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A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
I just noticed Joseph's comment in his question about Markov chains. My observations about the correctness of trying to use Markov chains to describe the rolling of a die, fair or unfair:
If by
state in the Markov chains, you mean just the "face" it is currently on or the "face" which is lower-most in attitude at a par... |
$ L^{p, q} $ estimates on the transport density
Laboratoire de Mathématiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay Cedex, France
In this paper, we show a new regularity result on the transport density $ \sigma $ in the classical Monge-Kantorovich optimal mass transport problem between two... |
Ivan Raikov About me
I am a researcher at Stanford University.
My CV is available here.
You can reach me at ivan (dot) g (dot) raikov (at) gmail (dot) com.
Software
I have a Github page.
Most of my recent software is written in Scheme for the Chicken Scheme compiler, or in Standard ML for the MLton compiler.
A list of ... |
Of course not.
But after reading a bit, some points make me believe it should be:
Let $S$ be a nice$^{\*}$ surface defined over $Spec\ \mathbb{Z}$.
The Brauer group $Br(S\otimes \bar{\mathbb{Q}})$ is an abelian divisible group, It is also a $Gal(\bar{\mathbb{Q}}/\mathbb{Q})$ module, For good primes there are reductions... |
To interpolate between data points \( \fvec{x}_i \) which are not somehow ordered in a grid structure the scattered data interpolation (Shepard-Interpolation) algorithm can be used\begin{equation*} f(\fvec{x}) = \sum_{i=1}^n \frac{w_i(\fvec{x}) f(\fvec{x}_i)}{\sum_{i=1}^n w_i(\fvec{x})}. \end{equation*}
The algorithm c... |
To prove $I=f^{-1}(I’)$ is an ideal of $R$, we need to check the following two conditions:
For any $a, b\in I$, we have $a-b\in I$.
For any $a\in I$ and $r\in R$, we have $ra\in I$.
Let us first prove condition 1. Let $a, b\in I$. Then it follows from the definition of $I$ that $f(a), f(b)\in I’$.Since $I’$ is an ideal... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Basic tutorial¶
This basic tutorial gives a brief overview of some of functionality of the
particles package. Details are deferred to more advanced tutorials. First steps: defining a state-space model¶
We start by importing some standard libraries, plus some modules from the package.
[12]:
%matplotlib inlineimport warn... |
If a matrix is diagonalizable, then the algebraic multiplicity of an eigenvalue is the same as the geometric multiplicity of the eigenvalue.
Recall that the geometric multiplicity of an eigenvalue is the dimension of the eigenspace of the eigenvalue.
Solution.
(a) Find the size of the matrix $A$
If $A$ is an $n\times n... |
It looks so. We start with inductive proof of
Steinitz Theorem. Let $A$ be a finite set of rays starting from the origin in $\mathbb{R}^d$. Assume that positive span of these rays is the whole $\mathbb{R}^d$. Then there exists a subset of at most $2d$ rays from $A$ with the same property.
Proof. Induction in $d$. Base ... |
I’m extremely agitated today. I dunno why. Maybe because there was some convulsion in the peaceful tidings of the house I live in, or the fact that I’m kinda hungry at the moment. Anyways, I don’t have time for chitchat. Let’s get to the studying.
The following is taken from
Foundations of Machine Learning by Rostamyar... |
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Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Let $a, b$ be arbitrary elements of the group $G$. We want to show that $ab=ba$.
By the given relation $(ab)^3=a^3b^3$, we have\begin{align*}ababab=a^3b^3.\end{align*}Multiplying by $a^{-1}$ on the left and $b^{-1}$ on the right, we obtain\[baba=a^2b^2,\]or equivalently we have\[(ba)^2=a^2b^2 \tag{*}\]for any $a, b\in ... |
Nontrivial Action of a Simple Group on a Finite Set
Problem 112
Let $G$ be a simple group and let $X$ be a finite set.Suppose $G$ acts nontrivially on $X$. That is, there exist $g\in G$ and $x \in X$ such that $g\cdot x \neq x$.Then show that $G$ is a finite group and the order of $G$ divides $|X|!$.
