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http://mathhelpforum.com/discrete-math/143065-another-probability-question.html | Thread:
1. Another probability question
A colony of rare spherical cocci bacteria lives deep under lunar ice. After thousands of years of slowly reproducing (a process that often results in abject failure and death) in this harsh climate, only one lonely bacteria named John remains.
Suppose that the probability of a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/tagged/projective | ## Tagged Questions
0answers
97 views
### projective plane and tetrahedra
suppose we have a tetrahedron with four adjacent ones in RP3 and the vertices of the central tetrahedron are [1,0,0,0,0] , [0,1,,0,0] , [0,0,1,0] , [0,0,0,1]. For each vertex doe …
0answers
106 views
### Projective spaces with nonconstant reg... | {"extraction_info": {"found_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/53986/component-of-force-field-tangent-to-a-curve | # Component of force field tangent to a curve
I recently had to solve the following problem:
A force $F=10\hat x- 8\hat y$ is applied to an object that is constrained to travel towards increasing values of x along the path defined by $y=x^2$ and $z=0$. Find the component of $F$ that is tangent to this path at the poi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 15, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/5122/impact-of-algorithms-for-factoring-using-elliptic-curves-over-mathbbq?answertab=oldest | # Impact of algorithms for factoring using elliptic curves over $\mathbb{Q}$
Recently a few papers have appeared that describe a new approach to factoring, using elliptic curves over $\mathbb{Q}$. See, e.g.,
• Factoring integers and computing elliptic curve rational points, Iftikhar A. Burhanuddin and Ming-Deh A. Hua... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/25986/list | ## Return to Answer
2 Corrected typo
Etimology
Etymology may help. Compact, from the Latin Compactus, past participle of the verb Compingere: "to pack together closely and firmly". You may have an idea of how strong is the hypothesis of compactness if you look at what happens when even total boundedness is lacking.
... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/53184/would-a-magnetic-rod-through-mars-shield-it-from-solar-wind | # Would a magnetic rod through Mars shield it from solar wind?
Would a magnetic rod going all the way through Mars shield it from solar wind?
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## 2 Answers
Theoretically yes.
It would have to produce a magnetic field of sufficient strength of course.
The Earth's magnetic field at the Earth's surface ranges 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": 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/94513/tracking-spectral-sequence-differentials | ## Tracking spectral sequence differentials
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I read a number of posts here on MO, but haven't quite found an answer to the question of where the differentials in a spectral sequence come from.
I came across a dif... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/pre-calculus/154058-multiplying-imaginary-factors-polynomial.html | # Thread:
1. ## [Solved] Multiplying imaginary factors of a polynomial
The problem:
$(x - e^{\frac{i\pi}{4}})(x - e^{\frac{-i\pi}{4}})$
My attempt:
I used the distributive rule to expand it, and got:
$x^2 - x(e^{\frac{i\pi}{4}} + e^{\frac{-i\pi}{4}}) + 1$
I recognise that $cos(\frac{\pi}{4}) = \frac{1}{2}(e^{\frac... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/98065/how-many-ways-can-b-balls-be-distributed-in-c-containers-with-no-more-than/98356 | # How many ways can $b$ balls be distributed in $c$ containers with no more than $n$ balls in any given container?
I think there are $\binom{b+ c - 1}{c-1}$ ways to distribute $b$ balls in $c$ containers. (Please correct me if that's a mistake.) How does this change if I am not allowed to place more than $n$ balls 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": 34, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math/195681-test-preparation-print.html | # Test preparation
Printable View
• March 7th 2012, 12:34 AM
KristianS
Test preparation
Hey guys
Im new here and its good to see that these forums are active and full of friendly people. I was wondering if someone could help me with some test preparation. My unit that I am revising on consists of Linear algebra/func... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/63020/eigenvalues-of-some-peculiar-matrices | # Eigenvalues of some peculiar matrices
While I was toying around with matrices, I chanced upon a family of tridiagonal matrices $M_n$ that take the following form: the superdiagonal entries are all $1$'s, the diagonal entries take the form $m_{j,j}=4 j (2 n + 3) - 8 j^2 - 6 n - 5$, and the subdiagonal entries take 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": 63, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://www.physicsforums.com/showthread.php?p=3732237 | Physics Forums
Simple problem: Gain after n trials given success rate and profibility
I'm stuck on what I'm sure is a very simple problem.
I'm trying to calculate predicted output for my share trading model.
For example, for a strategy the probability of it winning on each trade may be 0.4 and hence a loss is 0.6.
