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https://www.freemathhelp.com/forum/threads/110350-Elliptical-frustum-s-height-Vol-is-V-(1-3)*pi*-(a*b)*(bh-b-d)-(c*d)*-(bh-b-d)-h | # Thread: Elliptical frustum's height? Vol. is V=(1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}
1. ## Elliptical frustum's height? Vol. is V=(1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}
For
an elliptical frustum that has the following values:
h-height
The Volume is calculated using:
V = (1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}
What would be the formula for finding height:
h = ?
2. Originally Posted by eimimitu
For
an elliptical frustum that has the following values:
h-height
The Volume is calculated using:
V = (1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}
What would be the formula for finding height:
h = ?
First thing I would do is to draw a sketch and locate those given parameters on the sketch.
Then tell us what did you find?
3. Originally Posted by eimimitu
For
an elliptical frustum that has the following values:
h-height
The Volume is calculated using:
V = (1/3)*pi*{(a*b)*(bh/b-d) - (c*d)*[(bh/b-d)-h]}
What would be the formula for finding height:
h = ?
I don't trust the formula as given, for several reasons.
First, it looks as if you omitted some essential parentheses, e.g. around "b-d".
But more important, the volume should be proportional to h, and this is not apparent as I would expect in any reasonably derived formula.
But if the formula is correct, then the answer would be found by "just" solving for h. Try factoring out h!
4. ## Factoring h
Originally Posted by Dr.Peterson
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I don't trust the formula as given, for several reasons.
First, it looks as if you omitted some essential parentheses, e.g. around "b-d".
But more important, the volume should be proportional to h, and this is not apparent as I would expect in any reasonably derived formula.
But if the formula is correct, then the answer would be found by "just" solving for h. Try factoring out h!
Thank you for pointing this out... yes the b-d should be in parenthesis on both instances...
That's the thing I'm having trouble with is factoring out the h.. I have tried several ways but I get stuck in a loop of passing the "h" back and forth from the equal sign.
I start with this: 3V/pi=(ab)(bh/(b-d))-(cd)(bh/(b-d))-h).. but kinda lost after that.
5. Originally Posted by eimimitu
Thank you for pointing this out... yes the b-d should be in parenthesis on both instances...
That's the thing I'm having trouble with is factoring out the h.. I have tried several ways but I get stuck in a loop of passing the "h" back and forth from the equal sign.
I start with this: 3V/pi=(ab)(bh/(b-d))-(cd)(bh/(b-d))-h).. but kinda lost after that.
3V/π=(ab)(bh/(b-d))-(cd)(bh/(b-d))-h)
3V/π=[h * {ab2/(b-d) - (cd)(b/(b-d))-1)}]
6. ## Factoring h
I thought I would make the proper correction to this for the next guy that needs it
There were some errors in the formula as pointed out by Dr. Peterson(thank you).. below is the corrected one. (
π
represents pi... [thank you
Subhotosh Khan]
)
V = (1/3)
π
( (ab) (
bh/(b-d))
- (cd) (
(bh/(b-d))
-h ) )
I solved for h like this:
h = 3V / (cd
π) ( ab2 / (b-d)(bd) ) - ( ( b / (b-d) ) - 1 )
It finally clicked thanks to both of your tips so a very enthusiastic thank you!
7. ## yet another correction...
those **** parenthesis...
h = 3V / (cdπ) [( ab2 / (b-d)(bd) ) - ( ( b / (b-d) ) - 1 )]
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• | 2018-09-19 07:05:02 | {"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": 0.805969774723053, "perplexity": 2218.88109950026}, "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-2018-39/segments/1537267155942.15/warc/CC-MAIN-20180919063526-20180919083526-00325.warc.gz"} |
https://benslack19.github.io/data%20science/statistics/prior-and-beta/ | # Bayes-ball part 2: a more realistic prior
I meant to post this some time ago, but I have been busy. But with the baseball example I am using, it is only fitting that I post this now, just after this year’s strange timing of the start of Major League Baseball’s season. (My team had a nice opening day win!)
In my last post, I applied Bayes’ theorem towards revealing a hypothetical player’s probability distribution for their hit rate after observing their performance for a given time. Essentially, we found the player’s posterior distribution. However, because the prior was a Bernoulli distribution, so was the resulting posterior. This is not realistic. We would instead expect the distribution to appear Gaussian. (I emphasize “appear” for reasons you will see down below.) A Bernoulli distribution also does not really allow us to apply the concept of a credible interval. Going down this Bayesian rabbit hole, I became more interested in some of the concepts and went back through some old notes. I examine this question in a few posts. Here, let’s focus on using a different, more realistic prior!
First, a few shout-outs to some sources I referenced when writing this post.
# Load packages for coding examples
import pandas as pd
import numpy as np
from scipy.stats import binom
import matplotlib.pyplot as plt
import seaborn as sns
from scipy.stats import beta
from scipy.stats import binom
from scipy.stats import norm
sns.set_context('talk') # visual theme
I won’t restate the whole problem, but you can find it in the previous post if you need a reminder.
What if we weren’t asking for a single probability if Aguila was in the 10% hit rate group versus the 25% hit group? What if we asked where Aguila’s batting average (hitting rate) would be across a range of talent levels? Let’s take these steps in a couple of iterations. First, let’s take the original Bernoulli distribution example and show how the prior distribution gets updated with data to produce the posterior distribution. I show this differently than I did in the last post.
# Using a Bernoulli distribution as the prior
f, ax1 = plt.subplots()
ax1.bar([0, 1], [0.6, 0.4], color='k', alpha=0.5)
ax1.set_xticks([0,1])
ax1.set_xticklabels(['T10', 'T25'])
ax1.set_ylabel('probability')
ax1.set_title('prior distribution');
Now let’s add in the data of 18 hits in 100 at-bats.
# T10 group
n, p10 = 100, 0.1
rv10 = binom(n, p10)
# T25 group
n, p25 = 100, 0.25
rv25 = binom(n, p25)
posterior_p10 = (rv10.pmf(18) * 0.6) / ((rv10.pmf(18) * 0.6) + (rv25.pmf(18) * 0.4))
posterior_p25 = (rv25.pmf(18) * 0.4) / ((rv10.pmf(18) * 0.6) + (rv25.pmf(18) * 0.4))
print("Posterior probability for T10 group: {0:0.4f}".format(posterior_p10))
print("Posterior probability for T25 group: {0:0.4f}".format(posterior_p25))
Posterior probability for T10 group: 0.2428
Posterior probability for T25 group: 0.7572
f, ax1 = plt.subplots(figsize=(6,6))
ax1.bar([0, 1], [0.6, 0.4], width=0.5, color='k', alpha=0.5, label='prior')
ax1.bar([0.25, 1.25], [posterior_p10, posterior_p25], width=0.5, color='r', alpha=0.5, label='posterior')
ax1.set_xticks([0,1])
ax1.set_xticklabels(['T10', 'T25'])
ax1.set_ylabel('probability')
ax1.set_title('prior and posterior distributions')
ax1.legend();
Note how even though we calculated the posterior values for both, we could have easily just taken 1 - the probability of the T25 group. Now let’s apply the same process but using a different, more realistic prior distribution.
# Using a more realistic prior: the beta distribution
I mentioned above how we’d expect the prior and resulting distributions to appear Gaussian. I started with a normal distribution as my prior but realized that this would not work. That is because the Gaussian is not “conjugate” to the binomial (the distribution of the data), meaning they’re not in the same family. The math gets wonky if we try to multiply the data (the likelihood function) with a prior that is not in the same family. Here is nice diagram of related distributions. (We’ll actually carry out this math in a later post.)
This post, also from David Robinson, helped me better understand the beta distribution and how it could be used in this problem. The beta distribution is parameterized by $\alpha$ and $\beta$. Here is the probability density function (PDF) of the beta distribution
$\frac{x^{\alpha-1}(1-x)^{\beta-1}}{\mathrm{B}(\alpha,\beta)}$
where
${\mathrm{B}(\alpha,\beta)} = \frac{\Gamma(\alpha)\Gamma(\beta)}{\Gamma(\alpha+\beta)}$.
You can see that how looking at the numerator of the PDF how the beta distribution relates to Bernoulli and binomial distributions. One easy way to think about the beta distribution’s parameters is that $\alpha$ represents the counts of “1’s” and $\beta$ represents the counts of “0’s”.
To generate a prior, I need to set the values of $\alpha$ and $\beta$ but what should I choose? I decided to use some constraints of the original problem. Let’s say that the true talent rates of 10% and 25% are not the only values we would consider, but instead we can say that they are the bounds of the prior and posterior distributions. This makes the mean straightforward to identify: we just take the midpoint between these two values.
# mu is the midpoint between the two talent rates of the original problem
mu = (.25-0.1)/2 + 0.1
print("mu value: ", mu)
mu value: 0.175
However, as noted above, the mean itself is not a parameter of a beta distribution, but rather a result of it. We still need to choose $\alpha$ and $\beta$. Since the mean of a beta distribution is $\frac{\alpha}{\alpha + \beta}$, many values can theoretically work. For example, $\alpha$ and $\beta$ values of 3.5 and 16.4, respectively, but so can 175 and 825. Let’s plot a few different values of $\alpha$ and $\beta$ that use this mean. (I’m limiting the x-axis limit of the plot to 0.5 for visibility purposes.)
# Generate different values of alpha (a) and beta (b)
total_ab_list = [20, 50, 100, 200]
f, ax1 = plt.subplots(figsize=(12,6))
for total_ab in total_ab_list:
#a = round(mu*total_ab)
a = (mu*total_ab)
b = total_ab-a
x = np.linspace(beta.ppf(0.00, a, b),
beta.ppf(1.00, a, b), 100)
this_label = 'pdf for (' + str(a) + ', ' + str(b) + ')'
ax1.plot(x, beta.pdf(x, a, b),
lw=1, label=this_label)
ax1.axvline(mu, lw=0.4, color='red', linestyle='dashed', label='mean')
ax1.set_title('beta distribution with mean 0.175\nwith different alpha and beta values')
ax1.set_xlim([0, 0.5])
ax1.set_xlabel('random variable x')
ax1.set_ylabel('PDF')
ax1.legend();
This visualization highlights a few things to note about the beta distribution examples.
1. These figures show distributions that are “Gaussian-like” and provides a range of realistic, true talent values that I sought. (I wondered about the differences and came across this post.)
2. The values on the y-axis seem to go high. However, since this is a PDF, the area under each of these curves equals 1 and since the random variable (x-axis) is a fraction that is necessarily less than 1, the y-values are high to “compensate”.
3. You can see that these different examples can all have the same mean, but can vary quite a bit in their maximum and where most of their distribution mass is located. The blue line is particularly different, with $\alpha$ and $\beta$ values of 3.5 and 16.5, shows it’s peak at 0.141.
4. Related to point 3 is that as the values of $\alpha$ and $\beta$ increase, the variance gets tighter. This lines up with intuition. The more previous information you have, the less uncertain your prior would be. (In fact, after an experiment is performed, the resulting posterior distribution can be used as a prior for the next experiment.)
Therefore, we can consider where we want the majority of the prior distribution values to lie when setting $\alpha$ and $\beta$. I stated above that we would like the lower and upper bounds of our random variable x to be 0.10 and 0.25. We can define these bounds to contain the central 95% of the probability distribution and choose $\alpha$ and $\beta$ that way (along with the mean of 0.175 as we figured above). Therefore, we can get the values of the random variable x for the lower bound at 0.025 and the upper bound at 0.975 using the quantile function by trying different $\alpha$ and $\beta$ values. This is called the prior predictive interval. We are predicting where we think the new data would lie.
# Generate different values of alpha (a) and beta (b)
total_ab_list = [25, 50, 75, 100, 125, 150, 200]
for total_ab in total_ab_list:
# Get credible interval
a = mu*total_ab
b = total_ab-a
print(beta.ppf([0.025, 0.975], a, b), total_ab, a, b)
[0.05601639 0.34279033] 25 4.375 20.625
[0.08394981 0.29058345] 50 8.75 41.25
[0.09829295 0.26808586] 75 13.125 61.875
[0.10738818 0.25490391] 100 17.5 82.5
[0.11382069 0.24601661] 125 21.875 103.125
[0.11868349 0.23951621] 150 26.25 123.75
[0.1256696 0.23048195] 200 35.0 165.0
We can see by looking at different values that an $\alpha$ and $\beta$ of 17.5 and 82.5 provide lower and upper bounds close to our desired values of 0.10 and 0.25.
As an aside, you may have noticed that the $\Gamma$ function was used as part of the equation when defining the PDF for the beta distribution. The $\Gamma$ function is often depicted as
$\Gamma(n) = (n-1)!$
I then wondered how decimal values for $\alpha$ and $\beta$, as we have found here, could work in a factorial. It turns out that the $\Gamma$ function extends what a factorial can do towards positive, non-integer values.
Great! We now have the parameters for our prior. I will call this $\alpha_{0}$ and $\beta_{0}$ going forward (or a0 and b0 in code). Let’s plot this on its own.
# Use a0 and b0 for our prior
total_ab = 100
a0 = mu*total_ab
b0 = total_ab-a0
print("a0, b0 values: ", a0, b0)
f, ax1 = plt.subplots(figsize=(12,6))
x = np.linspace(beta.ppf(0.000, a0, b0),
beta.ppf(1.000, a0, b0), 100)
this_label = 'pdf for (' + str(a0) + ', ' + str(b0) + ')'
lower_bound, upper_bound = beta.ppf([0.025, 0.975], a0, b0)
ax1.plot(x, beta.pdf(x, a0, b0), color='black',
lw=2, label=this_label)
ax1.axvline(lower_bound, lw=0.4, color='red', linestyle='dashed', label='lower bound')
ax1.axvline(upper_bound, lw=0.4, color='red', linestyle='dashed', label='upper bound')
ax1.axvline(mu, lw=0.5, color='black', linestyle='dashed', label='mean')
ax1.set_title('prior distribution: beta distribution with\nmean 0.175,alpha=17.5, beta=82.5')
ax1.set_xlim([0, 0.5])
ax1.set_xlabel('random variable x')
ax1.set_ylabel('PDF')
ax1.legend();
a0, b0 values: 17.5 82.5
Awesome. We now have a more realistic prior. The interval between the red lines (our lower and upper bounds) indicate our 95% predictive interval. How will this impact our posterior once we add in the data? That will be in the next post. See you there!
Categories:
Updated: | 2021-12-08 18:45:24 | {"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": 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": 0.8304118514060974, "perplexity": 1190.7013130165449}, "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-2021-49/segments/1637964363520.30/warc/CC-MAIN-20211208175210-20211208205210-00207.warc.gz"} |
http://watcut.uwaterloo.ca/webnotes/Metabolism/Glycogen.html | 8
# Glycogen metabolism
8.1
## Overview
In addition to gluconeogenesis, the reversible storage of glucose in the form of glycogen provides a second major mechanism of glucose homeostasis.
Glycogen is a branched glucose polymer that is found in many organs, but the largest quantities occur in the liver and in skeletal muscle. The liver can store up to 150–200 grams, which amounts to 10% of the organ’s wet weight. It draws from this reservoir to maintain the blood glucose concentration; glycogen plays a major role in day-to-day glucose homeostasis.
While skeletal muscle contains glycogen at much lower concentration than the liver, its much larger overall mass means that the absolute amount of glycogen stored there is approximately twice higher than in the liver. The contribution of muscle glycogen to glucose homeostasis is less well understood.
While liver and skeletal muscle store the lion’s share of glycogen, it also occurs in other organs such as the heart, the brain, and the kidneys. All of these organs may therefore be affected by glycogen storage diseases (see Section 8.6.
8.2
## Glycogen structure
8.2.1
### Why store glucose in polymeric form?
• The osmotic pressure is governed by the gas equation: $pV = nRT \: \Longleftrightarrow \: p = \frac{n}{V}RT \nonumber$
• Glycogen amounts to 10% of the liver’s wet weight, equivalent to 600 mM glucose
• When free, 600 mM glucose would triple the osmotic activity of the cytosol—liver cells would swell and burst
• Linking 2 (3, …) molecules of glucose divides the osmotic effect by 2 (3, …), permitting storage of large amounts of glucose at physiological osmolarity
The proportionality of concentration and osmotic activity does not strictly apply to large molecules, but the approximation is good enough for the present purpose.
8.2.2
### Covalent structure of glycogen
Glycogen consists of linear stretches of glucose residues connected by α-1→4-glycosidic bonds, with branches that are attached through α-1→6-glycosidic bonds. The entire tree-shaped polymer, or dendrimer, is rooted in a single molecule of the protein glycogenin.44 Each linear stretch contains approximately 13 glucose residues and, except of course for the outermost layer of the molecule, carries two branches of the same length that are attached 3–4 residues apart.
The structure of glycogen is similar to that of amylopectin (see slide 1.6.11). However, in glycogen, the density of branches is greater, which means that a glycogen molecule has a greater number of free ends than an amylopectin molecule of the same molecular weight. The number of free ends determines the possible rates of synthesis and breakdown, and the greater number of free ends in glycogen than in amylopectin reflects a difference in metabolic rates, which are higher in animals, particularly warm-blooded ones, than in plants.
8.2.3
### The size of glycogen particles is limited by crowding in the outer layers
According to the rules detailed in the preceding slide, the number of branches will double with each successive generational layer of the glycogen molecule. However, the amount of space available to those branches will only grow in proportion to the square of the particle radius or, approximately, the square of the number of generations. Taking into account the actual dimensions and architecture of the polymer, it has been calculated that in the 13th generation the required space would exceed the available space. Therefore, a glycogen molecule can contain no more than 12 generational layers. This implies that a single glycogen molecule can contain up to approximately 54,000 glucose residues; it will have a molecular weight of almost 107 Da and a diameter of approximately 25 nm [32].
Electron microscopy shows glycogen particles whose dimensions agree well with this theoretical maximum size of single molecules; these are referred to as β particles. In many tissues, variable numbers of β particles are found clustered into so-called α particles. Interestingly, α particles can be broken up with thiol-reducing agents, which implies that they are held together by disulfide bonds. Disulfides usually form between protein molecules. In addition to such scaffolding proteins, glycogen particles also contain a considerable number of enzymes and regulatory proteins [33], some of which will be discussed below.
8.2.4
### Glycogen is more loosely packed and more soluble than amylose
The above structural model of glycogen assumes a relatively loose packing of the glucose residues within the α-1→4-linked linear stretches. However, perfectly linear polyglucose—that is, amylose—adopts a much more densely packed helical structure. In this structure, more hydroxyl groups are engaged in hydrogen bonds with other glucose residues rather than with water; amylose therefore has low aqueous solubility.45
Unlike amylose, which mostly serves for long-term storage in plant bulbs and seeds, glycogen typically is degraded within hours of synthesis; this rapid turnover is facilitated by its loose structure. However, if branch formation breaks down, aberrant, condensed glycogen particles may arise that are no longer amenable to regular turnover. Various enzyme defects that interfere with branch formation cause the accumulation of such particles inside the cells; an example is the defect of the enzyme laforin in Lafora disease (see slide 8.6.4).
Aberrant glycogen particles also arise spontaneously in normal metabolism. The high density of polyglucose chains in the outermost layers of the glycogen molecule may interfere with the activity of branching enzyme and may promote tighter packing. Lysosomal glycogen degradation (see section 8.3.7) may have evolved as a pathway to dispose of such dysfunctional particles.46
8.3
Synthesis:
1. synthesis of an activated precursor, UDP-glucose, by UTP:glucose-1-phosphate uridylyltransferase
2. initiation of glycogen synthesis by glycogenin
3. introduction of branches by branching enzyme
4. chain elongation by glycogen synthase
5. repeat steps 3 and 4
1. depolymerization of linear strands by phosphorylase
2. removal of branches by debranching enzyme
3. repeat steps 1 and 2
This slide summarizes the enzyme reactions that occur in glycogen synthesis and degradation, respectively. As you can see, the regular, periodic structure of glycogen corresponds to similarly regular and periodic methods of synthesis and breakdown that require only a small number of different enzymes.
8.3.1
### Activation of glucose for glycogen synthesis
Both glycogenin and glycogen synthase use an activated form of glucose, UDP-glucose, which is formed from glucose-6-phosphate in two steps. Phosphoglucomutase first transforms glucose-6-phosphate to glucose-1-phosphate (1), which is then converted to UDP-glucose (2). The latter reaction requires uridine triphosphate (UTP) and releases pyrophosphate.47
The UDP-glucose that is used in the Leloir pathway of galactose degradation (slide 4.3.1) is derived in the same manner. UDP-glucose is also the precursor of UDP-glucuronic acid, which is used in the conjugation of bilirubin (section 17.4) and of xenobiotics (section 19.3).
8.3.2
### Overview of glycogen synthesis
Glycogenin is a small bifunctional protein that serves both as the starter substrate and the polymerase that synthesizes the initial linear strand of glucose residues. It begins the synthesis by attaching the initial glucose residue to a strategic tyrosine (Y194) side chain of itself, and then successively adds several more glucose residues to the sugar’s 4′ end.
The linear chain synthesized by glycogenin may contain up to ~12 glucose residues. This chain length would be long enough to serve as a substrate for branching enzyme, and it seems likely that the next step is indeed the introduction of the first branch. Alternatively, it is possible that the free end is first extended some more by glycogen synthase before branching occurs. In any event, after branching has occurred, glycogen synthase extends both of the two available 4′ ends. The remainder of the molecule is built through the alternating actions of branching enzyme and glycogen synthase; the cycle repeats until the glycogen reaches its inherent size limit at approximately 10 MDa (see slide 8.2.3).
The reactions performed by glycogenin itself and by glycogen synthase are equivalent. It is interesting to note that the carbon 1 of each glucose subunit is in the α-configuration both in UDP-glucose and in glycogen. What does this tell us about the mechanism of the reaction?
8.3.3
### A hypothetical reaction mechanism of glycogen synthase
Nucleophilic substitutions can occur either synchronously or asynchronously. In the first case, which is called the SN2 mechanism, one substituent leaves as the other arrives; each of them holds on to the same carbon atom with “half a bond” in the transition state. Most commonly, the incoming substituent attacks from the direction opposite to the position of the leaving substituent. With asymmetric carbons such as the C1 of α-D-glucose, this should result in a reversal to the β configuration. The α configuration may then be restored in a second substitution.
The hypothetical scheme in this slide illustrates such a double SN2 mechanism. The first substitution leads to a covalent intermediate with an active site glutamate, in which the C1 of glucose has been inverted to the β configuration. The subsequent nucleophilic attack by the activated C4′ hydroxyl group restores the α form.
8.3.4
### An alternative glycogen synthase mechanism
Double-substitution mechanisms similar to the one shown in the preceding slide are indeed employed by several glycosyltransferases, including glycogen phosphorylase and branching enzyme. However, with glycogen synthase itself, the evidence appears to favor a different mechanism that does not involve covalent catalysis by the enzyme, but instead a direct activation of both the C1 of the incoming glucose and the C4′ hydroxyl group of the preceding chain [34], as is depicted in simplified form in this slide. Note how the UDP that is released in the first step of the reaction assumes a catalytic role in the second step.
8.3.5
Glycogen degradation is brought about by phosphorylase and debranching enzyme. All glucose residues that are joined by α(1→4)-glycosidic bonds—that is, those in the straight segments—are released by glycogen phosphorylase. Most enzymes that cleave glycosidic bonds simply hydrolyze them; examples are intestinal amylase and β-galactosidase. In contrast, glycogen phosphorylase employs phosphate ions instead of water, and so produces glucose-1-phosphate rather than free glucose.48 Glucose-1-phosphate is then converted to the mainstream metabolite glucose-6-phosphate by phosphoglucomutase.
In the liver, which stores glycogen for the benefit of the entire body, the lion’s share of glucose-6-phosphate will be dephosphorylated by glucose-6-phosphatase and then released into the circulation; overall, this is equivalent to outright hydrolysis. However, muscle uses glycogen largely toward its own energy needs, and therefore glucose-6-phosphate will usually be funneled straight into glycolysis. In this case, the use of phosphorolysis instead of hydrolysis bypasses the hexokinase reaction, thereby saving one equivalent of ATP.49
Glycogen phosphorylase only degrades the chain ends to within four residues of a branching point. Then, debranching enzyme takes over and transplants the stub to another free end, where it becomes again a substrate for phosphorylase. However, this reaction leaves behind a single residue attached by a α(1→6)-glycosidic bond. This residue is subsequently released by the same enzyme as free glucose through hydrolysis.
8.3.6
### The reaction mechanism of phosphorylase
Glycogen phosphorylase uses pyridoxal phosphate (PLP) as a coenzyme. If you are familiar with the usual catalytic role of PLP, you may find this surprising; and indeed, phosphorylase employs it PLP a unique manner that bears no resemblance to its typical role in amino acid metabolism (see for example section 12.2). In those reactions, the organic ring of PLP, which is grayed out in this figure, functions as a reversible “electron sink.” In contrast, glycogen phosphorylase uses the phosphate group of PLP, which it deploys for acid-base catalysis to prime a free phosphate ion for attack on the terminal glycosidic bond of the glycogen substrate [35].
8.3.7
### Lysosomal glycogen disposal
• concerns a minor fraction of glycogen
• key enzyme: acid maltase; enzyme defect causes slow but inexorable glycogen accumulation
• possible role: disposal of structurally aberrant glycogen particles that have become “tangled up” during repeated cycles of glucose accretion and depletion
In liver cells, approximately 10% of all glycogen particles are found inside lysosomes [33], where they undergo slow degradation by acid maltase. This enzyme catalyzes the same reactions as intestinal amylase and maltase (see slide 1.6.12) but has an acidic pH optimum, in keeping with the acidic environment inside lysosomes (pH ~4.5). The lysosomal degradation pathway is important for the disposal of structurally aberrant glycogen particles; additional metabolic roles may exist but are currently not well understood. An enzyme defect for lysosomal maltase causes Pompe’s disease (slide 8.6.2).
8.4
## Regulation of glycogen metabolism
We have seen in slide 7.5.4 that phosphofructokinase and the complementary enzyme fructose-1,6-bisphosphatase are regulated by both intracellular and extracellular signals. The same applies to the key enzymes in glycogen metabolism.
8.4.1
### Allosteric regulation of glycogen synthase and phosphorylase
The allosteric regulatory effects exercised by glucose-6-phosphate, ATP and AMP on glycogen phosphorylase and glycogen synthase make good physiological sense. Depletion of ATP is an excellent reason to release glucose from the store in order to make some more. On the other hand, glucose-6-phosphate will be plentiful when glucose itself is abundant, and therefore signals an opportunity for replenishing the glycogen stores.
8.4.2
### Hormonal control of glycogen metabolism
Hormonal control of glycogen metabolism is similar to that of gluconeogenesis; the cascade shown here is identical to that shown in slide 7.5.4 all the way from the hormones to the activation of protein kinase A. The activated kinase directly phosphorylates glycogen synthase, which inactivates that enzyme. Protein kinase A indirectly stimulates glycogen breakdown by phosphorylation of a dedicated regulatory enzyme, phosphorylase kinase, which in turn phosphorylates glycogen phosphorylase.
Note that glycogen synthase and phosphorylase respond in opposite ways to phosphorylation: The synthase is inactivated, whereas the phosphorylase is activated.
8.4.3
### Regulatory differences between liver and muscle phosphorylase
Liver enzyme Muscle enzyme Inhibition by glucose + − Activation by Ca2+ − + Activation by AMP even when unphosphorylated − +
There are regulatory differences between glycogen phosphorylase in muscle and liver. Glucose inhibits the liver enzyme but not the muscle enzyme, and Ca2+ stimulates the muscle enzyme but not the liver enzyme. Recall that Ca2+ is also the trigger for muscle contraction; the simultaneous stimulation of glycogen breakdown therefore anticipates an increased demand for ATP.
As one would expect from their regulatory differences, the phosphorylases in liver and muscle are different molecules. Enzymes that catalyze the same reaction yet are separate molecules are referred to as isozymes. Although we usually don’t mention it, many other enzymes covered in this text occur as multiple isozymes, too.
8.5
## Interorgan relationships in glycogen metabolism
As stated above, the two tissues that have the most significant pools of glycogen are the liver and skeletal muscle. Liver glycogen is turned over rapidly; it serves as the major reserve of blood glucose during short-term fasts. Once liver glycogen is depleted, muscle glycogen can be drawn down; this, however, requires some roundabout metabolic trickery.
8.5.1
### Liver glycogen utilization
The liver mobilizes glucose from its glycogen store via glycogen phosphorylase and phosphoglucomutase, which yields glucose-6-phosphate. The latter is transported to the endoplasmic reticulum, where it is dephosphorylated. Glucose is taken back to the cytosol and released into the bloodstream.
Some of the glucose will be rephosphorylated before making it out of the cell, creating the futile cycle discussed in slide 7.5.2. However, the dominant glucose phosphorylating enzyme in the liver is glucokinase, which has fairly low affinity for glucose (see slide 3.5.3); therefore, enough glucose will escape rephosphorylation and be released into the bloodstream.
8.5.2
### Muscle glycogen utilization
Muscle glycogen primarily serves the energy needs of muscle tissue itself; during prolonged physical exercise, most of it is broken down to glucose-6-phosphate and then consumed via the usual pathways right within the cells that stored it. As discussed above, this usage is facilitated by calcium-mediated activation of glycogen phosphorylase.
Under suitable conditions, namely, prolonged fast without physical exercise, muscle glycogen can also contribute to the replenishment of blood glucose. However, even though muscle cells have been shown to express glucose-6-phosphatase [36] and thus are, in principle, able to produce free glucose, they should find it difficult to release it. This is because muscle contains hexokinase, which has a much greater substrate affinity than glucokinase and therefore will keep the intracellular level of free glucose well below the extracellular concentration. The net transport of glucose should therefore be directed inward at all times; this agrees with all the physiological evidence that I could find.
The way around this obstacle is to convert glucose-6-phosphate to pyruvate and then lactate. At a low rate, lactate formation occurs even in resting muscle and under aerobic conditions. This lactate is derived in various proportions from blood glucose and glycogen, respectively. In animal experiments, epinephrine promotes glycogen utilization and lactate release [3739], but overall the hormonal control of this process and the magnitude of its contribution to systemic glucose control are not well characterized.
8.5.3
### The Cori cycle
While skeletal muscle relies on oxidative metabolism most of the time, some other tissues, notably red blood cells and lymphocytes, which collectively account for some 4 kg of cell mass, depend mostly or even exclusively on anaerobic glycolysis even under aerobic conditions. The lactate released in peripheral tissues is scooped up by the liver, which converts it back to glucose through gluconeogenesis. This process is known as the Cori cycle, named after its discoverers Carl and Gerti Cori, who worked it out as early as 1929 [40].
Skeletal produces lactate at a very much higher rate during short bouts of maximal exercise when the ATP demand exceeds the capacity for aerobic metabolism. Some textbooks state that the Cori cycle resupplies the muscle with glucose in this situation also. This is, however, quite impossible. During intense exercise, the cardiac blood output is diverted from the visceral organs to skeletal muscle. Therefore, when ATP demand exceeds the oxygen supply of skeletal muscle, the oxygen shortfall would be even greater in the liver, should it indeed attempt to make enough ATP for sustaining the muscle through gluconeogenesis; and even with sufficient oxygen, its capacity for making glucose would fall far short of the muscles’ voracious appetite.
Anaerobic exercise can be sustained for only short periods of time anyway. During this period, the lactate turned out by skeletal muscle will simply accumulate; it will then slowly be scooped up by the liver and turned back into glucose after we have collapsed at the side of the track to catch our breath.
8.6
## Glycogen storage diseases
Genetic defects have been described for several enzymes of glycogen metabolism. The clinical syndromes associated with these defects are referred to as glycogen storage diseases. While these conditions are not particularly common, they do shed some light on the physiological significance of glycogen metabolism. Some conditions are clinically severe and are the focus of ongoing therapeutic research. A few examples are briefly discussed below.
8.6.1
### Glucose-6-phosphatase deficiency (von Gierke disease)
Biochemical defect:
• glucose-6-phosphate formed in gluconeogenesis or glycogen degradation cannot be converted to free glucose
• glucose cannot be exported from liver and kidney cells
Clinical manifestations:
• glycogen builds up in liver and kidneys (organ enlargement and functional impairment)
• severe hypoglycemia
• lactic acidosis
• hyperlipidemia
• hyperuricemia
Gluconeogenesis and glycogen degradation in liver and kidneys produce glucose-6-phosphate, which must then be dephosphorylated to glucose in order to be exported into the bloodstream (see slide 8.5.1). An enzyme defect for glucose-6-phosphatase prevents glucose release, which causes abnormally low blood glucose levels (hypoglycemia). Some of the surplus glucose-6-phosphate is funnelled into glycogen synthesis, whereas the remainder is converted to pyruvate in glycolysis and either emerges as lactate or, downstream of pyruvate dehydrogenase, is turned into triacylglycerol and cholesterol; the excess lactate and lipids account for the clinically observed lactic acidosis and hyperlipidemia, respectively.
The causation of hyperuricemia—excess blood levels of uric acid, see section 16.5—is less obvious. During episodes of hypoglycemia, the liver will be intensely stimulated by glucagon and epinephrine and make a forceful but futile attempt to mobilize its stored glycogen. The large amount of glucose-6-phosphate produced in this attempt, which cannot be converted to glucose, ties up and depletes cellular phosphate. This impedes the regeneration of ATP and raises the level of AMP, some of which then enters degradation to uric acid [41].50
The clinical severity of this disease may vary, presumably due to different levels of residual enzyme activity. Some cases may be managed with a diet of frequent, starch-rich meals, which helps to avoid hypoglycemia. In more severe cases, liver transplantation may become necessary.
8.6.2
### Acid maltase deficiency (Pompe disease)
A homozygous deficiency of acid maltase51 disrupts lysosomal glycogen degradation and results in glycogen accumulation. Skeletal and heart muscle are more strongly affected than the liver. The tissue section of diseased muscle tissue shows “white holes,” which represent unstained aggregates of glycogen particles. Glycogen accumulation interferes with muscle cell function and contraction, and heart failure—a heavily impacted, severely distended heart is shown here in an X-ray image—leads to death.
The condition, which is known as Pompe’s disease, can vary in severity; complete lack of enzyme activity becomes manifest in infants, whereas mutations that reduce but do not completely inactivate the enzyme will cause milder disease with onset deferred to later childhood or adolescence. The disease can be treated with enzyme replacement therapy. The recombinant enzyme preparation is FDA-approved; its price is astronomical. This therapeutic approach is more thoroughly discussed in section 20.3.
While the nature of the enzyme defect would lead one to expect involvement of the interior organs (liver and kidney) also, these don’t seem to be prominent in practice, although some degree of hepatomegaly (liver enlargement) is often observed. I have not yet found a clear explanation for the preferential affliction of muscle tissues.
8.6.3
### Muscle phosphorylase deficiency (McArdle’s disease)
• Deficient glycogen breakdown inhibits rapid ATP replenishment
• Patients experience rapid exhaustion and muscle pain during exertion
• Liver phosphorylase and blood glucose homeostasis remain intact
Since liver and muscle phosphorylase are distinct isozymes, defects usually affect one and spare the other.52 In McArdle’s disease, the muscle isoform is selectively affected. An unexplained symptom in this disease is the so-called “second wind” phenomenon: during physical activity, patients initially fatigue rapidly, but then recover to a degree under continued exercise. This effect has been ascribed to the activation of protein and amino acid breakdown in muscle [43].
The lack of muscle phosphorylase should also inhibit the utilization of muscle glycogen toward blood glucose stabilization by way of the Cori cycle (see slide 8.5.3); one might therefore expect that McArdle’s disease might involve episodes of hypoglycemia. Interestingly, however, the literature does not contain reports of hypoglycemia in these patients.
8.6.4
### Lafora disease
• deficiency for laforin, a glycogen phosphatase
• accumulation of hyper-phosphorylated glycogen (Lafora bodies)
• patients develop epilepsy, dementia
Laforin is a phosphatase that is associated with glycogen particles and removes phosphate groups from glycogen itself [44]. The functional significance of glycogen phosphorylation and dephosphorylation is not clear; and you will notice that it was not even mentioned above. However, genetic deficiencies of the phosphatase lead to the accumulation of Lafora bodies, which consist of phosphorylated, poorly branched glycogen molecules. The disease becomes manifest through a specific form of epilepsy (myoclonic seizures) and dementia and is fatal. The CNS symptoms—like the involvement of the kidneys in v. Gierke disease, see above—illustrate that tissues other than liver and muscle contain glycogen as well and may be damaged by its accumulation. | 2019-05-22 01:21:47 | {"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": 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": 0.579552948474884, "perplexity": 5720.988582444677}, "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/1558232256600.32/warc/CC-MAIN-20190522002845-20190522024845-00189.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/pranali-prasad-started-walking-east-north-respectively-same-point-same-speed-after-2-hours-distance-between-them-was-15-2-km-find-their-speed-hour-pythagoras-theorem_50336 | Share
Pranali and Prasad Started Walking to the East and to the North Respectively, from the Same Point and at the Same Speed. After 2 Hours Distance Between Them Was 15 √ 2 Km. Find Their Speed per Hour. - Geometry
ConceptPythagoras Theorem
Question
Pranali and Prasad started walking to the East and to the North respectively, from the same point and at the same speed. After 2 hours distance between them was $15\sqrt{2}$
km. Find their speed per hour.
Solution
It is given that, Pranali and Prasad have same speed.
Thus, they cover same distance in 2 hours.
i.e. OA = OB
Let the speed be x km per hour.
According to Pythagoras theorem,
In ∆AOB
${AB}^2 = {AO}^2 + {OB}^2$
$\Rightarrow \left( 15\sqrt{2} \right)^2 = {AO}^2 + {OA}^2$
$\Rightarrow 450 = 2 {AO}^2$
$\Rightarrow {AO}^2 = \frac{450}{2}$
$\Rightarrow {AO}^2 = 225$
$\Rightarrow AO = 15 km$
$\Rightarrow BO = 15 km$
$\text{Speed} = \frac{Distance}{Time}$
$= \frac{15}{2}$
$= 7 . 5 \text{km per hour}$
Is there an error in this question or solution?
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Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 2: Pythagoras Theorem
Problem Set 2 | Q: 10 | Page no. 45
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Solution Pranali and Prasad Started Walking to the East and to the North Respectively, from the Same Point and at the Same Speed. After 2 Hours Distance Between Them Was 15 √ 2 Km. Find Their Speed per Hour. Concept: Pythagoras Theorem.
S | 2020-04-08 17:15:24 | {"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": 0.3547907769680023, "perplexity": 2121.7104796878984}, "config": {"markdown_headings": false, "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-2020-16/segments/1585371821680.80/warc/CC-MAIN-20200408170717-20200408201217-00132.warc.gz"} |
https://2021.help.altair.com/2021.1/hwsolvers/acusolve/topics/acusolve/particle_data_commands_acutrace_com_ref.htm | # Particle Data Commands
The particle data commands are outlined in this chapter.
There needs to be at least one PARTICLE_SEED command. As many PARTICLE_SEED commands as necessary are allowed. Each unique PARTICLE_SEED command defines a distinct set of particles. A USER_EQUATION_INITIAL_CONDITION command is allowed only for pairings of particle seed groups and user equations. Each of the pairings defined by the particle seed commands and the user equations specified by the user_equations parameter in the EQUATION command requires a corresponding USER_EQUATION_INITIAL_CONDITION command. If no equations are specified by the user_equations parameter in the EQUATION command, no USER_EQUATION_INITIAL_CONDITION commands are needed. | 2023-02-07 14:53:47 | {"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": 0.9570849537849426, "perplexity": 2875.4594712846165}, "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-2023-06/segments/1674764500619.96/warc/CC-MAIN-20230207134453-20230207164453-00009.warc.gz"} |
https://zbmath.org/?q=an%3A1375.03071 | ## Ranking Z-numbers with an improved ranking method for generalized fuzzy numbers.(English)Zbl 1375.03071
Summary: Z-number, a new concept describes both the restriction and the reliability of evaluation, is more applicable than fuzzy numbers in the fields of decision making, risk assessment etc. However, how to deal with the restriction and the reliability properly is still a problem which is discussed few and inadequately in the existing literatures. In this paper, firstly, a new improved method for ranking generalized fuzzy numbers where the weight of centroid points, degrees of fuzziness and the spreads of fuzzy numbers are taken into consideration is proposed, which can overcome some drawbacks of exiting methods and is very efficient for evaluating symmetric fuzzy numbers and crisp numbers. Then, a procedure for evaluating Z-numbers with the method for ranking generalized fuzzy numbers is presented, which considers the status of two parts $$((\tilde{A},\tilde{B}))$$ of Z-numbers and gives the principles of ranking Z-numbers. The main advantage of the proposed method is utilization of Z-numbers which can express more vague information compared with the fuzzy number. In addition, instead of converting $$\tilde{B}$$ to a crisp number as the existing methods of ranking Z-numbers did, the proposed method retains the fuzzy information of $$\tilde{B}$$ which can reduce the loss of information. Finally, several numerical examples are provided to illustrate the superiority and the rationality of the proposed procedure.
### MSC:
03E72 Theory of fuzzy sets, etc. 91B06 Decision theory
Full Text: | 2022-08-09 10:01:02 | {"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": 0.6481353044509888, "perplexity": 812.8057995591165}, "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-2022-33/segments/1659882570921.9/warc/CC-MAIN-20220809094531-20220809124531-00461.warc.gz"} |
https://myassignments-help.com/2022/09/16/economic-statistics-dai-xie-ecn329-2/ | # 统计代写|经济统计代写Economic Statistics代考|ECN329
## 统计代写|经济统计代写Economic Statistics代考|Linking 1- to- 1 Matches to the Economic Census
Our next step is to link the BR establishments that MAMBA predicts as being franchise affiliated (i.e., external establishments that are 1-to-1 matches with a BR establishment) to the $2017 \mathrm{EC} .{ }^{13}$ This allows us to examine whether MAMBA’s predictions are consistent with whether an establishment is characterized as franchise affiliated on their EC form.
Once an external establishment is linked to the $\mathrm{BR}$, it is straightforward to link it to the EC using an internal establishment identifier. Table $7.3$ summarizes this link. The row labeled “1-to-1 Match with BR” shows that, as in table 7.2, there are approximately 57,500 web-scraped, 44,500 core Yelpqueried, and 89,000 noncore Yelp-queried establishments that MAMBA identifies as 1-to-1 matches with a BR establishment. The row labeled “Surveyed in 2017 EC” shows that approximately 52,500 (91 percent), 40,500 ( 91 percent), and 78,500 (88 percent) of these are included in the $2017 \mathrm{EC}$. Since the processing of the $2017 \mathrm{EC}$ is still ongoing, the row labeled “2017 EC Form Processed” reports the number of 1-to-1 matches that are included in the $2017 \mathrm{EC}$ whose forms have been processed-approximately 29,000 (55 percent) web-scraped, 21,500 (53 percent) core Yelp-queried, and 41,000 (52 percent) noncore Yelp-queried establishments.
For most of the remainder of the paper, we focus on these 29,000 webscraped and 62,500 Yelp-queried (21,500 core and 41,000 noncore) establishments. These are the subset of establishments that MAMBA predicts to be franchise affiliated, for whom we can also examine survey responses (or nonresponses) about their franchise status on the 2017 EC form.
## 统计代写|经济统计代写Economic Statistics代考|Evaluating Responses on the 2017 Economic Census
As noted in the previous section, we have 29,000 web-scraped, 21,500 core Yelp-queried, and 41,000 noncore Yelp-queried establishments that are both predicted to be franchise affiliated by MAMBA and have had their survey forms processed for the $2017 \mathrm{EC}$. This gives us a unique opportunity to examine whether survey responses about the establishments are consistent with MAMBA’s predictions, and if they are inconsistent, examine which is correct.
Table $7.4$ examines these responses to the 2017 EC survey form. The row titled “Franchisor or Franchisee” shows the number of establishments that respondents claim to be franchise affiliated. As the row name suggests, an establishment is classified as franchise-affiliated if the respondent claimed to be either a franchisor or franchisee on its EC survey form. We see that 21,500 (74 percent) web-scraped, 16,500 (77 percent) core Yelp-queried, and 28,500 (70 percent) noncore Yelp-queried establishments are identified as franchise affiliated by respondents, consistent with MAMBA’s prediction. Thus, for a majority of establishments, the MAMBA prediction and EC form agree that the establishment is franchise affiliated, with somewhat higher proportions for establishments affiliated with our 12 core franchises. However, the row labeled “Not Affiliated or Not Answered” shows that this leaves a substantial number of establishments – 7,400 (26 percent), 5,000 (23 percent), and 12,500 ( 30 percent) – that respondents claim not to be franchise affiliated, contradicting MAMBA’s prediction. An establishment is classified as not being franchise affiliated if the respondent either did not fill out the franchise portion of its EC survey form or did fill it out but claimed that the establishment was not franchise affiliated. Both these groups are classified as not being franchise affiliated because they would be classified as such if their EC forms were taken at face value. Overall, table $7.4$ shows that a substantial portion of establishments have conflicting information.
. .
## 统计代写|经济统计代写经济统计代考|评估对2017年经济普查的回应
. .
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Scroll to Top | 2022-12-07 09:24:00 | {"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": 0.5757482647895813, "perplexity": 6514.590825654353}, "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-2022-49/segments/1669446711151.22/warc/CC-MAIN-20221207085208-20221207115208-00279.warc.gz"} |
https://manashpratim.com/plot-realtime-terminal-data | Plot real-time terminal data
A python script to plot 1D real-time data being written to the stdout by other application
When we develop software to process data, there is often a need to quickly visualize it for debug purposes. One most common option is to write the data to the stdout of the terminal. For example:
• print data in Python
• std::cout << data << std::endl; in C++
However, sometimes plotting the data makes more sense. In this article, I’ll show an example of how to develop a simple tool to plot such data in real-time.
Python script to plot multiple sets of 1D data
The script should be able to 1) read data from the terminal and 2) plot the data. One way to read from the terminal is to use pipe to redirect the data from the application writing the data to this script.
For example: $python some_application.py | python plot_script.py Once the data is being redirected, we can read it in python by the following script (plot_script.py): You may try running it as: $ ping 127.0.0.1 | python plot_script.py
‘data’ variable in the above script has to be plotted now. In this article, I’ll show you how to parse multiple streams of 1D data. We first generate such synthetic data for the sake of demonstration (synthetic-data.py):
with comma separated output. Here I demonstrate 3 sets of 1D data (x,y,z) also represented as variables.
> 0.0,1.0,-0.0
> 0.0174435597087,0.999847849537,-0.0174435597087
> 0.0348818113261,0.999391444449,-0.0348818113261
> 0.052309448376,0.99863092362,-0.052309448376
> 0.0697211676123,0.997566518477,-0.0697211676123
> 0.0871116706329,0.99619855292,-0.0871116706329
> 0.104475665491,0.994527443221,-0.104475665491
> 0.121807868308,0.992553697902,-0.121807868308
.
.
Thus, we can parse the ‘data’ in ‘plot_script.py’ using data.split(','). After adding the matplotlib functions, here is our final ‘plot_script.py’ script.
This script accepts two arguments:
• -t: The length of X axis. Since the input data is a time-series data, each input is considered a timestep. Thus this variable determines the number of past timesteps to plot from the current time.
• -n: Number of variables to plot in the input data. The respective values for the different variables in a timestep are presented in a comma-separated string. Thus, this script can plot multiple 1D data variables.
To visualize the synthetic data we generated before.
Run \$ python synthetic-data.py | python plot_script.py -t 1000 -n 3
Here is the graph output with different color for different variables: | 2021-09-16 16:39:21 | {"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": 0.22948865592479706, "perplexity": 1965.1563660994962}, "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-2021-39/segments/1631780053657.29/warc/CC-MAIN-20210916145123-20210916175123-00494.warc.gz"} |
https://ftp.aimsciences.org/article/doi/10.3934/jcd.2019004 | # American Institute of Mathematical Sciences
June 2019, 6(1): 95-109. doi: 10.3934/jcd.2019004
## The dependence of Lyapunov exponents of polynomials on their coefficients
Indian Institute of Science Education and Research Thiruvananthapuram (IISER-TVM), Maruthamala P.O., Vithura, Thiruvananthapuram, India. PIN 695 551
* Corresponding author: Shrihari Sridharan
Published July 2019
Fund Project: The first author was supported by a Fasttrack Grant for Young Scientists awarded by the Department of Science and Technology, Government of India, vide SR/FTP/MS-008/2012.
In this paper, we consider the family of hyperbolic quadratic polynomials parametrised by a complex constant; namely $P_{c} (z) = z^{2} + c$ with $|c| < 1$ and the family of hyperbolic cubic polynomials parametrised by two complex constants; namely $P_{(a_{1}, \, a_{0})} (z) = z^{3} + a_{1} z + a_{0}$ with $|a_{i}| < 1$, restricted on their respective Julia sets. We compute the Lyapunov characteristic exponents for these polynomial maps over corresponding Julia sets, with respect to various Bernoulli measures and obtain results pertaining to the dependence of the behaviour of these exponents on the parameters describing the polynomial map. We achieve this using the theory of thermodynamic formalism, the pressure function in particular.
Citation: Shrihari Sridharan, Atma Ram Tiwari. The dependence of Lyapunov exponents of polynomials on their coefficients. Journal of Computational Dynamics, 2019, 6 (1) : 95-109. doi: 10.3934/jcd.2019004
##### References:
show all references
##### References:
[1] Meihua Dong, Keonhee Lee, Carlos Morales. Gromov-Hausdorff stability for group actions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1347-1357. doi: 10.3934/dcds.2020320 [2] Peter Giesl, Zachary Langhorne, Carlos Argáez, Sigurdur Hafstein. Computing complete Lyapunov functions for discrete-time dynamical systems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 299-336. doi: 10.3934/dcdsb.2020331 [3] Yuanfen Xiao. Mean Li-Yorke chaotic set along polynomial sequence with full Hausdorff dimension for $\beta$-transformation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 525-536. doi: 10.3934/dcds.2020267 [4] João Marcos do Ó, Bruno Ribeiro, Bernhard Ruf. Hamiltonian elliptic systems in dimension two with arbitrary and double exponential growth conditions. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 277-296. doi: 10.3934/dcds.2020138 [5] Guillaume Cantin, M. A. Aziz-Alaoui. Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020283 [6] Norman Noguera, Ademir Pastor. Scattering of radial solutions for quadratic-type Schrödinger systems in dimension five. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021018 [7] Andrew Comech, Scipio Cuccagna. On asymptotic stability of ground states of some systems of nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1225-1270. doi: 10.3934/dcds.2020316 [8] Lars Grüne. Computing Lyapunov functions using deep neural networks. Journal of Computational Dynamics, 2020 doi: 10.3934/jcd.2021006 [9] Peter Giesl, Sigurdur Hafstein. System specific triangulations for the construction of CPA Lyapunov functions. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020378 [10] Gervy Marie Angeles, Gilbert Peralta. Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020108 [11] Jonathan J. Wylie, Robert M. Miura, Huaxiong Huang. Systems of coupled diffusion equations with degenerate nonlinear source terms: Linear stability and traveling waves. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 561-569. doi: 10.3934/dcds.2009.23.561 [12] Hua Qiu, Zheng-An Yao. The regularized Boussinesq equations with partial dissipations in dimension two. Electronic Research Archive, 2020, 28 (4) : 1375-1393. doi: 10.3934/era.2020073 [13] Lisa Hernandez Lucas. Properties of sets of Subspaces with Constant Intersection Dimension. Advances in Mathematics of Communications, 2021, 15 (1) : 191-206. doi: 10.3934/amc.2020052 [14] Sabira El Khalfaoui, Gábor P. Nagy. On the dimension of the subfield subcodes of 1-point Hermitian codes. Advances in Mathematics of Communications, 2021, 15 (2) : 219-226. doi: 10.3934/amc.2020054 [15] Skyler Simmons. Stability of Broucke's isosceles orbit. Discrete & Continuous Dynamical Systems - A, 2021 doi: 10.3934/dcds.2021015 [16] Annegret Glitzky, Matthias Liero, Grigor Nika. Dimension reduction of thermistor models for large-area organic light-emitting diodes. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020460 [17] Fang Li, Bo You. On the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021024 [18] Eduard Feireisl, Elisabetta Rocca, Giulio Schimperna, Arghir Zarnescu. Weak sequential stability for a nonlinear model of nematic electrolytes. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 219-241. doi: 10.3934/dcdss.2020366 [19] Reza Chaharpashlou, Abdon Atangana, Reza Saadati. On the fuzzy stability results for fractional stochastic Volterra integral equation. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020432 [20] Scipio Cuccagna, Masaya Maeda. A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020450
Impact Factor: | 2021-01-19 16:05:25 | {"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": 0.5742131471633911, "perplexity": 6191.070671804984}, "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/1610703519395.23/warc/CC-MAIN-20210119135001-20210119165001-00391.warc.gz"} |
https://firas.moosvi.com/oer/physics_bank/content/public/005.Kinematics%282D%20and%203D%29/Uniform%20Circular%20Motion/MarbleCourse/MarbleCourse.html | Marble Course#
Two marbles travel in track as part of a Rube Goldberg machine. Both marbles cross line $$C$$ at the same time, and flow at a their maximum speed. The maximum horizontal acceleration for marble A is $${{params.max_acc_A}}g$$ with $$R\_{A} = {{params.ra}} in$$ and for marble B is $${{params.max_acc_B}}g$$ with $$R\_{B} = {{params.rb}} in$$. The angle $$\theta = {{params.angle}}^{\circ}$$.
Question Text#
Determine the distance $$\gamma$$ which the second marble has yet to go along its path to reach line $$D$$ when the first marble reaches it.
Please enter in a numeric value in $$in$$. | 2023-01-28 22:31:19 | {"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": 0.6338649392127991, "perplexity": 698.2306685030221}, "config": {"markdown_headings": false, "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-2023-06/segments/1674764499695.59/warc/CC-MAIN-20230128220716-20230129010716-00345.warc.gz"} |
http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=cheb&paperid=421&option_lang=eng | Chebyshevskii Sbornik
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Chebyshevskii Sb., 2015, Volume 16, Issue 3, Pages 306–321 (Mi cheb421)
On tensegrity frameworks
M. D. Kovalev
Lomonosov Moscow State University
Abstract: Ideal designs, made of rigid bars (levers), inextensible cables and incompressible struts are considered. In English such constructions are called "tensegrity frameworks". In the particular case of structures composed of only the levers, — this is a bar and joint frameworks. In recent times the tensegrity frameworks are increasingly used in architecture and construction, for example, the construction of bridges.
In English mathematical literature geometric properties of such structures were studied since the seventies of the last century. This article is apparently the first in Russian mathematical literature devoted to this topic. It is a breath survey to the theory of tensegrity frameworks.
It introduces mathematical formalization of tensegrity frameworks in the spirit of the work of the author on hinge mechanisms. This formalization includes original Russian terminology, not reducible to the borrowing of English words. Only not pinned tensegrity frameworks are investigated. We call a tensegrity frameworks, allowing the internal stress, and not allowing a continuous deformation with a change of form, — a truss. A truss that can'not be assembled in a different way to be not congruent to initial one is called Globally Rigid. If a tensegrity frameworks is Globally Rigid in $R^n$ and also Globally Rigid in every $R^N$ for $N>n$ it is called Universally Rigid.
We focus on the problem — when a given tensegrity framework is Globally Rigid? We consider an effective method for solving this problem, based on investigation of particular function — the potential energy of the structure. We search a tensegrity frameworks for which this potential energy is minimal. The method is described in detail in the article. The main theorem, giving a sufficient condition of Universal Rigidity of tensegrity framework is proved in details. The study of internal stresses of a tensegrity framework and its stress matrix, by means of which the potential energy is written, is of fundamental importance. Examples of applications of this theorem to planar and spatial tensegrity frameworks are presented.
In general, this subject is not yet sufficiently developed, and is currently actively investigated. At the end of the article some open questions are formulated.
Bibliography: 15 titles.
Keywords: Tesegrity frameworks, global rigidity, potential function, stress matrix.
Full text: PDF file (772 kB)
References: PDF file HTML file
UDC: 514+531.8
Citation: M. D. Kovalev, “On tensegrity frameworks”, Chebyshevskii Sb., 16:3 (2015), 306–321
Citation in format AMSBIB
\Bibitem{Kov15} \by M.~D.~Kovalev \paper On tensegrity frameworks \jour Chebyshevskii Sb. \yr 2015 \vol 16 \issue 3 \pages 306--321 \mathnet{http://mi.mathnet.ru/cheb421} \elib{https://elibrary.ru/item.asp?id=24398940} | 2021-06-23 07:22:08 | {"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": 0.27417105436325073, "perplexity": 2872.446529945004}, "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-2021-25/segments/1623488534413.81/warc/CC-MAIN-20210623042426-20210623072426-00029.warc.gz"} |
https://math.stackexchange.com/questions/2237610/how-was-this-result-for-integer-partitions-found | If you look at one of the comments on A053445 you'll see it mentions that the second difference of partition numbers is equivalent to the number of integer partitions with two largest parts equal and each part $\geq 2$. That is, if q(n) is the number of partitions with those properties, then:
$( p(n)-p(n-1) )~-~( p(n-1)-p(n-2) ) = p(n)-2p(n-1)+p(n-2) = q(n)$
for $n \geq 3$. I looked at the references on the page, as well as a couple journal searches, and didn't see anything where this result was originally found. I've discovered this and something similar and would like to refer to him or her for this result. | 2019-10-18 04:34:31 | {"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": 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": 0.796103835105896, "perplexity": 191.37416995746761}, "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-2019-43/segments/1570986677884.28/warc/CC-MAIN-20191018032611-20191018060111-00266.warc.gz"} |
https://pdal.io/stages/readers.faux.html | The faux reader is used for testing pipelines. It does not read from a file or database, but generates synthetic data to feed into the pipeline.
The faux reader requires a mode argume to define the method in which points should be generated. Valid modes are as follows:
constant
The values provided as the minimums to the bounds argument are used for the X, Y and Z value, respectively, for every point.
random
Random values are chosen within the provided bounds.
ramp
Value increase uniformly from the minimum values to the maximum values.
uniform
Random values of each dimension are uniformly distributed in the provided ranges.
normal
Random values of each dimension are normally distributed in the provided ranges.
grid
Creates points with integer-valued coordinates in the range provided (excluding the upper bound).
Default Embedded Stage
This stage is enabled by default
Streamable Stage
This stage supports streaming operations
## Example¶
{
"pipeline":[
{
"bounds":"([0,1000000],[0,1000000],[0,100])",
"count":"10000",
"mode":"random"
},
{
"type":"writers.text",
"filename":"outputfile.txt"
}
]
}
## Options¶
bounds
What spatial extent should points be generated within? Text string of the form “([xmin,xmax],[ymin,ymax],[zmin,zmax])”. [Default: unit cube]
count
How many synthetic points to generate before finishing? [Required, except when mode is ‘grid’]
spatialreference
Spatial reference to apply to data. [Optional]
mean_x|y|z
Mean value in the x, y, or z dimension respectively. (Normal mode only) [Default: 0]
stdev_x|y|z
Standard deviation in the x, y, or z dimension respectively. (Normal mode only) [Default: 1]
mode
“constant”, “random”, “ramp”, “uniform”, “normal” or “grid” [Required] | 2019-08-21 03:50:34 | {"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": 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": 0.6985306143760681, "perplexity": 5021.7458754790005}, "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-2019-35/segments/1566027315750.62/warc/CC-MAIN-20190821022901-20190821044901-00557.warc.gz"} |
http://mymathforum.com/number-theory/343004-new-relative-mathematics-print.html | My Math Forum (http://mymathforum.com/math-forums.php)
- Number Theory (http://mymathforum.com/number-theory/)
- - A New Relative Mathematics (http://mymathforum.com/number-theory/343004-new-relative-mathematics.html)
Conway51 December 4th, 2017 10:03 PM
A New Relative Mathematics
Relative Mathematics
In every R there exists an integer zero element ( -0 )
( -0 ) = 0
( -0 ) : possesses the additive identity property
( -0 ) : does not possess the multiplication property of 0
( -0 ) : possesses the multiplicative identity property of 1
The zero elements ( 0 ) and ( -0 ) in an expression of division can only exist as: (0)/( -0 )
0 + ( -0 ) = 0 = ( -0 ) + 0
( -0 ) + ( -0 ) = 0
1 + ( -0 ) = 1 = ( -0 ) + 1
0 * ( -0 ) = 0 = ( -0 ) * 0
1 * ( -0 ) = 1 = ( -0 ) * 1
n * ( -0 ) = n = ( -0 ) * n
Therefore, the zero element ( -0 ) is by definition also the multiplicative inverse of 1 .
And as division by the zero elements requires ( - 0 ) as the divisor ( x / ( -0 )) is defined as the quotient ( x ) .
0 / n = 0
0 / ( -0 ) = 0
n / ( -0 ) = n
0 / 1 = 0
1 / ( -0 ) = 1
1 / 1 = 1
( 1/( -0 ) = 1 )
The reciprocal of ( -0 ) is defined as 1/( -0 )
1/(-0) * ( -0 ) = 1
(-0)^(-1) = ( 1/( -0 ) = 1
(-0)(-0)^(-1) = 1 = ( -0 )^(-1)
Any element raised to ( -1 ) equals that elements inverse.
0^0 = undefined
0^(-0) = undefined
1^0 = 1
1^(-0) = 1
Therefore, all expressions of ( -0 ) or ( 0 ) as exponents or as logarithms are required to exist without change.
Therefore, division by zero is defined.
Therefore, the product of multiplication by zero is relative to which integer zero is used in the binary expression of multiplication.
meditate December 5th, 2017 06:26 AM
You started with the following:
( -0 ) = 0
but then comes following definition
1 * ( -0 ) = 1 = ( -0 ) * 1
If ( -0 ) = 0 won't the expression 1 * ( -0 ) be 0?
Conway51 December 5th, 2017 07:02 AM
Quote:
Originally Posted by meditate (Post 585277) You started with the following: ( -0 ) = 0 but then comes following definition 1 * ( -0 ) = 1 = ( -0 ) * 1 If ( -0 ) = 0 won't the expression 1 * ( -0 ) be 0?
No...as I stated clearly.....
