text stringlengths 28 2.36M | meta stringlengths 20 188 |
|---|---|
\begin{document}
\markboth{V. Millot \& A. Pisante} {Symmetry of local minimizers for the three dimensional Ginzburg-Landau functional}
\title{SYMMETRY OF LOCAL MINIMIZERS
FOR THE THREE DIMENSIONAL GINZBURG-LANDAU FUNCTIONAL}
\author{VINCENT MILLOT}
\address{D\'epartement de Math\'ematiques\\
Universit\'e de Cer... | {"config": "arxiv", "file": "0804.0128/GLlocmin.tex"} |
TITLE: What rules were used to find that $\sin(2/x)-(2/x)\cos(2/x)$ is the derivative of $y= x\sin( 1/x)$?
QUESTION [0 upvotes]: I am little confused as to what rule I use to find the derivative of $y=x\sin(1/x)$. Is it the Chain rule or a combination of the product rule and the chain rule? The answer is $\sin (2/x) - ... | {"set_name": "stack_exchange", "score": 0, "question_id": 1190700} |
TITLE: question concerning continuous and locally bound functions in relation to continuous almost everywhere
QUESTION [3 upvotes]: I have a question from Munkres' Analysis on Manifolds text, under the section 15 Improper Integrals, question 8.
$\newcommand{\R}{\mathbb{R}}$
The question reads as follows: Let $A$ be op... | {"set_name": "stack_exchange", "score": 3, "question_id": 349840} |
chapter \<open>Inductive inference of recursive functions\label{c:iirf}\<close>
theory Inductive_Inference_Basics
imports Standard_Results
begin
text \<open>Inductive inference originates from work by
Solomonoff~\cite{s-ftiip1-64,s-ftiip2-64} and Gold~\cite{g-lil-67,g-lr-65}
and comes in many variations. The common... | {"subset_name": "curated", "file": "formal/afp/Inductive_Inference/Inductive_Inference_Basics.thy"} |
\section{Explicit formulas}
\label{sec:formulas}
In this appendix we list explicit formulas for categorical invariants
of Euler characteristic $\chi\geq -3$.
The formulas will be written in terms of partially directed graphs.
Our conventions when drawing such a graph $(G,L_G^{\sf in}\coprod
L_G^{\sf out},E^{\sf dir},... | {"config": "arxiv", "file": "2009.06659/formulas.tex"} |
TITLE: Ellipse Tangents in 3D
QUESTION [1 upvotes]: I know that we can find the tangent of the ellipse in 2D by taking the derivative of the equation defining the ellipse.
But I'm little bit confused about finding the ellipse tangent in 3D. Where the ellipse orientation could be in any direction.
Suppose we have the fo... | {"set_name": "stack_exchange", "score": 1, "question_id": 655853} |
TITLE: Hierarchy of Mathematical Spaces
QUESTION [5 upvotes]: I really got lost among all those many different spaces in mathematics, and I got really confused what is special case of what.
For example, I knew for long time vector spaces, then Hilbert spaces, that I thought about as infinite dimensional vector spaces, ... | {"set_name": "stack_exchange", "score": 5, "question_id": 1364375} |
TITLE: Arranging Couples in a Row
QUESTION [1 upvotes]: Three couples are sitting in a row. Compute the number of arrangements in which no person is sitting next to his or her partner. Answer is 240.
From wikipedia, This problem is called the menage problem have a fourmula called Touchard's formula:
Let $M_n$ denote th... | {"set_name": "stack_exchange", "score": 1, "question_id": 110762} |
TITLE: Limit of $\lim_{n\to\infty} n-ne\left(1-\frac{1}{n}\right)^n$?
QUESTION [1 upvotes]: How do I calculate
$$\lim_{n\to\infty} n-ne\left(1-\frac{1}{n}\right)^n$$
Edit: changed it to correct question with $1-1/n$
REPLY [0 votes]: \begin{align}
n-ne\left(1-\frac{1}{n}\right)^n
&= n-nee^{n\ln\left(1-\frac{1}{n}\ri... | {"set_name": "stack_exchange", "score": 1, "question_id": 2867565} |
\begin{document}
\title{Finite-Memory Prediction as Well as \\ the Empirical Mean}
\author{Ronen~Dar and
Meir~Feder,~\IEEEmembership{Fellow,~IEEE}
\IEEEcompsocitemizethanks{
The work of Ronen Dar was supported by the Yitzhak and Chaya Weinstein research institute for signal processing.
The work w... | {"config": "arxiv", "file": "1102.2836/Thesis_Journal_arxiv.tex"} |
\begin{document}
\begin{abstract}
We investigate the asymptotics of the expected number of real roots of random trigonometric polynomials
$$
X_n(t)=u+\frac{1}{\sqrt{n}}\sum_{k=1}^n (A_k\cos(kt)+B_k\sin(kt)), \quad t\in [0,2\pi],\quad u\in\R
$$
whose coefficients $A_k, B_k$, $k\in\N$, are independent identically distri... | {"config": "arxiv", "file": "1601.01841/hfarxiv.tex"} |
\begin{document}
\maketitle
\begin{abstract}
Model order selection (MOS) in linear regression models is a widely studied problem in signal processing. Techniques based on information theoretic criteria (ITC) are algorithms of choice in MOS problems. This article proposes a novel technique called residual ratio thresh... | {"config": "arxiv", "file": "1805.02229/residual_ratio_thresholding.tex"} |
TITLE: Deformation Retraction and Projection/Closest Vector
QUESTION [1 upvotes]: How do I compute the projection/closest vector to a subset? I have been thinking about this for far too long without any progress. If it helps, I am working in $\Bbb{R}^2$, but I would like formalue in terms of norms and inner products, i... | {"set_name": "stack_exchange", "score": 1, "question_id": 3068599} |
TITLE: Cardinal numbers of Setminus
QUESTION [0 upvotes]: Could you help me check the following fact?
