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http://mathoverflow.net/questions/55575?sort=oldest | ## Why is the dual of a torus the same as its fundamental group?
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The set of continuous homomorphisms from a torus ${\mathbb T}^n = ({\mathbb R}/{\mathbb Z})^n \to {\mathbb R}/{\mathbb Z}$ can be identified 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": 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/98237/approaching-the-circumference-of-a-circle?answertab=votes | # Approaching the circumference of a circle
We had a lengthy discussion yesterday, on how to prove that the circumference of a circle is $2\pi r$. By using google, the most commonly found proof starts in the following way.
"Consider the regular n-gon inside the circle touching the circle at its vertices, and the regu... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/152614-find-value-function-continuous.html | Thread:
1. find the value for which the function is continuous
f(x)= ln x/(x-1), if 0<x not =1
c , if x=1
and what kind of discontinuity is present if c does not have this value?
can someone help me with this problem?
2. This is nearly impossible to read...
Is it
$f(x) = \begin{cases}\frac{\ln{x}}{x - 1}\textrm{ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/180507/how-to-resize-an-image?answertab=oldest | # How to resize an image?
I am not sure about the title of this question, so if someone knows an appropriate one, please rename it. It's a programming related question (but doesn't involve any programming). I posted it on stack overflow but didn't get any responses so I am trying here.
I need to map a piece of rectan... | {"extraction_info": {"found_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/260962/boundedness-of-a-family-of-functions-in-c10-1?answertab=oldest | # Boundedness of a family of functions in $C^{1}[0,1]$
Suppose we have a set $S$ which contains all functions $v \in C^{1}[0,1]$ so that $v(0) = 0$ and
$$\int_{0}^{1} |v'(x)|^2 dx = 1.$$
How can I show that $S$ is bounded with the infinity norm. That is, how can I show that
$$sup_{v\in S}\lVert v\rVert_{\infty}$$
... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/220331/parameter-optimization-in-probabilistic-models/234967 | # Parameter optimization in probabilistic models
Task: Suppose we model a variable $y = Wx + \mu$ as a linear transformation of $x$ plus some Gaussian noise $\mu\sim\mathcal N(0,\sigma I)$. Our aim is to minimize the estimation error of $x$ given $y$ in terms of $W$, i.e. we want to minimize the entropy $H(x|y,W)$ as ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=558684 | Physics Forums
## A Unitary Matrix and Hermitian Matrix
Its true that one can say a unitary matrix takes the form
$U=e^{iH}$
where $H$ is a Hermitian operator. Thats great, and it makes sense, but how can you compute the matrix form of $H$ if you know the form of the unitary matrix $U$. For example, suppose you wan... | {"extraction_info": {"found_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://mathoverflow.net/questions/41931?sort=oldest | ## About isogeny theorem for elliptic curves
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$K$ a number field, $G_K$ its Galois group, $E_1, E_2$ two elliptic curves defined over $K$. The isogeny theorem says that if for some prime number $\ell$, The Tate mo... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/34591?sort=newest | Probability of generating the symmetric group
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The statement is simple:
What is the probability that a set of n-1 transpositions generates the symmetric group, $S_n$?
The motivation is that I remembered reading that... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/18359/motivation-of-surgery/76981 | ## motivation of surgery
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an $n$-surgery on m dim manifold M is to cut out $S^n\times D^{m-n}$and replace it by $D^{n+1}\times S^{m-n-1}$. I want to know how this is invented? I do know that the effect of passing ... | {"extraction_info": {"found_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://mathhelpforum.com/trigonometry/86956-factoring-trig-function-print.html | # factoring a trig function
Printable View
• May 2nd 2009, 01:30 PM
brentwoodbc
factoring a trig function
I can do the basic ones, but when they have a coefficient in front of the first term I dont know what to do.
$2cos^2x-7cosx-3$
I thought maybe you do
(2cosx-1)(cosx-3)
Edit nevermind That is right.
BUt 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": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/192687-show-p-not-complete.html | # Thread:
1. ## Prove that D is connected
Let $D \subset R$, and let f: D-->R be continuous. Prove that D is connected if { $x,f(x): x \in D$}, the graph of f, is a connected subset of $R^2$
2. ## Re: Prove that D is connected
Originally Posted by wopashui
Let $D \subset R$, and let f: D-->R be continuous. Prove th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 24, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/194206/is-there-a-generalized-formula-to-solve-the-nth-exponent-of-an-m-dimensional | # Is there a generalized formula to solve the $n$th exponent of an $m$ dimensional square matrix?
