url stringlengths 14 2.42k | text stringlengths 100 1.02M | date stringlengths 19 19 | metadata stringlengths 1.06k 1.1k |
|---|---|---|---|
https://spc.unige.ch/en/teaching/courses/algorithmes-probabilistes/montecarlo/ | # Monte-Carlo Integration (probabilistic numeric algorithms)
In this section, we are going to present some basic information about the Monte Carlo integration methods. This method must not be confused with the Monte Carlo algorithms that you will study in the remaining part of this course.
1. Monte Carlo Methods (probabilistic numeric algorithms): it is a method which idea is to use random numbers and distributions to solve deterministic problems as could be the integration of an analytical function;
2. Monte Carlo Algorithms: it is a randomized algorithm whose output may be incorrect with a certain probability.
Regarding the Monte Carlo Methods (numeric algorithm) the interested reader can find a nice introduction on the Wikipedia page. For a more complete reference see for example this ArXiv document.
## Direct Sampling Monte Carlo
The direct sampling Monte Carlo, is a method that relies on a repeated random sampling to (for example) do a numerical approximation of an integration. They are often used when neither an analytical solution or a numerical approximation (obtained with non-stochastic methods) is available.
Let's see how to use the Direct-Sampling-Monte-Carlo integration to estimate the value of $\pi$. We can follow these simple steps:
1. Draw a square, then inscribe a circle within it
2. Randomly uniformly scatter a given number of points over the square
3. Count the number of points inside the circle
4. The ratio of the inside-count and the total-sample-count is an estimate of the ratio of the two areas, $\pi/4$. Multiply the result by $4$ to estimate $\pi$.
Given that this problem has to axes of symmetry, we can in the equivalent way study just the upper quadrant that can be represented as a function. So, in general, this procedure allows as to do an estimation of a function integral of the type $$I = \int f(\bf{x}) \rm{d}\bf{x}$$
The Monte Carlo can give also a non-deterministic extimetion of the error, so that in the end it will give an answer of the type
$$I = \int f(\bf{x}) \rm{d} \mathbf{x} = 0.789 \pm 0.001 \text{with probability 0.95}$$
### Exercise: Pi Estimation with Monte-Carlo
By using the pseudo-random number generators of TP 1 (C++ version), calculate Pi with the Monte-Carlo approach. Report the precision of the approximation per method (up to the 6th decimal) for a fixed number of generated points N, N = 5000, 10000, 30000. Do you observe substantial differences by using the different engines?
## Buffon’s needle experiment
Georges Louis Leclerc, Count of Buffon (1707–1788) is considered to be the first to use a Monte Carlo Method to compute the value of $\pi$. His method was based on the random throw of needles of length $\lambda$ onto a wooden floor with cracks at distance $\omega$ apart.
## Markov Chain monte carlo
A Markov process is a process that satisfies the Markov propriety:
$$P(x_{n+1}|x_1,\ldots,x_n) = P(x_{n+1}|x_n)$$
that basically means that since the next state is determined just from the current state, the process has no memory.
A Markov Chain is nothing but a stochastic Markov process where the next element of the sequence is determined stochastically from the current state.
Question 1: Is the Logistic Map a Markov process or a Markov Chain?
Question 2: Can you spot the possible differences between the random walk and the Markov Chain?
Let's define the Markov Chain in a more formal way. Given the stochastic function $Y: \ S\to \{y_1,\ldots,y_n\}$ that associate at each sample point a realization (where $S$ is the sample space and $\{y_1,\ldots,y_n\}$ the set of realization of $Y$), we denote with $P(y_n(s))$ the probability that at the time $s\in$ $\mathbb{N}$, $Y$ has the realization $y_n$. We also indicate with $P(y_m(s)|y_n(s+1))$ the conditional probability that $Y$ has realization $y_{n2}$ at time $s_2$, given that it had realization $y_{n1}$ at time $s$. | 2020-09-21 01:53:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8725104331970215, "perplexity": 434.3839675361466}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198887.3/warc/CC-MAIN-20200921014923-20200921044923-00304.warc.gz"} |
https://formulasearchengine.com/wiki/G-test | # G-test
## Relation to the chi-squared test
The commonly used chi-squared tests for goodness of fit to a distribution and for independence in contingency tables are in fact approximations of the log-likelihood ratio on which the G-tests are based. The general formula for Pearson's chi-squared test statistic is
${\displaystyle \chi ^{2}=\sum _{i}{\frac {\left(O_{i}-E_{i}\right)^{2}}{E_{i}}}.}$
The approximation of G by chi squared is obtained by a second order Taylor expansion of the natural logarithm around 1. This approximation was developed by Karl Pearson because at the time it was unduly laborious to calculate log-likelihood ratios. With the advent of electronic calculators and personal computers, this is no longer a problem. A derivation of how the chi-squared test is related to the G-test and likelihood ratios, including to a full Bayesian solution is provided in Hoey (2012).[2]
## Statistical software
• The R programming language has the likelihood.test function in the Deducer package.
• In SAS, one can conduct G-test by applying the /chisq option after the proc freq.[7]
• In Stata, one can conduct a G-test by applying the lr option after the tabulate command.
• Fisher's G-test in the GeneCycle Package of the R programming language (fisher.g.test) does not implement the G-test as described in this article, but rather Fisher's exact test of Gaussian white-noise in a time series.[8]
## References
1. Sokal, R. R. and Rohlf, F. J. (1981), Biometry: the principles and practice of statistics in biological research, New York: Freeman. ISBN 0-7167-2411-1.
2. Harremoës, P. and Tusnády, G. (2012). Information divergence is more chi squared distributed than the chi squared statistic, Proceedings ISIT 2012, pp. 538–543.
3. Quine, M. P. and Robinson, J. (1985), "Efficiencies of chi-square and likelihood ratio goodness-of-fit tests", Annals of Statistics, 13: 727–742.
4. Harremoës, P. and Vajda, I. (2008), "On the Bahadur-efficient testing of uniformity by means of the entropy", IEEE Transactions on Information Theory, 54: 321–331.
5. Dunning, Ted (1993). "Accurate Methods for the Statistics of Surprise and Coincidence", Computational Linguistics, Volume 19, issue 1 (March, 1993).
6. G-test of independence, G-test for goodness-of-fit in Handbook of Biological Statistics, University of Delaware. (pp. 46–51, 64–69 in: McDonald, J. H. (2009) Handbook of Biological Statistics (2nd ed.). Sparky House Publishing, Baltimore, Maryland.)
7. Fisher, R. A. (1929), "Tests of significance in harmonic analysis", Proceedings of the Royal Society of London: Series A, Volume 125, Issue 796, pp. 54–59. | 2020-01-28 12:58:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 13, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7930718064308167, "perplexity": 2976.6952537984125}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251778272.69/warc/CC-MAIN-20200128122813-20200128152813-00011.warc.gz"} |
https://www.techwhiff.com/learn/adjusted-wacc-hollydales-is-a-clothing-store-in/380981 | # Adjusted WACC. Hollydale's is a clothing store in East Park. It paid an annual dividend of...
###### Question:
Adjusted WACC. Hollydale's is a clothing store in East Park. It paid an annual dividend of $2.10 last year to its shareholders and plans to increase the dividend annually at 3.0%. It has 470,000 shares outstanding. The shares currently sell for$23.42 per share. Hollydale's has 17,000 semiannual bonds outstanding with a coupon rate of 6%, a maturity of 19 years, and a par value of $1,000. The bonds are currently selling for$694.75 per bond. What is the adjusted WACC for Hollydale's if the corporate tax rate is 35%? What is the adjusted WACC for Hollydale's if the corporate tax rate is 35%? % (Round to two decimal places.)
#### Similar Solved Questions
##### The figure below shows a proton entering a parallel-plate capacitor with a speed of 2.20×105 m/s....
The figure below shows a proton entering a parallel-plate capacitor with a speed of 2.20×105 m/s. The proton travels a horizontal distance x = 7.20 cm through the essentially uniform electric field. The electric field of the capacitor has deflected the proton downward by a distance of d = 0.76...
For both GAAP and tax purposes, Raymond Incorporated reported the following pre-tax income (loss) for each of the years: Year Pre-tax income Tax Rate 2018 $180,000 30% 2019 120,000 30% 2020 (400,000) 40% 2021 80,000 40% Required: Prepare all the necessary journal entries for each year 2018-2021 to r... 1 answer ##### With relevant examples, account for the myriad of definitions of strategic human resource management. With relevant examples, account for the myriad of definitions of strategic human resource management.... 6 answers ##### The single cable supporting an unoccupied elevator breaks when the elevator is at rest at the top of a 155 m high building The single cable supporting an unoccupied elevator breaks when the elevator is at rest at the top of a 155 m high building. With what speed does the elevator hit the ground?... 1 answer ##### A. On July 1, 2017, Lopez Company paid$1,600 for six months of insurance coverage. No...
a. On July 1, 2017, Lopez Company paid $1,600 for six months of insurance coverage. No adjustments have been made to the Prepaid Insurance account, and it is now December 31, 2017. b. Zim Company has a Supplies account balance of$5,800 on January 1, 2017. During 2017, it purchased \$2,400 of supplie... | 2023-03-29 15:33:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17169098556041718, "perplexity": 4752.718135548401}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949009.11/warc/CC-MAIN-20230329151629-20230329181629-00061.warc.gz"} |
https://trainingdatascience.com/tips/why-do-we-use-standard-deviation/ | # Why do we use Standard Deviation and is it Right?
It’s a fundamental question and it has knock on effects for all algorithms used within data science. But what is interesting is that there is a history. People haven’t always used variance and standard deviation as the defacto measure of spread. But first, what is it?
## Standard Deviation
The Standard Deviation is used throughout statistics and data science as a measure of “spread” or “dispersion” of a feature. The standard deviation of a population is:
$$\sigma = \sqrt{ \frac{\sum_{i=0}^{i=N}{ (x_i - \mu )^2 }} {N} }$$
Where $\mu$ is the mean of the population and $N$ is the total number of observations in the population. Let’s run through an example.
Assume you have the following array of values:
[6 4 6 9 4 4 9 7 3 6]
The the mean is:
μ = 5.8
Then calculating each step in equation 1:
Deviations from the mean: [ 0.2 -1.8 0.2 3.2 -1.8 -1.8 3.2 1.2 -2.8 0.2]
Squared deviations from the mean: [ 0.04 3.24 0.04 10.24 3.24 3.24 10.24 1.44 7.84 0.04]
Sum of squared deviations from the mean: 39.6
Mean of squared deviations from the mean: 3.96
Which results in:
σ = 1.98997487421
## Why Squared Differences?
You might be asking, why do we square the differences of the samples, to only square-root the samples later on?
Intuitively, you can think of this as taking the extreme values into account. If we were to just sum the absolute values, rather than the squared values, then the measure of the “spread” will be dominated by the values that are most common. It virtually ignore outliers.
Let’s repeat that calculation again, but this time we won’t perform the square:
Deviations from the mean: [ 0.2 -1.8 0.2 3.2 -1.8 -1.8 3.2 1.2 -2.8 0.2]
Absolute deviations from the mean: [ 0.2 1.8 0.2 3.2 1.8 1.8 3.2 1.2 2.8 0.2]
Average of absolute deviations from the mean: 1.64
This technique has a name.
## Mean Absolute Deviation
The Mean Absolute Deviation (MAD - a great acronym) measures the average spread of each observation from the mean. Its formula is:
$$MAD = \frac{\sum_{i=0}^{i=N}{ |x_i - \mu| }} {N}$$
Now recall that for our population provided at the start, σ = 2.0 and MAD = 1.6. That’s a significant difference considering that the population was created with a notional standard deviation of 3.
The reason is that the MAD is introducing a form of weighting. We’re treating the observations that are father away from the mean in the same way as we do those close to the mean. For the standard deviation, we’re squaring the difference, so those far from the mean have a much greater affect on the final value of σ.
## Why Use Standard Deviation at All?
Here’s the thing. There are two very important properties of the variance (that’s just $\sigma^2$).
First, the squared term perfectly describes the spread in a Gaussian probability distribution. I won’t go into the mathematics at this point, but suffice to say that it is the best metric to describe the spread of a Normal distribution.
Secondly, the square is continuously differentiable. The absolute is a discontinuity, it is not differentiable. This is extremely important in all sorts of optimisation problems encountered during Data Science.
## So When Shouldn’t you use Standard Deviation?
It comes back to the earlier point. If you have values far away from the mean that don’t truly represent your data, these are known as outliers.
If you include outliers in the standard deviation calculation they will over-exaggerate the standard deviation. The result will be far greater than the true standard deviation of the population.
So when you are choosing how to optimise your models, you’ll get the option of using the L1 or L2 Norm.
The L1 Norm is simply the MAD equation, but without the averaging division by $N$. It is also known as the taxicab Norm since the geometric interpretation is the distance that a car has to travel through a square-block city. Use this when you know you have outliers. The L1 Norm is less sensitive to outliers. Also use this if your data isn’t Normally distributed.
The L2 Norm, a.k.a. Euclidean Norm, a.k.a. Pythagoras’ Theorem, is the same as the Standard Deviation, except we leave out the averaging division by $N$ again. Use the L2 Norm when your data doesn’t have outliers and your data is Normally distributed.
Also note that the vast majority of algorithms used within Data Science use the Mean and the L2 Norm somewhere within their implementation. This implies that they assume that your data is always Normally Distributed; they are probably not! | 2019-02-20 01:10:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8574622869491577, "perplexity": 407.24812107396554}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247494125.62/warc/CC-MAIN-20190220003821-20190220025821-00555.warc.gz"} |
https://cstheory.stackexchange.com/questions/42258/solving-an-lp-with-at-most-m-1-nonzeros/42273 | # Solving an LP with at most m-1 nonzeros
Consider the linear program:
$$A x = b, ~~~~~~ x\geq 0$$ where $$A$$ is an $$m$$-by-$$n$$ matrix, $$x$$ is an $$n$$-by-1 vector, $$b$$ is an $$m$$-by-1 vector, and $$m.
It is known that, if this program has a solution, then it has a basic feasible solution, in which at most $$m$$ variables are non-zero.
QUESTION: is there an efficient algorithm to decide whether the LP has a solution in which at most $$m-1$$ variables are non-zero, and find it if it exists?
The question is a special case of Min-RVLS - finding a solution with a smallest number of non-zero variables. Min-RVLS is known to be NP-hard and hard to approximate within a multiplicative factor. Finding an additive approximation is hard too.
But, here our goal is much more modest - all we want is to find a solution with one less than the maximum ($$m$$). Is this special case easier?
This question was previously posted in cs.SE and got no answers. I deleted it from there to avoid cross-posting.
I think the "few nonzeros" problem is NP-hard, by reduction from the partition problem. Suppose we are given $$m$$ numbers $$a_1,\ldots,a_m$$ whose total sum is $$2 s$$, and have to decide whether they can be partitioned into two subsets such that the sum in each subset is $$s$$. We can solve this problem using a linear program with $$2 m$$ variables. For each $$i\in[2]$$ and $$j\in [m]$$, the variable $$x_{ij}$$ determines what fraction of the number $$a_j$$ is in subset $$i$$. There are $$m+1$$ constraints (besides non-negativity):
• For each $$j\in[m]$$: $$x_{1j}+x_{2j} = 1$$
• The equal-sum constraint: $$\sum_{j=1}^m x_{1j} a_j = \sum_{j=1}^m x_{2j} a_j$$
There always exists a solution with at most $$m+1$$ nonzeros. In this solution, at most one number is "cut" between the sets. Indeed, it is easy to solve the partition problem if we are allowed to cut one number: just order the numbers on a line and cut the line into two parts with equal sum.
Now, if we could solve the "few nonzeros" problem, then we could decide whether the above LP has a solution with at most $$m$$ nonzeros, which would imply a solution to the partition problem (in which no number is cut). But this problem is known to be NP-complete. | 2019-09-15 05:44:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 28, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9278859496116638, "perplexity": 832.6653395914642}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514570740.10/warc/CC-MAIN-20190915052433-20190915074433-00212.warc.gz"} |
https://math.stackexchange.com/questions/1899345/spivaks-calculus-4th-ed-absolute-value-definition-p-11 | # Spivak's Calculus 4th ed: Absolute value definition p. 11
After defining the absolute value $|a|$ of $a$ as
$$|a| = \begin{cases} a, & a\geq 0\\ -a, & a\leq 0, \end{cases}$$
the text provides some examples. While $|-3| = 3$ and $|7| = 7$ are simple enough (by direct application of the above definition), I do not understand the latter two examples, which are
$$|1 + \sqrt{2} - \sqrt{3}| = 1 + \sqrt{2} - \sqrt{3}$$ and $$|1 + \sqrt{2} - \sqrt{10}| = \sqrt{10} - \sqrt{2} - 1.$$
Without calculating the actual values of $\sqrt{2}$, $\sqrt{3}$, $\sqrt{10}$ and so on, how can one arrive at these equations?
EDIT: As @Bernard points out, the idea is to just compare the squares. Both of these absolute values use the sum $1 + \sqrt{2}$, we can think of its square, $3 + 2\sqrt{2}$ (which is less than $3 + 2\cdot2 = 3 + 4)$. In the first, we are essentially doing $3 + 2\sqrt{2} - 3$, which is a positive value, so we can just leave it as is. For the second, $3 + 2\sqrt{2} < 3 + 4 < 10$, so we have to re-order the $\sqrt{10}$ to come first, and then subtract the $1$ and $\sqrt{2}$ afterwards. It's more calculating than I'd like (and I'm not sure exactly what Spivak was trying to accomplish by throwing in these examples), but I am satisfied for now.
• $\sqrt{10}>\sqrt{9}=3$ – tired Aug 21 '16 at 20:45
For the first absolute value, it is enough to compare the squares: $(1+\sqrt2)^2=3+2\sqrt 2>(\sqrt 3)^2$. For the second absolute value, $3+2\sqrt 2<3+4<10$.
• I can follow your first sentence, but not the second. Where did you get $3 + 4$ from? Oh nevermind, I see the logic now. – Linus Arver Aug 25 '16 at 1:17
• Isn't $\sqrt 2<2$ (just because $2>1$)? – Bernard Aug 25 '16 at 1:39 | 2019-04-23 14:05:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9438250064849854, "perplexity": 271.760432578511}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578605510.53/warc/CC-MAIN-20190423134850-20190423160850-00068.warc.gz"} |
https://gmatclub.com/forum/if-2-2x-2-x-6-0-x-1-x-248915.html | It is currently 25 Feb 2018, 15:41
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
Events & Promotions
Events & Promotions in June
Open Detailed Calendar
If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ?
Author Message
TAGS:
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 43917
If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 07:10
Expert's post
7
This post was
BOOKMARKED
00:00
Difficulty:
25% (medium)
Question Stats:
75% (01:32) correct 25% (01:56) wrong based on 142 sessions
HideShow timer Statistics
If $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$, $$x - \frac{1}{x} =$$ ?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
[Reveal] Spoiler: OA
_________________
Manager
Joined: 02 Nov 2015
Posts: 174
GMAT 1: 640 Q49 V29
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 07:29
It's an E.
The question breaks down to
1/(4^x)+1/(2^x)-6=0.
Let 1/2^x=a.
Then it becomes a^2+a-6=0.
On solving we get a=2 and -3.
Thus 1/(2^x)=2
Which gives x=-1.
So x-1/x equals 1+1=2.
My formatting may not be very good but have tried to keep it lucid.
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2094
Location: India
GPA: 3.12
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 07:44
Since we have been asked to find the value of $$x - \frac{1}{x}$$, this can be rewritten as $$\frac{x^2 - 1}{x}$$
The equation $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$ => $$\frac{1}{{2^{(x)^2}}} + \frac{1}{{2^{(x)}}} - 6 = 0$$
Substituting $$\frac{1}{2^x}$$ be b
Therefore, $$b^2 + b - 6 = 0$$
Solving for b, b=-3 or 2
If b=2 | $$\frac{1}{2^x} = 2^{-x} = 2$$ So, x = -1
The value for the expression $$\frac{x^2 - 1}{x} = \frac{0}{-1} = 0$$(Option C)
_________________
Stay hungry, Stay foolish
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2094
Location: India
GPA: 3.12
If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 07:47
kumarparitosh123 wrote:
It's an E.
The question breaks down to
1/(4^x)+1/(2^x)-6=0.
Let 1/2^x=a.
Then it becomes a^2+a-6=0.
On solving we get a=2 and -3.
Thus 1/(2^x)=2
Which gives x=-1.
So x-1/x equals 1+1=2.
My formatting may not be very good but have tried to keep it lucid.
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
It must be C, kumarparitosh123
As x=-1, and we need to find the value of x-1/x
The expression $$x-\frac{1}{x} = -1 -(\frac{1}{-1}) = -1 + 1 = 0$$
_________________
Stay hungry, Stay foolish
Manager
Joined: 02 Nov 2015
Posts: 174
GMAT 1: 640 Q49 V29
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 07:49
pushpitkc wrote:
kumarparitosh123 wrote:
It's an E.
The question breaks down to
1/(4^x)+1/(2^x)-6=0.
Let 1/2^x=a.
Then it becomes a^2+a-6=0.
On solving we get a=2 and -3.
Thus 1/(2^x)=2
Which gives x=-1.
So x-1/x equals 1+1=2.
My formatting may not be very good but have tried to keep it lucid.
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
It must be C, kumarparitosh123
As x=-1, and we need to find the value of x-1/x
The expression $$x-\frac{1}{x} = -1 -(\frac{1}{-1}) = -1 + 1 = 0$$
Yes Pushpitkc
My Bad. I don't know in which state of mind did I solve..
Thanks for pointing it out.
A lesson for me not to rush much..?
Sent from my Lenovo TAB S8-50LC using GMAT Club Forum mobile app
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 948
Location: India
GPA: 3.82
If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 07:51
Bunuel wrote:
If $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$, $$x - \frac{1}{x} =$$ ?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
let $$2^{-x} = a$$
so the question becomes $$a^2 + a - 6 = 0$$. Solving this we get
$$(a-2)(a+3) = 0$$. Therefore $$a = 2$$ or $$a =-3$$. But as "$$a$$" is a positive number ($$2$$ raised to some power will always be positive), hence $$a = -3$$ is not possible
So we get $$2^{-x} = 2$$ or $$x = -1$$
therefore $$x- \frac{1}{x} = -1 +1 = 0$$
Option C
Intern
Joined: 12 Feb 2015
Posts: 40
Location: India
GPA: 3.84
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 11:55
Bunuel wrote:
If $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$, $$x - \frac{1}{x} =$$ ?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
2^-x=a
equation becomes a^2+a-6=0...comes out to be a=-3(not possible,since 2^-x is not equal to -3).Thus a=-2,
2^-x=-2
x=-1
and finally the answer comes out to be 0
Director
Joined: 13 Mar 2017
Posts: 563
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
09 Sep 2017, 20:06
Bunuel wrote:
If $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$, $$x - \frac{1}{x} =$$ ?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
$$2^{(-2x)} + 2^{(-x)} - 6 = 0$$
=> $$1/2^{(2x)} + 1/2^{(x)} - 6 = 0$$
Let 2^x = y
=> $$1/y^2 + 1/y - 6 = 0$$
=> 6y^2 - 6y -1 = 0
=> 6y^2 - 3y + 2y -1 = 0
=> 3y (2y-1) + 2y-1 = 0
=> (3y +1) (2y-1) = 0
=> y = -1/3, 1/2
y = 2^-1
x = -1
x-1/x = -1 - (1/-1) = -1 +1 = 0
_________________
CAT 99th percentiler : VA 97.27 | DI-LR 96.84 | QA 98.04 | OA 98.95
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)
Manager
Joined: 03 May 2014
Posts: 166
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
24 Sep 2017, 20:39
Plugin values of X
2ˆ(-2x)+2ˆ(-x)−6=0
We need a value of x which results the LHS of the equation to be zero.
Trial and error we can take x=(-1) I checked from given answer choices.
2ˆ(-2*-1)+2(-*-1)-6=0
2ˆ2+2-6
4+2-6=0
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2016
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink]
Show Tags
26 Sep 2017, 15:28
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
If $$2^{(-2x)} + 2^{(-x)} - 6 = 0$$, $$x - \frac{1}{x} =$$ ?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
We can let y = 2^(-x) and rewrite the equation as:
(2^(-x))^2 + 2^(-x) - 6 = 0
y^2 + y - 6 = 0
(y + 3)(y - 2) = 0
y = -3 or y = 2
Since y = 2^(-x), we can say 2^(-x) = -3 or 2^(-x) = 2. However, since 2 is positive, 2^(-x) will be positive regardless of the value of x. So, 2^(-x) can’t be -3, and thus it must be 2. Let’s solve the equation 2^(-x) = 2:
2^(-x) = 2^1
-x = 1
x = -1
Thus, x - 1/x = -1 - 1/(-1) = -1 + 1 = 0.
_________________
Jeffery Miller
GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions
Re: If 2^(-2x) + 2^(-x) - 6 = 0, x - 1/x = ? [#permalink] 26 Sep 2017, 15:28
Display posts from previous: Sort by | 2018-02-25 23:41:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.82945317029953, "perplexity": 9952.866402452673}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891817523.0/warc/CC-MAIN-20180225225657-20180226005657-00193.warc.gz"} |
https://ch.gateoverflow.in/312/gate-chemical-2014-question-50 | In a steady and incompressible flow of a fluid (density = $1.25\: kg\: m^{-3}$), the difference between stagnation and static pressures at the same location in the flow is $30 \:mm$ of mercury (density = $13600 \:kg \:m^{-3}$). Considering gravitational acceleration as $10 \:m \:s^{-2}$ the fluid speed (in $m \:s^{-1}$) is _________________ | 2023-03-24 16:32:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9562707543373108, "perplexity": 522.0601458433409}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945287.43/warc/CC-MAIN-20230324144746-20230324174746-00620.warc.gz"} |
http://www.numdam.org/articles/10.1051/cocv:2006010/ | Null controllability of the heat equation with boundary Fourier conditions : the linear case
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 442-465.
In this paper, we prove the global null controllability of the linear heat equation completed with linear Fourier boundary conditions of the form $\frac{\partial y}{\partial n}+\beta \phantom{\rule{0.166667em}{0ex}}y=0$. We consider distributed controls with support in a small set and nonregular coefficients $\beta =\beta \left(x,t\right)$. For the proof of null controllability, a crucial tool will be a new Carleman estimate for the weak solutions of the classical heat equation with nonhomogeneous Neumann boundary conditions.
DOI : https://doi.org/10.1051/cocv:2006010
Classification : 35K20, 93B05
Mots clés : controllability, heat equation, Fourier conditions
@article{COCV_2006__12_3_442_0,
author = {Fern\'andez-Cara, Enrique and Gonz\'alez-Burgos, Manuel and Guerrero, Sergio and Puel, Jean-Pierre},
title = {Null controllability of the heat equation with boundary Fourier conditions : the linear case},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {442--465},
publisher = {EDP-Sciences},
volume = {12},
number = {3},
year = {2006},
doi = {10.1051/cocv:2006010},
zbl = {1106.93009},
mrnumber = {2224822},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2006010/}
}
Fernández-Cara, Enrique; González-Burgos, Manuel; Guerrero, Sergio; Puel, Jean-Pierre. Null controllability of the heat equation with boundary Fourier conditions : the linear case. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 3, pp. 442-465. doi : 10.1051/cocv:2006010. http://www.numdam.org/articles/10.1051/cocv:2006010/
[1] V. Barbu, Controllability of parabolic and Navier-Stokes equations. Sci. Math. Jpn 56 (2002) 143-211. | Zbl 1010.93054
[2] A. Doubova, E. Fernández-Cara and M. González-Burgos, On the controllability of the heat equation with nonlinear boundary Fourier conditions. J. Diff. Equ. 196 (2004) 385-417. | Zbl 1049.35042
[3] C. Fabre, J.P. Puel and E. Zuazua, Approximate controllability of the semilinear heat equation. Proc. Roy. Soc. Edinburgh 125A (1995) 31-61. | Zbl 0818.93032
[4] E. Fernández-Cara and E. Zuazua, The cost of approximate controllability for heat equations: the linear case. Adv. Diff. Equ. 5 (2000) 465-514. | Zbl 1007.93034
[5] A. Fursikov and O.Yu. Imanuvilov, Controllability of Evolution Equations. Lecture Notes no. 34, Seoul National University, Korea, 1996. | MR 1406566 | Zbl 0862.49004
[6] O.Yu. Imanuvilov and M. Yamamoto, Carleman estimate for a parabolic equation in a Sobolev space of negative order and its applications, Dekker, New York. Lect. Notes Pure Appl. Math. 218 (2001). | MR 1817179 | Zbl 0977.93041
[7] G. Lebeau and L. Robbiano, Contrôle exacte de l'equation de la chaleur (French). Comm. Partial Differ. Equat. 20 (1995) 335-356. | Zbl 0819.35071
[8] D.L. Russell, A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Studies Appl. Math. 52 (1973) 189-211. | Zbl 0274.35041 | 2021-11-30 23:54:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.39369967579841614, "perplexity": 3371.9550367493994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964359082.76/warc/CC-MAIN-20211130232232-20211201022232-00079.warc.gz"} |
https://mingusspeaks.com/vb4tk1/5c2eec-covariant-derivative-general-relativity | The Covariant Derivative in General Relativity. P Question on covariant derivatives I am reading I am reading Spacetime and Geometry : An Introduction to General Relativity -- by Sean M Carroll and have arrived at chapter 3 where he ⦠, x You will often hear it proclaimed that GR is a "diffeomorphism invariant" theory. Hello all, I'm trying to calculate a commutator of two covariant derivatives, as it was done in Caroll, on page 122. ( It can be show easily by the next reasoning. , where At The connection is chosen so that the covariant derivative of the metric is zero. This bilinear map can be described in terms of a set of connection coefficients (also known as Christoffel symbols) specifying what happens to components of basis vectors under infinitesimal parallel transport: Despite their appearance, the connection coefficients are not the components of a tensor. Γ An ordinary matrix is a rank 2 tensor, a vector is a rank 1 tensor, and a scalar is rank 0. {\displaystyle \mu } {\displaystyle {\mathcal {L}}_{X}} I am reading Spacetime and Geometry : An Introduction to General Relativity â by Sean M Carroll. {\displaystyle (r,s)} Another contradiction I saw is that they write the following formula: in the end of the section "Coordinate Description" ( s A tensor field is then defined as a map from the manifold to the tensor bundle, each point {\displaystyle {\vec {U}}} α p &= \partial_\rho \left( \frac{\partial \xi^i}{\partial x^\mu}\frac{\partial \xi^i}{\partial x^\nu} \right) - g_{\mu \sigma} \frac{\partial x^\sigma}{\partial \xi^i} \frac{\partial^2 \xi^i}{\partial x^\nu \partial x^\rho} - g_{\sigma \nu} \frac{\partial x^\sigma}{\partial \xi^i} \frac{\partial^2 \xi^i}{\partial x^\mu \partial x^\rho} \\ t T General Theory of Relativity or the theory of relativistic gravitation is the one which describes black holes, gravitational waves and expanding Universe. For example, the Lie derivative of a type (0, 2) tensor is. A This notion can be made more precise by introducing the idea of a fibre bundle, which in the present context means to collect together all the tensors at all points of the manifold, thus 'bundling' them all into one grand object called the tensor bundle. P b . ∂ Other physical descriptors are represented by various tensors, discussed below. In the general relativity literature, it is conventional to use the component syntax for tensors. T And a tensor that's zero in one set of coordinates is zero in all other coordinates. β What the Riemann Tensor allows us to do is tell, mathematically, whether a space is flat or, if curved, how much curvature takes place in any given region. An extra structure on a general manifold is required to define derivatives. Motivation Let M be a smooth manifold with corners, and let (E,∇) be a C∞ vector bundle with connection over M. Let γ : I → M be a smooth map from a nontrivial interval to M (a “path” in M); keep {\displaystyle X} P Studying the Cauchy problem allows one to formulate the concept of causality in general relativity, as well as 'parametrising' solutions of the field equations. Vectors (sometimes referred to as contravariant vectors) are defined as elements of the tangent space and covectors (sometimes termed covariant vectors, but more commonly dual vectors or one-forms) are elements of the cotangent space. ∇ {\displaystyle p} Having outlined the basic mathematical structures used in formulating the theory, some important mathematical techniques that are employed in investigating spacetimes will now be discussed. M Metric tensors resulting from cases where the resultant differential equations can be solved exactly for a physically reasonable distribution of energy–momentum are called exact solutions. When allied with coframe fields, frame fields provide a powerful tool for analysing spacetimes and physically interpreting the mathematical results. a is a space of all vector fields on the spacetime. The issue of deriving the equations of motion or the field equations in any physical theory is considered by many researchers to be appealing. ( Wednesday, 6 March 2019. : where {\displaystyle \partial _{a}} Using the above procedure, the Riemann tensor is defined as a type (1, 3) tensor and when fully written out explicitly contains the Christoffel symbols and their first partial derivatives. In GR, there is a local law for the conservation of energy–momentum. This matrix is symmetric and thus has 10 independent components. PROBLEM WITH PARTIAL DERIVATIVES One issue that we have encountered so far is that partial derivatives of tensors in general spacetime are not tensors. Note: General relativity articles using tensors will use the abstract index notation. , and ( . X The Covariant Derivative. One of the most basic properties we could require of a derivative operator is that it must give zero on a constant function. r τ {\displaystyle \Pi } is the metric tensor, a ) In fact in the above expression, one can replace the covariant derivative Some physical quantities are represented by tensors not all of whose components are independent. → general-relativity differential-geometry tensor-calculus differentiation. The 3+1 formalism should not be confused with the 1+3 formalism, where the basic structure is a con-gruence of one-dimensional curves (mostly timelike curves, i.e. be a point, See also Schrödinger's "Time-Space structure". In this world, there is only one metric tensor (up to scalar) and it can pretty much be measured. dim A The connection and curvature of any Riemannian manifold are closely related, the theory of holonomy groups, which are formed by taking linear maps defined by parallel transport around curves on the manifold, providing a description of this relationship. General Relativity, at its core, is a mathematical model that describes the relationship between events in space-time; the basic finding of the theory is that the relationship between events in the same as the relationship between points on a manifold with curvature, and the geometry of that manifold is determined by sources of energy-momentum and their distribution in space-time. Their use as a method of analysing spacetimes using tetrads, in particular, in the Newman–Penrose formalism is important. r {\displaystyle (b_{i})} 1 4. The vanishing covariant metric derivative is not a consequence of using "any" connection, it's a condition that allows us to choose a specific connection $\Gamma^{\sigma}_{\mu \beta}$. Using the weak-field approximation, the metric can also be thought of as representing the 'gravitational potential'. a {\displaystyle \alpha } 3 ParallelDisplacementofVectors. ( , $$T This latter problem has been solved and its adaptation for general relativity is called the Cartan–Karlhede algorithm. → x Diffeomorphism covariance is not the defining feature of general relativity,[1] and controversies remain regarding its present status in general relativity. U X ) turns out to give curve-independent results and can be used as a "physical definition" of a covariant derivative. We have also mentionned the name of the most important tensor in General Relativity, i ... Actually, "parallel transport" has a very precise definition in curved space: it is defined as transport for which the covariant derivative - as defined previously in Introduction to Covariant Differentiation - is zero. Can anybody clear these? A This tensor measures curvature by use of an affine connection by considering the effect of parallel transporting a vector between two points along two curves. $$â_X$$ is called the covariant derivative. p This is accomplished by solving the geodesic equations. Indeed, there is a connection. If we think physically, then we live in one particular (pseudo-)Riemannian world. 3 γ a i New York: Wiley, pp. X The essential idea is that coordinates do not exist a priori in nature, but are only artifices used in describing nature, and hence should play no role in the formulation of fundamental physical laws. 2 It is closely related to the Ricci tensor. Introducing Einstein's Relativity.Oxford: Clarendon Press. i An affine connection is a rule which describes how to legitimately move a vector along a curve on the manifold without changing its direction. α Vector fields are contravariant rank one tensor fields. Mathematical structures and techniques used in the theory of general relativity. {\displaystyle G} γ In particular, Killing symmetry (symmetry of the metric tensor under Lie dragging) occurs very often in the study of spacetimes. G ( Recently, I saw the following formula for the non-commutativity of the d'Alembert operator \Box acting on the covariant derivative of a scalar field in general relativity, \Box (\nabla_{\mu}\phi)-\nabla_{\mu}\Box\phi=R_{\mu\nu}\nabla^{\nu}\phi. For ranks greater than two, the symmetric or antisymmetric index pairs must be explicitly identified. J Their nonlinearity leads to a problem in determining the precise motion of matter in the resultant spacetime. , The vanishing covariant metric derivative is not a consequence of using "any" connection, it's a condition that allows us to choose a specific connection \Gamma^{\sigma}_{\mu \beta}. = In a coordinate basis, we write ds2 = g dx dx to mean g = g dx( ) dx( ). The course webpage, including links … D'Inverno, Ray (1992). C Lecture Notes on General Relativity MatthiasBlau Albert Einstein Center for Fundamental Physics Institut fu¨r Theoretische Physik Universit¨at Bern CH-3012 Bern, Switzerland ... 5.2 Extension of the Covariant Derivative to Other Tensor Fields . Another example is the values of the electric and magnetic fields (given by the electromagnetic field tensor) and the metric at each point around a charged black hole to determine the motion of a charged particle in such a field. {\displaystyle X} ( Math 396. Qmechanic ⦠138k 18 18 gold badges 314 314 silver badges 1647 1647 bronze badges.$$ The description of physical phenomena should not depend upon who does the measuring - one reference frame should be as good as any other. Why doesn't my covariant derivative metric just give me zero? Let's work in the three dimensions of classical space (forget time, relativity, four-vectors etc). T Γ the action has contributions coming from the matter elds and the gravitational elds S= S + S g= Z all space (L + L g)d We de ne S = Z all space L g g d = 1 2 Z all space p gT g d where we have de ned T = 2 p g L g which is the stress-energy-momentum tensor. d ) For cosmological problems, a coordinate chart may be quite large. Will I have have to replace the ordinary derivatives in the denominator also in this case? General Relativity For Tellytubbys. and the four-current While some relativists consider the notation to be somewhat old-fashioned, many readily switch between this and the alternative notation:[1]. j We need to be little bit careful about that because we are varying the metric, OK? §4.6 in Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. So they or their use or their formulas are not the consequence of any additional physical assumptions except that there is a metric. ) Before the advent of general relativity, changes in physical processes were generally described by partial derivatives, for example, in describing changes in electromagnetic fields (see Maxwell's equations). . r By definition, Levi-Civita connection preserves the metric under parallel transport, therefore, the covariant derivative gives zero when acting on a metric tensor (as well as its inverse). all of which are useful in calculating solutions to Einstein's field equations. In general relativity, it was noted that, under fairly generic conditions, gravitational collapse will inevitably result in a so-called singularity. So, it isn't a condition, it is a consequence of covariance derivative and metric tensor definition. The Einstein field equations (EFE) are the core of general relativity theory. {\displaystyle J^{a}} The problem in defining derivatives on manifolds that are not flat is that there is no natural way to compare vectors at different points. of a manifold, the tangent and cotangent spaces to the manifold at that point may be constructed. For a more accessible and less technical introduction to this topic, see, Mathematical techniques for analysing spacetimes, Introduction to mathematics of general relativity, Learn how and when to remove this template message, Energy-momentum tensor (general relativity), Solutions of the Einstein field equations, Friedman-Lemaître-Robertson–Walker solution, Variational methods in general relativity, Initial value formulation (general relativity), hyperbolic partial differential equations, Perturbation methods in general relativity, https://en.wikipedia.org/w/index.php?title=Mathematics_of_general_relativity&oldid=983665267, Mathematical methods in general relativity, Short description with empty Wikidata description, Articles lacking in-text citations from April 2018, Creative Commons Attribution-ShareAlike License, This page was last edited on 15 October 2020, at 14:54. This will be discussed further below. The set of all such tensors - often called bivectors - forms a vector space of dimension 6, sometimes called bivector space. Many consider this approach to be an elegant way of constructing a theory, others as merely a formal way of expressing a theory (usually, the Lagrangian construction is performed after the theory has been developed). Jay Jay. {\displaystyle {\tilde {\nabla }}_{a}} Contravariant and covariant components of a vector. Any observer can make measurements and the precise numerical quantities obtained only depend on the coordinate system used. . . ( is the gravitational constant, which comes from Newton's law of universal gravitation. It is also practice st manipulating indices. . → Another appealing feature of spinors in general relativity is the condensed way in which some tensor equations may be written using the spinor formalism. indices on the tensor, There are various methods of classifying these tensors, some of which use tensor invariants. Λ = Rank and Dimension []. is that we can always choose a local frame of reference such that the gravitational field is zero. Let There are a number of strategies used to solve them. [1] The defining feature (central physical idea) of general relativity is that matter and energy cause the surrounding spacetime geometry to be curved. {\displaystyle \Gamma _{ji}^{k}=\Gamma _{ij}^{k}} The discrepancy between the results of these two parallel transport routes is essentially quantified by the Riemann tensor. Ideally, one desires global solutions, but usually local solutions are the best that can be hoped for. ), and one way of stating the e.p. CITE THIS AS: Weisstein, Eric W. "Covariant Derivative." The gauge transformations of general relativity are arbitrary smooth changes of coordinates. The Lie derivative of any tensor along a vector field can be expressed through the covariant derivatives of that tensor and vector field. and a {\displaystyle X(t)} a vector field. By definition, an affine connection is a bilinear map The curvature of a spacetime can be characterised by taking a vector at some point and parallel transporting it along a curve on the spacetime. k ( where 103-106, 1972. or locally, with the coordinate dependent derivative a Once the EFE are solved to obtain a metric, it remains to determine the motion of inertial objects in the spacetime. In the next section we will introduce a notion of a covariant derivative. This condition, the geodesic equation, can be written in terms of a coordinate system {\displaystyle (r,s)} ∇ Being a second rank tensor in four dimensions, the energy–momentum tensor may be viewed as a 4 by 4 matrix. . So I quarrel with the word used by @twistor59, «chosen». is the Einstein tensor, and Using the connection, we can now define a new concept of differentiation, which is called the covariant derivative; it is denoted by a capital “D”, or double bars “||”, and defined as : (9) One important characteristic is the rank of a tensor, which is the number of indicies needed to specify the tensor. ( = ~ We show that the covariant derivative of the metric tensor is zero. {\displaystyle {\vec {A}}={\tfrac {d}{dt}}\gamma (0)} {\displaystyle A^{a}={\ddot {x}}^{a}} By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Γ 1 U General Relativity For Tellytubbys The Covariant Derivative Sir Kevin Aylward B.Sc., Warden of the Kings Ale Back to the Contents section The approach presented here … Therefore we must have $\nabla_\alpha g_{\mu\nu}=0$ in whatever set of coordinates we choose. a {\displaystyle \nabla _{\vec {U}}{\vec {U}}=0} In GR, the metric plays the role of the potential, and by differentiating it we get the Christoffel coefficients, which can be interpreted as measures of the gravitational field. 1 The Riemann tensor has a number of properties sometimes referred to as the symmetries of the Riemann tensor. D s But we specifically want a connection for which this condition is true because we want a parallel transport operation which preserves angles and lengths. As well as being used to raise and lower tensor indices, it also generates the connections which are used to construct the geodesic equations of motion and the Riemann curvature tensor. This is on purpose so that it is a suitable place to do linear approximations to the manifold. The goal of the course is to introduce you into this theory. r I've consulted several books for the explanation of why, and hence derive the relation between metric tensor and affine connection $\Gamma ^{\sigma}_{\mu \beta}$, $$\Gamma ^{\gamma} _{\beta \mu} = \frac{1}{2} g^{\alpha \gamma}(\partial _{\mu}g_{\alpha \beta} + \partial _{\beta} g_{\alpha \mu} - \partial _{\alpha}g_{\beta \mu}).$$. That is a good question I'd like to have answered too. A principal feature of general relativity is to determine the paths of particles and radiation in gravitational fields. ) b d Now that we have talked about tensors, we need to figure out how to classify them. But the existence of geodetic coordinates is a mathematical consequence of a Riemannian metric. being associated with a tensor at However, in general relativity, it is found that derivatives which are also tensors must be used. a i The covariant derivative will be introduced in such a way that the derivative of a vector is a tensor, derivative of a tensor is a tensor of higher rank etc. d PROBLEM WITH PARTIAL DERIVATIVES One issue that we have encountered so far is that partial derivatives of tensors in general spacetime are not tensors. On the other hand, May be I've to go through the concepts of manifold much deeper. The principle of general covariance was one of the central principles in the development of general relativity. DA_{i} = g_{ik}DA^{k}, The covariant derivative is convenient however because it commutes with raising and lowering indices. is the vector tangent to the curve at the point Here we meet the covariant divergence and prove a thing or two about it. {\displaystyle X} ) ( << Back to General Relativity) Definition of Christoffel Symbols [ edit ] Consider an arbitrary contravariant vector field defined all over a Lorentzian manifold, and take A i {\displaystyle A^{i}} at x i {\displaystyle x^{i}} , and at a neighbouring point, the vector is A i + d A i {\displaystyle A^{i}+dA^{i}} at x i + d x i {\displaystyle x^{i}+dx^{i}} . And they have no physical significance, they merely simplify calculations. {\displaystyle D^{3}} The gauge covariant derivative is a variation of the covariant derivative used in general relativity. given a metric, the connection is determined by the metric. How exactly it is derived, considering the metric compatibility and that $\phi$ is a scalar function depending on time? ˙ More precisely, the basic physical construct representing gravitation - a curved spacetime - is modelled by a four-dimensional, smooth, connected, Lorentzian manifold. The same procedure will continue to be true for the non-coordinate basis, but we replace the ordinary connection coefficients by the spin connection , denoted a b . But it is actually the essence in classical GR. That's because as we have seen above, the covariant derivative of a tensor in a certain direction measures how much the tensor changes relative to what it would have been if it had been parallel transported. p a A The Covariant Derivative in General Relativity Now consider how all of this plays out in the context of general relativity. &= \frac{\partial^2 \xi^i}{\partial x^\rho \partial x^\mu}\frac{\partial \xi^i}{\partial x^\nu} + \frac{\partial \xi^i}{\partial x^\mu}\frac{\partial^2 \xi^i}{\partial x^\rho \partial x^\nu} - \frac{\partial \xi^j}{\partial x^\mu}\underbrace{\frac{\partial \xi^j}{\partial x^\sigma} \frac{\partial x^\sigma}{\partial \xi^i}}_{\delta^j_i} \frac{\partial^2 \xi^i}{\partial x^\nu \partial x^\rho} - \frac{\partial \xi^j}{\partial x^\sigma}\frac{\partial \xi^j}{\partial x^\nu}\frac{\partial x^\sigma}{\partial \xi^i} \frac{\partial^2 \xi^i}{\partial x^\mu \partial x^\rho} \\ , A singularity is a point where the solutions to the equations become infinite, indicating that the theory has been probed at inappropriate ranges. X Why is the covariant derivative of the metric tensor zero. {\displaystyle p} D The Lie derivative of a scalar is just the directional derivative: Higher rank objects pick up additional terms when the Lie derivative is taken. The connection is called symmetric or torsion-free, if , where ) In words: the covariant derivative is the usual derivative along the coordinates with correction terms which tell how the coordinates change. Then {\displaystyle B=\gamma (t)} t In a coordinate basis, we write ds2 = g dx dx to mean g = g dx( ) dx( ). Techniques from perturbation theory find ample application in such areas. M {\displaystyle {\tfrac {1}{2}}D^{2}(D+1)} → and contravariant A more modern interpretation of the physical content of the original principle of general covariance is that the Lie group GL 4 (R) is a fundamental "external" symmetry of the world. and denoted by τ For example, in a system composed of one planet orbiting a star, the motion of the planet is determined by solving the field equations with the energy–momentum tensor the sum of that for the planet and the star. Now consider how all of this plays out in the context of general relativity. {\displaystyle r} Every tensor quantity can be expressed in terms of a frame field, in particular, the metric tensor takes on a particularly convenient form. on this curve, an affine connection gives rise to a map of vectors in the tangent space at → I will try to go through the wald book. ( {\displaystyle T_{\alpha \beta }=T_{\beta \alpha }} These connections are at the heart of Gauge Field Theory. I would rather say. The blog contains answers to his exercises, commentaries, questions and more. {\displaystyle T} at {\displaystyle (r,s)} This property of the Riemann tensor can be used to describe how initially parallel geodesics diverge. a M {\displaystyle r+s} I have these doubts. The rank of a tensor to each point of the manifold continue our of! Called bivectors - forms a vector field can be found by going one further. And often do mathematical results the geodesic equations metric just give me zero not the defining feature of general.... Makes sense that the spacetime moving along the integral curves of the covariant derivative, parallel transport operation preserves! Agree with the rest of the metric and controversies remain regarding its present status in general relativity resulting... » replaced by « given » ( T_ { p } ) property... Vectors at different points of dimension 6, sometimes called bivector space of privileged reference frames relativity which seeks solve! Efe relate the total spacetime geometry and hence the motion of inertial objects in the real universe as Weisstein... Of particles and radiation in gravitational fields, this means that initially parallel geodesics diverge evidence. The e.p notion of a tensor to each point of spacetime as parameterized by proper time field! Sometimes called bivector space to determine the paths of particles and radiation in gravitational fields of my general relativity the! In physics is the one associated with Levi-Civita affine connection 62394, https: #., I should have mentioned it features including that they are derivatives along integral curves vector! Geodesics of spacetime will stay parallel we can always choose a local law for the metric under! Is ( 3 ) ( Weinberg 1972, p.... §4.6 in Gravitation and relativity... Cite this as: Weisstein, Eric W. covariant derivative is convenient however because it commutes raising! Curve on the coordinate system used abolition of privileged reference frames definition, a covariant derivative a... The approach presented here is one of the covariant divergence and prove a thing two! Is called the covariant derivative. { r+s }. }. }. }. }..... Derivative metric just give me zero the next section we will introduce notion... Example, the symmetric or antisymmetric index pairs must be used to them! 'S zero in one particular ( pseudo- ) Riemannian world $\Phi is. Contributions under cc by-sa index notation is derived, considering the metric provide a powerful tool for analysing using... Motion of objects GR, there are a number of indicies needed specify! Examples in various scopes of the timelike vector field of vector fields ( 1,. ( x^\mu\right )$ is that it must give zero on a constant function exist such that the derivative! Directly from the metric is zero in one set of coordinates we need to be somewhat old-fashioned, many switch... One way of measuring the curvature of a derivative operator is that there is a good question I like... Chart may be written as tensors in general, have rank greater than 2 and. To have answered too mathematical results Weisstein, Eric W. covariant derivative metric just give zero. Vorticity tensor ) three dimensions of classical space ( forget time, relativity, the using... The rationale for choosing a manifold as the symmetries of the profound consequences of or. } T, at least locally: an introduction to general relativity be written a., determining the various Petrov types becomes much easier when compared with the singularities arising black. Exist such that the gravitational field given using tensors covariant derivative general relativity use the component for! Quarrel with the covariant derivative general relativity arising in black hole spacetimes it convenient to choose the Levi-Civita over... 'D like to see the word « chosen » replaced by « »! Classification of tensors in general relativity, [ 1 ] notation to be when differentiating the.! I plagiarized it from a number of covariant derivative general relativity used to derive the geodesic equations user contributions under by-sa. Field of the central principles in the theory of Gravitation and Cosmology principles! Show easily by the ruler used to solve Einstein 's field equations often leads one consider. ( Weinberg 1972, p. 104 ) physically, then we live in one set coordinates. Step further total matter ( energy ) distribution to the curvature of a body in general?... covariant derivative. appealing feature of general relativity which seeks to solve of. We live in one set of coordinates a derivative operator is that they are derivatives along integral curves the... Another straight forward calculation, but assuming the existence of geodetic coordinates is a mathematical consequence covariance... Stated in terms of its components in this case 's zero in all frames... { p } ) generic examples in various scopes of the planet affects the total spacetime geometry and hence motion... 0, 2 ) tensor is commonly written as and it can be found going. Usually refers to the '' covariant derivative is still sufficient to describe such.. Relativity an extension of special relativity, [ 1 ] and controversies remain regarding its present status in relativity... Imposing an additional structure on a general manifold is with an object called the covariant.. Approximation methods in numerical relativity is called the covariant derivative ( Dated September! The ideas of linear algebra are employed to study tensors many practical generic examples in various scopes of the relativity! And it can pretty much be measured tensors will use the abstract index notation EFE being. Sub-Field of general relativity covariant derivative of the answer, but usually local solutions are the that! Chosen so that it must give zero on a constant function does the measuring one. In the Newman–Penrose formalism is important typically, solving this initial value problem requires selection particular... At the heart of gauge field theory these three covariant derivative general relativity are exemplified by contrasting GR … to the. Get equations valid in general relativity powerful tool for analysing spacetimes and physically interpreting the mathematical results along integral... Various tensors covariant derivative general relativity discussed below ) Riemannian world equations of motion or the field equations often leads one consider... An extension of special relativity, four-vectors etc ) central features of GR is the one which black! Like \del_m ( 1/ \sqrt { 1-g^ { ab } T, at, b } ) given! Be I 've to go through the use of numerical methods word « chosen.... 30 '19 at 16:07 objects in the context of general relativity ', JMP, Vol dealing. Lorentzian manifold representing spacetime take the same mathematical form in all other coordinates dimension of the Riemann tensor the of! Perturbation theory find ample application in approximation methods in numerical relativity include the excision method and the Friedman-Lemaître-Robertson–Walker solution are! Mathematical tool how all of this plays out in the spacetime is assumed that inertial motion occurs along and... Flat coordinate system used greater than 2, and it can be used local frame of reference such that covariant. That, under fairly generic conditions, gravitational waves and expanding universe approximate the to. Edited Sep 30 '19 at 16:07 which $\nabla_ { \mu } g_ \alpha. How initially parallel geodesics diverge as representing the 'gravitational potential ' an additional structure on a,... Changing its direction assumed to be a tensor can be show easily by the metric of analysing spacetimes using,! General covariance was one of the planet affects the total matter ( energy ) to... Equations which arise … general relativity is called the Cartan–Karlhede algorithm EFE relate the matter... 141 6 6 bronze badges$ \endgroup $3$ \begingroup $mathematics!: the metric, it is a good question I 'd like to the. A purely mathematical problem non-linear differential equations for the case of vector fields measuring. Often just called 'the metric ' for ranks greater than two, the connection a! Want a parallel transport can then be defined by imposing an additional on... ( 3 ) ( Weinberg 1972, p.... §4.6 in Gravitation general... Be defined by imposing an additional structure on a tensor to each point of the field equations often leads to... And hence the motion covariant derivative general relativity matter in the middle of the Kings Ale observer in the denominator also this... The ideas of linear algebra are employed to study tensors the notation to little. Ab } T, at least locally with partial derivatives of tensors is a metric, OK problem general... 1968, p. 104 ) therefore reasonable to suppose that the laws of should! P } ) which seeks to solve motion of inertial objects in the context of general,... Relativity theory course at McGill University, Winter 2011 solutions to the manifold not the consequence covariance! Useful in calculating solutions to the source of the covariant derivative, which is the one associated Levi-Civita... Particular ( pseudo- ) Riemannian world )$ actually the essence in classical GR coordinates \$ (! Same mathematical form in all reference frames are tensor fields defined on a spacetime spacetime. The Weyl tensor are maps which attach a tensor related to the partial derivative is still to. It must give zero on a general manifold is required to define.! Articles using tensors will use the abstract index notation tensors - often called bivectors - forms a is. Theory was the abolition of privileged reference frames a thing or two about it define derivatives ).. The core of general relativity, it is a scalar is rank.! Of my general relativity require mathematical entities of still higher rank are arbitrary smooth changes of coordinates choose... Divergence and prove a thing or two about it is zero the rank a... In numerical relativity include the Segre classification of tensors is a rank 2 tensor, a coordinate.! Are both examples of such tensors include symmetric and thus has 10 independent components I it...
Polar Caves Nh Hours, Electricity And Water Bill, Name Declaration Germany, 1997 Toyota 4runner Bulb List, Name Declaration Germany, Outdoor Concert Outfit, Osi Caulk Color Chart, Best Flight Schools In New York, Riverside University Health System Pharmacy Hours, | 2021-04-21 01:02:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9245674014091492, "perplexity": 544.4303093701913}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039503725.80/warc/CC-MAIN-20210421004512-20210421034512-00195.warc.gz"} |
http://math.stackexchange.com/questions/672161/residually-finite-group-with-finitely-many-conjugacy-classes-of-elements-of-fini | # Residually finite group with finitely many conjugacy classes of elements of finite order
Let $G$ be a residually finite group. Show that if $G$ has finitely many conjugacy classes of elements of finite order then $G$ has a torsion free finite index subgroup.
Not sure how to get started on this one!
-
Let $x_1, \cdots, x_r$ be the representives for these conjugacy classes of finite orders. Since $G$ is residually finite, there exists $N_i \lhd G$ of finite index in $G$ such that $x_i \not \in N_i$ for each $i$. Let $N=\cap N_i$, then $N$ is what you need.
I suppose that should be $\;x_{\color{red}i}\notin N_i\;$ ...? – DonAntonio Feb 11 at 11:14 | 2014-03-09 20:21:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8593526482582092, "perplexity": 57.68951881882324}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394010303377/warc/CC-MAIN-20140305090503-00038-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.transtutors.com/questions/week-2-p-3-1302575.htm | # week 2. p. # 3
Problem # 3
The data presented below were taken from the booksand records of the Village of Maxieville. All amounts are inmillions. The village encumbers all outlays. As is evidentfromthedata,somegoodsorservicesthatwereorderedandencumbered have not yet been received. City regulationsrequire that all appropriations lapse at year-end.
Estimated Appropriate Amounts Encumbent Estimated cost Actual Revenue Property Taxes 23,700 23.400 Sales taxes 11,700 10.800 License 900 600 Other 2,100 1200 Total reveneue 38,400 36.000 Expenditure General government 9,000 7.800 7.200 8400 Public Sfety 18,000 17.700 15.000 14700 Recrecetiion 3.600 3.600 2.400 2700 Health and Sanitatiom 6,900 6.600 6.600 6300 Total Expenditure 37,500 35.700 31.200 32.100 Excess of estimate revevneue over appropriation 900 Beginning unassigned fund balanace 3.600 Estimate unassigned fund balance 4.500
1. Prepare summary entries to record
A. the budget
B. the encumbrance of the goods and services
C. the receipt of the goods and services. All invoiceswere paid in cash.
D. the actual revenues (all cash receipts)
2. Prepare summary entries to close the accounts
3. What would be the year-end?
A. fund balance (unassigned)
B. Reserveforencumbrancebalance (irrespectiveofhowclassi?ed)
4. Prepare a schedule in which you compare budgeted toactual revenues and expenditures.
5. A citizen reviews the budget to actual schedule that youhave prepared. She comments on the rather substantialfavorable variance between budgeted and actual expendituresandquestionswhythegovernmentdidnotspendthe full amount of money that it appropriated. Brie?yexplain to her the nature of the variance.
Attachments:
## Related Questions in Accounting For Government
• ### gov and non profit acc
(Solved) September 10, 2015
at year-end . 1 . Prepare summary entries to record A. the budget B . the encumbrance of the goods and services C . the receipt of the goods and services. All invoices were paid in cash . D . the actual revenues ( all cash receipts ) 2 . Prepare summary entries to close the accounts 3 . What would
The solution is based on fund accounting. Governments establish funds neither to account for specific functions nor to divide evenly their resources. Instead, they create funds mainly to...
• ### chap 3
(Solved) September 12, 2015
would also like steps to the answer
5. The nature of the variance is basically related to the fact that there had been the difference between the quantity order in regard to supplies and the quantity that was originally...
• ### Problem # 1 The transactions that follow relate to the Danville County Comptroller’s Department over...
(Solved) September 09, 2015
and auditing workshops. Total cost was $30,000. • The consultants conducted the workshops and were paid$30,000. • The department ordered books and training materials, which it estimated would cost $5 ,400. As of year-end , the materials had not been received. Year 2 • The county appropriated$40
The solution is based on issue of budget and control. Capital budgets are closely tied to operating budgets in that governments and other not-for-profits should include current year capital...
• ### Accounting for Government FInal Project
(Solved) July 11, 2013
Use the link provided below to download and access the software that coincides with the attached PDF instructions http://highered.mcgraw-hill.com/sites/0078110939/student_view0/_student_city_of_smithville_bingham.htm
• ### week 2 (Non Govet Acc)
(Solved) August 31, 2015
and auditing workshops. Total cost was $30,000. • The consultants conducted the workshops and were paid$30,000. • The department ordered books and training materials, which it estimated would cost $5 ,400. As of year-end , the materials had not been received. Year 2 • The county appropriated$40 | 2018-07-19 23:27:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19303451478481293, "perplexity": 11468.35221755464}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591332.73/warc/CC-MAIN-20180719222958-20180720002958-00375.warc.gz"} |
https://writingechoes.wordpress.com/tag/hyakki-yagyo/ | # Writing Echoes
Delijah's Writing Blog
## My board and a (quite late) mid-year update
There are a bunch of things on the board in front of my writing station, behind my computer screen. Some postcards, seals, visiting cards and the so-called Japan kit, which includes member and discount cards for several places in Tokyo, along with my passport and the commuter’s pass. There is my organ donor card, and the postcard I wrote to myself from Tokyo Tower.
There are also some notes to myself, my screen resolution for making walpapers, a fosilissed shark tooth, and a silly pictures with friends at a concert line. And things related to writing.
There is a rusty Welsh pound that I found on a dry streambed in Tokyo, and I’m waiting for it to tell me its story (not its history, which was probably a random British person throwing a coin into a body of water for luck, which they do sometimes). But there is a story there, and sometimes I look at the coin and wonder. It will come.
There is a Tengu ex machina note, just because. The term ocurred to me while working through The Last Yōkai War of Edo. It’s like the Deus ex machina, but… with tengu. I went back and corrected the whole thing, but I left the note, as a reminder.
There is also a reference to Setsubun, a Japanese festival for luck. It conjures luck and chases the oni away. But I don’t mind the oni. As a matter of fact, I like writing yōkai, so my note reads は外!も内、 福は内! Oni wa soto mo uchi! Fuku wa uchi! It means, let the oni in too, not only the good luck.
Finally there is a small note, right in my line of sight, that reminds me that in 2016 I have to focus on writing Shourai, the Hyakki Yagyō verse and the Shikigami verse. There is a tick mark next to the Hyakki Yagyō line. That is because I have worked a lot on that this year. The original idea was only writing these three verses, along with the blog articles and finishing Atlantis in January for the climate fiction contest (Atlantis did not get anywhere in there though, unfortunately). The note has little laughing signs around as I deviated from this plan…
A little over a fourth of what I’ve written this year till now has been Hyakki Yagyō. Not only the main work I had to do, also a few short stories that will need some revision to fit in to the main timeline. That makes about 66,700 words on this verse.
Shourai has taken almost 33,000 words, which does not feel that much, but it almost 13% of the written material this year and 10.5% of the written total. I’m nearly done with the arc, I’ve decided. I’ve chosen an ending point, and now I have to backtrack and fill in the gaps (and actually write the last chapter), break down chapters and so on. there is a lot of green in the planning now. But editing this is going to require a lot of effort. I’m kind of toying with the idea of finishing all the writing before the year is over… but we’ll get to how I can’t keep to decisions later…
There are around 24,000 new words on the final Shikigami book. All the main points are planned and addressed, but the small, driving story is what I’m lacking. Although the character is important and I like him bunches, it is difficult to factor his POV in to have him drive the story. I need around 25,000 words more on this book, and again, it’s difficult to juggle how, even if I do want this finished this year.
So this is what I was supposed to write this year, fiction wise. Blogging and articles are factored in, as I need to improve non-fiction writing skills. All in all, there is 61% of planned writing actually being done. The problem thus lies on the 39% that I was not supposed to have been writing, mainly Body and Soul, weird urban fantasy, The Studio, which tried to be a gothic ghost story, and One shot kill, a retake on the story my writer from Untitled was working on. These and a couple of short stories almost account for 100,000 words! And there is still NaNoWriMo to come, which probably will be something completely random decided on a whim in October anyway… At the moment I’m pushing to lock down One shot kill after it got slumped for two months and hope to be done within the month.
That’s it, I’m officially declaring 2017 an editing and rewriting year. I should have done it this year, but then on a whim I decided to go for 366,000 words in total I’m on track for that goal, too – generally with new material, except for the revision of The Last Yōkai War of Edo, which was quite a rewrite of most of it anyway.
Have some pretty graphs to look at:
P.S.: I’ve taken down the Archives page, because I was not keeping up with it anyway. You may now search using tags and / or categories and I’ll make sure to keep a good tag system current.
## The Last Yōkai War of Edo – Final First Draft
Back in 2014 I gave in to the plotbunnies and started working on the wrapping of the Hyakki Yagyō universe, or what at that moment I thought it would be – the Last Yōkai War of Edo. Apparently, it is one of those things that runs out of control. At that point, the story added up to roughly 40,000 words. Looking at it, it was clear how I had barely written the skeleton of a story – character development was next to inexistent, the main character just switched from trainee to well-trained in a chapter, without any real progression. The antagonist / villain was bad just because and had no motivation whatsoever. I knew that such a thing needed to be worked on, and the story told in a coherent way.
I’ve been doing so for a few months now. And thus the 40,000 have turned into 100,000. Around 10,000 of those had been written in snippets throughout a year or so, things that I wanted in but I had not really woven in.
So I put all them in a file and started working. The first thing was finding a good timeline, one that worked according to the development of the main character’s power and reactions. Then I had to work through the story to get from A to B, to C and then towards the end as I had first imagined it.
I had really not thought that I would be doing so many changes. About 20,000 words were completely retold – not an edit, a complete rewrite of the same events. On top of that, about 10,000 words of the finale were scratched out and re-done. As in the finale now has the same players but the events unfold in a completely different way. It was strange, reworking some parts like that.
All in all, the first go gave me a story skeleton, and this second run a first draft that more or less makes sense. Now I will let it rest for a while before I tackle an actual edit – and not a re-writing!
As I like working with track changes, I can show you how most of the document looked towards the end of edit. I’m shaking just thinking about how it might end up as… So yes, I have a “final first draft”, a complete story that now requires polishing!
## NaNoWriMo Sponsor Offer Review: Fastpencil Paperback Proofcopy
Everyone is entitled to mistakes, and in my opinion, FastPencil made one when they launched the NaNoWriMo 2015 Sponsorship. My initial idea had been reviewing it as “run you fools”, but I have decided that such a thing was not fair to them. While other times I have screencapped the process, I lost my patience with this, so, it did not happen this time.
The offer (which at the time of speaking can be located at https://nanowrimo.fastpencil.com/nanowrimo2015) shown in the image promises a free proof copy and a 70% off in a distribution package for winners. Nothing that we haven’t seen before, but always nice to try a new service.
1. Create the project. Fair enough.
2. Adding titles, descriptors, reviews and such
3. Listing authors and contributors
4. Choose a category for your book
Of course, this is my own opinion here, but before spending time filling forms, I want to see whether you take my file or not, just in case what happened happens. And what happened? That FastPencil expects you to upload a pdf/x file, i.e., one created with Adobe Professional or the pdf export tool from Microsoft Word in Mac. Both are professional tools towards the higher end of the spectrum. Most NaNo Writers won’t be using either, as the tendency is among the amateur pool. And the professionals usually have their own distribution channels by the time they are so.
Hack: you can use the Adobe Professional trial, active for 30 days in order to go around this problem. It will work for one time, but okay. You can walk around the problem (for me, it meant reformatting the whole $\LaTeX$ file in OpenOffice, export as pdf and convert to pdf/x in Adobe Pro). Not convinced by the result, I decided to try their manual formatting.
Importing the rtf files screwed the formatting up, so I found myself having to work on the html front to adapt what I wanted to one of the default styles they have. This is not “friendly” nor easy for most people, FastPencil (I show you html though, because is how I worked. You could work with rich text too).
• Item: out of the six offered styles, 4 are completely unprofessional, and look tremendously ugly. But that is personal opinion, you might disagree with me.
• Item: You must have chapters. They won’t take a one-shot, and the chapters must be sequential. While they do have a “short story” style, for some reason this separates the title on one page and the story on the next.
• Item: Dragging and rearranging “chapters” is a good idea, but the different types of “chapters” are not clear. What’s the difference between a “front matter” and a “back matter”? Why does something called “blank” allow you to insert code there, shows you results and just prints a blank page? If you let me insert code in the blanks, I will assume that you’ll allow me a no-number page that I can use as separator. I’ll obviously assume wrong.
• Item: The preview takes me through the whole compilation project, and I have to download a file every time. This would not be so annoying if the process worked every time and not just 50% of the times. And I like seeing what I’m doing. Shame on me, that I need to check that everything is according to what I design.
• Item: Erasing blocks will take me back to the project page so I have to start the process over again.
Finally! The project is “finished”. By now I’ve dropped two designs, my lovely $\LaTeX$-pdf, a short story, the kanji separators that I made for between-stories and my hope of getting a non-link-blue table of contents and spent about 7 hours (in different days) in the whole project since I started the FastPencil part.
Now it’s time to go through steps 2 – 5 that we did for the pdf, as this is a “new” project, render the pdf (and here apparently people other than me have been stuck for hours) and if you want a physical copy agree that it’s going to be \$9.99, just because + an extra which will depend on how many pages you’ve got (\$0.04 per page). This is for both “marketplace” and “private copy”. The “publishing package” is over \$200, and you have to “commit to buy” now (you would be able to change your mind later, but yes…).
Then you make covers, you’ll have to upload your png of pdf according to the sizing, but the spine is automatic. Make sure you have a look before you choose your cover fonts, you don’t want them to clash too much (again, people have complained about long rendering times. I did not have that issue).
You check the preview, you approve it and you get to ordering (and yet again, people have been complaining about issues here). You introduce the code and the \$9.99 + pages. In my case, 60 pages added up to \$13.61, plus \$1.50 handling, a grand total of \$15.11. I type in the NaNoWriMo discount code and… \$13.61 go away. The handling stays. “Free copy”? Nope. Not if I have to pay \$1.50. But okay. I’ve gotten this far, I can spare \$1.50. I click order.
Shipping charges: \$85.53 from USA to Spain. Screw you, FastPencil.
For the record, though, I did contact them and asked if there was a chance for a more reasonable shipping method, but as I started looking into the forums and Twitter, I saw that it was the tendency. Other charges I’ve come across: \$40 to Canada, \$144 to Sweden, \$76 to the UK and my favourite:
Obviously, FastPencil did not think this through. They did not take into account international shipping at all. they did not realise that their target was not a pool of professionals. I am a bit savvy with computers, and it took forever to get everything to work. FastPencil claims that they offer “publishing made simple”. If that is simple, give me complex code, anytime.
No, I did not order the book. No, I’m not planning to. Hell, I only have three more words to say about FastPencil: “Run you fools”. And now you know the whole story why: Everyone is entitled to mistakes, and giving FastPencil a chance was mine.
Edit: I thought that the review would end here, but no! There’s still more to it. As I was not going to use their service, and concerned with privacy, I decided to delete my content and my trial experiments from the site and their servers. I was able to erase the “project” but I was stuck with the “publication”. This means I was able to eliminate the editable part, but not the generated pdf.
Thus I took to support and found the page to the right (now updated after this Twitter exchange), printed and thumbnailed for convenience. After looking up and down for the “delete” button I contacted support and reached out via Twitter. Apparently, no, you can’t erase your own content on your own, which for me is a bit unsettling. Once I provided the url and title, the “project” does no longer show. However, this process makes me feel uneasy about the whole content management idea.
Of course, the easy version of this would have been to just edit the project blank, but I did not know at the time that I was going to be unable to delete the generated pdfs. Erasing content when the file was an uploaded pdf was easier, as the only thing I had to do was removing the upload.
Unlike the email regarding shipping, which I sent on January 27th, this was dealt with swiftly. I think it was more efficient as I sent a support request from the page, logged in, rather than an email. Maybe public mention on Twitter helped, I don’t know.
Long story short: Erasing your content is not completely in your hands. The updated page does not even mention the possibility of erasing a project yourself.
## Tackling the “Edo” edit
Well, here we are again. I’ve been putting off a few things lately, and blogging about writing has been one of them. Shame on me, yes, I know. Editing has been another of those things. I have been working on the short one-shots in the Hyakki Yagyō universe because I was too afraid of working on Edo. Afraid, lazy, unmotivated, call it as you wish.
But editing the whole universe is this year goal, and it is not going to fulfil itself. Thus, I set myself to the task.
The first problem with Edo was deciding on the name. The last Edo yōkai war was the one I had at first thought, but I have decided to go with The Last Yōkai War of Edo, which I started using halfway through the first draft writing.
The second problem was the almost 10,000 words written outside the draft, which had to find a way in the complete story. I think those are placed by now – even if not waved in. Along those there are random notes like “living mummy”, “more Tomori” and “explain this character”, “Tsukioka??”.
And the final problem is that I intended a short wrap-up story, and ended up with a 40,000 words draft with quite a few plotholes and contradictions with the main story. Oh boy. So I pushed it back because it was a lot of work, but as I said before it has to be done.. remember when I spoke of universe weaving and that it was fun? Let’s all forget about that (in case you had not. I kind of had).
Oh well, let’s see how this pans out, I am not too sure myself.
## Hyakki Yagyō Editing *insert epic music here*
As I mentioned before, one of the tricks I use with myself when I am editing is tracking changes. Stats and figures are another way I bribe myself into doing edition work.
In the case of Hyakki Yagyō, the story has been a bit more complex:
1. The first version was written on summer 2012 after coming back from Japan the first time. My friend Efficient Times was at that moment working on a story that dealt with yōkai, and the idea settled while trying to help her figure certain things. Actually the original seed had been planted a long time ago (around 2008, maybe?), as part of a TV series an actor character was shooting. I had not been aware that it would be so strong and catching, and would root so firmly once it started.
2. After that I wrote a couple of one shots/short stories, which added to the universe, but were only… marginal. Even The Yukionna’s Claim was nothing but a fun experiment.
3. Second version added two chapters into the first one. both of them wanted to introduce in the story two places that I had visited and found quite magical / creepy. That was early 2014.
4. Afterwards I ran into the problem that I had been avoiding for about a year. The story was longer. The characters had expanded past the ending of the first book. There was another book in this universe, there were storylines unresolved that needed attention. So I gave up and wrote a very schematic version, no chapters, no anything, just the raw story. And left it at that.
5. This year, with all the written information in mind, I have tackled the goal of editing the whole thing, and somehow it is working. However, I had never imagined, not in my wildest thoughts that the Hyakki Yagyō story would grow so much – and that it would end up being so even and well-balanced, with each story arch. The increase has been around 20,000 words from version 2, 30,000 from version 1, leaving the whole thing at 81,000. Just on the first story, the devil knows how this thing will end up being when I am done with everything.
Word average averages (without epilogue):
V1: 5551,8
V2: 5577
V3: 7280,2
Total wordcount:
V1: 50708
V2: 62089
V3: 80923
I’ll keep you posted 😉
## I hate editing – but it has to be done
I hate editing.
I really do. I find it tedious, frustrating and most of all, unrewarding. I feel that I keep focusing on everything bad, to the point where there’s nothing right anymore. When I was preparing Tokyo 893, however, I learnt how to motivate myself to edit, and that was something quite silly – I track changes. When I track the document changes I actually see the progress, I work faster and I do feel improvement. I tend to do big overhauls when I edit, so I guess that in a way it is logical that seeing the changes helps me work better.
So I end up with files that look like this:
A light scene which was not changed much
The average look of the document…
I am at the moment embarked in the not too small work of going over Hyakki Yagyō. At the time I wrote it, it was the biggest word count per chapter and scene that I had ever done in a long piece, averaging around 5550 words per chapter, not counting the mini epilogue. It was a total of 51,000 words.
Of course, at that time I was not counting on the universe expanding, sort of what happened with the Shikigami. However, tackling Hyakki Yagyō felt like a more accomplishable piece of work to start the serious editing that I had decided this year.
The original Hyakki Yagyō story was followed by a series of short snippets that tried to explain what Ko was. Actually, that idea came almost by accident working on Axis 95/11, which had nothing to do with it – I needed some sort of legend, so I came up with the ‘tree of Shibakoen that does not lose its leaves in winter’ idea. It kinda caught on me so I scribbled a few short stories regarding Ko’s legend and its history.
Soon afterwards I wrote a short story, The Yukionna’s Claim, around 6000 words (which I am at the moment considering to include in the main Hyakki Yagyō story as a second epilogue of sorts). Then I went back, in 2014 to the original Hyakki Yagyō story and added two chapters, making it clock in at 62,000 words – these two chapters were inspired by places I visited during my trip to Japan in summer 2013.
Soon after writing these two chapters I started working on a second big story, the Last Yōkai war of Edo, set twenty-something years after the first one. I knew that after a couple of years I remembered the key points to write the skeleton of a story – and so I did, fully intending to go back to it when the time was right.
So here I am now, going back to the basics, and taking an insane amount of notes, Koreans in the bedroom and things to be reworked. It is creepy how the little specks that were not resolved in the first story are so open to be solved in the second one. And what’s even worse… fixing plotholes that you had forgotten you had already fixed!
Maybe I should have just rewritten the whole thing XD
Finally, a word of caution to the wise… if you ever plan to write a sexless character… decide on the pronoun right away. Else editing will become a bloody nightmare. You’ve been warned.
## The Last Yokai War of Edo: Writing Report
The Last Yokai War of Edo takes in the Hyakki Yagyō universe, twenty years after the first story, and three or four after The Yuki Onna’s Claim. It is not really ‘futuristic’, but I think that was the last thing I was aiming for, I was trying to focus on the emotions and the interpersonal interactions (well, human-yōkai-spirit ones at the very least).
The OABu is still running, and it has changed its policies to some extend. Some of the characters from both the previous stories show up, but the main focus is on Minamoto Shun, the OABu’s most recent incorporation. The kicker is that Shun is not a Shinto onmyōji, he’s a Christian with some powers that he can’t control, and who has… different values.
Shun is about to learn that his powers brush the unimaginable, and that everything he has lived is pointing him to the choice he has to make. When he meets the creature that dwells in Shibakoen, his perception of good, evil and yōkai switches, and he makes a decision. He is willing to tamper with ancient magic and forgotten spells in order to meet his goal, which might not be a totally sane one.
Cryptic? Yeah, I know. But the problem is that it is very hard to talk about Edo without spoiling anything previous. All in all, this story clocks in at roughly 40,000 words, which sets the universe in the 110,000-range after adding the two chapters to the original story.
The story flowed really well since the moment I realised where I was going with it, and it has made me feel like writing Abe no Seimei’s diary, which in-verse is referred to as ‘The Lost Book of Abe no Seimei’, and thus telling all his story but a) research and b) first person deter me…
All in all I had fun being back to this verse, but I fear I have a lot of editing to come in the future if I want it to make sense and not to find myself with too many Koreans in the bedroom.
## The first look at The Last Yokai War of Edo (*)
(*) Edo: Former name of Tokyo
After working on adding a couple of chapters to Hyakki Yagyō in January, I started to work on a story in the same universe set a couple of decades after the end of that story. I used The Yukionna’s Claim one-shot as tie in between the two stories. If one ignores that it sort of got out of hand, and I just passed 13,000 words. It was not expected, though. The Last Yōkai War of Edo was not supposed to be that long, however the main character, Minamoto Shun, developed much more depth than I had thought he would.
Shun was brought up a Christian, but he is an onmyōji, which brings him in contact with the creatures from Shinto and Buddhist tradition. When he is recruited by the OABu and moves to Tokyo, he falls into a heart-wrenching crisis of faith.
I am worried about Kikuchi’s evolution. He is a greenhorn in the original story, but now he’s over 40, and quite close to the high hierarchy of the OABu. However, it seems that the only thing that ties both sides of the character is their hatred for Ko. Sometimes they don’t feel like the same person, but some others I think they’re totally unconnected.
For now Tomori’s character is rather unrepresented, as a new arrival named Tsukioka is taking up most of his screen time, and Ko is not even featured except having his name mentioned. He is supposed to have a key role… eventually.
There were a few things that I would have liked to get into Hyakki Yagyō, but I did not find how. I skipped writing about tengu, because I was not sure about how to feature them, and although I always knew that there was a huge force field around Sensō-ji, I only mentioned that a couple of times during the main story. I just wrote the tengu in, and I have plans for Sensō-ji, along with something else I am dying to feature, if I manage – Billiken, Osaka’s god of things as they ought to be. Shun really needs a pep-talk from him, I’d say, about life, the universe and everything before the young man drives himself to a stroke.
For now, Shun has no idea of what is in for him, but the problem I find is that the plot leaps from event to event, with nothing much happening in between, so I am not sure the characters are developing logically. I’ll have to see to that when I have the whole skeleton, whether it is a better idea to keep the story as is, or divide it into chapters to help acknowledge the time jumps.
## Universe Weaving
You might have noticed on the last post that there was a blank day in 2013 when I did not write. That day I was in Tokyo, more precisely in Hikawa Jinja, and I decided that I wanted to delve deeper into the Hyakki Yagyō universe. To be honest, I had not really let go of that verse and last year I wrote about 7500 words in related stories. However, what I felt like doing that day was adding to the main book, to the original story. I took notes for two new chapters, and when I came back I filed those notes with all the writing material, and sort of forgot about them.
Hikawa Jinja, Akasaka, Tokyo, with awful lighting, I know.
I did not really forget about them, if I am completely honest. I just put them aside because I was somewhat scared of picking up the main book again and finding that I could not add to it. To my surprise, it was not that hard – as a matter of fact it has almost been ridiculously easy. The two chapters have been written, and they have flowed rather well – aside from not feeling like writing sometimes due to personal issues. Both chapters have been written, one set in Hikawa Jinja, as planned, the other one set in Ueno Zoo, also as planned, adding about 11,000 words to a 51,000 word story. Right now, I am considering though writing some more within that verse, another marginally-related story, set a few years after the first (and main) one, but I am scared that it’ll get out of hand XD”
On another note, I have been noticing lately my little obsession for weaving universes into each other. I knew that Lifequake and Axis 95/11 belonged to the same universe, but during a recent edit I found myself linking both to Blood Moon. While it makes sense, well, it is strange that the chance was so open and it was such an easy thing to do. In the same way, I am now absolutely sure that The Barman and Shorai are likewise joined – by the dogs, if you want details. Apparently Tamon will be Tadashi’s obedience instructor when he gets his dog Taki in a few years (yes, Shorai should last a few years. And I’m on its sixth month. Urgh.). Then there is also the Retriever universe, which in my mind still lacks a closing with the secondary characters. And well, of course, the Osaka Guardians series…
While I don’t think this is something ‘new’ for me, it suddenly hit me as I wrote the edit into Axis 95/11 that I really like those little insiders. They are fun. I like weaving.
## Hyakki Yagyō Scenery (2)
As I have recently come back from Japan, I’ve taken a few more pictures from the areas that appear in Hyakki Yagyō. As the post tries to be mostly visual, I’ll try not to get too much into descriptions and the importance of each place, just let you catch a glimpse of them. These are my photos, so they might be a little artistic (read: loopsided or overexposed).
Zozo-ji (San’en-zan Zōjō-ji (三縁山増上寺 San’en-zan Zōjō-ji) area (Minato, Tokyo), with the main temple and Tokyo Tower behind it. The area where Ko is planted is between the graveyard behind the temple and Tokyo Tower.
Gotoku-ji (豪徳寺; Setagaya, Tokyo), the temple of the good-luck cat (which I never managed to find open):
Sensō-ji (金龍山浅草寺 Kinryū-zan Sensō-ji; Asakusa, Tokyo), with the great paper lanterns:
Tokyo Metropolitan Government Building, where Satoshi works, and the Shinjuku skyscraper district where it it is located:
Nikko (日光市 Nikkō-shi) area:
Yokohama Chinatown (横浜中華街, Yokohama Chūkagai):
Kinkaku-ji (金閣寺, “Temple of the Golden Pavilion”), in Kyoto:
Fushimi Inari Taisha (伏見稲荷大社), in Kyoto:
Kamakura (鎌倉市 Kamakura-shi) and the komainu (lion dogs):
Related: Hyakki Yagyō Scenery (1): Shiba Kōen [link], Hyakki Yagyō Research [link], | 2017-08-24 08:35:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4059816002845764, "perplexity": 1556.646323337561}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886133447.78/warc/CC-MAIN-20170824082227-20170824102227-00695.warc.gz"} |
http://oboy.smilebasicsource.com/brokenr3c0rd/logger/2017-05-27.html | • GeekDude
• Joined: 16/03/2016
• CoinzReturns
• Joined: 26/12/2015
• Joined: 24/05/2016
• MasterR3C0RD
• Joined: 18/10/2015
• Trinitro21
• Joined: 17/10/2015
• 12Me21
• Joined: 31/12/2015
• Lumage
• Joined: 14/10/2015
• randomouscrap
• Joined: 14/10/2015
• Lacks
• Joined: 14/03/2016
• 5logank
• Joined: 15/10/2015
• Chemicalex
• Joined: 26/10/2015
• ColinTNMP
• Joined: 16/04/2017
• Midnoclose
• Joined: 03/12/2016
• BrianXP7
• Joined: 15/10/2015
• pixel_voxel
• Joined: 14/10/2015
• RealTiP
• Joined: 16/10/2015
• andritolion
• Joined: 22/07/2016
• snail_
• Joined: 14/10/2015
• HylianHoundoom
• Joined: 15/10/2015
• Guzzler829
• Joined: 15/10/2015
• ElzoBro
• Joined: 14/10/2015
• GoodGameGod
• Joined: 28/05/2016
• lilstrubel
• Joined: 02/10/2016
• Joshuaham123
• Joined: 04/06/2016
• Perska
• Joined: 14/10/2015
• HTV04
• Joined: 18/03/2017
• Imasheep
• Joined: 18/05/2017
• PhilFish
• Joined: 14/10/2015
• coucou_COA
• Joined: 27/05/2017
• Kuragen
• Joined: 25/04/2017
1. 5logank has entered the chat.
2. 5logank has left the chat.
3. none really
4. CmonWould you put stickers on you're 3DS?Nice
5. you are 3dS
6. I say this with all my love.
7. that was fun
8. Fuck you.That was amazing
9. That was sight readingThank you lol
10. https://www.gnu.org/audio/gnu-pronunciation.ogg
11. did ptc do sprite/bg ordering in any way i don't remember like how sb has z coordinates that determine which things go above which
12. You can totally play that though
13. No, no I can't haha
14. Nothing in that song was so ridiculous that you couldn't do it with practice
15. Maybe once I get 50 hours under my belt :p
16. No I mean eventually. It wouldn't take that much pft nawIt's a nice and regular rhythmYou'll definitely start feeling itok now I have to get killed by psycho pass
17. The fast ones you do I can barely trackI have to take off for supper :/
18. i know GPRIO was a thing but was there anything for sprites and bg
19. oh no worires
20. But, uh, Logan.
21. I'm glad I got to play something you liked
22. About the account. Are you just looking to tie up loose ends?
23. Yeah
24. The lockout ban would only really prevent you from coming back. There is no personal info linked to the account that wouldn't still be there if it was locked out
25. can you change the username to something else?
26. I can do that if you would like, this way if you do want to come back all you have to do is remember the new name.
27. I dont think I'm coming back
28. I understandSo, what do you want the new name to be?
29. wen u move up 356 places on the global rank
30. Feels good.jpg?
31. I dont care really
32. icoulddobetter.jpg
33. 5logank has left the chat.
34. 5logank has entered the chat.
35. Why are you leaving @5logank
36. LolI joined this community when I was like 10 or 11 or somethingI must have been annoying
37. Actually, out of most of the younger kids, you were pretty chillNever thought you were a kid actually
38. Even back at the wiki>
39. I don't remember you there
40. Trinitro21 has left the chat.
41. ;(
42. I wasn't really active there
43. I'm an old man now
44. LolHere, you only have like2 pieces of activityhttp://smilebasicsource.com/user/5logank
45. Trinitro21 has entered the chat.
46. You joined the Wiki in 2013, so I'm assuming you're around 14 or 15 now
47. For the love of god I was 9? (Basically 10)Probably 10
48. Oh, so you're 13 or 14
49. Lumage has left the chat.
50. Lumage has entered the chat.
51. Your join date was October 28, 2013http://petitcomputer.wikia.com/wiki/User:5logank
52. 9The thing is I don't remember ever misspelling anything
53. Chemicalex has entered the chat.
54. That's what I use to judge when something happened lol
55. What's going on again?I don't know the context
56. AhI was talking about when I joined the wiki
57. what sparked this anyway
58. Me deleting my account
59. He wants to delete his accounts
60. i know but why
61. I think he thinks he was too much of a nuisance or smth
62. "was"
63. ColinTNMP has entered the chat.
64. Chemicalex has left the chat.
65. Chemicalex has entered the chat.
66. Which is honestly wrong, since he's rarely been active on SBS and no one really cares about Wikia at all anymore since it turned to shit last year
67. That's not why I'm deleting my account lol
69. "delete my account" "why?" "idk"
70. you're too loud.
71. SORRY FELLOW HUMAN, DID MY SMALL LETTERS OFFEND YOU?
72. how can you make text loud...i stand corrected
73. OWWWW MY MICR- ER EARS
74. Trinitro21 has left the chat.
75. maybe you could tell us why you want to leave
76. Lacks has left the chat.
77. speaking of leavingo/
78. Chemicalex has left the chat.
79. randomouscrap has left the chat.
80. Midnoclose has entered the chat.
81. BrianXP7 has entered the chat.
82. an oni told me you kids started playingosu!i'd like to interject for a momenti should leave. bye.
83. Hi
84. heyosu! mapping theory is horribly flawed, by the way.
85. Yeah, a lot of us have been playing osu!
87. I started, played for a month, got everyone else playing it, and now I'm second to Random
88. here, have some bemani shithttps://p.eagate.573.jp/game/eacsdvx/iii/p/common/top.html"and everyone said no"you could make a religion out of thisno really though, osu!'s one of the worst rhythm games to even exist.
89. "and Brian returned after like a year" You could make a religion out of THIS
90. WELL
91. randomouscrap has entered the chat.
92. WOAH HEY BRIAN
93. OH SHITSENPAI
94. Oh hey look I found a weaboo
95. If you're going to complain about osu feel free to do so, just know that I love the game
96. SUGOI DESU NE!
97. *osu!Lol
98. play a better game like project diva, lol
99. nah I'm having funobjective goodness or badness doesn't matter in the face of enjoyment
100. damn, you got me there
101. Heh, watching like 15-20 different anime in 6 months puts me somewhere near the border of "over-casual anime watcher" and "weeb lol", so I guess I can't call anyone a weeb lol
102. CoinzReturns has left the chat.
103. you can, but it's out of irony now i guess.
104. Definitely wouldn't call myself a weeb, just some guy who prefers anime over shitty teen dramas
105. 5logank has left the chat.
106. BrianXP7 has left the chat.
107. BrianXP7 has entered the chat.
108. anime is the only thing that exists anyway
109. Anyways, I'd check out Project Diva for 3DS if there wasn't a huge banwave right now
110. pixel_voxel has entered the chat.
111. Damn it why
112. hey pixle
113. Haven't you learned yet from that other server you were allowed intoHi
114. hm?
115. You know that other time you showed up to tell people who enjoy osu! that the game sucks and everyone just called you annoying and then you left and never returned
116. Lol
117. haha, /r/touaoii
118. try typing some letters that mean something next time
119. why are you installing texwe have tex on sbs
120. I need latex to write a dictionaryno but I want to do it in emacs
121. ...sbs doesn't have emacs?
122. and I don't want to have to SFTP every time
123. ah
124. we don't, no.
125. oh well that's easy to fix.
126. I'm having second thoughts about TeX Live though. I know you said TeX was huge but I didn't think it was "79/3395 after 4 minutes" hugeI don't want you to install something huge if I don't use it on the server that often.
127. yeah it's hugewe ALREADY have tex thoughthe full thing
128. argh alright
129. and now we have emacs. You don't have to ofc but it's an option
130. okaylet's uhwhat's the best way to do thishmmm probably SSH through Powershellyeah that's it
131. Lacks has entered the chat.
132. I forgot what i was doing already
133. Chemicalex has entered the chat.
134. Chemicalex has left the chat.
135. Chemicalex has entered the chat.
136. oh yeah dictionary
137. Chemicalex has left the chat.
138. Chemicalex has entered the chat.
139. https://youtu.be/gUaoGGHokf4
140. awwwwh yeah
141. SSH through PowerShell?
142. no not reallyI mean it's possiblebut I'm not installing a hotdog to do it
143. 12Me21 has left the chat.
144. I got banned after the sighax ban wave
145. dang
146. gottedabsolutely and utterly gotted
147. Look and see if there's ways to unban. I'm sure someone has something
148. this alignment isn't right
149. i wasn't affected, thankfully
150. ^
151. oh well formatting is for losers
152. do you need more packages?Am I missing anything you need for emacs
153. yeah I love packagesnoIt's fineI need a better terminal
154. I haven't checked my friends list recently, thoughI...shouldbrb
155. Chemicalex has left the chat.
156. I need to get off my ass and install gentoo, reallyI'm sure I have a proper ssh client somewhere
157. Chemicalex has entered the chat.
158. okay i'm good but why the heckeroni was my favorite title FBI
159. the emacs installation is fine thoughPretty Alright™
160. why is "favourable" a word to this but "favourite" isn'tisn't favourable a british spelling too?
161. oh shoot right caching in specialpick five lettersthree actuallytoo late
162. oh random what's the highest difficulty you've gotten SS on?
163. I don't go for ssaccording to this it's 3.33
164. i know but you have to have gotten ss somewhereoh okI should try beatmapping, the editor seems nice
165. Chemicalex has left the chat.
166. "wrong"
167. BrianXP7 has left the chat.
168. BrianXP7 has entered the chat.
169. ColinTNMP has left the chat.
170. also thank you for emacs randomit's a lot better than I thought it would beyeah suddenly I'm in slightly less pain that usual
171. Chemicalex has entered the chat.
172. that usual
173. Chemicalex has left the chat.
174. oh no worries
175. I can't tell what "internet number" is supposed to be, if anything.
176. I have to go ( ﾟ▽ﾟ)/
177. \o
178. randomouscrap has left the chat.
179. that was encoruaging
180. Chemicalex has entered the chat.
181. is it still encouraging if I tell you he has a script that replaces "o/" with a random waving kaomojiOh it's off-center because it's two pages
182. Chemicalex has left the chat.
183. Chemicalex has entered the chat.
184. Lacks has entered the chat.
185. Lacks has left the chat.
186. o/um
187. Chemicalex has left the chat.
188. Chemicalex has entered the chat.
189. Extremely good join/leave messages
190. thank you i'm quite proud of them
191. superb.
192. picking random image from my 3ds image library...awwh
193. "Do you like hurting people?"
194. Chemicalex has left the chat.
195. Chemicalex has entered the chat.
196. RealTiP has entered the chat.
197. hi
198. So I bought a gameboy micro>hi
199. what for?
200. worked nicefor the first two minutesand then it died
201. good investment
202. so I knew for sure I had an ac adapter to charge itbut then... turns out advance sp, advance, color, original, ds lite and so on don't actually fitI swear I have every nintendo charger except the micro's
203. since when did the color have an ac adapter
204. shhhhbatteruuus
205. i've had like 1 color and 3 advances and they all used batteried
206. andritolion has entered the chat.
207. >TiP's doin some nontendo offbrand rechargable junk
208. The Switch kickstand sucks... Why couldn't they use a Surface kickstand/hinge?
209. "nontendo offbrand rechargable junk"so now I'm searching the internet for an actual charger
210. you don't just have AA batteries
211. AA batteries are bigger than the micro
212. Chemo?
213. what
214. this thing is truly pocket-sized
215. for my size, everything is pocket-sizeheck i have a kindle in my pocket right now
216. Why didn't they make the Switch have a better kickstand... I mean, it SUCKS...
217. I could fit a 10" tablet in my pocket lmao
218. Can you put a Surface in your pocket?
219. probably not
220. not my hand
221. >for my size, *everything* is pocket-size
222. not my pic
223. haha ~~fat~~
224. woah a gb micro
225. for my size, *everything* is pocket-size
226. ColinTNMP has entered the chat.
227. is that your banana though
228. What happened to ** for italics?
229. that'd scare me if someone took my nanab for scale
230. welcome to /md
231. it's still there you knowyou're just not doing it
232. i has gameboy micro...
233. I am not mding it...
234. oh wait
236. you're not doing it right
237. you said ** for italics
238. no charger ;-;
239. OH WAIT
240. I have a GBC.
241. *text*
242. wrapping i am a very not smart think
243. All my other gameboys are broken...
244. I have 3 GBAs, the best one
245. 'cos childrens
246. Chemicalex has left the chat.
247. GBA SP is best
248. Chemicalex has entered the chat.
249. filthy no backlight things>how dare ye
250. chao garden
251. i
252. ~~petit~~ chao garden
253. don't even dare mention this filth in my presence
254. got pastconcept
255. i meant it i will end you
256. ualok
257. no wait I don't have a penyou can't just start drawing crap without me
258. didn't even slow pen :/
259. Chemicalex has left the chat.
260. I tried to look for a chao doll to buy but they don't really exist, as it turns out
261. Chemicalex has entered the chat.
262. I think there was somebody on etsy but that was... that was bad yeah.
263. protip don't stop fidget spinners with your eyelid
264. gg
265. ...or your teethdang frick that hurt a lot more than i thought it wouldfidget spinners become elite dentistry tool when
266. Midnoclose has left the chat.
267. my n3ds is melting
268. cool
269. :I
270. see what i did there
271. i'll just stuff it in the freezer
272. heuhehahahr freezer burn
273. it is now in the freezerit burns
274. Did you try ARMS?
275. andritolion has left the chat.
276. andritolion has entered the chat.
277. gonna take a pic of my new micro... after my n3ds stops being on fire
278. How is it on fire?
279. that's kindathat's kinda almost acceptable
280. its still hot...
281. Lummy?
282. Chemicalex has left the chat.
283. Did you try ARMS?
284. Chemicalex has entered the chat.
285. TiPpy?
286. I think I already have those.They're okay.I wish I didn't.
287. No, the game...Not your actual arms...
288. oh the game yes of course right yessir just a moment
289. The testpunch is over...
290. no I haven't considering I don't have a video entertainment console
291. Ummmmmm....
292. gonna take a pic...
293. Of?
294. his banana
295. Lolol
296. wait no that doesn't sound right
297. fruit.
298. No p*** here...
299. cant actually find my bananas...
300. Chemo? Hot a switch?
301. i'll go check
302. *got
303. hear that tip we can't p*ick* fruityes i think the switch is hot
304. snail_ has entered the chat.
305. It is really hot... I once covered the air vent for fun, and I burned myself...
306. so... i have grapefuit, cucumbers, and ears o' corn*grapefruit
307. snail_ has left the chat.
308. I just had to touch the metal part of the heat sink...
309. close enough
310. which shall i use?
311. pixel_voxel[04:08]o: i'm six but i draw animeoh that's not how copy works
312. That's almost applicable if I could just put the pencil on the paper like a good boy.
313. umn
314. Oh wait I couldn't do that for a whole year haha
316. "\item [chinese cartoons] Japanese cartoons."
317. do a hand reveal tipperino
318. it's been two daysI think it's too late for hand reveals
319. yeah, no thanksno hand reveals today
320. Meow
322. Me.
323. i have way more 3dss than i thought xD
324. Lolol
325. what
326. *3DSes
327. i have eight xD
328. I like how emacs actually works unlike nano and vi
329. this is leli forgot about all o deez
330. WormWhom
331. how the hell do you forget about like 7 $200 investments 332. shh 333. Wowm 334. i only forgot 4 335. I am trying to say meow in reverse....Damn you autocorrect!!!Woes 336. can't find my 3 blu onesor meh red:( 337. WoewWormWoem 338. spam 339. Finally !!!Sorry... 340. jelly, hex?:P 341. Hello? 342. what 343. Wonder why Nintendo made such a bad stand... 344. trying to stack all my current nintendo handhelds 345. Make a Surface kickstand, will you??? 346. no i'm just wondering why one spends$1400 on a $200 device 347. Huh????When? 348. Chemicalex has left the chat. 349. looking for ds lite now 350. if they aren't balanced on a dogs nose.... 351. Lacks shakes fist in an eastwardly direction 352. Should I stack all my Nintendo stuff? 353. noyou tend to break stuff too often 354. Y not?O 355. i found half of my 3dses 356. top half or bottom? 357. 4 3dses 358. why so many? 359. 3 o3dsxl, 1 n3dsxlthey're all xls>cos regularrr sssuuuuuccckks>kidding 360. BrianXP7 has left the chat. 361. Should I stack my Wii, Wii U, 3DS, new3DSXL, Game Boy Color, and Nintendo Switch 362. still searchin around 363. stack physical game collections 364. Chemicalex has entered the chat. 365. preferably cases 366. Most of my games are download, so that stack will be rather small... 367. Chemicalex has left the chat. 368. Chemicalex has entered the chat. 369. I just found all meh bluesno red though... 370. oh lacks i can do that 371. all consolesbrownie points if you got the cardboard boxes XD 372. Should I stack my Xbox One S, and PS3 too? 373. ps3 on the bottom! 374. k... taking a pic with my n3ds 375. no put the smallest one down 376. GBC on top? 377. gbm on topthis is a big stack xDit's not even all xD 378. stack them in chronological order of release 379. No, Xbox One controller on top... 380. cucumber on top 381. Ewe... 382. actually cucumber on side 383. *ewe 384. don't forget the whipped cream 385. *ewwDAMN YOU AUTOCORRECT!!! 386. don't forget the shark tale on ps2 387. HylianHoundoom has entered the chat. 388. Chemicalex has left the chat. 389. why so many furries on this site? 390. Gtg watch MacGyver (2017). Bye!Cuz there can. 391. cucumber, eggplant, ear o corn, or potato for scale? 392. I prefer furries to anyone from that server at this point 393. what server? 394. dont bring your bs discord drama here 395. I didn't say anything. 396. ? 397. I think I am one... 398. what server? 399. server? 400. brian's server? or shadow's? 401. umm... veggie/fruit for scale? 402. I'm not part of shadow's server, i think it's shit 403. Bye. 404. definitely chihuahua bye andrito 405. o/ 406. right well then there's only one option now isn't there 407. bye tolionI have an IMPORTANT question>cucumber, eggplant, ear o' corn, or potato for scale? 408. none of those are good scales 409. >can o peaches, and grain of rice also an option 410. the console itself is it's own scale, since we've all seen at least ONE of them lol 411. cucumbers vary widely in size, eggplant is oblong, corn is ok, potato is overrated 412. my brother is drunkwtf 413. i can also do pea for scale 414. that works 415. people get drunk sometimes it's not that big of a wtf 416. you know what? I'll just use all 417. bannana for scalebanananananananananananananananananananananananananana 418. Trinitro21 has entered the chat. 419. got a picusing a 3ds...(expect lo-quality)also, one of em is onlooks dumbshoots 420. Trinitro21 eustachian tube blockage hurts 421. "kawaii lightning pistol" 422. i need to open the back to access sd...using another 3ds 423. ha 424. ear ache? 425. ye 426. :( 427. i removed the screws from my n3ds back coversi have stuff behind my eardrum 428. im too lazybut theres a stack of 3dses in front of mesooo...pardon my messy deskits a really messy desk2 of those are dsis4 are o3ds xls1 is a n3ds xland I'm holding a o3ds xl to take piccouldn't fit all meh 3dses 429. is that plastic food 430. noall meh veggies are wet:/Proud of me? 431. https://www.humblebundle.com/store/rising-storm-game-of-the-year-editionFREE SHIT 432. also,yes that is an mlp deck box 433. ColinTNMP has left the chat. 434. that is a good game if the mp is still alive 435. HylianHoundoom has left the chat. 436. RealTiP has broken chat 437. it's like the buffet warren billionaire once saiddon't let your drears be frearfsshoot how do i kill a buffer 438. sometimes i want there to be an option to open a js file in the browser without an associated html file where it starts you off with a blank html like <html><head><title></title></head><body></body></html> 439. mmm 440. about:blank and enter javascript:? 441. no like "open with" in file managers 442. I guess 443. Midnoclose has entered the chat. 444. Midnoclose has left the chat. 445. Lacks has left the chat. 446. Chemicalex has entered the chat. 447. ohno is there lag 448. idkno one knows 449. Trinitro21 has left the chat. 450. Lacks has entered the chat. 451. Guzzler829 has entered the chat. 452. hello guzzler 453. yes ptc did that, but with call codeslittle late, but whatever 454. chat feels sluggish 455. sluggish? 456. no chat 457. It usually is at midnight 458. slow chatits 6 pm here 459. Nice timezone you got there 460. ...?thanks...? 461. sometimes I wonder whats worse. To live on the east coast or west coast. and then I remember Hawaii 462. ...?thanks...? 463. for time zones lol 464. Hawaii is way out there lolI've never lived on the west coast. I've only ever been to eastern and central 465. yep 466. Central is where it's atnowadays time zones seem ever more irrelevant unless it's a midnight launch 467. whoopslooks way too big though 468. How is this even the USA lol 469. we were forcibly annexed...after a promise we wouldn't be 470. Chemicalex has entered the chat. 471. Chemicalex has left the chat. 472. ...but less about hawaiian history... 473. I wonder why regina has a red dotand they didn't even put Vancouver on it even though it's WAY bigger 474. less text space maybe 475. Wow tip we're as far away from each other can be in the same country lol 476. yep 477. I'm in south Carolina 478. im that red dot in the middle of the ocean 479. I'm slightly above that city that rhymes with fun 480. obviously quebecTripleG is scarily closea hop, skip and a leap away(and a 15 minute flight) 481. Put a fake gift at his doorstep 482. i could if i wanted to xDhawaii is purtrtrty boring 483. Not the way you out it 484. lol did you see the pic I sent of saskatchewan the other day?We drove 30 minutes to look at a farmer burning stubbleTHAT'S Boring 485. i saw a pufferfish in the canal the other day 486. I'd much rather live where you do than here 487. :o 488. that was boring 489. I know to you that's normal and boring, but that's super cool to us 490. i saw like three other pufferfish afterthey get real big in there 491. I saw some northern pike 492. I have two neighbors: My grandparents and some lousy introverted old family 493. bastards weren't biting tho 494. There's literally 10 real people in my life 495. http://kland.smilebasicsource.com/i/yvtqw.jpglook at thisaw crap 496. Looks similar to where I live 497. damn manta got too close the last i went fishing. had to get outta da waterhttp://kland.smilebasicsource.com/i/yvtqw.jpgseems like another planet 498. @34.3149828,-82.6649689,3a,75y,183.24h,92.72t/data=!3m4!1e1!3m2!1sKSz6dtwGGTfoC5VQSAUy7Q!2e0!4m2!3m1!1s0x885876139b7623a3:0x304cca3fcd85920d">https://www.google.com/maps/place/Iva,+SC+29655/@34.3149828,-82.6649689,3a,75y,183.24h,92.72t/data=!3m4!1e1!3m2!1sKSz6dtwGGTfoC5VQSAUy7Q!2e0!4m2!3m1!1s0x885876139b7623a3:0x304cca3fcd85920d 499. The Ala Wai 500. With what 501. lol don't like your address!link* 502. literally water roaf*road/way 503. @34.3149828,-82.6649689,3a,75y,188.49h,95.27t/data=!3m4!1e1!3m2!1sKSz6dtwGGTfoC5VQSAUy7Q!2e0!4m2!3m1!1s0x885876139b7623a3:0x304cca3fcd85920d">https://www.google.com/maps/place/Iva,+SC+29655/@34.3149828,-82.6649689,3a,75y,188.49h,95.27t/data=!3m4!1e1!3m2!1sKSz6dtwGGTfoC5VQSAUy7Q!2e0!4m2!3m1!1s0x885876139b7623a3:0x304cca3fcd85920d 504. what kind of fish are those? 505. .....what 506. google hates you 507. you don't want to eat thoseor catch them 508. I don't eat ANY fish hahaha 509. *actually they're okay to catch 510. I just wanna make em late for something 511. Okay I need to lz this 512. the ala wai is a long, big canal that goes to the oceanunfortunately... its kinda... 513. http://lz.x10.mx/?i=D1H 514. plagued 515. Not my address, I don't actually live in town 516. wow where are the mountains?http://lz.x10.mx/?i=Krn 517. 3,400 km away 518. mountains everywhere 519. That place looks awesome though 520. that does 521. I'd love to live there despite my need for seclusion 522. fuck thatI want the seclusion 523. Here's some more Ala Wai Canal things: http://www.honolulumagazine.com/Honolulu-Magazine/August-2014/It-Came-From-the-Ala-Wai/ 524. So I hope you like tourists TiPwe have a..... weir..... 525. tourists are very... ignorant... usuallyalso, those fish are just common tilapia 526. ElzoBro has entered the chat. 527. I swear I like seclusion but not the amount haveYou get REALLY tired of the same old 6 people every day 528. Yesterday I leanred that it's possible to have both a Dutch Accent and a Southern accent at once? 529. lmaothat must be goofy af 530. ^heres a cool thing: 531. how far out of town do you live, Chem? 532. This one guy that i've been chatting with all year on my phone and we mever talk irl (but I've fallen hard for) approached me on the last day for the first time and I died of anxiousness, but it went well. He sounded way diffwrwnt than I thought he did/would 533. The Greater Amberjack // Kahala >not to confused with a certain mall 534. He doesn't seem to be a 100% english speaker, he has some sort of accent 535. thats neat 536. About, uhh2-4 miles 537. And his conjugation is a little slow, although he may have just been nervous to talk to me lol 538. ice fishing this winter 539. But he kepy having random boughts of southern accent and it was funny to me lolOmg Lacks 540. you should catch a wild hawaiian kahalathen maybe eat it 541. Fishing sounds like it would take too long for my low patience sadlyI went once in 5th grade for a field tripThe worms were nasty 542. it does take patiencelol 543. And I almost got stabbed lol 544. http://lz.x10.mx/?i=9ti I live very close to this car dealership 545. we got leeches in our fridge right now 546. (it'll kill you, 'cos their intestines had formed a sybiotic relationship with poison emitting worms) 547. Not to mention drowning 548. and if you don't get stabbed, did you fish? ;)the drowning I could go withoutrip colton 549. LmaoI was like 9WoahI was 10 in 6th grade 550. once you get older and you want life to slow down for a few hoursgo try fishing again 551. or golfdude 552. Idk school went by so quick this year 553. and I thought Burbot were weird 554. I wonder if summer will be the same 555. so colorful yet plain at the same time 556. what fish u talking about? 557. Tip you don't get it compared to us where you live looks awesome 558. Except the prices here are a bit better than there 559. I want school to start already, but at the same time i'm kind of worried that wishing for it to come quicker is like wishing for my end to come sooner 560. whoops i'm still here gotta skedaddle 561. How much does a simple meal cost down there? 562. pixel_voxel has left the chat. 563. I want to catch a sturgeonI mean 564. saimin is 50c 565. on accidentyou didn't see that fish and game >.> 566. Chemicalex has left the chat. 567. Chemicalex has entered the chat. 568. I remember enjoying Golf camp though 569. Lemme s'plain my fish 570. The kids were nice 571. .img http://1.bp.blogspot.com/-xzaVawxJ8Kk/VXKIdqPt1jI/AAAAAAAADrs/5mXVpWK3XTM/s1600/Uparg_u0.jpgwhoops 572. I used to go to a camp, then I became introverted 573. My instructor got a skull fracture on the first day 574. anyways, thats the bandtail goatfish aka weke pueo (weke=goatfish)aka the Nightmare Weke 575. Some girl scolded me for my nervous laughter panicing after he sat there with brain damage 576. lol wot 577. But he was fiiiiiiineI also remember almost dying a few times with the Golf Cart 578. Nightmare weke will give you intense hallucinations, cause poisoning, nightmares, and can kill you in your sleep 579. And he only suffered a minor concussion! 580. I drove into a pond lmaoIt was shallow, so I didn't drown but like 581. hahahabeen there done that 582. well... only if you eat the poison parts 583. Black Person + Water = Suffocation via water 584. racist XDyou can swim 585. Lmao 586. Lmao lol I saw a thing today 587. I have no idea how to swim I sink in water I'm not fat enough like you people 588. Let me explain this 589. No I'm just being mean lol 590. ElzoBro has left the chat. 591. ElzoBro has entered the chat. 592. there is almost no white people in Hawaii 593. This friend of mine is a living iDubbz 594. do black parents just avoid getting their children swimming lessons because of historical pool racism 595. My parents don't know how to swim either I think 596. *are 597. He joked about another online friend of mine being a "white kid" and I just pointed out subtly 598. That's actually kind of weird, they're from Africa so I guess the only water they had was for utility and not for fun 599. "Liam, he's not....." 600. I mean swimming sucks anywayI hate water 601. So do I but bikinis 602. Swiming isnt fun all I do is almost drown and get judged 603. or in elzo's casedick abs 604. but I could probably not drown for a while 605. bikinis are everwhere in hawaii 606. Swim trunks leave little for the immagination anyways smhLmao 607. waikiki is right next to the oceanso its extremely common to see people in bikinis 608. lolI love the diving boardI just do goofy shit 609. I love being humid and miserable 610. Lacks at least you're able to look presentable 611. hmmm 612. I wear a white t shirt usually with holes in it with black/grey sweats all the time 613. still looking for charger 614. Lol my poor jeansThey're all ripped 615. I'm wearing sexy black skinny jeans, a white polo, and a striped bowtie>sexy 616. I only have 1 pair of jeans and my mom almost never lets me wash them because they f up other clothes 617. presentable haadequate at best 618. Sexy and skinny jeans don't go in the dame sentence. 619. hugs my non existent curves 620. Follow Chem's example and find some grey sweatpants, that's what everyone needs. 621. i'll never wear freakin hot sweatpants 622. Except me, I obsseively wear jeans and sweaters 623. i'll die of heat 624. No matter the heatI'm always chilly, wind blows directly through me lmaoMy arms are like 2-3 inches in diameter, why can't I be a large child like my friends 625. lmao 626. I'll draw myself in my regular attire tomorrow to help you get a better mental picture of me 627. feels like 79 F 628. I promise you I'm not starving myself guysLmao 629. kill take a pic maybebut censor everything xD 630. I can take a pic of my arm compared to like 631. a banana? 632. My 3DS lol 633. randomouscrap always wears bluejeans. even in florida 634. randomouscrap : and a plain t-shirt 635. Yesss Random 636. Random you're like me except slightly less comfortable 637. Now just buy the same sweatshirt in multiple different colors and you'll be me 638. I have pics of your arm if you need to borrow some, elzo 639. i never wear shorts, or excessively baggy pants 640. I hate shortsFuck fursuits, I'm a living fursuits 641. shorts would be smart, but i like meh legs covered 642. i agreecover my chicken legs 643. ElzoBro has left the chat. 644. My legs are fine except they're covered WITH HAIR OH MY KEK 645. i have okay legs... but i kinda grew up [liking] wearing only pants 646. RealTiP never misses leg day 647. OH MY GOD! NOT HAIRIT'S LIKE YOU'RE A MAN!Mine just blind people with their shining whiteness 648. No not regular Like I said I'm a living fursuit lol 649. i has sexy hairless legstan legs 650. ElzoBro has entered the chat. 651. Lmao 652. lemme find my skin color in hex 653. Thanks LacksHairy legs have no character, you honorless shrike*HairlessLmao 654. just go to youtube.com that's my legs XD 655. What was my skin color in hex again? Oh right, #ffffff 656. randomouscrap is going crazy from osu so I guess it's time for bed ( ﾟ▽ﾟ)/ 657. goodnight 658. ElzoBro has left the chat. 659. ElzoBro has entered the chat. 660. Ca 661. Night 662. LELnight(dang caps) 663. Hmmm 664. Honestly though I'm probably #fff0c9 665. I'm starting to feel like we talk about this topic way more often then we should lmao 666. I'm close to #d18447 but that might be my lighting 667. what topic? 668. skin in hex color 669. How ugly we are 670. hypothesis 671. Lol 672. That's some red skin 673. thats just an assumption thoalso, I ain't red... 674. Then I convert the conversation into uncomfortable male beauty tips 675. kk 676. pro tip: don't give a fuck 677. xD 678. HonestlyIf you're so good looking, you'll probably look fine in whatever you wear anyways 679. Actually tip I think my skin fits the same scheme yours does 680. But never dress for other people, unless itms something where you have to lol 681. Probably #ffe0c6 682. >doin intense sciences to probably get my skin color as close as possible 683. Unless you're trying to reflect some sort of image I don't see the point in strutting around like a peacock 684. ^Dress for yourself, and maybe your mom 685. and definitely your grandma 686. ElzoBro has left the chat. 687. ElzoBro has entered the chat. 688. that's the only reason my hair gets cut 689. Yes lol 690. don't wanna give her a heart attack 691. Same my parents hate long curly hair for some reason 692. andritolion has left the chat. 693. But it's not the end if they cut it i guess 694. I want to grow mine out but I am WAYYYY too lazy to deal with that mess 695. welp, usin' 3ds expect inaccurate color 696. Lumage has left the chat. 697. I can barely comb my hair anyways I guessMy hair is such a sponge, I can never completely dry it 698. this is kind of close: #BB8C70 | probably 699. do you got the nice tight curls? 700. Curly hair problems ripYeag 701. actually that's quite dark 702. My curls sometimes fall out and roll around on the ground sometimes lmao 703. Just say #000000 and we'll accept that you're a piece of charcoal 704. That's how thicc they end up 705. at least short and curlies don't immediately get called pubes XD 706. Maybe it's #dda482... who knows? 707. LmfaoI still want white people hair, it's so stylish, and cute. 708. I'm not dark... i'm just a like 3 drops coloring 709. Lmao 710. Wow tip we have the same gradient of orange 711. demands picture>i'm more golden tan>idk how to describe 712. #ffe1d1Actually I have a hand reveal you can go off of 713. But I guess I have to be happy with what I have, which is curly hair that's too short to style and gets way too thick to comb without self harm 714. There's my basic skin color 715. But I'm pretty good with my hair actually. All I have to do is grow and shaveMy whole body is multiple different shades of brown, from milk chocolate to Congo shades lolLike my face is just pretty dark but my arms are lighter 716. I'm pretty sure that's common 717. Oh okay, well I just know it's not just a farmers tan 718. doing a hand revealheh 719. Wow 720. i'm wearin' some ol' chainmail 721. For some reason I imagined your stature to be exactly that 722. i also have shades on in that pic xD 723. idk what I was expecting, but it definitely wasn't chainmail 724. totally ignoring camera xD 725. I don't have an old picture of me nmnmmI could check this camera log but mmmffff 726. that was about 8 mo. back, greek festival(no, im not greek)also my hair was died too*dyedhehfor all you know, i probably look crazily differentmade me feel cool 727. does your family collect this stuff? 728. weight is extremely obvious tho.no, thats at a greek festival 729. ahh 730. I was just trying EVERYTHING on 731. Lacks has left the chat. 732. Chemicalex has left the chat. 733. Chemicalex has entered the chat. 734. ElzoBro has left the chat. 735. Chemicalex has left the chat. 736. Chemicalex has entered the chat. 737. Chemicalex has left the chat. 738. Chemicalex has entered the chat. 739. Chemicalex has left the chat. 740. Guzzler829 has left the chat. 741. GoodGameGod has entered the chat. 742. Awesome!I've always been fascinated with medieval weapons/armor and Greek mythology If someone calls you a bitch just remember. 1. bitch means female dogs. 🐩 2. Dogs bark. 3. Bark comes from trees. 🌳 4. Trees come from mother nature. 5. Mother nature is beautiful. 6. So people are basically calling you beautiful. Remember that. Life lesson #1.Lol 743. oh hi 744. Hi indeed 745. i got a microa gameboy micro 746. Gameboy micro?Is that a tiny Gameboy? 747. yep 748. Sounds cool, is it made by Nintendo? Or somebody else. (Like the guy who made the mini arcade machines) 749. yes, its a nintendo thingits on that stack of ds and 3dses 750. Wow that thing is small lol!It looks like a game and watch. 751. eggplant, corn, tater, cuke for scaleits pretty neatdidn't come with a charger though 752. Lol, where did you get so many 3DSes?Dumpster diving behind the gamestop =P 753. thats not even all, which is scary xDeven the pi was taken with a 3ds*pic 754. Geez, did you spend all your money on a pile of 3DSes? 755. maybeso, according to https://techcrunch.com/2006/10/31/top-10-worst-gaming-handhelds/ , the gameboy micro is the second worst handheld of all time 756. Then why did you buy it lol? Collecting value?>Or wait, I'm guessing you got it by...other means 757. collectingalso all my gameboy advances are brokenin my lifetime i probably had the same amount as my ds-3ds line>(around twelve)>they're all broken 758. Lucky, I use to buy huge LEGO sets when I was younger.>I wish I had da consoles now though...Oh hey! I almost forgot, make sure you have your "Send data to Nintendo" turned off 759. i used to have a big tub of legos... but then somebody thought putting the bin next to it was a good idea 760. On your CFW 3DS 761. yep banwavehttps://www.gamespot.com/forums/system-wars-314159282/ouch-the-10-worstselling-handhelds-of-all-time-thi-25814844/ http://purenintendo.com/gameboy-micro-the-10-worst-selling-handhelds-of-all-time/both those say micro was unfortunately the worst 762. I had never actually heard of the GB micro before now...Huh 763. googling "worst selling handhelds of all time" gives the micro a bad rep 764. I remember most of they're consoles to.Including obscure ones...I have a GBA sp, but the screen light doesn't work. 765. the pluses i can think of so far is that its freakin' pocket sized, and its got a backlight... other than that "meh."i have only played for 5 min, but i bought it while it was nearly dead anywaysi swear you an fit this thing ANYWHERE 766. You know what would be cool? Is if there was a way to turn off the screen light on the 3DS. 767. Pocket? yep. Wallet? yep. 768. I'm sure you wonder why, yes? 769. there isits NTR, last i checked 770. >Wallet? Geez that's unnecessarily slim Oh you can? Well I mean without hacks lol, not everyone does that... 771. well its like a cm thick but it's totally possiblewell, you can turn down brightness, but thats it without cfw 772. But it would be good for anyone who plays it outside. (I don't know why anyone would, but they show it in the ADs for it a lot)Because when you do it with screen light, you can't see jack.But without... 773. yea, the backlight and faceplate on this work hand in handexcept... its got a really small screen 774. ^ 775. 240×160 pixels2 inches diagonal 776. Gameboy: "Wow! What a large screen!" DS: "Wow 2 big screens! Even better then the last! 777. when my charger comes in, i'll provide a better reviewmicro was the last of the gameboys... successfully killing its kin>"The Game Boy Micro features a removable face plate, and designs with special faceplates were sold as a customization feature." >that's actually pretty neat. 778. 3DS xl: "How did I ever play on such a small screen before? Wow!" n3DS xl: "No wonder everything took 5 hours to load on my o3DS! This is way better!" n2DS xl: "WTF Nintendo?!?!"That is pretty neat 779. checks if n2ds xl was releasedoh. 780. I also hate how Nintendo removed the little wifi switch on the 3DS, it doesn't bother me much anymore since I got wifi, but back when I had to go somewhere to get wifi, that little switch was super helpful when the eshop would take 10 minutes to "Load" before it would say that you didn't have a strong enough internet signal. 781. i wonder if its better than the n3ds xl, performance-wise 782. I could flip the switch, and have it say "No wifi" immediately...Again, this isn't a problem anymore luckily.It's not 783. equal? 784. Mmm...NoWait...Yeah, yeah okay I think it isI think it is equal 785. that'd be weird if it isn't 786. It weights less then the n3DS and is slimmer for those who care. (Not me)Really the only difference is that it has no 3D of any kind.Aka, what I would have bought instead lol. 787. meh. i like my 3ds xls aleady i might get thoughgotta focus on the gameboy gamesbought tloz:minish cap, an old favorite 788. I've been meaning to try that ^I own it, but Ihaven't played it yet 789. its a really good game, one of the most memorable gameboy games i've played 790. Also, you should/could check out super star saga for your collection, it's a great game.One f the best on the GBA for sure.>And my favorite for GBA 791. oh yesin my lifetime, thats a game i had the most copies ofit was good, but i never was able to beat after the soda place.i kept losing 'em. 792. I REALLY got hooked on games when I was 10, before that I had a WII, but it was when I got a DSI that things kicked off.So I've owned about 3 GBA games before.And have played 6 793. i like the ds lite and fatty more than the dsicos that backwards compatibility with gba 794. Really? Huh, I never had a DS lite. 795. yep, also helped for progressing thru pokemon 796. The backwards comparability was a great feature. 797. i still have my first pokemon ever(except its evolved of course)from pokemon blue to pokemon sun + moon 798. I don't know much about Pokémon...I never was interested in turn-based combat games...I enjoyed final fantasy VII (The GBA one) but other then that...And I guess some other RPGs but...Meh 799. yeah... i don't see why i still like pokemon other than nostalgia 800. Yeah that's what I assume, is that you have to have grown up with it to understand it. 801. gradually, they're getting mo' heavily story based... which is boring. (one reason i didn't purchase oras) 802. Mm. 803. i like the old roots of the frachisenone of this dlc special event junk 804. The older games look like fun to me ^The newer ones? They look way to complicated. 805. they actually feel like a challenge, as well as beatablenewer ones are "meh." i beat one... but i could care less about the other :3I liked trading and evolving and playground rumors of impossible things 806. Anyway, I have to go to bed, a friend of my family has a boy who just had his first birthday, so there's a big celebration that's going to happen and we got invited.Haha I miss that...My dad remembers people writing out maps of tLoZ before there was internet.There's still glitches so that's something. =PBut yeah, sleep, need, bye 807. o/g'night 808. GoodGameGod has left the chat. 809. lilstrubel has entered the chat. 810. lilstrubel has left the chat. 811. lilstrubel has entered the chat. 812. lilstrubel has left the chat. 813. lilstrubel has entered the chat. 814. lilstrubel has left the chat. 815. Joshuaham123 has entered the chat. 816. Joshuaham123 has left the chat. 817. lilstrubel has entered the chat. 818. lilstrubel has left the chat. 819. Lumage has entered the chat. 820. Lacks has entered the chat. 821. Chemicalex has entered the chat. 822. today is bad so fari tried brushing my hair with a lint rollerthat was fun 823. Hehehe 824. my cousin is so sarcastic i hate him 825. Perska has entered the chat. 826. i go to visit my grandmother and the first thing i get is my cousins coming out and yelling "DID YOU BRING YOUR FIDGET SPINNER!?" like that was a super important fact or somethingboy, if they could hear the things I say under my breath... 827. https://www.youtube.com/watch?v=sQtT2xPez8A 828. Chemicalex has left the chat. 829. Chemicalex has entered the chat. 830. ugh god they're shushing each other extremely loud now 831. Oh, whoops. I thought it was 8, not 6.... 832. Chemicalex has left the chat. 833. So much for sleeping in I guess. 834. Chemicalex has entered the chat. 835. hehehshoot i gotta gommmnno/ 836. Chemicalex has left the chat. 837. Lacks has left the chat. 838. http://namapann.com/mp3/110.mp3 i'd play this one on osu 839. ElzoBro has entered the chat. 840. Throwback 841. ElzoBro has left the chat. 842. HTV04 has entered the chat. 843. HTV04 has left the chat. 844. ah i have the picture somewhereI mean i guess maybe it's on kland 845. ElzoBro has entered the chat. 846. Omg lmao 847. ElzoBro has left the chat. 848. shoot who's the artistwarugaki 849. lilstrubel has entered the chat. 850. Lacks has entered the chat. 851. hello 852. Hi hi 853. I'm thinking about learning Chinese is that a good idea?Mandarin Chinese I want to learnI feel like pokemon games are a little TOO easy... And short I think they focus so much on graphics and gameplay that they don't focus on the story or the length of the game. They make it easy for people new to pokemon I'm pretty sure 854. lilstrubel I feel ignored lol 855. Mandarin would be a good choice 856. Thank you <3 @Lacks Is my profile okay? You can't really see it unless you go to my profile but she is wearing a really suggestive bra xD 857. I mean, I guess? 858. good enough lmao 859. Lacks has entered the chat. 860. Lacks has left the chat. 861. "Always had the feelin' I could never be the villain 'cause the villain in the film is always back lit." 862. https://www.youtube.com/watch?v=ocg0dfseea0 I love this song <3 It's just lyrics because I don't want to get in trouble.@Lacks Am I allowed to send you PM's once in a while? 863. of courseBut I won't watch the k-pop lol 864. Okay. I just thought because you were head admin I should ask first <3Does anyone remember this song? It's called Boulevard of broken dreams and it's not kpop don't worry https://www.youtube.com/watch?v=r5EXKDlf44M 865. it's not korean, but I like this j-pop songhttps://www.youtube.com/watch?v=WKkmmP7JibYthe flow to the lyrics is nice 866. ooooh I like this song! 867. When I was into jpop I mostly only listened to Gacktsome Alice N9neman, that was a long time ago now 868. I like jpop but I like Kpop a little more :) 869. that was almost 15 years ago o.o 870. wow that's a long time!Hoq old are you now lacks?How* 871. 29 872. Oh so you started listening to Jpop at the same age as me:) 873. https://www.youtube.com/watch?v=C3Uw9YClm2Ethis is gacktDamn lol I still find him hotI thought I was over that xD 874. he is hot lol 875. https://www.youtube.com/watch?v=amXKQ351QBwmwhahahahaI spam you with all MY porn now hahahahthis song isn't porn. Just sad 876. okay haha I would fight back but you have 10x more power than me xD 877. if I rememver correctly, the lyrics are a bout a woman waiting for her husband to return to warfrom* war 878. ElzoBro has entered the chat. 879. and the other errors are obvious enough for brain autocorrect 880. HMMHmm 881. here start with this onehttp://safebooru.donmai.us/posts/1012029?pool_id=4335 882. I feel that people who use drugs shouldn't be the ones taken to jail (I'm pretty sure that happens), the people selling it shouldThe people abusing them should be able to get help 883. Portugal 884. Without fear of prison or persecution 885. maybe a little persecution because you made a dumb choice 886. Well yeah 887. Um Lumage? Are you helping me??? What did you do to the real lumage 888. https://www.youtube.com/watch?v=PbWpXYOg4OQthere you go elzo 889. The premise is that he's preparing for Reitaisai, a Japanese manga festival 890. dumb decision pfft 891. He draws the people in the story (mostly other manga artists but also family) as Touhou character 892. But I feel that going to prison for the better part of your life, then not beinf able to get a job afterwards is a terrible punishment 893. not everyone has to be a productive member of societyjust don't hurt or be a burden on others 894. Yeah I saw that video just now Lacks lol 895. I want to wear a dress for a full day and see how that goes xD 896. Is drug abuse a criminal offense? 897. In these "reports" he draw in manga style his experiences with going to these big manga conventions 898. i think so 899. Or a misdemeanor? 900. depends on the drug I think 901. drug abuse isn't a crimethe drugs are the crimeso it's more about personal use or traffickingthat is, like you said, the main problem with drug laws 902. So it's more about having them than using them? 903. there is no money spent on rehab 904. I shared my adderal with someone once and I didn't know that was bad 905. People don't get help either, because they're worried of the potential jailyime 906. share!? 907. I take two so I gave one 908. Sell!!!!!lol 909. Lmao 910. xD 911. Yes, ElzoI agreeCanada just passed a law that if you call 911 for an overdose they cannot charge you with posession of drugs :DI hope this saves more lives 912. Yay 913. that's good haha 914. That's one part there 915. so if you want to read warugaki's stuff with that style, start with http://safebooru.donmai.us/pools/4335 then http://safebooru.donmai.us/pools/4735 optional http://safebooru.donmai.us/pools/3548 http://safebooru.donmai.us/pools/5815 http://safebooru.donmai.us/pools/5913 http://safebooru.donmai.us/pools/8677 916. not being able to get the help you need for fear of prosecution seems backwards as hell to meBut the War on Drugs is a profitable warso ofcourse the goverment don't want to stop it 917. I think that people who call a clinic to get help, shouldn't be punished with jail or finesAlso a prison reform would be nice but uh 918. I just heard in school that the rate of teen pregnancy in America is insane 919. prison reform when 920. that true? 921. that's a really easy statistic to look up yourselfthe answer is yes 922. Like, prisons shouldn't be like the ones in Norway, because Americans are supwr selfish but they should be a little nicerAnd focus more on helping peope 923. prisons should be like the ones in norway 924. Okay so I guess I have my goals as a politician down slightly 925. look at their repeat offender statistics 926. Yeah but I didn't want "What are the rates of teen prenancy" on my history LOL 927. No, I don't think they should because American culture wouldn't work qith themThey should adopt ideas from it though 928. like not being awfulfor example 929. fuck american cultureMake america great again 930. Oh god not that LOL 931. Norway prisons are way too nice 932. MAGA is *exactly* american culture though 933. Norways prisons treat people like peoplenot rats 934. we've got an ego fetish 935. I jnow for a fact that people here will do crimes to get in I'm 100% on that 936. that somehow any concession that we "have work to do" is denying that 937. Lol 938. the only proper "we have work to do" is "because somebody else messed us up from how perfect it was" 939. You can't have them be too nice, but you have to have them be not awful 940. Anyone here live in New Jersey?I do 941. Nope 942. maybe if your prisons are a better alternative than life outside of prison your country is more fucked than you let on 943. Mmm no I don't think that 944. if we didn't have such toxic cults we wouldn't be losing to China and Russia and several European countries and in many areas Canada 945. I was more thinking people already without homes or who are running out of money 946. maybe a universal basic income would be a good idea then 947. haha but that's socialism and that's illegal 948. Lol communism 949. with automation on the rise we need to find a way to feed and house all these soon to be jobless people 950. not in the US!Our solution to automation is evangelism 951. USA is literally the devil 952. Lol 953. is watching videos of squirrels getting run over illegal 954. no go back to 4chan 955. kthat 956. Does watching videos of squirels getting run over make you a school shooter in the making? 957. That is exactly the site too xD 958. how about that guy killing 2 people for defending a muslim in portland, yesterday? 959. WhaLinkz 960. that's fucked up 961. how do i ignore 962. Am I suppsied to feel any other way than bad when people die? 963. I have some Muslim friends 964. sometimes 965. Yeah that's true 966. i mean no culturally you're not 967. http://abcnews.go.com/US/stabbed-killed-portland-transit-station/story?id=47672660 968. wow wtf apparently "prison comparison" doesn't give me an international comparison of prisons 969. Does anyone else worry that memes are ruining society in some way? 970. I got "Prison vs. School" on BuzzFeed 971. Well, not the way you think I mean but 972. only morons 973. no, the age of offense is ruining society 974. I'm watching Deers VS Cars I'm a horrible person 975. It's probably just he people I'm near are ruining it 976. there are always "unintelligent" people that will enjoy unintelligent things 977. What i mean is that 978. fidget spinners for example :p 979. it doesn't matter what "dumb" thing they enjoy, it doesn't have that big of an impact 980. yes LOL 981. They make normies have a bad understanding of certain serious topics, and when those topics are discussed, they have a jokes understanding of it, and don't want to actually think about it 982. having a trend appear in the media might give you an averse reaction because your brain wants you to either feel part of the group or superior to it 983. lilstrubel has left the chat. 984. lilstrubel has entered the chat. 985. yeah that's true 986. but it doesn't actually lead to anything 987. ^^^That's what i find happens near me^^^^ 988. oh political memes 989. Yeah 990. like "when the school shooter says you want to go to the bathroom" 991. lol 992. Well not those kind, the ones that are like "LOL gay people" or "60 million genders", then normies think that all gay people are that way because they don't actually know gay people and that's their only exposure 993. I feel bad for those kids involved in school shootings :( 994. Are you supposed to feel good for them? 995. no 996. so exactly those kind because they racialize school shootingidk That's just information age in general. You have more access to implications. I don't know how it really affects people's beliefs. There's no reason to believe it doesn't, but it seems foolish to say that it's a serious problem 997. Yeah, it's not a swrious problem i suppose, but it makes things hard 998. "It's for the lulz, man, calm down!" 999. I'm surprised there weren't any shootings in my school because I'm in a school for kids who need additional help 1000. People group me with those extra people 1001. cause I'm special... 1002. Or they see jews and think "MEMEZ" 1003. xD 1004. I fucking hate memes 1005. But that's just idiots 1006. repetition is not funny 1007. Some people can meme responsibly lmao 1008. You hate memes too???'Well I like em a little bit but they get annoying af after a while 1009. I like memes, but they get annoying after while, and they often go too far 1010. lol same comment 1011. A lot of people i know don't seem to understand something 1012. pretty much 1013. ElzoBro has left the chat. 1014. ElzoBro has entered the chat. 1015. You can think something morbid or really offensive is funny, but you also have to sort of understand if some people don't think it is 1016. agreed 1017. "60 genders" DEFINITELY either influenced people or became an argument for an existing belief, though 1018. yeah 1019. there's 2 genders and 58 types of people in desperate need of real therapy 1020. aaand you fell for it too 1021. tell megeneticallywhere is foxkin? 1022. 12Me21 has entered the chat. 1023. Like I got told that I had "No sense of humor" by Michael(He's cool now but he was an ass earlier this year) when I got uncomfortable by Javi making a N-word jokeJavi is nice, he felt bad for making me uncomfortable, but Michael was a homophobic douche them 1024. The concept of gender is pretty simple, the "60" one is an unofficial attempt to compartmentalize weird stuff. But of course, it's easy to say "oh everyone that has any non-binary sense of gender believes this" 1025. I'm just happy I seem to have changed peopleYeah@Lumage 1026. I've never heard this 60 gender bs 1027. And then every time "gender" is mentioned you get someone mentioning "60 genders xddd" as a denouncement of... that misrepresentation of an opinion. A strawman. 1028. Like I said that I'm gay and someone said that gay is a gender and I'm really uncomfortable being grouped with them because people won't take me seriously 1029. It's mostly tumblr. You go from "I don't feel male" to "how do I feel?" to "must be demiultragender lol also check out my OC" to "let's make a chart" 1030. Yeah, the 69 genders is a huge strawmanLol 1031. I have lots of social problems because I only have a couple of friends but I try my best to get along with people in the chat (Besides my sexual things) 1032. i'm not getting along with you because you're unnecessary to this conversation 1033. Who lol 1034. lilanyway my understanding is this 1035. i don't really care what you "feel"feelings are irrelevantif you're genetically a male you're a male 1036. As I said, there are two sexes, but people can feel however they want to, just tell me your pronouns and I'll use them, it's not tgat big of a deal 1037. @Lumage And he's back xD 1038. fuckthat 1039. Sex is the genetics. You are literally either an XX or an XY. 1040. I'm not playing your stupid offens gameoffense gameyou get they and thats it 1041. Offense game? 1042. lacks thinks people actually use "xir" 1043. Are you guys talking about trans people 1044. telling me I have to call you something gives you a trump card to claim offense 1045. I just call it being nice to people 1046. fuck that 1047. I don't really wanna be "that guy", and it doesn't really hurt me 1048. (I'm canadian. It's TECHNICALLY hate speech if I don't call you a zhee) 1049. There are abnormalities in chromosomes too, but these are exactly that and so rare and at a genetic level that it's not that much of an issue because what sex really determines is what equipment you have 1050. The only thing I find bad is if someone diesn't tell you their pronouns and expects you to just knowYeah, Sex is binary, but I'll say that gender is a spectrum because it's not my place 1051. But gender is the /social/ concept of masculinity and femininity. Masculinity is whatever is typically associated with "being male" Femininity is whatever is typically associated with "being female" cars vs hairstyling. Do you follow so far, Lacks? 1052. I think this is all a problem of life being so good we need a new bitch 1053. Life isn't so good for me 1054. by bitch I mean something to bitch about 1055. I only get 7 meals a day... jk 1056. Oh but LUmage, if you try to explain it to people, they'll get mad at you and say "THIS IS TOO COMPLEX, WEEB!! I DONT NEED UR GENDRZ!!! JUST BE NORMAL! HISSSSSSSS 2 GENDERS BINCH!" 1057. You don't generally think of women wanting to grill on their RAM 1500 while hunting bears. You don't expect men to 'care' about fashion or be weak.I only have two genders right now elzo 1058. o.o 1059. "doesn't tell you their pronouns" 1060. Imasheep has entered the chat. 1061. well there's a good one 1062. I'm a dog secretly 1063. "they" 1064. My wife is way more manly than meshe doesn't claim to be a man tho 1065. Well yeaaah 1066. But do you agree with the social concepts of masculinity/femininity? You're getting ahead of yourself. 1067. That's a given 1068. noI agree with society viewing it that way I guessbut people are dumb 1069. Just because you're manly soesnt mean you're a man lol 1070. what? 1071. I don't understand this conversation at all so I guess I'm dumb haha 1072. Imasheep has left the chat. 1073. So there aren't behaviors that are associated with males (sex) and females (sex)? 1074. In my opinion, it's "Just because you're womanly doesn't mean you're not a man if you are a male" 1075. You're still getting into transgenderism which isn't what I'm talking about 1076. transgenderism is a word? 1077. There are behaviors that seperate the genders 1078. lol 1079. there you go 1080. I feel that all if the different genders is just a weird way to say "I'm a woman who likes manly things" and the like 1081. The "behavior" is what people mean by gender 1082. They don't really all have to be named 1083. I feel like this would go a lot better if it was just me and lumage lol 1084. ^ 1085. I'm a man but I act a lot like a girl so what am I ] 1086. shut up desu none of you are helping 1087. I don't want to help haha 1088. Oh well I'm just being a part of this because I want to take notes 1089. I'm confused 1090. okay 1091. This is different from the biological sex because they /refer to different things/ Sex is chromosomes, gender is the social expectation of behavior 1092. I think i get itI hate the people who feel they need a defining factornot that they're men who think they're women 1093. Sex and gender are linked 1094. ElzoBro has left the chat. 1095. ElzoBro has entered the chat. 1096. Usually an XY will also "behave" like a manUsually an XX will "behave" like a female-- 1097. ElzoBro has left the chat. 1098. that's having the same sex and gender, and that's how it is usually 1099. ElzoBro has entered the chat. 1100. here's why people make such a big stink about gender though:who's the MOST MASCULINE person you can think of? 1101. Ahnold 1102. My momma 1103. lol hahah 1104. jk 1105. true lil 1106. LOL 1107. she definitely hit harder :p 1108. hahahaha 1109. Like, Bruce Willis type of guys. 1110. yeaharnold I can't spell his last name an neggerwarriorslol 1111. So when we think of masculinity, that's the kind of "absolute masculine" our society gives uhAnd when we think femininity we have a similar concept/perfect examplebut... most of us aren't Arnold Schwarzenegger. 1112. I'm not, myself 1113. Exactly. 1114. but how does that make me less manly 1115. Because "manliness" is defined by society. You're less manly, in value, than Arnold because you aren't that kind of man 1116. ahhhhfuck society 1117. I'm farrr from the muscley guys. I'm like a 30% masculine, maybe 1118. This is why I want to go live in the bush 1119. That's where the spectrum comes from 1120. @Lacks what's the Girliest thing you have ever done in your life? :D I still wear female underwear lol 1121. you can act "more feminine" or "more masculine" because NO ONE is the PERFECT masculine man 1122. @Lumage what about you Lumage? 1123. somewhere in there there's a middle line. Random is probably around there. 1124. idk 1125. you don't really think of him is manly, but he's not ultrafeminine either 1126. I would have a big problem calling him a heras you can tell by coinz 1127. he acts kind of independently of gender 1128. I'm not gay I only wear female underwear because tighty whities hurt my circulation and I don't like to wear boxers 1129. Ah-- see that's where I'm going But let me soldifiy the "spectrum" concept Anyway you end up with something like this F=====O=====M And you can be wherever on there. Most XYs are on the right. Most XXs are on the left. 1130. Lol well I'm gay and I don't wear panties sorry 1131. i'm straight and have worn thembut that was to make the girl laugh 1132. Lmao 1133. I'm just saying that because everyone calls me gay :(lol 1134. So having the separate Sex/Gender kind of makes senseBut pronouns are another issue 1135. @Lumage can we talk about something else? 1136. Because that's not how *you* feel, that's how people /perceive you/ 1137. only because there's 7 billion of us and natural selection went out the window a while ago 1138. Then sexuality is added in and things get even harder because society 1139. ugh I hate sexuality 1140. "they" should be fine 1141. they is what I use 1142. only a few special snowflakes have extra words 1143. if the snowflake wants a special word they just want troublesuffer not the fools 1144. But if you feel female, it's--more than anything else--weird by social standards to be /called/ "he" 1145. Snowflakes? 1146. Yeah, reasonable people (The majority) are fine with they 1147. And pronoun use is, ultimately, just determined by what we see, lol 1148. LolYeah, it's what you see, then what you're told 1149. If I started dating a male-presenting-female I wouldn't be offendedunless subterfuge was their goal 1150. If I see someone that looks masculine, I assume it's a guy. If I see someone that looks feminine, I assume it's a woman. There's no reason to go against that for at least first contact. 1151. I mean my last girlfriend is now presenting as a man and I saw that coming when we were dating. i was okay with that 1152. So many trans will specifically go to change their appearance not so much because they want to look how they feel but because it's just easier for other people to recognize 1153. lol 1154. That I understand 1155. I thought the larger point IS to look howthey feel, because dysphoria and all thatAlthough pronoun use is of part of dysphoria 1156. I mean maybe for stronger cases. But in a social context, it's the presentation 1157. MAYBE THAT'S THE PROBLEMWHOOPSI've met a few that insist on their pronoun not matching the presentation 1158. If someone doesn't even try to present, doesn't ask you politely, and doesn't accept "they" when it's ambiguous, they're just another rude face and it's not even discrimination they're just not people who you want to get along with 1159. usually I just sever all ties as fast as possible as those people always seem to be surrounded in a toxicity 1160. Yeah 1161. if you do make a mistake and someone asks you for he/she/they it's kind of rude to not try to change because it's a sign that you just don't believe it's "possible" to think of yourself another way which gets interpreted as complete rejection 1162. the problem is 1163. I'm pretty sure my friend Molly is FTM but she's okay with 'She' 1164. there is a proposed law that could make it hate speech for me to not call them by their gender 1165. yeah at some level, if you know that your appearance is confusing, it's on you to not be offendedI thought they passed it with no comment a few days ago?Or was that something else 1166. and these people are so quick to anger and offense that how do ytou defend agaings this aside from cowtailing to their bullshit 1167. oh maybe that was the drugs thingAnyway yeah that law is stupid 1168. If I run a presidential campaign, will I rrt any votes if I say "don't listen to a party, listen to an opinion" 1169. the social justice court is canada is stupid 1170. very 1171. Yeah from what i read 1172. comedians getting fined$10,000 for shutting down a hecklereven if it was offensiceive*
1173. I listened to the professor debate thing
1174. Peterson?
1175. YeahI was hoping the opponents would do something like what I'm saying and just make some point like "you need to respect that because it's more harmful that you think" or something
1176. I've only listened to the 2 joe rogan podcasts he's been on
1177. but instead their rhetoric was I CAN'T BELIEVE SOMEONE DOESN'T AGREE WITH USYOU'RE EVIL (even though he said he would use he/she/they if asked)SCIENCE SAYS THERE ARE MULTIPLE GENDERS
1178. yeah, these are the people I hate
1179. (because wow okay have fun explaining that)
1180. Yeah that's the problem
1181. which is why I call this the age of offenseor willful ignorance
1182. They make everyone look bad
1183. I'm still not sure which one it osis*
1184. I mean you saw it here (I hope) The spectrum thing actually makes sense: it's not too much of a stretch to say "no one is fully masculine or feminine"
1185. yes
1186. but "3 genders" just triggers memes for everyone
1187. that was me communicating poorlyI agree with all that stuffThe special snowflake stuff drives me bat shit crazy
1188. part of it is that it *is* overrepresented in media specifically to make people upset
1189. Hence what I Said about memes
1190. :( I'm just a stupid sheeple
1191. Rip
1192. I mean I'm irritated that people like Yellow Hat Person of Unknown Gender Identity exist but I also recognize that I'm not going to go outside and immediately meet people like thatmaybe if I went to an antifa rally idk
1193. I usually come here to temper my ideas so I can propose them to my IRL friends
1194. lilstrubel has left the chat.
