id stringlengths 27 136 | text stringlengths 4 1.05M |
|---|---|
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10700 | # 2020? But it's still 2015!
Algebra Level 5
$\large f(x+1) = (5^{2^{x-1}} + 1)(x+1)^{2}f(x)$
Suppose we define a function of $$x$$ as described above for $$x$$ is a non-negative integer with $$f(0)=\sqrt{5} - 1$$.
If the value of $$f(2020)$$ can be written in form $$(5^{p} - 1)(q!)^{2}$$, for positive integers $$p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10702 | # Solutions to Problem Set 2
Math 345/504
1-29-2018
1. An operation is defined on the set of integers by
(a) Show that is associative and commutative.
(b) Find the identity element for , verifying that the identity axiom holds.
(c) Find a formula for the inverse of an element x, verifying that the inverse axiom h... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10692 | # John's strange quadrilateral
Geometry Level 3
Convex quadrilateral $$ABCD$$ has sides $$AB = BC = 21$$, $$CD = 15$$ and $$AD = 9$$. Given additionally that $$\angle ABC = 60^\circ$$, what is the length of $$BD$$?
This problem is proposed by John.
×
Problem Loading...
Note Loading...
Set Loading... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10698 | Graph of a continuous function $f:[a,b]\to(0,\infty)$ is measurable only if $f$ is differentiable?
I am studying measure theory, and I came across the following problem:
Let $f: [a, b]\to (0, \infty)$ be continuous, and let $G = \{ (x, y): y = f(x)\}.$ Prove that $G$ is measurable only if $f$ is differentiable in $(a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10699 | Free Version
Difficult
# Two Forces Acting on an Object: A Push-Me-Pull-You
APPHMC-VHAUV1
In the original Dr. Dolittle movie (from 20th Century Fox, 1967) one of the strange animals is a Push-Me-Pull-You, which looks like a llama with two torsos, two pairs of front legs, and no hindquarters. (Don't ask how its diges... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10701 | RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB
General information Latest issue Forthcoming papers Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archiv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_10703 | ## Stochastic Cahn-Hilliard equation.(English)Zbl 0838.60056
This paper is concerned with the study of a stochastic Cahn-Hilliard equation of the form: $\begin{cases} dX + \bigl( \Delta^2 X - \Delta f(X) \bigr) dt = dW, \\ X(0) = x. \end{cases} \tag{1}$ Here $$\Delta$$ represents the Laplace operator on $$\mathbb{R}^n... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1984 | # Talk:Supernatural number
(Redirected from Talk:Supernatural numbers)
WikiProject Mathematics (Rated Stub-class, Low-priority)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the pro... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1985 | # Restricted OLS problem
Here is my problem:
Let $1\leq l<k$ be integers and write the design matrix $X$ as $X=[X_1\; X_2]$, where $X_1$ is an $n\times l$-dimensional matrix, and where $X_2$ is an $n\times (k-l)$-dimensional matrix. Show that the restricted LS estimator $\beta^*$ subject to the restriction $R\beta=r$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1987 | # LMIs in Control/pages/Robust H inf State Feedback Control
## Robust Full State Feedback Optimal ${\displaystyle H_{\infty }}$ Control
Full State Feedback is a control technique which places a given system's closed loop system poles in locations specified by desired performance specifications. One can use ${\display... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1988 | Floor and ceiling functions
Last updated
Floor and ceiling functions
Floor function
Ceiling function
In mathematics and computer science, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted floor(x) or x. Similarly, the cei... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1989 | ## K values
$PV=nRT$
Philipp_V_Dis1K
Posts: 32
Joined: Fri Sep 28, 2018 12:20 am
### K values
Since K values smaller than 10^-3 are considered small, and large ones are greater than 10^3, what do the values between 10^-3 and 10^3 represent?
Kavvya Gupta 1H
Posts: 35
Joined: Fri Sep 28, 2018 12:21 am
### Re: K val... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1990 | Canadian Mathematical Society www.cms.math.ca
location: Publications → journals
Search results
Search: MSC category 46 ( Functional analysis )
Expand all Collapse all Results 1 - 25 of 231
1. CMB Online first
Liu, Zhichao
Injectivity of the connecting homomorphisms in inductive limits of Elliott-Thomsen ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1992 | Let $$W$$ be a set, and let $$v$$ be a finitely additive probability measure on $$2^W$$.
