content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Linear system solutions using Gauss-Jordan elimination
January 28th 2011, 10:35 AM #1
Newbie
Joined
Jan 2011
Posts
2
Linear system solutions using Gauss-Jordan elimination
$<br /> \left\{<br /> \begin{matrix}<br /> ax - 3y + z = a\\<br /> -x + 6y = -2\\<br /> x + 5z = 4\\<br /> \end{matrix}\right.<br />$... | 4 | [
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-0.0625,
-0.071289062... | 38,200 | 38200 | |
Power and Product Rule
June 2nd 2009, 11:21 AM #1
Member
Joined
May 2009
Posts
93
Power and Product Rule
Differentiate the given function (two methods)
I only know how to do the chain rule which I get 8(4x-7)
please show how to do this so I can master the rest of the questions my self..thanks
... | 5 | [
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-... | 38,201 | 38201 | |
Base 26
Date: 01/27/97 at 21:41:44
From: ac
Subject: Base numbers
Question 1 Consider a base-twenty-six number system wherein the
letters of the alphabet are the digits. That is, A=0, B=1, C=2, ...,
Z=25 in base ten. Calculate TWO+TWO in this system. Express your
answer in base ten.
Question 2 Express 1997 i... | 4 | [
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0... | 38,202 | 38202 | |
containment of intersection problem
May 15th 2010, 02:24 PM
nhk
containment of intersection problem
Suppose K is a normal subgroup of a finite group G and S is a p-Sylow subgroup of G. Prove that K intersect S is a p-Sylow subgroup of K. So I know that K is a unique p-sylow group by definition,
is that enoug... | 5 | [
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Is a reductive adelic group a Type I group?
up vote 14 down vote favorite
3
I foresee that to experts of automorphic forms this question will sound unimportant or useless or even not worthy of an answer; but none of these are going to stop me from asking it!
The question is simple: let $G$ be a reductive (or even sem... | 4 | [
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Finding the difference in range of a projectile (air resistance vs. free)
August 22nd 2012, 04:46 PM
Shakespoe
Finding the difference in range of a projectile (air resistance vs. free)
We were give two equations that show the position as a function of time on the x and y axis where there is a linear drag force o... | 4 | [
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0.03... | 38,205 | 38205 | |
2 Polynomial Problems
April 17th 2008, 12:39 PM #1
Newbie
Joined
Feb 2006
Posts
16
2 Polynomial Problems
Problem 147. The numbers 1 and 2 are roots of polynomial P. Prove that P is divisible by (x-1)(x-2).
I have the solution but I don't understand one of the steps.
Solution. P is divisible by ... | 4 | [
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-0... | 38,206 | 38206 | |
Math Help
November 1st 2009, 02:12 AM #1
Newbie
Joined
Apr 2009
Posts
19
Regression
Hi guys,
I have a question that I have done a bit of...
just need checking
and if sumone can tell me how to do the rest...coz im confused
thanks
A chemist is interested in determining the weight l... | 5 | [
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-0.005... | 38,207 | 38207 | |
pre-calc/trig
December 17th 2008, 06:24 PM #1
Newbie
Joined
Dec 2008
Posts
4
pre-calc/trig
My teacher always confuses me when she throws T into the mix. i tried replacing with X, didnt help my problem either. i saw in a thread by yovivo, that the help posted could somewhat be applied.
so i tried for ... | 4 | [
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Series and Sequences, Sigma notation.
June 19th 2012, 10:26 AM #1
Newbie
Joined
Jun 2012
From
Singapore
Posts
2
Series and Sequences, Sigma notation.
Given that r^2 +1 = (r+2)(r+1) - 3(r+1) + 2
Show that Sigma r=1 r=n (r^2 + 1)r! = n(n+1)!
Help please ><
Re: Series and Sequences, Sigma not... | 4 | [
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dy
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Here's the question you clicked on:
mathcalculus Group Title
helpppp: find the... | 4 | [
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0.0167236328125,
-0.039794921875,... | 38,210 | 38210 | |
kernal and image with complex numbers
August 13th 2012, 07:04 AM #16
Newbie
Joined
Aug 2012
From
Bolton
Posts
8
Re: kernal and image with complex numbers
For the kernel I get so far
Ker = { z in C* : z / (the complex conjugate) z = 1}
= { z in C* : z = (the complex conjugate) z }
Then ... | 5 | [
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differential eq problem
March 10th 2008, 12:12 PM #1
Newbie
Joined
Mar 2008
Posts
15
differential eq problem
A radar controlled tracking system is described by the following diff eqn:
X''(o)+100X'(o)+10,000X(o)= 10,000X(d)
X(d)=angular position of the target (in radians)
X(o)=angular p... | 5 | [
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Derivative of invert tan?
March 28th 2006, 02:19 PM
tttcomrader
Derivative of invert tan?
I read from the rules that the derivative of (tan^-1)x is (1/x^2+1), but I cannot figure out why and I can't find any explantations on the web.
Anyone have any ideas?
Thank you.
March 28th 2006, 06:57 PM
ThePerf... | 5 | [
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Smooth unitary irreducible finite-dimensional representations of U(n)
up vote 3 down vote favorite
2
I want to make sure I completely understand the isomorphism classes of smooth unitary irreducible finite-dimensional representations of $U(n)$. We have the irreducible defining representation $R$,
and we can apply any ... | 4 | [
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splitting field L
March 22nd 2009, 10:41 PM #1
Member
Joined
Apr 2006
Posts
91
B is a real number Sqrt(7 + 2*sqrt(7))
basically i have done the parts of finding the minimal polynomial mu of B over Q, and all the zeros of mu.
but i got stuck on the part where i need to find the degree [L :Q] and ... | 5 | [
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0.0125122... | 38,215 | 38215 | |
Finding height of cone
September 8th 2009, 11:20 AM #1
Finding height of cone
The radius of a traffic cone is 14 centimeters and the lateral surface of the cone is 1617 square centimeters. Find the height of the cone.
