相关论文: Bead sliding and convex inequalities

We exhibit a class of classical or tropical posynomial systems which can be solved by reduction to linear or convex programming problems. This relies on a notion of colorful vectors with respect to a collection of Newton polytopes. This…

We overview the main ideas and techniques of the functional-analytical approach to some extremal problems of convex geometry that stem from the Queen Dido problem.

We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \textit{scaling inequalities} used in analysing the…

We provide an overview of the connections between Bell's inequalities and algebraic structure.

We introduce and analyze several variations of Penney's game aimed to find a more equitable game.

While discounted payoff games and classic games that reduce to them, like parity and mean-payoff games, are symmetric, their solutions are not. We have taken a fresh view on the properties that optimal solutions need to have, and devised a…

A quadratic inequality is formulated in the paper. An estimate on the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations.

We consider a strictly convex billiard table with $C^2$ boundary, with the dynamics subjected to random perturbations. Each time the billiard ball hits the boundary its reflection angle has a random perturbation. The perturbation…

Problems involving rotating systems analyzed from an inertial frame, without invoking fictitious forces, is something that freshman students find difficult to understand in an introductory mechanics course. One of the problems that I…

We establish several inequalities for manifolds with positive scalar curvature and, more generally, for the scalar curvature bounded from below, in the spirit of the classical bound on the distances between conjugates points in surfaces…

Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…

We define convexity canonically in the setting of monoids. We show that many classical results from convex analysis hold for functions defined on such groups and semigroups, rather than only on vector spaces. Some examples and…

This paper surveys our results on integrable billiards. We consider various models of billiards, including Birkhoff, outer, magnetic, and Minkowski billiards. Also, we discuss wire billiards and billiards in cones. For four models of convex…

Flow games coincide precisely with the fundamental class of non-negative totally balanced games. However, the conditions for their convexity have remained elusive. In this paper, we resolve this challenge by providing a complete…

This paper studies the problem of perturbed convex and smooth optimization. The main results describe how the solution and the value of the problem change if the objective function is perturbed. Examples include linear, quadratic, and…

We provide infinitely many solutions of a Dirichlet problem on balls.

Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…

A protocol for considering decoherence in quantum games is presented. Results for two-player, two-strategy quantum games subject to decoherence are derived and some specific examples are given. Decoherence in other types of quantum games is…

We consider a mathematical model for the classical Sudoku puzzle, which we call the primal problem and introduce a corresponding dual problem. Both problems are constraint satisfaction models and a duality relation between them is proved.…

We are interested in solving convex optimization problems with large numbers of constraints. Randomized algorithms, such as random constraint sampling, have been very successful in giving nearly optimal solutions to such problems. In this…