url stringlengths 17 172 | text stringlengths 44 1.14M | metadata stringlengths 820 832 |
|---|---|---|
http://pediaview.com/openpedia/Four_color_theorem | # Four color theorem
Example of a four-colored map
A four-coloring of a map of the states of the United States (ignoring lakes).
In mathematics, the four color theorem, or the four color map theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than fou... | {"extraction_info": {"found_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": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stochastix.wordpress.com/2012/10/02/deterministic-finite-automata-in-haskell/ | # Rod Carvalho
## Deterministic Finite Automata in Haskell
Consider the deterministic finite automaton [1] illustrated below
[ state diagram courtesy of Michael Sipser [1] ]
Henceforth, we will call this automaton $M_1$. Note that $M_1$ has three states, labeled $q_1$, $q_2$, and $q_3$. The start state is $q_1$ (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": 0, "wp_latex": 88, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/discrete-math/156312-number-iterations-print.html | # Number of Iterations
Printable View
• September 15th 2010, 02:49 PM
aarnold
Number of Iterations
How many times does the innermost loop execute:
Code:
for k = 1 to n
for j = 1 to k
for i = 1 to j
#the inner loop
end for
end for
end for
I did the first few by hand to see if I noticed anything.
Looking at Pascal'... | {"extraction_info": {"found_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/revisions/67265/list | ## Return to Question
3 added 270 characters in body
It is well known that $4$ general points in $\mathbb{P}^2$ are complete intersection of two conics. On the other hand, if $d \geq 3$, $d^2$ general points are not a complete intersection of two curves of degree $d$. More precisely, if $d =3$ there is only one cubic... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 61, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/05/07/adding-and-multiplying-measurable-real-valued-functions/?like=1&_wpnonce=401286028f | # The Unapologetic Mathematician
## Adding and Multiplying Measurable Real-Valued Functions
One approach to the problem of adding and multiplying measurable functions on a measurable space $X$ would be to define a two-dimensional version of Borel sets and Lebesgue measure, and to tweak the definition of a measurable ... | {"extraction_info": {"found_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": 53, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/tagged/mean-square-error+standard-deviation | # Tagged Questions
0answers
45 views
### What is the purpose of subtracting the mean from data when standardizing?
What is the purpose of subtracting the mean from data when standardizing? and What is the purpose of dividing by the standard deviation?
2answers
81 views
### Step by step correlation calculation
I 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": 4, "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/57076/list | ## Return to Answer
2 added 13 characters in body
The niceness condition you want is on the action, not on the space $X$. Specifically, you want to have that $X\to X/G$ is a principle $G$-bundle, so that we have a Serre spectral sequence as you describefor $G\to X\to X/G$. Of course, since you're assuming that $G$ is... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 25, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/15804?sort=votes | ## When does a probability measure take all values in the unit interval?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $\mathbb{P}$ be a probability measure on some probability space $(\Omega,\mathcal{A})$. Are there conditions on the $\sigma$-algebra $\... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://planetmath.org/TheoryOfRationalAndIrrationalNumbers | # theory of rational and irrational numbers
The following entry is some sort of index of articles in PlanetMath about the basic theory of rational and irrational numbers, and it should be studied together with its complement: the theory of algebraic and transcendental numbers. The reader should follow the links in eac... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 21, "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/8294/how-much-of-a-star-falls-into-a-black-hole | # How much of a star falls into a black hole?
http://blogs.discovermagazine.com/badastronomy/2011/04/05/astronomers-may-have-witnessed-a-star-torn-apart-by-a-black-hole/
A lot of the star in the disc, a lot of the star in the jets, precisely how much of the star actually falls into the black hole?
-
## 1 Answer
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": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.physicsforums.com/showthread.php?p=3405942 | Physics Forums
## How to visualize diff eq?
I don't feel that I can truly appreciate a math without being able to visualize it in my head. Generally speaking: calculus flows into areas, trig builds shapes, and linear algebra builds spaces, but I cannot for the life of me look at a diff eq and 'see' it, so to speak. 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": 1, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2011/03/28/local-rings/?like=1&source=post_flair&_wpnonce=c1ce40f6e1 | # The Unapologetic Mathematician
## Local Rings
Sorry for the break last Friday.
