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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18520 | The Duplicators, Part I: Eutocius' Collection of Cube Duplications - Notation
Author(s):
Colin B. P. McKinney (Wabash College)
For readability, I’ve “translated” some of the mathematical statements into what I think is an abbreviated form. Table 1.1 gives a brief list.
tri.(ABΓ) The triangle with vertices A, B, Γ. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18521 | # How useful is knowing every torsionfree $\mathcal O(D)$ module is flat?
One of the corollaries of Weiertrass' factorization theorem plus the theorem of Mittag Leffler is that $\mathcal O(\Bbb C)$, more generally $\mathcal O(D)$ for some region $D$ is such that every finitely generated ideal is principal$^1$, since i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18522 | ### Home > PC > Chapter 2 > Lesson 2.1.1 > Problem2-10
2-10.
1. Factor out (x + 2) from each expression, then simplify. Homework Help ✎
1. (x + 2)2 − 3(x + 2)
2. (x + 2)3 − 4(x + 2)
3. 2(x + 2)2 + 6(x + 2) |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18523 | # Sprague-Grundy Theorem
This week, we continue our study of Impartial Games by learning about the Sprague-Grundy Theorem.
You may first choose to read the post Winning Positions if you have not already done so.
How would you solve the following?
1) The game Turning Turtles is played with a row of $n$ turtles, each... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18525 | # Math Help - I need help with finding sin and cos please.
1. ## I need help with finding sin and cos please.
The problem is $tan= -\frac{2} {3}$. I can't find sin or cos, How can I find them? I know Tangent is $\frac{x} {y}$ I know it can't be sin=-2 and cos=3, can it?
Thanks
Jason
2. First, you can't simply writ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18526 | How many arrangements?
Given all four digits odd numbers.How many of them have exactly two even numbers?
The sample set is $\{0,1,2,3,4,5,6,7,8,9\}$. To have a odd number, the last digit have to be odd, so there are five possible ways to the last digit. In order to have a four digit number, the first can't be zero. I... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18527 | Enable contrast version
# Tutor profile: Nicolaus S.
Inactive
Nicolaus S.
Third Year Mathematics Major at UC Davis
Tutor Satisfaction Guarantee
## Questions
### Subject:Pre-Calculus
TutorMe
Question:
What is $$sec(45)$$?
Inactive
Nicolaus S.
Secant is the opposite of cosine. Cosine is $$\dfrac{adjacent}{hypoten... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18512 | ## The future of the MLS program
University of Maryland (am affiliated, but not with this effort) just wrapped up an effort to look at what the MLS should be for the next few years. Many librarians gripe about their programs - how they didn't learn what they needed or learned stuff they don't use or isn't relevant. Th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18513 | • 333,079
# Posts Tagged ‘free ebooks’
## Project gutenberg has “Calculus Made Easy” by Silvanus P. Thompson
Posted by peeterjoot on May 4, 2013
One of my favorite books [1], a great little book that my grandfather gave me, is now available on project gutenburg (free ebooks transcribed from old out of print materia... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18519 | ## Calculating Percent Dissociation
#### Learning Objective
• Calculate percent dissociation for weak acids from their Ka values and a given concentration.
#### Key Points
• Percent dissociation is symbolized as α (alpha) and represents the ratio of the concentration of dissociated hydrogen ion [H+] to the concentr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18524 | # 1st and 2nd moment of interia of curves and surfaces
1. ### Jhenrique
686
If I can to calculate the 1st and 2st moment of inertia of areas and volumes, I can compute for curves and surfaces too?
2. ### SteamKing
8,789
Staff Emeritus
First, you must define what you mean by the moment of inertia of a curve or surfa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13760 | # Examples of Besov functions of power-logarithmic type $|x|^{\alpha} |\log |x||^{\beta}$
I'm stuck on the following exercise 17.9 from Leoni's text A first course in Sobolev Spaces (second edition). This is from the chapter on Besov spaces, but this is really just a integral inequality which should only need basic an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13763 | 1. ## Differentiate
I don't understand the attached question. There might be a misprint.