Don't know where to go from this.
Hi A Beautiful Mind,
The L.A. of a cone is give... | 4 | [
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Navigating Z/pZ
up vote 30 down vote favorite
13
Let's consider a silly-looking question first. Consider Z/pZ. Say I am allowed the two operations x->x+1 and x->2*x. Then, starting from 0, I can express every given element y of Z/pZ in O(log p)
steps; moreover, I can figure out how to do it in time O(log p).
The answ... | 5 | [
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Probability Proof
January 30th 2011, 12:15 PM #1
Member
Joined
Oct 2010
Posts
150
Probability Proof
Problem:
Let A and B be two events, show that:
P(A) + P(B) -1 $\leq$ P(A U B) $\leq$ P(A)+P(B)
Questions/Attempts:
Am I supposed to assume that A and B are the only events in the sample... | 4 | [
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-0.046386718... | 38,218 | 38218 | |
[SOLVED] Prove a finite subgroup is normal, given order conditions.
January 20th 2010, 11:54 AM #1
Senior Member
Joined
Feb 2008
Posts
410
[SOLVED] Prove a finite subgroup is normal, given order conditions.
Let $G$ be a finite group, and let $n$ be a divisor of $|G|$. Show that if $H$ is the only subgrou... | 5 | [
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Unbiased estimators
August 3rd 2009, 05:50 AM
chella182
Unbiased estimators
So I'm revising my stats by doing a past exam paper, and I'm stuck on one of the questions about unbiased estimators. The question goes...
Suppose that $X_1$, $X_2$,..., $X_n$ are a random sample from a population with mean $\mu$ a... | 5 | [
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Historical question in analytic number theory
up vote 11 down vote favorite
3
The analytic continuation and functional equation for the Riemann zeta function were proved in Riemann's 1859 memoir "On the number of primes less than a given magnitude." What is the earliest
reference for the analytic continuation and func... | 5 | [
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Hyper-optimistic conjecture
From Polymath1Wiki
Gil Kalai and Tim Gowers have proposed a “hyper-optimistic” conjecture.
Let $c^\mu_n$ be the maximum equal-slices measure of a line-free set. For instance, $c^\mu_0 = 1$, $c^\mu_1 = 2$, and $c^\mu_2 = 4$.
As in the unweighted case, every time we find a subset B of the ... | 4 | [
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Proof of Krylov-Bogoliubov Theorem
up vote 12 down vote favorite
3
Where can I find a proof (in English) of the Krylov-Bogoliubov theorem, which states if $X$ is a compact metric space and $T\colon X \to X$ is continuous, then there is a $T$-invariant Borel
probability measure? The only reference I've seen is on the W... | 4 | [
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0... | 38,223 | 38223 | |
Herstein: Normal subgroup proof.
October 15th 2011, 11:23 AM #1
Junior Member
Joined
Oct 2011
Posts
28
Herstein: Page 74 #18 (sect 2.5)
If H is any subgroup of G and N = ∩(a∈G) a^-1Ha, prove that N◅G.
I am extremely lost. So lost, it hurts.
Re: Herstein: Normal subgroup proof.
first of a... | 5 | [
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Using Complex Conjugate Numbers
Date: 09/14/1999 at 12:29:29
From: Larry Carroll
Subject: Conjugate Numbers
We are using electronic hardware to measure impedance, structural
return loss, and other properties of CATV cables that we manufacture.
The process has been automated by using a combination of HPBasic and
dBas... | 4 | [
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-0.014099... | 38,225 | 38225 | |
Definite Integrals!
$\int^1_0 arcsin\left(\frac{2x}{1+x^2}\right)$ PS. How do you get the brackets to enclose the entire expression?
Last edited by polymerase; January 21st 2008 at 06:34 PM.
I was tryin' to find a nice way to tackle this but I couldn't. Looks like it's pretty straightforward. Integrate by parts: $u =... | 5 | [
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Ordinary differential equations
October 8th 2010, 09:52 AM #1
Ordinary differential equations
1 ) SOLVE
dy/dx + y*cot(x) =5*e^cos(x) if y=-4 and x=5/4
2)
solve
dy/dx + (y logy)/x = y(logy)^2/(x^2)
3)SOLVE
(x*y^2)dx - e^(1/(x^3))dx - x^2*y dy = 0
Thank you very much.
For clari... | 5 | [
-0.0673828125,
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0.05517578125,
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0.06396484375,
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0.068359375,
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0.02185... | 38,227 | 38227 | |
Meshfree Methods
EFG Matlab Routines
These used to be hosted at Northwestern, but the files were taken down some time ago. The original 1d and 2d Matlab routines for the element-free Galerkin method are now located at
http://www.duke.edu/~jdolbow/EFG/programs.html
These routines are described in detail in the paper
... | 4 | [
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0.007720947265625,
0.0185546875,
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0.0966796875,
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0.0205078125,
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0.0400390625,
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... | 38,228 | 38228 | |
Complex number problem!
August 12th 2010, 04:50 AM
GreenMile
Complex number problem!
Find $Re(z)$ and $Im(z)$ if:
$z=\sqrt[3]{ \frac{2}{-\sqrt{2+i\sqrt{2}}}}$
My idea was to simplify the expression to the normal form $x+iy$ (The problem is that i don't know how). And then, by De Moivre's formula I can ... | 5 | [
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0.031982421875,
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0.047119140625,
-0.004150390625,
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0.034423828125,
0.044921875,
0.029541015625,
0.07666015625,
-0.00787353515625,
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0.0888671875,
0.09765625,
-0.000736236572265625,
-0.09814453125,
0.0... | 38,229 | 38229 | |
evalute this limit
Hints: Limit of a power = Power of the limit. Limit of a sum = Sum of the limit.
