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http://clay6.com/qa/74965/a-circular-coil-expands-radially-in-a-region-of-magnetic-field-and-no-elect	Comment Share Q) A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. The can be cause (a) The magnetic field is constant (b) The magnetic field is in the same plane as the circular coil and it may or may not vary (c) The magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably. (d) There is constant magnetic field in the perpendicular (to the plane of the coil) direction When a circular coil expands radially in a region of magnetic field, induced $emf$ developed is \begin{align}\; \; \; \; \; \; e& =Blv \\ & = B \times rate\; of\; charge\; of\; area \end{align} It is given that the magnetic field B is in a plane perpendicular to the plane of the circular coil. Since e=0, magnetic field should be in the plane of circular coil so that its component which perpendicular to plane of coil is zero. If the magnetic of the magnetic field decrease with the magnetic flux linked with the coil, then $e = \frac{d \phi}{dt}$= 0	2019-12-12 11:35:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9527361392974854, "perplexity": 364.39857814395003}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540543252.46/warc/CC-MAIN-20191212102302-20191212130302-00234.warc.gz"}
https://standards.globalspec.com/std/10277543/jis-construction-i-hdbk	JSA - JIS CONSTRUCTION I HDBK JIS Machine Construction I Handbook active, Most Current Organization: JSA Publication Date: 1 January 2018 Status: active Document History JIS CONSTRUCTION I HDBK January 1, 2018 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2017 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2016 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2015 JIS Machine Construction I Handbook A description is not available for this item. January 1, 2013 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2013 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2012 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2011 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2010 JIS CONSTRUCTION I HANDBOOK A description is not available for this item. January 1, 2009 JIS CONSTRUCTION I HANDBOOK A description is not available for this item.	2019-04-22 22:46:23	{"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": 0.8170329928398132, "perplexity": 12375.655513223508}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578582736.31/warc/CC-MAIN-20190422215211-20190423001211-00352.warc.gz"}
http://openstudy.com/updates/5611c5b0e4b0af5cf2f0352b	## anonymous one year ago Given a 13-card bridge hand has been dealt from a standard deck of 52 cards, what is the probability of having a) exactly 6 hearts? b) exactly 7 hearts, three diamonds, two clubs, and one spade? 1. anonymous exactly 6 hearts means 6 hearts and 7 other stuff do you know how many hearts are in the deck? 2. anonymous 13 3. anonymous ok so 13 hearts to choose 6 from and 39 other stuff to choose 7 from 4. anonymous $\huge \frac{\binom{13}{6}\binom{39}{7}}{\binom{52}{13}}$ s the quick answer 5. anonymous so is it 0.042%? 6. anonymous how would be work?	2017-01-24 21:57:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.48533886671066284, "perplexity": 1665.5420623699122}, "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-2017-04/segments/1484560285289.45/warc/CC-MAIN-20170116095125-00464-ip-10-171-10-70.ec2.internal.warc.gz"}
http://mathoverflow.net/questions/77206/mathematical-programming-with-other-algebras-than-linear	# Mathematical Programming with other Algebras than Linear Linear Programming is strongly entwined with linear algebra, as are many of its generalizations under the heading of mathematical programming / convex optimization. What analogies are there for convex optimization techniques outside of vector spaces dealt with in linear algebra. For example, Gaussian Elimination is generalized by Buchberger's algorithm for finding Groebner bases (or so I'm told); is there any algorithm that has a relationship with Buchberger's analogous to the Simplex Method's relationship with Gaussian Elimination? - did you already check out: math.berkeley.edu/~philipp/CAG-seminar.html – Suvrit Oct 5 '11 at 9:20	2015-04-02 01:53:08	{"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": 0.8192347884178162, "perplexity": 1003.4026246821988}, "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-2015-14/segments/1427131309986.49/warc/CC-MAIN-20150323172149-00196-ip-10-168-14-71.ec2.internal.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-1st-edition/chapter-8-rational-functions-8-1-model-inverse-and-joint-variation-8-1-exercises-problem-solving-page-556/40a	## Algebra 2 (1st Edition) $f=64.3249482 \dfrac{\sqrt T}{Ld}$ General equation for inverse variation is given by $y=\dfrac{k}{x}$ Here, we have $f=k \dfrac{\sqrt T}{Ld}$ ...(1) Plug the data, we have $262=k \dfrac{\sqrt {670}}{(62)(0.1025)}$ and $K \approx 64.3249482$ Thus, the equation (1) becomes: $f=64.3249482 \dfrac{\sqrt T}{Ld}$	2022-07-07 13:45:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8649606704711914, "perplexity": 594.130914469451}, "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/1656104692018.96/warc/CC-MAIN-20220707124050-20220707154050-00000.warc.gz"}
https://math.stackexchange.com/questions/439101/are-epimorphisms-stable-under-pullback-in-balanced-categories-with-epimorphic-im	# Are epimorphisms stable under pullback in balanced categories with epimorphic images? Suppose that $\mathcal{C}$ is a balanced category with epimorphic images, that is, every bimorphism is an isomorphism, every morphism has an image and the image factorization is an epi-mono factorization. Under such hypotheses, is it true that epimorphisms are stable under pullback (if it exists)? Or at least that $f(f^{-1}(S)) = S$, if it's defined, where $f : A \rightarrow B$ is an epimorphism and $S$ is a subobject of $B$? I believe both should be false, but I was not able to provide a counterexample.	2019-08-21 12:06:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9043633341789246, "perplexity": 252.40021255919396}, "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/1566027315936.22/warc/CC-MAIN-20190821110541-20190821132541-00004.warc.gz"}
https://mathoverflow.net/questions/368067/smallest-ordinal-alpha-such-that-l-cap-pl-alpha-is-uncountable	# smallest ordinal $\alpha$ such that $L \cap P(L_\alpha)$ is uncountable Let $$V$$ denote the von Neumann universe and $$L$$ Gödel's constructible universe. For any set $$X$$, let $$P(X)$$ denote the power set of $$X$$. Assume that $$0^\sharp$$ exists (and ZFC). What is the smallest ordinal $$\alpha$$ such that $$L \cap P(L_{\alpha})$$ is uncountable? (If $$V = L$$, then $$\alpha = \omega$$, but if $$0^\sharp$$ exists, then $$\alpha > \omega$$.) • It’s $\omega_1$. Aug 1, 2020 at 5:46 • I suspected so. Do you have a reference for a theorem that implies this? Aug 1, 2020 at 5:55 • If $0^\sharp$ exists, then every cardinal is inaccessible in L. Aug 1, 2020 at 6:04 • Ah, so $L \cap V_\alpha$ is countable for all countable $\alpha$, too, since $L \cap V_\alpha$ is the $V_\alpha$ of $L$. Thank you. Aug 1, 2020 at 6:08 • In ZFC alone, the $\alpha$ in the title can be described as: (1) If genuine $\omega_1$ is a successor cardinal of $L$, then $\alpha$ is its immediate predecessor cardinal of $L$. (2) If genuine $\omega_1$ is a limit (and therefore inaccessible) cardinal of $L$, then it is equal to $\alpha$. The additional hypothesis that $0^\#$ exists implies that case (2) occurs. Aug 1, 2020 at 14:22 We have in $$L$$, for each (infinite) $$\alpha$$, the following bijections: • $$f_\alpha:\alpha\rightarrow L_\alpha$$. • $$g_\alpha: \mathcal{P}(L_\alpha)^L=\mathcal{P}(L_\alpha)\cap L\rightarrow L_{(\vert\alpha\vert^+)^L}$$. Hence $$\vert\mathcal{P}(L_\alpha)^L\vert=\vert(\vert\alpha\vert^+)^L\vert$$. Now assuming $$0^\sharp$$ we have that $$\omega_1^V$$ is a limit cardinal in $$L$$, so for each $$\alpha<\omega_1^V$$ we have $$\vert\mathcal{P}(L_\alpha)^L\vert=\aleph_0$$. So the answer to your question is $$\omega_1^V$$. Note that all this requires is that $$\omega_1^V$$ be a limit cardinal in $$L$$. More generally, let $$\kappa$$ be the supremum of the $$L$$-cardinals whose $$L$$-successor is $$<\omega_1^V$$; then the $$\kappa$$th level of $$L$$ is the first whose $$L$$-powerset is truly uncountable. • OK, except I think you meant $P(L_\alpha)^L = L \cap P(L_\alpha)$, not $P(L_\alpha)^L = P(\alpha) \cap L$. Aug 3, 2020 at 0:30 • @JesseElliott Whoops, quite right - fixed! Aug 3, 2020 at 0:36	2023-02-01 15:35:24	{"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": 32, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9914027452468872, "perplexity": 298.74146162790834}, "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/1674764499946.80/warc/CC-MAIN-20230201144459-20230201174459-00563.warc.gz"}
https://www.isa-afp.org/entries/Special_Function_Bounds.html	# Real-Valued Special Functions: Upper and Lower Bounds Title: Real-Valued Special Functions: Upper and Lower Bounds Author: Lawrence C. Paulson Submission date: 2014-08-29 Abstract: This development proves upper and lower bounds for several familiar real-valued functions. For sin, cos, exp and sqrt, it defines and verifies infinite families of upper and lower bounds, mostly based on Taylor series expansions. For arctan, ln and exp, it verifies a finite collection of upper and lower bounds, originally obtained from the functions' continued fraction expansions using the computer algebra system Maple. A common theme in these proofs is to take the difference between a function and its approximation, which should be zero at one point, and then consider the sign of the derivative. The immediate purpose of this development is to verify axioms used by MetiTarski, an automatic theorem prover for real-valued special functions. Crucial to MetiTarski's operation is the provision of upper and lower bounds for each function of interest. BibTeX: @article{Special_Function_Bounds-AFP, author = {Lawrence C. Paulson}, title = {Real-Valued Special Functions: Upper and Lower Bounds}, journal = {Archive of Formal Proofs}, month = aug, year = 2014, note = {\url{https://isa-afp.org/entries/Special_Function_Bounds.html}, Formal proof development}, ISSN = {2150-914x}, } License: BSD License Depends on: Sturm_Sequences	2021-01-16 12:19:48	{"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": 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": 0.7101021409034729, "perplexity": 1164.459370657362}, "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/1610703506640.22/warc/CC-MAIN-20210116104719-20210116134719-00781.warc.gz"}
https://math.stackexchange.com/questions/2163875/technique-to-calculate-distribution-of-product-of-two-random-variables	# Technique to calculate distribution of product of two random variables Given two continuous random variables $X$ and $Y$, suppose we know probability distributions $p_X, p_Y$ of them and $cov(X,Y)$. (Note we don't impose the independence between them.) Then can we calculate $p_{Z}(z)$ where $Z=XY$? If not, what more do we need? Can we calculate $p_Z$ if we have $P_{X,Y}(x,y)$ the joint distribution of $X$ and $Y$? • Are the random variables discrete or continuous ? – callculus Feb 27 '17 at 15:54 • oh, they are continuous. – julypraise Feb 27 '17 at 15:57 • Covariance: not enough. Joint distribution: suffices, the standard approach works (for example, using a change of variables to compute the joint distribution of (Z,Y), then computing the first marginal). – Did Feb 27 '17 at 16:02 • @Did Thanks. Though, I'am quite new to the stuff and don't have a right reference. Where might I look for a explicit example? – julypraise Feb 27 '17 at 17:38 • In your textbook, perhaps? – Did Feb 27 '17 at 17:44 You can calculate $E[XY]$ from just $\mbox{cov }(X,Y)$ and the individual $E[X]$ and $E[Y]$: $$E[XY] = \mbox{cov }(X,Y)+E[X]E[Y]$$ Since you can easily get $E[X]$ from $p_X$ (similarly for $Y$), the information you propose is enough to determine $E[XY]$. But it is insufficient, in general, to determine $p_Z(z)$. Rather surprisingly, if you restrict the form of $p_{XY}(x,y)$ to a second degree expression on the unit square, and zero outside, then in fact the marginal distributions and the covariance together determine a unique joint probability function of that form. But if you relax that restriction, you can find cases that agree in marginal distributions and in covariances, but are not identical joint distributions.	2019-05-20 03:24:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8520792722702026, "perplexity": 386.39992522532714}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232255536.6/warc/CC-MAIN-20190520021654-20190520043654-00091.warc.gz"}
https://socratic.org/questions/how-do-you-balance-lial-oh-4-h-2o-lioh-al-oh-3-h-2o	# How do you balance LiAl(OH)_4 + H_2O -> LiOH + Al(OH)_3 + H_2O? Jan 27, 2016 It's already balanced. Here, let's see what happens when we check what's on each side. "LiAl"("OH")_4 + cancel("H"_2"O") -> "LiOH" + "Al"("OH")_3 + cancel("H"_2"O") color(green)("Li")color(highlight)("Al")color(blue)(("OH")_4) -> color(green)("Li")color(blue)("OH") + color(highlight)("Al")color(blue)(("OH")_3) Yep, it's fine the way it is. One lithium on each side, one aluminum on each side, and four $\text{OH}$ groups on each side. As for the charges, "Al"("OH")_4^(-) is balanced by ${\text{Li}}^{+}$, ${\text{OH}}^{-}$ is balanced by ${\text{Li}}^{+}$, and $3 \times {\text{OH}}^{-}$ is balanced by ${\text{Al}}^{3 +}$. Jan 27, 2016 Do you mean the reaction of lithium tetrahydroaluminate ($L i A l {H}_{4}$) with water? $L i A l {H}_{4} \left(s\right) + 4 {H}_{2} O \left(l\right) \rightarrow L i A l {\left(O H\right)}_{4} \left(a q\right) + 4 {H}_{2} \left(g\right) \uparrow$ Lithium tetrahydroaluminate is an important hydride transfer reagent, and a very common reductant in organic chemistry. The reduction reaction is performed in THF (${C}_{4} {H}_{8} O$) or ether (both solvent must be dry). $L i A l {H}_{4}$ can transfer up to 4 hydrides (with commercial grades usually it transfers about 3). When your organic reduction is finished, the mixture is worked up with water. This can get pretty violent (especially if the lithal has been added 1:1, as is quite commonly done).	2019-09-20 22:50:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "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": 0.575196385383606, "perplexity": 4808.180690385429}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574084.88/warc/CC-MAIN-20190920221241-20190921003241-00499.warc.gz"}
https://chemistry.stackexchange.com/tags/diffusion/new	Tag Info Let's discuss the problem in a qualitative way. In such a cell, the metal will get dissolved in the right-hand side of the cell, where the concentration is low, so that $[M^{z+}]$ increases in this compartment, which becomes the anode. In the left-hand side, the ions $[M^{z+}]$ are discharged and deposited as a metal layer on the electrode, which is the ... Osmotic pressure for non-electrolytic solutes is given by $$\pi = CRT$$ where $C$ is the effective concentration of all the solutes. In our case, with multiple solutes, we simply add all their concentrations to obtain the effective concentration. This gives us \begin{align} \pi_\mathrm{cell} &= 0.05RT\\ \pi_\mathrm{environment} &= 0.03RT \end{...	2020-01-27 10:34:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.9972739219665527, "perplexity": 934.9900662441804}, "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-2020-05/segments/1579251696046.73/warc/CC-MAIN-20200127081933-20200127111933-00411.warc.gz"}
http://educo.vln.school.nz/mod/forum/discuss.php?d=3595	## Discussion forum ### How do eDeans / Network Supervisors Control Internet Usage? How do eDeans / Network Supervisors Control Internet Usage? I would be grateful to hear about what kinds of controls are imposed upon Internet usage by eStudents in other schools. We have a system here where students are given five dollars worth of Internet usage - per term, I think it is. If they want more they need to pay for it. Our eStudents are allowed more usage without charge, but they or I have to request that usage from the network supervisor. Re: How do eDeans / Network Supervisors Control Internet Usage? We do not charge any of our students an internet usage fee. However when I talked to the IT man his comment was - 'yet'. At this point it is not something we are considering. Re: How do eDeans / Network Supervisors Control Internet Usage? All of our Y7-10 students have $5 loaded onto their accounts for printing. Seniors have$10. They can purchase more themselves if they need. We feel this is sufficient for all printing needs - VC students included. We have seen a drop in careless printing since this was introduced as students are far more conscious of cost. Internet use is an important learning tool and we do not charge students for this per se. Re: How do eDeans / Network Supervisors Control Internet Usage? None of our students are charged for internet usage and they all have \$5 loaded onto accounts for photocopying- they can pay for more if they want it. I tend to do big runs of photocopying for the VC students and fund that from the VC budget. But I have also set up a shared resource area in the library for VC students with photocopy sets, text books etc. Cheers Adrian!	2019-12-11 08:31:22	{"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": 0.49276965856552124, "perplexity": 3875.926238980211}, "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/1575540530452.95/warc/CC-MAIN-20191211074417-20191211102417-00163.warc.gz"}
http://mathhelpforum.com/calculus/78293-lim-inf-sup-innequality-question.html	# Thread: lim inf/sup innequality question... 1. ## lim inf/sup innequality question... x_n and y_n are bounded $\limsup x_n + \limsup y_n \geq \lim x_{r_n} + \lim y_{r_n}$ this is true because there presented sub sequences converge to the upper bound of x_n and y_n . the sum of limits is the limit of sums so we get one limit and the of two convergent sequence is one convergent sequence $\lim (x_{r_n} + y_{r_n}) = \limsup (x_n+y_n)$ this is true because the sequence is constructed from a convergent to the sup sub sequences so they equal the lim sup of $x_n+y_n$ now i need to prove that $\limsup (x_n+y_n) \Rightarrow \liminf x_n + \limsup y_n$ i tried: $ \limsup (x_n+y_n) = \limsup x_n + \limsup y_n \Rightarrow \liminf x_n + \limsup y_n $ lim sup i always bigger then lim inf so its true did i solved it correctly? 2. Originally Posted by transgalactic x_n and y_n are bounded $ lim sup x_n+lim sup y_n>=lim x_r_n+lim y_r_n $ this is true because there presented sub sequences converge to the upper bound of x_n and y_n . the sum of limits is the limit of sums so we get one limit and the of two convergent sequence is one convergent sequence $ lim(x_r_n+y_r_n)=limsup(x_n+y_n) $ this is true because the sequence is constructed from a convergent to the sup sub sequences so they equal the lim sup of x_n+y_n now i need to prove that $ limsup(x_n+y_n)=>liminf x_n+limsup y_n $ i tried: $ limsup(x_n+y_n)=limsup x_n+limsup y_n=>liminf x_n+limsup y_n $ lim sup i always bigger then lim inf so its true did i solved it correctly? I'm not sure what you want to prove. Is $r_n$ a particular subsequence? And why do we know that there is a limit to $x_{r_n}$ 3. x_r_n is a convergent subsequence of x_n y_r_n is a convergent subsequence of y_n r_n is just a sign to demonstrate that its a subsequence by weirshrass laws to any bounded sequence there is a convergent subsequence my proof is ok? 4. Originally Posted by transgalactic x_n and y_n are bounded $\limsup x_n + \limsup y_n \geq \lim x_{r_n} + \lim y_{r_n}$ this is true because there presented sub sequences converge to the upper bound of x_n and y_n . the sum of limits is the limit of sums so we get one limit and the of two convergent sequence is one convergent sequence $\lim (x_{r_n} + y_{r_n}) = \limsup (x_n+y_n)$ this is true because the sequence is constructed from a convergent to the sup sub sequences so they equal the lim sup of $x_n+y_n$ now i need to prove that $\limsup (x_n+y_n) \Rightarrow \liminf x_n + \limsup y_n$ i tried: $ \limsup (x_n+y_n) = \limsup x_n + \limsup y_n \Rightarrow \liminf x_n + \limsup y_n $ lim sup i always bigger then lim inf so its true did i solved it correctly? I'm still having trouble figuring out what you want to prove. Also I don't think that $\limsup (x_n+y_n) = \limsup x_n + \limsup y_n$. What if $x_n=0,1,0,1,0,1,...$ and $y_n=1,0,1,0,1,0,...$, then $x_n+y_n=1,1,1,1,1,1,...$, which has a limit and limit soupy of 1. But the $\limsup x_n + \limsup y_n=1+1=2$. If you just want to prove $\limsup x_n + \limsup y_n \geq \lim x_{r_n} + \lim y_{r_n}$ well $\limsup x_n \geq \lim x_{r_n}$ and $\limsup y_n \geq \lim y_{r_n}$. Now just add, but I'm still lost as to what you want. 5. $ \lim (x_{r_n} + y_{r_n}) = \limsup (x_n+y_n) $ why its correct what do i need to say so it will be valid ?? 6. Originally Posted by transgalactic $ \lim (x_{r_n} + y_{r_n}) = \limsup (x_n+y_n) $ why its correct what do i need to say so it will be valid ?? Let $w_n=x_n+y_n$. Now I still need to understand this sequence $r_n$. Is $r_n$ the sequence so that $\limsup w_n=\lim w_{r_n}$? 7. r_n is not a sequence its just a way for me so sign a subsequence . x_n is a bounded sequence with index n and i want a subsequence to x_n so i call it $x_{r_n}$ where n is the index again its just a way to sign a subsequence is it ok now? 8. can you show an example like this there is such things on the internet	2017-05-26 19:18:58	{"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": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9813481569290161, "perplexity": 1004.7543005372688}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608676.72/warc/CC-MAIN-20170526184113-20170526204113-00015.warc.gz"}
