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http://mathoverflow.net/questions/39406/how-do-you-handle-numerical-issues-when-converting-optimization-problems-to-decis/39414 | ## How do you handle numerical issues when converting optimization problems to decision problems?
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The trick of converting an optimization problem to a decision problem is well-known - you add a real number input ... | {"extraction_info": {"found_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/gravity+quantum-gravity | # Tagged Questions
3answers
570 views
### Why is gravity such a unique force?
My knowledge on this particular field of physics is very sketchy, but I frequently hear of a theoretical "graviton", the quantum of the gravitational field. So I guess most physicists' assumption is ...
1answer
175 views
### Is the quanti... | {"extraction_info": {"found_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/65396-integral.html | # Thread:
1. ## Integral
I want to evaluate the volume inside $r=cos(\theta)$.
Thanks.
2. $\begin{aligned}r & = \cos \theta \\ r^2 & = r\cos \theta \\ x^2 + y^2 & = x \\ (x-\tfrac{1}{2})^2 + y^2 & = \tfrac{1}{4} \end{aligned}$
Revolving it around the x-axis produces a sphere with radius $\tfrac{1}{2}$ .
3. That is... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://quant.stackexchange.com/questions/103/how-does-the-risk-neutral-pricing-framework-work | # How does the “risk-neutral pricing framework” work?
I've struggled for a long time to understand this - What is this? And how does it affect you?
Yes I mean risk neutral pricing - Wilmott Forums was not clear about that.
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1
Can you please elaborate on your question a little? "how does it affect you?" Also, maybe... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 40, "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/37130?sort=oldest | ## Integrability of distributions close to a given one.
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In this and this papers Thurston proves that every distribution is homotopic to an integrable one (in the first one for codimension greater than one and 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": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/93825-solved-few-beg-trig-probs-angles.html | # Thread:
1. ## [SOLVED] Few beg. Trig Probs Angles
So when you have 90-x in a right triangle that you are trying to solve cos sin and tang etc.. those questions, how do you include angle degrees into your calculations.. For instance,
l there is a h(3) line
4 l i just can't
l draw online
l_____________x
5
I know 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": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/27224/list | ## Return to Answer
1 [made Community Wiki]
In my dissertation I developed an algorithm for finding bounds on $H_2$ of a finitely presented group with finite field coefficients. I was motivated by a conjecture Quillen on the (co)homology of linear groups. As such, I included an appendix with presentations of several ... | {"extraction_info": {"found_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=4181344 | Physics Forums
## Variant of Bocard's Problem
[All numbers as assumed to be integers]
Bocard's problem asks to find the solutions to the Diophantine equation $n!=m^2-1$. The only known $(n,m)$ pairs are $(4,5),(5,11),(7,71)$, and it is conjectured that there are no more. A generalization of this problem would be $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": 68, "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/83591-likelihood-ratio-test-likelihood-function.html | # Thread:
1. ## Likelihood Ratio Test & Likelihood Function
Suppose that X_1,X_2,...,X_n1, Y_1,Y_2,...,Y_n2, and W_1,W_2,...,W_n3 are independent ranom samples from normal distributions with respective unknown means μ1, μ2, and μ3 and variances (σ1)^2, (σ2)^2, (σ3)^2.
Find the likelihood ratio test for H_o: (σ1)^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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/statistics/88730-placing-identical-distinct-objects.html | # Thread:
1. ## Placing Identical/Distinct Objects
Hello:
Suppose there are 10 identical red balls and 10 different blue balls. I am wondering if the following is correct. Suppose we want to put those balls into 4 boxes such that:
(a) there is a box containing exactly 2 red balls.
I assume this means that the box 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=42390 | Physics Forums
## Understanding set theory
I'm trying to prove something small with set theory and since I'm new to it, I've run into a problem. I can't understand what the following means exactly and how to proceed further. Or where the mistake is, if there is one. I think there is, because it seems... freaky.
$$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": 0, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/75795?sort=oldest | ## In an arbitrary abelian category, does chain complex homology commute with coproduct?
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On page 55 of Weibel's Introduction to homological algebra the following passage appears:
Here are two consequences that u... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.reference.com/browse/Vacuum+bubble | Definitions
Nearby Words
Feynman diagram
In quantum field theory a Feynman diagram is an intuitive graphical representation of the transition amplitude or other physical quantity of a quantum system.
