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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18210 | # Convergence or divergence of series
Does this series $$\sum_{k=2}^{\infty}\dfrac{\zeta{(k+1)}}{\zeta{(k)}}$$ converge or diverge?
Here $$\zeta{(k)}=\dfrac{1}{1^k}+\dfrac{1}{2^k}+\dfrac{1}{3^k}+\cdots+\dfrac{1}{n^k}+\cdots$$ If it converges, how to find the value?
If it diverges, how to prove it?
Thank you
Discus... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18211 | 172 views
The internal bisector of an angle $\text{A}$ in a triangle $\text{ABC}$ meets the side $\text{BC}$ at point $\text{D. AB = 4, AC = 3}$ and angle $\text{A} = 60^{\circ}$. Then what is the length of the bisector $\text{AD}?$
1. $\frac{12 \sqrt{3}}{7}$
2. $\frac{12 \sqrt{13}}{7}$
3. $\frac{4 \sqrt{13}}{7}$
4. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18212 | 64 US gallons in US customary cups
Conversion
64 US gallons is equivalent to 1024 US customary cups.[1]
Conversion formula How to convert 64 US gallons to US customary cups?
We know (by definition) that: $1\mathrm{usgallon}\approx 16\mathrm{uscup}$
We can set up a proportion to solve for the number of US customary... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18214 | Solving specific PDE
by stanley.st
Tags: solving, specific
P: 31 Hello, I derived a model in the form $$\begin{array}{rcl}\frac{\partial U(\vec{x},t)}{\partial t}&=&\gamma^2\Vert\nabla U(\vec{x},t)\Vert,\\\int_{\Omega}U(\vec{x},t)\, d \Omega&=&U_0,\quad\forall t\\U(\vec{x},0)&=&f(\vec{x}).\end{array}$$ I don't know t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18216 | leaf classification dataset
13 Dec leaf classification dataset
I. Generally speaking, efforts are focused on two directions: It may be good to start with some feature that is easy and generative and then check how much accuracy can be squeezed out of it. This website contains many algorithms for time series. The trai... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18217 | # The Solution of the Kadison-Singer Problem Adam Marcus (Crisply, Yale) Daniel Spielman (Yale) Nikhil Srivastava (MSR/Berkeley) IAS, Nov 5, 2014.
## Presentation on theme: "The Solution of the Kadison-Singer Problem Adam Marcus (Crisply, Yale) Daniel Spielman (Yale) Nikhil Srivastava (MSR/Berkeley) IAS, Nov 5, 2014."... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18218 | Question
# Magnetic field of light ray is given by →B=(3^i+4^j)×10−4 sin (kz+ωt) & electric field is given by →E=(α^i+β^j)×104 sin(kz+ωt), then what is the relation between α & βα=βαβ=2αβ=−43αβ=43
Solution
## The correct option is C αβ=−43→E.→B=0
Suggest corrections |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18220 | > {-# OPTIONS_GHC -fno-warn-missing-methods #-}
> module Virtual where
>
> import Control.Applicative
> import Test.QuickCheck
Yesterday on #haskell, augur asked me to explain how subtraction works for combinatorial species. (For an introduction to species, see my paper from the 2010 Haskell Symposium.) For example, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18221 | # Modified Bessel function Calculator
## Calculates the modified Bessel functions of the first kind Iv(x) and the second kind Kv(x), and their derivatives I'v(x) and K'v(x).
order v real number x complex number 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
$\normal Modified\ Be... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18222 | # Solve each of the following quadratic equations:
Question:
Solve each of the following quadratic equations:
$3\left(\frac{7 x+1}{5 x-3}\right)-4\left(\frac{5 x-3}{7 x+1}\right)=11, \quad x \neq \frac{3}{5}, \quad-\frac{1}{7}$
Solution:
$3\left(\frac{7 x+1}{5 x-3}\right)-4\left(\frac{5 x-3}{7 x+1}\right)=11, \qua... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18223 | Image of a function
Not all the elements of the domain need to belong to the real numbers.
Consider the function $f(x)=\displaystyle \sqrt{x-3}$ where we take the positive solution of the square root, only has positive images.
We will only consider those $x$ in the domain that belong to the real number, in which cas... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18209 | # Group is Inverse Semigroup with Identity
## Theorem
A group is an inverse semigroup with an identity.
