content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
A plausible positivity
up vote 4 down vote favorite
2
After getting stuck with the previous positivity (it probably sounds too complex), I would like to give a version of the problem which is of most interest to me.
Consider a sequence of real numbers $a_1,a_2,\dots,a_n,\dots$ with absolute values bounded above by th... | 5 | [
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0.05322265625,
0.04345703125,
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0.008056640625,
0.0142822265625,
0.06640625,
0.0859375,
-0.03369140625,
-0.0037689208984375,
0.09814453125,
-0.0319... | 37,500 | 37500 | |
Outer automorphisms of Borel subgroup
up vote 3 down vote favorite
Let $B$ be the group of upper triangular $n$-by-$n$ matrices of determinant $1$ over a finite field $F$. What is the group of outer automorphisms of $B$? More generally, what are outer automorphisms
of the Borel subgroup of a finite Chevalley group?
g... | 4 | [
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0.07568359375,
-0.004058837890625,
... | 37,501 | 37501 | |
mad hatter practice problems
February 29th 2008, 05:07 PM
jmmsan
mad hatter practice problems
i'm going over same previous problems from the mad hatter math contest, and i need help with a few.
28. Two congruent 30-60-90 triangles are placed so that they overlap partly and their hypotenuses coincide. If the ... | 4 | [
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-0.004974365234375,
-0.0849609375,
-0.07... | 37,502 | 37502 | |
Are there any finitely generated artinian modules that are not notherian?
up vote 4 down vote favorite
3
It is well known that for rings, Artinian implies Noetherian (the famous Hopkins–Levitzki theorem) and it is also well known that there are Artinian modules which are not Noetherian. A simple example
can be found i... | 5 | [
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0.03491210937... | 37,503 | 37503 | |
Linear algebra inequality
up vote 0 down vote favorite
I'm wondering (hoping) if an inequality is true. Please can anyone help me?
Let $V$ be a complex vector space $dim_{\mathbb{C}}(V)=n$ with a hermitian scalar product $h$. Let $v,a, b \in V$.
Is it true that
$(h(v,v)h(a,a)-{|h(v,a)|}^{2})(h(v,v)h(b,b)-{|h(v,b)|}... | 5 | [
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0.028564453125,
0.06884765625,
0.048583984375,
-0... | 37,504 | 37504 | |
polynomial maps
up vote 4 down vote favorite
1
A prolongation of the question composition-of-polynomial-functions-which-gives-the-identity: Let $f_1,\ldots,f_n, g_1,\ldots, g_n$ be polynomials in $\mathbb{Q}[X_1,\ldots,X_n]$ such that if $g=(g_1,
\ldots,g_n)$ then $f_i(g(x_1,\ldots,x_n))=x_i$ for all $i=1,\ldots,n$. D... | 5 | [
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0.0260009765625,
-0.03173828125,
0.0111694... | 37,505 | 37505 | |
Separable Differential Equations-Please help!
September 22nd 2008, 02:41 AM #1
Newbie
Joined
Nov 2007
Posts
14
Separable Differential Equations-Please help!
I've got a few of these separable differential questions to ask. The thing I'm most confused about is what to do with the constant when you are give... | 5 | [
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0.03369140625,
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-0.02294921875,
-0.05078125,
-0.01940917968... | 37,506 | 37506 | |
volume enclosed by spheres
Find the volume enclosed by the spheres $x^{2}+y^{2}+z^{2}=9$ and $x^{2}+y^{2}+(z-2)^{2}=4$
If we use spherical coordinates $(\rho,\theta,\phi)$, the spheres are thus $\rho=3$ and $\rho=4\cos\theta$. We see our volume is bounded by $\rho=3$ for $0\le\theta<\arccos\frac{3}{4}$ and $\rho=4\
co... | 5 | [
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0.02404785156... | 37,507 | 37507 | |
Is this Problem solvable as written?
September 8th 2012, 08:43 AM #1
Newbie
Joined
Sep 2012
From
Indiana
Posts
2
I'm normally not bad at word problems. This problem comes from a take home test my instructor gave us Tuesday.
The problem reads:
A boat takes five hours to move upstream against ... | 4 | [
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-0.009338378... | 37,508 | 37508 | |
Finding coefficients using asymptotic methods
March 4th 2010, 06:06 PM #1
Finding coefficients using asymptotic methods
The ordered bell numbers can be defined by the power coefficients
$\frac{1}{2-e^z} = \sum_{n=0}^{\infty} \frac{b(n)}{n!} z^n$ which is convergent in a neighbourhood of z=0.
Determine t... | 5 | [
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0.0245361328125,
-0.0033111572265625... | 37,509 | 37509 | |
expoential problem
December 3rd 2008, 09:17 PM
Steph07
expoential problem
Given: There are 7 billion, that is, 7*10^9
people on Earth. If a bird flu virus starts
with one person and within 5 days two
people are infected, then each of those two
people in 5 days infects 2 people each,
and so on... | 4 | [
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The physics of Michael Jackson’s moonwalk
Was the moonwalk fake? No, not the Apollo landings. I am talking about Michael Jackson’s moonwalk. You got to admit, he had a big impact on a lot of stuff and this is my way to give him respect –
physics.
