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http://mathoverflow.net/questions/66812?sort=votes | ## Ramanujan’s eccentric Integral formula
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The wikipedia page on Srinivasa Ramanujan gives a very strange formula:
Ramanujan: If $0 < a < b + \frac{1}{2}$ then, $$\int\limits_{0}^{\infty} \frac{ 1 + x^{2}/(b+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": 31, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/34110/algebraic-geometry-examples/34179 | ## Algebraic geometry examples
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What are some surprising or memorable examples in algebraic geometry, suitable for a course I'll be teaching on chapters 1-2 of Hartshorne (varieties, introductory schemes)?
I'd 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": 221, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathforum.org/mathimages/index.php?title=Blue_Wash&redirect=no | # Blue Wash
### From Math Images
Blue Wash
Field: Fractals
Image Created By: Paul Cockshott
Website: Fractal Art
Blue Wash
This image is a random fractal that is created by continually dividing a rectangle into two parts and adjusting the brightness of each resulting part.
# Basic Description
This image is consid... | {"extraction_info": {"found_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": 15, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/186265/if-kappa-is-a-cardinal-aleph-is-any-aleph-number-and-if-kappa-leq-a | # If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.
I'm having trouble understanding the statement:
If $\kappa$ is a cardinal, $\aleph$ is any $\aleph$-number, and if $\kappa\leq\aleph$ then $\kappa$ can be well ordered as well.
I underst... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "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/120694/how-are-modal-logic-and-graph-theory-related/120710 | ## How are Modal Logic and Graph Theory related?
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I am currently taking a graduate logic course on Modal Logic and I can't help notice that there are a certain class of graphs characterized by the modal axioms suc... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/65082/list | ## Return to Answer
2 added remarks
I don't know whether this is useful in practice, but the straightforward generalization of your 0-connectedness criterion to a 1-connectedness criterion goes as follows.
Any 1-cycle of the form $[(a_0, a_1), (a_1, a_2), \ldots, (a_k, a_0)]$ can be transformed into the trivial (emp... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 57, "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/259805/how-does-this-textbook-go-from-this-step-to-the-next-im-very-confused | # How does this textbook go from this step to the next? I'm very confused.
Here's a picture detailing the question:
In the second half of the picture where it says
$$1 = 4 - 1 \cdot (11 - 2 \cdot 4)\\ 1 = 3 \cdot 4 - 1 \cdot 11$$
How did they jump from that first equation to the next? Where'd the $3$ come from?
-
... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/47969/einsteins-equations-as-a-dirichlet-boundary-problem | # Einstein's equations as a Dirichlet boundary problem
Can Einstein's equations in vacuum $R_{ab} - \frac{1}{2}Rg_{ab} + \Lambda g_{ab}= 0$ be treated as a Dirichlet problem?
I am thinking of something along those lines: Consider a compact manifold $M$ with boundary $\partial M$. For a given metric $g_{ab}$ on $\part... | {"extraction_info": {"found_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://lukepalmer.wordpress.com/ | # Luke Palmer
Functional programming and mathematical philosophy with musical interludes
# Polyamory and Respect
I have been in an open, polyamorous relationship with my partner Amanda for about a year and a half. The relationship began as open for somewhat coincidental reasons, but over its course, I have developed... | {"extraction_info": {"found_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": 59, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/140854-chord-length-circle-inscribed-rectangle.html | Thread:
1. Chord length of a circle inscribed in a rectangle
The picture is of a rectangle whose base is greater than its height. A circle is drawn in the rectangle, which is tangent to the top, left, and bottom edges. the diagonal from the bottom left corner to the top right corner meets the circle in points E and 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": 0, "codecogs_latex": 33, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/79850/software-for-computing-baker-campbell-hausdorff/79911 | ## Software for Computing Baker-Campbell-Hausdorff
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Does anyone have a recommendation for software which can efficiently calculate the Baker-Campbell-Hausdorff series in classical Lie algebras?
