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http://crypto.stackexchange.com/questions/2753/in-the-sha-hash-algorithm-why-is-the-message-always-padded/2755 | # In the SHA hash algorithm, why is the message always padded?
In the SHA hash algorithm the message is always padded, even if initially the correct length without padding; the padding is of the form "1" followed by the necessary number of 0s.
Why is it necessary that the message always be padded?
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I edited your q... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/41030/why-is-int-dp-2-pi-p-rangle-langle-p-1/41246 | # Why is $\int (dp/2\pi) |p \rangle\langle p| = 1$?
In quantum mechanics, why is $\int (dp/2\pi) |p \rangle\langle p| = 1$ where $|p \rangle$ represents momentum eigenstate?
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Are you sure about the two pi? A family of orthonormal vectors spans the whole space (is 'complete') is the sum of all the projectors onto ea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/95/what-current-alternatives-are-there-to-the-standard-concordance-model-of-cosmolo/130 | # What current alternatives are there to the standard concordance model of cosmology?
The current "standard model" or concordance model of cosmology is Lambda CDM which includes late time acceleration due to a cosmological constant, cold dark matter as the missing matter component and an inflationary period at very ea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/128055/how-to-show-a-sequence-is-not-uniformly-integrable | # How to show a sequence is not uniformly integrable
Let $(X,\Omega,\mu)$ be a measure space. A sequence $f_n$ is said to be uniformly integrable if for every $\epsilon \gt 0$ there is a $\delta \gt 0$ such that for every measurable set $A$ with $\mu(A)\lt \delta$, $\int_A |f_n|~d\mu \lt \epsilon$, for every $n\in \ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 70, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://LAJEANNA.PARKER@ssa.gov/policy/docs/statcomps/income_pop55/2004/apn.html | # Appendix
Because the figures in this report are based on a sample of the older population, all reported statistics (counts, percentages, and medians) are only estimates of population parameters and may deviate somewhat from their true values—that is, from the values that would have been obtained from a complete cens... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=613040 | Physics Forums
## Magnetic potential energy
Dear all,
I'm reading a paper on finite element magnetic field analysis. Basically there are two approaches to this. One is to use Maxwell equation and the other is to define an energy functional, discretize the problem and minimize the functional with respect to the unkno... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/211799/uniqueness-of-induced-representation/211815 | # uniqueness of induced representation
I am studying the book "Representation Theory" by Fulton and Harris. And I just can not understand the part where they prove the uniqueness of induced representation. If someone could explain it I'd greatly appreciate it! It's on page 33 and it goes:
Choose a representative $g_{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/108624/constructing-the-lebesgue-stieltjes-integral-as-a-functional-on-c1-a-b | # Constructing the Lebesgue-Stieltjes Integral as a Functional on $C^1 ([a,b])$
This is based on an approach to a homework problem from last year that I discarded but would like to fill in the details of now. Unfortunately I can't see the necessary inequality.
Suppose we are given a function $g$ of bounded variation ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 48, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/223534/analyzing-a-function | # Analyzing a function
I am having a problem with the following function:
$f(x)=\sin^2(x)-\cos(3x)$
I need to examine the sign of $f'(x)$
I noticed that f is $2\pi$-periodic, therefore we need to analyze f(x) on $[0;2\pi]$
In addition to that $f(x)=-4\cos^3(x)-\cos^2(x)+3\cos(x)+1$
Hence $\forall x \in ]0;2\pi[, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/22648/spinor-integration | # Spinor integration
I am learning on-shell methods for one loop integrals from this paper: Loop amplitudes in gauge theory: modern analytic approaches by Britto. Starting with formula (18) spinor integration is explained. One first writes the loop momentum as $$(l)_{a\dot{a}}=t\lambda_a\tilde{\lambda}_\dot{a},$$ wher... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/tagged/quantiles?sort=active&pagesize=15 | # Tagged Questions
The quantiles of a distribution refer to points on its cumulative distribution function. Some common quantiles are quartiles and percentiles.
1answer
189 views
### How to calculate median of distributed data?
How to find the median (or approximate median) of n chunks of values. The values in each... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61784?sort=oldest | ## cohomology of BG, G compact Lie group
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It has been stated in several papers that $H^{odd}(BG,\mathbb{R})=0$ for compact Lie group $G$. However, I've still not found a proof of this. I believe that the proof is ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 107, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/tagged/lie-algebras | ## Tagged Questions
1answer
22 views
### Algorithm to find exponential map of differential operators acting on function
I am trying to write a computer program which computes the action of the exponential of a differential operator on a function, for any given differential operator. Examples: \$\ex …
0answers
168 vi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/10971?sort=newest | ## Why isn’t Likelihood a Probability Density Function?
