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http://gauravtiwari.org/tag/ordered-pair/ | # MY DIGITAL NOTEBOOK
A Personal Blog On Mathematical Sciences and Technology
Home » Posts tagged 'Ordered pair'
# Tag Archives: Ordered pair
## A Trip to Mathematics: Part III Relations and Functions
Read these statements carefully:
‘Michelle is the wife of Barak Obama.’
‘John is the brother of Nick.’
‘Robert 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 21, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/114340/what-does-following-matrix-says-geometrically?answertab=active | # what does following matrix says geometrically
Let $M\subset \mathbb C^2$ be a hypersurface defined by $F(z,w)=0$. Then for some point $p\in M$, I've $$\text{ rank of }\left( \begin{array}{ccc} 0 &\frac{\partial F}{\partial z} &\frac{\partial F}{\partial w} \\ \frac{\partial F}{\partial z} &\frac{\partial^2 F}{\parti... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 60, "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/32011/direct-proof-of-irrationality/32030 | ## Direct proof of irrationality?
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There are plenty of simple proofs out there that $\sqrt{2}$ is irrational. But does there exist a proof which is not a proof by contradiction? I.e. which is not of the form:
Sup... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 93, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/tagged/special-relativity?page=2&sort=active&pagesize=30 | Tagged Questions
The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.
3answers
81 views
How do we measure the range of distant objects despite relativistic effects?
When we observe astronomical objects like distant galaxies there are 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": 22, "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/28720/how-to-get-planck-length/28724 | # How to get Planck length
I know that what Planck length equals to.
1. The first question is, how do you get the formula $$\ell_P~=~\sqrt\frac{\hbar G}{c^3}$$ that describes the Planck length?
2. The second question is, will any length shorter than the Planck length be inaccessible? If so, what is the reason behind... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/advanced-algebra/158100-matrix-question.html | # Thread:
1. ## Matrix Question
Having some problems with this question.
The transformation T in the plane consists of an anticlockwise rotation through $90^{\circ}$ about the origin by a translation in which the point (x,y) is transformed to the point (x+1,y+2).
(a) Show that the matrix representing T is
\begin{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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://cs.stackexchange.com/questions/tagged/lower-bounds | # Tagged Questions
The lower-bounds tag has no wiki summary.
1answer
48 views
### Time complexity in Big O notation for Harmonic series with first k terms missing
Firstly, let's suppose there exists an algorithm where $i$ iterates from $1$ to $n$, spending $\frac{n^2}{i}$ time in each iteration. Thanks to the well ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 36, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/70866/list | ## Return to Question
2 replaced one of the tags
1
# Question on Linear Operators
Let $V$ be a normed infinite dimensional vector space. Let $L: V \longrightarrow V$ be a bounded linear operator. Moreover assume that $L$ is 'locally nilpotent' that is: $$\forall v \in V \quad \exists n \in \mathbf{N}: L^n (v) = 0.$$... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/85441/velocity-field-of-fluid-and-maurer-cartan-form | ## Velocity field of fluid and Maurer-Cartan form?
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Chatting with an engineer, he suggested me to have a look to a certain book in order to understand what fluid mechanics is about (I know nothing about the subjec... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 33, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/39197/most-suitable-metric-for-the-solar-system | # Most suitable metric for the Solar system?
1. If I wanted to solve the Einstein equations for the solar system, which choice of $g_{\mu\nu}$ and $T_{\mu\nu}$ is more suitable?
2. I thought about using a Schwarzschild metric near each planet, but how to connect them?
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## 2 Answers
Solving the Einstein equation 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": 5, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://unapologetic.wordpress.com/2007/05/26/natural-transformations-and-functor-categories/?like=1&source=post_flair&_wpnonce=8cb43e0c56 | The Unapologetic Mathematician
Natural Transformations and Functor Categories
So we know about categories and functors describing transformations between categories. Now we come to transformations between functors — natural transformations.
This is really what category theory was originally invented for, and the ter... | {"extraction_info": {"found_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": 46, "mimetex.cgi": 0, "/images/ma... |
http://asmeurersympy.wordpress.com/2010/05/ | # Aaron Meurer's SymPy Blog
My blog on my work on SymPy and other fun stuff.
## More information on my Google Summer of Code project this year
May 26, 2010
So, as I noted here, I have been accepted into the Google Summer of Code program again this year. I mentioned that my project involved improving the integrator,... | {"extraction_info": {"found_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": 1, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-math-topics/57562-l-1-space-integrable-functions.html | Thread:
1. L-1 space of integrable functions
If f is in L1 and delta > 0, then the L1 norm of f(delta*x)-f(x) goes to zero as delta goes to 1. I have been studying my text for two hours and still really don't understand it. Any thoughts?