Let $A,B,C$ be sets such that $C\subseteq A$ and $C\subseteq B$. Then
$1.$ $|A\setminus C|=|A|−|C|$
$2.$ $|A\setminus C|=|B\setminus C|$ if and only if $|A|=|B|$
where $|A|$ is the cardinal number of $A$ and $A\setminu... | {"set_name": "stack_exchange", "score": 0, "question_id": 939853} |
TITLE: How do I stop overcomplicating proofs?
QUESTION [30 upvotes]: I'm a third year student majoring in Math.
Whenever I sit down and try to prove something, I just don't know what and where to start with. The first proofs course I took was graded very strictly so missing a very tiny detail made me lose a lot of mark... | {"set_name": "stack_exchange", "score": 30, "question_id": 4546324} |
TITLE: Approach for optimization problem with polynomial constraints?
QUESTION [0 upvotes]: I have a problem where the objective function is linear and constraints have polynomials (in one variable). So, my question is what are the main approaches to this issue? I can construct a small example, just to illustrate it.
$... | {"set_name": "stack_exchange", "score": 0, "question_id": 1408419} |
\begin{document}
\begin{frontmatter}
\title{On Strong Data-Processing and Majorization Inequalities
with Applications to Coding Problems}
\author[First]{Igal Sason}
\address[First]{The Andrew and Erna Viterbi Faculty of Electrical Engineering,
Technion - Israel Institute of Technology,
Technion City,\\ Haifa 320000... | {"config": "arxiv", "file": "2103.16901/sason.tex"} |
TITLE: how to solve this differential equation $\tau\frac{dc}{dt} = -(1-\lambda)c(t) + \textbf{k}\cdot \textbf{h}(t)$
QUESTION [1 upvotes]: I haven't solved diff eq in a very long time and I'm having trouble with the following differential equation:
$$\tau\frac{dc}{dt} = -(1-\lambda)c(t) + \textbf{k}\cdot \textbf{h}(t)... | {"set_name": "stack_exchange", "score": 1, "question_id": 3262100} |
TITLE: Physical meaning of the sign basis in quantum mechanics
QUESTION [5 upvotes]: If we take a hydrogen atom as qubit, let
$\lvert0\rangle$ = unexcited state
$\lvert1\rangle$ = excited state
then what is the meaning of measuring the qubit value in the sign basis? If the atom may only be in excited or unexcited state... | {"set_name": "stack_exchange", "score": 5, "question_id": 34924} |
TITLE: Why the Feynman diagrams contributing to the effective action $\Gamma[\phi_{\rm cl}]$ are stripped/amputated/have no external lines?
QUESTION [8 upvotes]: I am reading P&S Chapter 11 and specifically I am trying to understand the derivation of $\Gamma[\phi_{\rm cl}]$. All the algebra is okay, but I am failing to... | {"set_name": "stack_exchange", "score": 8, "question_id": 693927} |
TITLE: Has this operator $0$ as an eigenvalue / where is my error?
QUESTION [3 upvotes]: I know of a theorem that tells me, that every compact linear operator
on an infinitedimensional Hilbert space has to have the eigenvalue
$0$. On the other hand I have the operator
\begin{eqnarray*}
& T:\ell^{2}\rightarrow\ell^{2}... | {"set_name": "stack_exchange", "score": 3, "question_id": 176103} |
TITLE: What is $\limsup\limits_{n\to\infty} \cos (n)$, when $n$ is a natural number?
QUESTION [3 upvotes]: I think the answer should be $1$, but am having some difficulties proving it. I can't seem to show that, for any $\delta$ and $n > m$, $|n - k(2\pi)| < \delta$. Is there another approach to this or is there someth... | {"set_name": "stack_exchange", "score": 3, "question_id": 136897} |
TITLE: How can infinite sine waves localize to a single pulse in space?
QUESTION [2 upvotes]: I have heard countless times (and not just when discussing the Heisenberg's Uncertainty Principle) that making a short pulse using sine waves requires more and more sine waves to localize the pulse closer and closer, and for a... | {"set_name": "stack_exchange", "score": 2, "question_id": 560127} |
/-
Copyright (c) 2022 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
import data.sum.order
import order.locally_finite
/-!
# Finite intervals in a disjoint union
This file provides the `locally_finite_order` instance for the disjoint sum... | {"subset_name": "curated", "file": "formal/lean/mathlib/data/sum/interval.lean"} |
TITLE: Estimating Gaussian parameters of a set of data points
QUESTION [2 upvotes]: I have a set of data points. When I draw a histogram of them, plotting their frequency of occurrence against them, I get a curve that looks like a normal curve. I am also able to perform test on the data set to know whether it follows a... | {"set_name": "stack_exchange", "score": 2, "question_id": 2735188} |
TITLE: If $S$ is an $R$-algebra, how does $S$ being a finitely generated $R$-module imply that $S$ is a finite-type $R$-algebra?
QUESTION [0 upvotes]: Let $R$ be a commutative ring.
