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https://test.biostars.org/p/191629/ | Biostar Beta. Not for public use.
vcf-consensus outputs sequence same as reference
1
Entering edit mode
4.4 years ago
seretnacho • 10
I downloaded a fasta file with a consensus sequence and a vcf file with the variant for certain individual (both files from 1000 genomes). I'm trying to get the sequence for that individual. To do that, i'm using vcf-consensus like this (let's say the consensus is master.fasta and the vcf is HG02291.vcf.gz):
tabix -p vcf HG02291.vcf.gz
cat master.fasta | vcf-consensus HG02291.vcf.gz > HG02291.fasta
After I do that, I compare HG02291.fasta with master.fasta and they are the exact same files (same headers and sequences), therefore vcf-consensus is not applying any changes to master.fasta. I've tried the same procedure with many other samples and it still does not work. What am I doing wrong?
1
Entering edit mode
3.7 years ago
liangjiao.xue • 100
United States
Here are two clues to consider:
1) Make sure the *vcf.gz file was zipped using bgzip. You could unzip them first and zip them again with bgzip from tabix
2) Make sure the chromosome IDs are same in VCF and fasta. Sometimes, it's "chr01" in one file, but "chr1" or "1" in another one.
0
Entering edit mode
2.5 years ago
i checked it twice but still showing problem> same output as reference fasta file
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Entering edit mode
Please use ADD COMMENT to answer to earlier reaction, as such this thread remains logically structured and easy to follow.
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Entering edit mode
Not a solution but I would recommend trying - a) rerunning with -s <sample_name> -i options b) running vcf-validator to check vcf
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Entering edit mode
i checked it twice but still showing problem> same output as reference fasta file | 2020-09-29 16:54:26 | {"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": 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": 0.20917849242687225, "perplexity": 10748.609252373846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400202418.22/warc/CC-MAIN-20200929154729-20200929184729-00456.warc.gz"} |
https://chemistry.stackexchange.com/questions/14276/butane-blowtorch-condensing-liquid-on-heating-surface | # Butane blowtorch condensing liquid on heating surface
I have a small Butane blowtorch, and use it to heat an Aluminium plate. The plate is thick so takes 20 seconds or so to really start heating up.
As soon as I apply the heat, droplets of some liquid start "condensing" on the surface of the metal around the general area of the flame.
The liquid is colorless and odorless and is at room temperature, note this happens when the metal is still at room temperature as it hasn't heated up much yet.
What is this liquid exactly and why/how does it form? I suspect it could be a $C_{4}H_{10} + O_{2}$ reactant but not sure. Thanks!
This is a guess - but I think it might be water formed as a byproduct of butane combustion precipitating on the plate:
$$\ce{2C4H10(g) + 13O2(g) -> 8CO2(g) + 10H2O(g)}$$
Aluminum has very high thermal conductivity, so it is possible that the plate is rapidly absorbing heat from the water vapor, causing it to condense. If this stops happening right around the point when the aluminum temperature reaches 100 C, that would be evidence to support this hypothesis.
• That sounds right to me then. I updated my question with a thought that the $C_{4}H_{10} + O_{2}$ reactant could involve water and that makes sense now, I'll try with a smaller piece of Al tomorrow to test the theory. Thanks! – baharini Jul 12 '14 at 1:58
• I added the reaction equation for you. If you try this, be sure to hold the thermometer right against the metal at the spot where the water is forming. That spot will heat up much faster than the rest of the plate. Also, make sure the thermometer is rated to around 600 C or you might break it accidentally. – thomij Jul 12 '14 at 2:12 | 2019-08-20 08:05:35 | {"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": 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": 0.6072215437889099, "perplexity": 718.0193555303977}, "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-2019-35/segments/1566027315258.34/warc/CC-MAIN-20190820070415-20190820092415-00557.warc.gz"} |
https://projecteuclid.org/euclid.bj/1432732038 | ## Bernoulli
• Bernoulli
• Volume 21, Number 3 (2015), 1824-1843.
### Extinction time for a random walk in a random environment
#### Abstract
We consider a random walk with death in $[-N,N]$ moving in a time dependent environment. The environment is a system of particles which describes a current flux from $N$ to $-N$. Its evolution is influenced by the presence of the random walk and in turn it affects the jump rates of the random walk in a neighborhood of the endpoints, determining also the rate for the random walk to die. We prove an upper bound (uniform in $N$) for the survival probability up to time $t$ which goes as $c\exp\{-bN^{-2}t\}$, with $c$ and $b$ positive constants.
#### Article information
Source
Bernoulli, Volume 21, Number 3 (2015), 1824-1843.
Dates
Revised: December 2013
First available in Project Euclid: 27 May 2015
https://projecteuclid.org/euclid.bj/1432732038
Digital Object Identifier
doi:10.3150/14-BEJ627
Mathematical Reviews number (MathSciNet)
MR3352062
Zentralblatt MATH identifier
1332.60137
#### Citation
De Masi, Anna; Presutti, Errico; Tsagkarogiannis, Dimitrios; Vares, Maria Eulalia. Extinction time for a random walk in a random environment. Bernoulli 21 (2015), no. 3, 1824--1843. doi:10.3150/14-BEJ627. https://projecteuclid.org/euclid.bj/1432732038
#### References
• [1] Blumenthal, R.M. and Getoor, R.K. (1968). Markov Processes and Potential Theory. New York: Academic Press.
• [2] De Masi, A. and Presutti, E. (1991). Mathematical Methods for Hydrodynamical Limits. Lectures Notes in Mathematics 1501. Berlin: Springer.
• [3] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2011). Current reservoirs in the simple exclusion process. J. Stat. Phys. 144 1151–1170.
• [4] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2012). Truncated correlations in the stirring process with births and deaths. Electron. J. Probab. 17 no. 6, 35 pp.
• [5] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2012). Non equilibrium stationary state for the symmetric simple exclusion with births and deaths. J. Stat. Phys. 146 519–528.
• [6] De Masi, A., Presutti, E., Tsagkarogiannis, D. and Vares, M.E. (2014). Exponential rate of convergence in current reservoirs. Bernoulli. To appear.
• [7] Ferrari, P., Presutti, E., Scacciatelli, E. and Vares, M.E. (1991). The symmetric simple exclusion process, I. Probability estimates. Stochastic Process. Appl. 39 89–105.
• [8] Karatzas, I. and Shreve, S.E. (1991). Brownian Motion and Stochastic Calculus. Graduate Texts in Mathematics 113. New York: Springer.
• [9] Lawler, L. and Limic, V. (2010). Random Walk: A modern Introduction. Cambridge University Studies in Advanced Mathematics 123. Cambridge: Cambridge Univ. Press.
• [10] Liggett, T. (1999). Stochastic Interacting Systems: Contact, Voter and Exclusion Processes. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 324. Berlin: Springer.
• [11] Liggett, T.M. (1985). Interacting Particle Systems. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences] 276. New York: Springer. | 2019-10-19 19:16:44 | {"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": 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": 0.6050815582275391, "perplexity": 3391.906951811357}, "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-2019-43/segments/1570986697439.41/warc/CC-MAIN-20191019164943-20191019192443-00554.warc.gz"} |
http://mathoverflow.net/questions/35461/interesting-complexity-classes-pr-subsetneq-c-subsetneq-r/35495 | # Interesting complexity classes $PR \subsetneq c \subsetneq R$
I'm working on a proof-checker that can verify termination proofs. The fundamental method it provides for constructing such proofs is to translate the program into primitive recursion. Basically, I provide a combinator $\rho$ typed as:
$\rho: \forall A,B:(A\rightarrow Nat \rightarrow A)\rightarrow (A \rightarrow B)\rightarrow A\rightarrow Nat \rightarrow B$
which, in the notation defined here, constructs $h$ given $f$ and $g$.
Although the term language contains a fixed-point combinator and is therefore Turing-complete, terms that use it have a "tentative" flag in their type that indicate this. The $\rho$ combinator and the fixed-point combinator are the only two language primitives that allow for recursion or looping of any sort (i.e., without either of these two combinators, all you've got is a finite-state machine). Therefore, all terms that are well-typed and non-tentatively typed are primitive recursive.
What I'm wondering is if there are any interesting complexity classes that you can build by starting with primitive-recursive constructions, and adding a finite number of other functions $Nat \rightarrow Nat$, each of which is in R but not in PR, and allowing composition with these functions. It's easy to come up with non-interesting examples of such classes, e.g. "primitive recursion plus the Ackermann function", but I'm looking for any that have sufficiently interesting properties that it would be worth adding the functions which characterize them as admitted axioms in the proof system.
-
Maybe I misunderstood something, but you seem to claim that membership in PR is decidable. It is not (see Rice’s theorem). I’m not sure, but it might be possible if your programs are written in some non-Turing-equivalent programming language. Could you clarify? – Antonio E. Porreca Aug 13 '10 at 10:59
...right, which is what I get for trying to ask coherent math questions at 5:30 AM. The system I'm working in is one based on Luo's Extended Calculus of Constructions. It contains a fixed-point combinator in addition to the above $\rho$ combinator and therefore is Turing-complete, but expressions that invoke it have their types flagged to indicate that they do. But, every well-typed term that is not so-flagged is in PR, because $\rho$ is the only other combinator that provides recursion. – dfranke Aug 13 '10 at 12:50
So, to rephrase my question without having to go into the gory details of the type calculus: can you get any interesting complexity classes by starting with a system that permits only primitive-recursive constructions, and augmenting it with certain $Nat \rightarrow Nat$ total functions that are not in PR. – dfranke Aug 13 '10 at 12:53
Could you please edit the original question according to your last comment? – Antonio E. Porreca Aug 13 '10 at 13:35
No problem. Done. – dfranke Aug 13 '10 at 14:03
First of all, it’s certainly possible to obtain some intermediate class by taking a language that only computes PR functions (say, an imperative programming language using only for loops) and adding any total computable but non PR function (e.g., Ackermann’s function). The resulting language L is non-universal, because it only computes total functions: you can still construct a computable but non-L-computable function by diagonalisation. However, L is clearly more powerful than the original language.
As for “interesting”, I guess it really depends on what you mean by that.
If “interesting” means “of practical use”, then one could answer that all computable functions of practical use are PR, since a non-PR function requires an amount of time to compute that is not, in turn, PR. Considering that time bounds such as 2n, 22n, 222n, …, are all PR, you see that there isn’t much hope to compute non-PR functions for large values of n.
If “interesting” means “logically interesting”, then I think the answer is “yes”. I’m somewhat familiar with Girard’s System F (also called “second order λ-calculus” or “polymorphic λ-calculus”), described for instance in Girard’s Proofs and Types (freely available here). The functions that can be computed in F are “exactly those which are provably total in [second order Peano arithmetic]” (page 123), and among these we have Ackermann’s function. There is an explicit λ-term for it on these slides (page 20).
If I recall correctly, the standard calculus of constructions includes System F and only computes total functions, so it also provides an example.
-
Sorry, I answered before your edit to the original question; now I see you already excluded the “PR + Ackermann” case. :-) – Antonio E. Porreca Aug 13 '10 at 14:08
Nifty. So the answer is that I don't even need $\rho$ as an axiom: the underlying system is already expressive enough to construct it and much more beyond it, and I need to finish wrapping my brain around the properties of that system. – dfranke Aug 13 '10 at 14:35
Alright, I get it now. What I was missing before was the essentialness of encoding natural numbers as iterator functions. That's where you get the "potential energy", so to speak, in order to compute complex functions without the need for a recursion operator. Thanks again. – dfranke Aug 15 '10 at 15:33 | 2015-05-30 05:02:38 | {"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": 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": 0.8294351696968079, "perplexity": 915.857849768393}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207930895.88/warc/CC-MAIN-20150521113210-00045-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/3056882/can-an-indefinite-integral-be-expressed-as-a-definite-integral-with-variable-bou | # Can an indefinite integral be expressed as a definite integral with variable bounds?
If I have a function $$f(t)$$, and an indefinite integral of this function, $$g(x) = \int f(t)\, dt$$, is there any way I can express $$g(x)$$ as a definite integral whose bounds depend on $$x$$?
I thought I saw somewhere that I could express it as $$g(x) = \int_a^x f(t)\, dt$$ but I don't know what $$a$$ is. Is this representation correct? Or is there a better way to express $$g$$?
• The second representation is correct. The first one doesn't represent $g$ as a function of $x$. Dec 30, 2018 at 14:50
No, not always.
In fact, the definite integral with variable bounds can be and is strictly more restrictive than the indefinite integral, in the most general case where both can be taken as sensibly existing to their fullest extent that we can say one defines the same kind of function as the other.
While it is true that if we have two functions $$F_1$$ and $$F_2$$ defined by definite integrals of the same function with different bounds, i.e.
$$F_1(x) := \int_{a_1}^{x} f(t)\ dt\ \mathrm{and}\ F_2(x) := \int_{a_2}^{x} f(t)\ dt$$
with $$a_1 \ne a_2$$, then we will have that $$F_1 - F_2$$ is a constant function, the range of possible such constants may be limited. A simple counterexample is to take $$f(x) := \sin(x)$$. Now the integral from any lower bound $$a$$ to $$x$$ is just $$\int_a^x \sin(t)\ dt = \cos(a) - \cos(x)$$, but here $$\cos(a)$$ - the "constant" of our integration - can only range in $$[-1, 1]$$ (and the difference of any two such "constants" only within $$[-2, 2]$$), but the constant in $$\int \sin(x)\ dx = -\cos(x) + C$$ can be any real number whatsoever, even one far outside this range, say assign $$C := \mbox{Graham's number}$$. Thus the integrals with variable bounds are not exhaustive of the full family of antiderivatives, which is what is represented by the indefinite integral, and if we are really pedantic should be truly written as the set it is: in "reality", not in the informalities of school calculus,
$$\int f(x)\ dx = \left\{ F(x) + C : C \in \mathbb{R} \right\}$$
where $$F'(x) = f(x)$$. Actually, if we want to be really correct - and in fact this is important but only in cases where the definite integral technically doesn't make sense as evaluable between arbitrary pairs of points - we should take
$$\int f(x)\ dx = \left\{ F(x) \in \mathbb{R}^\mathbb{R} : \mbox{F' exists and F'(x) = f(x)}\ \right\}$$.
• +1 I thought about going to this level of sophistication in my much shorter answer but decided the OP needed just the central points I made. Now they can see both views. Dec 30, 2018 at 15:12
• Very pedantic answer that is 100% valid and makes a distinction I had never thought about. +1 from me too. Heck, I'd give it a +5 if it was possible/allowed. Dec 30, 2018 at 15:14
• I'm having a hard time understanding this, as I'm new to Calculus, but it's ok. Dec 30, 2018 at 18:16
That fixed but arbitrary lower limit is essentially the "arbitrary constant" you use when finding antiderivatives, because $$g(x) = \int_a^x f(t)\, dt = \int_b^x f(t)\, dt + \int_a^b f(t)\, dt .$$ The second term in that sum is just a number.
The fundamental theorem of calculus says that both integrals with upper limit $$x$$ have derivative $$f$$ with respect to $$x$$.
The "indefinite integral" with no limits specified refers to the whole set of antiderivatives, not any particular one of them.
Edit in response to comment.
A loose common way to describe the indefinite integral is to say $$\int f(t)\, dt = F(x) + c$$ for a function $$F$$ whose derivative is $$f$$ and any real number $$c$$. That's really a set of functions, one for each value of $$c$$.
In my answer you can take $$F(x) = \int_b^x f(t)\, dt \quad \text{ and } \quad c = \int_a^b f(t)\, dt$$ to get the $$g(x)$$ in the question.
• I'm almost following what you're saying, but not quite. I understand that both integrals with upper limit $x$ have derivative $f$ with respect to $x$, but how does that make the constant integral the arbitrary constant? Dec 30, 2018 at 16:52
• @clabe45 See my edit. Dec 30, 2018 at 19:02
• Ahh that makes more sense now. Dec 31, 2018 at 2:17 | 2022-06-28 20:51:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 35, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.934647798538208, "perplexity": 211.67642711365176}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103617931.31/warc/CC-MAIN-20220628203615-20220628233615-00275.warc.gz"} |
https://brilliant.org/discussions/thread/cauchy-schwarz-is-too-useful/ | # Cauchy Schwarz is too useful...
The famous Cauchy Schwarz Inequality is a very very useful result in $\color{#D61F06}{\textbf{inequalities}}$
Simplest form of it is
$\displaystyle \left| ac+bd \right| \leq \sqrt{a^2+b^2} \sqrt{c^2+d^2}$,
and it's generalized form is
For any two sets of real numbers {$a_1,a_2,a_3,...,a_n$} and {$b_1,b_2,b_3,...,b_n$} , the following inequality holds :-
$\displaystyle \left| \sum_{j=1}^n a_jb_j \right| \leq \biggl( \sum_{j=1}^n a_j^2 \biggr)^{\frac{1}{2}} \biggl( \sum_{j=1}^n b_j^2 \biggr) ^{\frac{1}{2}}$
$\color{#3D99F6}{\textbf{What's important is that}}$
in solving problems, you have to chose your sets {$a_i$} and {$b_i$} $\color{#D61F06}{\textbf{S}} \color{#20A900}{\textbf{M}} \color{#3D99F6}{\textbf{A}}\color{#EC7300}{\textbf{R}}\color{#69047E}{\textbf{T}} \color{limegreen}{\textbf{L}}\color{#95D3FE}{\textbf{Y}}$ to reach your required answer...
For practice, here is one problem (Not made by me, but i changed the numericals than what I had seen). Try this, and it uses the result told above....
For $a,b,c,d \in \mathbb{R} ^+$, prove the following -
$\displaystyle \dfrac{1}{a} +\dfrac{9}{b}+\dfrac{25}{c}+\dfrac{49}{d} \geq \dfrac{256}{a+b+c+d}$
5 years, 10 months ago
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$\displaystyle (\sqrt{a}^{2}+\sqrt{b}^{2}+\sqrt{c}^{2}+\sqrt{d}^{2})((\frac{1}{\sqrt{a}})^{2}+(\frac{3}{\sqrt{b}})^{2}+(\frac{5}{\sqrt{c}})^{2}+(\frac{7}{\sqrt{d}})^{2}) \geq (\sqrt{a}\frac{1}{\sqrt{a}}+\sqrt{b}\frac{3}{\sqrt{b}}+\sqrt{c}\frac{5}{\sqrt{c}}+\sqrt{d}\frac{7}{\sqrt{d}})^{2}$
- 5 years, 10 months ago
lol it went through the space
Do you have any more problems for us to practice Cauchy Schwarz's inequality? Thank you ^__^
- 5 years, 10 months ago
Yes my friend, I will post some problems rather than notes now :D
Imgur
- 5 years, 10 months ago
Thank you meow!!! ^__^
- 5 years, 10 months ago
in general, we can just try to prove the Engel form of CS inequality. this will be proved automatically then.
- 5 years, 10 months ago | 2020-06-01 14:04:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 20, "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": 0.9905155301094055, "perplexity": 3498.6605036693472}, "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-2020-24/segments/1590347417746.33/warc/CC-MAIN-20200601113849-20200601143849-00169.warc.gz"} |
https://chbe241.github.io/Module-0-Introduction/MATH-152/Solving%20Sets%20of%20Linear%20Equations.html | # Solving Sets of Linear Equations¶
## Learning Objectives¶
By the end of this section you should be able to:
1. Solve a linear system using the substitution method.
2. Solve a linear system using the row reduction method.
3. Use Python to solve a linear system.
## Introduction¶
Being able to solve sets of linear equations is very important to a chemical engineer. There will be times where you have over 10 unknown variables and need to solve for them. This can be done by hand and can also be solved using a computer, more specifically, a programming language, such as python.
## By Hand¶
### Substitution Method for Solving Linear Systems¶
One of the simplest methods to solve a system of linear equations is the substitution method. The substitution method functions by substituting one of the variables for another. Here is an example:
$y = 2x + 4$
$3x + y = 9$
We can now substitute the y in the first equation into the second equation and solve.
$3x + (2x + 4) = 9$
$5x = 5$
$x = 1$
Finally, we can solve for y using x.
$y = 2(1) + 4$
$y = 6$
### Row Reduction Method for Solving Linear Systems¶
A more complicated but more practical method, for large systems, to solve large matrices is row reduction. Row reduction is done through matrix manipulation. There are four main rules to matrix manipulation:
1. Multiply a row by a non-zero constant.
2. Add one row to another.
3. Interchange between rows.
4. Add a multiple of one row to another.
We will be using these rules to help us solve a system of linear equations.
In this example, we must first convert the system of linear equations into a matrix. Then, we must row reduce the matrix until we get ones along the diagonal of the matrix and a lower triangle of zeros. Here is the system of equations:
$x + y - z = 5$
$2x + y + 3z = 2$
$4x - y + 2z = -1$
We must convert this system into an augmented matrix.
$\begin{split}\begin{vmatrix} 1 & 1 & -1 & | & 5 \\ 2 & 1 & 3 & | & 2 \\ 4 & -1 & 2 & | & -1 \end{vmatrix}\end{split}$
Now we shall row reduce the augmented matrix using the previous rules stated. First, we will $:raw-latex:\mathbf{R}_2 - 2:raw-latex:mathbf{R}_1$
$\begin{split}\begin{equation*} \begin{vmatrix} 1 & 1 & -1 & | & 5 \\ 0 & -1 & 5 & | & -8 \\ 4 & -1 & 2 & | & -1 \end{vmatrix} \end{equation*}\end{split}$
Second, we will $:raw-latex:\mathbf{R}_3 - 4:raw-latex:mathbf{R}_1$
$\begin{split}\begin{vmatrix} 1 & 1 & -1 & | & 5 \\ 0 & -1 & 5 & | & -8 \\ 0 & -5 & 6 & | & -21 \end{vmatrix}\end{split}$
Next, we will $-1 :raw-latex:\times :raw-latex:mathbf{R}_2$
$\begin{split}\begin{vmatrix} 1 & 1 & -1 & | & 5 \\ 0 & 1 & -5 & | & 8 \\ 0 & -5 & 6 & | & -21 \end{vmatrix}\end{split}$
After this, we will $:raw-latex:\mathbf{R}_3 + 5:raw-latex:mathbf{R}_2$
$\begin{split}\begin{vmatrix} 1 & 1 & -1 & | & 5 \\ 0 & 1 & -5 & | & 8 \\ 0 & 0 & -19 & | & 19 \end{vmatrix}\end{split}$
Finally we will $:raw-latex:\frac{\mathbf{R}_3}{-19}$
$\begin{split}\begin{vmatrix} 1 & 1 & -1 & | & 5 \\ 0 & 1 & -5 & | & 8 \\ 0 & 0 & 1 & | & -1 \end{vmatrix}\end{split}$
Since now we know
$z = -1$
we can solve for y which is
\begin{align}\begin{aligned}y = 3\\and finally solve for x which is\end{aligned}\end{align}
$x = 1$
## Using Python¶
As stated before, Python is a very powerful high-level programming language that can be used to compute tedious and complex arithmetic questions. Here is a simple example of how you can use Python to solve a system of linear equations.
Let’s say we have the same system of equations as shown above. Let’s solve it using Python!
$x + y - z = 5$
$2x + y + 3z = 2$
$4x - y + 2z = -1$
In [8]:
import numpy as py
from scipy.linalg import solve
A = [[1, 1, -1], [2, 1, 3], [4, -1, 2]]
b = [[5], [2], [-1]]
x = solve(A,b)
x
Out[8]:
array([[ 1.],
[ 3.],
[-1.]])
Here you can see what took multiple steps of matrix manipulation is easily solved in a few lines of code in Python.
Now you try using Python to solve this system of linear equations!
$x + 3y - z = 2$
$2x + 5 + 3z = 1$
$x - 3y + 2z = -4$
In [ ]: | 2023-02-07 05:10:57 | {"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": 2, "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": 0.6989792585372925, "perplexity": 434.78731097290773}, "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-2023-06/segments/1674764500384.17/warc/CC-MAIN-20230207035749-20230207065749-00437.warc.gz"} |
https://physics.stackexchange.com/questions/430833/speed-of-light-as-a-maximum-speed-limit | # Speed of Light As a Maximum Speed Limit [duplicate]
I know the speed of light problem has been beaten do death by hundreds of questions and answers, but I wanted to explore a new possibility and perhaps show an indication that light-speed as a constant is a man-made theoretical limit.
Would you please tell me if my musings are incorrect?
Now onto the subject at hand.
Suppose somewhere in the universe there are about 5000 different celestial bodies in a gargantuan solar system, each spread out the distance between the earth and the moon, each weighing approximately the size of 1 earth.
If by certain miracle, the orbits of those celestial bodies (planetoid objects) are arranged as such that 1) they are on the same plane, and b) all bodies line up almost perfectly with one another (at the time of the experiment).
It follows that if we launch a space vehicle, say a shuttle, and use gravity assist around those celestial bodies, we could theoretically increase the speed of that vehicle (provided that it doesn't rip itself apart from the inertia) 5000 times. As we have already achieved speeds of 150,000 mph using gravity assist in the past - wouldn't it follow that doing this 5000 times in sequence would eventually break the light speed barrier?
• You have successfully argued that if you assume Newton's laws are correct, then you can exceed the speed of light. If, instead, you assume that relativity is correct, then of course your argument, which uses Newton's laws, does not apply. – WillO Sep 26 '18 at 0:03
• I believe the answer here is quite relevant to this question: The one thing to keep in mind is that in order to perform a gravity-assist maneuver, you need to be able to enter a hyperbolic orbit around a given body that is moving relative to your destination. And, in order to be in such an orbit, there is a specific range of velocities for every object that you must have (dependent on mass of the object). ... – Alfred Centauri Sep 26 '18 at 0:19
• ... So the fastest you can get to by gravity-assist is much less than relativistic speeds because at relativistic speeds, you would not be able to enter into a proper hyperbolic orbit. – Alfred Centauri Sep 26 '18 at 0:19
• @AlfredCentauri: Your comments convince me that my earlier comment ("You have successfully argued...") was much too hasty. – WillO Sep 26 '18 at 2:29
• A superluminal speed is not something that hypothetically exists, but is prohibitively hard to achieve. Local superluminal speeds just don't exist in the hyperbolic geometry of our spacetime, so there simply is nothing to achieve. It is like going to the North of the North Pole. Such a direction simply doesn't exist. Every road from the North Pole goes South. – safesphere Sep 26 '18 at 8:21
Without seeing the math in relativity, it's hard to see where you're going wrong.
In relativity, the kinetic energy of an object is given by:
$$KE = (\gamma-1) m v^2$$
where $$v$$ is the object's velocity, $$m$$ is its mass, $$\gamma$$ is $$\sqrt{\frac{1}{1-v^2/c^2}}$$, and $$c$$ is the speed of light.
You can do gravitational assists to increase the body's kinetic energy, but the faster the body goes, the larger $$\gamma$$ gets, and the more energy you must put into the body to make it go even faster. You can never actually reach the speed of light: at that point $$\gamma$$ is infinite and you need an infinite amount of energy.
The gravitational assist scenario you describe just adds energy to the object. You can't add an infinite amount, so you can't reach the speed of light. You'll indeed go faster and faster, but while the first round of acceleration might add 5000mph, the second won't - it'll be less. This is because the formula for addition of velocities changes at relativistic speeds.
tl; dr: you can't break the light speed barrier with gravitational assists.
No, as you approach the speed of light relative to any of those bodies, that body's ability to accelerate you decreases according to the parameters of relativity.
Maybe a helpful analogy will be to think of yourself sailing and each of those bodies to be a 30mph gust of wind. The first gust you get a 2mph speed boost. But as you keep going you get less and less of a speed boost from each gust, with an eventual limit of 30 mph that you can never cross.
• That's not a good analogy since there is no such limit to a sailboat's speed. The current world speed record over a 500m course is 65.45 knots, by SailRocket, set in winds estimated to be about 25 knots. – D. Halsey Sep 25 '18 at 23:49
• @D.Halsey that's only possible with tacking. The analogy is fine if you exclude tacking (which most people don't know about anyway) – Señor O Sep 26 '18 at 0:40
• The analogy is only good going perfectly straight downwind. Tacking is something else altogether. – D. Halsey Sep 26 '18 at 1:57
It is important to understand that the speed of light is not a limit the way you think of it. The speed of light is c when measured locally, in vacuum. It is the same speed for EM waves and gravitational waves.
It is a common misconception to think that you can speed up to the speed of light. That is not correct. SR tells us three things:
1. anything with rest mass travels with a speed less then c, and will always do so
2. anything with no rest mass travels with the speed of light, and will always do so
3. anything that travels faster then the speed of light will always do so.
People usually do not even know about 3.
It is not that the speed of light is the maximum speed limit. It is just that anything that has rest mass will always travel slower then light (in vacuum when measured locally).
Now you are thinking about this the wrong way. You think you can speed up, but it is actually the other way around. The only speed is the speed of light. Light does not move in the time dimension, its speed in the time dimension is 0. Light does not experience time the way we do. If you want to experience time, you need to slow down in the spatial dimensions. The way to do that is to gain rest mass. If you gain rest mass, you will start moving in the time dimension, and start experiencing time the way we do.
In your case, your spaceship has rest mass. Let's assume it has unlimited fuel. As it starts to speed up, at about 0.8c, relativistic effects will become dominant, and ass the spaceship tries to speed up, it gains more mass. Having more rest mass will make it even harder for it to speed up. At this point, as it nears the speed of light, it would need infinite energy to speed up, so it becomes impossible.
Now there is an easy way to think about this. Anything in the universe has a speed relative to the speed of light (in vacuum when measured locally). Your spaceship has a speed of let's say 0.8c. When you do the slingshots, you just increase the speed to 0.81c etc. The increments in the speed of the spaceship are also relative to the speed of light. Even the lightest thing, the neutrino is traveling at a speed relative to the speed of light. As you go closer to the speed of light, the relative increases will need even more energy, and after a while, they will need infinite energy, so your spaceship will not speed up anymore, but will just gain more mass.
This form of use of relativistic mass is not in use in particle physics anymore, because it becomes confusing. In particle physics, they use rest mass, invariant mass.
I am using this example only for your question with the spaceship.
And I would like to mention a nice example for you. The way you describe it, imagine a neutrino traveling through space from far away, lets say passing by black holes, starts etc. Every time it passes by a star or black hole, it might do a slingshot, and speed up. By the time it gets to Earth, it would be possible to find a neutrino that has done slingshots the way you describe it and has sped up to speeds more then c. But we have not found any so far, and that is because even if the neutrino would do slingshots and speed up, it would still just speed up relative to the speed of light, and would always still travel slower then light. | 2021-06-21 08:21:47 | {"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": 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": 8, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6685870289802551, "perplexity": 259.0185835366461}, "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/1623488268274.66/warc/CC-MAIN-20210621055537-20210621085537-00426.warc.gz"} |
https://paul-mora.com/time%20series/python/DengAI-Predicting-Disease-Spread-STL-Forecasting-ARIMA-Box-Jenkins/ | # DengAI: Predicting Disease Spread — STL Forecasting/ ARIMA/ Box-Jenkins
Using the STL Forecasting Method with an ARIMA model, which is parameterized through the Box-Jenkins Method.
This post builds on our first blogpost which dealt with the initial data-transformation of the exogenous variables. Now we build a first model using only target variable itself. This is done by using the STL Forecasting method. This allows us to model time series which are affected by seasonal effects, by first removing the specified seasonality through a STL decomposition and then modeling the deseasonalized time series with a model of our choice — which is an Autoregressive Integrated Moving Average Model (ARIMA).
For those not familiar with the forecasting challenge, this competition deals with the prediction of dengue fever in two cities, or in the words from DrivenData themselves:
Your goal is to predict the total_cases label for each (city, year, weekofyear) in the test set. There are two cities, San Juan and Iquitos, with test data for each city spanning 5 and 3 years respectively. You will make one submission that contains predictions for both cities.
In order for better readability, this blogpost only shows and discusses graphs from the city San Juan. Further, the related code for every graph is found directly below each graph. Additionally the entire code (for both cities) is found at the bottom of this blogpost, or on GitHub.
In the center of our prediction approach is the aforementioned so-called STL method. STL stands for Seasonal-Trend decomposition method using LOESS. This method decomposes a time series into three components, namely its trend, its seasonality and its residuals. LOESS stands for locally estimated scatterplot smoothing and is extracting smooth estimates of the three aforementioned components.
## Structural Changes
Looking at the time series of dengue fever in San Juan, several things are worth pointing out. For once there is a strong seasonal component visible. In the first half of the data it looks like the seasonal pattern is yearly (52 weeks), whereas in the second half of the time series the pattern somewhat switched to a two-yearly pattern. The other predominant characteristic of the time series are the few but stark spikes. Especially in the first half of the time series we see two outbursts in the target variable of a magnitude which is unparalleled in the second half.
def plot_cutoff_comparison(time_series, cutoff, city_name):
first_half = time_series[:cutoff]
first_half.name = "First Half"
second_half = time_series[cutoff:]
second_half.name = "Second Half"
fig, axs = plt.subplots(nrows=2, ncols=1, figsize=(10, 10))
axs[0].plot(time_series, label="Complete Series")
axs[0].axvline(cutoff, color="r", linestyle="--", label="Cutoff")
axs[1].plot(second_half,
label="Series from observation {} onwards".format(cutoff))
axs = axs.ravel()
for axes in axs.ravel():
axes.legend(prop={"size": 16}, loc="upper right")
axes.tick_params(axis="both", labelsize=16)
fig.tight_layout()
fig.savefig(r"{}/{}/{}_cutoff_plot.png".format(output_path,
approach_method,
city_name),
bbox_inches="tight")
return first_half, second_half
At this point it is important to stress the higher importance of newer data compared to older data within time series problems. Normally within data science projects, we are very always interested in gathering more data, as this would in general increase the robustness and accuracy of our model. Though, when it comes to time series data, we have to weight the importance of new data on when exactly the data was sampled. If we are for example interested in predicting the stock price for a certain company, the company’s financial statements of the last couple of years, are undoubtely more important than the company’s performance 100 years ago. Why is that so? Because it could be possible that underlying data generating process changed over time. That would imply that older data is not giving us any information about future data and is therefore not only incorrect, but could also hurt our model performance.
The three charts below visualize the differences between the first and second half of the time series.
def difference_in_distribution(series1, series2, city_name):
# CDF
def ecdf(data):
""" Compute ECDF """
x = np.sort(data)
n = x.size
y = np.arange(1, n+1) / n
return x, y
test_results = pd.DataFrame(index=["KS 2 Sample Test", "ANOVA"],
columns=["Statistic", "P Value"])
test_results.iloc[0, :] = st.ks_2samp(series1, series2)
test_results.iloc[1, :] = st.f_oneway(series1, series2)
fig, axs = plt.subplots(ncols=3, figsize=(40, 15))
# Time series
axs[0].plot(np.arange(len(series1)), series1, color="b",
label=series1.name)
axs[0].plot(np.arange(len(series2)), series2, color="r",
label=series2.name)
axs[0].set_title("Level Data", fontsize=40)
axs[0].legend(prop={"size": 30})
# Boxplots
axs[1].boxplot([series1, series2])
axs[1].set_title("Boxplots", fontsize=40)
axs[1].set_xticklabels([series1.name, series2.name],
fontsize=30,
rotation=45)
x, y = ecdf(series1)
axs[2].scatter(x, y, color="b", label=series1.name)
x, y = ecdf(series2)
axs[2].set_title("Empirical Cumulative Distribution Function",
fontsize=40)
axs[2].scatter(x, y, color="r", label=series2.name)
axs[2].legend(prop={"size": 30})
for ax in axs.ravel():
ax.tick_params(axis="both", labelsize=30)
fig.tight_layout()
fig.savefig(r"{}/{}/{}_cutoff_plot.png".format(output_path,
approach_method,
city_name),
bbox_inches="tight")
return test_results
Next to individual visual judgement, there are also several tests to formally check whether the distribution of the data is different, namely the Chow Test, the Kolmogrov Smirnov 2-Sample test, and an Analysis of Variance (ANOVA). For the latter two we find the test results between the first half and the second half of the data below.
The significance test results confirm our initial hypothesis of a structural difference in the data generating process between the first and second half of the data.
Though it is important to note that only because the data is found to be different, we do not necessarily have to discard all observations from the first half. Instead we will winsorize and use the seasonality found in the second half of the data.
## Winsorizing
Winsorizing presents a valid alternative compared to simply dropping the data. This method is used when instead of throwing out potential outliers, we would like to keep them but alter their magnitude. This is done by specifying by much a potential outlier should be adjusted. A winsorizing value of X% for example means that all values which are higher than the (100-X) percentile are set to the value of the (100-X) percentile. A more thorough explanation of the process can be found here.
The chart below shows the impact of winsorizing our data to the 2.5% level (a value that is chosen to equalize the outbursts in the first half of the data). When looking at the scale of the y-axis the effect of the measure becomes apparent, the magnitude of the outliers has dampened.
def winsorizer(time_series, level, city_name):
decimal_level = level / 100
wind_series = st.mstats.winsorize(time_series, limits=[0, decimal_level])
fig, axs = plt.subplots(nrows=2, ncols=1, figsize=(10, 10))
axs[0].plot(time_series, label="Original Time Series")
axs[1].plot(wind_series,
label="Winsorized at the {}% level".format(level))
axs = axs.ravel()
for axes in axs.ravel():
axes.legend(prop={"size": 16}, loc="upper right")
axes.tick_params(axis="both", labelsize=16)
fig.tight_layout()
fig.savefig(r"{}/{}/{}_win.png".format(output_path,
approach_method,
city_name),
bbox_inches="tight")
return wind_series
Of course this does measure does not come without any risks. Winsorizing, or outlier altering in general, implies that we do not expect to see levels as high as the altered values. Given that the second half of the time series, which spans eight years of data, does not exhibit outbursts in any comparable magnitude, we feel confident to proceed with the winsorization.
## Seasonality Detection
When using a STL decomposition, we need to specify which periodicity the seasonality is supposed to have. In order to find that out, we can either specify an appropriate time index and let the frequency be inferred automatically, or we can look at the autocorrelation function (ACF) of the time series. The ACF shows us the correlation between time series observations and observations with various lagged version of the very same time series. A high autocorrelation with the first lag would for example describe a process where the value today is very much alike the value yesterday. Following the same logic, it is also possible to spot a potential seasonality in the data. Namely, by finding a timely reoccurring amplitude in the ACF of a time series.
Below we can see in the upper plot the actual target variable, namely the number of Dengue Fever cases in San Juan. The plot underneath shows the discussed autocorrelation function of that time series. The ACF plot indicates that initially (up until lag 400) we find a yearly pattern. That means that the amplitude is occurring at multiple of 52 (52 weeks equal a year). Beyond lag 400 we find a different pattern though. Something that resembles rather a two-year seasonality. Given the aforementioned higher importance of more recent data, we will therefore continue with a 104 week (or 2 year) seasonality.
def acf_plots(y, max_lags, city_name):
fig, axs = plt.subplots(nrows=2, figsize=(20, 10))
sm.graphics.tsa.plot_acf(y.values.squeeze(),
lags=max_lags, ax=axs[1], missing="drop")
axs[1].set_title("Autocorrelation Plot", fontsize=18)
axs[0].set_title("Original Time Series", fontsize=18)
axs[0].plot(y)
for ax in axs.ravel():
ax.tick_params(axis="both", labelsize=16)
fig.tight_layout()
fig.savefig(r"{}/{}/{}_raw_acf.png".format(output_path, # Individual output path
approach_method, # Individual folder
city_name),
bbox_inches="tight")
## Autoregressive Integrated Moving Average Model
Next in line is the parameterization of the ARIMA model. For that we have to remember that the STL Forecasting function is applying the prediction model on the deasonalized time series data, and not on the raw data. We therefore have to deseasonalize our data before examining it. This is by using the STL decomposition, specifying aforementioned 14 as our period.
In the image below we can see the original series at the very top, followed by the seasonality and the difference between the original series and the seasonality. It is the latter time series we will use to identify the appropriate paramerterization of the ARIMA model.
def stl_decomposing(y, period, city_name):
time_series = y.copy()
res = STL(time_series, period=period, robust=True).fit()
fig, axs = plt.subplots(3, 1, figsize=(30, 20))
time_series.plot(ax=axs[0], label="Original Series")
time_series_wo_season = time_series - res.seasonal
res.seasonal.plot(ax=axs[1])
time_series_wo_season.plot(ax=axs[2])
axs[0].set_title("Original Series", fontsize=30)
axs[1].set_title("Seasonality", fontsize=30)
axs[2].set_title("Original Series Minus Seasonality", fontsize=30)
for ax in axs.ravel():
ax.tick_params(axis="both", labelsize=25)
fig.tight_layout()
fig.savefig(r"{}/{}/{}_decomposed_acf.png".format(output_path,
approach_method,
city_name),
bbox_inches="tight")
return time_series_wo_season
Given that the deasonalized time series does not suffer from any kind of non-stationarity, we do not have to worry about the number of integration within the ARIMA model, since none is necessary. The bigger question is how many autoregressive (AR) and moving averages (MA) lags are necessary. In practice the lag length of the AR and MA processes are denoted by the letter p and q respectively.
One well-known approach for specifying the optimal lag length of AR and MA processes is the so-called Box-Jenkins method. This method involves three steps:
1. After ensuring stationarity, use plots of the autocorrelation function (ACF) and the partial autocorrelation function (PACF) to make an initial guess of the lag length for the AR and MA process
2. Use the parameters gauged from the first step and specify a model
3. Lastly check the residuals of the fitted model for serial correlation (independence of each other) and for stationarity. The former can be achieved using a Ljung-Box test. If the specified model fails these tests, go back to step 2 and use slightly different parameter for p and/or q
Following the three steps outlined above, we start by plotting the autocorrelation function and the partial autocorrelation function. These can be seen in the graph below.
A partial autocorrelation is the amount of correlation between a variable and a lag of itself that is not explained by correlations at all lower-order-lags. That is done by regressing the time series with all n-1 lags and therefore controlling for them when assesing the n-th partial correlation. It contrasts with the autocorrelation function, which does not control for other lags.
def acf_pacf_plots(time_series, nlags, city_name):
# Plotting results
no_nan_time_series = time_series.dropna()
fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(20, 10), sharey=True)
sm.graphics.tsa.plot_acf(no_nan_time_series,
lags=nlags, fft=True, ax=axs[0])
sm.graphics.tsa.plot_pacf(no_nan_time_series,
lags=nlags, ax=axs[1])
for ax, title in zip(axs.ravel(), ["ACF", "PACF"]):
ax.tick_params(axis="both", labelsize=16)
ax.set_title(title, fontsize=18)
ax.set_title(title, fontsize=18)
fig.tight_layout()
fig.savefig(r"{}/{}/{}_acf_pacf.png".format(output_path,
approach_method,
city_name),
bbox_inches="tight")
The way of how to identify the appropriate lag length from the two plots above is summarized in the following table:
From that we can see that the appropriate lag length of the AR process is the number of initial non-zero lags in the partial autocorrelation function. Looking at the plot above, we can see that this should be around 6, given that the seventh lag lies within the boundaries of the 95% confidence interval and is therefore not significant. It is to be noted that the very first vertical line represent the partial autocorrelation with itself and should be not counted.
The number of MA processes is taken by counting the number of initial non-zero terms within the autocorrelation function. In our example, we find rather many, namely around 20. It is important to note that the exact number is not too important as will empirically check a multitude of models before deciding for one.
It is important to stress that the Box-Jenkins method builds on the parsimony principal. Quoting the Oxford econometrician Kevin Sheppard:
Parsimony is a property of a model where the specification with the fewest parameters capable of capturing the dynamics of a time series is preferred to other representations equally capable of capturing the same dynamics.
That means that if we find multiple models which meet our conditions regarding serial correlation, we will choose the model with the smallest amount of lags. Therefore we check the results of the Ljung-Box serial correlation test not only for the lag lengths 6 and 20 (which is already way too many), but for all smaller lengths as well. The p-values of the Ljung-Box tests are captured in the image below.
It is visible that nearly all model parameterization find a significant Ljung-Box test, signaling serious serial correlation. Luckily, we also find some model parameterizations with non-significant serial correlation within the residuals. Applying the parsimony principle leads us then to take the AR-2 MA-2 model.
def box_jenkins_lb_finder(y, p, q, year_in_weeks, city_name):
lb_df = pd.DataFrame(columns=["MA_{}".format(x) for x in range(1, q)],
index=["AR_{}".format(x) for x in range(1, p)])
for i in range(1, p+1):
for j in range(1, q+1):
stlf = STLForecast(y, ARIMA, period=year_in_weeks, robust=True,
model_kwargs=dict(order=(i, 0, j), trend="c"))
stlf_res = stlf.fit()
results_as_html = stlf_res.summary().tables[2].as_html()
lb_df.loc["AR_{}".format(i),
"MA_{}".format(j)] = results_df.iloc[0, 0]
# Create heatmaps out of all dataframes
fig, axs = plt.subplots(figsize=(20, 10))
sns.heatmap(lb_df.astype(float), annot=True, fmt=".2f",
ax=axs, annot_kws={"size": 18},
vmin=np.min(lb_df.values),
vmax=np.percentile(lb_df.values, 25))
axs.set_xlabel("MA Terms", fontsize=20)
axs.set_ylabel("AR Terms", fontsize=20)
axs.tick_params(axis="both", labelsize=20)
fig.tight_layout()
fig.savefig(r"{}/{}/{}_lb_comp.png".format(output_path, approach_method,
city_name),
bbox_inches="tight")
## In-Sample Check and Forecasting
Finally it is time to look at some predictions from our model. It is important to note that in this forecasting challenge we are not interested in one-step ahead predictions, but a 260-step ahead forecast. In order to validate our performance we therefore need to specify a dynamic prediction method. That means that the model does not treat prior values as realized from a defined point onward, but is aware that these are predictions themselves.The graph below shows predictions of 260 values with the aforementioned dynamic forecasting method. The mean absolute error of 15.7 still represents an in-sample value and can therefore not be taken as representative for out-of-sample performance.
After applying the same steps for the other city in our data, we can then hand in our prediction results. From the picture below we can see that our predictions are far away from being competitive. Though, it has to be said that this performance, which is more or less equally good compared to the benchmark model provided by DrivenData, did not make use of any exogenous variable, meaning that there is still a lot improvement potential.
Categories:
Updated: | 2022-09-27 07:55:32 | {"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": 0.5802816152572632, "perplexity": 1520.8496074713933}, "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/1664030334992.20/warc/CC-MAIN-20220927064738-20220927094738-00409.warc.gz"} |
https://studyfinance.com/working-capital-ratio/ | # Working Capital Ratio
## Did you know?
The working capital ratio is a liquidity tool that gauges a company’s ability to settle its current debts with its current assets. It is sometimes referred to as the current ratio. The working capital ratio is crucial to creditors because it is an indicator of a company’s liquidity.
Creditors prefer current liabilities to be paid with current cash. This could include cash equivalents and marketable securities as well. This is because these assets are easily convertible to cash, unlike fixed assets. Faster cash conversion means more timely debt payments.
This metric is called the working capital ratio because it comes from the working capital calculation. Companies whose current assets are greater than their current liabilities have sufficient capital to sustain their everyday operations. In short, they have enough working capital. The calculation is essentially a comparison between current assets and current liabilities.
## Working Capital Ratio Formula
$Working\: Capital\: Ratio = \dfrac{Current\: Assets}{Current\: Liabilities}$
Current accounts and current liabilities are entered into a company’s balance sheet separately. This presentation makes it easier for investors and creditors to analyze a business. In financial statements, current assets and current liabilities always come before long-term assets and long-term liabilities. This calculation shows the portion of a company’s current assets that will cover its current liabilities.
You can see how changes to a company’s current liabilities and current assets directly affect the ratio. Specifically, a company’s working capital ratio is directly proportional to its current assets but inversely proportional to its current liabilities.
Because this ratio measures assets as a portion of liabilities, a higher ratio is better for companies, investors and creditors. A ratio of 1 is typically considered the middle ground. While it’s not technically high-risk, it is not very safe either. It means the firm would have to dispose of all current assets before it can pay off its current liabilities.
A ratio below 1 is significantly risky for creditors and investors. It proves the company isn’t operating efficiently, meaning, it cannot settle its obligations properly. A ratio below than 1 is always negative and is aptly called negative working capital. On the other hand, a ratio higher than 1 shows the company is capable of paying all its liabilities, while still keeping some current assets. Hence, it is called positive working capital.
## Working Capital Ratio Example
By the end of 2019, CREV Retail Co had total current assets at $9.97 million and total current liabilities at$9.06 million. What is the company’s working capital ratio?
Let’s break it down to identify the meaning and value of the different variables in this problem.
• Current assets: 9.97m
• Current liabilities: 9.06m
We can now apply the values to our variables and calculate the working capital ratio:
$Working\: Capital\: Ratio = \dfrac{9{,}970{,}000}{9{,}060{,}000} = 1.1$
In this case, CREV Retail Co would have a working capital ratio of 1.1.
CREV Retail Co’s WCR is above 1 which means it is clearly capable of paying its debt. While a ratio of 1 is considered safe, it is still not safe enough because this means the company will have to sell all its assets before it can pay its debt. In this example, the ratio is slightly higher than 1 which means they would not have to sell all of their assets to pay off debt. If the company applies for a new loan, it will have to pay off some of its debt in order to improve its working capital ratio and lower its risk to creditors.
## Working Capital Ratio Analysis
Because the working capital ratio has two key moving components – assets and liabilities – it important to study how they operate together.
It is also important to understand the difference between positive working capital and negative working capital. The former is always preferable as it means the business is likely to cover its short-term liabilities with its liquid assets. At the same time, this means the business can continue growing without having to incur additional debt or issue new stocks.
Conversely, a company with a negative working capital means the business lacks liquid assets to cover its current or short-term liabilities, usually due to poor asset management and cash flow. In case a company has insufficient cash to cover its bills when they are due, it will have to loan money, thereby increasing its short-term debt.
In any case, negative working capital is always a sign of a company whose finances are not doing well, but not necessarily to the extent it is going bankrupt. A lot of big companies usually have negative working capital and are fine. This is possible when inventory is so fast they can still pay their short-term liabilities. Such companies – usually big box stores and similar businesses – get their inventory from suppliers and sell the products immediately away for a low margin.
Working capital management demands coordinated actions and strategies for optimal inventory and accounts receivables as one part of the company’s liquidity. For instance, even if a company has a net working capital of 1.8, it can still have a slow inventory turnover or slow collection of receivables. Both potential issues can lead to delays in the availability of actual liquid assets.
On the flip side, when companies depend on credit lines and loans, it can lower their ratios. This is because they obtain assets from creditors only they need to settle outstanding liabilities, reducing net working capital. In the end, the value of a working capital ratio is only as good as the company’s accounts receivables, credit, and inventory management.
## Working Capital Ratio Conclusion
• The working capital ratio is a metric that reflects a company’s ability to pay off its debts with its assets.
• This formula requires two variables: Current Assets and Current, Liabilities.
• The working capital ratio is expressed as a number.
• A higher working capital ratio shows a company has more ability to pay its debt, making it less risky to creditors and investors.
• A working capital ratio of 1 indicates that a company will have to sell all its assets to be able to pay its debt.
• The working capital ratio is one of the many metrics that can be used to assess a company’s potential for insolvency.
## Working Capital Ratio Calculator
You can use the working capital ratio calculator below to quickly determine how easily a company can repay its debt with its assets by entering the required numbers. | 2020-11-29 19:21:25 | {"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": 2, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35279375314712524, "perplexity": 2221.9002044977688}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141202590.44/warc/CC-MAIN-20201129184455-20201129214455-00208.warc.gz"} |
https://math.temple.edu/more/toolbox/join/ | # Join the Web Site
For faculty, your bio should be 300 or so words (see the bio's under People) with selected pubs if applicable (e.g. your 3 favorite papers). For pubs, use an ordered list (see Creating Your Own Web Page under Toolbox). Separate paragraphs with blank lines. Blank lines will automatically be replaced by <p> tags.
You may insert HTML or $\LaTeX$ into the bio (click on Toolbox above for HTML or $\LaTeX$ instructions).
This would be a rectangular photo of you (preferably smiling) taken with a reasonably new phone. Crop the photo image so that its height is no more than 120% of its width, otherwise the web site image may be distorted. The photo should include your face, neck, and shoulders, not your whole body. Have a friend take a picture of you outdoors on a sunny day and e-mail it to yourself, then upload.
Your personal or course web site should be entered, it's https://math.temple.edu/~username or similar.
The web site automatically adds your faculty title. If you have an additional title (e.g. your faculty title is "Instructor" but you are also "Director of XYZ"), enter it below.
Once you hit "Submit", the changes are immediate and may be viewed on the math web site.
Enter Temple E-mail: * | 2017-02-20 01:41:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.20854006707668304, "perplexity": 4515.421994722722}, "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-2017-09/segments/1487501170380.12/warc/CC-MAIN-20170219104610-00295-ip-10-171-10-108.ec2.internal.warc.gz"} |
https://www.mysciencework.com/publication/show/cluster-variables-certain-double-bruhat-cells-type-u-e-monomial-realizations-crystal-bases-type-50b0f34a | # Cluster Variables on Certain Double Bruhat Cells of Type $(u,e)$ and Monomial Realizations of Crystal Bases of Type A
Authors
Type
Published Article
Publication Date
Apr 23, 2015
Submission Date
Sep 30, 2014
Identifiers
DOI: 10.3842/SIGMA.2015.033
Source
arXiv
Let $G$ be a simply connected simple algebraic group over $\mathbb{C}$, $B$ and $B_-$ be two opposite Borel subgroups in $G$ and $W$ be the Weyl group. For $u$, $v\in W$, it is known that the coordinate ring ${\mathbb C}[G^{u,v}]$ of the double Bruhat cell $G^{u,v}=BuB\cap B_-vB_-$ is isomorphic to an upper cluster algebra $\bar{{\mathcal A}}({\bf i})_{{\mathbb C}}$ and the generalized minors $\{\Delta(k;{\bf i})\}$ are the cluster variables belonging to a given initial seed in ${\mathbb C}[G^{u,v}]$ [Berenstein A., Fomin S., Zelevinsky A., Duke Math. J. 126 (2005), 1-52, math.RT/0305434]. In the case $G={\rm SL}_{r+1}({\mathbb C})$, $v=e$ and some special $u\in W$, we shall describe the generalized minors $\{\Delta(k;{\bf i})\}$ as summations of monomial realizations of certain Demazure crystals. | 2018-10-21 23:34:36 | {"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": 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": 0.7892025709152222, "perplexity": 290.40451076495435}, "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-2018-43/segments/1539583514437.69/warc/CC-MAIN-20181021224001-20181022005501-00244.warc.gz"} |
http://proiscorp.com/bts-bon-duqc/aaa89c-centroid-of-a-right-trapezoid | The figure shows a trapezoid broken into a triangle and a rectangle. Solution: Let a and b be the parallel sides of a trapezoid. Example. Go to your Tickets dashboard to see if you won! Question: Find the centroid of a trapezium of height 5 cm whose parallel sides are 6 cm and 8 cm. Click HERE to see a step-by-step construction of the centroidal mean in a trapezoid. Problem 238 The beam AB in Fig. Pro Subscription, JEE Let a and b be the parallel sides of a trapezoid. The sides that are parallel to each other are called bases. It is to find the centre of the trapezoid. Calculate the magnitude and position of the resultant load. The point where the diagonals of the square intersect each other is the centroid of the square. Please note that the centroid in a right triangle is at a distance one third the width of the triangle as measured from its base. All a student needs to do is follow the instructions line by line and practice example problems. Vedantu has provided a simple explanation to calculate the centroid of a trapezium. Now, trapezoid is interesting. In a trapezoid with bases of lengths "a" and "b," the centroidal mean, "g," is the length of the segment that is parallel to the bases and that also passes through the centroid of area of the trapezoid. Diagonal is a line from one vertices to another that is non adjacent. We divide the complex shape into rectangles and find bar(x) (the x-coordinate of the centroid) and bar(y) (the y-coordinate of the centroid) by taking moments about the y-and x-coordinates respectively. In the figures, the centroid is marked as point C. Its position can be determined through the two coordinates x c and y c, in respect to the displayed, in every case, Cartesian system of axes x,y.General formulas for the centroid of any area are provided in the section that follows the table. Using the centroid of trapezoid formula, A quadrilateral is a four-sided shape with only one pair of parallel sides and non-parallel sides are equal in length. The point where the diagonals of the square intersect each other is the centroid of the square. The centroid of a trapezoid lies between the two bases. Cyclic quadrilateral: the four vertices lie on a circumscribed circle. The lengths of its parallel sides are, Find the centroid of a trapezium of height, Vedantu The top section is a triangle, similar to the original, with a similarity ratio of 2/3. What is the location of F R, i.e., the distance d? Trapezoid (a two-dimensional figure) is a quadrilateral that has a pair of parallel opposite sides. Centroid of a Square. Centroid of A Right Angle Triangle. Trapezoid Definition. The perimeter and the area of an isosceles Trapezoid is given as – P-238 supports a load which varies an intensity of 220 N/m to 890 N/m. Any isosceles trapezoid may be formed by sectioning an isosceles triangle along a line parallel to its base. The Formula for Centroid of a Trapezoid. In the figures, the centroid is marked as point C. Its position can be determined through the two coordinates x c and y c, in respect to the displayed, in every case, Cartesian system of axes x,y.General formulas for the centroid of any area are provided in the section that follows the table. Repeaters, Vedantu If the parallel sides of trapezoid measures 8 cm, 10 cm and the height 9 cm, then find its centroid. Geometrically it is between the two bases or in other words lies on the median of trapezoid. What is the formula to find the centroid of a trapezium? June's. Your email address will not be published. Centroid of A Right Angle Triangle. The centroid lies between the parallel bases. The below online Centroid of a Trapezoid Calculator calculates the center of mass of trapezoid. The trapezium OABC is placed such that the origin coincides with one of its vertices. They form the same angle with this line. Problem 238 The beam AB in Fig. The above isosceles trapezoid property calculator is based on the provided equations and does not account for all mathematical limitations. The lengths of its parallel sides are AB = a and OC = b and its height is h. The coordinates of the centroid of the trapezium are given by the following formula. A trapezoid is a quadrilateral with two sides parallel. Here is an online geometry calculator to calculate the centroid of a right angled triangle. Here, the x‐centroid is found by requiring the moment of the weight of the pieces to equal the moment of the total weight. Let's assume that angle φ 1 is given. Trapezoids are called Trapezium in the UK. Students can be assured that the formula is accurate as it is provided by top experts at Vedantu. The centroid of a right angle triangle is the point of intersection of three medians, drawn from the vertices of the triangle to the midpoint of the opposite sides. mass (and weight) per unit length is taken as constant. Which website explains the centroid of a trapezoid formula clearly with examples? Trapezoid is a quadrilateral with two parallel sides and centroid of a trapezoid lies between two bases. The other sides are called legs. The centroid of a trapezoid can be found out by using the formula given below: Important Questions for CBSE Class 10 Maths Chapter 9 - Some Applications of Trigonometry. A right trapezoid is a trapezoid having two right angles.The area of the trapezoid is(1)(2)(3)The geometric centroid lies on the median between the base and top, and if the lower left-hand corner of the trapezoid is at the original, lies at(4)(5)(6)(cf. Let’s look at an example to see how to use this formula. Types of Trapezoids Right Trapezoid A right trapezoid has two right angles. Trapezoid is a convex quadrilateral with only one pair of parallel sides. So this is definitely also a parallelogram. A) 2 m B) 3 m C) 4 m D) 5 m E) 6 m 2. The heights of the legs are identical with each other leg. The perimeter and the area of an isosceles Trapezoid is given as – The y‐centroid is found by the composite object (line) theorem. Finding the lengths of the non parallel sides c and d, can be done if one interior angle of the trapezoid is known. Calculate the magnitude and position of the resultant load. 1 1 Centroid for BCSR, M 2 = ( (c b), w) The centroid of the trapezoid is considered as a point of 2 2 balance for the trapezoid. 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If F 1 = 1 N, x 1 = 1 m, F 2 = 2 N and x Trapezoid (a two-dimensional figure) is a quadrilateral that has a pair of parallel opposite sides. Consider the following trapezium in which. The center of gravity of a trapezoid can be estimated by dividing the trapezoid in two triangles. The center of gravity is the intersection between the middle orange line and the line between the triangles centers of gravity. Mackinaw's. Perimeter of a trapezoid is defined as the sum of the length of the bases and legs of the trapezoid is calculated using Perimeter=Side A+Side B+Side C+Side D.To calculate Perimeter of a trapezoid, you need Side A (a), Side B (b), Side C (c) and Side D (d).With our tool, you need to enter the respective value for Side A, Side B, Side C and Side D and hit the calculate button. Right Trapezoid Calculator. Trapezoid - from wolfram mathworld. Learn more about centroid of a trapezoid formula at CoolGyan.org and also download free pdf format of Textbook Solutions, Revision Notes and Board Questions Papers. A right trapezoid is a trapezoid having two right angles. Scalene Trapezoid A scalene trapezoid doesn´t have equal sides or angles. Trapezoid, Theorems and Problems- Index . Centroid of a trapezoid is a very useful tool. Give the gift of Numerade. Learn more about centroid of a trapezoid formula at vedantu.com and also download free pdf format of Textbook Solutions, Revision Notes and Board Questions Papers. Circumcircle is a circle that passes through all the vertices of a two-dimensional figure. Now consider a triangle dissected by a horizontal line through its centroid. The complexity is O(#edges). It is Find Centroid of a Polygon (Centroid of a Trapezoid, Centroid of a Rectangle, and others): If you want to calculate a polygon’s centroid, G(Cx,Cy) that is defined by its n vertices (x0,y0),(x1,y1),…(xn-1,yn-1), then you just need to use these given formulas: Centroid of a trapezoid is a very useful tool. Median of a Trapezoid, Theorems and Problems. Main & Advanced Repeaters, Vedantu Index.. Geometry Problem 1424. A convex quadrilateral is cyclic if and only if opposite angles sum to 180°. Centroid of a geometric object is defined by its centre of mass having uniform density. A parallelogram is an obtuse trapezoid with two pairs of parallel sides. Centroid, Area, Moments of Inertia, Polar Moments of Inertia, & Radius of Gyration of a Isosceles Trapezoid Home Calculators Forum Magazines Search Members Membership Login What is the best way to find the centroid of a polygon given that the polygon may be concave, convex and have many many sides of various lengths? If your isosceles triangle has legs of length l and height h, then the centroid is described as: G = (l/2, h/3) Centroid of a right triangle. A right trapezoid has two adjacent right angles. What is the best way to find the centroid of a polygon given that the polygon may be concave, convex and have many many sides of various lengths? Median of a Trapezoid, Theorems and Problems. Acute angle measures less than 90°. $a = 6\,cm,\,\,b = 8\,cm,\,\,h = 5\,cm$, ${G_y} = \frac{{b + 2a}}{{3\left( {a + b} \right)}}h = \frac{{8 + 12}}{{3\left( {8 + 6} \right)}} \times 5 = \frac{{20 \times 5}}{{42}} = 2.38\,cm$. Tangential trapezoid: a trapezoid where the four sides are tangents to an inscribed circle. Centroid of a trapezoid formula with solved examples. ... Actually it is easier if you break it into right trapezoids using a clever trick. Find the centroid of the isosceles trapezoid with vertices (-a, 0),(a, 0),(-b, c), and (b, c). An isosceles trapezoid is an acute trapezoid if its lateral sides have the same length, and the base angles have the same mea-sure. The centroid of a triangle is the point of intersection of its medians (the lines joining each vertex with the midpoint of the opposite side). In another words, Centroid of a Trapezoid is geometrically lies on the median. Hence, the centroid is 2 cm from the side whose length is 8 cm. Trapezoid is a convex quadrilateral with only one pair of parallel sides. In this section, we will look at the trapezoid centroid and the centroid formula for the trapezoid. Question: Find the centroid of a trapezium of height 4.5 cm whose parallel sides are 4 cm and 8 cm. There are two popular types of Trapezoid – one is isosceles and the another is right-angled Trapezoid. ... Actually it is easier if you break it into right trapezoids using a clever trick. CONCEPT QUIZ 1. Sorry!, This page is not available for now to bookmark. Centroid of a geometric object is defined by its centre of mass having uniform density. $G\left( {\frac{h}{2},\,\frac{{b + 2a}}{{3\left( {a + b} \right)}}h} \right)$. The trapezoid then approaches the shape of a triangle, as near as we please. A Trapezium or a trapezoid is a quadrilateral with at least one pair of parallel sides (Bases). The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides. Centroid, Area, Moments of Inertia, Polar Moments of Inertia, & Radius of Gyration of a Isosceles Trapezoid If your isosceles triangle has legs of length l and height h, then the centroid is described as: G = (l/2, h/3) Centroid of a right triangle. An isosceles trapezoid is a trapezoid in which the base angles are equal so c=d. Find below formula for the centroid of trapezoid located a distance of x, Question 1: Find the centroid of trapezoid with the given dimensions; a = 12′ ; b = 5′ ; h = 5′, x = $\frac{5 + 2 \times 12}{3(12 + 5)}$ × 5. I'll let you discover it. The above isosceles trapezoid property calculator is based on the provided equations and does not account for all mathematical limitations. The centroid lies between the parallel bases. To do this, I need to first find the geometric centroid of the trapezoid. Next, we want to find the coordinates of the centroid, $(\bar{x},\bar{y})$. Centroid of an isosceles triangle. The legs may or may not be parallel to each other. The corresponding rules are given in Figure 10. A trapezoid is a 4 sided polygon that has at least one pair of sides parallel. Area… The centroid, as the name indicates, lies at the centre of a trapezoid. Centre of Mass (Centroid) for a Thin Plate. Trapezoids The trapezoid or trapezium is a quadrilateral with two parallel sides. I'll let you discover it. Ans: The centroid of a trapezoid formula can be found on Vedantu’s website. (a) 2 cm from the side whose length is 4 cm, (b) 2 cm from the side whose length is 8 cm, (c) 3 cm from the side whose length is 4 cm, (d) 3 cm from the side whose length is 8 cm, $a = 4\,cm,\,\,b = 8\,cm,\,\,h = 4.5\,cm$, ${G_y} = \frac{{b + 2a}}{{3\left( {a + b} \right)}}h = \frac{{8 + 8}}{{3\left( {8 + 4} \right)}} \times 4.5 = \frac{{16 \times 4.5}}{{3 \times 12}} = \frac{{72}}{{36}} = 2\,cm$. Centroid of Right Triangle Formula. Diagonal is a line from one vertices to another that is non adjacent. For a right triangle, if you're given the two legs b and h, you can find the right centroid formula straight away: G = (b/3, h/3) Ans: A trapezium or a trapezoid is a quadrilateral with at least one pair of parallel sides. The center of gravity of a trapezoid can be estimated by dividing the trapezoid in two triangles. This is a trapezoid with two adjacent right angles. The below online Centroid of a Trapezoid Calculator calculates the center of mass of trapezoid. Trapezoid, Theorems and Problems- Index . mass (and weight) per unit length is taken as constant. The following is a list of centroids of various two-dimensional and three-dimensional objects. Tetra. Isosceles trapezoid (a two-dimensional figure) is a trapezoid with only one pair of parallel edges and having base angles that are the same. A 3{sides equal trapezoid is an isosceles trapezoid with three sides of the same length. Centroid of trapezium can be determine by using formula h/3((b+2a)/(b+a)) Centroid of trapezium is bit tricky to determine. Q4. Centroid of an isosceles triangle. This video shows the method of "how to find the centroid of Trapezoid". Trapezoid is a quadrilateral with two parallel sides and centroid of a trapezoid lies between two bases. The centroid of the right triangle is at the intersection of the median lines. Pro Lite, CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane. Here, the x‐centroid is found by requiring the moment of the weight of the pieces to equal the moment of the total weight. Centroid of an Area by Integration Moments of Inertia (I) Parallel Axis Theorem (PAT) Radius of Gyration (r) =∫ 2 x A I ydA =∫ 2 y A IxdA= + JI Iox y 2 II Adcx o=Σ +Σ = x x I r A = y y I r A = O o J r A = ∫ ∫ A A xdA x dA = ∫ ∫ A A ydA y dA 2 II Adcy o=Σ +Σ Jo = Polar Moment of Inertia ˘ Let's assume that angle φ 1 is given. A right trapezoid (also called right-angled trapezoid) has two adjacent right angles. Using simple geometrical principles, for the right triangles, with sides c, d as hypotenuses (see figure below), the calculation of … Tnsnames ora example. Centroid of a right triangle Locate the centroid of the right triangle shown. There are two popular types of Trapezoid – one is isosceles and the another is right-angled Trapezoid. Isosceles Trapezoid Formula. As you must already know, a trapezoid is a quadrilateral that has two sides parallel. You need to recreate a right trapezoid … You need to recreate a right trapezoid … The calculator has been provided with educational purposes in mind and should be used accordingly. The center of the circumcircle is the intersection of the perpendicular bisectors of … Solution 12.2-1 Centroid of a right triangle dA x dy b (1 y h) dy Similarly, x b y Q x A h 3 bh 2 6 Q x y dA h 0 yb (1 y h) dy bh 2 A dA h 0 b (1 y h) dy y y d y x h b O C x y x b (1 y 12 Review of Centroids and Moments of Inertia 3) h Problem 12.2-2 Determine the distance y to the centroid C of a trapezoid … Q3. Trapezoid is a quadrilateral with two parallel sides and centroid of a trapezoid lies between two bases. Finding the lengths of the non parallel sides c and d, can be done if one interior angle of the trapezoid is known. Calculations at a right trapezoid (or right trapezium). The centroid divides each of the medians in the ratio 2:1, which is to say it is located ⅓ of the distance from each side to the opposite vertex (see figures at right). Consider the following trapezium in which AB || CD. Vedantu academic counsellor will be calling you shortly for your Online Counselling session. Isosceles Trapezoid Formula. And so does this side. A right trapezoid is a trapezoid having two right angles.The area of the trapezoid is(1)(2)(3)The geometric centroid lies on the median between the base and top, and if the lower left-hand corner of the trapezoid is at the original, lies at(4)(5)(6)(cf. G is its centroid. Q2. is its centroid. I have found the formulas online. Centroid, Area, Moments of Inertia, Polar Moments of Inertia, & Radius of Gyration of a General Trapezoid P-238 supports a load which varies an intensity of 220 N/m to 890 N/m. A quadrilateral is a four-sided shape with only one pair of parallel sides and non-parallel sides are equal in length. The parallel sides are called the bases of the trapezoid and the other two sides are called the legs or the lateral sides. In another words, Centroid of a Trapezoid is geometrically lies on the median. Enter the lengths of the two parallel sides a … For a right triangle, if you're given the two legs b and h, you can find the right centroid formula straight away: G = (b/3, h/3) Why don’t you try to solving a problem for practice? For a given trapezoid that has parallel side a and b where the b is Practice example problems dissected by a horizontal line through its centroid following trapezium in AB... Tickets dashboard to see a step-by-step construction of the legs are identical with each.. 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https://en.wikipedia.org/wiki/User_talk:CBM/Archive_10 | # User talk:CBM/Archive 10
## Peer review
Hi Carl, this may be on interest to you, Ruhrfisch ><>°° 15:47, 13 August 2008 (UTC)
## Wikipedia:Articles on elections has been marked as a guideline
Wikipedia:Articles on elections has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:47, 13 August 2008 (UTC)
## More WP bot
Hi, CBM. I finally got an account in the toolserver running, so I can get around all the initialization problems I had been having. However, if I understand database_routines.pl correctly, the bot is using a 'wp10' database table that
SELECT server FROM toolserver.wiki WHERE dbname='wp10';
can't find. Since we were thinking about having a public database, would it be appropriate to change the database to a _p database? Also, help setting up stuff would be appreciated... Titoxd(?!? - cool stuff) 21:08, 13 August 2008 (UTC)
Also, there's several dependencies on NewMath or something like that, which is not in a publically-viewable directory. Would it be possible to put those in the SVN repo? Titoxd(?!? - cool stuff) 00:40, 14 August 2008 (UTC)
You can look at the files in /home/cbm/wp10.2g/alpha as an example of how I reconfigured things for toolserver. — Carl (CBM · talk) 01:59, 14 August 2008 (UTC)
Ah, that's helpful. You just use a lib call to force perl to open that directory. I see. When I try to run the tool on the toolserver, though, I get a permission denied error when trying to access /home/cbm/veblen/api.credentials (which makes sense). From a cursory review of the code, it seems like I can comment out that line without causing any problems, but I'd rather ask before making that change... also, to have the bot run through only a few projects, do you manually override wp10_routines::download_project_list, or do you do something fancier? Titoxd(?!? - cool stuff) 02:55, 15 August 2008 (UTC)
You can leave off the api.credentials; the reason I use that is to have the script log in under a username that is flagged as a bot, which allows it to request more pages per query from the API. As long as you stick to smallish projects, you don't need to do that. The script currently never edits the wiki, so it can run without logging in.
To download just one project, pass it as an argument to the script:
perl download.pl 'Tropical cyclones'
The argument is checked in download.pl. — Carl (CBM · talk) 03:03, 15 August 2008 (UTC)
The other thing you'll have to do is create the database tables. Run mysql -hsql u_titoxd < tables.sql from the source code directory. The output should show success four times, once for each table in that file. If you need to add new tables (like for GA and FA articles) then you should add the table creation commands to tables.sql. I can give you access to commit your code back to my svn repository. — Carl (CBM · talk) 03:08, 15 August 2008 (UTC)
I had made the tables manually via phpMyAdmin before (table u_titoxd_wp10_p), and I got the code to download projects into the database. I'm working now on abstracting the database connection a bit more (so we don't have to have login details on every file), but that is not going too well... The svn access sounds nice, but let me get the code running properly first... Titoxd(?!? - cool stuff) 04:05, 15 August 2008 (UTC)
Also, I'm not really sure if it is visible, but if it is, my code is in /home/titoxd/public_html, in case you want to have a look at it. I'll move it to a sub-folder once I know the code works, just so I don't introduce additional breakage on top of breakage... Titoxd(?!? - cool stuff) 04:07, 15 August 2008 (UTC)
• I added a bunch of raw, maybe fragile code to wp10routines.pl, and the code can now extract WikiProject preferences (although it doesn't do anything with them yet...) That code is available on /home/titoxd/public_html/wp10_routines.pl Titoxd(?!? - cool stuff) 10:05, 15 August 2008 (UTC)
I have uploaded a new version of database_routines.pl. The new code reads a file 'db.conf' (you can look at mine on toolserver) instead of hard-coding the login information. On the next update I will also make the library locations configurable, so that it isn't necessary to customize the actual perl files for each server. — Carl (CBM · talk) 12:00, 15 August 2008 (UTC)
I looked quickly through your code for wikiproject prefs. That overall layout is great. Near the end, instead of using two arrays @key and @value, you should use a single hash. That will make it easier to work with the data later.
There are quite a few ratings that the template will include:
• The project's homepage
• Info about the parent of the project
• Info about extra ratings.
I have a mockup at Category:Mathematics articles by quality. The homepage should be stored in the projects table, while the info on extra ratings should go in the ratings table.
