content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Groups problem...(Axioms)
June 29th 2010, 02:29 PM #1
Newbie
Joined
Jun 2010
Posts
5
Groups problem...(Axioms)
Say S is a set of elements (finitely or infinetly). Suppose that S is closed under the operation *, and that the associative law holds. If a*e=a and there exists -a (the inverse element) such
... | 4 | [
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0.058... | 36,600 | 36600 | |
Hecke-algebras in your field of mathematics
up vote 5 down vote favorite
4
(How) do Hecke-algebras arise naturally in your field of mathematics and why are they important?
How would you define them and how do you think about them? e.g. generators and relations, functions on some space, grothendieck group...
hecke-al... | 4 | [
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Work problem
November 18th 2006, 07:20 PM #1
Newbie
Joined
Nov 2006
Posts
10
Work problem
find how much work it takes to empty a full hemispherical water reservoir of radius 5m by pumping the water to a height of 4 m above the top of the reservoir. water weighs 9800 N/m^3.
I need to find the volume ... | 5 | [
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sub u w/ trig?
December 4th 2011, 07:50 PM #1
Member
Joined
Sep 2011
Posts
106
Thanks
1
sub u w/ trig?
I have been getting better but I am having trouble with this evil integral.
Evalute the following integrel:
$\int_{}{} sin^2(3x+\frac{\pi}{8}) dx$
The answer is = $\frac{x}{2}- \frac{... | 4 | [
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... | 36,603 | 36603 | |
ion
Recently, I analyzed the subspace comm range issue a bit. Cabman and AlexD pointed out that subspace comm has less range than the manual and online help suggest. I figured out now that this problem
is related to the so called "corrupted maps":
The main map is a grid. Let us assume there are two systems with these ... | 4 | [
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... | 36,604 | 36604 | |
The Reference Frame
Have you seen this cute video? (Via G.D.)
In the previous posting, we tried a couple of thought experiments. One of them was to imagine that the "global temperature" behaves like Brownian motion (which is approximately as good an
approximation as the "random noise" around a "long-term average" in w... | 5 | [
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-... | 36,605 | 36605 | |
second shifting theorem
October 2nd 2009, 05:22 AM
ArTiCK
second shifting theorem
Hi all,
I am having trouble gettin the answer to the attached question. I need to find f(t) and then find L[f(t)] using the t -shifting theorem.
I tried working it out...
f(t) = e^t - e^t u(t-2)
But when i take ... | 5 | [
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Magic square on an infinite lattice
up vote 6 down vote favorite
1
This question came to me while reading the discussion of magic square in the complex plane with equal integrals along every horizontal, vertical and diagonal "magic square in the complex plane with
equal integrals along every horizontal, vertical and d... | 5 | [
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Patent US20030147471 - Cross correlated trellis coded quatrature modulation transmitter and system
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application is a divisional of U.S. application Ser. No. 09/496,135 filed Feb. 1, 2000, which is a continuation of U.S. application Ser. No. 09/412,348, filed Oct. 5, 1... | 4 | [
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questions on central simple algebras
up vote 10 down vote favorite
6
Suppose $A$ is a finite dimensional central simple algebra over a field $F$, $B$ is a simple subalgebra of $A$. $C$ is the centralizer of $B$ in $A$.
From Wedderburd-Artin theorem and the double centralizer theorem We know
1. $A\cong M_n(\Delta_A)... | 5 | [
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ABNF
Defining a language
A grammar defines a language.
In computer science, the most common type of grammar is the context-free grammar, and these grammars will be the primary focus of this article.
Context-free grammars have sufficient richness to describe the recursive syntactic structure of many (though certain... | 4 | [
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π Day Special! Estimating π using Monte Carlo
In honour of π day (03.14 – can’t wait until 2015~) , I thought I’d share this little script I wrote a while back for an introductory lesson I gave on using Monte Carlo methods for integration.
The concept is simple – we can estimate the area of an object which is inside a... | 4 | [
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What Factors Affect the Resistance of a Wire? (2)
Nicola Tregay
Mill Chase School, Bordon, Hampshire, UKhttp://www.sci-journal.org/index.php?template_type=report&id=26&htm=reports/vol3no1/../vol3no2/v3n2a3.html&link=reports/home.phpHypothesis:
Does the Diameter of the wire affect the Resistance?
Ohms law states t... | 4 | [
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double integral
May 4th 2010, 06:17 PM #1
Member
Joined
May 2008
Posts
77
double integral
I = ∫∫R (x + y)dA where R is the region bounded by the curve y = x² and the line y = 1.
(a) Calculate I by integrating first in y and then in x.
(b) Calculate I by integrating first in x and then in y.
... | 5 | [
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-0... | 36,613 | 36613 | |
[SOLVED] solving linear equations in one variable????
July 23rd 2009, 06:25 AM
student897
[SOLVED] solving linear equations in one variable????
here are the problems i need help with. can u tell me the steps to solve these problems?? thank you!(Bow)
first problem: a(x+b)=c
second problem: 9x+2a=-3a+4x
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Help with this integral
December 31st 2005, 08:27 AM #1
Global Moderator
Joined
Nov 2005
From
New York City
Posts
10,616
Thanks
9
Help with this integral
Define, for $x \geq y \geq 0$
$\Lambda(x,y)=\frac{\Gamma(x+1)}{\Gamma(y+1)\Gamma( x-y+1)}$
Then proof for all $n>0$
$\int^n_{0}\Lam... | 4 | [
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Determinant from Cofactor
October 1st 2012, 03:36 PM
Hartlw
Determinant from Cofactor
Generally, a determinant A is defined as e[ijk..n]a[1i]a[2j]a[3k].. Then a co-factor A[rs] is defined and it is shown (arduously) that A=a[Li]A[Li]. Or, a determinant is defined inductiveley in
terms of defined A[rs], in wh... | 4 | [
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Linear disjointness of subfields of a centrally finite division algbera
up vote 6 down vote favorite
I am looking for papers or books which discuss this problem. Thank you for reading:
Let K and L be two subfields of a non-commutative division algebra D with the center Z. Suppose that K and L contain Z and that D is ... | 5 | [
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Subgroups, isomorphic
December 1st 2010, 08:00 PM #1
Senior Member
Joined
Apr 2008
From
Vermont
Posts
318
Subgroups, isomorphic
Let H be a subgroup of G and let a be in G. Show that aHa^-1 is a subgroup of G that is isomorphic to H.
