text stringlengths 256 16.4k |
|---|
May 16th, 2016, 08:34 AM
# 1
Senior Member
Joined: Dec 2014
From: The Asymptote
Posts: 142
Thanks: 6
Math Focus: Certainty
Temperature Gradient
You are part of a team of engineers designing an electric power plant that makes use of the temperature gradient in the ocean. The system is to operate between 20.0°C (surface-... |
@DavidReed the notion of a "general polynomial" is a bit strange. The general polynomial over a field always has Galois group $S_n$ even if there is not polynomial over the field with Galois group $S_n$
Hey guys. Quick question. What would you call it when the period/amplitude of a cosine/sine function is given by anot... |
Here is the URL: https://github.com/avaneev/biteopt
I've tested it on numerous global optimization benchmarking functions (included), and on real-world hyperparameter optimization problems I have. Seems to be working quite well except in comparison to deterministic methods it's necessary to make several attempts at dif... |
Dear Uncle Colin, If $e = \left( 1+ \frac{1}{n} \right)^n$ when $n = \infty$, how come it isn’t 1? Surely $1 + \frac{1}{\infty}$ is just 1? - I’m Not Finding It Natural, It’s Terribly Yucky Hi, INFINITY, and thanks for your message. You have fallen into one of maths’s classicRead More →
What are they? I thought, until ... |
The Strauss conjecture on negatively curved backgrounds
1.
Department of Mathematics, Johns Hopkins University, Baltimore, MD 21218, USA
2.
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, China
This paper is devoted to several small data existence results for semi-linear wave equations on negativ... |
Event detail
Seminar | March 4 | 12:10-1 p.m. | 939 Evans Hall
Nicolai Reshetikhin, UC Berkeley
For finite dimensional representations $V_1, \dots , V_m$ of a simple finite dimensional Lie algebra $\mathfrak g$ consider the tensor product $W=\otimes _{I=1}^m V_i^{\otimes N_i}$. The first result, which will be presented... |
Search
Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Search
Now showing items 1-10 of 20
Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c w... |
I am trying to prove the following inequality:
EDIT: Almost immediately after I posted this question, I discovered that the inequality I am being asked to prove is called Cantelli's inequality. When I wrote this up, I didn't realize this particular inequality had a name. I have found multiple proofs through Google, so ... |
Reference
For a bounded nonexample of integrability see: Riemann Integral: Bounded Nonexample
For a convergence theorem on integral see: Riemann Integral: Uniform Convergence
For a comparison of integrals see: Uniform Integral vs. Riemann Integral
Definition
Given a measure space $\Omega$ and a Banach space $E$.
Consid... |
I'm having a bit of a struggle with the following proof.
Statement: Prove that $N((0,0);1)$ is an open set in $\mathbb{R}\times\mathbb{R}$ with metric $d((x_1,x_2),(y_1,y_2))=|x_1-y_1|+|x_2-y_2|$.
Attempt: Let $x\in N((0,0);1)$. We need $N(x;\epsilon)=\{(a_1,a_2):|x_1-a_1|+|x_2-a_2|<\epsilon \} \subseteq N((0,0);1)=\{(... |
Is there an algorithm for finding the shortest path in an undirected weighted graph?
All-Pairs-Shortest Path
Given a graph $G = (V, E)$ find the shortest path between
any two nodes $u,v \in V$. It can be solved by Floyd-Warshall's Algorithm in time $O(|V|^3).$ Many believe the APSP problem requires $\Omega(n^3)$ time, ... |
In the classic crypto textbook "Introduction to Modern Cryptography" by Jonathan Katz and Yehuda Lindell, there is a definition for indistinguishable encryption in the presence of an eavesdropper as such that for every probabilistic polynomial time adversary A there is a negligible function negl(n) such that
$\Pr[PrivK... |
The problem with your code is that
N[Product[...]] calls
NProduct[...] which turns integers into reals before
Prime can evaluate, causing the error: See
Details and Options section of documentation of
NProduct.