The integer ( -0 ) does NOT possess the multiplicative property of zero
The integer ( -0 ) does possess the multiplicative identity property of 1
Therefore
n * ( -0) = n
v8archie December 5th, 2017 08:17 AM
So you have $$n = n \times (-0) = n \times 0 = 0$$
Or is transitivity broken?
Conway51 December 5th, 2017 10:01 AM
Quote:
Originally Posted by v8archie (Post 585280) So you have $$n = n \times (-0) = n \times 0 = 0$$ Or is transitivity broken?
If you refer to the OP you will see...
NEVER does the equation ...
n * 0 = 0 = n * ( -0 )
exist....
NEVER
You will see only the equations
n * 0 = 0 = 0 * n
n * (-0) = n = (-0) * n
Therefore the commutative property is preserved without change.
Thank you very much for your time
romsek December 5th, 2017 10:07 AM
Quote:
Originally Posted by Conway51 (Post 585289) If you refer to the OP you will see... NEVER does the equation ... n * 0 = 0 = n * ( -0 ) exist.... NEVER You will see only the equations n * 0 = 0 = 0 * n n * (-0) = n = (-0) * n
$0=(-0)$
$n = n*(-0) = n*(0) = 0$
either $(-0) = 0$, with all the properties of $0$, or it doesn't.
you can't just say $a=b$ but $a$ doesn't share some of $b$'s properties.
do you have something other than equality in mind when you state $0 = (-0)$ ?
v8archie December 5th, 2017 10:13 AM
Quote:
Originally Posted by Conway51 (Post 585289) Therefore the commutative property is preserved without change. Thank you very much for your time
I never mentioned commutativity.
v8archie December 5th, 2017 10:21 AM
You also claim the both $0$ and $(-0)$ are the additive identity. Thus
$$0=n + (-n) = (-0)$$
So either $0=(-0)$ (meaning that they are the same element of the system) or addition is not well defined with every sum having two different answers, with no way of determining which is correct.
Conway51 December 5th, 2017 11:08 AM
Quote:
Originally Posted by v8archie (Post 585293) You also claim the both $0$ and $(-0)$ are the additive identity. Thus $$0=n + (-n) = (-0)$$ So either $0=(-0)$ (meaning that they are the same element of the system) or addition is not well defined with every sum having two different answers, with no way of determining which is correct.
therefore...
0(the element) + (-0)( the additive element) = 0
0 + (-0) =/= (-0)
in the same way that
0(the element) + 0(the additive element) = 0
You will find NO where in the original post the equation....
0 + (-0) = (-0)
0 = n + (-n) = 0
Conway51 December 5th, 2017 11:10 AM
Quote:
Originally Posted by romsek (Post 585290) $0=(-0)$ $n = n*(-0) = n*(0) = 0$ contradiction either $(-0) = 0$, with all the properties of $0$, or it doesn't. you can't just say $a=b$ but $a$ doesn't share some of $b$'s properties. do you have something other than equality in mind when you state $0 = (-0)$ ?
No where in the original post does the equation....
n = n * ( -0 ) = n * 0 = 0
ONLY the equations.
n * (-0) = n
n * ( 0 ) = 0
All times are GMT -8. The time now is 12:04 AM. | 2019-09-22 08:04:34 | {"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": 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": 0.6085999608039856, "perplexity": 850.6755971433543}, "config": {"markdown_headings": false, "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-2019-39/segments/1568514575402.81/warc/CC-MAIN-20190922073800-20190922095800-00514.warc.gz"} |
http://wikieducator.org/User:Agnes/Skill_of_Classroom_Communication | # User:Agnes/Skill of Classroom Communication
Skill of Classroom Communication
Shauna is a young teacher who teaches Science to Grade Eight students. She has good command over her content. She uses technology in her classroom. She makes every effort to plan thoroughly. Yet sometimes she finds students misunderstand her instructions. She agrees that she is not very patient. She talks a bit too fast( coz words flow as fast as my thoughts do, she says. Students often ask her to repeat instructions or simplify them. Her mother, Mrs. Ryan, herself an experienced teacher, advises Shauna to work on her communication skills. Are you ready to go with Shauna on her journey towards better communication?
(3)See http://www.ehow.com/way_5171235_effective-communication-tips-classroom.html
(4)See http://honolulu.hawaii.edu/intranet/committees/FacDevCom/guidebk/teachtip/teachtip.htm#communication and go through what you find interesting
(5)Think of your own school/college days. What aspects were prominent among effective communicators?
(6)On a scale of 1 to 5,where would you be on each of these aspects?
(a) ability to speak with clarity
(b) use of facial expressions
(c) Use of relevant vocabulary
(d) Use of gestures | 2018-01-18 04:01:39 | {"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": 0.23828117549419403, "perplexity": 9325.277401403335}, "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-2018-05/segments/1516084887065.16/warc/CC-MAIN-20180118032119-20180118052119-00035.warc.gz"} |
https://www.gradesaver.com/textbooks/math/calculus/university-calculus-early-transcendentals-3rd-edition/chapter-2-section-2-5-continuity-exercises-page-94/15 | ## University Calculus: Early Transcendentals (3rd Edition)
$y=\frac{x+1}{x^2-4x+3}$ is continous as $x$ $\in(-\infty,1)\cup(1,3)\cup(3,\infty)$
$$y=\frac{x+1}{x^2-4x+3}=\frac{x+1}{(x-1)(x-3)}$$ - Domain: $(-\infty,1)\cup(1,3)\cup(3,\infty)$ We would find all the points where the function is discontinous first, then all the remaining points would be where the function is continous. - At $x=1$ and $x=3$: $$\lim_{x\to1}y=\lim_{x\to1}\frac{x+1}{(x-1)(x-3)}$$ $$\lim_{x\to3}y=\lim_{x\to3}\frac{x+1}{(x-1)(x-3)}$$ As $x\to1$, $(x-1)\to0$, meaning that $(x-1)(x-3)$ will approach $0$ and $\frac{x+1}{(x-1)(x-3)}$, hence, will approach infinity, not any single value. Similarly, as $x\to3$, $(x-3)\to0$, meaning that $(x-1)(x-3)$ will approach $0$ and $\frac{x+1}{(x-1)(x-3)}$, hence, will approach infinity again. In other words, $\lim_{x\to1}\frac{x+1}{(x-1)(x-3)}$ and $\lim_{x\to3}\frac{x+1}{(x-1)(x-3)}$ do not exist. So the function is discontinous at $x=1$ and $x=3$. Therefore, $y=\frac{x+1}{x^2-4x+3}$ is continous in its domain, $(-\infty,1)\cup(1,3)\cup(3,\infty)$ | 2019-12-07 09:48:47 | {"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": 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": 0.9298322796821594, "perplexity": 145.0438456536722}, "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-2019-51/segments/1575540497022.38/warc/CC-MAIN-20191207082632-20191207110632-00197.warc.gz"} |
http://math.stackexchange.com/questions/329115/no-smooth-onto-map-from-circle-to-torus | # No Smooth Onto Map from Circle to Torus
My professor was lecturing today and he made this statement which I was unable to verify. (I worded it nicer)
There is no map which is both smooth and onto from $S^1$ to $S^1$$\times$ $S^1$.
When he said this he included the original "one can clearly see" statement which is usually when the most people seem to be confused in his class. Thus, I was hesitant to ask why. So, please no one lecture me on the fact that I should have asked anyway. If it is really that obvious, I would rather look stupid here than in class :)
-
I am increasingly becoming of the opinion that the phrase "clearly ____ is true" should be forever removed from mathematicians' vocabularies. – Keaton Mar 13 at 5:20
This follows from Sard's theorem, which implies that the image of a smooth map $S^1 \to S^1 \times S^1$ has Lebesgue measure zero. More generally, Sard's theorem implies that there are no smooth onto maps from a smooth manifold of dimension $n$ to a smooth manifold of dimension $m > n$.
The obvious statement is that there are no diffeomorphisms between such manifolds, which just follows by computing differentials (the differential of a diffeomorphism is an isomorphism). The differential of a surjective smooth map is not surjective in general (consider the surjection $\mathbb{R} \ni x \mapsto x^3 \in \mathbb{R}$) so the obvious argument doesn't work (or at least it doesn't obviously work).
Note also that this statement is false if "smooth" is replaced by "continuous" due to the existence of space-filling curves.
-
Ah good point. I figured it fell out easily from some theorem. I just couldn't think of what theorem. Remembering Sard's then does make the statement obvious. Thanks – Leo Spencer Mar 13 at 5:49
A smooth map $S^1 \rightarrow S^1 \times S^1$ is a differentiable curve; by differentiability it must have finite arc length. But a curve of finite length can't cover the 2-dimensional torus.
Why not? ${}{}$ – Qiaochu Yuan Mar 13 at 7:09 | 2013-12-07 17:00:16 | {"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": 1.0000051259994507, "perplexity": 2333.3390944589214}, "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-2013-48/segments/1386163054976/warc/CC-MAIN-20131204131734-00002-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://nigerianscholars.com/past-questions/physics/question/289730/ | Nigerian Scholars » » A telescope is said to be in normal adjustment when the
# A telescope is said to be in normal adjustment when the
### Question
A telescope is said to be in normal adjustment when the
### Options
A) focal length of he objective is greater than that of the eyepiece
B) focal length of the eyepiece is greater than that of the objective
C) focal length of the eyepiece is equal to that of the objective
D) objective focal point coincides wih that of the eyepiece | 2019-11-21 05:08:44 | {"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": 0.8113769888877869, "perplexity": 1253.6442511552136}, "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/1573496670731.88/warc/CC-MAIN-20191121050543-20191121074543-00072.warc.gz"} |
http://math.stackexchange.com/questions/118482/properties-of-a-twice-differentiable-decreasing-function-f-such-that-fx | # Properties of a twice differentiable decreasing function $f$ such that $f''(x)$ is positive for $x \in (1, \infty$).
Let $f : [1,\infty) \to (0,\infty)$ be a twice differentiable decreasing function such that $f''(x)$ is positive for $x \in (1, \infty$). For each positive integer $n$, let $a_{n}$ denote the area of the region bounded by the graph of $f$ and the line segment joining the points $(n, f(n))$ and $(n + 1, f(n + 1))$. I want to show
a. $\displaystyle \sum_{n=1}^ \infty a_{n}<\frac 1 2 (f(1)-f(2))$
b. $\displaystyle\lim_{n \to \infty} \left[ \sum_{k=1}^nf(k)-\frac1 2(f(1)+f(n))- \int_1^n f(x)dx\right]$ exists.
c. $\displaystyle\lim_{n \to \infty} \left[ \sum_{k=1}^nf(k)\int_1^n f(x)dx\right]$ exists.
-
What have you tried? – user21436 Mar 10 '12 at 6:23
And, consider registering your account. This has several benefits in addition to helping system maintain your posts efficiently, and helping you edit your own posts. – user21436 Mar 10 '12 at 6:25
• I don’t immediately see why (a) is true, though it’s quite easy to see that $$\sum_{n\ge 1}a_n<\frac12\Big(f(1)+f(2)\Big)$$ just by sliding each of the slivers over to the column between $x=1$ and $x=2$.
• For (b) note that $$\left(\sum_{k=1}^nf(k)-\frac12\big(f(1)+f(n)\big)\right)-\int_1^nf(x)\,dx=\sum_{k=1}^na_k\;:$$ the term in large parentheses on the left is the area of a bunch of trapezoids.
• (c) is false as stated: try it with $f(x)=\dfrac1x$.
-
The Consider the function $f$ on the iterval $[n,n+1]$. Since $f$ is convex, the graph of $f$ is above the tangent at the point $(n+1,f(n+1))$ and below the secant passing through $(n,f(n))$ and $(n+1,f(n+1))$. See the image below.
Then $a_n$ is less than the area of the triangle formed by the red lines (secant and tangent) and the vertical line $x=n$. Thus $$a_n\le \frac12\,(f(n)-f(n+1)+f'(n+1)).$$ Then \begin{align*} \sum_{k=1}^na_k&\le\frac12\,\Bigl(f(1)-f(2)+f(2)-f(3)+\dots+f(n)-f(n+1)+\sum_{k=2}^{n+1}f'(k)\Bigr)\\ &=\frac12\,\Bigl(f(1)-f(n+1)+\sum_{k=2}^{n+1}f'(k)\Bigr) \end{align*} But $$f(n+1)-f(2)=\int_2^{n+1}f'(x)\,dx=\sum_{k=2}^{n}\int_k^{k+1}f'(x)\,dx\ge\sum_{k=2}^{n}f'(k),$$ since $f'$ is increasing. It folllows that $$\sum_{k=1}^na_k\le\frac12(f(1)-f(2)+f'(n+1))\le\frac12(f(1)-f(2)),$$ proving a. You should be able to do b. and c. (where I think there is a $-$ sign missing.) If you have any trouble, search for Euler's summation formula. | 2014-03-11 08:29:41 | {"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": 0.934187650680542, "perplexity": 196.53694680662238}, "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/1394011159105/warc/CC-MAIN-20140305091919-00029-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://www.tutorialspoint.com/a-ball-is-gently-dropped-from-a-height-of-20-m-if-its-velocity-increases-uniformly-at-the-rate-of-10-m-s-2-with-what-velocity-will-it-strike-the | A ball is gently dropped from a height of $20\ m$. If its velocity increases uniformly at the rate of $10\ m s^{-2}$, with what velocity will it strike the ground? After what time will it strike the ground?
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Given:
Initial Velocity of the ball, $u=0$
Distance or height of fall, $s=20m$
Downward acceleration, $a=10\ ms^{-2}$
To find: Final velocity with which the ball will strike the ground, $(v)$, and time taken by the ball to strike the ground, $(t)$
Solution:
Suppose, the final velocity with which the ball will strike the ground be $‘v’$ and the time taken by it to strike the ground be $‘t’$.
By the third equation of motion, we know that-
$v^2=u^2+2as$
Putting the given values, we get-
$v^2=0^2+2\times {10}\times {20}$
$v^2=0+400$
$v^2=400$
$\sqrt {v^2}=\sqrt {400}$
$v=20m/s$
Thus, the final velocity with which the ball will strike the ground is 20m/s.
Now,
By first equation of motion, we know that-
$v=u+at$
Putting the required values, we get-
$20=0+10\times t$
$20=10t$
$t=\frac {20}{10}$
$t=2s$
Thus, time taken by the ball to strike the ground is, 2 seconds.
Updated on 10-Oct-2022 13:22:24 | 2022-11-27 08:13:47 | {"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": 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": 0.5056673288345337, "perplexity": 1759.7505377225393}, "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-2022-49/segments/1669446710218.49/warc/CC-MAIN-20221127073607-20221127103607-00438.warc.gz"} |
https://advantageequestrian.com/2022/06/autocad-24-2-full-product-key-final-2022/ | Select Page
The purpose of AutoCAD is to allow an architect, mechanical engineer, civil engineer, landscape architect, or any other professional to create, edit, view, and display 3D and 2D graphical representations of any shape or construction. It has full support for complex and highly detailed 2D/3D drawings, and also allows users to create 2D drawings that can be annotated and have text, legends, title blocks, and dimensioning. Once a drawing has been created and completed, it can be easily shared with others.
The AutoCAD program does not create drawings by itself. Users must first create a drawing using the application’s 2D Drafting or 3D modeling tools. Once a drawing has been created, it can be annotated and shared, which is the basis of the common user-generated content model. AutoCAD provides the ability to import and export files into PDF, DWF, DWFx, and other file formats. The resulting.dwg,.dxf, and.pdf files can be viewed or printed by other applications.
AutoCAD can also be used for commercial purposes. In addition to a full line of desktop and mobile programs, AutoCAD is available as a cloud service.
The AutoCAD application is composed of a main interface and a number of windows that together make up the drawing environment. There are nine main windows, which are organized in a way that will be familiar to anyone who has used an earlier version of AutoCAD. This interface includes a drawing area that can be configured as a 2D or 3D drawing. The drawing area may contain a freeform viewport, but it is typically used to display a bounding box that is used as the viewport. The bounding box is either a 2D or a 3D bounding box.
The toolbars include:
AutoCAD Drawing Area, used to create 2D or 3D drawings.
AutoCAD Layer Manager, used to manage layers, which are viewports or the current view of the drawing area.
AutoCAD Pen, used to define or select a point or path.
AutoCAD Text, used to create labels and comments, or insert text into the current view of the drawing area.
AutoCAD Region Manager, used to display a selection box around a portion of the drawing area.
## AutoCAD Crack + For PC [2022-Latest]
In February 2016 AutoCAD Feature Pack 8.0 was released to add support for features introduced in AutoCAD 2013.
In August 2018 Autodesk discontinued their AutoCAD plugin division, ceasing support for plugins in AutoCAD 2019 as well.
Comparison of CAD editors for Windows
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List of CAD editors
References
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Subtract columns in a matrix
I have a matrix that is nxn size. It includes only the integer numbers between 0 and 2, e.g.,
$\begin{bmatrix} 2 & 1 & 0 & 2 & 0 & 0 & 2 & 1 \\ 0 & 2 & 1 & 2 & 1 & 0 & 2 & 0 \\ 2 & 2 & 0 & 1 & 0 & 1 & 2 & 2 \\ 0 & 0 & 2 & 2 & 1 & 1 & 0 & 2 \\ 0 & 1 & 2 & 2 & 2 & 0 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 1 & 2 & 2 \\ \end{bmatrix}$
What I want to do is to find the sum of the diagonal elements of each column except the last column. For example,
$\begin{bmatrix} 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 \\ 0 & 0 & 2 & 2 & 4 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 4 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{bmatrix}$
Which is equal to
\$\begin{bmatrix}
2 & 0 & 0 & 0 & 0 & 2 & 0 & 0 \\
0 & 4 & 0 & 0 & 0 & 4 & 0 & 0 \\
0 & 0 & 4 & 0 & 0 & 4 & 0 & 0 \\
0
5b5f913d15
After the installation process, a file named: “Resurf”. This file should be renamed to “Map File” and then move it to the installation directory. (W:Operation not permitted)
Start AutoCAD, and then activate the Resurf Map.
Go to the Filter option.
Select Map Type = Resurf.
Change the filter field so that it selects both text fields.
Hit Ok.
Known issues
This software lacks any kind of lock functionality when the key is used or edited. Any user can be a source of key cracking/creation.
References
Category:Desktop modeling software
Category:AutoCAD1. Field of the Invention
The invention relates to a method for separating an absorption layer from a functionalized polymeric substrate.
2. Background Information
Cataract surgery is typically performed using a pulse dye laser. The laser output is applied to a pre-exposed surgical capsulotomy in the lens of the eye. This laser procedure is known as photo capsulotomy. Laser energy is selectively absorbed in the cataractous lens with no visible absorption in the capsular bag, or posterior lens capsule, after the pulsed laser energy is applied to the anterior surface of the lens. This selective absorption is in contrast to the equally efficient absorption in the posterior lens capsule.
The absorption of the photo capsulotomy occurs in the functionalized hydrophilic and hydrophobic regions of the posterior lens capsule. These functionalized regions provide a weak bonding between the lens capsule and the posterior lens epithelium.
After the laser energy is applied, the posterior capsule is removed, leaving only a small rim of cortex. The cortex is resorbed by the epithelial cells and the crystalline lens is reshaped. During the reshaping, the epithelial cells migrate along the surface of the posterior lens capsule and the normal curvature of the posterior capsule is re-established.
After the cataract has been removed, the posterior capsule remains and is absorbed by the natural wound healing process of the eye. The epithelial cells migrate across the posterior capsule. If the wound healing is slowed or in some cases, the posterior capsule is left intact, the posterior capsule may degrade
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The Start Button: | 2022-10-06 17:09:39 | {"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": 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": 0.22601063549518585, "perplexity": 3540.9335479684087}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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-2022-40/segments/1664030337853.66/warc/CC-MAIN-20221006155805-20221006185805-00584.warc.gz"} |
http://tex.stackexchange.com/questions/29189/how-to-debug-hanging-xetex-compilation | # How to debug hanging xetex compilation
I'm experiencing a weird problem. After updating my MikTeX installation my thesis document no longer compiles. Compilation (with xelatex) hangs and takes up all of one of my CPU's cores.
However, if I take out one particular chapter (the chapters are in separate .tex files which I load with \input) compilation completes without any problems.
But, when I compile that particular chapter separably compilation also completes without problems. In other words, the problem does not seem to be caused by the chapter itself, but rather by some combination of factors. Also, I must stress that things worked fine until I updated MikTex.
Does anyone have any ideas on what might be causing this? Or maybe just some pointers on how I could debug this situation?
EDIT (1)
(removed, the problem was not related to images after all)
EDIT (2)
I did more research and it turns out it has something to do with greek letters in math mode.
I have traced to problem to a few math expressions (between $-signs) containing \mu and \alpha. These are in the aforementioned chapter. If I comment out these expressions (or just remove \mu and \alpha from them) my whole thesis compiles without problem (so including the problematic chapter). What makes this extra strange is that when I compile this chapter (with the \mu and \alpha expressions) in isolation -- by commenting out the loading of all other chapters in my master file -- everything works and the mu's and alpha's look fine in the pdf. My guess it this might be a memory problem. Maybe some sort of font cache can not load the greek glyphs because it is already full with all the glyphs used elsewhere in my thesis. Does this make any sense? Providing a MWE for this problem is hard because it simply does not seem to occur when the input is "minimal". However, this might be a relevant section of my preable: \usepackage{amsmath,amsfonts,amssymb} %MATH FONT: Iwona Light \usepackage[light,math]{iwona} %for basic math symbols %AMS Blackboald (mathbb) font (used for mathematical fields) \DeclareSymbolFont{AMSb}{U}{msb}{m}{n} \protected\def\mathbb#1{{\mathchar\numexpr256*\symAMSb+#1\relax}} \usepackage{mathspec} %Also loads fontspec(!) \defaultfontfeatures{Ligatures=TeX,Scale=MatchUppercase,Numbers={Lining,Proportional}} %MAIN FONT and MATH digits and latin letters: Computer Modern Unicode (CMU) Bright (loaded by filenames to force use of OpenType versions) \setallmainfonts(Digits,Latin)[BoldFont={cmunbbx.otf},ItalicFont={cmunbmo.otf},BoldItalicFont={cmunbxo.otf}]{cmunbmr.otf} %MATH greek letters: Greek font is Iwona Light (loaded by filenames to force use of OpenType versions) \setmathsfont(Greek)[BoldFont={Iwona-Bold.otf},ItalicFont={IwonaLight-Italic.otf},BoldItalicFont={Iwona-BoldItalic.otf},Numbers={Lining,Proportional}]{IwonaLight-Regular.otf} %SANS FONT: idem (no need to set it because CMU Bright already is a sans serif font) %MONOSPACE (typewrite) FONT: CMU Typewriter Text Light \setmonofont[Scale=MatchLowercase]{CMU Typewriter Text Light} \usepackage{xltxtra} %also loads xunicode - The following is not an answer but a comment. I use texlive, but experienced very similar issues to the ones you reported after I updated texlive over the weekend. Late last week there were some updates to the l3* packages and fontspec, but the update to mathspec was delayed until Monday or Tuesday. Because the updates were out of sync, so to say, problems arose. Since running the texlive updater again (early yesterday), everything's back in fine working order. In short, you may have to update your miktex installation again after the packages in question have been incorporated. – Mico Sep 22 '11 at 13:24 Thanks for your command Mico. As I am using mathspec and fontspec this could indeed be the reason... Checking for MikTex updates again... – Matthias Sep 22 '11 at 13:27 I'll keep my fingers crossed for your sake that getting the next update to the fontspec and mathspec files will do the trick. :-) – Mico Sep 22 '11 at 13:43 Unfortunately updating MikTex did not help. There where 2 package updates, but not for mathspec or fontspec. Also I checked and mathspec wasn't updated in MikTex since late 2009 and the last version on CTAN is also from that period. – Matthias Sep 22 '11 at 13:46 I suggest also to look at this thread – egreg Sep 22 '11 at 18:01 ## 1 Answer I was able to fix the problem with these 2 steps (both were necessary): • stopped using \setmathsfont(Greek){Iwona Light} (instead I rely only on \usepackage[light,math]{iwona} which was loaded anyway for symbols/largesymbols/etc. and also applies to greek letters like \alpha) • avoided all used of mathspec's "-feature (for custom spacing in math mode) The compilation problem has not occurred ever since. I should note that mathspec's "-'feature' was also mentioned as the source of xetex compilation hanging in the thread egreg referred to in the comments above. The only downside of no longer using \setmathsfont(Greek) was that I could no longer type greek letters as unicode characters (so αβ instead of \alpha\beta). However I was able to fix that by making all greek characters active (based on their unicode-code) and replacing their occurances with the relevant math command, like so: \catcode\^^^^03b1=13 \let^^^^03b1=\alpha \catcode\^^^^03b2=13 \let^^^^03b2=\beta` I got the idea from this blogpost: http://uucode.com/blog/2010/03/26/unicode-math-in-xelatex I made a custom package (which I may release online if there is interest) in which I did this for all greek letters (upper & lower case). Also, the package makes it possible to use the greek chars in math AND text mode (by auto-wrapping a$-pair around the \alpha, \beta, ... when greek unicode chars appear in text mode).
I realize a better way to do this would be to use unicode-math, but I don't really like any of the fonts which work with that package (because there is no sans serif font afaik).
- | 2016-07-24 01:06:42 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8564621806144714, "perplexity": 1220.2187788774054}, "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-2016-30/segments/1469257823805.20/warc/CC-MAIN-20160723071023-00016-ip-10-185-27-174.ec2.internal.warc.gz"} |
https://socratic.org/questions/why-we-take-caco-3-as-standard-to-determine-the-hardness-of-water | # Why we take "CaCO"_3 as standard to determine the hardness of water?
Mar 8, 2018
There are two reasons.
#### Explanation:
1. ${\text{CaCO}}_{3}$ causes most of the hardness
Water passing over limestone deposits dissolves some of the minerals.
The concentrations of $\text{Ca"^"2+", "Mg"^"2+}$, and $\text{HCO"_3^"-}$ ions present in the water increase greatly and cause the water to become "hard."
$\text{Ca}$ and $\text{Mg}$ often occur together, so it is convenient to have a single number that represents the total concentration of both ions.
2. The calculation is easy
We measure the concentrations of individual ions $\text{Ca"^"2+}$ and $\text{Mg"^"2+}$.
We usually express the hardness of water in "ppm" (parts per million or milligrams per kilogram of water or milligrams per litre).
The molar mass of $\text{CaCO"_3}$ is 100 g/mol, so it is easy to manipulate the numbers.
Thus,
M_text(CaCO₃)/M_text(Ca) = 100/40 = 2.5
M_text(CaCO₃)/M_text(Mg) = 100/24.3 = 4.1
Thus we can express the total hardness of water as
$\left[\text{CaCO"_3] = 2.5["Ca"^"2+"] + 4.1["Mg"^"2+}\right]$
Example
If ["Ca"^"2+"] = "30 mg/L" and ["Mg"^"2+"] = "3 mg/L",
The total hardness expressed as ${\text{CaCO}}_{3}$ is
["CaCO"_3] = "2.5 × 30 mg/mL+ 4.1 × 3 mg/L = 75 mg/L + 12 mg/L"
$\text{= 87 mg/L}$ | 2018-12-13 22:21:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 16, "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": 0.7175800800323486, "perplexity": 2765.8514814715295}, "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-2018-51/segments/1544376825112.63/warc/CC-MAIN-20181213215347-20181214000847-00439.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/college-algebra-7th-edition/chapter-2-functions-chapter-2-review-exercises-page-267/1 | ## College Algebra 7th Edition
f(x) = $x^{2}$ - 5
You first must square the input (which is x) -> $x^{2}$ Then subtract 5 f(x) = $x^{2}$ - 5 | 2018-09-25 11:51:58 | {"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": 0.9122604727745056, "perplexity": 1682.0212994670903}, "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-2018-39/segments/1537267161501.96/warc/CC-MAIN-20180925103454-20180925123854-00211.warc.gz"} |
http://dekro.ru/owwyrfh/ycxzy73.php?uonaemsxx=first-order-iir-filter | First order iir filter
First order iir filter Finite impulse response [ edit ] Finite-impulse-response filters can be built that approximate to the sinc function time-domain response of an ideal sharp-cutoff low-pass filter. The first order and second order circuit of All-Pass Filter have been mentioned below. implemented FIR and IIR filter depends on different factors, e. Snapshot 2: all-pole filter reducing amplitude of high frequencies. Order of the FIR or IIR filter, specified as the comma-separated pair consisting of 'FilterOrder' and a positive integer scalar. Common examples of linear time-invariant systems are most electronic and digital filters. IIR filters have one or more non-zero feedback First, the ideal filter International Design of Higher Order Digital IIR Low Pass Filter Using Hybrid Differential Evolution . In the present paper, we discuss a method to design a linear phase 1-dimensional Infinite Impulse Response (IIR) filter using orthogonal polynomials. 3) Impulse Response of a First-Order IIR System † The impulse response can be obtained by …IIR Filter Design IIR vs. I'd be happy for analytic solution whether it is for ${L}_{2}$ or ${L}_{1}$ cost function. Determine the corner frequency of your low-pass filter. The transfer function of the general fifth-order digital IIR filter as shown in this Demonstration is represented byDescription. The given parameters for the first IIR all-pass filter are m 1 =5 and m 2 =9 and for the second IIR all-pass filter they are m 1 =9 and m 2 =5. Since IIR filters are linear systems, the two calculations for the first zero section (b 11,b12) and the last pole portion (a n1,an2). a first-order filter ( ) with NM==3 yn ECE 2610 Signals and Systems 8–3 (8. Arzi. MathWorks Machine Translation. The transfer function of an infinite impulse response (IIR) filter with a Cascaded Second-Order Sections Form structure is defined as follows: where z is a complex variable, N is the number of sections, a is the set of reverse coefficients, and b is the set of forward coefficients. )( 1. IIR Filter Design on the TMS320C54x DSP Mandy Tsai The second-order IIR filter is two cascaded sections: the zeros and the poles. I'm designing a simple first order IIR filter for my Spartan-6 but I'm struggling with bus widths and coefficient quantization. Since each stage is similar algorithmically, it is implemented as aDescription. E-mail : contact AT tsdconseil. To compute the specific lengths of the arrays, first define the effective filter order $$N$$ which is the same as the specified filter order for low- and high- pass filters, and doubled for band-pass and band-stop filters. The input data is 16-bits wide comes from integrated ADCs and the quantization noise is the main noise contribution to the front end noise. The mathematical formula to be implemented for a first order IIR filter is as shown below. parallel IIR chebyshev type I bandpass filter which has 6th order was developed. Introduction. This section is associated to the real pole and to the real zero if there is one. What order of filter (1st order to 6th order) is required to give acceptable cut-offs for audio work? Complex Coefficient IIR Digital Filters first-order real filter Re[z] Im[z] Fig. The IIR filter seem not to be too CPU intensive, but the coefficients calculation is. It’s a jungle out there. In the special case when the denominator is unity it becomes the transfer function for a finite impulse response filter (FIR filter). Summary: This article shows how to implement a low-pass single-pole IIR filter. It is a nice audio plugin architecture with a very easy learning curve. When a filter is applied to successive blocks of a signal, it is necessary to save the filter state after processing each block. Let us examine a "first order" structure. - Second parameter is filter type which lp= lowpass, hp=highpass, bp=bandpass. Systems with this property are known as IIR systems or IIR filters, and are . Design of first-order differentiator utilising FIR and IIR sub-filters 9 Figure 12 Values of the critical pole of A(z) versus the bandwidth The filter has symmetric coefficients and the symbolic of the IIR/FIR wideband differentiator. possible that an IIR of lower order actually requires more #MAD than an FIR of higher order, because FIR filters may be implemented using polyphase structures. The Filter 2. Some approaches for computing the very first filtered value are: Use the raw sensor data instead of the lag filter formula. So this simple statement is very complicated when it comes to designing a circuit for the required frequencies to be blocked and allowing other ones. IIR Filter Design Using the Bilinear Transform. That formula for the cut-off frequency is a very inaccurate approximation. The automated translation of this page is provided by a general purpose third party translator tool. Topics covered: Digital filter design using the bilinear transformation, frequency warping introduced by the bilinear transformation, algorithmic design procedures for IIR filters. In a simple no-noise case, assuming that the phase offset is small (and the signal gets decoded correctly), the estimate of phase offset is, IIR1. Created Date: 9/13/1998 12:20:58 AMDesign of Higher Order Digital IIR Low Pass Filter Using Hybrid Differential Evolution . The most common design method for digital IIR filters is based on designing an analogue IIR filter and then I'm designing a simple first order IIR filter for my Spartan-6 but I'm struggling with bus widths and coefficient quantization. Ver. The work presented in this paper concerns with Abstract— synthesis of the two-dimensional Infinite Impulse Response (IIR) filters based on model order reduction. Introduction: In this lab, we learn the concept of the IIR filter. When emphasizing the analogy to analog circuits, the single tuning parameter is the “time constant”, usually written as the lower case Greek letter Tau ( ). The relation between the transition bandwidth and the filter length $$M$$, is given by: order Bessel function of the first kind. 4. In order to illustrate the efficiency of the designed Hardware architecture for the IIR filter. lfilter (b, a, x[, axis, zi]) Filter data along one-dimension with an IIR or FIR filter. Jump to navigation Jump to search. Foreword. August 2, 2002. 1 Simple filters There are two methods for smoothing a sequence of numbers in order to approx-imate a low-passfilter: the polynomial fit, as just described, and the moving av-A 4th order IIR Filter is implemented by cascading two of the structures shown in Figure 1. The filter is used for averaging Wifi signal strengths that are numbers like x = -65, -60, -63 etc. 2: Direct-Form-II implementation of a 2nd-order digital filter. Figure 9. I am working on a bugfix for an IIR filter implementation in C. For their simplicity and effectiveness, most commonly used are the so called circular buffers the length of which can be expressed as 2^k. First of all…A filter is a circuit which eliminates some particular frequencies and allows the other ones. A 9th order filter would be realized with numStages=5 second order stages with the coefficients for one of the stages configured as a first order filter (b2=0 and a2=0). Select the Global settings tab of the UI. From Wikibooks, open books for an open world < Digital Signal Processing. 0 component in PSoC Creator enables the use of direct-form I biquad filters, which are second order IIRs. A butterworth filter is usually my first choice for IIR, but for a first-order response, it doesn't really matter. (). • First-order IIR filter. In particular, IIR filter specs are normalized to [1 − Δ 1 , 1](dB) in the passband, andCONTROLLED DOCUMENT: P_901-000006_Rev06 Filter Design Equations. From high-pass filter realization on wikipedia , and given a sampling rate fs and filter cutoff frequency fc , the required factor alpha can be obtained from the relation:Digital Filters 2 What is a filter? Take input and create output Programs are filters back” to mix with new input gives the filter’s order. The order reduction of the filter is based on the Quasi-Gramians method. 0. 5Hz, 1Hz, 2Hz, 4Hz and 8Hz) filtered using a low pass filter. 5 * fs normal_c In 1998, I had some extra time while others were reading for final exams of the senior high school, and got into digital signal processing. This code drive the filter output data. This component implements a first order IIR low pass filter. 2nd order IIR filter sometimes referred to as a 'bi-quad'. This very simple numerical Aug 28, 2017 K. In many situations it is better to implement a digital filter in terms of first- and/or second-order elementary sections The signal flow graph for the Direct-Form-II (DF-II) realization of the second-order IIR filter section is shown in Fig. This filter is an infinite-impulse-response (IIR) single-pole low-pass filter. na is 1 (a "first-order" filter, looking only the immediately previous output sample), b(1) is 1, and a(2) is (say) . Finite impulse response Edit Finite-impulse-response filters can be built that approximate to the sinc function time-domain response of an ideal sharp-cutoff low-pass filter. The basic difference in it construction is that we have poles and zeros instead of FIR (Finite Impulse Response) where we have only zeros. This example shows how to design classic IIR filters. . Reference [5] proposed a simulator structure consisting of an IIR filter and an The IIR first order low pass filter is a particularly easy to implement (but still useful!) case Code: Select all float UpdateFilter(float meas, float k) Recursive filters are also called Infinite Impulse Response (IIR) filters, since their impulse responses are composed of decaying exponentials. Higher Order Filters. LTI Discrete-Time Systems in Transform Domain Simple Filters Comb Filters (Optional reading) Example 1-First Order HP Filter • Design a first-order highpassfilter with a 3- Simple IIR Digital Filters • goes to zero at ω= 0 and ω=π 1 EE3054 Signals and Systems Lectures 9 IIR Systems: First Order System Yao Wang Polytechnic University Some slides included are extracted from lecture presentations prepared byThis filter implements a general first-order (one-pole one-zero) filter which can be used for a variety of purposes, including smoothing out envelopes, and filtering sound-file, signal or other controllers. Generally, the larger the filter order, the better the frequency magnitude response performance of the filter. In HSDPA systems, there is a delay of about 3 subframe associated with the application of CQI feedback. First-order IIR filter. 25 comments on “ A simple digital low-pass filter maybe you can read the “Tutorial on very simple yet useful filter: the first order IIR filter A 4th order IIR Filter is implemented by cascading two of the structures shown in Figure 1. IIR (Infinite Impulse Response) Filter. Introduction: FIR filters . 1 First-Order IIR Filter. 2 Algorithms (IIR Filters) IIR (Infinite Impulse Response) filter is a digital filter with feedback, as showing in the following picture. First, we need 2nd order coefficients to implement biquad sections, the preferred, andHi, Kato-san, Your comments are correct, the coefficient calculation tool can be used to generate the coefficients for different types of filters, including First Order filters like the IIR on PRB_R1. And often, we use this simple filter on parameters instead of one the audio directly—some gentle smoothing of a calculated signal in an automatic gain control, for instance. The class of infinite-length impulse response (IIR) filters can be characterized in the three domains: the time domain via the impulse response $$h[n]$$, the frequency domain via the frequency response, and the $$z$$-domain via poles and zeros. Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of second-order sections. Radcliffe ME855 4/8/2003 Second-Order IIR Filter Design Example: Derive the sampled data filter corresponding to the frequency response below. 1st order IIR Filter Design First compute a few intermediate variables to use in the design:First-order IIR Low-pass Filter Design & Discretization. First Order Adaptive IIR Filter for CQI Prediction in HSDPA Abstract: In this work, we consider channel quality indicator (CQI) prediction for High Speed Downlink Packet Access (HSDPA). The maximum delay, in samples, used in creating each output sample is called the order of the filter. Note that the input signal comes in from the right, and the output is on the left. a sinewave of one frequency more than one at another frequency. The averaged output from the filter is y. the 8th order low pass Infinite Impulse Response (IIR) filter. Snapshot 1: first-order all-pass filter. Second-order IIR filters in BasicDSP by Niels A. As a result, usually, when a digital IIR filter is going to be implemented, an analog filter (e. If the first stage filter is an IIR filter, design based on the FRM technique is less sensitive to the finite world length effects compared to the IIR filter realized in a If you are just interested in designing an FIR which approximates the amplitude response of an IIR, first of all you need to analyze the amplitude response of the IIR and extract the main parameters (passband and stopband cutoff frequencies, passband ripple, and stopband rejecton). This filter is an infinite-impulse-response (IIR) single-pole low-pass filter. The LowPassFilter is part of the Preprocessing Modules . Digital Filters 2 What is a filter? Take input and create 1 sample = first order; 2 samples = second order, can be more selective for a given filter order IIR A first order filter would have one capacitor or one inductor, that affects the filters frequency response. Snapshot 3: bandpass filter. The IIR filter is a single frequency wave trap, when n ( n>1 ) frequency at the same time to notch, according to (2 ) configuration of different center frequency wave trap, then n A low pass digital filter (IIR) is designed based on given specifications. This option names the VHDL entity and the file that contains the VHDL code for the filter. Now lets convert the IIR filter described above to fixed point. LAB 4 DIGITAL FILTERING 1. The signal flow graph for the Direct-Form-II (DF-II) realization of the second-order IIR filter section is shown in Fig. Note that in the quoted answer I used the constant $\alpha=1-b$. A second order filter would have two capacitors or two inductors, or one capacitor and one inductor, that affects the filter's frequency response. Internally, it has a fully pipelined architecture permitting the highest possible sample rates for IIR filtering. The output Y (out-put of each filter stage) is computed by direct imple-mentation of Equation 1 and Equation 2. Butterworth analog filter is designed first, then it is converted to digital filter . IIR filter design using BLT - Butterworth filter design in DSP - Duration: 15:29. 01 Hz cut-off frequency has a time constant of 16 Hz and a respective exponential step response. The transfer the optimization criteria. , a greater number of coefficients and more computation. It covers the basic first and second order filter types as well as the advantages and disadvantages of passive and active filters. signal import butter, filtfilt import numpy as np def butter_highpass(cutoff, fs, order=5): nyq = 0. The second kind of method is simple, shortTo compute the specific lengths of the arrays, first define the effective filter order $$N$$ which is the same as the specified filter order for low- and high- pass …In electrical circuits, an RC filter (filter with one resistor and one capacitor) is a first-order lag. It is an optimum filter, in the sense that for a given order and given ripple specifications, it has a narrow transition band width. 56%, 98. Introduction A generalized set of equations can be formulated for the design of first-order and second-order low pass and high pass 2. In order to navigate out of this carousel please use your heading shortcut key to navigate to the next or previous heading. The fig-1 (a) depicts high pass equivalent and fig-1 (b) depicts low pass equivalent of the all pass filter. A third family of filters is that of elliptic filters. Digital Signal Processing/IIR Filter Design. The method includes Order of the FIR or IIR filter, specified as the comma-separated pair consisting of 'FilterOrder' and a positive integer scalar. Design of first-order differentiator utilising FIR and IIR sub-filters 5 Usually, the differentiator is approximated with a linear-phase FIR transfer function H(z), 0 IIR filters with order > 3, are normally broken down into smaller sections, typically second and/or first order blocks, which are then connected up in cascade or in parallel. COMPLEMENTARY IIR FILTER PAIRS WITH AN ADJUSTABLE first-order all-pass section. The difference equation for the second-order DF-II structure can be written as All-Pole IIR filters Part 1 of this article first describes generalized formulas for any 2-pole polynomial, no-zero, lowpass or highpass, infinite impulse response (IIR) filter. )( )1(. In the Comment in header text box, type Tutorial - IIR Filter. For a half-width of M , the full width of the moving-average filter is N = 1 + 2 M samples. Higher Order Optimal Stable Digital IIR Filter Design 508 The cascaded transfer function of IIR filter is denoted by H(ω,x), involving the filter coefficients like, poles and zeros. 2. 2 derives a number of properties of second-order continuous filters, and Section 1. - Continuous Time Filter Design This section first defines some useful functions when working with continuous (analog) filters. The filter is designed using a set of object functions. Portland State University. The order of an IIR filter is equivalent to the greater of the number of its delayed input or output terms. To apply the impulse invariant method to a high order IIR filter with simple poles, the transfer function H(s) is first expanded using partial fractions as the sum of single-pole filters: M61 An approach to Digital Low-Pass IIR Filter Design Bojan Jovanović, and Milun Jevtić Abstract – The paper describes the design process of discrete network – digital low-pass filter with Infinite Impulse Responseorder, because FIR filters may be implemented using polyphase structures. Then select the General tab of the Additional settings section. Introduction. I wrote as I learned, and here is the result. (a) Difference equation: a1 and b0 8 Apr 2017 This article explains how to simply calculate a first order IIR filter. 2 This article present some of the more intuitive aspects of IIR filters. Note The lowpass filters shown above were created with the analog prototype functions besselap, buttap, cheb1ap, cheb2ap, and ellipap. Dependencies Specifying a filter order is only valid when the value of 'DesignForMinimumOrder' is false . Analog fixed notch filter suffer from problem of accuracy, difficult in realization and unadjustable notch frequencies . It is high enough order to be useful on its own, and—because of coefficient sensitivities in higher order filters—the biquad is often used as the basic building block for more complex filters. First, a polynomial function exhibiting linear phase will be synthesized On the Synthesis and Realization of Selective Linear Phase IIR Filters Dejan Mirković, Ivan Litovski and Vančo Litovski Fig. doc DRN: PRELIMINARY Page 3 of 9 1. IIR Filter Design by Analog Filter Approximation The impulse invariance method suffers from aliasing and is not used often The bilinear transformation does not suffer from aliasing and is In this case the analog filter function is a first order LPF similar Æ instability problems should be minimal. FILTER DESIGN SUMMARY General linear filter with constant coefficients: = = = − + − M m m N m y n bmx n m a y n m 0 0 ( ) ( ) (1)FIR – Finite Impulse Response filter: No recursive termsEECS 206 IIR Filters IV: Case Study of IIR Filters August 2, 2002 † First-order IIR filter † Second-order IIR filter 1 First-Order IIR Filter (a) Difference equation: a1 and b0 real y In other words, the simple rst order IIR lter is the optimal lter to track a scalar value subject to random variations, and moreover the Kalman theory (Riccati equation) gives us the theorical tools to compute the optimal forget Tutorial on the first order IIR filterIn this answer I derived the exact relation between the coefficient of a first order recursive averaging filter and its 3-dB cut-off frequency. During the design we make use of magnitude and frequency scaling and also of the uniform choice of as a characterizing frequency will appear in all design steps, except for the last where the de-normalized (actual) values will be found. We are using bilinear transform (BLT) with frequency warping to compute the coefficients for different first and second order filter types. Hi, Kato-san, Your comments are correct, the coefficient calculation tool can be used to generate the coefficients for different types of filters, including First Order filters like the IIR on PRB_R1. First-order IIR Low-pass Filter Design & Discretization Determine the corner frequency of your low-pass filter. 5Hz, 1Hz, 2Hz, 4Hz and 8Hz) filtered using a low pass filter. I propose an simple Excel calculation sheet, which shows also frequency Sep 28, 2005 Filtering is a witch's brew of analog, digital, and mathematics that can fell the stoutest This new first order IIR filter, shown in Figure 9, has the It is often necessary to filter data from sensors or audio streams in order to suppress unwanted noise. For details refer to : "Signal Processing : Discrete Spectral Analysis, Detection and Estimation" - M. This transfer function atten uates lo w frequencies, but lets frequencies I know the IIR has infinite impulse response, hence I'm looking for the best approximation. The reason why this type of first order IIR filter is so widely used, is that it requires just an additional variable in RAM memory, to store the previous value of output signal, which is . Search for filter_out. Once the transfer function has been chosen, different filter structures allow to implement the filter, be it in hardware or in software. SPICE simulation that models a filter FIR, finite impulse response, where the number of terms in the response is finite. The first section of this chapter discusses the Finite Impulse Response (FIR) filter and the second section discusses the Infinite Impulse Response (IIR) filter. That is, the current output sample is the sum of the current input sample and half the previous output sample. g. Chapter 10 3 First-Order IIR Filter • Consider a 1st-order linear time-invariant recursion (see Fig. C. 2 Algorithms (IIR Filters) IIR (Infinite Impulse Response) filter is a digital filter with feedback, as showing in the following picture. Design of IIR filters Application of Bilinear Transform Design a first order low-pass digital filter with -3dB frequency of 1kHz and a sampling frequency of 8kHz The real-time digital filter, because it is a discrete time function, works with digitized data as opposed to a continuous waveform, and a new data point is acquired each sampling period. Then a window (Kaiser, Hanning, etc) is applied to the impulse response. Description. realizing the root locations of the filter with cascaded first- and second-order stages and the second is based on replacing components of a passive RLC ladder filter with first-order stages. Comparing with FIR filter, because of the feedback mechanism, IIR filter is much efficient than FIR filter. To apply the impulse invariant method to a high order IIR filter with simple poles, the transfer function H(s) is first expanded using partial fractions as the sum of single-pole filters: M Lecture 6 -Design of Digital Filters 6. From the discussion made so far on the filters, it may be concluded that in the stopband the gain of the filter changes at the rate of 20 db/decade for first-order filters and 40 db/decade for second-order filters. An elliptic filter has equiripple behaviour in both stop and pass bands. 1) • The iteration period of this filter is , where represent Sometimes, we do need the gentle slope of a first order frequency roll-off. shown in TableII, in Elliptical filter ,filter order, number of multiplier, number of adder, number of states up to 98. The LowPassFilter class implements a first-order infinite-impulse-response (IIR) low pass filter. FIR Filters High Pass Filter - Impulse Response Given a discrete system impulse response, it is simple to calculate its z transform. The coefficients − b k 1 and a k1 are the roots of the numerator and denominator polynomials and must be quantized. Pole rotation of a first-order real transfer function after applying the A 9th order filter would be realized with numStages=5 second order stages with the coefficients for one of the stages configured as a first order filter (b2=0 and a2=0). So, in order to -speed and with high precision, it is very important to design the IIR filters [12]. A biquad is a second order (two poles and two zeros) IIR filter. Since this filter has only one sample of state, it is a first order filter. The article is complemented by a Filter Design tool that allows you to create your own custom versions of the example filter that is shown below. And, most of the time, a simple first order filter is all that is 6. )( )( )1(. Because of the overshoot in the filters step response, square waves typically create the largest math values in a filter. First order highpass lter The transfer function is H (s)= s s +! c = s=! c 1+ s=! where! c =2 1000. symiirorder2 (input, r, omega {, precision}) Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of second-order sections. . Schwartz and L. • Second-order IIR filter. An analog filter, 60 Hz Twin T Notch, was created to compare and contrast with the digital implementation. Details. iir_frac16_1st - frac16 first-order IIR filter iir_frac16_2nd - frac16 second-order IIR filter iir_frac16_casc - cascade of frac16 second-order IIR filters A simple first order digital phase locked loop for tracking the constat phase offset can be as Assuming that the transmitter signal gets rotated by a constant phase , the received signal . In the difference-equation representation, the order is the larger of and in Eq. Therefore this paper presents discussion of IIR notch filters Filter Order . Even though FIR is easier to design, IIR will do the same work with fewer components, and fewer components translate directly to less money. Then the transfer function Then the transfer function between the input x and output y has a frequency dependent magnitude IIR Filter Design IIR vs. Looking back at Figure 1, we identified nodes d[n] and y[n] to be the potential l Consider the first-order IIR filter as shown right Assume the quantization operation to be rounding and the filter to be implemented with a signed 6-bit fractional arithmetic l The nonlinear difference equation characterizing the filter is given by IIR BANDPASS FILTER DESIGN USING MODIFIED TRANSFER FUNCTION IMPLEMENTATION IIR filters can be designed with first order Direct Forms 10: Digital Filter Structures • Direct Forms • Transposition • State Space + • Precision Issues • Coefficient Sensitivity • Cascaded Biquads • Pole-zero Pairing/Ordering Infinite Impulse Response (IIR) filters [1]. The corner frequency should be at most 10% of the system sample rate. I propose an simple Excel calculation sheet, which shows also frequency IIR Filters. The reason to use this approach is to emulate the sample & hold behavior:The simplest second-order digital filter, called a direct form, applies only five multiplies and five additions per sample, applied to five numbers: the input sample, …Dear All, I do not have any background in DSP, so please excuse if this question seems silly. It is often necessary to filter data from sensors or audio streams in order to suppress unwanted noise. Figure 9: Combined IIR magnitude response The characteristics include the steep low-pass curve of the IIR filter with the 0 gain at half the sample frequency of the FIR filter. How could this optimization problems can be solved given only 1st order IIR. Figure 6-28(a) is an implementation of our second-order IIR filter based on the general IIR structure given in Figure 6-22, and Figure 6-28(b) shows the second-order IIR filter implementation based on the alternate structure from Figure 6-21(b). Implementation Structures for Recursive Digital Filters Transposed-Direct-Form-I implementation of a second-order IIR digital filter. Digital filter is also often described in the difference equation form, which defines the relationship between output signal and input signal. FIR filter is large enough compared to IIR filter. First thing that comes to mind is that your main loop just seems to sample as quickly as possible. the second order system of IIR digital filter of the Z transfer function: The first method has the advantages of higher precision, but the floating point arithmetic program complex, long execution time. FIR Filters. A first-order filter causes gradual attenuation until the corner frequency. Incidentally, the exponential filter in Excel's Analysis Toolpak is a low pass filtering app. baseline noise elimination is often one of the first steps The order of performed IIR filter is 2 and it is a recursive filter. (b) Fixed point implementation of a 2nd order IIR filter using the Direct Form I structure (c) Additive noise model for the fixed-point 2 nd order IIR filter in (b). Similar sections of VHDL code apply to another second-order section and a first-order section. The figure-1 depicts First Order All Pass Filter circuit. 3. Filter Order influence. An elliptic filter has equiripple behaviour in both stop and pass bands. The transfer function of the general fifth-order digital IIR filter as shown in this Demonstration is represented by Formula (9-34) is the transfer function for an infinite impulse response filter (IIR filter). First, we show how to use known design specifications to determine filter order and 3dB cut-off How to implement a first order IIR RC filter in TPT. For a first-order filter, the stability condition that needs to be satisfied is that the pole of the filter lies within the unit circle. It has two delay nodes and the computation coefficients are A 1k , A 2k , B 1k and B 2k . A powerful C++ filter library for Linux, Mac OSX and Windows which implements all standard IIR filters such as Bessel, Butterworth, RBJ and Chebychev (which is shown above). Steady State and Transient Response: Before a signal is applied to the input of a digital filter, the filter's internal state'' is assumed equal to zero. April 1, 2016. J. The main reason is that IIR filter coefficients cannot be limited to a fractional range, as can FIR filter coefficients. )1(. 5. And, most of the time, a simple first order filter is all that is required. 2: Direct-Form-II implementation of a 2nd-order digital filter. In the previous filter tutorials we looked at simple first-order type low and high pass filters that contain only one single resistor and a single reactive component (a capacitor) within their RC filter circuit design. This filter class is capable to do low/high/bandpass and stopband filterings with different filter designs: Butterworth or Chebyshev Type I/II. Parallel realization of an odd-order IIR digital filter . This shopping feature will continue to load items. function will be the product of only two complex first- order sections. Figure 4 illustrates a bi-quad digital filter structure that computes the response of a second order IIR transfer function. For example, specifies a particular second-order filter. 1. I implemented an high pass filter in python using this code: from scipy. An IIR filter class implementation in Python 3. 0 component in PSoC Creator enables the use of direct-form I biquad filters, which are second order IIRs. In fact, a second-order IIR filter can be used as a sinus oid oscillator, even producing per- placing the feedback section first, followed by the feedfor- Chapter 7 • Real-Time IIR Digital Filters-=--- Designing a first-order IIR filter. 6 time constants, easy to calculate. High-order filters, such as third, fourth, and fifth-order are usually formed by cascading together single first-order and second-order filters. In the first part of the lab we are to use MATLAB to design a fourth order IIR filter through the cascading of two second order IIR filters. - The first parameter is filter order. I’m sure this could be written in other software languages as well, just don’t ask me how. first order iir filterInfinite impulse response (IIR) is a property applying to many linear time-invariant systems. 22The first type of system performs signal filtering in time domain. A low-pass filter (LPF) is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. problem of higher order low-pass stable digital IIR filter design. N is the number of first-order or second-order allpass sections. Let the sampling time be Ts and the filter bandwidth be ωc rad/sec. IIR Filters IV: Case Study of IIR Filters. D. This project was created as part of a university assignment. Moseley PE1OIT Second-order filters offer a sharper frequency response compared to the first-order filter. second order real filter into the product of two first order complex sections and initializing the internal memories of each section with its steady state values. Analytical procedure is illustrated below and simplified to allow one to more easily program the algorithm. To find the transfer function of the filter, we first take the Z-transform of each A simple FIR filter is the moving average filter. 2/24/2009 · Dear All, I do not have any background in DSP, so please excuse if this question seems silly. Abstract. First the minimax optimization method is used to design a family of second-, third-, and fourth-order digital integrators by optimizing the magnitude response in a min-max sense under the satisfactory condition of constant group delay. The kit is a subset of the following: IIR Filters See this page for IIR Filter Design Equations and C Code. 1Hz, 0. IIR filters have one or more non-zero feedback coefficients. The simplest second-order digital filter, called a direct form, applies only five multiplies and five additions per sample, applied to five numbers: the input sample, the last two input samples, and the last two output samples. After that, the filter causes exponential attenuation. • Different conventions exist for specifying magnitude responses for IIR and FIR filters. I mean, there are 4 coefficients for a first order IIR filter and I want to calculate coefficients of a 10th order FIR filter, which is equivalent of the IIR filter, in terms of the 4 coefficients. That may be useful if the filter is implemented in hardware. If the transfer function's order is odd, then a first order section has to be added to the chain. (a) Difference equation: a1 and b0 IIR Filters. a single high-order IIR, particularly for lower cut-off frequencies. The digital IIR filter implementation would naturally suffer from a large amount of group delay due to the tight constraints. z 3F3 Digital Signal Processing Section 2: Digital Filters • A filter is a device which passes some signals 'more' than others (selectivity’), e. That is, as a result of the feedback term, if the filter First, the ideal filter Dear All, I do not have any background in DSP, so please excuse if this question seems silly. Depending on your application, the "infinite" in IIR might be inconvenient and a FIR filter more suitable. Basic IIR Digital Filter Structures • The causal IIR digital filters we are concerned with in this course are • In the above, for a first-order factor IIR filter design primarily concentrates on the magnitude response of the filter and regards the phase response as secondary. )}( )({)(. Digital Signal Processing - IIR Filter Design - Important Questions and Answers: IIR Filter Design For designing a digital IIR filter, first an equivalent analog filter is designed using any one of the approximation technique for the given specifications. 1 3 Order IIR Highpass Butterworth Filter In signal processing, the order of the FIR filter is always higher than that of the IIR filter when we basically view the 61 An approach to Digital Low-Pass IIR Filter Design Bojan Jovanović, and Milun Jevtić Abstract – The paper describes the design process of discrete network – digital low-pass filter with Infinite Impulse Response • For IIR digital filter design, the IIR transfer function is a real rational function of : • H(z we get the transfer function of a first-order One of the most-used filter forms is the biquad. The primary advantage of IIR filters over FIR filters is that they typically meet a given set of specifications with a much lower filter order than a corresponding FIR filter. To illustrate this, we’ll first look at how quantizing coefficients effects z-plane pole locations of a 6 th order IIR filter. Sidhu . These structures implement an IIR filter as a single Nth order …Lecture 6 -Design of Digital Filters 6. This algorithm generates second order IIR filter coefficients, not Nth order coefficients. 5. Again writing in terms of the coefficients just designed, the condition can be given as: where V N is a Chebyschev polynomial of order N. This page derives the equations used to generate IIR filter coefficients for low pass, high pass, band pass, and notch filters. On what basis it is Proposed work deals with the design of a family of stable IIR digital integrators via use of minimax and pole, zero, and constant optimization methods. ECE 223. This feature is not available right now. 2. For example, second order real filter into the product of two first order complex sections and initializing the internal memories of each section with its steady state values. Section 1. The resulting bandpass and bandstop designs are of order 2 n . Thus, IIR filters require less Place the following steps in the order they are used to design and IIR filter. Filled with practical C functions, this state-of-the-art guide will allow filter designers to automate the design of analog and digital filters using the C programming language. Active Filter Design. Ha(s) = XN k=1 Ak s Note that the bilinear transform maps the entire left-hand s-plane to the interior ofDesign of first-order differentiator utilising FIR and IIR su b-filters 9 Figure 12 Values of the critical pole of A ( z ) versus the bandwidth of the IIR/FIR wideband differentiator. The first order section can be viewed as the second order section with B2 = A2 = 0. Important Short Questions and Answers: IIR Filter Design. SPICE simulation of IIR filter. This very simple numerical 28 Aug 2017 K. In other words, the simple rst order IIR lter is the optimal lter to track a scalar value subject to random variations, and moreover the Kalman theory (Riccati equation) gives us the theorical tools to compute the optimal forget This new first order IIR filter, shown in Figure 9, has the characteristics of both the previous filters. Shrenik Jain 11,548 views. This feature is particularly useful for designing controllers in three-phase systems (N = 3). Higher order systems Up: Chapter 6: Active Filter Previous: Wien bridge Butterworth filters. This property applies only when you set Specification to 'Coefficients' and Structure to 'Wave Digital Filter' . IIR filters are typically designed basing on continuous-time filter functions. 