As long as we’re in the neighborhood — so to speak — we may as well define the concept of a “local ring”. This is a commutative ring which contains a unique maximal ideal. Equivalently, it’s one in which the sum of any two noninvertible... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 36, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/78250?sort=oldest | ## Can taking the projective closure of an affine variety increase the degrees of its ideal generators?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Say we have some equations $f_1(x)=0, \ldots f_k(x)=0$ defining a variety $X$ in ${\mathbb C}^n$ (not necess... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 65, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/49993/distinguishing-between-valid-and-fallacious-arguments-propositional-calculus | # Distinguishing between valid and fallacious arguments (propositional calculus)
I am having some difficulties understanding logical arguments. I was taught that the notion of a valid argument is formalized as follows:
"An argument $P_1, P_2,\cdots , P_n ⊢ Q$ is said to be valid if $Q$ is true whenever all the premis... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/174669/a-sum-of-terms-like-1-sin2x-1 | # A sum of terms like $(1 + \sin^2x)^{-1}$
How to prove that $$\frac12\frac1{1+\sin^2 x} + \frac12\frac1{1+\cos^2 x} + \frac12\frac1{1+\sec^2 x}+ \frac12\frac1{1+\csc^2 x} = 1?$$ Some genius please help me I have been stuck at this for one whole day.
-
2
Please be clearer about the equation. Some would read 1/2(1+si... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/243972/probability-question-on-picking-letters/243974 | # Probability question on picking letters
5 letters: a, b, c, d, e I randomly pick 3 letters, whats the chance of having a and b in those 3 letters
-
## 1 Answer
You have a total of $5$ letters and you are choosing $3$ from them. Hence, the total number of ways of choosing three letters is $\dbinom{5}3$.
Number of... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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/39577/list | ## Return to Question
4 tag added
3 added 12 characters in body
Given a pair of Koszul dual algebras, say `$S^*(V)$` and `$\bigwedge^*(V^*)$` for some vector space $V$, one obtains an a triangulated equivalence between their bounded derived categories of finitely-generated graded modules.
Given a pair of Koszul dual... | {"extraction_info": {"found_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/28158/a-learning-roadmap-request-from-high-school-to-mid-undergraduate-studies/28175 | ## A Learning Roadmap request: From high-school to mid-undergraduate studies
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Dear MathOverflow community,
In about a year, I think I will be starting my undergraduate studies at a Dutch university. I have decide... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=507141 | Physics Forums
Page 1 of 3 1 2 3 >
## Faster than light time travel
Hello, i'm a high school senior interested in studying physics in college. I was listening to a podcast by Neil deGrasse Tyson in which he stated that if one could travel faster than the speed of light, it might be possible to travel back 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": 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/tagged/inertia | # Tagged Questions
The inertia tag has no wiki summary.
2answers
73 views
### Does inertia increase with speed?
I have heard that when the speed of the object increase, the mass of the object also increase. (Why does an object with higher speed gain more (relativistic) mass?) So inertia which is related to ...
0ans... | {"extraction_info": {"found_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/52094/exciton-energy-splitting-in-indirect-semiconductor/52459 | # Exciton energy splitting in indirect semiconductor
Let's take an indirect bulk semiconductor and imagine the exciton that build up at the indirect gap. Since we have a bulk semiconductor we should find three p-like orbitals: $p_x,p_y,p_z$. Would their energy levels be degenerate due to the mass anisotropy which we 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": 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/84120?sort=oldest | ## Fubini’s theorem and unique mean value
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Following the terminology of Rosenblatt, I will say that a bounded function $f:\mathbb Z\rightarrow\mathbb R$ has a unique mean value if for every pair of finitely additi... | {"extraction_info": {"found_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://www.physicsforums.com/showpost.php?p=3788761&postcount=2 | View Single Post
Recognitions: Gold Member Science Advisor Staff Emeritus No, amazingly, you are wrong and your teacher is right! Since that integrand does not exist at x= 0, you have to use the definition: $$\int_{-1}^1 \frac{dx}{x}= \lim_{\alpha\to 0^-}\int_{-1}^\alpha \frac{dx}{x}+ \lim_{\beta\... | {"extraction_info": {"found_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://mathoverflow.net/questions/29247/catenary-curve-under-non-uniform-gravitational-field/29523 | Catenary curve under non-uniform gravitational field
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
The catenary curve is the shape of a chain hanging between two equal-height poles under the influence of gravity. But the derivation of the (hyperbolic cosine) cur... | {"extraction_info": {"found_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://meetings.aps.org/Meeting/MAR11/Event/142863 | # Bulletin of the American Physical Society
## APS March Meeting 2011 Volume 56, Number 1
Monday–Friday, March 21–25, 2011; Dallas, Texas
### Session W29: Symmetric Discrete Structures for Finite Dimensional Quantum Systems
11:15 AM–2:15 PM, Thursday, March 24, 2011
Room: C148
Sponsoring Unit: GQI
Chair: Christop... | {"extraction_info": {"found_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": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://catalog.flatworldknowledge.com/bookhub/reader/1?e=baranoff-ch07_s04 | Please wait while we create your MIYO...