Right now, I have ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/60341?sort=oldest | ## applications of the sphere theorem
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I am looking for interesting applications of the 1/4-pinched sphere theorem. The theorem says: A compact, simply connected riemannian manifold whose sectional curvature K sat... | {"extraction_info": {"found_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/56078?sort=newest | ## Geometric interpretation of $BN$-pairs
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My question is relative to a geometric interpretation of the $BN$-pairs that arise in Tits' theory of buildings. Here is a definition that comes from an article by G. Str... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "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/24139-work-pump-empty-tank-full-work-lift-full-tank.html | # Thread:
1. ## Work to pump an empty tank full = Work to lift the full tank
The center of a spherical tank of radius R is at a distance H > R above the ground. A liquid of weight density p is at ground level. Show that the work required to pump the initially empty tank full of this liquid is the same as that to lift... | {"extraction_info": {"found_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://math.stackexchange.com/questions/111440/examples-of-apparent-patterns-that-eventually-fail/111452 | # Examples of apparent patterns that eventually fail
Often, when I try to describe mathematics to the layman, I find myself struggling to convince them of the importance and consequence of 'proof'. I receive responses like: "surely if the Collatz Conjecture is true up to $20 \times 2^{58}$, then it must always be true... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 173, "mathjax_display_tex": 21, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://physics.stackexchange.com/questions/46228/averaging-decibels | # Averaging decibels
Wikipedia:
The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level.
If I measure some physical quantity in decibels, then what is the preferred way to calculate the mean of the measured... | {"extraction_info": {"found_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/27186/is-there-a-majorana-like-representation-for-singlet-states/27188 | # Is there a Majorana-like representation for singlet states?
I mean the Majorana representation of symmetric states, i.e., states of $n$ qubits invariant under a permutation of the qudits. See, for example, D. Markham, "Entanglement and symmetry in permutation symmetric states", arXiv:1001.0343v2.
By Majorana repres... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?s=c6726230d0bb7c500dde31e04d1c04ea&p=4277220 | Physics Forums
## Best way to solve Schrodinger's wave equation numerically.
I have been trying to research the best way to solve the Schrodinger wave equation numerically so that I can plot and animate it in Maple. I'd also like to animate as it is affected by a potential. I have been trying for weeks to do this 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": 2, "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/1?e=baranoff-ch03_s02 | # Risk Management for Enterprises and Individuals, v. 1.0
by Etti Baranoff, Patrick L. Brockett, and Yehuda Kahane
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 product that lets you ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 11, "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/ma... |
http://mathoverflow.net/revisions/36992/list | ## Return to Answer
4 deleted 25 characters in body
Just a quick thought about showing that $3^n\alpha_n$ is integral. It's not too hard to prove via the Catalan number generating function that `\[\sum_{k=0}^{p-1} C_kx^k\equiv \frac{1-(1-4x)^{(p+1)/2}}{2x}-x^{p-1}\quad\bmod (p,x^p).\]` Now apply $D=x\frac{d}{dx}$ a b... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/208923-lipschitz-continuous.html | # Thread:
1. ## Lipschitz continuous
This question is about lipschitz continuous, i think the way to check if the solutions can be found as fixed points is just differentiating f(t), but i'm not sure about this. Can anyone give me some hints please? I will really appreciate if you can give me some small hints.
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 39, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=204051 | Physics Forums
## Magnetisation due to conduction electrons
1. The problem statement, all variables and given/known data
Due to its spin, the electron possesses a magnetic moment μB.
Treating the conduction electrons in a metal as a free electron gas, obtain an expression for the magnetization due to the magnetic 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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/96078/are-semi-direct-products-categorical-limits | ## Are semi-direct products categorical limits?
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Products, are very elementary forms of categorical limits. My question is whether in the category of groups, semi-direct products are categorical limits.
As was 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": 78, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=2586394 | Physics Forums
Is curvature guaranteed if only one connection coefficient is 'large'
A (3-d or higher) metric which is flat except for one non-trivial metric function of a different coordinate - eg changing dx2 to f(y)dx2 in Euclidean or Minkowski metric [but not f(x)dx2] - is curved if f(y) has a non-zero second der... | {"extraction_info": {"found_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": 38, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/128239-sine-cosine.html | # Thread:
1. ## Sine and Cosine
Not sure what this question is asking me, when their is no numbers to calculate, can someone please explain this to me
If Cos(x)=m then what is the value of Cos (180-x)?
Thanks
2. $\cos(a-b) = \cos a \cos b + \sin a \sin b$
3. It's a trigonometric identity.
cos(180 - x) is always ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/83628/list | ## Return to Question
Post Closed as "too localized" by Felipe Voloch, Dror Speiser, fedja, Igor Rivin, Emil Jeřábek
3 \$
"On a Diophantine Equation" paper of Erdös, at some point it is said that it is well known that $C(n,2)=x^2$ has infinitely many integer solutions. I am just wondering the formula generating all ... | {"extraction_info": {"found_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/calculus/47135-chapter-one-calculus-question.html | # Thread:
1. ## Chapter One Calculus Question
This is due monday...
The entirety of information I have is as follows:
lim 6=
x-->3
That's it. No instructions. There's about six of these. How am I supposed to handle them?