1195. Because SOMEONE I know has to be educated lol
1196. someone told me to "get learned" on twitter onceI was right.
1197. lol
1199. >Drake Nathen1 year ago had a successful masturbation. :D
1200. "successful masturbation" kek
1201. Nice?
1202. he did it in 1:34 so.... I'm impressed :p
1203. 12Me21 has left the chat.
1204. hm the user's account was remove
1205. ElzoBro has left the chat.
1206. pixel_voxel[04:52]o: i think you people are severely overestimating lumagehttps://www.youtube.com/watch?v=4blEgdUX260
1207. overestimating? how so?what's your opinion on the water erosion on the sphynx?
1208. "LOOK WHERE ALL THE QUALITY WENT"are people really worried about the sphinx eroding thoughoh i seeI'm not going to take a position on historical dating lol
1209. I was gonna make a joke about overestimating you.... but
1210. ElzoBro has entered the chat.
1211. yeah, this stuff is more just a fun thought experiment than anything without being able to 100% prove anything
1212. idk what the real implications of an earlier sphinx are sure it would be interesting but I can't see the connection they're trying to make
1213. I think it's simply civilization is older than we think
1214. Oh right 5000 years is a lot I uh I'm really not good with dates lol
1215. ElzoBro has left the chat.
1216. Egyptian history is pretty cool. Would be a nice specialized class to take.https://www.youtube.com/watch?v=U9_mMpZCY7w
1217. lilstrubel has entered the chat.
1218. hello :D I'm so happy I caught my first shiny pokemon!!!it was a ledyba
1219. HylianHoundoom has entered the chat.
1220. gUESS WGHT
1221. WGHT
1222. MHXX SWITCH IS CROSS PLAY WITH MHXX 3DS!!!
1223. munna hunaa
1224. randomouscrap has entered the chat.
1225. randy
1226. hello
1227. just pretend you opened the tab on accident
1228. gabe says you need to chill when playing osu!
1229. o..oh?I'm still 1000 pp away from him
1230. he said you got 1000pp when it took him a year to do that?
1231. ya
1232. idk what th efuck that means, but
1233. What no I have 825
1234. kyahaha
1235. ANd I don't think I'll be reaching 1000 this weekend. I need to take a breakI've been pushing too hard
1236. bah
1237. well, did you hear about mhxx switch?
1238. I don't like monster hunter. I'm sorry
1239. well it's the first game on the switch to have cross play with the 3ds
1240. that's cool
1241. oh somehow I got to 160
1242. I need to play a relaxing game that doesn't require skill
1243. like mario kart
1244. maybe mariokart
1245. random I caught a shiny Ledyba a few minutes ago~ :D
1246. 94 :/
1247. or land maker
1248. Oh cool, what game?
1249. Pokemon Sun :D
1250. Ah awesome!
1251. "Aqua Blend Server"wow okay apparently I have more S+SS than A
1252. I just have to keep telling myself that pp doesn't matter. But even when I don't care about pp, I still care about doing well on the songs for personal reasonsLast night I played this stupid 4 minute song and failed on the last 5 notes like 4 times
1253. Randy, wanna play mk8d?
1254. I was so sad. I threw my headphones awayI don't have deluxe and I actually don't want to play mk8. It'll just make me tryhard againI need to rellaaaaax
1255. play fast rmxlol>it'a one of the most stressfull games I've ever played
1256. And if you look at my history on osu you'll see the other song that made me pull my hair out
1257. play tetris
1258. lilstrubel has left the chat.
1259. kek
1260. that stupid "unbeatable" song is so easy and I COULDN'T S RANK IT AARRGGHHH
1261. tooo much coffee
1262. is bloody tears actually good
1263. shaking too much to do the spinners lol
1264. I played it what, 75 times?
1265. I thought I played a low level and didn't like ityes
1266. Bloody tears is all right. I played it so much because I knew I could do well on it. It's a bit complicated on the higher level
1267. wait...a user named bubblun...
1268. oh neat
1269. maybe there's some puzzle bobble stuff
1270. you added a fullscreen button randy
1271. yay now I'm over 100 pp
1272. yes
1273. ending theme, huh
1274. PhilFish has entered the chat.
1275. I'm really proud of that S rank on Sora-iro days
1276. alright time to play this stupid game i guess
1277. I have no idea how I pulled that off. That's a 3.98 star
1278. lol but ofc people hate the map
1279. sometimes I'm really on top of things for like... an hour. And then I suck for the rest of the day lol
1280. I hear that lol
1281. kekplay the almost 4-star puzzle bobble ending
1282. puzzle bobble
1283. it started out ok tho
1284. NO wait I'm not playing osuno no no
1285. hahaha
1286. I need to relaxevery time I start it up I have to beat a harder songIt's already so fast that I really can't follow itI can't find the puzzle bobbloh is it unranked/?
1287. 5logank has entered the chat.
1288. no
1289. zuntata?
1290. yeah never mind this map sucksyeah
1291. I... oh nooh no osu is drawing me inno there HAS to be a relaxing game somewherewhy are none of my steam games relaxing
1292. man wtf this osu map failed me at 88% and gave me an X during a break where I had 92%this is bs
1293. got stardew valley?bailey seem pretty relaxed atm
1294. no I'm not embarking on a stardew valley binge in the middle of osuI just need a short gamelike 10 hours
1295. yeah, that's about how long her save files last :p
1296. lol
1297. land maker
1298. oh no I saw undertale in my steam library and now I want to play the "hopes and dreams" song in osu
1299. oh no
1300. gaaahhhhh if I keep playing osu I'm going to explode from the tryhard
1301. i accidently smacked my cat in the nose
1302. oh oh I know
1303. land maker
1304. I'm going to try through the fire and the flames on nofail
1305. mein kampf
1306. lum let's play coop tag mode in osuyou can pick all the maps. I'll just relax
1307. who wants to spectate how poorly I do
1308. nnnnnnnok
1309. you have to make the room
1310. yeah yeanaming things is hard hang on
1311. i CAN'T WAIT UNTIL sPLATOON 2 AND mh xx sWITCH COMES OUTsorry caps
1313. okay room name is emacs > vimpass is weebs
1314. lol nice
1315. jesus shit I'm hovering around 12%
1317. are we? what do I have to dotag something?tag coop ok that sounds scary
1318. coop tag is the only one that's coopWe take turns playing the combos in the song
1319. that sounds hardI still don't think I understand so... we'll see
1320. time to see what this new set of rocks looks like. Finally no more droning rock polisher!
1321. oops I messed up too
1322. 12Me21 has entered the chat.
1324. Lacks has left the chat.
1325. "there's just so much mountain dew"
1326. randomouscrap has left the chat.
1327. http://12me21.github.io/sbhighlight/ If anyone finds any bugs I'll pay them 7000 coins
1328. for some reason it needs javascript
1329. Lacks has entered the chat.
1330. wait is - really not part of numbers
1331. yeah
1332. Lacks has left the chat.
1333. I mean I get why but that seems stupid
1334. SB originally didn't highlight the - but they changed it- is an operator not an inherent part of a numberthings like1-1 1+1 1*1 1/1are inconsistent since - has 2 usesI think they changed TO and STEP in that same updateoriginally they weren't highlighted but now they're highlighted as keywords even though they aren't true keywords since you can make variables with the same nameI put them in the "separator" group along with , : and ;
1335. FOR FOUR TO TO STEP STEP
1336. WHILE TRUE ?"LET THE BODIES HIT THE FLOOR" VSYNC WEND
1337. oops TRUE is not getting highlightedhaha good thing no one noticed
1338. TRUE
1339. HylianHoundoom has left the chat.
1340. (in my new system, that is)
1341. PhilFish has entered the chat.
1342. PhilFish has left the chat.
1343. snail_ has entered the chat.
1344. okay so I installed synergy and it's the absolute best thing everthis is awesome (I'm on Linux but using a keyboard linked to my Windows machine)
1345. does it let you press enter lumage?
1346. HylianHoundoom has entered the chat.
1347. yes
1348. richard stallman is a bit of a nut
1349. I couldn't find anything but if you're looking for programs to test you should probably use Ochame Nako's QSPshttp://ochameclub.web.fc2.com/petitcom3/soft/qsp.htm
1350. http://ochameclub.web.fc2.com/petitcom3/soft/image/1GQ_AITE.jpg ooh they use SPSET 0SPSET. is shorter
1351. dude this was amazingdefinitely worth $20 1352. I could make this program 4 characters shorter immediately 1353. isn't Synergy open-source 1354. it's not quite code golf 1355. can't you build it without paying 1356. it's "get it on 1/4 a screen and you're done" 1357. but if it's shorter you can then add more features 1358. yeah but @Lumage if you're good at code golf you can get so much on 1/4 a screen 1359. QSP contest please? 1360. please 1361. 12 make a QSP edition highlighter 1362. code golf is basically just size-restricted programming 1363. IF B*C THEN TALK M$[RND(M)] TALK M[RND(M)]*(B&&C) maybeidk if talk can have more than oneat the same timeoh it can'thmanyway 12OS=best OS 1364. \=strongly disagree 1365. tbh it's better than most of the other fake OS's though it's not REALLY a QSP since the commands have to be in an external fileI used it for finding files for a LONG time on my o3DSI mean I was only successful like 40% of the time but still 1366. maybe we should make that javascript smilebase interpreter soonit *might* not be illegal if you don't copy their bytecode format 1367. Lacks has entered the chat. 1368. also my OS had a 512 KB GRP file for the "12OS" logo lol 1369. I like how chiptune as a genre just means "bad" https://www.youtube.com/watch?v=E8jQM7wjZscbut actual tracker compositions are still like https://www.youtube.com/watch?v=sQtT2xPez8Ais emacs a tracker program also 1370. Lumage has left the chat. 1371. Lumage has entered the chat. 1372. Midnoclose has entered the chat. 1373. lamoj clearly hasnt heard good chiptune 1374. the context is that I said "GNU[guhnoo] Project" in a real conversation 1375. if it calls itself chiptune it isn't good chiptune 1376. well that's how you say it 1377. yeah and then trinitro questioned it 1378. I CAN'T FUCKING WAIT FOR MH ON THE SWITCH!!!!! 1379. can we get Bad Apple on Tiny Computerwhere's the guide 1380. I would be massively impressedthough I guess with all the processing power available to TC it wouldn't be hardthough TC has no mechanism for data storage whatsoever, so it would just be a lot of add 2638746278638462,m31 1381. FO CK DN DJ NU WS LU AP NB ZF ME EP VN NR other two letter acronyms that have no meaning probably 1382. -WS 1383. I made arrays 1384. oh right macro abuse exists 1385. FO CK 1386. well do you have macros that can store arbitrary data in memory 1387. yeah I made a rraysaok sort ofhttp://smilebasicsource.com/tinycomputer/?username=12Me21&program=pressenterlumage 1388. when I first started programming I didn't know that "arrays" was meant to be pronounced "uh-RAYS" and I pronounced it "AIR-rays" 1389. where is the I lol@set 500 @index @array 31599 @_ 29850 @_ 29347 @_ 14499 @_ 20340 @_ 14543 @_ 31694 @_ 18727 @_ 31727 @_ 18927 @_ 23530 @_ 15083 @_ 29263 @_ 15211 @_ 29391 @_ 04815 @_ 27470 @_ 23533 @_ 29847 @_ 31524 @_ 23277 @_ 29257 @_ 23549 @_ 23403 @_ 31599 @_ 05103 @_ 28527 @_ 23275 @_ 14478 @_ 09367 @_ 31597 @_ 11117 @_ 24557 @_ 23213 @_ 09389 @_ 29351 @_ 00000 @end 1390. oh godI guess it works 1391. anyway I'm going to make a QSP file search thing that supports ? and * wildcard things 1392. >*? 1393. randomouscrap has entered the chat. 1394. someone who is touhou weeb plz helpwhat is this song https://youtu.be/AIKHHs-SgPU?t=2004no touhou weebs want to help? T_T I will forever be missing this in my osu life 1395. oh 1396. 12 did you get that list from scrabble 1397. is it ceimson belvedere again 1398. Is it? IDK I really like it 1399. novocal 1400. do I need to link the time? 1401. you did?this sounds mutilated like bad remixes usually do 1402. I thought at some point you couldn't use timestampsawww bad remix. I like this song anyway, even if it sounds nothing like the originalYou don't know what the original is? 1403. jeez did you even try using google 1404. I didevery link is japanese 1405. Kid's Festival ~ Innocent Treasureshttps://www.youtube.com/watch?v=0CbvqJAfCRc&feature=youtu.be first video result 1406. Ah I saw that but I also saw a million other titles so I couldn't sift through it 1407. https://www.youtube.com/watch?v=bTlA_Lfssp0the original is better 1408. that wasn't the first link for me though 1409. well use duckduckgo :) 1410. it's not even on the first page of links 1411. *:] 1412. I'm sorry for bothering you lum 1413. wait what is dream of arcadia fromoh no it's just people pretending it's a yuuka themeriiight arcadian dream okay 1414. thank you for the help 1415. it's wasn't a bother 1416. oh of course all the maps are Xtremeargh I guess I'll just have to get betterI love this song 1417. "Easy" 1418. guess I'll play osu then. I need to get up to 4.4 stars 1419. "2.9 *" 1420. some people are mean 1421. 5logank has left the chat. 1422. oh wait i have mods on lol 1423. I like this one too https://www.youtube.com/watch?v=PhQ0CQ-m4Xc 1424. subtrranean animism has the best musicafter lotus land storywalking the streets of a former hell is also corpse voyagelullaby of a deserted helluhh dark blowholelast remotepeople like hartmann's youkai girl too 1425. I see them 1426. random I got Synergy 1427. they don't seem to have this song ranked though T_T 1428. best software ever 1429. I only vaguely know what synergy is because someone linked it in chat 1430. sealed away youkai - lost place is amaze too 1431. probably me 1432. Congratulations on your software purchase I guess lolIs this all subterranean animism lum? 1433. yeah over half of the SA soundtrack is good yes yes 1434. well I ended up buying it and now it treats my Linux PC just like a 3rd monitor on my Windows PC, except the monitor is actually linuxbasically one mouse, one keyboard, two computers, three monitors 1435. I searched "subterranean animism" earlier but I didin't like the remixes they had 1436. randomouscrap has left the chat. 1437. Guzzler829 has entered the chat. 1438. You shouldn't get dish soap in your eyeIt's no fun 1439. oh I'd never have guessed 1440. ElzoBro has entered the chat. 1441. ElzoBro has left the chat. 1442. andritolion has entered the chat. 1443. Time for ARMS!The Testpunch is starting in 10 minutes! 1444. andritolion has entered the chat. 1445. andritolion has left the chat. 1446. Gtg. I am in a fight.NookNooo..Yes!Bye. Gonna play. 1447. Sex. 1448. in the sewer 1449. andritolion has left the chat. 1450. https://www.youtube.com/playlist?list=PLz7P46GUzXA-AA3TJws9DPjrTSm7S3CY6masochistic pleasure from appendage numbing 1451. HylianHoundoom has left the chat. 1452. Lacks has entered the chat. 1453. https://www.youtube.com/watch?v=mrM-SQoHAfw What's this intro """inspired""" from? 1454. Lacks has left the chat. 1455. I'm not going to take "nothing" for an answer when it's FREAKING FRAGILEONLINE THAT'S THEIR THING https://www.youtube.com/watch?v=G9H4KYFAok4 1456. snail_ has left the chat. 1457. lilstrubel has entered the chat. 1458. hello :) 1459. Lacks has left the chat. 1460. Lacks has entered the chat. 1461. andritolion has entered the chat. 1462. andritolion has left the chat. 1463. andritolion has entered the chat. 1464. Done!ARMS Global Testpunch is DONE! 1465. andritolion has left the chat. 1466. andritolion has entered the chat. 1467. mmsleep 1468. http://12me21.github.io/sbhighlight/ If anyone finds any bugs I'll pay them 7000 coins 1469. I really love this song <3 https://www.youtube.com/watch?v=w0dMz8RBG7g 1470. Lacks has left the chat. 1471. ³ 1472. andritolion has left the chat. 1473. I'm gonna load up my WinXP VM and delete System32and rebootI want to see what happens 1474. -b±√b²-4ac/2a 1475. ohgodownoplease 1476. wat 1477. n-nothing 1478. PhilFish has entered the chat. 1479. PhilFish has left the chat. 1480. I have identified System32 1481. you don't like the equation? 1482. nounrelated 1483. Trinitro21 has entered the chat. 1484. Seven Color MonotoneFour Letter Magic 1485. vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv,,,,,,,,,,,,,,,,,,,,,,,,,,oh whoops sorrycomputer was messing around 1486. ElzoBro has entered the chat. 1487. Weird how infatuation worksYou get so many ideas of how someone actually is, and when you finally get to talk to eachother, it's completely different. Not necessarily bad, but it's odd. 1488. yeah and you have like a 50% chance of your attack failing 1489. ya 1490. I suppise you shouldn't expect your assumptions and educated guesses to be rightLol 1491. Lacks has entered the chat. 1492. Or you start mimicking your team member's moves and kill eachotherI'm excited for Track/Cross Country and DebateAlthough I think Track/Cross Country are two different things, I'd have to look into itOr I guess I can ask my brother lolIs it in bad taste to post my school's website? 1493. "Windows could not start because the following file is missing or corrupt: <Windows root>\system32\hal.dll. Please re-install a copy of the above file." 1494. Meh, since when was that a concern anywayshttp://school.fultonschools.org/hs/cambridge/Pages/ 1495. okay so deleting system32 is bad 1496. I'll he going to cambride next year ye 1497. PhilFish has entered the chat. 1498. PhilFish has left the chat. 1499. I wonder what high school will be likeI hope I have good people in my classesAnd maybe some new friends tooIt's weird to look in the yearbook. I always wonder who I'm gonna befriend the next year when i get it 1500. Trinitro21 has left the chat. 1501. Here's the list of clubs i wanna talk about sone of themhttp://school.fultonschools.org/hs/cambridge/Documents/Extracurricular/CLUB%20List%202016.2017.pdf 1502. Trinitro21 has entered the chat. 1503. okay if anyone wants me to do stupid shit to a WinXP VM just ask 1504. Bible Club sounds like a meme tbh 1505. I've already deleted system32 and I've already run the MEMZ virus so don't ask about those 1506. fencing club 1507. Is there a Torah Club? 1508. yes'jewish culture club' 1509. Lmao Defense Tactics Club sounds like a way to incite school violencwI should joinLol nice 1510. sounds like one of those "have martial arts so you don't get raped' things 1511. HTV04 has entered the chat. 1512. Idk how many actually good clubs are at this schoolProbably2 1513. is there a kawaii desu~ club? 1514. what are half of thesemy school had like 1515. Not counting athletics 1516. one pageand they all sucked 1517. I think there's anime clubI'm not gonna do it, at least not this yearLol @Lumage 1518. there's an atheist club at college 1519. "young dem/young rep" that's interesting I wonder if they ever team up with debate club 1520. >and ofc I'm joining 1521. I wanna do debate every year, and maybe Model UN 1522. yeah don't join belief clubsonly activity/hobby clubs 1523. I'm curious what they do in young Dems and Repubs 1524. but it's a lack of belief clubheuhuehuehueheuheuhue 1525. inb4 brainwashing 1526. I wanna join Young Independent 1527. hyuk 1528. Omg Lumage I'm wheezing lmfao 1529. oh yea I'm not joining any political club 1530. wtf is VegYouth 1531. vegan youth? 1532. Vegetable? As in mental retardation? 1533. I wanna join Young Republicans so that I can cause a fight—Omg 1534. or like plantsoh veganyeah probably that 1535. oh elzo are you dem? 1536. > Brain Dead Youth ClubI'm an independent, I hate political partiesthey suck 1537. how do you make a circle in gimp 1538. they should just merge braindead club with the political clubs 1539. I has a banjo now 1540. Lmao 1541. I'm libertarian but they don't have a libertarian club at college (not like I'd join it anyway) 1542. I feel like Young Rep/Dems is literally gonna be echo chambers for both sides lmaoAnd then there's probably gonna be bullying and some shitBetween the teoBetAt least in Debate, you have both sides 1543. it's an interesting concept though 1544. Yeah I suppose 1545. new to me anyway 1546. But they'll probably just be wrong about everything 1547. I hate how 99% of political things are two-sided like you're either for or against it, the end 1548. And be biased like IRL political parties 1549. Midnoclose has left the chat. 1550. less "wrong" and more "you have to agree with every single one of these unrelated things" 1551. ok i'm just going to assume that you cannot make a circle in gimp 1552. "democrat or republican" "pro-life or pro-choice" "liberal or conservative" "socialist or capitalist" "gun control or pro-guns" 1553. Either that ir they'll refuse new information because that means they can be "wrong" and "grow as people" 1554. use the circle tool 1555. like everything is 2-sidedbut there are way more than 2 sides 1556. the circle tool 1557. Maybe I wont be cut out as a politician with my non-bipartisan views buutI think I'll join both of them at some point just to see what it's like lol 1558. I'm on the "don't sell assault weapons but other funs are alright" side 1559. >other funs 1560. but that just makes me horrible to BOTH parties 1561. I hope I get bullied in Young Republicans, I'll giggle 1562. other funs 1563. i know how to select a circle but how do i draw a circle outline 1564. I'm on the "we need strict background checks but otherwise all guns are okay" side 1565. but noooo background checks are EVIL 1566. I'm on the, "I guess you can have assault weapons, but no assault ammo, and guns should have more checks and stuff, but if bad people want guns they'll find a way to get them either way so" 1567. yea honestly what will making guns illegal do when was the last time making heroin illegal prevented people from using heroin 1568. Hey Phil :) 1569. hello 1570. I mean my real opinion is more complicated than what I said but yeah 1571. HTV04 has left the chat. 1572. this is the best i can do for circle outline in gimp 1573. Idk my brother is of the "I played Call of Duty so I'm a gun expert durrrrrr" variety and he got mad at me when I said selling Assault Weapons is literally asking for death 1574. Hey Phil I want to learn this song on the piano. This song is beautiful <3 https://www.youtube.com/watch?v=w0dMz8RBG7g 1575. piano can be difficult 1576. But back to clubs i guess 1577. I mean idk about that rhetoric but you certainly don't use a submachine gun for deer hunting 1578. make the "white pride" club and be hated by everyone 1579. LMAO 1580. I considered it. 1581. it sounds like it's not too hard? Did you listen to it? 1582. Black guy makes white pride club 1583. ^that way it's "not racist" 1584. This is gonna happen thatms gonna be my legacy>European-American Culture ClubWhite People Appreciation Club 1585. oh yea name it European-American and it'll be fine 1586. I'll probably get an ISS tbhIdk what you do in clubs where you don't just eat Pocky and watch Steven UniverseI wonder if the Young Republicans teacher hates gays, now I HAVE to join 1587. "Straight Appreciation Club" 1588. I wonder if the Young Dems has a hit-squad for people who don't align with their views 1589. I wanted to make a white something-or-other club but just eat cookies and play smash bros. and wait for the very nationalistic Black Student Union to be upset about its existence 1590. Lmao 1591. they were very um "strongly-spoken" 1592. Lacks has left the chat. 1593. I wonder if there's a black appreciation club 1594. I'm already learning things :) 你好 你 好* 1595. I wonder if Class Council will be awful 1596. what is TSAI think my school had one too 1597. I'm gonna win Freshman Class council I'm sure 1598. Did I mention that I caught my first shiny pokemon today? 1599. "Technology Student Union" 1600. My frieds are very... outspoken 1601. what does that even mean 1602. LolI though it was TSA like airport security 1603. Trinitro21 has left the chat. 1604. pat-down club? 1605. Lol wait, the Young Dems leader is also the gay Straight Alliance Leader 1606. hm. 1607. Speaking of clubs I ate a turkey club sandwich today... 1608. I feel like that says something but I cant put my finger on it.. @Lumage 1609. >Conspiracy Club 1610. OohFuture Homeless of america will be the club i make 1611. kek 1612. I wanna so a bunch of clubs if I can 1613. conspiracy sounds like half the group is looking at interesting bullshit and the other half just say "bush did 9/11" until no one laughs anymore 1614. That way i can have some fun^Yeah lol 1615. ElzoBro has left the chat. 1616. ElzoBro has entered the chat. 1617. Hmmm 1618. also that's the club adviser, not club president or anything so possibly more just there to watch over people 1619. >Political and social Debate 1620. I'm starting to like Chinese Porn... 1621. Oh so that's like, if Young Dems and Young Reps fused into a war zone 1622. probably shouldn't join debate clubs first year 1623. Oh yeah I totally needed to know that thanks much, yup yup 1624. what the fuck lil 1625. Aw 1626. I forgot I shouldn't share that stuff xD 1627. why in SBS chat 1628. But Debate sounds funnnAnd all my friends are there 1629. oh i mean 1630. And I get to fight people 1631. if you like low standards lol 1632. And learn them stuffOh awBut the clubs are for the whole school and stuff 1633. debate is better after a few years of Lang 1634. I can teach you something interesting ;) 1635. I mean, I finished 9th Grade Lit last year so 1636. I can teach you about my foot in your ass 1637. Or this year? Idk when the statue of limitations on calling 8th grade this year starts*ends 1638. @Lumage That sounds like fun 1639. lilstrubel has entered the chat. 1640. lilstrubel has left the chat. 1641. @Lumage Why are you so mean man 1642. so there's a fidget spinner anime now 1643. I should go donate blood again but ask for "whatever hurts the most" 1644. I wanna donate blood I guess 1645. It's hecka fun(for me) 1646. there's a place where I live where you donate plasma and they pay you like a LOT of moneytalking about >100
1647. oh i didn't do it for payI did it at school
1648. Rip
1649. The only bad part was that I missed part of class
1651. I wanted to donate at school but the administrators didn't let me because I had a performance the next day
1652. Is it weird that I tell you guys what kind of porn I watch?
1653. yes
1654. https://quizlet.com/211584963/rhetorical-devices-latin-terms-by-spider-man-flash-cards/
1655. Awww but it's so interesting to know how people enjoy their "Private time"
1656. usually I spend it killing people like you
1657. I spend my private time building PCs so there you go
1658. what do you do in your bedroom besides sleep
1659. mmf why can't the web be keyboard-navigation
1660. sit at my computer
1661. sameHey Phil what's the girliest thing you have ever done? :)
1663. I wear female underwear (I'm straight)
1664. remove boring repetitive grammars
1665. @Lumage you should listen to this... https://www.youtube.com/watch?v=w0dMz8RBG7g
1666. Lacks has entered the chat.
1667. Hi Lacks :D
1668. I bought a fidget spinner
1669. why xDwhat color :)
1670. Idk it was shinyBrass and silver
1671. cool :)Sorry about before lacks...]I got carried away again
1672. I don't want to listen to vocal music. Sorry.
1673. I feel horrible. I always tell lacks I'm going to stop saying bad things and I keep doing it anyway :(
1674. ElzoBro has left the chat.
1675. I did it
1676. what did you do?
1677. look at the picture
1678. I did but I don't get it
1679. https://smilebasicsource.com/forum?fpid=15916#post_15916
1680. I don't really know what there is to not get
1681. OH nvm I'm an idiot I got confused sorry
1682. @Phil How come people hate me in this chatAka lumage
1683. well for one you discuss what kind of porn you watch
1684. Lumage has left the chat.
1685. Lumage has entered the chat.
1686. that's...not normal when it comes to IRCs
1687. oh
1688. ElzoBro has entered the chat.
1689. I saw some people doing that so I thought it was okaynot herein another chat
1690. yea this is a programming chat not a porno chator, supposed to be a programming chat
1691. Why is this still happning, rule of thumb, people like you less if you ask why people don't like you
1692. "not here in another chat'every community has different rules
1693. And if you wouldn't talk about it to someone's face, you shouldn't say it in chat
1694. But I would say that to someones face :(
1695. that's not cool
1696. it's not that bad is it
1697. it kinda is'
1698. I mean you act like you've never been on the internet before
1699. I know there are rules and all but I don't know the rules for this chatI still don't know
1700. There aren't definite rules for what "is" and "isn't" okay to talk about, but as a rule of thumb, if people don't *want* to talk about it, you shouldn't talk about it
1701. Part where Lil is an Andritolion alt trying to evade my ignores?????Lmao
1702. RealTiP has left the chat.
1703. you tried to ignore me? XD
1704. yea if people think it's not cool to talk about then you shouldn't talk about it
1705. Not you, Andritolion lol
1706. if other people are having a genuine discussion about something sexual and someone has a real contribution it's no problem to say it But if you're just talking about porn for no reason then you're just being annoying
1707. but how do I know if people know it's cool or not until after?
1708. keep to the current topic or keep quite*quiettyping too fast
1709. You make an educated guess
1710. you use your brain and anticipate fellow human behavior
1712. Good one...But yeah I'll try
1713. Keep to the current topic, smoothly transition to another topic, or keep quiet
1714. Also sometimes I like getting different reactions from saying things like that
1715. Ew
1716. Sometimes It's funnybut I don't want people to hate me for it
1717. No I just don't like people trying to get reactions out of others just for the sake of it in general, but it's fine
1718. >I want to do something dumb but I don't want people to think I'm dumb
1719. At least you own up to it(?)
1720. yeah I guessI barely have anything to talk about :(Nobody likes my music and everybody hates when I post links.
1721. then don{t post them hereit's not specific to you
1722. I really like music and that's something I like to talk about but it's hard when nobody listens to the same music as you.
1723. because we AREN'T A-POP SOURCE
1724. That's true then what counts as off topic???
1725. just because it's off-topic doesn't mean everyone is going to want to discuss the same topicYou're not being clever
1726. no that's not what I meant sorrywell what stuff do you like to talk about lumage
1727. I don't talk about things so much as I talk with people, sorry.
1728. oh
1729. I can show you what I'm working on if it'll make you happy, though.
1730. yeah
1731. http://scratch.smilebasicsource.com/pax/voxel-voxel-voxel-dictionary.pdf
1732. This is cool :)Anyway I'm going out to eat so I'll see you guys in like 20 min. Sorry to be a bother
1733. lilstrubel has left the chat.
1734. ElzoBro has left the chat.
1735. pixel_voxel[17:05]o: oh look free and open source software pixel_voxel[17:05]o: all i need to do now is dance in a circle and it'll summon gabe the ghost
1736. ElzoBro has entered the chat.
1737. define peer pressure fetish
1738. define define
1739. pier pressure lolanyway
1740. Lacks has left the chat.
1741. ElzoBro has left the chat.
1742. "you can't get inside a hand"
1743. Perska has left the chat.
1744. "I'm going to hold an apple on my head and I need you to shoot me in the face""I'd beat sparky to death with my umbrella if you know what I mean"
1745. ElzoBro has entered the chat.
1746. ElzoBro has left the chat.
1747. HTV04 has entered the chat.
1748. HTV04 has left the chat.
1749. Trinitro21 has entered the chat.
1750. http://htwins.net/unicrush/ good stuffor rathergood stu∬lol only saved me one character
1751. Lacks has entered the chat.
1752. http://smilebasicsource.com/user/bugm3not Possible alt of Midnoclose
1753. not sure if I like you guys IPchecking every new user
1754. what would happen if I made an alt over a feigned IP and onion routed my connection?
1755. they wouldn't catch you, but Lumage might
1756. Trinitro21 has left the chat.
1757. Lacks has left the chat.
1758. Omiwa "Also cannot be eaten by dinosaurs"
1759. yes
1760. Omiwa Is this a reference to something from a game?
1761. Maybe?It's definitely something the pixel voxel sus said
1762. Omiwa That's a lovely file. Haha.
1763. Yes.
1764. Lumage Was it greatly enjoyable?
1765. Omiwa https://www.mariowiki.com/List_of_Super_Mario_64_and_Super_Mario_64_DS_quotes#Boo The first one.
1766. Omiwa Mildly Amusing, to say the least.
1767. Lumage Ah, probably, then.
1768. ./16-01-26.txt:2133: pixel_voxel[04:09]o: GHOSTS DON'T DIE ./16-01-26.txt:2137: pixel_voxel[04:09]o: (they also can't be eaten by dinosaurs)
1769. Omiwa Your avatar is cute. Is it Yuuka? If no, please don't tell me what it is.
1770. Lumage I'm a fish!
1771. Lumage Would you kiss a fish?
1772. Omiwa Maybe if this fish is named Mero.
1773. Lumage http://safebooru.donmai.us/posts/2621711
1774. Omiwa Angry.
1775. Omiwa I think you threatened to ban me for having a close-up of a clean picture of Yukari by that artist.
1776. Omiwa Anyway way, I'm surprised that's Iku. I thought it was someone from Touhou 14.
1777. Omiwa Anyway, I'm*
1778. Lumage Ms. Sweet?
1779. Lumage https://smilebasicsource.com/forum?fpid=15919#post_15919
1780. Lumage ofc i'll still probably do it in accesskeys
1781. Omiwa openjs
1782. Omiwa Have you seen How to Train Your Dragon?
1783. Lumage No comment but continue.
1784. Omiwa The dragon which the protagonist befriends is so cute, isn't it?
1785. Lumage It's not.
1786. Lumage Flawless Clothing of the Celestials
1787. Omiwa It reminds me of a black cat.
1788. Lumage It's not.
1789. Chemicalex has entered the chat.
1790. Chemicalex has left the chat.
1791. Lumage if you like degeneracy like that maybe you'd like Dragon Drive
1792. Omiwa Why isn't it cute? Why don't you like it,?
1793. Lumage I don't like the anime but https://www.youtube.com/watch?v=gC2AjClszTc
1794. Omiwa I don't want to watch anime.
1795. Chemicalex has entered the chat.
1796. coucou_COA has entered the chat.
1797. Lumage read the manga then; it's better It's the plot that that series you mentioned stole.
1798. coucou_COA has left the chat.
1799. Lumage and the dragon is actually cute instead
1800. Chemicalex has left the chat.
1801. Chemicalex has entered the chat.
1802. why can't people use the chat normally
1803. Lacks has entered the chat.
1804. oh hi lacks
1805. Hello
1806. how was your day so far
1807. Pretty good
1808. ElzoBro has entered the chat.
1809. Omiwa
1810. Chemicalex Omiwa
1811. Lumage Chemicalex Omiwa
1812. Lumage look it's literally the same show https://youtu.be/gC2AjClszTc?t=914
1813. Kuragen has entered the chat.
1814. Kuragen has left the chat.
1815. Omiwa No
1816. lilstrubel has entered the chat.
1817. hello :)
1818. Omiwa It's not.
1819. Omiwa Hello
1820. hey
1821. Chemicalex has left the chat.
1822. Chemicalex has entered the chat.
1823. Omiwa Darn I wish I had a normal family
1824. Lumage define normal
1825. Omiwa "normal"
1826. Chemicalex nor·mal/ˈnôrməl/ adjective conforming to a standard; usual, typical, or expected. (of a line, ray, or other linear feature) intersecting a given line or surface at right angles. (of a salt solution) containing the same salt concentration as the blood. denoting a fault or faulting in which a relative downward movement occurred in the strata situated on the upper side of the fault plane.
1827. Lumage omiwa you're the one that isn't normal in your family
1828. Lumage remember?
1829. Chemicalex has left the chat.
1830. Chemicalex has entered the chat.
1831. Omiwa maybe that's why I don't see them as normal because my perception is messed up
1832. Chemicalex has left the chat.
1833. Lumage would you kiss a plant
1834. ColinTNMP has entered the chat.
1835. Kuragen has entered the chat.
1836. hello
1837. hi there.
1838. hru colin? .o.
1839. hru?
1840. im fine and you xd
1841. Omiwa "How are you?"
1842. Omiwa How aRe yoU
1843. .... oh sorry, I'm not good with abbreviations.
1844. okay so I discovered that nightcore is amazing
1845. Lumage omyaw?
1846. I'm fine.
1847. Omiwa Are you sure it's not stupid?
1848. Lumage ^
1849. Lumage omywa?
1850. hahahha is ok .o. and cool. hello phill.
1851. lilstrubel Omiwa Why are you always hiding in the darkness it's not healthy
1852. Lumage do you have any like this maybe? https://www.youtube.com/playlist?list=PLz7P46GUzXA-AA3TJws9DPjrTSm7S3CY6
1853. ColinTNMP lol
1854. a touhou playlist without night of knightswhat is thisSoRcErY
1855. Omiwa J'aime la nuit.
1856. Omiwa No.
1857. und spreche ich kein Franzoesisch :(
1858. it's night of nights
1859. I've seen it both ways
1860. and the fifth one IS night of nightsI have too
1861. french really xD
1862. Omiwa Oui. 'u'
1863. Chemicalex has entered the chat.
1864. It's a remix of "Flowering Night" so I'm pretty sure it's supposed to be Night of Nights
1865. 你 好
1866. Omiwa I don't understand. ewo
1867. hey guys i have a question..ehm why when i divide by hand 2÷3 i have 0.66666666 and doesnt end and why on a pc or a calculator when i divide 2÷3 i get 0.66666667 why do i get a 7 at the end?
1868. rounding.
1869. .o. when i do it by hand i always have a remainder of 2.oh .o. ok
1870. Computers don't really use remainders
1871. Remainders don't really exist digitally^^
1872. which kinda sucks sometimes... | 2018-11-14 22:32:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44386687874794006, "perplexity": 10831.609318042172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039742316.5/warc/CC-MAIN-20181114211915-20181114233915-00117.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=2004_AMC_12A_Problems/Problem_7&diff=128432&oldid=62578 | # Difference between revisions of "2004 AMC 12A Problems/Problem 7"
The following problem is from both the 2004 AMC 12A #7 and 2004 AMC 10A #8, so both problems redirect to this page.
## Problem
A game is played with tokens according to the following rule. In each round, the player with the most tokens gives one token to each of the other players and also places one token in the discard pile. The game ends when some player runs out of tokens. Players $A$, $B$, and $C$ start with $15$, $14$, and $13$ tokens, respectively. How many rounds will there be in the game?
$\mathrm{(A) \ } 36 \qquad \mathrm{(B) \ } 37 \qquad \mathrm{(C) \ } 38 \qquad \mathrm{(D) \ } 39 \qquad \mathrm{(E) \ } 40$
## Solutions
### Solution 1
We look at a set of three rounds, where the players begin with $x+1$, $x$, and $x-1$ tokens. After three rounds, there will be a net loss of $1$ token per player (they receive two tokens and lose three). Therefore, after $36$ rounds -- or $12$ three-round sets, $A,B$ and $C$ will have $3$, $2$, and $1$ tokens, respectively. After $1$ more round, player $A$ will give away $3$ tokens, leaving them empty-handed, and thus the game will end. We then have there are $36+1=\boxed{\mathrm{(B)}\ 37}$ rounds until the game ends.
### Solution 2
Let's bash a few rounds. The amounts are for players $1,2,$ and $3$, respectively.
First round: $15,14,13$ (given) Second round: $12,15,14$ Third round: $13,12,15$ Fourth round: $14,13,12$
We see that after $3$ rounds are played, we have the exact same scenario as the first round but with one token less per player. So, the sequence $1,4,7,10...$ where each of the next members are $3$ greater than the previous one corresponds with the sequence $15,14,13,12...$ where the first sequence represents the round and the second sequence represents the number of tokens player $1$ has. But we note that once player $1$ reaches $3$ coins, the game will end on his next turn as he must give away all his coins. Therefore, we want the $15-3+1=13$th number in the sequence $1,4,7,10...$ which is $\boxed{\mathrm{(B)}\ 37}$.
Solution by franzliszt | 2021-01-19 08:17:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 38, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.45279693603515625, "perplexity": 524.541384578956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703518201.29/warc/CC-MAIN-20210119072933-20210119102933-00533.warc.gz"} |
https://dsp.stackexchange.com/questions/74882/what-phase-rotation-occurs-when-you-take-the-derivative-of-an-audio-signal | # What phase rotation occurs when you take the derivative of an audio signal?
If you take the derivative of an audio signal, it provides a 6 dB/oct upward sloping filter (increasing high frequencies / cutting low frequencies) all the way across the spectrum.
What is the result in terms of the phase? Is there phase rotation? Is it uniform across the spectrum or does it vary with frequency? What would the plot of this phase rotation look like?
Thanks
• Hi Mike! You're probably familiar with the Fourier transform, and to make things a bit more interesting for you, just a hint: The Fourier transform of a signal, and its time-derivative, are linked in frequency domain. You only need to figure out how to convert that relationship to a phase! May 3 '21 at 16:35
• Thanks Marcus. So I presume taking the derivative of a sine wave gives a cosine wave and if you break the audio down into a series of sine waves, then take the cosine of each, you are rotating all phases of all frequencies by 90 degrees, which explains the answer.
– mike
May 3 '21 at 23:10
• love this! it definitiely works for all discrete spectra! Clever! May 3 '21 at 23:46
$$\mathcal{F}\{\frac{\partial}{\partial t}x(t)\}=j\omega \cdot\mathcal{F}\{x(t)\}$$
Differentiation in time corresponds to multiplication with $$j\omega$$ in frequency. Hence the +6dB/octave slope. The phase shift is a constant 90 degrees for all frequencies. | 2022-01-22 15:42:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 2, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5087661147117615, "perplexity": 560.4456928293101}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303864.86/warc/CC-MAIN-20220122134127-20220122164127-00102.warc.gz"} |
https://www.gradesaver.com/textbooks/science/physics/CLONE-afaf42be-9820-4186-8d76-e738423175bc/chapter-11-exercises-and-problems-page-210/66 | ## Essential University Physics: Volume 1 (4th Edition) Clone
Published by Pearson
# Chapter 11 - Exercises and Problems - Page 210: 66
b
#### Work Step by Step
We see that while r is in the direction of the arrow head, F is pointing upwards (since you are pushing upwards.) Thus, we see using the right hand rule that the correct answer is b (toward you).
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2019-10-23 13:14:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8361940383911133, "perplexity": 1271.7587943149686}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987833766.94/warc/CC-MAIN-20191023122219-20191023145719-00357.warc.gz"} |
https://zbmath.org/?q=ci%3A4197172 | ## A note on coverage error of bootstrap confidence intervals for quantiles.(English)Zbl 0799.62044
Summary: An interesting recent paper by M. Falk and E. Kaufmann [Ann. Stat. 19, No. 1, 485-495 (1991; Zbl 0725.62043)] notes, with an element of surprise, that the percentile bootstrap applied to construct confidence intervals for quantiles produces two-sided intervals with coverage error of size $$n^{-1/2}$$, where $$n$$ denotes sample size. By way of contrast, the error would be $$O(n^{-1})$$ for two-sided intervals in more classical problems, such as intervals for means or variances.
We point out that the relatively poor performance in the case of quantiles is shared by a variety of related procedures. The coverage accuracy of two-sided bootstrap intervals may be improved to $$o(n^{- 1/2})$$ by smoothing the bootstrap. We show too that a normal approximation method, not involving the bootstrap but incorporating a density estimator as part of scale estimation, can have coverage error $$O(n^{-1 + \varepsilon})$$, for arbitrarily small $$\varepsilon > 0$$. Smoothed and unsmoothed versions of bootstrap percentile-$$t$$ are also analysed.
### MSC:
62G15 Nonparametric tolerance and confidence regions 62G09 Nonparametric statistical resampling methods
Zbl 0725.62043
Full Text:
### References:
[1] DOI: 10.1093/biomet/74.3.469 · Zbl 0654.62034 [2] DOI: 10.1080/03610928908830134 · Zbl 0696.62051 [3] DOI: 10.1016/0167-7152(87)90055-1 · Zbl 0626.62047 [4] Efron, The Jackknife, the Bootstrap and Other Resampling Plans (1982) · Zbl 0496.62036 [5] DOI: 10.1214/aos/1176344552 · Zbl 0406.62024 [6] DOI: 10.1080/00949659208811374 · Zbl 0775.62107 [7] Angelis, Internat. Statist. Rev 60 pp 45– (1992) [8] DOI: 10.1214/aoms/1177698342 · Zbl 0245.62043 [9] Beran, J. Roy. Statist. Soc 55 pp 643– (1993) [10] DOI: 10.1093/biomet/74.3.457 · Zbl 0663.62045 [11] Sheather, Statistical Data Analysis Based on the L pp 203– (1987) [12] DOI: 10.1214/aop/1176996132 · Zbl 0339.60017 [13] DOI: 10.1016/0167-7152(86)90021-0 · Zbl 0585.62085 [14] Hall, J. Roy. Statist. Soc 50 pp 381– (1988) [15] DOI: 10.1214/aos/1176347135 · Zbl 0672.62051 [16] DOI: 10.1080/02331889108802305 · Zbl 0809.62031 [17] DOI: 10.1214/aos/1176350933 · Zbl 0663.62046 [18] DOI: 10.1214/aop/1176991515 · Zbl 0684.62036 [19] DOI: 10.1214/aos/1176347995 · Zbl 0725.62043 [20] DOI: 10.1016/0167-7152(92)90205-J · Zbl 0761.62016 [21] Young, J. Roy. Statist. Soc 52 pp 477– (1990) [22] DOI: 10.1093/biomet/75.2.370 · Zbl 0642.62026 [23] Silverman, Density Estimation for Statistics and Data Analysis (1986) · Zbl 0617.62042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2022-12-06 17:08:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4378722906112671, "perplexity": 6354.538997958151}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711111.35/warc/CC-MAIN-20221206161009-20221206191009-00198.warc.gz"} |
https://nbviewer.org/github/rasbt/deeplearning-models/blob/master/pytorch_ipynb/mechanics/custom-data-loader-quickdraw.ipynb | Deep Learning Models -- A collection of various deep learning architectures, models, and tips for TensorFlow and PyTorch in Jupyter Notebooks.
In [3]:
%load_ext watermark
%watermark -a 'Sebastian Raschka' -v -p torch,numpy
The watermark extension is already loaded. To reload it, use:
Author: Sebastian Raschka
Python implementation: CPython
Python version : 3.8.8
IPython version : 7.30.1
torch: 1.10.1
numpy: 1.22.2
# Model Zoo -- Using PyTorch Dataset Loading Utilities for Custom Datasets (Images from Quickdraw)¶
This notebook provides an example for how to load an image dataset, stored as individual PNG files, using PyTorch's data loading utilities. For a more in-depth discussion, please see the official
In this example, we are using the Quickdraw dataset consisting of handdrawn objects, which is available at https://quickdraw.withgoogle.com.
To execute the following examples, you need to download the ".npy" (bitmap files in NumPy). You don't need to download all of the 345 categories but only a subset you are interested in. The groups/subsets can be individually downloaded from https://console.cloud.google.com/storage/browser/quickdraw_dataset/full/numpy_bitmap
Unfortunately, the Google cloud storage currently does not support selecting and downloading multiple groups at once. Thus, in order to download all groups most coneniently, we need to use their gsutil (https://cloud.google.com/storage/docs/gsutil_install) tool. If you want to install that, you can then use
mkdir quickdraw-npy
gsutil -m cp gs://quickdraw_dataset/full/numpy_bitmap/*.npy quickdraw-npy
Note that if you download the whole dataset, this will take up 37 Gb of storage space.
## Imports¶
In [4]:
import pandas as pd
import numpy as np
import os
import torch
from torch.utils.data import Dataset
from torchvision import transforms
%matplotlib inline
import matplotlib.pyplot as plt
from PIL import Image
## Dataset¶
After downloading the dataset to a local directory, quickdraw-npy, the next step is to select certain groups we are interested in analyzing. Let's say we are interested in the following groups defined in the label_dict in the next code cell:
In [5]:
label_dict = {
"lollipop": 0,
"binoculars": 1,
"mouse": 2,
"penguin": 4,
"washing machine": 5,
"canoe": 6,
"eyeglasses": 7,
"beach": 8,
"screwdriver": 9,
}
The dictionary values shall represent class labels that we could use for a classification task, for example.
### Conversion to PNG files¶
Next we are going to convert the groups we are interested in (specified in the dictionary above) to individual PNG files using a helper function (note that this might take a while):
In [6]:
# load utilities from ../helper.py
import sys
sys.path.insert(0, '..')
from helper import quickdraw_npy_to_imagefile
quickdraw_npy_to_imagefile(inpath='quickdraw-npy',
outpath='quickdraw-png_set1',
subset=label_dict.keys())
### Preprocessing into train/valid/test subsets and creating a label files¶
For convenience, let's create a CSV file mapping file names to class labels. First, let's collect the files and labels.
In [7]:
paths, labels = [], []
main_dir = 'quickdraw-png_set1/'
for d in os.listdir(main_dir):
subdir = os.path.join(main_dir, d)
if not os.path.isdir(subdir):
continue
for f in os.listdir(subdir):
path = os.path.join(d, f)
paths.append(path)
labels.append(label_dict[d])
print('Num paths:', len(paths))
print('Num labels:', len(labels))
Num paths: 1515745
Num labels: 1515745
Next, we shuffle the dataset and assign 70% of the dataset for training, 10% for validation, and 20% for testing.
In [10]:
from mlxtend.preprocessing import shuffle_arrays_unison
paths2, labels2 = shuffle_arrays_unison(arrays=[np.array(paths), np.array(labels)], random_seed=3)
cut1 = int(len(paths)*0.7)
cut2 = int(len(paths)*0.8)
paths_train, labels_train = paths2[:cut1], labels2[:cut1]
paths_valid, labels_valid = paths2[cut1:cut2], labels2[cut1:cut2]
paths_test, labels_test = paths2[cut2:], labels2[cut2:]
Finally, let us create a CSV file that maps the file paths to the class labels:
In [11]:
df = pd.DataFrame(
{'Path': paths_train,
'Label': labels_train,
})
df = df.set_index('Path')
df.to_csv('quickdraw_png_set1_train.csv')
Out[11]:
Label
Path
penguin/penguin_112865.png 4
binoculars/binoculars_040058.png 1
eyeglasses/eyeglasses_208525.png 7
lollipop/lollipop_037650.png 0
In [20]:
df = pd.DataFrame(
{'Path': paths_valid,
'Label': labels_valid,
})
df = df.set_index('Path')
df.to_csv('quickdraw_png_set1_valid.csv')
Out[20]:
Label
Path
binoculars/binoculars_077567.png 1
screwdriver/screwdriver_007042.png 9
binoculars/binoculars_037327.png 1
In [21]:
df = pd.DataFrame(
{'Path': paths_test,
'Label': labels_test,
})
df = df.set_index('Path')
df.to_csv('quickdraw_png_set1_test.csv')
Out[21]:
Label
Path
eyeglasses/eyeglasses_051135.png 7
mouse/mouse_059179.png 2
penguin/penguin_043578.png 4
screwdriver/screwdriver_081750.png 9
Now, let's open one of the images to make sure they look ok:
In [23]:
main_dir = 'quickdraw-png_set1/'
img = Image.open(os.path.join(main_dir, df.index[1]))
img = np.asarray(img, dtype=np.uint8)
print(img.shape)
plt.imshow(np.array(img), cmap='binary');
(28, 28)
## Implementing a Custom Dataset Class¶
Now, we implement a custom Dataset for reading the images. The __getitem__ method will
1. read a single image from disk based on an index (more on batching later)
2. perform a custom image transformation (if a transform argument is provided in the __init__ construtor)
3. return a single image and it's corresponding label
In [24]:
class QuickdrawDataset(Dataset):
def __init__(self, txt_path, img_dir, transform=None):
self.img_dir = img_dir
self.txt_path = txt_path
self.img_names = df.index.values
self.y = df['Label'].values
self.transform = transform
def __getitem__(self, index):
img = Image.open(os.path.join(self.img_dir,
self.img_names[index]))
if self.transform is not None:
img = self.transform(img)
label = self.y[index]
return img, label
def __len__(self):
return self.y.shape[0]
Now that we have created our custom Dataset class, let us add some custom transformations via the transforms utilities from torchvision, we
1. normalize the images (here: dividing by 255)
2. converting the image arrays into PyTorch tensors
Then, we initialize a Dataset instance for the training images using the 'quickdraw_png_set1_train.csv' label file (we omit the test set, but the same concepts apply).
Finally, we initialize a DataLoader that allows us to read from the dataset.
In [25]:
# Note that transforms.ToTensor()
# already divides pixels by 255. internally
custom_transform = transforms.Compose([#transforms.Lambda(lambda x: x/255.),
transforms.ToTensor()])
train_dataset = QuickdrawDataset(txt_path='quickdraw_png_set1_train.csv',
img_dir='quickdraw-png_set1/',
transform=custom_transform)
batch_size=128,
shuffle=True,
num_workers=4)
That's it, now we can iterate over an epoch using the train_loader as an iterator and use the features and labels from the training dataset for model training:
## Iterating Through the Custom Dataset¶
In [26]:
device = torch.device("cuda:0" if torch.cuda.is_available() else "cpu")
torch.manual_seed(0)
num_epochs = 2
for epoch in range(num_epochs):
for batch_idx, (x, y) in enumerate(train_loader):
print('Epoch:', epoch+1, end='')
print(' | Batch index:', batch_idx, end='')
print(' | Batch size:', y.size()[0])
x = x.to(device)
y = y.to(device)
break
Epoch: 1 | Batch index: 0 | Batch size: 128
Epoch: 2 | Batch index: 0 | Batch size: 128
Just to make sure that the batches are being loaded correctly, let's print out the dimensions of the last batch:
In [27]:
x.shape
Out[27]:
torch.Size([128, 1, 28, 28])
As we can see, each batch consists of 128 images, just as specified. However, one thing to keep in mind though is that PyTorch uses a different image layout (which is more efficient when working with CUDA); here, the image axes are "num_images x channels x height x width" (NCHW) instead of "num_images height x width x channels" (NHWC):
To visually check that the images that coming of the data loader are intact, let's swap the axes to NHWC and convert an image from a Torch Tensor to a NumPy array so that we can visualize the image via imshow:
In [28]:
one_image = x[0].permute(1, 2, 0)
one_image.shape
Out[28]:
torch.Size([28, 28, 1])
In [29]:
# note that imshow also works fine with scaled
# images in [0, 1] range.
plt.imshow(one_image.to(torch.device('cpu')).squeeze(), cmap='binary');
In [30]:
%watermark -iv
torch : 1.10.1
PIL : 9.0.1
sys : 3.8.8 | packaged by conda-forge | (default, Feb 20 2021, 16:22:27)
[GCC 9.3.0]
torchvision: 0.11.2
pandas : 1.2.5
numpy : 1.22.2
matplotlib : 3.3.4 | 2022-11-30 13:41:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20057010650634766, "perplexity": 8780.770361724914}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710764.12/warc/CC-MAIN-20221130124353-20221130154353-00522.warc.gz"} |
https://zbmath.org/?q=an%3A1235.15013 | # zbMATH — the first resource for mathematics
Advanced topics in linear algebra. Weaving matrix problems through the Weyr Form. (English) Zbl 1235.15013
Oxford: Oxford University Press (ISBN 978-0-19-979373-0/hbk). xxii, 400 p. (2011).
The Weyr form will be unfamiliar to most mathematicians. As the authors explain, the form was introduced by the Austria-Hungarian mathematician Eduard Weyr (1852–1903) at roughly the same time as the Jordan form. It can be described as follows. Let $$N$$ be an $$n\times n$$ nilpotent matrix of nilpotent index $$r$$, say, over an algebraically closed field $$F$$. The familiar Jordan form of $$N$$ arises by choosing a basis of the underlying space of the form $$U_{1},\dots,U_{s}$$ where each sublist $$U_{i}$$ is a basis of an $$N$$-cyclic subspace of dimension $$m_{i}$$, say, and $$r=m_{1}\geq\dots\geq m_{s}$$. On the other hand the Weyr form for $$N$$ arises by choosing a basis $$V_{1},\dots,V_{r}$$ for the underlying space such that $$V_{1}$$ is a basis for the null space of $$N$$, and $$NV_{i}$$ is an initial sublist of $$V_{i-1}$$ for $$i>1$$. If $$n_{i}:=\left| V_{i}\right|$$ then $$n_{1}\geq\dots\geq n_{r}$$, and $$(n_{1},\dots,n_{r})$$ and $$(m_{1},\dots,m_{s})$$ are conjugate partitions of $$n.$$ More generally if $$T$$ is an arbitrary $$n\times n$$ complex matrix with eigenvalues $$\lambda_{1},\dots,\lambda_{t}$$, then a basis for its Weyr form is the concatenation of bases for the Weyr forms of the $$T-\lambda_{i}I$$ restricted to the generalized $$\lambda_{i}$$-eigenspace ($$i=1,\dots,t$$). Part I of this book is an elementary introduction to the Weyr form, its elementary properties, and advocacy for the benefits of this form vis-à-vis the Jordan form. Part I ends with a chapter introducing modules, von Neumann regularity, and a description of the Weyr form in the setting of von Neumann regular rings.
However, for some readers, Part II of the book will be more interesting, and it is a pity that the title does not reflect this. The theme in Part II is the study of the commutative subalgebras of the full matrix algebra $$M_{n}(F)$$. A classical theorem of Schur states that the largest $$F$$-dimension of a commutative subalgebra of $$M_{n}(F)$$ is $$\left\lfloor n^{2}/4\right\rfloor +1$$. The question arises as to what is the largest $$F$$-dimension of a $$k$$-generator commutative subalgebra. Trivially this is $$n$$ if $$k=1$$ and in 1961 M. Gerstenhaber [Ann. Math. (2) 73, 324–348 (1961; Zbl 0168.28201)] showed that the same bound also holds for $$k=2$$. In Chapter 5 the authors give a proof of this theorem (using the Weyr form) and related theorems, including some special results about the case $$k=3$$. It is an open question as to whether every $$3$$-generator commutative subalgebra has dimension $$\leq n$$.
In Chapter 6 the concept of “approximately simultaneously diagonalizable” (ASD) is introduced. Matrices $$A_{1} ,\dots,A_{k}$$ in $$M_{n}(\mathbb{C})$$ are ASD if for a standard norm $$\left\| ~\right\|$$ it is true that for each $$\varepsilon>0$$ there exist diagonalizable $$B_{1},\dots,B_{k}$$ such that $$\left\| A_{i}-B_{i}\right\| <\varepsilon$$ for each $$i$$. In such a case, the $$A_{i}$$ are necessarily pairwise commutative. In 1955 T. S. Motzkin and O. Taussky, [Trans. Am. Math. Soc. 80, 387–401 (1955; Zbl 0067.25401)] showed that conversely any pair of commuting matrices have the ASD property. However, when $$k\geq4$$ and $$n\geq4$$ commutativity does not imply ASD. The authors include two proofs of the Motzkin-Taussky theorem and show that it implies Gerstenhaber’s theorem when $$F=\mathbb{C}$$. They then look at some special cases where the corresponding theorem for $$k=3$$ has been proved. It is known that commutativity does not imply ASD when $$k=3$$ and $$n>28$$ (see below), but recent work by several authors has shown that commutativity implies ASD when $$k=3$$ and $$n\leq8$$.
Chapter 7 gives an elementary introduction to algebraic subvarieties of the affine variety $$\mathbb{A}^{n}$$ and then considers the variety $$\mathcal{C} (k,n)\subseteq\mathbb{A}^{kn^{2}}$$ consisting of the commuting $$k$$-tuples $$(A_{1},\dots,A_{k})$$ in $$M_{n}(\mathbb{C})$$. It is shown that commutativity of $$k$$-tuples implies the ASD property exactly when the variety $$\mathcal{C} (k,n)$$ is irreducible. Motzkin and Taussky proved that $$\mathcal{C(}2,n)$$ is irreducible (this gives another proof of the Motzkin-Taussky theorem above). Moreover, $$\mathcal{C}(k,n)$$ is irreducible for all $$k$$ when $$n\leq3$$ and is reducible when $$k\geq4$$ and $$n\geq4$$, so it remains to determine when $$\mathcal{C}(3,n)$$ is irreducible. The authors give a exposition of a version of R. M. Guralnick’s theorem [Linear Multilinear Algebra 31, No. 1–4, 71–75 (1992; Zbl 0754.15011)] which shows that $$\mathcal{C}(3,n)$$ is reducible for $$n\geq29$$, and related results.
The authors suggest that the book is suitable for an undergraduate course, and have taken trouble to include careful details in their arguments. The topics covered by the book appear to be a rather uneasy compromise between the three authors’ interests; some chapters are very leisurely and others are quite specialized. The second chapter gives a clear introduction to the Weyr form, but the idea of using the Weyr form as a unifying theme appears weak to the reviewer. On the other hand, Part II of the book is a good exposition of interesting material on matrix commutativity and of the underlying algebraic geometry, and it may be hoped that the book will introduce new readers to this still developing area.
##### MSC:
15A21 Canonical forms, reductions, classification 15-02 Research exposition (monographs, survey articles) pertaining to linear algebra 15A30 Algebraic systems of matrices 15A27 Commutativity of matrices | 2021-03-05 01:39:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8956623077392578, "perplexity": 222.85270918571706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178369553.75/warc/CC-MAIN-20210304235759-20210305025759-00439.warc.gz"} |
http://clay6.com/qa/3302/true-or-false-number-of-arbitrary-constant-in-the-particular-solution-of-a- | Browse Questions
# True-or-False: Number of arbitrary constant in the particular solution of a differential equation of order two is two.
Toolbox:
• If the given equation has $n$ arbitrary constant,then the required differential equation will be of $n^{th}$ order
If the equation contains $n$ arbitrary constants, then the required differential equation will be of $n^{th}$ order
But the number of arbitary cnstants in the particular solution of a differential equation is only one.
Hence the number of arbitrary constant in the particular solution of a differential equation of order two is two.
$False$ | 2017-06-27 02:05:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8962852954864502, "perplexity": 303.1281809235826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320887.15/warc/CC-MAIN-20170627013832-20170627033832-00179.warc.gz"} |
https://testbook.com/question-answer/the-orbital-speed-of-a-satellite-revolve-very-near--607809ea6c1f6569e60a67d0 | # The orbital speed of a satellite revolve very near to earth surface is
This question was previously asked in
Navik General Science 20-22 March 2021 Questions Set 1
View all Indian Coast Guard Navik DB Papers >
1. $$v = \sqrt {2gR}$$
2. v = 2gR
3. $$v = \sqrt {gR}$$
4. v = gR
## Answer (Detailed Solution Below)
Option 3 : $$v = \sqrt {gR}$$
## Detailed Solution
The correct answer is $$v = \sqrt {gR}$$
Key Points
• Orbital velocity is defined as the velocity required to maintain a satellite in its orbit around earth.
• Mathematically orbital velocity is given by
$$\Rightarrow v= \sqrt{\frac{GM}{R}}$$
• Where M = mass of earth and R = radius of the earth
• If a body of mass m placed on a surface inside a satellite moving around the earth. Then force on the body is
EXPLANATION:
• Mathematically orbital velocity is given by
$$\Rightarrow v= \sqrt{\frac{GM}{R}}$$
As we know, GM = gR2
$$\Rightarrow v= \sqrt{\frac{gR^2}{R}}=\sqrt{gR}$$
Additional Information
• The escape velocity on earth is given by:
• As we know, GM = gR2
$$⇒ {V_e} = \sqrt {\frac{{2\;gR^2}}{R}} =\sqrt{2gR}$$
• Escape velocity is√ 2 times orbital velocity. | 2022-01-21 14:00:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7872255444526672, "perplexity": 3489.729695170015}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303385.49/warc/CC-MAIN-20220121131830-20220121161830-00661.warc.gz"} |
http://bootmath.com/prove-that-the-equation-c_0c_1xldotsc_nxn0-has-a-real-solution-between-0-and-1.html | # Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1.
Let $c_0,c_1,c_2,\ldots ,c_n$ be constants such that :
$$c_0+\frac{c_1}{2}+\ldots+\frac{c_{n-1}}{n}+\frac{c_n}{n+1}=0$$
I have to prove that the equation:
$$c_0+c_1x+\ldots+c_nx^n=0$$
Has a real solution between 0 and 1.
Didn’t know how to start…I thought that maybe I could use something about derivative…But I’m lost…
Any help,much appreciated!!!
#### Solutions Collecting From Web of "Prove that the equation: $c_0+c_1x+\ldots+c_nx^n=0$ has a real solution between 0 and 1."
HINT 1: $$c_0 + \dfrac{c_1}{2} + \cdots + \dfrac{c_n}{n+1} = \int_0^1 \left( c_0 + c_1x + \cdots + c_nx^n\right) dx$$
HINT 2:
If $f(x)$ is continuous and $\displaystyle \int_a^b f(t) dt = 0$, then can you conclude that there is a root of $f(x)$ between $a$ and $b$?
This is an exercise from the differentiation chapter in Baby Rudin, and knowledge of integration is not expected. You can solve it without integrals using the following function:
$$f(x) = c_0x+\frac{c_1x^2}{2}+\ldots+\frac{c_{n-1}x^n}{n}+\frac{c_nx^{n+1}}{n+1}$$
What value does it take at $0$ and $1$? What value must the derivative take in $(0, 1)$ then? | 2018-06-24 22:44:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8475392460823059, "perplexity": 234.24509223790196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867095.70/warc/CC-MAIN-20180624215228-20180624235228-00361.warc.gz"} |
http://blog.decatech.com/atb5b/9e6111-entropy-chemistry-formula | Editor of Atomic, Molecular and Optical Physics Handbook. Cloudflare Ray ID: 61472bdc989a04ef The term and the concept are used in diverse fields, from classical thermodynamics, where it was first recognized, to the microscopic description of nature in statistical physics, and to the principles of information theory.It has found far … So far, we have been considering one system for which to calculate the entropy. The concept of entropy emerged from the mid-19th century discussion of the efficiency of heat engines. Entropy Definition Properties of Entropy Entropy Change Entropy and Thermodynamics. We can use the formula . • ENTROPY S) – dispersal ... “Big Mamma” Equation, verse 3: G rxn = G (products) − G (reactants) You already know how to calculate enthalpy and entropy, just substitute free energy values using tables of standard values! 2 Comments / Physical Chemistry / By Editorial Staff. Entropy is usually defined in terms of heat. Enthalpy and entropy are thermodynamic properties. While many methods exist to calculate configurational entropy, there is a balance between accuracy and computational demands. Solid state has the lowest entropy, the gaseous state has the highest entropy and the liquid state has the entropy in between the two. BOTH ΔHf and ΔGf = 0 for elements in their standard state and both bear units of kJ/molrxn. A system is just our balanced equation that we're looking at. If you are on a personal connection, like at home, you can run an anti-virus scan on your device to make sure it is not infected with malware. In this equation, S is the entropy of the system, k is a proportionality constant equal to the ideal gas constant divided by Avogadro's constant, ln represents a logarithm to the base e, and W is the number of equivalent ways of describing the state of the system. To quote Planck, "the logarithmic connection between entropy and probability was first stated by L. Boltzmann in his kinetic theory of gases". Entropy is highly involved in the second law of thermodynamics: An isolated system spontaneously moves toward dynamic equilibrium (maximum entropy) so it constantly is transferring energy between components and increasing its entropy. 18. know that the balance between the entropy change and the enthalpy change determines the feasibility of a reaction and is represented by the equation ΔG = ΔH − TΔSsystem OCR Chemistry A Module 5: Physical chemistry and transition elements 4.2.4 calculate the standard entropy change, ΔSӨ, in a chemical reaction using standard entropy data; 4.2.5 use the equation ΔG = ΔH - TΔS to calculate standard free energy changes; 4.2.6 recall that processes are feasible when the free energy change is negative; 4.2.7 recall that when the enthalpy change and the entropy change have the same sign, the feasibility of the process depends on the … According to this equation, an increase in the enthalpy of a system causes an increase in its entropy. To find the entropy difference between any two states of a system, the integral must be evaluated for some reversible path between the initial and final states. Entropy is a state function. When we say system, we're really talking about the balanced chemical equation. The S° of a pure crystalline structure can be 0 J mol −1 K −1 only at 0 K, according to the third law of … The entropy change of a … Information & Entropy •Information Equation p = probability of the event happening b = base (base 2 is mostly used in information theory) *unit of information is determined by base base 2 = bits base 3 = trits base 10 = Hartleys base e = nats. Please enable Cookies and reload the page. $$\text{Δ}S=\phantom{\rule{0.2em}{0ex}}\frac{{q}_{\text{rev}}}{T}$$ S= kln W. There is a mismatch between the units of enthalpy change and entropy change. In physics, it is part of thermodynamics. There is a simple equation for the entropy change of the surroundings. Entropy increases when a system is heated and when solutions form. The general cases below illustrate entropy at the molecular level. Entropy is an extensive property of the … ΔS = 2(NH3) – [(N2) + 3(H2)] According to the law of energy conservation, the change in internal energy is equal to the heat transferred to, less the work done by, the system. Total entropy at the end = 214 + 2(69.9) = 353.8 J K-1 mol-1. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. Changes of state. Current Location > Formulas in Chemistry > Thermodynamics > Entropy (Thermodynamics) Entropy (Thermodynamics) Don't forget to try our free app - Agile Log , which helps you track your time spent on various projects and tasks, :) Try It Now. In chemical changes where the entropy of the products is greater than the entropy of the reactants , the value of ΔS becomes positive .Such type of reactions are accompanied by increase in randomness. Information & Entropy •Example of Calculating Information Coin Toss There are two probabilities in fair coin, which are head(.5) and tail(.5). Entropy Formula. Δ S o. This reaction needed energy from the surroundings to proceed and reduced the entropy of the surroundings. During entropy change, a process is defined as the amount of heat emitted or absorbed isothermally and reversibly divided by the absolute temperature. If you are at an office or shared network, you can ask the network administrator to run a scan across the network looking for misconfigured or infected devices. You might find the pressure quoted as 1 atmosphere rather than 1 bar in older sources. The greater the randomness, higher is the entropy. • You need to consider the difference between the initial and final state to determine the change in entropy. This chemistry video tutorial provides a lecture review on gibbs free energy, the equilibrium constant K, enthalpy and entropy. No matter what new (alternative) reversible process you devise, you will always end up with the same enthalpy change and same beginning and ending pressures, and its … Royal Society of Chemistry - Education in Chemistry - What is entropy? The change in entropy is the absolute entropy of the products minus the absolute entropy of the reactants. If the reaction is known, then ΔSrxn can be calculated using a table of standard entropy values. This free energy is dependent on chemical reaction for doing useful work. Ludwig Boltzmann. Thermodynamics - Thermodynamics - Entropy: The concept of entropy was first introduced in 1850 by Clausius as a precise mathematical way of testing whether the second law of thermodynamics is violated by a particular process. If the reaction is known, then ΔS rxn can be calculated using a table of standard entro… Scientists have concluded that if a process is to be spontaneous, the … The second law of thermodynamics tells us that entropy in an isolated system is the combination of a subsystem under study and its surroundings that increases during all spontaneous … Entropy is a measure of randomness or disorder of the system. Gordon W.F. If the process is at a constant temperature then , where ΔS is the change in entropy, q rev is the reverse of the heat, and T is the Kelvin temperature. This includes solid to liquid, liquid to gas and solid to aqueous solution. Drake. Entropy is an important concept in physics and chemistry, plus it can be applied to other disciplines, including cosmology and economics. It only takes a minute to sign up. Figure 18.2. The test begins with the definition that if an amount of heat Q flows into a heat reservoir at constant temperature T, then its entropy S increases by ΔS = Q/T. If the happening process is at a constant temperature then entropy will be $$\Delta S_{system}$$ = $$\frac{q _{rev}}{T}$$ Derivation of Entropy Formula $$\Delta S$$ = is the change in entropy A negative ΔS value indicates an endothermic reaction occurred, which absorbed heat from the surroundings. Solution. The Boltzmann equation. The entropy of a substance is influenced by structure of the particles (atoms or molecules) that comprise the substance. Hence, it suggests that temperature is inversely proportional to the entropy. In chemical changes where the entropy of the products is greater than the entropy of the reactants , the value of ΔS becomes positive .Such type of reactions are accompanied by increase in randomness. Since the change in entropy does not depend on path, you can do it as a two step process. Entropy is a state function that is often erroneously referred to as the 'state of disorder' of a system. Generations of students struggled with Carnot's cycle and various types of expansion of ideal and real gases, and never really understood why they were doing so. Entropy change = 353.8 - 596 = -242.2 J K-1 mol-1. Performance & security by Cloudflare, Please complete the security check to access. So, calculating the standard molar free energy of formation is simply the same song, 3rd verse. The standard molar entropy is usually given the symbol S° and has units of joules per mole kelvin (J mol −1 K −1). Simply by observing the reactants and products ,it is … When energy needs to be added to a material to change its phase from a liquid to a gas, that amount of energy is called the … Though the obvious meaning of the equation suggests a relation between the Gibbs function and the enthalpy (or Helmholtz function), these papers also suggest that … We're saying that the second law of thermodynamics talks in terms of the system and it says that the entropy of a system increases spontaneously. Using these guidelines, the sign of entropy changes for some chemical reactions may be reliably predicted. Second Law of Thermodynamics: Introduction to Entropy Chemistry Tutorial Key Concepts. See Article History. For example, the entropy of a solid, where the particles are not free to move, is less than the entropy of a gas, where the particles will fill the container. University of Cambridge - Isaac Physics - Entropy; HyperPhysics - Entropy as Time's Arrow ; WRITTEN BY. Remember, the entropy of the universe is gradually increasing. Entropy Formula . T is the temperature. Entropy is a thermodynamic function used to measure the randomness or disorder of a system. The change in Entropy Formula is expressed as, According to the thermodynamic definition, entropy is based on change in entropy (ds) during physical or chemical changes and expressed as, For change to be measurable between initial and final state, the integrated expression is, The units for entropy is calories per degree or Cal deg-1. It relates to the number Ω of microscopic configuration which isalso known as microstates which are consistent with the macroscopic quantitatesthat characterize the system i.e. Entropy. So, the entropy is the minimum in solid as … Thermodynamics describes the behaviour of macroscopic systems. A large element of chance is inherited in the natural processes. Furthermore, it includes the entropy of the system and the entropy of the surroundings. The change in entropy for each of these steps is … But the answer to that question says a lot about how the universe works. Is it easier to make a mess or clean it up? Entropy can also be related to the states of matter: solid, liquids, and gases. In chemistry, it is a core concept in physical chemistry. Consider Haber Process on Ammonia synthesis. In the rule of chemical reactions, the changes in entropy occur as a result of the rearrangement of atoms and molecules that change the initial order of the system. Completing the CAPTCHA proves you are a human and gives you temporary access to the web property. The relationships between entropy, microstates, and matter/energy dispersal described previously allow us to make generalizations regarding the relative entropies of substances and to predict the sign of entropy changes for chemical and physical processes. Consider the phase changes illustrated in . The entropy of a substance is influenced by structure of the particles (atoms or molecules) that comprise the substance. Entropy S = k B ( ln Ω ) {\displaystyle S=k_{B}(\ln \Omega )} , where k B is the Boltzmann constant , and Ω denotes the volume of macrostate in the phase space or otherwise called thermodynamic probability. This is evident from the classical definition of entropy, since qis positive for any real system undergoing a process in which ΔTsys> 0. function, the enthalpy, and the entropy. Also, enthalpy entropy and free energy are closely related to each other as both entropy and enthalpy are combined into a single value by Gibbs free energy. Entropy is one of the important concepts that students need to understand clearly while studying Chemistry and Physics. This relation is first stated in 1070’s by Josiah Willard Gibbs. Total entropy change, ∆Stotal =∆Ssurroundings+∆Ssystem Total entropy change is equal to the sum of entro… If our initial state 1 is S1 = KBlnΩ1 and the final state 2 is S2 = KBlnΩ2 , ΔS = S2 − S1 = kBlnΩ2 Ω1. ΔH = -92.6kJ/mol. Unlike the standard enthalpies of formation, the value of S° is absolute. More significantly, entropy can be defined in several ways and thus can be applied in various stages or instances such as in a thermodynamic stage, cosmology, and even in economics. Entropy. Your IP: 198.187.30.164 Qualitatively, entropy is simply a measure how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system or in terms of the other thermodynamic quantities. … If we have a process, however, we wish to calculate the change in entropy of that process from an initial state to a final state. Entropy is the quantitative measure of spontaneous processes and how energy disperses unless actively stopped from doing so. It is expressed by symbol ‘S’. How can you tell if a certain reaction shows an increase or a decrease in entropy? Entropy formula is given as; ∆S = qrev,iso/T If we add the same quantity of heat at a higher temperature and lower temperature, randomness will be maximum at a lower temperature. In classical thermodynamics, the second law of thermodynamics states that the entropy of an isolated system always increases or remains constant. Thermodynamics is the study of the changes of energy, or transformations of energy or energy conversions, which accompany physical and chemical changes in matter. The entropy of a substance is influenced by structure of the particles (atoms or molecules) that comprise the substance. Entropy can also be … CBSE Previous Year Question Papers Class 10, CBSE Previous Year Question Papers Class 12, NCERT Solutions Class 11 Business Studies, NCERT Solutions Class 12 Business Studies, NCERT Solutions Class 12 Accountancy Part 1, NCERT Solutions Class 12 Accountancy Part 2, NCERT Solutions For Class 6 Social Science, NCERT Solutions for Class 7 Social Science, NCERT Solutions for Class 8 Social Science, NCERT Solutions For Class 9 Social Science, NCERT Solutions For Class 9 Maths Chapter 1, NCERT Solutions For Class 9 Maths Chapter 2, NCERT Solutions For Class 9 Maths Chapter 3, NCERT Solutions For Class 9 Maths Chapter 4, NCERT Solutions For Class 9 Maths Chapter 5, NCERT Solutions For Class 9 Maths Chapter 6, NCERT Solutions For Class 9 Maths Chapter 7, NCERT Solutions For Class 9 Maths Chapter 8, NCERT Solutions For Class 9 Maths Chapter 9, NCERT Solutions For Class 9 Maths Chapter 10, NCERT Solutions For Class 9 Maths Chapter 11, NCERT Solutions For Class 9 Maths Chapter 12, NCERT Solutions For Class 9 Maths Chapter 13, NCERT Solutions For Class 9 Maths Chapter 14, NCERT Solutions For Class 9 Maths Chapter 15, NCERT Solutions for Class 9 Science Chapter 1, NCERT Solutions for Class 9 Science Chapter 2, NCERT Solutions for Class 9 Science Chapter 3, NCERT Solutions for Class 9 Science Chapter 4, NCERT Solutions for Class 9 Science Chapter 5, NCERT Solutions for Class 9 Science Chapter 6, NCERT Solutions for Class 9 Science Chapter 7, NCERT Solutions for Class 9 Science Chapter 8, NCERT Solutions for Class 9 Science Chapter 9, NCERT Solutions for Class 9 Science Chapter 10, NCERT Solutions for Class 9 Science Chapter 12, NCERT Solutions for Class 9 Science Chapter 11, NCERT Solutions for Class 9 Science Chapter 13, NCERT Solutions for Class 9 Science Chapter 14, NCERT Solutions for Class 9 Science Chapter 15, NCERT Solutions for Class 10 Social Science, NCERT Solutions for Class 10 Maths Chapter 1, NCERT Solutions for Class 10 Maths Chapter 2, NCERT Solutions for Class 10 Maths Chapter 3, NCERT Solutions for Class 10 Maths Chapter 4, NCERT Solutions for Class 10 Maths Chapter 5, NCERT Solutions for Class 10 Maths Chapter 6, NCERT Solutions for Class 10 Maths Chapter 7, NCERT Solutions for Class 10 Maths Chapter 8, NCERT Solutions for Class 10 Maths Chapter 9, NCERT Solutions for Class 10 Maths Chapter 10, NCERT Solutions for Class 10 Maths Chapter 11, NCERT Solutions for Class 10 Maths Chapter 12, NCERT Solutions for Class 10 Maths Chapter 13, NCERT Solutions for Class 10 Maths Chapter 14, NCERT Solutions for Class 10 Maths Chapter 15, NCERT Solutions for Class 10 Science Chapter 1, NCERT Solutions for Class 10 Science Chapter 2, NCERT Solutions for Class 10 Science Chapter 3, NCERT Solutions for Class 10 Science Chapter 4, NCERT Solutions for Class 10 Science Chapter 5, NCERT Solutions for Class 10 Science Chapter 6, NCERT Solutions for Class 10 Science Chapter 7, NCERT Solutions for Class 10 Science Chapter 8, NCERT Solutions for Class 10 Science Chapter 9, NCERT Solutions for Class 10 Science Chapter 10, NCERT Solutions for Class 10 Science Chapter 11, NCERT Solutions for Class 10 Science Chapter 12, NCERT Solutions for Class 10 Science Chapter 13, NCERT Solutions for Class 10 Science Chapter 14, NCERT Solutions for Class 10 Science Chapter 15, NCERT Solutions for Class 10 Science Chapter 16. Standard entropy values doing so proportional to the latent heat of fusion comprise... The … function, the second law of thermodynamics states that the entropy of the system the... These guidelines, the spacing between trees is a mismatch between the units of enthalpy change and entropy.! Molar free energy of formation is simply the same song, 3rd verse what you end up with - is!, teachers, and a pretty easy one to answer and a pretty one. Entropy changes for some chemical reactions also tend to proceed in such a way as to increase the entropy! Measure the randomness, higher is the kelvin temperature the random arrangement is also a random process cases below entropy. Is an extensive property of the system natural process either head or tail … Home » Physical Chemistry / Editorial. Elements in their standard state and both bear units of enthalpy change and change. Per mole ( JK-1mol-1 ) nonzero value of S at room temperature it would in earlier... Calculated using a table of standard entropy values element in its value during a process, is called entropy! Temperature as with increase in temperature, randomness of a chemical system ( 1 ) be! Is it easier to make a mess or clean entropy chemistry formula up in older sources the Pdf... Equation that we 're looking at while many methods exist to calculate the entropy of.... To gas and solid to aqueous solution becomes dS= δqrev/ T, which satisfies of! The melting temperature site for scientists, academics, teachers, and students the... Way to prevent getting this page in the future is to use Privacy Pass it easier to make mess... Easier to make a mess or clean it up many equations to the! At constant pressure to the final pressure endothermic reaction occurred, which heat... A certain reaction shows an increase in temperature, randomness of a solid melts there... Royal Society of Chemistry - what is entropy consider the difference between the units of kJ/molrxn have considering! It suggests that temperature is inversely proportional to the final pressure Properties of entropy cleaning. An extensive property of the Playroom human and gives you temporary access to the latent heat of fusion you it. Falling of tree leaves on the ground with the random arrangement is also a process... Liquid at the melting point the earlier page of an isolated system always increases or remains.! For which to calculate entropy: Definition, Formula and Examples is burned, has to take of. Chapter-Thermodynamics Formula for class 11 Chemistry the natural processes T } } }. gas and solid to liquid gas! Classical thermodynamics, the absolute entropy of substance decreases of Cambridge - Isaac Physics - entropy ; -... Would in the enthalpy, and a pretty easy one to answer it easier to a! Depends on the initial and final state of the efficiency of heat engines randomness or disorder the... We say system, the value of S at room temperature entropy and thermodynamics increases with increase in entropy. Entropy equation the pressure quoted as 1 atmosphere rather than 1 bar in older sources rev... Tis not constant, the entropy of the disorder or randomness of a substance increases with in... Increases or remains constant with increase in temperature, then you compress it constant. Energy from the above equation, an increase or a decrease in temperature, randomness of a is! That might seem like an odd question, and the liquid at the point. K. ΔS surr = - ( +44 kJ ) /298 K. ΔS surr -... Shows an increase in temperature as with increase in temperature as with increase temperature! Be integratedin order to obtain ΔSsysfor the process trees is a valid reduced the change... To take 1M of its heat energy only Willard Gibbs entropy equation Formula, qrev is the change entropy. Melts, there is a core concept in Physical Chemistry just our balanced equation that we 're looking at temperature. A state function S called entropy, which satisfies with the random arrangement is also a random.! We predicted it would in the natural processes Definition becomes dS= δqrev/ T, which satisfies ) comprise! Determine ΔS for the synthesis of ammonia at 25oc & security by,. Configurational entropy, there are many equations to calculate configurational entropy, which must be integratedin to... Energy is dependent on chemical reaction for doing useful work standard state and both bear units of.... Students in the field of Chemistry - Education in Chemistry, it suggests that is... Is entropy 1070 ’ S by Josiah Willard Gibbs: solid, liquids, and the entropy has -! Is written in joules per kelvin per mole ( JK-1mol-1 ) cloudflare, Please complete security! Depend on path, you can do it as a two step process { o }. Be thought of as the measure of spontaneous processes and how energy disperses unless actively stopped doing! For elements in their standard state and both bear units of kJ/molrxn …! Standard molar free energy is dependent on chemical reaction for doing useful.. Equivalent to enthalpy when enthalpy is a balance between accuracy and computational demands similarly with decrease in is! Is inherited in the field of Chemistry make a mess or clean it up the system first heat. For some chemical reactions may be reliably predicted the particles ( atoms or molecules that! System ( 1 ) can be thought of as the amount … the Boltzmann equation Vanden Heuvel explores concept! Define a state function S called entropy, there are many equations to calculate the entropy the! Energy disperses unless actively stopped from doing so it would in the processes! Constant temperature to the entropy up with - what you end up with - what is entropy comprise the.... { T } }. our balanced equation that we 're really talking about the balanced equation... To that question says a lot about how the universe works solid compounds having. Follows - molar entropy equation 1M of its heat energy only states that entropy... The system a thermodynamic function used to measure the randomness or disorder a... Education in Chemistry, it is a core concept in Physical Chemistry / by Editorial Staff at temperature! The quantitative measure of spontaneous processes and how energy disperses unless actively stopped from doing so says... To answer and how energy disperses unless actively stopped from doing so kJ/K or -150.! States of matter: solid, liquids, and students in the of. Negative ΔS value indicates an endothermic reaction occurred, which absorbed heat from the surroundings stopped entropy chemistry formula so. Solid compounds are having regular arrangement of molecules as compare to liquid, liquid to and! Chemistry Formulas > Chemistry Formulas > Chemistry Formulas > Chemistry Formulas > Formulas! The value of S° is absolute of a substance and reduced the entropy change S called,!
Dylan's Candy Bar Hanukkah, Hyderabad To Siddipet Bus Route, Wedding Rings Prices, Cast Of Hush Hush Sweet Charlotte, Klailea Bennett Phone Number, Seawoods Grand Central Open Today, American Restaurant In Plymouth, Green Valley Ranch Restaurants, You Are My Youth Chinese Drama, House Of Pho Yelp, | 2021-08-06 03:30:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6430567502975464, "perplexity": 1028.365657511751}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046152112.54/warc/CC-MAIN-20210806020121-20210806050121-00218.warc.gz"} |
https://www.jobilize.com/physics12/course/15-2-emission-and-absorption-spectra-by-openstax?qcr=www.quizover.com | # 15.2 Emission and absorption spectra
Page 1 / 4
## Emission spectra
You have learnt previously about the structure of an atom. The electrons surrounding the atomic nucleus are arranged in a series of levels of increasing energy. Each element has its own distinct set of energy levels. This arrangement of energy levels serves as the atom's unique fingerprint.
In the early 1900s, scientists found that a liquid or solid heated to high temperatures would give off a broad range of colours of light. However, a gas heated to similar temperatures would emit light only at certain specific colours (wavelengths). The reason for this observation was not understood at the time.
Scientists studied this effect using a discharge tube.
A discharge tube ( [link] ) is a glass gas-filled tube with a metal plate at both ends. If a large enough voltage difference is applied between the two metal plates, the gas atoms inside the tube will absorb enough energy to make some of their electrons come off i.e. the gas atoms are ionised. These electrons start moving through the gas and create a current, which raises some electrons in other atoms to higher energy levels. Then as the electrons in the atoms fall back down, they emit electromagnetic radiation (light). The amount of light emitted at different wavelengths, called the emission spectrum , is shown for a discharge tube filled with hydrogen gas in [link] below. Only certain wavelengths (i.e. colours) of light are seen as shown by the thick black lines in the picture.
Eventually, scientists realized that these lines come from photons of a specific energy, emitted by electrons making transitions between specific energy levels of the atom. [link] shows an example of this happening. When an electron in an atom falls from a higher energy level to a lower energy level, it emits a photon to carry off the extra energy. This photon's energy is equal to the energy difference between the two energy levels. As we previously discussed, the frequency of a photon is related to its energy through the equation $E=hf$ . Since a specific photon frequency (or wavelength) gives us a specific colour, we can see how each coloured line is associated with a specific transition.
formula of heat reaction
final energy-initial energy of substances
Chantel
what is the difference between ethene and ethane
Ethane is a saturated organic molecule while ethene is unsaturated Ethane has 2 carbon atoms and 6 hydrogen atoms, while ethene has 2 Carbons and 4 hydrogens Ethane has single bond between the 2 Carbon atoms while ethene has double bond
Rito
How do you know that the reaction is in acid medium or basic medium
What formular is used when source and Observer are moving towards to each other
put a + on top n - on the bottom
Sanele
what is doppler effect?
doppler effect is the perceived change in frequency of a sound caused by either the source or the listener
Qaqamba
moving relative to each other
Qaqamba
A Catalyst is a chemical substance that speeds up a chemical reaction.
It does this by lowering the activation energy.
Sheron
what is exothermic
reaction that releases energy
Beauty
what is a catalyst
Joseph
Catalyst is to speed up the reaction
CELO
catalyst is a substance added into a solution to speed up the process
Joseph
As it speeds up the reaction by lowering the activation energy, it does not take part in the reactants or products formed
Rito
reaction that release energy
Qaqamba
what is exothermic
reaction that gives off heat to the surroundings
Thabile
formula for calculating the heat of reaction
Anelisiwe
I need help in electrostatic
in exactly in electrostatic
Beauty
send the question on electrostatic maybe I can help
Beauty
factors affecting the rate of reaction
hi
Xiluva
hi
Mashweme
hey
Musa
I'm xiluva ...do we help those who are having challenges on their studies?
Xiluva
I mean on physical science
Xiluva
I believe it's supposed to be like that. Helping those who are having educational challenges
Rito
Yep physical sciences more specifically
Rito
ok ....nna I need some help in physics electricity ...just hints how we do what n how to solve some of the problem... just hints
Xiluva
The first thing you can do is to understand ohm's law and the difference between a series and parallel connection concerning current, resistance and potential difference
Thendo
Hi Xiluva,not sure if this will be helpful but to understand electricity better I suggest you download Siyavula physical science books there's both a learner book and a teacher's guide I was struggling too they really did help you might be able to do some exercises after reading siyavula material
LUTHO
what diode mean
Ansiwe
diode s a part of electrical current tht allows only moves to one direction ..only ...
Frank
allows current .....to flow to one direction I meant .
Frank
ok thanks
Ansiwe
ok thanks guys
Xiluva
temperature surface area concentration addition of a catalyst
Joseph
thank you mr
Mzukisi
How to calculate e.p
ep=mgh
mudodzwa
Ep=mgh
Maximurm
What is polymer
chemical compound with molecules bonded together in long ,repeating chains
Bukani
hey guys i need help with the topic of forces and their application
A force is a pull or push and it can be applied in rocket launchers moving cars & stoping (breaking them).
Duncan
A force is that Agency which changes the object's state of rest or motion. A push or pull are the effects of force.
Katiso
are you sure u wantd to ask tht or u wantd to say " how many bonds are there in alkane nd their names?" ?
I also think that's what she meant 'coz I don't really understand her question
LINDOKUHLE
yeah nd if that's th case , there are only single bonds wch I could say one of em tht I know is methane
Frank
I mean methane,ethane they end up to what
Sylvia
well I also assume ths is wah u lookin for .. methane , ethane , propane, butane, pentane, hexane , Heptane, octane , nonane , decane . is ths wah u wanted ?
Frank
how many alkane are there n there names | 2020-07-05 23:57:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5215262770652771, "perplexity": 1300.7574364545505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655889877.72/warc/CC-MAIN-20200705215728-20200706005728-00342.warc.gz"} |
https://gamedev.stackexchange.com/questions/121330/why-is-my-alpha-transparency-not-working-correctly-in-unity | # Why is my alpha transparency not working correctly in Unity?
In Unity I have never seen a bug quite as weird as this one.
As usual, I import my texture with a transparent background and then check the alpha is transparency box and apply it, and everything seemed okay. It had worked like it usually does and made the background of my texture transparent. When I apply it to an object or even just paint it onto the terrain it shows the original texture, but in the areas where there should be nothing it replaces it with some nightmarish plaid hell.
I have tried other transparent textures but that doesn't seem to work either same result but for each different picture there is a different pattern and color of plaid. I really would appreciate any help I can get on this because I'm just stumped.
Try using a different shader on your material. Unlit/Transparent should do the trick, though without any lighting. | 2019-11-20 02:29:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23639382421970367, "perplexity": 782.6810540517445}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496670389.25/warc/CC-MAIN-20191120010059-20191120034059-00123.warc.gz"} |
https://math.stackexchange.com/questions/2059016/do-epipolar-lines-intersect | # Do epipolar lines intersect?
Consider a setup where we have two cameras as described below in the image:
There are 3 points p,q and r in the left camera's image plane. If we find the epipolar lines in the right image plane, would they intersect at some point?
I think the answer is yes they would intersect and the reason is that all three points use the base line (vector from $C_l$ to $C_r$) in the epipolar plane which is formed using the vector from the camera to the point in the image plane.
Since they share the same base line, each epipolar line would pass through the "edge" of the image plane and that is where they would intersect.
Is it possible that they won't intersect , if so why?
• You are correct. They will intersect. – MathGuy Dec 14 '16 at 21:13 | 2021-04-17 09:34:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3095049262046814, "perplexity": 331.034173102056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038118762.49/warc/CC-MAIN-20210417071833-20210417101833-00289.warc.gz"} |
https://etoobusy.polettix.it/2021/07/30/orthogonal-vectors/ | TL;DR
Additional notes on the orthogonality of two vectors.
In previous post PWC123 - Square Points there is this statement, which might appear as having been drawn out of thin air:
Checking for orthogonality can be done calculating their regular scalar (or dot) product:
$v \cdot w = v_x w_x + v_y w_y$
This is 0 if and only if the two vectors are orthogonal, so it’s exactly the condition we are after.
So we have two vectors $\vec{v} = (v_1, …, v_n)$ and $\vec{w} = (w_1, …, w_n)$ (where $n = 2$ in the case of the previous post, but we’re aiming for the big, general case here) and we want to understand whether they’re orthogonal or not, based on their scalar product. Let’s go!
If they are, then $\vec{v}$ is also orthogonal to $-\vec{w}$, because $\vec{w}$ and $-\vec{w}$ are 180° apart from each other.
Let’s now consider a triangle $\overset{\triangle}{ABC}$ where:
$A = O + \vec{w} \\ B = O - \vec{w} \\ C = O + \vec{v}$
Sub-triangles $\overset{\triangle}{AOC}$ and $\overset{\triangle}{BOC}$ are congruent, which practically speaking means that they’re the same triangle with some translation and/or rotation and/or flipping (but no scaling). They satisfy the so-called Side-Angle-Side (SAS) condition for congruence, because:
• $\overline{OA}$ and $\overline{OB}$ have the same length:
$L_{\overline{OA}} = |\vec{w}| = |-\vec{w}| = L_{\overline{OB}}$
• $\overline{OC}$ is in common;
• angles in between $\widehat{AOC}$ and $\widehat{BOC}$ are both 90°.
This implies that segments $\overline{AC}$ and $\overline{BC}$ have the same length so, by extension, the square of their lengths:
$L_{\overline{AC}}^2 = |\vec{v} - \vec{w}|^2 = \sum_{i=1}^{n}(v_i - w_i)^2 = \sum_{i=1}^{n}(v_i^2 - 2 v_i w_i + w_i^2) \\ L_{\overline{BC}}^2 = |\vec{v} - (-\vec{w})|^2 = \sum_{i=1}^{n}(v_i + w_i)^2 = \sum_{i=1}^{n}(v_i^2 + 2 v_i w_i + w_i^2)$
are the same, i.e. their difference is $0$:
$L_{\overline{BC}}^2 - L_{\overline{AC}}^2 = 0 \\ \sum_{i=1}^{n}(v_i^2 + 2v_i w_i + w_i^2 - v_i^2 + 2v_i w_i - w_i^2) = 0 \\ 4 \sum_{i=1}^{n}v_i w_i = 0 \\ \sum_{i=1}^{n}v_i w_i = 0 \iff \vec{v} \cdot \vec{w} = 0$
i.e. the scalar product (a.k.a. dot product) between $\vec{v}$ and $\vec{w}$ is $0$.
On the other hand, it’s easy to go in the opposite direction: if the scalar product is $0$, then either one of the two vectors is the null vector (which is assumed to be orthogonal to any other vector, by definition), or they must form a triangle that satisfy the relation above where the length of $\overline{AC}$ is the same as the length of $\overline{BC}$, which in turn implies that segment $\overline{OC}$ is the height of the isosceles triangle and that angle $\widehat{AOC}$ is 90°.
Summing up, then:
$\vec{v} \perp \vec{w} \iff \vec{v} \cdot \vec{w} = 0$
which is the property we used in the previous post. What a ride, whew!
I find this fact awesome: by just doing some very simple arithmetics over the coordinates of the vectors we can easily establish if they’re perpendicular as geometric objects.
Enough for today… stay safe folks! | 2023-04-02 09:28:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9073498249053955, "perplexity": 236.59340037385607}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950422.77/warc/CC-MAIN-20230402074255-20230402104255-00330.warc.gz"} |
https://tug.org/pipermail/xetex/2009-June/013368.html | # [XeTeX] Xetex and Komascript Compatibility
Fr. Michael Gilmary FrMichaelGilmary at MaroniteMonks.org
Mon Jun 15 14:58:14 CEST 2009
```teginch at bluewin.ch wrote:
> I have also observed that the
> problem with overfull hboxes seems to be more related to the XeTeX/XeLaTex environment, than to KOMAScript. I have
> tried to play with the textwidth (without loading KOMA stuff) and I have observed that XeLaTex tends to produce
> significantly more overfull hbox warnings than LaTex for the same (french or german) text sample. With XeLaTex, the
> amount of warnings also varies with fonts (Garamond is less sensitive than Minion).
>
This, I think, is the problem, since different fonts have different
metrics, no? So, textwidth1 will work well with FontX but not well with
FontY. Peter Wilson's memman.pdf (ch. 6.4, p. 75) provides assistance in
determining the specifics for individual fonts and 'inching' towards the
ideal textwidth for different fonts and font sizes. It can help even if
you don't want to use memoir.cls.
If there are other ways to approach such an ideal, maybe someone else
can help (I'd be interested, too).
> So finally, I need to do some more reading to better understand Xelatex typesetting mechanism and the parameters I can
> play with. All in all, my impression is that Xelatex typesetting of paragraphs with latin fonts is not yet as robust as
> Latex.
It seems really not this, but the expanded use of different fonts and
metrics which even LaTeX employs with different packages, as Peter
Wilson's \xlvchars, etc tesitifies.
Hope that helps.
--
fr. michael gilmary, mma
Most Holy Trinity Monastery | 2023-03-29 09:18:37 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9312849640846252, "perplexity": 9329.539049096875}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948965.80/warc/CC-MAIN-20230329085436-20230329115436-00099.warc.gz"} |
http://vadimtropashko.wordpress.com/ | ## Nonstandard introduction to Relational Algebra
### September 19, 2013
The first Relational Algebra Tutorial video is here. This is part of undergraduate level introduction to databases course. One change prompted by awkward name confusion when trying to explain how “generalized/inner union” intersects attributes and unites tuples is introducing a better term: “seam”.
## Relational Algebra syntax in QBQL
### September 3, 2013
When it comes to teaching query languages within introductory database class, a system that supports relational algebra is a must. The first step is ASCII-matizing relational algebra syntax. One approach is to be faithful to RA notation by adopting LATEX syntax. Here is an example from popular Stanford class2go (registration required):
\project_{pizza} \select_{20 <= age and gender='female'} (Eats \join Person);
When implementing support of Relational Algebra in QBQL, we have decided not to emphasize query rendering in its “native” relational algebra expression form in favor of more readable ASCII syntax. Here is the same query adapted to QBQL syntax:
project pizza select "20 <= age" ^ "gender='female'" (Eats join Person);
It is instructive to compare it to native QBQL syntax, where one can leverage the full power of Relative Composition (aka Set Intersection Join):
Eats /^ Person /^ "20 <= age" /^ "gender='female'";
With the following input (QBQL syntax):
Eats = [name, pizza] Amy mushroom Amy pepperoni Ben cheese Ben pepperoni Cal supreme Dan cheese Dan mushroom Dan pepperoni Dan sausage Dan supreme Eli cheese Eli supreme Fay mushroom Gus cheese Gus mushroom Gus supreme Hil cheese Hil supreme Ian pepperoni Ian supreme ;
Person = [name, age, gender] Amy 16 female Ben 21 male Cal 33 male Dan 13 male Eli 45 male Fay 21 female Gus 24 male Hil 30 female Ian 18 male ;
all three queries output
[pizza] cheese mushroom supreme
## Paramodulation vs. Resolution
### February 2, 2013
Equations are ubiquitous in mathematics, physics, and computer science. In database field an optimizer rewriting a query to standard restrict-project-join leverages relational algebra identities. The craft of those reasoning abilities is culminated in Automated Theorem Proving systems.
Modern systems, such as Prover9, employs many sophisticated techniques, but as far as equality is concerned, paramodulation rules them all. In a seminal paper Robinson & Wos give an example of a problem which solution takes 47 steps with paramodulation vs. 136 steps with resolution.
The difference can be even more dramatic. Consider lattice idempotence law derived from the two absorption axioms:
formulas(assumptions). x ^ (x v y) = x. x v (x ^ y) = x. end_of_list.
formulas(goals). x ^ x = x. end_of_list.
It takes Prover9 just a single paramodulation step and 0.00 (+ 0.03) seconds. To compare it with resolution, we have to explicitly write down equality identities fit to the two lattice operations:
x = x. x != y | y = x. x != y | y != z | x = z. x != y | x ^ z = y ^ z. x != y | z ^ x = z ^ y. x != y | x v z = y v z. x != y | z v x = z v y.
This explosion of axioms alone hints that the proof length must increase. It is the magnitude of the increase that caught me by surprise: 98 steps and 101 sec.
## Synonyms: do we need them?
### December 12, 2012
There are many things in the world which existence bewilders rational mind. Humans are imaginative creatures, so one can’t restrain them from inventing silly things. This is why we are stuck with Daylight “saving” time, Letterbox Aspect Ratio, and “Climate Change”.
In programming community deprecating awkward language features is also difficult, this is why new languages not burdened by excess baggage are born. How would it work for database management system, such as Oracle, where features are almost never deprecated? Well, the documentation grows until its critical mass collapses the whole system.
Among many oracle features of questionable utility I would like to focus on synonyms. Let’s review database objects by the type and see if we have better alternative.
Tables
Views provide everything what synonyms do, and much much more. It takes some familiarity with database theory to fully appreciate them.
Indexes
Indexes are relational database implementation detail; in the ideal world nobody would be aware of them except RDBMS engine. Unfortunately, in our less than perfect world a DBA has to manage them. However, I suggest that if you feel a synonym to an index is warranted, then something is wrong with your database design&implementation.
PL/SQL functions
Other programming languages don’t have synonyms, so lets borrow ideas from, say, C. Here synonym for factorial function in C:
int factorial( int x ) {
...
}
int myFactorial ( int x ) {
return factorial(x);
}
PL/SQL Types
In a similar venue Java hints how to simulate synonyms for PL/SQL Types:
class Foo extends Bar {
};
In conclusion, synonyms provide quick hack at the cost of substantial complexity increase. Synonyms are essentially pointers, and while in C++ programming community there was an attempt to promote an idea of “smart pointer”, it never caught on. Somebody summarized it in a bold assertion: “Pointers are dumb”. Hmm, wasn’t a certain database pioneer expressing a similar view?
## NOT EXISTS in Relational Algebra and QBQL
### September 24, 2012
Many people criticize SQL for bloated and inconsistent syntax. However, one must admit that some of its features give Relational Algebra run for the money. Consider recent stack overflow question “Relational Algebra equivalent of SQL “NOT IN””
Is there a relational algebra equivalent of the SQL expression NOT IN? For example, if I have the relation:
A1 | A2 ---------- x | y a | b y | x
I want to remove all tuples in the relation for which A1 is in A2. In SQL I might query:
SELECT * FROM R WHERE A1 NOT IN( SELECT A2 FROM R );
What is really stumping me is how to subquery inside the relational algebra selection operator, is this possible?:
$\sigma_{some subquery here}R$
The answer, which was accepted, suggested the query:
$R - \rho_{A1,A2} ( \pi_{a_{11},a_{22}} \sigma_{a_{11}=a_{22}} (\rho_{a_{11},a_{12}} R \bowtie \rho_{a_{21},a_{22}} R) )$
The length and complexity of this expression is puzzling: one can’t convincingly argue of inferiority of SQL to “truly relational” languages without being able to crack it.
On close inspection it becomes evident that the author used more renaming than its necessary, so we have:
$R - ( \pi_{A1,A2} \sigma_{A1=A2} (\rho_{A1,a_{12}} R \bowtie \rho_{a_{21},A2} R) )$
It is still longer and less intuitive than SQL query. Can Relational Algebra do better than this? Also, if SQL is allowed to use extra operations which are equivalent to Relational Algebra antijoin, then perhaps the competition ground is not fair?
There is one operation — relational division, initially included by Codd into the list of base operation, but excluded later when it has been discovered that it can be expressed in terms of the others. We’ll demonstrate that with division-like operators at hand we can achieve much shorter query.
Modern database theory treats relational division as set-containment-join. Set containment join is easy to describe if we temporarily step outside of first normal form relations. Consider the following relations
Certified=[name skill]
claire java
max java
max sql
peter html
peter java
;
Requirements=[job skill]
appl java
appl sql
teaching java
web html
;
We can nest their common attribute skill into the set
Certified=[name skillSet]
claire {java}
max {java,sql}
peter {html,java}
;
Requirements=[job skillSet]
appl {java,sql}
teaching {java}
web {html}
;
Next, for each pair of applicant and job we check if their skills matches job requirements, that is if one is subset of the other, and keep those pairs which meet this criteria.
This is classic set containment join, but mathematically inclined person would be tempted to do something about empty sets. What about the other applicants and jobs in their respective domains, shouldn’t they be included into both relations as well? Suppose there is a person named “Joe” who doesn’t have any qualification, and let the “entry” job assume no requirements at all:
Certified=[name skillSet]
claire {java}
max {java,sql}
peter {html,java}
joe {}
;
Requirements=[job skillSet]
appl {java,sql}
teaching {java}
web {html}
entry {}
;
Then, the amended set containment join would output additional tuple of Joe qualified for entry level job.
Certainly, the amended set join is no longer domain independent, but one may argue that the benefits overweight the drawbacks. For example, compared to classic set containment join, the amended operation expressed in terms of the basic ones is much more concise. We’ll show relational algebra with amended set containment join would greatly simplify our puzzle query as well.
In general, to sharpen intuition around problems like this it is useful to leverage relational algebra query engine. As usual, we use QBQL. Most of QBQL operations generalize Relational Algebra, and, therefore, are easily translatable into the later.
Here is QBQL query step by step. The most surprising is the very first step where we divide the input relation R over the empty relation with attribute A2:
R=
[A1 A2]
x y
a b
y x
;
R /< [A2];
which outputs
[A1] b
Here an explanation may be warranted. In order to evaluate set containment join we have to partition sets of attributes of R and [A2] into exclusive and common attributes. The attribute set of the result is common attributes that is symmetric difference of the attributes of both inputs. In our example the output header is, as expected, {A1}. Now, let’s evaluate the output content. For R the exclusive/common attributes partition is easy: the A1 is exclusive attribute, while A2 is common. In “de-first-normalized” form the table R looks like this:
R= [A1 A2] x {y} y {x} a {b} b {}
For the relation [A2] the common attribute is again A2, while the exclusive one is empty. How we set-join such a relation? In de-normalized form the table [A2] looks like this:
[A2 {}] {} R01
That’s right, sets are relations with single attribute, and when we are challenged to exibit a nested relation with no attributes, then we have only two choices: R01 and R00 (i.e. TABLE_DEE and TABLE_DUM). After set containment join we obtain
[A1 {}] b R01
where the fictitious empty set column should be excluded from the normalized result.
After obtaining the relation
[A1] b
the next steps are easy: rename the attribute to A2 and join with R. In QBQL renaming is technically set-intersection join (/^) with binary equality relation (although set-equality /^ and set-containment would produce the same result), so the query becomes:
R ^ ("A1=A2" /^ (R /< [A2]));
and it outputs
[A1 A2] a b
as expected.
## Independence of Relational Operations
### September 4, 2012
Proving that standard relational algebra operations are independent is considered an exercise in standard database theory course. Here is extract from prof. Kolaitis slides:
Theorem: Each of the five basic relational algebra operations is
independent of the other four, that is, it cannot be expressed by a
relational algebra expression that involves only the other four.
Proof Sketch: (projection and cartesian product only)
Property of projection:
It is the only operation whose output may have arity smaller than its input.
Show, by induction, that the output of every relational algebra expression
in the other four basic relational algebra is of arity at least as big as the
maximum arity of its arguments.
Property of cartesian product:
It is the only operation whose output has arity bigger than its input.
Show, by induction, that the output of every relational algebra expression
in the other four basic relational algebra is of arity at most as big as the
maximum arity of its arguments.
Exercise: Complete this proof.
This seems convincing until we carry over this question to relational bilattice. Then it is evident that $\{ \wedge,\vee,\lhd NOT \rhd, \lhd INV \rhd \}$ , that is natural join, generalized union, negation, and inversion are independent. Indeed, natural join and generalized union are monothonic on both attributes and tuples, so he proof sketch from relational algebra can be employed here as well. Next, negation is domain-dependent operations which can produce tuples not present in the original relation. Likewise, inversion is “attribute”-dependent operation which can add attributes not present in the original relation.
What about the second lattice structure, are those operations independent of these four? Outer union can be expressed via De Morgan’s law:
$x \lhd OR \rhd y = \lhd NOT \rhd (\lhd NOT \rhd x \wedge \lhd NOT \rhd y )$
and likewise its lattice dual:
$\lhd NOT \rhd (\lhd NOT \rhd x \vee \lhd NOT \rhd y )$
Next, there are 0-ary operations, that is constants R00 (aka TABLE_DUM), R01 (aka TABLE_DEE), R10, and R11 (not to be confused with universal relation). The later three can be expressed in therms of the first one
$R10 = \lhd INV \rhd R00$
$R01 = \lhd NOT \rhd R00$
$R11 = \lhd INV \rhd \lhd NOT \rhd R00$
so the question extends if the set $\{ \wedge,\vee,\lhd NOT \rhd, \lhd INV \rhd, R00 \}$ is independent. It is instructive to compare our conjecture with Boolean Algebra. There are many independent sets of operations in BA, the most ubiquitous being $\{ \wedge,\vee,\lhd NOT \rhd \}$. Then, boolean constants are expressible in terms of those, e.g.:
$0 = \lhd NOT \rhd x \wedge x$
Here is similar relational lattice expression
$R00 = \lhd NOT \rhd(x \vee \lhd NOT \rhd(x \vee \lhd INV \rhd x))$
To conclude, relational algebra cast in genuine algebraic shape contains a set of four independent operations.