Equip $$2^W$$ with the Borel sigma-algebra $$\mathcal{B}$$ generated by the sub-basic sets of the form $$\{a: w \in a\}$$ and $$\{a: w \notin a\}$$, where $$w \in W$$.
I am interested in characterizing those probability measures $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1993 | # Match the subtraction expression with the corresponding addition expression. −9−5
###### Question:
Match the subtraction expression with the corresponding addition expression.
−9−5
### A rectangular prism has a length of 4 cm, a width of 112 cm, and a height of 212 cm. The prism can be filled with unit cubes that ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1994 | # Irrational Equations
• October 4th 2008, 04:18 PM
BlakeRobertsonMD
Irrational Equations
Hi
I'm supposed to prove that all the solutions to X^2 = X + 1 are irrational.
I'm not sure exactly where to begin. I know by contradiction I would make it rational and replace x with A/B. Then work the problem through. After I... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1995 | Can $n^2+4n$ be a perfect square?
Do there exist positive integers $n,k$ such that $n^2+4n=k^2$? I'm not sure how to attack this question. I was able to get that $n=\frac{-4\pm\sqrt{16+4k^2}}{2}$, but I don't think it is of any use.
• Suppose you had such $n$ and $k$. Evidently $k > n$. So write $k = n + a$. What wou... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1996 | ### Calendar Capers
Choose any three by three square of dates on a calendar page...
### Have You Got It?
Can you explain the strategy for winning this game with any target?
### Pair Sums
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
# Top-heavy Pyramids
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1998 | # Tag Info
28
For $x < 1$, we have the Taylor series expansion: $$f(x):= \frac{-1}{4} \log \left(- \frac{x - x^{-1}}{x + x^{-1}} \right) = \frac{x^2}{2} + \frac{x^6}{6} + \frac{x^{10}}{10} + \frac{x^{14}}{14} + \ldots$$ Then $$f(x) + \frac{f(x^2)}{2} + \frac{f(x^4)}{4} + \frac{f(x^8)}{8} + \ldots = \frac{x^2}{2} + \f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1999 | # §14.18 Sums
## §14.18(i) Expansion Theorem
For expansions of arbitrary functions in series of Legendre polynomials see §18.18(i), and for expansions of arbitrary functions in series of associated Legendre functions see Schäfke (1961b).
## §14.18(iii) Other Sums
### ¶ Dougall’s Expansion
For a series representati... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1986 | ## College Algebra (10th Edition)
Published by Pearson
# Chapter 9 - Section 9.3 - Geometric Sequences; Geometric Series - 9.3 Assess Your Understanding: 59
#### Answer
The series diverges because $r=\dfrac{3}{2}$.
#### Work Step by Step
RECALL: (1) The common ratio $r$ of a geometric sequence is equal to the quo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1991 | # A Tutorial on Solving Equations Part 3
This is the third part of the series of tutorials on solving equations. In this part, we will solve more complicated equations especially those that contain fractions. The first part and the second part of this series discuss 10 sample equations. We start with the 11th example... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1997 | JMU F18 Wk7
#### Start
2018-10-12 18:30 UTC
## JMU F18 Wk7
#### End
2018-10-18 20:00 UTC
The end is near!
Contest is over.
Not yet started.
Contest is starting in -32 days 2:32:05
145:30:00
0:00:00
# Problem CTri Tiling
In how many ways can you tile a $3\times n$ rectangle with $2\times 1$ dominoes?
Here is a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1360 | # Chapter 5 - Section 5.1 - Exponents and Scientific Notation - Exercise Set: 130
$.0668$ square kilometers
#### Work Step by Step
We are given that Hagerman Fossil Beds National Monument in Idaho contains $6.68\times10^{-2}$ square kilometers of privately owned land. Since the exponent is negative, move the decimal... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1362 | # Tag Info
## Hot answers tagged conservation-laws
4
Since $\pi^0$ is a pseudoscalar particle, we have $$\langle 0|J^\mu_{em}|\pi^0 \rangle =0,$$ and the pion cannot decay into two leptons with a simple photon exchange. In the Standard Model, the leading-order contributions for this process are a box diagram and a $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1364 |
# 9.4 Orthonormal bases
We now define the notions of orthogonal basis and orthonormal basis for an inner product space. As we will see later, orthonormal bases have many special properties that allow us to simplify various calculations.
