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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1073 | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RS... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1074 | # Symbols:Greek/Gamma
Previous ... Next
## Gamma
The $3$rd letter of the Greek alphabet.
Minuscule: $\gamma$
Majuscule: $\Gamma$
The $\LaTeX$ code for $\gamma$ is \gamma .
The $\LaTeX$ code for $\Gamma$ is \Gamma .
### Gamma Function
$\map \Gamma z$
The Gamma function $\Gamma: \C \to \C$ is defined, for the o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1075 | # DO
While DOLIST and DOTIMES are convenient and easy to use, they aren’t flexible enough to use for all loops. For instance, what if you want to step multiple variables in parallel?
(do (variable-definition*)
(end-test-form result-form*)
statement*)
— Practical Common Lisp
— Peter Seibel
.
(defun split-if (fn l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1076 | # A new game is being introduced at the Hard Rock Cafe A ball is spun around a wheel until it comes to
A new game is being introduced at the Hard Rock Cafe A ball is spun around a wheel until it comes to rest in one of many spots Whatever is listed in that spot will be the player’s winnings If the wheel has 13 spots l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1078 | # Q7.25 (b) A small town with a demand of $800 kW$ of electric power at $220V$ is situated $15km$ away from an electric plant generating power at $440V$. The resistance of the two wire line carrying power is $0.5\Omega$ per km.The town gets power from the line through a $4000-220V$ step-down transformer at a sub-stat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1079 | # Estimation of Heteroscedasticity in Regression Analysis
The Annals of Statistics
Vol. 15, No. 2 (Jun., 1987), pp. 610-625
Stable URL: http://www.jstor.org/stable/2241329
Page Count: 16
You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
## A... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1081 | ## The Annals of Probability
### Maxima of Partial Samples in Gaussian Sequences
Yashaswini Mittal
#### Abstract
Let $\{X_n, n \geqq 0\}$ be a Gaussian sequence with $EX_i \equiv 0; V(X_i) \equiv 1$ and $EX_iX_j = r_{ij}$. Define $M_n = \max_{0\leqq i \leqq n}X_i$ and $m_{n,k} = \max (X_i; i \in G_n)$ where $G_n = ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1082 | TheInfoList
In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883. Through consideration of this set, Cantor and others helpe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1083 | # The small cardinality selection axiom
## Idea
The small cardinality selection axiom (SCSA) is a weak form of the axiom of choice, which asserts in a certain precise way that choice fails “in at most a small way”. It was introduced by Michael Makkai for the study of anafunctors, and thus it also has consequences for... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1086 | ## anonymous 5 years ago Hey everyone, need help finding the arc length of the curve y^2=x^3 from (0,0) to (1/4,1/8).
1. anonymous
I know the formula and I think y'=(3x^2)/(2y)
2. anonymous
let me try this, see if it works. $y=x^\frac{3}{2}$ yes?
3. anonymous
ok right, do we only take the +x^3/2?
4. anonymous
$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1087 | The graph of a non-invertible function $f$ is shown below.
Also shown is a horizontal line which you can click and drag to different heights. If that line intersects the graph of the function $f\text{,}$ the point(s) of intersection will be shown.
Next, the graph of an invertible function $g$ is shown.
1. According to ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1077 | +0
# Number Theory
0
176
2
Let n be a positive integer with exactly 3 positive prime divisors. If n^2 has 27 divisors, how many does n have?
Sep 24, 2021
#1
+1
n==30
30==2 * 3 * 5==3 prime factors
30==(1, 2, 3, 5, 6, 10, 15, 30)>>Total = 8 divisors
30^2= (1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1084 | # Dummy variables in integration: Is $\int x^2\,dx=\int y^2\,dy$?
My understanding was that when writing out indefinite integrals, the variable we use (customarily $$x$$) is merely a dummy variable that can be replaced by any other letter.
So for example, we may write $$\int x^2 \,dx=\int y^2 \,dy=\int z^2 \,dz=\int ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1085 | # Solve differential equation xy'= 6y+12x^4 y^(2/3)
Yasmin 2020-11-09 Answered
Solve differential equation$x{y}^{\prime }=6y+12{x}^{4}{y}^{\left(}2/3\right)$
You can still ask an expert for help
Expert Community at Your Service
• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Persona... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1080 | # How do you find the amplitude and period of Arc Sec?