# Risk Management for Enterprises and Individuals, v. 1.0
by Etti Baranoff, Patrick L. Brockett, and Yehuda Kahane
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... | {"extraction_info": {"found_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://unapologetic.wordpress.com/2008/08/ | # The Unapologetic Mathematician
## Convergence of Power Series
Now that we’ve imported a few rules about convergent series of complex numbers we can talk about when the series we get from evaluating power series converge or not.
We’ll just consider our power series to be in $\mathbb{C}[[X]]$, because if we have a 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 172, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/questions/45253/almost-linear-ode-how-node-becomes-a-spiral | ## Almost linear ODE: how node becomes a spiral
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Most introductory ODE books contain a discussion of almost linear systems, and there are two cases when the behavior of an almost linear system near an equilbrium 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": 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/68100/what-are-the-requirements-for-a-rotation-matrix?answertab=oldest | # What are the requirements for a rotation matrix?
Generally speaking, what are the necessary and sufficient properties of a matrix to make it a rotation matrix?
Is det(A) = 1 enough?
-
## 3 Answers
No, not by far. The matrix needs to be orthogonal, which means that $A^tA=I$ where $A^t$ is the transposed matrix --... | {"extraction_info": {"found_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://mathoverflow.net/questions/66584/optimal-tax-rate/66589 | ## Optimal tax Rate
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Assume you have two countries A and B, with a tax rates $T_A$ and $T_B$. The tax is redistributed to each people equally. Hence if you live in A and you make $I$ as income then you will finall... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/1513/why-does-my-watch-act-like-a-mirror-under-water/1514 | # Why does my watch act like a mirror under water?
I have a digital watch, rated to go underwater to $100 \rm m$. When it is underwater it can be read normally, up until you reach a certain angle, then suddenly, it becomes almost like a mirror, reflecting all the light that hits it, almost perfectly (you cannot read 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": 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/revisions/36961/list | Return to Answer
2 capitalization
There is a direct connection between Hall's marriage theorem (combinatorics) and Linear programming (linear inequalities). Of course, the latter is about finite dimensions, but prominently features duality and convexity, two important tools in functional analysis.
To elaborate on Ha... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/47499/list | 2 edited tags
1
# multiplicity under specialization
Let $C$ be a projective non-singular curve defined over a field $K$ with the characteristic zero. Let $y,z$ be non-constant rational functions defined $K$ such that $y$ is defined at all poles and zeros of $z$ and gives an injective mapping of this set into the alge... | {"extraction_info": {"found_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://en.wikipedia.org/wiki/Molecular_mass | # Molecular mass
Assuming hydrogen and oxygen are standard weights in this image (as opposed to deuterium oxide) the molecular mass should be 18.01528 u.
The molecular mass (ma) is the mass of a molecule.
## Units
The SI unit of mass is kg. However, for molecular mass more commonly the atomic mass unit (symbol u 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/94378/on-continuous-markov-chains-statistics-of-recurrent-states | On continuous Markov chains: statistics of recurrent states
Given a continuous Markov chains (and given the transition rates between the states) I would like to know the following:
1. mean time of permanence for all states.
2. higher order moments (i.e., variance and, possibly, CDF?)
In particular, I am also interes... | {"extraction_info": {"found_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/125396/solve-int-infty-infty-fraceqiy-k-sqrt-lambda-a-iy-sqrt-lambda?answertab=active | # solve $\int_{-\infty}^{\infty}\frac{e^{qiy -K(\sqrt{\lambda -a-iy}-\sqrt{\lambda})}}{a+iy}$?
Is there any way to solve this integral?
$$\int_{-\infty}^{\infty}\frac{e^{qiy -K(\sqrt{\lambda -a-iy}-\sqrt{\lambda})}}{a+iy} dy$$ where $K,\lambda, a$ and $q$ are real numbers and $K>0$, $a>0$, $\lambda > 0$ and $q<0$
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": 13, "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/47905/integers-in-a-triangle-and-differences/47947 | ## Integers in a triangle, and differences
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I read about the following puzzle thirty-five years ago or so, and I still do not know the answer.
One gives an integer $n\ge1$ and asks to place the integers $1,2,\ldo... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/120322/distribute-n-objects-to-k-boxes-such-that-no-box-has-more-than-c-objects-i | # Distribute $N$ objects to $K$ boxes such that no box has more than $c$ objects in it
I'm trying to find a way to calculate a problems such as this: if you have $n$ objects and $k$ indistinguishable boxes, how do you put in $n$ objects such that each box has no more than $C$, where $C \le k$.
For example, I have $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": 56, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/17087/why-is-the-space-of-surjective-operators-open | # Why is the space of surjective operators open?
Suppose $E$ and $F$ are given Banach spaces. Let $A$ be a continuous surjective map. Why is there a small ball around $A$ in the operator topology, such that all elements in this ball are surjective?