Definition 9.4.1. Let $$V$$ be an inner product space with inner product $$\inne... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1365 | # Absolute Value Basic
Algebra Level 2
Let $x$ be a real number. Which of the answers is equal to the below?
$|-x|$
×
Problem Loading...
Note Loading...
Set Loading... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1367 | FoCM 2014 conference
Workshop B5 - Information Based Complexity
December 17, 18:00 ~ 18:30 - Room B23
## Approximation of piecewise Hölder classes from inexact information
We study algorithms for $L^p$-approximation ($1\le p<\infty$) of functions $f:[a,b]\to{\mathbb R}$ that are piecewise $r$-times continuously dif... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1368 | ## Transitive closures
Hi,
I'm trying to find this example since 4 hours, but can't find one. I'm starting thinking it's impossible...
Find an example of relations $R_1$ and $R_2$ on some set $A$ such that, if we let $R = R_1 \setminus R_2$ and we let $S_1$, $S_2$ and $S$ be the transitive closures of $R_1$, $R_2$ a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1369 | # Tag Info
42
The most logical way to transform hour is into two variables that swing back and forth out of sync. Imagine the position of the end of the hour hand of a 24-hour clock. The x position swings back and forth out of sync with the y position. For a 24-hour clock you can accomplish this with x=sin(2pi*hour/2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1370 | 💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!
# Differentiate the function.$G(q) = (1 + q^{-1})^2$
## $$G^{\prime}(q)=0+2\left(-1 q^{-2}\right)+\left(-2 q^{-3}\right)=-2 q^{-2}-2 q^{-3}$$
Derivatives
Differentiation
### Discussion
You must be sign... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1373 | # Branching rules for ramified principal series representations of GL3 over a p-adic field - Mathematics > Representation Theory
Abstract: We decompose the restriction of ramified principal series representations ofthe $p$-adic group $\mathrm{GL}3,\mathrm{k}$ to its maximal compact subgroup$K=\mathrm{GL}3,\mathscr{R}$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1374 | ### Course
19S1 D. Anselmi
Theories of gravitation
Program
PDF
### Book
D. Anselmi
From Physics To Life
A journey to the infinitesimally small and back
In English and Italian
Available on Amazon:
US: book | ebook (in EN)
IT: book | ebook (in IT)
## 22A2 Damiano AnselmiFakeons versus Lee-Wick ghosts: physical... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1375 | ## Invariants of Legendrian knots
Series:
Geometry Topology Seminar
Tuesday, May 31, 2016 - 14:00
1 hour (actually 50 minutes)
Location:
Skiles 006
,
Duke University
Organizer:
Given a plane field $dz-xdy$ in $\mathbb{R}^3$. A Legendrian knot is a knot which at every point is tangent to the plane at that point. One ca... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1366 | # Evaluate $\int_0^\infty\frac{\sin(\varphi_1x)}x\frac{\sin\varphi_2x}x\cdots\frac{\sin\varphi_nx}x\frac{\sin(ax)}x\cos(a_1x)\cdots\cos(a_mx) \, dx$
How to evaluate
$$\int_0^\infty \frac{\sin(\varphi_1x)}{x}\frac{\sin\varphi_2x}{x} \cdots \frac{\sin\varphi_nx}{x} \frac{\sin(ax)}{x}\cos(a_1x) \cdots \cos(a_mx) \, dx \... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1371 | ### Using algebra tiles to solve polynomials
Algebra tiles can be used to represent polynomials. We can also use those tiles to solve polynomials. In this lesson, we will try to solve some polynomials using algebra tiles. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1372 | Landau's function
In mathematics, Landau's function g(n), named after Edmund Landau, is defined for every natural number n to be the largest order of an element of the symmetric group Sn. Equivalently, g(n) is the largest least common multiple (lcm) of any partition of n, or the maximum number of times a permutation o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1361 | Find the error bound
Hey guys I am unsure how to find the error bound. Use the langrange interpolating polynomial of degree 3 or less and four digit chopping arithmetic to approximate $\cos(.750)$ using the following values. Find an error bound for the approximation.
