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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10124 | # Closed-forms for several tough integrals
These integrals came up in the process of finding solution to Vladimir Reshetnikov's problem. I wonder if there are closed-forms for the following integrals: \begin{array}{1,1} &[\text{1}] &\quad\int_0^1\frac{\operatorname{Li}_3(ax)}{1+2x}\ dx\\[12pt] &[\text{2}] &\quad\int_0... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10125 | Next: The Influence of the Up: The Stochastic Web Previous: Symmetries of the Web Contents
The Skeleton of the Web
The iteration of the web map (1.24) for () typically yields phase portraits like those shown in figure 1.7.
In figures 1.7a through 1.7e one can observe the stochastic web for evolving under the itera... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10126 | # Are they known properties for the self-convolution application $H : f \mapsto f \star f$?
I was wondering if the application $$H : L^1(\mathbb{R}) \rightarrow L^1(\mathbb{R})$$ defined by :
$$H(f) := f \star f, \quad \forall f \in L^1(\mathbb{R})$$ had some known properties ? For example we know that , using Young ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10127 | # Homework Help: QM: Spin-orbit and wavefunctions for H
1. May 19, 2009
### Niles
1. The problem statement, all variables and given/known data
Hi all.
I wish to evaluate the following dipole moment
$$<1| x |2>,$$
where |1> and |2> are stationary states of the hydrogen atom when one accounts for spin-orbit couplin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14752 | # Computing the derivative from the definition
Using the limit definition of the derivative which I know is: $$f'(x)=\lim_{h\to0}\left(\frac{f(x+h)-f(x)}{h}\right)$$ I am trying to solve this problem $$f(x)= \frac{x}{x+2}$$
How do I go about properly solving this, I seemed to get
$$\frac{x}{x+2}\$$ as my answer agai... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14753 | Mathematics
# One obtuse angle and one acute angle can make a pair of supplementary angles.
True
##### SOLUTION
let, $A=120^0$ be obtuse angle and $B=60^0$ be acute angle.
So, $A+B=180^0$
That means $A$(obtuse angle) and $B$(acute angle) are supplementary
So, given statement is true
You're just one step away
TRUE/... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14754 | # Construction of a field
Given the polynomial
$$f(x)= x^4-16x^2+4$$
which has $a=\sqrt 3+\sqrt 5$ as one of its roots in $\Bbb C$, can you use $f(x)$ to construct a field $E$ of the form $Q[x]/I$ for some appropriate ideal $I$?
And does $f(x)$ factorize over this field $E$?
Any help would be appreciated thankyou!... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14755 | # Finding a general term for the sequence
Find a general term in simplest form for the sequence: $$2, 1, -4, 7, -10, 13, -16$$
This is what I tried:
$a_n = a_1 + (n - 1)\cdot d$
$a_n = 2 + (n-1)\cdot 3$
$a_n = (-1)^n (2+(n-1)\cdot 3)$
which doesn't work.
I am pretty confused regarding the first two terms of the se... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14756 | # Thermodynamics problem involving piston and spring
Tags:
1. Feb 8, 2016
### Titan97
1. The problem statement, all variables and given/known data
2. Relevant equations
$$W=P\Delta V$$
$$\Delta U=nC_v\Delta T$$
3. The attempt at a solution.
The gas is slowly heated. The temperature increases and the pressure incr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14757 | # Random geometries
Let $M$ be a smooth $n$-dimensional manifold, and let $FM = GL(M)$ indicate its tangent frame bundle. Let $G$ be a fixed linear subgroup of $GL(n)$, and consider the space $\mathcal S$ of all $G$-structures on $M$. Each element $Q \in \mathcal S$ is a $G$-subbundle of the frame bundle $FM$. For exa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14758 | # How do you find the solution to 6cos^2theta+5costheta-4=0 if 0<=theta<360?
Then teach the underlying concepts
Don't copy without citing sources
preview
?
#### Explanation
Explain in detail...