Since $G$ acts on ... |
Article Непрерывные потоки Морса–Смейла с тремя состояниями равновесия
We consider the class of continuous Morse-Smale flows defined on a topological closed manifold $M^n$ of dimension n which is not less than three, and such that the stable and unstable manifolds of saddle equilibrium states do not have intersection. ... |
Isomorphism Criterion of Semidirect Product of Groups Problem 113
Let $A$, $B$ be groups. Let $\phi:B \to \Aut(A)$ be a group homomorphism.
The semidirect product $A \rtimes_{\phi} B$ with respect to $\phi$ is a group whose underlying set is $A \times B$ with group operation \[(a_1, b_1)\cdot (a_2, b_2)=(a_1\phi(b_1)(a... |
Event detail BLISS Seminar: Phase Transitions in Generalized Linear Models
Seminar | April 30 | 3-4 p.m. | 540 Cory Hall
Leo Miolane, INRIA
We consider generalized linear models (GLMs) where an unknown $n$-dimensional signal vector is observed through the application of a random matrix and a non-linear (possibly probab... |
What are the consequences of having complete problems in $NP\cap coNP$?
This is a (wide) open problem; as in, we know almost nothing. Specifically, because of the trickiness in
proving $NP \cap coNP$-complete problems, we need very different proof techniques than currently exist. As such, a discussion of consequences s... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
In geometry, the term
semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. Ellipse
The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape. The semi-major axis is one half of... |
Difference between revisions of "Printing with FLTK"
m (Minor format changes)
(One intermediate revision by one other user not shown) Line 1: Line 1:
Printing with graphics_toolkit FLTK has some known limitations:
Printing with graphics_toolkit FLTK has some known limitations:
−
* Tex/Latex symbols won't show up in the... |
Answer
The longest three wavelengths in the Lyman series are $121.5~nm$, $102.6~nm$, and $97.23~nm$
Work Step by Step
The longest three wavelengths in the Lyman series would be the three transitions with the least amount of energy, that is, the transitions from level 2 to the ground state, from level 3 to the ground st... |
The
Inhomogeneous Short Integer Solution (ISIS) problem is as follows: given an integer $q$, a matrix $A \in \mathbb Z^{n\times m}_q$, a vector $b\in \mathbb Z^n_q$, and a real $\beta$, find an integer vector $e\in \mathbb Z^m$ such that $Ae = b \mod q $ and $||e||_2 \leq \beta$.
Now assume $e_0$ is a solution to the I... |
This interactive simulation estimates the value of the fundamental constant, pi (π), by drawing lots of random points to estimate the relative areas of a square and an inscribed circle.
Pi, (π), is used in a number of math equations related to circles, including calculating the area, circumference, etc. and is widely u... |
A ring $R$ is called Artinian if it satisfies the defending chain condition on ideals.That is, whenever we have ideals $I_n$ of $R$ satisfying\[I_1\supset I_2 \supset \cdots \supset I_n \supset \cdots,\]there is an integer $N$ such that\[I_N=I_{N+1}=I_{N+2}=\cdots.\]
Proof.
Let $x\in R$ be a nonzero element. To prove $... |
As I understand from the survey "Progress on Polynomial Identity Testing - II" a polynomial-time algorithm for solving PIT for $\Sigma \Pi \Sigma \Pi (2, r)$ is unknown.