## Proof
Let $\struct {S, \circ}$ be a group.
Let $a \in S$.
Then:
$\ds e$ $=$ $\ds a \circ a^{-1}$ Group Axiom $\text G 3$: Existence of Inverse Element $\ds \leadsto \ \$ $\ds e \circ a$ $=$ $\ds a \circ a^... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18215 | Volume 9, Issue 4
Second Order Convergence of the Interpolation Based on $Q^c_1$-Element
Numer. Math. Theor. Meth. Appl., 9 (2016), pp. 595-618.
Published online: 2016-09
Preview Purchase PDF 79 3804
Export citation
Cited by
• Abstract
In this paper, the second order convergence of the interpolation based on $Q^c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18219 | Try to answer the following questions here:
• What is this question used for?
• What does this question assess?
• What does the student have to do?
• How is the question randomised?
• Are there any implementation details that editors should be aware of?
### History and Feedback
#### Checkpoint description
Describe ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18213 | # Difference between revisions of "2019 AIME I Problems/Problem 14"
## Problem 14
Find the least odd prime factor of $2019^8+1$.
## Solution 1
The problem tells us that $2019^8 \equiv -1 \pmod{p}$ for some prime $p$. We want to find the smallest odd possible value of $p$. By squaring both sides of the congruence, w... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18352 | # Math Help - Geometry, perimeter, area of a triangle
1. ## Geometry, perimeter, area of a triangle
* *
***** 20
****** *
* ****** *
* **********
* ********** *
* ************* *
*******************
16
please show me how to find the perimter and area of above triangle. thanks.
suwanee
2. Originally Posted by Suwane... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18353 | # RD Sharma Solutions Class 9 Surface Area And Volume Of Sphere Exercise 21.1
## RD Sharma Solutions Class 9 Chapter 21 Exercise 21.1
Q1. Find the surface area of a sphere of radius:
(i) 10.5cm (ii) 5.6cm (iii) 14cm
Sol.
Surface area= $4\pi r^{2}$
$=4\times \frac{22}{7}\times \left ( 10.5 \right )^{2}$
=1386$cm^... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18354 | - Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
Reliability anal... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18355 | Calculus (3rd Edition)
The general solution is $$y=\ln \frac{1}{c-e^x}.$$
We have $$y'-e^{x+y}=0\Longrightarrow e^{-y}dy=e^{x}dx\\ \Longrightarrow\int e^{-y}dy=\int e^{x}dx+c\\ \Longrightarrow -e^{-y} =e^{x}+c\\ \Longrightarrow e^{-y} =c-e^{x}\Longrightarrow -y =\ln(c-e^x).$$ Hence, the general solution is $$y=\ln \fr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18356 | # Euler’s Formula, Fibonacci, the Bayer-Billera Theorem, and Fine’s CD-index
Bill Gessley proving Euler’s formula (at UMKC)
In the earlier post about Billerafest I mentioned the theorem of Bayer and Billera on flag numbers of polytopes. Let me say a little more about it.
## 1. Euler
Euler’s theorem asserts that for... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18357 | It is well known that $\overline{M}_{0,5}$, the moduli space of $5$-pointed rational curves, can be realized as the blow-up of $\mathbb{P}^2$ in four general points. Therefore, we may interpret $\overline{M}_{0,5}$ as the blow-up of a smooth quadric surface $Q\subset\mathbb{P}^3$ in three general points.
Now let $Q\su... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18358 | What is a witness string in a zero knowledge proof?
I had earlier asked the question What is a witness string? I unable to understand the concept
From the answers I got, it seems that a witness is more or less the answer. For e.g. in the padlock example given in the accepted answer, the witness is the padlock combina... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18359 | # 2 41 polytope
Jump to: navigation, search
Orthogonal projections in E6 Coxeter plane 421 142 241 Rectified 421 Rectified 142 Rectified 241 Birectified 421 Trirectified 421
In 8-dimensional geometry, the 241 is a uniform 8-polytope, constructed within the symmetry of the E8 group.
Coxeter named it 241 by its bifur... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18361 | # How to Solve Inverse Variation?
Inverse variation indicates an inverse relationship between two quantities. In this step-by-step guide, you will learn more about inverse variation.
