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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3068 | # Week 8: Turing Machines¶
In [1]:
from tock import *
from IPython.display import IFrame, HTML
## Tuesday¶
We have been climbing up the Chomsky hierarchy of language classes (cf. Figure 4.10):
Unit Language class Automaton Grammar
III Turing-recognizable languages Turing machines Unrestricted grammars
Context-sens... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3069 | # Thread: Covering integers with arithmetic sequences
1. ## Covering integers with arithmetic sequences
Are there 11 infinite arithmetric sequences (consist of positive integers) with differences 10, 11, ... ,20 that cover (starting somewhere) all positive integers?
Thank you very much in advanve!
2. The question i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3070 | # What is unitary space
In http://www.encyclopediaofmath.org/index.php/Unitary_space, unitary space seems to be Hilbert space. But in http://www.answers.com/topic/unitary-space, "finite dimensional" is required. My question is, which definition of unitary space is commonly used?
-
Answers.com is wrong. Unitary space... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_3071 | # Math Challenge - February 2020
• Challenge
• Featured
@fresh_42 I think I have the solution using the hint. That hint is quite a good idea, it's probably useful to remember in general.
First, we use Riesz representation theorem to define a mapping $T: \mathcal{H}^* \rightarrow \mathcal{H}$, which defines the mapping... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15440 | 1. ## Proof question about homomorphism 1?
(a) Prove that for any isomorphism φ: G-->H, |φ(x)|=|x| for all x∈G. Is the result still true if φ is only assumed to be a homomorphism?
(b) Using (a) or otherwise show that any two isomorphic groups have the same number of elements of order n, for every positive integer n.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15441 | Browse by: Author name - Classification - Keywords - Nature
XV: 40, 590-603, LNM 850 (1981)
STROOCK, Daniel W.; YOR, Marc
Some remarkable martingales (Martingale theory)
This is a sequel to a well-known paper by the authors (Ann. ENS, 13, 1980) on the subject of pure martingales. A continuous martingale $(M_t)$ with $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15442 | # Hausdorff Distance In R
Unfortunately, the simplicity of its definition renders the Hausdorff distance vulnerable to outliers and potentially an inaccurate estimate of one's intuitive notion of distance. Hausdorff distance is to get the maximum distance between two shapes. Fully automated 3D aortic segmentation of 4D... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15443 | # DMD:Background:The DMD Model Equations
Introduction Background Basic Layout Examples Problems Run Simulation Assessment Credits Etomica Modules
The relationship between time and position gives:
${\displaystyle (1)r_{ij}=r_{i}-r_{j}=(r_{i}^{0}+u_{i}(t-t_{0}))-(r_{j}^{0}+u_{j}(t-t_{0}))}$
${\displaystyle =(r_{ij}^{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15444 | # Equation $H(q,p)=E$ is the equation of motion or energy-conservation law?
I do not completely understand, why do we consider Hamilton–Jacobi equation $H(q,p)=E$ as equation of motion, whereas it is looks like energy-conservation law?
-
That is not the hamilton-jacobi equation. What you have above is an equality be... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15445 | This is [Theorem 4.4, Hall-coherent]
Lemma 97.22.2. Let $S$ be a locally Noetherian scheme. Let $\mathcal{X}$ be a category fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$. Assume
1. $\Delta : \mathcal{X} \to \mathcal{X} \times \mathcal{X}$ is representable by algebraic spaces,
2. $\mathcal{X}$ has (RS*),
3. $\m... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15446 | # Relaxation
The (unscaled, see Non-identity DR Scaling) SCS update equations are:
\begin{split}\begin{align} \tilde u^{k+1} &= (I + \mathcal{Q})^{-1} w^k \\ u^{k+1} &= (I + N_{\mathcal{C}_+})^{-1} (2 \tilde u^{k+1} - w^k) \\ w^{k+1} &= w^k + \alpha (u^{k+1} - \tilde u^{k+1}) \\ \end{align}\end{split}
where $$\alph... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15447 | # $x_1 \cdot \dots \cdot x_n=1 \implies x_1 + \dots + x_n \ge n$
Suppose $x_1, \dots, x_n$ are positive real numbers such that $x_1 \cdot \ldots \cdot x_n = 1$. Prove $x_1 + \dots + x_n \ge n$.