2. Originally Posted by Oscar201
This is due monday...
The entirety of information I have 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": 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/Rotation_matrix | # Rotation matrix
In linear algebra, a rotation matrix is a matrix that is used to perform a rotation in Euclidean space. For example the matrix
$R = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \\ \end{bmatrix}$
rotates points in the xy-Cartesian plane counter-clockwise through an angle θ... | {"extraction_info": {"found_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": 124, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/204277-implicit-differentiation.html | # Thread:
1. ## Implicit Differentiation
I've tried differentiating this over again, and took me a while to get it. but Im not sure, my answer were (1/3, 4/3)
heres the question
At what point on the curve xy=(1-x-y)^2 is the tangent line parallel to the x-axis.
Thank you very much
2. ## Re: Implicit Differentiatio... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/2455/what-happens-to-light-after-it-enters-an-eye/2459 | # What happens to light after it enters an eye
What happens to the light [energy] after it enters an eye and hits the rods and cones? I presume the energy becomes electrical, and it must be near 100% perfect, else our eyes would heat up? Or am I missing something?
The motivation of this question is solar panel techno... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://regularize.wordpress.com/category/math/signal-and-image-processing/ | # regularize
Trying to keep track of what I stumble upon
### Signal and image processing
Archived Posts from this Category
August 25, 2012
## ISMP over – non-convex and non-smooth minimization, l^1 and l^p
Posted by Dirk under Conference, Math, Optimization, Signal and image processing, Sparsity | Tags: Basis pur... | {"extraction_info": {"found_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": 340, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/322085/differentiation-of-logarithmic-functions | # Differentiation of logarithmic functions
I'm going over my homework from calc, and am having some trouble with a few questions. It seems as if I'm just not understanding how to solve the problem:
1. $$f(x) = \sqrt[5]{\ln x}$$
2. $$f(x) = \sqrt{x}\ln x$$
3. $$f(x)= \ln \dfrac{({2x+1})^3}{({3x-1})^4}$$
For the fir... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/265801/probability-distribution-of-number-of-times-required-to-roll-all-of-a-certain-se?answertab=votes | # Probability distribution of number of times required to roll all of a certain set of k numbers?
Consider a 12-sided fair die. What is the distribution of the number T of rolls required to roll a 1, a 2, a 3, and a 4?
Taking inspiration from the Coupon Collector's Problem, I believe that the expected number of rolls... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/305559/critiques-on-proof-showing-sqrt12-is-irrational?answertab=active | # Critiques on proof showing $\sqrt{12}$ is irrational.
My only exposure to proofs was in a math logic class I took in University. I was wondering if my attempt at proving that $\sqrt{12}$ is irrational is OK.
$$\Big(\frac{m}{n}\Big)^2 = 12$$ $$\Big(\frac{m}{2n}\Big)^2 = 3$$ $$m^2=3*(2n)^2$$
This implies $m$ is even... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 131, "mathjax_display_tex": 25, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/87919?sort=newest | ## Difficulties with the mod 2 Moore Spectrum
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I have been informed that there is a reference out there which specifically details what goes wrong with the mod 2 Moore spectrum, i.e. why it is not $A_\infty$ or so... | {"extraction_info": {"found_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/differential-equations/170754-second-order-non-homogeneous-differential-equation.html | # Thread:
1. ## Second order non homogeneous differential equation
I have to solve this DE
((x+2)^2)y'' -2y=4
the hint says to get rid of the x+2 but I have no idea where to start from... do I have to replace x+2 with another variable or what?
2. I would replace the $x+2$ with $t=x+2,$ and you get
$\dfrac{dy}{dt}=... | {"extraction_info": {"found_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://math.stackexchange.com/questions/193351/markov-chain-reach-one-state-before-another?answertab=votes | # Markov Chain Reach One State Before Another
I'm stumped on a problem. Here's my transition matrix:
$$P = \begin{bmatrix} \frac{3}{4}&\frac{1}{4}&0&0&0&0&0 \\\\ \frac{1}{2}&\frac{1}{4}&\frac{1}{4}&0&0&0&0 \\\\ \frac{1}{4}&\frac{1}{4}&\frac{1}{4}&\frac{1}{4}&0&0&0 \\\\ \frac{1}{4}&0&\frac{1}{4}&\frac{1}{4}&\frac{1}{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": 29, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/13301/assuming-u-sim-n0-sigma2-when-y-is-highly-skewed | Assuming $u\sim N(0,\sigma^2)$ when y is highly skewed
does it make sense to assume $u\sim N(0,\sigma^2)$ when I know from a histogram that $y$ is highly skewed. Because from the assumption $u\sim N(0,\sigma^2)$ it follows that $y\sim N(x\beta,\sigma^2)$ and I'm absoluteley not sure if the assumption $u\sim N(0,\sigma... | {"extraction_info": {"found_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://mathoverflow.net/questions/42512/awfully-sophisticated-proof-for-simple-facts/42514 | ## Awfully sophisticated proof for simple facts [closed]
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It is sometimes the case that one can produce proofs of simple facts that are of disproportionate sophistication which, however, do not involve any circula... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 194, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/47078/what-is-the-laughlin-argument | # What is the Laughlin argument?
