content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
A heat kernel for Schrödinger operator with low-order terms
up vote 1 down vote favorite
In "Schrödinger Operator: Heat Kernel and Its Applications", Feng computes the heat kernels associated to Schrödinger operators with at most quadratic potentials.
I am trying to see how these work in one variable. So consider his... | 5 | [
0.0022430419921875,
-0.022705078125,
0.0260009765625,
0.0091552734375,
-0.01446533203125,
0.036865234375,
0.00653076171875,
-0.0361328125,
0.06689453125,
0.03857421875,
0.10009765625,
-0.006378173828125,
-0.0286865234375,
-0.0234375,
0.0771484375,
0.027099609375,
-0.020263671875,
-... | 35,200 | 35200 | |
cotangent bundle symplectic reduction and fibre bundles
up vote 12 down vote favorite
10
Suppose a compact Lie group $G$ acts on a manifold $M$ with only one orbit type $G/H$ ($H$ denotes the stabiliser group). Then the manifold $M$ becomes a fibre bundle over the quotient manifold $X:=M
/G$ with typical fibre $G/H$ a... | 5 | [
-0.0390625,
-0.00177764892578125,
0.11376953125,
-0.01544189453125,
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0.006927490234375,
0.017578125,
0.031494140625,
0.011474609375,
0.026123046875,
0.11669921875,
0.00994873046875,
-0.0245361328125,
-0.0128173828125,
0.0269775390625,
0.00927734375,
0.000197410583496... | 35,201 | 35201 | |
Koch's Snowflake
Koch’s Snowflake
December 23, 2011
F++F++F, rewriting rule F → F-F++F-F, and angle 60 degrees (in the Lindenmayer notation, F means move forward, + is a right turn and - is a left turn).
Your task is to write a program to draw the Koch Snowflake. When you are finished, you are welcome to read or run... | 5 | [
-0.030517578125,
-0.007232666015625,
0.00933837890625,
-0.05322265625,
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0.07421875,
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0.041259765625,
-0.008544921875,
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0.0027618408203125,
-0.00714111328125,
-0.072265625,
0.02294921875,
-0.01361083984375,
0.0225830078125,
-0.14257... | 35,202 | 35202 | |
coordinate geometry-
October 19th 2010, 08:47 AM #1
Junior Member
Joined
Sep 2009
Posts
66
The points have the following coordinates:
A(3,-2)
B(p,3)
C(6,2)
D(q,r)
The figure ABCD is a rhombus. Find the values of p, q and r.
Even though I used the midpoint formula and the distance f... | 4 | [
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0.047607421875,
-0.0625,
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0.11865234375,
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0.04296875,
-0.008056640625,
-0.0791015625,
-0.021484375,
-0.053466... | 35,203 | 35203 | |
Find gcd of 7^(4n+3) − 4^(10n+3) + 11^(10n+2)
... the GCD of that expression and which other one?
I gooot you... Then, the idea is the following: prove that your expression is always divisible by 400 = 16 x 25. Since 400 belongs to the range of it, you are done.
Last edited by coquitao; September 15th 2009 at 02:51 A... | 5 | [
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0.09619140625,
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0.11181640625,
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-0.006072998046875,
-0.049072265625,
... | 35,204 | 35204 | |
undetermined coefficients
February 6th 2010, 04:50 PM #1
Newbie
Joined
Oct 2009
Posts
6
undetermined coefficients
I'm supposed to find the solution this initial value problem using the method of undetermined coefficients
$<br /> y'' - 2y' - 3y = 3te^{2t}, y(0)=1, y'(0)=0.$
My guess was to use $Y... | 5 | [
-0.0732421875,
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0.03662109375,
0.0093994140625,
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0.03173828125,
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-0.0673828125,
0.04931640625,
-0.01470947265625,
-0.0274658203125,
-... | 35,205 | 35205 | |
TrueSkill™ Ranking System: Details - Microsoft Research
TrueSkill™ Ranking System: Details
The TrueSkill™ ranking system is a skill based ranking system for Xbox Live developed at Microsoft Research.
Overview
Most games have at their root a metric for judging whether the game’s goals have been met. In the case of ma... | 4 | [
-0.0242919921875,
-0.057373046875,
-0.07470703125,
-0.018798828125,
0.054443359375,
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0.052001953125,
-0.00897216796875,
-0.054443359375,
0.026611328125,
-0... | 35,206 | 35206 | |
Involute of a Circle
Date: 01/22/99 at 10:44:30
From: EDWARD MALONE
Subject: Formula for the involute of a circle
I know how to construct the involute of a circle, but I can't find a
formula for it.
Date: 01/22/99 at 11:53:45
From: Doctor Anthony
Subject: Re: Formula for the involute of a circle
A string is wound... | 4 | [
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0.03173828125,
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-0.0... | 35,207 | 35207 | |
continuity of extension of maps along curves
up vote 1 down vote favorite
1
Let $a\le b$ and $k\ge 0$ be given and fixed. Let furthermore $x$ and $y$ denote two different elements of a Hilbert space $H$. Suppose $u:\mathbb{R}\rightarrow H$ is a $C^k$-embedding connecting $x$
and $y$, s.t. the derivatives up to order $... | 4 | [
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0.06591796875,
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-0.00439... | 35,208 | 35208 | |
Dimensional regularization of the radiation field
8.4 Dimensional regularization of the radiation field
We now address the similar problem concerning the binary’s radiation field (3PN beyond the Einstein quadrupole formalism), for which three ambiguity parameters, [45 , 44 ] (see Section 8.2).
