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http://math.stackexchange.com/questions/4238/finite-non-abelian-group-with-centre-but-no-outer-automorphism?answertab=active | # Finite non-abelian group with centre but no outer automorphism
The two element group has a centre (of course it does, it's abelian) but no outer automorphisms. I can come up with a (convoluted) countably infinite non-abelian example. Is there a finite one? If so what is the smallest?
Is there a name for this sort 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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cms.math.ca/10.4153/CJM-2011-049-0 | Canadian Mathematical Society
www.cms.math.ca
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| Site map | | | CMS store | |
location: Publications → journals → CJM
Abstract view
# Lifting Quasianalytic Mappings over Invariants
Read article
[PDF... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/57426/are-there-any-non-linear-solutions-of-cauchys-equation-fxyfxfy-with | ## Are there any non-linear solutions of Cauchy’s equation ($f(x+y)=f(x)+f(y)$) without assuming the Axiom of Choice?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be s.t. $f(x+y) = f(x) + f(y), \ \forall x, y$
It ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "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/140254/schwarz-christoffel-complex-mapping | # Schwarz-Christoffel Complex Mapping
Verify that the Schwarz-Christoffel mapping of $\mathbb H$ onto the infinite half strip described by $|\Re(z)|<\frac \pi 2$ and $\Im(z)>0$ is given by the arcsine function.
What does that mean and how do I do it?
Schwarz-Christoffel formula for the half-plane $\mathbb H$ 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": 8, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-math-topics/168556-problems-continuous-dynamical-systems.html | # Thread:
1. ## Problems with Continuous Dynamical Systems
Hi there, I'm new to this but I was wondering if you could help me with my understanding of Dynamical Systems.
I have a continuous dynamical system given by the equations:
dx1/dt = x1(x2-x3)
dx2/dt = x2(x3-x1)
dx3/dt = x3(x1-x3)
Which I need to analyse. 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://programmingpraxis.com/2009/07/21/pollards-p-1-factorization-algorithm/?like=1&source=post_flair&_wpnonce=27cac980df | Programming Praxis
A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer
Pollard’s P-1 Factorization Algorithm
July 21, 2009
Fermat’s little theorem states that for any prime number $p$, and any other number $a$, $a^{p-1} \equiv 1 \pmod{p}$. Rearranging terms, we have $a^{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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 29, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikipedia.org/wiki/D-brane | # D-brane
String theory
Superstring theory
Theory
Concepts
Related topics
Scientists
In string theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Ho... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/136848/fourier-transform-probability-distribution | # Fourier transform probability distribution
Suppose I have 1,000 independent random values with a uniform distribution $[+1, -1]$. Now suppose I take the discrete Fourier transform of this data. What the heck is the probability distribution of the resulting Fourier coefficients?
(I'm guessing it's either uniformly 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": 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/differential-geometry/143127-what-finite-subcover.html | # Thread:
1. ## what is a finite subcover?
I'm trying to write up a proof and getting really stuck on this idea of "finite subcover."
The problem is to prove that given any closed and bounded interval [a,b] in R, any cover of [a,b] with open intervals contains a finite subcover.
I saw a proof by contradiction sketc... | {"extraction_info": {"found_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://math.stackexchange.com/questions/266199/how-do-you-prove-this-set-problem?answertab=active | # how do you prove this set problem?
I'm trying to teach myself set-theory. I have been unable to prove algebraically that:
$(A \cup B) \cap \overline{(A \cap B)} = (A \cap \overline{B}) \cup (\overline{A} \cap B)$
I know it's elementary but I just want to see an example. (The book doesn't provide one.)
Correct me ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 51, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/10.4153/CMB-2011-063-8 | Canadian Mathematical Society
www.cms.math.ca
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| Site map | | | CMS store | |
location: Publications → journals → CMB
Abstract view
# From Matrix to Operator Inequalities
Read article
[PDF: 182KB]
h... | {"extraction_info": {"found_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/22398/direction-of-rotation-of-proton-in-magnetic-field-opposite-to-a-dipole/22402 | # Direction of rotation of proton in magnetic field--opposite to a dipole
Chatroom created by @pcr for discussing this: http://chat.stackexchange.com/rooms/2824/direction-of-rotation-of-proton-in-magnetic-field
Here's a small paradoxical question I was asked a long time ago (and have been asked twice since). I think ... | {"extraction_info": {"found_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://mathoverflow.net/questions/103279/isoperimetry-and-poincare-inequality | ## Isoperimetry and Poincare Inequality
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What are the known relations between isoperimetric and Poincare inequalities on manifolds?
