url stringlengths 17 172 | text stringlengths 44 1.14M | metadata stringlengths 820 832 |
|---|---|---|
http://mathoverflow.net/questions/97827?sort=oldest | ## A Parameter related to fractional chromatic number and Kneser Graphs
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $t \gt 0$ be an integer and $G$ is a simple graph with $\chi_f(G) = t$. Then $t$= inf `$\{ \frac{n}{k}| G \rightarrow KG(n,k)\}$` where ... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/7515/what-are-some-techniques-for-sampling-two-correlated-random-variables | # What are some techniques for sampling two correlated random variables?
What are some techniques for sampling two correlated random variables:
• if their probability distributions are parameterized (e.g., log-normal)
• if they have non-parametric distributions.
The data are two time series for which we can compute... | {"extraction_info": {"found_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/discrete-math/124768-determine-truth-values-following-statements.html | # Thread:
1. ## Determine the truth values of the following statements
Let S(a,b) be the statement "ab=a/b".
Given that the domain (or universe of discourse) for both variables consists of all positive, non-zero integers, what are the truth values of these two statements?
a) ∀a∃b S(a,b)
b) ∀b∃a S(a,b)
Explain your... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/83877?sort=votes | Are Kazhdan-Lusztig $R$-polynomials the Poincare polynomials of the corresponding affine varieties
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $x$ and $y$ be two elements of $S_n$. Let $U(x,y)$ be the intersection $(BxB \cap B_{-} y B)/B$ inside the flag 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": 35, "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/17997/deriving-symmetries-of-a-gauge-theory/18082 | ## Deriving symmetries of a Gauge theory
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hello, I don't know if this is a good place for exposing my problem but I'll try...
I have a gauge theory with action:
`$S=\int\;dt L=\int d^4 x \;\epsilon^{\mu\nu\rho\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": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/tags/velocity/hot | Tag Info
Hot answers tagged velocity
28
Double light speed
One of the results of special relativity is that a particle moving at the speed of light does not experience time, and thus is unable to make any measurements. In particular, it cannot measure the velocity of another particle passing it. So, strictly speaki... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/brownian-motion+control-theory | Tagged Questions
0answers
51 views
Controlling auto-correlated 1D Brownian motion
I have 1D Brownian motion process $x(t)$, and ability to control it. The control allows to shift the $x$ by $D$ at any time. I need the controlled process to be zero-mean, and to use the control ... | {"extraction_info": {"found_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/76708/how-to-determine-a-shape-is-convex-by-giving-polar-form-polynomial-equation | # How to determine a shape is convex by giving polar form polynomial equation?
It is easy to determine concave, convex curve in xy coordinate. But I am placing a question that I only have a polar polynomial equation like r(ang) = a4*ang^4 + a3*ang^3 + .... + a0;
How I can tell whether it is convex shape by given a eq... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/83698-tell-me-sequence-below-question.html | # Thread:
1. ## tell me the sequence in the below question;
Find the 15th term of the following sequence
1/2,1/4,1/8,... ( Use sequence formula)
2. $a_n = \frac{1}{2^n}$
3. ## sequence formula
sir please tell me more easily
i cant understand that how can i solve my question according to your given formula..
pleas... | {"extraction_info": {"found_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://mathhelpforum.com/number-theory/86539-sum-certain-consecutive-odd-numbers-57-2-13-2-find-numbers-print.html | # The sum of certain consecutive odd numbers is 57^2 – 13^2. Find the numbers.
Printable View
• April 29th 2009, 06:52 PM
chakravarthiponmudi
The sum of certain consecutive odd numbers is 57^2 – 13^2. Find the numbers.
Problem.
The sum of certain consecutive odd numbers is $57^2$– $13^2.$ Find the numbers.
solution
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cstheory.stackexchange.com/questions/10169/from-edge-disjoint-paths-to-independent-paths | # From edge-disjoint paths to independent paths
Let $\mathcal{G}_k$ denote the set of all graphs that contain two vertices $x,y$ and $k$ edge-disjoint $x-y$ paths.
Define $f(k)$ to be the maximum such that for every graph $G\in \mathcal{G}_k$ there are two vertices $x',y'$ with $f(k)$ independent $x'-y'$ paths in $G$... | {"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": 48, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cstheory.stackexchange.com/questions/3692/dijkstra-parallelization/3693 | # Dijkstra parallelization
I'd like to know what is the best method to parallelize the Dijkstra algorithm.
Thanks.