I don't want to use the AM-GM inequality to prove this (from which this statement would follow).
I suppose induction is the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15448 | # Questions Asked onOctober 18, 2017
1. ## River hieghts
What is the fraction of 6 gallons?
2. ## Physics
A bal is batted straight up and returns to the level of the batter after 6.5s. Determine how high the ball went. A=-9.8m/s^2
3. ## Physics
A ball is battled straight up and returns to the level of the batter ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15449 | Volume 18, Issue 1
Solving Trust Region Problem in Large Scale Optimization
J. Comp. Math., 18 (2000), pp. 1-12
Preview Full PDF BiBTex 298 636
• Abstract
This paper presents a new method for solving the basic problem in the "model-trust region" approach to large scale minimization: Compute a vector x such that $1/2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15450 | # Special Linear Lie Algebra
Hi,
Show that the Special linear Lie algebra is simple.
I tried it with induction but without result.
I is an ideal of L if $$x\in L, y\in I \Rightarrow [x,y]\in I$$
The matrices whose trace is 0 form the special linear lie algebra $$sl_n(\mathbb{C})$$. The special linear lie algebra is t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15451 | # In how many ways can 6 graduates line up to receive their diplomas, if there are 4 girls and 2 boys and the girls will receive their diplomas first?
Jul 19, 2016
48
#### Explanation:
this corresponds to how many ways girls can line up and then for each of these ways how we can include the boys lined up. Lets Cons... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15452 | GRE Math : How to find the height of a right triangle
Example Questions
Example Question #1 : How To Find The Height Of A Right Triangle
An equilateral triangle has a side length of 4. What is its height?
Possible Answers:
2√2
4
2√3
2
16
Correct answer:
2√3
Explanation:
If an equilateral triangle is divide... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15453 | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Archive Impact factor Subscription Search papers Search references RSS Latest issue Current issues Archive issues What is RSS
Algebra i Analiz: Year: Volume: Issue: Page: Find
Algeb... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15454 | # Question #d1d14
Mar 16, 2017
This is true, and the answers to questions above are:
Q4 - yes
Q5 - no
Q6 - yes
#### Explanation:
There are lots of divisibility rules. They're basically shortcuts for working out if you can divide by a number with no remainders leftover. Another example is that a number has to be eve... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15455 | # zbMATH — the first resource for mathematics
Non-abelian Hodge theory for algebraic curves in characteristic $$p$$. (English) Zbl 1330.14015
Let $$C$$ be a Riemann surface, and $$G_c$$ be a compact Lie group with its complexification $$G$$. In this case, one gets a bijection between stable $$G$$-Higgs bundles with va... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4048 | # DEVJERRY - Editorial
Author: Praveen Dhinwa
Tester: Kevin Atienza and Sergey Kulik
Editorialist: Kevin Atienza
### PROBLEM:
Jerry the mouse is in an n\times n grid, is at the location S := (s_x,s_y). He wants to move to the location E := (e_x,e_y). However, there is a bomb placed at B := (b_x,b_y) and so he has to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4049 | # Overlapping sample t-test
I have 10 people working together. They work in groups for 6 days: Three days in week 1, three days in week 2. In each day I don't have the full set of people, but a subset of them. In each day I measure the individual performances.
I have to say if the general performance was higher in we... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4050 | Respected Mathematicians, I would like to prepare a function, which will generate Pythagorean quadruples (a, b, c, d) = $d^2$ = $a^2$ + $b^2$ + $c^2$...-> (1). How far I am correct I don't know. For some set of integers a and b, consider $a^2$ + $b^2$ = m and d = c + ε. Now by (1), c = (m - $ε^2$)/2ε)....>(2) Now I wil... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4051 | # Coriolis & Centrifugal forces
1. ### PhMichael
132
1. The problem statement, all variables and given/known data
The picture speaks for itself: one man "A" is standing of a rotating disk whose angular velocity is $$\omega$$ CCW, and another one "B" is standing still on earth. I'm riquired to find the coriolis and c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4052 | # What is the important term?