I am sure you know about the moonwalk. Maybe you can even do the dance m... | 4 | [
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0.1513671875,
-0.0... | 37,511 | 37511 | |
Mean Curvature
May 18th 2013, 11:02 AM #1
Newbie
Joined
Dec 2011
Posts
9
Mean Curvature
On page 256 http://zakuski.utsa.edu/~jagy/papers/Michigan_1991.pdf there is a formula for the mean curvature of a level set of a function. Im interested in the case n=3. How do you prove this
formula? I can prove ... | 5 | [
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... | 37,512 | 37512 | |
fractions and powers
November 17th 2008, 01:59 AM #1
Newbie
Joined
Nov 2008
Posts
1
fractions and powers
If a fraction is in a bracket and is raised by the power of another fraction how would you evaluate it?
e.g (15/18)2/3 the 2/3 obviously raised as a power
Just looking for the rule as I can'... | 4 | [
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0.04150390625,
0.0966796875,
0.076171875,
-0.04052734375,
0.06640625,
-0.064453... | 37,513 | 37513 | |
mathschallenge.net
Polynomial Roots
Problem
Let $P(x) = x^n + c_{n-1}x^{n-1} + ... + c_{2}x^2 + c_{1}x + c_0$, where each of the coefficients, $c_{k}$, are integer. Prove that the roots of the equation $P(x) = 0$ will either be irrational or
integer.
Solution
It is clear that irrational roots exist. For example, $P... | 4 | [
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Statement of consistency in Godel's second incompleteness theorem
up vote 3 down vote favorite
1
This is a question from Stefan Bilaniuk's very good free online book A Problem Course in Mathematical Logic:
Problem 18.6. Suppose $\Sigma$ is a recursive set of sentences of LN. Find a sentence of LN, which we'll denote ... | 5 | [
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0.0068054199... | 37,515 | 37515 | |
Uniqueness in Composition of Polynomials
up vote 9 down vote favorite
The following situation came up in my research:
Suppose two functions $f$ and $g$ map $[0,\infty)$ to (a subset of) itself. The function $f$ is linear and $g$ is quadratic, but $g$ is one-to-one on the interval $[0,\infty)$.
My conjecture/desired ... | 5 | [
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0.040283203125,
0.03051757812... | 37,516 | 37516 | |
Random permutations of Z_n
up vote 21 down vote favorite
6
In http://www.springerlink.com/content/y19u81675243r237/fulltext.pdf, the author states the following without proof (equation 3.1):
"Consider a random permutation $\pi$ of $\mathbb{Z}_n$. What is the probability that $\pi(i+1)−\pi(i) \mod{n} < n/2$ for all $i... | 5 | [
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0.07568359375,
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0... | 37,517 | 37517 | |
Prove: every set with an infinite subset is infinite
March 31st 2009, 02:05 PM
noles2188
Prove: every set with an infinite subset is infinite
Prove that every set that has an infinite subset is infinite.
Also, prove that every subset of a finite set is finite.
March 31st 2009, 02:12 PM
Plato
March 31st 200... | 4 | [
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-0.07... | 37,518 | 37518 | |
Fraction beginner (or refresher)
June 11th 2008, 07:11 PM
mdudley
Fraction beginner (or refresher)
I have this problem: 3/4x - 5 = 2/3x
I do not know what to do after I do this:
3/4x - 5 + 5 = 2/3x + 5
3/4x = 5 2/3x
Do I take the 5 and mulitply it with the 2 and the 3 to get
10/15x to lo... | 4 | [
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0.1337890625... | 37,519 | 37519 | |
posterior probability question
December 24th 2008, 10:30 PM #1
Newbie
Joined
Dec 2008
From
Riyadh
Posts
6
hi
in the attachment is the question
I have problem solving it
from question I just knew the Prior Probability for that their claim correct is =0.2 and not correct =0.8
after he di... | 5 | [
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0.08154296875,
-0.028564... | 37,520 | 37520 | |
Math Help
February 10th 2008, 02:08 AM #1
Member
Joined
Jan 2008
Posts
154
identity
How do you prove the following: Given the direction cosines of two lines $\cos \alpha, \ \cos \beta, \ \cos \gamma$ and $\cos \alpha ', \cos \beta ', \cos \gamma ',$, then the cosine of the angle
$\theta$ between the... | 4 | [
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... | 37,521 | 37521 | |
Related Rates Problem
January 17th 2011, 08:19 PM
onanyc
Related Rates Problem
Let ABC be a right triangle with fixed hypotenuse, c= 10 inches. If x (the angle at vertex A) is increasing at a rate of 4pi radians/min, find the rate at which a (the side opposite A) is
increasing at the instant that x = pi/3 ra... | 4 | [
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0.07128... | 37,522 | 37522 | |
Prove Solution to PDE Vanishes
January 31st 2010, 04:29 PM
lvleph
Prove Solution to PDE Vanishes
I am not getting anywhere on this problem
Let $u$ be a solution of
$<br /> a(x,y)u_x + b(x,y)u_y = -u<br />$
of class $C^1$ in the closed unit disk $\Omega$ in the $xy$-plane. Let $a(x,y)x + b(x,y)y>0$ on... | 4 | [
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-0.0301513671875,
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Sum of Unit Fractions
Date: 07/17/2001 at 20:28:27
From: Candyce
Subject: Java programing class
Suppose that p/q is a fraction in lowest terms such that
1/(n+1) < p/q < 1/n for some positive integer n. Show that
(p/q) - (1/(n+1)) is a fraction which in its lowest terms has
numerator less than p. Hence by induction, ... | 4 | [
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0.043212890625,
0.056884765625,
0.1088... | 37,524 | 37524 | |
Gaussian Periods
up vote 3 down vote favorite
1
I attempted to get some information on this from MSE, but did not even receive a comment, so i'm trying my luck here:
Let p be an odd prime number and $p-1=m d$ a decomposition into positive factors. Then there is a unique cyclic extension $K_d/\mathbb Q$ of degree d ra... | 5 | [
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... | 37,525 | 37525 | |
Exploring i
Date: 03/16/98 at 04:21:12
From: Matthew Lilley
Subject: i^0 and i^2
I have been reading about imaginary numbers on the Internet as I am
interested in Fractals, and was wondering whether i^0 is 1. I have
asked my maths teachers at school, and none of them know, but they
all seem to think it isn't one.