To apply dimensional re... | 4 | [
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-0.02294921875,
-0.0361328125,
-0.09326171875,
0.029... | 35,209 | 35209 | |
Calculating the Shapley value in a weighted voting game.
up vote 0 down vote favorite
Given a special case of WVG (Weighted Voting Game) of $a$ 1s and $b$ 2s and a quota q, $ [q:1,1,1,1..1,2,2,..2] $. I need help with calculating the Shapley value of a player with a weight of $2$ and
a player with a weight of $1$ as a... | 5 | [
0.031982421875,
0.00970458984375,
-0.029052734375,
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0.0908203125,
0.02490234375,
0.03015136718... | 35,210 | 35210 | |
SAT HELP: finding range
January 28th 2007, 07:16 AM #1
Member
Joined
Nov 2006
From
chicago
Posts
156
SAT HELP: finding range
Hello! I already mentioned this in a previous topic, but anyways, I bought an SAT practice book for getting ready for the big test. It was pretty well formated, except it only ... | 4 | [
-0.004669189453125,
0.00494384765625,
-0.07080078125,
0.00775146484375,
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0.0625,
-0.020263671875,
-0.0673828125,
0.07421875,
0.016845703125,
0.05517578125,
-0.014892578125,
0.034912109375,
0.04296875,
-0.0260009765625,
-0.0247802734375,... | 35,211 | 35211 | |
is this proof ok?
January 23rd 2013, 03:09 PM #1
Newbie
Joined
Jan 2013
From
sweden
Posts
13
is this proof ok?
let A and B be subsets of the universal set, prove that: A = AUB IIF B is a subset of A.
Suppose x is in A then x is in (AUB). which implies that B is a subset of A.
conversely Supp... | 4 | [
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0.048828125,
-0.01000976... | 35,212 | 35212 | |
Converting from Parametric to Implicit
October 4th 2008, 10:08 AM #1
Newbie
Joined
Oct 2008
Posts
1
Converting from Parametric to Implicit
Hi!
I was hoping that someone could give me a few guidelines as to how to find the Implicit representation of parametric equations, an example i need to solve ha... | 4 | [
-0.0869140625,
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0.03662109375,
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0.02392578125,
0.03076171875,
0.006591796875,
0.039306640625,
-0.0830078125,
-0.06152... | 35,213 | 35213 | |
Factoring Strategies
Date: 11/01/2002 at 09:02:37
From: Verna Snedacar
Subject: Factoring strategies
Hi Dr. Math,
I am returning to school and I am having a very hard time in a math
for elememtary teachers class. The objective is to teach for
understanding.
My assignment is to explore strategies that help you find ... | 4 | [
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-0.001861572265625,
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0.05712890625,
-0.03271484375,
0.00872802734375,
-0.059082031... | 35,214 | 35214 | |
Questions about Zero - Undefined or Indeterminate?
From: Norman Rogers
Subject: Nothing about nothing
Date: Wed, 16 Aug 95 22:56:55 EDT
1/ Is 0,0,0,... a geometric sequence ?
2/ What is the value of 0/0 ? (is it really undefined or are there an
infinite number of values)
3/ What is the value... | 4 | [
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0.12255859375,
-0.00078582763671875,
0.0277099609375,
-0.07080078125,
-0.0... | 35,215 | 35215 | |
The Green-Tao theorem and positive binary quadratic forms
up vote 10 down vote favorite
4
Some time ago I asked a question on consecutive numbers represented integrally by an integral positive binary quadratic form. It has occurred to me that, instead, the Green-Tao theorem may include a
result on arithmetic progressi... | 4 | [
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0.09375,
0.036865234375,
-0.0284423828125,
0.01007080078125,
-0.000537872314453125,
-0.014099121... | 35,216 | 35216 | |
Is this done correctly?
September 2nd 2007, 05:26 PM #1
Junior Member
Joined
Sep 2007
Posts
64
Is this done correctly?
$= \int [sec(\frac{x}{2}) + tan(\frac{3x+1}{5} )+ tan(7x)] dx$
$= \int sec(\frac{x}{2}) + \int tan(\frac{3x+1}{5} ) + \int tan(7x) dx$
$= 2ln|sec\frac{x}{2} + tan\frac{x}{2}| +... | 5 | [
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0.04931640625,
-0.0181884765625,
-0.05810546875,
-0.03125,
0.0062866210937... | 35,217 | 35217 | |
An Upper Bound for the Average of Top Order Statistics
up vote 3 down vote favorite
The following problem arises when we try to bound the expected offline optimal value of a simple online assignment problem with random values and unit weights, by its deterministic approximation.
The Problem
Consider a sequence $\{X_... | 5 | [
-0.049560546875,
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0.01373291015625,
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0.03955078125,
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-0.07275390625,
-0.032470703125,
-0.0111083984375,
0.091796875,
-0.03002929... | 35,218 | 35218 | |
Geometric Interpretation of Integral
November 15th 2009, 02:01 PM #1
Senior Member
Joined
Jul 2008
Posts
347
Could someone please explain to me what it means when I have to give a geometric interpretation of each term of the integral, say, $\sqrt{a^2-x^2}$ between x = b and x = 0?
From what I can mak... | 5 | [
0.039794921875,
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0.0089111328125,
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0.058837890625,
0.058837890625,
-0.010498046875,
0.0038909912109375,
0.0222167968... | 35,219 | 35219 | |
Solving for Variables
July 11th 2010, 06:48 AM #1
Newbie
Joined
Jul 2010
Posts
2
Solving for Variables
Okay, so I'm having a difficult time understanding how to solve problems such as
Solve for B1: A=1/2(B1+B2)h
Help please!?
Thanks.
Your first step should be to make B1 not be in the... | 4 | [
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-0.054931640625,
-0.0791015625,
0.027099609375,
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0.0029296875,
0.029296875,
-0.00008630752563476562,
0.154296875,
-0.005584716796875,
0.049... | 35,220 | 35220 | |
Euler's Method
April 6th 2011, 02:57 PM
hansbahia
Euler's Method
-Let’s consider the initial-value problem
Dy/dt = 2-y, y(0)=1
How can I compute three different approximate solutions corresponding, for an example, to Δt= 1.0, 0.5 and 0.25 over the interval 0 ≤ t ≤ 4 by using Euler’s method. Also how can ... | 4 | [
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-0.0546875,
... | 35,221 | 35221 | |
Three questions on $\operatorname{hocolim}$
up vote 7 down vote favorite
4
I posted this on math.stack.exchange but didn't get a helpful response, so please let me try it here.
Let $D$ be a small category and $F:D\to sSets$ a functor.
There is a bisimplicial set indicated by $$ ...\begin{array}{c}\to \\ \to\\\to\end... | 5 | [
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0.068359375,
... | 35,222 | 35222 | |
Show that the sum of a convergent and divergent series is divergent
March 26th 2010, 11:29 AM #1
Member
Joined
Jan 2010
Posts
232
Show that the sum of a convergent and divergent series is divergent
I am completely stumped on this one, so I could really use a hand with it.