I was trying to do something like a general formula, and testing, I came with this:
$$\left( \begin{array}{cc} a & b \\ a' & b' \\ \end{array} \right)^2=\left( \begin{array}{ccc} a^2+a'b & b(a+b') \\ a'(a+b') & b'^2+a'b ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61336?sort=votes | Existence of sequence of examples of braking ‘Cancellation law in homeomorphic products’
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I know there are manifolds (with or without boundary) $A$ and $B$ such that $A\times C$ is homeomorphic to $B\times C$ but $A$ ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/23060/set-theory-and-model-theory/23065 | ## Set theory and Model Theory
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This question probably doesn't make any sense, but I don't see why, so I ask it here hoping someone will illuminate the matter:
There is this whole area of study in Set Theory abou... | {"extraction_info": {"found_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://math.stackexchange.com/questions/40059/is-fracm-1x-an-unbiased-estimator-of-theta-for-given-pdf | # Is $\frac{m-1}{x}$ an unbiased estimator of $\theta$ for given pdf?
Let $X$ be a continuous random variable with pdf, $$f(x;\theta)=\frac {\theta^m.x^{m-1}e^{-\theta x}} {(m-1)!} ; x\geq0, \theta>0$$ Is $\frac{m-1}{x}$ an unbiased estimator of $\theta$ for given pdf?
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2
If this is a homework question, please indi... | {"extraction_info": {"found_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/98452?sort=oldest | ## Conditional expectation and algebraic expressions
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Let $\mathcal{A}$ and $\mathcal{B}$ be two sub-$\sigma$-algebras in a measure space. To each one, there is a conditional expectation associated, respectively $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/189223/asymmetric-normal-probability-distribution?answertab=active | # Asymmetric Normal Probability Distribution
I'm looking for a continuous probability distribution a little bit like the normal distribution but asymmetric. In my opinion this distribution applies to phenomenons related to response time in environments marked by resource contention.
Examples I have in mind are:
• 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": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/79785-spherical-coordinates-print.html | # spherical coordinates!!!
Printable View
• March 21st 2009, 10:32 AM
althaemenes
spherical coordinates!!!
Hi,
For the following problem, how would I setup the triple integral? Do I have to convert it to spherical coordinates first:
many thanks....
Problem:
Integrate the function https://instruct.math.lsa.umich.ed... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://homotopical.wordpress.com/tag/homotopy-theory/ | # Posts Tagged ‘Homotopy theory’
## London workshop on arithmetic geometry and homotopy theory
Posted by Andreas Holmstrom on May 8, 2012
At Imperial College London, from May 30th to June 1st. Many interesting talks, but the main theme appears to be the recent work of Harpaz and Schlank in which they use etale homot... | {"extraction_info": {"found_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": 67, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/69156-countability-proof.html | # Thread:
1. ## Countability Proof
Fix $n >= 1$. Show that if A1,A2, . . . ,An are countable, then A1×A2× . . . × An is countable.
Does this require knowledge of the fact that N x N is countably infinite?
Thanks in advance.
2. Hello,
Originally Posted by h2osprey
Fix $n >= 1$. Show that if A1,A2, . . . ,An are cou... | {"extraction_info": {"found_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://mathoverflow.net/questions/93148?sort=newest | ## Unitary representations of Quantum Groups
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Let $\mathfrak{g}$ be a finite-dimensional complex simple Lie algebra and let $U_q(\mathfrak{g})$ be some incarnation of the quantized universal enveloping algebra 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": 20, "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/4266/sobolev-norms-of-eigenfunctions | ## Sobolev norms of eigenfunctions
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Let D be a domain in R^n, and let f be an eigenfunction of the Laplacian with Dirichlet boundary condition with eigenvalue $\lambda$. Assume that f has L^2 norm 1. I want to kno... | {"extraction_info": {"found_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/145277-simple-graph-proof-question.html | # Thread:
1. ## Simple graph proof question
Hi,
The exercise is as follows:
A simple graph, also called a strict graph, is an unweighted, undirected graph containing no graph loops or multiple edges. A well-known theorem states that the sum of the degrees of the vertices of a simple graph equals twice the number 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/3568/temperature-of-a-system-of-molecules?answertab=oldest | # Temperature of a System of molecules
Suppose I have a closed system with N molecules in it which are vibrating and all motion equations (rotation, translation and vibration) of the system are known along with any EM field equations in the region. Given all these information how do we calculate (not measure) the temp... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/abc-conjecture/ | What’s new
Updates on my research and expository papers, discussion of open problems, and other maths-related topics. By Terence Tao
# Tag Archive
You are currently browsing the tag archive for the ‘abc conjecture’ tag.