For example, for manifolds with a lower bound on Ricci curvature, the Cheeger-Bu... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/10870?sort=votes | ## Which topological spaces admit a nonstandard metric?
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My question is about the concept of nonstandard metric space that would arise from a use of the nonstandard reals R* in place of the usual R-valued metric.
... | {"extraction_info": {"found_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://math.stackexchange.com/questions/218137/the-necessary-and-sufficient-condition-for-diffeomorphism/218213 | # The necessary and sufficient condition for diffeomorphism
I came to the following proposition:
Let $M$ and $N$ be two smooth manifolds with respective maximal atlases $\mathcal{A}_M,\mathcal{A}_N$. Then a bijection $f:M \rightarrow N$ is a diffeomorphism if and only if the following codition holds:
$$(U,y)\in\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": 46, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Solving_Triangles&diff=23733&oldid=23732 | # Solving Triangles
### From Math Images
(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": 54, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/tags/hash-collision/hot | # Tag Info
## Hot answers tagged hash-collision
40
### Best way to reduce chance of hash collisions: Multiple hashes, or larger hash?
The risk of collision is only theoretical; it will not happen in practice. Time spent worrying about such a risk of collision is time wasted. Consider that even if you have $2^{90}$ ... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/3930/how-to-simulate-cointegrated-prices/3932 | # How to simulate cointegrated prices
Is there any simple way to simulate cointegrated prices?
-
There are some previous questions about correlation rather than cointegration that may be helpful: How to simulate correlated assets for illustrating portfolio diversification? and How to generate a random price series wi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/15277/plotting-a-complicated-vector-field?answertab=active | Plotting a complicated vector field
If we consider the vector $\left ( A \cdot \nabla \right) \: B$, we have in Cartesian coordinates
$$\left ( A \cdot \nabla \right) \: B = \left ( A \cdot \nabla B_x \right ) e_x + \left ( A \cdot \nabla B_y \right ) e_y + \left ( A \cdot \nabla B_z \right ) e_z,$$ which gives in fu... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/04/29/examples-of-convergent-series/?like=1&source=post_flair&_wpnonce=c1ce40f6e1 | # The Unapologetic Mathematician
## Examples of Convergent Series
Today I want to give two examples of convergent series that turn out to be extremely useful for comparisons.
First we have the geometric series whose terms are the sequence $a_n=a_0r^n$ for some constant ratio $r$. The sequence of partial sums is
$\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": 35, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-topics/115097-2d-plane-intersection-point.html | # Thread:
1. ## 2D plane intersection point
Hello all,
i need help with the following question:
Given a 2d plane which has 4 distinct points, C, D, A, B. Points A and B define an infinite line. At time t=0 a player starts moving at a constant velocity from point C to point D, where he arrives at t=1. Determine, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/121645/presumably-simple-laplace-transform-question/121647 | # Presumably Simple Laplace Transform Question
I have a (presumably simple) Laplace Transform problem which I'm having trouble with:
$$\mathcal L\big\{t \sinh(4t)\big\} = ?$$
How would I go about solving this? Would you please show working if possible, or alternatively point me in the right direction regarding how 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": 15, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/1858/is-there-some-way-to-generate-a-non-predictable-random-number-in-a-decentralised/3383 | Is there some way to generate a non-predictable random number in a decentralised network?
Is there a way to generate a random number with given restrictions:
• It will be used in a decentralised network with a big number of peers (no central authority to generate it)
• Its generation should not rely on any third-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": 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/questions/14858/k3-surface-of-genus-8 | ## K3 surface of genus 8
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $V$ be a complex vector space of dimension 6 and let $G\subset {\mathbb P}^{14}\simeq {\mathbb P}(\Lambda^2V)$ be the image of the Plucker embedding of the Grassmannian $Gr(2, V)$.
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": 56, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/146844/how-to-divide-aleph-numbers?answertab=oldest | # How to divide aleph numbers
Recently, I was wondering how division of aleph numbers would work. First, I thought about how finite cardinality division would work. What I came up with was that the result of $A/B$ where $A$ and $B$ are both cardinalities, is the number of times that each element of $B$ had to be mappe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 56, "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/203347/cutting-the-corners-of-a-cube?answertab=active | # Cutting the corners of a cube
Do you know of any way to cut the corners of a cube by means of rotation assuming that the cube is centered in the origin of XoYZ?