Within the canonical formulation of quantum field theory a Feynman diagram represents a term in the Wick's expansion ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 153, "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/m... |
http://mathhelpforum.com/differential-geometry/112144-integrate-using-complex.html | # Thread:
1. ## Integrate using complex
I stuck with this question I need any hint in it thanks in advance
show that
$\int_{0}^{\pi} \sin ^{2n} \theta d\theta =\frac{(2n)! \pi}{2^{2n} (n!)^2}$
my work
let
$z=e^{i\theta}$
$d\theta = \frac{dz}{iz}$
and
$\sin \theta = \frac{1}{2i}\left(z-\frac{1}{z} \right)$
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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 47, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/27164/why-is-fourier-analysis-so-handy-for-proving-the-isoperimetric-inequality/27192 | ## Why is Fourier analysis so handy for proving the isoperimetric inequality?
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I have just completed an introductory course on analysis, and have been looking over my notes for the year. For me, although it was ce... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/25911/random-walks-in-z2-z2-intrinsic-characterization-of-euclidean-distance-part/25947 | Random Walks in $Z^2$/$Z^2$-intrinsic characterization of Euclidean distance Part II
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For some context see http://mathoverflow.net/questions/25846/random-walks-in-z2-z2-intrinsic-characterization-of-euclidean-distance... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 71, "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/112467/is-the-domain-of-an-one-to-one-function-a-set-if-the-target-is-a-set?answertab=oldest | # Is the domain of an one-to-one function a set if the target is a set?
This is probably very naive but suppose I have an injective map from a class into a set, may I conclude that the domain of the map is a set as well?
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2
Perhaps you should clarify what is meant by "map" in this question. The answers using replac... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/46653-laurent-s-theorem.html | # Thread:
1. ## Laurent's Theorem
Hi just a bit of help needed here as I don;t know where to start:
Part (A)
----------------------------
Suppose $f(z) = u(x,y) + iv(x,y)\;and\;g(z) = v(x,y) + iu(x,y)$ are analytic in some domain D. Show that both u and v are constant functions..?
I guess we have to use the CRE her... | {"extraction_info": {"found_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://math.stackexchange.com/questions/138792/cardinality-does-ab-2b-if-a-le-2b/138810 | # Cardinality: does $|A^B|=|2^B|$ if $|A| \le |2^B|$?
Taking finite powers of a countably infinite set still yields a countable set: $$|\mathbb{N}|=|\mathbb{N}^k|.$$
It's also known that countable powers of the continuum still have the same cardinality as the continuum: $$|2^\mathbb{N}|=|\mathbb{R}|=|\mathbb{R}^k|=|\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 19, "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/38132/calculate-intersection-of-2-points | # Calculate intersection of 2 points
I have 2 points with bearing's coming from them, I need to calculate a 3rd point(intersection of bearing's from point 1,2) but am unsure of the maths required to do this. Could someone give me an example of how to do this.
Edit - The bearing's I am referring to are degree's from 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": 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/67039/decomposition-of-l-02gl-2-mathbbq-backslash-gl-2a-psi/67064 | Decomposition of $L_0^2(GL_2({\mathbb{Q}}) \backslash GL_2(A), \psi)$
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Two questions concerning the decomposition of $L_0^2(GL_2({\mathbb{Q}}) \backslash GL_2(A), \psi)$, where $\psi$ is a Hecke character on the adeli... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-software/146743-maple-logical-question.html | # Thread:
1. ## Maple / a logical question
My lecturer gave us the following question:
$f(x):=\frac{x}{x^{sin(x)}-1}$
Using Maple, find the limit of f(x) in $x=0^+$.
In order to approve Maple's answer, find the answers of the following equations:
* $f(x)=-0.1$ ( I got something with $10^-4$)
* $f(x)=-0.01$ ( I got ... | {"extraction_info": {"found_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://micromath.wordpress.com/2008/04/14/donald-knuth-calculus-via-o-notation/?like=1&_wpnonce=5e79d40c83 | # Mathematics under the Microscope
Atomic objects, structures and concepts of mathematics
Posted by: Alexandre Borovik | April 14, 2008
## Donald Knuth: Calculus via O notation
Continuing the theme of alternative approaches to teaching calculus, I take the liberty of posting a letter sent by Donald Knuth to to the 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 144, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/44295/a-property-of-continuous-maps-with-respect-to-compact-subsets | ## A property of continuous maps with respect to compact subsets
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I'm interested in continuous maps between topological spaces $f:X\to Y$ such that for any compact subset $L$ of $Y$ contained in $f(X)$, there is 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": 30, "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/104051/list | ## Return to Answer
1 [made Community Wiki]
I like the phrase counting in two different ways'' -- which I learned in a math camp. If you're not sure what it means, I suggest the exercise of trying to prove that $2^n = \sum_{i=0}^n {n\choose i}$ by looking for a proof which could be aptly described by this phrase. | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/21466-logs.html | # Thread:
1. ## Logs
Evaluate the expression without using a calculator.
log3^3^11
2. Originally Posted by soly_sol
Evaluate the expression without using a calculator.
log3^3^11
is this log to the base 10?