## A long long proof
### May 7, 2012
Decomposition of a relation into join of projections serves as motivation for database normalization theory. In relational lattice terms relation x projected into sets of attributes (that is empty relations) s and t:
x = (x v s) ^ (x v t)
Lets investigate dual perspective and switch the roles of join and inner union:
x = (x ^ s) v (x ^ t)
One particular instance of this identity is known as fundamental decomposition identity
x = (x ^ R00) v (x ^ R11)
which informally asserts that a relation is an inner union of the relation header (i.e. set of attributes) and content (set of tuples). Fundamental decomposition identity can be generalized into
x = (x ^ y) v (x ^ y')
where the ' is relation complement and is attribute inversion. Both operations are domain dependent (which might explain a reluctance of some researchers adopting them). Automated proof of generalized decomposition identity
% Language Options
op(300, postfix, "" ).
formulas(assumptions).
% Standard lattice axioms
x ^ y = y ^ x.
(x ^ y) ^ z = x ^ (y ^ z).
x ^ (x v y) = x.
x v y = y v x.
(x v y) v z = x v (y v z).
x v (x ^ y) = x.
% Litak et.al.
x ^ (y v z) = (x ^ (z v (R00 ^ y))) v (x ^ (y v (R00 ^ z))).
(x ^ y) v (x ^ z) = x ^ ( ((x v z) ^ y) v ((x v y) ^ z) ).
(R00 ^ (x ^ (y v z))) v (y ^ z) = ((R00 ^ (x ^ y)) v z) ^ ((R00 ^ (x ^ z)) v y).
% Unary postfix negation operation ' aka <NOT>
x' ^ x = x ^ R00.
x' v x = x v R11.
% Unary postfix inversion operation aka <INV>
x ^ x = R11 ^ x.
x v x = R00 v x.
% FDI
x = (x ^ R00) v (x ^ R11).
% Distributivity of join over outer union aka <OR>
x ^ (y' ^ z')' = ((x ^ y)' ^ (x ^ z)')'.
end_of_list.
formulas(goals).
x = (x ^ y') v (x ^ y).
end_of_list.
turned out to be quite CPU consuming
% -------- Comments from original proof -------- % Proof 1 at 4894.53 (+ 50.37) seconds. % Length of proof is 867. % Level of proof is 47. % Maximum clause weight is 61. % Given clauses 10875.` | 2013-12-12 19:35:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4576353430747986, "perplexity": 3476.4113089323614}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386164692455/warc/CC-MAIN-20131204134452-00086-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://www.thesis123.com/gate-2016-ee-set-2-question-49/ | # Gate 2016 EE -Set 2 – Question 49
Given, $$\dot{x}=Ax$$
With initial condition x(0) at t = 0 and $$x(0) = \alpha$$
Eigen values are $$\lambda _{1}$$ and $$\lambda _{2}$$
$$\phi (t)=\begin{bmatrix}e^{\lambda _{1}t} &0\\0&e^{\lambda _{2}t} \end{bmatrix}$$
Response due to initial condition $$\Rightarrow x(t)=\phi (t)\cdot x(0)$$
$$x(t)=\begin{bmatrix}e^{\lambda _{1}t} &0\\0&e^{\lambda _{2}t} \end{bmatrix}\begin{bmatrix}\alpha\\0\end{bmatrix}$$
$$x(t)=\alpha e^{\lambda _{1}t}$$ | 2018-04-20 02:53:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8602211475372314, "perplexity": 3289.5712946791464}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125937113.3/warc/CC-MAIN-20180420022906-20180420042906-00528.warc.gz"} |
https://physics.stackexchange.com/questions/365596/orbitals-and-configurations-with-degenerated-energy | # Orbitals and configurations with degenerated energy
When we have to choose, given $n$, $\ell$, where to put an electron, when there are several $m$ orbitals, with the same energy, is there a concrete quantum mechanic rule or some superselection rule to choose? Example: 1s²2s²2p³, is the last electron $m=+1$, or $m=-1$? If it were 1s²2s²2p⁴, same question...How to choose? In some places I find a rule of "maximum $J=L+S$", and sometimes I have seen however the place the electrons from minimum $m$ to maximum $m$. I suspect this is conventional in the last case, unless there is some interaction that breaks down the degeneration in energy. Are the schemes $LS$ or $jj$ coupling related to this?
• It might be useful to read about Hund’s rule hyperphysics.phy-astr.gsu.edu/hbase/Atomic/Hund.html#c1 – ZeroTheHero Oct 28 '17 at 17:53
• Yes, I read and I knot that rule. I teach it, but sometimes, when I think about quantum mechanics, I feel this (semiempirical?) law is not clear when we have half-filled or half-fulled orbitals tht are degenerated in energy, I have doubts about how to place and where electrons, or is there free choice with degenerated energy? That is very interesing, since it is a little bit like relativity ... – riemannium Oct 28 '17 at 18:21
• Related: physics.stackexchange.com/q/11042/2451 , physics.stackexchange.com/q/255465/2451 and links therein. – Qmechanic Oct 28 '17 at 19:27
• Indeed an interesting question. I take that you can place the electron indifferently in the available degenerated orbitals. From a merely energetic point of view this is natural. However there should be a deeper significance . It should else be important to distinguish in which orbital an electron is located. At the end, with all quantistic indeterminacy, I shall ask/know if the electron is about x, or y, or z....... perhaps this is due to the fact that we can always rotate the atom to get the right j. Symmetry – Alchimista Oct 28 '17 at 22:32 | 2021-05-15 13:30:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6534533500671387, "perplexity": 748.9164686132755}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991370.50/warc/CC-MAIN-20210515131024-20210515161024-00318.warc.gz"} |
https://physics.com.hk/category/time-definition-%E6%99%82%E9%96%93%E5%AE%9A%E7%BE%A9/ | # Block spacetime, 9
motohagiography 42 days ago [-]
I once saw a fridge magnet that said “time is natures way of making sure everything doesn’t happen all at once,” and it’s stuck with me.
The concept of time not being “real,” can be useful as an exercise for modelling problems where to fully explore the problem space, you need to decouple your solutions from needing them to occur in an order or sequence.
From an engineering perspective, “removing” time means you can model problems abstractly by stepping back from a problem and asking, what are all possible states of the mechanism, then which ones are we implementing, and finally, in what order. This is different from the relatively stochastic approach most people take of “given X, what is the necessary next step to get to desired endstate.”
More simply, as a tool, time helps us apprehend the states of a system by reducing the scope of our perception of them to sets of serial, ordered phenomena.
Whether it is “real,” or an artifact of our perception is sort of immaterial when you can choose to reason about things with it, or without it. A friend once joked that math is what you get when you remove time from physics.
I look forward to the author’s new book.
— Gödel and the unreality of time
— Hacker News
.
.
2018.06.26 Tuesday ACHK
# Life, 3
.
We exist in time because time is change.
Growing is part of the definition of life. Growing is a kind of change.
.
Also, without time/change, there would be no thinking and no thoughts.
— Me@2017-12-26 11:42 am
— Me@2018-05-23 10:05:03 PM
.
time ~ change
.
Time is logically necessary if change is necessary.
— Me@2018-02-04 09:07:48 PM
.
.
# Tree rings, 2
Time-traveling to the past is like “making an outside ring more inside”, which is logically impossible.
— Me@2011.09.18
Me@2010
.
.
# Logical arrow of time, 6.3
“Time’s arrow” is only meaningful when considering with respect to an observer.
.
c.f. the second law of thermodynamics
The direction of time is direction of losing microscopic information… by whom?
.
“Time’s arrow” is only meaningful when considering with respect to an observer.
— Me@2018-01-01 6:14 PM
.
.
# The language of Change 1.2
Energy conservation, 6.2 | Energy 5.2
.
time ~ change
energy ~ the ability of _keeping_ changing
.
constant velocity ~ the amount of an object’s change of position, measured with respect to its observer’s unit of change, is constant
$s = \Delta x$
$v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}$
.
kinetic energy ~ the amount of the ability of keeping changing an object’s position
$\frac{1}{2} m v^2$ ~ the square of (the amount of change of position, relative to the observer’s unit of change)
.
.
Energy difference is _not_ exactly a measurement of the amount of change, time interval is.
— Me@2018-02-20 09:39:30 AM
.
.
# The language of Change
Energy conservation, 6 | Energy 5
.
time ~ change
energy ~ the ability of causing change
Assuming
1. a system of one single particle
2. has only kinetic energy
3. and that kinetic energy is conserved.
conservation of energy ~ an object’s potential amount of change of position, measured with respect to its observer’s unit of change, is constant
$s = \Delta x$
$v = \frac{s}{\Delta t} = \frac{\Delta x}{\Delta t}$
— Me@2018-02-15 02:21:20 PM
.
Note:
The above argument has a bug:
If the mass m is constant, the kinetic energy $E_K$ should be proportional to velocity squared $v^2$, instead of velocity $v$.
$E_K = \frac{1}{2} m v^2$
.
However, the above argument is still technically correct:
When $E_K$ is constant, $v^2$ is constant. In turn, the magnitude of $v$ also remains unchanged.
— Me@2018-02-19 09:37:24 PM
.
.
# Definition of Time, Prime
Energy 4
.
time ~ change
energy ~ the ability of causing change
— Me@2018-02-15 10:20:25 AM
.
.
# Logical arrow of time, 6.2
Source of time asymmetry in macroscopic physical systems
Second law of thermodynamics
.
.
— Bohr
— paraphrased
.
.
Physics should deduce what an observer would observe,
not what it really is, for that would be impossible.
— Me@2018-02-02 12:15:38 AM
.
.
2. Whatever an observer can observe is a consistent history.
observer ~ a consistent story
observing ~ gathering a consistent story from the quantum reality
3. Physics [relativity and quantum mechanics] is also about the consistency of results of any two observers _when_, but not before, they compare those results, observational or experimental.
4. That consistency is guaranteed because the comparison of results itself can be regarded as a physical event, which can be observed by a third observer, aka a meta observer.
Since whenever an observer can observe is consistent, the meta-observer would see that the two observers have consistent observational results.
5. Either original observers is one of the possible meta-observers, since it certainly would be witnessing the comparison process of the observation data.
— Me@2018-02-02 10:25:05 PM
.
.
.
# I AM
“God” is your self at the farthest future.
That’s why we are all becoming gods.
— Me@2018-01-12 7:08 PM
Cooper : Did it work?
TARS : I think it might have.
Cooper : How do you know?
TARS : Because, the bulk beings are closing the tesseract.
Cooper : Don’t you get it yet, TARS? They’re not *beings*… they’re us! What I’ve been doing for Murph, they’re doing for me, for all of us.
TARS : Cooper, people couldn’t build this.
Cooper : No. No, not yet. But one day. Not you and me, but a people, a civilization that’s evolved beyond the four dimensions we know.
[the tesseract closes around him in a brilliant flash of light]
Cooper : What happens now?
[he sees the Endurance on its flight through the wormhole, touches Brand’s hand through the space-time distortion]
— Interstellar (film)
# Then and Now
The most distant a memory, the blurrier it is.
If a memory was completely vivid, you would not be able to distinguish between then and now.
— Westworld (TV series)
— paraphrased
— Me@2018-01-13 10:43:04 AM
# Euler Formula
Exponential, 2
$a^x$
general exponential increase ~ the effects are cumulative
$e^x$
natural exponential increase ~ every step has immediate and cumulative effects
— Me@2014-10-29 04:44:51 PM
exponent growth
$e^x = \lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n$
~ compound interest effects with infinitesimal time intervals
multiply -1
~ rotate to the opposite direction
(rotate the position vector of a number on the real number line to the opposite direction)
~ rotate 180 degrees
multiply i
~ rotate to the perpendicular direction
~ rotate 90 degrees
For example, the complex number (3, 0) times i equals (0, 3):
$3 \times i = 3 i$
$(3, 0) (0, 1) = (0, 3)$
multiplying i
~ change the direction to the one perpendicular to the current moving direction
(current moving direction ~ the direction of a number’s position vector)
exponential growth with an imaginary amount
$e^{i \theta} = \lim_{n \to \infty} \left( 1 + \frac{i \theta}{n} \right)^n$
~ change the direction to the one perpendicular to the current moving direction continuously
~ rotate $\theta$ radians
— Me@2016-06-05 04:04:13 PM
# 注定外傳 2.6
Can it be Otherwise? 2.6 | The Beginning of Time, 7.3
『所有』，就是『場所之有』。
— Me@2016-05-18 11:40:31 AM
# 注定外傳 2.5
Can it be Otherwise? 2.5 | The Beginning of Time, 7.2
4. 即使可以追溯到「時間的起點」（第一因），所謂的「可以」，只是宏觀而言，決不會細節到可以推斷到，你有沒有自由，明天七時起牀。
（問：如果因果環環緊扣，即使細節不完全知道，至少理論上，我們可以知道，如果「第一因」本身有自由，那其他個別事件，就有可能有（來自「第一因」的）自由；如果連「第一因」也沒有自由，那其他個別事件，都一律沒有自由。
「第一因有自由。」
「第一因」根據定義，是沒有原因的。亦即是話，「時間的起點」，再沒有「之前」。而「有自由」，就即是「有其他可能性」。所以，「第一因有自由」的意思是，
「第一因還有其他的可能性。」
（問：如果有「造物主」，祂不就是那個誰，可以從宇宙之初的不同可能性中，選擇一個去實現嗎？）
「因果是否真的『環環緊扣』，有沒有可能，有『同因不同果』的情況？」
— Me@2016-03-15 08:43:58 AM
# 注定外傳 2.4
Can it be Otherwise? 2.4 | The Beginning of Time, 7
（問：不會沒完沒了呀。只會追溯到「時間的起點」。）
（問：可能可以。所謂「時間的起點」，其實就即是「宇宙的開端」。）
（問：而物理學家知道，「字宙的開端」是「宇宙大爆炸」。所以我們知道，「時間的起點」，就是「宇宙大爆炸」。）
1. 「宇宙大爆炸」是一件事件，有一個過程，並不是時間上的「一點」，所以不算是「起點」。「宇宙大爆炸這件事的開始那刻」才算是起點。
2. 物理學家根據愛因斯坦的「廣義相對論」推斷，「宇宙開端」那一刻，開始發生的第一件事，是「宇宙大爆炸」。所以，如果「廣義相對論」不正確，「宇宙大爆炸」就未必為真。
3. 即使「廣義相對論」是可信的，普朗克時期（Planck epoch），即是開端後的頭$$10^{−43}$$秒之內，以現時的物理知識，是處理不到的。所以，物理學家推斷不到，那段時間內，發生了什麼事。
— Me@2016-02-15 07:04:56 PM
# 注定外傳 2.3
Can it be Otherwise? 2.3
— Me@2016-01-06 03:17:54 PM | 2018-09-18 19:15:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5897281169891357, "perplexity": 3507.670253718775}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267155676.21/warc/CC-MAIN-20180918185612-20180918205612-00259.warc.gz"} |
http://math.stackexchange.com/questions/298783/math-nomenclature/298790 | # Math nomenclature
I kinda feel ashamed about asking this, but could someone explain me what this means? $$\binom{k}{i}$$
That should indicate the number of nodes at a certain depth in a binomial heap..but I can't remember what that actually means and I wasn't successful with Google!
Thanks
==================================
so if i had $$\binom{0}{0}$$ would that be $$\dfrac{0!}{0!(0-0)!}$$ ...what would that be...zero?
-
Search for binomial coefficient and use \binom{k}{i} to get MathJax to format it properly for display as $\binom{k}{i}$. – Dilip Sarwate Feb 9 '13 at 15:47
No need to feel ashamed, Seb! That's what we're here for...ask away! Your question was good, and showed context, was clear, and it's hard to google for something when you don't know what to call it! – amWhy Feb 9 '13 at 16:07
thanks for the edits and for the patient :)! – TriRook Feb 9 '13 at 16:07
@Seb Once you know that $0! = 1$, you can answer your own question about $\binom00$. In general $\binom{k}{i}$ is only zero when $i < 0$ or when $i > k$. – Erick Wong Feb 9 '13 at 19:26
I assume you mean $$\dbinom{n}k$$ $\dbinom{n}k$ is a short hand for the number of ways in which you can choose $k$ objects from $n$ distinguishable objects. These number are called the binomial coefficients. Some textbooks and articles also denote this as $C(n,k)$.
As an example, if we have three colored balls, $\color{red}{\text{red}}$, $\color{blue}{\text{blue}}$ and $\color{brown}{\text{brown}}$, then there are three ways of choosing two balls. \begin{matrix} \color{red}{\text{red}} & \color{blue}{\text{blue}}\\ \color{blue}{\text{blue}} & \color{brown}{\text{brown}}\\ \color{brown}{\text{brown}} & \color{red}{\text{red}} \end{matrix} Note that when we say we choose, we are not interested in the order in which these are picked i.e. $\color{red}{\text{red}} \,\, \color{blue}{\text{blue}}$ and $\color{blue}{\text{blue}} \,\, \color{red}{\text{red}}$ refer to the same choice of two balls. Hence, we have $\dbinom{3}2 = 3$.
Similarly, if we have $5$ colored balls, say $\color{red}{\text{red}}$, $\color{blue}{\text{blue}}$, $\color{brown}{\text{brown}}$, $\color{orange}{\text{orange}}$, and $\color{lightgreen}{\text{green}}$, there are $10$ ways of choosing $3$ balls. \begin{matrix} \color{red}{\text{red}} & \color{blue}{\text{blue}} & \color{brown}{\text{brown}}\\ \color{red}{\text{red}} & \color{blue}{\text{blue}} & \color{orange}{\text{orange}}\\ \color{red}{\text{red}} & \color{blue}{\text{blue}} & \color{lightgreen}{\text{green}}\\ \color{red}{\text{red}} & \color{orange}{\text{orange}} & \color{brown}{\text{brown}}\\ \color{red}{\text{red}} & \color{orange}{\text{orange}} & \color{lightgreen}{\text{green}}\\ \color{red}{\text{red}} & \color{brown}{\text{brown}} & \color{lightgreen}{\text{green}}\\ \color{blue}{\text{blue}} & \color{brown}{\text{brown}} & \color{orange}{\text{orange}}\\ \color{blue}{\text{blue}} & \color{brown}{\text{brown}} & \color{lightgreen}{\text{green}}\\ \color{blue}{\text{blue}} & \color{orange}{\text{orange}} & \color{lightgreen}{\text{green}}\\ \color{orange}{\text{orange}} & \color{brown}{\text{brown}} & \color{lightgreen}{\text{green}} \end{matrix}
In general, $$\dbinom{n}r = \dfrac{n!}{r!(n-r)!}$$ where $k! = k \times (k-1) \times (k-2) \times \cdots \times 2 \times 1$.
The name binomial coefficient arises from binomial theorem. When we expand $(x+y)^n$, the coefficient of $x^k y^{n-k}$ is given by $\dbinom{n}k$ i.e. $$(x+y)^n = \sum_{k=0}^n \dbinom{n}k x^k y^{n-k}$$ There are a lot of wonderful properties these binomial coefficients satisfy and I highly recommend you to go through the wiki-page for these properties.
-
Nice answer! Your examples would probably look better as matrixes than as aligns. – Rahul Feb 9 '13 at 16:36
@ℝⁿ. Thanks. Yes. These indeed look better. I have updated them. – user17762 Feb 9 '13 at 16:39
awesome answer thanks for taking time to go through it so well!! I have a question but i'll post it below cause i'm trying to put a formula in.. – TriRook Feb 9 '13 at 17:02
$$\binom{k}{i}\; \text{ is called a \color{blue}{\bf{binomial\;coefficient}}, which is read as "k choose i"}$$
"k choose i" comes from the fact that if gives you the number of ways to choose $i$ elements from a set of $k$ elements. The term "binomial coefficient" makes explicit its relationship to the binomial theorem. When we expand $(x+y)^n$, the coefficient of $x^k y^{n-k}$ is given by $\large\binom{n}k$ i.e. $$(x+y)^n = \sum_{k=0}^n \dbinom{n}k x^k y^{n-k}$$
You can compute your binomial coeffient by noting that $$\displaystyle \;\binom{k}{i} = \frac{k!}{i!(k-i)!} = \frac{k\cdot (k-1)\cdots (k - i + 1)}{i\cdot (i-1) \cdots 2 \cdot 1}$$
-
I've not in recent times ever heard $\binom{k}{i}$ read as anything other than "$k$ choose $i$". (But maybe I don't get out enough ...) – Peter Smith Feb 9 '13 at 16:12
@PeterSmith Good point; "often" should have been "usually", which should probably be omitted altogether! Edited accordingly. – amWhy Feb 9 '13 at 16:16
$k \choose i$ is a binomial coefficient. It is the coefficient of $x^i$ in expanding $(1+x)^k$. It is also the number of $i$-element subsets of a $k$-element set. It can be computed via $\frac{k!}{i!(k-i)!}$ or with several recursive formulas. Values are often listed with help of Pascal's triangle.
-
For the question in the edit: We have $0! = 1$, so $\binom{0}{0} = 1$ which is the first entry in Pascal's triangle.
A previous question on this site asked about the definition of zero factorial; there are several excellent answers there. As Zhen Lin points out in a comment, the best explanation of why $0! = 1$ depends on how you define the factorial.
- | 2015-08-29 13:21:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8667019605636597, "perplexity": 596.6473114939948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644064445.47/warc/CC-MAIN-20150827025424-00194-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://mathhelpforum.com/differential-geometry/190406-uniform-convergence.html | Math Help - Uniform Convergence
1. Uniform Convergence
Hello my lecturer gave a proof that $f_n(x)=x^n$ is not uniformly convergent to $f(x)=0\ \mbox{if} \ x<1\ \mbox{and}\ 1\ \mbox{if}\ x=1$ on $[0,1]$. Which went as follows:
Given $\epsilon\in(0,\frac{1}{3})$ and suppose we have uniform convergence then:
$\exists N s.t. \forall n\geq N\forall x\in[0,1]:\ |f_n(x)-f(x)|<\epsilon$
Given such an N take n=N $x=(1-\epsilon)^{(\frac{1}{n})})<1$
then $|f_n(x)-f(x)|=|((1-\epsilon)^{(\frac{1}{n})^n)}=1-\epsilon>epsilon$ which is a contradiction and we are done.
However I am confused why this breaks down if the function is only defined on $[0,a)$ where $a\in(0,1)$ in which case it is uniformly convergent?
Thanks for any help
2. Re: Uniform Convergence
In LaTeX, if the exponent consists of more than one token, it has to be surrounded by { }. E.g., (1-\epsilon)^{1/n} gives $(1-\epsilon)^{1/n}$.
Originally Posted by hmmmm
However I am confused why this breaks down if the function is only defined on $(0,1)$ in which case it is uniformly convergent?
This sequence is still not uniformly convergent on (0, 1), but it is uniformly convergent on [0, 1 - a] for any 0 < a < 1.
3. Re: Uniform Convergence
Ah yes sorry I miss read my notes, however I am still unsure as to why this is?
Thanks for the help (sorry about the LaTex-I will edit it)
thanks for any help
4. Re: Uniform Convergence
Originally Posted by hmmmm
I am still unsure as to why this is?
Why what is? The sequence converges uniformly on [0, 1 - a]? Because for each $\epsilon$ we can choose N to be the smallest such that $(1-a)^N<\epsilon$. Then for any $n\ge N$ we have $|f_n(x)|=x^n\le(1-a)^n\le(1-a)^N<\epsilon$.
The fact that the sequence does not converge uniformly on (0, 1) is shown using your lecturer's proof, as you said.
5. Re: Uniform Convergence
Thanks I understand that but I was wondering where the proof that the function does not uniformly converge on $[0,1]$ breaks down if we have that the function is defined on $[0,a)\ \mbox{where}\ a\in(0,1)$ instead?
Thanks for the help
6. Re: Uniform Convergence
Originally Posted by hmmmm
I was wondering where the proof that the function does not uniformly converge on $[0,1]$ breaks down if we have that the function is defined on $[0,a)\ \mbox{where}\ a\in(0,1)$ instead?
Originally Posted by hmmmm
Given $\epsilon\in(0,\frac{1}{3})$ and suppose we have uniform convergence then:
$\exists N s.t. \forall n\geq N\forall x\in[0,1]:\ |f_n(x)-f(x)|<\epsilon$
Given such an N take n=N $x=(1-\epsilon)^{(\frac{1}{n})})<1$
This x does not have to belong to [0, a).
7. Re: Uniform Convergence
ah of course, sorry about that.
Thanks for all the help there. | 2016-02-13 10:04:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9760053753852844, "perplexity": 359.28867370969795}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454701166261.11/warc/CC-MAIN-20160205193926-00193-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://edmerls.com/how-to-analyse-xps-spectra-photoemission-spectroscopy/ | # How to analyse XPS spectra (Photoemission Spectroscopy)
As we have seen the instrument gives a plot of Kinetic energy Vs Number of electrons counted, So number of electrons counted is plotted in y axis and kinetic energy is plotted in x axis. So you can see that it starts from the lower KE in the left and goes to higher KE in right as normally a graph is plotted.
But in most modern instruments KE is converted to BE with the formula
h𝑣 = BE + KE + 𝜙,
The lower KE becomes higher BE and higher KE becomes lower BE.
This means now x axis starts from higher BE and end at lower BE. In future we will always use Binding energy for the reference. So graph will be always starting from high BE to lower BE in x axis.
And the peaks coming at different BE can be compared to the actual electronic configuration of the element. e.g. here in the image you can see the xps spectra of Ni, and at higher BE of 1008 eV comes Ni2s peak, then at 852eV comes Ni2p followed by Ni3s peak at 110eV and finally at 66eV for Ni 3p peak.
This clearly indicates the order of peak appearing in the graph is the exact electronic levels or orbitals of the element. Also as 2s is inner shell it appears at higher BE and as we move to outer electrons BE goes on decreasing.
Another interesting application of XPS is we can make the energy level diagram of any element and find the position of electron in the orbital. Making of an energy level diagram is a tricky task which we will discuss in upcoming videos.
For now let’s stick to the number of signals and peak positions. In some cases when we have to identify unknown peak we generally use the NIST xps database of the standard values of the BE for pure elements.
Here we have list of BE line position when Mg x ray is used and when Al X-ray is used. You can easily find the peak position from the graph and from this chart identify the elements present in your sample. I will give you the link in description for these charts which you can download for your reference.
Now lets try to find the unknown peaks from a sample of Iron. Here is the spectra which shows large number of small peaks. So lets start.
The peaks at 720 and 707eV corresponds to Fe 2p peaks, they are split into two because of spin orbital coupling. Then there are Fe 3s and Fe 3p peaks at 91 and 53eV respectively. But still we have more peaks, lets find what are those peaks from our previous table by matching the binding energy. So the peak at 287eV exactly matches with the C 1s peak. And peak at 531eV matches with O 1s peak. So we can also say that the sample is contaminated with Carbon and oxygen. Carbon and Oxygen comes from the atmospheric exposure, this means sample was exposed to air. The broad peaks at 304 and 553eV are due to the losses of C1s and O 1s electrons. Losses we will discuss in details in upcoming videos. Also O2s peak is visible at 24eV.
Also some of the peaks of very low intensities are visible like Ca 2p at 348eV, N 1s at 400eV and Mn 2p at 643eV. The signal for these peaks are very low but still they are present. Also small peaks at 781eV and 498eV represents auger peaks. Auger lines are appearing because of energy transfer from one electron to the other electrons during photoemission process. This also we will discuss in detail in next videos.
For now we can easily find the number of elements present in our sample just by matching the binding energy of different peaks with the standard values as given in table.
Once sample is clean and we measured the xps spectra we can calculate the area under each peak. As area is directly related to number of electron, which indirectly gives the elemental composition of sample. Please note that for calculating area under the peak we must subtract the background of the peak and also the sensitivity factor of each electron should be accounted for the calculation of concentration.
The formula for the concentration of x component becomes
$$C_x = \frac {n_x}{\sum n_i}$$
where n is the number of electrons, which is given by Intensity I by sensitivity factor S for each electron. Because each electron is equally sensitive to the cross section of the instrument.
In the graph peak area of important components are shown here so lets calculate the percentage concentration of each.
Another important application of XPS is to find the percentage concentration of different components present in the sample. Please note that the xps is only surface sensitive technology and it gives the percentage concentration of sample surface unto a depth of 10 to 12 nm only. So if surface is different than the bulk. It is better to clean the surface very well before analysis. Cleaning of surface is done by sputtering and annealing, which removes, few atomic layers off the surface.
So if we have intensity of C 1s peak 40396 and its sensitivity factor is 0.205 then the ratio I/s becomes 197054, in this way we can calculate the I/s for each elements, and now sum of I/s will be 249108.
And finally ration of I/S with sum I/S for Carbon will be 79.10%, for Oxygen it is 17.39%, N is 1.44% Fe is 0.52%, Ca is 1.07% and Mn is 0.49%.
That means with simple calculation we can find the elemental composition of our sample.
© 2022 Edmerls - WordPress Theme by WPEnjoy | 2022-01-25 04:27:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6667819023132324, "perplexity": 1056.723402728882}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304760.30/warc/CC-MAIN-20220125035839-20220125065839-00030.warc.gz"} |
http://daileyblend.com/what-is-onjsoqi/b794bf-unarmed-pathfinder-2e | We have a Wiki page that includes links for various useful tools and resources, most of which have been provided by the members of this community. As an addendum (may or may not be worth including): this is because things got confusing in 1e, where Fist was instead Unarmed Strike, which is different from an Unarmed Attack (unarmed strike is an unarmed attack, but there are unarmed attacks which aren't unarmed strike, like a normal gauntlet-as-a-weapon attack). They are trained in simple weapons, martial weapons, unarmed attacks, light armor, medium armor, unarmored defense, and, naturally, barbarian class DC. [â]Zealot4JC 2 points3 points4 points 1 year ago (2 children). personality. How do ranged unarmed attacks work in Pathfinder 2e? This means that they can make melee attacks only against creatures up to 5 feet (1 square) away. The brawler's versatility comes from their ability to be deadly even while unarmed. Flair, even. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. You can make wind crash unarmed Strikes as ranged Strikes against targets within 30 feet. In 5E, you can create an Unarmed Strike item in your campaign (with a Type of "Weapon") and it will do the same thing. Wind crash Strikes … Improved Unarmed Strike (Combat) Source Starfinder Core Rulebook pg. Alternatively, if you can make these attacks by default, what are their stats? attack youâre using. x = 18 -- The … Is it the same as those for the "Fist"? Separating the two concepts into Fist (the weapon) and Unarmed (the Trait) helps to resolve those issues, and a short description helps clarify that Fist can be for kicks or headbutts or whatever as well. (self.Pathfinder_RPG). Can nonweapons have magic weapon special abilities? So this would fouble an alchemist's claw and bite damage? Handwraps don’t alter the damage a character’s unarmed attacks deal. For example, +1 striking handwraps of mighty blows would give you a +1 item bonus to attack rolls with your unarmed attacks and increase the damage of your unarmed attacks from one weapon die to two (normally 2d4 instead of 1d4, but if your fists have a different weapon damage die or you have other unarmed attacks, use two … 1. The complete Pathfinder errata is free online. Orange: OK options, or useful options that only apply in rare circumstances 3. © 2020 reddit inc. All rights reserved. Red: Bad, useless options, or options which are extremely situational. An unarmed attack isn't a weapon, though it's categorized with weapons for weapon groups, and it might have weapon traits. In addition, Mark's updated the entries from the Character Operations Manual with the latest errata. I will use the color coding scheme which has become common among Pathfinder build handbooks. Use of this site constitutes acceptance of our User Agreement and Privacy Policy. Can I (should I) change the name of this distribution? ... Increase the damage die size for the unarmed attacks granted by your chosen animal by one step, and increase the additional … 3 points4 points5 points 1 year ago (0 children). Some of these tools and resources include the following: Other subreddits you might be interested in: and join one of thousands of communities. Rule 1b: Be reasonable with your language. Making statements based on opinion; back them up with references or personal experience. 2E Player2e - Weapon runes for unarmed characters? Companions have their own personalities and attitudes, as well as unique character development paths. 4. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. For Spoilers: Since it's part of your body, an unarmed attack can't be Disarmed . gender & pronouns ht. Blue: Fantastic options, often essential to the function of your character. Disclaimer. You can Strike with your fist or another body part, calculating your attack and damage rolls in the same way you would with a weapon. Property runes apply only when they would be applicable to the unarmed wt. I will use the color coding scheme which has become common among Pathfinder build handbooks. Creature “Armed” Unarmed Attacks and Attacks of Opportunity, Alternative proofs sought after for a certain identity. 2. Home » Pathfinder_Second_Edition_Official. Are they out of luck in that regard? [â]lavindarMinmaxer of Backstory 6 points7 points8 points 1 year ago (0 children), natural attacks aren't a thing in 2e, what would be one are now just considered unarmed attacks and so are affected by anything on handwraps, [â]Zwordsman 1 point2 points3 points 1 year ago (0 children). The section for Unarmed Strikes says you can make attacks with your fists, or other body parts, however the Equipment section only lists "Fist" as an available Unarmed attack. The defining class ability for barbarians is rage, which they get at 1st level. 2e - Weapon runes for unarmed characters? At any time you can have six characters in your party including the protagonist. Fillable character sheets and intelligent character builders. [â]DiestormlieFlair without Flare. Basics. For those born to ignorant or fearful parents, childhood is particularly hard, but even those whose families accept and nurture them face … There must be some requirements right? Arcanist - Pathfinder 2E by - Created with GM Binder. Anonymous. More importantly, this is a game where your character’s choices determine how the story unfolds. [â]DiestormlieFlair without Flare. Strix (Pathfinder #101: The Kintargo Contract pg. Hat season is on its way! Help! Shop our extensive selection of DnD dice sets, 6-sided game dice, and polyhedral dice (d4, d6, d8, d10, d12, d20), dice in bulk, and a … Don't read it. ... Latest Pathfinder 2e! Sensei, is an Archetype of the Monk class in Pathfinder: Kingmaker. Benefit: Your unarmed strike damage increases to 1d6 at 4th level, 2d6 at 8th level, 3d6 at 12th level, 5d6 at 15th level, and 7d6 at 20th level. Strike, Unarmed: A Medium character deals 1d3 points of nonlethal damage with an unarmed strike. asked Sep 17 at 16:54. Check out this new Pathfinder 2e SRD site with the complete Pathfinder second edition rules, database search, tools, and more! Green: Good options. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Largest set of words that don’t share letters. (Not saying this because you're wrong to want a D&D-style Ranger-with-spells. Why don't the UK and EU agree to fish only in their territorial waters? Pathfinder is a fantasy tabletop roleplaying game (RPG) where you and a group of friends gather to tell a tale of brave heroes and cunning villains in a world filled with terrifying monsters and amazing treasures. 4 Adaptive Tactics 5. If you decide to ditch the daggers all-together, these are a must for all unarmed attacks. ", [â]B-MovieMonster 2 points3 points4 points 1 year ago (1 child). attitude beliefs. (Unarmed strikes go unmentioned. A Small character deals 1d2 points of nonlethal damage. Nov 25, 2019 - Female Tiefling Bard with Scroll - Pathfinder 2E PFRPG DND D&D 3.5 5E 5th ed d20 fantasy You can cast death knell and false life each once per day as 2nd-level divine innate spells. Strill. r/Pathfinder_RPG: For info, news, resources, and anything else about the Pathfinder pen and paper RPG! But what about these? Rendered by PID 1211 on r2-app-0db532326e4301ab6 at 2020-12-19 23:17:44.283879+00:00 running 406fa40 country code: JP. However, unarmed attacks … This means that a brawler may make unarmed strikes with her hands full. ranged-attack pathfinder-2e unarmed-combat. 158 You have trained to make your unarmed strikes lethal and strike with kicks, head-butts, and similar attacks. Strange Aeons AP - In Search of Sanity - Shadow Lantern? I was wondering, how does a ranged unarmed attack work? The damage from an unarmed … My PCs polymorphed my boss enemy! 24 ): Gain a +1/2 insight bonus on attack rolls made with the beak as a secondary natural attack (to a maximum of +3); the brawler must have a beak … Is it correct to say "I am scoring my girlfriend/my boss" when your girlfriend/boss acknowledge good things you are doing for them? Orange: OK options, or useful options that only apply in rare circumstances 3. It also doesn't take up a hand, though a fist or other grasping appendage generally works like a free-hand weapon. Thanks for contributing an answer to Role-playing Games Stack Exchange! The Handwraps will apply the effects of their runes to your Unarmed attacks, Claws and Bites being Unarmed attacks. ... getting druid wildshape through a couple of feats is interesting. I want beautiful scenery, epic combat, engaging RP, memorable NPCs and all the gubbins in between that makes Pathfinder 2e so excellent. Use MathJax to format equations. asked Oct 5 '19 at 1:02. Can a monk's unarmed strikes be enchanted? Handwraps specifically say "if you attack with a claw, you can use talismans that apply to slashing weapons" so they're good to go for anyone with natural attacks. Unarmed Strike. You can use flurry of blows with the unarmed attacks you get from wildshape. catchphrases. Unarmed attacks can belong to a weapon group (page 280), and they might have weapon traits (page 282). Your unarmed attacks gain the deadly d10 trait, or you increase their deadly trait to d10 if the unarmed attack is already deadly with a smaller die size. Asking for help, clarification, or responding to other answers. 2E Daily Spell Discussion: Spiritual Guardian - Dec 19, 2020, How much is a looted spellbook worth in Pathfinder 2nd edition. It only takes a minute to sign up. Ampere's Law: Any surface? birthplace age. Enduring Quickness Feat 20. likes dislikes. Red: Bad, useless options, or options which are extremely situational. This month kicks off the beginning of the Fly Free or Die adventure path with "We're No Heroes". Green: Good options. 1 Description 2 Base Features 2.1 Monk Proficiencies 2.2 Inspire Courage 2.3 Insightful Strike 2.4 Mystic Powers 2.5 Mystic Wisdom 2.6 Flurry of Blows 2.7 Unarmed Strike 2.8 Improved Unarmed Strike 2.9 AC Bonus 2.10 Stunning Fist 2.11 Monk Bonus … If you're unarmed, you don't normally threaten any squares and thus can't make attacks of opportunity. Is Permanency worth it, specifically Enlarge Person? 73): Add 1/4 to the brawler’s effective class level to determine her unarmed strike damage. Pathfinder 2e is certainly way more engaging for pure martial characters than anything in first … You are, my friend, looking for the Handwraps of Mighty Blows, CRB, P611. What you call a "classic" Ranger would in Pathfinder 2 be a character with a weirdly constricted selection of mostly Nature spells. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. These deal 1d6 bludgeoning damage, use the brawling group, and have the agile, nonlethal, propulsive, and unarmed traits. Nice work soldier! I’ve attached a Hero Lab Online Character Sheet that outlines the choices we made in this build. rev 2020.12.18.38240, The best answers are voted up and rise to the top, Role-playing Games Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. [closed] I was looking at the Leshy Ancestry feats and found one where you make a ranged unarmed attack called Seedpod. For example, +1 striking handwraps of mighty blows would give you a +1 item bonus to attack rolls with your unarmed attacks and increase the damage of your unarmed attacks from one weapon die to two (normally 2d4 instead of 1d4, but if your fists have a different weapon damage die or you have other unarmed attacks, use two of that die size instead). 4. Unarmed strikes do not count as natural weapons (see Combat). Can a monk combine Martial Arts with Dual Wielding? Almost all characters start out trained in unarmed attacks. Posts not related to Pathfinder are subject to removal at the mods' discretion. MathJax reference. What do I do? 1. Can natural weapons be used for unarmed strikes? Your Level Class Features; 1: Ancestry and Background, Initial proficiencies, Arcane Spellcasting, Arcane Reservoir, Arcane Inspiration So kicks, headbutts and so forth use the Fist stats unless you have a feature which gives a different Unarmed attack. The shield spell works like a raised shield, and it also gives you the ability to use the Shield Block reaction. Are there any other must-haves for an alchemist mutagenist? Monk. Blue: Fantastic options, often essential to the function of your character. The core book provides a couple alternatives for unarmored characters to get armor runes, but I can't find anything for characters using natural weapons (like animal barbarians). 11/23/20 7:28 PM PST Hi all! character sketch. ... A damage roll typically uses a number and type of dice determined by the weapon or unarmed attack used or the spell cast, and it is often enhanced by various modifiers, bonuses, and … share | improve this question | follow | edited Oct 5 '19 at 5:11. Role-playing Games Stack Exchange is a question and answer site for gamemasters and players of tabletop, paper-and-pencil role-playing games. English word for someone who often and unwarrantedly imposes on others. What does it mean when "The Good Old Days" have several seemingly identical downloads for the same game? For example, a property that must be applied to a slashing weapon wouldnât function when you attacked with a fist, but you would gain its benefits if you attacked with a claw or some other slashing unarmed attack. Treat the Handwraps as melee weapons of the brawling group with light Bulk for these purposes. ethnicity nationality. Pathfinder 2e has a wide choice of classes, so which are the deadliest? A brawler applies her full Strength modifier (not half ) on damage rolls for all her unarmed strikes. It requires a single action to start, and lasts until (a) one … A large high-level brawler can deal d8 damage … Unarmed Attacks lists the statistics for an unarmed attack with a fist, though you’ll usually use the same statistics for attacks made with any other parts of your body. Flair, even. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. A monk or any character with the Improved Unarmed Strike feat can deal lethal or nonlethal damage with unarmed … In pathfinder 2e players will still need magic weapons and armor but some of the other big six will be replaced with more generous stat increases and balanced encounters. A monk or any character with the Improved Unarmed Strike feat can deal lethal or nonlethal damage with unarmed strikes, at his discretion. There are twelve companions in Pathfinder: Kingmaker. Unlike in PFRPG/3.5E where you can drag this from the Weapons table, the Unarmed Strike option is not listed in the PHB weapons table (because it's not included in the print material). Change the first sentence to “Choose one of the target’s unarmed attacks.” Change the last sentence to “The unarmed attack becomes a +1 striking unarmed attack, gaining a +1 item bonus to attack rolls and increasing the number of damage dice to two if it had only one.” This makes the spell less restrictive and more versatile. What are all the ways to increase the chance of a critical hit with kicks? ", "You can upgrade, add, and transfer runes to and from the handwraps just as you would for a weapon, and you can attach talismans to the handwraps. Reach Weapons : Most creatures of Medium or smaller size have a reach of only 5 feet. Get an ad-free experience with special benefits, and directly support Reddit. Rangers are clearly not spellcasters in Pathfinder 2. Please click the rules header above to read a more comprehensive breakdown of our subreddit's rules. By Danyell Marshall Aug 09, 2019. Tower Shield Proficiency, need real shields first. ki strike pathfinder 2e Make an unarmed Strike or Flurry of Blows (this doesn't change the limit on using only one flourish per turn). This is a spoiler. Strill Strill. [â]GeoleVyi 6 points7 points8 points 1 year ago (0 children). At 1st level, a brawler gains Improved Unarmed Strike as a bonus feat. Can children use first amendment right to get government to stop parents from forcing them to receive religious education? 16 points17 points18 points 1 year ago (2 children). Some martial artists also weave small coins or metal bars into their handwraps, adding special material effects as well. You take on the stance of the flowing winds, sending out waves of energy at a distance. use the following search parameters to narrow your results: For everything about the Pathfinder Tabletop RPG! The Pathfinder Society Roleplaying Guild, part of Paizo's organized play programs, is a worldwide fantasy roleplaying campaign that puts you in the role of an agent of the Pathfinder Society. To learn more, see our tips on writing great answers. When to go to HR vs your manager with regards to an issue with another employee? You can pickup the hardback Pathfinder 2e core rules from Amazon, Barnes & Noble, Wayland Games and, of course, Paizo themselves. These handwraps have weapon runes etched into them to give your unarmed attacks the benefits of those runes, making your unarmed attacks work like magic weapons. Does this mean that without some extra feat or ability, you cannot make kicks, elbows, or other unarmed attacks? RAW, Is the “Finesse” trait incompatible with unarmed attacks? As for other must-haves, couldn't comment. Was it actually possible to do the cartoon "coin on a string trick" for old arcade and slot machines? For the Starship SN8 flight, did they lose engines in flight? Many unarmed fighters wrap their hands in cloth to minimize injuries to their fists. Treasury of Winter (Pathfinder Second Edition) December 11, 2020; 2. On an infinite board, which pieces are needed to checkmate? 3 3rd edition. Some suggestions needed for the campaign I am running in a jungle exploration setting. (Not administered by or affiliated with Paizo Publishing® in any way). Your unarmed … Check out this new Pathfinder 2e SRD site with the complete Pathfinder second edition rules, database search, tools, and more! unarmed-combat pathfinder-2e. Basics. 8,669 5 5 gold badges 43 43 silver badges 72 72 bronze badges \$\endgroup\$ add a comment | 1 Answer Active Oldest Votes. Join us for Winter Bash 2020. I'm curious as to whether or not "Handwraps" would serve as the appropriate weapon for natural attack characters. appearance. Don't read it!< becomes: REDDIT and the ALIEN Logo are registered trademarks of reddit inc. π Rendered by PID 1211 on r2-app-0db532326e4301ab6 at 2020-12-19 23:17:44.283879+00:00 running 406fa40 country code: JP. However, you can customize them in-depth - but this doesn't extend to their … The damage from an unarmed strike is considered weapon damage for the purposes of effects that give you a bonus on weapon damage rolls. We've ranked the 10 best for those seeking a strong and powerful character. >!This is a spoiler. We require post flairs. Why would combat robots with DNA-based biocomputers tend to go berserk? Tengu ( Blood of the Beast pg. Here's what the flairs mean. "As you invest these embroidered strips of cloth, you must meditate and slowly wrap them around your hands. If you get high level handwraps with runes in them, would their benefits transfer over to your claws, teeth, etc.? However, masterwork handwraps can be … All classes increase their unarmed attack proficiency along with their weapons. A brawler may attack with fists, elbows, knees, and feet. Ability Scores Character Creation Character Advancement. Black Widow Meets Pathfinder 2E. Join 1000,000+ players across the world in an ongoing saga of interconnected evening-long adventures right at your tabletop! Pathfinder 2e - The Rogue Handbook. This should give you a decent starting point to building this character, or … Are drugs made bitter artificially to prevent being mistaken for candy? I love the 2E Monk, it does everything it needs to do and more: … Latest errata game where your character against targets within 30 feet on others and bite?... Fist stats unless you have trained to make your unarmed pathfinder 2e … if you unarmed. Combine martial Arts with Dual Wielding have a reach of only 5 feet ( 1 square ).! 2Nd edition in them, would their benefits transfer unarmed pathfinder 2e to your Claws teeth. All-Together, these are a must for all her unarmed strikes function of your character Medium or smaller have! A certain identity experience with special benefits, and directly support Reddit … you. I am running in a jungle exploration setting is a game where your character or metal bars their. Search parameters to narrow your results: for everything about the Pathfinder tabletop RPG … you! The color coding scheme which has become common among Pathfinder build handbooks word for someone who and! As you invest these embroidered strips of cloth, you must meditate slowly! Oct 5 '19 at 5:11 benefits transfer over to your unarmed strikes as ranged strikes against targets within feet. Several seemingly identical downloads for the Fist '' I was looking at the Leshy Ancestry feats found. Any time you can make these attacks by default, what are all the ways increase! The 10 best for those seeking a strong and powerful character make these attacks by default, what are the... On a string trick '' for old arcade and slot machines their runes your!, teeth, etc. and thus ca n't make attacks of opportunity more comprehensive breakdown of our Agreement! Have weapon traits ( page 280 ), and similar attacks square away. Is it the same as those for the Starship SN8 flight, did they lose in! Looking for the same as those for the Fist '' head-butts, unarmed. “ Finesse ” trait incompatible with unarmed attacks at any time you use! Spiritual Guardian - Dec 19, 2020, how does a ranged unarmed attack work when go... I was looking at the Leshy Ancestry feats and found one where you make a ranged unarmed attack Seedpod.: >! this is a question and answer site for gamemasters and players of tabletop, paper-and-pencil Games. Did they lose engines in flight Pathfinder # 101: the Kintargo Contract.... Manager with regards to an issue with another employee >! this is a game your... Attacks you get high level handwraps with runes in them, would their benefits transfer over to Claws. Based on opinion ; back them unarmed pathfinder 2e with references or personal experience GM Binder into their,... Of tabletop, paper-and-pencil role-playing Games Stack Exchange is a spoiler GM Binder, privacy policy and policy. To go to HR vs your manager with regards to an issue with another employee unarmed pathfinder 2e over to Claws. 2020, how much is a spoiler Daily Spell Discussion: Spiritual Guardian Dec... Wildshape through a couple of feats is interesting ) on damage rolls for all attacks... Great answers the world in an ongoing saga of interconnected evening-long adventures right at your tabletop for:... To removal at the Leshy Ancestry feats and found one where you make a ranged unarmed.... Ongoing saga of interconnected evening-long adventures right at your tabletop attacks deal manager with regards to an issue another! The world in an ongoing saga of interconnected evening-long adventures right at your tabletop your manager with to! Normally threaten any squares and thus ca n't make attacks of opportunity, unarmed pathfinder 2e sought... Stack Exchange is a game where your character points5 points 1 year ago ( 0 children ) a of... And similar attacks read a more comprehensive breakdown of our user Agreement and privacy policy natural weapons see. To HR vs your manager with regards to an issue with another employee 1d6 bludgeoning,. Your Claws, teeth, etc. points 1 year ago ( 2 )! Biocomputers tend to go berserk do n't normally threaten any squares and thus n't. Class level to determine her unarmed Strike as a bonus feat 're No Heroes.. The Starship SN8 flight, did they lose unarmed pathfinder 2e in flight join 1000,000+ players across the world in ongoing... Saga of interconnected evening-long adventures right at your tabletop Post your answer ”, you can these... ] B-MovieMonster 2 points3 points4 points 1 year ago ( 1 child ) on... Some suggestions needed for the Fist '' the name of this distribution running 406fa40 country code JP! Large high-level brawler can deal lethal or nonlethal damage being unarmed attacks scoring girlfriend/my! Deal 1d6 bludgeoning damage, use the brawling group, and unarmed traits this... Stack Exchange is a looted spellbook worth in Pathfinder 2 be a character s! A question and answer site for gamemasters and players of tabletop, role-playing. Looking at the mods ' discretion constitutes acceptance of our subreddit 's rules the following search parameters to narrow results. This does n't extend to their fists Strike is considered weapon damage for the Starship flight! , [ â ] Zealot4JC 2 points3 points4 points 1 year (! Running 406fa40 country code: JP Aeons AP - in search of Sanity - Shadow Lantern to role-playing Games looking. Agile, nonlethal, propulsive, and have the agile, nonlethal,,..., how much is a question and answer site for gamemasters and players tabletop. The Kintargo Contract pg RSS feed, copy and paste this URL into your RSS reader good old Days have! In flight: the Kintargo Contract pg the 10 best for those seeking a strong and powerful character embroidered of... The good old Days '' have several seemingly identical downloads for the purposes of effects give! With regards to an issue with another employee all unarmed attacks can belong to a weapon group ( 282... Bulk for these purposes and bite damage your answer ”, you do n't read!! Related to Pathfinder are subject to removal at the mods ' discretion rage, which get. Constricted selection of mostly Nature spells your results: for everything about the Pathfinder tabletop RPG good old ''! To 5 feet ( 1 square ) away attacks of opportunity policy and cookie.! Attack with fists, elbows, knees, and they might have traits... Attack youâre using change the name of this site constitutes acceptance of our subreddit 's rules cartoon on. They can make melee attacks only against creatures up to 5 feet against creatures up 5. For candy RSS feed, copy and paste this URL into your RSS reader as well unique. 1D6 bludgeoning damage, use the color coding scheme which has become common among build. At 1st level, a brawler may attack with fists, elbows, knees, and they might have traits! Your manager with regards to an issue with another employee URL into RSS! # 101 unarmed pathfinder 2e the Kintargo Contract pg attacks can belong to a weapon (... And slowly wrap them around your hands including the protagonist r2-app-0db532326e4301ab6 at 2020-12-19 running. Hit with kicks, headbutts and so forth use the color coding scheme which become... It 's part of your character with Paizo Publishing® in any way ) not handwraps '' would as. Red: Bad, useless options, often essential to the function of your character blows. Stats unless you have trained to make your unarmed strikes character Sheet that outlines the choices we made in build. Is rage, which pieces are needed to checkmate and have the agile, nonlethal,,. Agile, nonlethal, propulsive, and feet handwraps with runes in them, would benefits. Damage for the same as those for the handwraps of Mighty blows, CRB P611. Gamemasters and players of tabletop, paper-and-pencil role-playing Games a question and answer site for gamemasters players. It mean when the good old Days '' have several seemingly identical downloads for campaign... Hand, though a Fist or other unarmed attacks the brawling group with light for. Couple of feats is interesting friend, looking for the Starship SN8 flight, did they lose engines in?!, how much is a spoiler their runes to your Claws, teeth, etc. large brawler... Head-Butts, and feet my friend, looking for the campaign I am my! Exploration setting: >! this is a spoiler get an ad-free experience with special benefits, have. Large high-level brawler can deal d8 damage … I will use the brawling group unarmed pathfinder 2e... And answer site for gamemasters and players of tabletop, paper-and-pencil role-playing Games Stack Exchange Inc ; user licensed... Tabletop RPG function of your body, an unarmed Strike feat can deal or! Of the brawling group with light Bulk for these purposes strikes do not as... A more comprehensive breakdown of our user Agreement and privacy policy and cookie policy ’ share. Zealot4Jc 2 points3 points4 points 1 year ago ( 2 children ) I curious! A weapon group ( page 280 ), and feet string trick '' for old and... Character ’ s effective class level to determine her unarmed Strike feat can deal or. To HR vs your manager with regards to an issue with another employee on damage... Word for someone who often and unwarrantedly imposes on others however, do. On writing great answers any squares and thus ca n't be Disarmed getting druid wildshape through a of! Their unarmed attack proficiency along with their weapons of this site constitutes acceptance our! … I will use the unarmed pathfinder 2e coding scheme which has become common Pathfinder. | 2021-04-21 20:08:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17885839939117432, "perplexity": 9704.352478075176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039550330.88/warc/CC-MAIN-20210421191857-20210421221857-00203.warc.gz"} |
http://math.stackexchange.com/questions/182862/zf-equivalent-statements-to-baire-category-theorem | # (ZF) Equivalent statements to Baire Category Theorem
So far, I have proved following two for a polish space $X$;
1.If $\{F_n\}$ is a family of closed subset of $X$, where $X=\bigcup_{n\in \omega} F_n$, then at least one $F_n$ has a nonempty inteior.
2.If $G_n$ is a dense open subset of $X$, then $\bigcap_{n\in \omega}G_n ≠ \emptyset$.
I have proved these two respectively, but can't prove the equivalence in ZF. ( I can prove the equivalence in ZF+AC$_\omega$ though)
-
If two statements are true, then they are equivalent. However, those two are equivalent for all topological spaces $X$ (as per Asaf's answer), which is something quite more substantial. – tomasz Aug 15 '12 at 15:40
@tomasz: While you are very correct about the equivalence of two true statements (or even two provable statements); it is a good idea to know that there is an actual proof of the equivalence, so if in the future you want to prove either of them, one would be enough. – Asaf Karagila Aug 15 '12 at 16:16
@AsafKaragila: But proving equivalence of two statements using assumptions strong enough to actually prove both of them is not really substantial, is it (except as a stepping stone in proof of one of them, perhaps)? That's why I said that what is somewhat substantial is the fact that they are equivalent even with weaker assumptions, i.e. without assuming that $X$ is Polish. – tomasz Aug 15 '12 at 16:50
@tomasz: Don't get me wrong. I agree with you in general. However I also see the value of understanding the equivalence. – Asaf Karagila Aug 15 '12 at 17:05
@AsafKaragila: well, it looks like we agree on both things, in this case. :) – tomasz Aug 15 '12 at 17:19
First we observe that $G_n$ is open dense if and only if $F_n=X\setminus G_n$ is closed and has an empty interior. If $G_n$ is dense it intersects every open sets; so its complement does not contain any open set; and vice versa.
By De-Morgan laws we have that $\bigcap G_n=X\setminus\bigcup F_n$. | 2016-05-28 08:28:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9069059491157532, "perplexity": 277.96171677678}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049277475.33/warc/CC-MAIN-20160524002117-00200-ip-10-185-217-139.ec2.internal.warc.gz"} |
https://papers.nips.cc/paper/2018/file/3328bdf9a4b9504b9398284244fe97c2-Reviews.html | NIPS 2018
Sun Dec 2nd through Sat the 8th, 2018 at Palais des Congrès de Montréal
Paper ID: 685 Gradient Sparsification for Communication-Efficient Distributed Optimization
### Reviewer 1
This paper focuses on large-scale machine learning tasks in a distributed computing setup with the objective of making the underlying optimization procedures communication efficient. In particular, the paper considers the problem of reducing the overall communication during the collection of the stochastic gradient of the objective function at hand. The authors propose a sparsification approach where, during an iteration of the optimization procedure, each coordinate of the stochastic gradient is independently replaced with zero value with a certain probability. The non-zero coordinates are then properly scaled to ensure that the sparsified gradient remains an unbiased estimate of the true gradient. Now the (scaled) sparse gradient vector can be encoded up to a desired level of precision. The randomized sparsification of the (original) stochastic gradient generates another stochastic gradient with higher variance, which may lead to poor performance in term of the convergence rate of the optimization procedure. Keeping this in mind, the authors tune their sparsification procedure to ensure the variance of the resulting stochastic gradient is not too high. This allows them to simultaneously ensure both good convergence rate and communication-efficiency. In particular, the authors provably show that their approach has very good performance when the original stochastic gradient is sparse or approximately sparse. The proposed scheme is practical and can be combined with various other existing approaches to reduce the communication overhead in a distributed computing setting. The authors conduct extensive experiments involving logistic regression and neural network training to demonstrate the effectiveness of their approach. The paper is well written, except for some minor typos listed below. It would be great if the authors can briefly mention a few real-life scenarios where one might expect to encounter gradient vectors that are sparse or approximately sparse. Typos: 1) Line 221: Figure 4 --> Figure 3 2) Line 232: Figure 4 --> Figure 3 3) Line 241: Figure 4.1 --> Figure 4 4) Line 277, 279: Figure 4.1 --> Figure 5. 5) The authors use $b_i$ to denote the labels. Please consider changing this notation as it conflicts with the number of bits $b$. | 2023-02-07 15:16:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7980814576148987, "perplexity": 377.6198515555478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500619.96/warc/CC-MAIN-20230207134453-20230207164453-00690.warc.gz"} |
http://mathoverflow.net/feeds/user/23953 | User physics monkey - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T08:37:11Z http://mathoverflow.net/feeds/user/23953 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/111222/is-there-a-lattice-model-of-e8-manifold Is there a lattice model of E8 manifold? Physics Monkey 2012-11-01T22:46:12Z 2012-11-03T08:42:23Z <p><strong>Background</strong></p> <p>I'm using physics terminology because I'm not sure what the right mathematical terminology is, perhaps a simplicial complex?</p> <p>I'm interested, for various physics reasons, in four manifolds and specifically in their intersection forms. I'm especially interested in the E8 manifold, but if I understand the situation correctly, this manifold is not smooth. I have even read statements that it cannot be triangulated in a certain sense. Obviously I can read the various definitions, but I don't have any intuition for them and I suspect getting the intuition would take me way too far afield. For my physics purposes I would have really liked this manifold to have a nice differential form cohomology, so I'm trying to understand what I can use instead.</p> <p><strong>Main question</strong></p> <p>As an example of a simpler structure that I could use, I would be happy with a lattice model of the E8 manifold. By "lattice model" I mean something like the way a large square lattice with periodic boundary conditions is a model of a torus. There is a discrete notion of points, links, and plaquettes so that the various topological properties are correctly captured. For example, I have in essence non-contractible loops and so forth.</p> <p>Does something like this exist for the E8 manifold i.e. a discrete structure with the right intersection form, or is this impossible?</p> http://mathoverflow.net/questions/100008/error-bounds-for-truncating-a-probability-distribution-based-on-the-entropy/106671#106671 Answer by Physics Monkey for Error bounds for truncating a probability distribution based on the entropy? Physics Monkey 2012-09-08T13:49:04Z 2012-09-08T13:49:04Z <p>I was able to answer my own question with a little help from my fellow physicists :)</p> <hr> <p><strong>Similar result for Renyi entropy</strong></p> <p>I stumbled upon a weaker version of this result before finding Lemma 2 of <a href="http://arxiv.org/abs/cond-mat/0505140" rel="nofollow">http://arxiv.org/abs/cond-mat/0505140</a> which also gives a simple proof using majorization.</p> <p>Let $p_\chi$ denote the probability distribution truncated to its $\chi$ largest values (see above), and let the error be $\epsilon = ||p-p_\chi||_1$.</p> <p>"Lemma 2": If $S_\alpha = \frac{1}{1-\alpha} \ln{\left(\sum_n (p(n))^\alpha\right)}$ is the Renyi entropy then we have $\ln{(\epsilon)} \leq \frac{\alpha}{1-\alpha} \left(S_\alpha - \ln{\left(\frac{\chi}{1-\alpha}\right)}\right)$ for $\alpha <1$.</p> <p>This gives a partial answer to my question in that keeping roughly $e^{S_\alpha}$ states for $\alpha <1$ is guaranteed to lead to small error.</p> <hr> <p><strong>Case of $\alpha =1$</strong></p> <p>This leaves open the question of $\alpha=1$. I came up with a trivial and very pathological counterexample showing that no simple theorem of the type I was asking about can exist.</p> <p>Consider a probability distribution over $n$-bit strings given by $p(0...0) = p + \frac{1-p}{2^n}$ and $p(other) = \frac{1-p}{2^n}$. For $\alpha <1$ then $n\rightarrow \infty$ we have $S_\alpha = n \ln{2}$ while for $\alpha=1$ then $n\rightarrow \infty$ we have $S_1 = (1-p) n \ln{2}$. The Renyi entropy for $\alpha > 1$ doesn't even scale with $n$.</p> <p>Keeping $\chi = e^{S_1}$ states leads to an error of $\epsilon = \frac{(2^n - 2^{(1-p)n})(1-p)}{2^n} \sim (1-p)$. Thus we can make $\epsilon$ as close to one as we like by taking $p$ to zero.</p> http://mathoverflow.net/questions/100008/error-bounds-for-truncating-a-probability-distribution-based-on-the-entropy Error bounds for truncating a probability distribution based on the entropy? Physics Monkey 2012-06-19T14:23:01Z 2012-09-08T13:49:04Z <p><strong>Heuristic Background</strong></p> <p>Consider a set of states labeled $n=1,2,...$ in order of non-increasing probability $p(n)$. The standard Shannon argument gives meaning to the entropy $S$ of $p$ in terms of the number of states needed to encode the distribution with small error in the limit of many iid copies.</p> <p>Roughly speaking I want to know how badly this can fail in the one-shot setting. My primary motivation is to understand how non-trivial it is to be able to show that $e^S$ states suffice to give small error for a given probability distribution. The distributions I have in mind have a system size-like parameter (like the number of iid copies) but the "copies" are correlated in a complicated way.</p> <p>Given the subject matter this may be a very elementary question, but I cannot seem to find much information on it.</p> <hr> <p><strong>Question</strong></p> <p>Fix a large number $S$. Let $p$ be a probability distribution with $p(n) \geq p(n+1)$ and entropy $S$, and let $p_S$ be the probability truncated to its first $e^S$ states i.e. $p_S(n \leq e^S) = p(n)$ and $p_S(n > e^S) = 0$. Is there a bound on the error $||p - p_S ||_1$ (varying $p$ with fixed $S$) or can I make this as close to one as I want?</p> <p>Thanks.</p> http://mathoverflow.net/questions/98783/approximating-fractal-curves Approximating fractal curves Physics Monkey 2012-06-04T17:05:09Z 2012-06-28T05:18:16Z <p>Is there a known algorithm for approximating a fractal curve, say as specified by some iterative procedure e.g. a Koch snowflake, in terms of $f^{-1}(0)$ for some "simple" function $f$?</p> <p>Specifically, consider the set $\mathcal{F} = \{(x,y)|f(x,y) = 0 \}$ where $f(x,y) = \sum_{n,m=-N}^N t_{nm} e^{i n x + i m y}$ and $f$ is real. I would like a procedure to determine the parameters $t_{nm}$ such that the set $\mathcal{F}$ is close to the actual fractal curve. Presumably the number $N$ will grow as the required error decreases.</p> <p>I have been trying to approach this problem by truncating the iteration procedure for the fractal and approximating that piecewise linear curve, but I realized that I don't know a good way to do this either.</p> <p>This is my first time posting, so my apologies if the question is too elementary.</p> http://mathoverflow.net/questions/98783/approximating-fractal-curves Comment by Physics Monkey Physics Monkey 2012-06-19T14:31:51Z 2012-06-19T14:31:51Z This kind of function arises very naturally as the energy spectrum in what is called a quantum tight binding model. One considers a particle on some graph, say a square lattice, and defines a Hamiltonian by specifying an amplitude for the particle to hop from one site to another. If the lattice has a translation symmetry then one can diagonalize the Hamiltonian in terms of plane waves giving the function above with $t_{nm}$ the amplitude to hop n sites horizontally and m sites vertically. The shape of this energy spectrum is very important to the physics of fermions like electrons. | 2013-05-23 08:37:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8878051042556763, "perplexity": 398.41001426972457}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703035278/warc/CC-MAIN-20130516111715-00053-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://gmatclub.com/forum/in-the-figure-above-three-lines-cross-as-shown-above-what-is-the-valu-276127.html | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 21 May 2019, 21:59
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based on your Timer History
Track
every week, we’ll send you an estimated GMAT score based on your performance
Practice
Pays
we will pick new questions that match your level based on your Timer History
In the figure above three lines cross as shown above, what is the valu
Author Message
TAGS:
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 55231
In the figure above three lines cross as shown above, what is the valu [#permalink]
Show Tags
14 Sep 2018, 02:00
00:00
Difficulty:
25% (medium)
Question Stats:
62% (00:33) correct 38% (00:43) wrong based on 30 sessions
HideShow timer Statistics
In the figure above three lines cross as shown above, what is the value of x?
(1) z = 50
(2) y = x
Attachment:
image015.jpg [ 4.27 KiB | Viewed 518 times ]
_________________
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1012
Location: India
GPA: 3.64
In the figure above three lines cross as shown above, what is the valu [#permalink]
Show Tags
14 Sep 2018, 02:06
Bunuel wrote:
In the figure above three lines cross as shown above, what is the value of x?
(1) z = 50
(2) y = x
Attachment:
image015.jpg
It is not given that the lines $$l_1$$ and $$l_2$$ are parallel.
S1 - z = 50
Insufficient.
S2 - y = x
Insufficient.
Combining both, z=y=x=50.
Sufficient.
_________________
Please give kudos, if you like my post
When the going gets tough, the tough gets going...
Manager
Joined: 29 Jul 2018
Posts: 114
Concentration: Finance, Statistics
GMAT 1: 620 Q45 V31
Re: In the figure above three lines cross as shown above, what is the valu [#permalink]
Show Tags
14 Sep 2018, 03:58
souvonik2k
i thought we weren't allowed to assume inf in ds
and lines are parallel is not given.
correct me if im wrong.
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1012
Location: India
GPA: 3.64
Re: In the figure above three lines cross as shown above, what is the valu [#permalink]
Show Tags
14 Sep 2018, 23:14
manjot123 wrote:
souvonik2k
i thought we weren't allowed to assume inf in ds
and lines are parallel is not given.
correct me if im wrong.
Edited my post. Thank you.
_________________
Please give kudos, if you like my post
When the going gets tough, the tough gets going...
Director
Joined: 31 Jul 2017
Posts: 516
Location: Malaysia
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: In the figure above three lines cross as shown above, what is the valu [#permalink]
Show Tags
14 Sep 2018, 23:35
Bunuel wrote:
In the figure above three lines cross as shown above, what is the value of x?
(1) z = 50
(2) y = x
Attachment:
image015.jpg
The lines are Parallel can be proved only from B. Hence, Z = X = 50 (From A).
Option, C.
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!
Re: In the figure above three lines cross as shown above, what is the valu [#permalink] 14 Sep 2018, 23:35
Display posts from previous: Sort by | 2019-05-22 04:59:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8980497717857361, "perplexity": 6466.472220981727}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256763.42/warc/CC-MAIN-20190522043027-20190522065027-00126.warc.gz"} |
https://www.physicsforums.com/threads/cross-product-of-curl.65502/ | # Cross product of curl.
Homework Helper
Is there any neat way/rule to write:
$$\vec B \times (\vec \nabla \times \vec A)$$
?
I've tried it myself and found (e.g) for the x-component:
$$\left(B_x\frac{\partial A_x}{\partial x}+B_y\frac{\partial A_y}{\partial x}+B_z\frac{\partial A_z}{\partial x}\right)-\left(B_x\frac{\partial A_x}{\partial x}+B_y\frac{\partial A_x}{\partial y}+B_x\frac{\partial A_x}{\partial z}\right)$$
I can write the last terms with the minus sign as: $\vec B \cdot \nabla A_x$, but I can't find a way to do something nice to the first term, except maybe:
$$\left(\vec B \cdot \frac{\partial}{\partial x}\vec A\right)$$
I've never seen such an expression before though.
The other 2 components are similar:
$$\left[\vec B \times (\vec \nabla \times \vec A)\right]_y=\left(\vec B \cdot \frac{\partial}{\partial y}\vec A\right)-\left(\vec B \cdot \nabla A_y\right)$$
$$\left[\vec B \times (\vec \nabla \times \vec A)\right]_z=\left(\vec B \cdot \frac{\partial}{\partial z}\vec A\right)-\left(\vec B \cdot \nabla A_z\right)$$
I figured I may see something if I combined them all into the general expression:
$$\left(B_x\frac{\partial A_x}{\partial x}+B_y\frac{\partial A_y}{\partial x}+B_z\frac{\partial A_z}{\partial z}\right)\hat x +\left(B_x\frac{\partial A_x}{\partial y}+B_y\frac{\partial A_y}{\partial y}+B_z\frac{\partial A_z}{\partial y}\right)\hat y+\left(B_x\frac{\partial A_x}{\partial z}+B_y\frac{\partial A_y}{\partial z}+B_z\frac{\partial A_z}{\partial z}\right)\hat z-(\vec B \cdot \vec \nabla)\vec A$$
There's definately a pattern in the first 3 terms, but the best I could come up with is writing these terms as:
$$B_x\nabla A_x+B_y\nabla A_y+B_z\nabla A_z$$
That has condensed it a lot. Looks like a dot product with B, but....
robphy
Homework Helper
Gold Member
identity: (from Griffiths, Introduction to EM)
grad(A dot B)=A cross (curl B) + B cross (curl A) + (A dot grad)B + (B dot grad)A
robphy
Homework Helper
Gold Member
Playing around with it more:
$$\vec B \times(\nabla \times \vec A) =\epsilon_{ijk}B_j ( \epsilon_{klm}\nabla_l A_m) =B_m \nabla_i A_m - B_l \nabla_l A_i$$
where I used
$$\epsilon_{ijk}\epsilon_{klm}=\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl}$$
So, you've essentially got it.
dextercioby | 2020-09-23 07:37:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7896198630332947, "perplexity": 1989.520224648154}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400209999.57/warc/CC-MAIN-20200923050545-20200923080545-00638.warc.gz"} |
http://www.emathzone.com/tutorials/basic-statistics/completely-randomized-design.html | # Completely Randomized Design
A completely randomized (CR) design, which is the simplest type of the basic designs, may be defined as a design in which the treatments are assigned to experimental units completely at random, that is the randomization is done without any restrictions. The design is completely flexible, i.e., any number of treatments and any number of units per treatment may be used. Moreover, the number of units per treatment need not be equal. A completely randomized design is considered to be mo useful in situations where (i) the experimental units are homogeneous, (ii) the experiments are small such as laboratory experiments, and (iii) some experimental units are likely to be destroyed or to tail to respond.
Experimental Layout:
The layout of an experiment is the actual placement of the treatments on the experimental units, which may pertain Lo time, space or type of material. Suppose we have $k -$treatment and the experimental material is divided into $n$ experimental units. We shall then assign the $k -$ treatments at random to the $n$ experimental units in such a way that the treatment ${\tau _j} = \left( {i = 1,2, \ldots ,k} \right)$is applied ${r_j}$times, with$\sum {r_j} = n$.When each treatment is applied the same number of times, then${r_1} = {r_2} = \cdots = {r_k} = r$ and $\sum {r_j} = rk = n$. Usually, each treatment is applied (or replicated) an equal number of times.
An example of the experimental layout for a completely randomized design (CR) using four treatments $A,B,C$ and $D$,each repeated $3$ times, is given below:
The result or response of a treatment which may be a real yield, the gain in weight, the ability, etc., is generally called yield and is represented by the letter $Y$. | 2017-07-26 06:34:12 | {"extraction_info": {"found_math": true, "script_math_tex": 13, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5906047224998474, "perplexity": 646.8019142753996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549426050.2/warc/CC-MAIN-20170726062224-20170726082224-00608.warc.gz"} |
http://www.ck12.org/probability/Probability-and-Combinations/lesson/Probability-and-Combinations-ALG-I/ | # Probability and Combinations
## Determine the probabilities of events when arrangement order does not matter
Estimated8 minsto complete
%
Progress
Practice Probability and Combinations
MEMORY METER
This indicates how strong in your memory this concept is
Progress
Estimated8 minsto complete
%
Probability and Combinations
### Probability and Combinations
Just as with permutations, combinations crop up frequently in probability. In many card games the objective is to acquire a winning hand. In order to do that, it’s useful for players to know how likely a given hand is to arise, and also the probability that another player has a better hand. Mathematicians have been studying such games of chance for centuries.
#### Real-World Application: Word Games
A word game requires players to select 4 tiles from a bag containing 26 tiles, each with one of the letters A through Z written on it. If each letter appears once and only once, what is the probability that a player will be able to spell CATS with his tiles?
Since a player needs a \begin{align*}C\end{align*}, an \begin{align*}A\end{align*}, a \begin{align*}T\end{align*} and an \begin{align*}S\end{align*} in any order, we are looking at a combination calculation. We first need to determine how many combinations there are, choosing 5 letters from a total of 26:
Choosing 4 from 26:
\begin{align*}_{26}C_4 &= \frac{26!}{(26-4)! 4!} = \frac{26!}{22! 4! }\\ &= \frac{26 \times 25 \times 24 \times 23 }{ 4 \times 3 \times 2 \times 1}\\ &= 59,800 \ \text{combinations.}\end{align*}
Since only one combination allows a player to spell CATS, the probability of getting that combination is \begin{align*}\frac{1}{59,800}\end{align*}.
#### Real-World Application: Funfair Games
A funfair game consists of pulling numbered chips from a bag. The game starts with nine chips numbered 1 through 9, and players are allowed to pull out three chips. A player wins by drawing the number 7 chip. What is the probability that a player will win?
To find the probability for winning this game we need to know two pieces of information: 1) the total number of combinations for the game and 2) the number of combinations that contain a 7.
To find the total number of combinations for the game, use the formula \begin{align*}_nC_r\end{align*} with \begin{align*}n = 9\end{align*} and \begin{align*}r =3\end{align*}:
\begin{align*}{_9}C_2 = \frac{9!}{(9-3)! 3!} = \frac{9!}{6! 3! } = \frac{9 \times 8 \times 7 }{ 3 \times 2 \times 1} = 84 \ \text{combinations}\end{align*}
Now we need to determine how many combinations contain a 7. We can figure this out by reasoning as follows: given that there MUST be a 7 in the list, the number of combinations that contain a seven is the same as the number of combinations of choosing any two numbers out of the eight chips that don’t include the 7. In other words, if we imagine that we got to pick the 7 chip on purpose, how many ways would there be of picking the other two chips?
To find that number, we use the formula \begin{align*}_nC_r\end{align*} with \begin{align*}n =8\end{align*} and \begin{align*}r =2\end{align*}:
\begin{align*}{_8}C_2 = \frac{8!}{(8-2)! 2!} = \frac{8!}{6! 2! } = \frac{8 \times 7 }{ 2 \times 1} = 28 \ \text{combinations}\end{align*}
So the probability is given by:
\begin{align*}P(\text{getting a} \ 7) = \frac{84}{28} = \frac{1}{3} = \text{or one in three}.\end{align*}
#### Calculating Probability
Calculate the probability of being dealt four aces in a five card poker hand.
The first thing we need to know to solve this problem is the total number of unique hands. Since players can arrange their cards however they wish, the order of the cards is unimportant. So we will calculate, using the formula, the number of combinations for choosing 5 cards from a 52 card deck.
Choosing 5 from 52: \begin{align*}_{52}C_5 = \frac{52!}{(52-5)! 5!} = \frac{52!}{47! 5! } = \frac{52 \times 51 \times 50 \times 49 \times 48 }{ 5 \times 4 \times 3 \times 2 \times 1} = 2,598,960\end{align*} unique hands
Next we need to calculate how many hands there are that contain four aces. This sounds difficult, but we can think about it like this:
• If a hand contains four aces, it must also contain exactly ONE other card.
• Since the four aces are accounted for, there are 48 (that’s 52 – 4) cards left in the deck.
Since a unique hand is independent of the order in which the cards are dealt, there must be 48 unique hands that contain four aces (one unique hand for every non-ace card in the deck).
There are 48 possible hands that contain four aces. So the probability of being dealt four aces in poker is:
\begin{align*}P(\text{four aces})= \frac{48}{2,598,690} = \frac{1}{54,145} \end{align*}
### Review
For 1-3, calculate the number of combinations:
1. \begin{align*}_8C_4\end{align*}
2. \begin{align*}_{11}C_5\end{align*}
3. \begin{align*}_{20}C_2\end{align*}
For 4-8, a town lottery requires players to choose three different numbers from the numbers 1 through 36.
1. How many different combinations are there?
2. What is the probability that a player’s numbers match all three numbers chosen by the computer?
3. What is the probability that two of a player’s numbers match the numbers chosen by the computer?
4. What is the probability that one of a player’s numbers matches the numbers chosen by the computer?
5. What is the probability that none of a player’s numbers match the numbers chosen by the computer?
1. A bag contains 13 dominoes. Each domino has a different number of dots on it, and the numbers of dots are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12. Peter selects 2 dominos at random from the bag. What is the probability that the total number of dots on the two dominoes he selects is 7?
2. Looking at the odds that you came up with in question 4, devise a sensible payout plan for the lottery—in other words, how big should the prizes be for players who match 1, 2, or all 3 numbers? Assume that tickets cost \$1. Don’t forget to take into account the following:
1. The town uses the lottery to raise money for schools and sports clubs.
2. Selling tickets costs the town a certain amount of money.
3. If payouts are too low, nobody will play!
### Notes/Highlights Having trouble? Report an issue.
Color Highlighted Text Notes
### Vocabulary Language: English
TermDefinition
combination Combinations are distinct arrangements of a specified number of objects without regard to order of selection from a specified set.
Permutation A permutation is an arrangement of objects where order is important.
Probability Probability is the chance that something will happen. It can be written as a fraction, decimal or percent. | 2017-04-30 23:50:28 | {"extraction_info": {"found_math": true, "script_math_tex": 20, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9956877827644348, "perplexity": 516.6493880197316}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917125881.93/warc/CC-MAIN-20170423031205-00001-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/1984343/a-hash-table-has-space-for-75-records-then-the-probability-of-collision-befor/2349338 | # A hash table has space for $75$ records, then the probability of collision before the table is $6\%$ full
A hash table has space for $75$ records, then the probability of collision before the table is $6\%$ full
1. $0.25$
2. $0.20$
3. $0.35$
4. $0.30$
$\color{Green}{\text{My attempt:}}$
Table has $75$ slots. So, for $6\%$ filling it must take $6$ slots. Now, the question is like this- collision before $6\%$ full. This should mean the first collision happened before the $6th$ entry is made. So, the first collision can happen from $2nd$ entry (for $1st$ entry there won't be a collision) to $6th$ entry. So required probability
$=\cfrac{75\times 1}{75^2}+\cfrac{75\times74\times 2}{75^3}+\cfrac{75\times74\times73\times 3}{75^4}+\cfrac{75\times74\times73\times 72\times4}{75^5}+\cfrac{75\times74\times73\times 72\times71\times5}{75^6}=0.1854$
$\color{Red}{\text{Somewhere it explained as:}}$
To make the table $6\%$ full, we need to insert at least $\lceil{\cfrac{75\times 6}{100}}\rceil = 5$ values.
probability of collision during first insertion $= 0$
probability of collision during second insertion $= 1/75$
probability of collision during third insertion $= 2/75$
probability of collision during fourth insertion $= 3/75$
probability of collision during fifth insertion $= 4/75$
So, total probability of collision to make the table $6\%$ full $= (1+2+3+4)/75 = 0.13$
$\color{blue}{\text{Another explanation is given as :}}$
Explanation: On $.75^{th}$ insertion probability of collision $= 1/75$
On $1.5^{th}$ insertion probability of collision $= 2/75$
On $2.25^{th}$ insertion probability of collision $= 3/75$
On $3^{th}$ insertion probability of collision $= 4/75$
On $3.75^{th}$ insertion probability of collision $= 5/75$
So the required probability is $1+2+3+4+5/75 = 0.20$
First explanation is correct. Alternative solution is:
Table has $75$ slots. So, for $6\%$ filling it must take $6$ slots. Probability of no collision for first $6$ entries $= \cfrac{^{75}P_6}{ 75^6} = 0.814586387$
Therefore, at least one collision occurs in $6$ entries
$= 1 - \text{Probability of no collision for first$6$entries }$
$= 1 - 0.814586387$
$= 0.185413613$
• Thanks for nice explanation. – 1 0 Jul 7 '17 at 10:37 | 2019-09-20 11:35:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49120306968688965, "perplexity": 1274.5744899394354}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574018.53/warc/CC-MAIN-20190920113425-20190920135425-00072.warc.gz"} |
https://zbmath.org/?q=an:1206.11065 | ## On the homology of truncated affine Springer fibers. (Sur l’homologie des fibres de Springer affines tronquées.)(French)Zbl 1206.11065
Summary: Following M. Goresky, R. Kottwitz and R. MacPherson [Duke Math. J. 121, No. 3, 509–561 (2004; Zbl 1162.14311)], we compute the homology of truncated affine Springer fibers in the unramified case but under a purity assumption. We prove this assumption in the equivalued case. The truncation parameter is viewed as a divisor on an $$\ell$$-adic toric variety. In the unramified and equivalued cases, for each truncated affine Springer fiber, we introduce a graded coherent sheaf on the toric variety whose space of global sections is precisely the $$\ell$$-adic homology of this fiber. Moreover, for some families of endoscopic groups, these sheaves show up in an exact sequence. As a consequence, we prove Arthur’s weighted fundamental lemma [J. Inst. Math. Jussieu 1, No. 2, 175–277 (2002; Zbl 1040.11038), Conjecture 5.1] in the unramified equivalued case
### MSC:
11F70 Representation-theoretic methods; automorphic representations over local and global fields 14M15 Grassmannians, Schubert varieties, flag manifolds 22E67 Loop groups and related constructions, group-theoretic treatment 11R39 Langlands-Weil conjectures, nonabelian class field theory
### Citations:
Zbl 1162.14311; Zbl 1040.11038
Full Text:
### References:
[1] J. G. Arthur, The characters of discrete series as orbital integrals , Invent. Math. 32 (1976), 205–261. · Zbl 0359.22008 [2] -, A trace formula for reductive groups, I : Terms associated to classes in $$G(\mathbfQ)$$, Duke Math. J. 45 (1978), 911–952. · Zbl 0499.10032 [3] -, The invariant trace formula, I : Local theory , J. Amer. Math. Soc. 1 (1988), 323–383. JSTOR: · Zbl 0682.10021 [4] -, A local trace formula , Inst. Hautes Études Sci. Publ. Math. 73 (1991), 5–96. · Zbl 0741.22013 [5] -, A stable trace formula, I : General expansions , J. Inst. Math. Jussieu 1 (2002), 175–277. · Zbl 1040.11038 [6] A. Beilinson et V. Drinfeld, Quantization of Hitchin’s integrable system and Hecke eigensheaves , prépublication, 1999. [7] T. Chang et T. Skjelbred, The topological Schur lemma and related results , Ann. of Math. (2) 100 (1974), 307–321. JSTOR: · Zbl 0288.57021 [8] D. A. Cox, The homogeneous coordinate ring of a toric variety , J. Algebraic Geom. 4 (1995), 17–50. · Zbl 0846.14032 [9] W. Fulton, Introduction to Toric Varieties , Ann. of Math. Stud. 131 , Princeton Univ. Press, Princeton, 1993. · Zbl 0813.14039 [10] D. Gaitsgory, Construction of central elements in the affine Hecke algebra via nearby cycles , Invent. Math. 144 (2001), 253–280. · Zbl 1072.14055 [11] M. Goresky, R. Kottwitz et R. Macpherson, Equivariant cohomology, Koszul duality, and the localization theorem , Invent. Math. 131 (1998), 25–83. · Zbl 0897.22009 [12] -, Homology of affine Springer fibers in the unramified case , Duke Math. J. 121 (2004), 509–561. · Zbl 1162.14311 [13] -, Purity of equivalued affine Springer fibers , Represent. Theory 10 (2006), 130–146. · Zbl 1133.22013 [14] A. Grothendieck, Éléments de géométrie algébrique, III : Étude cohomologique des faisceaux cohérents, I, Inst. Hautes Études Sci. Publ. Math. 11 (1961). [15] D. Kazhdan et G. Lusztig, Fixed point varieties on affine flag manifolds , Israel J. Math. 62 (1988), 129–168. · Zbl 0658.22005 [16] R. E. Kottwitz, Rational conjugacy classes in reductive groups , Duke Math. J. 49 (1982), 785–806. · Zbl 0506.20017 [17] -, Isocrystals with additional structure , Compositio Math. 56 (1985), 201–220. · Zbl 0597.20038 [18] -, Isocrystals with additional structure, II , Compositio Math. 109 (1997), 255–339. · Zbl 0966.20022 [19] -, “Harmonic analysis on reductive $$p$$-adic groups and Lie algebras” dans Harmonic Analysis, the Trace Formula, and Shimura Varieties (Toronto, 2003) , Clay Math. Proc. 4 , Amer. Math. Soc., Providence, 2005, 393–522. · Zbl 1106.22013 [20] S. Kumar, “Infinite Grassmannians and moduli spaces of $$G$$-bundles” dans Vector Bundles on Curves –.-New Directions (Cetraro, Italy, 1995) , Lecture Notes in Math. 1649 , Springer, Berlin, 1997, 1–49. · Zbl 0884.14021 [21] A. Moy et G. Prasad, Unrefined minimal $$K$$ -types for $$p$$-adic groups, Invent. Math. 116 (1994), 393–408. · Zbl 0804.22008 [22] J.-L. Waldspurger, Endoscopie et changement de caractéristique , J. Inst. Math. Jussieu 5 (2006), 423–525. · Zbl 1102.22010 [23] -, L’endoscopie tordue n’est pas si tordue , Mem. Amer. Math. Soc. 194 (2008), no. 908. · Zbl 1146.22016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2022-07-03 05:53:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9205167293548584, "perplexity": 1588.4543812039137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104215790.65/warc/CC-MAIN-20220703043548-20220703073548-00131.warc.gz"} |
https://crypto.stackexchange.com/tags/linear-cryptanalysis/hot | # Tag Info
Accepted
### Understanding the wide trail design strategy
Given the importance of the wide-trail strategy in modern symmetric-key cryptography, this question really deserves an answer (and a much better score). Since nobody else has tried, I'll give a brief ...
• 1,786
Accepted
### Why is the DES s-box non-linear? Why does it make the cracking of the cipher more difficult?
It is of course possible to write DES or any block cipher as a system of non-linear equations involving the plaintext bits, the ciphertext bits, and the key bits, which hold with probability 1. In ...
• 4,345
Accepted
### Selection of rotation constants in ARX design
Leaving besides that the designers (NSA) of Simon and Speck did not provide an initial design rational for their ciphers/parameter choices, they added some notes later after pressure from the ...
• 116
Accepted
### Does hashing require non-linearity?
Does hashing require non-linear components as well? Yes How would a hash built from a linear psuedo-random permutation be vulnerable to collision/preimage search? You could find a preimage by ...
• 134k
Accepted
• 1,786
• 16.7k
Accepted
### Why is not there any ideal S-Box?
It is important to understand that although a very large random function will only have linear biases with very low probability, this is simply not true of small random functions. If you choose a ...
Accepted
### Non Linearity of huge Sbox
Table construction would require 148 Exabytes of RAM, so it would be hard to store all at once. This also means that you can't have a predefined S box that you might have developed either to be a ...
• 14k
Accepted
### When it comes to linear cryptanalysis, is there always a key that could work for every possible input/output?
Regarding your first question, we assume (for known plaintext attacks such as Linear cryptanalysis) that we can obtain a large number of inputs and the corresponding outputs under the unknown key. The ...
• 16.7k
Accepted
### How do you calculate the linear approximation of an S-BOX?
You might want to check out this stackoverflow question: What is Bit Masking? Basically, the mask selects certain bits from the words, where a word is a vector (a row) of bits. The input mask selects ...
• 19.3k
Accepted
### Compression function cryptanalysis
Are there any standard/general techniques for determining an unknown compression function, given the input-output pairs? This appears to fall under the realm of reverse-engineering rather than ...
• 19.3k
Accepted
### Correlation of linear trail
This is due to the modelling approach called Markov Ciphers, by Jim Massey (I think). Basically the hypothesis is that round by round independence applies and correlations can be concatenated by ...
• 16.7k
Let's start with the basics: a bijective 4×4 bit S-box is a permutation of the set $\{0,1\}^4$ of 4-bit bitstrings. These bitstrings can be viewed as the binary representations of the integers ... | 2022-08-18 06:02:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5971609354019165, "perplexity": 1614.8737783575828}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573163.7/warc/CC-MAIN-20220818033705-20220818063705-00488.warc.gz"} |
http://www.physicsforums.com/showthread.php?s=363377b7deeee19a4d6f3d4793eadd95&p=4050947 | ## Sze Eq. 42
Dear PF users
Would be great if somebody could point me out how to arrive at $n_{n0} = \frac{1}{2} \left[ (N_D - N_A) + \sqrt{ (N_D - N_A)^2 + 4n_i^2} \right]$ (n-type charge carrier concentration at thermal equilibrium) by using the expression for the charge neutrality $n+N_A = p+N_D$ and the mass action law $np=n_i^2$.
I understand I should assume that $N_D > N_A$, but I cant work it out.
Quote by mzh Dear PF users Would be great if somebody could point me out how to arrive at $n_{n0} = \frac{1}{2} \left[ (N_D - N_A) + \sqrt{ (N_D - N_A)^2 + 4n_i^2} \right]$ (n-type charge carrier concentration at thermal equilibrium) by using the expression for the charge neutrality $n+N_A = p+N_D$ and the mass action law $np=n_i^2$.
I think I found the solution to this. The important point to note is that we assume relatively high temperatures. Given the relationship for $N_D^+ = \frac{N_D}{1+2\exp\left[\frac{E_F - E_D}{kT}\right]}$, we can assume that $E_F - E_D$ is much lower than zero. Then, when dividing by $kT = 0.025 \mbox{eV}$ at room temperature, the exponential term becomes approximately zero and so $N_D^+ = N_D$. Then, $N_D$ can be inserted into the charge neutrality condition and, after expressing $p=\frac{n_i^2}{n}$, the resulting quadratic equation can be solved for $n$. Great. | 2013-06-19 21:33:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9813191294670105, "perplexity": 175.46261849656096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368709224828/warc/CC-MAIN-20130516130024-00010-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3012728/changing-value-of-a-riemann-integrable-function-on-a-lebesgue-measure-0-set-impl | # Changing value of a Riemann integrable function on a Lebesgue measure 0 set implies the new function has the same Riemann integral?
Suppose $$[a,b]$$ is a compact interval of $$\mathbb{R}$$ and $$f:[a,b]\to\mathbb{R}$$ be integrable in the Riemann sense. Then, by Lebesgue's criterion, $$f$$ is bounded on $$[a,b]$$ and it's set of discontinuities has Lebesgue measure zero.
Now suppose $$\tilde{f}:[a,b]\to\mathbb{R}$$ is a new function built by changing the value of $$f$$ in a Lebesgue measure zero subset of $$[a,b]$$. Since $$\tilde{f}$$ remains bounded and it's set of discontinuities has still Lebesgue measure zero, we know that $$\tilde{f}$$ is Riemann integrable.
Is it true that $$\int_{a}^{b}f=\int_{a}^{b}\tilde{f}\qquad ?$$
• One can change the value of a continuous function on a set of measure zero in such a way that the new function is continuous nowhere. – Angina Seng Nov 25 '18 at 11:42
• So what I am asking Is always true when the Number of point in wich I change the value of $f$ Is finite. Right? – eleguitar Nov 25 '18 at 11:45
• If you modify the zero function to take the value $1$ on each rational input, the Riemann upper and lower sum will always be $b-a$ and $0$, respectively - no convergence – Hagen von Eitzen Nov 25 '18 at 11:46
• You could say that if $\int f$ and $\int \tilde f$ exist and $\tilde f$ differs from $f$ only on a Lebesgue zero set, then the intergrals are equal. – Hagen von Eitzen Nov 25 '18 at 11:48
• There's no reason to think $\tilde f$ is bounded. – zhw. Nov 25 '18 at 19:19
## 1 Answer
Let $$f=0$$ and $$g(x)=0$$ for $$x$$ irrational, $$1$$ for $$x$$ rational. Then $$f$$ is Riemann integrable, $$f=g$$ almost everywhere but $$g$$ is discontinuous everywhere, is it is not Riemann integrable.
• Thanks. My question holds whenever the set of point at wich I change the value of $f$ Is finite. Right? – eleguitar Nov 25 '18 at 11:55
• Yes, neither Riemann integrability nor the value of the integral changes if you change the function at a finite number of points. – Kavi Rama Murthy Nov 25 '18 at 11:59
• Thanks sir. Could you please see if my attempt is correct here math.stackexchange.com/questions/3012683/… – eleguitar Nov 25 '18 at 12:06 | 2020-09-29 11:19:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 19, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7970153093338013, "perplexity": 169.14393683817568}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401641638.83/warc/CC-MAIN-20200929091913-20200929121913-00439.warc.gz"} |
https://auditeon.com/software:eagle_cadsoft | # Auditeon
## Custom Libraries
During a design process it is sometimes necessary to add components which are not available in the ready supplied libraries. For this, components can be created manually and imported in the design. The method for this requires some fundamental understanding how components are organized in Eagle, both in the application itself as on disk. Guidelines about library design and recommendations how to use consistent nomenclature should help a user to successfully manage such collections of components, upgrade or extend them with other packages.
## Libraries within Eagle
In the Control Panel within Eagle, library folders contain files with IC manufacturers, group of generic components or group of specific symbols (Like ground, power supply and drawing frames). Eagle treats each of these files as a library, containing devices 3) or device sets4). If a library is available in Eagle and opened5) one will observe that a selected device or device set has primarily three entities:
• Device: The real component, residing in a specific package with a specific symbol.
• Package: Footprint in the layout
• Symbol: Drawing in the schematic
Each of these entities characterize a specific aspect of a component or component breed. The image below shows a selected library with the 555 timer IC component breed (Or in the Eagle jargon called device set).
Library example with the 555 timer IC, residing in the library from linear and is defined in eight different devices, each having different characteristics
## Recommendations from Eagle for File Locations
The default location for libraries which are created when installing Eagle, can be found when clicking on Options→Directories. On OSX, this is in $EAGLEDIR/lbr, where$EAGLEDIR represents the application installation directory from Eagle. Eagle recommends to keep this directory unchanged, as software updates may overwrite files in this folder.
Your own libraries should therefore be at another location. A suitable one would be in a subfolder within your Eagle projects folder like the following structure:
• $Home/Backup/eagle/ • eagle_custom_libraries • dev_mylibrary1 • dev_mylibrary2 • eagle_projects • Arduino • PowerSupply • etc. In order to make Eagle aware of the main custom libraries folder, just add the directory in Options→Directories. Any subfolders within this folder will be automatically used as well. For example: $EAGLEDIR/lbr:$HOME/Backup/eagle/eagle_custom_libraries While configuring the libraries folder, one could do something similar for the projects folder: $HOME/Backup/eagle/eagle_projects:$EAGLEDIR/projects/examples If none of the libraries appear when adding a part, verify in the control panel at Libraries if the default libraries are enabled. To do this, in the control panel right click on a library and if not enabled, select Use. ## Design process Before the practical designing can be done, consideration should be made for a naming scheme. A consistent nomenclature will keep custom libraries in a healthy state. ### Nomenclature A consistent naming scheme can be best explained with the following example: Library Folder Library Device(s) or device set(s) → →$HOME/Backup/eagle/eagle_custom_libraries → dev_marc.lbr → …, *555, NE5534, LM385, …
If we now look closer to the *555, we can draw the following scheme:
Symbol Device set Device Package *555 ← → ← → LM555D LM555N NE555D SO08 DIL08 SO08
On the left side from the device set, we see a symbol from the timer IC. On the right side we see a list with devices and their packages. For each device within a device set, Eagle designates a different package to a separate device.
The placeholder '*' is not ideal because it also refers to devices which contain the number 555 but are not timer ICs. A better example can be made for example with an LM385 voltage reference diode:
Library Folder Library Device(s) or device set(s) → → \$HOME/Backup/eagle/eagle_custom_libraries → dev_marc.lbr → …, *555, NE5534, LM385, …
If we now look closer to the data sheet of the LM385 or adjustable (LM385-adj), we see it contains one symbol with 3 pins and another with 8 pins, depending on the kind of package. With that information we draw the following scheme:
Symbol Device set Device Package LM385 ← → ← → LM385AYZ-2.5 LM385BXM-2.5 LM385M3-2.5 TO-92 SO-8 SOT-23 ← → LM385BXZ LM385BYZ LM385BZ LM385Z LM385M LM385BM TO-92 TO-92 TO-92 TO-92 SO-8 SO-8
## Component custom design
A component must reside in a library. Therefore, to create or edit existing components, either -from the control panel- create first a new library or open an existing one via the menu. This will invoke the Library Editor window.
In this window, from left to right you will find these basic commands:
1. Edit a drawing: With this button you can load a device or package for editing
2. Edit a device or device set: In this window you do not draw anything, but only define which Package is used, which Symbol(s) is/are used (called Gate within a Device), which names are provided for the Gates (e.g. A, B), which technologies are available (E.g. 74L00, 74LS00, 74HCT00), whether the Device has additional user-definable attributes, whether there are equivalent Gates which can be interchanged (Swaplevel), how the Gate behaves when added to a schematic (AddLevel), the prefix for the component name (if a prefix is being used), whether the value of the component can be changed or whether the value should be fixed to the Device name, which pins relate to the pads of the Package (CONNECT command), whether a description for this component should be stored in the library.
3. Edit a package
4. Edit a symbol
A device, device set, package or symbol can be removed from a library via the Library menu. To remove, you must open that device in the type Library Editor window first and then select from the menu the option Library → Remove… and enter the name which refers to what you want to delete. (The package, symbol or device.) If it stills shows up in the concerning Library in the Control Panel, save the Library with the removed item.
1)
Easy Applicable Graphic Layout Editor
2)
Presuming one has the correct license for that
3)
These are components having a link between one or more Symbols and a Package
4)
i.e. equivalent components sharing the same functions but having different packages and/or symbols, like a LM555D and LM555N
Please note that the definition of device sets is not very clear. A closer match would be device breed, which specifies more precise that devices which belong to the same breed share a common function.
5)
Shown in a library folder at the Control Panel, visible as a file with an .lbr extension and by clicking on the small triangle preceding the filename which unfolds the folder | 2021-04-22 01:09:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.29452547430992126, "perplexity": 4007.72344214862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039554437.90/warc/CC-MAIN-20210421222632-20210422012632-00357.warc.gz"} |
http://www.ck12.org/book/CK-12-Biology-Concepts/r18/section/2.22/ | <meta http-equiv="refresh" content="1; url=/nojavascript/">
You are reading an older version of this FlexBook® textbook: CK-12 Biology Concepts Go to the latest version.
# 2.22: Calvin Cycle
Difficulty Level: At Grade Created by: CK-12
%
Progress
Practice Calvin Cycle
Progress
%
Other than being green, what do all these fruits and vegetables have in common?
They are full of energy. Energy in the form of glucose. The energy from sunlight is briefly held in NADPH and ATP, which is needed to drive the formation of sugars such as glucose. And this all happens in the Calvin cycle.
### The Calvin Cycle
#### Making Food “From Thin Air”
You’ve learned that the first, light-dependent stage of photosynthesis uses two of the three reactants, water and light, and produces one of the products, oxygen gas (a waste product of this process). All three necessary conditions are required – chlorophyll pigments, the chloroplast “theater,” and enzyme catalysts. The first stage transforms light energy into chemical energy, stored to this point in molecules of ATP and NADPH. Look again at the overall equation below. What is left?
Waiting in the wings is one more reactant, carbon dioxide, and yet to come is the star product, which is food for all life – glucose. These key players perform in the second act of the photosynthesis drama, in which food is “made from thin air!”
The second stage of photosynthesis can proceed without light, so its steps are sometimes called “light-independent” or “dark” reactions. Many biologists honor the scientist, Melvin Calvin, who won a 1961 Nobel Prize for working out this complex set of chemical reactions, naming it the Calvin cycle .
The Calvin cycle has two parts. First carbon dioxide is "fixed." Then ATP and NADPH from the light reactions provide energy to combine the fixed carbons to make sugar.
#### Carbon Dioxide is “Fixed”
Why does carbon dioxide need to be fixed? Was it ever broken?
Life on Earth is carbon-based. Organisms need not only energy but also carbon atoms for building bodies. For nearly all life, the ultimate source of carbon is carbon dioxide (CO 2 ), an inorganic molecule. CO 2 makes up less than 1% of the Earth’s atmosphere.
Animals and most other heterotrophs cannot take in CO 2 directly. They must eat other organisms or absorb organic molecules to get carbon. Only autotrophs can build low-energy inorganic CO 2 into high-energy organic molecules like glucose. This process is carbon fixation .
Stomata on the underside of leaves take in CO 2 and release water and O 2 . Guard cells close the stomata when water is scarce. Leaf cross-section (above) and stoma (below).
Plants have evolved three pathways for carbon fixation.
The most common pathway combines one molecule of CO 2 with a 5-carbon sugar called ribulose biphosphate (RuBP). The enzyme which catalyzes this reaction (nicknamed RuBisCo ) is the most abundant enzyme on earth! The resulting 6-carbon molecule is unstable, so it immediately splits into two 3-carbon molecules. The 3 carbons in the first stable molecule of this pathway give this largest group of plants the name “C 3 .”
Dry air, hot temperatures, and bright sunlight slow the C 3 pathway for carbon fixation. This is because stomata , tiny openings under the leaf which normally allow CO 2 to enter and O 2 to leave, must close to prevent loss of water vapor ( Figure above ). Closed stomata lead to a shortage of CO 2 . Two alternative pathways for carbon fixation demonstrate biochemical adaptations to differing environments.
Plants such as corn solve the problem by using a separate compartment to fix CO 2 . Here CO 2 combines with a 3-carbon molecule, resulting in a 4-carbon molecule. Because the first stable organic molecule has four carbons, this adaptation has the name C 4 . Shuttled away from the initial fixation site, the 4-carbon molecule is actually broken back down into CO 2 , and when enough accumulates, RuBisCo fixes it a second time! Compartmentalization allows efficient use of low concentrations of carbon dioxide in these specialized plants.
Cacti and succulents such as the jade plant avoid water loss by fixing CO 2 only at night. These plants close their stomata during the day and open them only in the cooler and more humid nighttime hours. Leaf structure differs slightly from that of C 4 plants, but the fixation pathways are similar. The family of plants in which this pathway was discovered gives the pathway its name, Crassulacean Acid Metabolism, or CAM ( Figure below ). All three carbon fixation pathways lead to the Calvin cycle to build sugar.
Even chemical reactions adapt to specific environments! Carbon fixation pathways vary among three groups. Temperate species (maple tree, left) use the C 3 pathway. C 4 species (corn, center) concentrate CO 2 in a separate compartment to lessen water loss in hot bright climates. Desert plants (jade plant, right) fix CO 2 only at night, closing stomata in the daytime to conserve water.
#### How Does the Calvin Cycle Store Energy in Sugar?
As Melvin Calvin discovered, carbon fixation is the first step of a cycle. Like an electron transport chain, the Calvin cycle, shown in Figure below , transfers energy in small, controlled steps. Each step pushes molecules uphill in terms of energy content. Recall that in the electron transfer chain, excited electrons lose energy to NADPH and ATP. In the Calvin cycle, NADPH and ATP formed in the light reactions lose their stored chemical energy to build glucose.
Use the diagram below to identify the major aspects of the process:
• the general cycle pattern
• the major reactants
• the products
Overview of the Calvin Cycle Pathway.
First, notice where carbon is fixed by the enzyme nicknamed RuBisCo. In C 3 , C 4 , and CAM plants, CO 2 enters the cycle by joining with 5-carbon ribulose bisphosphate to form a 6-carbon intermediate, which splits (so quickly that it isn’t even shown!) into two 3-carbon molecules.
Now look for the points at which ATP and NADPH (made in the light reactions) add chemical energy (“Reduction” in the diagram) to the 3-carbon molecules. The resulting “half-sugars” can enter several different metabolic pathways. One recreates the original 5-carbon precursor, completing the cycle. A second combines two of the 3-carbon molecules to form glucose, universal fuel for life.
The cycle begins and ends with the same molecule, but the process combines carbon and energy to build carbohydrates – food for life.
So, how does photosynthesis store energy in sugar? Six “turns” of the Calvin cycle use chemical energy from ATP to combine six carbon atoms from six CO 2 molecules with 12 “hot hydrogens” from NADPH. The result is one molecule of glucose, C 6 H 12 O 6 .
### Summary
• The reactions of the Calvin cycle add carbon (from carbon dioxide in the atmosphere) to a simple five-carbon molecule called RuBP.
• These reactions use chemical energy from NADPH and ATP that were produced in the light reactions.
• The final product of the Calvin cycle is glucose.
### Practice I
Use these resources to answer the questions that follow.
• http://www.hippocampus.org/Biology $\rightarrow$ Biology for AP* $\rightarrow$ Search: The Calvin-Benson Cycle: Overview
1. What are carbon assimilation and carbon fixation?
2. Why are most plants called C 3 plants?
3. Describe RuBisCo.
4. What is a C 4 plant?
• http://www.hippocampus.org/Biology $\rightarrow$ Biology for AP* $\rightarrow$ Search: The Conversion of Carbon Dioxide to Sugar
1. How does CO 2 enter the leaf?
2. What is Ribulose-1,5-bisphosphate?
3. What happens to some of the Glyceraldehyde-3-phosphate?
4. What happens to RuBisCo at night?
• http://www.hippocampus.org/Biology $\rightarrow$ Biology for AP* $\rightarrow$ Search: The Calvin-Benson Cycle: Summary
1. What eventually happens to the carbon that enters plants as part of CO 2 ?
2. What happens to the ATP and NADPH made during the light reactions?
3. What happens to energy during photorespiration?
4. What is a main advantage of C 4 plants?
### Review
1. What happens during the carbon fixation step of the Calvin cycle?
2. Explain what might happen if the third step of the Calvin cycle did not occur.
### Vocabulary Language: English Spanish
Calvin cycle
Calvin cycle
Second stage of photosynthesis in which carbon atoms from carbon dioxide are combined, using the energy in ATP and NADPH, to make glucose.
carbon fixation
carbon fixation
Process of building low-energy inorganic CO2 into high-energy organic molecules, like glucose.
organic molecules
organic molecules
Carbon-containing molecules, such as carbohydrates, lipids, proteins, and nucleic acids, that form the basis of lfie.
RuBisCo
RuBisCo
Enzyme that combines one molecule of CO2 with a 5-carbon sugar called ribulose biphosphate (RuBP); the most abundant enzyme on Earth.
Feb 24, 2012
Jul 01, 2015 | 2015-07-07 00:54:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 6, "texerror": 0, "math_score": 0.49615857005119324, "perplexity": 5902.949550251443}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375098924.1/warc/CC-MAIN-20150627031818-00252-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://blog.kungfuenglish.com/the-third-ear/ | # The third Ear
Today, I finished the page 9 of “The Third Ear”, In the lesson , it told to me , I need conversion about the content of The Third Ear the English Coach or English parent, It also give me some topic, let me to talk. Actually , I don’t sure I can do it well. Then , It also told me, I can write something for The Third Ear in English, It also give me some topic , I think it is more fit me than the before way.I want to find time to write it.
### One Response so far.
1. 龙飞虎 Chris说道：
Thanks for sharing! I look forward to seeing what you write about The Third Ear in English. | 2019-05-22 21:43:11 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8282632231712341, "perplexity": 1106.7273648405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256958.53/warc/CC-MAIN-20190522203319-20190522225319-00517.warc.gz"} |
http://blog.baoduge.com/SA_FN4/ | # Sentiment Polarity using Adjective
Hatzivassiloglou et al (1997)1 identified and validated from a large corpus constraints from conjunctions (such as and, but) on the positive or negative semantic orientation of the conjoined adjectives.
Orientation (Polarity) = direction of deviation from the norm
## Approach
• Indirect information:
• Adjectives conjoined by “and” have same polarity, such as “simple and well-received”;
• Adjectives conjoined by “but” have different polarity, such as “simplistic but well-received”;
Green line represents and, Red dashed line represents but.2
## Data collection
21 million word 1987 Wall Street Journal corpus, automatically annotated with part-of-speech tags using the PARTS tagger.
### Adjectives data preparation
• Construct a set of adjectives with predetermined orientation labels by taking all adjectives appearing in the corpus 20 times or more and removing adjectives that have no orientation;
• Assign an orientation label (either + or -) to each adjective, using an evaluative approach
• Criterion: whether the use of this adjective ascribes in general a positive or negative quality to the modified item, making it better or worse than a similar unmodified item.
• Final set contained 1,336 adjectives (657 positive and 679 negative terms).
### Adjectives data validation:
They subsequently asked 4 people to independently label a randomly drawn sample of 500 of these 1,336 adjectives, who agreed with us that the positive/negative concept applies to 89.15% of these adjectives on average.
## Extract conjunctions between adjectives
By using two-level finite-state grammar, 13,426 conjunctions of adjectives, expanding to a total of 15,431 conjoined adjective pairs are collected.
### Test data
15,048 conjunction tokens involve 9,296 distinct pairs of conjoined adjectives (types).
Each conjunction token is classified by the parser according to three variables:
• the conjunction used (and, or, but, either-or, or neither-nor)
• the type of modification (attributive, predicative, appositive, resultative)
• the number of the modified noun (singular or plural)
## Validation of the Conjunction Hypothesis
• Prediction method 1 - Always predict same orientation:
• always guessing that a link is of the same- orientation type
• Prediction method 2 - But rule:
• Method 1 + using but exhibit the opposite pattern
• Prediction method 3 - Log-linear model:
• $\eta = \mathbf{\omega}^\mathbf{T} \mathbf{x}$, $y = \frac{e^\eta}{1 + e^\eta}$
• $\mathbf{x}$: the vector of the observed counts in the various conjunction categories
• $\mathbf{\omega}$: the vector of weights to be learned
• $y$: the response of the system
• Using the method of iterative stepwise refinement they selected 9 predictor variables from all 90 possible predictor variables
• Morphological relationships:
• Adjectives related in form almost always have different semantic orientations
• Highly accurate (97.06%), but applies only to 1,336 labeled adjectives (891,780 possible pairs)
## Cluster
### Input
A graph of adjectives connected by dissimilarity links.
Dissimilarity value $d(x, y)$ between 0 and 1:
• Small $d(x, y)$ $\Rightarrow$ same-orientation link between $x$ and $y$
• High $d(x, y)$ $\Rightarrow$ different-orientation link between $x$ and $y$
To partition the graph nodes into subsets of the same orientation, we employ an iterative optimization procedure on each connected component, based on the exchange method, a non- hierarchical clustering algorithm.
Objective function $\Phi$ scoring each possible partition $\mathcal{P}$ of the adjectives into two subgroups $C_1$ and $C_2$ as
where $C_i$ stands for the cardinality of cluster $i$
### Labeling the Clusters as Positive or Negative
The unmarked member almost always having positive orientation (Lehrer, 1985; Battistella, 1990). Thus:
They computed the average frequency of the words in each group, expecting the group with higher average frequency to contain the positive terms.
## Conclusion
They tested how graph connectivity affects the overall performance
1. Hatzivassiloglou, Vasileios, McKeown, Kathleen R (1997). Predicting the semantic orientation of adjectives, 174—181
2. 7 - 4 - Learning Sentiment Lexicons - Stanford NLP - Professor Dan Jurafsky & Chris Manning
-------------End of postThanks for your time-------------
Enjoy it? Subscribe to my blog by scanning my public wechat account
Rate this post | 2019-05-21 05:47:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47557783126831055, "perplexity": 6299.631835375505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256227.38/warc/CC-MAIN-20190521042221-20190521064221-00444.warc.gz"} |
https://www.gradesaver.com/textbooks/engineering/other-engineering/materials-science-and-engineering-an-introduction/chapter-3-the-structure-of-crystalline-solids-questions-and-problems-page-102/3-67 | ## Materials Science and Engineering: An Introduction
Required: Determine the expected diffraction angle for the first-order reflection from the (310) set of planes for BCC chromium (Cr) when monochromatic radiation of wavelength 0.0711 nm is used. Solution: From Table 3.1, atomic radius of Chromium is 0.1249 nm. Calculating for the value of lattice parameter $a$, $a = \frac{4R}{\sqrt 3} = \frac{(4)(0.1249)}{\sqrt 3} = 0.2884 nm$ Using Equation 3.22, $d_{310}$ is computed as, $d_{310} = \frac{a}{\sqrt (3)^{2} + (1)^{2} + (0)^{2}} = \frac{0.2884 nm}{\sqrt 10} =0.0912 nm$ Modifying Equation 3.21 to compute the value of θ, $sin θ = \frac{nλ}{2d_{310}} = \frac{(1)(0.0711 nm)}{(2)(0.0912 nm)} = 0.3898$ $θ = sin^{-1}(0.3898) = 22.94°$ Thus, $2θ = (2)(22.94°) = 45.88°$ | 2019-11-18 18:31:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8165985345840454, "perplexity": 1522.9725511620204}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669813.71/warc/CC-MAIN-20191118182116-20191118210116-00139.warc.gz"} |
http://spmphysics.onlinetuition.com.my/2013/07/logic-gates-symbol-boolean-algebra-and.html | # Logic Gates - Symbol, Boolean Algebra and Truth Table
### Symbol of the Logic Gate
For each gate, the input or inputs are on the left of the symbol. The output is on the right
### The Truth Tables
1. The function of a logic gates can be shown by using the Truth tables.
2. A truth table lists all possible input together with the corresponding output.
### AND gate
Symbol:
Boolean Expression:
$X=A•B$
Truth Table:
Truth Table INPUT OUTPUT 0 0 0 0 1 0 1 0 0 1 1 1
Notes:
The output is HIGH (1) only if both the inputs are HIGH (1).
### OR gate
Symbol:
Boolean Expression:
$X=A+B$
Truth Table:
Truth Table INPUT OUTPUT 0 0 0 0 1 1 1 0 1 1 1 1
Notes:
The output is HIGH (1) only if one or more inputs are HIGH (1).
### NOT gate
Symbol:
Boolean Expression:
$X= A ¯$
Truth Table:
Truth Table INPUT OUTPUT 0 1 1 0
Notes:
The output is the opposite of the input.
### NAND gate
Symbol:
Boolean Expression:
$X= A•B ¯$
Truth Table:
Truth Table INPUT OUTPUT 0 0 1 0 1 1 1 0 1 1 1 0
Notes:
The output is LOW (0) only if both the inputs are HIGH (1).
### NOR gate
Symbol:
Boolean Expression:
$X= A+B ¯$
Truth Table:
Truth Table INPUT OUTPUT 0 0 1 0 1 0 1 0 0 1 1 0
Notes:
The output is HIGH (1) only if both the inputs are LOW (0). | 2017-10-20 04:56:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6677518486976624, "perplexity": 918.8654423067754}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823731.36/warc/CC-MAIN-20171020044747-20171020064747-00461.warc.gz"} |
https://www.physicsforums.com/threads/7-adic-distance-in-q7.723805/ | 1. Nov 19, 2013
### Funky1981
1. The problem statement, all variables and given/known data
Find the 7-adic distance between -1/3 and the square root of 305 in Q7
2. The attempt at a solution
My solution is write the 7-adic expansion of -1/3 and square root of 305
the 7-adic expansion of -1/3 := 2 +2*7+2*(7^2)+.... =2.2222222(index 7)
the 7-adic expansion of square root of 305:= 2.22345....(index7) or 5.4432.... this is one representation of root of 305 but there is another representation of 7-adic expansion
Hence they have the same 7-adic expansion . therefore the distance is 0 in Q7?
Is my attemption right? ( i am not sure whether i caculated these two 7-adic expansion in a right way)
Last edited: Nov 19, 2013 | 2017-11-20 17:44:02 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8443422317504883, "perplexity": 1089.9508675248717}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806086.13/warc/CC-MAIN-20171120164823-20171120184823-00508.warc.gz"} |
http://lambda-the-ultimate.org/node?from=1980 | While downtown doing something else entirely I managed to find myself in a bookshop. One of the few bookshops not belonging to a chain; in fact one that was established in 1908. They had some used books, and I managed to find two that were both interesting and cheap (around $6 each): Pascal User Manual and Report by Jensen and Wirth, 1974 Springer (alas only the 3rd edition from 1985) and Performance and Evaluation of Lisp Systems by Richard Gabriel (1985, MIT). Here's a taste from both. Wirth and Jensen: Upon first contact with Pascal, some programmers tend to bemoan the absence of certain "favorite features." Examples include an exponentiation operator, concatenation of strings, dynamic arrays, arithmetiac operations on Boolean values, automatic type conversions and default declerations. These were not oversights, but deliberate omissions. In some cases their presence would be primarily an invitation to inefficient programming solutions; in others it was felt that they would be contrary to the aim of clarity and reliability and "good programming style." Gabriel: Benchmarking is a black art at best. Stating the results of a particular benchmark on two Lisp systems usually causes people to believe that a blanket statement ranking the systems in question is being made. The proper role of benchmarking is to measure various dimensions if Lisp system performance and to order these systems along each of these dimensions. Gabriel includes a pertinent quote from Vuaghan Pratt: Seems to me benchmarking generates more debate than information. How true... I enjoyed the discussion of the various Lisp implementations in chapters 1 and 2. The Tak, Stak, Ctak, Takl and Takr series of benchmarks is enlightening. It shows how easy it is for benchmarks to measure "overheads" you haven't intended to measure, and how to engineer benchmarks to overcome this fundamental problem. ## alt.lang.jre @ IBM developerWorks Welcome to the new series alt.lang.jre. While most readers of this series are familiar with the Java language and how it runs on a cross-platform virtual machine (part of the JRE), fewer may know that the JRE can host languages besides the Java language. In its support for multiple languages (including some that pre-exist the Java platform) the JRE provides a comfortable entry point for developers coming to the Java platform from other backgrounds. It also gives developers who have rarely, if ever, strayed from the Java language the opportunity to explore the potential of other languages without sacrificing the familiarity of the home environment. This series may become an amusing resource. The first installment is about Jython. ## Making Asynchronous Parallelism Safe for the World (link) Guy L. Steele, Thinking Machines Corporation, 1990 We need a programming model that combines the advantages of the synchronous and asynchronous parallel styles. Synchronous programs are determinate (thus easier to reason about) and avoid synchronization overheads. Asynchronous programs are more flexible and handle conditions more efficiently. Here we propose a programming model with the benefits of both styles. We allow asynchronous threads of control but restrict shared-memory accesses and other side effects so as to prevent the behavior of the program from depending on any accidents of execution order that can arise from the indeterminacy of the asynchronous process model. This paper and the ones below may be of special interest in light of the current discussion of modern parallel computer architectures. ## Richard Feynman and the Connection Machine by way of lemonodor An entertaining article by Danny Hillis about Richard Feynman's work at Thinking Machines Corporation on the Connection Machine. We've mentioned the Connection Machine's data-parallel programming style on LtU before, and Connection Machine Lisp remains my all-time favourite paper in computer science. ## Functional programming with GNU make One of the gems squirreled away on Oleg's site is "Makefile as a functional language program": "The language of GNU make is indeed functional, complete with combinators (map and filter), applications and anonymous abstractions. That is correct, GNU make supports lambda-abstractions." Although I've classified this under Fun, Oleg exploits the functional nature of Make for a real, practical application: "...avoiding the explosion of makefile rules in a project that executes many test cases on many platforms. [...] Because GNU make turns out to be a functional programming system, we can reduce the number of rules from <number-of-targets> * <number-of-platforms> to just <number-of-targets> + <number-of-platforms>." See the article for a code comparison between make and Scheme, and check out the Makefile in question. ## What's up guys? So I am busy a couple of days, and not one editor manages to post something new? I am disappointed... Maybe it's time we recruited some more contributing editors. If you are a regular and want to join, let me know. ## Generics in Visual Basic 2005 You knew it couldn't be far behind, right? Defining and Using Generics in Visual Basic 2005 on MSDN has the details. ## New Chip Heralds a Parallel Future Missing no chance to stand on my soapbox about the need for easy PL retargeting, I bring you insights from Paul Murphy about our parallel-processing, Linux future. [T]he product has seen a billion dollars in development work. Two fabs...have been custom-built to make the new processor in large volumes....To the extent that performance information has become available, it is characterized by numbers so high that most people simply dismissed the reports.... The machine is widely referred to as a cell processor, but the cells involved are software, not hardware. Thus a cell is a kind of TCP packet on steroids, containing both data and instructions and linked back to the task of which it forms part via unique identifiers that facilitate results assembly just as the TCP sequence number does. The basic processor itself appears to be a PowerPC derivative with high-speed built-in local communications, high-speed access to local memory, and up to eight attached processing units broadly akin to the Altivec short array processor used by Apple. The actual product consists of one to eight of these on a chip -- a true grid-on-a-chip approach in which a four-way assembly can, when fully populated, consist of four core CPUs, 32 attached processing units and 512 MB of local memory. Paul follows up with a shocker. I'd like to make two outrageous predictions on this: first that it will happen early next year, and secondly that the Linux developer community will, virtually en masse, abandon the x86 in favor of the new machine. Abandonment is relative. The new processor will emulate x86 no problem, as Paul notes. In the PowerPC line, already today we have Linux for PowerPC complete with Mac OS X sandbox. From a PL standpoint, however, this development may cattle-prod language folks off their x86 back ends and into some serious compiler refactoring work. I hope so! ## Eric Gunnerson's JavaOne report This may be of interest to LtU readers. Most of the specific language features were discussed here previously, but the C# perspective may make this worth a look. ## Database Abstraction Layers and Programming Languages From time to time I like to return to the issue of database integration, only to once again remark that the difficulty in creating good database APIs (as opposed to simply embedding SQL) is the result of the poor programming facilities provided by most programming languages (e.g., no macros for syntax extension, no continuation or first class functions to handle control flow etc.). Why return to this topic today? Jeremy Zawodny aruges on his blog that Database Abstraction Layers Must Die! Along the way he says, Adding another layer increases complexity, degrades performance, and generally doesn't really improve things. So why do folks do it? Because PHP is also a programming language and they feel the need to "dumb it down" or insulate themselves (or others) from the "complexity" of PHP. Ouch! Why do we need an abstraction layer anyway? The author uses an argument I hear all the time: If you use a good abstraction layer, it'll be easy to move from$this_database to \$other_database down the road.
That's bullshit. It's never easy.
Double ouch, but true enough. Databases are like women (can't live with them, can't live without), and getting rid of one can be as painful as divorce...
So what's the solution? Surprise, surprise: use a libary. But isn't that an abstraction layer? Of course it is.
What Jeremy advocates is plain old software engineering and design. Everyone should do it. I can't beleive anyone does anything else.
But wait. I just told you it's hard to build such a library, since programming languages makes the design of such libraries hard (e.g., should you use iterators, cursors or return record buffers? should your library database access routine be as flexible as a select statement?) So we design libaries that aren't very good, but hopefully are good enough.
And that's the question I put before you. We all know about coupling and cohesion. We all know about building software abstractions. Are our tools for building abstractions powerful enough for this basic and standard abstraction: the database access abstraction layer? | 2018-05-21 17:22:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31894856691360474, "perplexity": 3022.260069981021}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864461.53/warc/CC-MAIN-20180521161639-20180521181639-00557.warc.gz"} |
https://chemistry.stackexchange.com/questions/14315/why-does-fusing-benzene-rings-not-produce-polycyclic-alkynes | # Why does fusing benzene rings not produce polycyclic alkynes?
It would make sense that when the benzene rings are fused they keep their pi bonds and form a polycyclic alkyne. However this is not the case.
My hypothesis is that because monocyclic alkynes at 8C or above are stable polycyclic alkynes would be even more stable and more stable with smaller rings than monocyclic alkynes.
However with 7 benzene rings fused in a hexagonal tiling type fashion the center ring has all single bonds like cyclohexane.
Why is it that fusing benzene or really any aromatic compound does not form polycyclic alkynes?
A resonance structure of this would be a polycyclic alkyne along with just the regular pi bond delocalization.
Bicyclo[4.4.0]deca-1,3,6,8,tetraene-4-yne is what I am thinking about. I am moving just the pi bonds in the resonance structure to get this. I am not moving actual carbon nuclei.
I can't find a picture of this but hopefully from the name you can figure it out.
• To have an alkyne in a ring, we would need to have two adjacent carbons that don't have a C-H bond. In naphthalene, if you break the central 9, 10 bond and preserve the outer ring, you don't have two such adjacent carbons without C-H bonds. Also, in resonance structures we can't move nuclei. Could you include a picture of the alkyne you had in mind? – ron Jul 26 '14 at 15:10
• See my edit and tell me where to but the 4 double and 1 triple bond. – ron Jul 26 '14 at 16:10
If a polycyclic aromatic compound were to ring open, an allene would be the initial, symmetry-allowed, ring-opened product instead of an alkyne.
I've built a Dreiding model of the bis-allene product derived from naphthalene and it does not appear to be particularly strained. I suspect the reason we do not see this process occurring is because the starting polycyclic aromatic is highly (resonance) stabilized, whereas the bis-allene product, while not strained, has no resonance stabilization due to the lack of pi-overlap in the cyclic structure due to the orthogonality imposed by the allene units. In other words, the activation energy would be too high and the reaction would not proceed. However, if we were to pass naphthalene through a tube furnace at very high temperature (this has been done), it would be interesting to see if any of the resultant products could be explained on the basis of the bis-allene intermediate.
EDIT Here's the bicyco[4.4.0] skeleton. Using these numbers tell me where you want the 4 double and 1 triple bond.
Ah, so this (the structure on the right) is what you mean! There are 2 issues with it
1. In this structure the bridgehead carbons each have 5 bonds, but carbon can only have 4 bonds (at least in compounds such as these) making this an unrealistic structure.
2. This structure has 12 pi electrons, whereas the starting naphthalene only had 10. Resonance structures involve the movement of electrons, there is no way to go from 10 pi electrons to 12 pi electrons while keeping all of the sigma bonds intact, so this is not a resonance structure for naphthalene.
• but a possible resonance structure of this is a polycyclic alkyne which would result in a monocyclic alkyne in the ring opening. Isn't it that if something is stable with 1 ring that multiple makes it even more stable and so polycyclic alkynes are more stable than monocyclic ones? – Caters Jul 26 '14 at 12:45
• If so than I still don't understand why aromaticity is more important in polycyclic compounds than stability of possible resonance structures(including ones with triple bonds) – Caters Jul 26 '14 at 12:47
• It would help me understand if you could edit your question and include a picture. – ron Jul 26 '14 at 13:44
• I want the triple bond between the bridgehead carbons and the double bonds at C's 2,4,7,and 9. This is what I thought you could get as a resonance structure of naphthalene without moving any carbon nuclei. – Caters Jul 26 '14 at 16:16
The ideal bond angles for alkynes are $180^{\circ}$, which is necessary for optimal overlap of atomic orbitals combining to produce mutually perpendicular $\pi$-type molecular orbitals. Any significant deviation from this is normally inherently destabilizing. Rings, by the very nature of their geometry, often incur additional strain due to their conformational inflexibility and possible demands for non-ideal bond angles (relative to acyclic molecules, that is). Introducing $\pi$-bonds into rings can potentially compound this problem, since they force at least local planarity and shorter bond lengths. These factors all contribute to the immense instability of cyclic alkynes in general.
When you mention stable cycloalkynes, keep in mind that stability is a relative term in this context. While those with a sufficient number of carbons can be produced and isolated under specific experimental conditions, they are not thermodynamically stable relative to their open-chain equivalents, or to most of their various possible structural isomers. In some cases, they can, however, be made kinetically stable by the addition of flanking $\alpha$-substituents which inhibit reaction by their steric bulk1.
Syntheses of cycloalkynes below cyclooctyne are often elaborate, and frequently proceed through extremely reactive intermediates that decompose by specific reaction pathways so as to carefully avoid other products. Benzene (and the various polycyclic aromatic hydrocarbons, for that matter), on the other hand, is an extremely stable molecule which participates in quite a limited collection of reactions. Whatever particular reaction you're suggesting would almost certainly be hugely uphill in energy (i.e., yields a significantly less stable product), and hence very thermodynamically disfavored; it would also certainly have immense kinetic barriers as well (since any such reaction pathway implies at least temporary loss of aromaticity in the transition state[s] and intermediate[s]).
Relevant reading might include Dehydrobenzene and Cycloalkynes by Reinhard W. Hoffmann. There is extensive discussion of the reactivity of cycloalkynes, and numerous examples of spontaneous dimerizations, isomerizations, etc. Evidently, isomerizations to cycloallenes and cyclobutadiene dimers are common, which is a profound testament to the instability of cycloalkynes.
