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http://mathoverflow.net/questions/13660?sort=votes | ## A comprehensive functor of points approach for manifolds
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This seems unrealistic, because the topology on a manifold doesn't have anything to do with the properties its structure sheaf, but I figured I might as... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "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/46267/the-four-clock-special-relativity-conundrum/48456 | # The Four-Clock Special Relativity Conundrum
Two open-car trains approach each other at fixed velocities. Each has a radar to see how quickly the other train is approaching, but apart from that the trains have no a priori knowledge of each other.
Each train has engineers on its first and last cars. Each engineer has... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 202, "mathjax_display_tex": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/advanced-algebra/173580-vector-problem-involving-orthogonal.html | # Thread:
1. ## Vector problem involving orthogonal
Hi, I'm struggling with this problem:
For $\vec{u} =$[-4, 1, 10]^T and $\vec{v} =$ [−12, −6, 8]^T find the vectors $\vec{u1}$ and $\vec{u2}$ such that:
(i) $\vec{u1}$ is parallel to $\vec{v}$
(ii) $\vec{u2}$ is orthogonal to $\vec{v}$
(iii) $\vec{u} = \vec{u1} + \... | {"extraction_info": {"found_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": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/243259/proof-that-certain-operators-are-compact | # Proof that certain operators are compact
I want to examine which of the following operators $T \colon C[0,1] \to C[0,1]$. are compact, by some I think I got the argument, but others I have no idea.
a) $Tx(t) = x(t^2)$
Guess it is compact, but i have no idea how to proof this?
b) $Tx(t) = x(0) + tx(1)$
Here the 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": 43, "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/76015?sort=newest | ## How much can a diagonal matrix change the eigenvalues of a symmetric matrix?
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Suppose that we have a symmetric matrix ${\bf S}$ with eigenvalue decomposition ${\bf S} = {\bf Q}{\bf \Lambda}{\bf Q}^T$. Assume th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "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/191243/is-this-a-typo-in-my-math-book | # Is this a typo in my math book?
I am doing homework which is submitted online. I came across a question asking if two functions are equal. $f(x)=3x+4$ and $g(x)=14+(8/x)+b(x-4)$. I set the two equations together and got 7 for an answer but the book says the answer is $\frac {7}{3}$.
Here is an image of the solution... | {"extraction_info": {"found_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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/196160/why-these-line-integrals-have-the-same-value | # Why these line integrals have the same value?
I'm posting with my phone so I cannot using latex. I will be thankful if somebody correct my post.
I want to integrate $x^2-iy^2$ on the complex plane with
(a) closed unit circle
(b) closed unit square $(+1+i, 1-i, -1+i, -1-i)$
By my calculation, the answers are same... | {"extraction_info": {"found_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://catalog.flatworldknowledge.com/bookhub/reader/2992?e=coopermicro-ch09_s01 | Please wait while we create your MIYO...
# Microeconomics: Theory Through Applications, v. 1.0
by Russell Cooper and A. Andrew John
Study Aids:
Click the Study Aids tab at the bottom of the book to access your Study Aids (usually practice quizzes and flash cards).
Study Pass:
Study Pass is our latest digital prod... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 9, "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/34687/two-elementary-games-in-number-theory | # two elementary games in number theory
I solved these two problems from a programming challenge website: numgame and numgame2.
These two problems are very similar. In the first one, the position is a number $n$ and each player can subtract from $n$ a divisor $d$ of $n$ with $1 \leq d < n$. Players Alice and Bob alte... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "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/193897/how-can-i-get-sequence-4-4-2-4-4-2-4-4-2-ldots-into-equation/193907 | # How can I get sequence $4,4,2,4,4,2,4,4,2\ldots$ into equation?
How can I write an equation that expresses the nth term of the sequence:
$$4, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2,\ldots$$
-
31
nth term of decimal expansion 442/999 ;) – wim Sep 11 '12 at 13:25
Why isn't this posted to tex stackexchange? – g33kz0r Sep 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": 33, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/65460/coefficients-of-lacunary-series-on-quasiconformally-transformed-unit-disk/67523 | Coefficients of lacunary series on quasiconformally transformed unit disk
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Say I have a lacunary $q$ series $s(q)=\sum_{n=0}^{\infty} a_{n}q^{n}$ , and I have a quasiconformal transformation $\xi$ which preserves 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": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?s=b13b5dbbbecd3e16f10b79c26b5cc69c&p=4275475 | Physics Forums
## Trying to determine initial thrust on an object from angular velocity?
Hi all,
I built an electric paper airplane launcher and I'm trying to figure out how much force or thrust is being applied to my paper airplane when it's launched. The setup looks like this:
The discs are 124mm in diameter, are... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2008/09/08/cauchys-condition-for-uniform-convergence/?like=1&source=post_flair&_wpnonce=2c354f29b9 | # The Unapologetic Mathematician
## Cauchy’s Condition for Uniform Convergence
As I said at the end of the last post, uniform convergence has some things in common with convergence of numbers. And, in particular, Cauchy’s condition comes over.
