content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Natural Numbers Problem
Date: 12 May 1995 05:11:20 -0400
From: Dana Murray
Subject: Question 5
Good morning Dr Math
Thank you for the hints with question 4.
How would you prove that one added to the product of four consecutive
natural numbers is a perfect square?
Thank you
Date: 16 May 1995 22:11:17 -0400
From:... | 4 | [
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-0.030639648437... | 39,100 | 39100 | |
Elementary short exact sequence of sheaves
up vote 13 down vote favorite
7
This question arised when I was trying to use this answer to understand Reid's "Young Person's guide to Canonical Singularities". In particular page 352 when computing the blow-up $Y\rightarrow A^2/\
mu_3$, the affine plane quotient the cyclic ... | 5 | [
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0.140625,
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0.0057373046875,
0.04248046875,
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0.01806640625,... | 39,101 | 39101 | |
Homology of abelian groups and their finite-index subgroups
up vote 1 down vote favorite
Fix some $1 \leq k \leq n$. I'm looking for finite-dimensional vector spaces $M_{n,k}$ over $\mathbb{Q}$ on which $\mathbb{Z}^n$ acts such that the natural map $H_k(\ell \mathbb{Z}^n,M_{n,k}) \
rightarrow H_k(\mathbb{Z}^k,M_{n,k})... | 5 | [
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0.0322265625,... | 39,102 | 39102 | |
nonagon
[DEL::DEL]
The Nonagon, from recognition to construction.
... | 4 | [
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Splitting principle for holomorphic vector bundles
up vote 12 down vote favorite
6
Let $E \to X$ be a vector bundle over a decent space $X$. Then there is a space $Z$ together with a map $p: Z \to X$ which induces a split injection on cohomology and such that $p^* E$ splits as a
direct sum of line bundles (take e.g. t... | 5 | [
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... | 39,104 | 39104 | |
Volume of a Cone
Date: 01/29/2001 at 21:55:37
From: cari
Subject: Volume of cones
Dr. Math,
I know HOW to find the volume of a cone(1/3area of base times height
divided by three) but my teacher wants to know WHY.
We know that filling the cone with water can prove it, but how does
it work with the actual shapes? If... | 5 | [
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-0.09765625,... | 39,105 | 39105 | |
Trig proof
Date: Wed, 30 Nov 1994 17:29:41 -0400 (EDT)
From: NAME NEERA
Subject: Math Question
Hello. I am a faculty member in math. I am trying to see how this
Dr.Math stuff works. Here is my question. Can you show me how
to prove arcsin(x)+arccos(x)=pi\2?
Date: Mon, 5 Dec 1994 17:07:41 -0500 (EST)
From: Dr. ... | 4 | [
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Author adam smith
10 definitions by adam smith
The study of choice in the face of scarcity.
Ignorant people who post idiotic definitions have scarce resources.
When yay just wont cut it
.....finding 50p in a public toilet
A mathematical rule useful for finding the derivative or instantaneous rate of change of a fu... | 4 | [
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0.03613... | 39,107 | 39107 | |
Math Help
Choose $k>n\Longrightarrow k=n+m\,,\,m>0\Longrightarrow 53\mid (2^{n+m}-2^n)= 2^n(2^m-1)\iff$ $\iff 53\mid (2^m-1)\iff 2^m=1\!\!\pmod{53}$ , and since 2 is not a primitive root modulo 53 (look here
Primitive root modulo n - Wikipedia, the free encyclopedia) , the above is true only when... Tonio Edit: Either... | 5 | [
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... | 39,108 | 39108 | |
Solution to ACL2 Quantifier Exercise 1
Author: Sandip Ray
In ACL2 documentation topic QUANTIFIER-TUTORIAL (Version 3.5 and later) one finds the following exercise.
Exercise 1. Formalize and prove the following theorem. Suppose there exists x such that (R x) and suppose that all x satisfy (P x). Then prove that t... | 5 | [
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If $X$ is a smooth and proper stack, does it admit a smooth and proper atlas?
up vote 5 down vote favorite
2
Fix a ground scheme $S$ (a field say). By atlas for an algebraic stack I mean a smooth and surjective morphism $Y \to X$ from a scheme (or algebraic space or affine scheme) $Y$. If the stack $X$ is
smooth then ... | 4 | [
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M - affine and H^1(M,Z)=H^2(M,Z) = 0 imply (?) Pic^algebraic(M) = 0. Note: in algebraic category NO exponential sequence
up vote 3 down vote favorite
1
Assume M affine algebraic manifold over C and we know that H^1(M,Z)=H^2(M,Z) = 0.
Question Does it imply Pic^algebraic(M) = 0 ?
Pic^algebraic means group of alg... | 5 | [
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geometric sequence
How many terms are in each sequence? 12, 4, 4/3, ......, 4/729 help i dont know how to get answer
Your terms are: $12, \frac{12}{3}, \frac{12}{9}, \frac{12}{27}......\frac{12}{2187}$ Or $\frac{12}{3^0}, \frac{12}{3^1}, \frac{12}{3^2}, \frac{12}{3^3}......\frac{12}{3^7}$
Hello, Vince604! How many te... | 4 | [
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Find the length of the curve r(t) - need help integrating
January 30th 2010, 10:23 AM #1
Newbie
Joined
Jan 2010
Posts
11
Find the length of the curve r(t) - need help integrating
Find the length of the curve $r(t)=<ln(5t), 2t , t^2> , 2\leq t \leq 3$
I am still trying to figure out how to use latex ... | 5 | [
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-0.0324707031... | 39,113 | 39113 | |
Sin(y)=Cos(y/3)
March 19th 2010, 02:54 PM #1
Junior Member
Joined
Sep 2009
Posts
62
Sin(y)=Cos(y/3)
Hello everyone, I came across an old trigonometry problem which I'm not able to solve again and it's driving me crazy, here it is:
find the value of tan(x+y) knowing that:
tan(x)=-sqrt(2)/2
si... | 4 | [
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help: solving equation (cos^2x)(sin^2x)=0
i need some help resolvong $\cos^2 x \sin^2 x = 0$ over the interval [0 degrees and 360 degrees]
Last edited by mr fantastic; April 14th 2009 at 06:48 PM. Reason: Clarified the latex and fixed a typo in the equation
I think i have the answer but i am not sure, can someone che... | 4 | [
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If the universal abelian group of two adjoint categories are isomoprhic, are the original two categories isomorphic?