$\log 3^{3^{11}} = 3^{11} \log 3$
if you can't use a calculator, you'd have to use a log table or something... | {"extraction_info": {"found_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/31239/poincare-bendixson-theorem | # Poincare-Bendixson Theorem
Can someone sketch some ideas of how to use the Poincare-Bendixson Theorem to prove that there must be a fixed point contained inside a periodic orbit?
-
I have a feeling that that statement is false. I do not have a counterexample though. – picakhu Apr 6 '11 at 2:43
I cant see the questi... | {"extraction_info": {"found_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://mathoverflow.net/questions/27794?sort=newest | ## Relative canonical sheaf
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Hi.
I want to know if for $f:X\to S$ a proper flat holomorphic map with n-dimensionnal fibers over reduced complex space S, the relative canonical sheaf $w_{X/S}:=H^{-n}(f^{!}O_{S})$ ... | {"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": 36, "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/295379/why-is-the-moduli-space-of-flat-connections-a-symplectic-orbifold/295505 | # Why is the moduli space of flat connections a symplectic orbifold?
In her Lectures on Symplectic Geometry on page 159, Ana Cannas da Silva writes "It turns out that $\mathcal{M}$ is a finite-dimensional symplectic orbifold."
Can somebody give me a reference for this result, preferably including a detailed definitio... | {"extraction_info": {"found_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": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/6098/reynolds-number-turbulence-regime-and-drag-force/6156 | # Reynolds number, turbulence regime, and drag force
I am trying to model a system in which cubes of about 2 cm in size are floating in a circular water thank of about 30 cm in diameter. The cubes move around under the influence of the fluid flow induced by four inlets that point toward the center of the tank, and are... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "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/76545?sort=oldest | ## Is it possible to reliably generate a particular approximation of an ideal knot via a simulated annealing approach?
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Say I take a cord, tie a loose knot in three-dimensional space, and pull tightly on the ends ... | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/78873/list | 3 edited tags
2 edited tags
1
# A model of CH +$\lnot \diamondsuit$
All of the models of CH which I know of also satisfy $\diamondsuit$. What is the easiest way to produce a model of CH wherein $\diamondsuit$ is false? | {"extraction_info": {"found_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://mathoverflow.net/questions/9854/uniformly-sampling-from-convex-polytopes/9871 | ## Uniformly Sampling from Convex Polytopes
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How to choose a point uniformly from a convex polytope $P \subset [0,1]^n$ defined by some inequalities, Ax < b ? (Here A is an m-by-n matrix, x is n-by-1 and b is m-by... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-statistics/182000-mann-whitney-u-test.html | # Thread:
1. ## Mann-Whitney U test
While I was analysing my data (regards to number of chemotherapy received by 2 groups of patients) I note the median values of both groups are same but applying the Mann-Whitney U test, it showed that there was significant difference in the number of chemptherapy received. Is it po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/5331/index?nomenu=1 | ## 'Decoding Transformations' printed from http://nrich.maths.org/
### Show menu
In this question, each of the letters $I$, $R$, $S$ and $T$ represents a different transformation.
We can do one transformation followed by another. For example, $R S$ means do $R$, then $S$''.
We can also undo transformations. For exa... | {"extraction_info": {"found_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": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/lebesgue-integral+limit | # Tagged Questions
0answers
64 views
### Show $f$ is in $L^1$ (d$\mu$) space and $_X\int f$ d$\mu=\lim_{n\to \infty}\int_X f_n d\mu$
Suppose $f$ is in $L^1$($\mu$). Prove that for each $\epsilon > 0$ , there exists a $\delta > 0$ so that the $\int |f|\mathrm d\mu$ < $\epsilon$ over the set $E$ whenever \$\mu(E) < ..... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=482183 | Physics Forums
## Exact meaning of a local base at zero in a topological vector space...
I am confused as to exactly what a local base at zero (l.b.z.) tells us about a topology. The definition given in Rudin is the following: "An l.b.z. is a collection G of open sets containing zero such that if O is any open set 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": 1, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/288656/product-rule-of-stochastic-exponents | # Product rule of stochastic exponents
we know that for standard exponents, $(e^x)(e^y)=e^{(x+y)}$. What is the product rule for stochastic exponents?
$E_n(U)E_n(V)=E_n(U+V+[U,V])$ where $U$ and $V$ are stocchastic sequences, $E_n$ is the stochastic exponent and $[U,V]_n$=$\sum_{k=1}^n(\Delta_Uk*\Delta_Vk)$.