Specifically, a sequence $f_n$ converges uniformly to a function $f$ if 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": 0, "wp_latex": 26, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/tagged/validation+regression | # Tagged Questions
1answer
55 views
### validating a regression model
I want to build a regression model to predict daily income from customers. I have 2 problems: 1. Choosing data for the training set - do I use daily income from 1 month ago, 6 month ago etc. 2. How do ...
0answers
87 views
### Question about 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": 5, "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/6384/why-does-dilation-invariance-often-imply-proper-conformal-invariance?answertab=active | # Why does dilation invariance often imply proper conformal invariance?
Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also invariant under proper conformal transformations 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": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/41988-complex-number.html | Thread:
1. Complex Number
Find the complex number $z$ which satisfies both $|z-3i|=3$ and $arg(z-3i)=\frac{3\pi}{4}$.
Thanks in advance.
2. Hi !
Originally Posted by Air
Find the complex number $z$ which satisfies both $|z-3i|=3$ and $arg(z-3i)=\frac{3\pi}{4}$.
Thanks in advance.
$z-3i=|z-3i|e^{i 3 \pi/4}$
$z-3i... | {"extraction_info": {"found_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": 32, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/104704?sort=newest | ## Azuma’s Inequality when the conditions hold with high probability?
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In Azuma's Inequality, is the statement true when $|X_k - X_{k-1}| < c_k$ almost surely rather than with probability 1? If not, is there anoth... | {"extraction_info": {"found_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/31754/quadripolar-moment-in-curved-space | # quadripolar moment in curved space
So, i'm going over the Thorne's derivation of the quadrupolar radiation term, and they write the core term as:
$$\frac{3 r_i r_j - 2 r^2 \delta_{ij}}{4 r^5}$$
But if i try to obtain this term by Covariant deriving the dipole term;
$$\nabla_{ij}{ \frac{1}{r}} = - \nabla_{j}{ \fra... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?s=ab7cfe3ab27334e5a4b9c6993334df0d&p=3975514 | Physics Forums
## Variable substitution in Langevin equation and Fokker-Planck equation
Dear all,
I have a question about the variable substitution in Langevin equation and Fokker-Planck equation and this has bothered me a lot. The general Langevin equation is:
$$\frac{dx}{dt}=u(x)+\sqrt{2 D(x)}\eta(t)$$
and the corr... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/8518/is-there-something-similar-to-noethers-theorem-for-discrete-symmetries/8519 | # Is there something similar to Noether's theorem for discrete symmetries?
Noether's theorem states that, for every continuous symmetry of a system, there exists a conserved quantity, e.g. energy conservation for time invariance, charge conservation for $U(1)$. Is there any similar statement for discrete symmetries?
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.em/1109106437 | On the Number of Perfect Binary Quadratic Forms
Francesca Aicardi
Source: Experiment. Math. Volume 13, Issue 4 (2004), 451-457.
Abstract
A perfect form is a form {\small $f=mx^2+ny^2+kxy$} with integral coefficients {\small $(m,n,k)$} such that {\small $f(\mathbb{Z}^2)$} is a multiplicative semigroup. The growth rat... | {"extraction_info": {"found_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://mathoverflow.net/questions/26676/incompleteness-and-nonstandard-models-of-arithmetic/27243 | ## Incompleteness and nonstandard models of arithmetic
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The following are a collection of doubts, some of which shall have concrete answers while others may have not. Any kind of help will be welcome.
Reading Pet... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2009/02/24/kernels-of-polynomials-of-transformations/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## Kernels of Polynomials of Transformations
When we considered the representation theory of the algebra of polynomials, we saw that all it takes to specify such a representation is choosing a single endomorphism $T:V\rightarrow V$. That is, once we pick a transformation $T$ we get 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": 0, "wp_latex": 17, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2009/11/04/parallelepipeds-and-volumes-iii/?like=1&source=post_flair&_wpnonce=8cb43e0c56 | # The Unapologetic Mathematician
## Parallelepipeds and Volumes III
So, why bother with this orientation stuff, anyway? We’ve got an inner product on spaces of antisymmetric tensors, and that should give us a concept of length. Why can’t we just calculate the size of a parallelepiped by sticking it into this bilinear... | {"extraction_info": {"found_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": 28, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/11/09/ | # The Unapologetic Mathematician
## Topologies as Categories
Okay, so we’ve defined a topology on a set $X$. But we also love categories, so we want to see this in terms of categories. And, indeed, every topology is a category!