## Step-by-step guide toinverse variation
There are two types of proportionalities. These are direct variation and inverse variation. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18362 | Mean Cholesterol Standard Deviation n Males 23.09 3.88 11 Females 25.889 2.522 9
From the values in the table above, is there evidence to believemales participating in the study have a significantly lowercholesterol level than females who participate in the study. Perform a hypothesis test at the .01 level of signific... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18364 | # Kernel SVM primal with Stochastic Gradient Descent
In short: I am currently reading Online Learning with Kernels (http://books.nips.cc/papers/files/nips14/AA33.pdf) for fun and I can't figure out how he got to equation 8 from equations 6 and 7.
The idea is: We want to minimize a risk function
$R_stoch$f,t$:=c(x_t,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18367 | +0
0
93
3
1) Compute the product$$\frac{(1998^2 - 1996^2)(1998^2 - 1995^2) \dotsm (1998^2 - 0^2)}{(1997^2 - 1996^2)(1997^2 - 1995^2) \dotsm (1997^2 - 0^2)}.$$
2) Let $$f(x) = \frac{3}{9^x + 3}.$$ Find $$f \left( \frac{1}{1001} \right) + f \left( \frac{2}{1001} \right) + f \left( \frac{3}{1001} \right) + \dots + f \l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18363 | Answers: 3 Show answers Another question on Mathematics. Example: The square root of 54 The square root of 54 is not an integer, since 54 is not a perfect square. Simplifying the square roots of powers. Advanced Placement (AP), 08.11.2019 02:31. This … QUESTION 17 radicals simplify and add/subtract a) Simplify the foll... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18365 | # Homework Help: Fourier Transform Time Shifting Property
1. Sep 10, 2011
### frenzal_dude
1. The problem statement, all variables and given/known data
I tried to work out the FT of a sin function with a time delay using first mathematical manipulation, and then using the time shifting property.
However I get two ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18366 | Probability of getting a bingo pattern with a certain number of balls drawn?
Let's say you have a fixed pattern on a standard 5x5 bingo card using all the standard bingo rules (center is a free space, B column has numbers 1-15, I has 16-30, etc. to 75). How can you calculate the probability of matching at least that p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18360 | # American Institute of Mathematical Sciences
August 2018, 12(3): 429-449. doi: 10.3934/amc.2018026
## Improved attacks on knapsack problem with their variants and a knapsack type ID-scheme
1 Aristotle University of Thessaloniki, Department of Informatics, P.O. Box 114, Thessaloniki 54124, Greece 2 Aristotle Unive... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6592 | # Normalizer of a cyclic subgroup of $\operatorname{GL}(2,\mathbb R)$
Find all the matrices in the subgroup $N(\langle A \rangle)$ of $\operatorname{GL}(2,\mathbb{R})$ where $|A|=4$. Is $N(\langle A \rangle)$ abelian? Is $N(\langle A \rangle)$ finite?
$\langle A \rangle$ is the cyclic subgroup of $GL(2,\mathbb{R})$ g... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6593 | New Titles | FAQ | Keep Informed | Review Cart | Contact Us Quick Search (Advanced Search ) Browse by Subject General Interest Logic & Foundations Number Theory Algebra & Algebraic Geometry Discrete Math & Combinatorics Analysis Differential Equations Geometry & Topology Probability & Statistics Applications Ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6595 | # Gauss sum for primitive real Dirichlet character
If $\chi$ is a real non-trivial primitive character modulo $q\ge 1$, then how could one show that $$\sum_{n\in \mathbb Z/q\mathbb Z} \chi(n)e\left(\frac nq\right) = \sum_{n\in \mathbb Z/q\mathbb Z} e\left(\frac {n^2}q\right)$$ where $e(z) = \exp(2\pi i z)$? I think on... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6596 | Mathematical and Applied Statistics Lesson of the Day – The Motivation and Intuition Behind Chebyshev’s Inequality
In 2 recent Statistics Lessons of the Day, I
Chebyshev’s inequality is just a special version of Markov’s inequality; thus, their motivations and intuitions are similar.
$P[|X - \mu| \geq k \sigma] \leq... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6597 | # equality of unions and intersections
Could you show me how to prove this?