$\cos(.698)=.7661, \cos(.733)=.7432, \cos(.768)=.7... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1363 | # Quickly Check my Work Please|Finding Derivatives
## Homework Statement
$$y=\frac{8x^4-5x^2-2}{4x^3}$$
Find y'.
2. The attempt at a solution
$$y=\frac{8x^4-5x^2-2}{4x^3}$$
$$y'=\frac{(32x^3-10x)(4x^3)-(12x^2)(8x^4-5x^2-2)}{(4x^3)^2}$$
$$y'=\frac{128x^6-40x^4-96x^6+60x^4+24x^2}{16x^6}$$
$$y'=\frac{32x^6+20x^4+24... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6369 | # Interpreting Structural Equation Model Estimates?
I am hoping someone can clarify how parameter estimates for structural equation models (SEM) are usually interpreted in practice.
By that I mean, suppose we have an SEM of the form
$$y = \mu + \Lambda \omega + \epsilon$$
$$\eta = \Gamma \xi + \delta$$
where $$\om... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6371 | Saturday
October 25, 2014
# Homework Help: Math: Calculus
calculus
Find the interval of convergence of the series. ∑(sinx/10)^n
Wednesday, May 7, 2014 at 7:34pm
Calculus
How much should be deposited into an account today if it is to accumulate to $32400 in 30 years if the account bears interest at 8.01% compounded m... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6373 | # Bolzano–Weierstrass theorem for random variables?
I am wondering if there is something similar to the Bolzano–Weierstrass theorem for random sequences. Namely, let $\{x_n\}$ be a bounded random sequence. Is it true that, under some reasonable conditions (I cannot be specific), there exists a subsequence of it that c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6374 | # New Additional Maths Syllabus (Syllabus 4047) TO BE IMPLEMENTED FROM YEAR OF EXAMINATION 2014
http://www.seab.gov.sg/oLevel/2014Syllabus/4047_2014.pdf
There are some minor changes to the A Maths Syllabus in 2014. Wishing everyone taking the new syllabus all the best!
Main Differences
– knowledge of $a^3+b^3=(a+b)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6375 | # How much does symbolic integration mean to mathematics?
(Before reading, I apologize for my poor English ability.)
I have enjoyed calculating some symbolic integrals as a hobby, and this has been one of the main source of my interest towards the vast world of mathematics. For instance, the integral below $$\int_0^{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6376 | If one has a simplicial complex how does one define the adjoint boundary operator from C_k into C_k+1?
This is an alternative to defining cohomology in terms of the dual space. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6377 | ## Regular graph
### Set
context $V,E$ … set
definiendum $\langle V,E,\psi\rangle \in \mathrm{it}(E,V)$
inclusion $\langle V,E,\psi\rangle$ … undirected graph
range $k\in \mathbb N$ range $v\in V$
postulate $\exists k.\ \forall v.\ d(v)=k$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6378 | 7 edited tags
6 added 5 characters in body; deleted 91 characters in body; edited title
WhatistheAsociated sum series of the Euler Product ofover the Twin Primes?
Please consider the (presumably infinite) Euler product over the twin primes:
$$f(z) = \prod_{p\in\mathbb{P}}^{\infty} \Big( 1 - \frac{1}{p(p+2)} frac{1}{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6379 | # Chapter 10 – Eigenvalues and Eigenvectors
###### Prerequisites & Objectives
• Prerequisites for Eigenvalues and Eigenvectors [PDF] [DOC]
• Objectives of Eigenvalues and Eigenvectors [PDF] [DOC]
###### Textbook Chapter
• Textbook Chapter of Eigenvalues and Eigenvectors [PDF] [DOC]
###### Digital Audiovisual Lectures
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6380 | # y=x^-4
y=x^-4
You can still ask an expert for help
• Questions are typically answered in as fast as 30 minutes
Solve your problem for the price of one coffee
• Math expert for every subject
• Pay only if we can solve it
Vertical Asymptotes: x=0
Horizontal Asymptotes: y=0
No Oblique Asymptotes |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6381 | # Properties of Complex Numbers
Properties of complex numbers are given as follows:
## Theorem 1: The operations of addition and multiplication of complex numbers satisfy the commutative, associative and distributive laws.