A square root is the same as taking to the power of $\frac{1}{2}$. So now use the fact that the limit of the power is the same as the power of the limit.
May be that there is a '+' instead of a '-' and the limit is... ... | 5 | [
0.0341796875,
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0.052734375,
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0.012939453125,
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-0.052490234375,
0.023681640625,
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0.07177734375,
0.001068115234375,
0.015869140625,
0.037353515625,
-0.021484375,
-0.0634765625,
0.0166015625,
-0.018676... | 38,230 | 38230 | |
Simple linear regression model
April 6th 2009, 06:58 AM #1
Newbie
Joined
Apr 2009
Posts
1
Simple linear regression model
The OLS estimator for the simple linear regression model can be written as
$<br /> b_2 = \beta_2 + \Sigma w_te_t$ where $w_t = \frac{(x_t - \overline{x})}{\Sigma(x_t - \overline{x}... | 4 | [
-0.0703125,
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0.042724609375,
0.0625,
0.0537109375,
0.01519775390625,
-0.0380859375,
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0.007415771484375,
0.0810546875,
-0.008544921875,
-0.0322265625,
-0.0834... | 38,231 | 38231 | |
Divergence of Dirichlet series
up vote 5 down vote favorite
3
Suppose $s$ is a complex number with $\Re(s) \in (0,1]$ and $\{a_n\}$ is a complex sequence converging to $a \neq 0$. Must the Dirichlet series $$\sum_{n=1}^\infty\frac{a_n}{n^s}$$ diverge?
I asked this question on math.stackexchange on 2011-12-13. Here is... | 5 | [
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0.05322265625,
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0.06298828125... | 38,232 | 38232 | |
Quadratic Inequalities.
April 20th 2010, 01:54 PM #1
Newbie
Joined
Dec 2009
Posts
8
Quadratic Inequalities.
I do NOT understand how to do this. Can someone explain in full detail/step by step how to do it?
1) y > -x^2 -10x
2) y< 4x^2+8x+4
3) y>x^2-3x-18
$y > -x^2 -10x \implies y> -x(x... | 4 | [
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0.0634765625,
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0.0263671875,
0.1044921875,
0.055908203125,
-0.059326171875,
-0.04003906... | 38,233 | 38233 | |
integral of arctan(1/x)
Could someone please show me step by step the solution to the integral of arctan(1/x)?
Hello, laura35066! $I \;=\;\int \arctan\left(\frac{1}{x}\right)\,dx$ Integrate by parts . . . . . $\begin{array}{ccccc}u &=& \arctan\left(x^{-1}\right) \\ \\[-3mm] du &=& \dfrac{\text{-}x^{-2}}{1 +
(x^{-1})^2... | 5 | [
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0.072265625,
-0.0299072265625... | 38,234 | 38234 | |
New to proofs...
January 25th 2011, 07:15 PM #1
Newbie
Joined
Jan 2011
Posts
7
New to proofs...
If $a \leq b$ and $b \leq a+c$, then $|a-b| \leq c$.
Ok this is what I need to prove. I am fairly new to this so i'm not too sure what i have done is right, but here is what i have.
$a \leq b \leq a+... | 4 | [
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0.09033203125,
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0.01611328125,
0.08544921875,
0.017578125,
-0.087... | 38,235 | 38235 | |
What is a Number Base?
Date: 04/19/2003 at 13:37:55
From: Cathy
Subject: Base Numbers
The base eight number 7n3 is equal to the base 7 number 1n35.
What digit does n stand for?
I don't know what a base number is.
Date: 04/19/2003 at 22:59:16
From: Doctor Samus
Subject: Re: Base Numbers
Hi Cathy,
In order to unde... | 4 | [
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-0.1171875,
... | 38,236 | 38236 | |
dividing an n-gon into rhombuses
September 10th 2010, 08:51 PM #1
Newbie
Joined
Sep 2010
Posts
15
dividing an n-gon into rhombuses
I'm trying to prove that any regular and convex 2n-polygon can be divided into rhombuses.
I proceed by induction.
BASE CASE: For n=2 this is obviously true because a... | 4 | [
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... | 38,237 | 38237 | |
Question regarding determinants and switching columns of square matrices
July 28th 2010, 12:42 AM
jayshizwiz
Question regarding determinants and switching columns of square matrices
$A$ is a square matrix length n and $b$ is a vector in $R^n$. For every $k$=1,2,...,n $A_k$ is the matrix that is received from $A$... | 5 | [
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0.08935546875,
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0.003967... | 38,238 | 38238 | |
[SOLVED] Help in Vector space: Linearly independent!
February 10th 2009, 08:57 PM
Vedicmaths
[SOLVED] Help in Vector space: Linearly independent!
I need help in this Linear independence problem...
Let U and V be distinct vectors in a vector space V. Show that {U,V} is linearly dependent iff U or V is a mult... | 4 | [
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0.0172119140625,
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0.00... | 38,239 | 38239 | |
Math Help
December 18th 2008, 05:47 AM #1
Member
Joined
Sep 2008
Posts
239
Matricies
The variables x, y, z satisfy the equations
x + 2y + 3y = 2
x + 3y + 2z = 1
2x + 2y + 𝛌z = 𝛍
where, 𝛌, 𝛍 are constants
a) using reduction to echelon form, or otherwise,
i) Find the value ... | 5 | [
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-0.068359375,
... | 38,240 | 38240 | |
Transition matrix for holomorphic vector bundles
up vote 1 down vote favorite
1
If we are given the local trivialities of a holomorphic vector bundle then by definition we can write down the transition matrix of that vector bundle.