By the way, I have some ideas--
If I can show that f is a continuous function ... | {"extraction_info": {"found_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": 22, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/142133/does-this-polynomial-evaluate-to-prime-number-whenever-x-is-a-natural-number/142140 | Does this polynomial evaluate to prime number whenever $x$ is a natural number?
I am trying to prove or disprove following statment:
$x^2-31x+257$ evaluates to a prime number whenever $x$ is a natural number.
First of all, I realized that we can't factorize this polynomial using its square root like $$ax^2+bx+c=a(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": 39, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/58804?sort=newest | ## Ostensibly different products on Ext-groups
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The following is presumably not the greatest generality in which this question makes sense.
1. Given a ring $k$, graded-commutative if it helps, and a Hopf-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": 77, "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/49918/integrate-frac1-sqrt1-x2 | # Integrate $\frac{1}{\sqrt{1 - x^2}}$
I have to calculate $\int \frac{1}{\sqrt{1 - x^2}} \operatorname{d}x$ forwards, using known rules like partial integration or substitution.
What I'm not allowed to do is simply show that $\frac{\operatorname{d}}{\operatorname{d} x} \arcsin x = \frac{1}{\sqrt{1 - x^2}}$, but I do... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 34, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2010/10/19/characters-of-permutation-representations/?like=1&source=post_flair&_wpnonce=55e0e6033e | # The Unapologetic Mathematician
## Characters of Permutation Representations
Let’s take $(\mathbb{C}S,\rho)$ to be a permutation representation coming from a group action on a finite set $S$ that we’ll also call $\rho$. It’s straightforward to calculate the character of this representation.
Indeed, the standard bas... | {"extraction_info": {"found_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/39802?sort=newest | ## Homotopic quotients of simplicial sets as infinity-groupoids
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Suppose $f:X \to Y$ is a function of sets. Then we can take the quotient $X/\text{~}$ by identifying $x \text{~} y$ if and only if $f(x)=f(y)$. Now ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 54, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/1230/whats-keeping-us-from-simply-redefining-avogadros-number-the-mole-as-a-defin | # What's keeping us from simply redefining Avogadro's Number / the Mole as a definite integer?
This might be a question to ask in a Chemistry site, but because there is a lot of talk about redefining many units of measurements in terms of Avogadro's Number / the Mole, I was wondering why we don't just redefine the Mol... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/trigonometry/105485-ok-im-stumpted-tan-cos-2-a.html | # Thread:
1. ## Ok Im Stumpted Tan - Cos^2
Hey I have a problem with some problems with an equation and got stuck when I got to a trig identity hope you can help
$4.6tan(x)-0.46cos^2(x)=50$
2. Originally Posted by Jonnyw2k
Hey I have a problem with some problems with an equation and got stuck when I got to a trig 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/40240/elementary-reference-for-algebraic-groups/40415 | ## Elementary reference for algebraic groups
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I'm looking for a reference on algebraic groups which requires only knowledge of basic material on the theory of varieties which you could find in, for example, Basic ... | {"extraction_info": {"found_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://medlibrary.org/medwiki/Cohomology | # Cohomology
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 medicat... | {"extraction_info": {"found_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... |
http://math.stackexchange.com/questions/1099/mandelbrot-like-sets-for-functions-other-than-fz-z2c/39534 | # Mandelbrot-like sets for functions other than $f(z)=z^2+c$?
Are there any well-studied analogs to the Mandelbrot set using functions other than $f(z)= z^2+c$ in $\mathbb{C}$?
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3
– yasmar May 2 '11 at 0:03
## 11 Answers
A variant on the M-set can be defined in straightforward fashion for any iterated function 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": 48, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathematica.stackexchange.com/questions/tagged/polynomials?sort=votes&pagesize=30 | # Tagged Questions
Questions on the functionality operating on polynomials
6answers
2k views
### Finding real roots of negative numbers (for example, $\sqrt[3]{-8}$)
Say I want to quickly calculate $\sqrt[3]{-8}$, to which the most obvious solution is $-2$. When I input $\sqrt[3]{-8}$ or Power[-8, 3^-1], Mathematic... | {"extraction_info": {"found_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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/53893/nmr-rotating-frame | # NMR rotating frame
I'm reading about a linearly polarized field (in the context of NMR). The field is given by
$${\bf H_{lin}}=2H_1({\bf i}cos(\omega_zt)).$$
This can be created by having a pulse field plus its mirror image; i.e.