If $S$ is a finitely generated $R$-module, then there is an onto $R$-module homomorphism $$R^{\oplus n} \to S.$$
If $S$ is a finite-type $... | {"set_name": "stack_exchange", "score": 0, "question_id": 3305081} |
TITLE: History of the theory of equations: John Colson
QUESTION [22 upvotes]: This is an EDIT version of my original question:
Recently I've been interested in the history of the Theory of Equations. The thing is that I learned about this mathematician named John Colson, he published a very interesting paper: Aequation... | {"set_name": "stack_exchange", "score": 22, "question_id": 493016} |
TITLE: why are motives more serious than "naive" motives?
QUESTION [16 upvotes]: I know my question is a bit vague, sorry for this.
Let $k$ be a field of characteristic zero. Consider the Grothendieck ring of varieties over $k$, usually denoted by $K_0(Var_k)$. This is generated by isomorphism classes of varieties over... | {"set_name": "stack_exchange", "score": 16, "question_id": 186290} |
TITLE: Observer in the double slit experiment with photons
QUESTION [1 upvotes]: In the double slit experiment with photons, the interacting observer is an instrument, detector…
If you replace the detector with a piece of metal with the same mass as the mass of the detector, the wave will collapse?
REPLY [1 votes]: I... | {"set_name": "stack_exchange", "score": 1, "question_id": 247329} |
\subsection{Complex surfaces}
Throughout this paper, $X$ will denote a complex surface, by which we mean a
connected compact complex manifold of complex dimension two. Usually
$X$ will be rational. The book \cite{BHPV} is a good
general reference for complex surfaces. Here we recount only needed facts.
Given divi... | {"config": "arxiv", "file": "math0505014/texfiles/background.tex"} |
TITLE: Supremum infimum on more general space
QUESTION [0 upvotes]: What is the definition of supremum and infimum on more general spaces, say $\mathbb{R}^2$, $\mathbb{R}^n$.
REPLY [1 votes]: Once we have a partially ordered set, we can define supremum and infimum, as the same way we define in $\mathbb{R}$. Now, we ca... | {"set_name": "stack_exchange", "score": 0, "question_id": 1764217} |
In mathematics, in the field of harmonic analysis, an oscillatory integral operator is an integral operator of the form
$$
T_\lambda u(x)=\int_{\R^n}e^{i\lambda S(x, y)} a(x, y) u(y)dy, \qquad x\in\R^m, \quad y\in\R^n,
$$
where the function S(x,y) is called the phase of the operator and the function a(x,y) is called t... | {"config": "wiki", "file": "wikipedia/2464.txt"} |
TITLE: Funny Time Dilation Relation
QUESTION [0 upvotes]: Today I was curiously calculating/comparing the times of moving observers and the time recorded by a corresponding stationary observer using Einstein's time dilation equation as detailed in Special Relativity. I was just trying to see the relation between the ti... | {"set_name": "stack_exchange", "score": 0, "question_id": 251396} |
TITLE: Show that this family of open sets forms a topology of pointwise convergence
QUESTION [0 upvotes]: This is Exercise 22.12 (b) on page 185 of Elementary Analysis, second edition, written by Kenneth Ross. I searched the site for similar questions and found a couple that looked similar (this and particularly this),... | {"set_name": "stack_exchange", "score": 0, "question_id": 3668419} |
\begin{document}
\title{Partial Euler Characteristic, Normal Generations and the stable $D(2)$
problem}
\author{Feng Ji and Shengkui Ye}
\maketitle
\begin{abstract}
We obtain relations among normal generation of perfect groups, Swan's
inequality involving partial Euler characteristic, and deficiency of finite
groups.... | {"config": "arxiv", "file": "1503.01987.tex"} |
TITLE: intersection of the complement of two disjoint sets is not disjoint
QUESTION [1 upvotes]: I have a question regarding whether the intersection of the complement of two disjoint set is disjoint or not.
I mean given say $A$ and $B$ with $A$ and $B$ disjoint, i.e. $A \subset X$ and $B \subset X$, and $A \cap B = \e... | {"set_name": "stack_exchange", "score": 1, "question_id": 2445856} |
TITLE: Prob. 6, Sec. 3.4 in Kreyszig's functional analysis book: The fourier coefficients minimise the distance.