## The probabilistic heuristic justification of the ABC conjecture
18 September, 2012 in math.N... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 76, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Identification_condition | Identifiability
(Redirected from Identification condition)
In statistics, identifiability is a property which a model must satisfy in order for inference to be possible. We say that the model is identifiable if it is theoretically possible to learn the true value of this model’s underlying parameter after obtaining 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": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://scicomp.stackexchange.com/questions/3307/recovering-coordinates-by-eigendecomposition-without-double-centering | # Recovering coordinates by eigendecomposition without double-centering
Suppose an Euclidean distance $D\in\mathbb{R}^{n\times n}$ matrix between a set of $n$ objects is given. To obtain inner-products (which will be further be used to recover coordinates), entries of $D$ are squared, and the matrix is double-centered... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/265925/where-do-cantor-sets-naturally-occur?answertab=active | # Where do Cantor sets naturally occur?
Cantor sets in general of course have many interesting properties on their own, and are also often used as examples of sets with these properties, but do they naturally occur in any application?
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Not clear what you mean by "naturally," since the Cantor set is an uncountably 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": 49, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Surface_area | Surface area
Surface area is the total area of the faces and curved surface of a solid figure. Mathematical description of the surface area is considerably more involved than the definition of arc length or polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surf... | {"extraction_info": {"found_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": 17, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/5286/what-concepts-were-most-difficult-for-you-to-understand-in-calculus/233392 | # What concepts were most difficult for you to understand in Calculus?
I'm developing some instructional material for a Calculus 1 class and I wanted to know from experience for yourself, tutoring others, and/or helping people on this site where is the most difficulty in Calculus?
If you had any good methods of helpi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 27, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/282271/scaled-lp-norm-and-geometric-mean | # “Scaled $L^p$ norm” and geometric mean
The $L^p$ norm in $\mathbb{R}^n$ is \begin{align} \|x\|_p = \left(\sum_{j=1}^{n} |x_j|^p\right)^{1/p}. \end{align} Playing around with WolframAlpha, I noticed that, if we define the "scaled" $L^p$ norm in $\mathbb{R}^n$ to be
\begin{align} \| x \|_p = \left(\frac{1}{n}\sum_{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": 50, "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/algorithms+statistics | # Tagged Questions
1answer
25 views
### How to compute conditional expectation of a log function
I've been studying the Expectation Maximization algorithm. According to the formula shown here, what I have to do in the M step is to compute a new $\theta$ that maximizes the conditional expectation ...
0answers
23 view... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://diracseashore.wordpress.com/2009/01/19/everyday-physics-boats-and-ice-float/ | # Shores of the Dirac Sea
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## Everyday physics: boats and ice float.
January 19, 2009 by dberenstein
As you might have noticed, some objects float and some others don’t. Here below I have a rendition of a boat and a cube of ice floating.
Various floating objects
Today, I will go on a bit abou... | {"extraction_info": {"found_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": 6, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/254953/algebraic-solution-of-x-3x-4 | # Algebraic solution of $x + 3^x < 4$
I solved graphically and found that $x + 3^x < 4$ is true for $x < 1$ but I can't find a way to prove it algebraiclly, any hints will be greatly appreciated!
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## 3 Answers
The left hand side is an increasing function of $x$. With $x=1$, its value is $4$.
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I suppose we just ... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/10/06/the-hodge-star-on-differential-forms/?like=1&source=post_flair&_wpnonce=671450efa2 | # The Unapologetic Mathematician
## The Hodge Star on Differential Forms
Let’s say that $M$ is an orientable Riemannian manifold. We know that this lets us define a (non-degenerate) inner product on differential forms, and of course we have a wedge product of differential forms. We have almost everything we need to 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": 36, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/328/angular-momentum-and-force/329 | # Angular Momentum and Force
I'm stuck on number 5. The answers to the first 4 are correct, but I dont know how to set up number 5. Any idea that I would have would require me having some kind of time information, but thats not given. Any suggestions?
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1
Our goal here is an answer conceptual questions as opposed to... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/201796/describe-the-locus-of-points-of-this-fraction?answertab=oldest | # Describe the locus of points of this fraction
What's the locus of: $$\mathrm{Im} \bigg(\frac{z-z_{1}}{z-z_{2}}\bigg)=0$$
I tried to figure it out and I get that it's a line. But it looks to me it will be wrong.
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## 3 Answers
Recall that $\frac{z-z_1}{z-z_2}$ is a complex number whose argument is the angle $z_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": 16, "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/333487/suppose-a-subset-0-1-b-subset-1-2-we-do-not-assume-they-are-lebesgue | # Suppose $A \subset [0,1]$, $B \subset [1,2]$. We do not assume they are Lebesgue measurable?