For your calculation, you actually do not need these. It looks like the result converges around $0.660162$:
T... |
Is the following theorem known, or can be easily derived from known results?
Consider the differential equation $$w''-kz^{-1}w'=(\lambda+\phi(z))w,$$ where $k>0$ is fixed, $\lambda$ is a large (complex) parameter and $\phi$ is a complex valued function analytic on $[0,1]$. It is known that there exists a unique solutio... |
Dana Scott had once proved that Zermelo's set theory $``\text{Z}"$ can be interpretable in the first order set theory whose axioms are just the axioms of:
Separation: if $\phi$ is a formula in which x doesn't occur, then: $\forall A \exists x \forall y (y \in x \iff y \subset A \wedge \phi)$ is an axiom. Infinity: the ... |
For the heat equation
\begin{equation} u_t(t,x) = \nu u_{xx}(t,x) \end{equation}
for $x \in [0,1]$ with boundary conditions $u(t,0) = u(t,1) = 0$ and initial value $u(0,x) = u_0(x)$ it is easy to show that the "energy" defined as
\begin{equation} E(t) = \frac{1}{2} \int_{0}^{1} u^2(t,x)~dx \end{equation}
decays over ti... |
If the density is bounded by a constant $C$ then I think the rate of convergence can be bounded as $\exp(-\delta t /C^2)$ for some fixed constant $\delta >0$. If the density is unbounded then I don't think there needs to be a uniform version of exponential convergence.
To elaborate on this, I will use my answer to the ... |
Is there a physical limit to data transfer rate (e.g. for USB $3.0$, this rate can be a few Gbit per second)? I am wondering if there is a physical law giving a fundamental limit to data transfer rate, similar to how the second law of thermodynamics tells us perpetual motion cannot happen and relativity tells us going ... |
Data is a general term for information (observations and/or measurements) collected during any type of systematic investigation.
A
data display is a visual format for organising and summarising data. Examples include box plots, column graphs, frequency tables, scatter plots, and stem plots.
A decimal is a numeral in th... |
$\newcommand{\Re}{\mathbb{R}}$I m looking for sufficient conditions that
may guarantee positive semidefiniteness (PSD) of a block matrix$$A = \begin{bmatrix} A_{1,1} & \cdots & A_{1,n} \\ \vdots & \ddots & \vdots \\ A_{n,1} & \cdots & A_{n,n}\end{bmatrix}$$with consistent block dimensions, $A_{i,j} \in \Re^{d_i \times ... |
I'm dealing with a coupled system of three transient, non-linear convection-diffusion equations. Let's just say to simplify the problem that they take the following form: $$ -\nabla\cdot(D_{1}(u_{2},u_{3})\nabla u_{1}) = -\nabla\cdot\mathbf{\chi}(u_{2},u_{3}) $$ $$ \frac{\partial u_{2}}{\partial t} + \nabla\cdot f_{1}(... |
I have been recently researching Happynet in terms of approximation and I have found out that there is a little interest in this topic.
What's the reason for this? Are there any related problems, that get better attention?
The Happynet problem is related to minimizing the energy in a Hopfield net.
The problem is define... |
According to
Uniformization theorem every compact Riemann surface $\Sigma$ of genus $g\ge2$ is isomorphic to a space that can be obtained by the action of a Fuchsian group on upper half plane $\mathbb{H}$
$$\Sigma\simeq\frac{\mathbb{H}}{\Gamma}$$
On the Teichmüller or moduli space of such Riemann surfaces, one can cons... |
Answer
b. 8 hours
Work Step by Step
We use the equation for period to find: $T=\sqrt{\frac{4\pi^2r^3}{GM_E}}$ $T=\sqrt{\frac{4\pi^2(20,200\times10^3)^3}{(6.67\times10^{-11})(5.97\times10^{24})}}\approx \fbox{8 hours}$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim... |
Search
Now showing items 1-10 of 33
The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
Let $X_n(\Bbb{Z})$ be the simplicial complex whose vertex set is $\Bbb{Z}$ and such that the vertices $v_0,...,v_k$ span a $k$-simplex if and only if $|v_i-v_j| \le n$ for every $i,j$. Prove that $X_n(\Bbb{Z})$ is $n$-dimensional...