For example if we have a square centered in the origin of XoY and we rotate this square 45 degrees the rotated square will cut all the corners of the origi... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/2579/law-of-an-integrated-cir-process-as-sum-of-independent-random-variables | # Law of an integrated CIR Process as sum of Independent Random Variables
It is known (see for example Joshi-Chan "Fast and Accureate Long Stepping Simulation of the Heston SV Model" available at SSRN) that for a CIR process defined as :
$$dY_t= \kappa(\theta -Y_t)dt+ \omega \sqrt{Y_t}dW_t$$ $Y_0=Y$ together with a c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/107009-equation-normal-curve-parallel-given-line.html | # Thread:
1. ## The equation of the normal to a curve which is parallel to a given line
this is the question:
find the equation of the normal to the curve y=3+2x-x^2 which is parallel to the line 2y-x-3=0
2. Originally Posted by mastermin346
this is the question:
find the equation of the normal to the curve y=3+2x... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/30732/how-can-i-evaluate-sum-n-0-infty-n1xn/30741 | # How can I evaluate $\sum_{n=0}^\infty (n+1)x^n$
How can if find the sum for:
$$\sum_{n=1}^\infty \frac{2n}{3^{n+1}}$$
I know the answer thanks to Wolfram Alpha. I'm more concerned with how to get to to that number. It cites tests to prove that it is convergent, but my class has never learned these before so I feel... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "mathjax_display_tex": 19, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.sagemath.org/doc/reference/modules/sage/modules/fg_pid/fgp_module.html | • index
• modules |
• next |
• previous |
• Modules »
# Finitely generated modules over a PID¶
You can use Sage to compute with finitely generated modules (FGM’s) over a principal ideal domain R presented as a quotient V/W, where V and W are free.
NOTE: Currently this is only enabled over R=ZZ, since it has not been... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/12120/calculating-time-for-a-fully-charged-ups/12121 | # Calculating time for a fully charged UPS
I have a UPS of 1000 Volts connected with 2 batteries each of 150 Amp. How much time it will take to consume the whole UPS (after fully charged) when a device of 1Amp is getting electricity form that UPS.
Please also explain me the calculation.
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## 3 Answers
There are 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-math-topics/160033-ratio-currents.html | # Thread:
1. ## ratio of currents
I solved this first in that this appears to be an inversion.
$\frac{\frac{V^2}{R_2}}{\frac{V^2}{R_1}}<br /> \Rightarrow<br /> \frac{I_1}{I_2}<br /> \Rightarrow<br /> \frac{[1+60(.005)]}{[1+60(.004)]}<br /> \times<br /> \frac{[1+10(.004)]}{[1+10(.005)]}<br /> \Rightarrow<br /> \frac{... | {"extraction_info": {"found_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": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/81517-rotation-triangle-print.html | # Rotation of triangle
Printable View
• March 30th 2009, 01:25 PM
Ian1779
1 Attachment(s)
Rotation of triangle
Hi
I am finding this question tough (attached), I think I may have stumbled on the answer but could do with some confirmation I'm on the right path.
Right, so far I have found the length $BC = \sqrt 82$ us... | {"extraction_info": {"found_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://mathhelpforum.com/algebra/146135-optimization-problems-print.html | # Optimization Problems
Printable View
• May 23rd 2010, 01:36 PM
lorica2000
Optimization Problems
I need an example or more of optimation problems - finding maximum values.
Thanks
• May 23rd 2010, 03:37 PM
SpringFan25
wow, choose your own question :D
I'll make an easy one then.
Find the maximum of $y=-(x-1)^2 + 15... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.m.wikipedia.org/wiki/Unit_hyperbola | # Unit hyperbola
The Unit Hyperbola is blue, its conjugate is green, and the asymptotes are red.
In geometry, the unit hyperbola is the set of points (x,y) in the Cartesian plane that satisfies $x^2 - y^2 = 1 .$ In the study of indefinite orthogonal groups, the unit hyperbola forms the basis for an alternative radial... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/3807/dimension-of-encryption-of-a-linearly-dependent-set-of-plaintexts?answertab=votes | # Dimension of Encryption of a linearly dependent set of plaintexts
Suppose I have an encryption scheme of the form $E(P)=C$ where $P$ is the plaintext and belongs in $\{0,1\}^N$, $C$ the ciphertext which belongs to $\{0,1\}^M$ and the encryption is performed under the key $K$ in $\{0,1\}^R$.