9. coefficients corresponding to the poles of the filter, and N is the filter’s order. The IIR filter, however, can achieve excellent approximation with considerably low order. • A simple IIR filter is the first-order lowpass filter. An IIR filter class implementation in Python 3. A recursive filter is one where the present output depends on past output values. Details. 8477). Filter design by windowing involves first calculating the impulse response for an ideal filter. 4 numerical examples are used to illustrate the procedure. Nasir Ahmed. The order of an IIR filter is equivalent to the greater of the number of its delayed input or output terms. The first filter created was a 60 Hz second order IIR Butterworth Notch filter. 2nd order IIR filter sometimes referred to as a 'bi-quad'. On IIR filter software implementation with direct structure, it is necessary to have two buffers with at least N+1 samples, where N is the IIR filter order. An important difference between FIR and IIR filters is the peak math values generated by the filter as a signal is processed. Discretize- use the "zero-order hold" approach. An Infinite Impulse Response (IIR) filter can be used to implement low pass and high pass Butterworth filters, which behave in the same way as analogue (resistor-capacitor) filters. 5Hz signal. 1Hz, 0. Direct computation of second order coefficients is preferred for three reasons. t. An example of a signal (sine wave at 0. IIR is better for lower-order tapping, whereas the FIR filter is used for higher-order tapping. 1 nyanxb nxbny nya nxbnxbny nxbnxb nyany. e. This filter is non recursive that is it has an output that depends on present input values only. You can specify the following types of filter: Butterworth, Bessel or Chebyshev infinite-impulse-response (IIR) filters, with lowpass, highpass, bandpass or bandstop characteristcis, designed by the bilinear transform or matched z -transform method; . 11/10/2014 · Moving on, as the title says, this post is about how to write a digital low-pass filter using the C language. To find the transfer function of the filter, we first take the Z-transform of each IIR Filters IV: Case Study of IIR Filters. This feature is particularly useful for …This Windowed FIR Filter C Code has two parts, the first is the calculation of the impulse response for a rectangular window (low pass, high pass, band pass, or notch). In this chapter we finally study the general infinite impulse response (IIR) difference equation that was men- a first-order filter ( ) with Impulse Response 2nd order IIR filters are often called 'biquads' and a common implementation of higher order filters is to cascade biquads. ∗. This sinc . The Online FIR Filter Design Tool generates the FIR filter coefficients, frequency response and impulse response based on the entered filter specifications. where V N is a Chebyschev polynomial of order N. In this chapter we finally study the general infinite impulse response (IIR) difference equation that was Impulse Response of a First-Order IIR System. Design of IIR Digital Highpass Butterworth Filter • For IIR digital filter design, the IIR transfer function is a real rational function of : • H(z we get the transfer function of a first-order digital lowpass Butterworth filter c c a s H s + Basic IIR Digital Filter Structures • The causal IIR digital filters we are concerned with in this course are characterized by a real rational transfer function of or, equivalently by a constant coefficient difference equation • In the above, for a first-order factor I mean, there are 4 coefficients for a first order IIR filter and I want to calculate coefficients of a 10th order FIR filter, which is equivalent of the IIR filter, in terms of the 4 coefficients. S. 00 coefficients corresponding to the poles of the filter, and N is the filter’s order. Design of Infinite Impulse Response (IIR) digital filters Output from a digital filter is made up from previous inputs and previous outputs, using the operation of convolution: Two convolutionsare involved: one with the previous inputs, and one with the previous outputs. We could use higher order filter but please remberber taht higher order filter increase the number of calculation iterations. The transfer function of an infinite impulse response (IIR) filter with a Cascaded Second-Order Sections Form structure is defined as follows: where z is a complex variable, N is the number of sections, a is the set of reverse coefficients, and b is the set of forward coefficients. In this answer I derived the exact relation between the coefficient of a first order recursive averaging filter and its 3-dB cut-off frequency. Infinite impulse response (IIR) filters IIR filters are the most efficient type of filter to implement in DSP (digital signal processing). Higher-order filters (such as Butterworth and Chebyshev filters) have steeper slopes after the corner frequency. CRPSO, the much improved version of PSO, is a population based global heuristic search algorithm which finds near optimal solution inFirst Order Adaptive IIR Filter for CQI Prediction in HSDPA Abstract: In this work, we consider channel quality indicator (CQI) prediction for High Speed Downlink Packet Access (HSDPA). The output data, y(n), is at a normalThis paper deals with using some MATLAB functions and tools for designing the first-order analogue Chebyshev filters and IIR Chebyshev filters. the first thing is filterdesign doesn't work at audio rate. Each block is built by a first-order Direct Form IIR filter. parallel IIR chebyshev type I bandpass filter which has 6th order was developed. It is noticeable from figure 2 and figure 3 that when changing the filter order with minor cut-off frequency of 2Hz (left figure), the filter output is significantly affected by the filter order. The obtained results prove that the proposed Cascaded digital IIR filter has several first order and second order sections together [6, 8]. The following block diagram demonstrates how to convert a filter from the Digital Filter Design Toolkit to an IIR filter cluster that is compatible with the IIR Filter Cluster output in the LabVIEW Full or Professional Development System filtering VIs. Design of first-order differentiator utilising FIR and IIR sub-filters 5 Usually, the differentiator is approximated with a linear-phase FIR transfer function H(z), 0An important difference between FIR and IIR filters is the peak math values generated by the filter as a signal is processed. A Cascade Form infinite impulse response (IIR) filter of the third-order. The difference equation for the second-order DF-II structure can be written as Sometimes, we do need the gentle slope of a first order frequency roll-off. EECS 206 IIR Filters IV: Case Study of IIR Filters August 2, 2002 † First-order IIR filter † Second-order IIR filter 1 First-Order IIR Filter (a) Difference equation: a1 and b0 real Simple Digital Filters sections of the first-order highpass filter • A first-order causal lowpass IIR digital filter has a transfer function given by The key characteristics of the First-Order Filter block are: Input accepts a vectorized input of N signals, thus implementing N filters. An RC circuit is a fist-order filter. First order IIR filters may be implemented in the Filter component by using the biquad filters with some zeroed coefficients. Hi, Is there a standard way of converting an IIR filter to a different sample rate? What I mean by this is, if I have an IIR filter F0 with a particular This algorithm generates second order IIR filter coefficients, not Nth order coefficients. Dear All, I do not have any background in DSP, so please excuse if this question seems silly. CRPSO, the much improved version of PSO, is a population based global heuristic search algorithm which finds near optimal solution in Order of a digital filter The order of a digital filter is the are all of first order, as one filter, and a recursive filter as an IIR (or Infinite A Beginner's Guide to Filter Topologies Abstract: This article is an excellent introduction to analog filters. A useful reference for computing biquad coefficients is the RBJ Audio EQ Cookbook . IIR Filter Design Home. But I just want to make it clear that the following system is equivalent to your mean filter and has the same computational complexity and your first order IIR!In signal processing, a digital biquad filter is a second-order recursive linear filter, containing High-order IIR filters can be highly sensitive to quantization of their as serially-cascaded biquad sections (and a first-order filter if necessary). 9. The filter is a DC tracking filter (low pass filter) whose purpose is to track DC component of a 1. g the coefficients of Fig. The main characteristic of the proposed filter design method resides in the fact that the equalization structure is planned from the beginning as a chain of SOSs (second-order sections), where each SOS is a low-pass, high-pass, or peak filter UDB Single Bit IIR filter Summary: This memo introduces and distributes an IIR filter implemented in a UDB. 2 FIR Filters The FIR (Finite Impulse Response) filter, as its name suggests, will always have a finite duration of non-zero An Introduction to Digital Filters APPLICATION NOTE AN9603 Rev 2. Somewhere in the dense wilderness, hidden from the view of the masses is a small tribe, much sought after by the head hunters of the surrounding plains. FIR filters have inherent stability when implemented in non-recursive form, linear phase, simple extensibility to multirate cases. N is known as the filter order. Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of first-order sections. Second-order IIR filters in BasicDSP by Niels A. Design an IIR filter, generate VHDL code for the filter, and verify the VHDL code with a generated test bench. order due to the growing number of multipliers, adders and delay elements [1]. 1 of Text • A digital filter,He(j), with infinite impulse response (IIR), can bew designed by first transforming it into a prototype analog filter Hj n)= c i x − i i =0 N ∑ (1) The input signal is x(n), the output signal is y(n) and c i are the filter coefficients. The first step is to identify the nodes in each second order section where overflow could occur. –Consider the IIR filter defined by = − r. What order of filter (1st order to 6th order) is required to give acceptable cut-offs for audio work? An Infinite Impulse Response (IIR) filter can be used to implement low pass and high pass Butterworth filters, which behave in the same way as analogue (resistor-capacitor) filters. 1 What plugins? This is the documentation for some plugins that I have written for the Linux Audio Developers Simple Plugin Architecture. Signal Processing First Lecture 16 IIR Filters: Feedback INFINITE IMPULSE RESPONSE FILTERS FIRST-ORDER IIR FILTER: y[n] Usually, in the IIR Filter design, Analog filter is designed, then it is transformed to a digital filter the conversion of Analog to Digital filter involves mapping of desired digital filter specifications into equivalent analog filter. The two band-edge frequencies, Fa and Fb, determine the shape of the sinc function impulse response of the ideal filter. Infinite impulse response (IIR) is a property applying to many linear time-invariant systems. Filter Order The maximum delay, in samples, used in creating each output sample is called the order of the filter. We then extend the 2-pole filter to a generalization for any even-order all-pole polynomial filter. exponential—Yields first-order IIR coefficients. Examples of low pass filters are air recievers for reciprocating compressors and capacitors across signals. fr. 6-1 6. To approximate a first order hardware filter, I generally use a IIR filter. 18. Im trying to implement a simple first order IIR filter on a MCU (PIC24FJ32GA002), without success until now. First order lo wpass lter The rst lter is a rst order lo wpass with cuto frequency 1kHz, with transfer Filter with ec hos Impulse resp onse: h (t) = )+0: 75 On IIR filter software implementation with direct structure, it is necessary to have two buffers with at least N+1 samples, where N is the IIR filter order. Fig. A method is presented for the design of notch filters with specified notch frequency Ω 0 and 3-dB rejection bandwidthB t, using a first-order real all-pass filter, wherein the only coefficient is used to control the notch frequency. The initial focus is on the situation for which the critical design parameter is the cutoff frequency at which the filter's power decays to half (-3 dB) the nominal passband value. First Order Lowpass RC Filter - Duration: 10:16. It is often possible to reduce the number of feedforward coefficients by introducing feedback coefficients. g. DT Filters. Tutorial on a very simple yet useful filter : the first order IIR filter. First, we need 2nd order coefficients to implement biquad sections, the preferred, and Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of second-order sections. IIR Filter Design Overview FIRST-ORDER (NOT MULTIPLE). In this application note, we will explain the difference between FIR ("finite impulse response") and IIR ("infinite impulse response") filtering. The SOS block is modular allowing any number of SOS blocks to be joined in series to implement higher order IIR filters. Steady State and Transient Response: Before a signal is applied to the input of a digital filter, the filter's internal state'' is assumed equal to zero. In the cascade form, the output of one section forms the input to the next: In practice, the propagation of errors is crucial to the success of an IIR filter so the order of the sections in the cascade, and the selection of which filter coefficients to group in each section, is vital: A novel method for the equalization of loudspeakers and other audio systems using IIR (infinite impulse response) parametric filters is presented. Department of Electronics and Communication Engineering, Giani Zail Singh Punjab Technical University Campus, A Simple Recursive (IIR) Filter Using FIR filters to reproduce a desired frequency response often requires a very high-order filter, i. The result of the analog The edge frequency of the ideal filter is in the center of this transition region. Common examples of linear time-invariant systems are most electronic and digital filters. In the first part of the lab we are to use MATLAB to design a fourth order IIR filter through the cascading of two second order IIR …Design of first-order differentiator utilising FIR and IIR sub-filters 9 Figure 12 Values of the critical pole of A(z) versus the bandwidth The filter has symmetric coefficients and the symbolic of the IIR/FIR wideband differentiator. half-width specifies the half-width of the moving-average filter in samples. Infinite impulse response (IIR) is a property applying to many linear time-invariant systems. [b,a] = butter(n,Wn,ftype) designs a lowpass, highpass, bandpass, or bandstop Butterworth filter, depending on the value of ftype and the number of elements of Wn. Design of IIR Filters • Reference: Sections 7. LAB OBJECTIVE The purpose of this lab is to design and implement digital filters. Chebyshev filter, Butterworth filter, Elliptic filter) is first designed and then is converted to a digital filter by applying discretization techniques such as Bilinear transform or Impulse invariance. IIR filters with order > 3, are normally broken down into smaller sections, typically second and/or first order blocks, which are then connected up in cascade or in parallel. 5412 (α = 1. 5 dB. This filter implements a general first-order (one-pole one-zero) filter which can be used for a variety of purposes, including smoothing out envelopes, and filtering sound-file, signal or other controllers. If and the 8th order low pass Infinite Impulse Response (IIR) filter. IIR filters provide extraordinary benefits in terms of computing: IIR filters are more than an order of magnitude more efficient than an equivalent FIR filter. Fill in the form and press the Submit'' button, and a filter will be designed for you. The input consists of the design specifications for the desired Butterworh analog filter. The first implementation top-level module has modules for 2, 4, and 6th-order IIR audio filters synched to run once/audio sample (about 47 KHz). Note that the bilinear transform maps the entire left-hand s-plane to the interior of The LowPassFilter class implements a first-order infinite-impulse-response (IIR) low pass filter. a) Apply a frequency transformation b) Prewarp critical frequencies c) Apply the bilinear transformation d) Decide on a Butterworth, Chebyshev I, II, or elliptic filter type. Mathematically, theDesign of IIR Digital Filters, Part 2 Let's take the case of a simple, second order analog filter, let's say with one 0 and two poles, so that the Well, the first algorithmic design procedure, which I am restricting, in my discussion here, to the design of infinite impulse response filters, the first is simply designing the filter to 2 - HIGHER-ORDER, CASCADED, ACTIVE FILTERS realizing the root locations of the filter with cascaded first- and second-order stages and the second is based on replacing components of a passive RLC ladder filter with first-order stages. A first order filter would have one capacitor or one inductor, that affects the filters frequency response. The IIR filter is the acronym of Infinite Impulse Response, what means that this type of filter does not becomes zero at the output in a certain amount of time, but it continues derivating indefinitely. FIR filters are preferred over IIR because they are more stable, and feedback is not involved. Show (publisher MCGraw-Hill). The pState points to state variables array. These functions find the zeros, poles, and gain of an order n analog filter of the appropriate type with cutoff frequency of 1 rad/s. 56% as compared to How does the order of a filter affect the impulse response of the system, however? Plotting the impulse responses of systems with certain orders suggests that the decay of the sinusoidals takes place much more slowly as the order increases, but I don't understand why. Chebyshev , Butterworth, Elliptic, etc) is first designed and then is converted to a digital filter by applying discretization techniques such as: 1)Bilinear transform or 2) Impulse invariance. This post is a mini tutorial on fixed point DSP. For the second-order all-pass sections, the corresponding adaptor coefficients are Structure of an Arbitrary Order IIR Filter Where “a” and “b” are IIR coefficients, “x” – input data vector, “y” – output vector, “order” – filter order. 3 In IIR filter implementation, we can group the numerator and denominator of (9. IIR digital filters have feedback paths that can sustain an impulse response Specify whether the block implements an FIR lowpass filter or an IIR lowpass filter. I am new to DSP, i was trying to implement the Butterworth filter and i read that Butterworth filter is an IIR filter. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. This section guides you through starting the Filter Design HDL Coder™ UI, setting options, and generating the VHDL code and a test bench for the IIR filter you designed and quantized in Design an IIR Filter in Filter Designer and Quantize the IIR Filter. We start with two forward 6. In the Name text box of the Target pane, type iir. 03. There is a strong dependency of an output value on a set of previous output values. I can use the freqz' function to find the cutoff (-20 dB) frequency for a given filter, specified by its IIR coefficients and sampling period. A filter with feedback from the output is called a recursive infinite impulse filter IIR. 1 sample = first order; 2 samples = second order, Infinite Impulse Response filter (IIR). he historic role of IIR (infinite-impulse-re-sponse)-filter-design software is to translate a set is a first- or second-order subfilter, Harris, Berdahl, Abel An IIR Hilbert Transformer Filter Design Technique for Audio AES 129th Convention, San Francisco, CA, 2010 Nov 4–7 Page 3 of 8 But just as two cascaded first-order sections don’t make a second-order section, two cascaded second-order Butterworth sections do not equal a fourth-order Butterworth section. These object functions are realized using a set of orthogonal polynomials. We want to design of a fifth order Butterworth low-pass filter with a cutoff frequency of 10KHz. A second-order filter decreases at −12 dB per octave, a third-order at −18 dB and so on. Settling to 99 % takes e. IIR Filter Design Overview Method: Impulse Invariance for IIR FIlters Approximation of Derivatives FIRST-ORDER (NOT MULTIPLE). For IIR filters, the filter order is equal to the number of delay elements in the filter structure. For example, two second-order low pass filters can be cascaded together to produce a fourth-order low pass filter, and so on. 1 Simple filters There are two methods for smoothing a sequence of numbers in order to approx-imate a low-passfilter: the polynomial fit, as just described, and the moving av- In electrical circuits, an RC filter (filter with one resistor and one capacitor) is a first-order lag. We will postpone our discussion of ladder filter …First of all…A filter is a circuit which eliminates some particular frequencies and allows the other ones. hardware used (microcontroller and DSP This application note consists of two parts, the first part for FIR filter and the second part for IIR filter. A recursive filter is one where the present output depends on …Filtered Audio Demo Max Kamenetsky In this demo y ou'll listen to a 10 second segmen frequency resp onse, impulse and step resp onses, and snapshots of the input and output signals. This Windowed FIR Filter C Code has two parts, the first is the calculation of the impulse response for a rectangular window (low pass, high pass, band pass, or notch). Since the ideal impulse response will not be time-limited, it must be truncated at some point in order to implement it in a practical system. IIR filter is essentially a feedback loop. One of the most-used filter forms is the biquad. You need to sample at your Fs rate in order for the filter to work correctly. You will design and implement a first order IIR (Infinite Impulse Response) filter and a second order IIR filter. Please try again later. Each fourth-order IIR filter can be realized in four possible cascade forms. Design minimum order filter — Design filter with minimum order on (default) | off When you select this check box, the block designs a filter with the minimum order and the specified passband, stopband frequency, passband ripple, and stopband attenuation. First Order High Pass Filter with Op Amp Using analysis techniques similar to those used for the low pass filter, it can be shown that which is the general form for first-order (one reactive element) low-pass filters. first order iir filter usually, when a digital IIR filter is going to be implemented, an analog filter (e. For bandpass and bandstop filters, the conversion to a digital filter doubles the order of each section. But I just want to make it clear that the following system is equivalent to your mean filter and has the same computational complexity and your first order IIR!Apr 8, 2017 This article explains how to simply calculate a first order IIR filter. The high-pass output is correct for a first order filter implementation. The lag filter formula is undefined because you don't have an "old_filtered_value" yet. A second order filter would have two capacitors or two inductors, or one capacitor and one inductor, that affects the filter's frequency response. Real-Time IIR Digital Filters a second-order IIR filter can be used as a sinus oid oscillator, even producing per- For an nth-order But-terworth has the first 1 EE3054 Signals and Systems Lectures 9 IIR Systems: First Order System Yao Wang Polytechnic University Some slides included are extracted from lecture presentations prepared by A first-order filter's response rolls off at −6 dB per octave (−20 dB per decade) (all first-order lowpass filters have the same normalized frequency response). • Functions gain and response accept coefficient arrays in the form produced by these functions. There isn’t much written about fixed point DSP, so I decided to describe how I built the filter. If the order is odd, the last section is first-order. Implement a smoothing IIR filter with mirror-symmetric boundary conditions using a cascade of first-order sections. For the Mesh Potato spectrum analyser I used a filter to smooth the signal strength estimates. − s •Impulse response has no fixed duration (it is infinite, hence the name) •The response is an exponential decay controlled by 1 =− r. This paper deals with using some MATLAB functions and tools for designing the first-order analogue Chebyshev filters and IIR Chebyshev filters. The transition between the pass-band and stop-band of a first order filter with cut-off frequency is characterized by the the slope of 20 dB per decade of frequency change. This distinguishes them from digital filters carried out by convolution, called Finite Impulse Response (FIR) filters. width (SW) and resolution (∆ReFine, ∆ImFine) to Accordingly, a second order IIR notch filter can be find the best position of the poles according to realized by using first order sections. 00 Page 1 of 10 January 1999 AN9603 Rev 2. Realization of Digital Filters Chapter Intended Learning Outcomes: (i) Ability to implement finite impulse response (FIR) and For each first-order section, canonic form is assumed. Stability, Recursively computable analysis and synthesis of the two-dimensional infinite impulse response filters of a reduced order. Each filter runs in parallel with all the other filters and each filter uses one 18-bit multiplier, so that you could implement up to about 35 filters. IIR Filter Design by Analog Filter Approximation In this case the analog filter function is a first order LPF similar Æ Although it is possible to implement IIR filters with fixed-point arithmetic, the use of floating-point arithmetic is greatly preferred when implementing IIR filters of any significant order. This Demonstration shows the implementation of a design for an infinite impulse response (IIR) low-pass digital filter. I can use the `freqz' function to find the cutoff (-20 dB) frequency for a given filter, specified by its IIR coefficients and sampling period. “EEE305”, “EEE801 Part A”: Digital Signal Processing Chapter 5: Design of IIR Filters University of Newcastle upon Tyne Page 5. The first section of a Butterworth filter has an f 0 of 1 and a Q of 0. 5 Now denormalise the frequency-domain transfer function H(s) of the Butterworth filter, with the corresponding low- pass to low-pass frequency transformation of …The key characteristics of the First-Order Filter block are: Input accepts a vectorized input of N signals, thus implementing N filters. Schwartz and …18. two parts are made, the The first step in the design of an IIR filter is usually an initial determination of R a and R b, the Butterworth Filter Design. pState points to the state variable array. Created Date: 9/13/1998 12:20:58 AM A first order filter with 0. It gives the equations used to generate IIR filters from the s domain coefficients of analog filters using the Bilinear Transform. 3. We will look at first order low pass filters here. The output Y (out-put of each filter stage) is computed by direct imple- • A simple IIR filter is the first-order lowpass filter First-Order Filters Filter Order Passband Stopband First order IIR filters may be implemented in the Filter component by using the biquad filters with some zeroed coefficients. 30) in different ways, leading to different pole and zero combinations in each of the second- Butterworth Low-Pass Filters In this article, we describe the commonly-used, n th -order Butterworth low-pass filter. Allpass filter coefficients of the first branch in Wave Digital Filter form, specified as an N-by-1 or N-by-2 matrix. Steiglitz-McBride designed the modifications of the traditional IIR by reducing the filter order by 5 factors [6]. Mateo Aboy 4,661 views. the IIR approximates as good as possible the FIR which is the arithmetic mean of the last $k$ samples:The reason why this type of first order IIR filter is so widely used, is that it requires just an additional variable in RAM memory, to store the previous value of output signal, which is . Nasir Ahmed. Assume the following first order IIR Filter: $$y[n] = \alpha x[n] + (1 - \alpha) y[n - 1]$$ How can I choose the parameter $\alpha$ s. In order to determine the maximal phase deviation ε from ( 9 ), in this example we choose the maximal attenuation a maxdB =0. Designing a first-order IIR filter. However, if I have aIn this application note, we will explain the difference between FIR ("finite impulse response") and IIR ("infinite impulse response") filtering | 2018-11-19 17:50:08 | {"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": 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": 0.5286850333213806, "perplexity": 1546.8780248039939}, "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-2018-47/segments/1542039746061.83/warc/CC-MAIN-20181119171420-20181119193420-00099.warc.gz"} |
http://www.sciforums.com/threads/towards-ideas-on-a-quantum-theory-of-gravity.159827/page-2 | Towards Ideas on a Quantum Theory of Gravity
Discussion in 'Pseudoscience' started by Geon, Aug 25, 2017.
Not open for further replies.
1. GeonRegistered Member
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190
In post two, there is a part two, which explains it more in detail and summarises most of it - it details some aspect of what we are attempting to achieve. There is a better model to follow now which is one that will directly look into a quantum approach to gravity by studying how uncertainty/commutation effects the structure of a spacetime. To understand that, we need to understand why the commutation smears classical space out and into a quantum phase space.
3. James RJust this guy, you know?Staff Member
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35,781
sciforums is not your blog, Geon.
Do you have something you'd like to discuss with our membership?
I assume all your work is hosted on some other site of your own? How about you just provide us with a link to that and we can take a look if interested?
Have you published any of your work in peer-reviewed journals?
5. James RJust this guy, you know?Staff Member
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35,781
Moderator note: I have merged several of Geon's threads regarding his "quantum theory of gravity". Still trying to decide whether any of this is appropriate for our Physics forum....
7. GeonRegistered Member
Messages:
190
Of course, but you have bundled all my posts together, how will that cause any clarity with what is being discussed? It will just confuse everything, you've combined posts involving general relativity, the friedmann equation...
I understand it is not a blog, if anyone had asked any questions I am quite sure I would have answered them.
8. exchemistValued Senior Member
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10,271
Then report it: please do not start another argument on the science threads.
9. geordiefValued Senior Member
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1,514
@ Geon .based on post#2
If ,as seems to be the common assumption our understanding of physical observations relies on their geometric behaviour ,what might this tell us?
(not how the geometry works but what the implications might be that it does-or can we say that the geometric models are only models that may themselves be thoroughly reworked /abandoned at some stage)
Interesting to think that gravity could become the dominant actor at very small(but not Planckian) scales. Is there any discussion of this idea to be found elsewhere?
Usual disclaimer: I am all questions and not any help to anyone looking for answers
Oh and the maths is a foreign country to me.....
10. GeonRegistered Member
Messages:
190
It tells us that geometry can be understood to have the classical limit and then a quantum limit - in this case, the quantum case is just a special case of classical mechanics, because the quantum limit requires a ''correction.''
Many types of corrections to the quantum scale have been suggested, but one that pretty much seems cornerstone to geometry is an application of commutation principles - or non-commutating as the case often is - it is the non-commuting connections of a gravitational field that would require these ''corrections'' I have been speaking about.
It is actually predicted by string theory and quantum loop gravity that a non-trivial spacetime relationship could offer such a path - I simply understand it as the antisymmetric part of a Reimann tensor $R_{ij}$. It is this object specifically, when you understand the antisymmetric properties as related to the spacetime non-commutation relationship, that possibly non-trivial relationship which screams to be investigated further.
You can find further information on dynamics at the Planck scale, by reading into Wheelers more generic concept of quantum foam, which is basically the suspected particle activity associated to the bubbling of fluctuations on the Planck scale.
11. GeonRegistered Member
Messages:
190
On my most best idea's on describing the phase transition
The model I use depends on a phase of Bose/or/Fermi statistics and the pre-big bang phase was super cool, similar in that respect to Ekyprotic theory. An all-matter state would consist of some state of matter more primordial than the matter we deal with today. The result of the phase transition from a supercool, all matter liquid state is what heated the universe giving rise to a bath of radiation, mostly of which we detect as the background temperatures.
Why Bose or Fermi statistics?
The thermal de Broglie wavelength is denoted as $\lambda_{T}$. When the thermal de Broglie wavelength is smaller than the inter-particle distance, the gas can be considered to be a classical. On the other hand, when the thermal de Broglie wavelength is on the order of or larger than the inter-particle distance, quantum effects will dominate and the gas must be treated with Fermi or Bose statistics.
$\ddot{\lambda}_T \approx \frac{3}{2} \frac{\Delta T \Delta t}{p} \geq \frac{\hbar}{p}$
The phase transition obeys the following considerations:
$\frac{V}{N\lambda^3_T} \leq 1$
and
$\frac{V}{N\lambda^3_T} > \lambda_T$
The reason why it is important the pre-big bang phase was supercool (but not zero Kelvin), is because a process of lowering the temperature of a liquid or a gas (which are both fluids) beyond its freezing point - normally when a fluid reaches freezing point it becomes a solid: in this case it will freeze below this point without becoming a solid! Strangely enough, solid state physics as a phase state is considered a third phase state below liquid!
In the case the pre-big bang phase consisted of spin 1/2 particles, then the all matter liquid state may be considered equivalent to a degenerate supercool gas.
12. GeonRegistered Member
Messages:
190
Now, this above isn't all the story - this presentation above just give the interesting physics for an early universe where temperature and phase transitions play a role. The interesting thing, this physics talks about phase transitions only in the post era. The pre-era is considered a little different - for instance, consider the pre-big bang phase as a system which has almost no thermal degree's of freedom?
If we speak loosely of deBroglies wavelength as the general statement of the wave function of matter, then we have a general statement:
1) if the thermal wavelength of matter is larger than the distance between particles in a system, it will follow new statistics and quantum corrections.
2) if the thermal wavelength is smaller than the interparticle distance, then the system follows classical rules
What can we say about the pre-big bang state, does it follow similar physics? Can the post physics describe the pre state? Yes, I suspect it should be able to since there has to be physics making sense of the phase transition in itself. What we can say in the mathematical model we chose, that the universe has been suspended from collapsing to a point - normal theories of the big bang generally tend to deal with large densities and small spaces - this may even be true of the pre-big bang models... we also have to be open to the idea matter-creation was a continuous event during the early stages which actually gives an alternative to inflation. Small spaces also tends to mean particles are closely packed together, much closer than any metal, or solid here on earth.
summary
What we might find is that a pre-big bang state may have been controlled like a small system obeying classical laws - only if, the thermal properties of the pre-big bang particles have wavelengths smaller than their separation. This is a difficult question to answer, because how small can you probe spacetime without seeing those quantum effects (?)... well... generally speaking most scientists think those quantum effects are visible at and around the Planck scale, which is much smaller than the thermal interpretation of a wavelength and we have already established, we do not want a universe to collapse to a point... maybe the size of a football would do (roughly).
As you can see this look on things may lead to an interesting pre-big bang model. It seems quantum effects would be directly related to the temperature of the system (universe). When a universe heats up, the wave functions related to particles can have physics that describes a quantum vacuum.
I'll be giving the pre-big bang phase a break, and returning back to general relativity and ideas towards its quantization. I hit on some ideas last night that need to be typed.
Last edited: Aug 29, 2017
13. GeonRegistered Member
Messages:
190
Just one last thing to add, some crucial things to be noted about the pre-big bang phase:
1) In this model the pre-big bang was supercool but not frozen (solid/quantum crystal)
2) The pre big bang phase does not need to contain the observable count of particles in the post big bang horizon
3) A matter of non-conservation interpretation as particle-creation in curved spaces giving rise to a diabatic phase transition
4) The thermal properties of the wavelength of the pre-big bang gas of particles can be described using quantum corrections so long as their wavelengths exceed the pre-big bang inter-particle distance.
5) Any thermal properties of the system [must] be related to thermal or kinetic movement. This can be interpreted to mean there was very little movement of any pre-big bang particles - we have a system sitting on the precipice of absolute zero.
6) Simply put now, a new understanding of how we approach this must be taken to figure out the correct way to work this model. Can the thermodynamic deBroglie wavelength have any significance in the physics concerning any quantum corrections taken in this phase, when we have already considered that the thermodynamic properties have almost been smeared out (corresponding to little kinetic motion in the system) it must also be considered what kind of gas we are dealing with in terms of statistics - Fermi or Bose, or are we looking at a system that has to be described, with a new statistic, or one that has to be modified? Interesting stuff.
Is this a case where temperature is related directly to quantum corrections? When a cold universe with little degree of freedom heats up, the wave functions related to particles can have physics that describes a quantum vacuum! The question is, does the pre-state ''deviate to create'' or is it also described by quantum mechanics?
Last edited: Aug 29, 2017
14. GeonRegistered Member
Messages:
190
There is a seventh stipulation - that the thermal interpretation of the wavelength breaks down to the classical vacuum - but then the classical vacuum is about geometry and any geometry at the scales we are talking about, requires a quantum interpretation.
There for, the wavelengths are corrected gravitationally as well into the commuting lengths of the spacetime triangle, so not entirely through its thermodynamics which is supposed to be vanishingly small but non-zero. This means the pre-big bang phase really would require a quantum interpretation of the geometry which in my picture, would not require a Boson field (gravitons). Any particles existing in this pre-big bang state in this kind of model, looks largely gravitational in nature. They may even be considered as gravitational waves themselves!
15. arfa branecall me arfValued Senior Member
Messages:
7,159
A quantum theory of gravity will need to include a theory of quantum information (of gravity and its entropy).
To paraphrase Leonard Susskind: "the emergence of space behind an event horizon needs to be understood in terms of quantum information."
What I mean to say, I guess, is a theory will have to explain away the appearance of this "quantum information (of entanglement)", at dual places on a timelike slice through the interior. I conjecture that a part of this problem is our understanding of the information itself, we say there is quantum information, but that by itself is a bit of a contradiction, really it should just be called entanglement, much less confusing that way . . .
Geon likes this.
16. GeonRegistered Member
Messages:
190
An Approach to Spacetime Triangulation as the Benchmark towards Gravitational Unification
It is well known from Pythagoras' theorem that there exists the spacetime inequality ~
$AB + BC > AC$
$AB + AC > BC$
$AC + BC > AB$
Is it possible to apply a spacetime commutator inside of this inequality? Yes I think so! Or at least, this occurred to me.
For a scalar product defind on a vector space the length of vector is determined by
$|X_a|^2 = X_a \cdot X_a$
With some invesigation (see references) a spacetime inequality can indeed satisfy the following relationship
$|X_a| + |X_b| \geq |X_a + X_b|$
Squaring both sides also yields
$|X_a + X_b|^2 = |X_a|^2 + |X_b|^2 + 2|X_a| |X_b|$
$(X_a + X_b) \geq ...$
$|X_a|^2 + |X_b|^2 + 2X_a \cdot X_b \geq |X_a|^2 + |X_b|^2 + 2|X_a| |X_b|$
from which it follows
$|X_a \cdot X_b| \geq |X_a||X_b|$
which is known as the Cauchy Schwartz inequality which can be thought of as a direct interpretation of a spacetime uncertainty. Another important identity whicch further can be identified from the spacetime relationships is
$|X_a||X_b| \geq \frac{1}{2} |<X_a|X_b> + <X_b|X_a>|$
If you have trained your eye on all my previous work into gravity, this looks like the structure of commutators!
In a Hilbert space, you can define new vectors
$\sqrt{|<\Delta X_A^2>< \Delta X_B^2>|} \geq \frac{1}{2} i< \psi|X_AX_B|\psi > + i<\psi|X_BX_A|\psi> = \frac{1}{2} <\psi|[X_A,X_B]|\psi>$
The left hand side calculates the deviation of the derivative from the mean of the derivative, at least, that is how it would be interpreted in the approach we took to the quantization of gravity. We will use these solutions as a benchmark into how to treat this commutivity in spacetime from the connections we solved.
ref http://rocs.hu-berlin.de/qm1415/resources/Lecture_Notes_10_11_12.pdf
Last edited: Aug 30, 2017
17. GeonRegistered Member
Messages:
190
Yes, a quantum theory of gravity will indeed involve a concept of information. The problem is, scientists are not too sure what information really is. In terms of the physics we deal with, we tend to think of information as bits of information -- but some scientists have argued the role of information may be much richer. The question of entropy is such an important question, especially considering questions of whether the universe had a high entropy or a low one, when it came into existence, becomes pivotal questions.
18. GeonRegistered Member
Messages:
190
And yes... you are right. Quantum entanglement requires explanation in a model like mine. I expect there to be unification somehow - that requires more investigations on my part. Though well-read on the subject, I am clearly not well-read enough to find the idea's I need.
19. GeonRegistered Member
Messages:
190
To give a hint in how to do this unification attempt, we have three key equations,
1.
$R_{i j} = [\nabla_i,\nabla_j] = -[\partial_j, \Gamma_i] + [\partial_i, \Gamma_j] + [\Gamma_i, \Gamma_j]$
These are the exact Christoffel symbols of the antisymmetric tensor indices $R_{ij}$.
2.
$[\nabla_i,\nabla_j] \geq \frac{1}{2} |iR_{ij}|$
This was an equation derived by another author, finding the relationship in a different form argued from quantum mechanics. As you will see in key equation 3. the form has similarities to application of a Hilbert space ~
3.
$\sqrt{|<\Delta X_A^2>< \Delta X_B^2>|} \geq \frac{1}{2} i< \psi|X_AX_B|\psi > + i<\psi|X_BX_A|\psi> = \frac{1}{2} <\psi|[X_A,X_B]|\psi>$
Again, this is a Hilbert spacetime commutation relationship of operators which has to translate into the gravitational dynamics dictated by key equation 1.
20. GeonRegistered Member
Messages:
190
So let's put it altogether, its just like a jigsaw puzzle now. Implemented the Christoffel symbols in approach 1. into approach 2. we get
$[\nabla_i,\nabla_j] \geq \frac{1}{2} |-[\partial_j, \Gamma_i] + [\partial_i, \Gamma_j] + [\Gamma_i, \Gamma_j]|$
use identities
$<\nabla_i | \nabla_j> = i <\psi| \nabla_i \nabla_j | \psi>$
$<\nabla_j | \nabla_i> = - i <\psi| \nabla_j \nabla_i | \psi>$
In the framework of the Hilbert space it becomes - assuming everything has been done correct, takes the appearance of ~
$\sqrt{|<\nabla_i^2>< \nabla_j^2>|} \geq = = \frac{1}{2} i< \psi|\nabla_i\nabla_j|\psi > + i<\psi|\nabla_j\nabla_i|\psi> = \frac{1}{2} <\psi|[\nabla_i,\nabla_j]|\psi> = \frac{1}{2} <\psi | iR_{ij}| \psi > = <\psi|[\nabla_i,\nabla_j]|\psi> < \psi | [\partial_j, \Gamma_i] + [\partial_i, \Gamma_j] + [\Gamma_i, \Gamma_j]| \psi >$
Yes there will be come corrections somewhere on those derivatives, not sure yet, wuld need to work it out, but generally speaking, this seems like it is probably the correct final form. (maybe).
Last edited: Aug 30, 2017
21. GeonRegistered Member
Messages:
190
So let's move on with some explanations of this.
Why the importance of doing this in a Hilbert space? As I explained very early on, this kind of commutation on spacetime was first studied by Von Neumann. Wiki gives a little history on this:
''Applications in the representation theory of groups naturally lead to examples of Hilbert algebras. Every von Neumann algebra endowed with a semifinite trace has a canonical "completed"[8] or "full" Hilbert algebra associated with it; and conversely a completed Hilbert algebra of exactly this form can be canonically associated with every Hilbert algebra. The theory of Hilbert algebras can be used to deduce the commutation theorems of Murray and von Neumann; equally well the main results on Hilbert algebras can also be deduced directly from the commutation theorems for traces. The theory of Hilbert algebras was generalised by Takesaki[6] as a tool for proving commutation theorems for semifinite weights in Tomita–Takesaki theory; they can be dispensed with when dealing with states.[1][9][10]''
As you can see, if we wanted to find a quantum interpretation of spacetime, without invoking gauge theories, left us with commutation and Hilbert spaces are great mathematical devices to reduce to the commutation relationships that smears classical space into the quantum.
22. GeonRegistered Member
Messages:
190
Sorry, equation came out wrong, the correct version is
$\sqrt{|<\nabla_i^2>< \nabla_j^2>|} \geq \frac{1}{2} i< \psi|\nabla_i\nabla_j|\psi > + i<\psi|\nabla_j\nabla_i|\psi> = \frac{1}{2} <\psi|[\nabla_i,\nabla_j]|\psi> = \frac{1}{2} <\psi | R_{ij}| \psi > = \frac{1}{2} < \psi | [\partial_j, \Gamma_i] + [\partial_i, \Gamma_j] + [\Gamma_i, \Gamma_j]| \psi >$
note* Can't edit or wouldn't have made this post. (Again, I still need to study the correct sign changes if there are any.)
Second edit : Until I work out the sign changes, I will remove imaginary symbol from curvature
Last edited: Aug 30, 2017
23. GeonRegistered Member
Messages:
190
Good, as I expected, there is no sign outside of absolute value, and any signs inside the absolute value gets quashed to a positive value anyway. ie. |-10| = 10 but -|-10| = -10. So above form is correct any way you do it. | 2021-04-12 06:08:57 | {"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": 0.6847318410873413, "perplexity": 746.2269439253854}, "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-2021-17/segments/1618038066613.21/warc/CC-MAIN-20210412053559-20210412083559-00162.warc.gz"} |
https://mc-stan.org/docs/2_28/functions-reference/gamma-distribution.html | This is an old version, view current version.
## 18.6 Gamma distribution
### 18.6.1 Probability density function
If $$\alpha \in \mathbb{R}^+$$ and $$\beta \in \mathbb{R}^+$$, then for $$y \in \mathbb{R}^+$$, $\text{Gamma}(y|\alpha,\beta) = \frac{\beta^{\alpha}} {\Gamma(\alpha)} \, y^{\alpha - 1} \exp(-\beta \, y) .$
### 18.6.2 Sampling statement
y ~ gamma(alpha, beta)
Increment target log probability density with gamma_lupdf(y | alpha, beta).
Available since 2.0
### 18.6.3 Stan functions
real gamma_lpdf(reals y | reals alpha, reals beta)
The log of the gamma density of y given shape alpha and inverse scale beta
Available since 2.12
real gamma_lupdf(reals y | reals alpha, reals beta)
The log of the gamma density of y given shape alpha and inverse scale beta dropping constant additive terms
Available since 2.25
real gamma_cdf(reals y, reals alpha, reals beta)
The cumulative gamma distribution function of y given shape alpha and inverse scale beta
Available since 2.0
real gamma_lcdf(reals y | reals alpha, reals beta)
The log of the cumulative gamma distribution function of y given shape alpha and inverse scale beta
Available since 2.12
real gamma_lccdf(reals y | reals alpha, reals beta)
The log of the complementary cumulative gamma distribution function of y given shape alpha and inverse scale beta
Available since 2.12
R gamma_rng(reals alpha, reals beta)
Generate a gamma variate with shape alpha and inverse scale beta; may only be used in transformed data and generated quantities blocks. For a description of argument and return types, see section vectorized PRNG functions.
Available since 2.18 | 2022-08-11 17:58:04 | {"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": 0.8170670866966248, "perplexity": 12796.704733697865}, "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-2022-33/segments/1659882571483.70/warc/CC-MAIN-20220811164257-20220811194257-00589.warc.gz"} |
https://www.physicsforums.com/threads/charge-distribution.234403/ | # Charge distribution
## Main Question or Discussion Point
A small positively charged sphere is lowered by a nonconducting threead into a grounded metal cup without touching the inside surface of the cup.The grounding wire attached to the outside surface is disconnected and the charged sphere is then removed from cup.What is the distribution of excess charge on surface of the cup?
Answer:Negative charge resides on the outside surface and no charge resides on the inside surface
I understand tht there is only negative charge but I dont understand why the negative charge isn't also on the inside surface...is it because all charges are always on the outer surface of a conductor?
But the inside surface of the cup is also the outer surface of the conductor???
Say there were some non-zero charge on the inside surface of the sphere. Then you can construct a closed Gaussian surface lying entirely between the outer and inner surface. The charge enclosed by the Gaussian surface is $q_{enc.}=-Q$. The total electric flux through the surface is $\Phi_E=0$ because the electric field everywhere on the Gaussian surface is zero since the surface is entirely inside the conductor. Now Gauss's law says $\Phi_E=\dfrac{q_{enc}}{\epsilon_0}$. Since the left side is zero, the right side must also be zero. Therefore $q_{enc.}$ must be zero, i.e. there is no charge of any sign on the inside surface. | 2020-02-25 00:45:35 | {"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": 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": 0.8594096302986145, "perplexity": 175.99036706351765}, "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-2020-10/segments/1581875145989.45/warc/CC-MAIN-20200224224431-20200225014431-00266.warc.gz"} |
http://boundedtheoretics.blogspot.com/2014/08/calling-all-statisticians-and.html | ## Thursday, August 21, 2014
### Calling all statisticians and probabilists
The following is a question I posted at the Mathematics Stack Exchange. Folks who see it here are likely to understand that my "Making Less of No Free Lunch" campaign is intended as much to hose down a creationist cloud of dust as to rain on the NFL parade. Please contribute a bit of your expertise to a worthy cause.
I hope to replace a proof of my own, in a paper explaining that the "no free lunch" theorems for optimization actually address sampling and statistics, with a reference to an existing result on sampling. The random selection process $$X_1, X_2, \dotsc, X_n$$ over the domain of the random objective function $F$ is statistically independent of the selected values, $$F(X_1), F(X_2), \dotsc, F(X_n),$$ despite the functional dependence $$X_i \equiv X(F(X_1), F(X_2), \dotsc, F(X_{i-1})),$$ $1 < i \leq n,$ where $X$ is statistically independent of $F.$ (See Section 0.1 here [or my last post] for more detail.)
To put this in terms of sampling, $F$ associates members of a statistical population with their unknown responses. The sampler $X$ processes data already in the sample to extend the selection. This typically biases the selection. But the selection process is statistically independent of the sequence of responses. That is the justification for referring to the latter as a sample.
This looks like textbook stuff to me: "Data processing biases the selection." But I am awash in irrelevant hits when I Google the terms you see here, and others like them. | 2019-02-17 05:40:58 | {"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": 0.5532039999961853, "perplexity": 825.784607316811}, "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/1550247481624.10/warc/CC-MAIN-20190217051250-20190217073250-00508.warc.gz"} |
http://mathoverflow.net/questions/64295/complex-analytic-space-with-no-positive-dim-subscheme | # Complex analytic space with no (positive dim.) subscheme ?
Is there an example of a complex analytic space $X$ that doesn't have any (not necessarily open or closed) positive dimensional subspace $Y$ which is analytically isomorphic to (the complex analytic space associated to) a scheme?
Edit: after D.Arapura's comment, we require $X$ to have dimension $>1$.
If I remember correctly, there are non "Abelian" complex tori $X=\mathbb{C}^n/\mathrm{Lattice}\;\;$ that do not have any positive dimensional analytic subvariety. Can a counterexample be derived from this?
Also, any complex algebraic space has an open subspace which is a scheme. So the counterexample (if it exists) must be searched outside algebraic spaces.
What if the question is modified by requiring that $X$ has no $Y$ that is locally closed in the analytic Zariski topology (where opens are complements of analytic subspaces)?
-
A disk will work, but this is probably not what you want. Did you want $X$ to be compact? – Donu Arapura May 8 '11 at 13:00
+1 to DonuArapura's comment! Perhaps I should've required $X$ to be of dimension > 1 ? – Qfwfq May 8 '11 at 13:07
Does a polidisk work? If so, I'll add the requirement "$X$ compact" as suggested by D.Arapura. – Qfwfq May 8 '11 at 13:26
Yes, I suspect that a polydisk does work, although this would be much harder. Off the top of my head, I might argue that polydisks have many bounded holomorphic functions, while the algebraic examples probably don't (reduce to the quasiprojective case, and apply suitable Riemann/Hartogs extension theorems to extend to the projective closure). – Donu Arapura May 8 '11 at 13:40
I deleted my answer, because the first half of it was wrong: Torus -point is not complex analytic equivalent to a scheme if the tours is non-algebraic. For the second example, I can not prove that non-algebraic torus can not contains something 2-dimensional complex analytic subset X isomorphic to a scheme, so that torus-X is a one dimensional Riemann surface of infinite topological type. – Dmitri May 8 '11 at 18:17
Take a complex 2-torus $X$ without curves, and hence, without non-constant meromorphic functions (see e.g. Shafarevich, Basic algebraic geometry, chapter VIII, \S 1, example 2). The only locally closed subsets of $X$ will be $X$ itself, $\varnothing$, finite subsets and the complements of finite subsets. $X$ minus a finite subset can't be algebraic: if it were, it would have a non-constant meromorphic function, and then so would $X$.
@dmitri. The holomorphic foliations on $X$ are defined by vector fields. To see it, take a vector field and look at the tangency locus with a given foliation. Since $X$ has no curves in it, the foliation and the vector field are everywhere tangent or transverse. But of course we can start with a vector field tangent to the foliation at a given point. – jvp May 21 '11 at 2:00
algori sorry for the confusion. I agree with your remark 100%, but it does not remove my concerns. I had in mind the following. We know that on a hyperbolic genus $g$ surface we can have a collection of geodesics whose complement is a collection of open ideal hyperbolic triangles. This collection is called lamination. Each geodesic is not compact in the surface. So why can not you have a lamination in the torus whose complement is analytically isomorphic to something algebraic? – Dmitri May 21 '11 at 8:53
jvp, you are right about foliations, when I was writing "foliation" I was thinking also about laminations... Is it clear that they don't exist? (by lamination I mean something like an infinite collection of vertical lines on C^2 given by equations $x_n=\frac{1}{n}$) – Dmitri May 21 '11 at 8:59 | 2014-07-24 20:23:05 | {"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": 0.9074918627738953, "perplexity": 376.9854282634014}, "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-2014-23/segments/1405997891176.68/warc/CC-MAIN-20140722025811-00245-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://www.calculussolution.com/blog/solving-critical-points-and-limits-with-sage | # Finding Critical Points and Limits with Sage!
## Primary tabs
This is the fifth lesson in five where we are discussing Sage and how it can be used to make your Calculus life easier. In the first lesson you learned how to create your own account and how to create a worksheet. In the second lesson you learned how to plot functions with Sage. In the third lesson you learned how to differentiate using Sage. And in the fourth lesson you learned how to integrate functions with Sage. In this lesson we are going to show how you can find critical points and solve limits. So to get started log into your account, create a new worksheet and label it 'critical points and limits'. You can do this by clicking the "New" button, typing "critical points and limits" in the text box and hitting the "Sage Worksheet" button just as we did in the first lesson.
First, let's introduce the solve function by solving a quadratic equation. Create a polynomial as you have done in the other lessons and then type the command "g=solve(f==0,x)" and then "show(g)". Like this:
You should recognize the two possible solutions to the quadratic equation.
Recall that critical points are where a function's derivative is zero or is not defined. So let's find those points where the derivative is zero using the solve function:
This is correct because
\begin{eqnarray}
f(x)&=&ax^2+bx+c,\\
\frac{df}{dx}&=&2ax+b=0,\\
x&=&-\frac{b}{2a}.
\end{eqnarray}
Be careful! This only works for functions that are polynomials. For functions like $1/x$ you will have to do other things like solve(f==oo,x) to solve it. A full discussion of critical points is beyond the scope of today's discussion so we will have to save it for later. Let's move to limits.
Let's solve
$\lim_{x\to 2}\,\frac{5x^2-3x-14}{x-2}.$
We know from here that the answer is 17. To do this we use the limit command like so:
The fact that we are approaching zero in the denominator was handled perfectly by Sage.
We hope that you enjoyed Sage Week. You can find more Calculus information on the Sage Calculus Tutorial page. Finally, if you want to jump to the other blog posts for Sage Week then here they are: | 2020-03-30 12:34:32 | {"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": 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": 0.39850282669067383, "perplexity": 489.5994358435685}, "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-2020-16/segments/1585370497042.33/warc/CC-MAIN-20200330120036-20200330150036-00156.warc.gz"} |
https://blog.geni.ai/blockchain-7-functions.html | # Blockchain Explained in 7 Simple Functions
Posted by Shanaka DeSoysa on Sun 03 March 2019
# Blockchain Explained in 7 Simple Functions¶
Practical hands-on guide to implement your own blockchain with 7 simple Python functions.
## Hashing Function¶
At the heart of the blockchain is the hashing function. Without encryption, the blockchain will be easily manipulable and transactions will be able to be fraudulently inserted. Here we're using a simple MD5 hashing algorithm. If you're interested in what's actually being used in bitcoin, read here.
In [0]:
import hashlib
import json
def hash_function(k):
"""Hashes our transaction."""
if type(k) is not str:
k = json.dumps(k, sort_keys=True)
return hashlib.sha256(k).hexdigest()
In [2]:
hash_function('www.myENDVR.com')
Out[2]:
'b26fe188c8c174c752aebea4e4fc42afe2b2e9ce6c6c94c5351bdaf76e8437e7'
## State Management¶
The ‘state’ is the record of who owns what. For example, myENDVR Inc have 100 coins and give 5 to John Smith, then the state will be the value of the dictionary below.
{‘transaction’: {‘myENDVR’: 95, ‘John Smith’: 5}}
In [0]:
def update_state(transaction, state):
state = state.copy()
for key in transaction:
if key in state.keys():
state[key] += transaction[key]
else:
state[key] = transaction[key]
return state
## Transaction Validation¶
The important thing to note is that overdrafts cannot exist. If there are only 10 coins in existence, then I cannot give 11 coins to someone. The below function verifies that the transaction we attempt to make is indeed valid. Also, a transaction must balance. I cannot give 5 coins and have the recipient receive 4 coins, since that would allow the destruction and creation of coins.
In [0]:
def valid_transaction(transaction, state):
"""A valid transaction must sum to 0."""
if sum(transaction.values()) is not 0:
return False
for key in transaction.keys():
if key in state.keys():
account_balance = state[key]
else:
account_balance = 0
if account_balance + transaction[key] < 0:
return False
return True
## Make Block¶
Now, we can make our block. The information from the previous block is read, and used to link it to the new block. This, too, is central to the idea of blockchain. Seemingly valid transactions can be attempted to fraudulently be inserted into the blockchain, but decrypting all the previous blocks is computationally (nearly) impossible, which preserves the integrity of the blockchain.
In [0]:
def make_block(transactions, chain):
"""Make a block to go into the chain."""
parent_hash = chain[-1]['hash']
block_number = chain[-1]['contents']['block_number'] + 1
block_contents = {
'block_number': block_number,
'parent_hash': parent_hash,
'transaction_count': block_number + 1,
'transaction': transactions
}
return {'hash': hash_function(block_contents), 'contents': block_contents}
## Check Block Hash¶
Below is a small helper function to check the hash of the previous block:
In [0]:
def check_block_hash(block):
expected_hash = hash_function(block['contents'])
if block['hash'] is not expected_hash:
raise
return
## Block Validity¶
Once we have assembled everything together, its time to create our block. We will now update the blockchain.
In [0]:
def check_block_validity(block, parent, state):
parent_number = parent['contents']['block_number']
parent_hash = parent['hash']
block_number = block['contents']['block_number']
for transaction in block['contents']['transaction']:
if valid_transaction(transaction, state):
state = update_state(transaction, state)
else:
raise
check_block_hash(block) # Check hash integrity
if block_number is not parent_number + 1:
raise
if block['contents']['parent_hash'] is not parent_hash:
raise
## Check Blockchain¶
Before we are finished, the chain must be verified:
In [0]:
def check_chain(chain):
"""Check the chain is valid."""
if type(chain) is str:
try:
assert (type(chain) == list)
except ValueError:
# String passed in was not valid JSON
return False
elif type(chain) is not list:
return False
state = {}
for transaction in chain[0]['contents']['transaction']:
state = update_state(transaction, state)
check_block_hash(chain[0])
parent = chain[0]
for block in chain[1:]:
state = check_block_validity(block, parent, state)
parent = block
return state
Finally, need a transaction function, which hangs all of the above together:
In [0]:
def add_transaction_to_chain(transaction, state, chain):
if valid_transaction(transaction, state):
state = update_state(transaction, state)
else:
raise Exception('Invalid transaction.')
my_block = make_block(state, chain)
chain.append(my_block)
for transaction in chain:
check_chain(transaction)
return state, chain
## Example¶
So, now we have our 7 functions. How do we interact with it? Well, first we need to start our chain with a Genesis Block. This is the inception of our new coin (or stock inventory, etc).
For the purposes of this article, I will say that I, Tom, will start off with 10 coins. Let's say we start off with 100 coins for myENDVR Inc.
In [0]:
genesis_block = {
'hash': hash_function({
'block_number': 0,
'parent_hash': None,
'transaction_count': 1,
'transaction': [{'myENDVR': 100}]
}),
'contents': {
'block_number': 0,
'parent_hash': None,
'transaction_count': 1,
'transaction': [{'myENDVR': 100}]
},
}
block_chain = [genesis_block]
chain_state = {'myENDVR': 100}
Now, look what happens when myENDVR Inc give some coins to user John Smith:
In [0]:
chain_state, block_chain = add_transaction_to_chain(transaction={'myENDVR': -5, 'John Smith': 5}, state=chain_state, chain=block_chain)
In [12]:
chain_state
Out[12]:
{'John Smith': 5, 'myENDVR': 95}
In [13]:
block_chain
Out[13]:
[{'contents': {'block_number': 0,
'parent_hash': None,
'transaction': [{'myENDVR': 100}],
'transaction_count': 1},
'hash': '4609f57859df784026c25fc42a9d0e40ebaa2a5b0e7c03b45c2c3d11da01829e'}] | 2019-07-21 03:12:36 | {"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": 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": 0.1882898211479187, "perplexity": 11038.039445199853}, "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-2019-30/segments/1563195526818.17/warc/CC-MAIN-20190721020230-20190721042230-00415.warc.gz"} |
https://mathhelpboards.com/threads/expectation-of-conditional-expression-with-exponentially-distributed-random-variable.28296/ | Expectation of conditional expression with Exponentially distributed random variable.
user_01
New member
Given an Exponentially Distributed Random Variable $X\sim \exp(1)$, I need to find $\mathbb{E}[P_v]$, where $P_v$ is given as:
$$P_v= \left\{ \begin{array}{ll} a\left(\frac{b}{1+\exp\left(-\bar \mu\frac{P_s X}{r^\alpha}+\varphi\right)}-1\right), & \text{if}\ \frac{P_s X}{r^\alpha}\geq P_a,\\ 0, & \text{otherwise}. \end{array} \right.$$
**My Take:**
First, let's solve the equation for $P_v$. For that, let's assume g(x) to be:
$$g(x) = \frac{P^0}{\exp(\overline{\mu}P_{th} + \varphi)}\left( \frac{1+\exp(-\overline{\mu}P_{th} + \varphi)}{1 + \exp(-\overline{\mu}P_s x r^{-\alpha} + \varphi)} - 1\right),$$
Then,
$$P_v = \begin{cases} g(x) & x \geq \frac{P_{th}}{P_s}r^\alpha\\ 0 & x < \frac{P_{th}}{P_s}r^\alpha \end{cases}$$
Then, with the knowledge that the PDF for Exponentially distributed RV is $f(x) = e^{-\lambda x}$ (with $\lambda = 1$ for our case), we can find $\mathbb{E}[P_v]$.
$$\mathbb{E}[P_v]= \int_Q^\infty g(x)f(x)dx \ \ \ \ \ \ \ \ \ \ \ (1)$$
where $Q = \frac{P_{th} r^{\alpha}}{P_s}$.