Calculus Level 2
$\large \lim_{x\to \infty} (e^{11x} - 7x)^{\frac1{3x}}$
If the limit above equals to $$e^{a/b}$$ for coprime positive integers $$a,b$$, find the value of $$a+b$$.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4053 | # Finding a non-differentiable function with these properties:
Wondering if anyone can point out a function $$f$$ from an open disc in $$\mathbb R^2$$ to $$\mathbb R$$, that:
• is defined and continuous at a point $$p$$;
• has(they exist) both of its partial derivatives at $$p$$;
• at least one of the partials is dis... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4054 | Asymptotes of a function
We define an asymptote as a straight line that can be horizontal, vertical or obliquous that goes closer and closer to a curve which is the graphic of a given function.
These asymptotes usually appear if there are points where the function is not defined.
Let's see an example, since it will ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4055 | # nLab Joseph A. Zilber
Joseph Abraham Zilber defended his PhD thesis at Harvard University in 1963. He was advised by Andrew Gleason and Raoul Bott.
## Selected writings
Introducing simplicial sets and semi-simplicial sets (see the historical remarks here):
Introducing the Eilenberg-Zilber theorem:
Last revised o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4056 | # Transversal Line
What are Transversal Line?
The line which intersects two distinct lines in a plane at two distinct points is called a transversal.
In the below figure, line 't' is transversal to lines l and m, intersecting these two lines at points A and B.
Also, we observe in the below figure, line 't' is not t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4057 | # Conformally invariant operators
On a general compact manifold $M$ with metric $g$, a metrically defined operator $A$ is said to be conformally invariant if under the conformal change in the metric $g_w=e^{2w}g$, the pair of the corresponding operators $A_w$ and $A$ are related by $A_w(\varphi)=e^{-bw} A(e^{aw}\varph... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4058 | ## Solution
Compression DP.
Let the particles with lifetime $i$ pass through all the planes first. And then calculate the particles with lifetime $i-1$.
We can notice that the particle with lifetime $i$ runs in the same direction, and is opposite to the direction of the particle with lifetime $i-1$.
Define $dp[i][j... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4059 | Last edited by Negal
Sunday, October 4, 2020 | History
2 edition of On the Wentzel-Brillouin-Kramers approximate solution of the wave equation found in the catalog.
On the Wentzel-Brillouin-Kramers approximate solution of the wave equation
Lloyd A. Young
# On the Wentzel-Brillouin-Kramers approximate solution of th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4060 | #### Vol. 305, No. 1, 2020
Recent Issues Vol. 305: 1 Vol. 304: 1 2 Vol. 303: 1 2 Vol. 302: 1 2 Vol. 301: 1 2 Vol. 300: 1 2 Vol. 299: 1 2 Vol. 298: 1 2 Online Archive Volume: Issue:
The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4061 | # American Institute of Mathematical Sciences
September 2020, 28(3): 1239-1255. doi: 10.3934/era.2020068
## On simultaneous recovery of sources/obstacles and surrounding mediums by boundary measurements
1 School of Mathematics and Statistics, Key Laboratory of Hunan Province for Statistical Learning and Intelligen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4062 | Math Help - Solving for a Constant Return to arrive at fixed end value
1. Solving for a Constant Return to arrive at fixed end value
Hi I am working on putting together an excel formula that will allow me produce the correct constant return number which will allow me to reach a fixed end value.
I have a fixed spendi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_4063 | # Cyclic vectors for the shift operator
Let $S:\ell^2\to\ell^2$ be the shift operator $$S(x_1,x_2,\dots)=(0,x_1,x_2,\dots).$$ Let $x\in \ell^2$ with $x_1=1$. Is $x$ cyclic for $S$? In other words, is the span of the vectors $x,Sx,S^2x,\dots$ dense in $\ell^2$? If this does not hold for every $x$, is there a handy crit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20240 | # Homework 12, Real Analysis
## Due date: October 27
### Problem 1
Let $x_n\to x, y_n\to y$ be convergent sequences in the normed space $(X,||\cdot||)$ over $\K$. Then
1. $x_n + y_n \to x + y$;
2. $\lambda_n x_n \to \mu x$ for all sequences $\lambda_n\to\lambda$ in $\K$.