However, there exists paper of Ankit Gupta "Algebraic Geometric Techniques for Depth-4 PIT & Sylvester-Gallai Conjectures for Varieties" that gives a ... |
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Now showing items 1-2 of 2
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
The L-band (1-2GHz) and S-band (2-4GHz) are traditionally used either as direct input or as an intermediate frequency (IF) when downconverting from a higher RF frequency (like in a Ku-band radar, for example). Rather than designing a heterodyne receiver to sample these bands at a lower frequency, system designers are e... |
Summary
Let $T : \Omega \rightarrow \mathbb{C}^{n \times n}$ be a matrix-valued function that is analytic on some simply-connected domain $\Omega \subset \mathbb{C}$. We call a point $\lambda \in \Omega$ an eigenvalue if the matrix $T(\lambda)$ is singular. Nonlinear eigenvalue problems arise in many applications, ofte... |
Observe the prime factorization $72=2^3\cdot 3^2$.Let $G$ be a group of order $72$.
Let $n_3$ be the number of Sylow $3$-subgroups in $G$.By Sylow’s theorem, we know that $n_3$ satisfies\begin{align*}&n_3\equiv 1 \pmod{3} \text{ and }\\&n_3 \text{ divides } 8.\end{align*}The first condition gives $n_3$ could be $1, 4, ... |
The Set of Vectors Perpendicular to a Given Vector is a Subspace
Problem 659
Fix the row vector $\mathbf{b} = \begin{bmatrix} -1 & 3 & -1 \end{bmatrix}$, and let $\R^3$ be the vector space of $3 \times 1$ column vectors. Define\[W = \{ \mathbf{v} \in \R^3 \mid \mathbf{b} \mathbf{v} = 0 \}.\]Prove that $W$ is a vector s... |
Geometry and Topology Seminar Contents 1 Fall 2016 2 Spring 2017 3 Fall Abstracts 4 Spring Abstracts 5 Archive of past Geometry seminars Fall 2016 Spring 2017
date speaker title host(s) Jan 20 Carmen Rovi (University of Indiana Bloomington) "The mod 8 signature of a fiber bundle" Maxim Jan 27 Feb 3 Rafael Montezuma (Un... |
I will begin by linking a previous post where I asked a general question for a stochastic setting which I describe below. It turns out that my "proof" for a restricted case had a mistake and there is a much simpler setting where showing hardness should be easier. Please let me know if I should amend the original questi... |
A variational approach to resonance for asymmetric oscillators
1.
Université Catholique de Louvain, Institut de Mathématique Pure et Appliquée, Chemin du Cyclotron, 2 , B-1348 Louvain-la-Neuve
$x'' + \alpha x^+ - \beta x^- + g(x) =p(t),$
where $x^+ =$ max{$x,0$} is the positive part of $x$, $x^- $ =max{$-x,0$} its nega... |
Tagged: matrix Problem 38
Let $A$ be an $m \times n$ real matrix.
Then the of $A$ is defined as $\ker(A)=\{ x\in \R^n \mid Ax=0 \}$. kernel
The kernel is also called the
of $A$. null space
Suppose that $A$ is an $m \times n$ real matrix such that $\ker(A)=0$. Prove that $A^{\trans}A$ is invertible.
(
Stanford Universit... |
Tips and Tricks for Modeling Induction Furnaces Today, we are pleased to introduce a new guest author, Vincent Bruyere of SIMTEC, who shares insight into the modeling of induction furnaces.
Induction heating has become an important process in many applications, from cooking meals to manufacturing. It is valued for its ... |
Answer
The total mass of matter and antimatter required is $1.35\times 10^4~kg$
Work Step by Step
We can find the kinetic energy of the starship: $K = (\gamma-1)mc^2$ $K = (\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1)mc^2$ $K = (\frac{1}{\sqrt{1-\frac{(0.3500~c)^2}{c^2}}}-1)(2.0\times 10^5~kg)(3.0\times 10^8~m/s)^2$ $K = (1.0... |
In the last post I have presented some historical context about programming and mathematical methodology. If you read it, then you should have an idea when and why programmers started to investigate on mathematical methodology. However, I haven’t mentioned any aspects of mathematical methodology that can help us to imp... |
SMC samplers¶
SMC samplers are SMC algorithms that sample from a sequence of target distributions. In this tutorial, these target distributions will be Bayesian posterior distributions of static models. SMC samplers are covered in Chapter 17 of the book.