Let $A_i \subset N$, $i \in I$, where $I$ is an arbitrary nonempty set. Prove that there exists at most countable set $J \subset I$ such that:
$\bigcup_{i \in I}A_i = \bigcup_{j \in J} A_j$ and $\bigcap_{i \in I}A_i = \bigcap_{j \in J} A_j$.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6598 |
# 3.2: Evaluating Algebraic Expressions
In this section we will evaluate algebraic expressions for given values of the variables contained in the expressions. Here are some simple tips to help you be successful.
## Tips for Evaluating Algebraic Expressions
1. Replace all occurrences of variables in the expression ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6599 | # Back-n-Forth or a Direct Isomorphism Between A Countable DLO Without Endpoints and $U = \{ \frac{m}{2^n} \}$
Note: I changed this question and deleted my answer, bringing it into the question for quick review. The proof now has the same brevity as the back-and-forth method found in wikipedia.
Let $$P$$ be a Countab... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6600 | # Sectional curvature and general relativity
Presented by:
G Hall [Aberdeen]
Date:
Friday 7th October 2005 - 16:00 to 17:00
Venue:
INI Seminar Room 1
Abstract:
The geometrical idea of sectional curvature in space-times is introduced and interpreted. It is then shown that, with the exception of plane waves and spaces ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6601 | # Ampere
From Wikipedia the free encyclopedia
ampere
Demonstration model of a moving iron ammeter. As the current through the coil increases, the plunger is drawn further into the coil and the pointer deflects to the right.
General information
Unit systemSI base unit
Unit ofElectric current
SymbolA
Named afterAndré-M... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6602 | # Show document
Title: Asymptotic automorphism groups of Cayley digraphs and graphs of abelian groups of prime-power order Dobson, Edward (Author) http://amc.imfm.si/index.php/amc/article/viewFile/120/116 English Not categorized 1.01 - Original Scientific Article IAM - Andrej Marušič Institute We show that almost ever... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6603 | # Division (mathematics)
(Redirected from Integer division)
$20 \div 4=5$
Division of numbers 0-10. Line labels = dividend. X axis = divisor. Y axis = quotient.
In mathematics, especially in elementary arithmetic, division (÷) is an arithmetic operation. Specifically, if b times c equals a, written:
a = b × c
where... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6594 | ## The Annals of Probability
### Finite Size Scaling in Three-Dimensional Bootstrap Percolation
#### Abstract
We consider the problem of bootstrap percolation on a three-dimensional lattice and we study its finite size scaling behavior. Bootstrap percolation is an example of cellular automata defined on the $d$-dime... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6604 | ## Linear inviscid damping in Gevrey spaces. (arXiv:1904.01188v1 [math.AP])
We prove linear inviscid damping near a general class of monotone shear flows in a finite channel, in Gevrey spaces. It is an essential step towards proving nonlinear inviscid damping for general shear flows that are not close to the Couette f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6606 | # Computing virtual work
1. Oct 9, 2012
### boeing_737
Hi all,
I've been trying to understand the vibration of a cantilever beam subjected to a forcing function using Lagrange's equation, but have got stuck at the virtual work part. I would appreciate your inputs here.
Using the assumed modes method, the transvers... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6607 | # Tag Archives: yahoo!
## How to Build the Best Fantasy Football Team, Part 2
UPDATE on 10/5/2015: Explained how to model a requirement of baseball leagues (Requirement 4).
UPDATE on 10/8/2015: Explained how to model a different objective function (Requirement 5).