The fundamental question is
Why is Hall conductance quantized?
Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the x-direction, then the y-direction develops a voltage $V_H$. The Hall conductance is $\sigma... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Big_Rip | # Big Rip
The Big Rip is a cosmological hypothesis first published in 2003, about the ultimate fate of the universe, in which the matter of the universe, from stars and galaxies to atoms and subatomic particles, is progressively torn apart by the expansion of the universe at a certain time in the future. According to ... | {"extraction_info": {"found_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": 13, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/262371/how-do-you-solve-the-area-of-a-trapezoid-using-diagonals | # How do you solve the area of a trapezoid using diagonals
The height of a trapezoid is $10$ cm. The lengths of the two diagonals of the trapezoid are $30$ cm and $50$ cm. Calculate the area of the trapezoid.
On the homework I solved this using $${D_1D_2\over 2}$$ and my teacher marked me wrong. So I don't know what ... | {"extraction_info": {"found_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://en.wikibooks.org/wiki/User:Daviddaved/Y-%CE%94_and_star-mesh_transforms | # User:Daviddaved/Y-Δ and star-mesh transforms
From Wikibooks, open books for an open world
Jump to: navigation, search
The effective conductivities and the Dirichlet-to-Neumann operator of a network are invariant under the following star-mesh transform,
Exercise (**). Use the Schur complement formula
$\Lambda = K/... | {"extraction_info": {"found_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://xorshammer.com/2008/08/15/axs-theorem/ | August 15, 2008 · 3:58 am
# Ax’s Theorem: An Application of Logic to Ordinary Mathematics
There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax’s Theorem.
Ax’s Theorem: For all polynomial ... | {"extraction_info": {"found_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": 55, "mimetex.cgi": 0, "/images/ma... |
http://psychology.wikia.com/wiki/First-order_logic?oldid=54339 | # First-order logic
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Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | ... | {"extraction_info": {"found_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": 28, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/2229/if-photons-have-no-mass-how-can-they-have-momentum/30430 | # If photons have no mass, how can they have momentum?
As an explanation of why a large gravitational field (such as a black hole) can bend light, I have heard that light has momentum. This is given as a solution to the problem of only massive objects being affected by gravity. However, momentum is the product of mass... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/6889/what-is-the-difference-between-a-zeta-function-and-an-l-function/112396 | ## What is the difference between a zeta function and an L-function?
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I've been learning about Dedekind zeta functions and some basic L-functions in my introductory algebraic number theory class, and I've been won... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/28245/monomial-distribution-of-xa-cdot-yb/28307 | # Monomial distribution of $X^a \cdot Y^b$
What is the distribution of the following monomial? $$X^a \cdot Y^b$$ where $X$ and $Y$ are normal random variables and $a$ and $b$ are natural numbers.
For example, when $X \sim N(0,1)$, $a=2$, and $b=0$ it is a Chi-squared distribution, which has a variance of 2.
What if ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/50099/list | Return to Answer
1 [made Community Wiki]
This may be a little tangential to the original question, but it avoids Choice, and 'works with all choices at once'. In Makkai's theory of anafunctors, one recognizes that 'the' functor $C^J \to C$ giving a limit of a (small) diagram $J \to C$ is only really defined via unive... | {"extraction_info": {"found_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/revisions/50964/list | ## Return to Answer
2 Corrected grammar, tried to clarify some language.
A position Positions of the car are in 1-1 correspondence with the isometry isometries of the plane that takes take it from its initial parked position to its current a given position. Define a driving metric that is the minimum total number of 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": 24, "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/46502/on-the-number-of-archimedean-solids/61477 | ## On the number of Archimedean solids
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Does anyone know of any good resources for the proof of the number of Archimedean solids (also known as semiregular polyhedra)?
