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http://mathoverflow.net/questions/71050?sort=votes | ## Can the twin prime problem be solved with a single use of a halting oracle?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
It occurred to me that if it were possible to determine whether a given program halts, that could be used to answer the twin primes 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": 73, "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/29408/what-is-the-expectation-of-a-normal-random-variable-divided-by-uniform-random-va?answertab=votes | # What is the expectation of a normal random variable divided by uniform random variable?
I have two random variables: $x = N(0, \sigma^2)$ and $y =U[0, b]$. I need to compute $E(x/(1+y))$. How does one go about doing this? They are independent so the joint pdf is just the product of the two pdfs but can the integral ... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-math-topics/48664-advanced-calculus-help.html | # Thread:
1. ## Advanced Calculus Help
A) For each part, find a function f: R -> R that has the desired properties: neither onto nor one-to-one
B)Under what conditions does A\(A\B) = B?
C)Define f:J -> N(natural numbers) where f(n) = 2n-1 for each n element of N(natural numbers).
D) Given A = {1,2,3,4,5}, B = {2,3... | {"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": 51, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://eventuallyalmosteverywhere.wordpress.com/2012/12/18/exploring-the-supercritical-random-graph/ | # Exploring the Supercritical Random Graph
Posted on December 18, 2012 by
I’ve spent a bit of time this week reading and doing all the exercises from some excellent notes by van der Hofstad about random graphs. I think they are absolutely excellent and would not be surprised if they become the standard text for an in... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 27, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/34587/determining-a-correction-factor-and-applying-it-to-a-second-set-of-numbers | # Determining a correction factor and applying it to a second set of numbers
1st- I would like to figure out the correction factor between two sets of numbers (time series).
2nd- I want to apply that correction factor to a second set of numbers.
As an example- say I have two temperature sensors, and I place them 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": 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/discrete-math/164731-countability-proof.html | # Thread:
1. ## Countability proof.
I need help on proving
(1) prove that if B A and A is countable, then B is countable
(2) prove that if B A, A is infinite, and B is finite, then A\B is infinite
I don't even know where to start... THx
2. I have a theorem which says
Suppose A is a set. The following statements 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": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/187620/blow-up-of-ode-solution | # Blow-up of ODE solution
I am a newcomer to ODE. The relevant theorem that I can think of is about the maximum open interval of existence of the solution. But I have not learned to find the interval on which the solution exists.
$f:\mathbb{R}^{n}\rightarrow\mathbb{R}^{n}$ is $C^{1}$ and bounded on $\mathbb{R}^{n}.$ ... | {"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": 8, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/51899-implicit-differentation.html | # Thread:
1. ## Implicit Differentation
$e^y+24-e^-1 = 5x^2+4y^2$
I can't figure this out....
I believe this stage is correct $e^y+e^-1=10x+8y*y'-y'$
But Need help on further solving it.
Help appreciate.
2. Actually the first step should be $y'e^y = 10x + 8yy'$
3. Where did you put the $e^-1$?
4. $e^{-1}$ is a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://engineering.wikia.com/wiki/Lift_(force) | # Lift (force)
Talk0
643pages on
this wiki
Lift consists of the sum of all the fluid dynamic forces on a body perpendicular to the direction of the external flow around that body.
There are a number of ways of explaining the production of lift; some are more complicated than others, some have been shown to be false.... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 11, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/tagged/gaussian-process?sort=unanswered&pagesize=15 | # Tagged Questions
The gaussian-process tag has no wiki summary.
1answer
53 views
### How to test if two samples are distributed from the same Gaussian process
Given a sequence $\mathbf{x} = (x_1,x_2,\dots,x_n)$ which is sampled from some Gaussian process $GP(\mu_1,\Sigma_1)$ and a "target" sequence $\mathbf{y} = (... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "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/91333/intuition-around-why-sine-of-x-angle-always-equals-same-result/108460 | # Intuition around why Sine of X angle always equals same result.
My understanding so far.
Sine represents a ratio of two sides of an interior angle within a right angle triangle. So given the three lengths of a triangle you can find the sine of any of the 3 interior angles.
Also if you are given the actual angle 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": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/math-topics/59722-find-slope-line.html | # Thread:
1. ## Find the slope of a line
Find the slope of the line joining $(2,4)$ and $(2+h, f(2+h))$ in terms of the nonzero number $h$
Ok I know that to find the slope of a line the formula is $m=\frac {y_2-y_1}{x_2-x_1}$, but when I try to solve for it I get $\frac {f(2+h)-4}{h}$. Is that right?