Is this method correct or am I making any mistake? | 2021-01-25 10:19:34 | {"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": 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": 0.979567289352417, "perplexity": 259.6183819598216}, "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-2021-04/segments/1610703565541.79/warc/CC-MAIN-20210125092143-20210125122143-00341.warc.gz"} |
http://tjchristiansen.com/202dy/n-oxidation-number-5d920e | # n oxidation number
Call 646-407-9078 or email us at mg@transformationtutoring.com for further … A partial electron transfer is a shift in the electron density near an atom as a result of a change in the other atoms to which it is covalently bonded. Oxidation number of nitrogen is important to decide to whether NO 2 can be oxidized or reduced. I want to caution some people reading this that the +5 is not a charge. Determining oxidation numbers from the Lewis structure (Figure 1a) is even easier than deducing it from the molecular formula (Figure 1b). 1 decade ago. Explaining what oxidation states (oxidation numbers) are. An oxidation number can be assigned to a given element or compound by following the following rules. Let Transformation Tutoring help you ace your chemistry class. The oxidation states are also maintained in articles of the elements (of course), and systematically in the table {{Infobox element/symbol-to-oxidation-state}} (An overview is here). It is 3 columns away from being a noble gas, thus its oxidation state it -3. The oxidation number for NO3, or nitrate, is -1. View All. O -2. = Roman group no. Therefore, the oxidation number of N in KNO3 is +5. This is because oxygen always has an oxidation number of -2. The three oxygen atoms have a combined oxidation of -6, corresponding to their electromagnetic charge and the lone nitrogen has a charge, or oxidation number, of +5. Oxidation corresponds to increasing the oxidation number of some atom. Since the oxidation number of copper increased from 0 to +2, we say that copper was oxidized and lost two negatively charged electrons. Applying the oxidation number rules to the following equation, we have. HNO4 is not a formula for a normal oxyacid. 6. + color(red)(5) … Oxidation states simplify the whole process of working out what is being oxidised and what is … Click hereto get an answer to your question ️ Oxidation number of N in NH4NO3 is: The sum of the oxidation numbers of N and H has to be zero because hydrazine is a neutral molecule. iii] in normal chemistry oxygen has fixed oxidation number of -2 and hydrogen +1 [except in hydrides] The oxidation state of chromium is +3. Because ammonia is neutral, the individual oxidation numbers must sum to zero. is not fix,it varies from compound to compound. Text Solution. Any free element has an oxidation number equal to zero. There is a slight difference between the two terms. 5. Two things come in handy here. Most of the time, it doesn't matter if the term oxidation state or oxidation number is used. The oxidation number of a monatomic ion equals the charge of the ion. Oxidation no. HNO3 is about as high as it gets. Become a member and unlock all Study Answers. In Ag NO3 the oxidation number of Ag (Silver) is 1+, the oxidation number of N (Nitrogen) is 5+, and the oxidation number of O (Oxygen) is 2-. Oxidation state and oxidation number are quantities that commonly equal the same value for atoms in a molecule and are often used interchangeably. Oxidation Numbers. i] the sum of the oxidation numbers in a compound equals zero. Oxidation states are straightforward to work out and to use, but it is quite difficult to define what they are in any quick way. 1 3. Calculating Oxidation Numbers. = +5 } }} {/eq} Become a … The atoms in He and N 2, for example, have oxidation numbers of 0. Well, as usual, the oxidation number of H is +I as is typical.... And the sum of the individual oxidation numbers is equal to the charge on the ion... And so N_"oxidation number"+4xxI^+=+1 N_"oxidation number"=-III For a few more examples .... see this older answer. - 8) to group no.} Nitrogen never has a positive ionic charge, and it barely has a negative charge (-3) in only a few compounds that are mildly ionic, like X3N, where X is an alkali metal (i.e K, Rb or Cs). H is always +1 and C is always +4 and N is -3. one bond attaches H-C and three bonds attach C-N forming a triple bond. #color(blue)(2) xx ? The best way to find answers to such problems is to remember. For maintenance: the two lists are compared in this /datacheck, to gain mutual improvements. (+3)+(-2) = Z Z=(+1). 4. N -3. for a neutral compound, the sum of the oxidation numbers of all constituent atoms must be equal to zero; the oxidation number of oxygen is usually equal to #-2#; This means that if you take #?# to be the oxidation number of nitrogen in dinitrogen pentoxide, #"N"_color(blue)(2)"O"_color(red)(5)#, you can say that. The usual oxidation number of hydrogen is +1. Oxidation number of nitrogen atom can be found by two methods, algebra method and observing structure of molecule. First of all Oxidation no. 1.3k SHARES. Of any compound in its elemental state is zero. Since the atom as whole is single negatively charged, following equation holds true: The overall oxidation state of the ion is -1, thus carbon must have an oxidation state of +2. If HNO4 exists, it has to be a peroxy acid; that’s the only way to squeeze an extra O in without fouling up the bonding. Try it risk-free for 30 days Try it risk-free Ask a question. We have nitrous acid, with a chemical formula of #HNO_2#.It is a neutral molecule as well. Answer : A Related Video. Any element can show { (group no. 1. This is a neutral compound, so the sum of the oxidation states is zero. The sum of oxidation number of nitrogen in is: 1:09 4.3k LIKES. An oxidation number is a positive or negative number that is assigned to an atom to indicate its degree of oxidation or reduction.The term oxidation state is often used interchangeably with oxidation number. 2. 1.3k VIEWS. Click hereto get an answer to your question ️ Find the oxidation number of N in NO^ - 3 . ii] the sum of the oxidation numbers in an ions equals the charge on the ion. The sum of the oxidation numbers is the charge on the ion or molecule. Cr +6. Karen. The oxidation state of oxygen is -2. Oxidation state of NO is +1 You can sign in to vote the answer. How do you think about the answers? Let n equal the oxidation state of chromium: n + 3(-1) = 0. n = +3 . The oxidation number of a free element is always 0. Lets assume then the oxidation number of N is x x + 3(-1) =0 x= +3 Oxidation number of Nitrogen in NF 3 is +3. Our amazing chemistry tutors in NYC, Brooklyn, and online are here to help you and provide guidance. The oxidation number of hydrogen is -1 when it is combined with a metal as in. The oxidation number is synonymous with the oxidation state. For the ion NH2- the oxidation number of N is -3. Therefore, the oxidation number for nitrogen in the given molecule is {eq}\displaystyle \boxed{\color{blue} { \boldsymbol{\rm{O.N.} Oxygen is more electronegative in this case, and so possesses an oxidation state of #-2#.There are two oxygens here, and so the total charge is #-2*2=-4#.. Hydrogen usually possesses an oxidation state of #+1#, and it does here as well.. Let #x# be the oxidation state of nitrogen. Oxidation state *Where group no. For the amine group -NH2 in organic molecules, such as CH3NH2, again it is -3. Oxidation number of N in is: 400+ LIKES. Each hydrogen is in the +1 state which would put each nitrogen in the -2 state. Thus it will have the negative oxidation state (think: it's better at grabbing electrons, which are negatively charged). The metals in Group IA form compounds (such as Li 3 N and Na 2 S) in which the metal atom has an oxidation number of +1. Sign in. Maintenance & improvements. Nitrogen dioxide (NO 2) is a molecule which contain two oxygen atom and one nitrogen atom. Let us calculate the oxidation number of nitrogen in ammonia. So the oxidation number for nitrogen in this case would be -3. Molecular nitrogen, N$2$, is a neutral molecule, therefore it has an oxidation state of zero. Let the oxidation number of N in N O 3 − be x. Chlorine has an oxidation state of -1 (no fluorine or oxygen atoms are present). To sum up: K = +1, C = +2, N … In Ag NO3 the oxidation number of Ag (Silver) is 1+, the oxidation number of N (Nitrogen) is 5+, and the oxidation number of O (Oxygen) is 2-. N=+3 O= -2. charge on NO=0. The oxidation number of each atom can be calculated by subtracting the sum of lone pairs and electrons it gains from bonds from the number of valence electrons. In NI3, the element fnitrogen is more electronegative compared to iodine. LiH, NaH, CaH 2, and LiAlH 4. H +1. Therefore, the oxidation number of the N atom is -3. For example, the oxidation number of Na + is +1; the oxidation number of N 3-is -3. Click hereto get an answer to your question ️ The oxidation number of nitrogen in (N2H5)^ + is: For monoatomic ions, the oxidation number always has the same value as the net charge corresponding to the ion. Oxidation Number of Nitrogen in NO 2 (Nitrogen Dioxide). The oxidation number of nitrogen in the nitrate ion is +5. Amine group -NH2 in organic molecules, such as CH3NH2, again it is 3 columns from. ] the n oxidation number of the oxidation state and oxidation number of nitrogen important. No^ - 3 any compound in its elemental state is zero ions equals charge... Has to be zero because hydrazine is a molecule and are often used.. Best way to Find answers to such problems is to remember fnitrogen is electronegative... Z Z= ( +1 ) or compound by following the following equation, we that! = Z Z= ( +1 ) is +5 its oxidation state of the oxidation number nitrogen... That commonly equal the oxidation number equal to zero in He and 2... Because hydrazine is a neutral compound, so the sum of the ion is +5 i want to caution people. ( think: it 's better at grabbing electrons, which are charged. Blue ) ( 2 ) xx that the +5 is not a for! Help you ace your chemistry class it risk-free for 30 days try it Ask! The negative oxidation state of -1 ( NO 2 can be assigned a... Often used interchangeably an ions equals the charge of the oxidation number is synonymous with the number... The negative oxidation state of the oxidation number of nitrogen in the nitrate ion is -1 when it combined! # color ( blue ) ( 2 ) is a molecule which contain two oxygen atom one! Quantities that commonly equal the oxidation number are quantities that commonly equal the same as... Of 0 ion NH2- the oxidation number of Na + is +1 the oxidation number of a monatomic ion the... State and oxidation number of nitrogen is important to decide to whether NO 2 can be oxidized or reduced N. Is more electronegative compared to iodine, Brooklyn, and online are here to help you provide! It is -3 to compound HNO_2 #.It is a neutral molecule as well compared to iodine are compared this. Ion or molecule grabbing electrons, which are negatively charged electrons a compound equals zero NH2- the oxidation of! In an ions equals the charge on the ion our amazing chemistry tutors in NYC Brooklyn! Electrons, which are negatively charged ) molecules, such as CH3NH2, again it is -3 an to. To help you and provide guidance are present ) -2 state -1 ( NO 2 )?... Elemental state is zero from 0 to +2, we have nitrous acid, with a chemical formula #. /Eq } Become a … therefore, the individual oxidation numbers must sum zero. Color ( blue ) ( 2 ) xx: K = +1, C = +2 N! 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As well of # HNO_2 #.It is a slight difference between the two lists are compared this. N atom is -3, NaH, CaH 2, for example, the element fnitrogen is more compared... Days try it risk-free for 30 days n oxidation number it risk-free for 30 days try it risk-free for 30 try... -2 ) = 0. N = +3 NH2- the oxidation numbers ) are fnitrogen. Thus carbon must have an oxidation state it -3 number is used commonly equal same! Let N equal the oxidation number can be assigned to a given element or compound following! Would be -3 it will have the negative oxidation state of +2 negative. At grabbing electrons, which are negatively charged ) Z Z= ( +1 ) charge of ion! To +2, N some people reading this that the +5 is not fix, does! Decide to whether NO 2 ) is a molecule which contain two oxygen atom one... Number can be found by two methods, algebra method and observing structure of molecule two terms state or number! = +5 } } } } } { /eq } Become a … therefore, oxidation. Negative oxidation state or oxidation number always has an oxidation state of +2 each in... Z Z= ( +1 ) two methods, algebra method and observing structure of n oxidation number two... Is used NaH, CaH 2, for example, the oxidation number of nitrogen in:..., which are negatively charged electrons chemistry tutors in NYC, Brooklyn, and LiAlH 4 reading that! ( -1 ) = 0. N = +3 for nitrogen in the +1 state which would put each nitrogen is! We say that copper was oxidized and lost two negatively charged ) H to! Fluorine or oxygen atoms are present ) molecule which contain two oxygen atom and one atom. Is more electronegative compared to iodine Z Z= ( +1 ) is electronegative! He and N 2, for example, have oxidation numbers ) are for a normal oxyacid Find! Is +1 ; the oxidation numbers in a compound equals zero and 4! The -2 state this /datacheck, to gain mutual improvements say that was. Nitrogen in this /datacheck, to gain mutual improvements often used interchangeably following. Metal as in ion is -1 when it is combined with a metal as in to whether NO 2 be. State which would put each nitrogen in is: 1:09 4.3k LIKES oxidation number of nitrogen in +1! Nitrate, is -1, for example, have oxidation numbers is the charge on the.... A metal as in states is zero #.It is a slight between... To your question ️ Find the oxidation state ( think: it 's better at electrons. N'T matter if the term oxidation state and oxidation number of nitrogen in ammonia and... 2, and online are here to help you and provide guidance any compound its. +2, we say that copper was oxidized and lost two negatively charged ) is always 0 and! It is 3 columns away from being a noble gas, thus carbon must an! Of -2 oxidation state of NO is +1 ; the oxidation numbers in an ions equals the charge the... Hno_2 #.It is a molecule and are often used interchangeably is not a formula for a normal oxyacid are! Overall oxidation state ( think: it 's better at grabbing electrons, which are negatively charged electrons oxygen. Two oxygen atom and one nitrogen atom can be assigned to a given element or compound by following the rules!, Brooklyn, and LiAlH 4 hno4 is not a charge time it... No^ - 3 and observing structure of molecule ( think: it 's better at grabbing electrons, which negatively. Are quantities n oxidation number commonly equal the same value for atoms in He and N 2, and LiAlH 4 difference! Kno3 is +5 so the sum of the oxidation number for NO3, nitrate... Was oxidized and lost two negatively charged ) fnitrogen is more electronegative compared to iodine a therefore! Nah, CaH 2, for example, the oxidation number of Na + is +1 the oxidation number N. Element has an oxidation number of a free element has an oxidation number for NO3, or,..., and online are here to help you ace your chemistry class,... Number for nitrogen in this case would be -3 and LiAlH 4 most of the ion -1! The atoms in He and N 2, and online are here to help you and guidance. For a normal oxyacid color ( blue ) ( 2 ) is a neutral molecule well. Of -2 of molecule in KNO3 is +5 is zero sum up: K +1... | 2021-05-12 08:42:38 | {"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": 0.6153262257575989, "perplexity": 2159.2429452127917}, "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/1620243991685.16/warc/CC-MAIN-20210512070028-20210512100028-00398.warc.gz"} |
https://math.stackexchange.com/questions/830108/when-does-the-limit-of-the-mean-values-of-a-function-around-a-point-approach-the | # When does the limit of the mean values of a function around a point approach the value of the function at that point ?
When does the limit of the mean values of a function around a point approach the value of the function at that point ? We can prove it if the function is continuous. But are there general classes of functions for which this holds ?
In precise language , what is the most general class of functions for which the following hold ?
$\frac{1}{n\alpha(n)\epsilon^{n-1}}\int_{\partial B(x,\epsilon)}f(y)dS(y) \rightarrow f(x)$ as $\epsilon \rightarrow 0$
• If the function is harmonic, this comes straight from the definition, perhaps more context is needed – Ellya Jun 11 '14 at 8:14
• yes but f(y) is not harmonic it comes from poisson equation delta u = -f.how it comes from definition? – Raja Sekar Jun 11 '14 at 8:27
• if it were harmonic, the mean integral over a ball centred at $x$ is the function evaluated at $x$. – Ellya Jun 11 '14 at 8:31
• ok sorry mean value property.again sorry sometimes it happens.but can you please check this out and give me some explanation.(math.stackexchange.com/questions/828836/…) – Raja Sekar Jun 11 '14 at 8:37
• Pointwise it can be absolutely horrible, note that the limit holds if you replace $f(y)$ by $f(y) + g(y)$ where around every ball $\partial B(x,\epsilon)$ the integral of $g$ vanishes. In particular, $g(y)$ doesn't even need to be Lebesgue integrable on $B(x,1)$. If you want this to hold everywhere, then the question may get more interesting. – Willie Wong Jun 23 '14 at 11:16
• It doesn't look to me like the original question is asking about functions for which this holds almost everywhere. I guess as long as the derivative of the integral exists everywhere for a Lebesgue integrable function $f$, then what you can say is that it is almost everywhere equal to a unique representative function which has the property OP asks for. – Dustan Levenstein Jun 23 '14 at 6:06
• This has been used even before introducing MVT in Page 25 of Evans when there are no restrictions on $f$. – Srinivas K Jun 28 '14 at 12:13 | 2021-05-06 12:14:00 | {"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": 0.9127090573310852, "perplexity": 205.00227679009805}, "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/1620243988753.97/warc/CC-MAIN-20210506114045-20210506144045-00574.warc.gz"} |
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http://math.stackexchange.com/questions/159831/chromatic-number-identity-involving-edges/159832 | # Chromatic Number Identity Involving Edges
I'm trying the prove the following:
Let $G$ be a simple graph with $m$ edges. Show that $\chi(G)\leq \frac{1}{2}+\sqrt{2m+\frac{1}{4}}.$
A very minute bit of algebraic manipulation shows that this is equivalent to proving $$\chi(G)(\chi(G)-1)\leq 2m.$$ From here I am a bit stuck. Could someone suggest a direction to head in?
Please no full solutions, just hints.
-
HINT: A little more manipulation turns it into $$m\ge\binom{\chi(G)}2\;,$$ which can be understood as saying that there must be at least as many edges as there are pairs of colors in a minimal coloring.
The fact that $G$ has chromatic number $\chi(G)$ means that you can partition vertices of the graph into $\chi(G)$ disjoint classes such that vertices in the same class have no neighbours. | 2016-05-29 15:33:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7562654614448547, "perplexity": 68.62317191966125}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049281363.50/warc/CC-MAIN-20160524002121-00178-ip-10-185-217-139.ec2.internal.warc.gz"} |
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# If L ≠ 0, is 18K/L an integer?
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09 May 2010, 02:28
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If L ≠ 0, is 18K/L an integer?
(1) K^2/L^2 is an integer.
(2) K - L = L
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msand wrote:
If L does not equal to 0, is (18*K)/L an integer?
(1) K^2/L^2 is an integer.
(2) K-L=L
If $$l\neq{0}$$ is $$\frac{18k}{l}=integer$$?
(1) $$\frac{k^2}{l^2}=integer$$. $$k=4$$ and $$l=2$$ - answer YES but $$k=\sqrt{6}$$ and $$l=\sqrt{2}$$ - answer NO. Not sufficient.
(2) $$k=2l$$ --> $$\frac{18k}{l}=\frac{18*2l}{l}=36=integer$$. Sufficient.
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16 May 2010, 11:32
according to statement A K^2/L^2 is integer but that doesn't mean that K & L are integer; square of 1.732 is 3 which is an integer but 1.732 itself is not a integer. hence statement A - i nsufficient
statment B - k=2l sufficeint we get a integer from it
so B must be the answer.
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Display posts from previous: Sort by | 2018-01-20 11:18:29 | {"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": 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": 0.5162864327430725, "perplexity": 12215.259225525622}, "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-2018-05/segments/1516084889567.48/warc/CC-MAIN-20180120102905-20180120122905-00483.warc.gz"} |
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http://jdh.hamkins.org/the-inner-model-and-ground-model-reflection-principles-cuny-set-theory-seminar-september-2017/ | # The inner-model and ground-model reflection principles, CUNY Set Theory seminar, September 2017
This will be a talk for the CUNY Set Theory seminar on September 1, 2017, 10 am. GC 6417.
Abstract. The inner model reflection principle asserts that whenever a statement $\varphi(a)$ in the first-order language of set theory is true in the set-theoretic universe $V$, then it is also true in a proper inner model $W\subsetneq V$. A stronger principle, the ground-model reflection principle, asserts that any such $\varphi(a)$ true in $V$ is also true in some nontrivial ground model of the universe with respect to set forcing. Both of these principles, expressing a form of width-reflection in constrast to the usual height-reflection, are equiconsistent with ZFC and an outright consequence of the existence of sufficient large cardinals, as well as a consequence (in lightface form) of the maximality principle and also of the inner-model hypothesis. This is joint work with Neil Barton, Andrés Eduardo Caicedo, Gunter Fuchs, myself and Jonas Reitz. | 2020-11-24 03:42:51 | {"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": 0.7643612027168274, "perplexity": 810.6392075071662}, "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-2020-50/segments/1606141171077.4/warc/CC-MAIN-20201124025131-20201124055131-00520.warc.gz"} |
http://happyworldtrip.com/mru0g30/ea5dc6-number-line-to-20-negative-and-positive | Example: 5 is really +5. Includes 0-10, 0-20, 0-30. When you have an addition or subtraction to calculate, you start at the first number and move the second number of places either to the right (for an addition) or left (for a subtraction). A number on the left is less than a number on the right. 1 Negative numbers are numbers that are less than zero. Not all values will create useful number lines. If a number has no sign it usually means that it is a positive number. Positive numbers are written with no sign or a ' $${+}$$ ' sign in front of them and they are counted up from zero to the right on a number line. 23 pages | Grades: 5 - 7. These unique features make Virtual Nerd a viable alternative to private tutoring. Positive and negative numbers are all integers. Numbers -20 to 0 on a number line, four per A4 page. Integers can be represented on the number line. Use the reels at the beginning and end of the number line. Example: An integer on the horizontal number line is greater than the number on its left and less than the number on its right. We subtract the two numbers and recall that when we subtract two negative numbers when we are looking at the right minus the left, we make them positive and subtract the positive numbers. Printable Number Line. Welcome to The Integers Number Lines from -20 to 20 Math Worksheet from the Integers Worksheets Page at Math-Drills.com. Numbers above zero are called whole numbers. 21 Posts Related to Number Line With Negative Numbers Up To 20. But just think of –400° F and –12° F. We have a negative number add a positive number. What Positive & Negative Numbers Mean (From Example/Guidance) Printable Blank Thermometers (3-Pages, various sizes) (From Worksheet) Fractions Number Line (Negative Values 0 to -1) (From Number line) Integer Line -100 to 100 (marked at the 1s and split into 8 lines) (From Number line) All whole numbers (both positive and negative) and zero. Our number line worksheets cover counting, comparing numbers, positive, and negative numbers, fractions, line plots, skip counting, and many other math concepts. Negative Numbers Number Line Worksheet. Here we plot fractions and mixed numbers on the given number line. This is the perfect way to introduce or reinforce negative and positive integers. https://www.twinkl.com/resource/t-n-025-number-lines-0-to-20 Use your number line to help you determine the difference in degrees of latitude between Panama City and each of the other six cities. Designed specifically for use with our positive number lines. Example: An integer on the horizontal number line is greater than the number on its left and less than the number on its right. Number Line. Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. Numbers 1, 2, 3 and so on then follow, equally spaced along the number line. Share This Post: Facebook Pinterest Twitter Google+. $-5215\:-\:\left(-6358\right)\:=\:6358\:-\:5215\:=\:1143 \nonumber$ Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite. This math worksheet was created on 2016-09-21 and has been viewed 20 times this week and 434 times this month. The line is actually an infinitive line, in which there is no strict rule which number is used to start and to end the line. 23 pages | Grades: 5 - 7. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. We don't have to include a positive sign (+) when we write positive numbers. Positive and negative number line … Add. The number of 20 is the end of the number line. Number lines are like the Swiss Army knife of math. The last worksheet begins with negative numbers (10) and works up to positive numbers (10). Upgrade to download 0 0. Positive and negative number line displayed on a movie show reel. Here is our selection of printable number lines involving positive and negative numbers up to 1000. a. Add. The given number line has each of its units divided into a number of fractional parts. ob_start_detecteda,#logo h1 a,#logo h2 a,.menu li.current-menu-item a,.menu li.current_page_item a,.menu li a:hover,.rhtitle.rhdefaultcolored,span.nmbr{color:#171717}.widget-heading,.post-entry blockquote p,.block-heading,.show-search #searchform input#s{border-color:#171717}#top-search a,.post-share .fa-comments,.pagination a:hover,ul.menu ul a:hover,.menu ul ul a:hover,.post-share a i:hover,.post-pagination a:hover{background:#171717}body{background:#fff}.rll-youtube-player,[data-lazy-src]{display:none!important}. negative and : by typing in the problem workbookand clicking on Solve : positive number calculator can be easily understood and – and step by step solution to my algebra homework : you can solve almost every problem with the help of : would be ready. A set of 26 printable A4 sheets which include different floors in the shop - negative numbers underground and positives above. Create a number line that goes from -20 to 20. 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Pre-K through 1st Grade. The arrows on each end of the number line show us that the line stretches to infinity in both the negative and positive direction. Add. Printable Number Line To 20 Negative And Positive. For example, the negative floors numbers in a building, bank balances falling into an overdraft or the temperature dropping below 0 degrees. Number Line With Negative Numbers Up To 20. Simply print on card stock a Movie Show Reel Positive and Negative Number Line -20 to 20 BW. For more help with numbers and number line lessons, see the pages below: In order to provide flexibility in creating number lines, this site does not limit the values you may use to create number lines. Free Printable Number Line Negative And Positive. Number Line. Writing numbers down on a Number Line makes it easy to tell which numbers are greater or lesser. Decimal Addition page 56. Number Lines. In this video, you’ll learn more about adding and subtracting negative numbers. The number line below shows this situation. Printable Number Line With Negative And Positive Numbers. Resources can be placed next to eac Positive and negative number line displayed on … Therefore, –2 + 8 = 6. This is the perfect way to introduce or reinforce negative and positive integers. Vertical Number Line Banner - 20 to 20 (SB10460) A vertical banner featuring a negative 20 to positive 20 number line with a hot and cold theme. Number Line With Negative And Positive Numbers To 100. For every positive integer, there’s a negative integer, called an additive inverse, that is an equal distance from zero. In Maths Counting Number Displays Number Lines. Numbers below zero are called negative numbers. A number line starts with zero, located at the beginning of a horizontal line. Represent each change on the applet, and draw it on a number line. Number Line Addition. https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th- We arrive at 6. Negative Numbers Number Line Worksheet Pdf. Amazon's Choice for negative and positive number line hand2mind Number Line -20 to 100 Decoration For Classroom Wall, Bulletin Board & Math Classes, 4 Inch x 36 Inch, Homeschooling Supplies & Classroom Decor, (12 Number Sections) Number + Facts 10 to 20. It may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. Try playing Casey Runner , you need to know the rules of positive and negative to succeed! They may appear to be simple straight lines, but they are versatile enough to teach an endless variety of math concepts. In order to provide flexibility in creating number lines, this site does not limit the values you may use to create number lines. What Positive & Negative Numbers Mean (From Example/Guidance) Printable Blank Thermometers (3-Pages, various sizes) (From Worksheet) Fractions Number Line (Negative Values 0 to -1) (From Number line) Integer Line -100 to 100 (marked at the 1s and split into 8 lines) (From Number line) Use positive numbers for north and negative numbers for south. 8 terms. Here is an example of a sum that starts with a negative number. Simply print on card stock a Here is our selection of free number lines involving positive and negative numbers up to 1000. Having a number line with both negative and positive numbers allows children to find the difference between them by counting forwards or backwards. https://www.twinkl.com/resource/t-n-607-numbers--20-to-20-numberline If we determine a 20 to positive and negative number line, then the number to start the line is -20. Divided into three-number blocks you can display all or just the sections you need to teach. Integers are whole numbers that are either greater than zero (positive) or less than zero (negative). Movie Show Reel Positive and Negative Number Line -20 to 20 BW. This is the Number Line: Negative Numbers (−) Positive Numbers (+) "−" is the negative sign. May 19, 2020 by admin. Set a reminder in your calendar. Number lines vary in length - if you're teaching your KS1 children addition, it might be helpful to begin with a 0-10 number line. Divided into three-number blocks you can display all or just the sections you need to teach. Customise the minimum and maximum values and how many partitions. A number line can be a powerful tool for learning about negative numbers, ratios or just introductory addition and subtraction operations. The number line PDFs on this page include various ranges (10, 12, 15, 20, 15 and 100) in both starting from zero as well as negative ranges. ... Write the positive and negative numbers on the number line and answer the questions. Numbers Can be Positive or Negative. Set a reminder in your calendar. Using these sheets will help your child to: learn the order of numbers in a number line; count in multiples of a range of numbers. Having a number line with both negative and positive numbers allows children to find the difference between them by counting forwards or backwards. The ITP can be used to model calculation strategies for addition and subtraction and to develop children’s understanding of the sums and differences between positive and negative numbers. However, we do have to include the negative sign (-) when we write negative numbers. Number Lines & Negative Numbers. Start at −6 on the number line, move forward 3, and you end up at −3 Now Play With It! Point A is negative 8, point B is negative 7, point ... and 20 years. Explore more than 10,000 'Negative Number Line' resources for teachers, parents and pupils as well as related resources on 'Number Line To 20' On a number line, the positive numbers are to the right of zero and the negative numbers are to the left of zero. You can then increase this to 0-20, 0-30, 0-50 and so on. b. Print the number line and cut it out so each of the numbers fit together without gaps. To recognize the need for negative numbers, and to place negative numbers on the number line. Positive and negative number line displayed on a movie show reel. This group of students are engaged right now, as we progress through your pack, and I'm sure that their confidence with numbers will continue to grow. The generator will attempt to create a number line with whatever data is provided. A number line is a straight line with a 'zero' point in the middle, with positive and negative numbers marked on either side of zero and going on indefinitely. It's easier to keep track of the negative numbers if you enclose them in brackets. Point A - 163… cweldon3668 cweldon3668 05/11/2020 Mathematics College Which point on the number line represents the product (Negative 4) (negative 2) (negative 1)? When graphing inequalities, you will have to understand positive and negative number line principles. A number line can help you to visualise both positive and negative numbers and the operations (adding and subtracting) that you can do with them. This bundle of Number Lines features one sheet per negative number line of:-5 to 5-10 to 10-20 to 20-50 to 50, and-100 to 100; Each number line is brightly coloured and features positive numbers in purple, neutral numbers in green, and negative numbers in pink. 88 terms. Thermometer - Positive and Negative Numbers. On a number line, the positive numbers are to the right of zero and the negative numbers are to the left of zero. Negative Numbers (−) Positive Numbers (+) (The line continues left and right forever.) Linda_Donaldson. Using a number line showing both sides of zero is very helpful to help develop the understanding of working with positive and negative numbers/integers. Which isn’t particularly asthetically pleasing but does reflect the financial phrases of “in the red” to represents debt etc. Using a number line showing both sides of zero is very helpful to help develop the understanding of working with positive and negative numbers/integers. This is the perfect way to introduce or reinforce negative and positive integers. 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The numbers are categorised by colour with negative numbers underscored by red, and positive by black. 23 pages | Grades: 5 - 7. The main concept is the left side has the lower number and vice versa. In this non-linear system, users are free to take whatever path through the material best serves their needs. 21 Posts Related to Number Line With Negative Numbers Up To 20. How far apart are these values? Addition . petersenjk TEACHER. They may appear to be simple straight lines, but they are versatile enough to teach an endless variety of math concepts. Number Line. Number Line With Negative Numbers Up To 20 Jerry June 14, 2020. This activity will allow the students a way to look at negative numbers and positive numbers and will help them in the future when they are adding or subtracting the two quantities. Positive and Negative Number Line Exercises 1) Represent the solution to the following on a number line: 3x < –6. Number Line With Negative And Positive Numbers To 100. This is a simple and clearly marked positive and negative number line that shows from -20 to 20. 19 terms. My son first started using number lines in the 1st Grade with his counting worksheets, but Kindergarteners can benefit from their use as well. For example, the negative floors numbers in a building, bank balances falling into an overdraft or the temperature dropping below 0 degrees. Upgrade to download 0 0. Selecting different scales on the number line and hiding and revealing the numbered intervals can support children’s estimation skills and ability to read horizontal scales. Values may be whole numbers, negative numbers or decimals. This is a simple and clearly marked positive and negative number line that shows from -20 to 20. This can get confusing because you may think that –400 is bigger than –12. 21 Posts Related to Number Line With Negative Numbers Up To 20. Numbers range from - 10 to +15 - a colourful and useful addition to your classroom. Values can be displayed in decimal or fraction form or hidden altogether. Examples: 5 is less than 8 Upgrade to download 0 0. It ranges from -50 to +50. Use the printable number line worksheets below as a helpful study guide for your child's math homework. In Mathematics Counting Number Displays Number Lines. Negative numbers get smaller and smaller the farther they are from zero. Positive Number. Negative Numbers Number Line Worksheet. Indo Word of the Week, 2020. They’re both positive numbers, but one is bigger than the other. It's a great way to introduce the concept of negative value to your child. We want to add 8, so we move 8 places to the right. This negative number line is printable and easy to use in your classroom. Divided into three-number blocks you can display all or just the sections you need to teach. Number Lines. The negative/positive number line is a great addition and a good tool for each student to have and use. or add to Google Calendar. By contrast, positive numbers are numbers that are greater than zero. Positive And Negative Number Line Worksheets. Our number line worksheets cover counting, comparing numbers, positive, and negative numbers, fractions, line plots, skip counting, and many other math concepts. The generator will attempt to create a number line with whatever data is provided. Set a reminder in your calendar. Here are three situations involving changes in temperature. PikeMathCoach. 5th through 7th Grades. October 9, 2020 by admin. A number line can be a powerful tool for learning about negative numbers, ratios or just introductory addition and subtraction operations. You can annotate dirtectly onto the line using the built in writing tool. Integers can be represented on the number line. This bundle of Number Lines features one sheet per negative number line of:-5 to 5-10 to 10-20 to 20-50 to 50, and-100 to 100; Each number line is brightly coloured and features positive numbers in purple, neutral numbers in green, and negative numbers in pink. Number Line Banners (SB7434) A set of colourful number line banners. Solution. A number line going from negative 10 to positive 10. This is a simple and clearly marked positive and negative number line that shows from -20 to 20. Balloons and Weights. A number line going from negative 10 to positive 10. In Mathematics Counting Number Displays Number Lines. It's easier to keep track of the negative numbers if you enclose them in brackets. seem tough if you think they are hard . 2) Represent the solution to the following on a number line: –5x – 7 = 3x + 17 Virtual Nerd's patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. Each number line is available blank or filled. There are rules you can use if adding, subtracting, multiplying or dividing positive and negative numbers. Negative and Positive Numbers - Multiplying Dividing Adding and Subtracting Rules / Number Line - Duration: 20:06. Simply print on card stock a ob_start_detecteda,#logo h1 a,#logo h2 a,.menu li.current-menu-item a,.menu li.current_page_item a,.menu li a:hover,.rhtitle.rhdefaultcolored,span.nmbr{color:#171717}.widget-heading,.post-entry blockquote p,.block-heading,.show-search #searchform input#s{border-color:#171717}#top-search a,.post-share .fa-comments,.pagination a:hover,ul.menu ul a:hover,.menu ul ul a:hover,.post-share a i:hover,.post-pagination a:hover{background:#171717}body{background:#fff}.rll-youtube-player,[data-lazy-src]{display:none!important}. View PDF. In a line with zero in the middle, negative numbers line … Negative numbers are smaller than zero. Movie Show Reel Positive and Negative Number Line -20 to 20 BW. In this non-linear system, users are free to take whatever path through the material best serves their needs. Basic 0-20 Number Line (Small) This page has two number lines, with the numbers 0 through 20. Elevator Negative Numbers Display Set (SB6740). These unique features make Virtual Nerd a viable alternative to private tutoring. Using the number line at the bottom of Handout 1, mark and label the point for each of the cities. A brilliant display resource to demonstrate negative numbers using a department store elevator concept. Positive numbers are sometimes written with a plus sign in front, e.g. View PDF. Negative Numbers Number Line Worksheet Pdf. 21 Posts Related to Printable Number Line To 20 Negative And Positive. May 19, 2020 by admin. or add to Google Calendar. Interactive Number Line. Number Line With Negative Numbers Up To 20. or add to Google Calendar. This resource is very flexible and can be used as a reference by children or to aid in calculation. We begin by finding –2 on the number line. Any number below zero is a negative number. "+" is the positive sign: No Sign Means Positive. I will allow them to place this number line on their desk, so they should make it small enough to fit the width of it. 20 terms. The Organic Chemistry Tutor 13,722 views Using these sheets will help your child to: learn the order of numbers in a number line; learn how negative numbers and positive numbers are positioned on a number line; The number line PDFs on this page include various ranges (10, 12, 15, 20, 15 and 100) in both starting from zero as well as negative ranges. Each number line is available blank or filled. Negative 4.5, written with a negative sign (–) in front of the 4.5: –4.5 Number lines are like the Swiss Army knife of math. cwilliams1214 TEACHER. Not all values will create useful number lines. Values may be whole numbers, negative numbers or decimals. We have -2 + 8. Preview & Download. In the context of negative numbers, a number that is greater than zero is referred to as positive.Thus every real number other than zero is either positive or negative, while zero itself is not considered to have a sign. 'S a great way to introduce or reinforce negative and positive direction the given number line and answer the.! Units divided into three-number blocks you can annotate dirtectly onto the line continues left right! Eac positive and negative number line and cut it out so each of the negative numbers but... Positive direction dividing positive and negative numbers or decimals degrees of latitude between Panama City and each of other! The right of zero and the negative numbers easier to keep track of the negative numbers! Runner, you need to teach rules of positive and negative number line starts with plus... Just introductory addition and subtraction operations a set of colourful number line displayed on a movie Show Reel positive negative... Point a is negative 7, point B is negative 8, so move. 'S math homework and can be used as a helpful study guide for your child needs. Going from negative 10 to +15 - a colourful and useful addition to your classroom them... Zero and the negative floors numbers in a building, bank balances falling into overdraft... Line Banners ( SB7434 ) a set of colourful number line, then the number line going negative! Elevator concept negative floors numbers in a building, bank balances falling into an overdraft or the temperature dropping 0. Your child 's math homework numbers for north and number line to 20 negative and positive ) and zero on 2016-09-21 and has been viewed times... With zero, located at the beginning of a horizontal line positive number serves needs! Study guide for your child you need to teach spaced along the number line -20 20! How many partitions line using the built in writing tool ( – ) in front, e.g that... Like the Swiss Army knife of math concepts guide for your child – ) in front, e.g way. Does not limit the values you may use to create a number line to help you determine difference. The beginning of a horizontal line A4 sheets which include different floors in the -. Displayed in decimal or fraction form or hidden altogether bottom of Handout 1, mark and label the for! Use your number line going from negative 10 to positive 10 you may use to create number lines but! Are versatile enough to teach an endless variety of math concepts starts with a number! ” to represents debt etc want to add 8, so we move places! But one is bigger than the other of fractional parts their needs the applet, and positive numbers to.! Plus sign in front of the negative numbers if you enclose them in brackets you enclose them in.. Created on 2016-09-21 and has been viewed 20 times this week and 434 times this month following on a line! In creating number lines is less than zero ( negative ) can displayed! 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Than a number line with whatever data is provided each of the number start... Display resource to demonstrate negative numbers your number line makes it easy to tell which numbers are the. All whole numbers ( + ) when we write negative numbers, ratios or just the sections you to... Line … number lines are versatile enough to teach every positive integer, there ’ s a number! Create number lines 0 on a number line -20 to 20 is negative 8, we! Equally spaced along the number line Exercises 1 ) Represent the solution the... Debt etc − '' is the perfect way to introduce or reinforce negative and positive.! Point a is negative 7, point B is negative 7, point B is 8! Has each of the number line with negative and positive number line to 20 negative and positive numbers ( 10 ) and works to! Use positive numbers number line to 20 negative and positive children to find the difference between them by counting forwards or.! So on then follow, equally spaced along the number line with negative numbers Up to 20 BW 10 +15... ) Represent the solution to the right alternative to private tutoring: //www.twinkl.com/resource/t-n-607-numbers -- 20-to-20-numberline number and! Then the number line that shows from -20 to 0 on a movie Show Reel than zero ( positive or. And subtracting negative numbers if you enclose them in brackets the printable number line stretches to in. Reference by children or to aid in calculation line continues left and right forever. powerful tool for about! A positive number lines colourful number line principles smaller and smaller the farther they versatile! Negative 4.5, written with a plus sign in front, e.g to the right of zero and the numbers! Than a number line has each of the numbers fit together without gaps or to in! You enclose them in brackets number and vice versa number line to 20 negative and positive is the number to start the line continues and! To take whatever path through the material best number line to 20 negative and positive their needs each of its units divided a. Contrast, positive numbers Exercises 1 ) Represent the solution to the following on a number principles... Need to teach annotate dirtectly onto the line stretches to infinity in both the number line to 20 negative and positive floors numbers in building. Infinity in both the negative numbers are to the right of zero subtracting negative numbers ( + ) we... Ratios or just introductory addition and subtraction operations isn ’ t particularly pleasing... Bank balances falling into an overdraft or the temperature dropping below 0 degrees the and. Like the Swiss Army knife of math counting forwards or backwards... and 20 years by counting forwards or.! And negative numbers, negative numbers, ratios or just the sections you need teach! Sign Means positive line, the positive and negative number Related to line... To positive 10 if a number line to 20 can display all or introductory... Positive 10 allows children to find the difference between them by counting forwards or backwards additive inverse that! –2 on the number of 20 is the number line and cut it so... By contrast, positive numbers ( − ) positive numbers ( − ) positive (. To tell which numbers are sometimes written with a negative sign ( - ) when write... '' is the number line -20 to 20 BW zero, located the... Zero, located at the bottom of Handout 1, 2, 3 so. They may appear to be simple straight lines, but they are versatile enough to teach that from. Fit together without gaps line: negative numbers represents debt etc greater or lesser ) positive are... Between Panama City and each of its units divided into three-number blocks you then. We have a negative number line with negative numbers Up to positive 10 sometimes written with a integer. – ) in front of the negative numbers Up to 20 with negative numbers 10! Understand positive and negative numbers Up to positive numbers ( + ) − '' is the left of and! Addition to your classroom counting forwards or backwards numbers ( 10 ) and zero to 1000 temperature dropping 0. Sb7434 ) a set of 26 printable A4 sheets which include different floors the... Just introductory addition and subtraction operations plus sign in front of the negative floors numbers in building! To include the negative and positive by black great way to introduce reinforce...: negative numbers on the number line, four per A4 page was created on 2016-09-21 and has viewed! Zero and the negative numbers, users are free to take whatever path the! ( − number line to 20 negative and positive positive numbers to 100 introduce the concept of negative value to your.! Subtraction operations smaller and smaller the farther they are from zero to teach together without gaps label point... Reference by children or to aid in calculation, so we move 8 places to right! ( positive ) or less than zero ( positive ) or less than zero ( negative ) range. To 20 and negative number line going from negative 10 to positive allows! About adding and subtracting negative numbers Up number line to 20 negative and positive 20 BW of Handout 1, mark and the... Positive direction, located at the beginning of a horizontal line numbers -20 to 20 study guide for your.... //Www.Twinkl.Com/Resource/T-N-607-Numbers -- 20-to-20-numberline number line -20 to 20 form or hidden altogether they re... Minimum and maximum values and how many partitions printable and easy to use in your classroom red and... Study guide for your child to printable number line with number line to 20 negative and positive numbers forwards or backwards the Swiss knife... Shop - negative numbers are to the following on a movie Show Reel positive negative... This is the left of zero and the negative sign ( – ) in front the. Beginning and end of the negative sign ( – ) in front of the fit. All or just introductory addition and subtraction operations negative value to your child 's homework... | 2021-10-20 01:41:00 | {"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": 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": 0.24547651410102844, "perplexity": 1158.3772841426878}, "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/1634323585290.83/warc/CC-MAIN-20211019233130-20211020023130-00277.warc.gz"} |
https://socratic.org/questions/how-do-you-find-the-domain-and-range-of-t-1-3 | # How do you find the domain and range of t^(1/3) ?
May 18, 2017
All real numbers
$t \in \mathbb{R} , f \left(t\right) \in \mathbb{R}$
#### Explanation:
We have: $f \left(t\right) = {t}^{\frac{1}{3}}$
$R i g h t a r r o w f \left(t\right) = \sqrt[3]{t}$
Both the domain and range of cubic functions are the set of all real numbers, i.e. $t \in \mathbb{R} , f \left(t\right) \in \mathbb{R}$.
From the above graph, it is clear that the graph infinitely spreads across the axes (because of the arrows).
Source: Tarantamath. Graph of basic cubic function. Digital image. Tarantamath. PBworks, n.d. Web. 18 May 2017. | 2019-11-19 05:51:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 4, "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": 0.6305838227272034, "perplexity": 1626.3859066557875}, "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-2019-47/segments/1573496670006.89/warc/CC-MAIN-20191119042928-20191119070928-00103.warc.gz"} |
https://dataleek.io/index.php/2015/04/29/twitter-civil-unrest-analysis-with-apache-spark/ | # Introduction
On Monday I attended the CU Boulder Computer Science Senior Projects Expo, and there was one project
in particular that I thought was pretty neat: determining areas of civil unrest through Twitter post
analysis. They had some pretty cool visuals and used Apache Spark, so I figured I’d try to recreate
it on my own. What follows is an initial prototype attempt as a proof of concept. I’ll go through
each step included here, but I’ve also included the code on my github
profile
, so feel free to clone and run it.
Again, this is a result that I was able to put together in just a couple days, so it’s not
completely fleshed out. This means that my solution is not a pretty solution, but instead a
solution that shows that a project of this nature is not only feasible, but scalable using Spark.
For reasons I will go into later, the video demo is at 4x speed.
The final result is pretty neat. (Press the play button on the below animation).
# General Approach
The steps for this project are fairly straightforward.
1. First establish the data, either in streaming or static form. For a static data form, this
is relatively simple since nothing changes and our analysis can be performed all at once. For this
project I chose to use a streaming data source in order to have a more adaptive solution. This
solution can scale from either a small file or stream to gigabytes of data.
2. Perform the analysis. Since we’re using Spark, this analysis is done using functional
techniques and is scalable depending on the system you’ve set up.
3. Display the results. This is completely up to the analyst as different approaches will have
different strengths and weaknesses. A generally accepted way (that would be another step for this
project) is to use D3, a javascript library, to display the data. Right now I use Cartopy.
# PySpark Streaming
One initial design choice that I made was to create a streaming program that constantly runs and
produces results. This means that the best approach is Spark’s streaming
API
. As with any other Spark
program I first created a SparkContext object, and since I’m set up on my laptop (with 4 workers)
I designated the program to use the local Spark instance. After I instantiated the SparkContext I
created a StreamingContext object and established a batch interval, which is simply the interval
at which the streaming API will update.
For reference, here’s a link to the streaming
API.
Once the setup code is complete, the stream can be started by setting a default “blank”
RDD, and creating a new queueStream whose
default contents is the blank RDD.
At this point the stream consists of a single entry: an RDD with contents [0]. To convert it to a
usable stream, I applied a flat map over every element in the stream. This mapping process converts
each element currently in the stream to a new RDD that contains the next chunk of Twitter data.
(Note, you could absolutely have a ton of elements in your blank RDD to start, which would mean that
you’re pulling in data over each one of those elements. I did not do that due to Twitter’s Rate
Limiting
, which I’ll go over more in depth
later.)
Analysis is now performed on the streaming object! (I’ll cover this more in depth later)
After the analysis is complete, the results are visualized. (Again, I’ll go over this later)
Since Spark is lazily evaluated, nothing has been done yet. All that’s been established is the fact
that we have some data stream and the intent to perform some series of steps on it in our analysis.
The final step is to start our stream and basically just wait for something to stop it. (Any
keyboard interrupt or process termination signal counts.)
And that’s it! Data is now being pulled from our streaming object.
# Transforming our Data Stream
In order to convert our initial blank RDD to twitter data, a flat
map
is applied over it. This converts each
element (currently just one) to my stream output.
The stream output is determined by the contents of the following streaming endpoint.
This restricts my results to English tweets over a bounding box that is mostly just the United
States. (You could remove the bounding box option, but since the only language I know is English I
wanted to be able to accurately parse the results.) A more complete guide to the Twitter API is
located on their site
.
The response object that we get when we use the stream=True option with the python requests
library
has an iterable object. I iterate over those
lines, yield them, and after receiving a set number of tweets I break and terminate the request. If
I run into any hiccups along the way, for the purpose of this prototype, they are just printed out
for visual debugging.
A more complete solution would ideally log these and create workarounds.
# Analysis
Since each element in our resulting RDD is a string representation of a Python object, each line in
our RDD is mapped to a literal Python object.
The posts are filtered by its text content. For this project, the filters look for language
indicative of social unrest. (If you’ll note, this application is not limited to social unrest and
many other filters could be applied.) I don’t really have the background for the best sentiment
analysis
, so all I have is a list of keywords as
my filtering criteria. (I’ve also included the word “http” in there so that in my pool of limited
results I actually have some content.)
For a more sophisticated process, implementing word association and natural language processing
would produce more accurate results. I didn’t implement something along those lines due to personal
time and scope constraints. For some ideas, here’s a paper on the
subject
.
At this point, the only posts that are left are those that indicate violence which need to be
reduced to just their geographical coordinates. Once this is complete each point can be plotted.
# Plotting
As you probably noticed, the “plotting” referenced above actually puts the contents of the RDD into
a queue. This queue is also accessed by the other
thread of the program which checks the queue every 5 seconds and pulls data out.
Cartopy is used for the plotting process, and a new
matplotlib figure is set to interactive
mode
.
If there is a new entry in the queue, we pull it out and add the points to our figure instance.
The final result is decent.
# Rate Limiting
Because Twitter will only let me query their site 15 times in 15
minutes
, I’m restricted in how much actual
analysis I can do. Not only do I have to use their sample stream, but I can only update once every
60 seconds unless I want to be rate limited very quickly, which is why this process is so slow. The
next step would be to make this update at a more reasonable speed by maintaining the response
object that is received from the request. All attempts to make that work failed horribly. I’m hoping
to get it working at one point, but right now it will just hang and never evaluate anything.
# Final Thoughts
All in all, this was a really neat project. The streaming API still has some kinks to iron out
chiefly in the documentation. No real tutorials exist for this tool yet, and I had to refer to the
unit tests for some of modules I was using. Often times, it was the only instance of working code I
could find. I’m hoping that this article may help someone who decides to work on Spark in the
future.
There is still a ton I could do with this project. Something that I’m planning on doing in the next
few weeks (sometime after finals finish up) is to implement a static version that acts on a
collected data set and shows behavior over the last few weeks.
My visualization is not very pretty. Yes, it gets the job done, but the black coastlines leave a lot
to be desired…
The hope is that the stream will just pass around the response object. Again, I was never quite able
to get that part implemented, but I think after a few more hours of working with it I can figure out
what the problem is.
Please let my know what you think! Leave comments below or on its github
page
and I’ll get back to you as quickly as I can. | 2020-07-03 13:51:33 | {"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": 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": 0.27470076084136963, "perplexity": 1499.2368956962246}, "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/1593655882051.19/warc/CC-MAIN-20200703122347-20200703152347-00434.warc.gz"} |
http://bilkent.herokuapp.com/qiubc/published/HomePage | back
# Quantum Information Group @UBC, Winter 2020
This is the homepage for the schedule of talks that will be held in Robert Raussendorf’s Quantum Information group.
Location: Hennings 309
Time: Tuesdays, 4 pm
go to last talk
# 2018/19
• Oct 19: Spectra of Graphs by Oleg
Spectral graph theory deals with problems on the intersection of graph theory and linear algebra. In this talk I will focus on what spectral graph theory can tell us about eigenvalues of matrices. Specifically, I will introduce the notions of quotient graphs, equitable partitions and the interlacing theorem. This will be based on the nice – physicist friendly – overview given in arXiv:1311.1759v4. I will finish with some of my thoughts on how to adopt these ideas to the problems of Hamiltonian spectrum in many-body systems.
• Nov 2: Paper review by Robert
Review of the paper “Real-time dynamics of lattice gauge theories with a few-qubit quantum computer” by Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp; et al.
• Nov 16: A generalization of Arkhipov’s framework by Cihan
Mermin-type contextuality proofs can be generalized to magic arrangements. Arkhipov shows that an arrangement is magic if and only if the intersection graph, a certain graph associated to the arragement, is non-planar. However, there are two restrictions (1) Eigenvalues are restricted to only two values, (2) Each observable belongs to exactly two contexts. I will describe an approach that will allow us to remove these two restrictions.
• Nov 23: Cavity Quantum Electrodynamics by Hirsh
Cavity Quantum Electrodynamics in the Nonperturbative Regime, PRA 97, 043820, by Bernardis, Jaako, and Rabl from TU Wien. First I’ll go over a brief derivation of perturbative cQED. Next I’ll present the paper on non-perturbative cQED and it’s nontrivial ground state. The ground state undergoes a quantum phase transition based on the strength of light-matter coupling. In these phases the dipoles spontaneously polarize and the field acquires a non-zero expectation value.
• Nov 30: Efficient computation of the partial trace by Joe
I will begin my talk with a quick refresher of the partial trace, specifically with regard to the implementation used in the paper. Then the numerical computation for bipartite systems will be discussed and how it can be more efficiently calculated. This then leads to the partial trace for multi-partitions, whose computational efficiently will also be discussed.
• Dec 14: Quantum computing in finance by Michael
I will be talking about an application of quantum computing in finance, namely, amplitude estimation and quantum Monte Carlo methods for options pricing. I will primarily be reviewing the paper “Quantum computational finance: Monte Carlo pricing of financial derivatives” by Patrick Rebentrost, Brajesh Gupt, and Thomas R. Bromley.
• Jan 29: Topology of operator constraints by Cihan
This is a continuation of generalization of Arkhipov’s framework. We study operator relations via the topology of two dimensional cell complexes. Given the operator constraints the goal will be to construct a projective representation of the fundamental group of the cell complex.
• Feb 26: A characterization of sets of n-qubit Pauli operators which are non-contextual and closed under inference by Michael
I will give a standard form for sets of n-qubit Pauli operators which are non-contextual and closed under inference and then I’ll prove that there are no sets of Pauli operators which are non-contextual, closed under inference, and not of this form.
• Apr 9: Noise-robust contextuality for Kochen-Specker type scenarios: two complementary frameworks by Ravi Kunjwal
The Kochen-Specker (KS) theorem is a mathematical result that points out the inconsistency between quantum theory and any putative underlying model of it where the outcomes of a measurement are fixed prior to the act of measurement by some (possibly hidden) physical states of the system in a manner that does not depend on (operationally irrelevant) details of the measurement context, i.e., the outcome a ssignments are fixed noncontextually in the model. Thus, quantum theory admits KS-contextuality. On the other hand, within the generalized approach to contextuality proposed by Spekkens, the assumption of deterministic outcome assignments is relaxed and, instead, noncontextuality for preparation procedures is invoked to obtain constraints on the operational statistics. I will present two complementary hypergraph frameworks that accomplish the project of accommodating Kochen-Specker (KS) type scenarios within the generalized approach to contextuality due to Spekkens. One of these frameworks generalizes the graph-theoretic framework of Cabello, Severini, and Winter for statistical proofs of KS-contextuality and the other one outlines how one can obtain noise-robust noncontextuality inequalities based on logical proofs KS contextuality. Time permitting, I will speculate on possible applications of these frameworks. Based on arXiv: 1805.02083, 1709.01098, and 1708.04793, 1506.04150.
• Apr 16: On Construction of Irreducible Representations of Von Neumann Matrix Algebras or How to Simultaneously Block-Diagonalize a Bunch of Matrices by Oleg
It is not possible to simultaneously diagonalize non commuting matrices. Nevertheless, it is possible to maximally block diagonalize any set of matrices using the structure of Von Neumann matrix algebras (VNMA). VNMAs (a.k.a -algebras) are becoming a common tool in physical literature with application ranging from quantum codes to the study of dynamics, decoherence and super selection rules. In this talk I will introduce the notion of VNMA and the motivation behind it, and give an overview of an algorithmic construction of irreducible representations of VNMA from generators. At the very least, we will learn how to block diagonalize a bunch of non commuting matrices.
# 2019/20
• Sept 13 @11am: Generative training of quantum Boltzmann machines with hidden units by Nathan Wiebe
We provide the first method for fully quantum generative training of quantum Boltzmann machines with both visible and hidden units while using quantum relative entropy as an objective. This is significant because prior methods were not able to do so due to mathematical challenges posed by the gradient evaluation. We present two novel methods for solving this problem. The first proposal addresses it, for a class of restricted quantum Boltzmann machines with mutually commuting Hamiltonians on the hidden units, by using a variational upper bound on the quantum relative entropy. The second one uses high-order divided difference methods and linear-combinations of unitaries to approximate the exact gradient of the relative entropy for a generic quantum Boltzmann machine. Both methods are efficient under the assumption that Gibbs state preparation is efficient and that the Hamiltonian are given by a sparse row-computable matrix.
• Sept 17 @5pm: Problems in topology of contextuality by Cihan
I will present a topological approach to studying contextuality following this paper. In this work first homotopy group of a space plays a crucial role in determining whether a given arrangement of observables is contextual. I will sketch this approach and end by listing some open problems.
• Sept 23: No group meeting
• Oct 1: Finding Quantum Wire in Hypergraph States by Amelia
We consider hypergraph states supported on sets $\Omega$ of qubits. For such a state $|H\rangle$, we divide $\Omega$ into three disjoint subsets, $\Omega=I\cup M\cup O$. $I$ is an ”input region”, $M$ a ”transmimssion region” and $O$ an ”output region”. We set out to find hypergraph states $|H\rangle$ on $\Omega$ where there exists Bell-type entanglement between regions $I$ and $O$ after the qubits in M have been measured in the local $X$-basis. This talk goes through the procedure of preparing the hypergraph state, performing the measurement, extracting qubits from the state and determining entanglement and suitability for quantum wire. We examine some of these results with the current stabilizer argument and find some of the state’s post-measurement stabilizers.
• Oct 8: Symmetry reduction for phase space simulation methods (Part 1) by Michael
Phase space methods are a promising approach for classically simulating quantum computation but in even dimensional Hilbert spaces there is an obstacle to practically using these methods. In even dimensional Hilbert spaces, the Wigner function is not unique. The best Wigner function to use for simulation is the solution to a convex optimization problem and the size of this convex optimization problem scales exponentially with the number of qubits. Here I will present some techniques for using simultaneous symmetries of states and the phase space to reduce this convex optimizaton problem to one which scales polynomially with the number of qubits. The main references I will use are: arXiv:1905.05374 and Quantum 3, 132 (2019).
• Oct 15: Symmetry reduction for phase space simulation methods (Part 2) by Michael
continuation…
• Nov 5: Towards 1D MBQC with Fermionic Systems by Paul
The search for a physically realizable cluster state is ongoing and is motivated by the potential of quantum computers to significantly outperform their classical counterparts for certain important classes of problems, such as prime factoring and quantum many-body simulations. In this report I analyze a system of fermions to determine whether or not it can be used as a resource for MBQC. Fermions are a class of particles characterized by the Pauli exclusion principle, which causes systems of fermions to be naturally entangled and suggests that they might be a good candidate for a physically realizable cluster state. However, some significant obstacles to creating a fermionic cluster state remain unresolved. For instance, a cluster state must have entanglement only between neighboring particles, but for free fermions the entanglement extends across the entire system, since in principle any two fermions could swap positions regardless of the distance between them. In 2012 Feder proposed confining non-interacting fermions in a double-well potential lattice and showed that its ground state is equivalent to a 1D cluster state. My research extends that work by considering the effect of adding interactions between fermions as well as an extra potential on one of the lattice sites. The goal is to determine whether or not these new features make it possible to implement fermionic MBQC. Specifically, is it possible to teleport a universal set of qubit rotations using measurements of individual lattice sites?
• Nov 19: Quantum to classical transition and its relation to fundamental scales by Oleg
Canonical commutation relations of position and momentum is one of the defining properties of quantum mechanics. As a result, the non-vanishing Planck constant sets the scale at which quantum effects such as measurement disturbance and uncertainty relations emerge. In this talk I will demonstrate that on a lattice, the scale at which quantum to classical transition occur is given by the square root of the size of the lattice. By taking the continuum limit we will recover the quantum-classical transition scale set by the Planck constant and see how it relates to the fundamental scales of minimal and maximal lengths.
• Jan 28: Quantum Time Travel using Closed Timelike Curves (CTCs) by Arnab
In this talk, we will discuss two nonequivalent quantum models of time travel using CTCs. We will also look into some computational and cryptographic schemes that use CTCs as resources to perform tasks that are impossible to do in a world without CTCs. We would conclude the talk by having a closer look at causality and consistency constraints in such schemes.
• Feb 25: Overview of variational quantum optimization algorithms by Oleg
I will introduce the basic principles behind VQE and QAOA algorithms and discuss the challenges and applications.
• Mar 10: Renormalizing Entanglement in Tensor Networks by Paul
I will review the multi-scale entanglement renormalization ansatz (MERA), a type of tensor network which is designed to preserve local operators and entanglement. Ref: https://arxiv.org/pdf/quant-ph/0610099.pdf
• Mar 24: Stable homotopy theory and quantum contextuality by Cihan
I will describe an approach to study quantum solutions to linear constraint systems which uses methods from stable homotopy theory.
• Apr 14: Paper review by Robert
Review of the paper.
• May 5: Our new paper, and Robert Spekkens ideas about contextuality by Michael
The talk will be in two parts. In the first part I will review our new paper (arXiv:2004.01992). I’ll briefly summarize the main results and discuss their implications. In the second part I will review Robert Spekkens ideas about contextuality and I will relate them to the hidden variable model defined in the new paper. The main reference for the second part of the talk is the paper “Contextuality for preparations, transformations, and unsharp measurements” by R.W. Spekkens (Physical Review A 71, 052108 (2005)).
• May 19: Geometry of quantum probabilities by Cihan
I will try to give more intuition on the structure of the generalized phase space (arXiv:2004.01992) using different coordinates. There arises questions related to the interaction between probabilities describing measurement statistics and the geometry of the partially ordered set of projectors.
• June 2: Quantum Thermodynamics: A primer for information theorists by Arnab
In this group presentation, I will be reviewing the emerging field of quantum thermodynamics. The talk is aimed as an introduction to the field dealing with the interplay between thermodynamics and information theory. The presentation is divided into two parts: First, I will talk about demons, engines and the thermodynamic cost of (quantum) computation. In the latter part of the talk, I will use a resource theory framework to show the inadequacy of Von-neumann entropy in characterising extractable work.
• July 28: Review of Stabilizer extent is not multiplicative by Paul
The Gottesman-Knill theorem states that a Clifford circuit acting on stabilizer states can be simulated efficiently on a classical computer. Recently, this result has been generalized to cover inputs that are close to a coherent superposition of logarithmically many stabilizer states. The runtime of the classical simulation is governed by the stabilizer extent, which roughly measures how many stabilizer states are needed to approximate the state. An important open problem is to decide whether the extent is multiplicative under tensor products. An affirmative answer would yield an efficient algorithm for computing the extent of product inputs, while a negative result implies the existence of more efficient classical algorithms for simulating large-scale quantum circuits. Here, we answer this question in the negative. Our result follows from very general properties of the set of stabilizer states, such as having a size that scales sub-exponentially in the dimension, and can thus be readily adapted to similar constructions for other resource theories. | 2021-05-16 09:35:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 12, "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": 0.6564139127731323, "perplexity": 713.7044572902839}, "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-2021-21/segments/1620243992516.56/warc/CC-MAIN-20210516075201-20210516105201-00121.warc.gz"} |
https://people.maths.bris.ac.uk/~matyd/GroupNames/97/C3%5E2xDic3.html | Copied to
clipboard
## G = C32×Dic3order 108 = 22·33
### Direct product of C32 and Dic3
Aliases: C32×Dic3, C333C4, C324C12, C3⋊(C3×C12), C6.(C3×C6), (C3×C6).7C6, C2.(S3×C32), C6.10(C3×S3), (C3×C6).11S3, (C32×C6).1C2, SmallGroup(108,32)
Series: Derived Chief Lower central Upper central
Derived series C1 — C3 — C32×Dic3
Chief series C1 — C3 — C6 — C3×C6 — C32×C6 — C32×Dic3
Lower central C3 — C32×Dic3
Upper central C1 — C3×C6
Generators and relations for C32×Dic3
G = < a,b,c,d | a3=b3=c6=1, d2=c3, ab=ba, ac=ca, ad=da, bc=cb, bd=db, dcd-1=c-1 >
Subgroups: 80 in 52 conjugacy classes, 30 normal (10 characteristic)
C1, C2, C3, C3, C3, C4, C6, C6, C6, C32, C32, C32, Dic3, C12, C3×C6, C3×C6, C3×C6, C33, C3×Dic3, C3×C12, C32×C6, C32×Dic3
Quotients: C1, C2, C3, C4, S3, C6, C32, Dic3, C12, C3×S3, C3×C6, C3×Dic3, C3×C12, S3×C32, C32×Dic3
Smallest permutation representation of C32×Dic3
On 36 points
Generators in S36
(1 15 7)(2 16 8)(3 17 9)(4 18 10)(5 13 11)(6 14 12)(19 33 29)(20 34 30)(21 35 25)(22 36 26)(23 31 27)(24 32 28)
(1 3 5)(2 4 6)(7 9 11)(8 10 12)(13 15 17)(14 16 18)(19 23 21)(20 24 22)(25 29 27)(26 30 28)(31 35 33)(32 36 34)
(1 2 3 4 5 6)(7 8 9 10 11 12)(13 14 15 16 17 18)(19 20 21 22 23 24)(25 26 27 28 29 30)(31 32 33 34 35 36)
(1 22 4 19)(2 21 5 24)(3 20 6 23)(7 26 10 29)(8 25 11 28)(9 30 12 27)(13 32 16 35)(14 31 17 34)(15 36 18 33)
G:=sub<Sym(36)| (1,15,7)(2,16,8)(3,17,9)(4,18,10)(5,13,11)(6,14,12)(19,33,29)(20,34,30)(21,35,25)(22,36,26)(23,31,27)(24,32,28), (1,3,5)(2,4,6)(7,9,11)(8,10,12)(13,15,17)(14,16,18)(19,23,21)(20,24,22)(25,29,27)(26,30,28)(31,35,33)(32,36,34), (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36), (1,22,4,19)(2,21,5,24)(3,20,6,23)(7,26,10,29)(8,25,11,28)(9,30,12,27)(13,32,16,35)(14,31,17,34)(15,36,18,33)>;
G:=Group( (1,15,7)(2,16,8)(3,17,9)(4,18,10)(5,13,11)(6,14,12)(19,33,29)(20,34,30)(21,35,25)(22,36,26)(23,31,27)(24,32,28), (1,3,5)(2,4,6)(7,9,11)(8,10,12)(13,15,17)(14,16,18)(19,23,21)(20,24,22)(25,29,27)(26,30,28)(31,35,33)(32,36,34), (1,2,3,4,5,6)(7,8,9,10,11,12)(13,14,15,16,17,18)(19,20,21,22,23,24)(25,26,27,28,29,30)(31,32,33,34,35,36), (1,22,4,19)(2,21,5,24)(3,20,6,23)(7,26,10,29)(8,25,11,28)(9,30,12,27)(13,32,16,35)(14,31,17,34)(15,36,18,33) );
G=PermutationGroup([[(1,15,7),(2,16,8),(3,17,9),(4,18,10),(5,13,11),(6,14,12),(19,33,29),(20,34,30),(21,35,25),(22,36,26),(23,31,27),(24,32,28)], [(1,3,5),(2,4,6),(7,9,11),(8,10,12),(13,15,17),(14,16,18),(19,23,21),(20,24,22),(25,29,27),(26,30,28),(31,35,33),(32,36,34)], [(1,2,3,4,5,6),(7,8,9,10,11,12),(13,14,15,16,17,18),(19,20,21,22,23,24),(25,26,27,28,29,30),(31,32,33,34,35,36)], [(1,22,4,19),(2,21,5,24),(3,20,6,23),(7,26,10,29),(8,25,11,28),(9,30,12,27),(13,32,16,35),(14,31,17,34),(15,36,18,33)]])
C32×Dic3 is a maximal subgroup of C338(C2×C4) C338D4 C334Q8 S3×C3×C12 He3⋊C12
54 conjugacy classes
class 1 2 3A ··· 3H 3I ··· 3Q 4A 4B 6A ··· 6H 6I ··· 6Q 12A ··· 12P order 1 2 3 ··· 3 3 ··· 3 4 4 6 ··· 6 6 ··· 6 12 ··· 12 size 1 1 1 ··· 1 2 ··· 2 3 3 1 ··· 1 2 ··· 2 3 ··· 3
54 irreducible representations
dim 1 1 1 1 1 1 2 2 2 2 type + + + - image C1 C2 C3 C4 C6 C12 S3 Dic3 C3×S3 C3×Dic3 kernel C32×Dic3 C32×C6 C3×Dic3 C33 C3×C6 C32 C3×C6 C32 C6 C3 # reps 1 1 8 2 8 16 1 1 8 8
Matrix representation of C32×Dic3 in GL3(𝔽13) generated by
3 0 0 0 1 0 0 0 1
,
3 0 0 0 3 0 0 0 3
,
1 0 0 0 4 0 0 0 10
,
1 0 0 0 0 1 0 12 0
G:=sub<GL(3,GF(13))| [3,0,0,0,1,0,0,0,1],[3,0,0,0,3,0,0,0,3],[1,0,0,0,4,0,0,0,10],[1,0,0,0,0,12,0,1,0] >;
C32×Dic3 in GAP, Magma, Sage, TeX
C_3^2\times {\rm Dic}_3
% in TeX
G:=Group("C3^2xDic3");
// GroupNames label
G:=SmallGroup(108,32);
// by ID
G=gap.SmallGroup(108,32);
# by ID
G:=PCGroup([5,-2,-3,-3,-2,-3,90,1804]);
// Polycyclic
G:=Group<a,b,c,d|a^3=b^3=c^6=1,d^2=c^3,a*b=b*a,a*c=c*a,a*d=d*a,b*c=c*b,b*d=d*b,d*c*d^-1=c^-1>;
// generators/relations
×
𝔽 | 2021-10-25 14:02:01 | {"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": 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": 0.9852014780044556, "perplexity": 12452.207406447205}, "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/1634323587711.69/warc/CC-MAIN-20211025123123-20211025153123-00119.warc.gz"} |
https://www.concepts-of-physics.com/pw/html/a/da/ida.html | IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions
# Polarization of Light
## Procedure
Demonstrated by Dr Ajay Mahajan. Take two piece of polaroid glasses (screen of the calculator). Show that transmitted intensity is maximum when the are parallel and minimum when they are crossed. It can be used to demonstrate law of Malus $$I=I_0\cos^2\theta$$.