Jul 5, 2015
arcsec does not have a (meaningful) amplitude or period.
You seem to have confused arcsec with the direct trigonometric functions
#### Explanation:
arcsec(x) is an angle; typically its value is restricted to angles in the range $\left[0 , 2 \pi\righ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10672 | # $\int_0^1 x^n \log^m (1-x) \, {\rm d}x$
Let $n \in \mathbb{N}$. We know that:
$$\int_0^1 x^n \log(1-x) \, {\rm d}x = - \frac{\mathcal{H}_{n+1}}{n+1}$$
Now, let $m , n \in \mathbb{N}$. What can we say about the integral
$$\int_0^1 x^n \log^m (1-x) \, {\rm d}x$$
For starters we know that $\displaystyle \log^m (1-x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10673 | # Finding the inverse of a matrix using elementary matricies
Can somebody help me understand what exactly is being asked here? I understand how to construct elementary matrices from these row operations, but I'm unsure what the end goal is. Am I to assume that $Y$ is built from these row operations?
Let $Y$ be the $4... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10675 | # Child Labor #1
Find natural number $$n$$ such that $$1! \times 2! \times 3! \times 4! \times . . . \times n!$$ has exactly $$n$$ trailing zeros.
###### Note: This is original problem.
×
Problem Loading...
Note Loading...
Set Loading... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10676 | What are the lengths that can be constructed with straightedge but without compass?
Most field theory textbooks will describe the field of constructible numbers, i.e. complex numbers corresponding to points in the Euclidean plane that can be constructed via straightedge and compass. This field is the smallest field of... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10677 | # Intertemporal equilibrium
At the equilibrium, factors are paid their marginal productivity, thus:
$$r_{t} = f^{\prime}(k_{t})$$
and
$$w_{t} = f(k_{t}) - f^{\prime}(k_{t})k_{t}.$$
## Definition of intertemporal equilibrium
An intertemporal equilibrium with perfect foresight is a sequence $(k_{t}, c_{t}) \in \mat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10678 | Question
# Begin with the graph of y = ln x and use transformations to sketch the graph of each of the given functions. y= ln (2-x)
Transformations of functions
Begin with the graph of y = ln x and use transformations to sketch the graph of each of the given functions. $$\displaystyle{y}={\ln{{\left({2}-{x}\right)}}}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10679 | # A word with maximal number of subwords
Let $W$ be a cyclic word of length $n$ in a 2-letter alphabet $\{0,1\}$. It is clear that it has at most $n^2$ different subwords (because the number of subwords of length $i$ is at most $n$ for each $i$) and that the actual number of subwords is less than $n^2$ (because the nu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10682 | # zbMATH — the first resource for mathematics
Partially mode-dependent design of $$H_{\infty }$$ filter for stochastic Markovian jump systems with mode-dependent time delays. (English) Zbl 1219.93134
Summary: This paper is concerned with the $$H_{\infty }$$ filtering problem for stochastic delay systems with Markovian... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10684 | # Search by Topic
#### Resources tagged with Mathematical reasoning & proof similar to Halving the Triangle:
Filter by: Content type:
Stage:
Challenge level:
### There are 181 results
Broad Topics > Using, Applying and Reasoning about Mathematics > Mathematical reasoning & proof
### Golden Eggs
##### Stage: 5 Cha... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10685 | # Proving $\sum\limits_{p \leq x} \frac{1}{\sqrt{p}} \geq \frac{1}{2}\log{x} -\log{\log{x}}$
How to prove this: $$\sum\limits_{p \leq x} \frac{1}{\sqrt{p}} \geq \frac{1}{2}\log{x} -\log{\log{x}}$$
From Apostol's number theory text i know that $$\sum\limits_{p \leq x} \frac{1}{p} = \log{\log{x}} + A + \mathcal{O}\Bigl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10686 | • Dmitri Kaledin, Witt vectors, commutative and noncommutative is a pretty preprint on (you'd never guess) Witt vectors. Its introduction is a really nice overview of the history of the subject, and explains in a nice way the interesting role that Witt vectors play in mathematics. The goal of the preprint is to describ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10687 | # How to prove that $a + 2 \sqrt{a^{2} + b^{2}} + 3 \sqrt{1+a^{2}} \geq 2 + \sqrt{1+b^{2}}$ for all $a,b >0$?