2. Hello there,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathinsight.org/differentiability_multivariable_definition | # Math Insight
• Top
• Introduction
• The definition
• In threads
When printing from Firefox, select the SVG renderer in the MathJax contextual menu (right click any math equation) for better printing results
### The definition of differentiability in higher dimensions
#### Suggested background
The definition of di... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 84, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/132348/how-to-evaluate-int-01-sin-frac1xdx/132355 | # how to evaluate $\int_0^1\sin(\frac{1}{x})dx$?
How can I evaluate the integral of $$\int_0^1\sin\left(\frac{1}{x}\right)dx.$$ Maybe it needs the cosine integral to evaluate it, but I cannot understand it very well.
Thanks a lot.
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2
Make a substitution so that you have $\sin t$ in there and then see what you get.... | {"extraction_info": {"found_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://mathoverflow.net/revisions/67298/list | Return to Answer
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This is indeed true. See for example Lemma 2.60 in Kollar-Mori Birational Geometry of algebraic varieties. In particular, it is shown that a Cartier divisor $D$ is big if and only if $mD \sim A + E$ for some ample divisor $A$ and effective divisor $E$. This is also prove... | {"extraction_info": {"found_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://mathhelpforum.com/discrete-math/1324-proof-induction.html | # Thread:
1. ## induction, how do i begin?
prove by induction that for every natural n and every x>0
(e^x) > 1 + x/1! + (x^2)/2! + ... + (x^n)/n!
it says we can assume that we know basic properties of derivatives and integrals, but i just am not sure where to begin.
2. Originally Posted by cen0te
prove by induction... | {"extraction_info": {"found_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://www.physicsforums.com/showpost.php?p=2278941&postcount=15 | View Single Post
Recognitions: Homework Help From first principles, an outcome to any sequence of 100 flips consists of a sequence of H (for Heads) and T (for Tails) of length 100, so $$\Omega$$ would be the set of all $$2^{100}$$ sequences, from all Ts through all Hs. One particular $$\omega$$ would be this o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/57540/list | Return to Question
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A covering map $p:X\to Y$ between topological spaces can be viewed as a fiber bundle $\Sigma\to X\to Y$ with a discrete group $\Sigma=Gal(X/Y)$ as fiber. Such a fiber bundle leads to a long exact sequence of homotopy groups. In this case, if $Y$ is contractible then, o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 22, "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/40958/how-does-gravity-work?answertab=oldest | # How does gravity work?
The math, I read, is
$F = G\frac{m_{1}m_{2}}{r^{2}}$
What I'm unclear about is how does it work in practice.
Say there are two identical pebbles massing 1 kilogram each outside Sol's gravity well close enough to attract each other.
What happens then? And, How long does each 'stage' take?
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/19294?sort=votes | ## Dispensing with the notion of infinity for the sake of coverings [closed]
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Instead of taking a one to one correspondence meaning each set has the same number of elements. why not use the concept of coverings 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": 9, "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/2008/01/15/some-compact-subspaces/?like=1&source=post_flair&_wpnonce=3fdfac1636 | # The Unapologetic Mathematician
## Some compact subspaces
Let’s say we have a compact space $X$. A subset $C\subseteq X$ may not be itself compact, but there’s one useful case in which it will be. If $C$ is closed, then $C$ is compact.
Let’s take an open cover $\{F_i\}_{i\in\mathcal{I}}$ of $C$. The sets $F_i$ are ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 35, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/6324/are-there-integer-solutions-to-9x-8y-1 | Are there integer solutions to $9^x - 8^y = 1$?
This came up in proving non-regularity of a certain language (powers of 2 over the ternary alphabet). Any clue to the above equation could help me move forward.
Edit: Of course, $x = 1, y = 1$ is a solution. I am looking for non-trivial solutions.
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5
yes x=1,y=1 is a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/19159-centralizer-subgroup.html | # Thread:
1. ## Is Centralizer subgroup?
Problem: Let G be a group, prove that the centralizers of G is a subgroup of G.
Proof: By definitions, the centralizers of G, $C(a) = \{ g \in G:ga=ag \} \forall a \in G$
Now, the identity element, e, has the property of $ea=ae$, thus e is in C(a). So C(a) is not an empty se... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 23, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/32409/examples-of-folk-theorems/33699 | ## Examples of “folk theorems”
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In this post, Justin gives a quote about Raoul Bott that has this line in it:
He talked about 'folk' theorems... theorems everyone knew, but were never written down.