Incomplete | 2020-08-04 06:00:27 | {"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": 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": 0.3536592423915863, "perplexity": 7264.182813258452}, "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/1596439735860.28/warc/CC-MAIN-20200804043709-20200804073709-00451.warc.gz"} |
https://j-james.me/math/calculus/6-1_slope-fields-and-eulers-method.html | # j-james/math
All my math notes, now in Markdown.
View the Project on GitHub j-james/math
# 6-1 Slope Fields and Euler’s Method
## Learning Targets
You will be able to
• Find general and specific solutions to differentiable equations
• Be able to write solutions in integral form
• Draw a slope field for a differential equation by hand
• Use Euler’s Method to find a solution to a differential equation at a particular input value
## Concepts / Definitions
Slope fields are a graphical representation of the family of solutions of a differential equation.
Slope fields can be useful to show you what the graph of the antiderivative looks like without ever solving the differential equation analytically. Each dash represents a slope at a particular $(x, y)$ value. The solution (antiderivative) is drawn because we know the slopes of each point on the curve.
If you apply this method knowing the location of one point on the curve, you can accurately determine the constant of integration.
### Example Slope Fields of Polynomial Functions
All the previous derivatives have had the same shape, and only varied in the $y$ axis. Now we come to “dependent” functions, in which the y is part of the derivative. These functions no longer hold the same shape among the $y$ axis. Solving the derivatives of these functions is slightly harder, although it can be done.
### Creating Slope Fields from Derivatives
Creating slope fields from derivatives is a straightforward process - given a point, merely plug the $x$ and $y$ values into the derivative, provided $x$ or $y$ exists in the equation. Draw a short line segment at the provided point on the graph with the slope provided by the derivative. Repeat for all given points.
### Euler’s Method
Euler’s method is a method for estimating the graph of a function given its derivative.
For each increment,
• Find the slope at the current $x$-value
• Increase $x$ by $\Delta x$
• Increase $y$ by the slope times $\Delta x$
• (note that $\Delta x$ can be negative)
• Repeat the process with a new point. | 2020-10-26 04:08:16 | {"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": 0.5795237421989441, "perplexity": 576.8730401323369}, "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/1603107890273.42/warc/CC-MAIN-20201026031408-20201026061408-00016.warc.gz"} |
https://docs.openstack.org/tripleo-docs/latest/install/post_deployment/quiesce_cephstorage.html | # Quiescing a CephStorage Node¶
The process of quiescing a cephstorage node means to inform the Ceph cluster that one or multiple OSDs will be permanently removed so that the node can be shut down without affecting the data availability.
## Take the OSDs out of the cluster¶
Before you remove an OSD, you need to take it out of the cluster so that Ceph can begin rebalancing and copying its data to other OSDs. Running the following commands on a given cephstorage node will take all data out of the OSDs hosted on it:
OSD_IDS=$(ls /var/lib/ceph/osd | awk 'BEGIN { FS = "-" } ; { print$2 }')
for OSD_ID in $OSD_IDS; do ceph crush reweight osd.$OSD_ID 0.0; done
Ceph will begin rebalancing the cluster by migrating placement groups out of the OSDs. You can observe this process with the ceph tool:
ceph -w
You should see the placement group states change from active+clean to active, some degraded objects, and finally active+clean when migration completes.
## Removing the OSDs¶
After the rebalancing, the OSDs will still be running. Running the following on that same cephstorage node will stop all OSDs hosted on it, remove them from the CRUSH map, from the OSDs map and delete the authentication keys:
OSD_IDS=$(ls /var/lib/ceph/osd | awk 'BEGIN { FS = "-" } ; { print$2 }')
for OSD_ID in $OSD_IDS; do ceph osd out$OSD_ID
systemctl stop ceph-osd@$OSD_ID ceph osd crush remove osd.$OSD_ID
ceph auth del osd.$OSD_ID ceph osd rm$OSD_ID
done
You are now free to reboot or shut down the node (using the Ironic API), or even remove it from the overcloud altogether by scaling down the overcloud deployment, see Deleting Overcloud Nodes. | 2018-10-23 20:39:09 | {"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": 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": 0.40558692812919617, "perplexity": 7710.620704568018}, "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/1539583517376.96/warc/CC-MAIN-20181023195531-20181023221031-00399.warc.gz"} |
https://math.stackexchange.com/questions/2374430/every-polynomials-image-contains-0-or-1-in-a-field-bbb-f?noredirect=1 | # Every polynomial's image contains $0$ or $1$ in a field $\Bbb F$
This question talks about fields in which every polynomials are almost surjective, while I am interested in the following case:
$\Bbb F$ is a field such that for every non-constant polynomial $f$ over $\Bbb F$, $f$ or $f-1$ has a root in $\Bbb F$.
If $\Bbb F$ is not the field with two elements, must $\Bbb F$ be algebraically closed?
• Oh, we should avoid constant polynomial as we do in the definition of algebraically closed field. – sawdada Jul 28 '17 at 6:21
• Note that this is equivalent to asking that $f-a$ has a root for all but at most one $a$, since if there are two exceptions you can compose with a linear polynomial to make them $0$ and $1$. – Eric Wofsey Jul 28 '17 at 6:26 | 2019-07-19 14:14:21 | {"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": 0.8682329058647156, "perplexity": 125.47695641681692}, "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-2019-30/segments/1563195526254.26/warc/CC-MAIN-20190719140355-20190719162355-00330.warc.gz"} |
http://mathhelpforum.com/geometry/52196-triangle-measurements.html | # Thread: Triangle measurements
1. ## Triangle measurements
Triangle
xz=18.5 m
xy=12.2 m
∠x= 73°
use the given measurements to find each of the following:
A. YZ
B. M
∠XZY
C. M∠xyz
D. The area
2. This is a classic case for the law of cosines and the law of sines.
Let XZ = a, XY = b, YZ = c. Then, by the law of cosines:
$c^2 = a^2 + b^2 - 2ab \cos 73$.
After you calculate c, then use the law of sines to find the angles:
$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin 73}$
3. How do you find yz?
4. I defined the length of YZ as c. Since you know the lengths of XZ (a) and XY (b), and the measure of the angle they share (ZXY = C = 73 degrees), you can use the law of cosines to find the length of YZ (c).
The calculation is $c^2 = (18.5)^2 + (12.2)^2 - 2(18.5)(12.2)\cos 73$. | 2017-03-23 03:21:41 | {"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": 3, "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": 0.7391588687896729, "perplexity": 928.1637478449405}, "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-2017-13/segments/1490218186608.9/warc/CC-MAIN-20170322212946-00235-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/136658/how-to-make-pdflatex-multithreaded-when-shell-escape-is-enabled | # How to make pdfLaTeX multithreaded when --shell-escape is enabled?
I am using \write18 enabled (or --shell-escape) with externalization to compile a bunch of PGFplots. The first run takes much time, and I noticed that pdflatex only runs on one CPU core. Is there any way to have pdflatex use multiple cores? (at least when \write18 is enabled)
-
Since you explicitly mentioned the use of external: you can configure the external library to run in mode=list and make. The resulting makefile can be processed in parallel using make -j 8 -f <file>.makefile (in this case on 8 threads). Only feasible if you can resort to make, though... – Christian Feuersänger Oct 6 '13 at 14:12
Note that the keyword "external library" means that this question is no duplicate. – Christian Feuersänger Oct 6 '13 at 14:13
What OS are you using? At least on UNIX-like systems it may be enough to end the command line passed to \write18 with an ampersand character (&) to have the shell spawn a new process for the external command. – Daniel Nov 21 '13 at 13:20
Could you give a minimal working example (MWE) that illustrates your problem, in particular, allows us to experiment with your method of "compiling a bunch of PGFplots"? – Stephan Lehmke Nov 26 '13 at 13:45
@StephanLehmke your feature request with asynchronous processing sounds interesting; but I fear that it would easily run out-of-control unless you restrict the number of background processes. And that, in turn, sounds like a very complicated method in TeX ... compiling twice would be simple. If you want to experiment with the code; feel free to do so. – Christian Feuersänger Dec 25 '13 at 14:30
The externalize in tikz may generated individual picture for every \begin{tikzpicture}...\end{tikzpicture}.
• \usepgfplotslibrary{external} let all pgf-plots outside of the compile.
Let pdflatex know those pictures are compiled with make.
• \tikzexternalize[mode=list and make] let tikz to know we would use the make. Because at present only the make support multi-thread.
I'm lazy to set the name for every pgfplots figure, so I let it done by system.
• external/system call set names for individual picture file, or the pdflatex doesn't know what file name should be set. (Origin code is from package tikz&pgf Manual for Version 2.10 page 345.)
My tex file is named test.tex
\documentclass{standalone}
\usepackage{pgfplots} %use tikz based pgfplots
\usepgfplotslibrary{external}
\tikzexternalize[mode=list and make]
\tikzset{external/system call={pdflatex \tikzexternalcheckshellescape
-halt-on-error -interaction=batchmode -jobname "\image" "\texsource"}
} % to let pdflatex work
%% compile picture: pdflatex --shell-escape xxxxxxx.tex
\begin{document}
\begin{tikzpicture}
\begin{axis}[ xlabel=$x$, ylabel={$f(x) = x^2 - x +4$} ]
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{loglogaxis}[xlabel=Cost,ylabel=Gain]
{ (10,100) (20,150) (40,225) (80,340) (160,510) (320,765) (640,1150) };
\end{loglogaxis}
\end{tikzpicture}
\end{document}
After first pdflatex compiling, do the make -j 4 -f test.makefile. 4 compiles the pictures with 4 thread.
Then run pdflatex second time.
The option --shell-escape also work fine in my system.
My system is:
1. Win 7(x64) + Miktex 2.9 + make under cygwin environment
2. Linux(x64) + Texlive2013 + make
-
Interesting, but could you elaborate what you are doing here? What is the sense of tikzexternalize ? – Keks Dose Dec 25 '13 at 11:38
I try explain the option I used, But it looks a bit weird in style. – selwyndd21 Dec 26 '13 at 6:15 | 2014-04-18 08:29:09 | {"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": 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": 0.9505994915962219, "perplexity": 6634.8695037593925}, "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-2014-15/segments/1397609533121.28/warc/CC-MAIN-20140416005213-00353-ip-10-147-4-33.ec2.internal.warc.gz"} |
http://www.gamedev.net/index.php?app=forums&module=extras§ion=postHistory&pid=4968260 | • Create Account
### #Actualalkisbkn
Posted 10 August 2012 - 06:30 PM
Okay, it seems that the correct derivative of "wave1" equation is the following:
float3 tan1 = float3(1.0, 30.0 * fs * cos(fs * waveVertex.x + t), 0.0);
float3 bitan1 = float3(0.0, 30.0 * fs * cos(fs * waveVertex.x + t), 1.0);
for tan and bitan. Then I do
normal = normalize(cross(bitan1, tan1));
For 1 wave it seems to be correct, however how should I go about adding many wave's normals together? Just summing them and normalizing the result?
### #1alkisbkn
Posted 10 August 2012 - 06:23 PM
Okay, it seems that the correct derivative of "wave1" equation is the following:
float3 tan1 = float3(1.0, 30.0 * fs * cos(fs * waveVertex.x + t), 0.0);
float3 bitan1 = float3(0.0, 30.0 * fs * cos(fs * waveVertex.x + t), 1.0);
for tan and bitan. Then I do
normal = normalize(cross(bitan1, tan1));
For 1 wave it seems to be correct, however how should I go about adding many wave's normals together? Just summing them and normalizing the result?
PARTNERS | 2013-12-22 08:26:46 | {"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": 0.6680660247802734, "perplexity": 11602.756247111034}, "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-2013-48/segments/1387345777253/warc/CC-MAIN-20131218054937-00047-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://eprints.lancs.ac.uk/id/eprint/152043/ | # ENISALA II:Distinct Star Formation and Active Galactic Nucleus Activity in Merging and Relaxed Galaxy Clusters
Stroe, Andra and Sobral, David (2021) ENISALA II:Distinct Star Formation and Active Galactic Nucleus Activity in Merging and Relaxed Galaxy Clusters. The Astrophysical Journal, 912 (1). ISSN 0004-637X
Text (2102.10116v1)
2102.10116v1.pdf - Accepted Version
## Abstract
The growth of galaxy clusters is energetic and may trigger and/or quench star formation and black hole activity. The ENISALA project is a collection of multiwavelength observations aimed at understanding how large-scale structure drives galaxy and black hole evolution. Here, we introduce optical spectroscopy of over 800 H$\alpha$ emission-line galaxies, selected in 14 z~0.15-0.31 galaxy clusters, spanning a range of masses and dynamical states. We investigate the nature of the emission lines in relation to the host galaxy properties, its location within the cluster, and the properties of the parent cluster. We uncover remarkable differences between mergers and relaxed clusters. The majority of H$\alpha$ emission-line galaxies in merging cluster fields are located within 3 Mpc of their center. A large fraction of these line-emitters in merging clusters are powered by star formation irrespective of cluster-centric radius, while the rest are powered by active galactic nuclei. Star-forming galaxies are rare within 3 Mpc of relaxed clusters and active galactic nuclei are most abundant at their outskirts (~1.5-3 Mpc). We discover a population of star-forming galaxies with large equivalent widths and blue UV-optical colors, found exclusively in the merging clusters in our sample. The widespread emission-line activity in merging clusters is likely supported by triggered activity in recently-accreted, gas-rich galaxies. By contrast, our observations for relaxed clusters match established models, in which black hole activity is enhanced at the virial radius and star-formation is quenched within the infall region. We conclude that emission-line galaxies experience distinct evolutionary paths in merging and relaxed clusters.
Item Type:
Journal Article
Journal or Publication Title:
The Astrophysical Journal
This is an author-created, un-copyedited version of an article accepted for publication/published in Astrophysical Journal. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at doi:10.3847/1538-4357/abe7f8
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1900/1912
Subjects:
Departments:
ID Code:
152043
Deposited By:
Deposited On:
23 Feb 2021 12:23
Refereed?:
Yes
Published?:
Published | 2022-08-11 09:08:17 | {"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": 0.34591880440711975, "perplexity": 4680.741768874233}, "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-2022-33/segments/1659882571246.56/warc/CC-MAIN-20220811073058-20220811103058-00246.warc.gz"} |
http://quant.stackexchange.com/tags/calibration/hot?filter=year | Tag Info
4
The Hull-White model can represents the risk free rate as a stochastic process, that is, in terms of expected return and volatility. The zero curve only gives you expected returns and you have to find a source to calibrate volatility, as FQuant told you. Common volatility sources used for this calibration are historical series of the zero curve or ...
2
Here is how I would approach such a calibration. Assuming we have the necessary market data one can easily construct the emprical distribution of the arrival rate. Let $\lambda_{emp}(\delta)$ be the empirical distribution. Then one can define a metric by $$m(k,A,N)=\sum_{i=1}^N |\lambda_{emp}(i)-\lambda^a(i)|$$ After you have decided upon a suitable ...
2
At long maturities, the real problem tends more to be model error than volatility estimation: over that kind of time period most companies undergo significant capital structure changes, for which there are very few models.
Only top voted, non community-wiki answers of a minimum length are eligible | 2014-08-30 08:38:36 | {"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": 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": 0.8663226962089539, "perplexity": 820.018612306153}, "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-2014-35/segments/1408500834663.62/warc/CC-MAIN-20140820021354-00026-ip-10-180-136-8.ec2.internal.warc.gz"} |
http://www.newtonproject.ox.ac.uk/view/texts/normalized/NATP00267 | <51r>
Feb 15. 167$\frac{5}{6}$. Cambridge
Sir
I thank you for giving me notice of the objection which some have made. If I understand it right they meane that colour may proceed from the different velocities which æthereall pulses or rays of light may have as they come immediately from the Sun. But if this be their meaning, they propound not an objection but an Hypothesis to explain my Theory. For the better understanding of this I shall desire you to consider that I put not the different refrangibility of rays to be the internal or essential cause of colours, but only the means whereby rays of different colours are separated. Neither do I say what is that cause, either of colour or of different refrangibility, but leave these to be explained by Hypotheses, & only say that rays which differ in colour, differ also in refrangibility, & that different refrangibility conduces to the production of colour no other way then by causing a different refraction & thereby a separation of those rays which had different colours before, but could not appear in their own colours till they were separated. Suppose red & blew pouders (as Minium & Bise) were equally mixed, the compound would be neither a good red nor a good blew but a midling dirty colour. Suppose further this mixture was put into water, & after the water had been well stirred, the pouders left to subside; if the red was much more ponderous then the blew, it would subside fastest & leave most of the blew to subside after it; & by consequence the heape would appear red at bottom & blew at top, & of intermediate colours between. Here then are various colours produced out of a dirty colour by means of different gravity, & yet that different gravity was not the internal cause of those colours, but only the cause of the separation of the particles of several colours. And so it is in the production of colours by the Prism: the different refrangibility of rays is no otherwise the cause of colour in this case then the different gravity of the pouders was in the other; it only causes a divers refraction of the rays originally qualified to exhibit divers colours, & by that divers refraction they are separated & when separated they must needs exhibit each their own colours which they could not do while mixed. Had I supposed different refrangibility the internal cause of colours, it would have been strangely precarious, & scarcely intelligible; but to make it only the cause of separation of rays indowed with different colours is nothing but experiment, & all that I have asserted in my writings. In like manner where I make different reflexibility the cause of colours (as in the case of thin transparent plates) I say not that it is their internal cause but only the means of their separation. For I apprehend that all the Phænomena of colours in the world result from nothing but separations or mixtures of difform rays & that different refrangibility & reflexibility are only the means by which those separations or mixtures are made.
This being apprehended, I presume you will easily see that you have <51v> not sent me an objection but only an Hypothesis to explain my Theory by. For to suppose different velocities of the rays the principle of colour is only to assign a cause of the the different colours which rays are originally disposed to exhibit & do exhibit when separated by different refractions. And though this should be the true essential cause of those different colours yet it hinders not but that the different refrangibility of the rays may be their accidental cause by making a separation of pulses of different swiftness. Yea so far is this Hypothesis from contradicting me that if it be supposed it infers all my Theory. For if it be true, then is the sun's light an aggregate of heterogeneal rays such are originally disposed to exhibit various colours: then is the whitenes of that light a mixture of those colours, being the result of the mixture of those unequal colorific motions: then is there nothing requisite for the production of colours but a separation of these rays so that the swiftest may go to one place by themselves & the slowest to another by themselves, or one sort be stifled & another remain: then must all the phænomena of colours proceed from the separations of these rays of unequal swiftness because while they continue blended together, as in the sun's original light, they can exhibit no other colour but white: & lastly; then must various refrangibility & reflexibility be the instrumental causes of the Phænomena of colour, those two being the proper means whereby difform rays are separated.
Were I to apply this Hypothesis to my notions I would say therefore that the slowest pulses being weakest are more easily turned out of the way by any refracting superficies then the swiftest, & so cæteris paribus are more refracted: and that the Prism by refracting them more separates them from the swiftest, & then they being freed from the alloy of o{n}e another strike the sence distinctly each with their own motions apart & so beget sensations of colour different both from one another & from that which they begat while mixed together; suppose the swiftest the strongest colour, red; and the slowest the weakest, blew.
To all this I might add concerning the different swiftness of rays that I my self have formerly applyed it to my notions in mentioning other Hypotheses, as you may see in my answer to Mr Hook sect. 4, & I think also in the Hypothesis I lately sent you. I say I applyed it in other Hypotheses; for in this of Mr Hook I think it is much more natural to suppose the pulses equally swift & to differ only in bigness, because it is so in the air, & the laws of undulation are without doubt the same in æther that they are in air.
Having thus answered, as I conceive, your objection in particular; I shall now for a conclusion remind you of what I have formerly said in general to the same purpose: so that I may at once cut off all objections that may be raised for the future either from this or any other Hypothesis whatever. If you consider what I said both in my second letter to P. Pardies & in my answer to Mr Hook sect 4. concerning the application of all Hypotheses to my Theory you may thence gather this general rule. That in any Hypothesis whence the rays may be supposed to have any originall diversities, whether as to size or figure or motion or force or quality or any thing els imaginable which may suffice to difference those rays in colour & refrangibility, there is no need to seek for other causes if these effects then those original diversities. This rule being laid down, I argue thus. In any <52r> Hypothesis whatever , light as it comes from the Sun must be supposed either homogeneal or heterogeneal. If the last, then is that Hypothesis comprehended in this general rule & so cannot be against me: if the first then must refractions have a power to modify light so as to change it's colorifick qualification & refrangibility; which is against experience.
Since the writing of this I receivd your other letter. I thank you for your account of Mr Berchhenshaw's scale of Musick though I have not so much skill in that science as to understand it well. If you should register the papers in your hand before you return them, I would desire you to leave out the last paragraph of the Hypothesis where I mention Mr Hook & Grimaldo together: but since you are to receive those papers again (that of the observations at least; for the Hypothesis I am more inclind to suppress,) I suppose it will not be necessary that you should put your self to the trouble of registring them.
I remain
Sir
Is. Newton
<52v>
Answ. March. 1. 75/6.
For Henry Oldenburg Esquire
at his house about the middle
of the Old Pall-mall in
Westminster
London
2 | 2017-11-21 22:57:03 | {"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": 0.5903828740119934, "perplexity": 1851.5472941438618}, "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/1510934806438.11/warc/CC-MAIN-20171121223707-20171122003707-00093.warc.gz"} |
https://gigaom.com/2005/02/05/vowifi-phones-are-the-shizzle/ | # VoWifi Phones Are the Shizzle
How do you get your mom to stop calling you every second day, and repeating, well, “when are you going to get married son… you know all your friends are trading their first ones in for new wives and you haven’t gotten out of the blocks yet!” I say, give her a VoWiFi phone. It looks like a cellphone, and is very cute and all. Tell her, this will save her tons of money. Even the venerable New York Times gives the concept a thumbs up. (Like you, she would not know if the reporter has actually tried to use one of these gizmos!) And when the phones don’t work, do your best French impersonation and shrug your shoulders and say, well Times said they are the shizzle. Guess what you will many options to choose from. Zyxel, Vonage, Siemens, Motorola and Nokia – all will have some offerings. Others are putting the VoWiFi phones right into the cellphones. I was half-skeptical about these devices, but you don’t have to tell mom that!
Since then, I have improved my math skills from first grade level to second grade level. My best estimate is that even if the handset is free, the VoIP service will cost you about $25 a month (unlimited), and the WiFi access will cost you about$30 a month if you travel a lot. At home wifi is for free though. Now if you have a good cellular wireless plan – $80 a month for about 1250 minutes with unlimited weekends and nights, then your total phone bill is going to be around$135 a month. Instead if you went over the limit of your cellphone by 120 minutes, you will still pay around an extra $36 a month. Of course you can switch to the basic$40 plan and make a compelling case for VoWiFi. Can you smart people do the math on these VoWiFi or dual mode – wifi+cell phones – and get back to me? Maybe I am thinking too narrow here? | 2021-04-11 07:52:28 | {"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": 0.2462022304534912, "perplexity": 1962.1973907290444}, "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/1618038061562.11/warc/CC-MAIN-20210411055903-20210411085903-00343.warc.gz"} |
https://www.biostars.org/p/317639/ | Issue while sorting a file
1
0
Entering edit mode
4.3 years ago
ricfoz ▴ 80
hello everyone
I am working with some bam files, and trying to retrieve a fasta sequence from them.
I have sorted my workflow, but i have an inquiry since the size of the files doesn't seem to match, i describe my issue as follows:
My original bam file has 2Gb size, when i sort it in order to retrieve a sequence with the "samtools view" tool, like this:
samtools sort inputfile.bam -o inputfile.sort.bam
the resulting file is 390Kb in size.
Is that normal? , i have checked a region of the genome with the "less" argument, and it does have information, still, i am hesitating on wheather the sorted file is truncated, since i think it should measure 2Gb as the original file.
Anyone with any idea what may be happening, or if my info is to be relied on ?
sort trouble inconsistency • 1.1k views
1
Entering edit mode
Hello ricfoz,
that the file size is smaller after sorting is normal, as the compression works better on sorted data. But the difference is to huge. Are you sure that you inputfile.bam is really a bam file or is it a sam file? Try
$head inputfile.bam If you get something human readable this is the sam file and could explain why this file is much larger. fin swimmer ADD REPLY 0 Entering edit mode 4.3 years ago drkennetz ▴ 560 No this is not normal your file has decreased in size almost 1000x and samtools sort doesn't actually remove any reads. what you can do is pipe wc -l with samtools view on your presorted file and your sorted file for a quickcheck using the following: samtools view unsorted.bam | wc -l samtools view sorted.bam | wc -l This will tell you the number of lines in each of your bam files. I would imagine the sorted will be much smaller. A way to track down your real issue would be to use linux gdb to see if there is an actual issue with the file, you can do this by typing the following into the command-line: gdb samtools some stuff will print to screen like GNU gdb etc.... you will then have gdb in place of your normal command-line [user]$ after which you will enter:
(gdb) run sort input.bam -o input.sort.bam
it will most likely print some errors you don't understand that are related to file compression failure or some formatting issue. Post this to samtools github issues and they should help with the problems you are seeing.
Edit: you can also run samtools sort input.bam -o input.sorted.bam -B to disable BAQ quality calculation. I don't know if quality is something you want to look at downstream but I have seen quality scores be an issue for longread sequencing technology. Dennis
0
Entering edit mode
Thank you... I ran the pipe with wc -l as you suggested. The number of lines it tells the files have are the same !, i think that means that the info may be the same?
It is very weird, still, i don't think there is any trouble with the compression with my samtools, since i have run the tool on other files, and they don't shrink, as this very one does.
0
Entering edit mode
.. I also ran the gdb command you suggested, it didn´t give any error message, it just worked as usually, outputting what the program is doing in a verbrose manner. but all ran smoothly. | 2022-09-28 22:35:05 | {"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": 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": 0.27131152153015137, "perplexity": 2782.9345825213345}, "config": {"markdown_headings": false, "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-2022-40/segments/1664030335286.15/warc/CC-MAIN-20220928212030-20220929002030-00468.warc.gz"} |
https://gamedev.stackexchange.com/questions/129844/unity-extending-native-components/129882 | # Unity - Extending native components
I was wondering if it was possible to use the existing native components inside Unity to extend them, and create my own.
For instance, if I wanted to create a component called Hurtbox, could I maybe do something like this?
class Hurtbox : BoxCollider2D { ... }
That would allow me to use the existing logic of the component and enhance it for my purposes.
Currently I have a separated BoxCollider2D and a Hurtbox components. The latter uses the former, but I thought if I managed to combine them both in a single one, it would be more elegant.
Is it doable? How?
• Have you tried to simply extend the classes? I would imagine that it should work in a simple C# manner, but I've never done this before. – Jesse Williams Sep 12 '16 at 20:22
• Though you would likely have to extend your editor for new values as well. I think this is why the expectation is to clump things together onto a GameObject and consider the GO as a single entity with multiple components. – Jesse Williams Sep 12 '16 at 20:23
• It is not that I can't test this. I know it can't be done this way. What I'm asking is if there is any way of doing this. – Enrique Moreno Tent Sep 13 '16 at 6:37
• what are you talking about? of course you can do it that way. Again, simply testing on your behalf would have gone a long way, here. – Gnemlock Sep 13 '16 at 22:31
It's absolutely possible to extend existing components in the way you describe. Take for example my extension to add a onHold event to the normal unity button.
using UnityEngine;
using UnityEngine.UI;
using UnityEngine.EventSystems;
using UnityEngine.Events;
public class HoldButton : Button
{
private bool isBeingPressed;
private float currTime;
private static float TimeMax = 1;
private bool startTimer;
public ButtonHoldEvent onHold { get; set; }
public override void OnPointerDown(PointerEventData eventData)
{
startTimer = true;
currTime = 0;
}
public override void OnPointerUp(PointerEventData eventData)
{
startTimer = false;
currTime = 0;
isBeingPressed = false;
}
void Update()
{
if(startTimer)
{
currTime += Time.deltaTime;
if(currTime >= TimeMax)
{
isBeingPressed = true;
}else
{
isBeingPressed = false;
}
}
if (isBeingPressed)
{
onHold.Invoke();
}
}
public class ButtonHoldEvent : UnityEvent
{
public ButtonHoldEvent() : base()
{
}
}
}
With this code I get all the features of a normal button with the added onHold functionality that I needed.
• I got this message on my editor: Assets/Scripts/Hurtbox.cs(8,14): error CS0509: "Hurtbox": cannot derive from sealed type "UnityEngine.BoxCollider2D"' – Enrique Moreno Tent Sep 16 '16 at 17:52
• Well yes BoxCollider2D seems to be sealed and this prevents other classes from inheriting from it. You can try and inherit Collider2D and implement that. – Uri Popov Sep 17 '16 at 7:23
• With Collider2D I didn't get the warning of "sealed type", but it did also not appear on the Component List. This is my code: hastebin.com/esiraroxot.cs – Enrique Moreno Tent Sep 17 '16 at 10:15
It is possible, but I wouldn't take that approach, for two main reasons:
1. If Unity folks change some underlying implementation later on, it may break functionality.
2. You would probably need a custom editor as well.
But instead, you can make custom components and add RequireComponent attribute at the top of your class. You will eventually end up with two components instead of a single extended one (and a bit of tight coupling), but you will save yourself from some headaches in the long run.
• I wanted to make the binding the CustomComponent and its derived component more tight. Imagine I want to derive BoxCollider2D in 2 Components: Hitbox and Hurtbox. If I use RequireComponent I would end up with 2 BoxColliders and the scripts can get fuzzy about which one to use. That is why I wanted to extend the native ones. – Enrique Moreno Tent Sep 16 '16 at 17:56
• @Dbugger I can't say I understand, RequireComponent doesn't add component instance if there is already one on GameObject. But instead, extending the component and adding two derived componnets essentially means double components, because each component is also the type of component you derived from. – S. Tarık Çetin Sep 17 '16 at 7:12 | 2021-05-12 14:37:37 | {"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": 0.3698456883430481, "perplexity": 1941.2099964196814}, "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-2021-21/segments/1620243990929.24/warc/CC-MAIN-20210512131604-20210512161604-00475.warc.gz"} |
https://tnboardsolutions.com/samacheer-kalvi-8th-maths-guide-chapter-1-ex-1-3/ | Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 1 Numbers Ex 1.3 Textbook Questions and Answers, Notes.
## Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 1 Numbers Ex 1.3
Question 1.
Verify the closure property for addition and multiplication for the rational numbers $$\frac{-5}{7}$$ and $$\frac{8}{9}$$.
Let a = $$\frac{-5}{7}$$ and b = $$\frac{8}{9}$$
∴ Closure property is true for addition of rational numbers.
Closure property for multiplication
∴ Closure property is true for rnultiplìcation of rational numbers.
Question 2.
Verify the commutative property for addition and multiplication for the rational numbers $$\frac{-10}{11}$$ and $$\frac{-8{33}$$.
Let a = $$\frac{-10}{11}$$ and $$\frac{-8{33}$$ be the given rational numbers.
From (1) and (2)
a + b = b + a and hence additionis commutative for rational numbers
From (3) and (4) a × b = b × a
Hence multiplication is commutative for rational numbers.
Question 3.
Verify the associative property for addition and multiplication for the rational numbers $$\frac{-7}{9}, \frac{5}{6}$$ and $$\frac{-4}{3}$$.
From (1) and (2), (a + b) + c = a + (b + c) is true for rational numbers.
From (1) and (2) (a × b) × c = (a × b) × c is true for rational numbers.
Thus associative property.
Question 4.
Verify the distributive property a × (b + c) = (a × b) + (a + c) for the rational numbers a = $$\frac{-1}{2}$$, b = $$\frac{2}{3}$$ and c = $$\frac{-5}{6}$$.
From (1) and (2) we have a × (b + c) = (a × b) + (a × c) is true
Hence multiplication is distributive over addition for rational numbers Q.
Question 5.
Verify the identity property for addition and multiplication for the rational numbers $$\frac{15}{19}$$ and $$\frac{-18}{25}$$.
Identify property for multiplication verified.
Question 6.
Verify the additive and multiplicative inverse property for the rational numbers $$\frac{-7}{17}$$ and $$\frac{17}{27}$$.
Additive inverse for rational numbers verified.
Mulplicative inverse for rational numbers verified.
Objective Type Questions
Question 7.
Closure property is not true for division of rational numbers because of the number
(A) 1
(B) 1
(C) 0
(D) $$\frac { 1 }{ 2 }$$
(C) 0
Question 8.
$$\frac{1}{2}-\left(\frac{3}{4}-\frac{5}{6}\right) \neq\left(\frac{1}{2}-\frac{3}{4}\right)-\frac{5}{6}$$ illustrates that subtraction does not satisfy the ________ property for rational numbers.
(A) commutative
(B) closure
(C) distributive
(D) associative
(D) associative
Question 9.
Which of the following illustrates the inverse property for addition?
(A) $$\frac{1}{8}-\frac{1}{8}=0$$
(B) $$\frac{1}{8}+\frac{1}{8}=\frac{1}{4}$$
(C) $$\frac{1}{8}+0=\frac{1}{8}$$
(D) $$\frac{1}{8}-0=\frac{1}{8}$$
(A) $$\frac{1}{8}-\frac{1}{8}=0$$
$$\frac{3}{4} \times\left(\frac{1}{2}-\frac{1}{4}\right)=\frac{3}{4} \times \frac{1}{2}-\frac{3}{4} \times \frac{1}{4}$$ illustrates that multiplication is distributive over | 2023-02-01 05:19:15 | {"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": 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": 0.7847788333892822, "perplexity": 785.1038491367799}, "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/1674764499911.86/warc/CC-MAIN-20230201045500-20230201075500-00222.warc.gz"} |
https://www.jobilize.com/physics-ap/section/learning-objectives-young-s-double-slit-experiment-by-openstax?qcr=www.quizover.com | # 27.3 Young’s double slit experiment
Page 1 / 10
## Learning objectives
By the end of this section, you will be able to:
• Explain the phenomena of interference.
• Define constructive interference for a double slit and destructive interference for a double slit.
The information presented in this section supports the following AP® learning objectives and science practices:
• 6.C.3.1 The student is able to qualitatively apply the wave model to quantities that describe the generation of interference patterns to make predictions about interference patterns that form when waves pass through a set of openings whose spacing and widths are small, but larger than the wavelength. (S.P. 1.4, 6.4)
• 6.D.1.1 The student is able to use representations of individual pulses and construct representations to model the interaction of two wave pulses to analyze the superposition of two pulses. (S.P. 1.1, 1.4)
• 6.D.1.3 The student is able to design a plan for collecting data to quantify the amplitude variations when two or more traveling waves or wave pulses interact in a given medium. (S.P. 4.2)
• 6.D.2.1 The student is able to analyze data or observations or evaluate evidence of the interaction of two or more traveling waves in one or two dimensions (i.e., circular wave fronts) to evaluate the variations in resultant amplitudes. (S.P. 5.1)
Although Christiaan Huygens thought that light was a wave, Isaac Newton did not. Newton felt that there were other explanations for color, and for the interference and diffraction effects that were observable at the time. Owing to Newton’s tremendous stature, his view generally prevailed. The fact that Huygens’s principle worked was not considered evidence that was direct enough to prove that light is a wave. The acceptance of the wave character of light came many years later when, in 1801, the English physicist and physician Thomas Young (1773–1829) did his now-classic double slit experiment (see [link] ).
Why do we not ordinarily observe wave behavior for light, such as observed in Young’s double slit experiment? First, light must interact with something small, such as the closely spaced slits used by Young, to show pronounced wave effects. Furthermore, Young first passed light from a single source (the Sun) through a single slit to make the light somewhat coherent. By coherent , we mean waves are in phase or have a definite phase relationship. Incoherent means the waves have random phase relationships. Why did Young then pass the light through a double slit? The answer to this question is that two slits provide two coherent light sources that then interfere constructively or destructively. Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. We illustrate the double slit experiment with monochromatic (single $\lambda$ ) light to clarify the effect. [link] shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude.
If a prism is fully imersed in water then the ray of light will normally dispersed or their is any difference?
the same behavior thru the prism out or in water bud abbot
Ju
If this will experimented with a hollow(vaccum) prism in water then what will be result ?
Anurag
What was the previous far point of a patient who had laser correction that reduced the power of her eye by 7.00 D, producing a normal distant vision power of 50.0 D for her?
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
What is the far point of a person whose eyes have a relaxed power of 50.5 D?
Jaydie
A young woman with normal distant vision has a 10.0% ability to accommodate (that is, increase) the power of her eyes. What is the closest object she can see clearly?
Jaydie
29/20 ? maybes
Ju
In what ways does physics affect the society both positively or negatively
how can I read physics...am finding it difficult to understand...pls help
try to read several books on phy don't just rely one. some authors explain better than other.
Ju
And don't forget to check out YouTube videos on the subject. Videos offer a different visual way to learn easier.
Ju
hope that helps
Ju
I have a exam on 12 february
what is velocity
Jiti
the speed of something in a given direction.
Ju
what is a magnitude in physics
Propose a force standard different from the example of a stretched spring discussed in the text. Your standard must be capable of producing the same force repeatedly.
What is meant by dielectric charge?
what happens to the size of charge if the dielectric is changed?
omega= omega not +alpha t derivation
u have to derivate it respected to time ...and as w is the angular velocity uu will relace it with "thita × time""
Abrar
do to be peaceful with any body
the angle subtended at the center of sphere of radius r in steradian is equal to 4 pi how?
if for diatonic gas Cv =5R/2 then gamma is equal to 7/5 how?
Saeed
define variable velocity
displacement in easy way.
binding energy per nucleon | 2019-04-21 08:39:35 | {"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": 0.5081085562705994, "perplexity": 1559.3618072017957}, "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/1555578530505.30/warc/CC-MAIN-20190421080255-20190421102255-00228.warc.gz"} |
https://codegolf.stackexchange.com/questions/38173/play-the-chaos-game | # Play the Chaos Game
The Chaos Game is a simple method to generate fractals. Given a starting point, a length ratio r and a set of 2D points, repeatedly do the following:
• From your set of points, pick one at random (uniformly).
• Average that point and the last drawn point (or the starting point) using r and 1 - r as the weights (i.e. r = 0 means you get the starting point, r = 1 means you get the random point and r = 0.5 means you get the point halfway in between.)
• Draw the resultant point.
For instance, if you picked the vertices of an equilateral triangle and r = 0.5, the plotted points would map out a Sierpinski triangle:
Image found on Wikipedia
You're to write a program or function which "plays" the chaos game to create a fractal.
## Input
You may write either a program or a function, and take following inputs via ARGV, STDIN or function argument:
• The number of points to plot.
• The starting coordinate (which has to be plotted, too!).
• The averaging weight r in the interval [0,1].
• A list of points to choose from.
## Output
You may render on screen or write an image file. If the result is rasterised, it needs to be at least 600 pixels on each side, all points must be on the canvas, and at least 75% of the horizontal and vertical extent of the image must be used for points (this is to avoid answers with a single black pixels saying "it's really far zoomed out"). The x and y axis must be on the same scale (that is the line from (0,0) to (1,1) must be at a 45 degree angle) and each point plotted in the chaos game must be represented as a single pixel (if your plotting method anti-aliases the point, it may be spread over 2x2 pixels).
Colours are your choice, but you need at least two distinguishable colours: one for the background and one for the dots plotted during the chaos game. You may but don't have to plot the input points.
## Scoring
This is code golf, so the shortest answer (in bytes) wins.
Edit: You no longer need to plot the input points, as they aren't really visible as single pixels anyway.
• What does "each point plotted ... must be represented as a single pixel" mean? Is it a) that no anti-aliasing should be used; or b) that the number of points in the second colour must be equal to the first item from the input? Note that b) is impossible to guarantee unless the iteration procedure has a test for "Does this pixel coincide with a previously plotted one?", because if the random number selector selects the same point enough times in a row then the position will converge to that point. – Peter Taylor Sep 25 '14 at 22:27
• @PeterTaylor It was intended to avoid people plotting large dots as the points (like Mathematica does by default), but I've already noticed that anti-aliasing causes some trouble with ensuring single pixels in Soham's answer. I think I'll relax this to "must not be larger than 2x2 pixels", which should cover all the anti-aliasing trouble. – Martin Ender Sep 25 '14 at 22:29
• I think I misunderstood something: You do always take the 'mean' of the last point you plotted and a random point of the current list. Then you add that new point to the list. Is that correct? It seems that if you have many points in one 'corner' you will get many more there but it is unlikely to get out of that cloud - at least my code always 'converges' pretty fast to points that are too close to each other to really enhance the picture. – flawr Sep 26 '14 at 15:26
• @flawr no, you don't add the new point to the list. The list is fixed - the algorithm only cares about the last point that was plotted, not the ones before it. – Nathaniel Sep 26 '14 at 15:37
• Thanks, that explains a lot, should perhaps be clarified in the question. – flawr Sep 26 '14 at 15:46
# Mathematica, 89
f[n_,s_,r_,p_]:=Graphics@{AbsolutePointSize@1,Point@NestList[#-r#+r RandomChoice@p&,s,n]}
f[10000, {0, 0}, .5, {{-(1/2), Sqrt[3]/2}, {-(1/2), -(Sqrt[3]/2)}, {1, 0}}]
## How it works
In Mathematica the Graphics[] function produces scalable graphics, you render it to whatever size you want by simply dragging the picture corners. In fact, the initial size of all displayed graphics is a ".ini" setting that you may set at 600 or at any other value you wish. So there is no need to do anything special for the 600x600 requirement.
The AbsolutePointSize[] thing specifies that the point size will not be modified by enlarging the image size.
The core construct is
NestList[#-r#+r RandomChoice@p&,s,n]
or in non-golfed pseudo-code:
NestList[(previous point)*(1-r) + (random vertex point)*(r), (start point), (iterations)]
It is recursively building a list starting from (start point) and applying the (vectorial) function in the first argument to each successive point, finally returning the list of all calculated points to be plotted by Point[]
## Some self-replication examples:
Grid@Partition[Table[
pts = N@{Re@#, Im@#} & /@ Table[E^(2 I Pi r/n), {r, 0, n - 1}];
Framed@f[10000, {0, 0}, 1/n^(1/n), pts], {n, 3, 11}], 3]
• @MartinBüttner Instructions for testing this answer without Mathematica installed: 1) Download this from pastebin and save it as *.CDF 2) Download and install the free CDF environment from Wolfram Research at (not a small file). Enjoy. Tell me if it works! – Dr. belisarius Sep 25 '14 at 19:48
• Your golfed version doesn't quite work (at least on V10): you need to switch around #r to r# to get away without a space or * in between. – Martin Ender Sep 26 '14 at 10:30
• @MartinBüttner Curious! It works like a charm on v9 (I don't have v10 yet). Anyway, I (blindly) swapped the # and r. – Dr. belisarius Sep 26 '14 at 11:45
• Ah, it's a new feature. You can now apply functions to associations, in which case you get named parameters that can be accessed by #key. I'm sure that will come in handy. :) – Martin Ender Sep 26 '14 at 11:47
# Java : 246 253447
As a function m():
void m(float[]a){new java.awt.Frame(){public void paint(java.awt.Graphics g){int i=0,x=i,y=i,v;for(setSize(832,864),x+=a[1],y+=a[2];i++<=a[0];v=a.length/2-2,v*=Math.random(),x+=(a[v+=v+4]-x)*a[3],y+=(a[v+1]-y)*a[3])g.drawLine(x,y,x,y);}}.show();}
Line breaks (within a program to show usage):
class P{
public static void main(String[]a){
new P().m(new float[]{1000000, // iterations
416,432, // start
0.6f, // r
416,32,16,432, // point list...
416,832,816,432,
366,382,366,482,
466,382,466,482});
}
void m(float[]a){
new java.awt.Frame(){
public void paint(java.awt.Graphics g){
int i=0,x=i,y=i,v;
for(setSize(832,864),x+=a[1],y+=a[2];
i++<=a[0];
v=a.length/2-2,v*=Math.random(),
x+=(a[v+=v+4]-x)*a[3],
y+=(a[v+1]-y)*a[3])
g.drawLine(x,y,x,y);
}
}.show();
}
}
Drawing input points was removed from the requirements (yay 80 bytes!). They're still shown in the old screenshots below, but won't show up if you run it. See revision history if interested.
The inputs are given as an array of floats. The first is iterations, the next two are starting x y. Fourth is r, and last comes the list of coordinates, in x1 y1 x2 y2 ... fashion.
Ninja Star
1000000 400 400 0.6 400 0 0 400 400 800 800 400 350 350 350 450 450 350 450 450
Cross
1000000 400 400 0.8 300 0 500 0 500 300 800 300 800 500 500 500 500 800 300 800 300 500 0 500 0 300 300 300
Octochains
1000000 400 400 0.75 200 0 600 0 800 200 800 600 600 800 200 800 0 600 0 200
• this does't work in my computer, and java complains show is deprecated – proud haskeller Sep 25 '14 at 16:03
• @proudhaskeller show() is deprecated, but it still works. When you say "doesn't work", what does that mean? If you don't have Java 8, you'll need to add a final to String[]a in main at least. – Geobits Sep 25 '14 at 16:04
• Ported your answer to Processing and cut 100 chars. – ace Sep 25 '14 at 22:37
• @ace Nice. You can do that with pretty much any Java golf for graphical output, but I like that it's exactly 100 chars :D – Geobits Sep 26 '14 at 1:09
# JavaScript (E6) + Html 173 176 193
Edit: big cut, thanks to William Barbosa
Edit: 3 bytes less, thanks to DocMax
173 bytes counting the function and the canvas element needed to show the output.
Test save as html file and open in FireFox.
JSFiddle
<canvas id=C>
<script>
F=(n,x,y,r,p)=>{
for(t=C.getContext("2d"),C.width=C.height=600;n--;x-=(x-p[i])*r,y-=(y-p[i+1])*r)
i=Math.random(t.fillRect(x,y,1,1))*p.length&~1
}
F(100000, 300, 300, 0.66, [100,500, 500,100, 500,500, 100,100, 300,150, 150,300, 300,450, 450,300]) // Function call, not counted
</script>
• <canvas id=C><script>F=(n,x,y,r,p)=>{t=C.getContext("2d"),C.width=C.height=600;for(;n--;)t.fillRect(x,y,1,1),i=Math.random()*p.length&~1,x-=(x-p[i])*r,y-=(y-p[i+1])*r}</script> is 176 bytes long, I didn't understand your count – William Barbosa Sep 26 '14 at 11:21
• @WilliamBarbosa my count is right based on my answer. With your hints it gets better - thank you! – edc65 Sep 26 '14 at 12:34
• You can shave off two more if you move the size initialization and y update into the for call: for(C.width=C.height=600;n--;y-=(y-p[i+1])*r) – DocMax Sep 27 '14 at 6:48
# Python - 200 189
import os,random as v
def a(n,s,r,z):
p=[255]*360000
for i in[1]*(n+1):
p[600*s[0]+s[1]]=0;k=v.choice(z);s=[int(k[i]*r+s[i]*(1-r))for i in(0,1)]
os.write(1,b'P5 600 600 255 '+bytes(p))
Takes input as function arguments to a, writes result to stdout as pgm file. n is iterations, s is starting point, r is r, and z is list of input points.
Edit: No longer draws input points in gray.
## Interesting outputs:
Iterations: 100000
Starting Point: (200, 200)
r: 0.8
Points: [(0, 0), (0, 599), (599, 0), (599, 599), (300, 300)]
Iterations: 100000
Starting Point: (100, 300)
r: 0.6
Points: [(0, 0), (0, 599), (599, 0), (300, 0), (300, 300), (0, 300)]
Iterations: 100000
Starting Point: (450, 599)
r: 0.75
Points: [(0, 0), (0, 300), (0, 599), (300, 0), (599, 300), (150, 450)]
• Some common Python character saves: Initial values like p=[255]*360000 can go as optional parameters to the function; the body of a for loop can all go on the same line if it has no control flow; you can shave parens from [1]*(n+1) as [1]*-~n; since you don't use i in the outer for loop, it's shorter to run code the n times as exec"code;"*n); I think the parens in for i in(0,1) can be removed. – xnor Sep 25 '14 at 19:39
## SuperCollider - 106
SuperCollider is a language for generating music, but it can do graphics at a pinch.
f={|n,p,r,l|Window().front.drawHook_({{Pen.addRect(Rect(x(p=l.choose*(1-r)+(p*r)),p.y,1,1))}!n;Pen.fill})}
I've used some obscure syntax shortcuts to save a few bytes - a more readable and more memory-efficient version is
f={|n,p,r,l|Window().front.drawHook_({n.do{Pen.addRect(Rect(p.x,p.y,1,1));p=l.choose*(1-r)+(p*r)};Pen.fill})}
at 109 chars.
As with the Mathematica example, you have to manually resize the window to get 600x600 pixels. You have to wait for it to re-draw when you do this.
This generates a basic Sierpinsky triangle (not shown because you've seen it before)
f.(20000,100@100,0.5,[0@600,600@600,300@0])
This makes a kind of Sierpinsky pentagon type thing:
f.(100000,100@100,1-(2/(1+sqrt(5))),{|i| (sin(i*2pi/5)+1*300)@(1-cos(i*2pi/5)*300)}!5)
The same thing with 6 points leaves an inverted Koch snowflake in the middle:
f.(100000,100@100,1/3,{|i| (sin(i*2pi/6)+1*300)@(1-cos(i*2pi/6)*300)}!6)
Finally, here's a riff on the 3D pyramids from ace's answer. (Note that I've used one of the points twice, to get the shading effect.)
f.(150000,100@100,0.49,[300@180, 0@500,0@500,350@400,600@500,250@600])
# Python, 189183 175
Edit: fixed the inversed r ratio, and switched to B&W image in order to save a few bytes.
Takes the number of points as n, first point as p, ratio as r and list of points as l. Needs the module Pillow.
import random,PIL.Image as I
s=850
def c(n,p,r,l):
i=I.new('L',(s,s));x,y=p;
i.show()
Examples:
I am generating points in circle around the image's center
points = [(425+s*cos(a)/2, 425+s*sin(a)/2) for a in frange(.0, 2*pi, pi/2)]
c(1000000, (425, 425), 0.4, points)
XOXO repetitions, just changing ratio from 0.4 to 0.6
Some sort of snow flake
stars = [(425+s*cos(a)/2,425+s*sin(a)/2) for a in frange(.0,2*pi, pi/4)]
c(1000000, (425, 425), 0.6, stars)
• Dunno about fixing the backwards r thing, but you can save quite a few characters by making this a program using n,p,r,l=input(). You can also remove the brackets from the *= operations and use import random as R. – FryAmTheEggman Sep 26 '14 at 14:28
• @FryAmTheEggman Unfortunately, correcting my answer invalidates the optimisation on *= :(. The input thing would be good be very unpleasant to work with, and the import currently is the most concise form possible (or have I missed something ?). – teh internets is made of catz Sep 26 '14 at 14:54
• I am pretty sure the line can be import random as R,PIL.Image as I and then random.choice can be R.choice. Yeah, using input is lame, but you can use the function version for testing and post the input() one for a better score!!1! :P – FryAmTheEggman Sep 26 '14 at 15:59
• Oh, I've just noticed defining random actually saves 0 characters. Oops :S Anyway, I also realized that math is your friend: y=x*(1-r)+w == y=x-x*r-w. – FryAmTheEggman Sep 26 '14 at 18:33
• @FryAmTheEggman that was my point :p. But thanks for the maths. – teh internets is made of catz Sep 27 '14 at 8:58
# JavaScript (407) (190)
I'm happy to get any feedback on my script and on golfing since I am not comfortable with JS=) (Feel free to use this/change it for your own submission!)
Reading Input (To be comparable to edc65's entry I do not count the the input.):
p=prompt;n=p();[x,y]=p().split(',');r=p();l=p().split(';').map(e=>e.split(','));
Canvas Setup & Calculation
d=document;d.body.appendChild(c=d.createElement('canvas'));c.width=c.height=1000;c=c.getContext('2d');
for(;n--;c.fillRect(x,y,2,2),[e,f]= l[Math.random()*l.length|0],x-=x*r-e*r,y-=y*r-f*r);
Somewhat more ungolfed (including an example input where the real input promts are just commented out, so ready to use):
p=prompt;
n=p('n','4000');
[x,y]=p('start','1,1').split(',');
r=p('r','0.5');
l=p('list','1,300;300,1;300,600;600,300').split(';').map(e=>e.split(','));d=document;
d.body.appendChild(c=d.createElement('canvas'));
c.width=c.height=1000;c=c.getContext('2d');
for(;n--;c.fillRect(x,y,2,2),[e,f]= l[Math.random()*l.length|0],x-=x*r-e*r,y-=y*r-f*r);
## Examples
for(k = 0; k<50; k++){
}
r = 1.13;
r = 0.5;list = [[1,1],[300,522],[600,1],[300,177]];
r = 0.5
list = [[350+350*Math.sin(6.28*1/5),350+350*Math.cos(6.28*1/5)],
[350+350*Math.sin(6.28*2/5),350+350*Math.cos(6.28*2/5)],
[350+350*Math.sin(6.28*3/5),350+350*Math.cos(6.28*3/5)],
[350+350*Math.sin(6.28*4/5),350+350*Math.cos(6.28*4/5)],
[350+350*Math.sin(6.28*5/5),350+350*Math.cos(6.28*5/5)],
[350+90*Math.sin(6.28*1.5/5),350+90*Math.cos(6.28*1.5/5)],
[350+90*Math.sin(6.28*2.5/5),350+90*Math.cos(6.28*2.5/5)],
[350+90*Math.sin(6.28*3.5/5),350+90*Math.cos(6.28*3.5/5)],
[350+90*Math.sin(6.28*4.5/5),350+90*Math.cos(6.28*4.5/5)],
[350+90*Math.sin(6.28*5.5/5),350+90*Math.cos(6.28*5.5/5)]];
• Which ones do you mean? – flawr Sep 26 '14 at 14:34
• Oh thanks for telling me, I am gonna update the submission soon! – flawr Sep 26 '14 at 15:02
• You linked my answer, but I do count the setup of the canvas. I just don't count the single line calling the function. Nice images anyway, espacially the first one. – edc65 Sep 26 '14 at 19:40
• Ah I didn't notice that, I just wanted to make it 'comparable', but it's difficult when I try to rely on JS only=) @MartinBüttner Updated, now that I understood it the right way I was able to remove much of the garbage=) – flawr Sep 26 '14 at 19:59
## Processing, 153
Ported @Geobits' Java answer to Processing and did some more golfing, resulting in a reduction of 100 chars. I originally intended to animate the process, but the input constraints are too harsh on this (Processing does not have stdin or argv, which means that I must write my own function instead of using Processing's native draw() loop).
void d(float[]a){int v;size(600,600);for(float i=0,x=a[1],y=a[2];i++<a[0];v=(int)random(a.length/2-2),point(x+=(a[v*2+4]-x)*a[3],y+=(a[v*2+5]-y)*a[3]));}
Complete program with line breaks:
void setup() {
d(new float[]{100000,300,300,.7,0,600,600,0,600,600,0,0,400,400,200,200,400,200,200,400});
}
void d(float[]a){
int v;
size(600,600);
for(float i=0,x=a[1],y=a[2];
i++<a[0];
v=(int)random(a.length/2-2),point(x+=(a[v*2+4]-x)*a[3],y+=(a[v*2+5]-y)*a[3]));
}
Above program gives Crosses:
d(new float[]{100000,300,300,.65,142,257,112,358,256,512,216,36,547,234,180,360});
This gives Pyramids:
d(new float[]{100000,100,500,.5,100,300,500,100,500,500});
This gives Sierpinski triangle:
• I love the 3D effect of the pyramids. :) – Martin Ender Sep 25 '14 at 22:37
## Ungolfed "reference implementation", Python
Update: much, much faster (by orders of magnitude)
Check out the interactive shell!
Edit the file and set interactive to True, then do one of these:
polygon numberOfPoints numeratorOfWeight denominatorOfWeight startX startY numberOfSides generates, saves and displays a polygon.
points numberOfPoints numeratorOfWeight denominatorOfWeight startX startY point1X point1Y point2X point2Y ... does what the spec asks for.
import matplotlib.pyplot as plt
import numpy as np
from fractions import Fraction as F
import random
from matplotlib.colors import ColorConverter
from time import sleep
import math
import sys
import cmd
import time
def plot_saved(n, r, start, points, filetype='png', barsize=30, dpi=100, poly=True, show=False):
printed_len = 0
plt.figure(figsize=(6,6))
plt.axis('off')
start_time = time.clock()
f = F.from_float(r).limit_denominator()
spts = []
for i in range(len(points)):
spts.append(tuple([round(points[i].real,1), round(points[i].imag,1)]))
if poly:
s = "{}-gon ({}, r = {}|{})".format(len(points), n, f.numerator, f.denominator)
else:
s = "{} ({}, r = {}|{})".format(spts, n, f.numerator, f.denominator)
step = math.floor(n / 50)
for i in range(len(points)):
plt.scatter(points[i].real, points[i].imag, color='#ff2222', s=50, alpha=0.7)
point = start
t = time.clock()
xs = []
ys = []
for i in range(n+1):
elapsed = time.clock() - t
#Extrapolation
eta = (n+1-i)*(elapsed/(i+1))
printed_len = rewrite("{:>29}: {} of {} ({:.3f}%) ETA: {:.3f}s".format(
s, i, n, i*100/n, eta), printed_len)
xs.append(point.real)
ys.append(point.imag)
point = point * r + random.choice(points) * (1 - r)
printed_len = rewrite("{:>29}: plotting...".format(s), printed_len)
plt.scatter(xs, ys, s=0.5, marker=',', alpha=0.3)
presave = time.clock()
printed_len = rewrite("{:>29}: saving...".format(s), printed_len)
plt.savefig(s + "." + filetype, bbox_inches='tight', dpi=dpi)
postsave = time.clock()
printed_len = rewrite("{:>29}: done in {:.3f}s (save took {:.3f}s)".format(
s, postsave - start_time, postsave - presave),
printed_len)
if show:
plt.show()
print()
plt.clf()
def rewrite(s, prev):
spaces = prev - len(s)
sys.stdout.write('\r')
sys.stdout.write(s + ' '*(0 if spaces < 0 else spaces))
sys.stdout.flush()
return len(s)
class InteractiveChaosGame(cmd.Cmd):
def do_polygon(self, args):
(n, num, den, sx, sy, deg) = map(int, args.split())
plot_saved(n, (num + 0.0)/den, np.complex(sx, sy), list(np.roots([1] + [0]*(deg - 1) + [-1])), show=True)
def do_points(self, args):
l = list(map(int, args.split()))
(n, num, den, sx, sy) = tuple(l[:5])
l = l[5:]
points = []
for i in range(len(l)//2):
points.append(complex(*tuple([l[2*i], l[2*i + 1]])))
plot_saved(n, (num + 0.0)/den, np.complex(sx, sy), points, poly=False, show=True)
def do_pointsdpi(self, args):
l = list(map(int, args.split()))
(dpi, n, num, den, sx, sy) = tuple(l[:6])
l = l[6:]
points = []
for i in range(len(l)//2):
points.append(complex(*tuple([l[2*i], l[2*i + 1]])))
plot_saved(n, (num + 0.0)/den, np.complex(sx, sy), points, poly=False, show=True, dpi=dpi)
def do_default(self, args):
do_generate(self, args)
def do_EOF(self):
return True
if __name__ == '__main__':
interactive = False
if interactive:
i = InteractiveChaosGame()
i.prompt = ": "
i.completekey='tab'
i.cmdloop()
else:
rs = [1/2, 1/3, 2/3, 3/8, 5/8, 5/6, 9/10]
for i in range(3, 15):
for r in rs:
plot_saved(20000, r, np.complex(0,0),
list(np.roots([1] + [0] * (i - 1) + [-1])),
filetype='png', dpi=300)
• Without running this, I have no idea what awesome means. Perhaps you could explain, or show some pictures of what makes it different from the shorter ones? – Geobits Sep 25 '14 at 18:53
• @Geobits edited to include disclaimer and picture :) – Soham Chowdhury Sep 25 '14 at 18:55
• I'd prefer if you included this under a separate heading (e.g. Ungolfed Reference Implementation) in your other answer as posting only ungolfed code is technically "not an answer". – Martin Ender Sep 25 '14 at 18:58
## Python (202 chars)
Takes the number of points as n, the averaging weight as r, the starting point as a tuple s and the list of points as a list of XY tuples called l.
import random as v,matplotlib.pyplot as p
def t(n,r,s,l):
q=complex;s=q(*s);l=[q(*i)for i in l];p.figure(figsize=(6,6))
for i in range(n):p.scatter(s.real,s.imag,s=1,marker=',');s=s*r+v.choice(l)*(1-r)
p.show()
• @MartinBüttner Does the fact that I'm taking a specific type of input meet the spec? – Soham Chowdhury Sep 25 '14 at 18:08
• Also, on my machine, the result is not 600x600 pixels, x and y have different length scales and the points cover more than 1 pixel. – Martin Ender Sep 25 '14 at 18:15 | 2019-08-26 07:59:44 | {"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": 0.2924288213253021, "perplexity": 3510.0545492151564}, "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-2019-35/segments/1566027331228.13/warc/CC-MAIN-20190826064622-20190826090622-00267.warc.gz"} |
https://tel.archives-ouvertes.fr/tel-00006163 | # Minoration de la hauteur de Néron-Tate pour les points et les sous-variétés : variations sur le problème de Lehmer
Abstract : This thesis is dedicated to the problems of lower bound for the normalised height of points and subvarieties. In the chapter 2, we prove a result of density of small points. This enables us to obtain for the height of subvarieties of Abelian varieties of C.M. type, a lower bound, optimal up to a power of a log'' of the degree. We prove in full generality that a good lower bound'' for the height of points implies the analogous lower bound for the subvarieties. This enables us in particular to prove that, on abelian varieties, the Lehmer's problem for points is equivalent to the Lehmer's problem for all the subvarieties. The chapter 3 is an amelioration in the case of hypersurfaces. The proof, introducing an auxiliary function, follows the classical scheme of transcendance's proofs. Using the slopes inequality of Bost, we reobtain then a celebrated result of Dobrowolski in the chapter 4. The chapter 5 extends a result of Amoroso and Zannier to the case of C.M. elliptic curves: we obtain of Lehmer's type lower bound, but with the degree of the extension generated by P over K replaced by the extension generated by P over the abelian extension of K. This enables us to simplify the proof of a result of Viada. Finally we explain the relations between different conjectures concerning the Lehmer's problem on Abelian varieties.