no kidding, my maths is foundations (basic logic but not pedantic), calc 1 which I'm pr... |
Title:
twolinesBfield
Post by:
ahmedelshfie on June 30, 2010, 07:21:22 pm
This following applet is
twolinesBfield
Created by prof Hwang Modified by Ahmed
Original project twolinesBfield (http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=1451)
There is current flow I in the z direction (along z-axis) which will produc... |
A new proof of the boundedness results for stable solutions to semilinear elliptic equations
1.
ICREA, Pg. Lluis Companys 23, 08010 Barcelona, Spain
2.
Universitat Politècnica de Catalunya, Departament de Matemàtiques, Diagonal 647, 08028 Barcelona, Spain
3.
BGSMath, Campus de Bellaterra, Edifici C, 08193 Bellaterra, S... |
I was reading the exponent Combination law in
proofwiki.org and got confused in one part of the proof. The proof is as follows:
Let $a \in R{> 0}$
Let $x, y \in R$
Let $a^x$ be defined as $a$ to the power of $x$
Then:
$a^x a^y = a^{x + y}$
Proof:
$a^{x+y}= $ $\displaystyle \exp \left({\left({x + y}\right) \ln a}\right)... |
Let's suppose we have
$$\gcd(a,b)\cdot\gcd(b,c)\cdot\gcd(c,a)\cdot \gcd(a,b,c) = abc$$
and look at a prime $p$ dividing at least one of $a,b,c$.
Suppose $p$ divides at most two of the three, say $p\nmid c$, and $a = p^\alpha\cdot a'$, $b = p^\beta\cdot b'$ with $p\nmid a'b'$. Then on the left hand side, $p$ does only o... |
I'm studying the quantum mechanics of an infinite square well from a computational standpoint.
My eigenfunctions are defined as $u_n(x)=\sqrt{2/L}\sin\left(n\pi x/L\right),\quad 0 \le x \le L, \quad n=1,2,3,\dots$ and zero outside of the $[0,L]$ interval.
I'd like to transform the wave function from position domain to ... |
It's easier to think about the Intermediate Value Theorem, which is equivalent to the Brouwer Fixed-Point Theorem for the unit interval.
The main issue is that dichotomy for (Cauchy) real numbers is not constructively valid: given two real numbers $\alpha,\beta$, there is no algorithm to decide whether $\alpha \leq \be... |
(Note: This question is related to my previous mathoverflow question, "Critical Points in $ZF$ without Choice".)
In the
Stanford Encyclopedia of Philosophy entry "Non-Wellfounded Set Theory" (Section 2.2, "The Foundation Axiom"), one has the following statement (my comments regarding it are in brackets):
The Foundation... |
Search
Now showing items 1-6 of 6
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
It does that whenever the Internet connection is temporarily down.muzik wrote:Looks like my apgsearch glitched out and submitted a mutant Siamese twin haul: I mean, not that that's a major problem or anything, just kinda interesting
For general discussion about Conway's Game of Life.