-
2
Perhaps it would be more profitable to ask why the nonsurjective... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 53, "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/61315/lie-group-examples/62023 | Lie group examples
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
I'm looking for interesting applications of Lie groups for an introductory Lie groups graduate course. In particular I'd like to hear of non-standard examples that at first sight do not seem to 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": 70, "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/18088/what-symmetry-causes-the-runge-lenz-vector-to-be-conserved/18093 | # What symmetry causes the Runge-Lenz vector to be conserved?
Noether's theorem relates symmetries to conserved quantities. For a central potential $V \propto \frac{1}{r}$, the Laplace-Runge-Lenz vector is conserved. What is the symmetry associated with the conservation of this vector?
-
2
– Dan Dec 21 '11 at 7:19
... | {"extraction_info": {"found_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": 25, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/Numerically_stable | # Numerical stability
(Redirected from Numerically stable)
In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms. The precise definition of stability depends on the context, but it is derived from the accuracy of the algorithm.
An opposite phenomenon ... | {"extraction_info": {"found_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": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/28422/does-the-poincare-series-of-a-coxeter-group-always-describe-a-flag-variety | ## Does the Poincare series of a Coxeter group always describe a “flag variety”?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let $W$ be a Coxeter group and let $P_W(q) = \sum_{w \in W} q^{\ell(w)}$ be its Poincare series. When $W$ is the Weyl group of a si... | {"extraction_info": {"found_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://mathhelpforum.com/math-topics/25946-physics1.html | # Thread:
1. ## Physics1
A hockey puck hits the board with a velocity of 10m/s at an angle of 20deg to the board. It is deflected with a velocity of 8m/s at 24deg to the board. If the time of impact is 0.03s, what is the average acceleration of the puck?
$(2.3 x 10^2m/s^2$ out from the board at an angle of 107deg)
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": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/geometry/120307-area-region.html | # Thread:
1. ## Area of Region
On each side of a unit square, an equilateral triangle of side length 1 is constructed. On each new side of each equilateral triangle, another equilateral triangle of side length 1 is contructed. The interiors of the square and the 12 triangles have no points in common. Let R be the 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": 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/tagged/locally-compact-groups | # Tagged Questions
Locally compact groups are among the main objects of study of abstract harmonic analysis. They arise e.g. in number theory, abstract Fourier analysis, representation theory, Lie theory, operator theory, etc. Their main property is the existence and uniqueness of Haar measure. Please combine with ...... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 122, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/Unitarity | # Unitary operator
(Redirected from Unitarity)
For unitarity in physics, see Unitarity (physics).
In functional analysis, a branch of mathematics, a unitary operator (not to be confused with a unity operator) is a bounded linear operator U : H → H on a Hilbert space H satisfying
$U^*U=UU^*=I \!$
where U∗ is the adj... | {"extraction_info": {"found_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": 10, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/5/how-can-you-prove-that-the-square-root-of-two-is-irrational/16544 | # How can you prove that the square root of two is irrational?
I have read a few proofs that $\sqrt{2}$ is irrational.
I have never, however, been able to really grasp what they were talking about.
Is there a simplified proof that $\sqrt{2}$ is irrational?
-
I can't edit yet, could someone edit "grash" to "grasp"? ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 120, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://mathoverflow.net/revisions/12453/list | ## Return to Answer
1 [made Community Wiki]
I would suggest the approach Tom Apostol takes in his linear algebra book. In chapter 1, after introducing abstract vector spaces, he goes on to Gram-Schmidt, and then immediately to best approximations. At the end of the first chapter, he solves questions like: "find the 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": 7, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathforum.org/mathimages/index.php?title=Four_Color_Theorem_Applied_to_3D_Objects&oldid=33869 | # Four Color Theorem Applied to 3D Objects
### From Math Images
Revision as of 13:42, 13 July 2012 by Pweck1 (Talk | contribs)
(diff) ←Older revision | Current revision (diff) | Newer revision→ (diff)
Four Color Theorem
Field: Graph Theory
Image Created By: [[Author:| ]]
Website: Chroma
Four Color Theorem
This pic... | {"extraction_info": {"found_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": 4, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Randomized_algorithm | # Randomized algorithm
Probabilistic
data structures
Part of a series on
Bloom filter · Quotient filter · Skip list
Random binary tree · Treap Rapidly exploring random tree
Randomized algorithm
Computer science Portal
A randomized algorithm is an algorithm which employs a degree of randomness as part of its logic.... | {"extraction_info": {"found_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": 38, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/07/30/ | # The Unapologetic Mathematician
## Roots of Polynomials I
When we consider a polynomial as a function, we’re particularly interested in those field elements $x$ so that $p(x)=0$. We call such an $x$ a “zero” or a “root” of the polynomial $p$.