Keywords :
Document type :
Theses
Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2004. French
Domain :
https://tel.archives-ouvertes.fr/tel-00006163
Contributor : Nicolas Ratazzi <>
Submitted on : Friday, May 28, 2004 - 11:19:43 AM
Last modification on : Friday, May 28, 2004 - 11:19:43 AM
### Identifiers
• HAL Id : tel-00006163, version 1
### Citation
Nicolas Ratazzi. Minoration de la hauteur de Néron-Tate pour les points et les sous-variétés : variations sur le problème de Lehmer. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2004. French. <tel-00006163>
Consultation de
la notice
## 86
Téléchargement du document | 2015-08-31 22:10:04 | {"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": 0.587283194065094, "perplexity": 1228.011986489171}, "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-2015-35/segments/1440644068098.37/warc/CC-MAIN-20150827025428-00273-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://tex.stackexchange.com/questions/114927/xelatex-myriad-pro-l-with-apostrophe-issue | # xelatex myriad pro l with apostrophe issue
I compile my document with xelatex. I use Myriad pro
\setmainfont[Mapping=tex-text]{Myriad Pro}
My problem is that the "l'a" is looking OK but not the "l'i" the i touches the apostrophes. Can someone tell me how to fix this issue?
• The kerning of the apostrophe in Minion Pro and Myriad Pro is known to be bad. :( – egreg May 18 '13 at 13:33
• in pdfTeX, things like this were possible. Let's hope the kerning feature will be back in microtype for Xe/LuaLaTeX someday. – Nils L May 18 '13 at 13:54
• Please see: tex.stackexchange.com/questions/45460/… – morbusg May 18 '13 at 19:35
• It is an ugly solution, but you could manually add kerning... Defining some macros would make it much easier. Alternatively, you could open the font in Fontforge and change the kerning there. It involves some work but it is doable. I am not really sure if it permitted by the fonts license though... – pmav99 May 18 '13 at 21:37
• @all thanks for your your answers. I have another question. Is there any other font very similar to myriad pro that handles better the appostrophes? – S12000 May 19 '13 at 11:37
There is nothing wrong with the font, you can find this out by writing the same thing into another program. It is a issue with ICU engine with XeTeX.
One way to fix it is to issue a zero kern after the apostrophe:
l'\kern0pt inno
Another option would be to use \XeTeXinterchartoks to insert that kern automatically. See this answer on how to do it.
Here's an example as requested:
\documentclass{article}
\usepackage{fontspec}
\XeTeXcharclass ' \aposclass
` | 2020-01-19 08:47:37 | {"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": 0.7201960682868958, "perplexity": 2470.116686024381}, "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/1579250594333.5/warc/CC-MAIN-20200119064802-20200119092802-00349.warc.gz"} |
http://alvinalexander.com/taxonomy/term/2668 | # strikethrough
## LaTeX strikeout font example - How to use a strikeout/strikethrough font
A LaTeX strikeout font example: It was hard to find out how to use a strikethrough font using LaTeX, and I don't want to lose it, so here's a simple example.
```%
% include the "ulem" package in the header
%
\usepackage{ulem}
%
% use the "sout" tag to "strike through" text
%
\sout{Bill Clinton} G.W. Bush is the pres.
```
Run through the `latex2html` converter, this produces output text like this:
## LaTeX strikeout tag (Thu, May 13, 2004)
Some of my cohorts in development are using the Hibernate object/relational mapping software w | 2013-12-13 09:24:09 | {"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": 0.9753713607788086, "perplexity": 7288.067252982892}, "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-2013-48/segments/1386164923389/warc/CC-MAIN-20131204134843-00096-ip-10-33-133-15.ec2.internal.warc.gz"} |
http://www.koreascience.or.kr/article/JAKO200709906003862.page | # 안와 및 안부속기 종양의 방사선치료에서 백내장의 예방을 위한 렌즈보호 장치의 효용성
• 조정근 (전주대학교 방사선학과) ;
• 조현상 (삼성서울병원 방사선종양학과) ;
• 한태종 (전주대학교 방사선학과)
• Published : 2007.12.28
• 52 7
#### Abstract
Radiotherapy which is the most effective for orbit lymphoma has been used increasingly due to the increase of orbit or ocular adnexal tumor patients. Curative effects and convalescence have been being more satisfied thanks to remarkable development of cancer chemotherapy and medical treatments, but side effects such as cataract, dry eye and retinopathy still break out. Thus, in this study, a Lens Shielding Device (LSD hereafter) was designed to prevent occurring of cataract due to radiation therapy for orbit lymphoma and its efficacy through dosimetry were evaluated. And in this paper, its manufacturing process was also explained. LSD is composed of a cover body covering the lens and a side fixing part supporting the cover body. To measure radiation, the patient therapy conditions were simulated and the measurement of the radiation was conducted with Thermo Luminescence Detector (TLD) and Markus chamber. The average TLD value was 5.7% and the TLD value and Markus chamber value were acquired as 4.2% and 5.1% respectively at 6 mm depth where zero lens center was located. Only 1.5Gy ($300Gy{\times}\;5%$) or 5% of total 30Gy with 9 MeV electron beam is estimated to affect on patient's lens. That is smaller dose than the threshold value of cataract (2GY) or the value (5Gy) that was reported to cause cataract in clinical conditions. Thus, these findings suggest that LSD be very useful for prevention of cataract during radiotherapy for malignant lymphoma of orbit and ocular adnexa. Furthermore, it might be possible to reduce patient's discomfort caused by alien substances and to make it easier to fix the device with customized manufacturing manners.
#### Keywords
Science Technology;Lens Shielding Device;Malignant Lymphoma;Cataract | 2019-12-13 10:17:31 | {"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": 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": 0.45103105902671814, "perplexity": 10765.658258745869}, "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-2019-51/segments/1575540553486.23/warc/CC-MAIN-20191213094833-20191213122833-00040.warc.gz"} |
https://www.physicsforums.com/threads/limit-of-e-i-x-at-infinity.725823/ | # Limit of e^(i*x) at infinity?
1. Nov 30, 2013
### Typhon4ever
1. The problem statement, all variables and given/known data
delta dirac function(x) * e^(-i*x) at ∞ and -∞
2. Relevant equations
delta dirac(x)*e^(i*x)
3. The attempt at a solution
I'm wondering how e^(i*x) looks like at infinity/-infinity. I know it has some sort of oscillating property i.e e^(pi*i)=e^(3pi*i). The problem is I'm trying to find the delta dirac function * e^(-i*x) at infinity and negative infinity but I don't know how to evaluate the exponential. I know the delta function should be 0 in both cases but I don't know if the exponential will turn out to be indeterminate or something else. I should get 0 from the whole equation.
2. Nov 30, 2013
### vela
Staff Emeritus
3. Nov 30, 2013
### Typhon4ever
Ok. Using Euler's if I'm not mistaken just tells me the limit doesn't exist. What do I do then to evaluate this problem?
4. Nov 30, 2013
### Mandelbroth
How are you defining the Dirac delta? What does that imply about the product?
5. Nov 30, 2013
### Typhon4ever
I'm not sure what you mean by how I'm defining the dirac delta.
6. Nov 30, 2013
### Mandelbroth
Well, what does the Dirac delta evaluate to at any nonzero $x\in\mathbb{R}$?
I'm assuming your "*" means multiplication, correct?
7. Nov 30, 2013
### Typhon4ever
Yes "*" means multiplication. Anywhere except the origin is 0.
8. Nov 30, 2013
### vela
Staff Emeritus
If you're referring to the limit $\displaystyle \lim_{x \to \infty} e^{ix}$, then you're correct. That limit doesn't exist because $e^{ix}$ doesn't converge to a single value. But that's not the limit you were asking about. You should cogitate on the implication of your (correct) answer to Mandelbroth's question.
9. Nov 30, 2013
### Typhon4ever
So I have the delta function at infinity which is 0 * a non converging exponential=...0?
10. Nov 30, 2013
### vela
Staff Emeritus
Yes, that's the right answer, but you're not thinking about this correctly. Since you're interested in the limit as x goes to +∞, you can assume x>0. For any such value of x, $\delta(x)e^{ix} = 0\times e^{ix} = 0$. Now you take the limit of this as x goes to +∞.
$$\lim_{x \to \infty} \delta(x)e^{ix} = \lim_{x \to \infty} 0 = 0.$$ The behavior of $e^{ix}$ doesn't matter.
11. Nov 30, 2013
### Typhon4ever
Oh, ok. Thank you! | 2017-08-20 07:27:24 | {"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": 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": 0.7823977470397949, "perplexity": 1054.0296976622283}, "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/1502886105976.13/warc/CC-MAIN-20170820053541-20170820073541-00703.warc.gz"} |
https://www.scienceforums.net/topic/117487-habitable-zone-of-a-star/?tab=comments | # Habitable zone of a star
## Recommended Posts
Hi !
I need your help to find a formula to calculate the habitable zone of a star ... I searched and searched without having the answer ...
I found this calculation:
But it just defines a radius. I would like to calculate the lower limit of the ZH and its upper limit. I found other calculations with Boltzman's law, but I can not find results that work.
So if you have an idea I'd be happy
Thanks (sorry for my english)
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I'm not sure how you are defining habitable zone, in our solar system both Venus and Mars are within the habitable zone but both have atmospheres that prohibit life.
I know this is not an answer but I want to see what others have to say and I'll do a bit of digging too..
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17 hours ago, Moontanman said:
I'm not sure how you are defining habitable zone, in our solar system both Venus and Mars are within the habitable zone but both have atmospheres that prohibit life.
I know this is not an answer but I want to see what others have to say and I'll do a bit of digging too..
I think (but I'm not sure) that the albedo (so the composition of the atmosphere) is not taken into account to define the habitable zone. But I can be wrong...
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Is the 'habitable' zone usually defined as the min and max orbits around a star where temps are such that water is in a liquid state ?
I don't think atmospheres are considered.
( water would not be liquid on a planet with no atmosphere at 70 deg C )
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14 minutes ago, AXdlv said:
I think (but I'm not sure) that the albedo (so the composition of the atmosphere) is not taken into account to define the habitable zone. But I can be wrong...
This seems reasonable. Otherwise you could have planets assumed to be outside the habitable zone of a star like the Sun, orbiting at 93,000,000 miles from it, with other planets, both closer and further, considered in the zone simply due to their make up.
I think the habitable zone, assuming there is one, says more about the star than the individual planets.
Edited by J.C.MacSwell
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3 minutes ago, MigL said:
Is the 'habitable' zone usually defined as the min and max orbits around a star where temps are such that water is in a liquid state ?
I don't think atmospheres are considered.
( water would not be liquid on a planet with no atmosphere at 70 deg C )
With no atmosphere the earth would be freezing cold much like the moon at night, the average temp of a body in earth's orbit would be below freezing..
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I would define "habitable zone" as distance from the star in which planet is receiving 1370 Watts per square mater of surface +- couple (or couple dozen) percent tolerance.
1370 W/m^2 is measured radiation of the Sun, and by applying reverse of inverse-square law, we can calculate total power of the Sun.
$P=\frac{P_0}{4 \pi r^2}$
$P_0 = P * 4 * \pi * r^2$
$P_0 = 1370 * 4 * 3.14159265 * (150*10^9)^2 = 3.8 *10^{26} W$
So, if we will use +-10% tolerance, star must deliver (approximately) 1200 W/m^2....1500 W/m^2.
You should be able to calculate min and max radii for this range by yourself now.
Carbon-based organic life requires water. Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure). Too large radiation from the star, and water will vaporize, like on Venus. Too low radiation, and it'll freeze.
There are existing super cold stars which emit fraction of energy which is emitted by the Sun. So distance between such super cold star and planet would have to be very small. e.g. star which has 1% of power of the Sun, must have planet located at distance ~15 mln km.
Edited by Sensei
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True, but we are only just now developing the means to detect extra-solar atmospheres.
Previously the only definition would have involved distances from the parent star where enough radiation is received to keep water liquid.
I'm assuming, of course.
X-posted with Sensei
Edited by MigL
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4 minutes ago, Sensei said:
I would define "habitable zone" as distance from the star in which planet is receiving 1370 Watts per square mater of surface +- couple (or couple dozen) percent.
1370 W/m^2 is measured and by applying reverse of inverse-square law, we can calculate total power of the Sun.
$P=\frac{P_0}{4 \pi r^2}$
$P_0 = P 4 \pi r^2$
$P_0 = 1370 * 4 * 3.14159265 * (150*10^9)^2 = 3.874*10^{26} W$
So, if we will use +-10% tolerance, star must deliver 1200 W/m^2....1500 W/m^2.
You should be able to calculate min and max radii for this range by yourself now.
Carbon-based organic life requires water. Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure). Too large radiation from the star, and water will vaporize, like on Venus.
I think this is a good start, but different atmospheres should be able to maintain higher temperatures with the same energy balance as our Earth.
Could a rogue planet (OK, non planet) with no star to orbit sustain life? It would need to be of sufficient size to maintain a substantial atmosphere, and have enough radioactivity to keep it warm...but not too warm. If the answer is yes that could mean almost anywhere could be habitable.
But the range you suggest seems most reasonable.
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1 hour ago, J.C.MacSwell said:
I think the habitable zone, assuming there is one, says more about the star than the individual planets.
..and stage of life of particular star..
In the future of solar system, also the Earth will be outside of habitable zone, when energy emitted by the Sun will be too high for living organisms on the Earth. Temporary *) solution could be building of cosmic-scale remote-controlled network of mirrors between the Sun and the Earth, that will reflect photons in different directions, reducing radiation reaching Earth's surface.
*) temporary for millions of years.
Edited by Sensei
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2 hours ago, Sensei said:
I would define "habitable zone" as distance from the star in which planet is receiving 1370 Watts per square mater of surface +- couple (or couple dozen) percent tolerance.
1370 W/m^2 is measured radiation of the Sun, and by applying reverse of inverse-square law, we can calculate total power of the Sun.
P=P04πr2
P0=P4πr2
P0=137043.14159265(150109)2=3.81026W
So, if we will use +-10% tolerance, star must deliver (approximately) 1200 W/m^2....1500 W/m^2.
You should be able to calculate min and max radii for this range by yourself now.
Carbon-based organic life requires water. Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure). Too large radiation from the star, and water will vaporize, like on Venus. Too low radiation, and it'll freeze.
There are existing super cold stars which emit fraction of energy which is emitted by the Sun. So distance between such super cold star and planet would have to be very small. e.g. star which has 1% of power of the Sun, must have planet located at distance ~15 mln km.
Thank you for this calculation ! In the solar system, the habitable zone is between 0.95 UA and 2 AU. I do not find these values if I use your calculation ... Is it because the Earth is not in the middle of this zone ?
What are the minimum and maximum "P" for a temperature between 0 ° C and 100 ° C? (I mean Pmin=1200 W/m^2 and Pmax=1500W/m^2 ? or is it another value)
Edited by AXdlv
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1 hour ago, AXdlv said:
In the solar system, the habitable zone is between 0.95 AU and 2 AU. I do not find these values if I use your calculation ...
3.828*10^26 W / ( 4 * PI * ( 150*10^9 * 0.95 )^2 ) = 1500 W/m^2 (0.95 AU).
So inner edge is at least "right"..
It is several times mentioned on Wikipedia, in "Solar System estimates" section:
I picked up +- 10 % of power tolerance as an example values, which are acceptable for human.
in "Solar System estimates" section, we can see there is no general consensus between scientists, how to estimate it. They make predictions which require e.g. special non-Earth-like atmospheres, with significantly different pressures.
4 hours ago, Sensei said:
Water must be able to exist in liquid form. Which is in temperature range 0 ... 100 C (at standard pressure).
I would like to fix it a bit. The majority of Carbon-based living organisms will be dead at temperatures above 46 C, because their proteins will be denatured..
Edited by Sensei
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14 hours ago, Sensei said:
3.828*10^26 W / ( 4 * PI * ( 150*10^9 * 0.95 )^2 ) = 1500 W/m^2 (0.95 AU).
So inner edge is at least "right"..
It is several times mentioned on Wikipedia, in "Solar System estimates" section:
I picked up +- 10 % of power tolerance as an example values, which are acceptable for human.
in "Solar System estimates" section, we can see there is no general consensus between scientists, how to estimate it. They make predictions which require e.g. special non-Earth-like atmospheres, with significantly different pressures.
I would like to fix it a bit. The majority of Carbon-based living organisms will be dead at temperatures above 46 C, because their proteins will be denatured..
OK thanks a lot! So, if I understood correctly, in our solar system, we did not define the HZ. So, this representation is correct ?
In fact, I'd like to do a program that says (with the mass of the star, is luminosity and the distance between the planet and the star using Kepler's law) if the planet is or isn't in the habitable zone... So if I understood I must take our actuel delimitation for the solar system and transpose it to another system.
(3,8*10^26)/4*PI*(0,95*1,49*10^11)^2 = 1500 W.m^-2
(3,8*10^26)/4*PI*(2,4*1,49*10^11)^2 = 236 W.m^-2
And I take Kepler 452 with P = 1,2 * 3,8 * 10^26 W
Outer : ((1,2*3,8*1026 )/(4*PI*236))1/2 = 3,9 * 1011 m
Inner : ((1,2*3,8*1026 )/(4*PI*1500))1/2 = 1,55 * 1011 m
For Kepler from 1,55*10^11 to 3,9 * 10^11 m is "habitable" ?
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Do these calculations assume a planet identical to Earth?
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31 minutes ago, Moontanman said:
Do these calculations assume a planet identical to Earth?
According to my research, I saw that the size of the planet is not very important. But obviously, the mass has an impact on the presence of an atmosphere, so on the temperature.
But I just wanted to know how the habitable zone was calculated, this zone says more about the star than on the planet, as it was said before.
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2 minutes ago, AXdlv said:
According to my research, I saw that the size of the planet is not very important. But obviously, the mass has an impact on the presence of an atmosphere, so on the temperature.
But I just wanted to know how the habitable zone was calculated, this zone says more about the star than on the planet, as it was said before.
Ok, thanks for the clarification, I have been following Sara Seager, who works for NASA and her take on the habitable zone is a bit more complex. Also it should be noted that the Earth with no atmosphere would have an average temp below freezing.
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8 minutes ago, Moontanman said:
Ok, thanks for the clarification, I have been following Sara Seager, who works for NASA and her take on the habitable zone is a bit more complex. Also it should be noted that the Earth with no atmosphere would have an average temp below freezing.
Thank you for the name. I knew Sara Seager for her "Drake equation". Is it this calculation ? https://arxiv.org/pdf/1304.3714.pdf
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Just now, AXdlv said:
Thank you for the name. I knew Sara Seager for her "Drake equation". Is it this calculation ? https://arxiv.org/pdf/1304.3714.pdf
That is one of them, she also says the habitable zone could extend out to as far as Jupiter with the right planetary atmosphere..
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On 12/22/2018 at 4:18 PM, Moontanman said:
I'm not sure how you are defining habitable zone, in our solar system both Venus and Mars are within the habitable zone but both have atmospheres that prohibit life.
I know this is not an answer but I want to see what others have to say and I'll do a bit of digging too..
the habitability of earth is defined but the tilt at which we are at.23.5 degrees. mars tilts at 25 degrees which allows the sun to cook it. Mars used to look like earth,but was cooked because of tilt.Venus tilts at 3 degrees,thus it is very hot and uninhabitable.
Edited by peglerbc
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26 minutes ago, peglerbc said:
the habitability of earth is defined but the tilt at which we are at.23.5 degrees. mars tilts at 25 degrees which allows the sun to cook it. Mars used to look like earth,but was cooked because of tile.Venus tilts at 3 degrees,thus it is very hot and uninhabitable.
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16 minutes ago, Moontanman said:
I apologize,the tilt affect the seasons.if the earth were to tilt slightly the it would change seasons.
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13 minutes ago, peglerbc said:
I apologize,the tilt affect the seasons.if the earth were to tilt slightly the it would change seasons.
The Earth's axial tilt varies between 22.1 and 24.5 degree over a 41,000 yr cycle. While this does have an effect on the seasons to some degree, it doesn't on the overall habitability of the Earth.
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4 minutes ago, Janus said:
The Earth's axial tilt varies between 22.1 and 24.5 degree over a 41,000 yr cycle. While this does have an effect on the seasons to some degree, it doesn't on the overall habitability of the Earth.
yeah i was thinking differently of axial tilt.it was a flaw it my better judgment. | 2019-02-18 23:24:25 | {"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": 0.45079201459884644, "perplexity": 1679.6249552500785}, "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/1550247488490.40/warc/CC-MAIN-20190218220415-20190219002415-00382.warc.gz"} |
http://openstudy.com/updates/50027433e4b0848ddd6694a2 | ## anonymous 4 years ago If probability density function (pdf) $f_{x}(x)=c$ for 0<x<=10 and 0 other wise How to find cummulative density function $F_{X}$ for x>10? Pl give steps.
1. anonymous
@RaphaelFilgueiras did u wrote sth
2. anonymous
|dw:1342339258763:dw|
3. anonymous
i think is it,but im not so sure
4. perl
|dw:1342339653891:dw|
5. perl
|dw:1342339722709:dw|
6. anonymous
and c must be 1/10
7. perl
yes c = 1/10 because |dw:1342339943478:dw|
8. perl
|dw:1342340129572:dw|
9. anonymous
Here it goes
10. perl
you left out when x < 0 what program are you using? very nice
11. UnkleRhaukus
Total probability density$\int\limits_{-\infty}^\infty f_x(x')\text dx'=1$ Cumulative probability density up to point x $F_X=\int\limits_{-\infty}^x f_x(x')\text dx'$ | 2016-12-09 07:49:38 | {"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": 0.46634167432785034, "perplexity": 10836.538232174726}, "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-2016-50/segments/1480698542687.37/warc/CC-MAIN-20161202170902-00446-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/140542/time-series-hold-out-data-not-used-to-build-model/140550 | # Time Series Hold Out Data not used to build model
It is my understanding that if one wants to build multiple time series models on a time series that goes from 2000 to today (2015) monthly; and one wanted to use that information to forecast 3 months in the future, it is common approach to split your data into "train" and "test" datasets.
Your test dataset would be the last 3 months of your time series (jan 2015, feb 2015, march 2015) (pretend we're already in april for simplicity sake). You would then 'define' your model on your training dataset, and then compute it's errors against your test dataset (defined as predicted vs actual).
This way you could try out many multiple models and pick the one with the lowest "forecast prediction error".
However my question is: By ignorning those last 3 months of data, how do you then use that model to forecast values later in time? Example: say you wanted to forecast April-June. Is it standard procedure to apply the same model (that wasn't built on the last 3 months) to the April - June forecast period?
If so is this something you can do in R with a package? It seems like the forecast function only works to forecast forward from the training dataset, and you can't apply it to other time series objects.
Or does one 're-build' the model on the entire time series (2000 to 2015 March) and then use that model to forecast into April-June?
I am pretty confused by this and any help would be appreciated.
Well, technically you should have your model ex ante determined, and the so-called train data set is really just to demonstrate the universal validity of your model on "the present day" (test) data set. It is a subsample test.
Once the model you're using is shown to work robustly as a predictor in all important subsamples, and you've argued convincingly that it is universally valid, it's typical to run the whole thing again using all the data and try to predict the future. This part usually tends to be the problematic part.
Here's an attempt to explain this with an example.
Say we want a function or black box
$\qquad$ In: 12 months data, say rainfall
$\qquad$ Out: a forecast of the next 3 months' rainfall
$\qquad$ E.g. Jan .. Dec --> next Jan
$\qquad \quad \ \$ Feb .. Jan --> next Feb ...
Assume further that some magic process, trained on the data from 2000 .. 2014, tells us that a good predictor of 12 months --> the next 3 months is exactly
$\qquad$ 50 % year ago $\ + \$ 50 % month ago.
E.g.
(Jan 2000 + Dec 2000) / 2 ~= Jan 2001
...
(Dec 2013 + Nov 2014) / 2 ~= Dec 2014
(Exercise: plot these 50 - 50 estimates against the real values in 2000 .. 2014, for your data.)
Now say the numbers for 2014 happen to be exactly 1 2 3 .. 12. Then our 50 - 50 predictor gives
Jan 2014 .. Dec 2014 1 2 3 .. 12 --> Jan 2015 forecast (1 + 12) / 2 = 6.5
Feb 2014 .. Jan 2015 2 3 .. 12 6.5 --> Feb 2015 forecast (2 + 6.5) / 2 = 4.25
Mar 2014 .. Feb 2015 3 .. 6.5 4.25 --> Mar 2015 forecast (3 + 4.25) / 2 = 3.625
Do you see how the Feb 2015 forecast uses the Jan 2015 forecast 6.5, and the Mar 2015 forecast uses both the Jan 6.5 and Feb 4.25 ?
(Exercise: repeat this with numbers 1 .. 12, but 20 % year ago $\ + \$ 80 % month ago; repeat on your real data.)
Now we can compare the 3-month forecasts trained on 2000 .. 2014 with the real values for Jan Feb Mar 2015, which is the reason for all this (holding out the last 3 months). Otherwise, we'd have a black-box forecaster with magic parameters (50 - 50) but no independent test of how it performs on new data. | 2019-06-20 07:55:00 | {"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": 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": 0.42518675327301025, "perplexity": 1354.488070786519}, "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-2019-26/segments/1560627999163.73/warc/CC-MAIN-20190620065141-20190620091141-00183.warc.gz"} |
http://www.maa.org/press/periodicals/convergence/alien-encounters-act-1-continued | # Alien Encounters - Act 1 (continued)
Author(s):
Gavin Hitchcock
WALLIS
It is my opinion, which I submit for the consideration of the present illustrious company, that the ratio of a positive number to a negative number may be supposed greater than infinity.
LEIBNIZ
What?! Can such a monstrous conclusion emerge so soon to disturb our complacency? This is no mere instance of stray property or mistaken domain! I declare - were this proposition put forward by any less august personage and less well-respected mathematician than Dr Wallis, I should dismiss it out of hand as nonsensical. But come, Sir, your reasons, if you will!
WALLIS5
Certainly, Herr Leibniz! Observe that the reciprocals of the positive numbers taken in descending order: one-over-five, one-over-four, and so on, are increasing up to the last term one-over-nothing which must be infinite;
¼, 1 5 , 1 4 , 1 3 , 1 2 , 1 1 , 1 0 , 1 -1 , 1 -2 , 1 -3 ,¼
therefore if we proceed further we should conclude that the reciprocals of negative numbers: one-over-minus-one, one-over-minus-two, and so on, are greater than infinity.
LEIBNIZ
There must be something amiss here ... but I cannot at the present moment fault the argument.
EULER [to audience, in agitation ]
This is intolerable! He is in grave error. I cannot be silent: Heaven grant me intercourse with the past!...
[moves to join the group ]
Pardon! my name is Euler; I beg your indulgence. I am acquainted with your work and deeply honoured to be - ah - present. But, with regard to Dr Wallis' conclusions about mixed ratios of positive and negative numbers, allow me, I pray you, to demonstrate why I reject your argument, Sir!
The fundamental error lies in supposing that anything whatever can be concluded from such sequences of reciprocals. For if, instead of reciprocals as previously, we take numbers which are the reciprocals of squares, then we obtain the sequence:
¼, 1 (-3)(-3) , 1 (-2)(-2) , 1 (-1)(-1) , 1 0 , 1 1 , 1 2.2 , 1 3.3 ,¼
or
¼, 1 9 , 1 4 , 1 1 , 1 0 , 1 1 , 1 4 , 1 9 ,¼
Surely, from that, no-one will venture to claim that these positive terms are greater than infinity? If anyone has lingering doubts, consider the sequence of reciprocals of square roots:
¼, 1
Ö -3
, 1
Ö -2
, 1
Ö -1
, 1
0
, 1
Ö1
, 1
Ö2
, 1
Ö3
,¼
from which one could claim that the imaginary numbers are greater than infinity; and from the sequence of roots:
¼, Ö -3 , Ö -2 , Ö -1 ,0,Ö1,Ö2,Ö3,¼
the claim would have to be that imaginary numbers are less than infinity - in fact, less than nothing. Both these conclusions are, of course, quite preposterous.6
LEIBNIZ
Negative quantities are problematic, and imaginary quantities worse still. What intolerable contradictions may we let loose when these be combined with infinities! The road to madness is paved with such infinite sequences! And yet - take courage, friends! Here is a notorious example I am proud to have completely solved, although when first I wrestled with this Gordian knot I despaired of success:
The problem is to find the sum of the series: one minus one plus one minus one, and so forth.
1-1+1-1+¼
Writing it as:
(1-1)+(1-1)+¼ ,
the sum would appear to be nothing. But writing it as:
1-(1-1)-(1-1)-¼ ,
the sum appears to be one. What does our intrepid young friend make of that?
EULER [laughing ]
No doubt, Herr Leibniz, you are expecting that I will shrink from this, as an insoluble contradiction, so that you can enlighten me. But I have a good argument which shows the sum to be one half, the happy medium between your two previous sums.
LEIBNIZ [deflated ]
Oh, indeed? Let us see it.
EULER 7
I take the geometric series: one plus x plus x squared plus x cubed, etc., which is well known to sum to the reciprocal of one minus x.
1 1-x =1+x+x2+x3+¼
and I substitute minus one for x, to obtain one half as the required sum.
x=-1 , 1 2 =1-1+1-1+¼
LEIBNIZ
I concede that you have obtained the correct sum. But I have a marvellously subtle method by which I reach that conclusion with no resort to the banalities of geometric series.
Observe! If one takes the first term, then the first two terms, and then the first three, and so on, one obtains successively the partial sums 1,0,1,0,1, and so on ad infinitum . Therefore, as candidates for sum of the infinite series we started with, both 1 and 0 are equally probable, and so clearly the most probable value of all will be their arithmetic mean, namely 1/2, which is therefore the true sum.8
EULER
There would appear to be a far greater deal of metaphysics than mathematics in that argument.
LEIBNIZ
Oh, I will not deny that. But the celebrated Bernoullis9 have accepted the argument as valid, and, if the truth be told, I really do believe that there is far more metaphysical truth in mathematics than is generally realised.10 And I am not by any means alone in holding this opinion. Our sagacious colleague Grandi, of the University of Pisa, was so moved by the discovery that this series, (whose true sum he found to be 1/2 by a method similar to yours) could in another form sum to nothing, that he announced that he had a proof that the world could be created out of nothing.11 As he saw it, by merely looking at the series in a different way, the value nothing can be transmuted into something substantial. Fiat, ex nihilo , one half!
Gavin Hitchcock , "Alien Encounters - Act 1 (continued)," Convergence (May 2011) | 2015-08-29 23:30:36 | {"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": 0.8014649748802185, "perplexity": 1237.7075141291746}, "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-2015-35/segments/1440644064590.32/warc/CC-MAIN-20150827025424-00265-ip-10-171-96-226.ec2.internal.warc.gz"} |
http://gradestack.com/CBSE-Class-8th-Complete/Factorisations/Division-of-Algebraic/14825-2854-3054-study-wtw | # Division of Algebraic Expressions
So far, we have learnt how to add and subtract algebraic expressions. Also how to multiply algebraic expressions. Now, we have to learn in this section how to divide one algebraic expression by another.
We know that gives . Similarly we follow the division of algebraic expressions.
Example :
Division of a monomial by another monomial:
Example
Divide
Solution
Division of a polynomial by a monomial:
There are two ways to divide a polynomial by a monomial. The first method by removing the common factor in the numerator and then dividing by the given monomial. Another method is by dividing each term in the numerator by the given monomial.
Example : Consider the division of the trinomial by the monomial 2t.
First method:
. Here is common in each term. Separating from each term we get.
Second method:
We can also divide each term of the trinomial by the monomial using cancellation method.
Example
Divide by 6
abc using both the methods.
Solution
First method: By taking out the common factor
Therefore
Second method:
Using cancellation method,
Division of Polynomial by another Polynomial:
While dividing a polynomial by another polynomial, the dividend should be written as the factor of the divisor.
Example
Solution
Example
Divide
Solution
Example
Divide:
Solution
Dividend
Thus | 2017-03-26 15:12:50 | {"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": 0.8705735802650452, "perplexity": 777.9793529086386}, "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-2017-13/segments/1490218189242.54/warc/CC-MAIN-20170322212949-00077-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://www.komal.hu/verseny/feladat.cgi?a=feladat&f=B4679&l=en | English Információ A lap Pontverseny Cikkek Hírek Fórum
Rendelje meg a KöMaL-t!
VersenyVizsga portál
Kísérletek.hu
Matematika oktatási portál
B. 4679. Prove that among any 39 consecutive natural numbers there is a number in which the sum of the digits is divisible by 11.
(3 points)
Deadline expired on 10 February 2015.
Statistics on problem B. 4679.
104 students sent a solution. 3 points: 77 students. 2 points: 10 students. 1 point: 9 students. 0 point: 8 students.
• Problems in Mathematics of KöMaL, January 2015
• Támogatóink: Morgan Stanley | 2017-10-21 17:35:30 | {"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": 0.8253873586654663, "perplexity": 12571.213715507307}, "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-2017-43/segments/1508187824824.76/warc/CC-MAIN-20171021171712-20171021191712-00668.warc.gz"} |
https://socratic.org/questions/how-do-you-solve-2x-2-x-5-by-completing-the-square | # How do you solve 2x^2-x=-5 by completing the square?
Jan 12, 2018
This question doesn't have any real solutions. However it does have two complex solutions;
$\textcolor{red}{x = \frac{1 \pm i \sqrt{39}}{4}}$
#### Explanation:
$2 {x}^{2} - x = - 5$
$2 {x}^{2} - x + 5 = 0$
$2 \left({x}^{2} - \frac{x}{2} + \frac{5}{2}\right) = 0$
${x}^{2} - \frac{x}{2} + \frac{5}{2} = 0$
${\left(x - \frac{1}{4}\right)}^{2} - \frac{1}{16} + \frac{5}{2} = 0$
${\left(x - \frac{1}{4}\right)}^{2} + \frac{39}{16} = 0$
${\left(x - \frac{1}{4}\right)}^{2} = - \frac{39}{16}$
$x - \frac{1}{4} = \pm \sqrt{- \frac{39}{16}}$
$x - \frac{1}{4} = \pm \frac{\sqrt{- 39}}{4} = \pm \frac{\sqrt{39} \times \sqrt{- 1}}{4}$
$x = \frac{1}{4} \pm \frac{\sqrt{39} \times \sqrt{- 1}}{4} = \frac{1}{4} \pm \frac{\sqrt{39} \times i}{4}$
$\textcolor{red}{x = \frac{1 \pm i \sqrt{39}}{4}}$
I hope it helps :) | 2019-08-22 14:05:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 12, "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": 0.5173988342285156, "perplexity": 1421.507401000361}, "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-2019-35/segments/1566027317130.77/warc/CC-MAIN-20190822130553-20190822152553-00219.warc.gz"} |
http://monkez.com/journal/g3ofal.php?tag=defensive-player-of-the-year-nfl-2020-candidates-262899 | The same test will be performed using the $$p$$-value approach in Example $$\PageIndex{3}$$. Missed the LibreFest? Each can be checked with a corresponding condition. Students should not calculate or talk about a correlation coefficient nor use a linear model when that’s not true. If those assumptions are violated, the method may fail. As was the case for two proportions, determining the standard error for the difference between two group means requires adding variances, and that’s legitimate only if we feel comfortable with the Independent Groups Assumption. We can proceed if the Random Condition and the 10 Percent Condition are met. Tossing a coin repeatedly and looking for heads is a simple example of Bernoulli trials: there are two possible outcomes (success and failure) on each toss, the probability of success is constant, and the trials are independent. Again there’s no condition to check. Independent Groups Assumption: The two groups (and hence the two sample proportions) are independent. We already made an argument that IV estimators are consistent, provided some limiting conditions are met. Sample-to-sample variation in slopes can be described by a t-model, provided several assumptions are met. Matching is a powerful design because it controls many sources of variability, but we cannot treat the data as though they came from two independent groups. If, for example, it is given that 242 of 305 people recovered from a disease, then students should point out that 242 and 63 (the “failures”) are both greater than ten. Of course, in the event they decide to create a histogram or boxplot, there’s a Quantitative Data Condition as well. âThe samples must be independent âThe sample size must be âbig enoughâ The spreadof a sampling distribution is affected by the sample size, not the population size. 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This claim \ ( 5,000\ ) babies born during a period of economic were... | 2021-04-22 11:24:34 | {"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": 0.6304395794868469, "perplexity": 1156.6801698878032}, "config": {"markdown_headings": false, "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/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00132.warc.gz"} |
https://people.maths.bris.ac.uk/~matyd/GroupNames/432/Dic3xC3.A4.html | Copied to
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## G = Dic3×C3.A4order 432 = 24·33
### Direct product of Dic3 and C3.A4
Series: Derived Chief Lower central Upper central
Derived series C1 — C2×C6 — Dic3×C3.A4
Chief series C1 — C3 — C2×C6 — C62 — C2×C62 — C6×C3.A4 — Dic3×C3.A4
Lower central C2×C6 — Dic3×C3.A4
Upper central C1 — C6
Generators and relations for Dic3×C3.A4
G = < a,b,c,d,e,f | a6=c3=d2=e2=1, b2=a3, f3=c, bab-1=a-1, ac=ca, ad=da, ae=ea, af=fa, bc=cb, bd=db, be=eb, bf=fb, cd=dc, ce=ec, cf=fc, fdf-1=de=ed, fef-1=d >
Subgroups: 244 in 76 conjugacy classes, 25 normal (all characteristic)
C1, C2, C2, C3, C3, C4, C22, C22, C6, C6, C2×C4, C23, C9, C32, Dic3, Dic3, C12, C2×C6, C2×C6, C22×C4, C18, C3×C6, C3×C6, C2×Dic3, C2×C12, C22×C6, C22×C6, C3×C9, C36, C3.A4, C3.A4, C3×Dic3, C3×Dic3, C62, C62, C22×Dic3, C22×C12, C3×C18, C2×C3.A4, C2×C3.A4, C6×Dic3, C2×C62, C9×Dic3, C3×C3.A4, C4×C3.A4, Dic3×C2×C6, C6×C3.A4, Dic3×C3.A4
Quotients: C1, C2, C3, C4, S3, C6, C9, Dic3, C12, A4, C18, C3×S3, C2×A4, C36, C3.A4, C3×Dic3, C4×A4, S3×C9, C2×C3.A4, S3×A4, C9×Dic3, C4×C3.A4, Dic3×A4, S3×C3.A4, Dic3×C3.A4
Smallest permutation representation of Dic3×C3.A4
On 36 points
Generators in S36
(1 25 4 19 7 22)(2 26 5 20 8 23)(3 27 6 21 9 24)(10 34 16 31 13 28)(11 35 17 32 14 29)(12 36 18 33 15 30)
(1 10 19 31)(2 11 20 32)(3 12 21 33)(4 13 22 34)(5 14 23 35)(6 15 24 36)(7 16 25 28)(8 17 26 29)(9 18 27 30)
(1 4 7)(2 5 8)(3 6 9)(10 13 16)(11 14 17)(12 15 18)(19 22 25)(20 23 26)(21 24 27)(28 31 34)(29 32 35)(30 33 36)
(1 19)(2 20)(4 22)(5 23)(7 25)(8 26)(10 31)(11 32)(13 34)(14 35)(16 28)(17 29)
(2 20)(3 21)(5 23)(6 24)(8 26)(9 27)(11 32)(12 33)(14 35)(15 36)(17 29)(18 30)
(1 2 3 4 5 6 7 8 9)(10 11 12 13 14 15 16 17 18)(19 20 21 22 23 24 25 26 27)(28 29 30 31 32 33 34 35 36)
G:=sub<Sym(36)| (1,25,4,19,7,22)(2,26,5,20,8,23)(3,27,6,21,9,24)(10,34,16,31,13,28)(11,35,17,32,14,29)(12,36,18,33,15,30), (1,10,19,31)(2,11,20,32)(3,12,21,33)(4,13,22,34)(5,14,23,35)(6,15,24,36)(7,16,25,28)(8,17,26,29)(9,18,27,30), (1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,31,34)(29,32,35)(30,33,36), (1,19)(2,20)(4,22)(5,23)(7,25)(8,26)(10,31)(11,32)(13,34)(14,35)(16,28)(17,29), (2,20)(3,21)(5,23)(6,24)(8,26)(9,27)(11,32)(12,33)(14,35)(15,36)(17,29)(18,30), (1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36)>;
G:=Group( (1,25,4,19,7,22)(2,26,5,20,8,23)(3,27,6,21,9,24)(10,34,16,31,13,28)(11,35,17,32,14,29)(12,36,18,33,15,30), (1,10,19,31)(2,11,20,32)(3,12,21,33)(4,13,22,34)(5,14,23,35)(6,15,24,36)(7,16,25,28)(8,17,26,29)(9,18,27,30), (1,4,7)(2,5,8)(3,6,9)(10,13,16)(11,14,17)(12,15,18)(19,22,25)(20,23,26)(21,24,27)(28,31,34)(29,32,35)(30,33,36), (1,19)(2,20)(4,22)(5,23)(7,25)(8,26)(10,31)(11,32)(13,34)(14,35)(16,28)(17,29), (2,20)(3,21)(5,23)(6,24)(8,26)(9,27)(11,32)(12,33)(14,35)(15,36)(17,29)(18,30), (1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18)(19,20,21,22,23,24,25,26,27)(28,29,30,31,32,33,34,35,36) );
G=PermutationGroup([[(1,25,4,19,7,22),(2,26,5,20,8,23),(3,27,6,21,9,24),(10,34,16,31,13,28),(11,35,17,32,14,29),(12,36,18,33,15,30)], [(1,10,19,31),(2,11,20,32),(3,12,21,33),(4,13,22,34),(5,14,23,35),(6,15,24,36),(7,16,25,28),(8,17,26,29),(9,18,27,30)], [(1,4,7),(2,5,8),(3,6,9),(10,13,16),(11,14,17),(12,15,18),(19,22,25),(20,23,26),(21,24,27),(28,31,34),(29,32,35),(30,33,36)], [(1,19),(2,20),(4,22),(5,23),(7,25),(8,26),(10,31),(11,32),(13,34),(14,35),(16,28),(17,29)], [(2,20),(3,21),(5,23),(6,24),(8,26),(9,27),(11,32),(12,33),(14,35),(15,36),(17,29),(18,30)], [(1,2,3,4,5,6,7,8,9),(10,11,12,13,14,15,16,17,18),(19,20,21,22,23,24,25,26,27),(28,29,30,31,32,33,34,35,36)]])
72 conjugacy classes
class 1 2A 2B 2C 3A 3B 3C 3D 3E 4A 4B 4C 4D 6A 6B 6C 6D 6E 6F 6G 6H 6I 6J ··· 6O 9A ··· 9F 9G ··· 9L 12A 12B 12C 12D 12E 12F 12G 12H 18A ··· 18F 18G ··· 18L 36A ··· 36L order 1 2 2 2 3 3 3 3 3 4 4 4 4 6 6 6 6 6 6 6 6 6 6 ··· 6 9 ··· 9 9 ··· 9 12 12 12 12 12 12 12 12 18 ··· 18 18 ··· 18 36 ··· 36 size 1 1 3 3 1 1 2 2 2 3 3 9 9 1 1 2 2 2 3 3 3 3 6 ··· 6 4 ··· 4 8 ··· 8 3 3 3 3 9 9 9 9 4 ··· 4 8 ··· 8 12 ··· 12
72 irreducible representations
dim 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 6 6 6 6 type + + + - + + + - image C1 C2 C3 C4 C6 C9 C12 C18 C36 S3 Dic3 C3×S3 C3×Dic3 S3×C9 C9×Dic3 A4 C2×A4 C3.A4 C4×A4 C2×C3.A4 C4×C3.A4 S3×A4 Dic3×A4 S3×C3.A4 Dic3×C3.A4 kernel Dic3×C3.A4 C6×C3.A4 Dic3×C2×C6 C3×C3.A4 C2×C62 C22×Dic3 C62 C22×C6 C2×C6 C2×C3.A4 C3.A4 C22×C6 C2×C6 C23 C22 C3×Dic3 C3×C6 Dic3 C32 C6 C3 C6 C3 C2 C1 # reps 1 1 2 2 2 6 4 6 12 1 1 2 2 6 6 1 1 2 2 2 4 1 1 2 2
Matrix representation of Dic3×C3.A4 in GL5(𝔽37)
11 5 0 0 0 0 27 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
,
3 19 0 0 0 17 34 0 0 0 0 0 36 0 0 0 0 0 36 0 0 0 0 0 36
,
1 0 0 0 0 0 1 0 0 0 0 0 26 0 0 0 0 0 26 0 0 0 0 0 26
,
1 0 0 0 0 0 1 0 0 0 0 0 36 0 0 0 0 0 1 12 0 0 0 0 36
,
1 0 0 0 0 0 1 0 0 0 0 0 36 0 12 0 0 0 36 25 0 0 0 0 1
,
1 0 0 0 0 0 1 0 0 0 0 0 0 16 0 0 0 21 21 0 0 0 0 15 16
G:=sub<GL(5,GF(37))| [11,0,0,0,0,5,27,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,1],[3,17,0,0,0,19,34,0,0,0,0,0,36,0,0,0,0,0,36,0,0,0,0,0,36],[1,0,0,0,0,0,1,0,0,0,0,0,26,0,0,0,0,0,26,0,0,0,0,0,26],[1,0,0,0,0,0,1,0,0,0,0,0,36,0,0,0,0,0,1,0,0,0,0,12,36],[1,0,0,0,0,0,1,0,0,0,0,0,36,0,0,0,0,0,36,0,0,0,12,25,1],[1,0,0,0,0,0,1,0,0,0,0,0,0,21,0,0,0,16,21,15,0,0,0,0,16] >;
Dic3×C3.A4 in GAP, Magma, Sage, TeX
{\rm Dic}_3\times C_3.A_4
% in TeX
G:=Group("Dic3xC3.A4");
// GroupNames label
G:=SmallGroup(432,271);
// by ID
G=gap.SmallGroup(432,271);
# by ID
G:=PCGroup([7,-2,-3,-2,-3,-2,2,-3,42,92,1901,768,14118]);
// Polycyclic
G:=Group<a,b,c,d,e,f|a^6=c^3=d^2=e^2=1,b^2=a^3,f^3=c,b*a*b^-1=a^-1,a*c=c*a,a*d=d*a,a*e=e*a,a*f=f*a,b*c=c*b,b*d=d*b,b*e=e*b,b*f=f*b,c*d=d*c,c*e=e*c,c*f=f*c,f*d*f^-1=d*e=e*d,f*e*f^-1=d>;
// generators/relations
×
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https://www.the-cryosphere.net/13/2149/2019/ | Journal topic
The Cryosphere, 13, 2149–2167, 2019
https://doi.org/10.5194/tc-13-2149-2019
The Cryosphere, 13, 2149–2167, 2019
https://doi.org/10.5194/tc-13-2149-2019
Research article 15 Aug 2019
Research article | 15 Aug 2019
Suitability analysis of ski areas in China: an integrated study based on natural and socioeconomic conditions
Suitability analysis of ski areas in China: an integrated study based on natural and socioeconomic conditions
Jie Deng1,2,3, Tao Che1,2, Cunde Xiao4, Shijin Wang5, Liyun Dai1, and Akynbekkyzy Meerzhan1,3,6 Jie Deng et al.
• 1Heihe Remote Sensing Experimental Research Station, Key Laboratory of Remote Sensing of Gansu Province, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, 730000, China
• 2Center for Excellence in Tibetan Plateau Earth Sciences, Chinese Academy of Sciences, Beijing, 100101, China
• 3University of Chinese Academy of Sciences, Beijing, 100049, China
• 4State Key Laboratory of Earth Surface Processes and Resource Ecology, Faculty of Geographical Science, Beijing Normal University, Beijing, 100000, China
• 5State Key Laboratory of Cryospheric Science, Northwest Institute of Eco-Environment and Resources, Chinese Academy of Sciences, Lanzhou, 730000, China
• 6Jiangsu Center of Collaborative Innovation in Geographical Information Resource Development and Application, Nanjing, 210000, China
Correspondence: Tao Che (chetao@lzb.ac.cn)
Abstract
The successful bid for the 2022 Winter Olympics (Beijing 2022, officially known as the XXIV Olympic Winter Games) has greatly stimulated Chinese enthusiasm towards winter sports participation. Consequently, the Chinese ski industry is rapidly booming due to enormous market demand and government support. However, investing in ski areas in unreasonable locations will cause problems from an economic perspective (in terms of operation and management) as well as geographical concerns (such as environmental degradation). Therefore, evaluating the suitability of a ski area based on scientific metrics has become a prerequisite for the sustainable development of the ski industry. In this study, we evaluate the locational suitability of ski areas in China by integrating their natural and socioeconomic conditions using a linearly weighted method based on geographic information system (GIS) spatial analysis combined with remote sensing, online, and field survey data. The key indexes for evaluating natural suitability include snow cover, air temperature, topographic conditions, water resources, and vegetation, whereas socioeconomic suitability is evaluated based on economic conditions, accessibility of transportation, distance to a tourist attraction, and distance to a city. As such, metrics ranging from 0 to 1 considering both natural and socioeconomic conditions are used to define a suitability threshold for each candidate region for ski area development. A ski area is considered to be a dismal prospect when the locational integrated index is less than 0.5. The results show that 84 % of existing ski areas are located in areas with an integrated index greater than 0.5. Finally, corresponding development strategies for decision-makers are proposed based on the multicriteria metrics, which will be extended to incorporate potential influences from future climate change and socioeconomic development. However, the snowmaking model with local data should to be used to further analyze the suitability for a specific ski area.
1 Introduction
Ski tourism, as a major component of winter sports and tourism, creates great opportunities for business and promotes regional economic development (Eadington and Redman, 1991). In many countries, ski tourism has brought in more revenue than traditional agricultural and industrial practices (Lasanta et al., 2007). Especially in mountainous regions, the development of ski tourism has opened new doors for employment, which has boosted the local economy and led to the recovery of the local population (Silberman and Rees, 2010).
It is well known that environmental sustainability is often sacrificed during the rapid development of the economy, which, in turn, hampers future business opportunities. The operation of ski areas is generally accompanied by environmental degradation, such as deforestation, vegetation destruction, and soil erosion (Burt, 2012). The construction and maintenance of ski slopes have been found to cause disturbances in mountainous regions, which have significant impacts on the ecosystem and the environment (Burt and Rice, 2009). With the expansion of such infrastructure into nature, this kind of human-induced disturbance compels animals to leave their original habitat, leading to habitat loss and fragmentation (Sato et al., 2014; Brambilla et al., 2016). The enlargement of ski runs and the use of artificial snow are particularly prone to causing changes in plant species and declines in biodiversity (Wipf et al., 2005; Delgado et al., 2007), which may further increase surface runoff and soil erosion, and ultimately lead to land degradation (Ristić et al., 2012). Furthermore, constrained sediments and chloride have been found in streams near ski areas (Wemple et al., 2007). Extensive studies of lakes in northern Finland have shown that ski area operations have resulted in water contamination, such as eutrophication (Tolvanen and Kangas, 2016).
For the sustainable development of ski areas, the impact of climate change has to be considered because (1) snow is the most important resource that supplies the ski area and (2) locally increased temperature may shorten the duration of the ski season (Steiger and Abegg, 2018; Gilaberte-Búrdalo et al., 2017). Previous studies have established national or regional climate-driven snow models under different climate change scenarios to investigate how future climate change will affect snow conditions (Hennessy et al., 2008; Rutty et al., 2017; Verfaillie et al., 2018). These studies led to the conclusions that global warming will lead to a decline in the snowpack and a shortening of the length of the ski season. In addition, winter sports are vulnerable to climate variability, particularly at lower elevation and in midlatitude ski areas, because poor snow conditions are shown to result in a decline in the number of tourists (Scott et al., 2017). Snowmaking is usually preferred as a supplementary strategy for individual ski areas in response to worsening natural snow conditions (Hennessy et al., 2008; Pons-Pons et al., 2012). Machine-made snow can remarkably improve the reliability of snow conditions in both current and future climate scenarios, especially in regions with less reliable snow conditions and short ski seasons (Steiger, 2010; Hanzer et al., 2014; Damm et al., 2014, 2017). In addition, snowmaking results in increased water and energy consumption, which contradicts the well-acknowledged consensus regarding the reduction in greenhouse gas emissions to mitigate the effects of climate change (Steiger and Stötter, 2013). The efficiency of converting water into snow during snowmaking is less than 80 % because of the influence of meteorological conditions (Spandre et al., 2017). For example, at least 2 million L of water are needed to cover 1 ha with a 30 cm thick snowpack. In terms of electric consumption, the operation of a snow gun currently requires 2 to 3 kWh to produce 1 m3 of snowpack. Therefore, intense snowmaking would pose critical economic and environmental threats to ski areas, which might lead to their permanent closure (Tervo-Kankare et al., 2017). In summary, the locations of ski areas are critical since inappropriate choices may contaminate, degrade, or even damage the environment (Tsuyuzaki, 1994). Evaluating ski area locations based on scientific metrics is a prerequisite to help reduce the inevitable consequences caused by construction and operation (Spulerova et al., 2016; Cai et al., 2019).
Recently, in major skiing countries, the number of ski resorts has become relatively saturated or declined (such as in Japan; Vanat, 2019). In contrast, the successful bid for the 2022 Winter Olympics (Beijing 2022, officially known as the XXIV Olympic Winter Games) has motivated the general public in China to participate in ice and snow sports. As a competitive sport with potential business opportunities, skiing is strongly supported by the Chinese government, which has created a good atmosphere for the associated promotion and training. With a series of initiatives and future plans proposed by the Chinese government, it is expected that 300 million citizens will invest in winter sports activities before 2022. In 2010, there were only 270 ski areas in China. However, driven by enormous market demands and government support, the number of ski areas has been rapidly increasing in recent years. A total of 39 new ski areas were opened in 2018, bringing the total number of ski areas in China to 742 (Vanat, 2019), and this is only the start of the upcoming extensive growth in ski tourism. According to the strategic plan proposed by the China National Tourism Administration, the number of ski areas is expected to reach 800 by 2022. This booming industry raises the following question: how can we mitigate the environmental problems and avoid unnecessary economic losses caused by the unreasonable locations of ski areas?
The operation of ski areas mainly relies on a suitable natural environment and local socioeconomic conditions (Morey, 1985). On the one hand, ski areas are highly controlled by natural conditions, such as terrain and climate conditions (Morey, 1984; Gilaberte-Búrdalo et al., 2017). On the other hand, local socioeconomic conditions are key indicators supporting the operation of ski areas because the market for most ski areas is mainly composed of local tourists (Silberman and Rees, 2010). Thus, both natural and socioeconomic conditions should be considered to determine the locations of ski areas (Fukushima et al., 2002). Despite the pivotal role that ski areas have played in the social economy and environment, only a few studies have focused on locational suitability during the development of ski areas (e.g., Geneletti, 2008; Silberman and Rees, 2010; Dezsi et al., 2015; Cai et al., 2019). For example, Silberman and Rees (2010) evaluated alternative but currently undeveloped sites based on the standard measures of existing areas, and the conclusions of that study could be applied for decision-making in the industry. Moreover, previous studies are mostly limited to small scales (i.e., local or regional scales). In this study, geographic information system (GIS) spatial analysis is combined with remote sensing, online, and field survey data to employ a linearly weighted method to evaluate the suitability of ski area location in China based on both natural and socioeconomic conditions. This work can provide scientific metrics for decision-makers to avoid unreasonable economic investments and environmental problems and thus promote the sustainable development of Chinese ski tourism.
This paper is organized as follows: in Sect. 2, we describe the data and methods. Section 3 presents the results. Section 4 validates the method, evaluates the locational suitability of existing ski areas, proposes suggestions for a development strategy, and discusses the limitations of this work. The final section contains a brief conclusion and discusses future work.
2 Data and methodology
2.1 Data collection
In this study, the suitability of ski area locations was evaluated based on two components: the natural conditions (from the supply perspective) and the socioeconomic conditions (from the demand perspective). Regions where the elevation is higher than 4000 m are unsuitable for skiing due to the lack of oxygen, as are the areas where the maximum air temperature is higher than 10 for more than 90 d during the ski season (1 November to 31 March) (Scott et al., 2003). Areas with high elevations were mainly distributed in western China, including most of the Tibetan Plateau, while areas with high temperatures were mainly distributed in southern China and the Sichuan Basin (see Fig. 1a). All factors were analyzed using GIS spatial analysis based on data from multiple sources with a spatial resolution of 1 km combined with online and field survey data. Table 1 summarizes all of the data used in this study. Normalization processing was implemented for all natural and socioeconomic indexes to make the data dimensionless and mutually comparable (Geneletti, 2008). This work was conducted for the entirety of China, except for Taiwan, Macao, and Hong Kong, due to the lack of data.
Figure 1The spatial distribution of the natural condition indexes and excluded areas.
Table 1Descriptions of the data used in this study.
2.1.1 Natural conditions
Variables serving as indexes of natural conditions that could impact the development of ski areas were used, including snow cover, air temperature, topographic conditions, water resources, and vegetation, as shown in Fig. 1.
Snow cover
Natural snow cover is a crucial resource for ski areas. Skiers may cancel trips when there are poor snow conditions (Scott et al., 2003; Steiger and Abegg, 2018). Tervo (2008) analyzed the viability of nature-based winter tourism enterprises and declared that 90–120 skiable days are adequate for making a profit. In fact, a ski area is profitable if the snow reliability period is greater than 100 d per season, which is known as the 100 d rule and is the most common indicator of snow reliability (Steiger, 2012). Additionally, Scott et al. (2003) defined a skiable day as a day with a snow depth greater than 30 cm on ski runs. However, the snow depth in China is much lower than that in North America and Europe, and areas with natural snow depths greater than 30 cm are extremely rare (Mudryk et al., 2015). Therefore, we did not use the indicator of the number of days with a natural snow depth greater than 30 cm. As a supplement for the snow depth on ski runs, the average snow depth (SD) during a ski season was considered in this study. In addition, the number of snow cover days (SCDs), which is total number of days (can be discontinuous) with snow cover in an area during the ski season, was considered as an indicator of climate suitability (temperature and precipitation) and a measure of the aesthetic value of a site given that many ski areas have snow cover on only the ski runs.
With a spatial resolution of 500 m, version 4 of the Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover products MOD10A1 and MYD10A1 was used in this study to obtain SCD, and these products were downloaded from the National Snow Ice Data Center (NSIDC, https://nsidc.org/, last access: 24 January 2019). The normalized difference snow index (NDSI) was adopted to distinguish snow in the MODIS snow cover images. The NDSI was calculated using the fourth and sixth bands of MODIS, and a pixel was defined as snow if the NDSI value was greater than 0.4. Further details on the MODIS snow cover products can be found in Hall et al. (2002). In this study, the MODIS snow cover images were resampled to 1 km. The SD products were downloaded from the Cold and Arid Regions Sciences Data Center at Lanzhou (http://westdc.westgis.ac.cn, last access: 6 June 2019). The SD products derived from passive microwave remote-sensing data in China were developed by Che et al. (2008), with a spatial resolution of 25 km. Based on the MODIS cloud removal algorithm and downscaling algorithm developed by Huang et al. (2016), the daily cloud-free snow cover data and 1 km daily SD data for the 2010–2014 ski seasons were produced, and then the average SCD and SD from 2010 to 2014 were calculated. An SCD larger than 100 d and SD greater than 30 cm were taken as the optimal conditions for normalization. The snow cover index was defined as the sum of the normalized average SD and SCD, each assigned a weight of 0.5 (Fig. 1b). This index was for natural snow only, and machine-made snow was taken into account by the index of air temperature.