Defining a static model¶
A static model is a Python object that r... |
A 60 degrees Rhombus in a 60 degrees Isosceles Trapezoid What is this about? A Mathematical Droodle
Created with GeoGebra, 24 November, 2016
Problem
Proof
WLOG, assume $AB=BC=AD=1\;$ and denote $AX=x.\;$ Since $\Delta ABC\;$ is isosceles with base angles of $30^{\circ},\;$ so is $\Delta AXM,\;$ implying $XM=AX=x\;$ and... |
In mathematics, for a given complex Hermitian matrix
M and nonzero vector x, the Rayleigh quotient [1] R(M, x), is defined as: [2] [3] R(M,x) := {x^{*} M x \over x^{*} x}.
For real matrices and vectors, the condition of being Hermitian reduces to that of being symmetric, and the conjugate transpose x^{*} to the usual t... |
Let $L \subseteq X^{\ast}$ be some language, then we define the
syntactic congruence as$$ u \sim v :\Leftrightarrow \forall x, y\in X^{\ast} : xuy \in L \leftrightarrow xvy \in L$$and the quotient monoid $X^{\ast} / \sim_L$ is called the syntactic monoid of $L$.
Now what monoids arise as syntactic monoids of languages?... |
Tagged: matrix Problem 121
Let $A$ be an $m \times n$ real matrix. Then the
null space $\calN(A)$ of $A$ is defined by \[ \calN(A)=\{ \mathbf{x}\in \R^n \mid A\mathbf{x}=\mathbf{0}_m\}.\] That is, the null space is the set of solutions to the homogeneous system $A\mathbf{x}=\mathbf{0}_m$.
Prove that the null space $\ca... |
Proving (-infinity, 0) is open
Hi, I've done most of the proof(I think), but I'm lost anyone willing to finish it off for me? I've spent a while on it and i'm stuck.
Let x be an element of (-infinity, 0) this implies x < 0 chose an r such that abs(r) < abs(x) let y be an element of (x -r, x+r).
This implies x-r<y<x+r w... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
№ 8
All Issues Volume 57, № 10, 2005
Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1315–1326
We suggest a method for obtaining a monotonically decreasing sequence of upper bounds of percolation threshold of the Bernoulli random field on $Z^2$. On the basis of this sequence, we obtain a method of
constructing approximations w... |
The Wikipedia page for Monad says just that for a monad $(T,\eta,\mu)$ we can define the category of all adjunctions that define the monad:
Let $\textbf{Adj}(C,T)$ be the category whose objects are the adjunctions $(F,G,e,\varepsilon)$ such that $(GF,e,G\varepsilon F)=(T,\eta,\mu)$ and whose arrows are the morphisms... |
A common question exists regarding the use of logarithm base 10 (\(\log\) or \(\log_{10}\)) vs. logarithm base \(e\) (\(\ln\)). The logarithm base \(e\) is called the
natural logarithm since it arises from the integral:
\[ \ln (a) = \int_1^a \dfrac{dx}{x}\]
Of course, one can convert from \(\ln\) to \(\log\) with a con... |
Computational Aerodynamics Questions & Answers
Very good question. We made this assumption only when deriving the GCI. So, within the $\rm GCI_{f}$ equation, you should change the term to $\left\vert\left(\frac{\triangle x_c}{\triangle x_f }\right)^p-1\right\vert$. That is, the GCI should always be positive. However, w... |
Suppose we have $3$ parties Alice, Bob and Charlie such that Alice can't talk with Bob.
Suppose that Alice has some string $x\in\{0,1\}^n$ and Bob has a string $y\in\{0,1\}^n$.
Suppose that Alice and Bob have access to a shared random string $r$ and a shared secret $s$.
Suppose that Charlie knows both $x$ and $y$ and h... |
Is it possible to approximate a monotone submodular function using a concrete coverage function, i.e.