up vote 2 down vote favorite
1
Suppose $F:C\to D$ is a left adjoint. Let $U:{\mathsf{Cat}}\to {\mathsf{Ab}}$ be the left adjoint to the fully faithful functor ${\mathsf{Ab}}\to {\mathsf{Cat}}$ that vie... | 5 | [
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Integration of Trigonometric Function by Substitution
Date: 03/18/98 at 20:05:21
From: Jennifer Haas
Subject: derivatives
Int[tan 2x dx]
I get confused when I need to do a u-substitution, or if this problem
actually needs one. At what point of the problem do I actually take
the derivative? Can you help me out pleas... | 5 | [
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...sum of all quadratic residues modulo p...
March 21st 2010, 04:12 PM
NikoBellic
...sum of all quadratic residues modulo p...
Let p be a prime > 3. Show that the sum of all the quadratic residues modulo p is divisible by p.
March 21st 2010, 04:49 PM
chiph588@
Quote:
Let $g$ be a primitive root modu... | 5 | [
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Measurable functions and unbounded operators in von Neumann algebras
up vote 4 down vote favorite
1
How do you define unbounded measurable functions for a general von Neumann algebra?
For the commutative algebra $L^\infty(X,\mu)$, we can consider the space of all measurable functions that are almost everywhere finite... | 4 | [
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0.00202941... | 39,119 | 39119 | |
About the continuity of coordinate projection
September 30th 2010, 09:59 AM #1
Newbie
Joined
Sep 2010
Posts
3
About the continuity of coordinate projection
I have attempted to solve this problem; however I couldn't do it.
Please, could someone give me a solution or a partial solution?
Thank you... | 4 | [
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Math Help
September 22nd 2006, 10:57 AM #1
Junior Member
Joined
Jul 2006
Posts
43
Divisibility
Had the following question:
If r is in Z and r is a non-zero solution of x^2+ax+b=0 (where a,b are in Z) prove that r divides b.
I solved it the following way:
Letting c and r be the roots of the... | 4 | [
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Probability Problems
October 15th 2009, 04:21 PM
loutja35
Probability Problems
Boods Types: The probability that a person in the United States has type AB+ blood is 3%. Five unrelated people in the United States are selected at random.
a.) Find the probability that all five have AB+ blood.
b.) Find the p... | 4 | [
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lagragian interpolation
April 20th 2010, 01:04 PM #1
Member
Joined
Jan 2008
Posts
175
lagragian interpolation
Let Q(t) be a quadratic polynomial such that Q(0) = 0,
Q(1) = 2, and Q(3) = 6. Use Lagrangian interpolation to
obtain Q(2).
im not understanding these things at all.
any help?
... | 4 | [
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Green's theorem question needs checking
May 18th 2010, 05:14 PM #1
Member
Joined
May 2008
Posts
77
Green's theorem question needs checking
Question:
Use Green's theorem to evaluate the following line integrals. Assume that the curve is transversed counterclockwise.
(a) $\oint_{\gamma}3xy.\partial... | 5 | [
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P6_C25
Plane-sweep: A general-purpose algorithm for 2-d problems … 1
25 Plane-sweep:
A general-purpose algorithm
for two-dimensional problems
illustrated using line segment intersection
Plane-sweep is an algorithm schema... | 4 | [
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-0.0140991... | 39,125 | 39125 | |
Math Forum Discussions - Re: Matheology § 224
Date: Apr 13, 2013 2:31 PM
Author: Frederick Williams
Subject: Re: Matheology § 224
Nam Nguyen wrote:
>
> On 13/04/2013 9:57 AM, Frederick Williams wrote:
> > Nam Nguyen wrote:
> >
> >> But if GC is undecidable in PA, there's no proof left in FOL but
> >> ... | 5 | [
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fractions with variables
2x/x^2-1 - 1/x+1 i got x+1 as my final answer
How have you got $x + 1$? I don't understand what you're trying to achieve. I'll presume the denominator on the left side is $x^2 - 1$ $\frac {2x}{(x^2 - 1)} - \frac{1}{(x + 1)}$ $\frac{(2x)(x + 1) -
(1)(x^2 - 1)}{(x^2 - 1)(x + 1)}$ $\frac{(2x^2 + ... | 4 | [
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0.017578125,
0.040283203125,
-0.036865234375,
-0.025634765625,
-0.07958984375,
0.068359375,
0.05615234375,
-0.08203125,
0.0028839111328125,
0.06591796875,
0.03759765625,
-... | 39,127 | 39127 | |
Designing Register Machines
Next: A Language for Describing Up: Computing with Register Machines Previous: Computing with Register Machines
Designing Register Machines
To design a register machine, we must design its data paths (registers and operations) and the controller that sequences these operations. To i... | 4 | [
-0.0810546875,
0.0230712890625,
-0.10302734375,
-0.09375,
-0.0751953125,
-0.07763671875,
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0.043212890625,
-0.0218505859375,
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-0.002166748046875,
0.0026397705078125,
0.054443359375,
-0.0286865234375,
0.0133056640625,
0.01953125,
-0.049560546875,
0.0... | 39,128 | 39128 | |
Derivation rules and Godel theorem
up vote 3 down vote favorite
1
Every formal theory is a collection of alphabet, axioms and derivation rules. My question is - what kind of "derivation rules" are acceptable here. For example, "from A B it follows $A \cup B$" is a
valid derivation rule. But what about, say, D: "from K... | 5 | [
-0.040771484375,
0.0037994384765625,
0.032958984375,
-0.0791015625,
0.01129150390625,
0.001129150390625,
0.01531982421875,
-0.030517578125,
0.08544921875,
0.0654296875,
-0.0140380859375,
-0.005828857421875,
0.060302734375,
0.01611328125,
0.005157470703125,
-0.0130615234375,
-0.006774... | 39,129 | 39129 | |
Lowest Integer That Can't Be Made
Date: 04/05/2004 at 11:49:41
From: Mary
Subject: algebra
You have an unlimited number of 'a' cent stamps and 'b' cent stamps.