First, remember that the collection of subsets of $X$, like the collection of subobjects ... | {"extraction_info": {"found_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": 14, "mimetex.cgi": 0, "/images/ma... |
http://www.timgittos.com/learning/mit-single-variable-calculus/week-1/ | # MIT OCW Single Variable Calculus - Week 1
### Differentiation
#### What is a derivative?
Geometric interpretation
Consider the problem of finding the tangent line to some function $$y=f(x)$$ at $$P=(x_0,y_0)$$:
The tangent line has an equation of the form $$y – y_0 = m(x – x_0)$$, where m is the slope or gradien... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 97, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/new-users/212618-using-sine-cosine.html | # Thread:
1. ## using sine and cosine
A scalene Triangle With a Side A 12m Long Side B 5m long and one angle which is opposite length A at 2.1 rad
help with knowing the rest of the angles in degrees and also the other side please
2. ## Re: using sine and cosine
Use the sine rule to find angle B.
Use the fact 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": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.mathplanet.com/education/pre-algebra/discover-fractions-and-factors/factorization-and-prime-numbers | # Factorization and prime numbers
A factor is a number that is divisible by another number and where the quotient is an integer.
Example
$\\ \frac{18}{2}=9\Rightarrow factor\\\\\\ \frac{18}{4}=4.5\Rightarrow not\: a\: factor \\$
2 is a factor of 18 because the answer is an integer (9). 4 is not a factor of 18 becau... | {"extraction_info": {"found_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/mat... |
http://terrytao.wordpress.com/category/mathematics/mathgn/page/2/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Category Archive
You are currently browsing the category archive for the ‘math.GN’ category.
## Covering a non-closed interval by disjoint closed intervals
4 October, 2010 in 245A ... | {"extraction_info": {"found_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": 250, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/23034/question-with-einstein-notation | # Question with Einstein notation
Let’s consider this equation for a scalar quantity $f$ as a function of a 3D vector $a$ as:
$$f(\vec a) = S_{ijkk} a_i a_j$$
where $S$ is a tensor of rank 4. Now, I’m not sure what to make of the index $k$ in the expression, as it doesn’t appear on the left-hand side. Is it a typo, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/248/list | ## Return to Answer
3 added 13 characters in body
1. Well, there are stupid examples like the fact that P^n $\mathbb{P}^n$ has Kähler structures where any rational multiple of the hyperplane class is the Kähler class which are compatible with the standard complex structure (you just rescale the symplectic structure an... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/81296/every-equalizer-is-monic | # Every equalizer is monic
Theorem I of section 3.10 of Goldblatt's Topoi states that every equalizer is monic. I don't understand the proof given. For reference, it is:
Suppose $i : e \rightarrow a$ equalizes $f,g : a \rightarrow b$. Suppose $i \circ j = i \circ l$ where $j,l : c \rightarrow e$. Since $$f \circ (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": 25, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.chegg.com/homework-help/questions-and-answers/identical-balls-mass-42-g-suspended-threads-length-116-m-carry-equal-charges-shown-figure--q1368628 | home / homework help / questions and answers / science / physics / two identical balls of mass...
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## Hanging Charges
Two identical balls of mass 4.2 g are suspended from threads of length 1.16 m and carry equal charges as shown in the figure. Each ball is 1.10 cm from the centerline.
1) Assume that the angle $... | {"extraction_info": {"found_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": 1, "/images/mat... |
http://quant.stackexchange.com/questions/96/what-is-a-coherent-risk-measure/2045 | What is a “coherent” risk measure?
What is a coherent risk measure, and why do we care? Can you give a simple example of a coherent risk measure as opposed to a non-coherent one, and the problems that a coherent measure addresses in portfolio choice?
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4 Answers
I'm just providing a global answer to the question, 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Fermi_level | # Fermi level
Not to be confused with Fermi energy.
In the context of solid state physics, the total chemical potential for electrons (or electrochemical potential) is known as the Fermi level, usually denoted by µ or EF. Identical in meaning to the electrochemical potential, the Fermi level of a body is the thermody... | {"extraction_info": {"found_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": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/111982/intuitive-interpretation-of-these-differential-forms | # Intuitive interpretation of these differential forms
Let $\pi: S^2-\{N\}\to \mathbb R^2$ be the stereographic projection map.
Let $\sigma:\mathbb R^2\to S^2-\{N\}$ be its inverse.
Let $p\in S^2-\{N\}$ and $x_1,x_2\in$ the tangent space of $S^2$
Would someone be nice enough to explain to me then what the following... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "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/38210/interpretation-of-field-operator | Interpretation of field operator
Consider a real scalar field operator $\varphi$. It can be written in terms of creation and anihilation operators as $$\varphi(\textbf{x})=\int \tilde{dk}[ a(k)e^{i\textbf{kx}}+a(k)^{\dagger}e^{-i\textbf{kx}}]$$ where $\tilde{dk}$ is a Lorenz-invariant measure. If $\varphi$ is interpre... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/173941-order-topology-vs-standard-one-print.html | # Order Topology vs. the standard one?