The inequality
$$a + 2 \sqrt{a^{2} + b^{2}} + 3 \sqrt{1+a^{2}} \geq 2 + \sqrt{1+b^{2}}$$
is related to some computation regarding the Shapley value of a stochastic cooperative game. Though I'm not sure it ho... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10680 | # 1 5.e – The Definite Integral as a Limit of a Riemann Sum (Numerical Techniques for Evaluating Definite Integrals)
## Presentation on theme: "1 5.e – The Definite Integral as a Limit of a Riemann Sum (Numerical Techniques for Evaluating Definite Integrals)"— Presentation transcript:
1 5.e – The Definite Integral as... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10681 | ## anonymous one year ago Can you please show me how to solve this?I would really appreciete it! (Limits and series) http://tinypic.com/r/dy3x4m/8
1. Jhannybean
$\lim_{x\rightarrow -1} \frac{x^2+3x+2}{2x^2-8} \\ \lim_{x\rightarrow -2} \frac{x^2+3x+2}{2x^2-8}$ $\lim_{x\rightarrow 1} \frac{\sqrt{1+3x}-2}{x-1}$ $\lim_{(... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10683 | # Thread: help me to correct my exercise on nested quantifier
1. ## help me to correct my exercise on nested quantifier
Let F(x,y) be the statement "x can fool y", where the domain consists of all people in the world. Use quantifiers to express each of these statements.
a. Nancy can fool exactly two people
$\exists ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10674 | # Explain Newton's second law.
The rate of change of momentum of a body is directly proportional to the unbalanced force applied in the direction of the force.
If a body of mass m is moving with initial velocity u along a straight line and is uniformly accelerated to a velocity v by applying a force F for time t then... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24336 | Principle of Non-Contradiction/Proof Rule
Theorem
The Principle of Non-Contradiction is a valid deduction sequent in propositional logic.
As a proof rule it is expressed in the form:
If we can conclude both $\phi$ and $\neg \phi$, we may infer a contradiction.
It can be written:
$\displaystyle {\phi \quad \neg \p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24337 | ## Intermediate Algebra (6th Edition)
The radical $\sqrt{-64}$ is not a real number because the radicand is a negative number and the index is even. Also, there is no real number such that when it is multiplied to itself will give a negative product. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24338 | # zbMATH — the first resource for mathematics
Extreme value theory for multivariate stationary sequences. (English) Zbl 0679.62039
The author considers multivariate extremal type theorems and some related problems in a setting where the assumptions of independence and linear normalization in the classical setting are ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24339 | ## Chemistry 9th Edition
a. $137.992\text{ grams}$ b. $31.\text{ grams Al}$ c. $7.0*10^{23}\text{ molecules Al}$ d. $4.8*10^2\text{ grams Bauxite}$
a. Molar Mass = $2*26.981538+5*15.9994+4*1.00794=137.992\text{ grams}$ b. $0.58\text{ moles Bauxite}*\frac{137.992\text{ grams Bauxite}}{1\text{ moles Bauxite}}*\frac{53.9... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24341 | # Maximum likelihood is equivalent to least squares in the presence of Gaussian noise
Note. Maximum likelihood estimation is equivalent to least squares estimation in the presence of Gaussian noise.
Let $y_i=f(x_i,\boldsymbol{\theta}) + r_i$ and let $r_i$ follow a normal gaussian distribution $r_i \asymp G(0,\sigma)$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24342 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 23 May 2019, 08:05
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24343 | # Calculate the characteristic function $\varphi_W$ of W
$p(x)=xe^{-x}$ for $x\geq 0$ or $0$ otherwise.
I tried to substitute $e^{-x}$ but then i found there is still a $x$ in front.
$$\phi_W(t)=\langle e^{\mathrm{i}tx}\rangle=\int_0^\infty dx\ x e^{-x}e^{\mathrm{i}tx}=-\mathrm{i}\frac{d}{dt}\int_0^\infty dx\ e^{-(1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24344 | # Permutations
### Permutations
Find the number of binary strings of length 40, for which, in any sub-string of length 6, there are maximum 3 "1".
All possible sub-strings are 35 (40-5+1).