Suppose $A \subset [0,1]$, $B \subset [1,2]$ (we do not assume they are Lebesgue measurable). Show that $m^{*}(A \cup B) = m^{*}(A) + m^{*}(B)$.
Just learned this. Not sure about it. I used $m^{*}(A \cup B)-m^{*}(B) \le 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": 43, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/35118/can-the-montevideo-interpretation-of-quantum-mechanics-do-what-it-claims | # Can the Montevideo interpretation of quantum mechanics do what it claims?
Partly inspired by the great responses to a my previous physics.SE question about "reversing gravitational decoherence, today I was rereading the intriguing papers by Gambini, Pullin, Porto, et al., about what they call the "Montevideo interpr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/227691/show-the-usual-schwartz-semi-norm-is-a-norm-on-the-schwartz-space/227702 | Show the usual Schwartz semi-norm is a norm on the Schwartz space
Let $f \in C^\infty(\mathbb R)$. Define the semi-norm $$\|f\|_{a,b}=\sup_{x \in \mathbb R} |x^af^{(b)}(x)|$$ where $a,b \in \mathbb Z_+$, and $f^{(b)}$ is the $b$-th derivative of $f$.
Show $\|\cdot\|_{a,b}$ is a norm on the Schwartz space $S(\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": 18, "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/109395/raising-a-power-series-by-a-power-series | # Raising a power series by a power series?
I know addition and multiplication are well defined operations on formal power series. Now say you have two formal power series $F(x),G(x)\in R[[x]]$, with $R\supset\mathbb{Q}$ is the coefficient ring.
Is there a way to define $F(x)^{G(x)}$? Is there a standard well defined... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=437669 | Physics Forums
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Associates and their Norms
Hello PhysicsForums:
I have two things I'd like to learn more about:
1. I was noticing that the norms of +-1+-i (which are associates) are the same. The same goes for +-(1-2i). Is there a general reason explaining why any two integers which are assoc... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 93, "mathjax_display_tex": 17, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/33750/is-temperature-an-extensive-property-like-density | # Is temperature an extensive property, like density?
I was thinking about it some time ago, and now that I've discovered this site I would like to ask it here because I couldn't work it out then.
I know that the higher temperature the air in my room has, the more energy the molecules have. But temperature isn't ener... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/19459/time-reversal-symmetry-and-t2-1 | # Time reversal symmetry and T^2 = -1
I'm a mathematician interested in abstract QFT. I'm trying to undersand why, under certain (all?) circumstances, we must have $T^2 = -1$ rather than $T^2 = +1$, where $T$ is the time reversal operator. I understand from the Wikipedia article that requiring that energy stay positiv... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/119939-nomenclature.html | # Thread:
1. ## Nomenclature
How exactly does this read:
(prove that) R[x]/<x^2+2> (is isomorphic to C)
And what exactly does the "/" imply algebraicly?
Thanks.
2. ...
3. Here, you are creating the complex numbers! This is very elegant. The $\mathbb{R}$ shows that you are in the reals, so $x^2$ can have any coeff... | {"extraction_info": {"found_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": 27, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/33063/does-the-expression-of-the-orbital-magnetic-dipole-moment-have-c?answertab=active | # Does the expression of the orbital magnetic dipole moment have $c$?
The orbital magnetic dipole moment of a particle with mass $m$ and charge $q$ can be shown to be related to the orbital angular momentum through the equation
$$\displaystyle \boldsymbol\mu_L=\frac{q}{2m}\bf{L}.$$
One of the quantum mechanics textb... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/30850/significance-of-matrix-vector-multiplication/30855 | # Significance of Matrix-Vector multiplication
Can someone give me an example illustrating physical significance of the matrix-vector multiplication?
1. Does multiplying a vector by matrix transforms it in some way?
2. Do left & right multiplication signify two different things?
3. Is matrix a scalar thing? (EDIT)
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": 68, "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/114824/how-to-solve-a-specific-multivariate-recurrence-relation-or-general-ones/114833 | ## How to solve a specific multivariate recurrence relation (or general ones)
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
How do you solve this recurrence (or multivariate recurrences in general)? Note that $p\in[0,1]$ and $n\in\mathbb{N}$ are given consta... | {"extraction_info": {"found_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://mathoverflow.net/questions/39485/are-there-motives-which-do-not-or-should-not-show-up-in-the-cohomology-of-any-s/39592 | Are there motives which do not, or should not, show up in the cohomology of any Shimura variety?
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $F$ be a real quadratic field and let $E/F$ be an elliptic curve with conductor 1 (i.e. with good reduction everywh... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=531143&page=4 | Physics Forums
Page 4 of 4 < 1 2 3 4
## What do these new symbols mean...?I can't start this without knowing
Oh if f = 1, then P = 1.