I want to show aHa^-1 is 1-1, onto and has a homomorphism proper... | 5 | [
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Cosine 20 Degrees
Date: 03/24/2002 at 15:41:35
From: Matthew Gallaher
Subject: The exact value for cosine 20 degrees
I have tried to find the exact value of cosine 20 degrees but have not
been able to come up with a solution. I tried to take a third of the
exact value of Cosine 60 degrees but that did not work. I t... | 5 | [
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Economics- Preferences
January 29th 2010, 02:17 AM #1
Newbie
Joined
Apr 2008
Posts
19
Economics- Preferences
Hey can someone help me on the following questions please.
After graduating, John receives a job offer which pays 42000/year. He knows that their is 1% chance the comapny might go bankrupt. A... | 5 | [
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Law of motion in angular form for a system of particles
The concept of angular momentum can easily be extended to include particles, constituting a system. Each of the particles can be associated with certain velocity. In angular parlance, we can assign
angular momentum to each of them, provided they are moving. They m... | 4 | [
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Difficult anti differentiation question
March 6th 2013, 10:28 PM
Bryanna
Difficult anti differentiation question
I have a curve, x^3 - 14x^2 + 59x -70 , and I need to run this line through it, mx - 70 , to make the area above the curve enclosed by the line equal to HALF of the area below the line enclosed
by... | 5 | [
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... | 36,622 | 36622 | |
Detailed proof of cup product equivalent to intersection
up vote 11 down vote favorite
5
Consider a smooth, closed, compact finite-dim manifold. We have Poincare Duality to relate the cocycles and cycles.
I would like to know where I can find a reference for a proof that the cup product of the Cohomology Ring is ... | 4 | [
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0.002... | 36,623 | 36623 | |
Common Logarithm and Natural Logarithm | Characteristic and Mantissa | Log-Table
Common Logarithm and Natural Logarithm
Here we will discuss about the common logarithm and natural logarithm.
In Logarithm we have already seen and discussed that the logarithmic value of a positive number depends not only on the number... | 4 | [
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Free and cellular G-action implies free G-complex?
up vote 1 down vote favorite
Recall that a CW-complex $X$ with an action of a group $G$ which permutes the cells (i.e., for any $g \in G$ and any cell $\sigma \subseteq X$, $g\sigma$ is a cell) is called a $G$-complex. If the
action permutes the cells freely ($g\sigma... | 5 | [
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-0.... | 36,625 | 36625 | |
Math Help
October 2nd 2008, 08:08 AM #1
Newbie
Joined
Sep 2008
Posts
7
slopes
Ok I think I've worked this out incorrectly so if someone could point me in the right direction that would be great.....
The question is find the equation of a line that passes through (-1,5) and (2,-4)
I know that
... | 4 | [
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0.0100... | 36,626 | 36626 | |
Need help with integral another proof
December 19th 2006, 12:18 PM #1
Newbie
Joined
Nov 2006
Posts
22
Need help with integral another proof
If f(x)>0 for all xElement-ofsymbol [a,b], then
b
Integral sign f>0
a
a) Give an example where f(x)>0 for all xElement-ofsymbol [a,b], and f(x)>0 fo... | 5 | [
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0.150390625,
0.016357421875,
-0.03100... | 36,627 | 36627 | |
Intersecting planes example
Find intersection of planes given by $x+y+z+1=0$ and $x + 2y + 3z +4=0$.
Solution: In three dimensions (which we are implicitly working with here), what is the intersection of two planes? As long as the planes are not parallel, they should intersect in a line. So our
result should be a line... | 5 | [
-0.07763671875,
-0.036865234375,
-0.1171875,
-0.039794921875,
0.01324462890625,
-0.01513671875,
0.07568359375,
-0.0091552734375,
-0.04052734375,
-0.00182342529296875,
-0.050537109375,
0.002410888671875,
0.0108642578125,
0.0234375,
-0.0693359375,
-0.00421142578125,
-0.1171875,
-0.06... | 36,628 | 36628 | |
Math Forum Discussions
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Topic: Computation of the matrix exponential
Replies: 6 L... | 4 | [
-0.068359375,
0.0035552978515625,
-0.1279296875,
-0.041748046875,
-0.0181884765625,
-0.09375,
-0.031005859375,
-0.08935546875,
0.045166015625,
0.08203125,
0.10986328125,
-0.029296875,
-0.033935546875,
0.033447265625,
0.060546875,
0.01177978515625,
-0.052978515625,
0.09375,
0.0086... | 36,629 | 36629 | |
Relatively Prime proof
February 17th 2014, 07:35 PM #1
Newbie
Joined
Feb 2014
From
Oregon
Posts
4
Relatively Prime proof
I am asked to prove that 2^100+1 and 2^100+3 are relatively prime using a=qb+r, gcd(a,b)=gcd(b,r). I'm not entirely sure how these two integers fit into the format a=qb+r...
Re: R... | 5 | [
-0.04833984375,
0.050537109375,
-0.0751953125,
-0.044189453125,
0.1103515625,
-0.007049560546875,
0.025634765625,
0.0888671875,
-0.06591796875,
0.04833984375,
-0.0142822265625,
-0.044189453125,
0.08154296875,
0.0537109375,
0.0556640625,
0.0267333984375,
-0.064453125,
-0.0634765625,... | 36,630 | 36630 | |
Counting pathways
December 5th 2006, 08:11 AM #1
Junior Member
Joined
Aug 2006
Posts
29
Counting pathways
Hello
I need to count the number of ways,from start to end,without passing through the red spots.
you can move one step at a time:forward or to the right.
thanks.
There are 49 path... | 5 | [
0.11669921875,
-0.07177734375,
-0.00970458984375,
0.00701904296875,
-0.03662109375,
0.0458984375,
-0.003875732421875,
-0.0458984375,
0.048095703125,
0.010009765625,
0.006134033203125,
0.057373046875,
0.0023345947265625,
0.0308837890625,
-0.04296875,
0.1103515625,
-0.054931640625,
-... | 36,631 | 36631 | |
Changing Word Problems to Algebra
Associated Topics || Dr. Math Home || Search Dr. Math
Changing Word Problems to Algebra
... | 4 | [
0.03662109375,
0.06298828125,
-0.0322265625,
-0.07568359375,
-0.1298828125,
0.06787109375,
0.0240478515625,
0.08056640625,
-0.1025390625,
0.0224609375,
-0.01318359375,
0.0341796875,
0.09130859375,
0.06591796875,
0.0390625,
0.016845703125,
-0.031005859375,
0.08056640625,
-0.096191... | 36,632 | 36632 | |
binary & decimal representations of int. - N, M are int, formed by reverse ...