Printable View
• March 9th 2011, 01:32 AM
aharonidan
Order Topology vs. the standard one?
on $R^2$ we define an order topology (lexicographic order) as follow: $(x1,y1)>(x2,y2)$ if $x1>x2$ or ( $x1=x2$ & $y1>y2$).
Is this topology equivalent to the standard topology? if not, whi... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/47547/why-do-many-people-say-vector-fields-describe-spin-1-particle-but-omit-the-spin/47550 | # Why do many people say vector fields describe spin-1 particle but omit the spin-0 part?
We know a vector field is a $(\frac{1}{2},\frac{1}{2})$ representation of Lorentz group, which should describe both spin-1 and spin-0 particles. However many of the articles(mostly lecture notes) I've read, when they talk about 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": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/10/23/group-representations/?like=1&_wpnonce=401286028f | # The Unapologetic Mathematician
## Group Representations
We’ve now got the general linear group $\mathrm{GL}(V)$ of all invertible linear maps from a vector space $V$ to itself. Incidentally this lives inside the endomorphism algebra $\hom_\mathbf{Vect}(V,V)$ of all linear transformations from $V$ to itself. In fact... | {"extraction_info": {"found_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": 23, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/93166-solved-basic-math-taken-next-level.html | # Thread:
1. ## [SOLVED] Basic math taken to a next level...
Hello everyone!
During my revision for my June exams (first year engineering) I came across this problem:
$<br /> <br /> \frac{2\sqrt{2} + 2 \sqrt{6}}{\sqrt{2+\sqrt{3}}}<br /> <br />$
Simple math as it seems it kept me busy for 5 hours and stil no result... | {"extraction_info": {"found_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/mat... |
http://mathematica.stackexchange.com/questions/20594/can-mathematica-resolve-this-equation/20599 | # Can mathematica resolve this equation?
Obviously，the equation $x^2-3 y^2=2 z^2$ doesn't have positive integer solutions.
I tried
````Exists[{x, y, z}, x > 0 && y > 0 && z > 0 && x^2 - 3 y^2 == 2 z^2]
Resolve[%, Integers]
````
and
````Exists[{x, y, z}, Element[{x, y, z}, Integers],
x > 0 && y > 0 && z > 0 && x^... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/fourier-series/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘Fourier series’ tag.
## 245C, Notes 2: The Fourier transform
6 April, 2009 in 245C - Real analysis, math.CA, math.GR... | {"extraction_info": {"found_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": 36, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/80175/proofs-from-the-book-bertrands-postulate-part-3-frac23np-leq-n-right | # Proofs from the BOOK: Bertrand's postulate Part 3: $\frac{2}{3}n<p \leq n \rightarrow$ no p divides $\binom{2n}{n}$
I have a very hard proof from "Proofs from the BOOK". It's the section about Bertrand's postulate, page 9:
I have to show, that for $\frac{2}{3}n<p \leq n$ there is no p which divides $\binom{2n}{n}$.... | {"extraction_info": {"found_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": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/38649/what-is-the-curvature-scalar-psi-4?answertab=active | # What is the curvature scalar $\Psi_{4}$?
What is the curvature scalar $\Psi_{4}$?
Is it related to the scalar curvature $R$?
What does its real and imaginary parts represent?
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## 1 Answer
It's one of the Weyl curvature scalars or coefficients, see the first page of http://arxiv.org/abs/1105.0781 - They're some... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.aps.org/articles/v2/89 | # Viewpoint: Slipping through blood flow
, , and , Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Published October 26, 2009 | Physics 2, 89 (2009) | DOI: 10.1103/Physics.2.89
Simulations provide insight into how viscous flow transforms the shapes of red blood c... | {"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/mat... |
http://physics.stackexchange.com/questions/23782/boundary-conditions-of-navier-cauchy-equation | # Boundary conditions of Navier-Cauchy equation
I'm having difficulties with Neumann boundary conditions in Navier-Cauchy equations (a.k.a. the elastostatic equations). The trouble is that if I rotate a body then Neumann boundary condition should be satisfied with zero force.
In math language: if deformation is given... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/55216/what-formulas-should-i-use-to-realistically-model-the-diffusion-of-a-drop-of-ink | # What formulas should I use to realistically model the diffusion of a drop of ink in a water?
I am a mathematician and am originally from the math side of stackexchange. I want to model the behaviour of a drop of ink diffusing in water. I dont want to simply use the diffusion equation $u_t(\mathbf{x},t)=D \triangledo... | {"extraction_info": {"found_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://math.stackexchange.com/questions/193605/what-is-the-probability-of-rolling-a-1-on-the-catenative-doomsday-dice-cascader | # What is the probability of rolling a 1 on the Catenative Doomsday Dice Cascader?
