content string | quality_label int64 | meta string | all-MiniLM-L6-v2_embedding list | doc_id int64 | unique_id string |
|---|---|---|---|---|---|
Stackelberg
The Stackelberg Model
Introduction
The eponymous Stackelberg model takes extends the basic quantity setting approach of the Cournot_Model but replaces simultaneous quantity choice by a sequential approach. Specifically in the
Stackleberg model quantities are chosen sequentially with later firms knowing th... | 5 | [
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-0.01214599609375,
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-0.00537109375,
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0.01806... | 39,800 | 39800 | |
non-locally trivial A^n bundles
up vote 11 down vote favorite
6
Let $f: X \to Y$ be a morphism of varieties such that its fibres are isomorphic to $\mathbb{A}^n$. Since the definition of a vector bundle stipulates that $f$ be locally the projection $U \times \
mathbb{A}^n \to U$, it is likely that there exist morphism... | 4 | [
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0.007354736328125,
-0.045654296875,
... | 39,801 | 39801 | |
Incircles Tangent to a Common Line
Date: 03/23/2001 at 00:20:23
From: Alice Klein
Subject: Circle Geometry
In triangle ABC, the incircle touches side AB at M. T is an arbitrary
point on BC. Show that the incircles of triangles BMT, AMT and ATC are
all tangent to a common line.
This problem proved really difficult t... | 4 | [
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0.078125,
-0.009033203125,
... | 39,802 | 39802 | |
Demand function
May 11th 2010, 01:52 PM #1
Member
Joined
Sep 2008
Posts
222
Demand function
the problem deals with applications of derivatives. the problem is: until recently hamburgers at the city sports arena costs $4 each the food concessionaire sold an average of 10,000 hamburgers
on a game night... | 5 | [
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... | 39,803 | 39803 | |
Are these Two Definitions of Quadratic Form (Algebraic, Topological) Related to Each Other?
up vote 2 down vote favorite
3
Hi, All:
I am trying to see if there is a nice relation between two different definitions of quadratic form q; a topological definition $q_T$, and an algebraic definition $q_A$, and, if there is,... | 4 | [
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0.03076171875,
-0.031982421875,
-0.06494140... | 39,804 | 39804 | |
Arbitrary small positive lower semi continuous functions
up vote 5 down vote favorite
1
This question is a generalization of the question posed in this page to lower semi continuous functions. so let me describe the Question in the following way.
Def: Let $(X,\tau)$ be a Tychonoff Topological space. we say that this ... | 5 | [
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0.09521484375,
-0.0059... | 39,805 | 39805 | |
Math Forum Discussions
Re: LOGIC & MATHEMATICS
Posted: May 28, 2013 3:24 PM
On May 27, 2:24 pm, Zuhair <zaljo...@gmail.com> wrote:
> On May 26, 9:52 am, Zuhair <zaljo...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>
> > Frege wanted to reduce mathematics to Logic by extending predicates by
> > objects in a general manner (i.e. ... | 4 | [
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-0.0231933593... | 39,806 | 39806 | |
Trig word problem. Help me please..
November 20th 2008, 05:06 AM #1
Newbie
Joined
Nov 2008
Posts
16
Trig word problem. Help me please..
A magician standing on a platform subtends an angle of 15degrees at a point on the ground. The angle of elevation of the platform from the same point is 45 degrees. The ... | 4 | [
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0.076... | 39,807 | 39807 | |
proof of limit
October 4th 2009, 09:13 AM #1
Banned
Joined
Oct 2009
Posts
4,261
Thanks
2
proof of limit
Hi:
how could one prove that if a_n --> A and A != 0 then
a_(n+1)/a_n --> 1 ?
I think some average inequalities could help here but I can't see it.
