Related papers: Bead sliding and convex inequalities
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
In this paper we introduce the novel framework of distributionally robust games. These are multi-player games where each player models the state of nature using a worst-case distribution, also called adversarial distribution. Thus each…
The convexification numerical method with the rigorously established global convergence property is constructed for a problem for the Mean Field Games System of the second order. This is the problem of the retrospective analysis of a game…
We define, in the frame of an abstract Wiener space, the notions of convexity and of concavity for the equivalence classes of random variables. As application we show that some important inequalities of the finite dimensional case have…
Using known entropic and information inequalities new inequalities for some classical polynomials are obtained. Examples of Jacobi and Legendre polynomials are considered.
In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain geometric meaning of basic invariants of vector distributions.
We present an experimental study of the movement of individual particles in a layer of vertically shaken granular material. High-speed imaging allows us to investigate the motion of beads within one vibration period. This motion consists…
This work presents a framework for billiards in convex domains on two dimensional Riemannian manifolds. These domains are contained in connected, simply connected open subsets which are totally normal. In this context, some basic properties…
A mapping M(t) is considered to obtain some preliminary results and a new trapezoidal form of Fejer inequality related to the h-convex functions. Furthermore the obtained results are applied to achieve some new inequalities in connection…
We review the basic ideas lying at the foundation of the recently developed theory of twisted symmetries of differential equations, and some of its developments.
Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium…
The billiard problem of statistical physics is considered in a new geometric approach with a symmetric phase space. The structure and topological features of typical billiard phase portrait are defined. The connection between geometric,…
The inequality of Berwald is a reverse-H\"older like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions…
We show that, by using multiplicative weights in a game-theoretic thought experiment (and an important convexity result on the composition of multiplicative weights with the relative entropy function), a symmetric bimatrix game (that is, a…
This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…
We demonstrate that the free motion of any two-dimensional rigid body colliding elastically with two parallel, flat walls is equivalent to a billiard system. Using this equivalence, we analyze the integrable and chaotic properties of this…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new…
We consider systems of "pinned balls," i.e., balls that have fixed positions and pseudo-velocities. Pseudo-velocities change according to the same rules as those for velocities of totally elastic collisions between moving balls. The times…
The dynamics of three soft interacting particles on a ring is shown to correspond to the motion of one particle inside a soft triangular billiard. The dynamics inside the soft billiard depends only on the {\it masses ratio} between…