#### Explanation:
I want someone to double check my answer
1
May 25, 2018
The solutions are $S = \left\{{60}^{\circ} , ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14759 | # Nonlinear optics waveform
1. Aug 30, 2010
### DanSandberg
From a textbook - The reason why the polarization plays a key role in the description of nonlinear optical phenomena is that a time-varying polarization can act as the source of new components of the electromagnetic field....... the wave equation in nonline... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14760 | # Cross product of two vectors
I have a very little knowledge of cross product of vectors and don't really understand why there is a need to calculate it.
I know that the cross product of two vectors gives a resultant in the direction which is perpendicular to both the vectors.
In a right-handed Cartesian coordinate... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14761 | # Math Help - Is this method effective enough or is there better?.
1. ## Is this method effective enough or is there better?.
Hi,
i'm measuring the distance of a boat moored on a 22.5 degree angle being the front nose hard up against the mooring and rear end hanging out on the 22.5 degree angle, i want to know the d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14762 | # When does regularity of the base scheme imply regularity of the top scheme?
My problem is the following:
I have a finite surjective morphism $f: X\rightarrow Y$ of noetherian schemes and know that $Y$ is a regular scheme. (Indeed, in my situation, the two schemes are topologically the same and the arrow is topologi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14763 | # Huge, almost huge and superhuge cardinals
A cardinal $\kappa$ is huge with target $\lambda$ if there is an elementary embedding $j:V\to M$ with critical point $\kappa$ such that $j(\kappa)=\lambda$ and $M^\lambda\subset M$.
## Almost huge
A cardinal $\kappa$ is almost huge with target $\lambda$ if there is an elem... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14764 | # How do you solve 4(m-4)<=4m-16?
There is no solution as $4 m - 16 \le 4 m - 16$ simplifies to $0 \le 0$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14765 | # How do you simplify ((3.2x 10^4) x ( 4.9 x 10^-4)) / (2.8 x 10^-7)?
##### 1 Answer
Mar 28, 2015
Group the coefficients and the exponents and process them separately:
$\frac{\left(3.2 \times {10}^{4}\right) \times \left(4.9 \times {10}^{- 4}\right)}{2.8 \times {10}^{- 7}}$
$= \frac{3.2 \times 4.9}{2.8} \times \fra... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14766 | Suppose $S\subset\mathbb{R}$ is dense without interior point, and for every open interval $I,J\subset\mathbb{R}$, $I\cap S$ is homeomorphic to $J\cap S$.
Is $S\times S$ homeomorphic to $S$?
By Luzin scheme, if $S$ is the set of rationals or irationals , I can see this statement is true.
-
Dear @user35739, your quest... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14767 | # What is the range of the function f(x)= 1 / ( 4 sin(x) + 2 ) ?
Apr 4, 2017
The range is $R = \left(- \infty , - \frac{1}{2}\right] \cup \left[\frac{1}{6} , + \infty\right)$
#### Explanation:
Note that the denominator is undefined whenever
$4 \sin \left(x\right) + 2 = 0$,
that is, whenever
$x = {x}_{1 , n} = \frac... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6640 | # Primes And A Double Product
Calculus Level 5
$\large f(n):=\prod_{a=1}^{p_n}\prod_{b=1}^{p_n}(1+\sqrt[p_n]{p_n}e^{2\pi i ab/p_n})$
Let $$\{p_n\}_{n=1}^\infty=\{3,5,7,11,\ldots\}$$ be the sequence of odd prime numbers in increasing order. Let us define the function above. Compute $\sum_{n=1}^{2016}\left( \frac{\sqr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6641 | ## Newton’s method
### Overview
• Gradient ascent is a very effective algorithm, but it takes baby steps at every single iteration and thus needs a lot of iterations to converge.
• Newton’s method is another algorithm for maximizing $$\ell(\theta)$$ which allows you to take much bigger steps and thus converge much ea... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6642 | # Why does $\lim\limits_{x\to\infty}\dfrac{(-1)^{x+1}}{x}$ converge to 0?