Show that if the series $\s... | 4 | [
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0.03369140625,
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0.08203125,
-0.00872802734375,
0.0... | 35,223 | 35223 | |
Find the values of x
such that $-2 < x^3 - 2x^2 + x - 2 < 0$.
$-2<x^3-2x^2+x-2<0$ $-2<(x-2)(x^2+1)<0$ $x^2+1$ is positive Dividing throughout by $x^2+1$, $-2<(x-2)<0$ $0<x<2$
Concentrate on one side of the inequality at a time. $-2 < x^3-2x^2+x-2$ $\implies\ 0<x^3-2x^2+x=x(x^2-2x+1)=x(x-1)^2$ Solive this, then go on ... | 4 | [
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0.03515625,
0.01495361328125,
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0.06201171875,
0.04931640625,
-0.091796875,
0.007354736328125,
-0.05517578125,
0.0654296875,
-0.0093994140625,
-0.0174560546875,
0.0004253387451171875,
0.01904296875,
-0.025756835... | 35,224 | 35224 | |
Version of Brauer-Nesbitt for summands
up vote 6 down vote favorite
The Brauer-Nesbitt theorem (well, one of them) says that if $k$ is a field and I have two semisimple representations (on finite-dimensional $k$-vector spaces) $r_1$ and $r_2$ of a $k$-algebra $A$
with the property that the char polys of $r_1(a)$ and $... | 5 | [
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0.0025787353515625,
-0.01287841796875,
-0.01531982421875,
-0.0751953125,
0.095703125,
0.0250244140625,
-0.00030517578125,
0.0703125,
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0.005340576171875,
0.0145263671875,
0.0537109375,
-0.03369140625,
0.01068115234375,
-0.0020751953125,
... | 35,225 | 35225 | |
Weather Forecasting
Date: 05/24/97 at 11:44:56
From: Brett
Subject: Probability (Conditional Prob. and Independence)
I have a hard time with theoretical questions and am stuck on a
particular problem.
As a simplified model for weather forecasting, suppose that the
weather (either wet or dry) tomorrow will be the sa... | 5 | [
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0.01312255859375,
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0.0026397705078125,
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0.0172119140625,
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0.023193359375,
-0.044189453125,
0.029541015625,
-0.09375,
-0.0727... | 35,226 | 35226 | |
Implicit Differentitationl;finding equation
June 25th 2008, 01:34 PM #1
Junior Member
Joined
Sep 2007
Posts
69
Implicit Differentitationl;finding equation
Find all the points of the elispe 3x^2+2y^2=12 where the tangent line has slope 1. Make a sketch of the elispe and the tangent line to confirm your an... | 5 | [
-0.007293701171875,
-0.06103515625,
-0.0419921875,
-0.06689453125,
0.01385498046875,
0.045166015625,
0.00921630859375,
0.06396484375,
0.064453125,
-0.0103759765625,
0.12353515625,
0.00141143798828125,
-0.00555419921875,
-0.1083984375,
-0.01300048828125,
0.0439453125,
-0.08837890625,
... | 35,227 | 35227 | |
Integrate the gaussian distribution PDF with limits [const,+inf) ?
up vote 1 down vote favorite
Hey all!
i want to find the integral pr = Integral(limits from a constant>0 to +infinite, and the function inside is the PDF of Gauss distribution)..
http://en.wikipedia.org/wiki/Normal_distribution
in this link u can se... | 5 | [
-0.0732421875,
-0.0040283203125,
-0.06005859375,
-0.0380859375,
0.029541015625,
-0.034912109375,
0.03515625,
0.0654296875,
-0.10693359375,
0.07177734375,
0.053955078125,
0.036865234375,
0.040771484375,
0.037109375,
-0.048583984375,
-0.0299072265625,
0.0196533203125,
-0.053955078125... | 35,228 | 35228 | |
write in algebraic form
Write the given expression in algebraic form err algebraic form?
let $\theta = \arcsin\left(\frac{x}{2}\right)$ then $\sin{\theta} = \frac{x}{2} = \frac{opposite}{hypotenuse}$ using Pythagoras ... $adjacent = \sqrt{4 - x^2}$ so ... $\cot\left[\arcsin\left(\frac{x}
{2}\right)\right] = \cot{\thet... | 4 | [
0.040283203125,
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0.0576171875,
0.0252685546875,
0.08056640625,
0.0108642578125,
0.03... | 35,229 | 35229 | |
Convolution in statistics
December 27th 2010, 01:56 PM
HHsts
Convolution in statistics
Dear all,
I learned, to derive the common probability distribution function $f_{Z}(i)$
of e.g. two independent distribution functions $f_{X}(i)$X and Y
$f_{X}(i)$, one can use the convolution.
$f_{Z}(i)=\sum_... | 5 | [
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0.109375,
0.03564453125,
0.040771484375,
-0.0390625,
-0.0791015625,
0.00424194335937... | 35,230 | 35230 | |
The Missing Point
July 13th 2011, 07:23 PM #1
,.hello everyone,.,can u help me with this??
Given points (-3,5) , (-2,-3) , (3,-4). find the fourth point in the first quadrant so that the quadrilateral made is both circumscribable and inscribable.