Can I jsut state that or should I write up more on nCr?
Mentor That can't be right. P(x) doesn't depend on f(x) at all. Try again.
In the summation I get $$\sum_{k=0}^{... | {"extraction_info": {"found_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": 11, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=191677 | Physics Forums
Thread Closed
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## Something I don't understand about String Theory
Hello, I have read a few books on the subject of String theory, including The Elegant Universe and Fabric of the Cosmos by Brian Greene (that guy is AWESOME!). Anyway, Mr. Greene may have answered my questions 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": 3, "mathjax_asciimath": 5, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/53662-simultaneous-equation-c1.html | # Thread:
1. ## Simultaneous Equation [C1]
I've been going through a textbook and I've came across Simultaneous equations by this point. I can do many, such as:
c = 7d - 2 [1]
3c - 4d = 11 [2]
To do this I subbed c in [2] and did this method:
3(7d-2) - 4d = 11
21d - 4d - 6 = 11
17d = 17
d = 1
And then went back 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": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php?title=Polar_Equations&oldid=24531 | # Polar Equations
### From Math Images
Revision as of 15:30, 12 July 2011 by Chanj (Talk | contribs)
A polar rose (Rhodonea Curve)
This polar rose is created with the polar equation: $r = cos(\pi\theta)$.
A polar rose (Rhodonea Curve)
Fields: Algebra and Calculus
Created By: chanj
# Basic Description
Polar equatio... | {"extraction_info": {"found_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": 49, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/193225-no-ways-seat-around-table-when-seats-numbered.html | # Thread:
1. ## No. of ways to seat around a table when seats are numbered
Three single men, two single women and two families take their places at a round table. Each of the two families consists of two parents and one child. Find the number of possible seating arrangements if the seats are numbered and each child 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/73246/why-is-mathbbr-infty-defined-the-way-it-is/73262 | ## Why is $\mathbb{R}^{\infty}$ defined the way it is?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I've been thinking about Grassmannians recently. Think of $\mathbb{R}^k$ as a $k$-dimensional vector space. Let $\text{Gr}_n(\mathbb{R}^k)$ denote the Grassm... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 95, "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/35264/congruences-for-fermat-quotients | # Congruences for Fermat Quotients
If $p$ is a prime number and $a$ is relatively prime to $p$, then by Fermat's Little Theorem, the Fermat quotient $q_p(a) = (a^{p-1}-1)/p$ is an integer. A well-known collection of theorems beginning with the work of Wieferich shows that if the first case of Fermat's Last Theorem hol... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/193939/error-bound-of-a-integration | # error bound of a integration
I have a function, which is $f(x) = e^{1/x}$. I want to calculate the error bound for the `Trapezoid Rule`, which formula is:
$$|E|\leq K\frac{(a-b)^3}{12\cdot n^2}$$
where $|f''(x)|\leq K$. What's the value of $K$ for the above function? If I calculated $f''(x)$ correctly, it 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": 14, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/85090/coloring-mathbbzk-and-a-fixed-point-theorem | ## Coloring $\mathbb{Z}^k$ and a fixed point theorem
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This is potentially another approach to this question. I put it as an update there, but perhaps it would be better to post it separately. If we color $\mathbb{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/number-theory/186551-prove-equation-solvable-print.html | # Prove that this equation is solvable
Printable View
• August 22nd 2011, 01:23 PM
alexmahone
Prove that this equation is solvable
Given any integers a, b, c and any prime p not a divisor of ab, prove that $ax^2+by^2\equiv c\ (mod\ p)$ is solvable.
• August 24th 2011, 01:04 AM
Opalg
Re: Prove that this equation is 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": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/148332/non-isomorphic-atomless-boolean-algebras | Non-isomorphic atomless Boolean algebras
All countable atomless algebras are isomorphic. Can one give an example of a pair of mutually non-isomorphic atomless Boolean algebras of cardinaliy continuum?
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1
I'm glad that you were happy with my answer but I suggest that you wait a little bit before accepting it (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": 77, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/11306/character-table-does-not-determine-group-vs-tannaka-duality/122367 | ## Character table does not determine group Vs Tannaka duality
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
From the example $D_4$, $Q$, we see that the character table of a group doesn't determine the group up to isomorphism. On the other hand, Tannaka dua... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 122, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/207955/prove-that-operatornamespec-sqrt2-contains-infinitely-many-powers-of-2 | # Prove that $\operatorname{Spec}\sqrt2$ contains infinitely many powers of $2$.