... | {"extraction_info": {"found_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://mathoverflow.net/questions/34390/on-proving-that-a-certain-set-is-not-empty-by-proving-that-it-is-actually-large/34410 | ## On proving that a certain set is not empty by proving that it is actually large
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
It happens occasionally that one can prove that a given set is not empty by proving that it is actually large. The word "large" ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 58, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/16262/why-is-the-principle-of-superposition-true-in-em-does-it-hold-more-generally/16269 | # Why is the Principle of Superposition true in EM? Does it hold more generally?
• In the theory of electromagnetism (EM), why is the principle of superposition true? Can we read it off from Maxwell's equations directly?
• Does it have any limit of applicability or is it a fundamental property of nature?
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## 4 Ans... | {"extraction_info": {"found_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://math.stackexchange.com/questions/184660/divisibility-for-numbers-like-13-17-and-19-compartmentalization-method?answertab=oldest | # divisibility for numbers like 13,17 and 19 - Compartmentalization method
For denominators like 13, 17 i often see my professor use a method to test whether a given number is divisible or not. The method is not the following : Ex for 17 : subtract 5 times the last digit from the original number, the resultant number ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/field-theory+definition | # Tagged Questions
2answers
652 views
### What is a non linear $\sigma$ model?
What exactly is a non linear $\sigma$ model? In many books one can view many different types of non linear $\sigma$ models but I don't understand what is the link between all of them and why it is ...
1answer
1k views
### Differentiating... | {"extraction_info": {"found_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://alanrendall.wordpress.com/2011/07/ | # Hydrobates
A mathematician thinks aloud
## Archive for July, 2011
### Cytokine dynamics, part 2
July 28, 2011
In a previous post I discussed a paper of Lev Bar-Or about the dynamics of the interactions between T cells and macrophages via the cytokines they produce. The model of that paper is a four-dimensional d... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 51, "mimetex.cgi": 0, "/images/ma... |
http://yehar.com/blog/?p=430 | # Marginal notes
These are miscellaneous notes and recipes.
## Mapping a pair of integers to an integer
2011-05-26
How to map from a pair of integers to an integer? Negative or positive, independent of the size of the two integers, you can convert them into balanced ternary to get rid of the signs and then interlea... | {"extraction_info": {"found_math": true, "script_math_tex": 29, "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": 29, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/14421/encrypting-algorithm/14424 | # Encrypting algorithm
I know there are some encrypting algorithm that once the text (the message) is encrypted there is no way to decrypt it.
I can think one way of doing this: using as encryption key the current date at the encryption moment. But there is one problem wiht that: Each time you encrypt the same messag... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/27632/about-the-definition-motivation-properties-of-the-twisted-chiral-superfield-in | # About the definition/motivation/properties of the twisted chiral superfield in ${\cal N}=2$ theories in $1+1$ dimensions
The following is in the context of the ${\cal N}=2$ supersymmetry in $1+1$ dimensions - which is probably generically constructed as a reduction from the ${\cal N}=1$ case in $3+1$ dimensions.
• ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 30, "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/22747/why-do-we-like-gauge-potentials-so-much | # Why do we like gauge potentials so much?
Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about magnetic monopoles?
And more generally, why do we like gauge potentials so much?... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?p=3858901 | Physics Forums
Page 2 of 2 < 1 2
## how to calculate required hp for machine
I have estimated the total MMOI as 16.5 kg-m^2, and on that basis, Bob_S value of 41 watts appears to be a reasonable estimate for the total power required to accelerate the roll (I calculated slightly less). The total energy of the 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": 1, "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/51111/calculating-point-on-a-circle-given-an-offset?answertab=oldest | # Calculating point on a circle, given an offset?
I have what seemed like a very simple issue, but I just cannot figure it out. I have the following circles around a common point:
The Green and Blue circles represent circles that orbit the center point. I have been able to calculate the distance/radius from the point... | {"extraction_info": {"found_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": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathandcode.com/ | # Wire Bead Toys with Mathematica
Posted on March 13, 2013 by
These are toys that I loved as a kid. It’s a dead simple toy, but it’s fun to flick a bead and watch it coast along the track. So what are the mathematics of this? What are some properties of it, and how can you simulate and animate it with Mathematica?
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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Gaussian_beam | # Gaussian beam
Instantaneous intensity of a Gaussian beam.