I managed to start with the solution. using my 3 points, i... | 5 | [
-0.025390625,
0.02587890625,
-0.043212890625,
-0.05126953125,
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0.01019287109375,
0.15234375,
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0.080078125,
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0.031005859375,
-0.0277099609375,
-0.0125732421875,
... | 35,231 | 35231 | |
Questions about lines
March 1st 2009, 10:03 PM #1
Newbie
Joined
Jan 2009
From
Australia
Posts
5
Questions about lines
ahh thanks! umm i actually have two more questions (sorry!)
um a) caculate the x and y intercept of the staright line with the equation 3x-2y=9
and
b) transpose the equ... | 4 | [
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0.0634765625,
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0.025146484375,
-0.1025390625,
0.046630859375,
0.0556640625,
-0.0634765625,
0.027587890625,
-0.00897216796875,
-0.024658203125,
0.07275390625,
-0.1572265625,
-0.02929687... | 35,232 | 35232 | |
Find the splitting field
December 13th 2008, 07:27 AM #1
Member
Joined
Feb 2008
Posts
125
Find the splitting field
Find the splitting field for f(x)=((x^2)+x+2)((x^2)+2x+2) over Z_3[x]
Write f(x) as a product of linear factors
I have no clue what this means, we haven't even discussed this, Pleas... | 5 | [
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0.0196533203125,
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0.04443359375,
0.08984375,
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-0.00897216796875,
-0.060546875,
0.02587890625,
-0.0021514892578125,
-0.022705078125,
-0.02490234375,
-0.002471923828125,
0.00811767578125,
0.01318359375,
-0.05224609375,
0... | 35,233 | 35233 | |
Proof of existence of recursively inaccessible and Mahlo ordinals
up vote 3 down vote favorite
As in title - I'm looking for a proof of the existence of a countable recursively inaccessible or recursively Mahlo ordinals, especially the first one. When looking for it in all the papers I
stumbled across their existence ... | 4 | [
-0.095703125,
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0.09375,
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0.02294921875,
-0.0264892578125,
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0.0223388671875,
0.01806640625,
-0.03857421875,
0.019775390625,
-0.0146484375,
-0.0302734375... | 35,234 | 35234 | |
Contour Maps in Python
This activity requires that the following software is installed on your system:
• Python 2.5 or higher.
• Numpy 1.1 or higher.
• Matplotlib 0.98.3.
• And a few other Python packages.
The simplest way to get a Python environment with all the packages needed for a successful scientific e... | 5 | [
0.00003314018249511719,
-0.05712890625,
-0.01446533203125,
-0.09423828125,
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0.07373046875,
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0.014404296875,
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-0.030029296875,
0.04248046875,
0.027099609375,
0.024169921875,
-0.0751953125,
... | 35,235 | 35235 | |
Minimal number of generators for $A^n$
up vote 15 down vote favorite
4
Let $A$ be a commutative ring and $n \in \mathbb{N}$. What is the minimal number $e_A(n)$ of generators of the $A$-algebra $A^n$? Here is what I already know (I can add proofs if necessary) from a
little joint work:
1. We have $e_A(n)=0$ for $n=0... | 4 | [
0.0140380859375,
0.049560546875,
-0.0869140625,
0.0203857421875,
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0.042724609375,
-0.0703125,
-0.007476806640625,
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0.07177734375,
-0.010986328125,
0.039794921875,
-0.076171875,
0.0024566650390625,
0.06396484375,
0.00897216796875,
-0.0071716... | 35,236 | 35236 | |
A Polynomial Inequality Proof
up vote 0 down vote favorite
Given $x_1,x_2, \ldots, x_n \ge 0, \alpha \ge 1$, show that
$\sum_{i}\alpha x_i(\sum_{j \le i}{x_j})^{\alpha-1} \ge (\sum_{i}x_i)^\alpha$
We're pretty sure the ineuqality holds for the given precondition. It can be validated using a small piece of matlab cod... | 5 | [
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0.11181640625,
0.036865234375,
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-0.0576171875,
0.0986328125,
0.01470947265625,
... | 35,237 | 35237 | |
Variation of parameters question
May 26th 2009, 08:27 AM
dankelly07
Variation of parameters question
Can someone help get me started with this I'm not sure where to begin..
$<br /> \begin{gathered}<br /> x\frac{{dy}}<br /> {{dx}} + (2 + 3x)\frac{{dy}}<br /> {{dx}} + 3y = r(x); \hfill \\<br /> \hfill \\<br... | 5 | [
-0.10400390625,
-0.041259765625,
-0.0093994140625,
-0.0267333984375,
-0.0169677734375,
0.0140380859375,
-0.00180816650390625,
-0.004058837890625,
-0.00811767578125,
-0.01483154296875,
0.00885009765625,
-0.1025390625,
0.010498046875,
-0.0169677734375,
0.09375,
-0.0035858154296875,
-0.... | 35,238 | 35238 | |
Necessary/Sufficient condition/Algorithm that tells me a function field is a kummer extension
up vote 0 down vote favorite
I start my question with an example. Suppose $F/K$ be the function field generated by $x^n - yx^{n-1} - 1 = 0$. It is not a cyclic over K(y), but if I set $t = yx^{n-1}$ then we have $K(x,t) \subs... | 4 | [
-0.020751953125,
0.053955078125,
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-0.030517578125,
0.0017547607421875,
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-0.019775390625,
0.006683349609375,
-0.06591796875,
0.046875,
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-0.03857421875,
0.017333984375,
0.006683349609375,
0.07958984375,
-0.0495605468... | 35,239 | 35239 | |
Mechanics Problem; Any help would be appreciated
March 26th 2011, 05:12 AM #1
Junior Member
Joined
Mar 2009
Posts
28
The details of the question are below;
Identical Cars A, B and C, are initially at rest in a straight line on a horizontal surface with their brakes off. Car A is pushed towards the o... | 5 | [
0.024658203125,
0.0771484375,
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0.039306640625,
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0.02978515625,
-0.06982421875,
0.09619140625,
0.006591796875,
0.00573730... | 35,240 | 35240 | |
seriously hitting my boiling point on these problems please help
March 14th 2014, 02:04 PM #1
Newbie
Joined
Mar 2014
From
