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http://physics.stackexchange.com/questions/32281/on-the-naturalness-problem | # On the naturalness problem
I know that there are several questions about the naturalness (or hierarchy or fine-tunning) problem of scalars masses in physics.stackexcange.com, but I have not found answers to any of the following questions. Suppose that we add to the SM Lagrangian the following piece:
$(\partial b)^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": 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/54736/about-the-1d-singularity-of-black-hole | # about the 1D singularity of black hole
I saw some responses here saying that the singularity into the black hole is one dimension object so my question is : is it possible that the singularity is simply a merger of the 4 dimensions of the spacetime ? Is it possible physically and mathematically that many dimensions ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/229297/transcendence-of-e-proof?answertab=oldest | # Transcendence of $e$ (proof)
I'm trying to get through the proof of transcendence of $e$ (the base of the natural logarithm) already for a couple of days, but now I got seriously stuck.
Proof is in most sources roughly the same. I followed this version.
We prove the transcendence of $e$ by contradiction - suppose 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": 32, "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/115149/is-there-a-composite-number-that-satisfies-these-conditions/115954 | ## Is there a composite number that satisfies these conditions?
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We know that if $q=4k+3$ ($q$ is a prime), then $(a+bi)^q=a-bi \pmod q$ for every Gaussian integer $a+bi$. Now consider a composite number $N=4k+3$ ... | {"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": 56, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/cl/nagdoc_cl23/html/F01/f01ecc.html | # NAG Library Function Documentnag_real_gen_matrix_exp (f01ecc)
## 1 Purpose
nag_real_gen_matrix_exp (f01ecc) computes the matrix exponential, ${e}^{A}$, of a real $n$ by $n$ matrix $A$.
## 2 Specification
#include <nag.h>
#include <nagf01.h>
void nag_real_gen_matrix_exp (Nag_OrderType order, Integer n, double ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 51, "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/ma... |
http://mendicantbug.com/tag/similarity/ | # The Mendicant Bug
Wanderings into computational linguistics, science, social media and life…
## The limits of collaborative filtering?
Posted: 25 June 2008 in Uncategorized
Tags: attributes, collaborative filtering, logic, machine learning, netflix prize, proportional analogies, recommender systems, relations, sim... | {"extraction_info": {"found_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://gowers.wordpress.com/2010/02/02/edp5-another-very-brief-summary/ | # Gowers's Weblog
Mathematics related discussions
## EDP5 — another very brief summary
I wasn’t expecting to have to write another post quite this soon, so this is another one where I don’t have much to say. Here are a few bits and bobs from the last lot of comments, but there’s plenty more in the comments themselve... | {"extraction_info": {"found_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": 440, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/169721/trying-to-prove-frac2n-frac12-leq-int-1-n11-n-sqrt1-sin/169899 | # Trying to prove $\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\sqrt{1+(\sin(\frac{\pi}{t}) -\frac{\pi}{t}\cos(\frac{\pi}{t}))^2}dt$
I posted this incorrectly several hours ago and now I'm back! So this time it's correct. Im trying to show that for $n\geq 1$:
$$\frac{2}{n+\frac{1}{2}} \leq \int_{1/(n+1)}^{1/n}\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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/90071/argument-principle-and-rouches-theorem-for-fz | # Argument principle and Rouché's theorem for $f(z)$
Say I have a complex valued polynomial $f(z)= z^4 -6z +3$. I'm trying to use the quarter disk $0 \leq \theta \leq \pi/2$, but on the real axis, it seems $f$ is positive only when $z \leq 0$. Does that mean that the change of argument is $- \pi$ for this particular p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/33709/epr-paradox-and-uncertainty-principle | # EPR paradox and uncertainty principle
In Wikipedia article EPR paradox,
The original paper purports to describe what must happen to "two systems I and II, which we permit to interact ...", and, after some time, "we suppose that there is no longer any interaction between the two parts." In the words of Kumar (2009),... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/46048/tachyon-vertex-operator-polchinskis-book?answertab=votes | # Tachyon vertex operator (Polchinski's book)
• I would like to know how does Polchinski in his book "derive" what is the "tachyon vertex operator" (..as say stated in equation 3.6.25, 6.2.11..) I can't locate a "derivation" of the fact that $:e^{ikX}:$ is the tachyon vertex operator.
(..I understand that it follows ... | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/10/15/a-new-definition-of-spans/?like=1&source=post_flair&_wpnonce=5d5a17dad5 | # The Unapologetic Mathematician
## A New Definition of Spans
I was trying to add in duals to the theory, and I ran into some trouble. The fix seems to be something I’d considered a little earlier for a possible generalization, but it seems that duals force the issue. We need to tweak our definition of spans.
