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http://mathoverflow.net/revisions/13581/list | ## Return to Question
3 deleted 222 characters in body
A quantum channel is a mapping between Hilbert spaces, `$\Phi : L(\mathcal{H}_{A}) \to L(\mathcal{H}_{B})$`, where `$L(\mathcal{H}_{i})$` is the family of operators on `$\mathcal{H}_{i}$`. In general, we are interested in CPTP maps. The operator spaces can be 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": 38, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Mandelbrot_set | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 21, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showpost.php?p=3197654&postcount=7 | View Single Post
Recognitions:
Gold Member
Homework Help
Quote by LCKurtz Don't quit yet, you almost have it. Take x > 0 to dispense with the || signs: $$R(x) = e^{\int-\frac 1{2x}dx}= e^{-\frac 1 2 \int\frac 1 x}\, dx = e^{-\frac 1 2 \ln x} = e^{\ln(x^{-\frac 1 2})} = x^{-\frac 1 2}$$ Also, a TeX no... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/75565/finite-simple-groups-and-conjugacy-classes-with-2p-elements/75672 | ## Finite simple groups and conjugacy classes with 2p elements
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $p$ be an odd prime number. Can a finite simple group have a conjugacy class with $2p$ elements?
-
2
Did you trawl the ATLAS for examples? – No... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 42, "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/38448/newton-2nd-law-does-vertical-force-mass-affect-the-horizontal-acceleration/38469 | # Newton 2nd Law: Does vertical force (mass) affect the horizontal acceleration?
I learnt before that if 2 forces are perpendicular to each other, they should not affect each other. However in a recent experiment setup (asked in another question):
I believe the theoratical equation by newton 2nd law is
$$\begin{alig... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/29249/quick-finite-intersection-property-question | ## Quick Finite Intersection Property Question [closed]
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I just need a quick clarification:
Given a sequence of sets `$\{a_n\}_{n \in \mathbb{N}}$` in some field $\mathbb{K}$, is saying that it satisfies the fini... | {"extraction_info": {"found_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://nrich.maths.org/2292 | ### Weekly Problem 14 - 2012
Weekly Problem 14 - 2012
### Lost
Can you locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
### Square Coordinates
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction 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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/171541-show-these-intervals-open-closed-sets-print.html | # Show these intervals are open and closed sets.
Printable View
• February 16th 2011, 04:09 PM
seamstress
Show these intervals are open and closed sets.
Show that the intervals (a, ∞) and (-∞, a) are open sets and that [b, ∞) and (-∞, b] are closed sets.
Thank you!
• February 16th 2011, 04:18 PM
Plato
Hello and welc... | {"extraction_info": {"found_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://mathhelpforum.com/differential-equations/156947-partial-differential-equations-problems.html | # Thread:
1. ## Partial Differential Equations Problems
Hello.
Question 1
Find the temperature distribution T(x,t) in a long thin bar $-a \leq x \leq a$ with given initial temperature $u(x,0) = f(x)$
The side walls of the bar are insulated, while heat radiates from the ends into the surrounding medium whose temperat... | {"extraction_info": {"found_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": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/148312-instantaneous-rate-word-problem.html | # Thread:
1. ## instantaneous rate word problem
So I was able to do the first part (hopefully it's right), but I'm having trouble trying to figure out what it's asking in the last parts. Here's my problem:
A business is prospering in such a way that its total (accumulated) profit after t years is $1000t^2$ dollars.
... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/dimensional-analysis+thermodynamics | # Tagged Questions
2answers
302 views
### Why are expressions such as $\operatorname{ln}T$ used in thermodynamics where $T$ is not dimensionless?
In all thermodynamics texts that I have seen, expressions such as $\operatorname{ln}T$ and $\operatorname{ln}S$ are used, where $T$ is temperature and $S$ is entropy, and ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "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/210614/proving-irrationals-are-dense-in-0-1 | # Proving irrationals are dense in (0, 1)
The definition of dense I'm using is the following: a subset $S$ of $(0, 1)$ is dense in $(0, 1)$ if for every $x \in (0, 1)$ and every $\epsilon > 0$ there exists $s \in S$ with $|s - x| < \epsilon$.
I'm trying to show that the set of irrationals in $(0, 1)$ (i.e. the set $\... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/38885/how-do-astronomers-measure-the-distance-of-the-planets-from-its-star/38887 | # How do astronomers measure the distance of the planets from its star?