November 5th 2008, 05:51 PM #1
binary & decimal representations of int. - N, M are int, formed by reverse ...
Bank ID number is 237(a4)18538 and has an illegible 4th digit.
Determine the value of a4.
They also give the check d... | 4 | [
0.01348876953125,
0.02783203125,
-0.044921875,
-0.0751953125,
-0.078125,
0.03125,
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0.047607421875,
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-0.03271484375,
-0.040771484375,
-0.00225830078125,
0.031982421875,
-0.029296875,
-0.0927734375,
0.0016632080078125,
-0.0380859375,
0.0106201171875,
-0.02... | 36,633 | 36633 | |
Bezout's Theorem for weighted homogeneous polynomials
up vote 12 down vote favorite
3
Bezout's Theorem states that for two homogeneous polynomials $f(x,y,z), g(x,y,z)$ over an algebraically closed field of degrees $m,n$ respectively, such that the two polynomials do not share a common
component, then the number of int... | 5 | [
-0.05322265625,
-0.01031494140625,
-0.060546875,
0.02294921875,
0.0145263671875,
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0.043212890625,
-0.051025390625,
-0.052734375,
-0.0264892578125,
0.03369140625,
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0.01123046875,
0.0159912109375,
0.0157470703125,
0.05712890625,
-0.08984375,
0.09423828125... | 36,634 | 36634 | |
GRANULARITY
limit the amount of parallelism
Major Section: PARALLEL-PROGRAMMING
This documentation topic relates to the experimental extension of ACL2 supporting parallel execution and proof; see parallelism.
Some function calls are on arguments whose evaluation time is long enough to warrant parallel execution, w... | 4 | [
-0.123046875,
0.060791015625,
-0.01171875,
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0.076171875,
0.046630859375,
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0.007354736328125,
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0.01251220703125,
-0.010986328125,
0.0274658203125,
-0.041259765625,
-0.04296875,
0... | 36,635 | 36635 | |
Question of Differential Equations
August 31st 2010, 05:15 AM
Paymemoney
Question of Differential Equations
1)Solve $y' = \sqrt{1-y^2}$
$y=sin(u)$$dy=cos(u) dy$
$y=\int \sqrt{1-y^2}$
$y=cos(u)$
what should i do next if this is correct?
2)Find the orthogonal trajectories for $y=Ce^{x}$
... | 5 | [
-0.00457763671875,
-0.04052734375,
0.03955078125,
0.0247802734375,
-0.01458740234375,
-0.07373046875,
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0.003875732421875,
-0.0556640625,
0.049560546875,
0.0810546875,
0.0228271484375,
0.00860595703125,
-0.00147247314453125,
-0.033447265625,
-0.04248046875,
0.0019683... | 36,636 | 36636 | |
Positive Definite Matrices
Date: 08/12/2008 at 23:27:25
From: Radhakrishnan
Subject: How to determine if a matrix is positive definite?
i have a correlation matrix and i want to check if the matrix is a
positive definite matrix, if not i want to make the matrix to be
positive definite......
in some places I found th... | 5 | [
-0.03076171875,
-0.021240234375,
-0.054931640625,
-0.020263671875,
-0.03662109375,
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0.010498046875,
-0.07666015625,
-0.017578125,
0.043701171875,
0.07763671875,
0.10546875,
-0.015869140625,
0.01190185546875,
-0.08935546875,
-0.03955078125,
0.1171875,
-0.00405883... | 36,637 | 36637 | |
Perimeters of random-walk polygons
up vote 11 down vote favorite
3
I have a random walk on $\mathbb{Z}^2$ that takes a step with equal probability in the three directions that avoid retracing the previous step. The walk proceeds until it returns to a lattice point
previously visited, at which time it pinches off a sim... | 4 | [
0.0142822265625,
-0.04541015625,
0.024169921875,
0.05029296875,
0.048828125,
-0.037841796875,
0.058349609375,
0.0159912109375,
0.0322265625,
-0.02490234375,
-0.004150390625,
0.00958251953125,
0.01287841796875,
0.091796875,
0.02978515625,
0.0024261474609375,
0.01373291015625,
0.0264... | 36,638 | 36638 | |
Products of Boolean algebras and probability measures thereon
up vote 2 down vote favorite
These are really two questions, but the second presupposes the first.
First, let $( B_i )_{i\in I}$ be an arbitrary family of Boolean algebras. I want to directly form a product of them that is like the product topology on the ... | 4 | [
-0.046630859375,
-0.037841796875,
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-0.0625,
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-0.068359375,
-0.087890625,
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0.017333984375,
-0.0218505859375,
0.06396484375,
0.032958984375,
0.04052734375,
... | 36,639 | 36639 | |
A question related to ultrapower embeddings.
up vote 5 down vote favorite
In Joel David Hamkins' "Forcing and Large Cardinals" a definition of $extender$ embeddings:
"An embedding $j:V \to M$ is an $extender$ embedding if every element of $M$ can be represented in the form $j(f)(\alpha)$ for some $f:\kappa \to V$ and... | 4 | [
0.02490234375,
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-0.0159912109375,
0.0167236328125,
0.0927734375,
0.0869140625,
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0.05615234375,
-0.000732421875,
-0.0262451171875,
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0.01287841796875,
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0.05322265625,
0.09423828125,
0.04223... | 36,640 | 36640 | |
The Vicar and the Curate (Ages of Three People)
Date: 03/20/2002 at 23:20:40
From: Jason Mooney
Subject: Crazy problem
This is a problem that I just can't figure out. Please help.
Note: Vicar and Curate are both terms for clergypersons (ministers,
pastors, priests). These words are more commonly used in England
th... | 4 | [
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0.041015625,
0.034423828125,
0.034912109375,
-0.052734375,
0.046142578125,
0.0595703125,
-0.052978515625,
0.0177001953125,
-0.09814453125,
-0.005981445... | 36,641 | 36641 | |
Puzzle : A number game
Well,
This is comparatively a simple puzzle with a nice observation. Given to me by tejas, who in turn, faced it in an entrance exam of CMI.