Let $z_1=(a,b)$, $z_2=(c,d)$ and $z_3=(e,f)$ be three complex numbers.
### i. Commutative Law... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6382 | # Structural Inductions
I'm looking at 2 versions of textbook for structural induction and I just can't understand structural induction and how to draw the rooted trees from it. Does anyone have a good resource or can help me lighten up my brain so that I can understand it?
Maybe it's better if I give an example... H... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6383 | # Order is Preserved on Positive Reals by Squaring/Proof 1
## Theorem
$x < y \iff x^2 < y^2$
## Proof
### Necessary Condition
Assume $x < y$.
Then:
$\ds x < y$ $\implies$ $\ds x \times x < x \times y$ Real Number Ordering is Compatible with Multiplication $\ds x < y$ $\implies$ $\ds x \times y < y \times y$ Rea... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6368 | # Prove that a function is an open mapping.
Let A be a set;let {$X_\alpha$}$_\alpha{_\in{_J}}$ be an indexed family of spaces and let {$f_\alpha$}$_\alpha{_\in{_J}}$ be an indexed family of functions $f_\alpha$:A $\rightarrow X{_\alpha}$. Let $\mathfrak J$ be the coarsest topology on A relative to which each of the fu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6370 | # Proving that the genus of a nonsingular plane curve is $\frac{(d-1)(d-2)}{2}$
I'm studying from Joseph Silverman's book The Arithmetic Of Elliptic Curves and I'm trying to do as many exercises as I can. Right now I'm trying to do Exercise 2.7 from chapter II which reads as follows.
Let $f(X, Y, Z) \in K[X, Y, Z]$ b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6372 | Articles in PressVolume 7, Issue 3 (2019)
Authors : Most. Ummey Kulsum and Shahanaj Pervin Title : Exact Travelling Wave Solutions of Some Non-linear Evolution Equations Using Rational Sine-Cosine Function Method Volume, Issue, Year : 7(3)(2019) Pages : 1−9
Abstract: In this paper, we establish a variety of exact tr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19648 | # December 5, 2020 Single Round Match 794 Editorials
#### FakeReportData
Even though the statement pretends that the data should be random, the easiest way is to come up with a fixed pattern.
What is a nice five-digit number that has all digits distinct? For example, 12345.
What’s another one, but now starting with... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19649 | Question
Troy travels 100 miles in 2 hours. Find the unit rate of speed by filling in the missing number.
100 miles/ 2hours = ? miles/ 1 hour = ? miles/hour
Answers
1. niczorrrr
Answer:
50 miles/1 hour = 50 miles/hour
Step-by-step explanation:
The fraction is reduced by dividing numerator and denominator by their c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19650 | Homework Help: Simplifying to a Geometric Series
1. Nov 30, 2011
xago
1. The problem statement, all variables and given/known data
I have a question with asks to solve a differential equation via power series and I've done everything up to finding the recurrence relation which is a$_{n+2} = -$$\frac{a_{n}}{n+2}$
Gi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19652 | Tags
#cfa #cfa-level-1 #economics #microeconomics #reading-13-demand-and-supply-analysis-introduction #study-session-4
Question
Positive income elasticity simply means that as [...] rises, [...] also rises.
income
Demand for the good
Tags
#cfa #cfa-level-1 #economics #microeconomics #reading-13-demand-and-supply-anal... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19653 | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Congruent Angles and Angle Bisectors ( Read ) | Geometry | CK-12 Foundation
You are viewing an older version of this Concept. Go to the latest version.
# Congruent Angles and Angle Bisectors
%
Best Score
Practice Congruent Angles and Angle Bisectors
Best Sco... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19654 | ## Calculus Question?
Find the equation of the tangent line to y =square root of x at P = (4; 2) by computing the limit of slopes of secant lines between the point P and a point Q on the graph which approaches P. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19655 | # Page 2 College-Level Mathematics Study Guide for the ACCUPLACER® test
#### Factoring
Factoring is the process of breaking down a unified whole into the product of its pieces. For example:
$24$ can be factored into $2 \cdot 2 \cdot 2 \cdot 3$
This particular case is also the prime factorization of the number. (Pri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19656 | # Proof verification and advice needed for a measure on a semialgebra
Note that the definition of a measure here is different than in most contexts.