I know they have accurate means of measuring the distance of the planets in the Solar System from the Sun. I'm skeptical how can they use the same tools or techniques for other systems so far away as 22 light years.
According to this link the pla... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/152021-indefinite-integral.html | # Thread:
1. ## Indefinite integral
Find the following indefinite integral, identifying any rules of calculus that you use:
$\int1/\sqrt{(1-x^2)*\arcsin(x)}$
I think I need to use integration by substitution, so have rearranged to give:
$\int(1-x^2)^{\-1/2} * (sin(x))^{1/2}$
I am not quite sure what to do next. 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": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/33504?sort=oldest | ## Degree sequences of multigraphs with bounded multiplicity
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I got to thinking about this problem while sifting through the math puzzles for dinner thread. There's a fun puzzle by rgrig which asks the guests to 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": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://motls.blogspot.com.au/2012/06/have-starkman-and-pals-shown-that.html | # The Reference Frame
## Sunday, June 24, 2012
... /////
### Have Starkman and pals shown that the hierarchy problem doesn't exist?
The Higgs mass around $125\GeV$ together with the Higgs vev around $246\GeV$ and the masses of related particles such as the W-bosons and Z-bosons are much smaller than some other 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": 7, "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-equations/58911-initial-value-problem.html | # Thread:
1. ## Initial value problem
Hi.
Solve the Initial value problem:
$\dot{u}(t) = \begin{pmatrix} a & 1 \\ 0 & b \end{pmatrix}\cdot u(t) \ , \ t\in [0,T] \ , \ u(0) = (1,1)^t$
(theres nothing said about 'a' and 'b')
does anyone know how to solve it, because i dont
Thanks so much!
Rapha
2. Originally Pos... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/data-analysis?sort=votes&pagesize=15 | # Tagged Questions
The data-analysis tag has no wiki summary.
2answers
1k views
### Did the researchers at Fermilab find a fifth force?
Please consider the publication Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in $p\bar{p}$ Collisions at $\sqrt{s} = 1.96$ TeV by the CDF-Collabo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.sagemath.org/doc/reference/matrices/sage/matrix/matrix_symbolic_dense.html | # Symbolic matrices¶
Symbolic matrices
Matrices with symbolic entries. The underlying representation is a pointer to a Maxima object.
EXAMPLES:
```sage: matrix(SR, 2, 2, range(4))
[0 1]
[2 3]
sage: matrix(SR, 2, 2, var('t'))
[t 0]
[0 t]
```
Arithmetic:
```sage: -matrix(SR, 2, range(4))
[ 0 -1]
[-2 -3]
sage: m = 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": 1, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/3750/aunt-and-uncles-fuel-oil-tank-dip-stick-problem?answertab=votes | # Aunt and Uncle's fuel oil tank dip stick problem
This problem first came to me in high school, and a couple times since, and I even assigned it for extra credit in one of my calculus classes after I became a teacher. So I know the solution. What I am looking for is other WAYS to obtain the solution. I've been told 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": 87, "mathjax_display_tex": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/tagged/convergence?sort=votes | # Tagged Questions
Convergence of sequences and different modes of convergence.
3answers
810 views
### Does the series $\sum\limits_{n=1}^{\infty} \frac{1}{n^{1 + |\sin(n)|}}$ converge or diverge?
Does the following series converge or diverge? I would like to see a demonstration. $$\sum_{n=1}^{\infty} \frac{1}{n^{1... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 135, "mathjax_display_tex": 21, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/24697?sort=newest | ## Isomorphism between direct sum of modules
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $M$, $N$ be two modules over ring $A$. If $M\oplus M\cong N\oplus N$, can we conclude $M\cong N$? In the case that $M$, $N$ are completely decomposable (e.g. finit... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?s=93fd6faac0552a57820d99f2c36e3921&p=4239043 | Physics Forums
## Z-Boson reasonance and the number of neutrino varieties
I've read that the experimental results of Z-Boson resonance confirm the theoretical expectations that there are 3-types of Neutrinos, not 2 or 4.