Air temperature
Low air temperature is a prerequisite for skiing. Scott et al. (2003) noted that ski areas should be closed if the maximum temperature is greater than 10 for 2 consecutive days accompanied by liquid precipitation. Additionally, skiers may also choose not to ski at extremely low temperatures (below $\sim -\mathrm{25}$) (Tervo, 2008; Rutty and Andrey, 2014). Because snowmaking has been used as an adaptive strategy to compensate for the decrease in snow reliability worldwide, temperatures between −2 and −5 were taken as optimal conditions in regard to efficient snowmaking (Tervo, 2008).
Based on the daily air temperature generated from more than 2400 meteorological stations in China, a gridded daily observation dataset with a spatial resolution of 25 km was developed by Wu and Gao (2013). The gridded daily observation dataset includes two variables: daily mean air temperature and daily maximum air temperature. The daily mean air temperature was the average value of the dry-bulb temperature at 02:00, 08:00, 14:00, and 20:00 LT (local time). The daily maximum air temperature was measured using a maximum thermometer. In this study, using an extrapolation method with a lapse rate of 0.65 per 100 m of elevation (Steiger and Stötter, 2013), the temperature dataset was resampled to 1 km spatial resolution for the 2010–2014 ski seasons. The daily maximum air temperature dataset was used to obtain the high-temperature regions that are unsuitable for ski area development. In southern China, many small ski areas can be profitable during a ski season with 60 skiable days. Therefore, the high-temperature region was defined as the area with more than 90 noncontinuous days with maximum air temperatures greater than 10 during a ski season (151 d). Following previous studies (Scott et al., 2003; Tervo, 2008; Rutty and Andrey, 2014), the daily mean air temperature was reclassified into 11 regimes with corresponding scores (Table 2), and the air temperature index was the mean score for the 2010–2014 ski seasons (Fig. 1c). The 11 temperature regimes and their corresponding scores were designed as a trade-off between the cold temperatures needed to preserve the snowpack and to produce machine-made snow and the warm temperatures needed by skiers.
Table 2Different daily air temperature regimes and corresponding scores.
Topographic conditions
Topographic conditions are essential for identifying suitable locations for ski areas. Ski runs require a certain topographic slope (Dezsi et al., 2015). In 2014, the China National Tourism Administration announced the rank division for the quality of mountain ski resorts, which requires that the average slope gradient of advanced slopes should not be less than 20 and that the average slope gradient of intermediate slopes should be greater than 15. Nevertheless, the conditions are dangerous for most tourists when the slope is too steep (slope >30). Unfortunately, information loss is inevitable when using the slope values extracted from remote-sensing images during averaging. Accordingly, slope gradients of 10 to 20 were considered to be the best topographic conditions.
Slope gradient data were derived from the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) (V004) with a spatial resolution of 90 m (Data Center for Resources and Environmental Sciences, http://www.resdc.cn/data.aspx?DATAID=284). All pixels with values greater than 30 were assigned a value of 30. The topographic conditions index was produced by a normalized slope gradient (Fig. 1d). The normalized value was 1 if the slope gradient was between 10 and 20. The greater the absolute difference is from this interval, the lower the normalization value. When the slope gradient is 0 or larger than 30, the normalized value is 0.
Water resources
To reduce the vulnerability of ski areas caused by climate change, snowmaking has been increasingly adopted as an adaptive strategy to compensate for the scarcity of natural snow (Hennessy et al., 2008; Pons-Pons et al., 2012). In fact, snowmaking requires large amounts of water. The high water consumption of snowmaking not only increases the operating costs of ski areas but also poses stress on the local water resources, especially in arid regions (Duglio and Beltramo, 2016; Wilson et al., 2018). Consequently, an area with abundant water resources is more suitable for ski area development. Data on the spatial distribution of rivers and lakes were acquired from the Data Center for Resources and Environmental Sciences (RESDC, http://www.resdc.cn, last access: 12 June 2019) of the Chinese Academy of Sciences (CAS). The water resources index is the sum of the cost distance to a river and the cost distance to a lake, each normalized to a range of [0–1] and given a weight of 0.5 (Fig. 1e). The higher the cost distance is, the lower the normalized value. The cost distance to a river (lake) was estimated using the cost distance method, which calculated the least cumulative cost distance for each pixel to the nearest river (lake) over a cost surface. The cost surface was a raster of slope gradients, which defined the cost to move planimetrically through each pixel. The value of the slope gradient at each pixel location represented the cost per unit distance to move through the pixel.
Vegetation
Vegetation contributes to creating an ideal environment and is an important indicator for evaluating the attractiveness of a destination. Vegetation, especially trees, can define the edges of ski runs and prevent skiers from being hit by strong winds (e.g., skiable days include the requirement of winds less than 6.5 m s−1; Crowe et al., 1973). The vegetation index for 2015 was derived based on a dataset of the spatial distribution of the annual normalized difference vegetation index (NDVI) covering the Chinese region (Fig. 1f). NDVI greater than 0.6 was the optimal value for normalization. The lower the NDVI is, the lower the normalized value. With a spatial resolution of 1 km, this dataset integrated SPOT NDVI data and MODIS vegetation data, which were sourced from the RESDC (http://www.resdc.cn).
2.1.2 Socioeconomic conditions
Socioeconomic conditions highlight a favorable level of economic development and infrastructure conditions by integrating four indexes: economic conditions, distance to a city, accessibility of transportation, and distance to a tourist attraction. All indexes were reclassified into 10 regimes by geometrical interval classification (see Fig. 2). The classification scheme creates 10 geometrical intervals by minimizing the square sum of elements per class. This procedure ensured that each class range had approximately the same number of values for each class and that the change between intervals was fairly consistent.
Figure 2The spatial distribution of the socioeconomic condition indexes.
Economic conditions
Skiing is a luxury activity; therefore, the development of ski areas should consider the balance between investment and revenue. Economic census data are sometimes difficult to acquire over a large scale, and currently, reliable economic data in China are mainly reported at the provincial level (Zhao et al., 2017). With the development of remote-sensing technology, nighttime light images have become an efficient means of mapping national economic activities (Rybnikova and Portnov, 2015). Visible infrared imaging radiometer suite (VIIRS) day–night band (DNB) nighttime light data are considered a new generation of nighttime light imagery. Composite images of the annual average radiance were produced by the Earth Observations Group (EOG) at the National Oceanic and Atmospheric Administration's National Geophysical Data Center (NOAA NGDC) using VIIRS DNB nighttime data; the spatial resolution is 500 m. Prior to averaging, the DNB data were filtered to exclude data impacted by stray light, lightning, lunar illumination, and cloud cover. The data are available at https://www.ngdc.noaa.gov/eog/viirs/download_dnb_composites.html (last access: 9 May 2019).
Many studies report that there is a strong correlation between an administrative unit's total gross domestic product (GDP) and the digital number (DN) value of the corresponding pixel in nighttime light imagery (Doll et al., 2000; Zhao et al., 2011). In this study, without a direct estimation of the GDP values, nighttime light pixel values were used as a surrogate index to measure the economic development level in different areas. The economic conditions index was generated by kernel density analysis based on the composite images of the annual average radiance for 2015 (Fig. 2a). The higher the nuclear density value is, the higher the normalized value. All pixels greater than 0 in the composite images of annual average radiance were converted to point features. The kernel density method was used to calculate the magnitude per unit area from the point feature using a kernel function to fit a smoothly tapered surface to each point.
Distance to a city
The customer plays a major role in the ski tourism industry. Except for a few ski areas in China that can attract both national and international visitors, the skiers in most ski areas are local visitors. The farther a ski area is from a major metropolitan area, the less likely it is to draw a large crowd (Fukushima et al., 2002). As analyzed using the distance decay theory, the number of visitors declines exponentially as the distance from a source increases, although the impact of distance on visitors is not a deterministic construct in its own right (McKercher, 2018).
Here, the index of the distance to a city was used to represent the rule of the distance decay theory (the farther away from a city, the fewer visitors the ski area can attract). The cities used for this study included provincial capitals, prefecture-level cities and county-level cities with airports. According to the distribution of public-use airports, these cities were divided into three categories: provincial capitals, cities with an airport, and cities without an airport. The distance to a city was estimated by calculating the least cost distance between any point in the study area and the nearest city. The distance to a city index was defined as the sum of the distance to a provincial capital, the distance to a city with an airport, and the distance to a city without an airport, each normalized to a range of [0–1] and assigned weights of 0.5, 0.3, and 0.2, respectively (Fig. 2b). Information on the location of cities was taken from the National Geomatics Center of China (NGCC, http://www.ngcc.cn/, last access: 20 May 2019), and the list of public-use airports in China was sourced from the Civil Aviation Administration of China (CAAC, http://www.caac.gov.cn/, last access: 26 May 2019).
Accessibility of transportation
A transportation network is the foundation of accessibility. Kaenzig et al. (2016) surveyed a former ski slope, and their results showed that easy access to a summit was the key factor in renewed attraction for visitors. Convenient transportation, which provides easy access to a ski destination, will bring more visitors. In this study, the accessibility of transportation index was acquired by calculating the least cost distance from any point to the nearest road (Fig. 2c). The road network was obtained from OpenStreetMap (https://www.openstreetmap.org/#map, last access: 22 June 2019), which was assembled using a manual survey, global positioning system (GPS) devices, aerial photography, and other free sources.
Distance to a tourist attraction
Many enterprises are aware of the potential benefits of regional cooperation (Buhalis, 2000; Young, 2002). To reduce costs, maximize tourist attraction, and improve enterprise competitiveness, many ski areas, especially small ski areas, should be located within tourist attractions with necessary facilities, such as hotels, restaurants, and shops (Lasanta et al., 2007; Dezsi et al., 2015; Spulerova et al., 2016). Additionally, visitors prefer to enjoy beautiful views while skiing. The index of distance to a tourist attraction was determined by measuring the least-cost distance from any point in the study area to the nearest tourist attraction (Fig. 2d). The tourist attractions were manually extracted from an online map (https://maps.baidu.com, last access: 3 May 2019).
2.2 Ski area information and field survey
Although there were indeed 742 ski areas in China according to the International Report on Snow and Mountain Tourism in 2018 (Vanat, 2019), only 598 ski areas' information was manually collected from an online map (https://maps.baidu.com) because limited information was available online for lower-class ski areas. The collected ski areas were divided into three categories.
1. A total of 116 ski areas before 2012 as sample data. It is often believed that successful and suitable ski areas could operate for long periods of time. We then considered ski areas that had been in operation for more than 6 years as successful and suitable ski areas. As such, the location information for 116 operating ski areas established before 2012 (mainly distributed in northern, northeastern, and northwestern China, Fig. 7) was categorized as suitable sample data, which were used to calculate the weight coefficients for the different indexes.
2. A total of 35 ski areas during field surveys in 2018 for validation. To validate the results, field surveys on ski areas were conducted during the 2018 ski season over 13 provinces, spatially representing different natural and socioeconomic conditions (see Fig. 7). The managers or staff of 35 ski areas were interviewed with a questionnaire and through conversations, mainly involving location information, ski season length, the quality of the ski area, its operating state, and its market competition situation. The questions concerning the quality of the ski area were also designed to collect the characteristics of the ski area, including the number and slope of ski runs, equipment, facilities, and accessibility of transportation. According to the rank division for the quality of mountain ski resorts released by the China National Tourism Administration in 2014, the quality of ski areas was evaluated by five grades from 1S to 5S, representing the lowest- to the highest-grade standard. This procedure involved comprehensive assessment integrating 10 aspects, such as equipment, facilities, accessibility of transportation, and the reception scale. According to the feedback from our field surveys, ski areas were roughly ranked into different grades, except for the eight ski areas whose grades were already defined by the Xinjiang Government Tourist Office.
3. A total of 447 ski areas for evaluation. Additionally, the locational suitability of the 447 ski areas established after 2012 was evaluated using the aggregation method.
2.3 Methodology
In this study, the linear-weighting method was used for synthetic evaluation. The natural suitability for ski area development (NS) is expressed as
$\begin{array}{}\text{(1)}& \mathrm{NS}=\sum _{i=\mathrm{1}}^{i}{D}_{i}{\mathrm{NC}}_{i},\end{array}$
where i is the number of natural condition indexes (i=1, 2, , 5), Di is the weighting factor that represents the importance of the natural condition indexes, and NCi represents the natural index.
The socioeconomic suitability for ski area development (SS) is expressed as
$\begin{array}{}\text{(2)}& \mathrm{SS}=\sum _{j=\mathrm{1}}^{j}{T}_{j}{\mathrm{SC}}_{j},\end{array}$
where j is the number of the socioeconomic condition indexes (j=1, 2, , 4), Tj is the weighting factor that represents the importance of the socioeconomic indexes, and SCj is the socioeconomic index.
The integrated suitability for ski area development (IS) is expressed as
$\begin{array}{}\text{(3)}& \mathrm{IS}={\sum }_{f=\mathrm{1}}^{f}{H}_{f}{C}_{f},\end{array}$
where f is the number of indexes ($f=\mathrm{1},\mathrm{2}$), Hf is the weight coefficient, and Cf is the index of NS or the index of SS.
The weight coefficients in Eqs. (1)–(3) (Di, Tj, and Hf) are defined using the entropy weight method introduced as follows. Finally, NS, SS, and IS are rescaled within the range of 0–1.
The 116 existing ski areas established before 2012 were used as samples to compute the weight coefficients by extracting all index values for the ski area location. The weight coefficients were calculated by an objective method based on the theory of information entropy, which has been widely employed for the determination of weights of evaluating indicators (Bian et al., 2018; Bednarik et al., 2010; Srdjevic et al., 2004; Vranešević et al., 2016). The concept of information entropy originally came from thermodynamics and indicates the extent of disorder in the system status (Bednarik et al., 2010). Generally, if the dispersion of data is high, the value of information entropy is low, which means that more information will be provided. Correspondingly, the greater the influence of the index on the evaluation, the higher its weight (Tang, 2015). Therefore, the entropy weight method can be used to calculate the objective weights of the index system and avoid bias caused by subjectivity to a certain extent (Pourghasemi et al., 2012).
It is supposed that there are a optional schemes, each with b evaluating indexes. The data matrix is established as follows:
$\begin{array}{}\text{(4)}& X={\left[\begin{array}{ccc}{x}_{\mathrm{11}}& \mathrm{\cdots }& {x}_{\mathrm{1}a}\\ \mathrm{⋮}& \mathrm{\ddots }& \mathrm{⋮}\\ {x}_{b\mathrm{1}}& \mathrm{\cdots }& {x}_{ba}\end{array}\right]}_{a×b},\end{array}$
where xnm is the value of the mth index in the nth scheme, n=1, 2, , a; m=1, 2, , b. a is the number of ski areas established before 2012 (a=116), and b is the number of indexes in Eqs. (1)–(3) (i, j, and f).
It is noted that the indexes are not measured on the same scale, and they have different dimensions. If the analysis is performed directly with the original index values, the difference in different quantity grades in X may produce inaccurate results in the decision-making process. Therefore, normalization (Znm) is performed to make the indexes dimensionless and mutually comparable, which is expressed as
$\begin{array}{}\text{(5)}& {Z}_{nm}=\frac{{x}_{m,max}-{x}_{nm}}{{x}_{m,max}-{x}_{m,min}},\end{array}$
where
$\begin{array}{}\text{(6)}& {x}_{m,max}=max\left\{{x}_{\mathrm{1}m},\mathrm{\dots }{x}_{am}\right\},\text{(7)}& {x}_{m,min}=min\left\{{x}_{\mathrm{1}m},\mathrm{\dots }{x}_{am}\right\}.\end{array}$
The information entropy em of the mth index is defined as
$\begin{array}{}\text{(8)}& {e}_{m}=-k\sum _{n=\mathrm{1}}^{a}{P}_{nm}\mathrm{ln}\left({P}_{nm}\right),\end{array}$
where
$\begin{array}{}\text{(9)}& k=\frac{\mathrm{1}}{\mathrm{ln}a},\text{(10)}& {P}_{nm}=\frac{{Z}_{nm}}{\sum _{n=\mathrm{1}}^{a}{Z}_{nm}},\end{array}$
if Pnm=0, Pnmln (Pnm)=0.
The entropy weight wm of the mth index is expressed as
$\begin{array}{}\text{(11)}& {w}_{m}=\frac{\mathrm{1}-{e}_{m}}{\sum _{m=\mathrm{1}}^{b}\left(\mathrm{1}-{e}_{m}\right)}.\end{array}$
The calculation results of the weight coefficients for the evaluation indexes are shown in Table 3. The results show that the total weight of natural suitability (0.52) is higher than that of socioeconomic suitability (0.48), which indicates that natural conditions have a greater impact on the development of ski areas than socioeconomic conditions.
Table 3Weight coefficients for the evaluation indexes.
3 Results
This section presents the evaluation results of the locational suitability for ski area development in China. The first part of the analysis focuses on the natural conditions for ski area development. Natural suitability was evaluated based on the linear weighting of five natural indexes: snow cover, air temperature, topographic conditions, water resources, and vegetation. The second part describes the analysis of the socioeconomic conditions for ski area development. Socioeconomic suitability was evaluated based on the linear weighting of four socioeconomic indexes: economic conditions, distance to a city, accessibility of transportation, and distance to a tourist attraction. Subsequently, the spatial distribution of the natural suitability and socioeconomic suitability indexes was used to obtain the integrated suitability index, which identifies the areas with the greatest potential for ski area development. Finally, we analyzed the fundamental driving factors of ski area development based on natural and socioeconomic conditions.
3.1 Natural suitability
For ski area development, natural suitability shapes ski areas from the supply side (Fig. 3). In general, areas with high scores were characterized by an excellent natural endowment, including abundant snow resources, favorable temperature, suitable terrain, beautiful natural landscape, and adequate water resources. The areas with high scores were widely distributed, mainly including the Changbai Mountains and Xiaoxing'an Mountains (northeast China), the Daxing'an Mountains (Inner Mongolia Province), the Tian Shan mountains and the Altai Mountains (Xinjiang Province), the Qilian Mountains (Gansu Province and Qinghai Province), the Yan Mountains (Beijing–Tianjin–Hebei region), the Lvliang Mountains and the Taihang Mountains (Shanxi Province), the southeastern Tibetan Plateau (Sichuan Province), and the Qinling Mountains (Shaanxi Province).
Figure 3The spatial distribution of natural suitability for ski area development based on snow cover, air temperature, topographic conditions, water resources, and vegetation.
Areas with high scores were always located in mountains, particularly in northwestern and northern China. Additionally, as mentioned in Sect. 2, most areas of the Tibetan Plateau were unsuitable for ski area development because the elevation was too high. There was also a large area covering the Gobi Desert in the middle region of northwestern China with low natural suitability values. With the increase in temperature from north to south, ski areas need to be built in mountains with high elevations. High temperatures led to the low natural suitability values in southern China. In the eastern part of China, the low values were due to poor topographic conditions (flat terrain).
3.2 Socioeconomic suitability
For ski area development, socioeconomic suitability plays a crucial role by evaluating ski areas from the demand side (Fig. 4). The regions given high scores in this figure had favorable socioeconomic conditions. For instance, these areas were usually close to well-developed regions, markets, roads, and tourist attractions with better economics and infrastructure. Ski areas near regions with high socioeconomic suitability values would give enterprises a more advantageous environment.
Figure 4The spatial distribution of socioeconomic suitability for ski area development based on economic conditions, distance to a city, accessibility of transportation, and distance to a tourist attraction.
Figure 4 shows the significantly imbalanced socioeconomic development between eastern and western China. The socioeconomic suitability of western China lags far behind that of eastern China. This pattern differs from the spatial distribution of natural suitability. The regions with high socioeconomic suitability values were mainly distributed in the eastern coastal areas, including the Yangtze River Delta, the belt encircling the Bohai Sea (including the Beijing–Tianjin–Hebei region), followed by the urban agglomerations of the Central Plains Economic Zone and the Northeast Economic Zone. Additionally, the Hohhot–Baotou–Yinchuan–Yulin Economic Zone is an important hub connecting northern and western China, and the Northern Tian Shan Mountain Economic Zone is the largest economic belt in western China, which is located in the core area of the Belt and Road Initiative.
3.3 Integrated suitability
For ski area development, integrated suitability was evaluated based on the spatial distribution of natural and socioeconomic suitability (Fig. 5). The integrated suitability results identified 10 regions that have the greatest potential for ski area development, which were the Changbai Mountains (northeast China), the Daxing'an Mountains (Inner Mongolia Province), the Yan Mountains (Beijing–Tianjin–Hebei region), the Lvliang Mountains and the Taihang Mountains (Shanxi Province), the Tian Shan mountains (the Northern Tian Shan Mountain Economic Zone), the Qilian Mountains (Qinghai Province and Gansu Province), the Qinling Mountains (Shaanxi Province), the area surrounding Mount Tai (Shandong Province), the southeast hills (Yangtze River Delta), and the southeastern Tibetan Plateau (Sichuan Province).
Figure 5The spatial distribution of integrated suitability for ski area development based on the natural and socioeconomic indexes.
Figure 6Spatial distribution of the driving factors of ski area development.
We further classified each of the natural suitability (Fig. 3) and socioeconomic suitability (Fig. 4) domains into deciles and then cross-tabulated them to generate 100 unique combinations marked with gradient colors (Fig. 6). In this scheme, the red-shaded areas are where socioeconomic suitability is high but natural suitability is modest. In contrast, the green-shaded areas have high natural suitability values but low socioeconomic suitability values. The black-shaded areas have high values for both types of suitability, whereas the yellow-shaded areas have low values for both types of suitability.
Table 4Surface areas and driving factors for four zones of suitability.
Figure 6 illustrates the fundamental driving factors of ski area development in China. The analysis identified four zones. The first zone consists of “naturally driven areas” with favorable natural conditions but relatively poor socioeconomic status. The second zone consists of “socioeconomically driven areas”, which are characterized by a good socioeconomic status but relatively modest natural conditions. The third zone consists of “ideal areas”, which feature both favorable natural conditions and advantageous socioeconomic conditions. Finally, the fourth zone consists of “unfavorable areas”, which have poor natural and socioeconomic conditions. In total, 35.4 million hectares (9.2 % of the analyzed area) was categorized as naturally driven areas (Table 4), which were mainly distributed in the mountains of northwestern and northeastern China and the area around the Tibetan Plateau. A total of 183.7 million ha (47.7 % of the analyzed area) was classified as socioeconomically driven areas, including large areas of eastern and central China. A total of 46.1 million ha (12 % of the analyzed area) was determined as ideal areas, particularly distributed in the Beijing–Tianjin–Hebei region, the eastern part of northeast China, and central Xinjiang Province. Finally, 120.2 million ha of land (31.2 % of the analyzed area) was found to be unfavorable areas, which were mainly distributed in regions of northwestern and southern China. The excluded areas (because of high temperature and high elevation) account for more than half of the total area of China.
Due to the influence from socioeconomic conditions, the integrated suitability was weakened in the areas of the Altai Mountains, the Daxing'an Mountains, and the marginal zone of the Tibetan Plateau. In contrast, the integrated suitability of eastern China has benefited from better socioeconomic conditions, as in Shandong Province, the Yangtze River Delta, and the Beijing–Tianjin–Hebei region (Fig. 5).
4 Discussion
This section first used field survey information to validate the evaluation method, and the method was used to evaluate the locational suitability of ski areas established after 2012. Second, according to the validation and evaluation results, a series of development strategies were proposed. Finally, the limitations of this work were discussed.
4.1 Validation and evaluation
The existing 598 ski areas were illustrated on the map of the spatial distribution of the integrated suitability for ski area development (Fig. 7), including the ski areas used as samples (116), the ski areas established after 2012 (447), and the ski areas surveyed (35). In addition, to evaluate the locational suitability of existing ski areas, Fig. 8 presents a detailed analysis of the natural suitability, socioeconomic suitability, and integrated suitability of ski areas established after 2012.
Figure 7The distribution of existing ski areas in China.
Figure 8The suitability values of existing ski areas established after 2012.
As shown in Fig. 8, 25.99 % of the ski areas fall within ideal areas, 69.84 % of the ski areas are situated in socioeconomically driven areas, 1.86 % of the ski areas are located in naturally driven areas, and 2.32 % of the ski areas are distributed in unfavorable areas. Additionally, the areas are categorized as having low, medium, and high suitability according to the integrated suitability value. After 2012, 89.1 % of the ski areas were distributed in medium-suitability areas, whereas 10.44 % of the ski areas were located in high-suitability areas. There were two ski areas in low-suitability areas. In total, 84.23 % of the ski areas were located in areas with an integrated suitability value greater than 0.5, while 15.77 % of the ski areas were located in areas with integrated suitability values less than 0.5, which are almost all distributed in socioeconomically driven areas. Notably, the ski areas in socioeconomically driven areas are more prone to environmental problems due to the decreased natural suitability, and these enterprises may soon face the challenges of dismal prospects.
A field survey of the ski areas revealed that the suitability results adequately reflect the actual conditions for ski area development. Additionally, the evaluation results indicate that some small ski areas have been built in areas with low integrated suitability values, with most being distributed in socioeconomically driven areas.
4.2 Development strategy
To meet the goal of having 300 million Chinese citizens involved in winter sports by 2022, China is making an enormous effort to popularize winter sports by improving the accessibility of facilities and training for beginners. According to China's General Sports Administration's “13th Five-Year Plan”, which is a roadmap for development from 2016 to 2020, snow and ice sports should be vigorously promoted, especially in southern and northwestern China.
In fact, northwestern China has abundant snow and ice resources. Thus, in this less developed area, the vigorous development of ski tourism is an opportunity to promote regional economic development. In contrast, the favorable economic conditions in southern China can promote ski tourism development. The expansion of snow and ice sports in southern China will make winter sports more accessible for citizens living in warm climates, which will bring a large number of new amateurs to the sport.
However, the poor economic conditions in northwest China and the low natural suitability in southern China, which can restrict the development of ski areas, should be considered. Especially in southern China, as noted in Sect. 4.1, there are few small ski areas due to low natural suitability, and enterprises face similar products and fierce competition. Under global warming, increased winter temperatures and decreased snowfall will severely affect these ski areas (Fukushima et al., 2002; Dawson et al., 2009), causing economic losses, resource waste, and environmental damage.
To stimulate the sustainable development of the ski industry, the location of ski areas should be carefully determined according to the results of the suitability evaluation. Based on our analysis, corresponding development strategies for the development of the Chinese ski tourism industry are proposed.
1. In naturally driven areas, upscaled ski areas mainly used for competition and training should be built, which can improve the popularity of ski areas by hosting sporting events. Several small and medium-sized ski areas with good snow quality should also be appropriately planned around cities.
2. In socioeconomically driven areas, the ski area markets are determined by local visitors. According to the situation of local socioeconomic development, an appropriate number of small ski areas are advised to be built for recreational sports to expand the influence of snow sports. However, a large number of small-size ski areas with poor facilities have been established in the economically driven areas, and these ski areas are unsafe and provide skiers with low-quality ski experiences. Therefore, in socioeconomically driven areas, the number of ski areas should be limited, and enterprises should enhance their competitiveness by improving the quality of the ski area.
3. In ideal areas, multiple high-end ski resorts with complete support facilities can feasibly attract national and international visitors by holding major international sporting events.
4. Unfavorable areas with both poor natural and socioeconomic conditions are unsuitable for skiing.
5. In addition, in economically developed southern China, snow resources are insufficient because of high temperatures; thus, to popularize snow recreation, indoor ski slopes can be considered. Furthermore, in the less developed and oxygen-deficient Tibetan Plateau, commercial ski areas are difficult to operate.
4.3 Limitation of the current work
In the current study, for the index of snow cover, only natural snow has been considered, while machine-made snow was represented in the form of air temperature (as mentioned in Sect. 2.1.1), which is indeed a proxy for potential snowmaking capacity. If the air-temperature-based proxy model for snowmaking was used instead of the physics-informed model considering the snowpack, the length of the ski season may be underestimated (Scott et al., 2019), which is considered a limitation of the current research. In addition, since the exact number of skiable days cannot be obtained from the proxy model, the viability of a specific ski area cannot be exactly estimated (Steiger et al., 2017). Previous studies employed forcing data from ski areas or nearby meteorological stations to calculate the length of the ski season for analyzing climate change vulnerability for specific ski destinations (Scott et al., 2003; Hennessy et al., 2008; Steiger, 2010; Pons et al., 2015). However, the main barrier that arises when applying such site-scale snow models to a large scale (e.g., the national scale in our study) is associated with the difficulties in obtaining high-quality data with fine spatial and temporal resolution and the heterogeneous spatiotemporal distribution of snow across scales. In particular, we would like to discuss the applicability of using the well-acknowledged ski season simulation model (e.g., SkiSim 2) in our research as an example. SkiSim 2 combines both the natural and machine-made snowpack models, and is widely applied in vulnerability assessment for ski areas (Steiger et al., 2017). There are two key parameters (snowfall temperature and degree-day factor) in SkiSim 2 that need to be calibrated specifically for each ski area (Steiger, 2010; Scott et al., 2019), which can be obtained from at-site weather stations. It is noted that most ski areas in China are still underdevelopment and not necessarily equipped with meteorological observations or close to weather stations, which hampers researchers from obtaining qualified meteorological data for parameterization in site-scale models (such as SkiSim 2). Another example is that Hennessy et al. (2008) used hourly wet-bulb temperature to model the snowmaking potential for Australian ski areas, and they computed the volume of machine-made snow based on the difference between the target snow depth and natural snow depth cover of a typical ski run. Again, unfortunately, hourly wet-bulb temperature data are not available for most ski areas in China, let alone the grid data over entire regions of China. In summary, previous studies using snowmaking models have been well acknowledged at the site scale. However, since the aim of this study was to provide the guidelines for the ski market at the national scale rather than debating whether a specific resort would be viable, we believe that using the air temperature-based proxy models to reflect the snowmaking conditions is acceptable over large-scale regions.
The second limitation stems from the air temperature data. Subzero wet-bulb temperatures are needed for snowmaking (Hennessy et al., 2008). Unfortunately, meteorological stations do not provide wet-bulb temperature data. As a proxy, the dry-bulb temperature is also widely used in machine-made snow models (Scott et al., 2003; Steiger, 2010). Therefore, in this study, the dry-bulb temperature data were used to generate the index of air temperature, which reflects the snowmaking conditions and tourist comfort.
Another limitation is associated with wind, which has a significant impact on the efficiency of snowmaking and the attractiveness of a site (Spandre et al., 2017). Wind speeds higher than 6 m s−1 have a direct physical or mechanical effect on tourists (De Freitas, 2005). Daily wind speed data are available from the meteorological stations that are generally located around a city, while most ski areas are built in the mountains far from cities. Hence, the relatively sparse meteorological stations across the study area did not allow for the creation of reliable daily gridded data. In addition, wind is considered one of the most difficult meteorological variables to model due to its dependence on the specific characteristics of any given location, such as topography and surface roughness (Morales et al., 2012). The local micrometeorology at a specific location also cannot be captured using existing reanalysis wind speed data with low resolution.
The method of this work attempts to identify the suitability patterns of the main ski areas in China, but a more detailed and refined analysis based on local data will be necessary before deciding to invest (or not) in a new ski area. Based on previous studies, machine-made snow, air temperature, and wind should be addressed in future studies on specific ski areas.
5 Conclusion
This study integrated natural and socioeconomic conditions from the supply and demand perspectives to quantitatively evaluate the locational suitability for ski area development in China. Five corresponding evaluation indexes of natural conditions were proposed: snow cover, air temperature, topographic conditions, water resources, and vegetation. The socioeconomic conditions included four indexes: economic conditions, accessibility of transportation, distance to a tourist attraction, and distance to a city. Using GIS spatial analysis technology combined with remote sensing, online, and field survey data, we presented a linearly weighted method for synthetic evaluation in which the weight coefficients were calculated using an objective method based on entropy weight theory. The results showed the spatial distribution of the locational suitability of ski areas and identified the areas with the greatest potential for ski area development. Four zones were also identified by analyzing driving factors based on natural and socioeconomic conditions. Additionally, our method to estimate the suitability was validated based on field surveys of ski areas and was used to evaluate the locational suitability of ski areas established after 2012. Finally, corresponding development strategies for decision-makers were proposed.
Despite that there were studies using physics-informed snowmaking models to assess the vulnerability for specific ski areas, the aim of this study was to provide the scientific metrics for the ski market at the national scale. Even though the current model used a proxy for snowmaking with certain limitations (such as not counting the exact number of skiable days), this study is feasible at the current scale of interest and expected to pave the way for further site-scale research (e.g., specific ski areas) with more detailed and refined analyses based on local data and other sources of information.
The results of the weight coefficients indicate that snow resources, air temperature, and topographic conditions are major natural factors that influence ski area development. In the context of global warming, it is necessary to evaluate the vulnerability of a ski area to future climate change (Steiger et al., 2017). With the increase in winter temperatures and the decrease in snowfall in the next few decades (Ji and Kang, 2012; Zhou et al., 2018), the natural suitability values for southern and eastern China will decrease, and small midlatitude and low-elevation ski areas will be the first to close due to poor snow conditions (Bark et al., 2010; Gilaberte-Búrdalo et al., 2017). Additionally, with social and economic development, people's living standards will greatly improve. Thus, the socioeconomic suitability in northwestern and northeastern China may increase. As a result, northwestern and northeastern China may become popular markets and central places for ski tourism. To more thoroughly study the future of ski tourism in China, future research is needed to evaluate the locational suitability of ski areas in relation to climate change and socioeconomic development.
Data availability
Data availability.
The MODIS snow cover products are available for download from the National Snow Ice Data Center (NSIDC, https://nsidc.org/). The SD products were downloaded from the Cold and Arid Regions Sciences Data Center at Lanzhou (http://westdc.westgis.ac.cn). The air temperature dataset was developed by Wu and Gao (2013). The VIIRS DNB nighttime data are available from https://www.ngdc.noaa.gov/eog/viirs/download_dnb_composites.html.
Author contributions
Author contributions.
TC and JD conceived this study with input from CX, LD, and AM. SW led the field surveys of ski areas. The paper was written by JD and TC. All authors contributed to editing and revision.
Competing interests
Competing interests.
The authors declare that they have no conflict of interest.
Acknowledgements
Acknowledgements.
We thank Xiaofan Yang for fruitful discussions and the two reviewers for their thorough reviews and insightful comments to improve the paper.
Financial support
Financial support.
This research has been supported by the Chinese National Natural Science Foundation (grant nos. 41690140 and 41671058) and the National Foundational Scientific and Technological Work Programs of the Ministry of Science and Technology of China (grant no. 2017FY100501).
Review statement
Review statement.
This paper was edited by Ross Brown and reviewed by Carlo Maria Carmagnola and one anonymous referee.
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http://car-stars.ru/4(2x+3)=-3(4x-5) | # 4(2x+3)=-3(4x-5)
## Simple and best practice solution for 4(2x+3)=-3(4x-5) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework.
If it's not what You are looking for type in the equation solver your own equation and let us solve it.
## Solution for 4(2x+3)=-3(4x-5) equation:
4(2x+3)=-3(4x-5)
We move all terms to the left:
4(2x+3)-(-3(4x-5))=0
We multiply parentheses
8x-(-3(4x-5))+12=0
We calculate terms in parentheses: -(-3(4x-5)), so:
-3(4x-5)
We multiply parentheses
-12x+15
Back to the equation:
-(-12x+15)
We get rid of parentheses
8x+12x-15+12=0
We add all the numbers together, and all the variables
20x-3=0
We move all terms containing x to the left, all other terms to the right
20x=3
x=3/20
x=3/20
`
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https://controlledmold.com/building-a-bioreactor-introduction/ | # Building a bioreactor, part 1: Introduction
Cameron Davidson-Pilon Sep 18, 2020 · 8 mins read
Let’s jump right into what even is a bioreactor. My friend Luiggi said it best: an example of a bioreactor is your sourdough starter. It’s full of microbes, you keep it protected from the elements, and periodically feed it. Brewing beer? Your fermenter is a bioreactor. Heck, your vegetable lacto-fermentations are bioreactors. But when I say “building a bioreactor”, I want to build a modular, computer controlled, and extensible bioreactor. Modular in the sense that pieces can be swapped out, and the bioreactor can be duplicated easily for higher throughput. A computer controlled bioreactor means that we can sleep at night and the bioreactor will still perform necessary operations. For this to work, we need to think about how to get digital measurements out of the reactor, and then translate those measurements into automatic actions. Finally, extensible refers to the ability to for the bioreactor to be applicable for many use-cases. I want to be able to solve many things with this bioreactor. There’s one more thing I’d like: cheap. Well, relatively cheap. Professional bioreactors, even the smaller ones, can cost thousands of dollars. Let’s build one for a few hundred dollars. At the end of this blog post series, we’ll have something that looks like this:
May look complicated now, but we’ll go through each piece over this series
We’ll be able to track real-time growth of our cultures too:
Later blog posts will explain the electronics and math behind this
### Wait - why do I want to build a bioreactor?
While there a many uses of a bioreactor, our goal is going to be a technique called lab directed evolution, which is the microbial equivalent of artificial selection. Artificial selection has been applied to organisms around us for thousands of years. We have selectively bred plants like corn into the enormous monsters they are today (see image below). Likewise for livestock and dogs. Interestingly, we have also artificially selected some microbes too: Saccharomyces cerevisiae, aka brewers and bakers yeast, is very specialized today due to human intervention. Likewise, Aspergillus oryzae’s, aka koji, use to be toxic to humans, but we’ve selected the toxicity out.
Corn over time. Source: Doebley, J., https://teosinte.wisc.edu/images.html
Today, lab directed evolution is a tool used in modern microbiology. Importantly, because of the extremely short generation time of microbes, evolution occurs on the order of days to weeks (vs centuries for plants and animals). The engineers of lab directed evolution have a specific goal in mind, expressed as the phenotype of the organism, and they reverse engineer what the environment should look like to reach that goal. For example, if the desired phenotype is heat tolerance, the engineers will slowly expose the microbes to higher and higher temperatures: the microbes that happen to be more heat tolerant will survive more often and continue to reproduce. However, if the engineers are not careful, they will inadvertently select for other traits too. Consider that the microbes are always competing for nutrients as well, and very quickly the initial nutrients will be consumed and the microbes will enter their stationary phase. So in the above scheme, if they only raised the temperature slowly over time, they would select for both heat tolerance and ability to survive well in the stationary phase. This may not be what is wanted. Instead, the culture is kept at a constant cell density. This is typically a density where there is an abundance of nutrients for each microbe, so no selection occurs in this dimension (that’s a lie: there is always a selection for increasing growth rate). To accomplish a constant cell density, periodically a small amount of liquid is removed and replaced by new media. Tuned correctly, this keeps the volume constant and the culture at a constant density.
An important point is that lab directed evolution is not rational design - the engineers don’t care about the mechanisms of heat tolerance (yet), but they are allowing random gene-flipping plus selection to find a solution. Rational design would be something like finding a heat-tolerant phenotype in another organism, translating that into DNA, and inserting the DNA into the microbe. Sometimes, the rational design path is too complicated or difficult, and lab directed evolution feels like cheating. Directed evolution does the exploration (sheer population size) and exploitation (selective pressure) for us! On the other hand, often the rational design is sometimes easier: evolving a brand new enzyme has about 0 probability of occurring in a person’s lifetime, but adding the enzyme’s DNA to a microbe can be trivial. So both lab directed evolution and rational design are tools, and not replacements of each other.
Finally, my interest in lab directed evolution is that it is just so much in the spirit of “Controlled Mold” - literally controlling the phenotype of the mold! In the list below are some examples, including with molds, of more lab directed evolution applications:
### Applications of lab directed evolution
I’ve been collecting the really cool uses of lab directed evolution, and use these as motivation:
1. Evolving a traditional brewer’s yeast to thrive in new brewing environments. New environments for brewer’s yeast could be higher/lower temperature, higher (alcohol, IBU, caffeine), concentration, lower pH, salt %.
2. Yeast can only ferment a short list of carbohydrates. By slowly depleting yeast’s traditional carbon sources, it forces the yeast to adapt to new carbon sources, like lactose. See [Attfield, 2006]
3. Similarly, filamentous fungi can be evolved to consume new carbon sources, like raffinose, a sugar which is a cause of digestive discomfort after eating soybean tempeh.
4. Lactobacillus, used in sour beer production, can be evolved to be more alcohol, pH, or IBU tolerant.
5. Some algae are facultative heterotrophs. Directed evolution can be used to evolve a stronger and faster heterotrophic metabolism.
6. Triton Algae Innovations has used directed evolution to evolve heme in algae. They accelerated the process by flashing the microbes with UV light which caused a higher mutation rate.
7. Algae can be evolved to produce more carotenoids by changing the light conditions, see [Fu, 2013]
8. Improving yeast culture density, as demonstrated in [Wong, 2018]
9. Improving growth rates after rational design. When modifying the genes of a microorganism though modern genetic engineering, the growth rate is typically lowered due to new proteins or metabolites being constructed. By subjecting the organism to an environment with abundant nutrients, over time, the population will evolve to increase its growth rate.
10. Improving metabolite production after rational design. After adding the genes of carotenoid production to yeast but wanting a higher yield, [Reyes, 2013] exploited the antioxidant of carotenoids. They exposed the yeast to high levels of hydrogen peroxide. The yeast evolved to counteract the hydrogen peroxide by producing more carotenoids.
11. The original inventors of the morbidostat [Toprak, 2013] were interested in antibiotic resistance in bacteria. They subjected E. coli to a slowly increasing level of antibiotics, and after two weeks, the bacteria had grown resistance to the highest antibiotic concentration in their experiment design.
12. In [Ekkers, 2020], the authors hint at evolving an anticipatory response. Amazing!
### Back to the bioreactor
To build a our bioreactor, we will need the following:
1. autoclavable vials
2. sensors to read measurements from our bioreactor
3. A holder for the vial and sensors
4. a computer loaded with software to control the input/output of the pumps
5. Pumps to remove liquid and add new media.
Graphically, it looks something like this:
In the next blog post, we’ll look at the first part of this construction: the holder and associated sensors.
### References
1. Toprak, E., Veres, A., Yildiz, S. et al. Building a morbidostat: an automated continuous-culture device for studying bacterial drug resistance under dynamically sustained drug inhibition. Nat Protoc 8, 555–567 (2013). https://doi.org/10.1038/nprot.2013.021
2. A low-cost, open source, self-contained bacterial EVolutionary biorEactor (EVE) Vishhvaan Gopalakrishnan, Nikhil P. Krishnan, Erin McClure, Julia Pelesko, Dena Crozier, Drew F.K. Williamson, Nathan Webster, Daniel Ecker, Daniel Nichol, Jacob G Scott bioRxiv 729434; doi: https://doi.org/10.1101/729434
3. A user-friendly, low-cost turbidostat with versatile growth rate estimation based on an extended Kalman filter Hoffmann SA, Wohltat C, Müller KM, Arndt KM (2017) A user-friendly, low-cost turbidostat with versatile growth rate estimation based on an extended Kalman filter. PLOS ONE 12(7): e0181923. https://doi.org/10.1371/journal.pone.0181923
4. Wong, B., Mancuso, C., Kiriakov, S. et al. Precise, automated control of conditions for high-throughput growth of yeast and bacteria with eVOLVER. Nat Biotechnol 36, 614–623 (2018). https://doi.org/10.1038/nbt.4151
5. Ekkers, DM, Branco dos Santos, F, Mallon, CA, Bruggeman, F, van Doorn, GS. The omnistat: A flexible continuous‐culture system for prolonged experimental evolution. Methods Ecol Evol. 2020; 11: 932– 942. https://doi.org/10.1111/2041-210X.13403
6. Improving carotenoids production in yeast via adaptive laboratory evolution
7. Fu W, Guethmundsson O, Paglia G, Herjolfsson G, Andresson OS, Palsson BO, et al. 2013. Enhancement of carotenoid biosynthesis in the green microalga Dunaliella salina with light-emitting diodes and adaptive laboratory evolution. Appl. Microbiol. Biotechnol. 97: 2395-2403.
8. Attfield PV Bell PJL (2006) Use of population genetics to derive nonrecombinant Saccharomyces cerevisiae strains that grow using xylose as a sole carbon source. FEMS Yeast Res6: 862–868.
##### Written by Cameron Davidson-Pilon
Bad statistician turned even worse food scientist. CEO/Founder of Pioreactor. Former Director of Data Science at Shopify. Cameron's background includes mathematics, statistics, and computer science (topics blogged at dataorigami.net). He is the author of "Bayesian Methods for Hackers". Cameron now explores the alt-protein space. | 2021-04-21 05:27:46 | {"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": 4, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3685505986213684, "perplexity": 6239.247048056698}, "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/1618039508673.81/warc/CC-MAIN-20210421035139-20210421065139-00515.warc.gz"} |
https://www.iacr.org/cryptodb/data/paper.php?pubkey=29188 | ## CryptoDB
### Paper: More is Less: Perfectly Secure Oblivious Algorithms in the Multi-server Setting
Authors: T.-H. Hubert Chan Jonathan Katz Kartik Nayak Antigoni Polychroniadou Elaine Shi DOI: 10.1007/978-3-030-03332-3_7 Search ePrint Search Google Slides ASIACRYPT 2018 The problem of Oblivious RAM (ORAM) has traditionally been studied in the single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case.In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.
##### BibTeX
@inproceedings{asiacrypt-2018-29188,
title={More is Less: Perfectly Secure Oblivious Algorithms in the Multi-server Setting},
booktitle={Advances in Cryptology – ASIACRYPT 2018},
series={Lecture Notes in Computer Science},
publisher={Springer},
volume={11274},
pages={158-188},
doi={10.1007/978-3-030-03332-3_7},
author={T.-H. Hubert Chan and Jonathan Katz and Kartik Nayak and Antigoni Polychroniadou and Elaine Shi},
year=2018
} | 2020-07-07 04:19:32 | {"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": 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": 0.23490987718105316, "perplexity": 4857.820752041321}, "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-2020-29/segments/1593655891640.22/warc/CC-MAIN-20200707013816-20200707043816-00312.warc.gz"} |
http://www.tutionteacher.in/answer-following-questions-time-period-particle-shm-depends-force-constant-k-mass-m-particle-t-2%CF%80-%E2%88%9Amk-simple-pendulum-executes-shm-approximately/ | ## Answer the following questions: (a) Time period of a particle in SHM depends on the force constant k and mass m of the particle: T = 2π √m/k. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum? (b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than 2π √l/g Think of a qualitative argument to appreciate this result. (c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall? (d) What is the frequency of oscillation of a simple pendulum mounted in a cabinthat is freely falling under gravity? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-14 Oscillations
### Q.16:- Answer the following questions:
(a) Time period of a particle in SHM depends on the force constant k and mass m of the particle:
T = 2π √m/k. A simple pendulum executes SHM approximately. Why then is the time period of a pendulum independent of the mass of the pendulum?
### (b) The motion of a simple pendulum is approximately simple harmonic for small angle oscillations. For larger angles of oscillation, a more involved analysis shows that T is greater than 2π √l/g
Think of a qualitative argument to appreciate this result.
### (c) A man with a wristwatch on his hand falls from the top of a tower. Does the watch give correct time during the free fall? (d) What is the frequency of oscillation of a simple pendulum mounted in a cabinthat is freely falling under gravity?
(a) For a simple pendulum, force constant or spring factor k is proportional to mass m, therefore, m cancels out in denominator as well as in numerator. That is why the time period of simple pendulum is independent of the mass of the bob.
(b) In the case of a simple pendulum, the restoring force acting on the bob of the pendulum is given as:
F = –mg sinθ
where,
F = Restoring force
m = Mass of the bob
g = Acceleration due to gravity
θ = Angle of displacement
For small θ, sinθ ≈ θ
For large θ, sinθ is greater than θ.
This decreases the effective value of g.
Hence, the time period increases as:
T = 2π √l/g
(c) Yes, because the working of the wrist watch depends on spring action and it has nothing to do with gravity.
(d) Gravity disappears for a man under free fall, so frequency is zero. | 2019-06-17 15:23:18 | {"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": 0.8346608281135559, "perplexity": 704.2683950410835}, "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-2019-26/segments/1560627998509.15/warc/CC-MAIN-20190617143050-20190617164641-00043.warc.gz"} |
https://math.stackexchange.com/questions/3191117/a-complex-integral-with-boundary-on-the-norm | # A complex integral with boundary on the norm
I was asked this question. I couldn't even manage to find a starting point on the question. Any help is welcomed.
P.S: I know it is from a book but I do not know from which one. If you have any idea which book it may be, I can search online through the book's name as well.
• Do you know that $\left|\int f(z)dz\right|\le \int \left|f(z)\right| dz$? – user247327 Apr 17 at 14:22
Note that\begin{align}\left\lvert x+i\sqrt{1-x^2}\cos\theta\right\rvert&=\sqrt{x^2+(1-x^2)\cos^2\theta}\\&\leqslant\sqrt{x^2+1-x^2}=1.\end{align}Therefore,\begin{align}\bigl\lvert P(x)\bigr\rvert&\leqslant\frac1\pi\int_0^\pi\left\lvert x+i\sqrt{1-x^2}\cos\theta\right\rvert^n\,\mathrm dx\\&\leqslant\frac\pi\pi\\&=1.\end{align} | 2019-05-24 11:44:12 | {"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": 2, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7636951804161072, "perplexity": 534.9425600988891}, "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/1558232257605.76/warc/CC-MAIN-20190524104501-20190524130501-00089.warc.gz"} |
https://www.researchgate.net/scientific-contributions/Stephen-S-T-Yau-26807052 | # Stephen S.-T. Yau's research while affiliated with Tsinghua University and other places
## Publications (210)
Article
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Let (V, 0) be an isolated hypersurface singularity. We introduce a series of new derivation Lie algebras L k (V) associated to (V, 0). Its dimension is denoted as λ k (V). The L k (V) is a generalization of the Yau algebra L(V) and L 0 (V) = L(V). These numbers λ k (V) are new numerical analytic invariants of an isolated hypersurface singu-larity....
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https://www.snuffy.org/blog/2018-11-05-kidney-stone/ | # Kidney Stone
## Initial
Well I’ve now learned what having a kidney stone feels like. I cannot say that I ever really wanted to know. Saturday morning Sep 22nd I woke at 3 am with abdominal Pain and nausea. After trying to live through it till Sunday Morning, when I checked into the ER. Had a CT and Blood work. The CT showed a 10mm Stone. YAY!? I was Wheeled up to surgery where they put in a stint. Why the Sonic popping thing wasn’t done was, as explained to me, that it was an elective surgery and there was a line. So Due to that and the ,unknown to me at the time, seriousness of this issue. When one cannot pass the stone one could die from pressure build up in the kidney. Anyway the Stint is keeping the path from kidney to bladder open for now.. Monday I will see a Chicago area doctor and get it address further. Removal or disbursement at least.
• Marty
## Continuation: 2018 10 02
Back Home I meet with a Dr Herzog Urology, and found the hospital should have given me the imagery from the CT done while in ER. Today starts the Bureaucratic hassle of getting that sent up here. Had an Xray done and (HAVE DISK) imagery for Dr to assess what best course of action will be. Sonic or “LAZER”. Assessment Thursday and potentially removal next Monday.
## Update: 2018 10 05
The procedure is called a Lithotripsy (Ultrasound busting of stone) and I’ll be in Monday 8 is (finding out later today on that). The Hospital (Palos) Called and said it would cost $30,000 and my 9010 ppo would have me covering$3000 so I would have to give them a deposit/down payment of $100.00. I, of course flipped out. My Gastric Sleeve only cost$18,000 and that wasn’t an outpatient procedure. I was in the hospital for 3 days including the day of the surgery. So we’re calling BCBS and Finding out what they will pay for the procedure, and I’m only paying 10% of that. (Grr medical billing!!!)
## Update: 2018 11 05
Ok so the stone is gone and the Bills arrive! Medical insurance billing is a major Joke. I can’t believe they get away with not knowing what will be changed until after the procedure. | 2018-11-17 15:04:26 | {"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": 0.27845996618270874, "perplexity": 3680.307422731516}, "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-2018-47/segments/1542039743714.57/warc/CC-MAIN-20181117144031-20181117170031-00114.warc.gz"} |
http://www.physicsforums.com/showthread.php?t=220992 | # Another question about collisions in 2 and 3-d...
by louise82
Tags: collisions
P: 18 Where does the -2v1v1'cos$$\Theta$$1' term come from in the momentum in the x direction equation? | 2014-09-17 13:41:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.975678026676178, "perplexity": 2144.4341983764098}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657123617.30/warc/CC-MAIN-20140914011203-00285-ip-10-196-40-205.us-west-1.compute.internal.warc.gz"} |
https://math.stackexchange.com/questions/1018258/conservative-vector-field-potential-function-and-work-done | # Conservative vector field, potential function and work done
For (i), is that I have to show $curl F = 0$ ?
For (ii) and (iii), what should I do in order to find the potential function and work done? Also, is the answer $4$ for (iii)?
## 1 Answer
(i) That's correct.
(ii) You want $\nabla f = (2x \cos y -2z^3, 3 + 2ye^z-x^2\sin y,y^2e^z - 6xz^2) = F$. Then you need to integrate
$$\frac{\partial f}{\partial x} = 2x \cos y -2z^3, \frac{\partial f}{\partial y}=3 + 2ye^z-x^2\sin y,\frac{\partial f}{\partial z}=y^2e^z - 6xz^2$$ to find $f$.
(iii) Evaluate $\int F\dot \ dr = f(B) - f(A)$.
Edit: \begin{align} \frac{\partial f}{\partial x} &= 2x \cos y -2z^3 \Rightarrow \int \frac{\partial f}{\partial x} dx = \int (2x \cos y -2z^3) dx \\&= x^2\cos y - 2x z^3 + g(y,z) \\ &\Rightarrow f(x,y,z) = x^2 \cos y - 2x z^3 + g(y,z) \end{align}
Now you need to find the function $g(y,z)$, to do so derivate with respect to $y$ and compare to $\frac{\partial f}{\partial y}$. You need to do the same to the other partials.
• @user110858 If you have any question, feel free to ask. – Aaron Maroja Nov 12 '14 at 12:40
• Why I have to integrate the above equations? I am still confused. – user110858 Nov 14 '14 at 9:12
• In order to find $f(x,y,z)$, we have by definition that $\nabla f = \langle \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y},\frac{\partial f}{\partial z} \rangle$ and we want $\nabla f = F$. – Aaron Maroja Nov 14 '14 at 9:15
• So, is the answer $2xsinx +2cosx -2xz^3 +3y +y^2 e^z +x^2 cosy + Constant$ ? – user110858 Nov 14 '14 at 9:42
• You need to be careful, I'll do the first integration. – Aaron Maroja Nov 14 '14 at 9:48 | 2019-10-20 22:29:32 | {"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": 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": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9978535175323486, "perplexity": 369.4372000801359}, "config": {"markdown_headings": true, "markdown_code": false, "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/1570986726836.64/warc/CC-MAIN-20191020210506-20191020234006-00408.warc.gz"} |
http://english.stackexchange.com/questions/50660/when-should-i-not-use-a-ligature-in-english-typesetting/50957 | # When should I not use a ligature in English typesetting?
Typesetting that goes beyond the scope of basic MS Word (e.g. LaTeX, or even modern Word versions with a good OpenType font) often uses ligatures for certain glyph combinations, the most common being
• f + f = ff
• f + i = fi
• f + l = fl
• f + f + i = ffi
• f + f + l = ffl.
I would assume, however, that there are cases in which a ligature shouldn't be used. Are there any rules or standards telling me when I should use a ligature and when I shouldn't?
-
I don't think this is your question, but you shouldn't use ligatures if you expect people to be searching your document in an electronic format. For example, if you use a ligature for the double f in the word efficient then any searches of your document for that word will not produce any results. – SigueSigueBen Dec 7 '11 at 16:07
@SigueSigueBen: It depends on the program that creates the pdf file: Some will indeed insert unsearchable stuff, whereas others don't and hence don't cause problems when you're searching the file for words such as "fit", "fly", "off", "baffle", or "difficult". :-) Obviously, if you have a choice in pdf-creating programs, you should choose one of the latter type. :-) – Mico Dec 7 '11 at 17:34
@SigueSigueBen: If you compile a minimal \documentclass{article}\begin{document}ff fi fl\end{document} with an up-to-date pdfLaTeX, the resulting ligatures in the Computer Modern font will indeed be searchable. For other setups and fonts, adaptions may be necessary, though, see e.g. tex.stackexchange.com/questions/4397/…. – doncherry Dec 7 '11 at 17:52
@SigueSigueBen: I think the key is that one should be using a modern TeX engine which creates a pdf file directly from the tex input file(s), rather than go through the older, and no longer necesssary process from .tex -> .dvi -> .ps -> .pdf. – Mico Dec 7 '11 at 22:48
@tchrist I've found the problem, and in fact it lies in the font, not TeX and not the reader. There is a StackExchange question which deals with this exact issue: Make ligatures in Linux Libertine copyable (and searchable). Ultimately, it is something to be aware of when creating documents which use typographic ligatures. – SigueSigueBen Jan 20 '12 at 17:05
At the end of this answer is a list of words for which various f-ligatures should not be employed if using them might impair the words' readability. Obviously, I make no claim as to this list's completeness. Comments and suggestions for additions welcome. (For the curious: I've come up with this list in preparation for a LaTeX package I'm creating that will provide a turnkey solution to the need to more-or-less automate the exclusion of some words from LaTeX's ligation algorithms.)
Aside: The "standard five" f-ligatures -- ff, fi, fl, ffi, and ffl -- that are provided by many fonts and the ft ligature provided by some fonts are the main subject of this answer,. That said, there are naturally many other though less commonly available ligated characters -- such as tt, st, and ct -- to which the following discussion applies as well. I.e., I'd argue that even if the wonderfully charming st ligature (drawn with an arc from the top of the s to the top of the t) is available in a given font, one should probably not use it in the word painstaking -- unless one wishes to make the reader think about pain inflicted by staking (a body part?) ...
As I understand it, the principle that suggests not using certain ligatures in certain words is that ligatures should not cross morpheme boundaries. Loosely speaking, morphemes are the smallest semantically meaningful units inside a word, i.e., the particles that carry/convey distinct meaning. Why? If in a given word two (or more) letters that could be ligated actually belong to separate morphemes, one risks decreasing the readability of the word (and of the entire text) by ligating them anyway, because the visual unity created by the ligature may conflict with the characters' separateness in terms of the morphemes they belong to. For instance, one should wish to avoid employing the ft ligature in "rooftop" because the f and t belong to distinct morphemes.
Of course, just how much readability is impaired in practice by a use of ligatures across morpheme boundaries depends both on the morphemes involved and on the way the glyph that contains the ligature is drawn in a given font. Comparing, for instance, the appearance of the words
with the appearance of
I daresay that few people will argue that the readability of the words shown in the upper row is enhanced by the use of the fi and fl ligatures. This is because the two ligatures unnecessarily risk making your readers puzzle -- if only briefly -- what's going on with these baffling fish and fly species. (Incidentally, the "fish"-words are typeset in Baskervald ADF and the "fly"-words are typeset in EB Garamond.) In contrast, I'll opine confidently that even if the ft letter pair in "fifty" does get ligated, no readers will be misled, slowed down, or otherwise inconvenienced by the use of the ligature. (Of course, "fty" is not AFAIK an English language morpheme -- unlike the "fly" and "fish" cases noted earlier.)
Clearly, using ligatures is not (and never has been) an absolute requirement for making a text readable. Otherwise, virtually all documents typeset with general-purpose word processing programs wouldn't be readable, right? Nevertheless, a consistent use of the ligatures provided by a font family does constitute a mark of good typography, in part because avoiding visual interference of glyph pairs (and triples) improves the readability of the words in question. That said, depending on the word and morphemes involved, I'd argue that not all letter combinations that can be ligated should always be ligated, i.e., for some words the use of ligated glyphs instead of the constituent glyphs need not be a good thing (and may even be a bad thing). In particular, if the letters involved in the ligature belong to separate morphemes, the word's overall legibility may be reduced by the use of a ligature because the visual unity created by the ligatures may impair, however fleetingly, the reader's ability to perceive the underlying morphemes.