Now, m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 44, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/37680/algorithm-to-tell-if-a-partial-recursive-function-is-0-everywhere?answertab=active | Algorithm to tell if a partial recursive function is 0 everywhere
Is there a (partial) recursive function that tells me, if a partial recursive function encoded by the number $c$ is the constant zero function ?
-
When writing questions, it's better practice to explain why you are interested in the question and 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": 59, "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/2010/10/13/hom-space-duals/?like=1&source=post_flair&_wpnonce=420e8d64d7 | # The Unapologetic Mathematician
## Hom Space Duals
Again, sorry for the delay but I was eager to polish something up for my real job this morning.
There’s something interesting to notice in our formulæ for the dimensions of spaces of intertwinors: they’re symmetric between the two representations involved. Indeed, ... | {"extraction_info": {"found_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": 42, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/243/compact-kaehler-manifolds-that-are-isomorphic-as-symplectic-manifolds-but-not-as/81475 | ## Compact Kaehler manifolds that are isomorphic as symplectic manifolds but not as complex manifolds (and vice-versa)
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1. What are some examples of compact Kaehler manifolds (or smooth complex projective varietie... | {"extraction_info": {"found_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/calculus/174445-alternating-series-estimation-theorem.html | # Thread:
1. ## Alternating Series Estimation Theorem
Use the alternating series estimation theorem to approximate the sum of $(-1)^n/(n!)$ from n=0 to infinity with an error of $.000005$.
I know that after summing a number of terms, the remainder(error) will be less than the first omitted term, so
I've set up the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 16, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/222044/what-is-the-distribution-of-a-data-set | # What is the distribution of a data set
I understand what the probability distribution is.
I also have a personal understanding/interpretation of the concept of distribution of a dataset. Whenever I see this expression I imagine a graph with frequency as the y-axis and the members of the data set on the x-axis, for ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/23540/list | ## Return to Answer
2 added 22 characters in body
As you note, if we choose two different embeddings $k^s \to k_v^s$, say $\imath_1$ and $\imath_2$, then we get two different $G_{k_v}$-module structures on $M$, call them $M_1$ and $M_2$, and two different restriction maps $r_1:H^n(k,M) \to H^n(k_v,M_1)$ and $r_2:H^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": 84, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/equation-solving | # Tagged Questions
Questions on the analytic and numeric equation solving functions of Mathematica (Solve, Reduce, NSolve, FindRoot, DSolve, RSolve, etc.).
0answers
91 views
### Find all the integer numbers $a$, $b$, $c$, $d$, $e$, $f$, $k$ to this equation have three integer different solutions?
How to choose all ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 5, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/223510/eigenvalues-and-determinant-of-conjugate-transpose-and-hermitian-of-a-complex-m | Eigenvalues and determinant of conjugate, transpose and hermitian of a complex matrix.
For a strictly complex matrix $A$,
1) Can we comment on determinant of $A^{*}$ (conjugate of entries of $A$) , $A^{T}$ (transpose of A) and $A^{H}$ (hermitian of $A$). I know that for real matrices, $\det(A)=\det(A^{T})$. Does it 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": 28, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://planetmath.org/admissibleidealsboundquiveranditsalgebra | # admissible ideals,, bound quiver and its algebra
Assume, that $Q$ is a quiver and $k$ is a field. Let $kQ$ be the associated path algebra. Denote by $R_{Q}$ the two-sided ideal in $kQ$ generated by all paths of length $1$, i.e. all arrows. This ideal is known as the arrow ideal.
It is easy to see, that for any $m\g... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 31, "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": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/31892-lost-equation.html | Thread:
1. Lost on this equation
I am trying to figure out the steps to solve this equation:
(t-5)^2=2t^2-7t-3
I dont even know how to start this.
And I cant seem to find an example in the book.
Thanks,
2. Originally Posted by GeinoD
I am trying to figure out the steps to solve this equation:
(t-5)^2=2t^2-7t-3
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/35472/is-multicollinearity-implicit-in-categorical-variables | # Is multicollinearity implicit in categorical variables?
I noticed while tinkering with a multivariate regression model there was a small but noticeable multicollinearity effect, as measured by variance inflation factors, within the categories of a categorical variable (after excluding the reference category, of cour... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/30592/warp-drive-with-gravitational-waves-in-the-nonlinear-regime | # warp drive with gravitational waves in the nonlinear regime
gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, maybe we should ask some physicists located a bit closer to t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "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/89142?sort=oldest | ## Are context-free languages with context-free complements necessarily deterministic context-free?