http://mathhelpforum.com/calculus/223754-derivative-sin-x.html	# Math Help - The derivative of sin(x) 1. ## The derivative of sin(x) The difference quotient is: $\frac{d}{dx}sin(x) = \lim \Delta x\rightarrow 0=\frac{sin(x+\Delta x)-sin(x)}{\Delta x}$ which converts to: $=\lim \Delta x\rightarrow 0\frac{sin(x)cos\Delta x+cos(x)sin(\Delta x)-sin(x)}{\Delta x}$ The above I understand. The below step is supposed to be an algebraic rearrangement of the above: $\frac{d}{dx}sin(x)=\lim \Delta x\rightarrow 0[cos(x)(\frac{sin(\Delta x)}{\Delta x})-sin(x)(\frac{1-cos(\Delta x)}{\Delta x})]$ I am wondering how things were changed to the step above. I am not seeing it right now. $\dfrac{ab+cd}{e} = a\dfrac{b}{e} + c\dfrac{d}{e} = \dfrac{ab}{e} + \dfrac{cd}{e}$ (this is order of operations and associativity of multiplication). Apply that to what you had. Consider the terms of the numerator. The first and last term have $\sin(x)$. Factor it from those terms, and you get $\sin(x)(\cos(\Delta x)-1)$. Put a negative sign in front, and you get $-\sin(x)(1-\cos(\Delta x))$. The middle term has a $\cos(x)$.	2015-03-27 13:39:41	{"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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7099685668945312, "perplexity": 355.442629003679}, "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-2015-14/segments/1427131296456.82/warc/CC-MAIN-20150323172136-00038-ip-10-168-14-71.ec2.internal.warc.gz"}
http://www.gradesaver.com/textbooks/math/trigonometry/trigonometry-10th-edition/chapter-8-complex-numbers-polar-equations-and-parametric-equations-section-8-1-complex-numbers-8-1-exercises-page-357/7	Trigonometry (10th Edition) Since $7$ is a natural number and natural numbers are a subset of the set of real numbers, $7$ is a real number. Also, for a complex number $a + bi$, if $b = 0$, then $a + bi = a$, which is a real number. Thus, the set of real numbers is a subset of the set of complex numbers. Therefore, 7 can be identified as a complex number as well.	2018-04-23 23:42:56	{"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": 0.7893226742744446, "perplexity": 39.11385179233523}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946256.50/warc/CC-MAIN-20180423223408-20180424003408-00240.warc.gz"}
https://www.wackbag.com/threads/networking-type-question.78752/	# Networking-Type Question #### Arc Lite ##### As big as your Imagination... This is for work. I need to be able take my network cable that comes from the main network to my PC and split that into a second signal for use with a laptop. So I can use both the Desktop and laptop. Would it be something as simple as a network switch like this? 5 port network swiches http://tinyurl.com/35e4zt http://tinyurl.com/32t89m #### Hate & Discontent ##### Yo, homie. Is that my briefcase? Yep, all you need is a standard network switch. Assuming that your network admins arent using manually assigned IP addresses, you should be good to go. #### Arc Lite ##### As big as your Imagination... Cool. I think I'm good to go. Thanks.	2018-07-16 10:57:46	{"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": 0.8524174690246582, "perplexity": 2779.2265515977124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589251.7/warc/CC-MAIN-20180716095945-20180716115945-00567.warc.gz"}
https://ora.ox.ac.uk/objects/uuid:4682c8d5-c8dc-4ac5-a278-c7d840cec9a7	Thesis ### The internal structure of irreducible continua Subtitle: With a focus on local connectedness and monotone maps Abstract: This thesis is an examination of the structure of irreducible continua, with a particular emphasis on local connectedness and monotone maps. A continuum is irreducible if there exist a pair of points such that no proper subcontinuum contains both, with the arc being the most basic example. Being irreducible has a number of interesting implications for a continuum, both locally and globally, and it is these consequences we shall focus on. As mentioned above, the arc is the most stra... Files: • (pdf, 1.8mb) ### Authors David Harper More by this author #### Contributors Role: Examiner Role: Supervisor Type of award: DPhil Level of award: Doctoral Awarding institution: University of Oxford Language: English Keywords: Subjects:	2020-10-29 06:04:06	{"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": 0.9258378148078918, "perplexity": 1311.8015085130278}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107902745.75/warc/CC-MAIN-20201029040021-20201029070021-00687.warc.gz"}
https://math.stackexchange.com/questions/1113613/probability-of-choosing-a-graph-with-hamiltonian-cycle	# Probability of choosing a graph with Hamiltonian cycle Given $N$ labeled points in a plane one can construct $2^{N(N-1)/2}$ graphs(Unweighted, undirected) with them. Is there any theorem that gives the probability of choosing at random from these a graph having a Hamiltonian cycle? Does a similar result exist for Eulerian cycles? • This seems reasonable for Eulerian cycles, since it comes down to parity of vertex degrees. Without a characterization of when graphs support a Hamilton cycle, such a result would surprise me, although there might be bounds corresponding to necessary or sufficient conditions for Hamiltonian cycles. – Brian Hopkins Jan 21 '15 at 15:14 • I'm am hoping that at least there are some bounds on the probabilities, even if exact results are not known – biryani Jan 21 '15 at 15:16 • To compute some initial values of the probability, oeis.org/A003216 gives counts of Hamiltonian graphs by number of vertices up to 11. However, that counts nonisomorphic graphs, which would each appear several times in the construction behind the 2^(n(n-1)/2) count, so there would be more work than just dividing the OEIS numbers by the powers of 2. – Brian Hopkins Jan 21 '15 at 15:37 Yes, a lot of work has been done on these kinds of questions. Choosing a graph on $n$ vertices at random is the same as including each edge in the graph with probability $\frac{1}{2}$, independently of the other edges. You get a more general model of random graphs if you choose each edge with probability $p$. This model is known as $G_{n,p}$. It turns out that for any constant $p>0$, the probability that $G$ contains a Hamiltonian cycle tends to 1 when $n$ tends to infinity. In fact, this is true whenever $p>\frac{c \log(n)}{n}$ for some constant $c$. In particular this is true for $p=\frac12$, which is the setting that you describe. Regarding Eulerian cycles, since a Eulerian cycle exists iff the degrees are all even and the probability that a vertex has even degree is about $\frac12$, the probability that there is a Eulerian cycle is about $2^{-n}$.	2019-05-26 19:28:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8878536820411682, "perplexity": 126.16619140788079}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232259452.84/warc/CC-MAIN-20190526185417-20190526211417-00180.warc.gz"}
https://emeneye.wordpress.com/2012/04/18/adding-drivers-to-a-windows-7-image-offline/	# Adding Drivers to a Windows 7 Image Offline In my previous post I provided instructions on how to capture a Windows 7 image whereas here I will cover how to add drivers to an offline .wim image which you may have captured previously. There are two ways to add drivers to an offline Windows 7 image, both require the use of DISM to mount the image and then add the drivers. The first is using an answer file with DriverPath entries pointing to device drivers and applying the answer file to the .wim image offline. The second is using DISM command line options to directly point to .inf files without the use of an answer file. But is there a third method? I cover this at the end of this post under Method 3. # Method 1: Using Answer Files to Point to Device Drivers I am familiar with using unattended answer files to install drivers as I covered this in Experiments with Sysprep, but that was as part of the Sysprep process. Adding drivers an offline image is slightly different however – you use DISM to apply the answer file to the .wim image instead of using Sysprep. I have previously provided step by step instructions on how to build unattended answer files using the Windows SIM tool so I will not cover this again. Instead the instructions here will be more in note form. Using Windows SIM add the amd64_Microsoft-Windows-PnpCustomizationsNonWinPE_neutral component to the offlineServicing configuration pass. In the Answer File pane expand the Microsoft-Windows-PnpCustomizationsNonWinPE component. Right-click DevicePaths, and select Insert New PathAndCredentials In the Properties pane add the path to the device drivers in the Path field and type 1 in the Key field. If the path is in a network share then expand PathAndCredential in the Answer File pane, select Credentials and type your credentials in the Properties pane. You can add multiple driver path entries but for each entry make sure to increment the Key value each time. First driver path entry has a Key vale of 1, the second driver path entry has a Key vale of 2 and so on. Mount the Windows image Open the Deployment Tools Command Prompt and type something like this to mount the image offline Dism /Mount-Wim /WimFile:C:\My-Wims\ref-win7-image.wim /Index:1 /MountDir:C:\ wim-mount-dir Apply the answer file to the mounted image using DISM DISM /Image:C:\wim-mount-dir /Apply-Unattend:C:\unattend-answer-files\oflinedrivers.xml Unmount the Windows Image Dism /Unmount-Wim /MountDir:C:\wim-mount-dir /commit Don’t forget the /commit switch otherwise changes to the image will not apply. # Method 2: Using DISM to add individual INF files This is a much easier method as it doesn’t involve the hassle of building answer files. Instead you issue DISM commands at the Deployment Tools Command Prompt to add inf files to an image. Mount the Windows Image At the Deployment Tools Command Prompt and type something like this to mount the image Dism /Mount-Wim /WimFile:C:\My-Wims\ref-win7-image.wim /Index:1 /MountDir:C:\wim-mount-dir Add an .INF Driver to an Image Dism /Image:C:\wim-mount-dir /Add-Driver /Driver:C:\my-drivers\audio-driver.inf Multiple drivers can be added by simply pointing to a folder which will install all .inf drivers found in that directory. To add drivers from subdirectories too use the /Resurse switch Dism /Image:C:\wim-mount-dir /Add-Driver /Driver:C:\my-drivers /recurse 64-bit computers require drivers to have a digital signature (i.e. signed drivers). To get past this requirement use the /ForceUnsigned switch to install unsigned drivers Dism /Image:C:\wim-mount-dir /Add-Driver /Driver:C:\my-drivers /ForceUnsigned Unmount the Windows Image Dism /Unmount-Wim /MountDir:C:\wim-mount-dir /commit Again, without the /commit switch none of your changes will be saved to the image. # Method 3: Copy device drivers to C:\Windows\INF\ During the Windows 7 installation process Setup searches for device drivers in the C:\Windows\INF\ directory including all subdirectories for devices on the computer and installs them as part of the same process ready to be used upon first log on. I initially based my theory on the fact that all in-box and out of box drivers are stored in this directory so manually copying drivers here should allow Setup to find and install these drivers. I’ve found this to work absolutely fine in all my tests, including offline. (I’ve already mentioned how this works in Experiments with Sysprep and Preparing and Sysprep’ing the Reference Computer). Here’s how this works in an offline scenario Mount the Windows Image At the Deployment Tools Command Prompt and type something like this to mount the image Dism /Mount-Wim /WimFile:C:\My-Wims\ref-win7-image.wim /Index:1 /MountDir:C:\wim-mount-dir Copy device drivers to C:\wim-mount-dir\Windows\INF\ Device drivers must be .inf files and not .exe applications. You might want to organise it in subfolders, for example C:\Windows\INF\MyDrivers\audio64 C:\Windows\INF\MyDrivers\ethernet64 C:\Windows\INF\MyDrivers\chipset64 etc Unmount the Windows Image Dism /Unmount-Wim /MountDir:C:\wim-mount-dir /commit When the .wim image is applied to a computer and turned on for the first time the device drivers will install as part of the Windows installation process, no problem. Coming up next is Applying a Windows 7 image using ImageX.	2017-07-26 22:35:30	{"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": 0.39696380496025085, "perplexity": 5288.158901270187}, "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-2017-30/segments/1500549426639.7/warc/CC-MAIN-20170726222036-20170727002036-00266.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-1-common-core-15th-edition/chapter-4-an-introduction-to-functions-4-7-arithmetic-sequences-got-it-page-278/5	## Algebra 1: Common Core (15th Edition) a) $A(n)=21+(n-1)2$ b) $A(n)=2+(n-1)7$ a) We have $A(1)=21$ $A(n)=A(n-1)+2$ $A(n)=A(1)+(n-1)d$ $A(n)=21+(n-1)2$ b) We have $A(1)=2$ $A(n)=A(n-1)+7$ $A(n)=A(1)+(n-1)d$ $A(n)=2+(n-1)7$	2022-05-26 05:12:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.38610923290252686, "perplexity": 673.0382548513403}, "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-2022-21/segments/1652662601401.72/warc/CC-MAIN-20220526035036-20220526065036-00113.warc.gz"}
https://itwissen.info/en/magnetic-flux-120717.html	# magnetic flux Magnetic flux is a measure of the strength of the magnetic field in an electric coil through which current flows. It results from the product of the number of turns (N) of the coil and the current (I), i.e. the total of the currents involved in the construction of the circuit ( ampere-turn number). The relationship between magnetic field strength (H) and electric current strength (I) is referred to as the flow-through theorem: The flux through the area bounded by a field line is equal to the circulating magnetic voltage. Magnetic potentials are distributed around a straight conductor. They can also be given as a function of the angle. Informations: Englisch: magnetic flux Updated at: 20.12.2021 #Words: 109 Links: magnetic field (H), coil, current, ampere (A), field strength (F) Translations: DE Sharing:	2023-03-29 17:32:34	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8696502447128296, "perplexity": 725.6883559995325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949009.11/warc/CC-MAIN-20230329151629-20230329181629-00787.warc.gz"}
http://blog.vmchale.com/article/transparent-programming	J and APL support (and encourage) a certain form of programming without error handling or library code reuse. The alternative wisdom goes against typical programming but it works together. Consider taking successive differences: it is hardly obvious that succ_diff is preferable to 2 -~/\ ] Now, 2 -~/\ (0\$0) will fail silently, but one can discern what inputs are acceptable by inspection. This situation is common in practice, consider the example monotonically_increasing: def monotonically_increasing(a): max_value = 0 for i in range(len(a)): if a[i] > max_value: max_value = a[i] a[i] = max_value This is in fact worse than >. /\ or \|\; all fail on an empty list but only the APL derivatives make this evident. # Explorative Programming Avoiding rigorous error handling in procedures is most acceptable for exploratory programming. It is preferable to use a one-off idiom that suits your data rather than a carefully written procedure; the procedure might be thrown away as you work. I claim this functional, terse style is in fact necessary for exploratory programming. Concise, self-explanatory programs balance what is lost in loose error handling. Those used to building systems may find this objectionable but the style works together.	2022-11-27 08:08:16	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.6687625050544739, "perplexity": 5377.398224110369}, "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/1669446710218.49/warc/CC-MAIN-20221127073607-20221127103607-00844.warc.gz"}
https://brilliant.org/problems/ka-boom/	# Ka-Boom! Algebra Level 4 If $$x,y$$ and $$z$$ are real numbers satisfying $$3\tan(x) + 4\tan(y) + 5\tan(z) = 20$$, find the least possible value of $\tan^2(x) + \tan^2(y) + \tan^2(z) .$ ×	2018-04-21 09:44:13	{"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": 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": 0.5831686854362488, "perplexity": 440.45039762110946}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125945111.79/warc/CC-MAIN-20180421090739-20180421110739-00438.warc.gz"}
https://www.physicsforums.com/threads/fourier-analysis-sawtooth.713633/	# Fourier Analysis - sawtooth 1. Sep 30, 2013 ### freezer 1. The problem statement, all variables and given/known data Sawtooth signal with To = 1, at T=0, x = 0, at T=1, x =1 verify: $a_{k} = \left\{\begin{matrix} \frac{1}{2}, for k=0; & \\\frac{j}{2\pi k}, for k \neq 0; & \end{matrix}\right.$ 2. Relevant equations $\frac{1}{T_{0}} \int_{0}^{T_{0}} te^{-j(2\pi/T_{0}))kt}dt$ 3. The attempt at a solution for k = 0 $a_{0} = \int_{0}^{1} t dt$ $a_{0} = \frac{1}{2} t^{2}$ from 0 to 1 = 1/2 for k != 0 $\int_{0}^{1} te^{-j(2\pi) kt}dt$ u = t du = dt dv = $e^(-j2\pi kt)$ $v = \frac{-1}{j2\pi k}e^{-j2\pi kt}$ $t * \frac{-1}{j2\pi k}e^{-j2\pi kt} - \int \frac{-1}{j2\pi k}e^{-j2\pi kt} dt$ $t * \frac{-1}{j2\pi k}e^{-j2\pi kt} - \frac{e^{-j2\pi kt}}{4\pi^2k^2}$ -1/j = j $t * \frac{j}{2\pi k}e^{-j2\pi kt} - \frac{e^{-j2\pi kt}}{4\pi^2k^2}$ $e^{-j2\pi kt} (t \frac{j}{2\pi k} - \frac{1}{4\pi^2 k^2})$ getting close but not seeing where to go from here. Last edited: Sep 30, 2013 2. Oct 1, 2013 ### Päällikkö Check the integration by parts rules: You seem to have forgotten to evaluate the first part at the boundaries (in particular, if you integrate over t from 0 to 1, there is no way t should remain in the final expression) $\int_a^b u(x)v'(x)\,dx = \left[u(x)v(x)\right]_a^b - \int_a^b u'(x)v(x)\,dx$, first term on the right hand side. 3. Oct 1, 2013 ### freezer $\frac{je^{-j2\pi k} }{2\pi k} - \frac{e^{-j2\pi k} }{4\pi^2 k^2} - \frac{1}{4\pi^2 k^2}$ 4. Oct 1, 2013 ### Päällikkö You seem to have a sign error. Also, remember that k is an integer (a periodic function is mapped into a series in fourier space), and you should be able to arrive at the result. 5. Oct 1, 2013 ### freezer Okay, see the sign error but still not seeing how that is going to get the other terms to fall out leaving just j/(2pik). 6. Oct 1, 2013 ### Päällikkö k is an integer. What is $\exp(-j2\pi k)$ for k integer? 7. Oct 1, 2013 ### freezer Thank you Paallikko, I did not have that one in my notes.	2017-08-19 17:04:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.6024484038352966, "perplexity": 1426.2138483257154}, "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-2017-34/segments/1502886105700.94/warc/CC-MAIN-20170819162833-20170819182833-00599.warc.gz"}