A 5 mW green laser pointer beam profile, showing the TEM00 profile
In optics, a Gaussian beam is a beam of electromagnetic radiation whose transverse electric field and intensity (irradiance) distributions are well approximated by Gaussian functions. Many la... | {"extraction_info": {"found_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": 105, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/39620?sort=oldest | ## Morphisms of a simple sheaf over an algebra to its double dual
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Given a smooth and projective surface $S$ over an algebraically closed field $k$ and a sheaf of Azumaya algebras $R$, i.e. $R$ is a locally free $... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/tagged/inequalities | ## Tagged Questions
3answers
193 views
### how to proof this Stirling related equation
here is what I need to proof, have no idea were to start. I know there is some connection with the Stirling theorem. \sum_{i=0}^{d}\binom{m}{i} \leq \left ( \frac{em}{d} \right …
0answers
109 views
### Bounding a sum of binomial... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Multivariate_Gaussian | # Multivariate normal distribution
(Redirected from Multivariate Gaussian)
"MVN" redirects here. For the airport with that IATA code, see Mount Vernon Airport.
Notation
Probability density function Many samples from a multivariate normal distribution, shown along with the 3-sigma ellipse, the two marginal distributio... | {"extraction_info": {"found_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": 102, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://stats.stackexchange.com/questions/10206/conditions-for-central-limit-theorem-for-dependent-sequences/10212 | # Conditions for Central Limit Theorem for dependent sequences
Cumbersome technical assumptions (e.g., mixing properties) are used in the literature to prove Central Limit Theorems for dependent sequences. I sketched a proof that does not require any of these technical assumptions. Can you help me figure out what is 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": 25, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/242724/monochromatic-squares-in-a-colored-plane | # Monochromatic squares in a colored plane
Color every point in the real plane using the colors blue,yellow only. It can be shown that there exists a rectangle that has all vertices with the same color. Is it possible to show that there exists a square that has all vertices with the same color ? If it is not possible,... | {"extraction_info": {"found_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/308024/truth-functional-completness-for-quantifiers | # Truth functional completness for quantifiers
There is a definition for truth-functional completness for a set of propositional connectives. Is there a definition for truth-functional completness of a set of quantifiers and propositional connectives ?
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## 1 Answer
There cannot be a direct analogue, because a form... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/102763/the-use-of-parentheses-to-mean-i-wont-tell-you-this-again/103060 | ## the use of parentheses to mean “I won’t tell you this again”
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
A reader of one of my drafts found fault with my use of parentheses; I put the word "bounded" in parentheses in a statement of a certain theorem, 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://physics.stackexchange.com/questions/21168/do-particles-have-different-spins-in-different-frames-of-reference | # Do particles have different spins in different frames of reference?
Let's say we have two photons, whose momentum vectors point to opposite directions. Also spin angular momentum vectors of the photons point to opposite directions. (Sum of spins is zero)
Now we change into a frame where the momentum vectors point 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": 12, "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/6392/could-use-an-explanation-of-the-notation-for-an-oracle-adversary/6394 | # Could use an explanation of the notation for an oracle adversary
In the definition below, what exactly does it mean for the adversary (not even sure that's the correct term?) to equal one?
$$\underset{K}{Pr} \left [A^{F_k(\cdot)} = 1 \right ]$$
Source (Page 22/35?) or Imgur Link
Thanks in advance!
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Asymptotic ... | {"extraction_info": {"found_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/19285?sort=newest | ## How do you axiomatize topology via nets?
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Let $X$ be a set and let ${\mathcal N}$ be a collection of nets on $X.$
I've been told by several different people that ${\mathcal N}$ is the collection of convergent ... | {"extraction_info": {"found_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://math.stackexchange.com/questions/30477/intuitive-idea-of-expectation-of-random-variable | # Intuitive idea of Expectation of random variable?
I'm studying probability for preparing myself for machine learning. I came across this notion of Expectation of (random variable) or (function of random variable) like $E[X]$ or $E[g(X)]$. Can anybody explain me the intuitive idea of the above notion (taking into con... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/70055-evaluate-integral.html | # Thread:
1. ## Evaluate the integral.
$<br /> \int \limits_0^{\frac{\\pi}{2}} \frac{cosx}{1+sin^2(x)}dx<br />$
2. Originally Posted by saiyanmx89
$<br /> \int \limits_0^{\frac{\\pi}{2}} \frac{cosx}{1+sin^2(x)}dx<br />$
Let $u = \sin x, \;\;\; \text{so} \;\;\; du = \cos x \, dx$
so (note the change of limits)
$\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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/mathematical-physics+quantum-mechanics | # Tagged Questions
0answers
6 views
### what is the magnetic quadrupole operator?
To find magnetic or electrical moments in quantum theory we must calculate the expectation value of an appropriate operator. the dipoles operator are similar and is easy to find but the magnetic ...