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Let $L \subseteq A^\star$ be a formal language over $A$ generated by a context-free grammar, and $L' = A^\star -... | {"extraction_info": {"found_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/94441/what-is-the-kolmogorov-extension-theorem-good-for?answertab=active | # What is the Kolmogorov Extension Theorem good for?
The Kolmogorov Extension Theorem says, essentially, that one can get a process on $\mathbb{R}^T$ for $T$ being an arbitrary, non-empty index set, by specifying all finite dimensional distributions in a "consistent" way. My favorite formulation of the consistency 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": 36, "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/3417/relative-security-of-a-vigenere-cipher?answertab=votes | # Relative security of a Vigenère cipher
Within a closed computer network, I am ciphering some plaintext data as an added security measure. This is below several other layers of protection. For various technical reasons, I am restricted to plain-text, UTF-8 data. To that end, I have been using a Vigenère cipher with p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/148953-sub-sequential-limit-point.html | # Thread:
1. ## Sub-sequential limit point
1) Is it Possible to find a sequence for which the set of sub-sequential limit points is [0,1]?
2)Is any closed set in R,the set of sub-sequential limit points of a sequence?
2. Originally Posted by math.dj
1) Is it Possible to find a sequence for which the set of sub-seq... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/201209/fredholm-operators | # Fredholm operators
How can I get the (Volterra) operator from an equation of the type
$$u''(x)+xu'(x)+u(x)=0\text{ ?}$$
I know that there is a general way of doing it, if you could point me at the proper book I'd be thankful!
-
It is simpler to solve this equations than to understand what you are asking about – ... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/36936/what-does-the-probabilistic-model-suggest-the-error-term-in-the-pnt-should-be/38272 | What does the probabilistic model suggest the error term in the PNT should be?
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Let $\Lambda(n)$ be the von Mangoldt function. The prime number theorem is equivalent to the statement that $\sum_{n \leq N} \Lambda(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": 31, "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/54846?sort=votes | ## Converse of the Banach fixed point theorem
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Let $f:X \to X$ ($X = R^d$ for some $d$) be a mapping such that $f^n (x) \to x^\ast$ for all $x \in X$ as $n \to \infty$ ($x^\ast$ is unique). Can we say anything abo... | {"extraction_info": {"found_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/algebra/164790-finding-stretch-compression.html | # Thread:
1. ## Finding stretch or compression
Hey everyone I'm trying to figure out how to find a stretch or compression of a parabola. I have a parabola with a vertex of (1,3) and points are (0,5) and (2,5).
The equation I have so far is y = _ (x-1)^2+3, but i can't find the stretch/compression. Thanks for your hel... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/134321-rate-change-cone-print.html | Rate of change of a cone
Printable View
• March 17th 2010, 02:20 PM
Frostking
Rate of change of a cone
I am trying to figure out a practice problem while studying for a calculus final and I do not know how to approach this problem. Any help would be much appreciated. The height of a cone is decreasing at 2 cm per sec... | {"extraction_info": {"found_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://mathoverflow.net/questions/87794/why-is-the-identity-element-of-a-group-denoted-by-e/87797 | ## Why is the identity element of a group denoted by $e$?
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The question was asked by a student, and I did not have a ready answer. I can think of the German word Einheit'', but since in German that is not how the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/110378/analogue-of-a-set-with-n-binary-operations/110379 | ## analogue of a set with n binary operations
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So a group is a type of structure with one binary operations that satisfies some list of axioms. A ring is a structure that has two binary operations that satisfy som... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 67, "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/22866-urgent-help-graphs-sine-cosine-2.html | # Thread:
1. Originally Posted by aikenfan
I'm sorry, I'm a bit confused...On 68, I thought that the Amplitude came from the graph...the line goes up to 2 (but the grid goes up to 3)
you labeled a point on the graph to be $(\pi, 3)$, how is it that the amplitude is 2? (you do not label a grid using coordinates, so if ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://nrich.maths.org/183/note | ### Homes
There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?
### Let's Investigate Triangles
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of diff... | {"extraction_info": {"found_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/revisions/41497/list | ## Return to Question
4 deleted 1092 characters in body
For the problem I am interested in I have additional information about the matrix $A$. For example I know it is a generalized vandermonde matrix.
Then the results of Schlickewei, Hans Peter; Viola, Carlo Generalized Vandermonde determinants. Acta Arith. 95 (200... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 66, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/wavefunction?page=1&sort=votes&pagesize=50 | # Tagged Questions
A complex scalar field that describes a quantum mechanical system. The square of the modulus of the wave function gives the probability of the system to be found in a particular state.