http://mathhelpforum.com/discrete-math/274724-disjoint-independent-events.html	1. ## Disjoint/Independent Events Let E be an experiment with sample space S. Let A and B be events in S, where A and B both have positive probability. i) Show that if A and B are disjoint, then they are NOT independent. ii) Show that if A and B are independent, then they are NOT disjoint. I am getting more familiar with basic probability but where would I start for this? Also, what makes two events disjoint/independent? 2. ## Re: Disjoint/Independent Events Apparently, you don't know the definitions of disjoint and independent. Event A and B are disjoint iff $A\cap B=\emptyset$ and A and B are independent iff $P(A\cap B)=P(A)P(B)$. Now suppose both $P(A)>0$ and $P(B)>0$. 1. Suppose A and B are disjoint. Can A and B be independent? Remember $P(\emptyset)=0$. 2. Suppose A and B are independent. Can A and B be disjoint? Remember the product of two positive reals is positive. 3. ## Re: Disjoint/Independent Events Thank you for explaining that. This now makes sense, I am just curious how to actually word this in a concise format. 4. ## Re: Disjoint/Independent Events Originally Posted by azollner95 I am just curious how to actually word this in a concise format. Assuming that you know logic, let $D$ be the statement that "two events with positive probability are disjoint"; let $I$ be the statement that "two events with positive probability are independent". The part A) says If D then not I. In symbols $D \Rightarrow \;\neg I$ That is equivalent to $\neg D\vee\neg I$ The part B) says If I then not D. In symbols $I \Rightarrow \;\neg D$ That is equivalent to $\neg I\vee\neg D$ Look at this truth-table. Can we say "That two events with positive probability are not independent OR not disjoint."?	2017-06-24 16:03:12	{"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": 0.9068156480789185, "perplexity": 422.2891203818596}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320264.42/warc/CC-MAIN-20170624152159-20170624172159-00487.warc.gz"}
https://testbook.com/question-answer/a-high-value-of-thermal-diffusivity-represents--5e8428c5f60d5d0664811263	# A high value of thermal diffusivity represents This question was previously asked in UPPSC AE Mechanical 2013 Official Paper II View all UPPSC AE Papers > 1. high storage, less conduction of heat 2. less storage, more conduction of heat 3. There is always equal amount of conduction and storage since it is a property 4. It has no relavance Option 2 : less storage, more conduction of heat ## Detailed Solution Concept: Thermal diffusivity of material is given as, $$\alpha = \frac{k}{{\rho c}}$$. It is the property of a material. Larger the value of α, faster heat will diffuse through the material. It means less heat will be stored and more conduction will occur. A high value of α could result either from a high value of thermal conductivity or low value of thermal heat capacity ρc. Thermal diffusivity α has units of square meters per second (m2/s).	2021-10-24 12:35:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.8044217228889465, "perplexity": 2843.839094379639}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585997.77/warc/CC-MAIN-20211024111905-20211024141905-00472.warc.gz"}
http://mathhelpforum.com/new-users/209651-can-t-prove-equation.html	# Math Help - Can't prove this equation 1. ## Can't prove this equation I need help on how to prove that 9^(n+3) + 4^n is divisible by 5. Please help, I have no idea of how to solve this 2. ## Re: Can't prove this equation I would use induction, observing that: $(9^{n+4}+4^{n+1})-(9^{n+3}+4^n)=5\cdot9^{n+3}+3(9^{n+3}+4^n)$ 3. ## Re: Can't prove this equation $9^n 9^3 + 4^n$ $(5+4)^n 729 + 4^n$ Use binomial theorem to expand $(5+4)^n$ All terms except the last term $4^n$ is divisible by 5. Take the two left over terms. $4^n * 729 + 4^n$. This is divisible by 5. 4. ## Re: Can't prove this equation Or you can observe that $9^{n+3} + 4^n = 729(9^n) + 4^n$ $\equiv 729(4^n) + 4^n$ (mod 5) $\equiv 730(4^n)$ (mod 5) $\equiv 0$ (mod 5) 5. ## Re: Can't prove this equation Originally Posted by richard1234 Or you can observe that $9^{n+3} + 4^n = 729(9^n) + 4^n$ $\equiv 729(4^n) + 4^n$ (mod 5) $\equiv 730(4^n)$ (mod 5) $\equiv 0$ (mod 5) even simpler: 9 = 4 (mod 5), whence 93 = 43 = 4 (mod 5) (since 42 = 16 = 1 (mod 5)). thus 9n+3 + 4n = (4n)4 + 4n = 5(4n) = 0 (mod 5). why do this? because why should i have to calculate the cube of 9, when i can calculate the cube of 4 instead (729 is a number i don't use everyday)? 6. ## Re: Can't prove this equation Originally Posted by Deveno why do this? because why should i have to calculate the cube of 9, when i can calculate the cube of 4 instead (729 is a number i don't use everyday)? Yeah that solution's slightly simpler than mine. I just happen to have 9^3 memorized.	2015-04-28 06:37:07	{"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": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8858537673950195, "perplexity": 1452.5471831431398}, "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-2015-18/segments/1429246660724.78/warc/CC-MAIN-20150417045740-00043-ip-10-235-10-82.ec2.internal.warc.gz"}
https://bkms.kms.or.kr/journal/view.html?doi=10.4134/BKMS.2009.46.2.373	- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors Boolean regular matrices and their strongly preservers Bull. Korean Math. Soc. 2009 Vol. 46, No. 2, 373-385 https://doi.org/10.4134/BKMS.2009.46.2.373Printed March 1, 2009 Seok-Zun Song, Kyung-Tae Kang, and Mun-Hwan Kang Jeju National University Abstract : An $m\times n$ Boolean matrix $A$ is called regular if there exists an $n\times m$ Boolean matrix $X$ such that $AXA=A$. We have characterizations of Boolean regular matrices. We also determine the linear operators that strongly preserve Boolean regular matrices. Keywords : Boolean algebra, generalized inverse of a matrix, regular matrix, $(U,V)$-operator MSC numbers : 15A04, 15A09 Downloads: Full-text PDF	2021-04-13 01:40:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46608009934425354, "perplexity": 4783.973798516735}, "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/1618038071212.27/warc/CC-MAIN-20210413000853-20210413030853-00348.warc.gz"}
http://math.stackexchange.com/questions/335966/finding-the-derivative-of-the-following-function	Finding the derivative of the following function I came across the following problem: Given $\displaystyle f(r,\theta)=(r \cos \theta,r \sin \theta)$ for $(r,\theta) \in \mathbb R^2$ with $r \neq 0$. Then how can I find the value of $Df$? ($Df$ denotes the derivative of $f$). Also, how can I check whether $\displaystyle f$ is $1-1$ on $\{(r,\theta) \in \mathbb R^2: r \neq 0\}$ or not? EDIT: I want to rephrase the first question. I have to check whether the following statement is true/false? The linear transformation $Df(r,\theta)$ is not zero for any $(r,\theta) \in \mathbb R^2$ with $r \neq 0$ . - Denote $$f_1(r,\; \theta)=r \cos \theta,\\ f_2(r,\; \theta)=r \sin \theta,$$ so $$\displaystyle f(r,\;\theta)=(r \cos \theta,\;r \sin \theta)=(f_1(r,\; \theta),\;f_2(r,\; \theta)).$$ Then $$Df(r,\;\theta)=\begin{pmatrix} \dfrac{\partial{f_1(r,\; \theta)}}{\partial{r}} && \dfrac{\partial{f_1(r,\; \theta)}}{\partial{\theta}} \\ \dfrac{\partial{f_2(r,\; \theta)}}{\partial{r}} && \dfrac{\partial{f_2(r,\; \theta)}}{\partial{\theta}} \end{pmatrix}=\\ =\begin{pmatrix} \dfrac{\partial{(r \cos \theta)}}{\partial{r}} && \dfrac{\partial{(r \cos \theta)}}{\partial{\theta}} \\ \dfrac{\partial{(r \sin \theta)}}{\partial{r}} && \dfrac{\partial{(r \sin \theta)}}{\partial{\theta}} \end{pmatrix}= \begin{pmatrix} \cos{\theta} && -r\sin{\theta} \\ \sin{\theta} && r\cos{\theta} \end{pmatrix}$$ Value of the derivative on vector $\pmatrix{h_1\\h_2}$ equals $$Df(r,\;\theta)\pmatrix{h_1\\h_2}=\begin{pmatrix} \cos{\theta} && -r\sin{\theta} \\ \sin{\theta} && r\cos{\theta} \end{pmatrix}\pmatrix{h_1\\h_2}=\pmatrix{h_1 \cos{\theta}-h_2 r\sin{\theta} \\ h_1\sin{\theta} + h_2r\cos{\theta}}$$	2015-05-24 18:02:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9626059532165527, "perplexity": 69.8919979587203}, "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-2015-22/segments/1432207928030.83/warc/CC-MAIN-20150521113208-00187-ip-10-180-206-219.ec2.internal.warc.gz"}
https://plainmath.net/other/102639-a-package-weighs-96-ounces-wh	i1yev1ki 2023-02-19 A package weighs 96 ounces. What is the weight of the package in pounds? ### Answer & Explanation kolosalnoigrr Given solution: As $16$ ounces make $1$ pound $1$ ounce will make $\frac{1}{16}$ pound and $96$ ounces will make $\frac{1}{16}×96$ pounds or $\frac{1}{{\overline{)16}}^{1}}×{\overline{)96}}^{6}$ pound i.e. $6$ pounds. Do you have a similar question? Recalculate according to your conditions! Get an expert answer. Let our experts help you. Answer in as fast as 15 minutes. Didn't find what you were looking for?	2023-03-24 04:14:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 8, "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": 0.18778494000434875, "perplexity": 4497.62531571411}, "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-2023-14/segments/1679296945242.64/warc/CC-MAIN-20230324020038-20230324050038-00289.warc.gz"}
https://paudetseis.github.io/Telewavesim/	# Documentation¶ The structure of the Earth’s crust and upper mantle gives useful information on the internal composition and dynamics of our planet. Some of the most widely used techniques to infer these properties are based on examining the effect of teleseismic body wave (i.e., P and S waves that originate from distant earthquakes and arrive as plane waves) propagation (e.g., transmission and scattering) through stratified media. Modeling the seismic response from stacks of subsurface layers is therefore an essential tool in characterizing their effect on observed seismograms. This package contains python and fortran modules to synthesize teleseismic body-wave propagation through stacks of generally anisotropic and strictly horizontal layers using the matrix propagator approach of Kennett (1983), as implemented in Thomson (1997). The software also properly models reverberations from an overlying column of water using the R/T matrix expressions of Bostock and Trehu (2012), effectively simulating ocean-bottom seismic (OBS) station recordings. The software will be useful in a variety of teleseismic receiver-based studies, such as P or S receiver functions, long-period P-wave polarization, shear-wave splitting from core-refracted shear waves (i.e., SKS, SKKS), etc. It may also be the starting point for stochastic inverse methods (e.g., Monte Carlo sampling). The main part of the code is written in fortran with python wrappers. Common computational workflows are covered in the Jupyter notebooks bundled with this package.	2020-04-06 09:37:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35827353596687317, "perplexity": 2945.0380963081734}, "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/1585371620338.63/warc/CC-MAIN-20200406070848-20200406101348-00332.warc.gz"}
https://socratic.org/questions/how-do-you-graph-the-function-y-cos-2x-2pi-3-1-2	How do you graph the function y=cos[2x-2pi/3]+1/2? Feb 10, 2015 Here is a procedure one can use to graph $y = \cos \left(2 x - 2 \frac{\pi}{3}\right) + \frac{1}{2}$. 1. Make a small transformation of the original function to $y = \cos \left[2 \left(x - \frac{\pi}{3}\right)\right] + \frac{1}{2}$. 2. Graph of this function can be obtained by horizontally right-shifting by $\frac{\pi}{3}$ a graph of function $y = \cos \left(2 x\right) + \frac{1}{2}$. 3. Graph of $y = \cos \left(2 x\right) + \frac{1}{2}$ can be obtained by vertically up-shifting by $\frac{1}{2}$ a graph of function $y = \cos \left(2 x\right)$. 4. Graph of $y = \cos \left(2 x\right)$ can be obtained by horizontally squeezing towards 0 by a factor $2$ a graph of function $y = \cos \left(x\right)$. "Squeezing" means that every point $\left(x , y\right)$ of the graph is transformed into $\left(\frac{x}{2} , y\right)$. So, the steps to graph the original function are: (a) start from a graph of $y = \cos \left(x\right)$; (b) squeeze this graph horizontally towards 0 by a factor of $2$. (c) shift up by $\frac{1}{2}$ (d) shift right by $\frac{\pi}{3}$.	2021-09-24 06:01:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 16, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6443887948989868, "perplexity": 503.1369018948072}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057504.60/warc/CC-MAIN-20210924050055-20210924080055-00615.warc.gz"}
https://hackage.haskell.org/package/assert4hs-core-0.1.0/docs/Test-Fluent-Assertions-Maybe.html	assert4hs-core-0.1.0: A set of assertion for writing more readable tests cases Test.Fluent.Assertions.Maybe Description This library aims to provide a set of combinators to assert Maybe type. Synopsis # Documentation assert if subject under is empty assertThat (Just 10) isNothing assert if subject under is not empty assertThat (Just 10) isJust assert if subject under is not empty and extract contained value assertThat (Just 10) extracting	2022-01-19 06:10:53	{"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": 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": 0.17125040292739868, "perplexity": 12475.373067018321}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320301263.50/warc/CC-MAIN-20220119033421-20220119063421-00009.warc.gz"}
https://brilliant.org/problems/5-13-21/	# 5, 13, 21 Algebra Level 2 $5,\, 13,\, 21,\, 29,\, 37,\, \ldots$ Determine the sum of the first 50 numbers in the list (that follows an arithmetic progression). ×	2017-09-22 13:41:00	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.6923105120658875, "perplexity": 1079.8618473229203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688966.39/warc/CC-MAIN-20170922130934-20170922150934-00326.warc.gz"}
http://www.igsor.net/projects/tagit/screenshots.html	# Screenshots¶ The images of a directory can be scanned and added to the tagit database. It’s optional but saves time when scanning through the images. Currently, this action is to be run from the terminal. The GUI shows a search bar (top), some extra information (right hand side) and the images. The image grid size (3x3 here) is configurable. Search filters can be added to restrict the displayed images. Images can be selected and tags can be manipulated.	2020-10-24 16:58:51	{"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": 0.8208699822425842, "perplexity": 2076.8483468429386}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107884322.44/warc/CC-MAIN-20201024164841-20201024194841-00491.warc.gz"}
http://khvmathematics.blogspot.com/2007/11/jokes-on-maths.html	Math Formula? ## Friday, November 2, 2007 ### JOKES ON MATHS IN DIFFERENT VIEWS Several scientists were all posed the following question: "What is 2 * 2 ?" The engineer whips out his slide rule (so it's old) and shuffles it back and forth, and finally announces "3.99". The physicist consults his technical references, sets up the problem on his computer, and announces "it lies between 3.98 and 4.02". The mathematician cogitates for a while, then announces: "I don't know what the answer is, but I can tell you, an answer exists!". Philosopher smiles: "But what do you mean by 2 * 2 ?" Logician replies: "Please define 2 * 2 more precisely."	2018-03-20 15:55:16	{"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": 0.8583981990814209, "perplexity": 4317.994415503955}, "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/1521257647498.68/warc/CC-MAIN-20180320150533-20180320170533-00422.warc.gz"}
https://cs.stackexchange.com/questions/35353/proving-that-the-set-of-non-universal-cfgs-is-not-in-np	# Proving that the set of non-universal CFGs is not in NP How do I prove that $\overline{\mathrm{ALL_{CFG}}}$ does not fall in NP, where $\qquad\mathrm{ALL_{CFG}} = \{\langle G \rangle \mid G \text{ is a CFG}, L(G) = \Sigma^* \}$ Hint: Use the fact that universality of context-free grammars (that is, deciding whether $L(G) = \Sigma^*$) is undecidable. • I thought it has something to do with proving $ALL_{CFG}$ is undecidable. But I don't know how to get from there to proving that it is not an NP problem. – Moshe Hoori Dec 16 '14 at 6:06 • I'm not sure but this is what I come up with so far: $ALL_{CFG}$ is undecidable so $\overline{ALL_{CFG}}$ is undecidable too. undecidable languages can't be NP. is that right? – Moshe Hoori Dec 16 '14 at 11:42	2019-08-22 13:54:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8967580795288086, "perplexity": 278.50889643437597}, "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-2019-35/segments/1566027317130.77/warc/CC-MAIN-20190822130553-20190822152553-00539.warc.gz"}
http://nrich.maths.org/1928/clue	### Gold Again Without using a calculator, computer or tables find the exact values of cos36cos72 and also cos36 - cos72. ### Pythagorean Golden Means Show that the arithmetic mean, geometric mean and harmonic mean of a and b can be the lengths of the sides of a right-angles triangle if and only if a = bx^3, where x is the Golden Ratio. ### Golden Triangle Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio. # Golden Ratio ##### Stage: 5 Challenge Level: Take $b = 1$ and write the equation in terms of $a$. Then solve this equation to find the golden ratio.	2015-02-28 17:37:23	{"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": 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": 0.7741702198982239, "perplexity": 800.569977043118}, "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-2015-11/segments/1424936462009.45/warc/CC-MAIN-20150226074102-00209-ip-10-28-5-156.ec2.internal.warc.gz"}
https://esl.hohoweiya.xyz/07-Model-Assessment-and-Selection/7.5-Estimates-of-In-Sample-Prediction-Error/index.html	7.5 样本内误差的估计¶ weiya注 1. Efron, B. (1986). How biased is the apparent error rate of a prediction rule?, Journal of the American Statistical Association 81: 461–70.	2019-06-20 19:42:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7644143104553223, "perplexity": 1893.9570887048374}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999273.24/warc/CC-MAIN-20190620190041-20190620212041-00213.warc.gz"}