With them, you will be able to make many different postages. Both a
and b are relatively prime positive integers.
I am interested in finding a cutoff point,... | 5 | [
-0.03564453125,
0.05419921875,
-0.04736328125,
-0.058837890625,
-0.03271484375,
0.024658203125,
0.018310546875,
0.0223388671875,
-0.03271484375,
0.02685546875,
-0.056640625,
0.039306640625,
0.0517578125,
0.017578125,
0.04345703125,
0.0556640625,
-0.0439453125,
-0.0089111328125,
-... | 39,130 | 39130 | |
On a limit at the boundary of $\mathbb{D}$ related to complex and harmonic analysis
up vote 0 down vote favorite
Let $p(z,t)=\frac{1}{2\pi}.\frac{1-|z|^2}{|z-t|^2}$ be the Poisson kernel on the open unit disk $\mathbb{D}$, fix $0<\alpha<1$ . Let $a\in \partial\mathbb{D}=S^1$ be fixed. Then my question is :
what is th... | 5 | [
-0.00127410888671875,
0.024658203125,
-0.05322265625,
-0.07861328125,
0.0341796875,
-0.008544921875,
0.05908203125,
0.0458984375,
-0.004302978515625,
-0.0198974609375,
0.043212890625,
0.038330078125,
0.0103759765625,
-0.03955078125,
-0.0286865234375,
-0.064453125,
0.031982421875,
-... | 39,131 | 39131 | |
Neat maps between manifolds with boundary
up vote 1 down vote favorite
1
Let us consider an embedding of smooth manifolds $i: (Y, \partial Y) \rightarrow (X, \partial X)$. It is neat (see Hirsh, "Differential topology") if $i(\partial Y) = i(Y) \cap \partial X$ and, for
every $y \in \partial Y$, there exists a boundar... | 5 | [
-0.0147705078125,
-0.0145263671875,
0.126953125,
-0.0732421875,
0.03662109375,
-0.03369140625,
0.08349609375,
0.026611328125,
-0.044189453125,
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0.057373046875,
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0.0380859375,
0.034423828125,
-0.0032501220703125,
0.0054931640625,
-0... | 39,132 | 39132 | |
cutting the cube
October 13th 2010, 12:53 AM #1
Member
Joined
Jul 2010
Posts
99
cutting the cube
Hi everyone,I got this puzzle and but I cannot solve it,can anyone please help me?
For a $3\times 3$ cube, it requires 6 cuts to cut it into 27 cubes.
Can the number of cuts be reduced if the cube ca... | 5 | [
0.0439453125,
-0.032470703125,
-0.0224609375,
-0.00823974609375,
-0.05908203125,
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0.0205078125,
-0.0034332275390625,
0.0263671875,
-0.134765625,
-0.03857421875,
-0.061279296875,
0.07275390625,
0.02587890625,
0.037109375,
-0.02685546875,
0.019165039... | 39,133 | 39133 | |
How Pi is Calculated
Date: 08/07/97 at 07:42:58
From: Krono
Subject: How pi is calculated
If pi is calculated by the circumference of a circle divided by its
radius, how can computers generate pi to billions of decimal places?
Do they draw really accurate circles or what? Is there a
straightforward function (eg. log... | 5 | [
-0.024658203125,
-0.00213623046875,
-0.035400390625,
0.06201171875,
-0.0615234375,
-0.0830078125,
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0.06982421875,
0.0810546875,
0.0213623046875,
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0.07763671875,
0.032470703125,
-0.035400390625,
-0.1142578125,
-0.050048828125,
-0.000432... | 39,134 | 39134 | |
Another Calculus Problem.
e ∫ (x^2-1)/(x) dx= 1 A) e- (1/e) B) e^2 - e C) (e^2/2)-e+ (1/2) D) e^2-2 E) (e^2/2)-(3/2)
frozenflames First find the antiderivative of $\int\frac{x^2-1}{x}dx$ Which is, $\int x-\frac{1}{x}dx$ Which is, $\frac{x^2}{2}-\ln |x|$, But it is taken from $[1,e]$ Which by the fundamental theorem
is... | 5 | [
0.041748046875,
-0.001556396484375,
0.07470703125,
-0.02587890625,
0.0267333984375,
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0.0439453125,
0.048583984375,
0.0177001953125,
0.0242919921875,
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0.007537841796875,
-0.0595703125,
-0.04052734375,
0.0157470703125,
-0... | 39,135 | 39135 | |
Absolute Max and Min on an Interval? =[
January 5th 2010, 07:44 PM
BoredBorad
Absolute Max and Min on an Interval? =[
Find the absolute maximum and absolute minimum of f on the interval (0,3] when f(x)=(x^3-4x^2+7x)/x
A. max:none, min: (3,4)
B. max(0,7), min:(3,4)
C. max: none, min: (2,3)
D. max ... | 4 | [
0.060791015625,
-0.0235595703125,
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-0.0791015625,
-0.029052734375,
0.0123291015625,
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0.11767578125,
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0.0478515625,
0.059326171875,
0.01153564453125,
0.00799560546875,
0.02465820312... | 39,136 | 39136 | |
A question about the additive group of a finitely generated integral domain
up vote 4 down vote favorite
2
Let $R$ be an integral domain of characteristic 0 finitely generated as a ring over $\mathbb{Z}$. Can the quotient group $(R,+)/(\mathbb{Z},+)$ contain a divisible element? By a "divisible element" I
mean an elem... | 5 | [
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0.03515625,
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0.0986328125,
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0.0250244140625,
... | 39,137 | 39137 | |
Continuity Functions
September 11th 2007, 07:15 PM #1
Newbie
Joined
Aug 2007
Posts
24
Continuity Functions
I'm at a loss on where to start with either of these problems. It seems you will use the same basic methods of solving each so I will list each of them.