Thanx
For large enough $... | 5 | [
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... | 39,808 | 39808 | |
trig question (correct me) [part 1]
June 26th 2009, 07:13 AM #1
Super Member
Joined
Jun 2009
From
Africa
Posts
641
hello
here's my function :
let $\mathbb{E} = [-\pi ,+\pi]$
$x \in \mathbb{E}$$;$$f(x) = \sqrt{\frac{1+cos(x)}{1-cos(x)}}$
and here's my questions :
Prove that $(\foral... | 4 | [
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0.06103515625,
-0.143554687... | 39,809 | 39809 | |
hey guys, need some help with a take home sheet
April 2nd 2007, 09:38 AM #1
Newbie
Joined
Apr 2007
Posts
20
hey guys, need some help with a take home sheet
1) what angle pheta is measured by a 7inch arc on a circle of radius=3
Find: Radians=
Degrees=
revs=
2) if the 8inch radius tires on... | 4 | [
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0.00131225... | 39,810 | 39810 | |
order of operations
what is the correct order of operations to solve this (3+3)(2)(3)^3+1 (Itwasntme)
Just remember the order of operations: Parentheses Exponents Division/Multiplication Addition/Subtraction Better known as PEMDAS therefore (3+3)(2)(3)^3+1 do parentheses: (6)(2)(3)^3 +1 do exponents:
(6)(2)(27) + 1 do... | 4 | [
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0... | 39,811 | 39811 | |
Laws of Vectors
Date: 4/10/96 at 13:31:28
From: Anonymous
Subject: Geometry - Vectors
Question - part 1: Use definitions I and II below to prove that
k[ (a, b) + (c,d) ] = k(a,b) + k(c,d)
I. Definition of Scalar Multiple k(a,b) = (ka, kb)
II. Definition of Vector Addition (a,b) + (c,d) = (a + c, b + d)
I ... | 4 | [
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orthogonality relation for quadratic Dirichlet characters
up vote 5 down vote favorite
1
Hello,
I've been working deriving the orthogonality relation for quadratic Dirichlet characters $\chi_d(n)$ (or real primitive characters). The statement I'm trying to prove is
$$\lim_{X \rightarrow \infty} \frac{1}{D} \sum_{0 <... | 5 | [
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Homework Help
Mia is approaching her goal of 119 points for the video game. She wants to put her initials on the computerized list of Top Ten Point Scorers forr the game, She moves Freddie the frog all over the
terminal screen and at last she does it. Freddie the Frog eats a total of 22 critters: worm ( worth 6 points ... | 4 | [
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Placing points on a sphere so that no 3 lie close to the same plane
up vote 17 down vote favorite
4
Motivation
I am working with arbitrary parallelopiped tilings given by projection from a higher dimensional space. The collection of tiles, and some properties of the higher dimensional space are specified by a
finite ... | 5 | [
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... | 39,815 | 39815 | |
Approximating commuting matrices by commuting diagonalizable matrices
up vote 15 down vote favorite
5
Suppose the matrices $A$ and $B$ commute. Do there exists sequences $A_n$ and $B_n$ of matrices such that
1. $A_n \rightarrow A$, $B_n \rightarrow B$.
2. Each $A_n$ is diagonalizable and the same for each $B_n$.
... | 4 | [
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Roots of an Equation
Date: 4/16/96 at 22:42:39
From: Jonathan Stone
Subject: Solving Quadratic Equations
I'm trying to help my daughter with these. Example 6x^2+x-2 = 0.
We can factor it to (3x+2)(2X-1), I think. We're not sure what to
do now to solve it to two numbers. A good method of factoring and
solving these ... | 4 | [
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Tangent space of the moduli stack of Drinfeld modules
up vote 4 down vote favorite
I am going through the proof of Thm 1.5.1 of Laumon, Cohomology of Drinfeld modular varieties, which says that a certain map of stacks is smooth. To prove this, Laumon considers the tangent space of
a moduli stack:
Very roughly, a Drin... | 4 | [
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Tweetable way to see that Willmore energy is Möbius invariant?
up vote 7 down vote favorite
1
Consider a compact orientable Riemannian manifold $M$ (without boundary) isometrically immersed into $\mathbb{R}^3$. The Willmore energy of $M$ is the functional
$$\mathcal{W} = \int_M H^2 dA$$
where $H$ is the induced mean... | 4 | [
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Stereographic Projection Maps Circles to Circles
A Geometric Proof, adapted from lecture notes by Bill Casselman
... | 4 | [
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INTRODUCTORY-CHALLENGE-PROBLEM-3-ANSWER
answer to challenge problem 3 for the new user of ACL2
Major Section: INTRODUCTION-TO-THE-THEOREM-PROVER
This answer is in the form of a script sufficient to lead ACL2 to a proof.
; Trying dupsp-rev at this point produces the key checkpoint:
; (IMPLIES (AND (CONSP X)
; ... | 4 | [
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question on subspaces and dimensions
October 11th 2010, 10:09 PM #1
Member
Joined
Aug 2008
Posts
249
question on subspaces and dimensions
Given that V and W are subspaces of R^n such that dim(V) + dim(W) ≥ n, show that dim(V ∩ W) ≥ dim(v) + dim(W) - n.
so i am given dim(V) + dim(W) ≥ n and since the... | 4 | [
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0.010070... | 39,822 | 39822 | |
Converting Polar Equations to Rectangular and vice versa...
February 12th 2006, 12:11 PM #1
telefl89
Guest
Converting Polar Equations to Rectangular and vice versa...