What do you do with ill crystallogr... |
Definitions: Let $T$ (for "time") be a random variable $T \sim \text{Exp}(\lambda)$ and $\Delta t$ is a realization (or called an observed value) of $T$. Let $D$ (for "delay") be a random variable $D \sim \text{Exp}(\mu)$. All the random variables (including those involved below) are mutually independent. Timed Balls-i... |
Current browse context:
astro-ph.HE
Change to browse by: Bookmark(what is this?) Astrophysics > High Energy Astrophysical Phenomena Title: The Optical Afterglow of GW170817: An Off-axis Structured Jet and Deep Constraints on a Globular Cluster Origin
(Submitted on 21 Aug 2019)
Abstract: We present a revised and complet... |
closed as no longer relevant by Robin Chapman, Akhil Mathew, Yemon Choi, Qiaochu Yuan, Pete L. Clark Aug 22 '10 at 9:00
This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicabl... |
How to Perform a Nonlinear Distortion Analysis of a Loudspeaker Driver
A thorough analysis of a loudspeaker driver is not limited to a frequency-domain study. Some desirable and undesirable (but nonetheless exciting) effects can only be caught by a nonlinear time-domain study. Here, we will discuss how system nonlinear... |
Ranked alphabet is very often used in Ranked Trees definition, like here for instance. In that example for given set $\Sigma=\{a,b,c\}$ ranks assigned by arity function $ar : \Sigma\rightarrow\mathcal{N}$ as:
$ar(a)=2, ar(b)=2, ar(c)=1$.
And Ranked Tree over $\Sigma$ is defined as:
$T_{\Sigma_r}$, the set of ranked tre... |
Taiwanese Journal of Mathematics Taiwanese J. Math. Volume 18, Number 6 (2014), 1957-1979. NON-NEHARI MANIFOLD METHOD FOR SUPERLINEAR SCHRÖDINGER EQUATION Abstract
We consider the boundary value problem \begin{equation} \tag{0.1} \left\{ \begin{array}{ll} -\triangle u+V(x)u=f(x, u), \ \ \ \ & x\in \Omega,\\ u=0, \ \ \ ... |
Finite Fourier Transform on a 2d waveHow does the finite fourier transform work exactly?The transform of f(x) is\widetilde{f}(\lambda_{n}) =\int^{L}_{0} f(x) X_{n} dxIf I had a 3d wave equation pde and I applied Finite fourier transform on the pde forz(x,y,t)=X(x)Y(y)T(t)...
1. Homework Statement [/prove f(x1,y1)-f(x0,... |
Consider the following so-called $U$-statistic of order 2: $$U = \frac1{\binom{m}{2}} \sum_{i < j} h(w_i,w_j)$$ where $w_1,\dots,w_m$ are IID from some distribution and $h$ is symmetric. If $|h(w_1,w_2)| \le B$ a.s., then a classical result gives the following concentration inequality: \begin{align} \mathbb P( | U - \m... |
This has been moved from math.stackexchange;
I am attempting to prove/disprove convergence of the following sum$$ \lim_{n \to \infty} \frac{1}{n} \sum_{p \leq n} \sum_{k=0}^\infty \ln p \left\{\frac{n}{(p-1)p^k} \right\}$$where $\{ x\}$ denotes the
fractional part of $x$.
Let $\epsilon_n$ denote the above double sum. I... |
But if you don't want to have a Google account: Chrome is really good. Much faster than FF (I can't run FF on either of the laptops here) and more reliable (it restores your previous session if it crashes with 100% certainty).
And Chrome has a Personal Blocklist extension which does what you want.
: )
Of course you alr... |
This is a really beautiful problem!
As there is some discussion in the question/comments/one of the answers about the history of this problem, let me narrate here what I found. I’m making this community-wiki as it is not exactly an answer to the question.
In
Mathematics Magazine, which is published five times a year by... |
The unit of illumination is the lux, lumens per square meter.
What is the minimum lux required for reading? How many lux does the Sun provide at distance D?
What is the minimum lux required for reading?
You can plug all sorts of numbers into this depending on how good your eyes are, how big the print is, and how close ... |
Corollaries to the Uniform Boundedness Principle
Corollaries to the Uniform Boundedness Principle
Recall from The Uniform Boundedness Principle page that if $X$ is a Banach space and $Y$ is a normed linear space where $\mathcal F$ is a collection of bounded linear operators from $X$ to $Y$ such that for every $x \in X$... |
The Chebyshev Metric
Recall from the Metric Spaces page that if $M$ is a nonempty set then a function $d : M \times M \to [0, \infty)$ is called a metric if for all $x, y, z \in M$ we have that the following three properties hold:
$d(x, y) = d(y, x)$. $d(x, y) = 0$ if and only if $x = y$. $d(x, y) \leq d(x, z) + d(z, y... |
Lovász theta-function of graphs¶
AUTHORS:
Dima Pasechnik (2015-06-30): Initial version
REFERENCE:
Functions¶
sage.graphs.lovasz_theta.