Problem : You are given integers from 1…2n. You are supposed to divide it in two sub sequence A and B such that, A and B both are of the same size n. A i... | 5 | [
-0.0595703125,
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0.0439453125,
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0.007659912109375,
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0.0089111328125,
0.060791015625,
0.006439208984375,
-0.059814453125,
0.041748046875,
0.0732421875,
-0.0054... | 36,642 | 36642 | |
Permutations Matrices Question
September 23rd 2010, 04:56 PM #1
Member
Joined
Sep 2010
Posts
151
Thanks
1
Permutations Matrices Question
This is a homework problem i had. Help!
Explain why the dot product of x and y equals the dot product of Px and Py.
Then From (Px)^T(Py)=x^Ty deduce that P... | 4 | [
-0.0164794921875,
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0.05859375,
-0.030517578125,
0.1298828125,
-0.0712890625,
0.01025390625,
0.04... | 36,643 | 36643 | |
Parametric Binomial Example - Demonstrate MTTF
From ReliaWiki
This example appears in the Life Data Analysis Reference book.
In this example, we will use the parametric binomial method to design a test that will demonstrate $MTTF=75\,\!$ hours with a 95% confidence if no failure occur during the test $f=0\,\!$. We... | 5 | [
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0.009033203125,
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-0.0181884765625,
0.043701171875,
-0.046630859375,
0.00775146484375,
-0.... | 36,644 | 36644 | |
rational function identity
up vote 13 down vote favorite
4
I just had to make use of an elementary rational function identity (below). The proof is a straightforward exercise, but that isn't the point. First, "my" identity is almost surely not original, but
I don't have a reference for it. Perhaps someone knows it (li... | 4 | [
-0.10986328125,
-0.0361328125,
0.0400390625,
-0.0267333984375,
0.021240234375,
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0.04443359375,
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-0.006103515625,
-0.06396484375,
0.10400390625,
-0.017578125,
0.018188... | 36,645 | 36645 | |
Odlyzko's method
From Polymath1Wiki
Odlyzko [O1993] has a method for computing π(x) in time/space x^1 / 2 + o(1); combining this with a binary search, one can locate a k-digit prime in time/space (10^k)^1 / 2 + o(1).
First observe that it suffices to compute π(x) to accuracy 1/2, since it is an integer. Next, it suf... | 4 | [
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0.00799560546875,
-0.0615234375,
-0.08447265625,
0.03515625,
0.02038574... | 36,646 | 36646 | |
NEED HELP FAST! Derivitives/cost application
April 13th 2009, 07:52 PM
jamman790
NEED HELP FAST! Derivitives/cost application
ok so i have this problem and i think ive got it figured just need a little help:)
we have a box with a square base and a volume of 4000cm^3
the sides and top cost 4.5$/m^2
... | 4 | [
0.08837890625,
0.0615234375,
0.0196533203125,
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0.09619140625,
-0.0255126953125,
0.08349609375,
0.04931640625,
0.10009765625,
... | 36,647 | 36647 | |
Cohomology of fibrations over the circle: how to compute the ring structure?
up vote 17 down vote favorite
8
This question is inspired by Cohomology of fibrations over the circle Moreover, it can be considered a subquestion of the above, but somehow it seems to me that some of the more interesting points
were not addr... | 4 | [
-0.032958984375,
0.095703125,
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0.0002765655517578125,
0.027099609375,
0.10205078125,
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0.047119140625,
0.046875,
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0.064453125,
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-0.0301513671875,
0.04931640625,
0.00677490234375,
-0.10498046875,
-0.... | 36,648 | 36648 | |
Homework Help
Posted by Jon on Tuesday, December 18, 2007 at 3:04pm.
A furniture company displays bedroom sets which require 21 square meters of space and living room sets which require 42 square meters of space. The company which has 546 square meters of available
space,wants to display at least 6 bedroom sets and at... | 4 | [
0.07763671875,
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0.030517578125,
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0.05078125,
0.02734375,
0.06787109375,
-0.0030670166015625,
0.01318359375,
... | 36,649 | 36649 | |
Math Forum Discussions
Re: Help me understand...INT (sin^5 x)
Posted: Dec 4, 2013 1:28 PM
On Wednesday, December 4, 2013 4:36:20 AM UTC-8, muhah...@hotmail.com wrote:
> Can you solve please (; dx/(cosx)5
If you mean to integrate cos(x)^5, the answer is
(1/5)sin(x)*cos(x)^4 +(4/15)sin(x)*cos(x)^2 + (8/15)sin(x) + C.
... | 5 | [
-0.057861328125,
0.005767822265625,
0.07470703125,
0.060791015625,
0.06787109375,
-0.0096435546875,
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-0.02978515625,
-0.0111083984375,
0.0167236328125,
0.038330078125,
-0.0274658203125,
-0.0196533203125,
0.057861328125,
-0.021484375,
0.04248046875,
-0.01416015625,... | 36,650 | 36650 | |
Proof of the Parallelogram Law
Date: 08/07/99 at 18:49:14
From: Kenneth
Subject: Proof of the Parallelogram Law
How do you prove the parallelogram law geometrically without using
vectors?