$${\bf H_1}=H_1({\bf i}cos(\omega_zt)+{\bf j}sin(\omega_zt)).$$
The mirror image fi... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/192097-question-about-multidimentional-gaussian-integration.html | # Thread:
1. ## Question about multidimentional gaussian integration
Dear all,
I know how to derive a multidimentional gaussian integration like this:
$\int_{-\infty}^{\infty} \mathrm{d} \mathbf{x} ~ \mathrm{exp} \left\{\mathbf{x}^T \mathbf{G} \mathbf{x} + \mathbf{H}^T \mathbf{x} \right\}$
where $\mathbf{x}=\left\{... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/155136-riemann-sums-print.html | # Riemann Sums
Printable View
• September 3rd 2010, 05:08 PM
stobs2000
Riemann Sums
hi this is a Riemann sum q:
Find U, the Riemann Upper Sum for f(x) = x2 on [0,2], using 4 equal sub-intervals
i know that n=0.5 so i thought the upper limit would be 0.5^2+ 1^2+1.5^2+2^2 which gives 7.5 but the answer is 3.75 so cou... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/75989/when-a-permutation-is-not-a-cycle | # When a Permutation is not a cycle
$\sigma = \pmatrix{1&2&3&4&5&6&7&8\\3 &8 &6 &7 &4 & 1 & 5 & 2} = (136)(28)(475)$
I just have a question about terminology. Would it be correct to say that $\sigma$ is not a cycle but $\sigma$ is a product of 3 disjoint cycles?
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8
I believe your last cycle should be (475). Also, ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 5, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/discrete-math/200126-simplify-formula-rate-change-volume.html | # Thread:
1. ## Simplify formula for rate of change of Volume
I need to simplify further the formula for the volume of a cylinder in pdf attached. I also need to interpret it.
Can you give me some hints? thanks
Attached Files
• cylinder.pdf (195.0 KB, 9 views)
2. ## Re: Simplify formula for rate of change of Volume
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/204031-factoring-question.html | # Thread:
1. ## Factoring Question
Hello,
I can't figure out how I should factor this expression.
$x^4 - 18x^2 + 1$
I know the answer is $(x^2 - 4x - 1)(x^2 + 4x - 1)$
But I don't know how it gets to this point. I've tried substituting x squared with y to get this...
$y^2 - 18y + 1$
but this can't really be fac... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 19, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/75131?sort=votes | ## How to detect frequency?
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Let $J$ be an arc in $\mathbb{S}^{1}\subset\mathbb{C}$ (no matter open or closed) and $\alpha\in(0,2\pi)$ be an angle such that $\alpha/\pi$ is irrational. Consider in $\mathbb{S}^{1}$... | {"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": 49, "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/47181/can-we-uniquely-define-a-graph-to-have-the-topology-of-a-polytope-via-proper-edge/47467 | ## Can we uniquely define a graph to have the topology of a polytope via proper edge length selection?
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I'll ask you to consider a situation wherein one has a series of edges for a graph, $(e_1, e_2, ..., e_N) \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": 55, "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/8176/are-newtons-gravity-waves-detectable-by-a-laser-interferometer | Are Newton's gravity waves detectable by a laser interferometer?
Newton's theory of gravity supports "gravity waves" in that moving objects cause changing gravitational fields. For example, two bodies rotating around their center of mass will have a stronger gravitational field when they are longitudinally oriented 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": 31, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/revisions/39255/list | 2 edited tags
1
# Determinant of a sum of a diagonal matrix, a dyadic product matrix, and a Hermitian Toeplitz matrix
Hi
From a physics problem, I am trying to evaluate exactly the following kind of determinant:
G = A + M + N.
A is diagonal M is a product of a column (of 1s) and a row matrix N is a Hermitian Toepl... | {"extraction_info": {"found_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/210300/poisson-process-arrival-probability | # Poisson Process Arrival Probability
Just a quick question regarding two Poisson Processes:
Let $X_t$ and $Y_t$ be two independent Poisson Processes with rate parameters $\lambda_1$ and $\lambda_2$, respectively, measuring the number of customers arriving in stores 1 and 2, respectively. What is the probability that... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://marcofrasca.wordpress.com/2012/06/04/turing-machine-and-landauer-limit/ | # The Gauge Connection
The curious ways to see the World of a theoretical physicist
## Turing machine and Landauer limit
My inactivity period was due to a lack of real news around the World. But I was not inactive at all. My friend Alfonso Farina presented to me another question that occupied my mind for the last 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 5, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/113885/list | Return to Answer
4 deleted 9 characters in body
As a matter of fact, P. L. Chebyshev knew already that for any $\epsilon > \frac{1}{5}$, there exists an $n(\epsilon) \in \mathbb{N}$ such that for all $n\geq n(\epsilon),$
$\pi((1+\epsilon)n)-\pi(n)>0.$
In [2], one can find a short report on the problem of determinin... | {"extraction_info": {"found_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://mathoverflow.net/questions/98466/how-many-points-are-there-on-an-elliptic-curve-reduced-at-a-bad-prime/98469 | ## How many points are there on an elliptic curve reduced at a bad prime?