Given a ground set $U$ and a monotone submodular function, $f:2^U\to \mathbb{R}$, the goal is to find another ground set, $V$, and map each element from $U$ to a subset of $V$ ($m:U \to 2^V$) such that $f(S) \leq g(S) ... |
Since $G$ is a $p$-group, its center is not trivial (see post 1 for a proof.)
If the center $Z(G)=G$, then $G$ is abelian so assume that $Z(G)$ is a proper nontrivial subgroup. Then the center must have order $p$ and it follows that the order of the quotient $G/Z(G)$ is $p$, hence $G/Z(G)$ is a cyclic group.
(b) The gr... |
Matrices Satisfying $HF-FH=-2F$ Problem 69
Let $F$ and $H$ be an $n\times n$ matrices satisfying the relation
\[HF-FH=-2F.\] (a) Find the trace of the matrix $F$. (b) Let $\lambda$ be an eigenvalue of $H$ and let $\mathbf{v}$ be an eigenvector corresponding to $\lambda$. Show that there exists an positive integer $N$ s... |
Every element of the ring $\Z[\sqrt{5}]$ can be written as $a+b\sqrt{5}$ for some integers $a, b$.The (field) norm $N$ of an element $a+b\sqrt{5}$ is defined by\[N(a+b\sqrt{5})=(a+b\sqrt{5})(a-b\sqrt{5})=a^2-5b^2.\]
Consider the case when $a=3, b=1$.Then we have\[(3+\sqrt{5})(3-\sqrt{5})=4=2\cdot 2. \tag{*}\]
We prove ... |
维基教科书:格式手册
The
Wikibooks Manual of Style serves to illustrate good structural and stylistic practices to help editors produce higher quality wikibooks. Wikibook titles编辑 See also Wikibooks:Naming policy for information on how to name books and their chapters.
Wikibooks should be titled based on their
aspect. This is a ... |
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1. Color connections of the four-quark Q Q Q ' Q ' system and doubly heavy baryon production in e + e - annihilation
Physics Letters B, ISSN 0370-2693, 12/2013, Volume 72... |
Example of an Infinite Algebraic Extension Problem 499
Find an example of an infinite algebraic extension over the field of rational numbers $\Q$ other than the algebraic closure $\bar{\Q}$ of $\Q$ in $\C$.
Contents
Definition (Algebraic Element, Algebraic Extension).
Let $F$ be a field and let $E$ be an extension of $... |
Asymptotic for the perturbed heavy ball system with vanishing damping term
1.
Institut Préparatoire aux Etude Scientifiques et Techniques, Université de Carthage, Bp 51 La Marsa, Tunisia
2.
Faculté des Sciences de Tunis, Laboratoire EDP-LR03ES04, Université de Tunis El Manar Tunis, Tunisia
3.
College of Sciences, Depar... |
Subspaces of Symmetric, Skew-Symmetric Matrices Problem 143
Let $V$ be the vector space over $\R$ consisting of all $n\times n$ real matrices for some fixed integer $n$. Prove or disprove that the following subsets of $V$ are subspaces of $V$.
(a) The set $S$ consisting of all $n\times n$ symmetric matrices. (b) The se... |
Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
$\left\{ \begin{array}{l} -\text{div}\big(\frac{\nabla u}{\sqrt{1-|\nabla u|^2}}\big) = λ f(x,u,\nabla u)\ \ \ \ \ \ &... |
Answer
$\text{Set Builder Notation: } \left\{ y|y\le-13 \right\} \\\text{Interval Notation: } \left( -\infty,-13 \right]$
Work Step by Step
$\bf{\text{Solution Outline:}}$ Use the properties of inequality to solve the given inequality, $ -5y\ge65 .$ Write the answer in both set-builder notation and interval notation. $... |
Answer
$\text{Set Builder Notation: } \left\{ t|t\ge-1 \right\} \\\text{Interval Notation: } \left[ -1,\infty \right)$
Work Step by Step
$\bf{\text{Solution Outline:}}$ To solve the given inequality, $ \dfrac{1}{2}t-\dfrac{1}{4}\le\dfrac{3}{4}t ,$ remove first the fraction by multiplying both sides by the $LCD.$ Then u... |
Helo, every one. May I ask for help about how to solve this problem?