One easy way to get this to happen is for $p$ to have a factor of $X-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": 0, "wp_latex": 18, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2008/07/24/the-inclusion-exclusion-principle/?like=1&source=post_flair&_wpnonce=4ca8fc8c32 | # The Unapologetic Mathematician
## The Inclusion-Exclusion Principle
In combinatorics we have a method of determining the cardinality of unions in terms of the sets in question and their intersection: the Inclusion-Exclusion Principle. Predictably enough, this formula is reflected in the subspaces of a vector space.... | {"extraction_info": {"found_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://mathhelpforum.com/algebra/45287-trinomial-factoring-help.html | # Thread:
1. ## Trinomial factoring help
Hello,
I have been learning how to factor trinomials and I am stuck..
2x^2+x-15 = (2x-5)(x+3)
3a^2-2a-5 = (3a-5)(a+1)
Fc^2+17c+14 = (fc+7)(c+2)
To factor these types of problems, is the only way real to just plug in factors and do a full test with foil?? I mean some of 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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/76093?sort=oldest | ## An inequality on Difference of Entropies
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi,
I have the following problem that came up. It is not a homework problem or something similar. I did my simulations and it seems to hold but i was unable to prove 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": 29, "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/255181/irreducible-subvariety-not-cut-out-by-one-equation | # Irreducible subvariety not cut out by one equation
Let $X$ be an irreducible nonsingular algebraic variety. Let $Y$ be an irreducible codimension 1 closed subvariety. An important theorem states that locally $Y$ is cut out by a single equation regular in the neighborhood of a given point. What would be an example wh... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 20, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.physicsforums.com/showthread.php?t=547728 | Physics Forums
## What is an unbiased estimator ??
I do not really understand what is an unbiased estimator during my statistic studies ~~ THANKS ~~
PhysOrg.com science news on PhysOrg.com >> Front-row seats to climate change>> Attacking MRSA with metals from antibacterial clays>> New formula invented for microsco... | {"extraction_info": {"found_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://mathematica.stackexchange.com/questions/11535/stationary-distribution-of-a-transition-matrix | # stationary distribution of a transition matrix
How can I solve the stationary distribution of a finite Markov Chain? In other words, how can I estimate the eigenvectors of a transition matrix?
-
2
Welcome to Mathematica.SE, whynot! Please let us know what you tried. In addition, may I suggest: 1) As you receive he... | {"extraction_info": {"found_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/38472/need-help-understanding-a-topos-theory-proof-any-topos-generated-by-subobjects-o/38483 | ## Need help understanding a topos theory proof (any topos generated by subobjects of 1 in whose subobject lattices are complete and Boolean satisfies AC)
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi all, I'm reading Mac Lane & Moerdijk's book "Sheaves 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": 68, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/211353-optimization-transformation-target-function-conditions.html | # Thread:
1. ## Optimization: transformation of target function and conditions
In a recent microeconomics lecture I was confronted with the following problem:
maxx1, x2, x3 2*sqrt(x1)
s.t.
2*sqrt(x2y)=64
y=2*sqrt(2x3)
x1+x2+x3=112
the professor reformulated the problem without explanation to
maxx1, x2, x3 4x1
s.t.
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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/3276/regularization-and-mean-estimation | # Regularization and Mean Estimation
Suppose I have some i.i.d. data $x_1, \ldots, x_n \sim N(\mu, \sigma^2)$, where $\sigma^2$ is fixed and $\mu$ is unknown, and I want to estimate $\mu$.
Instead of simply giving the MLE of $\mu = \bar{x}$, one could estimate
(1) $\mu = \lambda \mu_0 + (1 - \lambda) \bar{x},$
for ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 29, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/4485/is-this-the-correct-way-to-calculate-mse-from-ss-texttreatments-df | # Is this the correct way to calculate $MSE$ from $SS_{\text{treatment(s)}}$, $df_{\text{treatment(s)}}$, $F$?
As described in a few of my previous questions (here and there), I am interested in deriving summary statistics from statistics reported in the literature.
I would very much appreciate any advice into the 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": 24, "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/100615/given-a-die-what-is-the-probability-that-the-second-roll-of-a-die-will-be-less/100742 | # Given a die, what is the probability that the second roll of a die will be less than the first roll?
If you are given a die and asked to roll it twice. What is the probability that the value of the second roll will be less than the value of the first roll?
-
13
It makes me very sad to see that everyone here is ass... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 62, "mathjax_display_tex": 10, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://en.wikipedia.org/wiki/Differential_equations | # Differential equation
(Redirected from Differential equations)
Not to be confused with Difference equation.