9answers
3k views
### About the complex nature of the wave function?
1. Why is the wave function complex? I've 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": 44, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/221613/how-do-we-find-the-length-of-the-following-curve | # How do we find the length of the following curve?
$r = \sin^2(\theta/3)$
I can't integrate the following expression:
$$\int \sqrt{\left(\sin^2 \frac x 3\right)^2 + \left(\frac 2 3 \sin \frac x 3 \cos \frac x 3\right)^2}dx$$
I got this in my mid-term and I was wondering what the hell is wrong with the teacher.
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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": 11, "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/218661/how-strong-is-an-egg?answertab=oldest | # How Strong is an Egg?
You have two identical eggs. Standing in front of a 100 floor building, you wonder what is the maximum number of floors from which the egg can be dropped without breaking it. What is the minimum number of tries needed to find out the solution?
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1
@Dennis: You can have more than two tries: an... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 135, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/tagged/brownian-motion+statistics | Tagged Questions
1answer
64 views
Strong markov property on max of brownian motion
For $B_t$ Brownian Motion with drift $\mu<0$, I have the max value, $X = \max_{0<t<\infty}B_t$ . I need to prove with the Strong Markov Property that, $P(X>c+d)=P(X>c)P(X>d)$ a. It ...
2answers
108 views
Max of Brownian motion with d... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 8, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2009/10/06/vector-valued-functions/?like=1&source=post_flair&_wpnonce=9916d21231 | # The Unapologetic Mathematician
## Vector-Valued Functions
Now we know how to modify the notion of the derivative of a function to deal with vector inputs by defining the differential. But what about functions that have vectors as outputs?
Well, luckily when we defined the differential we didn’t really use anything... | {"extraction_info": {"found_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": 52, "mimetex.cgi": 0, "/images/ma... |
http://www.math.uah.edu/stat/games/PokerDice.html | $$\newcommand{\P}{\mathbb{P}}$$ $$\newcommand{\E}{\mathbb{E}}$$ $$\newcommand{\R}{\mathbb{R}}$$ $$\newcommand{\N}{\mathbb{N}}$$ $$\newcommand{\bs}{\boldsymbol}$$ $$\newcommand{\var}{\text{var}}$$
## 3. Simple Dice Games
In this section, we will analyze several simple games played with dice--poker dice, chuck-a-luck, ... | {"extraction_info": {"found_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": 85, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/292/how-does-asymmetric-encryption-work/516 | How does asymmetric encryption work?
I've always been interested in encryption but I have never found a good explanation (beginners explanation) of how encryption with public key and decryption with private key works.
How does it encrypt something with one key and decipher it with another key?
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2
It would be usefu... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathforum.org/mathimages/index.php?title=Newton's_Basin&diff=3342&oldid=3341 | # Newton's Basin
### From Math Images
(Difference between revisions)
| | ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 7, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/91716-solved-addition-multiplication-tables.html | # Thread:
1. ## [SOLVED] addition and multiplication tables
I have these two Cayley tables. The addition table is complete and the multiplication table is not. The instructions say to use the distributive laws, but I can't seem to find the solutions using the distributive laws. I can only find the solution using the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=124396 | Physics Forums
Thread Closed
Page 1 of 2 1 2 >
To find logarithm of a complex number
#2
Hi,
Well can anyone tell me how to find the natural logarithm of a complex number p + iq.
Also please tell me how to convert it into logarithm to the base 10.
An external link to a webpage (where all the details are given)... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/87024/criterions-for-reflexiveness-of-sheaves-and-a-special-case/87029 | ## Criterions for Reflexiveness of sheaves and a special case
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A coherent sheaf $V$ on a say noetherian scheme is called reflexive if the canonical map $V \rightarrow \mathcal Hom_{\mathcal O_X}(\mathcal Hom_{\mat... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/23547/ | ## Does pi contain 1000 consecutive zeroes (in base 10)?
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The motivation for this question comes from the novel Contact by Carl Sagan. Actually, I haven't read the book myself. However, I heard that one of the 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": 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/advanced-algebra/60380-module-homomorphism-ring-subset.html | # Thread:
1. ## module homomorphism, ring, subset
Background: Let $R$ be a ring, $S \subseteq R$ a multiplicatively closed subset, and let $M$, $N$ be $R-$modules. Let $\phi : M \rightarrow N$ be an $R-$module homomorphism, and let $\phi_s : S^{-1}M \rightarrow S^{-1}N$ denote the $S^{-1}R-$module homomorphism, and l... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 91, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/142167-confused-taylor-series-problem.html | # Thread:
1. ## Confused with this Taylor series problem.