In some very natural situations, we are not given local trivialities of that vector bu... | 5 | [
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-0.0859375,
0.03735... | 38,241 | 38241 | |
Tugboat problem
September 9th 2007, 11:27 PM #1
Newbie
Joined
Sep 2007
Posts
3
Tugboat problem
I am desperately in need of help for this problem..Please help! A tugboat of mass m = 200,000 kg pushes a barge with a mass of 800,000 kg so that starting from rest, they reach a speed of 2.9 m/s
after 10s.... | 4 | [
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0.1064453125,
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0.06787109375,
-0.049560546875,
0.07763671875,
0.09033203125,
-0.07666015625,... | 38,242 | 38242 | |
exactly equal
September 7th 2009, 04:06 AM #1
exactly equal
Hi everyone
I am new here looking for a bit of help. Hopefully in the future I will be able to offer others some help.
I have been brushing up on my maths skills as I am starting a Home study maths degree. I have come accross the following ques... | 4 | [
0.0157470703125,
0.061767578125,
-0.04638671875,
-0.0079345703125,
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0.0712890625,
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-0.044921875,
0.01116943359375,
0.052978515625,
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0.0068359375,
0.0888671875,
0.0228271484375,
0.0634765625,
0.06689453125,
-0.0556640625,
-0.050537109375... | 38,243 | 38243 | |
Hypothesis Test Problem
April 6th 2013, 05:10 PM
jeff2222
Hypothesis Test Problem
Hello,
I have a problem involving making a Hypothesis Test for a treatment being performed. The outcome is measured with a health rating FIM. There are 203 patients before treatment and 203 after
treatment , each has a hea... | 5 | [
0.02294921875,
0.053466796875,
0.0201416015625,
0.020751953125,
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0.2060546875,
-0.0283203125,
0.076171875,
0.01416015625,
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0.04150390625,
0.03759765625,
-0.0146484375,
-0.0052490234375,
0.06884765625,
-0.087890625,
... | 38,244 | 38244 | |
The Strong Law of Large Numbers
November 12th 2005, 06:13 PM #1
Global Moderator
Joined
Nov 2005
From
New York City
Posts
10,616
Thanks
9
The Strong Law of Large Numbers
I never studied statistics and read that The Strong Law of Large Numbers is a famous theorem. Could someone explain it to me wi... | 4 | [
-0.0150146484375,
-0.07080078125,
0.00482177734375,
0.04296875,
0.045654296875,
0.028076171875,
0.00830078125,
0.0869140625,
0.032470703125,
0.08154296875,
-0.01080322265625,
0.03271484375,
0.028076171875,
-0.03662109375,
0.04931640625,
-0.01507568359375,
0.041748046875,
-0.0385742... | 38,245 | 38245 | |
expected value and variance (continuous random variables)
Hello,
I would like your help!
X1, X2, … are independent continuous random variables with E[x]=2, V(X)=9.
Yi=(0.5^i)Xi, i=1,2,…
Tn=Y1+Y2+…+Yn
An=(1/n) Tn
E and V of Yn, Tn, An ???
E[Yn] = E[(0.5^i)Xi] = (0.5^i)E[Xi] = 2(0.5^i)... | 4 | [
0.07421875,
-0.023193359375,
0.0830078125,
-0.0306396484375,
0.034423828125,
0.0123291015625,
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0.006591796875,
0.0162353515625,
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0.03759765625,
0.0166015625,
0.00634765625,
0.04931640625,
-0.00848388671875,
0.037841796875,
-0.07373046875,
-0.048583984375,
... | 38,246 | 38246 | |
Integral problem
i know a solution that covers double integration, but, have you covered double integrals so that you can get my solution?
okay first we integrate by parts to get: $\int_{0}^{\infty }{\frac{\sin x}{x}\,dx}=\int_{0}^{\infty }{\frac{1-\cos x}{x^{2}}\,dx},$ now on the last integral we use the fact that $\... | 5 | [
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0.0703125,
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0.023681640625,
0.043212890625,
-0.061279296875,
0.0458984375,
-0.049072265625,
0.055419921875,
-0.09228515625... | 38,247 | 38247 | |
Lines in a Plane 10
September 5th 2009, 03:47 PM #1
Senior Member
Joined
Nov 2008
Posts
425
Lines in a Plane 10
Prove that the shortest distance from a point to a line is the distance measured along the perpendicular from the point to the line.
Assume it isn't -- take a point $p$ which is on the lin... | 5 | [
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0.07568359375,
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-0.06640625,
-0.03759765625,
0.1328125,
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0.041015625,
0.07275390625,
0.0308837890625,
0.033447265625,
0.0732421875,
-0.01361083984375,
0.1279296875,
-0.09375,
0.07666015625,
-0.0205078125,
-0.049560546875,
0.00381469726... | 38,248 | 38248 | |
Critical Numbers
October 30th 2008, 12:04 PM #1
Junior Member
Joined
Sep 2008
Posts
54
Critical Numbers
I need some help with these problems I have to find the critical numbers fo the problems.
First I need to differentiate the problem and then I need to set it equal to 0 and solve for the variable.... | 4 | [
-0.037841796875,
-0.0020751953125,
-0.0031585693359375,
0.01025390625,
-0.044189453125,
-0.0133056640625,
-0.0245361328125,
0.03564453125,
-0.0004367828369140625,
0.040771484375,
0.1025390625,
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0.06787109375,
0.01312255859375,
-0.005828857421875,
0.0201416015625,
-0.... | 38,249 | 38249 | |
is localization of category of categories equivalent to |Cat|
up vote 8 down vote favorite
5
It might be a stupid question. Suppose There is a category of categories,denoted by CAT,where objects are categories, morpshims are functors between categories
Take multiplicative system S={category equivalences}. Then we tak... | 4 | [
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0.004150390625,
-0.0224609375,
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0.0269775390625,
-0.0086669921875,
-0.01422119140625,
0.1162109375,
0.03979... | 38,250 | 38250 | |
A Diophantine Determined with a Data-Driven Approach
Date: 06/24/2012 at 01:41:55
From: Mohammad
Subject: Solve 4 x^2 y^2 +x^2 +y^2=n^2
I'm working on an Euler problem, which I have been able to simplify down
to solving the Diophantine equation
4*x^2*y^2 + x^2 + y^2 = n^2
I have tried searching for an online Dio... | 5 | [
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0.07861328125,
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0.0250244140625,
0.0034637451171875,
0.0... | 38,251 | 38251 | |
Noncompact Kahler manifolds with nonzero Ricci tensor but vanishing scalar curvature
up vote 2 down vote favorite
2
Let us consider a noncompact K\"{a}hler manifold with vanishing scalar curvature but nonzero Ricci tensor. I'm wondering what can it tell us about the manifold. The example (coming from physics) has
the ... | 4 | [
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0.06298828125,
0.042236328125,
-0.04638671875,
-0.0050048828125,
-0.... | 38,252 | 38252 | |
Products of Digits
Date: 03/02/2003 at 18:24:08
From: Liz
Subject: Product of digits
The product of digits in the number 234 is 24: 2*3*4 = 24.