How are these theoretical expectations calculated? I.e. how does the number of neutrino 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": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.citizendia.org/Hexagonal_number | A hexagonal number is a figurate number, The nth hexagonal number will be the number of points in a hexagon with n regularly spaced points on a side, as shown in [1]. A figurate number is a number that can be represented as a regular and discrete geometric pattern (e
The formula for the nth hexagonal number is:
$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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://katlas.math.toronto.edu/0506-Topology/index.php?title=Classnotes_for_January_10&oldid=765 | # Classnotes for January 10
### From 0506Topology
Revision as of 14:18, 6 Feb 2006; view current revision
## Group-Theoretical Defintions
The goal of this lecture is to state van Kampen's theorem (also known as the Seifert-van Kampen theorem), give a brief explanation of its plausibility, and supply several example... | {"extraction_info": {"found_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": 36, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/66830/list | ## Return to Answer
2 added 2 characters in body
Yes, this is true. It follows from the fact that the average $$\lim_{T\to\infty} {1\over T}\int_0^T\cos(\lambda_i t+\phi_i)\sum A_i\cos(\lambda_i t+\phi_i)\,dt$$ t+\phi_i)\sum_j A_j\cos(\lambda_j t+\phi_j)\,dt is $A_i/2$. Clearly the average is bounded by the supremum ... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/221887/probability-involving-two-poisson-constants?answertab=votes | # Probability involving two Poisson constants.
A discrete stochastic variable $X$ is defined as the number of eggs laid by a bird at a certain time. Depending on the specie of the bird, the Poisson constant for this distribution is $\lambda = \lambda_1$ or $\lambda_2$. What is $\text {Pr}(X = k)$?
Am I crazy to think... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/67562/weak-convergence-of-measures-on-non-metrizable-spaces/67577 | ## Weak convergence of measures on non-metrizable spaces
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
(ZF + Countable Choice)
Let $\langle X,\mathcal{T} \hspace{.06 in} \rangle$ be a second-countable Hausdorff space. Let $\mu$ be a Borel measure on $X$.
Le... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/121340/plus-construction-considerations/121368 | ## Plus construction considerations.
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In order to realise the K-groups of a ring as the homotopy groups of some space associated to that ring, Quillen proposed the following (roughly-sketched) construction:
Recal... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 2, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/79019-solved-calculating-limit-sequence.html | # Thread:
1. ## [SOLVED] Calculating limit of a sequence
Can someone help me with a good strategy for finding the limit of a sequence? I am just not understanding the best way to solve these. What I have been trying to do to first take the limit. If i got an indeterminate, I changed it to a function and took the deri... | {"extraction_info": {"found_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": 64, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=288086 | Physics Forums
## Reflection and Refraction, much index of refraction
1. The problem statement, all variables and given/known data
1. The index of refraction for water is 1.33 and that of glass is 1.50.
a. What is the critical angle for a glass-water interface?
b. In which medium is the light ray incident for total... | {"extraction_info": {"found_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": 14, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/39791?sort=oldest | ## Explicit metrics
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Every surface admits metrics of constant curvature, but there is usually a disconnect between these metrics, the shapes of ordinary objects, and typical mathematical drawings of surfaces.
Can... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 57, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/tagged/machine-learning?sort=faq&pagesize=15 | # Tagged Questions
Methods and principles of building "computer systems that automatically improve with experience."
12answers
13k views
### The Two Cultures: statistics vs. machine learning?
Last year, I read a blog post from Bendan O'Connor entitled "Statistics vs. Machine Learning, fight!" that discussed some 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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikibooks.org/wiki/Numerical_Methods/Errors_Introduction | Numerical Methods/Errors Introduction
When using numerical methods or algorithms and computing with finite precision, errors of approximation or rounding and truncation are introduced. It is important to have a notion of their nature and their order. A newly developed method is worthless without an error analysis. Nei... | {"extraction_info": {"found_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": 5, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/213762/question-about-linear-operators-on-hilbert-spaces | Question about linear operators on Hilbert spaces
I have the following question: "Let $V$ be a Hilbert space and let $T$ be a linear operator on $V$. If $S$ is any linear operator on $V$ that satisfies $\langle Tv,w \rangle = \langle Sv,w \rangle$ for all $v,w \in V$, then $S = T$."
My attempt at the problem went 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": 21, "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/44113/whats-the-value-of-sum-limits-k-1-infty-frack2k/44120 | # What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
For some series, it is easy to say whether it is convergent or not by the "convergence test", e.g., ratio test. However, it is nontrivial to calculate the value of the sum when the series converges. The question is motivated from the simple exercise 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": 31, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/29039/list | ## Return to Answer
1 [made Community Wiki]
A polynomial, solvable in radicals, whose splitting field is not a radical extension (of $\bf Q$). Let $f(x)$ be any cyclic cubic, that is, any cubic with rational coefficients, irreducible over the rationals, with Galois group cyclic of order 3. Then $f(x)=0$ is solvable 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": 15, "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/139108/explicit-example-of-a-toric-flip?answertab=oldest | # Explicit example of a toric flip
I am looking for a toy example of a flip between toric projective 3-folds. More precisely, I would like to see their defining fans (or polytopes).