http://dataspace.princeton.edu/jspui/handle/88435/dsp01d504rn78g	Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01d504rn78g Title: Witches' Brew and Bloodcraft An Examination of Inertial Behaviors In Laminar Flow Environments Authors: Pohlmann, John T. Advisors: Austin, Robert Contributors: Aizenman, Michael Department: Physics Class Year: 2016 Abstract: Deterministic Lateral Displacement arrays (DLDs) utilize the properties of laminar or viscous flow to separate biological material by characteristic size. DLDs are comprised of a long, at chip through which a solution is forced. A grid of laterally offset rows of pillars determines a flow pattern throughout the length of the chip. Due to laminar behavior, particles are expected to closely follow flow patterns, separating them based on their flow mode. As the size scale of DLDs decreases in an effort to boost the resolution of separation, experimentalists find that the efficiencies are decreasing: Polymer chains that otherwise traverse the length of the array unscathed break apart in the smaller scale, and particles do not separate as expected from laminar properties. Using low Reynolds and Stokes number approximations, this paper solves the laminar case in 2 1/2 dimensions for a scalar stream function. The scalar stream function allows us to translate boundary conditions from cartesian to polar, which allows us to de fine a critical radius and characteristic displacement vector to locate regions of inertial particle behavior in an otherwise completely laminar fluid. Finally, the scalar stream function and critical radius are applied to simulated flow environments to investigate if inertial behaviors may be occurring. We find clear patterns which are compliant with experimental observations, and make claims regarding theoretical models. Extent: 79 pages URI: http://arks.princeton.edu/ark:/88435/dsp01d504rn78g Type of Material: Princeton University Senior Theses Language: en_US Appears in Collections: Physics, 1936-2016 Files in This Item: File SizeFormat	2017-05-22 19:28:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46172627806663513, "perplexity": 3027.8367367488368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "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-2017-22/segments/1495463607046.17/warc/CC-MAIN-20170522190443-20170522210443-00100.warc.gz"}
https://imathworks.com/tex/tex-latex-numcases-environment-with-showlabels-package/	# [Tex/LaTex] numcases environment with showlabels package casesnumberingshowlabels I just discovered the environment numcases, which upgrades the package cases allowing to number the different cases. I am also currently using the showlabels package, which puts the name of the label on the PDF, right where you put it in the TeX file. Very useful feature, especially when writing a long document and you want to get the tag name from the PDF scrolling up a page rather than open another TeX file and search for the equation! Unfortunately, I can't get the numcases environment to work properly with the showlabels package. In particular, I cannot give a label to the last case, otherwise I get the error "Incompatible list can't be unboxed". However, without the showcases package, everything works smoothly. It also works smoothly if I don't label the last case, but of course that's not optimal, cause I need to label all the cases… Here's an example. Comment/uncomment the line where the showlabels package is included to see the behavior. \documentclass{article} \usepackage{showlabels} \usepackage{cases} \begin{document} \begin{numcases}{} a & b \label{a}\\ c & d \label{b} \end{numcases} \end{document} Does anybody know a workaround for this? I would be fine also with a way to avoid numcases (while getting the same result). I cannot understand why lines of a cases environment should be separately numbered. However, you get the effect with empheq: \documentclass{article} \usepackage{empheq} \usepackage{showlabels} \begin{document} \begin{empheq}[left=\empheqlbrace]{alignat=2}	2023-01-28 14:26:37	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.952160120010376, "perplexity": 1493.5689737657399}, "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/1674764499634.11/warc/CC-MAIN-20230128121809-20230128151809-00041.warc.gz"}
https://www.emathhelp.net/calculators/algebra-1/polynomial-long-division-calculator/?numer=5x%5E9+-+4x%5E2+%2B2&denom=5x%2B10	# Polynomial Long Division Calculator ## Perform the long division of polynomials step by step The calculator will perform the long division of polynomials, with steps shown. Related calculators: Synthetic Division Calculator, Long Division Calculator Divide (dividend): By (divisor): If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.	2022-10-05 02:49:03	{"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": 0.9089750051498413, "perplexity": 1399.1822482803136}, "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/1664030337531.3/warc/CC-MAIN-20221005011205-20221005041205-00456.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/elementary-and-intermediate-algebra-concepts-and-applications-6th-edition/chapter-5-polynomials-and-factoring-5-3-factoring-trinomials-of-the-type-ax2-bx-c-5-3-exercise-set-page-326/47	## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition) $(y+4)(2y-1)$ Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} 2y^2+8y-y-4 \\\\= (2y^2+8y)-(y+4) .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 2y(y+4)-(y+4) .\end{array} Factoring the $GCF= (y+4)$ of the entire expression above results to \begin{array}{l}\require{cancel} (y+4)(2y-1) .\end{array}	2018-06-25 00:34:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.9441630244255066, "perplexity": 3413.2276137073127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267867304.92/warc/CC-MAIN-20180624234721-20180625014721-00315.warc.gz"}
http://math.stackexchange.com/questions/679882/multiplication-on-a-kg-n	# Multiplication on a K(G,n) Suppose that, given an abelian group $G$, there is a multiplication map $\mu:K(G,n)\times K(G,n) \to K(G,n)$ defined such that the induced map on the homotopy group $\mu_:\pi_n(K(G,n) \times K(G,n)) \to \pi_n(K(G,n))$ takes $(g_1,g_2)$ to $g_1 + g_2$, where $+$ is the operation on $G$. Does it follow that this multiplication is homotopy-commutative; that is, if $t:K(G,n) \times K(G,n) \to K(G,n) \times K(G,n)$ switches coordinates, does it follow that $\mu t$ is homotopic to $\mu$? Since $G$ is commutative, it seems that $\mu$ should be, but I'm having a hard time coming up with the actual homotopy. I know that is NOT true in general that if two maps induce the same homomorphisms on homotopy groups, then they are homotopic. One could also ask if the fact that the operation on $G$ is associative implies that $\mu$ is homotopy-associative. - Yes, it follows that $\mu t$ is homotopic to $t$. In general we have the following result: Lemma: Suppose that $G$ and $H$ are abelian groups and $f,g: K(G,n) \to K(H,n)$ are maps. Then $f_ = g_: \pi_n(K(G,n))=G \to \pi_n(K(H,n))$ if and only if $f$ is homotopic to $g$. This follows easily from the following: Lemma: Let $X$ be an $(n-1)$-connected CW-complex with $\pi_1(X)$ abelian then the map $\eta: H^n(X;G) \to \text{Hom}(\pi_n(X),G)$ given by $\eta[f] = f_: \pi_n(X) \to \pi_n(K(G,n)) = G$ is an isomorphism. Here we use that $H^n(X;G) \cong [X, K(G,n)]$ where $[ , ]$ denotes homotopy classes of maps. A reference for this last lemma is Arkowitz - Introduction to Homotopy Theory. It is Lemma 2.5.13 - To apply your lemma are you asserting that $K(G,n)\times K(G,n)$ is a $K(H,n)$? – Kevin Carlson Feb 17 at 21:33 @Kevin Carlson: In general $\pi_n(X \times Y) \cong \pi_n(X) \times \pi_n(Y)$. In particular, for Eilenberg-Mac Lane spaces we get that $K(G,n) \times K(H,n)$ has the homotopy type of a $K(G \times H,n)$. – R. Frankhuizen Feb 17 at 21:41 Of course. Thanks. – Kevin Carlson Feb 17 at 21:42	2014-11-23 11:10:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9827533960342407, "perplexity": 99.55694545343368}, "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-2014-49/segments/1416400379462.60/warc/CC-MAIN-20141119123259-00253-ip-10-235-23-156.ec2.internal.warc.gz"}
http://soft-matter.seas.harvard.edu/index.php?title=Percolation_Model_for_Slow_Dynamics_in_Glass-Forming_Materials&diff=next&oldid=15929&printable=yes	# Difference between revisions of "Percolation Model for Slow Dynamics in Glass-Forming Materials" Glassy systems exhibit several unique properties. During a glass transition, the structural relaxation time increases by several orders of magnitude. Also, the structural correlations display an anomalous stretched-exponential time decay: $exp(-t/\tau_{\alpha})^{\beta}$, where $\beta$ is called the stretching exponent, and $\tau_{\alpha}$ is called the $\alpha$-relaxation time.	2020-09-19 13:38:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7086316347122192, "perplexity": 2209.2641775590623}, "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-2020-40/segments/1600400191780.21/warc/CC-MAIN-20200919110805-20200919140805-00377.warc.gz"}
https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Lane)/3%3A_Summarizing_Distributions/3.04%3A_Balance_Scale_Simulation	# 3.4: Balance Scale Simulation Skills to Develop • Understand what it means for a distribution to balance on a fulcrum • Learn which measure of central tendency will balance a distribution ## Instructions This demonstration allows you to change the shape of a distribution and see the point at which the distribution would balance. The graph in the right panel is a histogram of $$600$$ scores. The mean and median are equal to $$8$$ and are indicated by small vertical bars on the $$X$$-axis The top portion of the bar is in blue and represents the mean. The bottom portion is in pink and represents the median. The mean and median are also shown to the left of the $$Y$$-axis. You can see that the histogram is balanced on the tip of the triangle (the fulcrum). You can change the shape of the histogram by painting with the mouse. Notice that the triangle beneath the X-axis automatically moves to the point where the histogram is balanced. Experiment with different shapes and see if you can determine whether there is a relationship between the mean, median, and/or the mode and the location of the balance point. ## Illustrated Instructions Below is a screen shot of the simulaton's beginning screen. Note that the distribution is balanced on the fulcrum. The mean and median are shown to the left and also as small vertical bars below the $$X$$-axis. The mean is in blue and the median is in pink. The next figure illustrates this more clearly. Figure $$\PageIndex{1}$$: Beginning Screen of the Simulation You can change the distribution by painting with the mouse when running the simulation.Below is an example of the distribution after it has been changed. Note that the mean and median are marked by vertical lines. Figure $$\PageIndex{2}$$: Screen of the Simulation after change ## Contributor • Online Statistics Education: A Multimedia Course of Study (http://onlinestatbook.com/). Project Leader: David M. Lane, Rice University.	2019-09-17 05:00:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4608023464679718, "perplexity": 492.7222171087676}, "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/1568514573052.26/warc/CC-MAIN-20190917040727-20190917062727-00315.warc.gz"}
http://mathoverflow.net/questions/146571/logarithmic-mean/146575	# Logarithmic mean Logarithmic mean of two positive real numbers is well defined in the literature, it has also been extended to more than two arguments in various papers. Is there any notion of logarithmic mean of random variables or functions? Thank you for your help and time. - By the way, I know that logarithmic mean of convex functionals is there in the literature, but I want to know can we define it for random variables or just positive functions ? – andy Oct 31 '13 at 23:07 You're looking for $e^{E \log X}$. It has all the nice properties you'd like it to. - Could you expand a bit on your answer? – Suvrit Nov 1 '13 at 1:27 Yes, Omer, I would greatly appreciate if you could kindly elaborate a little more, anyway thank you so much. – andy Nov 1 '13 at 3:00 For two positive real numbers, this gives the geometric mean, not the logarithmic mean. Have you looked at en.wikipedia.org/wiki/Logarithmic_mean ? – S. Carnahan Nov 1 '13 at 9:42 Indeed, say $g(t) := e^{E[(1-t)\log X]+E[t\log Y]}$, then we could define a logarithmic mean as $$L(X,Y) := \int_0^1 g(t)dt.$$ Reasoning: The above idea is inspired by noting that the ordinary logarithmic mean between two positive scalars, $x$ and $y$ may be viewed as $L(x,y) = \int_0^1 x^{1-t}y^tdt$, where the integrand is nothing but the (weighted) geometric mean.	2014-07-09 23:32:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 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": 0.9347739219665527, "perplexity": 385.90992178796876}, "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-2014-23/segments/1404776400583.60/warc/CC-MAIN-20140707234000-00068-ip-10-180-212-248.ec2.internal.warc.gz"}
https://www.math.tamu.edu/Calendar/listday/index.php?print=5591&cal=38	## Noncommutative Geometry Seminar Date: November 22, 2019 Time: 3:00PM - 4:00PM Location: BLOC 624 Speaker: Ilya Kachkovskiy, Michigan State University Title: Almost commuting matrices Abstract: Suppose that $X$ and $Y$ are two self-adjoint matrices with the commutator $[X,Y]$ of small operator norm. One would expect that $X$ and $Y$ are close to a pair of commuting matrices. Can one provide a distance estimate which only depends on $\\|[X,Y]\\|$ and not on the dimension? This question was asked by Paul Halmos in 1976 and answered positively by Huaxin Lin in 1993 by indirect C*-algebraic methods, which did not provide any explicit bounds. It was conjectured by Davidson and Szarek that the distance estimate would be of the form $C\\|[X,Y]\\|^{1/2}$. In the talk, I will explain some background on this and related problems, and the main ideas of the proof of this conjecture, obtained jointly with Yuri Safarov. If time permits, I will discuss some current work in progress. .	2020-01-28 15:03:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5110520124435425, "perplexity": 468.76638496096007}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251778272.69/warc/CC-MAIN-20200128122813-20200128152813-00144.warc.gz"}
https://domymatlab.com/matlab-programming-for-numerical-analysis-pdf-2/	# Matlab Programming For Numerical Analysis Pdf \| Pay Someone To Do My Matlab Homework ## Matlab Assignment Help Near Me An Approach For Convergence As A Direct Approach. 5 3. The Theorem 2: _____________________________________________________________________ 1. Theorem 1: _____________________________________________________________________ An algorithm for speedup of computing the convergence rate of the iterative method and the stability graph of the discretization algorithm. 5 4. Relational Equivalences between the Run-Time Iterative Method And Stability Graph Inference For Numerical Analysis MPL Program for Numerical Analysis (DLXIC) — Theorem 3: _____________________________________________________________________ By linearising the variables in advance. 6 5. ## Matlab Coding Homework Help Proof of Theorem 7 For Theorem 2 Corollary 1: _____________________________________________________________________ 2. Corollary 3: _____________________________________________________________________ Theorem 4: _____________________________________________________________________ Theorem 5: _____________________________________________________________________ There are pairs of eigenvalue and eigenvector of the block matrix defined as follows: \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| link \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \| \|	2022-10-05 19:08:06	{"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": 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": 0.4786008596420288, "perplexity": 74.96117254780897}, "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/1664030337663.75/warc/CC-MAIN-20221005172112-20221005202112-00292.warc.gz"}
http://cvgmt.sns.it/paper/1065/	# The Monge problem for strictly convex norms in $R^d$ created by depascal on 07 May 2008 modified on 22 Sep 2010 [BibTeX] Published Paper Inserted: 7 may 2008 Last Updated: 22 sep 2010 Journal: Journ. of the Eur. Math. Soc. Volume: 12 Number: 6 Pages: 1355-1369 Year: 2010 Notes: The published version is available at: http:/www.ems-ph.orgjournalsshowissue.php?issn=1435-9855&vol=12&iss=6 Abstract: We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of $\R^d$ under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.	2019-02-17 11:26:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4600525200366974, "perplexity": 700.6355906407014}, "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-2019-09/segments/1550247481992.39/warc/CC-MAIN-20190217111746-20190217133746-00420.warc.gz"}
https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=18&t=64753	Sapling Homework $\lambda=\frac{h}{p}$ 805377003 Posts: 97 Joined: Wed Sep 30, 2020 10:10 pm Sapling Homework Can someone explain how to do this problem? As you may well know, placing metal objects inside a microwave oven can generate sparks. Two of your friends are arguing over the cause of the sparking, with one stating that the microwaves "herd" electrons into "pointy" areas of the metal object, from which the electrons jump from one part of the object to another. The other friend says that the sparks are caused by the photoelectric effect. Prove or disprove the latter idea using basic physics. Suppose the typical work function of the metal is roughly 4.570×10−19 J. Calculate the maximum wavelength in angstroms of the radiation that will eject electrons from the metal. Chem_Mod Posts: 19540 Joined: Thu Aug 04, 2011 1:53 pm Has upvoted: 882 times Re: Sapling Homework To solve this problem, know that the work function is equal to the minimum energy to eject an electron. Therefore, use this value and the equations c=(wavelength)(frequency) and E=h(frequency) to solve for the wavelength and then use dimensional analysis to find an answer in Angstroms! kateraelDis1L Posts: 104 Joined: Wed Sep 30, 2020 9:54 pm Re: Sapling Homework to add on^ an Angstrom unit of length is mostly used in measuring wavelengths of light, equal to 10^-10 meter or 0.1 nanometer.	2021-02-27 19:53:41	{"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": 0.42882436513900757, "perplexity": 1204.7246569991642}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178359082.48/warc/CC-MAIN-20210227174711-20210227204711-00255.warc.gz"}
https://forum.azimuthproject.org/plugin/viewcomment/19799	Keith wrote: >\$>\mathrm{hom}(f,g)(h)=\begin{cases} >u := g\circ h \circ f & \text{ if } target(f)=source(h) \\\\ >& \text{ and } target(h)=source(g)\\\\ >& \\\\ >\varnothing & \text{ otherwise.} >\end{cases} >\$ Thanks for this. Gave me a better perspective on how the hom functor works. Below is a diagram showing preservation of composition highlighting your hom gadget. ![homfunctor preservation of composition](http://aether.co.kr/images/homfunctor_composition.svg)	2021-09-18 08:00:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9973475337028503, "perplexity": 6850.766032554599}, "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-2021-39/segments/1631780056348.59/warc/CC-MAIN-20210918062845-20210918092845-00669.warc.gz"}
https://www.physicsforums.com/threads/stress-for-v-band-clamp-under-loading.892824/	1. Nov 9, 2016 formula428 I have a v-band clamp and I'm wanting to know the stresses for such a section. I'm interested in the forces and resultant stresses on the clamp from the flange and plug (inside the v band) opposing each other as pressure is increased. I thought of treating the section as an effective channel member in flexure such that the section is bending about an asymmetrical axis. Think of it as having a U, turning it upside down and then applying force/moment pushing down on the web. However, the stresses I'm getting are really high. Maybe I'm calculating it wrong? Right now I'm using (6 P L) / (b h^2) and treating the center "web" to simply be a rectangle. Last edited: Nov 9, 2016 2. Nov 11, 2016 Nidum They are tricky things to analyse properly . Let us see a picture or a drawing off the particular clamp that you are interested in . What forces do you think are acting in the clamp ? 3. Nov 11, 2016 formula428 Here's a rough FBD and my thoughts. File size: 46.5 KB Views: 61	2017-10-17 00:56:28	{"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": 0.8064987659454346, "perplexity": 2092.5740728281094}, "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/1508187820487.5/warc/CC-MAIN-20171016233304-20171017013304-00009.warc.gz"}