Given: triangle ABC with midpoint M on side AC
Prove: (AB)^2 + (AC)^2 = (AM)^2 + (BM)^2
I was reading a book on vector calculus... | 4 | [
0.004119873046875,
0.0322265625,
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0.01519775390625,
0.01361083984375,
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0.06689453125,
-0.0673828125,
... | 36,651 | 36651 | |
Solutions - Winona State University
Properties of Solutions
Terminology
Solvation Compositions Solubility Rules
... | 5 | [
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0.... | 36,652 | 36652 | |
Reed-Solomon Error Correction
Transmission media, such as telephone lines, wide-area networks, and satellite links, or storage media, like optical/magnetic disk and tape, are usually imperfect. To make digital data transmission
and storage reliable, error-correcting codes are indispensable. The efficient Reed-Solomon c... | 4 | [
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-0.055908203125,
-0.06689453125,
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0.12890625,... | 36,653 | 36653 | |
Quadratic Equations Shortcut
A lot of GMAT students strongly dislike algebra. Hate is a strong word, but you get my drift. Moreover, of all the algebra topics tested on the GMAT, quadratic equations tend to give students the
most pause. You may be one of those students. Well, fear not! I’m about to make your life a wh... | 4 | [
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-0.032470703125,
0.01831054... | 36,654 | 36654 | |
Simple Differentiation
The general fromula for f= a^(u(x)) f ' = ln(a) a^(u(x))du/dx For 3^(5x) f ' = ln(3)3^(5x)5 = 5ln(3)3^(5x)
A general method for problems like this is to take the logarithm of both sides. If $y= 3^{5x}$ then $ln(y)= ln(3^{5x})= 5x ln(3)$. Now differentiate both sides with respect to x. The deriva... | 5 | [
0.0030670166015625,
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-0.01080322265625,
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0.09375,
-0.004638671875,
0.01470947265625,
0.04736328125,
0.05078125,
0.004608154296875,
-0.1357421875,
0.043701171875,
... | 36,655 | 36655 | |
What Does It Mean to Distribute
Date: 08/25/2007 at 22:59:01
From: Andrea
Subject: distributive property
I understand the basics of the distributive property but I don't
understand all the different parts of it, like there's the
distributive property of multiplication over addition and over
subtraction and the distri... | 4 | [
-0.029541015625,
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0.040771484375,
0.0250244140625,
-0.040771484375,
0.032470703125,
0.0042724609375,
0.00653076171875,
0.06103515625,
0.044677734375,
0.04150390625,
0.0137939453125,
0.049560546875,
-0.00144195556640625,
0.0130615234375,
0.053955078125,
-0.0791015625,... | 36,656 | 36656 | |
do geometric fibers determine scheme-theoretic image?
up vote 4 down vote favorite
1
Let $X,Y,Z$ be reduced algebraic varieties, and let $Y$ and $Z$ be normal. Let $f:X \to Y$ and $g:X \to Z$ two surjective projective morphisms of algebraic varieties such that the geometric fibers of
$f$ and $g$ coincide. Is there an ... | 5 | [
-0.0113525390625,
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0.034423828125,
0.0238037109375,
0.06787109375,
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-0.0189208984375,
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0.0439453125,
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-0.005859375,
0.022216796875,
0.044921875,
0.005401611328125,
-0.031494140625,
-0.0... | 36,657 | 36657 | |
Integrate ln(a + b.cosx)
Hi All, Can anyone prove this, please... $\int_{0}^{\pi}ln(a+b.cosx)dx=\pi.ln(\frac{a+\sqrt{ {a}^{2}+{b}^{2}}}{2})$ ~Kalyan.
Last edited by kalyanram; June 22nd 2008 at 10:28 AM.
$<br /> J\left( \theta \right) = \int_0^\pi {\ln \left( {1 + \theta \cdot \cos \left( x \right)} \right)dx} \Right... | 4 | [
-0.01470947265625,
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0.050048828125,
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0.035400390625,
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0.02978515625,
-0.00133514404296875,
0.0595703125,
0.0162353515625,
-0.055419921875,
-0.00494384765625,
0.057373046875,
-0.02233886... | 36,658 | 36658 | |
Dividing a Line Segment into Seven Equal Parts
Date: 07/04/2003 at 01:36:51
From: Erik
Subject: Dividing a line segment into seven equal parts
I need to divide a segment with the length of X into seven equal parts
using only a compass and straightedge.
I also have to construct a line segment the length squareroot of... | 4 | [
-0.04443359375,
0.018310546875,
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0.034912109375,
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0.029296875,
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0.0595703125,
-0.030029296875,
0.03662109375,
-0.126953125,
-0.012... | 36,659 | 36659 | |
The broken weight problem: solutions and further exploration
First of all, let me say to all my readers how fantastic it felt to post a puzzle, after not posting anything for two months, and get eighteen thoughtful, insightful comments in just three days; it’s
every blogger’s dream. You all are fantastic and make this... | 5 | [
-0.10009765625,
-0.0224609375,
-0.00592041015625,
0.0439453125,
-0.01177978515625,
-0.033935546875,
0.01007080078125,
0.041748046875,
0.020263671875,
-0.004058837890625,
-0.058349609375,
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0.000576019287109375,
0.044921875,
-0.0159912109375,
-0.026123046875,
-0.0603027... | 36,660 | 36660 | |
What is the homotopy type of the space of the homeomorphisms of the n-ball such that the homeomorphism restricted to the boundary is isotopic to the identity?
up vote 8 down vote favorite
3
Consider the set of homeomorphisms of the topological n-ball to itself with the compact open topology. Sitting inside this space... | 4 | [
0.041259765625,
0.032470703125,
0.037841796875,
0.0264892578125,
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-0.0093994140625,
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-0.02587890625,
0.027099609375,
-0.0849609375,
-0.02197265625,
0.005950927... | 36,661 | 36661 | |
How to find the sequence?
September 21st 2011, 10:12 AM #1
Junior Member
Joined
Sep 2011
Posts
33
How to find the sequence?
Find all such sequences $(x_1, x_2, x_3, ..., x_{63})$ consisting of different positive integers that for $n=1,2,3,...,62$ the number $x_n$ is a divisor of $x_{n+1}+1$ and $x_{63}$ ... | 4 | [
-0.10595703125,
0.042724609375,
-0.048095703125,
-0.0966796875,
0.052490234375,
0.033935546875,
0.0272216796875,
-0.0185546875,
-0.0179443359375,
-0.0196533203125,
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0.057373046875,
-0.01171875,
-0.052978515625,
0.00115966796875,
-0.068359375,
-0.1201171875,
0.023925... | 36,662 | 36662 | |
03Lect6BoundLayer
Wind loading and structural response
Lecture 6 Dr. J.D. Holmes
Atmospheric boundary layers and
turbulence I
Atmospheric boundary layers and turbulence
153 metres 64 metres ... | 4 | [
0.01202392578125,
0.0205078125,
0.1298828125,
0.0299072265625,
-0.01116943359375,
-0.042724609375,
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-0.0086669921875,
0.004241943359375,
-0.06640625,
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-0.0576171875,
-0.04296875,
-0.09130859375,
0.045654296875,
0.08642578125,
0.014404296875,
-0.0046386718... | 36,663 | 36663 | |
Homework Help
Posted by Elyse on Thursday, June 6, 2013 at 3:10pm.