If I pick a subspace of ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/47859/the-definition-of-an-inertial-reference-frame-in-einsteins-relativity/47872 | # The definition of an inertial reference frame in Einstein's relativity
I'm reading Sean Carroll's book on general relativity, and I have a question about the definition of an inertial reference frame. In the first chapter that's dedicated to special relativity, the author describes a way of constructing a reference ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/6303/elgamal-signature-forging-a-signature-of-a-specific-form | # ElGamal signature: Forging a signature of a specific form
I have a question I can't solve from one of the courses I'm currently taking:
Show that given a legitimate ElGamal signature $(S,R)$ on a given message $m$, an attacker
can compute a signature on messages of the form: $m'=(m+bS)a\mod p - 1$,
when $b\in Z_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": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=211934 | Physics Forums
## some higher order differential equations
1. The problem statement, all variables and given/known data
a) s^2*t''+st*t'=s
b) y(dx/dy)^2=x^2+1
c) 17y''''-t^6*y"-4.2y^5=3cost(t)
2. Relevant equations
3. The attempt at a solution
For part a I thought about doing a reduction of order but I can't 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": 22, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4056508 | Physics Forums
Intersection of concave functions
Hi all,
I have a question. Suppose f : [ 0, l) $\rightarrow$ ℝ is concave , increasing and continuous where l < ∞ and g : [ 0, l) $\rightarrow$ ℝ is also concave, nondecreasing and continous on the same interval. Can we claim that f and g intersect finitely many times ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/96289-notes-wrong.html | # Thread:
1. ## Are the notes wrong?
I've highlighted parts of the image I'm concerned with:
In other words, they want a cubic polynomial, i.e. $P_3$, and if they say that a given polynomial's degree is $n+1$, they must choose $n=2$ so that $n+1=3$.
Perhaps they should have written the degree of the poly is $n$, no... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/74875/dual-space-of-the-space-of-finite-measures | # Dual space of the space of finite measures
Since I am reading some stuff about weak convergence of probability measures, I started to wonder what is the dual space of the space consisting of all the finite (signed) measures (which is well known to be a Banach space with the norm being total variation). Is there 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": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/2720/brute-force-a-ciphered-message/2724 | # Brute force a ciphered message?
I wrote my own cipher to encrypt messages. I would like to test a sample ciphered message to see how strong it is. Are there any tools for such task either in Windows or Linux ?
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## 2 Answers
There's no way to verify the strength of a cipher in any automated way, especially 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": 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/questions/68041/showing-block-diagonal-structure-of-matrix-by-reordering | ## Showing block diagonal structure of matrix by reordering
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose we have a block-diagonal matrix $M$, but the block diagonal structure is not immediately apparent from looking at the matrix because the rows/co... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/44789/list | ## Return to Answer
3 Fixed errors in the references...
If $A$ is symmetric, then the matrices that you mention are called:
Conditionally positive definite (CPD) --- these are intimately related to the venerable infinitely divisible matrices
There is a vast amount of literature on these matrices, some useful pointe... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/13903/list | ## Return to Answer
1 [made Community Wiki]
Tarski ran into some trouble when he tried to publish his result that the Axiom of Choice is equivalent to the statement that an infinite set $X$ has the same cardinality as $X \times X$.
From Mycielski:
"He tried to publish his theorem in the Comptes Rendus but Frechet 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://mathoverflow.net/questions/64365/natural-transformations-as-categorical-homotopies/75686 | ## Natural transformations as categorical homotopies
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Every text book I've ever read about Category Theory gives the definition of natural transformation as a collection of morphisms which make the well known diag... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 183, "mathjax_display_tex": 9, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://unapologetic.wordpress.com/2008/01/02/connectedness/?like=1&source=post_flair&_wpnonce=a832ba55c5 | # The Unapologetic Mathematician
## Connectedness
Tied in with the fundamental notion of continuity for studying topology is the notion of connectedness. In fact, once two parts of a space are disconnected, there’s almost no topological influence of one on the other, which should be clear from an intuitive idea of wh... | {"extraction_info": {"found_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": 27, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/272057/maximal-dimension-of-subspace-of-matrices-whose-products-have-zero-trace | Maximal dimension of subspace of matrices whose products have zero trace
In the space of all real matrices with dimension $n$, find the maximal possible dimension of a subspace $V$ such that $\forall X,Y\in V,\, \operatorname{tr}(XY)=0$.
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2 Answers
If $V$ is a subspace of real matrices of size $n$ with the propert... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://ams.org/bookstore?fn=20&arg1=survseries&ikey=SURV-89.S | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Ana... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=141301 | Physics Forums
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## The Massless Photon
(I hope I've chosen the right sub-forum for this question...)
Hi folks - I've recently joined here to see if people who are more knowledgeable than me can help me understand some physics issues I have struggled with for a long time.
My... | {"extraction_info": {"found_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": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/40564/what-is-the-symmetry-between-the-definitions-of-the-bounded-universal-existentia/40570 | # What is the symmetry between the definitions of the bounded universal/existential quantifiers?
What is the symmetry between the definitions of the bounded universal/existential quantifiers?