What are some... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 23, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/53106/does-increasing-the-density-of-a-solution-decrease-the-rate-of-temperature-chang?answertab=active | # Does increasing the density of a solution decrease the rate of temperature change?
I did an experiment to compare whether salt water (5% concentration of salt) or fresh water of the same volume took longer to heat up to a certain temperature. We found that salt water took longer to heat up than fresh water.
Is this... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/81466/list | ## Return to Answer
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The question itself seems too elementary for this site, since it just involves the standard axiomatic treatment of root systems as in Bourbaki Groupes et algebres de Lie, VI.1.7. The question is really about an arbitrary reductive algebraic group (with nontrivial der... | {"extraction_info": {"found_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://mathoverflow.net/revisions/120290/list | ## Return to Answer
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Here is a more bare hands explanation. Let $\phi$ be the field automorphism of ${\rm SL}_n(q^2)$ that acts by applying $x \mapsto x^q$ for to the matrix entries. Let $\gamma$ be the graph automorphism that maps matrices $A$ to their inverse-tranpose $A^{- \mathrm{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": 54, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://nrich.maths.org/2821/index?nomenu=1 | ## 'Multiplication Square' printed from http://nrich.maths.org/
### Show menu
Take a look at the multiplication square below:
Pick any 2 by 2 square and add the numbers on each diagonal.
For example, if you take:
the numbers along one diagonal add up to $77$ ($32 + 45$)
and the numbers along the other diagonal add ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/146661/help-me-evaluate-limit-of-sequence/146682 | # Help me evaluate limit of sequence
I have this limit, and i have no idea of approach: $$\lim_{n \rightarrow + \infty } \left(\frac{n^3}{4n-7}\right)\left(\cos\left(\frac1n\right)-1\right)$$ turns out to be of indeterminate form, how to solve it?
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As $n \to\infty$ we get a $"0\cdot\infty"$ kind of a limit to calcul... | {"extraction_info": {"found_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": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/44023/does-adding-corefinements-to-a-grothendieck-pretopology-change-the-topos/44390 | ## Does adding “co”refinements to a Grothendieck pretopology change the topos?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose we have a Grothendieck pretopology $\tau$ on a category C with fibered products. Now define a new Grothendieck pretopology $\... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 63, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-statistics/97961-prior-posterior-distributions.html | # Thread:
1. ## Prior and posterior distributions
A geologist researching seismic activity in south-east Turkey is able to specify her prior beliefs regarding the parameter of the Poisson distribution. She tells us that $\theta$ can be modelled with a gamma distribution, i.e. $\theta\sim\Gamma(\alpha,\lambda)$, and s... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=4271803 | Physics Forums
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| View Poll Results: What do observed violation of Bell's inequality tell us about nature?... | {"extraction_info": {"found_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/questions/49641/plurisubharmonic-sublevel-sets | ## plurisubharmonic sublevel sets
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Let $X$ be a complex manifold, let $\Omega \subseteq {\bf C} \times X$ be defined by $\Omega = \{ (z,p) \in {\bf C} \times X : a(p) < Im z < - b(p) \}$ where $a$ and $b$ are plur... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/251598/product-of-positive-definite-matrices | # Product of Positive Definite Matrices
Let $X,Y,Z$ be positive definite matrices such that $XYZ$ is hermitian . How can we show that $XYZ$ is also a positive definite matrix?
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– Inquest Dec 5 '12 at 15:39
## 2 Answers
Since by hypothesis $XYZ$ is Hermitian, then it is enough to show that its eigenvalues are posi... | {"extraction_info": {"found_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://mathoverflow.net/questions/76913/is-the-nc-torus-a-quantum-group/83343 | ## Is the nc torus a quantum group?
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The non-commutative n-torus appears in many applications of non-commutative geometry. To stay in the setting $n=2$: it is a C$^\ast$-algebra generated by unitaries $u$ and $v$,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "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/29011?sort=votes | ## Birkhoff ergodic theorem for dynamical systems driven by a Wiener process
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At the risk of asking a stupid question I have the following problem.
Suppose I have a measure preserving dynamical system `$(X, \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": 10, "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=3906553 | Physics Forums
## some lagrangian question
If we considered some coordinate as being a generalized one, like when we are considering spherical coordinates-let us suppose that I chose theta and phi as generalized coordinates. After deriving the Lagrangian equation it turned out that the equation doesnt depend on phi. ... | {"extraction_info": {"found_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://mathhelpforum.com/differential-geometry/170221-normal-vector.html | # Thread:
1. ## Normal vector
Given the curve $C$ on $\mathbb R^3$ parametrized by $r(t).$ Find the normal vector on $r(1)=(3,1,3)$ if the osculator plane on that point is $3y-x=0$ and $r(1)\cdot N(1)>0$ with $r'(1)=(6,2,2).$ (I don't know if "osculator" makes sense here.)