I have seen a couple of algebraic discussion... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php?title=Law_of_cosines&diff=17470&oldid=17466 | # Law of cosines
### From Math Images
(Difference between revisions)
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http://psychology.wikia.com/wiki/Autocorrelation | # Autocorrelation
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Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Statistics: Scientific 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": 20, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2012/09/12/lie-algebra-modules/?like=1&source=post_flair&_wpnonce=d0199d491e | # The Unapologetic Mathematician
## Lie Algebra Modules
It should be little surprise that we’re interested in concrete actions of Lie algebras on vector spaces, like we were for groups. Given a Lie algebra $L$ we define an $L$-module to be a vector space $V$ equipped with a bilinear function $L\times V\to V$ — often ... | {"extraction_info": {"found_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://aimath.org/textbooks/beezer/LTsection.html | Linear Transformations
Early in Chapter VS:Vector Spaces we prefaced the definition of a vector space with the comment that it was "one of the two most important definitions in the entire course." Here comes the other. Any capsule summary of linear algebra would have to describe the subject as the interplay of linear ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 123, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/189612-let-b-b-being-real-numbers-b-1-show-m-b-random-m-print.html | # let a<b with a, b being real numbers and b-a>1. Show that a<m<b for a random m
Printable View
• October 5th 2011, 07:02 AM
juanma101285
let a<b with a, b being real numbers and b-a>1. Show that a<m<b for a random m
Hi, I have the following three problems, but I only want to know what the first one is like... I am 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/59738/the-complex-version-of-nashs-theorem-is-not-true/59771 | ## “The complex version of Nash’s theorem is not true”
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The title quote is from p.221 of the 2010 book, The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions by Shing-Tung Ya... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 112, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.newworldencyclopedia.org/entry/Frequency | # Frequency
From New World Encyclopedia
Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above. The horizontal axis represents time.
Frequency is a measure of the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The per... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/7396/what-all-is-needed-to-solve-for-the-metric-in-gr | # What all is needed to solve for the metric in GR?
Einstein's field equations are:
$R_{ab} - {1 \over 2}g_{ab}\,R + g_{ab} \Lambda = {8 \pi G \over c^4} T_{ab}$
And since the Ricci curvature tensor is "less information" than the Riemann curvature tensor because:
$R_{ab} = R^c{}_{acb}$
and the Riccie curvature sca... | {"extraction_info": {"found_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://math.stackexchange.com/questions/238995/are-all-projection-maps-in-a-categorical-product-epic?answertab=votes | # Are all projection maps in a categorical product epic?
Are all $\Pi A_\alpha \stackrel{\pi_i}\longrightarrow A_\alpha$ projection maps epic, given that $\Pi A_\alpha$ be the product of $A_\alpha$s? Of course, assuming that the product exists.
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## 4 Answers
In an arbitrary category, it suffices to have a zero obj... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=3843428&postcount=17 | View Single Post
The relevant inequality for this problem is $|f_n(x)-f(x)| \leq ||f_n-f||_{\infty}$ for all $x \in [0,1]$. But honestly, based on your threads in the homework help forums, you really lack the mathematical maturity to be dealing with convergence in function spaces. It would be worthwhile for you to go ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/2694/what-is-the-importance-of-the-collatz-conjecture | # What is the importance of the Collatz conjecture?
I have been fascinated by this problem since I first heard about it in high school. From the Wikipedia article http://en.wikipedia.org/wiki/Collatz_problem:
Take any natural number $n$. If $n$ is even, divide it by $2$ to get $n / 2$, if $n$ is odd multiply it by $3... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "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/8227/a-mirror-flips-left-and-right-but-not-up-and-down/8230 | # A mirror flips left and right, but not up and down
Why is it that when you look in the mirror left and right directions appear flipped, but not the up and down?
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2
On which plane are your (2) eyes oriented? – user4577 Jul 21 '11 at 19:00
It COULD flip you upside down, depending on the type of mirror (flat vs conc... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/51915/can-one-raise-indices-on-covariant-derivative-and-products-thereof | # Can one raise indices on covariant derivative and products thereof?
Can the following be true?
1. $g^{\sigma\rho}\nabla_{\rho}\nabla_{\mu} = \nabla^{\sigma}\nabla_{\mu}$
2. $g^{\sigma\rho}\nabla_{\nu}\nabla_{\sigma} = \nabla_{\nu}\nabla^{\rho}$
3. $g^{\sigma\rho}\nabla_{\nu}\nabla_{\mu}T_{\sigma\rho} = \nabla_{\nu}... | {"extraction_info": {"found_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://math.stackexchange.com/questions/35537/metalogic-prove-neg-p-1-to-p-2-vdash-neg-p-2-to-p-1-without-using-t | Metalogic: Prove $\{\neg P_1 \to P_2\} \vdash (\neg P_2\to P_1)$ without using the Deduction Theorem
I want to prove that $$\{\neg P_1\to P_2\} \vdash (\neg P_2\to P_1)$$ without using the Deduction Theorem.