The problem says, "Write down the Taylor series of $Cos(x)$ about $x=0$ and sum the series $\sum_{0}^{inf} (-\pi ^2)^n / (2n)! 9^n$"
First question is, when do you stop writing terms of the series if it doesn't tell you?
Also, what does the second series hav... | {"extraction_info": {"found_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": 23, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/26297?sort=oldest | ## Which finite groups are generated by n involutions?
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One of the interesting problems in abstract polytope theory is to determine, for a given finite group, when that group is the automorphism group of a regular... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 18, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/254356/choosing-a-5-member-team-out-of-12-girls-and-10-boys/254359 | Choosing a 5 member team out of 12 girls and 10 boys
We must choose a 5-member team from 12 girls and 10 boys. How many ways are there to make the choice so that there are no more than 3 boys on the team?
The correct answer is (22 choose 5) - (12 choose 1)(10 choose 4) - (10 choose 5).
I understand the (22 choose 5)... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/moon?sort=active&pagesize=15 | # Tagged Questions
The moon tag has no wiki summary.
learn more… | top users | synonyms
2answers
69 views
### What is our estimated running speed on Moon's surface?
I was wondering if we have the chance to run on the Moon's surface, how would you expect it look like? I expect our velocity will increase for the sam... | {"extraction_info": {"found_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/94610/smoothing-a-sobolev-function/192888 | # smoothing a Sobolev function
Let $u \in H^1({\mathbb R}^n)$, $n \geq 2$. Let $\varphi \in C^\infty_0({\mathbb R}^n)$ with $\varphi \geq 0$. Let $\eta$ be a smoothing kernel with $\eta \in C^\infty_0({\mathbb R}^n)$, $\eta \geq 0$, $\int \eta \,dx = 1$. For $t > 0$, define $\eta_t$ by $\eta_t(x)=\frac{1}{t^n}\eta(\fr... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/61684/generalized-vector-bundles-with-singularities-on-riemann-surfaces | ## Generalized vector bundles with singularities on Riemann surfaces
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Let $X$ be a Riemann surface of genus $g \geq 2$ or in other words a complex curve.
Let $P_1, \ldots, P_m$ be points in $X$ and $E \rightarrow... | {"extraction_info": {"found_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/advanced-statistics/31855-clearification-poisson-distribution.html | # Thread:
1. ## Clearification on Poisson Distribution
Q: A parking lot has 2 entrances. Cars arrive at entrance 1 and 2 according to a Poisson distribution an average of 3/hour, and entrance 2 at an average of 4/hour, respectively. What is the probability that a total of 3 cars will arrive at the parking lot in a gi... | {"extraction_info": {"found_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://matthewkahle.wordpress.com/2010/09/ | The fundamental group of random 2-complexes
Eric Babson, Chris Hoffman, and I recently posted major revisions of our preprint, “The fundamental group of random 2-complexes” to the arXiv. This article will appear in Journal of the American Mathematical Society. This note is intended to be a high level summary of the ma... | {"extraction_info": {"found_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://mathoverflow.net/questions/51531/theorems-that-are-obvious-but-hard-to-prove/51532 | Theorems that are ‘obvious’ but hard to prove
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There are several well-known mathematical statements that are 'obvious' but false (such as the negation of the Banach--Tarski theorem). There are plenty more that are '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": 58, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/trigonometry/196412-isosceles-triangle-problem-using-right-triangle-trig.html | 2Thanks
• 1 Post By Prove It
• 1 Post By cshanholtzer
# Thread:
1. ## Isosceles triangle problem Using right triangle trig
I am not understanding how to solve this one, so any help would be greatly appreciated!
Problem: An isosceles triangle has equal sides of length 10 cm and a base of 8 cm. Find the angles of the ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/19802?sort=newest | ## How much complex geometry does the zeta-function of a variety know
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From Weil conjecture we know the relation between the zeta-function and the cohomology of the variety, however it appears that there are certa... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/43/is-there-a-standard-model-for-market-impact/277 | # Is there a standard model for market impact?
Is there a standard model for market impact? I am interested in the case of high-volume equities sold in the US, during market hours, but would be interested in any pointers.