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Given an elliptic curve $E$ defined over $\mathbb{Z}$, and a prime $p$, I know that Hasse's theorem gives, when $p$ is a good prime, a rel... | {"extraction_info": {"found_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://cs.stackexchange.com/questions/10014/how-can-i-argue-that-3-mathsfsat-leq-p-mathsfindset-is-polynomial-in-time | # How can I argue that $3\mathsf{SAT}\leq_p \mathsf{IndSet}$ is polynomial in time?
Given the reduction $3\mathsf{SAT}\leq_p \mathsf{IndSet}$ as follows:
How can I argue that it's in polynomial time? I understand how the reduction works, but even though it appears rather trivial, I can't explain why it's efficient.
... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://motls.blogspot.com.au/2012/05/psychology-of-dark-matter-denial.html | # The Reference Frame
## Thursday, May 24, 2012
... /////
### Psychology of dark matter denial
Sean Carroll mentioned some developments concerning dark matter that have been discussed on this blog, too. His short text is another example of the fact that his comments are sometimes right, however rare these events ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 6, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/pre-calculus/6624-stuck-one-first-post.html | # Thread:
1. ## stuck on this one - first post
just joined so don't let me down
Can't sort this one:
y = 3x
2y(squared) - xy = 15
Tried substituting y = 3x and x = y/3. I only get half of the right answer using x = y/3 as y = -3 and x= -1. Can't seem to get the full right answer.
Any ideas
Becca.
2. Originally ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/30243/computing-places-over-x-in-f-kx/30348 | ## Computing places over x in F/K(x)
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Let $F$ be a function field of "transcendental degree one" over its full constant field $K$. Let $x \in F \backslash K$. We know the divisor of $(x) = (x) - (1/x)$ in $K(x)$. ... | {"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": 110, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://crypto.stackexchange.com/questions/5966/is-it-possible-to-break-a-hash-based-block-cipher/5968 | Is it possible to break a hash-based block cipher?
Let's define the following block cipher:
$C_n = M_n \oplus H(k + n)$ where $C_n$ is the nth block of ciphertext, $M_n$ is the nth block of plaintext, $H$ is a cryptographic hash function, and $k$ is the secret key.
Decryption can be performed trivially, by computing... | {"extraction_info": {"found_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": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://crypto.stackexchange.com/tags/differential-analysis/hot?filter=year | # Tag Info
## Hot answers tagged differential-analysis
4
### S-box with differential uniformity = 2
There are 256! possible 8x8 S-boxes (i.e., bijective functions from $\{0,1\}^8$ to $\{0,1\}^8$. This is an absolutely enormous number. You couldn't possibly enumerate all of them within the lifetime of the universe. ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/176392-orthogonal-matrices.html | # Thread:
1. ## orthogonal matrices
Show that if A and B are orthogonal matrices, then AB is an orthogonal matrix.
I think I need to show that the columns of A are orthonormal to each other, but I don't know how.
2. Originally Posted by Jskid
Show that if A and B are orthogonal matrices, then AB is an orthogonal ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/calculus/19009-normal-have-two-differing-gradients-one-point.html | # Thread:
1. ## Is it normal to have two differing gradients for one point?
I have an exam tomorrow and part of it will consist of dervitives...
I was given a revision sheet and this is one of the questions:
Find the average rate of change of f(x) = x^3 - 4x^2 + x +2 from x=1 to x=4
So, I found the derivitive: f'(... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://stats.stackexchange.com/questions/4445/model-for-population-density-estimation | Model for population density estimation
A database of (population, area, shape) can be used to map population density by assigning a constant value of population/area to each shape (which is a polygon such as a Census block, tract, county, state, whatever). Populations are usually not uniformly distributed within thei... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/4600/a-basic-question-on-the-derivation-of-the-wave-equation | # A basic question on the derivation of the wave equation
Today I saw the derivation of the wave equation in class, and I did not understand the following step.
We are modeling a uniform-density string as being made up of tiny masses spaced a small amount $h$ apart connected by springs obeying Hooke's law. Let $y_i(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": 37, "mathjax_display_tex": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/number-theory/173518-affine-cipher-encryption.html | # Thread:
1. ## Affine Cipher Encryption
Hi!
Anyone any good with codebreaking?....
Let plaintext be written in the alphabet a, b, . . . , y, z and let ciphertext be
written in the alphabet A, B, . . . , Y, Z. Both alphabets have N = 26 letters.
Consider the affine cipher on digraphs with encryption
E( $\pi$) = 9 ... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/53549/is-there-an-infinite-increasing-sequence-of-primes-with-bounded-second-or-larger | Is there an Infinite increasing sequence of primes with bounded second or larger differences?