-
Try a literature search for parallel shortest path. You could start with e.g. "A Randomized Parallel Algorithm for Single-Source Shortest Paths" by Philip N. Klein and Sairam Subramanian in J. of Alg... | {"extraction_info": {"found_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://sumidiot.wordpress.com/2009/11/05/neighbors-in-farey-sequences/ | # ∑idiot's Blog
The math fork of sumidiot.blogspot.com
## Neighbors in Farey Sequences
I was reading about Ford circles today, and was planning on writing about them. But then I noticed that one of the things I wanted to say was based on some things I didn’t say about Farey sequences when I talked about them a few 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": 105, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/statistics/57651-continuous-random-variables-probability-density-functions.html | # Thread:
1. ## Continuous random variables – probability density functions
The following could represent a probability density function (p.d.f.) or not. If could, find the value of k.
$<br /> f(x) = \begin{cases} <br /> k(x + x^2), <br /> & \text {$-1 \le x \le 1,$} \\ 0, & \text {otherwise.} \end{cases}<br />$
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": 0, "codecogs_latex": 34, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/34784/how-would-be-tv-reception-in-a-spaceship-travelling-close-to-speed-of-light | # How would be tv reception in a spaceship travelling close to speed of light?
My little brother has made me a tough question (specially for a computer science engineer).
Imagine that there is a spaceship orbiting earth close at nearly speed of light (say 99%). Someone in earth transmits a tv signal to spaceship.
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": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/148181-algebra-2-graphing-help.html | Thread:
1. Algebra 2 graphing help
Hey guys, what's up? I know this is going to sound dumb, but I forgot how to do it.
xy=-3. How would you graph that? Im drawing a blank right now. Thanks for the help!
2. Originally Posted by robot214
Hey guys, what's up? I know this is going to sound dumb, but I forgot how to 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/trigonometry/67832-trigonometric-concepts.html | # Thread:
1. ## trigonometric concepts
Reading this, something rings in my mind, but I cant find the room the ring comes from I did this last year, but since I took an online class and therefor have no teacher,it's difficult to get the infos. The only thing I can remember is how to calculate sin,cos,tan using a scien... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/21425/what-meaning-do-changes-in-the-absolute-value-of-gibbs-free-energy-have-in-a-sim/21644 | # What meaning do changes in the absolute value of Gibbs free energy have in a simple expansion process?
Below is a simple representation of the thermodynamics of a steam turbine. Stream kinetic and potential energy changes are neglected and no other type of non-PV work is done besides shaft work. Enthalpy and entropy... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/307011/how-many-integer-solutions-of-a-exist-for-this-equation | How many integer solutions of “a” exist for this equation?
$a\times b = 8 \times (a + b)$
I have used Wolfram Alpha and it has given me 14 integer solutions.
But how can we find those solutions ? Which method ?
edit: integer solutions are as following:
$a = [-56, -24, -8, 0, 4, 6, 7, 9, 10, 12, 16, 24, 40, 72]$
$... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/37010?sort=newest | ## Product Measure Only Possible Measure?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $X$ be a separable complete metric space and $Z$ be the set of all integers. Let $\nu$ be a Borel probability measure on $X^Z$ invariant under the shift function $S:X... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://simple.wikipedia.org/wiki/Partial_derivative | # Partial derivative
In calculus, an advanced branch of mathematics, the partial derivative of a function is basically the derivative of one named variable, and the unnamed variable of the function is held constant. In other words, the partial derivative takes the derivative of certain indicated variables of a functio... | {"extraction_info": {"found_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://micromath.wordpress.com/2008/05/26/calculus-without-limits/?like=1&source=post_flair&_wpnonce=b467bcc1c8 | # Mathematics under the Microscope
Atomic objects, structures and concepts of mathematics
Posted by: Alexandre Borovik | May 26, 2008
## Calculus without limits
I re-publish my old post from my old blog, with comments (some of them new) included in the body.
My post:
Thanks to Michael Livshits, I became aware 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": 0, "codecogs_latex": 0, "wp_latex": 15, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikipedia.org/wiki/Montonen%E2%80%93Olive_duality | # Montonen–Olive duality
In theoretical physics, Montonen–Olive duality is the oldest known example of S-duality or a strong-weak duality. It generalizes the electro-magnetic symmetry of Maxwell's equations. It is named after Finnish Claus Montonen and British David Olive.