As the title states, why does$\lim\limits_{x\to\infty}\dfrac{(-1)^{x+1}}{x}$? It seems like this would produce the indeterminate form of $\frac{\infty}{\infty}$ at which point I would use L'Hospital's rule but I don't even know how to take the d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6643 | If = then it (a) Let fx ngbe a sequence in X. is a metric. Other articles where Discrete metric is discussed: metric space: …any set of points, the discrete metric specifies that the distance from a point to itself equal 0 while the distance between any two distinct points equal 1. This distance is called a discrete me... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6644 | # Can anyone help find the derivatives of a given function? 1) y=(lnx)/(3x-1+x^2) Thank's
lfryerda | Certified Educator
calendarEducator since 2012
starTop subjects are Math and Science
If you have more than one question, you need to make separate posts.
To find the derivative of the function, we need to use the q... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6645 | Elementary mathematics refers to courses in categories of numbers, inequalities, algebraic equations, calculus-like sequences, functions, integrals, and differential equations. If the student manages to accumulate a solid foundation in this type of mathematics, then he can study advanced mathematics without any problem... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6646 | # The symmetric group
Before defining anything, we shall provide a little motivation for some general notions which will arise later.
Let be any finite set and let denote the set of all permutations of onto itself:
This set has the following properties:
1. if belong to then (the composition of these permutations) al... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6647 | ## Algebra 1: Common Core (15th Edition)
Published by Prentice Hall
# Chapter 2 - Solving Equations - Chapter Review - Page 154: 26
Identity
#### Work Step by Step
We first use the distributive property on both sides to get that $3h-12=-12+3h$. We then simplify by subtracting 3h on both sides to get that $-12=-12$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6648 | # How do I show for nonzero constants $a$ and $b$ that $\operatorname{Corr} (x,y) = -1$ or $1$?
Let $X$ be a random variable with a mean of $\mu$ and a variance of $\sigma^2$ and let $Y = aX +b$. Show for non-zero constants $a$ and $b$ that $\operatorname{Corr}(X; Y ) = +1$ or $-1$.
-
Use the fact that $$\text{Corr}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6649 | # Wigner Symbols¶
Wigner, Clebsch-Gordan, Racah, and Gaunt coefficients
Collection of functions for calculating Wigner 3j, 6j, 9j, Clebsch-Gordan, Racah as well as Gaunt coefficients exactly, all evaluating to a rational number times the square root of a rational number [Rasch03].
Please see the description of the i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6650 | # Truncated Platonics
There are several Archimedean solids that are formed by the truncation (cutting off) of each corner of a Platonic solid.
These can be shown in successive truncations from one shape to its dual.
Original Truncation Rectification Bitruncation Birectification (dual)
Truncated Tetrahedron
Tetrate... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6651 | # Thread: mean squared error vs. root mean square
1. ## mean squared error vs. root mean square
what is the difference please? I cannot get it |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6652 | What are Lorentz Transformations? 1
When you study theory of relativity, one of the notions you will first stumble onto is about Lorentz transformations. It is actually a pretty big deal. Without knowing Lorentz transformations, you can’t study theory of relativity. So what are Lorentz transformations? A short answer ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6653 | # Invariant for group actions
Hello everybody!
Define the action of $SL_4({\mathbb{Z}})$ on alternating 2-forms or simply skew-symmetric matrices of degree 4 according to the following:
For $B \in SL_4({\mathbb{Z}})$ and an alternating matrix like $M$ define: $B.M = BMB^{T}$
Question: Why the single invariant for t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6654 | Question on Partitions of Unity
I was reading John Lee's Introduction to Smooth manifolds, and I came across this question:
• Let $M$ be a smooth manifold, and let $\delta : M \rightarrow \mathbb{R}$ be a positive continuous function. Using a partition of unity, show that there is a smooth function $\tilde{\delta} : ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_6655 | 3 added 175 characters in body
How about this one: $f(n)=1$ if $2^{2^n}+1$ is prime, and $f(n)=0$ otherwise.
Or: $f(n)$ is the largest prime factor of $2^{2^n}+1$.