Use Green's theorem to evaluate the integral:
y^(2)dx+xy dy
where C is the boundary of the region lying between the graphs of y=0,
y=sqrt(x), and x=9
• Calculus - Steve, Thursday, June 6, 2013 at 4:22pm
Using the definition, we have
P = ... | 5 | [
0.01806640625,
0.051513671875,
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0.0478515625,
0.0673828125,
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0.1083984375,
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0.0546875,
0.06884765625,
-0.08349609375,
-0.0986328125,
-0.... | 36,664 | 36664 | |
Math Forum Discussions
quasi
Posts: 10,188
Registered: 7/15/05
Re: An optimization problem
Posted: Sep 8, 2013 6:17 AM
Peter Percival wrote:
>quasi wrote:
>> William Elliot wrote:
>>> analyst41@hotmail.com wrote:
>>>
>>>> consider f(x1,x2,...xn) = {1 + sum(xi)^2)} / {1 +sum{x(i)}
>>>> 0 <=xi <=1 for all i.
>>>>
>>>> ... | 5 | [
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0.0213623046875,
0.06298828125,
... | 36,665 | 36665 | |
Linear algebra inequalities - please give hints
June 15th 2013, 03:57 AM
Crystuls
Linear algebra inequalities - please give hints
Three friends decide to buy some fish and chips.
One piece of fish costs $2.50
One scoop of chips costs $2.00
The friends only have $20 between them to spend.
They wan... | 4 | [
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0.05126953125,
-0.041259765625,
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0.03759765625,
0.002197265625,
0.034912109375,
0.04296875,
-0.0004043... | 36,666 | 36666 | |
Tangent Planes
July 3rd 2009, 08:22 AM
JoAdams5000
Tangent Planes
I am trying to find all planes that are tangent to both x^2 + y^2 + z^2 = 1 and x^2 + y^2 + 2z = 0.
I tried using gradient to get the general equation of the planes for each but after that I got stuck.
Any suggestions would be greatly ap... | 5 | [
-0.04833984375,
-0.031982421875,
-0.001800537109375,
-0.004119873046875,
0.0791015625,
-0.008544921875,
0.026611328125,
0.07421875,
0.0255126953125,
-0.0179443359375,
0.00201416015625,
-0.053466796875,
-0.043212890625,
-0.01214599609375,
-0.0810546875,
0.05517578125,
-0.07080078125,
... | 36,667 | 36667 | |
Solving an exponential equation
January 6th 2011, 01:40 PM
youngb11
Solving an exponential equation
I'm a little stuck (again:().
How would I go about solving an equation like this:
$4^2^x-4^x-20=0$
And a more complicated one such as:
$2^x+12(2)^-^x=7$
All help greatly appreciated!
Janu... | 4 | [
0.000820159912109375,
-0.017333984375,
0.0086669921875,
0.0927734375,
0.020751953125,
-0.0537109375,
0.04443359375,
0.0003871917724609375,
-0.025146484375,
0.05126953125,
0.044677734375,
-0.0322265625,
0.06884765625,
0.043701171875,
0.026123046875,
0.019287109375,
-0.0262451171875,
... | 36,668 | 36668 | |
Line of Best Fit For Points in Three Dimensional Space
Date: 11/22/2005 at 08:44:19
From: Abhi
Subject: fitting a line to points in 3D space
I have a problem where I have a set of points in 3D space. I know the
(X,Y,Z) coordinates of the points. I have to fit a line so that the
line is least distant from the points... | 4 | [
-0.12109375,
0.00604248046875,
-0.036376953125,
-0.052490234375,
0.0162353515625,
0.0150146484375,
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0.01171875,
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0.0296630859375,
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0.0033416748046875,
-0.064453125,
0.08251953125,
-0.03857421875,
-0.05126... | 36,669 | 36669 | |
Equations of the Hirzebruch surface embedded in a large space.
up vote 2 down vote favorite
1
Let $\mathbb{F}_1$ be the Hirzebruch surface $\mathbb{P}(\mathcal{O}\oplus\mathcal{O}(-1))$ and let $D$ be the very ample divisor $3C_0+5f$ on $\mathbb{F}_1$ (notation as in [Hartshorne, Algebraic
geometry, p. 373]). Then $|D... | 5 | [
-0.0546875,
-0.00130462646484375,
0.0028533935546875,
-0.028564453125,
0.11328125,
-0.09228515625,
0.017578125,
0.052978515625,
-0.09765625,
-0.04736328125,
0.0810546875,
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-0.08740234375,
0.02978515625,
-0.027099609375,
0.01409912109375,
-0.07666015625,
-0.02001953125... | 36,670 | 36670 | |
Solving an Equation
Pronunciation: /sɒlv iŋ ən ɪˈkweɪ ʒən/ ?
Most math problems you will find in algebra involve solving equations. The idea is to find a solution to the equation. A solution is a set of one or more values that, when substituted for the
variable(s), make the equation true.
Solving equations is one of... | 4 | [
-0.0198974609375,
-0.00927734375,
-0.0400390625,
0.0400390625,
-0.095703125,
0.0260009765625,
0.006988525390625,
0.0003108978271484375,
0.01361083984375,
0.0142822265625,
0.0390625,
-0.028564453125,
0.07470703125,
0.0260009765625,
0.0201416015625,
0.0225830078125,
-0.08447265625,
0... | 36,671 | 36671 | |
venn diagram
June 29th 2007, 12:06 PM #1
Junior Member
Joined
Jun 2007
Posts
40
venn diagram
Is the venn diagram for $(A - (A \cap B)) \cup (B - (A \cap B))$, the same as $(A-B) \cup (B-A)$
where as $A \cap B eq \varnothing$
The reason is :
$(A-(A\cap B))\cup(B - (A \cap B))$ = $((A-A)\cup(... | 5 | [
0.011962890625,
0.03857421875,
0.03271484375,
-0.08203125,
-0.0281982421875,
0.03466796875,
0.091796875,
-0.0196533203125,
-0.0546875,
-0.0022125244140625,
-0.04248046875,
-0.08837890625,
0.10205078125,
0.04833984375,
0.009765625,
0.03759765625,
-0.040771484375,
-0.0031585693359375... | 36,672 | 36672 | |
Complex Numbers
From Math Images
Definition
Complex numbers are numbers which take the form $a+bi$, where $a$ and $b$ are real numbers and $i = \sqrt{-1}$ .