I hope you guys can help, I have an exam on... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/combinatorics-on-words | Tagged Questions
1answer
181 views
A property of periodic words
Question is edited Perhaps this formulation is clearer. It is well known that if a power of a primitive (i.e. not a proper power) word $u$ contains two different occurrences of a …
4answers
384 views
Subwords of cube-free binary words
I'm currently wo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 35, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/59007?sort=oldest | ## Multiplicity one prime in the factorisation of p-N
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I'm wondering if analytic number theorists can prove results which have the following flavor:
So let $N$ be a large positive integer.
Q: Can you always find... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/schrodinger-equation?page=2&sort=newest&pagesize=30 | # Tagged Questions
Partial differential equation which describes the time evolution of the wavefunction of a quantum system. It is one of the first and most fundamental equations of quantum mechanics.
2answers
271 views
### What does the general solution of the Schrodinger equation represent for the particle in a bo... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/95294/does-the-following-characterization-of-subgroups-of-gl-2-mathbbf-p-generali | ## Does the following characterization of subgroups of $GL_2(\mathbb{F}_p)$ generalise?
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Let $p$ be a prime number. By a Cartan subgroup of $GL_n(\mathbb{F}_p)$ I mean an absolutely semisimple maximal abelian subg... | {"extraction_info": {"found_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/revisions/9732/list | ## Return to Answer
2 added 91 characters in body
I don't think so (but I haven't checked this argument very thoroughly):
First we claim that any such $f$ has degree two. Clearly the leading term of $f$ cannot be odd, so suppose by contradiction that $f$ has degree at least four. Pick a constant $R$ large enough so ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 46, "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/152747-volume-slicing.html | # Thread:
1. ## Volume By Slicing
The question is read as follows: Solid lies between planes perpendicular to the x-axis at x=1 and x=-1 . The cross sections are perpendicular to the x-axis are circular disk.s whose diamters run from the parabola y=x^2 to the parabola y=2-x^2 FInd the volume of the solid.
I tried do... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/tagged/soft-question+mathematical-physics | # Tagged Questions
3answers
515 views
### Are Mathematical Physics and Occam's Razor compatible?
Occam's Razor and mathematical beauty appear to be compatible when reviewing Michael Atiyah's video. But are the high levels of complexity associated with mathematical physics compatible with ...
0answers
51 views
### R... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.aps.org/story/print/v6/st22 | # Focus: Why Now?
Published November 16, 2000 | Phys. Rev. Focus 6, 22 (2000) | DOI: 10.1103/PhysRevFocus.6.22
Cosmologists wonder why we happen to live in the era when the three major components of the Universe exist in similar quantities. One explanation involves only the most basic parameters from high energy ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 13, "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://stats.stackexchange.com/questions/5450/what-if-interaction-wipes-out-my-direct-effects-in-regression/5455 | # What if interaction wipes out my direct effects in regression?
In a regression, the interaction term wipes out both related direct effects. Do I drop the interaction or report the outcome? The interaction was not part of the original hypothesis.
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2
you could probably get a better answer if you provided more detai... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/07/21/pullbacks-on-cohomology/?like=1&source=post_flair&_wpnonce=a34a077b61 | # The Unapologetic Mathematician
## Pullbacks on Cohomology
We’ve seen that if $f:M\to N$ is a smooth map of manifolds that we can pull back differential forms, and that this pullback $f^*:\Omega(N)\to\Omega(M)$ is a degree-zero homomorphism of graded algebras. But now that we’ve seen that $\Omega(M)$ and $\Omega(N)$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 28, "mimetex.cgi": 0, "/images/ma... |
http://scicomp.stackexchange.com/questions/3262/how-to-choose-a-method-for-solving-linear-equations | # How to choose a method for solving linear equations
To my knowledge, there are 4 ways to solving a system of linear equations (correct me if there are more):
1. If the system matrix is a full-rank square matrix, you can use Cramer’s Rule;
2. Compute the inverse or the pseudoinverse of the system matrix;
3. Use matr... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/18328/what-is-a-single-word-that-describes-the-idea-of-the-second-time-derivative-of-e/18338 | # What is a single word that describes the idea of the second time derivative of energy?