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The opposite question is if for any infinite increasing sequence of primes and any $k$ the sequence of the $k$-th order di... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 41, "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/53384/in-noethers-theorem-what-is-a-classical-solution-of-the-equations-of-motion/53388 | # In Noether's theorem, what is a “classical solution of the equations of motion”?
I'm reading a book which states that:
for each generator of a global symmetry transformation, there is a current $j^{\mu}_{a}$ which, when evaluated on a classical solution of the equations of motion $\phi_{cl}$, is conserved. I.e. $\p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 10, "mathjax_display_tex": 4, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://skullsinthestars.com/2009/10/02/the-first-paper-on-invisibility-1902/ | The intersection of physics, optics, history and pulp fiction
## The first paper on invisibility? (1902)
Posted on October 2, 2009 by
When discussing the history of invisibility physics, I typically cite Ehrenfest’s 1910 paper on radiationless motions as the first publication dedicated to the subject. Ehrenfest’s p... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 9, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/52023?sort=newest | ## Is there a Poincare-Hopf Index theorem for non compact manifolds?
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Does Poincare-Hopf index theorem generalizes in any way to non compact manifolds ? In particular, I am interested in the case of a smooth vecto... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 67, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/9239/how-to-find-the-effective-mass-of-a-hole/9241 | # how to find the effective mass of a hole
how can we find out the effective mass of a hole,since a hole in the valence band is just an absence of electron?
-
Conceptually, a hole is a virtual object. That virtual object behaves like a real particle, occupying energy levels, "moving" in the lattice, etc. Mathematica... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/822/is-angular-momentum-truly-fundamental/828 | # Is Angular Momentum truly fundamental?
This may seem like a slightly trite question, but it is one that has long intrigued me.
Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and generally rotational dynamics) can be fully derived from normal (linear) momentum... | {"extraction_info": {"found_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://quant.stackexchange.com/tags/volatility/new | # Tag Info
## New answers tagged volatility
1
### Is my VaR calculation correct?
you need to use the forecast for both the mean and sigma. It should look something like this: forecast = ugarchforecast(modelfit, n.ahead = 1, data = mydata); sigma(forecast); fitted(forecast) Then plug these values into the equation: ... | {"extraction_info": {"found_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/75023/is-this-pleasing-polynomial-irreducible/75028 | ## Is this pleasing polynomial irreducible?
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Let:
$f(x)=x^n+2x^{n-1}+3x^{n-2}+4x^{n-3}+\ldots + (n-1)x^2+nx+(n+1)$.
Is $f(x)$ irreducible?
In light of the answers to this question, I now know that this is true ... | {"extraction_info": {"found_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": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/78910?sort=oldest | Computer algebra system for calculation of characteristic polynomial of sparse matrix
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I have a $n \times n$ matrix, for which i need to calculate the characteristic polynomial. The matrix is over $GF(2)$, and $n \app... | {"extraction_info": {"found_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://mathoverflow.net/questions/39885?sort=newest | ## What spaces have well known horofunctions?
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Following Gromov, take a metric space $(X,d)$ and consider $C(X)/\mathbb{R}$ the set of continuous functions to $\mathbb{R}$ with the topology of uniform convergence ... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/tagged/coulombs-law+dimensions | # Tagged Questions
4answers
501 views
### Why are so many forces explainable using inverse squares when space is three dimensional?
It seems paradoxical that the strength of so many phenomena (Newtonian gravity, Coulomb force) are calculable by the inverse square of distance. However, since volume is determined by 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": 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/27335/matrix-geometry-for-f-strings?answertab=votes | # Matrix geometry for F-strings
A stack of N D-branes has the strange property that the traverse D-brane coordinates are matrix-valued. When the matrices commute, they can be interpreted as ordinary coordinates for N indistinguishable objects. But in general they correspond to something classical geometry doesn't desc... | {"extraction_info": {"found_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/84557/list | 2 edited tags
1
# Is there any literature about inner-replacement rule?
Hello all,
If you have a theorem $\vdash \alpha \rightarrow \beta$ and a theorem $\vdash \gamma$ then if $\alpha$ is a sub-expression of $\gamma$, and this sub-expression has an even number of negations within $\gamma$ (and it is not within a xo... | {"extraction_info": {"found_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://mathhelpforum.com/advanced-algebra/158772-find-basis-subspace-s-r3-spanned.html | # Thread:
1. ## Find a basis for the subspace S of R3 spanned by....
Hi, i am struggling with the idea of basis and dim.
Find a basis for the subspace S of R3 spanned by
{ v1 = (1,2,2), v2 = (3,2,1), v3 = (11,10,7), v4 = (7,6,4) }.
What is dim s ?