Differential equations
Scope
Classification
Operations
Attributes of variables
Relation to processes
• Difference (discrete analogue)
• stochastic
• Delay
Solutions
Solution topics
Mathematicians
Visualizatio... | {"extraction_info": {"found_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": 9, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/47762/list | ## Return to Answer
2 fixed a typo noted by a reader, used markdown instead of abusing MathJax
I
$\DeclareMathOperator{\Hom}{Hom}\newcommand{\amod}{\mathscr{A}\text{-}{\bf Mod}}\newcommand{\scrA}{\mathscr{A}}\newcommand{\scrE}{\mathscr{E}}\newcommand{\Ab}{\mathbf{Ab}}\DeclareMathOperator{\Lex}{\mathbf{Lex}}\DeclareM... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 80, "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/2192/index?nomenu=1 | There are six dots in a Braille cell. Each dot can be either raised or left blank. A black dot is raised on the paper so you can feel it (circles represent dots that have not been used). A quick calculation should tell you that there are $2^6$ possible arrangements of the six dots. However, some would be difficult to t... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/51992/how-i-calculate-degree-of-the-algebraic-curve | ## How I calculate degree of the algebraic curve?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Let F be algebraically closed field. Let C be a curve in F^n defined as zeroes of polynomials $p_1(x_1,\ldots,x_n),..,p_{n-1}(x_1,\ldots x_n)$. Let us define degr... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 39, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/285882/group-automorphisms-of-the-non-zero-elements-of-a-field | Group automorphisms of the non-zero elements of a field
I would like to know what is $Hom_{Groups}(K^*,K^*)$, at least in the case $K$ is a complete non-archimedean (valued) field. Is this $\mathbb{Z}$?
-
1 Answer
Much bigger than $\mathbb Z$, at least if (as is standard) you mean by “$K^*$” the set of nonzero elem... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/283636/linear-optimization-of-line-under-points | # Linear optimization of line under points.
I have a set of points in two-dimensional space. I'd like to find the line of best fit that minimizes the distance between the line and the points such that the line is below all points. How can I find the slope and intercept of a line that minimizes this distance?
-
Yes, 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cstheory.stackexchange.com/questions/16216/searching-for-the-first-item-satisfying-property-with-penalty-for-every-test | # Searching for the first item satisfying property with penalty for every test
The problem in terms of a step function on integers: A step function of integers is $0$ until $s$ (the "item" in question) and then $1$. That is, $s$ is the first integer that satisfies the property $f(s) = 1$. The only way to find out 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": 42, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/math/27940-riemann-hypothesis-print.html | Riemann Hypothesis
Printable View
Show 40 post(s) from this thread on one page
• February 10th 2008, 07:15 PM
ThePerfectHacker
Riemann Hypothesis
Today I recieved an e-mail from my mathematics advisor (not sure how to call him). He is an expert in complex analysis.
Quote:
I heard today that there will soon be an 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 7, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/287067/y-8-cos8x-32y-with-y0-1-initial-value-problem-diffeq | $y'=(8\cos8x)/(3+2y)$ with $y(0)=-1$ Initial Value Problem: DiffEq
Im told to find the explicit form $y(x)$ from the given differential equation and its initial value. Then find where the solution $x=?$ attain a maximum. What I did was:
$3+2ydy=8\cos 8xdx$ integrated both sides
$3y+y^2=\sin8x+c$
Im stuck because 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": 16, "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/29985/would-the-rate-of-ascent-of-an-indestructible-balloon-increase-as-function-of-it | # Would the rate of ascent of an indestructible balloon increase as function of it's altitude?
Assume a balloon filled with Hydrogen, fitted with a perfect valve, and capable of enduring vacuum (that is to say, it would retain it's shape and so well insulated that the extremes of temperature at high altitudes and in 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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/72851/asymptotic-behaviour-of-the-solution-to-a-certain-pde | ## Asymptotic behaviour of the solution to a certain PDE
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
$\delta M=\beta(x-y)M_y+\mu x(y-1)M_x+\delta y$, where $M(x,y)=\sum_{n=0}^{\infty}{\sum_{k=0}^{\infty}{s_{n,k}x^ny^k}}$ is the generating function for a ce... | {"extraction_info": {"found_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/92867/testing-what-probability-model-to-use/92884 | # Testing what probability model to use
Suppose we have some random variable $X$ that ranges over some sample space $S$. We also have two probability models $F$ and $G$. Let $f(x)$ and $g(x)$ be the probability density functions for these distributions. Does the following quantity $$\log \frac{f(x)}{g(x)} = \log \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": 50, "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/239802/gauss-divergence-theorem | # Gauss divergence theorem
I'm trying to solve the following problem using the Gauss divergence theorem. I have to calculate the Flux through a sphere. The sphere is given as $$x^2 +y^2+z^2==4$$ where as the z is resticted from $$\sqrt{3} \; to \; 2$$ I determined the divergence to $$4z$$ I first tried to use spherica... | {"extraction_info": {"found_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": 6, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cstheory.stackexchange.com/questions/tagged/chernoff-bound | # Tagged Questions
The chernoff-bound tag has no wiki summary.