Added 1: Inspired by Barry Cipra's comment, here is a function which is unknown in principle, not just in practice: Let $r(m)$ denote the number of latti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19072 | ## Algebra 1
a) $-2 * 1/2 = -1$ The product is -1, so the numbers are opposite reciprocals. b) $1/4 * 4 = 1$ The product is 1, so the numbers are not opposite reciprocals. c) $5 * -5 = -25$ The product is -25, so the numbers are not opposite reciprocals. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19073 | ## Variable Selection in Machine Learning
I've had a discussion with a colleague on the selection of variables in a model. The discussion boils down to the following question:
Is it better to supply all the variables that you have into the model and risk overfitting or should you start out small and add values to mak... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19074 | Projectile motion on a hemisphere
1. Mar 11, 2012
1. The problem statement, all variables and given/known data
A person standing on the top of a hemispherical rock of radius R kicks a ball (initially at rest on the top of the rock) to give it horizontal velocity $v_i$
What must be it's minimum initial speed if the ba... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19075 | # Problem of the Week Problem E Fold Once
A rectangular piece of paper, $$PQRS$$, has $$PQ = 30$$ cm and $$PS = 40$$ cm. The paper has grey lines on one side and is plain white on the other.
The paper is folded so that the two diagonally opposite corners $$P$$ and $$R$$ coincide. This creates a crease along line segm... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19076 | Post Undeleted by Aleksey
3 added 36 characters in body
The homology analogue of this question is answered affirmatively by Proposition 2.1 in math/0605535. By The proof provides $U$ with $H_p(U;{\mathbb Z})$ torsion-free and so implies the Universal Coefficient Theorem, it answers affirmative answer to the original q... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19077 | # Functions and More Functions
$\frac { f\big( \sqrt { 6 } \big) -f\big( \sqrt { 8 } \big) }{ \sqrt { 6 } -\sqrt { 8 } }$
Given the function $f\left( x \right) =\frac { 3 }{ 5 } x+\sqrt { 3 },$ evaluate the expression above.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19078 | # kronecker sum properties
If X and Y do not have the same number of dimensions, the smaller array is padded with dimensions of size one. Keywords: Hadamard (Schur) product, Kronecker sum, Kronecker product, matrix of matrices. The use of Kronecker product in some fields has been used extensively. From Wikipedia, the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19079 | Could you please explain if this code is giving a positive definite or a semi-positive definite matrix? eig ( A ) Q = np . The $<0$ eigenvalue of $A$ is $\approx -0.06$. Another suggestion is to look at the space of eigenvectors with positive eigenvalues. matrix ( eigvec ) xdiag = np . You might also reconsider your ap... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19080 | Lemma 71.3.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Assume $f$ is locally of finite type and $Y$ is locally Noetherian. Let $y \in |Y|$ be a point of codimension $\leq 1$ on $Y$. Let $X^0 \subset |X|$ be the set of points of codimension $0$ on $X$. Assume in addition one of ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19081 | # Proving $k$ is divisible by $3$ iff the sum of the digits of $k$ is divisible by 3 [duplicate]
I am trying to prove that $k$ is divisible by $3$ iff the sum of the digits of $k$ is divisible by 3 for all $k \in Z$.
I am not even sure what tags to use because I am not sure of right methods to use to solve this probl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19082 | # fsolve
Solve system of nonlinear equations
## Syntax
``x = fsolve(fun,x0)``
``x = fsolve(fun,x0,options)``
``x = fsolve(problem)``
``````[x,fval] = fsolve(___)``````
``````[x,fval,exitflag,output] = fsolve(___)``````
``````[x,fval,exitflag,output,jacobian] = fsolve(___)``````
## Description
Nonlinear system solv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19083 | # zbMATH — the first resource for mathematics
Inferring the residual waiting time for binary stationary time series. (English) Zbl 1308.62067
Summary: For a binary stationary time series define $$\sigma_{n}$$ to be the number of consecutive ones up to the first zero encountered after time $$n$$, and consider the probl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19084 | # Become a Linear Algebra Expert
back
Lesson /10
Directed Line Segment
To find the vector that forms between two points, you subtract two points. For example, if we have point $p = (P_1,P_2,P_3)$ and $q = (Q_1,Q_2,Q_3)$, then the vector that is going to form that connects from P to Q is:
\begin{split}
\vec{PQ} &= q ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19085 | ## Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 20-03-2023 al 26-03-2023
Lunedì 20 marzo 2023
Ore 11:00, aula "Roberta Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19086 | # Math Help - [SOLVED] Instantaneous velocity and Average velocity
1. ## [SOLVED] Instantaneous velocity and Average velocity
An airplane maintains a constant acceleration of 4.0m/s^2 [E] as it speeds up from 16m/s [E] to 28m/s [E].
a) What is the average velocity?