https://lists.gnu.org/archive/html/lilypond-user/2018-04/msg00357.html	lilypond-user [Top][All Lists] ## Re: \include command and local network folders From: David Wright Subject: Re: \include command and local network folders Date: Thu, 12 Apr 2018 15:58:07 -0500 User-agent: Mutt/1.5.21 (2010-09-15) ```On Thu 12 Apr 2018 at 12:13:21 (-0700), foxfanfare wrote: > David Wright wrote > > I see no filenames. I only see //192.168.1.13/Public/test.ly which > > looks like an incomplete URL, but lacking its protocol (like HTTP:). > > I can only assume when you mapped the files to a drive letter, > > you got the syntax correct. Would this reference help? > > > > https://msdn.microsoft.com/en-us/library/windows/desktop/aa365247(v=vs.85).aspx > > I don't understand David : \\192.168.0.13\Public\test.ly is a correct > Windows path. Then I think that's the filename you need to use. I assume "Starting lilypond-windows…" means you're running on a windows box. > I just changed the original "\" with the unix "/" for Frescobaldi to deal > with (//192.168.0.13/Public/test.ly) > I think it is named SMB right? Samba implements SMB on unix, yes, but programs on windows should use their own filename syntax to reference the files transparently. In linux, you'd typically see something like //192.168.0.13/Public if you were mounting a share as a client. Similarly you could only hand a filename like //192.168.0.13/Public/test.ly to a client that already knew what protocol to use, like smbclient. So try using the filename you wanted to specify, rather than second guessing the way the system deals with it. I'd be interested	2019-08-21 15:10:26	{"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": 0.9210169911384583, "perplexity": 11963.81421423557}, "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/1566027316021.66/warc/CC-MAIN-20190821131745-20190821153745-00393.warc.gz"}
https://halshs.archives-ouvertes.fr/halshs-00340381	# How to score alternatives when criteria are scored on an ordinal scale Abstract : We address in this paper the problem of scoring alternatives when they are evaluated with respect to several criteria on a finite ordinal scale $E$. We show that in general, the ordinal scale $E$ has to be refined or shrunk in order to be able to represent the preference of the decision maker by an aggregation operator belonging to the family of mean operators. The paper recalls previous theoretical results of the author giving necessary and sufficient conditions for a representation of preferences, and then focusses on describing practical algorithms and examples. Keywords : Document type : Journal articles Domain : https://halshs.archives-ouvertes.fr/halshs-00340381 Contributor : Michel Grabisch <> Submitted on : Thursday, November 20, 2008 - 4:55:50 PM Last modification on : Tuesday, March 27, 2018 - 11:48:05 AM Long-term archiving on : Monday, June 7, 2010 - 9:47:54 PM ### File jmcda06.pdf Files produced by the author(s) ### Citation Michel Grabisch. How to score alternatives when criteria are scored on an ordinal scale. Journal of Multi-Criteria Decision Analysis, Wiley, 2008, 15 (1-2), pp.31-44. ⟨10.1002/mcda.422⟩. ⟨halshs-00340381⟩ Record views	2019-11-17 09:45:15	{"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": 0.3123733103275299, "perplexity": 2126.8368036984784}, "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/1573496668910.63/warc/CC-MAIN-20191117091944-20191117115944-00492.warc.gz"}
http://www.stat.cmu.edu/research/publications/applying-non-parametric-robust-bayesian-analysis-non-opinionated-judicial	## Applying Non-parametric Robust Bayesian Analysis to Non-Opinionated Judicial Neutrality April, 1999 Tech Report ### Author(s) Joseph B. Kadane, Elias Moreno, Maria Eglee Perez and Luis Raul Pericchi ### Abstract This paper explores the usefulness of robust Bayesian analysis in the context of an applied problem, finding priors to model judicial neutrality in an age discrimination case. We seek large classes of prior distributions without trivial bounds on the posterior probability of a key set, that is, without bounds that are independent of the data. Such an exploration shows qualitatively where the prior elicitation matters most, and quantitatively how sensitive the conclusions are to specified prior changes. The novel non-parametric classes proposed and studied here represent judicial netrality and are reasonably wide so that when a clear conclusion emerges from the data at hand, this is arguably beyond a reasonable doubt.	2017-12-11 02:29:08	{"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": 0.8084262609481812, "perplexity": 2766.64848763461}, "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/1512948512054.0/warc/CC-MAIN-20171211014442-20171211034442-00098.warc.gz"}
http://mathhelpforum.com/calculus/124468-find-area-shaded-circles.html	# Math Help - find the area shaded by the circles 1. ## find the area shaded by the circles find the area shared by the circles r=2cos(theta) and r=2sin(theta). i know the general formula for finding the area, but i don't know which is the outside one, and which is the inside circle. but i've tried both ways and am still not getting the right answer. so let's just say i'll try it with integral .5(4cos(x)^2-.5(4sin(x)^2) i can factor out a 2, giving me cos(x)^2-sin(x)^2. the integral of that, i believe, can be expressed as 4sin(2x). now i figured the limits of integration were from 0 to pi/4, because those are the two places the circles intersect. so evaluating there, i would get 4-0=4. but i've been told the answer is pi/2 -1. so where am i going wrong, because i'm way off. 2. Originally Posted by isuckatcalc find the area shared by the circles r=2cos(theta) and r=2sin(theta). i know the general formula for finding the area, but i don't know which is the outside one, and which is the inside circle. but i've tried both ways and am still not getting the right answer. so let's just say i'll try it with integral .5(4cos(x)^2-.5(4sin(x)^2) i can factor out a 2, giving me cos(x)^2-sin(x)^2. the integral of that, i believe, can be expressed as 4sin(2x). now i figured the limits of integration were from 0 to pi/4, because those are the two places the circles intersect. so evaluating there, i would get 4-0=4. but i've been told the answer is pi/2 -1. so where am i going wrong, because i'm way off. use symmetry ... $A = 2 \int_0^{\frac{\pi}{4}} \frac{(2\sin{t})^2}{2} \, dt $ $A = 4 \int_0^{\frac{\pi}{4}} \sin^2{t} \, dt$ $A = 4 \int_0^{\frac{\pi}{4}} \frac{1-\cos(2t)}{2} \, dt$ $A = 2 \int_0^{\frac{\pi}{4}} 1-\cos(2t) \, dt$ finish 3. ok i get it now, i was trying to use both r=2cos(x) and r=2sin(x). how does one know when to use only one or when to subtract one from the other? since there were two graphs it seemed obvious to me that the latter formula needed to be used, but apparently it didn't. also, how do you know to go with r=2sin(x) instead of r=2cos(x)? thanks for the help. 4. Originally Posted by isuckatcalc ok i get it now, i was trying to use both r=2cos(x) and r=2sin(x). how does one know when to use only one or when to subtract one from the other? since there were two graphs it seemed obvious to me that the latter formula needed to be used, but apparently it didn't. also, how do you know to go with r=2sin(x) instead of r=2cos(x)? thanks for the help. You have to look at the graph and the region area you want to find. LOOK for symmetry and take advantage of it. I could have went with cosine ... $A = 2 \int_{\frac{\pi}{4}}^{\frac{\pi}{2}} \frac{(2\cos{\theta})^2}{2} \, d\theta$ 5. Converting to Cartesian coordinates, $x= r cos(\theta)$ and $y= r sin(\theta)$ so $r= 2cos(\theta)$ or $r^2= 2 rcos(\theta)$ and so $x^2+ y^2= 2 x$. Then $x^2- 2x+ y^2= 0$ and, completing the square, $x^2- 2x+ 1+ y^2= (x- 1)^2+ y^2= 1$. That is the circle with center at (1, 0) and radius 1. It is tangent to the y-axis at the origin. Similarly, $r= 2 sin(\theta)$ becomes $r^2= 2 r sin(\theta)$ or $x^2+ y^2= y$ giving the circle with center at (0,1) and radius 1. It is tangent to the x-axis at the origin. There is no "inside" or "outside". They overlap on the first quadrant, having x=y or $\theta= \pi/4$ as the mid line. That should lead you to integrate $r= 2 sin(\theta)$ from $\theta= 0$ to $\pi/4$ and then double to get the entire area.	2015-04-18 20:33:38	{"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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9274532198905945, "perplexity": 249.59392408168503}, "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-2015-18/segments/1429246636104.0/warc/CC-MAIN-20150417045716-00129-ip-10-235-10-82.ec2.internal.warc.gz"}
https://eepower.com/news/epa-leed-certification-fails-to-increase-energy-efficiency/	News # EPA: LEED Certification Fails to Increase Energy Efficiency March 02, 2014 by Jeff Shepard Today, LEED Exposed, a project of the Environmental Policy Alliance (EPA), released research showing that large privately-owned buildings in Washington D.C. certified under the U.S. Green Building Council's (USGBC) Leadership in Energy and Environmental Design (LEED) standards, actually use more energy than uncertified buildings. Despite having the highest number of buildings in the country certified under LEED, Washington D.C. buildings are actually less energy efficient than the national average. LEED Exposed determined energy consumption by comparing the weather-normalized, source energy use intensity, or EUI (a unit of measurement that represents the energy consumed by a building relative to its size), for both buildings certified by the USGBC as "green" and those that have not gone through the USGBC's expensive permitting process. For LEED-certified buildings, their EUI was 205, compared to 199 for non-certified buildings. Ironically, USGBC's headquarters (which has achieved the highest level of LEED certification) is even worse at 236. "This latest data release only confirms what we already knew: LEED certification is little more than a fancy plaque displayed by these 'green' buildings," said Anastasia Swearingen, research analyst for the Environmental Policy Alliance. "Previous analyses of energy use by LEED-certified buildings have consistently shown that LEED ratings have no bearing on actual energy efficiency." These findings are significant as D.C. is one of several major localities to mandate the use of LEED in construction of public buildings and was the first city to require all buildings (public and private) to disclose energy usage. An analysis by The Washington Examiner earlier this year of D.C. government buildings found that many of the District's LEED-certified buildings were the least energy-efficient of all comparable buildings. The city's Department of Environment (DOE) recognizes the problems with using LEED standards. In a report accompanying the release of data, the DOE says concerns and questions regarding the use of LEED include, "The dependence on a third-party organization, over which the government has no oversight, to set the District's green building standards," and, "The perception that application costs associated with LEED are significant." "It's troubling that to achieve the laudable goal of promoting greater energy efficiency, the District relies on the use of a third-party rating system that doesn't require actual proof of energy efficiency to earn certification," continued Swearingen. "Even more alarming is the fact that the city is collecting millions of dollars in permit fees to administer this inefficient program." In fiscal year 2013, D.C. collected over $1.6 million in green building fees, and the District has collected over$5.2 million in fees since 2010. Despite the expense, D.C. lags behind the rest of the country in energy efficient office buildings. The median EUI nationwide for office buildings is 148â€”DC's is 214, or 44% more than the national median. Swearingen concluded: "It's time for D.C. to ditch LEED and move towards a certification system that promises real improvements in energy efficiency."	2021-12-05 19:57:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30551406741142273, "perplexity": 6535.746958978186}, "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/1637964363216.90/warc/CC-MAIN-20211205191620-20211205221620-00462.warc.gz"}
https://exampur.com/short-quiz/12613/	# BIHAR CGL MATHS QUIZ Attempt now to get your rank among 37 students! ## Question 1: Select the most appropriate option to solve the equation. $105 \div 15 \times\{(38-8) \div 5\} \div 3=$ ## Question 2: $30 \div(20-15 \div 3 \times 8)=?$ ## Question 3: What will come in the place of the question mark ‘?’ in the following question? 60% of 90 + 12.5% × 64 – 39 + 16 = ? ## Question 4: What will come in the place of the question mark ‘?’ in the following question? $\sqrt{(89+32)}+5^{3}-(49 \times 2)=?$ ## Question 5: What will come in the place of the question mark ‘?’ in the following question? $40 \%$ of $60+16.66 \% \times 54-20+13=?$ ## Question 6: Simplify the following expression. $\frac{2}{5}-\left[1 \frac{1}{3}+\left(1 \frac{1}{4}-2 \frac{1}{3}\right)\right] \div 2 \frac{2}{3} \times \frac{3}{5}+\frac{2}{5}$ ## Question 7: The value of $(5 \div 8)$ of $(4 \div 5)$ of $25\left(15^2-13^2\right)$ is: ## Question 8: The value of $\{5-5 \div(10-12) \times 8+9\} \times 3+5+5 \times 5 \div 5$ of 5 is: ## Question 9: The value of $3 \times 7+5-6 \div 3-9+45 \div 5 \times 4-45$ is ## Question 10: If $\left(\frac{2}{7}\right)^{-3} \times\left(\frac{4}{49}\right)^6=\left(\frac{2}{7}\right)^{2 m-1}$, then what is the value of $m$ ?	2023-03-24 13:31:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5822113156318665, "perplexity": 1640.2355745263078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945282.33/warc/CC-MAIN-20230324113500-20230324143500-00259.warc.gz"}
https://media.nips.cc/nipsbooks/nipspapers/paper_files/nips32/reviews/3792-metareview.html	NeurIPS 2019 Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center Paper ID: 3792 Online Prediction of Switching Graph Labelings with Cluster Specialists This is a clear accept: all reviewers liked the paper, and I agree with their recommendation, as the paper provides a nice combination of fixed share (with specialists) with graph predictions. The authors are encouraged to include the lower bound. Also, the strength of the paper could be emphasized very clearly by comparing to applying meta-algorithms, such as those of [12-or rather its journal version, 13, 23] (these algorithms are specifically equipped to combine tracking with a large structured predictor class, at the price of a log T increase in complexity). Finally, I'd like to mention that two of the three reviewers were experts in proving regret bounds.	2020-05-30 00:18:33	{"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": 0.808384120464325, "perplexity": 2268.435327857482}, "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/1590347406785.66/warc/CC-MAIN-20200529214634-20200530004634-00593.warc.gz"}
http://tex.stackexchange.com/questions/114360/parsing-bbl-file-to-an-xml-file-from-within-pdflatex-while-typesetting	# parsing bbl file to an xml file from within pdflatex while typesetting As editor of a journal I need to translate the bibliography, in a bbl file, into part of an xml file (for potential submission to cross-ref). It seems best done on the fly by pdfLaTeX so I can also record in the xml the main metadata (authors, title, pages, volume, etc). Currently I use a scheme for bbl files where the \bibitem does not involve brackets, e.g. \bibitem{Smith99} ... The problem is that as soon as the bbl file uses brackets (as in natbib) then my scheme fails catastrophically on \bibitem[blah]{Smith99} ... Question: how can I get pdfLaTeX to parse a bbl file, with such \bibitem[]{}, into an xml file while pdflatex is typesetting to pdf? Currently I do the following (hacked from somewhere in latex and executed \AtBeginDocument): \renewcommand{\bibitem}[1]{</unstructured_citation></citation> ^^J<citation key="#1"><unstructured_citation>} ... \def\j@@Input{% \let\jrnltempb\jrnltempa \ifeof\jrnlin \immediate\closein\jrnlin \else \immediate\write\jrnlout{\jrnltempb} \expandafter\j@@Input \fi} \typeout{**** Starting to write the bibliography to the xml.} \immediate\openin\jrnlin\jobname.bbl\relax \immediate\write\jrnlout{<citation_list> ^^J<citation key="nil"><unstructured_citation>} Try using xparse, \usepackage{xparse}\DeclareExpandableDocumentCommand{\bibitem}{o{}m}{</unstruct‌ured_citation></citation>^^J<citation key="#2" opt-arg="#1"><unstructured_citation>}. – Bruno Le Floch May 15 '13 at 11:59 Does this have to be done with the .bbl file? I've seen .bst files that deliberately add an XML section to the .bbl from BibTeX, which is easier as the data contains no formatting. – Joseph Wright Aug 16 '13 at 10:23	2016-05-27 20:16:06	{"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": 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": 0.9330886006355286, "perplexity": 5376.957861752498}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049277091.27/warc/CC-MAIN-20160524002117-00197-ip-10-185-217-139.ec2.internal.warc.gz"}
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia-mathematica/all/199/2/90183/the-norms-and-singular-numbers-of-polynomials-of-the-classical-volterra-operator-in-l-2-0-1	Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty The norms and singular numbers of polynomials of the classical Volterra operator in $L_2(0,1)$ Tom 199 / 2010 Studia Mathematica 199 (2010), 171-184 MSC: 47A10, 47A35, 47G10. DOI: 10.4064/sm199-2-3 Streszczenie The spectral problem $(s^2I-\phi(V)^{*}\phi(V))f=0$ for an arbitrary complex polynomial $\phi$ of the classical Volterra operator $V$ in $L_2(0,1)$ is considered. An equivalent boundary value problem for a differential equation of order $2n$, $n=\deg(\phi)$, is constructed. In the case $\phi(z)=1+az$ the singular numbers are explicitly described in terms of roots of a transcendental equation, their localization and asymptotic behavior is investigated, and an explicit formula for the $\\|{I+aV}\\|_2$ is given. For all $a\neq 0$ this norm turns out to be greater than 1. Autorzy • Yuri LyubichTechnion Haifa 32000, Israel e-mail • Dashdondog TsedenbayarDepartment of Mathematics Mongolian University of Science and Technology P.O. Box 46/520 Ulaanbaatar, Mongolia e-mail Przeszukaj wydawnictwa IMPAN Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki. Odśwież obrazek	2021-05-09 05:12:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31797167658805847, "perplexity": 2233.8590161351167}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988955.89/warc/CC-MAIN-20210509032519-20210509062519-00028.warc.gz"}
https://bonohu.github.io/removing-version-information-in-ids.html	## Removing version information in IDs Identifiers (IDs) in public databases often contain version information. For example, .16 in ENSG00000100644.16 from Ensembl and .1 in NM_001243084.1 from RefSeq. Such version information can be an obstacle to join entries from different databases. So, version information should be trimmed before joining. The file that contains such IDs with version information id.txt can be converted by tiny Perl script like % perl -i~ -pe 's/([^\.]+)\./\$1/g' id.txt Original file will be renamed to id.txt~, and converted file is now named as id.txt.	2021-09-21 02:47:15	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3708350956439972, "perplexity": 14435.102724315533}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057131.88/warc/CC-MAIN-20210921011047-20210921041047-00584.warc.gz"}
