content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Limit of multivariable function using definition?
August 12th 2010, 10:03 AM #1
Junior Member
Joined
Feb 2010
Posts
54
Limit of multivariable function using definition?
I need to prove that the following limits exist but i have to use the definition of a limit.(the definition being that lim[(x,y)tends to... | 4 | [
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-0... | 38,500 | 38500 | |
fourier transforms
December 31st 2007, 03:59 AM #1
Junior Member
Joined
Jun 2007
Posts
43
fourier transforms
if $B(x)$ is a scalar field in (3d space) with fourier transform $\widetilde{B}(p)$ and $x\rightarrow x'$ is a finite isometry (i.e a rotation and translation $x'=Rx-a$ what is the fourier
tra... | 5 | [
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... | 38,501 | 38501 | |
Curves with infinitely many integral points consecutive Fibonacci numbers
up vote 1 down vote favorite
I suspect the Granville-Langevin conjecture implies this.
Let $F(x,y)=0$ be a curve with infinitely many integral points $(F_n,F_{n+1})$.
Is it true that either $x^2+x y - y^2 -1$ or $x^2+ x y -y ^2 +1$ divides $F(... | 5 | [
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-0.0986328125,... | 38,502 | 38502 | |
Equation of circle
September 25th 2010, 07:56 AM #1
Super Member
Joined
Dec 2009
Posts
755
Equation of circle
Find the equation of the circle with passes through the points $(0,1)$ and $(3,-2)$ and has its centre lying on the line $y=x-2$
If the point $(a,b)$ is the center then
$r=\sqrt{(0-a)^2... | 4 | [
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Formalizing Euclid's proof of the infinitude of primes
up vote 10 down vote favorite
2
Euclid's proof of the infinitude of primes requires me to take an arbitrary finite set of primes and multiply them together. If I want to formalize this proof in Peano Arithmetic, I need to know that
any finite set of numbers has a ... | 4 | [
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0.0673828125... | 38,504 | 38504 | |
Are maximal Cohen-Macaulay modules supported everywhere?
up vote 0 down vote favorite
1
Let $A$ be a local CM ring, and $M$ a maximal CM $A$-module. Is it true that $\operatorname{Supp}M=\operatorname{Spec}A$ ? This suspicion stems from such statements as:
• If $\omega$ is a canonical module of $A$, then $\omega_{\... | 5 | [
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Cubic Polynomial
June 23rd 2010, 05:25 AM
rtblue
Cubic Polynomial
A Cubic Polynomial with integral coefficients has a root $(3-4i)$ and possesses the form:
$y=x^3+ax+b$ Find AB/25
Have no clue where to start with this one. Any help is appreciated.
June 23rd 2010, 05:41 AM
Ackbeet
If you know one... | 5 | [
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... | 38,506 | 38506 | |
Surface Integrals
April 11th 2009, 10:58 AM #1
Junior Member
Joined
Mar 2009
Posts
32
Surface Integrals
Hi,
is the formula for ds equal to
$<br /> ds = sqrt(( (pz/px)^2 + (pz/py)^2 + 1))$
where p = partial derivative
many thanks
Problem:
For the parametrically defined surface... | 4 | [
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Posts about Hash function on The Pseudo Random Bit Bucket
In Pcompress, I have implemented a variant of the rolling hash based Content Defined Chunking that provides both deduplication accuracy and high performance. This post attempts to explain the
chunking process, covers the chunking computations that are done in Pc... | 4 | [
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I can not get the answer from the book could you please explain
November 14th 2008, 07:45 PM #1
I can not get the answer from the book could you please explain
Estimate the volume in metric units and compute the acual volume of the item:
Oil in a barrel that has a height of 1 m and a diameter of 0.5m
Th... | 4 | [
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Subset Sum
March 27, 2012
Instead of a matrix, we use a hash table; that way we don’t have to figure out all the sums ahead of time. Here’s the code:
(define (subset-sum xs t)
(let ((h (make-hash identity = #f 99991)))
(let loop1 ((xs xs))
(if (null? xs) #f
(let loop2 ((ys (cons (cons 0 (list)) (h 'enlist))))
(cond ... | 5 | [
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What is the probability that two numbers are relatively prime?
up vote 7 down vote favorite
1
The basic question that I have is in the title, but let us make it more rigorous below.
Let $N=\{1, 2, ..., n\}$, and put the (normalized) counting measure, $\mu_n$, on $N\times N$.
Let $\mathcal{S}_n= \{ (a, b)\in N\times ... | 5 | [
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Rates of change
July 12th 2009, 11:16 PM #1
Junior Member
Joined
Sep 2008
Posts
73
Rates of change
Sand being poured from a conveyor belt forms a cone with height h and a semi-vertical angle of 60 degrees. Let the volume of the sand is $\pi h^3$.
Suppose that the sand is being poured at a constant r... | 5 | [
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Characterization of amenable actions
up vote 5 down vote favorite
2
Let $(X,\mu)$ be a $G$-space, i.e. a measure space with a Borel quasi-invariant $G$-action. Say that $X$ is amenable (equivalently, that the action is amenable) if there is a $G$-fixed point in every
affine space over $X$ with an $\alpha$-twisted acti... | 4 | [
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Sample and Population Standard Deviation
Date: 03/03/2001 at 11:18:08
From: Lara Brook
Subject: Standard deviation
What letters represent theoretical and 'real' standard deviation,
mean, and variance?