22m/s [E]
b) How long does the airplane accelerat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19087 | # Example please for matrix norm
My book goes on to say:
"If we consider both C^n and C^m with norms, then we define the norm of an M x N matrix A by.."
Then the formula says norm of A=sup (over abs(v)=1) of abs(Av) = sup (over v does not equal 0) abs(Av)/abs(v)
Can someone please provide me at least one example of wh... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10576 | # Recent questions tagged q3-i
Questions from:
### A committee of 7 has to be formed from 9 boys and 4 girls.In how many ways can this be done when the committee consists of Exactly 3 girls?
To see more, click for the full list of questions or popular tags. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10577 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# Triangle Inequality Theorem
## Sum of the lengths of any two sides of a triangle is greater than the third side.
Estimated5 minsto complete
%
Progress
Practice Triangle Inequality The... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10578 | # Perverse sheaf
The mathematical term perverse sheaves refers to a certain abelian category associated to a topological space X, which may be a real or complex manifold, or a more general topologically stratified space, usually singular. This concept was introduced by Joseph Bernstein, Alexander Beilinson, Pierre Del... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10579 | Heatmap Centrality
Definition
A new centrality measure, termed the heatmap centrality, utilizes both local and global network information by comparing the farness of each node with the average sum of the farness of its neighbor nodes. In particular, the heatmap centrality for node $v_i$, denoted as $CHM_{(v_i)}$, is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10580 | # Lots of Parallelepiped
A,B,C,D are four points which are not on the same plane.
How many different parallelepiped can be constructed whose vertices are these points?
Parallelepiped is a solid figure with six faces having all parallelograms.
• +1 Very nice question. – hexomino Aug 29 '18 at 8:58
The points could ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10581 | Harmonic osilator energy using derivatives
1. Dec 12, 2013
dawozel
1. The problem statement, all variables and given/known data
Show that the energy of a simple harmonic oscillator in the n = 2 state is 5Planck constantω/2 by substituting the wave function ψ2 = A(2αx2- 1)e-αx2/2 directly into the Schroedinger equat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10582 | 2 added 134 characters in body; deleted 1 characters in body; [made Community Wiki]
Kind of a cheat, but define $f : \mathbb{N} \to \mathbb{N}$ so that $f(n)$ is the initial position (to the right of the decimal point) of the first occurance of $n$ consecutive $5$s in the the decimal expansion of $\pi$, and $0$ if suc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10583 | # Do inner models of unique measurable cardinals have a regular behavior? (Edited and Revised Version)
We know that if $\kappa$ is a measurable cardinal and $\mu$ be a two-valued non-trivial$\kappa$-additive measure on it then the corresponding inner model produced by Mostowski collapse of S... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10584 | BREAKING NEWS
Finite set
## Summary
In mathematics (particularly set theory), a finite set is a set that has a finite number of elements. Informally, a finite set is a set which one could in principle count and finish counting. For example,
${\displaystyle \{2,4,6,8,10\}}$
is a finite set with five elements. The nu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10585 | # Evaluate the following limit : lim(x→0) (2x)/√(a +x) - √(a - x)
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Evaluate the following limit : $\lim\limits_{\text x \to 0}\cfrac{2\text x}{\sqrt{a+\text x}-\sqrt{a-\text x}}$
lim(x→0) (2x)/√(a +x) - √(a - x)
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Given $\lim\limits_{\text x \to 0}\cfrac{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10586 | ## Solvability of a mixed problem for the nonlinear Schrödinger equation.(English. Russian original)Zbl 0658.35017
Math. USSR, Sb. 58, 525-540 (1987); translation from Mat. Sb., Nov. Ser. 130(172), No. 4, 520-536 (1986).