$\forall x \in A, B(x)$ means $\forall x (x \in A \rightarrow B(x))$
$\exists x \in A, B(x)$ means $\exists x (x \in A \land ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/4844/distributions-of-point-charges/5326 | Distributions of point charges
Problem
$N$ point charges are distributed in the unit ball in $\mathbb{R}^k$, $k=2,3$. Given locations of the particles $x_1,\ldots,x_N$ the potential energy is
$E=\sum_{j=1}^{N-1}\sum_{k=j+1}^N |x_j-x_k|^{-1}$
where $|x_j-x_k|$ is Euclidean distance between $x_j$ and $x_k$. I'm inter... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/new-users/198145-trying-remember-maths-after-40-years.html | # Thread:
1. ## Trying to remember maths after 40 years
I have forgotten some/ most / all of my maths knowledge.
I am trying to solve
x=10-x2 *t
for x with respect to t.
I know that I used to be able to do this and I also know that I thought it was simple but my memory has gone and who keeps text books for 40 years... | {"extraction_info": {"found_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.m.wikibooks.org/wiki/General_Relativity/Reissner-Nordstr%C3%B6m_black_hole | # General Relativity/Reissner-Nordström black hole
<General Relativity
Reissner-Nordström black hole is a black hole that carries electric charge $Q$, no angular momentum, and mass $M$. General properties of such a black hole are described in the article charged black hole.
It is described by the electric field of 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": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/143144-algebraic-word-problems.html | # Thread:
1. ## algebraic word problems
1)a 60% acid solution is to be mixed with a 80% acid solution to produce 20 liters of a 65% acid solution. how many liters of each solution is needed?
2)the ratio between two positive numbers is 6 to 5. if the difference between the two numbers is 8, what are the 2 numbers?
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://terrytao.wordpress.com/category/teaching/254a-random-matrices/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 ‘254A – random matrices’ category.
## 254A, Notes 1: Concentration of measure
3 January, 2010 in 254A - ran... | {"extraction_info": {"found_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": 25, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=95585 | Physics Forums
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## my paper on the Born rule...
Hi,
A while ago I discussed here about a paper I wrote, which you can find on the arxiv: quant-ph/0505059
Proponents of the Everett interpretation of Quantu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/238521/is-lim-n-to-infty-fracnn-frac1n-e-any-easier-than-stirling | # Is $\lim_{n \to \infty} \frac{n}{(n!)^\frac{1}{n}} = e$ any easier than Stirling? [duplicate]
Possible Duplicate:
Showing that $\frac{\sqrt[n]{n!}}{n}$ $\rightarrow \frac{1}{e}$
Stirling's approximation says that $$\lim_{n \to \infty} \frac{n^n \sqrt{n}}{n! e^n } = \frac{1}{\sqrt{2 \pi}}.$$ Since $\lim_{n \to \inft... | {"extraction_info": {"found_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": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/T-symmetry | # T-symmetry
In theoretical physics, T-symmetry is the theoretical symmetry of physical laws under a time reversal transformation:
$T: t \mapsto -t.$
Although in restricted contexts one may find this symmetry, the observable universe itself does not show symmetry under time reversal, primarily due to the second law ... | {"extraction_info": {"found_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": 21, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/242537/calculate-asymptotes-and-local-extreme-values | # Calculate asymptotes and local extreme values
I'm fed up with this question from my book. I've calculated the constants to this equation but got stuck at the asymptotes and local extreme values calculations which I need to plot the graph, perhaps anyone could help me out or guide me towards the solution of calculati... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?p=3768147 | Physics Forums
## Change in Density due to Temperature and Pressure Change
1. The problem statement, all variables and given/known data
Estimate the percent change in density of iron when it is still a solid, but deep in the Earth where the temperature is $2000^\circ C$ and it is under $5000$ atm of pressure. Take 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": 11, "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/86058/saturated-ideals | ## saturated ideals
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Is it possible to have a saturated ideal on a successor cardinal which does not extend the nonstationary ideal? (i.e. some nonstationary set is positive for this ideal)
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## 1 Answer
Yes, 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": 8, "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/11026/inverse-of-a-monoid-homomorphism | # Inverse of a monoid homomorphism
It is a well-known fact that
$f\colon a \mapsto \left(\begin{array}{cc} 1 & 1\\ 0 & 1\\ \end{array}\right), ~ b \mapsto \left(\begin{array}{cc} 1 & 0\\ 1 & 1\\ \end{array}\right)$
is a monomorphism from the free monoid generated by $a$ and $b$ to the matrix monoid $\mathbb{Z}^{2\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": 16, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Probability | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_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": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/199986-set-open.html | 1Thanks
• 1 Post By mfb
# Thread:
1. ## Is this set open?