Date: 03/05/2001 at 10:22:11
From: Doctor Jordi
Subject: Re: Standard deviation
Hello, Lara - thanks for writing ... | 5 | [
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0.000... | 38,514 | 38514 | |
integration by substitution xe^x^2
October 5th 2008, 09:44 PM #1
Member
Joined
Jun 2008
Posts
175
integration by substitution xe^x^2
Question is to calculate the integral $\int\limits_0^2 {xe^{x^2 } dx} =$
This is what I have done, however looks to be incorrect.
I let $u = e^{x^2 }$
and so... | 5 | [
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Geometric progression?
April 28th 2009, 05:29 AM #1
Geometric progression?
If $a_{i}\in\mathbb{R}, i = 1,2,3,...N$and all $a_{i}\ 's$ are distinct such that:
$\left(\sum_{i = 1}^{n - 1} a_{i}^2\right)x^2 + 2\left(\sum_{i = 1}^{n - 1} a_{i}a_{i + 1}\right)x + \sum_{i = 2}^{n} a_{i}^2\leq 0$
,then show that... | 5 | [
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Permutation Groups
April 25th 2012, 07:55 PM #1
Newbie
Joined
Apr 2012
From
USA
Posts
1
Permutation Groups
Hi everyone,
I could really use some help with this problem:
Let H be the subset of S[3] consisting of all the permutations that leave the element 2 fixed.
(i) Prove that H is a s... | 5 | [
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Domain and Range
October 20th 2011, 09:47 PM #1
Domain and Range
Hi,
I'm just wondering if I'm correct and also what notation I should use here.
The question is asking for the domain and range of $f(x,y)=e^{y-x^2}$
I think the domain is $Domain \subset R^2$ and $Range>0$
Thanks for your help.
... | 4 | [
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Area between two curves
May 17th 2008, 08:42 PM
casemeister
Area between two curves
Find the area of the regions by the lines and curves given below.
$y= 8cos(x)$ and $y = sec^2(x)$ between $\frac{-\pi}{3} \leq x \leq \frac{\pi}{3}$
May 17th 2008, 08:53 PM
o_O
First notice that the curves both inters... | 5 | [
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integral (partial fraction)
find $\int \frac{4 x^2 + 10 x + 24}{(x - 5)(x^2+4)} dx$
$\frac{4 x^2 + 10 x + 24}{(x - 5)(x^2+4)} = \frac{A}{x - 5} + \frac{B x + C}{x^2+4}$
$4x^2+10x+24 = A(x^2+4)+(Bx+C)(x-5)$
I was able to find A by: $170 = A(29), A= 6$
need help finding B and C
| 4 | [
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0.0... | 38,520 | 38520 | |
integral with radical and trigonometry
September 27th 2013, 10:06 AM
infraRed
integral with radical and trigonometry
Is there anyone who could walk me through this practice problem?:
$\int{\sqrt{1 + \frac{cosx}{sinx}}}\,dx$
I really struggle with integrals involving radicals or trigonometry.
September... | 5 | [
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Data Management Problem Help
July 17th 2008, 01:35 PM #1
I know I may be asking too much on this one, but please hear me out. I'm taking a data management course in summer school, summer school is only 3 weeks long. So basically, I'm learn a large
amount of material everyday for six hours, material that would ... | 4 | [
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-0.... | 38,522 | 38522 | |
quadratic equation from amazing lil boy
November 25th 2007, 11:01 AM
pitt
quadratic equation from amazing lil boy
hi there i want help with this quadratic equation.. im quiet young.. so try to explain it step by step so i can understand :)
y= 2x3+3x+19
p.s. the first 3 is squared
can someone ident... | 4 | [
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Bijections
Date: 04/28/2003 at 13:08:03
From: Mandy
Subject: Bijections
Find a bijection from (0, 1) to (0, 1]. (Be sure to prove that your
function has the proper properties.)
Date: 04/28/2003 at 16:52:15
From: Doctor Rob
Subject: Re: Bijections
Thanks for writing to Ask Dr. Math, Mandy.
The trick here is to pic... | 5 | [
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-0.0011825561523437... | 38,524 | 38524 | |
Integrated Rate Laws
CAcT HomePage
Integrated Rate Laws
This is a continuation of Rate and Order of Reactions
Skills to develop
• Apply either the differential rate laws or integrated rate laws to solve chemical kinetic probl... | 5 | [
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Complete Residue Systems Problem
May 21st 2010, 04:46 PM
1337h4x
Complete Residue Systems Problem
Hello everyone, I have a question on complete residue systems that I do not understand.
1. Are there any twin primes (like 11 and 13, or 3 and 5) of the form (2^n)-1, (2^n) +1, for n > 2?
If there are, do ... | 4 | [
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... | 38,526 | 38526 | |
Another Goodness of Fit test....GRRRR
August 18th 2008, 08:08 PM #1
Newbie
Joined
Jul 2008
Posts
5
Another Goodness of Fit test....GRRRR
I'm so confused with this goodness of fit stuff. I'm trying to solve the following problem...can anyone help??