The existence and uniqueness of the solution of a mixed problem for the nonlinear Schrödinger equa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10587 | # Exponential family
"Natural parameter" links here. For the usage of this term in differential geometry, see differential geometry of curves.
In probability and statistics, an exponential family is a set of probability distributions of a certain form, specified below. This special form is chosen for mathematical con... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10588 | # Archimedes
For other senses of this word, see Archimedes (disambiguation).
File:Archimedes.jpg
Archimedes of Syracuse.
Archimedes (Greek: ΑΡΧΙΜΗΔΗΣ) (287 BC212 BC) was an ancient mathematician, physicist, engineer, astronomer and philosopher born in the Greek seaport colony of Syracuse. He is considered by some mat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10589 | # Definition:Automorphic Number
## Definition
An automorphic number is a positive integer all of whose powers end in that number.
## Sequence of Automorphic Numbers
The sequence of automorphic numbers begins as:
$\displaystyle 1$ $:$ $\displaystyle 1^2$ $\displaystyle = 1$ $\displaystyle 5$ $:$ $\displaystyle 5^2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10590 | # Lesson 3Cyclic PolygonsSolidify Understanding
### 1.
The three angle bisectors of triangle are shown. Use a compass to construct an inscribed circle with center .
### 2.
The three angle bisectors of triangle are shown. Use a compass to construct an inscribed circle with center .
### 3.
The three angle bisectors... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10591 | If A is mapping-reducible to B and is not mapping-reducible to co-B, is A Turing-reducible to co-B?
If $A \leq_m B$ and $A$ is not mapping reducible to $co\text{-}B$, then $A \leq_T co\text{-}B$.
Is this true?
My intuition is false even if we can find some special case to make it true such as $A=B=co\text{-}A_{TM}$.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14416 | # Dashed underline under a inequality symbol
I'm trying to find (or create) a symbol that is like \geq but with a dashed/dotted line under the inequality symbol. It should look like this:
• Excuse me but it's just a curiosity. But where is this symbol used in Mathematics? – Sebastiano Aug 14 '18 at 20:23
• I use this... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14417 | ## SOS - bipartite graphs
How do I prove: Given a connected d-regular graph G, if (-d) is an eigenvalue of G's adjacency matrix, then G is bipartite? (the reverse is pretty easy to see) |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14418 | # Mysterious Triangle
Geometry Level 1
A triangle has perimeter 14 and area $$2\sqrt{14}.$$ If the shortest side has length 3, find the positive difference between the lengths of other two sides. Give your answer to 3 decimal places.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14419 | n moles of an ideal gas undergoes a process A→B as shown in figure….
Q: n moles of an ideal gas undergoes a process A→B as shown in figure. Maximum temperature of the gas during the process is:
(a) $\displaystyle \frac{3 P_0 V_0}{2 n R}$
(b) $\displaystyle \frac{9 P_0 V_0}{4 n R}$
(c) $\displaystyle \frac{9 P_0 V_0... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14420 | # Séminaires : Séminaire d'Algèbre
Equipe(s) : gr, Responsables : J. Alev, D. Hernandez, B. Keller, Th. Levasseur, et S. Morier-Genoud. Email des responsables : Jacques Alev , David Hernandez , Bernhard Keller , Thierry Levasseur , Sophie Morier-Genoud Salle : 001 Adresse : IHP Description
Orateur(s) Natalia IYUDU ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14421 | # Approximation Property
It seems to be a folk result that l_infinity has the approximation property, even the bounded approximation property, and also, I think, even the so-called propery pi (approximation property) of Lindenstrauss.