2. $f(x) = 6 \sin (x) + \sqrt{2} \cos (x)$
$f'(x) = 6 \cos (x) - \sqrt{2} \sin (x)$
$f''(x) = -6 \sin (x) - \sqrt{2} \cos (x) = -[6 \sin (x) + \sqrt{2} \cos (x)] = -f(x)$
3. Thanks, I can see now its a standard notation for th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13764 | # mathr / blog / #
## Atom domain coordinates
Previously I wrote about atom domain size estimates in the Mandelbrot set. A logical step given $$G(c) = 0$$ at the center and $$|G(c)| = 1$$ on the boundary is to take $$G(c)$$ as the atom domain coordinate for $$c$$. It turns out to make sense to make $$1 \le q \lt p$$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13765 | # Are there seemingly paradoxical consequences of the axiom of determinacy?
So I've been thinking about the axiom of choice (AC) and the axiom of determinacy (AD), which are known to be inconsistent with each other. Some qualitative similarities of them are:
• they are both trivial in the 'finite' case
• they have us... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13766 | # MATH 135
Mathematical proofs.
Section 004
Instructor:
Name: Ross Willard
Office: MC5058
Email: rdwillar@uwaterloo.ca, ross.willard@uwaterloo.ca
Office Hours: Tuesdays 9:00AM-10:00AM , Fridays 1:00PM-2:00PM, in MC 5058
Tutorials: Tuesdays 4:30PM-7:20PM (Drop-in to Biology 1 Room 271)
# 9/9/13
Show $$\sqrt{x}(x-\s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13767 | # Tag Info
## Hot answers tagged functional-analysis
4
Under the assumption that $\epsilon$ is constant across $a$, then no additional assumptions are needed. Suppose that $x_a$ is the fixed point of $f_a$, and choose $e>0$. Then there is a $\delta$ such that for all $b$ within $\delta$ of $b$, you have $e\epsilon\g... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13768 | # Integrating $\int x\sin x dx$
Could someone outline the step-by-step approach for the following indefinite integral?
$$\int x\sin x \ dx$$
I know the solution is $\sin(x)-x\cos(x)$, but cannot see how one would go about step-wise solving for it in a logical manner that does not include arbitrary guessing (even wit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13769 | Contents
topos theory
# Contents
## Statement
###### Proposition
Let $(\mathcal{C}, \tau)$ be a small site. Then the full subcategory inclusion $i \colon Sh(\mathcal{C},\tau) \hookrightarrow PSh(\mathcal{C})$ of its category of sheaves (Grothendieck topos) into its category of presheaves is a reflective subcategor... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13771 | Home > Standard Error > Standard Error As Percentage
# Standard Error As Percentage
## Contents
Compare portfolio manager performance using the information ratio. In regression analysis, the term "standard error" is also used in the phrase standard error of the regression to mean the ordinary least squares estimate ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13772 | Search by Topic
Resources tagged with Factors and multiples similar to Filling the Gaps:
Filter by: Content type:
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There are 91 results
Broad Topics > Numbers and the Number System > Factors and multiples
Divisibility Tests
Stage: 3, 4 and 5
This article takes the reader through divisibili... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13773 | # When can we assume this identity about series?
Suppose we are given that $$\sum_{i =a} ^b f (i)g (i) =\sum_{i =a} ^b f (i)h (i) \tag {1}$$ when can we conclude that $$\forall i =a,…,b:g(i)=h(i) \tag {2}$$ ?
For example, if $g, h$ are both linear and $\sum_i i f(i)\not = 0$ then $(1)\implies (2)$.
Is there a name f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13775 | 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 1180.47040
Cianciaruso, Filomena; Marino, Giuseppe; Muglia, Luigi; Ya... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13761 | # Is there any relation between the eigenvalues of possibly non-Hermitian matrix A and those of exp(A)?
Is there any relation between the eigenvalues of possibly non-Hermitian matrix A and those of exp(A)?
For hermitian matrices, they are just exponentials of the corresponding values. But in general, any relation?
T... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13762 | Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13770 | ### Home > INT3 > Chapter 4 > Lesson 4.3.2 > Problem4-81
4-81.
1. $\sqrt { x } + 2 = x$
First isolate the radical by subtracting $2$ from both sides.
$\sqrt{x} = x - 2$
Square both sides.