0answers
5 views
### what is the ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 31, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/contest-math?sort=faq&pagesize=15 | # Tagged Questions
Many people have their first exposure to real math in the form of a mathematics competition. Math contests show the competitors that math is a subject that makes great use of creativity. For those already initiated, math contests are a source of fantastic problems that often lead to extended ...
3a... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 117, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/... |
http://mathoverflow.net/questions/100693 | ## Can we extend a continuous function with keeping Hausdorff dimension?
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Let X be a compact subset of R^d, and K be a compact subset of X, such that Dim_H(X)=Dim_H(K). Let F be a continuous function on K, Can we ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/2696/do-all-massive-bodies-emit-hawking-radiation | # Do all massive bodies emit Hawking radiation?
It is known that any accelerated observer is subject to a heat bath due to Unruh radiation. The principle of equivalence suggests that any stationary observer on the surface of a massive body should also experience heat bath. Indeed by substituting surface gravity g into... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/13638/transformation-of-angles-in-special-relativity/13644 | # Transformation of angles in special relativity
My question is about the problem below
Depicted are two space ships (the USS Voyager and the USS Enterprise), each with velocity $v=c/2$ relative to the space station (Babylon 5). At the exact moment the two space ships are closest together (at a distance d) the USS En... | {"extraction_info": {"found_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": 7, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/81176/hyperbolicity-of-a-fundamental-group | ## Hyperbolicity of a fundamental group
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Let G be the fundamental group of a compact 3-manifold which supports on its interior a complete non positively curved Riemannian metric and is a cilinder near de metric. 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": 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/85830/how-to-use-the-extended-euclidean-algorithm-manually/252923 | # How to use the Extended Euclidean Algorithm manually?
I've only found a recursive algorithm of the extended Euclidean algorithm. I'd like to know how to use it by hand. Any idea?
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2
I'm not sure what you mean. The Extended Euclidean Algorithm is inherently recursive. When you use it by hand, you use it recursivel... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/46279/if-q-is-a-subset-of-the-plane-of-size-less-than-continuum-then-does-every-closed | ## If Q is a subset of the plane of size less than continuum, then does every closed F in Q extend to a closed connected G in the plane with the same trace on Q? (Or is this independent of ZFC?)
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This question ari... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 112, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/quantum-field-theory?page=2&sort=active&pagesize=15 | # Tagged Questions
Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 49, "mathjax_display_tex": 9, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/93297-change-basis-matrix.html | # Thread:
1. ## Change of Basis Matrix
Hey guys, I have a question on change of basis.
Find the change of basis matrix from the standard basis {(1,0,0),(0,1,0),(0,0,1)} to {(-1,1,1),(1,-1,1),(1,1,-1)}.
I'm having some trouble in figuring out what to do. Thanks in advance!
2. Let $[a,b,c]=p[-1,1,1]+q[1,-1,1]+r[1,1,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 18, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/239096/probability-for-winning?answertab=oldest | # probability for winning
it is a well known game played in india.is there any theory for winning this game.it is possible where it falls How it works:in a shuffled deck the dealer offers a cut. You then bet on that card will be dealt on the inside or the outside. He then deals the cards one a time alternating between... | {"extraction_info": {"found_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-geometry/189131-how-modify-hahn-banach-seperation-theorem.html | # Thread:
1. ## how to modify Hahn-Banach Seperation Theorem?
Suppose X is a real normed space, B is a non-empty open convex subset of X, E is a linear subspace of X, B don't intersect with E.
Then there exists a linear functional f, such that f(x)=0 when x belong to E, and f(x)>0 when x belong to B.
i don't know how... | {"extraction_info": {"found_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://math.stackexchange.com/questions/3861/what-is-your-favorite-proof-that-eix-has-a-period-of-2-pi/3865 | # What is your favorite proof that $e^{ix}$ has a period of $2\pi$?
as a function of a real variable, apparently. Part of the freedom in choosing a proof is that you get to choose what definition of $e^{ix}$ to start from -- do you use a differential equation? a power series? a definition in terms of trig functions? 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": 22, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/67/what-is-an-elliptic-curve-and-how-are-they-used-in-cryptography?answertab=oldest | # What is an elliptic curve, and how are they used in cryptography?