As seen here. Assume that each cascader bubble begins with a d6, as opposed to being determined by the prime bubble along with the number of cascader bubbles; the scene makes it ambiguous.
$\frac{1}{36} = 0.02777...$ provides a simple ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "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/119012/mod-3-moore-spectrum | ## Mod 3 Moore spectrum
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I only know through stories that mod 3 moore spectrum is not associative. I do not know of any proof. I have been informed that Toda had proved it in the paper "Extended $p^{th}$ power". 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": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://antimeta.wordpress.com/2007/12/01/foundations-of-category-theory/ | # Antimeta
A general distrust of strong metaphysical claims in mathematics and philosophy.
## Foundations of Category Theory
1 12 2007
Yesterday, Solomon Feferman from Stanford was up at Berkeley to give the logic colloquium, and he had a very interesting discussion of foundations for category theory. I figured I’d... | {"extraction_info": {"found_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": 4, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/96191/operator-theoretical-models-for-k-mathbbz-3 | ## Operator Theoretical Models for $(K(\mathbb{Z}, 3)$
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am looking for a reference concerning operator theoretical Models of $K(\mathbb{Z},3)$. Stolz-Teichner briefly say in "what is an elliptic object" that 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": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-equations/198274-tough-differential-equation-problem.html | # Thread:
1. ## Tough Differential Equation Problem
I need to find a function F such that it is continuous everywhere and
$y'(t)=F(y(t))$ and $y(0)=0$
The only thing i could think of is $y(t)=e^t$ but that obviously doesnt satisfy the initial value. Any help or hints is greatly appreciated.
2. ## Re: Tough Differe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Wiles'_proof_of_Fermat's_Last_Theorem | # Wiles's proof of Fermat's Last Theorem
(Redirected from Wiles' proof of Fermat's Last Theorem)
Wiles' proof of Fermat's Last Theorem is a proof of the modularity theorem for semistable elliptic curves released by Andrew Wiles, which, together with Ribet's theorem, provides a proof for Fermat's Last Theorem. Wiles f... | {"extraction_info": {"found_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": 19, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/6234/whats-the-value-of-this-vieta-style-product-involving-the-golden-ratio?answertab=oldest | # What's the value of this Vieta-style product involving the golden ratio?
One way of looking at the Vieta product $${2\over\pi} = {\sqrt{2}\over 2}{\sqrt{2+\sqrt{2}}\over 2}{\sqrt{2+\sqrt{2+\sqrt{2}}}\over 2}\dots$$ is as the infinite product of a series of successive 'approximations' to 2, defined by $a_0 = \sqrt{2}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "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/68178/finding-roots-of-polynomials-with-rational-coefficients | # Finding roots of polynomials with rational coefficients
I'm looking for a general approach (or approaches) for finding the roots of polynomials with rational coefficients of higher degrees than $4$. The problem is that I need to find the exact roots and not their approximations. And also I need to find both real 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": 5, "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/82349/uniformization-theorem-via-ricci-flows/82392 | ## uniformization theorem via ricci flows
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi, I have a question about the positive Euler characteristic case. My question is: why is it so difficult as compared to the zero and negative cases? I am more intereste... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/26519-series-solution.html | # Thread:
1. ## series solution...
Find a series solution y(x) of the IVP
y'' -xy' + 5y = 0, y(0) = 0, y'(0) = 1
Show that for the given initial conditions the series terminates and hence the solution reduces to a fifth order polynomial.
I seriously do not have a clue where to start on this problem! Can anyone ple... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/96687-jacobian-matrix-exercise.html | # Thread:
1. ## Jacobian matrix exercise
Hi everyone,
I'm trying to do an exercise about jacobian matrix but I don't really know how to do it can you help me? The exercise says:
$H:R \rightarrow R^3$ is a $C^1$ vectorial field in $R$ and $G:R^2 \rightarrow R^3$ is defined as follow:
$G(x,y) = H(x^2+3y)$
Calculate... | {"extraction_info": {"found_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": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/179879-function-problem.html | # Thread:
1. ## Function problem
hi ! can someone help me with this problem??
2. I see you've written that a proof by contradiction is the way to go. What have you done so far in that direction?
3. erm i know is using prof by contradiction, however i do not know how to apply that in this question!
4. Originally Po... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=661331 | Physics Forums
## Condition of continuity of E field at a boundary
I am trying to understand the derivation of Snell's law using Maxwell's equation and got stuck.
My text book says that "the E field that is tangent to the interface must be continuous" in order to consider refraction of light.
If it were static E fie... | {"extraction_info": {"found_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/61704/complicated-with-the-quotient-topology-mobius-strip-two-distinct-quotients | # Complicated with the quotient topology (Möbius strip) two distinct quotients
Let follow this definition of manifold. An n-manifold is a Hausdorff Topological space, Such That Each point you have an open neighborhood homeomorphic to the open disc $$U^n = \left\{ {x \in R^n :\left| x \right| < 1} \right\}$$
Let 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": 33, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/32189/does-gravity-slow-the-expansion-of-the-universe/32198 | # Does gravity slow the expansion of the universe?