$x=x^2−4x+4$
Set the equation equal to $0$.
$x^2−5x+4=0$
Factor.
$(x−4)(x−1)=0$
$x=4$ ($x=1$ is extraneous)
1. $\sqrt { x } ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_13774 | # The discretization trick
I explain the discretization trick that I mentioned in my previous post (Posterior consistency under possible misspecification). I think it was introduced by Walker (New approaches to Bayesian consistency (2004)).
Let $\mathbb{F}$ be a set of densities and let $\Pi$ be a prior on $\mathbb{F... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15154 | # NCERT Class 12-Mathematics: Chapter – 9 Differential Equations Part 17 (For CBSE, ICSE, IAS, NET, NRA 2023)
Get unlimited access to the best preparation resource for CBSE/Class-12 : get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-12.
Question 76: Fill in the blanks of the follow... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15155 | # Rectifiability of metric flat chains and fractional masses
created by stepanov on 16 Nov 2007
modified on 11 Oct 2010
[BibTeX]
Published Paper
Inserted: 16 nov 2007
Last Updated: 11 oct 2010
Journal: J. Math. Sciences (N.Y.)
Volume: 167
Number: 3
Pages: 406-417
Year: 2010
Notes:
(preprint 2007)
Abstract:
It i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15156 | # Minimum distance between closed sets.
I understand that if given a compact set K and a closed set C,that are disjoint, of a metric space then it follows that there is a minimum distance between them(You can prove this via a continuous function $\varphi_C:K\to R$ that contains the distance information and show that i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15158 | # zbMATH — the first resource for mathematics
Friable values of binary forms. (English) Zbl 1268.11136
Let $$P^+(n)$$ denote the largest prime factor of $$n$$ and let $$F\in\mathbb Z[X,Y]$$ be an integral binary form of degree $$t\geq 2$$. The authors consider the problem of how small $$y$$ can be as a function of $$x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15159 | # Counterexamples around Cauchy condensation test
According to Cauchy condensation test: for a non-negative, non-increasing sequence $$(u_n)_{n \in \mathbb N}$$ of real numbers, the series $$\sum_{n \in \mathbb N} u_n$$ converges if and only if the condensed series $$\sum_{n \in \mathbb N} 2^n u_{2^n}$$ converges.
Th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15160 | ## Intermediate Algebra (6th Edition)
We are given that $h(x)=7$. $h(-\frac{3}{4})=7$ In this example, h(x) does not depend on x and will be equal to 7 for any value of x. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15161 | My Math Forum Finite mapped on infinite set
User Name Remember Me? Password
Number Theory Number Theory Math Forum
February 26th, 2018, 09:49 PM #1 Senior Member Joined: May 2015 From: Arlington, VA Posts: 410 Thanks: 27 Math Focus: Number theory Finite mapped on infinite set Can a finite set ever be mapped onto... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15162 | # Find the probability that 8 or more will feel that the system is adequate. Find the probability that exactly 8 will feel that the system is adequate.
Only 20% of the people in a large city feel that its mass transit system is adequate. If 20 persons are selected at random, find the probability that 8 or more will fe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15163 | 2 Cu(OH) 2(s) → 2 CuO (s) + 2 H 2 O (l) + O 2(g) Reactions [ edit ] Copper(II) oxide dissolves in mineral acids such as hydrochloric acid , sulfuric acid or nitric acid to give the corresponding copper(II) salts: [4] Step 7: CuO(s) + H2SO4(aq) -> CuSO4 + H2O(l) – Double Replacement Step 9: Zn(S) + H2SO4(aq) -> ZnSO4(a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15164 |
# 7.1: Rational and Irrational Numbers
Skills to Develop
• Identify rational numbers and irrational numbers
• Classify different types of real numbers
be prepared!
Before you get started, take this readiness quiz.