1.) For what value of the constant
... | 4 | [
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0.08935546875,
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0.078125,
-0.06103515625,
0.041259765625,
0.1220703125,
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-0.04833984375,
-0.00872802734375,
-0.0087890625,
0.034912109375,
-0.08544921875,
-... | 39,138 | 39138 | |
arithmetic sequence
I can't find a common difference. Is that the way to start?
You can assume without loss of generality that $a \le b \le c$. Edit: Actually, easier to assume $\frac{1}{b+c} \le \frac{1}{c+a} \le \frac{1}{a+b}$ (perhaps this is what they meant anyway), and then
equate (the second term minus the first... | 4 | [
-0.068359375,
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0.0712890625,
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0.0888671875,
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0.02587890625,
0.007293701171875,
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0.04345703125,
0.033203125,
-0.064453125,
0.03466796875,
0.0308837890625,
... | 39,139 | 39139 | |
Find Derivative Using Delta Process
February 15th 2009, 12:44 PM #1
MHF Contributor
Joined
Jul 2008
From
NYC
Posts
1,489
Find Derivative Using Delta Process
Find the derivative using the delta process.
f(x) = kx + c
MY WORK:
f'(x) = lim as h--->0 for kx + c
f'(x) = lim as --->0 f(... | 4 | [
-0.03125,
0.02587890625,
0.0361328125,
0.0040283203125,
-0.041259765625,
0.0235595703125,
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-0.056884765625,
-0.01025390625,
0.056640625,
0.07373046875,
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0.0301513671875,
-0.0234375,
0.0008087158203125,
-0.009765625,
-0.031982421875,
0.0218505859375,
-... | 39,140 | 39140 | |
Does the Hirsch conjecture hold for $n < 2d$?
up vote 7 down vote favorite
1
The Hirsch conjecture asserts that the graph (i.e. $1$-skeleton) of a $d$-dimensional convex polytope with $n$ facets has diameter at most $n - d$.
After being open for decades, Francisco Santos has recently proved that this fails in general... | 5 | [
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0.044921875,
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0.0250244140625,
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0.01385498046875,
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0.0308837890625,
... | 39,141 | 39141 | |
counter examples in real analysis
March 11th 2007, 09:07 PM #1
Newbie
Joined
Mar 2007
Posts
21
counter examples in real analysis
For each of the following, prove or give a counter example:
a) if (Sn) converges to S, then (|Sn|) converges to |S|
b) if (|Sn|) is convergent, then (Sn) is convergent
... | 4 | [
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0.00799560546875,
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0.051025390625,
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0.0211181640625,
0.022... | 39,142 | 39142 | |
Simple Arithmetic Series Question
October 10th 2009, 01:17 PM #1
Member
Joined
Sep 2009
Posts
79
Simple Arithmetic Series Question
In an arithmetic series the 20th term is 14 and the 40th term is -6. Find the 10th term.
How do I do this?
$U_n = a+(n-1)d$
Where
□ $U_n$ is the nth ter... | 4 | [
-0.08056640625,
0.06396484375,
0.0751953125,
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-0.01287841796875,
-0.018310546875,
-0.04296875,
-0.032470703125,
-0.013... | 39,143 | 39143 | |
On "Mannian" Smoothing
A
recent thread
at Climate Audit revisited the topic of "Mannian" smoothing. There's a long history here -
here
, for example, is a thread to which this seems to be a sequel.
The "Mannian" smoothing to which they refer is described, under the name of Minimum Roughness Criterion, by Mann
GRL... | 4 | [
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0.0264892578125,
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-0.0172119140625,
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-0.056396484375,
0.023193359375,
-0.0038757... | 39,144 | 39144 | |
ASAP Calculus Integration help (by parts and trig)
February 11th 2009, 01:28 PM #1
Newbie
Joined
Feb 2009
Posts
7
Hi guys, I'm new on the forum and need a little assistance... we were given this to integrate:
/int x^3/sqrt (x^2+1)dx
And were instructed to integrate by trig integration and integr... | 5 | [
-0.042236328125,
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0.0703125,
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0.04833984375,
-0.0279541015625,
-0.0859375,
0.013427734375,
0.0240478515625,
... | 39,145 | 39145 | |
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Topic: An experiment . . . at random in intra-Permutation... | 4 | [
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-0.03955078125,
0.06787109375,
0.018310546875,
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0.01458740234375,
0.080078125,
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0.0400390625,
0.053955078125,
-0.07568359375,
-0.09912109375,
0.052001953125,
0.0498046875,
-0.01043701... | 39,146 | 39146 | |
determinant of fibonacci-sum graphs
up vote 3 down vote favorite
2
We have a simple graph with vertices $\{v_1, v_2, ... v_n\}$.
The adjacency matrix of this graph is $A= (a_{ij})$ so that
• $a_{ij}=1$ if $i+j$ belongs to the Fibonacci sequence;
• $a_{ij}=0$ if $i+j$ doesn't belong to the Fibonacci sequence.