I hear a lot about Elliptic Curve Cryptography these days, but I'm still not quite sure what they are or how they relate to crypto...
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## 3 Answers
Here is a super nice powerpoint on the subject!
http://www.math.brown.edu/~jhs/Presentations/Wyomi... | {"extraction_info": {"found_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/18062/how-do-electromagnetic-waves-carry-quantised-energy/18068 | # How do electromagnetic waves carry quantised energy?
If an electron oscillates about a mean position, it will create a time varying electric filed which in turn will create a time varying magnetic field and so on to create an electromagnetic wave. How does this wave carry energy , in which amount and how can this be... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/questions/21691/proofs-by-induction/21701 | ## Proofs by induction [closed]
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Background
I'm interested in the issue of "explanatory" mathematical proofs and would like to try to find out what intuitions mathematicians have about induction, because there 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": 90, "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/130354/surface-measure-for-lipschitz-domain?answertab=votes | # Surface measure for Lipschitz domain
Let $D\subset R^d$ be a bounded Lipschitz domain. Must there exist a bounded function $\Phi$ on $\partial D$ and collections of subsets $(\partial D )^{\epsilon} \subset \partial D$ (indexed by $\epsilon$) such that for all bounded continuous function $g$ on $\partial D$ we have ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/47952/proving-interesting-theorems-about-s-n-using-its-character-table/48003 | ## Proving interesting theorems about S_n using its character table.
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Hi, i wonder if there are interesting proofs about $S_n$ (group theoretic or not) using its character table. Using the Murnaghan-Nakayama rule ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 43, "mathjax_display_tex": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/46871/how-to-calculate-dual-frames-under-constraints | # How to calculate dual frames under constraints?
Denote orthonormal basis in $\mathbb{R}^2$: $(\epsilon_1,\epsilon_2)=\begin{pmatrix}1&0\\0&1\end{pmatrix}$ and $A=\begin{pmatrix}1&0&\frac{\sqrt{2}}{2}&\frac{\sqrt{2}}{2}\\0&1&\frac{\sqrt{2}}{2}&-\frac{\sqrt{2}}{2}\end{pmatrix}$.
Now let frames $(e_1,e_2,e_3,e_4)=(\ep... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/58828/list | Return to Answer
5 added 534 characters in body; added 6 characters in body
Actually, one can show the following stronger result:
Proposition
Assume that a finite abelian group $A$ admits a non-degenarate, bilinear alternating form $\psi$. Then $A$ has a lagrangian decomposition, i.e. there exists a subgroup $G$, 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": 70, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikisource.org/wiki/Page:Zur_Thermodynamik_bewegter_Systeme.djvu/7 | # Page:Zur Thermodynamik bewegter Systeme.djvu/7
From Wikisource
and isochorically brought to velocity zero. The arising function of $\beta$ plays here the role of a constant, so it is irrelevant. Of course, it must have the same value for all bodies.
Since we see $\beta$ as constant in this case, it is
$dQ=\frac{\... | {"extraction_info": {"found_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://mathhelpforum.com/geometry/46491-easy-question.html | # Thread:
1. ## Easy Question
When we want to find the area of a two dimensional figure and there are more than one type of shapes that can be used to find the whole figure, we find the areas of the shapes comprising the figure one step at a time. Then finally adding the areas of the shapes together to find area of 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/209019/linearly-separate-a-cube/209210 | # Linearly separate a cube
I am facing the problem of the linear separability of a three dimensional cube.
Let's take the opposite vertexes of the cube as $(0, 0, 0), (1, 1, 1)$. It is possible to split it with a plane in two tetrahedron-like parts, and so define two sets, each containing lying points lying on a 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": 12, "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/41830?sort=votes | ## isogenies between abelian varieties that induce isomorphisms?
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Let $\varphi : A \to B$ be an isogeny between 2 abelian varieties of dimension $g$. Are there known conditions for the $\ker\varphi$ so that this 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": 28, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.sacredduty.net/2013/01/18/revenge-combinatorics/ | A Protection Paladin Blog
# Revenge Combinatorics
Posted on January 18, 2013 by
Since January is apparently “Warrior Month” here at Sacred Duty, I figured I’d share a little side project I’ve been working on. Omega (of DBM fame) and I were having a conversation about warriors on Lei Shi, and what effect the lack 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": 190, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://nrich.maths.org/1882/note | ### Exploring Wild & Wonderful Number Patterns
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
### I'm Eight
Find a great variety of ways of asking questions which make 8.