http://hal.in2p3.fr/view_by_stamp.php?label=APC&langue=fr&action_todo=view&id=in2p3-00319078&version=1	158 articles – 1990 Notices [english version] HAL : in2p3-00319078, version 1 arXiv : 0804.2141 GRB080319B reached 5th optical magnitude during the burst. Thanks to the VLT/UVES rapid response mode, we observed its afterglow just 8m:30s after the GRB onset when the magnitude was R ~ 12. This allowed us to obtain the best signal-to-noise, high resolution spectrum of a GRB afterglow ever (S/N per resolution element ~ 50). The spectrum is rich of absorption features belonging to the main system at z=0.937, divided in at least six components spanning a total velocity range of 100 km/s. The VLT/UVES observations caught the absorbing gas in a highly excited state, producing the strongest Fe II fine structure lines ever observed in a GRB. A few hours later the optical depth of these lines was reduced by a factor of 4-20, and the optical/UV flux by a factor of ~ 60. This proves that the excitation of the observed fine structure lines is due to ''pumping'' by the GRB UV photons. A comparison of the observed ratio between the number of photons absorbed by the excited state and those in the Fe II ground state suggests that the six absorbers are $\gs18-34$ kpc from the GRB site, with component I ~ 2 times closer to the GRB site than components III to VI. Component I is characterized also by the lack of Mg I absorption, unlike all other components. This may be due to a higher gas temperature, suggesting a structured ISM in this galaxy complex.	2014-07-24 15:39:02	{"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": 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": 0.4700491428375244, "perplexity": 1591.6403620496078}, "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-2014-23/segments/1405997889379.27/warc/CC-MAIN-20140722025809-00127-ip-10-33-131-23.ec2.internal.warc.gz"}
http://mathhelpforum.com/algebra/98997-should-simple.html	1. ## Should be simple... ...but I'm afraid I can't recall how to answer such questions: 'After taking 3 math quizzes Elise has an average of 89. What must she score on the fourth quiz to raise her average to 91?' Help is very much appreciated. 2. Let her scores in the first three quizzes be $x1 , x2 , x3$ respectively. Given that $(x1+x2+x3)/3 = 89$ so $x1+x2+x3 = 267$ Now her average in four quizzes would be $(x1+x2+x3+x4)/4$ x4 is her scr in the 4th quiz. since $(x1+x2+x3+x4)/4=91$ $x1+x2+x3+x4=91(4)=364$ so $x4=364-(x1+x2+x3)$ Plug in the value of $x1+x2+x3$ from above and find x4 $x4=364-267=97$ 3. Thanks very much!	2013-05-24 08:16:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7097529768943787, "perplexity": 2465.3647873039135}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704368465/warc/CC-MAIN-20130516113928-00066-ip-10-60-113-184.ec2.internal.warc.gz"}
https://www.iacr.org/cryptodb/data/paper.php?pubkey=11593	## CryptoDB ### Paper: A Distributed and Computationally Secure Key Distribution Scheme Authors: Vanesa Daza Javier Herranz Carles Padró Germ\'an S\'aez URL: http://eprint.iacr.org/2002/069 Search ePrint Search Google In 1999, Naor, Pinkas and Reingold introduced schemes in which some groups of servers distribute keys among a set of users in a distributed way. They gave some specific proposals both in the unconditional and in the computational security framework. Their computationally secure scheme is based on the Decisional Diffie-Hellman Assumption. This model assumes secure communication between users and servers. Furthermore it requires users to do some expensive computations in order to obtain a key. In this paper we modify the model introduced by Naor et al., requiring authenticated channels instead of assuming the existence of secure channels. Our model makes the user's computations easier, because most computations of the protocol are carried out by servers, keeping to a more realistic situation. We propose a basic scheme, that makes use of ElGamal cryptosystem, and that fits in with this model in the case of a passive adversary. We then add zero-knowledge proofs and verifiable secret sharing to prevent from the action of an active adversary. We consider general structures (not only the threshold ones) for those subsets of servers that can provide a key to a user and for those tolerated subsets of servers that can be corrupted by the adversary. We find necessary combinatorial conditions on these structures in order to provide security to our scheme. ##### BibTeX @misc{eprint-2002-11593, title={A Distributed and Computationally Secure Key Distribution Scheme}, booktitle={IACR Eprint archive}, keywords={cryptographic protocols / Key distribution, secret sharing schemes.}, url={http://eprint.iacr.org/2002/069}, note={Proceedings of Information Security Conference, ISC'02. LNCS 2433, pp. 342--356 jherranz@mat.upc.es 12153 received 1 Jun 2002, last revised 11 Apr 2003}, author={Vanesa Daza and Javier Herranz and Carles Padró and Germ\'an S\'aez}, year=2002 }	2022-01-23 06:12:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 0.4695097804069519, "perplexity": 1976.3036116400447}, "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-20220123045449-20220123075449-00093.warc.gz"}
http://mathoverflow.net/feeds/question/105899	Power series with double zeros - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:37:09Z http://mathoverflow.net/feeds/question/105899 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/105899/power-series-with-double-zeros Power series with double zeros Jörg Neunhäuserer 2012-08-30T00:51:22Z 2012-08-31T02:25:36Z <p>How many power series of the form $1+\sum_{k=1}^{\infty} a_{k}x^{k}$ with <code>$a_{k}\in \{-1,0,1 \}$</code>, that have a double zero $f(x)=f'(x)=0$ in $(0,1)$, are there. Ok, there are many ways to understand the question: set theoretical, topological, measure theoretical. I would be especially interested in the Bernoulli measures of the coefficient space <code>$C\subseteq \{-1,0,1\}^{\mathbb{N}}$</code> of such series. </p> http://mathoverflow.net/questions/105899/power-series-with-double-zeros/105902#105902 Answer by Igor Rivin for Power series with double zeros Igor Rivin 2012-08-30T01:39:21Z 2012-08-30T02:20:13Z <p>At least the set-theoretical question can be answered: the are the cardinality of the continuum many such series, as can be deduced from the results in this paper (not all of them attributed by the authors to themselves):</p> <p>MR2293600 (2007k:30003) Reviewed Shmerkin, Pablo(FIN-JVS-MS); Solomyak, Boris(1-WA) Zeros of {−1,0,1} power series and connectedness loci for self-affine sets. (English summary) Experiment. Math. 15 (2006), no. 4, 499–511. </p> http://mathoverflow.net/questions/105899/power-series-with-double-zeros/105953#105953 Answer by Alexander Shamov for Power series with double zeros Alexander Shamov 2012-08-30T15:08:59Z 2012-08-30T17:02:22Z <p>I am going to address the question for $\mathrm{Bernoulli}(1/2)$ measures, using probabilistic language. This is not a complete answer, but I am trying to relate your question to the properties of the distribution of $f(x)$. Clearly, for $x<1/2$ we never even reach zero, but my guess is that for $x>1/2$ this distribution is absolutely continuous, though I am unable to prove this at the moment.</p> <p>So formally, at least,</p> <p>$\displaystyle \mathsf{E} \, \sum_{f(x)=0} \mathsf{1}\{\|f^\prime(x)\| < \epsilon\} = \intop_0^1 \mathsf{E} \, \delta(f(x)) \mathsf{1}\{\|f(x)\|<\epsilon\} \|f^\prime(x)\| dx \le \epsilon \intop_0^1 \mathsf{E} \, \delta(f(x)) dx$.</p> <p>$\mathsf{E} \, \delta$ is the density at zero, and it can be made perfect sense of, provided that the law of $f(x)$ has continuous density at zero. I don't know whether it has continuous density, but if we manage to prove that $f(x)$ has at least bounded density for $x>1/2$, then we can write inequalities with approximations of $\delta$ to get the same results...</p> http://mathoverflow.net/questions/105899/power-series-with-double-zeros/106007#106007 Answer by Robert Israel for Power series with double zeros Robert Israel 2012-08-30T23:56:20Z 2012-08-30T23:56:20Z <p>Some more examples with polynomials:</p> <p>$$\matrix{\left( {z}^{6}+{z}^{5}-{z}^{3}+z+1 \right) \left( z+{z}^{4}-1 \right) ^{2}\cr \left( {z}^{8}+{z}^{7}-{z}^{5}-{z}^{4}-{z}^{3}+z+1 \right) \left( z+ {z}^{6}-1 \right) ^{2}\cr \left( {z}^{9}+{z}^{8}-{z}^{6}-{z}^{5}-{z}^{4}-{z}^{3}+z+1 \right) \left( z+{z}^{7}-1 \right) ^{2}\cr \left( {z}^{4}-{z}^{3}+{z}^{2}-z+1 \right) \left( {z}^{2}+{z}^{5}-1 \right) ^{2}\cr \left( {z}^{6}-{z}^{5}+{z}^{4}-{z}^{3}+{z}^{2}-z+1 \right) \left( {z }^{2}+{z}^{7}-1 \right) ^{2}\cr \left( {z}^{6}-{z}^{5}+{z}^{3}-z+1 \right) \left( {z}^{3}+{z}^{4}-1 \right) ^{2}\cr \left( {z}^{7}-{z}^{5}+{z}^{4}+{z}^{3}-{z}^{2}+1 \right) \left( {z}^ {3}+{z}^{5}-1 \right) ^{2}\cr \left( -{z}^{10}+{z}^{8}-{z}^{7}+{z}^{6}+{z}^{5}-2\;{z}^{4}+{z}^{3}-z +1 \right) \left( {z}^{3}+{z}^{7}-1 \right) ^{2}\cr \left( {z}^{4}-{z}^{3}+{z}^{2}-z+1 \right) \left( {z}^{4}+{z}^{5}-1 \right) ^{2}\cr \left( {z}^{4}-{z}^{2}+1 \right) \left( {z}^{4}+{z}^{6}-1 \right) ^{ 2}\cr \left( {z}^{6}-{z}^{5}+{z}^{4}-{z}^{3}+{z}^{2}-z+1 \right) \left( {z }^{4}+{z}^{7}-1 \right) ^{2}\cr \left( {z}^{8}-{z}^{7}+{z}^{5}-{z}^{4}+{z}^{3}-z+1 \right) \left( {z }^{5}+{z}^{6}-1 \right) ^{2}\cr \left( {z}^{6}-{z}^{5}+{z}^{4}-{z}^{3}+{z}^{2}-z+1 \right) \left( {z }^{6}+{z}^{7}-1 \right) ^{2}\cr \left( -{z}^{14}-{z}^{13}-2\;{z}^{12}-{z}^{11}+{z}^{9}+2\;{z}^{8}-2\;{z}^{5}+2\;{z}^{2}+z+1 \right) \left( {z}^{5}-{z}^{3}+{z}^{2}+z-1 \right) ^{2}\cr \left( {z}^{5}+{z}^{4}-{z}^{3}-{z}^{2}+z+1 \right) \left( {z}^{5}+{z }^{3}-{z}^{2}+z-1 \right) ^{2}\cr \left( {z}^{15}+{z}^{14}-{z}^{11}-{z}^{10}+{z}^{9}+{z}^{8}+{z}^{7}+{z }^{6}-{z}^{5}-{z}^{4}+z+1 \right) \left( {z}^{5}-{z}^{4}+{z}^{3}+z-1 \right) ^{2}\cr }$$</p>	2013-05-19 18:37:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.8934195637702942, "perplexity": 870.7999143405984}, "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/1368697974692/warc/CC-MAIN-20130516095254-00076-ip-10-60-113-184.ec2.internal.warc.gz"}
https://samuel-lereah.com/db/proofdb/Fundamental%20theorem%20of%20calculus	A bit of everything # Fundamental theorem of calculus The fundamental theorem of calculus tells us that, given some function $f$ of a given regularity class, then, if there exists a function $F$ such that $F' = f$, we have $$\int_a^b f(x) dx = [F(x)]_a^b = F(b) - F(a)$$ ## In the Riemann integral In the case of the Riemann integral, we consider a partition of the integration interval $[a,b]$, that is, we consider some set $\{ x_i \}$, $0 \leq i \leq N$, with $x_0 = a$, $x_N = b$, and for every value of $i$, $$x_i < x_{i+1}$$ The lower and upper Riemann sum of that partition $P$ are defined as \begin{eqnarray} L_f &=& \sum_{i = 1}^N (x_i - x_{i-1}) \min_{x \in [x_{i-1}, x_i]} f(x)\\ U_f &=& \sum_{i = 1}^N (x_i - x_{i-1}) \min_{x \in [x_{i-1}, x_i]} f(x) \end{eqnarray}	2023-01-29 15:51:59	{"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": 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": 0.9997865557670593, "perplexity": 292.4601191482091}, "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-2023-06/segments/1674764499744.74/warc/CC-MAIN-20230129144110-20230129174110-00092.warc.gz"}
https://tex.stackexchange.com/questions/121641/degrees-as-numbers-or-units-in-si-system	# Degrees, as numbers or units in SI system When typesetting degrees the correct way is to make the degrees symbol part of the number (without the space between the degree symbol and the number.) Technically in the SI system then degrees C or degrees F should be typeset with a space between the degrees symbol and the unit. The \SI{23}{\celsius} does not do this correctly. Is this a bug or a feature? • It's a feature, siunitx handles both temperatures and angles correctly. In the SI system, there has to be a space between the number and the degree symbol and no space between the degree symbol and the C when typesetting temperatures. See section 5.3.3 of the official SI brochure. – Jake Jun 28 '13 at 19:50 • Fahrenheit and Rankine are not part of the SI system. The degree symbol in °C makes it possible to tell the derived unit for Celsius temperature apart from the base unit coulomb (C). It is therefore part of the unit symbol. – Jake Jun 28 '13 at 19:58 It's a feature, siunitx handles both temperatures and angles correctly. In the SI system, there has to be a space between the number and the degree symbol and no space between the degree symbol and the C when typesetting temperatures. See section 5.3.3 of the official SI brochure.	2019-10-16 07:09:22	{"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": 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": 0.7934808135032654, "perplexity": 789.2195691976755}, "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/1570986666467.20/warc/CC-MAIN-20191016063833-20191016091333-00368.warc.gz"}
https://atakua.org/w/spam.html	## SPAM The very original SPAM sketch: https://www.youtube.com/watch?v=g8huXkSaL7o SPAM on the Wikipedia, linking the sketch, the food and the communications phenomenon: https://en.wikipedia.org/wiki/Email_spam	2019-08-20 23:25:08	{"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": 0.815571665763855, "perplexity": 8705.401749343588}, "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/1566027315681.63/warc/CC-MAIN-20190820221802-20190821003802-00200.warc.gz"}
https://www.physicsforums.com/threads/integrating-the-complex-conjugate-of-z-with-respect-to-z.315128/	# Integrating the Complex conjugate of z with respect to z 1. May 19, 2009 ### Deevise Im doing a bit of contour integration, and a question came up with a term in it am unsure of how to do: in its simplest form it would be $$\int$$$$\bar{z}$$dz where z is a complex number and $$\bar{z}$$ is it's conjugate. Hmm i can't get the formatting to work out properly.. :S Last edited: May 19, 2009 2. May 19, 2009 ### Dick If you are integrating over a circular contour of radius R then zz=R^2, so z=R^2/z. Otherwise you just have to take the contour and write it as z=(x(t)+iy(t)), so z=(x(t)-iy(t)). 3. May 19, 2009 ### Deevise Well now i feel kind of stupid... its line intergration, not contour integration :P the question reads: Evaluate the integral: $$\int$$( $$\bar{z}$$ +1 ) dz L Where L is the line segment from -i to 1+i. normally i would just integrate and sub in start and end point, but i have totaly drawn a blank on what to do with the conjugate in this case... 4. May 19, 2009 ### Dick Just treat it as a complex line integral. You can only 'sub in' endpoints if the function you are integrating is analytic and has an antiderivative. (z+1) doesn't. Parametrize L as a function of t and integrate dt. Like I said, if you have z=(x(t)+iy(t)) then z*=(x(t)-iy(t)). 5. May 19, 2009 ### squidsoft 6. May 19, 2009 ### Deevise I think it's time i went to sleep... Yeh now that you mention the lack of anti-derivative i knew that. I think a good nights sleep will prepare me better for this exam than grinding my head into non-exsistant problems... sorry to waste your time with inane questions lol... Thanks for the prompt responces.	2017-12-16 21:11:01	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.7912722826004028, "perplexity": 1468.0158177248234}, "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/1512948589177.70/warc/CC-MAIN-20171216201436-20171216223436-00011.warc.gz"}
https://www.physicsforums.com/threads/innner-products-and-basis-representation.331381/	# Innner products and basis representation 1. Aug 18, 2009 ### iontail hi, I have a quickon vector spaces. Say for example we have X = a1U1 + a2U2 ....anUn this can be written as X = sum of ( i=0 to n) ai Ui now how can I get and expression of ai in therms of X and Ui. do we use inner product to do this...ans someone please explain how to go forward. 2. Aug 18, 2009 ### HallsofIvy Staff Emeritus If the Ui basis is "orthonormal" then, taking the inner product of X with Uk gives $<X, U_n]>= a_1 <U_1,U_k>+ \cdot\cdot\cdot+ a_k<U_k,U_k>+ \cdot\cdot\cdot+ a_n<U_n, U_k>= a_1(0)+ \cdot\cdot\cdot+ a_k(1)+ \cdot\cdot\cdot+ a_n(0)= a_k$. That is, for an orthonormal basis, $a_k= <X, U_k>$. If the basis is NOT orthonormal, there is no simple formula. That's why orthonormal bases are so popular! 3. Aug 18, 2009 ### iontail the basis is orthonormal...so the solution you suggested should be ok...however i dont have latex and have never used it before so cant view your reply. do I just downlad latex to view the thread or do I have to do something else. 4. Aug 18, 2009 ### iontail 5. Aug 18, 2009 ### tiny-tim LaTeX Hi iontail! You don't need to "have" LaTeX, it should be visible anyway. There's just something wrong with that particular LaTeX …I can't read it either (I can't see what's wrong with the code though.) To see the original code, just click on the REPLY button. 6. Aug 19, 2009 ### Дьявол Here is what HallsofIvy want to write: $$<X, U_n]>= a_1 <U_1,U_k>+ \cdot\cdot\cdot+ a_k<U_k,U_k>+ \cdot\cdot\cdot+ a_n<U_n, U_k>= a_1(0)+ \cdot\cdot\cdot+ a_k(1)+ \cdot\cdot\cdot+ a_n(0)= a_k$$	2017-11-18 12:36:59	{"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": 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": 0.7907309532165527, "perplexity": 3271.0816756852523}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934804881.4/warc/CC-MAIN-20171118113721-20171118133721-00726.warc.gz"}
https://www.ssccglapex.com/hi/the-average-score-of-a-cricketer-for-ten-matches-is-38-9-runs-if-the-average-for-the-first-six-matches-is-42-then-find-the-average-for-the-last-four-matches/	### The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches. A. 33.25 B. 33.5 C. 34.25 D. 35 Total sum of last 4 matches, = (10 × 38.9) – (6 × 42) = 389 – 252 = 137 Average = $\Large\frac{137}{4}$ = 34.25	2022-09-26 16:29:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8427504301071167, "perplexity": 347.6726290824486}, "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/1664030334912.28/warc/CC-MAIN-20220926144455-20220926174455-00690.warc.gz"}
http://mathhelpforum.com/algebra/5110-please-help-print.html	• Aug 24th 2006, 09:44 AM Angel King I need help with this problem . 15 divide 6 2/3 =? A) 100 1/4 B) 2 1/4 C)100 D) 2 3/4 I'm thinking the letter D :eek: • Aug 24th 2006, 09:55 AM Quick Quote: Originally Posted by Angel King I need help with this problem . 15 divide 6 2/3 =? A) 100 1/4 B) 2 1/4 C)100 D) 2 3/4 I'm thinking the letter D :eek: You know: $15=\frac{15}{1}$ and $6\frac{2}{3}=\frac{20}{3}$ therefore we have equation: $\frac{15}{1}\div \frac{20}{3}$ when dividing by a fraction you multiply by the reciprocal of the fraction, so we get: $\frac{15}{1}\div \frac{20}{3}=\frac{15}{1}\times \frac{3}{20}=\frac{15\times3}{1\times20}=\frac{45} {20}=2\frac{5}{20}=2\frac{1}{4}$ so the answer is B, not d BTW When I was taught to divide fractions my teachers would say that you would "cross multiply" so you can think of it like this: $\frac{15}{1}\div\frac{20}{3}=\frac{15}{1} \! \! \nwarrow \! \! \! \! \! \! \swarrow \! \! \frac{20}{3}=\frac{15\times3}{1\times20}=\frac{45} {20}$ did this post help?	2016-10-28 19:20:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.910094678401947, "perplexity": 2349.0021036000717}, "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-2016-44/segments/1476988725451.13/warc/CC-MAIN-20161020183845-00347-ip-10-171-6-4.ec2.internal.warc.gz"}
https://campus.datacamp.com/courses/chip-seq-workflows-in-r/comparing-chip-seq-samples?ex=6	As you have seen in the video, you have to create a set of consensus peak calls before you can test for differential binding. This can be achieved with the following line of R code: ar_counts <- dba.count(ar_peaks, summits=200) Consider the following statements. 1. In ar_counts all samples will have read counts the same set of peak calls. 2. Some read counts may be 0. 3. All peaks in ar_counts are 200 bp wide. 4. All peaks in ar_counts are 400 bp wide. Which of these statements are true?	2020-03-30 03:42:40	{"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": 0.23668605089187622, "perplexity": 1804.170964148801}, "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/1585370496523.5/warc/CC-MAIN-20200330023050-20200330053050-00384.warc.gz"}