That is... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/140922/karhunen-loeve-expansion-of-poisson-process?answertab=oldest | # Karhunen-Loève expansion of Poisson process
Let $X_t,t\geq 0$ be a Poisson process with rate parameter $\lambda$. Compute the Karhunen-Loève expansion of $X$ in interval $[0, T]$. How about the KL expansion of the centered process $X_t−\lambda t$?
The auto-correlation function of Poisson process is $R(s,t)=\lambda^... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/240667/determining-conjugates-of-sqrt-5-sqrt-6-over-mathbbq/240679 | # Determining conjugates of ${\sqrt 5 + \sqrt 6 }$ over $\mathbb{Q}$
The easy part is algebraic manipulation:
$x - \left( {\sqrt 5 + \sqrt 6 } \right) = 0 \Rightarrow {x^2} = 5 + 6 + 2\sqrt {30} \Rightarrow {x^2} - 11 = 2\sqrt {30} \Rightarrow p\left( x \right) = {x^4} - 22{x^2} + 1 = 0$. Solutions to this equation 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": 30, "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/18877/are-there-countable-index-subrings-of-the-reals | ## Are there countable index subrings of the reals?
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1. Does ${\mathbb R}$ have proper, countable index subrings? By countable I mean finite or countably infinite. By subring I mean any additive subgroup which is ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "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/97138/functions-holomorphic-on-a-region-minus-a-cantor-set | ## Functions holomorphic on a region minus a Cantor set
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Let $X$ and $Y$ be simply connected open regions of $\mathbb{C}$, and let $Z \subset X$ be a Cantor set. Assume we have a homeomorphism $f$ from $X$ to $Y$,... | {"extraction_info": {"found_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://samjshah.com/tag/calculus/ | # Some Random Things I Have Liked
Posted on May 10, 2013 by
## The Concept of Signed Areas
In calculus, after first introducing the concept of signed areas, I came up with the “backwards problem” which really tested what kids understood. (This was before we did any integration using calculus… I always teach integrat... | {"extraction_info": {"found_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": 18, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/97428/understanding-tensor-product-surfaces?answertab=active | # Understanding tensor product surfaces
Recently I bought a book about curves and surfaces (Curves and Surfaces for Computer Graphics by David Salomon), and I'm having trouble understanding the tensor product surfaces.
I think I understand the idea behind the basic curves:
• Linear interpolation
• Lagrange polynomia... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/17396/can-a-group-be-a-finite-union-of-left-cosets-of-infinite-index-subgroups | ## Can a group be a finite union of (left) cosets of infinite-index subgroups?
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To be more precise (but less snappy): is there an example of a group G with finitely many infinite-index subgroups H_1, ..., H_n and ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/43790/where-is-noncommutativity-in-the-state-effect-formalism-of-quantum-mechanics?answertab=active | # Where is noncommutativity in the state-effect formalism of quantum mechanics?
In quantum information theory, one can adopt the basic formalism where every system is given by an operator algebra, state preparation procedures correspond to linear functionals on that algebra (macroscopic systems preparing quantum syste... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3961676 | Physics Forums
## Is potential energy real?
Potential energy has always bothered me. Is it just an accounting trick to describe that energy is always conserved ( E = K + U)? Because if so, there are probably other ways we can describe this.
PhysOrg.com physics news on PhysOrg.com >> Promising doped zirconia>> New ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/65721/uses-of-lebesgues-covering-lemma | # Uses of Lebesgue's covering lemma
Consider Lebesgue's covering lemma in the following form:
Let $(X,d)$ be a compact metric space and let $\{U_i\}_{i\in I}$ be an open cover of $X$. Then there exists $\delta>0$ such that each subset $Y$ of $X$ of diameter less than or equal to $\delta$ lies within some $U_i$.
What... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/statistics/5388-very-very-urgent-plz-help.html | # Thread:
1. ## Very Very Urgent!! Plz Help
a) how many times must a die be thrown to be sure that the same number occurs twice?
b) How many times must two dice be thrown to be sure that the same total occurs at least six times?
c) How many times must n dice be thrown to be sure that the same total score occurs at ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/254814/why-must-we-distinguish-between-rational-and-irrational-numbers/254836 | # Why must we distinguish between rational and irrational numbers?
The difference between rational and irrational numbers is always stated as: rational numbers can be written as the ratio of two integers, and irrational numbers can't. However, why do mathematicians make a distinction between these two types of numbers... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/41697/what-is-the-spin-rotation-operator-for-spin-1-2 | # What is the spin rotation operator for spin > 1/2?