Do you mind if we switch to email for discussing the code? I think that's a better medium than wiki pages. — Carl (CBM · talk) 12:18, 15 August 2008 (UTC)
Sure, email works. Or even better, nobody uses irc:#wikipedia-1.0 most of the time, so we can work there as well. Titoxd(?!? - cool stuff) 16:07, 15 August 2008 (UTC)
## SelectionBot interwiki count
Hi CBM, I've been doing more "principal articles" and I've spotted a couple of wrong interwiki scores (zeroes). See these:
Clearly these are wrong, do you know what could be causing this glitch? Cheers, Walkerma (talk) 22:55, 13 August 2008 (UTC)
I don't know what caused that, but both those articles now have large interwiki counts with the updated data I made over the weekend. If we notice more issues like this, I can scan the database for articles that have high pagelinks but low interwiki links. — Carl (CBM · talk) 01:39, 14 August 2008 (UTC)
Thanks! Another strange feature that I've seen once or twice before, pages like this which don't show the importance templates. I don't care about the formatting, but can you check that the score is including the WikiProjects importance assessment? Cheers, Walkerma (talk) 04:34, 14 August 2008 (UTC)
That was a flaw in the bot - the project categories capitalize the word importance, but the script didn't realize that was possible. I added some code to fix the capitalization. I'll also add some more debugging code to flag other non-standard names so I can add them as exceptions. — Carl (CBM · talk) 11:18, 14 August 2008 (UTC)
Thanks! I'm glad we're finding these little bugs. Walkerma (talk) 16:40, 15 August 2008 (UTC)
## WP:ECON C-class for VeblenBot
VeblenBot is fantastic and he's an absolute boon for WikiProject Economics. Is it possible for the chart to be modified to include a C-class, per the new assessment table? I've been reassessing many economics articles lately to account for the new class, and it would be useful to see our progress. Thanks again. -FrankTobia (talk) 01:45, 17 August 2008 (UTC)
No problem. I also created the list of Economics articles by hitcount at Wikipedia:WikiProject Economics/Frequently viewed articles. — Carl (CBM · talk) 02:03, 17 August 2008 (UTC)
Thanks so much. I really appreciate all the work you've been doing, for WP:ECON especially. -FrankTobia (talk) 10:40, 17 August 2008 (UTC)
You rock, CBM. Thanks lots. CRETOG8(t/c)
## Wikipedia:WikiProject Micronations/Micronation convention has been marked as a guideline
has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:47, 18 August 2008 (UTC)
## Goofy request
Hi Carl, I have been busy and somehow have forgotten to do the SAPRs for the past two days - see User:PeerReviewBot/Logs/SA links. I have now run the script for all PRs without a SAPR. Would you mind running the bot an extra time to link the SAPRs (otherwise some reviews will wait three days for their SAPR). Thanks and sorry, Ruhrfisch ><>°° 11:04, 19 August 2008 (UTC)
No problem. — Carl (CBM · talk) 12:50, 19 August 2008 (UTC)
Thanks so much, I'll try to be better. Ruhrfisch ><>°° 13:04, 19 August 2008 (UTC)
I'm amazed you do such a good job in updating the reviews daily; I don't think anyone will fault you for missing a day. — Carl (CBM · talk) 13:42, 19 August 2008 (UTC)
## Incompleteness theorem article
I think the rewriting of the incompleteness theorem is on the right track. (I'm stuck in Wyoming without a computer except this one at the public library, so I'm out of the loop). I like the proof sketch. Bill Wvbailey (talk) 00:24, 21 August 2008 (UTC)
## date bug
I'd say that there's a bug where it updates the tagged since date. — Dispenser 13:13, 22 August 2008 (UTC)
Thanks for pointing that out. It should be fixed now. The current data will still be wrong, but new entries should behave correctly again. — Carl (CBM · talk) 15:24, 22 August 2008 (UTC)
## Template:ArticleHistory
Since you protected the template, can you change from the silver lock to the gold lock? Thank you. --Splat5572 (talk) 05:09, 23 August 2008 (UTC)
The template is on the unprotected doc subpage.[1] — Carl (CBM · talk) 05:12, 23 August 2008 (UTC)
## Wikipedia:Manual of Style (dates and numbers)/Date autoformatting has been marked as a guideline
has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 25 August 2008 (UTC)
## Wikipedia:Disambiguation and abbreviations no longer marked as a guideline
has been edited so that it is no longer marked as a guideline. It was previously marked as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 25 August 2008 (UTC)
## Wikipedia:Burden of evidence has been marked as a guideline
Wikipedia:Burden of evidence has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 26 August 2008 (UTC)
## User:VeblenBot/Mathematicians
A while back you deleated User:VeblenBot/Mathematicians with the list of mathematicians by importance. Was the a reason for this, I can't seem to find any breakdown of mathematician articles by class or priority. --Salix alba (talk) 16:47, 27 August 2008 (UTC)
It was just a reorganization of file names. The new location is User:VeblenBot/Math/field:Mathematicians. — Carl (CBM · talk) 16:53, 27 August 2008 (UTC)
Cool, nice one for fixing the broken links. --Salix alba (talk) 17:25, 27 August 2008 (UTC)
## Thanks
Thanks for your help yesterday.--Alnokta (talk) 21:33, 27 August 2008 (UTC)
## Template:Notorphan
Where did you see I wrote that? I've never even seen that template before. Calliopejen1 (talk) 06:37, 28 August 2008 (UTC)
Never mind, I tracked it down. It's an automated message as part of Howcheng's image maintenance script I use. I've asked if he can fix it. Calliopejen1 (talk) 06:57, 28 August 2008 (UTC)
## question
I'm not sure where to send this question to, so I posted it on the discussion for the 8 (number) page... http://en.wikipedia.org/wiki/Talk:8_(number)
thanks —Preceding unsigned comment added by Thespyofcharles (talkcontribs) 11:52, 28 August 2008 (UTC)
## Holy cow
The Barnstar of Diligence For taking the time to investigate. Moonriddengirl (talk) 12:51, 28 August 2008 (UTC)
## Moving forward on the BC mess
Hello Ryan, CBM, Jennavecia (same message on all three talk pages). Seems like the ANI thread has gone stale although this idea of small-committee discussion has received pretty solid support. Look, we're never going to have 30 people agreeing on who should be working on this so I'd suggest you three take a shot at it. Am I dumping this thankless task on you guys? I sure am. I don't mind helping out but BC has gotten this idea that I'm out to get him so that might just increase drama. I know Jennavecia has expressed concern that she might be viewed as a BC cheerleader but you're all reasonable people and, as Jennnavecia put it, I think you all "understand the grievances of most editors who want to see Beta banned and at the same time, find great value in his contributions". CBM has bot experience, Ryan has MedCom experience, you're all admins, you've all been around and you've all followed the various BC ANI threads and ArbCom cases enough to understand the situation. I expect that both ends on the BC-love spectrum will spit at whatever compromise you come up with but at this stage it'll have to do and cooler-heads can probably prevail... Pascal.Tesson (talk) 01:46, 28 August 2008 (UTC)
Yes, I'm willing to help there. I'll be pretty occupied over the weekend (Labor Day holiday) but can discuss with the others in the coming week. — Carl (CBM · talk) 00:08, 29 August 2008 (UTC)
## Wikipedia:Burden of evidence no longer marked as a guideline
Wikipedia:Burden of evidence has been edited so that it is no longer marked as a guideline. It was previously marked as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 28 August 2008 (UTC)
## Wikipedia:GlobalBlocking has been marked as a policy
Wikipedia:GlobalBlocking has recently been edited to mark it as a policy. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 29 August 2008 (UTC)
## Wikipedia:WikiProject/Naming convention has been marked as a guideline
Wikipedia:WikiProject/Naming convention has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 29 August 2008 (UTC)
## Wikipedia:WikiProject Medicine/Reliable sources has been marked as a guideline
has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 1 September 2008 (UTC)
## Wikipedia:Rollback feature has been marked as a guideline
Wikipedia:Rollback feature has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 1 September 2008 (UTC)
## TfD nomination of Template:Citations missing
Template:Citations missing has been nominated for deletion. You are invited to comment on the discussion at the template's entry on the Templates for Deletion page. Thank you. — SMcCandlish [talk] [cont] ‹(-¿-)› 01:19, 2 September 2008 (UTC)
## User:VeblenBot/PERtable
The bot seems to have a bug. It's using the syntax [[Category:Wikipedia semi-protected edit requests]] ([[Category:Wikipedia semi-protected edit requests#editprotected|request]]) which is causing categorization issues. --MZMcBride (talk) 07:43, 2 September 2008 (UTC)
Thanks for the note, it's fixed now. — Carl (CBM · talk) 12:17, 2 September 2008 (UTC)
## non-standard calculus
Note that there is an ongoing discussion at WP math. Katzmik (talk) 13:41, 2 September 2008 (UTC)
## Wikipedia:Bureaucrat discussion has been marked as a guideline
Wikipedia:Bureaucrat discussion has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:45, 2 September 2008 (UTC)
## Wikipedia:Reliable sources (medicine-related articles) has been marked as a guideline
has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:46, 2 September 2008 (UTC)
I am a retired mathematician, formerly at Stanford for eleven years. So I have some familiarity for scholarly criteria.
This is my first attempt to write a Wikipedia article.
I provided links to Kalnins' own website of videotapes of him stating these exact things. I quotes directly from the actual videotapes. There is no more direct form of knowledge.
Your editor suggested that there should be no article on Ed Kalnins, but only a reference on his notable parishoer's site Sarah Palin. I tried to create a reference to Ed Kalnins and a link to Ed Kalnins as well as to the already existing explicit reference of Wassila Assembly of God from the Sarah Palins page on Wikipedia. Yet such references are not being allowed by someone at Wikipedia. And the link for Wassila Assembly of God has been misdirected.
Your editor suggested that an article must be "balanced". But if a person is of note only because of controversial remarks or actions, balance is not applicable. Is Wikipedia claiming to be like the FCC, and an article on evolution to be balanced by one on "intelligent design" and "Hindu creation myths"?
Furthermore, the discussion page was deleted.
I will admit, that if Wikipedia censors his controversial remarks, then Ed Kalnins is no more notable than Sarah Palin's current pastor. The deleted remarks are the prionciple basis of his being notable.
Since my articles were deleted almost as quickly as I tried to edit them, and I can get no specifics from Wikipedia, I can only assume that someone delited the links to the actual videotapes from which the quotes were derived.
I will attempt to rewrite the article, including links by which you can verify the controversial statements yourself. EricDiesel (talk) 01:55, 3 September 2008 (UTC)
## Sarah Palin's Pastor Ed Kalnins
Yeah, I dropped that mathematician thing when I saw "Nonstandard Calculus" a few notches above. I was Alonzo Church's student at UCLA, before going up to Stanford.
I ran into an African guy reading "Nonstandard Analysis" in the cafeteria at Stanford on one of my first days there, and I sat down at his table, never having met a black mathematician before and never having met anyone who read that book, and I started quoting from the book just to freak him out. We became best friends, doing anti-apartheid stuff. He neglected to mention his father was a Chemist at Chapel Hill who was to be crowned the King of Eboland in Nigeria. I found out by seeing the ceremony on CBS, and when I asked if he was related to the new King he said, "Oh, yeah, thats my dad".
I started out as Ian Hacking's Student when he chaired Philosophy at Stanford, before he punched the cop who was trying to evict him from the chair's office when a prakster called in that a drunk had broken into the chairs office. Hacking wrote a book, "The Emergence of Probability" back in the 1980's, about evidence, which is relevant to the present situation.
Hacking described the etymology of "probability" as deriving from the same word as "probity", which was used in a court of law as a measure of evidence. If a noble person, a person of "probity", testified, then his probity was considered to have greater evidentiary weight than empirical evidence, such as seeing something with ones own eyes. (Probability after Rudolph Carnap has almost the exact opposite meaning from probity as far as evidence is concerned).
The link I provided is to Kalnins' videotaped sermons, from which I transcribed the quotes, from which one can verify my transcriptipons with ones own eyes and ears.
I suppose it is unreasonable to expect editors to go through the videotapes to verify my transcriptions, but the Huffington post author picked the very same quotes as I did (and more), and transcribed them the same way. So we have links by which the reader can check with their own eyes and ears, but lack the "probity" of a New York Times reproter.
One is reminded of Galileo being accused of claiming that his telescope showed fixed stars (moons)moving around a planet, which was impossible by Church doctrine, but being unable to get any tribunal member to look in the telescope (which is physically easier than watching Kalnins' crazy videotapes in the links).
If the transcribed quotes are not allowed until probity is Is there any way to directly refer to the videotapes of Kalnins' sermons: http://www.wasillaag.net/all.html, rather than to the church site.
Here are the bios of the Huffington post authors who quoted from the tapes with identical quotes as I had (and more):
Nico Pitney is National Editor at the Huffington Post. He was previously Deputy Research Director at the Center for American Progress and Managing Editor of ThinkProgress. He lives in Washington, DC, and has appeared on CNN, MSNBC, NPR, and the BBC. Nico can be reached at pitney@huffingtonpost.com.
Sam Stein is a Political Reporter at the Huffington Post, based in Washington, D.C. Previously he has worked for Newsweek magazine, the New York Daily News and the investigative journalism group Center for Public Integrity. He has a masters from the Columbia University Graduate School of Journalism and is a graduate of Dartmouth College. Sam can be reached at stein@huffingtonpost.com.
One of your editors suggested that the article I wrote was "clearly biased", but would not suggest how to include the information of the quotes without bias. The Wikipedia fairness doctrine he quoted reads like the FCC equal time requirement, or worse, like requiring an article on "Evolution" to also discuss "intelligent design" and "Hindu creation myths". But maybe I am too biased to see what else to include. —Preceding unsigned comment added by EricDiesel (talkcontribs) 02:53, 3 September 2008 (UTC)
## New categories for old
Hi - could you ask VB to list Category:September 2008 peer reviews, Category:GAR/39 and Category:GAR/40? The July peer review category and the 38th GAR archive have been stabilized. Geometry guy 20:07, 30 August 2008 (UTC)
Thanks for doing this. WP:Peer review/September 2008 appears not to be working yet, however. Geometry guy 09:54, 3 September 2008 (UTC)
Unfortunately I had typed 'Septembar'. I'm going to see if I can implements a system that will allow you to add and remove these using a web page on toolserver; that would be more efficient. — Carl (CBM · talk) 12:42, 3 September 2008 (UTC)
See http://toolserver.org/~cbm/cgi-bin/cats/cats.pl . I sent a password by email. — Carl (CBM · talk) 17:03, 3 September 2008 (UTC)
## WP:SCG
Thanks Carl, but per WP:TWOSHORTCUTS, let's pick our favorite two; do you like WP:SCICITE or WP:CITESCI better? (Feel free to respond anywhere.) - Dan Dank55 (send/receive) 16:57, 3 September 2008 (UTC)
Of those two (I didn't know either one existed), I think SCICITE is more parallel to the page title. — Carl (CBM · talk) 16:59, 3 September 2008 (UTC)
Delldot just added one this morning and I responded by adding another. Okay, I concur with you. (Taking this page off watchlist.) - Dan Dank55 (send/receive) 17:22, 3 September 2008 (UTC)
## controversy over Cantor
The current version of the article refers to "whole numbers" in the sense of "natural numbers". Is this accepted usage? Katzmik (talk) 13:38, 4 September 2008 (UTC)
It's pretty common in American primary schools at least. Some authors will use one term for the set {0,1,2,...} and another term for the set {1,2,3,...} but in the context of that article the status of 0 is unlikely to cause confusion. — Carl (CBM · talk) 13:41, 4 September 2008 (UTC)
## Putative edit warring over Sarah Palin
Re your comment on my talk page, concerning this edit: Interesting you should criticize me for not using the talk page less than 10 minutes after my edit, when I haven't even had a chance to do so. As an admin, you ought to have your AGF together better than that. As for the edit: The last time I checked, it's OK (desirable even) to restore material that is well-sourced. The sources in that section were mainly from ABC News. Were you aware of that? I trust you'll be leaving a warning on the user page of the editor who deleted it, asking them not to delete well-sourced material? Thanks. Comesincolors2 (talk) 15:39, 4 September 2008 (UTC)
## Peer review bugs?
Hi Carl, could you take a look at this thread at the Peer Review talk page Wikipedia_talk:Peer_review#Strange_behaviour and the one below it - looks like archived PR requests are not being removed and new PR requests are not being added - perhaps a bug in Veblenbot? Thanks, Ruhrfisch ><>°° 16:25, 4 September 2008 (UTC)
Thanks as always for all of your help, both via the bots and being ready to fix them so quickly, Ruhrfisch ><>°° 17:20, 4 September 2008 (UTC)
## 2 Questions re: "Notability is not contagious and UnDeleting 4 different articles for at least five days
Thanks for your comment on my discussion page.
I am new, and have been asking questions about this without a response from anyone and maybe you can help me understand the deletion of my four articles.
Palin's history teacher is clearly NOT notable. However, if Palin were a politician known for her denial of the Holocaust, her history teacher WOULD be notable, especially if the history teacher was a Holocaust denier.
Similarly, I would think Hegel’s history teacher would be notable because Hegel’s is notable for his theories on history, while Hegel’s sewing teacher would not be notable.
The general point is that a relation of B to notable A does NOT automatically transfer notability from A to B, but a relationship of B with the CAUSE of A’s notability WOULD, in addition to the mere simple relationship of B to A.
• 1, Is this correct at Wikipedia?
• 2. Would it be possible to reopen the pages for Wasilla Assembly of God, Ed Kalnins, Wasilla Bible Church, and Larry Kroon and let them independently evolve for five days, especially as completely different facts were being added by many on each page? A videotape of speaking in tongues in an independent church in remote Alaska, would be appropriate on not be appropriate on the Wasilla Bible Church page, but not on the Sarah Palin page (unless this independent church’s doctrine was to do this at home, like at the White House?). The international coverage is different for the four topics. E.g., Larry Kroon isgetting coverage in the Israeili press, but not Ed Kalnins, BECAUSE the two are NOTABLE for DIFFERENT reasons. since
A third Sarah Palin pastor has been in the media more, but this appears to be ONLY for his being her pastor, so would not be notable.
I am sending this to you since no one in control seems to understand the argument about relationships in order to respond to it, and I have made it pretty simple.
Thanks. EricDiesel (talk) 23:21, 4 September 2008 (UTC)
I think I follow the argument you are making. Unfortunately, it doesn't match the practice here. I'm going to avoid using any links, and just give a very brief summary. I can give links later if it helps. I'm also going to describe things based on my experience, rather than on how some people might claim things work.
There are several factors that people use to decide if a person is "notable" enough to have an article. The term "notable" should be viewed as jargon; no other place uses it like Wikipedia does.
The first question that people will ask is about sources. The more reliable, third-party sources you can provide provided, the more likely it is that the article can be justified. Not all sources are equal: professional media such as national newspapers and national television networks are good, but blogs are generally bad. The motivation there is that national media are better known for professional editorial standards than blogs.
It isn't enough for you to argue (regardless of merit) that the person should have been covered by the media. If the media have not found a person interesting enough to cover, we tend to use that as an indicator of that person's lack of "notability".
The second question is whether the person is only in the news because of one event. In general, if there is a controversy involving one person, and a second person is mentioned in the media only in connection to that one controversy, the second person is not considered "notable" independently.
Unfortunately, there is currently a lot of "controversy" surrounding Sarah Palin's article here and, by association, all articles on topics associated with her. I'm quite neutral on the matter, but there are a significant number of users who fear that these articles might be used to emphasize negative aspects beyond their due weight.
We have a principle called "neutral point of view", which roughly means, "write articles like they would be written by a disinterested person who is trying to be neutral and fair in her writing". Because of the atmosphere of tension about Palin, it's particularly important to avoid even the impression that an article is written to be primarily negative. — Carl (CBM · talk) 23:58, 4 September 2008 (UTC)
## Long Shot Question
Are you the logician/compscientist Carl who started as Paul Cohen's student in the late 80's, sat in the right fourth row (your right facing me) in Cubberly Auditorium every every Tarkovsky film I screened and lectured on, and had the cute younger sister who sat in the front row center at the film lecture/screenings?
If so, I coincidentally ran into your sister again at night at the beach in San Francisco the week the American remake of Solaris came out in 2003, and ran into that eccentric British physicist, Jonathan, who sat in the right third or fifth row, the same night in San Francisco. He suddenly left Stanford to be a destitute writer in Saint Petersburgh in the 1990's I left in 1992 to make money. EricDiesel (talk) 00:03, 5 September 2008 (UTC)
Sorry, that's not me. I only saw Cohen once before he passed away, at a panel at the 2005 AMS meetings about the continuum hypothesis. — Carl (CBM · talk) 00:17, 5 September 2008 (UTC)
## PSTS Policy & Guidelines Proposal
Since you have been actively involved in past discussions regarding PSTS, please review, contribute, or comment on this proposed PSTS Policy & Guidelines.--SaraNoon (talk) 18:59, 7 September 2008 (UTC)
== Admins and Editors Calling me "Unethical", "Trash" re: David Brickner ==
• In response to my post on David Brickner, GRBerry wrote “…it is both 'garbage' and… our obligation is to get rid of the ‘trash’…” and "stuffing 'garbage' into the encyclopedia”.
• CobaltBlueTony wrote he “agreed wholeheartedly with GRBerry"… and then called me “unacademic, unethical, and unacceptable”. I have repeatedly been accused of having a POV. Others have called me a “vandal”, and written NUMEROUS derogatory remarks.
• 1. Why am I ‘’’“Unethical”, “Garbage”, “Trash”, etc.’’’? EricDiesel (talk) 12:05, 8 September 2008 (UTC)
==Reliable Sources==
• In response to my post on David Brickner, GRBerry wrote “…most of the sources were either ‘not reliable’ upon examination (e.g. unedited partial copies of blogs)..." CobaltBlueTony wrote he “agreed wholeheartedly with GRBerry"
The sources were Jewish Journal, Israeli News, Atlantic Monthly, and ABC News. Which ones are "not considered reliable sources”. How do I tell? EricDiesel (talk) 14:27, 8 September 2008 (UTC)
== Coatrack re David Brickner ==
• In response to my post on David Brickner, GRBerry wrote it is a coatrack. CobaltBlueTony wrote he “agreed wholeheartedly with GRBerry" EricDiesel (talk) 12:09, 8 September 2008 (UTC)
• 1. ‘’’Coatrack’’’ – Please specify which sentences in article is not about Brickner and is a coatrack, what it is a coatrack for, and I will post the sentences in the article that this article is alleged to be a coatrack for. The information is rejected by the same people when I post it elsewhere.
"Brickner has long been the subject of international press coverage for his controversial statements, and is the subject of monitoring by Jewish anti defamation groups. In mid August 2008, Alaskan pastor Larry Kroon invited Brickner to deliver a guest sermon at the Wasilla Bible Church, and do fundraising there for Jews for Jesus there by taking collections. He commented one of the most widely reported terror attacks of the year, in which a Palestinian terrorist used a bulldozer to crush civilians. Brickner asserted that Jews were responsible, as the deaths were “God’s punishment” for Jews having failed to convert to Christianity. A Jewish Defense League spokesperson compared this with conversion efforts of the Inquisition, stating that it was not as bad as the Inquisition. The governor of Alaska happened to be in the audience for the sermon, and her spokespeople quickly issued statements that she did not know who Brickner was before going to the sermon, and that she would not have gone if she had known. When the sermon received further press coverage following the nomination of the governor for vice president, spokespeople for the governor quickly made clear that she categorically did not share Brickner’s views." EricDiesel (talk) 12:09, 8 September 2008 (UTC)
== Articles Not About Brickner ==
• In response to my post on David Brickner, GRBerry wrote "... most of the sources... had 'no material that is about Brickner'. CobaltBlueTony wrote he “agreed wholeheartedly with GRBerry"
• Please specify which of these articles “had no material that is about Brickner”.
• My posted sources were –
1 Jewish Journal – “a speech at her church suggested that violence against Israelis resulted from God’s judgment against Jews who have failed to embrace Jesus. David Brickner, the executive director of Jews for Jesus, suggested in his Aug. 17 sermon at Wasilla Bible Church that the refusal to accept Jesus was responsible for the long history of devastation visited upon Jerusalem. He also described his group’s successful targeting of Israeli Jews, both in Israel and elsewhere. ‘Judgment is very real, and we see it played out on the pages of the newspapers and on the television,’ said Brickner, according to a transcript posted on the church’s Web site. ‘It’s very real. When [my son] Isaac was in Jerusalem he was there to witness some of that judgment—some of that conflict—when a Palestinian from East Jerusalem took a bulldozer and went plowing through a score of cars, killing numbers of people. Judgment—you can’t miss it’.”
2 ‘‘‘Wall Street Journal’‘‘ - This was my error, and should have been a source on WAoG church, it is here by misplacement.
3 Israeli News – Actual video of Brickner’s sermon posted.
4 Atlantic Monthly – “this Jews For Jesus pamphlet (PDF) [link to pamphlet posted] from 2004 that reveals more details” (Brickner was in charge in 2004 and discussed “liberating” the Wailing Wall from the Jews in the pamphlet, causing the controversy in which I first saw him on cable news in 2004.)
5 Israel News – “…the Wasilla Bible Church gave its pulpit over to a figure viewed with deep hostility by many Jewish organizations: David Brickner, the founder of Jews for Jesus…” and “David Brickner, an activist for the missionary group ‘Jews for Jesus’, considered quite controversial among many American Jews. The Anti-Defamation League of B'nai Brith has criticized Brickner for ‘targeting Jews for conversion with subterfuge and deception’. Brickner in his sermon described terrorist attacks on Israelis as part of ‘an ongoing reflection of the fact that there is judgment’ by God of those who have not accepted Jesus as their savior.”
6 ABC News - (This is a blog, but the blog follows a news story by Jake Tapper, ABC News' Senior National Correspondent based in the network's Washington bureau.) “sermon by David Brickner, an activist for the missionary group ‘Jews for Jesus’, considered quite controversial among many American Jews. The Anti-Defamation League of B'nai Brith has criticized Brickner for "targeting Jews for conversion with subterfuge and deception." EricDiesel (talk) 14:26, 8 September 2008 (UTC)
== "Pray to Convert Gays to Straights" a coathanger ==
I put a sentence on the Wasilla Assembly of God article that “In 2008, the church promoted a conference to pray to convert gays into heterosexuals.” And cited an AP story. It was deleted “coatrack”. I was threatened not to post again or I would be blocked from posting. Why is this a coatrack? EricDiesel (talk) 14:29, 8 September 2008 (UTC)
## Nonstandard Calculus
In the first example of Nonstandard Calculus, it should be an "equality" if delta x is “infinitesimal”, and an "approximate equality" if delta x is “sufficiently small”, using the Wikipedia definition of infinitesimal. Anyone would understand the point made, but one purpose of creating a Nonstandard Calculus is to get rid of a lack of rigor in symbol manipulation, so being a hair splitter is appropriate. Of course, what is written is true, since it would be an approximately equality if delta x were zero. I am not going to make the edit until I know if it will cause a firestorm arguing over "infinitesmal", like trying to put a controversial church quote on a chruch artifcle. EricDiesel (talk) 16:42, 8 September 2008 (UTC)
## Strike till easy to read
Carl, I am striking all of the above so I don’t waste your time. If I can not quickly state what I am saying on such a trivial quantity of content, then I should switch fields. My mentors Church and Cohen must be turning in their graves (assuming they did not make it into hell) for having failed to teach me the concepts of elegance and triviality in so many years of one on one talks. So I am not going to ask for a response until I can write something that does not take you more than a couple of minutes to read. EricDiesel (talk) 18:39, 8 September 2008 (UTC)
Thanks. I was planning to try to look through it this evening. Apart from replying to you on my talk page I have been avoiding the Sarah Palin stuff. I'm afraid it will be a long time before articles related to her have any level of calm discourse. I'll look at the nonstandard calculus talk page next to see what's there. — Carl (CBM · talk) 21:31, 8 September 2008 (UTC)
Sorry,I forgot to put the nonstandardC edit in, and I accidentally deleted all but the first silly point. I see from the post after this that math edits have the same kind of passion as Palin. I am also discovering that there is a huge range of skill levels, knowledge levels, and culture types. And that it is kind of a waste of time to argue early on, since it is like being on a see saw. I will stick in the little thing left of my nonstandard analysis edit. I had a much worse deletion in May, since I owned that redwood forest that burned downn in Santa Cruz, Ca, and all of my in progress pre-computer research was burned (all my research is in progress, so I guess that was redundant). And I collected antiquarian science books. I had the Electromagnetism book written by Gauss that Gauss gave to Mach. And it had blood stains in it! EricDiesel (talk) 21:47, 8 September 2008 (UTC)
Yeah, writing an article here is like writing a paper with several coauthors, except coauthors usually want to keep you in their good graces. — Carl (CBM · talk) 21:55, 8 September 2008 (UTC)
## function
You've made no edits between the time of (19:23, 4 September 2008 to current) which is the time I first submitted my article, so again don't play dumb with me like Arthur Rubin trying to synthesize something up. Hope you and Arthur aren't the same person with different account.
Note: I am referring to the signifcant paragraph or the purpose (the paragraph). --Ramu50 (talk) 21:22, 8 September 2008 (UTC)
I don't see why I should I accept the act of listening to you guys, if you guys are immaturely not willing to discuss it.--Ramu50 (talk) 21:31, 8 September 2008 (UTC)
I'm sure all mathematicians seem (to you) to think and act the same way. You can rest assured there's more than one of them around, and (horrors) they are watching the function article. VasileGaburici (talk) 22:26, 8 September 2008 (UTC)
Let's discuss this at Talk:function (mathematics) instead of here. — Carl (CBM · talk) 22:41, 8 September 2008 (UTC)
I've done a lot of edit war, but most of them have legitimate reasons in the talk page and I am quite sure the admin will know me fairly on the edit war list. I will risk the chances for the dream project that I believe, that is the only reason I have lived. Otherwise to be dead honest I would've suicide, seeing almost every part of society for such long time, humans seem to only live for the greed of money, sex, inifinite entertainment, recognition for everything they done. Even the priest, buddha have greed of narvana, and none the less how wise they are, most of them they can't even apply it to life, unlike the worthy priest who can question the ethics of society such as religious church practice ethics. I have no time and care about that useless purpose of life in which and you and them live for, that is why when you look at my contribs I've participated so much article. Thus be my words and take it with a grain of salt. --Ramu50 (talk) 23:12, 8 September 2008 (UTC)
Many people have suicide for hope of lost, pressure, but I probably will be the only one or first to suicide for hatred, full happyness (which at many I see and you do not see, of course madness as it may sound). Yet it only sound madness, because I don't intend on putting it nicely as the sections of types of function. But if you can't have the basic foundation of linking some many things at once in a small paragraph, then I suggest having the basic management skill as a foundation.
By linking I mean able to utilize one data from a field of science and incorporate them to the field of science in which you feel. Tis a mockery and bragging if you want to take it that way, or tis a reference of the successful and meaningful life in your future is also one way you can take it. See ya I gtg --Ramu50 (talk) 23:18, 8 September 2008 (UTC)
== Slow Down - Pastor David Brickner, Pastor Paul Riley, Pastor Ed Kalnins, Pastor Larry Kroon, and Pastor David Brickner ==
I should have slowed down until I researched and wrote this and there might not have been a controversy. Is this an improvement?
Paul Riley should be added to the Religion section of the Sarah Palin article. Associated Press reports “Her pastor for most of her time at Wasilla Assembly of God, Paul Riley”. http://ap.google.com/article/ALeqM5jCeGgS4vbVt6qpxTpahCgGn_R-dQD92VOKVG0
• 1. Paul Riley is NOT notable, as he only appears in the media talking about Palin as far as I know, and notability cannot be inherited. If he becomes controversial, or is the subject of media stories for some other notable thing, only then he should only then get an article.
• 2. The “controversial figure” Ed Kalnins IS notable, since the content of the many media articles in which he is featured regards his controversial remarks. These remarks should NOT be on the Palin page, as there is no information I am aware of that directly links Palin to the controversial remarks. E.G., USA Today reports “The Rev. Ed Kalnins had no way of knowing he'd be a controversial figure in the 2008 presidential race.” http://www.usatoday.com/news/politics/election2008/2008-09-03-palin-pastor_N.htm . So Kalnins should have his own article in which his controversial remarks can be documented, as well as his bio, and any information about him that can be sourced.
• 3. Larry Kroon IS notable. He is in many major media stories linking him as far back as 2004 to the highly controversial Jews for Jesus and David Brickner. The Atlantic Monthly magazine reports this Jews For Jesus pamphlet (PDF) from 2004 that reveals more details about Palin's pastor.” This is a year 2004 association, long predating Palin’s rise from mayor. http://andrewsullivan.theatlantic.com/the_daily_dish/2008/09/palins-pastor-a.html Numerous other news articles report on Kroon, e.g. The Chicago Tribune http://www.chicagotribune.com/news/nationworld/chi-alaska-palin_monsep01,0,3504940.story . The 2004 stuff is unrelated to Palin, so Kroon should have his own article. It is unclear Palin knew Kroon would be speaking when she recently sat through his sermon.
EricDiesel (talk) 16:10, 5 September 2008 (UTC)
This is a lot of information for me to work through. I looked at the first two references, and they are both from September 2008. Your case for independent notability would be much stronger if there are references about these people from before Palin was nominated. — Carl (CBM · talk) 01:55, 6 September 2008 (UTC)
:: One of the sources is from 2004, relating David Brickner with Wasilla Bible Church. Please see next section on your talk page where I quote from the sources.
Please skip reading the above and read the following section instead. Thnx EricDiesel (talk) 11:29, 8 September 2008 (UTC)
Carl, at WP:ANI#Palin edit warrior spamming talk pages you asked for some time to try working with this editor. Do you have any significant update to give? GRBerry 18:22, 5 September 2008 (UTC)
As you can see, we're talking about it. — Carl (CBM · talk) 01:55, 6 September 2008 (UTC)
Unfortunately, he doesn't seem to be learning. If I see him coatracking this stuff with unreliable sources again, he is going to be blocked. GRBerry 02:07, 8 September 2008 (UTC)
:::GBerry, I am trying to learn, but you are not responding to my questions. For example, I put a sentence on the Wasilla Assembly of God article that “In 2008, the church promoted a conference to pray to convert gays into heterosexuals.” I cioted the Associated Press as the source. It was deleted “coatrack”. I was threatened not to post again or I would be blocked. No explanation was given to me despite multiple requests. Why is this a coatrack? EricDiesel (talk) 14:32, 8 September 2008 (UTC)
## Fixing protection?
Hi CBM. Now you have made me curious: I see that tonight you have unprotected and then re-protected several templates to the same protection level (full protection). For instance Template:·. You used the edit summary "fixing protection". What were there to fix? As far as I can see they were already fully protected.
--David Göthberg (talk) 05:13, 9 September 2008 (UTC)
It's a long story, and I had to do some more testing this morning to be sure what was happening to explain it here. Until some time in 2007, page protection information was stored in the page table in Mediawiki. At some point a page_restrictions table was added. However, the old page table entries were not all removed; they are only moved to the page_restrictions table when the protection status of the page changes. There are still about 8400 pages that have non-empty protection status in the page table.
I have a tool that uses API.php to determine the protection status of templates. Unfortunately, there is a bug in the API that I need to work around. Consider the results here. The protection entries with a source= field are generated by cascading protection; the ones without source= are due to the protection of the page itself. If a page is cascade protected, and the page's own protection status is stored in the page table instead of the page_restrictions table, then the API will not show the protection of the page itself, only the cascading protection. Changing the protection status "fixes" this problem by putting the protection in the page_restrictions table where the API can find it. — Carl (CBM · talk) 12:30, 9 September 2008 (UTC)
Since replying to you made me verify exactly what was going on, I reported the problem at bugzilla:15535. — Carl (CBM · talk) 12:45, 9 September 2008 (UTC)
Ah, so it was a problem of the kind I expected. That is, a database problem. Thanks for your detailed answer. (I just learnt how to use parts of the API some week ago, and I used to work with databases, so I understood your explanation.) There are of course some more things I wonder, but that is not relevant. I am now satisfied that you know what you are doing.
It seems the best thing would be if the devs did a database run to move the protection status from the page table to the page_restrictions table. Having database inconsistencies like that usually means trouble. Just like the API problem you point out.
--David Göthberg (talk) 13:28, 9 September 2008 (UTC)
That would be nice, but I can understand why it's a low priority for them. The real issue is the bug in the API, which needs to handle both types of protection entries. I'm sure they'll fix that soon. — Carl (CBM · talk) 13:55, 9 September 2008 (UTC)
## Coatrack Argument for Deletions
I wrote an essay on "Coatrack Argument For Deletions", User:EricDiesel/Coatrack Argument for Deletions, based on the not-so-well-defined definition of "coatrack" and "coat" in WP:COAT. The intent was to get something out of all these Obama and Palin debates to save admin and editor time in future debates, which I now see can get hot even in long settled math issues. Religeon stuff must be really crazy. It is at WP:Coatrack Argument for Deletions.
1. I don't know if it is appropriate to write such essays, or how to write an essay abstracting debates, in a way that others can add their knowledge.
2. If you have time, or know someone who has a rough idea of what a definition is who has time, edits, comments, and corrections would be appreciated.
(Or at least I thought I created it, before I just saw WP:Coatrack Argument For Deletions in "red", not "blue", in the preview frame here. I'll go check for typos.) EricDiesel (talk) 15:38, 9 September 2008 (UTC) Its here User:EricDiesel/Coatrack Argument for Deletions. Is there a way to get it discussed? EricDiesel (talk) 17:11, 9 September 2008 (UTC) Sorry about all the garbage, still learning.
## Wikipedia:Avoid weasel words has been marked as a guideline
Wikipedia:Avoid weasel words has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:51, 9 September 2008 (UTC)
## Wikipedia:Avoid weasel words is no longer marked as part of the manual of style
Wikipedia:Avoid weasel words has been edited so that it is no longer marked as part of the manual of style . This is an automated notice of the change (more information). -- VeblenBot (talk) 18:51, 9 September 2008 (UTC)
## 3 Palin Church Questions
Ok, boiled down my questions. Still referred to you for answers.
1. RE Wasilla Bible Church - Wasilla Assembly of God was trending KEEP with each new “revelation”, so the article was not deleted. Now it has much encyclopedia info growing on it, since there is a place to put the info. But Wasilla Bible Church is much more notable, as it is about to hold a widely protested convention to pray for gays to become straights. (They are even holding counter prayers in SF.) Also because it said that it owed its very existence to its long term relation with David Brickner, who made his most famous statement at the church while there on invitiation to the church, (the statement was even, favorably, compared to the Inquisition by the Jewish Defense League, etc.). THere is lots more, all deleted, "Coatrack". Now that notablity can be established better even than for WaoG., why should Wasilla Assembly of God be kept, but Wasilla Bible Church not? Also, why was the article deleted withuot a 5 day debate?
2. The last bit of info that anyone cares about was just deleted out of Wasilla Bible Church as “irrelevant” to Wasilla. Why is all the info on WBC not allowed under its allowed section header in Wiki?
3. The positions of Wasilla Asembly of God, as put forth in its sermons and by its invited speakers (Palin is but one), is of huge interest to anyone who looks in an encyclopedia about the church. The info has nothing to do with Palin (except by speculation in comparing her views with their possible roots). All of the stuff the church is known for is kept off, since it is called "coatrack". Why is any info that makes the church notable, information one would expect to find in an encyclopedia article on the church, not being allowed to be in the article?
If you look at the talk pages, a handful of editors keep deleting all info, threaten the contributors with shutting them down, and wear them out. Most info is deleted from the Wasilla article and from the Wasilla Assembly of God article. I am afraid to contrib since I was told that if I do I will be blocked from Wiki. Please check my deleted edits, and those of others, and if they should have been made. ThnxEricDiesel (talk) 03:05, 10 September 2008 (UTC) Articles and Information Were Restored. EricDiesel (talk) 15:59, 10 September 2008 (UTC)
Info deleted again in both church articles. EricDiesel (talk) 21:38, 10 September 2008 (UTC)
## Names
Hello, sir. I saw on a signature the C stands for Carl. However, what's the B and M?--Chris Wattson (talk) 18:39, 11 September 2008 (UTC)
## Details, details...
In the last notification at WT:MoS, "manual of style" in the heading was not properly capitalised, and the first sentence had a space before the full stop. I assume these are in the standard message, so I request their correction for the future notifications.
I realise most people don't even notice these trivialities, but this is the Manual of Style we are talking about, and some people there are fussy. I, for instance. :-) Waltham, The Duke of 04:59, 12 September 2008 (UTC)
I capitalized Manual of Style and removed the extra space. — Carl (CBM · talk) 13:44, 12 September 2008 (UTC)
Thank you, o Botmaster. Waltham, The Duke of 15:49, 12 September 2008 (UTC)
## Mathematicians
I happened to notice that Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Mathematicians was breaking the "too many expensive parser functions" limit. I recoded the row template so that it only uses one #ifexist instead of two per row. A side effect is that I've swapped two of the columns (dates and class). These no longer match the header generated by VeblenBot. Can you fix? Geometry guy 10:52, 13 September 2008 (UTC)
## WikiProject scoring
Hi CBM, I just saw this; I had thought that after subtracting 1000 we were dividing by 3, not by 2. Am I wrong on that? Thanks, Walkerma (talk) 14:30, 11 September 2008 (UTC)
We had gone back and forth on that by email; maybe we didn't ever come to a consensus about it, since I mentioned it along with other things in a long message. I thought at the time that dividing by 2 would be better. It results in a distribution with the 10th and 90th percentiles around -100 and 100, respectively, not an unreasonable range. A 100 point change is the same as changing High to Top or vice-versa.
I can very easily change the code to make it divide by 3 instead. I'm sure the effect will be to add more articles from projects with lower scores and decrease the number of articles from projects with higher scores. I don't have any data to justify a preference for dividing by 2, it just feels better to me for some reason. — Carl (CBM · talk) 14:49, 11 September 2008 (UTC)
OK, that sounds good for now; I thought the 3 had come in your last email to me on the topic, that's why I wanted to check. If there are projects in the lowest 10% that slide off the scale, they can always make manual nominations if they feel "badly done to"! BTW, I've asked for shepbot's help with the list announcements. Thanks for the updates to the SelectionBot page. Walkerma (talk) 15:46, 11 September 2008 (UTC)
I do think we should accept "manual nominations" for some period of time, with some sort of fixed criteria. That will also resolve an issue Titoxd pointed out to me, that because the database dump is getting more out of date, there are a few new FAs that should be selected but won't be on the computer-generated lists.
Using ShepBot is a good idea. I can also use the 'SelectionBot' user to post announcements or update wikipages, if needed. Once the last selection run is made, it looks like the next task is to make a list of selected articles that are in cleanup or maintenance categories. — Carl (CBM · talk) 15:57, 11 September 2008 (UTC)
I agree with ShepBot, definitely. I also told Carl that for the final selection, I think it would be better to do an API run (that is, gather data from the live wiki) to avoid the stale database problems. We can also have a short-term nominations process to avoid parts of sets to be left out.
One more thing: will there be any articles that were in v0.5 that won't be bot-selected for 0.7? We also need to include those. Titoxd(?!? - cool stuff) 19:05, 11 September 2008 (UTC)
I think that there will be some way for projects to manually propose articles that are missed by that automatic selection. If that's true, I'd rather use that for the articles that have been reassessed since the database dump. If I used the API, it would take a lot of manual work to follow up on articles that have been renamed since the database dump, which I would like to avoid. — Carl (CBM · talk) 20:18, 11 September 2008 (UTC)
(unindent) You're right that probably the next task after selection is to flag all articles with cleanup tags; User:Dank55 is interested in organizing a copyediting campaign to help clean up with worst offenders, which would be great. Another task will be to find a way to merge the automated selection in with the manual selection (many will be duplicates, of course. To save a lot of reviewer time, it'd also be really nice to find out which articles have already been included from the current nominations - including set nominations, where lists are transcluded in.
Another question - can you find out why WikiProject:Schools articles aren't appearing in the latest list? They appear in the 1.0 bot list (under W for WikiProject) but they don't show up here. I know I did a principal article for the project (School), so it was picked up by the bot. This was flagged by a project member here. Could there be other projects missing, or was this a single anomaly? Thanks, Walkerma (talk) 07:53, 12 September 2008 (UTC)
I'm looking into the issue with the Schools project. — Carl (CBM · talk) 13:27, 12 September 2008 (UTC)
As usual, there are several issues here. The Schools project wasn't listed because SelectionBot was being more picky about category naming than WP 1.0 bot. That will be fixed at the next upload.
The other things I noticed are a few new projects that were formed since the last database dump. These are listed at User:SelectionBot/Sandbox. I think it's best to go through and assign principal articles for these, so they can be included in the selection. The easiest thing would be to just annotate that page with the relevant information. I'll be able to work on it this evening. — Carl (CBM · talk) 15:00, 12 September 2008 (UTC)
Once I have the main article for each of those, I'll add them to the selection list and create a new data set. I should be able to finish that either this evening or tomorrow. — Carl (CBM · talk) 15:00, 12 September 2008 (UTC)
OK, I looked over that sandbox list. Many are not new, they are on the Sept 2 list, so I put the ones from that list into the sandbox page. I'll work on assigning the rest later. So hopefully we'll get our selection in the next 24 hours!? Thanks, Walkerma (talk) 20:28, 12 September 2008 (UTC)
Yes, I can work on it later tonight. — Carl (CBM · talk) 20:35, 12 September 2008 (UTC)
The list is done, I think, so I think you can go ahead. Then when you get time, could you respond to Stepshep here? Thanks! Walkerma (talk) 01:25, 13 September 2008 (UTC)
Thanks for finishing those. Barring any more unforseen difficulties I can post the selection Saturday morning. — Carl (CBM · talk) 02:30, 13 September 2008 (UTC)
Can you review this rough draft of a posting and give your comments? Thanks, Walkerma (talk) 22:13, 13 September 2008 (UTC)
## Wikipedia:Transclude text has been marked as part of the Manual of Style
Wikipedia:Transclude text has recently been edited to mark it as part of the Manual of Style. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 14 September 2008 (UTC)
## Need some help with ORish definitions at Semigroup action
The User:Geometry guy has done some work "disambiguating" the notions of M-act and S-act, which I've not seen disambiguated that way in any book on the topic I have on hand. He claims he copied those from Monoid, but that page doesn't make the dissambiguation. I'm fairly familiar with the area, because I use some of those results for my own reaseach, but I don't do reasearch in that area per se. I you know someone more authoritative active on Wikipedia, perhaps a you could ping him. Thanks, VasileGaburici (talk) 19:23, 14 September 2008 (UTC)
The main point was actually to disambiguate semiautomaton and monoid action. The distinction between monoid action and semigroup action is pretty minor, but both are used and they are different. I don't much care for the terms M-act and S-act, but was following previous editors and what literature I could find online. Any illumination you can provide would be welcome. Geometry guy 20:31, 14 September 2008 (UTC)
## Template for ambiguous (or not yet settled) terminology?
Is there a template for something like "Warning: the terminology in this article does not have a wide acceptance" and/or "there is little consensus amongst authors/sources for the terminology used in this article". I think that something like this is needed for some math/cs articles... VasileGaburici (talk) 19:11, 15 September 2008 (UTC)
No, there isn't. The underlying problem is that only very rarely do mathematics authors actually take time to discuss how widespread their terminology is. This is particularly true for contemporary research (vis-a-vis historical essays). They just define the terms and move on. In practice, we rely on editorial discussion on the talk page to figure out how to explain terminology. I think that a "scare tag" at the top is much less useful to the reader than a clear explanation of what's going on.
I'm sure that we can find a wording that everyone can agree with, in the end. Sometimes it's best to simply say "terminology varies from one author to another", explain how it varies, and be explicit about which definition is being used in the article at hand. — Carl (CBM · talk) 19:21, 15 September 2008 (UTC)
In the end, I always remind myself that, fundamentally, it's mathematics that we're trying to document, not terminology. Often, disputes about terminology have no corresponding dispute about actual mathematical content. In those cases, I think that extended arguments about terminology just churn water and take time that could be spent editing other articles. — Carl (CBM · talk) 19:27, 15 September 2008 (UTC)
Good point. VasileGaburici (talk) 20:02, 15 September 2008 (UTC)
## Re: math illustrations
See Wikipedia talk:WikiProject_Mathematics#Mathematical illustrators for my reply. Oleg Alexandrov (talk) 06:39, 16 September 2008 (UTC)
## wiki 0.7, SelectionBot, selection
Hey, would it be possible to modify the selected list? esp., to rmv a few items? Some of the WP:ETHNIC articles (in a link at WT:ETHNIC) may be a little controversial or sticky or something... Ling.Nut (talkWP:3IAR) 09:34, 16 September 2008 (UTC)
You should mention those particular articles at Wikipedia talk:Version 0.7. It is certainly possible to remove articles from the selection. — Carl (CBM · talk) 11:35, 16 September 2008 (UTC)
Thanks, will do. Ling.Nut (talkWP:3IAR) 23:31, 16 September 2008 (UTC)
## page views
HI, You referred to "a steady stream of page views" to abstract nonsense. Does one have access to this type of data? Katzmik (talk) 13:45, 16 September 2008 (UTC)
The data can be viewed at http://stats.grok.se, run by User:Henrik. I have my own local copy of the data for an independent project. Henrik's data does not take care of redirects, so you have to combine the results for General abstract nonsense and Abstract nonsense to get the total page views. I also made a list of the Top 500 math articles by hitcount, although it needs to be updated. — Carl (CBM · talk) 14:35, 16 September 2008 (UTC)
## Article score fomula can penalize importance assessments
Moved to the SelectionBot talk page, with a reply. — Carl (CBM · talk) 21:51, 16 September 2008 (UTC)
## Wikipedia:Article series has been marked as a guideline
Wikipedia:Article series has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 17 September 2008 (UTC)
## Wikipedia:Article series no longer marked as a guideline
Wikipedia:Article series has been edited so that it is no longer marked as a guideline. It was previously marked as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 19 September 2008 (UTC)
## Peer Review Bot not running?
Hi Carl, it would appear that User:PeerReviewBot did not run on the 20th (neither archives nor SAPRs). Ruhrfisch ><>°° 02:00, 21 September 2008 (UTC)
A change in the MediaWiki code made my previously-functional bot script unable to log in. I fixed my code to match the new system and ran the code by hand. — Carl (CBM · talk) 13:46, 21 September 2008 (UTC)
Thanks as always for your hard work on this. Ruhrfisch ><>°° 17:19, 21 September 2008 (UTC)
## Wikipedia:Wikipedia doesn't use Allwiki has been marked as a guideline
Wikipedia:Wikipedia doesn't use Allwiki has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 21 September 2008 (UTC)
## Wikipedia:WikiProject Ships/Guidelines has been marked as part of the Manual of Style
Wikipedia:WikiProject Ships/Guidelines has recently been edited to mark it as part of the Manual of Style. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 21 September 2008 (UTC)
## Version 0.7
Hi CBM, thanks a lot for the the new bot run, which I see now includes Primate and Electronic articles. Can you add in the WP:Palaeontology (UK spelling, with an "a) articles too, using Paleontology (US spelling) as principal article? The categories were set up wrongly, so they got a stats table but didn't show up on the main index page. The result was that we never generated a list for WP:Palaeontology, and now they're asking to be included in V0.7.
How we will deal with the new results, bearing in mind that articles already in the old list may have been re-assessed, renamed, had new interwikis, etc.? We can't reasonably just de-select articles that were selected last week, or add in new ones. I'd suggest that we generate an addendum page just for projects that were missed out of the original list - Primate, Electronic, Palaeontology, and any others you know of - and leave the existing selections alone. Many projects have put in hours of work on the current selection, so I regard it as set; we have the manual nomination and the "please deselect" option available to deal with corrections to the original list, and those options seem to be working fine. What do you think?
Once we sort that out, we'll have to send a formal message to all the projects that got missed out in the main selection. Should I do that manually, or are there more projects than we thought?
I hope to talk to you on IRC tomorrow at 4pm EDT. I may lurk on the 1.0 channel this evening while I do some 0.7 work. My conference last week went very well, BTW, but I'm still catching up.
Thanks again, Walkerma (talk) 19:45, 21 September 2008 (UTC)
PS: Ling Nut has produced a rough on-wiki list of the selection here, but be warned, it's big! He is doing an AWB run through every article, doing basic cleanup. Walkerma (talk) 20:04, 21 September 2008 (UTC)
I think the addendum idea is sound. Apart from the projects that were left off before, there are only 85 articles added to the selection. So those articles can be handled by the nominations page without redoing all the data. I'll still post the updated data in case anyone is interested in looking at it. I added Palaeontology, which I had thought I was not going to include, so that will require another upload to toolserver. I should have the new data in place later this evening. — Carl (CBM · talk) 21:26, 21 September 2008 (UTC)
Thanks, that sounds great! Walkerma (talk) 00:19, 22 September 2008 (UTC)
## Wikipedia:Manual of Style (Macedonia-related articles) no longer marked as a guideline
has been edited so that it is no longer marked as a guideline. It was previously marked as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 22 September 2008 (UTC)
## Wikipedia:Manual of Style (Macedonia-related articles) is no longer marked as part of the Manual of Style
has been edited so that it is no longer marked as part of the Manual of Style. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 22 September 2008 (UTC)
Both these are wrong. The page has long been marked {{proposed}}; VeblenBot is reacting to a change of category, in this edit, which made the cats agree with the text of the article. It might be better to have the bot watch the presence of {{guideline}} tags instead. Septentrionalis PMAnderson 19:18, 22 September 2008 (UTC)
## Joke
Is there a mathematician-phycisist-engineer-CS joke posting board? (Seriously.) If so, with the wider readership at Wikipedia as compared to the departments at Caltech and UCLA, I might finally be able to find someone who will actually LAUGH at one of my jokes for the first time. EricDiesel (talk) 19:21, 22 September 2008 (UTC)
I don't know of any. I do think the new content at mathematical proof looks fine, it resolves my concerns from earlier. In my copious free time I'd like to polish it up a little. — Carl (CBM · talk) 22:26, 22 September 2008 (UTC)
User:Gandalf61 wants to nix the whole "Mathematics without Proof" section. I agree with his points (sectoin is poorly written, too long, fringeish POV) but I don't agree such a section does not belong in a mathematical proof article. His same objections apply to most of what I wrote in the other sections, in that it they all needs a rewrite, but I think the section headers are all appropriate. The reality is that computers will soon be as good at proving anything as they now are at anagrams.. then chess... then medicine. All that will be left for us humans will be hyper-meta stuff and exploratory intuition. They would then strongly object to such a section, and mention of humans in a history of math article with more than a passing reference. That is a joke, but also accurate. EricDiesel (talk) 00:29, 23 September 2008 (UTC)
Its here[2]. Thanks to User:Gandalf61 for indirectly locating it. Tautologist (talk) 18:10, 24 September 2008 (UTC)
## Template help for screen readers
Can you help us out, Carl? I've been having a conversation with User:Graham87, who is a blind admin with huge numbers of edits to Wikipedia (whose judgment on screen readers I completely trust), that goes like this:
I looked through the talk archives at WP:ACCESS and can't find that we discussed this. Would it work for you to have the first image in a section directly above the heading rather than directly below? Do screen readers have a hard time with that for some reason? ...- Dan Dank55 (send/receive) 02:48, 24 September 2008 (UTC)
No I much prefer it if images are below the heading. If the image is above the heading, because screen readers read linearly, the image seems unrelated to the text because I won't know about the heading below it. Graham87 03:08, 24 September 2008 (UTC)
The problem is the rule not to sandwich text; if there are more images than text, then the images drop down into the next section, which is bad, or we dump a bunch of white space in the article, also bad. Is there any image code which will let me put the link for the image under the heading, but force it to show up higher, either on the same line or even a little above that? - Dan Dank55 (send/receive) 03:26, 24 September 2008 (UTC)
... I don't know about any code for controlling the image position... Graham87 03:41, 24 September 2008 (UTC)
Well, I'm out of ideas. I know that some of the wikiprojects have images in their articles on the same line as headings (that is, the image link is directly above the heading), and they don't read (many of) the style guidelines. If you come up with a solution that works for you, please let me know.
... It's not such a big deal, but I'd be happy if there was an intuitive way to fix the problem that works for both sighted and blind users. Graham87 04:17, 24 September 2008 (UTC)
I'd be glad to try to help, but I don't quite follow what you're asking for. Could you give me a couple specific pages where the problem comes up, and a description of how you'd like them to be fixed? — Carl (CBM · talk) 13:52, 24 September 2008 (UTC)
P.S. I meant that MOS:IMAGE doesn't like lines of text that have images on both sides. - Dan Dank55 (send/receive) 16:09, 24 September 2008 (UTC)
Did you find out anything, Carl? I can pass the buck to G-guy, or we can just harass the guys that make the screen readers. - Dan Dank55 (send/receive) 18:31, 25 September 2008 (UTC)
Sorry, I got distracted. I can see where the screen readers would get confused - if the image literally precedes the heading in the HTML, the screen reader can't tell what section it is in. I don't know any way to cause them to appear in the other order in the HTML but get the effect that you want, unfortunately. — Carl (CBM · talk) 20:12, 25 September 2008 (UTC)
Thanks, I'll punt this to G-Guy. - Dan Dank55 (send/receive) 20:26, 25 September 2008 (UTC)
## Suggested deletion from Super-recursive algorithm
The current version contains the following in the first paragraph:
"Indeed, since mid 1980's, the AI community has produced a large body of work on anytime algorithms for solving such problems as real-time search, constraint satisfaction, planning and scheduling, and diagnosis (Horvitz 1986; Boddy and Dean 1989; Zilberstein 1996). Traditional algorithms either run to completion or they provide no useful solution information. Anytime algorithms, however, are able to return a partial answer, whose quality depends on the amount of computation they were able to perform. An example is the Newton-Raphson iteration applied to finding the square root of a number. This iteration cannot be modeled by a Turing machine and demands more powerful mathematical models, such as limit Turing machines. Theoretical results show that limit Turing machines are more powerful than Turing machines and thus are super-recursive algorithms. Thus, super-recursive algorithms exist not only in theory but are already used in computing practice."
I suggest deleting it. There are several things wrong with it..
(1) Nobody working on anytime algorithms (that I know of) calls their algorithms "super-recursive". To claim they are is to be violating WP:NOR.
(2) When I added my comments about anytime algorithms, I brought them up as an example of how the CS community has been able to get by without this useless category of "super-recursive algorithm" and get results anyway. Burgin claims that the very concept of super-recursive algorithm will liberate CS from Turing-computability shackles; clearly, CS researchers didn't need any such liberation. Now Multipundit is claiming anytime algorithms under the umbrella of "super-recursive", as he does for many other things.
(3) Anytime algorithms do not return "partial" answers -- they return approximate answers, with the quality of the answer typically related in a predictable way to the amount of computing done.
(4) It's not "Newton-Raphson", it's Newton's algorithm, that's used to compute square roots.
(5) Newton iteration can clearly be modeled by Turing machines -- in fact, I've worked on floating point microcode and approximation lookup tables for division and square root using Newton's method -- software, hardware and firmware realizations go way back. Any floating point software or hardware is necessarily going to implement Newton's method in a way that can be modeled with a Turing machine. If what Multipundit means is that doing true Newton's method means using true real numbers, not floating point approximations thereof, then perhaps he's right. But in that case, it's not practical because no computer (not even analog computers) use true real numbers, which require infinite storage to represent in the worst case. (And the worst case is much more "frequent" -- there are only countably many Turing machine programs, but the reals are uncountable.)
(6) The final two sentence start out talking about theoretical results showing limit Turing machines being more powerful, then conclude in a way suggesting that any such theory has been reduce to practice. Really? Show me a real computer that uses the reals, not floating point numbers, and carries out Newton's method on square root to an infinite number of steps.
How could matters be any more confused?
I'd make the change myself, but I got far too disgusted with Multipundit's behavior last time I tangled with him. Maybe you have the patience. I think he's in WP:FRINGE, and where he makes specific reference to anytime algorithms as super-recursive algorithms (an idea he obviously got from me, ironically), he's also engaged in WP:NOR. Every time he adds something not in the peer-reviewed literature, he's in WP:NOR I'm surprised you put up with it. Yakushima (talk) 10:29, 25 September 2008 (UTC)
I can only work on so many things at a time, and at some point I stopped following that article very closely. The claim about Newton's method is clearly bad - I can program my calculator to find sqrt(2) with Newton's method. I also find the claim that contemporary computers are performing non-recursive algorithms very dubious.
Anyway, I'll trim the lede down some, but I don't have an enormous amount of time to try to improve the article. — Carl (CBM · talk) 13:40, 25 September 2008 (UTC)
## Peano arithmetic vs primitive-recursive arithmetic vs Goedel's theorems
A humble question: why do we need to consider both PA and PRA for Goedel's proofs? Isn't primitive recursion all that we need? Is PA also required so that the symbols of the axioms are there to be Goedelized, and then PR is just represent "the formation rules" required to manipulate the numbers (this doesn't sound right to me). It seems to me that PRA contains "enough arithmetic", albeit in an intuitionistic formulation. I'm thinking in context of Feferman's "Predicativity" p. 26-27, Church's Thesis, Goedel's later assertion (1964) that Turing's machines present an adequate basis for a "formal" arithmetic system, and Goedel's theorem V. Bill Wvbailey (talk) 16:32, 25 September 2008 (UTC)
PA is the easiest one to handle. It is not necessary to think about PA at all for Gödel's theorem; PA is just one of many axioms systems for arithmetic to which the theorem applies. PA is primarily of interest as a strong but well motivated theory of arithmetic in which most elementary number thoery can be carried out. A minimal system to which the theorem applies is Robinson arithmetic.
The way that people typically think about PRA is not as a first-order theory. They view it as a quantifier-free theory with free variables, which is about the same as saying a theory with universal quantification that cannot be negated - and thus no existential quantification.
The main interest in PRA in the study of metamathematics is:
1. PRA is extremely finitistic. Thus it is used to play the role of a finitistic base system whose consistency is not in doubt. PRA is usually studied with a classical proof system, including the excluded middle, although it could be studied with an intuitionistic system.
2. PRA is able to prove Gödel's theorem and many other syntactical results of proof theory. Thus if someone asks "how much logical apparatus is required to prove Gödel's theorem?" the answer is "very little". This is the main reason people bring up PRA in the context of the incompleteness theorems.
— Carl (CBM · talk) 20:40, 25 September 2008 (UTC)
This is what I suspected. Thanks! Bill Wvbailey (talk) 22:32, 25 September 2008 (UTC)
## request
can you give me a copy of my article it is on my discussion. your name was on the list. (The Perfect Enso (talk) 03:58, 25 September 2008 (UTC))
You need to tell me the title of the article. — Carl (CBM · talk) 03:59, 25 September 2008 (UTC)
aggreement in principle (The Perfect Enso (talk) 04:17, 25 September 2008 (UTC))
OK, thanks. The article was deleted because it had been moved to http://en.wiktionary.org/wiki/agreement_in_principle at some point. I can email you the source of the deleted page, if you set an email address in your preferences. If you don't want to use your real email address, just make a throwaway account on gmail or some other free email system. — Carl (CBM · talk) 04:23, 25 September 2008 (UTC)
Can you put it in my subpage instead? (The Perfect Enso (talk) 01:46, 27 September 2008 (UTC))
The content was "In law, An agreement in principle is a stepping stone to a final agreement. Such agreements with regards to the principle are usually considered fair and equitable." along with three links [3] [4] [5] — Carl (CBM · talk) 01:54, 27 September 2008 (UTC)
## Discepancy
Hi CBM, do you have any thoughts on this discrepancy? Good to see some VersionIDs coming in, though! Walkerma (talk) 05:51, 26 September 2008 (UTC)
I don't know what's up there, but I'm planning to finish updating the selection tomorrow afternoon, which will include updating all those pages (while keeping any data that has been entered, of course). — Carl (CBM · talk) 00:10, 28 September 2008 (UTC)
## Wikipedia:Deletion policy/Proposal has been marked as a policy
Wikipedia:Deletion policy/Proposal has recently been edited to mark it as a policy. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 27 September 2008 (UTC)
## Wikipedia:Preparing images for upload no longer marked as a guideline
Wikipedia:Preparing images for upload has been edited so that it is no longer marked as a guideline. It was previously marked as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 27 September 2008 (UTC)
What do I put in the edit summary box that sometimes appears above save page what is this for? —Preceding unsigned comment added by The Perfect Enso (talkcontribs) 23:20, 27 September 2008 (UTC)
The edit summary box is used to make a brief comment describing your edit. These edit comments are what you see when you click the "history" button on an article. — Carl (CBM · talk) 00:11, 28 September 2008 (UTC)
Are they required to do? The Perfect Enso (talk) 04:03, 28 September 2008 (UTC)
## CAT:ESP
Hi, would it be possible to have User:VeblenBot make a table for Category:Wikipedia semi-protected edit requests like the one it makes for WP:PER? 23:41, 27 September 2008 (UTC)
I have never seen the point of semi-protected edit requests, and so I don't see the point of tracking them. People who want to edit semi-protected pages can do so by simply registering an account, which is what we encourage all serious editors to do anyway. — Carl (CBM · talk) 23:55, 27 September 2008 (UTC)
## Troublesome PR
Hi Carl, the article on Rudolf Wanderone has a peer review at Wikipedia:Peer review/Rudolf Wanderone/archive1 but it is not showing up on WP:PR. The article was listed there, then I did the semi-transclusion trick to save space. The nominator then thought it had been archived and moved it to Wikipedia:Peer review/Rudolf Wanderone, AND copied the semi-automated peer review to it. I have removed the SAPR and thought I moved it back properly, but it still is not showing. Could you please take a look and figure out what the problem is? I alsready asked G guy and he thought it was a VeblenBot issue. Thanks in advance, Ruhrfisch ><>°° 11:54, 28 September 2008 (UTC)
Never mind - I just checked again and it is now listed there. Sorry for the mixup, Ruhrfisch ><>°° 11:56, 28 September 2008 (UTC)
## Release Version Nominations
Hi CBM, I'd like to have a big push on reviewing all the manual nominations that have appeared at Wikipedia:Release_Version_Nominations, but we can't really do productively until we know which ones on the page have already been selected by SelectionBot. I tried doing this with AWB list comparer (against Ling.nut's list, but it maxes about at around 5000 so I'm only getting A-C. I remember you said that this should be possible for you to do, can you help? Also, is there a good time for you to chat about getting an index done? Thanks, Walkerma (talk) 05:46, 28 September 2008 (UTC)
Here's a tool that scans Wikipedia:Release Version Nominations and compares it with a selection list: http://toolserver.org/~cbm/cgi-bin/nominations.cgi Tools like that are generally very fast to write, so just let me know the specs of any reports you need, and I'll work out a way to generate them.
I could discuss the index anytime today (Sunday Sep 28) before about 9pm EST, or Monday evening. — Carl (CBM · talk) 16:46, 28 September 2008 (UTC)
## Easy as pi?: Making mathematics articles more accessible to a general readership
The discussion, to which you contributed, has been archived, with very much additional commentary,
at Wikipedia:Village pump (proposals)/Archive 35#Easy as pi? (subsectioned and sub-subsectioned).
A related discussion is at
(Temporary link) Talk:Mathematics#Making mathematics articles more accessible to a general readership and
(Permanent link) Talk:Mathematics (Section "Making mathematics articles more accessible to a general readership"). Another related discussion is at
(Temporary link) Wikipedia talk:WikiProject Mathematics#Making mathematics articles more accessible to a general readership and
(Permanent link) Wikipedia talk:WikiProject Mathematics (Section "Making mathematics articles more accessible to a general readership").
-- Wavelength (talk) 01:30, 29 September 2008 (UTC)
## Mullins Lab
Dr. Bill Mullins of Mullins Labs, now retired, had 5 sons. The youngest was Michael Mullins. He is the the Michael Mullins who was listed in Boulder Daily Camera on November 18, 1996 for attempting to kill his pregnant wife. She is now speaker on Domestic Violence Awareness. Please see Boulder Daily Camera newspaper article, "The Boulder Shootings," for more information. It was also ran on every major broadcast network on November 17, 1996 and November 18, 1996. As for the lab, since Dr. Bill's retirement, his son Steve has sold off most of it. There is not much left of the family business. Michael committed suicide after shooting his wife and the family recently lost another son, this one to alcoholism, per Augusta Chronicle, March 2008 —Preceding unsigned comment added by 209.213.20.39 (talk) 02:33, 29 September 2008 (UTC)
## Bulletin Board System
Hi CBM,
I noticed that you removed the "ANSI scroller" image from the Bulletin Board System artical, with the comment "Perl WP:NFCC" and I was wondering if you could explain this to me. I looked up the Wikipedia artical on Non-free content criteria compliance, but I don't belive it applies to this image which is a free non-copyrighted ANSI image created by the ANSI group named "Ice" back in the 1990's. I see the image was previously deleted by Fairusebot. Is there something that needs to be changed in this image in order to allow it to be used in the BBS artical? Thanks in advance.
Pcmicro (talk) 15:37, 30 September 2008 (UTC)
No problem. The image in question, Image:Krux-ice-dec94.png, is not tagged as a free image. Unless the art pack was explicitly released under a free license, the image is copyrighted by default. If the autor were willing to release it under a free license, then we could certainly use it. But without any evidence of a free license, we can't. — Carl (CBM · talk) 16:18, 30 September 2008 (UTC)
My name is Leon Friedrichsen and have been a participant of the Encierros for 18 years. During these years at Pamplona many Spanish folks have mentioned that San Fermin was never "dragged" through the streets anywhere. I think thats the media of some sort making their claim to the usual dramatic sillyness so common in our current, shallow society. It seems as though they have too much to lose from telling the truth.
San Fermin was beheaded in Amiens, France after being stabbed in his side as he was spreading the Christian faith abroad. Hence the red scarf and sash. The bull fight came much later and after the fiestas were combined and moved to July in the 15th century, an arena was erected at the Plaza Del Castilo. At that time the bulls were run through the streets to the arena, were fought with honor and then ran back to the corals. They were not killed at that time. —Preceding unsigned comment added by 209.33.43.129 (talk) 05:26, 1 October 2008 (UTC)
## Wikipedia:External links has been marked as a guideline
Wikipedia:External links has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:51, 2 October 2008 (UTC)
## Wikipedia:External links is no longer marked as part of the Manual of Style
Wikipedia:External links has been edited so that it is no longer marked as part of the Manual of Style. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 2 October 2008 (UTC)
Mullins Labs Mullins Labs Logs indicate, as does the family, that there was not a threat issued concerning the lab, but the family. There has not been a company directed threat made. Please correct your information. Is there anyway that you know that those with whom you have had these posting interactions were not members of the Mullins Family. —Preceding unsigned comment added by 209.213.20.39 (talk) 20:23, 2 October 2008 (UTC)
## Wikipedia:Naming conventions (law enforcement agency categories) has been marked as a guideline
has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:51, 3 October 2008 (UTC)
## Wikipedia:Avoid statements that will date quickly has been marked as part of the Manual of Style
has recently been edited to mark it as part of the Manual of Style. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 3 October 2008 (UTC)
## NTWW and perennial issues
We're having a discussion about the inclusion/deletion debate over at WP:NTWW tomorrow (saturday) at 22:00 UTC. Since you were participating in the AN thread, I figured I'd let you know. Xavexgoem (talk) 22:09, 3 October 2008 (UTC)
## Wikipedia:Naming conventions (law enforcement agency categories) has been marked as part of the Manual of Style
has recently been edited to mark it as part of the Manual of Style. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 3 October 2008 (UTC)
Carl, the page hasn't had any edits since it was created, and I see nothing on the page that I can connect to the Manual of Style (whatever that is :). It's marked as a naming convention; is that what produced the notice? - Dan Dank55 (send/receive) 20:56, 3 October 2008 (UTC)
Yes. I have complete documentation at User:VeblenBot/PolicyNotes. The "naming conventions" category is currently treated both as a guideline and a style guide. If that isn't optimal, I can change the behavior. Let me know, — Carl (CBM · talk) 19:18, 5 October 2008 (UTC)
I think the Duke's suggestion has been accepted (at least by the people who read WT:MOS every day, otherwise we/they would have said something) at WT:MOS#Wikipedia: Naming conventions (law enforcement agency categories) has been marked as part of the Manual of Style. - Dan Dank55 (send/receive) 19:14, 8 October 2008 (UTC)
P.S. I can't get the section link to work, but you get the idea. - Dan Dank55 (send/receive) 19:16, 8 October 2008 (UTC)
I removed the naming conventions category from the MoS list. It is still included in the policy/guideline list. I don't have a third list yet just for naming conventions, but I could set that up at some point. — Carl (CBM · talk) 21:06, 8 October 2008 (UTC)
Thanks. - Dan Dank55 (send/receive) 03:27, 9 October 2008 (UTC)
## User:Yecril
Hi,
Do you think this is worth taking to ANI for wider input? This user looks to have a history of following his own interpretation of our guidelines even when there's abundant evidence that he's in the wrong. Chris Cunningham (not at work) - talk 08:56, 7 October 2008 (UTC)
I thought the discussion he and I had yesterday was going well. Everybody always disagrees about style. If I can't prevail on him to discuss his style changes first, then some other form of dispute resolution may be needed. — Carl (CBM · talk) 12:50, 7 October 2008 (UTC)
I started a discussion [6] on the math project page. The best resolution here will involve getting a good sense of the overall consensus regarding the {{math}} template. — Carl (CBM · talk) 13:33, 7 October 2008 (UTC)
## „Aus dem Paradies, das Cantor uns geschaffen hat, soll uns niemand vertreiben können."
replied on cantor's talk. Ling.Nut (talkWP:3IAR) 13:59, 9 October 2008 (UTC)
...and a slightly expanded provenance is on page 525n3 of "Mathematics and the Divine" By T Koetsier, L Bergmans. Ling.Nut (talkWP:3IAR) 14:09, 9 October 2008 (UTC)
Thanks. — Carl (CBM · talk) 14:30, 9 October 2008 (UTC)
## Wikipedia:Facial hair is required for administratorship has been marked as part of the Manual of Style
has recently been edited to mark it as part of the Manual of Style. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:51, 9 October 2008 (UTC)
## Gauss's law
Hi,
Looks like the recent curly quotes shenanigans has resulted in this article being moved to a title which consensus seems to have formed against. Can you shift both article and talk to Gauss's law, please? Chris Cunningham (not at work) - talk 23:53, 11 October 2008 (UTC)
It looked to me that the page was moved on Feb 16 [7] to Gauss' law, and then moved on Sep 17 [8] from Gauss' law to Gauss’s law (with the curly quote). Was the page ever named Gauss's law in between? My main goal was to undo back to whatever name was established before Sep 17; if that was Gauss's law then that's fine with me. — Carl (CBM · talk) 01:34, 12 October 2008 (UTC)
The ongoing discussion on that article started in April, but the conclusive edit was on September 15. Even accounting for Yecril's spat of page moves, this would appear to be entirely in line with a move in conjunction with talk page consensus on that date. Chris Cunningham (not at work) - talk 02:04, 12 October 2008 (UTC)
If that's the agreement there, I don't object to it. The people discussing it on the talk page seem to be confused about the difference between grammar and editorial style, but there are other things that interest me more. I was confused by the interaction with Yecril's move. I'll undo my move and apologize to an editor I contacted earlier. — Carl (CBM · talk) 02:15, 12 October 2008 (UTC)
Thanks. Chris Cunningham (not at work) - talk 02:29, 12 October 2008 (UTC)
## Keeping info out by provoking a page protection by edit warring
Protection lifted so strike comment Wasilla Assembly of God is the church attended by Sarah Palin and at which she gave a widely covered speech about a sermon at the church. The church, its pastor, and a frequent church guest pastor have been the subject of international news coverage since 1999, including for controversial sermons given at Wasilla Assembly of God in 2005 and 2008.
There was initially a dispute as to whether this article should be deleted. The article was kept. One or two editors then attempted to keep sourced information out of the article by constant deletions, vaguely citing “BLP” and “Coatrack” without specificity, and ignoring requests for specificity. They were successful, in that they created enough edit wars that they kept the information out by getting the article blocked.
There have now been three consensus suggestions for three sections for two weeks or so. All talk page suggestions made in them have been addressed.
The content of speeches and sermons given at this church has been the subject of almost a million web pages and thousands of news stories. Yet the information that is the subject of the international coverage, sourced with respected journalists and actual photos and video footage of the sermons is not in the article.
This article should be restored, with the three consensus sections as worded and sourced in the talk page, here[9], here[10], and here[11]. There are two editors who will object to any information about the speeches or sermons, but they have not made comment on the consensus suggestions for two weeks, and all concerns they voiced previously were addressed. If the consensus sections are not added, the editors who engaged in edit wars to keep information out will have succeeded in keeping the well sourced information out through provoking a protection by edit warring.
Here is an example of the "reasoning" by User:Jclemens. Thomas Muthee is a Kenyan pastor who delivered at least eleven sermons at this church between 2005 and 2008, who was singled out for credit by the governor of Alaska for her gubernatorial victory in her speech to the graduates at the church’s “Masters Commission” for his sermons and prayers given at this church, and who is the subject of a large number of international press stories for the content of his sermons given to this church. JClemens deletes all information about Muthee’s guest sermons reasoning as follows:
“So you added a section about the activities (1) of a person [Muthee] (2) mentioned by a guest speaker [Palin] (3) at a commencement ceremony [Master’s Commision] (4) for a ministry (5) of the church? I'm sure Kevin Bacon must fit in here somewhere—I count five degrees of separation from the actual church itself. (bold added)
• 1. How can consensus be reached with this kind of reasoning? (JClemens is the editor who was edit warring with variuous other editors, including me.)
• 2. I do not want to cause unneeded bad feelings by pointing out reasoning difficulties, so left this message on your talk page. Am I using the talkback at the top of the page correctly for this? Tautologist (talk) 19:29, 13 October 2008 (UTC)
## IRC
Hi CBM, I was just wondering if you're going to be around for the Version 0.7 IRC on #wikipedia-1.0 at 2000h UTC (4pm US Eastern Daylight time? We only have a week left before our deadline, I think we need to review what's left. I'd really appreciate learning about how we will handle the merge of the addendum with the main bot list and main manual selection, and how to remove articles that people have requested removed. Cheers, Walkerma (talk) 19:00, 14 October 2008 (UTC)
## This is new to me, so.
Had a bit of vandalism on my user page, the same IP keeps adding a bit of vandalism/unsourced (and untrue) info to Scott Menville's page as well. Any advice or assistance appreciated.Mr T (Based) (talk) 15:50, 15 October 2008 (UTC)
It looks to me like one person who is changing IPs. The 66.203.xx.xx IPs are from a school district in Ohio. Since the IPs change so often, there's no benefit in blocking them individually. If you have more problems with your user page or with Scott Menville, I'll semiprotect the pages. — Carl (CBM · talk) 17:46, 15 October 2008 (UTC)
Right, thank you.Mr T (Based) (talk) 17:47, 15 October 2008 (UTC)
I went ahead and semiprotected your user page for a month; the edit there was really out of line. The protection will expire automatically, and you can edit the page normally as long as you are logged in. — Carl (CBM · talk) 17:52, 15 October 2008 (UTC)
Much appreciated! Didn't find it offensive as it was all well wide of the mark, but it's one less thing for me to keep track of. :-)Mr T (Based) (talk) 17:56, 15 October 2008 (UTC)
## Wikipedia:Administrators' noticeboard/Arbitration enforcement has been marked as a guideline
has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:51, 15 October 2008 (UTC)
## Requesting rollback right
Since I've reorganized Criticism of Wikipedia, and also worked a bit on Reliability of Wikipedia, those two pages seem to be a magnet for vandals, e.g. like this. I saw that you are listed on the Category:Wikipedia_administrators_willing_to_grant_rollback_requests, and since we had constructive interactions before, I hope you will grant me this right. I understand that rollback is to be used only for clear cut cases of vandalism. Also, I've read WP:NAS/R. Thanks, VG 13:49, 16 October 2008 (UTC)
No problem, it's done. — Carl (CBM · talk) 14:29, 16 October 2008 (UTC)
Thanks, VG 17:08, 16 October 2008 (UTC)
Hi CBM, a little while back you helped add Saskatchewan Communities & Neighbourhoods to the WikiProject Canada banner. I was wondering if you could take a look at a bug mentioned at Template_talk:WikiProject_Canada#Bug. Many thanks, --Jh12 (talk) 03:14, 22 October 2008 (UTC)
## article rating in priority categories
Hello,
you are the one behind these cute assessment tables, right? Is it possible to enhance the bot so that pages like Category:Top-Priority_mathematics_articles also show an overview over the quality of the articles in that category? Thanks, Jakob.scholbach (talk) 18:47, 20 October 2008 (UTC)
If you have time, could you also have a look at Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Algebra and the like? It would be great to have a table there, as well. Thank you again! Jakob.scholbach (talk) 12:43, 21 October 2008 (UTC)
I think the tables you're interested in are already generated; the page Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Table lists all of them. We could transclude the first table from that page onto the category pages; it has breakdowns by quality and importance.