Let's check what happens in each string of length 6:
In order to find all possible arrangements so as to have at most 3 1s, we ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24345 | $$p$$ is a odd prime, then
1. there are infinite primes $$q$$ such that $$q$$ is a quadratic residue modulo $$p$$;
2. there are infinite primes $$q$$ such that $$q$$ is a quadratic nonresidue modulo $$p$$.
$a_0=q, a_1=q+p,a_2=q+pa_1,a_3=q+pa_1a_2,\dotsc, a_n=q+pa_1a_2\dotsb a_{n-1},\dotsc$
$\bigg(\dfrac{kq_1q_2q_3\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24346 | Advances in Differential Equations
On front propagation problems with nonlocal terms
Pierre Cardaliaguet
Abstract
We investigate the evolution of compact hypersurfaces of $\mathbb R^N$ depending, not only on terms of curvature of the surface, but also on non local terms such as the measure of the set enclosed by th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24347 | Question
# Can you explain me how to do distributive property on multiplication over addtion and multiplication over subtraction
Solution
## Distributive Property of Multiplication over Addition The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24348 | # Revision history [back]
Thanks to Juanjo's answer to my question here I've managed to get a script which gives us an analytical solution for our hicksian demand equations. This is:
x1, x2, l, p1, p2, a, b, R= var('x1, x2, l, p1, p2, a, b, R')
U = x1^a*x2^b
m = p1*x1+p2*x2;
L = m+ l * (R-U);
dLdx = L.diff(x1);
dLd... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24349 | # User:JaviPrieto/Integrals
${\displaystyle \int _{a}^{b}\!f(x)\,dx\,}$
${\displaystyle \int _{a}^{b}\!f(x)\,dx=F(b)-F(a)\,}$
Isaac Newton used a small vertical bar above a variable to indicate integration, or placed the variable inside a box. The vertical bar was easily confused with ${\displaystyle {\dot {x}}}$ or ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24350 | # Permanent Income Hypothesis - Changes in r
I want to analyze the changes in the interest rate $r$ when dealing with the permanent income hypothesis. First of all,
$r$ is the interest rate $0<\beta<1$ is the discount factor, $Y_t$ is the labor income for period $t$, $A_t$ is the net asset wealth, $C_t$ is the consum... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24351 | My Math Forum Locus
Algebra Pre-Algebra and Basic Algebra Math Forum
November 8th, 2010, 07:00 PM #1 Senior Member Joined: Apr 2009 Posts: 106 Thanks: 0 Locus Identify the locus of all points P(x, y) in the plane satisfying each of the following expressions: a. x^2 + y^2 < R^2 b. x^2 + y^2 - 2x + 2y + 4 = 0
Nove... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24340 | MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
I am not sure what your criteria would be for a proof to be given a geometric interpretation, but the reason why weights "disappear" when we take the inverse limit on... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14434 | My Math Forum (http://mymathforum.com/math-forums.php)
- Physics (http://mymathforum.com/physics/)
- - high school homework help?? (http://mymathforum.com/physics/47564-high-school-homework-help.html)
xcortx November 3rd, 2014 02:57 PM
high school homework help??
A stunt driver for a movie needs to make a 254... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14435 | # Thabit number
In number theory, a Thabit number, Thâbit ibn Kurrah number, or 321 number is an integer of the form $3 \cdot 2^n - 1$ for a non-negative integer n.
The first few Thabit numbers are:
2, 5, 11, 23, 47, 95, 191, 383, 767, 1535, 3071, 6143, 12287, 24575, 49151, 98303, 196607, 393215, 786431, 1572863, ..... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14436 | Lemma 37.62.11. Let $f : X \to Y$ be a morphism of schemes. The following are equivalent
1. $f$ is weakly étale, and
2. for $x \in X$ the local ring map $\mathcal{O}_{Y, f(x)} \to \mathcal{O}_{X, x}$ induces an isomorphism on strict henselizations.