canada
Posts
7
seriously hitting my boiling point on these problems please help
The two problems require to approximate the series to four decimal points. both are assumed to be c... | 5 | [
-0.00830078125,
0.05322265625,
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0.11572265625,
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0.030029296875,
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0.08447265625,
-0.087890625,
-0.061279296875,
0.0673828125,
-0.0... | 35,241 | 35241 | |
Prove: each square is the sum of 2 consecutive triangular numbers
October 1st 2010, 01:24 AM #1
Is the following an acceptable proof (be harsh
$t_k=1+2+3+\ldots+k=\frac{(k+1)k}{2}$
$t_{k-1}=1+2+3+\ldots+(k-1)=\frac{k(k-1)}{2}$
$\Longrightarrow t_{k-1}+t_k=k^2 \text{ } \square ?$
I mean, is the in... | 4 | [
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0.03857421875,
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-0.07568359375,
-0.037841796875,
0.03... | 35,242 | 35242 | |
double integral
May 31st 2010, 11:36 PM #1
Newbie
Joined
Mar 2010
From
Melbourne
Posts
20
double integral
I'm trying to show that
$\int\int_{0\leq x,y\leq 1}\Bigg\vert\frac{x^2-y^2}{(x^2+y^2)^2}\Bigg\vert\hspace{1mm}dxdy = 2\int_{0}^{1}\int_{0}^{1}\frac{x^2-y^2}{(x^2+y^2)^2}dxdy$
so that I ... | 5 | [
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0.053955078125,
-0.05615234375,
0.042236328125,
0.0191650390625,
-0.10205... | 35,243 | 35243 | |
Euclidean Spaces
October 10th 2008, 11:39 AM #1
Member
Joined
Jun 2008
Posts
170
Euclidean Spaces
Let's say if we have $\bold{x} \in \mathbb{R}^{n}$ and we want to show that $B_{r}(\bold{x})$(open ball of radius $r >0$) is convex. We know that $d(\bold{x}, \bold{y}) = |\bold{x}- \bold{y}|$
(e.g. the ... | 4 | [
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0.00732421875,
0.07275390625,
-0.100097656... | 35,244 | 35244 | |
Urgent Proving Identities
January 12th 2009, 02:45 AM #1
Newbie
Joined
Dec 2008
From
Philippines
Posts
15
Urgent Proving Identities
Prove that
tan A - (sec A sin^3A / 1 + cos A ) = sin A
Obtained from my Workings
(sin A / cos A) - (sin^3A / cos A + cos^2 A )(From here on I don't know wh... | 4 | [
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0.0732421875,
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-0.0013885498046875,
0.0405273... | 35,245 | 35245 | |
-webit-transform matrix3d
Matrix3d
When you dive into apples documentation of matrix3d you will find a short definition "Specifies a 3D transformation as a 4 x 4 matrix." following by the function definition in code:
matrix3d(m00, m01, m02, m03,
m10, m11, m12, m13,
m20, m21, m22, m23,
m30... | 4 | [
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0.0272216796875,
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0.01007080078125,
0.01708984375,
0.04345703125,
-0.01025390625,
0.1494140... | 35,246 | 35246 | |
A question on almost simple groups
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
We know that if $G$ is a simple group with $p+1$ Sylow $p$-subgroups, then $G$ is 2-transitive. Now let $G$ be almost simple group with $p+... | 5 | [
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0.005035400390... | 35,247 | 35247 | |
Maximizing number of factors contributing in the sum of sorted array bounded by a value
up vote 0 down vote favorite
I have a sorted array of integers of size n. These values are not unique. What I need to do is : Given a B, I need to find an i<A[n] such that the sum of |A[j:1 to n]-i| is lesser than B and to that
par... | 5 | [
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0.09375,
0.09375,
0.041259765625,
-0.006... | 35,248 | 35248 | |
Soluble Groups....
April 2nd 2009, 08:55 AM #1
Junior Member
Joined
Mar 2009
Posts
36
Soluble Groups....
Hi guys,
How can you prove that S3, S4 & A4 are soluble, & that A5 & S5 are not?
I know that every group of order less than 60 is soluble, but how would you proove it without using that fact... | 5 | [
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-0.02... | 35,249 | 35249 | |
A hard question that came in my midterms
Find the Center and Radius: A circle w/ (-5,4) & (-6,-3) as ends of a diameter
If the ends of the diameter are (-5,4) and (-6,-3), then the center of the circle is the midpoint of the said diameter, which is ((-5+(-6))/2,(4+(-3))/2) = (-5.5,0.5) -------------answer. The radius
... | 4 | [
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0.0234375,
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0.1171875,
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0.0693359375,
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0.010986328125,
... | 35,250 | 35250 | |
Intro to Real Analysis Proof
September 28th 2008, 02:38 PM
ilikedmath
Intro to Real Analysis Proof
I am really having a hard time in this intro to real analysis class. I feel as if I'm the only one in class who isn't getting it. I have an extremely hard time thinking abstractly and
constructing my own proofs... | 5 | [
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0.024658203125,
0.0625,
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0.042724609375,
0.029296875,
0.0196533203125,
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0.0291748046875,
0.06201171875,
-0.01953125,
0.0108642578125,
-0.02783203125,
0.01373291015625,
-0.0260009765625,... | 35,251 | 35251 | |
dy
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Here's the question you clicked on:
burhan101 Group Title
Trig identity.. I do... | 4 | [
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0.01055908203125,
-0.036376953125,
0.000033855438232421875,
-0.006256103515625... | 35,252 | 35252 | |
Spectral decomposition and invertibility
December 3rd 2009, 07:12 PM #1
Spectral decomposition and invertibility
Question: Let $T$ be a normal operator on a finite-dimensional complex inner product space $V$. Consider spectral decomposition $T = \lambda_1 T_1 + ... + \lambda_k T_k$ and prove that $T$ is
inver... | 5 | [
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0.021484375,
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0.04150390625,
-0.004058837... | 35,253 | 35253 | |
Limits of functions with converging zeros
up vote 0 down vote favorite
1
What can one say about the derivatives of a smooth function of several variables that is a limit of smooth functions with converging zeros?