I'm not sure how to proceed. The class notes are all we have to work from, no text to work on similar proofs.
... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/122090-generate-random-matrix-given-condition-number.html | # Thread:
1. ## Generate a random matrix given a condition number
If I am given the condition number , how can i generate a random matrix with that condition number. The matrix can have any number of rows and columns. please help...
2. The "condition number" of a matrix, A, is defined as [tex]||A||||A^{-1}|| For sym... | {"extraction_info": {"found_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://gilkalai.wordpress.com/2009/05/21/extremal-combinatorics-vi-the-frankl-wilson-theorem/?like=1&source=post_flair&_wpnonce=a082172354 | Gil Kalai’s blog
## Extremal Combinatorics VI: The Frankl-Wilson Theorem
Posted on May 21, 2009 by
Rick Wilson
The Frankl-Wilson theorem is a remarkable theorem with many amazing applications. It has several proofs, all based on linear algebra methods (also referred to as dimension arguments). The original 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 108, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/131113/showing-f-1y-is-poincare-dual-to-f-operatornamevol/131196 | Showing $[f^{-1}(y)]$ is Poincare dual to $f^*(\operatorname{vol})$.
Let $f: N^n \to M^m$ be a smooth map between closed oriented manifolds. Then I'm trying to show that for almost all $y \in M$, the homology class $[f^{-1}(y)] \in H_{n-m}(N)$ is Poincare dual to $f^* \operatorname{vol}_M$, where $\operatorname{vol}_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": 24, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/48993-tangent-circle-question.html | # Thread:
1. ## tangent circle question
The radius of the incircle of a triangle is 4 cm and the segments in to which one side is divided by the point of contact are 6cm and 8 cm , determine the other two sides of the triangle.
Oh and yeah, R = 4cm and the other R is the name of the contact point..no relation..PLEASE... | {"extraction_info": {"found_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://mathoverflow.net/questions/67029/extension-theory-with-bump-function/67369 | ## Extension theory with bump function
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Let $B_t(0)$ denote the $n$ dimensional ball of radius $t$ centered at the origin. Does there exist a $\phi\in C(\mathbb{R}^n)$ function with the properties:
$\phi (x) = \b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 65, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://jaswindercbse.nuvvo.com/lesson/11786-probability | # LearnHub
## probability
Author
jaswinder_singh_saini
Probability, or chance, is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 18, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Algebraic_number | Algebraic number
In mathematics, an algebraic number is a number that is a root of a non-zero polynomial in one variable with rational coefficients (or equivalently—by clearing denominators—with integer coefficients). Numbers such as π that are not algebraic are said to be transcendental; almost all real and complex 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": 43, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Problem_of_Apollonius&oldid=10372 | # Problem of Apollonius
### From Math Images
Revision as of 13:35, 4 November 2009 by AnnaP (Talk | contribs)
This an example of a fractal that can be created by repeatedly solving the Problem of Apollonius.
Fields: Geometry and Fractals
Created By: Paul Nylander
# Basic Description
Image by: Wikipedia
The problem ... | {"extraction_info": {"found_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": 91, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3971178 | Physics Forums
## Contravariant and covariant vectors transformations
Hi all,
I am new to General Relativity and I started with General Relativity Course on Youtube posted by Stanford (Leonard Susskind's lectures on GR).
So first thing to understand is transformation of covariant and contravariant vectors. Before 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": 37, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/puzzle+matrix | Tagged Questions
3answers
278 views
How do we solve Eight Queens variation using primes?
Using a $p_n$x $p_n$ matrix, how can we solve the Eight queens puzzle to find a prime in every row and column? ...