Such numbers frequently appear in mathematical equations, even in those describing physical systems. Extending our notion of numbers to include complex numbers... | 4 | [
-0.07275390625,
-0.00836181640625,
-0.068359375,
0.029296875,
-0.08349609375,
-0.1201171875,
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0.01202392578125,
0.1357421875,
-0.0439453125,
0.043212890625,
-0.033447265625,
0.0625,
0.095703125,
0.0361328125,
-0.06591796875,
-0.061279296875,
0.10791015625,
-... | 36,673 | 36673 | |
Pythagorean Triples Divisible by 5
Date: 11/17/2000 at 17:44:40
From: Simon Essex
Subject: Do all integer right-angled triangles
I am trying to find the answer to whether all right-angled triangles
with integer side lengths have a side with a length divisible by 5. I
have no idea how to answer this.
Thanks.
Date:... | 4 | [
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0.0498046875,
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0.050537109375,
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0.11376953125,
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-0.061279296875,
0.01611328125,
-0.0062... | 36,674 | 36674 | |
Need help with power series representation of function
November 5th 2012, 05:31 PM
kimsanders82
Need help with power series representation of function
I need help with the following:
Find the power series representation of the function defined by:
F(x) = the integral from 0 to x of cos (t^1/2/2) dt
... | 5 | [
-0.037353515625,
-0.0289306640625,
0.03173828125,
0.1259765625,
0.087890625,
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0.051025390625,
-0.007232666015625,
0.03173828125,
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-0.033447265625,
-0.0267333984375,
-0.03515625,
-0.02294921875,
-0.007354736328125,
-0.... | 36,675 | 36675 | |
Radical Concepts -- Simplifying Radicals
The property abab size 12{ sqrt { ital "ab"} } {}= aa size 12{ sqrt {a} } {}bb size 12{ sqrt {b} } {} can be used to simplify radicals. The key is to break the number inside the root into two
factors, one of which is a perfect square.
Example 1: Simplifying a Radical
... | 4 | [
0.04443359375,
0.035888671875,
-0.045654296875,
-0.031982421875,
-0.038330078125,
-0.0198974609375,
-0.0206298828125,
-0.0208740234375,
-0.0537109375,
0.09033203125,
0.01519775390625,
0.111328125,
0.01080322265625,
-0.00433349609375,
0.056884765625,
0.05029296875,
-0.10302734375,
0... | 36,676 | 36676 | |
Rate of Change as moving toward a point
Find the rate of change of f(x,y,z) = ln(x+yz^2)-sin(y+z)+xe^y at the point (0,1,-1) as you move toward the point (4,1,2)
you want the directional derivative here. first, find the vector from (0,1,-1) to (4,1,2). then find the unit vector in that direction then use the formula: ... | 4 | [
0.06298828125,
-0.041015625,
-0.031494140625,
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-0.025390625,
-0.016357421875,
-0.00092315673828125,
-0.0194091796875,
-0.0306396484375,
0.052978515625,
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0.03662109375,
0.0595703125,
-0.036376953125,
-0.004486083984375,
-0.07861328125,
-... | 36,677 | 36677 | |
Brauer group elements associated to conic bundles
up vote 4 down vote favorite
1
Let $X$ be a non-singular projective variety over a field $k$ (perhaps not of characteristic $2$), and let $\pi:Y\to X$ be a conic bundle over $X$ i.e. a proper morphism all of whose fibres are
isomorphic to plane conics. Let $Z \subset X... | 4 | [
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0.11376953125,
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-0.04541015625,
-0.009765625,
0.043212890625,
0.0213623046875,
-0.025146484375,
-0.0... | 36,678 | 36678 | |
Simplying Log Problems
January 11th 2010, 11:20 PM #1
Junior Member
Joined
Dec 2009
Posts
49
Simplying Log Problems
Hi My Friends
I need ur help to simply the following problem
can u please explain the steps to solve the problem
Thanks in Advanced
Hello metallica007
The definition... | 4 | [
-0.0252685546875,
0.000606536865234375,
0.0162353515625,
0.047119140625,
0.0036163330078125,
-0.08203125,
0.10205078125,
-0.003753662109375,
-0.003204345703125,
0.0732421875,
-0.025390625,
-0.0009918212890625,
0.048583984375,
0.06884765625,
0.0869140625,
0.12890625,
-0.1376953125,
... | 36,679 | 36679 | |
Two more questions (cont.)
April 8th 2008, 02:35 PM
shadow_2145
Two more questions (cont.)
This is the 2nd part to my questions:
I don't know if the following definition is needed, but I will include it.
$k$ is a positive integer and $f,g$ and $h$ are arithmetic functions. $\hat{f}$ denotes the Dirichl... | 5 | [
-0.044677734375,
0.10595703125,
0.01904296875,
0.00628662109375,
0.0927734375,
0.11865234375,
0.126953125,
-0.013671875,
0.004608154296875,
-0.041259765625,
0.0400390625,
-0.032958984375,
0.011474609375,
-0.08544921875,
-0.0654296875,
-0.0673828125,
-0.0174560546875,
-0.05297851562... | 36,680 | 36680 | |
Rewrite variable in given constants and variables
January 30th 2013, 05:00 AM #1
Newbie
Joined
Jan 2013
From
Netherlands
Posts
5
Rewrite variable in given constants and variables
Hello everyone,
English isn't my native language, so I hope I can make myself clear. I'm new on this forum, because I... | 4 | [
-0.0439453125,
0.01019287109375,
-0.0062255859375,
-0.0035400390625,
0.0128173828125,
0.08203125,
0.1142578125,
-0.033447265625,
0.0093994140625,
0.09619140625,
-0.016845703125,
0.0458984375,
0.052490234375,
-0.0091552734375,
-0.0751953125,
-0.00860595703125,
-0.046875,
-0.03588867... | 36,681 | 36681 | |
Two Heads After N Tails
Date: 05/20/99 at 10:45:32
From: jack wilson
Subject: Probability of two heads after n tails
Hi Doc,
I'm sure this is probably a simple question but I can't seem to get
past the initial phase. I believe it is similar to the picking the
same ball problem, but I'm interested in a portion of th... | 5 | [
-0.00872802734375,
-0.0167236328125,
0.09033203125,
-0.0810546875,
-0.00286865234375,
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0.0169677734375,
0.03857421875,
0.03515625,
0.040283203125,
0.025146484375,
-0.0179443359375,
-0.020751953125,
-0.0228271484375,
0.052978515625,
0.041259765625,
0.005157470703125,
... | 36,682 | 36682 | |
Linear programming problem
June 11th 2008, 06:36 PM
Stormy-1
Linear programming problem
Would very much appreciate some assistance with a Linear modelling problem. Facts: 2 production lines, 2 products, 8 hours per line (480 min), profit for each product, a is $42, b is $87
Line 1 Line 2
Product a 3 min... | 4 | [
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0.005706787109375,
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-0.044189453125,
0.0576171875,
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0.06884765625,
-0.05029296875,
0.0634765625,
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0.042724609375,
0.061767578125,
-0.00860595703125,
0.0247802734375,
0.11181640625,
0.0159912109375,
-0.06884... | 36,683 | 36683 | |
Equation of a Circle
August 5th 2008, 09:47 PM #1
Newbie
Joined
Aug 2008
Posts
4
Equation of a Circle
If I have two Circles:
(x+100)^2 + (y-20)^2 = 20^2
(x-100)^2 + (y-10)^2 = 10^2
and a straight line
y=1
How can I find the equation of a circle which touch to two circle and tangent t... | 4 | [
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-0.0070800781... | 36,684 | 36684 | |
Find the sum of the series and determine the radius and interval of convergence
Let f(x)= ln (1+x^2). Find f^15(0) I know the answer is 0 but why?