1. Write 3.19 as an improper fraction. If you missed this problem, review Example 5.1.4.
2. Write $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15165 | # Spin glasses overlap
Suppose you have a spin glass simulation in which the standard Metropolis MC algorithm is used to sample phase space. The we calculate the equivalent for the lattice system of the self intermediate scattering function, namely: $$C(\tau) = \frac{1}{N}\sum_i^N\left<\sigma_i(t)\sigma_i(t+\tau)\righ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15167 | Stringy Things
# Notes on String Theory: Conformal Group in 2-dimensions
1. Introduction: Conformal Group in 2-dimensions
Following our previous study of the d-dimensional conformal group and the generators of conformal transformations, we now turn our attention to the study of the conformal group in 2-dimensions. A... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15153 | # [pdftex] pdflatex and algorithms package
Roberto Posenato roberto.posenato at univr.it
Sat Sep 10 10:02:28 CEST 2005
Hi everyone,
I would like to know if anyone has already seen the following algorithms
package
compilation problem with pdflatex.
*CURRENT CONFIGURATION*
--------------------------------
I'm writing... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15157 | # Attempt at Finding the Best Linear Unbiased Estimator (BLUE)
Let $$X_1,...X_n$$ be iid $$N(0,\sigma^2)$$ where $$\sigma$$ is unknown. My task is to find the BLUE for $$\sigma$$ within the set of linear functions of $$|X_i|$$ for $$i=1,...,n$$. Here is my work thus far:
First, let $$T=\sum_{i=1}^nc_i|X_i|$$ be an es... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15166 | # $T :\mathbb {R^7}\rightarrow \mathbb {R^7}$ is defined by $T(x_1,x_2,\ldots x_6,x_7) = (x_7,x_6,\ldots x_2,x_1)$ pick out the true statements.
Consider the linear transformations $T :\mathbb {R^7}\rightarrow \mathbb {R^7}$ defined by $T(x_1,x_2,\ldots x_6,x_7) = (x_7,x_6,\ldots x_2,x_1)$. Which of the following stat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15152 | # Sorry I don't know why it cropped like that but this is all the important information...
###### Question:
Sorry I don't know why it cropped like that but this is all the important information
##### Suppose you are the president of the student government. You wish to conduct a survey to...
Suppose you are the presi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1888 | # Betti sequence of finite dimensional commutative algebras
Given a finite dimensional commutative local $$K$$-algebra $$A$$ for a field $$K$$. Associated to $$A$$ is its dimension $$d_A$$ and the Betti-sequence $$c_i=dim(Ext_A^i(S,S))$$ where $$S$$ is the unique simple $$A$$-module.
Question: Are there only finitely... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1889 | ## Precalculus (6th Edition) Blitzer
Fill the blank with: $\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
The equation for the quadratic formula is $x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ You can find it in the text just before example 10. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1891 | # A mathematical model for early retirement
Earlier I wrote about a mathematical model for beard growth and awesomeness. In that discussion I briefly described a similar model for net worth growth. It turns out, though, that your actual net worth number is not a particularly useful measure for determining when you can... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1892 | <meta http-equiv="refresh" content="1; url=/nojavascript/">
You are reading an older version of this FlexBook® textbook: CK-12 Chemistry - Intermediate Go to the latest version.
# 24.2: Half-Life
Difficulty Level: At Grade Created by: CK-12
## Lesson Objectives
• Define half-life as it relates to radioactive nuclid... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1893 | ## Hiroshima Mathematical Journal
### Geodesic orbit manifolds and Killing fields of constant length
Yuriĭ G. Nikonorov
#### Abstract
The goal of this paper is to clarify connections between Killing fields of constant length on a Rimannian geodesic orbit manifold $(M,g)$ and the structure of its full isometry group... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1896 | # Problem 5, 1968 IMO
Problem
Let a\gt 0 be a real number and f(x) a real function defined on all of \mathbb{R}, satisfying for all x\in\mathbb{R},</p>
f(x)=\frac{1}{2}+\sqrt{f(x)-f^2(x)}.
a) Prove that the function f is periodic; i.e., there exists b\gt 0 such that for all x, f(x+b)=f(x).
b) Give an example of su... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1897 | How do you write 30 8/10 as a decimal?
How do you write 30 8/10 as a decimal?