2answers
590 views
Tiling a square
I wondered if there was a way to automate the process of finding a way to ti... | {"extraction_info": {"found_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/71155/multiplicative-functions-whose-dirichlet-series-have-essential-singularities/71183 | Multiplicative functions whose Dirichlet series have essential singularities
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What can be said about the partial sums of a complex-valued completely multiplicative function, let's say bounded by 1 in absolute value, 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": 21, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathinsight.org/determinant_linear_transformation | # Math Insight
• Top
• Overview
• 1D
• 2D
• 3D
• In threads
When printing from Firefox, select the SVG renderer in the MathJax contextual menu (right click any math equation) for better printing results
### Determinants and linear transformations
#### Suggested background
A linear transformation $\vc{T}: \R^n \to \... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 148, "mathjax_display_tex": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/32527/measures-of-the-complexity-of-a-metric/32922 | ## Measures of the complexity of a metric
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I am seeking a measure of the "complexity" of a surface $S$, a quantity that reflects how widely the metric varies from spot to spot. I am primarily interested in surface... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://scicomp.stackexchange.com/questions/3275/gram-schmidt-method-to-identify-linearly-dependent-vectors | # Gram-Schmidt method to identify linearly dependent vectors
A method to orthogonalize a set of vectors (vectors of unit length that are mutually orthogonal) is the Gram-Schmidt process: http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process
Note that the the nested for loops imply that the difference is between 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": 37, "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/152082/differentiable-function-of-two-variables/152088 | # Differentiable function of two variables
Find the domain of a function $f(x,y)=\log_xy$. Does $f\in C^1$? (I don't know if this symbol is common - it means that $f$ is at least once differentiable, and its first derivative is continuous).
from basic facts the domain is: $D=\mathbb{R}^2 \setminus \left\{ (x,y) : 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/10/10/first-degree-homogeneous-linear-equations-with-constant-coefficients/?like=1&source=post_flair&_wpnonce=5092e672ce | # The Unapologetic Mathematician
## First-Degree Homogeneous Linear Equations with Constant Coefficients
Now that we solved one differential equation, let’s try a wider class: “first-degree homogeneous linear equations with constant coefficients”. Let’s break this down.
• First-degree: only involves the undetermined... | {"extraction_info": {"found_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": 22, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/70953/show-by-example-that-the-minkowski-sum-of-two-sets-xy-may-be-convex-even-if-n | # Show by example that the Minkowski sum of two sets $X+Y$ may be convex even if neither $X$ nor $Y$ are convex
There were two parts to this question. I proved that the Minkowski sum of two sets $X+Y$ is convex whenever $X$ and $Y$ are convex, but how do I prove this second part? "Show by example that the Minkowski su... | {"extraction_info": {"found_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://www.openwetware.org/wiki/Physics307L_F08:People/Smith/Notebook/7 | # Lab 7: Poisson Statistics
Lab Partner: Kyle Martin
## Preface
The lab manual we have been using for this class, which is last year's lab manual written by Dr. Gold, has a very sparse section for the Poisson Statistics lab. Kyle and I referred to it for the basic premise of the measurements we took and I referred 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": 0, "mathjax_asciimath": 0, "img_math": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/52355/what-do-the-j-and-m-stand-for-in-j-m-rangle-for-angular-momentum-in-quant | # What do the $j$ and $m$ stand for in $|j,m\rangle$ for angular momentum in quantum mechanics?
I'm assuming it is a jth state with m value as total angular momentum?
-
Wikipedia discusses quantization of angular momentum e.g. here and here. – Qmechanic♦ Jan 28 at 1:45
– Chris White Jan 28 at 2:13
## 1 Answer
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": 19, "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/40689?sort=newest | ## What is the angle between two complex vectors?
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Let $x, y\in R^n$ and $x, y$ are nonzero, it is well known $\frac{x^Ty}{\parallel x\parallel_2\parallel y\parallel_2}(\parallel x\parallel_2+\parallel y\parallel_... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 53, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physicspages.com/2011/02/08/harmonic-oscillator-series-solution/ | Notes on topics in science
## Harmonic oscillator – series solution
Required math: calculus
Required physics: harmonic oscillator
Reference: Griffiths, David J. (2005), Introduction to Quantum Mechanics, 2nd Edition; Pearson Education – Sec 2.3.
The complete Schrödinger equation for the harmonic oscillator potenti... | {"extraction_info": {"found_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": 116, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/49734/taking-the-second-derivative-of-a-parametric-curve?answertab=active | # Taking the second derivative of a parametric curve
I understand that for the parametric equations
$$\begin{align*}x&=f(t)\\ y&=g(t)\end{align*}$$
If $F(x)$ is the function with parameter removed then $\displaystyle F'(x) = \frac{\text{d}y}{\text{d}t}\big/\frac{\text{d}x}{\text{d}t}$
But the procedure for taking t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/31504/skeleton-of-a-braided-monoidal-category | ## Skeleton of a braided monoidal category
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Does every (lax) braided monoidal category have a braided monoidal skeleton? That is, I want to define a (lax) braided monoidal structure on a skeleton so that it is bra... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/56482/using-frac1ai-epsilon-pv-frac1a-i-pi-deltaa-in-feynman-integrals | # Using $\frac{1}{A+i\epsilon} = PV\frac{1}{A}-i\pi\delta(A)$ in Feynman Integrals
Are the following operations O.K.? This is related to the Feynman parameter trick.