Proof. Let $x \in X$ be a point with image $y = f(x)$ in $Y$. Choose... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14437 | # JAK/STAT guarantees robust neural stem cell differentiation by shutting off biological noise
## Abstract
Organismal development is precisely regulated by a sequence of gene functions even in the presence of biological noise. However, it is difficult to evaluate the effect of noise in vivo, and the mechanisms by whi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14438 | Proving No Solution in Extension Field
1. May 18, 2013
Szichedelic
1. The problem statement, all variables and given/known data
Let $\beta=\omega\sqrt[3]{2}$, where $\omega=e^{2\pi i/3}$, and let $K=\mathbb{Q}(\beta)$. Prove that the equation $x^{2}_{1}+\cdots+x^{2}_{k}=-1$ has no solution with $x_{i}$ in $K$.
2. R... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14439 | # Dimensions of Angular Speed
## Dimensional Formula of Angular Speed
The dimensional formula of angular speed is given by,
M0 L0 T-1
Where,
• M = Mass
• L = Length
• T = Time
### Derivation
Angular speed (ω) = 2π × [Time]-1 . . . . . (1)
⇒ The dimensional formula of time = [M0 L0 T1] . . . . (2)
And, π is a d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14440 | ## The Annals of Mathematical Statistics
### An Application of a Generalized Gamma Distribution
Gerald S. Rogers
#### Abstract
Let $\{x_{i1}, \cdots, x_{in_i}\}, i = 1, 2, \cdots, k, k \geqq 2, n_i \geqq 2$, be random samples from stochastically independent Gaussian populations with unknown means $\mu_i$ and unknow... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14441 | Homework Help: Electric circuit
1. Aug 2, 2006
teng125
http://www.savefile.com/files/7288537 [Broken]
find the current I(B) by calculation
Use the current function and KVL
the function is given as I(B)=0.01 (V(B) - 0.65V)^2
Can somebody pls show me the KVL ??
i tried to write the KVL as V(i) - I(B)R(i) - V(B) =0
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14442 | # Center of a group with finite index
1. Nov 30, 2014
### mahler1
1. The problem statement, all variables and given/known data
Let $G$ be a group such that its center $Z(G)$ has finite index. Prove that every conjugacy class has finite elements.
2. Relevant equations
3. The attempt at a solution
I know that $[G:... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14445 | An incompressible fluid (i.e., density is constant) enters a U-shaped conduit flowing at a steady 1 answer below »
1. An incompressible fluid (i.e., density is constant) enters a U-shaped conduit flowing at a steady flow rate of Q gpm (Figure 3.41). The conduit has a circular cross section all along its length and the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14446 | # Step By Step Calculus » 15.1 - Indefinite Integrals
Synopsis
Now we want to reverse the differentiation process: Given a derivative ff we want to find another function FF such that F'(x)=f(x)F'(x)=f(x). This FF is called an antiderivative for f.f. Two antiderivatives for ff can differ by at most a constant. Therefor... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14447 | # Math question
• July 30th 2012, 05:38 PM
hacker804
Math question
Hi.Can any one help me with these questions.They are really simple but i cannot seem to get them.Thanks
Q1.Show That:
http://i3.lulzimg.com/5b157758d4.gif
Q2.Prove that:
http://i3.lulzimg.com/1192859b6c.gif
Q3.Prove that:
http://i3.lulzimg.com/aca910... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14432 | # multivalued holomorphic function on Riemann surfaces
Let $$M$$ be an open Riemann surface and $$f$$ a multivalued holomorphic function from $$M$$ to $$\mathbb{H}$$, where $$\mathbb{H}$$ is the upper half plane. Suppose that the monodromy of $$f$$ lies in the two-dimensional Lie subgroup $$A$$ of $$PSL(2,\mathbb{R})$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14433 | # Fejér summation method
A summation method of arithmetical averages (cf. Arithmetical averages, summation method of), applied to the summation of Fourier series. It was first applied by L. Fejér [1].