The safety director of Honda USA took samples at ran... | 4 | [
0.024169921875,
0.05419921875,
0.05322265625,
-0.04345703125,
0.111328125,
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0.05615234375,
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0.052734375,
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... | 38,527 | 38527 | |
Splitting of primes in cubic fields with limited ramifications.
up vote 4 down vote favorite
3
Let $\mathbb{F}$ be a cubic field, i.e, $\mathbb{F} = \mathbb{Q}(\alpha)$ where $\alpha$ is a root of a cubic irreducible polynomial over $\mathbb{Q}$, satisfying $disc(\mathbb{F}/\mathbb{Q})$ is a
prime or a power of a prim... | 5 | [
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0.02880859375,
0.07275390625,
-0.09912109375,
0.0299072265625,
0.03173828125,
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0.061767578125,
0.0439453125,
0.04150390625,
-0.06689453125,
0.030151367187... | 38,528 | 38528 | |
Solving simultaneously involving logs.
July 18th 2009, 11:23 PM
smmmc
Solving simultaneously involving logs.
1) 52=x*10^m
2) 80=x*10^3m
my attempt
from 1) rearrange to get x=52/10^m
then sub into 2)
so
80=52/10^m * 10^3m
so
log 10(80) = log10(52) - log10(10^m) + log10(10^3m)
... | 4 | [
0.00787353515625,
0.0908203125,
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0.0625,
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0.0986328125,
-0.... | 38,529 | 38529 | |
Probability Problem in a Lewis Carroll Book
Date: 12/13/2008 at 18:09:24
From: James
Subject: Probability problem in a Lewis Carroll book
In Lewis Carroll's "A Tangled Tale" he asks the following:
"Say that 70 per cent of a group of soldiers have lost an eye — 75 per
cent an ear — 80 per cent an arm — 85 per cent a ... | 5 | [
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0.08642578125,
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0.07421875,
0.0179443359375,
0.0026092529296875,
-0.09326171875,
-0.02124023437... | 38,530 | 38530 | |
Norm inequality for stochastic maps
up vote 1 down vote favorite
I know that if $\Lambda$ is a stochastic positive linear map, i.e., $\Lambda(I) = I$, it is true that
\[ \|\Lambda(B)\| \leq \| B \| \]
For any operator $B$, where $\|\cdot\|$ is the standard operator norm $\|B\| := \max_{|v|= 1} |Bv|$. Is it true for ... | 4 | [
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-0.0126953125,
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0.15234375,
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-0.000755310058... | 38,531 | 38531 | |
Prove if 7 divides x^3+y^3+z^3 then it also divides xyz
October 24th 2012, 06:11 AM #1
Junior Member
Joined
Nov 2011
From
Karachi
Posts
36
Prove if 7 divides x^3+y^3+z^3 then it also divides xyz
Hello guys!
We are to prove that if 7 divides $x^3+y^3+z^3$, then it also divides $xyz$. How do we go... | 4 | [
-0.046875,
0.000728607177734375,
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0.0771484375,
0.0498046875,
-0.0228271484375,
-0.10205078125,
0.04077... | 38,532 | 38532 | |
Is there a natural distance between skew hermitian matrices?
up vote 2 down vote favorite
Working in machine learning, I try to find a way to compare time series, which can be considered as semi-continuous matrices belonging to $\mathbb R^{n \times \mathbb R}$ (a column corresponds to
n-dimensional the value of the ti... | 4 | [
-0.05712890625,
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-0.0380859375,
0.056640625,
0.0264892... | 38,533 | 38533 | |
Need help solving some 2nd order DEs
August 14th 2009, 08:03 AM #1
Newbie
Joined
Aug 2009
Posts
1
Need help solving some 2nd order DEs
Hi to everyone. I need help. I have few equations that i can not solve. If there is anyone that can help...please solve them step by step. I need them as fast as posible.... | 5 | [
-0.07470703125,
-0.04443359375,
0.0233154296875,
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-0.0216064453125,
-0.039794921875,
-0.02685546875,
0.06884765625,
-0.0654296875,
-0.003692626953125,
-0.00872802734375,
0.03271484375,
-0.000522613525390625,
0.014343261718... | 38,534 | 38534 | |
Conversion of Pure Recurring Decimal into Vulgar Fraction | Worked-out Examples
Conversion of Pure Recurring Decimal into Vulgar Fraction
Follow the steps for the conversion of pure recurring decimal into vulgar fraction:
(i) First write the decimal form by removing the bar from the top and put it equal to n (any var... | 4 | [
-0.04443359375,
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0.0101318359375,
-0.0380859375,
-0.013916015625,
0.09375,
0.0206... | 38,535 | 38535 | |
Integrating factor on Exact, Homogeneous DE
September 12th 2011, 03:26 PM #1
Junior Member
Joined
Aug 2010
Posts
41
Integrating factor on Exact, Homogeneous DE
Problem: $y*(1+x)+2xy'=0$
I have rearranged the equation to put it in exact form, resulting in the equation:
$(y+xy)dx+2xdy=0$
Afte... | 5 | [
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0.03125,
0.005889892578125,
-0.036132812... | 38,536 | 38536 | |
closed curve, trace
January 27th 2010, 06:11 PM #1
Newbie
Joined
Dec 2008
Posts
17
closed curve, trace
Let $\gamma$ be a closed path in a domain $D$ such that $W(\gamma, \zeta)=0$ for all $\zeta ot \in D$. Suppose that $f(z)$ is analytic on $D$ except possibly at a finite number of isolated
singulari... | 4 | [
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-0.039794921875,
-0.10498046875,
0.033447265625,
-0.02062988281... | 38,537 | 38537 | |
Decomposition of an abelian von Neumann algebra
up vote 1 down vote favorite
1
Hi, I came across the statement below and I couldn't figure out why it is true. I was hoping someone could explain it or give me a good reference. Thank you in advance. "Let $\pi$ be a non-degenerate
representation of a separable C*-algebra... | 4 | [
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0.06201171875,
... | 38,538 | 38538 | |
Partitions of n into non-negative powers of 2.