## Overview
In a four-dimensional Yang-Mill... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?p=4128573 | Physics Forums
## From what I understand, there s some sort of computer calculating pi...
... and for a long time, I took this for granted, but now I'm starting to wonder how it is doing this. From my knowledge, the only way one could calculate pi is to measure the diameter and radius of a circle, and find the ratio,... | {"extraction_info": {"found_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://mathoverflow.net/questions/5568/categorifying-the-group-representations | ## Categorifying the group representations
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Given a Lie algebra $g$, one constructs $\mathcal A$, a category whose $K_0$ is the universal enveloping algebra of $g$. Conjecture: any $\mathcal A$-acted triangulated ... | {"extraction_info": {"found_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://mathhelpforum.com/pre-calculus/111504-please-help-i-kind-know-how-do-but-i-dont-know-if-my-answer-right.html | # Thread:
1. ## Please help! I kind of know how to do this, but I dont know if my answer is right.
y=f(x)=6x^2-x-2/3x^2-11x-20
What are the intervals, test point k, f(k)?
y=f(x)=x^3+x^2-12x/x^2-2x-8
This is an oblique asymptote
What are the intervals, test point k, f(k)?
2. Originally Posted by Jluse7
y=f(x)=6x^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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://gilkalai.wordpress.com/2008/07/03/helly-cayley-hypertrees-and-weighted-enumeration-iii/?like=1&source=post_flair&_wpnonce=d42062ed33 | Gil Kalai’s blog
## Helly, Cayley, Hypertrees, and Weighted Enumeration III
Posted on July 3, 2008 by
This is the third and last part of the journey from a Helly type conjecture of Katchalski and Perles to a Cayley’s type formula for “hypertrees”. (On second thought I decided to divide it into two devoting the seco... | {"extraction_info": {"found_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": 45, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/91319/work-problems-a-deeper-look?answertab=oldest | # Work problems: A Deeper Look
We all know that work problems are some applications of algebra in reality. But the equation that corresponds to work problems is not as clearly stated as investment, mixture and uniform-motion problems.
Now, suppose we have the set of workers $A$ and each worker $a_i \in A$ where $n$ 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": 20, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/241629/sum-of-two-sine-curves | # Sum of two sine curves
How can we compute the sum $$\sin(f_1) + \sin(f_2)$$ I know it is $$2\sin\left(\frac{f_2 + f_1}{2}\right) \cos\left(\frac{f_2 - f_1}{2}\right)$$ but how can it be derived with elementary trigonometric identites?
-
## 3 Answers
The sine angle addition rule reads:
$$\sin(u\pm v)=\sin(u)\cos(... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/50156/are-standardized-betas-in-multiple-linear-regression-partial-correlations | # Are standardized betas in multiple linear regression partial correlations?
Since standardized betas are correlation coefficients in bivariate regression, is it the case that standardized betas in multiple regression are partial correlations?
-
Short answer: No. – Glen_b Feb 17 at 2:51
Because the value of a beta 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": 24, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/139574-logarithmic-function.html | Thread:
1. logarithmic function
how do i show that $\frac{d^2}{dx^2}\int_{-1} ^1 {log|x-t|}dt$= $\int_{-1}^1 \frac{-1}{(x-t)^2}dt$ is INCORRECT?
i know that to interchange limit and integral, a function must be uniformly convergent to its limit. but i dont know exactly how to show it.
2. Originally Posted by Kat-M
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/94894-looking-integration-pointer-print.html | # Looking for an integration pointer!
Printable View
• July 11th 2009, 12:29 PM
superduper
Looking for an integration pointer!
Hey guys, I got two problems here, that are probably extremely basic; but i'm having a hard time with these. When I finally find a $u$-substitution path I can generally work my way through, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 81, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/tagged/centering+resampling | # Tagged Questions
1answer
259 views
### Is centering needed when bootstrapping the sample mean?
When reading about how to approximate the distribution of the sample mean I came across the nonparametric bootstrap method. Apparently one can approximate the distribution of $\bar{X}_n-\mu$ by the ...
1answer
163 views
... | {"extraction_info": {"found_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/5995/positive-systems-in-n-the-n-1-simplex/6040 | ## “Positive systems” in n * the (n-1)-simplex
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let S := the nonnegative integer solutions to {$a_1 + ... + a_n = n$}, and center := (1,1,1,...,1). Call a vector v generic if v.s = v.center <=> s = center. Then ea... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikibooks.org/wiki/Vectors | # Vectors
A Wikibookian believes this page should be split into smaller pages with a narrower subtopic. You can help by splitting this big page into smaller ones. Please make sure to follow the naming policy. Dividing books into smaller sections can provide more focus and allow each one to do one thing well, which ben... | {"extraction_info": {"found_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": 133, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/number-theory/1589-convergence-primes.html | # Thread:
1. ## Convergence of primes
Let $p_n$ represent the n-th prime number. Determine what $\lim_{n\rightarrow \infty}\frac{p_{n+1}}{p_n}=?$. Does it even have a convergence?