Can you describe a general procedure for figuring out how many x-digit
numbers have a product equal to p, where x and p are counting numbers?
How many different three-digit... | 4 | [
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0.018310546875,
-0.031982421875,
-0.068359375,
0.026611328125,
-0.03564453125,
... | 38,253 | 38253 | |
Prime Numbers
September 20th 2010, 08:52 AM #1
Junior Member
Joined
Apr 2010
Posts
58
Prime Numbers
Here is my problem:
Let a,b be nonzero integers. Prove that (a,b) = 1 if and only if (a+b, ab) = 1.
Any suggestion on where to start?
You could try playing around with Bezout's identity.
... | 5 | [
-0.06298828125,
0.00604248046875,
-0.0419921875,
-0.044677734375,
-0.01007080078125,
0.0111083984375,
0.1298828125,
-0.03515625,
-0.0272216796875,
-0.0205078125,
-0.00107574462890625,
0.038818359375,
0.045166015625,
0.044189453125,
0.02392578125,
0.01019287109375,
-0.041015625,
-0.... | 38,254 | 38254 | |
Strange real functions
up vote 6 down vote favorite
I know there are a lot of strange functions $f~:~\mathbb R \to \mathbb R$.
I'm looking for an "elementary but complete" exposition of a result discovered by W. Sierpi\'nski and A. Zygmund in "Sur une fonction qui est discontinue sur tout ensemble de puissance du con... | 5 | [
-0.09326171875,
-0.07177734375,
0.018310546875,
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0.04833984375,
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0.10546875,
0.01483154296875,
0.023681640625,
0.04638671875,
-0.052001953125,
0.0206298828125,
0.107421875,
0.0419921875,
-0.043701171875,
-0.11767578125,
0.05224609375,
-0.044921875,
... | 38,255 | 38255 | |
Surjectivity of the natural map of injective module to its localization
up vote 3 down vote favorite
1
Hello all,
The lemma 3.3 page 214 in Hartshorne Algebraic Geometry book states:" If $I$ is an injective module over a Noetherian ring $A$. Then for any $f\in A$, the natural map of $I$ to its localization $I_f$
is s... | 4 | [
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0.0133056640625,
0.0118408203125,
0.0220947265625,
0.019287109375,
0.0072... | 38,256 | 38256 | |
How to foil this equation...
January 12th 2009, 04:10 PM #1
Newbie
Joined
Jan 2009
Posts
1
How to foil this equation...
4
[ v(2x+2) - v(x-3)][ v(2x+2) - v(x-3)] = 4
*By the way , that v symbol means SQuare root. CAn someplease walk me through this process.
$(\sqrt{a} - \sqrt{b})^2 = a - 2\... | 4 | [
0.016845703125,
0.023193359375,
0.00634765625,
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0.0439453125,
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-0.003997802734375,
0.06640625,
0.052978515625,
-0.04541015625,
0.0... | 38,257 | 38257 | |
Many-worlds interpretation
Talk0
34,135pages on
this wiki
Assessment | Biopsychology | Comparative | Cognitive | Developmental | Language | Individual differences | Personality | Philosophy | Social |
Methods | Statistics | Clinical | Educational | Industrial | Professional items | World psychology |
Philosophy Ind... | 4 | [
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0.06982421875,
0.0130615234375,
0.0289306640625,
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... | 38,258 | 38258 | |
ultisampling
Archive for the ‘adaptive multisampling’ tag
I recently added a first pass at area lights in the ray tracer. They are rather limited at the moment as the only point lights are supported and their shape is fixed as a sphere of user-controllable
radius r. The sampling is only an approximation and non-unifor... | 4 | [
-0.0693359375,
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0.031494140625,
0.0625,
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0.0228271484375,
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0.03759765625,
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0.0004634857177734375,
0.08935546875,
-0.026123046875,
-0.01806640625,
0.0888671875,
0.0189208984375,
0.05517578... | 38,259 | 38259 | |
Simultaneous Equations (LAME theory).
July 18th 2011, 07:18 AM #1
Newbie
Joined
Jul 2011
Posts
2
Simultaneous Equations (LAME theory).
Hi,
I have come to a standstill while trying to follow an example. I have attached the full example but need some assistance in the method used to solve the simultan... | 4 | [
-0.0322265625,
0.053466796875,
-0.0162353515625,
0.03564453125,
-0.0634765625,
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-0.0123291015625,
0.019775390625,
-0.000728607177734375,
0.01190185546875,
0.10302734375,
-0.0157470703125,
0.0712890625,
0.07470703125,
0.0281982421875,
0.126953125,
-0.08935546875,
... | 38,260 | 38260 | |
Brute force
Brute Force
1. Selection sort
2. Brute-Force string matching
3. Polynomial Evaluation
4. Closest pair problem by brute force
5. Exhaustive search
Traveling salesman problem
Knapsack problem
Assignment problem
... | 4 | [
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0.00087738037109375,
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0.0771484375,
-0.002655029296875,
-0.040771484375,
0.04736328125,
0.028076171875,... | 38,261 | 38261 | |
Cutting An Equal Number of Slices of Cake
Date: 07/13/98 at 17:13:39
From: Katherine Gonzalez
Subject: Question
I have had difficulties solving and understanding the following math
problem and that's why I writing you, to ask for your help.