October 21st 2008, 08:21 PM #1
Member
Joined
May 2008
From
Melbourne Australia
Posts
210
Thanks
23
Partitions of n into non-negative powers of 2.
10. (Solved)
Let b(n) denote the number of partitions of n into non-negative powers of 2. Prove that... | 5 | [
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0.060546875,
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-0.06884765625,
... | 38,539 | 38539 | |
Rings and Fields query
November 23rd 2007, 01:07 PM
musicmental85
Rings and Fields query
Hi,
Just trying to work on my rings and fields.
If its not too much trouble could someone explain how to do this for me? Its not so much a solution I'm looking for as the method as I really need to understand it
... | 5 | [
-0.0791015625,
0.03125,
-0.0908203125,
0.03564453125,
0.0308837890625,
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0.06884765625,
0.016845703125,
-0.01019287109375,
-0.08935546875,
0.0145263671875,
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0.053955078125,
0.050537109375,
-0.0264892578125,
-0.049072265625,
-0.045654296875,
-0.04565... | 38,540 | 38540 | |
Transformation Matrix
From Math Images
A transformation matrix is a special matrix that can describe 2d and 3d transformations. Transformations are frequently used in linear algebra and computer graphics, since transformations can be
easily represented, combined and computed.
Computing Transformations
If you have a... | 4 | [
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-0.007537841796875,
-0.055908203125,
-0.06689453125,
-0.0203857421875,
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-0.01397705078125,
-0.042724609375,
0.06787109375,
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0.036376953125,
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0.004638671875,
0.034423828125,
-0.025146484375,
0.037109375,
-0.0756835937... | 38,541 | 38541 | |
Finding First Derivatives by Definition
Associated Topics || Dr. Math Home || Search Dr. Math
Finding First Derivatives by Definition
... | 4 | [
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0.00970458984375,
0.05810546875,
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-0.033203125,
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0.0086669921875,
-0.0400390625,
-0.07... | 38,542 | 38542 | |
Joint PDF
May 6th 2009, 04:35 AM #1
Junior Member
Joined
Nov 2008
Posts
45
Joint PDF
The joint probability distribution is given by,
$f_{(X,Y)}(x,y) = 2$ if $0 \leq x \leq y \leq 1$, 0 otherwise.
(i) Determine the marginal density functions of X and Y. Check that it is indeed a pdf.
(ii) C... | 4 | [
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-0.06884765625,
0.0140380859375,
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-0.006103515625,
-... | 38,543 | 38543 | |
Solving Equations - using addition property
February 19th 2006, 02:40 PM #1
Obviously I don't know what I'm doing here. The book gives an answer of -8, so any hints on where my method is flawed would be appreciated.
z + 9 = 1
z + 9 = + (-1) = 1 + (-1)
z + 8 = 0
z = -1
Euclid Alexandria
Ob... | 4 | [
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-0.059326171875,
-0.02734375,... | 38,544 | 38544 | |
Prove that E is disconnected
November 25th 2011, 04:41 PM
wopashui
Prove that E is disconnected
Prove that a closed subset E of a metric space (M,d) is disconnected iff there exists disjoint nonempty closed sets E1, E2 such that E=E1UE2.
for the --> direction, we have E is disconnected, then by definition t... | 4 | [
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-0.00141143798828125,
0.0108032226562... | 38,545 | 38545 | |
Continued Fractions
October 21st 2007, 03:22 PM #1
Newbie
Joined
Sep 2007
Posts
11
Continued Fractions
Hello, I can't seem to understand how to use continued fractions to find the value of x in: x^2 + x - 72 = 0
Can someone please explain how to solve this problem? Basically, I need to prove that x ... | 5 | [
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-0.0174560546875,
0... | 38,546 | 38546 | |
This Linear Equation Answer Can't be Correct
November 5th 2012, 02:49 AM #1
Junior Member
Joined
Oct 2012
From
Australia
Posts
26
This Linear Equation Answer Can't be Correct
Linear Equation: 7x+5/3=11 Answer: x=4/3 ... I'm not getting that answer and don't know in which step I went wrong.
Can s... | 4 | [
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0.031982421875,
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0.01190185546875,
-0.07666015625,
0.11425... | 38,547 | 38547 | |
Poisson's
My watch list
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Poisson's ratio
When a sampl... | 4 | [
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0.00469970703125,
0.0218505859375,
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0.0634765625,
0.00160980224609375,
-0.0673828125,
0.0281982421875,
-0.004... | 38,548 | 38548 | |
Magnetic Fields Produced by Currents: Ampere’s Law
Magnetic fields have both direction and magnitude. As noted before, one way to explore the direction of a magnetic field is with compasses, as shown for a long straight current-carrying wire in
Figure 1. Hall probes can determine the magnitude of the field. The field a... | 5 | [
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0.0225830078125,
-0.169921875,
0.00... | 38,549 | 38549 | |
Orthocenter
May 19th 2008, 01:58 PM
tehc0ffee
Orthocenter
Heres the problem : Given triangle RST, with R= (-3,2), S=(4,5) , T= (7,-2), find the cords of the orthocenter.