2. A basis is a spanning set that is also independent. You are gi... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://physics.stackexchange.com/questions/46316/harmonic-oscillator-and-lorentz-symmetry/46317 | # Harmonic oscillator and Lorentz symmetry
There is a analog between harmonic oscillator $x=\frac{1}{\sqrt{2\omega}}(a+a^\dagger)$ and quantum field $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, which is used to quantize the field operator.
However, one thing confuse me... | {"extraction_info": {"found_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": 5, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://www.reference.com/browse/be+advised | Definitions
# Axiom of choice
In mathematics, the axiom of choice, or AC, is an axiom of set theory. Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if there are infinitely man... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 2, "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://en.wikipedia.org/wiki/Kullback-Leibler_divergence | # Kullback–Leibler divergence
(Redirected from Kullback-Leibler divergence)
Not to be confused with divergence in calculus.
In probability theory and information theory, the Kullback–Leibler divergence[1][2][3] (also information divergence, information gain, relative entropy, or KLIC) is a non-symmetric measure 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": 81, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/58573?sort=votes | ## About a Delzant polytope. (In particular dodecahedron)
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Hi. I have a question.
Definition. Delzant polytope $P$ is a rational convex simple polytope with the smooth condition. Here, "smooth" means that for eac... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://unapologetic.wordpress.com/2007/10/10/monoidal-structures-on-span-2-categories/?like=1&source=post_flair&_wpnonce=39170bc4ce | # The Unapologetic Mathematician
## Monoidal Structures on Span 2-Categories
Now we want to take our 2-categories of spans and add some 2-categorical analogue of a monoidal structure on it.
Here’s what we need:
• An object $\mathbf{1}$ called the unit object.
• For objects $A_1$ and $A_2$, an object $A_1\otimes A_2... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 54, "mimetex.cgi": 0, "/images/ma... |
http://physics.stackexchange.com/questions/45648/euler-equation-of-fluid-dynamics?answertab=active | # Euler equation of fluid dynamics
I'm trying to obtain Euler equation for a perfect fluid in laminar or stationary flow. A particle fluid is submitted at volume forces and surface force. The fist, in my case, is giving only by gravity and the second by pressure. By Newton's second law I obtain:
$$\vec{F}_V + \vec{F}... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 9, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/advanced-algebra/142520-solved-homogeneous-system.html | # Thread:
1. ## [SOLVED] Homogeneous system
If A is a 3x3 matrix and $a_1+2a_2-a_3=0$, then A must be singular.
True since $\begin{bmatrix}<br /> 0\\ <br /> 0\\ <br /> 0<br /> \end{bmatrix}$ and $\begin{bmatrix}<br /> 1\\ <br /> -2\\ <br /> -1<br /> \end{bmatrix}$ are solutions to the equations Ax=b.
2. true since,... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 3, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/revisions/85846/list | ## Return to Question
3 added 2 characters in body
Hello
While working on understanding the space spanned by certain integer relations of real numbers I have come across the following problem. Given $v_1,\dots, v_n \in \mathbb{Z}^m$ I am would like to find $w_1, \ldots w_n \in \mathbb{Z}^m$ such that
$$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": 31, "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/33222/how-do-you-start-self-learning-physics/46347 | # How do you start self-learning physics [closed]
I think this question has its place here because I am sure some of you are "self-taught experts" and can guide me a little through this process.
Considering that :
• I don't have any physics scholar background at all.
• I have a little math background but nothing too... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 3, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/math-topics/164424-classical-mechanics-problem-print.html | # classical mechanics problem
Printable View
• November 25th 2010, 10:23 PM
magus
classical mechanics problem
A ball is thrown with initial speed $v_0$ up an inclined plane. the plane is at an angle $\phi$ and the ball's initial velocity is at angle $\theta$. Choose an axis with x measured up the slope, y normal, 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 41, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/48290/finding-a-simple-basis-having-the-minimal-and-characteristic-polynomial?answertab=oldest | # finding a simple basis, having the minimal and characteristic polynomial
If I have a minimal polynomial ( p irred) $\ p(x)^n$, for example $(x^2+x+1)^3$ a characteristic polynomial $p(x)^2$ , how can i get a simple basis using the rational theorem? i dont understand it
-
5
It is difficult to understand what you ar... | {"extraction_info": {"found_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": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/calculus/189265-differentiate-find-maximum-minimum-turning-point.html | # Thread:
1. ## differentiate and find maximum and minimum turning point
2(x^2/3) + (x^4/5) +11
i differnetiated this to get
4/3(x^-1/3) + 4/5(x^-1/5)
i know then, that i have to set the differentiated formula = 0. Please help with what i have to do next.