This is the problem:
Before checking with the caterer, a cook cuts a cake i... | 4 | [
0.0184326171875,
0.07080078125,
0.005767822265625,
-0.076171875,
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-0.0272216796875,
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-0.00958251953125,
-0.037841796875,
-0.0093383... | 38,262 | 38262 | |
Schemes associated to vector spaces
up vote 1 down vote favorite
1
Let $k$ be a field. Let $F$ be a covariant functor on the category of $k$-algebras to the category of sets. Assume that the opposite functor $F^{op}$ on the category of affine $k$-schemes is a sheaf.
(This last assumption might not be necessary.)
Now,... | 5 | [
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0.09130859375,
0.057861328125,
0.01141357421875,
0.0235595703125,
0.0603027... | 38,263 | 38263 | |
Wierd reationship in spheres
March 4th 2009, 01:52 AM
espen180
Wierd reationship in spheres
I found a strange relationship between a sphere's volume and area, and a circle's area and circumference.
For spheres:
$\frac{d}{dr}V=\frac{d}{dr}\frac{4}{3}\pi r^3=4\pi r^2=A$
Where V is the volume and A is ... | 5 | [
-0.0022125244140625,
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0.053955078125,
0.0230712890625,
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-0.03515625,
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0.1357421875,
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0.05712890625,
-0.01611328125,
-0.08984375,
0.064453125,
... | 38,264 | 38264 | |
Characteristics of an IFR pdf
April 9th 2009, 12:01 AM
Xavier_B
Characteristics of an IFR pdf
Hi,
I am looking for help in solving a problem that crept up in my doctoral thesis.
Let f be a pdf, twice differentiable and F its cdf. Both are defined over $\mathbb{R}^+$.
I wish to prove that
$\frac... | 4 | [
-0.04248046875,
-0.0155029296875,
0.058837890625,
-0.0186767578125,
0.0615234375,
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-0.01611328125,
0.0654296875,
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0.0947265625,
-0.0255126953125,
0.000804901123046875,
0.08984375,
-0.00408935546875,
0.005218505859375,
-0.003875732421875,
-0.0062255859... | 38,265 | 38265 | |
Civil Engineering
Engineering:
Civil Engineering
CRAFTY Curriculum Foundations Project
Clemson University, May 4–7, 2000
... | 5 | [
-0.080078125,
0.0159912109375,
0.0400390625,
-0.031005859375,
-0.10498046875,
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0.01153564453125,
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0.0299072265625,
0.00830078125,
0.0255126953125,
-0.0615234375,
-0.0649414062... | 38,266 | 38266 | |
Mean Value Theorem follow on question
July 21st 2009, 07:45 AM #1
Newbie
Joined
Jul 2009
Posts
4
Mean Value Theorem follow on question
Hi, please could someone help me with the following
f(x) = square root (x), x>0
Apply the Mean Value Theorem to f(x) on the interval [100,102] to prove that
... | 5 | [
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0.02099609375,
0.035400390625,
-0.054931640625,
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0.1171875,
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0.060791015625,
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0.041015625,
0.06640625,
0.08251953125,
0.01080322265625,
0.004119873046875,
0.034912109375,
0.016357421875,
-... | 38,267 | 38267 | |
Base 12 Fractions
Date: 11/05/2001 at 06:59:05
From: Karla Killian
Subject: Decimal conversion of Base 12
I have read through the FAQ's and I do not understand the method for
doing decimals in base 12. The formulas were too complicated for me to
understand. I need a simple way to understand how to do and interpret
d... | 5 | [
0.01806640625,
0.0888671875,
0.003662109375,
-0.016845703125,
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0.0191650390625,
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0.1328125,
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0.036865234375,
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-0.004974365234375,
-0.050048828125,
0.01708984375,
-0.10546875,
... | 38,268 | 38268 | |
Equivalence Relations
August 26th 2009, 07:49 AM
Monkey D. Johnny
Equivalence Relations
I need help to get started with proving the 'only if' part of the following claim:
Let r be a relation. Define ~ to be the intersection of all equivalence relations containing r (So ~ is an equivalence relation.)
Sh... | 5 | [
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0.006500244140625,
0.0341796875,
0.0211181640625,
0.0089111328125,
-0.0471... | 38,269 | 38269 | |
Cramer's Rule and a System of Two Equations
Associated Topics || Dr. Math Home || Search Dr. Math
Cramer's Rule and a System of Two Equations
... | 4 | [
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0.00518798828125,
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-0.01696... | 38,270 | 38270 | |
Math Help
September 20th 2008, 04:46 AM #1
Newbie
Joined
Aug 2008
Posts
21
Suma
Demonstrate that:
$\<br /> \frac{1}{{\sum\limits_{k = 1}^n {\left( {\log _{a_k } x} \right)^{ - 1} } }} = \log _{a_1 *...*a_n } x.<br /> \<br />$
argh! it's hard for me to give a substantial hint here, so i will let... | 5 | [
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-0.00982666015625,
0.0732421875,
... | 38,271 | 38271 | |
Do Baumslag-Solitar Group von Neumann algebras have Property $\Gamma$?
up vote 11 down vote favorite
2
A type $II_{1}$ factor $M$ with trace $\tau$ has Property $\Gamma$ if for every finite subset $\{ x_{1}, x_{2},..., x_{n} \} \subseteq M$ and each $\epsilon >0$, there is a unitary element $u$ in $M$
with $\tau (u)=0... | 5 | [
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0.033203125,
0.038330078125,
-0.022460937... | 38,272 | 38272 | |
A question about to computing a integration
up vote 1 down vote favorite
2
Let $M$ be a smooth manifold of 2n-dim, $v$ be a map from $M$ to the matrix of order $m\times m$. We call $p\in M$ is the singularity, if $v(p)$ is non-invertible. Suppose $v$ is smooth and the
singularity is submanifold. Let $C$ be a connecte... | 5 | [
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0.004669189453125,
-0.1005859375,
0.016845703125,
-0.0272216796875,
0.06640625,
0.... | 38,273 | 38273 | |
related rates: rolling wheel
A wheel with radius 2 m rolls at 18 rad/s. How fast is a point on the rim of the wheel rising when the point is pi/3 radians above the horizontal (and rising)? (Round your answer to one decimal
place.)