More precisely, suppose that $f_i: R^n \to R^m$ is a sequence of smooth functions converging uniformly in... | 4 | [
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0.04052734375,
0.07421875,
0.059326171875,
0.034912109375,
-0.0400390625,
0.04443359375,
0.00537109375,
-0.02197265625,
-0.009826... | 35,254 | 35254 | |
probability
April 15th 2008, 07:44 AM #1
Newbie
Joined
Apr 2008
Posts
8
probability
1, In a particular departmental store customers arrive at a check up counter
according to poisson distribution at an average of 5 per hour
During a particular 1 hour period,
a,what is the probability that at l... | 5 | [
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-0.0067138671875,
0.045166015625,
-0.06298828125,
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0.125,
-0.036865234375,
0.02978515625,
0.0400390625,
0.0791015625,
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-0.0164794921875,
-0.00396728515625,
0.10400390625,
0.0281982421875,
0.031982421875,
-0.095214843... | 35,255 | 35255 | |
horizontal asymptotes
July 17th 2008, 04:19 AM
robasc
horizontal asymptotes
I am helping a friend and I am trying to remember if this is the correct way to figure out this horizontal asymptote?
equation:
1.493x^2 - 39.06x + 273.5
D = ---------------------------
0.0051x^2 - 0.1398x + 1
1.49... | 4 | [
0.004119873046875,
-0.029052734375,
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0.0673828125,
0.083984375,
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-0.01202392578125,
0.0274658203125,
0.06689453125,
0.01385498046875,
0.004669189453125,
-0.05004882812... | 35,256 | 35256 | |
Integral trig
$I=\int x\sin^2(x)\cos(x)dx$ Use product rule: $\int uv' = uv -\int u'v$ $Let \ u=x \ \ so: \ \ u'=1$ $Let \ v'=sin^2xcosx \ \ so: \ \ v=\frac{1}{3}sin^3x$ $I=uv - \int u'v = \frac{1}{3}xsin^3x - J$
where $J=\frac{1}{3}\int sin^3xdx$ $=\frac{1}{3}\int sinx(1-cos^2x)dx$ $=\frac{1}{3}\int sinx-cos^2xsinxdx$... | 5 | [
-0.0047607421875,
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... | 35,257 | 35257 | |
f(x) continuous at c
December 4th 2012, 03:08 PM
cloeannx3
f(x) continuous at c
Please Help!!
Prove that if c is irrational f(x) is continuous at c.
I would appreciate any type of hints or just where to start.
December 4th 2012, 03:33 PM
skeeter
Re: f(x) continuous at c
think it would help if y... | 5 | [
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0.125,
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0.078125,
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-0.03515625,
-0.038330078125,
-0.0266113281... | 35,258 | 35258 | |
Requiring references
up vote 1 down vote favorite
Assume $V$ be a genus larger than 1 handlebody, $S=\partial_{+} V$.
Denote $N$ be the normal closure of $MCG(V)$ in $MCG(S)$.
Is there any material related to the quotient group $MCG(S)/N$ ? Thanks!
mapping-class-groups gt.geometric-topology
@l.Mosher:sorry I ... | 5 | [
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-0.03271484375,
0.... | 35,259 | 35259 | |
spectral radius of a matrix as one element changes
up vote 2 down vote favorite
4
Here's my question --
Let $A$ be an $n \times n$ real matrix, and suppose that the spectral radius $\rho(A)$ is less than one (spectral radius = max eigenvalue). Let's choose some $1 \leq i \leq N$ and look at $A_{N,i}$.
Namely, let's r... | 4 | [
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0.0888671875,
... | 35,260 | 35260 | |
Summer Math Problem driving me crazy
June 22nd 2010, 02:05 PM #1
Newbie
Joined
Jun 2010
Posts
2
Summer Math Problem driving me crazy
This is a pre-calculus review to help me get ready for ap calc. I could not simplify the expression so I entered it into wolfram mathematica. I don't understand its second ... | 4 | [
-0.01373291015625,
0.024169921875,
0.04150390625,
0.0096435546875,
-0.0322265625,
0.010498046875,
-0.11669921875,
0.0262451171875,
0.00640869140625,
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-0.038818359375,
0.005462646484375,
0.0947265625,
0.01904296875,
-0.0458... | 35,261 | 35261 | |
Sum to Infinity
May 9th 2008, 11:51 PM #1
Junior Member
Joined
Dec 2007
Posts
59
Sum to Infinity
Hi again guys!
Once again I need help with what should be relatively simple, because once again my maths textbook refuses to explain things properly
Ok so its about the Sum to Infinity of a Geometri... | 4 | [
-0.0115966796875,
0.02490234375,
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0.0135498046875,
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... | 35,262 | 35262 | |
confused
January 4th 2009, 07:23 PM
frog09
confused
If $f'(x)=cos(x^2-1) and f(-1)=1.5, then f(5)= ?$
so far i have:
$\int_{-1}^5 cos(x^2-a) dx= f(5)-f(-1)$
i let $u=x^2-1$
$du=2x$
change the limits from x=5 to u=24, x=-1 to u=0
and have
$1/2 \int_0^{24} cos(u) du + f(-1)$
w... | 5 | [
-0.029052734375,
0.0164794921875,
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... | 35,263 | 35263 | |
Are there Heronian triangles that can be decomposed into three smaller ones?
up vote 4 down vote favorite
1
Is there anything known about the existence of Heronian triangles ABC (i.e. with rational side lengths and rational area) that can be decomposed into three Heronian triangles ABD, BCD, CAD?
Equivalently, is ther... | 5 | [
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0.0305... | 35,264 | 35264 | |
Finding the Circumcenter of a Sphere
Date: 09/24/2003 at 07:01:08
From: Chich-Hsiung Yeh
Subject: How to find the circumcenter (Xc,Yc,Zc) of a sphere
I am trying to write a computer program to find the circumcenter
(Xc,Yc,Zc) of a sphere given 3 points (x1,y1,z1), (x2,y2,z2) and
(x3,y3,z3) on the sphere, along with t... | 4 | [
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0.0198974609375,
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... | 35,265 | 35265 | |
Understanding Kinematics and Newton’s Laws of Motion—Wolfram|Alpha Blog
Throughout the history of physics, scientists have postulated laws and theories about the nature of the world around them. Some were proven false, while others have grown to be the basis of entire
fields of study. One such field is classical mechan... | 5 | [
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Any metric spaces can be viewed as a subset of normed spaces
December 15th 2011, 01:34 PM #1
Newbie
Joined
Oct 2010
Posts
3
Any metric spaces can be viewed as a subset of normed spaces
Consider a metric space (X, d). Let (B(X), ||.||) be the vector space of bounded real valued functions on X with the sup... | 4 | [
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0.02734375,
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0.10009765625,
-0.028686... | 35,267 | 35267 | |
Help me with graphing parabolas
February 20th 2007, 04:31 PM #1
Newbie
Joined
May 2006
Posts
19
Help me with graphing parabolas
failed a unit test retaking it but I don't know how to do some of the questions please help explain..