2answers
96 views
### Chernoff Bounds for settings with limited dependence
Could someone point me to a way of bounding the tail probability of sums of bernoulli variables each generated by the same distribution but the condition of independence is only ... | {"extraction_info": {"found_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://www.physicsforums.com/showthread.php?t=562548 | Physics Forums
## Please explain Dopler effect of light
How can there be any shifting of light frequency due to dopler effect? Frequency is just a fancy way of stating 'wave' or, as depicted on all explanitory diagrams, a sinusoidal wave. Each cycle of the wave represents one part of the total waves measured in a giv... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/100060/convexity-of-the-set-of-gradients-of-a-convex-function | # Convexity of the set of gradients of a convex function
If $\vec{y}_1$ and $\vec{y}_2$ are the gradients of a differentiable convex function $f(x)$ at points $\vec{x}_1$ and $\vec{x}_2$ does there exist a $\nabla f^{-1}( \alpha \vec{y}_1 + (1-\alpha)\vec{y}_2)$ in the domain of $f.$
The forward image of the domain 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": 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/180744/compute-int-frac-sinx-sinx-cosx-mathrm-dx/180746 | # Compute $\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$
I've got troubles in computing the below integral: $$\int \frac{\sin(x)}{\sin(x)+\cos(x)}\mathrm dx$$ I hope it can be expressed in elementary functions. I've tried simple substitution as $u=\sin(x)$ and $u=\cos(x)$ but not so effective the results were.
Any ... | {"extraction_info": {"found_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": 8, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/2523/is-there-a-limit-to-loudness/2525 | # Is there a limit to loudness?
Is there any reason to believe that any measure of loudness (e.g. sound pressure) might have an upper boundary, similar to upper limit (c) of the speed of mass?
-
## 4 Answers
Let's talk about the sound waves in the air first. Physically they are longitudinal waves of pressure. The b... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/84510/irreducibility-of-induced-representation-over-arbitrary-field/84518 | ## Irreducibility of Induced Representation over arbitrary field
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In representation theory of finite groups, there is Mackey test for irreducibility of an induced representation (Serre- Linear Representations of 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": 35, "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/88581/how-do-i-prove-the-following-inequality-involving-exponential-functions | How do I prove the following inequality involving exponential functions
Let $R>2$ be a real number. Then, for any $n\geq 1$, it holds that
$$\frac{ \exp(n R)+ 1}{\exp( n R) - \exp(\pi R/2)} \leq \exp( R/n^2).$$
How do I prove this?
-
2
For $n=1$ the inequality: $$e^R+1\leq e^R(e^R-e^{\pi R/2})$$ is false, because ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 11, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/228754/prove-rmcolb-subseteq-rmnulla/228758 | # Prove : $\rm{col}(B) \subseteq \rm{null}(A)$
Let $A$ be an $m\times n$ matrix and $B$ be a $n\times m$ matrix.
Prove that:
$$AB = 0 \iff \rm{col}(B) \subseteq \rm{null}(A)$$
Here is the problem in my textbook. I just have a simple solution if $B$ is transpose of $A$. But at general case, I don't have result yet.
... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/questions/767/how-to-fairly-select-a-random-number-for-a-game-without-trusting-a-third-party?answertab=votes | # How to fairly select a random number for a game without trusting a third party?
Several people are playing a game with random events and require a way to produce a random number. (Such as dice rolls or a lottery.)
Can this be done such that each player has the power to be reasonably sure that the random number was ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 95, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/differential-geometry/131805-question-jordan-content.html | # Thread:
1. ## A question on Jordan content
If A is Jordan-measurable with Jordan content c(A), $B\subseteq A$ and is of content zero. Prove that A-B is also Jordan-measurable with the Jordan-content equal to c(A). Thanks!
2. I finally proved it. First we prove A-B is Jordan-measurable. This is equivalent to showin... | {"extraction_info": {"found_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": 72, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://stats.stackexchange.com/questions/30162/sampling-for-imbalanced-data-in-regression | # Sampling for Imbalanced Data in Regression
There have been good questions on handling imbalanced data in the classification context, but I am wondering what people do to sample for regression.