Does anyone know where I can find something like this?
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## 1 Answer
Consider the cube with vertices $(\pm1,\pm1,\pm1)$ and subdivide... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/136856/definition-of-isomorphism-of-vector-spaces | # Definition of isomorphism of vector spaces
Suppose that $V_1$ is a vector space over the field $K_1$ and $V_2$ is a vector space over the field $K_2$. What is the definition of an isomorphism between these two vector spaces?
My best guess would be that $K_1$ and $K_2$ have to be isomorphic as fields. Say $\xi:K_1\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": 20, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/25878/relevance-of-the-complex-structure-of-a-function-algebra-for-capturing-the-topolo | ## Relevance of the complex structure of a function algebra for capturing the topology on a space.
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This question is the outcome of a few naive thoughts, without reading the proof of Gelfand-Neumark theorem.
Give... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 104, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/121018/intersections-of-anisotropic-tori-with-split-levi-subgroups | ## Intersections of anisotropic tori with split Levi subgroups
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Let G be a connected reductive group defined and split over a finite field k with Frobenius morphism F. Let T be an F-stable minisotropic maximal tor... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/31358/can-a-mathematical-definition-be-wrong/31431 | ## Can a mathematical definition be wrong?
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This question originates from a bit of history. In the first paper on quantum Turing machines, the authors left a key uniformity condition out of their definition. Three... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/65233/lifting-varieties-from-char-p-to-char-0-after-alterations | ## Lifting varieties from char. $p$ to char. 0 after alterations
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The question is related to this MO question:
http://mathoverflow.net/questions/25337/lifting-varieties-to-characteristic-zero
Let $X$ be a projec... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/36167/does-juggling-balls-reduce-the-total-weight-of-the-juggler-and-balls/36212 | # Does juggling balls reduce the total weight of the juggler and balls?
A friend offered me a brain teaser to which the solution involves a $195$ pound man juggling two $3$-pound balls to traverse a bridge having a maximum capacity of only $200$ pounds. He explained that since the man only ever holds one $3$-pound obj... | {"extraction_info": {"found_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": 12, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/139929/how-to-apply-the-poincare-formula-to-a-regular-n-gon | # How to apply the Poincaré formula to a regular n-gon?
I've been trying to solve the following home task:
Choose $n$ points ($n\ge 2$) on the circle's circumference and connect them all with each other using chords. In result, the circle is divided into $R$ number of regions. Let $P$ be the number of intersection po... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "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/83149?sort=votes | ## When is a reflective subcategory of a topos a topos?
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Suppose $\mathcal{E}$ is a topos and $\mathcal{F}\subseteq \mathcal{E}$ is a reflective subcategory with reflector $L$, say. Under what conditions is $\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": 68, "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/126610/problem-on-linear-diophantine-equation-over-3-variables | # Problem on Linear Diophantine Equation over 3 variables
How to solve $ax+by+cz=d$ over integers where $a,b,c,d$ are integers?
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what is given in your equation? – Victor Mar 31 '12 at 17:14
@Victor: $a,b,c,d$, obviously – t.b. Mar 31 '12 at 17:16
Some details depend on relationships between greatest common divisors... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://regularize.wordpress.com/2012/04/04/the-augemented-lagrangian-with-variational-inequalities-and-on-necessary-conditions-for-variational-regularization/ | # regularize
Trying to keep track of what I stumble upon
April 4, 2012
## The Augmented Lagrangian with variational inequalities and on necessary conditions for variational regularization
Posted by Dirk under Math, Regularization | Tags: ill-posed problems, regularization |
Leave a Comment
Today I’d like to blog a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 59, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/46092/computing-singular-value-question | # Computing Singular Value question
Good afternoon.
I'm studying for my finals of this year, currently studying for the exam "Numerical Linear Algebra". I'm trying to solve some of the questions the teacher asked the past years (for preparation), but I can't seem to figure out a few, namely this one. We've got this 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": 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/39431/the-residue-class-functor-from-a-frobenius-category-to-its-stable-category-induce | ## The residue class functor from a Frobenius category to its stable category induces a functor on cube-shaped diagrams - is it dense?