A... | 4 | [
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-0.044677734375,
-0.087890625,
-0.0607... | 37,526 | 37526 | |
Cardinal number exercise
March 28th 2008, 11:53 PM
Jameson
Cardinal number exercise
5.10 Exercise: Give examples of infinitely many infinite sets no two of which have the same cardinal number.
-------------
My text defines "countably infinite" to be a set that is countable but not infinite. Also it defin... | 5 | [
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... | 37,527 | 37527 | |
Having Trouble Solveing Equalities with Variables on Each Side
EDIT: One more problem I'm having with fuctions... solve: f(2/3) = (x^2+3)/(x-5) having a hard time here
Last edited by emximer; September 18th 2008 at 04:02 PM.
I'll do the second rational equation ... you try the first one after I show you how ... $\fra... | 4 | [
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0.... | 37,528 | 37528 | |
How to multiply algebraic fractions?
October 22nd 2012, 08:32 AM #1
Junior Member
Joined
Jul 2012
From
London
Posts
57
How to multiply algebraic fractions?
x+1/3 * 3x+3/2
As I would do with a normal fraction (I was told to treat algebraic fractions as normal ones) I would multiply the numerator ... | 4 | [
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0.0206298828125,
-0.... | 37,529 | 37529 | |
Show a solution satisfies the DE
hey . i need the solution :
1- y‘= 1+y^2 . y= tan (x+c)
2- y‘‘+2y‘+10y=0 . y= a cos pi x + b sin pi x
3- y‘‘‘= cos x . y= - sin x + ax^2 + bx + c
| 4 | [
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0.019653320312... | 37,530 | 37530 | |
second order differential equation for IVP
1. May 22nd 2011, 08:52 AM #1
2. May 22nd 2011, 09:34 AM #2
What the hint is tell you is notice that
$\frac{2}{x}y'-\frac{2}{x^2}y=\frac{d}{dx}\left( \frac{2}{x}y\right)$
So using this identity we get that
$\frac{d}{dx}(y')=\frac{d}{dx}... | 4 | [
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0.06982421875,
-0.027587... | 37,531 | 37531 | |
Motion of Charged Particle Question
May 15th 2008, 02:16 PM #1
Member
Joined
Sep 2007
Posts
140
Motion of Charged Particle Question
"Two electrons are held, at rest, 1.0x10^-12m apart, then released. With what kinetic energy and speed is each moving when they are a "large" distance apart."
I need he... | 5 | [
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0.03295898... | 37,532 | 37532 | |
Why is it important that partial derivatives commute?
up vote 17 down vote favorite
9
I am asking this in the context of differential geometry (specifically Riemannian).
When the Levi-Civita Connection is defined, we require that the torsion tensor is 0, which in local coordinates translates to the requirement that $... | 4 | [
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0.08642578125... | 37,533 | 37533 | |
2logan = loga18 + loga ( n - 4 )
May 23rd 2010, 08:11 AM #1
Junior Member
Joined
Nov 2009
Posts
28
2logan = loga18 + loga ( n - 4 )
Given that:
2logan = loga18 + loga ( n - 4 )
find the possible values of n.
>>how do i get to logan^2 = loga 18(n-4)
is it correct that
2logan = 2 l... | 4 | [
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0.048095703125... | 37,534 | 37534 | |
evaluate the integral using FTC
April 13th 2009, 10:45 AM #1
Junior Member
Joined
Oct 2008
Posts
34
evaluate the integral using FTC
∫10 (e^(-9x)) / (e^(-9x) + 6)) dx
8
Evaluate the integral using the fundamental theorem of calculus.
I don't know how to do rational numbers, i know that it is... | 5 | [
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0.091796875,
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-0.046875,
0.0095214... | 37,535 | 37535 | |
Math Help
March 4th 2012, 03:13 PM #1
cube
Each face of a cube is given a single narrow stripe painted from the center of
one edge to the center of its opposite edge. The choice of the edge pairing ismade at random and independently for each face. What is the probability thatthere is a continuous stripe enc... | 4 | [
0.0235595703125,
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simplify
I need to simplify 2 expressions: a) $\frac{7}{(x-4)(x-4)}$ b) $\frac{-3\sqrt{x-2}}{2(x-2)^2}$
Are you meant to use index laws? If so then note: a) $\frac{7}{(x-4)(x - 4)} = \frac{7}{(x-4)^2} = 7 (x - 4)^{-2}$ (the last is a debatable simplification). b) $\sqrt{x - 2} = (x - 2)^{1/2}$. Now use
the fact that $... | 4 | [
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converters
Analog-Digital Converters
What do you need to know to understand this topic?
• Basic electronics
• Digital representation
Sections
What is an analog-digital converter?
An Analog-Digital Converter (ADC) is a widely used electronic component that converts an analog electric signal (usually a voltage)... | 4 | [
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Circumradius and inradius.
July 7th 2010, 08:35 PM
earthboy
Circumradius and inradius.
prove that for any triangle ,R>= 2r,where R and r are the circumradius and inradius of the triangle respectively.
post in different proofs (Hi)
July 7th 2010, 09:12 PM
Also sprach Zarathustra
Not standard way...
... | 4 | [
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-0.003829956... | 37,539 | 37539 | |
Vopenka's Theorem on L(A) and Large Cardinals from Weaker Assumptions?
up vote 6 down vote favorite
3
I know that sometime ago Vopenka proved this:
Theorem: Assume there is a strongly compact cardinal. Then for any set $A$, $V \neq L(A)$.
Can we get by with a consistency-wise strictly weaker assumption?
Namely, cal... | 4 | [
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0.0549... | 37,540 | 37540 | |
Geometric sequence question.
September 24th 2012, 06:51 AM #1
Newbie
Joined
Sep 2012
From
The Planet Earth
Posts
7
Geometric sequence question.