I noticed that the list page for algebra (that you linked) is broken, as is the geometry page. We seem to have hit some template limit there. I'll try to patch over that (we have a system to break the long pages into subpages). But it will take a while for me to get to it, because I have some urgent deadlines to attend to. — Carl (CBM · talk) 19:11, 21 October 2008 (UTC)
Sure, take your time with this (if you want to do this at all). However, I still can't find what I'm looking for. I look for a table counting all top-priority articles, indexed by field and quality. The site you mention has every other type of combination but not this one. Jakob.scholbach (talk) 21:58, 21 October 2008 (UTC)
Now I think I see. You want something like User:VeblenBot/Math/table:FIELDS.QUALITY but only including Top-priority articles? I can do that very easily. — Carl (CBM · talk) 22:17, 21 October 2008 (UTC)
Here are the tables, which will update automatically:
When I get time, I may add a "total" row to the bottom. That will be a duplicate of the corresponding row in the main table, so for now you have to transclude User:VeblenBot/Math/table:MATHEMATICS to get totals. — Carl (CBM · talk) 22:34, 21 October 2008 (UTC)
Great, thank you! I tried -- and failed -- to include these tables into the categories mentioned above. Is there some template that copies the code at the bot's subpages?
Since you seem to have a mighty engine roaring in the background, here is another suggestion: it would be very handy to have a link to a even finer query at every number shown in the tables. Example: in the table listing top-priority articles, in the intersection of field=algebra and quality=stub, there could be a link to yet another subpage listing all articles meeting these three criteria. Jakob.scholbach (talk) 14:07, 22 October 2008 (UTC)
I added the tables to Category:High-Priority mathematics articles and its siblings. I see what you're asking for with the finer links inside the tables, but that will have to wait for the updated WP 1.0 bot in development. The updated bot will use a database to generate article lists on demand without having to upload them as wiki pages. I'll probably still upload the tables to the wiki, so we can transclude them, but the numbers in the table cells will link to the dynamic tool instead of linking to other wiki pages. I expect the new version of the bot to be live sometime in winter 2009. — Carl (CBM · talk) 14:26, 22 October 2008 (UTC)
Note that the lists are generated, for example at Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Foundations,_logic,_and_set_theory. It's just that the format of the lists isn't right to link to a specific field/priority/quality combination, and the time it would take me to change the layout and fix all the wiki pages would be better spent on developing the new bot, which will have this functionality as well. I still need to fix the template limits problem with the algebra page. Fixed now. — Carl (CBM · talk) 14:34, 22 October 2008 (UTC)
Alright. Thanks again. I appreciate your working on these issues. I believe this assessment is crucial for pushing WP further. Jakob.scholbach (talk) 17:09, 22 October 2008 (UTC)
## Wikipedia:Portal guidelines has been marked as a guideline
Wikipedia:Portal guidelines has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:55, 23 October 2008 (UTC)
## Wikipedia:Romanization of Ukrainian/Archive 20081024 has been marked as a guideline
has recently been edited to mark it as a guideline. This is an automated notice of the change (more information). -- VeblenBot (talk) 18:52, 25 October 2008 (UTC)
## Wikipedia's Expert Peer Review process (or lack of such) for Science related articles
Hi - I posted the section with the same name on my talk page. Could you take part in discussion ? Thanks ARP Apovolot (talk) 21:35, 25 October 2008 (UTC)
## WikiProject-requested changes to 0.7
Hi CBM, I started this page for notes on changes to be made. If you have any lists like that, can you let me know the link, or update my page? Things are very slow - I'm trying to do this, review nominations, and also to write the index words, all while doing my day job - so I'm afraid I won't have the index done in time for you to use it by the 30th. I'm hoping I can finish it next weekend, if I get the other stuff out of the way before then. Cheers, Walkerma (talk) 06:05, 26 October 2008 (UTC)
That page looks like a great start. I should be able to help with the review noms in the coming week, in the evenings. I have company in town this weekend, which is very nice but keeps me busy. — Carl (CBM · talk) 12:52, 26 October 2008 (UTC)
## A discussion on WP:SYNTH
Since you have previously been involved in discussions about the policy WP:NOR, it appears that you have a depth of understanding about this policy. I would appreciate your comments concerning an application of this policy's section WP:SYNTH here. Thank you. 300wackerdrive (talk) 15:18, 27 October 2008 (UTC)
## PeerReviewBot down?
Hi Carl, I see PeerReviewBot has not yet run today (and I forgot to do the SAPRs the day before). Just a heads up, Ruhrfisch ><>°° 18:23, 27 October 2008 (UTC)
It isn't down, just taking a break while the computer was turned off. Thanks for reminding me to run it by hand today. The automatic execution will resume tomorrow, this was just a temporary situation. — Carl (CBM · talk)
## non-standard analysis
Hi, Your comments suggest that I may have introduced some inaccuracies in the introduction to transfer principle, please feel free to edit it as you see fit. Katzmik (talk) 15:23, 29 October 2008 (UTC)
I'm afraid I would have to get the references and spend a long time thinking about the material before I could edit the articles sensibly.
My general advice, in order to prevent accidental misstatements, is to be meticulously clear about exactly which class of formulas the transfer principle applies to. The clearest way to describe it would be to give both the signature and a description of the exact forms of quantification that are permitted.
One complication is that if the formulas allow any element of the superstructure to be included, they will be in typed first order logic instead of regular first order logic. Also, the signature is going to have to include a set membership relation or some other way of handling the higher-type objects. This makes the technical details more slightly more involved. — Carl (CBM · talk) 15:39, 29 October 2008 (UTC)
## McCain, Obama, Palin, Biden
Hi CBM. I agree with continuing the lockdown thru November 5. However, the huge tag at the top of each of the articles is hideous. The small padlock symbol would work just as well, and anyone would understand what's happening from reading the tag at the top of each of the talk pages. The McCain article has already been locked up for a couple days without using the huge tag at the top of the article. This issue arose previously, and it was decided to keep the Palin article frozen but get rid of the huge tag at the top.Ferrylodge (talk) 07:58, 30 October 2008 (UTC)
Well, I'm not going to change the tags again, but I think it makes more sense to have the large tag. If we're going to protect the articles (which I find regrettable but unavoidable), we should be up front about it in a way that all potential editors can see. Only very experienced editors know what the little padlock means. So my attitude is that the more high-profile an article is, the higher the need for the large protection template. I don't see how the appearance of the tag makes much difference, as long as it isn't neon green and blinking. — Carl (CBM · talk) 13:04, 30 October 2008 (UTC)
Carl...My angry words were intended for others not you...sorry...I know McCain was protected. My feeling re:protection is more relevant to Sara Palin article. That is where the load of Manure was delivered. --Buster7 (talk) 13:53, 30 October 2008 (UTC)
## Watching empty categories before deletion
I've recently been in discussion with an experienced editor who in good faith was slapping the C1 template on categories immediately after removing their contents, thinking that there was a waiting period like PROD. However, admins then deleted the categories the same day, likewise in good faith.
I note that last year you said you'd put watching C1 tags on your list. This discussion also identified the need for a mechanism to watch empty categories before deleting them.
Do you think it is feasible to automate this? - Fayenatic (talk) 10:01, 30 October 2008 (UTC)
Yes. I would make a bot that runs at regular intervals. It keeps a local list of categories that are tagged for C1, and how long they have been empty. When it runs, it updates the local list and makes sure they are all empty. It will make a table in a user subpage that lists all the C1 candidates and how long they have been empty. Admins will need to check the table before deleting the cat. Thoughts? — Carl (CBM · talk) 13:15, 30 October 2008 (UTC)
That sounds excellent. Presumably we would also change the C1 template like PROD to (i) require subst:'ing, (ii) record the date tagged and calculate the date 4 days later, (iii) link to your page, (iv) how about categorising by date?
Could you also make a bot that puts the C1 daily sub-categories with dates 4 or more days old into the into CSD category? We want them to stop showing up as current candidates for speedy deletion until the 4 days are up. - Fayenatic (talk) 13:56, 30 October 2008 (UTC)
## McCain protection
Looks like we got our wires crossed - immediately after I announced that I was unprotecting it, I noticed the below section (and subsequently the ANI thread) and posted a reversal of my announcement. Sarcasticidealist (talk) 13:53, 30 October 2008 (UTC)
## PeerReviewBot not running
Hi Carl, sorry to bug you again but PeerReviewBot has not run since Oct. 28. There was an error that day linking a SAPR, so I tried fixing the PR page - not sure if that will work or not. Thanks as always for all you do, Ruhrfisch ><>°° 14:43, 30 October 2008 (UTC)
Sorry about the bot problems lately. This wasn't related to the outage over the weekend. I had switched to a different library and forgot to enable it. It should be back to normal now. The problem with that SAPR was the lack of a comment in the PR page to let the bot know where to put the SAPR link. That error message always indicates that particular problem. I fixed it. — Carl (CBM · talk) 14:58, 30 October 2008 (UTC)
Please don't apologize - I really appreciate not having to archive PRs and link all the SAPRs by hand! Thanks too for the explanation - I looked at a PR that already had the SAPR linked for comparison and so missed that. Ruhrfisch ><>°° 15:05, 30 October 2008 (UTC)
I'm wondering if PeerReviewBot has a page somewhere that explains its methodology? I ask not because I have any criticisms of it (I actually think it's quite neat) but because I'm wondering how to interpret some of its recommendations. For example, it recently told me to check for redundancies, which is always good advice, but I'm wondering what it means in this case. Does it automatically tell everybody to do that? Did it find certain red flag phrases in the article that suggested possible redundancy? Did it calculate the average sentence length and find that it was too long? Thanks, Sarcasticidealist (talk) 16:23, 30 October 2008 (UTC)
The code to make the reviews is at User:AndyZ/peerreviewer.js and was written by User:AndyZ. The way things work, Ruhrfisch runs that javascript to make the semi-automated review, and then the PeerReviewBot edits the peer review page to link to the review that has been generated. I have thought about porting the javascript code to perl, so that it could be fully automated, but it seemed like a daunting task. It would be very nice if a javascript programmer could use AJAX to automate the creation of the reviews; I may be able to do that someday. — Carl (CBM · talk) 16:52, 30 October 2008 (UTC)
## uniform continuity
Hi, thanks for your comment at the talk page there. I have responded to it, even though this may not be obvious due to multiple edits. I would like to add that it would be helpful if everybody could try to give non-standard analysis the benefit of the doubt at least until the mathematical issues are sorted out, as we are all laboring under the intertial weight of our standard education that has made us see things in a certain way. Katzmik (talk) 09:26, 28 October 2008 (UTC)
I'm very interested to follow your argument there; I just don't yet see that a local property of an extension of a function qualifies as local property of the original function. If I were convinced of that for the particular property in question, then I think that it would be worthwhile to add a sentence pointing to the nonstandard calculus article.
Here is a very trivial example: suppose f is continuous on [0,1). Extend this to a function from [0,1] to the extended real numbers by setting
${\displaystyle f(1)=\lim _{a\to 1}\sup _{x>a}|f(x)|}$
Then the original function f is bounded above on [0,1) if and only if the extension has a finite value at 1. Does this mean that if I permit myself to use extended real numbers then boundedness on an open interval is a local property of a continuous function? — Carl (CBM · talk) 13:32, 28 October 2008 (UTC)
P.S. Concerning your edit at non-standard calculus: do you mind if I add "by undergraduate standards"? Otherwise the remark is not entirely clear. Katzmik (talk) 09:29, 28 October 2008 (UTC)
My concern with "undergraduate standards" is that it doesn't seem to have the right tone for an encyclopedia. It also seems very open to interpretation - many undergraduates would find it perfectly reasonable to prove x^2 is not uniformly continuous, while many others would find it impossible. But I think that if the task is harder for undergrads, it is harder for everyone, in a relative sense. Certainly you or I would have to think a few more seconds about a rigorous proof using the standard definition, vs. a rigorous proof using the nonstandard definition.
I tried to think of some way of explaining precisely how the standard definition is more difficult than the nonstandard definition. One trick I have learned for WP writing is that it is often possible to replace subjective judgments with the objective reasons used in forming the judgment, and this results in a better article. It seems to me that the reason for the difficulty is the depth of the nested quantifiers in the standard version; but I've never seen that explanation in print, so I think it may just be my opinion. That's why I didn't add an explanation to the sentence. — Carl (CBM · talk) 13:16, 28 October 2008 (UTC)
I remember saying this somewhere at uniform continuity or (ε, δ)-definition of limit, I'd have to check. I do think this is the right reason. Katzmik (talk) 17:10, 28 October 2008 (UTC)
Carl, could this quote be helpful? "The number of quantifiers in a mathematical statement gives a rough measure of the statement’s complexity. Statements involving three or more quantifiers can be difficult to understand. This is the main reason why it is hard to understand the rigorous definitions of limit, convergence, continuity and differentiability in analysis as they have many quantifiers. [new paragraph] In fact, it is the alternation of the \forall and \exists that causes the complexity." Kevin Houston, How to Think Like a Mathematician, ISBN 9780521719780. -- Jitse Niesen (talk) 15:49, 29 October 2008 (UTC)
Kevin Houston certainly thinks like this mathematician :) Katzmik (talk) 15:54, 29 October 2008 (UTC)
Thanks Jitse, that reference will be very helpful. — Carl (CBM · talk) 17:15, 29 October 2008 (UTC)
Regarding the page on Kevin Houston: I'd really rather not edit the page of a mathematician who's at the same university as me, but having the quote on his page makes it seem like this is something very central to what he does, while I think it's just a side remark that many people have made. A short web search also brings up "The logical complexity of [the standard definition of a limit] (two alternations of quantifiers) explains why most students find it hard to understand the concept of a limit." [12] and "There’s no problem writing longer sequences of nested quantifiers, but it’s a general rule of thumb that people really have to work, cognitively, to handle more than two. This is why most of us have such a hard time digesting the definition of a limit when we first learn it in calculus:" [13]. I think it may be hard to defend the page on Houston at AfD. And he's not a professor. -- Jitse Niesen (talk) 15:02, 31 October 2008 (UTC)
I didn't notice that the page had been created, thanks for pointing it out. — Carl (CBM · talk) 15:25, 31 October 2008 (UTC)
## Template:Archive box
As you're the last person to edit the template I thought I'd let you know I've left a question on the talkpage §hep¡Talk to me! 03:09, 1 November 2008 (UTC)
## AfD nomination of 3103 (number)
An article that you have been involved in editing, 3103 (number), has been listed for deletion. If you are interested in the deletion discussion, please participate by adding your comments at Wikipedia:Articles for deletion/3103 (number). Thank you. JohnCD (talk) 22:24, 1 November 2008 (UTC)
## Partial Function
ok, the thing is it was inconsistent before since it said it associated *each* element of the domain, and then went on to say it didn't have to associate every element of the domain. —Preceding unsigned comment added by 209.195.87.241 (talk) 03:15, 2 November 2008 (UTC)
## Re my proposal
OK, though I wouldn't call it spamming, but since you are Administrator so I have to obey. Would you please help to place my proposal to one of those two places, pointed by you ? Apovolot (talk) 23:57, 2 November 2008 (UTC)
## Question
CBM, please take a look at the creator of Image:LaFranceFireEngine.jpg and see if you could justify an unblock, assuming that the user is now completely reformed? Katmairock (talk) 06:09, 7 November 2008 (UTC)
## Beta question
Hi Carl, with respect to this ANI thread (which I kinda regret initiating), I was never clear on Beta's restrictions imposed by the "ad-hoc" committee of yourself, Ryan and Lara - were you guys taking on an ongoing monitor/mentoring role, or just crafting the sanctions? And/or do y'all have comments on that recent little kerfuffle? I ask only as looking for a way to counter the "he's out of control/ban him now" sentiment which unfortunately arose in the thread. Beta's not such a bad guy imo, but interlocutors were and still are helpful, it would seem. Franamax (talk) 06:34, 9 November 2008 (UTC)
## Unprotection of {{Chinese name}}
Hi, you protected {{Chinese name}} in July 2008. Would you consider temporarily unprotecting it to enable me to merge {{Chinese name2}} into that template and to move the documentation to a separate subpage using {{Documentation}}? I think it is unnecessary to have a separate {{Chinese name2}} template when it can be incorporated into {{Chinese name}} using a parser function. — Cheers, JackLee talk 13:25, 11 November 2008 (UTC)
OK, I'm done. Thanks! — Cheers, JackLee talk 14:11, 11 November 2008 (UTC)
## Monthly/yearly page view dumps
Hello CBM,
Sorry for not letting hear from me earlier, and that it took me so long to finally publish the requested monthly/yearly logs. It's just that it has been relatively time and resource intense (for my PC ;-); but now it's done :-) Some (daily/~monthly) logs have been available earlier (you may have noticed it?), but I had to move all public logs to external services (after having aggregated data for 150 days (5 months) now). I hope with up to 150 days of counted page views you will have a pretty good basis for your WP 0.7/1.0 analyses now.
Consider subscribing to the RSS feed (e-mail) for keeping track. --- Best regards, Melancholie (talk) 23:45, 12 November 2008 (UTC)
## Python and atan2
I ran python's atan2 function:
>>> math.degrees(math.atan2(0,1))
0.0
>>> math.degrees(math.atan2(1,0))
90.0
>>> math.degrees(math.atan2(0,-1))
180.0
>>> math.degrees(math.atan2(-1,0))
-90.0
Which doesn't appear to match up with your graph. However... it could be that the behavior of atan2 depends on the language. Not certain.
The issue is that atan2 takes arguments in the order y,x. So to compute the atan2 of the point x=1, y=0 you compute atan2(0,1). I believe every language follows this pattern. See the python docs. — Carl (CBM · talk) 01:35, 14 November 2008 (UTC)
## Template stuff
Carl, can you take a minute to look at this? Check out CAT:CONTENT, and you'll see it claims that WP:NFC is a content policy, but check out WP:NFC and you'll see it ain't so. The problem is almost certainly being caused by the transclusion of WP:NFCC. Notice that I've put a noinclude beginning and end tag around {{policy|...}}; that could easily be causing the problem, but if I don't do it, then the policy template is transcluded, and that puts the WP:NFC page in the "Wikipedia policy" cat, which is no good. Perhaps I could subst the policy template and remove the offending cat from that location, but people will probably find that confusing; they're expecting the usual policy template at the top of a policy page. - Dan Dank55 (send/receive) 02:59, 15 November 2008 (UTC)
The noinclude is the right thing to do. For some reason it was necessary to do a null edit on WP:NFC to fix its categorizations. When you view a page, the categories displayed may not match the actual categories that the database thinks the page is in. When the page is edited (even a null edit) the database is updated and the categorization will be fixed. — Carl (CBM · talk) 03:07, 15 November 2008 (UTC)
Thanks!! - Dan Dank55 (send/receive) 03:34, 15 November 2008 (UTC)
## Re:Tagging math pages
Hello. Thank you for telling me about doing that. I must have done it a while ago because I can't find those math pages in my contributions. Can you please show me where those pages are? I would be happy to fix those pages once I know where to find them. Captain panda 23:52, 16 November 2008 (UTC)
## Bot doesn't show articles with slashes correctly
On User:VeblenBot/C/Wikipedia featured list candidates, "Bookseller/Diagram Prize for Oddest Title of the Year" is appearing as "Bookseller" because of the slash. A minor bug. Gary King (talk) 17:11, 17 November 2008 (UTC)
This should be fixed now. — Carl (CBM · talk) 23:26, 19 November 2008 (UTC)
## 3RR bot code
I'm interested to read the code for the 3RR bot to see what heuristic it's using, if you don't mind sharing it. You didn't create a talk page for the bot, by the way. — Carl (CBM · talk) 21:55, 16 November 2008 (UTC)
I can probably get you the source code this weekend. I don't want to hand it out right now as the framework I setup for the config files is not completed yet, and more importantly there is a bug in my rc parser which I want to clean up my ugly hack. —— nixeagle 17:24, 17 November 2008 (UTC)
As far as the hueriestic, it is basically reading the RC feed with the following "filters" on it.
1. Discard all non-mainspace edits/logentries.
3. Place all edits onto the end of a 300 edit buffer. (Assuming buffer is full do next step).
4. If buffer is full, take the item at the start of the buffer and check the rest of the buffer for an edit that is by the same user on the same article. If the user has another edit in the queue, discard the top edit and wait. (This prevents multiple pointless checks on users doing many edits in a short period of time... we only check when the editor has left the article alone for about 10 minutes).
5. If the edit has not yet been discarded, do a mysql query that returns the revisions that the user has edited the page in the last 24 hours. If there are fewer then 4 revisions returned, discard the edit... there is no way the user can violate 3RR without doing at least 4 edits to a page in one day.
6. Finally if all these prior steps don't cause an edit to be discarded we must check the diffs themselves, load each diff, strip information that will screw up the MD5 hash. (Timestamp, comments etc), and hash it. Compare the hashes.
1. There is a subcheck that is done, if the count of matching hashes is "1" (means no edits are the same change), and there is only 1 edit left to check, we simply say there is no 3RR violation.
—— nixeagle 17:32, 17 November 2008 (UTC) I'll get you the code, but that is the algorithm in english.
## Veblenbot
Carl, I am doing a lot of copyediting at FAC. I watchlist Veblenbot for new articles, but it would be really helpful if there were a quick way for me to be able to tell whether an article is related to math/sci/tech or not, without having to check every article that shows up (unless the article title makes it obvious). Can Veblenbot give me any help with this? - Dan Dank55 (send/receive) 12:39, 19 November 2008 (UTC)
The best way would probably be to list the WikiProjects that each article belongs to, but that would probably also make the page messier than it needs to be. Gary King (talk) 15:15, 19 November 2008 (UTC)
That's what I was thinking too; although it would be nice if everyone agreed how to classify articles, we don't, so there's probably no way around just listing the wikiprojects. I don't know if people want that information at WP:FACL, but if they don't and if there's a way to automatically represent that information on some other page, it would be a big help. Even at WP:GAN, where you could argue that this is a non-issue because the articles are already arranged nicely, it would be nice to have some snappier way of being notified when the articles in categories I most care about show up. - Dan Dank55 (send/receive) 15:46, 19 November 2008 (UTC)
Unfortunately this can't be done with just the framework that is already in place. That framework basically just downloads a list of articles in the category and uploads it to the wiki wrapped into templates. So there's no place in the code to check for the wikiprojects. It would be possible to make a separate system to do this, but I'm too swamped right now to think about it. — Carl (CBM · talk) 23:25, 19 November 2008 (UTC)
## User:VeblenBot/C/Good article nominees awaiting review
Could the page please be listed in reverse chronological order just like the page for featured article and featured lists? And link the date to the article, since there is no nomination page to link to? Gary King (talk) 16:48, 19 November 2008 (UTC)
No problem. — Carl (CBM · talk) 23:23, 19 November 2008 (UTC)
Articles with an ampersand in their title don't seem to show up properly on the page. All text after the ampersand is removed. Gary King (talk) 21:11, 21 November 2008 (UTC)
It looks like the issue is that these pages actually exist, made by DYKBot: Talk:Drum &, Talk:Tropical Storm Becky &. — Carl (CBM · talk) 21:21, 21 November 2008 (UTC)
Ah okay. I guess the bot needs fixing then. Gary King (talk) 21:32, 21 November 2008 (UTC)
## Algebra stub template
Dear CBM,
I know this has gone long enough and has wasted a lot of time, but according to another administrator, Template:Algebra-stub should have no image. User:Trovatore disagrees and so do other users but User:MSGJ held a vote towards the bottom of the section on 'algebra stub template' and the vote is clearly (currently) for the Rubik's cube. Despite this, User:MSGJ removed the image entirely. I proposed an image of the circle (as a group) but there was no response (probably because no one wants to waste their time in this discussion). I don't dare to edit Template:Algebra-stub in the fear of being blocked by User:Moondyne (he threatened to block me three times so far). Could you please add the Rubik's cube (or whichever one you feel is the best/circle as a group image)? I don't think anyone will argue anymore regarding this and because you are an admin, User:Moondyne can't block you.
Topology Expert (talk) 08:10, 22 November 2008 (UTC)
I'm very reluctant to get involved there any more than I already was. My wiki time is already committed to other tasks, and so some things I have to just stay out of. If there isn't an image on the template, that's less than ideal, but not so bad that it has to be remedied right away. I'd say: wait a month, then come back to it. — Carl (CBM · talk) 14:52, 22 November 2008 (UTC)
## This user makes statements with the intent of preserving convention at the expense of truth.
This user has demonstrated a willingness to express disagreement with arguments he has yet to understand presumably with the reasoning that if it goes against convention it can not possibly be correct. (Bandwagon Fallacy) —Preceding unsigned comment added by 96.32.188.25 (talk)
This anonymous contributor is obviously referring to halting problem, where they are currently arguing for original research. --Hans Adler (talk) 15:40, 23 November 2008 (UTC)
## Giano discussion
Regarding your discussion with PhilKnight, I think you are missing the fact that Giano very obviously feels he is being harassed by a group of people who are more interested in process than in writing an encyclopedia. Such Michael Kohlhaas situations can only get worse if the "authorities" routinely follow their processes to the letter whenever it can be used for legal, though not necessarily just, actions against the griper, while still not even keeping up the illusion of due process in connection with the griper's concern. Michael Kohlhaas was a tragic character in the proper sense of the word in that he had no choice. Ultimately the question is: What's more important? Protecting en.wikipedia's incredibly lax checkuser privacy standards and DG's abused admin bit, or preventing that Giano is forced into the same mode of operation in which other former content contributors like Peter Damian already are? It's incomprehensible to me how you can use legalistic arguments to justify measures against a user who has just been told very clearly, though implicitly, that his privacy and freedom from harassment is an IAR matter because he can't keep his temper.
Another question is the authority of Arbcom. You are assuming that it still exists, and that it is absolute. Giving the general quality of their output recently I don't agree. There are serious problems, especially with FT2's contributions. --Hans Adler (talk) 15:35, 23 November 2008 (UTC)
I'm just leaving the computer. I'll send you an email later today or tonight with my thoughts. My overall impression is that then entire situation sucks and no one person is to blame. — Carl (CBM · talk) 15:38, 23 November 2008 (UTC)
I couldn't agree more. --Hans Adler (talk) 15:40, 23 November 2008 (UTC)
It seems that Michael Kohlhaas has started the siege of Wittenberg; it seems likely that it will lead to similar results.
Just in case it wasn't clear: I didn't want to criticise you. In fact I have a very high opinion of your judgement and your approach to wikipedia; sometimes I agree with you, but I am always able to accept your position as a reasonable one, which is more than I can say about quite a few other people. There isn't much that I can say in response to your mail that I haven't already said publicly. Just one thing: It seems clear to me by now that we cannot change Giano, at least not by blocking. I think there could actually be a general consensus on this statement if we leave the reasons open (it's impossible in principle, or it's impossible because of the support Giano is getting). What follows for me is that we have the choice between trying other approaches, doing nothing, and banning Giano. In a situation where there is no consensus to ban Giano, I see "civility paroles" and blocks based on harmless jokes as nothing but overt mobbing. It is disturbing that ArbCom is engaging in this unethical behaviour. If the jury can't make up their collective mind whether to execute the delinquent or not, the pillory is in no way an acceptable alternative. And it has severe consequences for the community norms. --Hans Adler (talk) 11:12, 25 November 2008 (UTC)
I do think that part of the current problem stems from the inability of arbcom to come to a (near) unanimous opinion about how to proceed. They're the group specifically charged with taking care of these sorts of situations, and in this case they've floundered somewhat. However, they don't have decades of experience to rely on, and so we can expect some mistakes and growing pains. And it seems to be very difficult to switch from a mindset of dispute resolution to a mindset of just dispute mitigation.
There have been signs for some time that arbcom will not pass civility sanctions in the future like the one the passed in the Giano/IRC case. And it looks like arbcom is about to pass a resolution that will stop individual admins from using the arbcom sanction. That should reduce the size of the mob, at least. This statement looks promising: [14] — Carl (CBM · talk) 14:05, 25 November 2008 (UTC)
Yes, I agree that's a good sign. --Hans Adler (talk) 16:56, 25 November 2008 (UTC)
## online book about logic by Schwichtenberg
I just came across this and am going to try to read it. I linked it to the main mathematical logic article too. It looks very good. I mention it here because it touches a lot of topics that you edit. 67.122.210.149 (talk) 13:09, 25 November 2008 (UTC)
## abiding by regulations
Hi, Nice to hear from you Carl. You may note that Houston's book is scheduled to be released on 31 december '08. Did I understand the discussion correctly that on 30 december '08 Houston is ineligible to have a page according to wikipedia policies, but on 31 december '08 he becomes eligible? If there is such a policy or regulation, we should certainly abide by it, see my recent edits at Yawning Heights. Katzmik (talk) 09:27, 28 November 2008 (UTC)
## Well, I seem to have killed off the conversation
I agreed with you at Wikipedia_talk:Manual_of_Style#Scaling factor instead of fixed size?, and I agree with your note on my talk page, but now the conversation seems to have stopped. Ideas for where to go next? - Dan Dank55 (send/receive) 16:50, 1 December 2008 (UTC)
I don't know about the scaling factor / fixed size. But I asked on the wikimedia-tech channel if it would be possible to change the default size to 240px, and it seems like it is. It would be necessary to have a clear sign of consensus on the wiki before the change would be made. Maybe a poll is in order? I'm afraid I'm too busy during the next couple weeks to coordinate anything. — Carl (CBM · talk) 19:16, 1 December 2008 (UTC)
Thanks Carl, I'll ask around. - Dan Dank55 (send/receive) 19:52, 1 December 2008 (UTC)
## User:VeblenBot/C/GAR
Why isn't the current version of User:VeblenBot/C/GAR showing at WP:GAR?--TonyTheTiger (t/c/bio/WP:CHICAGO/WP:LOTM) 14:18, 2 December 2008 (UTC)
I'm not sure what problem you are seeing. When I compare them, the table of contents on GAR matches VeblenBot's list. Try forcibly reloading the GAR page. If that doesn't work, let me know which article on VeblenBot's list is not showing up on GAR. — Carl (CBM · talk) 14:25, 2 December 2008 (UTC)
## Vassyana and WP:NOR
It seems you were active on WP:NOR at the time when SlimVirgin and Vassayana had what appears to be an interminable argument: almost 500 posts from Vassyana according to SlimV, which seems confirmed by [15], but SlimV also has a comparable number of edits there, and Kenosis has more. SlimV brought up Vassyana's insistence as argument against him in the election. No way I'm going to read that many diffs, so I'm asking you as a trusted third-party for a summary of what this was all about. Thanks, Pcap ping 03:04, 4 December 2008 (UTC)
• The overall discussion, which went on for a very long time and never really was resolved, was about the relative roles of primary and secondary sources on Wikipedia. An underlying issue is that there is more than one definition of "primary source" and so different editors may enter the discussion with different ideas about which sources are primary and which are secondary. The discussion involved quite a few editors, many more than just SlimVirgin, Vassyana, and me. It went on for months.
• The discussion was often about the correct usage of primary sources, their potential for misuse, and similar questions for secondary sources. I was concerned that the language might be changed in a way that would make it harder to correctly use peer-reviewed research papers as sources in scientific articles. Other people were concerned with other potential problems for other sorts of articles.
• I don't believe that Vassyana ever claimed secondary sources are "more" likely to be biased, only that they "can" be biased. At least this is what the diffs I have seen show.
• I looked up current edit counts on toolserver, and found these total edit counts:
Editor Edits to WP:OR Edits to WT:OR CBM 7 (tied #41) 141 (#24) COGDEN 77 (#3) 492 (#5) Kenosis 61 (#4) 850 (#1) SlimVirgin 243 (#1) 659 (#2) Slrubenstein 89 (#2) 526 (#4) Vassyana 53 (#6) 565 (#3)
• Vassyana did comment at the time on the perceived frequency of his posts [16]. The full context of that thread is at [17]. I had the impression that Vassyana was participating in the conversation there in very good faith. I thought he was hoping to improve the language of the policy page and trying to help resolve the disputes that had arisen about the primary/secondary source issue. By the end of the very long discussion, everyone's nerves had frayed somewhat.
• I hope this actually addresses your question. If there's a more specific question I can address, let me know and I'll do my best. — Carl (CBM · talk) 04:33, 4 December 2008 (UTC)
Thanks for all the details. From the few diffs I had sampled I reached the same conclusions as you did. Pcap ping 12:22, 4 December 2008 (UTC)
## User:Topology Expert
Hi. TE has got himself blocked, requests a "math admin" ... Martin 18:58, 5 December 2008 (UTC)
## VeblenBot
Hi Carl, thanks for the comment on my talk page. I wonder if you could update VeblenBot to use the categories Category:Unassessed mathematics articles and Category:Unknown-Priority mathematics articles rather than, respectively, Category:Unassessed quality mathematics articles and Category:Unassessed importance mathematics articles which are now empty. Thanks.
By the way I didn't realise until recently that you operate the WP 1.0 bot as well. I recently made a template (currently in my sandbox) for WikiProject Articles for creation to track the number of articles in each class. This could easily be adapted for any project. Do you think there could be a use for it? Martin 08:58, 6 December 2008 (UTC)
Can't we use Category:Unassessed-Priority mathematics articles rather than "Unknown"? It's very hard to keep everything straight when "Unassessed" is used for some categories and "Unknown" is used for others. I can change the category for unassessed quality articles without too much trouble.
The template you made looks nice. The thing the bot does that can't be done on-wiki is to keep track of assessment changes and to keep a log of assessments. I don't really have much to do with the on-wiki aspects of the assessment program except for the mathematics project. — Carl (CBM · talk) 13:40, 6 December 2008 (UTC)
Of course we could use "unassessed" rather than "unknown" if you think it's better. It was just in the interests of standardising again. If you look at Category:Unknown-importance articles you'll see that the vast majority of projects use "unknown" for importance. There are a few "unassessed-importance" and "no-importance" is another non-standard one. I guess the 1.0 bot recognises all of these, does it? Martin 13:49, 6 December 2008 (UTC)
The non-orthogonal category names are mainly tough on human editors like me. The WP 1.0 bot handles every existing convention, but VeblenBot has a different code base that is made specifically for the math project, so the categories there are hard coded. My goal is that the next version of the WP 1.0 bot will include all the functionality that VeblenBot has, and then VeblenBot can stop duplicating effort. — Carl (CBM · talk) 14:01, 6 December 2008 (UTC)
## I've replied to a comment of yours
Hi Carl, I've replied to a comment of yours here. Regards, Paul August 15:49, 6 December 2008 (UTC)
And again here. Paul August 18:19, 6 December 2008 (UTC) | 2017-12-12 01:18:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "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": 0.48319536447525024, "perplexity": 2262.515030761494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948514238.17/warc/CC-MAIN-20171212002021-20171212022021-00799.warc.gz"} |
https://stacks.math.columbia.edu/tag/0AUW | Lemma 15.22.11. Let $A$ be a Dedekind domain (for example a discrete valuation ring or more generally a PID).
1. An $A$-module is flat if and only if it is torsion free.
2. A finite torsion free $A$-module is finite locally free.
3. A finite torsion free $A$-module is finite free if $A$ is a PID.
Proof. Proof of (1). Since a PID is a Dedekind domain (Algebra, Lemma 10.120.15), it suffices to prove this for Dedekind domains. By Lemma 15.22.6 and Algebra, Lemma 10.39.18 it suffices to check the statement over $A_\mathfrak m$ for $\mathfrak m \subset A$ maximal. Since $A_\mathfrak m$ is a discrete valuation ring (Algebra, Lemma 10.120.17) we win by Lemma 15.22.10.
Proof of (2). Follows from Algebra, Lemma 10.78.2 and (1).
Proof of (3). Let $A$ be a PID and let $M$ be a finite torsion free module. By Lemma 15.22.7 we see that $M \subset A^{\oplus n}$ for some $n$. We argue that $M$ is free by induction on $n$. The case $n = 1$ expresses exactly the fact that $A$ is a PID. If $n > 1$ let $M' \subset R^{\oplus n - 1}$ be the image of the projection onto the last $n - 1$ summands of $R^{\oplus n}$. Then we obtain a short exact sequence $0 \to I \to M \to M' \to 0$ where $I$ is the intersection of $M$ with the first summand $R$ of $R^{\oplus n}$. By induction we see that $M$ is an extension of finite free $R$-modules, whence finite free. $\square$
Comment #3540 by Laurent Moret-Bailly on
Typo in proof of (3): "induction on $M$". Also, why write "PID or discrete valuation ring" since one class contains the other?
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2021-10-28 13:59:36 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9805812239646912, "perplexity": 198.14474963546917}, "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/1634323588341.58/warc/CC-MAIN-20211028131628-20211028161628-00410.warc.gz"} |
https://electronics.stackexchange.com/questions/425262/figuring-out-the-principal-working-of-constant-current-source | # Figuring out the principal working of constant current source
I've the following circuit:
simulate this circuit – Schematic created using CircuitLab
I was told that this is a constant current source. I think that the resistors $$\\text{R}_1\$$ and $$\\text{R}_2\$$ determine the current in trough the load. Is that true and how is the output current related to those resistor values or other components in the circuit?
• Assume a fixed 3.3V on the positive input of the OpAmp. Next, assume there is a current of 0A running through R3. Use Ohms law for R3 and consider what happens to the OpAmp and next to the mosfet. Then, assume 2A is running through R3 and consider again what happens to the OpAmp and to the mosfet. Last, for 1A. Mar 2 '19 at 17:21
• @Huisman I've have realy no idea (Dutch: en goed om een Nederlander te zien hier :) & English: good to sea another Dutchman over here)! Mar 2 '19 at 17:24
• This circuit work thanks to the negative feedback magic. The opamp simply compares the voltage divider output voltage with the voltage produced by the current flowing through R3 resistor and the MOSFET V_R3 = I_load x R3. And if this voltage is lower than the voltage divider voltage the opamp will turn on the MOSFET harder to make sure that the voltage drop across R3 is equal to the voltage given by the voltage divider.
– G36
Mar 2 '19 at 17:25
• @G36 So, how does the loadcurrent depend on the resistor values? Mar 2 '19 at 17:26
• two comments. First - It's best to break this up into 2 parts. (1) Iout depends on voltage across resistor, which depends on voltage at input of amplifier. (2) Voltage at amplifier depends on Vload+ R1 and R2. Normally you'd use something more accurate than 'Vload+' to set the voltage to the opamp. Second - OP27 won't work here, it's an old-style dual-rail not R2R output, so the output won't go down to GND, neither will the input common mode go to ground. Use dual rails, or a -ve amplifier supply of -5v or more, or a modern R2R opamp. Mar 2 '19 at 17:42
The opamp is in a non-inverting amplifier configuration with a gain of 1. As always, the output of the opamp will do whatever it takes to make the voltages at the + (non-inverting) and - (inverting) inputs identical. Because the forward gain is 1, and the top of R3 is connected to the - input, the opamp will do whatever it takes to make the voltage at the top of R3 equal to the voltage at the + input. As R1 and R2 change, the + input voltage changes, and the opamp makes sure that voltage is at the top of R3.
Now for the fun part. Between the opamp output and R3 is the FET, which is essentially a voltage-controlled resistor. As the output of the opamp goes up and down, the resistance of the FET between its drain and source terminals (called Rds) goes down and up. The higher the gate voltage, the lower the resistance.
If the circuit were simply the load and R3 in series, then if the load resistance changed, the current through the string would change (Ohm's Law). But that FET is in there; its resistance is in series with the load. The load, FET, and R3 form a series string, and the opamp can adjust the FET's resistance. If the load resistance changes, the current through the string changes, the voltage at the top of R3 changes, and the opamp adjusts the FET's resistance to keep the R3 voltage equal to the input voltage. R3 is called the sense (or shunt) resistor. The opamp works to keep the voltage across it constant, and thanks to Ohm's Law that means the current through it (and the rest of the string) is constant. By constant I mean constant as long as the input voltage is constant. Change the input voltage, and the opamp adjusts the FET so the string current is correct for that voltage.
The net result is that the current through the load is not determined by the resistance of the load. Over the range of voltages that the circuit can handle, the current through the load is a constant even when the load resistance changes. The only thing that changes the load current is the + input voltage.
Simply the OP drives the gate of the drain follower ( with conditions $$\ R_{dsOn} < R_3\$$ to make $$\ V_{in+}=V_{in-}\$$ and $$\V_{load} > 2Vt\$$ , Vt= FET threshold voltage, a.k.a. $$\V_{gs(th)}\$$.
Then $$V_{R_2} = V_{R_3}=I_{R_3}*R_3,$$ and $$\V_{R_2}\$$is a ratio of $$\ V_{in}\$$.
# Details
Typically, R3 is small like = 50 to 100mV drop at Imax current, as the current shunt sensor to limit waste heat of Pd in R3 but not too small. where Vin offset contributes to error budget. This sensor loop area should be small as possible, so that transients do not cause overshoot for a step input from stray reactance and crosstalk from output current load mutual (inductive or capacitive) coupling. | 2021-11-27 17:21:06 | {"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": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5724375247955322, "perplexity": 1268.9333744580715}, "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/1637964358208.31/warc/CC-MAIN-20211127163427-20211127193427-00102.warc.gz"} |
https://www.physicsforums.com/threads/question-about-cosets-and-lagranges-theorem.788751/ | # Question about Cosets and Lagrange's Theorem
PsychonautQQ
If a is an element of G and H is a subgroup of H, let Ha be the right coset of H generated by a.
is Ha a subgroup?
I have this question because i feel like the answer should be know, yet my textbook notation makes it look like it is.
Why I think it should only be a set:
Let G = <a> and H = <a^3>. and |a| = 6,.
Then H = {1,a^3}, Ha = {a,a^4} Ha^2 = {a^2,a^5}.
To me it looks like Ha and Ha^2 can not be subgroups because they are not closed under the operation, unless the operation is multiplying the elements by a^3.. I don't know i'm confused.
But then I think they should be considered subgroups, because it goes on to say that Ha = H iff a is in H. So Ha must be a subgroup if it equals a subgroup... Anyway, anyone have insight here?
Ahmed Abdullah
The problem doesn't not say that $a$ must be an element of $H$. What the textbook goes on to say about the case when $a$ is an element of $H$ is not relevant to the problem.
Homework Helper
Gold Member
is Ha a subgroup?
##Ha## is a subgroup if and only if ##Ha = H## if and only if ##a \in H##.
One easy way to see this is that if ##Ha \neq H## then ##Ha## and ##H## are disjoint, so ##Ha## does not even contain the identity element.
PsychonautQQ
so when you create G out of disjoint cosets, you are joining H (a subgroup of G) with Ha, Hg, Hh, etc etc, which are only disjoint sets of elements of G? | 2022-08-19 08:53:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8525652289390564, "perplexity": 690.4586568569866}, "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/1659882573630.12/warc/CC-MAIN-20220819070211-20220819100211-00397.warc.gz"} |
https://calculator.uservoice.com/forums/126269-numerics-calculator-converter/filters/top?status_id=465259 | # Numerics Calculator & Converter
Thank you for your suggestions and feedback. We read your messages carefully and try to make Numerics as useful for you as possible.
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1. ## 121 Square Yards = 1 Gunta, 40 Guntas = 1 Acre
the area of a land in Telangana region in Andhra Pradesh State, India usually measures in Acres & Guntas. Guntas are fraction of acres.
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• ## calculating %
it would be good to become working calculating %. (10+10%= E?)
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• ## Calculus calculator
Derivatives, integrations, limits etc
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• ## Digit Grouping
Is good to have digit grouping in the calculator field.
E.g One million = 1,000,000
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• ## option to pick decimal mark between comma and dot
option to pick decimal mark between comma and dot
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• ## Display conversions for: Gallons per minute, Liters per minute (Flow Rate)
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• ## give an option to use degrees, radians and grads from the trig functions
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you can use degrees just by putting “deg” after the number e.g. sin(45 deg)
• ## Convert angles from degrees to radians & vice versa
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• ## Add conversion for torque.
Like they have it here: http://www.statman.info/conversions/torque.html
I use in-lbs and Nm mostly.
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• ## Integral and Derivative are welcome. You have done a good job. Congratulation!
Integral and Derivative are welcome. You have done a good job. Congratulation!
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• ## Shoe size converter
It could be great to convert your shoe size into like the US shoe sizes or European show size... Because nobody really think of this, and it isn't the hardest thing to do:-)
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thanks for the idea ;)
• ## fuel consumption converter
fuel consumption converter
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• ## percent bug
50%=0.25 ?
50+50*50%=5625 ?
50+50%=2550.25 ?
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• ## Add Script (functions) Library
This will allow users to write custom script and publish them to shared library, where other users will be able to use them
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One can add/edit scripts. Now we need to allow saving them
This is good for all those petrolheads that want to convert n*m to kgf*m.
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• ## make it so you can enter ratios and it can solve them
Such as 16 X
--- = ----
25 100
x=?
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• ## show a typeset mathematical expression above input field
This would be great to check, if everything is entered correctly. Just like http://texify.com/?$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
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• ## Pressure: Kgf/cm2 should be added
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• ## (2^1000000)%1000000007
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• ## torque conversion.
as in: foot pound to inch pound to newton meters.
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Reset | 2018-01-20 01:31:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5875939130783081, "perplexity": 13393.560187875257}, "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-2018-05/segments/1516084888341.28/warc/CC-MAIN-20180120004001-20180120024001-00554.warc.gz"} |
https://mran.revolutionanalytics.com/snapshot/2021-11-01/web/packages/kgrams/vignettes/kgrams.html | # Classical $$k$$-gram Language Models in R
library(kgrams)
## Introduction
kgrams provides R users with a set of tools for training, tuning and exploring $$k$$-gram language models1. It gives support for a number of common Natural Language Processing (NLP) tasks: from the basic ones, such as extracting (tokenizing) $$k$$-grams from a text and predicting sentence or continuation probabilities, to more advanced ones such as computing language model perplexities2 and sampling sentences according the language model’s probability distribution. Furthermore, it supports many classical $$k$$-gram smoothing methods, including the well-known modified Kneser-Ney algorithm, first described in (Chen and Goodman 1999), and widely considered the best performing smoothing technique for $$k$$-gram models.
$$k$$-gram language models are notoriously demanding from the space point of view, and many of the toolkits available for $$k$$-gram based NLP employ various techniques and data structures to achieve the data compression required by the large scales of industry (and, sometimes, academic) applications (see (Pibiri and Venturini 2019) for a recent review). On the other hand, at such large scales, neural language models are often the most economic and best performing choice, and this is likely to become more and more so in the future. In developing kgrams, I made no special attempt at data compression, and $$k$$-grams and count estimates are stored in plain C++ STL hash-tables, which can grow rapidly large as the size of corpora and dictionaries increases.
On the other hand, most focus is put on providing a fast, time efficient implementation, with intuitive interfaces for text processing and for model evaluation, and a reasonably large choice of pre-implemented smoothing algorithms, making kgrams suitable for small- and medium-scale language model experiments, for rapidly building baseline models, and for pedagogical purposes.
In the following Sections, I illustrate the prototypical workflow for building a $$k$$-gram language model with kgrams, show how to compute probabilities and perplexities, and (for the sake of fun!) generate random text at different temperatures.
## Building a $$k$$-gram language model
This section illustrates the typical workflow for building a $$k$$-gram language model with kgrams. In summary, this involves the following main steps:
1. Load the training corpus, i.e. the text from which $$k$$-gram frequencies are estimated.
2. Preprocess the corpus and tokenize sentences.
3. Store $$k$$-gram frequency counts from the preprocessed training corpus.
4. Build the final language model, by initializing its parameters and computing auxiliary counts possibly required by the smoothing technique employed.
We illustrate all these steps in the following.
kgrams offers two options for reading the text corpora used in its computations, which are basically in-memory and out-of-memory solutions:
• in-memory. The corpus is simply loaded in the R session as a character vector.
• out-of-memory. The text is read in batches of fixed size from a connection. This solution includes, for instance, reading text from a file, from an URL, or from the standard input.
The out-of-memory solution can be useful for training over large corpora without the need of storing the entire text into the RAM.
In this vignette, for illustration, we will train a language model on an online text source. We will use William Shakespeare’s “Much Ado About Nothing” (text of the entire play) as training corpus, which is freely available on shakespeare.mit.edu:
# Create an URL connection to Shakespeare's "Much Ado About Nothing"
txt_con <- url("http://shakespeare.mit.edu/much_ado/full.html")
### Step 2: preprocessing and tokenizing sentences
One can (and usually should) apply some transformations to the raw training corpus before feeding it as input to the $$k$$-gram counting algorithm. In particular, the algorithm considers as a sentence each entry of its pre-processed input, and pads each sentence with Begin-Of-Sentence (BOS) and End-Of-Sentence (EOS) tokens. It considers as a word any substring of a sentence delimited by (one or more) space characters.
For the moment, we only need to define the functions used for preprocessing and sentence tokenization. We will use the following functions, which leverage on the basic utilities kgrams::preprocess() and kgrams::tknz_sent(), and perform some additional steps, since we will be reading raw HTML lines from the URL connection created above.
.preprocess <- function(x) {
# Remove speaker name and locations (boldfaced in original html)
x <- gsub("<b>[A-z]+</b>", "", x)
# Remove other html tags
x <- gsub("<[^>]+>||<[^>]+$||^[^>]+>$", "", x)
# Apply standard preprocessing including lower-case
x <- kgrams::preprocess(x)
# Collapse to a single string to avoid splitting into more sentences at the end of lines
x <- paste(x, collapse = " ")
return(x)
}
.tknz_sent <- function(x) {
# Tokenize sentences
x <- kgrams::tknz_sent(x, keep_first = TRUE)
# Remove empty sentences
x <- x[x != ""]
return(x)
}
### Step 3: get $$k$$-gram frequency counts
We can now obtain $$k$$-gram frequency counts from Shakespeare with a single command, using the function kgram_freqs(). The following stores $$k$$-gram counts for $$k$$-grams of order less than or equal to $$N = 5$$:
freqs <- kgram_freqs(txt_con, # Read Shakespeare's text from connection
N = 5, # Store k-gram counts for k <= 5
.preprocess = .preprocess, # preprocess text
.tknz_sent = .tknz_sent, # tokenize sentences
verbose = FALSE, # If TRUE, prints current progress info
max_lines = Inf, # Read until the end-of-file
batch_size = 100 # Read text in batches of 100 lines
)
freqs
#> A k-gram frequency table.
The object freqs is an object of class kgram_freqs, i.e. a $$k$$-gram frequency table. We can obtain a first informative summary of what this object contains by calling summary():
summary(freqs)
#> A k-gram frequency table.
#>
#> Parameters:
#> * N: 5
#> * V: 3046
#>
#> Number of words in training corpus:
#> * W: 26174
#>
#> Number of distinct k-grams with positive counts:
#> * 1-grams:3048
#> * 2-grams:14389
#> * 3-grams:21208
#> * 4-grams:22706
#> * 5-grams:22975
The parameter V is the size of the dictionary, which was created behind the scenes by kgram_freqs(), using all words encountered in the text. In alternative, we could have used a pre-specified dictionary through the argument dict, and specify whether new words (not present in the original dictionary) should be added to it, or be replaced by an Unknown-Word (UNK) token, by the argument open_dict; see ?kgram_freqs for further details. The number of distinct unigrams is greater than the size of the dictionary, because the former also includes the special BOS and EOS tokens.
Notice that the functions .preprocess() and .tknz_sent() we defined above are passed as arguments of kgram_freqs()3. These are also saved in the final kgram_freqs object, and are by default applied also to inputs at prediction time.
The following shows how to query $$k$$-gram counts from the frequency table created above:4
# Query some simple unigrams and bigrams
query(freqs, c("leonato", "enter leonato", "thy", "smartphones"))
#> [1] 38 6 52 0
# Query k-grams at the beginning or end of a sentence
query(freqs, c(BOS() %+% BOS() %+% "i", "love" %+% EOS()))
#> [1] 208 0
# Total number of words processed
query(freqs, "")
#> [1] 26174
# Total number of sentences processed
query(freqs, EOS())
#> [1] 2270
The most important use of kgram_freqs objects is to create language models, as we illustrate in the next step.
### Step 4. Build the final language model
kgrams provides support for creating language models using several classical smoothing techniques. The list of smoothers currently supported by kgrams can be retrieved through:
smoothers()
#> [1] "ml" "add_k" "abs" "kn" "mkn" "sbo" "wb"
The documentation page ?smoothers provides a list of original references for the various smoothers. We will use Interpolated Kneser-Ney smoothing (Kneser and Ney 1995; see also Chen and Goodman 1999), which goes under the code "kn". We can get some usage help for this method through the command:
info("kn")
#> Interpolated Kneser-Ney
#> * code: 'kn'
#> * parameters: D
#> * constraints: 0 <= D <= 1
As shown above, Kneser-Ney has one parameter $$D$$, which is the discount applied to bare $$k$$-gram frequency counts or continuation counts. We will initialize the model with $$D = 0.75$$, and later tune this parameter through a test corpus.
To train a language model with the $$k$$-gram counts stored in freqs, use:
kn <- language_model(freqs, "kn", D = 0.75)
kn
#> A k-gram language model.
This will create a language_model object, which can be used to obtain word continuation and sentence probabilities. Let us first get a summary of our final model:
summary(kn)
#> A k-gram language model.
#>
#> Smoother:
#> * 'kn'.
#>
#> Parameters:
#> * N: 5
#> * V: 3046
#> * D: 0.75
#>
#> Number of words in training corpus:
#> * W: 26174
#>
#> Number of distinct k-grams with positive counts:
#> * 1-grams:3048
#> * 2-grams:14389
#> * 3-grams:21208
#> * 4-grams:22706
#> * 5-grams:22975
The parameter D can be accessed and modified through the functions parameters() and param(), which have a similar interface to the base R function attributes() and attr():
parameters(kn)
#> $N #> [1] 5 #> #>$V
#> [1] 3046
#>
#> \$D
#> [1] 0.75
param(kn, "D")
#> [1] 0.75
param(kn, "D") <- 0.6
param(kn, "D")
#> [1] 0.6
param(kn, "D") <- 0.75
We can also modify the order of the $$k$$-gram model, by choosing any number less than or equal to $$N = 5$$ (since we stored up to $$5$$-gram counts):
param(kn, "N") <- 4 # 'kn' uses only 1:4-grams
param(kn, "N")
#> [1] 4
param(kn, "N") <- 5 # 'kn' uses also 5-grams
In the next section we show how to use this language model for basic tasks such as predicting word and sentence probabilities, and for more complex tasks such as computing perplexities and generating random text.
## Using language_model objects
So far we have created a language_model object using Interpolated Kneser-Ney as smoothing method. In this section we show how to:
• Obtain word continuation and sentence probabilities.
• Generate random text by sampling from the language model probability distribution.
• Compute the language model’s perplexity on a test corpus.
### Word continuation and sentence probabilities
We can obtain both sentence probabilities and word continuation probabilities through the function probability(). This is generic on the first argument, which can be a character for sentence probabilities, or a word_context expression for continuation probabilities.
Sentence probabilities can be obtained as follows (the first two are sentences from the training corpus):
probability(c("Did he break out into tears?",
"We are predicting sentence probabilities."
),
model = kn
)
#> [1] 2.720954e-05 8.628460e-07 9.230391e-19
Behind the scenes, the same .preprocess() and .tknz_sent() functions used during training are being applied to the input. We can turn off this behaviour by explicitly specifying the .preprocess and .tknz_sent arguments of probability().
Word continuation probabilities are the conditional probabilities of words following some given context. For instance, the probability that the words "tears" or "pieces" will follow the context "Did he break out into" are computed as follows:
probability("tears" %|% "Did he break out into", model = kn)
#> [1] 0.5813743
probability("pieces" %|% "Did he break out into", model = kn)
#> [1] 9.992621e-06
The operator %|% takes as input a character vector on its left-hand side, i.e. the list of candidate words, and a length one character vector on its right-hand side, i.e. the given context. If the context has more than $$N - 1$$ words (where $$N$$ is the order of the language model, five in our case), only the last $$N - 1$$ words are used for prediction.
### Generating random text
We can sample sentences from the probability distribution defined by our language model using sample_sentences(). For instance:
set.seed(840)
sample_sentences(model = kn,
n = 10,
max_length = 10
)
#> [1] "i have studied officers ; <EOS>"
#> [2] "truly by in your company thing that you ask for [...] (truncated output)"
#> [3] "i protest i love the gentleman is wise ; <EOS>"
#> [4] "for it . <EOS>"
#> [5] "the best befits can i for your own hobbyhorses hence [...] (truncated output)"
#> [6] "but by this travail fit the length july cham's beard [...] (truncated output)"
#> [7] "don pedro she doth well as being some attires and [...] (truncated output)"
#> [8] "exeunt all ladies only spots of grey all the wealth [...] (truncated output)"
#> [9] "heighho ! <EOS>"
#> [10] "exit margaret ursula friar . <EOS>"
The sampling is performed word by word, and the output is truncated if no EOS token is found after sampling max_length words.
We can also sample with a temperature different from one. The temperature transformation of a probability distribution $$p(i)$$ is defined by:
$p_t(i) = \dfrac{\exp(\log{p(i)} / t)} {Z(t)},$ where $$Z(t)$$ is the partition function, defined in such a way that $$\sum _i p_t(i) \equiv 1$$. Intuitively, higher and lower temperatures make the original probability distribution smoother and rougher, respectively. By making a physical analogy, we can think of less probable words as states with higher energies, and the effect of higher (lower) temperatures is to make more (less) likely to excite these high energy states.
We can test the effects of temperature on our Shakespeare-inspired language model, by changing the parameter t of sample_sentences() (notice that the default t = 1 corresponds to the original distribution):
sample_sentences(model = kn,
n = 10,
max_length = 10,
t = 0.1 # low temperature
)
#> [1] "i will not have to do with you . <EOS>"
#> [2] "i will go before and show him their examination . [...] (truncated output)"
#> [3] "i will not be sworn but love may transform me [...] (truncated output)"
#> [4] "i will not have to do with you . <EOS>"
#> [5] "i will not be sworn but love may transform me [...] (truncated output)"
#> [6] "i will not think it . <EOS>"
#> [7] "i will not be sworn but love may transform me [...] (truncated output)"
#> [8] "i will not be sworn but love may transform me [...] (truncated output)"
#> [9] "i will not be sworn but love may transform me [...] (truncated output)"
#> [10] "i will not have to do with you . <EOS>"
sample_sentences(model = kn,
n = 10,
max_length = 10,
t = 10 # high temperature
)
#> [1] "pleasantspirited minds wants valuing peace speech libertines after offered being [...] (truncated output)"
#> [2] "braggarts smell fiveandthirty from possible knowest sickness tonight panders agony [...] (truncated output)"
#> [3] "show'd where's give intelligence princes finer tire scab brought rearward [...] (truncated output)"
#> [4] "deserved heart's evening virtues holds c hadst persuasion can finer [...] (truncated output)"
#> [5] "churchbench modesty thinks noncome remorse epitaphs consented mortifying whom hath [...] (truncated output)"
#> [6] "expectation impossible yielded deceive wedding mouth unclasp absentand qualify twelve [...] (truncated output)"
#> [7] "giddily certainly nightraven prized grief laugh claw invincible tyrant blessed [...] (truncated output)"
#> [8] "'i senseless beat time denies 'hundred ten forth hire' reenter [...] (truncated output)"
#> [9] "toothache laughed civil kill'd mean hero's yea foundation deformed appetite [...] (truncated output)"
#> [10] "hour studied figure nine leonato enough ever herself confess authority [...] (truncated output)"
As explained above, sampling with low temperature gives much more weight to probable sentences, and indeed the output is very repetitive. On the contrary, high temperature makes sentence probabilities more uniform, and in fact our output above looks quite random.
### Compute language model’s perplexities
Perplexity is a standard evaluation metric for the overall performance of a language model. It is given by $$P = e^H$$, where $$H$$ is the cross-entropy of the language model sentence probability distribution against a test corpus empirical distribution:
$H = - \dfrac{1}{W}\sum _s\ \ln (\text {Prob}(s))$ Here $$W$$ is total number of words in the test corpus (following Ref. (Chen and Goodman 1999), we include counts of the EOS token, but not the BOS token, in $$W$$), and the sum extends over all sentences in the test corpus. Perplexity does not give direct information on the performance of a language model in a specific end-to-end task, but is often found to correlate with the latter, which provides a practical justification for the use of this metric. Notice that better models are associated with lower perplexities, and that $$H$$ is proportional to the negative log-likelihood of the corpus under the language model assumption.
Perplexities can be computed in kgrams using the function perplexity(), which can read text both from a character vector and from a connection. We will take our test corpus again from Shakespeare’s opus, specifically the play “A Midsummer Night’s Dream”, which is example data from kgrams namespace:
midsummer[840]
#> [1] " when truth kills truth o devilishholy fray !"
We can compute the perplexity of our Kneser-Ney $$5$$-gram model kn against this corpus as follows:
perplexity(midsummer, model = kn)
#> [1] 376.8554
We can use perplexity to tune our model parameter $$D$$. We compute perplexity over a grid of values for D and plot the results. We do this for the $$k$$-gram models with $$k \in \{2, 3, 4, 5\}$$:
D_grid <- seq(from = 0.5, to = 1.0, by = 0.01)
FUN <- function(D, N) {
param(kn, "N") <- N
param(kn, "D") <- D
perplexity(midsummer, model = kn)
}
P_grid <- lapply(2:5, function(N) sapply(D_grid, FUN, N = N))
oldpar <- par(mar = c(2, 2, 1, 1))
plot(D_grid, P_grid[[1]], type = "n", xlab = "D", ylab = "Perplexity", ylim = c(300, 500))
lines(D_grid, P_grid[[1]], col = "red")
lines(D_grid, P_grid[[2]], col = "chartreuse")
lines(D_grid, P_grid[[3]], col = "blue")
lines(D_grid, P_grid[[4]], col = "black")
par(oldpar)
We see that the optimal choices for D are close to its maximum allowed value D = 1, for which the performance of the 2-gram model is slightly worse than the higher order models, and that the 5-gram model performs generally worse than the 3-gram and 4-gram models. Indeed, the optimized perplexities for the various $$k$$-gram orders are given by:
sapply(c("2-gram" = 1, "3-gram" = 2, "4-gram" = 3, "5-gram" = 4),
function(N) min(P_grid[[N]])
)
#> 2-gram 3-gram 4-gram 5-gram
#> 324.8595 320.5757 319.9021 319.9982
which shows that the best performing model is the 4-gram one, while it seems that the 5-gram model is starting to overfit (which is not very surprising, given the ridiculously small size of our training corpus!).
## Conclusions
In this vignette I have shown how to implement and explore $$k$$-gram language models in R using kgrams. For further help, you can consult the reference page of the kgrams website. Development of kgrams takes place on its GitHub repository. If you find a bug, please let me know by opening an issue on GitHub, and if you have any ideas or proposals for improvement, please feel welcome to send a pull request, or simply an e-mail at .
## References
Chen, Stanley F, and Joshua Goodman. 1999. “An Empirical Study of Smoothing Techniques for Language Modeling.” Computer Speech & Language 13 (4): 359–94.
Kneser, Reinhard, and H. Ney. 1995. “Improved Backing-Off for M-Gram Language Modeling.” 1995 International Conference on Acoustics, Speech, and Signal Processing 1: 181–84 vol.1.
Pibiri, Giulio Ermanno, and Rossano Venturini. 2019. “Handling Massive N -Gram Datasets Efficiently.” ACM Transactions on Information Systems 37 (2): 1–41. https://doi.org/10.1145/3302913.
1. Here and below, when we talk about “language models”, we always refer to word-level language models. In particular, a $$k$$-gram is a $$k$$-tuple of words.↩︎
2. Perplexity is a standard evaluation metric for language models, based on the model’s sentence probability distribution cross-entropy with the empirical distribution of a test corpus. It is described in some more detail in this Subsection.↩︎
3. Strictly speaking, a single argument .preprocess would suffice, as the processed input is (symbolically) .tknz_sent(.preprocess(input)). Having two separate arguments for preprocessing and sentence tokenization has a couple of advantages, as explained in ?kgram_freqs.↩︎
4. The string concatenation operator %+% is equivalent to paste(lhs, rhs). Also, the helpers BOS(), EOS() and UNK() return the BOS, EOS and UNK tokens, respectively.↩︎ | 2022-12-03 22:37:47 | {"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": 2, "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": 0.4196259379386902, "perplexity": 5968.462546701134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710941.43/warc/CC-MAIN-20221203212026-20221204002026-00058.warc.gz"} |
https://docs.digitalearthafrica.org/en/latest/sandbox/notebooks/Real_world_examples/Water_extent_WOfS.html | Mapping longer-term changes in water extent with WOfS¶
Keywords: data used; WOfS, water; extent, analysis; time series, visualisation; animation
Background¶
The United Nations have prescribed 17 “Sustainable Development Goals” (SDGs). This notebook attempts to monitor SDG Indicator 6.6.1 - change in the extent of water-related ecosystems. Indicator 6.6.1 has 4 sub-indicators: > i. The spatial extent of water-related ecosystems > ii. The quantity of water contained within these ecosystems > iii. The quality of water within these ecosystems > iv. The health or state of these ecosystems
This notebook primarily focuses on the first sub-indicator - spatial extents.
Description¶
The notebook demonstrates how to load, visualise, and analyse the WOfS annual summary product to gather insights into the longer-term extent of water bodies. It provides a compliment to the Water_extent_sentinel_2 notebook which focussing on more recent water extents at seasonal time intervals.
Getting started¶
To run this analysis, run all the cells in the notebook, starting with the “Load packages” cell.
Import Python packages that are used for the analysis.
[1]:
%matplotlib inline
import datacube
import numpy as np
import xarray as xr
import seaborn as sns
import matplotlib.pyplot as plt
from IPython.display import Image
from matplotlib.colors import ListedColormap
from matplotlib.patches import Patch
from deafrica_tools.bandindices import calculate_indices
from deafrica_tools.plotting import display_map, xr_animation
Connect to the datacube¶
Activate the datacube database, which provides functionality for loading and displaying stored Earth observation data.
[2]:
dc = datacube.Datacube(app='water_extent')
Analysis parameters¶
The following cell sets the parameters, which define the area of interest and the length of time to conduct the analysis over.
The parameters are:
• lat: The central latitude to analyse (e.g. 10.338).
• lon : The central longitude to analyse (e.g. -1.055).
• lat_buffer : The number of degrees to load around the central latitude.
• lon_buffer : The number of degrees to load around the central longitude.
• start_year and end_year: The date range to analyse (e.g. ('1990', '2020').
If running the notebook for the first time, keep the default settings below. This will demonstrate how the analysis works and provide meaningful results. The example covers part of the Lake Sulunga. Tanzania.
[3]:
# Define the area of interest
lat = -5.9460
lon = 35.5188
lat_buffer = 0.03
lon_buffer = 0.03
# Define the start year and end year
start_year = '1990'
end_year = '2021'
# Combine central lat,lon with buffer to get area of interest
lat_range = (lat - lat_buffer, lat + lat_buffer)
lon_range = (lon - lon_buffer, lon + lon_buffer)
View the area of Interest on an interactive map¶
The next cell will display the selected area on an interactive map. The red border represents the area of interest of the study. Zoom in and out to get a better understanding of the area of interest. Clicking anywhere on the map will reveal the latitude and longitude coordinates of the clicked point.
[4]:
display_map(lon_range, lat_range)
[4]:
Make this Notebook Trusted to load map: File -> Trust Notebook
[5]:
#Create a query object
query = {
'x': lon_range,
'y': lat_range,
'resolution': (-30, 30),
'output_crs':'EPSG:6933',
'time': (start_year, end_year),
}
**query)
print(ds)
<xarray.Dataset>
Dimensions: (time: 32, y: 255, x: 194)
Coordinates:
* time (time) datetime64[ns] 1990-07-02T11:59:59.999999 ... 2021-07...
* y (y) float64 -7.534e+05 -7.534e+05 ... -7.61e+05 -7.61e+05
* x (x) float64 3.424e+06 3.424e+06 3.424e+06 ... 3.43e+06 3.43e+06
spatial_ref int32 6933
Data variables:
count_wet (time, y, x) int16 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0
count_clear (time, y, x) int16 3 3 3 3 3 3 3 3 ... 21 21 21 18 19 19 19 20
frequency (time, y, x) float32 0.0 0.0 0.0 0.0 0.0 ... 0.0 0.0 0.0 0.0
Attributes:
crs: EPSG:6933
grid_mapping: spatial_ref
Facet plot a subset of the annual WOfS summaries¶
[6]:
ds.isel(time=[5,10,15,20,25]).frequency.plot(col='time', col_wrap=5, cmap=sns.color_palette("mako_r", as_cmap=True));
Animating time series¶
In the next cell, we plot the dataset we loaded above as an animation GIF, using the xr_animation <../Frequently_used_code/Animated_timeseries.ipynb>__ function. The output_path will be saved in the directory where the script is found and you can change the names to prevent files overwrite.
[7]:
out_path = 'annual_water_frequency.gif'
xr_animation(ds=ds,
output_path=out_path,
interval=400,
bands=['frequency'],
show_text='WOfS Annual Summary',
show_date = '%Y',
width_pixels=300,
annotation_kwargs={'fontsize': 15},
imshow_kwargs={'cmap': sns.color_palette("mako_r", as_cmap=True), 'vmin': 0.0, 'vmax': 0.9},
colorbar_kwargs={'colors': 'black'},
show_colorbar=False)
# Plot animated gif
plt.close()
Image(filename=out_path)
Exporting animation to annual_water_frequency.gif
[7]:
<IPython.core.display.Image object>
Calculate the annual area of water extent¶
The number of pixels can be used for the area of the waterbody if the pixel area is known. Run the following cell to generate the necessary constants for performing this conversion.
[8]:
pixel_length = query["resolution"][1] # in metres
m_per_km = 1000 # conversion from metres to kilometres
area_per_pixel = pixel_length**2 / m_per_km**2
Threshold WOfS annual frequency to classify water/not-water¶
Calculates the area of pixels classified as water (if ds.frequency is > 0.20, then the pixel will be considered regular open water during the year)
[9]:
water_threshold = 0.20
[10]:
#threshold
water_extent = ds.frequency > water_threshold
#calculate area
ds_valid_water_area = water_extent.sum(dim=['x', 'y']) * area_per_pixel
Plot the annual area of open water¶
[11]:
plt.figure(figsize=(18, 4))
ds_valid_water_area.plot(marker='o', color='#9467bd')
plt.title(f'Observed Annual Area of Water from {start_year} to {end_year}')
plt.xlabel('Dates')
plt.ylabel('Waterbody area (km$^2$)')
plt.tight_layout()
Determine minimum and maximum water extent¶
The next cell extract the Minimum and Maximum extent of water from the dataset using the min and max functions, we then add the dates to an xarray.DataArray.
[12]:
min_water_area_date, max_water_area_date = min(ds_valid_water_area), max(ds_valid_water_area)
time_xr = xr.DataArray([min_water_area_date.time.values, max_water_area_date.time.values], dims=["time"])
print(time_xr)
<xarray.DataArray (time: 2)>
array(['1992-07-01T23:59:59.999999000', '2021-07-02T11:59:59.999999000'],
dtype='datetime64[ns]')
Dimensions without coordinates: time
Plot the dates when the min and max water extent occur¶
Plot water classified pixel for the two dates where we have the minimum and maximum surface water extent.
[13]:
water_extent.sel(time=time_xr).plot.imshow(col="time", col_wrap=2, figsize=(14, 6));
Compare two time periods¶
The following cells determine the maximum extent of water for two different years. * baseline_year : The baseline year for the analysis * analysis_year : The year to compare to the baseline year
[14]:
baseline_time = '2019'
analysis_time = '2021'
baseline_ds, analysis_ds = ds_valid_water_area.sel(time=baseline_time, method ='nearest'), ds_valid_water_area.sel(time=analysis_time, method ='nearest')
Plotting¶
Plot water extent for the two chosen periods.
[15]:
compare = water_extent.sel(time=[baseline_ds.time.values, analysis_ds.time.values])
Calculating the change for the two nominated periods¶
The cells below calculate the amount of water gain, loss and stable for the two periods
[16]:
analyse_total_value = compare.isel(time=1).astype(int)
change = analyse_total_value - compare.isel(time=0).astype(int)
water_appeared = change.where(change == 1)
permanent_water = change.where((change == 0) & (analyse_total_value == 1))
permanent_land = change.where((change == 0) & (analyse_total_value == 0))
water_disappeared = change.where(change == -1)
The cell below calculate the area of water extent for water_loss, water_gain, permanent water and land
[17]:
total_area = analyse_total_value.count().values * area_per_pixel
water_apperaed_area = water_appeared.count().values * area_per_pixel
permanent_water_area = permanent_water.count().values * area_per_pixel
water_disappeared_area = water_disappeared.count().values * area_per_pixel
Plotting¶
The water variables are plotted to visualised the result
[18]:
water_appeared_color = "Green"
water_disappeared_color = "Yellow"
stable_color = "Blue"
land_color = "Brown"
fig, ax = plt.subplots(1, 1, figsize=(10, 10))
compare[1].plot.imshow(cmap="Pastel1",
ax=ax)
water_appeared.plot.imshow(
cmap=ListedColormap([water_appeared_color]),
ax=ax,
)
water_disappeared.plot.imshow(
cmap=ListedColormap([water_disappeared_color]),
ax=ax,
)
permanent_water.plot.imshow(cmap=ListedColormap([stable_color]),
ax=ax)
plt.legend(
[
Patch(facecolor=stable_color),
Patch(facecolor=water_disappeared_color),
Patch(facecolor=water_appeared_color),
Patch(facecolor=land_color),
],
[
f"Water to Water {round(permanent_water_area, 2)} km2",
f"Water to No Water {round(water_disappeared_area, 2)} km2",
f"No Water to Water: {round(water_apperaed_area, 2)} km2",
],
loc="lower left",
)
plt.title("Change in water extent: " + baseline_time + " to " + analysis_time);
Next steps¶
Return to the “Analysis parameters” section, modify some values (e.g. latitude, longitude, start_year, end_year) and re-run the analysis. You can use the interactive map in the “View the selected location” section to find new central latitude and longitude values by panning and zooming, and then clicking on the area you wish to extract location values for. You can also use Google maps to search for a location you know, then return the latitude and longitude values by clicking the map.
Change the year also in “Compare Two Time Periods - a Baseline and an Analysis” section, (e.g. base_year, analyse_year) and re-run the analysis.
Contact: If you need assistance, please post a question on the Open Data Cube Slack channel or on the GIS Stack Exchange using the open-data-cube tag (you can view previously asked questions here). If you would like to report an issue with this notebook, you can file one on Github.
Compatible datacube version:
[19]:
print(datacube.__version__)
1.8.6
Last Tested:
[20]:
from datetime import datetime
datetime.today().strftime('%Y-%m-%d')
[20]:
'2022-05-01' | 2022-05-22 08:51:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.26030245423316956, "perplexity": 8742.062067278439}, "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-2022-21/segments/1652662545090.44/warc/CC-MAIN-20220522063657-20220522093657-00298.warc.gz"} |
https://www.shaalaa.com/question-bank-solutions/write-remainder-obtained-when-1-2-3-200-divided-14-concept-of-permutations_53732 | Advertisement Remove all ads
Write the Remainder Obtained When 1! + 2! + 3! + ... + 200! is Divided by 14 ? - Mathematics
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
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Solution
Every number after 6! (i.e. 7! onwards) till 200! will consist a power of 2 and 7, which will be exactly divisible by 14.
So, we need to divide only the sum till 6!.
1! + 2! + 3! + 4! + 5! + 6! = 1 + 2 + 6 + 24 + 120 + 720 = 873
When 873 is divided, the remainder would be same as when 1! + 2! + 3! + ... + 200! is divided by 14.
Remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 = Remainder obtained when 873 is divided by 14 = 5
Is there an error in this question or solution?
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Forgot password? | 2021-04-14 11:43:16 | {"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": 0.9094932675361633, "perplexity": 661.3101789433063}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077810.20/warc/CC-MAIN-20210414095300-20210414125300-00582.warc.gz"} |
https://bq9.blogspot.com/2012/02/variables-in-gyp.html | ## 8.2.12
### variables in gyp
These are the ways to set variables you can reference in your gyp files.
Variables are referenced using the expansion character '<', like so '<(foo)'.
This happens in ExpandVariables, see [input.py]. There is also an "expand to list" variant '<@', which works if the context expects a list and if the string being expanded does not contain anything else.
Here is a toy .gyp file that references a variable foo
{
'targets': [
{
'target_name': 'foo_target',
'type': 'executable',
'sources': [ 'yo.c' ],
'actions': [
{
'action_name': 'greet',
'action': [ 'echo', 'hello world <(foo)', ],
'inputs': [],
'outputs': [ 'yo.c' ],
}]}]}
Now you could either add a variables section before 'targets' like so
'variables' : {
'foo': 'bar'
},
However, most of the time you will want to set these separately. You can do this in two ways.
1) include a separate file.
For this we would dreate a file some_vars.gypi that contains just this:
{
'variables' : {
'foo': 'bar'
},
}
and add an include to the original .gyp file
'includes': [ 'some_vars.gypi' ]
Here is the result:
$GYP_GENERATORS=ninja gyp --depth=0 --toplevel-dir=pwd \ simple_action.gyp$ ninja -C out/Default all
ninja: Entering directory out/Default'
[1/3] ACTION foo_target: greet
hello world bar
[...]
2) Set it on the command line.
gyp offers a "define" facility with the -D flag, which is also used to pass definitions down to the C/C++ compiler. The code says "-D is for default", so if the variable is already defined, that value is going to be used instead of your command line value.
Using the original .gyp file, we do
$GYP_GENERATORS=ninja gyp --depth=0 --toplevel-dir=pwd \ simple_action.gyp -Dfoo=baz$ ninja -C out/Default all
ninja: Entering directory out/Default'
[1/3] ACTION foo_target: greet
hello world baz
For an example with list expansion, check out the [Actions example] in the gyp language spec. | 2018-03-21 18:52:06 | {"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": 0.2937297821044922, "perplexity": 13434.544557052688}, "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-2018-13/segments/1521257647681.81/warc/CC-MAIN-20180321180325-20180321200325-00716.warc.gz"} |
http://mathematica.stackexchange.com/questions/35074/document-settings-for-online-viewing | # Document settings for online viewing
I'm trying to figure out how to prepare a notebook for NICE online viewing when it's been converted to PDF form. The students I am working with (sadly!) will not be able to use the CDFPlayer to view existing documents. I'm to use Google Docs and save the notebooks in PDF form.