W... | 4 | [
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0.029541015625,
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0.0322265625,
-0.052734375,
-0.041015625,
-0.0322265625,
-0.00399780... | 39,147 | 39147 | |
Three Binary Algorithms
January 15, 2010
We begin with the operations that are built-in to most hardware. R5RS Scheme does not provide bit operations, but most implementations provide an arithmetic-shift function, sometimes called ash as in
Lisp. R6RS standardizes the arithmetic-shift function. Simple versions that w... | 5 | [
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0.01263427734375,
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0.039306640625,
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0.00775146484375,
-0.0040283203125,
-0.03662109375,
0.03515625,
-0.08203125,
0.08... | 39,148 | 39148 | |
Method For Performing Wedge Analysis For Assessing Wedge Instabilities In Underground Openings - Patent 6757642
United States Patent: 6757642
( 1 of 1 )
United States Patent
6,757,642
Boudreau
, et al.
June 29, 2004
Method for performing w... | 4 | [
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0.004058837890625,
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0.041015625,
0.019287109375,
0.0147705078125,
0.06689453125,
-0.044189453125,
0.0532... | 39,149 | 39149 | |
Last non-zero digit of a factorial
Home
>
Number theory
,
Olympiad
,
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> Last non-zero digit of a factorial
Last non-zero digit of a factorial
Find a method to calculate the last non-zero digit of $n!$, where $n \in \mathbb{N}^*$ and $n!=1\cdot 2\cdot ... \cdot n$.
Solution: We have the following... | 5 | [
-0.0888671875,
0.0257568359375,
-0.00127410888671875,
-0.1083984375,
-0.024658203125,
0.08349609375,
0.0849609375,
0.07568359375,
-0.0191650390625,
0.0291748046875,
-0.00179290771484375,
-0.004852294921875,
0.0157470703125,
0.09130859375,
-0.01483154296875,
0.0262451171875,
-0.054687... | 39,150 | 39150 | |
absolute max and min
May 29th 2009, 12:18 PM
lisa1984wilson
absolute max and min
find the absolute maximum and absolute minimum (if any) of the given function on the specified interval:
f(x)=x^2 + 4x + 5; -3=<x=<1
the book has:
max (1, 10)
min (-2, 1)
The book is a terrible resource, its ... | 4 | [
-0.0169677734375,
-0.00872802734375,
0.0252685546875,
-0.0634765625,
-0.001800537109375,
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0.1435546875,
0.020751953125,
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0.072265625,
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0.1220703125,
0.031494140625,
-0.0654296875,
0.033935546875,
0.0390625,
-0.0546875,
-0... | 39,151 | 39151 | |
Remainder Theorem and Synthetic Substitution
Associated Topics || Dr. Math Home || Search Dr. Math
Remainder Theorem and Synthetic Substitution
... | 4 | [
-0.07177734375,
0.044189453125,
0.07666015625,
0.0634765625,
-0.015869140625,
0.0030975341796875,
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0.0252685546875,
0.0157470703125,
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0.083984375,
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0.0284423828125,
-0.004913330078125,
0.04345703125,
-0.061279296875,
0.0... | 39,152 | 39152 | |
Spatially Variant Apodization - Patent 5349359
United States Patent: 5349359
( 1 of 1 )
United States Patent
5,349,359
Dallaire
, et al.
September 20, 1994
Spatially variant apodization
Abstract
Spatially variant apodization is a digit... | 4 | [
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0.0284423828125,
0.0177001953125,
-0.0693359375,
-0.0654296875,
-0.0498046875,
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0.038818359375,
0.024658203125,
0.0206298828125,
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0.034423828125,
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-0.0213623046875,
-0.01953125,
0.055664062... | 39,153 | 39153 | |
transitive permutation groups have fixed point free elements
September 29th 2010, 10:50 AM
robeuler
transitive permutation groups have fixed point free elements
Let $G$ be a permutation group on $n$ letters. So a subgroup of $S_{n}$.
There is a theorem of Fein, Kantor and Schacher (1981) that if $G$ is tran... | 4 | [
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-0.01904296875,
-0.0272216796875,
-0.012878417... | 39,154 | 39154 | |
Help with Lines/Planes/Vectors
September 8th 2009, 03:47 PM #1
Junior Member
Joined
Sep 2009
Posts
49
Help with Lines/Planes/Vectors
I'm having trouble with these following problems. Appreciate all the help,
1.) Write an equation of the indicated plane through the origin and parallel to the plane wi... | 5 | [
-0.03759765625,
-0.013427734375,
-0.0108642578125,
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0.095703125,
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0.04296875,
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0.036865234375,
-0.06494140625,
0.0245361328125,
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Look at the recursive
I´m having a hard time getting through these sum understanding exercises
This one in particular, If you have some idéa, I value some explaining more then solution so please no: Hey stupid, what the hell, just to the "inversetriangular root extraction recursive
absolute value differenti... | 4 | [
-0.1455078125,
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0.01434326171875,
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0.0252685546875,
0.009765625,
-... | 39,156 | 39156 | |
Method and Apparatus for Estimating Rotor Position in a Sensorless Synchronous Motor
Patent application title: Method and Apparatus for Estimating Rotor Position in a Sensorless Synchronous Motor
Sign up to receive free email alerts when patent applications with chosen keywo... | 4 | [
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0.025390625,
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0.031494140625,
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0.0166... | 39,157 | 39157 | |
Tower of Hanoi
Date: 10/16/97 at 00:59:22
From: Forrest Bankston
Subject: Tower of Hanoi
I'm looking for mathematical solution, not a trial and error one.
I have done several net searches but can find no solution - just
histories of the puzzle and games for trial-and-error fun.
My students are exasperated and want a... | 4 | [
-0.052734375,
-0.0030059814453125,
-0.03271484375,
-0.12060546875,
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0.06201171875,
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0.07861328125,
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0.010... | 39,158 | 39158 | |
A question on the number of subgroups of a given exponent of a finite abelian p-group
Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
Is it known an explicit formula for the number of subgroups of a given exponent of a fin... | 4 | [
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-0.02... | 39,159 | 39159 | |
Sum of cubes.