For spin $\frac{1}{2}$, the spin rotation operator $R_\alpha(\textbf{n})=\exp(-i\frac{\alpha}{2}\vec{\sigma}\cdot\textbf{n})$ has a simple form:
$$R_\alpha(\textbf{n})=\cos\biggl(\frac{\alpha}{2}\biggr)-i\vec{\sigma}\cdot\textbf{n}\sin\biggl(\frac{\alpha}{2}\biggr)... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/2150-trig-theory-question.html | # Thread:
1. ## Trig Theory Question
In order to have an inverse a normal function must be one to one, What must happen to the trigonometric functions in order for them to have inverses.
Thanks alot
2. Originally Posted by aussiekid90
In order to have an inverse a normal function must be one to one, What must happe... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-statistics/156548-time-series.html | # Thread:
1. ## Time series
I have a book series of time and says in part:
An example of time series would be:
$Y_t = 0.8Y_{t -1} + \epsilon_t,$ $t = 1, 2 ...$
Then they say, this series can also be expressed as:
$Y_t = \displaystyle\sum_{i=1}^t{0.8^{t - i}} \epsilon_i$
How do they do and why they develop the 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": 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/revisions/72329/list | ## Return to Answer
3 added 296 characters in body
Here is a trial proof for the question over $Q_p$.
Write $J[f(x)^k]$ for the general Jordan form of a irreducible $f$, being $k$ identical blocks joined by 1's in general (minimal polynomial of block is $f^k$).
Let $A$ be finite order over $Q_p$, so $A\sim\oplus J[... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 105, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/geometry/1679-circle-proof.html | # Thread:
1. ## Circle proof
No idea how to get this one out, i know it is probably simple, just can't see it...grrr
Attached Thumbnails
2. Originally Posted by jacs
No idea how to get this one out, i know it is probably simple, just can't see it...grrr
There is something wrong here, or in my interpretation of this
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/43964?sort=votes | ## Folner sequences of amenable groups of exponential growth
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Let $G$ be an amenable group of exponential growth and let $S$ be a finite symmetric generating set. For each $k$, let $B_{k}$ be the closed ball of ra... | {"extraction_info": {"found_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://mathhelpforum.com/algebra/96781-radicals.html | # Thread:
1. ## Radicals
I have no clue how to do these, and the book I have does not help at all.
$(\sqrt{3} + \sqrt{5})^2$
On this one i got stuck after $8+\sqrt{15}+\sqrt{15}$
Multiply. $(\sqrt{14}+\sqrt{5})(\sqrt{14}+\sqrt{5})$
Solve. $\sqrt[3] {x-7}=2$
Solve $\sqrt{2x+1}=2x-5$
2. Originally Posted by alexl1... | {"extraction_info": {"found_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": 44, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/suvat-equations+homework | # Tagged Questions
1answer
45 views
### Projectile's angle in midflight
For a missile travelling from (0,0) at angle $\theta$ (to the horizontal) and initial velocity $u$, the y (vertical) position at time t is given by $s_{y} = u\sin (\theta) t - 0.5gt^{2}$ and the x ...
2answers
90 views
### Doubt in Kinematics
... | {"extraction_info": {"found_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://cdsmith.wordpress.com/2009/09/14/on-inverses-of-haskell-functions/?like=1&_wpnonce=f652223489 | software, programming languages, and other ideas
September 14, 2009 / cdsmith
Recall that given a function $f : A \to B$, a function $g : B \to A$ is called a left inverse of f in case $g \circ f = \mathrm{id}_A$. In other words, we want g to undo whatever f did to its parameter. A function has a left inverse if 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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/21473/linear-algebra-and-regular-orbits/21477 | ## Linear algebra and regular orbits
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
If A is an n×n matrix over a field, and Ak = I, with k the least positive integer such that this occurs, then must there be some vector v such that { v, Av, A2v, …, Ak−1v } = ... | {"extraction_info": {"found_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/calculus/66981-nasty-looking-but-actually-easy.html | # Thread:
1. ## nasty looking but actually easy
I ran across this integral that looks horrendous, but is actually quite simple. I am sure a lot of you will see it right off, but it is kind of fun.
$\int sin(x)^{x}\left(ln(sin(x))+xcot(x)\right)dx$
Just thought I would share.
2. Originally Posted by galactus
I 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/29991/list | ## Return to Question
2 Clarified question
One manifestation of the uncertainty principle is the fact that a compactly supported function $f$ cannot have a Fourier transform which vanishes on an open set. As stated, this phenomenon applies when $f$ lives on the integers, or on Euclidean space, but it is false for, sa... | {"extraction_info": {"found_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://www.abstractmath.org/Word%20Press/?tag=algebra | # Gyre&Gimbleposts about math, language and other things that may appear in the wabe
## Explaining math
2013/03/26 — SixWingedSeraph
To manipulate the demos in this post, you must have Wolfram CDF Player installed on your computer. It is available free from the Wolfram website. The source for the demos is the Mathem... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 254, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/23198/a-question-regarding-particle-trajectories-in-the-symplectic-manifold-formalism | A question regarding particle trajectories in the symplectic manifold formalism
How to solve a free particle on a 2-sphere using symplectic manifold formalism of classical mechanics ?