I have no idea what to do, my teacher gave this to us and im confused..
thanks (:
May 19th 2008, 02:12 PM
Incendiary
Quote:
... | 4 | [
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0.08642578125,
-0.08203125,
... | 38,550 | 38550 | |
How can I tell if a variety is normal?
up vote 12 down vote favorite
3
Suppose $R$ is a subalgebra of ${\mathbb C}[x_1,...,x_N]$ generated by polynomials $p_1,...,p_k.$ I know that ${\mathbb C}[x_1,...,x_N]$ is the integral closure of $R$. Is there an algorithm to
determine if $R={\mathbb C}[x_1,...,x_N]$ which would ... | 4 | [
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0.0255126953125,
0.0... | 38,551 | 38551 | |
Modular representation theory: central idempotents in $\mathbb{Z}_p[G]$
up vote 7 down vote favorite
3
Let $G$ be a finite group and let $p$ be a prime dividing the order of $G$. Let $\chi$ be a $\mathbb{C}_p$-valued irreducible character of $G$ and let $e_{\chi} = |G|^{-1}\chi(1)\sum_{g \in G} \chi(g
^{-1})g$ be the ... | 5 | [
-0.0301513671875,
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0.027587890625,
-0.0274658203125,
-0.0... | 38,552 | 38552 | |
how to calculate final velocity of car
September 17th 2011, 06:49 PM
moonnightingale
how to calculate final velocity of car
If a car accelerates uniformly from rest at 3.2m/s(2). when the car has traveled a distance of 40. meters, its speed will be.
I tried to use equation
v-u/a= t
but there r two... | 4 | [
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-0.017578125,
0.0177001953125,
0.07128906... | 38,553 | 38553 | |
Introduction to Linear and Exponential Growth
Date: 11/04/2003 at 19:12:07
From: Christina
Subject: Exponentially Growth
As a biology project, Nicole is investigating how fast a particular
beetle population will grow under controlled conditions. She started
her experiment with 5 beetles. The next month she counted ... | 4 | [
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-0.07470703... | 38,554 | 38554 | |
Valuation Criterion of Properness, (Irreducible) Varieties
up vote 3 down vote favorite
Greetings,
(I suspect this question has nothing to do with the Valuation Criterion of Properness, but I don't know for sure - feel free to modify my title)
This question arises in section 2.4 of Fulton's book on Toric Varieties -... | 4 | [
0.044677734375,
0.00021457672119140625,
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0.0069580078125,
0.0898437... | 38,555 | 38555 | |
an easy particle problem
July 13th 2010, 07:49 PM #1
Newbie
Joined
Jul 2010
Posts
23
an easy particle problem
Hi, just want to double check my answers and how it is set up! My prof. grades HW very harshly :/
V(t)=t^2-2t-8 1(<=) t (<=) 6
I did this using definite integrals.
Thanks
ye... | 4 | [
0.0184326171875,
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0.09375,
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0.05517578125,
0.0104370117... | 38,556 | 38556 | |
symmetric difference
Hello, $A \Delta B=(A \cup B) \backslash (A \cap B)$, this is according to the definition you're given. It is pretty obvious that it is commutative, by commutativity of $\cap$ and $\cup$. As for
associativity, you have to prove that $(A \Delta B) \Delta C=A \Delta (B \Delta C)$. Just use the defini... | 5 | [
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0.05615234375,
0... | 38,557 | 38557 | |
Calculus test questions
September 7th 2010, 01:49 AM
johnsy123
Calculus test questions
1) The curve with equation y=f(x) passes through the point (3,-1) and f '(x)=2x+5. find f(x).
2) find s in terms of t, if ds/dt=t+3-1/t^2 and s=6 and t=1.
September 7th 2010, 01:53 AM
Prove It
1) $f'(x) = 2x + 5... | 5 | [
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-0.0186767578125,
-0.0201416015625,
-0.00131225585937... | 38,558 | 38558 | |
What is the cohomology of this complex?
up vote 4 down vote favorite
1
I have a feeling that this may be a very easy question for some people on MO, but it isn't for me.
Take a finite pointed set $X$, with $*$ the base-point. Build a cosimplicial set which in degree $n \ge 1$ is $X^n$ (the cartesian product of $n$ co... | 5 | [
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0.099609375,
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... | 38,559 | 38559 | |
Linear Algebra Primer: Part 3- Basis, Span,
Linear Algebra Primer: Part 3- Span, Basis, and Dimension
This tutorial will focus on the concepts of span, basis, and dimension. Graph theory analogues will also be discussed in the context of basis.
Attached is a LaTeX typeset version for those who would prefer to view t... | 4 | [
-0.046142578125,
-0.039794921875,
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0.037353515625,
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-0.0235595703125,
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0.06982421875,
0.0888671875,
0.007476806640625,
-0.031494140625,
-0.058349609375,
0.000293731689453125,
-0.0... | 38,560 | 38560 | |
Square Root Proof Problem
June 23rd 2008, 07:23 PM
cryptocrow
Square Root Proof Problem
Hi. I'm having trouble with these problems.
p is and odd prime for both.
Prove x = 0 mod p if x = -x mod p.
Prove x = +/-y mod p^2 if x^2 = y^2 mod p^2, neither x nor y are 0 mod p.
Thanks...