### Dice and Spinner Numbers
If yo... | {"extraction_info": {"found_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://math.stackexchange.com/questions/152167/laplace-transform-of-simple-function/268487 | # Laplace transform of simple function
I have the function below:
$$3-2t+3t^2$$
I tried to get the transfer function, but my solution seems to be wrong, can someone please tell me what I am doing wrong:
$$\frac{1}{s}+\frac{1}{s^3}$$
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3
Are we just finding $\int_0^\infty (3-2t+3t^2)e^{-st}\,dt$? If so (using inte... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/243043/decompose-matrix | # Decompose matrix
The following $m$ x $n$ matrix, decompose the first standard basis vector $e_1 = w + z \in \mathbb{R^n}$, where $w \in$ rowspace(A) and $z\in kerA$. Verify your answer by expressing $w$ as a linear combination of the rows of $A$.
a.) $\pmatrix{1&-2&1\\2&-3&2}$
b.) $\pmatrix{1&-1&0&3\\2&1&3&3\\1&2&... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 13, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/28644/the-isomorphism-inference-rule/28785 | ## The isomorphism inference rule
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Suppose we are writing very detailed proofs, absolutely without any gaps (for example, for checking proofs by computer).
In such formal proofs every step (even a trivial one) mu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 24, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2011/08/02/integration-on-the-standard-cube/ | # The Unapologetic Mathematician
## Integration on the Standard Cube
Sorry for the delay, I’ve had a packed weekend.
Anyway, we’re ready to start getting into integration on manifolds. And we start with a simple case that everything else will be built on top of.
We let $[0,1]^k\subseteq\mathbb{R}^k$ be the “standar... | {"extraction_info": {"found_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": 20, "mimetex.cgi": 0, "/images/ma... |
http://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch06_s07 | # Elementary Algebra, v. 1.0
by John Redden
Study Aids:
Click the Study Aids tab at the bottom of the book to access your Study Aids (usually practice quizzes and flash cards).
Study Pass:
Study Pass is our latest digital product that lets you take notes, highlight important sections of the text using different co... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 36, "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://www.sagemath.org/doc/reference/rings_standard/sage/rings/finite_rings/integer_mod_ring.html | Ring $$\ZZ/n\ZZ$$ of integers modulo $$n$$¶
EXAMPLES:
```sage: R = Integers(97)
sage: a = R(5)
sage: a**100000000000000000000000000000000000000000000000000000000000000
61
```
This example illustrates the relation between $$\ZZ/p\ZZ$$ and $$\GF{p}$$. In particular, there is a canonical map to $$\GF{p}$$, but not in 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": 15, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/44086/is-there-a-ruler-and-compass-construction-of-the-common-perpendicular-of-two-geod | ## Is there a ruler and compass construction of the common perpendicular of two geodesics in H^3?
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Assume we have two geodesics in the Poincaré ball model of $\mathbb{H}^3$, viewed as arcs intersecting the boundar... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 79, "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/35399/is-this-true-mathrmcovx-y-sqrt-mathrmvarx-sqrt-mathrmvary/35404 | # Is this true: $\mathrm{Cov}(X,Y) = \sqrt{\mathrm{Var(X)}}\sqrt{\mathrm{Var}(Y)}$?
I just want to confirm whether this is correct or not:
The covariance of $X$ and $Y$ is equal to the standard deviation of $X$ times the standard deviation of $Y$.
or, in mathematical notation,
$$\mathrm{Cov}(X,Y) = \sqrt{\mathrm{Va... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 47, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://pediaview.com/openpedia/Associative_algebra | # Associative algebra
In mathematics, an associative algebra A is a (not necessarily unital) associative ring that has a compatible structure of a vector space over a certain field K or, more generally, of a module over a commutative ring R. Thus A is endowed with binary operations of addition and multiplication satis... | {"extraction_info": {"found_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": 29, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://en.wikipedia.org/wiki/Quadratic_function | # Quadratic function
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (October 2010)
It has been suggested that this 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": 64, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/1586/what-if-physical-constants-were-increased-or-decreased | What if physical constants were increased or decreased?
(Probably related to this one, and probably should be CW.)
A very long time ago, I had the good fortune to read George Gamow's excellent series of Mr. Tompkins books. That introduced me to the idea of a world where the usual physical constants (e.g. the speed 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://mathoverflow.net/revisions/64577/list | ## Return to Question
3 deleted 72 characters in body
Let $X$ be a compact complex manifold. By definition, $Pic(X)={\rm H^1}(X,\mathcal{O}^\times)$. We know a lot about this group. What is known about the groups ${\rm H^n}(X,\mathcal{O}^\times)$ for $n\ge 2$? Another question: when $X$ is an Abelian variety, are 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": 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/tagged/gauss-law?sort=faq&pagesize=30 | # Tagged Questions
The gauss-law tag has no wiki summary.