Does gravity slow the expansion of the universe?
I read through the thread http://www.physicsforums.com/showthread.php?t=322633 and I have the same question. I know that the universe is not being stopped by gravity, but is the force of gravity slowing it down in any ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "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/175380/solution-af-a-system-of-2-quadratic-equations?answertab=active | # Solution af a system of 2 quadratic equations
I have a system of two quadratic equations with unknowns $x$ and $y$:
$$a_{1 1} x y + a_{1 2} x^2 + a_{1 3} y^2 + a_{1 4} x + a_{1 5} y + a_{1 6} = 0,\\ a_{2 1} x y + a_{2 2} x^2 + a_{2 3} y^2 + a_{2 4} x + a_{2 5} y + a_{2 6} = 0,$$
where $a_{i j}$ are arbitrary scala... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/159713/solve-y-x-y/159714 | # Solve $y' = x + y$
I am suppose to use the substitution of $u = x + y$
$y' = x + y$
$u(x) = x + y(x)$
I actually forget the trick to this and it doesn't really make much sense to me. I know that I need to get everything in a variable with x I think but I am not sure how to manipulate the problem according to math... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.physicsforums.com/showthread.php?s=3c6e864be97c1387737927bfeafa691c&p=4232261 | Physics Forums
## Mersenne Sieve
Following is a list of 39 Mersenne numbers. Some are prime and some are not. These are generated with x =( 2^n) -1. Many of the largest primes known are Mersenne primes.
I would like to point out that a sieve may be used to block out many non prime Mersenne numbers.
For example for ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/55422/list | ## Return to Answer
4 added 57 characters in body
ADDED: here is a proof of the statement you need (namely the square free monomial ideal $I$ is a intersection of primes generated by subsets of parameters) without using the modularity property. We will use induction on $N=$ the total numbers of times the parameters 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": 117, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathhelpforum.com/statistics/76970-poker-type-question.html | # Thread:
1. ## a poker-type question
A standard 52 card deck is shuffled and you and your opponent are dealt two 'hole' cards each. now the next three cards from the deck are exposed (the flop) and it contains two of the deck's four aces.
Does the fact that two aces were exposed make it less likely, more likely, or... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/higgs-field | # Tagged Questions
The higgs-field tag has no wiki summary.
0answers
55 views
### Higgs boson/field symmetries and local symmetries
In the SM with gauge group U(1)xSU(2)xSU(3), those factors are associated to the gauge bosons associated with a local symmetry and the Higgs field provides masses to the elementary fer... | {"extraction_info": {"found_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://mathhelpforum.com/geometry/177613-how-find-largest-square-inside-triangle-print.html | # How to find the largest square inside a triangle?
Printable View
• April 11th 2011, 10:12 PM
Medusa
How to find the largest square inside a triangle?
I am wondering how you would go about to find the largest square that would fit inside a triangle?
An example of what i am asking is:
What is the side length of 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/216471/show-that-there-exists-a-bijection-from-abc-into-ab-times-c?answertab=active | # Show that there exists a bijection from $(A^B)^C$ into $A^{B \times C}$
Notation: Let A and B be sets. The set of all functions $f:A \rightarrow B$ is denoted by $B^A$.
Problem: Let A, B, and C be sets. Show that there exists a bijection from $(A^B)^C$ into $A^{B \times C}$. You should first construct a function 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": 38, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/102504/help-with-tensor-product-of-two-bit-operators-in-quantum-computing | # Help with tensor product of two bit operators (in quantum-computing)
I'm having trouble understanding how to put together two one-bit operators to get a two-bit operator. For example, suppose I have two electrons in the spin state:
$$\frac{1}{\sqrt{2}}(|\text{up},\text{up}\rangle+|\text{down},\text{down}\rangle)$$
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "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/160631-stuck-proof-induction.html | # Thread:
1. ## Stuck on proof by induction
Hello,
I start to solve this, but got stacked. Have no idea how to move on
Anybody help me ?
Code:
```5+8+11+…+ (3n+2) = 1/2n(3n+7)
n=1
5+8+11+…+ (3*1+2) = 1/2 *1 (3*1+7) => 5=5
n=k
5+8+11+…+ (3k+2) = 1/2 k(3k+7)
n=k+1
5+8+11+…+ (3(k+1)+2) = 1/2(k+1) (3(k+1)+7)
5+8+11... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/6023/is-it-safe-to-use-rsa-as-a-proof-of-work-system/6024 | # Is it safe to use RSA as a proof-of-work system?