Let $\mathcal{C}$ be a semialgebra. A function $\mu: \mathcal{C} \to [0, \infty]$ is a measure if:
1. $\mu(\emptyset) = 0$
2. For any sequence of pairwise disjoint sets... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19658 | # Using integrals to get volume, center of mass, and surface area
1. Nov 28, 2007
### ns5032
1. The problem statement, all variables and given/known data
For the homogeneous ice-cream cone that is given in spherical coordinates by rho= pi/4 (the bottom part) and phi=cos(rho) (the top part), find the volume, the cen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19659 | # Representing a stochastic integral as product of a unknown random variable and a standard normal random variable
Consider a probability space $(\Omega,\mathcal F, (\mathcal F_t)_{t\geq0},\mathbb P)$ where $\mathbb F=(\mathcal F_t)_{t\geq0}$ is generated by $B=(B_t)_ { t \geq 0}$ a standard brownian motion starting a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19660 | Limited access
List Settings
Sort By
Difficulty Filters
Page NaN of 1946
Let $A=(1,0,2)$, let $B=(1,2,3)$, and let $C=(2,3,4)$.
If the area of the triangle $ABC$ is $\sqrt{T}$, what is $T$?
Accuracy 0%
Select an assignment template |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19662 | # What is 4/7 as a decimal?
## Solve it
Recurring decimals are decimal numbers that have one digit or a sequence of digits that are repeated or recurring.
These decimals are the results of long division from certain fractions. It is not necessary that the long division of all fractions give the remainder 0.
The lon... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19663 | Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 10 Ordinary Differential Equations Ex 10.1 Textbook Questions and Answers, Notes.
## Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 10 Ordinary Differential Equations Ex 10.1
Question 1.
For each of the following equations, determ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19657 | ## Insight Things
### A scientific blog revealing the hidden links which shape our world
#### Tag: mean
An often forgotten formula for the mean of a random variable $X$ is given by:
$\displaystyle \mu=E(X)=\sum_{x=0}^{\infty} \Big(1-F(x)\Big)$
And for the continous case:
$\displaystyle \mu=E(X)=\int_{x=0}^{\infty... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19651 | # Point Charge Given Field Maps
Tags:
1. Feb 6, 2015
### END
1. The problem statement, all variables and given/known data
The electric field map is shown below. (Take it to be a self-consistent scale drawing at a particular moment in time.)
where $\mathrm{q}_4 = +10 C, \mathrm{q}_6 = +10 C$
What is the charge of $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19661 | An interlacing property of order statistics
In this post, we present an interlacing property of order statistics.
Suppose we have a distribution ${F}$ on real line ${\mathbb{R}}$ and ${\theta_i \overset{\text{iid}}{\sim} F}$ where ${i=1,\dots, n}$ and ${\overset{\text{iid}}{\sim}}$ means “independently and identicall... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20000 | # Forsaken Fortress Strategy Free Download [pack] PORTABLE
The Infectious Madness of Charles Charles Charles Charles of the Waltons Charles Dickens Charles Dickens Charles Dickens of Nineteen-Eighty Charles Dickens – The Prisoner Charles Dickens – Oliver Twist Charles Dickens – David Copperfield Charles Dickens – Grea... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20001 | # Separate limits in binomial coefficient series
In reading an old book I stumbled upon this expression
$$\sum_{k=0}^n {n \choose k} q^k (1-q)^{n-k} f(n,k)=0$$
With the trick of setting $\lambda=nq$ the author lets $n \to \infty$ and $q \to 0$, resulting in
$$\sum_{k=0}^{\infty} e^{-\lambda} \frac{\lambda^k}{k!} \l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20002 | # WIR_20B_M251-H1.pdf - Math 251 Summer 2020 Week-In-Review 1...
• 3
This preview shows page 1 - 2 out of 3 pages.