I've been working with settings for margins and page sizes and paper sizes, I'll admit I'm out of my depth completely.
Specifically, I'd like two things.
FIRST When I save as PDF, I'd like the pages to be like actual slides in terms of size. It would be nice if each page was viewable on screen like a nice "distinct" slide.
Below, a 2 second pdf creation, being viewed in Google Docs.
B Is there any way to set the stylesheets so I would be able to 'see' in Mathematica what my pages would look like so I can edit, space, page break accordingly.
I know, I expect my question is too vague and may get "punted", but I'll need to get going on this ASAP and I simply can't get my mind around it myself.
I have tons of content all ready to go in existing notebooks and now find I am faced with a massive reformatting task.
I can simply format for nice "regular" pages and students would scroll, but I figured since they were viewing documents on computer, there HAVE to be ways to capitalize on that.
Tom
-
Have you tried New > Slideshow... from the Mathematica File menu? – m_goldberg Oct 30 '13 at 14:23
Hi, yes, the slide show looks great but doesn't (at least in my test) have printing to PDF setting that maintain the look of the document. The key here is that I have to export to PDF (which is crazy, the CDF format has so much more to offer) The specific dilemma for me is posting my notebooks to Google Docs... not horrible since I can "simply" export as they are, I was just hoping for more of an "online" viewing solution. – Tom De Vries Oct 30 '13 at 14:48
What OS are you on? On my system, OS X, the PDF I get from choosing File > Print and them choosing to save as PDF in the Print dialog looks pretty good when the proper printer setup options are made. – m_goldberg Oct 30 '13 at 15:05
Thanks, yes, I did try that, it does work, I think I am working around the same issues as this poster mathematica.stackexchange.com/questions/5925/… since an automated solution would be needed, and I'm having to reset the print settings each time... – Tom De Vries Oct 30 '13 at 16:00
@TomDeVries to get the right look when you print you'll have to examine the StyleData[All, "Printout"] in your stylesheet as well as the StyleData["cell type", "Printout"] for each type of cell. I'd compare them to the slideshow styles and adjust accordingly. – Mike Honeychurch Oct 30 '13 at 21:35
I do this kind of things regularly. The view of the PDF documents I obtain I find to be satisfactory. Sometimes there appears a conflict of the embedded figure and the page length. This may give rise to something like a part of the page with no text. If this is strongly unwanted, I fix this up manually (also not a big deal). To make the PDF file I simply save a notebook in question as a pdf. This works, though it may work not from the first trial, but after few of them. Generally, the larger is the notebook, the higher is the chance that I need to retry saving.
I guess that this satisfactory appearance is to extent due to the JournalArticle StyleSheet I use for my documents. It is a nice StyleSheet covering practically all my needs. It may be good for communication with students as well, especially in natural sciences.
It has only one drawback: the fonts used for text, captions and formulas are too small. Reading from the screen one should zoom-in considerably, especially if his vision is weak. When the original notebook is printed, it becomes still smaller. The workaround is to make a new style sheet using the JournalArticle one as a starting point, where you can increase the necessary fonts (also in the Printing environment) and add/remove some things according to your personal preferences.
I did that by rewriting the StyleSheet many times until achieving to the one I like. Then the CDF had emerged on the scene. Now I cannot use the personalized StyleSheet, since it will not be installed on the reader's machine. So I had to return to the original JournalArticle. However, for the purposes you explained this may be a solution.
Anyway, if you like, I can send you examples of one of the original notebooks and their pdf versions as well as my customized StyleSheet to begin with. I do not see, how to do that through the StackExchange environment. Therefore, if you would like to have that write me to abo@iee.lu
- | 2015-08-02 14:32:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.4769478440284729, "perplexity": 1200.747942725164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042989126.22/warc/CC-MAIN-20150728002309-00154-ip-10-236-191-2.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/schrodinger-equation-help.96652/ | # Schrodinger equation help
1. Oct 25, 2005
### mathlete
I'm given the value of a normalized wave function at t=0 (see attachment) and i'm asked to find the wave function at some time t. I have no idea where to even begin, the book has zero examples of anything and I'm just stuck
#### Attached Files:
• ###### equations.PNG
File size:
1.3 KB
Views:
55
2. Oct 25, 2005
### Tom Mattson
Staff Emeritus
What does your book have to say about the time evolution of a wavefunction? More specifically, have you been told what the time evolution operator is?
3. Oct 25, 2005
### Physics Monkey
mathlete,
I can't see yout attachment so I don't know what level you're at, therefore I'm going to give a fairly basic approach. If I have an exact energy state $$\psi_E(x)$$ that satisfies the time independent Schrodinger equation $$H \psi_E = -\frac{\hbar^2}{2m} \frac{d^2\psi_E}{dx^2} + V \psi_E= E \psi_E,$$ then how does $$\psi_E$$ change in time? Hint: use the time dependent Schrodinger equation. | 2016-12-05 14:50:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.6494830250740051, "perplexity": 719.3825066159534}, "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-2016-50/segments/1480698541697.15/warc/CC-MAIN-20161202170901-00354-ip-10-31-129-80.ec2.internal.warc.gz"} |
https://stacks.math.columbia.edu/tag/067W | $\xymatrix{ Z \ar[r]_ i \ar[rd]_ j & X \ar[d]^ f \\ & Y }$
be a commutative diagram of schemes where $i$ and $j$ are formally unramified and $f$ is formally smooth. Then the canonical exact sequence
$0 \to \mathcal{C}_{Z/Y} \to \mathcal{C}_{Z/X} \to i^*\Omega _{X/Y} \to 0$
of Lemma 37.7.11 is exact and locally split.
Proof. Denote $Z \to Z'$ the universal first order thickening of $Z$ over $X$. Denote $Z \to Z''$ the universal first order thickening of $Z$ over $Y$. By Lemma 37.7.10 here is a canonical morphism $Z' \to Z''$ so that we have a commutative diagram
$\xymatrix{ Z \ar[r]_{i'} \ar[rd]_{j'} & Z' \ar[r]_ a \ar[d]^ k & X \ar[d]^ f \\ & Z'' \ar[r]^ b & Y }$
In the proof of Lemma 37.7.11 we identified the sequence above with the sequence
$\mathcal{C}_{Z/Z''} \to \mathcal{C}_{Z/Z'} \to (i')^*\Omega _{Z'/Z''} \to 0$
Let $U'' \subset Z''$ be an affine open. Denote $U \subset Z$ and $U' \subset Z'$ the corresponding affine open subschemes. As $f$ is formally smooth there exists a morphism $h : U'' \to X$ which agrees with $i$ on $U$ and such that $f \circ h$ equals $b|_{U''}$. Since $Z'$ is the universal first order thickening we obtain a unique morphism $g : U'' \to Z'$ such that $g = a \circ h$. The universal property of $Z''$ implies that $k \circ g$ is the inclusion map $U'' \to Z''$. Hence $g$ is a left inverse to $k$. Picture
$\xymatrix{ U \ar[d] \ar[r] & Z' \ar[d]^ k \\ U'' \ar[r] \ar[ru]^ g & Z'' }$
Thus $g$ induces a map $\mathcal{C}_{Z/Z'}|_ U \to \mathcal{C}_{Z/Z''}|_ U$ which is a left inverse to the map $\mathcal{C}_{Z/Z''} \to \mathcal{C}_{Z/Z'}$ over $U$. $\square$
There are also:
• 7 comment(s) on Section 37.11: Formally smooth morphisms
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2023-01-31 00:22:28 | {"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": 2, "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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9967092871665955, "perplexity": 149.0763265156856}, "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/1674764499831.97/warc/CC-MAIN-20230130232547-20230131022547-00029.warc.gz"} |
https://matheducators.stackexchange.com/questions/9874/why-do-we-conventionally-treat-trig-functions-as-going-anti-clockwise-from-the-r/9893 | # Why do we conventionally treat trig functions as going anti-clockwise from the right?
I realise that teachers tend to focus on right-angled triangles when introducing trig functions, and for those I can see that the most intuitive approach seems to be starting with the opposite and adjacent sides of a triangle matching the right and bottom of a rectangle. But otherwise, it's always struck me as odd that we go anti-clockwise from the right, rather than clockwise from the top - which gives the same results, but with sine corresponding to the horizontal direction, and cosine on the vertical. This is how bearings are conventionally given, after all, and even in the digital age the analogue clock-face is something almost everyone's familiar with. And it's not so hard to draw a triangle with its point facing downwards, right?
I'm just wondering if I'm missing something here. Would I be doing my students a terrible disservice if I introduced them to trig functions treating them as going clockwise from 12 o'clock?
• How would they react if you drew Cartesian coordinate planes with the positive x-axis going vertically and the positive y-axis going to the right? And then graph a function y=f(x)? You can buck conventional notation, but at some point your students will have to deal with conventions used in other contexts. Point out the differences. Gerhard "If You Dare To Differ" Paseman, 2015.10.29 – Gerhard Paseman Oct 29 '15 at 21:28
• Really asking two questions here. First is why the tradition originated and second is whether you should teach it differently. I also wonder about the origin, but I would never let that wonder dictate how I taught students unless it was some type of advanced graduate level proofs or theory course. – oemb1905 Oct 30 '15 at 1:22
• In addition, compass directions are also (not surprisingly) measured in a clockwise direction. – copper.hat Oct 30 '15 at 2:41
• Might have some luck on MSE. I added a question: math.stackexchange.com/questions/1504483/…. – copper.hat Oct 30 '15 at 3:07
• From Wikipedia: "it is known that the systematic introduction of the 360° circle came a little after Aristarchus of Samos composed On the Sizes and Distances of the Sun and Moon (ca. 260 BC)". Note the link between astronomy and using a circle for trigonometry. I mention that because when the solar system is viewed from above the Earth's north pole, the planets revolve anti-clockwise. That is a possible source for the direction of rotation. – Todd Wilcox Oct 30 '15 at 14:38
There is no such thing as a natural sign/direction convention until long after the fact. Consider another answerer's comment that anyone using the left hand rule to construct the cross product of two vectors would be mistreated. Of course, the left hand rule is exactly the correct rule to use for the path of electrons in a magnetic field? Why? Because the convention of positive and negative charge was set before anyone knew that the mobile charge carriers had been called "negative". Thanks, Ben Franklin.
Consequently, conventions are made and the ones that achieve critical mass succeed and overwhelm the alternatives. Frequently, it is the ones that can be described as somehow natural. In this context:
• I teach my trigonometry students that all three pairs of (cos, sin), (adjacent, opposite), and ($x$,$y$) are in alphabetical order.
• I teach them that angles are measured from the positive half of the first ($x$-) axis in the direction of the positive half of the second ($y$-) axis.
• Reference triangles have two points on the $x$-axis, in fact, their first two points. That is, start at the origin with the first point, go along the first axis to the second point, then turn at right angles and go parallel to the second axis to the third point. For some students, it even helps to see this as a sequence: "$(0,0), \xrightarrow{x}, 1, \xrightarrow{y} 2$".
Later, I explain to them that bearings are different and for a very practical reason: bearings are measured from the direction compasses point (North). I also warn them that there are many, many mismatched conventions. (Nearly every "reasonable" reference vector has been used in a navigation system at some point in the past 600 years). Although North is a common reference vector now, for astronomy and stellar navigation, it was common to use South as the reference vector, as it was then zero at the same time that the hour angle of a star was zero. Then, once one is in this mode of comparing bearings to times and star positions, it is only sane to measure angles clockwise so that positive offset times correspond to positive offset angles. That is, the conventions of navigation in the past were based on the need to have an easily interpretable table of stars and times, but the conventions of navigation in the present are based on the underlying convention that North is the basis of bearing measurements (which is largely a consequence of gradually narrowing cartographic convention in the last half of the second millenium).
However, none of that explains why angles are measured up from right. Early applications of trigonometry were to astronomy and navigation (see prior paragraph) and architecture. In architecture, the problem is to pile up building materials (either in preparation to construction or placed in the constructing itself). Consequently, one is measuring grades of piled up or placed materials. Then one measures angles in quadrants I or II up from the $x$-axis. One always puts the angles at the origin so that the sine and cosine actually correspond to the coordinates of the third point (projected onto the unit circle) because the practical historical problem is to measure an angle up from the horizon.
One can see this in Euclid's Elements, Prop. 1. The construction of an equilateral triangle from a given line segment AB. The point $A$ is drawn at the lower left, the segment AB proceeds to the right, and the third point is constructed above the segment AB (even though constructing it below is just as easy). That is, the author finds it natural to place the starting segment horizontally with the starting point at the left. (The next few triangle propositions are about isosceles triangles, which are drawn with the first point on a vertical symmetry axis -- i.e., modeling a pile of stuff. I recall reading that this was intended, but I have no hope of dredging up a reference.)
The final reason to do this is so that derivatives work in the expected way in Calculus: a slope of zero does not correspond to a vertical tangent line. Having to unlearn this will be a significant disservice to your students.
Edit: (More on the Calculus reason) Pick a point on a function at which the function is continuous and translate that point to the origin (just to make the rest of this clearer). Positive derivatives at that point correspond to tangent lines lying in quadrants I and III. Negative derivatives correspond to tangent lines lying in quadrants II and IV. Further, a derivative of zero corresponds to a horizontal tangent line. If we arrange angles to be measured in the right-handed orientation from the horizontal axis, then a zero angle coincides with a zero derivative, a positive angle with a positive derivative, and a negative angle with a negative derivative. We can actually finish this correspondence by observing that the tangent of the angle (measured in the standard way) of a tangent line is the slope of that tangent line. That is, the slope is the $\frac{\text{rise}}{\text{run}} = \frac{\Delta y}{\Delta x} = \tan \theta$. And I've seen "the lightbulb" for students when they realize the tangent line's angle's tangent is the slope. (I don't know that this is a valid "Aha!". There's linguistic repetition, but the ideas are really unrelated. But some students seem to make progress with this association.)
• That's a very good answer, but I'm not sure I follow your last point - could you possibly elaborate a little? – Oolong Nov 1 '15 at 10:19
• +1 This is a wonderful and comprehensive answer, well worth the wait. – mweiss Nov 1 '15 at 14:57
• Also, I see this is your first post on MESE. Welcome to the site! – mweiss Nov 1 '15 at 14:58
• @Oolong : I've elaborated the last paragraph. It's early here; please let me know if it's not quite coherent. (I haven't had my second cup of coffee yet.) – Eric Towers Nov 1 '15 at 16:03
• Thanks Eric, I think that makes sense. I'm still a bit unsure on one point though - it seems to me that going clockwise from the top, the tangent actually represents the gradient of a line tangent to the circle. Going anticlockwise from the right, it's instead the gradient of the radial line (the hypotenuse) - which is also nice, but seems harder to relate to the name of the function. Am I confused? – Oolong Nov 5 '15 at 17:18
Regarding the second part of your question:
Would I be doing my students a terrible disservice if I introduced them to trig functions treating them as going clockwise from 12 o'clock?
I think it's important to stress that the convention is just a convention, and there is no intrinsic reason why one convention is better than another. But at the same time, this particular convention is a nearly universal one, and teaching your students a nonstandard convention is roughly equivalent to a language teacher teaching his or her students a dialect that nobody else speaks. As soon as they leave your classroom they will find themselves in a mathematical world that does things differently, and you are doing them a disservice if they are not thoroughly used to the conventions that everybody uses.
• Actually I disagree with your answer based on the reasons I gave in my answer. A lot of mathematical objects that seem tied to the anti-clockwise direction are nowhere near arbitrary but have to do with the way we have chosen to position the coordinate axes on paper. For example signed area is positive for anti-clockwise traversal of a non-self-intersecting polygon in the plane. The relation between the anti-clockwise contour integral around a pole and the residue there as given by the Laurent series is another. Not coincidental at all. – user21820 Oct 30 '15 at 13:40
• Seems like we could just as well write complex analysis based on CW-loops. It'd just introduce a few signs here and there. Maybe CCW is just what we're used to. – James S. Cook Oct 31 '15 at 1:21
• To me, the most important takeaway from this question is this: "As soon as they leave your classroom they will find themselves in a mathematical world that does things differently, and you are doing them a disservice if they are not thoroughly used to the conventions that everybody uses." +1 – Todd Wilcox Oct 31 '15 at 8:53
• I don't think we should be upvoting this so much, since it does not answer the main question. Am I wrong on protocol here? – oemb1905 Nov 2 '15 at 2:11
• @oemb1905 If by "the main question" you mean "the question in the title", remember that the title is a just a headline; the question is what's in the body of the post. This particular post asks two questions; the second one asks about teaching, the first one about historical origins. It may be worth noting that it is only the second question that makes this on-topic for MESE; the first question by itself would be better for MSE or HSM. – mweiss Nov 2 '15 at 2:42
My guess is that it comes from drawing complex numbers. Putting real numbers on the $x$-axis from left to right and imaginary numbers on the $y$-axis from bottom to top matches with the way we tend to think (in cultures based on Latin at least). Once you establish that, then the function $x\mapsto e^{2\pi ix}$ takes you anti-clockwise from the positive $x$-axis.
On the other hand, if I'm not missing something, a clock face is based on living in the northern hemisphere.
• Interesting! I wonder if that is indeed how it started. I'm not sure what you mean about 'a clock face is based on living in the northern hemisphere'? – Oolong Oct 29 '15 at 21:54
• @Oolong A clock face is based on the position of a shadow moving on a sundial during the day. – PVAL Oct 29 '15 at 23:30
• The problem with this answer is that it is definitely false because Euler's identity came long after the definition and use of the trigonometric functions. As in my answer, I'm not saying that this isn't a good reason, but it certainly wasn't the original reason. =) – user21820 Oct 30 '15 at 13:36
• @user21820 Is it more about when the trig functions were invented or when the unit circle was developed as a way to understand and represent them? The history of the use of the unit circle is something I've been looking for all morning and haven't yet really found. If it post-dates Euler, then this answer could very well be a very good one. – Todd Wilcox Oct 30 '15 at 14:27
• My understanding was that the question was about why we now draw triangles oriented a particular way, not about why sin and cos are defined the way they are. Did those using trig before Euler always draw their triangles the same way? I would assume they spent their time on real-life questions, not school exercises. – Jessica B Oct 30 '15 at 15:30
I would avoid teaching it only as clockwise. If you wanted to teach it that way, I would recommend showing both throughout the process, and pointing out that while clockwise might make more intuitive sense at first, the world will expect you to think of it anti-clockwise later.
The reason I point it out is not a mathematics one. I am an engineer, who deals with things like coordinate conventions every day of my life. Even after doing it for years, coordinate conventions still confuse engineers enough to make machines break and planes crash every year (hopefully simulated machines and simulated planes! We do like to fix these things before they get manufactured!) The topics we have to deal with are so exacting that we oft do not have the spare brain-power to consider what might happen if our coordinate system is wrong.
How bad is it? I work on a simulation where we support multiple frames / coordinate systems because the work done in the simulation is too complicated to do them in the wrong frame. We support, at any time, at least 5 frames and another dozen or so coordinate systems associated to those frames. We handle Euler angles and Tait-Bryan angles, all 1000+ combinations thereof (did you know there were that many? Most people I work with are aware of 2 or 4!). I admit I get a sadistic gleam in my eye whenever anyone asks me to read in some Euler angle data, and I ask "which convention are you using?" It's especially satisfying when I make them go back to the vendors to make sure both vendors supplying data are using the same definitions! (usually they do. Most of our vendors follow the DIS convention, thank goodness)
You can call it a very powerful group-think, which it is, but its important for young engineers to learn the conventions we use, because we will use them. Circular, but true. Initially teach it however your instincts recommend, but please make sure your students are comfortable with the conventional way of doing it before they leave your class. In the best of worlds, a new engineer who is totally comfortable switching conventions is the best of all. However, a new engineer who has an alien convention is a liability until they can be trained to group-think like the rest of us.
And that's where I leave it to you. I'm no educator. I'm just a guy in the field. If you think you can train students to switch conventions in their mind without sweating it, please do so. Minds that can switch on a whim are tremendously valuable. If you think some of the students might have great trouble switching later on, I'd think twice (especially if you think any of those students might enter STEM fields).
• As an amusing aside, we do have one convention we all agree upon in engineering: right handed coordinate systems. Thank goodness for that. I oft joke that we have the "engineering gang sign," the thumb index and middle fingers of the right hand splayed out into a right handed coordinate system. If anyone flipped us the left-handed gang sign, we might murder them. – Cort Ammon Oct 30 '15 at 19:45
• You're probably right, but I'm still wondering how much difference it actually makes when that convention does come along. So many things come out the same if you mirror the whole thing around the a line from the top-right to the top left... – Oolong Oct 31 '15 at 15:23
• I am truly torn between saying "try it," because that's what learning is all about, and we need to try new things... and knowing that we've pelted the surface of Mars with slugs of what-was-a-rover-at-one-point for smaller convention mistakes ;-) – Cort Ammon Oct 31 '15 at 18:17
It's starting on the positive branch of the real number line; and passing through the positive quadrant first.
• Agreed - the convention predates complex numbers by many years. – oemb1905 Oct 30 '15 at 1:24
• @oemb1905 This answer doesn't really make sense without complex numbers, since it views the 'real number line' as significant. – Jessica B Oct 30 '15 at 8:00
• @JessicaB Complex numbers were discovered nearly five thousand years, possibly ten thousand years after the usage of the unit circle, degree measure, arc length, etc., for astronomy. If the question is about the origins of the convention, then I am not sure the work of Hamilton and Gibbs will inform the historical basis for that convention. – oemb1905 Oct 30 '15 at 15:56
Perhaps the convention is rooted in how the big dipper rotates around the north star--in a counterclockwise direction. Also think about how the earth rotates around its axis--in a counterclockwise direction.
Since the origins of trigonometry are inextricably tied to navigation, you would think our modern convention might descend from this.
• Of course, technically the Earth only rotates anticlockwise viewed from above the North pole... – DavidButlerUofA Oct 30 '15 at 3:19
• And yet, navigators use bearings clockwise from North instead... – Oolong Oct 30 '15 at 8:19
• Longitude on the celestial sphere is measured as eastward along the ecliptic plane from the vernal equinox, which serves as 0. So in the northern hemisphere this is a counterclockwise orientation. – user52817 Oct 30 '15 at 18:03
Question 1 - Why: it has to do with the right-handed coordinate system (Ampere's invention). X and Y are not the only axes, there is a third one- Z. In a right handed CS, if X points to the right and Y points up, then Z must point out of the wall (towards observer). Almost everything in physics, engineering and math relies on the right handed CS. The Cross-product X(cross)Y = +Z, Y(cross)Z = +X, Z(cross)X = +Y, whereas Y(cross)X = -Z. Positive moments are defined following the cross product notation: positive moment (or rotation) about Z axis goes from X towards Y axis. Take a screw for example - rotate it counterclockwise and it goes out of the wall towards the observer (positive Z direction), rotate it clockwise - it goes into the wall (negative Z direction). Question 2 - Since this convention is ubiquitous across all the scientific fields, teaching in a left handed CS will do a disservice to students, since re-learning is more difficult than learning from scratch.
PS I know at least one public clock that goes the other way around.
I did a google search for "right triangle". The first image I got is
Suitable for viewing angles counterclockwise from East or clockwise from South.
*: I use the compass points for direction, since I find phrases like "clockwise from down" awkward, and did not want to use "counterclockwise from the positive $x$ axis", since sometimes people do have the $y$ axis pointing East and the $x$ axis pointing either North or South
The second image I got was
suitable for viewing angles clockwise from West, or counterclockwise from South.
The twenty-fourth image was
and is the first triangle suitable for having an angle measured clockwise from North.
This is by no means conclusive, but if we were to believe the idea of measuring angles from coordinate axes and extending the trig functions to the whole circle came about as an extension of measuring right triangles, it's plausible that the way we tend to write triangles had some influence.
• It is, however, also plausible that the way we draw triangles is influenced by the convention that angles should run anti-clockwise from the right... – Oolong Oct 31 '15 at 15:26
• @Oolong: The images seem to be mostly split evenly between the first two types: I think the relevant bias is more likely to be that the base of the triangle should be on the bottom than anything else. – Hurkyl Nov 1 '15 at 23:40
• I'm not seeing the connection between this answer and the question. What did I miss? You say it's "plausible" but how? Every image is the same when viewed from somewhere else ... – oemb1905 Nov 2 '15 at 2:10
A large source of problems that trigonometry solved was astronomy. Our solar system is "right handed". If you point your thumb "north", your fingers will curl in the direction that the planets revolve around the sun. The orbits of most (not all) of the planets in our solar system are also right handed. It makes sense then to use the right hand rule to describe the direction in which angles increase.
• I see no natural reason to prefer north over south. If you look at the solar system from the opposite side, the planets revolve the other way. It is true that the conventions of preferring north and that of preferring counter-clockwise direction are compatible with each other, but neither choice seems obvious. – Joonas Ilmavirta Oct 31 '15 at 23:13
• There is no natural reason, just historical. Astronomy from the days of yore was mostly developed by people in the northern hemisphere who centered things around Polaris, or the "North Star." – user52817 Nov 1 '15 at 2:17
There are many possible reasons why it should be defined that way, but I'm not sure what were the initial motivating reasons. $\def\nn{\mathbb{N}}$ $\def\rr{\mathbb{R}}$
Firstly, $(\cos,\sin)$ is a basis for all the real-valued functions satisfying $f''=-f$. It is then natural to choose the basis elements so that $\cos(0) = 1$ and $\cos'(0) = 0$ and $\sin(0) = 0$ and $\sin'(0) = 1$. Another viewpoint is that this differential equation immediately implies that if they have a Taylor series $x \mapsto \sum_{k\in\nn} a_k \frac{x^k}{k!}$, then the coefficients $(a_n)_{n\in\nn}$ would have to satisfy $a_{n+2}=a_n$ for any $n\in\nn$. If we do not want to invoke the Taylor theorem we could also have defined them by the infinite series, prove that it converges, and then prove directly that it satisfies the differential equation. Either way, we obviously want the basis elements to be $(1,0,-1,0,\cdots)$ and $(0,1,0,-1,\cdots)$.
As a side note, harmonic motion is often started off with nonzero displacement but zero velocity, corresponding to a multiple of $\cos$, whereas $\sin$ corresponds to zero initial displacement but nonzero initial velocity. In some sense, rest is simpler than motion, just as first-order terms in a Taylor series are 'more' important than second-order terms.
Secondly, $\exp(it)$ goes round the unit circle for $t\in\rr$. We can see this from the properties of $\exp$ that follows from the infinite series definition, which is motivated by the differential equation $f'=f$. The other definitions do not reveal the underlying structure. We can then choose $\cos,\sin$ as the $x,y$ coordinates.
In both reasons above, they do not fix a starting point or direction for the path traced by $(\cos,\sin)$ in the plane. What fixes it is the choice of our coordinate system where the $y$-axis is $90^\circ$ anti-clockwise from the $x$-axis, and we plot a pair with the first element as $x$-coordinate and the second element as $y$-coordinate.
In fact, a lot of mathematical objects that seem tied to the anti-clockwise direction are nowhere near arbitrary but have to do with the way we have chosen to position the coordinate axes on paper. For example signed area is positive for anti-clockwise traversal of a non-self-intersecting polygon in the plane. The relation between the anti-clockwise contour integral around a pole and the residue there as given by the Laurent series is another. Not coincidental at all. (I decided to put this paragraph in because amazingly people don't seem to get that my answer explains all these seemingly arbitrary conventions at one go.)
• But why give the basis as $(\cos, \sin)$ rather than $(\sin, \cos)$? The latter seems (to beginners) much more "obvious". – mweiss Oct 30 '15 at 13:23
• @mweiss: Simply because we write the first coordinate first. So the question that should be asked is not about $\cos,\sin$ but about the choice of depicting the cartesian plane on paper. – user21820 Oct 30 '15 at 13:31
• @mweiss: It's the same reason we list the standard basis elements of $\mathbb{R}^2$ as $(1,0),(0,1)$ just as in the identity matrix rather than the other way around. It won't be the identity matrix if we switch the order but want to keep the same meaning of the matrix action on vectors. – user21820 Oct 30 '15 at 13:34
• No, I'm not asking "Why not list $y$ before $x$?". My question is Why does $\cos$ come first? Why not choose $\sin, \cos$ as the $x,y$ coordinates? Then with our current conventions about how we represent the coordinate system on paper, we would follow the proposal in the OP -- i.e. to start at $(0,1)$ and move clockwise. – mweiss Oct 30 '15 at 13:44
• But I think your second reason is the real one. The fact that $\exp(it) = \cos(t) + i sin(t)$, together with our conventions about writing complex numbers in the order "real part + imaginary part", argues for thinking about $\cos$ as the "first" function and $\sin$ as the "second". – mweiss Oct 30 '15 at 13:45
I am so interested in finding an answer for the first part of the question that I copy (as community wiki) my "answer" to this somehow the same MSE question, hoping that it helps us to understand the roots of this particular "convention".
This is by no means answering the question as it is. However, It is just to give a historical piece (taken from "The history of Stokes' Theorem" written by Katz) that might come handy when thinking of the first part of the question (CW vs. CCW or ACW).
As it can be seen, Green's theorem as introduced by Cauchy (1846) is undecided about the orientation of the curve.
I repeat that I didn't attempt to answer the question as asked. I just tried to extend the question a bit hoping that it helps us to find the answer (if any) to the original question.
I'm looking at the unit circle -
and it seems to me that if we deemed Y to be cosine, and X, sine, i.e. flip the graph about the Y=X line, we would achieve your goal. Right?
But, as Hurkyl indicates, the orientation of a 45 degree right triangle results in
and that would appear to be a bit disorienting to students. In the end, it's the combination of Cartesian coordinates being established as well as the 'comfortable' orientation for the 0-90 degree right angle triangles that dictated the placement. | 2019-09-20 11:06:43 | {"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": 0.687466561794281, "perplexity": 485.08326658776497}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573988.33/warc/CC-MAIN-20190920092800-20190920114800-00277.warc.gz"} |
https://math.stackexchange.com/questions/1351032/schwarz-lemma-of-complex-analysis | # Schwarz Lemma of Complex Analysis
Let be $f:B(0,1)\to B(0,1)$ holomorphic function such that $$f(0)=f'(0)=\cdots=f^{(n-1)}(0)=0$$ but $f^{(n)}(0)\neq 0.$ Show that $|f(z)|\le |z|^n,$ for every $z\in B(0,1)$ and $|f^{(n)}(0)|\le n!.$
I think that I will use the Schwarz Lemma, cause by the Lemma, I have that $|f(z)|\le |z|$, but I don't know how I can to use the conditions about the derivatives.
Any suggestion? Thanks.
• You don't use the Schwarz lemma, but you mimic its proof. By the assumption, $$g(z) := \frac{f(z)}{z^n}$$ is holomorphic on the open unit disk. Use the maximum modulus principle. – Daniel Fischer Jul 6 '15 at 6:56
• Hi @DanielFischer, I don't understand why $g$ is holomorphic in z=0 (z=0 is a polo of order n of $g$). Thanks you for your help. – Irddo Jul 6 '15 at 11:06
• Since $0$ is a zero of order $n$ of $f$, it is not a pole of $g$ but a removable singularity (and since $n$ is the precise order of the zero, we have $g(0) \neq 0$, but that is not important). – Daniel Fischer Jul 6 '15 at 11:10
• Yes, I get it. So, I need to show there is $z_0\in B (0, 1)$ such that $|g (z)|\le g |(z_0)|$, for every $z\in B (0, 1)$ to conclude that $g$ is constant? Is it? – Irddo Jul 6 '15 at 11:44
• But $g$ need not be constant, consider e.g. $f(z) = z^n\cdot e^{z-1}$. You need to show that $\lvert g(z)\rvert \leqslant 1$ for all $z\in B(0,1)$. – Daniel Fischer Jul 6 '15 at 11:48
By the assumption that $f(0) = f'(0) = \dotsc = f^{(n-1)}(0) = 0$, the Taylor series of $f$ centred at $0$ is
$$f(z) = \sum_{k = n}^\infty a_k z^k.$$
Hence the function
$$g(z) = \frac{f(z)}{z^n} = \sum_{k = n}^\infty a_k z^{k-n} = \sum_{k = 0}^\infty a_{n+m}\cdot z^m$$
is holomorphic on $B(0,1)$.
By the maximum modulus principle, for $0 < r < 1$, we have
$$\lvert g(z)\rvert \leqslant \max \{ \lvert g(\zeta) : \lvert \zeta\rvert = r\} = \max \biggl\{ \biggl\lvert \frac{f(\zeta)}{\zeta^n}\biggr\rvert : \lvert \zeta\rvert = r\biggr\} \leqslant \frac{1}{r^n},\tag{1}$$
for $\lvert z\rvert \leqslant r$, since $\lvert f(\zeta)\rvert < 1$. We thus have
$$\lvert g(z)\rvert \leqslant \inf \{ r^{-n} : \lvert z\rvert \leqslant r < 1\} = 1$$
for all $z\in B(0,1)$.
Hence, we have
$$\lvert f(z)\rvert = \lvert z^n\cdot g(z)\rvert = \lvert g(z)\rvert\cdot \lvert z\rvert^n \leqslant \lvert z\rvert^n$$
on $B(0,1)$.
The estimate for $f^{(n)}(0)$ follows similarly from the integral formula:
$$f^{(k)}(z) = \frac{k!}{2\pi i} \int_{\lvert \zeta\rvert = r} \frac{f(\zeta)}{(\zeta-z)^{k+1}}\,d\zeta$$
for $\lvert z\rvert < r < 1$, whence
$$\lvert f^{(k)}(0)\rvert \leqslant \frac{k!}{2\pi} \cdot (2\pi r)\cdot \frac{1}{r^{k+1}} = \frac{k!}{r^k}.$$
Since that inequality holds for all $r < 1$, it follows that
$$\lvert f^{(k)}(0)\rvert \leqslant k!$$
for all $k\in \mathbb{N}$. Note that for this estimate, it was immaterial that $f$ has a zero at $0$, only that $\lvert f\rvert$ is bounded by $1$ is required. | 2020-02-27 15:30:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9884909391403198, "perplexity": 141.27242003935214}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875146714.29/warc/CC-MAIN-20200227125512-20200227155512-00064.warc.gz"} |
https://openscholarship.wustl.edu/iwota2016/Contributed/contributedtalksMondayA/3/ | ## Contributed talks session A (Monday)
#### Location
Cupples I Room 207
#### Start Date
7-18-2016 3:00 PM
#### End Date
18-7-2016 3:20 PM
#### Description
\noindent We give a solvability criterion for the following $\mu$-synthesis problem. Let $\mu$ be the structured singular value for the diagonal matrices with entries in $\Bbb{C}$. \vspace{0.2cm} \noindent\text{\bf{Problem.}} Given distinct points $\lambda_1,\dots,\lambda_n$ in the open unit disc $\Bbb{D}$ and target $2\times2$ complex matrices $W_1, \dots, W_n$ such that $\mu(W_j)\leq 1$ for all $j=1,\dots, n$, find a holomorphic $2\times2$ matrix function $F$ on $\Bbb{D}$ such that $F(\lambda_j)=W_j$ for each $j$, and $\mu(F(\lambda))\leq1$ for all $\lambda\in\Bbb{D}$. \vspace{0.2cm} \noindent By [1, Theorem 9.2], this problem is equivalent to the following interpolation problem: does there exist a holomorphic function $x$ from the disc to the tetrablock $\overline{\Bbb{E}}$ such that $x(\lambda_j)=(w_{11}^j,w_{22}^j,\det{W_j})$ for each $j$? The tetrablock is the domain in $\Bbb{C}^3$ defined by $\overline{\Bbb{E}}:=\{(x_1,x_2,x_3)\in\Bbb{C}^3:1-x_1z-x_2w+x_3zw\neq0\text{ for all }z,w\in\Bbb{D}\}.$ \vspace{0.2cm} \noindent In this talk we show such an $x$ exists if and only if, for distinct $z_1,z_2,z_3\in\Bbb{D}$, there are positive $3n$-square matrices $[N_{il,jk}]$, of rank $1$, and $[M_{il,jk}]$ such that $\left[1-\overline{\frac{z_lx_{3i}-x_{1i}}{x_{2i}z_l-1}}\frac{z_kx_{3j}-x_{1j}}{x_{2j}z_k-1}\right] \geq[(1-\overline{z_l}z_k)N_{il,jk}]+[(1-\overline{\lambda_i}\lambda_j)M_{il,jk}],$ where $(x_{1j},x_{2j},x_{3j})=(w_{11}^j,w_{22}^j,\det{W_j})$ for each $j$.\\ \noindent The talk is based on a joint work with Z. A. Lykova and N. J. Young.\\ \noindent [1] A. A. Abouhajar, M. C. White and N. J. Young, A Schwarz lemma for a domain related to $\mu$-synthesis, \emph{J. Geom. Anal. 17}, (2007), pp. 717-750
#### Share
COinS
Jul 18th, 3:00 PM Jul 18th, 3:20 PM
A criterion for the solvability of a $\mu$-synthesis problem
Cupples I Room 207
\noindent We give a solvability criterion for the following $\mu$-synthesis problem. Let $\mu$ be the structured singular value for the diagonal matrices with entries in $\Bbb{C}$. \vspace{0.2cm} \noindent\text{\bf{Problem.}} Given distinct points $\lambda_1,\dots,\lambda_n$ in the open unit disc $\Bbb{D}$ and target $2\times2$ complex matrices $W_1, \dots, W_n$ such that $\mu(W_j)\leq 1$ for all $j=1,\dots, n$, find a holomorphic $2\times2$ matrix function $F$ on $\Bbb{D}$ such that $F(\lambda_j)=W_j$ for each $j$, and $\mu(F(\lambda))\leq1$ for all $\lambda\in\Bbb{D}$. \vspace{0.2cm} \noindent By [1, Theorem 9.2], this problem is equivalent to the following interpolation problem: does there exist a holomorphic function $x$ from the disc to the tetrablock $\overline{\Bbb{E}}$ such that $x(\lambda_j)=(w_{11}^j,w_{22}^j,\det{W_j})$ for each $j$? The tetrablock is the domain in $\Bbb{C}^3$ defined by $\overline{\Bbb{E}}:=\{(x_1,x_2,x_3)\in\Bbb{C}^3:1-x_1z-x_2w+x_3zw\neq0\text{ for all }z,w\in\Bbb{D}\}.$ \vspace{0.2cm} \noindent In this talk we show such an $x$ exists if and only if, for distinct $z_1,z_2,z_3\in\Bbb{D}$, there are positive $3n$-square matrices $[N_{il,jk}]$, of rank $1$, and $[M_{il,jk}]$ such that $\left[1-\overline{\frac{z_lx_{3i}-x_{1i}}{x_{2i}z_l-1}}\frac{z_kx_{3j}-x_{1j}}{x_{2j}z_k-1}\right] \geq[(1-\overline{z_l}z_k)N_{il,jk}]+[(1-\overline{\lambda_i}\lambda_j)M_{il,jk}],$ where $(x_{1j},x_{2j},x_{3j})=(w_{11}^j,w_{22}^j,\det{W_j})$ for each $j$.\\ \noindent The talk is based on a joint work with Z. A. Lykova and N. J. Young.\\ \noindent [1] A. A. Abouhajar, M. C. White and N. J. Young, A Schwarz lemma for a domain related to $\mu$-synthesis, \emph{J. Geom. Anal. 17}, (2007), pp. 717-750 | 2020-04-06 12:59:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8963378071784973, "perplexity": 276.4156768632224}, "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/1585371624083.66/warc/CC-MAIN-20200406102322-20200406132822-00416.warc.gz"} |
http://mathhelpforum.com/statistics/205282-determining-correlation-print.html | # Determining the correlation
• October 14th 2012, 01:28 AM
algorithm
Determining the correlation
Hi,
I am computing the correlation between two vectors by simply averaging loads of correlation values:
Repeat 100 times:
$Y = X + Noise$, where $Noise$ is AWGN with a normal distribution.
$C = \sigma_{XY}/\sqrt\(\sigma_{X}\sigma_{Y})$
Y and X are vectors of the same length. For my purposes $X$ is just contains known constants.
What I'd like to know is how I can determine the correlation analytically?
Thanks.
• October 14th 2012, 11:07 PM
chiro
Re: Determining the correlation
Hey algorithm.
Hint: How do you calculate the covariance and variance analytically? | 2016-06-30 05:41:55 | {"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": 4, "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": 0.6786454319953918, "perplexity": 1509.154279559075}, "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-2016-26/segments/1466783398075.47/warc/CC-MAIN-20160624154958-00143-ip-10-164-35-72.ec2.internal.warc.gz"} |
https://socratic.org/questions/krypton-79-mg-has-a-half-life-of-35-h-how-many-half-lives-have-passed-after-105- | # Krypton-79 mg has a half-life of 35 h. How many half-lives have passed after 105 h?
Jun 12, 2017
$3$ half-lives
#### Explanation:
This question is rather simple; we're given a half-life ($35$ $\text{h}$) and asked how many occur in a given time ($105$ $\text{h}$).
To solve this, divide the time interval by the half-life:
$\left(105 \cancel{\text{h"))/(35cancel("h}}\right) = 3$ $\text{half-lives}$
It makes sense, as there are three $35 \text{-}$ hour intervals within $105$ hours. | 2020-01-18 17:55:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 9, "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": 0.8331981301307678, "perplexity": 1335.821397821864}, "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/1579250593295.11/warc/CC-MAIN-20200118164132-20200118192132-00258.warc.gz"} |
http://www.burningcutlery.com/derek/winsetup/ | Making Windows Usable
Some of us can't avoid using Windows, whether for work or for software that won't run elsewhere. But there are things one can do to make using Windows more bearable. I've compiled here the steps I typically take to transform a Windows box into something a little more usable, with things we take for granted on other operating systems: powerful command-line tools, remote access, etc.
Contents
The most important software to install is cygwin, which provides both a set of UNIX tools and a set of UNIX compatibility libraries. IMO, Windows is completely unusable without cygwin's shells and utilities, in particular bash, perl, ssh, sshd, rsync, grep, and awk.
Installing cygwin
Install cygwin by running setup.exe from http://www.cygwin.com/. The default installation path is c:\cygwin, which I will assume has been chosen from here on. Choose the UNIX file format as the default. The package selection interface is difficult to use. If you have the disk space, I would recommend just installing everything by clicking the circular arrow next to All until it says Install (it may take a few seconds to change). Cygwin is getting larger and larger (recent installs of everything occupy nearly 2.5GB of disk space), however. If you don't want everything, go through the package list and select what you want. There are typically a number of packages not included by default that I want to have, like rsync. You can always re-run the installer later and add any packages you missed (it remembers what it already installed).
If you plan on installing cygwin on multiple machines and do not want every package, you should download locally the packages you want. Then you can point the installation GUI at the local source and tell it to install everything, which will be limited to what you downloaded and not the entire set of packages.
Mounts
Cygwin's current mounts can be displayed with the mount command:
% mount
C:\cygwin\bin on /usr/bin type system (binmode)
C:\cygwin\lib on /usr/lib type system (binmode)
C:\cygwin on / type system (binmode)
Windows drives are accessible as /cygdrive/c/, /cygdrive/d/, etc. I typically mount each drive as /c, /d, etc. for shorter paths in accessing them:
mkdir /c; mount c: /c
Mounts used to be persistent by default, so you only had to issue the mount command once. On modern Cygwin versions, however, the /etc/fstab file should be edited to make persistent mounts by adding a line like this:
c:/ /c ntfs binary,posix=0,user 0 0
The posix=0 option turns off case sensitivity.
Many cygwin and some Windows applications can also handle mixed paths (with a drive letter but with forward slashes) such as c:/cygwin/home. The cygpath utility can be used to convert paths between Windows, 8.3, UNIX, and mixed formats. Here are some examples:
% cygpath -u c:\\cygwin\\bin\\ls.exe
/usr/bin/ls.exe
% cygpath -w /cygdrive/c/cygwin/usr/bin/ls.exe
c:\cygwin\usr\bin\ls.exe
% cygpath -m c:/cygwin/usr/bin/ls.exe
c:/cygwin/usr/bin/ls.exe
% cygpath -d /c/Program\ Files/emacs-21.3/
c:\PROGRA~1\emacs-21.3\
% cygpath -u cygpath -d /c/Program\ Files/emacs-21.3/
/c/PROGRA~1/emacs-21.3/
PATH
I recommend adding c:\cygwin\bin to your Windows PATH for use in non-cygwin programs like Emacs or the Windows cmd shell. To edit your Windows PATH, open up:
In general, edit your own path, not the system one. The editing dialog is horribly done, as it cannot be resized. You could also edit the registry directly. Note that changes to environment variables are broadcast to the system, but only some applications (such as explorer.exe) listen for such events. You will have to restart cmd or cygwin shells to pick up any new values (as they are children of explorer.exe they will inherit the new values).
For your cygwin path, set it within your .bashrc as usual. You may want something like:
export CYGSYSROOT=cygpath -u $SYSTEMROOT export PATH="/usr/local/bin:/c/program files/emacs-21.3/bin:/usr/bin:/bin:/usr/X11R6/bin:${CYGSYSROOT}/system32:${CYGSYSROOT}/system32/wbem" Home directory Cygwin provides a default home directory under c:/cygwin/home/, which is mounted as /home/. I prefer to use the same home directory for both cygwin and non-cygwin applications, so I want a shorter non-cygwin path. Thus I typically create a top-level directory c:/derek. Edit /etc/passwd to update your cygwin home directory to point at your preferred home directory. Some non-cygwin applications such as Emacs will read your HOME environment variable. Create such a variable using the same method as editing your path above and point it at your home directory. I use a mixed path c:/derek for HOME. You could also try to change the Windows application-specific default directories by messing with other environment variables that default to the script-unfriendly Documents and Settings, though I have not yet tried this: APPDATA='C:\Documents and Settings\derek\Application Data' HOMEPATH='\Documents and Settings\derek' USERPROFILE='C:\Documents and Settings\derek' Recent Windows versions use the Users directory instead. Rxvt c:\cygwin\bin\rxvt.exe -sb -sl 2000 -fn "fixedsys" -bg lightgrey -e c:/cygwin/bin/ssh-agent.exe c:/cygwin/bin/bash.exe You can select other fonts such as -fn "CourierNew-16". Rxvt has Shift+PgUp, easy cut and paste (via Shift+Insert or the mouse middle button/scroll wheel), etc., all the features that you'll soon be banging your head against the wall wishing for if you run bash in the cmd window. You can also customize the title of your rxvt window. I set mine via my prompt settings in my .bashrc file to indicate the hostname (to tell me whether I'm ssh-ed to a remote machine in that window) and the current directory: if [ "$PS1" ]; then # interactive
# set primary prompt to put host in window title
PS1="\n$\033]0;\h: \w\007$\@ \w\n% "
fi
Note that Ctrl+Z to suspend and then bg to move a foreground job into the background does not work in any cygwin window I've used. So plan your background jobs ahead of time.
If you do find yourself in cmd, you should learn the keyboard shortcuts for cutting and pasting.
X
I personally do not use cygwin's X server and use more of a mixture of UNIX and Windows. I find it impossible to avoid interacting with native Windows applications, so I can't completely isolate myself in the UNIX environment. The X server has caused problems for me, like preventing hibernation on my laptop. And Windows underlies it all anyway, so it may be unrealistic to try and achieve a true native UNIX feel. The UNIX and Windows environments co-exist in an uneasy truce. (Note that some of my bias here is coming from warts with older versions of cygwin where the X server involved a separate root window and X clients were separated from native Windows clients. More recent versions are getting better at integrating transparently.)
Miscellaneous Tools
You'll want to run updatedb so you can use locate to find files. You can use cygwin's cron to set up regular updates. You can also manage Windows scheduled tasks from the command line with the schtasks program (on XP and later).
For converting text file formats, use the dos2unix and unix2dos utilities.
Note that Task Manager will refuse or fail to kill certain processes. You can write a program that acquires maximum privileges to more reliably kill processes, and from the command line. You can also use the debugger:
ntsd -p PID -c q
Cygwin's symbolic links are only understandable by Cygwin. When the target is a directory, you can instead create NTFS junctions, which are understood both by Cygwin and by native Windows applications.
Creating junctions needs the SeCreateSymbolicLinkPrivilege privilege, which by default is not granted to non-administrators. To give yourself this privilege, run secpol.msc and then navigate to Security Settings | Local Policies | User Rights Assignment | Create symbolic links.
To create a junction from a Cygwin shell, route the command through cmd:
cmd /c mklink /J localname 'c:\path\to\target'
Cygwin comes with a version of Emacs, and it is useful when logged in over ssh. But for interactive use I prefer a native Windows Emacs to one that requires the X server be running. You can obtain Windows Emacs and documentation from GNU. After unpacking the tarball you'll need to run the addpm program to add a Start Menu entry for it.
Windows Emacs can handle mixed paths as well as Windows paths, but it does not know about cygwin mounts.
Conveniently, you can drag-and-drop files into Emacs. Just like on UNIX you can change the font with Shift-LeftClick.
Emacs will honor your HOME environment variable. Put your .emacs file there. Also set a SHELL environment variable with a value of c:/cygwin/bin/bash.exe. This will allow you to use Emacs features that require a shell, such as compiling, running grep, or of course M-x shell.
I put Windows Emacs ahead of cygwin's Emacs on my PATH, except when over ssh:
if [[ -n $TERM ]] && [[ -n$SSH_CLIENT ]]; then
# prefer cygwin emacs
export PATH_EMACS="/usr/bin:/bin:/c/program files/emacs-22.2/bin"
else
# presumably logged in via Windows, so prefer Windows Emacs
export PATH_EMACS="/c/program files/emacs-22.2/bin:/usr/bin:/bin"
fi
export PATH="/usr/local/bin:${PATH_EMACS}:/usr/X11R6/bin:${CYGSYSROOT}/system32:\${CYGSYSROOT}/system32/wbem"
UNIX Emacs typically uses X resources to set its geometry and position. On Windows I set them directly in my .emacs file:
; subsequent frames are to the right
(setq default-frame-alist
'((top . 0) (left . 687)
(width . 91) (height . 50)
(font . "-*-couriernew-bold-r-normal-*-12-*-*-*-*-*-*-*")
(cursor-color . "black")
(cursor-type . box)
(foreground-color . "black")
(background-color . "white")))
; initial frame is top-left
(setq initial-frame-alist '((top . 0) (left . 0)))
Keyboard Shortcuts
Useful keyboard shortcuts:
• Alt+Tab: switch focus and raise window
• Win+e: launch Windows Explorer
The Win key is the one with the Windows logo on it, on the left of most standard keyboards between Ctrl and Alt. Some smaller laptops do not have such a key.
• Win+d: minimize all windows
• Win+l: switch user
• Alt+F4: close window
• Alt+Space: open the window menu
You can minimize a window with Alt+Space n.
Also of note is how to cut and paste in the cmd window: invoke Edit|Mark (Alt+Space e m) to enter selection mode (a strange rectangular selection mode) and Edit|Paste (Alt+Space e p) to paste from the clipboard. Alternatively, on Windows XP and later, if you enable QuickEdit in the Properties for cmd you can use the right mouse button to copy selected text or paste from the clipboard. As pointed out by Hugo De Vries, this is also available on Windows NT and 2000 via a registry tweak.
For convenient launching of custom applications, you can create a directory of shortcuts (Windows' version of symbolic links: create one by right-dragging a target file to the location where you want the shortcut and then select Create Shortcuts Here on the menu that pops up) and add it to the task bar. But there's no way to access it without using the mouse. The better solution is to stick the directory of shortcuts on the start menu. I put mine at the top level by placing a shortcut to my directory of shortcuts at:
I call it Quickstart. Then I can access it by pressing Win q.
I set up a different shortcut for each of 3 rxvt windows, with names like 1 rxvt, 2 rxvt, and 3 rxvt, for quickly placing them on my laptop with a few keystrokes (Win q 1, e.g.):
C:\cygwin\bin\rxvt.exe --geometry 80x40-8-55 -sb -sl 2000 -fn "fixedsys" -bg white -e c:/cygwin/bin/ssh-agent.exe c:/cygwin/bin/bash.exe
C:\cygwin\bin\rxvt.exe --geometry 80x40+0-55 -sb -sl 2000 -fn "fixedsys" -bg white -e c:/cygwin/bin/ssh-agent.exe c:/cygwin/bin/bash.exe
C:\cygwin\bin\rxvt.exe --geometry 80x40+350-200 -sb -sl 2000 -fn "fixedsys" -bg white -e c:/cygwin/bin/ssh-agent.exe c:/cygwin/bin/bash.exe
"Double-Clicking" from the Command Line
I wrote a simple program called dclick that lets me launch applications from the command line using the file extension database as though I had double-clicked on the file in Windows Explorer. You can download the source code and executable from the file list. It acts like the start command in cmd. You can launch Explorer for the current directory with
dclick .
SSH Agent
For password-less access to remote machines, you'll want to generate an RSA key pair on your local machine and then use the ssh agent. Be sure to keep your private key secure.
ssh-keygen -t rsa
Enter a passphrase to protect your key. Then copy your public key to the remote machine's authorized_keys file:
scp ~/.ssh/id_rsa.pub remote-machine:.ssh/tmp
ssh remote-machine "cat .ssh/tmp >> .ssh/authorized_keys; rm .ssh/tmp"
Now you need to invoke the ssh agent. I run each of my bash instances under ssh-agent as shown earlier. Unlike on UNIX, on cygwin there is no single ancestor process (like the window manager) that we can easily run under ssh-agent. However, it turns out that a single ssh-agent process can be shared among all shells running on the machine. As long as that ssh-agent is alive the other shells can use its stored key. See the function "ssh-setup" in the sample .bashrc. The procedure is to invoke ssh-add (and type in your passphrase) in the first shell started after logging in. So long as you keep that shell alive, all later-started shells will be able to use its key without re-invoking ssh-add.
SSH Server
An ssh server can be installed on cygwin, giving remote command-line access, which is invaluable for scripting and low-bandwidth access. Here are instructions:
1. Install cygwin packages openssh and cygrunsrv
2. Set global env var CYGWIN=ntsec tty
3. Make sure c:\cygwin\bin is on global Path env var
4. Run ssh-host-config, say "yes" to privilege separation and installing sshd as a service, and have ntsec and tty in CYGWIN
5. net start sshd
6. sshd uses user info from its own /etc/passwd. To add users created since cygwin was installed (back up the passwd file first of course):
mkpasswd -l > /etc/passwd
Unfortunately you cannot copy the passwd file from another machine as the entries refer to guids on the local machine.
7. If your home directory is not /home/user, change /home/user in /etc/passwd to the proper value (e.g., /c/user).
8. For public key authentication: make sure .ssh/authorized_keys is o+r and that StrictModes is no in /etc/sshd_config. See also the command ssh-user-config.
When logging in over ssh, to source your .bashrc on login, you need a .bash_profile that sources it, as this is a login shell. Unfortunately a non-interactive remote login (giving a command to ssh to run) is not detected as being started by sshd (it is so detected on Linux) and so does not source .bashrc. I tried setting BASH_ENV (indicates what non-interactive bashes should source) as a global env var and restarting sshd but it didn't work. My solution is to explicitly source .bashrc in any non-interactive scripts that need it.
Hosts
On Windows the hosts file is at %SYSTEMROOT%\system32\drivers\etc\hosts (on Windows NT and 2000, %SYSTEMROOT% is c:\WINNT, while on Windows XP+ it is c:\WINDOWS, assuming c: is your %SYSTEMDRIVE%). Cygwin links up /etc/hosts to the same file.
Other network tools
Other tools you should be aware of:
• ipconfig: analogue of ifconfig on Linux, lists network device configuration.
ipconfig /all lists MAC addresses, DNS servers, etc.
ipconfig /renew obtains a new DHCP lease.
• ping: like its Linux counterpart, uses ICMP to query a remote host
• tracert: like its Linux counterpart traceroute
• arp: like its Linux counterpart, manipulates the ARP cache
• nbtstat: shows NetBIOS information
• netstat: like its Linux counterpart, shows TCP/IP information
• netsh: a new command-line utility on Windows XP and later (finally!) for controlling network configuration. For example, you can set an explicit DNS server with:
netsh interface ip set dns name="Local Area Connection" source=static addr=24.92.226.9 register=PRIMARY
• net: command-line control over services (net start spooler, e.g.), shares (net use \\remote-machine\share, e.g.), and more.
• rsync: available with cygwin, rsync is invaluable in backing up data and synchronizing files and directories on remote machines.
I don't understand why Windows users put up with such a weak desktop and window manager. Fortunately there are options to add power to the interface.
Virtual desktop
There are several virtual desktop programs out there, such as Vern and Cool Desk. I use VirtuaWin, which at the time I evaluated alternatives seemed the most stable. I've been very happy with it. I set it up to not switch desktops when the mouse hits the screen edge unless Ctrl is pressed, and I use Win+arrow keys to switch between desktops. I also set a key combination to stick a window and use it to move windows from one desktop to another, un-sticking when at the destination.
Focus-follows-mouse
Believe it or not, Windows does support focus-follows-mouse, though there is no GUI configuration exposing it. Instead you must edit a registry key and then log out and back in for the change to become effective. You can use regedit to edit the key.
On Windows NT, set the following registry key to have a value of 1:
HKEY_CURRENT_USER\Control Panel\Mouse\Active Windows Tracking
On NT it has some bugs: some apps auto-raise on focus, and alt-tab doesn't move the mouse.
On Windows 2000 or higher, you need to change a binary-valued registry key:
This is a little-endian bitmask. For focus-follows-mouse, add the flag 0x1. For example, my XP SP2 laptop originally had a value of 9E 3E 05 80, which is 0x80053E9E. To activate focus-follows-mouse I changed to 0x80053E9F, or 9F 3E 05 80 in regedit.
According to http://www.winguides.com/registry/display.php/18/ you can also achieve raise-on-focus by adding the flag 0x40. I haven't tested that as I don't like raise-on-focus.
I typically install a few miscellaneous tools:
• Winzip, since Windows comes with no archive tools, is useful for installing things prior to setting up cygwin as well as auto-expanding archives when not near a command line.
• Postscript viewer: I use GSview for viewing postscript files on Windows. First, install AFPL Ghostscript for Windows via the latest version's self-extracting executable. Then install GSview via the latest self-extracting executable.
Sysinternals
Sysinternals produces a number of excellent utilities for Windows aimed toward the power user. I always install Process Explorer. Autoruns is very useful for cleaning out the various auto-start programs that infest Windows computers. There are other command-line utilities for process-control, etc.
Using the Microsoft cl Compiler from the Command Line
To use the Visual C++ compiler from the command line, you need to set some environment variables. My sample .bashrc shows how I've adapted the batch file that Microsoft provides (typically at
C:\Program Files\Microsoft Visual Studio\VC98\Bin\VCVARS32.BAT
) for use with bash.
Debuggers
The best debugger on Windows is windbg. Its underlying engine is also present in two command-line-only debuggers: ntsd, which ships with Windows (though it's an older version) and cdb. The latter is identical to the former except it does not open a new window, which makes it useful for scripting. The kernel debugger kd also shares the same innards.
Install windbg by installing the Debugging Tools for Windows.
windbg is quite powerful. Most importantly, it exposes all of its power in its command-line interface yet still supports graphical interaction for times when that's the better way to view information.
Native OpenGL
Recent versions of cygwin use OpenGL libraries from freeglut targeting cygwin's own X server rather than the native Windows OpenGL libraries. This means that you cannot run your GL programs without first starting the X server, and you cannot have some else run them without installing cygwin.
There are two sets of header files and of libraries:
• stdcall ones that use native GL are in /usr/include/w32api and /usr/lib/w32api
• C calling convention ones that use X are in /usr/X11R6/include and /usr/X11R6/lib
To use the native libraries rather than X libraries, you need to do two things when compiling your application:
1. Specify the proper include path:
-I/usr/include/w32api
make sure /usr/X11R6/include is NOT also on the include path earlier than w32api. If it is you will get link errors stemming from the calling convention mismatch.
2. Link with the cygwin libraries that import from the native Windows libraries:
-lopengl32 -lglu32 -lglut32 -L/usr/lib/w32api
To ensure you're using the right libraries you can launch your executable under the debugger that ships with Windows, ntsd. Look at the module list that is printed out by default on startup. correctly using windows libraries. The correct list should include C:\WINDOWS\system32\OPENGL32.dll:
ModLoad: 00400000 00566000 image00400000
By contrast, if you're using the X libraries instead, you'll see X11R6 dlls:
ModLoad: 00400000 004bc000 image00400000
Dual-Boot Machines
If your machine also boots Linux, you may want to try Explore2fs, a tool for reading ext2 and ext3 partitions from Windows. And since Linux can read ntfs, you can transfer files in both directions. However, for both reading and writing from either operating system, a FAT32 partition is still the best way to go.
Remote Desktop Access
There are Remote Desktop Protocol (RDP) clients for Linux that allow you to connect to Terminal Services servers or Windows XP machines that allow Remote Desktop access. I use rdesktop on my Fedora box. To enable Remote Desktop on Windows XP, check the Allow box in
Control Panel|System|Remote
With old versions of X and rdesktop (prior to Fedora Core 2), I had to tweak the default X key mappings to get the Windows key to be forwarded to the remote host. I used this .xmodmaprc file:
keycode 115 = Hyper_L
keycode 116 = Hyper_R
clear MOD3
There was no support for forwarding the context menu key (keycode 117). But, recent versions need no tweaking and automagically forward the Windows key and the context menu key. Note that the right Alt key is not forwarded by default.
There are also VNC clients and servers for both Linux and Windows. When using vncviewer on Linux, unset Alt+F4 as otherwise pressing it when inside vncviewer will not be forwarded and will close the client instead of a target remote Windows application.
Windows X Server
There are several X servers available for Windows, enabling display of applications running on remote UNIX machines on your local Windows screen. With recent cygwin versions you can use cygwin's own X server for this purpose. In the past I've used Exceed, a commercial X server. New versions of Exceed may be different, but I had to copy my Linux .Xresources file into
c:/Documents and Settings/All Users/Application Data/Hummingbird/Connectivity/7.00/Exceed/xrdb.txt
and then tell Exceed to reload XRDB for Screen 0. I also liked to change the keyboard configuration to make both Alt keys go to X.
You can install Exceed's fonts as Windows fonts via the Control Panel's Fonts window. Search Exceed's database to find the file for the X font name you're interested in.
Besides unplugging your computer from the network, the best thing you can do is to keep your computer fully patched. Use Windows Update to install all service packs and security updates.
There are many features of Windows that are potential attack vectors yet don't really need to be enabled. Turn off all Windows services that you don't need, such as WWW Publishing Service, SMTP, and Messenger . You can use the MMC graphical interface (with my .bashrc simply type dclick services.msc from the cygwin command line, or type services.msc in the Start Menu | Run box, or select Administrative Tools | Services), or the new sc command-line utility on Windows XP and later. From the graphical interface, use the context menu (right-click) to bring up the Properties page and both turn the service off if currently running and change its startup type to Manual. With sc, issue this command:
sc config "servicename" start= demand
You should consider other measures like disabling the guest account and disabling hidden shares. Here is a good list of these and other key steps for better securing your computer
Contact | 2014-10-21 11:55:00 | {"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": 2, "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": 0.35848599672317505, "perplexity": 7648.890262256856}, "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-2014-42/segments/1413507444385.33/warc/CC-MAIN-20141017005724-00152-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://answers.opencv.org/questions/123597/revisions/ | # Revision history [back]
Hello,
i know this was asked already several times but i am still confused about how the acceptanceRatio based on the maxFalseAlarmRate training parameter breaks my model training with showing the message "Required leaf false alarm rate achieved. Branch training terminated"
I also read the book "OpenCV 3 Blueprints" wroten by Joseph Howse,Steven Puttemans,Quan which tells :
The training breaks if the acceptanceRatio < then maxFalseAlarmRate^NumStages
But i can't apply this statement to my training, for example:
I used to detect some arizona bottles using the traincascade with the following parameters:
opencv_traincascade.exe -data data -vec bottle.vec -bg bg.txt -numPos 1000 -numNeg 2100 -numStages 8 -minHitRate 0.995 -maxFalseAlarmRate 0.3 -w 40 -h 100 -featureType HAAR
I got in total:
Pos Pictures: 1071
Neg Pictures: 2165
I trained my cascade about one day ending up with 7 stages because of the break statement:
===== TRAINING 6-stage =====
<BEGIN
POS count : consumed 1000 : 1009
NEG count : acceptanceRatio 2100 : 0.000171474
Precalculation time: 30.145
+----+---------+---------+
| N | HR | FA |
+----+---------+---------+
| 1| 1| 1|
+----+---------+---------+
| 2| 1| 1|
+----+---------+---------+
| 3| 0.996| 0.447143|
+----+---------+---------+
| 4| 0.999| 0.35381|
+----+---------+---------+
| 5| 0.997| 0.267619|
+----+---------+---------+
END>
Training until now has taken 0 days 23 hours 9 minutes 46 seconds.
===== TRAINING 7-stage =====
<BEGIN
POS count : consumed 1000 : 1012
NEG count : acceptanceRatio 0 : 0
Required leaf false alarm rate achieved. Branch training terminated.
But i still dont understand why it broke the training.
If i take from the parameters maxFalseAlarmRate^NumStages = 0.3^8 this is still bigger than the last given acceptanceRatio : 0.000171474
Did i maybe thought wrong and its maxFalseAlarmRate^CurrentStageDepth= 0.3^7 ?
Although my cascade is very decent in detecting arizona bottles (sometimes 1-2 false positives) and i know it will only detect them at least on the dimensions -w 40 -h 100 but if there are any suggestions to improve my detection parameterwise please feel free to tell me (increasing overall dataset is planned in future) | 2019-06-19 16:41:43 | {"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": 0.2861967086791992, "perplexity": 11771.114282237471}, "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/1560627999003.64/warc/CC-MAIN-20190619163847-20190619185847-00048.warc.gz"} |
https://math.stackexchange.com/questions/723025/solving-pde-only-using-method-of-characteristics/723443 | # Solving PDE only using method of characteristics
Solve $aU_x+bU_y+cU$=0 using characteristic method. I know how to solve this by change of coordinates as in this article.
But without changing coordinates how to do it with the method of characteristics? I know how to solve if it was $aU_x+bU_y=0$by using directional derivative.
Also in page 10 of that article they have used Jacobian.Please explain why Jacobian is used there. | 2020-04-08 18:58:55 | {"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": 0.5007965564727783, "perplexity": 204.55450506035663}, "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/1585371821680.80/warc/CC-MAIN-20200408170717-20200408201217-00174.warc.gz"} |
http://mathhelpforum.com/geometry/96054-dividing-line-given-ratio-print.html | # Dividing a line in a given ratio
• July 25th 2009, 02:36 PM
Jenna.fernandes
Dividing a line in a given ratio
Given A(1,3) , B(5,1) and P|AB in ratio 3:1 , determine point P
A.(4,3/2) B.(9/2,3/2) C.(9/2,1) D.(9/2,2) E.(4,1)
• July 25th 2009, 02:58 PM
AlephZero
Couple of things:
1. Many of us sort of frown upon the insistent, borderline rude titles of which your post serves as an example. We often ignore such posts, and so, it's in your own interest to give them a simple, courteous title descriptive of the problem at hand. You'll probably get better results that way.
2. We also frown upon threads started in categories with which they have nothing to do, such as yours. It is, so far as I can tell, a basic geometry question, having nothing directly to do with Calculus. So for the same reasons as given above, you might want to pay attention to where you post things in the future.
3. Lastly, you need to be more clear in describing your question. I assume, but only after some considerable effort, that the "A" and "B" in your question are points in the plane, making AB a line. I'm not sure what P | AB is supposed to indicate, nor what the 3:1 ratio has to do with it. Is P a segment of AB having one third AB's length? 3 times it's length?
In summary, you need to give a little to get a little. Many of us would love to help you out if only you would take a moment or two to make things a bit easier on us.
• July 25th 2009, 03:01 PM
Jester
Quote:
Originally Posted by Jenna.fernandes
Given A(1,3) , B(5,1) and P|AB in ratio 3:1 , determine point P
A.(4,3/2) B.(9/2,3/2) C.(9/2,1) D.(9/2,2) E.(4,1)
Hint - the point $P$ must be on the line connecting $A$ and $B$.
• July 25th 2009, 04:46 PM
mr fantastic
Quote:
Originally Posted by AlephZero
Couple of things:
1. Many of us sort of frown upon the insistent, borderline rude titles of which your post serves as an example. We often ignore such posts, and so, it's in your own interest to give them a simple, courteous title descriptive of the problem at hand. You'll probably get better results that way.
2. We also frown upon threads started in categories with which they have nothing to do, such as yours. It is, so far as I can tell, a basic geometry question, having nothing directly to do with Calculus. So for the same reasons as given above, you might want to pay attention to where you post things in the future.
3. Lastly, you need to be more clear in describing your question. I assume, but only after some considerable effort, that the "A" and "B" in your question are points in the plane, making AB a line. I'm not sure what P | AB is supposed to indicate, nor what the 3:1 ratio has to do with it. Is P a segment of AB having one third AB's length? 3 times it's length?
In summary, you need to give a little to get a little. Many of us would love to help you out if only you would take a moment or two to make things a bit easier on us.
These comments are no longer relevant because the post in question has been Moderated. However, I have not deleted these comments because they are a timely reminder to all members of things to consider when posting a question.
A relevant thread regarding how to post a question: http://www.mathhelpforum.com/math-he...-get-help.html | 2014-08-21 16:44:59 | {"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": 0.5877950191497803, "perplexity": 666.6779899644023}, "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-2014-35/segments/1408500820617.70/warc/CC-MAIN-20140820021340-00289-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://cstheory.stackexchange.com/questions/17504/how-fast-can-we-group-clauses-with-few-variables-in-common-in-k-sat | # How fast can we group clauses with few variables in common in k-SAT?
Given a k-SAT problem with $C$ clauses and $V$ variables, we can group the clauses together into groups of $g$ clauses with few exceptions, where the exceptions contain $g-1$ or fewer clauses. If we add the constraint that each group should contain at most $n$ variables in common, and no clause is in more than one group, how quickly can we find a "grouping" that satisfies these conditions?
I'm wondering if this problem has been considered before, and in what circumstances this problem needs to be resolved. My motivation for considering this question stems from another attempt at making use of the clause counting that I describe in this question. | 2020-01-18 10:20:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36470794677734375, "perplexity": 215.87979953800235}, "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/1579250592394.9/warc/CC-MAIN-20200118081234-20200118105234-00283.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/pc3/chapter/3/lesson/3.2.2/problem/3-108 | ### Home > PC3 > Chapter 3 > Lesson 3.2.2 > Problem3-108
3-108.
Suppose $f\left(g\left(x\right)\right)=\frac{1}{x+7}$. Write a possible set of equations for functions $f$ and $g$. (Note: $f(x)\ne g(x)\ne x$) | 2021-01-28 05:15:16 | {"extraction_info": {"found_math": true, "script_math_tex": 4, "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": 0.7218983173370361, "perplexity": 2501.0329472950652}, "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/1610704835901.90/warc/CC-MAIN-20210128040619-20210128070619-00396.warc.gz"} |
https://mathematics21.org/2016/04/23/conjecture-2/ | # An important conjecture about funcoids. Version 2
This conjecture appeared to be false.
Now I propose an alternative conjecture:
Let $A$, $B$ be sets.
Conjecture Funcoids $f$ from $A$ to $B$ bijectively corresponds to the sets $R$ of pairs
$(\mathcal{X}; \mathcal{Y})$ of filters (on $A$ and $B$ correspondingly) that
1. $R$ is nonempty.
2. $R$ is a lower set.
3. every $\left\{ \mathcal{X} \mid (\mathcal{X} ; \mathcal{Y}) \in R \right\}$ is a dcpo for every $\mathcal{Y} \in \mathfrak{F}B$ and every $\left\{ \mathcal{Y} \mid (\mathcal{X} ; \mathcal{Y}) \in R \right\}$ is a dcpo for every $\mathcal{X} \in \mathfrak{F}A$
by the mutually inverse formulas:
$(\mathcal{X} ; \mathcal{Y}) \in R \Leftrightarrow \mathcal{X} \times^{\mathsf{FCD}} \mathcal{Y} \sqsubseteq f \quad \mathrm{and} \quad f = \bigsqcup^{\mathsf{FCD}} \left\{ \mathcal{X} \times^{\mathsf{FCD}} \mathcal{Y} \mid (\mathcal{X} ; \mathcal{Y}) \in R \right\}$. | 2020-07-07 00:16:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 32, "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": 0.883295476436615, "perplexity": 974.9996836724566}, "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/1593655890566.2/warc/CC-MAIN-20200706222442-20200707012442-00405.warc.gz"} |
http://openstudy.com/updates/51858ebce4b09587cd39ca2e | Here's the question you clicked on:
Ambition Find an equation for the nth term of the sequence. -2, -8, -32, -128, ... 10 months ago 10 months ago
• This Question is Closed
1. kausarsalley
$a_n=a_1 \times r ^{n-1}$
2. kausarsalley
a(n)=nth term a(1)=first term of the sequence r=common ratio | 2014-03-10 23:30:51 | {"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": 0.8403060436248779, "perplexity": 2912.3067720822046}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394011044030/warc/CC-MAIN-20140305091724-00006-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://engineering.stackexchange.com/tags/materials/hot | # Tag Info
24
TL;DR: Its not the air that's enclosed inside that creates the force, but the lack of air - or more precisely pressure. First of all some nomenclature (this is for the closed type, there is also the open type): When you press a suction cup on a surface what happens is that the air inside it is pushed out. During the compression phase of the cup the air ...
7
As your construction is 3D printed, increasing the strength at the point of current breaking will more likely transfer the damage to a new location. The obvious and possibly impractical solution is to solve the jamming problem, rather than to try to power through it. If it's not practical to prevent the jamming, consider to convert the jamming related ...
5
You might consider dealing with it in software. Sense the stepper motor current, and when it exceeds a certain threshold that indicates jamming, perform a high speed reverse rotation for one or more revolutions. Then proceed in the forward direction.
5
Build the auger around a stronger shaft which has a better connection to the motor shaft. Perhaps a carbon fibre or even a steel centre. But then consider what will be the next breaking point. Or make a joint between the auger and the motor that fails if the mechanism gets jammed - just make it easy to replace.
4
For me a good (compromise of a) solution would be to redesign the shaft with an rectangular slot (although I am still unclear as to the fracture type, so I suspect is torsional). Like so Then you can use a rectangularly shaped metallic shaft along the length, which will be able to transmit more gradually the torque. *Figure 2: rectangular shaft image ...
3
CTE characterizes dimensional change, with no load. It corresponds to a relatively fundamental physical principle, making it easy to use in a design calculation Heat Deflection test characterizes the deformation under heat AND load, which includes a variety of phenomena happening at the same time. The result is dependent on the particular geometry and ...
3
When you push that onto a flat surface it pushes most of the air out. The elasticity of the item makes want to flex and come off but the air pressure is pushing it onto the surface.
3
In machine tools where an auger is used to remove scrap metal chips, the current in the auger motor is sensed. If it exceeds a certain level due to jamming, the electronics temporarily reverses the auger direction which can clear the jam. Lubrication of the material-auger interface is very important with augers, which have a huge swept surface area.
2
TLDR: look at Viton / FKM PTFE has poor mechanical stability, would be careful whether to use it in most sealing apps (unless it has mechanical backup). Look at other fluoroelastomers, in particular Viton (FKM) or Kalrez/Chemrez (FFKM). The other common elastomer substitutes for NBR are EPDM and silicone (PDMS). Those are the most common ones you can usually ...
2
If you know the torque, or a close approximation of it, you can size the auger shaft more appropriately. From Machinery's Handbook the max torque T a shaft can handle is T= S_S* Z_P S_S = allowable torsional shear stress of material Z_P = polar section modulus (0.196 * diameter^3) Make sure your units are consistent. So you can either use a stronger ...
2
It won't help prevent swinging, and in all likelihood would keep the door swinging longer after an impulse force is applied. As the comments suggest, most inside doors have a guide on the floor (usually in the retracted region, not the doorframe itself). If you have a barn-door-type sliding door, there may well be a guide/stabilizer near the top of the door.
2
For a rectangular beam under a load, P, at the end the deflection is $$\delta= \frac{PL^3}{3EI}$$ therefore if you have the E as half you need to double the I of the part. In rectangular beams and roughly rectangular tabs: $$I= \frac{BH^3}{12}$$ So you ned a tab thicker by the ratio of $T_{new}= T_{old}*\sqrt[3]{2}$ edit if we are concerned with a yield ...
1
The coefficient of thermal expansion is the change in size of the material as the temperature changes, which is obvious when looking at the units: a length change per metre per degree. Heat deflection is not about a change in length.
1
If I understand correctly you need the part to be able to rotate around point B, so that the AB section remains vertical, while the BCD rotates. In that case, the following is not really an answer, just a heads up, that there are other properties that will have a detrimental effect on the properties: The horizontal distance between the fulcrum and the ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2021-05-18 00:56:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.5488319396972656, "perplexity": 1102.7813097991618}, "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/1620243991650.73/warc/CC-MAIN-20210518002309-20210518032309-00560.warc.gz"} |
http://math.stackexchange.com/tags/trace/hot | # Tag Info
9
The trace of an endomorphism $f : X \to X$ of a dualizable object $X$ in a monoidal category is the composition $1 \xrightarrow{\eta} X \otimes X^* \xrightarrow{f \otimes \mathrm{id}} X \otimes X^* \cong X^* \otimes X \xrightarrow{\epsilon} 1$. This coincides with the usual definition in the category of vector spaces. There is a more general categorical ...