QUESTION [0 upvotes]: Let $n \in \mathbb{N}$, let $\{ e_1, \ldots, e_n \}$ be an orthonormal set in an inner product space $X$, let $x \in X$, let $y(x) \colon= \sum_{j=1}^n \langle x, e_j \rangle e_j$, and ... | {"set_name": "stack_exchange", "score": 0, "question_id": 1752394} |
\begin{document}
\begin{abstract} We extend the results of \cite{ZZ} on LDP's
(large deviations principles) for the empirical measures $$ Z_s: = \frac{1}{N} \sum_{\zeta: s(\zeta) = 0}
\delta_{\zeta}, \;\;\; (N: = \# \{\zeta: s(\zeta) = 0)\}$$
of zeros of Gaussian random polynomials $s$ in one variable to
$P(\phi)... | {"config": "arxiv", "file": "1009.5142.tex"} |
TITLE: Find direction of tangent vector based on trajectory along circle
QUESTION [1 upvotes]: A particle travels along an arc (in green) from A = $(x_A, y_A)$ to B= $(x_B, y_B)$. The arc is on a circle defined by its center C = $(x_C, y_C)$ and its radius r. The vector u points from C to A and the vector v points from... | {"set_name": "stack_exchange", "score": 1, "question_id": 2680855} |
TITLE: Conditional Probablity
QUESTION [0 upvotes]: 100 coins with two sides (head and tail)
20 coins are fair (50% of getting head and 50% of getting tail)
80 coins are biased (70% of getting head and 30% of getting tail)
What is the probability of get head if we throw a randomly chosen coin from the 100 coins once
... | {"set_name": "stack_exchange", "score": 0, "question_id": 236809} |
TITLE: Find maximum and minimum argument of $f(z)=(z^4-1)/4$ where $z$ belongs to square with vertices $\{1,i,-1,-i\}$
QUESTION [0 upvotes]: let z be a complex number with |z|<1,
now how to find the max and min argument of $(z^4-1)/4$
This original problem given below comes from kheavan.files.wordpress.com/2011/10/mat... | {"set_name": "stack_exchange", "score": 0, "question_id": 3562208} |
\section{Proofs of Section~\ref{jc}}
\subsection{Proof of Lemma~\ref{pk}} \label{wx}
Fix $X,$ and let $W$ be its orthogonal projection onto the closed subspace $\calV.$ Consider the symmetric matrix $\bM=\BE[\bV \bV^T].$ Since $\bc^T \bM \bc = \BE[|\bc^T \bV|^2]$ for each $\bc\in \BR^{n+1},$ linear independence of th... | {"config": "arxiv", "file": "2109.00649/Appendix/Generalizations.tex"} |
TITLE: Show that there exists a $c\in \mathbb{C}$ such that $f(z)=c \bar{z}$ for all $\vert z\vert=1$.
QUESTION [2 upvotes]: The problem is:
Suppose that $f(z)$ is continuous on a domain $D$ that contains the unit circle, and that $f(z)$ satisfies: $$\vert f(e^{i\theta})\vert \leq M \; \forall \theta \, \in [0, 2\pi )... | {"set_name": "stack_exchange", "score": 2, "question_id": 478642} |
\begin{document}
\title
[Stable broken {${\boldsymbol H}(\ccurl)$} polynomial extensions \&
$\MakeLowercase{p}$-robust \revision{broken} equilibration]
{Stable broken {${\boldsymbol H}(\MakeLowercase{\ccurl})$} polynomial extensions\\
and $\MakeLowercase{p}$-robust a posteriori error estimates
\revision{by broken patc... | {"config": "arxiv", "file": "2005.14537/chaumontfrelet_ern_vohralik_2020b.tex"} |
\begin{document}
\date{\today}
\subjclass{}
\keywords{}
\begin{abstract}
We study two--generated subgroups $\langle f,g\rangle<\Homeo^+(I)$ such that $\langle f^2,g^2\rangle$ is isomorphic to Thompson's group $F$, and such that the supports of $f$ and $g$ form a chain of two intervals. We show that this class conta... | {"config": "arxiv", "file": "1704.03112.tex"} |
\begin{document}
\maketitle
\baselineskip=0.9
\normalbaselineskip
\vspace{-3pt}
\begin{center}{\footnotesize\em $^{\mbox{\tiny\rm 1}}$Centre for the
mathematical sciences, Numerical Analysis, Lund University, Lund, Sweden\\ email: peter.meisrimel\symbol{'100}na.lu.se, azahar.sz\symbol{'100}gmail.com, philipp.birken... | {"config": "arxiv", "file": "2007.00410/DNWR_multirate_MeisrimelMongeBirken_arxiv.tex"} |
TITLE: Terminal Paths in Kleene's O
QUESTION [6 upvotes]: I'm stuck on a problem in Sack's Higher Recursion Theory (#2.4)- any hints are welcome. He defines Kleene's O in the usual way, and the corresponding order $<_O$. A path through O is a linearly ordered subset Z s.t. $w<_Ov\in Z\rightarrow w\in Z$. A path can be... | {"set_name": "stack_exchange", "score": 6, "question_id": 227093} |
TITLE: Does a collar along the boundary always find an embedding in the manifold?
QUESTION [2 upvotes]: Suppose we have a smooth manifold $M$ with boundary $K$. $K$ always finds a natural embedding inside $M$. Can we extend this embedding to an embedding of $K\times [0,\epsilon)$ inside $M$ in general ?
It seems to be... | {"set_name": "stack_exchange", "score": 2, "question_id": 1983503} |
\begin{document}
\title{\bf Some non-standard ways to generate SIC-POVMs in dimensions 2 and 3}
\author{Gary McConnell\\\it
Controlled Quantum Dynamics Theory Group\\\it
Imperial College London\\\rm
\texttt{g.mcconnell@imperial.ac.uk}}
\date{\today}
\maketitle
\bf The notion of Symmetric Informationally Complet... | {"config": "arxiv", "file": "1402.7330/HadMultSICs.tex"} |
TITLE: Asymptotic of integral
QUESTION [2 upvotes]: I have this definite integral:
$$ \int_{0}^{\frac \pi 2} \left( 1 + t^2 \cot^2\theta \right )^{-\frac{n-1}{2}} d \theta , t\in (0,1)$$
where $n$ is an integer. I need to find the asymptotic as a function on $n$.
I suspect it should be $O(\frac{1}{\sqrt{n}})$ but wasn... | {"set_name": "stack_exchange", "score": 2, "question_id": 2062149} |
TITLE: Find the tangent to the curve
QUESTION [0 upvotes]: The equation of the tangent to the curve $y=sin²(\frac{\pi x^3}{6})$ at $x=1$ is?