Math 251 - Summer 2020 Week-In-Review 1 Math 251 - Week-In-Review 1 Justin Cantu Problem Statements You should attempt the problems yourself first. The next section contains the solutions. 1. What does ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20003 | # The Strong Measure Zero Game
## Background
Originally, my first post was going to be an introduction to selection principles, especially those in topology, and a few other related concepts. I decided I could not do justice to the subject in one post (especially with my minimal knowledge), and have opted to present ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20004 | # On quasi-zero divisor graphs of non-commutative rings
Document Type : Research Paper
Authors
Faculty of Mathematical sciences, Shahrood University of Technology, Shahrood, Iran.
10.29252/asta.5.2.1
Abstract
Let $R$ be an associative ring with identity. A ring $R$ is called reversible if $ab=0$, then $ba=0$ for ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20005 | # nLab Mostowski's collapsing lemma
Mostowski’s collapsing lemma states that any extensional well-founded relation is isomorphic to a (necessarily unique) transitive set.
Mostowski’s lemma can be proven in ZF set theory using the axiom of replacement and axiom of separation. In set theories that are not powerful enou... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20006 | # Hausdorff dimension for bounded set
Let $$F$$ be the set of of numbers $$x\in [0,1]$$ with base 3 expansions $$0.a_1a_2...$$ for which there exists an integer k such that $$a_i\neq 1$$ for all $$i\geq k$$. Find the Hausdorff dimension of $$F$$.
Note that $$F$$ is the countable union of $$F_k$$ where $$F_k$$ is the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20007 | ## exponential plateau graph
Exponential Growth. Often you will set that to a constant value based on your experimental design, but otherwise Prism can fit it. fitting Y = Ae^rX to a set of given a set of x,y points? Join Yahoo Answers and get 100 points today. Characteristics of exponential distribution. © 1995-2019 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20008 | #### Volume 21, issue 1 (2017)
Recent Issues
The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
Sharp geometric and f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20009 | Show Summary Details
More options …
Wood Research and Technology
# Holzforschung
### Cellulose – Hemicelluloses – Lignin – Wood Extractives
Editor-in-Chief: Faix, Oskar
Editorial Board: Daniel, Geoffrey / Militz, Holger / Rosenau, Thomas / Salmen, Lennart / Sixta, Herbert / Vuorinen, Tapani / Argyropoulos, Dimitris... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20010 | # Necessary Condition for Rectifiability Involving Wasserstein Distance W2
@inproceedings{Dkabrowski2020NecessaryCF,
title={Necessary Condition for Rectifiability Involving Wasserstein Distance W2},
author={Damian Dkabrowski},
year={2020}
}
A Radon measure μ is n-rectifiable if μ ≪ H n and μ-almost all of supp μ can b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20012 | Workers and employment - class-VII
Description: workers and employment Number of Questions: 59 Created by: Amit Pandey Tags: livelihood and struggles of urban workers employment: growth, informalisation and other issues social science economic sources employment and unemployment in india - problems and policies econo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20013 | Evaluate the Integral $$\int_{0}^{\infty} x^{s-1} \cos(2\pi ax) \mathrm{d}x$$
How to evaluate
\int\limits_{0}^{\infty} x^{s-1} \cos(2\pi ax) \mathrm{d}x
\tag{1}
\label{eq:mtc-1}
was part of a question posed at Mathematics Stack Exchange. Note that this is the Mellin transform of the indicated cosine function.
The o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20015 | Language: Search: Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.
Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 0880.34018
El-Reheem, Z.F.A.
On some trace formula for the Sturm-Liou... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20014 | # Quantum math revisited
It’s probably good to review the concepts we’ve learned so far. Let’s start with the foundation of all of our math, i.e. the concept of the state, or the state vector. [The difference between the two concepts is subtle but real. I’ll come back to it.]
#### State vectors and base states
We us... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20011 | Example 5-2-1 - Maple Help
# Online Help
###### All Products Maple MapleSim
Chapter 5: Applications of Integration
Section 5.2: Volume of a Solid of Revolution
Example 5.2.1
If $A$ is the plane region bounded by the $x$-axis and the graphs of $y={x}^{2}$ and $x=1$, use the method of disks to calcul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9568 | Next: 12.6 Trigonometric Functions Up: 12. Power Series Previous: 12.4 The Exponential Function Index
# 12.5 Logarithms
12.37 Definition (Logarithm.) Let . The logarithm of is the unique number such that . We denote the logarithm of by , Hence
(12.38)
12.39 Remark. Since is the unique number such that , it fo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9569 | Rank of a matrix
1. The problem statement, all variables and given/known data
Find all possible values of rank(A) as a varies.