June 23rd 20... | 4 | [
-0.01318359375,
0.037353515625,
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0.038818359375,
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0.03955078125,
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0.012451171875,
-0.025390... | 38,561 | 38561 | |
[Numpy-discussion] Interpolation via Fourier transform
M Trumpis mtrumpis@berkeley....
Thu Mar 5 13:51:44 CST 2009
Hi Nadav.. if you want a lower resolution 2d function with the same
field of view (or whatever term is appropriate to your case), then in
principle you can truncate your higher frequencies and do this:
... | 4 | [
-0.045654296875,
0.0033111572265625,
0.031494140625,
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0.0361328125,
-0.03662109375,
-0.006805419921875... | 38,562 | 38562 | |
Normal subgroups of the Galois group
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I am trying to teach myself Galois theory. Is it true that every for a field extension K->L, that every normal subgroup of Gal(L:K) is of ... | 4 | [
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0.08837890625,
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0.0189208... | 38,563 | 38563 | |
word problem
I claim 103138 divides that number for all positive integer values of n. This is done by observing that $a-b$ divides $a^n - b^n$ and then rearranging the given number into sums of such differences.
For example, $278 = 2141-1863$ and $-278 = 1492 - 1770$ Thus $278|2141^n -1863^n + 1492^n - 1770^n$ Similarl... | 5 | [
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-0.033447265625,
0.... | 38,564 | 38564 | |
Finding equation of Tangent.
April 3rd 2010, 09:48 AM #1
Newbie
Joined
Apr 2010
From
Reading, Berkshire.
Posts
5
Finding equation of Tangent.
The curve y = √8x + 1 and the tangent at the point P(3,5) on the curve. This tangent meets the y-axis. Find the equation of the tangent at P.
Can anyone p... | 4 | [
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0.0625,
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0.030517578125,
0.0120849609375,
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0.10546875,
-0.031494140625,
0.0859375,
-0.10400390625,
-0.036376953125,
0.002... | 38,565 | 38565 | |
Isotropic subspaces in cohomology
up vote 5 down vote favorite
3
Hello,
Here is a problem I encountered in the study of Kähler manifolds but there is a natural generalisation of this for topological spaces. If $X$ is a topological space, denote by $g_\mathbb{R}$ the real
genus of $X$, that is the maximal dimension of... | 5 | [
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0.041015625,
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0.107421875,
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0.0007781982421875,
-0.03076171875,
-0.1298828125,
0.00927734375,
0.0216064453125,
... | 38,566 | 38566 | |
Trigonometry and Complex Exponentials
Amazingly, trig functions can also be expressed back in terms of the complex exponential. Then everything involving trig functions can be transformed into something involving the exponential
function. This is very surprising.
In order to easily obtain trig identities like , let's ... | 5 | [
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0.06494140625,
... | 38,567 | 38567 | |
Explicit description of the "simplicial tensor product" of chain complexes
up vote 7 down vote favorite
3
Recall that there is an equivalence of categories (Dold-Kan) $$N:\mathrm{s}\mathbf{Ab}\simeq \operatorname{Ch}_{\geq 0}(\mathbf{Ab}):\Gamma$$ between simplicial abelian groups and (connective) chain
complexes, whe... | 4 | [
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0.06591... | 38,568 | 38568 | |
Galois Groups vs. Fundamental Groups
up vote 44 down vote favorite
54
In a recent blog post Terry Tao mentions in passing that:
"Class groups...are arithmetic analogues of the (abelianised) fundamental groups in topology, with Galois groups serving as the analogue of the full fundamental group."
Can anyone explain t... | 4 | [
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0.... | 38,569 | 38569 | |
A brief vector question
March 1st 2009, 12:23 AM #1
Junior Member
Joined
Mar 2009
Posts
66
A brief vector question
This vector question has three parts, and I've done the first two, finding the point of intersection and acute angle between them. It's the third bit I don't understand.
L1 = 2i-j+3k + ... | 5 | [
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-0.080078125,
... | 38,570 | 38570 | |
Independence of rotated spherical harmonics
up vote 0 down vote favorite
1
Hi,
Consider a spherical harmonic of degree $l$, denoted by $y_l^m$. I rotate this harmonic using $2l+1$ different rotations. The set of functions I get is not an orthogonal set, but the functions are
still harmonics. The question is: does thi... | 4 | [
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0.04296875,
-0.0069580078125,
-0.0869140625,
-0.0186767578125,
-0.04687... | 38,571 | 38571 | |
BEATCALC
BEATCALC: Beat the Calculator!
Back to Calculation Tips & Tricks
┏━━━━━━━━━━━━━━━━━━━━━┯━━━━━━━━━━━━━━... | 4 | [
0.0035247802734375,
0.001251220703125,
-0.016357421875,
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-0.11669921875,
0.034423828125,
-0.072265625,
0.0159912109375,
-0.0230712890625,
-0.0233154296875,
-0.019287109375,
-0.0576171875,
0.050537109375,
-0.0145263671875,
-0.0272216796875,
-0.022705078125,
-0.108398437... | 38,572 | 38572 | |
MMSE estimator expressed through cumulants
up vote 0 down vote favorite
I have a linear model $$Y=HX+N,$$ where $H$ is a matrix and $X$ are drawn from $p_X(X)$, and $N$ is Gaussian noise variates.