I know the question is pretty simple and straight but I would like to cross check my answer which is
$y=\frac14 + \frac{\pi\sqrt3}{4}(x-1)$
REPLY [2 votes]: You are indeed corre... | {"set_name": "stack_exchange", "score": 0, "question_id": 2780881} |
TITLE: Let all eigenvalues of $A$ have a negative real part ( i.e. $A$ is stable ). Why does the following hold?
QUESTION [2 upvotes]: Let all eigenvalues of $A$ have a negative real part ( i.e. $A$ is stable ). Why does the following hold?
$$\int_{0}^{\infty} [Ae^{A\tau}BB^*e^{A^*\tau}+e^{A\tau}BB^*e^{A^*\tau}A^*] \, ... | {"set_name": "stack_exchange", "score": 2, "question_id": 2113746} |
\begin{document}
\title[Exact asymptotics for constrained exponential random graphs]{Large deviations and exact asymptotics for constrained exponential
random graphs}
\author{Mei Yin}
\thanks{Mei Yin's research was partially supported by NSF grant DMS-1308333.}
\address{Department of Mathematics, University of Denv... | {"config": "arxiv", "file": "1412.6001.tex"} |
TITLE: Span and Dimension: A subspace
QUESTION [5 upvotes]: If $A$ is finite set of linearly independent vectors then the dimension of the subspace spanned by $A$ is equal to the number of vectors in $A$.
This is obviously true. Since $A$ is a finite set of linearly independent vectors and spans a subspace, $A$ is a b... | {"set_name": "stack_exchange", "score": 5, "question_id": 692721} |
TITLE: Solution curve for three-variable differential system
QUESTION [2 upvotes]: Show that the functions $F(x,y,z)=x+y+z$ and $G(x,y,z)=x^2+y^2+z^2$ are integrals of the system of equations $dx/dt=y-z, dy/dt=z-x, dz/dt=x-y$, i.e. on any solution curve $(x(t),y(t),z(t))$ these functions are constant. Interpret the res... | {"set_name": "stack_exchange", "score": 2, "question_id": 543746} |
TITLE: Dimension of a space of matrices
QUESTION [4 upvotes]: Let $m,n\in\mathbb{Z}$ and $r<\min$(m,n). Denote by $M$ the set of $m\times n $ matrices over a field $k$, and let $M_r$ be the subset of matrices of rank at least equal to $r$.
Now fix a matrix $A\in M_r$ and a subspace $W\in G(n-r,n)$ of dimension $n-r$ in... | {"set_name": "stack_exchange", "score": 4, "question_id": 524761} |
TITLE: Radian, an arbitrary unit too?
QUESTION [2 upvotes]: Why is the radian defined as the angle subtended at the centre of a circle when the arc length equals the radius? Why not the angle subtended when the arc length is twice as long as the radius , or the radius is twice as long as the arc length? Isn't putting 2... | {"set_name": "stack_exchange", "score": 2, "question_id": 526043} |
TITLE: Does Russel's paradox preclude us from using the power set to generate every possible set?
QUESTION [0 upvotes]: Suppose I have the set of all things $\{a, b, c,... \}$.
It seems to me that $ \mathcal P \{a, b, c,... \} $ would be the set of all sets, which sounds like it includes the set of all sets that do no... | {"set_name": "stack_exchange", "score": 0, "question_id": 1249171} |
\begin{document}
\maketitle
\begin{abstract}
We consider the defocusing cubic nonlinear Schr\"odinger equation (NLS) on the
two-dimensional torus. The equation admits a special family of elliptic invariant
quasiperiodic tori called finite-gap solutions. These are inherited from the
integrable 1D model (cubic NLS o... | {"config": "arxiv", "file": "1810.03694/GHHMP4amsart11.tex"} |
TITLE: differentiability and compactness
QUESTION [1 upvotes]: I have no idea how to show whether this statement is false or true:
If every differentiable function on a subset $X\subseteq\mathbb{R}^n$ is bounded then $X$ is compact.
Thank you
REPLY [0 votes]: If $X$ is unbounded, take some variant of $\|x\|$. If $X... | {"set_name": "stack_exchange", "score": 1, "question_id": 257473} |
TITLE: How to show that the graded dual of the universal enveloping algebra of a free Lie algebra on a finite set is the shuffle algebra
QUESTION [4 upvotes]: In the article, the universal enveloping algebra of a free Lie algebra on a set X is defined to be the free associative algebra generated by X.
It is said that ... | {"set_name": "stack_exchange", "score": 4, "question_id": 255472} |
TITLE: Tails of sums of Weibull random variables
QUESTION [7 upvotes]: Suppose that $X_1, X_2, \ldots, X_n$ are i.i.d random variables distributed according to Weibull distribution with shape $0 < \epsilon < 1$ (it means that $\mathbf{Pr}[X_i \geq t] = e^{-\Theta(t^{\epsilon})}$).