I think about position, its time derivative speed, and its second time derivative, acceleration. I would like to identify a single word that can be used as a handle for the second time derivative of energy (i.e., the time derivati... | {"extraction_info": {"found_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/calculus/131280-contour-integrals.html | # Thread:
1. ## contour integrals
Compute integral of:
Integral over C of 1/z dz
where C is the unit circle centered at some point z.
|z.| >2
2. well a unit circle in 1 not z= 2
try putting z into polar form and then do a contour integral
3. the center of the circle is at a point z, |z|>2 its just saying the unit ... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-statistics/68660-binomial-distribution-problems.html | # Thread:
1. ## Binomial Distribution Problems
I believe that all of these are binomial distribution problems, but I'm not really sure how to approach them. Any help would be appreciated greatly.
1. Estimate the probability that, in a group of five people, at least two of them have the same zodiacal sign. (There are... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/219943/approximation-of-stochastic-differential-equations?answertab=active | # Approximation of stochastic differential equations
Consider the two following real Stochastic Differential Equations (SDE) starting from the same initial condition: $$dx_t = f(x_t)dt + \sigma dB_t$$ $$dy_t = f(y_t)g_{\epsilon}(y_t)dt + \sigma dB_t$$
where $f$ and $g_{\epsilon}$ are such that there exists strong sol... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/155495/solve-the-general-cubic-by-factoring?answertab=oldest | # Solve the general cubic by factoring
After learning Cardano's solution of the cubic, I decided to look at Ferrari's solution of the quartic (both articles on Wikipedia). At the end of the article on the quartic function was an an alternate method to solve the cubic by factoring into two quadratic terms - something 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": 4, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/22203/unbiased-estimate-of-the-variance-of-an-unnormalised-weighted-mean/59403 | ## Unbiased estimate of the variance of an *unnormalised* weighted mean
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I have a follow-up question to this one:
http://mathoverflow.net/questions/11803/unbiased-estimate-of-the-variance-of-a-weighted-mean
Spec... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/algebra/97957-counting-lattice-points.html | # Thread:
1. ## Counting lattice points.
Let n be a positive integer, and R be the region defined by the simultaneous conditions x-y< n , x+y < n and x > 0. In terms of n
how many lattice points are contained in R?
If I didn't misunderstand the question I got 0 points for n=1 , 1 for n=2, 4 for n=3, 9 for n=4 . 16 f... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/46626/list | ## Return to Question
3 added 138 characters in body; deleted 6 characters in body; added 1 characters in body
Let $c_0$ be the Banach space of doubly infinite sequences $$\lbrace a_n: -\infty\lt n\lt \infty, \lim_{|n|\to \infty} a_n=0 \rbrace.$$ Let $T$ be the space of $2\pi$ periodic functions integrable on $[0,2\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": 18, "mathjax_display_tex": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/228182/how-many-solutions-does-cos97x-x-have | # How many solutions does $\cos(97x)=x$ have?
How many solutions does $\cos(97x)=x$ have?
I have plot the function. However I don't know how to solve the problem without computer.
Can anyone give a fast solution without a computer?
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## 2 Answers
Let us concentrate on $[0,1]$ as suggested by Siminore. The period ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=134996 | Physics Forums
Thread Closed
Page 1 of 2 1 2 >
## The true nature of length contraction
I stumbled on a book that seems to throw the concept of length contraction upside down to me. Maybe someone can help me here.
All the books I've read to date, a popular example might be Elegant Universe, say that an object... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/277235/two-identical-point-charges-cant-collide/278355 | two identical point charges can't collide
I've convinced myself intuitively that if you place two massless classical particles with the same charge in $\mathbb{R}^n$, with arbitrary initial velocities and (distinct) positions, they will never collide. However, I'm have a heck of a time trying to prove it, and would ap... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-math-topics/56241-finding-norm-scalar-product-sin-ax-cos-bx-vector-space-c-0-pi-print.html | # Finding the norm and scalar product of sin(aX),cos(bX) in the vector space C(0,Pi)
Printable View
• October 28th 2008, 01:23 PM
partickrock
Finding the norm and scalar product of sin(aX),cos(bX) in the vector space C(0,Pi)
Hi im trying to calculate the norm and scaler product of sin ax and cos bx in vector space C(... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/5036/spectra-of-c-algebras/5058 | ## Spectra of $C^*$ algebras
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Gelfand-Naimark structure theorem for $C^*$ algebras gives a canonical isometric * isomorphism between any commutative unital $C^*$ algebra $A$ and the algebra of continuous complex-v... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "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/121454/how-can-we-determine-if-every-matrix-of-mathbbr2-times-2-can-be-written/121718 | # How can we determine if every matrix of $\mathbb{R}^{2 \times 2}$ can be written as a linear combination of specific $A, B$ matrices
We have these two matrices:
$$K = \left(\begin{matrix} 2 & 1 \\ 8 & 7\end{matrix}\right), \quad L = \left(\begin{matrix} 2 & 1 \\ 2 & 7 \end{matrix} \right)$$
We have been asked if e... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 37, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/298661/saying-a-in-b-in-category-theory/298681 | # Saying $a \in b$ in category theory
Suppose I have a category $C$ of sets, and $a,b \in C$. How can I express, in the language of category theory, that $a \in b$? (To clarify: the objects of $C$ are actually sets, and I want to express that $a$ actually is a member of $b$, in the underlying set theory.) I am aware o... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 72, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/105246/undergraduate-topology/105258 | ## Undergraduate Topology
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I am developing an introductory topology course for undergraduates, and I am wondering what topics to cover. At my institution, real analysis is not a prerequisite for the course, so it ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/29314-probability-help-please.html | # Thread:
1. ## Probability help please
Hey guys, I need some help on this problem please
---
Verify the following extension of the addition rule by a) an appropriate Venn diagram and b) by a formal argument using the axioms of probability and the propositions in the chapter.