### Problem 2
Let $(X,||\cdot||)$ be a nor... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20241 | # Naive Bayes classifier
## Introduction
The naive Bayes classifier is a generative model for classification. Before the advent of deep learning and its easy-to-use libraries, the Naive Bayes classifier was one of the widely deployed classifiers for machine learning applications. Despite its simplicity, the naive Bay... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20242 | # Math Help - Primes in Q Fields with Norms less than 6 (Interesting!)
1. ## Primes in Q Fields with Norms less than 6 (Interesting!)
Hello All,
I've been trying to get the hang of understanding how primes interact with Quadratic fields and then the respective norms. (You can see because over the past month I've had... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20243 | # Discrete Contraction and Inner Product
Let $$\alpha$$ and $$\beta$$ be two 1-forms. Their inner product can be expressed as
$(\alpha,\beta)=\langle\alpha^{\sharp},\beta\rangle=\langle\beta^{\sharp},\alpha\rangle=(\alpha^{\sharp},\beta^{\sharp})$
where $$\langle\cdot,\cdot\rangle$$ represents the pairing between a ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20244 | It is currently 23 Oct 2020, 19:31
### 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.
Customized
for You
we will pick new questions that match your level based o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20245 | # Lazard Lie category
## Definition
### As the category of Lazard Lie rings
The Lazard Lie category can be defined as the following concrete category:
Item Value
Objects Lazard Lie rings, i.e., Lie rings for which there exists a finite $c$ such that the Lie ring has 3-local class at most $c$ and is powered over all... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20246 | # Complex_Number
As you know, the imaginary number is defined as: where $a \in \mathbb{R}$
ai = a\sqrt{-1}
And therefore complex number $c \in \mathbb{C}$ is imaginary number plus a real number.
Imaginary number relates to rotation. For detailed intuitive understanding of imaginary number, see this article
Differe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20247 | How do you find the slope given (2, -1) and (-3, 4)?
Apr 4, 2016
$\frac{\delta y}{\delta x} = - 1$
Explanation:
Slope is $\text{rise"/"run}$, or the change in $y$ divided by the change in $x$. Mathematically this is shown as
$\frac{\delta y}{\delta x}$
To find the change in a value, take the second one and subtra... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20248 | ## College Algebra (10th Edition)
$x=\frac{3}{4}$ or $x=\frac{4}{3}$
$\displaystyle \frac{1}{(x-1)^{2}}+\frac{1}{x-1}=12$ We multiply both sides by $(x-1)^2$: $1+(x-1)=12(x-1)^2$ $12(x-1)^2-(x-1)-1=0$ $[4(x-1)+1][3(x-1)-1]=0$ $(4x-4+1)(3x-3-1)=0$ $(4x-3)(3x-4)=0$ $(4x-3)=0$ or $(3x-4)=0$ $x=\frac{3}{4}$ or $x=\frac{4}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20249 | Matrix Multiplication Review
Overview
Matrices are a way of grouping numbers, and are organized into rows and columns. Matrices are often used as a way of representing several equations in an easier to organize format, however to solve these systems of equations we must be able to perform matrix operations such as mu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20250 | ## On reasonably sure proofs
I happened to come across a 1993 opinion piece, Theorems for a price: Tomorrow's semi-rigorous mathematical culture by Doron Zeilberger. I think it's a rather fascinating document as it questions the future of mathematical proof. Its basic thesis is that some time in the future of mathemat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20251 | # 10th Physics | Light | Linear Magnification Produced by Mirrors
## Linear Magnification Produced by Mirrors
The linear magnification produced by a spherical mirror (concave or convex) is defined as the ratio of the height of the image (h¢) to the height of the object (h). It is a pure ratio and has no units. It is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20252 | # Two tangents to the parabola y=1-x^2 intersect at point (2,0). Find the coordinates of points on parabola on which these are tangents?