Now, if $X$ is multivariate Gaussian, then a linear estimator $\hat{X}=A+BX$ solves the problem $$\mathcal{E}(|\hat{X}-X|... | 4 | [
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0.07373046875,
0.109375,
-0.0108642578125,
-0.00671... | 38,573 | 38573 | |
Yr 10 Maths Level 1:Quadratics Investigation
August 17th 2008, 01:52 AM #1
Newbie
Joined
Aug 2008
Posts
1
the equation is h=-0.4 d^2 + 2d.
h=height above water, d=horizontal distance.
Q1) how high above the water is the dolphin when it has travelled 2 m horizontally from its starting point?
... | 4 | [
0.0235595703125,
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0.08984375,
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0.053466796875,
-0.0322265625,
-0.0008544... | 38,574 | 38574 | |
Kronecker-Weber false for number fields distinct from $\mathbb{Q}$
up vote 1 down vote favorite
1
Keith Conrad's History of Class Field Theory notes has a comment that given any number field $K\neq \mathbb{Q}$, then $K$ has an abelian extension which is not contained in $K(\zeta_\infty)$, so the
Kronecker-Weber theore... | 4 | [
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0.080078125,
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0.01647949... | 38,575 | 38575 | |
Discrete Mathematics Project
Index
Discrete Mathematics Project
Counting Techniques/Probability Activity
Title
"What's In the Bag?" (Jim Arnow)
Goals
... | 5 | [
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0.0830078125,
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0.0908203125,
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0.058349609375,
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0.027099609375,
-0.0224609375,
-0.000247955322... | 38,576 | 38576 | |
Find a and b where a, b \in\mathbb{Z}^+
1. June 22nd 2010, 05:31 PM #1
Find a and b where a, b \in\mathbb{Z}^+
$gcd(a,b)=20 \ \mbox{and} \ lcm(a,b)=840$
What is an easy, efficient way to do these sort of problems?
2. June 22nd 2010, 06:05 PM #2
$20=2^2\cdot5$ and $840=2^3\cdot3\cd... | 4 | [
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0.048583984375,
-0.056396484375,
-0.05419921875,
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0.041748046875,
-0.130859375,
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0.038330078125,
0.111328125,
0.020751953125,
0.036376953125,
0.08642578125,
-0.0074462890625,
0.03491210... | 38,577 | 38577 | |
Econometrics by Simulation
Original Code
* A frequent assumption in economics is that the coefficient that is being estimated is constant throughout the population.
* That is, the effect of the exogenous variable is the same for all individuals.
* This assumption is implicit in the notation:
* Y = XB + u
* Because... | 4 | [
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0.034912109375,
-0.04345703125,
... | 38,578 | 38578 | |
Voids - H.J. Rood
Annu. Rev. Astron. Astrophys. 1988. 26: 245-294
Copyright © 1988 by . All rights reserved
3.2. Theoretical Studies
3.2.1. DYNAMICAL EVOLUTION OF VOIDS A typical void has a radius R[v] ~ 25 Mpc and a sharp contiguous shell of superclusters with a non-Hubble velocity (assumed outward relative to... | 4 | [
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0.04345703125,
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0.03076171875,
-0.054443359375,
0.026611328125,
-0.11328125,
0.08984375,
-0.066894531... | 38,579 | 38579 | |
Negative Gromov-Witten invariants
up vote 9 down vote favorite
5
I understand the heuristic reason why Gromov-Witten invariants can be rational; roughly it's because we're doing curve counts in some stacky sense, so each curve $C$ contributes $1/|\text{Aut}(C)|$
to the count rather than $1$.
However, I don't understa... | 4 | [
-0.0703125,
-0.055908203125,
-0.000823974609375,
0.0224609375,
-0.0322265625,
-0.0546875,
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0.05712890625,
0.07861328125,
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0.07568359375,
-0.044189453125,
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-0.046630859375,
-0.03369140625,
... | 38,580 | 38580 | |
Reduction to single higher-order linear ODE
June 30th 2012, 05:53 PM #1
Newbie
Joined
Jun 2012
From
canada
Posts
12
Reduction to single higher-order linear ODE
I need to reduce the following system to a single higher-order linear ODE for y
x'(t) - y'(t) + z(t) = 0
x(t) + y'(t) - z'(t) = 1
... | 4 | [
-0.10205078125,
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0.048095703125,
0.004547119140625,
-0.026123046875,
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0.00274658203125,
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0.051025390625,
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0.0084228515625,
-0.00141143798828125,
... | 38,581 | 38581 | |
arithmetic seq. !
July 14th 2006, 01:04 PM #1
Member
Joined
Sep 2005
Posts
136
please help !
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence?
Which one of the basic functions (linear, quadratic, rational, or exponential) is related ... | 4 | [
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0.00433349609375,
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0.004150390625,
-0.08642578125,
0.0030... | 38,582 | 38582 | |
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Topic: Product with elementary methods
Replies: 2 Last Po... | 5 | [
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Math Help
February 9th 2010, 05:22 PM #1
Member
Joined
Nov 2009
Posts
81
Hi
I am find it hard to figure this series out?
Would anyone have any ideas?
1 +2/3+ 8/15 + 48/105 +384/945+ 3840/10395 + 46080/135135 + 645120/2027025 +10321920/34459425+...