ReportAnswer 1
$30.8$
Explanation:
As an example :
$\text{ } 9.2354 \to 9 + \frac{2}{10} + \frac{3}{100} + \frac{5}{1000} + \frac{4}{10000}$ and so on
So $30 \frac{8}{10} \to 30 + \frac{8}{10} \to 30.8$
Add Answer of: How do you write ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1898 | Tag Info
65
This is a bit of a can of worms. Let's unpack a little. We were given no additional information other than that stated in the page. This is your daughter's homework, not yours. Be careful with this distinction, because coloring a child's question with adult interpretations can lead to trouble (and does in... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1899 | # A cast iron pipe of diameter 600 mm and length 400 m carries water from a tank and discharges freely into air at a point 4.5 m below the water surface in the tank. The friction factor of the pipe is 0.018. Consider acceleration due to gravity as 9.81 m/s2. The velocity of the flow in pipe (in m/s, (round off to two d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1900 | # regression to the mean saying
Rather, the characteristics in the offspring regress towards a mediocre point (a point which has since been identified as the mean). In no sense does the future event "compensate for" or "even out" the previous event, though this is assumed in the gambler's fallacy (and the variant law ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1901 | Jordan Watts' Homepage
## Differential Forms on Singular Spaces
Differential forms are an extremely useful concept for smooth manifolds. They are the input for integration, allowing one to find volumes, centres of mass, among other measurements; they are the foundation for global invariants such as de Rham cohomology... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1902 | # I Need for Lorentz transformation in pre-relativity period
Tags:
1. Jan 23, 2017
### faheemahmed6000
What was the need for Lorentz transformation in pre-relativity period?
Why was it necessary for the velocity of light to be invariant between different inertial frames and hence what was the need for Lorentz trans... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1894 | # American Institute of Mathematical Sciences
• Previous Article
Optimal $L^2$-control problem in coefficients for a linear elliptic equation. I. Existence result
• MCRF Home
• This Issue
• Next Article
Transformation operators in controllability problems for the wave equations with variable coefficients on a half-axi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1895 | # Problem with nonhomogeneous ODE
I'm trying to find the general solution for the ODE $$f''(t)+f(t)=\frac16\sin^3t,\tag{1}$$ but something keeps going wrong. I first set $x_1=f$, $x_2=x_1'$, so letting $$A=\left[\begin{array}{cc}0 & 1\\-1 & 0\end{array}\right],\quad x=\left[\begin{array}{c}x_1\\x_2\end{array}\right],\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1903 | # Uniqueness of a SDE with non-negativity constraint
I am working on the following SDE (but we will dealing only with deterministic object: $\omega\in\Omega$ is fixed): $$\label{sde}%sde x_t=\underbrace{\xi_0+\int_0^tb(s,x_s)\,ds+\int_0^t\sigma(s,x_s)\,dW_s}_{=:z_t}+y_t$$ where $y_t=\sup_{0\le s\le t}(z_s)^{-}$ is the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1890 | Homework Help: Probability w/ continuous R.V
1. Jan 2, 2014
DotKite
1. The problem statement, all variables and given/known data
A commercial water distributor supplies an office with gallons of water once
a week. Suppose that the weekly supplies in tens of gallons is a random
variable with pdf
f(x) = 5(1-x)^4 , 0... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4256 | # How do you use FOIL to multiply (x-2)^2 (x+17)?
Jun 23, 2015
FOIL will only get you part of the way, but...
${\left(x - 2\right)}^{2} \left(x + 17\right)$
$= \left({x}^{2} - 4 x + 4\right) \left(x + 17\right)$
$= {x}^{3} + 13 {x}^{2} - 64 x + 68$
#### Explanation:
FOIL will only get you part of the way since o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4257 | # zbMATH — the first resource for mathematics
Generalized Deligne-Lusztig characters. (English) Zbl 0812.20024
Let $${\mathbf G}^ 0$$ be a connected reductive algebraic group defined over the algebraic closure of a finite field $${\mathbf F}_ q$$ and let $$\sigma$$ be an outer automorphism of $$\mathbf G^ 0$$. Form th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4260 | # Do harmonic numbers have a “closed-form” expression?
One of the joys of high-school mathematics is summing a complicated series to get a “closed-form” expression. And of course many of us have tried summing the harmonic series $H_n =\sum \limits_{k \leq n} \frac{1}{k}$, and failed. But should we necessarily fail?
M... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4261 | Are equivalent rational polynomials still equivalent if not all of their limits at corresponding points are equal?
Apologies if I've used terms incorrectly. What I mean:
1. Far as I know, the limit of $x-5$ exists for all real numbers.
2. $\displaystyle\frac{(x-5)(x+5)}{x+5} = x-5$
3. But the limit of the left-hand... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4263 | # Points of intersection to find area inside a region
1. Apr 12, 2010
### edough
1. The problem statement, all variables and given/known data
Use a dounble integral to find the area of the region inside r = 1+ cos (theta) and outside r = 2sin (theta). sketch region and indecate the points of intersection.
I'm conf... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4264 | # Transformations
• April 28th 2010, 11:47 AM
Transformations
I am just a little confused by the wording of this problem and I am hoping that someone might have a better idea of how to go about solving this.
Suppose that $\int\int_{D}f(x,y) dA= 3$ where D is the disk $x^2 + y^2 \leq 1$. Now suppose that E is the disk... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4265 | ## Algebraic & Geometric Topology
### Satellites of Legendrian knots and representations of the Chekanov–Eliashberg algebra
#### Abstract
We develop a close relation between satellites of Legendrian knots in $ℝ3$ and the Chekanov–Eliashberg differential graded algebra of the knot. In particular, we generalize the we... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4266 | Expii
# What Are Periodic Functions? - Expii
A function is periodic if its graph repeats after a given length (called the period), sort of like a wave. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4267 | Under the auspices of the Computational Complexity Foundation (CCF)
REPORTS > DETAIL:
### Paper:
TR16-143 | 15th September 2016 09:12
#### An Almost Cubic Lower Bound for $\Sigma\Pi\Sigma$ Circuits Computing a Polynomial in VP
TR16-143
Authors: Nikhil Balaji, Nutan Limaye, Srikanth Srinivasan
Publication: 15th Sep... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4268 | # Is it possible to generalize Lebesgue-Stieltjes measure in this way?
Riemann-Stieltjes integration is available when a integrator is monotonically increasing. However, three texts i have, all define Lebesgue-Stieltjes measure with respect to monotonically increasing right-continuous function.
I don't understand why... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4269 | ## Introductory Algebra for College Students (7th Edition)
m=$\frac{y_2-y_1}{x_2-x_1}$ m=$\frac{4-1}{3-2}$ m=$\frac{3}{1}$ m=1 The slope is a positive number, therefore the line rises. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4270 | # zbMATH — the first resource for mathematics
## Huang, Ming-Deh A.
Compute Distance To:
Author ID: huang.ming-deh-a Published as: Huang, Ming-Deh; Huang, Ming-Deh A.
Documents Indexed: 56 Publications since 1984, including 2 Books
all top 5
#### Co-Authors
6 single-authored 13 Adleman, Leonard Max 7 Cheng, Qi 4... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4258 | # How do you know if 9x^2 +12x - 4 is a perfect square trinomial and how do you factor it?
Jun 7, 2015
$\textcolor{b l u e}{9 {x}^{2}}$ is a perfect square : $= \textcolor{b l u e}{{\left(3 x\right)}^{2}}$
$\textcolor{red}{4}$ is also a perfect square : $= \textcolor{red}{{2}^{2}}$
And $\textcolor{p u r p \le}{12 x} ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4262 | # The hypotenuse is 10 and the area is 24, how do you find the other lengths on the triangle?
Dec 29, 2015
$6$ and $8$.
#### Explanation:
Let the other side lengths be $a$ and $b$ and area be $A$. Then,
$\textcolor{w h i t e}{\times} A = 24$
$\implies \frac{a b}{2} = 24 \textcolor{w h i t e}{\times \times \times \t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4271 | # Thread: How to compute this double integral?
1. ## How to compute this double integral?
How to compute this double integral?$I=\displaystyle\int\displaystyle\int_{R( xy)}(3x+6y)^2dA$. How to find out R(xy) here? In the original problem $R(xy)$ region is given where A,B,C,D are labels for sides.
$A=x+2y=2,B=x-2y=2,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4259 | # Why is the integral of 1/x ln x?
