Related papers: Ten Lectures on the Moment Problem
The following is an improved version of Chapter 12 of my book [Sm17]. Among others, we present a new unified approach to the Archimedean Positivstellens\"atze for quadratic modules and semirings in Section 12.4 and we add a number of new…
In this paper we improve the bounds for the Carath\'eodory number, especially on algebraic varieties and with small gaps (not all monomials are present). We provide explicit lower and upper bounds on algebraic varieties, $\mathbb{R}^n$, and…
In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear…
Assorted questions: Time as a parameter in Quantum Mechanics. No-Go theorems for a time operator. Localization, time and causality. Causality violation. Localization again. Lesson 1: Evading the troubles: Im E finite. Lights and shadows of…
A moment body is a linear projection of the spectraplex, the convex set of trace-one positive semidefinite matrices. Determining whether a given point lies within a given moment body is a problem with numerous applications in quantum state…
These are the lecture notes of a course given by the first author on December 27, 2012 - January 4, 2013, held at the Academy of Mathematics and Systems Science Chinese Academy of Sciences in Beijing.
In this paper we give a complete solution of the following "polynomial moment problem" which arose about 10 years ago in connection with Poincare's center-focus problem. For a given polynomial P(z) to describe polynomials Q(z) orthogonal to…
We study the optimization problem over the weakly Pareto set of a convex multiobjective optimization problem given by polynomial functions. Using Lagrange multiplier expressions and the weight vector, we give three types of representations…
We continue the study of truncated matrix-valued moment problems begun in arXiv:2310.00957. Let $q\in\mathbb{N}$. Suppose that $(\mathcal{X},\mathfrak{X})$ is a measurable space and $\mathcal{E}$ is a finite-dimensional vector space of…
When using a finite difference method to solve an initial--boundary--value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze…
In May 2015, a conference entitled "Groups, Geometry, and 3-manifolds" was held at the University of California, Berkeley. The organizers asked participants to suggest problems and open questions, related in some way to the subject of the…
I give a pedagogical introduction to the concepts and the tools that are necessary to study particle physics models in higher dimensions. I then give a more detailed presentation of warped compactifications and discuss their possible…
In this prelinimary version of paper, we propose to give a complete solution to the Truncated Multidimensional Trigonometric Moment Problem (TMTMP) from a system and signal processing perspective. In mathematical TMTMPs, people care about…
The optimal power flow (OPF) problem minimizes power system operating cost subject to both engineering and network constraints. With the potential to find global solutions, significant research interest has focused on convex relaxations of…
Concentration inequalities, a major tool in probability theory, quantify how much a random variable deviates from a certain quantity. This paper proposes a systematic convex optimization approach to studying and generating concentration…
Moment methods are classical approaches that approximate the mesoscopic radiative transfer equation by a system of macroscopic moment equations. An expansion in the angular variables transforms the original equation into a system of…
This document is built around a list of thirty-two problems in enumeration of matchings, the first twenty of which were presented in a lecture at MSRI in the fall of 1996. I begin with a capsule history of the topic of enumeration of…
This document is the aggregation of six discussions of Lopes et al. (2010) that we submitted to the proceedings of the Ninth Valencia Meeting, held in Benidorm, Spain, on June 3-8, 2010, in conjunction with Hedibert Lopes' talk at this…
A summary of the session on Particle Astrophysics at the Rencontre de Vietnam, 2006.
We consider univariate distributions with finite moments of all positive orders. The moment problem is to determine whether or not a given distribution is uniquely determined by the sequence of its moments. There is a huge literature on…