A=[1, 2, a]
[-2, 4a, 2]
[a, -2, 1]
A is 3x3, just merge the 3 row vectors.
3. The attempt at a solution
I have the solution but I create this thread to find the most effective/efficient p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9570 | # action of symmetric group on the second exterior power
Let $$e_i \wedge e_j \ (i < j)$$ be a basis for the $$\mathbb Z$$-module $$\wedge^2 \Gamma$$, where $$\Gamma = \mathbb Z^n$$. Clearly $$S_n$$ acts on the module $$\wedge^2 \Gamma$$ via $$\pi(e_i \wedge e_j) = e_{\pi(i)} \wedge e_{\pi(j)} \ \ \ \forall \pi \in S_... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9571 | # How prove that $\lim\limits_{x\to+\infty}f(x)=\lim\limits_{x\to+\infty}f'(x)=0$ if $\lim\limits_{x\to+\infty}([f'(x)]^2+f^3(x))=0$?
Question:
Let $f$ be differentiable on $[0,+\infty)$, such as$$\lim_{x\to+\infty}\left([f'(x)]^2+f^3(x)\right)=0$$show that $$\lim_{x\to\infty}f(x)=\lim_{x\to\infty}f'(x)=0$$
I think ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9572 | Question
# Evaluate the indefinite integral as an infinite series. \int \frac{\cos x-1}{x} dx
Integrals
Evaluate the indefinite integral as an infinite series. $$\int \frac{\cos x-1}{x} dx$$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9573 | # Find the average velocity of the ball over the time interval from 4 to 4+h seconds when h cant = 0? When a ball is thrown vertically upwardinto the air with a velocity of 67 ft/sec itsheight, y(t), in feet after t seconds is given byy(t) = 67t − 16t^2 .
By definition, the average velocity on the time interval `[t_1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9577 | Sal adds (5+2i) and (3-7i) . Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
We're asked to add the complex number 5 plus 2i to the other complex number 3 minus 7i. And as we'll see, when we're adding complex numbers, you can only add the real parts to each other and you can on... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9578 | # Probabilistic interpretation of prime number theorem
Suppose there is a function f(x) which is the "probability" that the integer x is prime. The integer x is prime with probability f(x), and then divides the larger integers with probability 1/x; so as x changes from x to x+1, f(x) changes to (roughly)
f(x).(1-f(x)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9581 | Search for a tool
Derangements
Tool for generating derangements. In mathematics, a derangement is a permutation of distinct objects without fixed point, ie that no object is in its original position.
Results
Derangements -
Tag(s) : Combinatorics,Mathematics
dCode and you
dCode is free and its tools are a valuable... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9582 | #### DOCUMENTA MATHEMATICA, Vol. 4 (1999), 285-340
Kengo Matsumoto
Presentations of Subshifts and Their Topological Conjugacy Invariants
We introduce the notions of symbolic matrix system and $\lambda$-graph system that are presentations of subshifts. They are generalized notions of symbolic matrix and $\lambda$-gra... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9574 | # Does the series $\sum_{n\in\mathbb{Z}} \exp\left(-\sum_{k=-n}^{+n}\cos(k)\right)$ converge or diverge?
Does the following series converge or diverge? $$\sum_{n\in\mathbb{Z}} \exp\left(-\sum_{k=-n}^{+n}\cos(k)\right)$$
-
What is $\mathbb{Z^2}$? – Ron Gordon Jan 19 '13 at 13:54
Use \exp instead of e^ when the exponen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9576 | # Honors Algebra 2: Extra Practice Conics
• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown
Calculator Active.
1. Identify the following by what kind of conic section it is:
1. $$\displaystyle x = -3\left(y + 1\right)^2 + 2$$
2. Solution
sideways parabola
3. $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9579 | # Home
Score : $500$ points
### Problem Statement
Snuke has two boards, each divided into a grid with $N$ rows and $N$ columns. For both of these boards, the square at the $i$-th row from the top and the $j$-th column from the left is called Square $(i,j)$.
There is a lowercase English letter written in each square... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.