I am having some difficulty with doing this. I am in a Pre-Calc class at my high school. My problem is, I was horrible at solving for identities, a... | 5 | [
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Decomposition of finite algebras over finite fields
up vote 6 down vote favorite
3
Let $K$ be a number field, $Z_K$ its ring of integers, and $p$ a rational prime number. Then $A_p = Z_K/(p)$ is a finite ${\mathbb F}_p$-algebra. Using ideal arithmetic in $Z_K$ and the Chinese
remainder theorem it is easily checked tha... | 4 | [
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Applications of DIfferentiation - Cylinder
September 6th 2006, 07:43 AM
classicstrings
Applications of DIfferentiation - Cylinder
I keep getting the wrong answer for this question, help appreciated.
A cylinder is designed so that it is always as high as its base diameter. It is expanding.
What is the r... | 5 | [
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0.00086212158203... | 39,825 | 39825 | |
What happens to inertia groups after blow ups?
up vote 2 down vote favorite
Say we have a branched $G$-Galois covering $X \rightarrow Y$ of surfaces, and assume that the branch locus (in $Y$) is a divisor with normal crossings. I will always assume that the ramification is
tame, and you can pretend we're doing this wi... | 4 | [
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Determining a function
June 3rd 2010, 09:27 AM #1
Member
Joined
May 2010
Posts
98
Determining a function
Hey all, i got a question im struggling with, and as of yet, i havent got anywhere..
It is a follows:
Determine a function $u: [0,\pi] \times [0,\infty[-> R <br />$ such that $<br /> \frac{d... | 5 | [
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0.03662109375,
-0.140625,
... | 39,827 | 39827 | |
Radii and centers in Banach spaces
up vote 9 down vote favorite
3
Suppose I have a Banach space $V$ and a set $A \subseteq V$ such that for all $\epsilon > 0$ there exists $v$ such that $A \subseteq \overline{B}(v, r + \epsilon)$. Does there exist $c$ such that $A
\subseteq \overline{B}(c, r)$?
The answer is clearly ... | 5 | [
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-0.032... | 39,828 | 39828 | |
eek
August 28, 1995
This Week's Finds in Mathematical Physics (Week 62)
John Baez
Now I'd like to talk about a fascinating subject of importance in both mathematics and physics, the subject of "ADE classifications". Here A, D, and E aren't abbreviations for anything; they are just
names for certain diagrams. But the... | 4 | [
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... | 39,829 | 39829 | |
Help Understanding a Proof
December 23rd 2009, 07:37 PM #1
Super Member
Joined
Jun 2009
From
United States
Posts
676
Thanks
19
Help Understanding a Proof
I'm having trouble understanding the proof of Theorem 1 on this page:
Pauls Online Notes : Linear Algebra - Finding Inverse Matrices
... | 4 | [
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-0.0170... | 39,830 | 39830 | |
Rings and Fields
February 24th 2009, 10:05 AM #1
Rings and Fields
If F is a field and R is a ring containing F as a subring, we can just as
easily regard R as a vector space over F as we can in the case that R itself
is field. Suppose that R is an integral domain containing the field F , and
as a vector ... | 5 | [
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-0.01519775390625,
0.087402... | 39,831 | 39831 | |
Measurement Uncertainty
Background
A measurement result is complete only when accompanied by a quantitative
statement of its uncertainty. The uncertainty is required in order to decide if the
result is adequate for its intended purpose and to ascertain if it is consistent with
ot... | 4 | [
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0.08935546875... | 39,832 | 39832 | |
Coconuts, Forwards and Backwards
Date: 02/02/2010 at 13:09:09
From: sue
Subject: x/3 +1 +(x/3 +1)/3 + 2/3 +(x/3) + 3 =22
Three sailors were marooned on an island. They worked all day
collecting coconuts, which left them too tired to settle up that
night; so they decided to divide the coconuts in the morning.
In the... | 4 | [
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0.0155... | 39,833 | 39833 | |
calc help
January 10th 2009, 08:25 AM
twilightstr
calc help
Make a substitution to express the integrand as a rational function and then evaluate the integral.
integral from 16 to 9 of (square root x)/ (x-4) dx (Let u= square root of x.)
Thanks
January 10th 2009, 08:44 AM
Jester
Quote:
$\int... | 4 | [
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0.006927490234375,
0.049072265625,
-0.021484... | 39,834 | 39834 | |
Modules with flat duals
up vote 3 down vote favorite
Let $R$ be a commutative ring, $M$ an $R$-module, $M^*=Hom_R(M,R)$ its dual. What are sufficient (and possibly necessary) conditions on $M$ that ensure that $M^*$ is flat? Is there a name for such
modules?