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Hi everyone, first post here...
I've been trying to get my head around why a likelihood isn't a probability density function. My understanding says that fo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/2763/one-dimensional-analog-of-cleansing-a-correlation-matrix-via-random-matrix-theor?answertab=oldest | # One dimensional analog of cleansing a correlation matrix via random matrix theory
The general idea of cleansing a correlation matrix via random matrix theory is to compare its eigenvalues to that of a random one to see which parts of it are beyond normal randomness. These are then filtered out and one is left with t... | {"extraction_info": {"found_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/mat... |
http://math.stackexchange.com/questions/158617/about-the-wasserstein-metric | # About the Wasserstein “metric”
I've just encountered the Wasserstein metric, and it doesn't seem obvious to me why this is in fact a metric on the space of measures of a given metric space $X$. Except for non-negativity and symmetry (which are obvious), I don't know how to proceed.
Do you guys have any advices or l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 74, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/102697?sort=newest | $H$-Hopf modules equal the tensor products of their coinvariants with H
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In a comment for this old question, it was said that
> There is a theorem that Hopf modules are (up to isomorphism) the tensor products of thei... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.cs.cmu.edu/~dsheehy/osu12new.html | Don Sheehy
Postdoc Inria Saclay, France, don.r.sheehy@gmail.com
A New Approach to Output-Sensitive Voronoi Diagrams and Delaunay Triangulations
Ohio State University, Oct 31, 2012
Voronoi diagrams and their duals, Delaunay triangulations, are used in many areas of computing and the sciences. Starting in 3-dimensions, t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/73089/finite-sum-of-the-fractional-type | Finite sum of the fractional type
Some special manipulations involving finite sums. How to solve this sum?
$\displaystyle{\sum_{k=1}^{n}}\frac{1}{4k^2 - 1}$
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1
Hint 1: the denominator can be factorised. Hint 2: Partial fractions. Hint 3: It telescopes. – ShreevatsaR Oct 16 '11 at 17:09
2 Answers
Hint: Note that ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3039031 | Physics Forums
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Gold Member
## "Locally Lorentz"
Mister Thorne Wheeler, "Gravitation" asks "What does it mean to say that the geometry of a sufficiently limited region of spacetime in the real physical world is Lorentzian?"
The follow this up with two answers... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/47865/are-angles-ever-multiplied?answertab=votes | # Are angles ever multiplied?
I recently explained multiplication of (non-zero) complex numbers to my Mathematics Fundamentals students, the usual bit about “multiply their lengths, and add their angles”. Of course, there is always at least one student who wants to know why the angles are added instead of multiplied –... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/15002/mathematically-oriented-treatment-of-general-relativity?answertab=active | # Mathematically-oriented Treatment of General Relativity
Can someone suggest a textbook that treats general relativity from a rigorous mathematical perspective? Ideally, such a book would
1. Prove all theorems used
2. Use modern "mathematical notation" as opposed to "physics notation", especially with respect to lin... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/232056/expectation-inequality-with-weight-matrix | # Expectation inequality with weight matrix
Given that $X$ is random matrix ($X'$ is transposed matrix) and $\Omega$ is invertible square matrix is inequality $$EX'X\cdot(EX'\Omega X)^{-1}\cdot EX'X\leq EX'\Omega^{-1}X$$ correct? All the expectations as well as inverse of $EX'\Omega X$ exist.
Maybe (but it is probabl... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/4763?sort=newest | ## SL(2,Z/N)-decomposition of space of cusp forms for Gamma(N)
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Since $\Gamma(N)$ is normal in $\mathrm{SL}(2,\mathbb{Z})$, the quotient group $\mathrm{SL}(2,\mathbb{Z}/N)$ acts on the spaces of cusp forms $S_k(\G... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/151651-help-needed-graphing-equations.html | # Thread:
1. ## Help Needed in Graphing Equations
I honestly don't know what I would do without this forum. This time, I am stumped by a graphing problem with equations. The question is...
Graph the equation 3y = 2x + 5 and calculate slope, x-intercept and y-intercept.
I have been working on this one problem for a ... | {"extraction_info": {"found_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/mat... |
http://www.physicsforums.com/showthread.php?p=2641769 | Physics Forums
## Energy conservation problem
1. The problem statement, all variables and given/known data
A string exerts a tension force of 55N on a 10kg block as it moves a distance of 5m up a frictionless incline. The string pulls parallel to the incline.
A) Find the total external work done on the block-earth s... | {"extraction_info": {"found_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": 18, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Law_of_cosines&oldid=21125 | # Law of cosines
### From Math Images
Revision as of 15:43, 20 June 2011 by Rscott3 (Talk | contribs)
Law of Cosines
Field: Geometry
Created By: rscott3
Website: [ ]
Law of Cosines
The law of cosines is a trigonometric extension of the Pythagorean Theorem.