The first term of a finite geometric series is 6 and the last term is 4374. The sum of all terms is 6558. Find the common ratio and the number of terms in th... | 4 | [
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-0.09326171875,
... | 37,541 | 37541 | |
Unit Vectors
Date: 07/02/2002 at 17:41:08
From: J. Smith
Subject: Unit Vectors.
I am trying to solve a math problem that I truly do not understand.
The problem reads:
"Find the two unit vectors that are collinear with each of the
following vectors. (a) vector A = (3, -5)"
That's the first question in this problem,... | 4 | [
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-0.04272... | 37,542 | 37542 | |
Rusty on my math
August 27th 2009, 07:15 PM #1
Junior Member
Joined
Feb 2009
Posts
31
Rusty on my math
If someone could step me through how to do the following equation again, it would be greatly appreciated. Hard for me to get back into the swing of things again, LOL!! The equation is as follows:
I... | 4 | [
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0.0219726... | 37,543 | 37543 | |
Combinatorial distance ≡ Euclidean distance
up vote 8 down vote favorite
3
Definition: A polytope has property X iff there is a function f:N^+ → R^+ such that for each pair of vertices v[i], v[j] the following holds:
dist[euclidean](v[i], v[j]) = f(dist[combinatorial](v[i], v[j]))
with dist[combinatorial](v[i], v[j]... | 4 | [
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0.0186767578125,
0.0302734375,
0.... | 37,544 | 37544 | |
A very annoying Inequality
November 9th 2008, 10:58 AM #1
Junior Member
Joined
Nov 2008
Posts
53
A very annoying Inequality
Can anyone help me with this question:
Show that if f is continuous on the closed interval [0,1] then,
[IMG]file:///C:/DOCUME%7E1/OWNER%7E1.UNC/LOCALS%7E1/Temp/moz-screens... | 5 | [
0.042724609375,
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0.0703125,
0.00933837890625,
0.0279541015625,
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0.062255859375,
0.09521484375,
0.07861328125,
-0.040771484375,
-0.001739501953125,
-0.00506591796875,
-0.... | 37,545 | 37545 | |
Intersection of two sphere
November 4th 2010, 08:06 PM #1
Junior Member
Joined
Oct 2008
Posts
65
Intersection of two sphere
Fid the constant c such that at any point of intersection of the two shpere
(x - c)^2 + y^2 + z^2 = 3 and x^2 + (y - 1)^2 + z^2 = 1
the corresponding tangent plane will be... | 4 | [
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0.00750732421875,
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-0.011... | 37,546 | 37546 | |
Math Help
I cant calculate this limit correctly... thank you very much for your help
Last edited by xxlvh; November 9th 2009 at 04:21 PM.
thanks for the help but your answer is wrong... you answered for the limit of one multiplier...but you got n multipliers...so its not that simple...but thanks anyway
nevemind I s... | 5 | [
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-... | 37,547 | 37547 | |
Where does the 2 go?
June 12th 2013, 03:36 AM
alyosha2
Where does the 2 go?
$\int \frac{2}{(4u^2 + 1)} du$
$s = 2u$
$= \int \frac{2}{(s^2 + 1)} ds$
$= 2 \int \frac{1}{(s^2 + 1)} ds$
$= tan^{-1} (2u)$
where does the 2 go?
June 12th 2013, 03:42 AM
chiro
Re: Where does the 2 go?
Hey... | 4 | [
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0.0308837890625,
0.0114746093... | 37,548 | 37548 | |
Why doesn't the power rule work with exponential functions?
Well, it's all in the title.
Any help is appreciated!
Re: Why doesn't the power rule work with exponential functions?
No, it's not!
Are you referring to the derivative of a constant power?
If so, why on earth would they be the same?!?... | 5 | [
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0.08447265625,
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0.06103515625,
0.07666015625,
0.0260009765625,
-0.05859375,
0.041015625,
... | 37,549 | 37549 | |
Lifespan Probability
Date: 03/26/99
From: Anonymous
Subject: Probability that a general pop will live past 85
My question is:
It is estimated that the probability that the general population will
live past their 85th birthday is 5.4%. Out of a sample of 600 people,
what is the probability that fewer than 30 will li... | 5 | [
0.052490234375,
0.0830078125,
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0.027099609375,
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0.06396484375,
-0.05419921875,
0.02294921875,
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0.038330078125,
-0.0030059814453125,
0.0135498046875,
0.03466796875,
-0.099609375,
-0.01586... | 37,550 | 37550 | |
Just Beatty It
[This is the 6th post in the current series about Wythoff's game: see posts #1, #2, #3, #4, and #5. Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the
comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show ... | 5 | [
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0.0274658203125,
... | 37,551 | 37551 | |
Finding Cartesian equation of parametric surface.
October 6th 2009, 06:37 PM
DairyDude
Finding Cartesian equation of parametric surface.
I'm a little confused with this problem.
Find the Cartesian equation of the parametric surface: [2cos(t)cos(s), 3sin(s), sin(t)cos(s)]
Find eqn. of the tangent plane ... | 5 | [
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0.05908203125,
0.029296875,
-0.03271484375,
-0.029296875,
-0.0203857421875,
-... | 37,552 | 37552 | |
Area and Perimeter in Polygons
Date: 06/24/99 at 15:15:39
From: Mike Hansen
Subject: Geometry
Dear Dr. Math,
I teach Algebra I to some very precocious 13-year-olds, and one in
particular who came up with a formula for area that I would like you
to look over for me.