$\newcommand{\spec}{\operatorname{Spec}}\spec\sqrt2=\{\lfloor k\sqrt2\rfloor: k \ge 0\}$.
I have no idea of how I can prove the statement in the question.
Prove that $\spec\sqrt2$ contains infinitely many powers of $2$.
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2
The most 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": 21, "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/tagged/fibration+category-theory | # Tagged Questions
1answer
86 views
### Beck Chevalley condition and maps of adjunctions
Suppose we have a split fibration $p : \mathbb{E}\to\mathbb{B}$ with (split) simple products. To fix notation, this means that for every projection $\pi_{I,J} : I\times J \to I$ in the base category, ...
2answers
149 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
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# Validity
(Redirected from Logical validity... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 15, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/05/12/topological-vector-spaces-normed-vector-spaces-and-banach-spaces/?like=1&source=post_flair&_wpnonce=671450efa2 | # The Unapologetic Mathematician
## Topological Vector Spaces, Normed Vector Spaces, and Banach Spaces
Before we move on, we want to define some structures that blend algebraic and topological notions. These are all based on vector spaces. And, particularly, we care about infinite-dimensional vector spaces. Finite-di... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 27, "mimetex.cgi": 0, "/images/ma... |
http://openwetware.org/index.php?title=Physics307L:People/sosa/formallabreport&oldid=271345 | # Physics307L:People/sosa/formallabreport
### From OpenWetWare
Revision as of 23:01, 15 December 2008 by David E. Sosa (Talk | contribs)
# Determining the Elementary Charge Via Millikan's Oil Drop Experiment
Author: David Sosa
Experimentalists: Manuel Franco Jr. and David Sosa
Location: Junior Lab, Department 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 41, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/110202-function-limits-f-g.html | # Thread:
1. ## Function limits-f and g
Let $h(x)=2f(x) - g(x)$, where $f$and $g$ are functions satisfying:
$\lim_{x\to3}f(x)=-2$,
$\lim_{x\to3}g(x)=4$,
$\lim_{x\to7}f(x)=6$,
$\lim_{x\to7}g(x)=-5$.
Find the following:
a. $\lim_{x\to3}h(x)$
b. $\lim_{x\to7}(g(x)/h(x))$
c. $\lim_{x\to3}f(x)*g(x+4)$
Here are th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/27141/some-questions-about-the-spectral-function?answertab=active | # Some questions about the spectral function
If you think that this question is likely to get closed then please do not answer and only say that in the comments since this system doesn't let me delete the question once it has answers.
Everytime I am faced with an analysis of the spectral function it looks like a "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": 25, "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/42149/compressing-the-mandelbrot-set | Compressing the Mandelbrot set
This question may not have a definitive answer. However, if someone is able to illuminate the topic for me, I would be very grateful.
The Mandelbrot set is the set obtained from the quadratic recurrence equation{1}:
$$\begin{equation} z_{n+1}=z_n^2 + c \end{equation}$$
I'm sure most 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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-applied-math/140892-matrix-estimation-problem.html | # Thread:
1. ## Matrix estimation problem
Imagine the following problem: we have a set of n matrix equations in the form of :
[b1] = [A] * [b0]
[b2] = [A] * [b1]
etc.
vertical vectors [b0], [b1], ... are GIVEN. We try to estimate matrix A. As there are many equations (more than cells in matrix A) the system has no 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": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/35409/why-is-a-nucleus-isotropic | # Why is a nucleus isotropic?
I believe in Neutron Scattering the neutrons after hitting a nucleus can bounce in any of 360*3 dimensions -> 1080 degrees?
Why is this so? Shouldn't it only bounce "off" the neutron in approximately the same "direction" that it came in such as when a particle bounces off a mirror -> bec... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/2516/mass-of-particle-near-light-speed-in-a-medium | # Mass of particle near light speed in a medium
I am trying to get a common understanding from these two previous questions:
Does the increase of mass occur only if the particle approaches c (speed of light in a vacuum) or if it simply approaches the speed of light in its current medium? For example, does the mass 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": 7, "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/28741/one-plaquette-action-and-su2s-irreducible-representations | # One-Plaquette Action and SU(2)'s Irreducible Representations
I have a typical single-plaquette partition function for a gauge-field $$Z=\int [d U_{\text{link}}] \exp[-\sum_{p} S_{p}(U,a)]$$ with $U$ as the product of the the $U$'s assigned to each link around a plaquette. Now the $U$'s are irreducible representation... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/2584/combine-n-normal-distribution-probability-sets-in-a-limited-float-range | # Combine n Normal distribution Probability Sets in a limited float range
I've got a fixed solution space defined by a minimum and maximum float which has no divisible slice.