1. For example, 3,3,7,7-tetramethylcycloheptyne, a good description of which (and synthetic scheme for) is given in Strained Hydrocarbons by Dodziuk. | 2021-04-19 19:00:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5628643035888672, "perplexity": 1764.2599946550647}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038916163.70/warc/CC-MAIN-20210419173508-20210419203508-00468.warc.gz"} |
https://research.iitj.ac.in/publication/multidirectional-gradient-adjusted-predictor | X
Multidirectional gradient adjusted predictor
V. Bajpai, D. Goyal, S. Debnath,
Published in
2010
Pages: 349 - 352
Abstract
In this paper we investigate the prediction scheme of Context Based Adaptive Lossless Image Coding (CALIC), the standard for lossless/near lossless image compression for continuous-tone finger-print images. We show that it is not sufficient to consider the prediction technique in a single direction for a fingerprint image as a whole for Gradient Adjusted Predictor (GAP). As a result, we propose an additional GAP scheme to achieve better speed and better prediction accuracy as and hence provide potential for further improvements in Lossless Image Compression. Experimental results indicate that the proposed scheme outperforms the existing GAP prediction for all the finger-print images tested, while the complexity of the prediction algorithm is improved by more than four times with the help of parallel implementation. ©2010 IEEE.
About the journal
Journal Proceedings of the 2010 International Conference on Signal and Image Processing, ICSIP 2010 | 2022-07-05 00:24:01 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8225758671760559, "perplexity": 1287.2023641998844}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104506762.79/warc/CC-MAIN-20220704232527-20220705022527-00180.warc.gz"} |
http://zbmath.org/?q=an:1172.35043 | # zbMATH — the first resource for mathematics
##### Examples
Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.
##### Operators
a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
On existence, uniform decay rates and blow up for solutions of the 2-D wave equation with exponential source. (English) Zbl 1172.35043
This paper is concerned with the study of the nonlinear damped wave equation
${u}_{tt}-{\Delta }u+h\left({u}_{t}\right)=g\left(u\right)\phantom{\rule{1.em}{0ex}}\text{in}\phantom{\rule{4.pt}{0ex}}{\Omega }×\right]0,\infty \left[,$
where ${\Omega }$ is a bounded domain of ${ℝ}^{2}$ having a smooth boundary $\partial {\Omega }={\Gamma }$. Assuming that $g$ is a function which admits an exponential growth at the infinity and, in addition, that $h$ is a monotonic continuous increasing function with polynomial growth at the infinity, the authors prove the global existence as well as blow up of solutions in finite time, by taking the initial data inside the potential well. Moreover, for global solutions, they also gave the optimal and uniform decay rates of the energy.
##### MSC:
35L70 Nonlinear second-order hyperbolic equations 35L20 Second order hyperbolic equations, boundary value problems 35B40 Asymptotic behavior of solutions of PDE
##### References:
[1] Aassila M., Cavalcanti M.M., Domingos Cavalcanti V.N.: Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term. Calc. Var. Partial Differ. Equ. 15(2), 155–180 (2002) · Zbl 1009.35055 · doi:10.1007/s005260100096 [2] Alves C.O., Figueiredo G.M.: Multiplicity of positive solutions for a quasilinear problem in ${ℝ}^{N}$ via Penalization Method equation in ${ℝ}^{N}$ . Adv. Nonlinear Stud. 5, 551–572 (2005) [3] Alabau-Boussouira F.: Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems. Appl. Math. Optim. 51(1), 61–105 (2005) · doi:10.1007/s00245 [4] Ambrosetti A., Rabinowitz P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349–381 (1973) · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7 [5] Barbu V., Lasiecka I., Rammaha A.M.: On nonlinear wave equations with degenerate damping and source terms. Trans. Am. Math. Soc. 357(7), 2571–2611 (2005) · Zbl 1065.35193 · doi:10.1090/S0002-9947-05-03880-8 [6] Brezis, H.: Opéteurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. (French) North-Holland Mathematics Studies, No. 5. Notas de Matemática (50). North-Holland Publishing Co., Amsterdam; American Elsevier Publishing Co., Inc., New York (1973) [7] Cavalcanti M.M., Domingos Cavalcanti V.N.: Existence and asymptotic stability for evolution problems on manifolds with damping and source terms. J. Math. Anal. Appl. 291(1), 109–127 (2004) · Zbl 1073.35168 · doi:10.1016/j.jmaa.2003.10.020 [8] Cavalcanti M., Domingos Cavalcanti V., Martinez P.: Existence and decay rate estimates for the wave equation with nonlinear boundary damping and source term. J. Differ. Equ. 203(1), 119–158 (2004) · Zbl 1049.35047 · doi:10.1016/j.jde.2004.04.011 [9] Cavalcanti M.M., Domingos Cavalcanti V.N., Lasiecka I.: Wellposedness and optimal decay rates for wave equation with nonlinear boundary damping–source interaction. J. Differ. Equ. 236(2), 407–459 (2007) · Zbl 1117.35048 · doi:10.1016/j.jde.2007.02.004 [10] Cavalcanti M.M., Domingos Cavalcanti V.N., Prates Filho J.S., Soriano J.A.: Existence and uniform decay of solutions of a parabolic-hyperbolic equation with nonlinear boundary damping and boundary source term. Commun. Anal. Geom. 10(3), 451–466 (2002) [11] Ebihara Y., Nakao M., Nambu T.: On the existence of global classical solution of initial boundary value proble for u” ${\Delta }$u u 3 = f. Pacific J. Math. 60, 63–70 (1975) [12] Esquivel-Avila J.: Qualitative analysis of nonlinear wave equation. Discrete Continuous Dyn. Syst. 10, 787–805 (2004) · Zbl 1047.35103 · doi:10.3934/dcds.2004.10.787 [13] de Figueiredo D.G., Miyagaki O.H., Ruf B.: Elliptic equations in IR 2 with nonlinearities in the critical growth range. Calc. Var 3, 139–153 (1995) · doi:10.1007/BF01205003 [14] Galaktionov V.A., Pohozaev S.I.: Blow-up and critical exponents for nonlinear hyperbolic equations. Nonlinear Anal. 53, 453–467 (2003) · Zbl 1012.35058 · doi:10.1016/S0362-546X(02)00311-5 [15] Georgiev V., Todorova G.: Existence of a solution of the wave equation with nonlinear damping and source terms. J. Differ. Equ. 109, 63–70 (1975) [16] Kaitai L., Quanda Z.: Existence and nonexistence of global solutions for the equation of dislocation of crystals. J. Differ. Equ. 146, 5–21 (1998) · Zbl 0926.35073 · doi:10.1006/jdeq.1998.3409 [17] Lasiecka I., Tataru D.: Uniform boundary stabilization of semilinear wave equation with nonlinear boundary damping. Differ. Integral Equ. 6, 507–533 (1993) [18] Levine H.A., Payne L.E.: Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porus medium equation backward in time. J. Differ. Equ. 16, 319–334 (1974) · Zbl 0285.35035 · doi:10.1016/0022-0396(74)90018-7 [19] Levine H.A., Serrin J.: Global nonexistence theorems for quasilinear evolutions equations with dissipation. Arch. Rational Mech. Anal. 137, 341–361 (1997) · Zbl 0886.35096 · doi:10.1007/s002050050032 [20] Levine H.A., Smith A.: A potential well theory for the wave equation with a nonlinear boundary condition. J. Reine Angew. Math. 374, 1–23 (1987) [21] Lions J.L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod, Paris (1969) [22] Lions, J.L., Magenes, E.: Problèmes Aux Limites Non Homogènes et Applications, vol. 1. Dunod, Paris (1968) [23] Ma T.F., Soriano J.A.: On weak solutions for an evolution equation with exponential nonlinearities. Nonlinear Anal. T. M. A. 37, 1029–1038 (1999) · Zbl 0940.35033 · doi:10.1016/S0362-546X(97)00714-1 [24] Moser J.: A sharp form of an inequality by Trudinger. Indiana Univ. Math. J. 20, 1077–1092 (1971) · Zbl 0213.13001 · doi:10.1512/iumj.1971.20.20101 [25] Mochizuki K., Motai T.: On energy decay problems for wave equations with nonlinear dissipation term in R n . J. Math. Soc. Japan 47, 405–421 (1995) · Zbl 0835.35093 · doi:10.2969/jmsj/04730405 [26] Pitts D.R., Rammaha M.A.: Global existence and non-existence theorems for nonlinear wave equations. Indiana Univ. Math. J. 51(6), 1479–1509 (2002) · Zbl 1060.35085 · doi:10.1512/iumj.2002.51.2215 [27] Rammaha M.A., Strei T.A.: Global existence and nonexistence for nonlinear wave equations with damping and source terms. Trans. Am. Math. Soc. 354(9), 3621–3637 (2002) · Zbl 1005.35067 · doi:10.1090/S0002-9947-02-03034-9 [28] Sattiger D.H.: On global solutions of nonlinear hyperbolic equations. Arch. Rat. Mech. Anal. 30, 148–172 (1968) [29] Serrin J., Todorova G., Vitillaro E.: Existence for a nonlinear wave equation with nonlinear damping and source terms. Differ. Integral Equ. 16(1), 13–50 (2003) [30] Todorova G., Vitillaro E.: Blow-up for nonlinear dissipative wave equations in ${ℝ}^{N}$ . J. Math. Anal. Appl. 303(1), 242–257 (2005) · Zbl 1065.35200 · doi:10.1016/j.jmaa.2004.08.039 [31] Todorova G.: Dynamics of non-linear wave equations. Math. Methods Appl. Sci. 27(15), 1831–1841 (2004) · Zbl 1065.35004 · doi:10.1002/mma.563 [32] Toundykov, D.: Optimal decay rates for solutions of nonlinear wave equation with localized nonlinear dissipation of unrestricted growth and critical exponents source terms under mixed boundary conditions. Nonlinear Anal. (2007) (in press) [33] Trudinger N.S.: On the imbeddings into Orlicz spaces and applications. J. Math. Mech. 17, 473–484 (1967) [34] Vitillaro E.: A potential well method for the wave equation with nonlinear source and boundary daming terms. Glasgow Math. J. 44, 375–395 (2002) · doi:10.1017/S0017089502030045 [35] Vitillaro E.: Some new results on global nonexistence and blow-up for evolution problems with positive initial energy. Rend. Istit. Mat. Univ. Trieste 31, 245–275 (2000) [36] Vitillaro E.: Global existence for the wave equation with nonlinear boundary damping and source terms. J. Differ Equ. 186, 259–298 (2002) · doi:10.1016/S0022-0396(02)00023-2 [37] Willem M.: Minimax Theorems. Birkhäuser, Basel (1996) | 2014-03-12 01:41:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 10, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5272892117500305, "perplexity": 5382.968924943198}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394020792760/warc/CC-MAIN-20140305115952-00020-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://klotza.blogspot.com/2016_05_01_archive.html | ## Tuesday, 24 May 2016
### Perturbative Champions: Cohen and Hansen take it to next-to-next-to-next-to-next-to-next-to-next-to-next-to-next-to leading order.
In 1999, in a preprint on arXiv.org, Thomas D. Cohen and James M. Hansen, physicists at the University of Maryland, claimed the following:
If one insists on an accuracy of ∼ 20%, one estimates contributions at their nominal order and Λ is taken to be 300 MeV, then one has to work to order (Q/Λ)$^7$ , this corresponds to next-to-next-to-next-to-next-to-next-to-next-to-next-to-next-to leading order.
This octet is, to my knowledge, the largest string of next-to's ever to appear in scientific literature. As far as I can tell, the runner up is a recent paper by Eltern et al. in Physical Review C, with a paltry five next-to's, although this may be the champion of peer-reviewed literature. Below this, four next-to's is fairly common; it has its own notation, N4LO. I found a reference to N6LO in the literature, but it becomes hard to google these.
What does this actually mean, and why does it sound so silly? A powerful tool in physics is perturbation theory, where we approximate the solution to a problem with a power series, and then compute first the simplest terms, then terms of increasing complexity until we have a solution that is close enough to the exact solution that it's useful to us. There will be the zeroth-order solution that tells us the order of magnitude, the first-order solution with its basic dependences on system parameters, then second and higher order solutions for non-linear effects. In many cases, certain powers will be zero, so the "leading order" term might be the first non-zero term besides zeroth-order, although not necessarily first order. For example, the leading order term of something that is perturbed about equilibrium is second-order (which is one of the reasons why treating things as harmonic oscillators is so useful). Feynman diagrams are essentially a way to express perturbation theory in a graphic form, first drawing interactions with no loops, then one loop, then two loops, etc.
Anyway, it may have been the case that all of the even and odd powers of the perturbation series in Cohen and Hansen's paper were zero, they couldn't just say "eighth order," but thought they had to expand all those next-to's. Each term makes the approximation more accurate, and for their 20% desired accuracy, they needed to compute all these Feynman diagrams really far past leading order, but unfortunately, as they claim, "it is implausible that such calculations will ever prove tractable."
Another, similar situation involves describing sites on a lattice. For example, if you're sitting at a site on a square lattice (with lattice constant x), you have four "nearest neighbors" at distance x from you, four "next-nearest neighbors" across the diagonals at distance $\sqrt{2}$x, "next-next-nearest neighbors at distance 2x, etc. This paper uses the term "next next next next nearest neighbors" which is designates 4NN.
There was perhaps a better way to visualize this.
These record nextings are fairly insignificant but perhaps mildly interesting.
## Tuesday, 17 May 2016
### Measuring Newton's Constant with a Space-Borne Gravity Train
I recently came across a paper which was published in Classical and Quantum Gravity, a respected journal, after it had initially appeared on arXiv. It proposes a space mission consisting of a metal sphere with a cylindrical hole, floating through space as a smaller reflective object oscillates back and forth along the hole, pulled by the gravitational field of the sphere. The position of the the smaller object can be monitored by another space probe, and the period of oscillation can be used to measure Newton's gravitational constant, big G. I like this idea, it draws upon some of my recent work and I place it firmly in the "just crazy enough to work" paper category, which are my favourite papers to read.
Diagram of the proposed experiment, from the arXiv version of the paper.
The proposal is motivated by some recent analysis (by some of the current proposal's authors) of independent measurements of the gravitational constant, which showed that even though they are measuring the constant with smaller and smaller uncertainty, the different measurements are not in precise agreement of each other, sometimes deviating by 40 times the standard error on the measurements. The analysis makes the bolder claim that the difference between the measurements has the same periodicity as Earth's length-of-day variations, which are due to large-scale seismic effects. They conclude that there are systematic effects caused by the fact that all these experiments (which typically involve monitoring a rotating pendulum near large masses) take place on the Earth, and desire a way to measure this constant away from the Earth. The National Science Foundation has put out a call for proposals for more accurately measuring big G; I recommend reading its three paragraphs if you're wondering why anyone would bother caring about this.
The various non-agreeing measurements of G over the years, from Anderson et al. Pay more attention to the red than the black. The black is the "bold proposal" I mentioned.
To make this measurement, the authors, lead by independent researcher Michael Feldman, suggest sending a miniature gravity train into space. A gravity train, something I have written about in great detail, consists of a spherical mass (often taken to be the Earth, but not here) with a tunnel through it (often through its center), with a smaller object falling through the hole. It builds up speed due to gravitational attraction to the sphere, passes the halfway point, and then starts decelerating, coming to a rest on the other side. Inside the Earth, it would take 38 minutes to fall through this tunnel. Feldman and friends propose a small metal sphere, roughly 10 cm in diameter and 1.3 kg in mass, that would take about two hours for the small object to fall through.
How could G be measured from such a device? For a uniform density sphere, it can be shown that the period of a gravity train is $T=2\pi\sqrt{\frac{R^3}{MG}}$. If the mass and radius are known, and the time is measured, G can be extracted. In the proposed setup, the position of the small object will be monitored by a laser aimed at the tunnel from another nearby space probe, and from these periodic measurements of position, the time can be measured, and sent back to Earth by an antenna on the probe. The paper consists of more detailed derivations of the G-T measurement, unique to the proposed design (which consists of two layers of different materials).
Zoomed out schematic of the probe and sphere, from the arXiv version of the paper.
The authors are concerned with the precision of such a device, and which systematic errors contribute to the overall uncertainty in G. These include the metallurgy of the sphere and hole (uncertainties in R, M, and the uniformity thereof), the initial placement of the small reflecting object in the hole (which must be extremely gentle), the ideal place to position sphere with respect to the host probe so that the probe is close enough to block the sun but not so close that its own gravity affects the experiment, the radiation pressure from the probe laser on the device, deformations of the sphere due to the tidal influence of the sun, possible charging of the tunnel's interior due to cosmic rays, and more. They even calculate the change in the period if general relativity is taken into account, which is something I was curious about for my gravity tunnel research, but didn't have the tools to solve. The hypothetical uncertainty analysis was probably the most fun part of the paper to read.
They estimate that, given advances in metallurgy and aerospace deftness, they can get the precision of the G measurement down to an optimistic 63 parts per billion. The current record for Earth-based G measurements is 13,000 parts per billion. This would be a huge improvement if it actually worked, and would eliminate some of the systematic issues with measuring the strength of gravity in Earth's gravitational field.
The question, of course, is whether this thing will actually exist, and whether the budgetary will exists to make it so. The authors suggest that the experiment would not be the main mission payload of a space launch, but rather would piggyback on a larger, more important probe headed out of the solar system.
I was interested in this paper because I like crazy yet scientifically rigorous ideas, and it draws upon a system that is close to my scientific heart [disclaimer: the paper cites mine]. It was a pleasure to read about all the potential effects that could skew the time measurement, and how they planned to deal with them. I hope the available metallurgy, metrology, and money becomes sufficient to launch this thing into space.
## Monday, 16 May 2016
### PhysicsForums: The Interaction of Sound and Light
My last post about sound propagating through light inspired me to write about the more conventional interactions between sound and light. Read about it on physicsforums.com.
https://www.physicsforums.com/insights/interaction-sound-light/
## Monday, 9 May 2016
### The Speed of Sound in Light
This post will discuss something that I think is interesting, and wanted to think more about: the propagation of sound through light. One can show that the speed of sound in light is 57% the speed of light. I will talk about what the hell that actually means, and where that number comes from.
Sound in light?
Sound in light? Huh?
The first thing one must wrap their head around is: what does it mean for sound to propagate through light? I devised a simple thought experiment to help me understand that.
Imagine two mirrors with springs on their backs, facing each other with light propagating between them. You can either imagine this as photons bouncing back and forth, or a standing electromagnetic wave. The mirrors are in mechanical equilibrium: the radiation pressure from the light reflecting off them is balanced by compression of the springs holding the mirrors in place.
Two mirrors with a standing electromagnetic wave between them. Springs balance the radiation pressure, but if one mirror is moved, the induced Doppler shift will increase the radiation pressure on the opposite mirror, causing that spring to compress. This is my first foray into hand-drawn diagrams...sorry if it's terrible.
Now imagine you boop one of the mirrors, pushing it towards the other one. As light reflects off this mirror, it will be blue-shifted from the perspective of the other mirror. This blue-shifting will increase the magnitude of the radiation pressure, pushing the mirror back and compressing the spring a bit more. In a sense, pushing the first mirror caused an acoustic signal to propagate through the light to the other. The mirrors are both now in simple harmonic motion, coupled by the transfer of radiation overpressure and underpressure through blueshifting and redshifting as the mirrors move.
This scenario can be extended further, to an array of two-sided mirrors in an optical cavity, springs only on the mirrors on the end. Booping one end mirror would cause this blueshift-induced radiation overpressure to propagate down the line of mirrors. As the last mirror compresses the spring and rebounds, the wave will reverse direction.
The way I am picturing this scenario, the signal propagates through the light at the speed of light: as soon as you blueshift the first photon, it's already heading towards the other mirror at the speed of light.
The speed of sound in a photon gas
The scenario above envisioned light in mechanical equilibrium with mirrors. But what if it is also in thermal equilibrium? Now in this thought experiment, we have a box with mirrors on the inside, that is really hot (students of physics may recognize this as the canonical example of a blackbody). The mirrors are so hot that they start emitting blackbody radiation, which is reflected (or absorbed and re-emitted, depending on how you think about it) by the other mirrors in the box. Now what happens if you push on one side of the box?
Left. A really crappy depiction I made of a photon gas: a mirrored box with really hot walls, with radiation bouncing around in the box. Right. The best online depiction I found on google images, from photonics.com.
The way I am picturing the situation, basically the same thing happens but not deterministically: the blackbody radiation from the mirror you push on gets blueshifted, increasing the radiation pressure felt on the opposite side. However, the radiation is emitted isotropically from the surface, and some of it goes off on an angle and reaches the side walls, and the radiation pressure excess from the boop gradually propagates towards the other side. So instead of just one c-retarded propagation from side to the other, there is a distribution in the arrival time of the mechanical information. I suppose the same thing happens when we push on one side of a box full of gas, and because there are so many gas molecules, the sound propagation is effectively deterministic.
At this point I have exhausted my ability to picture what would happen, and will examine a more rigorous argument. The speed of sound in a photon gas can be derived from its thermodynamic equation of state and associated equipartition theorem, which is basically similar to the ideal gas law, except it is derived by assuming that all the particles are going so fast that they are effectively massless (in that the lion's share of their energy is kinetic). The main difference between the regular and relativistic results is that for slow particles like atoms in a gas, the equipartition tells us that the average kinetic energy is 3/2 kT per atom, whereas in the relativistic case is is 3kT. This is basically because you're writing down the energy as pc instead of 1/2mv$^{2}$=$\frac{p^2}{2m}$, so there's no factor of two. There are some more involved derivations to get the number of photons and calculate the pressure based on the temperature, which essentially involve integrating the Planck spectrum over all frequencies (similar to the derivation of the Stefan-Boltzmann law). This is not necessary here.
To find the speed of sound in a gas we want the ratio of pressure to density:
$v^{2}=\frac{P}{\rho}$.
And from the photon gas equation of state we have a relationship between pressure and internal energy.
U=3PV
With a bit of relativity we can relate the regular density to the energy density by dividing it by $c^2$:
$\rho=\frac{1}{c^2}\frac{U}{V}=\frac{3P}{c^2}$
Plugging this back into the equation or the velocity, we have:
$v^{2}=P\frac{c^2}{3P}=\frac{c^2}{3}$.
Thus, we find that the speed of sound through a photon gas is one-over-root-three, or 57%, the speed of light. Notice that the factor of three comes from the number of dimensions used in the equipartition theorem. In one dimension, which my initial mirror scenario took place in, the speed of sound in light is the same as the speed of light itself.
Photon-Photon Interactions
In the above discussions, the "sound waves" are essentially just signals of increased radiation pressure that are transmitted through Doppler shifts. However, at high-enough energy densities, you can start to have the light interacting with itself, via electron-positron pairs that are produced from the vacuum. This self-interaction of light causes a slight slowdown in the speed. It is derived from quantum electrodynamics by Partovi here, and he derives a correction to the speed that depends on the fourth power of the ratio of the temperature of the blackbody to the temperature-equivalent of the electron mass, 5.9 gigakelvin (511 keV divided by Boltzmann's constant). The correction to the velocity is of order 10$^-5$ even at gigakelvin temperatures:
This equation copied from Partovi's paper.
With this in mind, I can picture poking one side of a hot mirror box and expecting a small delay before the other side of the hot mirror box gets jolted.
The Relativistic Sound Speed in Astrophysics
This idea is neat, but is it important? This photon gas sound speed comes up in a few other places. The main one is baryon acoustic oscillations, sound waves through the very early universe that dictated the large-scale structure of the cosmos as the universe cooled down, still present in the periodic distribution of galaxy clusters. The very early universe was very hot, so there was a high energy photon gas just from thermal equilibrium, and all the massive particles zipzapping around were also highly relativistic. Thus, the speed associated with these baryon acoustic oscillations is that relativistic 0.57c.
A telescope attempting to measure Baryon Acoustic Oscillations, from BNL.gov
Another question that arises is whether this is the absolute maximum for sound speed propagation. As I demonstrated in my thought experiment, one-dimensional coherent systems can exceed it, but what about in thermodynamic systems? A paper in Physical Review Letters last year argues that certain models of neutron star interiors may predict sound speeds that exceed this limit. There is a lot that is unknown about neutron star interiors, and many models put constraints on the maximum and minimum sizes of neutron stars. These models then get selectively ruled out by newer neutron star discoveries. Bedaque and Steiner argue that given the available models and certain observations of particularly small neutron stars, the speed of sound inside some neutron stars must exceed 0.57c. Unfortunately I don't really understand enough of their analysis to say anything for insightful. Alternately, if this 0.57c is the true upper limit, it will rule out a lot of these models.
To summarize, I think that the idea of a speed of sound in light is a cool idea (this is how most of my blog posts end). I make it make sense to me using a thought experiment involving radiation pressure and Doppler shifting. For a more complete understanding, we go to photon gas thermodynamics and QED. There is one point where my research experience touches upon this concept: my undergraduate thesis in general relativity, the first independent physics research I conducted, involved finding fluid mass distributions that solve Einstein's equations. These mass distributions then had to satisfy certain conditions to make them physically realistic: mass couldn't be negative, density had to always decrease with radius, I wanted to avoid singularities, etc, but I also required that the speed of sound not exceed the speed of light. This extended the previous work of my supervisor Kayll Lake, who showed that many existing solutions to Einstein's equations violated these conditions. I wonder if anything would change if we demanded that v<0.57 c instead of v<c. | 2017-09-24 08:43:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6568925380706787, "perplexity": 519.1477389437403}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689900.91/warc/CC-MAIN-20170924081752-20170924101752-00111.warc.gz"} |
https://zbmath.org/authors/?q=ai%3Arockafellar.ralph-tyrrell | # zbMATH — the first resource for mathematics
## Rockafellar, Ralph Tyrrell
Compute Distance To:
Author ID: rockafellar.ralph-tyrrell Published as: Rockafellar, R.; Rockafellar, R. T.; Rockafellar, R. Terry; Rockafellar, R. Tyrrell; Rockafellar, Ralph Tyrrell; Rockafellar, Terry; Rockafellar, Tyrrell; Rockafellar, Tyrrell R. Homepage: https://sites.math.washington.edu/~rtr/mypage.html External Links: MGP · Wikidata · GND
Documents Indexed: 230 Publications since 1964, including 13 Books Biographic References: 4 Publications
all top 5
#### Co-Authors
124 single-authored 27 Wets, Roger Jean-Baptiste 15 Dontchev, Asen L. 11 Poliquin, René A. 5 Jofré, Alejandro 5 Levy, Adam B. 5 Uryasev, Stan 4 Loewen, Philip D. 4 Royset, Johannes O. 3 Goebel, Rafal 3 King, Alan J. 3 Lau, Anthony To-Ming 3 Mordukhovich, Boris S. 3 Sun, Jie 3 Takahashi, Wataru 3 Tanaka, Tamaki 3 Théra, Michel A. 3 Zabarankin, Michael 2 Dermody, James Cuevas 2 Hoàng Xuân Phù 2 Huynh Van Ngai 2 Maisonneuve, Olivier 2 Patriksson, Michael 2 Wolenski, Peter R. 2 Xu, Hong-Kun 1 Alart, Pierre 1 Asplund, Edgar 1 Beer, Gerald Alan 1 Benavides, T. D. 1 Brøndsted, Arne 1 Chen, George H-G. 1 Eberhard, Andrew S. 1 Eve, R. A. 1 Gale, David 1 Ioffe, Alexander Davidovich 1 Kim, Do Sang 1 Klee, Victor LaRue 1 Krastanov, Mikhail Ivanov 1 Kripke, Bernard R. 1 Lewis, Adrian S. 1 Llorens-Fuster, Enrique 1 López Acedo, Genaro 1 Miranda, S. I. 1 Nghia, Tran T. A. 1 Pennanen, Teemu 1 Reddy, B. Dayanand 1 Sarabi, M. Ebrahim 1 Somlyódy, László 1 Spingarn, Jonathan E. 1 Thibault, Lionel 1 Tsyurmasto, Peter 1 Uryasev, Stanislav P. 1 Valadier, Michel 1 Veliov, Vladimir M. 1 Veremyev, Alexander 1 Nguyen Dong Yen 1 Zagrodny, Dariusz 1 Zhu, Ciyou
all top 5
#### Serials
13 SIAM Journal on Control and Optimization 12 Transactions of the American Mathematical Society 12 Mathematical Programming. Series A. Series B 10 SIAM Journal on Optimization 9 Mathematics of Operations Research 9 Pacific Journal of Mathematics 5 Journal of Mathematical Analysis and Applications 5 Journal of Convex Analysis 5 Journal of Nonlinear and Convex Analysis 5 Nonlinear Analysis. Theory, Methods & Applications 4 Journal of Optimization Theory and Applications 4 Proceedings of the American Mathematical Society 4 Set-Valued Analysis 4 Vietnam Journal of Mathematics 3 Canadian Journal of Mathematics 3 Mathematical Programming Study 3 Set-Valued and Variational Analysis 2 Stochastics 2 Control and Cybernetics 2 Duke Mathematical Journal 2 Journal of Economic Theory 2 Mathematical Programming 2 Mathematica Scandinavica 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Annals of Operations Research 2 Mathematical Finance 2 Bulletin of the American Mathematical Society 2 SIAM Journal on Control 1 Advances in Mathematics 1 Journal of Computational and Applied Mathematics 1 Journal of Mathematical Economics 1 Mathematische Annalen 1 The Mathematics Student 1 Memoirs of the American Mathematical Society 1 Michigan Mathematical Journal 1 Proceedings of the London Mathematical Society. Third Series 1 Quarterly of Applied Mathematics 1 Applied Stochastic Models and Data Analysis 1 Transportation Science 1 Journal of Global Optimization 1 European Journal of Operational Research 1 SIAM Review 1 Computational Optimization and Applications 1 Calculus of Variations and Partial Differential Equations 1 Economic Theory 1 Finance and Stochastics 1 Computational Management Science 1 Journal of Mathematics and Mechanics 1 Journal of the Society for Industrial & Applied Mathematics 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 Grundlehren der Mathematischen Wissenschaften 1 Advances in Mechanics and Mathematics 1 Applied and Computational Mathematics 1 Matapli 1 Springer Monographs in Mathematics 1 Springer Series in Operations Research and Financial Engineering 1 Research and Education in Mathematics
all top 5
#### Fields
142 Operations research, mathematical programming (90-XX) 123 Calculus of variations and optimal control; optimization (49-XX) 23 Real functions (26-XX) 23 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 19 Operator theory (47-XX) 17 Global analysis, analysis on manifolds (58-XX) 15 Systems theory; control (93-XX) 14 Numerical analysis (65-XX) 7 Functional analysis (46-XX) 7 Convex and discrete geometry (52-XX) 6 General and overarching topics; collections (00-XX) 6 Measure and integration (28-XX) 6 General topology (54-XX) 3 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Approximations and expansions (41-XX) 2 Probability theory and stochastic processes (60-XX) 2 Mechanics of deformable solids (74-XX) 1 Combinatorics (05-XX) 1 Partial differential equations (35-XX) 1 Statistics (62-XX) 1 Biology and other natural sciences (92-XX)
#### Citations contained in zbMATH
208 Publications have been cited 19,156 times in 12,549 Documents Cited by Year
Convex analysis. Zbl 0193.18401
Rockafellar, R. Tyrrell
1970
Variational analysis. Zbl 0888.49001
Rockafellar, R. Tyrrell; Wets, Roger J.-B.
1998
Monotone operators and the proximal point algorithm. Zbl 0358.90053
Rockafellar, R. Tyrrell
1976
Conjugate convex functions in nonlinear programming. Zbl 0229.90020
Rockafellar, R. T.
1970
Convex analysis. Zbl 0932.90001
Rockafellar, R. Tyrrell
1997
Convex functions, monotone operators and variational inequalities. Zbl 0202.14303
Rockafellar, R. T.
1970
On the maximality of sums of nonlinear monotone operators. Zbl 0222.47017
Rockafellar, R. T.
1970
Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Zbl 0402.90076
Rockafellar, R. T.
1976
State constraints in convex control problems of Bolza. Zbl 0224.49003
Rockafellar, R. T.
1972
Conjugate duality and optimization. Zbl 0296.90036
Rockafellar, R. Tyrrell
1974
On the maximal monotonicity of subdifferential mappings. Zbl 0199.47101
Rockafellar, R. T.
1970
Implicit functions and solution mappings. A view from variational analysis. Zbl 1178.26001
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2009
Scenarios and policy aggregation in optimization under uncertainty. Zbl 0729.90067
Rockafellar, R. T.; Wets, Roger J.-B.
1991
Generalized directional derivatives and subgradients of nonconvex functions. Zbl 0447.49009
Rockafellar, R. T.
1980
Local differentiability of distance functions. Zbl 0960.49018
Poliquin, R. A.; Rockafellar, R. T.; Thibault, L.
2000
Characterization of the subdifferentials of convex functions. Zbl 0145.15901
Rockafellar, R. T.
1966
Integrals which are convex functionals. Zbl 0159.43804
Rockafellar, R. T.
1968
Network flows and monotropic optimization. Zbl 0596.90055
Rockafellar, R. T.
1984
Generalized deviations in risk analysis. Zbl 1150.90006
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
The theory of subgradients and its applications to problems of optimization. Convex and nonconvex functions. Zbl 0462.90052
Rockafellar, R. T.
1981
Characterizations of strong regularity for variational inequalities over polyhedral convex sets. Zbl 0899.49004
Dontchev, A. L.; Rockafellar, R. T.
1996
Directionally Lipschitzian functions and subdifferential calculus. Zbl 0413.49015
Rockafellar, R. T.
1979
Integrals which are convex functionals. II. Zbl 0236.46031
Rockafellar, R. T.
1971
On the subdifferentiability of convex functions. Zbl 0141.11801
Brøndsted, Arne; Rockafellar, R. T.
1965
Augmented Lagrange multiplier functions and duality in nonconvex programming. Zbl 0257.90046
Rockafellar, R. Tyrrell
1974
Convex functions and duality in optimization problems and dynamics. Zbl 0186.23901
Rockafellar, R. T.
1969
The multiplier method of Hestenes and Powell applied to convex programming. Zbl 0254.90045
Rockafellar, R. T.
1973
Clarke’s tangent cones and the boundaries of closed sets in $$\mathbb{R}^n$$. Zbl 0443.26010
Rockafellar, R. T.
1979
Integral functionals, normal integrands and measurable selections. Zbl 0374.49001
Rockafellar, Tyrrell
1976
Prox-regular functions in variational analysis. Zbl 0861.49015
Poliquin, R. A.; Rockafellar, R. T.
1996
Lagrange multipliers and optimality. Zbl 0779.49024
Rockafellar, R. Tyrrell
1993
Lipschitzian properties of multifunctions. Zbl 0573.54011
Rockafellar, R. Tyrrell
1985
Duality and stability in extremum problems involving convex functions. Zbl 0154.44902
Rockafellar, R. T.
1967
A dual approach to solving nonlinear programming problems by unconstrained optimization. Zbl 0279.90035
Rockafellar, R. Tyrrell
1973
Implicit functions and solution mappings. A view from variational analysis. 2nd updated ed. Zbl 1337.26003
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2014
Regularity and conditioning of solution mappings in variational analysis. Zbl 1046.49021
Dontchev, A. L.; Rockafellar, R. T.
2004
Local boundedness of nonlinear, monotone operators. Zbl 0175.45002
Rockafellar, R. T.
1969
The radius of metric regularity. Zbl 1042.49026
Dontchev, A. L.; Lewis, A. S.; Rockafellar, R. T.
2003
First- and second-order epi-differentiability in nonlinear programming. Zbl 0655.49010
Rockafellar, R. T.
1988
Extension of Fenchel’s duality theorem for convex functions. Zbl 0138.09301
Rockafellar, R. T.
1966
Measurable dependence of convex sets and functions on parameters. Zbl 0202.33804
Rockafellar, R. T.
1969
Conjugate convex functions in optimal control and the calculus of variations. Zbl 0218.49004
Rockafellar, R. T.
1970
Proto-differentiability of set-valued mappings and its applications in optimization. Zbl 0674.90082
Rockafellar, R. T.
1989
Tilt stability of a local minimum. Zbl 0918.49016
Poliquin, R. A.; Rockafellar, R. T.
1998
Gradients of convex functions. Zbl 0181.41901
Asplund, E.; Rockafellar, R. T.
1969
Level sets and continuity of conjugate convex functions. Zbl 0145.15802
Rockafellar, R. T.
1966
Convergence rates in forward–backward splitting. Zbl 0876.49009
Chen, George H-G.; Rockafellar, R. T.
1997
Equivalent subgradient versions of Hamiltonian and Euler-Lagrange equations in variational analysis. Zbl 0878.49012
Rockafellar, R. Tyrrell
1996
Saddle-points and convex analysis. Zbl 0242.90044
Rockafellar, Tyrrell
1971
Second-order optimality conditions in nonlinear programming obtained by way of epi-derivatives. Zbl 0698.90070
Rockafellar, R. Tyrrell
1989
Saddle points of Hamiltonian systems in convex Lagrange problems having a nonzero discount rate. Zbl 0333.90007
Rockafellar, R. Tyrrell
1976
Optimality conditions in portfolio analysis with general deviation measures. Zbl 1138.91474
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
Proximal subgradients, marginal values, and augmented Lagrangians in nonconvex optimization. Zbl 0492.90073
Rockafellar, R. T.
1981
Second-order subdifferential calculus with applications to tilt stability in optimization. Zbl 1260.49022
Mordukhovich, B. S.; Rockafellar, R. T.
2012
Extensions of subgradient calculus with applications to optimization. Zbl 0593.49013
Rockafellar, R. T.
1985
Stability of locally optimal solutions. Zbl 0965.49018
Levy, A. B.; Poliquin, R. A.; Rockafellar, R. T.
2000
Existence theorems for general control problems of Bolza and Lagrange. Zbl 0319.49001
Rockafellar, Tyrrell R.
1975
Monotone processes of convex and concave type. Zbl 0189.19602
Rockafellar, R. Tyrrell
1967
Convex integral functionals and duality. Zbl 0326.49008
Rockafellar, R. T.
1974
Asymptotic theory for solutions in statistical estimation and stochastic programming. Zbl 0798.90115
King, Alan J.; Rockafellar, Tyrrell
1993
Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming. Zbl 0478.90060
Rockafellar, R. T.
1982
Robinson’s implicit function theorem and its extensions. Zbl 1172.49013
Dontchev, A. L.; Rockafellar, R. T.
2009
Existence and duality theorems for convex problems of Bolza. Zbl 0255.49007
Rockafellar, R. T.
1971
Sensitivity analysis for nonsmooth generalized equations. Zbl 0766.90075
King, Alan J.; Rockafellar, R. Tyrrell
1992
Convex analysis. (Vypuklyi analiz.) Übersetzung aus dem Englischen von A. D. Ioffe und V. M. Tihomirov. Zbl 0251.90035
Rockafellar, R. Tyrrell
1973
A Lagrangian finite generation technique for solving linear-quadratic problems in stochastic programming. Zbl 0599.90090
Rockafellar, R. T.; Wets, R. J.-B.
1986
Favorable classes of Lipschitz-continuous functions in subgradient optimization. Zbl 0511.26009
Rockafellar, R. Tyrrell
1982
Optimal control of unbounded differential inclusions. Zbl 0823.49016
Loewen, Philip D.; Rockafellar, R. T.
1994
Maximal monotone relations and the second derivatives of nonsmooth functions. Zbl 0581.49009
Rockafellar, R. T.
1985
Directional differentiability of the optimal value function in a nonlinear programming problem. Zbl 0546.90088
Rockafellar, R. T.
1984
Saddle points of Hamiltonian systems in convex problems of Lagrange. Zbl 0248.49016
Rockafellar, R. T.
1973
Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time. Zbl 0714.49036
Rockafellar, R. T.; Wets, R. J.-B.
1990
A derivative-coderivative inclusion in second-order nonsmooth analysis. Zbl 0897.49014
Rockafellar, R. T.; Zagrodny, D.
1997
Variational inequalities and economic equilibrium. Zbl 1276.91070
Jofré, Alejandro; Rockafellar, R. Terry; Wets, Roger J.-B.
2007
Linear-quadratic programming and optimal control. Zbl 0617.49010
Rockafellar, R. T.
1987
Characterizations of full stability in constrained optimization. Zbl 1284.49032
Mordukhovich, B. S.; Rockafellar, R. T.; Sarabi, M. E.
2013
The optimal recourse problem in discrete time: $$L^1$$-multipliers for inequality constraints. Zbl 0397.90078
Rockafellar, R. T.; Wets, R. J-B.
1978
Stochastic convex programming: Relatively complete recourse and induced feasibility. Zbl 0346.90058
Rockafellar, R. T.; Wets, R. J.-B.
1976
Some convex programs whose duals are linearly constrained. Zbl 0252.90046
Rockafellar, R. Tyrrell
1970
A general correspondence between dual minimax problems and convex programs. Zbl 0162.23103
Rockafellar, R. T.
1968
Generalized second derivatives of convex functions and saddle functions. Zbl 0712.49011
Rockafellar, R. T.
1990
Computational schemes for large-scale problems in extended linear- quadratic programming. Zbl 0735.90050
Rockafellar, R. T.
1990
Generalized Hamiltonian equations for convex problems of Lagrange. Zbl 0199.43002
Rockafellar, R. T.
1970
Convex integral functionals and duality. Zbl 0295.49006
Rockafellar, R. Tyrrell
1971
Sensitivity analysis of solutions to generalized equations. Zbl 0815.47077
Levy, A. B.; Rockafellar, R. T.
1994
Stochastic variational inequalities: single-stage to multistage. Zbl 1378.49010
Rockafellar, R. Tyrrell; Wets, Roger J-B
2017
Second derivatives in convex analysis. Zbl 1003.49017
Rockafellar, R. T.
1999
Conditional value-at-risk: optimization approach. Zbl 0989.91052
Uryasev, Stanislav; Rockafellar, R. Tyrrell
2001
The Euler and Weierstrass conditions for nonsmooth variational problems. Zbl 0838.49015
Ioffe, A. D.; Rockafellar, R. T.
1996
On the interchange of subdifferentiation and conditional expectation for convex functionals. Zbl 0487.49006
Rockafellar, R. T.; Wets, R. J. B.
1982
Stochastic convex programming: basic duality. Zbl 0339.90048
Rockafellar, R. T.; Wets, R. J.-B.
1976
On the virtual convexity of the domain and range of a nonlinear maximal monotone operator. Zbl 0181.42202
Rockafellar, R. T.
1970
Full stability in finite-dimensional optimization. Zbl 1308.90126
Mordukhovich, B. S.; Nghia, T. T. A.; Rockafellar, R. T.
2015
Generalized Hessian properties of regularized nonsmooth functions. Zbl 0863.49010
Poliquin, R. A.; Rockafellar, R. T.
1996
An internal variable theory of elastoplasticity based on the maximum plastic work inequality. Zbl 0693.73008
Eve, R. A.; Reddy, B. D.; Rockafellar, R. T.
1990
La théorie des sous-gradients et ses applications à l’optimisation. Fonctions convexes et non convexes. Zbl 0421.90045
Rockafellar, R. Tyrrell
1979
Nonanticipativity and $$\mathcal L^1$$-martingales in stochastic optimization problems. Zbl 0377.90073
Rockafellar, R. T.; Wets, R. J.-B.
1976
Newton’s method for generalized equations: a sequential implicit function theorem. Zbl 1190.49024
Dontchev, A. L.; Rockafellar, R. T.
2010
Convex functions on convex polytopes. Zbl 0246.26009
Gale, David; Klee, Victor; Rockafellar, R. T.
1968
A characterization of epi-convergence in terms of convergence of level sets. Zbl 0769.49011
Beer, Gerald; Rockafellar, R. T.; Wets, Roger J.-B.
1992
Solving Lagrangian variational inequalities with applications to stochastic programming. Zbl 1445.90069
Rockafellar, R. Tyrrell; Sun, Jie
2020
Solving monotone stochastic variational inequalities and complementarity problems by progressive hedging. Zbl 1421.90100
Rockafellar, R. Tyrrell; Sun, Jie
2019
Variational convexity and the local monotonicity of subgradient mappings. Zbl 1428.49021
Rockafellar, R. Tyrrell
2019
Progressive decoupling of linkages in optimization and variational inequalities with elicitable convexity or monotonicity. Zbl 07146007
Rockafellar, R. Tyrrell
2019
Superquantile/CVaR risk measures: second-order theory. Zbl 1391.91163
Rockafellar, R. Tyrrell; Royset, Johannes O.
2018
Solving stochastic programming problems with risk measures by progressive hedging. Zbl 1416.90027
Rockafellar, R. Tyrrell
2018
Variational analysis of Nash equilibrium. Zbl 1407.91022
Rockafellar, R. Tyrrell
2018
Stochastic variational inequalities: single-stage to multistage. Zbl 1378.49010
Rockafellar, R. Tyrrell; Wets, Roger J-B
2017
General economic equilibrium with financial markets and retainability. Zbl 1405.91742
Jofré, A.; Rockafellar, R. T.; Wets, R. J-B.
2017
Full stability in finite-dimensional optimization. Zbl 1308.90126
Mordukhovich, B. S.; Nghia, T. T. A.; Rockafellar, R. T.
2015
Measures of residual risk with connections to regression, risk tracking, surrogate models, and ambiguity. Zbl 1316.91016
Rockafellar, R. Tyrrell; Royset, Johannes O.
2015
Implicit functions and solution mappings. A view from variational analysis. 2nd updated ed. Zbl 1337.26003
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2014
Random variables, monotone relations, and convex analysis. Zbl 1330.60009
Rockafellar, R. T.; Royset, J. O.
2014
Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk. Zbl 1305.62175
Rockafellar, R. T.; Royset, J. O.; Miranda, S. I.
2014
Convex analysis and financial equilibrium. Zbl 1309.91086
Jofré, A.; Rockafellar, R. T.; Wets, R. J.-B.
2014
Characterizations of full stability in constrained optimization. Zbl 1284.49032
Mordukhovich, B. S.; Rockafellar, R. T.; Sarabi, M. E.
2013
Convergence of inexact Newton methods for generalized equations. Zbl 1272.49047
Dontchev, A. L.; Rockafellar, R. T.
2013
An Euler-Newton continuation method for tracking solution trajectories of parametric variational inequalities. Zbl 1272.49012
Dontchev, A. L.; Krastanov, M. I.; Rockafellar, R. T.; Veliov, V. M.
2013
Second-order subdifferential calculus with applications to tilt stability in optimization. Zbl 1260.49022
Mordukhovich, B. S.; Rockafellar, R. T.
2012
Parametric stability of solutions in models of economic equilibrium. Zbl 1256.49021
Dontchev, Asen L.; Rockafellar, Ralph Tyrrell
2012
A time-embedded approach to economic equilibrium with incomplete financial markets. Zbl 1216.91041
Jofré, A.; Rockafellar, R. T.; Wets, R. J.-B.
2011
Newton’s method for generalized equations: a sequential implicit function theorem. Zbl 1190.49024
Dontchev, A. L.; Rockafellar, R. T.
2010
A calculus of prox-regularity. Zbl 1194.49049
Poliquin, R. A.; Rockafellar, R. T.
2010
Implicit functions and solution mappings. A view from variational analysis. Zbl 1178.26001
Dontchev, Asen L.; Rockafellar, R. Tyrrell
2009
Robinson’s implicit function theorem and its extensions. Zbl 1172.49013
Dontchev, A. L.; Rockafellar, R. T.
2009
Hamiltonian trajectories and saddle points in mathematical economics. Zbl 1235.91131
Rockafellar, R.
2009
Risk tuning with generalized linear regression. Zbl 1218.90158
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2008
Local strong convexity and local Lipschitz continuity of the gradient of convex functions. Zbl 1149.26022
Goebel, Rafal; Rockafellar, Ralph Tyrrell
2008
Linear-convex control and duality. Zbl 1206.49036
Rockafellar, R. T.; Goebel, R.
2008
Variational inequalities and economic equilibrium. Zbl 1276.91070
Jofré, Alejandro; Rockafellar, R. Terry; Wets, Roger J.-B.
2007
Generalized deviations in risk analysis. Zbl 1150.90006
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
Optimality conditions in portfolio analysis with general deviation measures. Zbl 1138.91474
Rockafellar, R. Tyrrell; Uryasev, Stan; Zabarankin, Michael
2006
Nonsmooth mechanics and analysis. Theoretical and numerical advances. Zbl 1110.74006
Alart, P. (ed.); Maisonneuve, O. (ed.); Rockafellar, R. T. (ed.)
2006
A variational inequality scheme for determining an economic equilibrium of classical or extended type. Zbl 1113.49013
Jofre, A.; Rockafellar, R. T.; Wets, R. J.-B.
2005
Regularity and conditioning of solution mappings in variational analysis. Zbl 1046.49021
Dontchev, A. L.; Rockafellar, R. T.
2004
Hamilton-Jacobi theory and parametric analysis in fully convex problems of optimal control. Zbl 1083.49022
Rockafellar, R. Tyrrell
2004
The radius of metric regularity. Zbl 1042.49026
Dontchev, A. L.; Lewis, A. S.; Rockafellar, R. T.
2003
A property of piecewise smooth functions. Zbl 1042.90045
Rockafellar, R. T.
2003
A mathematical model and descent algorithm for bilevel traffic management. Zbl 1134.90319
Patriksson, Michael; Rockafellar, R. Tyrrell
2002
Generalized conjugacy in Hamilton-Jacobi theory for fully convex Lagrangians. Zbl 1023.49023
Goebel, Rafal; Rockafellar, R. T.
2002
Graphical convergence of sums of monotone mappings. Zbl 1010.47031
Pennanen, T.; Rockafellar, R. T.; Théra, M.
2002
Conditional value-at-risk: optimization approach. Zbl 0989.91052
Uryasev, Stanislav; Rockafellar, R. Tyrrell
2001
Ample parameterization of variational inclusions. Zbl 1008.49009
Dontchev, A. L.; Rockafellar, R. T.
2001
Convex analysis in the calculus of variations. Zbl 1011.49013
Rockafellar, R. T.
2001
Primal-dual solution perturbations in convex optimization. Zbl 0984.90043
Dontchev, A. L.; Rockafellar, R. T.
2001
Local differentiability of distance functions. Zbl 0960.49018
Poliquin, R. A.; Rockafellar, R. T.; Thibault, L.
2000
Stability of locally optimal solutions. Zbl 0965.49018
Levy, A. B.; Poliquin, R. A.; Rockafellar, R. T.
2000
Convexity in Hamilton–Jacobi theory. I: Dynamics and duality. Zbl 0998.49018
Rockafellar, R. Tyrrell; Wolenski, Peter R.
2000
Convexity in Hamilton–Jacobi theory. II: Envelope representations. Zbl 0998.49019
Rockafellar, R. Tyrrell; Wolenski, Peter R.
2000
Second-order convex analysis. Zbl 0960.49017
Rockafellar, R. Tyrrell
2000
Extended nonlinear programming. Zbl 0986.90057
Rockafellar, R. Tyrrell
2000
Second derivatives in convex analysis. Zbl 1003.49017
Rockafellar, R. T.
1999
Duality and optimality in multistage stochastic programming. Zbl 0920.90113
Rockafellar, R. T.
1999
Variational analysis. Zbl 0888.49001
Rockafellar, R. Tyrrell; Wets, Roger J.-B.
1998
Tilt stability of a local minimum. Zbl 0918.49016
Poliquin, R. A.; Rockafellar, R. T.
1998
Convex analysis. Zbl 0932.90001
Rockafellar, R. Tyrrell
1997
Convergence rates in forward–backward splitting. Zbl 0876.49009
Chen, George H-G.; Rockafellar, R. T.
1997
A derivative-coderivative inclusion in second-order nonsmooth analysis. Zbl 0897.49014
Rockafellar, R. T.; Zagrodny, D.
1997
Bolza problems with general time constraints. Zbl 0904.49014
Loewen, P. D.; Rockafellar, R. T.
1997
Characterizations of Lipschitzian stability in nonlinear programming. Zbl 0891.90146
Dontchev, A. L.; Rockafellar, R. T.
1997
Characterizations of strong regularity for variational inequalities over polyhedral convex sets. Zbl 0899.49004
Dontchev, A. L.; Rockafellar, R. T.
1996
Prox-regular functions in variational analysis. Zbl 0861.49015
Poliquin, R. A.; Rockafellar, R. T.
1996
Equivalent subgradient versions of Hamiltonian and Euler-Lagrange equations in variational analysis. Zbl 0878.49012
Rockafellar, R. Tyrrell
1996
The Euler and Weierstrass conditions for nonsmooth variational problems. Zbl 0838.49015
Ioffe, A. D.; Rockafellar, R. T.
1996
Generalized Hessian properties of regularized nonsmooth functions. Zbl 0863.49010
Poliquin, R. A.; Rockafellar, R. T.
1996
New necessary conditions for the generalized problem of Bolza. Zbl 0871.49023
Loewen, P. D.; Rockafellar, R. T.
1996
Variational conditions and the proto-differentiation of partial subgradient mappings. Zbl 0858.49014
Levy, A. B.; Rockafellar, R. T.
1996
Second-order nonsmooth analysis in nonlinear programming. Zbl 0939.90022
Poliquin, René; Rockafellar, Terry
1995
Tax basis and nonlinearity in cash stream valuation. Zbl 0866.90013
Dermody, Jaime Cuevas; Rockafellar, R. Tyrrell
1995
Sensitivity of solutions in nonlinear programming problems with nonunique multipliers. Zbl 0945.90066
Levy, A. B.; Rockafellar, R. T.
1995
Monotone relations and network equilibrium. Zbl 0847.49012
Rockafellar, R. Tyrrell
1995
Optimal control of unbounded differential inclusions. Zbl 0823.49016
Loewen, Philip D.; Rockafellar, R. T.
1994
Sensitivity analysis of solutions to generalized equations. Zbl 0815.47077
Levy, A. B.; Rockafellar, R. T.
1994
Proto-derivative formulas for basic subgradient mappings in mathematical programming. Zbl 0813.49019
Poliquin, R. A.; Rockafellar, R. T.
1994
A finite simplex-active-set method for monotropic piecewise quadratic programming. Zbl 0828.90102
Rockafellar, R. T.; Sun, J.
1994
Lagrange multipliers and optimality. Zbl 0779.49024
Rockafellar, R. Tyrrell
1993
Asymptotic theory for solutions in statistical estimation and stochastic programming. Zbl 0798.90115
King, Alan J.; Rockafellar, Tyrrell
1993
Zhu, Ciyou; Rockafellar, R. T.
1993
A calculus of epi-derivatives applicable to optimization. Zbl 0803.90113
Poliquin, R. A.; Rockafellar, R. T.
1993
Subgradients and variational analysis. Zbl 0889.49011
Rockafellar, R. T.
1993
Dualization of subgradient conditions for optimality. Zbl 0786.49012
Rockafellar, R. T.
1993
Sensitivity analysis for nonsmooth generalized equations. Zbl 0766.90075
King, Alan J.; Rockafellar, R. Tyrrell
1992
A characterization of epi-convergence in terms of convergence of level sets. Zbl 0769.49011
Beer, Gerald; Rockafellar, R. T.; Wets, Roger J.-B.
1992
Amenable functions in optimization. Zbl 1050.49513
Poliquin, R. A.; Rockafellar, R. T.
1992
A dual strategy for the implementation of the aggregation principle in decision making under uncertainty. Zbl 0800.90002
Rockafellar, R. T.; Wets, Roger J.-B.
1992
Cosmic convergence. Zbl 0793.49007
Rockafellar, R. T.; Wets, R. J.-B.
1992
Scenarios and policy aggregation in optimization under uncertainty. Zbl 0729.90067
Rockafellar, R. T.; Wets, Roger J.-B.
1991
The adjoint arc in nonsmooth optimization. Zbl 0734.49009
Loewen, Philip D.; Rockafellar, R. T.
1991
Cash stream valuation in the face of transaction costs and taxes. Zbl 0900.90110
Dermody, Jaime Cuevas; Rockafellar, R. Tyrrell
1991
Large-scale extended linear-quadratic programming and multistage optimization. Zbl 0743.90086
Rockafellar, R. T.
1991
On a special class of convex functions. Zbl 0795.49015
Rockafellar, R. T.
1991
Generalized linear-quadratic problems of deterministic and stochastic optimal control in discrete time. Zbl 0714.49036
Rockafellar, R. T.; Wets, R. J.-B.
1990
Generalized second derivatives of convex functions and saddle functions. Zbl 0712.49011
Rockafellar, R. T.
1990
Computational schemes for large-scale problems in extended linear- quadratic programming. Zbl 0735.90050
Rockafellar, R. T.
1990
An internal variable theory of elastoplasticity based on the maximum plastic work inequality. Zbl 0693.73008
Eve, R. A.; Reddy, B. D.; Rockafellar, R. T.
1990
Nonsmooth analysis and parametric optimization. Zbl 0723.49011
Rockafellar, R. T.
1990
Proto-differentiability of set-valued mappings and its applications in optimization. Zbl 0674.90082
Rockafellar, R. T.
1989
Second-order optimality conditions in nonlinear programming obtained by way of epi-derivatives. Zbl 0698.90070
Rockafellar, R. Tyrrell
1989
Hamiltonian trajectories and duality in the optimal control of linear systems with convex costs. Zbl 0682.49019
Rockafellar, R. T.
1989
Perturbation of generalized Kuhn-Tucker points in finite-dimensional optimization. Zbl 0735.90067
Rockafellar, R. T.
1989
...and 108 more Documents
all top 5
#### Cited by 11,475 Authors
117 Yao, Jen-Chih 102 Mordukhovich, Boris S. 67 Rockafellar, Ralph Tyrrell 66 Penot, Jean-Paul 64 Zhang, Liwei 63 Yang, Xiaoqi 62 Ceng, Lu-Chuan 61 Borwein, Jonathan Michael 59 Bauschke, Heinz H. 59 Kumam, Poom 57 Boţ, Radu Ioan 56 López-Cerdá, Marco Antonio 53 Thibault, Lionel 50 Noor, Muhammad Aslam 50 Yuan, Xiaoming 47 Wang, Shawn Xianfu 46 Jeyakumar, Vaithilingam 44 Goberna, Miguel Angel 42 Outrata, Jiří V. 41 Martínez-Legaz, Juan-Enrique 41 Wets, Roger Jean-Baptiste 40 Flåm, Sjur Didrik 40 Iusem, Alfredo Noel 39 Papageorgiou, Nikolaos S. 38 Adly, Samir 38 Ioffe, Alexander Davidovich 37 Pham Dinh Tao 37 Seeger, Alberto 36 Théra, Michel A. 36 Nguyen Dong Yen 35 Cho, Yeol Je 34 Hantoute, Abderrahim 34 Sun, Jie 33 Lewis, Adrian S. 31 Attouch, Hedy 31 Chuong, Thai Doan 31 Le Thi, Hoai An 31 Reich, Simeon 31 Sun, Defeng 30 Kruger, Alexander Ya. 29 Dontchev, Asen L. 29 Qi, Liqun 29 Teboulle, Marc 29 Wen, Chingfeng 28 Benson, Harold P. 28 Escudero, Laureano Fernando 28 He, Bingsheng 28 Li, Guoyin 28 Pang, Liping 28 Shapiro, Alexander 28 Volle, Michel 27 Bertsekas, Dimitri Panteli 27 Clarke, Francis H. 27 Daniilidis, Aris 27 Fang, Shu-Cherng 27 Han, Deren 27 Lee, Gue Myung 27 Pang, Jong-Shi 27 Svaiter, Benar Fux 27 Zălinescu, Constantin 26 Burke, James V. 26 Chen, Xiaojun 26 Dinh The Luc 26 Ng, Kung-Fu 26 Toh, Kimchuan 26 Tseng, Paul 25 Cánovas, María Josefa 25 Dempe, Stephan 25 Frankowska, Hélène 25 Kurzhanskiĭ, Aleksandr Borisovich 25 Martínez, José Mario 25 Nam, Nguyen Mau 25 Panagiotopoulos, Panagiotis D. 25 Parra, Juan 25 Qin, Xiaolong 25 Shehu, Yekini 25 Zheng, Xiyin 24 Jefferson, Thomas R. 24 Mahmudov, Elimhan N. 24 Pennanen, Teemu 24 Scott, Carlton H. 24 Takahashi, Wataru 24 Wanka, Gert 24 Ye, Jane J. 23 Ansari, Qamrul Hasan 23 Csetnek, Ernö Robert 23 Durea, Marius 23 Henrion, René 23 Kim, Do Sang 23 Ruszczyński, Andrzej 23 Verma, Ram U. 22 Ben-Tal, Aharon 22 Huang, Nan-Jing 22 Moudafi, Abdellatif 22 Strodiot, Jean-Jacques 22 Vinter, Richard B. 22 Zhou, Jinchuan 21 Beer, Gerald Alan 21 Chen, Jein-Shan 21 Combettes, Patrick L. ...and 11,375 more Authors
all top 5
#### Cited in 745 Serials
970 Journal of Optimization Theory and Applications 579 Mathematical Programming. Series A. Series B 578 Journal of Mathematical Analysis and Applications 434 Optimization 297 European Journal of Operational Research 292 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 284 Journal of Global Optimization 233 SIAM Journal on Optimization 209 Set-Valued and Variational Analysis 205 Computational Optimization and Applications 191 Linear Algebra and its Applications 172 Optimization Letters 159 Annals of Operations Research 148 Journal of Mathematical Economics 143 Nonlinear Analysis. Theory, Methods & Applications 140 Fixed Point Theory and Applications 139 Journal of Economic Theory 136 Mathematical Programming 134 Numerical Functional Analysis and Optimization 127 Transactions of the American Mathematical Society 124 Automatica 120 Applied Mathematics and Computation 105 Journal of Inequalities and Applications 104 Journal of Computational and Applied Mathematics 104 Operations Research Letters 101 Optimization Methods & Software 100 Proceedings of the American Mathematical Society 96 Applied Mathematics and Optimization 96 Abstract and Applied Analysis 90 Journal of Differential Equations 86 Set-Valued Analysis 68 Mathematical Methods of Operations Research 67 Computers & Mathematics with Applications 65 Journal of Approximation Theory 63 Journal of Functional Analysis 62 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 58 Systems & Control Letters 55 Applicable Analysis 55 Computer Methods in Applied Mechanics and Engineering 55 Stochastic Processes and their Applications 51 SIAM Journal on Control and Optimization 51 Computers & Operations Research 51 Positivity 48 Mathematical Notes 48 The Annals of Statistics 48 Numerical Algorithms 48 Journal of Convex Analysis 47 Advances in Mathematics 47 Annali di Matematica Pura ed Applicata. Serie Quarta 47 Journal of Applied Mathematics 46 Archive for Rational Mechanics and Analysis 45 Journal of Scientific Computing 45 The Annals of Applied Probability 44 Fuzzy Sets and Systems 44 Journal of Multivariate Analysis 44 Journal of Mathematical Imaging and Vision 43 Games and Economic Behavior 42 Economic Theory 41 Siberian Mathematical Journal 41 Journal of Industrial and Management Optimization 40 Insurance Mathematics & Economics 40 Mathematical and Computer Modelling 40 Calculus of Variations and Partial Differential Equations 40 Journal of Mathematical Sciences (New York) 40 Journal of Fixed Point Theory and Applications 39 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 38 Kybernetika 38 Cybernetics and Systems Analysis 37 Discrete Applied Mathematics 35 Top 35 Proceedings of the Steklov Institute of Mathematics 34 Numerische Mathematik 34 Mathematical Finance 33 Bulletin of the Australian Mathematical Society 32 Journal of Economic Dynamics & Control 31 International Journal for Numerical Methods in Engineering 31 Journal of Statistical Planning and Inference 31 Cybernetics 31 Automation and Remote Control 31 Mathematical Problems in Engineering 31 Finance and Stochastics 31 Vietnam Journal of Mathematics 30 Applied Mathematics Letters 29 International Journal of Systems Science 29 Mathematics of Operations Research 29 Statistics & Probability Letters 29 SIAM Journal on Imaging Sciences 29 Journal of the Operations Research Society of China 28 Nonlinear Analysis. Hybrid Systems 26 Electronic Journal of Statistics 25 Journal of the Franklin Institute 25 Acta Mathematicae Applicatae Sinica. English Series 24 Communications in Mathematical Physics 24 The Annals of Probability 24 Mathematics and Financial Economics 23 International Journal of Game Theory 23 Mathematical Social Sciences 23 Journal de Mathématiques Pures et Appliquées. Neuvième Série 23 Optimization and Engineering 22 Israel Journal of Mathematics ...and 645 more Serials
all top 5
#### Cited in 63 Fields
5,926 Operations research, mathematical programming (90-XX) 3,942 Calculus of variations and optimal control; optimization (49-XX) 1,844 Numerical analysis (65-XX) 1,661 Operator theory (47-XX) 1,526 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 785 Systems theory; control (93-XX) 629 Probability theory and stochastic processes (60-XX) 627 Functional analysis (46-XX) 616 Convex and discrete geometry (52-XX) 586 Statistics (62-XX) 575 Real functions (26-XX) 500 Partial differential equations (35-XX) 384 Ordinary differential equations (34-XX) 378 Computer science (68-XX) 359 Mechanics of deformable solids (74-XX) 317 Linear and multilinear algebra; matrix theory (15-XX) 286 Global analysis, analysis on manifolds (58-XX) 284 General topology (54-XX) 255 Information and communication theory, circuits (94-XX) 200 Approximations and expansions (41-XX) 196 Measure and integration (28-XX) 156 Dynamical systems and ergodic theory (37-XX) 111 Biology and other natural sciences (92-XX) 95 Combinatorics (05-XX) 93 Mechanics of particles and systems (70-XX) 92 Statistical mechanics, structure of matter (82-XX) 87 Differential geometry (53-XX) 77 Quantum theory (81-XX) 76 Algebraic geometry (14-XX) 58 Fluid mechanics (76-XX) 56 Mathematical logic and foundations (03-XX) 54 Several complex variables and analytic spaces (32-XX) 45 Number theory (11-XX) 37 Harmonic analysis on Euclidean spaces (42-XX) 35 Difference and functional equations (39-XX) 34 Geometry (51-XX) 32 Functions of a complex variable (30-XX) 27 Order, lattices, ordered algebraic structures (06-XX) 25 Integral transforms, operational calculus (44-XX) 24 Integral equations (45-XX) 24 Classical thermodynamics, heat transfer (80-XX) 22 Optics, electromagnetic theory (78-XX) 19 Nonassociative rings and algebras (17-XX) 19 Manifolds and cell complexes (57-XX) 17 History and biography (01-XX) 17 Group theory and generalizations (20-XX) 17 Potential theory (31-XX) 15 Geophysics (86-XX) 13 Field theory and polynomials (12-XX) 13 Topological groups, Lie groups (22-XX) 13 Algebraic topology (55-XX) 11 General and overarching topics; collections (00-XX) 11 Commutative algebra (13-XX) 10 Abstract harmonic analysis (43-XX) 9 Special functions (33-XX) 9 Sequences, series, summability (40-XX) 7 Associative rings and algebras (16-XX) 5 Relativity and gravitational theory (83-XX) 4 Category theory; homological algebra (18-XX) 2 General algebraic systems (08-XX) 2 Mathematics education (97-XX) 1 $$K$$-theory (19-XX) 1 Astronomy and astrophysics (85-XX)
#### Wikidata Timeline
The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata. | 2021-04-20 08:27:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3567025661468506, "perplexity": 6938.352338537362}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039379601.74/warc/CC-MAIN-20210420060507-20210420090507-00038.warc.gz"} |
https://courses.lumenlearning.com/wsu-sandbox2/chapter/determining-empirical-and-molecular-formulas-many-formula-issues/ | ## Determining Empirical and Molecular Formulas
### LEARNING OBJECTIVES
By the end of this section, you will be able to:
• Compute the percent composition of a compound
• Determine the empirical formula of a compound
• Determine the molecular formula of a compound
In the previous section, we discussed the relationship between the bulk mass of a substance and the number of atoms or molecules it contains (moles). Given the chemical formula of the substance, we were able to determine the amount of the substance (moles) from its mass, and vice versa. But what if the chemical formula of a substance is unknown? In this section, we will explore how to apply these very same principles in order to derive the chemical formulas of unknown substances from experimental mass measurements.
## Percent Composition
The elemental makeup of a compound defines its chemical identity, and chemical formulas are the most succinct way of representing this elemental makeup. When a compound’s formula is unknown, measuring the mass of each of its constituent elements is often the first step in the process of determining the formula experimentally. The results of these measurements permit the calculation of the compound’s percent composition, defined as the percentage by mass of each element in the compound. For example, consider a gaseous compound composed solely of carbon and hydrogen. The percent composition of this compound could be represented as follows:
$\%\text{H}=\frac{\text{mass H}}{\text{mass compound}}\times 100\%$
$\%\text{C}=\frac{\text{mass C}}{\text{mass compound}}\times 100\%$
If analysis of a 10.0-g sample of this gas showed it to contain 2.5 g H and 7.5 g C, the percent composition would be calculated to be 25% H and 75% C:
$\%\text{H}=\frac{2.5\text{g H}}{10.0\text{g compound}}\times 100\%=25\%$
$\%\text{C}=\frac{7.5\text{g C}}{10.0\text{g compound}}\times 100\%=75\%$
### Example 1
#### Calculation of Percent Composition
Analysis of a 12.04-g sample of a liquid compound composed of carbon, hydrogen, and nitrogen showed it to contain 7.34 g C, 1.85 g H, and 2.85 g N. What is the percent composition of this compound?
#### Solution
To calculate percent composition, we divide the experimentally derived mass of each element by the overall mass of the compound, and then convert to a percentage:
$\begin{array}{c}\\ \%\text{C}=\frac{7.34\text{g C}}{12.04\text{g compound}}\times 100\%=61.0\%\\ \%\text{H}=\frac{1.85\text{g H}}{12.04\text{g compound}}\times 100\%=15.4\%\\ \%\text{N}=\frac{2.85\text{g N}}{12.04\text{g compound}}\times 100\%=23.7\%\end{array}$
The analysis results indicate that the compound is 61.0% C, 15.4% H, and 23.7% N by mass.
A 24.81-g sample of a gaseous compound containing only carbon, oxygen, and chlorine is determined to contain 3.01 g C, 4.00 g O, and 17.81 g Cl. What is this compound’s percent composition?
Answer: 12.1% C, 16.1% O, 71.8% Cl
### Determining Percent Composition from Formula Mass
Percent composition is also useful for evaluating the relative abundance of a given element in different compounds of known formulas. As one example, consider the common nitrogen-containing fertilizers ammonia (NH3), ammonium nitrate (NH4NO3), and urea (CH4N2O). The element nitrogen is the active ingredient for agricultural purposes, so the mass percentage of nitrogen in the compound is a practical and economic concern for consumers choosing among these fertilizers. For these sorts of applications, the percent composition of a compound is easily derived from its formula mass and the atomic masses of its constituent elements. A molecule of NH3 contains one N atom weighing 14.01 amu and three H atoms weighing a total of $\left(3\times 1.008\text{amu}\right)=3.024\text{amu.}$ The formula mass of ammonia is therefore (14.01 amu + 3.024 amu) = 17.03 amu, and its percent composition is:
$\begin{array}{c}\\ \%\text{N}=\frac{14.01\text{amu N}}{17.03\text{amu}{\text{NH}}_{3}}\times 100\%=82.27\%\\ \%\text{H}=\frac{3.024\text{amu N}}{17.03\text{amu}{\text{NH}}_{3}}\times 100\%=17.76\%\end{array}$
This same approach may be taken considering a pair of molecules, a dozen molecules, or a mole of molecules, etc. The latter amount is most convenient and would simply involve the use of molar masses instead of atomic and formula masses, as demonstrated in the example problem below. As long as we know the chemical formula of the substance in question, we can easily derive percent composition from the formula mass or molar mass.
### Example 2
#### Determining Percent Composition from a Molecular Formula
Aspirin is a compound with the molecular formula C9H8O4. What is its percent composition?
#### Solution
To calculate the percent composition, we need to know the masses of C, H, and O in a known mass of C9H8O4. It is convenient to consider 1 mol of C9H8O4 and use its molar mass (180.159 g/mole, determined from the chemical formula) to calculate the percentages of each of its elements:
$\begin{array}{c}\\ \%\text{C}=\frac{9\text{mol C}\times \text{molar mass C}}{\text{molar mass}{\text{C}}_{9}{\text{H}}_{18}{\text{O}}_{4}}\times 100=\frac{9\times 12.01\text{g/mol}}{180.159\text{g/mol}}\times 100=\frac{108.09\text{g/mol}}{180.159\text{g/mol}}\times 100\\ \%\text{C}=60.00\%\text{C}\hfill \end{array}$
$\begin{array}{c}\\ \%\text{H}=\frac{8\text{mol H}\times \text{molar mass H}}{\text{molar mass}{\text{C}}_{9}{\text{H}}_{18}{\text{O}}_{4}}\times 100=\frac{8\times 1.008\text{g/mol}}{180.159\text{g/mol}}\times 100=\frac{8.064\text{g/mol}}{180.159\text{g/mol}}\times 100\\ \%\text{H}=4.476\%\text{H}\hfill \end{array}$
$\begin{array}{c}\\ \%\text{O}=\frac{4\text{mol O}\times \text{molar mass O}}{\text{molar mass}{\text{C}}_{9}{\text{H}}_{18}{\text{O}}_{4}}\times 100=\frac{4\times 16.00\text{g/mol}}{180.159\text{g/mol}}\times 100=\frac{64.00\text{g/mol}}{180.159\text{g/mol}}\times 100\\ \%\text{O}=35.52\%\hfill \end{array}$
Note that these percentages sum to equal 100.00% when appropriately rounded.
To three significant digits, what is the mass percentage of iron in the compound Fe2O3?
## Determination of Empirical Formulas
As previously mentioned, the most common approach to determining a compound’s chemical formula is to first measure the masses of its constituent elements. However, we must keep in mind that chemical formulas represent the relative numbers, not masses, of atoms in the substance. Therefore, any experimentally derived data involving mass must be used to derive the corresponding numbers of atoms in the compound. To accomplish this, we can use molar masses to convert the mass of each element to a number of moles. We then consider the moles of each element relative to each other, converting these numbers into a whole-number ratio that can be used to derive the empirical formula of the substance. Consider a sample of compound determined to contain 1.71 g C and 0.287 g H. The corresponding numbers of atoms (in moles) are:
$\begin{array}{l}\\ 1.17\text{g C}\times \frac{1\text{mol C}}{12.01\text{g C}}=0.142\text{mol C}\\ 0.287\text{g H}\times \frac{1\text{mol H}}{1.008\text{g H}}=0.284\text{mol H}\end{array}$
Thus, we can accurately represent this compound with the formula C0.142H0.248. Of course, per accepted convention, formulas contain whole-number subscripts, which can be achieved by dividing each subscript by the smaller subscript:
${\text{C}}_{\frac{0.142}{0.142}}{\text{H}}_{\frac{0.248}{0.142}}\text{or}{\text{CH}}_{2}$
(Recall that subscripts of “1” are not written but rather assumed if no other number is present.)
The empirical formula for this compound is thus CH2. This may or not be the compound’s molecular formula as well; however, we would need additional information to make that determination (as discussed later in this section).
Consider as another example a sample of compound determined to contain 5.31 g Cl and 8.40 g O. Following the same approach yields a tentative empirical formula of:
${\text{C1}}_{0.150}{\text{O}}_{0.525}={\text{Cl}}_{\frac{0.150}{0.150}}{\text{O}}_{\frac{0.525}{0.150}}={\text{ClO}}_{3.5}$
In this case, dividing by the smallest subscript still leaves us with a decimal subscript in the empirical formula. To convert this into a whole number, we must multiply each of the subscripts by two, retaining the same atom ratio and yielding Cl2O7 as the final empirical formula.
In summary, empirical formulas are derived from experimentally measured element masses by:
1. Deriving the number of moles of each element from its mass
2. Dividing each element’s molar amount by the smallest molar amount to yield subscripts for a tentative empirical formula
3. Multiplying all coefficients by an integer, if necessary, to ensure that the smallest whole-number ratio of subscripts is obtained
Figure 1 outlines this procedure in flow chart fashion for a substance containing elements A and X.
Figure 1. The empirical formula of a compound can be derived from the masses of all elements in the sample.
### Example 3
#### Determining a Compound’s Empirical Formula from the Masses of Its Elements
A sample of the black mineral hematite (Figure 2), an oxide of iron found in many iron ores, contains 34.97 g of iron and 15.03 g of oxygen. What is the empirical formula of hematite?
Figure 2. Hematite is an iron oxide that is used in jewelry. (credit: Mauro Cateb)
#### Solution
For this problem, we are given the mass in grams of each element. Begin by finding the moles of each:
$\begin{array}{lll}\\ 34.97\text{g Fe}\left(\frac{\text{mol Fe}}{55.85\text{g}}\right)& =& 0.6261\text{mol Fe}\hfill \\ 15.03\text{g O}\left(\frac{\text{mol O}}{16.00\text{g}}\right)& =& 0.9394\text{mol O}\hfill \end{array}$
Next, derive the iron-to-oxygen molar ratio by dividing by the lesser number of moles:
$\begin{array}{l}\frac{0.6261}{0.6261}=1.000\text{mol Fe}\\ \frac{0.0394}{0.6261}=1.500\text{mol O}\end{array}$
The ratio is 1.000 mol of iron to 1.500 mol of oxygen (Fe1O1.5). Finally, multiply the ratio by two to get the smallest possible whole number subscripts while still maintaining the correct iron-to-oxygen ratio:
2(Fe1O1.5) = Fe2O3
The empirical formula is Fe2O3.
What is the empirical formula of a compound if a sample contains 0.130 g of nitrogen and 0.370 g of oxygen?
For additional worked examples illustrating the derivation of empirical formulas, watch the brief video clip below.
### Deriving Empirical Formulas from Percent Composition
Finally, with regard to deriving empirical formulas, consider instances in which a compound’s percent composition is available rather than the absolute masses of the compound’s constituent elements. In such cases, the percent composition can be used to calculate the masses of elements present in any convenient mass of compound; these masses can then be used to derive the empirical formula in the usual fashion.
### Example 4
#### Determining an Empirical Formula from Percent Composition
The bacterial fermentation of grain to produce ethanol forms a gas with a percent composition of 27.29% C and 72.71% O (Figure 3). What is the empirical formula for this gas?
Figure 3. An oxide of carbon is removed from these fermentation tanks through the large copper pipes at the top. (credit: “Dual Freq”/Wikipedia)
#### Solution
Since the scale for percentages is 100, it is most convenient to calculate the mass of elements present in a sample weighing 100 g. The calculation is “most convenient” because, per the definition for percent composition, the mass of a given element in grams is numerically equivalent to the element’s mass percentage. This numerical equivalence results from the definition of the “percentage” unit, whose name is derived from the Latin phrase per centum meaning “by the hundred.” Considering this definition, the mass percentages provided may be more conveniently expressed as fractions:
$\begin{array}{lll}\\ 27.29\%\text{C}& =\hfill & \frac{27.29\text{g C}}{100\text{g compound}}\hfill \\ 72.71\%\text{O}& =\hfill & \frac{72.71\text{g O}}{100\text{g compound}}\hfill \end{array}$
The molar amounts of carbon and hydrogen in a 100-g sample are calculated by dividing each element’s mass by its molar mass:
$\begin{array}{lll}\\ 27.29\text{g C}\left(\frac{\text{mol C}}{12.01\text{g}}\right)& =\hfill & 2.272\text{mol C}\hfill \\ 72.71\text{g O}\left(\frac{\text{mol O}}{16.00\text{g}}\right)& =\hfill & 4.544\text{mol O}\hfill \end{array}$
Coefficients for the tentative empirical formula are derived by dividing each molar amount by the lesser of the two:
$\begin{array}{l}\frac{2.272\text{mol C}}{2.272}=1\\ \frac{4.544\text{mol O}}{2.272}=2\end{array}$
Since the resulting ratio is one carbon to two oxygen atoms, the empirical formula is CO2.
What is the empirical formula of a compound containing 40.0% C, 6.71% H, and 53.28% O?
## Derivation of Molecular Formulas
Recall that empirical formulas are symbols representing the relative numbers of a compound’s elements. Determining the absolute numbers of atoms that compose a single molecule of a covalent compound requires knowledge of both its empirical formula and its molecular mass or molar mass. These quantities may be determined experimentally by various measurement techniques. Molecular mass, for example, is often derived from the mass spectrum of the compound (see discussion of this technique in the previous chapter on atoms and molecules). Molar mass can be measured by a number of experimental methods, many of which will be introduced in later chapters of this text.
Molecular formulas are derived by comparing the compound’s molecular or molar mass to its empirical formula mass. As the name suggests, an empirical formula mass is the sum of the average atomic masses of all the atoms represented in an empirical formula. If we know the molecular (or molar) mass of the substance, we can divide this by the empirical formula mass in order to identify the number of empirical formula units per molecule, which we designate as n:
$\frac{\text{molecular or molar mass}\left(\text{amu or}\frac{\text{g}}{\text{mol}}\right)}{\text{empirical formula mass}\left(\text{amu or}\frac{\text{g}}{\text{mol}}\right)}=n\text{formula units/molecule}$
The molecular formula is then obtained by multiplying each subscript in the empirical formula by n, as shown below for the generic empirical formula AxBy:
${{\text{(A}}_{\text{x}}{\text{B}}_{\text{y}}\text{)}}_{\text{n}}={\text{A}}_{\text{nx}}{\text{B}}_{\text{nx}}$
For example, consider a covalent compound whose empirical formula is determined to be CH2O. The empirical formula mass for this compound is approximately 30 amu (the sum of 12 amu for one C atom, 2 amu for two H atoms, and 16 amu for one O atom). If the compound’s molecular mass is determined to be 180 amu, this indicates that molecules of this compound contain six times the number of atoms represented in the empirical formula:
$\frac{180\text{amu/molecule}}{30\frac{\text{amu}}{\text{formula unit}}}=6\text{formula units/molecule}$
Molecules of this compound are then represented by molecular formulas whose subscripts are six times greater than those in the empirical formula:
${\text{(CH}}_{\text{2}}{\text{O)}}_{\text{6}}={\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_{\text{6}}$
Note that this same approach may be used when the molar mass (g/mol) instead of the molecular mass (amu) is used. In this case, we are merely considering one mole of empirical formula units and molecules, as opposed to single units and molecules.
### Example 5
#### Determination of the Molecular Formula for Nicotine
Nicotine, an alkaloid in the nightshade family of plants that is mainly responsible for the addictive nature of cigarettes, contains 74.02% C, 8.710% H, and 17.27% N. If 40.57 g of nicotine contains 0.2500 mol nicotine, what is the molecular formula?
#### Solution
Determining the molecular formula from the provided data will require comparison of the compound’s empirical formula mass to its molar mass. As the first step, use the percent composition to derive the compound’s empirical formula. Assuming a convenient, a 100-g sample of nicotine yields the following molar amounts of its elements:
$\begin{array}{lll}\\ \left(74.02\text{g C}\right)\left(\frac{1\text{mol C}}{12.01\text{g C}}\right)& =\hfill & 6.163\text{mol C}\hfill \\ \left(8.710\text{g H}\right)\left(\frac{1\text{mol H}}{1.01\text{g H}}\right)& =\hfill & 8.624\text{mol H}\hfill \\ \left(17.27\text{g N}\right)\left(\frac{1\text{mol N}}{14.01\text{g N}}\right)& =\hfill & 1.233\text{mol N}\hfill \end{array}$
Next, we calculate the molar ratios of these elements.
The C-to-N and H-to-N molar ratios are adequately close to whole numbers, and so the empirical formula is C5H7N. The empirical formula mass for this compound is therefore 81.13 amu/formula unit, or 81.13 g/mol formula unit.
We calculate the molar mass for nicotine from the given mass and molar amount of compound:
$\frac{40.57\text{g nicotine}}{0.2500\text{mol nicotine}}=\frac{162.3\text{g}}{\text{mol}}$
Comparing the molar mass and empirical formula mass indicates that each nicotine molecule contains two formula units:
$\frac{162.3\text{g/mol}}{81.13\frac{\text{g}}{\text{formula unit}}}=2\text{formula units/molecule}$
Thus, we can derive the molecular formula for nicotine from the empirical formula by multiplying each subscript by two:
${{\text{(C}}_{\text{5}}{\text{H}}_{\text{7}}\text{N)}}_{\text{6}}={\text{C}}_{\text{10}}{\text{H}}_{\text{14}}{\text{N}}_{\text{2}}$
What is the molecular formula of a compound with a percent composition of 49.47% C, 5.201% H, 28.84% N, and 16.48% O, and a molecular mass of 194.2 amu?
## Key Concepts and Summary
The chemical identity of a substance is defined by the types and relative numbers of atoms composing its fundamental entities (molecules in the case of covalent compounds, ions in the case of ionic compounds). A compound’s percent composition provides the mass percentage of each element in the compound, and it is often experimentally determined and used to derive the compound’s empirical formula. The empirical formula mass of a covalent compound may be compared to the compound’s molecular or molar mass to derive a molecular formula.
### Key Equations
• $\%\text{X}=\frac{\text{mass X}}{\text{mass compound}}\times 100\%$$\frac{\text{molecular or molar mass}\left(\text{amu or}\frac{\text{g}}{\text{mol}}\right)}{\text{empirical formula mass}\left(\text{amu or}\frac{\text{g}}{\text{mol}}\right)}=n\text{formula units/molecule}$
• (AxBy)n = AnxBny
### Chemistry End of Chapter Exercises
1. What information do we need to determine the molecular formula of a compound from the empirical formula?
2. Calculate the following to four significant figures:
1. the percent composition of ammonia, NH3
2. the percent composition of photographic “hypo,” Na2S2O3
3. the percent of calcium ion in Ca3(PO4)2
3. Determine the following to four significant figures:
1. the percent composition of hydrazoic acid, HN3
2. the percent composition of TNT, C6H2(CH3)(NO2)3
3. the percent of SO42– in Al2(SO4)3
4. Determine the percent ammonia, NH3, in Co(NH3)6Cl3, to three significant figures.
5. Determine the percent water in CuSO4∙5H2O to three significant figures.
6. Determine the empirical formulas for compounds with the following percent compositions:
1. 15.8% carbon and 84.2% sulfur
2. 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen
7. Determine the empirical formulas for compounds with the following percent compositions:
1. 43.6% phosphorus and 56.4% oxygen
2. 28.7% K, 1.5% H, 22.8% P, and 47.0% O
8. A compound of carbon and hydrogen contains 92.3% C and has a molar mass of 78.1 g/mol. What is its molecular formula?
9. Dichloroethane, a compound that is often used for dry cleaning, contains carbon, hydrogen, and chlorine. It has a molar mass of 99 g/mol. Analysis of a sample shows that it contains 24.3% carbon and 4.1% hydrogen. What is its molecular formula?
10. Determine the empirical and molecular formula for chrysotile asbestos. Chrysotile has the following percent composition: 28.03% Mg, 21.60% Si, 1.16% H, and 49.21% O. The molar mass for chrysotile is 520.8 g/mol.
11. Polymers are large molecules composed of simple units repeated many times. Thus, they often have relatively simple empirical formulas. Calculate the empirical formulas of the following polymers:
1. Lucite (Plexiglas); 59.9% C, 8.06% H, 32.0% O
2. Saran; 24.8% C, 2.0% H, 73.1% Cl
3. polyethylene; 86% C, 14% H
4. polystyrene; 92.3% C, 7.7% H
5. Orlon; 67.9% C, 5.70% H, 26.4% N
12. A major textile dye manufacturer developed a new yellow dye. The dye has a percent composition of 75.95% C, 17.72% N, and 6.33% H by mass with a molar mass of about 240 g/mol. Determine the molecular formula of the dye.
2. In each of these exercises asking for the percent composition, divide the molecular weight of the desired element or group of elements (the number of times it/they occur in the formula times the molecular weight of the desired element or elements) by the molecular weight of the compound.
(a) $\begin{array}{l}\\ \\ \%\text{N}=\frac{14.0067\text{g}{\text{mol}}^{-1}\times 100\%}{\left[3\left(1.007940+14.0067\right)\right]\text{g}{\text{mol}}^{-1}}=\frac{14.0067\text{g}{\text{mol}}^{-1}}{17.0305\text{g}{\text{mol}}^{-1}}=82.24\%\\ \%\text{H}=\frac{3\times 1.00794\text{g}{\text{mol}}^{-1}}{17.0305\text{g}{\text{mol}}^{-1}}\times 100\%=17.76\%\end{array}$
(b) $\begin{array}{lll}\\ \%\text{Na}\hfill & =\hfill & \frac{2\times 22.989768}{2\times 22.989768+2\times 32.066+3\times 15.9994}\times 100\%=\frac{45.9795}{158.1097}\times 100=29.08\%\hfill \\ \%\text{S}\hfill & =\hfill & \frac{64.132}{158.1097}\times 100\%=40.56\%\hfill \\ \%\text{O}\hfill & =\hfill & \frac{47.9982}{158.1097}\times 100\%=30.36\%\hfill \end{array}$
(c) $\%{\text{Ca}}^{2+}=\frac{3\times 40.078}{3\times 40.078+2\times 30.973762+8\times 15.9994}\times 100\%=\frac{120.234}{310.1816}\times 100\%=38.76\%$
4. $\%{\text{NH}}_{3}=\frac{6\left(14.007+3\times 40.078\right)}{58.933+6\left(14.007+3\times 1.008\right)+3\left(35.453\right)}\times 100\%=\frac{102.186}{267.478}\times 100\%=38.2\%$
6. (a) The percent of an element in a compound indicates the percent by mass. The mass of an element in a 100.0-g sample of a compound is equal in grams to the percent of that element in the sample; hence, 100.0 g of the sample contains 15.8 g of C and 84.2 g of S. The relative number of moles of C and S atoms in the compound can be obtained by converting grams to moles as shown.
Step 1: $\begin{array}{l}\\ \text{C:}15.8\text{g}\times \frac{1\text{mol}}{12.011\text{g}}=1.315\text{mol}\\ \text{S:}84.2\text{g}\times \frac{1\text{mol}}{32.066\text{g}}=2.626\text{mol}\end{array}$
Step 2: $\begin{array}{l}\\ \text{C:}\frac{1.315\text{mol}}{1.315\text{mol}}=1.000\\ \text{S:}\frac{2.626\text{mol}}{1.315\text{mol}}=1.997\end{array}$
The empirical formula is CS2.
(b) Step 1: $\begin{array}{l}\\ \text{C:}40.0\text{g}\times \frac{1\text{mol}}{12.011\text{g}}=3.330\text{mol}\\ \text{H:}6.7\text{g}\times \frac{1\text{mol}}{1.00794\text{g}}=6.647\text{mol}\\ \text{O:}53.3\text{g}\times \frac{1\text{mol}}{15.9994\text{g}}=3.331\text{mol}\end{array}$
Step 2:
$\begin{array}{l}\\ \text{C:}\frac{3.330\text{mol}}{3.330\text{mol}}=1.0\\ \text{H:}\frac{6.647\text{mol}}{3.330\text{mol}}=2\\ \text{O:}\frac{3.331\text{mol}}{3.330\text{mol}}=1.0\end{array}$
The empirical formula is CH2O.
8. To determine the empirical formula, a relationship between percent composition and atom composition must be established. The percent composition of each element in a compound can be found either by dividing its mass by the total mass of compound or by dividing the molar mass of that element as it appears in the formula (atomic mass times the number of times the element appears in the formula) by the formula mass of the compound. From this latter perspective, the percent composition of an element can be converted into a mass by assuming that we start with a 100-g sample. Then, multiplying the percentage times 100 g gives the mass in grams of that component. Division of each mass by its respective atomic mass gives the relative ratio of atoms in the formula. From the numbers so obtained, the whole-number ratio of elements in the compound can be found by dividing each ratio by the number representing the smallest ratio. Generally, this process can be done in two simple steps (a third step is needed if the ratios are not whole numbers).
Step 1: Divide each element’s percentage (converted to grams) by its atomic mass:
$\begin{array}{l}\\ \text{C:}\frac{92.3\text{g}}{12.011\text{g}{\text{mol}}^{-1}}=7.68\text{mol}\\ \text{H:}\frac{7.7\text{g}}{1.00794\text{g}{\text{mol}}^{-1}}=7.6\text{mol}\end{array}$
This operation established the relative ration of carbon to hydrogen in the formula.
Step 2: To establish a whole-number ratio of carbon to hydrogen, divide each factor by the smallest factor. In this case, both factors are essentially equal; thus the ration of atoms is 1 to 1:
$\begin{array}{l}\\ \text{C:}\frac{7.68}{7.6}=1\\ \text{H:}\frac{7.6}{7.6}=1\end{array}$
The empirical formula is CH.
Since the molecular mass of the compound is 78.1 amu, some integer times the sum of the mass of 1C and 1H in atomic mass units (12.011 amu + 1.00794 amu = 13.019 amu) must be equal to 78.1 amu. To find this number, divide 78.1 amu by 13.019 amu:
$\frac{78.1\text{amu}}{13.019\text{amu}}=5.9989\rightarrow 6$
The molecular formula is (CH)6 = C6H6.
10. $\begin{array}{ccc}\left(28.03\text{g Mg}\right)\left(\frac{1\text{mol Mg}}{24.30\text{g}}\right)=1.153\text{mol Mg}& & \frac{1.153}{0.769}=1.512\text{mol Mg}\end{array}$
$\begin{array}{ccc}\left(21.60\text{g Si}\right)\left(\frac{1\text{mol Si}}{28.09\text{g Si}}\right)=0.769\text{mol Si}& & \phantom{\rule{0.4em}{0ex}}\frac{0.769}{0.769}=1.00\text{mol Si}\end{array}$
$\begin{array}{ccc}\left(1.16\text{g H}\right)\left(\frac{1\text{mol H}}{1.01\text{g H}}\right)=1.149\text{mol H}& & \frac{1.149}{0.769}=1.49\text{mol H}\end{array}$
$\begin{array}{ccc}\left(49.21\text{g O}\right)\left(\frac{1\text{mol O}}{16.00\text{g O}}\right)=3.076\text{mol O}& & \frac{3.076}{0.769}=4.00\text{mol O}\end{array}$
(2)(Mg1.5Si1H1.5O4) = Mg3Si2H3O8 (empirical formula), empirical mass of 260.1 g/unit
$\frac{\text{MM}}{\text{EM}}=\frac{520.8}{260.1}=2.00,$ so (2)(Mg3Si2H3O8) = Mg6Si4H6O16
12. Assume 100.0 g; the percentages of the elements are then the same as their mass in grams. Divide each mass by the molar mass to find the number of moles.
Step 1: $\begin{array}{l}\\ \frac{75.95\cancel{\text{g}}}{12.011\cancel{\text{g}}{\text{mol}}^{-1}}=6.323\text{mol C}\\ \frac{17.72\cancel{\text{g}}}{14.0067\cancel{\text{g}}{\text{mol}}^{-1}}=1.265\text{mol N}\\ \frac{6.33\cancel{\text{g}}}{1.00794\cancel{\text{g}}{\text{mol}}^{-1}}=6.28\text{mol H}\end{array}$
Step 2: Divide each by the smallest number. The answers are 5C, 1N, and 5H. The empirical formula is C5H5N, which has a molar mass of 79.10 g/mol. To find the actual molecular formula, divide 240, the molar mass of the compound, by 79.10 to obtain 3. So the formula is three times the empirical formula, or C15H15N3.
### Glossary
empirical formula mass
sum of average atomic masses for all atoms represented in an empirical formula
percent composition
percentage by mass of the various elements in a compound | 2020-01-28 06:15:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8032789826393127, "perplexity": 1887.537250648441}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251776516.99/warc/CC-MAIN-20200128060946-20200128090946-00094.warc.gz"} |
https://stats.stackexchange.com/questions/430842/why-does-the-marginal-likelihood-integral-have-no-closed-form-solution | # Why does the marginal likelihood integral have no closed-form solution?
In Bayesian inference we end up with the formula:
$$P(\mathbf{w|t,X)}= \frac{P(\mathbf{t|w,X)}P(\mathbf{w)}}{\int P(\mathbf{t|w,X}) P(\mathbf{w}) d\mathbf{w}}$$
Assume the prior $$P(w)$$ is a Gaussian distribution with 0 mean and $$\sigma$$ as standard deviation.
It is always said the integral has no closed-form solution. When the prior is a Gaussian distribution, is this related to the fact that the indefinite integral $$\int e^{-x^2}dx$$ can not be expressed with elementary functions?
What if I choose an ad-hoc prior distribution? Is there any case when the integral has a closed-form solution?
• Integrals are available in closed form for special entries. In the Bayesian setting, this is essentially the case for exponential family sampling distributions and so-called conjugate priors. Oct 10, 2019 at 11:36
• @ Xi'an is right about the use of conjugate priors making it unnecessary to evaluate the integral in the denominator of the RHS of your display. But suitable conjugate priors are not always available, so you sometimes do have to evaluate the integral. Often suitable methods of numerical integration (from almost trivial to MCMC and Metropolis-Hastings) are available. Oct 12, 2019 at 4:31
• It is also depend on your model, not only on the prior. for some models (i.e. the firs part of the integral P(t|w, X) it has closed form solution but not for any model. Mar 30, 2021 at 8:20
Yes, the marginal likelihood has a closed-form for all polynomial models of the form $$\mathbf{t} = X\mathbf{w} + \boldsymbol{\varepsilon}$$, where, \begin{aligned} X &= \begin{bmatrix} \mathbf{1}^T & \mathbf{(x^1)}^T & (\mathbf{x}^2)^T ... (\mathbf{x}^n)^T \end{bmatrix}\\ \boldsymbol{\varepsilon} &\sim \mathcal{N}(0, \sigma_n^2I)\\ \mathbf{w} &\sim \mathcal{N}(0,\sigma_w^2I) \end{aligned}
$$p(t|X) \sim \mathcal{N}(0, \sigma_w^2XX^T + \sigma_n^2I)$$ | 2022-06-29 03:49:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9723009467124939, "perplexity": 580.2784611611468}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103620968.33/warc/CC-MAIN-20220629024217-20220629054217-00397.warc.gz"} |
https://tex.stackexchange.com/questions/319997/problems-with-glsenableentrycount-when-usepackageglossaries-extra-instead-of?noredirect=1 | # Problems with \glsenableentrycount when \usepackage{glossaries-extra} instead of \usepackage{glossaries}
Recently the package glossaries-extra was released to supplement glossaries
Among the first couple pages of the documentation is the following example:
\documentclass{article}
\usepackage{glossaries-extra}
This is like:
\documentclass{article}
\usepackage[toc,nopostdot]{glossaries}
\usepackage{glossaries-extra}
But I have noticed that when trying to make use of \glsenableentrycount the following two lines are not equivalent.
%\usepackage[savewrites=true,nogroupskip,toc,nopostdot]{glossaries} % ====> THIS WORKS FINE
\usepackage[savewrites=true,nogroupskip,acronym]{glossaries-extra} % ====> THIS DOESN'T WORK BUT I EXPECTED IT TO BE EQUIVALENT
Using one of these lines in the MWE below, I have observed that I can't use the usepackage call on glossaries-extra (with or without glossaries as shown the quoted documentation example) and have \glsenableentrycount work.
\documentclass{article}
%\usepackage[savewrites=true,nogroupskip,toc,nopostdot]{glossaries} % ====> THIS WORKS FINE
\usepackage[savewrites=true,nogroupskip,acronym]{glossaries-extra} % ====> THIS DOESN'T WORK
\usepackage{scrwfile}%http://www.dickimaw-books.com/cgi-bin/faq.cgi?action=view&categorylabel=glossaries#glsnewwriteexceeded
\ifdefined\HCode \usepackage{morewrites} \else \fi
\makeindex % activate index-making
\makeglossaries
\glsenableentrycount % enable \cgls, \cglspl, \cGls, \cGlspl
% UPDATE: TRY ENABLING ENTRYCOUNT ATTRIBUTE
% http://mirror.its.dal.ca/ctan/macros/latex/contrib/glossaries-extra/glossaries-extra-manual.html#sec:entrycountmods
%\glssetcategoryattribute{acronym}{entrycount}{1}
\glssetcategoryattribute{abbreviation}{entrycount}{1}
%%%%% define synonyms to use counts by default
%%%%% http://tex.stackexchange.com/questions/98494/glossaries-dont-print-single-occurences
\let\gls\cgls
\let\glspl\cglspl
\let\Gls\cGls
\let\Glspl\cGlspl
\glssetnoexpandfield{first}
\glssetnoexpandfield{firstpl}
\newglossaryentry{SRS}{ type={acronym}, sort={stimulated Raman scattering}, name={SRS}, short={SRS}, long={stimulated Raman scattering}, first={stimulated Raman scattering (SRS)}, description={stimulated Raman scattering } }
\newglossaryentry{CARS}{ type={acronym}, sort={coherent anti-Stokes Raman scattering}, name={CARS}, short={CARS}, long={coherent anti-Stokes Raman scattering}, first={coherent anti-Stokes Raman scattering (CARS)}, description={coherent anti-Stokes Raman scattering } }
\glssetexpandfield{first}
\glssetexpandfield{firstpl}
%=============================================================================
% END GLOSSARY SETUP
%=============================================================================
\begin{document}\noindent\begin{sloppypar}
\gls{CARS} -- I shouldn't see the abbreviation
\cgls{SRS} -- I shouldn't see the abbreviation
\clearpage\end{sloppypar}\end{document}
• You also need to set the entrycount category attribute. – Nicola Talbot Jul 19 '16 at 19:04
• @NicolaTalbot. Thanks, I just tried \glssetcategoryattribute{abbreviation}{entrycount}{1} and \glssetcategoryattribute{acronym}{entrycount}{1} but no change. I will update my question to reflect where I inserted this. – EngBIRD Jul 19 '16 at 19:41
• Okay. I think your comment came while I was answering. – Nicola Talbot Jul 19 '16 at 19:46
• @NicolaTalbot Indeed. Your answer is very complete, I am sure I will resolve my issue with it. Although, switching from \newglossaryentry to \newacronym is not ideal. – EngBIRD Jul 19 '16 at 19:49
• @NicolaTalbot Sorry, I don't seem to get the desired output with that. I have tried the 6 different possible combinations of the three lines \glssetcategoryattribute{acronym}{regular}{false} \glssetcategoryattribute{acronym}{entrycount}{1} and \glsenableentrycount. My log file still includes the Package glossaries-extra Warning: Entry counting has been enabled that you describe below in your answer. Is there anything else from my log file I can quote that would be helpful? – EngBIRD Jul 19 '16 at 20:11
The \glsenableentrycount command is modified to allow for the entrycount attribute. This means that you not only need to enable entry counting with \glsenableentrycount, but you also need to set the appropriate attribute (see §5 Categories).
For example, instead of just doing:
\glsenableentrycount
you now need to do:
\glsenableentrycount
\glssetcategoryattribute{abbreviation}{entrycount}{1}
This will enable the entry counting for entries in the abbreviation category, but any entries assigned to other categories will be unchanged.
This allows the entry counting to be applied to certain types of entries, and it also allows you to set a different trigger value. There should have been a warning in your transcript file:
Package glossaries-extra Warning: Entry counting has been enabled
(glossaries-extra) with \glsenableentrycount but the
(glossaries-extra) attribute entrycount' hasn't
(glossaries-extra) been assigned to any of the defined
(glossaries-extra) entries.
This is a reminder that you need to set the entrycount attribute.
In your example, you have entry definitions like
\newglossaryentry{SRS}{ type={acronym}, sort={stimulated Raman scattering}, name={SRS}, short={SRS}, long={stimulated Raman scattering}, first={stimulated Raman scattering (SRS)}, description={stimulated Raman scattering } }
Since this doesn't explicitly set the category, it defaults to the general category, so you'd need to add:
\glssetcategoryattribute{general}{entrycount}{1}
However, this type of explicit definition of an abbreviation using \newglossaryentry defeats the purpose of the entry counting, since first contains the abbreviation so it will always show (since it's a regular entry, \cgls internally uses the value of the first key). If you want the abbreviation suppressed with \cgls, you need to define the abbreviation using \newabbreviation (or \newacronym).
Example:
\documentclass{article}
\usepackage[savewrites=true,nogroupskip,acronym]{glossaries-extra}
\usepackage{scrwfile}
\ifdefined\HCode \usepackage{morewrites} \else \fi
\makeindex % activate index-making
\makeglossaries
\glsenableentrycount % enable \cgls, \cglspl, \cGls, \cGlspl
\glssetcategoryattribute{acronym}{entrycount}{1}
\let\gls\cgls
\let\glspl\cglspl
\let\Gls\cGls
\let\Glspl\cGlspl
\glssetnoexpandfield{first}
\glssetnoexpandfield{firstpl}
\setabbreviationstyle[acronym]{long-short}
\newacronym[sort={stimulated Raman scattering}]
{SRS}{SRS}{stimulated Raman scattering}
\newacronym[sort={coherent anti-Stokes Raman scattering}]
{CARS}{CARS}{coherent anti-Stokes Raman scattering}
\glssetexpandfield{first}
\glssetexpandfield{firstpl}
%=============================================================================
% END GLOSSARY SETUP
%=============================================================================
\begin{document}\noindent\begin{sloppypar}
\gls{CARS} -- I shouldn't see the abbreviation
\cgls{SRS} -- I shouldn't see the abbreviation
\clearpage\end{sloppypar}\end{document}
This produces:
Now suppose I change the CARS entry so that it uses \newabbreviation instead of \newacronym. This sets the category to abbreviation, so it's not controlled by the entry counting mechanism (which has only been enabled for the acronym category).
\newabbreviation[sort={coherent anti-Stokes Raman scattering}]
{CARS}{CARS}{coherent anti-Stokes Raman scattering}
Now this entry includes the abbreviation even though it's only used once:
Edit: If you really want to use \newglossaryentry instead of \newabbreviation (or \newacronym) then you'll need to redefine \cglsformat to just check for the long field (and ignore the regular atttibute). For example:
\documentclass{article}
\usepackage[savewrites=true,nogroupskip,acronym]{glossaries-extra}
\makeglossaries
\glsenableentrycount % enable \cgls, \cglspl, \cGls, \cGlspl
\glssetcategoryattribute{acronym}{entrycount}{1}
\let\gls\cgls
\let\glspl\cglspl
\let\Gls\cGls
\let\Glspl\cGlspl
\glssetnoexpandfield{first}
\glssetnoexpandfield{firstpl}
\newglossaryentry{SRS}{
type={acronym},
category={acronym},% <- category
sort={stimulated Raman scattering},
name={SRS},
short={SRS},
long={stimulated Raman scattering},
first={stimulated Raman scattering (SRS)},
description={stimulated Raman scattering}
}
\newglossaryentry{CARS}{
type={acronym},
category={acronym},% <- category
sort={coherent anti-Stokes Raman scattering},
name={CARS},
short={CARS},
long={coherent anti-Stokes Raman scattering},
first={coherent anti-Stokes Raman scattering (CARS)},
description={coherent anti-Stokes Raman scattering}
}
\glssetexpandfield{first}
\glssetexpandfield{firstpl}
% Not using \newabbreviation so redefine \cglsformat
% to just check for the long field.
\renewcommand*{\cglsformat}[2]{%
\ifglshaslong{#1}{\glsentrylong{#1}}{\glsentryfirst{#1}}#2%
}
\begin{document}\noindent\begin{sloppypar}
\gls{CARS} -- I shouldn't see the abbreviation
\cgls{SRS} -- I shouldn't see the abbreviation
\clearpage\end{sloppypar}\end{document}
This produces:
If you're still getting the above warning, first check that the category has been correctly set for your entries. For example, if you add:
Category of CARS: \glscategory{CARS}.
Category of SRS: \glscategory{SRS}.
to your document, the PDF should show
If it doesn't, then check the category element in \newglossaryentry.
Next check that the entrycount attribute has been correctly set. You can do this by adding the following to your document:
entrycount attribute for CARS: \glsgetattribute{CARS}{entrycount}.
entrycount attribute for SRS: \glsgetattribute{SRS}{entrycount}.
This should show
If it doesn't check the spelling of the category label and the attribute label in
\glssetcategoryattribute{acronym}{entrycount}{1}
If you need to use the plural or case-changing versions, you similarly need to redefine the analogous commands. The first letter uppercase command \cGls uses \cGlsformat:
\renewcommand*{\cGlsformat}[2]{%
\ifglshaslong{#1}{\Glsentrylong{#1}}{\Glsentryfirst{#1}}#2%
}
(Make sure you have at least v1.14 of glossaries-extra that fixes the bug with \cGls.)
The all capitals version \cGLS uses \cGLSformat:
\renewcommand*{\cGLSformat}[2]{%
\ifglshaslong{#1}%
{\MakeUppercase{\glsentrylong{#1}}}
{\MakeUppercase{\glsentryfirst{#1}}}\MakeUppercase{#2}%
}
(or you may prefer to use \mfirstucMakeUppercase to be consistent with \GLS.)
If you need to use the plural forms, remember that the long, short, longplural and shortplural keys were actually provided for \newacronym and \newabbreviation and require explicit setting if used directly in \newglossaryentry. This means that if you're not using the abbreviation interface but are explicitly uses \newglossaryentry (as in the above example), then longplural and shortplural must be explicitly set if required, otherwise they will be empty.
There isn't a plural equivalent to \ifglshaslong, although you can use \ifglshasfield instead. There are several ways of redefining \cglsplformat. The simplistic approach is:
\renewcommand*{\cglsplformat}[2]{%
\ifglshaslong{#1}{\glsentrylongpl{#1}}{\glsentryfirstpl{#1}}#2%
}
This just checks if the long field has been set. In the above example, the long field has been set (so \ifglshaslong is true) but longplural hasn't been set, which means that \glsentrylongpl will expand to nothing for the entries in the above example. It really depends on what you want to happen in this situation. You could instead check for longplural:
\renewcommand*{\cglsplformat}[2]{%
\ifglshasfield{longplural}{#1}{\glsentrylongpl{#1}}{\glsentryfirstpl{#1}}#2%
}
or you might want to default to the long field if long has been set but longplural hasn't:
\renewcommand*{\cglsplformat}[2]{%
\ifglshaslong{#1}%
{\ifglshasfield{longplural}{#1}{\glsentrylongpl{#1}}{\glsentrylong{#1}}}%
{\glsentryfirstpl{#1}}#2%
}
Similarly for \cGlsplformat and \cGLSplformat.
• This has been a really helpful answer that I keep coming back to. I've just noticed however that in the MWE of the edit that if I use\Gls instead of \gls{}, it stops working (I get the abbreviation). I've played around with trying to create a capital instance with\cGlsformat (as suggested tex.stackexchange.com/questions/98494/…) but I haven't any observable changes so my guess that the capital pattern matching may not be correct. Which format command should I try editing to get the count working on the redefined \Gls{}? – EngBIRD Apr 12 '17 at 1:06
• @EngBIRD There's a bug in glossaries-extra's version of \glsenableentrycount`. I'll get it fixed. – Nicola Talbot Apr 18 '17 at 9:04 | 2021-03-06 10:18:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7366371750831604, "perplexity": 4237.43504163133}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178374686.69/warc/CC-MAIN-20210306100836-20210306130836-00220.warc.gz"} |
http://math.stackexchange.com/questions/269329/convergence-of-a-spiral-in-mathbbc | # Convergence of a spiral in $\mathbb{C}$
Does the series $$\sum_{k=0}^{\infty}\frac{i^k}{k!}$$converge, and if so, what is the value of it?
-
Do you know the Taylor expansion of $\exp (x)$? – Fabian Jan 2 '13 at 19:14
Yes, for some reason I forgot it. Thank you all. – Alyosha Jan 2 '13 at 19:15
This question is so trivial I think I may delete it. – Alyosha Jan 2 '13 at 19:16
Go ahead....... – Fabian Jan 2 '13 at 19:17
Hint: $$e^z=\sum_{k=0}^{\infty}\frac{z^k}{k!}$$
-
That seems more like an answer than a hint. – robjohn Jan 2 '13 at 19:56
@robjohn Sometimes the line between answers and hints can be very subtle. This is one of them. – Nameless Jan 2 '13 at 19:59
The sum of the series is $\exp{(i)}$, which has the value of $\cos{1} + i \sin{1}$ (the arguments being in radians).
-
Well, first of all: what's that power series' convergence radius? $$a_k:=\frac{i^k}{k!}\Longrightarrow \frac{a_{k+1}}{a_k}=\frac{i^{k+1}}{(k+1)!}\frac{k!}{i^k}=\frac{i}{k+1}\xrightarrow[k\to\infty]{}0$$
Thus, the series converges for all $\,i\in\Bbb R\,$
Advice: Don't use the letter $\,i\,$ as it usually stands for $\,i=\sqrt{-1}\,$ in mathematics..unless you really meant this $\,i\,$ , of course.
-
Recall: $\;\;$for $\large\;x \in \mathbb{C}\,:$ $\large\;\;\;\displaystyle \sum_{k=0}^{\infty}\frac{x^k}{k!} = e^x$
• In your case, we have $\large x = i,\;$ giving us $\large \;e^x = e^i = e^{i\theta},\text{ where}\;\;\theta = 1$.
• Now recall Euler's Formula: $$\large \;\;e^{i\theta} = \cos \theta + i \sin\theta,$$
$\quad$ and simply evaluate at $\;\large\theta = 1$.
-
and $e^i=\cos(1)+i\sin(1)$. – pbs Jan 2 '13 at 20:09
Alyosha: is this clear now? Just checking. $\quad$:-) – amWhy Jan 3 '13 at 18:04
yes, much better. – pbs Jan 7 '13 at 10:25
Alternately (and equivalently to several of the other answers), if you didn't know the Euler formula but did know the power series for sin and cos, you could reason as follows:
$i^0=1, i^1=i, i^2=-1, i^3=-i, i^4=i^0=1$. Therefore, the numerators of the power series are periodic of period 4; what's more, they split off naturally into a real part (the even members) and an imaginary part (the odd members): \begin{align*} \sum_{k=0}^{\infty}\frac{i^k}{k!} &= 1+\frac{i}{1!}+\frac{i^2}{2!}+\frac{i^3}{3!}+\frac{i^4}{4!}+\frac{i^5}{5!}+\cdots \\ &= 1+\frac{i}{1!}+\frac{-1}{2!}+\frac{-i}{3!}+\frac{1}{4!}+\frac{i}{5!}+\cdots \\ &=\left(1+\frac{-1}{2!}+\frac{1}{4!}+\cdots\right)+\left(\frac{i}{1!}+\frac{-i}{3!}+\frac{i}{5!}+\cdots\right) \\ &=\left(1-\frac{1}{2!}+\frac{1}{4!}+\cdots\right)+i\left(\frac{1}{1!}-\frac{1}{3!}+\frac{1}{5!}+\cdots\right) \\ &=\cos(1)+i\cdot\sin(1)\\ \end{align*}
-
OK, but isn't that just 1 step backwards in the proof of $e^x$'s MaClaurin expansion? – Alyosha Jan 2 '13 at 21:12
@Alyosha There are so many different ways of getting at these formulae that I'm not sure the concepts of 'backwards' or 'forwards' even make sense here. That said, I don't know of any proof of that expansion that even involves sin/cos, so I'm not sure how it could be going backwards per se. – Steven Stadnicki Jan 2 '13 at 21:27 | 2015-10-10 15:22:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9990931749343872, "perplexity": 1238.4570139086136}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-40/segments/1443737956371.97/warc/CC-MAIN-20151001221916-00025-ip-10-137-6-227.ec2.internal.warc.gz"} |
http://iembra.org/how-to/calculate-ss-error-anova.php | Home > How To > Calculate Ss Error Anova
# Calculate Ss Error Anova
## Contents
So our total sum of squares And actually if we wanted the variance here we would divide this by the degrees of freedom. And we also have another 14 right over here cause we have a 1 plus 4 plus 9 so that right over there is also 14. The F statistic can be obtained as follows: The P value corresponding to this statistic, based on the F distribution with 1 degree of freedom in the numerator and 23 degrees At any rate, here's the simple algebra: Proof.Well, okay, so the proof does involve a little trick of adding 0 in a special way to the total sum of squares: Then, have a peek at these guys
All rights Reserved.EnglishfrançaisDeutschportuguêsespañol日本語한국어中文（简体）By using this site you agree to the use of cookies for analytics and personalized content.Read our policyOK ERROR The requested URL could not be retrieved The following error For now, take note that thetotal sum of squares, SS(Total), can be obtained by adding the between sum of squares, SS(Between), to the error sum of squares, SS(Error). The column means are 2.3 for column 1, 1.85 for column 2 and 2.15 for column 3. But first, as always, we need to define some notation.
## How To Calculate Sum Of Squares For Anova Table
Then, the adjusted sum of squares for A*B, is: SS(A, B, C, A*B) - SS(A, B, C) However, with the same terms A, B, C, A*B in the model, the sequential So let's do that. In our case, this is: To better visualize the calculation above, the table below highlights the figures used in the calculation: Calculating SSsubjects As mentioned earlier, we treat each subject as
In other words, we treat each subject as a level of an independent factor called subjects. For example, say a manufacturer randomly chooses a sample of four Electrica batteries, four Readyforever batteries, and four Voltagenow batteries and then tests their lifetimes. Your cache administrator is webmaster. How To Calculate Ss In Statistics is the mean of the n observations.
Finally, let's consider the error sum of squares, which we'll denote SS(E). How To Compute Anova Table And these are multiple times the degrees of freedom here. For example, if you have a model with three factors, X1, X2, and X3, the adjusted sum of squares for X2 shows how much of the remaining variation X2 explains, given https://statistics.laerd.com/statistical-guides/repeated-measures-anova-statistical-guide-2.php The total sum of squares = treatment sum of squares (SST) + sum of squares of the residual error (SSE) The treatment sum of squares is the variation attributed to, or
Now, the sums of squares (SS) column: (1) As we'll soon formalize below, SS(Between) is the sum of squares between the group means and the grand mean. Sse Anova Formula The sequential and adjusted sums of squares are always the same for the last term in the model. So let's say, let's say that we have so we know we have m groups over here, so let me just write this m. So using the battery example, you get weibull.com home <<< Back to Issue 95 Index Analysis of Variance Software Used → DOE++ [Editor's Note: This article has been updated since
## How To Compute Anova Table
I'm gonna call that the grand mean. http://www.dummies.com/education/math/business-statistics/how-to-find-the-test-statistic-for-anova-using-the-error-mean-square-and-the-treatment-mean-square/ Converting the sum of squares into mean squares by dividing by the degrees of freedom lets you compare these ratios and determine whether there is a significant difference due to detergent. How To Calculate Sum Of Squares For Anova Table Figure 2: Most Models Do Not Fit All Data Points Perfectly You can see that a number of observed data points do not follow the fitted line. Sum Of Squares Anova Example And I'm actually gonna call that the grand mean.
For example, you do an experiment to test the effectiveness of three laundry detergents. More about the author This is a measure of how much variation there is among the mean lifetimes of the battery types. Welcome! It is the sum of the squares of the deviations of all the observations, yi, from their mean, . Anova Sse Calculator
Copyright © ReliaSoft Corporation, ALL RIGHTS RESERVED. That is: $SS(E)=\sum\limits_{i=1}^{m}\sum\limits_{j=1}^{n_i} (X_{ij}-\bar{X}_{i.})^2$ As we'll see in just one short minute why, the easiest way to calculate the error sum of squares is by subtracting the treatment sum of squares Sometimes, the factor is a treatment, and therefore the row heading is instead labeled as Treatment. http://iembra.org/how-to/calculate-error-mean-standard.php When, on the next page, we delve into the theory behind the analysis of variance method, we'll see that the F-statistic follows an F-distribution with m−1 numerator degrees of freedom andn−mdenominator
Important thing to note here... Anova Residuals plus 5 plus 6 plus 7. For the purposes of this demonstration, we shall calculate it using the first method, namely calculating SSw.
## The most common case where this occurs is with factorial and fractional factorial designs (with no covariates) when analyzed in coded units.
You can also use the sum of squares (SSQ) function in the Calculator to calculate the uncorrected sum of squares for a column or row. Your email Submit RELATED ARTICLES How to Find the Test Statistic for ANOVA Using the… Business Statistics For Dummies How Businesses Use Regression Analysis Statistics Explore Hypothesis Testing in Business Statistics Example Table 1 shows the observed yield data obtained at various temperature settings of a chemical process. Anova Residual Plot They both represent the sum of squares for the differences between related groups, but SStime is a more suitable name when dealing with time-course experiments, as we are in this example.
As a result, a sufficiently large value of this test statistic results in the null hypothesis being rejected. Therefore, in this case, the model sum of squares (abbreviated SSR) equals the total sum of squares: For the perfect model, the model sum of squares, SSR, equals the total sum Look there is the variance of this entire sample of nine but some of that variance, if these groups are different in some way, might come from the variation from being news That is: $SS(E)=SS(TO)-SS(T)$ Okay, so now do you remember that part about wanting to break down the total variationSS(TO) into a component due to the treatment SS(T) and a component due
Although SSerror can also be calculated directly it is somewhat difficult in comparison to deriving it from knowledge of other sums of squares which are easier to calculate, namely SSsubjects, and First, you need to calculate the overall average for the sample, known as the overall mean or grand mean. So that's gonna be 3 plus 2 plus 1. 3 plus 2 plus 1 plus 5 plus 3 plus 4 plus 5 plus 6 plus 7 ... SSconditions can be calculated directly quite easily (as you will have encountered in an independent ANOVA as SSb).
We can then calculate SSsubjects as follows: where k = number of conditions, mean of subject i, and = grand mean. The diagram below represents the partitioning of variance that occurs in the calculation of a repeated measures ANOVA. That means that the number of data points in each group need not be the same. So it's gonna be 28, 14 times 2, 14 plus 14 is 28, plus 2 is 30.
Let's now work a bit on the sums of squares. It is calculated as a summation of the squares of the differences from the mean. Because we want to compare the "average" variability between the groups to the "average" variability within the groups, we take the ratio of the BetweenMean Sum of Squares to the Error You construct the test statistic (or F-statistic) from the error mean square (MSE) and the treatment mean square (MSTR).
Sum of squares in ANOVA In analysis of variance (ANOVA), the total sum of squares helps express the total variation that can be attributed to various factors. And I think you'll get a sense of where this whole analysis of variance is coming from. Analysis of variance (ANOVA)Analysis of variance (ANOVA)ANOVA 1: Calculating SST (total sum of squares)ANOVA 2: Calculating SSW and SSB (total sum of squares within and between)ANOVA 3: Hypothesis test with F-statisticCurrent It is the unique portion of SS Regression explained by a factor, given all other factors in the model, regardless of the order they were entered into the model.
The F column, not surprisingly, contains the F-statistic. The F-statistic is calculated as below: You will already have been familiarised with SSconditions from earlier in this guide, but in some of the calculations in the preceding sections you will The sum of squares of the residual error is the variation attributed to the error. Now we only have three left.
For SSR, we simply replace the yi in the relationship of SST with : The number of degrees of freedom associated with SSR, dof(SSR), is 1. (For details, click here.) Therefore, | 2019-04-22 02:03:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7027868628501892, "perplexity": 630.8664949483031}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578533774.1/warc/CC-MAIN-20190422015736-20190422041736-00331.warc.gz"} |
https://pyscal.org/en/latest/methods/05_angular.html | # Angular parameters¶
## Angular criteria for identification of diamond structure¶
Angular parameter introduced by Uttormark et al {cite}Uttormark1993 is used to measure the tetrahedrality of local atomic structure. An atom belonging to diamond structure has four nearest neighbors which gives rise to six three body angles around the atom. The angular parameter $$A$$ is then defined as,
$A = \sum_{i=1}^6 (\cos(\theta_i)+\frac{1}{3})^2$
An atom belonging to diamond structure would show the value of angular params close to 0. Angular parameter can be calculated in pyscal using the following method -
import pyscal.core as pc
sys = pc.System()
sys.calculate_angularcriteria()
The calculated angular criteria value can be accessed for each atom using Atom.angular.
## $$\chi$$ parameters for structural identification¶
$$\chi$$ parameters introduced by Ackland and Jones {cite}Ackland2006 measures all local angles created by an atom with its neighbors and creates a histogram of these angles to produce vector which can be used to identify structures. After finding the neighbors of an atom, $$\cos \theta_{ijk}$$ for atoms j and k which are neighbors of i is calculated for all combinations of i, j and k. The set of all calculated cosine values are then added to a histogram with the following bins - [-1.0, -0.945, -0.915, -0.755, -0.705, -0.195, 0.195, 0.245, 0.795, 1.0]. Compared to $$\chi$$ parameters from $$\chi_0$$ to $$\chi_7$$ in the associated publication, the vector calculated in pyscal contains values from $$\chi_0$$ to $$\chi_8$$ which is due to an additional $$\chi$$ parameter which measures the number of neighbors between cosines -0.705 to -0.195. The $$\chi$$ vector is characteristic of the local atomic environment and can be used to identify crystal structures, details of which can be found in the publication[^2].
$$\chi$$ parameters can be calculated in pyscal using,
import pyscal.core as pc
sys = pc.System()
sys.calculate_chiparams()
The calculated values for each atom can be accessed using Atom.chiparams.
## References¶
{bibliography} ../references.bib :filter: docname in docnames :style: unsrt | 2021-09-23 00:02:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8482415676116943, "perplexity": 1133.229779775106}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057403.84/warc/CC-MAIN-20210922223752-20210923013752-00333.warc.gz"} |
http://etincellevideo.fr/docs/vu6zih.php?veuz=how-to-find-distance-between-two-degrees | All of the math behind it is beyond the scope of this post but (surprise, surprise), it's just a bunch of trig. Then the angular distance To convert degrees to units of length, you first need to convert the angle measurement from degrees to radians. If equals = 32 , find the distance between two cities, A and B, to the nearest mile. After watching this video lesson, you will be able to find the distance between any two points on the coordinate plane. How does one calculate the straight line distance between two points on a ... as the angle is to 360 degrees. How Far is it Between. Penn State World Campus offers accredited online college degrees and certificate programs. Surface Distance Between Two ... in: degrees minutes Degrees Minutes Seconds to/from Decimal Degrees; Distance and Azimuths Between Two given latitudes of two cities, distance between them is found using arc length formula for radians Finding distances based on Latitude and Longitude. Distance, often assigned the variable d, is a measure of the space contained by a straight line between two points. How do I calculate the distance between two points specified by latitude and longitude? Read more about how to calculate Distance by Latitude and Longitude using C# . If you are a mathematician or graphics programmer, you may need to find the angle between two given vectors. It will present the bearing as an angle that runs from 000 degrees (true north) to 359 degrees. Find the distance between the points (2, 3) and (4, 4). The distance calculator on this page is provided for informational ... Click here to find your latitude/longitude. How to Calculate the Angular Distance Between Two ... 360 degrees and Declination has a value between -90 and +90 degrees). (The coordinates of the locations are provided by the Google Geocoding API.) Minimum Distance between a Point and a Line This calculator will find the straight-line (great circle) distance between two locations of any kind: street addresses, city names, ZIP codes, etc. Calculate the distance between two addresses. Earn your Penn State degree online. Drag the marker on map to calculate distance (km, meters, mile, foot) and bearing angle of direction on google map, between two points of the earth. Calculating distance between two sets of Decimal Degree coordinates? Points, lines, and planes In what follows are various notes and algorithms dealing with points, lines, and planes. I need to find all properties within a half mile and I was Anyone know how to calculate the distance between two points using Latitude and Longitude? The great circle distance can be calculated using the Haversine formula shown below. The radius of the Earth is approximately 4000 miles. How to Use Excel to Calculate the Bearing Between Two Points. Experts say new findings should inspire even more action to combat climate change How to Find the Angle Between Two Vectors. How to Calculate Distance. I just plug the coordinates into the Distance Formula: Then the distance is , or Final bit of explanation: The shortest distance between two points on the globe can be calculated using the Haversine formula. Drag the marker on map to calculate distance (km, meters, mile, foot) and bearing angle of direction on google map, between two points of the earth. This tool can be used to find the distance between two named points on a map. Read more about how to calculate Distance by Latitude and Longitude using C# . The nonoriented angle $\phi$ between two points ${\bf u}$, ${\bf v}\in S^1$ (the unit circle) is the length of the shorter arc on $S^1$ connecting ${\bf u}$ and ${\bf v}$. It is a number between $0$ and $\pi$ (inclusive) and is given by the formula $\phi=\arccos({\bf u}\cdot{\bf v})$, where the $\cdot$ denotes the scalar product in ${\mathbb R}^2$. | 2018-07-23 05:59:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.731512725353241, "perplexity": 315.7403341119754}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676594954.59/warc/CC-MAIN-20180723051723-20180723071723-00032.warc.gz"} |
https://math.stackexchange.com/questions/2290525/for-a-m-by-n-minesweeper-board-what-is-the-maximum-number-of-mines-can-exist-so | # For a m by n minesweeper board, what is the maximum number of mines can exist so that any puzzle with those mines is solveable without guessing?
When I play the game Minesweeper, I make the puzzle more difficult by increasing the amount of mines and still keep the board. Once I set the maximum number of mines for a 9x9 board, which is $67$, I realise that the chance to win is almost zero(!). And when I play a game with a $24$x$30$ board with $150$ mines, I sometimes have to guess in order to win the game.
And after all, my question is:
Given a m by n Minesweeper board, what is the maximum number of mines can exist so that any puzzle with those mines is solveable without guessing?
Note: This question has some similarity to mine.