According to James, he saw a pattern in the areas... | 5 | [
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0.0625,
-0.03857421875,
0.0268554687... | 37,553 | 37553 | |
dense orders are saturated
up vote 9 down vote favorite
2
In a FOM msg of Fri May 21 19:59:44 EDT 1999, http://www.cs.nyu.edu/pipermail/fom/1999-May/003149.html Simpson gave a short proof of the following theorem:
Theorem. Let F be a real closed ordered field and suppose that the ordering of F is $\kappa$-dense, i.e.... | 4 | [
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0.0498046875,
0.06494140625,
-0.0322265625,
0.05126953125,
-0.050537109375,
-... | 37,554 | 37554 | |
Volume-like property to upper bound lattice points in a convex body
up vote 7 down vote favorite
2
The following question arises in passing in a joint paper that I am working on. Let $K$ be a centrally symmetric convex body in an $n$-dimensional real vector space $V$ which contains a lattice $L$.
$L$ yields a natural ... | 4 | [
-0.0206298828125,
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0.0108642578125,
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0.00009918212890625,
-0.0277099609375,
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0.068... | 37,555 | 37555 | |
Turing machines and decidability.
November 22nd 2010, 04:36 PM
girgishf
Turing machines and decidability.
1. Let SUBSETTM = {<M1,M2> : M1 and M2 are Turing machines and L(M1) L(M2)}. Is
SUBSETTM decidable? Prove your answer is correct.
2. Let L = {<M> : M is a Turing machine that accepts at least 2 diff... | 5 | [
-0.031494140625,
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0.05517578125,
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-0.045654296875,
0.0096435546875,
0.1005859375,
0.0152587890625,
-0.026733... | 37,556 | 37556 | |
a function of Bernoulli variables?
up vote 0 down vote favorite
Let $X_1,X_2,...,X_n$ be a fixed number of Bernoulli random variables. My problem is to find a distribution for $Y$ such that for some function $f$, we have $Y=f(X_1,X_2,...,X_n)$. There are two
candidate functions to use, $max$ or $avg$. I have no idea ... | 4 | [
-0.057373046875,
-0.10986328125,
0.0137939453125,
-0.059814453125,
0.044921875,
-0.049072265625,
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0.0146484375,
-0.005828857421875,
-0.0146484375,
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0.0654296875,
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0.053955078125,
0.048583984375,
0.1044921875,
0.02099609375,
-0.02490234375,
... | 37,557 | 37557 | |
Homotopy equivalence between the Grassmannian Gr_{n,m} and Gr_n \times Gr_m.
up vote 6 down vote favorite
1
The following assertion appears in a paper I am reading, and I can't seem to verify it.
Let $\text{Gr}_{n,m}$ denote the set of pairs $(V,W)$ where $V$ and $W$ are as follows.
1. $V$ is an $n$-dimensional sub... | 4 | [
-0.115234375,
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0.034423828125,
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-0.0252685546875,
-0.05126953125,
0.0517578125,
0.01531982421875,
-0.03051... | 37,558 | 37558 | |
Determinant of an updated Covariance matrix
up vote 3 down vote favorite
I am faced with the following problem :
Originally (at time 0) I have a number of data samples $x^0_{1...n}$ (normalised : $E[x] = 0, Var[x] = 1$) from which I have calculated the covariance matrix $C^0 = X^T X$ (where $X$ is the matrix of
data ... | 5 | [
-0.0242919921875,
-0.00604248046875,
0.0037841796875,
-0.058837890625,
0.07861328125,
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-0.038818359375,
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0.07421875,
0.047119140625,
0.037841796875,
-0.030029296875,
-0.01458740234375,
-0.04736328125,
0.01153564453125,
0.0373535156... | 37,559 | 37559 | |
Integration of inverse hyperbolic functions
September 1st 2010, 10:46 PM #1
Senior Member
Joined
Jul 2009
From
Singapore
Posts
338
Integration of inverse hyperbolic functions
Prove that:
$\displaystyle \int^1_{\frac{4}{5}} arsech xdx=2\arctan 2-\frac{\pi}{2}-\frac{4}{5}\ln 2$
I found $arsech... | 5 | [
0.03759765625,
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0.001190185546875,
-0.09033203125,
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-0.005615234375... | 37,560 | 37560 | |
Taylor series
From Encyclopedia of Mathematics
2010 Mathematics Subject Classification: Primary: 26A09 Secondary: 30B10 [MSN][ZBL]
Also known as Maclaurin series. The series was published by B. Taylor in 1715, whereas a series reducible to it by a simple transformation was published by Johann I. Bernoulli in 1694.
... | 4 | [
-0.08056640625,
0.0028533935546875,
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0.08203125,
0.0257568359375,
0.0059814453125,
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0.015869140625,
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0.02392578125,
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-0.04833984375,
-0.0732421875,
-0.0252685546875,
-0.05615234375,
-0.0878906... | 37,561 | 37561 | |
equivalence relation on a partition..help.
July 29th 2009, 12:28 PM #1
Junior Member
Joined
Feb 2009
Posts
48
equivalence relation on a partition..help.
Lets A = {1,2,3,4,5,6,7,8,9,10} and let P be the partition of A given by
P = {{1,2},{3,4,5},{6,7},{8,10},{9}}
Give the equivalence relation R o... | 5 | [
-0.0771484375,
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0.08056640625,
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0.033447265625,
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0.031494140625,
-0.059814453125,
0.0198974609375,
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0.10400390625,
0.039794921875,
-0.0157470703125,
0.005218505859375,
-0.037597... | 37,562 | 37562 | |
Math Forum Discussions
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Topic: [math-learn] Algebra as a spatial motion game of l... | 4 | [
-0.00021457672119140625,
-0.034423828125,
-0.0361328125,
-0.03466796875,
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0.0067138671875,
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0.039794921875,
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0.01220703125,
0.05322265625,
-0.036865234375,
0.02685546875,
-0.052490234375,
... | 37,563 | 37563 | |
Math Forum Discussions
Re: G_delta
Posted: Jan 20, 2013 1:14 AM
On Sat, 19 Jan 2013, Butch Malahide wrote:
> On Jan 19, 3:13 am, William Elliot <ma...@panix.com> wrote:
> >
> > > > > > Does this generalize to every uncountable limit ordinal eta,
> > > > > > that f in C(eta,R) is eventually constant and thusly the Cech... | 4 | [
-0.04296875,
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0.02294921875,
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0.009765625,
... | 37,564 | 37564 | |
Help with a congruence proof
October 11th 2012, 01:46 PM #1
Newbie
Joined
Sep 2012
From
Canada
Posts
7
Help with a congruence proof
The question asks you to find if a statement is true, if it is, prove it. If it is not, give a counterexample.