Notice the following
$p_n<p_{n+1}<2p_n$ (Betrand's Conjecure)
thus,
$1<\frac{p_{n+1}}{p_n}<2$
Thus, by the limit limitation theorem,
$1\l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=246182 | Physics Forums
## Ideal Gas Law and Isobaric Processes
Hi,
So let's take the standard example of a gas in a container with a piston at the top. Charles' Law states that at constant pressure, an increase in temperature (kinetic energy of gas molecules) will increase the volume. This makes sense both conceptually 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": 0, "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/19904/generalisation-of-reversible-equation-to-non-reversible-situations-because-it-on?answertab=votes | # Generalisation of Reversible Equation to Non-Reversible Situations Because it Only Contains 'Properties of the System'
I've just been reading through Van Ness' Understanding Thermodynamics, and I'm having a little trouble following his argument at one point. He is deriving the useful differential equation:
$$dU=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": 6, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/45704?sort=votes | ## Shimura datum of family of fake elliptic curves
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose we have a PEL type $(H,\phi ,*;T,O,V)$ where H is a rational nonsplit quaternion algebra, $\phi$is an embedding of Q-algebra $\phi : H-->M(2,R)$, and * 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": 36, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/5259/approximating-pi-using-monte-carlo-integration/5287 | # Approximating $\pi$ using Monte Carlo integration
I'm trying to approximate $\pi$ using Monte Carlo integration; I am approximating the integral
$$\int\limits_0^1\!\frac{4}{1+x^2}\;\mathrm{d}x=\pi$$
This is working fine, and so is estimating the error (variance), $\sigma$. However, when I then try to use importanc... | {"extraction_info": {"found_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": 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=4160636&postcount=3 | View Single Post
What you need is this. You'll find its derivation in any standard thermodynamics text. $\left(\frac{\partial U}{\partial V}\right)_T = T\left(\frac{\partial P}{\partial T}\right)_{V} - P.$ I agree, though, with Studiot. It is impolite not to acknowledge attempts to help. It's perfectly in order to 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": 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/17182?sort=votes | Is an irreducible holomorphic symplectic manifold a simple Lie algebra?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The tangent bundle of a hyper-Kahler manifold gives a quadratic Lie algebra in the derived category. Can this be regarded as a simple Lie algebr... | {"extraction_info": {"found_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=78f45efb5c8e28edb4f98af11b81a095&p=4004258 | Physics Forums
## Cannot tell when a probability generating function converges for |s|<1
Hi, I have a problem that is already solved... I thought 3 of the 4 functions were probability generating functions, but I got one wrong and don't know why.
The solution says $g(s)=1+s-s^2$ is not a probability generating functi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/100620/good-reduction-of-abelian-varieties-s-t-why-is-this-ring-henselian/100621 | ## Good reduction of abelian varieties [S-T] — Why is this ring henselian?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
First of all, I find it hard to formulate a good title for this question. Sorry that it is so vague.
Let's move on te the question itsel... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/134838/finding-a-vector-in-a-n-l-s?answertab=votes | # Finding a vector in a n.l.s.
Let $X$ be a normed linear space and $Y$ a closed proper subspace. Prove that for all $\varepsilon > 0$, there is an $x \in X$ with $\|x\| = 1$ and such that $\|x − y\| ≥ 1 − \varepsilon$ for all $y \in Y$ .
-
## 1 Answer
This is a basic result in functional analysis sometimes called ... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Resolution_(logic) | # Resolution (logic)
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic. In other words, iteratively applying the resolution rule in a suitable way allows for telling whether... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 24, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/quantum-interpretations+quantum-mechanics | # Tagged Questions
0answers
17 views
### Showing that the CHSH inequality is not violated
I can usually work out whether CHSH inequality is violated when the observables that we are measuring and the state we are in is given explicitly, but I'm struggling with the generality of the ...
2answers
111 views
### Is eve... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/harmonic-oscillator | # Tagged Questions
The term "harmonic oscillator" is used to describe any system with a "linear" restoring force that tends to return the system to a equilibrium state. There is both a classical harmonic oscillator and a quantum harmonic oscillator. Both are used to as toy problems that describe many physical systems.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 60, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/differential-geometry/207056-function-distance-point-outside-sphere-any-point-its-surface-print.html | # function for distance from a point outside a sphere to any point on its surface
Printable View
• November 8th 2012, 10:28 AM
mosibat
1 Attachment(s)
function for distance from a point outside a sphere to any point on its surface
Hi
I have a point m outside a sphere. The sphere center is o and r is the radius of 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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/32538/finite-axiom-of-choice-how-do-you-prove-it-from-just-zf/32545 | ## Finite axiom of choice: how do you prove it from just ZF?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The axiom of choice asserts the existence of a choice function for any family of sets F. Suppose, however, that F is finite, or even that F just has on... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculators/82873-implicit-differentiation-ti-nspire-cas.html | # Thread:
1. ## Implicit Differentiation on TI-Nspire CAS
Hi there, I'm trying to do the following implicit differentiation on my TI-Nspire CAS, and I can't figure it out.