\[\begin{align} max_{x_i} \quad |\sum_{i=1}^{4} a_i x_i | \\ s.t. \quad \sum_{i=1}^4 x_i^2=1\end{align}\]
The goal is to find the optimal \(x_i\), the \(a_i\) is known.
Thank you very much.
Intuitively, the optimal \(x\) will be proportional to \(a\).... |
Each element of $G/N$ is a coset $aN$ for some $a\in G$.Let $aN, bN$ be arbitrary elements of $G/N$, where $a, b\in G$.
Then we have\begin{align*}(aN)(bN)&=(ab)N \\&=(ba)N && \text{since $G$ is abelian}\\&=(bN)(aN).\end{align*}Here the first and the third equality is the definition of the group operation of $G/N$.
Rema... |
Suppose $G$ is a finite group. We will say, that it force solvability if any finite group $H$, such that $G$ is isomorphic to its maximal proper subgroup, is solvable. Does there exist some sort of classification of such groups?
On one hand, all such groups have to be solvable. On the other hand, there are several larg... |
Rikka with Number
Time Limit: 8000/4000 MS (Java/Others)
Memory Limit: 65536/65536 K (Java/Others)
Description
As we know, Rikka is poor at math. Yuta is worrying about this situation, so he gives Rikka some math tasks to practice. There is one of them:
In radix $d$, a number $K=(A_1A_2...A_m)_d(A_i \in [0,d),A_1 \neq ... |
Viscous Flow Questions & Answers
This is a good question. The conservative form is not necessary to solve most viscous flow problems in this course, so I prefer to derive only the non-conservative form. In other courses (like Intro to CFD for instance), then we need the conservative form because it's easier to discreti... |
№ 8
All Issues Türkmen E.
↓ Abstract
Ukr. Mat. Zh. - 2019. - 71, № 3. - pp. 400-411
Over an arbitrary ring, a module $M$ is said to be $\scr{Z^{ \ast}}$ -semilocal if every submodule $U$ of $M$ has a $\scr{Z^{ \ast}}$ -supplement $V$ in $M$, i.e., $M = U + V$ and $U \cap V \subseteq \scr{Z^{ \ast}} (V )$, where $\scr{Z... |
Finance theory suggests that capital markets reflect all available information about firms in the firms' stock prices. Given this basic premise, one can study how a particular event changes a firm's prospects by quantifying the impact of the event on the firm's stock. Finance scholars have developed the 'event study me... |
Many inductive arguments work by projecting an observed pattern onto as-yet unobserved instances. All the ravens we’ve observed have been black, so all ravens are. All the emeralds we’ve seen have been green, so all emeralds are.
The assumption that the unobserved will resemble the observed seems to be central to induc... |
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cond-mat.stat-mech
Change to browse by: References & Citations Bookmark(what is this?) Condensed Matter > Statistical Mechanics Title: Correlation Function and Simplified TBA Equations for XXZ Chain
(Submitted on 30 Dec 2010 (v1), last revised 8 Jan 2011 (this version, v2))
Abstract: The calcula... |
№ 8
All Issues Volume 62, № 3, 2010
Ukr. Mat. Zh. - 2010. - 62, № 3. - pp. 291–300
We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment $[–1, 1]$ with respect to a measure, or, more precisely, with respect to the functional $μ(f) = \text{mes}\le... |
I'm trying to get a conclusive numerical value for Mean Squared Error (MSE) as the performance metric of a few CS sparse recovery algorithms. To do this, I vary the number of measurements ($M$) taken from an $N$-dimensional vector with $M\ll N$ using the sensing matrix $\mathbf A \in \mathbb K^{M\times N}$. The goal is... |
A Concentration Phenomenon for Semilinear Elliptic Equations
Article
First Online:
529 Downloads Citations Abstract
For a domain \({\Omega \subset \mathbb{R}^{N}}\) we consider the equation
with zero Dirichlet boundary conditions and \({p\in(2, 2^*)}\). Here \({V \geqq 0}\) and
$$-\Delta{u} + V(x)u = Q_n(x)|{u}|^{p-2}u... |
Computational Aerodynamics Questions & Answers
You don't necessarily need to express $\phi$ as a function of $U$ to determine $\partial \phi/\partial U$ in the same way as you don't need to express $F$ as a function of $U$ to obtain $\partial F/\partial U$.