You then have 0..N Normal distribution probability sets which I need to combine.
In the end I neeed
Method to define probability set with a 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": 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/86760/on-the-generalisation-of-the-laplace-transform | ## On the generalisation of the Laplace transform
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I consider a measure transform $A$ given by $$A\mu(x) = \int\limits_{\mathbb{R}^n_{+}} e^{-g(x,y)} \mu(dy)$$ where $g(x,y)$ is some positive smooth function, $\mu... | {"extraction_info": {"found_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://mathoverflow.net/questions/99411?sort=newest | ## Sequence of permutations without a fixed point
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I need to find $m$ permutations $A_1,..,A_m$ where each $A_i$ is a permutation on $n$ objects such that any of the compositions $A_jA_{j+1}..A_{j+k}$; $1 \leq 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": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://cms.math.ca/Reunions/ete12/abs/oa | Réunion d'été SMC 2012
Hôtels Regina Inn et Ramada (Regina~Saskatchewan), 2 -4 juin 2012 www.smc.math.ca//Reunions/ete12
Algèbres des opérateurs
Org: Martin Argerami, Juliana Erlijman et Remus Floricel (Regina)
[PDF]
BERNDT BRENKEN, University of Calgary
Universal C*-algebras of *-semigroups and the C*-algebra 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": 23, "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/120365/first-eigenvalue-of-delta-on-kaehler-manifold-with-ricci-ge-k | ## First eigenvalue of $\Delta$ on Kaehler manifold with $Ricci\ge k$.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $M$ be a Kaehler manifold of complex dimension $n$. Let $\Delta$ be the real Laplacian of the underline Riemannian manifold. Let's assume... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/88692?sort=oldest | ## Why should I care about Heegaard-Floer theory?
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I would like to collect a list of applications of Heegaard-Floer theory. By applications, I don't mean things like "it can detect the unknot" or "it can detect kn... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/300575/integration-involving-the-absolute-function | # Integration Involving the Absolute Function
How do I integrate the double integral of the form $|x^2-y|$ with the boundaries $-1\leq x\leq 1$ and $-1\leq y\leq 1$?
-
1
Separate the integral into two regions, one with $x^2>y$ and one with $x^2 \leq y$. – copper.hat Feb 11 at 21:28
## 1 Answer
You can break it int... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/87923?sort=newest | ## Sequences without long arithmetic progressions
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First, a bit of notation. If we have an arithmetic progression $a, a+k, a+2k, \ldots, a+(n-1)k$ we will call $k$ the distance, and $n$ the length.
While trying 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": 51, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://blog.eqnets.com/2010/02/ | # Equilibrium Networks
Science, networks, and security
## Martingales from finite Markov processes, part 1
15 February 2010
In an earlier series of posts the emerging inhomogeneous Poissonian nature of network traffic was detailed. One implication of this trend is that not only network flows but also individual pac... | {"extraction_info": {"found_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": 37, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Saddle_points | # Saddle point
(Redirected from Saddle points)
A saddle point on the graph of z=x2−y2 (in red)
Saddle point between two hills (the intersection of the figure-eight $z$-contour)
In mathematics, a saddle point is a point in the domain of a function that is a stationary point but not a local extremum. The name derives f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.gap-system.org/Manuals/doc/ref/chap44_mj.html | [MathJax off]
### 44 Matrix Groups
Matrix groups are groups generated by invertible square matrices.
In the following example we temporarily increase the line length limit from its default value 80 to 83 in order to get a nicer output format.
```gap> m1 := [ [ Z(3)^0, Z(3)^0, Z(3) ],
> [ Z(3), 0*Z(3)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 65, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/mass+equivalence-principle | # Tagged Questions
2answers
163 views
### Why equivalence principle is principle and not law?
We can prove that the inertial mass and the gravitational mass should be the same (equivalence principle) from the $f=mg=ma$ then $g=a$, so we have equivalence law! But why we said equivalence ...
5answers
959 views
### 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": 2, "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=4247166 | Physics Forums
## The vector nature of Angular Momentum
Here is an animation from Wikipedia : http://en.wikipedia.org/wiki/File:Torque_animation.gif
The angular momentum is given by the Cross product of r and p
We can see that the direction would be perpendicular to the direction of rotation of the particle (as show... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/16018/does-a-photon-have-a-rest-frame | # Does a photon have a rest frame?
Quite a few of the questions given on this site mention a photon having a rest frame such as it having a zero mass in its rest frame. I find this contradictory since photons must travel at the seed of light in all frames according to special relativity
Does a photon have a rest fram... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/174145/what-is-the-relation-between-the-representation-of-a-hecke-algebra-and-the-repre | What is the relation between the representation of a Hecke algebra and the representation of the Coxeter group?