5answers
2k views
### Does Coulomb's Law, with Gauss's Law, imply the existence of only three spatial dimensions?
Coulomb's Law states that the fall-off of the strength of the electrostatic force is inversely proportional to the distance squared of the charg... | {"extraction_info": {"found_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/questions/67576?sort=votes | ## basic measure theory question - measure on the natural numbers [closed]
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I am looking for a succinct way to describe a subset of the natural numbers which has measure zero" in the following sense: Let X_1 \subs... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathematica.stackexchange.com/questions/tagged/expression-manipulation?sort=faq&pagesize=15 | # Tagged Questions
How to manipulate expressions structurally, not necessarily complying with the rules of algebra.
2answers
696 views
### Head and everything except Head?
I have been working on picking expressions apart using Head and Part and encountered a little mystery. Consider the canonical ...
3answers
395 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": 3, "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/134229/derive-density-of-log-of-theta-when-theta-follows-a-uniform-distribution | # Derive density of log of theta when theta follows a uniform distribution
I'm learning bayesian and I need to do some proofs that I'm not quite sure I can do. Any help will be very welcome!
If $\theta \text{~Unif}(0,1)$
What's the density of $y = - \log\theta$?
And what's density of $\theta \ (1-\theta)$?
Finally... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/126732/minimal-subset-of-x-1-x-2-x-100-that-xors-to-y | # Minimal subset of $x_1, x_2, …, x_{100}$ that XORs to $y$
Given a 64-bit positive integer $y$ and a set of $100$ $64$-bit positive integers: $X = \{ x_1, x_2, \dots, x_{100} \}$
I want to find a smallest possible $Z = \{z_1, z_2, \dots, z_n\} \subset X$, such that:
$$\begin{align} y = z_1 ⊕ z_2 ⊕ \dots ⊕ z_n \end{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 21, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/72009/truel-extended-to-n-persons/72097 | ## Truel extended to n persons
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n players numbered 1~n play a shooting game. Their accuracy rates p1~pn are strictly between 0 and 1, and strictly increases from p1 to pn. This is common knowledge.
Before the gam... | {"extraction_info": {"found_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/180307/a-geometry-problem-measure-of-an-angle?answertab=active | # a geometry problem - measure of an angle
We have a square and the following information:
1) $E \in [AB]$, $E$ an arbitrary point
2) $[AC] \cap [DE]= \{P\}$ and
3)$FP \perp ED$, where $F \in BC$ .
We have to prove that the measure of the angle $\angle EDF = 45^{\circ}$.
Thanks a lot !
-
## 2 Answers
It's easy... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 14, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/28118?sort=newest | ## Does the norm of a normed linear space determine the form of its dual spaces elements?
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Hello everybody,
As an introductory example, suppose $U \subset R^n$ is open and bounded, let $p = 2$. Then there is 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": 43, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://psychology.wikia.com/wiki/Root_mean_square?oldid=26564 | # Root mean square
Talk0
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(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | 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": 31, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/869/sim-security-for-two-messages | # SIM security for two messages
Here SIM means the simulation based security
Consider a two message encryption scheme:$$Enc:K \times M \times M \rightarrow C \times C$$
and $Enc(K, m, m')=(K \oplus m, K \oplus m')$, In the real world experiment, the adversary $Eve$ gets $(K \oplus m, K \oplus m')$ as ciphertext, 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": 36, "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-algebra/64779-find-splitting-field.html | # Thread:
1. ## Find the splitting field
Find the splitting field for f(x)=((x^2)+x+2)((x^2)+2x+2) over Z_3[x]
Write f(x) as a product of linear factors
2. Originally Posted by mandy123
Find the splitting field for f(x)=((x^2)+x+2)((x^2)+2x+2) over Z_3[x]
Write f(x) as a product of linear factors
Let $f(x)$ be a 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/31649-setting-g-x-zero.html | # Thread:
1. ## Setting g'(x) to zero
(I know this is the pre-cal forum, but the calculus isn't my problem here ... it's the basics that are dogging me.)