PS I would call such a module coflat if this term were not ... | 4 | [
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0.0625,
0.0233154296875,
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0.013549... | 39,835 | 39835 | |
Find a special element in group algebra
up vote 0 down vote favorite
Let $$G=\langle x, y, z\mid xyx^{-1}=zy, xzx^{-1}=z, yz=zy\rangle,$$ denote $l^1(G)^{\times}$ to be the set of units in $l^1(G)$, which we have considered as a ring with multiplication defined by the
usual convolution, i.e., $(\sum_{g\in G}\lambda_gg... | 4 | [
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0.10693359375,
-0.04736328125,
0.0659... | 39,836 | 39836 | |
Scaffold Towers
Jump Over Left Menu
The Strength of Scaffold Towers under Vertical Loading
H S Harung, E Lightfoot, D M Duggan
January 1975
The Structural Engineer
H. S. Harung, Royal Norwegian Navy; E. Lightfoot and D. M. Duggan, Department of Engineering Science, University of Oxford
Synopsis
Several single-st... | 4 | [
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0.010498046875,
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0.0035552978515625,
-0.08740234375,
... | 39,837 | 39837 | |
NetanelD.Seminar
Mutual Exclusion Using Atomic
Registers
Lecturer: Netanel Dahan
Instructor: Prof. Yehuda Afek
B.Sc. Seminar on Distributed Computation
Tel-Aviv University 11.03.07
Based on the book ‘Synchro... | 4 | [
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0.018310546875,
-0.046... | 39,838 | 39838 | |
cost function.
November 5th 2009, 04:03 PM #1
Junior Member
Joined
Sep 2008
Posts
41
cost function.
For the given cost function
C(x)=52900+200x+x2 find:
a) The cost at the production level 1000 = $1252900
b) The average cost at the production level 1000 = $1252.9
c) The marginal cost at t... | 5 | [
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0.... | 39,839 | 39839 | |
Area Problem
March 18th 2006, 12:15 PM
frozenflames
Area Problem
12. The area of the region enclosed by the graph of y = x^2 + 1 and the line y = 5 is
(A) 14/3
(B) 16/3
(C) 28/3
(D) 32/3
(E) 8p
March 18th 2006, 01:52 PM
CaptainBlack
Quote:
Originally Posted by frozenflames
1... | 5 | [
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Locker Problem
Date: 11/21/97 at 19:52:10
From: Jim Boyer
Subject: Locker Problem
Here is the problem: A new high school has just been completed.
There are 1,000 lockers in the school and they have been numbered from
1 through 1,000. During recess (remember this is a fictional problem),
the students decide to try a... | 4 | [
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0.0256347... | 39,841 | 39841 | |
Infinite Series Problem
Date: 01/15/2002 at 14:41:02
From: Flori
Subject: Infinite series and geometric sequences
Hi,
I have been given the task of finding the correct answer to an
infinite series question:
You have three people, a, b, and c. Each throws a die once, in turn.
If a gets a 6 on his first throw, he wi... | 4 | [
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-0.008... | 39,842 | 39842 | |
rate of change problem
March 27th 2013, 07:29 AM
kopklan
rate of change problem
Hi, I'm new here and I would be very grateful if you guys can help me with these 2 exercises :-)
---
1. A container in the shape of a right circular cone of heighr 20 cm and radius 5cm is held vertex downward and filled with ... | 5 | [
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0.042724609... | 39,843 | 39843 | |
False Existential
February 23rd 2008, 10:34 PM #1
Newbie
Joined
Feb 2008
Posts
3
False Existential
Rusty returning student stuck on this one proof:
Prove false:
There exists an integer n such that $6n^2 + 27$ is prime.
I know to do this, I have to prove the universal negation true.
For ... | 4 | [
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0.03... | 39,844 | 39844 | |
Structure theorem for Finitely Generated modules over PID's using localization
up vote 1 down vote favorite
I have been trying to work out a proof of structure theorem for finitely generated modules over PID's using localization. This is what my plan is:
1.Prove that every finitely generated torsion free module over ... | 4 | [
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... | 39,845 | 39845 | |
How much larger is the powerset of a transfinite set?
up vote 8 down vote favorite
5
This may seem a vague question, but in the process of explaining the hierarchy of transfinite sets to my students, I've had to use the Cardinality(powerset(S)) > Cardinality(S) argument, which
appeared to me to be extremely weak in in... | 5 | [
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... | 39,846 | 39846 | |
Lecture 17:
1
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... | 5 | [
0.046142578125,
0.0390625,
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0.... | 39,847 | 39847 | |
Evaluate line integral with 3 dimensions
May 14th 2010, 09:12 AM #1
Junior Member
Joined
Aug 2008
Posts
52
Evaluate line integral with 3 dimensions
Where C is the loop
with a clockwise orientation when viewed from above.