lovasz_theta(
graph)¶
Return the value of Lovász theta-function of graph
For a graph \(G\) this function is denoted by \(\theta(G)\), and it can be computed in polynomial time. Mathemat... |
Hyperplane in $n$-Dimensional Space Through Origin is a Subspace
Problem 352
A hyperplane in $n$-dimensional vector space $\R^n$ is defined to be the set of vectors\[\begin{bmatrix}x_1 \\x_2 \\\vdots \\x_n\end{bmatrix}\in \R^n\]satisfying the linear equation of the form\[a_1x_1+a_2x_2+\cdots+a_nx_n=b,\]where $a_1, a_2,... |
Multiple Products of Riemann-Stieltjes Integrable Functions with Increasing Integrators
Recall from The Product of Riemann-Stieltjes Integrable Functions with Increasing Integrators page that if $f$ and $g$ are functions defined on $[a, b]$ and $\alpha$ is an increasing function on $[a, b]$ then if $f$ and $g$ are Riem... |
There is a question in Mark Srednicki's Book (Problem 24.4, p.160) about $Sp(2N)$, but I am not sure I understand the significance (application?) of this group. In that chapter, he talks about $SO(N)$ and $SU(N)$, which are part of the Standard Model and from accepted answer of this I gather that the structure of the S... |
Surface plasmon resonance (SPR).
Surface plasmon resonance ( SPR) is the resonant oscillation of conduction electrons at the interface between a negative and positive permittivity material stimulated by incident light. The resonance condition is established when the frequency of incident photons matches the natural fre... |
The Field of Real Numbers
We will now look at some axioms regarding the set of real numbers $\mathbb{R}$. We will note that an "axiom" is a statement that isn't meant to necessarily be proven and instead, they're statements that are given. These axioms are rather straightforward and may seem trivial, however, we will s... |
Physics of Rotational Motion
The laws and equations that govern nature and natural phenomena are described by physics. One prime focus of physics is motion. We have dealt in detail about translational motion (objects that move along a straight or curved line) in the previous chapters, and now we will expand our view to... |
I know that the geodesics for Euclidean Space are straight lines and likewise in the absence of forces like gravity, the geodesics are straight lines. But what if you took some curved lines and tried to work backwards to determine the geometry of the space consisting of the curved geodesics. How would one go about dete... |
Is the Set of All Orthogonal Matrices a Vector Space? Problem 611
An $n\times n$ matrix $A$ is called
orthogonal if $A^{\trans}A=I$. Let $V$ be the vector space of all real $2\times 2$ matrices.