In order to make a wiggle graph, I need to find where my slopes are zero. The formula of my derivative is:
$g'(x) = 6x^2 - 7x - 3$
So my question is, when g'(x) = ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 5, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/82030/size-of-a-union-of-two-sets | # Size of a union of two sets
We were ask to prove that $|A \cup B| = |A| + |B| - |A \cap B|$. It was easy to prove it using a Venn diagram, but I think we might be expected to do if more formally. Is there a formal way?
-
What does $|A|$ mean? Is $|\cdot|$ a measure? Or maybe the sets are finite? – Jeff Nov 14 '11... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ijm/1258138306 | ### The spectrum of differential operators in $H\sp p$ spaces
Dashan Fan, Liangpan Li, Xiaohua Yao, and Quan Zheng
Source: Illinois J. Math. Volume 49, Number 1 (2005), 45-62.
#### Abstract
This paper is concerned with linear partial differential operators with constant coefficients in $H^p(\mathbf{R} ^n)$. In 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": 8, "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/27089/necessary-and-sufficient-criteria-for-non-trivial-derivations-to-exist/27093 | ## Necessary and sufficient criteria for non-trivial derivations to exist?
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Off hand, does anyone know of some useful conditions for checking if a ring (or more generally a semiring) has non-trivial derivations? (... | {"extraction_info": {"found_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://mathhelpforum.com/trigonometry/168162-never-learned-how-change-cosine-into-frational-form.html | # Thread:
1. ## never learned how to change a cosine into frational form
I was wondering if someone could help me out with how to change a cosine into fractional from: example cos 45 = sqrt2/2 and cos 150 = sqrt3/2
I know that if I take the inverse of the cosine decimal form I can take the answer do square it, make ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/16003/what-is-rich-structure-actually/16040 | ## What is “rich structure”, actually? [closed]
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An ubiquitous claim in mathematics is that such-and-such mathematical entity has a rich structure or more structure than another one. Most oftenly the entity is a 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": 27, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/8296/plotting-a-path-in-a-vector-field | # Plotting a path in a vector field
I am trying to make a visual representation of the curve $y=x^{2}$, with $x\in\left[0,1\right]$ in the vector field defined by $\vec{F}=\left[-y,x\right]$.
However, as far as I can tell there does not seem to be any facility which allows me to do this in Mathematica (I've looked 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": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/44523/riemann-roch-as-an-index-theorem | ## Riemann-Roch as an index theorem [closed]
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I am sorry to make this a new question. I would have liked to leave a comment, but I suppose I don't have enough rep for that....
So, in the accepted answer to this q... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/5088/number-of-continuous-0-1-to-0-1-functions-for-given-arc-length | # Number of continuous $[0; 1] \to [0; 1]$ functions for given arc length
Just out of pure curiosity ...
Suppose I want to connect the two points $(0|0)$ and $(1|1)$ with the graph of some continuous and differentiable function
$$f : [0; 1] \to [0; 1]$$
and let $s$ be the arc length of that function in $[0; 1]$.
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": 43, "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/123159/when-is-a-substack-closed/123165 | ## When is a substack closed?
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For this question we will consider the Zariski site of affine schemes and a stack $\mathcal{M}$ over it. I don't know what a substack is, but I have a guess. The stack $\mathcal{M}$ ... | {"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": 19, "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/229912/roc-analysis-detection-probability-when-false-alarm-is-maximized | # ROC analysis: detection probability when false alarm is maximized.
I am wondering if detection probability always goes to 1 as false alarm probability goes to 1.
Let's assume binary hypothesis problem:
$\mathcal{H}_0: x(t) =n(t)$
$\mathcal{H}_1: x(t) = s(t) + n(t)$ where $s(t)$ and $n(t)$ are the desired signal 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": 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/questions/74359/algorithm-to-compute-certain-poset-from-a-given-poset/74476 | ## Algorithm to compute certain poset from a given poset.
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Hi. Associated with a finite poset $P$, one can consider the poset $S(P)$, whose elements are the intervals of $P$, ordered by inclusion. (See http://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": 32, "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/galois-representations | # Tagged Questions
The galois-representations tag has no wiki summary.
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### Galois representations and normal bases
I am not very familiar with the theory of Galois representations, but I do know a bit about both Galois theory and representation theory. Recently I learned about the notion of a norm... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://medlibrary.org/medwiki/Continuous_group | # Continuous group
Welcome to MedLibrary.org. For best results, we recommend beginning with the navigation links at the top of the page, which can guide you through our collection of over 14,000 medication labels and package inserts. For additional information on other topics which are not covered by our database of m... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 6, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
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