Yesterday, I wrote a post describing an optimizatio... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_6605 | # Evaluate the following double integral
1. May 18, 2005
### brendan_foo
Just had an exam and I had to evaluate the following double integral, with limited success
$$\int_0^1 \int_0^{\pi} y\sin(xy) {dy} {dx}$$
I managed to compute the first integral, that was ok, using parts. But trying to integrate that with resp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9488 | Many important applied problems involve finding the best way to accomplish some task. Often this involves finding the maximum or minimum value of some function: the minimum time to make a certain journey, the minimum cost for doing a task, the maximum power that can be generated by a device, and so on. Many of these pr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9489 | # American Institute of Mathematical Sciences
• Previous Article
Analysis of the Hessian for inverse scattering problems. Part III: Inverse medium scattering of electromagnetic waves in three dimensions
• IPI Home
• This Issue
• Next Article
Image denoising: Learning the noise model via nonsmooth PDE-constrained optim... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9490 | # Search by Topic
#### Resources tagged with Multiplication & division similar to Clever Carl:
Filter by: Content type:
Stage:
Challenge level:
### There are 160 results
Broad Topics > Calculations and Numerical Methods > Multiplication & division
### Slippy Numbers
##### Stage: 3 Challenge Level:
The number 101... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9493 | # After the math contest, Basil noticed that there were four extra- large pizzas that were left untouched. In addition, another three slices of pizza were uneaten. If there were a total of 51 slices of pizza left, how many slices does an extra-large pizza have? MATH CONTEST 3:30 RM 105 EX PIZZA EX.16. DIZZA XG. PIZZA X... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9494 | ## anonymous 3 years ago Use The Inequality -4t-8≤12 To Fill In The Missing Numbers . A.t≥? B.t+4≥? C.t-?≥0 D.t+10≥? E.3t≥? F.t≥-5 -
1. anonymous
@satellite73
2. anonymous
that was wrong, lets do it right
3. anonymous
Lol Okay
4. anonymous
$-4t-8≤12$ add 8 get $-4t\leq 20$ divide by -4 and change the inequality... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9495 | # Structure of Measurable Subsets of the Unit Square
If A is a (Lebesgue-)measurable subset of the unit square that has positive measure, does there exist a subset B contained in A that has a product structure (is the product of two subsets of the real line) and that has positive measure?
-
Consider a measurable subs... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9496 | # Who are you calling broken?
I’m feeling the morning-after shame of attempted profundity via wordle. When I was young my mother told me, “Riley, when you can’t quite think of the right way to say something, remember: anything’s better than wordle.”
Or something like that. Maybe the exact details are eluding me. Fo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9497 | • ### Unit 8: Momentum and Collisions
We use the term momentum in various ways in everyday language. For example, we often speak of sports teams gaining and maintaining the momentum to win. Generally, momentum implies a tendency to continue on course (to move in the same direction) and is associated with mass and velo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9498 | Eliminating NDSolve Instability
pde = {D[Q[t, ϕ, θ], t] == -Cos[θ]*D[Q[t, ϕ, θ], ϕ] + Sin[θ]*D[Q[t, ϕ, θ], θ, ϕ]/2,
Q[t, 0, θ] == Q[t, 2*Pi, θ], Q[t, ϕ, 0] == 0,
Q[0, ϕ, θ] == ((1 - Cos[ϕ]*Sin[θ])^2 - 1)/4};
sol = NDSolveValue[pde, Q, {t, 0, 5}, {ϕ, 0, 2*Pi}, {θ, 0, Pi}, MaxStepSize -> {.01, .25, .25}]
generates the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9500 | # Tag Info
## Hot answers tagged differential-geometry
24
Einstein himself told the story in his Kyoto address of 1922, which I quote from Pais's biography titled Subtle is the Lord: "If all systems are equivalent, then Euclidean geometry cannot hold in all of them. To throw out geometry and keep laws is equivalent ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9501 | 1. Math
3. linear algebra find the standard matrix for these linear transformations...
# Question: linear algebra find the standard matrix for these linear transformations...
###### Question details
Linear Algebra. Find the standard matrix for these Linear Transformations:
1.) The dot product, . Assume so that you ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9503 | geometric quotient
Let $S$ be a base scheme. Let $X$ be a scheme over $S$ and let $G$ be a group scheme over $S$ acting on $X$ via $\sigma: G \times_S X \to X$. Suppose that we have a scheme $Y$ over $S$ together with $\varphi: X \to Y$ such that $\varphi \circ \sigma = \varphi \circ p_2$ (where $p_2: G \times_S X \to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9491 | Courses
# RD Sharma Solutions - Ex - 4.3 & Ex - 4.4, Rational Numbers, Class 7, Math Class 7 Notes | EduRev
## Class 7 : RD Sharma Solutions - Ex - 4.3 & Ex - 4.4, Rational Numbers, Class 7, Math Class 7 Notes | EduRev
The document RD Sharma Solutions - Ex - 4.3 & Ex - 4.4, Rational Numbers, Class 7, Math Class 7 No... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9492 | # Definition:Continuous Real Function/Open Interval
Let $f$ be a real function defined on an open interval $\left({a \,.\,.\, b}\right)$.