$$F:= \int_0^1 \mathrm{d}x\int_0^{1-x}\mathrm{d}y \frac{1}{f(x,y)+\mathrm{i}\epsilon}.$$ Now using
$$\frac{1}{A+i\epsilon} = PV\frac{1}{A}-i\pi\delta(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": 13, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/1847/how-can-one-compute-the-greeks-on-vix-futures | # How can one compute the Greeks on VIX Futures
I am guessing the short answer to this question is "use the chain rule and linearity of the derivative," but I am looking for more specific advice on how to compute the derivatives of a VIX futures contract. Roughly speaking, the VIX index represents a rolling weighted p... | {"extraction_info": {"found_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/123131/motivation-behind-the-definition-of-flat-module?answertab=active | Motivation behind the definition of flat module
Can someone explain what is the motivation behind the definition of a flat module? I saw the definition but I don't really know why it is important to work with these structures.
-
Tensor products conserve almost every property you could ask for. Tensors with flat modul... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 66, "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/71885?sort=newest | ## Units in cyclotomic fields
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Let $q$ and $r$ be distinct prime numbers. I noticed (computing a few cases) that $\zeta_{2q} + \zeta_{2q}^{-1} + \zeta_{2r} + \zeta_{2r}^{-1}$ is a unit (in $\mathbb{Z}[\zeta_{2qr}]... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 65, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/35731/what-is-the-estimation-bias-of-the-top-estimate-in-a-list-sorted-by-value | # What is the estimation bias of the top estimate in a list sorted by value?
Let's make the problem as simple as possible. Assume two related random variables, $X_1$ and $X_2$. On the basis of some data we estimate their true means $\mu_{X_1}$ and $\mu_{X_2}$ by sample means $\hat\mu_{X_1}$ and $\hat\mu_{X_2}$. These ... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/6162/list | ## Return to Answer
3 TeXified
It is easier to take the derivative, and consider the volume of the n-1-sphere (i.e., the "surface area" of the boundary of the ball).
Start with the integral of e-x_1^2 $\int_{\mathbb{R}^n} e^{-x_1^2 - ... - x_n^2 over Rn} dx_1 \dots dx_n$. Fubini's theorem lets you decompose this int... | {"extraction_info": {"found_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/52775/help-with-a-derivative | # Help with a derivative
I need to take the derivative of the following function w.r.t. $x$.
(This is the General Beta of the Second Kind density function.)
$$\frac{a}{bB(p,q)}\frac{(x/b)^{ap-1}}{(1+(x/b)^a)^{p+q}}$$
$B(p,q)$ is the beta function.
Don't need the answer per se, but would appreciate some advice on 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": 13, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/36079/unit-of-torque-with-radians/36090 | # Unit of torque with radians?
Usually, the angular frequency $\omega$ is given in $\mathrm{1/s}$. I find it more consistent to give it in $\mathrm{rad/s}$. For the angular momentum $L$ is then given in $\mathrm{rad \cdot kg \cdot m^2 / s}$.
However, the relation for torque $\tau$ says: $$\tau \cdot t = L$$
So the 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": 27, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/1832/solution | ### Fraction and Percentage Card Game
Match the cards of the same value.
# Tiny Nines
##### Stage: 4 Challenge Level:
Good solutions to this were sent in by Chen of The Chinese High School, Singapore, Anders and Sammy of Bentley Park College, Rebecca of Henry Box School and Andrei of School 205, Bucharest, Romania.... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/21028/second-law-of-thermodynamics-why-is-it-only-almost-always-true-that-entropy-i/21036 | # Second law of Thermodynamics: Why is it only “almost” always true that entropy is non-decreasing?
The venerable Wikipedia states the second law of Thermodynamics as such:
````...that the entropy of any closed system not in thermal equilibrium almost always increases.
````
Er, "almost"? Of course I understand 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": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.haskell.org/haskellwiki/index.php?title=User:Michiexile/MATH198/Lecture_9&diff=31624&oldid=31612 | # User:Michiexile/MATH198/Lecture 9
### From HaskellWiki
(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": 40, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.cfd-online.com/W/index.php?title=Heat_transfer&diff=7497&oldid=7496 | [Sponsors]
Home > Wiki > Heat transfer
# Heat transfer
### From CFD-Wiki
(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": 16, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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