# Basic Description
The law of cosines is a formula that ... | {"extraction_info": {"found_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": 59, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/1222/white-holes-and-time-reversed-oppenheimer-snyder-collapse | # White Holes and Time-Reversed Oppenheimer-Snyder collapse
So, the canned explanation that I always hear about why the white hole solution of the extended Schwarzschild solution is non-physical is that "The matter distribution cuts off the white hole solution."
If I look at Oppenheimer-Snyder collapse, however, the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/92272/finding-the-limit-of-a-sequence?answertab=oldest | # finding the limit of a sequence
If there were a regular square root I would multiply the top by its adjacent and divide, but I've tried that with this problem and it doesn't work. Not sure what else to do have been stuck on it.
$$\lim _{n\to \infty } \sqrt [3]{n^2} \left( \sqrt [3]{n+1}- \sqrt [3]{n} \right) .$$
-... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/776 | ### Continued Fractions I
An article introducing continued fractions with some simple puzzles for the reader.
### LOGO Challenge - Circles as Bugs
Here are some circle bugs to try to replicate with some elegant programming, plus some sequences generated elegantly in LOGO.
### Spirals Instead of Sunflowers
Using lo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/43429-solved-convergence-infinite-series.html | # Thread:
1. ## [SOLVED] Convergence of an infinite series
I've to show whether the following infinite series converges or not. The problem is that I tried to prove it's divergent by induction, by the root test and by trying to bound it from below. But I couldn't reach any conclusion.
Here it comes : $\sum_{n=1}^{+\i... | {"extraction_info": {"found_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/ma... |
http://mathoverflow.net/questions/109661/polarizable-variations-of-mixed-hodge-structures | ## Polarizable variations of (mixed) Hodge structures
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I am trying to come to grips with Saito's theory of mixed Hodge modules (slightly) beyond just the basic axiomatic formalism. I will take my Hodge structures ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/17121-power-sets.html | # Thread:
1. ## Power sets
I have a homework problem that I knew the answer but dont know how to do the proof. Can anyone help me?
List all the subsets of the set X={a,b,c}. How many are there? Next, try with X={a,b,c,d). Now suppose that the set X has n elements: how many subsets does X have? Try to justify your an... | {"extraction_info": {"found_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/mat... |
http://gowers.wordpress.com/2008/08/ | # Gowers's Weblog
Mathematics related discussions
## Archive for August, 2008
### Princeton Companion latest
August 28, 2008
A quick post to give an update on the Princeton Companion to Mathematics. It’s been off my hands for a few weeks now. If all goes well it will be printed by the middle of September and shoul... | {"extraction_info": {"found_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": 6, "mimetex.cgi": 0, "/images/mat... |
http://jmanton.wordpress.com/tag/measure-theory/ | # Jonathan Manton's Blog
Thoughts and ideas on mathematics, engineering, neuroscience and academia
### Archive
Posts Tagged ‘Measure Theory’
## Measure-theoretic Probability: Still not convinced?
June 22, 2010
This is a sequel to the introductory article on measure-theoretic probability and accords with my belief... | {"extraction_info": {"found_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": 237, "mimetex.cgi": 0, "/images/m... |
http://unapologetic.wordpress.com/2010/11/25/induced-matrix-representations/?like=1&source=post_flair&_wpnonce=5d5a17dad5 | # The Unapologetic Mathematician
## Induced Matrix Representations
Sorry I missed posting this back in the morning…
We want to work out the matrices of induced representations. Explicitly, if $V$ is a left $H$-module of degree $d$, where $H$ is a subgroup of $G$, then $V\!\!\uparrow_H^G$ is a left $G$-module. If we ... | {"extraction_info": {"found_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": 60, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/71958/why-is-this-function-differentiable?answertab=oldest | # Why is this function differentiable?
I know that the piecewise function $f(x) = \left\{ \begin{array}{lr} 2x & , x < 1\\ x+1 & , x \geq 1 \end{array} \right.$ is differentiable because $2x$ and $x + 1$ converge at different rates based on their slope but why is $f(x) = \left\{ \begin{array}{lr} \frac{x^2-1}{x-1} & ,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/121095-finding-area.html | # Thread:
1. ## finding the area
I am not sure what to do here for this problem.
Sketch the region enclosed by x+ y^2= 42 and x+y = 0. Decide whether to integrate with respect to x or y. Then find the area of the region.