Then $f$ is continuous on $\left({a \,.\,.\, b}\right)$ if and only if it is continuous at every point of $\left({a \,.\,.\, b}\right)$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9499 | ### Theory:
Operators in LibreOffice Calc:
An operator is a character or set of characters that determine the action that is to be performed or considered.
Relational Operators:
Relational operators are used to comparing two values. They form relational expressions. These operators always give a single value as a r... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9502 | # Math Help - Evaluate The Following Limit (3).
1. ## Evaluate The Following Limit (3).
Hello
$\lim_{n\to\infty} (cos(n))^n$
What the hell is this ?
I can not do anything
2. It oscillates from -1 to 0 to 1 and back again.
For natural k...
When $n=2k\pi,\ Cos(n)=1$
When $n=k\pi,\ Cos(n)=-1$
Odd powers of this is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9456 | # Math Help - Expressing a non-trivial linear dependency relationship
1. ## Expressing a non-trivial linear dependency relationship
I've been ask to see if a set of vectors is linearly independent, and if not, find a non-trivial linear dependency relationship.
I believe I've correctly determined that the set is line... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9457 | # Precalculus Examples
Determine if Bijective (One-to-One)
,
A bijection is a function giving an exact pairing of the elements of two sets. Every element of one set should be paired with exactly one element of the other set, and every element of the other set should be paired with exactly one element of the first set,... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9459 | # Definite integrals of absolute values
1. Dec 9, 2007
### Hurricane3
1. The problem statement, all variables and given/known data
$$\int|x^{2}+x-2|dx$$ from -2 to 2
2. Relevant equations
The integral of f(x) from a to b = F(b) - F(a)
|x| = { x if x >= 0; -x if x < 0
---
Ok, I don't know how to do the definite in... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9460 | ## Intermediate Algebra (6th Edition)
Published by Pearson
# Chapter 5 - Section 5.1 - Exponents and Scientific Notation - Exercise Set - Page 262: 65
-2
#### Work Step by Step
We are given the expression $3^{0}-3t^{0}$. $3^{0}-3t^{0}=1-3(t^{0})=1-3\times1=-2$ In general, $a^{0}=1$ when a is nonzero. In the second... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9462 | # Sequence of smooth functions approximating a 2d cylinder step function
Let $f(x,y)=1$ if $(x,y)$ is in the unit disk and $f=0$ otherwise. I would like to approximate $f$ by a sequence of smooth functions. The functions need to be evaluated quickly so the results I'm getting from mollification are to awkward to deal ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9463 | There are infinitely many complex values $z$ for which $z^z = z$. Find the exact value of any of them (must have a non-zero imaginary part). |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9464 | # How do you convert ml to l?
Jul 8, 2017
There are 1000 mL (milliliters) in 1 L (liter).
So, to convert from mL to L, divide by 1000.
I hope this helps a lot! :)
Jul 8, 2017
Divide by 1000
#### Explanation:
The m in ml is short for milli which refers to a quantity of ${10}^{-} 3$.
${10}^{-} 3$ is equivalent to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9465 | # ASP，需要使用SFTP
0
## 9 答案
Let me tell you what I know about the cohomology of congruence subgroups of Sp_{2g}(\Z). As far as cohomology with rational coefficients goes, this was determined by Borel. In the limit as g->\infty, it is isomorphic to a polynomial algebra with generators in degrees 4k+2. See his paper
A. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9467 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 15 Dec 2018, 12:59
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9468 | 1
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
Ship A is sailing towards north-east with velocity $$\mathop v\limits^ \to = 30\mathop i\limits^ \wedge + 50\mathop j\limits^ \wedge$$ km/hr where $$\mathop i\limits^ \wedge$$ points east and $$\mathop j\limits^ \wedge$$ , north. Ship B is at a distance of 80 km eas... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9469 | # which expression is equivalent to 2w?
A student starts working for $12 per hour. 3c+3. To ensure the best experience, please update your browser. symbol. A driver uses 35.5 gallons of gas to drive from the Enanol canyon in the golden bridge, a distance of 787.25 miles. For addition and subtraction, use the standard ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9471 | # What is the relationship between symmetry and degeneracy in quantum mechanics?
Let me remind you about the following classical examples in quantum mechanics.