July 27th 2010, 01:19 PM #1
Junior Member
Joined
Jul 2010
Posts
25
Sum of cubes.
$<br /> <br /> \begin{array}{l}<br /> prove\;that\; \\ <br /> \\ <br /> 1^3 + 2^3 + 3^3 + ............ + 100^3 = (\frac{{100 \times 101}}{2})^2 \\ <br /> \\ <br /> \end{array}<br /> <br /> <br />
$
Las... | 4 | [
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0.025634765625,
-0.02... | 39,160 | 39160 | |
Example: solution of the hyperbolic equation
Example: solution of the hyperbolic equation
Dynamics of pressures in the pipeline with a liquid
Let's consider dynamic p... | 4 | [
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-0.073... | 39,161 | 39161 | |
Find an integer n for which (1+2cos(π/9))^n rounded to nearest integer is divisib...
July 25th 2010, 12:52 PM #1
Newbie
Joined
Jul 2010
Posts
20
Find an integer n for which (1+2cos(π/9))^n rounded to nearest integer is divisib...
Find an integer n for which (1+2cos(pi/9))^n rounded to the nearest integer... | 5 | [
-0.0322265625,
0.049072265625,
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0.040771484375,
0.01904296875,
-0.09423828125,
0.0250244140625,
-0.... | 39,162 | 39162 | |
Divergence of the Dirichlet series for the Riemann zeta function for Re s = 1, Im s <> 0
up vote 2 down vote favorite
1
Consider the Dirichlet series $\sum_{n=1}^{\infty} n^{-s}$, with $s=\sigma+it$, $\sigma$ and $t$ real. How can one prove that this series diverges for $\sigma=1$ and $t\neq 0$?
In all the other comb... | 5 | [
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0.0625,
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-0.0625,
-0.1044921875,
0.08203125,
-0.06982421875,
0.049072265625... | 39,163 | 39163 | |
Using SPSS for One Way Analysis of Variance
This tutorial will show you how to use SPSS version 12 to perform a one-way, between- subjects analysis of variance and related post-hoc tests.
This tutorial assumes that you have:
• Downloa... | 5 | [
0.058837890625,
0.00127410888671875,
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0.033935546875,
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-0.0439453125,
0.0277099609375,
-0.0164794921875,
-0.026123046875,
0.030517578125,... | 39,164 | 39164 | |
X not simply connected and X-x contractible
up vote 3 down vote favorite
1
Hello,
I was wondering if there is a nice counterexample to the following question.
Suppose $X$ is a CW-complex which is not simply connected and there is a point $x\in X$ such that $X-x$ is contractible. Is $X$ homotopy equivalent to a wedge... | 5 | [
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-0.08837890625,
-0.02844... | 39,165 | 39165 | |
Fast Perlin Noise
by Ben Weston
I’m a POV-Ray fanatic, using it for everything from art to drawing graphs. Those years of using POV have given me a lot of skills with procedurally generated textures & shapes that I seldom get a
chance to use in my day job. So, I figured I’d leverage those abilities into my hobby prog... | 4 | [
-0.050048828125,
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0.0791015625,
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0.0299072265625,
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-0.0030517578125,
-0.0478515625,
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0.037841796875,
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... | 39,166 | 39166 | |
showing its a cauchy sequence
Show $i^n/n$ is a cauchy sequence. need $|(mi^n-ni^m)/nm| < e$whenever $n,m>_N$.
Silly question, I suppose, but does $i=\sqrt{-1}$ in this problem? If so, why not just use the triangle inequality?
The sequence converges, and so it's trivially Cauchy. It converges to zero because each ter... | 5 | [
-0.006744384765625,
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0.02490234375,
0.044921875,
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0.0859375,
0.0130615234375,
-0.06640625,
0.000885009765625,
0.12060546875,
-0.0213... | 39,167 | 39167 | |
Some Mathematics in O()-notation
Posted by: Alexandre Borovik | April 14, 2010
Some Mathematics in O()-notation
From Dmitri Fon-Der-Flaass:
There are infinitely many prime numbers.
Proof: Assume that there are only $k$ prime numbers. Then the number of all ways to multiply $m$ of them (perhaps with repetitions) ... | 4 | [
0.0040283203125,
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0.080078125,
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0.033935546875,
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0.06494140625,
0.03369140625,
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0.09423828125,
0.0595703125,
-0.06103515625,
-0.0159912109375,
0.080078125,
-0.0164794921875,
0.009765625,
0... | 39,168 | 39168 | |
Symmetric Ricci Tensor
up vote 4 down vote favorite
4
Let $M$ be a pseudo-Riemannian manifold. Assume that $M$ comes with a zero-torsion affine connexion $\nabla.$ There is no need for $\nabla$ to be the Levi-Civita connexion. Recall that the curvature
tensor of $\nabla$ is given by $R(X,Y)Z = \nabla_X\nabla_YZ - \nab... | 4 | [
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0.057861328125,
0.0245361328125,
0.046630859375,
-0.04296875,
0.0... | 39,169 | 39169 | |
RLC Circuit Question
April 17th 2013, 05:19 AM #1
Newbie
Joined
Oct 2012
From
Australia
Posts
24
RLC Circuit Question
I have the following question to work out:-
A defibrillator consists of a open circuit containing a capacitor of 40 $\mu$F and an inductor of 0.05H. A patient has a resistance of... | 4 | [
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-0.0322265625,
-0.0800781... | 39,170 | 39170 | |
1+3+5+...+(2n+1)
Hi Emma,
Suppose that we use S to designate this sum, that is
S = 1 + 3 + 5 + ... + (2n+1)
There is a nice way to evaluate S that starts with evaluating 2S by writing the sum forwards and and then backwards.