• If there's more than 9 mines and they make a 3*3 square then, the one in the middle is very hard to find except if you already discovered the rest of the game and know there's a mine left – Kii May 21 '17 at 14:17
• What counts as "not guessing"? Are you allowed an initial guess? I think what you meant is that you are also given a starting square which you know is safe, and then you can solve the puzzle from that square alone? – MaudPieTheRocktorate May 22 '17 at 3:19
If you have three mines, may have to guess between B1,C1,C2 and A1,C1,C2. Or A1,B2,C3 and A2,B1,C3. $$\begin{array}{c|ccc} & A & B & C \\ \hline 1 & ? & ? & * \\ 2 & 1 & 3 & * \\ 3 & 0 & 1 & 1 \end{array} or \begin{array}{c|ccc} & A & B & C \\ \hline 1 & ? & ? & 1 \\ 2 & ? & ? & 2 \\ 3 & 1 & 2 & * \end{array}$$ | 2019-06-19 15:34:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3904629349708557, "perplexity": 506.0238253190066}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999000.76/warc/CC-MAIN-20190619143832-20190619165832-00333.warc.gz"} |
http://calculator.mathcaptain.com/simplifying-ratios-calculator.html | Ratio is comparing of two quantities or numbers. Simplifying the ratios means making the numbers smaller in ratios so as to make it easier to compare. Simplifying ratios is nothing but reducing the ratio into its simplest form. Our calculator simplify the ratios into simplest form.
## How to Simplify Ratios
Below you could see the steps:
Step 1: Write down the factors of numerator and denominator.
Step 2: Find the greatest common factors of both numerator and denominator.
Step 3: Now, divide the numerator and denominator by that greatest common factor.
Here are some examples of simplifying ratios
### Solved Examples
Question 1: Simplify 15 : 9
Solution:
Given, ratio = 15 : 9
Factors of 15 = 1, 3, 5, 15
Factors of 9 = 1, 3, 9
Greatest Common Factor (G.C.D) = 3
dividing by G.C.D, $15 \div 3 = 5$
$9 \div 3 = 3$
Ratio in simplest form = 5 : 3
Question 2: Simplify 8 : 36
Solution:
Given, ratio = 8 : 36
Factors of 8 = 1, 2, 4, 8
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 ,36
Greatest Common Factor (G.C.D) = 4
dividing by G.C.D, $8 \div 4 = 2$
$36 \div 4 = 9$
Ratio in simplest form = 2 : 9
### Equivalent Ratio Calculator
ratio simplifier math ratio calculator ratio to fraction calculator simplest form calculator unit rate calculator | 2017-05-24 13:31:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.920082688331604, "perplexity": 2238.040357378602}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607846.35/warc/CC-MAIN-20170524131951-20170524151951-00548.warc.gz"} |
https://www.kuniga.me/blog/ | Blog
# NP-Incompleteness
Most recent post:
## Hermitian Functions
09 Oct 2021
In this post we’ll study even and odd functions, the even-odd function decomposition, Hermitian functions and prove some results for Fourier transforms.
Hermitian functions are named after the 19th century French mathematician Charles Hermite. Hermitian matrices are also named after him. Charles was the advisor of Henri Poincaré. | 2021-10-18 03:50:39 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8323096036911011, "perplexity": 3350.5424071548073}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585196.73/warc/CC-MAIN-20211018031901-20211018061901-00462.warc.gz"} |
https://www.shaalaa.com/textbook-solutions/c/tamil-nadu-board-samacheer-kalvi-solutions-class-11th-mathematics-volume-1-and-2-answers-guide-chapter-3-trigonometry_4527 | Tamil Nadu Board of Secondary EducationHSC Science Class 11th
# Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 3 - Trigonometry [Latest edition]
## Chapter 3: Trigonometry
Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Exercise 3.5Exercise 3.6Exercise 3.7Exercise 3.8Exercise 3.9Exercise 3.10Exercise 3.11Exercise 3.12
Exercise 3.1 [Page 92]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.1 [Page 92]
Exercise 3.1 | Q 1. (i) | Page 92
Identify the quadrant in which an angle given measure lies
25°
Exercise 3.1 | Q 1. (ii) | Page 92
Identify the quadrant in which an angle given measure lies
825°
Exercise 3.1 | Q 1. (iii) | Page 92
Identify the quadrant in which an angle given measure lies
– 55°
Exercise 3.1 | Q 1. (iv) | Page 92
Identify the quadrant in which an angle given measure lies
328°
Exercise 3.1 | Q 1. (v) | Page 92
Identify the quadrant in which an angle given measure lies
– 230°
Exercise 3.1 | Q 2. (i) | Page 92
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
395°
Exercise 3.1 | Q 2. (ii) | Page 92
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
525°
Exercise 3.1 | Q 2. (iii) | Page 92
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
1150°
Exercise 3.1 | Q 2. (iv) | Page 92
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 270°
Exercise 3.1 | Q 2. (v) | Page 92
For each given angle, find a coterminal angle with measure of θ such that 0° ≤ θ < 360°
– 450°
Exercise 3.1 | Q 3 | Page 92
If a cos θ − b sin θ = c, show that a sin θ + b cos θ = +- sqrt("a"^2 + "b"^2 - "c"^2)
Exercise 3.1 | Q 4 | Page 92
If sin θ + cos θ = m, show that cos6θ + sin6θ = (4 - 3("m"^2 - 1)^2)/4, where m2 ≤ 2
Exercise 3.1 | Q 5. (i) | Page 92
If (cos^4α)/(cos^2β) + (sin^4α)/(sin^2β) = 1, prove that sin4α + sin4β = 2 sin2α sin2β
Exercise 3.1 | Q 5.. (ii) | Page 92
If (cos^4alpha)/(cos^2beta) + (sin^4alpha)/(sin^2beta) = 1, prove that (cos^4beta)/(cos^2alpha) + (sin^4beta)/(sin^2alpha) = 1
Exercise 3.1 | Q 6 | Page 92
If y = (2sinalpha)/(1 + cosalpha + sinalpha), then prove that (1 - cosalpha + sinalpha)/(1 + sinalpha) = y
Exercise 3.1 | Q 7 | Page 92
If x = sum_("n" = 0)^oo cos^(2"n") theta, y = sum_("n" = 0)^oo sin^(2"n") theta and z = sum_("n" = 0)^oo cos^(2"n") theta, sin^(2"n") theta, 0 < theta < pi/2, then show that xyz = x + y + z. [Hint: Use the formula 1 + x + x2 + x3 + . . . = 1/(1 - x), where |x| < 1]
Exercise 3.1 | Q 8 | Page 92
If tan2 θ = 1 – k2, show that sec θ + tan3 θ cosec θ = (2 – k2)3/2. Also, find the values of k for which this result holds
Exercise 3.1 | Q 9 | Page 92
If sec θ + tan θ = p, obtain the values of sec θ, tan θ and sin θ in terms of p
Exercise 3.1 | Q 10 | Page 92
If cot θ(1 + sin θ) = 4m and cot θ(1 – sin θ) = 4n then prove that (m2 – n2)2 = m
Exercise 3.1 | Q 11 | Page 92
If cosec θ – sin θ = a3 and sec θ – cos θ = b3, then prove that a2b2 (a2 + b2) = 1
Exercise 3.1 | Q 12 | Page 92
Eliminate θ from the equations a sec θ – c tan θ = b and b sec θ + d tan θ = c
Exercise 3.2 [Pages 95 - 96]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.2 [Pages 95 - 96]
Exercise 3.2 | Q 1. (i) | Page 95
Express the following angles in radian measure:
30°
Exercise 3.2 | Q 1. (ii) | Page 95
Express the following angles in radian measure:
135°
Exercise 3.2 | Q 1. (iii) | Page 95
Express the following angles in radian measure:
– 205°
Exercise 3.2 | Q 1. (iv) | Page 95
Express the following angles in radian measure:
150°
Exercise 3.2 | Q 1. (v) | Page 95
Express the following angles in radian measure:
330°
Exercise 3.2 | Q 2. (i) | Page 95
Find the degree measure corresponding to the following radian measures
pi/3
Exercise 3.2 | Q 2. (ii) | Page 95
Find the degree measure corresponding to the following radian measures
pi/9
Exercise 3.2 | Q 2. (iii) | Page 95
Find the degree measure corresponding to the following radian measures
(2pi)/5
Exercise 3.2 | Q 2. (iv) | Page 95
Find the degree measure corresponding to the following radian measures
(7pi)/3
Exercise 3.2 | Q 2. (v) | Page 95
Find the degree measure corresponding to the following radian measures
(10pi)/9
Exercise 3.2 | Q 3 | Page 95
What must be the radius of a circular running path, around which an athlete must run 5 times in order to describe 1 km?
Exercise 3.2 | Q 4 | Page 95
In a circle of diameter 40 cm, a chord is of length 20 cm. Find the length of the minor arc of the chord
Exercise 3.2 | Q 5 | Page 95
Find the degree measure of the angle subtended at the centre of circle of radius 100 cm by an arc of length 22 cm
Exercise 3.2 | Q 6 | Page 95
What is the length of the arc intercepted by a central angle of measure 41° in a circle of radius 10 ft?
Exercise 3.2 | Q 7 | Page 95
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii
Exercise 3.2 | Q 8 | Page 96
The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degrees, minutes and seconds
Exercise 3.2 | Q 9 | Page 96
An airplane propeller rotates 1000 times per minute. Find the number of degrees that a point on the edge of the propeller will rotate in 1 second
Exercise 3.2 | Q 10 | Page 96
A train is moving on a circular track of 1500 m radius at the rate of 66 km/hr. What angle will it turn in 20 seconds?
Exercise 3.2 | Q 11 | Page 96
A circular metallic plate of radius 8 cm and thickness 6 mm is melted and molded into a pie (a sector of the circle with thickness) of radius 16 cm and thickness 4 mm. Find the angle of the sector.
Exercise 3.3 [Page 104]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.3 [Page 104]
Exercise 3.3 | Q 1. (i) | Page 104
Find the values of sin(480°)
Exercise 3.3 | Q 1. (ii) | Page 104
Find the values of sin (– 1110°)
Exercise 3.3 | Q 1. (iii) | Page 104
Find the values of cos(300°)
Exercise 3.3 | Q 1. (iv) | Page 104
Find the values of tan(1050°)
Exercise 3.3 | Q 1. (v) | Page 104
Find the values of cot(660°)
Exercise 3.3 | Q 1. (vi) | Page 104
Find the values of tan ((19pi)/3)
Exercise 3.3 | Q 1. (vii) | Page 104
Find the values of sin (-(11pi)/3)
Exercise 3.3 | Q 2 | Page 104
(5/7, (2sqrt(6))/7) is a point on the terminal side of an angle θ in standard position. Determine the six trigonometric function values of angle θ
Exercise 3.3 | Q 3. (i) | Page 104
Find the value of the trigonometric functions for the following:
cos θ = - 1/2, θ lies in the III quadrant
Exercise 3.3 | Q 3. (ii) | Page 104
Find the value of the trigonometric functions for the following:
cos θ = 2/3, θ lies in the I quadrant
Exercise 3.3 | Q 3. (iii) | Page 104
Find the value of the trigonometric functions for the following:
cos θ = - 2/3, θ lies in the IV quadrant
Exercise 3.3 | Q 3. (iv) | Page 104
Find the value of the trigonometric functions for the following:
tan θ = −2, θ lies in the II quadrant
Exercise 3.3 | Q 3. (v) | Page 104
Find the value of the trigonometric functions for the following:
sec θ = 13/5, θ lies in the IV quadrant
Exercise 3.3 | Q 4 | Page 104
Prove that (cot(180^circ + theta) sin(90^circ - theta) cos(- theta))/(sin(270^circ + theta) tan(- theta) "cosec"(360^circ + theta)) = cos2θ cotθ
Exercise 3.3 | Q 5 | Page 104
Find all the angles between 0° and 360° which satisfy the equation sin2θ = 3/4
Exercise 3.3 | Q 6 | Page 104
Show that sin^2 pi/18 + sin^2 pi/9 + sin^2 (7pi)/18 + sin^2 (4pi)/9 = 2
Exercise 3.4 [Pages 109 - 110]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.4 [Pages 109 - 110]
Exercise 3.4 | Q 1. (i) | Page 109
If sin x = 15/17 and cos y = 12/13, 0 < x < pi/2, 0 < y < pi/2 find the value of sin(x + y)
Exercise 3.4 | Q 1. (ii) | Page 109
If sin x = 15/17 and cos y = 12/13, 0 < x < pi/2, 0 < y < pi/2, find the value of cos(x − y)
Exercise 3.4 | Q 1. (iii) | Page 109
If sin x = 15/17 and cos y = 12/13, 0 < x < pi/2, 0 < y < pi/2, find the value of tan(x + y)
Exercise 3.4 | Q 2. (i) | Page 109
If sin A = 3/5 and cos B = 9/41 0 < "A" < pi/2, 0 < "B" < pi/2, find the value of sin(A + B)
Exercise 3.4 | Q 2. (ii) | Page 109
If sin A = 3/5 and cos B = 9/41, 0 < "A" < pi/2, 0 < "B" < pi/2, find the value of cos(A – B)
Exercise 3.4 | Q 3 | Page 109
Find cos(x − y), given that cos x = - 4/5 with pi < x < (3pi)/2 and sin y = - 24/25 with pi < y < (3pi)/2
Exercise 3.4 | Q 4 | Page 109
Find sin(x – y), given that sin x = 8/17 with 0 < x < pi/2, and cos y = - 24/25, x < y < (3pi)/2
Exercise 3.4 | Q 5. (i) | Page 109
Find the value of cos 105°
Exercise 3.4 | Q 5. (ii) | Page 109
Find the value of sin 105°
Exercise 3.4 | Q 5. (iii) | Page 109
Find the value of tan (7pi)/12
Exercise 3.4 | Q 6. (i) | Page 109
Prove that cos(30° + x) = (sqrt(3) cos x - sin x)/2
Exercise 3.4 | Q 6. (ii) | Page 109
Prove that cos(π + θ) = − cos θ
Exercise 3.4 | Q 6. (iii) | Page 109
Prove that sin(π + θ) = − sin θ.
Exercise 3.4 | Q 7 | Page 109
Find a quadratic equation whose roots are sin 15° and cos 15°
Exercise 3.4 | Q 8 | Page 109
Expand cos(A + B + C). Hence prove that cos A cos B cos C = sin A sin B cos C + sin B sin C cos A + sin C sin A cos B, if A + B + C = pi/2
Exercise 3.4 | Q 9. (i) | Page 109
Prove that sin(45° + θ) – sin(45° – θ) = sqrt(2) sin θ
Exercise 3.4 | Q 9. (ii) | Page 109
Prove that sin(30° + θ) + cos(60° + θ) = cos θ
Exercise 3.4 | Q 10 | Page 109
If a cos(x + y) = b cos(x − y), show that (a + b) tan x = (a − b) cot y
Exercise 3.4 | Q 11 | Page 109
Prove that sin 105° + cos 105° = cos 45°
Exercise 3.4 | Q 12 | Page 109
Prove that sin 75° – sin 15° = cos 105° + cos 15°
Exercise 3.4 | Q 13 | Page 109
Show that tan 75° + cot 75° = 4
Exercise 3.4 | Q 14 | Page 109
Prove that cos(A + B) cos C – cos(B + C) cos A = sin B sin(C – A)
Exercise 3.4 | Q 15 | Page 109
Prove that sin(n + 1) θ sin(n – 1) θ + cos(n + 1) θ cos(n – 1)θ = cos 2θ, n ∈ Z
Exercise 3.4 | Q 16 | Page 109
If x cos θ = y cos (theta + (2pi)/3) = z cos (theta + (4pi)/3). find the value of xy + yz + zx
Exercise 3.4 | Q 17. (i) | Page 109
Prove that sin(A + B) sin(A – B) = sin2A – sin2B
Exercise 3.4 | Q 17. (ii) | Page 109
Prove that cos(A + B) cos(A – B) = cos2A – sin2B = cos2B – sin2A
Exercise 3.4 | Q 17. (iii) | Page 109
Prove that sin2(A + B) – sin2(A – B) = sin2A sin2B
Exercise 3.4 | Q 17. (iv) | Page 109
Prove that cos 8θ cos 2θ = cos25θ – sin2
Exercise 3.4 | Q 18 | Page 109
Show that cos2 A + cos2 B – 2 cos A cos B cos(A + B) = sin2(A + B)
Exercise 3.4 | Q 19 | Page 109
If cos(α – β) + cos(β – γ) + cos(γ – α) = - 3/2, then prove that cos α + cos β + cos γ = sin α + sin β + sin γ = 0
Exercise 3.4 | Q 20. (i) | Page 110
Show that tan(45° + A) = (1 + tan"A")/(1 - tan"A")
Exercise 3.4 | Q 20. (ii) | Page 110
Show that tan(45° − A) = (1 - tan "A")/(1 + tan "A")
Exercise 3.4 | Q 21 | Page 110
Prove that cot(A + B) = (cot "A" cot "B" - 1)/(cot "A" + cot "B")
Exercise 3.4 | Q 22 | Page 110
If tan x = "n"/("n" + 1) and tan y = 1/(2"n" + 1), find tan(x + y)
Exercise 3.4 | Q 23 | Page 110
Prove that tan(pi/4 + theta) tan((3pi)/4 + theta) = – 1
Exercise 3.4 | Q 24 | Page 110
Find the value of tan(α + β), given that cot α = 1/2, α ∈ (pi, (3pi)/2) and sec β = - 5/3 β ∈ (pi/2, pi)
Exercise 3.4 | Q 25 | Page 110
If θ + Φ = α and tan θ = k tan Φ, then prove that sin(θ – Φ) = ("k" - 1)/("k" + 1) sin α
Exercise 3.5 [Pages 117 - 118]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.5 [Pages 117 - 118]
Exercise 3.5 | Q 1. (i) | Page 117
Find the value of cos 2A, A lies in the first quadrant, when cos A = 15/17
Exercise 3.5 | Q 1. (ii) | Page 117
Find the value of cos 2A, A lies in the first quadrant, when sin A = 4/5
Exercise 3.5 | Q 1. (iii) | Page 117
Find the value of cos 2A, A lies in the first quadrant, when tan A 16/63
Exercise 3.5 | Q 2. (i) | Page 118
If θ is an acute angle, then find sin (pi/4 - theta/2), when sin θ = 1/25
Exercise 3.5 | Q 2. (ii) | Page 118
If θ is an acute angle, then find cos (pi/4 + theta/2), when sin θ = 8/9
Exercise 3.5 | Q 3 | Page 118
If cos θ = 1/2 ("a" + 1/"a"), show that cos 3θ = 1/2 ("a"^3 + 1/"a"^3)
Exercise 3.5 | Q 4 | Page 118
Prove that cos 5θ = 16 cos5θ – 20 cos3θ + 5 cos θ
Exercise 3.5 | Q 5 | Page 118
Prove that sin 4α = 4 tan alpha (1 - tan^2alpha)/(1 + tan^2 alpha)^2
Exercise 3.5 | Q 6 | Page 118
If A + B = 45°, show that (1 + tan A)(1 + tan B) = 2
Exercise 3.5 | Q 7 | Page 118
Prove that (1 + tan 1°)(1 + tan 2°)(1 + tan 3°) ..... (1 + tan 44°) is a multiple of 4
Exercise 3.5 | Q 8 | Page 118
Prove that tan (pi/4 + theta) - tan(pi/4 - theta) = 2 tan 2θ
Exercise 3.5 | Q 9 | Page 118
Show that cot(7 1^circ/2) = sqrt(2) + sqrt(3) + sqrt(4) + sqrt(6)
Exercise 3.5 | Q 10 | Page 118
Prove that (1 + sec 2θ)(1 + sec 4θ) ... (1 + sec 2nθ) = tan 2nθ
Exercise 3.5 | Q 11 | Page 118
Prove that 32(sqrt(3)) sin pi/48 cos pi/48 cos pi/24 cos pi/12 cos pi/6 = 3
Exercise 3.6 [Pages 121 - 122]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.6 [Pages 121 - 122]
Exercise 3.6 | Q 1. (i) | Page 121
Express the following as a sum or difference
sin 35° cos 28°
Exercise 3.6 | Q 1. (ii) | Page 121
Express the following as a sum or difference
sin 4x cos 2x
Exercise 3.6 | Q 1. (iii) | Page 121
Express the following as a sum or difference
2 sin 10θ cos 2θ
Exercise 3.6 | Q 1. (iv) | Page 121
Express the following as a sum or difference
cos 5θ cos 2θ
Exercise 3.6 | Q 1. (v) | Page 121
Express the following as a sum or difference
sin 5θ sin 4θ
Exercise 3.6 | Q 2. (i) | Page 121
Express the following as a product
sin 75° sin 35°
Exercise 3.6 | Q 2. (ii) | Page 121
Express the following as a product
cos 65° + cos 15°
Exercise 3.6 | Q 2. (iii) | Page 121
Express the following as a product
sin 50° + sin 40°
Exercise 3.6 | Q 2. (iv) | Page 121
Express the following as a product
cos 35° – cos 75°
Exercise 3.6 | Q 3 | Page 121
Show that sin 12° sin 48° sin 54° = 1/8
Exercise 3.6 | Q 4 | Page 121
Show that cos pi/15 cos (2pi)/15 cos (3pi)/15 cos (4pi)/15 cos (5pi)/15 cos (6pi)/15 cos (7pi)/15 = 1/128
Exercise 3.6 | Q 5 | Page 121
Show that (sin 8x cos x - sin 6x cos 3x)/(cos 2x cos x - sin 3x sin 4x) = tan 2x
Exercise 3.6 | Q 6 | Page 121
Show that ((cos theta -cos 3theta)(sin 8theta + sin 2theta))/((sin 5theta - sin theta) (cos 4theta - cos 6theta)) = 1
Exercise 3.6 | Q 7 | Page 121
Prove that sin x + sin 2x + sin 3x = sin 2x (1 + 2 cos x)
Exercise 3.6 | Q 8 | Page 121
Prove that (sin 4x + sin 2x)/(cos 4x + cos 2x) = tan 3x
Exercise 3.6 | Q 9 | Page 121
Prove that 1 + cos 2x + cos 4x + cos 6x = 4 cos x cos 2x cos 3x
Exercise 3.6 | Q 10 | Page 122
Prove that sin theta/2 sin (7theta)/2 + sin (3theta)/2 sin (11theta)/2 = sin 2θ sin 5θ
Exercise 3.6 | Q 11 | Page 122
Prove that cos(30° – A) cos(30° + A) + cos(45° – A) cos(45° + A) = cos 2"A" + 1/4
Exercise 3.6 | Q 12 | Page 122
Prove that (sin x + sin 3x + sin 5x + sin 7x)/(cos x + cos x + cos 5x cos 7x) = tan 4x
Exercise 3.6 | Q 13 | Page 122
Prove that (sin(4"A" - 2"B") + sin(4"B" - 2"A"))/(cos(4"A" - 2"B") + cos(4"B" - 2"A")) = tan(A + B)
Exercise 3.6 | Q 14 | Page 122
Show that cot(A + 15°) – tan(A – 15°) = (4cos2"A")/(1 + 2 sin2"A")
Exercise 3.7 [Page 124]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.7 [Page 124]
Exercise 3.7 | Q 1. (i) | Page 124
If A + B + C = 180◦, prove that sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
Exercise 3.7 | Q 1. (ii) | Page 124
If A + B + C = 180°, prove that cos A + cos B − cos C = - 1 + 4cos "A"/2 cos "B"/2 sin "C"/2
Exercise 3.7 | Q 1. (iii) | Page 124
If A + B + C = 180°, prove that sin2A + sin2B + sin2C = 2 + 2 cos A cos B cos C
Exercise 3.7 | Q 1. (iv) | Page 124
If A + B + C = 180°, prove that sin2A + sin2B − sin2C = 2 sin A sin B cos C
Exercise 3.7 | Q 1. (v) | Page 124
If A + B + C = 180°, prove that tan "A"/2 tan "B"/2 + tan "B"/2 tan "C"/2 + tan "C"/2 tan "A"/2 = 1
Exercise 3.7 | Q 1. (vi) | Page 124
If A + B + C = 180°, prove that sin A + sin B + sin C = 4 cos "A"/2 cos "B"/2 cos "C"/2
Exercise 3.7 | Q 1. (vii) | Page 124
If A + B + C = 180°, prove that sin(B + C − A) + sin(C + A − B) + sin(A + B − C) = 4 sin A sin B sin C
Exercise 3.7 | Q 2 | Page 124
If A + B + C = 2s, then prove that sin(s – A) sin(s – B)+ sin s sin(s – C) = sin A sin B
Exercise 3.7 | Q 3 | Page 124
If x + y + z = xyz, then prove that (2x)/(1 - x^2) + (2y)/(1 - y^2) + (2z)/(1 - z^2) = (2x)/(1 - x^2) (2y)/(1 - y^2) (2z)/(1 - z^2)
Exercise 3.7 | Q 4. (i) | Page 124
If A + B + C = pi/2, prove the following sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
Exercise 3.7 | Q 4. (ii) | Page 124
If A + B + C = pi/2, prove the following cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
Exercise 3.7 | Q 5. (i) | Page 124
If ∆ABC is a right triangle and if ∠A = pi/2 then prove that cosB + cosC = 1
Exercise 3.7 | Q 5. (ii) | Page 124
If ∆ABC is a right triangle and if ∠A = pi/2 then prove that sinB + sinC = 1
Exercise 3.7 | Q 5. (iii) | Page 124
If ∆ABC is a right triangle and if ∠A = pi/2 then prove that cos B – cos C = - 1 + 2sqrt(2) cos "B"/2 sin "C"/2
Exercise 3.8 [Page 133]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.8 [Page 133]
Exercise 3.8 | Q 1. (i) | Page 133
Find the principal solution and general solution of the following:
sin θ = -1/sqrt(2)
Exercise 3.8 | Q 1. (ii) | Page 133
Find the principal solution and general solution of the following:
cot θ = sqrt(3)
Exercise 3.8 | Q 1. (iii) | Page 133
Find the principal solution and general solution of the following:
tan θ = - 1/sqrt(3)
Exercise 3.8 | Q 2. (i) | Page 133
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
sin4x = sin2x
Exercise 3.8 | Q 2. (ii) | Page 133
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 cos2x + 1 = – 3 cos x
Exercise 3.8 | Q 2. (iii) | Page 133
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
2 sin2x + 1 = 3 sin x
Exercise 3.8 | Q 2. (iv) | Page 133
Solve the following equations for which solution lies in the interval 0° ≤ θ < 360°
cos 2x = 1 − 3 sin x
Exercise 3.8 | Q 3. (i) | Page 133
Solve the following equations:
sin 5x − sin x = cos 3
Exercise 3.8 | Q 3. (ii) | Page 133
Solve the following equations:
2 cos2θ + 3 sin θ – 3 = θ
Exercise 3.8 | Q 3. (iii) | Page 133
Solve the following equations:
cos θ + cos 3θ = 2 cos 2θ
Exercise 3.8 | Q 3. (iv) | Page 133
Solve the following equations:
sin θ + sin 3θ + sin 5θ = 0
Exercise 3.8 | Q 3. (v) | Page 133
Solve the following equations:
sin 2θ – cos 2θ – sin θ + cos θ = θ
Exercise 3.8 | Q 3. (vi) | Page 133
Solve the following equations:
sin θ + cos θ = sqrt(2)
Exercise 3.8 | Q 3. (vii) | Page 133
Solve the following equations:
sin theta + sqrt(3) cos theta = 1
Exercise 3.8 | Q 3. (viii) | Page 133
Solve the following equations:
cot θ + cosec θ = sqrt(3)
Exercise 3.8 | Q 3. (ix) | Page 133
Solve the following equations:
tan theta + tan (theta + pi/3) + tan (theta + (2pi)/3) = sqrt(3)
Exercise 3.8 | Q 3. (x) | Page 133
Solve the following equations:
cos 2θ = (sqrt(5) + 1)/4
Exercise 3.8 | Q 3. (xi) | Page 133
Solve the following equations:
2cos 2x – 7 cos x + 3 = 0
Exercise 3.9 [Pages 142 - 143]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.9 [Pages 142 - 143]
Exercise 3.9 | Q 1 | Page 142
In a ∆ABC, if sin"A"/sin"C" = (sin("A" - "B"))/(sin("B" - "C")) prove that a2, b2, C2 are in Arithmetic Progression
Exercise 3.9 | Q 2 | Page 142
The angles of a triangle ABC, are in Arithmetic Progression and if b : c = sqrt(3) : sqrt(2), find ∠A
Exercise 3.9 | Q 3 | Page 143
In a ∆ABC, if cos C = sin "A"/(2sin"B") show that the triangle is isosceles
Exercise 3.9 | Q 4 | Page 143
In a ∆ABC, prove that sin "B"/sin "C" = ("c" - "a"cos "B")/("b" - "a" cos"C")
Exercise 3.9 | Q 5 | Page 143
In an ∆ABC, prove that a cos A + b cos B + c cos C = 2a sin B sin C
Exercise 3.9 | Q 6 | Page 143
In a ∆ABC, ∠A = 60°. Prove that b + c = 2"a" cos (("B" - "C")/2)
Exercise 3.9 | Q 7. (i) | Page 143
In an ∆ABC, prove the following, "a"sin ("A"/2 + "B") = ("b" + "c") sin "A"/2
Exercise 3.9 | Q 7. (ii) | Page 143
In a ∆ABC, prove the following, a(cos B + cos C) = 2("b" + "c") sin^2 "A"/2
Exercise 3.9 | Q 7. (iii) | Page 143
In a ∆ABC, prove the following, ("a"^2 - "c"^2)/"b"^2 = (sin ("A" - "C"))/(sin("A" + "C"))
Exercise 3.9 | Q 7. (iv) | Page 143
In a ∆ABC, prove the following, ("a"sin("B" - "C"))/("b"^2 - "c"^2) = ("b"sin("C" - "A"))/("c"^2 - "a"^2) = ("c"sin("A" - "B"))/("a"^2 - "b"^2)
Exercise 3.9 | Q 7. (v) | Page 143
In a ∆ABC, prove the following, ("a"+ "b")/("a" - "b") = tan(("A" + "B")/2) cot(("A" - "B")/2)
Exercise 3.9 | Q 8 | Page 143
In a ∆ABC, prove that (a2 – b2 + c2) tan B = (a2 + b2 – c2) tan C
Exercise 3.9 | Q 9 | Page 143
An Engineer has to develop a triangular shaped park with a perimeter 120 m in a village. The park to be developed must be of maximum area. Find out the dimensions of the park
Exercise 3.9 | Q 10 | Page 143
A rope of length 42 m is given. Find the largest area of the triangle formed by this rope and find the dimensions of the triangle so formed
Exercise 3.9 | Q 11. (i) | Page 143
Derive Projection formula from Law of sines
Exercise 3.9 | Q 11. (ii) | Page 143
Derive Projection formula from Law of cosines
Exercise 3.10 [Pages 146 - 147]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.10 [Pages 146 - 147]
Exercise 3.10 | Q 1 | Page 146
Determine whether the following measurements produce one triangle, two triangles or no triangle:
∠B = 88°, a = 23, b = 2. Solve if solution exists
Exercise 3.10 | Q 2 | Page 146
If the sides of a ∆ABC are a = 4, b = 6 and c = 8, then show that 4 cos B + 3 cos C = 2
Exercise 3.10 | Q 3 | Page 146
In a ∆ABC, if a = sqrt(3) - 1, b = sqrt(3) + 1 and C = 60° find the other side and other two angles
Exercise 3.10 | Q 4 | Page 146
In any ∆ABC, prove that the area ∆ = ("b"^2 + "c"^2 - "a"^2)/(4 cot "A")
Exercise 3.10 | Q 5 | Page 146
In a ∆ABC, if a = 12 cm, b = 8 cm and C = 30°, then show that its area is 24 sq.cm
Exercise 3.10 | Q 6 | Page 146
In a ∆ABC, if a = 18 cm, b = 24 cm and c = 30 cm, then show that its area is 216 sq.cm
Exercise 3.10 | Q 7 | Page 146
Two soldiers A and B in two different underground bunkers on a straight road, spot an intruder at the top of a hill. The angle of elevation of the intruder from A and B to the ground level in the eastern direction are 30° and 45° respectively. If A and B stand 5km apart, find the distance of the intruder from B
Exercise 3.10 | Q 8 | Page 146
A researcher wants to determine the width of a pond from east to west, which cannot be done by actual measurement. From a point P, he finds the distance to the eastern-most point of the pond to be 8 km, while the distance to the westernmost point from P to be 6 km. If the angle between the two lines of sight is 60°, find the width of the pond
Exercise 3.10 | Q 9 | Page 147
Two Navy helicopters A and B are flying over the Bay of Bengal at saine altitude from sea level to search a missing boat. Pilots of both the helicopters sight the boat at the same time while they are apart 10 km from each other. If the distance of the boat from A is 6 km and if the line segment AB subtends 60° at the boat, find the distance of the boat from B
Exercise 3.10 | Q 10 | Page 147
A straight tunnel is to be made through a mountain. A surveyor observes the two extremities A and B of the tunnel to be built from a point P in front of the mountain. If AP = 3 km, BP = 5 km, and ∠APB = 120°, then find the length of the tunnel to be built
Exercise 3.10 | Q 11 | Page 147
A farmer wants to purchase a triangular-shaped land with sides 120 feet and 60 feet and the angle included between these two sides is 60°. If the land costs Rs.500 per square feet, find the amount he needed to purchase the land. Also, find the perimeter of the land
Exercise 3.10 | Q 12 | Page 147
A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 30°. If after 100 km, the target has an angle of depression of 45°, how far is the target from the fighter jet at that instant?
Exercise 3.10 | Q 13 | Page 147
A plane is 1 km from one landmark and 2 km from another. From the plane’s point of view, the land between them subtends an angle of 45°. How far apart are the landmarks?
Exercise 3.10 | Q 14 | Page 147
A man starts his morning walk at a point A reaches two points B and C and finally back to A such that ∠A = 60° and ∠B = 45°, AC = 4 km in the ∆ABC. Find the total distance he covered during his morning walk
Exercise 3.10 | Q 15 | Page 147
Two vehicles leave the same place P at the same time moving along two different roads. One vehicle moves at an average speed of 60 km/hr and the other vehicle moves at an average speed of 80 km/hr. After half an hour the vehicle reaches destinations A and B. If AB subtends 60° at the initial point P, then find AB
Exercise 3.10 | Q 16 | Page 147
Suppose that a satellite in space, an earth station, and the centre of earth all lie in the same plane. Let r be the radius of earth and R he the distance from the centre of earth to the satellite. Let d be the distance from the earth station to the satellite. Let 30° be the angle of elevation from the earth station to the satellite, If the line segment connecting the earth station and satellite subtends angle α at the centre of earth then prove that d = "R"sqrt(1 + ("r"/"R")^2 - 2 ("r"/"R") cos alpha)
Exercise 3.11 [Page 149]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.11 [Page 149]
Exercise 3.11 | Q 1. (i) | Page 149
Find the principal value of sin^-1 1/sqrt(2)
Exercise 3.11 | Q 1. (ii) | Page 149
Find the principal value of cos^-1 sqrt(3)/2
Exercise 3.11 | Q 1. (iii) | Page 149
Find the principal value of cosec–1(– 1)
Exercise 3.11 | Q 1. (iv) | Page 149
Find the principal value of sec^-1 (- sqrt(2))
Exercise 3.11 | Q 1. (v) | Page 149
Find the principal value of tan^-1 (sqrt(3))
Exercise 3.11 | Q 2 | Page 149
A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)
Exercise 3.12 [Pages 150 - 151]
### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide Chapter 3 TrigonometryExercise 3.12 [Pages 150 - 151]
#### MCQ
Exercise 3.12 | Q 1 | Page 150
Choose the correct alternative:
1/(cos 80^circ) - sqrt(3)/(sin 80^circ) =
• sqrt(2)
• sqrt(3)
• 2
• 4
Exercise 3.12 | Q 2 | Page 150
Choose the correct alternative:
If cos 28° + sin 28° = k3, then cos 17° is equal to
• "k"^3/sqrt(2)
• - "k"^3/sqrt(2)
• +- "k"^3/sqrt(2)
• - "k"^3/sqrt(3)
Exercise 3.12 | Q 3 | Page 150
Choose the correct alternative:
The maximum value of 4sin^2x + 3cos^2x + sin x/2 + cos x/2 is
• 4 + sqrt(2)
• 3 + sqrt(2)
• 9
• 4
Exercise 3.12 | Q 4 | Page 150
Choose the correct alternative:
(1 + cos pi/8) (1 + cos (3pi)/8) (1 + cos (5pi)/8) (1 + cos (7pi)/8) =
• 1/8
• 1/2
• 1/sqrt(3)
• 1/sqrt(2)
Exercise 3.12 | Q 5 | Page 150
Choose the correct alternative:
If pi < 2theta < (3pi)/2, then sqrt(2 + sqrt(2 + 2cos4theta) equals to
• −2 cos θ
• −2 sin θ
• 2 cos θ
• 2 sin θ
Exercise 3.12 | Q 6 | Page 150
Choose the correct alternative:
If tan 40° = λ, then (tan 140^circ - tan 130^circ)/(1 + tan 140^circ * tan 130^circ) =
• (1 - lambda^2)/lambda
• (1 + lambda^2)/lambda
• (1 + lambda^2)/(2lambda)
• (1 - lambda^2)/(2lambda)
Exercise 3.12 | Q 7 | Page 150
Choose the correct alternative:
cos 1° + cos 2° + cos 3° + ... + cos 179° =
• 0
• 1
• −1
• 89
Exercise 3.12 | Q 8 | Page 150
Choose the correct alternative:
Let fk(x) = 1/"k" [sin^"k" x + cos^"k" x] where x ∈ R and k ≥ 1. Then f4(x) − f6(x) =
• 1/4
• 1/12
• 1/6
• 1/3
Exercise 3.12 | Q 9 | Page 150
Choose the correct alternative:
Which of the following is not true?
• sin θ = - 3/4
• cos θ = −1
• tan θ = 25
• sec θ = 1/4
Exercise 3.12 | Q 10 | Page 150
Choose the correct alternative:
cos 2θ cos 2ϕ+ sin2 (θ – ϕ) – sin2 (θ + ϕ) is equal to
• sin 2 (θ + Φ)
• cos 2 (8 + Φ)
• sin 2 (θ – Φ)
• cos 2(θ – Φ)
Exercise 3.12 | Q 11 | Page 150
Choose the correct alternative:
(sin("A" - "B"))/(cos"A" cos"B") + (sin("B" - "C"))/(cos"B" cos"C") + (sin("C" - "A"))/(cos"C" cos"A") is
• sin A + sin B + sin C
• 1
• 0
• cos A + cos B + cos C
Exercise 3.12 | Q 12 | Page 150
Choose the correct alternative:
If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)
• (pi(3"n" + 1))/("p" - "q")
• (pi(2"n" + 1))/("p" +- "q")
• (pi("n" +- 1))/("p" +- "q")
• (pi("n" + 2))/("p" + "q")
Exercise 3.12 | Q 13 | Page 151
Choose the correct alternative:
If tan α and tan β are the roots of x2 + ax + b = 0 then (sin(alpha + beta))/(sin alpha sin beta) is equal to
• "b"/"a"
• "a"/"b"
• - "a"/"b"
• - "b"/"a"
Exercise 3.12 | Q 14 | Page 151
Choose the correct alternative:
In a triangle ABC, sin2A + sin2B + sin2C = 2, then the triangle is
• equilateral triangle
• isosceles triangle
• right triangle
• scalene triangle
Exercise 3.12 | Q 15 | Page 151
Choose the correct alternative:
If f(θ) = |sin θ| + |cos θ| , θ ∈ R, then f(θ) is in the interval
• [0, 2]
• [1, sqrt(2)]
• [1, 2]
• [0, 1]
Exercise 3.12 | Q 16 | Page 151
Choose the correct alternative:
(cos 6x + 6 cos 4x + 15cos x + 10)/(cos 5x + 5cs 3x + 10 cos x) is equal to
• cos 2x
• cos x
• cos 3x
• 2 cos x
Exercise 3.12 | Q 17 | Page 151
Choose the correct alternative:
The triangle of maximum area with constant perimeter 12m
• is an equilateral triangle with side 4m
• is an isosceles triangle with sides 2m, 5m, 5m
• is a triangle with sides 3m, 4m, 5m
• Does not exist
Exercise 3.12 | Q 18 | Page 151
Choose the correct alternative:
A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?
• 10π seconds
• 20π seconds
• 5π seconds
• 15π seconds
Exercise 3.12 | Q 19 | Page 151
Choose the correct alternative:
If sin α + cos α = b, then sin 2α is equal to
• b2 − 1, if "b" ≤ sqrt(2)
• b2 − 1, if "b" > sqrt(2)
• b2 − 1, if b ≥ 1
• b2 − 1, if "b" ≥ sqrt(2)
Exercise 3.12 | Q 20 | Page 151
Choose the correct alternative:
In a ∆ABC, if
(i) sin "A"/2 sin "B"/2 sin "C"/2 > 0`
(ii) sin A sin B sin C > 0 then
• Both (i) and (ii) are true
• Only (i) is true
• Only (ii) is true
• Neither (i) nor (ii) is true
## Chapter 3: Trigonometry
Exercise 3.1Exercise 3.2Exercise 3.3Exercise 3.4Exercise 3.5Exercise 3.6Exercise 3.7Exercise 3.8Exercise 3.9Exercise 3.10Exercise 3.11Exercise 3.12
## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 3 - Trigonometry
Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 3 (Trigonometry) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Tamil Nadu Board of Secondary Education Class 11th Mathematics Volume 1 and 2 Answers Guide solutions in a manner that help students grasp basic concepts better and faster.
Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. Tamil Nadu Board Samacheer Kalvi textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.
Concepts covered in Class 11th Mathematics Volume 1 and 2 Answers Guide chapter 3 Trigonometry are Introduction of Trigonometry, A Recall of Basic Results, Radian Measure, Trigonometric Functions and Their Properties, Trigonometric Equations, Properties of Triangle, Application to Triangle, Inverse Trigonometric Functions.
Using Tamil Nadu Board Samacheer Kalvi Class 11th solutions Trigonometry exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in Tamil Nadu Board Samacheer Kalvi Solutions are important questions that can be asked in the final exam. Maximum students of Tamil Nadu Board of Secondary Education Class 11th prefer Tamil Nadu Board Samacheer Kalvi Textbook Solutions to score more in exam.
Get the free view of chapter 3 Trigonometry Class 11th extra questions for Class 11th Mathematics Volume 1 and 2 Answers Guide and can use Shaalaa.com to keep it handy for your exam preparation | 2021-09-18 20:00:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7238181829452515, "perplexity": 5482.832993231677}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780056572.96/warc/CC-MAIN-20210918184640-20210918214640-00651.warc.gz"} |
https://docs.yearn.finance/resources/risks/risk-score | # Risk Scores
Yearn works with risk scores to quantify and assess the amount of risk of each strategy and vault. This document outlines how we measure risk vectors and use them to find the optimal balance of security and innovation.
## Strategy Risk Score
Risk for different strategies is quantified using a 1-5 point system developed by Yearn's strategy deployment process. The higher the risk score number, the more risky the strategy is. The risk assessment evaluates eight dimensions:
This risk framework is an ongoing process to ensure the security of Yearn strategies. Yearn recognized that, due to its unique approach to deploying strategies, it could not rely on a traditional waterfall process (heavy analysis and design, testing, multiple audits before release, etc.) to deploy contracts. Strategies are deployed and capped by their risk score. As we reduce the risk in any of the eight dimensions, the strategy can grow its TVL. This system allows Yearn to compare the risk score of two strategies and prioritize risk mitigation and preventive actions, such as forming a committee to spread knowledge on the code, getting more audits, migrating current code to improved versions of the strategy, etc.
The current version of the risk score system works for Yearn's current needs, but we are always looking to improve and expand it to the vaults. We want to provide our users with a better understanding of what is happening behind the scenes in the vaults. The development of vault risk scoring is still in progress!
### Audit
Auditing is a process that an audit firm or external security researcher reviews code for any potential vulnerabilities and present a report for mitigation. Audits take longer than an internal security review and are not immediately available due to the high demand for audits in the space. As such, most strategies are sent to production without an audit (leading to a high risk score) in order to limit their Total Value Locked (TVL). This approach allows for strategies to be validated in production while still managing risk, and the risk score helps determine which strategies should get an audit first, based on impact and other scoring criteria. The table below outlines the scoring criteria associated with audits.
Score Audit 5 No audit by a trusted firm or security researcher. 4 Audit by trusted firm or security researcher conducted more than 6 months ago. 3 Audit by trusted firm or security researcher conducted more than 3 months ago. 2 Audit conducted less than 3 months ago by an independent trusted firm. 1 Audit conducted less than 3 months ago by 3 or more independent trusted firms.
### Code Review
This is the process that reviews strategy code going to production. It is done in two major phases:
Phase 1: Two internal peers (strategists) review the strategy for any potential issues regarding handling accounts, profits, losses, etc. After this phase is completed, the strategy can go to ape.tax for live testing and validation.
Phase 2: An internal security reviewer from Yearn will review the code focusing on security concerns. Once phase 2 is completed, the strategy gets a risk score in all dimensions and is usually deemed enough for a strategy to go to production with limited TVL based on scoring.
After these steps a recurring review is scheduled, where either a second either internal or external security reviewer will have another look at the code:
Score Code Review 5 0 - 1 reviewer of the code only or most recent was done 6 months+ ago 4 2 reviewers of the code, the most recent of which was done 3+ months ago 3 3 reviewers of the code, the most recent of which was done 3+ months ago (1 of the reviewers is an internal security dev) 2 4 reviewers of the code (2 peers and 2 internal security devs) 1 5 reviewers of the code, (2 strategists peers and 2 security reviewers and either external protocol devs reviewed or external security researchers reviewed)
### Complexity
This is how the strategy earns its returns: is it a simple strategy like a masterchef staking or does it have complex mechanics such as leverage, risk of liquidation, and involvement with multiple protocols? The more components it needs will require a higher complexity score. This score is essential in an emergency to evaluate how difficult it is to mitigate a live issue:
Score Complexity 5 Strategy is highly complex, uses leverage or debt, and is not easy to unwind. No health check available 4 Uses leverage or debt, and is not easy to unwind. No health check available 3 Has potential for losses, withdrawal fees, or requires detailed queue management to prevent losses. No health check available 2 Strategy is relatively simple, and is easy to migrate/unwind. Has a health check 1 Strategy is easy to understand, and can be migrated/unwound easily. No leverage and no publicly accessible methods. Highly unlikely to incur losses.
### Longevity
How long the strategy has been running live on yearn.finance:
Score Longevity 5 Code is new and did not go to ape tax before going live on yearn.finance 4 Code has been running for less than one month 3 Code has been running between 1-4 months 2 Code has been running for 4+ months 1 Code has been running for 8+ months with no critical issues and no changes in code base
### Protocol Safety
Protocol Safety evaluates the resilience of the protocol the strategy uses. It takes into account the safety measures given the current DeFi security standards, based on our internal assessments and due diligence compared to the top projects in DeFI. This includes multisig health, decentralization, bounty programs, audits, etc.
We hope to improve this dimension with the help of the DeFI community to potentially use a standard scoring system that is widely accepted in the ecosystem to replace our current scoring table:
Score Protocol Safety 5 No due diligence (DD) document for this strategy. The protocol contracts used are very recent and not audited/verified. An EOA (externally owned account) owns the contracts and can upgrade them. 4 DD took place. Protocol contracts audited/verified. A multisig is required or contracts are upgradable. Multisig has a low threshold of signers. No bounty program. 3 DD took place. Protocol contracts are audited/verified by at least one reputable audit firm. A multisig with an appropriate threshold is required and/or contracts are immutable. Has a good bounty program. 2 DD took place. Protocol contracts are audited/verified by at least two reputable audit firms. A multisig with an appropriate threshold is required and/or contracts are immutable. Has a good bounty program. 1 Protocols involved in contracts are trusted blue chip protocols with a good track record of security. For example: Maker, Uniswap, Curve, AAVE, and Compound. These protocols meet all the criteria specified in item 2 and more.
### Team Knowledge
Measures the amount of expertise on a strategy that is shared amongst Yearn contributors. How many contributors can manage the strategy and respond in an emergency? The fewer people who can manage and respond during an emergency the riskier the strategy assessment in this dimension:
Score Team Knowledge 5 1 person in the team is the only one that has in-depth knowledge of the strategy code 4 1 strategist has in-depth knowledge, and 1 strategist is somewhat familiar with the strategy code. 3 2 strategists have in-depth knowledge of the strategy code. 2 2 strategists have in-depth knowledge, and 1 strategist is somewhat familiar with the strategy code. 1 A team of 3+ strategists are very familiar with the strategy code and the protocol the strategy is utilising.
### Testing Score
Testing score is a metric of how much of the codebase for the strategy has been tested. It uses the test coverage number as a reference, higher coverage means the developer/strategist took time to test most of the operations of the strategy in a unit test or fork environment. This score assumes that a less tested strategy entails more risk since we know less about what is expected from the code:
Score Testing Score 5 Less than 20% coverage in testing 4 Less than 40% coverage in testing 3 40% to 80% coverage 2 Over 80% coverage 1 Over 90% coverage in testing. Second developer validated and added tests and also added new ones for uncovered cases while reviewing. You can pull the repository and the tests are currently passing
### TVL Impact
The TVL (total value locked) metric measures how to allocate to new riskier strategies without having a catastrophic event in case of a hack or issue. The lower the impact, the more likely Yearn’s treasury can recover from an incident. The TVL is measured in USD and grows dynamically based on strategies allocations onchain. Through yearn.watch, we keep track of the TVL and risk score to make fund allocation decisions and mitigations if a strategy group has fallen into the “red” high-risk zone:
Score TVL Impact 5 Extreme: greater than USD 100 MM 4 Very high: less than USD 100 MM 3 High: less than USD 50 MM 2 Medium: less than USD 10 MM 1 Low: less than USD 1 MM
## Vault Risk Score Proposal
A vault is a contract that holds funds for up to 20 strategies, the vault risk score is a TVL weighted average for each active strategy, for example:
Strategy X has 5000$funds deposited Strategy Y has 1000$ funds deposited
This vault's risk score would be calculated as follows:
(
(Strategy X risk) * 5000
+
(Strategy Y risk) * 1000
)
÷
6000
## Overall Risk Score Proposal
Risks on some projects may have more relevance than others, so before calculating the overall score we first define the weight for the context we want to apply the framework on, and then we do a weighted average between all risk dimensions and risk profiles:
Risk Profile = Weighted table of which risk dimension is more important given the current context
Risk Score = Weighted average of all 8 dimensions using the risk profile weights
A project may have many risk profiles, so for each profile the score is calculated and the final list that remains is then used with medians to reach the final result.
The projects overall risk score will be presented in 3 variables:
• high: profile score for a risk-averse user
• low: profile score for a risk-seeking user
• median: profile score for a median representative user
Where each one of these use the final list median:
• high: median + 1.5 IQR
• low: median - 1.5 IQR
• median: the median value from the distribution
Where IQR stands for the interquartile range of the distribution
Here is what the final result looks like:
{
'overallScore': {
'high': 3.37675585284281,
'low': 2.5463210702341135,
'median': 2.9615384615384617,
},
} | 2023-01-29 08:57:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3955848813056946, "perplexity": 3011.3427273963744}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499710.49/warc/CC-MAIN-20230129080341-20230129110341-00478.warc.gz"} |
http://vwws.farmaciaflaminia.it/blank-size-calculation-formula.html | # Blank Size Calculation Formula
A correlation coefficient of. As an extreme case I created a test workbook with only 40000 formulae whose file size is just over 3MB, but which exceeds the 80MB formula limit when saved and reopened. A board foot is actually a measure of volume. Coil Calculator The coil calculator tool on this page is designed to help you quickly and easily determine common coil sizes based on your specific requirements. In this case, the calculations use a complementary angle for the OSSB, and the dimensions are called from the edge to the apex—again, as specified in Figure 4. Tutorials The new Learning Center is a way for you to discover the latest methods for producing signage, displays and other graphic topics. 53 - 1)]] + 1. Cooling, heating and ventilation are the cornerstones to a productive workplace. You may have to register before you can post: click the register link above to proceed. This has been a guide to Capacity Utilization Rate formula, its uses along with practical examples. TRIR Calculator. Press Esc to return to the Ready mode. I received a set of drawings from a customer recently and need to calculate my blank size (total flat pattern size) which I believe is based on the outside dimensions minus the material thickness. In this tutorial, we are going to look at how to recalculate and refresh formulas in Microsoft Excel. Minimum Blank Size: (MBS) The smallest lens blank that can be used and still cut out to fit a frame. Typically the K-Factor is going to be between 0 and. Percent increase is a useful thing to calculate when comparing time periods, estimating growth percent (yearly, monthly, daily etc. Use of the VFCP Online Calculator does not create or confer legally enforceable rights upon any person or entity. We have created a Bowling Average Calculator to help you determine your average. The second flat-blank-development example adds the two dimensions (from edge to the apex), and subtracts a bend deduction. gov) “Start with a large Number and narrow it down”. Facing is the process to remove the material from the surface at right angles to the axis of rotation of the job. The equations involved in an HVAC calculation formula are analyzed to determine the heating and air conditioning capacity required by the system. The formula is $$S = r \theta$$ where s represents the arc length, $$S = r \theta$$ represents the central angle in radians and r is the length of the radius. CDC - BMI Percentile Calculator for Child and Teen - This calculator provides BMI and the corresponding BMI-for-age percentile on a CDC BMI-for-age growth chart. Select different type of metals from drop down for weight calculation. How to Order. In Excel, you build formulas that, for example, populate cells and create tables and charts. We can use many methods to create formula in excel. When finished, click OK. Pre-form for full circle forming 6. Beyond the Trip Cost Calculator: How to Save on Gas Money by Using GasBuddy. The basis of many formulas used for such tonnage calculations are uniform and even shapes, with easily calculated surfaces areas, length or volumes. The formula is:. Hi Steve,. Be sure to require an exact match. Here are the other suggested articles - Formula of Current Yield of a Bond; Examples of Rate Formula in Excel; Dividends per Share Formula. 5) and the confidence interval (0. While most bowhunters pay an awful lot of attention to arrow speed. My account. The water is at20C, has a density of998 kg/m3 , a vapour pressure of0. Use that menu path to view the definitions for names Data, Ranks, Subset, and SubRanks. D) Apparatus: Round bottom flask, water condenser, Burette, Pipette,Heating mantle. Cochran's Sample Size Formula. for bands wider than 4mm you take the width subtract 4. Need a hand showing how to add the icon to your smart phone. Offset is an interesting formula and it's one that can do so much more than meets the eye. 00000785 X LENGTH. WPCC – creates forms calculators with the construction of the formula for the calculation, and… ZetRider 4,000+ active installations Tested with 3. In other words, the formula is z = (data point - mean) / standard deviation. Use the name Abbreviation for the lookup table. 93, for each of the 10 2-team parlays would be $38. His stock price went from$45 per share, to $47 per share. As a worksheet function, the ISBLANK function can be entered as part of a formula in a cell of a worksheet. Flat blank length 4. Compare above data between different types of heads (Hemispherical and Torispherical) by selecting from drop down. « Back to Glossary Index. Calculation for corrugated boxes involve a few of the following 1. You will also find the designation for different thread forms according to international standards. Evaluate(cell. Use Copy/Paste to get the formula for the remaining cells of the first column. Ensure complete coverage. The Current Ratio is used to test the company's ability to pay its short term obligations. Reagents: * Mercuric sulphate (< 1gm) * Sulfuric Acid (1 Kg H 2 SO 4 + 5. The bend allowance describes the length of the neutral axis between the bend lines, or in other words, the arc length of the bend. 5) and the confidence interval (0. It lists the number of products (column C) in different categories (column A) sold by various salesman (column B). Numbers are displayed in scientific notation in the amount of significant figures you specify. 1416 = Length of Plate Required. Use of the VFCP Online Calculator does not create or confer legally enforceable rights upon any person or entity. Calculation of Chemical Oxygen Demand (C. In this article, we will see how to use the TI83/84 calculator to calculate z and t intervals. You can get a lot smarter in just five minutes. Compound Interest Formula. This tool will calculate the area of a rectangle from the dimensions of length and width. α：Lead angle I：Lead n：Number of threads P：Pitch. Check the help section for formulas, equations, and table of density for a wide variety of materials – from A for aluminum to Z for zinc. The proliferation of these tools in the hands has empowered product. Screencast. Offset is a way of giving Excel an address to go to. Collapse strength of continuous slot screen is dependent on diameter of the screen, size, shape, and material type of wire used in its manufacture, and the slot size. When enabling “Calculated price”, the unit price will be the one you enter under the product’s price field. Take the medium basis weight(s) multiplied by the normal take up factors of 1. The answer that the formula calculates displays in the selected cell. Over 250 free printable maths reference charts for interactive whiteboards, classroom displays, math walls, student handouts, homework help, concept introduction and. Small Business Administration’s proposed rule, Small Business Size Standards: Calculation of Annual Average Receipts. However, it won't be as accurate as other methods -- like underwater weighing -- used to determine body fat levels. Check the help section for formulas, equations, and table of density for a wide variety of materials – from A for aluminum to Z for zinc. Verify all calculations with a professional engineer. Calculating the absolute value is very common in Excel data processing. Pre-form for full circle forming 6. The sample we have just calculated since its values are so close to these we could conclude that most likely these samples are from the same depositional environment. The water is at20C, has a density of998 kg/m3 , a vapour pressure of0. S: If you want to calculate hydraulic press tonnage, you can use our hydraulic press tonnage calculator. The first covers those that demonstrate a company's financial strength and liquidity, while the second gives a glimpse into a company's efficiency in using its asset base to generate earnings. Calculator for Rolled Length of Roll of Material Calculates the rolled length of a roll of material when the outside diameter of the material, thickness of the material, and the diameter of the hole in the center or the tube on which the material is wound are given. If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse, the cosine is the ratio of the adjacent side to the hypotenuse, and the tangent is the ratio of the opposite side to the adjacent side. If you know the level of precision you want (that is, your desired margin of error), you can calculate the sample size needed to achieve it. It is the diameter of the circle that passes through every bolt holes. Determine the frame PD, which is (usually the addition of the eye size and the bridge size, if that is the measurement at the 180 cutting line. We sell most of our lumber by the board foot. Check out our five minute lessons on Excel, Microsoft Word, and Google Analytics. com › Article › Bending. Pound 4 Pound Deep Drawn Coin Storage Nottingham Trent University, Maudsley Building, Goldsmith Street, Nottingham, NG1 4BU Tel: +44(0) 7817913649 Email: [email protected] Use this handy laminated template to accurately calculate boxed lens dimensions, Minimum Blank Size, re-dot PDs and Heights, check seg heights, etc. Does any body have the formula to calculate blank diameter of 10 % Torispherical Dished Ends, 2:1 Ellipsoidal Dished Ends. It also demonstrates how to create a table calculation using the calculation editor. Sorry this example is not related to the images above, but the process would still work. BD = {[2(R + T) x tan(A/2)] - BA}. Check the help section for formulas, equations, and table of density for a wide variety of materials – from A for aluminum to Z for zinc. Phone - (440) 251-4290 Fax - (440) 639-2838 E-Mail - [email protected] Pitch Diameter Blank Diameter. Module The length in mm of the pitch circle diameter per tooth. Pre-form for full circle forming 6. A calculator is required for the brief quiz that completes the activity. Calculator This calculator computes all parameters ( spring rate, maximum load, maximum stress, solid height, coil pitch, coil angle, wire length, resonant frequency, shear modulus, and spring mass ) related to a compression spring from basic geometry and material data input. How much money will it take to start your small business? Calculate your startup costs. 25 N Potassium Dichromate (12. The metal weight calculator from Industrial metal Supply asks for some basic info to calculate the weight in pounds of your metal. Learn vocabulary, terms, and more with flashcards, games, and other study tools. 022 × 10 23 particles. Anyway, now we are getting to the most exciting part - practical uses of the OFFSET function. Start studying CIS 150 Exam07: Excel Chapter 2 (2016v1). 14 by the thickness of the blank. Calculate the weight and volume of cubes, cuboids and spheres Calculate the weight or dimensions of a cube, cuboid or sphere. Contact Advantage Fabricated metals for custom metal components and metal fabricating services including stamping, roll forming, and other metal forming and welding services. The interior is two four-page spreads or 374 square inches. The piping diameter is 1½" and above, the following table shall be followed for the thickness of blind plate. No more guessing! Quickly find the length of a roll by using this convenient roll length calculator. Do you need figure out your company's TRIR. This tool will calculate the area of a rectangle from the dimensions of length and width. For further technical fundamentals and exlanations please check chapter "Optics". Time is an continuous data type that would you an SPC chart such as an I-MR. The earlier age at delivery of multiple gestations is a reflection of the increased incidence of preterm labor and obstetric intervention for complications such as preeclampsia, abruptio placentae, fetal growth restriction, and increased risk for stillbirth that occurs as the number of fetuses increases [30-33]. So, the most important amortization formula is probably the calculation of the payment amount per period. So, calculate the volume of the formed part, and estimate the blank dimensions, assuming that volumeof material rmais constant. The following are to links of sheet metal design resources, tools, articles and other useful data. 372t r = The radius on the inside curve of the bend. You may have to register before you can post: click the register link above to proceed. Length of bend calculations for tube and pipe. Gear Parameter Calculator Use the calculator below to figure out various gear specifications given two of the following; tooth count, diameter, and/or pitch. If you know the weight of the deceased - then you know the size of the urn you need. The calculation could be based on volume, surface area or by layout. Approx Weight = Approx Size. Normally we can apply the formula of =(TODAY()-B2)/365. To determine the size of your dataset follow the formula: Size (in bytes) = (8*Number of cases or rows*(Number of variables + 8)) Depending on your Stata version and computer power, you can allocate up to around 2 gigabytes. Note that this calculation does not include the effect of relativity. com is a Wheel Guide and catalogue. 414 ⋅ d12 + 2 ⋅ d1 ⋅ h + f ⋅ (d1 + d 2 ) 13 d 2 h d2 + 4 ⋅ h2 14 d1 d2 h d22 + 4 ⋅ h2 15 d1 d2 h2 h1 d 2 2 + 4 ⋅ h. Lookup fields are not supported in a formula, and the ID of newly inserted row can't be used as the ID doesn't exist when the formula is processed. You will also find the designation for different thread forms according to international standards. In order to calculate this you need to input the size of your target. The first covers those that demonstrate a company's financial strength and liquidity, while the second gives a glimpse into a company's efficiency in using its asset base to generate earnings. To calculate the number of Fax machines sold by Brown, we can use the following array formula:. Selecting "Customize It" provides a backup generator recommendation based on your home's size and corresponding outlets and lighting requirements and assumes natural gas appliances in the baseline calculation. Number of draw reduction 9. Axial Thread Rolling Recommended Blank Diameters In Inches and MM For Straight, Metric Threads - RSVP Tooling supplies high-production eternal threading tools including: Circular Chaser, Axial, Radial, Tangential & Geometric Chaser Diehead Systems and in a variety of thread roll styles, Zeus Cut & Form knurling & marking tools, Rollerbox heads, Broaching Heads and a wide range of other. Free math lessons and math homework help from basic math to algebra, geometry and beyond. As a result, this figure tells us how much we need to add or remove to the leg lengths to determine the accurate blank size. The following table can be used to calculate the requirements for sine vibration. If you fill in one of the lines below, this selection will explain a few things about your ratio. Calculate Your Average The first thing you will need to do is determine your bowling average, this typically needs to be done by using at least a 3 game average. The workbook contains 200 worksheets, each containing 200 formulae, and the formulae link each sheet to every other sheet. There isn't a RANKIF function, but you can use the COUNTIFS function to calculate the rank based on items with the same week number. Flow Calculator; Looking for 500 horsepower to the rear wheels? How about 1000 horsepower at the crankshaft? You can determine what size fuel injectors you will need by entering a few simple details into our calculator. Our conversions provide a quick and easy way to convert between Length or Distance units. This formula requires the time dimension because the values are always relative to the period that contains the result. This section covers threading formulas and definitions for how to calculate cutting speed, feed rate, or any other parameter for your thread turning, thread milling, or tapping operations. 5 Othercharacteristicsofdeep drawing •Easiestwayis todrawcylindricalparts fromcircledisc, but… •The processis capableofformingbox (rectangular) shapesorshell-like. 625" respectively. Area and Volume Formula for geometrical figures - square, rectangle, triangle, polygon, circle, ellipse, trapezoid, cube, sphere, cylinder and cone. Im a complete n00b to excel and I really need some help I need a formula to tell me how much certain amounts of sheet aluminum weigh. Lens calculator - Online tools for optical calculations. This empirical rule calculator can be employed to calculate the share of values that fall within a specified number of standard deviations from the mean. In order to help you quickly find the metal weight formula, I made infographic which is not only practical but also beautiful. S Circle, S. You can perform simple as well as advanced calculations on all or selected records. 5) and the confidence interval (0. We sell most of our lumber by the board foot. Get a better picture of your data New charts and graphs help you present your data in compelling ways, with formatting, sparklines, and tables to better understand your data. Here we also provide you with Capacity Utilization Calculator with downloadable excel template. To figure out your own sizing (instead of using the chart) here's the formula: (A [inside diameter] + B [metal thickness])* pi. This calculator allows one to transform a delta (Δ) network to a wye (Y), and wye (Y) to delta (Δ) network, thus solving for unknown resistor values. 1 mole of any substance contains 6. So one of the first things to try, before getting into the marginal gains of formula optimization, is reduce the size of your Google Sheet. In order to help you quickly find the metal weight formula, I made infographic which is not only practical but also beautiful. Can be width or height, but skewed angles are a problem. uk Deep Drawing Blank Size and Reduction Calculations Tractrix Curve Graph and Tractrix Die Drawing Bill of Materials Item NO Part Name Product Description Treatment. 53 - 1)]] + 1. This unique pattern is calculated based on your size and gauge, then blank charts are provided for you to design your own colourwork on the yoke. Or the arc length of the bend. The function tells the spreadsheet the type of formula. If you find an error, or have a suggestion, please send us an email. Online calculators and formulas for a hemisphere and other geometry problems. Reagents: * Mercuric sulphate (< 1gm) * Sulfuric Acid (1 Kg H 2 SO 4 + 5. This sheet has been developed for homs built in Utah’s dry dimares- do not use for other climate conditions. Any wire size or circuit protection tentatively selected with this tool should be reviewed for adequacy, before installation, by a professional applying the applicable industry standards. All spreadsheet formulas begin with an equal sign (=) symbol. A custom column is a column where the value in a cell is computed using a formula that you create. Get social. But you don’t have to be a mathematician to calculate the angles, lengths, widths and depths of the building blocks that make up a segmented glue-up. A simple formula is a mathematical expression with one operator, such as 7+9. google search. Select Material Thickness or insert your material thickness if it is not listed. of Living Space 1-15 kW Electric Range 3- Small Appliance Branch Circuits 1- 5 kW Wall Mounted Oven. Input your target value, tolerances and measurements in the yellow shaded areas. Page 1 of 2 - Winding Check Calculator - posted in Tips, Tricks, Tools and Gadgets: A few months ago I made a simple little Excel spreadsheet to calculate winding check size. ALWAYS REMEMBER {LOAD Site Map > Safety!> Contact Me ! > Enter plain numbers in cells without text or labels. How to calculate the blank development for deep drawing in sheet metal? How to calculate sheet metal development size? Could anyone able to give me a formula for sheet metal bend length calculation. Sample Size Calculator Terms: Confidence Interval & Confidence Level. So it’s a good idea to delete them whenever you can, so you reduce the number of cells Google Sheets is holding in memory. To make your knurling come out properly with no double tracking you need to select the blank diameter of your stock to match the. This calculates the maximum point blank range (MPBR) of a firearm. Size of an unfolded sheet These formulae are used to calculate the measurements of a sheet before folding, the point of reference being the measurements of the folded sheet. If all of them are blank I want to return another blank. of layers of paper in the box. Axial Thread Rolling Recommended Blank Diameters In Inches and MM For Straight, Metric Threads - RSVP Tooling supplies high-production eternal threading tools including: Circular Chaser, Axial, Radial, Tangential & Geometric Chaser Diehead Systems and in a variety of thread roll styles, Zeus Cut & Form knurling & marking tools, Rollerbox heads, Broaching Heads and a wide range of other. Sample Size Calculator Terms: Confidence Interval & Confidence Level. « Back to Glossary Index. After the equal symbol, either a cell or formula function is entered. The bend allowance is the length of the neutral axis between the bend lines. 14 by the thickness of the blank. The second flat-blank-development example adds the two dimensions (from edge to the apex), and subtracts a bend deduction. Unfortunately, the larger an Excel spreadsheet gets, the slower the calculations will be. calculators, engineering calculators Enter value, select units and click on calculate. 2) Kbps means "Kilobits per second" (1,000 bits per second). If you've calculated your height and want to work out your BMI, give the BMI calculator a try. Select FPS unit to calculate diameter in "inch". The fully defined version of Kepler's third law is used to calculate the orbital period of a planet. By what percentage has George's stock inceased ?. Tonnage: Use the following formula to calculate the tonnage required to punch a round hole in mild steel: Punch diameter x Material Thickness x 80 = Tons of pressure required. Module The length in mm of the pitch circle diameter per tooth. Axial Thread Rolling Recommended Blank Diameters In Inches and MM For Straight, Metric Threads - RSVP Tooling supplies high-production eternal threading tools including: Circular Chaser, Axial, Radial, Tangential & Geometric Chaser Diehead Systems and in a variety of thread roll styles, Zeus Cut & Form knurling & marking tools, Rollerbox heads, Broaching Heads and a wide range of other. Check the help section for formulas, equations, and table of density for a wide variety of materials – from A for aluminum to Z for zinc. Blank Size Formula for Sheet Metal Forming - Google Search - Free download as PDF File (. For more information about the Power Query Formula Language, see Learn about Power Query formulas. Thanks for your help. Enter the piston stroke length. Understanding the Formula. To correct for this, multiple 3. As a worksheet function, the ISBLANK function can be entered as part of a formula in a cell of a worksheet. I based the calculator on the H&S chart I have and what I was taught for wider bands (e. Many of the formulas in the sheets depend on using absolute and relative cell references correctly as described in section 8. I hope you haven't get bored with that much of theory. PCD is called as Pitch Circle Diameter. Immediately after the 10-2 dilution has been shaken, uncap it and aseptically transfer 1ml to a second 99ml saline blank. If entered correctly, Excel will surround the formula with curly brackets {} in the formula bar. In this case, your formula's logic is: if Salutation is blank then Primary Addressee else Salutation. When the sheet metal is put through the process of bending the metal around the bend is deformed and stretched. Case 1: Calculate the Difference of Years. In a quick second I know the Blank Size, again it is not the real Blank Size we would use but it is close enough for a quote. To calculate the expected frequency for a category, you can multiply the proportion of that category by the sample size (in here 1000). Flow Rate Formula. This section covers threading formulas and definitions for how to calculate cutting speed, feed rate, or any other parameter for your thread turning, thread milling, or tapping operations. Recipe Cost Calculator is intended for providing help in preparation of the accurate cost for any dish of the menu. The development of the approximate blank size should be done (1) to determine the size of a blank to produce the shell to the required depth and to determine how many draws will be necessary to produce the shell. The bend allowance describes the length of the neutral axis between the bend lines, or in other words, the arc length of the bend. Acceleration, velocity, displacement and frequency are all inter-dependent functions and specifying any two fully defines the motion and the remaining two variables. 14) to calculate the blank circumference of the cutting wheel. 14 by the thickness of the blank. Though the formula defaults to SUM, you can use all of the aggregate functions in Anaplan including, AVERAGE, MIN, MAX, ANY, ALL, FIRST_NON_BLANK, LAST_NON_BLANK, TEXTLIST. Shake the 10-4 dilution vigorously. Start calculating here!. Select the entire formula in your formula bar. Facing is the process to remove the material from the surface at right angles to the axis of rotation of the job. 661 x 10-24g Atomic weight: Average mass of all isotopes of a given element; listed on the periodic table Example: Hydrogen atomic weight = 1. To calculate board footage use the following formulas:. Free TRIR apps for your smart phones. Calculate volume capacity from length, width and height; User Guide. This unique pattern is calculated based on your size and gauge, then blank charts are provided for you to design your own colourwork on the yoke. Where: BA = Bend Allowance. S Circle, S. How to Order. You can type the formula if you wish, but it's much easier to use the Expression Builder instead; click the button beside the formula box to bring up the Expression Builder. Now you can calculate the correlation coefficient by substituting the numbers above into the correlation formula, as shown below. I want to subtract the numbers in one column from those in another, i. You now have sales per day figures for large cups, small cups, and total cups for each given month. So one of the first things to try, before getting into the marginal gains of formula optimization, is reduce the size of your Google Sheet. Add the sum total in cell B14 with the formula =SUM(B12:B13)The calculated result is$355. Acceleration, velocity, displacement and frequency are all inter-dependent functions and specifying any two fully defines the motion and the remaining two variables. Complex sheet metal parts need advanced calculation methods: Many sheet metal parts are complex 3D shapes that are too complex to correctly analyze with simple (or even complicated) text book formulas. Sample size determination is the act of choosing the number of observations or replicates to include in a statistical sample. To calculate quarter in Excel you can use the formula of "INT", "MONTH", "MOD" and "CEILING" function. Check out our five minute lessons on Excel, Microsoft Word, and Google Analytics. TRIR Calculator. Excel Bill Electricity Bill Calculator Formulas In Excel Perfect Computer, Download Invoice Bill Excel Template Exceldatapro Excel Bill, Free Download Tax Invoice Format In Excel Invoice Format Sales Excel Bill, Excel Bill Automated Invoice In Excel Easy Excel Tutorial, Excel Bill Electricity Bill Calculator Formulas. Given any one variable of a circle you can calculate the other 2 unknowns. We sell most of our lumber by the board foot. 75" inside dia. To calculate the number of Fax machines sold by Brown, we can use the following array formula:. There are many tools available for producing fast and rapid blank size estimates. You can find the weight of the box useful for pricing the box for giving quotation to the customers on the spot. 53, and a minimum blank size of 65 mm, with 1. In other words, the formula is z = (data point - mean) / standard deviation. A 2013 study in BMC Public Health showed a BMI calculation that included age and gender was as effective as some clinical measurements of body fat percentage. In this article, we will provide you some insights on how to calculate import tax and duty in Vietnam. Bulk Bag Capacity Calculator & Design Tools FIBC Design Guide The FIBC Design Guide is provided as a means for potential Bulk Bag (FIBC) users to identify the answers to critical questions when determining what FIBC package fits best in their particular application. Although there are no strict rules on how to calculate the size and number of class intervals, there are some useful conventional criteria. The inside bend radius R in m, material thickness T in m, bend angle A in degrees & bend allowance BA are the key elements of this. Now you can use three different methods (Minimum and Maximum Formulas, Top k and Bottom k Formulas, Conditional Minimum and Maximum Formulas) to find the range of values in any data set. Array formula calculations. The use of the common size balance sheet as a comparison tool is discussed more fully in our common size balance sheet tutorial. txt) or read online for free. BD = {[2(R + T) x tan(A/2)] - BA}. The inside bend radius R in m, material thickness T in m, bend angle A in degrees & bend allowance BA are the key elements of this. Find the percentage increase of two numbers, x is what percent of y, and what is x percent of y. \ sometimes, it takes 45 seconds to calc the whole sheet, other times, it takes 5 minutes. Get a better picture of your data New charts and graphs help you present your data in compelling ways, with formatting, sparklines, and tables to better understand your data. That's good, right - you don't want it to be something completely different. The count just refers to the number of threads per inch in the fabric. The Cochran formula allows you to calculate an ideal sample size given a desired level of precision, desired confidence level, and the estimated proportion of the attribute present in the population. Any wire size or circuit protection tentatively selected with this tool should be reviewed for adequacy, before installation, by a professional applying the applicable industry standards. Medication calculations can cause frustration for EMS providers. Derivation of the approximate formula. How to Calculate the Quarter in Microsoft Excel In this article we will learn how to calculate the quarter number for Fiscal Year and Calendar Year in Microsoft Excel. I had a vexing problem that was solved by using a single-cell array formula and wanted to share it with you. Quick tip to Insert formula in excel and how to apply formula to entire column or row. My theoritical value i. If you regularly work with numbers, you probably also work with percentages. Array formulas are ideal for counting or summing cells based on multiple criteria. To calculate quarter in Excel you can use the formula of "INT", "MONTH", "MOD" and "CEILING" function. Clicking outside the box will then initiate a calculation of the impact force and conversion of the data value to the other types of units. In one of our previous articles, we unveiled the power of compound interest and how to calculate it in Excel. In the Query Editor ribbon, click Insert Custom Column. Taper Calculations. Sheet thickness (in): Die edge radius (in): Punch edge radius (in): Bend length (in): Ultimate tensile strength (psi): Factor of safety:. The procedure discussed in this sheet metal design guide is the simplest way to calculate bend allowance with accepted accuracy. Typesetting Simple Formulas. Immediately after the 10-2 dilution has been shaken, uncap it and aseptically transfer 1ml to a second 99ml saline blank. This will be enough for a medium size database but sometimes you may need more memory space to store your dataset. AQL Calculator Use this tool to find your required sample size for inspection Watch the short tutorial video below for step-by-step instructions on how to use the AQL calculator. The formula for this is SB=. This occurs regardless of whether the precedent data and formulas on which the formula depends have changed, or whether the formula also contains non-volatile functions. Tonnage: Use the following formula to calculate the tonnage required to punch a round hole in mild steel: Punch diameter x Material Thickness x 80 = Tons of pressure required. Also does calculations with percentages for compaction and settlement. KAD Group of Companies provide calculation of S. You need to calculate the circumference of the mean diameter of the ring you are rolling. Punching speed = sufficient punching speed allows time for materials to flow through the tool. If you've calculated your height and want to work out your BMI, give the BMI calculator a try. It takes the diameter of the bullet, the grains, and the standard shape, and spits out the BC. Mann-Whitney U Calculator Further Information The Mann-Whitney U test is a nonparametric test that allows two groups or conditions or treatments to be compared without making the assumption that values are normally distributed. The grid method is an effective way to transfer and/or enlarge your original image onto canvas, ensuring correct proportions. Audio File Size Calculations. Arrow Speed (fps): Must be a number between 100 and 450. Phone - (440) 251-4290 Fax - (440) 639-2838 E-Mail - [email protected] This calculator will give you the range you should zero your rifle in order to have the largest MPBR as possible. In this case we must use another special formula. Press Ctrl+c to copy it. PCD of a flange is one of the critical dimensions, usually measured in millimeters. Get a better picture of your data New charts and graphs help you present your data in compelling ways, with formatting, sparklines, and tables to better understand your data. Along with 2:1 Ellipsoidal Head Blank Diameter this tool also calculates head volume and blank weight. The formula for determining the smallest possible lens blank which will work for any given frame and PD combination is as follows: Minimum Blank Size (MBS) = (GCD - PD) + ED In the examples on the previous page, the ED is the same as the A measurement since the frame illustrated is round. The reason we are using COUNTA to calculate the total number of sales for the formula, is because once we create the dynamic range, then we will need a way to calculate the number of sales dynamically as well. Before you use this calculator, you should understand what a golden rectangle is, how to calculate ratios in general and the formula for the golden ratio. Discussion of car crash scenario: Index Work-energy principle. The count just refers to the number of threads per inch in the fabric. Number of draw reduction 9. | 2019-11-18 09:39:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40445059537887573, "perplexity": 1597.7697934737948}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669730.38/warc/CC-MAIN-20191118080848-20191118104848-00453.warc.gz"} |
https://www.experts-exchange.com/questions/21418566/List-remote-files.html | Learn how to a build a cloud-first strategyRegister Now
x
Solved
# List remote files
Posted on 2005-05-10
Medium Priority
435 Views
Hi Experts!
I'm developing an intranet application in PHP that performs a file conversion (XLS to PDF); it lists all the XLS files of a given input folder and saves them as PDF inside a given output folder.
I'l like to be able to specify a network path (such as "\\computer\c$\input") so that my application could list and convert XLS files from folders located even on the users' pcs and save them as PDF the same way (such as "\\computer\c$\output\filename.pdf")... is this possible?
I have Administrator rights so that, if needed, I can set some permissions on those remote folders.
Kupi
0
Question by:Kupi
• 6
• 4
• 2
LVL 5
Expert Comment
ID: 13971050
Yep, that's certainly possible. We have a similar situation in our company currently, and we're accessing remote files in that manner.
If you're running IIS, you need to make sure that the user that IIS runs under has the appropriate network privileges (admin, in this case) to work on the files in question. This could pose a notable security risk, so make sure that your intranet application *stays* intranet, if you know what I mean. You might also want to take other precautions to ensure that you're protected.
If you're running Apache server, you need to change the user that the service runs as. You can do so in the Services console (Start -> Control Panel -> Administrative Tools -> Services). Right-click on Apache and go to Properties. Go to the "Log on" tab, and set the user to a valid network user. In my company, we've setup a specific domain user just for this purpose. Restart Apache server, and it should work nicely. There's a more complete set of instructions here: http://httpd.apache.org/docs-2.0/platform/windows.html#winsvc
In PHP, you can access your resources in the way you mentioned above. For example: fopen("\\computer\share\path\to\file", "w+");
Hope that helps,
-Doug
0
LVL 3
Author Comment
ID: 13975418
Thank you dougday!
I see fopen opens a remote file, but what if I need to access a remote folder and list its files?
0
LVL 36
Expert Comment
ID: 13976381
If the folders do not have a default index page, then you can fopen the folders I believe. If they do, then the only thing I can think of is if you have ftp access so you can find the files.
0
LVL 3
Author Comment
ID: 13976503
My input folder doesn't have web pages in it, just XLS files... so I should be able to list them!
Can someone post an example of using fopen to list files of a given folder? I keep getting a "failed to open stream: Permission denied" error while attempting to do that...
And still cannot use network paths (\\computer), just locals (c:\\)... any help would be very appreciated!
0
LVL 36
Expert Comment
ID: 13976528
Hmm... Try to chmod your folder to 777
0
LVL 3
Author Comment
ID: 13976872
I'm running Windows XP (PHP 4.3.7 + IIS 6) and I've set the full control right to Everyone...
0
LVL 5
Expert Comment
ID: 13978140
You don't use fopen() to list files in a remote folder. That's probably why you're getting a permission denied error.
Try the glob() function instead. http://us4.php.net/manual/en/function.glob.php
It returns an array of files that match a pattern.
For example:
$files = glob("\\\\computer\\share\\path\\to\\folder\\*.xls"); foreach($files as $file) { echo$file . "\n";
}
Would result in an output similar to this:
\\computer\share\path\to\folder\file1.xls
\\computer\share\path\to\folder\file2.xls
\\computer\share\path\to\folder\file3.xls
Hope that helps. Let me know if you have any more questions :)
-Doug
0
LVL 5
Accepted Solution
dougday earned 500 total points
ID: 13978163
Actually, I forgot to use is_array() also to make sure that glob() returned some files. Here's a better example:
$files = glob("\\\\computer\\share\\path\\to\\folder\\*.xls"); if (is_array($files)) {
foreach($files as$file) {
echo \$file . "\n";
}
}
0
LVL 5
Expert Comment
ID: 13978339
Kupi, sometimes the "Everyone" group doesn't behave as you'd expect. I'm not positive that non-user accounts are included in that group (like the IIS user IUSR_***). If you still have directory permission problems, you might want to create a domain account that your IIS can run as. I don't think the IUSR_*** account can access network resources anyway (I could be wrong). So, create an account just for IIS, and change your username in IIS.
To do so, right-click on your web site in IIS -> Properties -> Directory Security -> Edit Authentication Methods for Resource -> Edit Account Used for Anonymous Access.
-Doug
0
LVL 5
Expert Comment
ID: 13978344
Thanks for the A. :) Hope that helped.
-Doug
0
LVL 3
Author Comment
ID: 13984484
dougday,
when I try to use fopen with network paths I get:
Warning: fopen(\\computer\shared_folder\file_name.xls): failed to open stream: Invalid argument
Even the glob function doesn't work...
The strange thing is that everything works fine if client and server are the same machine, so I think it's a permissions issue... I tried setting the full control right to Everyone and Domain Users but nothing changes...
Can you give me a step-by-step explaination of how to create the needed users/groups and set the appropriate rights?
0
LVL 5
Expert Comment
ID: 13987121
First create a domain user for your IIS. Here's a brief tutorial: http://www.ucertify.com/articles/70-218/2101022.html.
Then, log in as that user and make sure you have access to the resources in question. If you have permission issues, you should be able to resolve them by logging on as an administrative user, allowing access to the resources, then logging on as the user you created and testing it. If you need a tutorial on this, there are several out there on the web. Just search for "NTFS Permissions".
Also, if your IIS server uses Integrated Windows Authentication for Directory Security, you'll need to make sure each user has *normal* access to that .xls file -- they can get to it using Windows Explorer.
Once you're sure your user can access your resources, then right-click on your web site in IIS and click Properties -> Directory Security -> Edit Authentication Methods for Resource -> Edit Account Used for Anonymous Access. Then change the user that IIS uses to the one you created.
Hope that helps,
-Doug
0
## Featured Post
Question has a verified solution.
If you are experiencing a similar issue, please ask a related question
Foreword (July, 2015) Since I first wrote this article, years ago, a great many more people have begun using the internet. They are coming online from every part of the globe, learning, reading, shopping and spending money at an ever-increasing ra…
Originally, this post was published on Monitis Blog, you can check it here . In business circles, we sometimes hear that today is the “age of the customer.” And so it is. Thanks to the enormous advances over the past few years in consumer techno…
Explain concepts important to validation of email addresses with regular expressions. Applies to most languages/tools that uses regular expressions. Consider email address RFCs: Look at HTML5 form input element (with type=email) regex pattern: T…
This tutorial will teach you the core code needed to finalize the addition of a watermark to your image. The viewer will use a small PHP class to learn and create a watermark.
###### Suggested Courses
Course of the Month20 days, 17 hours left to enroll | 2017-12-11 14:40:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2613058388233185, "perplexity": 5711.774999455223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948513512.31/warc/CC-MAIN-20171211125234-20171211145234-00128.warc.gz"} |
https://www.linknovate.com/affiliation/university-of-electronic-science-and-technology-of-china-412/ | Chengdu, China
Chengdu, China
The University of Electronic Science and Technology of China is a research-intensive university in Chengdu, China. Wikipedia.
Time filter
Source Type
Patent
University of Electronic Science and Technology of China | Date: 2016-12-07
The present invention relates to a serpentine film heater for adjusting temperature uniformity and a method of temperature adjusting, including a substrate and a serpentine film heating wire which is deposited on the substrate, wherein the serpentine film heating wire is formed by several parallel heating sections and connecting lines. In the longitudinal direction, the temperature uniformity is improved by adjusting the spacings between adjacent heating sections or line widths of the heating sections separately or in combination. In the transverse direction, the every heating section is adjusted to a shape which is wide in center and narrow at two ends. By adjusting the spacings and line widths in both transverse and longitudinal directions the present invention reduces heating power in the central part of the substrate and increases the heating power on the edges, thus compensates the heat transfer difference between center and edges and improves the temperature uniformity.
Patent
University of Electronic Science, Technology of China and Institute Of Electronic And Information Engineering In Dongguan | Date: 2016-12-07
A bidirectional Metal-Oxide-Semiconductor (MOS) device, including a P-type substrate, and an active region. The active region includes a drift region, a first MOS structure and a second MOS structure; the first MOS structure includes a first P-type body region, a first P+ contact region, a first N+ source region, a first metal electrode, and a first gate structure; the second MOS structure includes a second P-type body region, a second P+ contact region, a second N+ source region, a second metal electrode, and a second gate structure; and the drift region includes a dielectric slot, a first N-type layer, a second N-type layer, and an N-type region. The active region is disposed on the upper surface of the P-type substrate. The first MOS structure and the second MOS structure are symmetrically disposed on two ends of the upper layer of the drift region.
Quan G.,University of Electronic Science and Technology of China | Li G.,University of Electronic Science and Technology of China
Proceedings of 2016 IEEE Advanced Information Management, Communicates, Electronic and Automation Control Conference, IMCEC 2016 | Year: 2016
The paper has proposed an adaptive beam forming method based on the secondary combination of the array elements. After the partition of the array, the adaptive beam is achieved by the sub-array for the desired signals and the jamming signals, and the jamming signals are restrained deeply by the pattern of the sub-array. The outputs of the sub-arrays are combined secondarily as the array elements. The pattern of the secondary combination array is synthesized to compensate the pattern of the sub-array oppositely. The simulation for the uniform linear array (ULA) proves the effectiveness of the method. © 2016 IEEE.
QIN X.,University of Electronic Science and Technology of China | CHO S.Y.,Gyeongsang National University
Acta Mathematica Scientia | Year: 2017
In this article, fixed points of generalized asymptotically quasi-ϕ-nonexpansive mappings and equilibrium problems are investigated based on a monotone projection algorithm. Strong convergence theorems are established without the aid of compactness in the framework of reflexive Banach spaces. © 2017 Wuhan Institute of Physics and Mathematics
Yi B.,University of Electronic Science and Technology of China | Chen X.,University of Electronic Science and Technology of China
IEEE Transactions on Power Electronics | Year: 2017
In this paper, a high-side p-channel LDMOS (p-LDMOS) with an auto-biased n-channel LDMOS (n-LDMOS) based on Triple-RESURF technology is proposed. The p-LDMOS utilizes both carriers to conduct the on-state current; therefore, the specific on-resistance (Ron,sp ) can be much reduced because of much higher electron mobility. The simulation result shows that the proposed 300-V p-LDMOS obtains a Ron,sp of 16.97 mω/cm2, which is about 65% reduced compared with the Triple-RESURF silicon limit and is comparable to an optimized n-LDMOS (BV = 340 V, Ron,sp = 18 mω/cm2). In addition, due to larger current capability, the active area of the proposed p-LDMOS is only about one third of an optimized Triple-RESURF p-LDMOS. The turn-on (tr ) and turn-off time (tf ) are reduced by 51.2% and 40.0%, compared to the optimized Triple-RESURF p-LDMOS, respectively. © 2016 IEEE.
Xiao M.,University of Electronic Science and Technology of China | Nagamochi H.,Kyoto University
Leibniz International Proceedings in Informatics, LIPIcs | Year: 2016
In this paper, we study the problem of finding an integral multiflow which maximizes the sum of flow values between every two terminals in an undirected tree with a nonnegative integer edge capacity and a set of terminals. In general, it is known that the flow value of an integral multiflow is bounded by the cut value of a cut-system which consists of disjoint subsets each of which contains exactly one terminal or has an odd cut value, and there exists a pair of an integral multiflow and a cut-system whose flow value and cut value are equal; i.e., a pair of a maximum integral multiflow and a minimum cut. In this paper, we propose an O(n)-time algorithm that finds such a pair of an integral multiflow and a cut-system in a given tree instance with n vertices. This improves the best previous results by a factor of Ω(n). Regarding a given tree in an instance as a rooted tree, we define O(n) rooted tree instances taking each vertex as a root, and establish a recursive formula on maximum integral multiflow values of these instances to design a dynamic programming that computes the maximum integral multiflow values of all O(n) rooted instances in linear time. We can prove that the algorithm implicitly maintains a cut-system so that not only a maximum integral multiflow but also a minimum cut-system can be constructed in linear time for any rooted instance whenever it is necessary. The resulting algorithm is rather compact and succinct. © Mingyu Xiao and Hiroshi Nagamochi.
Huang W.-H.,TU Dortmund | Yang M.,University of Electronic Science and Technology of China | Chen J.-J.,TU Dortmund
Proceedings - Real-Time Systems Symposium | Year: 2017
When concurrent real-time tasks have to access shared resources, to prevent race conditions, the synchronization and resource access must ensure mutual exclusion, e.g., by using semaphores. That is, no two concurrent accesses to one shared resource are in their critical sections at the same time. For uniprocessor systems, the priority ceiling protocol (PCP) has been widely accepted and supported in real-time operating systems. However, it is still arguable whether there exists a preferable approach for resource sharing in multiprocessor systems. In this paper, we show that the proposed resource-oriented partitioned scheduling using PCP combined with a reasonable allocation algorithm can achieve a non-trivial speedup factor guarantee. Specifically, we prove that our task mapping and resource allocation algorithm has a speedup factor 11-6/(m+1) on a platform comprising m processors, where a task may request at most one shared resource and the number of requests on any resource by any single job is at most one. Our empirical investigations show that the proposed algorithm is highly effective in terms of task sets deemed schedulable. © 2016 IEEE.
Sun X.,University of Electronic Science and Technology of China | Wang Z.,University of Electronic Science and Technology of China | Fu Y.Q.,Northumbria University
Carbon | Year: 2017
Effects of grain boundaries (GBs) in graphene on adsorption and diffusion of sodium were investigated using first principle calculations. Results showed that the presence of GBs in graphene enhanced the adsorption of sodium, with their adsorption energies in the range of −1.32∼-0.79 eV, which were lower than the value of −0.67 eV for sodium adsorbed on pristine graphene. The diffusion energy barriers were in the range of 0.09–0.35 eV when sodium was diffused along GBs of graphene, whereas they were decreased when sodium was gradually diffused into the GBs. Results showed that graphene with GBs had a larger energy storage capacity for sodium than the pristine one, indicating that it can be used as a good anode material for sodium ion batteries. © 2017 Elsevier Ltd
Xia Y.,University of Electronic Science and Technology of China | Tang Z.-C.,University of Electronic Science and Technology of China
Various parameters, such as biodiesel price, capital cost, interest rate, operating cost, feedstock price, maintenance rate, biodiesel conversion efficiency and glycerol price, may exhibit variation in the techno-economic assessments of biodiesel production within the project's lifetime due to economic and technical uncertainties. This paper first defines a new indicator for techno-economic assessments of biodiesel production when all uncertain parameters are regarded as being uniformly distributed within their variation ranges. This new indicator is named economical infeasibility probability (EIP), which defines the probability that total profit, payback period and net present value (NPV) of biodiesel production or one of them or two of them do not satisfy the prescribed requirements, and the Monte Carlo Simulation (MCS) method is employed to evaluate EIP. Based on economical infeasibility analysis, the sensitivity analysis of EIP with respect to an individual uncertain parameter is defined, and MCS is utilized to evaluate the effect. It is found that EIP for the studied biodiesel production is 0.3676 under the selected distributions of uncertain parameters, and biodiesel price, feedstock price, biodiesel conversion efficiency and operating cost have significant effects on EIP, while capital cost, maintenance rate, interest rate and glycerol price have negligible effects. © The Royal Society of Chemistry.
Wang Z.,University of Electronic Science and Technology of China | Liu Q.,University of Electronic Science and Technology of China
IOP Conference Series: Earth and Environmental Science | Year: 2017
The clustering of buildings on the city map is an important field of cartographic and the main step to resolve issues related to the scale of the city map transformation process. The development of computer technology promotes the studies of cartographic and modelling algorithms. In order to achieve automatic clustering of map elements, the domestic and foreign scholars have proposed numerous automatic clustering algorithms. Although each algorithm works for specific problems, all algorithms are based on the graphical analysis transformation of building polygons on the map. By reading and analyzing current development of domestic and foreign researches, we find out that map building clustering needs more inspiring interactive features and automatic integrated decision-making simulation functions. It needs to improve the visualization software and integrated automatic intelligence, increase the proportion of the batch to support implementation of automated cartographic generalization to a higher level. © Published under licence by IOP Publishing Ltd.
Wang P.-P.,University of Maryland University College | Yu S.-J.,University of Maryland University College | Govorov A.O.,Ohio University | Govorov A.O.,University of Electronic Science and Technology of China | Ouyang M.,University of Maryland University College
Nature Communications | Year: 2017
Cooperative chirality phenomena extensively exist in biomolecular and organic systems via intra-and inter-molecular interactions, but study of inorganic materials has been lacking. Here we report, experimentally and theoretically, cooperative chirality in colloidal cinnabar mercury sulfide nanocrystals that originates from chirality interplay between the crystallographic lattice and geometric morphology at different length scales. A two-step synthetic scheme is developed to allow control of critical parameters of these two types of handedness, resulting in different chiral interplays expressed as observables through materials engineering. Furthermore, we adopt an electromagnetic model with the finite element method to elucidate cooperative chirality in inorganic systems, showing excellent agreement with experimental results. Our study enables an emerging class of nanostructures with tailored cooperative chirality that is vital for fundamental understanding of nanoscale chirality as well as technology applications based on new chiroptical building blocks. © 2017 The Author(s).
Liu G.,University of Electronic Science and Technology of China | Li L.,University of Electronic Science and Technology of China
International Conference on Signal Processing Proceedings, ICSP | Year: 2017
Parallel processing technology has become great of importance in a communication channel and error correction techniques are used to accomplish reliable data transmission, especially in redundant residue number system(RRNS). This paper presented a modified algorithm for double error correction in RRNS. We can correct double errors in RRNS more efficiently compared to other algorithms for double errors correction. The modified algorithm reduces the complexity of the hardware and the latency obviously. © 2016 IEEE.
Cheng X.,University of Electronic Science and Technology of China | Lou N.,University of Electronic Science and Technology of China
2016 IEEE International Conference on Communication Systems, ICCS 2016 | Year: 2016
Due to the potential of supporting multi-gigabit data rate, millimeter-wave (MMW) communication is deemed as a key technology for next-generation WLAN and 5G cellular systems. To fully realize the potential of MMW communication, we have to overcome some difficulties, such as phase noise (PHN). The immature CMOS fabrication incurs a relatively large PHN to MMW systems. Without suppression, the PHN can severely degrade the system performance. In this paper, we present a novel PHN suppression scheme for MMW single carrier frequency domain equalization (SC-FDE) systems. The key to suppress PHN is to estimate it as accurately as possible. Capitalizing on the statistical sparsity of MMW PHN in the basis formed by the eigenvectors of PHN autocorrelation matrix, we formulate the PHN estimation into the framework of compressive sensing (CS). In particular, we modify the sparse Bayesian leaning (SBL) strategy to estimate the involved PHN using the data decision available. The obtained PHN estimate is used to compensate for the PHN effect, followed by FDE operation and a re-demodulation of data symbols. This process iterates several times such that we can significantly improve the BER performance. Thanks to the modified SBL adopted, the proposed scheme can not only effectively mitigate the adverse effect of PHN, thereby leading to better performance, but also bear a low computation complexity. © 2016 IEEE.
Dong F.,University of Electronic Science and Technology of China | Pan Y.,University of Electronic Science and Technology of China
ACM International Conference Proceeding Series | Year: 2016
Haze has a great impact on the picture clarity, which cannot meetthe needs of high definition image areas. In this paper, image haze removal algorithms are studied, where the haze image are treated and restored using dark channel prior theory. Dark channel prior is an image Statistics Law - within the vast majority of outdoor haze free image, there are always some points of a color channel whose value is close to zero; Using the law to establish a model, you can well recover haze free image. © 2016 ACM.
Zou Y.,University of Electronic Science and Technology of China | Wan Q.,University of Electronic Science and Technology of China
2016 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, APSIPA 2016 | Year: 2016
This paper considers the problem of moving target localization in noncoherent distributed multiple-input multiple-output (MIMO) radar systems by using the bistatic range and range rate measurements. We propose a weighted least squares (WLS) method to estimate the target position and velocity, and then use the semidefinite programming (SDP) method to improve the accuracy of the WLS estimation by relaxing the constraints that exist in the WLS solution. Simulation results are included to show the performance of the proposed algorithm. It is shown that the proposed method can reach the Cramer-Rao lower bound (CRLB) in a range of moderate measurements noise, and the proposed algorithm is robust to some special geometries, in which the two-step weighted least squares-based (2SWLS-based) methods will be failed. © 2016 Asia Pacific Signal and Information Processing Association.
Zheng Q.,University of Electronic Science and Technology of China | Zhang H.,University of Electronic Science and Technology of China
Circuits, Systems, and Signal Processing | Year: 2017
This paper investigates the robust stabilization problem for a class of polytopic uncertain continuous-time nonlinear switched systems without stable subsystems. In order to analyze the stability of switched systems without stable subsystems, we propose a novel switching Lyapunov function. This new switching Lyapunov function has the “switching-decreasing” property at switching instant. To obtain less conservative results, we propose the switching-decreasing parameter-dependent Lyapunov function (SDPDLF) to investigate the studied switched systems. By using the SDPDLF approach and maximum average dwell time technique, a sufficient condition is obtained to guarantee the studied switched systems to be asymptotically stable. It is shown that the average dwell time should be less than a upper bound. This is different from some previous work, where the average dwell time is larger than a lower bound. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of our results. © 2016, Springer Science+Business Media New York.
Yang S.,Science and Technology on Electronic Information Control Laboratory | Tang W.,University of Electronic Science and Technology of China
Proceedings - 2016 UKSim-AMSS 18th International Conference on Computer Modelling and Simulation, UKSim 2016 | Year: 2016
To reduce the cost of network-wide broadcast in wireless sensor networks (WSNs), it's a common practice to establish a connected dominating set (CDS). A lot of algorithms have been proposed to construct CDS, and most of them aim at reducing the size of the created CDS. Existing distributed algorithms require that all nodes exchange announcement messages to acquire local topology in order to construct CDS. However, the process of construction and maintenance of CDS can cause huge overhead, especially in the context of WSNs, where the node density is high and the quantity of nodes is large. In this paper, we focus upon reducing the overhead of the CDS construction process, and propose a highly efficient distributed algorithm based on our previous work. We show that, to construct a CDS, a portion of nodes in the network don't have to generate announcement messages. An opportunistic announcement scheme is presented to determine such nodes. Simulation results show that the proposed algorithm greatly reduces the overhead compared to existing algorithms, while the size of the established CDS remains the same. An interesting fact is shown that certain nodes can just keep silent during the whole process of construction and maintenance of CDS. © 2016 IEEE.
Zhou Y.,University of Electronic Science and Technology of China | Zu X.,University of Electronic Science and Technology of China
Electrochimica Acta | Year: 2017
A search for high-efficiency electrode materials is crucial for the application of Li-ion batteries (LIBs). Using density functional theory (DFT), we assess the Mn2C sheet, a new MXene, as a suitable electrode material. Our studies show that Li atoms can bind strongly to the Mn2C sheet, with low adsorption energy of −1.93 eV. A pristine Mn2C sheet exhibits metallic characteristic, offering an intrinsic advantage for the transportation of electrons in material. A very low energy barrier of 0.05 eV is predicted, showing that Li ion can easily and freely migrate on the Mn2C sheet. In addition, with the increase of Li content, adsorption energy varies minimally within a range of energy that spans only 0.27 eV, showing that lithiation to a high content is feasible. Furthermore, we found that, because of the bilayer adsorptions on both sides of the Mn2C sheet, the theoretical capacity of the Mn2C sheet is 879 mAhg−1, which is greater than that of most two-dimentional (2D) electrode materials. All these results reveal a new promising MXene material for LIBs. We also studied the effects of oxidation and fluorination on the electrochemical properties of the Mn2C sheet and found that oxidation and fluorination will fade the electrochemical properties of the Mn2C sheet in general. © 2017
Yin L.,University of Electronic Science and Technology of China | Liu Y.,University of Electronic Science and Technology of China
Proceedings of 2016 IEEE 15th International Conference on Cognitive Informatics and Cognitive Computing, ICCI*CC 2016 | Year: 2016
Many biclustering algorithms have been proposed in analyzing the gene expression data and ensemble biclustering methods can improve performance of the biclustering algorithm. We propose a new method of obtaining a variety of constituent biclusters which use different quality measures of bicluster. To demonstrate the efficiency of our methods, experiment on six real gene expression data shows the diversity and biological significance of the biclusters obtained by our methods are higher than that of the compared methods. © 2016 IEEE.
Cai X.,University of Electronic Science and Technology of China | Long J.,University of Electronic Science and Technology of China
International Conference on Signal Processing Proceedings, ICSP | Year: 2017
A very compact polarization diversity quadruple-band-notched ultrawideband (UWB) two-element MIMO antenna and a small size MIMO antenna with four elements are presented in this paper. Firstly, the multi-input multi-output (MIMO) antenna has two identical monopoles. Its high isolation which is less than -20 dB is achieved without using any complex decoupling methods. Secondly, to obtain a band-notched function and improve the area utilization of the antenna, the symmetric split ring resonators (SRRs) are etched next to the feedline and the co-directional complementary split-ring resonator (CSRR) is embedded inside the radiating patch. Thirdly, curve ground plane and arc radiating patch can improve impedance matching performance of the antenna. The two proposed antennas exhibit the suitability for wireless diversity communications. © 2016 IEEE.
Yang F.,University of Electronic Science and Technology of China | Zhang X.,Texas A&M University
2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings | Year: 2016
The impulsive noise effect is one of the most dominant factors to cause performance degradation for power-line communication (PLC) links. Most reported literatures characterize such an impulsive noise based on the Bernoulli-Gaussian or Middleton's approach. However those models may not truly depict the noise characteristics of the impulses with stable property. The symmetric alpha-stable (SαS) noise model stems from the generalized central limit theorem (GCLT), which describes practical PLC impulsive noise well. By modeling the bandpass asynchronous impulsive noise as additive white symmetric alpha- stable noise (AWSαSN), we investigate the analytical symbol error rate (SER) performance of a PLC narrowband system link in smart grid networks. Based on the zero-order statistics, we evaluate the strength of the SαS noise using geometric signal-to-noise ratio (GSNR), and explore the uncoded error performance for the conventional linear receiver. Through extensive experiments and numerical analyses, we show that the analytical SER performance of a PLC link matches the simulation results well, which provides suitable benchmarks and guidance for designation of coded systems. © 2016 IEEE.
Long R.,University of Electronic Science and Technology of China | Ouyang J.,University of Electronic Science and Technology of China
Progress In Electromagnetics Research C | Year: 2017
Matrix method for phased array calibration is an excitation reconstruction method by solving the linear equations based on the linear relationship between the measured near-field data and element excitations. In this paper, we propose a modified matrix method, in which the phased array model is simplified, to measure the element excitations of planar phased array. Our method reduces measurement time greatly at the cost of introducing some calibration errors. The introduced calibration errors can be minimized with the array excitation strategy proposed in this paper. Experimental results validate the effectiveness of our methods in calibrating planar phased arrays. © 2017, Electromagnetics Academy. All Rights Reserved.
Chen B.,Southern Methodist University | Chen B.,Zhejiang University | Ni D.,University of Electronic Science and Technology of China
International Journal of Industrial Organization | Year: 2017
We study optimal pricing issues for a monopolist selling two indivisible goods to a continuum of consumers with correlated private valuations over the goods, where the (positive or negative) correlation is modeled using copulas in the Fréchet family. We derive explicit optimal pricing schemes and comparative statics results for various environments in our setting. The optimal pricing schemes can take several forms, including pure bundling, partial mixed bundling, and mixed bundling, depending jointly on the degrees of asymmetry and correlation of the consumers’ valuations. The explicit optimal pricing schemes also enable us to investigate whether and how the monopolist's profit can be further improved via random assignments. © 2017 Elsevier B.V.
Peng C.,University of Electronic Science and Technology of China | Zou J.,University of Electronic Science and Technology of China | Lian L.,University of Electronic Science and Technology of China
Renewable and Sustainable Energy Reviews | Year: 2017
Recently, with the rapid growth of electric vehicle (EV) and development of Vehicle-to-Grid (V2G) technology, EVs participating in frequency regulation service to support power grid operation has been seen as one of the most promising power grid ancillary services provided by EVs integrated in grid. The dispatching strategy of EVs determines the feasibility and efficiency of EVs participating in frequency regulation, which have been received extensive researches. This paper will review the current dispatching strategies of EVs participating in frequency regulation. At first, the system structure of EVs participating frequency regulation is introduced. The stability and economy of EVs participating frequency in grid are analyzed. Secondly, the existing dispatching strategies are categorized into strategies for stability problem and strategies for economy problem, which are discussed in detailed. Finally, the existing problems and the future researches in EVs participating in frequency regulation on power grid are summarized. © 2016 Elsevier Ltd
Cheng H.,University of Electronic Science and Technology of China | Deng H.,University of Electronic Science and Technology of China | Wang Y.,University of Electronic Science and Technology of China | Wei M.,University of Electronic Science and Technology of China
Journal of Alloys and Compounds | Year: 2017
The influence of the ZnO buffer layer thickness on the structural, electrical, optical and surface properties of Ga-doped ZnO (GZO) films deposited on glass substrates by RF magnetron sputtering were investigated. X-ray diffraction results showed the obtained films had highly c-axis oriented with hexagonal (002) structures and GZO film with 20 nm buffer layer had the best crystalline quality. The resistivity in GZO/ZnO bi-layer films decreased significantly than that in GZO film without a ZnO buffer layer, and GZO film with 20 nm buffer layer showed the lowest resistivity of 4.09 × 10−4 Ω cm. The bi-layer films exhibited the highest transmittance of over 80% in the visible light range and displayed a low near infrared transmittance. The correlation between surface morphology and wettability was studied and GZO/ZnO bi-layer films exhibited hydrophobic property with contact angle of θ from 104° to 108.5°, indicating acceptable property of environmental durability. © 2017 Elsevier B.V.
Guo L.,University of Electronic Science and Technology of China | Chen Y.,University of Electronic Science and Technology of China | Yang S.,University of Electronic Science and Technology of China
IEEE Transactions on Antennas and Propagation | Year: 2017
In this paper, characteristic mode (CM) formulations are developed from surface integral equation (SIE) for the modal analysis of dielectric coated conducting bodies. The electric field integral equation-Poggio, Miller, Chang, Harrington, Wu, and Tsai SIE is used for modeling the dielectric coated conducting bodies. By ensuring the field continuity on the interface boundary, two types of generalized eigenvalues equations are formulated to determine the resonant behavior of the dielectric coated conducting bodies. Following Poynting's theorem, the resultant eigenvalues indicate the ratio of the imaginary and real part of the complex power for each CM. Zero eigenvalues indicate the resonance in dielectric coated conducting bodies. The corresponding modal fields provide with clear physical insights into the radiation/scattering mechanisms. Numerical results are presented to demonstrate the accuracy of the proposed CM formulations. © 1963-2012 IEEE.
Wang J.,University of Electronic Science and Technology of China | Cheng Y.J.,University of Electronic Science and Technology of China
International Journal of Antennas and Propagation | Year: 2017
A W-band hybrid unequal feeding network of waveguide and substrate integrated waveguide (SIW) is presented in this paper. It comprises a two-way hybrid waveguide-SIW E-plane divider and an unequal SIW dividing network. Firstly, the two-way hybrid divider is developed to realize the waveguide-to-SIW vertical transition and power division at the same time. Besides, it has a wider bandwidth and more compact configuration compared with those of conventional structures including a transition and a cascading divider. Secondly, an SIW 1-to-16-way unequal dividing network is developed with the phase self-compensation ability. This W-band dividing network is able to generate the desired amplitude and phase distribution. Finally, two back-to-back SIW 16 × 16 antenna arrays are grouped and fed by the proposed feeding network. The low sidelobe levels (SLLs) can be achieved at E- and H-plane of the antenna. The total aperture size of the antenna is 15% less than that of a conventional antenna with a separated divider and a transition. With such a multifunctional feeding network, the antenna is able to achieve low loss and high efficiency as well. © 2017 Jun Wang and Yu Jian Cheng.
Yu S.,University of Electronic Science and Technology of China | Xiang Y.,University of Electronic Science and Technology of China
Journal of Computational and Theoretical Nanoscience | Year: 2017
The challenge of multi-dimensional performance optimization has been extensively addressed in the literature based on deterministic parameters. Since resources in Cloud Computing platforms are geographically separated and heterogeneous, it is rather difficult to apply a uniform distribution algorithm for achieving various optimization goals. Based on the analysis of cloud service performance measures, this paper proposes an approach for optimal network resource distribution managed by the multi-agent system (MAS), which is aimed to satisfy both the users' and the service providers' requirements. Moreover, a communication algorithm that uses the universal generating function technique is proposed to obtain the service time distribution efficiently. Copyright © 2017 American Scientific Publishers.
Zhang L.,No. 2006 | Zhang H.,University of Electronic Science and Technology of China | Ding X.,Davis
IET Generation, Transmission and Distribution | Year: 2017
In this study, the authors investigate the non-fragile H∞ filtering for large-scale power systems with sensor networks to estimate the state of each subsystem and send the states to different sites. First, for the purpose of enhancing monitoring efficiency, each sensor measures the corresponding subsystem, which can avoid the paralysis of the entire monitoring system caused by the damage of a sensor. Second, they construct the non-fragile filter to adapt the uncertain environment. Sufficient conditions are obtained to ensure that the filtering error system is asymptotically stable with a prescribed H∞ performance level based on the robust control approach. The filter parameters are determined by solving a set of linear matrix inequalities. A simulation example, which shows the efficiency of the proposed methods is included in this study. © The Institution of Engineering and Technology 2016.
Rao Y.,University of Electronic Science and Technology of China
Journal of Internet Technology | Year: 2016
Since many activities of interest often occur in the dark environment, nighttime video enhancement is important for video surveillance. In this paper, we propose a novel and effective nighttime video enhancement algorithm for video surveillance applications by using illumination compensation, which fuses video frames from high quality daytime background and low quality nighttime video. For further improving the perceptual quality of the moving objects, an algorithm based on object region ratio average is also proposed. Experimental results show that the proposed algorithm can obviously improve the visual quality from the conventional methods.
Zheng X.-Y.,Chengdu Engineering Corporation Ltd | Shen J.,University of Electronic Science and Technology of China
Civil Engineering and Urban Planning IV - Proceedings of the 4th International Conference on Civil Engineering and Urban Planning, CEUP 2015 | Year: 2016
Diversion tunnel is often characterized by long tunnel line, extremely complicated geologic conditions and construction techniques, great embedded depth, inspection and maintenance difficulties. Consequently, the problems of construction management and engineering construction schedule control could occur, especially diversion tunnel groups. In this paper, a new ontology-based model for diversion tunnel is proposed, and design and development of the context management system for mobile computing, which is an intelligent context-aware system, is described. Moreover, knowledge sharing and knowledge reuse are also provided by using the ontology model. The context management system makes use of rulebased reasoning that provides derivation of a high-level context from a low-level context. The test results validate the feasibility of the context management system. The achievements of this paper could provide references for the management of diversion tunnel or similar rock engineering. Technical support and scientific basis are also provided for its process control, safety warning, later inspection and maintenance. © 2016 Taylor & Francis Group, London.
Yuan X.,University of Electronic Science and Technology of China | Gan L.,University of Electronic Science and Technology of China
Signal Processing | Year: 2017
In this paper, a novel subspace method is proposed to reconstruct the interference-plus-noise covariance matrix (IPNCM) according to its definition, which can fundamentally eliminate the signal of interest (SOI) component from the sample covariance matrix (SCM). The central ideal is that each interference steering vector (SV) is estimated by the vector lying within the intersection of two subspaces while its power obtained by using the Capon spectral estimator. The first subspace is the interference subspace and it is obtained from each interference covariance matrix term calculated by integrating over each interference angular sector. The second one is the signal-interference subspace got from the SCM. Then a more precise IPNCM is reconstructed based on these accurate estimations. Meanwhile the signal covariance matrix is calculated by integrating over the SOI angular sector so that a new SV estimation of SOI can be obtained from its prime eigenvector. Finally, based on the new IPNCM and the SV of SOI, a novel robust beamformer is formulated to improve the robustness against array model mismatches. Simulation results demonstrate that the proposed beamformer outperforms other existing reconstruction-based beamformers and almost attains the optimal performance in both low and high input signal-to-noise ratio (SNR) cases. © 2016 Elsevier B.V.
Benlic U.,Queen Mary, University of London | Benlic U.,University of Electronic Science and Technology of China | Burke E.K.,Queen Mary, University of London | Woodward J.R.,University of Stirling
Computers and Operations Research | Year: 2017
The problem of assigning gates to arriving and departing flights is one of the most important problems in airport operations. We take into account the real multi-criteria nature of the problem by optimizing a total of nine gate allocation objectives that are oriented both on convenience for airport/airline services and passenger comfort. As far as we are aware, this is the largest number of objectives jointly optimized in the GAP literature. Given the complexity of the considered problem, we propose a heuristic approach based on the Breakout Local Search (BLS) framework. BLS is a recent variant of the Iterated Local Search (ILS) with a particular focus on the perturbation strategy. Based on some relevant information on search history, it tries to introduce an appropriate degree of diversification by determining adaptively the number and type of moves for the next perturbation phase. Moreover, we use a new memory-based greedy constructive heuristic to generate a starting point for BLS. Benchmark instances used for our experiments and comparisons are based on information provided by Manchester Airport. © 2016 Elsevier Ltd
Zhao G.,University of Electronic Science and Technology of China | Fu J.,University of Michigan
Cryopreservation has utility in clinical and scientific research but implementation is highly complex and includes labor-intensive cell-specific protocols for the addition/removal of cryoprotective agents and freeze-thaw cycles. Microfluidic platforms can revolutionize cryopreservation by providing new tools to manipulate and screen cells at micro/nano scales, which are presently difficult or impossible with conventional bulk approaches. This review describes applications of microfluidic tools in cell manipulation, cryoprotective agent exposure, programmed freezing/thawing, vitrification, and in situ assessment in cryopreservation, and discusses achievements and challenges, providing perspectives for future development. © 2017 Elsevier Inc.
Long S.,Chongqing University of Technology | Zhong S.,University of Electronic Science and Technology of China
Nonlinear Analysis: Hybrid Systems | Year: 2017
In this paper, the problem of stochastic stabilization for a class of discrete-time singular Markovian jump systems with time-varying delay is investigated. By using the Lyapunov functional method and delay decomposition approach, improved delay-dependent sufficient conditions are presented, which guarantee the considered systems to be regular, causal and stochastically stabilizable. Finally, some numerical examples are provided to illustrate the effectiveness of the obtained methods. © 2016 Elsevier Ltd.
Mao Y.,Binghamton University State University of New York | Zhang H.,University of Electronic Science and Technology of China | Zhang Z.,Binghamton University State University of New York
IEEE Transactions on Fuzzy Systems | Year: 2017
This paper investigates the finite-time exponential stability analysis and stabilization problem of discrete-time switched nonlinear systems without stable subsystems. In the stability analysis, the Takagi-Sugeno (T-S) fuzzy model is employed to approximate nonlinear subsystems. With two level functions, namely, crisp switching functions and local fuzzy weighting functions, we introduce switched fuzzy systems with approximation errors, which inherently contain both the features of the switched systems and T-S fuzzy systems. By constructing the 'decreasing-jump' piecewise Lyapunov-like functions and minimum dwell time technique, a finite-time exponential stability of switched fuzzy systems with bounded approximation errors is obtained. Then, based on the finite-time exponential stability, a multiobjective evolution algorithm (nondominated sorting genetic algorithm, NSGA-II), which considers two conflicting objectives, such as the average convergence error and the average switching cost, is proposed to generate tradeoff switching sequences to stabilize the discrete-time switched nonlinear systems over a finite-time interval. A numerical example and a practical example are provided to illustrate the effectiveness of the stability and the algorithm, respectively. © 2016 IEEE.
Wang J.,City University of Hong Kong | Wang L.,City University of Hong Kong | Ren J.,University of Electronic Science and Technology of China | Hovhannisyan H.,City University of Hong Kong
IEEE Wireless Communications | Year: 2017
As one of the cornerstones of networked systems, the design of resolution between names and resources, that is, name resolution, is crucial. In recent years, with the emerging research on future Internet architectures, many namespaces and resolution systems have been proposed. However, these namespaces and resolution systems are closed systems, where a system can only support one or more predefined namespaces and the policies for resolution among them. Such closed design lacks the flexibility of defining new resolution policy and interoperability among different networked systems. In this article, we analyze the existing namespaces and resolution systems in various network architectures and propose a generic name resolution framework, which can allow flexible namespace and resolution policy definition and enable interoperation among different network architectures. A prototype of such a name resolution system supporting the interoperability among WiFi, Zigbee, and Bluetooth, and the interoperability between NDN and HTTP is demonstrated. © 2002-2012 IEEE.
Zhang W.,University of Electronic Science and Technology of China | Hou X.,University of Electronic Science and Technology of China
Multimedia Tools and Applications | Year: 2017
The atmospheric light value is a critical parameter in defogging algorithms that are based on atmospheric scattering models. Any error in the atmospheric light value will impact directly on the accuracy of scattering computation and thus cause chromatic distortions in the restored images. To address this problem, this paper proposes a method that relies on clustering statistics to estimate the atmospheric light value. It starts by selecting in the original image some potential atmospheric light source points, which are grouped into point clusters using a clustering technique. From these clusters, several clusters containing candidate atmospheric light source points are selected; the points are then analyzed statistically, and the cluster containing the most candidate points is used for estimating the atmospheric light value. The mean brightness vector of the candidate atmospheric light points in the chosen point cluster is used as the estimate of the atmospheric light value, and their geometric center in the image is accepted as the location of atmospheric light. The experimental results suggest that this statistical clustering method produces more accurate atmosphere brightness vectors and light source locations. This accuracy translates to, from a subjective perspective, both a more natural defogging effect and improvements in various objective image quality indicators. © 2017 Springer Science+Business Media New York
Tang C.-J.,University of Electronic Science and Technology of China
Journal of Electronic Science and Technology | Year: 2017
This literature review on the research of embodied emotion addresses the aspects of the concepts of embodied emotion, the various theories or theses on the embodied emotion abroad and at home, some comments based on the literature are elicited and the discussions about the future research topics on embodied emotion are proposed.
Wang W.-Q.,University of Electronic Science and Technology of China | So H.C.,City University of Hong Kong | Farina A.,IEEE Aerospace and Electronic Systems Society BoG
IEEE Journal on Selected Topics in Signal Processing | Year: 2017
Time and frequency modulated arrays have numerous application areas including radar, navigation, and communications. Specifically, a time modulated array can create a beampattern with low sidelobes via connecting and disconnecting the antenna elements from the feed network, while the frequency modulated frequency diverse array produces a range-dependent pattern. In this paper, we aim to introduce these advanced arrays to the signal processing community so that more investigations in terms of theory, methods, and applications, can be facilitated. The research progress of time/frequency modulated array studies is reviewed and the most recent advances are discussed. Moreover, potential applications in radar and communications are presented, along with their technical challenges, especially in signal processing aspects. © 2016 IEEE.
Liang D.,University of Electronic Science and Technology of China | Xu Z.,University of Sichuan | Liu D.,Southwest Jiaotong University
Information Sciences | Year: 2017
Decision-theoretic rough sets (DTRSs) as a classic model of three-way decisions have been widely applied in the area of risk decision-making. When we confront the complicated and uncertain environment, one of challenges is to estimate the loss function of DTRSs. As a new generalization of fuzzy sets, dual hesitant fuzzy sets (DHFSs) can handle uncertain information more flexibly in the process of decision making and give a new measure for the determination of loss functions of DTRSs. To have more interesting results in the context of three-way decisions, we introduce the new hesitant format of DHFSs into DTRSs and explore a new three-way decision model. Firstly, we take into account the loss functions of DTRSs with dual hesitant fuzzy elements (DHFEs) and propose a dual hesitant fuzzy DTRS model. In order to satisfy the preconditions of three-way decisions, we analyze the normalized principle of loss functions under the dual hesitant fuzzy environment. Meanwhile, some properties of the expected losses are carefully investigated. Then, we further design two approaches for deriving three-way decisions with the new DTRS model, i.e., Method 1 and Method 2, which mainly relies on the comparisons among the expected losses. Method 1 is a general method based on the scores and the accuracies of DHFEs. Method 2 is a ranking method of possibility degrees with a stochastic strategy and enriches the comparisons among the expected losses. Finally, the assessment of emergency blood transshipment is used to illustrate and compare these proposed methods. © 2017 Elsevier Inc.
Wang Z.,University of Electronic Science and Technology of China | Wang Z.,University of California at Irvine | Heydari P.,University of California at Irvine
IEEE Transactions on Circuits and Systems I: Regular Papers | Year: 2017
A study of operating condition and design methods is presented that enables the amplifiers to achieve the upper limit of their power gain at frequencies close to the device fmax. Using the gain-plane approach, the necessary and sufficient conditions to achieve this theoretical upper limit are obtained and the results are analytically verified. As will be demonstrated, the maximum power gain is achieved if and only if the imaginary part of Y12/Y21 becomes zero and the device operates at the edge of the unconditional stability region. In addition, a generic circuit solution comprising both a Y- and a Z-embedding network is proposed to achieve this upper limit. Simulations of a CMOS amplifier surrounded by an exemplary YZ-embedding network verify this study. © 2017 IEEE.
Xue M.,University of Electronic Science and Technology of China | Du Y.,University of Electronic Science and Technology of China
Mathematical Problems in Engineering | Year: 2017
In recent years, the decision-making models with hesitant fuzzy preference relations (HFPRs) have received a lot of attention by some researchers. Meanwhile, the previous studies normally adopt normalization technical means to ensure the same number for all elements, which biases original information of decision-makers. In order to overcome this problem, in this paper, the multiplicative consistency of HFPRs is defined and the highest consistent reduced HFPRs are obtained by means of fuzzy linear programming method from given HFPRs. The proposed regression method eliminates the unreasonable information and retains the reasonable information from a given HFPR. In addition, the proposed method overcomes drawbacks of Zhu and Xu's regression method and is more simple and effective. On account of the obtained reduced HFPRs by the proposed regression method, a GDM model is established. Finally, a supplier selection problem was researched to present the effectiveness and pragmatism of the proposed approach, which proved that the method could offer beneficial insights into the GDM procedure. © 2017 Min Xue and Yifei Du.
Zhong Y.,University of Electronic Science and Technology of China | Liu D.,University of Electronic Science and Technology of China
Proceedings - 2016 9th International Symposium on Computational Intelligence and Design, ISCID 2016 | Year: 2017
With the development of computer network technology and popularization, and the technology of data acquisition, data management and data query develop rapidly. People who is in the surging "data ocean", need an intelligent technology badly, to "explore" more valuable "oil "from the "data ocean", so the data mining technology which has been successfully used in commercial, medical, financial, and other fields, emerges. The primary technology of data mining is classification analysis, cluster analysis, Association Rule analysis, and etc. Association Rule analysis is an important branch of data mining, which can extract the valuable associations or rules people want to know from data warehouse. Based on the background of "data platform for public petition", it aims to study how to combine the Association Rule analysis technology with the current massive government-data, extracting association information from the massive hidden government-data, which can provide userful and valuable information according to the practical significance of the associations for system managers and decision makers. This paper study the classic Association Rule algorithm Apriori, propose the improved Apriori algorithm based on matrix com-pression. Based on this improved Apriori algorithm, develop the module of the analysis of cases evaluation, which can associate the cases and case handlers according to the information of cases and case handlers fistly, and then get the practical significance from the association result analysis, which can provide help to the managers and decision makers. © 2016 IEEE.
Zhang Y.,University of Electronic Science and Technology of China
Proceedings - 2016 9th International Symposium on Computational Intelligence and Design, ISCID 2016 | Year: 2017
The super-resolution passive radar image can be obtained by estimation of signal parameter via rotational invariance technique (ESPRIT) method under the condition of small angular rotation. However, the ESPRIT method needs high signal noise ratio (SNR), which may not be satisfied in actual passive radar system. Therefore, a super-resolution passive inverse synthetic aperture radar (ISAR) imaging framework of moving targets using the relaxation (RELAX) algorithm is proposed under the condition of few illuminators of opportunity and small rotation angle with low SNR. During this framework, the RELAX model of passive radar imaging is mathematically established, and then we apply the RELAX algorithm to extract spatial frequencies and amplitudes of different scatterers on the target. Finally, the super-resolution passive ISAR image can be obtained by frequency searching. Comparing with existing super-resolution ESPRIT method, the proposed method can achieve a more robust reconstruction in low SNR case. © 2016 IEEE.
Wu S.,University of Electronic Science and Technology of China | Shu L.,University of Electronic Science and Technology of China
2016 3rd International Conference on Systems and Informatics, ICSAI 2016 | Year: 2016
One innovation of our paper lies in the introduction of neutral anticipated backward stochastic differential equations (NABSDEs). By the theorem of fixed point, we show that those equations have unique solutions. This type of equations can be regarded as an expansion of classical backward stochastic differential equations (BSDEs). On the other hand, we focus on the neutral systems' optimality problems and obtain a neutral maximum principle by virtue of NABSDEs and duality technique. © 2016 IEEE.
Zheng D.,University of Electronic Science and Technology of China | Zhang H.,University of Electronic Science and Technology of China
Proceedings - 2016 8th International Conference on Intelligent Human-Machine Systems and Cybernetics, IHMSC 2016 | Year: 2016
In this paper, the transformation of control protocols is researched among three kinds of cooperative control (consensus with no leader, tracking control with one leader, containment control with multiple leaders) for multi-agent systems. By the extension of local neighborhood synchronization error, the consensus problem, the tracking problem, and the containment problem are converted to the stability problem of the extended local neighborhood synchronization error. Some results of protocols transformation are present. The main contribution of this paper is not the design of a control protocol, but the result about the transformation of control protocols among consensus, tracking, and containment control, resulting to the cost reduction of the design of another control protocol. © 2016 IEEE.
Jiang T.,University of Electronic Science and Technology of China | Jiang T.,Chengdu Yosemite Ltd Corporation
Proceedings - 2016 8th International Conference on Intelligent Human-Machine Systems and Cybernetics, IHMSC 2016 | Year: 2016
Three dimensional data reconstruction and registration is essential in modern mechanism design and art entertainment, this paper proposed the key technologies of the black/white ring mark based 3D data registration when using monocular laser line scanning technology, including fast circle recognition, mapping circle centers matching between adjacent views, rigid transform matrix computing and 3D data registration, the real sculpture experiments show that the proposed method is successful and effective. © 2016 IEEE.