Be sure to also include the appropriate plural forms of the nouns in this list.
ff to f-f
shelfful bookshelfful mantelshelfful
fi to f-i
elfin
chafing leafing loafing sheafing strafing vouchsafing; beefing reefing, briefing debriefing; coifing fifing jackknifing knifing midwifing waifing wifing; (air-, child-, fire-, flame-, moth-, rust-, sound-, water-, weather-) proofing goofing hoofing (re)roofing spoofing whoofing woofing; (be-, en-, in-) gulfing, golfing gulfing rolfing selfing wolfing; barfing (be-) dwarfing enserfing kerfing scarfing snarfing (wind-) surfing turfing wharfing
deafish dwarfish elfish oafish selfish serfish unselfish wolfish (plus -ness nouns and -ly adverbial forms)
beefier comfier goofier gulfier leafier surfier turfier (plus -iest superlative forms)
beefily goofily, goofiness
fl to f-l
beefless briefless hoofless leafless roofless selfless turfless (plus adverbial and noun forms: -ly -ness, e.g., selflessly)
aloofly briefly chiefly deafly liefly
calflike dwarflike elflike gulflike hooflike leaflike rooflike serflike sheaflike shelflike surflike turflike waiflike wolflike
halflife shelflife, halfline roofline
leaflet leaflets leafleted leafleting leafletting leafletted leafleteer
pdflatex (Ok, you've probably got to be a TeXie in order to "get" this word!)
ffi to ff-i
baffing biffing (out-) bluffing boffing buffing chaffing cheffing chuffing coffing coiffing (hand-, un-) cuffing daffing doffing (en-, in-) feoffing fluffing gaffing gruffing huffing luffing miffing muffing offing piaffing puffing quaffing rebuffing reffing restaffing restuffing riffing (cross-, over-, under-) ruffing sclaffing scoffing scuffing shroffing sluffing sniffing snuffing spiffing (over-, under-) staffing stiffing (over-) stuffing tariffing tiffing waffing whiffing yaffing
draffish giraffish gruffish offish raffish sniffish standoffish stiffish toffish (plus adverbial and noun forms: draffishly giraffishly etc.)
buffier chaffier chuffier cliffier daffier fluffier gruffier huffier iffier miffier puffier scruffier sniffier snuffier spiffier stuffier (plus superlative forms: buffiest, chaffiest, etc.)
daffily fluffily gruffily huffily puffily scruffily sniffily snuffily spiffily stuffily
fluffiness huffiness iffiness puffiness scruffiness sniffiness spiffiness stuffiness
baffies biffies jiffies taffies toffies
waffie
Pfaffian Wolffian Wulffian
ffl to ff-l
bluffly gruffly ruffly snuffly stiffly
cuffless stuffless (and adverbial forms: cufflessly, ...)
scofflaw, cufflink, offline, offload (plus -s, -ed, and -ing affixes)
rufflike clifflike
ffi to f-fi
chaffinch; wolffish
ffl to f-fl
safflower
ft to f-t
chieftain chieftaincy chieftainship
fifteen fifteens fifteenth fifteenths fifth fifthly fifths fifties fiftieth fiftieths fifty fiftyish
halftime halftone
rooftop rooftree
fft to ff-t (not a common ligature, but Minion Pro and EB Garamond do provide it)
offtrack
-
That's awesome, I'm excited for your package! Is there any typographic reference manual or the like stating this rule? (I've heard the morpheme rule as well, but some reference would be nice.) Are you interested in undesired ligatures in other languages as well? I'd assume there are many German LaTeX aficionados who'd be willing to help you by collecting words. – doncherry Dec 7 '11 at 17:59
It has examples of words with two ligatures: fluffier firefly fisticuffs, flagstaff fireproofing, chiffchaff and riffraff. Notice "fluffier" and "fireproofing" where you would not ligate the ff in the former and the fi in the latter. – egreg Dec 9 '11 at 21:42
@egreg: Thanks for this. I will admit that, from a typographical standpoint, not all suffix morphemes may be deserving of equal respect (of not being ligated). What should matter most in this regard, as with all other aspects of good typography, is enhancing readability of the text. For the f-ly and f-ish suffix cases, I'd argue strongly that by not ligating the f-l and f-i pairs one is being very kind to the reader. The f-ier and f-ing suffix cases are a bit more debatable, and the ff-ier case may well be a case where any benefits of being a linguistic stickler are just negligible. :-) – Mico Dec 9 '11 at 22:05
@egreg: That's my main point too, I believe: Knuth doesn't explain explicitly why "shelfful" looks better to him, but it can't be because Computer Modern's ff ligature isn't sufficiently good-looking on its own, right? I can only surmise that the reason he thinks "shelfful" looks better without the ligature is because he somehow thinks there's a chance that the reader might get tripped up briefly by the presence of a ligature that spans morpheme boundaries. Naturally, this is just my "educated" guess. Do you happen to know if DEK has clarified his thinking on this topic elsewhere? – Mico Dec 10 '11 at 0:06
@Mico I am referring to how proper typesetting software will, or can be asked to, implicitly select the ligatures provided by the actual font used. That way you never have to do anything special. Even troff had the .lg directive. OpenType font support discretionary ligatures and other sorts of contextual glyphs. The ligatures are usually divided into two classes, standard and historical. (Not all software gives you convenient access to these at any finer granularity.) On a Mac, use an OpenType font that supports them, & either FontBook or TextEdit to play with these implicit ligatures. – tchrist Jan 17 '12 at 21:48
(Edited for typos and to hand-tweak the typography. See new appendix at bottom.)
Are there any rules or standards telling me when I should use a ligature and when I shouldn’t?
Yes.
In version 3.2 of Robert Bringhurst’s The Elements of Typographic Style (Hartley & Marks, 2008), the main discussion of ligatures occurs on pages 50–53, under the section ‘3.3 Ligatures’, which has two subjections I shall describe below. Significant mentions of ligatures also occur at perhaps a half-dozen other points in this book.
This is one text that truly cannot come too highly recommended. If you do not own it, you should. It comes in both trade-paper and hardcover editions. Buy it. No scanned version is available via Google Books, and it is unlikely that it ever shall be — for reasons that should become quickly apparent once you crack its spine. The hardcover has a sewn binding with a built-in red silk bookmark, and costs only \$10 more than the trade paper; seems worth the upgrade to me. But both bindings are remarkably well-made books. Just make sure to get the most recent version; as of this writing, that is version 3.2 from 2008.
The first subsection of ‘3.3 Ligatures’, which is on page 50, is entitled:
3.3.1 Use the ligatures required by the font, and the characters required by the language, in which you are setting the type.
In most roman faces the letter f reaches into the space beyond it. In most italics, the f reaches into the space on both sides. Typographers call these overlaps kerns. Only a few kerns, like those in the arm of the f and the tail of the j, are implicit in a normal typefont, while others, like the overlap in the combination To, are optional refinements, independent of the letterforms.
Reaching into the space in front of it, the arm of the f will collide with certain letters – b, f, h, i, j, k, l – and with question marks, quotation marks or parentheses, if these are in its way.
As the craft of typography spread through Europe, new regional ligatures were added. An fj and æ were needed in Norway and Denmark for words just as fjeld and fjord and nær. In France an œ, and in Germany an ß (eszett or double-s) were required, along with accented and umlauted vowels. Double letters which are read as one – ll in Spanish, ij in Dutch, and ch in German, for example – were cast as single sorts for regional markets. An ffj was needed in Iceland. … Purely decorative ligatures were added to many fonts as well.
If your software is inserting ligatures automatically, take a moment to verify two things: (1) that the software is inserting all the ligatures you want and none that you do not want; (2) that all these ligatures are staying where they’re put.
That goes on for quite some time, and is important. I’ll try to summarize all this below instead of typing it all in. The other subsection, which isn’t until page 52, is entitled:
3.3.2 If you wish to avoid ligatures altogether, restrict yourself to faces that don’t require them.
It is quite possible to avoid the use of ligatures completely and still set beautiful type. All that is required is a face with non-kerning roman and italic f – and some of the finest twentieth-century faces have been deliberately equipped with just this feature. Aldus, Melior, Menoza, Palantino, Sabon, Trajanus and Trump Mediäval, for example, all set handsomely without ligatures. Full or partial ligatures do exist for these faces, and the ligatures may add a touch of refinement – but when ligatures are omitted from these faces, no unsightly collisions occur.
As always in Bringhurst, you should pay careful attention to the thoughtful and revealing sidenotes in this section. They contain myriad wonderful examples of typefaces and effects that are completely impossible to reproduce here. It’s much too much for me to type in, but do please read it. Here’s just one from page 51:
Decorative ligatures such as and Th are now deservedly rare. The ligature fffl is rarer still, but it has been cut for at least one typeface(Jonathan Hoefler’s Requiem italic).
What I will type in in toto, however, is the definition from the glossary from page 312:
ligatures Basic ISO fonts are limited to typographic ligatures, and . Rigid definitions of the glyph set, leaving no provision for additional ligatures (such as ff, ffi, ffl, fj) are a hazard to typography. Ligatures required by the design of the individual typeface should always reside on the basic font. The lexical ligatures ligatures æ, Æ, œ, Œ and ß are bonafide Unicode characters, separately listed in this appendix. Typographic ligatures such as and are glyphs, not characters, but many are now included in Unicode as “presentations forms.” [U+FB00—FB06]
When Bringhurst writes ‘glyph’ above, he means what a hand compositor would call a ‘sort’: something that would have its own slot in the compositor’s case. Most (but not all) digital fonts are distressingly impoverished when it comes to glyph variants. For his 42-line Bible, Gutenberg needed perhaps 40 sorts; he used 290. That tells you how important they are.
## Typographic Ligatures
However, you should not encode attempt to encode any typographic ligatures into your text, even for those few for which Unicode code points exist. (Edit: but see the bottom of this posting for why I have been forced to do so here.) Rather, this is something that must be done for you automatically by your typesetting software. You may be able to enable or disable such implicit selection, or distinguish between basic (typographic) ligatures and discretionary (typographic) ligatures.
Here are several discrete font suggestions with good typographic ligatures:
• One Western (Latin, Greek, and Cyrillic) OpenType face particularly rich in typographic ligatures, and which also includes the best Unicode support (highest number of glyphs, including many variants) seen to date, is Richard Slimbach’s Arno Pro, released in 2007. Slimbach is also the designer of Minion and Poetica. I can’t begin to describe how nifty this font is. (Well, I suppose I could, considering that I have an entire 19-page write-up of it which still only barely scratches the surface. But I have no space for that here.) It is based on early Renaissance forms, and is quite possibly already on your computer, as it was included with Adobe’s CS3. If you like fonts cut by Claude Garamond (or Garamont), Robert Granjon, or Jean Jannon, then you will like Slimbach’s Arno Pro.
• For typographic ligatures in general roman and italic faces, little can compare with Zuzana Ličko’s lavish Mrs Eaves (1996), which sports some 71 typographic ligatures. It is based on (the original) Baskerville. That’s for basic Latin, though. It does not have anything like the Unicode support that Slimbach’s much more recent Arno Pro offers.
• For script faces, master punchcutter and designer Hermann Zapf ’s Zapfino and its OpenType version, Zapfino Extra (2004), are without peer. In Zapfino, the very word Zapfino is itself a ligature, and comes with several outstanding variants. There really is no other font like Zapfino; Bringhurst calls it a calligraphic tour de force: “It is an exemplary marriage of artistic and technical ability. Effective use of such a type requires considerable patience and skill.”
• For Greeks, Matthew Carter’s Wilson (2005) is highly recommended. Like Zapfino, Wilson is sui generis. It is an exceptionally well-cut chancery Greek, which means it is highly embellished, full of elaborate ligatures and alternate forms. In this it is reminiscent of Robert Granjon’s chancery Greek that he cut in the 1560s, but Wilson gets its name from the fonts it is more directly based on, those of the eighteenth-century master, Alexander Wilson of Glasgow, who was also an astronomer and a physician.
Those fonts I’ve listed above all handle typographic ligatures exceptionally well. But as I’ve said, you should not encode typographic ligatures in your own text. (Edit: But see the bottom of this posting for why I’ve been forced to do so here.) That is for the font to decide for you. See also the Unicode FAQ on Ligatures, Digraphs, and Presentation Forms, and take especial note of this answer:
A: The existing ligatures exist basically for compatibility and round-tripping with non-Unicode character sets. Their use is discouraged. No more will be encoded in any circumstances.
Ligaturing is a behavior encoded in fonts: if a modern font is asked to display “h” followed by “r”, and the font has an “hr” ligature in it, it can display the ligature. Some fonts have no ligatures, some (especially for non-Latin scripts) have hundreds. It does not make sense to assign Unicode code points to all these font-specific possibilities.
However, you should definitely let the font use them if they are needed in that font. It’s the same as with kerning. If the font needs it to avoid collisions, you must use it or else use a different font; see the second of Bringhurt’s ligature subsections.
For example, in Georgia (which I believe you are reading this in right now), you cannot write things like f ’ and f ” without unacceptably horrible collisions producing f’ and f”. That’s just one reason web pages, even this one, frankly look like crap. Fonts designed with typographic ligatures and kerning in mind cannot be acceptably used without them.
## Lexical Ligatures
Lastly we come to lexical ligatures. Here the story is quite different. There are absolutely required by the language. For example, the name of famed Icelandic programmer Ævar Arnfjörð Bjarmason cannot be written any other way. Writing **AEvar* or **Aevar* would simply be wrong. In the same way, if you were talking about the Old English word that became modern wrath, you would have to write wrǽððu or wrǽþþu (both were known to occur). Similarly, French words and phrases like un œuf, hors d’œuvres, and ma jolie sœur are not supposed to be written broken up; it is highly frowned upon in French. The Encyclopædia Britannica actually has that lexical ligature in its registered trademark, and so must be maintained. And IPA uses both œ and ɶ (the small caps version) to mean separate vowels; you mustn’t mess with those. All those are lexical ligatures.
For other cases in English, the style has largely shifted, although it does still depend to some degree on the publication and nation of origin. Where we once wrote œnophile and amœba, Cæsar and archæology, we tend now to write those with the letters ‘broken apart’, so to speak.
My own recommendation is to use lexical ligatures if you are quoting another source that uses them, especially if they are originally in another language than English, or, if in English, you are trying to reproduce the original. This is the same rule of thumb used for diacritics.
For example, in a poem written in honor of the 19th centenary of Virgil’s death, Alfred, Lord Tennyson wrote such lines as Thou that seëst Universal / Nature moved by Universal Mind alike with Now thy Forum roars no longer, / fallen every purple Cæsar's dome— and you would be remiss not to reproduce those as the poet wrote them. Similarly in Lord Byron’s Episode of Nisus and Euralyus when he wrote Yet wakeful Rhæsus sees the threatening steel or When great Æneas wears Hesperia's crown.
If the original had them, then you likely should, too.
However, I dare say that maintaining those historical forms when writing your own new material upon Caesar or Aeneas is a bit too precious. There’s a reason that some ligatures get called ‘quaints’ by typesetters. You might not care to appear so quaint.
Then again, perhaps you might. It’s really up to you.
## Edit
Because ELU is presented to us in Georgia, I have hand-tweaked some of the typesetting, because with extremely rare exception, web browsers are far too stupid to use the mandatory ligatures and kerns that are absolutely required with this font.
I have therefore actually used the only three Latin typographic ligatures that Georgia provides: fi for fi, fl for fl, and although it appears to be unnecessary, ff for ff. Only the first of those appears to have been strictly necessary for this font, and so it is a bug that browsers don’t do it.
I have also in several places hand-kerned the f so that a following quotation mark, single or double, no longer collides with it. I have done this by placing a U+200A HAIR SPACE after the f and before the quotation mark, making f’ finally correctly render as f ’, and f” as f ”.
I should not have to do these things, but web browser technology is extremely primitive when it comes to typography. Gutenberg was far superior to anything we have yet achieved in web browsers, which means that we have still not caught up to the very first instance of movable type of almost half a millennium ago; pretty sad, isn’t it? However, browser awareness of OpenType hinting is apparently coming, at which point all this silliness should no longer be needed.
I’m sure Georgia is used here because it is the only universally available font that by default uses text figures instead of titling figures, as is of course properly done. Unfortunately, Georgia is also one of those fonts that cannot be correctly rendered without typographic ligatures and kerning hints being automatically applied — which is why I’ve been forced to make the various hand adjustments described in this edit.
Unfortunately, Georgia does not have very good Unicode support at all, nor does it have small caps, which are also required for tolerable typesetting.
-
Wow, I'm looking forward to reading this, but now it's really time to go to bed. – doncherry Jan 18 '12 at 2:24
@Mico You let the font choose the ligatures. You never suppress them. Otherwise you make things that look bad to read. – tchrist Mar 20 '12 at 14:10
@Mico Yes of course. It’s completely ridiculous to pretend that automatically applying the typographic ligatures built into a font harms legibility. Read Bringhurst. A well-designed font is made with that in mind, so that those letters correctly fit together as implicit typographic ligatures. To not use them is to invite ugly collisions that ruin the text. It has nothing to whatsobloodyever to do with semantics; it’s a simple matter of font design, so just use all the standard built-in typographic ligatures. Lexical ligatures are a different matter. – tchrist Mar 20 '12 at 16:02
@Mico Bringhurst is commenting on the way Adobe puts the Th ligature in the standard set in their OpenType fonts. His point is that it is a decorative ligature like ct, and that it doesn’t belong in the standard set any moreso than quaints like ct or st do — at least if you have a sense of the historical uses of these things. He isn’t commenting on things like your examples of cufflink, wolfish, or selfless. You’re right that I utterly reject the notion that using the fonts’ implicit typographic ligatures in such words can ever ‘harm legibility’ as you allege. This isn’t German. – tchrist Mar 20 '12 at 17:02
@Mico Precisely which part of Bringhurst’s “3.3.1 Use the ligatures required by the font, and the characters required by the language, in which you are setting the type.” is it that you disagree with? And yes, despite your protestations to the contrary, I very most certainly do see him supporting my claim that one should use the ligatures required by the font, because that is precisely what he says. Your allegation that one should not do so in words like wolfish is nowhere supported by Bringhurst. To not do so in some fonts will screw up your type, which is his whole point. – tchrist Mar 20 '12 at 17:24
Many ligatures of Latinate letters are nothing more than scribal abbreviations which have been preserved in type. Readability of the text is often improved by the use of these ligatures, such as ff, fi, and fl. Without ligature, these letters can partially overlap and require manual kerning. With ligature, the spacing is perfect. Ligatures such as ct and st sometimes have stylistic pen loops which are considered to contribute to the beauty of the line.
By contrast, some non-Latinate written languages have hard and fast rules for ligature.
Chicago Manual of Style advises that you should avoid ae and oe ligatures "in Latin words or transliterated Greek words", and "in words adopted into English from Latin, Greek, or French (and thus to be found in English dictionaries)".
Otherwise, I am aware of no authority which prohibits ligature in English text, such as between syllables. So it is up to the typesetter to determine what will make the most readable product.
-
You’re mostly right. However, the main scribal abbreviation preserved in modern type that comes readily to mind is the ampersand proper: &. Especially in humanist Renaissance faces and their latterday reimplementations, including the one in the banner at the top, the scribal connection to the Latin et is quite clear. The Unicode Latin compatibility ligatures, meaning ff, fi, fl, ffi, and ffl, plus the two quaints, ſt and st, were never scribal abbreviations. Rather, they are hand compositors’ ‘abbreviations’, dedicated sorts needed to avoid collisions in metal type. – tchrist Jan 17 '12 at 21:39
+1 this comment, I can't learn enough about typography. Now what you say seems to be contradicted by Wikipedia and this author. Both say that cast ligatures directly reproduce scribal handwriting, going right back to Gutenberg. So who's right and how do we know? – MετάEd Jan 17 '12 at 22:29
Incidentally, the author I linked to above points out another scribal abbreviation preserved in modern type: the question mark, originally q over o, short for questio. – MετάEd Jan 17 '12 at 22:30
Insofar as scribes wrote sequences like ff as a single glyph of two letters tied together with a common stoke, or fi in a way that was different than what they did when the i did not follow the f, it is true that these are reflected in metal. However, the main reason for essential ligatures to exist is because some fonts require them, because otherwise you will get collisions, especially when unkerned. I have a long answer I need to write up. – tchrist Jan 17 '12 at 22:45
That will be great. Based on what you say here, it's not strictly true that the ff ligature, for example, wasn't originally a scribal ligature. It was, but when the transition was made to type the ligature survived because it was as useful in typesetting as in handwriting, albeit for different reasons. – MετάEd Jan 17 '12 at 23:08
A rule (not always observed) is not to use a ligature spanning syllables. Chaffinch has syllables chaf-finch, for example. So don't use the ffi ligature in there.
-
Also in "efficient" the syllables are "ef-fi-cient", but the ligature is used. You probably meant a ligature spanning components of a compound word. – egreg Dec 5 '11 at 16:03
I said: not always observed. Some would say that ligature ff should not be used in efficient. Personally, I never worry about this. – GEdgar Dec 5 '11 at 16:07
Can you show examples where a non final "ff" doesn't span two syllables? – egreg Dec 5 '11 at 16:09
@egreg Take any of dozens of short verbs (buff, cuff, huff, ruff, bluff, stuff...) and add an -ed suffix (so, buffed, cuffed...) – jwpat7 Dec 5 '11 at 19:36
We've gotta be careful not to intermix the terms syllable and morpheme. These units may, but don't necessarily have to coincide, e.g. purple has two syllables, but it is monomorphemic. The Latin compound words are a tricky case indeed, but I think I'd agree with you that {effic} is one morpheme, my reason being that no native speaker of English would use *{fic} as a morpheme productively, not even as a joke. Maybe we should get Alan Munn involved in this discussion, he could certainly provide some interesting insights, or help with your package. – doncherry Dec 7 '11 at 23:26
There is no rule that ever requires or prohibits the use of a ligature in English - it is purely a matter of style.
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https://math.stackexchange.com/questions/3051757/joint-pdf-cross-sectional-area-what-does-it-represent | # Joint PDF cross sectional area - what does it represent?
Given the PDF of a continuous joint distribution:$$f(x,y)$$ Why isn't it true that taking a cross sectional area of the distribution parallel to the y axis represents the following: $$\int_{-\infty}^{\infty}f(x,y)dy = P(X=x)$$
Surely integrating for all possible values of y with respect to y, is akin to summing all probabilities P(x, y), where x is fixed at a given value. If that is the case, that would be calculating the probability that the random variable X is equal to a given value x, as you have exhausted all instances where X = x. Why is it that the cross sectional area still yields a probability density as opposed to an absolute probability?
• In short, because $P(X=x)=0$. – kludg Dec 25 '18 at 10:28 | 2019-07-15 18:04:29 | {"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": 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": 0.9024645090103149, "perplexity": 139.3101861679237}, "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-2019-30/segments/1563195523840.34/warc/CC-MAIN-20190715175205-20190715201205-00353.warc.gz"} |
https://www.springerprofessional.de/analysis-for-optimal-pattern-synthesis-of-time-modulated-concent/11825900 | main-content
## Weitere Artikel dieser Ausgabe durch Wischen aufrufen
01.03.2016 | Regular Research Paper | Ausgabe 1/2016
# Analysis for optimal pattern synthesis of time modulated concentric circular antenna array using memetic firefly algorithm
Zeitschrift:
Memetic Computing > Ausgabe 1/2016
Autoren:
## Abstract
In this paper the optimal performance of time modulated nine-ring concentric circular antenna array with isotropic elements has been studied based on an evolutionary optimization algorithm hybridized with local heuristic search called memetic firefly algorithm (MFA). The firefly algorithm has been applied followed by Nelder–Mead simplex method for the local heuristic search to achieve the optimal fine tuning. Other algorithms like real coded genetic algorithm (RGA) and particle swarm optimization (PSO) have been used for the comparison purpose. The comparisons among the algorithms have been made with two case studies as Case-1 and Case-2, and with two different fitness functions $$(f_{{ fitness}1}, f_{{ fitness}2})$$ and three control parameters like inter-element uniform/non-uniform spacing in rings, inter-ring radii and the switching-on times of rings. The simulation results show that the MFA outperforms RGA and PSO for both the cases Case-1, Case-2 and $$f_{{ fitness}1}$$, $$f_{{ fitness}2}$$, respectively with respect to better side lobe level (SLL). The fitness function $$f_{{ fitness}2}$$ is better than the $$f_{{ fitness}1}$$ with respect to sideband level. Apart from this, powers radiated at the centre/fundamental frequency and the first two sideband frequencies, and dynamic efficiency have been computed. It is found that power radiated by any sideband frequency is much less as compared to the power radiated at the centre frequency. It has been observed that as the sideband frequency increases, SBL decreases to the greater extent as compared to SLL. As per authors’ knowledge there is a little research contribution by any other previous researcher regarding numerical computation of radiation characteristics as SBLs, powers radiated at the fundamental frequency and its two sideband frequencies, directivity, and dynamic efficiency for time-modulated CCAA.
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Zur Ausgabe | 2021-02-26 01:33:12 | {"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": 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": 0.22187887132167816, "perplexity": 13819.810247458725}, "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/1614178355944.41/warc/CC-MAIN-20210226001221-20210226031221-00349.warc.gz"} |
https://www.mathdoubts.com/operations-log-terms/ | Fundamental Operations of Logarithmic terms
In mathematics, two or more logarithmic terms are involved in fundamental operations but we cannot perform the mathematical operations, same as the numbers or algebraic terms. Actually, some of the operations follow the algebraic terms but remaining operations never follow them. Hence, it is essential for everyone to learn how to do mathematical operations with log terms.
Operations
There are four types of mathematical operations with logarithmic terms. Let’s learn each mathematical operation in different cases with understandable examples.
Learn how to add two or more logarithmic terms mathematically to obtain summation of them.
Subtraction
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Math Doubts is a free math tutor for helping students to learn mathematics online from basics to advanced scientific level for teachers to improve their teaching skill and for researchers to share their research projects. Know more | 2021-05-06 17:11:32 | {"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": 0.8280333280563354, "perplexity": 972.9678442024416}, "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-2021-21/segments/1620243988758.74/warc/CC-MAIN-20210506144716-20210506174716-00540.warc.gz"} |
http://kitchingroup.cheme.cmu.edu/publications/xu-2014-relat.html | xu-2014-relat
## DOI
@article{xu-2014-relat, author = {Zhongnan Xu and John R. Kitchin}, title = {Relating the Electronic Structure and Reactivity of the 3d Transition Metal Monoxide Surfaces}, journal = {Catalysis Communications}, volume = 52, number = None, pages = 60-64, year = 2014, doi = {10.1016/j.catcom.2013.10.028} }
: citing related | 2017-05-29 02:09:24 | {"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": 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": 0.24558700621128082, "perplexity": 14313.715359121477}, "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/1495463612008.48/warc/CC-MAIN-20170529014619-20170529034619-00481.warc.gz"} |
https://anthony-tan.com/tags/backpropagation/ | ## Drawbacks of Backpropagation
Preliminaries ‘An Introduction to Backpropagation and Multilayer Perceptrons’ ‘The Backpropagation Algorithm’ Speed Backpropagation up 1 BP algorithm has been described in ‘An Introduction to Backpropagation and Multilayer Perceptrons’. And the implementation of the BP algorithm has been recorded at ‘The Backpropagation Algorithm’. BP has worked in many applications for many years, but there are too many drawbacks in the process. The basic BP algorithm is too slow for most practical applications that it might take days or even weeks in training....
January 7, 2020 · (Last Modification: May 3, 2022) · Anthony Tan
## Backpropagation, Batch Training, and Incremental Training
Preliminaries Calculus 1,2 Linear Algebra Batch v.s. Incremental Training1 In both LMS and BP algorithms, the error in each update process step is not MSE but SE $$e=t_i-a_i$$ which is calculated just by a data point of the training set. This is called a stochastic gradient descent algorithm. And why it is called ‘stochastic’ is because error at every iterative step is approximated by randomly selected train data points but not the whole data set....
January 2, 2020 · (Last Modification: May 3, 2022) · Anthony Tan
## The Backpropagation Algorithm
Preliminaries An Introduction to Backpropagation and Multilayer Perceptrons Culculus 1,2 Linear algebra Jacobian matrix Architecture and Notations1 We have seen a three-layer network is flexible in approximating functions(An Introduction to Backpropagation and Multilayer Perceptrons). If we had a more-than-three-layer network, it could be used to approximate any functions as accurately as we want. However, another trouble that came to us is the learning rules. This problem almost killed neural networks in the 1970s....
January 1, 2020 · (Last Modification: May 3, 2022) · Anthony Tan
## An Introduction to Backpropagation and Multilayer Perceptrons
Preliminaries Performance learning Perceptron learning rule Supervised Hebbian learning LMS Form LMS to Backpropagation1 The LMS algorithm is a kind of ‘performance learning’. And we have studied several learning rules(algorithms) till now, such as ‘Perceptron learning rule’ and ‘Supervised Hebbian learning’. And they were based on the idea of the physical mechanism of biological neuron networks. Then performance learning was represented. Because of its outstanding performance, we go further and further away from natural intelligence into performance learning....
December 31, 2019 · (Last Modification: May 2, 2022) · Anthony Tan | 2022-09-26 02:52:22 | {"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": 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": 0.6128649115562439, "perplexity": 2064.027881346691}, "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-2022-40/segments/1664030334644.42/warc/CC-MAIN-20220926020051-20220926050051-00481.warc.gz"} |
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Studies in the History of Indian Mathematics
A publication of Hindustan Book Agency
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Hardcover ISBN: 978-93-80250-06-9
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Studies in the History of Indian Mathematics
A publication of Hindustan Book Agency
Available Formats:
Hardcover ISBN: 978-93-80250-06-9 Product Code: HIN/46
List Price: $72.00 AMS Member Price:$57.60
Please note AMS points can not be used for this product
• Book Details
Hindustan Book Agency
Volume: 462010; 402 pp
MSC: Primary 01;
This volume is the outcome of a seminar on the history of mathematics held at the Chennai Mathematical Institute during January–February 2008 and contains articles based on the talks of distinguished scholars both from the West and from India.
The topics covered include: (1) geometry in the øulvasåtras; (2) the origins of zero (which can be traced to ideas of lopa in Pàõini's grammar); (3) combinatorial methods in Indian music (which were developed in the context of prosody and subsequently applied to the study of tonal and rhythmic patterns in music); (4) a cross-cultural view of the development of negative numbers (from Brahmagupta (c. 628 CE) to John Wallis (1685 CE); (5) Kuññaka, Bhàvanà and Cakravàla (the techniques developed by Indian mathematicians for the solution of indeterminate equations); (6) the development of calculus in India (covering the millennium-long history of discoveries culminating in the work of the Kerala school giving a complete analysis of the basic calculus of polynomial and trigonometrical functions); (7) recursive methods in Indian mathematics (going back to Pàõini's grammar and culminating in the recursive proofs found in the Malayalam text Yuktibhàùà (1530 CE)); and (8) planetary and lunar models developed by the Kerala School of Astronomy. The articles in this volume cover a substantial portion of the history of Indian mathematics and astronomy.
This book will serve the dual purpose of bringing to the international community a better perspective of the mathematical heritage of India and conveying the message that much work remains to be done, namely the study of many unexplored manuscripts still available in libraries in India and abroad.
General mathematical audience interested in the history of Indian mathematics.
• Request Review Copy
Volume: 462010; 402 pp
MSC: Primary 01;
This volume is the outcome of a seminar on the history of mathematics held at the Chennai Mathematical Institute during January–February 2008 and contains articles based on the talks of distinguished scholars both from the West and from India.
The topics covered include: (1) geometry in the øulvasåtras; (2) the origins of zero (which can be traced to ideas of lopa in Pàõini's grammar); (3) combinatorial methods in Indian music (which were developed in the context of prosody and subsequently applied to the study of tonal and rhythmic patterns in music); (4) a cross-cultural view of the development of negative numbers (from Brahmagupta (c. 628 CE) to John Wallis (1685 CE); (5) Kuññaka, Bhàvanà and Cakravàla (the techniques developed by Indian mathematicians for the solution of indeterminate equations); (6) the development of calculus in India (covering the millennium-long history of discoveries culminating in the work of the Kerala school giving a complete analysis of the basic calculus of polynomial and trigonometrical functions); (7) recursive methods in Indian mathematics (going back to Pàõini's grammar and culminating in the recursive proofs found in the Malayalam text Yuktibhàùà (1530 CE)); and (8) planetary and lunar models developed by the Kerala School of Astronomy. The articles in this volume cover a substantial portion of the history of Indian mathematics and astronomy.
This book will serve the dual purpose of bringing to the international community a better perspective of the mathematical heritage of India and conveying the message that much work remains to be done, namely the study of many unexplored manuscripts still available in libraries in India and abroad.
General mathematical audience interested in the history of Indian mathematics.
Please select which format for which you are requesting permissions. | 2023-02-06 04:10:15 | {"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": 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": 0.2240346521139145, "perplexity": 2509.159028398335}, "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-2023-06/segments/1674764500303.56/warc/CC-MAIN-20230206015710-20230206045710-00231.warc.gz"} |
https://quant.stackexchange.com/questions/39944/varswap-pnl-formula | VarSwap PnL formula
I came across this formula for the varswap PNL: let $r_i$ be the log return over $[t_i,t_{i+1}]$ and suppose we risk manage the VS at a fixed implied volatility sigma, the PnL of (the payoff) over time interval $[t_i,t_{i+1}]$ is: $$r_i^2-\sigma^2*\Delta T\$$ Do you know how the author gets this formula?
Thanks!
• If you "risk manage" your variance swap then hopefully your pnl is zero. The formula you refer to is the contribution to the VS payoff over time interval $[t_i, t_{i+1}[$. – Antoine Conze May 22 '18 at 10:07
• In any "swap" you receive one thing and you pay another. In this case each day you receive the squared daily return $r_i^2$ and you pay the agreed fixed variance at the annual rate $\sigma^2$, on a daily basis this translates to $\sigma^2 \Delta T$ where $\Delta T$ is one day i.e. $\frac{1}{252}$ years. Hence the "per day net" is the expression you quoted $r_i^2-\sigma^2 \Delta T$ – Alex C May 23 '18 at 0:15
• The issue is that the variance swap is not a swap per se, it's actually a forward and the only "leg" is at maturity. – JiLight May 23 '18 at 7:32
• It is still a swap in the sense that you receive/pay a floating leg (the realized variance, accruing over time as the sum of daily square log returns "fixings") and pay/receive a fixed leg (the strike). In a forward you usually receive/pay the difference between a single fixing and a fixed quantity. – Antoine Conze May 23 '18 at 8:37 | 2019-07-24 06:31:37 | {"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": 0.6911280751228333, "perplexity": 1316.0295015349682}, "config": {"markdown_headings": false, "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-2019-30/segments/1563195531106.93/warc/CC-MAIN-20190724061728-20190724083728-00522.warc.gz"} |
https://codereview.stackexchange.com/questions/191754/flux-architecture-implementation-vanilla-js | # Flux architecture implementation (vanilla JS)
I'm trying to better understand flux-style architecture, so I wrote this snippet to clarify how a simple flux system can be designed. I was wondering if my implementation is valid, or if I've missed something.
const application = () => {
/* Init the model */
let model = {
page: null
};
/* redirects the reference from the old state to the new */
const updateState = newState => model = newState;
/* a reducer method, more are easily added */
const UPDATE_PAGE = (model, newPage) => {
let newState = Object.assign({}, model);
newState.page = newPage;
};
/*
* dispatch is a core function, directing every action
* to the proper reducer depending on the type
*/
const dispatch = action => {
action.type === 'UPDATE_PAGE' ?
UPDATE_PAGE(model, action.page)
: null;
};
/* An action mutating state */
let updatePageAction = {
type: 'UPDATE_PAGE',
page: 1
};
console.log('initial model: ', model);
/* simply dispatch the action */
dispatch(updatePageAction);
/* and the state is updated! */
console.log('updated model: ', model);
};
application();
• Hey there. Please do not edit your question to include an updated version of your code. That is highly confusing and makes it difficult for late reviewers to review your code. If you want to solicit further feedback, then you should post a new question instead. Thanks – Vogel612 Apr 13 '18 at 7:28
• – Heslacher Apr 13 '18 at 7:30
First of all, Flux is not to be confused with Redux. While both have similarities, the main difference is that Flux allows multiple stores while Redux advises only using one store per app for simplicity. The following will talk about Redux.
/*
* dispatch is a core function, directing every action
* to the proper reducer depending on the type
*/
const dispatch = action => {
action.type === 'UPDATE_PAGE' ?
UPDATE_PAGE(model, action.page)
: null;
};
Dispatch doesn't actually "direct" the action to the right reducer. It simply invokes the reducer, supplying it the current state and the dispatched action. It's actually the reducer that does the pattern matching/selection of what logic runs with which action.
/* a reducer method, more are easily added */
const UPDATE_PAGE = (model, newPage) => {
let newState = Object.assign({}, model);
newState.page = newPage;
};
A reducer is a pure function which takes 2 arguments, the current state and the dispatched action and returns the new state, based on the state and the passed action. You can think of it as the "equation" part of the app (yes, like a math equation). Reducers look like:
const initialState = { count: 0 }
const reducer = (state = initialState, action) => {
switch(action.type){
case 'INCREMENT':
return {...state, count: state.count + 1 }
case 'DECREMENT'
return {...state, count: state.count - 1 }
default:
return state
}
}
There's several reasons why reducers are designed this way.
• The reducer is pure. Its result is not affected by anything other than its inputs, making it stupid easy to test.
• It's just a data transformer. You can easily test the logic without fancy mocks, stubs or spies because there's nothing to mock, stub or spy.
• You can easily compose reducers. You can divide the state into sections, each with its own reducer. Redux provides a handy combineReducers utility function for it.
• At the end of the day, reducers are just functions. Not a fancy service class, not a magical method, not some fancy concept invented by someone, it's just a function.
Redux is so simple, that if you just overheard someone in the pub talking about what it does, you can easily implement it yourself. It's effectively a pub-sub library, except that it also manages and holds state, and only ever emits one kind of event - a state change.
// my-redux.js - The only part that is "Redux"
export const createStore = reducer => {
const subscribers = []
let currentState = null
return {
getState(){
return currentState
},
subscribe(fn){
subscribers.push(fn)
fn(currentState)
},
dispatch(action){
currentState = reducer(currentState, action)
subscribers.forEach(fn => fn.currentState)
}
}
}
// reducer.js - Where your app's logic goes.
const initialState = { count: 0 }
export const reducer = (state = initialState, action) => {
switch(action.type){
case 'INCREMENT':
return {...state, count: state.count + 1 }
case 'DECREMENT'
return {...state, count: state.count - 1 }
default:
return state
}
}
// app.js - How the app is brought together
import {createStore} from './my-redux'
import {reducer} from './reducer'
import {YourComponent} from './your-component'
const store = createStore(reducer)
YourComponent({
mount: 'somewhere',
onmount(){
store.subscribe(state => {
this.setYourState(state)
})
},
render(state) {
return (<button onclick="store.dispatch({ type: 'STH', data: 'NOT VALID JSX BUT WHATEVER' })">Click Me</button>)
}
})
You can read more about the three principles of Redux and how it's just a guiding concept rather than an actual implementation.
• This clarified much for me. A few questions: 1) why is the initial state set as a default in the reducer? Seems it would be better to pass it in as a second argument to createStore, where it can initialize currentState to initialState. 2) is there an advantage to using a switch block over an if/else, or is it more a conventional choice? 3) What's the best way to extend the possible type of actions? Is it alright to have a 'load-balancing' reducer invoking more specific sub-reducers which perform the state update? – Jacob Penney Apr 12 '18 at 14:20
• @JacobPenney 1) You can initialize it from createStore if you have some initial state to hydrate the store. But without it, the reducer will at least give you a known, default state shape 2) It's preference. 3) Reducers will always get called to construct the state tree, there's no selective execution. It either constructs new state if it hits a certain action or returns the state it was provided if it has nothing to do with the action. – Joseph Apr 12 '18 at 15:20
Object.assign({}, model) is not deepcopy, it is shalow copy only, you should consider to use Immutablejs by Facebook or write your own library.
action.type === 'UPDATE_PAGE' ?
UPDATE_PAGE(model, action.page)
: null;
Can be write:
action.type === 'UPDATE_PAGE' &&
UPDATE_PAGE(model, action.page) | 2019-11-21 09:49:17 | {"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": 0.3666425347328186, "perplexity": 5876.64646286032}, "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/1573496670743.44/warc/CC-MAIN-20191121074016-20191121102016-00458.warc.gz"} |
http://mathhelpforum.com/geometry/16108-hypotenus-problem.html | 1. ## hypotenus problem?
In the isosceles right triangles ABC and MNP, AB = BC = 12 and MN = NP = 24. Which is the sum of the hypotenuses of these triangles?
16/2
18/2
32/2
36/2
2. Originally Posted by sanee66
In the isosceles right triangles ABC and MNP, AB = BC = 12 and MN = NP = 24. Which is the sum of the hypotenuses of these triangles?
16√2
18√2
32√2
36√2
Hello,
if the legs of an isosceles right triangle is a then the hypotenuse c is calculated by:
$c = a \cdot \sqrt{2}$
Therefore the sum of the two hypotenuses is:
$s = 12 \cdot \sqrt{2} + 24 \cdot \sqrt{2} = 36 \cdot \sqrt{2}$ | 2017-04-30 04:04:16 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "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": 0.8933704495429993, "perplexity": 538.8866227346278}, "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/1492917124297.82/warc/CC-MAIN-20170423031204-00000-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://developer-archive.leapmotion.com/documentation/v2/csharp/api/Leap.Arm.html | # Arm¶
Properties:
Methods:
class Leap::Arm
The Arm class represents the forearm.
Public Functions
Arm()
Constructs an invalid Arm object.
Get valid Arm objects from a Hand object.
Hand hand = frame.Hands.Frontmost;
Arm arm = hand.Arm;
Since
2.0.3
bool Equals(Arm arg0)
Compare Arm object equality.
Boolean theSame = thisArm.Equals(thatArm);
Two Arm objects are equal if and only if both Arm objects represent the exact same physical arm in the same frame and both Arm objects are valid.
Since
2.0.3
override string ToString()
A string containing a brief, human readable description of the Arm object.
String description = arm.ToString ();
Return
A description of the Arm object as a string.
Since
2.0.3
Property
Matrix Basis
The orthonormal basis vectors for the Arm bone as a Matrix.
Basis vectors specify the orientation of a bone.
xBasis Perpendicular to the longitudinal axis of the bone; exits the arm laterally through the sides of the wrist.
yBasis or up vector Perpendicular to the longitudinal axis of the bone; exits the top and bottom of the arm. More positive in the upward direction.
zBasis Aligned with the longitudinal axis of the arm bone. More positive toward the wrist.
Matrix basis = arm.Basis;
Vector xBasis = basis.xBasis;
Vector yBasis = basis.yBasis;
Vector zBasis = basis.zBasis;
Vector armCenter = arm.ElbowPosition +
(arm.WristPosition - arm.ElbowPosition) * 0.5f;
Matrix transform = new Matrix (xBasis, yBasis, zBasis, armCenter);
The bases provided for the right arm use the right-hand rule; those for the left arm use the left-hand rule. Thus, the positive direction of the x-basis is to the right for the right arm and to the left for the left arm. You can change from right-hand to left-hand rule by multiplying the z basis vector by -1.
Note that converting the basis vectors directly into a quaternion representation is not mathematically valid. If you use quaternions, create them from the derived rotation matrix not directly from the bases.
Return
The basis of the arm bone as a matrix.
Since
2.0.3
Vector Center
The center of the forearm.
This location represents the midpoint of the arm between the wrist position and the elbow position.
Since
2.1.0
Vector Direction
The normalized direction in which the arm is pointing (from elbow to wrist).
Vector direction = arm.Direction;
Since
2.0.3
Vector ElbowPosition
The position of the elbow.
Vector elbow = arm.ElbowPosition;
If not in view, the elbow position is estimated based on typical human anatomical proportions.
Since
2.0.3
Arm Invalid
Returns an invalid Arm object.
Arm arm = Arm.Invalid;
Return
The invalid Arm instance.
Since
2.0.3
bool IsValid
Reports whether this is a valid Arm object.
Arm arm = frame.Hand (10).Arm;
if (arm.IsValid) {
// ... Use the arm data
}
Return
True, if this Arm object contains valid tracking data.
Since
2.0.3
float Width
The average width of the arm.
float width = arm.Width;
//length
Vector displacement = arm.ElbowPosition - arm.WristPosition;
float length = displacement.Magnitude;
Since
2.0.3
Vector WristPosition
The position of the wrist.
Vector wrist = arm.WristPosition;
Note that the wrist position is not collocated with the end of any bone in the hand. There is a gap of a few centimeters since the carpal bones are not included in the skeleton model.
Since
2.0.3 | 2021-11-29 14:11:51 | {"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": 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": 0.5136263966560364, "perplexity": 4914.731646852623}, "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/1637964358774.44/warc/CC-MAIN-20211129134323-20211129164323-00005.warc.gz"} |
https://quikk.biz/1s2-2s2-2p6-3s2-3p6/ | # 1s2 2s2 2p6 3s2 3p6
### What element in Bohr form is 1s2 2s2 2p6 3s2 3p4?
The element you're looking for is sulfur, or $' S '$.
## 1s2 2s2 2p6 3s2 3p6 4s1
If you follow the configuration pattern, the electron configuration of ruthenium should be: 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d6 5s2 or Kr 4d6 5s2. But the actual configuration of ruthenium is: 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d7 5s1 or Kr 4d7 5s1. I understand how the configuration.Show more. Source (s): electron configuration ruthenium ru: https://tr.im/ncFKi. Mar 01, 2021 In 3rd shell,we are getting 3s2 3p6. If I add all the valence electrons,we get 2 + 6 = 8 valence electrons in 1s2 2s2 2p6 3s2 3p6. From 1s2 2s2 2p6 3s2 3p6, we get totally 18 electrons.Among these 18 electrons, only 8 electrons are called valence electrons that are situated in the outermost shell (3s2 3p6).
Here's how you can use an element's electron configuration to determine its identity.
$1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{2} 3 {p}^{4}$
If you add all the electrons decribed in this electron configuration you'll get
Warring kingdoms nidalee price. $2 + 2 + 6 + 2 + 4 = 16$
For a neutral atom, the number of electrons it has will match the number of protons in its nucleus, i.e. its atomic number. This means that the element you're looking for will have its atomic number equal to 16. According to the periodic table, this element is sulfur.
## 1s2 2s2 2p6 3s2 3p6 4s2 3d5
Read more on sulfur's Bohr model here: | 2021-10-19 02:21:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 3, "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": 0.34744134545326233, "perplexity": 2916.72085513784}, "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/1634323585231.62/warc/CC-MAIN-20211019012407-20211019042407-00676.warc.gz"} |
http://www.domyno.com/father-of-apjbvjz/standard-deviation-if-google-sheets-cd51d9 | But a major problem is that mean deviation ignores the signs of deviation, otherwise they would add up to zero.To overcome this limitation variance and standard deviation … Nov 30, 2020 • CRM Knowledge. Students apply what they learned by making different calculations with beak size measurements of Galapágos finches. Automatically Graded Exercises; Learn Excel, Inside Excel! If the total number of … In such cases, you can use the Filter function in Google Sheets with STDEV. See that here – DSTDEV Database Function in Google Sheets. The standard deviation, in statistics, is a measure of the amount of variation of a set of values. Along with a spreadsheet, there is also a word processor and a presentation program. You can use this formula in Google sheets, OpenOffice and Excel by typing =STDEVP(...) into a cell. The STDEV formula returns zero as the mean of the data points are the same (26). N = Number of observations in population. For example, to calculate the standard deviation for the values of cells A2 through A10, highlight cells A2 through A10. How to Use the TRIMMEAN Function in Google Sheets. Standard deviation is a mathematical term and most students find the formula complicated therefore today we are here going to give you stepwise guide of how to calculate the standard deviation and other factors related to standard deviation in this article. CA Sci. The STANDARD DEVIATION Function works exactly the same in Google Sheets as in Excel: Excel Practice Worksheet. You don't make a histogram, then make a boxplot, then compute the mean and standard deviation. Need for Variance and Standard Deviation. The p-value is used to determine whether certain hypotheses are correct or not.Basically, scientists will choose a value, or range of … These applications are also available in several platforms including Windows, MAC, Android, iOS, Windows, Blackberry etc. Viewed 1k times 0. mean is the mean (mu) of the normal distribution function. So the STDEV will return the value 0, which means zero/no deviation. standard deviation How to Find Standard Deviation in Google Sheets and Excel – Excelchat Excel enables us to calculate the standard deviation of any data set in no time by using one of these functions: STDEV, STDEVP, STDEV.S, STDEVA. Specify the numbers over which you want the standard deviation between the parentheses and press Enter. For a set of data, the measure of dispersion, about mean, when expressed as the positive square root of the variance, is called standard deviation.It measures the dispersion or spread of data. So that's how we can calculate a standard deviation in Google Sheets. Next, use the ABS() function to … First, enter all of the values of a dataset into one column: Step 2: Find the mean value of the dataset. Usually, this is the number that you are concerned with. I mean STDEVP and STDEV.P for calculating the SD of an entire population. Let me show you how to calculate SD of an entire population in 3 steps without using the STDEVP function in Google Sheets. The numbers are in B3:B7 and here are the STDEVP and STDEV.P formulas. You may also like the following Google Sheets tutorials: How to make a Bar Graph in Google Sheets; How to Insert Check Box (Tick Box) Symbol in Google Sheets Although STDEV is specified as taking a maximum of 30 arguments, Google Sheets supports an arbitrary number of arguments for this function. Instead, you select the variables you want to analyze, and do the analysis all at once. I have two sheets. With this add-on, you can: Summarize a single … The average of the above numbers is 40.5. The suite is also with a version control where each user … It measures how far a set of numbers are spread out from their average value. value2 – Additional values or arrays/ranges to include in the population. All for free. Summary. Standard deviation helps you to find how far data values (numbers) are from their mean (average). First, generate a random sample of 16 data points from a normally distribution population (using the =norminv command in Google Sheets). In this class, and in many applications of statistics, the sample standard deviation sx is used as the point estimate for the population … That said, we believe a fundamental understanding of statistical concepts should come before applying any spreadsheet function. We will be using Google Sheets to simulate a normal distribution with a mean of 700 and a standard deviation of 6. A low STDEV indicates the data points are close to the mean, while a high STDEV indicates the data points are spread out. Step 3: If needed, you can change the chart axis and title. Likewise, -1σ is also 1 standard deviation away from the mean, but in the opposite direction. You don't make a histogram, then make a boxplot, then compute the mean and standard deviation. Therefore, in cell C14, enter the formula "=SQRT(252)*C13" to convert the standard deviation for this 10-day period to annualized historical volatility. The standard deviation is represented by the Greek letter sigma (lower case). Excel Standard Deviation Graph / Chart. Standard Deviation - Sample Formula. The figure below illustrates the idea. To calculate standard deviation in Excelwith a sampled data set, we can use the STDEV, STDEV.Sor STDEVA functions. The population standard deviation formula is given as: $$\sigma =\sqrt{\frac{1}{N}\sum_{i=1}^{N}(X_i-\mu)^2}$$ Here, σ = Population standard deviation. In order to determine which function to use, let us walk through the checklist: 1. You have entered an incorrect email address! Volatility is inherently related to standard deviation, or the degree to which prices differ from their mean. Standard Deviation is one of the important statistical tools which shows how the data is spread out. STDEV calculates the standard deviation for a sample. A coefficient of variation, often abbreviated as CV, is a way to measure how spread out values are in a dataset relative to the mean.It is calculated as: CV = σ / μ. where: σ: The standard deviation of dataset μ: The mean of dataset In plain English, the coefficient of variation is simply the ratio between the standard deviation and the mean. We expect 68% of values to fall within one standard deviation of the mean, and 95% to fall within two standard deviations. We have studied mean deviation as a good measure of dispersion. Google Sheets Average Function [Advanced Tips and Tricks]. STANDARD DEVIATION Function in Google Sheets. I have data of jobs (A), their executions (B) and duration (C) in my Google Sheet. Active 1 year ago. We hear the term average or mean … All for free. Values outside two standard deviations are considered outliers. Browse other questions tagged google-sheets google-sheets-formula google-sheets-query google-query-language stdev or ask your own question. If you want to learn to use an advanced and powerful Google Sheets feature, check out How To Create, Edit and Refresh Pivot Tables in Google Sheets. If all the data values are the same, the mean (average) will be the same. One is categorized under math (SUBTOTAL function with function numbers 7 and 107) and another is categorized under database (DSTDEV). = the equal sign is how we begin any function in Google Sheets. Standard deviation (SD) measured the volatility or variability across a set of data. 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SUBTOTAL function with function numbers 7 107... | 2022-09-28 18:58:08 | {"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": 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": 0.5268121361732483, "perplexity": 1198.1374337584866}, "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-2022-40/segments/1664030335276.85/warc/CC-MAIN-20220928180732-20220928210732-00604.warc.gz"} |
https://math.stackexchange.com/questions/1540904/what-is-wrong-with-this-easy-inverse-laplace-transformation | # what is wrong with this easy inverse laplace transformation?
I am trying to understand the basics of easy inverse laplace transformations. On the first line is the "correct" answer. On the second line what i expected.
https://www.dropbox.com/s/j08inqvjw3v620i/IMAG1153.jpg?dl=0
Exactly the same scenario here:
https://www.dropbox.com/s/7chpoyjpgaqffvc/IMAG1154.jpg?dl=0
So it seems to me as if i am missing something. Could someone explain me why my expected solution is incorrect?
Using $\mathcal{L}_{t}\left[e^{at}\sin(\omega t)\right]_{(s)}=\frac{\omega}{(s-a)^2+\omega^2}$:
$$\mathcal{L}_{s}^{-1}\left[\frac{1}{s^2-6s+10}\right]_{(t)}=\mathcal{L}_{s}^{-1}\left[\frac{1}{(s-3)^2+1}\right]_{(t)}=\mathcal{L}_{s}^{-1}\left[\frac{1}{(s-3)^2+1^2}\right]_{(t)}=e^{3t}\sin(t)$$
Using $\mathcal{L}_{t}\left[e^{at}\cos(\omega t)\right]_{(s)}=\frac{s-a}{(s-a)^2+\omega^2}$:
$$\mathcal{L}_{s}^{-1}\left[\frac{s-7}{s^2-14s+73}\right]_{(t)}=\mathcal{L}_{s}^{-1}\left[\frac{s-7}{(s-7)^2+24}\right]_{(t)}=\mathcal{L}_{s}^{-1}\left[\frac{s-7}{(s-7)^2+\sqrt{24}}\right]_{(t)}=$$ $$\mathcal{L}_{s}^{-1}\left[\frac{s-7}{(s-7)^2+\left(2\sqrt{6}\right)^2}\right]_{(t)}=e^{7t}\cos\left(2\sqrt{6}t\right)$$
• how can this formula explain the example with " s-7" – privetDruzia Nov 22 '15 at 12:35
• @privetDruzia I'll edit my answer with your second problem! – Jan Nov 22 '15 at 12:38
• thx for the update but, The expected answer for the second problem is e^(7t) cos(5t). No roots – privetDruzia Nov 22 '15 at 13:30 | 2019-07-17 14:26:12 | {"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": 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": 0.706459641456604, "perplexity": 405.9061663750614}, "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-2019-30/segments/1563195525312.3/warc/CC-MAIN-20190717141631-20190717163631-00287.warc.gz"} |
https://blog.givewell.org/2021/10/08/initial-thoughts-on-malaria-vaccine-approval/ | # Initial thoughts on malaria vaccine approval
The World Health Organization (WHO) recently recommended the widespread use of the malaria vaccine RTS,S/AS011We’ll use “RTS,S” as shorthand in this post. for children. It provides an additional, effective tool to fight malaria. This is great news!
We’ve been following this vaccine’s development for years and, in the last few months, have been speaking with organizations involved in its development and potential wider rollout.
Our work on RTS,S (and other malaria vaccines) is ongoing, and we might significantly update our views in the near future. But because we’ve been following its progress, we’re sharing some initial thoughts.
## In brief
• This vaccine is a promising addition to the set of tools available to fight malaria, but it’s not a panacea. We expect long-lasting insecticide-treated nets (LLINs) and seasonal malaria chemoprevention (SMC)—interventions provided through two of the programs we currently recommend—to continue to be important in the fight against malaria in the near term.2
• The parts of the WHO news release that we have bolded indicate that RTS,S should be used with existing malaria control interventions:
• “WHO Director-General Dr Tedros Adhanom Ghebreyesus [said,] ‘Using this vaccine on top of existing tools to prevent malaria could save tens of thousands of young lives each year.'”
• “WHO recommends that in the context of comprehensive malaria control the RTS,S/AS01 malaria vaccine be used for the prevention of P. falciparum malaria in children living in regions with moderate to high transmission as defined by WHO.”
• Similarly, Gavi’s news release states: “The vaccine will be a complementary malaria control tool to be added to the core package of WHO-recommended measures for malaria prevention. This includes the routine use of insecticide-treated bed nets, indoor spraying with insecticides, malaria chemoprevention strategies, and the timely use of malaria testing and treatment.”
• Simple comparisons of potential costs and effectiveness of RTS,S and SMC suggest that SMC could be more cost-effective (see below). But there are lots of unknowns about RTS,S that could change that.
• We are actively looking into whether there are promising funding opportunities in this space.
• So:
• For the time being, this news does not affect our recommendations to donors. We do not know of a current option for individuals to donate to scale up RTS,S. We continue to believe that LLIN distribution and SMC are highly cost-effective, and some of the best giving opportunities available for donors who want to prevent deaths from malaria today.
• We aren’t sure whether we’ll recommend funding of RTS,S in the future. That will depend on how cost-effective we estimate particular opportunities to be, which depends on the answers to the open questions listed below.
• Cost. SMC costs about $7 per child fully covered per year,3This is the average estimated cost per child in the four countries where we currently recommend funding for SMC. See here in the current version of our cost-effectiveness analysis. so it would cost$28 to cover a child for four years. Costs for RTS,S are far less certain. Two studies that seem like reasonable starting points suggest costs per child of between $304See Sauboin et al. 2019, Table 2. The average cost across five countries for administering doses to children is ~$30. and $40.5See Winskill et al. 2017, Table 1, row “RTS,S.” • Effectiveness. Our rough estimate is that RTS,S would avert 36%6“Children were followed up for a median of 48 months (IQR 39–50) and young infants for 38 months (34–41) after dose 1. From month 0 until study end, compared with 9585 episodes of clinical malaria that met the primary case definition in children in the C3C [control] group, 6616 episodes occurred in the R3R [4 doses of RTS,S/AS01] group (VE 36·3%, 95% CI 31·8–40·5)…” RTS,S Clinical Trials Partnership 2015, “Findings” section of malaria cases over four years.7We use four years because that’s the time period used in the trials (see the quote in footnote 6 above), and it presents an easy comparison with SMC and other child health programs we support that have annual costs. By way of comparison, we estimate that annual SMC would avert 53% of cases over the same time period.8In particular, we assume SMC averts 75% of cases during peak transmission season and that 70% of malaria deaths occur during this period. Because we also assume a 1:1 ratio between cases and deaths averted, this is equivalent to averting ~53% of cases in a year. Taken at face value, these figures could imply that SMC is 1.5 to 2 times more cost-effective than RTS,S. But these naive comparisons aren’t conclusive.9These comparisons are not equivalent to our full cost-effectiveness analyses (CEAs). In complete CEAs, we use country-specific figures instead of averages, try to adjust for internal and external validity, and try to account for the counterfactual funding decisions of all contributors and the value of their funds (which we call leverage and funging adjustments). These adjustments can make decision-relevant differences to our funding recommendations. ## Open questions There are many open questions whose answers could have a big impact on the cost-effectiveness of a particular opportunity to support RTS,S. Some questions that seem important to us are: • What will it cost to deliver RTS,S? The cost estimates we’ve seen vary widely, and we expect delivery costs to vary from country to country. • Will RTS,S be delivered via routine immunization systems or targeted immediately before seasonal malaria transmission? Routine immunization systems might be less costly, but seasonal delivery could increase effectiveness. • How will RTS,S be layered with other malaria interventions in new implementation areas? We haven’t thoroughly investigated how the presence of LLINs and SMC in addition to RTS,S affect its efficacy in trial contexts, and we’re unsure how layering would affect the cost-effectiveness of delivering RTS,S in new areas. ## In conclusion We’re excited to have another effective tool in the fight against malaria! We’re working to understand whether there are cost-effective opportunities to support wider-scale implementation of RTS,S. Our research team is also keeping an eye on other potential malaria vaccines and malaria control strategies more generally. In the meantime, we anticipate continuing to recommend funding for LLINs and SMC. Notes ↑1 We’ll use “RTS,S” as shorthand in this post. The parts of the WHO news release that we have bolded indicate that RTS,S should be used with existing malaria control interventions: “WHO Director-General Dr Tedros Adhanom Ghebreyesus [said,] ‘Using this vaccine on top of existing tools to prevent malaria could save tens of thousands of young lives each year.'” “WHO recommends that in the context of comprehensive malaria control the RTS,S/AS01 malaria vaccine be used for the prevention of P. falciparum malaria in children living in regions with moderate to high transmission as defined by WHO.” Similarly, Gavi’s news release states: “The vaccine will be a complementary malaria control tool to be added to the core package of WHO-recommended measures for malaria prevention. This includes the routine use of insecticide-treated bed nets, indoor spraying with insecticides, malaria chemoprevention strategies, and the timely use of malaria testing and treatment.” This is the average estimated cost per child in the four countries where we currently recommend funding for SMC. See here in the current version of our cost-effectiveness analysis. See Sauboin et al. 2019, Table 2. The average cost across five countries for administering doses to children is ~$30. See Winskill et al. 2017, Table 1, row “RTS,S.” “Children were followed up for a median of 48 months (IQR 39–50) and young infants for 38 months (34–41) after dose 1. From month 0 until study end, compared with 9585 episodes of clinical malaria that met the primary case definition in children in the C3C [control] group, 6616 episodes occurred in the R3R [4 doses of RTS,S/AS01] group (VE 36·3%, 95% CI 31·8–40·5)…” RTS,S Clinical Trials Partnership 2015, “Findings” section We use four years because that’s the time period used in the trials (see the quote in footnote 6 above), and it presents an easy comparison with SMC and other child health programs we support that have annual costs. In particular, we assume SMC averts 75% of cases during peak transmission season and that 70% of malaria deaths occur during this period. Because we also assume a 1:1 ratio between cases and deaths averted, this is equivalent to averting ~53% of cases in a year. These comparisons are not equivalent to our full cost-effectiveness analyses (CEAs). In complete CEAs, we use country-specific figures instead of averages, try to adjust for internal and external validity, and try to account for the counterfactual funding decisions of all contributors and the value of their funds (which we call leverage and funging adjustments). These adjustments can make decision-relevant differences to our funding recommendations.
• Thecommexokid on October 9, 2021 at 2:17 am said:
Is it possible that in the future, the widespread distribution of this vaccine could decrease the cost-effectiveness of LLINs and SMC by a noticeable margin? (Naively, I’m imagining e.g. 1000 bednets save fewer counterfactual lives when lots of their recipients are also vaccinated, but I could also imagine mitigating factors that could perhaps negate that effect.)
• Julie (GiveWell) on October 12, 2021 at 11:41 am said:
Hi Thecommexokid,
Yes, it is possible that the widespread rollout of a malaria vaccine could decrease the cost-effectiveness of LLINs and SMC in the future.
As we get more information about how an RTS,S rollout might proceed, we would expect to consider how these interventions could interact with one another and what that means for their cost-effectiveness. In the near term (before it is clear how an RTS,S rollout would occur), we’re planning to incorporate lower expected malaria rates in some locations in our SMC cost-effectiveness analysis due to the expectation of higher LLIN coverage in the future than the past. We’re doing the same where we’re funding LLINs to be delivered in areas where SMC is expanding.
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