If a^2 = b^2 (mod p), then a = b (mod p), where p is p... | 4 | [
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0.0546875,
... | 37,565 | 37565 | |
Find the partial sum
September 28th 2009, 09:24 PM
flexus
Find the partial sum
find the partial sum
100
∑ 6n
n=10
ok this is what i did but i didnt get the same answer as the book can someone tell me what i did wrong please?
100
∑ 6n
n=10
60+66+72+78+...
a1=60 d=66-60-->... | 4 | [
-0.07763671875,
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-0.034423828125,
-0.0712890625,
-0.031005859375,
-0.06689453125,
0.028... | 37,566 | 37566 | |
Decision Tree Learning - ID3
Decision tree examples
ID3 algorithm
Occam Razor
Top-Down Induction in Decision Trees
Information Theory
gain from property P
Training Examples
Day Outlook Temp. Humidity Wind Play Tennis
D1 Sunny ... | 5 | [
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0.005401611328125,
-0.031494140625,
0.047119140625,
0.056884765625,
0.0036163330078125,... | 37,567 | 37567 | |
Mapping 3D Line Segments
Date: 10/06/97 at 20:12:39
From: Dave Ice
Subject: How do I map 3D line segments onto a 2D perspective as seen
from an arbitrary point in space?
This thought experiment has me stumped. I'm writing a computer program
where a stick figure is seen from different perspectives. When the
stick fin... | 4 | [
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0.04345703125,
-0.03955078125,
0.005767822265625,
-0.0703125,
0.021728515625,
0.0... | 37,568 | 37568 | |
Convergence
Member
Registered: 2009-11-13
Posts: 222
Re: Convergence
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 81,417
Re: Convergence
Hi;
Here is a nice video:
In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not ye... | 5 | [
-0.059326171875,
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0.0439453125,
-0.08837890625,
-0.000640869140625,
0.0693359375,
-0.130859... | 37,569 | 37569 | |
Epsilon - Delta Proof Question
October 10th 2011, 01:18 PM #1
Newbie
Joined
Oct 2011
Posts
11
Epsilon - Delta Proof Question
lim ((1/(x+4)) = 1/2
x-> -2
or
a=-2
L=1/2
f(x)= (1/(x+4))
The question says we will need a constraint on |x+2|, so it says to assume |x+2|<1.
This is... | 5 | [
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0.033447265625,
-0.08935546875,
... | 37,570 | 37570 | |
Euler Equation
Date: 09/13/97 at 17:19:49
From: Oliver Dale
Subject: Euler function and radians
I have seen the famous Euler equation e^i*pi-1 = 0 and know something
abut its derivation. Specifically, it follows from the infinite series
that define sin, cos and e^x. My question is: does the equation still
work if we... | 5 | [
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0.0625,
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0.015380859375,
0.022705078125,
0.07373046875,
-0.1416015625,
-0.0615234375,
-0.0099487304687... | 37,571 | 37571 | |
typo in mass calculation
04-28-2009 #1
Registered User
Join Date
Jan 2009
Posts
5
typo in mass calculation
Hay
I have a very easy question but I can't find my typo...
I want to calculate the mass of a globe. I have two methods and I need both and they should give the same result of course...
... | 4 | [
0.0252685546875,
0.04541015625,
-0.05078125,
0.0272216796875,
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0.0849609375,
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0.053466796875,
0.01177978515625,
-0.0306396484375,
-0.00677490234375,
0.039306640625... | 37,572 | 37572 | |
arc length - are of the zone of a sphere by revolving about the y
October 22nd 2011, 12:18 PM #1
Member
Joined
Aug 2011
Posts
117
arc length - are of the zone of a sphere by revolving about the y
I have a problem where i dont understand how the solutions manual is doing the steps.
Problem: Find the ... | 4 | [
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0.0166015625,
-0.01275634765625,
-0.0400390625,
0.004638671875,
-0.061279296875... | 37,573 | 37573 | |
Point modules of quantum projective space $\mathbb{P}^n$
up vote 8 down vote favorite
5
Let $A$ be a quantum $\mathbb{P}^n$ defined by $$ A=\mathbb{C}\langle x_1,x_2,\dots,x_{n+1}\rangle/(x_ix_j-r_{ij}x_jx_i)_{1\le i < j\le n+1}. $$ I would like to know the set $X$ of isomorphism
classes of point modules for $A$. Here... | 5 | [
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0.0556640625,
0.10107421875,
0.004425048828125,
0.041015625,
... | 37,574 | 37574 | |
Limit of zero to the zero
August 21st 2012, 05:58 AM #1
Junior Member
Joined
Jun 2010
Posts
59
Limit of zero to the zero
$\lim\limits_{n \to \infty} \left(\frac{1}{n}\right)^\frac{1}{n}$. The answer is 1, but how do I show this?
My textbook says for this scenario take $y = f(x)^{g(x)}$, take $\ln y$... | 5 | [
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-0.04541015625,
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0.0133056640625,
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0.06005859375,
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0.0556640625,
-0.0025482177734375,
0.04833984375,
-0.036376953125,
-0.06... | 37,575 | 37575 | |
Generating a Random Point within a Circle
Date: 04/02/2007 at 17:41:13
From: PC
Subject: Random point within a circle.