The Fourier series
$$\frac12+\sum_{n=1}^\infty(a_n\cos nx+b_n\sin nx)\label{1}\tag{1}$$
of a function $f\in L(-\pi,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14443 | # Normalization condition
1. Feb 26, 2010
### nklohit
In Peskin's textbook, he uses the spin sum as $$\sum u\bar{u} = \gamma^{\mu}p_{\mu} +m$$ ;
on the other hand, in Kaku's book and in Zee's book, they use $$\sum u\bar{u} = \dfrac{\gamma^{\mu} p_{\mu} + m}{2m}$$ . But why aren't there any diffferent in the differen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14444 | # Weighted Estimates for Maximal Commutators of Multilinear Singular IntegralsAcademic research paper on "Mathematics"
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## Academic research paper on topic "Weighted Estimates for Maximal Commutators of Multilinear Singular Integrals"
Hindawi Publishing Corpo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19697 | # Toronto Math Forum
## APM346-2016F => APM346--Tests => TT1 => Topic started by: Victor Ivrii on October 19, 2016, 10:26:33 PM
Title: TT1-P2
Post by: Victor Ivrii on October 19, 2016, 10:26:33 PM
(a) Find solution $u(x,t)$ to
\begin{align}
&u_{tt}-u_{xx}= (x^2-1)e^{-\frac{x^2}{2}},\label{eq-1}\\
\end{align}
(b) (1 p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19699 | # Newton's Method, Analytical Formula
Currently I am learning about Netwon's Method. Given the function f: $\frac{1}{5} x^5 - \frac{2}{3}x^3 + x$ and $x^{(0)} = \sqrt{\frac{ 25+2\sqrt{55} }{27} }$, I want to analytically determine the sequence $x^{(n+1)} = \Psi(x^{(n)})$ with $\Psi(x) := x - \frac{f(x)}{f'(x)}$. Can s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19700 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 16 Aug 2018, 14:43
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19701 | Question
# A bus decreases its speed from $80km{h}^{-1}$ to $60km{h}^{-1}$ in $5s$, find the acceleration of the bus.
Open in App
Solution
## Step 1: Given dataInitial velocity, $u=80km{h}^{-1}=22.2m{s}^{-1}$Final velocity, $v=60km{h}^{-1}=16.7m{s}^{-1}$Time, $t=5s$Step 2: Formula used$v=u+at$Where “a” is the accele... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19703 | What is the integral of e^(0.5x)?
$2 {e}^{0.5 x} + C$
Explanation:
$\setminus \int {e}^{0.5 x} \setminus \mathrm{dx}$
$= \setminus \int {e}^{0.5 x} \frac{1}{0.5} d \left(0.5 x\right)$
$= \frac{1}{0.5} \setminus \int {e}^{0.5 x} \setminus d \left(0.5 x\right)$
$= 2 {e}^{0.5 x} + C$
Jul 18, 2018
$2 {e}^{\frac{1}{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19704 | 1. Torbjorn
It would be nice if you changed all the $$..$$ to $..$, the former is not recommended to use in LaTeX.
• tom
Thanks for the heads up. I changed to code accordingly.
2. The code above re-numbers the lemma from 1.1. How can I set the counter so that the lemma’s number continues the theorem’s number? (theo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19705 | ×
Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 4.2 - Problem 37e
Get Full Access to Fundamentals Of Differential Equations - 8 Edition - Chapter 4.2 - Problem 37e
×
In 37–41, find three linearly independent solutions (see
ISBN: 9780321747730 43
Solution for problem 37E Chapter 4.2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19706 | How do you find the equation of the circle given center at the (10, 5) and a radius of 11?
Mar 20, 2018
${\left(x - 10\right)}^{2} + {\left(y - 5\right)}^{2} = 121$
Explanation:
$\text{the standard form of the equation of a circle is}$
$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \tex... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19707 | View Single Post
P: 9 Hi, Thank you for your reply. I am only interested in the case with B=0. The expression for the magnetization is $M=[1-\sinh^{-4}(2/k_B T)]^{1/8}$. The susceptibility is obtained from $\chi = \frac{- ^2}{k_B T}$. But I don't know the analytical expression for $\chi$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19708 | Question
# The boat goes $24$ km upstream and $28$ km downstream in $6$ hours. It goes $30$ km upstream and $21$ km downstream in $6\dfrac{1}{2}$ hours. Find the speed of the boat in still water and also speed of the stream.