Last edited by hebby; February 9th 20... | 5 | [
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Karolyi's theorem for finite groups and its extensions
up vote 1 down vote favorite
Suppose that $\mathbb A = (A, +)$ is a (possibly non-commutative) group, and denote by $p(\mathbb A)$ the minimum of $|S|$ as $S$ ranges in the set of non-trivial subgroups of $\mathbb A$, with the
convention of taking $p(\mathbb A) :=... | 4 | [
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-... | 38,585 | 38585 | |
First Order Differential
March 11th 2013, 01:49 PM #1
Member
Joined
Jan 2011
Posts
88
First Order Differential
$2r(s^2+1)dr+(r^4+1)ds=0$
This is the second question in the textbook and I am able to do every question after it, so perhaps there is something simple that I am not seeing? The answer has ... | 5 | [
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Diferentiation
How do you differentiate function like x^(1/4) or x^(3/5) ect?
Given $f(x)= x^{\alpha}$, where $\alpha$ is an arbitrary real or even complex constant, its derivative by definition is... $\displaystyle f^{'}(x) = \lim_{\delta \rightarrow 0} \frac{(x+\delta)^{\
alpha} - x^{\alpha}}{\delta}$ (1) Now is... ... | 4 | [
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... | 38,587 | 38587 | |
vertices of a square, coordinate geometry and differentiation
January 5th 2012, 10:20 PM
furor celtica
vertices of a square, coordinate geometry and differentiation
The origin O and a point B(p, q) are opposite vertices of the square OABC. Find the coordinates of the point A and C
A line l has gradient q/p. ... | 4 | [
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2-class group of a quadratic imaginary extension
up vote 1 down vote favorite
2
Let $p\equiv 5 [8]$ be a prime number, and consider $K=\mathbb{Q}(\sqrt{-p})$.
I would like to check that the $2$-Sylow subgroup of the class group $C_K$ has order $2$ (I'm pretty sure it's true).
Apparently, this can be done using genus... | 5 | [
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can you colve for x?
First note that 256=4^4 so we change the question into $4^{x-x^2}=\frac{1}{(4^4)^x}=\frac{1}{4^{4x}}$ Multiply both sides by $4^{4x}$ to get $4^{4x}\cdot 4^{x-x^2}=1$ $4^{4x+x-x^2}=1$ $4^{5x-x^2}=1$
And we need the exponent to be 0 since $x^0=1$ (you can take the log of both sides, but log 1=0 so w... | 4 | [
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... | 38,590 | 38590 | |
Math Help
Question:
If $f(r)=r(r+1)(r+2)$, find $f(r+1)-f(r)$ and deduce that $\sum_{r=1}^nr^2=\frac{1}{6}n(n+1)(2n+1)$
My solution:
$f(r+1)-f(r)$
$=(r+1)(r+2)(r+3)-r(r+1)(r+2)$
$=(r+1)(r+2)[(r+3)-r]$
$=3(r+1)(r+2)$
$=3r^2+9r+6$
Let,
$u_r= f(r+1)-f(r)$
$u_r=3r^2+9r+6$
... | 5 | [
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0.017944335... | 38,591 | 38591 | |
Space of Morphisms of Vector Spaces (Linear Transformations)
AUTHOR:
A VectorSpaceHomspace object represents the set of all possible homomorphisms from one vector space to another. These mappings are usually known as linear transformations.
For more information on the use of linear transformations, consult the docum... | 5 | [
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[SOLVED] Sum of divisors
May 18th 2010, 01:49 PM #1
[SOLVED] Sum of divisors
Let $k$ denote the number of positive divisors of the positive integer $n$, and $S$ the sum of the positive divisors of $n$. Show that
$k\sqrt{n} < S < \sqrt{2k}n$
Last edited by Bruno J.; May 18th 2010 at 02:17 PM.
we al... | 5 | [
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Derivation of Kinetic energy formula and worked examples
Where there are no opposing forces, a moving body needs noforce to keep it moving with a steady velocity ( Newton's first law of motion ). If, however, a resultant force does act on a moving body in
the direction of its motion, then it will accelerate ( Newton's ... | 4 | [
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Conservapedia
Chain rule
From Conservapedia
$\frac{d}{dx} \sin x=?\,$ This article/section deals with mathematical concepts appropriate for a student in late high school or early university.
The chain rule in calculus is a formula for determining the derivative of a composite function:
$f(g(x))' = f'(g(x))\tim... | 4 | [
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Changing the orientation of a Landweber exact cohomology theory
up vote 4 down vote favorite
1
Let the ring R be a MU[*]-module via a ring homomorphism φ and suppose it satisfies the condition of the Landweber exact functor theorem such that we obtain a cohomology theory $R^*(-) := R \otimes_
{MU_*} MU^*(-)$. If ω den... | 4 | [
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Homogeneous Linear Differential Equations
Date: 05/06/2001 at 11:29:06
From: Tim
Subject: Solving linear differential equations
Hi,
I have a couple of questions on solving differential equations of
higher order. (note: the " ' " in y' stands for the first derivative
of y(x). I do know calculus.
How would one solve... | 5 | [
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help...inductive proof???
February 16th 2008, 07:44 AM #1
Newbie
Joined
Feb 2008
Posts
8
can someone help me how to prove this...?
Prove by induction that the number of 2-subsets of an n-set A equals n(n-1)/2. [hint: Let x be any object of A and B=A-{x}. Then a 2-subset of A is either a 2-subset of B... | 4 | [
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Optimum Design of Space Trusses with Buckling Constraints by Means of Spreadsheets
Turk J Engin Environ Sci
25 (2001) , 355 – 367.
¨ ˙
c TUBITAK
Optimum Design of Space Trusses with Buckling Constraints by
Means of Spreadsheets
... | 5 | [
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