As usual, I have trouble with the third dimension. I have a problem l... | 5 | [
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-0.1337890625,
-... | 39,848 | 39848 | |
Solving of inequalities involving modulus
June 10th 2011, 06:02 AM #1
Newbie
Joined
Jun 2011
Posts
20
Solving of inequalities involving modulus
"Solve the inequality 1/(x-a) < 4|x-a|, where a is a positive constant, leaving your answer in terms of a." The answers are x <a and x > a + 1/2.
What I've ... | 4 | [
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0.044677734375,
-0.0947265625... | 39,849 | 39849 | |
Is there a lower bound for variance in terms of curvature?
up vote 2 down vote favorite
1
If the Gaussian curvature of the metric $g= f^2(x,y)(dx^2+dy^2)$ is nonzero then $f$ cannot be constant. This can be expressed by stating that the (probabilistic) variance $Var(f)$ of $f$ is nonzero
(in a suitable domain). If the... | 5 | [
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-0.0334472... | 39,850 | 39850 | |
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Topic: Series Convergence
Replies: 4 Last Post: Jan 26, 2... | 5 | [
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... | 39,851 | 39851 | |
Estimation theory
is a branch of
statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of
surveys and experiments....
and
signal processing
Signal processing is ... | 4 | [
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-0.017578125,
0.026611328125,
-0.04150390625... | 39,852 | 39852 | |
Does $\Pi^1_{\infty}$ comprehension imply ATR$_0$?
up vote 3 down vote favorite
$\Pi^1_{\infty}\text{-}\mathsf{CA}_0$ proves existence of models of ATR$_0$. But I think it does not imply ATR$_0$, because Axiom Beta is a kind of replacement axiom. Is that right?
lo.logic proof-theory
I'm puzzled with your referen... | 5 | [
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-0.024169921875,
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0.05... | 39,853 | 39853 | |
The Dual Isogeny II
Apologies that I haven’t been posting recently. Sage days was this past weekend along with 6 inches of snow in Georgia(read: power outages), the Arizona Winter school in a week and everything else,
it’s been very busy.
I’ve also been thinking about the comments on my last post, and how to deal with... | 4 | [
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0.041015625,
-0.11962890625,
-0.001220... | 39,854 | 39854 | |
Polynomials with rational coefficients
up vote 20 down vote favorite
10
Long time ago there was a question on whether a polynomial bijection $\mathbb Q^2\to\mathbb Q$ exists. Only one attempt of answering it has been given, highly downvoted by the way. But this answer
isn't obviously unsuccessful, because the followin... | 5 | [
-0.0306396484375,
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0.04248046875,
-0.0014801025390625,
0.0164794921875,
0.123046875,
-0.0159912109375,
-0.0488281... | 39,855 | 39855 | |
College Physics
Posted by Phillip on Saturday, February 11, 2012 at 8:17pm.
An artificial satellite is moving in a circular orbit with a speed of 6.5 km/s and a period of 80.0 min. A retarding rocket fires in a direction opposite to the motion. This provides a retarding
deceleration of 21.0 m/s2. What is the acute ang... | 5 | [
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... | 39,856 | 39856 | |
Definition of Sum
December 11th 2011, 09:54 AM #1
Newbie
Joined
Nov 2011
Posts
8
Definition of Sum
I have been trying to find an acceptable definition of the "sum" of two natural numbers. Wikipedia has come close to what I am looking for. They begin by saying:
Let n' be the successor of n, that is t... | 4 | [
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-0.01019287109... | 39,857 | 39857 | |
Circles problem.
August 1st 2009, 11:26 PM #1
Newbie
Joined
May 2009
Posts
5
Circles problem.
1. If from any point on the common chord of two intersecting circles , tangents be drawn to the circles , prove that they are equal.
2. From an external point P , tangents PA and PB are drawn to a circle wi... | 4 | [
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0.0013... | 39,858 | 39858 | |
is f a polynomial provided that it is "partially" smooth?
up vote 21 down vote favorite
8
Let $f$ be a $C^\infty$ function on $(c,d)$ ,and let $O=\cup_{n\in \mathbb{Z}^+} (a_n,b_n)$ where $(a_n,b_n)$ are disjoint open interval in $(c,d)$ and $O$ is dense in $(c,d)$. Suppose for each $n\in
\mathbb{Z}^+$ ,$f$ coincides ... | 5 | [
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-0.02... | 39,859 | 39859 | |
acmc of vsi connected to the grid
Journal of ELECTRICAL ENGINEERING, VOL. 55, NO. 3-4, 2004, 77–82
AVERAGE CURRENT MODE CONTROL OF A VOLTAGE SOURCE INVERTER CONNECTED TO THE GRID: APPLICATION TO DIFFERENT FILTER CELLS
Mustapha Raoufi — Moulay Tahar Lamchich
∗
In this paper the a... | 4 | [
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0.045... | 39,860 | 39860 | |
linear programming
May 24th 2008, 10:25 AM
deragon999
linear programming
OK I have attempted 2 Linear Programming questions and i would like to know if i have got all the equations correct for the first question, and some help on the second one would be much
appreciated.