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Let $\mathcal{E}$ be a Frobenius category, i.e. an exact category with suffic... | {"extraction_info": {"found_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?p=4257779 | Physics Forums
Page 2 of 2 < 1 2
## How can evaporation occur?
to confirm my understanding the overall temperature will be the same even when some particles have more KE than others.
So long as their kinetic energies average to get the specified temperature, yes.
However, usually we would say that the tempera... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/99590/the-properties-of-functions-from-w-21 | ## The properties of functions from $W_{2}^{1}$ [closed]
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Is it true that the product of the two functions from $W_{2}^{1}(0,1)$ belongs to $W_{2}^{1}(0,1)$?
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2
yes, because they are in $L^\infty$ with derivat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://euler.slu.edu/escher/index.php/Angles_of_Polygons_and_Regular_Tessellations_Exploration | # Angles of Polygons and Regular Tessellations Exploration
### From EscherMath
Objective: Calculate the interior angles of polygons and classify the regular tessellations of the plane.
## Exploration
### Interior Angles of Polygons
1. Check that the sum of the angles in a triangle is 180° as follows: Cut out a tri... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/9936/kummerian-fields/9937 | ## “Kummerian” fields?
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This is sort of a random, spur of the moment question, but here goes:
We define [with apologies to Conan the Barbarian] a field K to be $\textbf{Kummerian}$ if there exists an index set 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": 30, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/45448?sort=votes | ## Aleph 0 as a large cardinal
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The first infinite cardinal, $\aleph_0$, has many large cardinal properties (or would have many large cardinal properties if not deliberately excluded). For example, if you do not 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": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/1955/clue | ### Logosquares
Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.
### Shape and Territory
If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
### So Big
One... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/939/counting-primes?answertab=active | # Counting primes
Let $\pi(x)$ be the number of primes not greater than $x$.
Wikipedia article says that $\pi(10^{23}) = 1,925,320,391,606,803,968,923$.
The question is how to calculate $\pi(x)$ for large $x$ in a reasonable time? What algorithms do exist for that?
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3
What's wrong with the ones given on the page?... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/155796-integral-square-root-print.html | # integral (square root)
Printable View
• September 10th 2010, 07:23 PM
mybrohshi5
integral (square root)
I am having trouble solving this integral
$\int ^2_1 \sqrt(4x^2+4+\frac{1}{x^2}) dx$
I think i can reduce the equation under the square root to an expression that is squared which would get rid of the square roo... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/810/what-is-the-difference-between-a-stream-cipher-and-a-one-time-pad/814 | # What is the difference between a stream cipher and a one-time-pad?
A (synchronous) stream cipher is an algorithm which maps some fixed-length key to an arbitrary-length key-stream (i.e. a sequence of bits): $C : \{0,1\}^k \to \{0,1\}^{\infty}$.
This key-stream is then XOR-ed with the plain text stream, giving the c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/73019/list | ## Return to Question
2 added 1110 characters in body
Let $c(r)$ be a nice, continuous function with compact support. For example, $c(r) = \tfrac 1 5 (1-r)^{11} \big( 5 + 55r + 239 r^2 + 429 r^3 \big)$ for $r \in [0,1]$, and $c(r) = 0$ otherwise.
On a rectangular domain $D$ in $\mathbb R^2$, we define $c(x,y) = c(|x... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "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/37356?sort=votes | ## Realizing groups as automorphism groups of graphs.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Frucht showed that every finite group is the automorphism group of a finite graph. The paper is here.
The argument basically is that a group is the automorphi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/169645-differentiate-respect-x.html | # Thread:
1. ## Differentiate with respect to x
Y = $\displaystyle \sqrt{(x^3+5)}$
2. Use the chain rule: $\dfrac{d}{dx} f[g(x)] = f'[g(x)] \cdot g'(x)$
In your case you have $f(x) = \sqrt{g(x)}$ and $g(x) = x^3+5$
3. $\dfrac{d}{dx}\left(\sqrt{u(x)}\right)=\dfrac{1}{2\ sqrt{u(x)}}\cdot u'(x)$
Fernando Revilla
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": 11, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/9335?sort=newest | ## Why is every symplectomorphism of the unit disk Hamiltonian isotopic to the identity?