$v = \frac{1}{3} \pi r^2 h$
I want to get: $\frac{dv}{dt} = \frac{2}{3} \pi r \frac{dr}{dt} \frac{dh}{dt}$
Is there any way to get the Nspire 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": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://programmingpraxis.com/2010/07/20/solving-systems-of-linear-equations/?like=1&_wpnonce=ef2a6945bd | # Programming Praxis
A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer
## Solving Systems Of Linear Equations
### July 20, 2010
In today’s exercise we continue the examination of matrix operations that we began previously. Our goal is to be able to solve a system of equ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/tagged/powers+calculus | # Tagged Questions
1answer
71 views
### Definite integral including the ratio and power functions of a single variable
I find trouble in calculating the following integral: $$\int_0^R \frac{m\cdot x}{m+s\cdot x^a} \,dx$$ Mathematica does not provide an output for this function, however, there seems to be an output .... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/4435/finding-alpha-such-that-f-alphaxy-fxfy?answertab=votes | # Finding $\alpha$ such that $f(\alpha(x+y))=f(x)+f(y)$
Problem taken from the link: http://web.mit.edu/rwbarton/Public/func-eq.pdf I am stating the question here
For which $\alpha$ does there exists a nonconstant function $f: \mathbb{R} \to \mathbb{R}$ such that $f(\alpha(x+y))=f(x)+f(y)$ for all $x,y \in \mathbb{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": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/102974-poincare-s-theorem.html | # Thread:
1. ## Poincare's Theorem
Let H1 & H2 be subgroups of G. How can it be shown that if H1 & H2 have finite index in G then so the intersection of H1 & H2.
2. Originally Posted by thomas_donald
Let H1 & H2 be subgroups of G. How can it be shown that if H1 & H2 have finite index in G then so the intersection o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3756127 | Physics Forums
Page 1 of 5 1 2 3 4 > Last »
## Bosons and Fermions in a rigorous QFT
I'm wondering, is there still a sharp distinction between Bosons and Fermions in a rigorous QFT, if exsits?
My question is motivated by the following, consider one of the equations of motion of QED:
$$\partial_\nu F^{\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": 0, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/24594/survey-articles-on-homotopy-groups-of-spheres/24598 | ## Survey articles on homotopy groups of spheres
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Are there general surveys or introductions to the homotopy groups of spheres? I'm interested especially in connections to low-dimensional geometry and topology.
-... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/156500-triple-integral.html | # Thread:
1. ## Triple integral
Find the volume of the ellipsoid $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1$ by solving the triple integral after making the transformation $x = au, y = bv$ and $z = cw$
I'm just a bit confused here because this does not seem like a Jacobian transformation. I know what the tri... | {"extraction_info": {"found_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/10512/theories-of-noncommutative-geometry/10533 | Theories of Noncommutative Geometry
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
[I have rewritten this post in a way which I hope will remain faithful to the questioner and make it seem more acceptable to the community. I have also voted to reopen it. -- PLC]
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/153097/flattening-a-2d-normal-distribution | # “Flattening” a 2D Normal Distribution
I would like to model the probability of a point being at a certain place on a 2D grid. The X coordinate of the point varies according to a normal distribution with mean $0$ and standard deviation $\sigma$. The Y coordinate varies according to a normal distribution with the same... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/08/11/internal-categories/?like=1&_wpnonce=34114a6dfa | # The Unapologetic Mathematician
## Internal Categories
Just like we have monid objects, we can actually define something we could sensibly call a “category object”. In this case, however, it will be a little more accurate to use the term “internal category”.
This is because a (small) category isn’t just a set with ... | {"extraction_info": {"found_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": 20, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/50441?sort=oldest | ## Forbidden mirror sequences
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $\cal{M}$ be a finite collection of two-sided mirrors, each an open unit-length segment in $\mathbb{R^2}$, and such that the segments when closed are disjoint. A ray of light tha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Uniqueness | Uniqueness quantification
From Wikipedia, the free encyclopedia
(Redirected from Uniqueness)
Jump to: navigation, search
"Unique" redirects here. For other uses, see Unique (disambiguation).