$P(A \cup B \cup C) = P(A) + P(B) + 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 4, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://psychology.wikia.com/wiki/Artificial_neural_network?diff=prev&oldid=106851 | Changes: Artificial neural network
Edit
Back to 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 67, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/70790?sort=votes | ## The NP version of Matiyasevich’s theorem
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
By Matiyasevich, for every recursively enumerable set $A$ of natural numbers there exists a polynomial $f(x_1,...,x_n)$ with integer coefficients such that for every $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": 24, "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/292633/regularity-up-to-the-boundary/299641 | # Regularity up to the boundary
Let $L$ be a second order linear elliptic differential operator on an open bounded subset $U\subset \mathbb R^n$, with smooth uniformly bounded coefficients. Suppose the boundary of $U$ is $C^\infty$. Suppose $f\in C_c^\infty(U)$ ($f$ is smooth and has compact support in $U$). Must ther... | {"extraction_info": {"found_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://motls.blogspot.com/2012/07/diphoton-higgs-enhancement-as-proof-of.html?m=1 | The Reference Frame
Our stringy Universe from a conservative viewpoint
Friday, July 20, 2012
Diphoton Higgs enhancement as a proof of naturalness
The first hep-ph preprint today is a paper I've known about since the July 4th Higgsfest and I've been looking forward to see it. The title is
2:1 for Naturalness at 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": 16, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/66545-basic-division-simplification.html | # Thread:
1. ## Basic division simplification
I have been given a logarithmic equation to simplify. I have simplified it down a couple of stages and am left with the below equation:
(3a)/((a^2)/(25))
Is it possible to remove the 'a' from the equation, or at least one of them, perhaps the lower one? I have tried qui... | {"extraction_info": {"found_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://mathoverflow.net/questions/70186/more-questions-about-log-structures/70193 | ## More questions about log structures
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I now have some more questions regarding the role of log structures in moduli problems (you can assume that the moduli problem is the compactification of $n$-marked genus $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": 26, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://planetmath.org/Discriminant | # Summary.
The discriminant of a given polynomial is a number, calculated from the coefficients of that polynomial, that vanishes if and only if that polynomial has one or more multiple roots. Using the discriminant we can test for the presence of multiple roots, without having to actually calculate the roots of the p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 47, "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://physics.stackexchange.com/questions/tagged/tensor-calculus+mathematics | # Tagged Questions
0answers
203 views
### Invariants of a tensor [closed]
I asked (almost) the same question in the math exchange. I'm teaching a course, and I need a simple and intuitive proof that the invariants of a matrix ($3\times3$, but it doesn't matter) can be ...
2answers
361 views
### What is the mathemat... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-statistics/108379-e-x_k-how-can-we-prove.html | # Thread:
1. ## E(∑ |X_k|) < ∞ ? How can we prove it?
Let |X_k| ≥ 0 be a sequence of random variables.
If we are given that
∞
∑ |X_k| < ∞ and
k=1
+∞
E(∑ |X_k|) < ∞ ,
k=1
does this imply that
k=n
E(∑ |X_k|) < ∞ ?
k=1
An infinite sum is by definition the limit of the sequence of partial sums and intuition seems to... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/8295/einsteins-box-unclear-about-bohrs-retort | # Einstein's box - unclear about Bohr's retort
I was reading a book on the history of Quantum Mechanics and I got intrigued by the gendankenexperiment proposed by Einstein to Bohr at the 6th Solvay conference in 1930.