Now consider the random variable $S_n ... | {"set_name": "stack_exchange", "score": 7, "question_id": 118562} |
TITLE: Solve nonlinear equation $-xu_x+uu_y=y$
QUESTION [4 upvotes]: Solve nonlinear equation
$$\left\{\begin{matrix}
-xu_x+uu_y=y & \\
u(x,2x)=0&
\end{matrix}\right.$$
using method of characteristic curves
my attempt:
for the pde we can write it as
$\frac{dx}{-x}=\frac{dy}{u}=\frac{du}{y}$
but i cant solve littl... | {"set_name": "stack_exchange", "score": 4, "question_id": 2443958} |
TITLE: Boundary conditions for $\mathbf D$ and $\mathbf H$
QUESTION [0 upvotes]: I understand the derivation for the boundary conditions for $\mathbf B$ and $\mathbf E$ as it was explained to me in Griffiths, but Griffiths states the following:
$$H_{\text{above}}^{\bot} - H_{\text{below}}^{\bot} = -(M_{\text{above}}^{\... | {"set_name": "stack_exchange", "score": 0, "question_id": 479204} |
TITLE: How to evaluate limiting value of sums of a specific type
QUESTION [2 upvotes]: We know that if $f$ is integrable in (0,1) then
$$
\lim_{n \to \infty} \frac{1}{n}\sum_{k=1}^{n}f(k/n) = \int_{0}^{1}f(x)dx.
$$
Recently I found the following sum
$$
\lim_{n \to \infty} \sum_{k=1}^{n}\frac{k}{n^2 + k^2} = \frac{\ln ... | {"set_name": "stack_exchange", "score": 2, "question_id": 400174} |
TITLE: Show that given set is smooth submanifold.
QUESTION [1 upvotes]: This is Exercise 2.1.14 of ``Lecture on the geometry of Manifold."
Let $Z=\{(x,a,b,c) \in \mathbb{R}^{4}: a \neq 0, ax^2+bx+c=0 \}$. Show that $Z$ is a smooth submanifold of $\mathbb{R}^{4}.$
Clearly, if we just assume $Z' = \{(x,a,b,c) \in \mat... | {"set_name": "stack_exchange", "score": 1, "question_id": 3355379} |
\begin{document}
\title{Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the 2nd kind}
\date{\today}
\author{J.~C.~De Los Reyes\footnotemark[3] \and C.~Meyer\footnotemark[4]}
\renewcommand{\thefootnote}{\fnsymbol{footnote}}
\footnotetext[3]{Research Center on M... | {"config": "arxiv", "file": "1404.4787/r_abl_VI2_2014.tex"} |
TITLE: Does the antidiagonal in this square matrix always contain a prime?
QUESTION [5 upvotes]: Does the antidiagonal in the square matrix with entries $1,2,\ldots,n^2$ row by row in that order always contain a prime?
For example:
For n=2: $\begin{bmatrix}1 & 2\\3 & 4\end{bmatrix}$ the antidiagonal contains two prime... | {"set_name": "stack_exchange", "score": 5, "question_id": 227671} |
TITLE: Explain why, if x, y and z is a primitive Pythagorean triple, then either x or y must be odd
QUESTION [1 upvotes]: "Three positive integers $x$, $y$ and $z$ are called a Pythagorean triple if $x^2 + y^2 = z^2$. A Pythagorean triple is called primitive if the only positive integer that is a factor of all three in... | {"set_name": "stack_exchange", "score": 1, "question_id": 2427497} |
TITLE: Symmetric random walk with bounds
QUESTION [4 upvotes]: can anyone help me with this:
We are considering a symmetric random walk that ends if level 3 is reached or level -1 is reached. Start=0
What is the expected number of walks? So I am looking for: $E[{\tau}]$ with $\tau$=the stopping time.
REPLY [0 votes]: ... | {"set_name": "stack_exchange", "score": 4, "question_id": 288298} |
TITLE: Why is $n \log (n)$ more significant than $n^2 \log (n)$ in terms of efficiency?
QUESTION [2 upvotes]: I am in a computer algorithms course where I was faced with a problem to determine the big theta efficiency of $n\log(n) + n^2\log(n)$. The solution is
$\Theta(n\log(n))$.
Why was this chosen over $n^2 \log(n... | {"set_name": "stack_exchange", "score": 2, "question_id": 1927661} |
TITLE: Derivative of Lagrangian with respect to velocity
QUESTION [2 upvotes]: My question revolves around this lecture notes on page $109$ equation $(5.1.10)$.
Let's stick to $\mathbb{R}^3$ and consider a particle in $3$-space with position vector $\mathbf{x} = (x, y, z)$. Denote its velocity by $\mathbf{v} = \dot{\m... | {"set_name": "stack_exchange", "score": 2, "question_id": 546882} |
TITLE: In how many ways can you choose between 5 places to visit, but two times each?
QUESTION [2 upvotes]: Lets suppose you want to visit 5 places, A B C D E, you also want to go to each one two times.
For example: You visit $A$, after a day you visit $B$, after a day you visit $B$ again, then $C$ and so on. The thing... | {"set_name": "stack_exchange", "score": 2, "question_id": 4304675} |
TITLE: Calculating closed forms of integrals
QUESTION [1 upvotes]: So I've been told that you can't find the closed form of $\int e^{-\frac{x^2}{2}}$.
Apparently, you know the exact result then you integrate over the whole of $\mathbb{R}$ but every other number needs to be calculated numerically.
What I'm wondering is ... | {"set_name": "stack_exchange", "score": 1, "question_id": 1188320} |
TITLE: Given the following set of equations, find: $xy + 2yz + 3zx$.
QUESTION [1 upvotes]: The positive reals x, y, z satisfy the equations
$$x^2 + xy + \frac{y^2}{3}=25$$
$$\frac{y^2}{3}+z^2 = 9$$
$$z^2+ zx + x^2 = 16$$
Find $$xy + 2yz + 3zx$$
My understanding:
What struck me first were the squares $9, 16, 25$. Th... | {"set_name": "stack_exchange", "score": 1, "question_id": 4149496} |
\begin{document}
\title{Global solutions for $H^s$-critical nonlinear biharmonic \\ Schr\"{o}dinger equation}
\author{Xuan Liu, Ting Zhang\\
\small{School of Mathematical Sciences, Zhejiang University,
Hangzhou 310027, China}}
\date{}
\maketitle
\begin{abstract}
We consider the nonlinear biharmonic Schr\"od... | {"config": "arxiv", "file": "2103.04293.tex"} |
TITLE: compound distribution in Bayesian sense vs. compound distribution as random sum?