Consider the subset
\[W:=\{A\in V \mid \text{$A$ is an orthogonal matrix}\}.\] Prove or disprove that $W$ is a subspace of $V... |
Partial Linearity of Integrals of Upper Functions on General Intervals
Recall from the Upper Functions and Integrals of Upper Functions page that a function $f$ defined on an interval $I$ is said to be an upper function on $I$ if there exists an increasing sequence of functions $(f_n(x))_{n=1}^{\infty}$ that converges ... |
Let $\mathscr{M}$ be a model category and let $\mathscr{I}$ be a small category. Consider any homotopy colimit functor $\text{hcolim}_{\mathscr{M}}^{\mathscr{I}}\colon\mathscr{M}^{\mathscr{I}}\longrightarrow \mathscr{M}$ of shape $\mathscr{I}$ on $\mathscr{M}$. Here I adopt the notion of homotopy colimit considered in ... |
A Comparison Theorem for Integrals of Upper Functions on General Intervals
Recall from the Upper Functions and Integrals of Upper Functions page that a function $f$ on $I$ is said to be an upper function on $I$ if there exists an increasing sequence of functions $(f_n(x))_{n=1}^{\infty}$ that converges to $f$ almost ev... |
The Set of all Subsets of Natural Numbers is Uncountable
Table of Contents
The Set of all Subsets of Natural Numbers is Uncountable
Theorem 1: The set $\mathcal P (\mathbb{N})$ of all subsets of $\mathbb{N}$ is uncountable. In the proof below, we use the famous diagonalization argument to show that the set of all subse... |
What is meant by Laplace Transform? asked | 579 views | 1 answers. Definition of Laplace Transform and give the basic Laplace Transforms and its application. MathematicsLaplaceTransform
0
Laplace transform is yet another operational tool for solving constant coefficients linear differential equations. The process of so... |
Differentiation and Integration of Power Series
We will now look at differentiating and integrating power series term by term, a technique that will be very useful. We first note that power series have terms which are polynomials, and polynomials are relatively easily to differentiate and integrate. The following theor... |
How Laplace Transform related to Fourier Transform? asked | 754 views | 1 answers. Difference between Laplace Transform and Fourier Transform and how they are related. LaplaceTransformFourier
0
This brief note is about Fourier transform and how related to Laplace Transform.
To begin, we first state the definition of th... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
A canon is fired Horizontal to the ground 80 meters above ground The canon ball is fired a $T=0$ and hits the ground at $T_g$. Calculate the height at the time $T_g/2$So far I have calculated time. which gives me the equation$$y=y_i+v_{iy}(4.05) - (0.5)(9.82)(4.05^2)$$Now my problem is that when I try to calculate $v_{... |
By what way and with which variables could you determine a plane's maximum rate of climb per time? If I'm not mistaken, I'm looking for V
Y.
By what way and with which variables could you determine a plane's maximum rate of climb per time? If I'm not mistaken, I'm looking for V
To calculate your possible climb speed $v... |
This is a crosspost from MSE. It's been up there for a few weeks now. A 200 rep bounty yielded no results (or even comments). I'm hoping someone here has some helpful ideas. See this post for the original.
Consider $U$ a nice compact region in $\mathbb{C}$ with boundary $\Gamma$. Let $S_1$ b the ideal of trace class op... |
The most frequently used evaluation metric of survival models is the concordance index (c index, c statistic). It is a measure of rank correlation between predicted risk scores $\hat{f}$ and observed time points $y$ that is closely related to Kendall’s τ. It is defined as the ratio of correctly ordered (concordant) pai... |
Edit My original answer was wrong. The pressure is in fact constant; if there were a gradient, then the layer between $z$ and $z+dz$ would have a net force on it, and the gas would not be in a steady state. This is in contrast to the fact that in a gravitational field, there must be a net force on such a layer that cou... |
It's been a while since my last time using Mactex + Texstudio, which worked fine back then. Now with fresh installation I'm getting the below error:
Package inputenc Error: Unicode character 〖 (U+3016)(inputenc) not set up for use with LaTeX. \end{align}Package inputenc Error: Unicode character 〗 (U+3017)(inputenc) not... |
Tagged: determinant of a matrix Problem 718
Let
\[ A= \begin{bmatrix} 8 & 1 & 6 \\ 3 & 5 & 7 \\ 4 & 9 & 2 \end{bmatrix} . \] Notice that $A$ contains every integer from $1$ to $9$ and that the sums of each row, column, and diagonal of $A$ are equal. Such a grid is sometimes called a magic square.
Compute the determinan... |
Prove that the Center of Matrices is a SubspaceLet $V$ be the vector space of $n \times n$ matrices with real coefficients, and define\[ W = \{ \mathbf{v} \in V \mid \mathbf{v} \mathbf{w} = \mathbf{w} \mathbf{v} \mbox{ for all } \mathbf{w} \in V \}.\]The set $W$ is called the center of $V$.Prove that $W$ is a subspace ... |
Let $F$ be a field and let $A\in M_n(F)$ be a matrix with $det(A) = \pm 1 $. How can I show that $A$ is a product of involutions ? Of course the converse is true and clear.