Q1:
A bank is attempting to ... | 4 | [
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... | 39,861 | 39861 | |
Stability of medians in Median graphs
up vote 1 down vote favorite
A Median graph is graph with the property, that for each three vertices $x,y,z$ there is a unique vertex $m(x,y,z)$ lying on shortest paths from $x$ to $y$, from $y$ to $z$ and from $z$ to $x$.
Examples are trees, the Cayley graph of $\mathbb{Z}^n$ (wi... | 5 | [
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0.010437011... | 39,862 | 39862 | |
Is there a function f = g' but not Riemann Integrable
November 29th 2009, 08:39 AM #1
Newbie
Joined
Nov 2009
Posts
23
Is there a function f = g' but not Riemann Integrable
The second fundamental theorem of calculus states that:
If f is integrable in [a, b] and f = g' for some function g, then
$... | 5 | [
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Examples of "inner products" of parallel morphisms in a dagger category
up vote 3 down vote favorite
There is a very interesting abstract notion of the trace of an endomorphism $f : c \to c$ of an object $c$ in a braided monoidal category (although the symmetric case is easier): see, for example,
Ponto and Shulman's T... | 4 | [
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It’s My Ritz in a Box.It's My Ritz in a Box.
This is the conclusion of the Ritz variation discussion we’ve been doing. Tomorrow we’ll get back to less arcane and more entertaining physics, I promise! We’re capping things off today by
demonstrating the actual technique in detail for an example where we already know the ... | 5 | [
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-0.00915... | 39,865 | 39865 | |
Why isn't $\langle x,y,z|xyzx^{-1}y^{-1}z^{-1}\rangle$ a hyperbolic surface group?
up vote 9 down vote favorite
3
The group mentioned in the title, $\langle x,y,z|xyzx^{-1}y^{-1}z^{-1}=1\rangle$, is in between the torus fundamental group $\langle x,y|xyx^{-1}y^{-1}=1\rangle$ and the two-holed torus fundamental
group $... | 4 | [
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How do I calculate the discriminant of a galois closure and its other subfields?
up vote 8 down vote favorite
4
Given a number field K of dimension d over Q, and galois closure of dimension d! over Q (i.e galois group Sd), can we relate the discriminant of the galois closure to that of the discriminant of K?
Assume no... | 5 | [
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trig substitution problem
How about $\int\sqrt{9-4x^2}\, dx=3\int \sqrt{1-\left(\tfrac{2}{3}x\right)^2}\, dx=\ldots$ Substituting $z := \tfrac{2}{3}x$, thus $dz = \tfrac{2}{3}dx$ and $dx = \tfrac{3}{2}dz$. This gives you $=3\
int \sqrt{1-z^2}\cdot \tfrac{3}{2}\,dz=\tfrac{9}{2}\int \sqrt{1-z^2}\, dz$ and, maybe, you kow... | 5 | [
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0.033... | 39,868 | 39868 | |
6.832 chapter 2_ Nonlinear dynamics of the simple pendulum
C H A P T E R 2
The Simple Pendulum
2.1 INTRODUCTION
Our goals for this chapter are modest: we’d like to understand the dynamics of a pendulum.
Why a pendulum? In part... | 5 | [
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0.0026702880... | 39,869 | 39869 | |
Math Help
January 30th 2009, 05:45 AM #1
Member
Joined
Oct 2008
Posts
124
Diffy Q
A function y = g(x) is described by some geometric property of its graph. Write a differential equation of the form dy/dx = f(x, y) having the function g as its solution (or as one of its
solutions).
"The line tan... | 5 | [
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... | 39,870 | 39870 | |
mods with prime powers
April 18th 2010, 08:41 PM #1
Super Member
Joined
Oct 2007
From
Santiago
Posts
517
mods with prime powers
Hey guys, cant get my head around this fact .If p is a prime, then $a^{p-1}$ = 1 (mod p) provided a $ot\equiv$ 0 mod p. If someone could explain with an clear example of som... | 4 | [
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Math Forum Discussions
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Math Forum » Discussions » Policy and News » geometry.ann... | 4 | [
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-0.042236328125,
-0.0480... | 39,872 | 39872 | |
Similar Triangles and Area
Date: 11/12/98 at 04:32:11
From: Anna
Subject: Geometry
Hi,
I'm having difficulty with this question:
P is a point on the segment joining the respective midpoints, D and E
of the sides AB and AC of a triangle ABC. Prove that the area of BPC is
twice the area of ADE.