8
Both sides are continuous. A standard proof goes by showing this for diagonalizable matrices, and then using their density in $M_n(\mathbb{C})$. But actually, it suffices to triangularize $$A=P^{-1}TP$$ with $P$ invertible and $T$ upper-triangular. This is possible as soon as the characteristic polynomial splits, which is obviously the case in ...
7
Let $A$ be the positive definite square root of $X$ and $B$ the positive definite square root of $Y$. You have $$\mbox{tr}(XY)=\mbox{tr}(AABB)=\mbox{tr}(BAAB)=\mbox{tr}((AB)^*AB)>0.$$ Indeed, the latter is the sum of all $c_{i,j}^2$ where $c_{i,j}=(AB)_{i,j}$. So it is nonnegative. And if it were zero, this would imply $AB=0$ hence $A=B=0$ since ...
6
Hint: Prove that $AB$ and $BA$ have the same characteristic polynomial. This can be done using only the determinant. And the determinant can be defined without reference to any basis, as you can see here: Formula of the determinant Now write, for every $n\times m$ matrix $A$ and every $m\times n$ matrix $B$: $$... 6 What is true is that the expansion of the characteristic polynomials is given by traces of powers of the matrix A; explicitly, the characteristic polynomial \chi_A(T)=\det(T\cdot{\rm Id}-A) is given by$$T^n-{\rm tr}(A)T^{n-1}+\frac{{\rm tr}(A)^2-{\rm tr}(A^2)}{2}T^{n-2}-\frac{{\rm tr}(A)^3-3{\rm tr}(A){\rm tr}(A^2)+2{\rm tr}(A^3)}{6}T^{n-3}+\cdots $$... 6 Let S_1, S_2 be two positive definite matrices. Let \Delta = S_2 - S_1 and for t \in [0,1], let$$\phi = (S_1 + t\Delta)^{-1} = ((1 - t) S_1 + t S_2)^{-1}$$We have:$$\begin{align} & \frac{d}{dt} \phi \;= - \phi \Delta \phi\\ \implies & \frac{d}{dt} \phi^2 \;= - \phi \Delta \phi^2 - \phi^2 \Delta \phi\\ \implies & ...
5
This is false. By the (finite-dimensional) spectral theorem, every symmetric matrix is diagonalizable, so we can write $S=QDQ^{-1}$. Thus we have $$\det(I+S)=\det(Q^{-1}(I+S)Q)=\det(I+D)=\prod\limits_{i=1}^n (1+d_i)\\\ne 1+\sum\limits_{i=1}^n d_i=1+\mathrm{trace}(D)=1+\mathrm{trace}(S).$$ Perhaps the formula $\prod\limits_{i=1}^n (1+d_i)$ may be of use, ...
5
$\newcommand{\tr}{\operatorname{tr}}$Here is an exterior algebra approach. Let $V$ be an $n$-dimensional vector space and let $\tau$ be a linear operator on $V$. The alternating multilinear map $$(v_1,\dots,v_n) \mapsto \sum_{k=1}^n v_1 \wedge\cdots\wedge \tau v_k \wedge\cdots\wedge v_n$$ induces a unique linear operator $\psi: \bigwedge^n V \to ... 5 Hint: Use that every complex matrix has a jordan normal form and that the determinant of a triangular matrix is the product of the diagonal. use that$\exp(A)=\exp(S^{-1} J S ) = S^{-1} \exp(J) S And that the trace doesn't change under transformations. \begin{align*} \det(\exp(A))&=\det(\exp(S J S^{-1}))\\ &=\det(S \exp(J) S^{-1})\\ ... 5 You don't need to choose any particular basis; all you need is the fact that\wedge V$is graded and$L_b$raises the degree by$1$, so if you choose any basis that respects the gradation, then$L_b$sends any basis vector to a different subspace, so the diagonal elements in such a basis all vanish. 4 Yes, it is. Consider$S(t) = A + t B$where$A$is symmetric positive definite and$Bis symmetric. It is enough to show that $$\left.\dfrac{d^2}{d t^2} \text{Tr}(S(t)^{-1})\right|_{t=0} \ge 0$$ Now $$S(t)^{-1} = (A (I + t A^{-1} B))^{-1} = A^{-1} - t A^{-1} B A^{-1} + t^2 A^{-1} B A^{-1} B A^{-1} + \ldots$$ so $$\left. \dfrac{d^2}{\partial t^2} ... 4 Hint: the trace is multiplicative, i.e. \mbox{Tr}(AB)=\mbox{Tr}(BA), as soon as the scalar field (or ring) is commutative. In particular, for every invertible matrix P and every matrix A in M_n(\mathbb{R}) or M_n(\mathbb{C}), we have$$ \mbox{Tr}\;(PAP^{-1})=\mbox{Tr}\; A. 4 You may do it by first computing matrix powers and then you may calculate whatever you want. Now question is how to calculate matrix power for a given matrix, say A? Your goal here is to develop a useful factorization A = PDP^{-1}, when A is n\times n matrix.The matrix D is a diagonal matrix (i.e. entries off the main diagonal are all zeros). Then ... 4 The proof in Martin Brandenburg's answer may look scary but it is secretly about moving beads around on a string. You can see all of the relevant pictures in this blog post and in this blog post. The proof using pictures is the following: In the first step g gets slid down on the right and in the second step g gets slid up on the left. You can also ... 3 If there's a basis |n \rangle in our vector space, you can expand the identity with 1 = \sum_n |n \rangle\langle n| $tr(AB) = \sum_n \langle n|AB |n \rangle =\sum_{m,n} \langle n|A|m \rangle \langle m|B |n \rangle$ and then you can run it backwards: \[ = \sum_{m,n} \langle m|B |n \rangle\langle n|A|m \rangle = \sum_{m} \langle m|B A|m \rangle ... 3 For clarification, following the question, let us emphasize some notations first. Let M_n be the collection of n\times n complex valued matrices, let H_n be the collection of n\times n complex valued Hermitian matrices, and given X,Y\in H_n, denote X\ge 0\Leftrightarrow X is positive semidefinite, and X\ge Y\Leftrightarrow X-Y\ge 0. Given ... 3 Yes, it holds true. Let A be a n\times m and B be a m \times n matrix over the commutative ring R, we have \begin{align*} \mathrm{tr}(AB) &= \sum_{i=1}^n (AB)_{ii}\\ &=\sum_{i=1}^n \sum_{j=1}^m A_{ij}B_{ji}\\ &= \sum_{j=1}^m \sum_{i=1}^n B_{ji}A_{ij}\\ &= \sum_{j=1}^m (BA)_{jj}\\ &= \mathrm{tr}(BA) \end{align*} ... 3 If you want to make the trace appear, you can use the following formula: y^Tz=\mbox{Tr} (yz^T). $$Then$$ \|y-X\beta\|^2+\lambda \beta^TS\beta=(y-X\beta)^T(y-X\beta)+\lambda \beta^TS\beta =\mbox{Tr}((y-X\beta)(y-X\beta)^T)+\lambda \mbox{Tr}(\beta \beta^TS^T) =\mbox{Tr}((y-X\beta)(y-X\beta)^T+\lambda \beta \beta^TS^T)) $$3 I have considered two different paths to this problem, one requires the diagonalization of A (so may be not so useful depending on A) and the other uses the Kronecker product properties. One other note at the end gives an equivalent skew form of the equation. The Kronecker seems to have the most usefulness for finding the desired trace. The rest is maybe ... 3 There's no failure, unless you count assuming that such a matrix X exists for any A. You've in fact given a proof that if \det{A}\leq0, there is no X (with real trace) such that e^X=A. If you allow \operatorname{Tr}(X) to be complex (so it is possible for e^{\operatorname{Tr}(X)} to be negative), then there does exist X with e^X=A for any ... 3 Let f(t)= \det(e^{tA}). Then f'(t)=D \det(e^{tA}) \cdot Ae^{tA}=\text{tr} \left(^t \text{com}(e^{tA})Ae^{tA} \right). But A and e^{tA} commute, and ^t\text{com}(e^{tA})e^{tA}=\det(e^{tA}) \operatorname{I}_n. Therefore, f'(t)=\text{tr}(A)f(t) and f(0)=1, hence f(t)=e^{\text{tr}(A)t}. For t=1, \det(e^{A})= e^{\text{tr}(A)}. 3 The claim results from the following statement: (*) If E/F is a degree n separable extension, then the trace$$ t(E/F):E\to F $$of E/F is nonzero. To prove (*), denote by$$ t(A/K):A\to K $$the trace of A over K, whenever K is a field and A a finite dimensional K-algebra. As$$ t((K\otimes E)/K)=K\otimes t(E/K): K\otimes E\to K ... 2 Unless some contextual details are missing, your book is wrong. For a counterexample, consider R=\begin{pmatrix}1&1\\1&2\end{pmatrix} and U=\begin{pmatrix}0&0\\0&1\end{pmatrix}. Clearly R is symmetric and tr(U^TU)=1. You may verify that \begin{align*} Q_1&=tr(URRU^T)-N^{-1}\left(tr(UR)\right)^2 ... 2 I would do it as follows: For (x,y) \in H \times H define an element of N(H) by x \,\tilde{\otimes}\, y = \langle \cdot , y \rangle x and note that \|x \, \tilde{\otimes}\,y\|_{1} = \|x\|\,\|y\|. For a functional \varphi \in N(H)' define a sesquilinear form on H by B_{\varphi}(x,y) = \varphi(x \,\tilde{\otimes}\, y). The map \varphi ... 2 Let F be the field of 2^N elements. If Tr(ax)=0 for all x\in F, then the polynomial p(x)=Tr(ax)=ax+a^2x^2+a^4x^4+\cdots+a^{2^{N-1}}x^{2^{N-1}}$has (at least)$2^N$distinct zeros in the field$F$, namely all its elements. If$a\neq0$, then this polynomial has degree$2^{N-1}$. Therefore$\ldots$2 Note that$\text{tr}(AB) = \sum_i \sum_j A_{ij} B_{ji}$so$\dfrac{\partial}{\partial A_{ij}} \text{tr}(AB) = B_{ji}$, i.e.$\text{grad}_A \text{tr}(AB) = B'$. Thus$ \text{grad}_A \text{tr}(ABDC) = (BDC)'=C'D'B'$, while$\text{grad}_A \text{tr}(DBA'C) = \text{grad}_A \text{tr}(CDBA') = \text{grad}_A \text{tr}(AB'D'C') = (B'D'C')' = CDB$. So (substituting ... 2 As commenters say,$L^* = \hom_K(L,K)$is a vector space over$K$of dimension$n$, the same dimension as$L$over$K$. You have a$K$linear map$T : L \to L^*$, such that$T(x)$is the linear form defined by$T(x)(y) = Tr(xy)$. Since there is a$y \in L$such that$Tr(y) \neq 0$,$T(1)$is not the zero map of$L^*$. Since$L$is a field, for any$\alpha ...
2
Your $\wedge^k A^m$ is just the polarization: $\wedge^k A^m = {N \choose m} \wedge^k(\underbrace{A,\dots,A}_m,1,\dots,1)$, the right-hand side refers to $\wedge^k$ as a $k$-linear form. As we know, $\wedge^N$ is the determinant, so $\wedge^N A^m$ are just the coefficients of the characteristic polynomial. Those are elementary symmetric functions of the ...
2
Minimizing $f(X)$ with respect to $X$ is equivalent to first minimizing $f(X)$ with respect to $X$ under the constraint $g(X)=c$ and then minimizing the result with respect to $c$. Thus the minimum with respect to $X$ must be the minimum with respect to $X$ under the constraint $g(X)=c$ for some value of $c$, and to find that you can introduce a Lagrange ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2013-05-21 10:00:15 | {"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": 2, "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": 0.9959558844566345, "perplexity": 674.913071900354}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368699881956/warc/CC-MAIN-20130516102441-00083-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://mobile.surenapps.com/2020/10/acids-bases-and-salts-revision-notes_30.html | ### Acids Bases and Salts - Revision Notes
CBSE Class 7 Science
Revision Notes
Chapter – 5
Acids, Bases and Salts
• There are three types of Substances: Acids, Bases and Salts
• Acids: Acids are sour in taste.
They are corrosive in nature. A concentrated acid cuts through clothes and eats away the wool. If it falls on the skin, it can cause burns.
They are good conductors of electricity, as they allow the passage of electric current through them.
• Types of Acids:
(i) Mineral Acids: These are acids prepared from minerals present in the earth’s crust.
(ii) Organic Acids: These are acids produced by plants and animals (except hydrochloric acid).
(iii) Weak Acids: These do not dissociate completely in solution. Example: tartaric acid, lactic acid.
(iv) Strong Acids: These dissociate completely in solution. Example: nitric acid, sulphuric acid.
• Neutralization: It is the reaction between an acid and a base which results in formation of salt and water.
Acid + Base $\to$ Salt + Water
Example: HCl + NaOH $\to$ NaCl + H2O
• Neutralisation in Everyday Life:
(i) Indigestion: Too much acid in stomach causes indigestion. It is neutralized by taking an antacid like milk of magnesia.
(ii) Ant sting: When an ant bites, it injects formic acid into the skin. The effect is neutralized by rubbing moist baking soda (sodium hydrogen carbonate) or calamine (containing zinc carbonate).
(iii) Soil treatment: When the soil is too acidic, it is neutralized by treating with quicklime (calcium oxide) or slaked lime (calcium hydroxide).
• Bases: Bases are bitter in taste and soapy to touch.
Types of Bases:
(i) Weak Bases: These naturally produce less hydroxide ions in solution. Example: magnesium hydroxide, ammonium hydroxide.
(ii) Strong Bases: These produce more number of hydroxide ions on dissolving in water. Example: Sodium hydroxide(NaOH), Potassium hydroxide (KOH)
• Substances which are neither acidic nor basic are called neutral.
• An acid and a base neutralise each other and form a salt. A salt may be acidic, basic or neutral in nature.
• Solutions of substances that show different colour in acidic, basic and neutral solutions are called indicators.
• Indicators: It is special chemical that changes its colour to indicate the presence of a chemical substance.
• It is used to confirm the presence of an acid, a base or a neutral solution.
• Classification of Indicators:
Natural Indicators:
(i) Litmus: It is extracted from lichens. It is available in the form of strips of paper or in the form of a solution.· Acid turns blue litmus red. Bases turn red litmus blue.
(ii) Turmeric: It remains yellow in neutral and acidic solutions but turns red in alkaline solutions.
(iii) China rose: It turns acidic solutions to dark pink (magenta) and basic solution to green.
(iv) Red cabbage: It turns acidic solutions to red and basic solutions to blue.
Other Indicators:
(i) Methyl Orange: It gives pinkish red colour with acidic solutions and yellow colour with bases.
(ii) Phenolphthalein: It is an acid-base indicator. It is colourless in acidic solutions but turns pink in alkali solutions. | 2021-10-23 20:07:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.6224409937858582, "perplexity": 7292.7132530160925}, "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/1634323585768.3/warc/CC-MAIN-20211023193319-20211023223319-00430.warc.gz"} |
https://www.ademcetinkaya.com/2022/12/ipviu-interprivate-iv-infratech_27.html | Outlook: InterPrivate IV InfraTech Partners Inc. Units assigned short-term Ba1 & long-term Ba1 estimated rating.
Dominant Strategy : Sell
Time series to forecast n: 27 Dec 2022 for (n+1 year)
Methodology : Modular Neural Network (Speculative Sentiment Analysis)
## Abstract
This paper examines the theory and practice of regression techniques for prediction of stock price trend by using a transformed data set in ordinal data format. The original pretransformed data source contains data of heterogeneous data types used for handling of currency values and financial ratios. The data formats in currency values and financial ratios provide a process for computation of stock prices. The transformed data set contains only a standardized ordinal data type which provides a process to measure rankings of stock price trends.(Vijh, M., Chandola, D., Tikkiwal, V.A. and Kumar, A., 2020. Stock closing price prediction using machine learning techniques. Procedia computer science, 167, pp.599-606.) We evaluate InterPrivate IV InfraTech Partners Inc. Units prediction models with Modular Neural Network (Speculative Sentiment Analysis) and Wilcoxon Rank-Sum Test1,2,3,4 and conclude that the IPVIU stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Sell
## Key Points
1. Technical Analysis with Algorithmic Trading
2. Should I buy stocks now or wait amid such uncertainty?
3. Fundemental Analysis with Algorithmic Trading
## IPVIU Target Price Prediction Modeling Methodology
We consider InterPrivate IV InfraTech Partners Inc. Units Decision Process with Modular Neural Network (Speculative Sentiment Analysis) where A is the set of discrete actions of IPVIU stock holders, F is the set of discrete states, P : S × F × S → R is the transition probability distribution, R : S × F → R is the reaction function, and γ ∈ [0, 1] is a move factor for expectation.1,2,3,4
F(Wilcoxon Rank-Sum Test)5,6,7= $\begin{array}{cccc}{p}_{a1}& {p}_{a2}& \dots & {p}_{1n}\\ & ⋮\\ {p}_{j1}& {p}_{j2}& \dots & {p}_{jn}\\ & ⋮\\ {p}_{k1}& {p}_{k2}& \dots & {p}_{kn}\\ & ⋮\\ {p}_{n1}& {p}_{n2}& \dots & {p}_{nn}\end{array}$ X R(Modular Neural Network (Speculative Sentiment Analysis)) X S(n):→ (n+1 year) $\begin{array}{l}\int {r}^{s}\mathrm{rs}\end{array}$
n:Time series to forecast
p:Price signals of IPVIU stock
j:Nash equilibria (Neural Network)
k:Dominated move
a:Best response for target price
For further technical information as per how our model work we invite you to visit the article below:
How do AC Investment Research machine learning (predictive) algorithms actually work?
## IPVIU Stock Forecast (Buy or Sell) for (n+1 year)
Sample Set: Neural Network
Stock/Index: IPVIU InterPrivate IV InfraTech Partners Inc. Units
Time series to forecast n: 27 Dec 2022 for (n+1 year)
According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Sell
X axis: *Likelihood% (The higher the percentage value, the more likely the event will occur.)
Y axis: *Potential Impact% (The higher the percentage value, the more likely the price will deviate.)
Z axis (Grey to Black): *Technical Analysis%
## IFRS Reconciliation Adjustments for InterPrivate IV InfraTech Partners Inc. Units
1. An example of a fair value hedge is a hedge of exposure to changes in the fair value of a fixed-rate debt instrument arising from changes in interest rates. Such a hedge could be entered into by the issuer or by the holder.
2. An entity applies IAS 21 to financial assets and financial liabilities that are monetary items in accordance with IAS 21 and denominated in a foreign currency. IAS 21 requires any foreign exchange gains and losses on monetary assets and monetary liabilities to be recognised in profit or loss. An exception is a monetary item that is designated as a hedging instrument in a cash flow hedge (see paragraph 6.5.11), a hedge of a net investment (see paragraph 6.5.13) or a fair value hedge of an equity instrument for which an entity has elected to present changes in fair value in other comprehensive income in accordance with paragraph 5.7.5 (see paragraph 6.5.8).
3. An entity has not retained control of a transferred asset if the transferee has the practical ability to sell the transferred asset. An entity has retained control of a transferred asset if the transferee does not have the practical ability to sell the transferred asset. A transferee has the practical ability to sell the transferred asset if it is traded in an active market because the transferee could repurchase the transferred asset in the market if it needs to return the asset to the entity. For example, a transferee may have the practical ability to sell a transferred asset if the transferred asset is subject to an option that allows the entity to repurchase it, but the transferee can readily obtain the transferred asset in the market if the option is exercised. A transferee does not have the practical ability to sell the transferred asset if the entity retains such an option and the transferee cannot readily obtain the transferred asset in the market if the entity exercises its option
4. Lifetime expected credit losses are not recognised on a financial instrument simply because it was considered to have low credit risk in the previous reporting period and is not considered to have low credit risk at the reporting date. In such a case, an entity shall determine whether there has been a significant increase in credit risk since initial recognition and thus whether lifetime expected credit losses are required to be recognised in accordance with paragraph 5.5.3.
*International Financial Reporting Standards (IFRS) adjustment process involves reviewing the company's financial statements and identifying any differences between the company's current accounting practices and the requirements of the IFRS. If there are any such differences, neural network makes adjustments to financial statements to bring them into compliance with the IFRS.
## Conclusions
InterPrivate IV InfraTech Partners Inc. Units assigned short-term Ba1 & long-term Ba1 estimated rating. We evaluate the prediction models Modular Neural Network (Speculative Sentiment Analysis) with Wilcoxon Rank-Sum Test1,2,3,4 and conclude that the IPVIU stock is predictable in the short/long term. According to price forecasts for (n+1 year) period, the dominant strategy among neural network is: Sell
### IPVIU InterPrivate IV InfraTech Partners Inc. Units Financial Analysis*
Rating Short-Term Long-Term Senior
Outlook*Ba1Ba1
Income StatementCaa2B2
Balance SheetCaa2Baa2
Leverage RatiosB2B1
Cash FlowB1Ba2
Rates of Return and ProfitabilityBaa2B1
*Financial analysis is the process of evaluating a company's financial performance and position by neural network. It involves reviewing the company's financial statements, including the balance sheet, income statement, and cash flow statement, as well as other financial reports and documents.
How does neural network examine financial reports and understand financial state of the company?
### Prediction Confidence Score
Trust metric by Neural Network: 93 out of 100 with 458 signals.
## References
1. Chow, G. C. (1960), "Tests of equality between sets of coefficients in two linear regressions," Econometrica, 28, 591–605.
2. K. Tuyls and G. Weiss. Multiagent learning: Basics, challenges, and prospects. AI Magazine, 33(3): 41–52, 2012
3. Athey S, Blei D, Donnelly R, Ruiz F. 2017b. Counterfactual inference for consumer choice across many prod- uct categories. AEA Pap. Proc. 108:64–67
4. Burgess, D. F. (1975), "Duality theory and pitfalls in the specification of technologies," Journal of Econometrics, 3, 105–121.
5. T. Morimura, M. Sugiyama, M. Kashima, H. Hachiya, and T. Tanaka. Nonparametric return distribution ap- proximation for reinforcement learning. In Proceedings of the 27th International Conference on Machine Learning, pages 799–806, 2010
6. Li L, Chu W, Langford J, Moon T, Wang X. 2012. An unbiased offline evaluation of contextual bandit algo- rithms with generalized linear models. In Proceedings of 4th ACM International Conference on Web Search and Data Mining, pp. 297–306. New York: ACM
7. Y. Le Tallec. Robust, risk-sensitive, and data-driven control of Markov decision processes. PhD thesis, Massachusetts Institute of Technology, 2007.
Frequently Asked QuestionsQ: What is the prediction methodology for IPVIU stock?
A: IPVIU stock prediction methodology: We evaluate the prediction models Modular Neural Network (Speculative Sentiment Analysis) and Wilcoxon Rank-Sum Test
Q: Is IPVIU stock a buy or sell?
A: The dominant strategy among neural network is to Sell IPVIU Stock.
Q: Is InterPrivate IV InfraTech Partners Inc. Units stock a good investment?
A: The consensus rating for InterPrivate IV InfraTech Partners Inc. Units is Sell and assigned short-term Ba1 & long-term Ba1 estimated rating.
Q: What is the consensus rating of IPVIU stock?
A: The consensus rating for IPVIU is Sell.
Q: What is the prediction period for IPVIU stock?
A: The prediction period for IPVIU is (n+1 year) | 2023-02-03 05:57:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.5161473155021667, "perplexity": 7787.423460525965}, "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/1674764500044.16/warc/CC-MAIN-20230203055519-20230203085519-00281.warc.gz"} |
https://mathhelpforum.com/threads/computing-square-roots.283202/ | # Computing Square Roots
#### xyz_1965
See attachment. Can someone get me started here? It looks like I need to plug each square root given for n in the formula and simplify.
#### romsek
MHF Helper
pick $a_0$ by taking a rough guess at the square root.
you know $\sqrt{9}=3$ so try $a_0 = 2.7$
you know $\sqrt{81}=9, ~\sqrt{100}=10$ so try $a_0 = 9.5$
#### greg1313
This is a consequence of the binomial theorem.
$$\displaystyle (a^2 + b)^{1/2} \$$
$$\displaystyle = \ \bigg(a^2\bigg)^{\tfrac{1}{2}} \ + \ \dfrac{1}{2}\bigg(a^2\bigg)^{\tfrac{-1}{2}}b^1 \ + \ ...$$
$$\displaystyle = \ a \ + \ \dfrac{1}{2}a^{-1}b \ + \ ...$$
$$\displaystyle \approx \ a \ + \ \dfrac{b}{2a}$$
$$\displaystyle 2.8^2 \ = \ 7.84 \$$ is 0.16 less than 8.
$$\displaystyle 2.9^2 \ = \ 8.41 \$$ is 0.41 more than 8
Then someone might use 2.8 for a and 0.16 for b.
$$\displaystyle \sqrt{8} \ \approx \ 2.8 \ + \ \dfrac{0.16}{2*2.8}$$
$$\displaystyle \sqrt{8} \ \approx \ 2.8 \ + \ 0.0285714...$$
$$\displaystyle \sqrt{8} \ \approx \ 2.8285714$$
Compare this first approximation to $$\displaystyle \ \sqrt{8} \ = \ 2.828427...$$ | 2020-01-26 23:23:02 | {"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": 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": 0.8770325183868408, "perplexity": 1108.5536622560176}, "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/1579251694071.63/warc/CC-MAIN-20200126230255-20200127020255-00334.warc.gz"} |
https://www.physicsforums.com/threads/pi-in-everything.187116/ | # Pi in everything
1. Sep 26, 2007
### Mindscrape
This has probably already been brought up at some point, but does anyone else think it is strange how much pi, the ratio of circumference to diameter, occurs in so much that has nothing to do with circles? I mean, why should an electric potential between two grounds have any significance with respect to the ratio of circumference to diameter (through the Fourier series)? Even more so, suddenly e, an equally strange appearance, comes into into play. They appear all over the place too, oscillations, orbits, etc. Mankind made a peculiar invention with math.
You more mathy folks might think its totally normal within the math context, but no one is going to look at the physical situation of two grounded conductors (without already seeing the solution) and say, "Oh, I bet that 2.72 and 3.14 play a big part."
2. Sep 26, 2007
### neutrino
Because we tend to approximate a lot of things to perfect circles and spheres. Even though some things may not actually involve circles or spheres, if you trace the steps backwards, you'll come across them somewhere.
As for e, it's usually the base of the logarithm used in calculus.
3. Sep 26, 2007
### ice109
periodic motion can be described by a circular coordinate system. do i really need to explain orbits? i don't know about fourier series and potential between 2 grounds but field drops off from a charge as 1/r^2 which sets up circlular equipotentials. you want a really weird occurrence of pi? look up some of the series that sum to pi. e.g.
$$\pi = \frac{4}{1}-\frac{4}{3}+\frac{4}{5}-\frac{4}{7}+\frac{4}{9}-\frac{4}{11}\cdots$$
4. Sep 26, 2007
### AlephZero
But if anybody can give a phyisical "explanation" as to why $e^{i\pi}+1=0$, that would be interesting.
Sure, pi relates to Euclidean geometry, and e relates to physical growth and decay phenomena - in a sense, it defines a natural measuremt of time to describe the processes.
But why should pi and e relate to each other through a simple equation? I guess the association between the complex plane and 2-D Euclidean space must figure somewhere in the link...
5. Sep 26, 2007
### mjsd
Perhaps, the sphere/spherical shape is everywhere, and that's why $$\pi$$ pops up so often. Not a coincident either (if you believe in that fact that our world is full of symmetries and symmetry is indeed the guiding principle in our axioms/laws and logics). Think of a perfectly symmetrical surface in 3D you get the sphere. in fact in all dimensions, you get some kind of a hypersphere and your old friend pi shall certainly drop by for a visit. How can anything be evenly distributed around a point? you get the sphere again. How to get reflection symmetry in all direction?... the sphere; rotation? sphere... the list goes on. It is this symmetry principle in stuffs, the space they reside in and their interactions that makes the "sphere"/circle and hence $$\pi$$ important.
6. Sep 26, 2007
### HallsofIvy
Staff Emeritus
There is no reason to expect or want a "physical" explanation of a purely mathematical expression. I suspect that any "physical" study of $\pi$ would founder on approximation issues and "physically" there is nothing special about e. Any exponential can be written using any base.
7. Sep 26, 2007
### AlephZero
What I was thinking was: pi and e are related to elementary Euclidean geometry, of circles and rectangular hyperbolas for example. The complex plane can be represented in Euclidean geometry. So, is there a geometrical (non-calculus-based) proof in terms that Euclid, Archimedes, etc would have recognized, that $e^{i\pi}+1 = 0$?
Obviously this is equivalent to a purely geometrical demonstration that $e^{i\theta} = \cos\theta + i\sin\theta$.
The Greeks were quite happy with (semi-pictorial) geometrical arguments about limits of areas, etc....
Apologies for bad use of the word "physical" - working as an ME, Euclidiean geometry is pretty much isomorphic to physical reality!
Last edited: Sep 26, 2007
8. Sep 26, 2007
### HallsofIvy
Staff Emeritus
Excellent! A purely geometrical demonstration would be mathematics and not at all "physical". I doubt that there would be such a demonstration that Euclid and Archimedes would have recognized because you will have to have "i" in there somewhere- and they wouldn't have recognized that.
(I suspect a physicist working in general relativity would NOT say "Euclidean geometry is pretty much isomorphic to physical reality"!
9. Sep 26, 2007
### Chris Hillman
If You Like Simplicity, Which Mathematicians Do, You Can't Avoid Pi
This is really a FAQ, but it's a good question nonetheless.
"Why" questions can be problematic if you are not expecting the kind of explanation likely to be offered by mathematicians--- which brings us to another FAQ, "What is mathematics?". The standard answer is that the definining characteristic of mathematical discourse is the notion of proof, and I don't disagree, but let me toss another idea into the mix. I like to define mathematics as the art of reliable reasoning about simple situations without getting confused. According to this definition, proof is merely a means to the end of reliable reasoning while avoiding confusion.
If you accept this, it follows that mathematically simple situations will turn up more often in the most successful mathematical theories, which are the ones most likely to appear in undergraduate math curricula. And be it noted: one component of what we call "mathematical genius" is the ability to recognize a simple phenomenon masquerading as an apparently complicated phenomenon.
Given this, the explanations I prefer are information theoretic: we define appropriate notions of complexity of differential equations and then show that the simplest differential equations are those which give rise to familiar trig, hyperbolic trig, exp, and (at the next stage) the best known special functions, such as Legendre, Bessel, elliptic, and hypergeometric functions. But of course we should not be too surprised if $\pi$ turn ups when we study circular trig functions (for example when integrating over the circle). And we can expect circular trig functions to turn up more than hyperbolic trig functions because the circle is compact.
(A principle which is challenged by the importance of the Lorentz group in physics, but in the interests of simplicity, let's ignore that. And one could turn this reasoning around and adduce the fact that by our definitions the ODE $\ddot{x} + x = 0$ is particularly simple as evidence that our definitions of "complexity" are reasonable, which might cause some to doubt that we are not simply talking in circles--- no pun intended!)
We should recall here the principle that the simplest differential equations tend to model more than one situation. This is the well known "paucity of low dimensional models" phenomenon. Also, this style of reasoning is not limited to differential equations; similar remarks hold for algebraic plane curves.
I note too that probability concerns measures, and when we normalize Lebesque measure on the unit circle, we introduce a factor of $1/\pi$, so we shouldn't be terribly surprised that this constant is involved in the computation of various probability problems in the real plane. Indeed, the most efficient way to derive the most often encountered probability distributions (Gaussian, Poisson, and so on) is via the Principle of Maximal Entropy. Many of these involve $\pi$ in some way, if you like because these distributions are expressed using the "usual suspects" such as the exponential function.
Trig functions also arise in higher dimensions because n-dimensional unit spheres contain (n-1)-dimensional unit spheres. Very often in mathematics we are interested in how functions decay with distance from "the origin", and analyzing such behavior leads naturally to harmonic decompositions in which integrations over spheres play a central role. (This is one way to explain the phenomenon mentioned by Halls, that spheres are everywhere in mathematics.) So here too we should expect $\pi$ to play a role, and it does.
All in all, it is not very surprising that the same special functions, and therefore the same constants associated with special functions, arise all over the mathematical map. It all comes down to the unity of mathematics, and ultimately one way of explaining the happy meeting of algebra, analysis, and geometry is the information theoretic principle that leads us to expect a preference for simple models, of which there are not many, hence these models are familiar friends to undergraduate math students.
If you read German, you can look in the papers of Hurwitz for some famous examples of this kind of reasoning.
As for Euler's formula, this is less mysterious if you know about Cayley-Dickson algebras, where the starting point is factoring a simple partial differential equation. In the simplest nontrivial cases ("elliptic, parabolic, and hyperbolic"), we obtain respectively circular trig, parabolic trig, and hyperbolic trig together with the appropriate "adjoined unit" (not a real number) obeying $e^2 = -1, \, e^2 = 0, \, e^2 = 1$ respectively, and with isotropy groups $SO(2), \, R, \, SO(1,1)$. Only the first is compact, so again by the principle of analysis which says that compactness tends to be associated with simplicity, we should expect circular trig to be more important than parabolic or hyperbolic trig. And it is.
(The fact that parabolic trig is associated with Galilean relativity and hyperbolic trig with special relativity challenges this notion, but overall, compactness wins, in my estimation.)
Last edited: Sep 26, 2007
10. Sep 26, 2007
### ice109
chris hillman who are you!
11. Sep 26, 2007
### matt grime
Someone about whom one can find details using google quite easily (Chris's contributions to Wikipedia and Usenet, you see).
12. Sep 26, 2007
### Mindscrape
I'm debating whether or not Chris answered everything to my heart's desire, or whether it's a genius oversimplification. He covered anything I could possibly mention, but at the same time almost anything can be stripped down to its roots and simplified to a very basic level, which I don't know if I would call genius or merely a sensible check. Things are complicated, and I feel that too much reduction does an injustice rather than a service to the problem, though I do see the point that it takes a lot of prowess to take a spherical harmonic and reduce it to nothing more than polynomials (legendre polys). At the same time, you are right that circles and circular derivatives do appear in many situations, which would imply the constant pi to be appear in at least an equal number of situations.
I see the point, and it has been argued very well, much better than I could possible do, but at the same time why should heat conduction care whether it follows a circular function or hexagonal one? Is it a coincidence that physical phenomena all like to oscillate and all like to relate to circular functions (why not oscillate triangularly?), something that has been determined by a higher power, or just something we are doing to make ourselves happy with our mathematical invention? Sure a pendulum follows a circular path, with small angles of course, but why should an atom follow the same principles?
13. Sep 27, 2007
### matt grime
As Chris eloquently points out, we have chosen trig functions as our preferred bases in so many situations that it is no great mystery that we see pi. Had we chosen other functions, we wouldn't see pi, or some multiple of a power of pi appearing, but entirely 'different' constants.
14. Sep 27, 2007
### ZapperZ
Staff Emeritus
It is because every physical problem that you deal with involves the GEOMETRY of the system. A physical pendulum follows a particular geometry whether you choose a cartesian or polar coordinates. An atom has to be solve in real and momentum space when you write down the Schrodinger equation. A waveguide would have to be solved using Poisson's equation that require the geometry of the fields and the boundary conditions.
The way you are asking is similar to someone asking why was it possible that I used a screw driver to work on my electronics, yet I also need a screw driver to build a house, or a screw driver to repair a toy. Was there some coincidence or a "higher power" involved here to make that screw driver applicable to all these different areas? It is the same with mathematics.
Zz.
15. Sep 27, 2007
### RetardedBastard
Yes, there WAS a higher intelligent power -- Henry F. Phillips :)
16. Sep 27, 2007
### ZapperZ
Staff Emeritus
But I wasn't using a Phillips screw driver!
:)
Zz.
17. Oct 3, 2007
### tony873004
The number of seconds in a year is coincidentally similar to pi: 3.15*107 seconds. I had an Astronomy teacher who loved to do "order of magnitude" solutions, and in problems that contained both pi, and seconds in a year, she would cancel out pi and the 3.15, leaving only 107. It was justified since some of the inputs to the problem were expressed to fewer than 2 significant figures.
18. Oct 9, 2007
### Cexy
A fleeting and whimsical thought: Could the propensity of pi to appear in mathematical formulae be explained by a kind of Zipf's law? That is, it would be especially surprising if there was no number which turned up more than any other. Given that we can expect some numbers to turn up more than others, we shouldn't be surprised about the exact form of that number - pi in this case.
It's like the philosophically-minded golfer who, reasoning that the probability of his landing his golf ball on any particular blade of grass is practically zero, congratulates himself on being a true pro when he takes a swing and finds that he does indeed manage to land his ball exactly on a blade of grass.
19. Oct 10, 2007
### alphachapmtl
"...it is strange how much pi, the ratio of circumference to diameter, occurs in so much that has nothing to do with circles..."
It's true, but at the same time if you dig a bit you will find a circle everywhere.
Example: How many ways for two integer square to sum to n ?
That is how many solutions of a^2+b^2=n ? Answer=PI on average.
Unexpected at first, but a^2+b^2=n is just the equation of a circle of radius n.
Of course, sometimes its not so clear.
20. Oct 10, 2007
### Count Iblis
Pi in the Sky :rofl: | 2017-04-23 20:10:06 | {"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": 0.7278396487236023, "perplexity": 764.7674622505423}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118743.41/warc/CC-MAIN-20170423031158-00147-ip-10-145-167-34.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/118060/question-about-maps-of-power-series-rings | # Question about Maps of power series rings
Suppose we have an injective homomorphism of power series rings
$$k[[x_1,...,x_m]]\to k[[y_1,...,y_n]]$$
can $x_i$ map to a unit in $k[[y_1,...,y_n]]$?
Of course in general, for injective homomorphisms of rings, non-units can become units in larger rings. For example, $\mathbb{Z}\to \mathbb{Q}$. I am also assuming that $k$ is fixed under the above embedding.
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any hypotesis on $m,n$? $m\le n$, $n\le m$, $m<n$, $n<m$? – tetrapharmakon Mar 9 '12 at 0:31
You'll have to know something about $k$. See this. – Dylan Moreland Mar 9 '12 at 0:59
@DylanMoreland: Sorry, I am unable to make a connection between my question and your link. Let's assume $k$ is algebraically closed for simplicity. – Merlin Mar 9 '12 at 1:15
@tetrapharmakon: I haven't thought of it, so I will leave it open. – Merlin Mar 9 '12 at 1:15
The answer is no (injective or not) at least if you consider homomorphisms of $k$-algebras. Suppose you have such a map $k[[x_1,\dots, x_n]]\to k[[y_1,\dots, y_m]]$. Composing with the evaluation at $(0,\dots, 0)\in k^m$, you get a map $$\phi: k[[x_1,\dots, x_n]]\to k$$ and you want to prove that $\phi(x_i)=0$ for all $i\le n$. Suppose for instance that $\phi(x_1)=\lambda\in k^*$. Then $\phi(x_1-\lambda)=0$. But $x_1-\lambda$ is an unit in $k[[x_1,\dots, x_n]]$ and $$0 = \phi(x_1-\lambda) \phi(1/(x_1-\lambda))=\phi(1).$$ Contradiction.
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Thank you, that's a neat trick. – Merlin Mar 9 '12 at 15:12
Very clever. Well done! – user5137 Mar 9 '12 at 16:22
I don't think this can be done without addressing the issue of infinite sums in $k$. If we have such a mapping $\varphi:k[[x_1,\cdots,x_m]]\rightarrow k[[y_1,\cdots,y_n]]$ with
$$\varphi(x_i)=a+g(y_1,\cdots,y_m)\in k[[y_1,\cdots,y_m]]$$ where $a\in K$, $a\not=0$, and $g(0,0,\cdots,0)=0$, then let $$f=1+x_i + x_i^2 + x_i^3 + \cdots$$
What is $\varphi(f)$? If it's something even close to obvious, then it's the power series that one obtains by substituting $\varphi(x_i)$ into each term. However, this gives us a constant term of $$1+a+a^2 + a^3 + \cdots$$ which is something that we know about if, say, $k\in \{\mathbb{Q},\mathbb{R},\mathbb{C}\}$, but I'm not aware of any kind of study of infinite series in general fields (off the top of my head, I don't think that a series whose terms aren't eventually zero could possibly converge in a finite field).
And even if, say $k=\mathbb{R}$ and, say $a=\frac{1}{2}$, then the constant term of $\varphi(f)$ would be 2, but then consider what $\varphi$ would do to the power series $$1+3 x_i + 9x_i^2 + 27 x_i^3 + \cdots + 3^n x_i^n + \cdots$$ In this case, the series formed by the constant term diverges. What then?
The issue here is why we have the word "formal" in the phrase "rings of formal power series": in a general algebraic setting, we don't care about convergence, and we don't plug anything into our power series except zero.
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I am gathering you are saying that such homomorphisms, if they exist cannot be substitution homomorphisms. Zariski-Samuel restrict to power series without constant terms while defining substitution homomorphisms. Although I am not sure whether there are no other homomorphisms between power series rings, which is what led me to this question. – Merlin Mar 9 '12 at 1:17
@Merlin: this is actually a good question. – user18119 Mar 9 '12 at 9:21
Yes, upon further thinking and after asking for feedback as to whether I was missing something obvious, this only works for homomorphisms that respect infinite sums. This clearly need not be the case. – user5137 Mar 9 '12 at 16:23 | 2016-02-10 02:53:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.9430370926856995, "perplexity": 210.97322081515856}, "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-2016-07/segments/1454701158601.61/warc/CC-MAIN-20160205193918-00153-ip-10-236-182-209.ec2.internal.warc.gz"} |
https://www.hackmath.net/en/math-problem/11871 | # The hemisphere
The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
Correct result:
R = 19.079 cm
#### Solution:
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At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area. | 2021-01-17 13:10:43 | {"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": 0.812504768371582, "perplexity": 551.9295729986958}, "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/1610703512342.19/warc/CC-MAIN-20210117112618-20210117142618-00211.warc.gz"} |
http://ai-su13.artifice.cc/k-nn.html | Home
# k-nearest neighbor classification
## Summary
• Classification is used for predicting the label on a new data point, using a model built from a set of training examples where the true labels were known.
• k-nearest neighbor determines the predicted label by asking the $$k$$-nearest neighbor points in the training set to “vote” for the label.
• k-nearest neighbor requires deciding upfront the value of $$k$$.
• This method is very simple but requires retaining all the training examples and searching through it.
Suppose we measure some properties of flowers, species of iris to be precise. But this time, we also know their true “labels” (species). We have a table like the following:
Sepal length (cm)Sepal width (cm)Petal length (cm)Petal width (cm)Species
5.13.51.40.2iris setosa
4.93.01.40.2iris setosa
4.73.21.30.2iris setosa
7.03.24.71.4iris versicolor
6.33.36.02.5iris virginica
Since we know the true labels, we do not need to use k-means clustering to find (approximate) the species clusters.
If we get a new set of measurements from a new plant, we can predict (approximate, guess) which species it is by calculating the mean of each species cluster and finding which mean is closest.
However, instead of calculating means we typically use a different approach. (Perhaps the two approaches are equivalent; I am not sure.)
Given a new set of measurements, perform the following test:
1. Find (using Euclidean distance, for example), the $$k$$ nearest entities from the training set. These entities have known labels. The choice of $$k$$ is left to us.
2. Among these $$k$$ entities, which label is most common? That is the label for the unknown entity.
What we have is a voting mechanism, where the most votes wins. Sometimes it is a good idea to give each vote a weight, such as the inverse of the entity’s distant from the unknown entity (so more distance votes count for less).
## TOC
### Choosing k
The article “Choosing $$k$$ for two-class nearest neighbour classifiers with unbalanced classes“ by Hand and Vinciotti provides more information and solutions for choosing $$k$$ when performing two-class assignment (i.e., Yes/No assignments) when one class is substantially larger than the other. They write in their conclusion,
Nearest neighbor supervised classification methods have many attractive properties. However, many of these are based on asymptotic arguments. In problems where the classification threshold lies near 0 or 1, as generally is the case in situations where one class is much larger than the other, the fact that $$k$$ is finite results in a non-monotonic relationship between the proportion of each class correctly classified as $$k$$ varies. This means that, in general, larger $$k$$ may not yield better performance than smaller $$k$$.
An example of how the choice of $$k$$ affects performance may be found in the document classification notes.
### Handwritten digit recognition
Consider the following dataset, available from UCI. Thirty people wrote 3823 digits (0-9), which were then scanned as images and translated into 64 features. Specifically, each digit was scanned into a 32x32 pixel black-and-white image, which was divided into 4x4 pixel blocks (64 of them); the number of black pixels in each 4x4 block was counted. These counts constitute the 64 features.
The plot below shows each of the 3823 entities in the testing set. Because the feature vector of each entity has 64 dimensions, we cannot simply plot the feature vectors themselves. Instead, I reduced the dimensionality to 2D using “multidimensional scaling.” This technique calculates the distance from each entity to each other entity, creating a 3823x3823 matrix of distances. Then these distances are reduced to two dimensions by finding an x,y pair for each entity that respects its distances to the other entities. The scaling is not perfect, but generally serves as a good approximation of how “different” each entity is from each other entity.
We see that each digit generally forms a cluster, although there is some overlap. The overlap may well be an artifact of the multidimensional scaling; perhaps there is no overlap if the data were to be graphed in more dimensions.
The k-nearest neighbor algorithm can be visualized using this plot. Say we get a new image, and we want our software to figure out which digit it is. We find the $$k$$ nearest examples from the training set, and figure out what is the most common digit among those examples. Looking at the plot, we can imagine that if the new entity would be placed in the bottom-middle area, that most of its nearest neighbors would be green, representing the digit 4.
In fact, tests with this dataset have shown that the following $$k$$ values produce the corresponding recognition accuracies:
k valueaccuracy
198.00
297.38
397.83
497.61
597.89
697.77
797.66
These are rather high accuracies for such a simple algorithm.
### How to handle noise
Some of the labeled training examples may be surround by the examples from the other classes. Such a situation may arise by plenty of reasons: (i) as a result of a random mistake, (ii) because insufficient number of training example of this class (an isolated example appears instead of cluster), (iii) because incomplete system of features (the classes are separated in other dimensions which we do not know), (iv) because there are too many training examples of other classes (unbalanced classes) that create too dense “hostile” background for the given small class and many other reasons. (source)
We can handle outliers by just removing them from the dataset. They won’t contribute any useful information for classification. Outliers can be detected by defining two values $$q \geq r > 0$$ and say that a point is an outlier with respect to some class if, among its $$q$$ nearest neighbors, there are more than $$r$$ examples from other classes.
## Applet
### Example exercise
Ensure that the parameters are at default settings
1. Create a class with green color by clicking at the top left corner of the work desk and also click on random to create some outliers
2. Create a second class with blue color by clicking at the bottom right corner of the work desk and also click on random to create some outliers
3. Test a query example at the center. (Hint: click on handle test menu, ensure the method is KNN and click at the center of the work desk. Example screen shot is shown below)
1. Classify the test query using different values of $$k$$ = 3, 5, 10 and 20. (To change $$k$$, Go to Parameter menu, change the Number of Nearest Neighbor, click Handle test Menu and click the point you want to classify, i.e., center of the work desk)
2. Does varying the value of $$k$$ affect the classification and which $$k$$ gives a better classification?
3. Calculate the map at the various $$k$$. What can you observe?
## Remarks
What is the inductive bias of k-nearest neighbor? The inductive bias corresponds to an assumption that the classification of an instance $$x$$, will be most similar to the classification of other instances that are nearby in Euclidean distance.
One practical issue in applying k-nearest neighbor algorithms is that the distance between instances is calculated based on all attributes of the instance (i.e., on all axes in the Euclidean space containing the instances). This lies in contrast to methods such as rule and decision tree learning systems that select only a subset of the instance attributes when forming the hypothesis. To see the effect of this policy, consider applying k-nearest neighbor to a problem in which each instance is described by 20 attributes, but where only 2 of these attributes are relevant to determining the classification for the particular target function. In this case, instances that have identical values for the 2 relevant attributes may nevertheless be distant from one another in the 20-dimensional instance space. As a result, the similarity metric used by k-nearest neighbor — depending on all 20 attributes-will be misleading. The distance between neighbors will be dominated by the large number of irrelevant attributes. This difficulty, which arises when many irrelevant attributes are present, is sometimes referred to as the curse of dimensionality. Nearest-neighbor approaches are especially sensitive to this problem.
[…]
One additional practical issue in applying k-nearest neighbor is efficient memory indexing. Because this algorithm delays all processing until a new query is received, significant computation can be required to process each new query. Various methods have been developed for indexing the stored training examples so that the nearest neighbors can be identified more efficiently at some additional cost in memory. One such indexing method is the $$kd$$-tree, in which instances are stored at the leaves of a tree, with nearby instances stored at the same or nearby nodes. The internal nodes of the tree sort the new query $$x_q$$, to the relevant leaf by testing selected attributes of $$x_q$$.
Machine Learning by Tom Mitchell, page 234.
AI Su13 material by Joshua Eckroth is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License. Source code for this website available at GitHub. | 2018-09-20 04:43:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4792110323905945, "perplexity": 738.8801987690267}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156416.22/warc/CC-MAIN-20180920041337-20180920061337-00229.warc.gz"} |
https://scicomp.stackexchange.com/questions/25187/looking-for-name-of-optimization-problem-in-form-min-mathrm-xt-mathrm-a-ma | # Looking for name of optimization problem in form $\min \mathrm x^T \mathrm A \mathrm x$ subject to $\|\mathrm x\| = 1$
I'm sorry for this silly question. Several times I faced with optimization problems which can be expressed as
$$\begin{array}{ll} \text{minimize} & \mathrm x^T \mathrm A \mathrm x\\ \text{subject to} & \|\mathrm x\| = 1\end{array}$$
where $\mathrm A$ is square matrix and $\mathrm x$ is vector.
(This kind of problem arises in PCA or rigid alignment of 3D point sets)
I know that solution of this problem is eigenvalue decomposition of $\mathrm A$. Smallest eigenvalue should be minimum of optimization problem and corresponding eigenvector should be solution.
I want to know is there exist special name for such optimization problem?
PS: Sorry for my poor English.
• Thank you for reply! I thought that well-known problems have own names like Least Squares, Linear/Quadratic/Convex programming, etc. So this fact is surprise for me. Can you rewrite your comment as answer? – Dark_Daiver Oct 13 '16 at 16:06
• Done! Glad to help. – Christian Clason Oct 13 '16 at 16:19
Since the optimization problem has a well-known closed-form solution, it is rarely used in itself and hence usually not given a name. The objective function $x^TAx$ (using $\|x\|=1$), however, is known under the name Rayleigh quotient; the set of its values is called field of values, or numerical range (of $A$).
More generally, this is a textbook example of a quadratic programming problem with a single differentiable equality constraints (if written as $\|x\|^2-1=0$).
• Due to the equality constraint and that $1-\|x\|$ is not a convex function, this isn't a convex constraint. – Deathbreath Nov 1 '16 at 15:41
• @Deathbreath Actually, it is convex if written as $g(x):=\|x\|^2-1=0$. I've made this explicit now. – Christian Clason Nov 1 '16 at 16:52
• that still isn't convex. To make it precise, a convex constraint is $g(x) \le 0$, where $g$ is a convex function. The above equality constraint is only a convex constraint for linear $g$. Since equality implies $g(x)\le 0$ and $-g(x) \le 0$ and $-g(x)=1-\|x\|^2$ is concave, this is not a convex problem. Or more to the point, the surface of a sphere is not a convex set, hence the feasible set here isn't convex. – Deathbreath Nov 1 '16 at 18:20
I know this should be a comment but I do not have enough reputation to comment. I just want to point out that for an arbitrary $A$ with real entries the solution (minimum) to this problem is the smallest eigenvalue of the symmetric part of $A$, namely $S(A)=\frac{(A+A^T)}{2}$, and in the special case when $A$ is symmetric this indeed (as in the original question) gives the smallest eigenvalue of $A$. | 2020-09-28 22:40:38 | {"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": 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": 0.9359346032142639, "perplexity": 257.7605751599312}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401614309.85/warc/CC-MAIN-20200928202758-20200928232758-00230.warc.gz"} |
http://openproblemgarden.org/op/primes_p_such_that_3_is_a_primitive_root_modulo_p | # 3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime
Importance: Medium ✭✭
Author(s):
Subject: Number Theory
Keywords:
Posted by: princeps on: February 25th, 2012
Conjecture is a primitive root modulo for all primes , where is prime.
## Bibliography
* indicates original appearance(s) of problem. | 2019-07-16 10:06:00 | {"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": 0.9867729544639587, "perplexity": 6280.155612190852}, "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/1563195524522.18/warc/CC-MAIN-20190716095720-20190716121720-00017.warc.gz"} |
https://forum.orekit.org/t/about-phasing-example-in-orekit-10-0/695 | # About Phasing Example in Orekit 10.0
Greetings. I am currently learning Orekit as an astronautical engineering student by following the given tutorials and examples. I am new in both java and orekit library. The library is awesome. Before asking my question I would like to thank to the community and the developers of the library especially Luc Maisonbe for the didactic examples.
My question is about the Phasing example in version 10.0. As far as I understand from this tutorial, we are trying to design sun synchronous and repeating ground track orbit. Somehow I understood the initialGuess and improveEarthPhasing methods, yet I have got stuck on improveSunSynchronization and improveFrozenEccentricity methods. In those methods, SecularAndHarmonic class has called and hence there are terms such as secular degrees and pulsations. For instance, in improveSunSynchronization code the SecularAndHarmonic class is used as follows;
// find all other latitude crossings from regular schedule
SecularAndHarmonic mstModel = new SecularAndHarmonic(2,
2.0 * FastMath.PI / Constants.JULIAN_YEAR,
4.0 * FastMath.PI / Constants.JULIAN_YEAR,
2.0 * FastMath.PI / Constants.JULIAN_DAY,
4.0 * FastMath.PI / Constants.JULIAN_DAY);
So, what should I understand from these evaluations? What are the 2 and 4 pi over julian day and year terms? (namely the pulsations.)
Also in this phasing example there is a comment like this.
// fit the mean solar time to a parabolic plus medium periods model
// we will only use the linear part for the correction
mstModel.fit();
What is the meaning of parabolic plus medium periods model?
In ApiDocs, SecularAndHarmonic class is defined as fitting evaluation of osculating orbital parameters. So, in these examples are we fitting osculating elements to mean or somethingelse ?
In addition, if you guys have any theoratical document about this example or the concept of the example, may I ask the references kindly?
Again, Thank you very much for this spectacular library.
Kind Regards,
Uzay
Hi @uzayt
Thanks for the kind words, it is appreciated.
The pulsation terms correspond to the \omega factor in an evolution model of the form c \cos \omega t + s \in \omega t. The c and s coefficients being the unknowns that will be fitted. In other words, the harmonic part in SecularAndHarmonics fits only the amplitude, not the frequency (or pulsation here) that must be provided by users. This approach has been selected rather than a Fourier transform because:
1. not all periods are multiple of each others so any sample, dues to its finite duration,
cannot be periodic for all terms, some will be truncated mid-period which will violate Fourier
transform hypothesis
2. the frequencies we want are discrete and not continuous
3. the frequencies we want are already known and related to identified physical causes
Fixing the pulsation helps fitting correctly the curve even if the sample range is not a whole number of periods. You can even fit something with yearly period on a sample that is only 8 months long for example. Beware, it is not magic! If you attempt to fit, as above, half day, one day, six months and one year and use a sample range limited to one week, you will end up with garbage. The fitting will find the closest model, but this closest model would only fit for this specific week as the least squares engine will most probably affect some part of the evolution to wrong terms, including the polynomial part that adds to this.
So the four pulsations in the phasing example correspond to terms with one year period, one half year period, one day period and one half day period. In space flight dynamics, pulsations are most often related to periods like \tau_p and \tau_p/2 where \tau_p is the period of the generating perturbation p. For example terms linked to Sun (or Earth revolution parameters) have \tau_\text{Sun} equal to one year. Terms linked to Moon third body attraction have \tau_\text{Moon} slightly below one month. Other periods that appear frequently are the day (linked to Earth rotation, mainly due to Earth gravity field) and the period of the satellite itself.
Parabolic plus mean periods means we want to identify an evolution of the form a + bt + ct^2+\sum_k\left(c_k \cos \omega_k t + s_k \sin\omega_k t\right), with \omega_k limited to medium periods (i.e. we want to remove the short periods). A classical way we do that with SecularAndHarmonics is that we first fit the curve with all known (or meaningful wrt. the sample range) terms to make sure we identified correctly all of them, and then either just consider a few terms, deliberately ignoring the extra ones we added just for getting a better fit, or refitting with a new made up sample built from the previous model and with denser sample points. As an example of the last point, we may have an initial sample that can only be one point per orbit (because for example we sample longitudes of nodes crossings), but for the second stage fit we add up new points between the nodes. This use is really expert use (or rather hack use ).
At the end, yes, this class is a workaround to compute mean elements that we set up before we had DSST model, which computes mean elements in a much much more rigorous way. It remains relevant now that we have DSST in cases we want to sort out some harmonics and not others, or when we know one effect is really periodic but with a long period and on a shorter time scale (say less than half its period) we want to model it as a polynomial.
1 Like
Another point I forgot.
The phasing tutorial is not really good. It was a hack I set up quickly for a study some years ago and I put it there just because it may interest other users, but it is definitely low quality. Not very good educationally speaking, and it fails to converge in many cases.
For the learning part, I think I should write it again, one day, with better explanations.
For the convergence part, I think I should write it again, one day, using a proper multi-dimensional optimization rather than a loop around three fixed-point iterations (one for period, one for inclination, one for eccentricity). Some times, the separate fixed-point methods creates an infinite loop, most probably between changes in semi-major axis and eccentricity.
So if you are using this as an educational tool, take care, it is not a good example and I am not proud of it. It is a hack.
1 Like | 2020-08-09 00:27:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.7184883952140808, "perplexity": 1210.738217868642}, "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-2020-34/segments/1596439738366.27/warc/CC-MAIN-20200808224308-20200809014308-00049.warc.gz"} |
https://ncatlab.org/nlab/show/judgment | Judgments
foundations
# Judgments
## Idea
In mathematics and especially in formal logic, by a judgement [Frege (1879, §2)] one means the assertion [Russell & Whitehead (1910, p. xviii)] or validation [Kochen (1961, p. 2)] of a proposition $P$, hence the claim (or even the specification) of a proof of $P$ [Church (1940, §5)].
To bring out the subtle (cf. jstor:43154266) but crucial distinction — eloquently amplified by Martin-Löf (1996, lectures 1-2) — between the notion of a proposition $P$ as such and the judgement/assertion/validation/proof of its truth, it is tradition to prefix the latter with the symbol “$\vdash$”, known as the Urteilsstrich (German: “judgement stroke”) of [Frege (1879, §2)] (see the historical pointers below), as:
(1)$\vdash \; P \,.$
For example, the Riemann hypothesis certainly is a proposition, but it remains open whether we may truthfully assert or validate it, hence we cannot yet judge that it holds true: No proof is known, even though it seems likely to be in fact true.
In other words, the judgement symbols “$\vdash \, P$ ” convey that we know (a proof of, hence the truth of) $P$ [Martin-Löf (1996, lectures 1-2)].
As such, judgements may be formalized as “meta-proposition”, namely propositions but in an ambient meta-language (the deductive system or logical framework) rather than to the object language in which the given $P$ itself is formulated. (More specifically, any deductive system includes, as part of its specification, which strings of symbols are to be regarded as the judgments. Some of these symbols may themselves express a proposition in the object language, but this is not necessarily the case.)
More generally, one considers hypothetical judgements (maybe first made explicit in [Church (1940, §5)]) which are such assertions/validations but conditioned on premises, hence claims/specifications of proofs based on assumptions $A$: Writing
(2)$A \;\;\vdash\;\; P$
is to express the judgement that given any assertion/validation/proof of $A$ we know how to produce (from that) a validation/proof of $P$.
In systems of (dependent) type theory (where such notation seems to go back to Hofmann (1995, p. 31), cf. below) this is quite literally the case in that the categorical semantics of such a hypothetical judgement is a given by a function (and typically a computable function, hence an algorithm) which maps proofs of $A$ to proofs of $P$.
More generally yet, in type theory the propositions $A$ and $P$ appearing here are allowed to be any (dependent) types (see at propositions as types). In this generality, the denotational semantics of hypothetical judgements (2) is given by (computable) functions/morphisms with domain $A$ and codomain $P$. In programming languages based on such type theories this translates to the denotation of an actual program which produces data of data type $P$ when run on input data of data type $A$.
Judgements are themselves subject to a calculus of natural deduction by which further judgements may be inferred from given ones. For example the notation
$\frac{ A \;\;\vdash\;\; P_1 ,\, \;\;\;\;\;\;\; A \;\;\vdash\;\; P_1 }{ A \;\;\vdash\;\; P_1 \times P_2 }$
traditionally expresses that whenever we can assert both $P_1$ as well as $P_2$ assuming a validation of $A$ (hence: given a pair of functions with domain type $A$), then with that same assumption we find assertion/validation/proof of their logical conjunction $P_1 \times P_2$ (namely a function with codomain to their product type).
Finally, to make explicit which particular assumptions a hypothetical judgement really depends on, it is common to adjoin a generic context symbol $\Gamma$ to the hypothesis on the left hand side of the Urteilsstrich: Notation such as
$\Gamma ,\,\;\; a \colon A \;\;\; \vdash \;\;\; p_a \,\colon\, P$
expresses the judgement that $P$ may be asserted given validation of $\Gamma \times A$, but that in doing so only the validation of $A$ is actually made use of, while $\Gamma$ may be any context of assumptions (whose validation might however be used in previous/further deduction steps).
## Examples
### In first-order logic
In first-order logic, a paradigmatic example of a judgement is the judgement that a certain string of symbols is a well-formed proposition. This is often written as “$P \;prop$”, where $P$ is a metavariable standing for a string of symbols that denotes a proposition.
Another example of a judgement is the judgement that these symbols form a proposition proved to be true. This judgment is often written as “$P\;true$”.
Neither of these judgements is the same thing as the proposition $P$ itself. In particular, the proposition is a statement in the logic, while the judgement that the proposition is a proposition, or is provably true, is a statement about the logic. However, often people abuse notation and conflate a proposition with the judgment that it is true, writing $P$ instead of $P\;true$.
### In type theory
The distinction between judgements and propositions is particularly important in intensional type theory.
The paradigmatic example of a judgment in type theory is a typing judgment. The assertion that a term $t$ has type $A$ (written “$t:A$”) is not a statement in the type theory (that is, not something which one could apply logical operators to in the type-theoretic system) but a statement about the type theory.
Often, type theories include only a particular small set of judgments, such as:
• typing judgments (written $t:A$, as above)
• judgments of typehood (usually written $A \;type$)
• judgments of equality between typed terms (written say $(t=t'):A$)
(In a type theory with a type of types, judgments of typehood can sometimes be incorporated as a special case of typing judgments, writing $A:Type$ instead of $A\;type$.)
These limited sets of judgments are often defined inductively by giving type formation/term introduction/term elimination- and computation rules (see natural deduction) that specify under what hypotheses one is allowed to conclude the given judgment.
These inductive definitions can be formalized by choosing a particular type theory to be the meta-language; usually a very simple type theory suffices (such as a dependent type theory with only dependent product types). Such a meta-type-theory is often called a logical framework.
## Hypothetical and generic judgments
It may happen that a judgment $J$ is only derivable under the assumptions of certain other judgments $J_1,\dots, J_2$. In this case one writes
$J_1,\dots,J_n \;\vdash J.$
Often, however, it is convenient to incorporate hypotheticality into judgments themselves, so that $J_1,\dots,J_n \;\vdash J$ becomes a single hypothetical judgment. It can then be a consequence of other judgments, or (more importantly) a hypothesis used in concluding other judgments. For instance, in order to conclude the truth of an implication $\phi\Rightarrow\psi$, we must conclude $\psi$ assuming $\phi$; thus the introduction rule for implication is
$\frac{\phi \;\vdash\; \psi}{\vdash\; \phi\Rightarrow\psi}$
with a hypothetical judgment as its hypothesis. See natural deduction for a more extensive discussion.
In a type theory, we may also consider the case where the hypotheses $J_1$ are typing judgments of the form $x:A$, where $x$ is a variable, and in which the conclusion judgment $J$ involves these variables as free variables. For instance, $J$ could be $\phi\;prop$, where $\phi$ is a valid (well-formed) proposition only when $x$ has a specific type $X$. In this case we have a generic judgement, written
$(x \colon X) \;\vdash\; (\phi \; prop).$
which expresses that assuming the hypothesis or antecedent judgement that $x$ is of type $X$, as a consequence we have the succedent judgement that $\phi$ is a proposition. If on the right here we have a typing judgment
$(x \colon X) \;\vdash\; (t \colon A)$
we have a term in context.
For more about the precise relationship between the various meanings of $\vdash$ here, see natural deduction and logical framework.
While this may seem to be a very basic form of (hypothetical/generic) judgement only, in systems such as dependent type theory or homotopy type theory, all of logic and a good bit more is all based on just this.
## History of the notion and notation
The terminology of judgement in formal logic, and the notation
$\vdash A$
for the judgement of content $A$ is due to Frege (1879, §2) (Frege’s das Urtheil – or das Urteil in modern German spelling – directly translates to: the judgement).
This notion and notation (often “Frege’s Urteilsstrich” – “judgement stroke”) was adopted by Russell & Whitehead (1910, p. xviii), who however speak of “assertion” instead of “judgement” — see Martin-Löf (1996, p. 6) for speculation that these authors may have wanted “to avoid any association with Kantian philosophy” (cf. below):
and then by Church (1940, §5) (without any attribution) — now allowing hypotheses/assumptions on the left of the Urteilsstrich — to mean provable under these assumptions:
Similarly, Kochen (1961, p. 2) introduced (in a context of model theory) the notation “$\mathfrak{A} \;\vDash\; P$” (apparently not actively remembering its historical origin, cf. Kochen (2017)) for a notion in model theory pronounced “$\mathfrak{A}$ validates $P$” — which is at least closely related to these hypothetical judgements (and often used synonymously, e.g. here):
The need (which had been contested by some logicians such as Wittgenstein, cf. jstor:43154266) for Frege’s distinction between a proposition “$A$”, as such, and its judgement/assertion/proof/validation “$\vdash A$” was eloquently argued for by Martin-Löf (1984, pp. 2), (1987) and in (1996, lectures 1-2), together with a re-promotion of Frege’s Urteilsstrich notation “$\vdash$” (ML84, p. 2, ML96, p. 2, 6):
The notation for hypothetical judgements
(3)$context \;\vdash\; judgement$
was then (without attribution to Church or Martin-Löf) adopted for dependent type theory in Hofmann (1995, p. 31), later published as Hofmann (1997, p. 82):
This eventually became the trademark of the practice of dependent type theory (though mostly used without any attribution), e.g.: Jacobs (1998, p. 2, 121, 586); Bauer, Haselwarter & Lumsdaine (2020).
(Curiously, apparently Martin-Löf did not actually use the general notation (3) in publications: When in 1996, p. 29 it comes to hypothetical judgements, he switched to using just a vertical “$\vert$” instead of “$\vdash$”.)
In summary:
terminologyauthor
judgementFrege (1879)
assertionRussell & Whitehead (1910)
proofChurch (1940)
validationKochen (1961)
judgementMartin-Löf (1984, 1996)
Hofmann (1995, 1997)
## References
Pre-history of the notion of judgement (Urteil) in (informal) logic:
The origin of the notion of “judgement” (and of the notation “$\vdash$” for it) in formal logic:
and under the name “assertion” in:
Keeping the symbol “$\vdash$”, now allowing hypothesis on the left, but pronouning it as “proof under assumptions”:
Discussion in the context of what became known as Martin-Löf dependent type theory:
Reviewed in:
Further discussion in
Textbook acccount in a context of programming languages:
The alternative notation “$\vDash$” for satisfaction with closely related (if different) usage seems to originate in
whose author
cannot recollect whether [he] originated it or took it from some other paper.
according to:
See also:
Last revised on January 25, 2023 at 16:56:26. See the history of this page for a list of all contributions to it. | 2023-02-07 14:04:24 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 84, "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": 0.8813743591308594, "perplexity": 1331.4408615252744}, "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-2023-06/segments/1674764500619.96/warc/CC-MAIN-20230207134453-20230207164453-00034.warc.gz"} |
https://math.stackexchange.com/questions/2982942/proof-that-a-b-is-neither-closed-nor-open | # Proof that $[a,b)$ is neither closed nor open?
Our professor gave us definitions for closed and open intervals.
A set $$U$$ is open if $$\forall x \in U$$, $$\exists \epsilon \gt 0$$ such that $$(x- \epsilon,x+ \epsilon)\subset U$$. A set is $$F$$ closed, if its complement is open.
I'm not too sure how to write the solution that is clear and understandable. This is what I've thought of so far.
To prove that the set $$U=[a,b)$$ is not open, I used proof by contradiction by assuming that it is open. Since $$a \in U$$, it follows that $$\exists \epsilon \gt 0$$ such that $$(a- \epsilon,a+ \epsilon)\subset U$$. However, this is not possible as there does not exist $$\epsilon \gt 0$$ such that $$a- \epsilon \in U$$. The proof that the set is not closed is similar to this.
• Do you mean $a$ in place of $x$ in the last paragraph? – Mario Carneiro Nov 3 '18 at 14:52
• oops, my bad. I fixed it now. – Bob Nov 3 '18 at 14:55
You have a slight error.
You say there is no $$\epsilon$$ so that $$a -\epsilon$$ is in $$U$$. But there is nothing in the definition that says $$a -\epsilon \in U$$. Then definition says $$(a-\epsilon, a + \epsilon) \not \subset U$$. ANd $$a-\epsilon \not \in (a-\epsilon, a+\epsilon)$$ so that does not contradict.
However as there exist for any $$\epsilon > 0$$ many (uncountably many) $$y \in (a-\epsilon, a)$$ so that $$a-\epsilon < y < a$$ and in particular, there is $$a - \frac \epsilon 2 \in (a-\epsilon, a + \epsilon)$$. $$a-\epsilon$$ is NOT a valid counter example point. But $$a - \frac \epsilon 2$$ (as is $$a-.99999\epsilon$$) is. And from that your argument follows.
......
To prove in is not closed is similar.
But let's go into detail. $$b \not \in [a,b)$$ so $$b \in [a,b)$$. ANd for $$b$$ there is no $$\epsilon > 0$$ so that $$(b-\epsilon,b+\epsilon) \subset [a,b)^c$$.
Why not? Because there are infinitely many $$y$$ so that $$\max(a, b-\epsilon) < y < b$$ and these are all in $$y \in [a,b)$$ so $$y \not \in [a,b)^c$$.
To not twist ourselfs into knots it is probably easier to put it this way:
If $$[a,b)^c$$ is open then there will be an $$\epsilon > 0$$ so that $$(b-\epsilon, b+\epsilon)\subset [a,b)^c$$. We might as well assume $$0 < \epsilon < b-a$$. [We can assume that because for any $$\epsilon$$ so that $$(b-\epsilon, b+\epsilon ) \subset U$$ then for any $$0 < \epsilon_2 < \epsilon$$ we'd have $$(b-\epsilon_2,b+\epsilon_2) \subset (b-\epsilon, b+\epsilon ) \subset U$$ ans we can always find an $$0 < \epsilon_2 < b-a$$]
Then let $$a < b - \frac \epsilon 2 < b$$ so $$b-\frac \epsilon 2 \in [a,b)$$ and $$b-\frac \epsilon 2\not \in [a,b)^c$$. But $$b-\frac \epsilon 2 \in (b-\epsilon, b+\epsilon)$$ so $$(b-\epsilon, b+\epsilon)\not \subset [a,b)^c$$. So $$[a,b)$$ is not closed.
....
Hmm, maybe that wasn't easier.
Welcome to MSE!
$$U=[a,b)$$ is not open means $$(\color{red}{\exists x} \in U \wedge\color{blue}{\forall \varepsilon>0}):(x-\varepsilon,x+\varepsilon) \subset U\;\;\text{is false}$$
You are right about that $$x$$ namely $$x=a$$. You assume the left endpoint of the nbd of $$a$$ does't in $$U$$. But $$a- \varepsilon$$ is not even in $$(a-\varepsilon,a+\varepsilon)$$. Note that every element of the portion $$(a-\varepsilon,a)$$ is not in $$U$$, so $$U$$ is not open
For other $$x$$'s in $$U$$, we have $$(x-\varepsilon,x+\varepsilon) \subset U$$ How to choose $$\varepsilon$$ in this case?
Seems correct.
If the set is closed, then $$I^{\text C}:=]-\infty,a[\cup[b,\infty[$$ is open; since $$b\in I^{\text C}$$, $$]b-\epsilon,b+\epsilon[$$ should also be contained in $$I^{\text C}$$, for some $$\epsilon > 0$$, which is a contradiction.
Of course you need to account what @Chinnapparaj R said, i.e. to show that there is $$\mu\in ]b-\epsilon,b[$$ that makes $$]b-\epsilon,b[ \not\subset I^{\text C}$$ | 2020-06-05 01:57:38 | {"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": 70, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9329825639724731, "perplexity": 117.2909681898141}, "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-2020-24/segments/1590348492427.71/warc/CC-MAIN-20200605014501-20200605044501-00468.warc.gz"} |
http://warholprints.com/library/collisions-rings-and-other-newtonian-n-body-problems-cbms-regional-conference-series-in | Collisions, Rings, and Other Newtonian N-Body Problems (Cbms
Format: Paperback
Language: English
Format: PDF / Kindle / ePub
Size: 8.93 MB
Downloadable formats: PDF
What is most striking to the contemporary eye, however, is that the compendious descriptions of the properties of matter were essentially empirical. Consider a one-dimensional elastic collision between particles of masses m1 and m2. Now there’s a spectrum of positions you could take. Your life will unfold perfectly, precisely and with unwavering certainty, just as you "believe" that it will. The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 5-Year Impact Factor: 1.325 ℹ Five-Year Impact Factor: To calculate the five year Impact Factor, citations are counted in 2015 to the previous five years and divided by the source items published in the previous five years. © Journal Citation Reports 2016, Published by Thomson Reuters
Pages: 235
Publisher: American Mathematical Society (May 1, 2005)
ISBN: 0821832506
Field Theory of Guided Waves
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Introduction to Field Quantization (International series of monographs in natural philosophy)
Stochastic Wave Propagation (Fundamental Studies in Engineering)
Optical Solitons: Theory and Experiment (Cambridge Studies in Modern Optics)
Gauge Theories and Experiments at High Energies (SUSSP publications)
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4.4 | 2017-07-21 16:57:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43612271547317505, "perplexity": 1274.838365523932}, "config": {"markdown_headings": false, "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-2017-30/segments/1500549423787.24/warc/CC-MAIN-20170721162430-20170721182430-00484.warc.gz"} |
http://www.bobbydurrettdba.com/2015/05/29/surprising-calibrate_io-result/ | # Surprising calibrate_io result
Recently I used DBMS_RESOURCE_MANAGER.calibrate_io to measure disk I/O performance using a call like this:
DECLARE
l_latency PLS_INTEGER;
l_iops PLS_INTEGER;
l_mbps PLS_INTEGER;
BEGIN
DBMS_RESOURCE_MANAGER.calibrate_io (num_physical_disks => 10,
max_latency => 20,
max_iops => l_iops,
max_mbps => l_mbps,
actual_latency => l_latency);
DBMS_OUTPUT.put_line('Max IOPS = ' || l_iops);
DBMS_OUTPUT.put_line('Max MBPS = ' || l_mbps);
DBMS_OUTPUT.put_line('Latency = ' || l_latency);
END;
/
Using this call I have a surprising result. This test returns very different results when run against two different databases on the same Linux virtual machine and the same filesystem.
database 1:
Max IOPS = 7459
Max MBPS = 863
Latency = 18
database 2:
Max IOPS = 39921
Max MBPS = 1105
Latency = 0
Both databases use direct and asynchronous I/O. The databases differ in size and configuration. It seems that something about the databases themselves affects the results since they share the same filesystem on the same machine.
I did not get useful numbers from calibrate_io and have wasted a lot of time trying to interpret its results. You may want to focus on other tools for measuring disk I/O performance.
– Bobby | 2017-02-24 03:35:58 | {"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": 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": 0.4777601361274719, "perplexity": 14305.38453375958}, "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-2017-09/segments/1487501171281.53/warc/CC-MAIN-20170219104611-00492-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://jahrme.github.io/treatise/Treatise-V/Lab-9.html | # Subsection2.1Background
In 1887 Heinrich Hertz observed that light striking a metal surface may release electrons. Philipp Lenard later showed that the emitted electrons have a maximum kinetic energy that depends on the wavelength but not the intensity of the light used. In 1905 Einstein correctly explained the photoelectric effect by invoking Planck's quantum hypothesis. According to Einstein, a photon of energy $hc\lambda^{-1}$ knocks an electron from the target, giving the electron a kinetic energy $hc\lambda^{-1}-W$, where $W$ is called the work function, the minimum amount of energy needed to release one electron from that particular metal.
# Subsection2.2Experimental Setup
We will measure the kinetic energy of the electrons by measuring the electric potential $V_0$, called the stopping potential (measured in volts, symbol V), required to stop the most energetic electrons released. You do that by adjusting the potential on your box until the electron current reads zero. Kinetic energy $K$ is related to stopping potential by $K=eV_0$, where $e$ is the electron's charge. The units for kinetic energy are electron volts (eV). If we measure say $V_0=1.5$ V, then the electron's kinetic energy was $1.5$ eV.
We can select a single wavelength by using a known light source, which produces a spectrum containing just a few visible wavelengths, and a filter that allows light of only a single wavelength to pass.
Using this, we begin by calibrating the box containing the photo-tube so that there is no current when the aperture is covered. From there, we insert the correct light filter and point the light into the box. We then adjust the voltage so as to get a current of $0$; this is our $eV_0$ for the current light's $\lambda$. It should be noted, though, that when using yellow light there can be some difficulty in getting an accurate measurement.