Any help would be great
2. Originally Posted by mbrez88
I am not sure what to do here for this... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://wikis.controltheorypro.com/index.php?title=Proportional_Control | • Search »
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Proportional Control
From ControlTheoryPro.com
| | | |
|----------------------------------------------------------------------------------------|------|--------... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/108200/where-should-the-exponent-be-written-in-numbers-with-units-of-measurement/108202 | # Where should the exponent be written in numbers with units of measurement?
If you are to calculate the hypotenuse of a triangle, the formula is:
$h = \sqrt{x^2 + y^2}$
If you don't have any units for the numbers, replacing x and y is pretty straightforward: $h = \sqrt{4^2 + 6^2}$
But what if the numbers are in me... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://johncarlosbaez.wordpress.com/2011/11/04/network-theory-part-16/ | # Azimuth
## Network Theory (Part 16)
We’ve been comparing two theories: stochastic mechanics and quantum mechanics. Last time we saw that any graph gives us an example of both theories! It’s a bit peculiar, but today we’ll explore the intersection of these theories a little further, and see that it has another inter... | {"extraction_info": {"found_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": 397, "mimetex.cgi": 0, "/images/m... |
http://planetmath.org/maximalsubgroup | # maximal subgroup
Let $G$ be a group.
A subgroup $H$ of $G$ is said to be a maximal subgroup of $G$ if $H\neq G$ and there is no subgroup $K$ of $G$ such that $H<K<G$. Note that a maximal subgroup of $G$ is not maximal among all subgroups of $G$, but only among all proper subgroups of $G$. For this reason, maximal s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 21, "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/ma... |
http://mathhelpforum.com/calculus/210056-prove-there-exists-inverse-function.html | # Thread:
1. ## prove there exists an inverse function
Hello. I'm quite new to calculus and frankly speaking I'm an autodidact. Could you tell me how to solve this:
$f: [\frac{\pi}{2}, \pi) \ni x \rightarrow \frac{1}{sinx} \in R$
Prove that there exists a inverese of $f$. In what set is $f^{-1}$ differentiable? Cal... | {"extraction_info": {"found_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": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/117791?sort=votes | ## What axioms are stronger than the Axiom of choice?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What other axioms in set theory are stronger than AC ? I mean what are those axioms that will imply AC ?
-
## 5 Answers
The axiom "every set is constructib... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 75, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/hyperbolic-geometry+conformal-geometry | # Tagged Questions
2answers
331 views
### How does a conformal mapping preserve angles in hyperbolic geometry?
Suppose I have a sector $D = \{0 < \arg z < \alpha\}$ where $\alpha \leq 2\pi$. If I apply the function $w = \frac{\zeta - i}{\zeta + i}$ from the upper half plane to the unit disc (\$\zeta = ...
2answers
1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/86351-e-x-exponential-random-variable-joint-density-elevators-cov-multinomial.html | # Thread:
1. ## E(x) of exponential random variable, joint density, and elevators +cov of multinomial
So, I've been working on a bonus review for a few hours now and have hit places where I'm not sure and places where I don't know where to start. I don't need help on all of these but it's simpler if I just post the w... | {"extraction_info": {"found_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": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/145598-solved-make-x-subject-y-2x-x-2-a.html | # Thread:
1. ## [SOLVED]Make x the subject in y = 2x - x^2.
Hi it's late but I can't seem to single out x in the following equation:
$y = 2x - x^2$
Can it be done?
I want to evaluate the volume by using washers even though I can just use shells
2. You can't solve that equation for x can you be more specific about... | {"extraction_info": {"found_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/ma... |
http://math.stackexchange.com/questions/tagged/linear-algebra?sort=active&pagesize=50 | # Tagged Questions
Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them. This includes: systems of linear equations, Hamel basis, dimension, matrices, determinant, trace, eigenvalues and eigenvectors, diagonalization, etc. For questions specifically concerning ...
4... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 151, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/145757-differentiation-application.html | # Thread:
1. ## Differentiation Application
Thanks to those who responded yesterday to my question regarding the differentiation in this problem. As it turns out, I wasn't off as far as I thought I might be. I believed that correctly differentiating the function was the root of my problem, but as it turns out, I'm no... | {"extraction_info": {"found_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": 38, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/276520/full-isomorphism-closed-reflective-subcategory-of-set | # Full isomorphism-closed reflective subcategory of Set
What are the full isomorphism-closed reflective subcategories of $\textbf{Set}$?
In the book "The Joy of Cats" it is mentioned (p. 58) that there are precisely three such subcategories. I can see two of them are:
1. the whole category $\textbf{Set}$
2. the subc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/18268/consecutive-birthdays-probability?answertab=active | Consecutive birthdays probability
Let $n$ be a number of people. At least two of them may be born on the same day of the year with probability: $$1-\prod_{i=0}^{n-1} \frac{365-i}{365}$$
But what is the probability that at least two of them are born on two consecutive days of the year (considering December 31st and Ja... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 114, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/36321/why-does-the-running-of-the-gauge-couplings-show-frac1-alpha-frac1?answertab=active | # Why does the running of the gauge couplings show $\frac{1}{\alpha}$ > $\frac{1}{\alpha_w}$ at low energy?