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That is, for any symplectomorphism $\psi: D^2 \to D^2$, there should be a time-dependent Hamiltonian Ht on D2 such that 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": 54, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/206575-difference-between-gradient-vector-surface-normal-vector-s.html | 1Thanks
• 1 Post By HallsofIvy
# Thread:
1. ## The difference between a gradient vector to a surface and the normal vector to that s
...urface. Plz help I don't understand this difference. Thanks
2. ## Re: The difference between a gradient vector to a surface and the normal vector to th
Hey nicksbyman.
If you 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": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/70468-college-calculus.html | Thread:
1. college calculus
Let p(x) be a polynomial function of degree n. Determine if each of the following statements is TRUE or FALSE and justify your answer in writing.
NOTE: If you can find a counterexample, the counterexample is enough to justify saying the statement is FALSE.
(a) The domain of p(x) is all re... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/differential-geometry/156579-2-simple-outer-measure-problems.html | # Thread:
1. ## 2 simple outer measure problems
Hello all.
These are homework problems, so partial solutions / advice would be preferred.
These come from the book Real Analysis (4th ed) by Royden and Fitzpatrick
Chapter 2 problems 15 and 20
15. Show that if E has finite measure and $\epsilon>0$, then E is the dis... | {"extraction_info": {"found_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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/32011/what-is-a-tensor | # What is a tensor?
I have a pretty good knowledge of physics but couldn't understand what a tensor is. I just couldn't understand it, and the wiki page is very hard to understand as well. Can someone refer me to a good tutorial about it?
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1
– Qmechanic♦ Jul 14 '12 at 7:45
I wrote a short one. The main problem is 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": 48, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://leifjohnson.net/post/on-database-wrangling | # Leif Johnson » On database wrangling
Wasn't I just sitting here writing about time passing quickly ? Well, as the end of the semester approaches and I find myself increasingly stressed, time just zips right along !
## Kohonen maps
This week I wrote up a little JavaScript visualization of a bimodal Kohonen map 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": 22, "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/2009/09/09/ | # The Unapologetic Mathematician
## Shears Generate the Special Linear Group
We established that if we restrict to upper shears we can generate all upper-unipotent matrices. On the other hand if we use all shears and scalings we can generate any invertible matrix we want (since swaps can be built from shears and scal... | {"extraction_info": {"found_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": 21, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/41701/how-does-one-compute-cos-pi-4k-1 | # How does one compute $\cos((\pi/4)(k-1 ))$?
How to compute $\cos \left( \frac{\pi}{4}(k-1) \right)$ ?
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## 2 Answers
Think about it; $\pi/4$ is $45°$. With each different value of $k$ you're summing up $45°$. Since $\pi/4$ divides $2\pi$, you'll eventually get a cycle of values for $\cos(k(\pi/4))$, and then you ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nanoexplanations.wordpress.com/2011/12/09/polygon-rectangulation-part-2-minimum-number-of-fat-rectangles/ | the blog of Aaron Sterling
# Polygon rectangulation, part 2: Minimum number of fat rectangles
Posted on December 9, 2011
This post is the second in a series on polygon rectangulation. In my previous post, I discussed methods to decompose an orthogonal polygon into a minimum number of rectangles. (See that post 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 32, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/105933/associated-graded-of-a-filtration-of-a-tensor-product | ## Associated graded of a filtration of a tensor product
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm trying to understand a part of the PhD thesis of Kenji Lefèvre-Hasegawa (e.g. available here). My question is about the proof of Lemma 1.3.2.3b stating... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/general-topology+compactness | # Tagged Questions
3answers
50 views
### Prove that $S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$.
Prove that $S=\{0\}\cup\left(\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}\right)$ is a compact set in $\mathbb{R}$, but $\bigcup_{n=0}^{\infty} \{\frac{1}{n}\}$ is not a 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": 171, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://stats.stackexchange.com/questions/45419/interpreting-correlation-coefficient-of-determination | # Interpreting correlation & coefficient of determination
Correlation (r) is a measure of linear association between two variables. Coefficient of determination (r^2), is a measure of how much of the variability in one variable can be "explained by" variation in the other.
For example, if r 0.8 is the correlation bet... | {"extraction_info": {"found_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://stats.stackexchange.com/questions/30560/how-to-give-entire-word-a-quality-score-to-account-for-the-phred-score-of-each-l | # How to give entire word a quality score to account for the phred score of each letter?