This is alluded to in a few texts, but I cannot seem to find the proof, which is pr... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14422 | # Square multiples of 24
Author: mathforces
Problem has been solved: 228 times
Русский язык | English Language
How many natural square numbers less than $1,000,000$ are also multiples of 24? |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14423 | # Inellastic Collision Problem
1. Mar 1, 2008
### klopez
The mass of the blue puck shown below is 30.0% greater than the mass of the green one. Before colliding, the pucks approach each other with momenta of equal magnitudes and opposite directions, and the green puck has an initial speed of 11.0 m/s. Find the speed... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14424 | # In a linear relationship two data points are (9,3) and (33,9). If the function is y=mx+b, we have?
## (a) $m = 4$ and $b = - 33$ (b) $m = \frac{1}{4}$ and $b = \frac{3}{4}$ (c) $m = 4$ and $b = - 123$ (d) $m = \frac{1}{4}$ and $b = 24$
Jan 8, 2017
Looking at my calculations and your question's structure you have a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14425 | # Understanding vector space axioms
I am completely lost on the idea of vector spaces. I have read notes and watched videos and I am so confused. Can someone give me the general idea as to how I am supposed to figure out how these two satisfy the axioms of the vector spaces?
Let $V$ be the set of vectors in $\mathbb ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14426 | When does improper Riemann integration fail for computing expected values?
Riemann integration requires bounded intervals of integration. However, some continuous random variables (like those from the normal or gamma distribution) have unbounded support sets.
For these 2 distributions, would improper Riemann integral... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14427 | ## 2bornot2b Group Title What is the difference between the terms denumerable and enumerable. 2 years ago 2 years ago
1. satellite73 Group Title
synonyms
2. 2bornot2b Group Title
What's the meaning of them?
3. satellite73 Group Title
a set is "denumarable" if you can count the elements first, second, third etc
4... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14428 | # Uniform convergence of ${(1-\frac{x^2}{n})^n}$
Uniform convergence of: $$f_n(x):={(1-\frac{x^2}{n})^n}$$
(a) In a closed interval $[-L, L]$ as $L>0$.
(b) In $\mathbb{R}$.
My try:
There is a pointwise convergence to $e^{-x^2}$.
Obviously, there is no uniform convergence in $\mathbb{R}$ as $\lim\limits _{x\to \in... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14429 | ### kostka's blog
By kostka, 2 months ago,
The last round of Google Kick Start 2020 will take place this Sunday (November 15) at 3:00 UTC and will last 3 hours. Make sure you participate!
See you at g.co/kickstart.
UPD: Thank you for participating! Analysis can be found in the problem view. See you next year!
• +4... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14430 | # Math Help - Triangle problem and one more
1. ## Triangle problem and one more
I've been working on these for 2 hours, and still cant get the answer, thanks!!!
Nevermind the picture below, the problem is with the two problems in the link
2. h(h+7) / 2 = 60
3. Originally Posted by Wilmer
h(h+7) / 2 = 60
which prob... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14431 | Hellenica World
# .
In mathematics, a Carnot group is a simply connected nilpotent Lie group, together with a derivation of its Lie algebra such that the subspace with eigenvalue 1 generates the Lie algebra. Carnot groups have a Carnot–Carathéodory metric. They were introduced by Pansu (1982, 1989) and Mitchell (1985... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14848 | Comment
Share
Q)
Fill in the blank for the the following : Equations of the lines through the point $(3, 2)$ and making an angle of $45^{\circ}$ with the line $x-2y=3$ are _______.
$\begin {array} {1 1} (A)\;3x+y=7 ; x-3y=9 & \quad (B)\;3x-y=7; x+3y=9 \\ (C)\;3x-y=-7; x-3y=-9 & \quad (D)\;3x+y=-7 ; x+3y=-9 \end {arra... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14849 | User:Fropuff/Draft 2
Draft in progress. Writing hyperbolic plane.
The hyperbolic plane is a two-dimensional surface with constant negative curvature equal to −1. According to the uniformization theorem in Riemannian geometry there are exactly three distinct simply connected surfaces with constant Gaussian curvature. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14850 | ## Repair What Does The Standard Error In The Mean Indicate (Solved)
Home > Standard Error > What Does The Standard Error In The Mean Indicate
# What Does The Standard Error In The Mean Indicate
## Contents
Of course, T / n {\displaystyle T/n} is the sample mean x ¯ {\displaystyle {\bar {x}}} . Or decreasing standa... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14851 | anonymous 4 years ago Prove that (14^n + 4)/2 is never prime.