By involution I mean a matrix whose square is the identity matrix.
Mathematics Stack Exchange is a question and answer site for people studying mat... |
I'm not able to come up with an argument that is fundamentally different from the "committee argument", but it is possible to cast the entire proof in geometric terms if one is willing to move into the third dimension.
Consider a three-dimensional grid analogous to your two-dimensional one. Your grid is a quadrant of a... |
Suppose you have a data set $Y_{1}, ..., Y_{n}$ from a continuous distribution with density $p(y)$ supported on $[0,1]$ that is not known, but $n$ is pretty large so a kernel density (for example) estimate, $\hat{p}(y)$, is pretty accurate. For a particular application I need to transform the observed data to a finite ... |
I assume that you are using the OLS estimator on this linear regression model. You can use the
, which will be the solution to a minimization problem under inequality constraints. Using standard matrix notation (vectors are column vectors) the minimization problem is stated as inequality constrained least-squares estim... |
I know that there are plenty of
Machine learning algorithms out there for prediction and classification tasks, but why then we need Neural networks even? Why Neural nets?
The basic idea of implementing neural networks is to mimic human
brain or simply develop a model that works like a human brain. In Machine learning t... |
NTS ABSTRACT
Return to NTS Spring 2017
Contents Sept 7
David Zureick-Brown Progress on Mazur’s program B I’ll discuss recent progress on Mazur’s ”Program B”, including my own recent work with Jeremy Rouse which completely classifies the possibilities for the 2-adic image of Galois associated to an elliptic curve over t... |
We are always introduced to magnets by pictures illustrating a parallepiped magnet, a horseshoe magnet, etc...
Anyway the first time we actually calculate a magnetic field is for eelectromagnets. Indeed I've rarely seen explaining or calculating the magnetic field of a permanent magnet. I know formulas for the magnetic... |
Electronic Journal of Probability Electron. J. Probab. Volume 20 (2015), paper no. 95, 35 pp. Random walk on random walks Abstract
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisso... |
This was one of those big questions in the 19th century. It still causes some consternation. If you have a composite system, such as the nucleus of an atom, some other force is necessary. This force of course is the nuclear interaction. This keeps the protons from flying apart, though for some unstable nuclei there are... |
The Character of a Group Representation
Definition: Let $G$ be a group and let $(V, \rho)$ be a group representation of $G$. The Character of $(V, \rho)$ is the function $\chi_V : G \to \mathbb{C}$ defined for all $g \in G$ by $\chi_V(g) = \mathrm{trace} (\rho(g))$. Recall that if $A$ is a square matrix then $\mathrm{t... |
Consider a doublet of complex scalar fields $\mathbf{\Phi}$. The $SU(2)$ transformation is $\textrm{exp}\left(it^{i}\tau_{i}\right)$ with generators $\tau_{i}=\frac{\sigma_{i}}{2}$, whilst the $U(1)$ transformation is $\textrm{exp}\left(\frac{1}{2}i\alpha I\right)$. Hence we may write an $SU(2)\times U(1)$ transformati... |
The Annals of Statistics Ann. Statist. Volume 13, Number 2 (1985), 689-705. Additive Regression and Other Nonparametric Models Abstract
Let $(X, Y)$ be a pair of random variables such that $X = (X_1, \cdots, X_J)$ and let $f$ by a function that depends on the joint distribution of $(X, Y).$ A variety of parametric and ... |
Dynamical zeta functions and topology for negatively curved surfaces
主讲人：Semyon Dyatlov
时间： 周二、周三14:00-15:30，2019-7-2
地点：清华大学近春园西楼第三会议室
摘要
For a negatively curved compact Riemannian manifold (or more generally, for an Anosov flow), the Ruelle zeta function is defined by $$\zeta(s)=\prod_\gamma (1-e^{-s\ell_\gamma} ),\q... |
As metioned in Wikipedia's biography, Shanks used Machin's formula$$ \pi = 16\arctan(\frac15) - 4\arctan(\frac1{239}) $$
The standard way to use that (and the various Machin-
like formulas found later) is to compute the arctangents using the power series
$$ \arctan x = x - \frac{x^3}3 + \frac{x^5}5 - \frac{x^7}7 + \fra... |
Scalar Multiples of Matrices
Definition: A scalar is a quantity that has a magnitude (size or length) but no direction.