Thanks
2. ## Re: differentiate and find maximum and minimu... | {"extraction_info": {"found_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://mathhelpforum.com/pre-calculus/38464-finding-center-conic-sections.html | # Thread:
1. ## Finding the center of conic sections
Hey guys, just ran across this question on a homework:
"Find the center of the conic section whose equation is: A x ²+B xy +C y ²+D x +E y +F=0"
How do I find them without any numbers in each term? Is there a general formula to solve for the center like -b/2a?
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": 15, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/11558/taylor-series-of-a-complex-function-that-is-not-holomorphic/11565 | ## Taylor series of a complex function that is not holomorphic
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I want to create Taylor series of a complex function that has complex conjugate in it. Obviously I cannot do a total derivative but derivations over ... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/4456/how-do-you-synthesize-a-probability-density-function-pdf-from-equally-weighted | # How do you synthesize a probability density function (pdf) from equally weighted price data?
What I'm working with: I have a collection of prices that has very few to no repeating values (depending on the look back period) ie each price value is unique, some prices are clustered and some can be spread apart by great... | {"extraction_info": {"found_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://catalog.flatworldknowledge.com/bookhub/reader/128?e=fwk-redden-ch01_s04 | # 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": 201, "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/m... |
http://physics.stackexchange.com/questions/31192/lorentz-transformations-of-the-polarization-vector | # Lorentz transformations of the polarization vector
Let $\bf{n}'$ be a unit vector in the direction of a wavevector in the plasma rest frame and $\bf{B'}$ be a unit vector along the magnetic field in the plasma rest frame. The electric field of a linearly polarized electromagnetic wave is directed along the unit vect... | {"extraction_info": {"found_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://physics.stackexchange.com/questions/24409/looking-for-references-about-operator-mixing-and-anomalous-dimensions?answertab=oldest | # Looking for references about “operator mixing” (and anomalous dimensions)
I am looking for some pedagogic references about the idea of "operator mixing" and its associated concept about when anomalous dimension has to be thought of as a matrix.
For example this idea is slightly touched upon in this article though 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": 6, "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/showpost.php?p=3795929&postcount=5 | View Single Post
Quote by kai_sikorski If you know that the realization is in A, then all you don't know is if step 5 was -1, or 1. You know everything else. Yes you can add this set to F4, but that doesn't mean that the stochastic process will go right 5 times. It means that, you're now allowed to 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": 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/9400/induced-emf-of-a-spinning-metal-rod | # Induced EMF of a spinning metal rod [closed]
Hey everyone, I'm currently taking an Eletricity and Magnetism course and I'm having dificulty answering this problem. I've gone to my tutor, but sadly, he hasn't taken E+M for a while now and couldn't recall off the top of his head how to go about solving this. We went 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": 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/21336/what-determines-color-wavelength-or-frequency | # What determines color — wavelength or frequency?
What determines the color of light -- is it the wavelength of the light or the frequency?
(i.e. If you put light through a medium other than air, in order to keep its color the same, which one would you need to keep constant: the wavelength or the frequency?)
-
## ... | {"extraction_info": {"found_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/234115/find-the-norm-of-an-operator-on-ell-2?answertab=oldest | # Find the norm of an operator on $\ell_2$
Let $(x_n) \subset \ell_2$ and let operator $L:\ell_2\to \mathbb R$ be defined by:
$\displaystyle L((x_n)) := \sum_{n=1}^{\infty} \frac{x_n}{\sqrt{n(n+1)}}$.
Find the norm of L.
-
Are you assigning homework to us? Please don't post in the imperative and without showing 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": 11, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/44428-reciprocal-opposites.html | # Thread:
1. ## reciprocal opposites
If two nonzero numbers are opposites of each other, are their reciprocals opposites of each other? Why or why not?
2. Hello,
Originally Posted by renmail2000
If two nonzero numbers are opposites of each other, are their reciprocals opposites of each other? Why or why not?
Let n 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": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathoverflow.net/questions/65491/voronoi-cell-of-lattices-with-the-same-profile | ## Voronoi cell of lattices with the same profile.
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
Definition 1. Given a body $V$ in $\mathbb R^n$, the function $$p_V(r)=\mathop{\rm vol} [V\cap B_r(0)]$$ will be called profile of $V$.
Definition 2. Define Vor... | {"extraction_info": {"found_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": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/156226/show-that-operatornameinta-cap-b-operatornameinta-cap-operatornam | # Show that $\operatorname{int}(A \cap B)= \operatorname{int}(A) \cap \operatorname{int}(B)$
It's kind of a simple proof (I think) but I´m stuck!
I have to show that $\operatorname{int} (A \cap B)=\operatorname{int} (A) \cap \operatorname{int}(B)$.