A is a subset of B, both sets are open.
Is the set B/A open?
My answer would be no, because the complement of an open set is always closed. Is this the correct definition in this case?
2. ## Re: Is this set open?
But a set can be both open and closed.
You... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/160662/what-transforms-under-su2-as-a-matrix-under-so3 | # What transforms under SU(2) as a matrix under SO(3)?
A vector $\boldsymbol{r}$ in $\mathbb{R}^3$ transforms under rotation $\boldsymbol{A}$ to $\boldsymbol{r}'=\boldsymbol{Ar}$. It is equivalent to an SU(2) "rotation" as $$\left( \boldsymbol{r}'\cdot\boldsymbol{\sigma} \right) = \boldsymbol{h} \left( \boldsymbol{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": 47, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/68552-cauchy-schwarz-inequality-integrals.html | # Thread:
1. ## Cauchy-Schwarz inequality for Integrals
Suppose that the functions $f,g,f^2,g^2, fg$ are integrable on the closed, bounded interval [a,b]. Prove that:
$\int ^b _a fg \leq \sqrt { \int ^b_a f^2 } \sqrt { \int ^b_a g^2 }$.
Proof.
Now, $0 \leq \sqrt { \int _a ^b (f- \lambda g)(f- \lambda g) } ^2$ $= \... | {"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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/116701?sort=newest | ## How would set theory research be affected by using ETCS instead of ZFC?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In "Rethinking Set Theory", Tom Leinster argues in favor of teaching axiomatic set theory via Lawvere's Elementary Theory of the Category... | {"extraction_info": {"found_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": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=260849 | Physics Forums
Right handed vs Left handed circular polarization
Hey,
I just wanted to clear up some confusion I've been having regarded which is which of these.
If I have the wave $$\vec{E}= E_{0X} cos(kz-\omega t)+ E_{0Y} sin(kz-\omega t)$$ and $$E_{0X}=E_{0Y}$$. Then at z=0, t=0 the field is pointing completely ... | {"extraction_info": {"found_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": 13, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://unapologetic.wordpress.com/2009/06/ | # The Unapologetic Mathematician
## Dirac notation I
There’s a really neat notation for inner product spaces invented by Paul Dirac that physicists use all the time. It really brings to the fore the way a both slots of the inner product enter on an equal footing.
First, we have a bracket, which brings together two 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 107, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/61252/why-do-bernoulli-numbers-arise-everywhere/61278 | ## Why do Bernoulli numbers arise everywhere?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I have seen Bernoulli numbers many times, and sometimes very surprisingly. They appear in my textbook on complex analysis, in algebraic topology, and of course, numbe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 76, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?s=4b7c6c19868f87b41f69b69f91f3ad9a&p=3986308 | Physics Forums
## Which method of integration for sin^2(x) dx
During maths class last semester this integral came up in the course of discussion and my lecturer gave a quick outline of how to solve it but I didn't grasp it at the time and we moved on. I'd like to know how to do it though! The integral is:
$\int sin^... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/112525-increasing-decreasing-functions.html | # Thread:
1. ## increasing and decreasing functions
I am to determine the interval on which f(x)=x-x^-2 is increasing. I came up with the derivative of f`(x) =x-x^-2 as f`(x)=1+2/x^3. Having said that, the graph on the left side of the y axis seems to travel in a positive direction until it gets to the y axis, then g... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://quant.stackexchange.com/questions/2152/how-to-perform-basic-integrations-with-the-ito-integral/2153 | # How to perform basic integrations with the Ito integral?
From the text book Quantitative Finance for Physicists: An Introduction (Academic Press Advanced Finance) I have this excercise:
Prove that
$$\int_{t_1}^{t_2}W(s)^ndW(s)=\frac{1}{n+1}[W(t_2)^{n+1}-W(t_1)^{n+1}]-\frac{n}{2}\int_{t_1}^{t_2}W(s)^{n-1}ds$$
Hint... | {"extraction_info": {"found_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": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://johncarlosbaez.wordpress.com/2011/03/04/network-theory-part-1/ | # Azimuth
## Network Theory (Part 1)
As a mathematician who has gotten interested in the problems facing our planet, I’ve been trying to cook up some new projects to work on. Over the decades I’ve spent a lot of time studying quantum field theory, quantum gravity, n-categories, and numerous pretty topics in pure 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 8, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/60375?sort=votes | ## Is R^3 the square of some topological space?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The other day, I was idly considering when a topological space has a square root. That is, what spaces are homeomorphic to $X \times X$ for some space $X$. $\mathbb... | {"extraction_info": {"found_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://math.stackexchange.com/questions/258332/prove-that-if-ax-by-abxy-then-xy-1?answertab=votes | # Prove that if $a^x=b^y=(ab)^{xy}$, then $x+y=1$.