I have a word representing a DNA sequence and each letter of that word is a nucleotide base (A,T,G,C). Each letter has a phred quality score. The formula used for the phred quality score is $Q=-10\log_{10} P$ where $Q$ is the phre... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/44773/vector-nature-of-angular-velocity/44795 | # Vector Nature Of Angular Velocity
I am currently reading about angular position, angular velocity, and angular acceleration. I came across this paragraph that was particularly confusing, and was wondering if someone could perhaps help me. Here is the paragraph:
"If a particle rotates in the $xy$ plane, the directio... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?p=1057320 | Physics Forums
## Prime Number Gaps
Hello everyone,
I'd first like to say that I am uninformed on this subject and that I have a question to the mathematicians on these forums who know about the subject.
In the set of all prime numbers, has the integer gaps between two prime numbers been studied? I mean, do mathema... | {"extraction_info": {"found_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/40224/probability-of-a-point-taken-from-a-certain-normal-distribution-will-be-greater | Probability of a point taken from a certain normal distribution will be greater than a point taken from another?
Let's say I have one point that will be taken randomly from a normal distribution with mean $\mu_1$ and standard deviation $\sigma_1$. Let's say I have another point that is taken much in the same way from ... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/5166/algorithm-to-calculate-the-control-points-of-a-cubic-bezier-curve?answertab=votes | # algorithm to calculate the control points of a cubic Bezier curve
I have all points where my curve pass through, but I need to get the coordinates of the control points to be able to draw the curve. How can I do to calculate this points?
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## 2 Answers
When what you already have is a set of points where your curv... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 28, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://dsp.stackexchange.com/questions/2654/what-is-the-difference-between-convolution-and-cross-correlation | # What is the difference between convolution and cross-correlation?
I've found on multiple sites that convolution and cross-correlation are similar (including the tag wiki for convolution), but I didn't find anywhere how they differ.
What is the difference between the two? Can you say that autocorrelation is also a k... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/200624-finding-area-between-parabolas.html | 3Thanks
• 1 Post By Reckoner
• 1 Post By skeeter
• 1 Post By Plato
# Thread:
1. ## Finding Area between Parabolas
The question is:
A shape has been formed by three intersecting parabolas, the equations of these parabolas are:
1. $y=-x^2-6x-9$
2. $y=x^2-4.5$
3. $y=-x^2+6x-9$
Using calculus, find the area of the sh... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/201787/recursive-curve-fitting?answertab=votes | # Recursive curve fitting
I have a few points for which I have to obtain a best fit. (I tried to use the least squares curve fitting method as Robert says, however, since it seems to be fitting rather poorly, any other suitable method would also work for me.)
However, the function is recursive and looks like this -
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/statistics/30976-can-any-one-help-normal-distribution-dont-have-much-time-left.html | # Thread:
1. ## Can any one help with Normal Distribution. dont have much time left!!
i have a last Q left to do for my maths coursework and it has completely stumped me. can anyone help. here is the whole Q:
A scientist was measuring oak trees in a woodland and noticed that their height was normally distributed. Un... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/70493/dg-lie-structure-on-hh-and-koszul-duality | ## dg-lie structure on $HH^*$ and Koszul duality
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
This is shamelessly close to my other question: http://mathoverflow.net/questions/70151/a-question-on-koszul-duality-and-b-infty-structures-on-hh. Maybe this one w... | {"extraction_info": {"found_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://crypto.stackexchange.com/questions/2153/unit-testing-a-library-rng-and-its-seeding-for-practical-security/2203 | # Unit testing a library RNG and its seeding for practical security
Suppose I have a cryptography library that provides me with a black-box random number generator that is supposed to be suitable for long-lived key generation. (Under the hood it may be assumed to use some combination of `/dev/random` or equivalent, 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": 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/146615/how-many-matrices-generate-2d-lie-algebra-i-e-c-1-c-2-k-1-c-1-k-2-c-2?answertab=active | # “How many” matrices generate 2d Lie algebra (i.e. $[c_1,c_2]=k_1 c_1 +k_2 c_2$)?
Consider a pair of matrices $(c_1, c_2)$. The words "it generates the 2-dimensional Lie algebra", means that there exists a pair of scalars $k_1$, $k_2$, such that $$[c_1, c_2] = k_1 c_1 + k_2 c_2,$$ where $[a,b]$ is the "commutator" $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": 15, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/energy-conservation?sort=faq&pagesize=15 | Tagged Questions
The law of conservation of energy, which states that the amount of energy in a system is constant. For questions about Earth's environment, see the climate-science tag instead.