y = ( x + 2)^2 -3 its not in y = a ( x - h)^2 + k so I don't use h,k fo... | 4 | [
0.043701171875,
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0.0233154296875,
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0.0155029296875,
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0.04443359375,
0.0120849609375,
... | 35,268 | 35268 | |
Chi-Square Test
Date: 04/24/2002 at 09:32:20
From: Dave Edwards
Subject: Probability
Four chiropractors examine a patient. Each can allocate the patient to
a category, 1, 2, or 3. I have calculated by percentage the number of
times the chiropractors agree for any combination of 2, 3, and all
4. I need to compare this... | 4 | [
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0.0208740234375,
-... | 35,269 | 35269 | |
Basic number theory problem
July 23rd 2012, 02:27 AM #1
Newbie
Joined
Jul 2012
From
Hanoi
Posts
3
Basic number theory problem
Let x and y be integers. Prove that 2x + 3y is divisible
by 17 iff 9x + 5y is divisible by 17.
Solution. 17 | (2x + 3y) ⇒ 17 | [13(2x + 3y)], or 17 | (26x + 39y) ⇒
... | 5 | [
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-0.0771484375,... | 35,270 | 35270 | |
y'' + 2/x y' = cy
March 8th 2014, 03:29 AM #1
Newbie
Joined
Mar 2014
From
Finland
Posts
5
y'' + 2/x y' = cy
Hello!
I have this second order differential equation which is causing me some trouble:
y'' + 2/x y' = c y
where c is a constant. I've got no clear idea of where to start solving... | 4 | [
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0.06103515625,
0.0189208984375,
0.0012817382812... | 35,271 | 35271 | |
Believe it or not... a log question which was briefly stumping us
Believe it or not… a log question which was briefly stumping us
Hi all,
A teacher approached me with the following question.
The function $\ln(x^{-2})$ has a graph that looks like:
It makes sense that the function exists for all negative x values, be... | 5 | [
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-0.0869140625,
-0.06201171875,
... | 35,272 | 35272 | |
Triple integral, I'm lost
June 8th 2009, 01:13 PM #1
Member
Joined
Dec 2008
Posts
228
Triple integral, I'm lost
(triple integral) x dv
Where R is bounded by the paraboloid x=4y^2+4z^2 and the plane x=4.
It would be so, so, so helpful if someone shows me the steps.
By the way... when you at... | 5 | [
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0.0712890625,
0.027099609375,
0.04248046875,
0.0062255859375,
0.00665283203... | 35,273 | 35273 | |
Linear independence of matrix set?
March 9th 2010, 05:29 PM
crymorenoobs
Linear independence of matrix set?
I need to show that the following set of 2x2 matrices forms a basis for the subspace that it spans, ie) that it is linearly independent.
{[1 1] [0 1] [2 0] }
{[1 0], [1 1], [0 -1]}
For a vect... | 4 | [
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-0.042236328125,
-0.04833984375... | 35,274 | 35274 | |
Fourier Series: Triangular waveform, Ao calc going wrong somewhere
January 7th 2010, 08:12 AM
emmv
Fourier Series: Triangular waveform, Ao calc going wrong somewhere
The question asked is calculate Fourier series for waveform
$f(t) = 5 + \frac{5}{\pi}\theta for -\pi < \theta < 0$
$f(t) = 5 - \frac{5}{\pi... | 5 | [
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-0.108... | 35,275 | 35275 | |
Fractional Brownian motion and Laplacian
up vote 4 down vote favorite
Having read this link on math stackexchange, I would like to submit to your wisdom the following questions.
Is it possible, mutatis mutandis, to repeat the same reasoning for a fractional Brownian motion?
More specifically: a real valued Gaussian ... | 4 | [
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0.07666015625,
0.... | 35,276 | 35276 | |
Rate of change
October 22nd 2008, 07:06 AM
ihmth
Rate of change
1.) A swimming pool os 40ft long 20ft wide 8ft deep at the deep end and 3ft deep at a shallow depth. The bottom being rectangular. If the pool is filled with by pumping water into it at the rate
of 100 cubic ft per min. How fast is the water lev... | 5 | [
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0.05126953125,
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0.11083984375,
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0.07958984375,
-0.035888671875,
0.05664062... | 35,277 | 35277 | |
binomial series expansion
March 9th 2010, 05:32 PM #1
Senior Member
Joined
Apr 2009
Posts
253
binomial series expansion
use the binomial series to expand the function as a power series.
$\sqrt{1+x}$
I know how to start the problem but i get stuck.
using:
$(1+x)^k = \sum_{n=0}^{\infty}\bin... | 4 | [
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0.03662109375,
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0.0439453125,
0.0074462890625,
0.0371093... | 35,278 | 35278 | |
Nasty limit...
May 14th 2011, 09:13 PM #1
Junior Member
Joined
Oct 2009
Posts
57
Nasty limit...
I have this really nasty limit that I've been banging my head on all night. The question asks me to calculate the following:
$\lim_{n\to\infty}\frac{n \times \left(\frac{2n-2}{2n-1}\right)^{2n-2}}{2n-1}$
... | 5 | [
-0.04443359375,
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-0.0220947265625,
0.02392578125,
-0.045... | 35,279 | 35279 | |
Money problem
November 1st 2008, 07:24 PM #1
Money problem
Tom borrowed a sum of money at 10% per annum compound interest. If he repaid the sum only after 2 years, he would have to repay $4356. I already found the sum of money that he had borrowed to be
$3600.
The question is if he repaid the sum by two ... | 4 | [
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0.00299072265625,
-0.0927734375,
0.04223632812... | 35,280 | 35280 | |
Need help with ff.
February 10th 2007, 10:47 PM #1
Newbie
Joined
Feb 2007
Posts
2
Need help with ff.
Hello all!
I'm not really good in math... recently, our prof announced we would be having a test in the coming week, and he gave us the ff. problems as review questions... trouble is, I'm having a he... | 5 | [
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-0.0013275146484375,
0.04443359375,
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confusing lagrange multiplier question
August 18th 2010, 01:19 AM
tsang
confusing lagrange multiplier question
f(x,y,z)=xy+z^3
subject to x^2+y^2+z^2=1
Find all the absolute maximum and minimum.