Prove that if $a^x=b^y=(ab)^{xy}$, then $x+y=1$.
How do I use logarithms to approach this problem? Any help would be appreciated, thanks.
-
## 4 Answers
Using logarithms:
Since $a^x = b^y$, $$\log a^x = \log b^y \quad \Rightarrow \quad x \log a = y \log b \quad \... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/22650-integral-problem.html | # Thread:
1. ## Integral problem
Find f(x) if f(1) = -1 and the tangent line at (x, f(x)) has slope 2e^x + 1
This is a problem that was thrown into my indefinite integral homework, and I'm kinda stuck.
any help appreciated.
2. Originally Posted by leviathanwave
Find f(x) if f(1) = -1 and the tangent line at (x, 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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/188001/membership-based-on-maximum-of-a-function-over-the-set?answertab=oldest | # Membership based on maximum of a function over the set.
Let $S\subset \mathbb{R}^n$ and let $f(x)$ be a continuous function over $\mathbb{R}^n$. Furthermore, define $s_{\text{max}}:= \sup_{x\in S} \{f(x)\}$ and let $f(x)$ attain its minimum for at least one element in $S$.
Under what conditions on $f(x)$ and $S$ do... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 82, "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-applied-math/180135-ivp-using-leibniz-formula.html | # Thread:
1. ## IVP using Leibniz formula
How does one formulate this integral equation as an initial value problem?
u(t)=1 + integral from 0 to t (s ln (s/t) u(s) ds)
we're supposed to use Leibniz formula but I'm not sure how to apply it. Thanks!
2. So your integral equation is
$u(t)=1+\int_{0}^{t}s\ln\left(\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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/08/15/an-example-of-an-enriched-category/?like=1&_wpnonce=274c59a080 | # The Unapologetic Mathematician
## An example of an enriched category
Sorry for the delay, but the cable setup took more than I’d expected (there will me more on this over at Yankee Freak-Out). Today, I’d like to run through an example of a monoidal category, and what sort of enriched categories it gives rise to.
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": 0, "codecogs_latex": 0, "wp_latex": 30, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/99850/how-can-i-solve-the-differential-equation-yy2-fx | How can I solve the differential equation? $y'+y^{2}=f(x)$
$y'+y^{2}=f(x)$
I know how to find endless series solution via endless integral or endless derivatives , and power series solution method if we know $f(x)$. And also I know how to find general solution if we know one particular solution ($y_0$)
I am looking ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/135042/help-me-prove-the-identity-overlinef0-frac12-pi-int-02-pi-frace?answertab=oldest | # Help me prove the identity $\overline{f(0)} = \frac{1}{2\pi}\int_0^{2\pi}\frac{e^{i\phi}}{e^{i \phi}-z}\overline{f(e^{i\phi})}d\phi$
Let f be an analytic function defined in an open set containing the closed unit disk and let z in ℂ be fixed. I've simplified a more complicated expression down to this identity, and 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": 56, "mathjax_display_tex": 21, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/math-challenge-problems/22996-r-2-2-r-4-2-r-2-a.html | Thread:
1. (r - 2)^2 + (r - 4)^2 = r^2?
How do I find the value of r?
(r - 2)^2 + (r - 4)^2 = r^2
I know what r is, coincidentally, (it's 10)
But how would I go about finding it if I didn't know?
Wasn't sure where to post this, it's not homework, I got it from a brain teaser (finding the radius of a circle which i... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 59, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.boredofstudies.org/wiki/Maths_Extension_2:Integration | # Maths Extension 2:Integration
BikiCrumbs: Integration
### From Biki
Why not add to it? Don't be intimidated - we welcome all contributions!
## Integration by Substitution
Examples: For, $\int\sqrt{a^2 + x^2}\,dx$ use the substitution x = tanθ.
## Partial Fractions & Rational Functions
### Handy Partial Fractio... | {"extraction_info": {"found_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": 50, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/124047/is-the-clustering-of-prime-powers-merely-coincidental | # Is the clustering of prime powers merely coincidental?