5answers
1k views
Conservation law of energy and Big Bang?
Did the law of conservation of energy apply to the earliest mom... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 9, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/44774/difference-between-maximal-element-and-greatest-element?answertab=votes | difference between maximal element and greatest element
I know that it's very elementary question but I still don't fully understand difference between maximal element and greatest element. If it's possible, please explain to me this difference with some examples etc.
I tried to explain this difference to myself usin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 68, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math-challenge-problems/127365-integral-over-head-light-contour-via-residue-theorem.html | # Thread:
1. ## Integral over head-light contour via Residue Theorem
This is a challenge question that I already know how to solve: Let $f(z)=\sqrt{1-z^2}$ and consider a smooth (differentiable) map $f(H(t))$ where $H$ is the general shape shown in the first plot below (loops around the branch-points,then looping aro... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/162790/levy-measure-and-compensation | # Lévy measure and compensation
In the Lévy-Itô decomposition it's necessary to compensate small jumps. That's clear. The small jumps are perhaps non-summable. But why are the jumps quared summalbe?
In the "ordinary" proofs of the Lévy Khintchine Formula or the Lévy-Itô Decomposition i can't get the point where we ex... | {"extraction_info": {"found_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/293766/beginners-in-calculus/293772 | beginners in calculus
i am using the Stewart calculus early transcendentals text and in chapter $2.4$there is a question:
use the given graph of f to find the number delta such that
if $0<|x-5|< \delta$ then $|f(x) -3|< 0.6$
Is the answer: right delta = 0.7 and left delta = 1.0? If so pick the smallest ,correct....... | {"extraction_info": {"found_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://mathforum.org/mathimages/index.php?title=Law_of_cosines&diff=17460&oldid=17456 | # Law of cosines
### 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": 32, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/302444/groups-of-symmetries-and-presentation-of-semi-direct-products | # Groups of Symmetries and presentation of Semi-direct products
Let $L$ the tessellation of the euclidean plane by equilateral triangles. Prove that the group $G = Sym(L)$ of isometries of $\mathbb{R}^2$ leading $L$ in $L$ is is a semi-direct product $\mathbb{Z} \times \mathbb{Z} \rtimes D_6$, and obtain a presentatio... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/88233?sort=votes | ## how many consecutive integers $x$ can make $ax^2+bx+c$ square ?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The following problem was raised in a Mathlinks thread:
If $a,b,c\in\mathbb Z$ such that $a\ne0$ and $b^2-4ac\ne 0$, for how many consecutive 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": 31, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3588462 | Physics Forums
Page 1 of 3 1 2 3 >
## The Lorentz Transformations and a Few Concerns
The derivation of the Lorentz transformations is based on the homogeneity[of space and time] and the isotropy of space.
Could one derive the same transformations wrt space which is not homogeneous or[not] isotropic?
You may c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 17, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/41460-pythag-question.html | # Thread:
1. ## Pythag Question
Hi,
This question is an extract from a book which i took a photo of
as I couldn't be bothered replicating it on the computer
http://i116.photobucket.com/albums/o...chet/Maths.jpg
Currently baffled as to what the answer is.
A Nudge in the right direction will be appreciated.
2. Origi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/83808?sort=newest | ## What is the relation between a ‘'homotopy fiber bundle’' and a Serre fibration?
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Since I got no responses to this question at Stack Exchange, please let me try my luck here.
Call a continuous map $\pi:E\to B$ ... | {"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": 26, "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/120548/list | ## Return to Answer
3 deleted 11 characters in body
The empty structure is ''disconnected'' and the definition of a tree is ''connected acyclic graph''.
For example to get from the generating series $G(t)$ of a connected species to the generating series of the set of its structures $G^*(t) F(t)$ the formula is $$G^*... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 12, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/118339?sort=oldest | ## Is there a general process for conditioning a stochastic process above a boundary?
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$(X_t, Y_t)$ is a two-dimensional Markov stochastic process that runs on time interval $[0, t_f]$. Given its transition functi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/299081/do-numbers-of-this-form-have-a-name | # Do numbers of this form have a name?
$$48625 = 4^{5} + 8^{2} + 6^{6} + 2^{8} + 5^{4}$$
Notice that the digits of the number are in digit order, while the exponents are the digits of the number in reverse order.
Do numbers of this form have a name?
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## 1 Answer
They are "tabulated" at OEIS. I use the quotes 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": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
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