Mar 15, 2017
Coordinates are $\left(2 + \sqrt{3} , - 5 - 4 \sqrt{3}\right)$ and $\left(2 - \sqrt{3} , - 5 + 4 \sqrt{3}\right)$
#### Explanation:
Equation of a line with slope $m$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20253 | 23 | 05 | 2019
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# An elementary proof of the Banach-Zarecki theorem
## Abstract
There is a very rich literature concerning the Banach-Zarecki Theorem, such as the books of Saks (Theory of the integral, 2nd. rev. ed.,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20254 | #### Volume 11, issue 5 (2011)
Recent Issues
The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear ISSN (electronic): 1472-2739 ISSN (print): 1472-2747
Erratum to the article Twisted Alexander polynomials and s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_20255 | # An Application of Convergence theorem
Let $$(X,M.\mu)$$ be a measure space and let $$f\colon X \rightarrow \mathbb{R}$$ be a measurable function. Show that $$\lim_{n \to \infty} \int_X \left(1-\left(\frac{2}{e^{f(x)}+e^{-f(x)}}\right)^n \right)d\mu=\mu(\{x \in X:f(x)\neq0\})$$
My attempt:
I think its an applicatio... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14016 | # Nth Order Differential Equations
1. Nov 22, 2011
### ahaanomegas
We know that there are a few forms for 1st order differential equations. Second-order differential equations have an extra term with an $x$ in it. My conjecture is that third-order differential equations have another extra term with an $x^2$ in it. A... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14017 | ## Semisimple Rings and Modules
After discussing simple modules, the next best thing is to look at semisimple modules, which are just direct sums of simple modules. Here’s a summary of the results we’ll prove:
• A module is semisimple iff it is a sum of simple submodules.
• Quotients, sums, direct sums and submodules... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14018 | # Abel inequality
Jump to: navigation, search
An estimate for the sum of products of two numbers. If sets of numbers $(a_k)$ and $(b_k)$ are given such that the absolute values of all sums $B_k = b_1 + \cdots + b_k$, $k=1,\ldots,n$, are bounded by a number $B$, i.e. $|B_k| \le B$, and if either $a_i \ge a_{i+1}$ or $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14019 | Gradient descent is an optimization algorithm used to minimize some function by iteratively moving in the direction of steepest descent as defined by the negative of the gradient. In machine learning, we use gradient descent to update the parameters of our model. Parameters refer to coefficients in Linear Regression an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14020 | # Reach the Last pole
Question: There are 20 poles with a constant distance between each pole. A car takes 24 second to reach the 12th pole. How much will it take to reach the last pole.
Answer:
The car will take 41.45 seconds to reach the last pole.
Let the distance between two poles is X.
The car takes 24 seconds ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14021 | Definitions
# escape velocity
escape velocity, the velocity a body must be given in order to escape the gravitational hold of some other larger body, e.g., the earth, moon, or sun. A body given less than the escape velocity will fall back toward the surface of the larger body; a body given a velocity equal to or grea... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14022 | It is currently 18 Jan 2018, 06:16
### GMAT Club Daily Prep
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14023 | # Basic definitions: magnetic flux, inductance,...
## Magnetic flux: definition
Let there be a filiform circuit closed-loop, defined by its contour C and provided with an electric current I.