A wheel with radius 2 m rolls at 18 rad/s. How fast is a point on the rim of the wheel r... | 5 | [
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0.00799560546875,
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0.0111083984375,
0.0198974609375,
0.08740234375,
-0.026123046875,
0.037... | 38,274 | 38274 | |
Determinant proof
July 14th 2009, 03:34 PM #1
Determinant proof
Q: Prove that if $|A|=|B|eq{0}$ and A and B are of the same size, then there exists a matrix C such that $|C|=1$ and A=CB.
A: Since $|A|=|B|eq{0}$ we know $A^{-1}$ and $B^{-1}$ exists. So,
$|A^{-1}||A|=|A^{-1}||B|$
$1=|A^{-1}||B|$
... | 5 | [
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0.01708984375,
-0.1005859375,
0.0703125,
0.029052734375,
-0.00872802... | 38,275 | 38275 | |
Partial fractions and integration
Thanks for the quick reply. What's a CAS? Darn, my first time using Latex and I forgot to put in the limits which was 3 and 0. Anyhow my partial fractions matches yours, but my answer(ln 8) after
integrating doesn't match the answer page of my book.
Last edited by mr fantastic; May 10... | 5 | [
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0.027587890625,
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-0.08056640625,
0.0016021728515625,... | 38,276 | 38276 | |
Tough Problem from Rotman's Group Theory, 3rd Ed
September 30th 2009, 10:15 AM #1
Newbie
Joined
Sep 2009
Posts
19
Tough Problem from Rotman's Group Theory, 3rd Ed
Given a group G of order (2^m)k, k odd. If G contains an element of order 2^m, then (show that) the set of elements of G having odd order is a... | 4 | [
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0.025146484... | 38,277 | 38277 | |
expand (e^2x)/(2x+1) up to x^3
January 27th 2014, 06:01 AM #2
MHF Contributor
January 27th 2014, 05:42 AM #1
Senior Member
expand (e^2x)/(2x+1) up to x^3
I want to expand (e^2x)/(2x+1) up to x^3. I can expand e^2x but I am then lost.
Re: expand (e^2x)/(2x+1) up to x^3
Re: expand (e^2x)/(2x+1) up to x^3
... | 5 | [
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0.0625,
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0.12109375,
-0.05395... | 38,278 | 38278 | |
Derivative question
March 17th 2007, 08:00 AM #1
Junior Member
Joined
Nov 2006
Posts
62
Derivative question
If f(x) = sqrt(3x)
then f'(x) = ?
and f' (4) = ?
I have done this problem over and over again and the result remains the same, incorrect. Here is what I did:
d/dx[sqrt(3x)] =
d/... | 4 | [
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-0.07568359375,
0.07373046875,
-0.0057373046875,
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0.0250244140625,
0.06494140625,
-0.01373291015625,
0.001983642578125,
-0.0751953125,
0.01782... | 38,279 | 38279 | |
Finding the Power Set of a Power Set
Date: 02/17/2005 at 04:45:48
From: Richard
Subject: "The second power set", or the power set of a power set
What is "the second power set", or the power set of the power set of
a set, say set <1,2,3>?
As we know, the power set of set <1,2,3> is
<< >,<1>,<2>,<3>,<1,2>,<1,3>,<2,... | 4 | [
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-0.0908203125,
0.048583984375,
0.06884765625,
-0.0255126953125,
-0.074... | 38,280 | 38280 | |
Loan
February 24th 2007, 10:10 AM
julie
Loan
James borrowed $5,000 from his friend 2 years ago; and, an additional $3,000 1 year ago. He wants to repay his friend the money that he borrowed plus interest at 8% compounded quarterly.
a) How much will James have to pay in 2 years time to fully repay his debt i... | 5 | [
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-0.05908203125,
-0.04248046875,
-0.048583984... | 38,281 | 38281 | |
Why is $\mathbb{Q}$-factoriality not local in the étale topology?
up vote 7 down vote favorite
3
I was reading Kollár and Mori's book today and stumbled on the following passage:
"The $\mathbb{Q}$-factoriality assumption is a very natural one if we start with smooth varieties, and it makes many proofs easier. On the ... | 4 | [
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0.05224609375,
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The CircuitCalculator.com Blog
The Excel based tool (see link below) calculates the capacitance and inductance per unit length as well as the impedance of a transmission line. It may be applied to wires, PCBs, etc.
A cross section of the transmission line is drawn into the Excel grids using different colors to represe... | 4 | [
-0.04736328125,
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Annuities
September 8th 2009, 05:09 PM
bart203
Annuities
a) Determine the present value on January 1, 2000, of payments of $200 every 6 months from January 1, 2000, through January 1, 2004, inclusive, and $100 every 6 months from July 1, 2004, through
January 1, 2010, inclusive, if i = .06.
I think it m... | 4 | [
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0.02429199... | 38,284 | 38284 | |
Trig Calculus Corner question
May 14th 2007, 09:09 AM #1
Junior Member
Joined
May 2007
Posts
25
Trig Calculus Corner question
This is my final review question I can't figure out from the trigonometry unit, I would appreciate any and all help. This week should open a whole new can of problems when I start... | 5 | [
0.0062255859375,
0.062255859375,
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0.... | 38,285 | 38285 | |
Sums of uniformly random vectors from the $n$-dimensional unit ball
up vote 3 down vote favorite
2
I'm interested in some instances of the following problem.