Example 1. Bound states in 1-dim potential V(x).
Let $V(x)$ be a symmetric potential i.e. $$V(x) = V(-x)$$ Let us introduce the parity operator $\hat\Pi$ in t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9458 | # Why does $S^n$ satisfy the local $n$-slice condition? (From Lee's Smooth Manifolds)
Example $5.9$ on page $103$ of John Lee's Smooth Manifolds says the following:
The intersection of $S^n$ with the open subset $\{x:x^i>0\}$ is the graph of the smooth function $$x^i=f(x^1,\dots,x^{i-1},x^{i+1},\dots,x^{n+1})$$ where... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9461 | # A face centred cubic element (atomic mass = 60) has a cell edge of 400 pm. What is its density ?
$6.23gcm^{-3}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9466 | # Linear relations and graphs
• July 25th 2012, 09:50 PM
bbutale
Linear relations and graphs
A triangle is made from the coordinate axes and the line 4x+5y+p=0 . The area of the triangle is 10 square units. What is the value of p?
• July 25th 2012, 10:22 PM
pickslides
Re: Linear relations and graphs
Solving for the x ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_9470 | # How do you solve by graphing y = 4x + 4 and 3x + 2y = 12?
May 29, 2015
A graph of the given equations (see below) may give an indication of the general area of the solution; but (unless it is drawn at a very large scale) it is unlikely to provide an exact solution.
Both equations are linear and the easiest point t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8768 | # Why are nets not used more in the teaching of point-set topology?
I just finished working through a proof of Tychonoff's Theorem that uses nets (specifically, as a corollary of the fact that a net in a product space converges iff the projected nets in the components do). While I might be missing steps (I based the p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8771 | # I Cantor's intersection theorem (Apostol)
1. Mar 25, 2016
### mr.tea
Hi,
I am reading "mathematical analysis" by Apostol right now for a course in analysis. Since I am trying to understand the author's proof of the above theorem(3.25 in the book), but I have something that I can't understand.
He assumes that each... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8772 | # How would I apply the limit laws to $\lim_{x\to 2}\frac{(3x-6)\sqrt{x^2+1}}{5x-10}$?
$$\lim_{x\to 2}\frac{(3x-6)\sqrt{x^2+1}}{5x-10}$$
I have tried to simplify, multiply by the conjugate of the denominator, but I cannot seem to figure out how to find the limit. Do I need to apply the limit laws in order to find the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8774 | # Definition for multiplication [duplicate]
I am serious.
What is the definition for multiplication ?.
Every book and resources online(the one's I have seen) tells multiplication is repeated addition. But that's only some defintion that can be called valid when one of the numbers is a positive integer. For eg: $5 \t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8775 | # How Do I Work Out the Percentage of a Number?
To work a percentage of a number, make a fraction of a 100 to the percentile number. For example to calculate 25% of 2000, it will be required to make a fraction of 25 out of 100 and the multiply it with 2000 to get the percentage of 25 in 2000.
Ask.com Answer for: how d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8776 | MathSciNet bibliographic data MR2299461 (2008c:20058) 20E42 (11F46 11F60 11F70 20G25) Shemanske, Thomas R. The arithmetic and combinatorics of buildings for ${\rm Sp}\sb n$${\rm Sp}\sb n$. Trans. Amer. Math. Soc. 359 (2007), no. 7, 3409–3423 (electronic). Article
For users without a MathSciNet license , Relay Station ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8777 | Publicité ▼
# définition - Azimuth
azimuth (n.)
1.the azimuth of a celestial body is the angle between the vertical plane containing it and the plane of the meridian
Merriam Webster
AzimuthAz"i*muth (�), n. [OE. azimut, F. azimut, fr. Ar. as-sum�t, pl. of as-samt a way, or perh., a point of the horizon and a circl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8779 | # Math Help - Solve the equation
1. ## Solve the equation
$\frac 1{\left(1+\sqrt{1+\sqrt{x}}\right)^4}+\frac 1{\left(1-\sqrt{1+\sqrt{x}}\right)^4}+\frac 2{\left(1+\sqrt{1+\sqrt{x}}\right)^3}+\frac 2{\left(1-\sqrt{1+\sqrt{x}}\right)^3}=0$
2. Originally Posted by james_bond
$\frac 1{\left(1+\sqrt{1+\sqrt{x}}\right)^4}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8780 | ## Understanding Integration III: Jacobians
Now, we’re going to talk a bit about the geometry of the periods, which were completely analytic in nature. As we mentioned, for a compact Riemann surface $X$, we have a period matrix $\Omega$ that encodes the complex integration theory on the surface.