I thought the coupling constants were something like:
$\alpha \approx 1/137$
$\alpha_w \approx 10^{-6}$
$\alpha_s \approx 1$
And yet if you look at any pictorial representation of the running of the coupling... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/66831-length-side-b.html | # Thread:
1. ## Length of Side b
In ΔABC, m<C = 30 and a = 24. If the area of the triangle is 42, what is the length of side b?
Is this a law of sines or law of cosines problem?
2. Originally Posted by magentarita
In ΔABC, m<C = 30 and a = 24. If the area of the triangle is 42, what is the length of side b?
Is thi... | {"extraction_info": {"found_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/mat... |
http://mathhelpforum.com/advanced-algebra/45521-eigen-vectors.html | # Thread:
1. ## Eigen vectors
I need to know how to compute T with respect to the basis b. and i need a way to know where b is a basis consisting of egeinvectors of T.
Let v= p_1(R), T(a+bx)= (6a-6b)+(12a-11b)x and the basis B={3+4x,2+3x}
Let V= R^3, T = $\begin{pmatrix}\ a \\ b \\ c\end{pmatrix}\$ = $\begin{pmatri... | {"extraction_info": {"found_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/mat... |
http://mathoverflow.net/questions/110273/can-one-ignore-primes-lying-over-l-in-the-fontaine-mazur-conjecture-counterexa | ## Can one ignore primes lying over $l$ in the Fontaine-Mazur conjecture? Counterexamples?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The Fontaine-Mazur conjecture predicts that an $l$-adic Galois representation of a number field is 'geometric' if it is u... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/latex-help/111343-triple-lower-limits-summation-sign-urgent.html | # Thread:
1. ## Triple lower limits in summation sign (urgent)
Hi!
How do I get several limits below each other using the summation sign? I.e. $\sum\limits_{i \neq j} A_{ij}$, but I would also like $i, j \neq r, s$ and $i, j \neq s, r$ on two lines below the first limit...
Thanks!
2. Originally Posted by Jodles
Hi... | {"extraction_info": {"found_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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=128272 | Physics Forums
## Parameterization
Hi, I am having a lot of trouble on the parameterization part of this problem:
Suppose there is a cylindrical container of liquid with circular flow velocity given in cylindrical coordinates by v(r,$$\theta$$,z) = <-f(r,z)sin$$\theta$$, f(r,z)cos$$\theta$$,0> for some function f(r,... | {"extraction_info": {"found_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": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/integral-transforms?sort=unanswered&pagesize=15 | # Tagged Questions
This covers all transformations of functions by integrals, including but not limited to the Radon, X-Ray, Hilbert, Mellin transforms. Use (wavelet-transform), (laplace-transform) for those respective transforms, and use (fourier-analysis) for questions about the Fourier and Fourier-sine/cosine ...
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 78, "mathjax_display_tex": 17, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/30556/what-does-ads-cft-have-to-say-about-quantum-gravity-in-our-world?answertab=oldest | # What does AdS/CFT have to say about quantum gravity in our world?
The Ads side of the AdS/CFT correspondence is a model of quantum gravity in 5 dimensional antidesitter space. What can it say about quantum gravity in our 4-spacetime dimensions? Or is it just a toy model to better our understanding of quantum gravity... | {"extraction_info": {"found_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/mat... |
http://math.stackexchange.com/questions/217926/requirements-for-a-linear-transformation?answertab=votes | # Requirements for a Linear Transformation
Let's say we have a transformation:
$$T: \mathbb{R}^n \rightarrow \mathbb{R}^m.$$
This is a linear transformation iff: for all $\vec{a} , \vec{b} \in \mathbb{R}^n$ and $c \in \Bbb{R}$,
1. $T(\vec{a} + \vec{b}) = T(\vec{a}) + T(\vec{b})$
2. $T(c \vec{a}) = cT(\vec{a})$
I'v... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/reference-request?page=3&sort=votes&pagesize=50 | # Tagged Questions
Use this tag for questions seeking a single specific paper or a short, non-open-ended list of references, like "What paper first discovered X?", "Where can I find the original derivation of X?", or "What is the canonical source for X?" etc.
4answers
383 views
### References for conceptual issues i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/226371/logic-and-geometry | # Logic and geometry
By delving into topos theory and sheaves one will eventually discover a "deep connection" between logic and geometry, two fields, which are superficially rather unrelated.