(The interior point of the intersection is the intersection of the 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": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathhelpforum.com/algebra/81653-staggering-algebra-problem.html | # Thread:
1. ## A staggering algebra problem.
x+(300-2x)+(170-x)+(150-x)=500
Need help with this problem. I know the solution is 200 but do not know how to achieve it.
2. Originally Posted by GeoBlockage
x+(300-2x)+(170-x)+(150-x)=500
Need help with this problem. I know the solution is 200 but do not know how to 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": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://en.wikipedia.org/wiki/Symbolic_logic | # Mathematical logic
(Redirected from Symbolic logic)
Mathematical logic (also symbolic logic, formal logic, or, less frequently, modern logic) is a subfield of mathematics with close connections to the foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the ma... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://math.stackexchange.com/questions/172688/calculating-a-number-when-its-remainder-is-given?answertab=oldest | # Calculating a number when its remainder is given
I am having difficulty solving the following problem:
Marge has n candies , where n is an integer between 20 and 50.If marge divides the candies equally among 5 children she will have 2 candies remaining . If she divided the candies among 6 children she will have 1 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": 89, "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/tagged/fuchsian-groups | ## Tagged Questions
2answers
241 views
### finite index subgroup of a fuchsian group
Given G, a fuchsian group and a finite sub set A of G. Does there exist a finite index subgroup H in G such that inter section of A with H is empty?
1answer
77 views
### Fundamental domain for subgroup of fuchsian Schottky group.
... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 35, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/68885/mathematica-package-for-obtaining-hypergeometric-function | Mathematica package for obtaining hypergeometric function
Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
In my current research in electromagnetics I am encountering integrals of the form $$\int_0^\infty dt J_0( r t) \frac{\exp(-h \sqrt{t^2 - a^2})}{\sqrt{t^2 - 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": 5, "mathjax_display_tex": 3, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/mat... |
http://mathhelpforum.com/number-theory/119938-how-do-you-find-last-digit-number-using-fermats-little-theorem-print.html | # How do you find the last digit of a number using Fermat's Little Theorem
Printable View
• December 11th 2009, 01:45 PM
steph3824
How do you find the last digit of a number using Fermat's Little Theorem
For example, what is the last digit of 17^(3241)? It would help a ton if someone could show how to solve this usin... | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 20, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://mathoverflow.net/questions/91174/on-unitary-fractions | ## On unitary fractions
### Remember to vote up questions/answers you find interesting or helpful (requires 15 reputation points)
My apologies if the question has already been discussed somewhere else, I did not found anything related to unitary fractions with the search tool...
It is a nice exercise for high-school... | {"extraction_info": {"found_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://quant.stackexchange.com/questions/7147/derivation-of-itos-lemma?answertab=active | # Derivation of Ito's Lemma
My question is rather intuitive than formal and circles around the derivation of Ito's Lemma. I have seen in a variety of textbooks that by applying Ito's Lemma, one can derive the exact solution of a geometric Brownian Motion. So, if one has
$dS = a(S,t)dt + b(S,t)dZ$
the first part on 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": 10, "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/43523/does-a-magnetic-field-have-gravity?answertab=active | # Does a magnetic field have gravity?
Re-reading http://physics.stackexchange.com/a/33156/5265; I find myself thinking if light, being EM in the humanly visible spectrum, may possess gravity - does a magnetic field also possess gravity?
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## 1 Answer
Per wikipedia, the electromagnetic tensor $F^{\mu \nu}$ contribut... | {"extraction_info": {"found_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://www.sagemath.org/doc/reference/plane_curves/sage/schemes/elliptic_curves/ell_local_data.html | # Local data for elliptic curves over number fields¶
Let $$E$$ be an elliptic curve over a number field $$K$$ (including $$\QQ$$). There are several local invariants at a finite place $$v$$ that can be computed via Tate’s algorithm (see [Sil2] IV.9.4 or [Ta]).
These include the type of reduction (good, additive, mult... | {"extraction_info": {"found_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": 25, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/ma... |
http://math.stackexchange.com/questions/148134/concrete-examples-of-2-categories/148138 | # Concrete examples of 2-categories
I've been reading some of John Baez's work on 2-categories (eg here) and have been trying to visualize some of the constructions he gives.
I'm interested in coming up with 'concrete' examples of 2-categories. As an example of what I don't mean, I know that the category Cat forms 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": 169, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/m... |
http://math.stackexchange.com/questions/573/varying-definitions-of-cohomology | # Varying definitions of cohomology
So I know that given a chain complex we can define the $d$-th cohomology by taking $\ker{d}/\mathrm{im}_{d+1}$. But I don't know how this corresponds to the idea of holes in topological spaces (maybe this is homology, I'm a tad confused).
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One can compute (co)homology of different... | {"extraction_info": {"found_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... |
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