Verified
156k+ views
Hint: Assume speed of boat in still water $=u$ km/h and speed of stream ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19709 | # Tag Info
8
This answer is for your "somewhat related question": In the following recent paper, Klee-Minty cubes were used explicitly to show that there exists a pivoting rule for the simplex method (not one of the standard ones, like Dantzig's pivoting rule analysed by Disser and Skutella) for which it is PSPACE-co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19710 | #### 9th Standard Maths English Medium Free Online Test 1 Mark Questions 2020 - 2021 Part - Nine
9th Standard
Reg.No. :
•
•
•
•
•
•
Maths
Time : 00:15:00 Hrs
Total Marks : 15
Part A
15 x 1 = 15
1. If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19711 | # zbMATH — the first resource for mathematics
$$C^ k$$-resolution of semialgebraic mappings, addendum to volume growth and entropy. (English) Zbl 0641.54037
In this addendum the inequality (*) is proved with $$\ell /k$$ instead of $$2\ell /k$$ and examples are given to show that this improved inequality is sharp. From... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19696 | # The derivation of the quantum information no-hiding theorem
+ 1 like - 0 dislike
428 views
I am reading Samuel L. Braunstein, Arun K. Pati, Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox. I am puzzling over the derivation in Section Perfect hidin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19698 | # Prove $\lim\limits_{n\to\infty}\int_0^1(\cos \frac1x)^n\mathrm dx=0$
Prove $$\lim_{n\to\infty}\int_0^1 \left(\cos{\frac{1}{x}} \right)^n\mathrm dx=0$$
I tried, but failed. Any help will be appreciated.
At most points $(\cos 1/x)^n\to 0$, but how can I prove that the integral tends to zero clearly and convincingly?... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19702 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 19 Feb 2019, 05:00
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10288 | New York Journal of Mathematics NYJM Monographs, Volume 2, 2007
NYJM Monographs
Michael T. Lacey
Issues related to Rubio de Francia's Littlewood-Paley inequality
Published: January 18, 2007 Keywords: Littlewood-Paley inequality, multipliers, square function, multipliers, BMO Subject: Primary: 42B25. Secondary: 42B... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10289 | # Right-continuity of filtrations
To this day I still ignore the reason why ,to define ,for instance, a filtration that is continuous to the right (based on an existing one),We write:
$D_{t}=D_{t+}^{0}=\bigcap_{\epsilon>0} D_{t+\epsilon}^{0}$ (isn't $\bigcap_{\epsilon \geq \alpha} D_{t+\epsilon}^{0}= D_{\alpha}^{0}?$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10290 | # NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY
@article{Alarcn2018NEWCA,
title={NEW COMPLEX ANALYTIC METHODS IN THE THEORY OF MINIMAL SURFACES: A SURVEY},
author={A. Alarc{\'o}n and F. Forstneri{\vc}},
journal={Journal of the Australian Mathematical Society},
year={2018},
volume={106},
page... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10291 | # 2.17. Detailed Colorspace Descriptions¶
## 2.17.1. Colorspace SMPTE 170M (V4L2_COLORSPACE_SMPTE170M)¶
The SMPTE 170M standard defines the colorspace used by NTSC and PAL and by SDTV in general. The default transfer function is V4L2_XFER_FUNC_709. The default Y’CbCr encoding is V4L2_YCBCR_ENC_601. The default Y’CbCr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10292 | Problem 62E
62. If $h(x)=\sqrt{4+3 f(x)}$, where $f(1)=7$ and $f^{\prime}(1)=4$, find $h^{\prime}(1)$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10293 | ### Park Jun-Yong (朴俊勇)
School of Mathematics
University of Minnesota
127 Vincent Hall
206 Church St. SE
Minneapolis, MN 55455
Office: 454 Vincent Hall
Email: junepark at math dot umn dot edu
I'm a doctoral student in pure mathematics at the University of Minnesota advised by Craig Westerland.
My interest lies in ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10294 | # American Institute of Mathematical Sciences
2015, 5(2): 211-231. doi: 10.3934/naco.2015.5.211
## Primal-dual interior-point algorithms for convex quadratic circular cone optimization
1 Department of Mathematics, Shanghai University, Shanghai 200444, China, China 2 College of Fundamental Studies, Shanghai Universi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10296 | # Is every quasicoherent sheaf $\mathscr{F}$ on $\operatorname{Proj}S$ of the form $\widetilde{M}$?