For context, the thought experiment is a failed attempt by Einstein to disprove Heisenberg's Uncerta... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/208909-mvt.html | # Thread:
1. ## MVT
Suppose f:[a,b]->R satisfies the following properties:
1. f is continuous on [a,b] and continuously differentiable on (a,b)
2. f(a) and f(b) are positive numbers
3. f(x)=0 for some x in (a,b)
Prove that there exists some c in (a,b) such that f'(c)=0.
I understand what the problem is asking and c... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 9, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/87649-double-integrals-problem.html | # Thread:
1. ## Double integrals problem
Well, my problem isn't with the double integral bit, it's just with the integration once I've switched the limits et cetera. The original problem is:
$\int_{0}^{1}\int_{\sqrt{y}}^{1}2x^5y\cos{(xy^2)}dx dy$
...and I'm told to solve it by changing the order of integration. I get... | {"extraction_info": {"found_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": 52, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/45320/why-does-an-object-with-higher-speed-gain-more-relativistic-mass | # Why does an object with higher speed gain more (relativistic) mass?
Today, in my high school physics class, we had an introductory class on electromagnetism. My teacher explained at some point that an object with a very high speed (he said it started to get somewhat clearly noticable when travelling at 10% of the sp... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://quant.stackexchange.com/questions/4021/st-petersburg-lottery-pricing-short-investing-horizons/4038 | # St Petersburg lottery pricing & short investing horizons
I am a statistician (no solid background in finance). Please forward me to a book \ chapter \ paper to resolve the following general question. Suppose we have a stock with the following monthly return distribution: P(R=1%)=0.999, P(R=10000%)=0.001. The mean mo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2010/06/09/equicontinuity-convergence-in-measure-and-convergence-in-mean/?like=1&source=post_flair&_wpnonce=9a71b83933 | The Unapologetic Mathematician
Equicontinuity, Convergence in Measure, and Convergence in Mean
First off we want to introduce another notion of continuity for set functions. We recall that a set function $\nu$ on a class $\mathcal{E}$ is continuous from above at $\emptyset$ if for every decreasing sequence of sets $E... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 88, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/92634-find-equation-tangent-line-curve-print.html | Find the equation of the tangent line to the curve.
Printable View
• June 12th 2009, 08:21 AM
mant1s
Find the equation of the tangent line to the curve.
Hi guys,
Could someone take a look at my work.. im lost.
Problem:
Code:
Find the equation of the tangent line to the curve
y= 4 tan x at the point ( pi/4 , 4).
... | {"extraction_info": {"found_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://math.stackexchange.com/questions/319431/how-was-the-isoperimetric-inequality-formulated | # How was the isoperimetric inequality formulated?
I'm tyring to understand how the isoperimetric inequality came into existence. It seems like finding the region which yields maximum area when enclosed by a curve of fixed length is an old problem. Queen Dido seems to have figured out the solution a long time ago: tha... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/981?sort=oldest | ## Rational maps with all critical points fixed
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
What can be said about rational self-maps of $\mathbb P^1$ for which all critical points are also fixed points ?
If all but one of the fixed points are critical, 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": 103, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathhelpforum.com/calculus/199102-convergence.html | # Thread:
1. ## Convergence
I have attached the question.
I have expanded $(1+h)^n$ using the binomial theorem, and the question after it I assume they want me to use the very same theorem to prove the convergence.
So this is what I had done;
$(n+1)^{1/n}=1+h \rightarrow n+1=(1+h)^n=1+nh+\frac{n!}{2!(n-2)!}+...+h^... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/258132/orthonormality-proof-on-outer-product-of-svd-unitary-matrices-columns | # Orthonormality proof on outer product of SVD unitary matrices columns
If I have the two unitary matrices from the SVD of an m x n matrix (U, V*) and I form a set of new matrices by doing $u_iv_i^H$ (forms an m x n matrix). Assuming $r = min(m, n)$ and my set is $X_1, X_2, ..., X_r$, how can I show that this is an or... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3837817 | Physics Forums
## Proper summation notation
Hi
Is it correct of me to say that I want to carry out the sum
[tex]
\sum_i{v_iw_i}
[/tex]
where $i\in\{x,y,z\}$? Or is it most correct to say that $i=\{x,y,z\}$?
Best regards,
Niles.