Given a circle C with center (xc, yc) and radius R, find a random
point within the circle. What's the best possible way to do that in
terms of computation?
Date: 04/03/2007 at 08:57:09
From: Doc... | 4 | [
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0.03125,
-0.04638671875,
0.056640625,
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0.0908203125,
0.0027618408203125,
0.06884765625,
-0.036376953125,
-0.000942230224609375,
-0.003... | 37,576 | 37576 | |
Parametric Arc Length
August 9th 2010, 03:24 PM #1
Member
Joined
May 2010
From
WI - USA
Posts
129
Parametric Arc Length
I am given a curve defined by:
$x=a\cos(t)+at\sin(t)$
$y=a\sin(t)-at\cos(t)$
"The a is a positive constant"
How do I handle this? Am I supposed to factor the a o... | 5 | [
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0.016845703125,
-0.06640625,
0... | 37,577 | 37577 | |
A question about a formal power series manipulation
up vote 1 down vote favorite
1
I want to find a function $f(x,y)$ which can satisfy the following equation,
$\prod _{n=1} ^{\infty} \frac{1+x^n}{(1-x^{n/2}y^{n/2})(1-x^{n/2}y^{-n/2})} = exp [ \sum _{n=1} ^\infty \frac{f(x^n,y^n)}{n(1-x^{2n})}]$
• I would like to... | 5 | [
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-0.0458984375,
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0.072265625,
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0.017578125,
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0.0267333984375,
0.0107421875,
0.06298828125,
-0.0000972747802734375,
-0.065... | 37,578 | 37578 | |
Finding the gradient
December 14th 2009, 03:49 PM #1
Super Member
Joined
Dec 2008
Posts
509
Finding the gradient
Hi
I few question i am having troubling finding the gradient:
1) Given that the curve y=ax^2+\frac{b}{x} has a gradient of -5 at the point (2, -2) find the value of a and b.
this... | 4 | [
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0.021728515625,
0.18359375,
-0.00732421875,
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-0... | 37,579 | 37579 | |
A morphism from proper to affine is constant?
up vote 6 down vote favorite
Let $S$ be a base scheme and $f \colon X \to S$ and $Y \to S$ finitely presented morphisms. Suppose that $g$ is affine and $f$ is faithfully flat and separated with connected reduced geometric
fibers. Also, suppose that $f$ is proper over a (to... | 4 | [
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0.000934600830078125,
0.00811767578125,
0.048095703125,
0.0235595703125,
0.095214... | 37,580 | 37580 | |
Math Forum Discussions
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Topic: Russian Peasant Multiplication: how does it work?
... | 4 | [
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0.0118408203125,
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-0.000370025634765625,
0.055419921875,
0.052978515625,
0.01806640625,
0.027587890625,
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0.03759765625,
-0.07568359375,
... | 37,581 | 37581 | |
Quaternary Numbers
Date: 28 Jun 1995 10:05:49 -0400
From: Jonathan Rose
Subject: Quaternery Numbers
How do quaternary numbers work? As I understand it, it's
q = r + a.i + b.j + c.k where r is real and i^2 = j^2 = k^2 = -1
but what happens when you start multiplying and dividing i, j and k?
does i x j = k or -k?
... | 5 | [
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-0.00811767578125,
-0.0556640625,
0.0023651123046875,
-0.096... | 37,582 | 37582 | |
Does any real number has a unique binary decimal representation...?
March 15th 2013, 07:16 AM
jojo7777777
Does any real number has a unique binary decimal representation...?
Any real number in [0,1] has a unique binary decimal representation o.b[1]b[2]b[3]..., where each b[i] is either 0 or1. Numerically, o.b[1]... | 5 | [
-0.072265625,
-0.1279296875,
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0.0269775390625,
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-0.00060272216796875,
... | 37,583 | 37583 | |
Finding mean E[X] using permutations of a combination??
September 27th 2009, 09:56 AM #1
Junior Member
Joined
Sep 2009
Posts
69
A permutation of the numbers 1, ... 12 is drawn at random, and written on a sheet of paper. For example,
9, 2; 5, 1, 8, 12, 10, 3, 6, 11, 4, 7. Consecutive pairs determine a ... | 4 | [
0.02392578125,
0.0380859375,
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0.00946044921875,
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0.12109375,
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0.0164794921875,
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-0.04882... | 37,584 | 37584 | |
Evaluating and simplifying limits
May 25th 2009, 10:23 PM #1
Evaluating and simplifying limits
I need help on this limit problem, we aren't given an equation....so I'm not really sure how to do these. We were supposed to have a lesson on limits but we didn't finish the lesson and our
teacher let us wander off... | 4 | [
-0.0458984375,
-0.01458740234375,
0.0296630859375,
0.00225830078125,
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0.017578125,
0.00750732421875,
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0.023193359375,
0.078125,
-0.000614166259765625,
0.04150390625,
-0.01348876953125,
... | 37,585 | 37585 | |
ariance
In
probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events:
mathematical abstractions of non-deterministic events or measured quantities that may either be s... | 4 | [
0.0439453125,
-0.02197265625,
-0.035400390625,
0.016845703125,
-0.05322265625,
0.0189208984375,
0.049072265625,
0.006927490234375,
0.10888671875,
0.034912109375,
-0.00982666015625,
0.0308837890625,
0.07177734375,
-0.0211181640625,
-0.0091552734375,
-0.0849609375,
0.0027008056640625,
... | 37,586 | 37586 | |
Inverse of an Inverse
Associated Topics || Dr. Math Home || Search Dr. Math
Inverse of an Inverse
Date: 01/20/200... | 5 | [
-0.058349609375,
0.01275634765625,
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0.0859375,
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0.0189208984375,
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0.00518798828125,
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0.02880859375,
-0.04248046875,
... | 37,587 | 37587 | |
Diagonalizing matrix problem with parameters
September 21st 2012, 10:46 AM #1
Junior Member
Joined
Aug 2011
Posts
38
Thanks
1
Diagonalizing matrix problem with parameters
Hi,
I have this problem I'm stuck on:
A is a 3x3 matrix
A=
a,b,c are real numbers
1) determine for what valu... | 5 | [
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-0.0174560546875,
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0.0023345947265625,
-0.0157470703125,
-0.05175... | 37,588 | 37588 | |
4 Variable Truth Table
TopA truth table is used to find the relation with Boolean Algebra, Boolean function and propositional Calculus.