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## 2 Answers
There is a family of models that is so commonly used among practitioners 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": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Appell%e2%80%93Humbert_theorem | # Appell–Humbert theorem
In mathematics, the Appell–Humbert theorem describes the line bundles on a complex torus or complex abelian variety. It was proved for 2-dimensional tori by Appell (1891) and Humbert (1893), and in general by Lefschetz (1921)
## Statement
Suppose that T is a complex torus given by V/U where ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/204529/prove-if-lim-n-to-inftya-n-l-and-a-n-a-for-all-n-then-l-geq-a | # Prove: If $\lim_{n\to\infty}a_n = L$ and $a_n > a$ for all $n$ then $L \geq a$
Prove: If $\lim_{n\to\infty}a_n = L$ and $a_n > a$ for all $n$ then $L \geq a$
Proof: We know from the definition of the limit that $\forall_{\epsilon > 0} \exists_n s.t. \forall_{n>N} |a_n - L| < \epsilon$. Now since $a_n > a$ for all $... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 65, "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/93452/a-question-on-taylor-series-and-polynomial/206673 | # A question on Taylor Series and polynomial
Suppose $f(x)$ that is infinitely differentiable in $[a,b]$.
For every $c\in[a,b]$ the series $\sum\limits_{n=0}^\infty \cfrac{f^{(n)}(c)}{n!}(x-c)^n$ is a polynomial.
Is true that $f(x)$ is a polynomial?
I can show it is true if for every $c\in [a,b]$, there exists a ne... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 202, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/6466/subgroups-klein-bottle | Subgroups - Klein bottle
Let $G$ be the fundamental group of the Klein bottle,
$G = \langle x,y \ ; \ yxy^{-1}=x^{-1} \rangle = {\mathbb Z} \rtimes {\mathbb Z} \ .$
What are the nilpotent subgroups of $G$?
I was only able to find a normal series of abelian subgroups with cyclic quotients in $G$, namely
$1\leq \lan... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 50, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/199856-prove-limit.html | # Thread:
1. ## Prove this limit
lim as x goes to 1 (x^(2)-2x+4)=3
2. ## Re: Prove this limit
If a function f is continuous at x0, then its limit as x -> x0 is f(x0).
3. ## Re: Prove this limit
Using what "basis"? If you know about "continuous functions" and in particular that all polynomials are continous for al... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/82917?sort=newest | ## R-matrices, crystal bases, and the limit as q -> 1
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I am seeking references for precise statements and rigorous proofs of some facts about the actions of quantum root vectors and $R$-matrices on crystal bases 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": 55, "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/65652/symplectic-classes-on-rational-surfaces | ## symplectic classes on rational surfaces.
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Hi. I have a stupid question. Let $M$ be a blow-up of the complex projective plane at $k$ generic points. Then we can choose an orthoginal basis (with respect to the cu... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/44732/is-string-theory-formulated-in-flat-or-curved-spacetime/44738 | # Is String Theory formulated in flat or curved spacetime?
String Theory is formulated in 10 or 11 (or 26?) dimensions where it is assumed that all of the space dimensions except for 3 (large) space dimensions and 1 time dimension are a compact manifold with very small dimensions. The question is what is assumed about... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/12330/calculating-angles-for-tetrahedral-molecular-geometry | # Calculating angles for tetrahedral molecular geometry
Let's say I have a molecular like CH3F (i.e. fluoromethane), and I'm able to measure the angle (theta) between the C-H bonds. Provided (theta) what is the angle between the C-F bond and the C-H bonds?
-
## 1 Answer
Use a coordinate system with the C at the ori... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?t=592619 | Physics Forums
## Quadratic Reciprocity
If a is a quadratic nonresidue of the odd primes p and q, then is the congruence $x^2 \equiv a (\text{mod } pq)$ solvable?
Obviously, we want to evaluate $\left( \frac{a}{pq} \right)$. I factored a into its prime factors and used the law of QR and Euler's Criterion to get rid ... | {"extraction_info": {"found_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/281254/question-on-cech-cohomology | # Question On Cech Cohomology
In section 16 of the topology book of Bott and Tu, there is a path fibration $\Omega S^2 \to PS^2 \to S^2$. The $E_2$ page of the spectral sequence of this fibration is $$E_2^{p,q}=H^p(S^2,H^q(\Omega S^2)).$$
This is a Cech Cohomology of $S^2$ with values in $H^q(\Omega S^2)$. My questio... | {"extraction_info": {"found_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/revisions/103005/list | Return to Answer
1 [made Community Wiki]
From Rick Kenyon's open problem list:
What are the minimal number of squares needed to tile an $a \times b$ rectangle?
Kenyon showed the correct order is $\log a$ assuming $a/b$ is bounded with $b \leq a$. However, there is plenty of room for improvement in the constant fact... | {"extraction_info": {"found_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://nrich.maths.org/5589/solution | nrich enriching mathematicsSkip over navigation
### Roots and Coefficients
If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?