The magnetic flux Φ associated with the contour C is defined by:
(1)
where:
• is the magnetic field created by the current ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14024 | Fibonacci sequence inversion - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-21T05:04:28Z http://mathoverflow.net/feeds/question/39124 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/39124/fibonacci-sequence-inversion Fibonacci sequence inversion Hernán Eche 20... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14025 | # Height of points over number fields
I'm beginning to read about height theory in this text by J.H. Silverman. In page $5$ he gives the following definition of height, considering a number field $K$:
The height of a point $P=[x_0:...:x_N]\in\mathbb{P}^N(\mathbb{Q})$ with $x_0,...,x_N\in\mathbb{Z}$ and $\gcd(x_0,...,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14026 | Is there a connected non-affine scheme $S$ such that it is the union of rings of integers of number fields? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T01:24:17Z http://mathoverflow.net/feeds/question/76349 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14027 | Copied to
clipboard
## G = SD16⋊3D7order 224 = 25·7
### The semidirect product of SD16 and D7 acting through Inn(SD16)
Series: Derived Chief Lower central Upper central
Derived series C1 — C28 — SD16⋊3D7
Chief series C1 — C7 — C14 — C28 — C4×D7 — D4⋊2D7 — SD16⋊3D7
Lower central C7 — C14 — C28 — SD16⋊3D7
Upper c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14028 | ## mathcalculus Group Title HELP: Use your knowledge of the derivative to compute the limit given below: The derivative that is being calculated is 11 months ago 11 months ago
1. mathcalculus Group Title
2. mathcalculus Group Title
im confused. am i suppose to use the power rule or quotient rule to find the derivati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14029 | • September 9th 2008, 01:12 PM
cecij22
I need help with this problem:
(sqroot 5)*(sqroot .0025)/(sqroot .0009)
• September 9th 2008, 01:15 PM
Matt Westwood
$\frac {\sqrt 5 \sqrt{.0025}}{\sqrt {.0009}}$
$= \sqrt {\frac {5 \times .0025}{.0009}}$
$= \sqrt {\frac {5 \times 25}{9}}$
$= \sqrt 5 {\frac {5}{3}}$
... I thi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14030 | # Virial theorem
(Redirected from Virial)
In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, $\left\langle T \right\rangle$, of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, $\lef... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14031 | الرئيسية Famous problems of elementary geometry
# Famous problems of elementary geometry
, ,
This short book, first published in 1897, addresses three geometry puzzles that have been passed down from ancient times. Written for high school students, this book aims to show a younger audience why math should matter and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7536 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 23 May 2019, 10:41
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7537 | # 2007 USAMO Problems/Problem 2
## Problem
(Gregory Galperin) A square grid on the Euclidean plane consists of all points $(m,n)$, where $m$ and $n$ are integers. Is it possible to cover all grid points by an infinite family of discs with non-overlapping interiors if each disc in the family has radius at least 5?
##... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7538 | # Find sequence whose sum of squares converges
Prove that for every sequence $\{a_n\}$ such that $\sum\limits_{n=1}^{\infty}a_n^2=+\infty$ there exists sequence $\{b_n\}$ such that $\sum\limits_{n=1}^{\infty}b_n^2$ converges but $\sum\limits_{n=1}^{\infty}a_nb_n$ diverges. How should I approach this problem?
• What i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7539 | # حالة مستقرة
(تم التحويل من حالة أرضية)
الحالة المستقرة stationary state هي حالة كمية يكون فيها كل القابلين للرصد مستقلين عن الزمن. وهي متجه ذاتي للهاملتونية.[1] وهذه تناظر حالة بطاقة محددة منفردة (بدلاً من تراكب كمي لطاقات مختلفة). كما تـُدعى متجه ذاتي للطاقة، حالة ذاتية للطاقة، دالة ذاتية للطاقة، أو كت ذاتي للطاقة... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7540 | Home > ACC7 > Chapter 9 Unit 6 > Lesson CC2: 9.2.2 > Problem9-66
9-66.
Use the rectangular prism shown at right to complete parts (a) through (d) below.
1. Calculate the surface area of the prism. Show all of your subproblems.
To find the surface area, find the area of each face of the prism.
There are $6$ faces i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7541 | # Sample quiz on properties of triangles and quadrilaterals Main home here.
1. In $\triangle ABC$, the slope of the line that joins the midpoints of sides $AB$ and $AC$ is $\cdots$
equal to one
equal to zero
equal to the slope of side $BC$
equal to the slope of side $AB$
2. In $\triangle ABC$, the length of the line t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7542 | ## Fix What Does It Mean When Standard Error Is High (Solved)
Home > Standard Error > What Does It Mean When Standard Error Is High
# What Does It Mean When Standard Error Is High
## Contents
For any random sample from a population, the sample mean will usually be less than or greater than the population mean. Beca... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7543 | # Unit 5Systems of Equations and Inequalities
## Lesson 1
### Learning Focus
Solve systems of linear equations that represent a context.