There are some types of logic operation which are given below.
1.
AND operator
- It is also known as conjunction operator.
The ‘AND’ operator is denoted by the symbol ‘∧’.
2.
OR... | 4 | [
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0.119140625,
-0.02783203125... | 37,589 | 37589 | |
Exponential form - Math Central
Hi Motaz. Let me demonstrate with a similar question:
Let z = log[5] (1/625).
Start by realizing that if the log is in base 5, we want to exponentiate with base 5 on both sides:
5^z = 5^ log[5] (1/625)
On the right hand side, the exponentiation and the log cancel each other, because ... | 4 | [
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0.1123046875,
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0.078125,
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0.023193359375,
... | 37,590 | 37590 | |
GCD of f(x) and f'(x) (simple question)
November 25th 2009, 12:38 PM #1
GCD of f(x) and f'(x) (simple question)
This seemed simple, but I keep getting ridiculous fractions.
For example, find the GCD of f(x) and f'(x) over Q of:
f(x)=x^3 -3x -2
The quotient becomes 1/3x with a remainder of -2x-2, whi... | 4 | [
-0.04638671875,
0.02392578125,
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0.01300048828125,
0.032958984375,
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0.030029296875,
-0.0162353515625,
-0.041015625,
0.005401611328125,
0.0419... | 37,591 | 37591 | |
Asymptotic lower/upper bounds for unconventional T(n)?
September 15th 2008, 06:14 AM
Shaitan00
Asymptotic lower/upper bounds for unconventional T(n)?
Similarily to my previous post, I am trying to find out how to solve the lower/upper bounds for a given T(n) - the book I have been reading refers to using the Mas... | 4 | [
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0.0478515625,
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... | 37,592 | 37592 | |
Modelling with differential equation
September 8th 2010, 02:05 AM
acevipa
Modelling with differential equation
A cyclist freewheeling on a level road experiences a negative acceleration which is proportional to the square of his speed. His speed is reduced from $20m/s$ to $10m/s$ in a distance of $100m$.
Fin... | 5 | [
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0.1328125,
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-0.0247802734375,
0.061767578125,
0.083984375... | 37,593 | 37593 | |
A natural center of a convex weakly compact set in Banach space
up vote 13 down vote favorite
2
Question: Let $S$ be a convex weakly compact set in Banach space $H$. Propose a natural way to define the unique center $O \in S$.
Motivation: A lot! For example, in game theory $S$ can be a set of possible (fair) allocati... | 4 | [
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0.080078125,
-0.02734375,
-... | 37,594 | 37594 | |
Series of Functions
Is... $\displaystyle f^{'} (x) = 1+x^{4}+x^{8} + ... + x^{4 n} + ... = \frac{1}{1-x^{4}} = \frac{\frac{1}{2}}{1+x^{2}} + \frac{\frac{1}{2}}{1-x^{2}}$ (1) ... so that is... $\displaystyle f(x) = \int_
{0}^{x} \frac{dt}{1-t^{4}} = \frac{1}{2}\ \tan^{-1} x + \frac{1}{4}\ \ln \frac{1+x}{1-x}$ (2) ... an... | 5 | [
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-0.1318359375,
-0.041015625,
0.034423828125,
-0.099609... | 37,595 | 37595 | |
How can I use my graphing calculator to solve this complex number problem?
August 14th 2007, 04:08 PM #1
Junior Member
Joined
Jun 2005
Posts
43
How can I use my graphing calculator to solve this complex number problem?
The question in my book says use a graphing calculator to represent -3+2i in trigonome... | 4 | [
-0.10400390625,
0.059814453125,
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-0.07421875,
-0.0498046875,
-0.03... | 37,596 | 37596 | |
Sum solving
July 16th 2012, 02:50 PM
Emilijo
Sum solving
Is it possible to find F(n), summation of the function f(k), where k=1,2...,n ( Is there some formula, general formula, for any f(k), of course if k is in domain of function)
sum_(k=1, to n) f(k) = F(n)
If it is not possible, why?
July 16th 2012... | 5 | [
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-0.0830078125,
-0.036132... | 37,597 | 37597 | |
Numerically Equivalent Sets
May 11th 2010, 07:18 PM #1
Banned
Joined
Sep 2009
Posts
502
Numerically Equivalent Sets
For infinite sets $A$ and $B$ to be numerically equivalent. Is bijective function
$f:A \rightarrow B$
the only requirement that needs satisfying?
I'm not sure what you mean b... | 4 | [
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0.050048828125,
-0.... | 37,598 | 37598 | |
Verify Trig Identities
November 14th 2012, 10:15 AM
Darion
Verify Trig Identities
Could someone please double-check this for me?
Find the exact value by using a half-angle identity.
tan(7pi/8)
My Answer: tan(7pi/8) can be turned into tan(7pi/4 /2). So then we use the half angle formula associated w... | 4 | [
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-0.02490234375... | 37,599 | 37599 |