This article includes a list of references, related reading or external links, but . (January 2013)
In mathematics and logic,... | {"extraction_info": {"found_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": 8, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/92473-finding-eigenvector-print.html | # Finding the eigenvector
Printable View
• June 10th 2009, 01:56 PM
Nerdfighter
Finding the eigenvector
Given a specific Eigenvalue $\lambda$, how do I find an eigenvector of a Matrix $A$?
Specifically, if $\lambda = 4$ and $A =$ $\left[\begin{array}{rrr}3&0&-1\\2&3&1\\-3&4&5\end{array}\right]$
By the way, is there... | {"extraction_info": {"found_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": 29, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=4240256 | Physics Forums
## Series and Future Stock Prices
1. The problem statement, all variables and given/known data
I have a question here that seems so simple, yet I can't seem to wrap my head around what they're asking.
It says that one method of pricing a stock is to set the share price equal to the sum of all future 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": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://programmingpraxis.com/2011/04/12/ | # Programming Praxis
A collection of etudes, updated weekly, for the education and enjoyment of the savvy programmer
## House Of Representatives
### April 12, 2011
The United States counts its citizens every ten years, and the result of that census is used to allocate the 435 congressional seats in the House of Rep... | {"extraction_info": {"found_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": 1, "mimetex.cgi": 0, "/images/mat... |
http://en.m.wikibooks.org/wiki/Sound_Synthesis_Theory/Sound_in_the_Digital_Domain | # Sound in the Digital Domain
## Introduction
Digital systems (e.g. computers) and formats (e.g. CD) are clearly the most popular and commonplace methods of storing and manipulating audio. Since the introduction of the compact disc in the early 1980s, the digital format has provided increasingly greater storage capac... | {"extraction_info": {"found_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": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/game-theory+decision-theory | # Tagged Questions
1answer
59 views
### Deducing probability of an event, when opponent's type is uncertain
Suppose, two players I and II, given a state space of three states$\{a,b,c\}$ with a common prior, $p(a) = p(b) =p(c) =1/3$, are endowed with two partitions of state space, \$\mathscr{P}_\text{I} = ...
1answer... | {"extraction_info": {"found_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/15710/why-is-it-that-mathbbq-cannot-be-homeomorphic-to-any-complete-metric-spac | # Why is it that $\mathbb{Q}$ cannot be homeomorphic to _any_ complete metric space?
Why is it that $\mathbb{Q}$ cannot be homeomorphic to any complete metric space?
Certainly $\mathbb{Q}$ is not a complete metric space. But completeness is not a topological invariant, so why is the above statement true?
-
1
Don'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": 108, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/56022/measurability-of-the-inverse-of-a-measurable-function/56061 | # Measurability of the inverse of a measurable function
Let $m$ denote Lebesgue measure, and let $f:[0,1] \to [0,1]$ be a (Lebesgue) measurable and bijective function. In general, it is not true that $f^{-1}$ is measurable. However, suppose that we now have the condition that $\forall A \subset [0,1]$, $m(A) = 0 \Righ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 63, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/86338-trig-transformation.html | # Thread:
1. ## trig transformation
hello, i need help with this particular transformation, I was just wondering if my answer is correct
the transformation is this f(x) = 3 cos 2 (x - π/4) + 1 it asks me to find the period, amplitude, phase shift, which I have as π, 3 and π/4 to the right respectively. It then goes ... | {"extraction_info": {"found_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/260436/equation-to-determine-radius-for-a-circle-that-should-intersect-a-given-point | # Equation to determine radius for a circle that should intersect a given point?
Simple question. I tried Google but I don't know what search keywords to use.
I have two points on a 2d plane. Point 1 = x1 and y1, and Point 2 = x2 and y2.
I'd like to draw a circle around Point 1, and the radius of the circle should 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": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/tagged/finite-population | # Tagged Questions
The finite-population tag has no wiki summary.
0answers
12 views
### How to handle samples with many replicates for population estimation,when sample size is small?
I have a sample with very small sample size ($n<10$) and I would like to estimate the population mean. However, some of the samples ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/47969/determing-x-y-increase-by-angle | # determing x,y increase by angle?
If I had a position of 0,0 and I had an angle of 45 degrees (or any number) and my velocity was 1 what would be the x,y increase?
For example if I had a 90 degree angle, and I had a velocity of 1. Then because my angle is straight up, my increase would be 1y and 0x.
Not sure if thi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/83809-n-1-prove-number-even-perm-n-equals-number-odd-perm-n.html | # Thread:
1. ## n > 1, prove the number of even perm. of [n] equals the number of odd perm. of [n]
For n > 1, prove that the number of even permutations of [n] equals the number of odd permutations of [n].