Use a 1D extrapolation polynomial. 2D is too time consuming to... |
I’m studying the paper of (Baum-Connes-Higson, ex 4.25), and I would like to give an explicit computation for the Connes-Kasparov conjecture for SL(2,R).
The idea is that each non-trivial representation of the compact circle group $K$ induces a discrete series representation. I have found a description of the discrete ... |
Problem 4 from the IMO 2013 What Might This Be About? Problem
Let $ABC$ be an acute triangle with orthocenter $H,$ and let $W$ be a point on the side $BC,$ lying strictly between $B$ and $C.$ The points $M and N$ are the feet of the altitudes from $B$ and $C,$ respectively. Denote by $\omega_1$ is the circumcircle of $... |
A friend of mine and me have decided to try the brute-force method and compute some values of $t$ for small values of $n$ and $d$. This is totally impossible without employing pruning, and we hope that the tricks we have found will give some insight in the rest of the problem. So far, we have not managed to get the dou... |
As a matter of fact, it isn't hard to construct a multiplicative sequence $a_n$ such that $f(z)$ is an entire function without zeroes. Unfortunately, it is completely useless for the questions that you brought up as "motivation".
Here is the construction.
Claim 1: Let $\lambda_j\in [0,1]$ ($j=0,\dots,M$). Assume that $... |
Multitype pair correlation function (cross-type)
Calculates an estimate of the cross-type pair correlation function for a multitype point pattern.
Usage
pcfcross(X, i, j, ..., r = NULL, kernel = "epanechnikov", bw = NULL, stoyan = 0.15, correction = c("isotropic", "Ripley", "translate"), divisor = c("r", "d"))
Argument... |
[Click here for a PDF of this post with nicer formatting]
This is my first set of notes for the UofT course ECE1229, Advanced Antenna Theory, taught by Prof. Eleftheriades, covering ch. 2 [1] content.
Unlike most of the other classes I have taken, I am not attempting to take comprehensive notes for this class. The clas... |
AliPhysics 5403132 (5403132)
Scripts used in the analysis Algorithms Corrections Monte-carlo code Mid-rapidity tracklet code for dN/deta Tasks Topical
file AliAODForwardMult.h Per-event \( N_{ch}\) per \((\eta,\varphi)\) bin. file AliFMDEventPlaneFinder.h file AliForwardUtil.h Various utilities used in PWGLF/FORWARD. f... |
I have a problem involving a time-indexed variable \(x_{it}\) representing the amount of a resource allotted to a task \(i\) in time \(t\).
The quantity of the (renewable) resource is constrained at a value \(R\) per period: $$ \sum_{i=1}^{I} x_{it}\leq R\,\,\,\forall t \in T $$
and I have to allott a given quantity \(... |
Laplace transforms were used to solve the MNA equations for time dependent systems, and to find the moments used to in MOR.