# Subsection2.3Our Results
Our data can be seen in Table 2.1, and is plotted in Figure 2.2.
# Subsection2.4Analysis
The maximum kinetic energy of an emitted electron is $K=eV_0$. According to Einstein's theory, this maximum kinetic energy is related to the wavelength of light and the metal's work function according to $eV_0=hc\lambda^{-1}-W.$ We would like to measure Planck's constant $h$, and in doing so verify the quantum (photon) nature of light. In this experiment it's easier to measure $hc$, which effectively measures Planck's constant, because the speed of light $c$ is well known. In our data, we measured the stopping potential $V_0$ for several different wavelengths $\lambda$. We have plotted $eV_0$ (in units of eV) versus $\lambda^{-1}$ (in units of nm) in Figure 2.2; the result is a straight line with a slope $hc$. The accepted result is $hc = 1240$ eV nm. We are within a factor of two of this result; as such, we can say we've measured the smallest constant in nature, Planck's constant.
As a bonus, the intercept of our graph gives us the metal's work function, in units of eV. Most metals have a work function between $0$ and $5$ eV and ours falls into that range at $0.97$.
##### Historical Significance
This experiment established the quantum notion of light whereby light (as well as matter, though that is another issue) exhibits both particulate and wavelike properties, suggesting that traditional mechanics can not always account for our physics. Additionally, the experiment was revolutionary as previously it had been believed that the amount of energy conveyed by light was dictated by the intensity of the light, in other words how bright it was. However, as can be seen in this experiment, it is the wavelength of light that really determines the energy conveyed when attempting to liberate electrons. | 2017-03-24 04:13:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.713090717792511, "perplexity": 383.881533356864}, "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/1490218187690.11/warc/CC-MAIN-20170322212947-00079-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/converting-ml-gal-to-gal-ml.534690/ | Converting ml/gal to gal/ml
1. Sep 28, 2011
asburypark
good afternoon,
good day,
is there some logic to assuming that ml/gal is the
exact same thing as gal/ml assuming that you are
dealing with 1 Liter in both ratios?
thank you so much
asburypark2010
2. Sep 28, 2011
Staff: Mentor
It makes about as much sense as assuming that 50 $/hour is the same as 50 hour/$. I have nothing against working for $50 per hour, but even in Chinese sweatshops they don't work 50 hours per$1.
3. Sep 28, 2011
Mike H
I'm not really sure what you're trying to do, but given that 1 gallon is ~ 3.75 liters (approximately - you will want to check for a more exact conversion factor), you will need to use the appropriate relationship depending on what you're trying to convert based on your dimensional analysis.
For example, let's convert 10 liters into gallons.
10 liters * (1 gallon/3.75 liters) = 2.67 gallons
On the other hand, let's convert 10 gallons into liters.
10 gallons * (3.75 liters/1 gallon) = 37.5 liters
The relationship of 1 gallon ~ 3.75 liters holds in both cases, but in one case, gal/L is used, while L/gal is used in the other.
4. Sep 29, 2011
sjb-2812
Last edited by a moderator: May 3, 2018
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook | 2018-05-28 10:02:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8043292164802551, "perplexity": 3552.954971673547}, "config": {"markdown_headings": false, "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-2018-22/segments/1526794872766.96/warc/CC-MAIN-20180528091637-20180528111637-00379.warc.gz"} |
https://www.sparrho.com/item/background-conditions-influence-the-estimated-cloud-radiative-effects-of-anthropogenic-aerosol-emissions-from-different-source-regions/1ece6e4/ | # Background Conditions Influence the Estimated Cloud Radiative Effects of Anthropogenic Aerosol Emissions from Different Source Regions
Research paper by Benjamin S. Grandey, Chien Wang
Indexed on: 17 Aug '18Published on: 17 Aug '18Published in: arXiv - Physics - Atmospheric and Oceanic Physics
#### Abstract
Using the Community Earth System Model, with the Community Atmosphere Model version 5.3, we investigate the cloud radiative effects of anthropogenic aerosols emitted from different source regions and global shipping. Due to transboundary transport and sub-linearity in the response of clouds to aerosols, the cloud radiative effects of emissions from a given source region are influenced by emissions from other source regions. For example, the shortwave cloud radiative effect of shipping is $-0.39 \pm 0.03$ W m$^{-2}$ when other anthropogenic emissions sources are present (the "present-day background" assumption) compared with $-0.60 \pm 0.03$ W m$^{-2}$ when other anthropogenic emissions sources are absent (the "natural background" assumption). In general, the cloud radiative effects are weaker if present-day background conditions are assumed compared to if natural background conditions are assumed. Assumptions about background conditions should be carefully considered when investigating the climate impacts of aerosol emissions from a given region. | 2022-01-23 05:10:44 | {"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": 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": 0.5473482012748718, "perplexity": 5655.325056269487}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304134.13/warc/CC-MAIN-20220123045449-20220123075449-00610.warc.gz"} |
https://indico.cern.ch/event/797094/contributions/3367687/ | # IoP Joint HEPP and APP Annual Conference 2019
Apr 7 – 10, 2019
Imperial College London
Europe/London timezone
## Search for long-lived neutral particles that decay into displaced jets in the ATLAS detector
Apr 8, 2019, 2:00 PM
15m
Huxley 340 (Imperial College London)
### Speaker
Ms Alice Morris (University College London (GB))
### Description
Long-lived particles feature in many extensions to the Standard Model that have been proposed to address some of its open questions. Decays of long-lived particles created in collider experiments would produce unique signatures that may have been overlooked by previous searches for promptly decaying particles.
A search for pairs of neutral long-lived particles (LLPs) decaying in the volume of the ATLAS detector (mainly in the hadronic calorimeter) is presented, which probes LLP decay lengths ranging between a few centimetres and a few tens of metres. The analysis uses a simplified Hidden Sector model as a benchmark, where scalar LLPs are pair-produced from decays of heavy bosons, and eventually decay to SM fermions (mainly b-quarks). If this decay occurs in the calorimeters, the two resulting fermions are reconstructed as a single displaced jet with unusual features compared to jets from SM processes. A series of machine learning techniques were employed to identify the displaced jets and reduce the contamination from background in the search region. A data-driven estimate of the remaining background was performed and limits were set on the production cross section times branching ratio, extrapolated as a function of the decay length of the LLPs. These are presented combined with limits from a search which looks for displaced jets in the ATLAS muon spectrometer. | 2022-08-08 11:29:57 | {"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": 0.8523777723312378, "perplexity": 2325.2691177266556}, "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/1659882570793.14/warc/CC-MAIN-20220808092125-20220808122125-00425.warc.gz"} |
https://stacks.math.columbia.edu/tag/0DI2 | Lemma 36.35.3. Let $f : X \to S$ be a morphism of schemes which is flat and locally of finite presentation. Let $E$ be an object of $D_\mathit{QCoh}(\mathcal{O}_ X)$. The following are equivalent
1. $E$ is $S$-perfect,
2. for any affine open $U \subset X$ mapping into an affine open $V \subset S$ the complex $R\Gamma (U, E)$ is $\mathcal{O}_ S(V)$-perfect.
3. there exists an affine open covering $S = \bigcup V_ i$ and for each $i$ an affine open covering $f^{-1}(V_ i) = \bigcup U_{ij}$ such that the complex $R\Gamma (U_{ij}, E)$ is $\mathcal{O}_ S(V_ i)$-perfect.
Proof. Being pseudo-coherent is a local property and “locally having finite tor dimension” is a local property. Hence this lemma immediately reduces to the statement: if $X$ and $S$ are affine, then $E$ is $S$-perfect if and only if $K = R\Gamma (X, E)$ is $\mathcal{O}_ S(S)$-perfect. Say $X = \mathop{\mathrm{Spec}}(A)$, $S = \mathop{\mathrm{Spec}}(R)$ and $E$ corresponds to $K \in D(A)$, i.e., $K = R\Gamma (X, E)$, see Lemma 36.3.5.
Observe that $K$ is $R$-perfect if and only if $K$ is pseudo-coherent and has finite tor dimension as a complex of $R$-modules (More on Algebra, Definition 15.83.1). By Lemma 36.10.2 we see that $E$ is pseudo-coherent if and only if $K$ is pseudo-coherent. By Lemma 36.10.5 we see that $E$ has finite tor dimension over $f^{-1}\mathcal{O}_ S$ if and only if $K$ has finite tor dimension as a complex of $R$-modules. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 2022-05-19 11:26:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.9808114171028137, "perplexity": 147.10285950525372}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662527626.15/warc/CC-MAIN-20220519105247-20220519135247-00484.warc.gz"} |
https://physics.stackexchange.com/questions/315330/berry-curvature-in-one-dimensional-parameter-space | # Berry curvature in one dimensional parameter space
Berry curvature is defined by
$$\Omega_{n,\mu\nu}(R) = \frac{\partial A_{n,\nu}}{\partial R^{\mu}} - \frac{\partial A_{n,\mu}}{\partial R^{\nu}}$$ where $R$ is an parameter in hamiltonian. I think it is well defined if the dimension of parameter $R$ is more than 2. But what if the dimension of parameter $R$ is 1? Is it possible to say something about Berry curvature if the dimension of parameter is 1? If the dimension is 1, I think even the closed path integral for Berry phase is not well derfined.
If the dimension of $R=1$, them $\mu=\nu=$ $\alpha$. The $\Omega_{n,\alpha,\alpha}=\partial_{\alpha}A_{n,\alpha}-\partial_{\alpha}A_{n,\alpha}=0$. On the other hand, a closed path, can be defined as $R(\alpha (t))=R(\alpha(t+T))$. So, I don't think any problem in defining the closed path in one parameter case, as a close path depends on the initial and final point.
• If $\Omega_{n,\nu\mu}=0$, Berry phase is always zero in 1 dimensional parameter space. But it can have any non-zero values in higher dimensions. What's the difference between one and higher dimension? – user42298 Feb 28 '17 at 11:50 | 2020-04-10 06:55:43 | {"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": 0.959545910358429, "perplexity": 111.6235241570599}, "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-2020-16/segments/1585371886991.92/warc/CC-MAIN-20200410043735-20200410074235-00488.warc.gz"} |
https://testbook.com/question-answer/permanent-teeth-formula-of-adult-cow-is--6043787d1d3ce81740d44573 | # Permanent teeth formula of Adult Cow is-
This question was previously asked in
RSMSSB Agriculture Supervisor 2018 Official Paper (Held on 3 March 2019)
View all RSMSSB Agriculture Supervisor Papers >
1. $$I \frac{0}{4} C \frac{0}{0} PM \frac{3}{3} M \frac{3}{3}$$
2. $$I \frac{4}{0} C \frac{0}{0} PM \frac{3}{3} M \frac{3}{3}$$
3. $$I \frac{0}{4}C \frac{3}{0}PM \frac{0}{3}M \frac{3}{3}$$
4. $$I \frac{0}{4}C \frac{0}{3}PM \frac{3}{0}M \frac{3}{3}$$
Option 1 : $$I \frac{0}{4} C \frac{0}{0} PM \frac{3}{3} M \frac{3}{3}$$
## Detailed Solution
The correct answer is - 0/4 - 0/0 PM - 3/3 M - 3/3.
• The number of each type of tooth varies from one species to another and the conventional way of describing them is by a "dental formula".
• The type of teeth are indicated by the first letter, and the number of teeth on one side of the upper jaw is indicated over the number of the same type of teeth on the lower jaw.
• Because the formula is for one side of the mouth the total number of teeth is the total in the formula x 2.
• The dental formula for cattle is as follows, where I = incisors, C = canines, P = premolars and M = molars:
• Cattle:
• Temporary teeth:
• - 0/4 - 0/0 - 3/3 - 0/0 = 10 x 2 = 20
• Permanent teeth:
• - 0/4 - 0/0 - 3/3 M - 3/3 = 16 x 2 = 32
• In cattle the permanent teeth are not fully erupted until 3.5-4 years of age | 2021-10-25 17:32:20 | {"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": 0.46497708559036255, "perplexity": 2291.951867533284}, "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/1634323587719.64/warc/CC-MAIN-20211025154225-20211025184225-00107.warc.gz"} |
https://docs.themeegg.com/eggnews/color-settings-and-typography-settings/ | # Typography Settings
Step1: Go to Appearance > Customize section.
Now, click on the Typography Setting.
Now you can see lots of options for typography setting, so, check them manually…
You can find lots of options, Here we mention some of them, But in this section available are listed below:-
Google Fonts, Header Fonts, Font size for the title, Footer font size options.
In this section, you can select all the google fonts options available in this theme.
Here, below is the screenshot of the google font options:-
Dashboard > Appearance >Customize > Typography Setting
Now you can see many lists of the typography Setting options, Now, you can check individually. Here you can find lots of options. We list some of them, they are given below…
• Header Font Size Options: In this section, you can find all the header font size settings, which cover header area.
Now you can see the screenshot of the header font size options: It makes your task very easy:
• Font sizes for the title: In this section, you can find Font size for the title (From h1 to h6 and post, page, Widget and comment title. It’s very easy to change the font size of the different title.
• Footer font size option: In this section covers all the Footer font size settings, which cover the footer area. | 2021-06-14 08:54:06 | {"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": 0.8354713320732117, "perplexity": 2169.9234190815673}, "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/1623487611641.26/warc/CC-MAIN-20210614074543-20210614104543-00624.warc.gz"} |
http://www.mumsadvice.co.uk/hi-just-a-quick-one-i-will-do-a-test-later-if-i-dont-come-on-just-wondering-if/ | # Hi just a quick one, I will do a test later if I don’t come on just wondering if…
0
34
Hi just a quick one, I will do a test later if I don’t come on just wondering if People know, I was on the pill I had a period on the 10th may for 5 days (my 7 day break) I then stopped taking the pill mid way on the 20th (due to personal problems we agreeed it will be better for my hormones) I then had a withdrawal bleed couple days later.. IS THIS CLASSED AS A PERIOD??? About 10 days ago we then decided to try for a baby, but I haven’t come on This month, and just wondering if I go by my original 10th may period or the 20th withdrawal bleed so I know if I’m late or not many thanks 😇
Source
SHARE | 2017-12-16 12:45:08 | {"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": 0.8291407227516174, "perplexity": 1188.8949283509298}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948588072.75/warc/CC-MAIN-20171216123525-20171216145525-00254.warc.gz"} |
http://theran.lt/papers/p002-bichromatic.html | # Lines induced by bichromatic point sets
Authors: Louis Theran Preprint: 1101.1488, 2011 Full text: arXiv
An important theorem of Beck says that any point set in the Euclidean plane is either “nearly general position” or “nearly collinear”: there is a constant $C>0$ such that, given $n$ points in the plane with at most $r$ of them collinear, the number of lines induced by the points is at least $Cr(n−r)$. Recent work of Gutkin-Rams on billiards orbits requires the following elaboration of Beck’s Theorem to bichromatic point sets: there is a constant $C>0$ such that, given $n$ red points and $n$ blue points in the plane with at most $r$ of them collinear, the number of lines spanning at least one point of each color is at least $Cr(2n−r)$. | 2018-02-19 09:32:10 | {"extraction_info": {"found_math": true, "script_math_tex": 9, "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": 0.6294980645179749, "perplexity": 326.3384892791954}, "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-2018-09/segments/1518891812579.21/warc/CC-MAIN-20180219091902-20180219111902-00099.warc.gz"} |
https://bitbucket.org/arigo/cpython-withatomic/src/84461011a1a0/Doc/libmacostools.tex | # cpython-withatomic / Doc / libmacostools.tex
The branch 'legacy-trunk' does not exist.
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Tip: You can also navigate files with Alt+j (next) and Alt+k (previous) and view the file with Alt+o. | 2014-04-18 21:10:17 | {"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": 0.19657710194587708, "perplexity": 3702.1926709817326}, "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-2014-15/segments/1397609535095.9/warc/CC-MAIN-20140416005215-00526-ip-10-147-4-33.ec2.internal.warc.gz"} |
https://www.zbmath.org/?q=ci%3A33.0449.04 | # zbMATH — the first resource for mathematics
On the combinatorial identities of Abel-Hurwitz type and their use in constructive theory of functions. (English) Zbl 1240.41058
Summary: This paper is concerned with the problem of approximation of multivariate functions by means of Abel-Hurwitz-Stancu type linear positive operators. Inspired by the work of D. D. Stancu [Rev. Anal. Numér. Théor. Approx. 31, No. 1, 115–118 (2002; Zbl 1084.41504)], we continue the discussions of the approximation of trivariate functions by a class of Abel-Hurwitz-Stancu operators in the case of trivariate variables, continuous on the unit cube $$K_3=[0,1]^3$$.
In Section 1, which is the Introduction, we give the generalization due to N. H. Abel [J. Reine Angew. Math. 1, 159–160 (1826; Zbl 02751789)] of the Newton binomial formula, and the very important extension of this formula due to A. Hurwitz [Acta Math. 26, 199–204 (1902; JFM 33.0449.04)]. Here also, an interesting combinatorial significance in cycle-free directed graphs is mentioned given by D. E. Knuth [The art of computer programming. Vol. 1: Fundamental algorithms. London: Addison-Wesley Publishing Company (1968; Zbl 0191.17903)]. Then, we present a main result given in 2002 by D. D. Stancu [2002, loc. cit.], where a variant of the Hurwitz identity was employed in order to construct and investigate a new linear positive operator, which is used in the theory of approximation of univariate functions.
In Section 2, we discuss in detail the trivariate polynomial operator of Stancu-Hurwitz type $$S^{(\beta),(\gamma),(\delta)}_{m,n,r}$$ associated to a function $$f\in C(K_3)$$, where $$K_3$$ is the unit cube $$[0,1]^3$$.
Section 3 is devoted to the evaluation of the remainder term of the approximation formula of the function $$f(x,y,z)$$ by means of the Stancu-Hurwitz type operator $$S^{(\beta),(\gamma),(\delta)}_{m,n,r}$$. Firstly, we present an integral form of this remainder, based on the Peano-Milne-Stancu result [D. D. Stancu, J. Soc. Ind. Appl. Math., Ser. B, Numer. Anal. 1, 137–163 (1964; Zbl 0143.07901)]. Then, we give a Cauchy type form for this remainder. By using a theorem of T. Popoviciu, we give an expression, using the divided differences of the first three orders. When the coordinates of the vectors $$(\beta),(\gamma),(\delta)$$ have, respectively, the same values, we are in the case of the second operator of E. W. Cheney and A. Sharma [Riv. Mat. Univ. Parma, II. Ser. 5, 77–84 (1964; Zbl 0146.08202)]. In this case, we obtain an extension of the results from papers by D. D. Stancu [2002, loc. cit.] and by I. Taşcu [“Approximation of bivariate functions by operators of Stancu-Hurwitz type”, Facta Univ., Ser. Math. Inf. 20, 33–39 (2005)].
##### MSC:
41A35 Approximation by operators (in particular, by integral operators) 41A20 Approximation by rational functions
##### Keywords:
Abel-Hurwitz-Stancu operators | 2021-02-28 10:56:11 | {"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": 0.6991379857063293, "perplexity": 877.768716394185}, "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/1614178360745.35/warc/CC-MAIN-20210228084740-20210228114740-00191.warc.gz"} |
http://askmetips.com/standard-error/standard-deviation-and-standard-error-of-the-mean.php | Home > Standard Error > Standard Deviation And Standard Error Of The Mean
# Standard Deviation And Standard Error Of The Mean
## Contents
Sep 16, 2013 Jesse Maurais · The University of Calgary The standard error is what you call the standard deviation of the sample, as opposed to the population from which it Well, let's see if we can prove it to ourselves using the simulation. Read Answer >> Related Articles Investing Explaining Standard Error Standard error is a statistical term that measures the accuracy with which a sample represents a population. To estimate the standard error of a student t-distribution it is sufficient to use the sample standard deviation "s" instead of σ, and we could use this value to calculate confidence my review here
Assets with higher prices have a higher SD than assets with lower prices. Investing Understanding the Simple Random Sample A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. For an upcoming national election, 2000 voters are chosen at random and asked if they will vote for candidate A or candidate B. So this is the variance of our original distribution.
## Difference Between Standard Deviation And Standard Error
We take 10 samples from this random variable, average them, plot them again. Notice that s x ¯ = s n {\displaystyle {\text{s}}_{\bar {x}}\ ={\frac {s}{\sqrt {n}}}} is only an estimate of the true standard error, σ x ¯ = σ n Investing What is a Representative Sample?
So we got in this case 1.86. Roman letters indicate that these are sample values. Larger sample sizes give smaller standard errors As would be expected, larger sample sizes give smaller standard errors. Standard Error In R JSTOR2682923. ^ Sokal and Rohlf (1981) Biometry: Principles and Practice of Statistics in Biological Research , 2nd ed.
Two data sets will be helpful to illustrate the concept of a sampling distribution and its use to calculate the standard error. Standard Error Of The Mean Excel Manage Subscriptions See All Newsletters Hot Definitions Gross Domestic Product - GDP The monetary value of all the finished goods and services produced within a country's borders in a specific time Another way of considering the standard error is as a measure of the precision of the sample mean.The standard error of the sample mean depends on both the standard deviation and For the purpose of this example, the 9,732 runners who completed the 2012 run are the entire population of interest.
All right. Standard Error Of The Mean Definition However, different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, The distribution of these 20,000 sample means indicate how far the mean of a sample may be from the true population mean.
## Standard Error Of The Mean Excel
All such quantities have uncertainty due to sampling variation, and for all such estimates a standard error can be calculated to indicate the degree of uncertainty.In many publications a ± sign this page In this scenario, the 2000 voters are a sample from all the actual voters. So we take 10 instances of this random variable, average them out, and then plot our average. The notation for standard error can be any one of SE, SEM (for standard error of measurement or mean), or SE. Standard Error Of The Mean Calculator
Blackwell Publishing. 81 (1): 75–81. Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time. ISBN 0-8493-2479-3 p. 626 ^ a b Dietz, David; Barr, Christopher; Çetinkaya-Rundel, Mine (2012), OpenIntro Statistics (Second ed.), openintro.org ^ T.P. http://askmetips.com/standard-error/standard-error-of-measurement-refers-to-the-standard-deviation-of.php Bence (1995) Analysis of short time series: Correcting for autocorrelation.
In statistics, a representative sample accurately represents the make-up of various subgroups in an entire data pool. Standard Error Of Estimate Formula All Rights Reserved. ISBN 0-521-81099-X ^ Kenney, J.
## This section helps you understand what these values mean.
I have had five UK visa refusals What could an aquatic civilization use to write on/with? Because the 5,534 women are the entire population, 23.44 years is the population mean, μ {\displaystyle \mu } , and 3.56 years is the population standard deviation, σ {\displaystyle \sigma } The formula for the SD requires a couple of steps. Standard Error Formula Statistics So let's say we take an n of 16 and n of 25.
Now the sample mean will vary from sample to sample; the way this variation occurs is described by the “sampling distribution” of the mean. Standard error of the mean (SEM) This section will focus on the standard error of the mean. So we could also write this. useful reference Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply.
So I think you know that, in some way, it should be inversely proportional to n. This is more squeezed together. So let's say you have some kind of crazy distribution that looks something like that. Notice that s x ¯ = s n {\displaystyle {\text{s}}_{\bar {x}}\ ={\frac {s}{\sqrt {n}}}} is only an estimate of the true standard error, σ x ¯ = σ n
The confidence interval of 18 to 22 is a quantitative measure of the uncertainty – the possible difference between the true average effect of the drug and the estimate of 20mg/dL. I'll show you that on the simulation app probably later in this video. Of the 2000 voters, 1040 (52%) state that they will vote for candidate A. Relative standard error See also: Relative standard deviation The relative standard error of a sample mean is the standard error divided by the mean and expressed as a percentage.
Standard deviation is going to be the square root of 1. So if this up here has a variance of-- let's say this up here has a variance of 20. Why does Deep Space Nine spin? doi:10.2307/2682923.
A practical result: Decreasing the uncertainty in a mean value estimate by a factor of two requires acquiring four times as many observations in the sample. Student approximation when σ value is unknown Further information: Student's t-distribution §Confidence intervals In many practical applications, the true value of σ is unknown. Compare the true standard error of the mean to the standard error estimated using this sample. v t e Statistics Outline Index Descriptive statistics Continuous data Center Mean arithmetic geometric harmonic Median Mode Dispersion Variance Standard deviation Coefficient of variation Percentile Range Interquartile range Shape Moments
Moreover, this formula works for positive and negative ρ alike.[10] See also unbiased estimation of standard deviation for more discussion. For the runners, the population mean age is 33.87, and the population standard deviation is 9.27. The standard deviation of the age was 3.56 years. | 2017-12-12 06:35:14 | {"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": 0.8285341262817383, "perplexity": 937.0368344217432}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948515309.5/warc/CC-MAIN-20171212060515-20171212080515-00107.warc.gz"} |
https://www.mathworks.com/help/matlab/ref/quiver.html | quiver
Quiver or vector plot
Syntax
``quiver(X,Y,U,V)``
``quiver(U,V)``
``quiver(___,scale)``
``quiver(___,LineSpec)``
``quiver(___,LineSpec,'filled')``
``quiver(___,Name,Value)``
``quiver(ax,___)``
``q = quiver(___)``
Description
example
````quiver(X,Y,U,V)` plots arrows with directional components `U` and `V` at the Cartesian coordinates specified by `X` and `Y`. For example, the first arrow originates from the point `X(1)` and `Y(1)`, extends horizontally according to `U(1)`, and extends vertically according to `V(1)`. By default, the `quiver` function scales the arrow lengths so that they do not overlap.```
````quiver(U,V)` plots arrows with directional components specified by `U` and `V` at equally spaced points. If `U` and `V` are vectors, then the x-coordinates of the arrows range from 1 to the number of elements in `U` and `V`, and the y-coordinates are all 1.If `U` and `V` are matrices, then the x-coordinates of the arrows range from 1 to the number of columns in `U` and `V`, and the y-coordinates of the arrows range from 1 to the number of rows in `U` and `V`. ```
example
````quiver(___,scale)` adjusts the length of arrows: When `scale` is a positive number, the `quiver` function automatically adjusts the lengths of arrows so they do not overlap, then stretches them by a factor of `scale`. For example, a `scale` of 2 doubles the length of arrows, and a `scale` of 0.5 halves the length of arrows.When `scale` is 0, such as `quiver(X,Y,U,V,0)`, then automatic scaling is disabled. ```
example
````quiver(___,LineSpec)` sets the line style, marker, and color. Markers appear at the points specified by `X` and `Y`. If you specify a marker using `LineSpec`, then `quiver` does not display arrowheads. To specify a marker and display arrowheads, set the `Marker` property instead.```
````quiver(___,LineSpec,'filled')` fills the markers specified by `LineSpec`.```
````quiver(___,Name,Value)` specifies quiver properties using one or more name-value pair arguments. For a list of properties, see Quiver Properties. Specify name-value pair arguments after all other input arguments. Name-value pair arguments apply to all of the arrows in the quiver plot.```
example
````quiver(ax,___)` creates the quiver plot in the axes specified by `ax` instead of the current axes (`gca`). The argument `ax` can precede any of the input argument combinations in the previous syntaxes.```
example
````q = quiver(___)` returns a `Quiver` object. This object is useful for controlling the properties of the quiver plot after creating it.```
Examples
collapse all
Load sample data that represents air currents over North America. For this example, select a subset of the data.
```load('wind','x','y','u','v') X = x(11:22,11:22,1); Y = y(11:22,11:22,1); U = u(11:22,11:22,1); V = v(11:22,11:22,1);```
Create a quiver plot of the subset you selected. The vectors `X` and `Y` represent the location of the base of each arrow, and `U` and `V` represent the directional components of each arrow. By default, the `quiver` function shortens the arrows so they do not overlap. Call `axis equal` to use equal data unit lengths along each axis. This makes the arrows point in the correct direction.
```quiver(X,Y,U,V) axis equal```
By default, the `quiver` function shortens arrows so they do not overlap. Disable automatic scaling so that arrow lengths are determined entirely by `U` and `V` by setting the `scale` argument to `0`.
For instance, create a grid of `X` and `Y` values using the `meshgrid` function. Specify the directional components using these values. Then, create a quiver plot with no automatic scaling.
```[X,Y] = meshgrid(0:6,0:6); U = 0.25*X; V = 0.5*Y; quiver(X,Y,U,V,0)```
Plot the gradient and contours of the function $z=x{e}^{-{x}^{2}-{y}^{2}}$. Use the `quiver` function to plot the gradient and the `contour` function to plot the contours.
First, create a grid of x- and y-values that are equally spaced. Use them to calculate z. Then, find the gradient of z by specifying the spacing between points.
```spacing = 0.2; [X,Y] = meshgrid(-2:spacing:2); Z = X.*exp(-X.^2 - Y.^2); [DX,DY] = gradient(Z,spacing);```
Display the gradient vectors as a quiver plot. Then, display contour lines in the same axes. Adjust the display so that the gradient vectors appear perpendicular to the contour lines by calling `axis equal`.
```quiver(X,Y,DX,DY) hold on contour(X,Y,Z) axis equal hold off```
Create a quiver plot and specify a color for the arrows.
```[X,Y] = meshgrid(-pi:pi/8:pi,-pi:pi/8:pi); U = sin(Y); V = cos(X); quiver(X,Y,U,V,'r')```
Create a grid of `X` and `Y` values and two sets of `U` and `V` directional components.
```[X,Y] = meshgrid(0:pi/8:pi,-pi:pi/8:pi); U1 = sin(X); V1 = cos(Y); U2 = sin(Y); V2 = cos(X); ```
Create a tiled layout of plots with two axes, `ax1` and `ax2`. Add a quiver plot and title to each axes. (Before R2019b, use `subplot` instead of `tiledlayout` and `nexttile`.)
```tiledlayout(1,2) ax1 = nexttile; quiver(ax1,X,Y,U1,V1) axis equal title(ax1,'Left Plot') ax2 = nexttile; quiver(ax2,X,Y,U2,V2) axis equal title(ax2,'Right Plot')```
Create a quiver plot and return the quiver object. Then, remove the arrowheads and add dot markers at the base of each arrow.
```[X,Y] = meshgrid(-pi:pi/8:pi,-pi:pi/8:pi); U = sin(Y); V = cos(X); q = quiver(X,Y,U,V); q.ShowArrowHead = 'off'; q.Marker = '.';```
Input Arguments
collapse all
x-coordinates of the bases of arrows, specified as a scalar, a vector, or a matrix.
If `X` and `Y` are vectors and `U` and `V` are matrices, then `quiver` expands `X` and `Y` into matrices. In this case, `size(U)` and `size(V)` must equal `[length(Y) length(X)]`. For more information about expanding vectors into matrices, see `meshgrid`.
If `X` and `Y` are matrices, then `X`, `Y`, `U`, and `V` must be the same size.
y-coordinates of the bases of arrows, specified as a scalar, a vector, or a matrix.
If `X` and `Y` are vectors and `U` and `V` are matrices, then `quiver` expands `X` and `Y` into matrices. In this case, `size(U)` and `size(V)` must equal `[length(Y) length(X)]`. For more information about expanding vectors into matrices, see `meshgrid`.
If `X` and `Y` are matrices, then `X`, `Y`, `U`, and `V` must be the same size.
x-components of arrows, specified as a scalar, vector, or matrix.
If `X` and `Y` are vectors, then `size(U)` and `size(V)` must equal `[length(Y) length(X)]`.
If `X` and `Y` are matrices, then `X`, `Y`, `U`, and `V` must be the same size.
y-components of arrows, specified as a scalar, vector, or matrix.
If `X` and `Y` are vectors, then `size(U)` and `size(V)` must equal `[length(Y) length(X)]`.
If `X` and `Y` are matrices, then `X`, `Y`, `U`, and `V` must be the same size.
Line style, marker, and color, specified as a character vector or string containing symbols. The symbols can appear in any order. You do not need to specify all three characteristics (line style, marker, and color).
If you specify a marker using `LineSpec`, then `quiver` does not display arrowheads. To specify a marker and display arrowheads, set the `Marker` property instead.
Example: `'--or'` is a red dashed line with circle markers
Line StyleDescription
`-`Solid line
`--`Dashed line
`:`Dotted line
`-.`Dash-dot line
MarkerDescription
`'o'`Circle
`'+'`Plus sign
`'*'`Asterisk
`'.'`Point
`'x'`Cross
`'_'`Horizontal line
`'|'`Vertical line
`'s'`Square
`'d'`Diamond
`'^'`Upward-pointing triangle
`'v'`Downward-pointing triangle
`'>'`Right-pointing triangle
`'<'`Left-pointing triangle
`'p'`Pentagram
`'h'`Hexagram
ColorDescription
`y`
yellow
`m`
magenta
`c`
cyan
`r`
red
`g`
green
`b`
blue
`w`
white
`k`
black
Arrow scaling factor, specified as a positive number. By default, the `quiver` function automatically scales the arrows so they do not overlap. The `quiver` function applies the scaling factor after it automatically scales the arrows.
Specifying `scale` is the same as setting the `AutoScaleFactor` property of the quiver object. For example, specifying `scale` as `2` doubles the length of the arrows. Specifying `scale` as `0.5` halves the length of the arrows.
To disable automatic scaling, specify `scale` as 0. When you specify `scale` as 0, the `AutoScale` property of the quiver object is set to `'off'` and the length of the arrow is determined entirely by `U` and `V`.
Target axes, specified as an `Axes` object. If you do not specify the axes, then the `quiver` function uses the current axes.
Name-Value Pair Arguments
Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.
Example: `'Color','r','LineWidth',1`
Note
The properties listed here are only a subset. For a complete list, see Quiver Properties.
Width of arrow stem and head, specified as a scalar numeric value greater than zero in point units. One point equals `1/72` inch. The default value is `0.5` point.
Example: `0.75`
Arrowhead display, specified as `'on'` or `'off'`, or as numeric or logical `1` (`true`) or `0` (`false`). A value of `'on'` is equivalent to `true`, and `'off'` is equivalent to `false`. Thus, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type `matlab.lang.OnOffSwitchState`.
• `'on'` — Display the vectors with arrowheads.
• `'off'` — Display the vectors without arrowheads.
Automatic scaling of arrow length, specified as `'on'` or `'off'`, or as numeric or logical `1` (`true`) or `0` (`false`). A value of `'on'` is equivalent to `true`, and `'off'` is equivalent to `false`. Thus, you can use the value of this property as a logical value. The value is stored as an on/off logical value of type `matlab.lang.OnOffSwitchState`.
• `'on'` — Scale the arrow length to fit within the grid-defined coordinate data and scale arrows so that they do not overlap. The `quiver` or `quiver3` function then applies the `AutoScaleFactor` to the arrow length.
• `'off'` — Do not scale the arrow lengths.
Scale factor, specified as a scalar. A value of `2` doubles the length of the arrows. A value of `0.5` halves the length of the arrows.
This property has an effect only if the `AutoScale` property is set to `'on'`.
Example: `2`
Tips
To create a quiver plot using polar coordinates, first convert them to Cartesian coordinates using the `pol2cart` function. | 2021-01-23 15:40:18 | {"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": 0.8785200715065002, "perplexity": 973.4469010831227}, "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-2021-04/segments/1610703538082.57/warc/CC-MAIN-20210123125715-20210123155715-00514.warc.gz"} |
http://physics.stackexchange.com/questions/53385/probability-and-probability-amplitude | # Probability and probability amplitude
What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the statistical mathematics a similar equation where we calculate probability like $P=\left|x\right|^2$ where $x$ is whatever?
-
"[F]or a detailed reconstruction of the historical origin of the Born rule within the context of quantum mechanics," see: J. Mehra and H. Rechenberg, The Historical Development of Quantum Theory. Vol. 6: The Completion of Quantum Mechanics 1926–1941. Part 1: The Probabilistic Interpretation and the Empirical and Mathematical Foundation of Quantum Mechanics, 1926-1936, Springer-Verlag, New York, 2000. Source. – Gugg Feb 8 at 13:46
I'm not quite sure what the historical origin was, but the Stern-Gerlach experiment and particularly variations with multiple Stern-Gerlach filters can teach us a lot about probabilities in QM. I might write up a more detailed answer in the future but at the moment I don't really have the time. – Wouter Feb 8 at 15:12
Earlier, related question by the same poster: physics.stackexchange.com/questions/51962/… – dmckee Feb 8 at 15:44 | 2013-05-23 04:42:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7874398827552795, "perplexity": 538.168937425629}, "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-2013-20/segments/1368702810651/warc/CC-MAIN-20130516111330-00041-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://docs.codegra.de/guides/use-codegrade-as-a-student.html | # How to use CodeGrade as a student¶
Using CodeGrade as a student is easy and offers you the ability to get a lot more feedback and optionally automated test results.
When you open an assignment in CodeGrade or your LMS (Blackboard, Brightspace, Canvas, Moddle, etc.) you are presented with a number of actions you can perform.
• Latest submission: Go to your latest submission.
• Set up Git: Show instructions on how to connect a Git provider to your assignment, this allows you to create submissions by pushing to a Git repository.
• Rubric: Show the rubric of this assignment.
• Groups: Create and/or join groups.
Note
Some of these are not available when they are not applicable, e.g. when an assignment is not set up as a group assignment, the groups button will be hidden.
## Handing in¶
1. Click the “Upload files” button.
2. Optionally, if the teacher has set hand-in instructions, they are displayed at the top of the page. Make sure to follow your teacher’s requirements when uploading files!
3. You can either drag and drop files onto the upload field or select them via your browser’s file picker dialog. You can either upload separate files, or an archive (such as a zip or tar). Archives are automatically extracted (but archives contained in other archives are not).
4. Press submit.
5. If the teacher enabled Continuous Feedback, you will now be able to see Automated Test results coming in (this might take a few minutes).
Note
Keep in mind that Continuous Feedback is preliminary, and the rubric will not yet be filled in. You only get a grade after the deadline when the teacher graded your assignment.
1. Click on tests to see why they succeeded or failed. Improve your code and try again.
Note
### Handing in with Git¶
Some CodeGrade assignments allow you to hand in code by pushing to a Git repository (GitLab or Github). If an assignment is set up to allow for Git submissions the “Set up Git” button shows you instructions on how to set up a deploy key and webhook URL for your repository.
Note
Working in a group and handing in using Git? Make sure all members of the group have opened the CodeGrade assignment in Canvas, Moodle, Blackboard or Brightspace before handing in. This does not apply to stand- alone usage of CodeGrade!
Warning
CodeGrade has a size limit for uploading submissions. Handing in via git can result in files exceeding this size limit to be silently deleted. Always check your submission in CodeGrade when working with large repositories. If the size limit is exceeded, a file named cg-size-limit-exceeded will show up in your submission. | 2020-04-09 19:34:34 | {"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": 0.2386312186717987, "perplexity": 3508.1196001921594}, "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/1585371876625.96/warc/CC-MAIN-20200409185507-20200409220007-00410.warc.gz"} |
https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-8-polynomials-and-factoring-8-2-multiplying-and-factoring-lesson-check-page-494/5 | ## Algebra 1: Common Core (15th Edition)
Find the greatest common factor. Find the factors of each term and multiply the factors that are common to all the terms. $21n^3=7×3×n×n×n$ $18n^2=6×3×n×n$ $GCF=3×n×n=3n^2$ | 2021-04-19 01:53:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.3917642831802368, "perplexity": 439.29231025614973}, "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/1618038863420.65/warc/CC-MAIN-20210419015157-20210419045157-00251.warc.gz"} |
http://math.stackexchange.com/questions/802043/what-does-this-question-about-a-matrix-mean/802047 | # what does this question about a matrix mean?
here is a question says :
what does that mean ?
I did my best to solve this question myself but i didn't find a way to solve it
is this question possible or there is something else that i don't understand it
the matrix is square ..
how it changes to singular?
-
## 1 Answer
A singular matrix is a matrix which does not have an inverse. A matrix has an inverse if and only if its determinant is nonzero. Take the determinant and find the value(s) of $\alpha$ which makes the determinant zero. Then just take the $\alpha$ such that it means the condition of the problem - that is, $0 \leq \alpha <2\pi$.
-
THANKS ! .......... ..... – Maher May 19 '14 at 21:18
but ! we know that a matrix of order " size " $n*n$ is called a square matrix .. and the above matrix is $2*2$ matrix .. so even if it has not an inverse it is still square ?? confusion ?? – Maher May 19 '14 at 21:32
We only consider the determinant for square matrices and the only consider matrices to even possibly having an inverse if the matrix is square. But keep in mind just because a matrix is square doesn't mean that it will have an inverse. So to sum up, for the question asking about a determinant of a matrix or its inverse, the question only makes sense if the matrix is square. But just being square isn't enough. There is more to check - that is, that the determinant of the matrix is not zero. You need both square AND nonzero determinant. – mathematics2x2life May 19 '14 at 21:36 | 2016-02-13 15:40:15 | {"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": 0.9012351632118225, "perplexity": 184.98013783330416}, "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-2016-07/segments/1454701166739.77/warc/CC-MAIN-20160205193926-00253-ip-10-236-182-209.ec2.internal.warc.gz"} |
http://www.benjaminborn.de/HANK_BusinessCycleAndInequality/build/linearization.html | # Linear perturbation around steady state
Note
The main functions of this section are in the folder 5_LinearizationFunctions.
The model is linearized with respect to aggregate variables. For this, we write the equilibrium conditions in the form of $F(X,X')=0$, where $X$ and $X'$ are (expected) deviations from steady state in two successive periods. Applying the total differential yields $A*X' = - B*X$, where $A$,$B$ are the first derivatives of $F$ with respect to $X'$,$X$. In the standard setting, we use the generalized Schur decomposition [Klein] to transform this equation into a linearized observation equation $d = gx*k$ and a linearized state transition equation $k' = hx*k$, where $k$ is a vector of the state variables and $d$ is a vector of the control variables ($X = \begin{bmatrix} k \\ d \end{bmatrix}$).
In our code, $F$ is implemented as HANKEstim.Fsys(), while differentiating and solving for $gx$ and $hx$ is done in HANKEstim.SGU(), and linearize_full_model() returns the results as a struct LinearResults:
HANKEstim.linearize_full_modelFunction
linearize_full_model()
Linearize the full model (i.e. including idiosyncratic states and controls) around the steady state, and solves using SGU().
Returns
struct LinearResults, containing
• A::Array{Float64,2},B::Array{Float64,2}: first derivatives of Fsys() with respect to arguments X [B] and XPrime [A]
• State2Control::Array{Float64,2}: observation equation
• LOMstate::Array{Float64,2}: state transition equation
source
## Overview of SGU()
HANKEstim.SGUFunction
SGU(sr, m_par, A, B; estim)
Calculate the linearized solution to the non-linear difference equations defined by function Fsys(), using Schmitt-Grohé & Uribe (JEDC 2004) style linearization (apply the implicit function theorem to obtain linear observation and state transition equations).
The Jacobian is calculated using the package ForwardDiff
Arguments
• sr: steady-state structure (variable values, indexes, numerical parameters, ...)
• A,B: derivative of Fsys() with respect to arguments X [B] and XPrime [A]
• m_par: model parameters
Returns
• gx,hx: observation equations [gx] and state transition equations [hx]
• alarm_sgu,nk: alarm_sgu=true when solving algorithm fails, nk number of predetermined variables
• A,B: first derivatives of Fsys() with respect to arguments X [B] and XPrime [A]
source
The function executes the following steps:
• generate devices to retrieve distribution and marginal value functions from compressed states/controls (Γ and DC,IDC)
• calculate the first derivative of HANKEstim.Fsys() with respect to X and XPrime. We use automatic differentiation (implemented in Julia by the package ForwardDiff). Partial derivatives are calculated using the ForwardDiff.jacobian() function. We exploit that some partial derivatives have known values (contemporaneous marginal value functions and the future marginal distributions) and set them directly instead of calculating them [BL].
• compute linear observation and state transition equations using the HANKEstim.SolveDiffEq() function
## Overview of SolveDiffEq()'
HANKEstim.SolveDiffEqFunction
SolveDiffEq(A, B, n_par; estim)
Calculate the solution to the linearized difference equations defined as P'BP xt = P'AP x{t+1}, where P is the (ntotal x r) semi-unitary model reduction matrix n_par.PRightAll of potentially reduced rank r.
Arguments
• A,B: matrices with first derivatives
• n_par::NumericalParameters: n_par.sol_algo determines the solution algorithm, options are:
• litx: Linear time iteration (implementation follows Reiter)
• schur: Klein's algorithm (preferable if number of controls is small)
Returns
• gx,hx: observation equations [gx] and state transition equations [hx]
• alarm_sgu,nk: alarm_sgu=true when solving algorithm fails, nk number of predetermined variables
source
• compute linear observation and state transition equations. The solution algorithm is set in n_par.sol_algo, with the options :schur (mentioned above) and :litx [lit]. The results are matrices that map contemporaneous states to controls [gx], or contemporaneous states to future states [hx]
## Overview of Fsys()
HANKEstim.FsysFunction
Fsys(X, XPrime, Xss, m_par, n_par, indexes, Γ, compressionIndexes, DC, IDC, DCD, IDCD)
Equilibrium error function: returns deviations from equilibrium around steady state.
Split computation into Aggregate Part, handled by Fsys_agg(), and Heterogeneous Agent Part.
Arguments
• X,XPrime: deviations from steady state in periods t [X] and t+1 [XPrime]
• Xss: states and controls in steady state
• Γ, DC, IDC, DCD,IDCD: transformation matrices to retrieve marginal distributions [Γ], marginal value functions [DC,IDC], and the (linear) interpolant of the copula [DCD,IDCD] from deviations
• indexes,compressionIndexes: access Xss by variable names (DCT coefficients of compressed $V_m$ and $V_k$ in case of compressionIndexes)
Example
julia> # Solve for steady state, construct Γ,DC,IDC as in SGU()
julia> Fsys(zeros(ntotal),zeros(ntotal),XSS,m_par,n_par,indexes,Γ,compressionIndexes,DC,IDC)
*ntotal*-element Array{Float64,1}:
0.0
0.0
...
0.0
source
The function HANKEstim.Fsys() proceeds in the following way:
1. set up vector F, that contains the errors to all equilibrium conditions. There are as many conditions as deviations from steady state (length of X,XPrime), and conditions are indexed with respective model variable in IndexStruct indexes
2. generate locally all aggregate variables (for both periods) using @generate_equations
3. construct the full-grid marginal distributions, marginal value functions, and the copula from the steady-state values and the (compressed) deviations (for the copula, the selection of DCT coefficients that can be perturbed ensures that also the perturbed function is a copula)
4. write all equilibrium condition-errors with respect to aggregate variables to F, using HANKEstim.Fsys_agg()
5. compute optimal policies with HANKEstim.EGM_policyupdate(), given future marginal value functions, prices, and individual incomes. Infer present marginal value functions from them (envelope theorem) and set the difference to assumed present marginal value functions (in terms of their compressed deviation from steady state) as equilibrium condition-errors (backward iteration of the value function)
6. compute future marginal distributions and the copula (on the copula grid) from previous distribution and optimal asset policies. Interpolate when necessary. Set difference to assumed future marginal distributions and copula values on the copula nodes as equilibrium condition-errors (forward iteration of the distribution)
7. compute distribution summary statistics with HANKEstim.distrSummaries() and write equilibrium conditions with their respective (control) variables
8. return F
Note that the copula is treated as the sum of two interpolants. An interpolant based on the steady-state distribution using the full steady-state marginals as a grid and a "deviations"-function that is defined on the copula grid generated in prepare_linearization(). The actual interpolation is carried out with HANKEstim.myinterpolate3(). Default setting is trilinear interpolation, the code also allows for 3d-Akima interpolation.
### Called functions / macros
HANKEstim.@generate_equationsMacro
@generate_equations()
Write out the expansions around steady state for all variables in aggr_names, i.e. generate code that reads aggregate states/controls from steady state deviations.
Equations take the form of (with variable r as example):
• r = exp.(Xss[indexes.rSS] .+ X[indexes.r])
• rPrime = exp.(Xss[indexes.rSS] .+ XPrime[indexes.r])
Requires
(module) global aggr_names
source
HANKEstim.Fsys_aggFunction
Fsys_agg(X, XPrime, Xss, distrSS, m_par, n_par, indexes)
Return deviations from aggregate equilibrium conditions.
indexes can be both IndexStruct or IndexStructAggr; in the latter case (which is how function is called by SGU_estim()), variable-vectors X,XPrime, and Xss only contain the aggregate variables of the model.
source
HANKEstim.myinterpolate3Function
myinterpolate3(xgrd1, xgrd2, xgrd3, ygrd, xeval1, xeval2, xeval3)
Trilineary project ygrd on (xgrd1,xgrd2,xgrd3) and use it to interpolate value at (xeval1,xeval2,xeval3).
Example
julia> xgrd = [1.0,6.0];
julia> f((x,y,z)) = x+y+z;
julia> ygrd = f.(collect(Iterators.product(xgrid,xgrid,xgrid));
julia> xeval = [3.0,5.0];
julia> mylinearinterpolate3(xgrd,xgrd,xgrd,ygrd,xeval,xeval,xeval)
2x2x2 Array{Float64,3}:
[:,:,1] =
9.0 11.0
11.0 13.0
[:,:,2] =
11.0 13.0
13.0 15.0`
source | 2022-10-04 07:14:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.7835186123847961, "perplexity": 6657.6703087510905}, "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/1664030337480.10/warc/CC-MAIN-20221004054641-20221004084641-00082.warc.gz"} |
https://support.bioconductor.org/p/125119/ | Question: DESeq2 indirect batch effect removal
0
7 weeks ago by
University Hospital Jena, Germany
Nicolas Huber0 wrote:
Hi, I use DESeq2 in R for differential expression calculation. I already know the design is terrible, but this is what I have to work with ;) Question 1: can I remove the batch effect between 2 groups if their samples do not share a batch, but some of their samples share a batch with a third group? (groups are different genotypes, batches are different experiments) Example: I want to compare group gA (samples s1, s2, s3) with group gC (samples s8, s9, s10, s11). These samples come from different batches (batch bX and bY), but no sample of group gA shares a batch with samples from group gC, so a batch effect removal would be impossible. However, there is group gB (samples s4, s5, s6, s7), which has 2 samples from batch bX and 2 from batch bY.
myColData <- data.frame(row.names=c("s1","s2","s3","s4","s5","s6","s7","s8","s9","s10","s11"),
group=c("gA","gA","gA","gB","gB","gB","gB","gC","gC","gC", "gC"),
batch=c("bX","bX","bX","bX","bX","bY","bY","bY","bY","bY", "bY"))
print(myColData)
myCounts <- matrix(round(runif(1100, 0, 20)), ncol=11, nrow=100)
My approach would be to 1) initiate a DESeq object, with known batch effect in the design 2) apply the DESeq function over it 3) calculate the results of that with only gC and gA given in the contrast
library(DESeq2)
myDE1 <- DESeqDataSetFromMatrix(myCounts, colData=myColData, design=~batch+group)
myDE2 <- DESeq(myDE1)
myDE3 <- results(myDE2, contrast=c("group", "gC", "gA"))
My 1st question: Is this a correct way to handle the batch effect? My 2nd question: Let's assume there is no batch here, just the groups. DESeq2 will give different results when I give as input (step 1) the whole matrix with all samples and then compare (in step 3) only the groups I care about (as done above, Input was gA, gB and gC but I am only interested in gC vs. gA), compared with when I give a matrix with only the groups of Interest to begin with. Is one of the ways incorrect? Shouldn't the results (myDE03 & myDE13) theoretically be the same?
#input whole matrix, compare only gC and gA in the end
myDE01 <- DESeqDataSetFromMatrix(myCounts, colData=myColData, design=~group)
myDE02 <- DESeq(myDE01)
myDE03 <- results(myDE02, contrast=c("group", "gC", "gA"))
myDE03
#input only samples from gC and gA and compare them
myDE11 <- DESeqDataSetFromMatrix(myCounts[,c(1:3,8:11)], colData=myColData[c(1:3,8:11),], design=~group)
myDE12 <- DESeq(myDE11)
myDE13 <- results(myDE12, contrast=c("group", "gC", "gA"))
myDE13
Any help is appreciated
deseq2 batch • 94 views
modified 6 weeks ago by Michael Love26k • written 7 weeks ago by Nicolas Huber0
Answer: DESeq2 indirect batch effect removal
2
6 weeks ago by
Michael Love26k
United States
Michael Love26k wrote:
> myColData
group batch
s1 gA bX
s2 gA bX
s3 gA bX
s4 gB bX
s5 gB bX
s6 gB bY
s7 gB bY
s8 gC bY
s9 gC bY
s10 gC bY
s11 gC bY
DESeq2 will give different results when I give as input (step 1) the whole matrix with all samples and then compare (in step 3) only the groups I care about (as done above, Input was gA, gB and gC but I am only interested in gC vs. gA), compared with when I give a matrix with only the groups of Interest to begin with. Is one of the ways incorrect?
This is a FAQ in our vignette.
thanks for the answer, I am just not sure I understand it correctly. So the first two code snippets I posted are the correct way to handle this situation with DESeq2?
The 2nd question (with the 3rd code snippet) is not about the batch effect, I just observed that results differ when having different matrix inputs, even though the samples that are compared are the same (just the presence of other samples changes the calculation apparently).
1
So the first two code snippets I posted are the correct way to handle this situation with DESeq2?
Yes
I just observed that results differ when having different matrix inputs, even though the samples that are compared are the same (just the presence of other samples changes the calculation apparently).
Yes, this is expected. And it is in our FAQ in the vignette. | 2019-11-20 05:52:20 | {"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": 0.4327246844768524, "perplexity": 3537.495120260471}, "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/1573496670448.67/warc/CC-MAIN-20191120033221-20191120061221-00336.warc.gz"} |
https://socratic.org/questions/what-are-the-intercepts-of-7x-5y-4 | # What are the intercepts of 7x-5y=4?
##### 1 Answer
Nov 25, 2015
Have a look at http://socratic.org/s/apEzpX45
Foe method of approach. | 2020-01-22 18:06:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 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": 0.4427984356880188, "perplexity": 10875.292719722964}, "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-2020-05/segments/1579250607314.32/warc/CC-MAIN-20200122161553-20200122190553-00130.warc.gz"} |
http://physics.stackexchange.com/questions/100982/what-is-the-cause-of-centripetal-centrifugal-force?answertab=votes | # What is the cause of centripetal/centrifugal force?
What is the cause of centripetal/centrifugal force? When an object of mass $m$ is moved in a circular orbit, it experiences a centrifugal force radially away from the center. What is the cause of this centrifugal force? Is these related to the four fundamental forces (gravity,electromagnetic,weak and strong forces)?
This force is equivalent to a force experienced while stopping a mass in motion (Inertia). But is this inertia caused by some force? or what causes inertia? A photon particle does not have inertia of rest.
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It experiences no such force. Who told you that? As an aside, I suggest you read an introductory Physics text to learn the difference between an applied force (e.g. pushing something) and force due to a field. – Carl Witthoft Feb 26 at 14:52
The force away from the center, which comes from the non-inertial coordinate system, is centrifugal force. The force toward the center, which keeps the object in orbit, is centripetal force. It can come from various sources: gravity, EM, tension in a string, etc. – Ross Millikan Feb 26 at 15:21
Though this question is a bit naive, I don't see the point in the down vote. It is a fair question. Anupam hits the nail on the head, by the way. – wgrenard Feb 26 at 16:05
Related: physics.stackexchange.com/q/8891/2451 and links therein. – Qmechanic Feb 26 at 17:48
Deepak i noticed that your question is changed. Do you know about centrifugal force too in detail? To answer the first line of your question i have to explain the cause of centrifugal force. – user31782 Feb 27 at 4:39
Firstly you need to understand Newton's law's. basically the second law. Concisely second law is :"whenever we apply a force on an object this force changes object's velocity's magnitude if it is in the same direction as that of the direction of motion and changes the direction of motion if the applied force is not in the direction of motion."
When an object rotates uniformly in a circular orbit it doesn't experience any force(real or/and pseudo) radially outward. What it experience is the centripetal force which is always radially inward as measured from the co-ordinate system in which it rotates and is given by
$F={\dfrac{mv^2}{r}}$ where $m$ is the mass of that object, $v$ is the tangential instantaneous speed and $r$ is the radius of the circle in which it is rotating.
See this picture to visualize this:
To deviate the motion of an object from straight to circular we have to apply a force radially inward because due to inertia the object tends to move in a straight line. The force we apply changes velocity of that object by changing the direction of motion.
It should be noted if the force is calculated from some non-inertial frame of reference then we will have to add a pseudo force on that object but the motion will not remain circular in this non-inertial frame.
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And to add to a good answer: centrifugal force is an illusion - it is just a name people give to the unrestricted, inertia-guided movement when a centripetal force stops (e.g. when a string snaps). – Amadan Feb 27 at 1:50
@Amadan CEntrifugal force is not an illusion. Nor it is inertia guided. It only comes into play when we switch our frame of reference to a revolving one. This appears to hold Newton's second law. I edit my answer soon. – user31782 Feb 27 at 10:55
A centripetal force is not a fundamental force. We call any force a centripetal force if it is acting towards the center of the direction of rotation, perpendicular to the direction of motion.
Rotating a rock tied on a string? Centripetal force = tension in the string
Satellite orbiting Earth? Centripetal force = gravity
Charged object rotating around an opposite charge? Centripetal force = electromagnetic force.
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In an important sense, centripetal force is not a force at all. Consider an object executing simple circular motion. Add up all the forces on the object. The resultant (net) force point toward the center, and we call it centripetal. The centripetal force is the sum of the real forces, not an interaction between two objects, not a separate force itself. – garyp Feb 26 at 22:33
Anupam has very well answered, I'll just add my modest contribution with a simple example: the inertial frame could be the Earth and the non-inertial frame a car moving in a circle. In that case the centripetal force is the reaction of the tyres on the ground due to their grip, but the most interesting thing about this case is that objects in the car seem to be pushed outward. In reality (meaning, in an inertial frame, which the Earth can be considered for a short duration) they simply tend to continue in a straight line: this force, the centrifugal force, is only fictitious and is due to the fact that the lines that solids tend to go along in inertial frames might not be lines in a non-inertial frame (viewpoint problem). The car itself experiences the centrifugal force because after all it is yet just another thing bound in a non rigid way (i.e. suspensions) to the tyres which propagate the centripetal force. This is why they can topple at great speeds (higher centrifugal force).
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Centripetal forces are not forces which are developed on their own; actually, it is produced under the action of different forces FOR EXAMPLE: If a man moves on a road in circular path. Centripetal force is provided by FRICTIONAL FORCE Similarly when earth moves around sun the centripetal force is provided by the gravitational force. So, the centripetal force is not a force itself; it can be produced under the action of several forces.
- | 2014-12-22 02:57:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5851700901985168, "perplexity": 398.456836512287}, "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-2014-52/segments/1418802773061.155/warc/CC-MAIN-20141217075253-00058-ip-10-231-17-201.ec2.internal.warc.gz"} |
https://maker.pro/forums/threads/understanding-magnitude-and-phase-bode-plots.252211/ | Understanding magnitude and phase Bode plots.
paris
Sep 15, 2012
2
I'm having problems understanding Bode plots. I've been studying from this website:
http://lpsa.swarthmore.edu/Bode/BodeExamples.html
And I understood the concept of poles, zeros, increasing at 20dB/decade, transfer functions, etc etc.. What I don't understand (taken Example 3) is how to draw the final construction of the these bode plots.. In the case of the magnitude plot of what I understood, isn't the final plot supposed to begin at 30dB, decrease to 20dB, decrease again to 0dB at real pole at -3 and increase at real zero at -10? However, I don't get why does the exact plot begins before 40dB and continues to decrease past the real pole at -3..
The same goes for the phase plot. I understood how to construct the plots according to each pole and zero, but I don't understand how to get to the final plot at the end. I hope I make some sense and I hope someone could help me clear some of my doubts.
paris
Sep 15, 2012
2
TYPO:
*continues to decrease past the real zero at -10..
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2K | 2022-09-30 19:59:50 | {"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": 0.8514429926872253, "perplexity": 821.7177378014142}, "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-2022-40/segments/1664030335504.22/warc/CC-MAIN-20220930181143-20220930211143-00550.warc.gz"} |
https://homework.cpm.org/category/CCI_CT/textbook/cc4/chapter/3/lesson/3.1.1/problem/3-13 | ### Home > CC4 > Chapter 3 > Lesson 3.1.1 > Problem3-13
3-13.
Draw a slope triangle and use it to write the equation of the line shown in the graph at right
Review the Math Notes box in Lesson 2.2.2.
$y = \frac{7}{2}\textit{x}+2$ | 2019-08-18 19:38:17 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "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": 0.37247657775878906, "perplexity": 2417.970287486666}, "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/1566027313996.39/warc/CC-MAIN-20190818185421-20190818211421-00101.warc.gz"} |
https://www.scienceforums.net/topic/122213-the-killing-of-george-floyd-the-last-straw/page/5/ | # The Killing of George Floyd: The Last Straw?
## Recommended Posts
1 minute ago, Moreno said:
This is bad, of course. But there is some difference between a racial genocide as covert/open government program and an individual psycho. Are an individual white racists more common than colored racists? Including police officers? If yes, why? I thought that all races are equal and therefore racism (and racism motivated crime) should be equally common among them all.
Because some people have been on the receiving end of racism for much longer than others, potentially making their experiences different. But the problem is that currently white people hold much more societal power than those with other skin colours and those that are parts of religions that are not Christianity. This means that even if there would be equal racism among all people, the consequences disproportionately affect non-white/non-Christian (in the western world!) people. Hence people speak of systemic racism, yes it may be (please note that I am not saying this is the case) the case that if most power in the USA and other western countries would lie in people of colour, they would be equally racist. But they are not in power (generally) and thus the current issue is that they are disproportionally discriminated against. If we ever get to a position where it is the other away around, then we have a different issue to solve.
• Replies 455
• Created
#### Posted Images
25 minutes ago, Moreno said:
This is bad, of course. But there is some difference between a racial genocide as covert/open government program and an individual psycho. Are an individual white racists more common than colored racists? Including police officers? If yes, why? I thought that all races are equal and therefore racism (and racism motivated crime) should be equally common among them all.
Even if prejudice is equally common across all groups, that is not the point. It misses the point by several light years.
White people are in positions of privilege, authority and power. They have the power to exploit and abuse black people (and other minorities) with impunity.
Even without that, they have advantages because of their privilege: they don't have to put up with daily insults because of their race, they don't get treated with suspicion whenever they go shopping, they don't have to worry about being repeatedly stopped by the police for no reason, they don't have to teach their children how not to be killed by the police.
17 minutes ago, Dagl1 said:
Because some people have been on the receiving end of racism for much longer than others, potentially making their experiences different.
Quote
But freedom is not enough. You do not wipe away the scars of centuries by saying: Now you are free to go where you want, and do as you desire, and choose the leaders you please.
You do not take a person who, for years, has been hobbled by chains and liberate him, bring him up to the starting line of a race and then say, “you are free to compete with all the others,” and still justly believe that you have been completely fair.
President Lyndon Johnson
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3 minutes ago, Strange said:
Even if prejudice is equally common across all groups, that is not the point. It missis the point by several light years.
White people are in positions of privilege, authority and power. They have the power to exploit and abuse black people (and other minorities) with impunity.
Even without that, they have advantages because of their privilege: they don't have to put up with daily insults because of their race, they don't get treated with suspicion whenever they go shopping, they don't have to worry about being repeatedly stopped by the police for no reason, they don't have to teach their children how not to be killed by the police.
President Lyndon Johnson
You said it more clearly than I did!
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53 minutes ago, Moreno said:
This is bad, of course. But there is some difference between a racial genocide as covert/open government program and an individual psycho. Are an individual white racists more common than colored racists? Including police officers? If yes, why? I thought that all races are equal and therefore racism (and racism motivated crime) should be equally common among them all.
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I do 'get' it, Dim, Zap, CY, INow, and all who have tried explaining.
My concern is that often we find 'hidden' meaning in certain words or phrases.
Usually because our perception of those words or phrases are colored by our life experiences.
And not to make light of a person losing his life to deliberate brutality, but this incident couldn't have come at a worse time.
In about a week there will be an explosion of Covid-19 cases all across the US.
And of course, predominantly in the communities that took part in the protests.
How many more will die ?
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8 hours ago, iNow said:
Your understanding isn’t accurate. You should fix that.
Please, quantify this. For “too many?” How many? I’ll accept and order if magnitude estimate. Becomes “too often?” How often? One in five? In ten? A hundred? A million?
Going by the rhetoric commonly espoused by political leaders probably 30%, but let's say it's half of that, 15% of those forming an opinion, and rising every time the rhetoric on one side gets repeated. (with the other side views getting polarized similarly as a result and with most willing to say anything mostly talking past each other
8 hours ago, iNow said:
Knowing you won’t be able answer my entirely reasonable request in an even remotely satisfactory way...
With respect to accuracy? Probably not. With respect to emotion? Definitely not.
8 hours ago, iNow said:
perhaps we can simply agree there is a problem affecting Americans of specific ethnicities in an asymmetric way and that we should be allies in making things better, even if better often falls short of perfect.
Agree.
The hard part is how best to proceed.
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10 minutes ago, MigL said:
And not to make light of a person losing his life to deliberate brutality, but this incident couldn't have come at a worse time.
In about a week there will be an explosion of Covid-19 cases all across the US.
And of course, predominantly in the communities that took part in the protests.
How many more will die ?
I don't think this is making light. It is likely to be a major problem. And, of course, it is blacks and other minorities who are worse hit by Covid-19 (for a variety of reasons).
Making light of it would be to suggest that Trump will be recommending tear gas as a cure.
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13 hours ago, iNow said:
I think that your fixation on the racial part of whats happening in the US for the past week/months/years is not healthy and certainly not giving the broad picture of whats really going on. I am not surprised to see that though, after all US is a highly racist place and always has been.
People, especially the lower middle class have had enough of the quarantine and are going nuts. The murder of George Floyd (I hope the cop never gets out of jail one way or another) was just a drop that tipped the scale. People started looting and burning down cities, dozens of the phone recorded clips Ive seen for the past week are all saying the same thing - people went nuts and need to be contained and unfortunately its that morons POTUS’s job to do so. I see this whole thing through the lens of firearms - if cops in the US weren’t afraid that every single person on the streets is carying a gun this whole situation would be completely different. I don’t know what needs to happen for Americans to understand this, Im not sure its even possible at this point.
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22 minutes ago, koti said:
People, especially the lower middle class have had enough of the quarantine and are going nuts.
While this may have exacerbated things, and encouraged more young (often white) kids to join in for the "fun" and looting, the underlying problem is real and almost entirely a problem of race. We have seen the same scenes pay out before (in the USA and the UK) for very similar reasons. Unfortunately, in the USA, almost nothing has changed.
After the Brixton riots, the local police did change their behaviour somewhat which improved the situation. But if you're a young, black male you are still going to be treated with suspicion.
27 minutes ago, koti said:
if cops in the US weren’t afraid that every single person on the streets is carying a gun this whole situation would be completely different.
Yeah, that doesn't help.
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1 hour ago, J.C.MacSwell said:
Going by the rhetoric commonly espoused by political leaders probably 30%, but let's say it's half of that, 15% of those forming an opinion, and rising every time the rhetoric on one side gets repeated
Well, since we're now just pulling numbers out of our ass, I'll tell you you're wrong, and that the number is actually less than 0.5%. See! Amazing how we can make any argument when we make up numbers.
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1 hour ago, MigL said:
I do 'get' it, Dim, Zap, CY, INow, and all who have tried explaining.
My concern is that often we find 'hidden' meaning in certain words or phrases.
Usually because our perception of those words or phrases are colored by our life experiences.
And not to make light of a person losing his life to deliberate brutality, but this incident couldn't have come at a worse time.
In about a week there will be an explosion of Covid-19 cases all across the US.
And of course, predominantly in the communities that took part in the protests.
How many more will die ?
Except you kind of are, and you're off topic.
If the protestor's are willing to face a foe that has a track record of openly killing people, with a leader who is actively encouraging them to do so.
I don't imagine the prosect of a cold, possibly worse, is much of a deterant.
Edited by dimreepr
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1 hour ago, J.C.MacSwell said:
The hard part is how best to proceed.
I knew you'd be willing to be an ally on this, so thanks. More than anything, we just need to ensure we actually DO move forward. It seems so often these conversations just die on the vine and we find ourselves in the exact same places again in just a few short weeks when it happens next time.
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34 minutes ago, koti said:
if cops in the US weren’t afraid that every single person on the streets is carying a gun this whole situation would be completely different.
If the cops in the US weren't "taught/trained" to be afraid that every single person on the streets is carying a gun this whole situation would be completely different. (FTFY)
De-escalation training has been shown to reduce death, in both the police and the public.
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35 minutes ago, koti said:
I think that your fixation on the racial part of whats happening in the US for the past week/months/years is not healthy
You're welcome to think whatever you want. My "fixation" is on the fact that these trends are deep rooted, well established, and persistent. We are all citizens equally protected, yet those protections are not equally applied. Whether it's in policing, experience with the justice system and imprisonment, education and dilapidated schools, red lined districts preventing home-ownership and creation of wealth, access to fresh foods, being spoke to as "less than" in daily interactions or viewed with suspicion for doing perfectly normal things like bird watching...
The "racial part" of what's happening is the important part right now, and suggesting that it's not is unfortunately indicative of little more than your own white privilege.
White guy guns down a church full of people praying or a school full of children? Gently walked out by authorities and respectfully given due process of the law. White guys arrive to a state capitols and start waving semi-automatic rifles around in the governors mansion or saying the only good democrat is a dead democrat? They're called very fine people and allowed to remain there to share their message of protest without intervention from the police.
But when a black guy sells some loose cigarettes on the street for a buck a pop, or 12 year old boy squirting water out of a squirt gun at a park, or man uses an allegedly forged $20 bill at a convenience store? Dead from police. A white guy using a forged$20 bill at a store has a fun story he tells at parties for the next few years. A black guy using a forged $20 bill at a store has a headstone and an orphaned family. What's not healthy is the american system of quote unquote justice and the way so many americans can't seem to see how drastically different their experience is from their neighbors, but if you wish to instead focus on me for rightly highlighting these facts and hoping to perhaps inspire some modicum of support for change and improvements, well... then that's your prerogative and you're fee to do so. 5 minutes ago, dimreepr said: If the cops in the US weren't "taught/trained" to be afraid that every single person on the streets is carying a gun this whole situation would be completely different. (FTFY) De-escalation training has been shown to reduce death, in both the police and the public. Studies have also shown that the police departments which purpose more retired equipment from the military for use in local towns tend to have higher rates of death by cop and restrictions to constitutionally protected freedoms in their areas. It's the "when all you have is a hammer everything looks like a nail" situation ##### Link to comment ##### Share on other sites 15 hours ago, Strange said: That is a ridiculous statement. If this statistic is related to white racism somehow, then it is curious to discover that white racist police officers hate other whites much more than Asians/Pacific Islanders as they kill their own whites much more often in relative proportions. Average income in USA by ethnicity. The wealthiest are East Indians at$132,746 by household. Followed by all other Asians.
Very strange "systematic racism" indeed.
Edited by Moreno
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6 minutes ago, Moreno said:
If this statistic is related to white racism somehow, then it is curious to discover that white racist police officers hate other whites much more than Asians/Pacific Islanders as they kill their own whites much more often in relative proportions.
Maybe it is an interesting thing to research yes, but does this, together with other people's explanation and Dimreepr's video explain to you the problem people (non-white/non-christian) are facing? Your previous posts seemed to ask why these things were problems, did these questions get answered and do you understand the problems and why people are currently battling racism coming from white people that is ingrained in the system (within the USA, and possibly other places in the western world)? Do you agree that white-people disproportionately hold power in society, and do you also agree with the fact (which is a strange question) that non-whites are more often victims of police misconduct, brutality, and assault.
Do you think things should be systematically changed because of these things that have been shown to you?
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7 minutes ago, Dagl1 said:
Do you agree that white-people disproportionately hold power in society
Not personally me. But I deserve for better.
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1 hour ago, iNow said:
You're welcome to think whatever you want. My "fixation" is on the fact that these trends are deep rooted, well established, and persistent. We are all citizens equally protected, yet those protections are not equally applied. Whether it's in policing, experience with the justice system and imprisonment, education and dilapidated schools, red lined districts preventing home-ownership and creation of wealth, access to fresh foods, being spoke to as "less than" in daily interactions or viewed with suspicion for doing perfectly normal things like bird watching...
The "racial part" of what's happening is the important part right now, and suggesting that it's not is unfortunately indicative of little more than your own white privilege.
White guy guns down a church full of people praying or a school full of children? Gently walked out by authorities and respectfully given due process of the law. White guys arrive to a state capitols and start waving semi-automatic rifles around in the governors mansion or saying the only good democrat is a dead democrat? They're called very fine people and allowed to remain there to share their message of protest without intervention from the police.
But when a black guy sells some loose cigarettes on the street for a buck a pop, or 12 year old boy squirting water out of a squirt gun at a park, or man uses an allegedly forged $20 bill at a convenience store? Dead from police. A white guy using a forged$20 bill at a store has a fun story he tells at parties for the next few years. A black guy using a forged \$20 bill at a store has a headstone and an orphaned family.
What's not healthy is the american system of quote unquote justice and the way so many americans can't seem to see how drastically different their experience is from their neighbors, but if you wish to instead focus on me for rightly highlighting these facts and hoping to perhaps inspire some modicum of support for change and improvements, well... then that's your prerogative and you're fee to do so.
There is a lot which I agree with in your above post, theres some with which I somewhat agree and some which I dont agree with at all. Racial issues which are always a part of everything USA are not necessarily something which is of an issue for every one else on this planet. I don’t know how much more of freedom and racial equality the US can take but judging by whats happening in the last week in major US cities I have a feeling that its not much more. Ive never seen in any other developed country so much straight up in your face racism from whites and blacks alike, its a disease and there is no singular cure.
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3 minutes ago, Moreno said:
Not personally me. But I deserve for better.
Nor me, poor white trash, but I just deserve the same.
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4 minutes ago, Moreno said:
Not personally me. But I deserve for better.
You do have more power and privilege than black people (or other minorities). The fact you are not ware of it is part of the problem.
Here, try this:
How many fingers do you have left?
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2 minutes ago, Strange said:
How many fingers do you have left?
I will do this test with my neighbour Tunde who was born and raised in Łódź, is 100% Polish and is as black as it gets (his Dad is Nigerian) I’ll get back to you.
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4 minutes ago, Moreno said:
Not personally me. But I deserve for better.
Together with your other statements, this answer seems as if you are not agreeing with the other points, or have not gotten any new knowledge or insight from peoples post, this could of course be completely untrue, but at the same time, based on the tendency of your previous answers and posts on other topics, it is not unreasonable (to me) to think that you still hold your initial believes, not understanding that systemic racism exists, denying its existence, or not seeing how the fact that it is currently a bigger issue for some people than for others (and should therefore first be solved for those people (referring back to the comment about every group of people (on average) possibly being equally as racist)).
Some post ago you asked people in this forum to help you comprehend; they have attempted to, did it make a difference, do you now understand more than before? If not, why? Again I could be completely misreading it, but to me it feels like you evaded the other questions I asked.
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1 minute ago, koti said:
I will do this test with my neighbour Tunde who was born and raised in Łódź, is 100% Polish and is as black as it gets (his Dad is Nigerian) I’ll get back to you.
I suspect that Polish (and other European) migrants in the UK would do pretty badly on this after the last few years.
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5 minutes ago, Strange said:
I suspect that Polish (and other European) migrants in the UK would do pretty badly on this after the last few years.
But doesn’t that tell us that white privilage is subjective?
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8 minutes ago, koti said:
But doesn’t that tell us that white privilage is subjective?
No, it tells us that privilege is real, the subjective part is how the privileged perceive a threat...
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https://darkmatterdarkenergy.com/tag/cosmic-microwave-background/ | # Tag Archives: cosmic microwave background
## Mini Black Holes as Dark Matter?
Ancient Voyager Satellite Says No for the Smallest Possible
Black holes can come in all sizes from about a billion tons up to billions of solar masses.
Because isolated black holes are difficult to detect, especially smaller mass ones, they have long been considered as candidates for dark matter, invoked to explain the extra gravitational accelerations measured at the outskirts of galaxies.
Stephen Hawking showed that black holes radiate low energy particles very slowly due to quantum thermodynamic effects. So the very lowest mass black holes evaporate away due to Hawking radiation during the life of the universe.
Voyager Satellites
The Voyager satellites were launched in 1977 and NASA has determined that Voyager 1 crossed the heliopause in 2012. This is the boundary for the solar wind, which holds back a large portion of galactic cosmic rays. Voyager 2 crossed the heliopause last year.
Forty-two years after launch, and having toured Jupiter, Saturn, Uranus, and Neptune, these remarkable satellites are still returning valuable data about the outer reaches of the Solar System.
What is the connection between black holes, dark matter, and Voyager 1?
In the early universe, large numbers of so-called primordial black holes (PBHs) of various sizes may have formed. The question arises, could these be the primary component of dark matter?
Primordial Black Holes as Dark Matter Candidates
The detection of gravitational waves from half a dozen mergers of black holes of intermediate mass has given new energy to this idea. Also, there is the continued failure to detect exotic particle candidates for dark matter in Earth-bound laboratory experiments.
A team of Japanese astronomers, searching for microlensing effects with stars in the Andromeda galaxy, have ruled out small black holes in the range of $10^{20}$ grams up to about 3 times the Earth’s mass. https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter has more detail.
Constraints from other lensing experiments (MACHO, EROS) and the cosmic microwave background appear to rule out more massive primordial black holes as the explanation for most dark matter.
What about the tiniest allowable black holes, from about $4 \cdot 10^{14}$ gm (smaller ones have evaporated already) up to $10^{20}$ gm?
Voyager 1 Constraints
With a recent analysis researchers at the Laboratoire de Physique Theorique et Hautes Energies (LPTHE) show that the Voyager 1 satellite now rules out primordial black holes with masses below $10^{17}$ gm as well, as the source of most dark matter. And it is because of the Hawking radiation that we do not detect.