I've drawn a diagram... | 4 | [
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-0.04931640625,
0.0025482177734375... | 39,873 | 39873 | |
Fibered products of cyclic groups
up vote 2 down vote favorite
2
Background
Let $m,n$ be positive integers and consider the cyclic group $\mathbb{Z}_{mn}$.
We have a natural epimorphism $\mathbb{Z}_{mn} \to \mathbb{Z}_n$ coming from the exact sequence
$$ 0 \to \mathbb{Z}_m \to \mathbb{Z}_{mn} \to \mathbb{Z}_n \to 0... | 5 | [
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... | 39,874 | 39874 | |
Solve for X values
So, first would probably be grouping. You would take the x^3 and group it with the 3x^2. Factor that into x^2 (x-3) + 3 Then it would just be (x^2+3) (x-3)
so factor for this eqn will be x= 3, and 2 imaginary fators will be there with "i"(iota)
Last edited by mr fantastic; October 20th 2009 at 06:2... | 5 | [
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-0.020874023437... | 39,875 | 39875 | |
Wireless Sensor Network-Based Projectile Trajectory Estimation
Institute for Software Integrated Systems
Vanderbilt University
Nashville Tennessee 37235
TECHNICAL REPORT
TR #: ISIS-05... | 4 | [
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0.008544921875,
0.01696... | 39,876 | 39876 | |
Complex Numbers
January 16th 2008, 09:35 PM #1
Banned
Joined
Oct 2007
Posts
158
Complex Numbers
I need to find the rectangular form of i ^ (-3) + i ^ (-2)
i = imaginary number
The answer in my book says -1 + i but i do not know how they got it
$i^{-3} = \frac{1}{i^3} = \frac{1}{i \times i \t... | 4 | [
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-0.04248046875,
-0.01275634765625,
-0.006103515625,
-0.0179443359... | 39,877 | 39877 | |
crossproducts of linearly independent vectors
January 30th 2013, 08:32 PM #1
Member
Joined
Dec 2012
From
-
Posts
77
crossproducts of linearly independent vectors
hello, i am asked to proof that, for 3 linearly independent vectors, the crossproducts of each of the pairs of vectors are also linealry in... | 5 | [
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0.1298828125,
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0.08349609375,
-0.013... | 39,878 | 39878 | |
Fitting an Arc to a Point and Two Tangent Lines
Date: 11/14/2004 at 23:11:39
From: Phill
Subject: Arc from point and 2 tangents
I'm wondering how to fit an arc to a point and two circles. I have a
picture of what I am trying to work out but I will try to describe it.
There is a vertical line segment of length 0.3 m,... | 5 | [
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0.068359375,
-0.059814453125,
0.0... | 39,879 | 39879 | |
Another combinatorial proof
July 4th 2010, 08:28 AM
oldguynewstudent
Another combinatorial proof
Give combinatorial or bijective proofs of the following. Part of your job is to determine all values of n,k, and/or m for which the identities are valid.
c) $\left({0\atop m}\right)+\left({1\atop m}\right)+\left... | 4 | [
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0.12890625,
0.064453125,
0.0537... | 39,880 | 39880 | |
Trisected Hypotenuse of a Triangle
Date: 12/20/98 at 14:30:43
From: Will Nuse
Subject: Trisected hypotenuse of a triangle
Here's the problem:
In right triangle ABC, with C as the right angle, it is known that
AD = DE = EB (the three segments of the hypotenuse) and that D and E
are points on hypotenuse AB. It is als... | 4 | [
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0.0306396484375,
0.0634765625,
-0.06689453125,
-0.10498046875,
0.0150146484... | 39,881 | 39881 | |
Math Forum Discussions
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Topic: Differentiability
Replies: 8 Last Post: Mar 1, 201... | 5 | [
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Distance Traveled
January 18th 2011, 08:08 PM
PPSSAGW
Distance Traveled
Hi everyone. I'm working on a calculus problem about distance. I haven't learned it yet, but I have done some research to find a way to solve it.
A particle moves on the x-axis so that its velocity at any time t≥0 is given by $v(t)=12t^... | 4 | [
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Mean or Median?
Date: 11/02/2003 at 16:53:27
From: Jill
Subject: Why do we use mean instead of median
In working on finding textbook readability for a math project, we have
to find the mean number of words per sentence.