Say the problem domain is very sensitive to the sign but only somewhat sensitive to the magnitude of the target. However 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": 4, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://www.haarp.alaska.edu/haarp/mbcalc.html | Search the Site
```
```
The Antenna System
IRI Performance Calculator
Diagnostic Instruments
Glossary of Terms
Site Map
How to Contact HAARP
Privacy Statement
Questions of a technical nature may be submitted via e-mail to:
Page updated January 20, 2008
### Calculation of the Expected Lunar Echo Receive Signal Stre... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "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/mat... |
http://mathoverflow.net/questions/35348/the-difference-between-a-sequential-space-and-a-space-with-countable-tightness/105551 | ## The difference between a sequential space and a space with countable tightness
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi, I have recently encountered these two definitions of a sequential space and a space of countable tightness. And I seem to 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": 23, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.nag.com/numeric/CL/nagdoc_cl23/html/S/s18eec.html | # NAG Library Function Documentnag_bessel_i_nu (s18eec)
## 1 Purpose
nag_bessel_i_nu (s18eec) returns the value of the modified Bessel function ${I}_{\nu /4}\left(x\right)$ for real $x>0$.
## 2 Specification
#include <nag.h>
#include <nags.h>
double nag_bessel_i_nu (double x, Integer nu, NagError *fail)
## 3 ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 34, "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://crypto.stackexchange.com/questions/1119/randomized-oblivious-transfer?answertab=oldest | # Randomized Oblivious Transfer
If we define Oblivious Transfer as following: Alice inputs $(x_0,x_1) \in F^2$, where $F$ is a field, and Bob inputs $b\in\{0,1\}$, then Alice gets a dummy output(for which she knows nothing about b), and Bob gets $x_b$. Now if we use a Random functionality R, which requires no input bu... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 45, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/265821/does-linearity-decompose-down-convex-sums | # Does linearity decompose down convex sums?
I'm doing some convex optimisation where I'm minimising sum function $f(x) = \sum g_i(x)$, where the $g$'s are convex (and hence so is $f$) and the sum is finite.
In doing so it turns out that $f$ is a linear function between any two (global) optima. Apparently $f$ being 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": 13, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/43638/list | ## Return to Question
6 added 537 characters in body
Let $\lambda$ denote a partition of size $n$. Let $$d_{\lambda}= \text{number of distinct parts of } \lambda$$ $$o_{\lambda}= \text{number of odd parts of } \lambda$$ $$f_{\lambda}= \text{number of standard Young tableau of shape } \lambda$$ Given an involution $\p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 56, "mathjax_display_tex": 37, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://physics.stackexchange.com/questions/tagged/definition+metrology | # Tagged Questions
1answer
53 views
### A sphere, a simple object?
In this video, the woman says that a sphere is a pretty simple object. What intrigues me is the use of a sphere for such a calculation. First of all, the sphere wouldn't be perfect as a perfect sphere ...
1answer
97 views
### Does the Kelvin have a ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/tagged/inverse+notation | # Tagged Questions
2answers
84 views
### What does this syntax mean: “$f^{-1} : N_{10} \Rightarrow N_b$ is the inverse of $f: N N_{b} \Rightarrow N_{10}$?”
I'm trying to solve this but I haven't seen syntax like this before. Can someone please explain the syntax? http://i.imgur.com/GO1Ki.png The image is Show that 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": 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/109687/is-it-true-that-the-orbit-space-of-a-free-finite-group-action-on-a-cw-complex-is/109763 | ## Is it true that the orbit space of a free finite group action on a CW-complex is also a CW-complex?
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Suppose a finite group G acts freely and continuously on an n-dimensional CW-complex X. Then can we conclude ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 81, "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/40832/what-are-relativistic-and-radiative-effects-in-quantum-simulation?answertab=votes | # What are relativistic and radiative effects (in quantum simulation)?
I'm reading about Quantum Monte Carlo, and I see that some people are trying to calculate hydrogen and helium energies as accurately as possible.
QMC with Green's function or Diffusion QMC seem to be the best ways to converge on the "exact" soluti... | {"extraction_info": {"found_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/75753?sort=votes | ## Elements of unit modulus in ring generated by root of unity
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
When thinking of an apparently unrelated problem I stumbled upon the following question, which is certainly elementary to many readers of this site. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 44, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/65517/useful-topology-on-space-of-smooth-structures-on-mathbb-r4 | # Useful topology on space of smooth structures on $\mathbb R^4$?
Mathoverflow is intimidating, so I thought I'd ask here first (second). If I don't get any useful answers here in a few days, I'll ask there.
$Q_0$: Is there any use for a topology on the (continuum of) smooth structures on $\mathbb{R}^4$?
$Q_1$: If 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": 9, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathcountsnotes.blogspot.com/ | # mathcounts notes
The best math program for middle school students
## Wednesday, May 15, 2013
### This Week's Work : Week 12 -- for Inquisitive Young Mathletes
Link to the online timed test on questions you mostly got wrong or not fast enough.
(sent through e-mail)
Common Pythagorean Triples:
3, 4, 5 and its deri... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.