QUESTION [0 upvotes]: I'm trying to sort out two different uses of the term "compound distribution" and figure out the relationship.
The Wikipedia article on compound distribution -- which I wrote -- defines a compound distribution ... | {"set_name": "stack_exchange", "score": 0, "question_id": 91877} |
\begin{document}
\title{Micro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equations
\footnote{The first and the third author was supported by the funding DOE--Simulation Center for Runaway Electron Avoidance and Mitigation. Th... | {"config": "arxiv", "file": "1809.00028/Arxiv_Submit.tex"} |
\begin{document}
\title{Enumeration of binary trees \\ compatible with a perfect phylogeny}
\author{Julia A. Palacios\thanks{Department of Statistics and Department of Biomedical Data Science, Stanford University, Stanford, CA, USA. Corresponding author: juliapr@stanford.edu} \\ Anand Bhaskar\thanks{Department of Ge... | {"config": "arxiv", "file": "2108.04849/Main.tex"} |
TITLE: 1-Factorizations of complete graphs sharing a unique 1-factor
QUESTION [2 upvotes]: The complete graph $K_6$ has 15 1-factors (i.e. perfect matching), and 6 1-factorizations (i.e. partitions of the edges into perfect matching). As you can see on the actual drawings, they have a nice property
Any two 1-factoriz... | {"set_name": "stack_exchange", "score": 2, "question_id": 3639450} |
TITLE: Algebraic identities
QUESTION [6 upvotes]: Given that $$a+b+c=2$$ and $$ab+bc+ca=1$$
Then the value of
$$(a+b)^2+(b+c)^2+(c+a)^2$$ is how much?
Attempt:
Tried expanding the expression. Thought the expanded version would contain a term from the expression of $a^3+b^3+c^3-3abc$, but its not the case.
REPLY [0 v... | {"set_name": "stack_exchange", "score": 6, "question_id": 2346162} |
TITLE: proof- can NOT be a linear combination
QUESTION [1 upvotes]: How can I prove that $X^2-Y,X-Y^2$ CAN NOT be written as a combination of $<X^3-Y^3,X^2Y-X>$ ?
REPLY [3 votes]: Suppose $X^2-Y=p(X,Y)(X^3-Y^3)+q(X,Y)(X^2Y-X)$. Evaluating at $X=0$ gives
$Y=p(0,Y)Y^3$, which is impossible. The same technique works for ... | {"set_name": "stack_exchange", "score": 1, "question_id": 543368} |
\begin{document}
\maketitle
\begin{abstract}
{\small \noindent A dynamic coloring of a graph $G$ is a proper coloring such that for every vertex
$v\in V(G)$ of degree at least $2$, the neighbors of $v$ receive at least $2$ colors. The smallest
integer $k$ such that $G$ has a dynamic coloring with $ k $ colors, is ca... | {"config": "arxiv", "file": "0911.4199/Dynamic_coloring.tex"} |
\begin{document}
\begin{abstract}
We show that there is no positive loop inside the component of a fiber in
the space of Legendrian embeddings in the contact manifold $ST^*M$,
provided that the universal cover of $M$ is $\RM^n$.
We consider some related results in the space of one-jets of functions on a compact manif... | {"config": "arxiv", "file": "1004.5263/pil13.tex"} |
\begin{document}
\maketitle
\abstract{We study initial-boundary value problems for linear evolution equations of arbitrary spatial order, subject to arbitrary linear boundary conditions and posed on a rectangular 1-space, 1-time domain. We give a new characterisation of the boundary conditions that specify well-posed ... | {"config": "arxiv", "file": "1104.5571/Well-posed_IBVP.tex"} |
TITLE: Number of undirected trees with unlabled vertices and labeled edges
QUESTION [0 upvotes]: I would appreciate some help coming up with an expression for the number of spanning trees of an undirected graph with m labeled edges but m+1 unlabled vertices.
The answer is supposed to be ${m+1}^{m-2}$, but the best I c... | {"set_name": "stack_exchange", "score": 0, "question_id": 3808153} |
TITLE: Euler–Lagrange equation (changing variable)
QUESTION [0 upvotes]: Create the Euler–Lagrange equation for the following questions (if it's necessary change the variables).
$$\tag{1}\int_{y_1}^{y_2}\dfrac{x'^2}{\sqrt{x'^2+x^2}}\,\mathrm{d}y$$
$$\tag{2}\int_{x_1}^{x_2}y^{3/2}\,\mathrm{d}s$$
$$\tag{3}\int\dfrac{y\cd... | {"set_name": "stack_exchange", "score": 0, "question_id": 407791} |
TITLE: Is this family of functions equicontinuous in $\mathbb{R}$?
QUESTION [3 upvotes]: Let $\{ \varphi_{\lambda}(x,y): \lambda \in \mathbb{R} \}$ be the family of functions defined by $$\varphi_{\lambda}(x,y):= \frac{1}{1 + x^4 + \frac{1}{2}\arctan(\lambda)\sin(y^6)}$$ for all $\lambda \in \mathbb{R}$. Is this family... | {"set_name": "stack_exchange", "score": 3, "question_id": 3989974} |
TITLE: $f,g$ continuous maps. $f = g$ a.e. equal, is $f = g$ on a locally compact group?