One question asks: Why does the forumla uses the mean number of words
per sentence insteand of th... | 4 | [
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[SciPy-user] Solving "difference" equations
Travis Oliphant oliphant at ee.byu.edu
Sun Aug 21 15:02:43 CDT 2005
Robert Kern wrote:
>Kumar Appaiah wrote:
>
>
>>Dear Scipy users,
>>I would like to know whether SciPy has a facility allowing one to
>>solve discrete-time difference equations. For example, equations lik... | 4 | [
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One more exponential equation
2^2x -2 x 2^x -8 = 0 Please help solve this equation. Thank you very much
2^2x -2 x 2^x -8 = 0 I'm sure that is 2^(2x) -2(2^x) -8 = 0 In another form, (2^x)^2 -2(2^x) -8 = 0 -----------(i) (i) is a quadratic erquation in 2^x. So if y = 2^x, then (i) becomes y^2 -2y -8 = 0
So, (y -4)(y+2) ... | 4 | [
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Build Your Own Logo with Mathematica (and a Few Friends)
Mathematica has powerful graphics capabilities that can be used to explore the space of graphical forms in a very flexible way. Wolfram Research itself has already published a blog post showing how
to manipulate various corporate logos, so it should be no surpris... | 4 | [
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Basic Trigonometry
April 17th 2009, 04:07 PM #1
Member
Joined
Oct 2008
Posts
157
Basic Trigonometry
The triangle ABC has sides AB [
a] Write down and simplify a quadratic equation satisfied by
b] Express sinBaC in the form
c] Express sinAcB in the form
I have no idea how to solve thes... | 4 | [
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Intersection of Two Spheres
January 2nd 2010, 03:12 PM #1
Intersection of Two Spheres
For quite sometime I have been intrigued by the curve created by the intersection of two spheres with the following properties/conditions:
Let both spheres have the same radius. Let's say a radius of 2.
Let one sphere b... | 5 | [
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Visual Symbols Slay the Distributive Property
Progress …
I made some progress yesterday helping a boy understand the distributive property, and it was mostly due to the use of visual symbols.
I’d like to share the process of my tutoring, for it shows how important it is to break an algebraic procedure into its const... | 4 | [
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The weight of a concrete cylinder - Math Central
Curtis,
You can use our volume calculator to find the volume of the cylinder but the weight is not as easy. The weight depends on the density of the concrete which varies considerably, depending on the
aggregate used. There are some densities at http://hypertextbook.com... | 4 | [
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Is every finite group a proper quotient of a finite primitive group?
up vote 11 down vote favorite
2
Let $G$ be a finite group. Is there necessarily a finite primitive permutation group $P$ and a normal subgroup $N>1$ of $P$ such that $P/N \cong G$?
If not, what restrictions are there on quotients of finite primitive... | 5 | [
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Graphing a function and solving value of x
January 18th 2007, 09:41 AM #1
Newbie
Joined
Jan 2007
Posts
10
Graphing a function and solving value of x
I really need help on these problems. I am lost. Don't have an idea of where to begin in solving and graphing these. Please see attachment. Thanks to anyone... | 4 | [
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The Falling Chimney
The Falling Chimney Web Page
By Gabriele Varieschi, Kaoru Kamiya (*) and Isabel Jully (*) - Dept. of Physics - LMU
... | 4 | [
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Proof by Induction
Using Mathematical Induction: Prove the sum of cubes of 3 consecutive pos. integers is divisble by 9.
The sum of the cubes of 1, 2, 3 is 1+8+27=36 which is divisible by 9. Now suppose that for some k: C(k)=k^3+(k+1)^3+(k+2)^3 is divisible by 9. Then: C(k+1)=C(k) - k^3 + (k+3)^3 = C(k) + 3 (k^2*3) + ... | 5 | [
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Use Definition to find Derivative
October 14th 2009, 02:33 PM #1
Use Definition to find Derivative
Find the derivative of $Secx$ using the definition below:
$\frac{d}{dx}(x) = \lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h}$
Note $y=Secx \rightarrow Cos^{-1}x$
$\frac{d}{dx}(Secx) = \lim_{h \righta... | 5 | [
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graphing problem
May 18th 2010, 11:52 PM
Anemori
graphing problem
i have this equation:
solve for x:
ln(x)+ln(x-3)=2
x=0, x=3
In addition:
graph f(x)=ln(x) and -f(x-3)+2 by using transformations. Explain the relationship between the solutions to the original equation and the points of int... | 4 | [
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Hashing
hashing 1
Observation: We can store a set very easily if
we can use its keys as array indices:
A: k 1 r e c o r d w ith k e y k 1
k2 r e c o r d w ith k e y k 2
e.g. SEARCH(A,k)
return A[k]
hashing ... | 4 | [
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Algebra.....units prove
February 28th 2006, 03:33 PM #1
Junior Member
Joined
Feb 2006
From
Canada
Posts
45
Suppose that R and S are rings with identity. Let (r, s) in R × S. Show that
(r, s) is unit in R × S <=> r is a unit in R and s is a unit in S.
Also, if (r, s) is a unit in R×S, show tha... | 5 | [
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