$2^3$ and $3^2$ are close together; $11^2$, $5^3$, and $2^7$ (121, 125, and 128) are close together; $3^5$, $2^8$, and maybe $17^2$ (243, 256, and 289) are close together. $7^3$ is close to $19^2$ (343 and 361). $3^7$ is very nearly $13^3$ (2187 and 2197), which... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 52, "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/8466/sun-symmetry-and-its-representations | # SU(N) symmetry and its representations
If a Lagrangian containing an N-multiplet of fields is invariant under global $\mathbf{SU}(N)$ transformations, does that necessarily imply it is invariant under $\mathbf{SU}(N-1)$, $\mathbf{SU}(N-2)$,... all the way down to $\mathbf{U}(1)$ as well, where the representations 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": 51, "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/168759-volume-involving-triple-integral.html | # Thread:
1. ## Volume involving a triple integral
Find the volume determined by z less than or equal to 6-x^2-y^2 and z greater than or equal to sqrt(x^2+y^2).
I'm not sure how to find the limits of integration for this question. I set the two inequalities to each other and found that x^2+y^2=9 and x^2+y^2=4, but a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://crypto.stackexchange.com/questions/3958/besides-key-and-ciphertext-sizes-what-are-other-advantages-of-elliptic-curve-ver?answertab=votes | # Besides key and ciphertext sizes what are other advantages of elliptic curve versions of various protocols?
There are elliptic curve variants of Diffie-Hellman, ElGamal, DSA and possibly other protocols/algorithms. I know that these elliptic curve variants have smaller key and ciphertext sizes which will make commun... | {"extraction_info": {"found_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.reference.com/browse/Exponential_utility | Definitions
# Exponential utility
In economics exponential utility refers to a specific form of the utility function, used in many contexts because of its convenience when uncertainty is present. Formally, exponential utility is given by:
$u\left(c\right)=-e^\left\{-a c\right\}$,
where $c$ is consumption and $a$ is... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "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://mathoverflow.net/questions/28967/a-characterization-of-convexity/29004 | ## A characterization of convexity
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
While doing some research on polytopes I came to the following question. Maybe it's already somewhere but anyway I'll post it here.
Let $X\subset \mathbb{R}^3$ be such that, fo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 99, "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/1873/the-concepts-of-path-integral-in-quantitative-finance | # The Concepts of Path Integral in Quantitative Finance
I realize that path integral techniques can be applied to quantitative finance such as option value calculation. But I don't quite understand how this is done.
Is it possible to explain this to me in qualitative and quantitative terms?
-
1
Although some physic... | {"extraction_info": {"found_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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/218626/how-many-subgroups-can-we-make-of-group-whose-order-is-a-multiple-of-prime | # How many subgroups can we make of group whose order is a multiple of prime
If a group has $n$ elements of order $p$ ($p$ is prime) how many subgroups of order $p$ do we get? If the group was cyclic than only one unique subgroup of order $p$, but what if the group is non-cyclic?
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## 2 Answers
Turn the question 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": 29, "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/116236/mean-value-property-with-fixed-radius | # Mean value property with fixed radius
I will focus on the real line. Let $f$ be a smooth function on $\mathbb{R}$, if $\forall x\in\mathbb{R}, r>0$, $$\frac{f(x-r)+f(x+r)}{2}=f(x),$$ we say that f has the spherical mean value property (MVP); if instead $$\frac{1}{2r}\int_{x-r}^{x+r}f(t)dt=f(x),$$ we say f has the ba... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 86, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/108213/the-multiplicative-system-in-a-symmetric-monoidal-category | ## The multiplicative system in a symmetric monoidal category
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Let $\mathcal{C}$ be a symmetric monoidal category. In the 1973 paper "Note on monoidal localisation" by Brian Day, the multiplicative system of morph... | {"extraction_info": {"found_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://mathoverflow.net/questions/17105/reference-for-the-expected-number-of-prime-factors-of-n-larger-than-nalpha-is-l/17114 | ## Reference for the expected number of prime factors of n larger than n^alpha is -log alpha
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Let $0 < \alpha < 1$ be a constant. The expected number of prime factors of a "random" integer near $n$ which are great... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/91454/simple-closed-curves-and-the-coefficent-of-expi-theta-in-the-associated-four/91784 | ## Simple closed curves and the coefficent of $\exp(i\theta)$ in the associated Fourier series
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Given a continuous map $f:S^1\to \mathbb{C}$ from the unit circle to the complex numbers, one can form its Fourier se... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 75, "mathjax_display_tex": 4, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/6690/solution | ### Rotating Triangle
What happens to the perimeter of triangle ABC as the two smaller circles change size and roll around inside the bigger circle?
### Doodles
A 'doodle' is a closed intersecting curve drawn without taking pencil from paper. Only two lines cross at each intersection or vertex (never 3), that is 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": 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/58534/formal-smoothness-versus-reducedness/58544 | ## formal smoothness versus reducedness
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Hi,
I have the following situation: $R,H$ schemes (can be assumed noetherian and of finite type) over a field $k$ which we can assume to be algebraically closed, with $H$ ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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