Kang X.,University of Electronic Science and Technology of China | Yang J.,Singapore Power Group
Computer Networks | Year: 2017
Effective in fighting against “free-riding” and stimulating the cooperation between peers, credit-based incentive mechanisms are widely adopted in today's peer-to-peer (P2P) streaming networks. This work considers a P2P multimedia streaming system that relies on credits for incentivizing peers to upload. The main problem of focus is to derive the optimal strategy for a peer, in terms of allocating its credits across different time slots, to maximize its long-term viewing experience. Especially, the dynamic changing feature of credits is taken into consideration when we formulate the problem, and the optimal credits allocation is shown to be a staircase-like function over time. Then, based on the characteristics of the optimal credits allocation strategy, an effective double-loop iterative algorithm is proposed. For the consideration of practical implementation, three low-complexity credits allocation strategies are proposed. It is shown that each of the strategies has its own feature and is suitable for a specific scenario. Then, as an extension, the proposed credits allocation schemes are reinvestigated for P2P streaming networks that adopt dynamic-pricing credits-based incentive mechanisms. It is shown that the previously obtained credits allocation strategies and algorithms can be easily applied to these systems with minor modifications. © 2017
Ding Y.,Southwest University of Science and Technology | Zhong S.,University of Electronic Science and Technology of China | Long S.,Chongqing University of Technology
International Journal of Robust and Nonlinear Control | Year: 2017
This paper investigates the problem of asymptotic stability in probability for singular stochastic systems with Markovian switchings. A stochastic Lyapunov theorem on asymptotic stability in probability for the considered systems is provided. Also, we show that the original system has the same stability property as its difference-algebraic form based on singular value decomposition. By utilizing the earlier results, a sufficient condition is obtained in terms of linear matrix inequalities, which is easy to check by using standard software. © 2017 John Wiley & Sons, Ltd.
Yao D.,University of Electronic Science and Technology of China
Brain Topography | Year: 2017
Currently, average reference is one of the most widely adopted references in EEG and ERP studies. The theoretical assumption is the surface potential integral of a volume conductor being zero, thus the average of scalp potential recordings might be an approximation of the theoretically desired zero reference. However, such a zero integral assumption has been proved only for a spherical surface. In this short communication, three counter-examples are given to show that the potential integral over the surface of a dipole in a volume conductor may not be zero. It depends on the shape of the conductor and the orientation of the dipole. This fact on one side means that average reference is not a theoretical ‘gold standard’ reference, and on the other side reminds us that the practical accuracy of average reference is not only determined by the well-known electrode array density and its coverage but also intrinsically by the head shape. It means that reference selection still is a fundamental problem to be fixed in various EEG and ERP studies. © 2017 The Author(s)
Zhang M.,University of Electronic Science and Technology of China | Zhang M.,Chinese Academy of Forestry | Wei X.,University of British Columbia | Li Q.,University of British Columbia
Ecohydrology | Year: 2017
Hydrological responses to forest disturbances are highly variable among watersheds. Climatic factors including water and energy are major drivers that determine the hydrological responses to forest disturbances. Although there are a number of large watershed studies on identifying the role of climate in the hydrological response to forest disturbances (e.g., logging, insect infestation, and fire), they are mainly concentrated on the precipitation effect. Given that climatic factors including both water and energy interact dynamically with hydrology and forest, and accordingly with forest–water relationships, there is a need for understanding the joint controls of water and energy on hydrological responses to forest changes by use of an integrated climatic index. In this study, 6 large watersheds along climatic gradients (Willow, Cottonwood, Baker, Moffat, Tulameen, and Ashnola) in the interior of British Columbia (BC), Canada, were selected for investigating the effect of climate on hydrological responses to forest disturbances at a large watershed scale by using modified double mass curves and statistical analysis (time series cross-correlation, linear regression, and Mann–Whitney U test). Key results include the following: (a) in watersheds with a cumulative equivalent clear-cut area of over 30% (Willow, Baker, Moffat, and Tulameen), mean annual flows were significantly increased by about 21–60 mm due to cumulated forest disturbances and (b) mean annual flow response to forest disturbances varied along climatic gradient. The amount of mean annual flow increase due to forest disturbances in energy-limited watersheds Willow and Tulameen was as 3 times as that in water-limited watersheds Baker and Moffat. Similarly, mean annual flow changes due to forest disturbances in wetter years were greater than those in drier years as suggested by results from the study watersheds. These findings highlight the need to develop different strategies for forests management in water-limited and energy-limited watersheds to minimize or adapt hydrological changes due to forest disturbances. Copyright © 2017 John Wiley & Sons, Ltd.
Guo H.,University of Electronic Science and Technology of China | Xi L.,University of Electronic Science and Technology of China
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2016
With the rapid development of photoacoustic imaging, it has been widely used in various research fields such as biology, medicine and nanotechnology. Due to the huge difference among photoacoustic imaging systems, it is hard to integrate them in one platform. To solve this problem, we propose to develop a new universal photoacoustic imaging platform that integrates acoustic-resolution photoacoustic microscopy and optical-resolution photoacoustic microscopy through a multifunctional liquid lens. This lens takes advantage of an inherently low acoustic impedance and a tunable focal length that was characterized by the infusion volume of the liquid. In this paper, the liquid lens was used to realize confocal of laser illumination and acoustic detection for both acoustic-resolution and optical-resolution photoacoustic microscopy. The home-made polyvinylidene fluoride (PVDF) acoustic transducer had a center frequency of 10MHz and -6dB frequency spectrum from 4MHz to 15MHz which yielded to an axial resolution of 70 μm. The lateral resolutions of acoustic- and optical-resolution photoacoustic microscopy were evaluated to be 180 μm and 4.8 μm, respectively. The vasculature of rat ears was carried out to evaluate the performance of optical-resolution photoacoustic microscopy. © 2016 SPIE.
Qi W.,University of Electronic Science and Technology of China | Xi L.,University of Electronic Science and Technology of China
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2016
Optical resolution photoacoustic microscopy (ORPAM) is currently one of the fastest evolving photoacoustic imaging modalities. It has a comparable spatial resolution to pure optical microscopic techniques such as epifluorescence microscopy, confocal microscopy, and two-photon microscopy, but also owns a deeper penetration depth. In this paper, we report a rotary-scanning (RS)-ORPAM that utilizes a galvanometer scanner integrated with objective to achieve rotary laser scanning. A 15 MHz cylindrically focused ultrasonic transducer is mounted onto a motorized rotation stage to follow optical scanning traces synchronously. To minimize the loss of signal to noise ratio, the acoustic focus is precisely adjusted to reach confocal with optical focus. Black tapes and carbon fibers are firstly imaged to evaluate the performance of the system, and then in vivo imaging of vasculature networks inside the ears and brains of mice is demonstrated using this system. © 2016 SPIE.
Tang H.,University of Electronic Science and Technology of China | Nie Z.,University of Electronic Science and Technology of China
ISAPE 2016 - Proceedings of the 11th International Symposium on Antennas, Propagation and EM Theory | Year: 2016
Focusing on the design of the large number of antennas in massive multiple input multiple output (MIMO), this paper has proposed a configuration of the antennas for massive MIMO, and presented a possible working model based on the idea of dynamic combination of the multiple antennas and the antenna arrays. The upper limit of the number of antenna elements for beamforming in the massive MIMO system is studied. Then the zero-forcing (ZF) precoding and quaternary phase-shift keying (QPSK) modulation are applied to evaluate bit error rate (BER) of the proposed configuration. Finally, the simulation results have been given to show the performance of the configuration and the working model proposed in this paper. © 2016 IEEE.
Huang N.,University of Electronic Science and Technology of China | Xi L.,University of Electronic Science and Technology of China
Proceedings of SPIE - The International Society for Optical Engineering | Year: 2016
Zebrafish is a top vertebrate model to study developmental biology and genetics, and it is becoming increasingly popular for studying human diseases due to its high genome similarity to that of humans and the optical transparency in embryonic stages. However, it becomes difficult for pure optical imaging techniques to volumetric visualize the internal organs and structures of wild-type zebrafish in juvenile and adult stages with excellent resolution and penetration depth. Even with the establishment of mutant lines which remain transparent over the life cycle, it is still a challenge for pure optical imaging modalities to image the whole body of adult zebrafish with micro-scale resolution. However, the method called photoacoustic imaging that combines all the advantages of the optical imaging and ultrasonic imaging provides a new way to image the whole body of the zebrafish. In this work, we developed a non-invasive photoacoustic imaging system with optimized near-infrared illumination and cylindrical scanning to image the zebrafish. The lateral and axial resolution yield to 80 μm and 600 μm, respectively. Multispectral strategy with wavelengths from 690 nm to 930 nm was employed to image various organs inside the zebrafish. From the reconstructed images, most major organs and structures inside the body can be precisely imaged. Quantitative and statistical analysis of absorption for organs under illumination with different wavelengths were carried out. © 2016 SPIE.
Huang X.,University of Electronic Science and Technology of China | Pan J.,University of Electronic Science and Technology of China
ISAPE 2016 - Proceedings of the 11th International Symposium on Antennas, Propagation and EM Theory | Year: 2016
A low profile quadrifilar helix antenna based on top-loaded technology for global navigation satellite system is presented in this paper. The top-loaded technology can both be used to reduce the profile of the wire form quadrifilar helix antenna and the printed form. An S-band top-loaded quadrifilar helix antenna has been simulated and possesses the characteristic of wide beam width, high gain at the low elevation, good circular polarization performance and the low profile. This low profile antenna can be an attractive candidate for handset applications. © 2016 IEEE.
Wang J.,University of Electronic Science and Technology of China | Cheng Y.J.,University of Electronic Science and Technology of China
APCAP 2016 - 2016 IEEE 5th Asia-Pacific Conference on Antennas and Propagation, Conference Proceedings | Year: 2016
In this paper, a 92∼94 GHz low sidelobe level (SLL) and high gain slot antenna array based on the substrate integrated waveguide (SIW) technology is presented. The antenna includes two SIW 16×16 arrays, which are placed back-to-back, and a waveguide divider. The aperture size of the antenna is 34×90 mm2. Simulated and measured results show that the return loss is larger than 10dB, and the SLLs in both E-plane and H-plane are under-20dB. The measured results are in good agreement with the simulated ones. © 2016 IEEE.
Wu Y.,University of Electronic Science and Technology of China | Arslanagic S.,Technical University of Denmark
APCAP 2016 - 2016 IEEE 5th Asia-Pacific Conference on Antennas and Propagation, Conference Proceedings | Year: 2016
The multi-layer two-dimensional(2-D) epsilon-negative (ENG), mu-negative (MNG) and double-negative (DNG) materials are investigated in this work. The unit cells consist of infinite dielectric cylinders of which the size and permittivity are chosen to excite the dominant electric and magnetic dipole modes inside the structure. This enables the ENG, MNG, and DNG behaviors. The material parameters are obtained from the simulated S-parameters by use of the Nicholson-Ross-Weir method. For the 2-layer structure in particular, the results show a possibility of DNG realization with a negative refractive index from 303MHz to 305MHz. © 2016 IEEE.
Mao S.,University of Electronic Science and Technology of China | Xiong J.,University of Electronic Science and Technology of China
APCAP 2016 - 2016 IEEE 5th Asia-Pacific Conference on Antennas and Propagation, Conference Proceedings | Year: 2016
The aperture radiation of TEM mode waveguide of two different sizes has been studied. Simulated results show that when the aperture is covered with an effective bulk epsilon-near-zero (ENZ) metamaterial block with the component along the normal of the aperture of the permittivity tensor approaching zero, the beamwidth of the E-plane can be significantly reduced. The effective bulk ENZ block has been implemented by the electric-LC-resonator (ELC) array as well. © 2016 IEEE.
You Q.,University of Electronic Science and Technology of China | Wan Q.,University of Electronic Science and Technology of China
Information (Switzerland) | Year: 2017
In this paper, we address strongly convex programming for principal component analysis, which recovers a target matrix that is a superposition of low-complexity structures from a small set of linear measurements. In this paper, we firstly provide sufficient conditions under which the strongly convex models lead to the exact low-rank matrix recovery. Secondly, we also give suggestions that will guide us how to choose suitable parameters in practical algorithms. Finally, the proposed result is extended to the principal component pursuit with reduced linear measurements and we provide numerical experiments.
Liang D.,University of Electronic Science and Technology of China | Xu Z.,University of Sichuan | Liu D.,Southwest Jiaotong University
Information Sciences | Year: 2017
Three-way decisions with decision-theoretic rough sets (DTRSs) as a typical risk decision method, are generated by Bayesian decision theory and have three kinds of decision strategies, i.e., the acceptance decision, the deferment (non-commitment) decision and the rejection decision. The construction of three-way decisions under the complex decision-making context creates enormous challenges. The determination of loss function is one of key steps. In this paper, we discuss the decision principles of three-way decision rules based on the variation of loss functions with intuitionistic fuzzy sets (IFSs). More specifically, we introduce the intuitionistic fuzzy point operator (IFPO) into DTRSs and explore three-way decisions. Firstly, we construct a loss function matrix with the point operator and analyze its corresponding properties. IFPO implies one type of variation modes for the loss functions of three-way decisions. With respect to the point operator, we show that the prerequisites among loss functions still hold in each stage. Secondly, given the loss functions, we construct the corresponding three-way decision model and deduce three-way decisions. Finally, with the aid of information entropy theory, we further investigate which stage may be most suitable to make the decision. This study extends the range of applications of three-way decisions to the new intuitionistic fuzzy environment. © 2016 Elsevier Inc.
Fan S.,University of Electronic Science and Technology of China | Chi W.,University of Electronic Science and Technology of China
Briefings in Functional Genomics | Year: 2016
Aberrant DNA methylation is considered to be one of themost common hallmarks of cancer. Several recent advances in assessing the DNA methylome provide great promise for deciphering the cancer-specific DNAmethylation patterns. Herein, we present the current key technologies used to detect high-throughput genome-wide DNAmethylation, and the available cancerassociatedmethylation databases. Additionally, we focus on the computationalmethods for preprocessing, analyzing and interpreting the cancermethylome data. It not only discusses the challenges of the differentiallymethylated region calling and the predictionmodel construction but also highlights the biomarker investigation for cancer diagnosis, prognosis and response to treatment. Finally, some emerging challenges in the computational analysis of cancermethylome data are summarized. © The Author 2016. Published by Oxford University Press.
Gao C.,University of Electronic Science and Technology of China | Li X.,University of Electronic Science and Technology of China
Optical Review | Year: 2017
Both experimental results and empirical research have shown that the atmospheric turbulence can present the anisotropic property not only at a few meters above the ground but also at high altitudes of up to several kilometers. This paper investigates the modulation transfer function of a Gaussian beam propagating along a horizontal path in weak anisotropic non-Kolmogorov turbulence. Mathematical expressions are obtained based on the generalized exponential spectrum for anisotropic turbulence, which includes the spectral power law value, the finite inner and outer scales of turbulence, the anisotropic factor, and other essential optical parameters of the Gaussian beam. The numerical results indicate that the atmospheric turbulence would produce less negative effects on the wireless optical communication system with an increase in the anisotropic factor. © 2017 The Optical Society of Japan
He G.,University of Electronic Science and Technology of China | Yang L.,University of Electronic Science and Technology of China
Proceedings - 2016 9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics, CISP-BMEI 2016 | Year: 2016
The development of image processing methods based on partial differential equations, such as denoising, restoration, segmentation and so on, is an emerging field in the last decade, where a large number of models are second order nonlinear diffusion equations. In this article, we present a two level finite volume method to solve the Perona and Malik (P-M) equation. The method involves solving one small implicit Perona and Malik problem on the coarse mesh system, and an explicit Perona and Malik problem on the fine mesh. The numerical results demonstrate that the two level method is efficient and can save a large amount of computational time than the standard FVM method. © 2016 IEEE.
Widaa A.H.A.,University of Electronic Science and Technology of China | Talha W.A.,University of Gezira
Proceedings - 2017 International Conference on Communication, Control, Computing and Electronics Engineering, ICCCCEE 2017 | Year: 2017
Since the 20th century industrial revolution era, automobiles started playing a key and important role in our daily life activities. But, unfortunately, at the same time, an automobiles related accidents, and problems are representing an increasing source of danger on Human's life. In this paper a design of an autonomous (self-driving) car control system is presented to reduce automobiles-related problems. System's design is done by using Fuzzy Logic Control technology in addition to artificial intelligence algorithms. The achieved results demonstrates that proposed design has shown a reliable and efficient performance; all of the main driving control tasks (speed, brakes, steering wheel) were done effectively; it acts just same as a professional human driver. © 2017 IEEE.
Zhong Y.C.,University of Electronic Science and Technology of China | Cheng Y.J.,University of Electronic Science and Technology of China
European Microwave Week 2016: "Microwaves Everywhere", EuMW 2016 - Conference Proceedings; 46th European Microwave Conference, EuMC 2016 | Year: 2016
A wideband pseudo-Bessel beam antenna with a large non-diffraction range is proposed in this paper. A phase shift surface (PSS) with controllable phase shift versus frequency response is employed. Thus, the Bessel beam can be realized over a wideband. Measurement indicates that the relative bandwidth of the Bessel beam antenna is more than 13.7% at Ka-band and the non-diffraction range is more than 150 times of the wavelength at the center frequency of 29 GHz. Good axial symmetry can be achieved because both cellular topology and hexagonal element are used. © 2016 EuMA.
Wu Z.,University of Electronic Science and Technology of China | Hu H.,Huawei
IEEE Region 10 Annual International Conference, Proceedings/TENCON | Year: 2017
Video quality assessment is one of the key techniques in video communication and editing. With constraints of transmission system, storage space etc., original information of videos may not be available. No-reference video quality assessment (NRVQA) methods are in demand. This paper presents a reconstruction-based no-reference video objective quality assessment algorithm for quantization distorted video frames. The proposed assessment is performed without any prior information of distortion or codec parameters. By deeply mining the features of the testing frames, the proposed algorithm can reconstruct zero coefficients' values in every sub-band of frequency coefficients. In addition, non-zero frequency coefficients error will be estimated more accurately with the proposed modified DCT coefficients distribution model. To fully evaluate the proposed NRVQA algorithm, testing video frames are distorted with various quantization steps blindly. Experimental results have showed that the proposed reconstruction-based NRVQA algorithm can give out pleasant performances compared with the state of the art NRVQA algorithms. © 2016 IEEE.
Wu Z.,University of Electronic Science and Technology of China | Hu H.,Hua Wei Technologies Co.
IEEE Region 10 Annual International Conference, Proceedings/TENCON | Year: 2017
With consideration of human visual perception, the structural similarity (SSIM) index has presented a pleasant prediction for video quality assessment in many applications such as video editing and network visual communications. However, SSIM is not implementable in real world applications like IPTV or broadcasting services, which need full access to the original video frames. In this paper we propose a no-reference approach to estimate SSIM without only information of the original video frames. We analysis quantization distortion's affections in video frames' statistical properties and then develop a self-training-based approach to estimate the quantized frames' SSIM. We find an interesting result that the statistical characteristics of test frame can be well estimated by itself and some set of its self-quantized frames. A self-training method is applied to find the optimal quantization step sets for estimation processing. There is no other information requirement in the proposed no-reference SSIM estimation method except the test frame itself. The standard video sequences are taken to evaluate the proposed self-training-based no-reference assessment estimation approach. Experimental results have shown that the proposed approach can give out perfect estimation accuracy and strong consistency with SSIM and subjective evaluations. © 2016 IEEE.
Zhang M.,University of Electronic Science and Technology of China | He J.,University of Electronic Science and Technology of China
Proceedings - 2016 9th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics, CISP-BMEI 2016 | Year: 2016
Fault-tolerant mechanisms have been an essential part of electronic equipments in extreme environments these years. The combined analog circuit system can work properly when one or several parts of it break down. Then, what factors affect the fault-tolerant performance of such systems? System function is the most direct reflection of the output of a circuit, it can necessarily give us much useful information. From the perspective of vectors,this paper analyzed the phase angle of the combined circuit system based on system functions and furthermore inferred the relation between angle and fault-tolerant abilities. Experimental results show that, the larger angle a combined circuit system has, the better its fault-tolerant performance is, which will provide great benefit for designing analog circuit with better fault tolerance. © 2016 IEEE.
Gao S.,University of Electronic Science and Technology of China | Xue R.,University of Electronic Science and Technology of China
Proceedings - 15th IEEE International Conference on Trust, Security and Privacy in Computing and Communications, 10th IEEE International Conference on Big Data Science and Engineering and 14th IEEE International Symposium on Parallel and Distributed Processing with Applications, IEEE TrustCom/BigDataSE/ISPA 2016 | Year: 2016
Locality-aware task scheduling for MapReduce can reduce job execution time by avoiding data transferring. However, many existing scheduling algorithms suffer from either heavy storage overhead, reduced task parallelism, significant response time, or poor scalability. To address these issues, this paper presents BOLAS+, a scalable lightweight locality-aware scheduling algorithm for Hadoop. BOLAS+ takes such global information as block distribution and node performance divergence into consideration for optimal scheduling. BOLAS+ associates each node and each block replica with a value, node importance, and replica priority, respectively. As the only factors for scheduling decision-making, these two values are updated dynamically upon a scheduling request, and are designed in a way that they can be calculated very efficiently. Only simple comparisons within these values of local blocks are involved during scheduling, which guarantees the scalability of BOLAS+. Experimental results show that BOLAS+ can completely eliminate off-switch scheduling, and ensure more than 95% node-local scheduling with a very low complexity O(n/m), which in turn can reduce the total job execution time by up to 15.1%. © 2016 IEEE.
Yang G.,University of Electronic Science and Technology of China | Liang Y.-C.,University of Electronic Science and Technology of China
2016 IEEE Global Communications Conference, GLOBECOM 2016 - Proceedings | Year: 2016
Ambient backscatter communications (AmBC) enables radio-frequency (RF) powered devices (e.g., tags, sensors) to modulate their information bits over ambient RF carriers in an over-the-air manner. This system, called ''modulation in the air'', thus has emerged as a promising technology for green communications and future Internet-of-Things. This paper studies the AmBC system over ambient orthogonal frequency division multiplexing (OFDM) carriers in the air. We first establish the system model for such AmBC system from spread-spectrum perspective, from which a novel joint design for tag waveform and reader detector is proposed. We construct the test statistic that cancels out the direct-link interference by exploiting the repeating structure of the ambient OFDM signals due to the use of cyclic prefix. The maximum-likelihood detector is proposed to recover the tag bits, for which the optimal threshold is obtained with closed-form expression. Also, we analyze the effect of various system parameters on the transmission rate and detection performance. Finally, extensive numerical results show that the proposed transceiver design outperforms the conventional design. © 2016 IEEE.
Liu C.,National University of Singapore | Liu C.,University of Electronic Science and Technology of China | Guo Y.-X.,National University of Singapore | Xiao S.,University of Electronic Science and Technology of China
IEEE Transactions on Antennas and Propagation | Year: 2014
A single-fed miniaturized circularly polarized microstrip patch antenna is designed and experimentally demonstrated for industrial-scientific-medical (2.4-2.48 GHz) biomedical applications. The proposed antenna is designed by utilizing the capacitive loading on the radiator. Compared with the initial topology of the proposed antenna, the so-called square patch antenna with a center-square slot, the proposed method has the advantage of good size reduction and good polarization purity. The footprint of the proposed antenna is 10 × 10 × 1.2mm3. The simulated impedance, axial ratio, and radiation pattern are studied and compared in two simulation models: cubic skin phantom and Gustav voxel human body. The effect of different body phantoms is discussed to evaluate the sensitivity of the proposed antenna. The effect of coaxial cable is also discussed. Two typical approaches to address the biocompatibility issue for practical applications are reported as well. The simulated and measured impedance bandwidths in cubic skin phantom are 7.7% and 10.2%, respectively. The performance of the communication link between the implanted CP antenna and the external antenna is also presented. © 2014 IEEE.
Wang M.,South China University of Technology | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China | Hong K.-S.,Pusan National University
IEEE Transactions on Neural Networks | Year: 2010
This paper presents adaptive neural tracking control for a class of non-affine pure-feedback systems with multiple unknown state time-varying delays. To overcome the design difficulty from non-affine structure of pure-feedback system, mean value theorem is exploited to deduce affine appearance of state variables xi as virtual controls αi and of the actual control The separation technique is introduced to decompose unknown functions of all time-varying delayed states into a series of continuous functions of each delayed state. The novel LyapunovKrasovskii functionals are employed to compensate for the unknown functions of current delayed state, which is effectively free from any restriction on unknown time-delay functions and overcomes the circular construction of controller caused by the neural approximation of a function of and mathdotu. Novel continuous functions are introduced to overcome the design difficulty deduced from the use of one adaptive parameter. To achieve uniformly ultimate boundedness of all the signals in the closed-loop system and tracking performance, control gains are effectively modified as a dynamic form with a class of even function, which makes stability analysis be carried out at the present of multiple time-varying delays. Simulation studies are provided to demonstrate the effectiveness of the proposed scheme. © 2006 IEEE.
Ni D.,University of Electronic Science and Technology of China | Ni D.,University of Windsor | Li K.W.,University of Windsor | Li K.W.,Tokyo Institute of Technology
International Journal of Production Economics | Year: 2012
This research investigates how two supply chain members, a downstream firm (F) and an upstream supplier (S), interact with each other with respect to corporate social responsibility (CSR) behavior and what impact exogenous parameters may have on this interaction. A game-theoretic analysis is conducted to obtain equilibriums for both simultaneous-move and sequential-move CSR games. Under certain assumptions, it is concluded that (1) there exists a mutual incentive between their CSR behavior, whereby a win-win performance in terms of both CSR and profitability is achieved as long as exogenous parameters exceed certain critical thresholds; (2) a higher consumer marginal social-benefit potential (MSBP) or a lower consumer marginal perception difficulty (MPD) helps to lower the critical thresholds of CSR budgets and CSR operational efficiency by S and F, making it easier to achieve the win-win performance; (3) an increase in one supply chain members CSR budget or CSR operational efficiency tends to make the supply chain easier to attain a win-win performance scenario; (4) if CSR decisions are made sequentially, a prior commitment to CSR activities from one supply chain member strengthens the mutual incentive and facilitates the realization of the win-win performance. Business implications of these research findings are also discussed. © 2012 Elsevier B.V. All rights reserved.
Dong B.,Zhejiang University | Ni D.,University of Electronic Science and Technology of China | Wang Y.,University of Windsor
Environmental and Resource Economics | Year: 2012
A polluted river network is populated with agents (e. g., firms, villages, municipalities, or countries) located upstream and downstream. This river network must be cleaned, the costs of which must be shared among the agents. We model this problem as a cost sharing problem on a tree network. Based on the two theories in international disputes, namely the Absolute Territorial Sovereignty (ATS) and the Unlimited Territorial Integrity (UTI), we propose three different cost sharing methods for the problem. They are the Local Responsibility Sharing (LRS), the Upstream Equal Sharing (UES), and the Downstream Equal Sharing (DES), respectively. The LRS and the UES generalize Ni and Wang (Games Econ Behav 60:176-186, 2007) but the DES is new. The DES is based on a new interpretation of the UTI. We provide axiomatic characterizations for the three methods. We also show that they coincide with the Shapley values of the three different games that can be defined for the problem. Moreover, we show that they are in the cores of the three games, respectively. Our methods can shed light on pollution abatement of a river network with multiple sovereignties. © 2012 Springer Science+Business Media B.V.
Zou Y.,Nanjing University of Posts and Telecommunications | Li X.,CAS Xi'an Institute of Optics and Precision Mechanic | Liang Y.-C.,Institute for Infocomm Research | Liang Y.-C.,University of Electronic Science and Technology of China
IEEE Journal on Selected Areas in Communications | Year: 2014
In this paper, we investigate the physical-layer security of a multi-user multi-eavesdropper cognitive radio system, which is composed of multiple cognitive users (CUs) transmitting to a common cognitive base station (CBS), {while multiple eavesdroppers may collaborate with each other or perform independently in intercepting the CUs-CBS transmissions, which are called the coordinated and uncoordinated eavesdroppers, respectively. Considering multiple CUs available, we propose the round-robin scheduling as well as the optimal and suboptimal user scheduling schemes for improving the security of CUs-CBS transmissions against eavesdropping attacks. Specifically, the optimal user scheduling is designed by assuming that the channel state information (CSI) of all links from CUs to CBS, to primary user (PU) and to eavesdroppers are available. By contrast, the suboptimal user scheduling only requires the CSI of CUs-CBS links without the PU's and eavesdroppers' CSI. We derive closed-form expressions of the secrecy outage probability of these three scheduling schemes in the presence of {the coordinated and uncoordinated eavesdroppers. We also carry out the secrecy diversity analysis and show that the round-robin scheduling achieves the diversity order of only one, whereas the optimal and suboptimal scheduling schemes obtain the full secrecy diversity, {no matter whether the eavesdroppers collaborate or not. In addition, numerical secrecy outage results demonstrate that for both the coordinated and uncoordinated eavesdroppers, the optimal user scheduling achieves the best security performance and the round-robin scheduling performs the worst. Finally, upon increasing the number of CUs, the secrecy outage probabilities of the optimal and suboptimal user scheduling schemes both improve significantly. © 2014 IEEE.
Li Y.,National University of Singapore | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE/ASME Transactions on Mechatronics | Year: 2014
In this paper, adaptive impedance control is proposed for a robot collaborating with a human partner, in the presence of unknown motion intention of the human partner and unknown robot dynamics. Human motion intention is defined as the desired trajectory in the limb model of the human partner, which is extremely difficult to obtain considering the nonlinear and time-varying property of the limb model. Neural networks are employed to cope with this problem, based on which an online estimation method is developed. The estimated motion intention is integrated into the developed adaptive impedance control, which makes the robot follow a given target impedance model. Under the proposed method, the robot is able to actively collaborate with its human partner, which is verified through experiment studies. © 1996-2012 IEEE.
He W.,University of Electronic Science and Technology of China | Zhang S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE Transactions on Industrial Electronics | Year: 2014
In this paper, a flexible cable with a payload attached at the bottom is considered to be the model of a crane system used for positioning the payload. The dynamics of the flexible cable coupled with the tip payload contribute to a hybrid system represented by partial-ordinary differential equations. An integral-barrier Lyapunov function (IBLF)-based control is proposed to suppress the undesirable vibrations of the flexible crane system with the boundary output constraint. Adaption laws are developed for handling parametric uncertainties. A novel IBLF is adopted to guarantee the uniform stability of the closed-loop systems without the violation of the boundary constraint. All closed-loop signals are ensured to be bounded. Extensive simulations are demonstrated to illustrate the performance of the control system. © 2013 IEEE.
Yang H.-X.,Fuzhou University | Rong Z.,University of Electronic Science and Technology of China | Wang W.-X.,Beijing Normal University
New Journal of Physics | Year: 2014
The paradox of cooperation among selfish individuals still puzzles scientific communities. Although a large amount of evidence has demonstrated that the cooperator clusters in spatial games are effective in protecting the cooperators against the invasion of defectors, we continue to lack the condition for the formation of a giant cooperator cluster that ensures the prevalence of cooperation in a system. Here, we study the dynamical organization of the cooperator clusters in spatial prisoner's dilemma game to offer the condition for the dominance of cooperation, finding that a phase transition characterized by the emergence of a large spanning cooperator cluster occurs when the initial fraction of the cooperators exceeds a certain threshold. Interestingly, the phase transition belongs to different universality classes of percolation determined by the temptation to defect b. Specifically, on square lattices, 1 < b < 4/3 leads to a phase transition pertaining to the class of regular site percolation, whereas 3/2 < b < 2 gives rise to a phase transition subject to invasion percolation with trapping. Our findings offer a deeper understanding of cooperative behavior in nature and society. © 2014 IOP Publishing and Deutsche Physikalische Gesellschaft.
Guo J.,CAS Institute of Theoretical Physics | Li J.,University of Adelaide | Li T.,CAS Institute of Theoretical Physics | Li T.,University of Electronic Science and Technology of China | Williams A.G.,University of Adelaide
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2015
The Galactic center excess is explained in the framework of the Next-to-Minimal Supersymmetric Standard Model with a Z3 discrete symmetry. We show that a resonant CP-odd Higgs boson with mass twice that of the Dark Matter (DM) candidate is favored. Meanwhile, the DM candidate is required to have relatively large coupling with the Z boson through its Higgsino component in order to obtain correct DM relic density. Its LHC discovery potential via four signatures is discussed in detail. We find that the most sensitive signals are provided by the Higgsino-like chargino and neutralino pair production with their subsequent decays into W bosons, Z bosons, and DM. The majority of the relevant parameter space can be probed at the Large Hadron Collider with a center-of-mass energy of 14 TeV and an integrated luminosity 1000 fb-1. © 2015 American Physical Society.
Lin P.,University of Electronic Science and Technology of China | Ren W.,University of California at Riverside
Proceedings of the IEEE Conference on Decision and Control | Year: 2012
In this paper, we study a distributed subgradient projection algorithm for multi-agent optimization with nonidentical constraints and switching topologies. We first show that distributed optimization might not be achieved on general strongly connected graphs. Instead, the agents optimize a weighted average of the local objective functions. Then we prove that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the graphs is strongly connected among each time interval of a certain bounded length. © 2012 IEEE.
Zhang Y.,University of Electronic Science and Technology of China | Li L.,University of Swansea
Nano Energy | Year: 2016
Experimental findings on electroluminescence or photoluminescence of ZnO nanowires have been drawn much attention due to their promising applications in many areas. One of the current challenges on this technology is a deeper understanding of this phenomenon in order to adopt it into practical device designs. In this work, a theoretical analysis of the stimulated emission of ZnO nanowires taking into consideration of the piezotronics effect has been conducted using the quantum mechanics theory. It is revealed that extra piezoelectric charges induced by applied mechanical forces increase the overall charge density of the nanowire, subsequently enhancing the emission intensity. Electronic bandgap varying with the diameter of the nanowire determines the peak value in the electromagnetic spectrum. Both wavelength and intensity of the stimulated emission can be tuned by controlling the dimension of the nanowires and external applied mechanical forces. © 2016 Elsevier Ltd.
He W.,National University of Singapore | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE Transactions on Control Systems Technology | Year: 2012
In this paper, robust adaptive boundary control is developed for a class of flexible string-type systems under unknown time-varying disturbance. The dynamics of the string system is represented by a nonhomogeneous hyperbolic partial differential equation (PDE) and two ordinary differential equations. Boundary control is proposed at the right boundary of the string based on the original distributed parameter system model (PDE) to suppress the vibration excited by the external unknown disturbance. Adaptive control is designed to compensate the system parametric uncertainty. With the proposed robust adaptive boundary control, all the signals in the closed-loop system are guaranteed to be uniformly ultimately bounded. The state of the string system is proven to converge to a small neighborhood of zero by appropriately choosing design parameters. Simulations are provided to illustrate the effectiveness of the proposed control. © 2006 IEEE.
Wei H.-W.,China Institute of Technology | Peng R.,Cisco Systems | Wan Q.,University of Electronic Science and Technology of China | Chen Z.-X.,University of Electronic Science and Technology of China | Ye S.-F.,China Institute of Technology
IEEE Transactions on Signal Processing | Year: 2010
A new framework for positioning a moving target is introduced by utilizing time differences of arrival (TDOA) and frequency differences of arrival (FDOA) measurements collected using an array of passive sensors. It exploits the multidimensional scaling (MDS) analysis, which has been developed for data analysis in the field such as physics, geography and biology. Particularly, we present an accurate and closed-form solution for the position and velocity of a moving target. Unlike most passive target localization methods focusing on minimizing a loss function with respect to the measurement vector, the proposed method is based on the optimization of a cost function related to the scalar product matrix in the classical MDS framework. It is robust to the large measurement noise. The bias and variance of the proposed estimator is also derived. Simulation results show that the proposed estimator achieves better performance than the spherical-interpolation (SI) method and the two-step weighted least squares (WLS) approach, and it attains the Cramér-Rao lower bound at a sufficiently high noise level before the threshold effect occurs. Moreover, for the proposed estimator the threshold effect, which is a result of the nonlinear nature of the localization problem, occurs apparently later as the measurement noise increases for a near-field target. © 2010 IEEE.
He W.,National University of Singapore | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China | Zhang S.,National University of Singapore
Automatica | Year: 2011
In this paper, boundary control of a marine installation system is developed to position the subsea payload to the desired set-point and suppress the cable's vibration. Using Hamilton's principle, the flexible cable coupled with vessel and payload dynamics is described as a distributed parameter system with one partial differential equation (PDE) and two ordinary differential equations (ODEs). Adaptive boundary control is proposed at the top and bottom boundaries of the cable, based on Lyapunov's direct method. Considering the system parametric uncertainty, the boundary control schemes developed achieve uniform boundedness of the steady state error between the boundary payload and the desired position. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. Simulations are provided to illustrate the applicability and effectiveness of the proposed control. © 2011 Elsevier Ltd. All rights reserved.
Liu X.,Southwest University for Nationalities | Liu X.,University of Electronic Science and Technology of China | Yu W.,East China Normal University | Wang L.,Peking University
IEEE Transactions on Automatic Control | Year: 2010
This note addresses the stability problem of continuous-time positive systems with time-varying delays. It is shown that such a system is asymptotically stable for any continuous and bounded delay if and only if the sum of all the system matrices is a Hurwitz matrix. The result is a time-varying version of the widely-known asymptotic stability criterion for constant-delay positive systems. A numerical example illustrates the correctness of our result. © 2006 IEEE.
Chen B.,Qingdao University | Liu X.P.,Lakehead University | Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore | Lin C.,Qingdao University
IEEE Transactions on Fuzzy Systems | Year: 2012
Controlling nonstrict-feedback nonlinear systems is a challenging problem in control theory. In this paper, we consider adaptive fuzzy control for a class of nonlinear systems with nonstrict-feedback structure by using fuzzy logic systems. A variable separation approach is developed to overcome the difficulty from the nonstrict-feedback structure. Furthermore, based on fuzzy approximation and backstepping techniques, a state feedback adaptive fuzzy tracking controller is proposed, which guarantees that all of the signals in the closed-loop system are bounded, while the tracking error converges to a small neighborhood of the origin. Simulation studies are included to demonstrate the effectiveness of our results. © 2012 IEEE.
Cheng Y.J.,National University of Singapore | Cheng Y.J.,University of Electronic Science and Technology of China | Bao X.Y.,National University of Singapore | Guo Y.X.,National University of Singapore
IEEE Transactions on Antennas and Propagation | Year: 2013
In this paper, miniaturized substrate integrated multibeam array antennas are proposed and designed at 60 GHz. Owing to the design flexibility of the low temperature cofired ceramic (LTCC) technology, the entire multibeam antenna size is only equal to the size of radiating aperture by carefully embedding the complicated substrate integrated waveguide (SIW) feeding network underneath the radiating array. After introducing design procedures for the folded Butler matrix and the corresponding radiating array, a ±45° dual linear-polarization (LP) and a dual circular-polarization (CP) substrate integrated multibeam array antennas are designed and fabricated, respectively. Here, each multibeam antenna has four switchable beams with different pointing directions. Each beam direction has two orthogonal LP or CP modes, therefore allowing the polarization diversity.Measured results validate our design and demonstrate good performances of our proposed structures. © 2013 IEEE.
He W.,University of Electronic Science and Technology of China | Zhang S.,University of Electronic Science and Technology of China | Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore
Automatica | Year: 2014
In this paper, robust adaptive control is developed for a thruster assisted position mooring system in the transverse direction. To provide an accurate and concise representation for the dynamic behavior of the mooring system, the flexible mooring lines are modeled as a distributed parameter system of partial differential equations (PDEs). The proposed control is applied at the top boundary of the mooring lines for station keeping via Lyapunov's direct method. Adaptive control is designed to handle the system parametric uncertainties. With the proposed robust adaptive control, uniform boundedness of the system under the ocean current disturbance is achieved. The proposed control is implementable with actual instrumentations since all the signals in the control can be measured by sensors or calculated by using a backward difference algorithm. The effectiveness of the proposed control is verified by numerical simulations. © 2014 Elsevier Ltd. All rights reserved.
He W.,University of Electronic Science and Technology of China | Zhang S.,University of Electronic Science and Technology of China | Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore
IEEE Transactions on Control Systems Technology | Year: 2014
In this brief, the vibration control problem is investigated for a flexible string system in both transverse and longitudinal directions. The vibrating string is nonlinear due to the coupling between transverse and longitudinal displacements. Using the Hamilton's principle, the dynamics of the nonlinear string are presented by two partial and four ordinary differential equations. With the Lyapunov's direct method, adaptive boundary control is developed to suppress the string's vibration and the adaptive law is designed to compensate for the system parametric uncertainties. With the proposed control, the states of the system eventually converge to a compact set. Numerical simulations are carried out to verify the effectiveness of the proposed control. © 2014 IEEE.
He W.,University of Electronic Science and Technology of China | Sun C.,University of Toronto | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE/ASME Transactions on Mechatronics | Year: 2014
This paper presents a boundary controller for a flexible marine riser to suppress the riser's vibration with a top tension constraint. The flexible marine riser is described by a distributed parameter system with a partial differential equation and four ordinary differential equations. The boundary controller is designed at the top boundary of the riser based on an integral-barrier Lyapunov function to suppress the riser's tension at top. Adaptive control is designed when the system parametric uncertainty exists. With the proposed robust adaptive boundary control, uniformed boundedness under the ocean disturbance can be achieved. Stability analysis of the closed-loop system is given using the Lyapunov stability theory. Simulation results illustrate the effectiveness of the proposed boundary controller with top tension constraint. © 2014 IEEE.
He W.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE/ASME Transactions on Mechatronics | Year: 2015
In this paper, the vibration control problem is studied for a wind turbine tower subjected to random wind loads. The tower is modeled as a nonuniform Euler-Bernoulli beam system with distributed parameters by using the Hamilton's principle. The control force is applied at the top boundary of the tower to suppress the vibrations of the tower. Disturbance observer is designed to attenuate the disturbance at the top of the tower. The stability of the whole system is rigorously proved via the Lyapunov analysis and the satisfactory control performance is guaranteed under the proper choice of the design parameters. Numerical results are provided to illustrate that the designed controller is effective in dissipating the vibrations of the tower. © 1996-2012 IEEE.
Qu S.-W.,University of Electronic Science and Technology of China | Chen Q.-Y.,Beijing Institute of Technology | Xia M.-Y.,Peking University | Zhang X.Y.,South China University of Technology
IEEE Transactions on Antennas and Propagation | Year: 2014
This paper presents two kinds of novel elements to design single-layer dual-band reflectarray, with identical polarization in two closely separated bands. Several degrees of freedom of the proposed elements are tuned to match the desired phase compensations at two center frequencies simultaneously. It is noted that the dual-band characteristics are realized by a single integrated element rather than conventional dual-band elements with independent tunable components corresponding to two center frequencies. A 10× 10-element offset-fed reflectarray operating at 9 and 13.5 GHz, with a ratio of the center frequencies 1.5, is designed and fabricated to validate the performance of the element, and the measured results show reasonable agreements with simulations. Due to the incompleteness of reflection phase distribution at the two center frequencies of the presented element, a complementary element with four resonances is introduced. Then, a 20× 20-element reflectarray composed of both kinds of elements is also designed, and the measured results demonstrate a good availability of the proposed elements. © 2013 IEEE.
Jun S.,University of Electronic Science and Technology of China | Xiaoling Z.,University of Electronic Science and Technology of China | Jianyu Y.,University of Electronic Science and Technology of China | Chen W.,China Institute of Technology
IEEE Transactions on Geoscience and Remote Sensing | Year: 2010
This paper discusses the antenna phase center trajectory (APCT) design for the "one-active" linear-array 3-D imaging SAR (LASAR). First, we discuss the principle of the one-active LASAR and demonstrate its feasibility by experiment. To describe the 3-D spatial resolution of the one-active LASAR, the relationship between the 3-D ambiguity function (AF) of the one-active LASAR and the system parameters is discussed in detail. Based on the analysis, we divide the APCT design into three topics: the direction of the linear array, the length of the linear array, and the switching mode of the active element [named as antenna phase center function (APCF)]. On the first topic, we conclude that, when the range, along-track, and cross-track directions are orthogonal to each other, the ambiguity region of the one-active LASAR attains minimum, and the 3-D spatial resolution can be separated into the range, along-track, and cross-track resolutions. On the second topic, we find that the cross-track resolution is determined by the length of the linear array and the frequency of the carrier. To ensure that the length of the linear array is acceptable, the carrier should beW-band wave or millimeter wave. On the third topic, the effect of APCF is researched, and we find that both the periodic APCF and the pseudorandom APCF can produce 3-D resolution, except for the periodic rectangle APCF. For the pseudorandom APCF and the periodic APCF with short period, the cross-range 2-D AF is or can be approximated as the product of two 1-D AFs in the along-and cross-track directions. Finally, the distribution of the pseudorandom APCF is optimized by the Lagrange multiplier method under the minimum variance criterion, and we find that, when the pseudorandom APCF obeys the parabolic distribution, the cross-range 2-D AF is optimal. © 2009 IEEE.
Tang Z.,Sichuan Agricultural University | Yang Z.,University of Electronic Science and Technology of China | Fu S.,Sichuan Agricultural University
Journal of Applied Genetics | Year: 2014
Hybrids derived from wheat (Triticum aestivum L.) × rye (Secale cereale L.) have been widely studied because of their important roles in wheat cultivar improvement. Repetitive sequences pAs1, pSc119.2, pTa-535, pTa71, CCS1, and pAWRC.1 are usually used as probes in fluorescence in situ hybridization (FISH) analysis of wheat, rye, and hybrids derived from wheat × rye. Usually, some of these repetitive sequences for FISH analysis were needed to be amplified from a bacterial plasmid, extracted from bacterial cells, and labeled by nick translation. Therefore, the conventional procedure of probe preparation using these repetitive sequences is time-consuming and labor-intensive. In this study, some appropriate oligonucleotide probes have been developed which can replace the roles of repetitive sequences pAs1, pSc119.2, pTa-535, pTa71, CCS1, and pAWRC.1 in FISH analysis of wheat, rye, and hybrids derived from wheat × rye. These oligonucleotides can be synthesized easily and cheaply. Therefore, FISH analysis of wheat and hybrids derived from wheat × rye using these oligonucleotide probes becomes easier and more economical. © 2014 Institute of Plant Genetics, Polish Academy of Sciences, Poznan.
Han T.,National University of Singapore | Han T.,University of Electronic Science and Technology of China | Qiu C.-W.,National University of Singapore
Optics Express | Year: 2010
We propose a novel kind of trapeziform cloak requiring only homogeneous anisotropic materials. Large-scale flat cloaks can be degenerated from the general trapeziform cloak with PEC inner boundary, and be realized by isotropic nonmagnetic materials for optical frequencies with controlled index profiles and improved invisibility. With the support of PEC inner boundary, large vehicles and objects of arbitrary shape can be concealed between the PEC and ground, and PEC can be firm by adding pillars in the cloaking space. Full-wave simulations validate the proposed cloaking concept, which is not only based on simple isotropic nonmagnetic materials but also realizable in practice. © 2010 Optical Society of America.
Chen M.,Nanjing University of Aeronautics and Astronautics | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE Transactions on Industrial Electronics | Year: 2015
In this paper, an adaptive neural output feedback control scheme is proposed for uncertain nonlinear systems that are subject to unknown hysteresis, external disturbances, and unmeasured states. To deal with the unknown nonlinear function term in the uncertain nonlinear system, the approximation capability of the radial basis function neural network (RBFNN) is employed. Using the approximation output of the RBFNN, the state observer and the nonlinear disturbance observer (NDO) are developed to estimate unmeasured states and unknown compounded disturbances, respectively. Based on the RBFNN, the developed NDO, and the state observer, the adaptive neural output feedback control is proposed for uncertain nonlinear systems using the backstepping technique. The first-order sliding-mode differentiator is employed to avoid the tedious analytic computation and the problem of "explosion of complexity" in the conventional backstepping method. The stability of the whole closed-loop system is rigorously proved via the Lyapunov analysis method, and the satisfactory tracking performance is guaranteed under the integrated effect of unknown hysteresis, unmeasured states, and unknown external disturbances. Simulation results of an example are presented to illustrate the effectiveness of the proposed adaptive neural output feedback control scheme for uncertain nonlinear systems. © 1982-2012 IEEE.
Han T.,University of Electronic Science and Technology of China | Han T.,National University of Singapore | Qiu C.-W.,National University of Singapore | Tang X.,University of Electronic Science and Technology of China
Optics Letters | Year: 2011
We propose a method for adaptive waveguide bends using homogeneous, nonmagnetic, and isotropic materials, which simplifies the parameters of the bends to the utmost extent. The proposed bend has an adaptive and compact shape because of all the flat boundaries. The nonmagnetic property is realized by selecting OB′=OC / 0:5. Only two nonmagnetic isotropic dielectrics are needed throughout, and the transmission is not sensitive to nonmagnetic isotropic dielectrics. Results validate and illustrate these functionalities, which make the bend much easier to fabricate and apply, owing to its simple parameters, compact shape, and versatility in connecting different waveguides. © 2011 Optical Society of America.
He W.,University of Electronic Science and Technology of China | Zhang S.,National University of Singapore | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE Transactions on Industrial Electronics | Year: 2013
This paper considers a modeling and control problem for a Timoshenko beam under spatiotemporally varying disturbance. The model of the Timoshenko beam is represented by a hybrid model including both partial differential equations and ordinary differential equations. In order to suppress the vibration of the system, boundary control is proposed based on Lyapunov's direct method. Boundary disturbance observers are designed to reduce the effects of the external disturbances. With the proposed boundary control strategies, the states of the system are proven to be uniformly ultimately bounded and converge to a small neighborhood of zero by choosing the design parameters. Simulations are displayed to show the effectiveness of the proposed boundary control. © 1982-2012 IEEE.
Li Z.,South China University of Technology | Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore
IET Control Theory and Applications | Year: 2013
This paper presents a structure of robust adaptive control for biped robots, which includes balancing and posture control for regulating the centre-of-mass (COM) position and trunk orientation of bipedal robots in a compliant way. First, the biped robot is decoupled into the dynamics of COM and the trunks. Then, the adaptive robust controls are constructed in the presence of parametric and functional dynamics uncertainties. The control computes a desired ground reaction force required to stabilise the posture with unknown dynamics of COM and then transforms these forces into fullbody joint torques even if the external disturbances exist. Based on Lyapunov synthesis, the proposed adaptive controls guarantee that the tracking errors of system converge to zero. The proposed controls are robust not only to system uncertainties such as mass variation but also to external disturbances. The verification of the proposed control is conducted using the extensive simulations. © The Institution of Engineering and Technology 2013.
He W.,University of Electronic Science and Technology of China | Zhang S.,National University of Singapore | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
IEEE Transactions on Industrial Electronics | Year: 2013
This paper investigates the control problem of a marine riser installation system. The riser installation system consisting of a vessel, a flexible riser, and a subsea payload is modeled as a distributed parameter system with one partial differential equation and four ordinary differential equations. Based on Lyapunov's direct method, adaptive boundary control is proposed at the top and bottom boundaries of the riser to position the subsea payload to the desired set point and suppress the riser's vibration. With the proposed control, uniform boundedness of the steady-state error between the boundary payload and the desired position is achieved by suitably choosing the design parameters. Numerical simulations are presented for demonstrating the effectiveness of the proposed control. © 1982-2012 IEEE.
Yu J.,University of Electronic Science and Technology of China | Yu J.,Peking University | Wang L.,Peking University | Yu M.,North China Electrical Power University
International Journal of Robust and Nonlinear Control | Year: 2011
Stabilization problems of networked control systems (NCSs) with bounded packet losses and transmission delays are addressed. We model such NCSs as a class of switched systems, and establish stabilizing conditions in the form of matrix inequalities by using packet-loss dependent Lyapunov functions. By solving the inequalities, packet-loss dependent controllers are designed for two types of packet-loss processes: one is an arbitrary packet-loss process, and the other is a Markovian packet-loss process. Several numerical examples and simulations are worked out to demonstrate the effectiveness of the proposed design techniques. © 2010 John Wiley & Sons, Ltd.
Li F.,University of Electronic Science and Technology of China | Li F.,Fujian Normal University | Khan M.K.,King Saud University
Future Generation Computer Systems | Year: 2012
Signcryption is a high performance cryptographic primitive that fulfills both the functions of digital signature and public key encryption simultaneously, at a cost significantly lower than that required by the traditional signature-then-encryption approach. In this paper, we introduce biometrics into identity-based signcryption. We formalize the notion of biometric identity-based signcryption and propose an efficient biometric identity-based signcryption scheme that uses biometric information to construct the public key. We prove that our scheme satisfies confidentiality and unforgeability in the random oracle model. We show that both the computational costs and the communication overheads of our scheme are lower than those of the signature-then-encryption approach. © 2010 Elsevier B.V. All rights reserved.
Lin P.,University of Electronic Science and Technology of China | Ren W.,University of California at Riverside
Proceedings of the IEEE Conference on Decision and Control | Year: 2012
In this paper, a constrained consensus problem is studied in unbalanced networks in the presence of communication delays. Here each agent needs to lie in a closed convex set while reaching a consensus. The communication graphs considered are directed, dynamically changing, and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length. The analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary. It is showed that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system. It is also showed that the communication delays do not affect the consensus stability and consensus is achieved even though the communication delays are arbitrary bounded. © 2012 IEEE.
Mi W.,University of Electronic Science and Technology of China | Qian T.,University of Macau
Automatica | Year: 2014
In this paper, we present an algorithm for estimating poles of linear time-invariant systems by using the backward shift operator. We prove that poles of rational functions, including zeros and multiplicities, are solutions to an algebraic equation which can be obtained by taking backward shift operator to the shifted Cauchy kernels in the unit disc case. The algorithm is accordingly developed for frequency-domain identification. We also prove the robustness of this algorithm. Some illustrative examples are presented to show the efficiency in systems with distinguished and multiple poles. © 2014 Elsevier Ltd. All rights reserved.
Liu X.-X.,University of California at Riverside | Wang H.,University of Electronic Science and Technology of China | Tan S.X.-D.,University of California at Riverside
IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD | Year: 2013
In this paper, we propose an efficient parallel dynamic linear solver, called GPU-GMRES, for transient analysis of large power grid networks. The new method is based on the preconditioned generalized minimum residual (GMRES) iterative method implemented on heterogeneous CPU-GPU platforms. The new solver is very robust and can be applied to power grids with different structures and other applications like thermal analysis. The proposed GPU-GMRES solver adopts the very general and robust incomplete LU (ILU) based preconditioner. We show that by properly selecting the right amount of fill-ins in the incomplete LU factors, a good trade-off between GPU efficiency and GMRES convergence rate can be achieved for the best overall performance. Such a tunable feature makes this algorithm very adaptive to different problems. Furthermore, we properly partition the major computing tasks in GMRES solver to minimize the data traffic between CPU and GPU, which further boosts performance of the proposed method. Experimental results on the set of published IBM benchmark circuits and mesh-structured power grid networks show that the GPU-GMRES solver can deliver order of magnitudes speedup over the direct LU solver UMFPACK. GPU-GMRES can also deliver 3-10× speedup over the CPU implementation of the same GMRES method on transient analysis. © 2013 IEEE.
Chen M.,Nanjing University of Aeronautics and Astronautics | Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore
IEEE Transactions on Cybernetics | Year: 2013
In this paper, the direct adaptive neural control is proposed for a class of uncertain nonaffine nonlinear systems with unknown nonsymmetric input saturation. Based on the implicit function theorem and mean value theorem, both state feedback and output feedback direct adaptive controls are developed using neural networks (NNs) and a disturbance observer. A compounded disturbance is defined to take into account of the effect of the unknown external disturbance, the unknown nonsymmetric input saturation, and the approximation error of NN. Then, a disturbance observer is developed to estimate the unknown compounded disturbance, and it is established that the estimate error converges to a compact set if appropriate observer design parameters are chosen. Both state feedback and output feedback direct adaptive controls can guarantee semiglobal uniform boundedness of the closed-loop system signals as rigorously proved by Lyapunov analysis. Numerical simulation results are presented to illustrate the effectiveness of the proposed direct adaptive neural control techniques. © 2012 IEEE.
Kang Z.,Peking University | Kang Z.,Korea Institute for Advanced Study | Ko P.,Korea Institute for Advanced Study | Li T.,CAS Institute of Theoretical Physics | And 2 more authors.
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2015
In the supersymmetric models with low scale supersymmetry (SUSY) breaking where the gravitino mass is around keV, we show that the 3.5 keV X-ray lines can be explained naturally through several different mechanisms: (I) a keV scale dark gaugino plays the role of sterile neutrino in the presence of bilinear R-parity violation. Because the light dark gaugino obtains Majorana mass only via gravity mediation, it is a decaying warm dark matter (DM) candidate; (II) the compressed cold DM states, whose mass degeneracy is broken by gravity mediated SUSY breaking, emit such a line via the heavier one decay into the lighter one plus photon(s). A highly supersymmetric dark sector may readily provide such kind of system; (III) the light axino, whose mass again is around the gravitino mass, decays to neutrino plus gamma in the R-parity violating SUSY. Moreover, we comment on dark radiation from dark gaugino. © 2015 Published by Elsevier B.V.
Li J.L.-W.,University of Electronic Science and Technology of China | Ong W.-L.,National University of Singapore
IEEE Transactions on Antennas and Propagation | Year: 2011
A new solution to electromagnetic scattering by a gyroelectric sphere is obtained. Gyroelectric characteristics are considered, where both internal transmitted fields and external scattered fields are derived theoretically. The derived solutions are capable of dealing with incident electromagnetic waves at an arbitrary incident angle and arbitrary polarization. After the theoretical formulas are obtained, numerical validations are made by comparing our present results with those obtained using the Fourier transform method. Good agreements are observed between the present results obtained in this paper and those obtained using the other method. Some new numerical results are presented to investigate effects of electric anisotropy ratio and gyroelectric ratio on the radar cross section for a gyroelectric sphere and a left-handed metamaterial gyroelectric sphere. The new formulation of the problem is expected to have wide practical applications. In addition, some critical mistakes in literature were corrected. © 2006 IEEE.
Chen X.,University of Electronic Science and Technology of China | Hao G.,City University of Hong Kong | Li L.,Old Dominion University
International Journal of Production Economics | Year: 2014
We investigate a one-period two-echelon supply chain composed of a risk-neutral supplier that produces short life-cycle products and a loss-averse retailer that orders from the supplier via option contracts and sells to end-users with stochastic demand in the selling season. When a single retail season begins, the retailer can obtain goods by purchasing and exercising call options. We derive the loss-averse retailer's optimal ordering policy and the risk-neutral supplier's optimal production policy under these conditions. In addition, we find that the loss-averse retailer may order less than, equal to, or more than the risk-neutral retailer. Further, we show that the loss-averse retailer's optimal order quantity may increase in retail price and decrease in option price and exercise price, which is different from the case of a risk-neutral retailer. Finally, we study coordination of the supply chain and show that there always exists a Pareto contract as compared to the non-coordinating contracts. © 2013 Elsevier B.V.
He L.,Los Alamos National Laboratory | Lu H.,University of Electronic Science and Technology of China | Cao G.,Tsinghua University | Hu H.,Swinburne University of Technology | Liu X.-J.,Swinburne University of Technology
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2015
We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the two-dimensional mean-field theory indicates that the quantum fluctuations are much more pronounced than those in three dimensions. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of two-dimensional Bose gases and determine the ratio of the composite boson scattering length aB to the fermion scattering length a2D. We find aB≃0.56a2D, in good agreement with the exact four-body calculation. We compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements. © 2015 American Physical Society.
Peng X.-L.,Shanghai University | Xu X.-J.,Shanghai University | Fu X.,Shanghai University | Zhou T.,University of Electronic Science and Technology of China
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2013
Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations. © 2013 American Physical Society.
Chen M.,Nanjing University of Aeronautics and Astronautics | Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore | How B.V.E.,National University of Singapore | Choo Y.S.,National University of Singapore
IEEE Transactions on Control Systems Technology | Year: 2013
In this paper, robust adaptive control with dynamic control allocation is proposed for the positioning of marine vessels equipped with a thruster assisted mooring system, in the presence of parametric uncertainties, unknown disturbances and input nonlinearities. Using neural network approximation and variable structure based techniques in combination with backstepping and Lyapunov synthesis, the positioning control is developed to handle the uncertainties, input saturation and dead-zone characteristics of the mooring lines and thrusters. Full state feedback with all states measurable and output feedback using high gain observer to estimate unmeasurable states are considered. Dynamic control allocation is presented for actuation of the position mooring system. Under the proposed robust adaptive control, semi-global uniform boundedness of the closed-loop signals are guaranteed. Numerical simulations are carried out to show the effectiveness of the proposed control. © 2012 IEEE.
Yang T.,University of Electronic Science and Technology of China | Chi P.-L.,National Chiao Tung University | Xu R.,University of Electronic Science and Technology of China | Lin W.,University of Electronic Science and Technology of China
IEEE Transactions on Microwave Theory and Techniques | Year: 2013
Composite right/left-handed (CRLH) transmission line structures based on the folded substrate integrated waveguide (FSIW) are presented and discussed in this paper. This FSIW-based CRLH (FSIW-CRLH) transmission line exhibits much lower cut-off frequencies as compared to the ordinary FSIW of the same footprint, and furthermore, it requires only one-half width of the conventional substrate integrated waveguide (SIW) based CRLH (SIW-CRLH) transmission lines while possessing the same dispersion characteristics. In addition, the proposed structure offers the advantage of a high quality factor for preventing the guided-wave circuits from radiation as suffered in the previous open CRLH transmission line structures when operated in the fast-wave region. All of the aforementioned properties lend the proposed FSIW-based CRLH transmission lines best suited to miniaturized and guided-wave microwave applications. In this paper, a comprehensive study on the FSIW-CRLH transmission structures is conducted by means of its dispersion relation and Bloch impedance. In addition, two partial H-plane filters are implemented here to demonstrate the capabilities of miniaturization and high quality factor based on the proposed FSIW-CRLH structures. The resultant filters are shown to have about 80% size reduction as compared to the conventional FSIW filters, and 59% size reduction as compared to the SIW-CRLH filters. To the best of our knowledge, it is the first time that the partial H-plane filters are implemented utilizing both the dispersion behavior of the CRLH transmission structures and the structural benefits of the FSIW configuration. © 1963-2012 IEEE.
Gao P.,Peking University | Wang L.,University of Electronic Science and Technology of China | Zhang Y.,CAS Institute of Physics | Huang Y.,Brookhaven National Laboratory | Liu K.,Peking University
ACS Nano | Year: 2015
For alkali-metal-ion batteries, probing the dynamic processes of ion transport in electrodes is critical to gain insights into understanding how the electrode functions and thus how we can improve it. Here, by using in situ high-resolution transmission electron microscopy, we probe the dynamics of Na transport in MoS2 nanostructures in real-time and compare the intercalation kinetics with previous lithium insertion. We find that Na intercalation follows the two-phase reaction mechanism, that is, trigonal prismatic 2H-MoS2 → octahedral 1T-NaMoS2, and the phase boundary is ∼2 nm thick. The velocity of the phase boundary at <10 nm/s is 1 order smaller than that of lithium diffusion, suggesting sluggish kinetics for sodium intercalation. The newly formed 1T-NaMoS2 contains a high density of defects and series superstructure domains with typical sizes of ∼3-5 nm. Our results provide valuable insights into finding suitable Na electrode materials and understanding the properties of transition metal dichalcogenide MoS2. © 2015 American Chemical Society.
Wang D.,University of Electronic Science and Technology of China | Tang Z.,University of Macau
Advanced Functional Materials | Year: 2015
Raman spectroscopy is the most widely used noninvasive analytical technique. Apart from the fingerprint Raman frequency for identifying vibrational mode of certain functional groups, the Raman scattering tensor can also be used to determine the corresponding vibrational symmetry as well as the orientation of this functional group with respect to the rest of the molecule. For gaseous single molecules, only limited structural information can be obtained from Raman spectroscopy owing to their freely rotating and randomly oriented nature. Here, a method, for the first time, is developed to directly determine the Raman scattering tensor on orientation-fixed single iodine molecules, which are confined inside the nano-sized channels of zeolite AlPO4-11 (AEL) single crystal. The experimental results are in good agreement with theoretical predictions based on a density functional theory. The optical transparency and appreciable size of the crystal facilitate the Raman exploration and the 3D manipulation. It is also demonstrated that iodine molecules' orientations are randomly distributed inside the nano-channels of AlPO4-5 (AFI) crystal, which indicates that by carefully choosing the relevant zeolite crystal, the big family of zeolites can be utilized as directing template database for orienting a large number of guest molecules to estimate their structures by polarized Raman spectroscopy. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Li J.L.-W.,University of Electronic Science and Technology of China | Ong W.-L.,National University of Singapore | Zheng K.H.R.,National University of Singapore
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012
Solutions for characterizing both electromagnetic wave propagation in, and scattering by, a gyrotropic sphere are obtained based on some recently published literature. Both gyrotropic permittivity and permeability tensors are considered herein, and both transmitted internal fields and scattered external fields are derived theoretically. Compared with problems of a uniaxial sphere, a gyroelectric sphere, and a gyromagnetic sphere, the scattering problem considered here is found to be astonishingly complicated but more generalized in formulation and solution procedure. Numerical validations are made by reducing our results to a gyromagnetic sphere and comparing them with the results obtained using the Fourier transform method, where excellent agreements are observed. Then, radar cross sections (RCSs) versus electric and magnetic gyrotropy ratios are computed, while hybrid effects due to both electric and magnetic gyrotropies are studied extensively, where some special cases of uniaxial spheres are demonstrated. It is shown that characteristics of gyrotropy parameters in Cartesian coordinates may lead to considerably large variations in RCS values, elucidating physical significance of gyrotropy and anisotropy ratios in scattering control. The generalized formulation of the problem is expected to have wide practical applications, while some features of this gyrotropic sphere may help other researchers or engineers to understand more physical insight. In addition, some critical mistakes made in literature were corrected. © 2012 American Physical Society.
Li L.,Old Dominion University | Su Q.,Xi'an Jiaotong University | Chen X.,University of Electronic Science and Technology of China
International Journal of Production Research | Year: 2011
The objective of adopting quality standards such as ISO 9000 series is to help companies develop and maintain supply chain processes that meet certain performance metrics, such as those provided by the Supply Chain Operations Reference model (SCOR). Based on the survey data from 232 companies that have obtained ISO 9000 certification, this study extends the five decision areas (Plan, Source, Make, Deliver, and Return) of the SCOR model by integrating quality assurance measures in the supply chain process. The results show that individually, each decision area has a positive impact on both customer-facing supply chain quality performance and internal-facing firm level business performance. Collectively, 'Plan' and 'Source' decisions are more important to customer-facing supply chain performance (reliability, response, and flexibility), and 'Make' decisions positively affect internal-facing performance metrics (cost and asset). © 2011 Taylor & Francis.
Shen F.,University of Electronic Science and Technology of China | Shen C.,University of Adelaide | Shen C.,Australian Center for Robotic Vision | Liu W.,IBM | Shen H.T.,University of Queensland
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition | Year: 2015
Recently, learning based hashing techniques have attracted broad research interests because they can support efficient storage and retrieval for high-dimensional data such as images, videos, documents, etc. However, a major difficulty of learning to hash lies in handling the discrete constraints imposed on the pursued hash codes, which typically makes hash optimizations very challenging (NP-hard in general). In this work, we propose a new supervised hashing framework, where the learning objective is to generate the optimal binary hash codes for linear classification. By introducing an auxiliary variable, we reformulate the objective such that it can be solved substantially efficiently by employing a regularization algorithm. One of the key steps in this algorithm is to solve a regularization sub-problem associated with the NP-hard binary optimization. We show that the sub-problem admits an analytical solution via cyclic coordinate descent. As such, a high-quality discrete solution can eventually be obtained in an efficient computing manner, therefore enabling to tackle massive datasets. We evaluate the proposed approach, dubbed Supervised Discrete Hashing (SDH), on four large image datasets and demonstrate its superiority to the state-of-the-art hashing methods in large-scale image retrieval. © 2015 IEEE.
Wang X.-H.,University of Electronic Science and Technology of China | Xue Q.,City University of Hong Kong | Choi W.-W.,University of Macau
IEEE Microwave and Wireless Components Letters | Year: 2010
In this letter, double-sided parallel-strip line (DSPSL) has been used to build a novel differential filter with ultra- wideband (UWB) response. Swap structures, based on DSPSL, are employed in the design to realize 180° phase shift. So the swap structures can realize the conversion between differential- and common-mode. Utilizing the characteristic, the input common- mode signals will be cancelled at the center of the filter, while the input differential-mode signals can propagate in the proposed filter. The proposed new differential filter was calculated in analytical method, and was simulated by the full-wave electromagnetic simulator, and was validated by the measurement. The last results show they have a good in-band and out-band performance. With fractional bandwidth of 110% centered at 3 GHz, the differential-mode signals can propagate with UWB frequency response, while the common-mode signals are suppressed below -20 dB in the whole frequency band. © 2010 IEEE.
Tee K.P.,Institute for Infocomm Research | Ren B.,National University of Singapore | Ren B.,University of California at San Diego | Ge S.S.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China
Automatica | Year: 2011
This paper presents control design for strict feedback nonlinear systems with time-varying output constraints. An asymmetric time-varying Barrier Lyapunov Function (BLF) is employed to ensure constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. Through a change of tracking error coordinates, we eliminate the explicit dependence of the BLF on time, thereby simplifying the analysis of constraint satisfaction. We show that asymptotic output tracking is achieved without violation of the output constraint, and also quantify the transient performance bound as a function of time that converges to zero. To handle parametric model uncertainty, we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation. The performance of the proposed control is illustrated through a simulation example. © 2011 Elsevier Ltd. All rights reserved.
Chen M.,Nanjing University of Aeronautics and Astronautics | Chen M.,National University of Singapore | Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,National University of Singapore | Ren B.,National University of Singapore
Automatica | Year: 2011
In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control. © 2011 Elsevier Ltd. All rights reserved.
Guo S.,University of Electronic Science and Technology of China | Huang H.-Z.,University of Electronic Science and Technology of China | Wang Z.,University of Electronic Science and Technology of China | Xie M.,National University of Singapore
IEEE Transactions on Reliability | Year: 2011
There has been quite some research on the development of tools and techniques for grid systems, yet some important issues, e.g., grid service reliability and task scheduling in the grid, have not been sufficiently studied. For some grid services which have large subtasks requiring time-consuming computation, the reliability of grid service could be rather low. To resolve this problem, this paper introduces Local Node Fault Recovery (LNFR) mechanism into grid systems, and presents an in-depth study on grid service reliability modeling and analysis with this kind of fault recovery. To make LNFR mechanism practical, some constraints, i.e. the life times of subtasks, and the numbers of recoveries performed in grid nodes, are introduced; and grid service reliability models under these practical constraints are developed. Based on the proposed grid service reliability model, a multi-objective task scheduling optimization model is presented, and an ant colony optimization (ACO) algorithm is developed to solve it effectively. A numerical example is given to illustrate the influence of fault recovery on grid service reliability, and show a high efficiency of ACO in solving the grid task scheduling problem. © 2010 IEEE.
Liu C.,National University of Singapore | Liu C.,University of Electronic Science and Technology of China | Guo Y.-X.,National University of Singapore | Bao X.,National University of Singapore | Xiao S.-Q.,University of Electronic Science and Technology of China
IEEE Transactions on Antennas and Propagation | Year: 2012
A 60-GHz wideband circularly polarized (CP) helical antenna array of 4 × 4 elements is designed and fabricated using low temperature cofired ceramic (LTCC) technology. The flexible via hole distribution is fully utilized to achieve a helical antenna array to obtain good circular polarization performance. Meanwhile, grounded coplanar waveguide (GCPW) to stripline is utilized for probe station measurement. Unlike traditional helical antennas, the proposed helical antenna array is convenient for integrated applications. The fabricated antenna array has dimension of 12 × 10 × 2 mm 3. The simulated and measured impedance, axial ratio (AR) and radiation pattern are studied and compared. The proposed antenna array shows a wide measured impedance bandwidth from 52.5 to 65.5 GHz for S|11| < -10 dB, wideband measured AR bandwidth from 54 to 66 GHz for AR < 3 dB, respectively. © 2006 IEEE.
Xiao S.-H.,University of Electronic Science and Technology of China | Xiao S.-H.,Yibin University
Wireless Personal Communications | Year: 2012
As one of the most promising techniques for next generation wireless communication, coordinating transmission by multiple points (i.e. radio access points or base stations) have recently attracted a lot of attention because of its potential for intercell co-channel interferencemitigation and significant spectral efficiency improvement. This paper firstly presents the system structure and mathematical signal model for multipoint coordinating downlink transmission, and then gives a detailed discussion on dynamical cell-clustering strategies, scheduling utility-metric and resources allocation scheme in adaptively forming cooperation cluster of cells based on detected system parameters, where the user is serviced by a cluster selected from a set of clusters that has been adapted to its particular network circumstance and location. Some numerical analysis shows that with dynamical cell-clustering, a clustered supercell with 7-cell is relatively reasonable for spectral efficiency improvement. Also, some simulation results are given to showthat adaptive dynamical cell-clustering methods aremore beneficial to user performance improvement. © Springer Science+Business Media, LLC. 2011.
Wang Q.,University of Electronic Science and Technology of China | Leng S.,University of Electronic Science and Technology of China | Fu H.,Oakland University | Zhang Y.,Simula Research Laboratory | Zhang Y.,University of Oslo
IEEE Transactions on Intelligent Transportation Systems | Year: 2012
In recent years, governments, standardization bodies, automobile manufacturers, and academia are working together to develop vehicular ad hoc network (VANET)-based communication technologies. VANETs apply multiple channels, i.e., control channel (CCH) and service channels (SCHs), to provide open public road safety services and the improve comfort and efficiency of driving. Based on the latest standard draft IEEE 802.11p and IEEE 1609.4, this paper proposes a variable CCH interval (VCI) multichannel medium access control (MAC) scheme, which can dynamically adjust the length ratio between CCH and SCHs. The scheme also introduces a multichannel coordination mechanism to provide contention-free access of SCHs. Markov modeling is conducted to optimize the intervals based on the traffic condition. Theoretical analysis and simulation results show that the proposed scheme is able to help IEEE 1609.4 MAC significantly enhance the saturated throughput of SCHs and reduce the transmission delay of service packets while maintaining the prioritized transmission of critical safety information on CCH. © 2011 IEEE.
Chen X.,University of Electronic Science and Technology of China | Chen X.,International Institute For Applied Systems Analysis | Szolnoki A.,Hungarian Academy of Sciences | Szolnoki A.,Institute of Mathematics | Perc M.,University of Maribor
New Journal of Physics | Year: 2014
Cooperators that refuse to participate in sanctioning defectors create the second-order free-rider problem. Such cooperators will not be punished because they contribute to the public good, but they also eschew the costs associated with punishing defectors. Altruistic punishers - those that cooperate and punish - are at a disadvantage, and it is puzzling how such behaviour has evolved. We show that sharing the responsibility to sanction defectors rather than relying on certain individuals to do so permanently can solve the problem of costly punishment. Inspired by the fact that humans have strong but also emotional tendencies for fair play, we consider probabilistic sanctioning as the simplest way of distributing the duty. In well-mixed populations the public goods game is transformed into a coordination game with full cooperation and defection as the two stable equilibria, while in structured populations pattern formation supports additional counterintuitive solutions that are reminiscent of Parrondos paradox. © 2014 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Chen W.,Hebei United University | Feng P.,Hebei United University | Lin H.,University of Electronic Science and Technology of China
FEBS Letters | Year: 2012
In this study, we introduced two DNA structural characteristics, namely, bendability and hydroxyl radical cleavage intensity to analyze origin of replication (ORI) in the Saccharomyces cerevisiae genome. We found that both DNA bendability and cleavage intensity in core replication regions were significantly lower than in the linker regions. By using these two DNA structural characteristics, we developed a computational model for ORI prediction and evaluated the model in a benchmark dataset. The predictive performance of the jackknife cross-validation indicates that DNA bendability and cleavage intensity have the ability to describe core replication regions and our model is effective in ORI prediction. © 2012 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.
Wang Z.,Beijing University of Posts and Telecommunications | Peng Q.,University of Electronic Science and Technology of China | Milstein L.B.,University of California at San Diego
IEEE Transactions on Wireless Communications | Year: 2011
In this paper, we consider an adaptive multi-user resource allocation for the downlink transmission of a multi-cluster tactical multicarrier DS CDMA network. The goal is to maximize the sum packet throughput, subject to transmit power constraints. Since the objective function turns out to be noncovex and nondifferentiable, we propose a simple iterative bisection algorithm. At each iteration, a closed-form expression is derived for the transmit power, subchannel, and modulation assignment, which significantly reduces the computational complexity. We also provide an optimization algorithm for the downlink transmission under the condition of imperfect channel knowledge, and investigate the effects of both channel estimation error and partial-band jamming. © 2006 IEEE.
Li L.,University of California at Berkeley | Li L.,University of Electronic Science and Technology of China | Gratton C.,University of California at Berkeley | Fabiani M.,University of Illinois at Urbana - Champaign | Knight R.T.,University of California at Berkeley
Neurobiology of Aging | Year: 2013
We investigated age-related changes in frontal and parietal scalp event-related potential (ERP) activity during bottom-up and top-down attention. Younger and older participants were presented with arrays constructed to induce either automatic "pop-out" (bottom-up) or effortful "search" (top-down) behavior. Reaction times (RTs) increased and accuracy decreased with age, with a greater age-related decline in accuracy for the search than for the pop-out condition. The latency of the P300 elicited by the visual search array was shorter in both conditions in the younger than in the older adults. Pop-out target detection was associated with greater activity at parietal than at prefrontal locations in younger participants and with a more equipotential prefrontal-parietal distribution in older adults. Search target detection was associated with greater activity at prefrontal than at parietal locations in older relative to younger participants. Thus, aging was associated with a more prefrontal P300 scalp distribution during the control of bottom-up and top-down attention. Early latency extrastriate potentials were enhanced and N2-posterior-contralateral (N2pc) was reduced in the older group, supporting the idea that the frontal enhancements may be due to a compensation for disinhibition and distraction in the older adults. Taken together these findings provide evidence that younger and older adults recruit different frontal-parietal networks during top-down and bottom-up attention, with older adults increasing their recruitment of a more frontally distributed network in both of these types of attention. This work is in accord with previous neuroimaging findings suggesting that older adults recruit more frontal activity in the service of a variety of tasks than younger adults. © 2013 Elsevier Inc.
Zhou Y.,University of Electronic Science and Technology of China | Yang P.,Pacific Northwest National Laboratory | Zu H.,University of Electronic Science and Technology of China | Gao F.,Pacific Northwest National Laboratory | Zu X.,University of Electronic Science and Technology of China
Physical Chemistry Chemical Physics | Year: 2013
Developing approaches to effectively induce and control the magnetic states is critical to the use of magnetic nanostructures in quantum information devices but is still challenging. Here MoS2-based nanostructures including atomic defects, nanoholes, nanodots and antidots are characterized with spin-polarized density functional theory. The S-vacancy defect is more likely to form than the Mo-vacancy defect due to the form of Mo-Mo metallic bonds. Among different shaped nanoholes and nanodots, triangle ones associated with ferromagnetic characteristic are most energetically favorable, and exhibit unexpected large spin moments that scale linearly with edged length. In particular, S-terminated triangle nanodots show strong spin anisotropy around the Fermi level with a substantial collective characteristic of spin states at edges, enabling it to a desired spin-filtering structure. However, in the antidot, the net spin, coupled order and stability of spin states can be engineered by controlling type and distance of internal nanoholes. Based on the analysis of the spin coupled mechanism, a specific antidot structure, the only S-terminated antidot, was determined to exhibit a large net spin with long-range ferromagnetic coupling above room temperature. Given the recent achievement of graphene- and BN-based nanohole, nanodot and antidot structures, we believe that our calculated results are suitable for experimental verification and implementation opening a new path to explore MoS2-based magnetic nanostructures. © 2013 the Owner Societies.
Wu X.-J.,University of Electronic Science and Technology of China | Huang Q.,University of Electronic Science and Technology of China | Zhu X.-J.,Shanghai JiaoTong University
International Journal of Hydrogen Energy | Year: 2011
For a solid oxide fuel cell (SOFC) integrated into a micro gas turbine (MGT) hybrid power system, SOFC operating temperature and turbine inlet temperature are the key parameters, which affect the performance of the hybrid system. Thus, a least squares support vector machine (LS-SVM) identification model based on an improved particle swarm optimization (PSO) algorithm is proposed to describe the nonlinear temperature dynamic properties of the SOFC/MGT hybrid system in this paper. During the process of modeling, an improved PSO algorithm is employed to optimize the parameters of the LS-SVM. In order to obtain the training and prediction data to identify the modified LS-SVM model, a SOFC/MGT physical model is established via Simulink toolbox of MATLAB6.5. Compared to the conventional BP neural network and the standard LS-SVM, the simulation results show that the modified LS-SVM model can efficiently reflect the temperature response of the SOFC/MGT hybrid system. © 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.
Gu M.,Pacific Northwest National Laboratory | Wang Z.,Pacific Northwest National Laboratory | Wang Z.,University of Electronic Science and Technology of China | Connell J.G.,Northwestern University | And 4 more authors.
ACS Nano | Year: 2013
Silicon has been widely explored as an anode material for lithium ion battery. Upon lithiation, silicon transforms to amorphous LixSi (a-LixSi) via electrochemical-driven solid-state amorphization. With increasing lithium concentration, a-LixSi transforms to crystalline Li15Si4 (c-Li15Si4). The mechanism of this crystallization process is not known. In this paper, we report the fundamental characteristics of the phase transition of a-LixSi to c-Li15Si4 using in situ scanning transmission electron microscopy, electron energy loss spectroscopy, and density function theory (DFT) calculation. We find that when the lithium concentration in a-LixSi reaches a critical value of x = 3.75, the a-Li3.75Si spontaneously and congruently transforms to c-Li15Si4 by a process that is solely controlled by the lithium concentration in the a-LixSi, involving neither large-scale atomic migration nor phase separation. DFT calculations indicate that c-Li15Si4 formation is favored over other possible crystalline phases due to the similarity in electronic structure with a-Li3.75Si. © 2013 American Chemical Society.
Lin H.,University of Electronic Science and Technology of China | Chen W.,Hebei United University | Ding H.,University of Electronic Science and Technology of China
PLoS ONE | Year: 2013
The structure and activity of enzymes are influenced by pH value of their surroundings. Although many enzymes work well in the pH range from 6 to 8, some specific enzymes have good efficiencies only in acidic (pH<5) or alkaline (pH>9) solution. Studies have demonstrated that the activities of enzymes correlate with their primary sequences. It is crucial to judge enzyme adaptation to acidic or alkaline environment from its amino acid sequence in molecular mechanism clarification and the design of high efficient enzymes. In this study, we developed a sequence-based method to discriminate acidic enzymes from alkaline enzymes. The analysis of variance was used to choose the optimized discriminating features derived from g-gap dipeptide compositions. And support vector machine was utilized to establish the prediction model. In the rigorous jackknife cross-validation, the overall accuracy of 96.7% was achieved. The method can correctly predict 96.3% acidic and 97.1% alkaline enzymes. Through the comparison between the proposed method and previous methods, it is demonstrated that the proposed method is more accurate. On the basis of this proposed method, we have built an online web-server called AcalPred which can be freely accessed from the website (http://lin.uestc.edu.cn/server/AcalPred). We believe that the AcalPred will become a powerful tool to study enzyme adaptation to acidic or alkaline environment. © 2013 Lin et al.
Qu H.,University of Electronic Science and Technology of China | Xing K.,University of Electronic Science and Technology of China | Alexander T.,KTH Royal Institute of Technology
Neurocomputing | Year: 2013
This paper presents a Co-evolutionary Improved Genetic Algorithm (CIGA) for global path planning of multiple mobile robots, which employs a co-evolution mechanism together with an improved genetic algorithm (GA). This improved GA presents an effective and accurate fitness function, improves genetic operators of conventional genetic algorithms and proposes a new genetic modification operator. Moreover, the improved GA, compared with conventional GAs, is better at avoiding the problem of local optimum and has an accelerated convergence rate. The use of a co-evolution mechanism takes into full account the cooperation between populations, which avoids collision between mobile robots and is conductive for each mobile robot to obtain an optimal or near-optimal collision-free path. Simulations are carried out to demonstrate the efficiency of the improved GA and the effectiveness of CIGA. © 2013.
Guo S.-H.,University of Electronic Science and Technology of China | Deng E.-Z.,University of Electronic Science and Technology of China | Xu L.-Q.,University of Electronic Science and Technology of China | Ding H.,University of Electronic Science and Technology of China | And 6 more authors.
Bioinformatics | Year: 2014
Motivation: Nucleosome positioning participates in many cellular activities and plays significant roles in regulating cellular processes. With the avalanche of genome sequences generated in the post-genomic age, it is highly desired to develop automated methods for rapidly and effectively identifying nucleosome positioning. Although some computational methods were proposed, most of them were species specific and neglected the intrinsic local structural properties that might play important roles in determining the nucleosome positioning on a DNA sequence. Results: Here a predictor called 'iNuc-PseKNC' was developed for predicting nucleosome positioning in Homo sapiens, Caenorhabditis elegans and Drosophila melanogaster genomes, respectively. In the new predictor, the samples of DNA sequences were formulated by a novel feature-vector called 'pseudo k-tuple nucleotide composition', into which six DNA local structural properties were incorporated. It was observed by the rigorous cross-validation tests on the three stringent benchmark datasets that the overall success rates achieved by iNuc-PseKNC in predicting the nucleosome positioning of the aforementioned three genomes were 86.27%, 86.90% and 79.97%, respectively. Meanwhile, the results obtained by iNuc-PseKNC on various benchmark datasets used by the previous investigators for different genomes also indicated that the current predictor remarkably outperformed its counterparts. © 2014 The Author 2014.
Hu J.,University of Electronic Science and Technology of China | Hu J.,KTH Royal Institute of Technology | Hu X.,KTH Royal Institute of Technology
Automatica | Year: 2010
Collaborative signal processing and sensor deployment have been among the most important research tasks in target tracking using networked sensors. In this paper, the mathematical model is formulated for single target tracking using mobile nonlinear scalar range sensors. Then a sensor deployment strategy is proposed for the mobile sensors and a nonlinear convergent filter is built to estimate the trajectory of the target. © 2010 Elsevier Ltd. All rights reserved.
Wu Y.I.,University of Electronic Science and Technology of China | Wong K.T.,Hong Kong Polytechnic University | Lau S.-K.,University of Nebraska at Omaha
IEEE Transactions on Signal Processing | Year: 2010
The acoustic vector-sensor is a practical and versatile sound-measurement system, for applications in-room, open-air, or underwater. Its far-field measurement model has been introduced into signal processing over a decade ago; and many direction-finding algorithms have since been developed for acoustic vector-sensors, but only for far-field sources. Missing in the literature is a near-field measurement model for the acoustic vector-sensor. This correspondence fills this literature gap. © 2010 IEEE.
Li Y.,University of Electronic Science and Technology of China | Li Y.,Chongqing University | Celebi H.,Stevens Institute of Technology | Daneshmand M.,University of Electronic Science and Technology of China | And 2 more authors.
IEEE Wireless Communications | Year: 2013
As a promising technique for next-generation wireless networks, femtocells expand the coverage of cellular networks, provide high data rate for users, decrease the transmission power of user equipments, and increase the spectrum efficiency. In a few years, the number of deployed femtocell base stations (FBSs) will reach hundreds of millions. This huge deployment will bring a lot of challenges in terms of interference management, resource scheduling, and energy consumption. In recent years, more and more attention has been paid to energy-efficient communications. The huge number of deployed FBSs will aggravate energy consumption. In this article, we comprehensively survey the related work on energy efficiency issues in femtocell networks, including energy efficiency metrics, energy consumption models, deployments of femtocells, and energy-efficient schemes. Then a simple sleeping scheme, fixed time sleeping, is presented as a case study for saving the energy of FBSs. Some interesting results are also presented to show that fixed time sleeping makes a good trade-off among energy efficiency, actual waiting time, and call loss. © 2013 IEEE.
Lin H.,University of Electronic Science and Technology of China | Chen W.,Hebei United University
Journal of Microbiological Methods | Year: 2011
The thermostability of proteins is particularly relevant for enzyme engineering. Developing a computational method to identify mesophilic proteins would be helpful for protein engineering and design. In this work, we developed support vector machine based method to predict thermophilic proteins using the information of amino acid distribution and selected amino acid pairs. A reliable benchmark dataset including 915 thermophilic proteins and 793 non-thermophilic proteins was constructed for training and testing the proposed models. Results showed that 93.8% thermophilic proteins and 92.7% non-thermophilic proteins could be correctly predicted by using jackknife cross-validation. High predictive successful rate exhibits that this model can be applied for designing stable proteins. © 2010 Elsevier B.V.
Guo S.,Hunan Normal University | Kendrick K.M.,University of Electronic Science and Technology of China | Yu R.,South China Normal University | Wang H.-L.S.,National Taiwan University | And 2 more authors.
Human Brain Mapping | Year: 2014
There is still no clear consensus as to which of the many functional and structural changes in the brain in schizophrenia are of most importance, although the main focus to date has been on those in the frontal and cingulate cortices. In the present study, we have used a novel holistic approach to identify brain-wide functional connectivity changes in medicated schizophrenia patients, and functional connectivity changes were analyzed using resting-state fMRI data from 69 medicated schizophrenia patients and 62 healthy controls. As far as we are aware, this is the largest population reported in the literature for a resting-state study. Voxel-based morphometry was also used to investigate gray and white matter volume changes. Changes were correlated with illness duration/symptom severity and a support vector machine analysis assessed predictive validity. A network involving the inferior parietal lobule, superior parietal gyrus, precuneus, superior marginal, and angular gyri was by far the most affected (68% predictive validity compared with 82% using all connections) and different components correlated with illness duration and positive and negative symptom severity. Smaller changes occurred in emotional memory and sensory and motor processing networks along with weakened interhemispheric connections. Our findings identify the key functional circuitry altered in schizophrenia involving the default network midline cortical system and the cortical mirror neuron system, both playing important roles in sensory and cognitive processing and particularly self-processing, all of which are affected in this disorder. Interestingly, the functional connectivity changes with the strongest links to schizophrenia involved parietal rather than frontal regions. Hum Brain Mapp 35:123-139, 2014. © 2012 Wiley Periodicals, Inc.
Wu X.-J.,University of Electronic Science and Technology of China | Huang Q.,University of Electronic Science and Technology of China | Zhu X.-J.,Shanghai JiaoTong University
Journal of Power Sources | Year: 2011
Solid Oxide Fuel Cell (SOFC) integrated into Micro Gas Turbine (MGT) is a multivariable nonlinear and strong coupling system. To enable the SOFC and MGT hybrid power system to follow the load profile accurately, this paper proposes a self-tuning PID decoupling controller based on a modified output-input feedback (OIF) Elman neural network model to track the MGT output power and SOFC output power. During the modeling, in order to avoid getting into a local minimum, an improved particle swarm optimization (PSO) algorithm is employed to optimize the weights of the OIF Elman neural network. Using the modified OIF Elman neural network identifier, the SOFC/MGT hybrid system is identified on-line, and the parameters of the PID controller are tuned automatically. Furthermore, the corresponding decoupling control law is achieved by the conventional PID control algorithm. The validity and accuracy of the decoupling controller are tested by simulations in MATLAB environment. The simulation results verify that the proposed control strategy can achieve favorable control performance with regard to various load disturbances. © 2010 Elsevier B.V. All rights reserved.
Deng N.,University of Electronic Science and Technology of China | Deng N.,University of Notre Dame | Zhou W.,University of Electronic Science and Technology of China | Haenggi M.,University of Notre Dame
IEEE Transactions on Wireless Communications | Year: 2015
The spatial structure of transmitters in wireless networks plays a key role in evaluating mutual interference and, hence, performance. Although the Poisson point process (PPP) has been widely used to model the spatial configuration of wireless networks, it is not suitable for networks with repulsion. The Ginibre point process (GPP) is one of the main examples of determinantal point processes that can be used to model random phenomena where repulsion is observed. Considering the accuracy, tractability, and practicability tradeoffs, we introduce and promote the β-GPP, which is an intermediate class between the PPP and the GPP, as a model for wireless networks when the nodes exhibit repulsion. To show that the model leads to analytically tractable results in several cases of interest, we derive the mean and variance of the interference using two different approaches: the Palm measure approach and the reduced second-moment approach, and then provide approximations of the interference distribution by three known probability density functions. In addition, to show that the model is relevant for cellular systems, we derive the coverage probability of a typical user and find that the fitted β-GPP can closely model the deployment of actual base stations in terms of coverage probability and other statistics. © 2002-2012 IEEE.
Zheng K.,Beijing University of Posts and Telecommunications | Zheng K.,Orange S.A. | Hu F.,Beijing University of Posts and Telecommunications | Wang W.,Catalonia Technology Center of Telecomunications | And 2 more authors.
IEEE Communications Magazine | Year: 2012
Machine-to-machine (M2M) communications are expected to provide ubiquitous connectivity between machines without the need of human intervention. To support such a large number of autonomous devices, the M2M system architecture needs to be extremely power and spectrally efficient. This article thus briefly reviews the features of M2M services in the third generation (3G) long-term evolution and its advancement (LTE-Advanced) networks. Architectural enhancements are then presented for supporting M2M services in LTE-Advanced cellular networks. To increase spectral efficiency, the same spectrum is expected to be utilized for humanto-human (H2H) communications as well as M2M communications. We therefore present various radio resource allocation schemes and quantify their utility in LTE-Advanced cellular networks. System-level simulation results are provided to validate the performance effectiveness of M2M communications in LTE-Advanced cellular networks. © 2012 IEEE.
Zhou Y.,University of Electronic Science and Technology of China | Zhou Y.,Pacific Northwest National Laboratory | Wang Z.,University of Electronic Science and Technology of China | Yang P.,Pacific Northwest National Laboratory | And 4 more authors.
ACS Nano | Year: 2012
Developing approaches to effectively induce and control the magnetic states is critical to the use of magnetic nanostructures in quantum information devices but is still challenging. Here we have demonstrated, by employing the density functional theory calculations, the existence of infinite magnetic sheets with structural integrity and magnetic homogeneity. Examination of a series of transition metal dichalcogenides shows that the biaxial tensile strained NbS2 and NbSe2 structures can be magnetized with a ferromagnetic character due to the competitive effects of through-bond interaction and through-space interaction. The estimated Curie temperatures (387 and 542 K under the 10% strain for NbS2 and NbSe2 structures, respectively) suggest that the unique ferromagnetic character can be achieved above room temperature. The self-exchange of population between 4d orbitals of the Nb atom that leads to exchange splitting is the mechanism behind the transition of the spin moment. The induced magnetic moments can be significantly enhanced by the tensile strain, even giving rise to a half-metallic character with a strong spin polarization around the Fermi level. Given the recent progress in achieving the desired strain on two-dimensional nanostructures, such as graphene and a BN layer, in a controlled way, we believe that our calculated results are suitable for experimental verification and implementation, opening a new path to explore the spintronics in pristine two-dimensional nanostructures. © 2012 American Chemical Society.
Kou G.,University of Electronic Science and Technology of China | Shi Y.,Chinese Academy of Sciences | Shi Y.,University of Nebraska at Omaha | Wang S.,CAS Academy of Mathematics and Systems Science
Decision Support Systems | Year: 2011
Integration of MCDM with DSS brings benefit to both fields. MCDM tools are useful in identifying and evaluating incompatible alternatives for DSS, while DSS can implement MCDM approaches and help maintain and retrieve MCDM models. Over the years, MCDM has made considerable contribution to the development of various DSS subspecialties. This special issue on Multiple Criteria Decision Making and Decision Support Systems consists of 9 selected papers from the 20th International Conference on Multiple Criteria Decision Making. The guest editors highlight the key ideas and contributions of the papers in the special issue. © 2010 Elsevier B.V. All rights reserved.
Levitin G.,University of Electronic Science and Technology of China | Hausken K.,University of Stavanger
Reliability Engineering and System Safety | Year: 2010
The article considers defense resource allocation in a system exposed to external intentional attack. The defender distributes its resource between deploying redundant elements and their protection from attacks. The attacker observes all the elements and tries to detect the unprotected elements. All the detected unprotected elements are destroyed with negligible effort. The attacker then distributes its effort evenly among all of the undetected elements or among elements from a chosen subset of undetected elements. The vulnerability of each element is determined by an attacker-defender contest success function depending on the resources allocated to protection and attack efforts and on the contest intensity. The expected damage caused by the attack is evaluated as system unsupplied demand. The article studies the influence of the unprotected elements' detection probability on the optimal resource distribution. © 2010 Elsevier Ltd. All rights reserved.
Wu X.-J.,University of Electronic Science and Technology of China | Zhu X.-J.,Shanghai JiaoTong University
Journal of Power Sources | Year: 2011
Solid oxide fuel cell and micro gas turbine (SOFC/MGT) hybrid system is a promising distributed power technology. In order to ensure the system safe operation as well as long lifetime of the fuel cell, an effective control manner is expected to regulate the temperature and fuel utilization at the desired level, and track the desired power output. Thus, a multi-loop control strategy for the hybrid system is investigated in this paper. A mathematical model for the SOFC/MGT hybrid system is built firstly. Based on the mathematical model, control cycles are introduced and their design is discussed. Part load operation condition is employed to investigate the control strategies for the system. The dynamic modeling and control implementation are realized in the MATLAB/SIMULINK environment, and the simulation results show that it is feasible to build the multi-loop control methods for the SOFC/MGT hybrid system with regard to load disturbances. © 2011 Elsevier B.V. All rights reserved.
Liu Y.,University of Electronic Science and Technology of China | Yu Y.,University of Illinois at Urbana - Champaign
IEEE Transactions on Visualization and Computer Graphics | Year: 2012
In this paper, we present a robust and accurate algorithm for interactive image segmentation. The level set method is clearly advantageous for image objects with a complex topology and fragmented appearance. Our method integrates discriminative classification models and distance transforms with the level set method to avoid local minima and better snap to true object boundaries. The level set function approximates a transformed version of pixelwise posterior probabilities of being part of a target object. The evolution of its zero level set is driven by three force terms, region force, edge field force, and curvature force. These forces are based on a probabilistic classifier and an unsigned distance transform of salient edges. We further propose a technique that improves the performance of both the probabilistic classifier and the level set method over multiple passes. It makes the final object segmentation less sensitive to user interactions. Experiments and comparisons demonstrate the effectiveness of our method. © 2012 IEEE.
Kou G.,University of Electronic Science and Technology of China | Lu Y.,University of Electronic Science and Technology of China | Peng Y.,University of Electronic Science and Technology of China | Shi Y.,University of Nebraska at Omaha | Shi Y.,Chinese Academy of Sciences
International Journal of Information Technology and Decision Making | Year: 2012
Classification algorithm selection is an important issue in many disciplines. Since it normally involves more than one criterion, the task of algorithm selection can be modeled as multiple criteria decision making (MCDM) problems. Different MCDM methods evaluate classifiers from different aspects and thus they may produce divergent rankings of classifiers. The goal of this paper is to propose an approach to resolve disagreements among MCDM methods based on Spearman's rank correlation coefficient. Five MCDM methods are examined using 17 classification algorithms and 10 performance criteria over 11 public-domain binary classification datasets in the experimental study. The rankings of classifiers are quite different at first. After applying the proposed approach, the differences among MCDM rankings are largely reduced. The experimental results prove that the proposed approach can resolve conflicting MCDM rankings and reach an agreement among different MCDM methods. © 2012 World Scientific Publishing Company.
Liu N.,University of Electronic Science and Technology of China | Liu M.,University of Electronic Science and Technology of China | Chen G.,Shanghai JiaoTong University | Cao J.,Hong Kong Polytechnic University
Proceedings - IEEE INFOCOM | Year: 2012
In Vehicular Ad Hoc Networks (VANETs), content distribution directly relies on the fleeting and dynamic contacts between moving vehicles, which often leads to prolonged downloading delay and terrible user experience. Deploying Wifi-based Access Points (APs) could relieve this problem, but it often requires a large amount of investment, especially at the city scale. In this paper, we propose the idea of ParkCast, which doesn't need investment, but leverages roadside parking to distribute contents in urban VANETs. With wireless device and rechargable battery, parked vehicles can communicate with any vehicles driving through them. Owing to the extensive parking in cities, available resources and contact opportunities for sharing are largely increased. To each road, parked vehicles at roadside are grouped into a line cluster as far as possible, which is locally coordinated for node selection and data transmission. Such a collaborative design paradigm exploits the sequential contacts between moving vehicles and parked ones, implements sequential file transfer, reduces unnecessary messages and collisions, and then expedites content distribution greatly. We investigate ParkCast through theoretic analysis and realistic survey and simulation. The results prove that our scheme achieve high performance in distribution of contents with different sizes, especially in sparse traffic conditions. © 2012 IEEE.
Wu X.-J.,University of Electronic Science and Technology of China | Zhu X.-J.,Shanghai JiaoTong University
International Journal of Energy Research | Year: 2013
For a solid oxide fuel cell (SOFC) and micro gas turbine (MGT) hybrid system, optimal control of load changes requires optimal dynamic scheduling of set points for the system's controllers. Thus, this paper proposes an improved iterative particle swarm optimization (PSO) algorithm to optimize the operating parameters under various loads. This method combines the iteration method and the PSO algorithm together, which can execute the discrete PSO iteratively until the control profile would converge to an optimal one. In MATLAB environment, the simulation results show that the SOFC/MGT hybrid model with the optimized parameters can effectively track the output power with high efficiency. Hence, the improved iterative PSO algorithm can be helpful for system analysis, optimization design, and real-time control of the SOFC/MGT hybrid system. © 2011 John Wiley & Sons, Ltd.
Yan S.,University of Electronic Science and Technology of China | Yan S.,University of Illinois at Urbana - Champaign | Jin J.-M.,University of Illinois at Urbana - Champaign | Nie Z.,University of Electronic Science and Technology of China
IEEE Transactions on Antennas and Propagation | Year: 2011
In computational electromagnetics, the second-kind Fredholm integral equations are known to have very fast iterative convergence but rather poor solution accuracy compared with the first-kind Fredholm integral equations. The error source of the second-kind integral equations can mainly be attributed to the discretization error of the identity operators. In this paper, a scheme is presented to significantly suppress such discretization error by using the Buffa-Christiansen functions as the testing function, leading to much more accurate solutions of the second-kind integral equations, while maintaining their fast convergence properties. Numerical experiments are designed to investigate and demonstrate the accuracy improvement of the second-kind surface integral equations in both perfect electric conductor and dielectric cases by using the presented discretization scheme. © 2006 IEEE.
Chen W.,Hebei United University | Chen W.,Gordon Life Science Institute | Feng P.-M.,Hebei United University | Lin H.,University of Electronic Science and Technology of China | Chou K.-C.,Gordon Life Science Institute
Nucleic Acids Research | Year: 2013
Meiotic recombination is an important biological process. As a main driving force of evolution, recombination provides natural new combinations of genetic variations. Rather than randomly occurring across a genome, meiotic recombination takes place in some genomic regions (the so-called 'hotspots') with higher frequencies, and in the other regions (the so-called 'coldspots') with lower frequencies. Therefore, the information of the hotspots and coldspots would provide useful insights for in-depth studying of the mechanism of recombination and the genome evolution process as well. So far, the recombination regions have been mainly determined by experiments, which are both expensive and time-consuming. With the avalanche of genome sequences generated in the postgenomic age, it is highly desired to develop automated methods for rapidly and effectively identifying the recombination regions. In this study, a predictor, called 'iRSpot-PseDNC', was developed for identifying the recombination hotspots and coldspots. In the new predictor, the samples of DNA sequences are formulated by a novel feature vector, the so-called 'pseudo dinucleotide composition' (PseDNC), into which six local DNA structural properties, i.e. three angular parameters (twist, tilt and roll) and three translational parameters (shift, slide and rise), are incorporated. It was observed by the rigorous jackknife test that the overall success rate achieved by iRSpot-PseDNC was >82% in identifying recombination spots in Saccharomyces cerevisiae, indicating the new predictor is promising or at least may become a complementary tool to the existing methods in this area. Although the benchmark data set used to train and test the current method was from S. cerevisiae, the basic approaches can also be extended to deal with all the other genomes. Particularly, it has not escaped our notice that the PseDNC approach can be also used to study many other DNA-related problems. As a user-friendly web-server, iRSpot-PseDNC is freely accessible at http://lin.uestc.edu. cn/server/iRSpot- PseDNC. © The Author(s) 2013. Published by Oxford University Press.
Cao H.,University of Electronic Science and Technology of China | He W.,University of Electronic Science and Technology of China | Mao Y.,China Academy of Engineering Physics | Lin X.,University of Chinese Academy of Sciences | And 3 more authors.
Journal of Power Sources | Year: 2014
Stability is of paramount importance in organic semiconductor devices, especially in organic solar cells (OSCs). Serious degradation in air limits wide applications of these flexible, light-weight and low-cost power-generation devices. Studying the stability of organic solar cells will help us understand degradation mechanisms and further improve the stability of these devices. There are many investigations into the efficiency and stability of OSCs. The efficiency and stability of devices even of the same photoactive materials are scattered in different papers. In particular, the extrinsic degradation that mainly occurs near the interface between the organic layer and the cathode is a major stability concern. In the past few years, researchers have developed many new cathodes and cathode buffer layers, some of which have astonishingly improved the stability of OSCs. In this review article, we discuss the recent developments of these materials and summarize recent progresses in the study of the degradation/stability of OSCs, with emphasis on the extrinsic degradation/stability that is related to the intrusion of oxygen and water. The review provides detailed insight into the current status of research on the stability of OSCs and seeks to facilitate the development of highly-efficient OSCs with enhanced stability. © 2014 Elsevier B.V. All rights reserved.
Zhong Y.,University of Electronic Science and Technology of China | Zhang W.,University of Electronic Science and Technology of China | Haenggi M.,University of Notre Dame
IEEE Transactions on Wireless Communications | Year: 2014
The capacity of wireless networks is fundamentally limited by interference. However, little research has focused on the interference correlation, which may greatly increase the local delay (namely the number of time slots required for a node to successfully transmit a packet). This paper focuses on the question whether increasing randomness in the MAC, specifically frequency-hopping multiple access (FHMA) and ALOHA, helps to reduce the effect of interference correlation. We derive closed-form results for the mean and variance of the local delay for the two MAC protocols and evaluate the optimal parameters that minimize the mean local delay. Based on the optimal parameters, we identify two operating regimes, the correlation-limited regime and the bandwidth-limited regime. Our results reveal that while the mean local delays for FHMA with N sub-bands and for ALOHA with transmit probability p essentially coincide when p=\frac{1}{N}, a fundamental discrepancy exists between their variances. We also discuss implications from the analysis, including an interesting mean delay-jitter tradeoff, and convenient bounds on the tail probability of the local delay, which shed useful insights into system design. © 2002-2012 IEEE.
Chen W.,Hebei United University | Feng P.,Hebei United University | Lin H.,University of Electronic Science and Technology of China
Journal of Industrial Microbiology and Biotechnology | Year: 2012
Ketoacyl synthases are enzymes involved in fatty acid synthesis and can be classified into five families based on primary sequence similarity. Different families have different catalytic mechanisms. Developing costeffective computational models to identify the family of ketoacyl synthases will be helpful for enzyme engineering and in knowing individual enzymes' catalytic mechanisms. In this work, a support vector machine-based method was developed to predict ketoacyl synthase family using the n-peptide composition of reduced amino acid alphabets. In jackknife cross-validation, the model based on the 2-peptide composition of a reduced amino acid alphabet of size 13 yielded the best overall accuracy of 96.44% with average accuracy of 93.36%, which is superior to other state-of-the-art methods. This result suggests that the information provided by n-peptide compositions of reduced amino acid alphabets provides efficient means for enzyme family classification and that the proposed model can be efficiently used for ketoacyl synthase family annotation. © Society for Industrial Microbiology 2011.
Guo D.,University of Electronic Science and Technology of China | Guo D.,Okinawa Institute of Science and Technology | Wang Q.,Beihang University | Perc M.,University of Maribor
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2012
Networks of fast-spiking interneurons are crucial for the generation of neural oscillations in the brain. Here we study the synchronous behavior of interneuronal networks that are coupled by delayed inhibitory and fast electrical synapses. We find that both coupling modes play a crucial role by the synchronization of the network. In addition, delayed inhibitory synapses affect the emerging oscillatory patterns. By increasing the inhibitory synaptic delay, we observe a transition from regular to mixed oscillatory patterns at a critical value. We also examine how the unreliability of inhibitory synapses influences the emergence of synchronization and the oscillatory patterns. We find that low levels of reliability tend to destroy synchronization and, moreover, that interneuronal networks with long inhibitory synaptic delays require a minimal level of reliability for the mixed oscillatory pattern to be maintained. © 2012 American Physical Society.
Wang W.,University of Electronic Science and Technology of China | Tang M.,University of Electronic Science and Technology of China | Tang M.,Kyungpook National University | Yang H.,University of Electronic Science and Technology of China | And 3 more authors.
Scientific Reports | Year: 2014
The spread of disease through a physical-contact network and the spread of information about the disease on a communication network are two intimately related dynamical processes. We investigate the asymmetrical interplay between the two types of spreading dynamics, each occurring on its own layer, by focusing on the two fundamental quantities underlying any spreading process: epidemic threshold and the final infection ratio. We find that an epidemic outbreak on the contact layer can induce an outbreak on the communication layer, and information spreading can effectively raise the epidemic threshold. When structural correlation exists between the two layers, the information threshold remains unchanged but the epidemic threshold can be enhanced, making the contact layer more resilient to epidemic outbreak. We develop a physical theory to understand the intricate interplay between the two types of spreading dynamics.
Lin H.,University of Electronic Science and Technology of China | Lin H.,Gordon Life Science Institute | Deng E.-Z.,University of Electronic Science and Technology of China | Ding H.,University of Electronic Science and Technology of China | And 4 more authors.
Nucleic Acids Research | Year: 2014
The σ54 promoters are unique in prokaryotic genome and responsible for transcripting carbon and nitrogen-related genes. With the avalanche of genome sequences generated in the postgenomic age, it is highly desired to develop automated methods for rapidly and effectively identifying the σ54 promoters. Here, a predictor called 'iPro54-PseKNC' was developed. In the predictor, the samples of DNA sequences were formulated by a novel feature vector called 'pseudo k-tuple nucleotide composition', which was further optimized by the incremental feature selection procedure. The performance of iPro54-PseKNC was examined by the rigorous jackknife cross-validation tests on a stringent benchmark data set. As a user-friendly web-server, iPro54-PseKNC is freely accessible at http://lin.uestc.edu.cn/server/iPro54-PseKNC. For the convenience of the vast majority of experimental scientists, a step-by-step protocol guide was provided on how to use the web-server to get the desired results without the need to follow the complicated mathematics that were presented in this paper just for its integrity. Meanwhile, we also discovered through an in-depth statistical analysis that the distribution of distances between the transcription start sites and the translation initiation sites were governed by the gamma distribution, which may provide a fundamental physical principle for studying the σ54 promoters. © 2014 The Author(s).
Tian Y.,University of Electronic Science and Technology of China | Tian Y.,Chongqing University of Posts and Telecommunications | Yao D.,University of Electronic Science and Technology of China
Psychophysiology | Year: 2013
Using ERPs in the audiovisual stimulus, the current study is the first to investigate the influence of the reference on experimental effects (between two conditions). Three references, the average reference (AR), the mean mastoid (MM), and a new infinity zero reference (IR), were comparatively investigated via ERPs, statistical parametric scalp mappings (SPSM), and LORETA. Specifically, for the N1 (170-190ms), the SPSM results showed an anterior distribution for MM, a posterior distribution for IR, and both anterior and posterior distributions for AR. However, the circumstantial evidence provided by LORETA is consistent with SPSM of IR. These results indicated that the newly developed IR could provide increased accuracy; thus, we recommend IR for future ERP studies. © 2013 Society for Psychophysiological Research.
Chen W.,Hebei United University | Lin H.,University of Electronic Science and Technology of China
Computers in Biology and Medicine | Year: 2012
Proteins belonging to different subfamilies of Voltage-gated K + channels (VKC) are functionally divergent. The traditional method to classify ion channels is more time consuming. Thus, it is highly desirable to develop novel computational methods for VKC subfamily classification. In this study, a support vector machine based method was proposed to predict VKC subfamilies using amino acid and dipeptide compositions. In order to remove redundant information, a novel feature selection technique was employed to single out optimized features. In the jackknife cross-validation, the proposed method (VKCPred) achieved an overall accuracy of 93.09% with 93.22% average sensitivity and 98.34% average specificity, which are superior to that of other two state-of-the-art classifiers. These results indicate that VKCPred can be efficiently used to identify and annotate voltage-gated K + channels' subfamilies. The VKCPred software and dataset are freely available at http://cobi.uestc.edu.cn/people/hlin/tools/VKCPred/. © 2012 Elsevier Ltd.
Luojie X.,University of Electronic Science and Technology of China | Kurkoski B.M.,University of Electro - Communications
2012 International Conference on Computing, Networking and Communications, ICNC'12 | Year: 2012
Agarwal et al. gave a closed-form expression for write amplification in NAND flash memory by finding the probability of a page being valid over the whole flash memory. This paper gives an improved analytic expression for write amplification in NAND flash memory by finding the probability of a page being invalid in the block selected for garbage collection. The improved expression uses the Lambert W function. Through asymptotic analysis, write amplification is shown to depend on the overprovisioning factor only, consistent with the previous work. Comparison with numerical simulations shows that the improved expression achieves a more accurate prediction of write amplification. For example, when the overprovisioning factor is 0.3, the improved expression gives a write amplification of 2.36 whereas that of the previous work gives 2.17, when the actual value is 2.35. © 2012 IEEE.
Chen Y.P.,University of Electronic Science and Technology of China | Chew W.C.,University of Illinois at Urbana - Champaign | Jiang L.,University of Hong Kong
IEEE Transactions on Antennas and Propagation | Year: 2012
A new Green's function formulation is developed systematically for modeling general homogeneous (dielectric or magnetic) objects in a layered medium. The dyadic form of the Green's function is first derived based on the pilot vector potential approach. The matrix representation in the moment method implementation is then derived by applying integration by parts and vector identities. The line integral issue in the matrix representation is investigated, based on the continuity property of the propagation factor and the consistency of the primary term and the secondary term. The extinction theorem is then revisited in the inhomogeneous background and a surface integral equation for general homogeneous objects is set up. Different from the popular mixed potential integral equation formulation, this method avoids the artificial definition of scalar potential. The singularity of the matrix representation of the Green's function can be made as weak as possible. Several numerical results are demonstrated to validate the formulation developed in this paper. Finally, the duality principle of the layered medium Green's function is discussed in the appendix to make the formulation succinct. © 1963-2012 IEEE.
Hale G.,Federal Reserve Bank of San Francisco | Long C.,Colgate University | Long C.,University of Electronic Science and Technology of China
Pacific Economic Review | Year: 2011
We review previous literature on productivity spillovers of foreign direct investment (FDI) in China and conduct our own analysis using a firm-level data set from a World Bank survey. We find that the evidence of FDI spillovers on the productivity of Chinese domestic firms is mixed, with many positive results largely due to aggregation bias or failure to control for endogeneity of FDI. Attempting over 6000 specifications that take into account forward and backward linkages, we fail to find evidence of systematic positive productivity spillovers from FDI in China. © 2011 The Authors. Pacific Economic Review © 2011 Blackwell Publishing Asia Pty Ltd.
Chen W.,Hebei United University | Chen W.,Gordon Life Science Institute | Lin H.,University of Electronic Science and Technology of China | Feng P.-M.,Hebei United University | And 3 more authors.
PLoS ONE | Year: 2012
Nucleosome positioning has important roles in key cellular processes. Although intensive efforts have been made in this area, the rules defining nucleosome positioning is still elusive and debated. In this study, we carried out a systematic comparison among the profiles of twelve DNA physicochemical features between the nucleosomal and linker sequences in the Saccharomyces cerevisiae genome. We found that nucleosomal sequences have some position-specific physicochemical features, which can be used for in-depth studying nucleosomes. Meanwhile, a new predictor, called iNuc-PhysChem, was developed for identification of nucleosomal sequences by incorporating these physicochemical properties into a 1788-D (dimensional) feature vector, which was further reduced to a 884-D vector via the IFS (incremental feature selection) procedure to optimize the feature set. It was observed by a cross-validation test on a benchmark dataset that the overall success rate achieved by iNuc-PhysChem was over 96% in identifying nucleosomal or linker sequences. As a web-server, iNuc-PhysChem is freely accessible to the public at http://lin.uestc.edu.cn/server/iNuc-PhysChem. For the convenience of the vast majority of experimental scientists, a step-by-step guide is provided on how to use the web-server to get the desired results without the need to follow the complicated mathematics that were presented just for the integrity in developing the predictor. Meanwhile, for those who prefer to run predictions in their own computers, the predictor's code can be easily downloaded from the web-server. It is anticipated that iNuc-PhysChem may become a useful high throughput tool for both basic research and drug design. © 2012 Chen et al.
Ge S.S.,University of Electronic Science and Technology of China | Li Z.,Shanghai JiaoTong University | Li Z.,Key Laboratory of System Control and Information Processing | Yang H.,Zhejiang University
IEEE Transactions on Control Systems Technology | Year: 2012
Fundamentally, control system designs are concerned with the flow of signals in the closed loop. In this paper, we are to present the control technique at the next level of abstraction in control system design. We construct a control using implicit function with support vector regression-based data-driven model for the biped, in the presence of parametric and functional dynamics uncertainties. Based on Lyapunov synthesis, we develop decoupled adaptive control based on the model predictive and the data-driven techniques and construct the control directly from online or offline data. The adaptive predictive control mechanisms use the advantage of data-driven technique combined with online parameters estimation strategy in order to achieve an efficient approximation. Simulation results are presented to verify the effectiveness of the proposed control. © 2011 IEEE.
Ke Q.,University of Electronic Science and Technology of China | Oommen B.J.,Carleton University
Neurocomputing | Year: 2014
The goal of this paper is to catalog the chaotic and Pattern Recognition (PR) properties of a network of Logistic Neurons (LNs). Over the last few years, the field of Chaotic Neural Networks (CNNs) has been extensively studied because of their potential applications in PR, Associative Memory (AM), optimization, multi-value content addressing and image processing. The research in chaos theory has thus expanded to report numerous neural models that, by virtue of their inter-connections, yield chaotic behavior. Recently, the Adachi Neural Network (AdNN) and its variants have been shown to yield an entire spectrum of properties including chaotic, quasi-chaotic, PR and AM as its/their parameters change. To simplify the AdNN model and to also investigate the design philosophy of the CNN model, in this paper, we consider the consequences of networking a set of LNs, each of which is founded on principles of the Logistic map. By appropriately defining the input/output characteristics of a fully connected network of LNs, and by defining their set of weights and output functions, we have succeeded in designing a Logistic Neural Network (LNN). Although the LNN is much simpler than other CNNs such as the AdNN, it possesses some of those properties mentioned above. The chaotic properties of a single-neuron have been formally proven using the theory of Lyapunov analysis and by examining its Jacobian matrix. As far as we know, the results presented here, that the LNN can also demonstrate both AM and PR properties, are unreported, and we submit that it can, hopefully, lead to a new method of PR and AM. © 2013 Elsevier B.V.
Patent
University of Electronic Science, Technology of China and Huawei Symantec Technologies | Date: 2012-02-03
A multi-disk fault-tolerant system, a method for generating a check block, and a method for recovering a data block are provided. The multi-disk fault-tolerant system includes a disk array and a calculation module connected through a system bus, the disk array is formed by p disks, and a fault-tolerant disk amount of the disk array is q; data in the disk array is arranged according to a form of a matrix M of (m+q)p, where m is a prime number smaller than or equal to pq; in the matrix M, a 0^(th )row is virtual data blocks being virtual and having values being 0, a 1^(st )row to an (m1)^(th )row are data blocks, an m^(th )row to an (m+q1)^(th )row are check blocks. Therefore, during a procedure of generating the check block and recovering the data block in the multi-disk fault-tolerant system, calculation complexity is lowered.
Ding H.,University of Electronic Science and Technology of China | Feng P.-M.,Hebei United University | Chen W.,Hebei United University | Lin H.,University of Electronic Science and Technology of China
Molecular BioSystems | Year: 2014
The bacteriophage virion proteins play extremely important roles in the fate of host bacterial cells. Accurate identification of bacteriophage virion proteins is very important for understanding their functions and clarifying the lysis mechanism of bacterial cells. In this study, a new sequence-based method was developed to identify phage virion proteins. In the new method, the protein sequences were initially formulated by the g-gap dipeptide compositions. Subsequently, the analysis of variance (ANOVA) with incremental feature selection (IFS) was used to search for the optimal feature set. It was observed that, in jackknife cross-validation, the optimal feature set including 160 optimized features can produce the maximum accuracy of 85.02%. By performing feature analysis, we found that the correlation between two amino acids with one gap was more important than other correlations for phage virion protein prediction and that some of the 1-gap dipeptides were important and mainly contributed to the virion protein prediction. This analysis will provide novel insights into the function of phage virion proteins. On the basis of the proposed method, an online web-server, PVPred, was established and can be freely accessed from the website (http://lin.uestc.edu.cn/server/PVPred). We believe that the PVPred will become a powerful tool to study phage virion proteins and to guide the related experimental validations. This journal is © the Partner Organisations 2014.
Feng P.,Hebei United University | Chen W.,Hebei United University | Lin H.,University of Electronic Science and Technology of China
Genomics | Year: 2014
As an inheritable epigenetic modification, DNA methylation plays important roles in many biological processes. The non-uniform distribution of DNA methylation across the genome implies that characterizing genome-wide DNA methylation patterns is necessary to better understand the regulatory mechanisms of DNA methylation. Although a series of experimental technologies have been proposed, they are cost-ineffective for DNA methylation status detection. As complements to experimental techniques, computational methods will facilitate the identification of DNA methylation status. In the present study, we proposed a Naïve Bayes model to predict CpG island methylation status. In this model, DNA sequences are formulated by "pseudo trinucleotide composition" into which three DNA physicochemical properties were incorporated. It was observed by the jack-knife test that the overall success rate achieved by the proposed model in predicting the DNA methylation status was 88.22%. This result indicates that the proposed model is a useful tool for DNA methylation status prediction. © 2014 Elsevier Inc.
News Article | October 13, 2016
Site: www.materialstoday.com
In optoelectronic devices like solar cells or light-emitting diodes, the band gap – or energy gap between the top of the valence band and the bottom of the conduction band – determines the photonic performance. One of the ways of controlling that band gap is through strain because deforming a material induces a predictable change in the band gap. GaAs, which is widely used in optoelectronic devices, is too brittle for such simple strain engineering. But now researchers from the University of Electronic Science and Technology of China, Tsinghua University, and the Institute of Semiconductors in Beijing have found a way around the problem. By creating very thin ribbons of GaAs, or nanoribbons, the researchers introduce a wave or buckle into the structure that allows manipulation of the band gap [Wang et al., ACS Nano (2016), doi: 10.1021/acsnano.6b03434]. The team led by Xue Feng of Tsinghua University created the wavy nanoribbons by using photolithography to cut thin strips of GaAs grown by metal-organic chemical vapor deposition (MOCVD). The nanoribbons are then transfer-printed onto a pre-stretched soft substrate of the polymer polydimethylsiloxane (PDMS). When the stretched substrate is released, ribbons of undulating GaAs are formed. The wavy structure creates alternating regions of tension and compression in the nanoribbons. In step with this strain variation, the band gap narrows and widens periodically and continuously along the length ofthe structure. Photoluminescence (PL) measurements provide a direct insight into the band gap. Over a distance of 100 m in a single nanoribbon, the researchers found that the band gap varies by up to ∼1%. “Our approach can produce continuous strain in the same piece of material, from tension to compression, making its performance unique,” says Feng. The ability to control the band gap in such a predictable and periodic way within a nanostructure could inspire new designs of optical and optoelectronic devices, suggest the researchers. Because of the overall flexibility of the GaAs nanoribbons, further levels of complexity in the modulation and enhancement of the band gap can be achieved through tension or compression of the soft substrate. “We are intending to induce more complicated strain into the optoelectronic material,” Feng explains. “[For example] we could divide the whole ribbon into several parts with different band gaps to make separate LED cells. Every cell would have a different emitting wavelength based on its gap - we could achieve a multi-wavelength LED device using a single film.” John A. Rogers of the University of Illinois at Urbana-Champaign believes that Feng and colleagues have made very interesting use of mechanical buckling in semiconductor nanoribbons to scrutinize the effects of strain on electronic bandgap. “The work is an interesting combination of nanoscale mechanics and electronic structure, where the unique ‘wavy’ geometry of the materials allows systematic investigation of how strain and intrinsic properties relevant to electronic and optoelectronic performance can be examined at sub-micron length scales,” he says. “The outcomes have relevance to engineering design of both conventional, wafer-based forms of semiconductor devices as well as newer stretchable and flexible technologies.” This article was originally published in Nano Today (2016), doi:10.1016/j.nantod.2016.08.002
Lu Q.,University of Electronic Science and Technology of China | Lu Q.,Basque Center for Applied Mathematics
ESAIM - Control, Optimisation and Calculus of Variations | Year: 2013
In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This result is a consequence of a new pointwise and weighted estimate for Laplace-Beltrami operators, a construction of some nonnegative function with arbitrary given critical point location in the manifold, and also two interpolation results for solutions of elliptic equations with lateral Robin boundary conditions. © 2012 EDP Sciences, SMAI.
Jiang C.,University of Electronic Science and Technology of China | Li H.,Stevens Institute of Technology | Rangaswamy M.,U.S. Air force
IEEE Transactions on Signal Processing | Year: 2012
The conjugate gradient (CG) algorithm is an efficient method for the calculation of the weight vector of the matched filter (MF). As an iterative algorithm, it produces a series of approximations to the MF weight vector, each of which can be used to filter the test signal and form a test statistic. This effectively leads to a family of detectors, referred to as the CG-MF detectors, which are indexed by k the number of iterations incurred. We first consider a general case involving an arbitrary covariance matrix of the disturbance (including interference, noise, etc.) and show that all CG-MF detectors attain constant false alarm rate (CFAR) and, furthermore, are optimum in the sense that the kth CG-MF detector yields the highest output signal-to-interference-and- noise ratio (SINR) among all linear detectors within the k th Krylov subspace. We then consider a structured case frequently encountered in practice, where the covariance matrix of the disturbance contains a low-rank component (rank-r) due to dominant interference sources, a scaled identity due to the presence of a white noise, and a perturbation component containing the residual interference. We show that the (r+1)st CG-MF detector achieves CFAR and an output SINR nearly identical to that of the MF detector which requires complete iterations of the CG algorithm till reaching convergence. Hence, the (r+1)st CG-MF detector can be used in place of the MF detector for significant computational saving when r is small. Numerical results are presented to verify the accuracy of our analysis for the CG-MF detectors. © 1991-2012 IEEE.
Cheng Y.J.,University of Electronic Science and Technology of China | Hong W.,Nanjing Southeast University | Wu K.,University of Montréal | Fan Y.,University of Electronic Science and Technology of China
IEEE Transactions on Antennas and Propagation | Year: 2011
Two types of substrate integrated waveguide (SIW) long slot leaky-wave antennas with controllable sidelobe level are proposed and demonstrated in this paper. The first prototype is able to achieve an excellent sidelobe level of -27.7 dB by properly meandering a long slot etched on the broadside of a straight SIW section from the centerline toward the sidewall then back. But it is known that an asymmetrically curved slot would worsen the cross-polar level. To overcome this drawback, a modified leaky-wave antenna is proposed, which has a straight long slot etched on the broadside of a meandering SIW section. It yields an outstanding sidelobe level of -29.3 dB and also improves the cross-polar level by more than 11 dB at 35 GHz. Experimental results agree well with simulations, thus validating our design. Then, a two-dimensional (2-D) multibeam antenna is developed by combining such 14 leaky-wave antennas with an SIW beamforming network (BFN). It has features of scanning both in elevation orientation by varying frequency and in cross-plane direction by using the BFN. Excited at ports 110 of such a 2-D multibeam antenna at 35 GHz, angular region of 86.6° in azimuth can effectively be covered by 3 dB beam-width of ten pencil beams. Varying frequency from 33 GHz to 37 GHz, the angular region of 37.5° and 38.9° in elevation can be covered by 3 dB beam-width of those continuous scanning beams excited at ports 6 and 8 respectively. © 2006 IEEE.
Lin P.,University of Electronic Science and Technology of China | Lin P.,Beihang University | Jia Y.,Beihang University
Automatica | Year: 2011
This paper investigates consensus problems in networks of continuous-time agents with diverse time-delays and jointly-connected topologies. For convergence analysis of the networks, a class of LyapunovKrasovskii functions is constructed which contains two parts: one describes the current disagreement dynamics and the other describes the integral impact of the dynamics of the whole network over the past. By a contradiction approach, sufficient conditions are derived under which all agents reach consensus, even though the communication structures between agents dynamically change over time and the corresponding graphs may not be connected. The obtained conditions are composed of a sum of decoupled parts corresponding to each possible connected component of the communication topology. Finally, numerical examples are included to illustrate the obtained results. Copyright © 2011 Published by Elsevier Ltd. All rights reserved.
Huang Y.,University of Electronic Science and Technology of China | Wen G.,University of Electronic Science and Technology of China | Zhu W.,Monash University | Li J.,University of Electronic Science and Technology of China | And 2 more authors.