QUESTION [2 upvotes]: In this question (functions $f=g$ $\lambda$-a.e. for continuous real-valued functions are then $f=g$ everywhere) it is stated that if $ f,g : \mathbb{R} \to \mathbb{R} $ are continuous and $ f = g $ a.e. equal... | {"set_name": "stack_exchange", "score": 2, "question_id": 830304} |
TITLE: Can a gauge anomaly be *removed* by quantum corrections?
QUESTION [4 upvotes]: Consider a classical gauge field coupled to a vector field $j^\mu$. Gauge invariance requires that $\mathcal A_\mathrm{cl}:=\partial_\mu j^\mu$ vanishes:
$$
\mathcal A_\mathrm{cl}\equiv 0
$$
In other words, the source of a classical g... | {"set_name": "stack_exchange", "score": 4, "question_id": 403987} |
TITLE: Inconsistency when solving IVP using Laplace Transform with Dirac Delta
QUESTION [3 upvotes]: solving $\dot{x}(t) + x(t) = \delta (t) $ Using Laplace transform for
$x(0) = 1$, we get:
$sX(s)-1 + X(s) = 1$
$X(s) = \frac{2}{s+1}$
so, $x(t) = 2e^{-t}$
However, evaluating at t=0,
$x(0) = 2 \neq 1$
This disagrees wit... | {"set_name": "stack_exchange", "score": 3, "question_id": 4281658} |
TITLE: Find the number of functions $f(x)$ with $f(f(n)) = n+2022$ for every nonnegative integer n.
QUESTION [1 upvotes]: Find the number of functions $f(x)$ from nonnegative integers to nonnegative integers so that $f(f(n)) = n+2022$ for every nonnegative integer n.
Let $a_0 = f(0)$ and let $a_n = f(a_{n-1})$ for $n\... | {"set_name": "stack_exchange", "score": 1, "question_id": 4538449} |
TITLE: Finding the maxima without second derivative test
QUESTION [0 upvotes]: How can I verify that a critical point is a maximum without using the second derivative test?
Here is the specific situation.
There is a function $f(x)\ge 0$ and $x\ge 0$ as they are both distances. Now I found that
$$
\frac {df}{dx}=\fra... | {"set_name": "stack_exchange", "score": 0, "question_id": 1441890} |
\begin{document}
\title[Cartan geometry and nef tangent bundle]{Holomorphic Cartan
geometry on manifolds\\[5pt] with numerically effective tangent bundle}
\author[I. Biswas]{Indranil Biswas}
\address{School of Mathematics, Tata Institute of Fundamental
Research, Homi Bhabha Road, Bombay 400005, India}
\email{indr... | {"config": "arxiv", "file": "1101.4192.tex"} |
\begin{document}
\pagestyle{headings}
\title{The Noncommutative Geometry of Graph $C^*$-Algebras I: The Index
Theorem}\footnote{\noindent This research was supported by
Australian Research Council and a University of Newcastle Project
Grant}
\author{David Pask}
\email{david.pask@newcastle.edu.au}
\author{Adam Renn... | {"config": "arxiv", "file": "math0508025/arxiversion.tex"} |
TITLE: Deriving Trapezoid Rule via Newton-Cotes formula
QUESTION [0 upvotes]: Newton-Cotes is given by
$$
\int_{a}^{b} f(x) d x \approx \sum_{i=0}^{n} f\left(x_{i}\right) A_{i}, \: A_{i}=\int_{a}^{b} \ell_{i}(x) d x, \quad i=0,1, \ldots, n
$$
For $n=1$, $a=x_0$ and $b=x_1$ I get:
$$
\int_{a}^{b} f(x) d x = \int_{x_0}^... | {"set_name": "stack_exchange", "score": 0, "question_id": 3877933} |
TITLE: Derivation of transformer equations
QUESTION [3 upvotes]: I've learnt in high school that in an ideal transformer, $$\frac{V_s}{N_s} = \frac{V_p}{N_p}$$ I looked for derivation for this formula, and in every source I look, the argument goes thus:
$$|V_p| = N_p \frac{d\Phi}{dt}$$ $$|V_s| = N_s \frac{d\Phi}{dt}$$ ... | {"set_name": "stack_exchange", "score": 3, "question_id": 224396} |
\begin{document}
\begin{center}
{\bf \Large Lebesgue measure and integration theory on non-archimedean real closed fields with archimedean value group}
\end{center}
\centerline{Tobias Kaiser}
\vspace{0.7cm}\noi \footnotesize {{\bf Abstract.} Given a non-archimedean real closed field with archimedean value group whic... | {"config": "arxiv", "file": "1409.2241.tex"} |
TITLE: Nim game variant
QUESTION [2 upvotes]: Statment is as follow
Given a number of piles in which each pile contains some numbers of stones/coins. In each turn, a player can choose only one pile and remove any number of stones (at least one) from that pile. The player who cannot move is considered to lose the game ... | {"set_name": "stack_exchange", "score": 2, "question_id": 2368702} |
\subsection{Bounds for DRLS \label{sec-all-bounds}}
We derive a new additive-multiplicative spectral approximation bound (Eqn. \ref{bound}) for the square of the submatrix $\mathbf{C}$ selected with DRLS.
\begin{theorem}\label{theorem-DRLS} \textit{Additive-Multiplicative Spectral Bound:}
Let $\mathbf{A} \in \mat... | {"config": "arxiv", "file": "1803.06010/bounds.tex"} |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.