Watch
Announcements
#1
Hello
We were doing FP1 topic on calculus and the teacher was about to do an example using 1/x but he was like oops it's an exception and the integral of 1/x is actually ln x.
I have no idea why this is true (my teacher didn't know/couldn't explain) and I have... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12290 | # Ding, Guoli
## Ding's tau_r vs. tau conjecture ★★★
Author(s): Ding
\begin{conjecture} Let $r \ge 2$ be an integer and let $H$ be a minor minimal \Def{clutter} with $\frac{1}{r}\tau_r(H) < \tau(H)$. Then either $H$ has a $J_k$ minor for some $k \ge 2$ or $H$ has Lehman's property. \end{conjecture}
Keywords: clutte... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12291 | ## 105.3 Thickenings
The following terminology may not be completely standard, but it is convenient. If $\mathcal{Y}$ is a closed substack of an algebraic stack $\mathcal{X}$, then the morphism $\mathcal{Y} \to \mathcal{X}$ is representable.
Definition 105.3.1. Thickenings.
1. We say an algebraic stack $\mathcal{X}'... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12292 | # Length-Norm inequality to root-n times Length (using 2|uv| <= |u|^2 + |v|^2)
1. Oct 3, 2014
### Sravoff
I've been reading "The Qualitative Theory of Ordinary Differential Equations, An Introduction" and am now stuck on an inequality I am supposed to be able to prove. I am pretty sure the inequality comes from line... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12293 | Question
# Find the principal unit normal vector to the curve at the specified value of the parameter r(t)=ti+\frac{6}{t}j , t=3
Vectors and spaces
Find the principal unit normal vector to the curve at the specified value of the parameter
$$r(t)=ti+\frac{6}{t}j , t=3$$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12294 | Math Help - Proving subsets =S
1. Proving subsets =S
Hello
Iv got an exam in a week and am trying to get through my whole course in that week. And am off to a horrible start =/
Can someone please tell how i should go about proving questions like the follwoing.
Q1)
A = {x <element_of> R | cos x = 1}
A = {x <element_... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12295 | # Integers such that all Coprime and Less are Prime
## Theorem
The following positive integers have the property that all positive integers less than and coprime to it, excluding $1$, are prime:
$1, 2, 3, 4, 6, 8, 12, 18, 24, 30$
There are no other positive integers with this property.
## Proof
Let $S_n$ denote t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12297 | # How do we check octet rule in resonance structures?
For example, this carbon has an incomplete octet:
Can we say this is because C has configuration $\mathrm{1s^2 2s^2 2p^2}$ and hence here its just forming 3 bonds whereas it should form 4 to make it $\mathrm{2p^6}$ and complete its octet? Or do we say that it's fo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12298 | Lemma 25.6.5. The category of affine schemes is equivalent to the opposite of the category of rings. The equivalence is given by the functor that associates to an affine scheme the global sections of its structure sheaf.
Proof. This is now clear from Definition 25.5.5 and Lemma 25.6.4. $\square$
In your comment you c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12299 | # dimension of momentum
There are two valid answers. Aristotle claimed that everything that is moving must be kept moving by something. by[40], Electromagnetic radiation (including visible light, ultraviolet light, and radio waves) is carried by photons.
We thus find that Kepler's equal-area law is equivalent to a st... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12300 | # How do you solve the system of equations 50x + 40= y and 30x + 45= y?
Apr 16, 2018
$x = 0.25 , y = 52.5$
#### Explanation:
$\therefore 50 x + 40 = y - - - - - - \left(1\right)$
$\therefore 30 x + 45 = y - - - - - - \left(2\right)$
$\therefore \left(1\right) - \left(2\right)$
$\therefore 20 x - 5 = 0$
$\theref... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12301 | # Open set x open set
1. Jun 18, 2011
### seydunas
Hi
i want to solve a problem about topology or analysis: Let U and V be open sets in R^n, i want to to show their dot product is open in R.
Tahnk you
2. Jun 18, 2011
### micromass
Hi seydunas!
The dot product is a composition of sums and products, so it actual... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12303 | # How do you use the binomial theorem to approximate (2.005)^10?