2. Originally Posted by qtpipi
For n > 1, prove that the number of even permutations of [n] equals the number o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/15841/can-someone-explain-the-color-pink-to-me?answertab=active | # Can someone explain the color Pink to me?
I just finished watching this interesting video:
http://youtu.be/S9dqJRyk0YM
It does a very quick explanation of how pink light doesn't exist, and that the concept of pink is our brain's attempt at filling in a gap in the spectrum.
My question is, how does our brain perce... | {"extraction_info": {"found_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": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=4238454 | Physics Forums
seeking derivation of real scalar field Lagrangian
Here and there I come across the following formula for the Lagrangian density of a real scalar field, but not a deriviation.
[tex]
\mathcal{L} = \frac {1}{2} [ \dot \phi ^2 - ( \nabla \phi ) ^2 - (m \phi )^2 ]
[/tex]
Could someone show me where this... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3781680 | Physics Forums
## Can the existence of nonstandard hyperreal extensions be proved?
I have begun to read about the hyperreals, and am wondering whether the natural extensions of real-valued functions to hyperreal-valued functions is simply a definition of the hyperreals, or can it be proved? Or is it accepted as an ax... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/54917/surely-space-time-curvature-does-not-explain-gravity-it-just-describe-its-effec | # Surely space-time Curvature does not explain gravity, it just describe its effects?
In special relativity co-moving objects see the other's 4-velocity as being only temporal.
When they move relative to each other they see the other's 4-velocity has rotated so that it points less in the temporal direction but now ha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/02/08/sets-and-functions/?like=1&source=post_flair&_wpnonce=d0199d491e | # The Unapologetic Mathematician
## Sets and functions
I’m soon going to need to really use the notion of a function, and I want to make sure that I lay the groundwork properly. This is also a good place to mention a few things about sets.
For most of my purposes, a naïve concept of sets will suffice. A set is a col... | {"extraction_info": {"found_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": 65, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/38517/in-relatively-simple-words-what-is-an-inverse-limit/38523 | # In (relatively) simple words: What is an inverse limit?
I am a set theorist in my orientation, and while I did take a few courses that brushed upon categorical and algebraic constructions, one has always eluded me.
The inverse limit. I tried to ask one of the guys in my office, and despite a very shady explanation ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 153, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/10648/why-is-a-circle-in-a-plane-surrounded-by-6-other-circles?answertab=votes | # Why is a circle in a plane surrounded by 6 other circles
When you draw a circle in a plane you can perfectly surround it with 6 other circles of the same radius. This works for any radius. What's the significance of 6? Why not some other number?
I'm looking for an answer deeper than "there are 6*60=360 degrees in 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": 36, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/200623-biased-ness-ols-estimates.html | # Thread:
1. ## Biased-ness of OLS estimates
If the picture is too small, please view attached pic.
Hey guys, so I'm just reading through the proof of the biased-ness of OLS estimates if an important independent variable is left out and I'm just stuck at the very end, basically the mathematical part that confuses 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": 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/97175/small-sums-of-entries-in-submatrices-strange-phenomenon/97293 | ## small sums of entries in submatrices - strange phenomenon
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose that $x \in \mathbb{R}^{n}$ is a vector of small positive fractions, i.e. $x_{i} \approx \frac{1}{n}$. The exact values are unknown. I form 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": 32, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://wiki.stat.ucla.edu/socr/index.php?title=SOCR_EduMaterials_Activities_LawOfLargeNumbers&redirect=no | # SOCR EduMaterials Activities LawOfLargeNumbers
## Overview
This is part I of a heterogeneous activity that demonstrates the theory and applications of the Law of Large Numbers (LLN). Part II and Part III of this activity contain more examples and diverse experiments. The SOCR LLN applet is available here.
### Goal... | {"extraction_info": {"found_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://math.stackexchange.com/questions/211265/continuity-of-floor-function-in-mathbb-z | # continuity of floor function in $\mathbb Z$
Suppose $$f(x)=\left|x-2\left\lfloor\frac{x+1}{2}\right\rfloor\right|$$ To prove the continuity of $f$ in $\mathbb {R}$ we have to prove it first in $\mathbb {Z}$ then at $\mathbb{R} - \mathbb{Z}$. But why do we have to prove the continuity if $x=2n$ and $x=2n-1$ ($n \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": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/30157/at-what-g-is-terminal-velocity-not-terminal/30162 | # At what g is terminal velocity not terminal?
How weak would gravity need to be in order for a human to reliably survive the terminal velocity of falling through air?