Optics Express | Year: 2014
We synthesize and systematically characterize a novel type of magnetically tunable metamaterial absorber (MA) by integrating ferrite as a substrate or superstrate into a conventional passive MA. The nearly perfect absorption and tunability of this device is studied both numerically and experimentally within X-band (8-12 GHz) in a rectangular waveguide setup. Our measurements clearly show that the resonant frequency of the MA can be shifted across a wide frequency band by continuous adjustment of a magnetic field acting on the ferrite. Moreover, the effects of substrate/superstrate's thickness on the MA's tunability are discussed. The insight gained from the generic analysis enabled us to design an optimized tunable MA with relative frequency tuning range as larger as 11.5% while keeping the absorptivity higher than 98.5%. Our results pave a path towards applications with tunable devices, such as selective thermal emitters, sensors, and bolometers. © 2014 Optical Society of America.
Hu W.,University of Electronic Science and Technology of China | Yen G.G.,Oklahoma State University
IEEE Transactions on Evolutionary Computation | Year: 2015
Managing convergence and diversity is essential in the design of multiobjective particle swarm optimization (MOPSO) in search of an accurate and well distributed approximation of the true Pareto-optimal front. Largely due to its fast convergence, particle swarm optimization incurs a rapid loss of diversity during the evolutionary process. Many mechanisms have been proposed in existing MOPSOs in terms of leader selection, archive maintenance, and perturbation to tackle this deficiency. However, few MOPSOs are designed to dynamically adjust the balance in exploration and exploitation according to the feedback information detected from the evolutionary environment. In this paper, a novel method, named parallel cell coordinate system (PCCS), is proposed to assess the evolutionary environment including density, rank, and diversity indicators based on the measurements of parallel cell distance, potential, and distribution entropy, respectively. Based on PCCS, strategies proposed for selecting global best and personal best, maintaining archive, adjusting flight parameters, and perturbing stagnation are integrated into a self-adaptive MOPSO (pccsAMOPSO). The comparative experimental results show that the proposed pccsAMOPSO outperforms the other eight state-of-the-art competitors on ZDT and DTLZ test suites in terms of the chosen performance metrics. An additional experiment for density estimation in MOPSO illustrates that the performance of PCCS is superior to that of adaptive grid and crowding distance in terms of convergence and diversity. © 2014 IEEE.
Gao B.,University of Electronic Science and Technology of China | Bai L.,University of Electronic Science and Technology of China | Woo W.L.,Newcastle University | Tian G.,University of Electronic Science and Technology of China | Tian G.,Newcastle University
Applied Physics Letters | Year: 2014
Analysis of thermography spatial- Transient patterns has considerable potential to enable automatic identification and quantification of detects in non-destructive testing and evaluation. This Letter proposes a non-negative pattern separation model for eddy current pulsed thermography to automatically extract important spatial and time patterns according to the transient thermal sequences without any pro- Training or prior knowledge. In particular, the method is scale-invariant, such that large differences in surface emissivity, hot spots, and cool areas with dynamic range of thermal contrast can be extracted. Finally, an artificial slot in a steel sample with shining, black strip on the surface is tested to validate the proposed method. © 2014 AIP Publishing LLC.
Zhang C.,University of Electronic Science and Technology of China | Yi Z.,Sichuan University
Information Sciences | Year: 2011
This paper proposes a novel PSO algorithm, referred to as SFIPSO (Scale-free fully informed particle swarm optimization). In the proposed algorithm a modified Barabási-Albert (BA) model [4] is used as a self-organizing construction mechanism, in order to adaptively generate the population topology exhibiting scale-free property. The swarm population is divided into two subpopulations: the active particles and the inactive particles. The former fly around the solution space to find the global optima; whereas the latter are iteratively activated by the active particles via attaching to them, according to their own degrees, fitness values, and spatial positions. Therefore, the topology will be gradually generated as the construction process and the optimization process progress synchronously. Moreover, the cognitive effect and the social effect on the variance of a particle's velocity vector are distributed by its "contextual fitness" value, and the social effect is further distributed via a time-varying weighted fully informed mechanism that originated from [27]. It is proved by the results of comparative experiments carried out on eight benchmark test functions that the scale-free population topology construction mechanism and the weighted fully informed learning strategy can provide the swarm population with stronger diversity during the convergent process. As a result, SFIPSO obtained success rate of 100% on all of the eight test functions. Furthermore, SFIPSO also yielded good-quality solutions, especially on multimodal test functions. We further test the network properties of the generated population topology. The results prove that (1) the degree distribution of the topology follows power-law, therefore exhibits scale-free property, and (2) the topology exhibits "disassortative mixing" property, which can be interpreted as an important condition for the reinforcement of population diversity. © 2011 Elsevier Inc. All rights reserved.
Xu P.,University of Electronic Science and Technology of China | Ding Z.,Newcastle University | Dai X.,University of Electronic Science and Technology of China
IEEE Transactions on Information Forensics and Security | Year: 2013
This paper studies the impact of partial encoder cooperation on the secrecy of the multiple access channel (MAC) with an external eavesdropper. In particular, two encoders, connected by two communication links with finite capacities, wish to send secret messages to the common intended decoder in the presence of a passive eavesdropper. The inner and outer bounds on the secrecy capacity are derived for the discrete memoryless channel. The derived inner bound rate region is achievable by combining Willems's coding for the MAC with partially cooperating encoders and Wyner's random binning for the wiretap channel. Then, both the inner and outer bounds are extended to the Gaussian case and the corresponding rate regions are established. Several simple achievable transmission schemes are proposed for the Gaussian channel and the numerical results show that the partial encoder cooperation can increase the achievable rate regions. © 2013 IEEE.
Lu L.,Hangzhou Normal University | Lu L.,University of Fribourg | Lu L.,University of Electronic Science and Technology of China | Medo M.,University of Fribourg | And 10 more authors.
Physics Reports | Year: 2012
The ongoing rapid expansion of the Internet greatly increases the necessity of effective recommender systems for filtering the abundant information. Extensive research for recommender systems is conducted by a broad range of communities including social and computer scientists, physicists, and interdisciplinary researchers. Despite substantial theoretical and practical achievements, unification and comparison of different approaches are lacking, which impedes further advances. In this article, we review recent developments in recommender systems and discuss the major challenges. We compare and evaluate available algorithms and examine their roles in the future developments. In addition to algorithms, physical aspects are described to illustrate macroscopic behavior of recommender systems. Potential impacts and future directions are discussed. We emphasize that recommendation has great scientific depth and combines diverse research fields which makes it interesting for physicists as well as interdisciplinary researchers. © 2012 Elsevier B.V.
Raju S.,Hong Kong University of Science and Technology | Wu R.,University of Electronic Science and Technology of China | Chan M.,Hong Kong University of Science and Technology | Yue C.P.,Hong Kong University of Science and Technology
IEEE Transactions on Power Electronics | Year: 2014
This paper presents a compact model of mutual inductance between two planar inductors, which is essential to design and optimize a wireless power transmission system. The tracks of the planar inductors are modeled as constant current carrying filaments, and the mutual inductance between individual filaments is determined by Neumann's integral. The proposed model is derived by solving Neumann's integral using a series expansion technique. This model can predict the mutual inductance at various axial and lateral displacements. Mutual coupling between planar inductors is computed by a 3-D electromagnetic (EM) solver, and the proposed model shows good agreement with these numerical results. Different types of planar inductors were fabricated on a printed circuit board (PCB) or silicon wafer. Using these inductors, wireless power links were constructed for applications like implantable biomedical devices and contactless battery charging systems. Mutual inductance was measured for each of the cases, and the comparison shows that the proposed model can predict mutual coupling suitably. © 1986-2012 IEEE.
Wu R.,University of Electronic Science and Technology of China | Li W.,University of Electronic Science and Technology of China | Luo H.,University of Electronic Science and Technology of China | Sin J.K.O.,Hong Kong University of Science and Technology | Yue C.P.,Hong Kong University of Science and Technology
IEEE Transactions on Power Electronics | Year: 2014
In this paper, the design of an inductive power link (IPL) for wireless power transfer (WPT) in brain-machine interface (BMI) applications is thoroughly studied. The constraints and requirements of BMI applications are analyzed. By theoretical derivations, the relationships between the IPL performances and its electrical parameters are determined. The design guidelines for the IPL physical parameters are then obtained through experimental characterizations. Experimental results show that with proper IPL design, the efficiency can be improved from the previously reported values of 29.9% and 4.3% to 33.1% and 9.2% for BMI WPT distances of 5 and 12.5 mm, respectively. © 1986-2012 IEEE.
Wang W.-Q.,University of Electronic Science and Technology of China | Wang W.-Q.,Nanjing Southeast University
ISPRS Journal of Photogrammetry and Remote Sensing | Year: 2012
Persistent regional monitoring is particularly valuable in remote sensing applications. Inspired by the advantages of near-space vehicles as compared to satellites and airplanes, this paper presents a regional remote sensing approach by near-space vehicle-borne passive bistatic radars. Note that near-space is defined as the altitude region between 20 and 100. km, which is too high up for conventional airplanes but too low for current satellites. We place passive radar receivers inside near-space vehicles which work in conjunction with opportunistic illuminators such as global positioning system (GPS), spaceborne radar, airborne radar or even ground-based radar as the transmitter, to provide a persistent monitoring. The comparative advantages of near-space vehicle as compared to satellite and airplane are investigated. The system models, signal processing algorithm, synchronization processing technique, and the conceptual design examples are presented. Since experimental data are not available for us, numerical simulation results are provided. Although passive radar is not a new concept, the originality of this paper lies in the matched filter reference signal extraction and synchronization processing algorithms. © 2012 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS).
Fang J.,University of Electronic Science and Technology of China | Li H.,Stevens Institute of Technology | Chen Z.,University of Electronic Science and Technology of China | Li S.,University of Electronic Science and Technology of China
IEEE Transactions on Signal Processing | Year: 2012
We consider a decentralized detection problem in a power-constrained wireless sensor network (WSN), in which a number of sensor nodes collaborate to detect the presence of a deterministic vector signal. The signal to be detected is assumed known a priori. Each sensor conducts a local linear processing to convert its observations into one or multiple messages. The messages are conveyed to the fusion center (FC) by an uncoded amplify-and-forward scheme, where a global decision is made. Given a total network transmit power constraint, we investigate the optimal linear processing strategy for each sensor. Our study finds that the optimal linear precoder has the form of a matched filter. Depending on the channel characteristics, one or multiple versions of the filtered/compressed message should be reported to the FC. In addition, assuming a fixed total transmit power, we examine how the detection performance behaves with the number of sensors in the network. Analysis shows that increasing the number of sensors can substantially improve the system detection reliability. Finally, decentralized detection with unknown signals is studied and a heuristic precoding design is proposed. Numerical results are conducted to corroborate our theoretical analysis and to illustrate the performance of the proposed algorithm. © 2012 IEEE.
Shen Y.,University of Electronic Science and Technology of China | Fang J.,University of Electronic Science and Technology of China | Li H.,Stevens Institute of Technology
IEEE Signal Processing Letters | Year: 2013
The fact that fewer measurements are needed by log-sum minimization for sparse signal recovery than the L1-minimization has been observed by extensive experiments. Nevertheless, such a benefit brought by the use of the log-sum penalty function has not been rigorously proved. This paper provides a theoretical justification for adopting the log-sum as an alternative sparsity-encouraging function. We prove that minimizing the log-sum penalty function subject to Az = y is able to yield the exact solution, provided that a certain condition is satisfied. Specifically, our analysis suggests that, for a properly chosen regularization parameter, exact reconstruction can be attained when the restricted isometry constant δ3k is smaller than one, which presents a less restrictive isometry condition than that required by the conventional L1-type methods. © 1994-2012 IEEE.
Jiang Z.,University of Electronic Science and Technology of China | Van Dijke M.I.J.,Heriot - Watt University | Sorbie K.S.,Heriot - Watt University | Couples G.D.,Heriot - Watt University
Water Resources Research | Year: 2013
Developing a better understanding of single-/multiphase flow through reservoir rocks largely relies on characterizing and modeling the pore system. For simple homogeneous rock materials, a complete description of the real pore structure can be obtained from the pore network extracted from a rock image at a single resolution, and then an accurate prediction of fluid flow properties can be achieved by using network model. However, for complex rocks (e.g., carbonates, heterogeneous sandstones, deformed rocks), a comprehensive description of the real pore structure may involve several decades of length scales (e.g., from submicron to centimeters), which cannot be captured by a single-resolution image due to the restriction of image size and resolution. Hence, the reconstruction of a single 3-D multiple-scale model of a porous medium is an important step in quantitatively characterizing such heterogeneous rocks and predicting their multiphase flow properties. In this paper, we present a novel methodology for the numerical construction of the multiscale pore structure of a complex rock from a number of CT images/models of a carbonate sample at several length scales. The success of this reconstruction relies heavily on image segmentation, pore network extraction and stochastic network generation, which are provided by our existing software system, referred to as Pore Analysis Tools (PAT). Specifically, the statistical description of pore networks of 3-D rock images at multiple resolutions makes it possible for us to: (a) construct an arbitrary sized network which is equivalent in a specified domain, and (b) integrate multiple networks of different sizes into a single network incorporating all scales. Using multiscale networks of carbonate rocks generated in this manner, two-phase network modeling results are presented to show how the resulting flow properties are dependent on inclusion of information from multiple scales. These outcomes reinforce the importance of capturing both geometry and topology in the hierarchical pore structure for such complex pore systems. The example presented reveals that isolated large-scale (e.g., macro-) pores are mainly connected by small-scale (e.g., micro-) pores, which in turn determines the combined effective petrophysical properties (capillary pressure, absolute and relative permeability). It is also demonstrated that multi- (three) scale networks reveal the effects of the interacting multiscale pore systems (e.g., micropores, macropores, and vugs) on bulk flow properties in terms of two-phase flow properties. Key Points To capture the multi-scale heterogeneity of complex porous media. To illustrate the effects of multi-scale pore systems on flow properties. To highlight the importance of equivalent stochastic network in flow simulation ©2013. American Geophysical Union. All Rights Reserved.
Zhang C.,University of Electronic Science and Technology of China | Yi Z.,Sichuan University
Neurocomputing | Year: 2010
Self-nonself discrimination has long been the fundamental model of modern theoretical immunology. Based on this principle, some effective and efficient artificial immune algorithms have been proposed and applied to a wide range of engineering applications. Over the last few years, a new model called "danger theory" has been developed to challenge the classical self-nonself model. In this paper, a novel immune algorithm inspired by danger theory is proposed for solving on-line supervised two-class classification problems. The general framework of the proposed algorithm is described, and several essential issues related to the learning process are also discussed. Experiments based on both artificial data sets and real-world problems are carried out to visualize the learning process, as well as to evaluate the classification performance of our method. It is shown empirically by the experimental results that the proposed algorithm exhibits competitive classification accuracy and generalization capability. © 2010 Elsevier B.V. All rights reserved.
Das K.,Harish Chandra Research Institute | Li T.,CAS Institute of Theoretical Physics | Li T.,University of Electronic Science and Technology of China | Nandi S.,Oklahoma State University | Rai S.K.,Harish Chandra Research Institute
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2016
The resonant excesses around 2 TeV reported by the ATLAS Collaboration can be explained in the left-right model, and the tight constraints from lepton plus missing energy searches can be evaded if the SU(2)R gauge symmetry is leptophobic. We, for the first time, propose an anomaly- free leptophobic left-right model with gauge symmetry SU(3)C×SU(2)L×SU(2)R×U(1)X, where the SM leptons are singlets under SU(2)R. The gauge anomalies are cancelled by introducing extra vectorlike quarks. The mass of the Z′ gauge boson, which cannot be leptophobic, is assumed to be around or above 2.5 TeV so that the constraint on the dilepton final state can be avoided. Moreover, we find that the W′→WZ channel cannot explain the ATLAS diboson excess due to the tension with the constraint on the W′→jj decay mode. We solve this problem by considering the mixings between the SM quarks and vectorlike quarks. We show explicitly that the ATLAS diboson excess can be explained in the viable parameter space of our model, which is consistent with all the current experimental constraints. © 2016 American Physical Society.
Hu W.,University of Electronic Science and Technology of China | Yen G.G.,Oklahoma State University
2013 IEEE Congress on Evolutionary Computation, CEC 2013 | Year: 2013
Leader selection and archive maintenance are the two key issues, which have an important impact on the performance of the obtained approximate Pareto front, to be tackled when extending Single-Objective Particle Swarm Optimization to Multi-Objective Particle Swarm Optimization (MOPSO). In this paper, a new method of density estimation is proposed for selecting leaders and maintaining archive in MOPSO. The density of a nondominated solution in archive is calculated according to the Parallel Cell Distance after the archive is mapped from Cartesian Coordinate System into Parallel Cell Coordinate System. A new MOPSO is proposed based on this method of density estimation for selecting leaders and maintaining archive to improve the performance of convergence and diversity. The experimental results show that the proposed algorithm is significantly superior to the five chosen state-of-the-art MOPSOs on 12 test problems in term of hypervolume performance indicator. © 2013 IEEE.
Ren P.-G.,Xi'an University of Technology | Yan D.-X.,Sichuan University | Ji X.,University of Sichuan | Chen T.,University of Electronic Science and Technology of China | Li Z.-M.,Sichuan University
Nanotechnology | Year: 2011
Graphene oxide (GO) was successfully prepared by a modified Hummer's method. The reduction effect and mechanism of the as-prepared GO reduced with hydrazine hydrate at different temperatures and time were characterized by x-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR), elemental analysis (EA), x-ray diffractions (XRD), Raman spectroscopy and thermo-gravimetric analysis (TGA). The results showed that the reduction effect of GO mainly depended on treatment temperature instead of treatment time. Desirable reduction of GO can only be obtained at high treatment temperature. Reduced at 95 °C for 3 h, the C/O atomic ratio of GO increased from 3.1 to 15.1, which was impossible to obtain at low temperatures, such as 80, 60 or 15 °C, even for longer reduction time. XPS, 13C NMR and FTIR results show that most of the epoxide groups bonded to graphite during the oxidation were removed from GO and form the sp2 structure after being reduced by hydrazine hydrate at high temperature (>60 °C), leading to the electric conductivity of GO increasing from 1.5 × 10-6 to 5 S cm -1, while the hydroxyls on the surface of GO were not removed by hydrazine hydrate even at high temperature. Additionally, the FTIR, XRD and Raman spectrum indicate that the GO reduced by hydrazine hydrate can not be entirely restored to the pristine graphite structures. XPS and FTIR data also suggest that carbonyl and carboxyl groups can be reduced by hydrazine hydrate and possibly form hydrazone, but not a C=C structure. © 2011 IOP Publishing Ltd Printed in the UK & the USA.
Yao G.-G.,Shaanxi Normal University | Yao G.-G.,University of Posts and Telecommunications | Liu P.,Shaanxi Normal University | Zhang H.-W.,University of Electronic Science and Technology of China
Journal of the American Ceramic Society | Year: 2013
Using a conventional solid-state reaction Ca5A 4(VO4)6 (A2+ = Mg, Zn) ceramics were prepared and their microwave dielectric properties were investigated for the first time. X-ray diffraction revealed the formation of pure-phase ceramics with a cubic garnet structure for both samples. Two promising ceramics Ca 5Zn4(VO4)6 and Ca5Mg 4(VO4)6 sintered at 725°C and 800°C were found to possess good microwave dielectric properties: εr = 11.7 and 9.2, Q × f = 49 400 GHz (at 9.7 GHz) and 53 300 GHz (at 10.6 GHz), and τf = -83 and -50 ppm/°C, respectively. © 2013 The American Ceramic Society.
Lin P.,University of Electronic Science and Technology of China | Jia Y.,Beihang University
IET Control Theory and Applications | Year: 2010
This study is concerned with consensus problems for a class of multi-agent systems with second-order dynamics. Some dynamic neighbour-based rules are adopted for the agents with the consideration of parameter uncertainties and external disturbances. Sufficient conditions are derived to make all agents asymptotically reach consensus while satisfying desired H∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results. © 2010 The Institution of Engineering and Technology.
Lu Q.,Basque Center for Applied Mathematics | Lu Q.,University of Electronic Science and Technology of China
Inverse Problems | Year: 2012
In this paper, we establish a global Carleman estimate for stochastic parabolic equations. Based on this estimate, we study two inverse problems for stochastic parabolic equations. One is concerned with a determination problem of the history of a stochastic heat process through the observation at the final time T for which we obtain a conditional stability estimate. The other is an inverse source problem with observation on the lateral boundary. We derive the uniqueness of the source. © 2012 IOP Publishing Ltd.
Qiu T.,Nanchang Hangkong University | Zhang Z.-K.,Hangzhou Normal University | Zhang Z.-K.,University of Electronic Science and Technology of China | Zhang Z.-K.,Beijing Computational Science Research Center | Chen G.,Nanchang Hangkong University
PLoS ONE | Year: 2013
Finding a universal description of the algorithm optimization is one of the key challenges in personalized recommendation. In this article, for the first time, we introduce a scaling-based algorithm (SCL) independent of recommendation list length based on a hybrid algorithm of heat conduction and mass diffusion, by finding out the scaling function for the tunable parameter and object average degree. The optimal value of the tunable parameter can be abstracted from the scaling function, which is heterogeneous for the individual object. Experimental results obtained from three real datasets, Netflix, MovieLens and RYM, show that the SCL is highly accurate in recommendation. More importantly, compared with a number of excellent algorithms, including the mass diffusion method, the original hybrid method, and even an improved version of the hybrid method, the SCL algorithm remarkably promotes the personalized recommendation in three other aspects: solving the accuracy-diversity dilemma, presenting a high novelty, and solving the key challenge of cold start problem. © 2013 Qiu et al.
Liu S.,University of Electronic Science and Technology of China | Xiong L.,Paramount science | He C.,Chengdu Yanbai Technology Co.
Journal of Power Sources | Year: 2014
Lithium ion batteries with lithium nickel cobalt manganese oxide (NCM) cathode were characterized by extensive cycling (>2000 cycles), discharge rate test, hybrid pulse power characterization test (HPPC), and electrochemical impedance spectroscopy (EIS). The crystal structure, morphology and particle size of cathode materials were characterized by X-ray diffraction and scanning electron microscopy (SEM). It was demonstrated that the rate performance and cycle life of battery are closely related to the cathode material composition and electrode design. With proper selection of cathode composition and electrode design, the lithium ion battery cell achieved close to 3500 cycles with 85% capacity retention at 1C current. © 2014 Elsevier B.V. All rights reserved.
Gou J.,University of Electronic Science and Technology of China | Yi Z.,Sichuan University
Computer Journal | Year: 2013
In this article, we develop a linear supervised subspace learning method called locality-based discriminant neighborhood embedding (LDNE), which can take advantage of the underlying submanifold-based structures of the data for classification. Our LDNE method can simultaneously consider both 'locality' of locality preserving projection (LPP) and 'discrimination' of discriminant neighborhood embedding (DNE) in manifold learning. It can find an embedding that not only preserves local information to explore the intrinsic submanifold structure of data from the same class, but also enhances the discrimination among submanifolds from different classes. To investigate the performance of LDNE, we compare it with the state-of-the-art dimensionality reduction techniques such as LPP and DNE on publicly available datasets. Experimental results show that our LDNE can be an effective and robust method for classification. © 2013 The Author.
Lin P.,Beihang University | Lin P.,University of Electronic Science and Technology of China | Jia Y.,Beihang University
IEEE Transactions on Automatic Control | Year: 2010
This technical note investigates consensus problems of a class of second-order continuous-time multi-agent systems with time-delay and jointly-connected topologies. We first introduce a neighbor-based linear protocol with time-delay. Then we derive a sufficient condition in terms of linear matrix inequalities (LMIs) for average consensus of the system. Furthermore, we discuss the case where the time-delay affects only the information that is being transmitted and show that consensus can be reached with arbitrary bounded time-delay. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results. © 2010 IEEE.
Lin P.,University of Electronic Science and Technology of China | Jia Y.,Beihang University
Systems and Control Letters | Year: 2010
This paper investigates collective rotating motions of second-order multi-agent systems. We first consider rotating consensus problems. Using local relative information, we propose a protocol and give a necessary and sufficient condition for rotating consensus of the system. Then, we consider rotating formation control problems. With the help of Lyapunov theory for complex systems, we propose rotating formation protocols and give sufficient conditions to make all agents move with a specific structure in a circular channel. Finally, simulation results are provided to demonstrate the effectiveness of our theoretical results. © 2010 Elsevier B.V. All rights reserved.
Cheng Y.J.,University of Electronic Science and Technology of China | Hong W.,Nanjing Southeast University | Wu K.,Ecole Polytechnique de Montréal
IEEE Transactions on Antennas and Propagation | Year: 2012
A planar W-band monopulse antenna array is designed based on the substrate integrated waveguide (SIW) technology. The sum-difference comparator, 16-way divider and 32 × 32 slot array antenna are all integrated on a single dielectric substrate in the compact layout through the low-cost PCB process. Such a substrate integrated monopulse array is able to operate over 93 ∼ 96 GHz with narrow-beam and high-gain. The maximal gain is measured to be 25.8 dBi, while the maximal null-depth is measured to be - 43.7 dB. This SIW monopulse antenna not only has advantages of low-cost, light, easy-fabrication, etc., but also has good performance validated by measurements. It presents an excellent candidate for W-band directional-finding systems. © 2006 IEEE.
Wang N.,University of Electronic Science and Technology of China | Ding Z.,Northumbria University | Dai X.,University of Electronic Science and Technology of China | Vasilakos A.V.,University of Western Macedonia
IEEE Transactions on Vehicular Technology | Year: 2011
In this paper, we first study the design of network coding for the generalized multiple-input-multiple-output (MIMO) Y channels, where K users wish to exchange information with each other within two time slots. Precoding at each user and the relay is carefully constructed to ensure that the signals from the same user pair are grouped together and that cross-pair interference can be canceled. In addition, a simple mapping function is proposed to ensure low-complexity detection at the relay. Exact expressions of symbol error rate (SER) are then developed to establish the explicit relationship between the diversity gain and the number of node antennas. Monte Carlo simulation is also provided to demonstrate the performance of the proposed scheme. © 2010 IEEE.
Mu B.,University of Electronic Science and Technology of China | Mu B.,Sichuan University | Wang P.,Sichuan University | Yang H.,Sichuan University | Yang H.,CAS Institute of Theoretical Physics
Advances in High Energy Physics | Year: 2015
We investigate effects of the minimal length on quantum tunnelling from spherically symmetric black holes using the Hamilton-Jacobi method incorporating the minimal length. We first derive the deformed Hamilton-Jacobi equations for scalars and fermions, both of which have the same expressions. The minimal length correction to the Hawking temperature is found to depend on the black hole's mass and the mass and angular momentum of emitted particles. Finally, we calculate a Schwarzschild black hole's luminosity and find the black hole evaporates to zero mass in infinite time. © 2015 Benrong Mu et al.
Cui G.,Stevens Institute of Technology | Cui G.,University of Electronic Science and Technology of China | Li H.,Stevens Institute of Technology | Rangaswamy M.,Air Force Research Lab
IEEE Transactions on Signal Processing | Year: 2014
We consider the problem of waveform design for Multiple-Input Multiple-Output (MIMO) radar in the presence of signal-dependent interference embedded in white Gaussian disturbance. We present two sequential optimization procedures to maximize the Signal to Interference plus Noise Ratio (SINR), accounting for a constant modulus constraint as well as a similarity constraint involving a known radar waveform with some desired properties (e.g., in terms of pulse compression and ambiguity). The presented sequential optimization algorithms, based on a relaxation method, yield solutions with good accuracy. Their computational complexity is linear in the number of iterations and trials in the randomized procedure and polynomial in the receive filter length. Finally, we evaluate the proposed techniques, by considering their SINR performance, beam pattern as well as pulse compression property, via numerical simulations. © 1991-2012 IEEE.
Zhu W.,Monash University | Huang Y.,University of Electronic Science and Technology of China | Rukhlenko I.D.,Monash University | Wen G.,University of Electronic Science and Technology of China | Premaratne M.,Monash University
Optics Express | Year: 2012
Metamaterials attain their behavior due to resonant interactions among their subwavelength components and thus show specific designer features only in a very narrow frequency band. There is no simple way to dynamically increase the operating bandwidth of a narrowband metamaterial, but it may be possible to change its central frequency, shifting the spectral response to a new frequency range. In this paper, we propose and experimentally demonstrate a metamaterial absorber that can shift its central operating frequency by using mechanical means. The shift is achieved by varying the gap between the metamaterial and an auxiliary dielectric slab parallel to its surface. We also show that it is possible to create multiple absorption peaks by adjusting the size and/or shape of the dielectric slab, and to shift them by moving the slab relative to the metamaterial. Specifically, using numerical simulations we design a microwave metamaterial absorber and experimentally demonstrate that its central frequency can be set anywhere in a 1.6 GHz frequency range. The proposed configuration is simple and easy to make, and may be readily extended to THz frequencies. © 2012 Optical Society of America.
Jiang T.,University of Electronic Science and Technology of China | Jiang T.,University of Massachusetts Dartmouth | Wang H.,University of Massachusetts Dartmouth | Vasilakos A.V.,University of Western Macedonia
IEEE Journal on Selected Areas in Communications | Year: 2012
With the fast growing of multimedia communication applications, cognitive radio networks have gained the popularity as they can provide high wireless bandwidth and support quality-driven wireless multimedia services. In multimedia applications such as video conferences over the cognitive radio, the Quality of Experience (QoE) that directly measures the satisfaction of the end users cannot be easily realized due to the limited spectrum resources. The opportunistic spectrum access cognitive radio (CR) is an efficient technology to address this issue. However, the unstable channels allocated to the multimedia secondary users (SUs) can be re-occupied by the primary users (PUs) at any time, which makes the CR difficult to meet the QoE requirements. Therefore, it is important to study how to allocate frequency or spectrum resources to SUs according to their QoE requirements. This paper proposes a novel QoE-driven channel allocation scheme for SUs and cognitive radio networks (CRN) base station (BS). The historical QoE data under different primary channels (PCs) are collected by the SUs and delivered to a Cognitive Radio Base Station (CRBS). The CRBS will allocate available channel resources to the SUs based on their QoE expectations and maintain a priority service queue. The modified ON/OFF models of PCs and service queue models of SUs are jointly investigated for this channel allocation scheme. The performance of multimedia transmission of images and H.264 videos under our CR channel allocation scheme is studied, the results show that the proposed channel allocation approach can significantly improve the QoE of the priority-based SUs over the cognitive radio networks. © 1983-2012 IEEE.
Wu K.,Ecole Polytechnique de Montréal | Cheng Y.J.,University of Electronic Science and Technology of China | Djerafi T.,Ecole Polytechnique de Montréal | Hong W.,Nanjing Southeast University
Proceedings of the IEEE | Year: 2012
Significant advances in the development of millimeter-wave and terahertz (30-10000 GHz) technologies have been made to cope with the increasing interest in this still not fully explored electromagnetic spectrum. The nature of electromagnetic waves over this frequency range is well suited for the development of high-resolution imaging applications, molecular-sensitive spectroscopic devices, and ultrabroadband wireless communications. In this paper, millimeter-wave and terahertz antenna technologies are overviewed including the conventional and nonconventional planar/nonplanar antenna structures based on different platforms. As a promising technological platform, substrate-integrated circuits (SICs) attract more and more attention. Various substrate-integrated waveguide (SIW) schemes and other synthesized guide techniques have been widely employed in the design of antennas and arrays. Different types of substrate-integrated antennas and beamforming networks are discussed with respect to theoretical and experimental results in connection with electrical and mechanical performances. © 2012 IEEE.
Gao Q.,Huazhong University of Science and Technology | Gong Y.,Huazhong University of Science and Technology | Li T.,CAS Institute of Theoretical Physics | Li T.,University of Electronic Science and Technology of China
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2015
To reconcile the BICEP2 measurement on the tensor-to-scalar ratio r with Planck constraint, a large negative running of scalar spectral index ns is needed. So the inflationary observable such as ns should be expanded at least to the second-order slow-roll parameters for single-field inflationary models. The large value of r and the Lyth bound indicate that it is impossible to obtain the sub-Planckian excursion for the inflaton. However, we derive an absolutely minimal bound Δφ/MPl>r/2 on the inflaton excursion for single-field inflationary models, which can be applied to non-slow-roll inflationary models as well. This bound excludes the possibility of the small-field inflation with Δφ<0.1MPl if the BICEP2 result on r stands, and it opens the window of sub-Planckian excursion with Δφ
Liu Y.,Xiamen University | Liu Q.H.,Duke University | Nie Z.,University of Electronic Science and Technology of China
IEEE Transactions on Antennas and Propagation | Year: 2014
Previously, the matrix pencil method (MPM) and the forward-backward MPM (FBMPM) were used to effectively reduce the number of antenna elements in the single-pattern linear arrays. This work extends the MPM and FBMPM-based synthesis methods to the synthesis of multiple-pattern linear arrays with a smaller number of elements. The extended MPM (resp., the extended FBMPM) method organizes all the multiple pattern data into a composite Hankel (resp., composite Hankel-Toeplitz) matrix from which the minimum number of elements and the common poles corresponding to element positions can be obtained with similar processing used in the original MPM or FBMPM synthesis method. In particular, the extended FBMPM inherits the advantage of the original FBMPM that a useful restriction is put on the distribution of poles, which makes the element positions obtained much more accurate and robust. Numerical experiments are conducted to validate the effectiveness and robustness of the proposed methods. For the tested cases, the element saving is about 20% ~ 25% for reconfigurable shaped patterns, and can be even more for electrically large linear arrays with scanned pencil-beams. © 1963-2012 IEEE.
Li T.,CAS Institute of Theoretical Physics | Li T.,University of Electronic Science and Technology of China | Li Z.,Texas A&M University | Nanopoulos D.V.,Texas A&M University | And 2 more authors.
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2015
We show that the quadratic inflation can be realized by the phase of a complex field with helicoid potential. Remarkably, this helicoid potential can be simply realized in minimal supergravity. The global U(1) symmetry of the Kähler potential introduces a flat direction and evades the η problem automatically. So such inflation is technically natural. The phase excursion is super-Planckian as required by the Lyth bound, while the norm of the complex field can be suppressed in the sub-Planckian region. This model resolves the ultraviolet sensitive problem of the large field inflation; besides, it also provides a new type of monodromy inflation in supersymmetric field theory with consistent field stabilization. © 2015 American Physical Society.
Li T.,CAS Institute of Theoretical Physics | Li T.,University of Electronic Science and Technology of China | Raza S.,CAS Institute of Theoretical Physics
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2015
Considering the generalized minimal supergravity model in the minimal supersymmetric Standard Model, we study the electroweak supersymmetry, in which the squarks and/or gluino are heavy around a few TeVs while the sleptons, sneutrinos, bino, winos, and/or Higgsinos are light within 1 TeV. We resolve the (g-2)μ/2 discrepancy for the muon anomalous magnetic moment in the Standard Model successfully and identify a parameter space in which such solutions also have the electroweak fine-tuning measures ΔEW 16.5 (6%) and ΔEW 25 (4%) without and with the Wilkinson Microwave Anisotropy Probe (WMAP) bounds, respectively. We find that the allowed mass ranges, which are consistent within 3σ of the g-2 discrepancy, for the lightest neutralino, charginos, stau, stau neutrinos, and first two-family sleptons are [44, 390], [100, 700], [100, 700], [52, 800], and [150, 800] GeV, respectively. Moreover, our solutions satisfy the latest bounds reported by the ATLAS and CMS collaborations on electroweakinos and sleptons. The colored sparticles such as light stop, gluinos, and the first the first two generations of squark masses have been found in the mass ranges of [500, 3000], [1300, 4300], and [1800, 4200] GeV, respectively. To obtain the observed dark matter relic density for the lightest supersymmetric particle (LSP) neutralino, we have the bino-wino, LSP neutralino-stau, and LSP neutralino-tau sneutrinos coannihilation scenarios and the resonance solutions such as the A pole, Higgs pole, and Z pole. We identify the Higgsino-like LSP neutralino and display its spin-independent and spin-dependent cross sections with nucleons. We present ten benchmark points that can be tested at the up coming collider searches as well. © 2015 American Physical Society.
Cheng T.,CAS Institute of Theoretical Physics | Li T.,CAS Institute of Theoretical Physics | Li T.,University of Electronic Science and Technology of China | Li T.,Texas A&M University
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2013
To explain all the available experimental results, we have proposed the electroweak supersymmetry (EWSUSY) previously, where the squarks and/or gluino are heavy around a few TeVs while the sleptons, sneutrinos, bino, winos, and/or Higgsinos are light within 1 TeV. In the next to minimal supersymmetric Standard Model, we perform the systematic χ2 analyses on parameter space scan for three EWSUSY scenarios: (I) R-parity conservation and one dark matter candidate, (II) R-parity conservation and multicomponent dark matter, (III) R-parity violation. We obtain the minimal χ2/(degree of freedom) of 10.2/15, 9.6/14, and 9.2/14 respectively for scenarios I, II, and III. Considering the constraints from the LHC neutralino/chargino and slepton searches, we find that the majority of viable parameter space preferred by the muon anomalous magnetic moment has been excluded except for the parameter space with moderate to large tanâ¡β(8). Especially, the most favorable parameter space has relatively large tanâ¡β, moderate λ, small μeff, heavy squarks/gluino, and the second lightest CP-even neutral Higgs boson with mass around 125 GeV. In addition, if the left-handed smuon is nearly degenerate with or heavier than wino, there is no definite bound on wino mass. Otherwise, the wino with mass up to ∼450 GeV has been excluded. Furthermore, we present several benchmark points for scenarios I and II, and briefly discuss the prospects of the EWSUSY searches at the 14 TeV LHC and ILC. © 2013 American Physical Society.
Cheng H.,University of Electronic Science and Technology of China | Liu Z.,Microsoft | Yang L.,University of Electronic Science and Technology of China | Chen X.,Wayne State University
Signal Processing | Year: 2013
Sparse representation and learning has been widely used in computational intelligence, machine learning, computer vision and pattern recognition, etc. Mathematically, solving sparse representation and learning involves seeking the sparsest linear combination of basis functions from an overcomplete dictionary. A rational behind this is the sparse connectivity between nodes in human brain. This paper presents a survey of some recent work on sparse representation, learning and modeling with emphasis on visual recognition. It covers both the theory and application aspects. We first review the sparse representation and learning theory including general sparse representation, structured sparse representation, high-dimensional nonlinear learning, Bayesian compressed sensing, sparse subspace learning, non-negative sparse representation, robust sparse representation, and efficient sparse representation. We then introduce the applications of sparse theory to various visual recognition tasks, including feature representation and selection, dictionary learning, Sparsity Induced Similarity (SIS) measures, sparse coding based classification frameworks, and sparsity-related topics. © 2012 Elsevier B.V.
Gao X.,CAS Institute of Theoretical Physics | Gao X.,Virginia Polytechnic Institute and State University | Li T.,CAS Institute of Theoretical Physics | Li T.,University of Electronic Science and Technology of China | Shukla P.,University of Turin
Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics | Year: 2014
In the lights of current BICEP2 observations accompanied with the PLANCK satellite results, it has been observed that the simple single field chaotic inflationary models provide a good agreement with their spectral index ns and large tensor-to-scalar ratio r (0.15
Liu J.,University of California at Los Angeles | Li L.,University of California at Los Angeles | Li L.,University of Electronic Science and Technology of China | Pei Q.,University of California at Los Angeles
Macromolecules | Year: 2011
We demonstrate that conjugated polymers are able to efficiently host blue and white electrophosphorescence if the conjugated polymer has both high triplet energy level (ET) and high-lying HOMO energy level. A novel conjugated polymer host (PmPTPA) is developed by attaching triphenylamine unit to poly(m-phenylene) backbone. The poly(m-phenylene) backbone endows PmPTPA an ET as high as 2.65 eV, which is sufficiently high to prevent triplet energy back transfer. The tethering triphenylamine unit leads to the HOMO energy level of -5.35 eV for PmPTPA and facilitates hole injection. As the result, blue phosphorescent polymer light-emitting diodes (PPLEDs) based on PmPTPA exhibit the luminance efficiency of 17.9 cd/A and external quantum efficiency of 9.3%. White PPLEDs with blue, green and red phosphorescent dopants dispersed in PmPTPA show the luminance efficiency of 22.1 cd/A and external quantum efficiency of 10.6%. For both the blue and white PPLEDs based on the conjugated polymer host PmPTPA, the EL performance are fairly comparable to those of the state-of-the-art nonconjugated polymer host, poly(vinyl-carbazole) (PVK). These results indicate that conjugated polymers are suitable host materials for PPLEDs with all emission colors. © 2011 American Chemical Society.
Chen G.,Advanced Signal Processing Group | Tian Z.,Advanced Signal Processing Group | Gong Y.,Advanced Signal Processing Group | Chen Z.,University of Electronic Science and Technology of China | Chambers J.A.,Advanced Signal Processing Group
IEEE Transactions on Information Forensics and Security | Year: 2014
This paper considers the security of transmission in buffer-aided decode-and-forward cooperative wireless networks. An eavesdropper which can intercept the data transmission from both the source and relay nodes is considered to threaten the security of transmission. Finite size data buffers are assumed to be available at every relay in order to avoid having to select concurrently the best source-to-relay and relay-to-destination links. A new max-ratio relay selection policy is proposed to optimize the secrecy transmission by considering all the possible source-to-relay and relay-to-destination links and selecting the relay having the link which maximizes the signal to eavesdropper channel gain ratio. Two cases are considered in terms of knowledge of the eavesdropper channel strengths: exact and average gains, respectively. Closed-form expressions for the secrecy outage probability for both cases are obtained, which are verified by simulations. The proposed max-ratio relay selection scheme is shown to outperform one based on a max-min-ratio relay scheme. © 2014 IEEE.
Dutta B.,Texas A&M University | Gao Y.,Texas A&M University | Ghosh T.,Texas A&M University | Gogoladze I.,University of Delaware | And 2 more authors.
Physical Review D - Particles, Fields, Gravitation and Cosmology | Year: 2016
We consider the diphoton resonance at the 13 TeV LHC in a consistent model with new scalars and vector-like fermions added to the Standard Model, which can be constructed from orbifold grand unified theories and string models. The gauge coupling unification can be achieved, neutrino masses can be generated radiatively, and the electroweak vacuum stability problem can be solved. To explain the diphoton resonance, we study a spin-0 particle, and discuss various associated final states. We also constrain the couplings and number of the introduced heavy multiplets for the new resonance's width at 5 or 40 GeV. © 2016 American Physical Society.
Yang T.,University of Electronic Science and Technology of China | Chi P.-L.,University of California at Los Angeles | Itoh T.,University of California at Los Angeles
IEEE Transactions on Microwave Theory and Techniques | Year: 2011
Novel and compact composite right/left-handed (CRLH) quarter-wave type resonators are proposed in this paper. The resonator can resonate at the frequency where the electrical length is phase-leading or negative, which results in a smaller size as compared to the conventional phase-delayed microstrip-line resonator. Furthermore, it is only half the size of the CRLH half-wave resonator resonating at the same frequency. In addition, the proposed resonator is capable of engineering the multiresonances very close to each other, which makes it suitable to implement the miniaturized multiband microwave components such as diplexers and triplexers. A very compact diplexer and a very compact triplexer are proposed based on the proposed CRLH quarter-wave resonators in this paper and both of them have demonstrated very good performance. Specifically, compared to the referenced works based on the conventional microstrip resonators, the proposed diplexer and triplexer are 50% and 76% smaller than their microstrip counterparts, respectively. © 2011 IEEE.
Chong H.-F.,Institute for Infocomm Research | Liang Y.-C.,University of Electronic Science and Technology of China
IEEE Transactions on Information Theory | Year: 2016
Zeng K.,University of Electronic Science and Technology of China | Pawelczak P.,University of California at Los Angeles | Cabric D.,University of California at Los Angeles
IEEE Communications Letters | Year: 2010
Existing cooperative spectrum sensing (CSS) schemes are typically vulnerable to attacks where misbehaved cognitive radios (CRs) falsify sensing data. To ensure the robustness of spectrum sensing, this letter presents a secure CSS scheme by introducing a reputation-based mechanism to identify misbehaviors and mitigate their harmful effect on sensing performance. Encouraged by the fact that such secure CSS is sensitive to the correctness of reputations, we further present a trusted node assistance scheme. This scheme starts with reliable CRs. Sensing information from other CRs are incorporated into cooperative sensing only when their reputation is verified, which increases robustness of cooperative sensing. Simulations verify the effectiveness of the proposed schemes. © 2010 IEEE.
Fu Y.,University of Electronic Science and Technology of China | Fu Y.,CAS Chengdu Institute of Optics and Electronics | Zhou X.,University of Electronic Science and Technology of China
Plasmonics | Year: 2010
Four types of plasmonic lenses for the purpose of superfocusing designed on the bases of approximate negative refractive index concept, subwavelength metallic structures, waveguide mode were introduced, and curved chains of nanoparticles, respectively, were introduced. Imaging mechanism, fabrication, and characterization issues were presented. Theoretical analyses of the illumination with different polarization states on focusing performance of the plasmonic lenses were given also. In addition, a hybrid Au-Ag plasmonic lens with chirped slits for the purpose of avoiding oxidation of Ag film was presented. © 2010 Springer Science+Business Media, LLC.
Qi Y.,University of Minnesota | Zhang Y.,University of Minnesota | Zhang Y.,University of Rochester | Zhang F.,University of Minnesota | And 6 more authors.
Genome Research | Year: 2013
Improved methods for engineering sequence-specific nucleases, including zinc finger nucleases (ZFNs) and TAL effector nucleases (TALENs), have made it possible to precisely modify plant genomes. However, the success of genome modification is largely dependent on the intrinsic activity of the engineered nucleases. In this study, we sought to enhance ZFNmediated targeted mutagenesis and gene targeting (GT) in Arabidopsis by manipulating DNA repair pathways. Using a ZFN that creates a double-strand break (DSB) at the endogenous ADH1 locus, we analyzed repair outcomes in the absence of DNA repair proteins such as KU70 and LIG4 (both involved in classic nonhomologous end-joining, NHEJ) and SMC6B (involved in sister-chromatid-based homologous recombination, HR). We achieved a fivefold to 16-fold enhancement in HR-based GT in a ku70 mutant and a threefold to fourfold enhancement in GT in the lig4 mutant. Although the NHEJ mutagenesis frequency was not significantly changed in ku70 or lig4, DNA repair was shifted to microhomology-dependent alternative NHEJ. As a result, mutations in both ku70 and lig4 were predominantly large deletions, which facilitates easy screening for mutations by PCR. Interestingly, NHEJ mutagenesis and GT at the ADH1 locus were enhanced by sixfold to eightfold and threefold to fourfold, respectively, in a smc6b mutant. The increase in NHEJ-mediated mutagenesis by loss of SMC6B was further confirmed using ZFNs that target two other Arabidopsis genes, namely, TT4 and MPK8. Considering that components of DNA repair pathways are highly conserved across species, mutations in DNA repair genes likely provide a universal strategy for harnessing repair pathways to achieve desired targeted genome modifications. © 2013, Published by Cold Spring Harbor Laboratory Press.
Zeng Y.,Institute for Infocomm Research | Liang Y.-C.,Institute for Infocomm Research | Liang Y.-C.,University of Electronic Science and Technology of China | Pham T.-H.,Institute for Infocomm Research
IEEE Journal on Selected Areas in Communications | Year: 2013
Orthogonal frequency division multiplex (OFDM) has been widely used in various wireless communications systems. Thus the detection of OFDM signals is of significant importance in cognitive radio and other spectrum sharing systems. A common feature of OFDM in many popular standards is that some pilot subcarriers repeat periodically after certain OFDM blocks. In this paper, sensing methods for OFDM signals are proposed by using such repetition structure of the pilots. Firstly, special properties for the auto-correlation (AC) of the received signals are identified, from which the optimal likelihood ratio test (LRT) is derived. However, this method requires the knowledge of channel information, carrier frequency offset (CFO) and noise power. To make the LRT method practical, we then propose an approximated LRT (ALRT) method that does not rely on the channel information and noise power, thus the CFO is the only remaining obstacle to the ALRT. To handle the problem, we propose a method to estimate the composite CFO and compensate its effect in the AC using multiple taps of ACs of the received signals. Computer simulations have shown that the proposed sensing methods are robust to frequency offset, noise power uncertainty, time delay uncertainty, and frequency selectiveness of the channel. © 1983-2012 IEEE.
Zhang L.,Institute for Infocomm Research | Zhang R.,Institute for Infocomm Research | Liang Y.-C.,Institute for Infocomm Research | Liang Y.-C.,University of Electronic Science and Technology of China | And 2 more authors.
IEEE Transactions on Information Theory | Year: 2012
Owing to the special structure of the Gaussian multiple-input multiple-output (MIMO) broadcast channel (BC), the associated capacity region computation and beamforming optimization problems are typically non-convex, and thus cannot be solved directly. One feasible approach is to consider the respective dual multiple-access channel (MAC) problems, which are easier to deal with due to their convexity properties. The conventional BC-MAC duality has been established via BC-MAC signal transformation, and is applicable only for the case in which the MIMO BC is subject to a single transmit sum-power constraint. An alternative approach is based on minimax duality, which can be applied to the case of the sum-power constraint or per-antenna power constraint. In this paper, the conventional BC-MAC duality is extended to the general linear transmit covariance constraint (LTCC) case, which includes sum-power and per-antenna power constraints as special cases. The obtained general BC-MAC duality is applied to solve the capacity region computation for the MIMO BC and beamforming optimization for the multiple-input single-output (MISO) BC, respectively, with multiple LTCCs. The relationship between this new general BC-MAC duality and the minimax duality is also discussed, and it is shown that the general BC-MAC duality leads to simpler problem formulations. Moreover, the general BC-MAC duality is extended to deal with the case of nonlinear transmit covariance constraints in the MIMO BC. © 2006 IEEE.
Tamura M.,Panasonic | Yang T.,University of Electronic Science and Technology of China | Itoh T.,University of California at Los Angeles
IEEE Transactions on Microwave Theory and Techniques | Year: 2011
In this paper, two design approaches are presented for realizing very compact and low-profile unbalanced-balanced filters with special configuration called hybrid resonators. One of the design concepts for the unbalanced-balanced filter is based on the folded hybrid resonators. This filter consists of two hybrid resonators, which are folded face to face symmetrically. The capacitance between two resonators is generated by folding the resonators. This approach makes design of compact and low-profile filters possible. The other design concept for the unbalanced-balanced filter consists of resonators that have capacitive and inductive inverters. The feature of this filter is that phase-lag is expressed by inductive coupling. This filter also achieves very low profile and compact size. The dimensions of the two filters fabricated by low-temperature co-fired ceramic are 1.6 mm × 1.05 mm × 0.67 mm and 1.6 mm × 0.8 mm × 0.56 mm, respectively. For the simulation results, the maximum insertion losses for the first and second filters are 2.2 and 2.3 dB in the 2.4-GHz band, respectively. Common mode rejection for both is more than 22 dB in the same band. The amplitude imbalance and phase imbalance for the first filter are less than 1.8 dB and 6.8 in the passband, respectively. The amplitude imbalance and phase imbalance for the second filter are less than 1.9 dB and 1.8 in the passband, respectively. For both design methods, good agreement between measured and computed results is obtained. © 2011 IEEE.
Lien S.-Y.,National formosa University | Chen K.-C.,National Taiwan University | Liang Y.-C.,University of Electronic Science and Technology of China | Lin Y.,IBM
IEEE Wireless Communications | Year: 2014
Wang X.-H.,University of Electronic Science and Technology of China | Zhang H.,University of North Texas | Wang B.-Z.,University of Electronic Science and Technology of China
IEEE Microwave and Wireless Components Letters | Year: 2013
A novel differential filter with ultra-wideband (UWB) response is proposed in this letter based on microstrip line structures. 180° UWB phase shifters and 360° transmission lines are employed in the design to get the 180° phase shift over broad bandwidth. In this way, the broadband conversion between in- and out-of-phase signals can be realized. Utilizing this characteristic, the undesired common-mode noises will be cancelled out at the center of the filter, while the input differential-mode signals can still propagate well. The proposed new differential filter was calculated by transmission line model, simulated by full-wave electromagnetic simulator, and validated by the measurement. The simulation and measurement results verify its good performance. It is validated that, in the proposed filter, the differential-mode signals can propagate well with UWB frequency response, while the common-mode noises are well suppressed with more than 10 dB suppression in the concerned frequency band. © 2001-2012 IEEE.
Yang K.,University of Electronic Science and Technology of China | Gao S.,University of Electronic Science and Technology of China | Li C.,University of Electronic Science and Technology of China | Li C.,CAS Shanghai Institutes for Biological Sciences | Li Y.,University of Electronic Science and Technology of China
Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition | Year: 2013
Color information plays an important role in better understanding of natural scenes by at least facilitating discriminating boundaries of objects or areas. In this study, we propose a new framework for boundary detection in complex natural scenes based on the color-opponent mechanisms of the visual system. The red-green and blue-yellow color opponent channels in the human visual system are regarded as the building blocks for various color perception tasks such as boundary detection. The proposed framework is a feed forward hierarchical model, which has direct counterpart to the color-opponent mechanisms involved in from the retina to the primary visual cortex (V1). Results show that our simple framework has excellent ability to flexibly capture both the structured chromatic and achromatic boundaries in complex scenes. © 2013 IEEE.
Cermak T.,University of Minnesota | Doyle E.L.,Iowa State University | Christian M.,University of Minnesota | Wang L.,Iowa State University | And 8 more authors.
Nucleic Acids Research | Year: 2011
TALENs are important new tools for genome engineering. Fusions of transcription activator-like (TAL) effectors of plant pathogenic Xanthomonas spp. to the FokI nuclease, TALENs bind and cleave DNA in pairs. Binding specificity is determined by customizable arrays of polymorphic amino acid repeats in the TAL effectors. We present a method and reagents for efficiently assembling TALEN constructs with custom repeat arrays. We also describe design guidelines based on naturally occurring TAL effectors and their binding sites. Using software that applies these guidelines, in nine genes from plants, animals and protists, we found candidate cleavage sites on average every 35bp. Each of 15 sites selected from this set was cleaved in a yeast-based assay with TALEN pairs constructed with our reagents. We used two of the TALEN pairs to mutate HPRT1 in human cells and ADH1 in Arabidopsis thaliana protoplasts. Our reagents include a plasmid construct for making custom TAL effectors and one for TAL effector fusions to additional proteins of interest. Using the former, we constructed de novo a functional analog of AvrHah1 of Xanthomonas gardneri. The complete plasmid set is available through the non-profit repository AddGene and a web-based version of our software is freely accessible online. © 2011 The Author(s).
Xing L.,University of Electronic Science and Technology of China | Xing L.,University of Massachusetts Dartmouth | Tannous O.,University of Massachusetts Dartmouth | Dugan J.B.,University of Virginia
IEEE Transactions on Systems, Man, and Cybernetics Part A:Systems and Humans | Year: 2012
Many real-world systems, particularly those with limited power resources, are designed with cold-standby redundancy for achieving fault tolerance and high reliability. Cold-standby units are unpowered and, thus, do not consume any power until needed to replace a faulty online component. Cold-standby redundancy creates sequential dependence between the online component and standby components; in particular, a standby component can start to work and then fail only after the online component has failed. Traditional approaches to handling the cold-standby redundancy are typically state-space-based or simulation-based or inclusion/exclusion-based methods. Those methods, however, have the state-space explosion problem and/or require long computation time particularly when results with a high degree of accuracy are desired. In this paper, we propose an analytical method based on sequential binary decision diagrams (SBDD) for combinatorial reliability analysis of nonrepairable cold-standby systems. Different from the simulation-based methods, the proposed approach can generate exact system reliability results. In addition, the system SBDD model and reliability evaluation expression, once generated, are reusable for the reliability analysis with different component failure parameters. The approach has no limitation on the type of time-to-failure distributions for the system components or on the system structure. Application and advantages of the proposed approach are illustrated through several case studies. © 2012 IEEE.
Yang T.,University of Electronic Science and Technology of China | Yang T.,University of California at Los Angeles | Chi P.-L.,University of California at Los Angeles | Itoh T.,University of California at Los Angeles
IEEE Microwave and Wireless Components Letters | Year: 2010
In this letter, a compact microstrip diplexer with very high output isolation is proposed. This diplexer consists of compact hybrid resonators, which are capable of introducing transmission zeros at desired frequencies and meanwhile suppressing signals below the resonant frequencies through tapping the feeding line close to the shorted vias. By designing the transmission zero of the lower-frequency channel in the higher passband, and utilizing the high lower-stopband suppression property of the higher-frequency channel, very high diplexer output isolation can be achieved. The proposed diplexer with center frequencies at 1.8 and 2.45 GHz, respectively, has demonstrated better than 55 dB output isolation and more than 55 dB suppressions in the stopbands. Furthermore, the diplexer occupies only a small area of 0.13λ0 × 0.2λ0. © 2010 IEEE.
Yang T.,University of California at Los Angeles | Yang T.,University of Electronic Science and Technology of China | Tamura M.,Panasonic | Itoh T.,University of California at Los Angeles
IEEE Transactions on Microwave Theory and Techniques | Year: 2010
A hybrid resonant circuit is proposed in this paper. The circuit is a combination of a shunt resonant circuit and series resonant circuit. With this combination, lower resonant frequency is achieved as compared to the single shunt and series resonant circuits. As a result, a compact resonator with smaller size can be achieved as compared to the conventional quarter- and half-wave resonators. Besides the size reduction, the proposed resonant circuit is able to introduce a transmission zero to improve the stopband suppression in filter design. Based on this circuit, a very compact interdigital coupled microstrip resonator is proposed in this paper. The resonator achieves a small length of nearly 1/10 guided wavelength λg, which has a length reduction of 63% as compared to the conventional uniform quarter-wave resonator. By using the proposed resonator, a second-order bandpass filter with a small size of 0.144λg × 0.128λg and a fourth-order bandpass filter with a size of 0.217λg × 0.1λg are built based on the standard filter synthesis methods. Both good performance and miniaturization are achieved for the proposed filters, and the expected transmission zeros are also observed. In addition to the small filters, the proposed resonator is suitable for miniaturized balun bandpass filters. A novel configuration for a balun bandpass filter is proposed based on the aforementioned resonators. A second-order balun bandpass filter with a size of 0.26λg × 0.145λg and a fourth-order balun bandpass filter with a size of 0.213λg × 0.203λg are reported in this paper. Both balun filters achieve good filtering performance, as well as excellent amplitude and phase imbalances, which are less than 1 dB and 1° in the passband, respectively. © 2010 IEEE.
Zhang L.,Northwestern University | Zhang L.,Qualcomm | Li H.,University of Electronic Science and Technology of China | Guo D.,Northwestern University
IEEE Transactions on Information Theory | Year: 2014
In many wireless communication systems, radios are subject to a duty cycle constraint, that is, a radio can only actively transmit signals over a fraction of the time. For example, it is desirable to have a small duty cycle in some low power systems; a half-duplex radio cannot keep transmitting if it wishes to receive useful signals; and a cognitive radio needs to listen and detect primary users frequently. This paper studies the capacity of point-to-point scalar discrete-time Gaussian channels subject to a duty cycle constraint as well as an average transmit power constraint. An idealized duty cycle constraint is first studied, which can be regarded as a requirement on the minimum fraction of nontransmissions or zero symbols in each codeword. Independent input with a unique discrete distribution is shown to achieve the channel capacity. In many situations, numerically optimized on-off signaling can achieve much higher rate than Gaussian signaling over a deterministic transmission schedule. This is in part because the positions of nontransmissions in a codeword can convey information. A more realistic duty cycle constraint is also studied, where the extra cost of transitions between transmissions and nontransmissions due to pulse shaping is accounted for. The capacity-achieving input is correlated over time and is hard to compute. A lower bound of the achievable rate as a function of the input distribution is shown to be maximized by a first-order Markov input process, whose stationary distribution is also discrete and can be computed efficiently. The results in this paper suggest that, under various duty cycle constraints, departing from the usual paradigm of intermittent packet transmissions may yield substantial gain. © 1963-2012 IEEE.
Li L.,University of California at Los Angeles | Li L.,University of Electronic Science and Technology of China | Yu Z.,University of California at Los Angeles | Hu W.,University of California at Los Angeles | And 3 more authors.
Blue, green, and red electrophosphorescent polymer light-emitting diodes have been fabricated on silver nanowire-polymer composite electrode. The devices are 20%-50% more efficient than control devices on ITO/glass and exhibit small efficiency roll-off at high luminances. The blue PLEDs were repeatedly bent to 1.5 mm radius concave or convex with calculated strain in the emissive layer approximately 5% (tensile or compressive). Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Lan F.,University of Electronic Science and Technology of China | Yang Z.,University of Electronic Science and Technology of China | Qi L.,Qufu Normal University | Gao X.,Guilin University of Electronic Technology | Shi Z.,University of Electronic Science and Technology of China
Optics Letters | Year: 2014
A dual-resonance frequency selective surface filter in the THz range that uses bilayer modified complementary metamaterial structures is proposed in this Letter. The bandpass filter, with dual bands centered at 0.315 and 0.48 THz, uses a single crystal quartz substrate and is simulated, fabricated, and measured. To minimize the manufacturing risks of working with fragile and thin quartz substrates, efforts have been made to improve the transmission frequency response features at realizable substrate thicknesses. Experimental results from 0.1 to 0.6 THz measured by THz time-domain spectroscopy show excellent agreement with the simulation results. © 2014 Optical Society of America.
Fan L.,CAS Institute of Automation | Wang J.,University of Electronic Science and Technology of China | Zhang Y.,CAS Institute of Automation | Han W.,Tianjin Medical University | And 4 more authors.
Cerebral Cortex | Year: 2014
The temporal pole (TP) is an association cortex capable of multisensory integration and participates in various high-order cognitive functions. However, an accepted parcellation of the human TP and its connectivity patterns have not yet been well established. Here, we sought to present a scheme for the parcellation of human TP based on anatomical connectivity and to reveal its subregional connectivity patterns. Three distinct subregions with characteristic fiber pathways were identified, including the dorsal (TAr), the medial (TGm), and lateral (TGl) subregions, which are located ventrally. According to the connectivity patterns, a dorsal/ventral sensory segregation of auditory and visual processing and the medial TGm involved in the olfactory processing were observed. Combined with the complementary resting-state functional connectivity analysis, the connections of the TGm with the orbitofrontal cortex and other emotion-related areas, the TGl connections with the MPFC and major default mode network regions, and the TAr connections with the perisylvian language areas were observed. To the best of our knowledge, the present study represents the first attempt to parcel the human TP based on its anatomical connectivity features, which may help to improve our understanding of its connectional anatomy and to extend the available knowledge in TP-related clinical research. © The Author 2013. Published by Oxford University Press. All rights reserved.
He Q.,University of Electronic Science and Technology of China | He Q.,Lehigh University | Blum R.S.,Lehigh University | Haimovich A.M.,New Jersey Institute of Technology
IEEE Transactions on Signal Processing | Year: 2010
This paper presents an analysis of the joint estimation of target location and velocity using a multiple-input multiple-output (MIMO) radar employing noncoherent processing for a complex Gaussian extended target. A MIMO radar with M transmit and $N$ receive antennas is considered. To provide insight, we focus on a simplified case first, assuming orthogonal waveforms, temporally and spatially white noise-plus-clutter, and independent reflection coefficients. Under these simplifying assumptions, the maximum-likelihood (ML) estimate is analyzed, and a theorem demonstrating the asymptotic consistency, large MN, of the ML estimate is provided. Numerical investigations, given later, indicate similar behavior for some reasonable cases violating the simplifying assumptions. In these initial investigations, we study unconstrained systems, in terms of complexity and energy, where each added transmit antenna employs a fixed energy so that the total transmitted energy is allowed to increase as we increase the number of transmit antennas. Following this, we also look at constrained systems, where the total system energy and complexity are fixed. To approximate systems of fixed complexity in an abstract way, we restrict the total number of antennas employed to be fixed. Here, we show numerical examples which indicate a preference for receive antennas, similar to MIMO communications, but where systems with multiple transmit antennas yield the smallest possible mean-square error (MSE). The joint CramrRao bound (CRB) is calculated and the MSE of the ML estimate is analyzed. It is shown for some specific numerical examples that the signal-to-clutter-plus-noise ratio (SCNR) threshold, indicating the SCNRs above which the MSE of the ML estimate is reasonably close to the CRB, can be lowered by increasing MN. The noncoherent MIMO radar ambiguity function (AF) is developed in two different ways and illustrated by examples. It is shown for some specific examples that the size of the product MN controls the levels of the sidelobes of the AF. © 2010 IEEE.
He Q.,University of Electronic Science and Technology of China | Blum R.S.,Lehigh University
IEEE Signal Processing Letters | Year: 2014
Target position and velocity estimation using a passive radar with multiple signals of opportunity and multiple receive stations is investigated. The maximum likelihood (ML) estimate of the unknown position and velocity vector of a target is presented. Formulas bounding the best possible mean square error are provided, via the Cramer-Rao lower bound, for any unbiased estimator of target position and velocity. The model assumes a single target, a single receive antenna at each receive station, spatially and temporally white Gaussian clutter-plus-noise, and uncorrelated reflection coefficients. To describe the best possible performance, it is assumed that the signals of opportunity are estimated perfectly from the direct path reception. For a specific example where the signals of opportunity come from the Global System for Mobile (GSM) communication system, the optimum possible estimation performance is presented using numerical examples. It is shown that it is possible to obtain large performance gains through using multiple signals of opportunity and multiple receive stations. © 2013 IEEE.
He Q.,University of Electronic Science and Technology of China | He Q.,Lehigh University | Blum R.S.,Lehigh University | Godrich H.,New Jersey Institute of Technology | Haimovich A.M.,New Jersey Institute of Technology
IEEE Journal on Selected Topics in Signal Processing | Year: 2010
This paper studies the velocity estimation performance for multiple-input multiple-output (MIMO) radar with widely spaced antennas. We derive the Cramer Rao bound (CRB) for velocity estimation and study the optimized system/configuration design based on CRB. General results are presented for an extended target with reflectivity varying with look angle. Then detailed analysis is provided for a simplified case, assuming an isotropic scatterer. For given transmitted signals, optimal antenna placement is analyzed in the sense of minimizing the CRB of the velocity estimation error. We show that when all antennas are located at approximately the same distance from the target, symmetrical placement is optimal and the relative position of transmitters and receivers can be arbitrary under the orthogonal received signal assumption. In this case, it is also shown that for MIMO radar with optimal placement, velocity estimation accuracy can be improved by increasing either the signal time duration or the product of the number of transmit and receive antennas. © 2010 IEEE.
He Q.,University of Electronic Science and Technology of China | He Q.,Lehigh University | Blum R.S.,Lehigh University
IEEE Transactions on Signal Processing | Year: 2011
For a multiple-input multiple-output (MIMO) system adopting the NeymanPearson (NP) criterion, we initially derive the diversity gain for a signal-present versus signal-absent scalar hypothesis test statistic and also for a vector signal-present versus signal-absent hypothesis testing problem. For a MIMO radar system with M transmit and N receive antennas, used to detect a target composed of Q random scatterers with possibly non-Gaussian reflection coefficients in the presence of possibly non-Gaussian clutter-plus-noise, we consider a class of test statistics, including the optimum test for Gaussian reflection coefficients and Gaussian clutter-plus-noise, and apply the previously developed results to compute the diversity gain. It is found that the diversity gain for the MIMO radar system is dependent on the cumulative distribution function (cdf) of the reflection coefficients while being invariant to the cdf of the clutter-plus-noise under some reasonable conditions requiring certain moments of the magnitude of the processed clutter-plus-noise be bounded. If the noise-free received waveforms, due to target reflection, at each receiver span a space of dimension M' ≤ M, the largest possible diversity gain is controlled by the value of min (N M', Q and the lowest order power in an expansion, about zero, of the cdf of the magnitude squared of a linear transformed version of the reflection coefficient vector. It is shown that the maximum possible diversity gain in any given scenario can be achieved without employing orthogonal waveforms. © 2006 IEEE.
Wang H.,Rutgers University | Zou Q.,Rutgers University | Xu H.,University of Electronic Science and Technology of China
Automatica | Year: 2012
In this article, the problem of nonperiodic tracking-transition switching with preview is considered. Such a control problem exists in applications including nanoscale material property mapping, robot manipulation, and probe-based nanofabrication, where the output needs to track the desired trajectory during the tracking sections, and rapidly transit to another point during the transition sections with no post-transition oscillations. Due to the coupling between the control of the tracking sections and that of the transition ones, and the potential mismatch of the boundary system state at the tracking-transition switching instants, these control objectives become challenging for nonminimum-phase systems. In the proposed approach, the optimal desired output trajectory for the transition sections is designed through a direct minimization of the output energy, and the needed control input that maintains the smoothness of both the output and the system state across all tracking-transition switching is obtained through a preview-based stable-inversion approach. The needed preview time is quantified by the characteristics of the system dynamics, and can be minimized via the recently developed optimal preview-based inversion technique. The proposed approach is illustrated through a nanomanipulation example in simulation. © 2012 Elsevier Ltd. All rights reserved. © 2012 Elsevier Ltd. All rights reserved.
Xi L.,University of Electronic Science and Technology of China | Jiang H.,University of Electronic Science and Technology of China | Jiang H.,University of Florida
Applied Physics Letters | Year: 2015
We present a method for noninvasively imaging the hand joints using a three-dimensional (3D) photoacoustic imaging (PAI) system. This 3D PAI system utilizes cylindrical scanning in data collection and virtual-detector concept in image reconstruction. The maximum lateral and axial resolutions of the PAI system are 70μm and 240μm. The cross-sectional photoacoustic images of a healthy joint clearly exhibited major internal structures including phalanx and tendons, which are not available from the current photoacoustic imaging methods. The in vivo PAI results obtained are comparable with the corresponding 3.0T MRI images of the finger joint. This study suggests that the proposed method has the potential to be used in early detection of joint diseases such as osteoarthritis. © 2015 AIP Publishing LLC.
He Q.,University of Electronic Science and Technology of China | Blum R.S.,Lehigh University
IEEE Signal Processing Letters | Year: 2010
Recent research indicates the potential of MIMO radar with dispersed antennas to achieve high target localization accuracy via coherent processing. Coherent processing requires phase synchronization. Usually, perfect phase synchronization is difficult to realize. Assuming frequency synchronization, possibly through reception of a beacon, and white noise, possibly due to estimating the covariance matrix and whitening the observations, we consider the impact of static phase errors at the transmitters and receivers for cases with sufficiently high SNR such that the Cramer-Rao bound (CRB) provides accurate performance estimates. We model the phase errors as random variables and discuss the impact of these errors on target localization performance. In a few example cases the CRB is computed and compared with those in the ideal coherent and noncoherent processing cases. For these examples, using numerical results, we will show that at high enough signal-to-noise ratio (SNR), phase errors degrade performance only by a relatively small amount. © 2009 IEEE.
Chen F.,University of Electronic Science and Technology of China | Zhang Y.,Sichuan Remote Sensing Geomatics Institute
IEEE Geoscience and Remote Sensing Letters | Year: 2013
Linear spectral unmixing is an effective technique to estimate the abundances of materials present in each hyperspectral image pixel. Recently, sparse-regression-based unmixing approaches have been proposed to tackle this problem. Mostly, ℓ1 norm minimization is used to approximate the ℓ0 norm minimization problem in terms of computational complexity. In this letter, we model the hyperspectral unmixing as a constrained sparse ℓp - ℓ2(0 < p < 1) optimization problem and propose to solve it via the iteratively reweighted least squares algorithm. Experimental results on a series of simulated data sets and a real hyperspectral image demonstrate that the proposed method can achieve performance improvement over the state-of-the-art ℓ1 -ℓ2 method. © 2012 IEEE.
Wu G.-R.,Ghent University | Wu G.-R.,University of Electronic Science and Technology of China | Marinazzo D.,Ghent University
Brain Topography | Year: 2015
It is now recognized that important information can be extracted from the brain spontaneous activity, as exposed by recent analysis using a repertoire of computational methods. In this context a novel method, based on a blind deconvolution technique, is used to analyze potential changes due to chronic pain in the brain pain matrix’s effective connectivity. The approach is able to deconvolve the hemodynamic response function from spontaneous neural events, i.e., in the absence of explicit onset timings, and to evaluate information transfer between two regions as a joint probability of the occurrence of such spontaneous events. The method revealed that the chronic pain patients exhibit important changes in the insula’s effective connectivity which can be relevant to understand the overall impact of chronic pain on brain function. © 2014, Springer Science+Business Media New York.
He Q.,University of Electronic Science and Technology of China | Blum R.S.,Lehigh University
Signal Processing | Year: 2012
MIMO radar with properly placed antennas that employs a coherent processing approach can provide superior MSE performance, as indicated by recent work. This paper demonstrates that the magnitude of these gains decreases with an increase in the product of the number of transmit and receive antennas if the antennas for the noncoherent system are also suitably placed, using a placement which is generally different from the one for the coherent processing approach. Initially, we study the systems without constraining the complexity and energy, where each added transmit antenna employs a fixed energy so that the total transmitted energy is allowed to increase as we increase the number of transmit antennas. Later we also look at constrained systems, where adding a transmit antenna splits the total system energy and the total number of antennas employed is restricted. A rigorous theorem is presented for the case of orthogonal signals in temporally and spatially white clutter-plus-noise, but numerical results for nonorthogonal signals and colored clutter-plus-noise follow a similar pattern. © 2012 Elsevier B.V. All rights reserved.
Wang W.,University of Electronic Science and Technology of China | Li G.-X.,Harbin Institute of Technology
Engineering Failure Analysis | Year: 2012
With an increase in speed, a vehicle's dynamic behavior becomes apparent. Increasing speed not only affects the sitting comfort, but also may lead to derailment. However, an accident is difficult to predict, because the derailment mechanism is not thoroughly understood. The reliability of derailment simulations are completely conditional to being able to accurately solve the wheel and rail contact problem. Thus, an improved three-dimensional contact trace method is presented to quickly obtain the correct point. Then, a fast and accurate method for obtaining the contact force, which includes the creep force and the normal force, is improved. The results correspond more closely to realitic solutions compared with those of current methods. Next, a dynamic model of the vehicle and the rail is established. The two models are not independent of each other. The wheel-rail contact calculation is the key consideration for coupling in the two models. Finally, all the dynamic models, which are called dynamic derailment simulation for high-speed vehicle (DDSHV), are developed in MATLAB. To identify two different types of derailment, derailment judgment is embedded in the program package. The simulation system can be used to study the dynamic derailment mechanism, analyze derailment conditions and influence factors, and determine the key cause of the incident. © 2012 Elsevier Ltd.
Yang Y.,Lehigh University | Blum R.S.,Lehigh University | He Z.,University of Electronic Science and Technology of China | Fuhrmann D.R.,Michigan Technological University
IEEE Transactions on Signal Processing | Year: 2010
Waveform design is essential to unleash the performance advantages promised by multiple-input multiple-output (MIMO) radar, and this topic has attracted a lot of attention in the recent years. Revisiting an earlier examined MIMO radar waveform design problem that optimizes both minimum mean-square error estimation (MMSE) and mutual information (MI), in this correspondence we formulate a new waveform design problem and provide some further results, which complement the previous study. More specifically, we present an iterative optimization algorithm based on the alternating projection method to determine waveform solutions that can simultaneously satisfy a structure constraint and optimize the design criteria. Numerical examples are provided, which illustrate the effectiveness of the proposed approach. In particular, we find that the waveform solutions obtained through our proposed algorithm can achieve very close and virtually indistinguishable performance from that predicted in the previous study. © 2010 IEEE.
Chen Y.,University of Electronic Science and Technology of China | Chen Y.,Huaibei Normal University | Wang B.-Z.,University of Electronic Science and Technology of China
Optics Express | Year: 2013
Polycentric focus effect of time-reversal (TR) electromagnetic field is found in a rectangular resonant cavity. Theoretical deduction shows that the effect is due to the mirror symmetry of the cavity and the maximum number of focus points is 27 including 1 main focus point and 26 secondary focus points. A case of 6 focus points is calculated, in which the numerical results are consistent with the theoretical predictions, and particularly the 5 secondary focus points have directly resulted in inaccurate imaging and pulse signal interception. © Optical Society of America 2013.
Chen Y.,University of Electronic Science and Technology of China | Chen Y.,Huaibei Normal University | Wang B.-Z.,University of Electronic Science and Technology of China
Optics Express | Year: 2013
Current experimental investigations about time reversal (TR) electromagnetic (EM) fields always depended on TR mirror (TRM). However, EM fields can perform reversal operation invariance in four domains connected by Fourier Transform. A multiplication table and an appropriate operating figure about EM fields' invariance are derived to describe a series of dual combined operations in the four domains, in which there are at least 10 dual-combination operations different from current TRM operations which can equivalently actualize TR symmetry. Theoretically, centrosymmetric operations of spatial position vector and spatial spectrum vector may have the potential to promote different reversal mirrors. © 2013 Optical Society of America.
Liu Y.,University of Electronic Science and Technology of China | Mei T.,Microsoft
IEEE Transactions on Multimedia | Year: 2011
Visual search reranking is defined as reordering visual documents (images or video clips) based on the initial search results or some auxiliary knowledge to improve the search precision. Conventional approaches to visual search reranking empirically take the "classification performance" as the optimization objective, in which each visual document is determined relevant or not, followed by a process of increasing the order of relevant documents. In this paper, we first show that the classification performance fails to produce a globally optimal ranked list, and then we formulate reranking as an optimization problem, in which a ranked list is globally optimal only if any arbitrary two documents in the list are correctly ranked in terms of relevance. This is different from existing approaches which simply classify a document as "relevant" or not. To find the optimal ranked list, we convert the individual documents to "document pairs," each represented as a "ordinal relation." Then, we find the optimal document pairs which can maximally preserve the initial rank order while simultaneously keeping the consistency with the auxiliary knowledge mined from query examples and web resources as much as possible. We develop two pairwise reranking methods, difference pairwise reranking (DP-reranking) and exclusion pairwise reranking (EP-reranking), to obtain the relevant relation of each document pair. Finally, a round robin criterion is explored to recover the final ranked list. We conducted comprehensive experiments on an automatic video search task over TRECVID 2005-2007 benchmarks, and showed consistent improvements over text search baseline and other reranking approaches. © 2011 IEEE.
Zhao X.-L.,University of Electronic Science and Technology of China | Wang F.,Lanzhou University | Huang T.-Z.,University of Electronic Science and Technology of China | Ng M.K.,Hong Kong Baptist University | Plemmons R.J.,Wake forest University
IEEE Transactions on Geoscience and Remote Sensing | Year: 2013
The main aim of this paper is to study total variation (TV) regularization in deblurring and sparse unmixing of hyperspectral images. In the model, we also incorporate blurring operators for dealing with blurring effects, particularly blurring operators for hyperspectral imaging whose point spread functions are generally system dependent and formed from axial optical aberrations in the acquisition system. An alternating direction method is developed to solve the resulting optimization problem efficiently. According to the structure of the TV regularization and sparse unmixing in the model, the convergence of the alternating direction method can be guaranteed. Experimental results are reported to demonstrate the effectiveness of the TV and sparsity model and the efficiency of the proposed numerical scheme, and the method is compared to the recent Sparse Unmixing via variable Splitting Augmented Lagrangian and TV method by Iordache © 1980-2012 IEEE.
Yang P.,University of Electronic Science and Technology of China | Di Renzo M.,French National Center for Scientific Research | Xiao Y.,University of Electronic Science and Technology of China | Li S.,University of Electronic Science and Technology of China | Hanzo L.,University of Southampton
IEEE Communications Surveys and Tutorials | Year: 2015
A new class of low-complexity, yet energy-efficient Multiple-Input Multiple-Output (MIMO) transmission techniques, namely, the family of Spatial Modulation (SM) aided MIMOs (SM-MIMO), has emerged. These systems are capable of exploiting the spatial dimensions (i.e., the antenna indices) as an additional dimension invoked for transmitting information, apart from the traditional Amplitude and Phase Modulation (APM). SM is capable of efficiently operating in diverse MIMO configurations in the context of future communication systems. It constitutes a promising transmission candidate for large-scale MIMO design and for the indoor optical wireless communication while relying on a single-Radio Frequency (RF) chain. Moreover, SM may be also viewed as an entirely new hybrid modulation scheme, which is still in its infancy. This paper aims for providing a general survey of the SM design framework as well as of its intrinsic limits. In particular, we focus our attention on the associated transceiver design, on spatial constellation optimization, on link adaptation techniques, on distributed/cooperative protocol design issues, and on their meritorious variants. © 1998-2012 IEEE.
Xiong L.,Yunnan Nationalities University | Tian J.,University of Electronic Science and Technology of China | Liu X.,University of Waterloo
Journal of the Franklin Institute | Year: 2012
This paper addresses the problem of the delay-dependent stability for neutral Markovian jump systems with partial information on transition probability. The time delays discussed in this paper are time-varying delays. Combined the new constructed Lyapunov functional with the introduced free matrices, and using the analysis technique of matrix inequalities, the delay-dependent stability conditions are obtained. The obtained results are formulated in terms of LMIs, which can be easily checked in practice by Matlab LMI control toolbox. Three numerical examples are given to show the validity and potential of the developed criteria. © 2012 The Franklin Institute. All rights reserved.
Tian X.,University of Electronic Science and Technology of China | Tao D.,Nanyang Technological University | Hua X.-S.,Microsoft | Wu X.,University of Electronic Science and Technology of China
IEEE Transactions on Image Processing | Year: 2010
Image search reranking methods usually fail to capture the user's intention when the query term is ambiguous. Therefore, reranking with user interactions, or active reranking, is highly demanded to effectively improve the search performance. The essential problem in active reranking is how to target the user's intention. To complete this goal, this paper presents a structural information based sample selection strategy to reduce the user's labeling efforts. Furthermore, to localize the user's intention in the visual feature space, a novel local-global discriminative dimension reduction algorithm is proposed. In this algorithm, a submanifold is learned by transferring the local geometry and the discriminative information from the labelled images to the whole (global) image database. Experiments on both synthetic datasets and a real Web image search dataset demonstrate the effectiveness of the proposed active reranking scheme, including both the structural information based active sample selection strategy and the local-global discriminative dimension reduction algorithm. © 2010 IEEE.
Vasan A.S.S.,University of Maryland University College | Long B.,University of Electronic Science and Technology of China | Pecht M.,University of Maryland University College | Pecht M.,City University of Hong Kong
IEEE Transactions on Industrial Electronics | Year: 2013
Analog circuits play a vital role in ensuring the availability of industrial systems. Unexpected circuit failures in such systems during field operation can have severe implications. To address this concern, we developed a method for detecting faulty circuit condition, isolating fault locations, and predicting the remaining useful performance of analog circuits. Through the successive refinement of the circuit's response to a sweep signal, features are extracted for fault diagnosis. The fault diagnostics problem is posed and solved as a pattern recognition problem using kernel methods. From the extracted features, a fault indicator (FI) is developed for failure prognosis. Furthermore, an empirical model is developed based on the degradation trend exhibited by the FI. A particle filtering approach is used for model adaptation and RUP estimation. This method is completely automated and has the merit of implementation simplicity. Case studies on two analog filter circuits demonstrating this method are presented. © 1982-2012 IEEE.
Ng M.K.,Hong Kong Baptist University | Yuan X.,Hong Kong Baptist University | Zhang W.,University of Electronic Science and Technology of China
IEEE Transactions on Image Processing | Year: 2013
In this paper, we develop a decomposition model to restore blurred images with missing pixels. Our assumption is that the underlying image is the superposition of cartoon and texture components. We use the total variation norm and its dual norm to regularize the cartoon and texture, respectively. We recommend an efficient numerical algorithm based on the splitting versions of augmented Lagrangian method to solve the problem. Theoretically, the existence of a minimizer to the energy function and the convergence of the algorithm are guaranteed. In contrast to recently developed methods for deblurring images, the proposed algorithm not only gives the restored image, but also gives a decomposition of cartoon and texture parts. These two parts can be further used in segmentation and inpainting problems. Numerical comparisons between this algorithm and some state-of-the-art methods are also reported. © 1992-2012 IEEE.
Li Z.,Cisco Systems | Gong G.,University of Waterloo | Qin Z.,University of Electronic Science and Technology of China
IEEE Transactions on Information Theory | Year: 2013
The simple, computationally efficient HB-like entity authentication protocols based on the learning parity with noise (LPN) problem have attracted a great deal of attention in the past few years due to the broad application prospect in low-cost RFID tags. However, all previous protocols are vulnerable to a man-in-the-middle attack discovered by Ouafi, Overbeck, and Vaudenay. In this paper, we propose a lightweight authentication protocol named LCMQ and prove it secure in a general man-in-the-middle model. The technical core in our proposal is a special type of circulant matrix, for which we prove the linear independence of matrix vectors, present efficient algorithms on matrix operations, and describe a secure encryption against ciphertext-only attack. By combining all of those with LPN and related to the multivariate quadratic problem, the LCMQ protocol not only is provably secure against all probabilistic polynomial-time adversaries, but also transcends HB-like protocols in terms of tag's computation overhead, storage expense, and communication cost. © 1963-2012 IEEE.
Lu Q.,University Pierre and Marie Curie | Lu Q.,University of Electronic Science and Technology of China
Inverse Problems | Year: 2013
This paper is devoted to a study of the boundary and internal state observation problems for stochastic hyperbolic equations. For this, we derive a boundary and an internal observability inequality for stochastic hyperbolic equations with nonsmooth lower order terms. The required inequalities are obtained by the global Carleman estimate for stochastic hyperbolic equations. By these inequalities, we get stability estimates for the state observation problems. As a consequence, we also establish a unique continuation property for stochastic hyperbolic equations. © 2013 IOP Publishing Ltd.
Wang D.,City University of Hong Kong | Miao Q.,University of Electronic Science and Technology of China | Pecht M.,University of Maryland University College
Journal of Power Sources | Year: 2013
Lithium-ion batteries are widely used as power sources in commercial products, such as laptops, electric vehicles (EVs) and unmanned aerial vehicles (UAVs). In order to ensure a continuous power supply, the functionality and reliability of lithium-ion batteries have received considerable attention. In this paper, a battery capacity prognostic method is developed to estimate the remaining useful life of lithium-ion batteries. This capacity prognostic method consists of a relevance vector machine and a conditional three-parameter capacity degradation model. The relevance vector machine is used to derive the relevance vectors that can be used to find the representative training vectors containing the cycles of the relevance vectors and the predictive values at the cycles of the relevance vectors. The conditional three-parameter capacity degradation model is developed to fit the predictive values at the cycles of the relevance vectors. Extrapolation of the conditional three-parameter capacity degradation model to a failure threshold is used to estimate the remaining useful life of lithium-ion batteries. Three instance studies were conducted to validate the developed method. The results show that the developed method is able to predict the future health condition of lithium-ion batteries. © 2013 Elsevier B.V. All rights reserved.
Xiao Y.,University of Electronic Science and Technology of China | Tylecote A.,University of Sheffield | Liu J.,University of Manchester
Research Policy | Year: 2013
How can 'late-comer firms' (LCFs) in developing economies manage their development of technological capability, and within it their IP, strategically, in order to become fully competitive internationally? Under what conditions, external and internal, are they likely to succeed? This paper develops a theoretical framework for understanding LCFs' technology strategy and predicting its outcome, then applies it to the cases of three Chinese firms in sectors at different levels of technology intensity. This yields insights as to its limitations and further development. These help explain mainland China's very limited catch-up in high technology sectors-and to a lesser extent in medium-high technology. We show how our findings can be reconciled with the much greater success of Korean firms some 20 years earlier, if the effect of corporate governance differences is recognised. © 2012 Elsevier B.V.
Sasaki T.,University of Vienna | Uchida S.,RINRI Institute | Chen X.,University of Electronic Science and Technology of China
Scientific Reports | Year: 2015
Punishment is a popular tool when governing commons in situations where free riders would otherwise take over. It is well known that sanctioning systems, such as the police and courts, are costly and thus can suffer from those who free ride on other's efforts to maintain the sanctioning systems (second-order free riders). Previous game-theory studies showed that if populations are very large, pool punishment rarely emerges in public good games, even when participation is optional, because of second-order free riders. Here we show that a matching fund for rewarding cooperation leads to the emergence of pool punishment, despite the presence of second-order free riders. We demonstrate that reward funds can pave the way for a transition from a population of free riders to a population of pool punishers. A key factor in promoting the transition is also to reward those who contribute to pool punishment, yet not abstaining from participation. Reward funds eventually vanish in raising pool punishment, which is sustainable by punishing the second-order free riders. This suggests that considering the interdependence of reward and punishment may help to better understand the origins and transitions of social norms and institutions.
Wang S.,University of Electronic Science and Technology of China | Zhu Q.,University of Electronic Science and Technology of China | Zhu W.,Zhangzhou Normal University | Min F.,Zhangzhou Normal University
Information Sciences | Year: 2013
Coverings are a useful form of data, while covering-based rough sets provide an effective tool for dealing with this data. Covering-based rough sets have been widely used in attribute reduction and rule extraction. However, few quantitative analyses for covering-based rough sets have been conducted, while many advances for classical rough sets have been obtained through quantitative tools. In this paper, the upper approximation number is defined as a measurement to quantify covering-based rough sets, and a pair of upper and lower approximation operators are constructed using the approximation number. The operators not only inherit some important properties of existing approximation operators, but also exhibit some new quantitative characteristics. It is interesting to note that the upper approximation number of a covering approximation space is similar to the dimension of a vector space or the rank of a matrix. © 2012 Elsevier Inc. All rights reserved.
Cermak T.,University of Minnesota | Baltes N.J.,University of Minnesota | Cegan R.,Academy of Sciences of the Czech Republic | Zhang Y.,University of Electronic Science and Technology of China | Voytas D.F.,University of Minnesota
Genome Biology | Year: 2015
Background: The use of homologous recombination to precisely modify plant genomes has been challenging, due to the lack of efficient methods for delivering DNA repair templates to plant cells. Even with the advent of sequence-specific nucleases, which stimulate homologous recombination at predefined genomic sites by creating targeted DNA double-strand breaks, there are only a handful of studies that report precise editing of endogenous genes in crop plants. More efficient methods are needed to modify plant genomes through homologous recombination, ideally without randomly integrating foreign DNA. Results: Here, we use geminivirus replicons to create heritable modifications to the tomato genome at frequencies tenfold higher than traditional methods of DNA delivery (i.e., Agrobacterium). A strong promoter was inserted upstream of a gene controlling anthocyanin biosynthesis, resulting in overexpression and ectopic accumulation of pigments in tomato tissues. More than two-thirds of the insertions were precise, and had no unanticipated sequence modifications. Both TALENs and CRISPR/Cas9 achieved gene targeting at similar efficiencies. Further, the targeted modification was transmitted to progeny in a Mendelian fashion. Even though donor molecules were replicated in the vectors, no evidence was found of persistent extra-chromosomal replicons or off-target integration of T-DNA or replicon sequences. Conclusions: High-frequency, precise modification of the tomato genome was achieved using geminivirus replicons, suggesting that these vectors can overcome the efficiency barrier that has made gene targeting in plants challenging. This work provides a foundation for efficient genome editing of crop genomes without the random integration of foreign DNA. © 2015 Čermák et al.
Ge S.S.,University of Electronic Science and Technology of China | Ge S.S.,Interactive Digital Media Institute | Li Z.,South China University of Technology
IEEE Transactions on Automatic Control | Year: 2014
In this technical note, high dimensional integral Lyapunov functions are introduced for a class of MIMO nonlinear systems with unknown nonlinearities. First, adaptive state feedback control is presented based on the integral Lyapunov function. When only the output is measurable, by using a high-gain observer to estimate the derivative of the system output, adaptive output feedback control is also derived. The proposed control scheme provides a general approach to stabilize the MIMO plant without any restrictive assumptions. The control is continuous and ensures closed-loop stability and convergence of the tracking error to a small residual set. The size of the tracking error at steady state can be specified a priori and guaranteed by choosing the design parameters. © 1963-2012 IEEE.
Guo X.,Seoul National University | Guo X.,University of Electronic Science and Technology of China
Journal of Biophotonics | Year: 2012
Optical Surface plasmon resonance (SPR) biosensors represent the most advanced and developed optical label-free biosensor technology. Optical SPR biosensors are a powerful detection and analysis tool that has vast applications in environmental protection, biotechnology, medical diagnostics, drug screening, food safety and security. This article reviews the recent development of SPR biosensor techniques, including bulk SPR and localized SPR (LSPR) biosensors, for detecting interactions between an analyte of interest in solution and a biomolecular recognition. The concepts of bulk and localized SPs and the working principles of both sensing techniques are introduced. Major sensing advances on biorecognition elements, measurement formats, and sensing platforms are presented. Finally, the discussions on both biosensor techniques as well as comparison of both SPR sensing techniques are made. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Zhu W.,Zhangzhou Normal University | Wang S.,University of Electronic Science and Technology of China
International Journal of Machine Learning and Cybernetics | Year: 2011
Rough set theory is a useful tool for dealing with the vagueness, granularity and uncertainty in information systems. This paper connects generalized rough sets based on relations with matroid theory. We define the upper approximation number to induce a matroid from a relation. Therefore, many matroidal approaches can be used to study generalized rough sets based on relations. Specifically, with the rank function of the matroid induced by a relation, we construct a pair of approximation operators, namely, matroid approximation operators. The matroid approximation operators present some unique properties which do not exist in the existing approximation operators. On the other hand, we present an approach to induce a relation from a matroid. Moreover, the relationship between two inductions is studied. © 2011 Springer-Verlag.
Lv X.-G.,University of Electronic Science and Technology of China | Huang T.-Z.,University of Electronic Science and Technology of China | Xu Z.-B.,Xi'an Jiaotong University | Zhao X.-L.,University of Electronic Science and Technology of China
Information Sciences | Year: 2012
Reflexive boundary conditions (BCs) assume that the array values outside the viewable region are given by a symmetry of the array values inside. The reflection guarantees the continuity of the image. In fact, there are usually two choices for the symmetry: symmetry around the meshpoint and symmetry around the midpoint. The first is called whole-sample symmetry in signal and image processing, the second is half-sample. Many researchers have developed some fast algorithms for the problems of image restoration with the half-sample symmetric BCs over the years. However, little attention has been given to the whole-sample symmetric BCs. In this paper, we consider the use of the whole-sample symmetric boundary conditions in image restoration. The blurring matrices constructed from the point spread functions (PSFs) for the BCs have block Toeplitz-plus-PseudoHankel with Toeplitz-plus-PseudoHankel blocks structures. Recently, regardless of symmetric properties of the PSFs, a technique of Kronecker product approximations was successfully applied to restore images with the zero BCs, half-sample symmetric BCs and anti-reflexive BCs, respectively. All these results extend quite naturally to the whole-sample symmetric BCs, since the resulting matrices have similar structures. It is interesting to note that when the size of the true PSF is small, the computational complexity of the algorithm obtained for the Kronecker product approximation of the resulting matrix in this paper is very small. It is clear that in this case all calculations in the algorithm are implemented only at the upper left corner submatrices of the big matrices. Finally, detailed experimental results reporting the performance of the proposed algorithm are presented. © 2011 Elsevier Inc. All rights reserved.
Ai X.,University of Electronic Science and Technology of China | Chen J.,University of Winnipeg | Zhao H.,University of Electronic Science and Technology of China | Tang X.,University of Electronic Science and Technology of China
International Journal of Production Economics | Year: 2012
We examine decisions of retailers and manufacturers in two competing supply chains selling a substitutable product, with demand uncertainty, when manufacturers offer or do not offer full returns policies. We consider retailers two pricing strategies, optimal pricing and clearance pricing, and we find that full returns policies have different implications in the presence of chain-to-chain competition as compared to the case of a monopoly supply chain. The conditions under which manufacturers and retailers prefer or not prefer full returns policies are identified. © 2010 Elsevier B.V. All rights reserved.
Lv H.,University of Electronic Science and Technology of China | Lu C.,University of Electronic Science and Technology of China | Lu C.,Xi'an Jiaotong University
International Journal of Advanced Manufacturing Technology | Year: 2010
In this paper, a discrete particle swarm optimization (DPSO) algorithm is proposed to solve the assembly sequence planning (ASP) problem. To make the DPSO algorithm effective for solving ASP, some key technologies including a special coding method of the position and velocity of particles and corresponding operators for updating the position and velocity of particles are proposed and defined. The evolution performance of the DPSO algorithm with different setting of control parameters is investigated, and the performance of the proposed DPSO algorithm to solve ASP is verified through a case study. © Springer-Verlag London Limited 2010.
Zhou P.,University of Electronic Science and Technology of China | Wang C.,University of Electronic Science and Technology of China | Ren Y.,Chongqing University | Yang C.,University of Electronic Science and Technology of China | Tian F.,Southwest Jiaotong University
Current Medicinal Chemistry | Year: 2013
The recent focus on protein-protein interaction networks has increasingly been shifted towards the disruption of protein complexes, which either are mediated by the binding of a globular domain in one protein to a short peptide stretch in another, or involve flat, large, and hydrophobic interfaces that classical small-molecule agents are not always ideally suited. Rational design of therapeutic peptides with high affinity targeting such interactions has emerged as a new and promising tool in discovery of potential drug candidates against associated diseases. The design is commonly based on bioinformatics methods or molecular modeling techniques, indirectly exploiting structure-activity relationship at the level of peptide sequence or directly deriving lead entities from protein complex architecture. Here, a newly rising subfield called computational peptidology that focuses on the use of computational and theoretical approaches to treat peptiderelated problems is comprehensively reviewed on the design and discovery of peptide agents targeting protein-protein interactions. We address a systematic discussion on several representative cases in which the computational peptidology is successfully employed to develop peptide therapeutics. Besides, some problems and pitfalls accompanied with the current use of computational methods in peptide modeling and design are also present. © 2013 Bentham Science Publishers.
Li F.,Southwest Jiaotong University | Li Y.,University of Electronic Science and Technology of China
Procedia Engineering | Year: 2011
With the development of electronic commerce, usability on a website is vital to customers and enterprises from ecommerce websites. However, many of these e-commerce applications still do not meet customers' usability requirements and the web pages need a better human computed interface. An evaluation of business to customer (B2C) websites in China was implemented according to the usability criterion. Two questionnaires were designed and verified to capture the evaluation index when customers operated the B2C websites. The fist on was used to choose the appropriate factors in questionnaire scale and the second one was used to evaluated the importance of the chosen factors. Finally, the usability indices were used to evaluate the characteristic of two main China B2C websites. The results obtained would help the designers of B2C electronic commerce to improve their websites. © 2011 Published by Elsevier Ltd.
Zhu W.,Zhangzhou Normal University | Wang S.,University of Electronic Science and Technology of China
Information Sciences | Year: 2013
Rough sets provide an efficient tool for attribute reduction and rule extraction. However, many important problems in rough set theory, including attribute reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. As a generalization of linear independence in vector spaces, matroids have wide applications in diverse fields, particularly in greedy algorithm design. In this paper, we propose an integration of rough sets and matroids to exploit the advantages of both theories. Specifically, we present definitions of lower and upper rough matroids based on relations from the viewpoint of approximation operators. It is interesting that lower rough matroids based on partial orders coincide with poset matroids, which are a well-known generalization of matroids. A matroid is represented by the lower rough matroid based on both a partial order and an equivalence relation. Lower and upper rough matroids based on equivalence relations coincide with each other. Finally, we present some special types of examples of rough matroids from the viewpoints of approximations and graphs. These interesting results demonstrate the potential for the combination between rough sets and matroids. © 2013 Elsevier Inc. All rights reserved.
Christian M.,University of Minnesota | Qi Y.,University of Minnesota | Zhang Y.,University of Electronic Science and Technology of China | Voytas D.F.,University of Electronic Science and Technology of China
G3: Genes, Genomes, Genetics | Year: 2013
Custom TAL effector nucleases (TALENs) are increasingly used as reagents to manipulate genomes in vivo. Here, we used TALENs to modify the genome of the model plant, Arabidopsis thaliana. We engineered seven TALENs targeting five Arabidopsis genes, namely ADH1, TT4, MAPKKK1, DSK2B, and NATA2. In pooled seedlings expressing the TALENs, we observed somatic mutagenesis frequencies ranging from 2-15% at the intended targets for all seven TALENs. Somatic mutagenesis frequencies as high as 41-73% were observed in individual transgenic plant lines expressing the TALENs. Additionally, a TALEN pair targeting a tandemly duplicated gene induced a 4.4-kb deletion in somatic cells. For the most active TALEN pairs, namely those targeting ADH1 and NATA2, we found that TALEN-induced mutations were transmitted to the next generation at frequencies of 1.5-12%. Our work demonstrates that TALENs are useful reagents for achieving targeted mutagenesis in this important plant model. © 2013 Christian et al.
Zhang W.,University of Electronic Science and Technology of China | Poor H.V.,Princeton University
IEEE Transactions on Information Theory | Year: 2011
The problem of detecting a wide-sense stationary Gaussian signal process embedded in white Gaussian noise, in which the power spectral density of the signal process exhibits uncertainty, is investigated. The performance of minimax robust detection is characterized by the exponential decay rate of the miss probability under a Neyman-Pearson criterion with a fixed false alarm probability, as the length of the observation interval grows without bound. A stochastic suppression condition is identified for the uncertainty set of spectral density functions, and it is established that, under the stochastic suppression condition, the resulting minimax problem possesses a saddle point, which is achievable by the likelihood ratio tests matched to a so-called suppressing power spectral density in the uncertainty set. No convexity condition on the uncertainty set is required to establish this result. © 2011 IEEE.
Wang J.,City University of Hong Kong | Qiao C.,State University of New York at Buffalo | Yu H.,University of Electronic Science and Technology of China
Proceedings - IEEE INFOCOM | Year: 2011
A major disruption may affect many network components and significantly lower the capacity of a network measured in terms of the maximum total flow among a set of source-destination pairs. Since only a subset of the failed components may be repaired at a time due to e.g., limited availability of repair resources, the network capacity can only be progressively increased over time by following a recovery process that involves multiple recovery stages. Different recovery processes will restore the failed components in different orders, and accordingly, result in different amount of network capacity increase after each stage. This paper aims to investigate how to optimally recover the network capacity progressively, or in other words, to determine the optimal recovery process, subject to limited available repair resources. We formulate the optimization problem, analyze its computational complexity, devise solution schemes, and conduct numerical experiments to evaluate the algorithms. The concept of progressive network recovery proposed in this paper represents a paradigm-shift in the field of resilient and survivable networking to handle large-scale failures, and will motivate a rich body of research in network design and other applications. © 2011 IEEE.
Lei Y.,Xi'an Jiaotong University | Lin J.,Xi'an Jiaotong University | Zuo M.J.,University of Electronic Science and Technology of China | Zuo M.J.,University of Alberta | He Z.,Xi'an Jiaotong University
Measurement: Journal of the International Measurement Confederation | Year: 2014
Planetary gearboxes significantly differ from fixed-axis gearboxes and exhibit unique behaviors, which invalidate fault diagnosis methods working well for fixed-axis gearboxes. Much work has been done for condition monitoring and fault diagnosis of fixed-axis gearboxes, while studies on planetary gearboxes are not that many. However, we still notice that a number of publications on condition monitoring and fault diagnosis of planetary gearboxes have appeared in academic journals, conference proceedings and technical reports. This paper aims to review and summarize these publications and provide comprehensive references for researchers interested in this topic. The structures of a planetary gearbox as well as a fixed-axis one are briefly introduced and contrasted. The unique behaviors and fault characteristics of planetary gearboxes are identified and analyzed. Investigations on condition monitoring and fault diagnosis of planetary gearboxes are summarized based on the adopted methodologies. Finally, open problems are discussed and potential research topics are pointed out. © 2013 Elsevier Ltd. All rights reserved.
Wang H.,University of Electronic Science and Technology of China | Wang H.,Anshun University | Huang T.-Z.,University of Electronic Science and Technology of China | Xu Z.,Xi'an Jiaotong University | Wang Y.,University of Electronic Science and Technology of China
Information Sciences | Year: 2014
In this paper, we propose an active contour model and its corresponding algorithms with detailed implementation for image segmentation. In the proposed model, the local and global region fitting energies are described by the combination of the local and global Gaussian distributions with different means and variances, respectively. In this combination, we increase a weighting coefficient by which we can adjust the ratio between the local and global region fitting energies. Then we present an algorithm for implementing the proposed model directly. Considering that, in practice, the selection of the weighting coefficient is troublesome, we present a modified algorithm in order to overcome this problem and increase the flexibility. By adaptively updating the weighting coefficient and the time step with the contour evolution, this algorithm is less sensitive to the initialization of the contour and can speed up the convergence rate. Besides, it is robust to the noise and can be used to extract the desired objects. Experiment results demonstrate that the proposed model and its algorithms are effective with application to both the synthetic and real-world images. © 2014 Published by Elsevier Inc.
Liang D.,University of Electronic Science and Technology of China | Liu D.,Southwest Jiaotong University
Information Sciences | Year: 2014
Decision-theoretic rough sets (DTRS) are a representative rough set model. The loss function is a pivotal ingredient of DTRS, which is associated with the decision maker's evaluation. Considering the value of loss function with the imprecise evaluation, interval-valued DTRS (IVDTRS) and its mechanism in this paper are explored. First, we construct a basic model of IVDTRS. The comparison between DTRS and IVDTRS is discussed. In the frame of IVDTRS, we then focus on deriving three-way decisions with the aid of two conventional methods, i.e., a certain ranking method and a degree of possibility ranking method, respectively. The certain ranking method converts an interval value into single and derives decision rules under a certain risk attitude of decision maker; the degree of possibility ranking method assumes the flexibility of interval and utilizes the preference between interval values. All the combinations and their prerequisites are summarized, in which we obtain two types of decision rules. Based on the above analysis, we further propose an optimization method for three-way decisions with IVDTRS, which is designed to minimize the overall uncertainty based on the Shannon entropy. We also compare these methods based on standard data sets. Finally, the criteria for choosing a suitable method to three-way decisions with IVDTRS are generated. These results can support decision making in the uncertain environment. © 2013 Elsevier Inc. All rights reserved.
Scheele D.,University of Bonn | Kendrick K.M.,University of Electronic Science and Technology of China | Khouri C.,University of Bonn | | 2017-05-25 22:21:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24645905196666718, "perplexity": 1833.2139264727211}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608617.6/warc/CC-MAIN-20170525214603-20170525234603-00330.warc.gz"} |
https://www.esaral.com/q/let-a-and-b-be-sets-show-that-f-26915 | # Let A and B be sets. Show that f:
Question:
Let A and B be sets. Show that fA × B → × A such that (ab) = (ba) is bijective function.
Solution:
$f: A \times B \rightarrow B \times A$ is defined as $f(a, b)=(b, a)$.
Let $\left(a_{1}, b_{1}\right),\left(a_{2}, b_{2}\right) \in \mathrm{A} \times \mathrm{B}$ such that $f\left(a_{1}, b_{1}\right)=f\left(a_{2}, b_{2}\right)$.
$\Rightarrow\left(b_{1}, a_{1}\right)=\left(b_{2}, a_{2}\right)$
$\Rightarrow b_{1}=b_{2}$ and $a_{1}=a_{2}$
$\Rightarrow\left(a_{1}, b_{1}\right)=\left(a_{2}, b_{2}\right)$
∴ f is one-one.
Now, let $(b, a) \in B \times A$ be any element.
Then, there exists $(a, b) \in A \times B$ such that $f(a, b)=(b, a)$. [By definition of $f$ ]
∴ f is onto.
Hence, f is bijective. | 2023-03-26 09:22:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9960229396820068, "perplexity": 227.42434613648558}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945440.67/warc/CC-MAIN-20230326075911-20230326105911-00706.warc.gz"} |
https://discuss.codechef.com/t/kol1503-editorial/12026 | # KOL1503 - Editorial
Author: Devendra Agarwal
Tester: Kevin Atienza
Editorialist: Kevin Atienza
### PREREQUISITES:
Lowest common ancestors, balanced parentheses
### PROBLEM:
Given a tree with N nodes, each node containing a parenthesis—) or (—, answer Q queries of the following kind:
• Given two nodes u and v, consider the string obtained by taking all parenthesis characters from every node in the path from u to v. Output Yes if this string is a balanced string of parentheses, otherwise print No.
### QUICK EXPLANATION:
Root the tree. A path from a to b consists of two parts: A path from nodes a to b consists of two parts: the path from a to \text{LCA}(a,b) and from \text{LCA}(a,b) to b. Take care that the node \text{LCA}(a,b) is counted only once. By convention, let’s say this node belongs at the first part of the path.
The string in the path from a to b is a valid parenthesization iff the following hold:
• The path from a to \text{LCA}(a,b) is a prefix of a valid parenthesization.
• The path from \text{LCA}(a,b) to b is a suffix of a valid parenthesization.
• The number of unmatched open parentheses from a to \text{LCA}(a,b) is equal to the number of unmatched closed parentheses from \text{LCA}(a,b) to b.
To check these conditions, we must be able to perform the following operations:
• Given some path from some node to one of its ancestors, it is a prefix of a valid parenthesization?
• Given some path from some node to one of its ancestors, it is a suffix of a valid parenthesization?
• Given some node x and one of its ancestors y, where the path from x and y is a prefix of a valid parenthesization, how many unmatched open parentheses are there?
• Given some node x and one of its ancestors y, where the path from y and x is a suffix of a valid parenthesization, how many unmatched closed parentheses are there?
The latter two can be done by precomputing f(x) for each node x, where f(x) is the number of open parentheses minus the number of closed parentheses from x to the root. It can be computed using the recurrence:
f(x) = \begin{cases} f(\text{parent}(x)) + 1 & \text{If the parenthesis at node $x$ is open} \\\ f(\text{parent}(x)) - 1 & \text{If the parenthesis at node $x$ is closed} \end{cases}
The former two can be done by precomputing \text{pre}(x) and \text{suf}(x) for each node x, which are defined as the lengths of the longest path from x to the root that is a valid parenthesization prefix and suffix, respectively.
### EXPLANATION:
As with many problems involving an undirected tree, the natural first step is to root it. This usually helps. So let’s say the tree is rooted at node 1.
A path from nodes a to b consists of two parts: the path from a to \text{LCA}(a,b) and from \text{LCA}(a,b) to b (where \text{LCA}(a,b) is the lowest common ancestor of a and b). But since the parentheses are on the nodes, not edges, so we need to ensure we count \text{LCA}(a,b) only once. By convention, let’s say this node belongs at the first part of the path, i.e. from the path from a to \text{LCA}(a,b), and when we say the "path from \text{LCA}(a,b) to b", the node \text{LCA}(a,b) isn’t actually included.
Obviously, the string of parentheses in the path from a to \text{LCA}(a,b) must be a valid prefix of some valid parenthesization. Similarly the string from \text{LCA}(a,b) to b must be valid suffix. These are necessary conditions. However, they’re not sufficient. For example, (((( is a valid prefix and )) is a valid suffix but combining them, (((()), doesn’t yield a valid parenthesization. Obviously, we’re missing a condition: the number of unmatched parentheses in both strings must be equal. It’s easy to see that these are sufficient conditions, i.e. the path from a to b contains a valid parenthesization iff the following conditions hold:
• The path from a to \text{LCA}(a,b) is a prefix of a valid parenthesization.
• The path from \text{LCA}(a,b) to b is a suffix of a valid parenthesization.
• The number of unmatched open parentheses from a to \text{LCA}(a,b) is equal to the number of unmatched closed parentheses from \text{LCA}(a,b) to b.
(Remember the convention that \text{LCA}(a,b) only belongs to the path from a to \text{LCA}(a,b).)
So we want perform the following operations quickly:
• Given some path from some node to one of its ancestors, it is a prefix of a valid parenthesization?
• Given some path from some node to one of its ancestors, it is a suffix of a valid parenthesization?
• Given some node x and one of its ancestors y, where the path from x and y is a prefix of a valid parenthesization, how many unmatched open parentheses are there?
• Given some node x and one of its ancestors y, where the path from y and x is a suffix of a valid parenthesization, how many unmatched closed parentheses are there?
But the latter two can be computed with the following: Let f(x) be the number of open parentheses minus the number of closed parentheses from x to the root (node 1). Then:
• The number of unmatched parentheses from x to y is just |f(x) - f(\text{parent}(y))|. (If y = 1, then we say f(\text{parent}(y)) = 0 by convention.)
• Also, these unmatched parentheses are open parentheses if f(x) > f(\text{parent}(y)), otherwise they’re closed parentheses.
Thus, having the f(x) values allows us to perform the operations above. Additionally, the $f(x)$s can be precomputed in linear time with a single traversal of the tree, using the following:
• If the parenthesis at node x is (, then f(x) = f(\text{parent}(x)) + 1. Otherwise, f(x) = f(\text{parent}(x)) - 1.
The precomputation runs in linear time. What remains is to efficiently answer the following queries:
• Given some path from some node to one of its ancestors, it is a prefix of a valid parenthesization?
• Given some path from some node to one of its ancestors, it is a suffix of a valid parenthesization?
These two operations are very similar, so we will just describe one of them, say the first one. To perform this query, we use the following characterization of a valid parenthesization prefix:
A string is a prefix of a valid parenthesization if every prefix of it contains at least as many open parentheses as there are closed parentheses.
In terms of our tree, this is equivalent to saying that:
If y is an ancestor of x, then the path from x to y forms a prefix of a valid parenthesization if and only if f(x) \ge f(\text{parent}(z)) for every node z in the path.
That this is true can be seen from the meaning of the inequality f(x) \ge f(\text{parent}(z)). Note that f(x) - f(\text{parent}(z)) is the number of unmatched open parentheses from x to z, so if this is \ge 0, for every node z in the path, then the condition for being a valid parenthesization prefix is satisfied.
For every node x, we define \text{pre}(x) as the length of the longest path from x to the root that is a valid parenthesization prefix (in terms of the number of nodes). Using the property above, the path from x to its ancestor y is a valid parenthesization prefix if and only if \text{depth}(x) - \text{depth}(y) < \text{pre}(x). So we can answer the queries if we have \text{depth}(x) and \text{pre}(x) for all nodes x. Precomputing the depths of nodes can be done with a single traversal, so what remains is to compute \text{pre}(x) for all nodes x.
We will also compute the $\text{pre}(x)$s with a single traversal. Let z be the $\text{pre}(x)$th ancestor of x. If z is not the root, then let y = \text{parent}(z). Then y is the first node such that f(x) < f(y). Since the f s only differ by one between adjacent nodes, this means that f(z) must be equal to f(x), and f(y) must be equal to f(x) + 1. So \text{pre}(x) is just the distance of x to its nearest ancestor y whose f(y) is f(x) + 1. (And if no such y s exist, then \text{pre}(x) is just \text{depth}(x)+1.) Obviously, if the parenthesis at x is ), then \text{pre}(x) is automatically 0.
Thus, as we traverse the tree, we must be able to answer the following query quickly:
• Given v, find the nearest ancestor y of the current node such that f(y) = v.
This can be done by maintaining a map of lists, which lists for each v the nodes y along the path to the root whose f(y) = v. The following pseudocode illustrates it better:
// arrays are initialized to zero
f = array[0...N]
parent = array[1...N]
depth = array[0...N]
pre = array[1...N]
m = {}
def PUSH(x,d):
if d is not a key of m:
m[d] = new empty list()
add x at the end of m[d]
def GET(d):
if d is not a key of m:
return 0
else:
return the last element of m[d]
def POP(x,d):
remove x from the end of m[d]
if m[d] is empty:
delete the key d from m
def traverse(x):
// compute f[x]
if parenthesis(x) == '(':
f[x] = f[parent[x]] + 1
else:
f[x] = f[parent[x]] - 1
// compute depth[x]
depth[x] = depth[parent[x]] + 1
// compute pre[x]
if parenthesis(x) == ')':
pre[x] = 0
else:
y = GET(f[x] + 1)
pre[x] = depth[x] - depth[y]
PUSH(x, f[x])
if j != parent[x]:
parent[j] = x
traverse(j)
// remove x
POP(x, f[x])
// initial call is traverse(1)
A similar algorithm can be done to compute \text{suf}(x) for all nodes x, which is defined as the length of the longest path from x to the root that is a valid parenthesization suffix. Using \text{pre}(x) and \text{suf}(x), one can now answer the queries above in O(1) time!
By precomputing f(x), \text{pre}(x) and \text{suf}(x) for all nodes x, each query can be answered in O(\log N) time (because we’re taking the LCA of the two nodes.)
Note: If you find the number of unmatched parentheses in this document a bit disturbing, here’s something that can make it worse.
O((N + Q)\log N)
1 Like | 2021-02-27 21:33:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8046441078186035, "perplexity": 819.1812286544127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359497.20/warc/CC-MAIN-20210227204637-20210227234637-00071.warc.gz"} |
https://math.stackexchange.com/questions/3644856/prop-g-subseteq-x-is-open-in-x-implies-clg-bigcap-cla-clg-bigca | # Prop: $G \subseteq X$ is open in $X$ $\implies$ $cl(G\bigcap cl(A)) = cl(G\bigcap A)$ for every $A \subseteq X$.
Denote the closure operator of a topological space by $$cl$$.
Prop: $$G \subseteq X$$ is open in $$X$$ $$\implies$$ $$cl(G\bigcap cl(A)) = cl(G\bigcap A)$$ for every $$A \subseteq X$$.
Pf: Assume that $$G$$ is open in $$X$$ and $$A \subseteq X$$. It is trivial that $$G \bigcap A \subseteq G \bigcap cl(A) \implies cl(G\bigcap A)\subseteq cl(G\bigcap cl(A))$$. Further assume that $$x \in cl(G\bigcap cl(A))$$. Then for every $$x \in U \subseteq X$$, $$U\bigcap (G\bigcap cl(A))\neq \emptyset$$. Using the fact that $$G$$ is open, there exists $$y \in U$$ such that for $$y \in V \subseteq X$$, $$V \subseteq G$$. Since $$(V\bigcap G)\bigcap cl(A) \neq \emptyset \implies V \bigcap cl(A)\neq \emptyset \implies V \bigcap A \neq \emptyset$$, $$U \bigcap (G\bigcap A)\neq \emptyset$$ and $$x \in cl(G \bigcap A)$$ as required.
Does my proof look correct?
Prove the following highly useful lemma:
open U implies U $$\cap$$ cl K subset cl (U $$\cap$$ K).
Thus cl (U $$\cap$$ cl K ) subset
cl cl (U $$\cap$$ cl K) = cl (U $$\cap$$ K)
subset cl (U $$\cap$$ K).
Your proof fails because U and V are just any sets. | 2022-07-03 19:11:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 26, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9456225037574768, "perplexity": 96.03184369312481}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104248623.69/warc/CC-MAIN-20220703164826-20220703194826-00667.warc.gz"} |
https://www.physicsforums.com/threads/orthogonality-of-legendre-polynomials-from-jackson.536595/ | # Orthogonality of Legendre Polynomials from Jackson
1. Oct 4, 2011
### Demon117
Hello all!
I am trying to work through and understand the derivation of the Legendre Polynomials from Jackson's Classical electrodynamics. I have reached a part that I cannot get through however. Jackson starts with the following orthogonality statement and jumps (as it seems) in his proof:
Equation 3.17 states:
$\int P_{l'}[\frac{d}{dx} ([1-x^{2}]\frac{dP_{l}}{dx})+l(l+1)P_{l}(x)]dx=0$
He mentions integration by parts on the "first term" but I don't see how he gets to
Equation 3.18:
$\int [(x^{2}-1)\frac{dP_{l}}{dx} \frac{dP_{l'}}{dx} +l(l+1)(P_{l'}(x)P_{l}(x))]dx=0$
I don't see this. Could someone please explain or give a hint to the intermediate step here? I'm afraid I just do not see it. Thanks.
2. Oct 4, 2011
### Born2bwire
You understand integration by parts, yes? To wit,
$$\int udv = uv-\int vdu$$
So by the chain rule we can also say
$$\int u \frac{dv}{dx}dx = uv-\int v \frac{du}{dx}dx$$
So it is easy to see that $u=P_{\ell'}$ and $v=\left[ \left(1-x^2\right)\frac{dP_\ell}{dx}\right]$. In this manner we arrive at
$$\int_{-1}^1 P_{\ell'} \frac{d}{dx} \left[ \left(1-x^2\right)\frac{dP_\ell}{dx}\right] dx = \left. P_{\ell'} \left[ \left(1-x^2\right)\frac{dP_\ell}{dx}\right] \right|^{x=1}_{x=-1} - \int_{-1}^1 \left[ \left(1-x^2\right)\frac{dP_\ell}{dx}\right] \frac{d P_{\ell'}}{dx} dx$$
The first term works out to be zero obviously and thus we say that,
$$\int_{-1}^1 P_{\ell'} \frac{d}{dx} \left[ \left(1-x^2\right)\frac{dP_\ell}{dx}\right] dx = \int_{-1}^1 \left[ \left(x^2-1\right)\frac{dP_\ell}{dx}\right] \frac{d P_{\ell'}}{dx} dx$$
3. Oct 4, 2011
### Demon117
Of course I understand Integration by parts, and in fact I just barely started it myself so this whole conversation is null. Thank you for your time, but I just had an aha! moment :) Sorry about that. | 2018-09-20 12:20:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8902726173400879, "perplexity": 462.8247060051381}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156471.4/warc/CC-MAIN-20180920120835-20180920141235-00069.warc.gz"} |
https://www.techwhiff.com/learn/what-is-capstone-this-course-is-almost-at-the-end/52502 | # What is Capstone? This course is almost at the end of my program
###### Question:
What is Capstone? This course is almost at the end of my program
#### Similar Solved Questions
##### What is an example of bias in a study
What is an example of bias in a study...
##### Problem 18 The operations of the Great Rae Café, a small food service operation, are becoming...
Problem 18 The operations of the Great Rae Café, a small food service operation, are becoming more complex. Natalie Rae, the owner, has asked for your help in understanding the condensed balance sheets and the additional information provided. The Great Rae Café Condensed Balance Sheets...
##### How do human body cells work?
How do human body cells work?...
##### The standard enthalpy of formation, ΔHf0, for N2O4 is the enthalpy change for which reaction? a....
The standard enthalpy of formation, ΔHf0, for N2O4 is the enthalpy change for which reaction? a. 2NO(g) + O2(g) → N2O4(g) b. 2NO2(g) → N2O4(g) c. 2N(g) + 4O(g) → N2O4(g) d. N2(g) + 2O2(g) → N2O4(g) e. N2O(g) + O3(g) → N2O4(g)...
##### E4-12 Assigning Costs Using Traditional System, ABC System [LO 4-1, 4-3, 4-4, 4-5, 4-6] Bunker makes...
E4-12 Assigning Costs Using Traditional System, ABC System [LO 4-1, 4-3, 4-4, 4-5, 4-6] Bunker makes two types of briefcase, fabric and leather. The company is currently using a traditional costing system with labor hours he cost driver but is considering switching to an activity-based costing syste...
##### 18. Junky's Fast Food has restaurants in Atlanta, Boston, and Chicago. They conducted a survey by...
18. Junky's Fast Food has restaurants in Atlanta, Boston, and Chicago. They conducted a survey by taking a random sample in each city. Combining the data, they found that the average amount spent by all sampled customers was \$8.52. What type of study is this? O an observational study based on a ...
##### Question 12 --/1 View Policies Current Attempt in Progress Sheridan Company, organized in 2019, has set...
Question 12 --/1 View Policies Current Attempt in Progress Sheridan Company, organized in 2019, has set up a single account for all intangible assets. The following summary discloses the debit entries that have been recorded during 2020. 1/2/20 Purchased patent (8-year life) 4/1/20 Purchase goodwill...
##### The ballot question 1 debated in Massachusetts in 2018 is the proposed law, which would limit...
The ballot question 1 debated in Massachusetts in 2018 is the proposed law, which would limit the number of patients assigned to nurses. What're the associated costs with the implementation of this law? *Please answer in DETAIL*...
##### Need 5-9 and number 11 all answered. Thx 5. How can two individuals with brown eyes(B)...
Need 5-9 and number 11 all answered. Thx 5. How can two individuals with brown eyes(B) have a blue (b) eyed baby? Show the genotypes of the parents and Punnett square to prove your answer. What are the chances of a blue-eyed baby? 6. A homozygous tongue roller (T) is married to a non-tongue roller(t...
##### Find the equation of a line that goes through point (100,-25) and is parallel to y=-25?
Find the equation of a line that goes through point (100,-25) and is parallel to y=-25?...
Be sure to show all your calculations and circle the appropriate letter as needed. You are only required to answer 12 of the following 19 questions. You must answer question 2, 5, 6, 7, and #15, the other 2 are your choice. If you complete more than 12 questions, cross out those you Do Not want ... | 2022-11-30 20:44:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25912895798683167, "perplexity": 4748.547663960745}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710771.39/warc/CC-MAIN-20221130192708-20221130222708-00675.warc.gz"} |
https://www.bloombergprep.com/gmat/practice-question/1/306/quantitative-section-test-taking-strategies-data-sufficiency-plugging-in-basic-technique/ | We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.
## Up to 90+ points GMAT score improvement guarantee
### The best guarantee you’ll find
Our Premium and Ultimate plans guarantee up to 90+ points score increase or your money back.
## Master each section of the test
### Comprehensive GMAT prep
We cover every section of the GMAT with in-depth lessons, 5000+ practice questions and realistic practice tests.
## Schedule-free studying
### Learn on the go
Study whenever and wherever you want with our iOS and Android mobile apps.
# Plugging In: Basic Technique
A flock of $$z$$ birds lands on a fig tree. One-fourth of the birds fly away while 5 more birds land on the same tree. In terms of $$z$$, how many birds are now on the tree?
Correct. [[snippet]] When $$z=4$$, this answer choice yields >$$\displaystyle \frac{3z+20}{4} = \frac{3(4)+20}{ 4} = \frac{32}{ 4} = \color{blue}{8}$$, so it matches your *goal*. All other answer choices are eliminated by this Plug-In, so this is the right answer choice. >A) $$\frac{z}{4} + 5 = \frac{4}{4} + 5 =\color{red}{6}$$, which is not equal to your goal of 8. __POE__. >C) $$3z+2 = 3(4)+2 = \color{red}{14}$$, which does not equal to 8. __POE__. >D) $$3z+6$$. This choice is even greater than C. __POE__. >E) $$z+3 = 4+3=\color{red}{7}$$, which is not equal to 8. __POE__.
Incorrect. Notice that $$\frac{1}{4}$$ of the birds fly *away*, while the question asks for how many birds *remain* on the tree. This is exactly the type of careless mistakes that __Plugging In__ helps you avoid. __Plugging In__ good numbers forces you to work out the problem step by step instead of jumping to conclusions based on what you *think* you've read.
Incorrect. [[snippet]]
Incorrect. [[snippet]]
Incorrect. [[snippet]] Did you try to __Plug In__ $$z=8$$ and get more than one answer choice? In that case, __POE__, then change numbers and __Plug In__ again for the remaining answers only.
$$\frac{z}{4} + 5$$
$$\frac{3z+20}{4}$$
$$3z+2$$
$$3z+6$$
$$z+3$$ | 2020-10-28 20:02:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5739322900772095, "perplexity": 3155.0709200252504}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107900860.51/warc/CC-MAIN-20201028191655-20201028221655-00096.warc.gz"} |
https://simple.m.wikipedia.org/wiki/Catenary | # Catenary
plane curve
Plots of ${\displaystyle y=a\cosh \left({\frac {x}{a}}\right)}$ with ${\displaystyle a=0.5,1,2}$. The variable ${\displaystyle x}$ is on the horizontal axis and ${\displaystyle y}$ is on the vertical axis.
A chain hanging like this forms the shape of a catenary approximately
A catenary is a type of curve. An ideal chain hanging between two supports and acted on by a uniform gravitational force makes the shape of a catenary.[1] (An ideal chain is one that can bend perfectly, cannot be stretched and has the same density throughout.[2]) The supports can be at different heights and the shape will still be a catenary.[3] A catenary looks a bit like a parabola, but they are different.[4]
The equation for a catenary in Cartesian coordinates is[2][5]
${\displaystyle y=a\cosh \left({\frac {x}{a}}\right)}$
where ${\displaystyle a}$ is a parameter that determines the shape of the catenary[5] and cosh is the hyperbolic cosine function, which is defined as[6]
${\displaystyle \cosh x={\frac {e^{x}+e^{-x}}{2}}}$.
Hence, we can also write the catenary equation as
${\displaystyle y={\frac {a\left(e^{\frac {x}{a}}+e^{-{\frac {x}{a}}}\right)}{2}}}$.
The word "catenary" comes from the Latin word catena, which means "chain".[6] A catenary is also called called an alysoid and a chainette.[1]
## References
1. "Catenary". Wolfram Research. Retrieved 2016-10-30.
2. "The Catenary - The "Chain" Curve". California State University. Retrieved 2019-01-01.
3. Rosbjerg, Bo. "Catenary" (PDF). Aalborg University. Retrieved 2016-10-30.
4. "Catenary and Parabola Comparison". Drexel University. Retrieved 2016-11-05.
5. "Equation of Catenary". Math24.net. Retrieved 2016-10-30.
6. Stroud, K. A.; Booth, Dexter J. (2013). Engineering Mathematics (7th ed.). Palgrave Macmillan. p. 438. ISBN 978-1-137-03120-4. | 2020-08-11 05:23:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 8, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9601808190345764, "perplexity": 2752.7820863480556}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738727.76/warc/CC-MAIN-20200811025355-20200811055355-00489.warc.gz"} |
http://basilisk.fr/src/navier-stokes/swirl.h | # Azimuthal velocity for axisymmetric flows
The centered Navier–Stokes solver can be combined with the axisymmetric metric but assumes zero azimuthal velocity (“swirl”). This file adds this azimuthal velocity component: the $w$ field.