2S = 1 + 3 + 5 + ... + 2n-3 + 2n-1 + 2n+1 +
2n+1 + 2n-1 + 2n-3 + ... | 4 | [
-0.09521484375,
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-0.036865234375,
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-0.0478515625,
0.025146484375,
-0.027221... | 39,171 | 39171 | |
Predict your climate
Via Steve McIntyre's blog (posting by John A.)
Dave Stockwell has created a script whose source is found here (mirror) and described here. If you click the image below, it opens in a separate window: you probably need to click because the image
does not quite fit here. Every time you reload the im... | 4 | [
-0.10009765625,
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-0.056884765625,
-0.08251953125,
-0.08740234375,
-0.1318359375,
-0.143... | 39,172 | 39172 | |
Inverse Laplace
November 1st 2008, 02:18 AM #1
Member
Joined
Mar 2008
From
http://en.wikipedia.org/wiki/Malaysia now stop asking me where is malaysia...
Posts
158
Inverse Laplace
Well i got this question from my tutorial. Given the answers as well with it.Still couldn't understand how my lecturer g... | 5 | [
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-0.0294189453125,
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0.046875,
-0.078125,
0.0054931... | 39,173 | 39173 | |
special primes with p'=4p+1
up vote 5 down vote favorite
2
How can I most quickly find a big prime, p, for which 4p+1 is also prime? For example, p=37 works. I wonder if these special primes have been researched and some characteristics are known. Are there
infinitely many of these primes?
prime-numbers
1 This br... | 4 | [
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0.01422119140625,
-0.07031... | 39,174 | 39174 | |
Math Forum Discussions
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Topic: Small but powerful triangles
Replies: 1 Last Post:... | 5 | [
-0.027099609375,
0.0791015625,
-0.0286865234375,
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0.03369140625,
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0.05078125,
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0.05224609375,
0.0186767578125,
-0.025146484... | 39,175 | 39175 | |
Probability/Two fair dice are tossed
May 28th 2009, 09:46 PM
change_for_better
Probability/Two fair dice are tossed
Two fair dice are tossed and the product of the outcomes is recorded:
(a)Write down the sample space s, the mode and median of S
S={1,2,3,4,5,6,2,4,6,8,10,12,3,6,9,12,15,18,4,8,12 ,16,20,... | 4 | [
-0.006988525390625,
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0.11181640625,
0.0498046875,
-0.00286865234375,
-0.0035858154296875,
0.00921630859375,
0.05029296875,
-0.0294189453125,
-0.0216064453125,
-0.018798828125,
-0.0197753906... | 39,176 | 39176 | |
Integrating a volume
February 22nd 2010, 07:33 PM
Latszer
Integrating a volume
We just started today and a problem I have is...
Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown in the figure below. Evaluate the integral exactly. Use your work to a... | 5 | [
-0.048583984375,
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0.028076171875,
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0.01513671875,
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0.06689453125,
-0.0380859375,
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0.004486083984375,
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-0.0400390625,
0.09912109375,
0.010986328125,
-0.00732421875,
-0.017822265... | 39,177 | 39177 | |
Math Forum Discussions
Math Forum
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Discussions
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Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Potter's electro-magnetic universal distance per m... | 4 | [
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0.0400390625,
-0.03759765625,
0.0277099609375,
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0.056396484375,
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0.1083984375,
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0.006134033203125,
0.002838134765625,
-0.054443359375,
0.01300048828125,
-... | 39,178 | 39178 | |
[SOLVED] set proof help
March 5th 2009, 10:30 AM #1
Junior Member
Joined
Sep 2007
Posts
30
[SOLVED] set proof help
Can anyone prove or disprove
$X \cap Z \subseteq Y \Leftrightarrow (X - Y) \cup (Y-Z) \subseteq Z^c$
I think you have to split it up into two parts, but whenever I do it one way I c... | 4 | [
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0.07373046875,
-0.01513671875,
0.040283203125,
-0.002838134765625,
0.01513671875,
-0.052... | 39,179 | 39179 | |
Under what conditions a bounded linear map can be extended ?
up vote 2 down vote favorite
I have two questions after reading the Hahn-Banach theorem from Conway's book ( I have googled to know the answer but I have not found any result yet. Also I am not sure that whether my questions
have been asked here somewhere on... | 4 | [
0.010986328125,
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0.0078125,
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0.050537109375,
-0.003814697265625,
0.002471923828125,
... | 39,180 | 39180 | |
Axioms Proving.
March 14th 2009, 07:45 PM
panda*
Axioms Proving.
Let A, B and C be any three events. Show that
(i) $P(A) = P(B)$if and only if $P(A \cap B^{c}) = P(A^{c} \cap B)$
(ii) Given $P(A) = 0.5$ and $P(A \cup (B^{c} \cap C^{c})^{c})= 0.8$, determine $P(A^{c} \cap (B \cup C))$
Show that for ... | 5 | [
0.039306640625,
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0.0003070831298828125,
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0.0279541015625,
0.0859375,
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0.010986328125,
0.08056640625,
0.0791015625,
0.050048828125,
-0.0439453125,
-0.01330566406... | 39,181 | 39181 | |
Triple Intergral
October 30th 2006, 06:18 PM #1
Triple Intergral
#14 f(x,y,z) = z W is the region in the first octant bounded by the cylinder y^2 + z^2 = 9 and the planes y = x, x = 0 and z = 0
My first intergral has the limits between x = 0 and x = y^2 + z^2 - 9
My second intergral has limits between z... | 4 | [
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0.11181640625,
-0.05712890625,
0.0079345703125,
-0.008544921875,
-0.0473632... | 39,182 | 39182 | |
Unimodular column property
up vote 1 down vote favorite
Hi, I know that if $R$ is a ring such that every projective $R$-module finitely generated is free then $R$ has the unimodular column property. I would like to know if there is a ring $R$ that doesn't
satisfy the unimodular column property but such that every fini... | 4 | [
-0.057861328125,
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... | 39,183 | 39183 | |
Math Help
November 23rd 2012, 04:44 AM #1
Senior Member
Joined
Sep 2012
From
Sweden
Posts
250
Thanks
6
Matrix
Hello i got a problem!
ima decide a inverkar to this Matrix A=1 0 -1 1 an it says clue ima set B= x y z tand decide x,y,z,t, for B shall be inverse to A.( its 2x2 the first 2 number ... | 5 | [
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construction
This Talk is Under Construction
Berkeley Math Circle 2001-2002
... | 4 | [
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Factoring Quadratics When a Doesn't = 1
Date: 03/24/2003 at 11:51:54
From: Tracy
Subject: Factoring quadratics when a doesn't = 1
A trick to solving quadratics was presented to me. I was wondering
if there is a proof for it.