### Target Six
Show that x = 1 is a solution of the equation x^(3/2) ... | {"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": 30, "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/10.4153/CMB-2008-044-8 | Canadian Mathematical Society
www.cms.math.ca
| | | | |
|----------|----|-----------|----|
| | | | | | |
| Site map | | | CMS store | |
location: Publications → journals → CMB
Abstract view
# On the Maximal Spectrum of Semiprimitive Multiplication Modules
... | {"extraction_info": {"found_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://mathoverflow.net/questions/36431?sort=oldest | eigenvalues of edge regular graphs
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In graph theory, an edge regular graph is defined as follows. Let G = (V,E) be a regular graph with v vertices and degree k. G is said to be edge regular if there is also integer λ ... | {"extraction_info": {"found_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-applied-math/120555-optimization-time-dependent-constraints-need-help-please.html | # Thread:
1. ## optimization with time dependent constraints, need help please~
Dear all,
I am trying to obtain the optimal solution from constraints that are represented in time function:
Minimize F = 100Ppv + 2Pdg
subject to:
$Ppv(t) + Pdg(t) \geq PL(t)$
$\sum Ppv(t) \leq 0.4 \times \sum PL(t)$
t is from 1 to 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": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/87276/an-equivalence-relation-on-the-power-set-of-the-plane | ## An equivalence relation on the power set of the plane.
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Let $R\subseteq\mathbb{R}^2$. Consider the set of all "horizontal sections" $H_R =$ {$Rb|b\in\mathbb{R}$} where $Rb=${$a\in\mathbb{R} | (a,b)\in R$}. Simi... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=87875&page=3 | Physics Forums
Thread Closed
Page 3 of 4 < 1 2 3 4 >
## A proof of RH using quantum physics...:)
i can,t prove it :( :( :( :( :( i can not prove the existence of the potential even with the variational principle for Schroedinguer equation:
$$J[\phi]=\int_{-\infty}^{\infty}dx(V(x)\phi^{2}/2-(\hbar^{2}/4m... | {"extraction_info": {"found_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": 45, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/73046/turning-a-measurable-function-to-a-bijection/73047 | ## Turning a measurable function to a bijection
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Let $f:(0,1)\rightarrow (0,1)$ be a borel measurable function such that for every $y$ in $(0,1)$ , $f^{-1}(y)$ is a borel set and $\mu(f^{-1}(y))=0$ and also $\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": 13, "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/9134/list | ## Return to Question
2 fixed up the formatting in a hacky way, \newline doesn't seem to work?
Thinking of arbitrary tensor products of rings, $A=\otimes_i A_i$ ($i\in I$, an arbitrary index set), I have recently realized that $Spec(A)$ should be the product of the schemes $Spec(A_i)$, a priori in the category of aff... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/91583?sort=votes | ## The rank of a symmetric space
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I would like to work a theorem on a article who deals with the rank one symmetric spaces.
i looked up the definition of symmetric spaces of rank one, but I did not find a satisfa... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/15680/only-head-on-collision/15695 | Only Head On collision?
Let us consider two spheres A and B. Suppose they are interacting with each other (In broad sense one can say they are colliding). Let for the time being refer to "striking by coming in contact as collision". Now suppose the sphere B collided in such a way that its direction of motion is not al... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "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/88733/metric-graphs-and-curvature | ## Metric graphs and curvature
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Consider a positively weighted connected simple graph with bounded degree $X$ . Denote by $d(x,y)$ the weight on the edge with endpoints $x$ and $y$. Suppose we have the following 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": 38, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://medlibrary.org/medwiki/Birational_transformation | # Birational transformation
Welcome to MedLibrary.org. For best results, we recommend beginning with the navigation links at the top of the page, which can guide you through our collection of over 14,000 medication labels and package inserts. For additional information on other topics which are not covered by our data... | {"extraction_info": {"found_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": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/165284-composite-functions-question.html | # Thread:
1. ## Composite Functions Question
Hope I've posted this question in the right place- I think I did.. But anyway.
Let a be a positive number, let f : [2,∞) → R, f (x) = a − x and let g: (−∞, 1] → R,
g(x) = x^2 + a. Find all values of a for which f ◦ g and g ◦ f both exist.
I've no clue how to do this coul... | {"extraction_info": {"found_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://www.sagemath.org/doc/reference/combinat/sage/combinat/rigged_configurations/bij_type_D.html | # Bijection classes for type $$D_n^{(1)}$$¶
Part of the (internal) classes which runs the bijection between rigged configurations and KR tableaux of type $$D_n^{(1)}$$.