But what if I have not the abilities or capacities of delving deeper into topos theory and sheaves? Does the deep connection ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/13647/why-does-the-riemann-zeta-function-have-non-trivial-zeros/50145 | ## Why does the Riemann zeta function have non-trivial zeros?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This is a very basic question of course, and exposes my serious ignorance of analytic number theory, but what I am looking for is a good intuitive exp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 90, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/982/how-to-easily-find-location-of-hidden-characters-that-causes-hard-to-find-syntax | # how to easily find location of hidden characters that causes hard to find syntax error in notebook?
For last 30 minutes (and I was lucky today, sometimes I spend 5 times as much time) I have been removing code little by little from my large one cell, (have to be one cell, it is Manipulate demo stylesheet) in order t... | {"extraction_info": {"found_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/mat... |
http://nrich.maths.org/962/note | nrich enriching mathematicsSkip over navigation
### Bracelets
Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?
### Is a Square a Rectangle?
How many rectangles can you find in this shape? Which ones are differently sized and which ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/15217?sort=newest | ## Proof of the Reidemeister theorem
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While preparing for my introduction to topology course, I've realized that I don't know where to find a detailed proof of the Reidemeister theorem (two link diagrams give isot... | {"extraction_info": {"found_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/mat... |
http://mathhelpforum.com/differential-geometry/163240-homeomorphism-circle.html | # Thread:
1. ## Homeomorphism of the circle
Let $f: \mathbb{S}^1 \rightarrow \mathbb{S}^1$ be an orientation preserving homeomorphism with at least one fixed point. Show that every periodic point of $f$ has period 1, i.e. is a fixed point.
Anybody got an idea?
2. Let p0 be a fixed point and p be a periodic point wi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2010/07/23/product-measures/?like=1&source=post_flair&_wpnonce=4ca8fc8c32 | # The Unapologetic Mathematician
## Product Measures
We continue as yesterday, considering the two $\sigma$-finite measure spaces $(X,\mathcal{S},\mu)$ and $(Y,\mathcal{T},\nu)$, and the product measure space $(X\times Y,\mathcal{S}\times\mathcal{T})$.
Last time we too a measurable set $E\subseteq X\times Y$ and def... | {"extraction_info": {"found_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": 31, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/linear-algebra+options | # Tagged Questions
1answer
319 views
### Linear Solve with Modular Arithmetic
I am interested in using LinearSolve[m,b] which will find a solution to the equation $m.x=b$, where I am in mod 2 arithmetic. Is there any way to perform this ... | {"extraction_info": {"found_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/mat... |
http://physics.stackexchange.com/questions/8770/if-you-put-a-latex-balloon-in-a-vacuum-how-much-would-it-expand?answertab=active | # If you put a latex balloon in a vacuum, how much would it expand?
If you put a latex balloon in a vacuum, how much would it expand? And would it pop? Assume it doesn't leak.
EDIT:
Some numbers: Ambient pressure is 100 KPa, balloon is perfectly spherical with a diameter of 300 mm, deflated it has a diameter of 25mm... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/29469/spontaneous-time-reversal-symmetry-breaking?answertab=votes | # Spontaneous Time Reversal Symmetry Breaking?
It is known that you can break P spontaneously--- look at any chiral molecule for an example. Spontaneous T breaking is harder for me to visualize. Is there a well known condensed matter system which is uncontroversial example where T is broken spontaneously?
I remember ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3945182 | Physics Forums
Significance of kinematic and dynamic viscosity
It is stated that kinematic viscosity is the ratio of dynamic viscosity to density. can anyone elaborate it further that what are the uses of both types of viscosities and why we differentiate them.does dynamic viscosity reates with static fluid?
PhysOrg... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/52974/what-is-the-last-digit-of-pi?answertab=oldest | # What is the last digit of $\pi$?
I want to know: what is the last digit of $\pi$?
Some people say there are no such thing, but they fail to mention why.
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Sometimes even rational numbers don't have a "last digit", think of 1/3=0.33333... – Vhailor Jul 21 '11 at 22:12
37
Nice Poem. ${}$ – jspecter Jul 21 '11 at... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/fans | ## Tagged Questions
0answers
379 views
### Reference for this polyhedral lemma
Recall the definition of a fan: Let $U$ be a finite dimensional real vector space. Then a fan is a collection $\mathcal{F}$ of cones in $U$ such that (1) If \$\sigma \in \mathcal{F …
0answers
224 views
### A question about a blue fan and... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/118479/orientations-for-pseudoholomorphic-curves-with-totally-real-boundary-condition/118483 | ## Orientations for pseudoholomorphic curves with totally real boundary condition
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I am trying to understand what the obstructions are to orienting moduli spaces of pseudoholomorphic curves with totally real bound... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/doppler-effect | # Tagged Questions
The doppler-effect tag has no wiki summary.