For any trinomial ax^2+bx+c you multiply ac, and then find factors of
the product that add t... | 4 | [
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... | 39,186 | 39186 | |
Line integral help
June 14th 2014, 06:27 AM #1
Super Member
Joined
Sep 2008
Posts
607
Line integral help
am stuck on the integration part, so far I have
x = cost , y = sint
dx = -sint dt dy = cost dt
$\int ( xy^{2}) dx + ( x^{2}y + 2x) dy$ subbing in the values for x,y, dx and dy
i ge... | 5 | [
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A property on the Green-St Venant strain tensor
up vote 0 down vote favorite
Green-St Venant strain tensor is defined by $E(u)={1\over 2}[\nabla u+(\nabla u)^T+(\nabla u)^T\nabla u]$, where $\nabla u$ is the displacement gradient.
Show that
$u\in H^1(\Omega), E(u)\in L^r(\Omega), r\ge1\Rightarrow u\in W^{1,2r}(\Omeg... | 5 | [
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Physics question I need some help with...
October 12th 2009, 08:03 PM #1
Newbie
Joined
Jun 2009
Posts
19
Physics question I need some help with...
A water balloon is dropped on some unsuspecting sunbathers from a stationary hot air balloon. The water balloon is 353 m above the beach. If the water balloon... | 4 | [
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confused while trying to factor this
October 30th 2010, 02:55 PM
NecroWinter
confused while trying to factor this
y^3-y^2+3y-3 is what im factoring
the book says the answer is (y-1)(y^2+3)
i dont know how it gets there
heres what i try to do:
(y^3-y^2)+(3y-3)
-y^2(y-1) + 3(y-1)
(y-1)(... | 4 | [
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Isometric embeddings of finite-dimensional normed spaces
Let $\ell_p^n$ denote the $n$-dimensional real space with the norm $\|x\|_p=\left(\sum_{k=1}^n|x_k|^p\right)^{1/p}$ or $\|x\|_\infty=\max_k |x_k|$. In two-dimensional case $n=2$ it is easy to plot
the unit notice the pattern: from squareness to roundness back to... | 5 | [
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0.012878... | 39,191 | 39191 | |
Mannings Equation
Flowrate equals the area of the flow times the velocity of the flow.
Q = AV
Q = Flowrate, A=Area, V = Velocity
So if the velocity in a rectangular channel, 2 metres wide and 1 metre deep was 3 metres per... | 5 | [
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Linear algebra toughy
May 4th 2008, 12:28 PM #1
Junior Member
Joined
Apr 2008
Posts
47
Linear algebra toughy
Suppose that n is a positive integer. Define T \ $in L(F^n)$ by:
T( $z_1$, ....., $z_n$)=(0, $z_1$,...., $z_n-1$).
Find a formula for T*( $z_1$, ....., $z_n$).
T*is the adjoint of T... | 5 | [
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decimal digit as final digit
Which decimal digits occur as the final digit of a forth power of an integer?
Reduce $x^{4}$ mod $10$. You can just reduce $0^4,1^4,...,9^4$ by mod $10$ since it will repeat. And those are the possibilities.
Think of a decimal number as $a_n \cdot 10^n + ~...~ + a_1 \cdot 10 + a_0$ So whe... | 4 | [
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... | 39,194 | 39194 | |
Factoring an equation to find its roots
October 12th 2012, 05:49 PM #1
Newbie
Joined
Sep 2012
From
US
Posts
18
Factoring an equation to find its roots
This is actually for my ODE class, but I'm stuck on a factorization type question.
r^5 - 3r^4 + 3r^3 - 3r^2 + 2r = 0
First thing I can do is... | 4 | [
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Celebrating Grassmann numbers
Off-topic rumor: the LHC will probably only restart at 13 TeV, not 14 TeV, in 2015, after the 2013-2014 break (upgrade).
Hermann Graßmann
was born in 1809 as the 3rd child to a math teacher (his father) in Stettin, currently in the Northwestern corner of Poland (Czech: Štětín; much o... | 4 | [
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Prove this ...
a,b,x,y are a positif reals and x<y Prove : $<br /> \frac{x}{y}\prec(\frac{ax+by}{bx+ay}\prec\frac{y}{ x}<br />$
Hello, dhiab! $a,b,x,y$ are positive reals and $x<y.$ Prove: . $\frac{x}{y} \:<\:\frac{ax+by}{bx+ay} \;<\:\frac{y}{x}$ $\begin{array}{ccccc}\text{We have:} & x \:<\:y \\<br /> \text{Square:} ... | 5 | [
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... | 39,197 | 39197 | |
Finding the roots through Newtons method
August 14th 2010, 06:51 AM #1
Member
Joined
May 2010
Posts
241
Finding the roots through Newtons method
In each of the following items approximate the zeros of $f$ using Newton's method. Continue iterating until making two successive approximations differ at most ... | 4 | [
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When are the units of R[x] exactly the units of R?
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.
I (Anton) have edited this question to be the question Pete and Zeb discuss in the first few comments.
... | 5 | [
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