(Context: watching scifi on a space station with a variety of artificial gravities, it occurred to me that medium-strength gravity would have some adv... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 17, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/17819?sort=newest | ## What’s the origin of the naming convention for the standard basis of sl_2?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
$\mathfrak{sl}_2(\mathbb{C})$ is usually given a basis $H, X, Y$ satisfying $[H, X] = 2X, [H, Y] = -2Y, [X, Y] = H$. What is 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": 16, "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/40337?sort=newest | ## Ingenuity in mathematics
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
[This is just the kind of vague community-wiki question that I would almost certainly turn my nose up at if it were asked by someone else, so I apologise in advance, but these sorts 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": 53, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://topologicalmusings.wordpress.com/tag/identity/ | Todd and Vishal’s blog
Topological Musings
Tag Archive
You are currently browsing the tag archive for the ‘identity’ tag.
A note on a simple polynomial-logarithmic algebraic identity
November 10, 2008 in Elementary Math Problem Solving, Problem Corner, Some theorems | Tags: gauss, identity, logarithmic, lucas, pol... | {"extraction_info": {"found_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": 48, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=144171 | Physics Forums
## Electric field arising from a uniform charge distribution of infinite extent
Consider a uniform charge distribution occupying all of (flat) spacetime,
$$\rho(t,x,y,z) = \text{constant} \;\;\;\;\; ,\; (t,x,y,z) \in R^{1,3}$$
Because this charge distribution is translationally invariant, it seems re... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/73071/a-constrained-topological-sort | A constrained topological sort?
Suppose that one has a directed, acyclic graph G, and each vertex $v$ contains a (positive) value $a_v$. Additionally, let $r$ be a constant. For my purposes, $r>1$, but this might not matter. Let $n$ be the number of vertices in G and let $[n]:=\{1,2,\ldots, n\}$.
A topological 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": 39, "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/792/how-to-perform-risk-factor-calculation/801 | # How to perform risk factor calculation?
I am studying Arbitrage Pricing Theory (APT) and I have a question about calculating factor exposures.
Assume:
\begin{equation} r = \beta_1r_1 + \beta_2r_2 + ... + \beta_kr_k + r_e \end{equation}
Where:
$\beta_i$ is the exposure of the asset to a factor
$r$ is the return ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/14262/the-problem-of-infinity/14276 | ## The problem of infinity [closed]
### Background and motivation
The following is copied from my blog since someone thought it was the clearest statement I had made regarding a problem I recently posed. On their advice, it is a community wiki. I would encourage, however, I discussion somewhere else (meta.MO perhaps?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 32, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/166541/ideal-generated-by-differential-forms/167442 | # Ideal generated by differential forms
I have troubles picturing what elements belong to a particular ensemble.
Let $\omega_1$,...,$\omega_r$ be differential 1-forms on a $C^\infty$ n-manifold that are independent at each point. Considering a complete base $\omega_1$,...,$\omega_r$,...,$\omega_{r+1}$,...,$\omega_{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": 22, "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/24607?sort=votes | ## What is a Module over a Lie algebroid?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $\alpha: \mathfrak g_A \to T_{A/k}$ be a Lie algebroid over a $k$-algebra $A$. Numerous facts about and its universal enveloping algebra comes from the theory of ring... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://luckytoilet.wordpress.com/2011/05/20/simplifying-a-sum-of-consecutive-cubes/ | # Lucky's Notes
Notes on math, coding, and other stuff
## Simplifying a sum of consecutive cubes
If you were asked to find the sum of the first four cubes, you would easily be able to do so:
$1^3 + 2^3 + 3^3 + 4^3 = 100$
But here you may notice something interesting:
$1^3 + 2^3 + 3^3 + 4^3 = (1+2+3+4)^2$
It turn... | {"extraction_info": {"found_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": 53, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/3264/thermal-radiation-spectrum-of-a-blackbody/3269 | # Thermal radiation spectrum of a blackbody
Why is it that thermal radiation of a black body usually described by a spectral distribution function rather than an intensity vs frequency curve?
I have a vague explanation for this: Any measured intensity of radiation will contain a spectrum of frequencies which are impo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/5268?sort=oldest | Functorial Whitehead Tower?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The Whitehead tower of a (pointed) space is a tower of spaces which successively kills the bottom homotopy groups. The first two spaces can be constructed functorially (at least for suitab... | {"extraction_info": {"found_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/tagged/statistical-mechanics | # Tagged Questions
The study of large systems through coarse graining microscopic descriptions, providing a more detailed understanding of thermodynamics.
0answers
26 views
### Lattice model completely constrained by boundary data
I am dealing with a lattice model that has the peculiar property that if I specify al... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 38, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.