2answers
81 views
### Is there a way to create a flickering frequency to be dependent on speed of the person looking at it?
Is there a way to make a screen or a road sign flash at different rates, depending on the velocity of the observer looking at it?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://wiki.xiph.org/index.php?title=Intra&oldid=13862&diff=prev | # Intra
### From XiphWiki
(Difference between revisions)
| | ... | {"extraction_info": {"found_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": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/137436-showing-tangent-curve-also-tangent-curve-another-point.html | # Thread:
1. ## Showing that the tangent to the curve is also tangent to curve at another point.
Show that the tangent to the curve y=(x^2 +x -2)^2 +3 at the point where x=1 is also tangent to the curve at another point.
So far this is what I did:
Subbed in 1 to the oringinal curve to find out that the point is (1,... | {"extraction_info": {"found_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/ma... |
http://math.stackexchange.com/questions/250194/is-the-optimal-solution-to-this-problem-to-row-straight-to-the-store | # Is the optimal solution to this problem to row straight to the store?
For my homework, I was given this brainteaser:
You’re sunbathing on the island shown on the map below. The island is six miles from shore at the closest point, and the nearest store is a convenience store seven miles down the beach. If you can ro... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/86874?sort=votes | ## Is every finite group a quotient of the Grothendieck-Teichmuller group?
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The Grothendieck-Teichmuller conjecture asserts that the absolute Galois group $Gal(\mathbb{Q})$ is isomorphic to the Grothendieck-Teichm... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/7795/what-is-5746-divided-by-17 | # What is $57^{46}$ divided by 17?
$$\frac{57^{46}}{17}$$
What is best and quickest way to evaluate an approximate answer to this by hand?
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Do you want the result $57^{46} / 17 \approx 3.5 \times 10^{79}$, the quotient, or the remainder? – KennyTM Oct 25 '10 at 13:00
3
Some of the answers below are interpreting... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 48, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/85329?sort=votes | ## Hovey’s unit axiom in monoidal model categories
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Let $\mathcal{C}$ be a monoidal model category in the sense of Hovey's book. He assumes the following unit axiom not considered in other references (e.g. Schwede... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/16742/how-to-explain-certain-patterns-appearing-after-kernel-averaging | # How to explain certain patterns appearing after kernel averaging?
Having a `2D map` filled `uniformly by random values` (Figure:top-left), the next maps are kernel averaged with a kernel of sizes 3x3, 5x5, ..., 11x11.
The questions are:
What are the patterns appeared in the kernel averaged maps?
What is the statisti... | {"extraction_info": {"found_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/mat... |
http://mathoverflow.net/questions/10083/computing-lengths-in-the-a-2-affine-weyl-group | computing lengths in the A_2 affine weyl group
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The A_2 affine Weyl group is the symmetry group of the triangulation of the plane by equilateral triangles. As Sean points out, it may be generated by reflections $r_1, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/133283-prime-decomposition-number-rings.html | # Thread:
1. ## Prime decomposition in number rings
Assume that the number field K contains a primitive n'th root of unity $u$.
Let $a$ in the integral ring of K and let I be an prime ideal of the integral ring of K such that $na$ is not in I.
Let L=K( $a^{1/n}$).
Show that $x^{n}-a$ is separable modulo I.
Thank you... | {"extraction_info": {"found_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/mat... |
http://physics.stackexchange.com/questions/34891/derivative-of-a-position-eigenket?answertab=oldest | # Derivative of a Position Eigenket
I was flicking through Zettili's book on quantum mechanics and came across a 'derivation' of the momentum operator in the position representation on page 126. The author derived that $\langle\vec{r}|\hat{\vec{P}}|\psi\rangle = -i\hbar\vec{\nabla}\langle\vec{r}|\psi\rangle$ (I've omi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/110721/invertibility-of-a-matrix-with-a-gaussian-perturbation | ## invertibility of a matrix with a Gaussian perturbation
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Suppose that $A$ is an arbitrary fixed $n\times n$ matrix and $G$ a random $n\times n$ matrix with i.i.d. $N(0,1)$ entries. Is there a simple proof that $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/205325-getting-root-equation.html | # Thread:
1. ## Getting to the root of the equation
The equation has two roots. Find the smaller and larger one?
so I came up with 2x2e-5x(3-3x)=0
Just not sure where to go from here?