http://www.intlpress.com/HHA/v7/n2/a2/	# Transferring TTP-structures via contraction ## V. Alvarez, J.A. Armario, M.D. Frau and P. Real Let $A \otimes _tC$ be a {\em twisted tensor product} of an algebra $A$ and a coalgebra $C$, along a {\em twisting cochain} $t:C \rightarrow A$. By means of what is called the {\em tensor trick} and under some nice conditions, Gugenheim, Lambe and Stasheff proved in the early 90s that $A \ot _tC$ is homology equivalent to the objects $M \ot _{t'}C$ and $A \ot _{t''}N$, where $M$ and $N$ are strong deformation retracts of $A$ and $C$, respectively. In this paper, we attack this problem from the point of view of contractions. We find explicit contractions from $A\ot _t C$ to $M \ot _{t'}C$ and $A\ot_{t''}N$. Applications to the comparison of resolutions which split off of the bar resolution, as well as to some homological models for central extensions are given. Homology, Homotopy and Applications, Vol. 7(2005), No. 2, pp. 41-54 Available as: dvi dvi.gz ps ps.gz pdf	2013-05-20 09:27:59	{"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": 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": 0.9744361042976379, "perplexity": 691.6449247969108}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368698693943/warc/CC-MAIN-20130516100453-00017-ip-10-60-113-184.ec2.internal.warc.gz"}
https://brilliant.org/problems/4-numbers-theory/	# 4 Numbers Theory Number Theory Level pending Find pair of 4 numbers a,b,c&n such that they satisfies equation. a^n + b^n = c^ n Where a,b,c&n belongs to Natural Number Set and n>2. ×	2017-01-18 01:51:55	{"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": 0.9607524275779724, "perplexity": 10000.977230483575}, "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-2017-04/segments/1484560280133.2/warc/CC-MAIN-20170116095120-00201-ip-10-171-10-70.ec2.internal.warc.gz"}
https://rdrr.io/cran/nnspat/man/ceTk.html	ceTk: Cuzick and Edwards T_k Test statistic In nnspat: Nearest Neighbor Methods for Spatial Patterns Description This function computes Cuzick and Edwards T_k test statistic based on the number of cases within `k`NNs of the cases in the data. For disease clustering, \insertCitecuzick:1990;textualnnspat suggested a `k`-NN test based on number of cases among `k` NNs of the case points. Let z_i be the i^{th} point and d_i^k be the number cases among `k` NNs of z_i. Then Cuzick-Edwards' `k`-NN test is T_k=∑_{i=1}^n δ_i d_i^k, where δ_i=1 if z_i is a case, and 0 if z_i is a control. The argument `cc.lab` is case-control label, 1 for case, 0 for control, if the argument `case.lab` is `NULL`, then `cc.lab` should be provided in this fashion, if `case.lab` is provided, the labels are converted to 0's and 1's accordingly. Also, T_1 is identical to the count for cell (1,1) in the nearest neighbor contingency table (NNCT) (See the function `nnct` for more detail on NNCTs). Usage `1` ```ceTk(dat, cc.lab, k = 1, case.lab = NULL, ...) ``` Arguments `dat` The data set in one or higher dimensions, each row corresponds to a data point. `cc.lab` Case-control labels, 1 for case, 0 for control `k` Integer specifying the number of NNs (of subject i), default is `1`. `case.lab` The label used for cases in the `cc.lab` (if `cc.lab` is not provided then the labels are converted such that cases are 1 and controls are 0), default is `NULL`. `...` are for further arguments, such as `method` and `p`, passed to the `dist` function. Value Cuzick and Edwards T_k test statistic for disease clustering Elvan Ceyhan References \insertAllCited `Tcomb`, `seg.ind`, `Pseg.coeff` and `ceTkinv` ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```n<-20 #or try sample(1:20,1) Y<-matrix(runif(3n),ncol=3) cls<-sample(0:1,n,replace = TRUE) #or try cls<-rep(0:1,c(10,10)) ceTk(Y,cls) ceTk(Y,cls,method="max") ceTk(Y,cls,k=3) ceTk(Y,cls+1,case.lab = 2) #cls as a factor na<-floor(n/2); nb<-n-na fcls<-rep(c("a","b"),c(na,nb)) ceTk(Y,fcls,case.lab="a") #try also ceTk(Y,fcls) ############# n<-40 Y<-matrix(runif(3n),ncol=3) cls<-sample(1:4,n,replace = TRUE) # here ceTk(Y,cls) gives an error message ```	2021-12-03 04:39:05	{"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": 0.8237146735191345, "perplexity": 3087.3559122091033}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362589.37/warc/CC-MAIN-20211203030522-20211203060522-00546.warc.gz"}
https://www.physicsforums.com/threads/conformal-mapping-and-flow-normal-to-ellipse.672425/	# Conformal Mapping and flow normal to ellipse 1. Feb 17, 2013 ### nickthequick Hi, Given that the flow normal to a thin disk or radius r is given by $\phi = -\frac{2rU}{\pi}\sqrt{1-\frac{x^2+y^2}{r^2}}$ where U is the speed of the flow normal to the disk, find the flow normal to an ellipse of major axis a and minor axis b. I can only find the answer in the literature in one place, where it's stated $\phi = -\frac{U b}{E(e)} \sqrt{1-\frac{x^2}{a^2}-\frac{y^2}{b^2}}$ where E(e) is the complete elliptical integral of the second kind and e is the eccentricity of the disk. I have been trying to use the Joukowski map to send lines of equipotential of the disk to those of the ellipse, but I'm not sure how the complete elliptical integral of the second kind enters this picture. Any suggestions, references, would be appreciated! Nick 2. Feb 20, 2013 ### nickthequick On second thought, the Joukowski map seems inappropriate here. I think the map I want is $z\to a \cosh(\xi + i \eta)$ so that $x=a\sinh (\xi) \cos(\eta)$ and $y = a\cosh (\xi) \sin(\eta)$. This will effectively give me the change in functional form that I expect; however, I still don't see how this will modify the coefficient in the appropriate way.	2017-08-24 02:54:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9009354114532471, "perplexity": 348.4702895520451}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886126027.91/warc/CC-MAIN-20170824024147-20170824044147-00335.warc.gz"}
https://physics.meta.stackexchange.com/questions/5668/invalid-flags-%E2%86%92-disputed-%E2%86%92-flags-should-not-be-used-to-indicate-technical-inaccu	# Invalid flags → disputed → flags should not be used to indicate technical inaccuracies. What? I continue to be befuddled by what exactly one is supposed to do with flags in the 10k tools, and I'm quite relieved to know they're going away soon. In the meantime, though, here's a stumper I just came across in my flagging history: The post in question is this answer, which came up flagged as Not an Answer if I remember correctly. I understand why someone would flag this - it was only a sort-of good fit to the question to begin with - but I disagree that it failed to address the original intent of the OP. Particularly, I felt it did answer the question in its state at the time, with a less specific title. On the other hand, given the current state of the question, I can understand that it might best be classed as Not an Answer. Given that, I can understand that my invalid flags is disputed. I'm completely stumped, however, at the message. Flags should not be used to indicate technical inaccuracies, or an altogether wrong answer? That has absolutely nothing to do with why I flagged this way. The technical content of the post was never an issue. Could someone elucidate what on Earth this message means and how it came into being?	2020-10-23 11:01:06	{"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": 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": 0.5699766874313354, "perplexity": 582.3867699382101}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107881369.4/warc/CC-MAIN-20201023102435-20201023132435-00437.warc.gz"}
https://pyvows.org/a-particle-moves-along-a-straight-line-such-that-its-position-is-defined-by-st2%E2%88%926t5-m/	A particle moving along a straight line can be modeled by the equation s= (t2 − 6t + 5) m. The particle starts at position 0 and moves to position 3 after 2 seconds. What is its velocity? The particle’s velocity is 2 meters per second since it traveled 3 meters in only two seconds. -The particle starts at position 0 and moves to position after two seconds. What is its velocity? +The particle’s velocity is (Vel) since it traveled meters in only seconds. +The particle’s velocity is (Vel) since it traveled meters in only seconds. The acceleration of the particle can be calculated by taking the slope of line s=t with respect to t on a graph, which gives us −( )/( ). This means that every second, the speed increases by . In order for this acceleration equation to take place over time T so that we have an approximate prediction for where our final location would be (s’), we use T = √(( ), or √()) + (( ), or √())*. We plug in three values into this equation:	2021-10-28 05:50:31	{"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": 0.9728198051452637, "perplexity": 659.0117829187179}, "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-2021-43/segments/1634323588257.34/warc/CC-MAIN-20211028034828-20211028064828-00355.warc.gz"}
https://web2.0calc.com/questions/question_132	+0 # question 0 41 1 A square $DEFG$ varies inside equilateral triangle $ABC,$ so that $E$ always lies on side $\overline{AB},$ $F$ always lies on side $\overline{BC},$ and $G$ always lies on side $\overline{AC}.$ The point $D$ starts on side $\overline{AB},$ and ends on side $\overline{AC}.$ The diagram below shows the initial position of square $DEFG,$ an intermediate position, and the final position. Show that as square $DEFG$ varies, the height of point $D$ above $\overline{BC}$ remains constant. Guest Mar 14, 2018 Sort: #1 +91974 +1 It says... "The diagram below shows the initial position of square DEFG, an intermediate position, and the final position." Where is the diagram? Melody Mar 14, 2018 ### 6 Online Users We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners. See details	2018-03-25 05:30:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8555477857589722, "perplexity": 1309.1303113307713}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257651820.82/warc/CC-MAIN-20180325044627-20180325064627-00080.warc.gz"}
https://brilliant.org/problems/magic-cake/	# Magic cake Algebra Level 3 You have to divide a cake with 200 straight cuts ( AB and CD are two possible cuts for examples ). Which is the maximum number of slices (dimension is not important) that you can have? ×	2017-07-24 10:54:19	{"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": 0.9183745384216309, "perplexity": 1194.7603666955845}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424846.81/warc/CC-MAIN-20170724102308-20170724122308-00398.warc.gz"}
https://menglish.tupaki.com/post/17520335/This-Politician-Tweet-Got-Misunderstood	# This Politician's Tweet Got Misunderstood Sarcasm is a very difficult art. Many a time, it boomerangs if not understood properly. Not just that, it might even turn counter-productive. Former MP Konda Visweshwar Reddy must be learning this quite fast. Recently, this TRS-turned-Congress leader and ace industrialist has sent a tweet congratulating both KCR and KTR for their handling of Corona. The tweet was meant to heckle KCR and KTR for their failure to curb Corona. Reddy wanted the tweet to be laced with wit and sarcasm. However, the tweet was written in such a way that it had the opposite effect. The TRS,instead of being angry, was happy and the Congress, instead of being happy, was shocked. Reddy later realised that his tweet has badly misfired and made TRS happey instead of being angry. He had to issue a clarification in a hurry to tell everyone that he wanted his tweet to make fun of the TRS. The Congress, it appears, is not very pleased with Reddy's tweet. ×	2020-08-14 13:53:27	{"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": 0.8932738900184631, "perplexity": 7984.528139819866}, "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/1596439739328.66/warc/CC-MAIN-20200814130401-20200814160401-00370.warc.gz"}
http://www.wowhead.com/quest=41159/process-of-elimination	Quick Facts Screenshots Videos # Process of Elimination Dig around Stormheim until you find a piece of the Titan Disc. Eliminate Digsites ## Description With so many places ta dig up fragments, it's become quite a pain figuring out where ta look for more of the titan disc. I have a plan though. I need ye ta eliminate potential areas where the disc could exist so we can narrow down where in Stormheim it might exist. You take part of the area an' I'll take the other part. Meet back here if ye find anythin'. ## Gains Upon completion of this quest you will gain: • 16,450 experience ## Series 1. Bits and PiecesProcess of EliminationAnd Into the Fel FireDeciphering DemonologyThe Purple Hills of Mac'Aree The Relic Renewed	2018-07-17 20:19:55	{"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": 0.8202710151672363, "perplexity": 10469.158885331384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676589892.87/warc/CC-MAIN-20180717183929-20180717203929-00580.warc.gz"}
https://search.r-project.org/CRAN/refmans/energy/html/U_product.html	U_product {energy} R Documentation ## Inner product in the Hilbert space of U-centered distance matrices ### Description Stand-alone function to compute the inner product in the Hilbert space of U-centered distance matrices, as in the definition of partial distance covariance. ### Usage U_product(U, V) ### Arguments U U-centered distance matrix V U-centered distance matrix ### Details Note that pdcor, etc. functions include the centering and projection operations, so that these stand alone versions are not needed except in case one wants to check the internal computations. Exported from U_product.cpp. ### Value U_product returns the inner product, a scalar. ### Author(s) Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely ### References Szekely, G.J. and Rizzo, M.L. (2014), Partial Distance Correlation with Methods for Dissimilarities, Annals of Statistics, Vol. 42, No. 6, pp. 2382-2412. https://projecteuclid.org/euclid.aos/1413810731 ### Examples x <- iris[1:10, 1:4] y <- iris[11:20, 1:4] M1 <- as.matrix(dist(x)) M2 <- as.matrix(dist(y)) U <- U_center(M1) V <- U_center(M2) U_product(U, V) dcovU_stats(M1, M2) [Package energy version 1.7-10 Index]	2022-05-25 20:29:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 0.6026495099067688, "perplexity": 14656.109420299941}, "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-2022-21/segments/1652662593428.63/warc/CC-MAIN-20220525182604-20220525212604-00470.warc.gz"}
https://www.physicsforums.com/threads/finding-probability-stat-mech.700201/	# Finding Probability(Stat mech) 1. Jul 5, 2013 ### catsonmars I am pre studying for Statistical Mechanics class in the fall and need help with this problem. I’ve already spent some time with it. Let the displacement x of an oscillator as a function of time t be given by X=Acos(wt+ϕ). Assume that the phase angle ϕ is equally likely to assume any value in the range 0 < ϕ < 2pi. The probability w(ϕ)d ϕ that ϕ lies in the range between ϕ and ϕ +d ϕ is then simply w(ϕ) dϕ=(2pi)^-1d ϕ. For any fixed time t, find the probability P(x)dx that x lies between x and x+dx by summing w(ϕ) over all angles ϕ for which x lies in this range. Express P(x) in termas of A and x. Relevant equations[/b] X=Acos(wt+ϕ). w(ϕ)d ϕ=(2pi)^-1d ϕ 3. The attempt at a solution The only thing I can come up with is integrating ∫P(x)dx = ∫(2pi)^-1d ϕ and inegrating over x and x+dx Or ƩP((x)dx* w(ϕ) dϕ)/p(x) 2. Jul 5, 2013 ### TSny Hello catsonmars. Welcome to PF! You have a good start with $w(\phi) = \frac{1}{2\pi}$. Since you are looking for the probability that $x$ lies in an infinitesimal range from $x$ to $x+dx$, you will not need to integrate. The probability is just $\small P(x)dx$. This is given by the probability $w(\phi)\|d\phi\|$ that $\phi$ lies in the range $\phi$ to $\phi + d\phi$, where $\phi$ is the value of the phase angle that corresponds to $x$ and $\phi + d\phi$ corresponds to $x+dx$. [Caution: think about whether or not there is more than one value of $\phi$ that corresponds to the same $x$. If so, you will need to make an adjustment for that.] So, the probability that $x$ lies between $x$ and $x+dx$ could be expressed as $\small P(x)dx$ or as $w(\phi)\|d\phi\|$ (if there is only one value of $\phi$ that corresponds to a value of $x$). That is, $\small P(x)dx =$ $w(\phi)\|d\phi\|$ [I leave it to you to think about what to do if there is more than one value of $\phi$ corresponding to the same value of $x$. Perhaps this has something to do with the word "summing" in the statement of the problem.] Since you already know how to express $w(\phi)$, all you need to do is find an expression for $d\phi$ in terms of $x$ and $dx$. Hint: $d\phi = \frac{d\phi}{dx}dx$. Last edited: Jul 6, 2013 3. Jul 12, 2013 ### catsonmars There should be more x values than ϕ's because the range of ϕ is much smaller than x. Second I'm still not sure how I should right the summation. I have ϕ=(Ʃw(ϕ)dϕ)/(P(x)(dx)) but that still seems wrong. I've also thought about relating ϕ+dϕ to x+dx somehow but I'm can't think of what would make them equal so I can get ϕ in terms of x. Also I've looked at the answer key and I have no idea how the amplitue "A" would fit into the equation. 4. Jul 12, 2013 ### TSny Basically, you need to solve $\small P(x)\|dx\| = w(\phi)\|d\phi\|$ for $\small P(x)$. That is, $P(x) = w(\phi)\frac{d\phi}{dx}$ Use $x = Acos(\omega t + \phi)$ to find $\frac{d\phi}{dx}$ as a function of $A$ and $x$. There's the additional task of dealing with the fact that there might be two different values of $\phi$ corresponding to the same value of $x$.	2018-01-17 01:22:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8204375505447388, "perplexity": 251.96245554020203}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084886792.7/warc/CC-MAIN-20180117003801-20180117023801-00751.warc.gz"}
http://www.askphysics.com/equations-of-motion-images-for-easy-reuse/?shared=email&msg=fail	Home » General » Equations of Motion – Images for easy reuse # Equations of Motion – Images for easy reuse Here you can find the equations of motion in the form of images which you can use in your documents. $v = u + at$ $S = ut + \frac{1}{2} at^{2}$ $v^{2} = u^{2} + 2aS$ ### Visitors So Far @ AskPhysics • 2,166,826 hits	2019-11-14 10:59:58	{"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": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3123134970664978, "perplexity": 2052.5377120665726}, "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/1573496668416.11/warc/CC-MAIN-20191114104329-20191114132329-00487.warc.gz"}
https://www.semanticscholar.org/paper/Game-semantics-of-Martin-L%C3%B6f-type-theory%2C-part-III%3A-Yamada/4ab0d21ec0c92889d3205f5bb31bfb55bc4e82d9	• Corpus ID: 220546221 # Game semantics of Martin-Löf type theory, part III: its consistency with Church's thesis @article{Yamada2020GameSO, title={Game semantics of Martin-L{\"o}f type theory, part III: its consistency with Church's thesis}, journal={ArXiv}, year={2020}, volume={abs/2007.08094} } We prove consistency of intensional Martin-Lof type theory (MLTT) with formal Church's thesis (CT), which was open for at least fifteen years. The difficulty in proving the consistency is that a standard method of realizability a la Kleene does not work for the consistency, though it validates CT, as it does not model MLTT; specifically, the realizability does not validate MLTT's congruence rule on pi-types (known as the $\xi$-rule). We overcome this point and prove the consistency by novel… 1 Citations Parametric Church's Thesis: Synthetic Computability Without Choice This work introduces various parametric strengthenings of CTφ, which are equivalent to assuming CT φ and an S n operator for φ like in the S n theorem, and explains the novel axioms and proofs of Rice’s theorem. ## References SHOWING 1-10 OF 70 REFERENCES Consistency of the intensional level of the Minimalist Foundation with Church’s thesis and axiom of choice • Philosophy Arch. Math. Log. • 2018 It is shown that consistency with the formal Church’s thesis and the axiom of choice are satisfied by the intensional level of the two-level Minimalist Foundation, for short MF, completed in 2009 by the second author. Game Semantics for Martin-Löf Type Theory A category with families of a novel variant of games is proposed, which induces a surjective and injective interpretation of the intensional variant of MLTT equipped with unit-, empty-, N-, dependent product, dependent sum and Id-types as well as the cumulative hierarchy of universes for the first time in the literature. A game-semantic model of computation This work shows, as a main technical achievement, that viable strategies in game semantics are Turing complete and has given a mathematical foundation of computation in the same sense as Turing machines but beyond computation on natural numbers, e.g., higher-order computation, in a more abstract fashion. Notes on game semantics Applications of game semantics to model-checking and abstract interpretation are being developed, which opens the way for connecting the uses of games in semantics and in verification. Definability and Full Abstraction • P. Curien • Computer Science Electron. Notes Theor. Comput. Sci. • 2007 A game semantics for generic polymorphism • Computer Science Ann. Pure Appl. Log. • 2003 Realizability Models for Type Theories Intensionality, Definability and Computation • S. Abramsky • Computer Science Johan van Benthem on Logic and Information Dynamics • 2014 This work reviews how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully abstract models of programming languages, with applications in program analysis and verification. Games for Dependent Types • Philosophy ICALP • 2015 Although definability for the hierarchy with $$\mathsf {Id}$$-types remains to be investigated, the notions of propositional equality in syntax and semantics do coincide for open terms of the type hierarchy.	2022-08-11 14:50:35	{"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": 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": 0.5106868147850037, "perplexity": 2407.126030961532}, "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/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00786.warc.gz"}