Is there a way to get coriolis effect directly, without going into Newton mechanics?
And is there a good textbook dealing with classi... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/35105/manifold-regularization-using-laplacian-graph-in-svm | # Manifold regularization using laplacian graph in SVM
I'm trying implement Manifold Regularization in Support Vector Machines (SVMs) in Matlab. I'm following the instructions in the paper by Belkin et al.(2006), there's the equation in it:
$f^{*} = argmin_{f \in H_k}\sum_{i=1}^{l}V(x_i,y_i,f)+\gamma_{A}\parallel 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": 17, "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/18823/how-do-we-visualise-antenna-reception-of-individua-radiowave-photons-building-up/18825 | # How do we visualise antenna reception of individua radiowave photons building up to a resonant AC current on the antenna?
I am a chemical/biological scientist by trade and wish to understand how quantum EM phenomena translates to our more recognizable classical world. In particular I want to get a mechanistic pictur... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/22686/quotient-of-a-category-by-a-group-action | ## Quotient of a category by a group action
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Let a group $G$ act on a small category $C$. If $G$ acts freely on objects, there is a sensible construction of the quotient $C/G$ (this is briefly spelt out here)
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... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/86800/heegaard-splitting-of-covering-hyperbolic-manifold | ## Heegaard splitting of covering hyperbolic manifold.
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I am curious about how the Heegaard genus changes after a finite covering.
Is there anyone constructing an closed hyperbolic 3-manifold $N$ such that
the 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": 3, "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/10283/is-there-a-size-cutoff-to-quantum-behaviour/10290 | # Is there a “Size” Cutoff to Quantum Behaviour?
We all know that subatomic particles exhibit quantum behavior. I was wondering if there's a cutoff in size where we stop exhibiting such behavior.
From what I have read, it seems to me that we still see quantum effects up to the nanometer level.
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## 3 Answers
The 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": 5, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/108835/would-you-show-how-many-different-orders-in-this-case-is-possible | # Would you show how many different orders in this case is possible?
You want to arrange your disks so that the cd's of the same artist come in a row and you have 20 cd's from five different artists four from each. How many different orders in this case is possible?
My solution
Firstly the cd's of each artist can be... | {"extraction_info": {"found_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/58622?sort=newest | ## Fano 3-fold of degree 4
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Let $X$ be the intersection of two quadrics in $P^5$. It is well known that the intermediate Jacobian $J(X)$ is isomorphic to $J(C)$ for a genus 2 curve, related to the pencil of quadri... | {"extraction_info": {"found_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://mathoverflow.net/questions/35420/how-to-compute-the-ring-of-invariants-of-so-3k-acting-on-a-polynomial-ring | ## How to compute the ring of invariants of SO_3(k) acting on a polynomial ring
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Let $k$ be a field and let $A$ be the polynomial ring over $k$ in $3n$ variables: $A = k[X_{ij} \vert i=1,2,3 \quad j=1,2,\cdots,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": 25, "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/204632/the-concept-of-infinity/204635 | # The concept of infinity
This evening I had a discussion with a friend of my about a mathematical riddle and the concept of 'infinite'
The riddle
Imagine a hotel with an infinite amount of rooms, and all of the rooms are occupied. At that moment a bus arrives with an infinite amount of people who all want a room 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": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.abstractmath.org/Word%20Press/?tag=mathematica | # Gyre&Gimbleposts about math, language and other things that may appear in the wabe
## Writing math for the web
2013/05/02 — SixWingedSeraph
## Abstractmath
I built my website abstractmath.org during the years 2002 through 2006. After that I made sporadic changes, but medical operations and then teaching courses 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": 168, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://pixelstoomany.wordpress.com/category/shadows/exponential-shadow-maps/ | # Pixels, Too Many..
## A conceptually simple(r) way to derive exponential shadow maps + sample code
June 12, 2008 — Marco Salvi
A few months ago, while working on an improved version of exponential shadow maps, I stumbled on a new way to derive ESM equations which looks more simple and intuitive than previous attem... | {"extraction_info": {"found_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": 13, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/140591/infinite-or-unknown/140602 | # Infinite or unknown?
If you have $0$ clients on Monday, and $5$ clients on Tuesday, how many times have the number of clients you had grown from Monday to Tuesday?