Let $n \geq 2$, and suppose we draw $k \geq 2$ vectors $v_1, \dots, v_k$ uniformly at random from the $n$-dimensional ball of radius $1$, $B_n(1)$. Consider... | 5 | [
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-0.0... | 38,286 | 38286 | |
Math 10 Pure Fractions! Add/Multiply/Factor
September 30th 2008, 06:05 PM #1
Newbie
Joined
Sep 2008
Posts
7
alright, my math is easy but theres always a few hard ones. just wondering if anyone can do these, show restrictions and show as much work as possible, or explain the steps.
4 | 5
---------... | 4 | [
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0.04... | 38,287 | 38287 | |
identify the curve
April 5th 2007, 12:36 PM
jeph
identify the curve
identify the curve by finding a Cartesian equation for the curve.
r=3sin(theta)
how do you get a circle of radius 3/2 centered at (0, 3/2)?
i got
r^2=3rsin(theta)
x^2+y^2=3y
did i do something wrong already? or do i j... | 4 | [
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0.03759765625,
0.0002460479736328125,
0.0184326171875,
-0.169921875,
-0.0529785... | 38,288 | 38288 | |
splitting fields
April 4th 2010, 03:24 PM
hamidr
splitting fields
Hi I do not understand the splitting fields, for example in the following:
find splitting field of (x^4)+1 over Q. all I know is that this function factors to (x^2+i)(x^2-i) but how do we know that this is the the end? how do we know this cann... | 5 | [
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0.0... | 38,289 | 38289 | |
Writing Games in Perl - Part 6 - Math for dummies
Following
posts 1,
2,
3,
4 and
5 on
the subject of writing games in Perl, now we are going to fix the math
in the game.
In the first post, I used a very naive simplification of the
movement calculation. I simply considered that the velocity was
constant during the time... | 5 | [
0.01190185546875,
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-0.059814453125,
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0.0234375,
... | 38,290 | 38290 | |
Matrices that are > 1 in a sense
up vote 3 down vote favorite
1
How can I characterize the class of square matrices such that: $ ||MN||_F \ge ||M||_F $?
In other words, when multiplied, they always give "bigger" products.
The norm is the Frobenius norm, which is the same as the Euclidean norm of the vectorization of... | 4 | [
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-0.0... | 38,291 | 38291 | |
Higher-Order Wave Equations and Matter Waves
The most common "wave equation" in one space and one time dimension is
where V is a constant equal to the phase velocity of a monochromatic wave. This has the general solution f(x+Vt) + g(x-Vt) for arbitrary functions f and g. Among the particular solutions of this
equatio... | 4 | [
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-0.... | 38,292 | 38292 | |
Probability of preserving connectivity between pair of vertices in weighted graph
up vote 0 down vote favorite
Let $G=(V,E)$ be an undirected graph and $p \colon E \mapsto (0,1]$ defines weights of its edges.
Let's fix two connected vertices $v_1, v_2 \in V$.
Random graph $G'=(V,E')$ is obtained from $G$ by removing... | 5 | [
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0.00347900390625,
0.01953125,
-0... | 38,293 | 38293 | |
Group with virtually cyclic positive part.
up vote 4 down vote favorite
1
Let $G$ be a group, $S$ its finite set of generators. Denote $G^+$ the subsemigroup of $G$ generated by $S$. Let $g\in G$, $H<G$ the subgroup generated by $g$ and let $g_1,...,g_k\in G$ be a finite
collection. Suppose $G^+\subset g_1H\cup\cdots\... | 5 | [
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-0.09228515625,
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-0.06689453125,
-0.026123046875,
-0.01... | 38,294 | 38294 | |
proof required...
February 8th 2010, 02:25 AM #1
Junior Member
Joined
Feb 2010
Posts
26
proof required...
if cosA+cosB+cosC=0=sinA+sinB+sinC
prove that
cos^2 A + cos^2 B + cos^2 C = sin^2 A + sin^2 B + sin^2 C = 3/2
I have no idea how to equate the two. This was part of the questions in the ... | 5 | [
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0.00775146484375,
-0.0036926269531... | 38,295 | 38295 | |
Replacement in von Neumann hierarchy of sets
up vote 3 down vote favorite
2
Is there an ordinal $\alpha$ such that $ZF$ believes that $V_{\alpha}$ is a model of $ZF$? (If it is problematic to state this since we have to check infinitely many axioms at once, formalize logic
in $ZF$. ) If $\alpha > \omega$ is a limit or... | 5 | [
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0.0341796875,
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0.044677734375,
0.024... | 38,296 | 38296 | |
Dirichlet series
Dirichlet series
Let $(\lambda_{n})_{{n\geq 1}}$ be an increasing sequence of positive real numbers tending to $\infty$. A Dirichlet series with exponents $(\lambda_{n})$ is a series of the form
$\sum_{n}a_{n}e^{{-\lambda_{n}z}}$
where $z$ and all the $a_{n}$ are complex numbers.
An ordinary Diri... | 4 | [
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0.0390625,
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0.03... | 38,297 | 38297 | |
Moving Particle Equation
May 20th 2008, 12:05 AM #1
Moving Particle Equation
Q: With the following two equations, find the value of $u$:
$2ut = 735 \ \ \ \ \ \ \ \ \ \ \ \ \dots (1)$
$0 = 3ut - 21 gt^2\ \ \ \ \dots (2)$.
The correct answer is $u=24.5$. I'm getting an incorrect answer. Can someone do ... | 4 | [
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Left adjoint of totalization?
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
There is a functor from bicomplexes to chain complexes sending a bicomplex to its associated total chain complex. Does this functor have a left... | 4 | [
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