Although Hawking radiation has never been detected, it is on very firm theoretical grounds that it should exist. Everything, including strange objects like black holes, has a quantum nature.
$T = 1.1 GeV / (m/10^{13} gm)$
Thus for an $m = 10^{16}$ gm black hole the Hawking temperature is about 1 MeV. (GeV or giga electron-Volt is a billion eV and around the rest mass energy of a proton, and an MeV or mega electron-Volt is a million eV and about twice the rest mass energy of an electron.)
Since these temperatures are in the MeV range, only very light particles such as neutrinos, electrons, and positrons would be emitted by the PBHs.
Figure 1 from the Boudaud and Cirelli paper shows the observed combined electron and positron cosmic ray flux from Voyager 1 in the energy range from 3 MeV to 50 MeV. It also shows results in the 1 to 10 GeV range from the Alpha Magnetic Spectrometer 2 experiment on the International Space Station (located well inside the heliopause). Two different models of how the energetic particles propagate through the galaxy are used.
Smallest possible Black Holes ruled out
PBHs with $10^{15}$ or $10^{16}$ grams are clearly ruled out; they would inject far too many energetic electron and positron cosmic rays into the interstellar medium that Voyager 1 has entered.
The authors state that no more than 0.1% of dark matter can be due to PBHs of mass less than $10^{16}$ grams (10 billion tons).
In Figure 1, a monotonic mass distribution was assumed (PBHs all have the same mass). They also consider various log-normal mass distributions and similar constraints on the allowable PBH mass were found.
What about at $10^{17}$ grams and above? Most mass regions are ruled out.
The mass region above $5 \cdot 10^{17}$ grams and up to about $10^{20}$ grams has been excluded as a primary source of dark matter from PBHs by a 2012* result from Barnacka, Glicenstein, and Moderski. They searched for gravitational lensing effects upon gamma ray burst sources due to intervening black holes.
So vast ranges of possible PBH masses are ruled out. However the mass region from $3 \cdot 10^{16}$ up to $5 \cdot 10^{17}$ grams remains a possibility as a dark matter hideout for PBHs.
*The same year that Voyager 1 crossed the heliopause, coincidentally
References
Boudaud, M. And Cirelli, M. 2019 “Voyager 1 electrons and positrons further constrain primordial black holes as dark matter” https://arxiv.org/abs/1807.03075
https://darkmatterdarkenergy.com/2017/12/07/primordial-black-holes-and-dark-matter/
Barnacka, A., Glicenstein, J.-F., Moderski, R. 2012 “New constraints on primordial black holes abundance from femtolensing of gamma-ray bursts” http://arxiv.org/abs/1204.2056
## No Dark Energy?
Dark Energy is the dominant constituent of the universe, accounting for 2/3 of the mass-energy balance at present.
At least that is the canonical concordance cosmology, known as the ΛCDM or Lambda – Cold Dark Matter model. Here Λ is the symbol for the cosmological constant, the simplest, and apparently correct (according to most cosmologists), model for dark energy.
Models of galaxy formation and clustering use N-body simulations run on supercomputers to model the growth of structure (galaxy groups and clusters) in the universe. The cosmological parameters in these models are varied and then the models are compared to observed galaxy catalogs at various redshifts, representing different ages of the universe.
It all works pretty well except that the models assume a fully homogeneous universe on the large scale. While the universe is quite homogeneous for scales above a billion light-years, there is a great deal of filamentary web-like structure at scales above clusters, including superclusters and voids, as you can easily see in this map of our galactic neighborhood.
##### Galaxies and clusters in our neighborhood. IPAC/Caltech, by Thomas Jarrett – “Large Scale Structure in the Local Universe: The 2MASS Galaxy Catalog”, Jarrett, T.H. 2004, PASA, 21, 396
Well why not take that structure into account when doing the modeling? It has long been known that more local inhomogeneities such as those seen here might influence the observational parameters such as the Hubble expansion rate. Thus even at the same epoch, the Hubble parameter could vary from location to location.
Now a team from Hungary and Hawaii have modeled exactly that, in a paper entitled “Concordance cosmology without dark energy” https://arxiv.org/pdf/1607.08797.pdf . They simulate structure growth while estimating the local values of expansion parameter in many regions as their model evolves.
Starting with a completely matter dominated (Einstein – de Sitter) cosmology they find that they can reasonably reproduce the average expansion history of the universe — the scale factor and the Hubble parameter — and do that somewhat better than the Planck -derived canonical cosmology.
Furthermore, they claim that they can explain the tension between the Type Ia supernovae value of the Hubble parameter (around 73 kilometers per second per Megaparsec) and that determined from the Planck satellite observations of the cosmic microwave background radiation (67 km/s/Mpc).
Future surveys of higher resolution should be able to distinguish between their model and ΛCDM, and they also acknowledge that their model needs more work to fully confirm consistency with the cosmic microwave background observations.
Meanwhile I’m not ready to give up on dark energy and the cosmological constant since supernova observations, cosmic microwave background observations and the large scale galactic distribution (labeled BAO in the figure below) collectively give a consistent result of about 70% dark energy and 30% matter. But their work is important, something that has been a nagging issue for quite a while and one looks forward to further developments.
Dark Energy and Matter content of Universe
## WIMPs or MACHOs or Primordial Black Holes
A decade or more ago, the debate about dark matter was, is it due to WIMPs (weakly interacting massive particles) or MACHOs (massive compact halo objects)? WIMPs would be new exotic particles, while MACHOs are objects formed from ordinary matter but very hard to detect due to their limited electromagnetic radiation emission.
Schwarzenegger (MACHO), not Schwarzschild (Black Holes)
Image credit: Georges Biard, CC BY-SA 3.0
Candidates in the MACHO category such as white dwarf or brown dwarf stars have been ruled out by observational constraints. Black holes formed in the very early universe, dubbed primordial black holes, were thought by many to have been ruled out as well, at least across many mass ranges, such as between the mass of the Moon and the mass of the Sun.
The focus during recent years, and most of the experimental searches, has shifted to WIMPs or other exotic particles (axions or sterile neutrinos primarily). But the WIMPs, which were motivated by supersymmetric extensions to the Standard Model of particle physics, have remained elusive. Most experiments have only placed stricter and stricter limits on their possible abundance and interaction cross-sections. The Large Hadron Collider has not yet found any evidence for supersymmetric particles.
Have primordial black holes (PBHs) as the explanation for dark matter been given short shrift? The recent detections by the LIGO instruments of two gravitational wave events, well explained by black hole mergers, have sparked new interest. A previous blog entry addressed this possibility:
The black holes observed in these events have masses in a range from about 8 to about 36 solar masses, and they could well be primordial.
There are a number of mechanisms to create PBHs in the early universe, prior to the very first second and the beginning of Big Bang nucleosynthesis. At any era, if there is a total mass M confined within a radius R, such that
2*GM/R > c^2 ,
then a black hole will form. The above equation defines the Schwarzschild limit (G is the gravitational constant and c the speed of light). A PBH doesn’t even have to be formed from matter whether ordinary or exotic; if the energy and radiation density is high enough in a region, it can also result in collapse to a black hole.
Cosmic Strings
Image credit: David Daverio, Université de Genève, CSCS supercomputer simulation data
The mechanisms for PBH creation include:
1. Cosmic string loops – If string theory is correct the very early universe had very long strings and many short loops of strings. These topological defects intersect and form black holes due to the very high density at their intersection points. The black holes could have a broad range of masses.
2. Bubble collisions from symmetry breaking – As the very early universe expanded and cooled, the strong force, weak force and electromagnetic force separated out. Bubbles would nucleate at the time of symmetry breaking as the phase of the universe changed, just as bubbles form in water as it boils to the surface. Collisions of bubbles could lead to high density regions and black hole formation. Symmetry breaking at the GUT scale (for the strong force separation) would yield BHs of mass around 100 kilograms. Symmetry breaking of the weak force from the electromagnetic force would yield BHs with a mass of around our Moon’s mass ~ 10^25 kilograms.
3. Density perturbations – These would be a natural result of the mechanisms in #1 and #2, in any case. When observing the cosmic microwave background radiation, which dates from a time when the universe was only 380,000 years old, we see density perturbations at various scales, with amplitudes of only a few parts in a million. Nevertheless these serve as the seeds for the formation of the first galaxies when the universe was only a few hundred million years old. Some perturbations could be large enough on smaller distance scales to form PBHs ranging from above a solar mass to as high as 100,000 solar masses.
For a PBH to be an effective dark matter contributor, it must have a lifetime longer than the age of the universe. BHs radiate due to Hawking radiation, and thus have finite lifetimes. For stellar mass BHs, the lifetimes are incredibly long, but for smaller BHs the lifetimes are much shorter since the lifetime is proportional to the cube of the BH mass. Thus a minimum mass for PBHs surviving to the present epoch is around a trillion kilograms (a billion tons).
Carr et al. (paper referenced below) summarized the constraints on what fraction of the matter content of the universe could be in the form of black holes. Traditional black holes, of several solar masses, created by stellar collapse and detectable due to their accretion disks, do not provide enough matter density. Neither do supermassive black holes of over a million solar masses found at the centers of most galaxies. PBHs may be important in seeding the formation of the supermassive black holes, however.
Limits on the PBH abundance in our galaxy and its halo (which is primarily composed of dark matter) are obtained from:
1. Cosmic microwave background measurements
2. Microlensing measurements (gravitational lensing)
3. Gamma-ray background limits
4. Neutral hydrogen clouds in the early universe
5. Wide binaries (disruption limits)
Microlensing surveys such as MACHO and EROS have searched for objects in our galactic halo that act as gravitational lenses for light originating from background stars in the Magellanic Clouds or the Andromeda galaxy. The galactic halo is composed primarily of dark matter.
A couple of dozen of objects with less than a solar mass have been detected. Based on these surveys the fraction of dark matter which can be PBHs with less than a solar mass is 10% at most. The constraints from 1 solar mass up to 30 solar masses are weaker, and a PBH explanation for most of the galactic halo mass remains possible.
Similar studies conducted toward distant quasars and compact radio sources address the constraint in the supermassive black hole domain, apparently ruling out an explanation due to PBHs with from 1 million to 100 million solar masses.
Lyman-alpha clouds are neutral hydrogen clouds (Lyman-alpha is an important ultraviolet absorption line for hydrogen) that are found in the early universe at redshifts above 4. Simulations of the effect of PBH number density fluctuations on the distribution of Lyman-alpha clouds appear to limit the PBH contribution to dark matter for a characteristic PBH mass above 10,000 solar masses.
Distortions in the cosmic microwave background are expected if PBHs above 10 solar masses contributed substantially to the dark matter component. However these limits assume that PBH masses do not change. Merging and accretion events after the recombination era, when the cosmic microwave background was emitted, can allow a spectrum of PBH masses that were initially less than a solar mass before recombination evolve to one dominated by PBHs of tens, hundreds and thousands of solar masses today. This could be a way around some of the limits that appear to be placed by the cosmic microwave background temperature fluctuations.
Thus it appears could be a window in the region 30 to several thousand solar masses for PBHs as an explanation of cold dark matter.
As the Advanced LIGO gravitational wave detectors come on line, we expect many more black hole merger discoveries that will help to elucidate the nature of primordial black holes and the possibility that they contribute substantially to the dark matter component of our Milky Way galaxy and the universe.
References
B. Carr, K. Kohri, Y. Sendouda, J. Yokoyama, 2010 arxiv.org/pdf/0912.5297v2 “New cosmological constraints on primordial black holes”
S. Cleese and J. Garcia-Bellido, 2015 arxiv.org/pdf/1501.07565v1.pdf “Massive Primordial Black Holes from Hybrid Inflation as Dark Matter and the Seeds of Galaxies”
P. Frampton, 2015 arxiv.org/pdf/1511.08801.pdf “The Primordial Black Hole Mass Range”
P. Frampton, 2016 arxiv.org/pdf/1510.00400v7.pdf “Searching for Dark Matter Constituents with Many Solar Masses”
Green, A., 2011 https://www.mpifr-bonn.mpg.de/1360865/3rd_WG_Green.pdf “Primordial Black Hole Formation”
P. Pani, and A. Loeb, 2014 http://xxx.lanl.gov/pdf/1401.3025v1.pdf “Exclusion of the remaining mass window for primordial black holes as the dominant constituent of dark matter”
NEW BOOK just released:
S. Perrenod, 2016, 72 Beautiful Galaxies (especially designed for iPad, iOS; ages 12 and up)
## The Supervoid
The largest known structure in the universe goes by the name of the Supervoid. It is an enormously large under-dense region about 1.8 billion light-years in extent. Voids (actually low density regions) in galaxy and cluster density have been mapped over several decades.
The cosmic microwave background radiation map from the Planck satellite and earlier experiments is extremely uniform. The temperature is about 2.7 Kelvins everywhere in the universe at present. There are small microKelvin scale fluctuations due to primordial density perturbations. The over-dense regions grow over cosmic timescales to become galaxies, groups and clusters of galaxies, and superclusters made of multiple clusters. Under-dense regions have fewer galaxies and groups per unit volume than the average.
The largest inhomogeneous region detected in the cosmic microwave background map is known as the Cold Spot and has a very slightly lower temperature by about 70 microKelvins (a microKelvin being only a millionth of a degree). It may be partly explained by a supervoid of radius 320 Megaparsecs, or around 1 billion light-years radius.
Superclusters heat cosmic microwave background photons slightly when they pass through, if there is significant dark energy in the universe. Supervoids cool the microwave background photons slightly. The reason is that, once dark energy becomes significant, during the second half of the universe’s expansion to date, it begins to smooth out superclusters and supervoids. It pushes the universe back towards greater uniformity while accelerating the overall expansion.
A photon will gain energy (blueshift) when it heads into a supercluster on its way to the Earth. This is an effect of general relativity. And as it leaves the other side of the supercluster as it continues its journey, it will lose energy (redshift) as it climbs out of the gravitational potential well. But while it is passing through the supercluster, that structure is spreading out due to the Big Bang overall expansion, and its gravitational potential is weakening. So the redshift or energy loss is smaller than the original energy gain or blueshift. So net-net, photons gain energy passing through a supercluster.
The opposite happens with a supervoid. Photons lose energy on the way in. They gain energy on the way out, but less than they lost. Net-net photons lose energy, become colder, when passing through supervoids. Now all of this is relative to the overall redshift that all photons experience as they travel from the Big Bang last scattering surface to the Earth. During each period that the universe doubles in size, the Big Bang radiation doubles in wavelength, or halves in temperature.
In a newly published paper titled “Detection of a Supervoid aligned with the Cold Spot in the Cosmic Microwave Background”, astronomers looked at the distribution of galaxies in the direction of the well-established Cold Spot. The supervoid core redshift distance is in the range z = 0.15 to z = 0.25, corresponding to a distance of roughly 2 to 3 billion light-years from Earth.
They find a reduction in galaxy density of about 20%, and of dark matter around 14%, in the supervoid, relative to the overall average density values in the universe. The significance of the detection is high, around 5 standard deviations. The center of the low density region is well aligned with the position of the Cold Spot in the galactic Southern Hemisphere.
Both the existence of this supervoid and its alignment with the Cold Spot are highly significant. The chance of the two being closely aligned to this degree is calculated as just 1 chance in 20,000. The image below is Figure 2 from the authors’ paper and maps the density of galaxies in the left panel and the temperature differential of the microwave background radiation in the right panel. The white dot in the middle of each panel marks the center of the Cold Spot in the cosmic microwave background.
A lower density of galaxies is indicated by a blue color in the left panel. Red and orange colors denote a higher density of galaxies. The right panel shows slightly lower temperature of the cosmic microwave background in blue, and slightly higher temperature in red.
The authors have calculated the expected temperature reduction due to the supervoid; using a first-order model it is about 20 microKelvins. While this is not sufficient to explain the entire Cold Spot temperature decrease, it is a significant portion of the overall 70 microKelvin reduction.
Dark Energy is gradually smearing out the distinction between superclusters and supervoids. Dark Energy has come to dominate the universe’s mass-energy balance fairly recently, since about 5 billion years ago. If there is no change in the Dark Energy density, over many billions of years it will push all the galaxies so far apart from one another that no other galaxies will be detectable from our Milky Way.
References
I. Szapudi et al, 2015 M.N.R.A.S., Volume 450, Issue 1, p. 288, “Detection of a supervoid aligned with the cold spot of the cosmic microwave background” – http://mnras.oxfordjournals.org/content/450/1/288.full
S. Perrenod and M. Lesser, 1980, P.A.S.P. 91:764, “A Redshift Survey of a High-Multiplicity Supercluster” http://www.jstor.org/discover/10.2307/40677683?uid=2&uid=4&sid=21106121183081
## Planck Mission Full Results Confirm Canonical Cosmology Model
Dark Matter, Dark Energy values refined
The Planck satellite, launched by the European Space Agency, made observations of the cosmic microwave background (CMB) for a little over 4 years, beginning in August, 2009 until October, 2013.
Preliminary results based on only the data obtained over the first year and a quarter of operation, and released in 2013, established high confidence in the canonical cosmological model. This ΛCDM (Lambda-Cold Dark Matter) model is of a topologically flat universe, initiated in an inflationary Big Bang some 13.8 billion years ago and dominated by dark energy (the Λ component), and secondarily by cold dark matter (CDM). Ordinary matter, of which stars, planets and human beings are composed, is the third most important component from a mass-energy standpoint. The amount of dark energy is over twice the mass-energy equivalent of all matter combined, and the dark matter is well in excess of the ordinary matter component.
This general model had been well-established by the Wilkinson Microwave Anisotropy Probe (WMAP), but the Planck results have provided much greater sensitivity and confidence in the results.
Now a series of 28 papers have been released by the Planck Consortium detailing results from the entire mission, with over three times as much data gathered. The first paper in the series, Planck 2015 Results I, provides an overview of these results. Papers XIII and XIV detail the cosmological parameters measured and the findings on dark energy, while several additional papers examine potential departures from a canonical cosmological model and constraints on inflationary models.
In particular they find that:
Ωb*h² = .02226 to within 1%.
In this expression Ωb is the baryon (basically ordinary matter) mass-energy fraction (fraction of total-mass energy in ordinary matter) and h = H0/100. H0 is the Hubble constant which measures the expansion rate of the universe, and indirectly, its age. The best value for H0 is 67.8 kilometers/sec/Megaparsec (millions of parsecs, where 1 parsec = 3.26 light-years). H0 has an uncertainty of about 1.3% (two standard deviations). In this case h = .678 and the expression above becomes:
Ωb = .048, with uncertainty around 3% of its value. Thus, just under 5% of the mass-energy density in the universe is in ordinary matter.
The cold matter density is measured to be:
Ωc*h² = .1186 with uncertainty less than 2% and with the h value substituted we have Ωc = .258 with similar uncertainty.
Since the radiation density in the universe is known to be very low, the remainder of the mass-energy fraction is from dark energy,
Ωe = 1 – .048 – .258 = .694
So in approximate percentage terms the Planck 2015 results indicate 69% dark energy, 26% dark matter, and 5% ordinary matter as the mass-energy balance of the universe. These results are essentially the same as the ratios found from the preliminary results reported in 2013. It is to be emphasized that these are present-day values of the constituents. The components evolve differently as the universe expands. Dark energy is manifested with its current energy density in every new unit of volume as the universe continues to expand, while the average dark matter and ordinary matter densities decrease inversely as the volume grows. This implies that in the past, dark energy was less important, but it will dominate more and more as the universe continues to expand.
Why is dark energy produced as the universe expands? The simplest explanation is that it is the irreducible quantum energy of empty space, of the vacuum. Empty space – space with no particles whatsoever – still has fields (scalar fields, in particular) permeating it, and these fields have a minimum energy. It also has ‘virtual’ particles popping in and out of existence very briefly. This is the cosmological constant (Λ) model for the dark energy.
This is the ultimate free lunch in nature. The dark energy works as a negative gravity; it enters into the equations of general relativity as a negative pressure which causes space to expand. And as space expands, more dark energy is created! A wonderful self-reinforcing process is in place. Since the dark energy dominates over matter, the expansion of the universe is accelerating, and has been for the last 5 billion years or so. Why wonderful? Because it adds billions upon billions of years of life to our universe.
The Planck Consortium also find the universe is topologically flat to a very high degree, with an upper limit of 1/2 of 1% deviation from flatness at large scales. This is an impressive observational result.
One of the most interesting results is Planck’s ability to constrain inflationary models. While a massive inflation almost certainly happened during the first billionth of a trillionth of a trillionth of a second as the Universe began, as indicated by the very uniformity of the CMB signal, there are many possible models of the inflationary field’s energy potential.
We’ll take a look at this in a future blog entry.
## BICEP2 Apparently Detects Quantum Nature of Gravity and Supports Inflationary Big Bang
Can a single experiment do all of the following?
1. Provide significant confirmation of the inflationary version of the Big Bang model (and help constrain which model of inflation is correct)
2. Confirm the existence of gravitational waves
3. Support the quantum nature of gravity (at very high energies)
4. Provide the first direct insight into the highest energy levels imagined by physicists – 10^16 GeV (10,000 trillion GeV) – 12 orders of magnitude beyond the LHC
Apparently it can! BICEP2 is a radio telescope experiment located at the South Pole, taking advantage of the very cold, dry air at that remote location for greater sensitivity. It is focused on measuring polarization of the cosmic microwave background radiation that is a remnant of the hot Big Bang of the early universe. (BICEP is an abbreviation of Background Imaging of Cosmic Extragalactic Polarization; this is the second version of the experiment).
The results announced by the BICEP2 team on March 17 at the Harvard-Smithsonian Center for Astrophysics, if they have been correctly interpreted, are the most important in cosmology in the 21st century to date. They are of such enormous significance that a Nobel Prize in Physics is highly likely, if the results and interpretation are confirmed.
We infer from a number of previous observations that there was likely an inflationary period very early on in the universes’s history. We are talking very, very, early – in the first billionth of a trillionth of a trillionth of a second. See this earlier post of mine here: https://darkmatterdarkenergy.com/2011/03/22/inflation/ This new result from BICEP2 is very supportive of inflationary Big Bang models, and that includes very simple models for inflation.
What is the observation? It is B-mode polarization in the cosmic microwave background radiation. The cosmic microwave background (CMB) is the thermal radiation left over from a time when the universe became transparent, at age 380,000 years, almost 14 billion years ago. There are two polarization modes for alignment of CMB radiation, the E-mode and the B-mode. The B-mode measures the amount of “curliness” in the alignment of CMB microwave photons (as you can easily see in the image below).
There are two known causes of B-mode polarization for the CMB. The first, also detected by the BICEP2 experiment, is due to intervening clusters of galaxies along the line of sight. These clusters bend the light paths due to their immense masses, in accordance with general relativity. These effects are seen at smaller spatial scales. At larger spatial scales, we have the more significant effect, whereby the gravitational waves generated during the inflation epoch imprint the polarization.
You can easily see the curly B-mode polarization with a quick glance at BICEP2’s results. (bicepkeck.org)
What is being seen in today’s CMB is due to this second and more profound cause, which is nothing less than quantum fluctuations in space-time in the very, very early universe revealing themselves due to the gravitational waves that they generated. And these gravitational waves in turn caused a small curling effect on the cosmic microwave background, until the time of decoupling of radiation and matter. This is seen in the image at angular scales of a few degrees.
At age 380,000 years the universe became transparent to the CMB radiation and it traveled for another 13.8 billion years and underwent a redshift by a factor of 1500 as the universe expanded. So what was optical radiation at that time, becomes microwave radiation today, with a characteristic temperature of 2.7 Kelvins (degrees above absolute zero), while still retaining the curly pattern seen by BICEP2.
This is the first observation that provides some direct insight into extremely high energy scales within the context of a single experiment. We are talking here of approximately a trillion times higher energy than the Large Hadron Collider, the world’s most powerful particle accelerator, where the Higgs boson was discovered.
The BICEP2 results are a single experiment that for the first time apparently ties quantum mechanics and gravity together. It supports the quantum nature of gravity, which occurs at very high energy scales. The Planck scale at which space-time would be quantized corresponds to an energy level of 10^18 or 10^19 GeV (ten million trillion GeV), and inflation in many models begins when the universe has an energy level somewhat lower, at 10^16 GeV (ten thousand trillion GeV, where 1 GeV is a little more than the rest mass-energy of a proton).
And take a look at this interview of Sean Carroll by PBS’s Gwen Ifill to get some more context around this (hopefully correct!) universe-expanding discovery. Other astronomers are already racing to confirm it.
References:
http://www.cfa.harvard.edu/CMB/bicep2/ – BICEP2 web site at Harvard-Smithsonian Center for Astrophysics
http://www.theguardian.com/science/2014/mar/17/bicep2-how-hot-big-bang-science-dark-energy
http://www.scientificamerican.com/article/gravity-waves-cmb-b-mode-polarization/
## More Dark Matter: First Planck Results
Credit: European Space Agency and Planck Collaboration
Map of CMB temperature fluctuations with slightly colder areas in blue, and hotter areas in red.
The first results from the European Space Agency’s Planck satellite have provided excellent confirmation for the Lambda-CDM (Dark Energy and Cold Dark Matter) model. The results also indicate somewhat more dark matter, and somewhat less dark energy, than previously thought. These are the most sensitive and accurate measurements of fluctuations in the cosmic microwave background (CMB) radiation to date.
Results from Planck’s first 1 year and 3 months of observations were released in March, 2013. The new proportions for mass-energy density in the current universe are:
• Ordinary matter 5%
• Dark matter 27%
• Dark energy 68%
Credit: European Space Agency and Planck Collaboration
The prior best estimate for dark matter primarily from the NASA WMAP satellite observations, was 23%. So the dark matter fraction is higher, and the dark energy fraction correspondingly lower, than WMAP measurements had indicated.
Dark energy still dominates by a very considerable degree, although somewhat less than had been thought prior to the Planck results. This dark energy – Lambda – drives the universe’s expansion to speed up, which is known as the runaway universe. At one time dark matter dominated, but for the last 5 billion years, dark energy has been dominant, and it grows in importance as the universe continues to expand.
The Planck results also added a little bit to the age of the universe, which is measured to be about 13.8 billion years, about 3 times the age of the earth. The CMB radiation itself, was emitted when the universe was only 380,000 years old. It was originally in the infrared and optical portions of the spectrum, but has been massively red-shifted, by around 1500 times, due to the expansion of the universe.
There are many other science results from the Planck Science team in cosmology and astrophysics. These include initial support indicated for relatively simple models of “slow roll” inflation in the extremely early universe. You can find details at the ESA web sites referenced below, and in the large collection of papers from the 47th ESlab Conference link.
References:
http://www.esa.int/Our_Activities/Space_Science/Planck/Planck_reveals_an_almost_perfect_Universe – news article at ESA site
https://darkmatterdarkenergy.com/2011/07/04/dark-energy-drives-a-runaway-universe/ – runaway universe blog
http://www.rssd.esa.int/index.php?project=planck – Planck Science Team site
http://www.sciops.esa.int/index.php?project=PLANCK&page=47_eslab – 47th ESlab Conference presentations on Planck science results
## The Big Bang model
Cosmic Microwave Background spectrum (credit: NASA)
The Big Bang theory describing the origin and expansion of the universe from a very tiny and energetic initial state was developed initially in the 1920s as a solution for Einstein’s equations of general relativity. It assumed, correctly, a uniform (homogeneous) density of matter and energy. While the universe around us today appears highly non-uniform, with visible matter apparently concentrated in groups of galaxies, and in individual galaxies, gaseous nebulae, and star clusters, stars, and planets, all the evidence indicates that matter was very uniformly distributed throughout the first one million years of existence. At that time there were no stars or galaxies, rather the universe consisted of hot dense, but expanding, gas and photons (light). Even today, on the largest scales of 500 million light years and beyond, the universe appears to be quite uniform on average.
The first great support for the Big Bang came from the detection of what we call the Hubble expansion, named for Edwin Hubble, who in 1929 first demonstrated that galaxy recession predominates and depends on distance from us. Galaxies on average are all moving away from each other, unless they are gravitationally bound to their neighbors. The rate of expansion is simply proportional to the distance to the galaxy; this is known as Hubble’s law. Every galaxy moves away from every other galaxy regardless of its position in the universe; this implies a global and uniform expansion.
How do we determine this relationship? The light from these distant galaxies is shifted to be redder than normal in proportion to the velocity away from our galaxy. The redshift is a measure of the velocity of recession and the velocity is found to be proportional to the distance from our Milky Way to the galaxy in question. To be clear, the galaxy velocity and distance follow a linear relation. If we were located in another galaxy, we would observe the same effect. Most of the galaxies would be receding from us as well, at rates proportional to their distance. This is just what one expects for a universe which is isotropic – the same in each direction – and which is expanding uniformly. Each dimension of three-dimensional space is getting larger with time. The gravitationally bound objects, such as the galaxies themselves, are not expanding, but the space between the galaxies is stretching and has been since the Big Bang initial event.
Since the rate of the expansion is proportional to distance, one can take the proportionality constant, known as Hubble’s constant, and by inverting that determine an approximate age of the universe. It amounts to ‘running the movie backward.’ The age works out to 14 billion years, which is very close to the current best estimate of the age of 13.8 billion years, about 3 times the age of the Sun and the Earth.
Another great success of the Big Bang model was in its prediction of the helium abundance. The same hydrogen fusion process that powers the Sun took place in the early universe during the first 20 minutes, when the temperature was millions of degrees. In the Sun hydrogen is fused to created helium. For the early universe, this is known as primordial or Big Bang nucleosynthesis. There was only time enough and the right conditions to create helium, the second lightest element in the periodic table, and also the heavy form of hydrogen known as deuterium, plus just a bit of the third element lithium. None of the heavier elements such as carbon, nitrogen, oxygen, silicon or iron were created – this would happen later inside stellar furnaces. The final result of this cosmological nucleosynthesis turned 25% of the initial available mass of hydrogen into helium, and into trace amounts of deuterium, lithium and beryllium. The primordial abundance observed in the oldest stars for helium and deuterium matches the predictions of the Big Bang nucleosynthesis model.
The Big Bang moved from being possible theory to well-established factual model describing the universe when the first detection of the cosmic microwave background was published in 1965 by Arno Penzias and Robert Wilson, who received the Nobel Physics prize for their discovery. The cosmic microwave background is blackbody thermal radiation at millimeter wavelengths in the radio portion of the electromagnetic spectrum., and as we observe it at present, it has a temperature of a little under 3 degrees above absolute zero (see image above which has the characteristic thermal blackbody shape). It fills space in every direction in which one observes, and is remarkably uniform in intensity. The cosmic microwave background dates from a time when the universe was about 380,000 years old, and the radiation was originally emitted at a temperature of around 3000 degrees on the Kelvin scale. It also has redshifted, by over 1000 times. Thus we detect today as radio waves photons that were originally emitted in the optical and infrared portions of the electromagnetic spectrum when the universe was only 380,000 years old. Unlike the hydrogen and helium atoms which are found in stars and on planets, these photons have stretched out in proportion to the expansion of the universe. | 2019-03-21 00:30:26 | {"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 14, "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": 0.49886423349380493, "perplexity": 836.6499816165586}, "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-2019-13/segments/1552912202474.26/warc/CC-MAIN-20190320230554-20190321012554-00480.warc.gz"} |
https://physics.stackexchange.com/questions/486147/change-in-magnetic-flux-eddy-currents-vs-moving-wire | # Change in Magnetic Flux: Eddy Currents vs Moving Wire
From what I have read, as a conducting rod moves perpendicular to a uniform magnetic field, this will lead to a change in magnetic flux and therefore an emf will be induced (area being swept as the conducting rod moves).
However, in terms of eddy currents, I have been told that when the metal plate is moving perpendicular to and within the uniform magnetic field, there is not change in magnetic flux and therefore no induced emf.
As the conducting rod moves and there is an induced emf (and therefore change in magnetic flux), how is it that there is no induced emf in the form of eddy currents as the metal plate is within the uniform magnetic field.
To me, I don't see where the difference lies between the two scenarios, they are both conductors moving within a uniform magnetic field.
Could someone please explain to me where my understanding is flawed.
• If an electric charge moves in a magnetic field the Lorenz forces (see your formula above) acts upon it. However, this is only true, if the motion is not parallel to the magnetic field. Therefore, could you please clarify the relative directions of the B-field and the motion of the metal plate. – Semoi Jun 15 '19 at 10:45
• @Semoi please see it now – Max604 Jun 16 '19 at 12:33
• Thank you for clarifying the directions. My second guess is, that the problem is due to wording. We usually use the term eddy currents if we like to address the induced currents which are produced by a change in the B-field, $dB/dt \propto I$. However, in the situation described above the B-field is constant. Therefore, although we obtain a voltage across the moving conductor, we usually do not speak of eddy currents. Nevertheless, the voltage across the plate exists. – Semoi Jun 16 '19 at 18:20
The flux of the magnetic field through any surface whose border lies inside the rod is defined as $$\int_S\vec{B}\cdot\hat{n}dS$$ where the integral is calculated over the whole surface and $$\hat{n}$$ is the versor perpendicular to the surface (point by point). For example if you consider a rectanguar border and the rectangle as the surface, the flux is simply given by $$\int_S\vec{B}\cdot\hat{n}dS=\vec{B}\cdot\hat{n}\cdot A$$ where $$A$$ is the area of the rectangle and $$\vec{B}\cdot\hat{n}$$ is the same in any point of the rectangle because the field is uniform. For this particular surface the flux is constant. Without actually calculating it but just by looking at the flux definition we can conclude that this is true for any surface with any border that moves with the rod because the field is uniform and if the rod moves perpendicularly to the field, the angle between $$\vec{B}$$ and $$\hat{n}$$ does not change over time. | 2021-04-15 18:04:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 7, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8033167123794556, "perplexity": 157.99976115897022}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038087714.38/warc/CC-MAIN-20210415160727-20210415190727-00535.warc.gz"} |
http://everything.explained.today/Siegel%27s_lemma/ | # Siegel's lemma explained
In transcendental number theory and Diophantine approximation, Siegel's lemma refers to bounds on the solutions of linear equations obtained by the construction of auxiliary functions. The existence of these polynomials was proven by Axel Thue;[1] Thue's proof used Dirichlet's box principle. Carl Ludwig Siegel published his lemma in 1929.[2] It is a pure existence theorem for a system of linear equations.
Siegel's lemma has been refined in recent years to produce sharper bounds on the estimates given by the lemma.[3]
## Statement
Suppose we are given a system of M linear equations in N unknowns such that N > M, say
a11X1+ … +a1NXN=0
aM1X1+ … +aMNXN=0
where the coefficients are rational integers, not all 0, and bounded by B. The system then has a solution
(X1,X2,...,XN)
with the Xs all rational integers, not all 0, and bounded by
(NB)M/(N-M).
[4]
gave the following sharper bound for the Xs:
max|Xj|\le\left(D-1\sqrt{\det(AAT)}\right)1/(N-M)
where D is the greatest common divisor of the M by M minors of the matrix A, and AT is its transpose.Their proof involved replacing the Dirichlet box principle by techniques from the geometry of numbers.
## References
• Bombieri. E.. Vaaler. J.. On Siegel's lemma. Inventiones Mathematicae. 73. 1. 1983. 11–32. 10.1007/BF01393823. harv. .
• Book: Hindry . Marc . Marc Hindry . Silverman . Joseph H. . Joseph H. Silverman . Diophantine geometry . . Berlin, New York . Graduate Texts in Mathematics . 978-0-387-98981-5 . 1745599 . 2000 . 201 . harv . .
• Wolfgang M. Schmidt. Diophantine approximation. Lecture Notes in Mathematics 785. Springer. (1980 [1996 with minor corrections]) (Pages 125-128 and 283-285)
• Wolfgang M. Schmidt. "Chapter I: Siegel's Lemma and Heights" (pages 1–33). Diophantine approximations and Diophantine equations, Lecture Notes in Mathematics, Springer Verlag 2000.
## Notes and References
1. Thue. Axel. Axel Thue. Über Annäherungswerte algebraischer Zahlen. J. Reine Angew. Math.. 135. 1909. 284–305. harv.
2. Siegel. Carl Ludwig. Carl Ludwig Siegel. Über einige Anwendungen diophantischer Approximationen. Abh. Preuss. Akad. Wiss. Phys. Math. Kl.. 1929. 41–69. harv., reprinted in Gesammelte Abhandlungen, volume 1; the lemma is stated on page 213
3. Bombieri. E.. Enrico Bombieri. Mueller, J. . On effective measures of irrationality for
{\scriptscriptstyle\sqrt[r]{a/b}}
and related numbers. Journal für die reine und angewandte Mathematik. 342. 1983. 173–196.
4. Lemma D.4.1, page 316. | 2020-05-25 08:50:36 | {"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": 0.9595077037811279, "perplexity": 3572.1656638768736}, "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-2020-24/segments/1590347388012.14/warc/CC-MAIN-20200525063708-20200525093708-00502.warc.gz"} |
http://math.stackexchange.com/questions/109309/a-question-about-dirichlet-test-for-converge-fx-sin-x-x-alpha | # A question about Dirichlet Test for converge $- f(x)=\sin x/x^{\alpha}$
I know how to solve and prove that
$$\int_{0}^{\infty} \frac{\sin(x)}{x^\alpha} \, dx$$ converge for $0 < \alpha < 2$ with regular tests and integration by parts.
But with the Dirichlet test, I just see that I have one function which is monotonic decreasing to $0$ for any given $\alpha$ and the integral on the $\sin(x)$ is bounded for $[0,\infty]$ because so it should converge. so it should converge for any $\alpha$.
Clearly I don't understand the Dirichlet test, but I've read its definition many times and still I don't understand where I got it wrong.
-
Don't abuse the display style! Use them appropriately. Thanks to Nunoxic for his substantial edit and I have as well edited the post substantially. There is a gap: because so. I don't think they ever go together. – user21436 Feb 14 '12 at 16:37
Does the behaviour of $1/x^\alpha$ near 0 play well with Dirichlet? – David Mitra Feb 14 '12 at 16:38
thanks. I just dont know how to add Latex in the same line, everytime i am inserting Latex code its just jumps to the next line without any \n newline character. and regarding 1/x^\alpha - isnt it monotonic decreasing for any given alpha? or that i am looking it wrong and because its not "proper" integrable in [0,infinity] i cant use it? – YNWA Feb 14 '12 at 16:42
Dirichlet Test
Let $f$, $g :[a,\infty)\rightarrow\Bbb R$ be such that:
1) $f$ is decreasing and $f(x)\rightarrow0$ as $x\rightarrow\infty$.
2) $g$ is continuous and there is an $M$ such that $\Bigl|\int_a^x g(t)\,dt\Bigr|\le M$ for all $x>a$.
Then $\int_a^\infty f(t)g(t)\,dt$ converges.
Now, is $f(x)={1\over x^\alpha}$ defined on all of $[0,\infty)$? Could you even define an extension of $f$ to $[0,\infty)$ so that it remains monotone?
-
you' the man...thank you! that part seemed to have vanished from my notebook – YNWA Feb 14 '12 at 18:47 | 2015-08-04 01:39:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9127391576766968, "perplexity": 437.37703089875265}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042990177.43/warc/CC-MAIN-20150728002310-00040-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://mathhelpforum.com/algebra/204520-shared-weight-limits-help.html | # Math Help - shared weight limits help
1. ## shared weight limits help
Ok, I don't know if I'm in the right section or not but here goes my question.
What is the calc for this. Say I have 1 person who can lift 100lbs. His limit is of ccourse 100lbs. But if I have 2 people who can lift 100lbs what is their combined lifting limit. Add a third person. I know there is a spesific calc for this but I can't remember it.
2. ## Re: shared weight limits help
Ans is 1 person= 100lbs
the calculation is average weight method.
one person can lift 100lbs and other can lift 100lbs
Then average of two people lift is 100lbs.
Got stuck with Average Weight problems ?
3. ## Re: shared weight limits help
Originally Posted by ugsquish
Ok, I don't know if I'm in the right section or not but here goes my question.
What is the calc for this. Say I have 1 person who can lift 100lbs. His limit is of ccourse 100lbs. But if I have 2 people who can lift 100lbs what is their combined lifting limit. Add a third person. I know there is a spesific calc for this but I can't remember it.
To me, this is a physics question, not a mathematics question...Am I correct in my assumption?
Anyways. I'm going to use KG instead of LBS.
A person can lift 100KG. That means that he uses the force: F=ma.
m = 100kg, a=9,8m/s^2 (gravity) and we get 980 N.
If two people can lift 100 kg each, then their combined lifting limit would be 980*2=m*9,8m/s^2=200kg.
I'm not sure if this is what you are asking...But I'll leave it here in case. | 2015-11-25 16:07:28 | {"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": 0.8636648058891296, "perplexity": 1598.6337941551342}, "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-2015-48/segments/1448398445208.17/warc/CC-MAIN-20151124205405-00263-ip-10-71-132-137.ec2.internal.warc.gz"} |
http://mathoverflow.net/revisions/115471/list | 2 Corrected formatting.
Using Engel's Theorem and Lie's Theorem, one can easily establish the following result:
Let $\frak{g}$ be a finite-dimensional Lie algebra over an algebraically closed field $\mathbb{F}$ of characteristic $0$. If $\frak{g}$ is solvable, then $[\frak{g},\frak{g}] {\frak{g}},{\frak{g}}]$ is nilpotent.
In order to apply the two theorems stated at the beginning, one must assume that (i) $\mathbb{F}$ is algebraically closed, (ii) $\mathbb{F}$ has characteristic $0$, and (iii) $\frak{g}$ is finite-dimensional. If we relax each of these three conditions in turn, are there certain well-known counterexamples?
1
A certain theorem about finite-dimensional Lie algebras over an algebraically closed field with zero characteristic.
Using Engel's Theorem and Lie's Theorem, one can easily establish the following result:
Let $\frak{g}$ be a finite-dimensional Lie algebra over an algebraically closed field $\mathbb{F}$ of characteristic $0$. If $\frak{g}$ is solvable, then $[\frak{g},\frak{g}]$ is nilpotent.
In order to apply the two theorems stated at the beginning, one must assume that (i) $\mathbb{F}$ is algebraically closed, (ii) $\mathbb{F}$ has characteristic $0$, and (iii) $\frak{g}$ is finite-dimensional. If we relax each of these three conditions in turn, are there certain well-known counterexamples? | 2013-05-21 16:23:24 | {"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": 0.8750520348548889, "perplexity": 50.56066519098263}, "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-2013-20/segments/1368700168711/warc/CC-MAIN-20130516102928-00024-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://www.quantize.maths-fi.com/node/16 | ## Asymptotic quantization error of continuous signals and the quantization dimension
Title Asymptotic quantization error of continuous signals and the quantization dimension Publication Type Journal Article Year of Publication 1982 Authors Paul L. Zador Journal IEEE Trans. Inform. Theory Volume IT-28 Pagination 139–149 Date Published March Keywords information-theory, nldr, rate-distortion, source-coding, vector-quantization Abstract Extensions of the limiting quantization error formula of Bennet are proved. These are of the form , where is the number of output levels, is the th moment of the metric distance between quantizer input and output, is the signal space dimension, and is the signal distribution. If a suitably well-behaved -dimensional signal density exists, , and does not depend on . For this reduces to Bennett's formula. If is the Cantor distribution on , and this equals the fractal dimension of the Cantor set . Random quantization, optimal quantization in the presence of an output information constraint, and quantization noise in high dimensional spaces are also investigated. | 2022-07-02 19:43:19 | {"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": 0.8305572271347046, "perplexity": 1574.8496127149901}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104204514.62/warc/CC-MAIN-20220702192528-20220702222528-00112.warc.gz"} |
http://www.saralstudy.com/study-eschool-ncertsolution/mathematics/application-of-derivatives/1183-the-total-revenue-in-rupees-received-from-the-sale | Question 16
# The total revenue in Rupees received from the sale of x units of a product is given byR (x) = 13x2 + 26x + 15Find the marginal revenue when x = 7.
Marginal revenue is the rate of change of total revenue with respect to the number of units sold.
\begin{align}MR=\frac{dR}{dx}\end{align}
∴Marginal Revenue
MR = 13(2x) + 26 = 26x + 26
When x = 7,
MR = 26(7) + 26 = 182 + 26 = 208
Hence, the required marginal revenue is Rs 208.
--> | 2019-04-21 10:13:09 | {"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": 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": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5673741698265076, "perplexity": 881.6164673758308}, "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-2019-18/segments/1555578530527.11/warc/CC-MAIN-20190421100217-20190421122217-00516.warc.gz"} |
https://www.albert.io/learn/ap-calculus-ab-bc/question/average-rate-of-change-from-graph | Limited access
What does the expression $\cfrac{k(2+h)-k(2)}{h}$ represent for the function $k(x)$ shown below?
A
The derivative at $x=2$.
B
$k'(2)$
C
The instantaneous rate of change of $k$ at $x=2$.
D
The average rate of change of $k$ over the interval $[2,2+h]$.
Select an assignment template | 2017-03-25 00:09:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22549398243427277, "perplexity": 832.8778303412765}, "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/1490218188717.24/warc/CC-MAIN-20170322212948-00616-ip-10-233-31-227.ec2.internal.warc.gz"} |
https://www.idpoisson.fr/agenda-de-lidp/?id=2393 | # Agenda de l’IDP
## Séminaire d'Analyse
We study whether the solutions of a fully nonlinear, uniformly parabolic equation with superquadratic growth in the gradient satisfy initial and homogeneous boundary conditions in the classical sense, a problem we refer to as the classical Dirichlet problem. Our main results are: the nonexistence of global-in-time solutions of this problem, depending on a specific largeness condition on the initial data, and the existence of local-in-time solutions for initial data $C^1$ up to the boundary. Global existence is know when boundary conditions are understood in the viscosity sense, what is known as the generalized Dirichlet problem. Therefore, our result implies loss of boundary conditions in finite time. Specifically, that a solution satisfying homogeneous boundary conditions in the viscosity sense eventually becomes strictly positive at some point of the boundary. This is joint work with Alexander Quaas. | 2020-02-26 06:18:12 | {"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": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8988239765167236, "perplexity": 242.33381475023552}, "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/1581875146187.93/warc/CC-MAIN-20200226054316-20200226084316-00477.warc.gz"} |
https://projecteuclid.org/euclid.die/1367846888 | ## Differential and Integral Equations
### Dirichlet problem for the Schrödinger operator in a half-space with boundary data of arbitrary growth at infinity
Alexander I. Kheyfits
#### Abstract
We consider the Dirichlet problem for the Schrödinger operator in a half-space with boundary data having an arbitrary growth at infinity. A solution is constructed as the generalized Poisson integral. Uniqueness of the solution is investigated also.
#### Article information
Source
Differential Integral Equations, Volume 10, Number 1 (1997), 153-164.
Dates
First available in Project Euclid: 6 May 2013
Permanent link to this document
https://projecteuclid.org/euclid.die/1367846888
Mathematical Reviews number (MathSciNet)
MR1424803
Zentralblatt MATH identifier
0879.35039
Subjects
Primary: 35J10: Schrödinger operator [See also 35Pxx]
#### Citation
Kheyfits, Alexander I. Dirichlet problem for the Schrödinger operator in a half-space with boundary data of arbitrary growth at infinity. Differential Integral Equations 10 (1997), no. 1, 153--164. https://projecteuclid.org/euclid.die/1367846888 | 2018-06-18 09:49:46 | {"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": 0.8290281891822815, "perplexity": 1842.8316807326457}, "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-2018-26/segments/1529267860168.62/warc/CC-MAIN-20180618090026-20180618110026-00110.warc.gz"} |
https://math.stackexchange.com/questions/1290546/if-g-is-cyclic-then-g-h-is-cyclic | # If $G$ is cyclic then $G/H$ is cyclic?
If $G$ is cyclic, then $G/H$ is cyclic?
The proof I got goes like this: $G$ is cyclic, so $G=<g>$ for some $g\in G$. So any coset in $G/H$ would be of the form $Hg'=Hg^n$ for some $n$. So $Hg$ is an generator of $G/H$. Thus, $G/H$ is cyclic.
I might just be confusing myself, but we have only shown that $Hg'$ is in form of $(Hg)^n$. But what if we are missing some $n\in\mathbb{N}$? That is, there is no quotient group of the form $Hg^2$, for example.
To make myself a little bit clearer, I think what the above proof has done was showing that $\forall Hg'\in G/H, Hg'\in <Hg>$, thus $G/H \subset <Hg>$. I feel that this is not a complete proof.
As other answers have noted, the quotient group is a group. Because $$G$$ is cyclic, every element of $$G$$ can be written in the form $$g^n$$ for some $$n \in \mathbb{N}$$. Thus, all the right cosets will be of the form $$Hg^n$$ for some $$n \in \mathbb{N}$$, and you can arrive at $$Hg^n$$ by "multiplying" (as it's been defined) $$Hg$$ by itself $$n$$ times. Also, if $$G/H$$ is smaller than $$G$$—which happens whenever $$H$$ is a nontrivial normal subgroup—then there will indeed be some $$n$$ missing, in a sense$$^\dagger$$: we will have $$Hg^n = Hg^m$$ for some $$n \neq m$$. But this will be of no consequence to the above proof.
Here is a different way of approaching this problem, sans cosets$$^\ddagger$$:
If $$H$$ is a subgroup of a cyclic group $$G$$, then $$H$$ is necessarily normal since every subgroup of an abelian group is normal (cyclic implies abelian). As such*, there exists a group $$G_1$$ and a surjective group homomorphism $$\phi:G \rightarrow G_1$$ such that $$\ker(\phi) = H$$. From the isomorphism theorem, we get $$G_1 \cong G/H$$.
So the problem is equivalent to determining whether the homomorphic image of a cyclic group is cyclic. This is rather immediate: assuming $$g$$ generates $$G$$, consider any $$a \in G_1$$. We have $$a = \phi(g^n)$$ for some $$n$$, and further $$\phi(g^n) = \phi(g)^n$$. So we see that $$\phi(g)$$ generates $$G_1$$.
$$\underline{\textbf{Footnotes}} \\[0.5em]$$
$$^\dagger$$This is to say: as we pass to the quotient, some elements are now regarded as "the same" modulo $$H$$. For more about this, see my post here for analogous discussion pertaining to rings and their quotients; for groups of course, there is only $$1$$ operation / operation table.
$$^\ddagger$$To be perfectly accurate, it's not that we aren't using cosets; rather, we are sweeping them under the rug of the isomorphism theorem.
*Indeed, in general, $$G/H$$ is a group $$\iff H$$ is normal. There are many equivalent notions for normality. Click here for further discussion.
One can make several arguments to the effect that $(Hg)^n$ is always an element of $G/H$. The simplest would be to appeal to the fact that quotient group is, in fact, a group - in particular, meaning that it is closed under products. If $(Hg)^2$ were not in the quotient, but $Hg$ was what would $Hg\cdot Hg$ be?
More elementarily, though, the quotient group $G/H$ is defined by looking at the cosets of $H$. So $Hx$ is in the quotient group for any $x$ in $G$ - so, since $g^n$ is in $G$, it follows that $Hg^n=(Hg)^n$ is in $H$.
• Put another way, $Hg^2$ may take you back to the identity, $H$, but it's definitely in $G/H$. – pjs36 May 20 '15 at 3:20
• Can I argue that, $G/H$ as a group is in the cyclic group generated by $Hg$. Since the subgroup of a cyclic group is cyclic as well, $G/H$ is cyclic as well? – 3x89g2 May 20 '15 at 3:22
• @Misakov You could, but it's not a sensible way to do it - the group generated by $Hg$ equals $G/H$, so it makes little sense to the latter being a subgroup of the former as the reason for them both being cyclic - they are both cyclic because $<Hg>$ is and they are equal. The fact that $Hg'=(Hg)^n$ tells you that $<Hg>$ contains $G/H$. The fact that $Hg$ is an element of $G/H$ tells you that every power of it is in $G/H$ - that is $G/H$ contains $<Hg>$. They are thus equal (as sets and as groups). – Milo Brandt May 20 '15 at 3:27
$G$ cyclic
$H \trianglelefteq G$
$G/H = \{aH: a \in G\}$
$\langle x \rangle = G$ where $x \not = e$
$a = x^k \Rightarrow aH = x^kH = (xH)^k$
This was for arbitrary element so done.
If $g'$ is any element of a group $G,$ and if $H$ is a subgroup of $G$, then $Hg$ is by definition a right coset of $H$ in $G.$ This includes the case that $g'=g^2$ for some $g\in G,$ regardless of whether $G$ is cyclic or $H$ is a normal subgroup of $G.$
You're pretty much done, as long as you can justify your claims.
In general homomorphism maps cyclic group to cyclic subgroup. We know that the quotient homomorphism $\pi$ maps $G$ onto $G/H$, i.e. $G/H=\pi(G)$. So if $G$ is cyclic, then $G/H$ must also be cyclic. | 2020-01-26 18:23:19 | {"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": 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": 39, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9447697997093201, "perplexity": 91.07245682303159}, "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/1579251690095.81/warc/CC-MAIN-20200126165718-20200126195718-00495.warc.gz"} |
https://www.gamedev.net/forums/topic/527924-per-pixel-point-light-glsl/ | Per-Pixel Point Light GLSL
Recommended Posts
Hey, having some real trouble with my shaders, it's been a week and I still can't sort it out, so for me, that's forum time :p. I need a picture to explain what's going wrong. As you can see, light is totally skipping that point. Here are my shaders, I'm doing light stuff in worldspace, because, if not, that strange effect shown in the picture, rotates around the light. *sigh*. Also, ignore "position", it's best not to ask why, but i'm using it to translate just for the minute. Ignore the specular stuff too, (the half vector) I know that's wrong. Vertex:
varying vec3 normal;
varying vec3 halfV;
varying vec4 lightVertexVec;
uniform vec4 position;
uniform mat4 modelViewMatrix;
//I get my eyeDIR (eye direction vector, for specular) and lightPOS (light position vector) from the APP
uniform vec3 eyeDIR;
uniform vec4 lightPIS;
void main()
{
//I need the world position of the vertex, so i can get a direction vector between it and the light
vec4 calculatedVertex = gl_Vertex - position;
//I need the light-vertex vector, to grab direction and distance off
lightVertexVec = ((lightPIS) - (calculatedVertex));
//Make sure everything that needs to be applied to the normal is
normal = gl_Normal;
//We only need one set of vertex co-ordinates
gl_TexCoord[0] = gl_MultiTexCoord0;
//Optmized setting of position
gl_Position = gl_ProjectionMatrix * gl_ModelViewMatrix * (gl_Vertex + position);
}
Fragment:
//sampler2D for diffuse map and specular map
uniform sampler2D tex, spec;
varying vec3 normal;
varying float Power, lightDistance;
varying vec3 halfV;
uniform vec3 eyeDIR;
varying vec4 lightVertexVec;
void main()
{
//I store the final specular value in a single float
float specPower;
vec4 specular;
float specFinal;
//Att = multiplyer for light distance stuff
float att;
//Quick ambient, I'm going to set ambient to uniform when i link it in with TINCS, so map makers can set it
vec4 ambient = vec4(0.03,0.03,0.03,0.03);
vec4 color = ambient;
//Now, I normalize the light-vertex vector to get the direction of the light to the vertex
vec4 lightDirection = normalize(lightVertexVec);
//Then I just get the length for distance
vec4 lightDistance = length(lightVertexVec);
//Calculate the halfVector, (for specular stuff) I think this code might be dodgey! Take a good look darkblu :P
halfV = normalize((lightDirection + (vec4(eyeDIR.x,eyeDIR.y,eyeDIR.z,0) * gl_ProjectionMatrix * gl_ModelViewMatrix)) / 2);
//Cacluate the power of the light, by getting the dot product of the normal and light direction
Power = max(dot(normalize(normal), normalize(lightDirection)),0.0);
//Get the diffuse value off the texture and if there is no diffuse, we set it to white
vec4 diffuse = texture2D(tex,gl_TexCoord[0].st);
if(diffuse == 0)
{
diffuse = vec4(2,1,1,1);
}
//Get the specular value off the specular texture
specular = texture2D(spec,gl_TexCoord[0].st);
float specMulti = specular;
//attenuation equals one over the linear and quadratic power of the light, lower you go, the more powerful the light is
att = 1 / (0.00001 * lightDistance + 0.1 * lightDistance * lightDistance);
//add the diffuse values onto the final color
color += att * (diffuse * Power);
if(specMulti < 1.0 && specMulti > 0.0)
{
//I've taken out the spec stuff for now, so we can solve this
//specPower = max(dot(normal, halfV),0.0);
//specFinal = 1 * pow(specPower,specMulti);
//color += att * specFinal;
}
//Get the final color!
gl_FragColor = color;
}
Any help is great. Thanks! EDIT: I've circled the light in the picture, the compression seems to make it invisible.
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I don't know how much of a help this is, but when I implemented shaders in one of my games, one user complained of not being able to see anything... and there was a strange red glow, somewhat like what you showed. It was later determined that his graphics card didn't have shader support.
It looked very similar to that, though.
Hope this helps,
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I've just made it a red light. No problem there. I'm running a 9600GT ;).
GLEW would spew errors if it wasn't supported also.
EDIT: The problem is the fact that the light stops, past an imaginary line cast from the bottom of the light, you see it stops to the right of the light. Yet, it's a point light, so it should be illuminated, but even more strangely, the plane past the area where light should be which is another mesh, has light applied to it. But again with the same strange cut off.
Also, my normals are fine.
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this looks a lot like a spot with an exponent applied to it (the lighting to the left). Are you sure it's a point light & calculated without spot exponent?
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Honestly, I have no idea half of those terms mean. The code is there, could you check for me?
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Quote:
Original post by ButtermanI've just made it a red light. No problem there. I'm running a 9600GT ;).
Oh ok, scratch my theory then. That's very odd, though. It looked almost the same, although said tester had an ATI Radeon 9000 mobile. ;)
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A/ only worry about diffuse lighting first
eg
gl_FragColor.xyz = vec3(dot( normal, light_vector ));
the same relates to any programming excercise when a bug occurs
B/
vec4 calculatedVertex = gl_Vertex - position;
why do u need a vec4 instead of vec3?
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I usually use
vec3 normal = normalize(gl_NormalMatrix * gl_Normal);
Besides that I have no idea. I sugest you recreate your math starting with this link
http://www.lighthouse3d.com/opengl/glsl/index.php?pointlight
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many times people mess up sending the light data to OpenGL during the fixed function operations.
Make sure you send a 4 component vector to glLightfv( GL_POSITION, vec4 position )
if you are using a point or spot light w = 1 ( because you are transforming point in homogenious coordinates )
and w = 0 if you are transforming a vector.
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It seem to me that there is someting wrong with normals. try a debug output.
I also think you can do it with much less expensive length() and normalize()functions.
Oh! why:
gl_Position = gl_ProjectionMatrix * gl_ModelViewMatrix * (gl_Vertex + position);
when you can do simply:
gl_Position= gl_ModelViewProjectionMatrix * (gl_Vertex + position);
?!
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Quote:
Honestly, I have no idea half of those terms mean. The code is there, could you check for me?
Sounds like you copy and pasted code and expect to be a pro at openGL. Try updating the position uniform that you have each frame. Allow yourself to move the that position and draw it at run time.
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Quote:
Quote:
Honestly, I have no idea half of those terms mean. The code is there, could you check for me?
Sounds like you copy and pasted code and expect to be a pro at openGL. Try updating the position uniform that you have each frame. Allow yourself to move the that position and draw it at run time.
Actually. That's the exact oposite of the truth. First I wrote what I understood about lamberts cosine law from physics, it worked, yay! Then, I started reading through tutorials about per-pixel lights and point lights. I implemented it as I understood it from those tutorials. Obviously, I've done somthing really wrong, because it's not working :D. If I had of copy-pasted it, wouldn't it have worked?
Anyway. Yes, I'm using homogenous co-ordinates, if you read the code you would have realised I'm not even using any fixed function stuff, I can't! This code is targetting ES 2.0, I'm going to have to replace the matricies with my own, because all matrix math is out of ES 2.0, that's why I'm multiplying matrices individually. Anyway, multiplication law, it dosen't make a difference what order I do it in.
The problem is in the multiplication of the matrices, while I understand physics concepts quite well, I'm not so great on maths. I need to pass the light in world-space.
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Original post by ButtermanThis code is targetting ES 2.0, I'm going to have to replace the matricies with my own, because all matrix math is out of ES 2.0, that's why I'm multiplying matrices individually. Anyway, multiplication law, it dosen't make a difference what order I do it in. The problem is in the multiplication of the matrices, while I understand physics concepts quite well, I'm not so great on maths. I need to pass the light in world-space.
Actually, you will find that the order of multiplication *does matter* for matrices, as they are not commutative with respect to multiplication.
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• 22 | 2017-10-20 03:44:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.49316731095314026, "perplexity": 3331.621512540389}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823630.63/warc/CC-MAIN-20171020025810-20171020045810-00343.warc.gz"} |
https://www.paris-billets.com/harry-potter-e-o-calice-de-fogo-dublado-720p-mp4-work | 04th Août2022
by carodah
I’ve tried search and removed » » + « ? » + space a lot of time, but no successful. A: I’m not 100% sure what your problem is, but if all you are trying to do is drop the spaces into the file, then you can use a loop: for %%x in (« %~1 ») do set « var=%%x » & SET « var=!var: =! » & SET « var=!var: \= » & SET « var=!var: \ « ! » & SET « var=!var: |= » & SET « var=!var: |! » & SET « var=!var: « ` » » The : will switch any spaces that are converted from your original string into \\, which is a escaped backslash. If you want to convert all characters in the string, you can replace the : with a single!. Q: Verification of $[\phi(x):\phi(y)]=e^{K(y-x)}$ Let $\mathbb{F}_p$ be the finite field of $p$ elements and $\phi : \mathbb{F}_p \rightarrow \mathbb{F}_p$ a linear surjective homomorphism with kernel $\langle 0 \rangle$. Let $K=\sum_{n=1}^\infty\frac{1}{p^n}$ and $x,y \in \mathbb{F}_p$. I want to show that $$[\phi(x):\phi(y)]=e^{K(y-x)}.$$ Attempt: Note that $|\ker(\phi)|=p^\ell$ for some $\ell \in \mathbb{Z}$. If $[\phi(x):\phi(y)]=e^{K(y-x)}$, then \begin{align} &[\phi(x):\phi(y)]^K[\phi(x):\phi(y)]=e^{K(y-x)\times K(y-x)}\\ &[\phi(x):\phi(y)]^Ke^{K(y-x)^2}=e^{K^2(y-x)^2}\\ &[\phi(x): | 2022-08-18 16:19:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.887589156627655, "perplexity": 545.6283414709809}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573242.55/warc/CC-MAIN-20220818154820-20220818184820-00085.warc.gz"} |
https://homework.cpm.org/category/CON_FOUND/textbook/a2c/chapter/9/lesson/9.3.2/problem/9-149 | ### Home > A2C > Chapter 9 > Lesson 9.3.2 > Problem9-149
9-149.
1. Given the equation x3 − 6x2 + 7x + 2 = 0. Homework Help ✎
1. Verify that x = 2 is a solution.
2. What is one factor of x3 − 6x2 + 7x + 2?
3. Use (b) to find another factor.
4. What are all the solutions of x3 − 6x2 + 7x + 2 = 0?
Substitute 2 into the equation for every x.
8 − 24 + 14 + 2 = 0
0 = 0
Use the value for x given in problem a to calculate the factor.
(x − 2)
Try using a generic rectangle.
(x2 − 4x −1)
See part (a) for one solution.
$\frac{4\pm\sqrt{16+4}}{2}$
Use the quadratic formula to find the other solutions in the equation x2 − 4x − 1.
$x=2, 2\pm\sqrt{5}$ | 2020-02-19 09:39:14 | {"extraction_info": {"found_math": true, "script_math_tex": 2, "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": 0.7373263239860535, "perplexity": 1090.0068038609836}, "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-2020-10/segments/1581875144111.17/warc/CC-MAIN-20200219092153-20200219122153-00344.warc.gz"} |
https://kb.osu.edu/dspace/handle/1811/16063 | COUPLED VIBRATIONS IN ALKALI HALOGENATES
Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/16063
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Title: COUPLED VIBRATIONS IN ALKALI HALOGENATES Creators: Soriaga, M. P.; Neufeld, J.; Andermann, G. Issue Date: 1973 Publisher: Ohio State University Abstract: Studies based on band shape analyses indicate that for alkali halogenates, such as $NaClO_{3}, KClO_{3}, NaBrO_{3}$, and $KBrO_{3}$, the external (lattice) modes may be described as those of independent, damped harmonic oscillators. The very short lifetimes of the excited states of these modes, on the other hand, indicate the presence of coupling. The inherent contradiction of the above statements may be removed if the dissipation of lattice energy is rationalized in terms of coupling schemes which are not due to phonon-phonon interactions but require the mechanisms based on interactions involving internal modes. Direct experimental evidence on combination modes will be offered and evaluated. Description: This work was supported in part by the National Science Foundation. Present address of J. Neufeld: Chemistry Department, University of North Carolina, Raleigh, North Carolina, 27607. Author Institution: Department of Chemistry and Hawaii Institute of Geophysics, University of Hawaii URI: http://hdl.handle.net/1811/16063 Other Identifiers: 1973-M-09 | 2016-05-01 00:42:06 | {"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": 0.37915605306625366, "perplexity": 2633.2712980421056}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860113541.87/warc/CC-MAIN-20160428161513-00141-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://ai.stackexchange.com/tags/gym/hot?filter=all | # Tag Info
7
You can try the actions yourselves, but if you want another reference, check out the documentation for ALE at GitHub. In particular, 0 means no action, 1 means fire, which is why they don't have an effect on the racket. Here's a better way: env.unwrapped.get_action_meanings()
4
OpenAI's Gym is a standardised API, useful for reinforcement learning, applied to a range of interesting environments many of which you can then access for free with little effort. It is very simple to use, and IMO worth learning if you want to practice RL using Python to any depth at all. You could use it to ensure you have good understanding of basic ...
3
There is a really small mistake in here that causes the problem: for index, (current_state, action, reward, next_state, done) in enumerate(minibatch): if not done: new_q = reward + DISCOUNT * np.max(future_qs_list) #HERE else: new_q = reward # Update Q value for given ...
3
This is a case of overfitting the Q function leading to compounding errors when selecting actions. You have been training your neural network as function approximator for too long on the same data distribution, so the neural network loses it's ability to generalize and slowly starts overfitting, i.e. learns the data exactly as it is or at least very closely....
3
To answer your question, the specifics of some of the OpenAI Gym environments can be found on their wiki: The episode ends when you reach 0.5 position, or if 200 iterations are reached. There is a deeper question in what you asked, though: My initial understanding was that an episode should end when the Car reaches the flagpost. The environment certainly ...
3
The episode ends when either the car reaches the goal, or a maximum number of timesteps has passed. By default the episode will terminate after 200 steps. You can customize this with the _max_episode_steps attribute of the environment.
3
You may be very interested to know that there was a bug in the v2 Lidar tracing, making the agent think there were phantom objects, and sometimes intersecting with its own legs: https://github.com/openai/gym/pull/1789 Finding this bug makes me even more impressed anyone has solved BipedalWalkerHardcore-v2 - it seems the observations from lidar have been ...
3
You can try to figure out what exactly does an action do using such script: action = 0 # modify this! o = env.reset() for i in xrange(5): # repeat one action for five times o = env.step(action)[0] IPython.display.display( Image.fromarray( o[:,140:142] # extract your bat ).resize((300, 300)) # bigger image, easy for visualization ) ...
2
There is no way to tell via the Gym API, and to any RL-based learning agent this is entirely unimportant, discrete actions are just arbitrary labels, and their effects are learned by trial and error in terms of reward and changes to state. If you need to know, you can read the code for each environment. Often it is described in a comment, or as constants. E....
2
There seems to be no difference between 2 & 4 and 3 & 5. The inconsistency mentioned by Icyblade is due to the mechanics of the Pong environment. "Each action is repeatedly performed for a duration of k frames, where k is uniformly sampled from {2,3,4}" So the action is just repeated a different number of times due to randomness
2
It is your choice. This can even be different between training and target system. The approach called "exploring starts" chooses a random start state (and action if you are assessing a deterministic policy for action values). In general, if you don't have a reason to pick exploring starts, you should aim for your env.reset() function to put the environment ...
2
It depends on the task the agent is trying to learn and of course on the environment constrains. In an Atari game agents have a pre-fixed starting point because that's part of the games rules, so I would say that this is enough of a justification to make each simulation start from that starting point. Moreover, you have to pay attention to the kind of ...
2
Since the environment has some randomness in it, purely memorizing a trajectory to victory will not work. You will have to memorize every single trajectory for that to work, and there are an infinite number of them. So, you will need to add some sort of bias to your learning model - i.e., what to do when the observations in your pickle file don't match the ...
2
What's exactly the point of time.sleep() in this code? I don't really understand it, you're simply stopping the execution of the program for $0.01$ seconds, how will that affect the simulator in any way ? It's not running in parallel, it does one step of the simulation when you call env.step function and returns the next state and reward. Calling sleep ...
2
What I was looking for is multi-agent RL, where I have multiple RL agents, each controlling actions of one user. All RL agents/user make an action in each environment step and each get their own reward. I represent my RL agents' actions as dict, containing the RL agent ID as key and its action as value. The different agents may either use the same or a ...
2
Yes, it is the state of the memory; this would mainly involve variables, since the code would be in ROM. Since it is only 128 bytes in size, the screen memory would also not be included in this. The idea is that all information relevant to the game is captured in these 128 bytes; they represent the state of the game world at any given time. Movements of the ...
1
After checking the Internet, you will probably find several resources such as https://github.com/mohammadasghari/dqn-multi-agent-rl https://rlss.inria.fr/files/2019/07/RLSS_Multiagent.pdf https://arxiv.org/abs/2011.00583 and others. Try to understand the principles first (see above). After some reasonable amount of coding you can adapt OpenAI gym. Good ...
1
The question is conceptually wrong, because of misunderstanding of area. Explanation: The idea is to replace open ai gym by something different. For example: web-site or computer game. There is no way to create an environment based on image. If you want to use implemented algorithm for open ai gym and want to change environment for your own, could do ...
1
I had to change the actions selection function for this and tune some hyper-parameters. Here's what I did to make it converge: Sampled the noise from a standard normal distribution instead of sampling randomly. Changed the polyak constant (tau) from 0.99 to 0.001 (I didn't have an idea of what it should be, so I had just set it randomly in the first try) ...
1
I don't recommend changing the rules of the environment. What you could do: Perform a method called bucketing i.e. take a value from a continuous state space see which discrete bucket it should go into and then let your agent use the bucket number as the observation. e.g. Say I do have a continuous state space with one variable in range $[-\infty,\infty]$ ...
1
I guess it would always be better if you can reuse existing environments to make it work for yourself. Since most of the environment codes is anyway opensourced, you can always edit it to your liking. If you want a custom environment, you can add an environment to gym like this.
1
Model your problem as an MDP To solve a problem with reinforcement learning, you need to model your problem as a Markov decision process (MDP), so you need to define the state space, the action space, and the reward function of the MDP. Understand your problem and the goal To do define these, you need to understand your problem and define it as a goal-...
1
I've actually implemented this game before using deep reinforcement learning. You are dealing with a dynamic action space here, where the action space may change at each time step of the game (or more generally the MDP). First, let's discuss the actual action spaces in each one of the two phases of Crib (or Cribbage) and formalize the question. Phase 1: The ...
1
The renowned book Reinforcement Learning: An Introduction (2nd edition), by Sutton and Barto, provides a different update rule than your first update rule for policy evaluation. Their update rule is more similar to your second update rule. See section 4.1. They also provide the pseudocode for policy evaluation on page 75 of the book. You can also find the ...
1
I thought about my input-layer. I had the 500 states one hot encoded. So 499 of every input node would be 0. And 0 is very bad in an neural network. I tried the same code with the "CardPole-v0" and it worked. So think about your input guys
1
I'm not sure why you need a continuing environment, but actually you can make most (if not all) OpenAI Gym environments continuing. When you perform a step, you receive information about the next state, the reward, a termination signal and a dictionary with additional information. Simply ignore the termination signal if you want the episodes to continue ...
1
It's not on your end, as a creator of flight simulator, to worry about what action should get the credit for the reward that happened some time after the action was taken. You should return the reward when the actual event happens not when the action that caused it happened. It's the job of the reinforcement learning agent to figure that out. For example if ...
1
I believe if you run a single agent in multiple parallel environments many times you will get similar actions in similar states, the reason behind multiple agents is that you will have different agents with different parameters and you can also have different explicit exploration policies so your exploration will be better and you will learn more from ...
1
https://github.com/openai/retro Current list of machines is Atari Atari2600 (via Stella) TurboGrafx-16/PC Engine (via Mednafen/Beetle PCE Fast) Game Boy/Game Boy Color (via gambatte) Game Boy Advance (via mGBA) Nintendo Entertainment System (via FCEUmm) Super Nintendo Entertainment System (via Snes9x) GameGear (via Genesis Plus GX) Genesis/Mega Drive (via ...
1
Ok, I found https://blog.openai.com/gym-retro/ but there may be other platforms?
Only top voted, non community-wiki answers of a minimum length are eligible | 2021-06-23 12:26:55 | {"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": 0.6171468496322632, "perplexity": 776.8153338980895}, "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/1623488538041.86/warc/CC-MAIN-20210623103524-20210623133524-00145.warc.gz"} |
https://www.passeidireto.com/arquivo/1021626/pinedo_problemas_deterministicos/29 | 251 pág.
# Pinedo_problemas_deterministicos
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V (q1, . . . , qF , u, h) = min
(
min
h\u2032\u2208G(q1,...,qF ,u,h)
(
V (q\u20321, . . . , q
\u2032
F , u, h
\u2032) + \u3c4
)
,
V (q\u20321, . . . , q
\u2032
F , u\u2212 1, h)
)
,
where q\u2032g = qg for g \ufffd= h, q\u2032h = qh \u2212 1, \u3c4 = sh\u2032h + pqh,h,
sh\u2032h = 0 if h = h\u2032, and where G(q1, . . . , qF , u, h) =
= {h\u2032 | h\u2032 \u2208 {0, 1, . . . , g}, V (q\u20321, . . . , q\u2032g, u, h\u2032) + \u3c4 \u2264 dqh,h};
for qg = 0, 1, . . . , ng, g = 1, . . . , F, and
u = 0, 1, . . . ,
\u2211F
g=1 qg and h = 1, . . . , F.
Optimal Value Function:
min
(
u | min
g=0,1,...,F
(
V (n1, . . . , nF , u, g)
)
<\u221e
)
||
In words, the procedure can be described as follows: the \ufb01rst term in the
minimization of the recursion selects job (qh, h) to be scheduled on time if this
is possible and chooses a batch h\u2032 for the previous on-time job; the second term
selects job qh of batch h to be late.
Note that the optimal value function is equal to the smallest value of u for
which
min
g=0,1,...,F
(
V (n1, . . . , nF , u, g)
)
<\u221e.
In order to determine the computational complexity of the procedure, note
that the number of states that have to be evaluated is again O(nFn F ). Since
4.6 Batch Processing 99
each recursive step requires O(F ) steps to solve, the time complexity of this
algorithm is O(F 2nF+1), which is polynomial for \ufb01xed F .
The more general problem 1 | fmls, sgh |
\u2211
wjUj can be solved in pseu-
dopolynomial time when F is \ufb01xed. This result follows from the fact that Al-
gorithm 4.5.7 can be generalized to minimize the weighted number of late jobs
in O(nFW ) time, where W =
\u2211n
j=1 wj .
The total tardiness objective
\u2211
Tj and the total weighted tardiness objective\u2211
wjTj turn out to be considerably harder than the
\u2211
Uj objective.
4.6 Batch Processing
Consider a machine that can process a number of jobs simultaneously, i.e., a
machine that can process a batch of jobs at the same time. The processing times
of the jobs in a batch may not be all the same and the entire batch is \ufb01nished
only when the last job of the batch has been completed, i.e., the completion
time of the entire batch is determined by the job with the longest processing
time. This type of machine is fairly common in industry. Consider, for example,
the \u201dburn-in\u201d operations in the manufacturing process of circuit boards; these
operations are performed in ovens that can handle many jobs simultaneously.
Let b denote the maximum number of jobs that can be processed in a batch.
Clearly, the case b = 1 refers to the standard scheduling environment considered
in previous sections. It is to be expected that the b = 1 case is easier than the
case b \u2265 2. Another special case that tends to be somewhat easier is the case
b = \u221e (i.e., there is no limit on the batch size). This case is not uncommon
in practice; it occurs frequently in practice when the items to be produced are
relatively small and the equipment is geared for a high volume. In this section
the case b = \u221e (or equivalently, b \u2265 n) is considered \ufb01rst; several objective
functions are discussed. Subsequently, the case 2 \u2264 b \u2264 n \u2212 1 is considered;
several objective functions are discussed.
When b = \u221e the minimization of the makespan is trivial. All jobs are pro-
cessed together and the makespan is the maximum of the n processing times.
However, other objective functions are not that easy. Assume p1 \u2264 p2 \u2264
· · · \u2264 pn. An SPT-batch schedule is de\ufb01ned as a schedule in which adja-
cent jobs in the sequence 1, . . . , n are assembled in batches. For example, a
possible batch schedule for an 8-job problem is a sequence of four batches
({1, 2}, {3, 4, 5}, {6}, {7, 8}). The following result holds for 1 | batch(\u221e) | \u3b3
when the objective function \u3b3 is a regular performance measure.
Lemma 4.6.1. If the objective function \u3b3 is regular and the batch size is
unlimited, then the optimal schedule is an SPT-batch schedule.
Proof. The proof is easy and left as an exercise (see Exercise 4.22). unionsq
Consider the model 1 | batch(\u221e) | \u2211wjCj . This problem can be solved
via dynamic programming. Let V (j) denote the minimum total weighted com-
100 4 Advanced Single Machine Models (Deterministic)
pletion time of an SPT-batch schedule that contains jobs j, . . . , n, assuming
that the \ufb01rst batch starts at t = 0. Let V (n + 1) denote the minimum total
weighted completion time of the empty set, which is zero. A backward dynamic
programming procedure can be described as follows.