I tried to solve the simutaneous equations, and I ended up with 14 critical points! (Headbang)
So I ... | 5 | [
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... | 35,282 | 35282 | |
center of the dihedral group
March 25th 2010, 07:21 PM #1
Junior Member
Joined
Jan 2010
Posts
41
center of the dihedral group
Hi,
my question is, "for n = 3 or greater, show $Z(D_n)$is trivial if n is odd and is {1, $a^{n/2}$} if n is even."
Any help would be appreciated; we haven't learned anyt... | 4 | [
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Halp! Linear equation questions.
September 17th 2008, 03:51 PM
bad_at_math
Halp! Linear equation questions.
I'm supposed to find the y-intercept, slope, and equation for a couple problems. I'm having a lot of trouble with these. This first one has the two points on a graph (0,3) and (6,6) The y
intercept is ... | 4 | [
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0.011... | 35,284 | 35284 | |
Constant Multiple Rule...Yes or No?
October 15th 2013, 06:52 PM
nycmath
Constant Multiple Rule...Yes or No?
Find s'(t).
Does the constant multiple rule apply here?
s(t) = [-2(2-t) * sqrt{1+t}]/3
I pulled out 1/3 but my answer is nothing like the book's answer.
Applying the constant rule, the ... | 5 | [
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Why can't subvarieties separate?
up vote 5 down vote favorite
3
I'm posting my answer to this question as its own question:
Let $V$ be an irreducible projective variety over $\mathbb{C}$. Let $U$ be a Zariski open set in $V$. I'll use $V(\mathbb{C})$ and $U(\mathbb{C})$ to mean $V$ and $U$ equipped with their Euclide... | 5 | [
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pre- calc test next period need help please ...
I assume you mean 68/4+i to mean: $\frac{68}{4+i}$ We get: $\frac{68}{4+i} - \frac{17}{4-i}$ Then you do something called multiply with the complex conjugat. You multiply both numerator and
denominator with (focusing on the first term), you multiply with $(4-i)$ So we get... | 4 | [
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0... | 35,287 | 35287 | |
Free splittings of one-relator groups
up vote 15 down vote favorite
9
Roughly speaking, I want to know whether one-relator groups only have 'obvious' free splittings.
Consider a one-relator group $G=F/\langle\langle r\rangle\rangle$, where $F$ is a free group. Is it true that $F$ splits non-trivially as a free pr... | 4 | [
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0.034912109... | 35,288 | 35288 | |
Radioactive decay
February 21st 2011, 10:40 PM #1
Newbie
Joined
Oct 2008
Posts
24
Radioactive decay
Radium-226 has a half life of 1620 years. Find the time period during which a given mass of this material is reduced by one-quarter.
Q= Ce^-rt should be the right equation?
Stumped on how to set ... | 4 | [
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The image of the point-pushing group in the hyperelliptic representation of the braid group
up vote 20 down vote favorite
4
Let $B_{2g+1}$ be the Artin braid group on $2g+1$ strands. There is a symplectic representation
$\rho: B_{2g+1} \rightarrow Sp_{2g}(\mathbf{Z})$
called the "hyperelliptic representation," which... | 5 | [
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Josephus Problem
Date: 04/18/2003 at 20:39:50
From: Jeremy
Subject: Determining an equation from a series
There are x people sitting around a table. Every other person at the
table is eliminated until there is only one person left. For
instance, at a four-person table, the second and fourth person are
eliminated; the... | 4 | [
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Math Forum Discussions
Re: disjunctive constraints in integer linear programming
Posted: Apr 13, 2013 11:02 AM
On Thursday, April 11, 2013 12:24:57 PM UTC-7, d.inf...@gmail.com wrote:
> I have an integer linear programming problem as follows:
>
>
>
> The constraints are either
>
>
>
>
>
> x >= 0
>
> y = u
>
> z = x + ... | 4 | [
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limit from sides in complex function..
July 12th 2010, 10:31 AM #1
MHF Contributor
Joined
Nov 2008
Posts
1,401
limit from sides in complex function..
i was told here that there is no +infinity and -infinity in complex functions
only infinity
but i have a solved question from a test which is solv... | 4 | [
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Map constructed from the coquasitriangular structure of SLq(2) which appears not to respect the standard commutation relations
up vote 0 down vote favorite
Let $A$ be a Hopf algebra dually paired with a quasi-triangular Hopf algebra $B$. If $x$ is some fixed element of $A$, then we can define a linear map $$ P_x: A \t... | 4 | [
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Hausdorf distance
August 28th 2010, 02:40 PM #1
Newbie
Joined
Aug 2010
Posts
1
Hausdorf distance
How can I determine the Hausdorf distance between 2 sets when the intersection of those sets is not empty?
For example,
$U = \{ (x,y) : \, 1 \leq x \leq 4 \text{ and } 1 \leq y \leq 2 \}$
$V = \... | 4 | [
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0.0751953125,
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Function equations, vetex, etc... Plz help!
May 2nd 2008, 06:28 AM #1
Newbie
Joined
May 2008
Posts
5
1. Write the equation of the constant function, if possible, which passes throught the point P(4,5).
2. Write the equation of the cubic function, if possible, which passes through the points A(0,1), B... | 5 | [
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Can't figure out this 3d vectors problem.
October 1st 2008, 10:29 AM #1
Junior Member
Joined
Oct 2008
Posts
29
Can't figure out this 3d vectors problem.
I've been trying to figure out how my teacher did this work question from a note she gave us, for two hours now and I still can't figure it out. If one ... | 4 | [
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Lie subgroups of SU(3)
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Apart from images of representations of subgroups of SU(2), what are the Lie subgroups of SU(3)? Where should I look for a reference?
up vote 7 down... | 4 | [
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Ricci flow as a gradient flow and its Lyapunov function
up vote 1 down vote favorite
1
In study of Ricci flow, for making Ricci flow as a gradient flow I faced $\mathcal{F}(g,f)=\int (R+|\nabla f|^2)e^{-f}$. I know that if we suppose $\frac{df}{dt}=-R$, then $\frac{d}{dt}\mathcal{F}
(g,f)=\int \langle-Ric-Hess(f),\dot... | 4 | [
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