Blog Entries: 1 Recognitions: Homework Help If you h... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/39284/how-many-different-ways-can-you-distribute-5-apples-and-8-oranges-among-six-chil | How many different ways can you distribute 5 apples and 8 oranges among six children?
How many different ways can you distribute 5 apples and 8 oranges among six children if every child must receive at least one piece of fruit? If there was a way to solve this using Pólya-Redfield that would be great, but I cannot fig... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 16, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?p=3932667 | Physics Forums
## How to calculate the height submerged of cylinder
A hollow cylinder (but not open ended) is allowed to float on a liquid. Can anyone please help me how to calculate the height (h) it submerge? I want to get a relationship between height and cylinder weight.
I can calculate the volume of submerged 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": 10, "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/67484/list | ## Return to Answer
2 added 113 characters in body
Infinite exponent partition relations are inconsistent with the axiom of choice, so in ZFC, this phenomenon does not exist, but nevertheless, in the context of $ZF+\neg AC$ there is a robust theory. See for example Andres Caicedo's discussion, this Kleinberg article,... | {"extraction_info": {"found_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/questions/51715/coproducts-of-complete-boolean-algebras | ## Coproducts of complete Boolean algebras
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Does the category of complete Boolean algebras have binary coproducts?
Note that this category does not have countable coproducts. Indeed, the coproduct of countably 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": 6, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=4084380 | Physics Forums
## Homogeneous Eqn of Line given 2 homogeneous pointspoints
I'm reviewing Projective Geometry. This is an exercise in 2D homogeneous points and lines. It is not a homework assignment - I'm way too old for that.
Given two points p1 (X1,Y1,W1) and p2 (X2,Y2,W2) find the equation of the line that passes ... | {"extraction_info": {"found_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/74804/software-for-some-universal-algebra-issues/111962 | # Software for some universal algebra issues
I am looking for some mathematical software that can help me with a very common task in the realm of universal algebra (as far as I know programs like prover9/mace4 and uacalc do not help with this issue).
The input of this software should be two different finite algebras,... | {"extraction_info": {"found_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://luckytoilet.wordpress.com/ | # Lucky's Notes
Notes on math, coding, and other stuff
## How to Write your own Minesweeper AI
December 23, 2012
A while ago, I wrote a minesweeper AI. I intended to publish a writeup, but due to university and life and exams, I never got around to writing it. But having just finished my Fall term, I have some time... | {"extraction_info": {"found_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": 47, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/36847/list | ## Return to Answer
2 added 2 characters in body
Maybe I'm underestimating your problem, but it seems Mikael above is right.
In your example you define $q:f_1\to f_2$, so if it's a kernel of some other map r, then $r$ must have $f_2$ for domain. $q$ can't possibly be a kernel of $p$, as the composition $pq$ does not... | {"extraction_info": {"found_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://mathhelpforum.com/calculus/46628-differentiating-integral.html | # Thread:
1. ## Differentiating an integral
Hi,
I am unsure how to differentiate an integral. The specific problem I am working on at the moment is:
$\frac{\partial }{\partial T} \int_t^T F(t;s) ds$
s is a dummy variable used to represent T. The solution to this is
$F(t;T)$
...but I am unsure why we would get th... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.m.wikibooks.org/wiki/Control_Systems/Feedback_Loops | # Control Systems/Feedback Loops
| | | | |
|----------------------------------------------------------|------------------------|--------------|-------------|
| The Wikibook of: Control Systems and Control Engineeri... | {"extraction_info": {"found_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": 20, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/94764-using-parameters.html | Thread:
1. Using Parameters
A question from my text is:
The simultaneous equations $x+2y+3z=13,\;-x-3y+2z=2$ and $-x-4y+7z=17$ have infinitely many solutions. Describe these solutions through the use of a parameter.
I understand how to do this. I just don't understand the purpose of using a parameter?
2. Originall... | {"extraction_info": {"found_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": 26, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/7485/list | ## Return to Answer
3 added 119 characters in body
Let me have a punt at this. $F$ alg closed inside $F'$ iff $\overline{F}\otimes_FF'$ is a field, right? So now it's easy because $\overline{L}$ is an algebraic closure of $F$, and I don't think I even assumed $L$ was simple over $F$. Did I miss something?
Edit: my 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": 63, "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/gauss-sums?sort=votes&pagesize=15 | # Tagged Questions
For questions on Gauss sums, a particular kind of finite sum of roots of unity.
1answer
82 views
### Gauss Sum of a Field with Four Elements
I need to calculate a couple of Gauss sums to solve a problem I'm working on, but I keep getting the wrong answer because the absolute value of what I calcu... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
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