Given a Coxeter group $W$, there is a corresponding Hecke algebra (Iwahori-Hecke algebra). There are many results on the representation of the Hecke algebra. But why is this motivated?
How is the representa... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/44014/rsa-is-it-easy-to-find-the-public-key-from-the-secret-key/44017 | # RSA: is it easy to find the public key from the secret key?
I know that it is not easy to find the secret key from the public key . Is it relatively easy to find the public key from the secret key for scientists in the field?
If the answer is yes then is there any cryptography system such that only a particular per... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 54, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.quantitativepoker.com/2011/01/utility-part-1-basics.html | # Quantitative Poker
math beyond the odds
## Saturday, January 22, 2011
### Utility, Part 1: The Basics
Before we can dive into any models of various poker decisions, we first need to establish the building blocks of models for rational preferences under uncertainty.
In economics, the foundation of any approach to... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://johncarlosbaez.wordpress.com/2011/10/23/a-math-puzzle-coming-from-chemistry/ | # Azimuth
## A Math Puzzle Coming From Chemistry
I posed this puzzle a while back, and nobody solved it. That’s okay—now that I think about it, I’m not sure how to solve it either!
It seems to involve group theory. But instead of working on it, solving it and telling you the answer, I’d rather dump all the clues 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 23, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/1489/how-to-determine-how-much-of-a-table-is-generated/1507 | # How to determine how much of a table is generated?
If I'm generating a table from a slow function, like this:
````foo = Table[SuperSlowExpression, {1000}]
````
is there a way to determine after submission (so it is too late to instrument the call) to find out how many values already have been generated (so that wh... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/103099-discriminant-question.html | # Thread:
1. ## Discriminant question
Find the range of values of a for which the following equations have two real roots:
x^2 - 2ax + 3a = 0
I've got it down to a^2-3a>0, where do i go from here?
Thanks
2. The equation $a^2-3a=0$ has the roots $a_1=0, \ a_2=3$
Then $a^2-3a\geq 0$ if $a\in(-\infty,0]\cup[3,\inft... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/79435?sort=votes | ## Question about 0-dimensional Polish spaces
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hello everybody,
I'm stuck with proving (or disproving) the following statement.
Statement: For every $0$-dimensional Polish space $(X,\mathcal{T}\ )$, and a counta... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?s=d6ac94b40ef73978d413d8e6e579f7dd&p=4194368 | Physics Forums
## Python and Rutherford Scattering
Hello everyone
I have been supplied with this eqn
$$n=\frac{Nat}{16r^2}(\frac{2Ze^2}{4\pi\epsilon_0E_K})^2cosec^4(\frac{\ph i}{2})$$
for Rutherford scattering.
$$N$$ is the number of alpha particles incident on a unit area of foil
$$t$$ is the thickness of the f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://quant.stackexchange.com/tags/artificial-intelligence/hot?filter=all | # Tag Info
## Hot answers tagged artificial-intelligence
13
### Multilayer Perceptron (Neural Network) for Time Series Prediction
First, let's speak about perceptrons in general: their input $X_0$ is a $K$-dimensional vector. So if you want to use $(P_{bid}(t),P_{ask}(t), Q_{bid}(t),Q_{ask}(t))$, it would mean that... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://sbseminar.wordpress.com/2009/03/25/hall-algebras-and-donaldson-thomas-invariants-i/ | ## Hall algebras and Donaldson-Thomas invariants I March 25, 2009
Posted by Joel Kamnitzer in Algebraic Geometry, conferences, homological algebra, quantum groups, things I don't understand.
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I would like to tell you about recent work of Dominic Joyce and others (Bridgeland, Kontsevich-Soibelman, Behrend,... | {"extraction_info": {"found_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": 41, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/202835/schwarz-lemma-extension/202876 | # Schwarz Lemma Extension
Let $f: \Omega \rightarrow \Omega$ be holomorphic where $\Omega \subset \mathbb{C}$ is a bounded region containing 0. If $f(0)=0$ and $f'(0)=1$, does $f(z)=z$?
This is true if $\Omega$ is a disk centered at 0 but does it hold if $D$ is only bounded?
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## 2 Answers
There is a substantial 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": 28, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/247425/is-there-a-vector-space-that-cannot-be-an-inner-product-space?answertab=oldest | # Is there a vector space that cannot be an inner product space?
Quick question: Can I define some inner product on any arbitrary vector space such that it becomes an inner product space? If yes, how can I prove this? If no, what would be a counter example? Thanks a lot in advance.
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The easy answer is, no. But I 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": 23, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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