Suppose I devised the following challenge-response proof-of-work system:
A server generates a 2048-bit RSA modulus, and uses the "public" exponent (usually 65537) to sign a random nonce a fixed number of times, say, 256.
The server then sends the signed nonce to 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": 70, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/6810/seifert-surfaces-of-torus-knots/6815 | ## Seifert surfaces of torus knots
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Does anyone know a nice description of a Seifert surface of a torus knot? I can construct such surfaces in band projection, but what I get is ugly and unwieldy. Is there some el... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Hodge_conjecture | # Hodge conjecture
The Hodge conjecture is a major unsolved problem in algebraic geometry which relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety. More specifically, the conjecture says that certain de Rham cohomology classes are algebraic, that is, they ar... | {"extraction_info": {"found_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": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/121205/periodicity-of-a-specific-non-linear-ode-of-second-order | ## Periodicity of a specific non-linear ODE of second order
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Consider the second-order ODE: $$\ddot{x} + x+x^2=0,$$ here $\ddot{x}$ is the second derivative w.r.t. $t$. Take initial values $x(0)=0.5$ and $\dot{x}(... | {"extraction_info": {"found_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://mathoverflow.net/revisions/70399/list | ## Return to Answer
3 added proof that the probabilities form a dense set
EDIT to add some details:Given a universal TM $M$ with tape alphabet $A$, and given a subinterval of $[0,1]$, choose an integer $n$ so large that your given interval includes one of the form $[k/|A|^n,(k+1)/|A|^n]$. Let $S$ be a set of $k$ word... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "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/194585/integration-of-int-sqrtx-sqrt2x-dx-and-int-3x-ex-dx?answertab=oldest | # Integration of $\int \sqrt{x\sqrt{2x}} dx$ and $\int 3^x e^x dx$
I try to evaluate this two integrals, but I don't know how to proceed:
i) $\int \sqrt{x\sqrt{2x}} dx = \int {2^{\frac{1}{4}}\cdot x^{\frac{3}{4}}}$
ii) $\int 3^x e^x dx$
What's the best way to evaluate them? Substitution or Intergration by parts?
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": 9, "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/48085/not-universal-operator-and-computational-basis/48087 | # NOT Universal Operator and Computational basis
This is the relationship between density operator and Bloch vector: $$\rho= \frac{1}{2}({\bf{\hat{1}}}+{\bf{b}}.\boldsymbol{\hat{\sigma}})$$
We define the NOT Universal Operator in the following way:
$$U: {\bf{b}}\to -{\bf{b}}/3$$
My question is - How does NOT Univer... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/string?sort=votes&pagesize=15 | # Tagged Questions
This tag is for non-relativistic material strings, such as, e.g., a guitar string. PLEASE DO NOT USE THIS TAG for relativistic strings and string theory.
5answers
1k views
### Why Won't a Tight Cable Ever Be Fully Straight?
I posted this picture of someone on a zipline on Facebook. One of my frie... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/56572/homogeneous-system-of-polynomial-equations/56976 | ## Homogeneous system of polynomial equations
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi all,
Previously I asked a question that currently has no satisfactory answer http://mathoverflow.net/questions/55939/least-sum-squares-given-constraints-on-subcom... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/7060/solution | ### Weekly Challenge 43: A Close Match
Can you massage the parameters of these curves to make them match as closely as possible?
### Weekly Challenge 44: Prime Counter
A weekly challenge concerning prime numbers.
### Weekly Challenge 28: the Right Volume
Can you rotate a curve to make a volume of 1?
# Weekly Chal... | {"extraction_info": {"found_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://mathoverflow.net/questions/62889?sort=newest | ## Question on PDE
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am looking for a reference where the following situation or something similar could have been studied. As a foreword, my question may not be very technical since I am from an engineering back... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/2604/what-do-we-get-from-having-higher-generations-of-particles/3201 | # What Do We Get From Having Higher Generations of Particles?
Background: I have written a pop-science book explaining quantum mechanics through imaginary conversations with my dog-- the dog serves as a sort of reader surrogate, popping in occasionally to ask questions that a non-scientist might ask-- and I am now wor... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/179762-logarithm-question.html | # Thread:
1. ## Logarithm question
If the sum is 2^x = 8, how do I work out x?
When I use my calculator, I press 'log', then 2 and then in brackets (8), so it looks like this "log2(8)". Why do I get the answer of 2.4082399.....
2. Originally Posted by yorkey
If the sum is 2^x = 8, how do I work out x?
When I use m... | {"extraction_info": {"found_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/calculus/79769-solving-differential-equations-using-change-variable.html | Thread:
1. Solving differential equations using a change of variable
My book is telling me
d/du((e^u)dy/dx)
=(e^u)dy/dx + (e^u)(d2y/dx2).(dx/du)
I understand where the first part has come from, but not sure how the second part was derived. Would anyone kindly provide me with an explanation?