### Lesson Summary
In this lesson, we reviewed strategies for solving systems of linear equations, including using tables, graphs, and algebra. We examined two different algebrai... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7544 | Summation help
1. Feb 27, 2009
hover
Hey everyone,
I need some help trying to figure out how to find the summation of
n
$$\sum_{}^{\6}i^p$$
i=0
I was looking on the web and found on Wikipedia this formula off the http://en.wikipedia.org/wiki/Summation" [Broken] page. It looks like this assuming I copied it right (... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7545 | # How do you solve f=(27.2*m)/t for m?
Multiply both sides of the equation by $\frac{t}{27.2}$
$f \times \frac{t}{27.2} = \frac{\cancel{27.2} \cdot m}{\cancel{t}} \times \frac{\cancel{t}}{\cancel{27.2}}$
$m = \frac{f \cdot t}{27.2}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7546 | ## Functions Modeling Change: A Preparation for Calculus, 5th Edition
Published by Wiley
# Chapter 11 - Polynomial and Rational Functions - Exercises to Skills Review for Chapter 11 - Page 494: 44
#### Answer
$\frac{7}{p^2+11}+\frac{p}{p^2+11}$
#### Work Step by Step
Splitting the fraction into a sum of fractions... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7547 | # Question about step used in solution manual for Problem 8b in Chapter 9 of Spivak's Calculus
Problem 8b in Chapter 9 of Spivak's Calculus reads as follows:
Prove that if $$g(x)=f(cx)$$, then $$g'(c)=c \cdot f'(cx)$$.
Spivak's first part of the solution is written as:
\begin{align}g'(x)&=\displaystyle \lim_{h\to 0... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7548 | # Is the quantization of the harmonic oscillator unique?
To put it a little better:
Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit?
I'm specifically, but not only, interested in an elaboration in terms of deformation quantization.
-
By deformation qu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7549 | # Help understanding notation of first fundamental form
I'm having a hard time understanding some stuff about the first fundamental form. Since I think I have decently understood what the first fundamental form means (inner product restricted to the tangent space of a surface) I think what confuses me is the notation.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7550 | # Which of the following is not the same as 0.032 liters
###### Question:
Which of the following is not the same as 0.032 liters
#### Similar Solved Works
?? PLEASE HELP $?? PLEASEEEEEEEE HELP$...
### 15 POINTSwrite an equation un point slope form for the line through the gives point with the given slope.(-3,4);m=... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_7551 | # Improper Integral using Comparison to determine Convergence/Divergence
## Homework Statement
Use a comparison to determine if the improper integral converges or diverges. If the integral converges, give an upper bound for the value.
Integral of d(theta) / (theta^3 + theta)^1/2 from 1 to infinity
N/A
## The Attem... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12832 | ## Lie, Jordan algebras and the associator identity
Before I continue the quantum mechanics algebraic series, I want to first state my happiness for the defeat of the far (alt)-right candidate in France despite Putin's financial and hacking support. Europe has much better antibodies against the scums like Trump than U... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12833 | # density of primes such that both $f(x)$ and $g(x)$ have roots
Let $f(x)$ and $g(x)$ be irreducible polynomials over rationals. I know that to find the density of the primes $p$ such that (say) $f(x)$ has a root mod $p$ can be found using Chebotarev density theorem, looking at the density of elements with fixed point... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12834 | Courses
Courses for Kids
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Find the angle which is equal to its complement:
Last updated date: 20th Mar 2023
Total views: 308.7k
Views today: 3.87k
Verified
308.7k+ views
Hint:- Sum of two complementary angles is ${90^0}$
As we all know that if $\theta$ be an angle then,
Comp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12835 | # GRE Subject Test: Math : Ratio Test
## Example Questions
### Example Question #1 : Ratio Test
Which of these series cannot be tested for convergence/divergence properly using the ratio test? (Which of these series fails the ratio test?)
Explanation:
The ratio test fails when . Otherwise the series converges abso... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12836 | # Capacitance of Non-concentric Spheres
We all know how to obtain the capacitance $C=\frac{ab}{b-a}$ (ignoring constants) for two concentric spheres of radii $a,b$.