Algorithm 4.6.2 (Minimizing Total Weighted Completion Time \u2013
Batch Size In\ufb01nite)
Initial Condition:
V (n+ 1) = 0
Recursive Relation:
V (j) = min
k=j+1,...,n+1
(
V (k) + pk\u22121
n\u2211
h=j
wh
)
j = n, . . . , 1.
Optimal Value Function:
V (1) ||
The minimization in the recursive relationship of the dynamic program se-
lects the batch of jobs {j, . . . , k \u2212 1} with processing time pk\u22121 for insertion at
the start of a previously obtained schedule that comprises jobs {k, . . . , n}. It is
clear that this algorithm is O(n2).
Consider now the model 1 | batch(\u221e) | Lmax. This problem also can be solved
via a backward dynamic programming procedure. Assume again that p1 \u2264 p2 \u2264
· · · \u2264 pn. Let V (j) denote now the minimum value of the maximum lateness for
SPT-batch schedules containing jobs j, . . . , n, assuming their processing starts
at time t = 0.
Algorithm 4.6.3 (Minimizing Maximum Lateness \u2013 Batch Size In\ufb01-
nite)
Initial Condition:
V (n+ 1) = \u2212\u221e
Recursive Relation:
V (j) = min
k=j+1,...,n+1
(
max
(
V (k) + pk\u22121, max
h=j,...,k\u22121
(pk\u22121 \u2212 dh)
))
j = n, . . . , 1.
4.6 Batch Processing 101
Optimal Value Function:
V (1) ||
The minimization in the recursive relationship assumes that if a batch of
jobs j, . . . , k \u2212 1 (with processing time pk\u22121) is inserted at the beginning of a
schedule for jobs k, . . . , n, then the maximum lateness of jobs k, . . . , n increases
by pk\u22121, while the maximum lateness among jobs j, . . . , k \u2212 1 is
max
h=j,...,k\u22121
(pk\u22121 \u2212 dh).
This algorithm also operates in O(n2).
Example 4.6.4 (Minimizing Maximum Lateness \u2013 Batch Size
In\ufb01nite)
Consider the following scheduling with \ufb01ve jobs, i.e., n = 5.
jobs 1 2 3 4 5
pj 2 3 8 10 27
dj 10 7 6 16 43
The initial condition is V (6) = \u2212\u221e. The recursive relationships result in
the following:
V (5) = max(V (6) + p5, p5 \u2212 d5) = \u221216.
V (4) = min
k=5,6
(
max(V (k) + pk\u22121, max
h=4,...,k\u22121
(pk\u22121 \u2212 dh))
)
= min
(
max(\u221216 + 10, 10\u2212 16) , max(\u2212\u221e, 11,\u221216)
)
= min(\u22126, 11) = \u22126
V (3) = min
k=4,5,6
(
max(V (k) + pk\u22121, max
h=3,...,k\u22121
(pk\u22121 \u2212 dh))
)
= min
(
max(\u22126 + 8, 8\u2212 6) , max(\u221216 + 10, 10\u2212 6, 10\u2212 16) ,
max(\u2212\u221e, 27\u2212 6, 27\u2212 16, 27\u2212 43)
)
= min(2, 4, 21) = 2
V (2) = min
k=3,...,6
(
max(V (k) + pk\u22121, max
h=2,...,k\u22121
(pk\u22121 \u2212 dh))
)
102 4 Advanced Single Machine Models (Deterministic)
= min
(
max(2 + 3, 3\u2212 7) , max(\u22126 + 8, 8\u2212 7, 8\u2212 6) ,
max(\u221216 + 10, 10\u2212 7, 10\u2212 6, 10\u2212 16),
max(\u2212\u221e, 27\u2212 7, 27\u2212 6, 27\u2212 16, 27\u2212 43)
)
= min(5, 2, 4, 21) = 2
V (1) = min
k=2,...,6
(
max(V (k) + pk\u22121, max
h=1,...,k\u22121
(pk\u22121 \u2212 dh))
)
= min
(
max(4,\u22128) , max(5,\u22127,\u22124) , max(2,\u22122, 1, 2),
max(\u22126, 0, 3, 4,\u22126) , max(\u2212\u221e, 17, 20, 21, 11,\u221216)
)
= min(4, 5, 2, 4, 21) = 2
Backtracking yields the following schedule: The fact that the minimum for
V (1) is reached for k = 4 implies that the \ufb01rst three jobs are put together
in one batch. The minimum for V (4) is reached for k = 5, implying that job
4 is put in a batch by itself. ||
The 1 | batch(\u221e) |\u2211Uj problem is slightly more complicated. In Chapter 3
it was already observed that there is not any backward algorithm for minimizing
the number of late jobs when b = 1. It turns out that no backward algorithm has
been found for the b =\u221e case either. However, the problem can be solved via
a forward dynamic programming algorithm. Let V (j, u, k) denote the minimum
makespan of an SPT-batch schedule for jobs 1, . . . , j, with u being the number
of late jobs among these j jobs and the last batch having a processing time pk
(implying that this last batch will end up containing also jobs j + 1, . . . , k, but
not job k + 1).
The dynamic program operates in a forward manner and distinguishes be-
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http://bettereconomics.blogspot.com/2011/02/ | ## Monday, February 28, 2011
Facing a \$25 billion state budget shortfall, Gov. Jerry Brown has proposed to cut hundreds of thousands of parents and their children from the welfare rolls on July 1. Additionally, law enforcement officials say the governor’s proposal to transfer thousands of convicted felons and parolees to county jails and oversight will “wreak havoc” on the criminal justice system.
“I don’t think there is any question the day of reckoning has arrived,” said Paul McIntosh, executive director of the California State Association of Counties, which has devoted a special section of its Web site — “Counties in Fiscal Crisis” — to educate officials about the situation. Calwatch
The poor would be better served if we break up the state.
### Check out this video of a Solar Eruption
Here, taken by NASA
### This author speaks my language
Most importantly, these thinkers refined the very definition of information, purifying the concept just as earlier generations of scientists had purified the meaning of "mass" and "energy". But whereas the crisp new definitions of mass and energy restricted the words' use to technical contexts, information's new definition, one based on bits and entropy (I = -∑pi log2 pi, to be precise) widened its applicability. Information theory soon colonised economics, genetics, thermodynamics and other fields. Today some physicists even argue that information is more fundamental than both mass and energy - that it may be the very bedrock of reality.
New Scientist has the review
James Gleick's The Information
### Looks like kazzillions of federal jobs.
The U.S. government has 15 different agencies overseeing food-safety laws, more than 20 separate programs to help the homeless and 80 programs for economic development.
These are a few of the findings in a massive study of overlapping and duplicative programs that cost taxpayers billions of dollars each year, according to the Government Accountability Office.
A report from the nonpartisan GAO, to be released Tuesday, compiles a list of redundant and potentially ineffective federal programs, and it could serve as a template for lawmakers in both parties as they move to cut federal spending and consolidate programs to reduce the deficit. Sen. Tom Coburn (R., Okla.), who pushed for the report, estimated it identifies between \$100 billion and \$200 billion in duplicative spending. The GAO didn't put a specific figure on the spending overlap. WSJ
Nice work Tom Coburn. Most of that is a result of my dingbat Senator, Babs Boxer.
### Reserve currency
What is it? Lets do what Mish does and go with the Investopeida definition:
"A foreign currency held by central banks and other major financial institutions as a means to pay off international debt obligations, or to influence their domestic exchange rate."
There are two parts, liquid and stable makes a reserve currency. The stable currencies are liquid over the largest domain, normally that is the US. By having the largest, liquid economy, the Dollar changes its relative value the slowest and remains liquid. So central banks do not have to constantly trade currencies over the global domain, they get a good representation value.
The world is changing, however, in one respect. Robots can do the trading for us. So liquidity and a measure of uncertainty are the two things we need to hold currencies over time. We need to measure entropy so the robots can propery trade currencies and get a measure of the global economy, no longer relying on a single large economy.
It is relativly simple to measure entropy if the robot has access to transaction data and can run the equivalent of a Huffman encoder. In the new world we have robots distributed to each of the central bankers, and these robots constantly measure the amount of mutual entropy among the currencies, and make trades to maintain minimal redundancy. As simple as that.
What makes this work is relatively transparant trade of goods, intra and inter national trade. China does not have that, the US does, Japan does, Europe does, Brazil does. There are no more reserve currencies, they are gone. There is simply the measure of transparancy in the various economies. Gold really doesn't work, it is too heavy to trade, and so there is always a paper trail between the gold and the trades.
You cannot beat the robots as long as you can gather good trading sets.
If you need a measure of mutual entropy, follow my blog and I will dig it out. Basically my approach is to constantly measure the combined real yield curve of all currencies by mutual quantization, a multi-variate Huffman encoder. Then the central bank need only trade to make the holdings a close match to the measured yield curve. Probably the best way to do this is the same method I do with the SP100 trades. I put them all into a group and encode them as one. Individual currency trades, then matched to the cobine curve generate trading vectors, directional trades. In fact, there will exist the ideal yield curve for all currencies, treated as if they we a single channel. That ideal curve will be the matching fibnacci set, just rrade each currency against the ideal.
Now, what can I use for the trading values. Probably the price of oil, copper, gold, wheat, and other internationally taded commodities would be a good start. Any graduate students out there? Let's see, I need my SQLite to hold trading sets, my R Project and SQL interface, and my Huffman encoder. Check, now I just need more data.
### There are always zero interest rates
The curve does not extend to infinity. Sumner makes the usual canard about zero interest rates.
When economists talk about Zero Interest rates, they mean a yield curve that would cause some bonds to go belly up because the borrower is belly up. He is really back to the Great Exogenous, some government bond god that insures no defaults can happen to the Lords favorite lenders.
Iceland didn't bother with the Great Exogenous, they just let the bond holders go belly up, and more power to them. My county here in Fresno is about to go belly up, and some existing lenders will realize losses, unless we can pass the losses on up Congress. Anybody in the Tea Party want to cover a billion in potential bond haircuts?
### Bill Gates still hasn't discovered the Internet
What should policymakers do? One approach is to get more students in front of top teachers by identifying the top 25 percent of teachers and asking them to take on four or five more students. Part of the savings could then be used to give the top teachers a raise. (In a 2008 survey funded by the Gates Foundation, 83 percent of teachers said they would be happy to teach more students for more pay.) The rest of the savings could go toward improving teacher support and evaluation systems, to help more teachers become great. He says.
That should say: "Get students in from of Lap Top teachers." The modern issue is to distinguish between teachers and baby sitters.
### Billy Kristol might just start a trillion dollar war
The Pentagon is deploying naval and air forces around Libya as the US and UK governments consider tougher measures to force Muammer Gaddafi from power, including the possible establishment of a no-fly zone.
“We must not tolerate this regime using military force against its own people,” David Cameron, UK prime minister, said. “In that context I have asked the Ministry of Defence and the Chief of the Defence Staff to work with our allies on plans for a military no-fly zone.”FT
California is not paying for this one.
### Cops starting the Civil War
Pajama media has the story about Cops now taking sides in the various protests. We have a real worry about that in Fresno County as we approach bankruptcy, here the cops and protesters are quick to grab the gun.
### I take a shot at Brad's puzzle
And yet, even though politicians who fail to safeguard economic growth and high employment tend to lose the next election, leaders in Europe and the US are clamoring to enact policies that would reduce output and employment in the short run.
He s going through the Great Exogenous mantra again.
What Brad wants are local policies adjusted to local conditions. Our unemployment levels are quite low and demand quite high relative to previous trading partners. In order for locality to reign, we have to decouple, that is, import much less goods and export much less socialized banking.
Our economy is now a smaller part of global distribution. Increasing central government spending yesterday made a smaller dent in a larger domain. Increasing spending today just makes central government huge relative to a smaller, local domain. Foreigners no longer fund our entitlements, nor to they fund municipal pension bonds.
The yield curve is low relative to equilibrium, but we do not yet have visibility about how to reach equilibrium. In the smaller domain, a central government that consumes 14% of GDP seems to be equilibrium.
### Model the revisions
Stolen chart from Calculaed Risk
Why are the revisions growing? Data is skewed because the global economy is still undergoing adaption. What we see is the still winding up of the gobal commodities shortages. We take the minimal number of steps to make adjustments to inventory levels. This occurs mainly in oil, and food. In the peripheral area of the supply chains, the future estimate of commodities demand is not determined until the shortage hits. At that point, we discover who is short and who is not, so we readjust orders to compenstate. It is a step by step process.
The normal macro estimates are way off, and it takes longer and longer to get accurate estimates of where things stand. The whole excercize in monetary and fiscal policy becomes unstable bullshit, quite frankly, they make a measurements on a time scale that was valid three years ago and expect the same time scale to be valid in the middle of the restructuring.
This makes nonsense of the paradox of thrift delusion which is still floating around. Government planning becomes absurd because we elect Congress from the periphery which is out of whack relative to macro measurements coming into DC. It means that the pipe Ben thinks he is filling with money is a different pipe than is being filled, so he doesn't get feed back until the bounce back.
### There must be two Moodys
Also, the acknowledgment by Moody's of a possible review and downgrade comes barely a month after analysts at both Moody's and Standard & Poor's Ratings Services warned that the U.S. could be downgraded if it doesn't make progress in shrinking its elevated debt levels. Moody's said in January that if the U.S. doesn't act in the next two years, the likelihood of a negative outlook on its rating would increase.
The U.S. is grappling with a national debt of about \$14 trillion and rising. Its debt is 66% of gross domestic product and is projected to hit 85% by 2015, the International Monetary Fund expects. WSJ
Then we have another Moody's:
The report, by Moody's Analytics chief economist Mark Zandi, offers fresh ammunition to Democrats seeking block the Republican plan, which would terminate dozens of programs and slash federal appropriations by \$61 billion over the next seven months.
Zandi, an architect of the 2009 stimulus package who has advised both political parties, predicts that the GOP package would reduce economic growth by 0.5 percentage points this year, and by 0.2 percentage points in 2012, resulting in 700,000 fewer jobs by the end of next year. WA Post
What is going on?
There is a plot afoot. The schophrenia has more to do with Moodys keeping their clients satisfied than telling the truth. They have, on the one hand, a number of big finance, like Goldman Sachs, who make a living selling Treasury paper, and want insurance on muncipal debt. On the other hand,... Wait, there is no other hand. If Treasury goes down, so does Moodys. If Big Finance goes down, so does Moodys, Moodys itself is so embedded in the government economy that is cannot escape.
Ben, Obama, Tim and Big finance have worked a scheme for QE3 and Amercan world socialist banking. But, the game is nearing the end, emerging markets have caught on, with an economy contracted, there is no path for the money. Getting close to default.
### Budgeting week by week seems fine to me
“We want to make sure that this continuing resolution that is worked out allows enough time for the negotiations that need to take place to produce a continuing resolution that takes us through the whole fiscal year, because what we believe is that if we keep returning to this process every couple of weeks that will be bad for the economy because of the uncertainty it creates and the tension around that,” Mr. Carney said.
WSJ
The Senate got us into this problem, so I say, keep them working 24/7 and manage the budget week by week. The economy remans in a contracted condition, that means we are all bunched around the short end of the curve. Overall, the transaction rates are lower, but the focus is on the short end. Congress has two choices, reform or focus on the short end.
### Th Great Exogenizers
Two-thirds of respondents–including majorities of Democrats, Republicans and independents–said that improving transportation infrastructure is “important.” And 80% agreed that federal funding to improve and modernize transportation systems would boost local economies and create jobs.
But only 27% said that raising the federal gasoline tax would be an “acceptable” way to provide more highway funding. The 18.4-cent federal tax on a gallon of gasoline provides most funding for transportation projects, and many groups, including the Chamber of Commerce, have called for raising the gas tax. WSJ
Politicians like Pauk Ryan cause this problem. They spread ignorance and lies. The solution is simple, you want to fix a bidge, get the money locally. Cut entitlements and use earnarks, another solution.
### Now Drum is passing around the bogus chart
The one Dean Baker issued, one that claims that eventually we will get to our eqilibrium rate of growth. Yes, we will gt there, but a whole lot of public sector workers will be laid off before we can achieve our natural rate once again.
This is the same scam big finance started when they issued their report on lower local government spending. It starts with a very bad analysis then progresses among the various supporters. It is Progressives and Oligarchs in a collusion.
The fact is public sector unions are holding us back from equilibrium rate of growth, the economy is waiting for that sector to reform. Kevin Drum is effectively pushing for local government default and restructuring. Fine, then say it. Otherwise Kevin is just an ingeniously repeating the line his funders give him, just like the Tea Party.
Go read Kevin Williamson from NRO,he gets it right.
### Billy Kristol touts the Communist line
The politician most responsible for the debt crisis will unite the Republicans? This is Billy Kristol, advocate for mammouth federal government, chief of oligarchs spouting the socialist line.
Billy has a problem, his Big Government solutions will eventually default, in the same manner that the progressives will eventually default. There is an implicit unity between the Paul Ryan, debt fueled spending and the progressive debt fueled spending. Both are based on transfering corporate expenses onto the central government.
### Bruce Bartlett on the money
Hatch did not address the fact that following the 1993 tax increase, which he and every other Republican in Congress opposed, federal spending fell from 21.4 percent of GDP to 18.3 percent in 2000. And, contrary to starve-the-beast theory, when Republicans slashed taxes during the George W. Bush administration, it did not put any downward pressure whatsoever on spending, which rose to 20.7 percent of GDP in Bush’s last year Here.
He is pointing to the Big Government element in the Tea Party. The danger here is that the Tea Party ultimately will opt to strangle their own constituents with more bailouts. Basically the Tea Party should be aware that their funders are pushing for socialism, for the oligarchs. That means shifting more corporate expenses onto the taxpayer.
The Tea Party needs to make up their mind, do they want an early default by Congress, or do they want more Big Government subsidies for their funders. If they chose the former, then an orderly restructuring of federal government is great news, but they should say so. Right now they are looking more and more like fools.
### Behind the scenes on the Goldman Sachs report
Eventually, Obama could also come under pressure from state officials and the financial industry to provide emergency aid to states and municipalities if they can't pay off their debts. Wash Post
Goldman Sachs issued a report on lower GDP due to lower state and local spending. The report was deliberately ingenious for a reason. Big finance wants more insurance from the Great Exogenous for its failure on due diligence. Public sector advocates picked the report up and ran with it, it appeared in hundreds of local newspaper op eds.
Its the game, finance uses our dependency on the government economy to force more Congressional bailouts of finance. Many economists are both part of the plot and the target of the plot. But the intention was to transfer taxpayer money to big finance. The plot is uncovered. The way to stop these delusions is to raise the progressive rates at the federal level.
### Look at revision history to estimate changes in growth
Tim Duy, and others, are using minimum variance estimates to get changes in GDP growth due to supply shocks. But the method assumes the economy is capable of infintesimal changes in inventory cycles and quant levels. A better estimate is to look at revision history, for the time being. Run the normal minimum variance estimate, then take the near term predicted growth and revise it down by the recent revision percentage. That should give you a lower bound for the near term, but it does not tell you how long we stay in the lowered condition. But I would expect something like 2.7% growth for the next quarter.
Supply chains will shorten for the next slowdown, however, I think poducers in the middle of the curve know this, and plan an orderly consolidation. Also, emerging markets have figured much of this out, they won't be caught off guard this time around. The real problem is going to be goverment adjustments here at home.
### Negative interest rates
The best way to achieve them is via bankruptcy. My county in Freasno will go bankrupt, and the people most responsible for that, Judy Case and Henry Perea are in the county supervisors office today sweating out how he will explain all this. It is hard to imagine a more loathsome bunch of corrupt liars then the Fesno Country supervisors.
You can look at the whole group here. They have basically been operatives of the local public sector unions, an have systematically robbed the county of wealth. All of them should be hauled before a grand jury and indicted. The problems go back even farther, but most of this bunch were part of the billion dollar theft when they secretly signed on to another billion dollars in pension giveaways to the public sector unions. Fresno County will be the next county in California to implement negative interest rates.
Speaking of negative interest rates, Tim Duy reports that we have to do some of that at the Federal level as a result of the ongoing oil shortages. If Ben wants to implement negative interest rates then he should be the state bankruptcy arbiter. His best approach would be to manage a break up of the Dollar currency zone, working with Illinois, California, Texas, Florida and New York to build their own cantral banks while negotiating haircuts for federal bond holders.
### Game changing in foreign currency markets
Emerging markets figure out the currency game.
As recently as last month, governments of emerging economies from South Africa to Brazil warned that competitive devaluations might be needed to keep their strengthening currencies from stifling economic growth.
Now, talk of currency controls is being abandoned and interest rates are rising as record food prices and oil at \$100 a barrel make inflation the bigger threat. That means developing nations will keep outperforming in the foreign-exchange market, according to Morgan Stanley.
They have discovered that American finance goes to their markets because they have the growth, we don't. So what does this mean for Sumner and his NGDP growth theoory? That if he wants near term accuracy, then his macro model better include more emerging markets and less domestic American markets.
It also means that America had better adapt products to emerging markets, not domestic markets. M1V will be dropping faster as we downgrade our consumer sector. It also means that foreign markets will build up their entitlement systems and quit loaning money to us.
Sure enough, in the next Bloomberg article.
Consumer spending in the U.S. probably rose at a slower pace in January as food and fuel prices climbed, economists said before a report today.
Americans’ purchases, which account for about 70 percent of the economy, rose 0.4 percent after a 0.7 percent gain in December, according to the median estimate of 59 economists surveyed by Bloomberg News. Other figures may show manufacturing continued to expand and home sales dropped.
I have been noting for some time that M1V has been on a downward trajectory for some time. Heterskedactic effects make is unobservable in macro summations, but not any more.
## Sunday, February 27, 2011
### I call it the Canadian Interpretation
The finding that inflation is not forecastable over the Great Moderation period is consistent with the predictions of the DSGE model given the strong monetary policy rule estimated for this period. Specifically, since under this rule the policymaker will alter the interest rate to counter forecastable deviations of inflation from the target, the rule will eliminate forecastable movements in inflation and leave only unforecastable shocks to drive fluctuations. Say Edge and Gurkaynak
In this study they find they central banks set interest rates by correcting their past errors. I call it the Canadian Interpretation because Nick Rowe mentioned is as part of his New Keynesian model. This is comparable to the Copehnagen interpretation of quantum physics.
What does it mean?
As my hords of readers should readily tell us, it means that the bankers yield curve are the variances in a Fibonacci sequence that matches the channel bandwidth to the signal to noise ratio of the bankers involved. It is the basis of the information theory, and implies that minimal redundancy is the norm to use. As we all know by now, I have said for three years the economy is based on a fixed uncertainty constant determined biologically.
I also implies that DSGE models are only valid for a short term look ahead and that heteroskedacity is not an artifact but a fundamental process of adjustment. I think this validates the Levine model and the Hidalgo-Hausmann model, ultimately. It certainly validates my model, and the trader's model of Fibonacci matching (Elliot Waves). It also should validate the Geoffrey West study of cities. It validates the Snap Back theorem, Schumpeter Creative Destruction. But more importantly, it tells us that information revolutions cause major disruptions because we are forced to requantize. It likely validates the idea of Fibonacci counters in our brains.
I think implies that we should be moving faster toward automated transportation, because we will quantize the Roadbots and adapt to them very fast. And, don't forget the theory of minimal government, which implies progressve tax rates on central gvernment, and redistricting of state boundaries.
Welcome aboard!
### Tom Juravich gets it wrong on public sector unions
He points out, correctly, that Gov Walker is sap for business and gave away a bunch of goodies causing a deficit. OK, granted, he guy is strategically stupid. He also points out that currently Wisconsis public workers , through their unions, have close to parity in wages.
Neither of these two issues touch upon the basic problem, public sector unions have received collective bargaining rights that take away from voter choicess, especially in education. Agreements between buyers of services and sellers of services needs to be done between those two groups, without some formal mandate from high government authority. This problem is espcially acute in the relationship between information technoogy and education. We have a situation where collective bagaining is forcing students into classrooms that have lost their utility, being replaced by information technlogy. Teachers, in the classroom, no longer earn the Risk Free Return, mainly because of technology. Educution is being broken up. dismemebered, and reassembled into smaller, specializes processes.
I presume this is about the Wisconsin equivalent of the Dills Act. If Gov Walker is a dunce, then recall the guy or vote him out of office. But that is no reason to retain an outmoded version of the Dills Act.
### Working on theory
The next step in Channel theory is mutual entropy, or how does on sector know it is safe to expand distribution. Looking back at the post on contraction, what we want is knowledge of the conditions that let all the various sectors move from the contracted yield curve to the expanded yield curve. We will find simplification in the problem because we know we have a constant value of signal to noise ratio at equilibrium.
It seems the mathematicians are hard at work on the problem. And it has become a big issue in Internet searching, how does one search trust the links established by previous searches, and how fast to a set of search links converge. In economics, it has to do with finding an agreement between the arrival of wages and the arrival of goods. When should a producer change delivery quants in order to short the queue waiting to buy goods. If he changes to much, then wages go down to far. it is not just price discovery, but quant discovery also. This is what distinguishes channel theory from the Keyesian and monetarists.
Example: When does a collection of taders at the corner become a market? When the mean their distribution over the variance reaches a sufficient value, we will create a matching function, in our heads, and forever quantize that place as the market.
Looking at Mutual Entropy definiton we need to estimat the mutual probability of arrivals in the first equation. If the merchant cannot get that right, then he invests a lot and gets no customers.
The mathematicians read my blog, they will help us out.
### Let's do a standard Krugman correction
In this case, Krugman is passing along the Baker analysis of returns on public pensions. In it, Krugman refers to the Risk Free Rate of return. What he means is the shape of the yield curve under equilbrium conditions. Behind this assumption is that distribution has minimized redundancy, and all economic components are operating with standard uncertainty. The value is constant because standard uncertainty is biologically determined.
Unfortunalely, and Krugman knows this, the public sector is one of the components that has to reach equilibrium to get the risk free return, and public sector unions are not at equilibrium..
Public sector unions are keeping us from equilibrium. How do I know? Because they consume 80% of the public taxes in California, California on the edge of bankruptcy and has been for quite some time. California, acording to our elected Governor, cannot reach equilibrium unitl we lay off a whole bunch of public sector unions employees. California is due to pay 15% of the DC debt, and cannot do so until it reaches equilibrium.
Krugman is playing the expectations game. The idea is to convince us that Public Sector Unions earn their risk free rate, and once convinced, then he can go ahead and update the national accounts and say all is well, it must be somebody else's fault. We also call this the Great Exogenous religion.
This is theory of economics based on deception. If public sector unions could always get the risk free rate, then why do they need the Dills Act?
### Restructure the political system and save entitlements
Seriously, accept that DC has reached its limits, and start to split up the liabilities and assets. Rather than than continue the delusions of the Great Exogenous. This nation is going nowhere by sending batches of economists to DC with various magical potions, none of which work.
There are half a dozen ways to get a restructuring.
Regional nullification, starting with California. California needs to default, default on the Dills Act, default on our part of the DC debt, simply declare that the time has come.
Central Bank rebellion. Why doesn't Ben propose a break up of the dollar into regional currencies. It won't be the first time.
Abolish the Senate. Start an amendment process to simply do away with the Senate completely.
City States: Large metropolitan cities should vote on their own statehood.
Do all of these, we have the Internet, we can sort a lot of it out in real time. We will have a lot of hysteria from the Great Exogenizers, but hysteria lasts a short time. Once they see the energy and enthusiasm of escaping from DC they will all be on board, an they can create their own, new Exogenous.
### NYT editorial says nothing about entitlements
TThe NYT editors go into a rant about Republicans and the need to trim the budget. Yet, the biggest budget busters are the ones supported by the Times, entitlements, about which the Times says nothing. The lack of leadership is at the NYT. The Times insructs us to follow Obama policies, the same Obama who just gat a FICA tax cut, I guess intending to reduce the impact of Social Security. If Obama wants to reduce Social Secuirty, then put it in his plan, and reduce it.
Best solution? Quit reading the new York Times, they only confuse the issue. There is much better analysis on the web, and we can fact check the web in real time.
### My home county, making the headlines
Fresno County leads the state with 35% of taxes going to pension obligations. Heaadlines in local Fresno Bee. Whokudanode? We all knew for ten years, Davis, Brown, local voters, unions, the Gubinator, we all knew. We were just picking the appropriate crash point is all. Our UC system which educates teachers knew, including Romer. The Dills Act, good for one generation only.
## Saturday, February 26, 2011
### The mathematics of a contraction
The economy operates with minimal redundancy, resulting in rank reduction, as I point out so many times. The result is that the yield curve takes discrete jumps from position to position. So, consider an economy that attempts to maintain goods flow under two different rank settings. I used a 7 and 6 length Fibonacci series. But in the N=6 case, I have to equalize goods flow goods flow. Let jump below the graph and look at the yield curve equation
Tis si the standard aggregate generalized yield curve, I have added vi in the numerator to sum over all ecomponents operating at rates v. Remember that the cargo size, -log(vi) is always uniformly dirstibuted modulo one, and the economy always works integers. The value -vi*log(vi) is always one to the nearest integer, as in R:
Here is the scaled, rank seven F series: 0.038 0.038 0.077 0.115 0.192 0.308 0.500
My fastest transationrate is .5, the spectra is normalized to 1.0, meaning the Beta in the eqution is 1.0.
What is my equivalent to the economic quantity eqution? It is -log(g7) cargos, transacted g7 times over the longest inventory cycle, which becomes:
> round(-g7*log(g7)+.5)
[1] 1 1 1 1 1 1 1
All ones. In the completely normalized case, this is the quantity of total goods at each transaction rate, and the total good transacted is 7, over the longest inventory cycle in the distribution chain.
What happens if I drop rank? The good transacted has to increase, I have fewer transactions over all. So the gamma in the exponent of the yield curve must go to 7/6, to preserve quantity, as in the economic standard:
From Wiki. Except of course, in channel theroy we are smart enough to eliminate money. We would replace the equation above with the mutual entropy operator between two yield curves.
But, the point is, when we drop rank, we ship larger cargos and we have a total (sum but not mean) reduced transaction rate. That is we have to adopt economies of scale. Inside the firm or household we will see larger inventory levels. The curve is not as steep, so gains from specialization are lower. Variance in inventory levels reduce, we are safer. But less focused on the long term.
But, bottom line, there are only so many discrete solutions. When oil gets too expensive, we will suddenly contract farther than any one really expects, unless they understand channel theory.
Why did I increase gamma in the yield curve eqution? That goes back to the shannon theory:
C/B = log(1 + SNR) The C is the number of cargos I can carry in B trucks. -log(g6) is the information carraige, I have essentially multiplied all my cargo sizes by 7/6, and it is factored out of the maximum entrpy formu;a -g6*log(g6) which you ill see in the Huffman encoder. I grew my bit size over all symbols.
### Dean Baker is wrong on the Social Security wage tax
Dean Baker claims Fact Check is wrong for treating Social Secutity taxes like any other tax on income.
Dean baker is of the Great Exogeneous, so he looks into the bible and finds the words "designated" ragarding the Social Secutiry deducton from wages. Unfortunately FICA tax law is written by Congress, who also write the bible for income taxes. It is that same wage channel they tax to cover debt service. The Supremes have already ruled that Congress will treat SS taxes like any other income tax.
Here, from the 2010 tax relief:
§ Reduces the employee Social Security tax rate for wages paid in 2011 from 6.2% to 4.2%; the employer rate remains at 6.2% How did Congress do that if the tax was designated?
Tell that idiot to go read the bill. And tell that idiot we have the internet, the era in which he can spout bullshit and get away with it is gone. We know these economists are not scientists, we now fact check their claims
Remember, this is the same person who missed the great oil shortage.
### So what about this NGDP growth thingy of Sumner's?
He wants more money poured down the pipe. The money will seek the shortest path toward liquidity. Congress can easily spend it, and Congress is borrowing most of it. The second biggest chunk is going overseas, and will for a while as long as bond holders feel Treasury bills remain liquid. Little of it goes into the American domestic sector because we are still jammed up, dealing with state bankruptcies, oil shortages, and sticky wages.
But Congress doesn't seem to be turning a profit, see the Crowding Out post. And the IRS has no authority to collect taxes over seas, nor are investors likely to return overseas profits back to the US any time soon.
So Scott Sumner does have to worry about output distribution, he has to worry about whether the money path corresponds to the macro economy he is measuring. If he is measuing national accounts in the US but much of the money flows to Eastern Asia, then he has a problem, he will continually advocate NGDP growth unit the results are not showing up on national acounts, as higher oil pirces
Have no fear, however, bond holders are much smarter. They will shut off the flow with crunching interest rates long before.
### The CBO does crowding out
Here in a projected baseline of GDP into the future. Crowding out means that Congress has more demand on future resources and the private sector must shrink (or go underground). Open it up, it has crowding out starting now, today right now.
It is a bit confusing. The letter is dated Aug 2010, the Pelosi Congress. If the Pelosi Congress intended to turn a profit, there would be no crowding out, and a bigger federal government would have a higher multiplier. Pelosi and the CBO disagree about this, I think.
Another problem. Romer was doing the business planning for Obama at the time, yet Romer still thinks the Pelosi Congress was profitable, Romer kept insisting on high multiplers throughout, and still does, even with the Tea Party Congress.
Somebody is runnng a scam here, maybe it is the same people running the Choo Choo scam.
### I still like earmarks
But Carl Hulse watches them go away. They are great for Congressional districts, and I much prefer them to entitlements. They meet the Hidalgo-hausmann test of great variability over smaller domains at faster transaction rates. I blame California Senators Barb and Diane, and NY Schumer and Illinois Durbin for their demise.
### Ms Romer wants a bit of hyperinflation
Chris Romer talking from the NYT explaining to us what determines the yield curve. . True,as she pointed out, defaulting on our gold promises in 1933 allowed us a bit of hyperinflation. She would like to repeat a partial default, how can we help in her cause?
Helping Ms Romer find some hyperinflation:
We need to shrink the domain over which dollars flow and prevent dollars from entering new monetary domains, then she gets her inflation in the residual domains, mainly DC.
We can adopt our own money here in California and the West. Can California citizens find a way to renounce our obligation toward the \$15 trillion? If we Californians can do that, then most of the dollars return to the East Coast where they become illiquid and hyperinflationary.
Sounds like a plan to me. I would first upgrade the Lockyer Laser Printer. The next step would be a declaration that California only accepts California Laserbacks for taxes. Our California Assembly mght be a bit of a problem, they still dream of the Great Exogenous. But they are discovering the Obama comes bearing tax bills and Choo Choo scams, not money. The idea of a Western money, complete free of the DC, would be an attraction to other Western states, and Texas could pursue a similar plan. we can upgrade the Casadian Nation in the Northwest. let Alaska join Canada.
The Internet can help:
Continue to refuse sale taxes for on-line sales. Help Facebook advance their concept of digital money. Use the Internet for exchanges of goods by barter. Spend more time on the Internet and less time in commerce. Use the internet to help build secessionist movements. Organize on-line tax revolts in the three largest states that subsidize DC.
If Ms. Romer was really serious then we have a more direct path. Just have Congress refuse to pay interest on the debt while Ben continues to credit Treasury with digital money.
### Yes, that is the plan
Gov. Scott Walker, a Tea Party-tinged Republican, is the advance guard of a new GOP push to dismantle public-sector unions as an electoral force. Says Fineman
The questionn is why does Fineman need to write about news that has been public knowledge for ten years. Why not remove a legally entrenched force preventing local voter from making local decisions. It is true that Gov Walker wants to put his own legally entrenched forces into national power, but the solution to all the mumbo jumbo is to reduce national political power and put power back to local voters.
### Public Sector Unon mandates, take another hit
Bipartison pension commission has bad news for public sector unions, and good news for voters. They find current taxpyars have no intention of paying off promises made a generation ago. Anothe fail for the Great Exogenous
### Here's a problem set
You go to the open air market, and see three people in line to buy a carton of eggs. Take out your watch and compute the interest rate of a 30 year mortgage. We know it is possible with a stable queuing network to do this, we have the tools. But, you say, I would have a terrible error. Would you?
Consider the second case. You go to the supermarket in a small town and meet a maid doing the grocery shopping for the mistriess. Can you guess the relative value of the mistress' home? Very likely you could, and you may even have a good guess of the neighborhood that the mistress lives in.
The two problems are closely related queueing problems in the economy. The arrangement of houses, towns, eggs and maids is easily understood in our heads, we do graph algebra in our heads, and the economic network executes our graph algebra.
### The fallacy of composition and graph algebras.
We run across economists who claim two things, one, the sum is not always equal to the whole, and two we can measure the sum in macro economics. Seems like a contradiction? The math the economy uses is not the same math the macroeconomists use.
If a business reports output-input = surplus, it is not the case that surplus + input = output. The later computation is invalid because the economy cannot do that, in general. We cannot take a car apart and return the parts into inventory, no general invertability. The second problem is the change of units accountants tend to use. Rather than count carburators in inventory, they report that number in units of carburator prices, which may have changed considerably. The other problem is round off error, units are always rounded to the nearest integer in inventory management. Probably all three fallacies are related.
If the fallacy of composition relates more to macroeconomists using the wrong rules of computation, then what should macroeconomists count? Units of goods moved over a specified cycle of exchanges, the count of inventory exchanges from the slowest transaction rate to the fastest. This composition works, it makes no assumptions about asymmetry of trade, it deals with integer units, and insures mass flow is consistent.
A lot of economists get this, mainly sector economists. They count the flow of automobiles to the consumer, and compare car sales totals from one business cycle to the next. Calculated risk does this all the time. I see it done with volumes flows for the stock market.
If we count the flows of money, we can add it up and compare it to flows of money from a similar business cycle. If we compute on a business cycle that is one generation long, that is the longest inventory cycle is a generation then we have to wait one generation before we get an accurate measure of NGDP. I see historical economists compute real gdp based on hundred year cycles.
Lets call NGDP(i) the measure of integer flows of money up to some cycle i.
The ensembale of inventory cycles is an integer set. So it is perfectly reasonable to estimate nominal gdp relative to a specified maximum cycle and cycles less than. So we have GDP relative to the yearly cycle and the quarterly cycle. If I have the data, I can get real time NGDP on a daily cycle, and the number is accurate, to the daily cycle, as long as I measure short enough to avoid inerference with the next integer inventory cycle up stream, and as long as I measure unit flows. But I can always capture the sum components down stream, because they have smaller inventory cycle.
What is real GDP then? It is total GDP measured in money using a complete algebra, it is remotely related to NGDP. Take a NGDP measure accurate to a specified inventory cycle, NGDP(i). Estimate the discount rate from the selected inventory cycle, i , out to a maximum known cycle, and apply that estimate to convert to RGDP.
So, when Scott Sumner wants to increase NGDP he really means he wants to increase the rank of money distribution, he wants to extend NGDP out to the next cyle.
## Friday, February 25, 2011
### Unfair restrictions on voters by public sector unions in California
From the Dill Act:
a) The state shall grant exclusive recognition to employee organizations designated or selected pursuant to rules established by the board for employees of the state or an appropriate unit thereof, subject to the right of an employee to represent himself.
Translated, in California voters are not allowed to hire and fire individuals, but are manadated to deal with public sector unions. This seems a clear violation of proportional representation to me. This debate seems to be about anti-democratic processes written into law by Jerry the Younger, and voters are well advised to terminate the Dill act, if they value democracy. The rights to assembly are not denied to public sector unions, indeed the SUpremes would not allow it. Voters have given up certain rights, and voters have the right to recover them with the democratic process.
In the case of Wisconsin it seems that voters have decide to recover their rights, a very good judgment in my opinion.
### The rise in bond yields was due to what?
A top Federal Reserve official said Friday long-term bond yields may have risen in the wake of the launch of the central bank’s bond-buying program because market participants expected more purchases than were ultimately announced. Says Yellen
It was no secret that the Fed wanted dollar inflation. From the time the Fed announced the word was, go buy foreign, before the dollar inflates. So the last quarter, as the Fed started, domestic private investment dropped and foreign dollar inestments started. Any change in monetary policy requires an adjustment period. Since the announcement, the trade weighted dollar is down 3 points, and the adjustment is likely finished.
### Economists still don't get forecasting right
"We had every reason to believe the U.S. economy will do extremely well this year," said Bernard Baumohl, chief global economist for the Economic Outlook Group. "Now we have to go back to the drawing boards."
Wa Post
No, you don't have to go back to the drawing board, all you have to do is follow Mish.
Or you could follow M1V, which has never stopped droping since the crash. The Problem Mr. Baumohl has is that he has been hired to lie, to say things about which he has no knowledge.
The same article says local budget cuts in government hurt the economy, failing to point out the central government borrowing has stuck the three major funding states with a \$200 billion dollar debt service costs, due in four year. The \$3 trillion that Krygman, DeLong, and Thoma decided should be borrowed by Obama are paid for by Illinois, New York, and California, three states who have had severe budget problems since before the crash. How are these states going to cover the DC borrowing costs? By cutting the local government work force.
The Post fails to point out that we had severe oil problems in July, 2008, the exact date of the crash, but the Obama government never once considered that the oil shortage caused the crash in the first place. Nor evidently did Mr. Baumol figure out that we crased on the day oil peaked at \$140.
### Dave Cay Johnson tries the old scam, with Thoma's help
Thus, state workers are not being asked to simply "contribute more" to Wisconsin' s retirement system (or as the argument goes, "pay their fair share" of retirement costs as do employees in Wisconsin' s private sector who still have pensions and health insurance). They are being asked to accept a cut in their salaries so that the state of Wisconsin can use the money to fill the hole left by tax cuts and reduced audits of corporations in Wisconsin.
He talks about the fact that public unions want future taxpayers to cover expenses private sector workers handle with current savings.
No one is asking public union anything accept to bargain based on current wages and do the saving for future events themselves. He fails the sanity test. What is the loss if public sector workers handle their own future costs? None, according to his calculations, so he argues for Gov Walker, have public sector employees handle their own benefits.
His hidden claim is that Wisconsin intends to stiff the teachers and putting benefits back into the individuals hands is a scam. Wrong again, he is pulling the scam. Teachers have every right to bagain for current wages, there is such a thing as a Due Process requirement. Notice that Krugman and Thoma help Dave in trying out this new scam.
The semantic trick is Krugman, Thoma and Johnson. Let's take Johnson at his word: Tell teachers to cover their own benefits and bargain for increased wages. If teachers do not get the increased wages they think they need, then they can go work elsewhere. After all, according to Johnson, this method works just fine for the private sector.
### Try printing the abstract
We use state and county level variation to examine the impact of the American Recovery and Reinvestment Act on employment. A cross state analysis suggests that one additional job was created by each \$170,000 in stimulus spending. Time series analysis at the state level suggests a smaller response with a per job cost of about \$400,000. These results imply Keynesian multipliers between 0.5 and 1.0, somewhat lower than those assumed by the administration. However, the overall results mask considerable variation for different types of spending. Grants to states for education do not appear to have created any additional jobs. Support programs for low income households and infrastructure spending are found to be highly expansionary. Estimates excluding education spending suggest fiscal policy multipliers of about 2.0 with per job cost of under \$100,000.
So what the study says, if you eliminate Romer and her allegiance to teachers unions, then the stimulus could have done a much better job. Which begs the question, how do we eliminate Romer?
Oh yes, we apply a government economic model, the election, where we see Gov Walker doing a good job of eliminating the Romer policy and thus raising state government multipliers.
Thank you Krugman and Baker for pointing out what Thoma tries to hide from us, public unions have very low multipliers.
But, key, Krugman is getting into Hidalgo-hausmann in Small is Beautiful. The real issue behind low density states having low unemployment is hat low density staes have less income spread. Large dense cities support lengthy production chains so in a recession a reduction in chain length implies a much larger layoff rate, the employment reduction goes as NlogN, the same as the spread on the minimal spanning tree of distribution. The more dense the economy, the larger the rank, N, and the greater the NlogN.
### Stumbling and Mumbling gets oil correct
He talks about how high oil prices cause unemployment, a subject keynesians prohibited in their censourship for three years. What does tell you about Keynes? He prefered socialism even if it meant unemployment, as in the first stimulus which caused a rise in oil immports and today's rise in unemployment. His post is a good read, and an indirect indictment against Romer and Obama. Implicit in his post is an affirmation of channel theory, rather then Keynes. He implies much of what I have said about oil prices causing a producer collapse.
### The Tea Party is part of the economy
Stan Collender, idiot extraordinaire. The man is too goddamned stupid to understand any real model of the economy, so it is he who creates a delusional religion of the great Exogenous, putting government outside the economy. Then when his idiotic model doesn't hold up to reality, he blames the Democratic process and implicitly demands Keynesian dictatorship.
Let me axplain to the bozo that the model of the Tea Party was predicted four years ago, during the primaries, predicated on the typical results we get, as in Clinton's mid term elections? But bozos like Stan sit in a delusion,. and when the model becomes reality claim, "Oh No, this cannot happen, it is agains my religion of the Great Exogenous"
George Lakoff??? If you cannot explain the delusions of Stan Collender then why the hell do you study the brain?
### An economist making the Keynesian error
In both cases, the fiscal and monetary authorities should be asking themselves whether they've overestimated the performance of these economies and their ability to handle big, and largely unnecessary, short-term budget cuts. Ryan Avent of Free Exchange
He is talking about the downward revision of GDP that was just released in which fourth quarter GDP is now 2.8%, a meager showing. The revisions reflect quantization error, we cannot measure things with the same accuracy as before because the network rank is reduced, we have a smaller set of transaction rates. Hence, no successful search to sustainable patterns of trade (Kling), less netork density (Hidalfo-hausmann), lower precision (me)
The cause of the quantization error is exactly Ryan Avents solution, central government is not adapting and is holding the economy in a reduced rank position. Going back to Hidalgo and Hausman, once again, what do they say? GDP growth is based on the ability of the economy to expand variability in products. Channel theory tells us that the economy cannot raise rank because some major component of the economy is stuck in reduced rank, mainly central government. minimal redundancy is an apation toward channel coherence. Ryan's solution makes things worse, not better.
Note: One of the major causes of the downward revision was... local governments are going broke. The govenrment channel is top heavy, and local govenrments cannot find solutions.
We see these continual downward revisions because the Keynesians are measuring the aggregate and ignoring the heteroskedacity. As in Leonhardt, measuring total government employment and calling is small, then what happens? When the revisions come out and examine the dispersion and notice less variability in the retail end of government.
Catherine Rampell and Leonhardt are repeating this error today an will repeat it tomorrow. Keynesians are unable to correct their curricula. Keynes gave them a pretend theory that allows fake socialism.
### More on Fibonnacci
When I want a finite set of quants to work with I select a Fibonacci series as a set of transaction rates, scaled such that the fastest rate is .5, like this: g = 0.015 0.029 0.044 0.074 0.118 0.191 0.309 0.500
Scaling my quants put
Taken from this: f = 1 2 3 5 8 13 21 34 by dividing by 68.
The plot of log(g) is uniform in the plot. Within an integer, the spread of log(g) is even across the series.
I cal the series log(g) the quants of a maximum entropy distribution which are delivered at rate g, so that:
-g*log(g) is the entropy measured over the whole network at rate g. It is also the total quantity of -log(g) delivered over the network.
This simple model would result from perfect encoding out of my Huffman encoder, and the distribution of quantity sizes would be uniform, hence this sequence defines a maximum entropy distribution network of rank 8, the number of quants in my series.
Looking at -g*log(g): 0.029 0.050 0.069 0.100 0.139 0.191 0.252 0.316 0.363 0.347
where I have increased the rank by two. The values are all within an integer of being equal.
round(-g*log(g)+.5), rounding g to the nearest integer, yields 1 1 1 1 1 1 1 1 1 1.
When I talk about maximum entropy, I also mean minimum redundancy, which is more intituitive in economics. It would be natural from the sense of Hayek that we would find sustainable patterns of trade by looking to remove redundancy. Integer soltions arrise naturally because of transaction costs, for us to entertain an infinite variety of transaction sizes would imply that there is no cost in a trip to the store for even the smallest item.
How do we find the proper price of an item? On the micro level we generally know only -log(g), not g itself. But we get an estimate of g by looking at the number of people in line to buy a -log(g). Computing the price of items over the whole economy involves estimating the yield curve of money with a discount rate.
Comparing the variance of money to the variaince of a good, in the minimum vaiance world, is equivalent to finding the mutual entropy between money and a good in the minimum redundancy world. Hidalgo and Hausmann compute conditional variance in the product space of final demand. But I suspect the entire economics profession will eventually adopt minimum redundancy.
Anyway, the result here is that the generalized yield curve can have either -g*log(g) in the numerator, or -log(g) in the numerator depending upon when one is working on the macro or micro level. The effort is always to find the approximate measure of the yield curve in some local space that is a mix of macro and micro, because that is the measure of heteroskedacity entrepreneurs look for, heteroskedacity is a measure of excess redundancy.
### I'm getting a new computer
My 15 year old computer with Windows 2000 is not up to snuff and crashes when I have to much web, especially Adobe Flash. I need speed to run my data research. I had this on the farm, it has a layer of dirt and grime, the fan doesn't cool well, I lost the cover, and it is a mishmash of old and new disk drives. My internet connetion is an old 40 year old twisted pair running along the ceiling in the basement, through a worm hole, into the garage and out to the roof edge where it competes in open space with a tree. One time I shook my keyboard and got half a joint. I have two CD drives and a small floppy which I have never used. Behind the thing is a huge knot of wires, the thing no longer plays video at all, and I can run Pandora for about an hour and it crashes with memory leaks. Someone put on a Netflix virus that crashes every so often. I put out the word, its gonna be replaced. Probably buy a much better five year old computer for a hundred bucks, technology is cheap.
### Japanese parents flip coin with child to get spare bedroom
Mish talking about the change in Japanese demographics and pension bonds. I am not too concerned, this is an issue with a country in export surplus in which most of the lending is between parents and children. Parents quit saving, children quit borrowing. The younger take the job and master bedroom, the older takes the spare bedroom and plays video games. They have enough export surplus to manage. The real problem is getting the children to invest in grandchldren, and with mom and dad hanging around to pester them into sex, they just might solve the demographics.
### Germany's secret to success
Michael Schuman is going to tell us in the next issue of time.
Why not repeat the Hidalgo-Hausmann research. Highly dense variable networks that allow entrepreneurs the ability to find Kling Sustainable patterns of trade. Hidalgo and Hausmann actually went into the maize and calculated probabilities of PSST discovery. Another way of stating it that Germans are able to find the maximum number os useful channel components in a restricted bandwidth channel, while reducing transaction intervals to increase total channel capacity. Or they mnimize the Levine chain risk while maximizing the Levine chain length. Also look at Geoffrey West's work on cities. It's all related.
## Thursday, February 24, 2011
### The efficiency of exchange
It is a fundamental method of reducing neuronal excitement in our heads, quite frankly. The work of trade is the work of quantization, we accept the shared quantization of a good, and that quant allos us to move things around with minimal redundancy.
If we were neurology scientists, we would look at minimal neuronal spike trains in our heads while trading, and neurologists do exactly that. If we were matheticians we would look for quantization relationships that define the minimal number of steps to move goods through a network, and mathematicians do just that. If we were information scientists we would look for the minimum number of channels to transmit the maximum amount of information, and we information scientists do just that. If we were physicists, ditto; stock traders ditto, babies with toys, ditto, fish in the sea, ditto. Minimizing redundancy, the fundamental process of nature.
### They went home
House lawmakers stayed until 4:41 a.m. Saturday to finish up a spending bill to keep the government open, and sent it over to the Senate — only to be met with an empty chamber. Senators had closed up shop two days before and went home for a 10-day break to honor George Washington's birthday.
“We will do our work, but where is the Senate? They’re on vacation,” said Rep. Denny Rehberg, a Montana Republican and member of the House Appropriations Committee who ran part of the floor debate over cutting spending for the new health care law. “Here we are knocking up against a March 4 deadline and they’re missing the deadline again.”
Washington Times
We get this problem beacuse the channel is skewed, the Senate does not have economies of scale when their disparate representation gives them no common ground. What they have in common is a Constitutional delusion, not strong enough to finsh the work of government. (George Lakoff, it the entropy maximization that we do in our heads)
I am beginning to think the channel coherance will dominate, we get a synchroous default from DC, Illinois and California, an unconscious desire from all parties to fix the problem.
### We know where Congress gets its paper
The red line is Congress borrowing the blue is Ben lending. So if Ben is lending, and Congress is borrowing, then Congress pays this back, right? Ben can't just forgive this debt because he wants the Treasuries to be tradable, and he has already traded much of them. So the Treasury bonds have to collect a debt service fees to be tradable. Hence, Obama has to schedule \$300 billion.year in debt service within five years. Any ideas?
### Whoops on municipal bonds
AIG said that “several” issuers of bonds it holds have been downgraded, amid budget pressures. As of Dec. 31, the company had more than \$700 million of state general-obligation bonds from California, which has the lowest Standard & Poor’s credit rating of any U.S. state. It also held more than \$200 million in the bonds from Illinois.Bloomberg
Had you asked me when these bonds were issued by Fresno, I would have told you we had no intention or money to cover the billion in debt costs. Much of this pension debt was concluded behind closed doors, fraudently, and hidden from voters. Look here, the grand jury investigated, found fault. Gov Davis ordered the pension increases rescinded, and the County supervisors went ahead and ordered them through. Likely a class action suit from Fresno taxpayers would win, and put AIG on the hook for our billion in losses. There is no way property taxpayers in Fresno should be bound to cover these costs, this was clearly fraud on the part of Fresno County sups, aided and abetted by bond insurers.
If the US Treasury wants to prosecute, go after this man, Henry Perea, as near as I can tell he was the crook in charge. This same man was also involved in the Ray LaHood Choo Choo scam during the last election, which resulted in the fraudulent election of Jim Costa for Congress.
### And he deliberately excluded dispersion
State vs Federal ,contractors, as well as military personell when Leonhardt produced this report. I tried to get the number of contractors employed by DC, it was no where to be seen in the BLS data banks.
Nor does this graph, reposted by Kevin Drum, include dispersion, by which I mean fewer government paychecks in California and more in Washington DC. A better measure is comparative housing.
Looking closely what to we see Kevin? Your town, Los Angeles gave up 10% of its housing wealth to Washington DC. Los Vegas is in the dumps. In other words, because Kevin don't do due dilligence, you make bad policy taking money from LA and giving it to Washington DC, hence the 25% preimum we pay on DC Delusional policy. San Diego is a loser here, as is Portland.
So, ask Leonhardt the following: If the better equilibrium is more industry in Washington DC, then why to Federal deficits rise faster the closer we get to that equilibrium?
Federal spending cuts deserve the most attention. They are the most likely of these issues to occur, and could have the largest magnitude. The assumption we incorporated into our recently revised budget estimates—discretionary spending cuts of \$25bn and \$50bn below the CBO baseline for FY2011 and FY2012 respectively—would shave nearly one percentage point off of the annualized rate of real GDP growth in Q2, but would fade quickly with a negligible effect on growth by year-end.
This is what the Gololdman Sachs report said, not what you implied.
Alec Phillips, the author of the report is simply calculating the adjustment cost as money is shifted out of the government sector and into the private sector. The entire gist of the report if one clicks into the link is that it will be business as usual because Republicans love big government just as much as Democrats. Goldman's entire bonus system is built on the continuing idea that Washington DC will somehow get California, Illinois and New York to cover the debt service fees.
It is the Internet, Yglesias readers may not follow through, but plenty of others will follow the links.
### Illinois you have a problem
A review of the document suggests a gap of more than \$3 billion between income and expenses in the coming year. On top of that, the state owes about \$8.7 billion to groups that provide services on government’s behalf, to corporations waiting for tax refunds and to the program that provides medical care for government employees.
So the total deficit could top \$12 billion. That’s one-third of state government’s total spending from general funds.
The 2005 tax foundation report has your state paying 25 cent premium on federal taxes. Who are your Senators? Why Senator Durbin, one of the men most responsible for moving Illinois taxes to DC where it is spread out to Republican states! Well, Illinois voted for your bankruptcy.
### The Volokh Conspiracy says what about the Republican party!!
The Libertarian Origins of the Republican Party
I don't read this guy, but I have news. We entered the civil war when John Fremont and Abe Lincoln proposed using federal subsidies for Manifest Destiny. Far from Libertarian, these two were big government stalinists. They were about government funding of railroads and canals. The South rebelled because slaves were excluded from Lincoln's big government subsidy plan.
He talks a lot about the 14th, and I might remind our readers that the 14th came about after a Big Government civil war, not the libertarian nonesense he parades.
Remind me not to click on his page again, this guy is about Big Government, of the Weekly Standard variety, as is Instapundit, the blogger who decides a trillion dollar war in Libya is fine and dandy!
### Internet search statistics
West Coast independence and secession generates 115,000 results. Let's watch this number, see how it moves as he debt debacle in DC continues.
During the search, by the way, I found plenty of formal intergovernmental management groups between Oerogn and Washignton State and Canada. One of these is actually a democraticaly operated forum, much like the EU.
While international boundaries continue to play an important role in Cascadia, studies have shown that citizens in the Pacific Northwest are the most likely in the United States and Canada to believe that international borders hinder progress, do not protect national interests and should be further eroded.[citation needed] Cascadia already leads the way in binational and regional cooperation, governing bodies as well as crossborder NGO's, and continues to strengthen these ties through the establishment of a crossborder state ID card in 2006, the 'Pacific Coast Collaboration' agreement (PCC) signed by the governors of California, Oregon, Washington and Alaska and the premier of British Columbia in 2008, the bioregional 'Cascadia Mayors Council' founded in 1996 and the establishment of the Pacific Northwest Economic Region in 1991, a regional U.S.-Canadian forum in which all legislative members and governors are voting members, along with a consortium of the regions most powerful non-profit, public and private sector companies.
We would like to see a group like this offer a script, discounted, but recognized as money by the participants, many of which are part of the Cascadia group and offer essential goods and services. This should easily be possilbe if they use Internet based accounting. A possible venture opportunity? A way to avoid the Dollar payments on federal debt?
Facebook runs a money center for their gaming operators. NGO's and business within this Cascadia group could adopt the same prninciple. The concpet could be extended among private groups in Fresno, CA easily. The relative cost of Inernet money is small and maps well to loosely assembled commercial exchange. What the Internet needs is a common money software protocol, one that can be adapted to different regions and groups wanting a money mapped to their particular ecology.
### Brown on the budget
"I want to make one thing clear, and that's another reason I came here: If we don't get the tax extensions, I am not going to sign a budget that is not an all-cuts budget," Brown said.
"And it's going to be turbulent," the governor added. "Because I don't want to be here four years and play games or evasion, and everything just erodes. I think we got to meet the moment of truth now. And it's either the tax extensions and the \$12 billion. Or it's \$25 billion or as close to that as we're going to get. And if we can't do that, then maybe we don't get a budget."
Brown is going to let nature take its course, and more power to him and more power to California. The last thing we need is a bunch of government dependents pushing and shoving at every corner, like Davis or the Gubinator.
### A independent California gains much more from immigrants
Brian Caplan promotes immigration for California. Lets look at the chart Brian posts from an NBER study:
Younger immigrants help California, great news. Now, remove the Federal premium California pays for the DC Delusionals. The gain from immmigrants go up, California tax income rising by 4-5%, an increase that puts our budget into the black and gets California out of the depreession.
What about our part of the \$15 trillion in DC debt? Well, California would likely get a fairly good deal in negotiations, since we hold a good chunk of potential debt service costs. Ignorant bond holders will need to take a haircut, of course, another bonus. California could take many of the Western states with us, the scale gains from independence multiply. Under that scenario, then fine, let the immigrants role in.
A West Coast move toward independence starts with a California default, we need to go on stike within the current DC dominated system.
### Economists deliberately avoid a government model
John Goodman on Government Failure:
Why is our perspective so different from so many other health policy analysts? I think the answer is: the vast majority of people in health policy do not understand the concept of “government failure.”
It is worse than John explains. Economists of the Keynesian variety deliberatly promote anti-democratic models, it is built in. There model presupposes that elites run around the nation discouraging the democratic process. Keynesians have deliberately taken advantage of the undemocratic Senate, look no further than the trashing of Nevada by Senator Reid, or the huge bills heaped upon Californian counties by larger government actors. Keynes whole principle was monarchy by the elite. They seek programs that prevent the adative adjustments in government structures, they cause depression and war.
Fortunately they have been caught in their scam. We now have network models that predict the damage and wars caused by Keynes and the elitists. e can hold them back for a while, but they always resurge and require constant vigilence.
HT Econoblog
### European economists want bond guarantees dropped
A lasting assurance of the EU that would guarantee the solvency of apparently only illiquid but in fact insolvent states via community credits would have extremely negative consequences. Favourable credit conditions and the liability of the European community of states would give over-indebted countries a powerful incentive to repeat the mistakes of the past and to continue a policy of indebtedness at the expense of their EU partners.EU Vox
These economists are smart, they do not want EU funds used to guarantee bad lending by big finance, as doing that causes bad lending. The idea is to keep borowing rates high enough, up front, to cover any losses by the PIIGS in the future. The alternative is the fiasco of bond holders having to go political to get their losses covered.
Tim Geithner, on the other hand, believes it perfectly reasonable to go globe trotting for Congressional funding while guaranteeing that California, flat on its back with no say in the matter, will somehow generate the debt service funds. Bond holders beware, when Obama comes calling on California we will likely pay off the debt with Laser Money.
### NY Congressman pushes Choo Choo
Rep. Nadler is pushing full steam ahead on a \$53 billion spending spree for High Speed Rail projects. This of course is after the 8 billion spent on High Speed Rail in the stimulus bill. Both barely begin to cover the estimated \$500 billion dollars required for the plan, which many state governments have already rejected due to the massive cost.
Congratulations Rep. Nadler, you are Citizens Against Government Waste’s Porkers of the Month for February, 2011!
New York ciizens will pay a 20 cent premium to rural states for every dollar of bondogle this guy orders up.
### Smart Citizens don't listen to Instapundit
Americans are wary of the current chaotic political situation in several Arab countries including Libya but strongly believe the United States should stay out of the picture. Rasmussen
That would be 67% of citizen's think the Welfare Queen from Alaska spouts her mouth off without thinking.
### Good news from the MiddleEast
The reason why Bahrain is very important is because in any negotiation you have to have some give-and-take, and it’s likely that the Bahraini monarchy will have to give some concession to the opposition. And once that happens, it will lead to an empowerment of the opposition, 70 percent of which is Shia — 70 percent of the population of the country is Shia — and that has very large-scale implications for the region, particularly for Saudi Arabia and Kuwait.Stratfor
The Shia religion has a lesser inclination to belt bomb, throw rocks and rape Western women than Arab Sunni men. Anything that advances Shia culture over Sunni is very good news for human civilization.
HT Zero Hedge
### Jeff Frankels is right about Republicans
Look no further than the hypocrisy if Keith Hennessey. It is the failure of far away government, and is the reason I predict the fragmetation of government. We do not have democaracy in theSenate, and the problem is getting worse. Ultimately one of the big subsidizing states will collapse, most likely California. Until California escapes, problems will get nothing but worse in DC. Rural Senatros will always run California dry, it matters little what their politics are.
### Obama sure imported too much oil with the stimulus
A reminder. that little peak in oil imports in 2010, cash to Arab dictators and a drain on current accounts, was the work of Obama and the Keynesian math challenged. If you all recall, Obama drove up the price of oil and we had a mini-crash about that time.
Now we have Kevin Drum begging for a repeat, and Berkely professors support this nonesene with oil now at \$110 per barrel? Isn''t this what got us into trouble in mid 2008, too much Bush stimulus driving up oil imports?
Has anyone noticed that the financial crisis committe when looking at 22 potential causes of the crash conveniently left out the oil price peak which occured exactly at the crash point? This is the delusional thinking that comes from Keynesian worship, the idea of skipping the obvious for fear the Great Exogenous might suffer embarrassment. I should remind Kevin that his policy ran up another \$300 billion in debt service, due from the very poor lining the streeets of LA.
How long did Krugman insist, after the crash, that we had surplus oil, needing to be used with stimulus? A wierd philosophy from an economist who just prior to the crash was warning us of oil shortages. Is the contradictory nonsense worth the worship? People, we import this stuff, it is not a surplus laying around the nation.
Let me helpd out my readers with a chart from Econobrowser.:
Event Date Lost output
Suez Crisis Nov 1956 10%
OPEC embargo Nov 1973 7.5%
Iranian revolution Nov 1978 7%
Iran-Iraq War Oct 1980 6%
Persian Gulf War I Aug 1990 9%
Venezuela and Persian Gulf War II Dec 2002 4%
This is a list of oil disruptions and the subsequent drop in GDP that resulted. This chart was disallowed by the financial crisis committee. But Jim collets the data, and thank him for it. Yglesias do you get it? Oil is imported, when we waste it, we crash, people become unemployed. Even Brad will admit that Keynesian policies do not work under shortages of essential goods. Where is the Drum/Yglesias evidence that more oil consumption by central government helps the unemployment problem? How does Krugman think the Congress can figure out some wedge between a sligtly less oil shortage in a recession and a severe shortages in post recession? How does Ray LaHood running around with Choo Choo scams during elections help?
### California flat on its back
California economy, 4% growth, cumulative growth since the recession.
"Our Index's November reading reinforced the unimpressive pattern of recovery in California over the course of 2010," said Dana Johnson, Chief Economist at Comerica Bank. "The state's recovery in 2010 has been uneven and inconsistent across sectors, creating choppiness in our Index. Looking ahead, California should make modest gains in 2011 against a background of a gradually accelerating national economy."
"Our Index's November reading reinforced the unimpressive pattern of recovery in California over the course of 2010," said Dana Johnson, Chief Economist at Comerica Bank. "The state's recovery in 2010 has been uneven and inconsistent across sectors, creating choppiness in our Index. Looking ahead, California should make modest gains in 2011 against a background of a gradually accelerating national economy."
The economic index is pegged to 2008, and is a three month average. Here is the unemployment rate:
Gee, I wonder what Obama will say to a state expected cover 13% of the federal debt service, growing to an additional \$300 billion by 2016. California, not growing at all, is expected to come up with another \$13 plus the 25% premium, or \$18 billion per year in federal taxes when our own budget is short by \$25 billion this year. Even if California could borrow or Laser Prints that money, it still does not cover the fact that Obama wants the additional \$18 billion in federal debt debt service. We are likely to grow at this rate, 1.5% per year for a number of years with our increasing pension crisis coming due, mainly in the cities where no one sees the problem.
Where is Tim going to find foreign investors willing to loan money when the largest state is unable to cover debt service. Somebody, likely the Keynesians, doesn't follow the trail down from the top to the bottom. With California on its back, then Nevada is in dire straights, and they pay a 30% premium price for federal borrowing.
The politicians responsible for this mess? Jerry brown the younger and Gray Davis, and Pete Wilson; with special mention for Karen Bass and incompetent County Supervisers in the Central Valley. Special mention to Boxer and Fenstein for bringing home a huge debt service from DC.
### Yglesias deliberately lies to his delusional collective
Boehner, for all his faults, has delivered a budget to the Senate. Where is the Senate response budget?
I think it’s pretty clear that we’re looking toward a scenario in which John Boehner shuts the government down in the near future. Yglesias, the Keynesian is anti-democratic.
The point he misses is that many of us want the government shutdown precisely because Obama is delusional enough to believe the Keynesians nonsense. Let me repeat the history. The Tea Party, regardless of their big government inclinations, was elected into the House. Reid is only elected because Obama ran the Choo Choo scam; proposing a train from Mojave to somewhere, a train which was never going anywhere. Citizens of Nevada have figured out they were scammed, they have become Tea Party supporters. Reid represents only three Congressional districts and he charges Nevadans a whopping 30% premium cost for more government concentration .
The complaint today, for example, is that Chris Christie is becoming soft in comparison to Gov Walker. The calls in California to shut down the unions are stronger, not weaker. Fewer foreign investors will be inclined to invest in Geithner's socialist banking because they know Americans have no intention of paying the insurance settlements. And I might remind Yglesias supporters that investors always make them pay for money they borrow via government, and Obama plans to take \$300 billion from Ygesias' supporters to pay debt service to the wealthy by 2016, a result Yglesias approves.
The Internet watchers are not neary as stupid as Yglesias' fans, we get the anti-democratic forces in Berkeley and the unions. The Tea party is becoming more powerful because of the desire of Berkeley professors to skirt the democratic process. We are bypassing the Keynesians, we know they cannot change, that their science never was.
### No Ms Bachmann, I won't support your Traditional Marriage ideas.
The Tea party is on the edge of becoming yet another Big Government swamp, and I suggest you get your members focused on their local constituents and getting out of central government moraility. Dunno if you are aware, but you are close to becoming yet another entitlement maven.
### Union of Concerned Scientists caught in a Scientific Fraud?
This posting from Next Big Future claims so. They seem to have a case, | 2017-10-22 19:14:41 | {"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": 1, "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": 0.2570019066333771, "perplexity": 4141.644991736697}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187825436.78/warc/CC-MAIN-20171022184824-20171022204824-00811.warc.gz"} |
https://www.jobilize.com/online/course/5-5-graphs-of-trig-functions-by-openstax?qcr=www.quizover.com | # 5.5 Graphs of trig functions
Page 1 / 3
## Graphs of trigonometric functions
This section describes the graphs of trigonometric functions.
## Graph of $sin\theta$
Complete the following table, using your calculator to calculate the values. Then plot the values with $sin\theta$ on the $y$ -axis and $\theta$ on the $x$ -axis. Round answers to 1 decimal place.
$\theta$ 0 ${}^{\circ }$ 30 ${}^{\circ }$ 60 ${}^{\circ }$ 90 ${}^{\circ }$ 120 ${}^{\circ }$ 150 ${}^{\circ }$ $sin\theta$ $\theta$ 180 ${}^{\circ }$ 210 ${}^{\circ }$ 240 ${}^{\circ }$ 270 ${}^{\circ }$ 300 ${}^{\circ }$ 330 ${}^{\circ }$ 360 ${}^{\circ }$ $sin\theta$
Let us look back at our values for $sin\theta$
$\theta$ ${0}^{\circ }$ ${30}^{\circ }$ ${45}^{\circ }$ ${60}^{\circ }$ ${90}^{\circ }$ ${180}^{\circ }$ $sin\theta$ 0 $\frac{1}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{\sqrt{3}}{2}$ 1 0
As you can see, the function $sin\theta$ has a value of 0 at $\theta ={0}^{\circ }$ . Its value then smoothly increases until $\theta ={90}^{\circ }$ when its value is 1. We also know that it later decreases to 0 when $\theta ={180}^{\circ }$ . Putting all this together we can start to picture the full extent of the sine graph. The sine graph is shown in [link] . Notice the wave shape, with each wave having a length of ${360}^{\circ }$ . We say the graph has a period of ${360}^{\circ }$ . The height of the wave above (or below) the $x$ -axis is called the wave's amplitude . Thus the maximum amplitude of the sine-wave is 1, and its minimum amplitude is -1.
## Functions of the form $y=asin\left(x\right)+q$
In the equation, $y=asin\left(x\right)+q$ , $a$ and $q$ are constants and have different effects on the graph of the function. The general shape of the graph of functions of this form is shown in [link] for the function $f\left(\theta \right)=2sin\theta +3$ .
## Functions of the form $y=asin\left(\theta \right)+q$ :
1. On the same set of axes, plot the following graphs:
1. $a\left(\theta \right)=sin\theta -2$
2. $b\left(\theta \right)=sin\theta -1$
3. $c\left(\theta \right)=sin\theta$
4. $d\left(\theta \right)=sin\theta +1$
5. $e\left(\theta \right)=sin\theta +2$
Use your results to deduce the effect of $q$ .
2. On the same set of axes, plot the following graphs:
1. $f\left(\theta \right)=-2·sin\theta$
2. $g\left(\theta \right)=-1·sin\theta$
3. $h\left(\theta \right)=0·sin\theta$
4. $j\left(\theta \right)=1·sin\theta$
5. $k\left(\theta \right)=2·sin\theta$
Use your results to deduce the effect of $a$ .
You should have found that the value of $a$ affects the height of the peaks of the graph. As the magnitude of $a$ increases, the peaks get higher. As it decreases, the peaks get lower.
$q$ is called the vertical shift . If $q=2$ , then the whole sine graph shifts up 2 units. If $q=-1$ , the whole sine graph shifts down 1 unit.
These different properties are summarised in [link] .
$a>0$ $a<0$ $q>0$ $q<0$
## Domain and range
For $f\left(\theta \right)=asin\left(\theta \right)+q$ , the domain is $\left\{\theta :\theta \in \mathbb{R}\right\}$ because there is no value of $\theta \in \mathbb{R}$ for which $f\left(\theta \right)$ is undefined.
The range of $f\left(\theta \right)=asin\theta +q$ depends on whether the value for $a$ is positive or negative. We will consider these two cases separately.
If $a>0$ we have:
$\begin{array}{ccc}\hfill -1\le sin\theta & \le & 1\hfill \\ \hfill -a\le asin\theta & \le & a\hfill \\ \hfill -a+q\le asin\theta +q& \le & a+q\hfill \\ \hfill -a+q\le f\left(\theta \right)& \le & a+q\hfill \end{array}$
This tells us that for all values of $\theta$ , $f\left(\theta \right)$ is always between $-a+q$ and $a+q$ . Therefore if $a>0$ , the range of $f\left(\theta \right)=asin\theta +q$ is $\left\{f\left(\theta \right):f\left(\theta \right)\in \left[-a+q,a+q\right]\right\}$ .
Similarly, it can be shown that if $a<0$ , the range of $f\left(\theta \right)=asin\theta +q$ is $\left\{f\left(\theta \right):f\left(\theta \right)\in \left[a+q,-a+q\right]\right\}$ . This is left as an exercise.
The easiest way to find the range is simply to look for the "bottom" and the "top" of the graph.
## Intercepts
The $y$ -intercept, ${y}_{int}$ , of $f\left(\theta \right)=asin\left(x\right)+q$ is simply the value of $f\left(\theta \right)$ at $\theta ={0}^{\circ }$ .
$\begin{array}{ccc}\hfill {y}_{int}& =& f\left({0}^{\circ }\right)\hfill \\ & =& asin\left({0}^{\circ }\right)+q\hfill \\ & =& a\left(0\right)+q\hfill \\ & =& q\hfill \end{array}$
## Graph of $cos\theta$ :
Complete the following table, using your calculator to calculate the values correct to 1 decimal place. Then plot the values with $cos\theta$ on the $y$ -axis and $\theta$ on the $x$ -axis.
$\theta$ 0 ${}^{\circ }$ 30 ${}^{\circ }$ 60 ${}^{\circ }$ 90 ${}^{\circ }$ 120 ${}^{\circ }$ 150 ${}^{\circ }$ $cos\theta$ $\theta$ 180 ${}^{\circ }$ 210 ${}^{\circ }$ 240 ${}^{\circ }$ 270 ${}^{\circ }$ 300 ${}^{\circ }$ 330 ${}^{\circ }$ 360 ${}^{\circ }$ $cos\theta$
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Got questions? Join the online conversation and get instant answers! | 2019-12-13 10:39:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 119, "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": 0.6687784790992737, "perplexity": 696.3662465064001}, "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-20191213094833-20191213122833-00035.warc.gz"} |
https://www.physicsforums.com/threads/simple-question-on-linear-equations.143188/ | # Simple question on linear equations.
1. Nov 10, 2006
### MathematicalPhysicist
we have the system a_i1x+a_i2y+a_i3z=b_i i=1,2,3
and we are given that it has a unique solution (1,2,0)
i need to find the set of solutions for the next system:
a_i1x+b_iy+a_i3z=a_i2
what i did is:
we have the solution for the first equation then we have a_i1+2a_i2=b_i
so we put it in the second equation and we have:
a_i1x+(a_i1+2a_i2)y+a_i3z=a_i2
(a_i1x+a_i2y+a_i3z)+(a_i1+a_i2)y=a_i2
b_i+(a_i1+a_i2)y=a_i2
(a_i1+2a_i2)+(a_i1+a_i2)y=a_i2
from here i found the solution, is this method valid?
2. Nov 10, 2006
### arildno
Hint:
Look up Cramer's rule, and see what you can find out with that.
3. Nov 11, 2006
### MathematicalPhysicist
do you know perhaps another method to solve this other than cramer's rule?
cause im not supposed to use it here.
4. Nov 11, 2006
### radou
Try to look at the corresponding vector equation: $$\vec{a}_{1}x + \vec{a}_{2}y + \vec{a}_{3}z = \vec{b}$$.
5. Nov 11, 2006
### MathematicalPhysicist
i don't understand, radou can you elaborate?
6. Nov 11, 2006
### radou
Well, after plugging the solution (x, y, z) = (1, 2, 0) into the vector equation, you find out that the vector b can be written as a linear combination of vectors a1 and a2, right? So, that means that the vector b lies in the same plane as a1 and a2 do. Hence, you know that the vectors a1, a2 and a3 are linearly independent. Now, after plugging in the linear combination a1 + 2a2 = b into the equation a1x + by + a3z = a2, and rearranging, you can use the fact that a1, a2 and a3 are linearly independent to solve the equation.
7. Nov 11, 2006
### MathematicalPhysicist
when you mean rearranging, you mean like i did i.e:
a1x+a2y+a3z+(a1+a2)y=a2
but how do i find for (x,y,z) with your approach?
i mean if they are independent then any combination of them, its coeffiencts are zero like this a1x+a2y+a3z=0 then x=y=z=0, but how do i use it here?
8. Nov 11, 2006
### radou
I meant a1x + (a1+2a2)y+a3z = a2 =>
a1(x+1) + a2(2y-1)+a3z = 0. Now use the fact that a1, a2 and a3 are linearly independent.
Edit: too bad you're not allowed to use Cramer's rule, as Arildno suggested, since this problem seems to be ideal for its application.
9. Nov 11, 2006
### MathematicalPhysicist
ok, thanks i understand now.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook | 2018-07-18 09:12:04 | {"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": 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": 0.7506746053695679, "perplexity": 967.645768656263}, "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-2018-30/segments/1531676590074.12/warc/CC-MAIN-20180718080513-20180718100513-00529.warc.gz"} |