AUTHORS:
• Travis Scrimshaw (2011-04-15): Initial version
TESTS:
```sage: KRT = TensorProductOfKirillovReshetikhinTableaux(['D', 4, 1], [[2,1]])
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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/177338/generalized-change-of-variables-theorem | # Generalized Change of Variables Theorem?
Is there a generalized form of the differentiable change of variables theorem for Lebesgue integrals? That is, if we consider the well known change of variables theorem: If $\phi : X \rightarrow X$ is a diffeomorphism of open sets in $\mathbb{R}^n$, $X \subseteq \mathbb{R}^n$... | {"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": 10, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/170513-find-basis-print.html | # find the basis
Printable View
• February 7th 2011, 07:00 PM
Taurus3
find the basis
Let L be the line spanned by v_1=[1, 1, 1]. Find a basis {v_2, v_3} for the plane perpendicular to L, and verify that B= {v_1,, v_2, v_3} is a basis for R3.
Let ProjL denote the projection onto the line L. Find the matrix B for Proj... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/96250-derivatives-tangent-lines.html | # Thread:
1. ## Derivatives and tangent lines
I'm having some trouble on these questions. On other questions for this I was using derivatives to get the answers but on these I don't know how to apply it. Can someone explain how to use derivatives to find these answers?
1. Find the equation of the tangent line to the... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/1685?sort=oldest | Range of a Certain Linear Operator
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Consider the following hermitian form on the sobolev space H^1(I), of an interval I: g(u,v):= \int_I (du/dt dv/dt - \rho(t) u v)dt, where \rho is a nice bounded function on I. Riesz... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/97173-permutation-involving-restriction.html | # Thread:
1. ## Permutation involving restriction
Decide in how many ways the letters of the word ABRACADABRA can be arranged in a row if C, R and D are not to be together.
My text says the answer is 78,624 ways, but I don't know how they arrived at this.
2. Instead of considering AB and CDR as seperate letters, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/111133/function-defined-by-infinite-series?answertab=active | # Function defined by infinite series
A function $f$ is defined as follow:
$$f(x)=\sum_{n=1}^{\infty}\frac{b_{n}}{(x-a_{n})^{2}+b_{n}^{2}}\;\;, x\in \mathbb R$$
where $(a_{n}, b_{n})$ are points in the $xy$-plane, $b_{n}>0$ for all $n$. When is the function $f(x)$ bounded away from zero? that is $f(x)\geq a>0$, for ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/40246/matrices-hermitian-and-unitary/40248 | # Matrices (Hermitian and Unitary)
Hey! I have some short proofs I’m quite stuck on below. I know the definitions but get stuck on how to use them to prove what’s required. If possible, can you please explain how to apply the definition to get these proofs so that I can try again? Thanks!
Q1. Show that if there exist... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/05/24/cardinals-and-ordinals-as-categories/?like=1&source=post_flair&_wpnonce=5b12459335 | # The Unapologetic Mathematician
## Cardinals and Ordinals as Categories
We can import all of what we’ve said about cardinal numbers and ordinal numbers into categories.
For cardinals, it’s actually not that interesting. Remember that every cardinal number is just an equivalence class of sets under bijection. So, gi... | {"extraction_info": {"found_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": 38, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/192431/finding-e-bigl-overliney2-bigm-overliney-vphantomy2-bigr-by-basus | # Finding $E\Bigl(\overline{Y^2}\Bigm|\overline{Y\vphantom{Y^2}}\Bigr)$ by Basu's theorem?
Suppose $Y_1,\ldots,Y_n$ are a random sample of normal distribution $\mathcal{N}(\mu,1)$. If $\overline{Y^2}=\displaystyle\frac{1}{n}\sum_{i=1}^n Y_i^2$, how can I find $E\Bigl(\overline{Y^2}\Bigm|\overline{Y\vphantom{Y^2}}\Bigr... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/118471-relations-question-print.html | # Relations Question
Printable View
• December 4th 2009, 08:38 AM
dre
Relations Question
Let A be the set {a, b, c, d, e, 1, 2, 3, 4, 5, x, y, z, w}
How many different reflexive relations are there and how many different symmetric relations are there? I know the total would be 2^196 because of the power set rule but... | {"extraction_info": {"found_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": 48, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://terrytao.wordpress.com/tag/padded-trees/ | 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 ‘padded trees’ tag.
## Random Martingales and localization of maximal inequalities
7 December, 2009 in math.CA, math.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 35, "mimetex.cgi": 0, "/images/ma... |
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