$A$ - Infinite times
$B$ - Unknown
$C$ - Undefined
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4
I'd go with "c - undefined". – mrf May 3 '12 at 21:14
## 2 Answers
To ask "how many times 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": 12, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/51234-solved-find-area-rectangle-abcd.html | # Thread:
1. ## [SOLVED] Find the area of rectangle ABCD
Hi, this is on the SAT OG Book page 747 #16
In rectangle ABCD, point E is the midpoint of line segment BC. If the area of quadrilateral ABED is $\frac{2}{3}$, what is the area of the rectangle ABCD?
a) $\frac{1}{2}$
b) $\frac{3}{4}$
c) $\frac{8}{9}$
d) 1
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/factorization+function-construction | # Tagged Questions
3answers
245 views
### Generating pairs of additive and multiplicative factors for integers
Given an integer $n$, I want two lists: a) the set of pairs of the divsors $a,b$ into exactly two factors $n=a\cdot b$, b) the set of pairs $a,b$ of two summands $n=a+b$. The code I came up ... | {"extraction_info": {"found_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://www.theresearchkitchen.com/archives/date/2012/06 | # Density Estimation of High-Frequency Financial Data
Posted on June 12, 2012 by
Frequently we will want to estimate the empirical probability density function of real-world data and compare it to the theoretical density from one or more probability distributions. The following example shows the empirical and theoret... | {"extraction_info": {"found_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": 63, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/128282/group-homomorphism-always-exist-between-two-groups | # Group homomorphism always exist between two groups.
Is there always exists a homomorphism between two groups $G_1$ and $G_2$? Why?
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## 1 Answer
If you require the homomorphism to be surjective, the answer is no; for example, there is no homomorphism of $\Bbb Z/3\Bbb Z$, the cyclic group of order $3$, onto $\Bbb ... | {"extraction_info": {"found_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://stochastix.wordpress.com/2012/06/29/runge-kutta-in-haskell/ | # Rod Carvalho
## Runge–Kutta in Haskell
Last time I implemented a Runge-Kutta method was in December 2001. Back then, I implemented the classical 4th order Runge-Kutta (RK4) method in C. However, in the past decade, whenever I needed a numerical solution of an ordinary differential equation (ODE), I used MATLAB. Now... | {"extraction_info": {"found_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": 39, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/6769/upward-force-on-a-object-at-rest/6770 | # Upward force on a object at rest
Is there an upward force on a object at rest? If yes, where does it come from?
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3
Can you be more specific about the situation? I have a feeling you're referring to an object in the Earth's gravitational field resting on some kind of surface? – dbrane Mar 12 '11 at 22:53
You mean ... | {"extraction_info": {"found_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/math-topics/74744-sign-charts-print.html | # Sign Charts
Printable View
• February 20th 2009, 03:31 PM
AlgebraicallyChallenged
Sign Charts
Dear Forum I have tried to figure this one out several times but I am still having no luck if anyone can help please let me know, it would be greatly appreciated.
Solve x^2 + 11x + 18 > 0 using the Critical Value (Sign Cha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/33669/trajectory-of-a-projectile-meets-a-moving-object-2d/34112 | # Trajectory of a projectile meets a moving object (2D)
First of all, I asked this question on Stackoverflow, but I realize this is a better place to ask the question. So i moved it here.
I've looked for quite some time now to find a nice math solution for my cannon firing a projectile at a moving target, taking into... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/69278?sort=votes | Hartshorne’s associated scheme for a variety
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This question comes from Proposition 2.6 in Chapter 2 of Hartshorne's Algebraic Geometry. In my edition, that's on page 78.
For a variety $V$, Hartshorne defines the topo... | {"extraction_info": {"found_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/148998/how-to-plot-z-in-mathbbc-z-izi/149002 | # How to plot $\{z \in \mathbb{C} : |z-i|>|z+i|\}$
How would I draw the set $\{z \in \mathbb{C} : |z-i|>|z+i|\}$ and $\{z \in \mathbb{C} : |z-i|\not=|z+i|\}$?
Im not sure how to solve the second one, and for the first one, I tried squaring both sides and trying to work something out, but I got no where.
$|z-i|^2>|z+... | {"extraction_info": {"found_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://sbseminar.wordpress.com/2007/06/27/john-brundan-and-the-centers-of-blocks-of-category-o/ | ## John Brundan and the centers of blocks of category O June 27, 2007
Posted by Ben Webster in Algebraic Topology, category O, Category Theory.
trackback
So, those of you who like the categorical approach to representation theory probably know about the center of a category:
Definition. The center of an abelian 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 73, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/2917/how-can-the-schmidtsamoa-cryptosystem-uniquely-decrypt-large-messages/2919 | # How can the Schmidt–Samoa cryptosystem uniquely decrypt large messages?
Suppose I choose $p=7$ and $q=11$.
This gives a public key of $p^2·q = 539$.
However, decryption occurs using a modulus of $p·q=77$.