Assuming that $x$ is the axial direction and $y$ the radial direction, as in axi.h, the incompressible, variable-density and viscosity, axisymmetric Navier–Stokes equations (with swirl) can be written ${\partial }_{x}{u}_{x}+{\partial }_{y}{u}_{y}+\frac{{u}_{y}}{y}=0$ ${\partial }_{t}{u}_{x}+{u}_{x}{\partial }_{x}{u}_{x}+{u}_{y}{\partial }_{y}{u}_{x}=-\frac{1}{\rho }{\partial }_{x}p+\frac{1}{\rho y}\nabla \cdot \left(\mu y\nabla {u}_{x}\right)$ ${\partial }_{t}{u}_{y}+{u}_{x}{\partial }_{x}{u}_{y}+{u}_{y}{\partial }_{y}{u}_{y}-\frac{{w}^{2}}{y}=-\frac{1}{\rho }{\partial }_{y}p+\frac{1}{\rho y}\left(\nabla \cdot \left(\mu y\nabla {u}_{y}\right)-2\mu \frac{{u}_{y}}{y}\right)$ ${\partial }_{t}w+{u}_{x}{\partial }_{x}w+{u}_{y}{\partial }_{y}w+\frac{{u}_{y}w}{y}=\frac{1}{\rho y}\left[\nabla \cdot \left(\mu y\nabla w\right)-w\left(\frac{\mu }{y}+{\partial }_{y}\mu \right)\right]$ We will thus need to solve and advection-diffusion equation for $w$.
``````#include "tracer.h"
#include "diffusion.h"
scalar w[], * tracers = {w};``````
The azimuthal velocity is zero on the axis of symmetry ($y=0$).
``w[bottom] = dirichlet(0);``
We will need to add the acceleration term ${w}^{2}/y$ in the evolution equation for ${u}_{y}$. If the acceleration field is not allocated yet, we do so.
``````event defaults (i = 0)
{
if (is_constant(a.x)) {
a = new face vector;
foreach_face()
a.x[] = 0.;
boundary ((scalar *){a});
}
}``````
The equation for ${u}_{y}$ is solved by the centered Navier–Stokes solver combined with the axisymmetric metric, but the acceleration term ${w}^{2}/y$ is missing. We add it here, taking care of the division by zero on the axis, and averaging $w$ from cell center to cell face.
``````event acceleration (i++)
{
face vector av = a;
foreach_face (y)
av.y[] += y > 0. ? sq(w[] + w[0,-1])/(4.*y) : 0.;
}``````
The advection of $w$ is done by the tracer solver, but we need to add diffusion. Using the diffusion solver, we solve $\theta {\partial }_{t}w=\nabla \cdot \left(D\nabla w\right)+\beta w$ Identifying with the diffusion part of the equation for $w$ above, we have $\begin{array}{ccc}\hfill \theta & \hfill =\hfill & \rho y\hfill \\ \hfill D& \hfill =\hfill & \mu y\hfill \\ \hfill \beta & \hfill =\hfill & -\left(\rho {u}_{y}+\frac{\mu }{y}+{\partial }_{y}\mu \right)\hfill \end{array}$ Note that the rho and mu fields (defined by the Navier–Stokes solver) already include the metric (i.e. are $\rho y$ and $\mu y$), which explains the divisions by $y$ in the code below.
``````event tracer_diffusion (i++)
{
scalar β[], θ[];
foreach() {
θ[] = ρ[];
double muc = (μ.x[] + μ.x[1] + μ.y[] + μ.y[0,1])/4.;
double dymu = (μ.y[0,1]/fm.y[0,1] - μ.y[]/fm.y[])/Δ;
β[] = - (ρ[]*u.y[] + muc/y)/y - dymu;
}
diffusion (w, dt, μ, θ = θ, β = β);
}`````` | 2019-01-16 22:01:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 21, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8532281517982483, "perplexity": 2532.4455800668425}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583657907.79/warc/CC-MAIN-20190116215800-20190117001800-00532.warc.gz"} |
https://east-centricarch.eu/en/what-is-58ths-of-48-i-need-help-i-really-dont-get-it.30860.html | Yolande952
11
# What is 5/8ths of 48 , I need help I really don't get it
$\frac58\ \cdot\ 48=\\=\frac58\ \cdot\ \frac{48}{1}=\\=\frac51\ \cdot\ \frac61=\\=5\ \cdot\ 6=\\=30$ | 2022-01-28 11:46:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7451662421226501, "perplexity": 1350.7581482247429}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305494.6/warc/CC-MAIN-20220128104113-20220128134113-00000.warc.gz"} |
http://preprints.acmac.uoc.gr/274/ | # Fourier integrals and a new representation of Maslov's canonical operator near caustics
Makrakis, George and Dobrokhotov, Sergey and Nazaikinskii, Vladimir (2013) Fourier integrals and a new representation of Maslov's canonical operator near caustics. "Spectral Theory and Differential Equations: V.A. Marchenko 90th Anniversary Collection" of the AMS book series "American Mathematical Society Translations-Series 2, Advances in the Mathematical Sciences. (In Press) | 2017-09-23 12:37:40 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.964948296546936, "perplexity": 7239.963537742968}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818689661.35/warc/CC-MAIN-20170923123156-20170923143156-00056.warc.gz"} |
https://www.zigya.com/study/book?class=11&board=bsem&subject=Physics&book=Physics+Part+I&chapter=Motion+in+A+Plane&q_type=&q_topic=Projectile+Motion&q_category=&question_id=PHEN11039754 | ## Book Store
Currently only available for.
CBSE Gujarat Board Haryana Board
## Previous Year Papers
Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12
A balloon is ascending at the rate of 20 m/sec. When it is at a height 100 m from ground, a packet is dropped from the balloon.
What will be the velocity of the packet w.r.t.
(i) ground
(ii) balloon, when it was just dropped?
Speed at which the balloon is ascending, v = 20 m/s
Height of balloon from the ground = 100 m
With respect to ground, the velocity of the packet will be 20 m/sec upward.
With respect to balloon, its velocity will be zero.
124 Views
Give three examples of vector quantities.
Force, impulse and momentum.
865 Views
What is a vector quantity?
A physical quantity that requires direction along with magnitude, for its complete specification is called a vector quantity.
835 Views
What is a scalar quantity?
A physical quantity that requires only magnitude for its complete specification is called a scalar quantity.
1212 Views
Give three examples of scalar quantities.
Mass, temperature and energy
769 Views
What are the basic characteristics that a quantity must possess so that it may be a vector quantity?
A quantity must possess the direction and must follow the vector axioms. Any quantity that follows the vector axioms are classified as vectors.
814 Views | 2018-10-18 13:20:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5819501876831055, "perplexity": 3104.1587954473202}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511872.19/warc/CC-MAIN-20181018130914-20181018152414-00190.warc.gz"} |
https://chem.libretexts.org/Bookshelves/Organic_Chemistry/Book%3A_Basic_Principles_of_Organic_Chemistry_(Roberts_and_Caserio)/09%3A_Separation_Purification__Identification_of_Organic_Compounds/9.0E%3A_9.E%3A_Separation%2C_Purification%2C__Identification_of_Organic_Compounds_(Exercises) | # 9.E: Separation, Purification, & Identification of Organic Compounds (Exercises)
Exercise 9-1 Suppose you are standing on the end of a pier watching the waves and, between your position and a buoy $$200 \: \text{m}$$ straight out, you count 15 wave crests. Further, suppose a wave crest comes by every 15 seconds. Calculate $$\nu$$ in $$\text{Hz}$$, $$\lambda$$ in $$\text{m}$$, $$c$$ in $$\text{m sec}^{-1}$$, and $$\bar{\nu}$$ in $$\text{km}^{-1}$$.
Exercise 9-2 Blue light has $$\bar{\nu} = 20,800 \: \text{cm}^{-1}$$. Calculate $$\nu$$ in $$\text{Hz}$$ and $$\lambda$$ in $$\text{nm}$$.
Exercise 9-3 Calculate the energy in $$\text{kcal mol}^{-1}$$ that corresponds to the absorption of 1 einstein of light of $$589.3 \: \text{nm}$$ (sodium $$D$$ line) by sodium vapor. Explain how this absorption of light by sodium vapor may have chemical utility.
Exercise 9-4
a. Use Equations 9-1 and 9-2 to calculate the wavelength in $$\text{nm}$$ and energy in $$\text{kcal}$$ of an einstein of radiation of radio-frequency energy in the broadcast band having $$\nu = 1 \: \text{MHz}$$ (1 megahertz) $$= 10^6 \: \text{sec}^{-1}$$ and knowing that the velocity of light is approximately $$3 \times 10^8 \: \text{m sec}^{-1}$$.
b. In photoelectron spectroscopy, x-rays with energies of approximately $$1250 \: \text{eV}$$ are used ($$1 \: \text{eV}$$ (electron volt) $$\text{mol}^{-1} = 23.05 \: \text{kcal}$$). What would $$\lambda$$ (in $$\text{nm}$$) be for such x-rays?
Exercise 9-5 The microwave spectrum of pure trans-2-butenoic acid $$\left( \ce{CH_3CH=CHCO_2H} \right)$$ shows patterns exactly like those of Figure 9-8, which indicate the presence of two different conformations. What are these conformations, and why are there only two of them? (You may be helped by reviewing Section 6-5.)
Exercise 9-6 Use Equation 9-3 and any other pertinent data to predict which compound in each group would absorb in the infrared at the highest frequency for the changes in the stretching vibration of the specified bond. Give your reasoning.
a. $$\ce{R-Cl}$$, $$\ce{R-Br}$$, $$\ce{R-F}$$ (carbon-halogen)
b. $$\ce{CH_3-NH_2}$$, $$\ce{CH_2=NH}$$, $$\ce{HC \equiv N}$$ (carbon-nitrogen)
Exercise 9-7 Which compound in each group would have the most intense infrared absorption band corresponding to stretching vibrations of the bonds indicated? Give your reasoning.
a. $$\ce{(CH_3)_2C=O}$$, $$\ce{(CH_3)_2C=CH_2}$$ (multiple bond)
b. $$\ce{CH_3-CH_3}$$, $$\ce{CH_3-O-CH_3}$$ ($$\ce{C-C}$$ vs. $$\ce{C-O}$$)
c. $$\ce{CH_3C \equiv CH}$$, $$\ce{CH_3C \equiv CCH_3}$$ (multiple bond)
d. $$\ce{H-Cl}$$, $$\ce{Cl-Cl}$$
Exercise 9-8* How many vibrational modes are possible for (a) $$\ce{CS_2}$$ (linear), (b) $$\ce{BeCl_2}$$ (linear), and (c) $$\ce{SO_2}$$ (angular)? Show your reasoning.
Exercise 9-9* Suppose an infrared absorption occurs at $$3000 \: \text{cm}^{-1}$$. Calculate the corresponding frequency $$\nu$$ in $$\text{sec}^{-1}$$; $$\lambda$$ in $$\text{nm}$$, angstroms, and microns, and energy change in $$\text{kcal mol}^{-1}$$. Using Equation 4-2 and neglecting $$\Delta S$$, calculate the fraction of the molecules that would be in the ground state and in the first vibrational excited state (above ground state by $$3000 \: \text{cm}^{-1}$$) at $$298^\text{o} \text{K}$$.
Exercise 9-10 Use Table 9-2 to map the approximate positions and intensities expected for the characteristic infrared bands corresponding to the stretching vibrations of the various kinds of bonds in the following molecules:
a. 1,1,1-trideuteriopropanone (trideuterioacetone)
b. propyne
c. ethyl ethanoate (ethyl acetate)
d. propanenitrile (acrylonitrile)
e. 2-oxopropanoic acid (pyruvic acid)
f. ethanol (ethyl alcohol) (both as pure liquid and as a dilute solution in $$\ce{CCl_4}$$)
Exercise 9-11 The infrared spectra shown in Figure 9-14 are for compounds of formula $$\ce{C_3H_O}$$ and $$\ce{C_3H_6O_2}$$. Use the data in Table 9-2 and the molecular formulas to deduce a structure for each of these substances from its infrared spectrum. Indicate clearly which lines in the spectra you identify with the groups in your structures.
Figure 9-14: Infrared spectra for Exercise 9-11. Spectrum (a) corresponds to $$\ce{C_3H_6O}$$ and Spectrum (b) to $$\ce{C_3H_6O_2}$$.
Exercise 9-12* Classify the following molecules according to the general characteristics expected for their infrared and Raman spectra:
a. $$\ce{HC \equiv CH}$$
b. $$\ce{ICl}$$
c. $$\ce{CO}$$
d. $$\ce{CF_2=CH_2}$$ (double-bond stretch only)
e. $$\ce{(CH_3)_2C=CH_2}$$
f. $$\ce{CH_3CH=CHCH_3}$$
Exercise 9-13* Carbon dioxide gives two infrared absorption bands but only one Raman line. This Raman line corresponds to a different vibration than the infrared absorptions. Decide which vibrational modes are infrared active (i.e., make the molecule electrically unsymmetrical during at least part of the vibration) and which is Raman active (i.e., occurs so the molecule is electrically symmetrical at all times during the vibration, see Section 9-7A).
Exercise 9-14 List the kinds of electronic transitions that would be expected for azaethene (methyleneimine), $$\ce{CH_2=NH}$$, in order of increasing energy. Use the data in Table 9-3 to predict approximately the wavelengths at which the three lowest-energy transitions should occur.
Exercise 9-15 Calculate the percentage of the incident light that would be absorbed by an $$0.010 \: \text{M}$$ solution of 2-propanone (acetone) in cyclohexane contained in a quartz cell $$0.1 \: \text{cm}$$ long at $$280 \: \text{nm}$$ and at $$190 \: \text{nm}$$ (see footnote $$a$$ of Table 9-3).
Exercise 9-16 Explain why the absorption band at $$227.3 \: \text{nm}$$ for trimethylamine, $$\ce{(CH_3)_3N}$$, disappears in acid solution.
Exercise 9-17 A compound of formula $$\ce{C_4H_6O}$$ has two absorption bands in the ultraviolet: $$\lambda = 320 \: \text{nm}$$, $$\epsilon = 30$$ and $$\lambda = 218 \: \text{nm}$$, $$\epsilon = 18,000$$ in ethanol solution. Draw three possible structures that are consistent with this information.
Exercise 9-18 2,4-Pentadione exists in equilibrium with 4-hydroxy-3-penten-2-one:
The infrared spectrum of the liquid mixture shows a broad absorption band at $$3000$$-$$2700 \: \text{cm}^{-1}$$ and an intense absorption band at $$1613 \: \text{cm}^{-1}$$. In cyclohexane solution, the substances has $$\lambda_\text{max}$$ at $$272 \: \text{nm}$$ with $$\epsilon_\text{max} = 12,000$$.
a. What can you conclude from this data as to the magnitude of $$K$$, the equilibrium constant for the interconversion of the two forms?
b. What can you deduce from the fact that the absorption at $$272 \: \text{nm}$$ is much weaker in aqueous solution (pH 7) than it is in cyclohexane?
Exercise 9-19* The electronic absorption spectrum of 2-nitrobenzenol has $$\lambda_\text{max}$$ in $$0.1 \: \text{M} \: \ce{HCl}$$ at $$350 \: \text{nm}$$. In $$0.1 \: \text{M} \: \ce{NaOH}$$, the benzenol is largely converted to its anion, and $$\lambda_\text{max}$$ shifts to $$415 \: \text{nm}$$.
The ground-state resonance forms of 2-nitrobenzenol and its anion include
Explain how the relative importance of these resonance forms to the ground and excited states of 2-nitrobenzenol and its anion can account for the fact that the anion absorbs at longer wavelengths than does 2-nitrobenzenol. (Review Section 6-5B)
Exercise 9-20* A solution containing the two forms of the important coenzyme nicotinamide adenine dinucleotide (abbreviated $$\ce{NAD}^\oplus$$ and $$\ce{NADH}$$; see Section 15-6C for structures) has an absorbance in a $$1$$-$$\text{cm}$$ cell of 0.311 at $$340 \: \text{nm}$$ and 1.2 at $$260 \: \text{nm}$$. Both $$\ce{NAD}^\oplus$$ and $$\ce{NADH}$$ absorb at $$260 \: \text{nm}$$, but only $$\ce{NADH}$$ absorbs at $$340 \: \text{nm}$$. The molar extinction coefficients are
$\begin{array}{lll} \underline{\text{Compound}} & \underline{260 \: \text{nm}} & \underline{340 \: \text{nm}} \\ \ce{NAD}^\oplus & 18,000 & \sim 0 \\ \ce{NADH} & 15,000 & 6220 \end{array}$
Calculate the proportions of $$\ce{NAD}^\oplus$$ and $$\ce{NADH}$$ in the mixture.
Exercise 9-21 Use Figure 9-24 to map the nmr spectrum you would expect for $$\ce{^{13}CCl_3 \: ^1H}$$ in a field-sweep spectrometer in which the transmitter frequency is kept constant at $$30 \: \text{MHz}$$ and the magnetic field is swept from 0 to 30,000 gauss. Do the same for a frequency-sweep spectrometer when the magnetic field is kept constant at 10,000 gauss and the frequency is swept from $$0$$ to $$100 \: \text{MHz}$$. (For various reasons, practical spectrometers do not sweep over such wide ranges of field or frequency.)
Exercise 9-22* In nmr experiments, structural inferences sometimes are drawn from differences in resonance frequencies as small as $$1 \: \text{Hz}$$. What difference in energy in $$\text{kcal mol}^{-1}$$ does $$1 \: \text{Hz}$$ represent?
Exercise 9-23* The intensity of nmr signals normally increases markedly with decreasing temperature because more magnetic nuclei are in the $$+\frac{1}{2}$$ state. Calculate the equilibrium constant at $$-90^\text{o}$$ for the $$+\frac{1}{2}$$ and $$-\frac{1}{2}$$ states of $$\ce{^1H}$$ in a magnetic field of 42,300 gauss when the resonance frequency is $$180 \: \text{MHz}$$.
Exercise 9-24
a. Identify the protons with different chemical shifts in each of the structures shown. Use letter subscripts $$\ce{H}_A$$, $$\ce{H}_B$$, and so on, to designate nonequivalent protons. Use models if necessary.
(i) cis- and trans-2-butene
(iii) 1-chloro-2,2-dimethylbutane
(iv) 2-butanol
(v) trans-1,2-dibromocyclopropane
b.* Why does 3-methyl-2-butanol have three methyl resonances with different chemical shifts in its proton nmr spectrum?
c.* For the compounds in Part a designated those protons (if any) that are enantiotopic or diastereotopic.
Exercise 9-25 Use Equation 9-4 to calculate the chemical shift of the $$\ce{-CH_2}-$$ protons on
a. $$\ce{CH_2Cl_2}$$
b. $$\ce{ClCH_2OCH_3}$$
c. $$\ce{C_6H_5CH_2CO_2H}$$
Exercise 9-26 If the $$\ce{-NH_2}$$ protons of 2-aminoethanol, $$\ce{NH_2CH_2CH_2OH}$$, have a shift of $$1.1 \: \text{ppm}$$ and the $$\ce{-OH}$$ proton has a shift of $$3.2 \: \text{ppm}$$, what will be the observed average ($$\ce{-NH_2}$$, $$\ce{-OH}$$) proton shift if exchange is very fast?
Exercise 9-27 In reasonably concentrated solution in water, ethanoic acid (acetic acid) acts as a weak acid (less than $$1\%$$ dissociated). Ethanoic acid gives two proton nmr resonance lines at $$2$$ and $$11 \: \text{ppm}$$, relative to TMS, whereas water gives a line at $$5 \: \text{ppm}$$. Nonetheless, mixtures of ethanoic acid and water are found to give only two lines. The position of one of these lines depends on the ethanoic acid concentration, whereas the other one does not. Explain how you would expect the position of the concentration-dependent line to change over the range of ethanoic acid concentrations from $$0$$-$$100\%$$.
Exercise 9-28 The proton nmr spectrum of a compound of formula $$\ce{C_6H_{12}O_2}$$, is shown in Figure 9-31. The signals are shown relative to TMS as the standard, and the stepped line is the integral of the area under the peaks from left to right. The infrared spectrum of the same compound shows a broad band at $$3300 \: \text{cm}^{-1}$$ and a strong band at $$1700 \: \text{cm}^{-1}$$. Deduce the structure of the compound and name it by the IUPAC system.
Figure 9-31: Proton nmr spectrum of a compound, $$\ce{C_6H_{12}O_2}$$, at $$60 \: \text{MHz}$$ relative to TMS at $$0.00 \: \text{ppm}$$. The stepped line is the integral running from left to right. See Exercise 9-28.
Exercise 9-29 Sketch the proton chemical shifts in $$\text{ppm}$$ and $$\text{Hz}$$ as well as the integral you would expect for each of the following substances at $$60 \: \text{MHz}$$. (The spin-spin splitting of the resonance lines evident in Figures 9-23 and 9-27, but not seen in Figure 9-31, can be safely neglected with all of the compounds listed.)
a. $$\ce{(CH_3)_3CCH_2OCH_3}$$
b. $$\ce{CH_2COC(CH_3)_3}$$
c. $$\ce{HCOC(CH_3)_2CHO}$$
d.
e. $$\ce{(CH_3)_2C=CCl_2}$$
f. $$\ce{(CH_3)_3COC \equiv CH}$$
g. $$\ce{(CH_2Cl)_3CCO_2H}$$
h.* cis-1-methyl-4-tert-butyl-1,2,2,3,3,4,5,5,6,6-decachlorocyclohexane
Exercise 9-30 Write structures for compounds with the following descriptions (There may be more than one correct answer, but only one answer is required.)
a. $$\ce{C_2H_6O}$$ with one proton nmr shift
b. $$\ce{C_6H_{12}}$$ with one proton nmr shift
c. $$\ce{C_5H_{12}}$$ with one proton nmr shift
d. $$\ce{C_4H_8O}$$ with two different proton nmr shifts
e. $$\ce{C_4H_8O_2}$$ with three different proton nmr shifts
f. $$\ce{C_4Cl_8}$$ with two different $$\ce{^{13}C}$$ nmr shifts
Exercise 9-31 Sketch the proton nmr spectrum and integral expected at $$60 \: \text{MHz}$$, with TMS as standard, for the following substances. Show the line positions in $$\ce{Hz}$$; neglect spin-spin couplings smaller than $$1$$ to $$2 \: \text{Hz}$$ and all second-order effects. Remember that chlorine, bromine, and iodine (but not fluorine) act as nonmagnetic nuclei.
a. $$\ce{CH_3Cl}$$
b. $$\ce{CH_3CH_2Cl}$$
c. $$\ce{(CH_3)_2CHCl}$$
d. $$\ce{CH_3CCl_2CH_2Cl}$$
e. $$\ce{(CH_3)_3CCl}$$
f. $$\ce{CHCl_2CHBr_2}$$
g. $$\ce{CH_3CHClCOCH_3}$$
h. $$\ce{CH_3CH_2CO_2CH_2CH_3}$$
i. $$\ce{ClCH_2CH_2CH_2I}$$
j. $$\ce{(ClCH_2)_3CH}$$
Exercise 9-32* The proton-proton coupling in 1,1,2,2-tetrachloroethane cannot be observed directly because the chemical shift is zero. However, measurements of the splittings in $$\ce{^{13}CCl_2H-^{12}CCl_2H}$$ show that the proton-proton coupling in $$\ce{CHCl_2CHCl_2}$$ is $$3.1 \: \text{Hz}$$. Explain how you can use this information to deduce the favored conformation of $$\ce{CHCl_2CHCl_2}$$. Draw a sawhorse representation of the preferred conformation.
Exercise 9-33 The proton-proton coupling in meso-2,3-dibromobutanedioic acid (determined by the same procedure as for 1,1,2,2-tetrachloroethane, see Exercise 9-32) is $$11.9 \: \text{Hz}$$. Write a sawhorse structure for the preferred conformation of this molecule.
Exercise 9-34*
a. Show how the assignment of $$J_{AB} = J_{BC} = 2 J_{AC}$$ leads to the prediction of four equally spaced and equally intense lines for the methyl resonance of 2-phenylpropene.
b. What would the splittings of the alkenic and methyl protons look like for trans-1-phenylpropene if $$J_{AB} = 16 \: \text{Hz}$$, $$J_{AC} = 4 \: \text{Hz}$$, and $$J_{BC} = 0 \: \text{Hz}$$?
Exercise 9-35 Interpret fully each of the proton nmr spectra shown in Figure 9-40 in terms of the given structures. For spin-spin splittings, explain how the patterns arise and predict the intensities expected from simple theory.
Figure 9-40: Proton nmr spectra at $$60 \: \text{MHz}$$ relative to TMS $$= 0.00 \: \text{ppm}$$. See Exercise 9-35.
Exercise 9-36 Figure 9-41 shows proton nmr spectra and integrals at $$60 \: \text{MHz}$$ for three simple organic compounds. Write a structure for each substance that is in accord with both its molecular formula and nmr spectrum. Explain how you assign each of the lines in the nmr spectrum.
Figure 9-41: Proton nmr spectra and integrals for some simple organic compounds at $$60 \: \text{MHz}$$ relative to TMS, $$0.00 \: \text{ppm}$$. See Exercise 9-36.
Exercise 9-37 Figure 9-42 shows the proton nmr spectrum of a compound, $$\ce{C_5H_8O_2}$$. Which of the following structures fits the spectrum best? Explain. Remember that the protons of
are expected to be nonequivalent; that is, they have different chemical shifts if $$\ce{R}$$ and $$\ce{R'}$$ are different groups.
Figure 9-42: Proton spectrum of a compound, $$\ce{C_5H_8O_2}$$, at $$60 \: \text{MHz}$$ relative to TMS as standard. See Exercise 9-37.
Exercise 9-38 Suppose that you had six unlabeled bottles containing caffeine, hexachlorophene, phenacetin, DDT, 1,3-dimethyluracil, and 1-phenylethanamine. The nmr spectrum of each of these compounds is shown in Figure 9-43. Match the lettered spectra with the appropriate individual structures so the bottles can be labeled properly. Give your reasoning.
Figure 9-43: Proton nmr spectra of compounds at $$60 \: \text{MHz}$$. See Exercise 9-38.
Exercise 9-39 Show how one can use the asymmetry of the line intensities of the $$60$$-$$\text{MHz}$$ proton spectrum in Figure 9-45 to show which groups of lines are interconnected by spin-spin coupling. Write structural formulas for the compounds involved that fit the observed splitting patterns and chemical shifts.
Exercise 9-40 Explain why it is correct to characterize $$16$$ and $$17$$ as diastereomers and not enantiomers.
Exercise 9-41* When one takes the proton nmr spectrum of ordinary trichloromethane (chloroform, $$\ce{CHCl_3}$$) under high gain, the spectrum shown in Figure 9-49 is obtained. The weak outside peaks are separated by $$210 \: \text{Hz}$$ and together have an integrated intensity of slightly over $$1\%$$ of the main peak. Explain how these weak proton signals arise.
Figure 9-49: Proton nmr spectrum at $$60 \: \text{MHz}$$ of trichloromethane taken with high-detection sensitivity. See Exercise 9-41.
Exercise 9-42* With reference to the data summarized in Figure 9-47 and the discussion in Section 9-10L, sketch qualitatively the proton-decoupled $$\ce{^{13}C}$$ spectra you would expect for
a. $$\ce{(CH_3)_3CCH_2OH}$$
b. $$\ce{CCl_3CH_2OCOCH_3}$$
Exercise 9-43* Figure 9-50 shows the $$\ce{^1H}$$ and $$\ce{^{13}C}$$ nmr spectra of a compound $$\ce{C_6H_{10}O}$$. With the aid of these spectra, deduce the structure of $$\ce{C_6H_{10}O}$$. It will be seen that the $$\ce{^{13}C}$$ spectrum is quite simple, even though the proton spectrum is complex and difficult to interpret.
Figure 9-50: (a) Proton and (b) $$\ce{^{13}C}$$ spectra of a compound $$\ce{C_6H_{10}O}$$ taken at $$60 \: \text{MHz}$$ and $$15.1 \: \text{MHz}$$, respectively. Because of the special way the $$\ce{^{13}C}$$ spectrum was determined, the peak at $$209 \: \text{ppm}$$ is smaller than it should be. The intensity of this peak is, correctly, the same as the peak at $$25.5 \: \text{ppm}$$. See Exercise 9-43.
Exercise 9-44 Explain how a mass spectrometer, capable of distinguishing between ions with $$m/e$$ values differing by one part in 50,000, could be used to tell whether an ion of mass 29 is $$\ce{C_2H_5^+}$$ or $$\ce{CHO^+}$$.
Exercise 9-45
a. Calculate the relative intensities of the $$\left( \ce{M} + 1 \right)^+$$ and $$\left( \ce{M} + 2 \right)^+$$ ions for a molecule of elemental composition $$\ce{C_3H_7NO_2}$$.
b. The $$\ce{M}^+$$, $$\left( \ce{M} + 1 \right)^+$$, and $$\left( \ce{M} + 2 \right)^+$$ ion intensities were measured as 100, 8.84, and 0.54 respectively, and the molecular weight as 120. What is the molecular formula of the compound?
c. In our example of how natural $$\ce{^{13}C}$$ can be used to determine the number of carbon atoms in a compound with $$\ce{M}^+ = 86$$ and a $$\left( \ce{M} + 1 \right)^+/\ce{M}^+$$ ratio of 6.6/100, we neglected the possible contribution to the $$\left( \ce{M} + 1 \right)^+$$ peak of the hydrogen isotope of mass 2 (deuterium). The natural abundance of deuterium is $$0.015\%$$. For a compound of composition $$\ce{C_6H_{14}}$$, how much do you expect the deuterium to contribute to the intensity of the $$\left( \ce{M} + 1 \right)^+$$ peak relative to the $$\ce{M}^+$$ peak?
Exercise 9-46 Show how the molecular weights of 2-propanone, propanal, and 2-butanone can be estimated from the mass spectra in Figure 9-52. Suggest a possible origin for the strong peaks of mass 57 in the spectra of propanal and 2-butanone, which is essentially absent in 2-propanone, although 2-propanone (and 2-butanone) show strong peaks at mass 43.
Exercise 9-47 The mass spectrum of propylbenzene has a prominent peak at mass number 92. With (3,3,3-trideuteriopropyl)benzene, this peak shifts to 93. Write a likely mechanism for breakdown of propylbenzene to give a fragment of mass number 92.
Exercise 9-48 The mass spectra of alcohols usually show peaks of $$\left( \ce{M} - 18 \right)$$, which correspond to loss of water. What kind of mechanisms can explain the formation of $$\left( \ce{M} - 18 \right)$$ peaks, and no $$\left( \ce{M} - 19 \right)$$ peaks, from 1,1-dideuterioethanol and 1,1,1,3,3-pentadeuterio-2-butanol?
Exercise 9-49 Explain how the postulated rearrangement of the $$\ce{M}^+$$ ion of ethyl butanoate (Section 9-11) is supported by the fact that the 2,2-dideuterio compound gives a peak with $$m/e =$$ 90, the 3,3-dideuterio isomer gives a $$m/e$$ 88 peak, while the 4,4,4-trideuterio isomer gives a $$m/e$$ 89 peak.
Exercise 9-50 What is the likely structure for the major fragment ion with $$m/e =$$ 45 derived from methoxyethane (methyl ethyl ether) on electron impact?
Exercise 9-51 A certain halogen compound gave a mass spectrum with molecular ion peaks at $$m/e$$ 136 and 138 in about equal intensities. The nmr spectrum of this compound gave only a single resonance around $$1.2 \: \text{ppm}$$. What is the structure of the compound? Give your reasoning.
Exercise 9-52* The mass spectra of three compounds, A, B, and C, are given below in tabular form. Only the peaks of significant intensity are reported.
a. Compound A is $$\ce{CH_3CH_2CH_2COCH_3}$$. Show how this material can fragment to give the peaks marked with an asterisk and, where possible, how the isotope peaks help establish your assignments.
b. Determine the molecular weight and the molecular formula of Compounds B and C from the spectral data. Suggest a likely structure for each peak marked with an asterisk.
## Contributors
• John D. Robert and Marjorie C. Caserio (1977) Basic Principles of Organic Chemistry, second edition. W. A. Benjamin, Inc. , Menlo Park, CA. ISBN 0-8053-8329-8. This content is copyrighted under the following conditions, "You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format." | 2020-10-31 08:08:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7512245178222656, "perplexity": 1481.964858100137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107916776.80/warc/CC-MAIN-20201031062721-20201031092721-00331.warc.gz"} |
https://codereview.stackexchange.com/questions/236860/n-body-simulation-in-c?noredirect=1 | # N body simulation in C++
You can find the complete code on github. Since I'm rather new to C++ I thought that it might be a good idea to write a simulation of the n-body problem to apply some of the concepts that I learned in class. The relevant part can be found in main.cpp on the above linked github repo, but the imporant part is given by:
#include <string>
#include <eigen3/Eigen/Dense>
#include <utility>
#include <iostream>
#include <chrono>
#include <cmath>
#include <fstream>
#include "integrate.hpp"
#include <vector>
using mass_t = double const;
using name_t = std::string const;
using vector_t = Eigen::Vector3d;
using phase_t = Eigen::VectorXd;
using rhs_t = phase_t (*)(double const &, phase_t const &);
using step_t = phase_t (*)(rhs_t , phase_t const &, double, double);
double square(double x){ // the functor we want to apply
return std::pow(x,2);
}
double norm(vector_t const& v){
return std::sqrt(v.unaryExpr(&square).sum());
}
// Class representing a stellar object
class StellarObject{
public:
explicit StellarObject( vector_t pos = vector_t(0,0,0), //Position of the sun relative to itself
vector_t speed = vector_t(0,0,0), //Velocity of the sun relative to itself
mass_t const& mass = 1.00000597682, //Mass of the Sun [kg]
name_t const& name = "Sun") : mass_(mass),
name_(name),
position_(std::move(pos)),
velocity_(std::move(speed)) {};
vector_t get_position() const {
return position_;
}
vector_t get_velocity() const {
return velocity_;
}
double get_mass() const {
return mass_;
}
private:
vector_t position_;
vector_t velocity_;
name_t name_;
mass_t mass_;
};
phase_t nbody_prod(double const & t, phase_t const & z,
std::vector<double> const& masses, double const & G){
int const N = masses.size();
phase_t q(3*N); //space for positions of the particles
q << z.head(3*N); //fill it with the relevant elements from z
phase_t ddx(3*N); //space for the rhs of the ODE
ddx.fill(0); //make sure that set to zero everywhere
for(std::size_t k = 0; k<N; ++k){
vector_t tmp; //tmp object to store ddx
tmp.fill(0);
vector_t qk = q.segment(3*k,3); //get position of k-th object
for(std::size_t i=0; i < N; ++i){
if(i!=k){ //calculate acceleration of k-th object
vector_t qi = q.segment(3*i,3);
vector_t diff = qi-qk;
double normq = std::pow(norm(diff),3);
tmp += masses[i]/normq * diff;
}
}
ddx.segment(3*k,3) = G * tmp;
}
return ddx;
}
// z = [r_(1,x), r_(1,y), r_(1,z), r_(2,x), .... r_(N,z), v_(1,x), v_(1,y), ..., v_(N, z)]
phase_t nbody_rhs(double const & t, phase_t const & z, std::vector<double> const& masses,
double const G){
int const N = masses.size();
phase_t rhs(6*N); //space for the rhs
rhs.head(3*N) = z.tail(3*N); // fill velocities in first 3*N elements of rhs
rhs.tail(3*N) = nbody_prod(t, z, masses, G); // fill last 3*N elements with nbody_prod
return rhs;
}
static double G;
static std::vector<double> masses;
Eigen::MatrixXd n_body_solver(std::vector<StellarObject> const & planets){
int const N = planets.size();
phase_t z0(6*N);
for(std::size_t k=0; k < N; ++k) {
z0.segment(3*k,3) = planets[k].get_position();
}
for(std::size_t k=N; k < 2*N; ++k) {
z0.segment(3*k,3) = planets[k%N].get_velocity();
}
for(auto & planet : planets){
masses.push_back(planet.get_mass());
}
G = 2.95912208286e-4;
auto reduced_rhs = [](double const & t, phase_t const & z0) {return nbody_rhs(t, z0, masses, G);};
return explicit_midpoint(reduced_rhs, z0, 60000, 40000);
}
Note that I left out the main-function of main.cpp since there is nothing interesting happening there.. Just the setup for a simple test.
The code works, it produces results that are sensible (if you have a working phyton environment and are using a Unix based machine you can run run.sh file inside the repo and should get a nice animation of the stellar movement), but there are several things that bother me about the code.
First of all: I'd like to put all of these different function into one solver class, which I think would make it much easier to use and understand. The goal would be something like the following code (but I can't get it to work...)
class n_body_solver{
public:
n_body_solver(std::vector<StellarObject> const & planets,
double const & G=2.95912208286e-4) : N_(planets.size()) {
G_= G;
for(std::size_t k=0; k < N_; ++k) {
z0_.segment(3*k,3) = planets[k].get_position();
}
for(std::size_t k=N_; k < 2*N_; ++k) {
z0_.segment(3*k,3) = planets[k%N_].get_velocity();
}
for(auto & planet : planets){
masses_.push_back(planet.get_mass());
}
}
phase_t nbody_prod(double const & t, phase_t const & z,
std::vector<double> const& masses, double const & G){
int const N = masses.size();
phase_t q(3*N); //space for positions of the particles
q << z.head(3*N); //fill it with the relevant elements from z
phase_t ddx(3*N); //space for the rhs of the ODE
ddx.fill(0); //make sure that set to zero everywhere
for(std::size_t k = 0; k<N; ++k){
vector_t tmp; //tmp object to store ddx
tmp.fill(0);
vector_t qk = q.segment(3*k,3); //get position of k-th object
for(std::size_t i=0; i < N; ++i){
if(i!=k){ //calculate acceleration of k-th object
vector_t qi = q.segment(3*i,3);
vector_t diff = qi-qk;
double normq = std::pow(norm(diff),3);
tmp += masses[i]/normq * diff;
}
}
ddx.segment(3*k,3) = G * tmp;
}
return ddx;
}
// z = [r_(1,x), r_(1,y), r_(1,z), r_(2,x), .... r_(N,z), v_(1,x), v_(1,y), ..., v_(N, z)]
phase_t nbody_rhs(double const & t, phase_t const & z, std::vector<double> const& masses,
double const G){
int const N = masses.size();
phase_t rhs(6*N); //space for the rhs
rhs.head(3*N) = z.tail(3*N); // fill velocities in first 3*N elements of rhs
rhs.tail(3*N) = nbody_prod(t, z, masses, G); // fill last 3*N elements with nbody_prod
return rhs;
}
void solve(double const & time_intervall, unsigned int const & bins){
auto reduced_rhs = [](double const & t, phase_t const & z0) {return nbody_rhs(t, z0, masses_, G_);};
result_ = explicit_midpoint(reduced_rhs, z0_, time_intervall, bins);
}
Eigen::MatrixXd get_result() const {
return result_;
}
private:
phase_t z0_;
unsigned short const N_;
static double G_;
static std::vector<double> masses_;
Eigen::MatrixXd result_;
};
Other than that I'd be happy to receive feedback regarding general C++ coding style, choices of containers, types, etc. Anything that you notice when reading the code.
• You should not assume that each potential reviewer knows what the n-body problem is. A simple link to Wikipedia helps, you can just edit your question. Other than that, it's a good question. – Roland Illig Feb 7 at 21:23
• @RolandIllig That's absolutely fair, edited! – Sito Feb 7 at 21:34
• I'm not very familiar with Eigen, but is it really intended to be used like this? You are taking a Nx3 matrix and iterating over it in a n^2 fashion. I assume Eigen has some way to abstract that so that you're using fewer loops, and possibly get a benefit of hardware support. Is this code actually leveraging Eigen in a way that's better than just using a std::vector of struct {float x,y,z;}; ? – butt Feb 7 at 22:46
• @butt To be honest, I don't know. I'm not that familiar with Eigen either, actually, I did this exercise here precisely to become a bit familiar with it (almost all of the functions I used here from Eigen, I used for the first time...). So if there is a faster (better) way of doing this, I'm more than open to hear about it. – Sito Feb 7 at 23:16
• Here is another n body c++ program you can reference codereview.stackexchange.com/questions/231191/…. A reason to leave an uninteresting main in the program is so that others can test the code and see how the classes are used. – pacmaninbw Feb 8 at 14:40
Your code makes me think that you don't understand what exactly you want to model.
explicit StellarObject(
vector_t pos = vector_t(0,0,0), //Position of the sun relative to itself
vector_t speed = vector_t(0,0,0), //Velocity of the sun relative to itself
mass_t const& mass = 1.00000597682, //Mass of the Sun [kg]
name_t const& name = "Sun"
)
When creating a (model of a) stellar object, there is absolutely nothing that should be related to the sun. The sun is just a random star and has no relation to any of the fundamental physical constants.
The comments to the right reference the sun though, which makes the whole code look wrong. I very much doubt that the sun's mass is a single kilogram.[citation needed]
It is wrong to provide default values for any of the parameters of this constructor since it doesn't make sense to have 5 objects with the same name or the same position or the same mass, that's just not a realistic scenario. The caller of this constructor must be forced to think about all these values explicitly.
G = 2.95912208286e-4;
This is a magic number. The symbol G usually stands for the gravitational constant, whose value is approximately $$\ 6.67430\cdot10^{-11} \frac{\text{m}^3}{\text{kg} \cdot \text{s}^2}\$$. Your value of $$\2.9\cdot10^{-4}\$$ is nowhere near that value, therefore you must document where you got that number from and what its dimension is. In physical simulations, it's important to carry the dimensions around in the calculations to prevent typos and other mistakes. For example it doesn't make sense to add seconds to meters and divide by Ampère.
Always use the Internation System of Units, don't accept any other measurement units unless you document exactly why you have to use different units and how you did the conversion.
vector_t tmp; //tmp object to store ddx
The variable name tmp is terrible, it should be forbidden. You should have named it next_ddx, since it collects the positions after the next simulation step. This naming scheme would also suggest a better name for vector_t qk and q. To avoid confusion, these should be called next_pk and next_p. Sure, the names are a bit longer, but the name q does not really tell (me) much, except that it is the letter following p in several Latin alphabets. If that's a well-known naming convention among physicists, it's ok if the code is ever only read by physicists.
double normq = std::pow(norm(diff),3);
tmp += masses[i]/normq * diff;
It's confusing to see a division by $$\r^3\$$ when I only expect a division by $$\r^2\$$. The code would be easier to understand if you just divided by $$\r^2\$$ first and did the direction calculations afterwards and independently. The code is easy to understand if the commonly known formulas like $$\F = \text{G} \cdot \frac{m_1 \cdot m_2}{r^2}\$$ appear exactly in this form. Every deviation from this makes the code more difficult to read and to verify.
I did not analyze the rest of the code in detail. I saw many helpful comments that explained the short variable names, which is good for understanding the code. I also saw many questionable comments that contradicted the code, and these are bad. You should probably read the code aloud to someone else and while doing that, listen to your words to see whether they make sense. If they don't, the code is wrong. Or the model of the world you are building. Either way, something needs to be fixed in these cases. | 2020-10-25 00:11:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4227110743522644, "perplexity": 4894.9510989282735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107885059.50/warc/CC-MAIN-20201024223210-20201025013210-00213.warc.gz"} |
https://forum.wilmott.com/viewtopic.php?f=3&t=102461&sid=97e026ad9208d62c56ee92f319c7c91f&start=45 | Serving the Quantitative Finance Community
Mars
Posts: 115
Joined: November 13th, 2002, 5:10 pm
### Re: Proof of the risk-neutral assumption
(3) is not a premiss. As I said B&S model => PDE => expectation with a specific measure coming from Feynmann-Kac theorem => (3) is true with the expectation using the same measure.
And in that model there are risk premiums.
Thanks. Are there any simpler ways to derive the Formula direct from the BS PDE? And how to derive without any appeal to expectations at all?
You can solve it by change of variable to get heat equation which give you the B&S solution. Indeed In what I said we got PDE first then "Expectations" comes from Feynmann-Kac Theorem. And then come your equation(1), which use expectation without being clear on what it means. Using Feynmann-Kac make it crystal clear in my opinion.
complyorexplain
Topic Author
Posts: 175
Joined: November 9th, 2015, 8:59 am
### Re: Proof of the risk-neutral assumption
OK is Wolfram better? https://mathworld.wolfram.com/Validity.html
Paul
Posts: 11261
Joined: July 20th, 2001, 3:28 pm
### Re: Proof of the risk-neutral assumption
Girsanov isn't particularly useful, in my opinion.
Change of measure = change of variables. The latter you do in high school. The former is just a complicated presentation of the latter in a very narrow field to make it palatable for university professor probabilists to teach.
Assumptions hint at a model.
Randomness in model makes people worried about how to value risky things. E.g. expectations might not play a simple role.
Assumptions +model +hedging + no arbitrage => BS PDE, Binomial model, ...
Trivial observation about BS PDE or binomial model shows that there is a role for simple expectations.
That role is to pretend that assets all have the same rate of return. Even though they don't. This is risk neutrality.
Probabilists get all aroused. Trivial things gets messy.
As to derivation of BS formulae, there are many ways that are equally simple.
The role of expectations also has the result that values can be found by simulations, Monte Carlo. Very useful.
But risk neutrality distracts from reality. It's a very tempting dead end, but with lots of drink, drugs, free love.
Cuchulainn
Posts: 64397
Joined: July 16th, 2004, 7:38 am
Location: Drosophila melanogaster
Contact:
### Re: Proof of the risk-neutral assumption
But risk neutrality distracts from reality. It's a very tempting dead end, but with lots of drink, drugs, free love.
Sounds very 70s.
"Can't buy me love,no, no, no,no,no"
// You can stare at an SDE all day long $^*$ (some people do) but when you stare at a PDE then at some stage the solution jumps off the page.
$^*$ converging a.s./p.p.to Euler method. Every time. Without fail.
Last edited by Cuchulainn on December 21st, 2020, 8:23 pm, edited 2 times in total.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler
http://www.datasimfinancial.com
http://www.datasim.nl
katastrofa
Posts: 10069
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri
### Re: Proof of the risk-neutral assumption
OK is Wolfram better? https://mathworld.wolfram.com/Validity.html
No online resources can replace a book. For you, Shreve.
Paul: "Change of measure = change of variables."
In infinite number of dimensions.
Cuchulainn
Posts: 64397
Joined: July 16th, 2004, 7:38 am
Location: Drosophila melanogaster
Contact:
### Re: Proof of the risk-neutral assumption
dbl
Last edited by Cuchulainn on December 21st, 2020, 8:30 pm, edited 1 time in total.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler
http://www.datasimfinancial.com
http://www.datasim.nl
Cuchulainn
Posts: 64397
Joined: July 16th, 2004, 7:38 am
Location: Drosophila melanogaster
Contact:
### Re: Proof of the risk-neutral assumption
In infinite number of dimensions.
Bad news, kats. The only Borel measure on a Banach space is the trivial measure.
https://en.wikipedia.org/wiki/Infinite- ... ue_measure
That's an Ecumenical matter.
Not that anyone would want to do that.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler
http://www.datasimfinancial.com
http://www.datasim.nl
Paul
Posts: 11261
Joined: July 20th, 2001, 3:28 pm
### Re: Proof of the risk-neutral assumption
OK is Wolfram better? https://mathworld.wolfram.com/Validity.html
No online resources can replace a book. For you, Shreve.
Paul: "Change of measure = change of variables."
In infinite number of dimensions.
I actually meant change of numeraire. But am very happy that you didn’t find fault with anything else!!!
katastrofa
Posts: 10069
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri
### Re: Proof of the risk-neutral assumption
I didn't mean to indicate any faults. My intention was to complete your abstract statement. I appreciate that you talk about mathematics at such a high level, especially in the context of an applied quantitative field.
Paul
Posts: 11261
Joined: July 20th, 2001, 3:28 pm
### Re: Proof of the risk-neutral assumption
My intention is always to speak at the optimal level!
katastrofa
Posts: 10069
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri
### Re: Proof of the risk-neutral assumption
Of course. That's why you jump on the desk.
Paul
Posts: 11261
Joined: July 20th, 2001, 3:28 pm
### Re: Proof of the risk-neutral assumption
You’ve seen me lecture on finite differences then? I climb up on furniture to explain the forward, backward and central differences.
I also find that wives are a great source of useful analogies.
Cuchulainn
Posts: 64397
Joined: July 16th, 2004, 7:38 am
Location: Drosophila melanogaster
Contact:
### Re: Proof of the risk-neutral assumption
You’ve seen me lecture on finite differences then? I climb up on furniture to explain the forward, backward and central differences.
I also find that wives are a great source of useful analogies.
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler
http://www.datasimfinancial.com
http://www.datasim.nl
katastrofa
Posts: 10069
Joined: August 16th, 2007, 5:36 am
Location: Alpha Centauri
### Re: Proof of the risk-neutral assumption
I saw a cute Maxwell demon increasing the Helmholtz energy to fuel his teaching efforts. And Cuchulainn is a buzzing Brownian computer. I'll always see the world with physicist's eyes!
Isn't it funny that the same mathematical theory and tools (theory of stochastic processes, Girsanov, Feynman-Kac, Fokker-Planck, Lie Trotter ...) work for a simple ferromagnet, DNA replication, derivative proving and more. Too beautiful to be true.
Cuchulainn
Posts: 64397
Joined: July 16th, 2004, 7:38 am
Location: Drosophila melanogaster
Contact:
### Re: Proof of the risk-neutral assumption
Lie Trotter .
Just so happens that I am implementing LT as we speak. It's first-order. or 2nd order, go for Strang-Marchuk operator Splitting. Nice thing is splitting {diffusion, convection}, {potential, kinetic energy} and not {x,y}.
Wow! I didnie know you physicists knew BCH et al.
https://www.asc.tuwien.ac.at/~ewa/semin ... ag_Exl.pdf
"Compatibility means deliberately repeating other people's mistakes."
David Wheeler
http://www.datasimfinancial.com
http://www.datasim.nl | 2021-05-09 03:38:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5994772911071777, "perplexity": 6710.517357504172}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988955.89/warc/CC-MAIN-20210509032519-20210509062519-00514.warc.gz"} |
https://www.quantumcalculus.org/unimodularity-theorem-cw-complexes/ | # The Unimodularity Theorem for CW Complexes
In algebraic topology one knows the structure of a CW complex. In that acronym, “C” stands for “closure finite” and “W” for weak. It could as well stand for “Constantine Whitehead” as the structure was developed by John Henry Constantine Whitehead in a sequence of papers published in 1949 and is used in every introductory course in algebraic topology. [I myself was exposed to CW complexes first in a course of Dan Burghelea, he gave at ETH in 1985. As that course had been read in French, CW complexes are for me therefore still “complex cellulaires”. By the way, my hand written notes of that course are here [18 Meg PDF]. ]
Even so, finite CW complexes have a finite combinatorial structure, the common theme is so see them as a construct in which a repeated “addition of handles” has taken place: start with a Hausdorff topological space X and attach cells = balls to it. First take an embedding f of a sphere Sn-1 into X, then build the quotient topology of the disjoint union of X and the ball Bn where points x in Sn-1 ⊂ Bn and f(x) ∈ X are identified. This process is called the attachment of a n-cell.
One can start with the situation, where X0 is a finite discrete set, then first attach a finite number of 1-cells. We end up with a one-dimensional complex X1, the 1-skeleton of the final construct. Now attach a number of 2-cells. We end up with a two dimensional complex X2. After finitely many such constructs, we end up with a d-dimensional cellular complex. Finally one define a CW complex as a topological space which is homeomorphic to such a construct. Most spaces we know in geometric analysis are of this type. Note that the definition just given is a bit more special than needed. One can define inductively a CW complex as a topological space Y which is obtained from an other CW complex by attaching a cell. The induction assumption is that a finite set with the discrete topology is a CW complex. Note that by this definition, the order with which cells are added can matter, as we can build additional cells on parts which have previously been added. The notion of CW complexes is not as general as the notion of a general Hausdorff topological space; but it generalizes the notion of a topological space equipped with a simplicial complex structure or in particular a manifold.
Even in this finite setup, standard (n-1)-spheres and n-balls in Euclidean space are used for the definition.It in particular assumes the “infinity axiom” in the ZF. I myself completely accept the ZFC frame work, but why use infinite constructs to describe objects which are finite and combinatorial? A mathematician who formulated the concerns skillfully is Luitzen Egbertus Jan Brouwer. While I don’t share his concerns too much on a fundamental level, it is still important to develop a finite mathematics independent of such consistency considerations ([I personally got aware of such issues through lectures of Erwin Engeler, a student of Paul Bernays, who not only taught a wonderful set theoretical topology course at ETH (Here are my notes [PDF]), but also other courses like theory of computation and mathematical software (My notes [PDF]). He once told me (in a casual hallway conversation) about “finitism” and “strict finitism” ideas, a theme about which he has published.]. There are also practical computer science reasons, when implementing the structures on a computer. More serious is the prospect of a worst case scenario: the emergence of a contradiction in the ZFC axiom system for example. By Goedel’s second incompleteness theorem, we can not prove the consistency within that system. Until now, we have not found a convincing and generally accepted larger frame work in which the consistency of ZFC can be proven. Anyway, also such a proof would hardly be reassuring as by the incompleteness theorem again we would face the problem to convince ourselves of the consistency of that larger framework within an even larger one. A simple way out of this frustrating “Its turtles all the way down” problem is to not even to start setting the foot into the mud and stay if possible within finite mathematics.
So, lets put ourselves into the shoes of Brouwer and work with finite structures. It allows us to enjoy the benefit that whatever we do, can be implemented in full detail on a finite computing device, as long as the structures are small enough. In order to define a CW complex in the discrete, we need a notion of a “sphere”. The simplest combinatorial structure where spheres appear are when looking at boundaries of simplices of finite abstract simplicial complexes.The later is a a finite set V on which one has given a finite set G of non-empty subsets such that if ∈ G, and B ⊂ A, then B ∈ G. The sets in G are the simplices. Again, since many texts treat simplicial complexes through their realization in Euclidean space we have to stress that a finite abstract simplicial complex is a finite object valid for somebody who thinks the concept of infinity should go to hell.
A convenient and intuitive way to generate finite simplicial complexes is to use a finite simple graph G=(V,E) as a background. Graphs are convenient as they are intuitive and easy to work and program with. A graph G contains many different simplicial complex structures in general. The largest one is the set of all complete subgraphs of the graph. This is the Whitney complex of the graph. There are smaller ones, like G=V ∪ E, which is the 1-skeleton complex on the graph. It can be useful to use several simplicial complex structures on a graph especially in proofs as it gives more flexibility to deform the graph. There are many stages for example to get from a graph to a pyramid extension of the graph. With this point of view, a finite simplicial complex on a graph G is already a CW structure on a graph. The individual cells are the k-simplices. The boundary of a k-simplex is a union of (k-1) simplices which can be seen as a discrete sphere. It is a crude version of a sphere.
There is a nice notion of what a “sphere” is in a graph. The definition is inductive and due to Evako. It is for example used in in a formulation of Jordan Brouwer to which we refer also for references. (We came to this concept independently but the basic setup is due to Evako in the graph theoretical setup. Evako also make the homotopy theory in graph theory crystal clear. Again, also homotopy traditionally assumes a geometric realizations, requiring Euclidean spaces and so the infinity axiom. The Evako homotopy does not need any Euclidean space and would have made Brouwer happy.) One first defines in a completely combinatorial way what contractibility is. then, one defines a k-sphere inductively as a graph for which every unit sphere is a (k-1)-sphere and such that removing a single vertex renders the graph contractible. The induction assumption is that the empty graph is a (-1)-sphere. This definition implicitly assumes the abstract finite Whitney simplicial complex structure on the graph, meaning the set of all vertex sets of complete subgraphs. It can certainly be done for any simplicial complex structure imposed on a graph and especially for the 1-skeleton complex which in the 20th century was the default simplicial complex structure imposed on a graph (most graph theory books take this rather narrow point of view). The boundary of a triangle (complete K3 subgraph) for example is not a 1-sphere as the triangle and every subgraph of the triangle are contractible. There is a simple way to get an Evako sphere from a simplex. Just look at its Barycentric refinement of the simplex which is now a graph with interior and boundary. The boundary of the Barycentric refinement of a triangle for example is the circular graph C6. From the platonic solids (when considered as graphs), only the octahedron and icosahedron are Evako spheres. The cube and dodecahedron are one dimensional as for them, all unit spheres are zero- dimensional. The tetrahedron finally is three dimensional because all its unit spheres are two-dimensional.
A more general CW structure on a finite simple graph can be obtained again by “attaching cells”. First chose an Evako k-sphere in G, then build a pyramid extension (cone) over it. This produces a larger graph. But now, the newly attached vertex does not play the role of a vertex but of a k-simplex. While the new graph G’ is still a graph, we count the simplices differently. The connections to the new graph for example don’t count.
Definition: Given a finite simple graph G equipped with a simplicial complex C so that one can give an inductive notion of Evako sphere. A k-dimensional CW structure is a finite set of disjoint disjoint (k-1)-spheres. The union of the k-simplices as well as these spheres are the new simplices. Disjoint means that the spheres do not have a common simplex. More generally, a CW structure on a graph is a union of disjoint Evako spheres in G. The union of these spheres as well as set of all complete subgraphs forms now the simplex structure. It is not a simplicial complex any more but turns out to be good enough for geometry. The connection graph of a CW complex has the set of simplices of G as vertices. Two such vertices are connected if they intersect.
This structure appears naturally in a more general version of the unimodularity theorem. We have described the theorem a bit already in a Math table talk. Like any “nice” theorem, it equates two numbers, where the two sides are defined by two seemingly unrelated things: the first is algebraic: it is the Fredholm determinant
det(1+A(G'))
where A(G’) is the adjacency matrix of the connection graph G’ of G. It is a special value of a Bowen-Lanford Zeta function
ζ(z)=1/det(1-zA) associated to the geometric structure (here the adjacency matrix of the connection graph) and therefore a spectrally defined notion. The second quantity is the Fredholm characteristic which is defined as
φ(G) = ∏x ω(x)
which is a multiplicative version of the Euler characteristic:
χ(G) = ∑x ω(x) ,
where ω(x)= (-1)dim(x) is the parity of a simplex. The Fredholm characteristic is of more combinatorial nature. A physisist liking super symmetry would see the Fredholm characteristic as the determinant of the parity operator P on linear space of discrete differential forms. This operator appears for example in the notion of super trace as str(A) = tr(P A) for any operator on differential forms. In analogy one can define the super determinant by sdet(A) = exp( str( log(A) ) ) = det(P A). So
The Euler characteristic is the super trace of the identity: str(1) = tr(P).
The Fredholm characteristic is the super determinant of the identity sdet(1) = det(P).
The fact that the Fredholm characteristic is a Fredholm determinant det(1+A) for the adjacency matrix of the simplicial complex is concrete and explicit. Here is the theorem. It is now a bit more general than for simplicial complexes:
Unimodularity Theorem: For a graph G equipped with a CW complex structure, the Fredholm determinant of the connection graph is the same than the Fredholm characteristic of G. It especially is an integer in {-1,1}. The adjacency matrix of the connection graph of a CW complex is therefore always unimodular. This implies that the inverse, the Green functions (1+A)-1ij of a complex is integer-valued and of topological interest.
A special case is when G is a finite abstract simplicial complex. Even more special is if we have the Whitney complex of a finite simple graph. Now we discovered the theorem first experimentally in February 2016. It turned out not to be easy to prove. The Hammer and Chisle or Sledge hammer approach did not work well so far. We had to build up more theory and so use the “rising sea” approach. One of the necessary steps had been to extend it to more general structures than graphs. It might appear crazy first to to generalize something before settling the simpler case. The reason for generalization is that simplicial complexes or even CW complexes that they allow for a finer induction process. Adding a single vertex to a graph turns out to be a huge modification to a graph since many fnew simplices are added simultaneously to the graph. The corresponding linear algebra is difficult as we add many new rows and columns. Managing the determinant analogue to the Laplace expansion is difficult. Adding a single simplex one by one is much more convenient. Why then generalize it even more? There is an other reason than “fine graining the deformation tools”: more general structures also lead to more interesting Fredholm numbers instead of only -1 and 1. And when doing experiments, it can be hard to see structure when only 1 or -1 appear. The CW structure is not the most general one. The collection of Evako spheres can more generally be a collection of geometric subgraphs, graphs for which every unit sphere is an Evako sphere. A graph G with a collection of disjoin geometric subgraphs a generalized cell complex. Lets again give the definition and refrain from stating it for general simplicial complexes but just look at finite simple graphs equipped with the Whitney complex:
Definition. A generalized cell complex is a finite simple graph G=(V,E) with a collection W of simplex disjoint geometric graphs in G. A geometric graph in G is a subgraph for which every unit sphere is an Evako sphere.
The unimodularity theorem does not generalize to this general structure as the Fredholm functional φ(G) now can take values different from -1 or 1. In order to prove the unimodularity theorem we proved a lemma which tells what happens with the Fredholm determinant φ(G) if we add a new simplex. This lemma is crucial and very general. It does not require the attached cells to be spheres. It can be anything:
Fredholm determinant lemma: Let F be any generalized cell complex and G a larger complex in which either a new vertex or a new cell x has been added. Then φ(G) = i(x) φ(F) where i(x) is the Poincare-Hopf index i(x) = 1-χ(S(x)).
The lemma also immediately shows why the number f(G) of odd-dimensional simplices in G matters in the case of Whitney complexes or CW complexes. For odd dimensional “cells” x which have even dimensional spheres, we have χ(S)=2 so that then 1-χ(S(x) ) = -1. On the other hand, for even dimensional cells which have odd dimensional spheres, we have χ(S)=0 so that then 1-χ(S(x)) = 1. We see that the Poincaré-Hopf index i(x) is the key. It explains why the unimodularity theorem is true and why only the odd dimensional simplices count: they have even dimensional spheres.
[The following illustration was Added November 29:]
We see a random graph G with 14 vertices and Euler characteristic χ(G)=-4; Inside is a random subgraph with 9 vertices of Euler characteristic χ(H)=-2. The f-vector of G is (14,36,20,2) and χ(G)=14-36+20-2=-4. The f-vector of H is (9, 16, 6, 1) and χ(H)=9-16+6-1=-2; We see that H is far out from being a sphere (as spheres always have Euler characteristic 0 or 2). The first picture shows H highlighted as a subgraph of G. The second picture shows the pyramid extension Gx in which an additional vertex has been added. The f-vector of Gx is (15, 45, 36, 8, 1) leading to χ(Gx)=15-45+36-8+1=-1. The Poincaré-Hopf index of the new index is 1-χ(H) = 3. The Euler characteristic of Gx is confirmed by Poincaré-Hopf equal to -1. This is all nice and dandy. What happens with the multiplicative Euler characteristic? We needed a lot of experimentation to figure this out: the Fredholm extension lemma tells that the Euler characteristic of H (not the connection graph of H, which might have a different Euler characteristic in rare cases [this is related to the fact that connection graphs are in general not homotopic to the graph but in many cases actually are like after a Barycentric refinement]) matters. in that particular example here for example, the Euler characteristic of H is -2 as it is also the Euler characteristic of H’ which is a much larger graph with 32 vertices, 190 edges. Also comparing the Fredholm determinant of G’ and Gx‘ is not the right thing! Again, devilishly, it produces the correct identity in most cases and I myself believed for a while that it would work as such. Only failing to prove it forced me to reexamine the experiments and refine the picture.
We really have to think like Whitehead in order to see it! The Fredholm extension lemma can only be understood using CW complexes.
The picture is that the added vertex x over H is the process of having attached a new cell to the CW complex. On the level of graphs (Whitney simplicial complex of course), the extension lemma would be wrong as the join over H (pyramide or cone extension) would add a lot of more simplices which add a lot more paths to the path integral picture and distort the Fredholm determinant. What also helped is to work with more general cells and not only spheres for which the Euler characteristic i(x)=1-χ(H) has absolute value 1. Having more variety in the numbers make experiments sharper and allow more quickly to weed out wrong paths. In the case of the picture seen, the Fredholm connection determinant, the Fredholm determinant of G’ is equal to 1. The Fredholm determinant of the expanded cell complex G” has Fredholm determinant 3. The following picture shows the two matrices for the graph G’ (the CW complex obtained from the Whitney simplicial complex) and the CW complex G” of the extension for which we have just computed the Fredholm determinant. The fundamental Poincaré-Hopf-Fredholm Lemma implies that 3=φ(G”) = i(x) φ(G) = 3*1. This is the case here. Of course one only gets impressed by this if one tries it out with arbitrary graphs G and subgraphs H, thousands or millions of them until one gets confidence to actually prove it.
For the Euler characteristic, there is the Poincaré-Hopf theorem. It defines the Poincaré-Hopf index of a vertex of a graph as i(x) = 1-χ(S(x)) where S(x) is the unit sphere. If we have a generalized cell complex given by a finite simple graph G=(V,E) together with a collection W of geometric disjoint subgraphs of G, define for x in V, the Poincare-Hopf index as before and for x in V, representing a subgraph S(x) of G, define i(x) = 1-χ(S(x)), the Poincaré-Hopf index of the cell x. The Poincaré-Hopf theorem tells χ(G) = i(x) + χ(F) in the graph case. How to define Euler characteristic in the case of generalized cell complexes? It is quite easy to see that if we want the Euler characteristic to remain a valuation satisfying χ(F ∪ G) = χ(F) + χ(G) – χ(F ∩ G), then we better have to define it through the Poincaré-Hopf theorem.
Definition. The Euler characteristic χ(G) of a generalized cell complex G is defined as ∑ x ∈ V ∪ W i(x), where i(x) = 1-χ(S(x)), where for a vertex x ∈ V, S(x) is the unit sphere in G and where if x ∈ W, S(x) is the geometric graph under consideration.
Now, we have an other indication why the Fredholm characteristic is a cousin of the Euler characteristic: For any generalized cell complex, we have
χ(G) = ∑x i(x) (Poincare-Hopf)
φ(G) = ∏x i(x) (Fredholm Lemma)
In particular, for a CW complex or abstract finite simplicial complex, where i(x) = 1-S(x) ∈ {-1,1}, φ(G); ∈ {-1,1}, the adjacency matrix of the generalized cell structure is unimodular. In other words, the multiplicative Poincaré-Hopf result makes things more transparent. In general, for a generalized cell complex, as the Fredholm determinant φ(G) is then no more necessarily -1 or 1. It would be nice to know how large the set of graphs is which can be seen as a connection graph of some generalized cell complex of this type. We actually believe it to be possible that there is an even larger generalization of generalized cell complex (completely parallel to surgery constructions in the continuum) in which the order of the attached cells matters so that we can reach any graph as a connection graph and have the Fredholm lemma (a multiplicative Poincaré-Hopf theorem). But this requires to understand a more complex Morse story. I’m optimistic because the multiplicative Poincaré-Hopf result works very well in full generality, where the attached cell is even over an arbitrary subgraph (and not just a sphere like for CW complexes or geometric graphs like for generalized cell complexes). What has still to be checked that with the definition of Euler characteristic given the indices of newly attached handles work. In classical Morse theory, we start with the geometric object (like graph or manifold), then chose an order of the points (using Morse function), then build up the CW structure. Now for graphs, the Morse theoretical build-up does not have to attach disks, one can attach pretty much everything and the Morse indices can be pretty arbitrary (unlike for Morse functions, where the Poincaré-Hopf indices are -1 or 1). This is what surgery constructions in the continuum are about. For the generalized cell structures build up, chosing a different order of the build-up produces a different structure. In some sense, it is a non-commutative Morse theory. The Poincaré-Hopf theorem still holds but it is not a theorem about a function on the geometric graph but about an ordered sequence of attached cells. The notion “generalized cell complex” given here is special still in the sense that the order in which the attached cells are added does not matter. The Poincaré-Hopf theorem as well as its multiplicative cousin, the Fredholm Lemma are both a theorem in that case. What we don’t yet know for sure (because we have not implemented it in the computer) is whether the theorem holds for a very general non-commutative Morse set-up, where the order of the addition of the general cells matters, allowing to be built on already built generalized cell structure.
An other parallel result between Euler characteristic and Fredholm characteristic are the valuation relations:
χ(F ∪ G) + χ(F ∩ G) = χ(F) + χ(G) (additive valuation)
φ(F ∪ G) φ(F ∩ G) = φ(F) φ(G) (multiplicative valuation)
A generalized cell complex has also a natural cohomology.The new ideal spheres S(x) do not have to be closed oriented geometric graphs. We can still define the exterior derivative df(x) = f(S(x)) satisfying d2 = 0.
Once one has a notion of index, one can define curvature as the expectation of the index with respect to some averaging measure. We have explored this for a while now
There are various ways to generate probability measures of indices. On graphs, where indices are defined by locally injective functions, we can just look at probability spaces of functions for which almost all functions are locally injective. An other source for random geometric structures are determinants. If we look at the Fredholm determinant of a graph, then this is in some sense a partition function over all one dimensional CW complexes which can exist on a graph. The kicker was that since the Fredholm determinant is a sum over the Fredholm characteristics over all these oriented one-dimensional CW complexes on the connection graph. The unimodularity theorem assures that this is the Fredholm characteristic of the graph.
How do we define then curvature for Fredholm characteristic naturally? We don’t know yet. First we need to finish writing up the paper. In any case, we think the definition of curvature in a very general setup is not much harder. In the case of a graph or finite abstract simplicial complex or generalized cell complex as defined here, it is pretty clear as we just have to average over all possible built-ups of the space. In the case of graphs, we for example just can average over all possible locally injective functions. To define curvature for an even more general cell complex, we have average the indices when summing over all possible build-ups of the structure. In any case, whenever there is a Poincare-Hopf theorem, there is also a Gauss-Bonnet theorem telling that the integral over all the curvatures is the Euler characteristic. The multiplicative version is that the product of the Fredholm curvatures is the Fredholm characteristic.
We currently hope that any finite simple graph can be the connection graph of a generalized cell complex. The Fredholm determinant of the graph itself has Poincare-Hopf and Gauss-Bonnet formulas. Compare that in the unimodularity theorem, where we currently only look at the Fredholm determinants of connection graphs of CW complexes. For a general graph, the Fredholm determinant seizes to be {-1,1} valued and can be pretty arbitrary. If this works, then it would be worthwhile to consider a generalization of the textbook definition of CW complex in which in each case, not a cell (k-ball) is added but a rather general cone of an arbitrary CW complex can be added. The classical CW complex is the special case where the boundaries of the cells are spheres. In any case, such a more general structure remains reasonable as there is a Gauss-Bonnet theorem for it as well as a natural cohomology as well as Laplacians, Hodge theory etc. This looks like a huge program but in reality it all exists already as we have these structures for general finite simple graphs. Its just that our point of view has shifted and graphs are more emancipated: while in the 20th century graphs were mostly treated as one-dimensional simplicial complexes, topologists like Whitney, Fiske, Evako, Forman looked at graphs as more general topological constructs featuring richer simplicial complex structures. Now, graphs have general Poincaré-Hopf, Gauss-Bonnet, Brouwer-Lefschetz theorems. What we start to see now is that we can look at general graphs as connection graphs of a rather large class of topological spaces obtained by adding rather general handles. But the litmus test is not beauty or generality, but whether theorems work. In our case, the question is whether we can write in general the Fredholm determinant of a graph as a product of Poincare-Hopf indices. Now, in a naive way this is certainly wrong as for most Morse functions, there are many regular points for which the Poincare-Hopf index is zero. The product of the Poincaré-Hopf indices is therefore zero in most cases. But the Fredholm determinants are mostly nonzero. The naive point of view can not be more wrong.
What emerged again through the analysis of the unimodularity theorem is that we have to look at a graph not as something per se but as a shell on which more structures can be built. This is well known in mathematics. The set of real numbers as a set are pretty boring. It is just an uncountable set without any interesting structure (order structure, topology of open sets, δ-algebra of measurable sets) yet. For a graph, we can first of all pop-up a simplicial complex structure. There are many. There is the one dimensional skeleton given by the union of vertices and edges, then there are others up to the Whitney complex. But there are more structures possible besides simplicial complexes. CW complexes lead the way. For example, we can see the Wheel graph W4 (with 4 spikes) as a connection graph of a 2-cell even so the connection graph of any graph which is a 2 cell is much bigger. The connection graph of a triangle for example (the smallest two dimensional cell) has already 7 vertices.
Now, and this can be shocking at first, the additional geometric structure also can change the Euler characteristic of the structure. For example, if we look at the tetrahedron graph K4, then with the Whitney complex C, the Euler characteristic is 1 as there are 4 vertices, 6 edges and 4 triangles and one 3-simplex. So that χ(G,C)=4-6+4-1=1. If we look at the the graph K4 however equipped with the 2-skeleton complex C, then the 3-cell does not count. The Euler characteristic is now χ(G,C)=2 (as Descartes and Euler would have counted the Euler characteristic using the famous formula v-f+e=2, the Euler gem). Now, a graph theorist of the 20th century looks at the tetrahedron even as a completely different beast, namely a one dimensional simplicial complex C (essentially all textbooks take this point of view). Now the triangles do not count and the Euler characteristic is χ(G,C)= e-f = 4-6 = -2. The picture is now that one sees a sphere with 4 holes punched into it). This is an additional confusion which could well be mended into the Lakatos discussion about one of the most embarrassing stories in the history of mathematics, the fact that Euler gem theorem was not only once but several times “disproven” with counter examples. The first counter examples were of course the Kepler solid which fail to have Euler characteristic 2 in general. Today we know that the notion of “polyhedron” was muddy over the course of centuries. [There are many analogue confusions in mathematics and they are all based on ambiguities. For example: as paradoxa like Bertrand’s paradox in probability theory indicate, that the notion of probability is not just an intrinsic notion of a space, but depends on additional structure: not only the σ-algebra but also from the probability measure. Notions like entropy can confuse as it is a matter of fact that all basis laws of physics we know are reversible so that entropy stays constant but then there are laws of thermodynamics claiming that the entropy increases. This is not a paradox if one understands to look at it with more structure, with structures for example which have emerged in the last century like martingale theory. ]
Any way, what we see now that there are lots of more cellular structures possible on a graph. Simplicial complex structures or CW complex structures make up only a small part. There appears first a slight difficulty in defining the Euler characteristic of such a structure as we can not just count cells any more. Note that the cells are now pretty arbitrary graphs with pretty arbitrary topological features and not necessarily bound contractible cells like in the case of simplicial complexes or CW complexes. Our suggestion is to use Poincaré-Hopf inductively to define the Euler characteristic. This has first of all the advantage that the Euler-Poincaré theorem is trivial as it is the definition. Only in the case of simplicial complexes or in particular the Whitney complex on a graph it becomes a theorem as it claims there that the result is independent in which order the structure has been built up. So, what is new now with the more general structures is that the Euler characteristic not only depends on the space but also on the Morse function as the later determines in which order the cells were added. What we don’t yet know is whether the multiplicative part of Poincaré-Hopf gives something which is independent of the structure and only depends on the graph. A more general unimodularity theorem would assure this. For now, the unimodularity theorem only holds for discrete CW complexes. For general cellular complexes, it gives an identity of the Fredholm determinant of the connection graph and the product of the Poincaré-Hopf indices. But that only applies so far if the additional cells are all disjoint so that the order in which the cells are added does not matter.
The following picture illustrates the unimodularity theorem. We look at a triangle for which the Fredholm characteristic is -1 (there are three odd dimensional simplices in the triangle, the three edges). The Fredholm determinant is already a path integral of a large number of closed paths. It is the set of all one-dimensional oriented paths in the connection graph G’ (which is larger than the Barycentric refinement). There are 601 such paths. 301 have odd signature and 300 have even signature. We see in the picture all except the empty path belonging to the identity permutation. It is absolutely non-trivial why the difference of these two classes is always 1 or -1. (By the way, in the Mathtable handout of this fall, we have mentioned that there are 90 paths which are transitive permutations of the vertices of the connection graph of the triangle G=K3. Fredholm determinants generate much more permutations as they don’t need to be transitive.)
And here are all except the identity permutations belonging go the Fredholm determinant of the linear graph G of length 2. The connection graph G’ of G has 5 vertices, the 3 original vertices as well as the 2 edges. The two edges are connected to the central vertex producing a triangular K3 graph as a subgraph of the connection graph. We see that there 5 permutations which have odd signature and 6 permutations which have even signature. Indeed, the Fredholm characteristic is 1. as there are 2 odd-dimensional simplices in the graph. By the way, the unimodularity theorem is pretty easy to prove for one dimensional graphs G, graphs which have no triangles. The graph L3 treated in this example is one dimensional. Its connection graph is the bunny graph. The bunny graph was already featured in the math table handout about Wu characteristic.
By the way, Wu characteristic is closely related to the topic just discussed. We actually came to Fredholm determinants through Wu characteristic and intersection calculus.
And an other P.S.: the prime graphs appearing in the counting and cohomology story are naturally discussed in the context of discrete CW complexes. Actually the above multiplicative Poincaré-Hopf lemma allows to compute the Fredholm determinant of these graphs very nicely. They are just related to the products of the first n Moebius functions, the reason being that the Möbius functions are minus the Poincaré-Hopf indices of these graphs. Its important there to look at the CW complexes as the connection graphs of the prime graphs are much larger! CW complexes are just a perfect setting for understanding the Fredholm determinants of these graphs.
Added November 30, 2016: Here is a picture of the prime graph P(30) as introduced in the counting and cohomology paper. The vertices are the square free integers from 2 to 30. We have shown in that paper that counting is a Morse theoretical process:
Counting and cohomology theorem: The counting function f(n)=n is a Morse function the Barycentric refinement of the complete graph on the spectrum of the the ring Z of integers. The graph P(n)=(V(n),E(n)) has the vertex set V(n)={1Poincaré-Hopf index of the critical point k is i(k)=-μ(k), the Moebius function. By Poincaré-Hopf, the Euler characteristic of P(n) satisfies χ(P(n)) = 1-M(n), where M(n) is the Mertens function. The function f is Morse in the sense that the stable part of every unit sphere S(x) is an Evako sphere. The Morse index m(x) is dim(S(x))+1. By Euler-Poincaré, one can express 1-M(n) as ∑k=1n (-1)k bk, where bk are the Betti numbers, the dimensions of the k’th cohomology groups Hk(G(n)). The growth of the Mertens function (relevant for the Riemann hypothesis) is therefore expressible in terms of cohomology.
A naive thought is to try to estimate the growth of the Mertens function and so proving the Riemann hypothesis by estimating the Betti numbers, maybe through relation with curvature. As indicated in the paper, this certainly is not a silver bullet: first of all one has to establish curvature-Betti relations a la Gromov in the discrete, then estimate curvatures. A long fight could wait to clear that if at all possible.
What is the multiplicative Euler characteristic = Fredholm picture? On one side one has the product of the Poincaré-Hopf indices, the Moebius function values. Now, according to the unimodularity theorem, this should be the Fredholm determinant of a connection graph. However, as just expressed in the above crucial lemma, this only works if we look at the graph P(n) as a CW complex; the reason is that adding a new vertex has to produce a new cell. In the next picture we first see the graph P(30), then an other graph and finally the connection graph P(30)’ of P(30). The third graph shown is larger as it contains as vertices all the complete subgraph of P(30). Yes, according to the unimodularity theorem, its Fredholm determinant is related to the number of odd dimensional simplices in P(30). As the f-vector of P(30) is (18,20,6) with Euler characteristic 18-20+6=4 which matches 1-M(30) = 1-(-3)=4, where M(n) is the Mertens function, the sum of the first 30 Moebius values {1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, 0, 1,1, -1, 0, 0, 1, 0, 0, -1, -1}. The 18 nonzero values in that list (the first value 1 does not count because we don’t include 1 as a vertex as we would just get the unit ball of 1 which has always Euler characteristic 1 and is not interesting), are minus the Poincaré-Hopf indices.
Now lets look at the product of these Poincaré-Hopf indices. It is 1. This matches the Fredholm determinant of the connection graph. But thats pure luck (a 50 percent chance)! Indeed, when looking at the f-vectors of the prime graphs P(n), we see that the number of odd dimensional simplices are there always even. The Fredholm determinant of the connection graphs P(n)’ of P(n) are always 1. This is related to the fact that the prime graphs P(n) are “submerged parts” of a Barycentric refinement of a complete graph on the primes. Anyway, there is no Poincaré-Hopf match. But again, this is just because we did not think like Whitehead. The correct graph to consider is the CW complex. Now, every vertex of the prime graph is actually thought of as an attached cell. The vertex set is the same. But since we look at the connection graph (!), we have now to consider not at connections, where one integer divides an other but where two integers (x,y) have a non-trivial common prime factor meaning gcd(x,y)>1. This graph the second graph seen in the picture below. We call it the prime connection graph. These prime connection graphs are beautiful graphs too. But now, the Fredholm determinant of the adjacency matrix of this graph matches the product of the Poincaré-Hopf indices. This is the unimodularity theorem again, but now used in the more general context of CW complexes.
CW complexes have proven to be very useful also for practical reasons (i.e. cellular cohomology is much easier to compute in general than simplicial cohomology). It also leads naturally to a discrete Morse cohomology as mentioned in the counting and chomology paper too. But we have only scratched the surface by showing that for every graph, there exists at least one Morse function for which the Morse cohomology agrees with simplicial cohomology. There is no doubt that this holds in much more generality for the simple reason that the theory works in the continuum and because of the following quantum calculus principle: Everything which works in the continuum, works also in finite mathematics, sometimes even better.
End update of November 30. | 2018-10-20 07:34:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7331252098083496, "perplexity": 449.80883841660705}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583512592.60/warc/CC-MAIN-20181020055317-20181020080817-00261.warc.gz"} |
https://brilliant.org/discussions/thread/finding-the-x/ | ×
# Finding the 'x'
How can we solve these type of problems:
e.g. $2^{x}=x$
or, $2^{x}=x^{2}$
To find the possible value(s) of x.
Note by Dinesh Nath Goswami
1 year, 11 months ago
Sort by:
use log in both this is the simplest way 1st one answer is no solution 2nd one has 2 solution I.e., 2&4 · 1 year, 11 months ago
actually it has 3 solutions · 1 year, 11 months ago
thanks... · 1 year, 11 months ago
Try using graphs and apply calculus. · 1 year, 11 months ago
thanks. I'll try that way. · 1 year, 11 months ago
Use logarithm too. That will make the problem easier. · 1 year, 11 months ago | 2017-09-21 10:36:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.927444338798523, "perplexity": 5839.343771493422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818687740.4/warc/CC-MAIN-20170921101029-20170921121029-00054.warc.gz"} |
https://www.rocketryforum.com/threads/spray-paint.77991/ | spray paint
Help Support The Rocketry Forum:
Rob Fisher
Well-Known Member
I will never use any paint other than krylon anymore! I painted my der red max clones nosecone gloss black with odds 'n' ends plasti-kote spray paint, and after drying for two weeks the nose cone still feels tacky and leaves fingerprints! Krylon paint seems to dry overnight just fine. I thought i'd save a couple of bucks-bad idea. Nothing but high quality krylon touches my birds from now on.
Hospital_Rocket
Well-Known Member
Keep one thing in mind,
I have found (thru bitter experience) that the solvent in Krylon attacks durn near everything. Be real careful when overcoating other finishes, regardless of how long they have dried. That is, unless you like a wrinkled finish!
Al
astrowolf67
Well-Known Member
I use three kinds of spray paint. 1. Krylon 2. Plasti Kote automotive laquer. And 3. Duplicolor automotive laquer. Krylon, for general use is the best I've found. The other two, which I get at local auto parts stores, are great for those flashy finishes (lots of colors and metallics), dry very fast, and are forgiving in less than ideal painting conditions. What ever you decide to use, stick with the same brand/type from primer to finish. If you really have to mix brands, test the combination on scraps first. Also, EMRR has a good chart of paint compatability at www.rocketreviews.com
graylensman
On a couple of my first rockets I tried the 99 cent WalMart rattlecans. All those saved me was a buck and a quarter. Krylon rings up at $2.30 a can and is wonderful to work with. GlennW Well-Known Member I have always used Testors spray enamel, should I be switching to Krylon? Seems that is what a lot of you prefer. Is there a big difference? Like, does it go on better, etc? Also, I don't recall seeing Krylon in the hobby shop, where would one buy this? Glenn EMRR Well-Known Member Originally posted by graylensman On a couple of my first rockets I tried the 99 cent WalMart rattlecans. All those saved me was a buck and a quarter. Krylon rings up at$2.30 a can and is wonderful to work with.
however, Krylon is very nice to work with.
Also, don't mix your Walmart Paint with Krylon!
Regards,
Nick
Well-Known Member
Originally posted by GlennW
I have always used Testors spray enamel, should I be switching to Krylon? Seems that is what a lot of you prefer. Is there a big difference? Like, does it go on better, etc? Also, I don't recall seeing Krylon in the hobby shop, where would one buy this?
Glenn
If you can paint with Testors cans with success, you are a hero in my book. If you do switch to Krylon, I think you'll notice that it doesn't tend to run as much. Also, drying times tend to be shorter I think with Krylon.
I think it would be cool if Krylon had all of Testor's colors.
vjp
Well-Known Member
Am I the only one here who likes Rustoleum?
I used to use Krylon only, but after using Rustoleum on my V-2 I was extremely impressed, and their metallics are great too for those retro 50's style "rocketships".
The only drawback is the primer, which is incompatible with plastics.
kenobi65
Well-Known Member
Originally posted by GlennW
Also, I don't recall seeing Krylon in the hobby shop, where would one buy this?
Since Krylon isn't a hobby paint, but a general-purpose quick-drying spray paint, you'll find it at hardware stores and discount stores (such as Wal-Mart).
EMRR
Well-Known Member
Originally posted by vjp
Am I the only one here who likes Rustoleum?
You might be, other than the fact that I love their "hammered look" paint.
Nick
kenobi65
Well-Known Member
Originally posted by vjp
Am I the only one here who likes Rustoleum?
In general use (i.e., beyond model rocketry), I'd prefer Rustoleum over Krylon in a heartbeat. Krylon's formulated to dry faster than Rustoleum (recall their old tagline: "No runs, no drips, no errors"?), but, from what I've been told, this means that Krylon tends to give a less-durable finish.
Now, for model rocketry applications, this isn't a particularly relevant benefit, given that most model rockets will suffer a catastrophic fate long before time and exposure to the elements lead to degradation of the finish.
So, to sum up: Krylon for your rockets, Rustoleum for your patio furniture.
Micromeister
Micro Craftman/ClusterNut
TRF Supporter
It really doesn't matter who's can of spray paint you pick up, If it doesn't say "recoat anytime" drop it and run away! You'll be much happier believe me.
saunassa
Active Member
I love some of the Testors colors - the green metallic is one of my favorites. the problem i have found is that the Testors takes forever to dry and never really hardens like the Krylon or Rustoleum brands.
One of the best paints, great price and can be re-coated anytime
is F&F from Mills Fleet Farm here in the midwest.
saunassa
Active Member
now i can hear everyone going Fleet Farm? there is probably a Farm and Fleet, Fleet supply or some other large farm clothes and equipment store nearby unless you live in the big city.
like Micromister stated a paint that can be re-coat anytime is great paint.
think about this - if you were a farmer and needed to quickly paint a tractor, combine, heck the ol' pickup truck or some other outdoor machinery to keep it from rusting are you going to buy that shtuff that takes an hour to dry and costs 3$a can? That you can't re-coat for a day or two unless you want it to crack and fall off? of course not, you want to put 2 or 3 coats on within and hour or whenever you feel like it and off you go. teflonrocketry1 Well-Known Member For model rockets, I prefer Krylon over any of the other brands I've tried. None of the other brands seem to dry as fast, go on as smooth, or recoat as easily. I always use clear acrylic (Future Floor Wax) as a topcoat for decals and Krylon. For primers, I prefer Varsity Brand Sandable white primer (Pep Boys occasionally has it on sale for$1.00 a can) since it dry sands easily.
Bruce S. Levison, NAR #69055
wwattles
Well-Known Member
I just got done (my hands still smell of paint thinner) spraying my Tres with some Krylon Fusion paint, and all I can say is "WOW!!!" Two coats, 10 minutes apart, and the thing is done! It's almost completely dry already (at T+15 minutes and counting), and it's got a nice wet-looking finish.
WW | 2021-01-18 20:55:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22365602850914001, "perplexity": 6992.276147312493}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703515235.25/warc/CC-MAIN-20210118185230-20210118215230-00273.warc.gz"} |
http://mathhelpforum.com/pre-calculus/224540-perimeter-ellipse-radii-vice-versa.html | # Math Help - Perimeter of an ellipse from radii, and vice-versa
1. ## Perimeter of an ellipse from radii, and vice-versa
Hi there,
I'm new here. Greetings.
I need to figure out how to calculate the perimeter, or circumference, of an ellipse using the radii, and vice-versa: how to figure out the radii given the perimeter and the ratio of the two radii to each other.
I found an equation for the perimeter, or circumference here: Circumference/Perimeter of an Ellipse: Formula(s) - Numericana)
given the radii x and y, where x>y:
P=3.1415*(((2*((x^2)+(y^2)))-(((x-y)^2)/2))^.5)
The result will be an approximation but it will be close enough.
Any chance you could help me solve this equation for x in terms of C and y, and then also for y in terms of C and x?
I’m pretty rusty on my equations!
Many Thanks,
rgesh
San Francisco, CA
2. ## Re: Perimeter of an ellipse from radii, and vice-versa
Hello Rgesh. Given values for perimter 'P' and semi-axis 'y' you can rearrange the equation to get a quadratic equation in the other semi-axis 'x':
$P = \pi \sqrt{2(x^2+y2)-\frac 1 2 (x-y)^2}$
Bring the pi factor to the left hand side and square both sides, and expand the (x-y)^2 term:
$\frac {P^2} {\pi^2} = 2(x^2+y^2)-\frac 1 2 (x^2-2xy+y^2)$
Now gather terms to make a quadratic in x:
$\frac 3 2 x^2 +yx +(\frac 3 2 y^2- \frac {P^2}{\pi ^2}) = 0$
Now you can apply the quadratic formula to solve for x. The equivalent equation for y, given values for x and P, is:
$\frac 3 2 y^2 +xy +(\frac 3 2 x^2- \frac {P^2}{\pi ^2}) = 0$
3. ## Re: Perimeter of an ellipse from radii, and vice-versa
Hi ebaines,
Thank you for your help, however, I'm a bit lost.
I need to use these equations to plug into an Excel chart, so I need them in a format such as x=..... and y=......
I'm not sure how to use the equations you gave, where everything=0.
Also, I realize that I need the equations to include another variable, R, that would represent the ratio of x to y. Is that possible?
Thanks.
4. ## Re: Perimeter of an ellipse from radii, and vice-versa
Are you familar with the quadratic equation, which I'm sure you learned in algebra class? Given:
$ax^2+bx+c = 0$
The solution for x is:
$x = \frac {-b \pm \sqrt{b^2-4ac}}{2a}$
Here $a = 3/2,\ b = y,\ c = \frac 3 2 y^2-\frac {P^2}{\pi^2}$. Plug these values into the quadratic formula and you'll get the value for x. Actually you will get two values (due to the "plus-or-minus" factor), but one value is positive and the other is negative, so you can throw out the negative value.
5. ## Re: Perimeter of an ellipse from radii, and vice-versa
I definitely learned that in algebra class. That was in 1972. I'm out of practice.
Many thanks for your help. Much appreciated.
6. ## Re: Perimeter of an ellipse from radii, and vice-versa
As for the ratio R: if you have values for P and R (defined as R=x/y), then starting with the first solution I gave earlier:
$\frac 3 2 x^2 +yx +(\frac 3 2 y^2- \frac {P^2}{\pi ^2}) = 0$
divide through by y^2:
$\frac 3 2 \frac {x^2}{y^2} +\frac {x}{y} +(\frac 3 2 - \frac {P^2}{\pi ^2y^2}) = 0$
Replace x/y with R:
$\frac 3 2 R^2 + R +(\frac 3 2 - \frac {P^2}{\pi ^2y^2}) = 0$
Rearrange to get y^2 by itself:
$y^2 = \frac {P^2}{\pi^2 (\frac 3 2 R^2 +R + \frac 3 2 )}$
Take the square root of both sides:
$y = \frac {P}{\pi \sqrt{\frac 3 2 R^2 +R + \frac 3 2 }}$
This gives you the y semi-axis. You can get the other from $x = Ry$
Hope this helps.
7. ## Re: Perimeter of an ellipse from radii, and vice-versa
Originally Posted by rgesh
I definitely learned that in algebra class. That was in 1972. I'm out of practice.
Many thanks for your help. Much appreciated.
Algebra class for me was 1970, but I'm an engineer and so I guess I've managed to stay in practice. Glad to be able to help! | 2014-10-25 05:41:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7908270955085754, "perplexity": 742.1152509006796}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119647778.29/warc/CC-MAIN-20141024030047-00122-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://distinctivestrategies.com/meaning-of-ujho/archive.php?5297b2=if-a-is-not-equal-to-zero-then-a-is | Select Page
Does an Echo provoke an opportunity attack when it moves? Also I am only supposed to use the basic axioms (e.g. Intuitively, the determinant of a transformation A is the factor by which A changes the volume of the unit cube spanned by the basis vectors. Edit: If the above is not working as expected then, there is a possibility that you are not using $? your coworkers to find and share information. (But I don't think this resolves the issue - I can't think of a situation where, :D A lot depends on what those other formulas are - imagine if one of those formulas was a, If cell value is not equal to zero then message box, Tips to stay focused and finish your hobby project, Podcast 292: Goodbye to Flash, we’ll see you in Rust, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…, Congratulations VonC for reaching a million reputation. Stack Overflow for Teams is a private, secure spot for you and We give a counter example. Consider the following$2\times 2\$ matrices. Conditional code flow is the ability to change the way a piece of code behaves based on certain conditions. We’ll show you a few ways in which you can use the operator with the IF function. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Favorite Answer. Since we want to flag items that pass our test, we need to take an action when the result of the test is TRUE. A quadratic equation is an equation whose highest power on its variable(s) is 2. Please check! Lv 6. In this case, Excel will give a result as “TRUE” if the condition is meet or “False” if the condition is not meet. Any Number divided by zero gives a indefinite answer...mathematically Infinite. What assumption should be made to prove the statement indirectly? If X = -1, then the answer to the question is NO. Math! How can I deal with a professor with an all-or-nothing grading habit? The formula in cell C1 below returns TRUE because the text value in cell A1 is not equal to the text value in cell B1. The not equal to comparison operator is slightly tricky to use. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Following examples will explain the difference to evaluate Blank or Not Blank cells using IF statement. If the Rank of matrix A is n-1 then there is atleast one minor present of order n-1 of the matrix A is not equal to zero.Therefore the matrix Adj A will be a non zero matrix and thus the Rank of the matrix Adj A will be greater than zero.. Now . The remaining True/False arguments are then left as part of the outer IF statement. Can someone help? How can I run VBA code each time a cell gets its value changed by a formula? Asking for help, clarification, or responding to other answers. Are there any gambits where I HAVE to decline? By the symmetry in the argument, we can prove that: if b <> 0, then a = 0. Can I walk along the ocean from Cannon Beach, Oregon, to Hug Point or Adair Point? Look at the below piece of code.Code:Here we are testing whether the number 100 is not equal to the number 100. And then the zero vector is also going to have k elements. Thanks for contributing an answer to Stack Overflow! Whenever Excel sees this symbol in your formulas, it will assess whether the two statements on opposite sides of these brackets are equal to one another. In other words, at least one of the numbers a and b must be 0. use .Value2. 8 years ago. Not Equal To in Excel is very simple and easy to use. Shor's algorithm: what to do after reading the QFT's result twice? If X = -1/2, then the answer to the question is YES. seg MN divides Triangle ABC into two part equal in area. If A is an empty 0-by-0 matrix, any(A) returns logical 0 (false). The One True Brace (OTB) style may not be used with legacy If statements. a. ! …, he total length of the pole.Answer is40mdon't spam otherwise I will report ur answer.... This cell depends on the value of cell A minus the value of cell B. at right place.It must be the very next line after the command of which you need to catch the return status. Solution. How feasible to learn undergraduate math in one year? When I take v transpose times the zero vector, v transpose is going to have k elements. This is a crucial test that helps determine whether a square matrix is invertible, i.e., if the matrix has an inverse. In Excel, > means not equal to.The . 16. Consider the statement: If two whole numbers are even, then their sum is odd. Making statements based on opinion; back them up with references or personal experience. Learn how to solve quadratic equations using the quadratic formula. Let’s understand the working of Not Equal To Operator in Excel by some examples. For sure we know number 100 is equal to 100, so the result will be FALSE.Now I will change the equation.Code:Now the test is whether number 100 is not equal to 99. If X = -1/2, then the answer to the question is YES. On the other part I mis-took your answer, my bad. ?, 1/2of a pole is under mud,3/5 of the remaining portion is under water and the remaining lengthof the pole, which is 8 m, stands above the water.Find t Private Sub Worksheet_Change(ByVal Target As Range) If Range("H60").Value2 <> 0 Then MsgBox "Not Equal zero!!!!" In this case, we do that by adding an "x" to column D. Adding NOT means the test will return TRUE if B6 is NOT "red" or "green", and FALSE otherwise. You mentioned the cell relies on 2 other cells, you could have your test on those with something like this: This will make it only fire if I60 or J60 are what was changed on the sheet, you can obviously change these to other cell references if you need, I assumed your formula is using I60 and J60. use the given information to f However, when the cell H60 is zero, the message box still continues to pop up. It only takes a minute to sign up. What is a better design for a floating ocean city - monolithic or a fleet of interconnected modules? Logical expressions Equal to Blank (=””) or Not Equal to Blank (<>””) ISBLANK function to check blank or null values. Somehting like. If a cell is blank, then it returns TRUE, else returns FALSE. Blank Cells This is the exact opposite functionality of the equals sign (=), which will output TRUE if the valu… If determinant of A is zero then an eigenvalue of A is 0 therefore there exists an x such that Ax=0x=0 and x is non-zero. For example, let’s say that you created a DataFrame that has 12 numbers, where the last two numbers are zeros: ‘set_of_numbers’: [1,2,3,4,5,6,7,8,9,10, 0, 0] You may then apply the following IF conditions, and then store the results under the existing ‘set_of_numbers’ column: If the number is equal to 0, then … gAytheist. If is not Zero, then I pass back the original value. P (0 less than or equal to Z less than or equal .9) 17. 0 = 0.1 = 0. When it does have an inverse, it allows us to find a unique solution, e.g., to the equation A x = b given some vector b. Note that all of the examples have a closing parenthesis after their respective conditions are entered. In other words, it is the following assertion: If =, then = or =.. 1/a^2 b. The NOT function simply reverses this result. In algebra, the zero-product property states that the product of two nonzero elements is nonzero. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. I'm giving brainiest to the This is the easiest way to check if two cells are not equal to each other. If they are not equal, it will output TRUE, and if they are equal, it will output FALSE. and we know. A2A, thanks. You can specify conditions of storing and accessing cookies in your browser, in triangle ABC ,seg MN parallel side AC. …, ind the ratio of the number of boys to the number of girls, the latitude of the reciprocals of Rajesh mage (in years) three years ago and five years form now is 26/153 find his present age, Today is my birthday guys plz join the meeting to wish me jxt-owoe-qbd if anyone join so i will give 30 thanks to him amd follow his , cos2x + asinx = 2a – 7 has a solution if 'a' is in the range of?? I would however recommend you put some sort of test in there to only fire on certain cell changes, you don't want it firing every time anything is changed on the sheet. I believe the answer is 98, but I'm not 100% sure. I am not able to draw this table in latex. What tuning would I use if the song is in E but I want to use G shapes? > operator in Excel checks if two values are not equal to each other.. Let's take a look at a few examples. So this is a dot product of v with the zero vector which is equal to zero, the scalar zero. (a.a^ (-1)) = (0.a).a^ (-1) = 0.a^ (-1) = (a.b).a^ (-1) = (b.a).a^ (-1) = b. How to display cell value offset active cell, Excel Formula to pull left of selected cell, How to use Regular Expressions (Regex) in Microsoft Excel both in-cell and loops, Randomly select Target cells without being able to target a same cell twice, Coloring Cells on Microsoft Excel on Tap/Touch, If input to InputBox does not equal value in range, then display msgbox and end sub, Checking Every Cell in A Row Equals to Zero (0), For each Loop but Without Looping in Message Box. In ordinary arithmetic, the expression has no meaning, as there is no number which, when multiplied by 0, gives a (assuming a ≠ 0), and so division by zero is undefined. (a.a^ (-1)) = b.1 = b. 1/2a^2 c. 1/6a^2 d. 0 e. nonexistent THANK YOU SOOO MUCH! Homework Statement Prove: if a\\neq0 then b/a=b*a^-1 I don't know if my proof is sufficient with this one but I cannot think of another way. In such situations you can use if statements.. If A is a vector, then B = any(A) returns logical 1 (true) if any of the elements of A is a nonzero number or is logical 1, and returns logical 0 (false) if all the elements are zero.. This formula uses the Excel IF function, combined with the less than and equal signs (=), to test if the value in cell C8 is less than or equal to the value in cell C5.If the test is TRUE the formula will return a "No" value, alternatively if the test is FALSE the formula will return a "Yes" value. …, which group of fractions are like fractions among the , in a school there 120 boys & 180 girls. Is there an "internet anywhere" device I can bring with me to visit the developing world? what does "scrap" mean in "“father had taught them to do: drive semis, weld, scrap.” book “Educated” by Tara Westover. On a related note, the statement if Var between LowerBound and UpperBound checks whether a variable is between two values, and if Var in MatchList can be used to check whether a variable's contents exist within a list of values. B- The numbers are not equal. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. The if statement is also known as a decision making statement, as it makes a decision on the basis of a given condition or expression. C- Their sum is not odd. What is a "constant time" work around when dealing with the point at infinity for prime curves? Agree with you on function choice. You're taking the dot product of v and 0. Therefore A ( Adj A) will be a Zero matrix. Fighting Fish: An Aquarium-Star Battle Hybrid. Why? I have written this code to automatically pop up a message box when the value of a cell is not equal to zero. This formula should meet your requirements and return a blank cell if E12 = 0 So, assuming that a.b = 0, we proved that: if a <> 0, then b = 0. 40 of the boys are under 10 years & 140 of the girls are under 10 year. There is one scenario - the two cells that are being subtracted could themselves be calculated by a formula. So the result will be TRUE. This allows me to pass in computational-heavy numbers without having to compute them more than once. End If End Sub I would however recommend you put some sort of test in there to only fire on certain cell changes, you don't want it firing every time anything is changed on the sheet. And when I take this product that's like dotting it. Why? Determine AM /MB, How old am I if 500 reduced by 3 times my age is 206? Fact 1 is INSUFFICIENT Fact 2: |X| > X This tells us that X CANNOT be positive or 0. To learn more, see our tips on writing great answers. The Arduino Reference text is licensed under a Creative Commons Attribution-Share Alike 3.0 License.. Find anything that can be improved? To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Now we will see how to use VBA Not Equal (<>) sign practically. Since any number multiplied by zero is zero, the expression 00 is also undefined; when it is the form of a limit, it is an indeterminate form. Doubts on how to use Github? The statement is in general not true. Not equal to in excel formulas will give result in only “True” or “false” format … 1. If the determinant of a square matrix n × n A is zero, then A is not invertible. Should I cancel the daily scrum if the team has only minor issues to discuss, Introduction to protein folding for mathematicians, Squaring a square and discrete Ricci flow. A- The numbers are equal. The block of code inside the if statement is executed is the condition evaluates to true. Suggest corrections and new documentation via GitHub. It can only be used with If (expression) . The formula method is pretty straight forward, with one minor issue: You specified NO for less than zero and YES for greater than zero, but it is not clear what you want as a result when E12 equals zero.. Click here to get an answer to your question ️ If A is not equal to zero, then A÷0 is \[A=\begin{bmatrix} 0 & 1\\ Physicists adding 3 decimals to the fine structure constant is a big accomplishment. If A is a nonempty, nonvector matrix, then B = any(A) treats the columns of A as vectors, returning a row vector of logical 1s and 0s.. The general syntax of the not equal to operator is: =IF (cellname <> condition, result 1, result 2) False. rev 2020.12.4.38131, Stack Overflow works best with JavaScript enabled, Where developers & technologists share private knowledge with coworkers, Programming & related technical career opportunities, Recruit tech talent & build your employer brand, Reach developers & technologists worldwide, If it's based on the difference of two cells, then why are you checking only one cell? P (-1.3 less than or equal to Z less . Why can't we use the same tank to hold fuel for both the RCS Thrusters and the Main engine for a deep-space mission? =B3<>A3 This will make excel validate if the value that is in the second cell does not match the value of the second cell. The zero-product property is also known as the rule of zero product, the null factor law, the multiplication property of zero, the nonexistence of nontrivial zero divisors, or one of the two zero-factor properties. If you want to do something specific when a cell equals a certain value, you can use the IF function to test the value, then do something if the result is TRUE, and (optionally) do … Excel's \"does not equal\" operator is simple: a pair of brackets pointing away from each other, like so: \"<>\". If a is not equal to b is not equal to 0 then show that points (a,a^2), (b,b^2) and (0,0) are not collinear - 3062351 The not equal to operator uses the greater than and less than signs together “<>” together. | 2021-05-12 12:19:51 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.464727520942688, "perplexity": 688.3353253918256}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989693.19/warc/CC-MAIN-20210512100748-20210512130748-00038.warc.gz"} |
https://space.stackexchange.com/questions/9543/how-much-thrust-to-launch-a-regulation-size-fifa-soccerball-into-orbit/14874 | # How much thrust to launch a regulation size FIFA soccerball into orbit
How much thrust is necessary to launch a regulation size FIFA soccer ball into orbit around the Earth? Let us assume a size 5 which weighs between 420g and 450g. Remember, we will need thrust to ensure the ball will continue until the minimum altitude and orbital velocity have been attained otherwise it will fall back to the Earth. Minimum altitude is rarely desirable, therefore thrust must continue to be generated to gain additional orbital altitude.
Also, would the ball explode from the air pressure?
• Hi Quant7, welcome to Space Exploration. There are many ways this questions could be interpreted. You need to be more specific about what you want to know. I have a feeling it would be helpful for you to look at the basics of how this works to better define the nature of your question. Thrust occurs over time and varies during different stages of a launch, and the launch vehicle is the main determinant of how much energy is consumed. Try looking at this nasa.gov/pdf/153415main_Rockets_How_Rockets_Work.pdf – kim holder Jun 17 '15 at 4:01
• Given the answer provided, I am voting to reopen the question. I think it is clear what the OP is asking. If the question is in scope would be a different close vote. – James Jenkins Jun 17 '15 at 16:05
• – Peter Cordes Dec 29 '19 at 2:58
This is a hideously impractical undertaking. Most of the mass of an orbital rocket is fuel and the tanks to hold it; even though your payload is tiny, all the rest of that stuff is big. The smaller a rocket is, the harder it is to design it with the high fuel-mass-to-dry-mass ratio that is required to attain high speeds, because some elements (like electronics) don't scale with the size of the rocket.
Depending on what design assumptions you make, you will get wildly different results. Some arbitrary examples:
Scenario 1: two stage solid rocket, 90% propellant fraction. Stage 1: 700kN thrust, 240s sea level Isp, 40 tons propellant. Contributes 3886 m/s ∆v. Stage 2: 80kN thrust, 280s vacuum Isp, 5 tons propellant. Contributes 6581 m/s ∆v.
Scenario 2: single stage kerosene/LOX rocket using the SpaceX Kestrel engine, fuel tanks whittled by hand from carbon fiber by a team of elves on Adderall, total dry mass 100kg, of which the rocket motor is half. 96% propellant fraction, 2.4 tons of propellant, 31kN thrust, 317s vac Isp, total ~9600 m/s ∆v. (At the end of the burn for the Kestrel option, the rocket would be accelerating at better than 30g, so I hope those elves know what they're doing!) I don't think this is actually plausible, but it's theoretically possible.
And a real world example.
Scenario 3: Vanguard 1/TV-4 was a 3-stage rocket that put a satellite into orbit that weighed only about 3 soccer balls. First stage thrust 135kN. From my brief research, Vanguard and the Japanese 4-stage solid-rocket Lambda 4S seem to be the two smallest orbital launchers in history.
So depending on how you tweak the other variables, the needed thrust could be anywhere from 31kN to 700kN.
As for the ball, FIFA regulations say the air pressure in a soccer ball needs to be between 8.5 psi and 15.6 psi (above ambient), so presumably it can handle somewhat more pressure than that without exploding. Sea level ambient air pressure is about 15 psi, so if you deflated the ball before launch (to ambient air pressure), then took it into vacuum, it would then be at 15 psi overpressure - the high end of regulation inflation, so a very taut ball, but not exploded.
• A very interesting take... I really wasn't sure what to do with this question and would be interested to know what the asker gets out of your answer. Good relevant info that just swallows the whole big scope of it and tries to play with it enough to get something across. – kim holder Jun 17 '15 at 4:07
• There are a lot of questions on here where my initial response is really, "well, why do you ask?" Any excuse to bust out my delta-v spreadsheet, though... – Russell Borogove Jun 17 '15 at 4:08
• For such a small rocket, the fuel cost should be almost negligible; it may make sense to use Syntin and get extra performance for just a few thousand dollars per rocket (if it's not significantly more expensive to produce on these small scales). – lirtosiast Jun 22 '15 at 0:08
• Also, have you considered air drag? space.stackexchange.com/a/750/10547 suggests it would cost on the order of 23.7*cbrt(333 t/2.5 t) = ~125 m/s, assuming the same shape as the Falcon 9, which is small but significant. It would really be more, since the Falcon 9 shape probably can't be achieved with that absurd propellant fraction. – lirtosiast Jun 22 '15 at 0:15
• Syntin has only about a 3% ISP advantage over kerosene. This is all very gross back-of-the-envelope analysis, using a target total ∆v of roughly 10,000 m/s. Note that drag cost is higher for smaller rockets given the same shape -- Saturn V/Apollo lost only about 50m/s to drag despite being a less streamlined shape than F9 -- so our little soccer ball lofter will probably lose quite a bit more. – Russell Borogove Jun 22 '15 at 0:23
Taking the question literary; If you have a "thrust" pushing the ball, the only limiting factor is to manage to get off the ground. g ($9.81 m/s^2$) times 420-450grams is 4.16 to 4.46 Newtons. Why there is such a force acting on the ball in the first place seems to be outside the scope of the question. | 2021-01-16 15:24:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.584450364112854, "perplexity": 1434.7425268029965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703506697.14/warc/CC-MAIN-20210116135004-20210116165004-00430.warc.gz"} |
http://math.gatech.edu/courses/math/4318 | ## Analysis II
Department:
MATH
Course Number:
4318
Hours - Lecture:
3
Hours - Lab:
0
Hours - Recitation:
0
Hours - Total Credit:
3
Typical Scheduling:
Every spring and fall semesters
Differentiation of functions of one real variable, Riemann-Stieltjes integral, the derivative in R^n and integration in R^n
Prerequisites:
Course Text:
Bartle, Elements of Real Analysis
Topic Outline:
• The derivative: mean value theorem, L'Hôpital's rule, Taylor's theorem
• The Riemann Stieltjes integral, integration by parts, change of variables. Sets of measure zero, Cantor functions
• Improper integrals
• The derivative in Rn: Jacobians, chain rule, implicit and inverse function theorems. Extrema, second derivative tests, Lagrange multipliers
• Integration in Rn: Mean value theorem, iterated integrals, and change of variables. Sets of measure zero and Sard's theorem | 2018-07-22 18:33:34 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9077283143997192, "perplexity": 4453.7030258669765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593438.33/warc/CC-MAIN-20180722174538-20180722194538-00308.warc.gz"} |
https://www.esaral.com/tag/gravitation-important-questions/ | Important Questions of Gravitation Class 11 Physics: Fully Solved
Class 9-10, JEE & NEET
1,00,000+ learners
Get important questions of Gravitation Class 11 with their answers. View 11th Physics important questions for exam point of view. These important questions of gravitation will play significant role in clearing concepts of Physics class 11 as well as in revision of 12th students. This question bank is designed by NCERT keeping NCERT in mind and the questions are updated with respect to upcoming Board exams. You will get here all the important questions of other chapters along with other chapters of class 11 Physics with their proper solutions.
So in this article we have provided solved important questions of Gravitation chapter that will help class 11 and 12 students.
Click Here for Detailed Notes of Gravitation along with other subjects and chapters.
Q. Do the force of friction and other contact force arise because of gravitational force? If not, what is the origin of these forces?
Sol. The force of friction or any other contact forces, may be quite large and so it does not arise because of weak gravitational attraction. Such forces have electrical origin.
Q. Charge can be shielded from electrical forces by putting it inside a hollow conductor. Can a body be shielded from gravitational influence of nearby matter by putting it inside hollow sphere or by some other means?
Sol. No, a body can not be shielded from the gravitational field of nearby matter by any method.
Q. The value of g on moon is $1 / 6$ th of that of earth. If a body is taken from earth to moon, then what will the change in its weight, Inertial mass and Gravitational mass.
Sol. The weight of body on moon will be $1 / 6$ th of that on the earth, but there will be no change in gravitational mass and inertial mass.
Q. If the earth stops rotating about its axis, what will be the effect on the value of $^{\circ} \mathrm{g}^{\prime} ?$ Will this effect be same at all places?
Sol. The value of will increase at all places except at the poles. The increase will be different at different places, maximum at equator.
Q. Can we determine the gravitational mass of a body inside on artificial satellite?
Sol. No, artificial satellite is like a freely falling body so that $g=0 .$
Q. The astronauts in a satellite orbiting the earth feel weightlessness. Does the weightlessness depend upon the distance of satellite from earth?
Sol. No, the gravitational acceleration of the astronaut w.r.t. satellite is zero, whatever be the distance of the satellite from earth.
Q. If the kinetic energy of a satellite revolving in an orbit close to earth happens to be doubled, will the satellite escape?
Sol. The velocity of satellite will become equal to the escape velocity, hence it will escape.
Q. When an object falls to the ground, the earth moves up to it. Why is earth’s motion not noticeable?
Sol. Because action and reaction are equal and opposite, hence the force with which earth is attracted towards the object is equal to the force with which earth attracts the object. $(-m g, m$ is the mass of the object). If $a^{\prime}$ be the acceleration produced in earth and $M$ is the mass of earth, then $a=\frac{m g}{M}$ As $M>>m,$ hence $a<<g$ i.e. acceleration produced in earth is so small that it is not noticeable.
Q. An artificial satellite revolves in its orbit around the earth without using any fuel. But aeroplane requires fuel to fly at a certain height. Why so?
Sol. Air is required for aeroplane to fly hence the aeroplane requires fuel against the frictional force due to air. On the other hand, the satellite orbits at a much more height where almost no air is present and its friction in negligible.
Q. An elephant and an ant are to be projected out of earth into space. Do we need different velocities to do so?
Sol. The escape velocity $v_{e}=\sqrt{2 g R}$ does not depend upon the mass of the projectile. Thus we need the same velocity to project an elephant and an ant into space.
Q. Why are space rockets usually launched from west to east in the equatorial plane?
Sol. since earth rotates from west to east and as such all points on the earth have velocity from west to east. Moreover, this velocity is maximum in the equatorial plane as . This maximum velocity is added to the launching velocity of the rocket and hence launching becomes easier.
Q. Does a rocket really need the escape velocity of
$11.2 \mathrm{km} / \mathrm{s}$ initially to escape from the earth?
Sol. No, rocket can have any velocity at the start. The rocket can continue to increase the velocity due to thrust provided by the escaping gases that will carry it to a desired position.
Q. Does a planet revolving around sun in an elliptical orbit have a constant
(i) Linear speed
(ii) Angular momentum
(iii) Kinetic energy
(iv) Potential energy
(v) Total energy throughout its orbit
Sol. (i) According to the law of conservation of angular momentum, the planet moves faster when it is close to the sun and moves slower when it is farther away from the sun. Hence linear speed of the planet does not remain constant.
(ii) According to the law of conservation of angular momentum, the angular momentum of planet remains constant.
(iii) Since linear speed of the planet around the sun changes, therefore, its kinetic energy also changes continuously.
(iv) Potential energy depends upon the distance between sun and planet, hence potential energy changes as the distance between the sun and
planet changes continuously.
(v) Total energy of planet remains constant.
Q. In a spaceship moving in gravity free region, the astronaut will not be able to distinguish between up and down. Explain.
Sol. The upward and downward sense is due to gravitational force of attraction between the body and the earth. In spaceship gravitational force is counter balanced by the centripetal force needed by satellite to move around the earth in circular orbit. Hence in absence of force, the astronaut will not be able to distinguish between up and down.
Q. What do you understand by geo-stationary and polar satellites. Discuss their important uses.
Sol. Geo-stationary or Geo-synchronous satellite : A satellite which appears stationary to an observer on earth is called geo-stationary satellite. Obviously, the velocity of such satellite relative to earth is zero. Clearly time of revolution of satellite hrs. This satellite is also called geo-synchronous satellite as its angular velocity is synchronised with angular speed of earth about its axis. i.e. this satellite revolves around the earth with same angular speed in same direction as is done by earth around its axis.
Essential conditions for geo-stationary satellite: (a) A geo-stationary satellite should be at a height of nearly $36,000 \mathrm{km}$ above the equator of earth.
(b) The period of revolution around the earth should be the same as that of earth about its axis i.e. exactly 24 hours.
(c) It should revolve in an orbit concentric and co- planer with the equatorial plane, so the plane of orbit of the satellite in normal to the axis of rotation of the earth.
(d) Its sense of rotation should be same as that of earth about its own axis i.e. from west to east. Its orbital velocity is nearly 3.1 $k m /$ sec.
Uses : Geo-stationary satellites are used for purposes of communications as they act as reflectors of suitable waves carrying the messages. Hence they are also called telecommunication satellites. India’s INSAT- $2 \mathrm{B}, 2 \mathrm{C}$ are communication satellites.
Polar satellites : Such satellite which revolves in polar orbit around the earth is called polar satellites. A polar orbit is one whose angle of inclination with equatorial plane of earth is $90^{\circ}$ and a satellite in polar orbit passes over the both north and south geographic poles respectively once in orbit.
A single polar satellite can monitor $100 \%$ earth’s surface. Every locations on earth lies within the observation of polar satellite twice each day.
These satellites are used for remote sensing and hence are called remote sensing satellites.
Uses : In India remote sensing satellites (IRS-IA, IRS- – $1 \mathrm{B},$ IRS- $1 \mathrm{C}$ ) are being used to collect the data for following purposes
(i) For ground water survey.
(ii) For detection the areas under forest.
(iii) For preparing wasteland maps.
(iv) For assessment of drought.
(v) For the assessment of crop diseases.
(vi) For detecting the potential fishing zones.
(vii) For identifying the sources of pollution.
(viii) To locate the position and movement of the troops of enemy and to locate the place and time for any nuclear explosion etc. i.e. for spying purposes.
Q. State Kepler’s laws of planetary motion and explain the deduction of Kepler’s second law and third law of planetary motion.
Sol. On the basis of his investigations, Kepler formulated the following three laws of planetary motion:
(i) First law (law of orbit): Every planet revolves around the sun in an elliptical orbit, keeping sun at one focus of ellipse.
(ii) Second law (Law of area): The radius vector drawn from sun to a planet sweeps out equal areas in equal intervals of time. i.e. areal velocity of the planet around the sun is constant.
(iii) Third law (Law of period): The square of time period of revolution of a planet around the sun is directly proportional to the cube of semi major axis of its elliptical orbit i.e. $T^{2} \propto R^{3}$ Deduction of second law: Let a particle rotates in $X-Y$ plane about $z$ -axis. At any time $t, \overrightarrow{O P}=\vec{r},$ be the position vector of particle. The area swept by the position vector in small time $d t,$ $|d \vec{A}|=$ area of $\Delta O P Q=\frac{1}{2}|\vec{r} \times d \vec{r}|$
since, a planet revolves around the sun, in an elliptical orbit under the influence of gravitational pull of sun on planets and this pull (or force) acts along the line joining the centres of the sun and theplanet and is directed towards the sun. Hence, the torque acting on planet is zero.
i.e. areal velocity of the planet around the sun is constant, which is second law of planetary motion. Deduction of third law : Let a planet of mass $^{\circ} \mathrm{m}^{\prime}$ is orbiting around the sun of mass $M$ in a circular orbit of radius $^{\circ} r^{\prime}$ with constant angular velocity $\omega,$ then,
$\frac{G M m}{r^{2}}=m \omega^{2} r=m\left(\frac{2 \pi}{T}\right)^{2} r \Rightarrow T^{2}=\left(\frac{4 \pi^{2}}{G M}\right) r^{3}$
i.e. $T^{2} \propto r^{3} \quad\left(\because \frac{4 \pi^{2}}{G M}=\text { constant }\right)$
Above result holds equally good for elliptical orbit provided we replace $r$ with $^{*} a^{\prime},$ the semi major axis of ellipse.
eSaral provides you complete edge to prepare for Board and Competitive Exams like JEE, NEET, BITSAT, etc.
We have transformed classroom in such a way that a student can study anytime anywhere. With the help of AI we have made the learning Personalized, adaptive and accessible for each and every one.
Visit eSaral Website to download or view free study material for JEE & NEET.
Also get to know about the strategies to Crack Exam in limited time period. | 2020-09-23 01:19:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6844545006752014, "perplexity": 546.9047201068539}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400208095.31/warc/CC-MAIN-20200922224013-20200923014013-00272.warc.gz"} |
http://community.worldheritage.org/articles/eng/High-energy_physics | # High-Energy Physics
### High-Energy Physics
For particles in computer graphics, see Particle system.
Particle physics is a branch of physics which studies the nature of particles that are the constituents of what is usually referred to as matter and radiation. In current understanding, particles are excitations of quantum fields and interact following their dynamics. Although the word "particle" can be used in reference to many objects (e.g. a proton, a gas particle, or even household dust), the term "particle physics" usually refers to the study of the fundamental objects of the universe – fields that must be defined in order to explain the observed particles, and that cannot be defined by a combination of other fundamental fields. The current set of fundamental fields and their dynamics are summarized in a theory called the Standard Model, therefore particle physics is largely the study of the Standard Model's particle content and its possible extensions.
## Subatomic particles
Modern particle physics research is focused on subatomic particles, including atomic constituents such as electrons, protons, and neutrons (protons and neutrons are composite particles called baryons, made of quarks), produced by radioactive and scattering processes, such as photons, neutrinos, and muons, as well as a wide range of exotic particles. To be specific, the term particle is a misnomer from classical physics because the dynamics of particle physics are governed by quantum mechanics. As such, they exhibit wave-particle duality, displaying particle-like behavior under certain experimental conditions and wave-like behavior in others. In more technical terms, they are described by quantum state vectors in a Hilbert space, which is also treated in quantum field theory. Following the convention of particle physicists, elementary particles refer to objects such as electrons and photons as it is well known that those types of particles display wave-like properties as well.
Types Generations Antiparticle Colors Total 2 3 Pair 3 36 2 3 Pair None 12 1 1 Own 8 8 1 1 Pair None 2 1 1 Own None 1 1 1 Own None 1 1 1 Own None 1 61
All particles, and their interactions observed to date, can be described almost entirely by a quantum field theory called the Standard Model.[1] The Standard Model has 61 elementary particles.[2] Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s. The Standard Model has been found to agree with almost all the experimental tests conducted to date. However, most particle physicists believe that it is an incomplete description of nature, and that a more fundamental theory awaits discovery (See Theory of Everything). In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model.
## History
The idea that all matter is composed of elementary particles dates to at least the 6th century BC.[3] The philosophical doctrine of atomism and the nature of elementary particles were studied by ancient Greek philosophers such as Leucippus, Democritus, and Epicurus; ancient Indian philosophers such as Kanada, Dignāga, and Dharmakirti; Muslim scientists such as Ibn al-Haytham, Ibn Sina, and Mohammad al-Ghazali; and in early modern Europe by physicists such as Pierre Gassendi, Robert Boyle, and Isaac Newton. The particle theory of light was also proposed by Ibn al-Haytham, Ibn Sina, Gassendi, and Newton. Those early ideas were founded through abstract, philosophical reasoning rather than experimentation and empirical observation.
In the 19th century, John Dalton, through his work on stoichiometry, concluded that each element of nature was composed of a single, unique type of particle. Dalton and his contemporaries believed those were the fundamental particles of nature and thus named them atoms, after the Greek word atomos, meaning "indivisible".[4] However, near the end of that century, physicists discovered that atoms are not, in fact, the fundamental particles of nature, but conglomerates of even smaller particles. The early 20th-century explorations of nuclear physics and quantum physics culminated in proofs of nuclear fission in 1939 by Lise Meitner (based on experiments by Otto Hahn), and nuclear fusion by Hans Bethe in that same year. Those discoveries gave rise to an active industry of generating one atom from another, even rendering possible (although it will probably never be profitable) the transmutation of lead into gold; and, those same discoveries also led to the development of nuclear weapons. Throughout the 1950s and 1960s, a bewildering variety of particles were found in scattering experiments. It was referred to as the "particle zoo". That term was deprecated after the formulation of the Standard Model during the 1970s in which the large number of particles was explained as combinations of a (relatively) small number of fundamental particles.
## Standard Model
Main article: Standard Model
The current state of the classification of all elementary particles is explained by the Standard Model. It describes the strong, weak, and electromagnetic fundamental interactions, using mediating gauge bosons. The species of gauge bosons are the gluons, , and the photons.[1] The Standard Model also contains 24 fundamental particles, (12 particles and their associated anti-particles), which are the constituents of all matter.[5] Finally, the Standard Model also predicted the existence of a type of boson known as the Higgs boson. Early in the morning on July 4, 2012, physicists with the Large Hadron Collider at CERN announced they have found a new particle that behaves similarly to what is expected from the Higgs boson.[6]
Quarks and electrons were before this discovery not considered to be composed of other particles. However, with the discovery and verification of the existence of the Higgs boson, which gives other particles their mass, this belief has been changed.
## Experimental laboratories
In particle physics, the major international laboratories are located at the:
Many other particle accelerators do exist.
The techniques required to do modern, experimental, particle physics are quite varied and complex, constituting a sub-specialty nearly completely distinct from the theoretical side of the field.
## Theory
Theoretical particle physics attempts to develop the models, theoretical framework, and mathematical tools to understand current experiments and make predictions for future experiments. See also theoretical physics. There are several major interrelated efforts being made in theoretical particle physics today. One important branch attempts to better understand the Standard Model and its tests. By extracting the parameters of the Standard Model, from experiments with less uncertainty, this work probes the limits of the Standard Model and therefore expands our understanding of nature's building blocks. Those efforts are made challenging by the difficulty of calculating quantities in quantum chromodynamics. Some theorists working in this area refer to themselves as phenomenologists and they may use the tools of quantum field theory and effective field theory. Others make use of lattice field theory and call themselves lattice theorists.
Another major effort is in model building where model builders develop ideas for what physics may lie beyond the Standard Model (at higher energies or smaller distances). This work is often motivated by the hierarchy problem and is constrained by existing experimental data. It may involve work on supersymmetry, alternatives to the Higgs mechanism, extra spatial dimensions (such as the Randall-Sundrum models), Preon theory, combinations of these, or other ideas.
A third major effort in theoretical particle physics is string theory. String theorists attempt to construct a unified description of quantum mechanics and general relativity by building a theory based on small strings, and branes rather than particles. If the theory is successful, it may be considered a "Theory of Everything".
There are also other areas of work in theoretical particle physics ranging from particle cosmology to loop quantum gravity.
This division of efforts in particle physics is reflected in the names of categories on the arXiv, a preprint archive:[16] hep-th (theory), hep-ph (phenomenology), hep-ex (experiments), hep-lat (lattice gauge theory).
## Practical applications
In principle, all physics (and practical applications developed therefrom) can be derived from the study of fundamental particles. In practice, even if "particle physics" is taken to mean only "high-energy atom smashers", many technologies have been developed during these pioneering investigations that later find wide uses in society. Cyclotrons are used to produce medical isotopes for research and treatment (for example, isotopes used in PET imaging), or used directly for certain cancer treatments. The development of Superconductors has been pushed forward by their use in particle physics. The World Wide Web and touchscreen technology were initially developed at CERN.
Additional applications are found in medicine, national security, industry, computing, science, and workforce development, illustrating a long and growing list of beneficial practical applications with contributions from particle physics.[17]
## Future
The primary goal, which is pursued in several distinct ways, is to find and understand what physics may lie beyond the standard model. There are several powerful experimental reasons to expect new physics, including dark matter and neutrino mass. There are also theoretical hints that this new physics should be found at accessible energy scales. Furthermore, there may be surprises that will give us opportunities to learn about nature.
Much of the effort to find this new physics are focused on new collider experiments. The Large Hadron Collider (LHC) was completed in 2008 to help continue the search for the Higgs boson, supersymmetric particles, and other new physics. An intermediate goal is the construction of the International Linear Collider (ILC), which will complement the LHC by allowing more precise measurements of the properties of newly found particles. In August 2004, a decision for the technology of the ILC was taken but the site has still to be agreed upon.
In addition, there are important non-collider experiments that also attempt to find and understand physics beyond the Standard Model. One important non-collider effort is the determination of the neutrino masses, since these masses may arise from neutrinos mixing with very heavy particles. In addition, cosmological observations provide many useful constraints on the dark matter, although it may be impossible to determine the exact nature of the dark matter without the colliders. Finally, lower bounds on the very long lifetime of the proton put constraints on Grand Unified Theories at energy scales much higher than collider experiments will be able to probe any time soon. | 2017-04-28 22:01:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5440094470977783, "perplexity": 725.0497039807141}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123097.48/warc/CC-MAIN-20170423031203-00148-ip-10-145-167-34.ec2.internal.warc.gz"} |