I was just thinking to myself, what would happen to the capacitance for non-concentric spheres?
Suppose we perturbed the inner sphere off the origin. Doe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12837 | # Commutators in second quantization
## Main Question or Discussion Point
Hi. I've been trying to calculate a couple of commutators, namely $[\Psi(r),H]$ and $[\Psi^{\dagger}(r),H]$ where H is a free particle hamiltonian in second quantization. I have attached my attempts and I would greatly appreciate if anyone coul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12838 | ## African Diaspora Journal of Mathematics
### Bounded and Compact Operators on the Bergman Space $L^{1}_{a}$ in the Unit Disk of $\mathbb{C}$
#### Abstract
We characterize boundedness and compactness of the Toeplitz operator $T_{\mu}$, on the Bergman space $L_{a}^{1}(\Delta)$, where the symbols, $\mu$, are complex ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12839 | Home > Standard Error > Compute Standard Error Sampling Mean
# Compute Standard Error Sampling Mean
## Contents
Using a sample to estimate the standard error In the examples so far, the population standard deviation σ was assumed to be known. So we take our standard deviation of our original distribution. Journal of... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12840 | Thread: Manifolds Question View Single Post
2013-05-21, 13:43 #2
R.D. Silverman
Nov 2003
22×5×373 Posts
Quote:
Originally Posted by jinydu Let M be a compact n-manifold with boundary. Show that there is an open set U containing the boundary that is diffeomorphic to (the boundary) x [0,1) -------- By definition of... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12841 | ## Section7.7Substitution
The formulas in differential form given at the end of Section 7.5 not only summarize the basic differentiation formulas, but also the basic integration formulas! In each case, one can integrate both sides of the expression, then use the Fundamental Theorem of Calculus, which says that
$$\int... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12842 | # Closed forms and trajectories of vector fields
This question is inspired by this recent one and this one; I hope it's not too elementary.
Let $M$ be a (closed) smooth manifold and $X$ a vector field on $M$. Fix any Riemannian metric $g$ on $M$ and let $X^{\flat}=g(X,\cdot)$ be the metric-dual differential form of $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12843 | Electronegativities of the elements (data page)
# Electronegativities of the elements (data page)
Main article: Electronegativity
## Contents
• 1 Electronegativity (Pauling scale)
• 2 Notes
• 3 Electronegativity (Allen scale)
• 4 References
• 4.1 WEL
• 4.2 CRC
• 4.3 LNG
• 4.4 Allen Electronegativities
## Electrone... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12844 | # nLab equivariant PL de Rham theorem
Contents
cohomology
### Theorems
#### Representation theory
representation theory
geometric representation theory
and
# Contents
## Idea
The equivariant PL de Rham theorem (Triantafillou 82, Theorem 4.9) is the generalization of the PL de Rham theorem to the equivariant P... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12845 | # P and K start from their office and walk in opposite directions, travelling 10 km each. Then P turns left and walks 10 km, whereas K turns right and walks 10 km. How far are they now from each other?
[ A ] 10 km [ B ] 30 km [ C ] 25 km [ D ] 20 km
Answer : Option D Explanation : |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12846 | # Let F : (2,0)R be a function defined by:F(m) = "The area of the region enclosed by y = In(r
###### Question:
Let F : (2,0) R be a function defined by: F(m) = "The area of the region enclosed by y = In(r 1),y = Vz +I,2 = 0,y = m and y 0" Write the formula of F in terms of m_ (Hint: While sketching the region you can... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_12847 | ## Essentials of Statistics (5th Edition)
$\alpha=1-0.95=0.05.$ Using the table: $z_{\alpha/2}=z_{0.025}=1.96.$ Standard deviation=$\frac{range}{4}=\frac{2.95-0}{4}=0.7375.$ Hence the sample size this way:$\left (\frac{z_{\alpha/2}\cdot \sigma}{E}\right)^2=\left (\frac{1.96\cdot0.7375}{0.2}\right)^2\approx53$. Using t... |
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