Hello,We know that $\ln(1+x)=-\sum_{n\geq 1}\frac{x^n}{n}$ So here, $f(x)=-\sum_{n\geq 1}\frac{x^{2n}}{n}$ So you can notice that the factors of the odd powers of x are 0. ... | 5 | [
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-... | 36,685 | 36685 | |
Playing Card Probability
August 30th 2009, 10:14 PM #1
Junior Member
Joined
Oct 2007
Posts
52
Playing Card Probability
How do I go about solving this?
4 cards are drawn from a pack of 52 playing cards without replacment. What is the probability that two are black and two are red?
The number of ... | 4 | [
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0.07373046875,
-0.11962890625,
-0.00958251953... | 36,686 | 36686 | |
commutative diagram, module homomorphisms
December 8th 2008, 06:32 PM #1
Newbie
Joined
Nov 2008
Posts
1
commutative diagram, module homomorphisms
Suppose $R$-modules and $R$-module homomorphisms.
(a) Suppose that $\phi$ is injective. Prove that the map $\phi_0 : \text{Ker } f \rightarrow \text{Ker } ... | 5 | [
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Degeneration of the Hodge spectral sequence
up vote 23 down vote favorite
7
Let $f\colon X \to S$ be a smooth proper morphism of schemes. If $S$ is of characteristic zero (i.e., $S$ is a $\mathbb Q$-scheme), then Deligne has shown:
1. $R^af_*\Omega^b_{X/S}$ is locally free for all $a,b \geq 0$.
2. The Hodge-De Rha... | 4 | [
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-0.052246093... | 36,688 | 36688 | |
FOCS 2013 Recaps, Part 2
We continue our FOCS 2013 recaps (Part 1) with recaps by Clément (a guest blogger from Columbia) and Michael.
Clément Canonne on Learning sums of independent integer random variables by Constantinos Daskalakis, Ilias Diakonikolas, Ryan O’Donnell, Rocco Servedio, and Li-Yang Tan.
Background: ... | 4 | [
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0.... | 36,689 | 36689 | |
Ask Dr. Math Tour
Archive Sample
Back to The Ar... | 4 | [
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What is known about the MMP over non-algebraically closed fields
up vote 11 down vote favorite
2
I would like to know how much of the recent results on the MMP (due to Hacon, McKernan, Birkar, Cascini, Siu,...) which are usually only stated for varieties over the complex numbers, extend to
varieties over arbitrary fie... | 4 | [
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Field extension containing the eigenvectors of a Hermitian matrix
up vote 8 down vote favorite
3
Let H be a (finite-dimensional) Hermitian matrix with algebraic numbers for its entries, all of which lie in some minimal field extension of the rational numbers; call this field ℚ(H) for short.
Let's assume that the eigen... | 5 | [
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Solution of Linear Programs by the Simplex Method
Next: Alternate Optimal SolutionsDegeneracy, Up: The Simplex Method Previous: Linear Programs in Standard
For simplicity, in this course we solve ``by hand'' only the case where the constraints are of the form
First, we convert the problem into standard form by a... | 5 | [
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0.054931640625,
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Ultraweak closure inside a closed ball
up vote 0 down vote favorite
Let $H$ be a Hilbert space, and $S\subseteq \mathcal{B}(H)$. We denote $\bar S$ the ultraweak closure of $S$, and $B_r$ the closed ball of center 0 and radius $r>0$ of the normed space $\mathcal{B}
(H)$.
If $S$ is a subalgebra of $\mathcal{B}(H)$, Do... | 5 | [
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Data Structures: Graph Theory- Bipartite Matching
This tutorial will introduce the concept of bipartite matching, including an algorithm to find the maximal matching and minimal cover of a bipartite graph.
First, let's define some terms. A matching is a set of edges in a Graph that do not share vertices. A cover is a ... | 5 | [
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Finding the marginal distribution
November 22nd 2010, 05:20 AM #1
Member
Joined
Oct 2008
Posts
206
Finding the marginal distribution
With $f_X(x)\propto \frac{f_{(X|Y)}(x|y_o)}{f_{(Y|X)}(y_o|x)}$
I am given that
$f_{(X|Y)}(x|y)\propto (y)exp(-yx)$ at interval $0\le x<b<+\infty$
and
$f_... | 5 | [
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0.09375,
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-0.113281... | 36,696 | 36696 | |
Inverse Statements
Date: 08/20/98 at 20:02:40
From: Axel Ishmael
Subject: Half empty or half full?
I have been studying inverses. It is my understanding that the same
situation can be described using an inverse statement.
For example, say that there are 3 + 4 times as many girls as boys. Is
this the same as saying ... | 4 | [
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-0.041... | 36,697 | 36697 | |
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Topic: ----- ----- impossible equation
Replies: 3 Last Po... | 5 | [
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Bounded Hamming distance
up vote 4 down vote favorite
Definition 1. For each $n\in\mathbb{Z}^+$, the $n$-dimensional Hamming cube is the set of ordered $n$-tuples of $\lbrace 0,1\rbrace$, denoted by $\lbrace 0,1\rbrace ^n$.
Definition 2. The binary operation that turns $\lbrace 0,1\rbrace ^n$ into a group is $\oplus$... | 4 | [
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