2. ## Re: Getting to the root of the equation
Originally Posted by M670
The equation has two roots. Find the smaller and larger on... | {"extraction_info": {"found_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/mat... |
http://en.wikipedia.org/wiki/Basis_(topology) | # Base (topology)
(Redirected from Basis (topology))
In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B. We say that the base generates the topology T. Bases are useful because many pr... | {"extraction_info": {"found_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": 60, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/132967/history-of-f-circ-g | # History of $f \circ g$
$f \circ g$ is usually interpreted as $f(g(x))$ although, as Google shows, $g(f(x))$ is used frequently too. My question: Does anybody know who was the first mathematician to use this symbol and what was his interpretation?
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$f\circ g$ is always interpreted as $f(g(x))$; more precisely, t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 68, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/74897/small-cycles-in-an-undirected-graph/75069 | # Small cycles in an undirected graph
Let $G=(V,E)$ be an undirected graph. I am using the usual convention that $n=|V|, m=|E|$. For $v \in V$, let $deg(v)$ be the degree of the vertex $v$.
I am trying to show that if we have $m > \frac{n^{3/2}}{2}$, it follows that $G$ has either a triangle $C_3$ or a square $C_4$. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/14363/hydrostatic-friction-why-do-water-droplets-stay-at-rest-on-an-inclined-glass-su/14369 | # Hydrostatic friction: why do water droplets stay at rest on an inclined glass surface?
Tjis is a non-expert question on a (seemingly simple) text-book topic. The question is about "hydrostatic friction", defined as follows.
Consider a drop of water resting on a flat surface. If the surface is slightly inclined, the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/74188/finding-centre-and-radius-of-circle/74205 | # Finding centre and radius of circle
Let $a,c \in \mathbb R$ with $a \neq 0$, and let $b \in \mathbb C$. Define $$S=\{z\in \mathbb C: az\bar{z}+b\bar{z}+\bar{b}z+c=0\}.$$
a. Show that $S$ is a circle, if $|b|^2 > ac$. Determine its centre and radius.
b. What is $S$ if $a=0$ and $b \neq 0$?
How would I get started i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/153358-solutions-triangle.html | # Thread:
1. ## solutions of a triangle
prove that: $\:\dfrac{c}{a+b}\:\ = \:\dfrac{1-tan\:\dfrac{A}{2}\:\tan\:\dfrac{B}{2}\ }{1 +tan\:\dfrac{A}{2}\:\tan\:\dfrac{B}{2} }$
where $\:\boxed{a,b,c}$ are the sides opposite to the angles $\:\boxed{A,B,C}$ respectively in a triangle
2. Let $P , Q , R$ be the points of tan... | {"extraction_info": {"found_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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/64420/is-there-a-faster-way-to-calculate-a-few-diagonal-elements-of-the-inverse-of-a-h | # Is there a faster way to calculate a few diagonal elements of the inverse of a huge symmetric positive definite matrix?
I asked this on SO first, but decided to move the math part of my question here.
Consider a $p \times p$ symmetric and positive definite matrix $\bf A$ (p=70000, i.e. $\bf A$ is roughly 40 GB usin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 73, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Logistic_map | # Logistic map
The logistic map for 100 generations of x (plotted left to right) as r moves from 0 to 4
The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equat... | {"extraction_info": {"found_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": 35, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.aps.org/articles/large_image/f1/10.1103/Physics.3.107 | Credit: Alan Stonebraker
Figure 1: (Top) Experimental configuration used by Minardi et al. to produce light bullets. $1550$-$nm$ laser pulses with $170$-$fs$ duration go into a hexagonal array of glass waveguides. The nonlinear optical interaction in the glass causes formation of solitons that are stable in time and s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "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/mat... |
http://gilkalai.wordpress.com/2008/09/16/a-diameter-problem-5/?like=1&source=post_flair&_wpnonce=81d32a40f7 | Gil Kalai’s blog
## A Diameter Problem (5)
Posted on September 16, 2008 by
### 6. First subexponential bounds.
Proposition 1: $F(d,n) \le F_k(d,n) \times F(d-k,n-k).$
How to prove it: This is easy to prove: Given two sets $S$ and $T$ in our family $\cal F$, we first find a path of the form $S=S_0, S_1, S_2, \dots,... | {"extraction_info": {"found_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": 130, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/49960/do-spheres-exist-in-nature/50017 | # Do spheres exist in nature?
Often in physics, Objects are approximated as spherical. However do any perfectly spherical objects actually exist in nature?
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1
I believe black holes are considered to be perfectly spherical, though I don't have the appropriate knowledge to elaborate on this. – Wouter Jan 11 at 21:18
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.m.wikipedia.org/wiki/Young's_inequality | # Young's inequality
In mathematics, Young's inequality is either of two inequalities: one about the product of two numbers,[1] and one about the convolution of two functions.[2] They are named after William Henry Young.
Young's inequality for products can be used to prove Hölder's inequality. It is also used widely ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 14, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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