2. Erghhhhhhh....:p
O... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/2572/how-can-we-find-public-key-have-only-8-or-16bits-how-many-messages-does-eve-nee/2573 | # How can we find Public key have only 8 or 16bits? How many messages does Eve need to know the Public key in RSA?
Suppose Alice sends messages to Bob by encrypting the messages with Bob's public key.
Eve knows that the data is encrypted using RSA, but does not know the public key. Can Eve figure out the public key j... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/21781?sort=newest | ## Oriention-Reversing Diffeomorphisms of a Manifold
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am trying to figure out when a closed, oriented manifold admits an orientation reversing diffeomorphism. My naive argument that the orientation cover should ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 35, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/203330-query-about-implementing-linear-discriminant-analysis.html | # Thread:
1. ## Query about implementing Linear Discriminant Analysis
Hi, I am trying to implement LDA on some fMRI data. Trying to do it myself rather that using a package as I'd like to understand whats going on under the bonnet as it were.
I have obtained a weight vector, $\mathbf{w}$, according to the formula
$... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/2853-induction-proof-print.html | # Induction Proof
Printable View
• May 6th 2006, 08:51 PM
AfterShock
Induction Proof
Here is the problem:
"Let S_n stand for the sum of all the products of the integers, taken two at a time, from 1 to n. For example, S_4 means:
S_4 = 1*2 + 1*3 + 1*4 + 2*3 + 2*4 + 3*4
Prove that S_n is given explicitly by:
S_n = [... | {"extraction_info": {"found_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://quantumweird.wordpress.com/category/quantum-mechanics/ | Explanation of the (formanlly) Weird Quantum World
# Category Archives: Quantum mechanics
## Thought Experiment – Photons up Close
Posted on January 3, 2008
Recently I published a paper on radio frequency photons: Thought Experiment- Photons at Radio Frequencies in which I described a photon from the time of emiss... | {"extraction_info": {"found_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": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/23071/find-the-net-force-the-southern-hemisphere-of-a-uniformly-charged-sphere-exerts?answertab=oldest | # “Find the net force the southern hemisphere of a uniformly charged sphere exerts on the northern hemisphere”
This is Griffiths, Introduction to Electrodynamics, 2.43, if you have the book.
The problem states Find the net force that the southern hemisphere of a uniformly charged sphere exerts on the northern hemisph... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/121731-maximum-distance-normal-center.html | Thread:
1. Maximum distance of normal from the center
Normal is drawn at a variable point 'P' of an ellipse $<br /> \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1<br />$
Find the maximum distance of the normal from the centre of the ellipse
2. 1) The question makes no sense. If a = b, all the Normals, extended both direction... | {"extraction_info": {"found_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/mat... |
http://mathoverflow.net/questions/117401?sort=oldest | ## Is every functor inducing a homotopy equivalence a composition of adjoint functors?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
It was asked here whether every functor is a composition of adjoint functors. The answer is no, because all adjoint functors ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/18902/intuitive-explanation-of-nakayamas-lemma?answertab=votes | # Intuitive explanation of Nakayama's Lemma
Nakayama's lemma states that given a finitely generated $A$-module $M$, and $J(A)$ the Jacobson radical of $A$, with $I\subseteq J(A)$ some ideal, then if $IM=M$, we have $M=0$.
I've read the proof, and while being relatively simple, it doesn't give much insight on why 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": 44, "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/70710?sort=newest | ## Continuous Measurement in Quantum Mechanics
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Let $\mathcal{P}(S^{\infty})$ denote the set of probability measures on the unit sphere $S^{\infty} \subset \mathcal{H}$ in the Hilbert space of states of a quantum ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/208259-trigonometric-hyperbolic-identities.html | # Thread:
1. ## Trigonometric and Hyperbolic identities
Question is as follows:-
Hence solve for t for values in the range 0 ≤ t ≤ 2 π rad:
5.5 Cos t + 7.8 Sin t = 4.5
Any help would be greatful, thanks
2. ## Re: Trigonometric and Hyperbolic identities
Originally Posted by boza100
Question is as follows:-
Hence ... | {"extraction_info": {"found_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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/94012/sum-of-reciprocal-prime-numbers?answertab=active | # Sum of reciprocal prime numbers
How can the following equation be proven?
$$\forall n > 2 : \sum_{p \le n}{\frac1{p}} = C + \ln\ln n + O\left(\frac1{\ln n}\right),$$ where $p$ is a prime number.
It's not homework; I just don't understand from where should I start.
-
## 2 Answers
Apostol gives a proof of this in... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=119052 | Physics Forums
## Is it intuitive that the Energy levels...
For a 1D infinite well, The energy levels of an electron trapped inside is dependent on the length of the well. The longer the length, the less its energy will be for each state.
I am aware how the formula is derived. The main form of the formula is a solut... | {"extraction_info": {"found_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... |
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