Unless otherwise specified, scalars in the context of Linear Algebra will be a real number $k \in \mathbb{R}$. We are now ready to define scalar multiplication on a matrix.
Definition: If $A$ is an $m... |
Question
Suppose you have a supply of inductors ranging from 1.00 nH to 10.0 H, and resistors ranging from $0.100 \textrm{ }\Omega$ to $1.00 \textrm{ M}\Omega$. What is the range of characteristic RL time constants you can produce by connecting a single resistor to a single inductor?
Final Answer
$\tau_{max} = 100 \tex... |
Too long for a comment: Here's a little intuitive tip: What do $~\dfrac{\sin t}t~$ and $~\dfrac{\cos t}{t^2}~$ both have in
common? They are even functions. So, if you notice various series or integrals whose summand
or integrand belongs to this category having a nice closed form, that should not surprise you. For
inst... |
Some Metrics Defined on Euclidean Space
Recall from the Metric Spaces page that if $M$ is a nonempty set then a function $d : M \times M \to [0, \infty)$ is called a metric if for all $x, y, z \in M$ we have that the following three properties hold:
$d(x, y) = d(y, x)$. $d(x, y) = 0$ if and only if $x = y$. $d(x, y) \l... |
If a Half of a Group are Elements of Order 2, then the Rest form an Abelian Normal Subgroup of Odd Order Problem 575
Let $G$ be a finite group of order $2n$.
Suppose that exactly a half of $G$ consists of elements of order $2$ and the rest forms a subgroup. Namely, suppose that $G=S\sqcup H$, where $S$ is the set of al... |
Most of the phenomena studied in the domain of Engineering and Science are periodic in nature. For instance, current and voltage in an alternating current circuit. These periodic functions could be analyzed into their constituent components (fundamentals and harmonics) by a process called Fourier analysis.
Periodic fun... |
Yes, except for the specific case in which the state is in an eigenstate of the measurement operator.Measurements with deterministic outcomesMore specifically, for any quantum (pure) state $|\psi\rangle$, there is just one class of measurements that can be performed without changing the state, and these are the measure... |
Answer
Stone house: 9 hours Wood house: 3 hours
Work Step by Step
We divide the value of Q by the rate at which heat is absorbed to find: $ \Delta t = \frac{ \Delta Q}{10^5} = \frac{75 \times 2000 \times .2 \times 30}{10^5 } = 9 \ hours$ For the wood house: $\Delta t = \frac{ \Delta Q}{10^5} = \frac{15 \times 2000 \tim... |
NTS ABSTRACTSpring2019
Return to [1]
Contents Jan 23
Yunqing Tang Reductions of abelian surfaces over global function fields For a non-isotrivial ordinary abelian surface $A$ over a global function field, under mild assumptions, we prove that there are infinitely many places modulo which $A$ is geometrically isogenous ... |
NTS ABSTRACTSpring2019
Return to [1]
Contents Jan 23
Yunqing Tang Reductions of abelian surfaces over global function fields For a non-isotrivial ordinary abelian surface $A$ over a global function field, under mild assumptions, we prove that there are infinitely many places modulo which $A$ is geometrically isogenous ... |
This answer says
A helicopter uses a LOT more fuel hovering than it does in forward flight.
Is this correct? Why?
Aviation Stack Exchange is a question and answer site for aircraft pilots, mechanics, and enthusiasts. It only takes a minute to sign up.Sign up to join this community
Yes it is correct that helicopters use... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.