For the record, the Laplace transform is defined as:
\begin{equation}\label{eqn:laplaceTransformVec:20}
\boxed{ \LL( f(t) ) = \int_0^\infty e^{-s t} f(t) dt. } \end{equation}
The only Laplace tran... |
Answer
(a) The electron moved to a lower potential. (b) $\Delta V = -190~J/C$
Work Step by Step
(a) By conservation of energy, the decrease in kinetic energy is equal in magnitude to the increase in electric potential energy. Since the charge on an electron is negative, the electron must have moved to a lower potential... |
Sorry I cannot find a clearer title for this question. I have a constraint like the following:
$$ \sum_{t \in T} w_{t} \cdot y_{t} \geq A $$
where \(w_t\) are given, positive weights, and \(y_t \in \{0,1\} \).
I want to add (if possible) the following constraint:
$$ y_{t} = \dots 0,0,1,1,1,0,0\dots $$
while this is not... |
If Two Matrices Have the Same Eigenvalues with Linearly Independent Eigenvectors, then They Are Equal
Problem 424
Let $A$ and $B$ be $n\times n$ matrices.Suppose that $A$ and $B$ have the same eigenvalues $\lambda_1, \dots, \lambda_n$ with the same corresponding eigenvectors $\mathbf{x}_1, \dots, \mathbf{x}_n$.Prove th... |
Churn is a really big deal in SaaS... but which is a "bigger" deal? Customer churn, or revenue churn?
Today, I'm looking at the differences between these two essential SaaS metrics, and helping you to use them to monitor and improve the growth of your own SaaS startup.
Customer Churn
Customer churn (also known as
"Logo... |
The zero element of $C(\mathbb{R})$ is the function $\mathbf{0}$ defined by $\mathbf{0}(x) = 0$. This shows that $\mathbf{0} \in W_a$ if and only if $a=0$.
We have shown that if $a \neq 0$, then $W_a$ is not a subspace as every subspace contains the zero vector. Now we consider the case $a=0$ and prove that $W_0$ is a ... |
Sample Quantiles
The generic function
quantile produces sample quantiles corresponding to the given probabilities. The smallest observation corresponds to a probability of 0 and the largest to a probability of 1.
Keywords univar Usage
quantile(x, …)
# S3 method for defaultquantile(x, probs = seq(0, 1, 0.25), na.rm = FA... |
Schönbrodt's and Perugini's method defines a point of stability (POS), a sample size beyond which one is reasonably confident that an estimate is within a specified range (labeled the corridor of stability, or COS) of its population value. For more details on how the point of stability is estimated, you can read either... |
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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 ... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
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 31-40 of 165
Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV
(Springer, 2012-09)
Measurements of the sphericity of primary charged particles in minimum bias proton--proton collisions at $\sqrt{s}$=0.9, 2.76 and 7 TeV ... |
July 11th, 2015, 05:37 AM
# 1
Senior Member
Joined: Jul 2015
From: Florida
Posts: 154
Thanks: 3
Math Focus: non-euclidean geometry
New Spherical Trig Function
I have recently begun sorting through some of our old writings and I came across what looks to me like a new spherical trigonometric function.
It goes like this:... |
Laustsen, Niels J. (2002)
Maximal ideals in the algebra of operators on certain Banach spaces. Proceedings of the Edinburgh Mathematical Society, 45 (3). pp. 523-546. ISSN 0013-0915
PDF (download.pdf)
download.pdf
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Abstract
For a Banach space $\mathfrak{X}$, let $\mathcal{B}(\mathfrak{X})$ denote the Ba... |
October 16th, 2014, 09:17 PM
# 11
Member
Joined: Oct 2014
From: UK
Posts: 62
Thanks: 2
October 16th, 2014, 09:22 PM
# 12
Global Moderator
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City
Posts: 7,963
Thanks: 1148
Math Focus: Elementary mathematics and beyond
That
is what's happening! The statement of th... |
In Absolute Value as Belief, Steven Daskal aims to save anti-Humeanism against Lewis’s attacks in the Desire as Belief papers by changing the connection between credences and values. I like the idea he’s trying to develop – trying to use the difference in value between \(A\) and \(\neg A\) to state the theory more care... |
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