Let $S$ be a graded ring, let $X=\operatorname{Proj}S$ be a sheaf, and $\mathscr{F}$ be a quasicoherent sheaf on $\mathscr{O}_X$. We know that for any graded $S$-module $M$, $\widetilde{M}$ is a quasicoherent $\mathscr{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10297 | # Imports/Exports in the equation of exchange
From the equation of exchange: $$MV=PY$$, where $$M$$ is the money aggregate, $$Y$$ is the real output, $$P$$ is the price level and $$V$$ is the velocity of money, we derive $$\% \Delta M + \% \Delta V = inflation + growth\ rate$$. How will these equations be affected by ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10298 | # Bullet trajectory: Aiming a gun
Tags:
1. Jun 28, 2017
### donaldparida
1. The problem statement, all variables and given/known data:
A person aims a gun at a bird from a point at a horizontal distance of 100m. If the gun can impart a speed of 500m/s to the bullet , then above what height of the bird he should aim ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10299 | # Why does this Laurent Series Vanish?
Let $\Phi_{l}(z;q)$ denote the Lerch Transcendent and $Li_{l}(z)$ denote the Polylogarithm function. For $l \in \mathbb{Z}_{\geq 0}$, we have the following Laurent expansion \begin{align} \Phi_{-l}(z;0) + (-1)^{l} Li_{-l}(1/z) = \sum_{k \geq 0} k^{l} z^{k} + \sum_{k \leq -1} k^{l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10300 | # Some sharp Hodge Laplacian and Steklov eigenvalue estimates for differential forms
Kwok Kun Kwong
8 引文 斯高帕斯（Scopus）
## 摘要
We give some sharp lower bounds of the first eigenvalue for the Hodge Laplacian acting on differential forms on the boundary of a Riemannian manifold. We also give some sharp estimates for the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10302 | The figure below shows the drive train of a bicycle that has wheels67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclistpedals at a steady angular rate of 79.0 rev/min. The chain engages with a frontsprocket 15.2 cm in diameter and a rear sprocket 6.50 cm in diameter. (a) Calculate the speedof a link of the ch... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10303 | # Finding Binomial expansion of a radical
I am having trouble finding the correct binomial expansion for $\dfrac{1}{\sqrt{1-4x}}$:
Simplifying the radical I get: $(1-4x)^{-\frac{1}{2}}$
Now I want to find ${n\choose k} = {\frac{-1}{2}\choose k}$
\begin{align} {\frac{-1}{2}\choose k} &= \dfrac{\frac{-1}{2}(\frac{-1}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10295 | # Families of algebraic spaces
Let U be a scheme. Let us define a family of d dimensions proper algebraic spaces over U to be a morphism X —> U from an algebraic space X to U which is flat, proper, locally of finite presentation, such that all geometric fibres are equidimensional of dimension d. Let Fam_d denote that ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10301 | ## An excursion approach to maxima of the Brownian bridge.(English)Zbl 1306.60115
Summary: Distributions of functionals of the Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18514 | # Definition:Algorithm/Analysis
## Definition
There are two primary methods for analyzing algorithms formally:
### Correctness
The primary method of validity for algorithms is using a Proof of Correctness.
This is correctness through verification of the algorithm accomplishing its purpose formally, and terminating... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18515 | Exercise from SICP:
Exercise 1.4.
Observe that our model of evaluation allows for combinations whose operators are compound expressions. Use this observation to describe the behavior of the following procedure:
(define (a-plus-abs-b a b)
((if (> b 0) + -) a b))
# Solution
There are two possible branches, if b is p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18516 | # Assembly parts
Nine machines produce 1,800 parts on nine machines. How many hours will it produce 2 100 parts on seven such machines?
Correct result:
t = 12 h
#### Solution:
$s=1800 / (9 \cdot \ 8)=25 \ \\ t=2100/(7 \cdot \ s)=2100/(7 \cdot \ 25)=12 \ \text{h}$
Our examples were largely sent or created by pupi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18517 | MathSciNet bibliographic data MR1631107 11F11 (33C05) Chan, Heng Huat On Ramanujan's cubic transformation formula for ${}\sb 2F\sb 1(\frac 13,\frac 23;1;z)$${}\sb 2F\sb 1(\frac 13,\frac 23;1;z)$. Math. Proc. Cambridge Philos. Soc. 124 (1998), no. 2, 193–204. Article
For users without a MathSciNet license , Relay Stati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18518 | An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure.
more_vert
An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB with downward vertical is $\theta$, then :
(1) $\t... |
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