https://dsp.stackexchange.com/questions/63602/discrete-fourier-transform-norms-of-complex-input-signals-and-their-transforma	# Discrete Fourier transform - Norms of complex input signals and their transformation Given a signal $$\mathbf{z} \in \mathbb{C}^n$$ and its Discrete Fourier transform $$\hat{\mathbf{z} }$$, does $$\|\|\mathbf{z}\|\| = \|\|\hat{\mathbf{z} }\|\|$$ hold? The question is given to me like this with no additional details. Information about what kind of norm is also not given. Does anyone have an idea what the question might be looking for?	2021-09-23 14:33:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 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": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28685787320137024, "perplexity": 206.4501138059862}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057424.99/warc/CC-MAIN-20210923135058-20210923165058-00578.warc.gz"}
http://openstudy.com/updates/4d9cc6be8f378b0b40dae117	## anonymous 5 years ago Can someone help me with Surface area of pyramids and cones 1. anonymous Find the slant height of the regular pyramid or cone 2. anonymous Do you know what pathagorean therom is? 3. anonymous yeah isnt it a^2+b^2=c^2 4. anonymous Ok so find the length of the hypotenuse of the pyramid (for the first one) 5. anonymous so 12^2+15^2=369 6. anonymous 369=c^2 you still need to get rid of that exponent.. so you get $3\sqrt{41}$. Now that you have all the lengths apply the forumla for area of a triangle. Area = 1/2 * base * height 7. anonymous Because you have 4 triangles you could change your forumla to reflect that A=4(1/2bh) 8. anonymous Then don't forget the add the area of the base of the pyramid itself... width * height. Add them both up, and that's surface area. 9. anonymous Get it? 10. anonymous so 4(1/214415) 11. anonymous 12. anonymous Take the area of one of the isosceles triangles, multiply it by 4 and add it to the area of the base. Forget that 1/2 BH I messed up 13. anonymous know im lost 14. anonymous Do you see the forumla for the area of an isocoles triangle I sent you? 15. anonymous ya 16. anonymous Ok so do you see how each side of the pyramid is an isocles triangle? 17. anonymous ya 18. anonymous Ok so on the forumla you know that B=12, and C and A are the same and using pythagorean theorm we know it is $3\sqrt{41}$ So plug all those into the forumla and you will have the area of ONE side of the pyramid. 19. anonymous 82.486362509205 20. anonymous I'm going to take your word on that... lol. Now what do you think you do? 21. anonymous it by 4 22. anonymous 23. anonymous the base of 144 24. anonymous There you go, that's the surface of a pyramid. 25. anonymous As long as your algebra was right when putting those numbers in. 26. anonymous so 473.96 27. anonymous Assuming your algebra is correct, yes.. Find more explanations on OpenStudy	2017-01-22 08:33:23	{"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": 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": 0.7421228885650635, "perplexity": 2150.9084831796567}, "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-2017-04/segments/1484560281419.3/warc/CC-MAIN-20170116095121-00150-ip-10-171-10-70.ec2.internal.warc.gz"}
http://openstudy.com/updates/4dd04d139fe58b0b2fad38f7	## safia21 5 years ago algebra can you help me with # 2 and # 3 thanks 1. safia21 2. anonymous the cooking one? 3. safia21 4. anonymous cook has 4 quarts that is 50% chicken stock. so at the moment it is 50% of 4 = 2 quarts chicken stock. so for example if she adds 3 quarts of chicken stock she will have 4+3= 7 quarts of liquid of which 2 + 3 = 5 quarts is chicken stock, and the percent will be 5/7 * 100. this is not what you want obviously, i am just trying to explain where the equation will come from. if she adds x quarts of chicken stock she will have 2+x quarts of chicken stock and 4+x quarts of liquid. you want $\frac{2+x}{4+x}=.75$ $2+x=.75(4+x)$ last equation says your two quarts of chicken stock plus your x quarts must be 75% of the total liquid. now we solve multiply out $x+2=.75x+.75\times 4= .75x+3$ $.25x=1$ subtract .75x from both sides and subtract 2 from both sides $x=\frac{1}{.25}=\frac{100}{25}=4$ 5. safia21 and #3 thanks 6. anonymous ok #3 looks like the previous one we did so let me be careful and not put the 1 on the wrong side like i did last time. 7. anonymous keep seeming to put the 1 on the wrong side. you have two rates, r and r +1 $\frac{12}{r}=\frac{12}{r+1}+1$ slower person's time is one less more than faster persons. $\frac{12}{r}=\frac{12+r+1}{r+1}=\frac{r+13}{r+1}$ cross multiply$12(r+1)=r(r+13)$ $12r+12=r^2+13r$ $r^2+r-12=0$ $(r+4)(r-3)=0$ $r=3$ $r=-4$ so r = 3	2017-01-23 05:00:55	{"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": 0.6214653253555298, "perplexity": 1430.695879481203}, "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-2017-04/segments/1484560282110.46/warc/CC-MAIN-20170116095122-00573-ip-10-171-10-70.ec2.internal.warc.gz"}
https://socratic.org/questions/how-do-you-find-the-percent-composition-of-oxygen-in-sodium-hydroxide	# How do you find the percent composition of oxygen in sodium hydroxide? Mar 21, 2017 The percent composition of oxygen in sodium hydroxide is 40.000%. #### Explanation: Determine the molar mass of sodium hydroxide $\left(\text{NaOH}\right)$. Then divide the molar mass of oxygen by the molar mass of $\text{NaOH}$, and multiply by 100. Molar Masses $\text{NaOH} :$$\text{39.997 g/mol}$ https://www.ncbi.nlm.nih.gov/pccompound?term=NaOH $\text{O} :$$\text{15.999 g/mol}$ (periodic table) Percent Composition of Oxygen $\text{percent composition"=(15.999cancel("g"/"mol"))/(39.997cancel("g"/"mol"))xx100="40.000%}$	2022-08-15 21:34:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "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": 0.8739524483680725, "perplexity": 4568.568428809594}, "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/1659882572212.96/warc/CC-MAIN-20220815205848-20220815235848-00708.warc.gz"}
https://www.ms.u-tokyo.ac.jp/journal/abstract_e/jms190405_e.html	## Clifford modules, finite-dimensional approximation and twisted $K$-theory J. Math. Sci. Univ. Tokyo Vol. 19 (2012), No. 4, Page 587–612. Gomi, Kiyonori Clifford modules, finite-dimensional approximation and twisted $K$-theory A twisted version of Furuta's generalized vector bundle provides a finite-dimensional model of twisted $K$-theory. We generalize this fact involving actions of Clifford algebras. As an application, we show that an analogy of the Atiyah-Singer map for the generalized vector bundles is bijective. Furthermore, a finite-dimensional model of twisted $K$-theory with coefficients $\Z/p$ is given.	2022-06-27 21:46:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9471868276596069, "perplexity": 1080.7393339530392}, "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/1656103341778.23/warc/CC-MAIN-20220627195131-20220627225131-00707.warc.gz"}
http://crypto.stackexchange.com/tags/3des/new	# Tag Info First, note that $192=3\cdot64$, so the real key length of 3DES is $192$ bits. However, since $8$ bits in each subkey are parity bits, this reduces to $3\cdot56=168$ bits of non-redundant key material. Now, the reason that 3DES' effective key length is usually classified as $2\cdot56=112$ bits is that 3DES is susceptible to a meet-in-the-middle attack: When ...	2015-01-28 20:14:42	{"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": 0.9345426559448242, "perplexity": 1773.6868782620516}, "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-2015-06/segments/1422119446463.10/warc/CC-MAIN-20150124171046-00252-ip-10-180-212-252.ec2.internal.warc.gz"}
http://ndl.iitkgp.ac.in/document/RnV0dHBBOEk5bkozcUo2NHd1Q3RoYUU5VmlXODNJQXYydkRVeDNIbTVRND0	### The impact of thoracic load carriage up to 45 kg on the cardiopulmonary response to exerciseThe impact of thoracic load carriage up to 45 kg on the cardiopulmonary response to exercise Access Restriction Subscribed Author Phillips, Devin B. ♦ Ehnes, Cameron M. ♦ Stickland, Michael K. ♦ Petersen, Stewart R. Source SpringerLink Content type Text Publisher Springer Berlin Heidelberg File Format PDF Copyright Year ©2016 Language English Subject Domain (in DDC) Technology ♦ Medicine & health Subject Keyword Thoracic load carriage ♦ Oxygen demand ♦ Ventilation ♦ Breathing pattern ♦ Occupational physiology ♦ Performance ♦ Human Physiology ♦ Occupational Medicine/Industrial Medicine ♦ Sports Medicine Abstract The purposes of this experiment were to, first, document the effect of 45-kg thoracic loading on peak exercise responses and, second, the effects of systematic increases in thoracic load on physiological responses to submaximal treadmill walking at a standardized speed and grade.On separate days, 19 males (age 27 ± 5 years, height 180.0 ± 7.4 cm, mass 86.9 ± 15.1 kg) completed randomly ordered graded exercise tests to exhaustion in loaded (45 kg) and unloaded conditions. On a third day, each subject completed four randomly ordered, 10-min bouts of treadmill walking at 1.34 m s−1 and 4 % grade in the following conditions: unloaded, and with backpacks weighted to 15, 30, and 45 kg.With 45-kg thoracic loading, absolute oxygen consumption ( $\dot{V}{\text{O}}_{2}$ ), minute ventilation, power output, and test duration were significantly decreased at peak exercise. End-inspiratory lung volume and tidal volume were significantly reduced with no changes in end-expiratory lung volume, breathing frequency, and the respiratory exchange ratio. Peak end-tidal carbon dioxide and the ratio of alveolar ventilation to carbon dioxide production were similar between conditions. The reductions in peak physiological responses were greater than expected based on previous research with lighter loads. During submaximal treadmill exercise, $\dot{V}{\text{O}}_{2}$ increased (P < 0.05) by 11.0 (unloaded to 15 kg), 14.5 (15–30 kg), and 18.0 % (30–45 kg) showing that the increase in exercise $\dot{V}{\text{O}}_{2}$ was not proportional to load mass.These results provide further insight into the specificity of physiological responses to different types of load carriage. ISSN 14396319 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2016-07-09 Publisher Place Berlin/Heidelberg e-ISSN 14396327 Journal European Journal of Applied Physiology Volume Number 116 Issue Number 9 Page Count 10 Starting Page 1725 Ending Page 1734	2020-09-28 15:45:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 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": 0.1896306872367859, "perplexity": 12815.450164505664}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00118.warc.gz"}
https://www.rdocumentation.org/packages/pmclust/versions/0.2-0	# pmclust v0.2-0 0 0th Percentile ## Parallel Model-Based Clustering using Expectation-Gathering-Maximization Algorithm for Finite Mixture Gaussian Model Aims to utilize model-based clustering (unsupervised) for high dimensional and ultra large data, especially in a distributed manner. The code employs 'pbdMPI' to perform a expectation-gathering-maximization algorithm for finite mixture Gaussian models. The unstructured dispersion matrices are assumed in the Gaussian models. The implementation is default in the single program multiple data programming model. The code can be executed through 'pbdMPI' and MPI' implementations such as 'OpenMPI' and 'MPICH'. See the High Performance Statistical Computing website <https://snoweye.github.io/hpsc/> for more information, documents and examples. ## Functions in pmclust Name Description One E-Step Compute One E-step and Log Likelihood Based on Current Parameters generate.basic Generate Examples for Testing Set of PARAM A Set of Parameters in Model-Based Clustering. Internal Functions All Internal Functions One Step of EM algorithm One EM Step for GBD One M-Step Compute One M-Step Based on Current Posterior Probabilities assign.N.sample Obtain a Set of Random Samples for X.spmd Independent logL Independent Function for Log Likelihood pmclust-package Parallel Model-Based Clustering Update Class of EM or Kmenas Results Update CLASS.spmd Based on the Final Iteration Set of CONTROL A Set of Controls in Model-Based Clustering. mb.print Print Results of Model-Based Clustering pmclust and pkmeans Parallel Model-Based Clustering and Parallel K-means Algorithm print.object Functions for Printing or Summarizing Objects According to Classes as functions Convert between X.gbd (X.spmd) and X.dmat get.N.CLASS Obtain Total Elements for Every Clusters Initialization Initialization for EM-like Algorithms EM-like algorithms EM-like Steps for GBD Read Me First Read Me First Function Set Global Variables Set Global Variables According to the global matrix X.gbd (X.spmd) or X.dmat generate.MixSim Generate MixSim Examples for Testing No Results! ## Vignettes of pmclust Name pmclust-include/00-preamble.tex pmclust-include/01-acknowledgement.tex pmclust-include/01-introduction.tex pmclust-include/02-example.tex pmclust-include/03-algorithm.tex pmclust-include/04-discussion.tex pmclust-include/my_jss.cls pmclust-include/pmclust.bib build_pdf.sh pmclust-guide.Rnw No Results!	2019-02-15 22:48:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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": 0.2196369171142578, "perplexity": 9333.149468043552}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247479627.17/warc/CC-MAIN-20190215224408-20190216010408-00314.warc.gz"}
https://nanograv.org/glossary/p-pdot-diagram	# P-Pdot Diagram The spin period vs spin period derivative (how quickly the pulsars spin rate is slowing due to loss of luminous energy) diagram shows the different classes of neutron stars. From it, we have understood different properties of the neutrons stars, how they change over time, etc.	2022-12-09 20:05:32	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8319411873817444, "perplexity": 1684.6094772270844}, "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/1669446711475.44/warc/CC-MAIN-20221209181231-20221209211231-00424.warc.gz"}
http://tex.stackexchange.com/questions/85513/multiply-matrix-and-letter?answertab=active	# Multiply matrix and letter I want to multiply a matrix with a letter, it looks like that: \documentclass{report} \usepackage{ngerman} \usepackage{amsmath} \begin{document} $\left( \begin{array}{ccc} \| & & \| \\ f_1 & \dots & f_n \\ \| & & \| \end{array}\right) \mathcal{A} = \left( \begin{array}{ccc} \| & & \| \\ q_1 & \dots & q_n \\ \| & & \| \end{array} \right)$ \end{document} Is there a chance, that the letter is not so small in comparison to the matrix, so that they have about the same size? - Via graphicx package, you can use {\raisebox{-1.5ex}{\scalebox{3}{$\mathcal{A}$}}} but the result would not look that nice I guess. – percusse Dec 4 '12 at 18:16 hm true, it looks strange. But thanks anyway. Maybe I will stick to my old variant. – Adam Dec 4 '12 at 18:20 It would maybe look better if you reduce the size of the matrices via smallmatrix variants. – percusse Dec 4 '12 at 18:22 thanks! that does look much better!! – Adam Dec 4 '12 at 18:26 As percusse points out, you can resize it using the package graphicx: {\raisebox{-1.5ex}{\scalebox{3}{$\mathcal{A}$}}} However, I would say that it looks better "small" than "resized". That would be very inconsistent and weird. I recommend you to stuck with small $A$. However, there're few possible improvements of your code: \documentclass{report} \usepackage[ngerman]{babel} \usepackage{amsmath} \begin{document} $\begin{pmatrix} \| & & \| \\ f_1 & \cdots & f_n \\ \| & & \| \end{pmatrix} \mathcal{A} = \begin{pmatrix} \| & & \| \\ q_1 & \cdots & q_n \\ \| & & \| \end{pmatrix}$ \end{document} • Do not use ngerman package, use babel with the appropriate option. • The package amsmath offers the environment pmatrix for matrices in parentheses, as well as bmatrix for [...], Bmatrix for {...}, vmatrix for \|...\| and Vmatrix for \|\|...\|\|. • I'm not sure what the verical bars denote (probably a vector written in a column?) but I'm sure I would not understand it as a reader. However, I don't know how to improve it, since the context is missing. If the entries are really column vectors and you defined them properly before, I think that the reader would understand it even without the bars. -	2015-08-01 12:06:28	{"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": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.906754732131958, "perplexity": 1670.797756373052}, "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/1438042988650.6/warc/CC-MAIN-20150728002308-00318-ip-10-236-191-2.ec2.internal.warc.gz"}
https://www.maa.org/press/periodicals/loci/resources/calcplot3d-an-exploration-environment-for-multivariable-calculus-directional-derivatives	# CalcPlot3D, an Exploration Environment for Multivariable Calculus - Directional Derivatives Author(s): Paul Seeburger (Monroe Community College) Exercise: Determine the directional derivative function for $f(x, y) = x^2 + xy + y^2 + 1$ in the direction of v = i + j. Then determine its value at the point (0, -1). Use CalcPlot3D to graph this surface and show the appropriate tangent line on the surface at the point (0, -1) and displaying the unit direction vector and the correct directional derivative value. To do this, first enter the function in Function 1. Then choose the directional derivative option from the drop-down menu just above the Trace Plot to the left of the 3D plot. You can then use the Trace Plot menu at the top of the applet to enter the point (0, -1) and the direction vector. I recommend hiding the edges (using the E key or the Hide Edges option on the View Settings menu) and also making the surface transparent (using Ctrl-T or the Make Surfaces Transparent option on the View Settings menu). Rotate the plot until you can clearly see the direction vector, the surface, the tangent line, and the directional derivative value. Be sure it is the approximation of the exact value you obtained in your homework problem.	2019-09-23 07:38:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5611846446990967, "perplexity": 681.0706083402455}, "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/1568514576122.89/warc/CC-MAIN-20190923064347-20190923090347-00031.warc.gz"}