We can use $\Omega$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8781 | # Tagged: Bernoulli random variable
## Problem 748
Suppose that $X$ is a random variable with Bernoulli distribution $B_p$ with probability parameter $p$.
Assume that the variance $V(X) = 0.21$. We further assume that $p > 0.5$.
(a) Find the probability $p$.
(b) Find the expectation $E(X)$.
## Problem 747
A rand... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8782 | # Pre RMO practice 2019
1) Determine whether the following functions are well-defined:
1a) $f: Q \rightarrow Z$ defined by $f(a/b)=a$
1b) $f: Q \rightarrow Q$ defined by $f(a/b)=a^{2}/b^{2}$
2) Determine whether the function $f: R^{+} \rightarrow Z$ defined by mapping a real number r to the first digit to the right... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8769 | Home > Error Function > Complementary Error Function
# Complementary Error Function
## Contents
doi:10.1090/S0025-5718-1969-0247736-4. ^ Error Function and Fresnel Integrals, SciPy v0.13.0 Reference Guide. ^ R Development Core Team (25 February 2011), R: The Normal Distribution Further reading Abramowitz, Milton; St... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8770 | # Polyhedral combinatorics
Last updated
Polyhedral combinatorics is a branch of mathematics, within combinatorics and discrete geometry, that studies the problems of counting and describing the faces of convex polyhedra and higher-dimensional convex polytopes.
## Contents
Research in polyhedral combinatorics falls ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8773 | ## Abstract and Applied Analysis
### An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations $AXB=E,$$CXD=F$
#### Abstract
The generalized coupled Sylvester systems play a fundamental role in wide applications in several areas, such as stability theory, control theory, pe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8783 | # Regular Points of a polynomial system
For a polynomial map $F:\mathbb{R}^n \rightarrow\mathbb{R}^n,$ let $F_{\delta}(\mathbf{x})$ denote the polynomial map obtained by perturbing each coefficient of $F$ by an amount less than $\delta.$ Let $V^R$ denote the regular solutions of the polynomial system $F(\mathbf{x})=0.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_8778 | # American Institute of Mathematical Sciences
December 2021, 11(4): 633-644. doi: 10.3934/naco.2021001
## Solving nonlinear differential equations using hybrid method between Lyapunov's artificial small parameter and continuous particle swarm optimization
Department of Mathematics, College of Computer Science and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19441 | # How to draw this finite state automaton?
I know that the following language $L$ = {$a^n$ where $n$ is a prime number bounded by some fixed $f$} is a regular language because it is finite. Because it's a regular language, I should be able to draw a NFA for it, but I'm stuck as to how. If the value of $f$ was given, I... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19442 | # 4.6 Exponential and logarithmic equations (Page 3/8)
Page 3 / 8
Solve $\text{\hspace{0.17em}}{2}^{x}={3}^{x+1}.$
$x=\frac{\mathrm{ln}3}{\mathrm{ln}\left(2}{3}\right)}$
Is there any way to solve $\text{\hspace{0.17em}}{2}^{x}={3}^{x}?$
Yes. The solution is $0.$
## Equations containing e
One common type of exp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19443 | # Discrete Mathematics and Combinatorics Commons™
## All Articles in Discrete Mathematics and Combinatorics
569 full-text articles. Page 1 of 18.
Minimum Rank Of Skew-Symmetric Matrices Described By A Graph, 2017 University of Wyoming
#### Minimum Rank Of Skew-Symmetric Matrices Described By A Graph, Mary Allison, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19446 | # Nyquist–Shannon sampling theorem
Example of magnitude of the Fourier transform of a bandlimited function
The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient con... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19447 | # $C^{*}$-algebra
## 1 Definition
$C^{*}$-algebras are a type of involutive Banach algebras which arise in the study of operators on Hilbert spaces, Lie group representations, locally compact topological spaces, knots, noncommutative , among other topics in mathematics and theoretical physics . Their study was initia... |
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