1. anonymous
* (14^n + 11)/2
2. Mr.Math
The expression you gave is never integer.
3. Mr.Math
$$14^n+11$$ is odd $$\forall n\in \mathbb{Z}$$, which implies $$\frac{14^n+11}{2}$$ is never integer and hence never prime.
4. anonymous
5. anonymous
14^n, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14852 | # Area of Square - Comparing squares
The question is:
If the area of a parallelogram $JKLM$ is $n$ and if length of $KN$ is $n+(1/n)$, then find the length of $JM$. (The answer is $n^2 /( n^2+1 )$.)
How would i go about solving this problem ?
-
Do you know the formula for the area of a parallelogramm? – Phira Jun ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14853 | # Finding the fixed points of a contraction
Banach's fixed point theorem gives us a sufficient condition for a function in a complete metric space to have a fixed point, namely it needs be a contraction.
I'm interested in how to calculate the limit of the sequence $x_0 = f(x), x_1 = f(x_0), \ldots, x_n = f(x_{n-1})$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14854 | ### Contact
A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?
# Approximating Pi
##### Stage: 4 and 5 Challenge Level:
By inscribing a circle in a square and then a square in a circle ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14855 | # Topological dimension of a countable dense set
I'm reading a (dynamical systems) paper in which topological dimension figures. In my situation, I'm trying to compute the topological dimension of the subset of the $d$-dimensional torus consisting of points with rational coordinates. I've looked at the online resource... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14856 | # Lifting of a proper map in the cover is a proper map
Let $$M$$ be an orientable surface without boundary$$($$I am not assuming $$M$$ is compact, it can be non-compact$$)$$. Let $$\Phi: M\to M$$ be a proper homotopy-equivalnce$$($$A proper homotopy-equivalence can be defined analog way as homotopy-equivalence, but he... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14857 | #### Vol. 12, No. 1, 2019
Recent Issues
The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Author Index Coming Soon Other MSP Journals
On the covering number of $S_... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14858 | # Number of natural and real numbers [duplicate]
I was reading Rubin and came across the fact that $2^{\aleph_0}$ is the cardinality of reals.
I follow the proof but I cant seem to understand physically what this attempts to say. Is there a nice intuitive explanation for this property?
-
It ways that there is a bije... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14859 | Courses
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# Write an equation of a horizontal parabola with the given vertex and passing through the given point. Vertex at (4,3) and passing through (6,2).
Last updated date: 27th Mar 2023
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Hint: A... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14860 | +7 (3412) 91 60 92
## Archive of Issues
Russia Izhevsk
Year
2012
Issue
3
Pages
19-24
Section Mathematics Title About Stone space of one Boolean algebra Author(-s) Golovastov R.A.a Affiliations Udmurt State Universitya Abstract We consider the Boolean algebra of the same type as algebra constructed by Bell, and the S... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14861 | Portal:Mathematics
The Mathematics Portal
Mathematics is the study of numbers, quantity, space, structure, and change. Mathematics is used throughout the world as an essential tool in many fields, including natural science, engineering, medicine, and the social sciences. Applied mathematics, the branch of mathematics... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14862 | Examveda
# The cost of packaging of the mangoes is 40% the cost of fresh mangoes themselves. The cost of mangoes increased by 30% but the cost of packaging decreased by 50%, then the percentage change of the cost of packed mangoes, if the cost of packed mangoes is equal to the sum of the cost of fresh mangoes and cost... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_14863 | # Math Help - sigma-algebra
1. ## sigma-algebra
Hi!
Trying to get a grasp on $\sigma-algebra$.
Let´s say I have a the set $\Omega = \left\{1,2,3}\right\}$.
Now, if I want to find the smallest $\sigma-algebra \, F$ that includes both 1 and 2. Would this be:
$F = \left\{\emptyset, \Omega, 1, 2, 3, \left\{1,2\right\}... |
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