Feb 20, 2017
$\approx 1049.6$
#### Explanation:
${\left(2.005\right)}^{10}$
$= {2}^{10} {\left(1.0025\right)}^{10}$
$= 1024 {\left(1 + 0.0025\right)}^{10}$
$= 1024 \left(1 + \left(10\right) 0.0025 + \setminus O \left({0.0025}^{2}\right)\right)$
$\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12289 | 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 0837.35065
Euler, M.; Euler, N.; Köhler, A.
On the construction of ap... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12296 | # Finite dimensional graded commutative algebras¶
AUTHORS:
• Michael Jung (2021): initial version
class sage.algebras.finite_gca.FiniteGCAlgebra(base, names, degrees, max_degree, category=None, **kwargs)
A finite dimensional graded commutative algebra $$A$$ is an integer-graded algebra satisfying the super-algebra ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12302 | HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Invariants in Non-Commutative Variables of the Symmetric and Hyperoctahedral Groups
Abstract : We consider the graded Hopf algebra $NCSym$ of symmetric functions with non-commutative variables, which is analo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12288 | Quantum questions
0 answers
## Quantum annealing vs adiabatic quantum computation
I had this impression that quantum annealing is an optimization technique which may or may not produce exact solutions. On the other hand adiabatic quantum computation always gives exact solutions ...
1 answer
## Is the D-Wave archit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_32 | # Consider a pair of perpendicular straight lines ax^(2)+3xy-2y^(2)-5x+5y+c=0. Distance between the orthocenter and the circumcenter of triangle ABC is
Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
Updated On: 24-4-2021
Apne doubts clear karein ab Whatsapp par bh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_34 | # What are the intercepts of : 8y= - 2x - 9?
Apr 9, 2016
$x$ intercept: $\left(- \frac{9}{2} , 0\right)$
$y$ intercept: $\left(0 , - \frac{9}{8}\right)$
#### Explanation:
$x$ intercepts where $y = 0$
Therefore, substitute $y = 0$ and solve for $x$.
$0 = - 2 x - 9$
$9 = - 2 x$
$- \frac{9}{2} = x$
Therefore, $x$ in... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_35 | 5
# Valueisplays the Experimental Probability Distribution.Four Dice Roll Welcome You have 630 points.Play Again? Occurrence #requency of SixesTotal rolls is 100...
## Question
###### Valueisplays the Experimental Probability Distribution.Four Dice Roll Welcome You have 630 points.Play Again? Occurrence #requency of... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_36 | GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
It is currently 23 Feb 2020, 19:29
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 Questi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_39 | # Proving
• November 24th 2012, 04:39 AM
Thorpelizts
Proving
I'm supposed to prove the question in the attachment.....
Ive done some steps, but still cannot solve it:(
• November 24th 2012, 05:12 AM
Plato
Re: Proving
Quote:
Originally Posted by Thorpelizts
I'm supposed to prove the question in the attachment..... Iv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_41 | # zbMATH — the first resource for mathematics
Metric theory of Pierce expansions. (English) Zbl 0598.10057
Every real number $$0<x\leq 1$$ has a unique representation of the form $$x=1/a_ 1-1/a_ 1a_ 2+1/a_ 1a_ 2a_ 3-...,$$ where the integers $$a_ j$$ are determined by the algorithm $$x=x_ 0$$, $$a_ j=[1/x_{j- 1}]$$ an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_42 | College Algebra 2e
# 7.7Solving Systems with Inverses
College Algebra 2e7.7 Solving Systems with Inverses
### Learning Objectives
In this section, you will:
• Find the inverse of a matrix.
• Solve a system of linear equations using an inverse matrix.
Soriya plans to invest $10,500 into two different bonds to spre... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_44 | # Finding POI's for the follow two curves
So I need to find the POI (point of intersection) of the following two curves: \begin{align*} r & = 1 + \cos \theta, \\ r & = 2 - 2\cos \theta. \end{align*} What I did was I just set both the equations equal to each other... $$1 + \cos \theta = 2 - 2 \cos \theta$$ then isolate... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_45 | # Question: Definite integral
August 28 2012 by
false
Maple 13
4
Maple 13 does not calculate the definite integral
int(x^4/(4*x^5+2), x=0..1);
although the corresponding indefinite integral is calculated correctly. The reason?
Thank you. |
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