If a person chooses to encrypt $500$ using my public key, how do I recover this value if the decryption modul... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "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/3969/why-are-elliptic-curve-variants-of-rsa-chiefly-of-academic-interest | # Why are elliptic curve variants of RSA “chiefly of academic interest”?
Yesterday I was thinking about elliptic curve variants of popular protocols/algorithms (ECDH, ECES[1], etc) and the thought occured that I had never seen an elliptic curve variant of RSA. My understanding of RSA and elliptic curves told me that 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": 43, "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/36065?sort=newest | ## irreducible subgroup of SL(n,R)
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Suppose a subgroup of SL(n,R) is irreducible; i.e. R^n contains no proper invariant real subspaces except {0}. Then is it irreducible as a subgroup of SL(n,C)? i.e. Does C^n con... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/12634/why-dont-astronauts-in-orbit-get-stuck-to-the-ceiling/12635 | # Why don't astronauts in orbit get stuck to the “ceiling”?
When a shuttle is in orbit, it is essentially rotating around the "centre" of the Earth at a great speed. So why does there seem to be no centrifugal force sticking them to the 'ceiling' of the shuttle?
Is it because the shuttle is not actually being rotated... | {"extraction_info": {"found_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://math.stackexchange.com/questions/217151/roots-of-unity-and-function-mu | # Roots of unity and function $\mu$
I need to prove that for each positive integer $n$ the sum of the primitive $n$th roots of unity in $\mathbb{C}$ is $\mu(n)$, where $\mu$ is the Möbius function.
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So what's the question? – Patrick Da Silva Oct 20 '12 at 0:02
Yes...or not: what's your question? ¿Cuál es tu pregunt... | {"extraction_info": {"found_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": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/112242/showing-something-is-an-asymptotic-sequence?answertab=active | # Showing something is an asymptotic sequence
I need to show that $\phi_n(z)=\ln(1+z^n)$ as $z \rightarrow 0$ is an asymptotic sequence, i.e. to show that $$\lim_{z\rightarrow 0}\frac{\phi_{n+1}(z)}{\phi_n(z)}=0.$$
Is it sufficient for me to say that as $z\rightarrow 0$, $$\frac{\phi_{n+1}}{\phi_n}=\frac{\ln(1+z^{n+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": 22, "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/234557/sum-of-squares-of-dimensions-of-irreducible-characters | Sum of squares of dimensions of irreducible characters.
For anyone familiar with Artin's Algebra book, I just worked through the proof of the following theorem, which can be seen here:
(5.9) Theorem Let $G$ be a group of order $N$, let $\rho_1,\rho_2,\dots$ represent the distinct isomorphism classes of irreducible 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": 24, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/254595/lipschitz-questions | # Lipschitz Questions
I want to ask one general question, and after that I would like to know if my method is correct (for determining whether a function is Lipschitz with respect to y)
Is the following statement true?
Suppose D is a convex domain, the function $f(x,y)$ is continuous and $f_y$ is continuous in D. Th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/77986/which-diophantine-equations-can-be-solved-using-continued-fractions/89438 | ## Which Diophantine equations can be solved using continued fractions?
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Pell equations can be solved using continued fractions. I have heard that some elliptic curves can be "solved" using continued fractions. Is... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 104, "mathjax_display_tex": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/120239?sort=oldest | ## When is PSU(2,q^2) = PSL(2,q) ?
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The context for this question is from page 284 - 287 of Berger's paper: http://pdn.sciencedirect.com/science?_ob=MiamiImageURL&_cid=272332&_user=209810&_pii=S0021869398976785&_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": 42, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/204263-analytic-geometry.html | 2Thanks
• 1 Post By MarkFL
• 1 Post By chiro
# Thread:
1. ## Analytic Geometry
Hello, everybody. I need help...
Show that, for all values of p, the point P given by x=ap2, y=2ap lies on the curve y2=4ax.
a) Find the equation of this normal to this curve at the point P.
If this normal meets the curve again at the poi... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/tagged/hypothesis-testing | # Tagged Questions
Hypothesis testing assesses whether data support a given hypothesis rather than being an effect of random fluctuations or some other process described by an alternative hypothesis.
0answers
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### Relation between observed power and p-value?
I am trying to understand the relation between ob... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/283167/given-an-algebraic-curve-fx-y-0-why-do-the-partial-derivatives-of-fx-y/283202 | # Given an algebraic curve $F(x,y)=0$, why do the partial derivatives of $F(x,y)$ being zero at a point imply the plane curve has a singularity?
I'm looking at algebraic plane curves of the form $F(x,y)=0$ and trying to figure out why for points on the curve such that $\frac{\partial F}{\partial x} = \frac{\partial 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": 40, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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