相关论文: An application of lattice points counting to shrin…

Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and…

We consider both geometric and measure-theoretic shrinking targets for ergodic maps, investigating when they are visible or invisible. Some Baire category theorems are proved, and particular constructions are given when the underlying map…

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.

Machine-learned normalizing flows can be used in the context of lattice quantum field theory to generate statistically correlated ensembles of lattice gauge fields at different action parameters. This work demonstrates how these…

Minkowski's second theorem on successive minima gives an upper bound on the volume of a convex body in terms of its successive minima. We study the problem to generalize Minkowski's bound by replacing the volume by the lattice point…

We solve the problem of finding a sharp upper bound on the minimum angle formed by $N$ points in the Euclidean and Hyperbolic planes.

In this paper, we present an algorithm for the computation of harmonic maps, and respectively, of the harmonic map heat flow between two closed Riemannian manifolds. Our approach is based on the totally geodesic embedding of the target…

We extend the famous result of Katok and Zemlyakov on the density of half-infinite geodesics on finite flat rational surfaces to half-infinite geodesics on a finite polycube translation $3$-manifold. We also extend this original result to…

This paper addresses the three concepts of \textit{ consistency, stability and convergence } in the context of compact finite volume schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of…

This paper proposes novel gradient-flow schemes that yield convergence to the optimal point of a convex optimization problem within a \textit{fixed} time from any given initial condition for unconstrained optimization, constrained…

It is a longstanding problem to determine the precise relationship between the geodesic length spectrum of a hyperbolic manifold and its commensurability class. A well known result of Reid, for instance, shows that the geodesic length…

We present a new lattice kinetic method to simulate fluid dynamics in curvilinear geometries. A suitable discrete Boltzmann equation is solved in contravariant coordinates, and the equilibrium distribution function is obtained by a Hermite…

The master-field approach to lattice QCD envisions performing calculations on a small number of large-volume gauge-field configurations. Substantial progress has been made recently in the generation of such fields, and this must be joined…

We establish central limit theorems for an action of a group G on a hyperbolic space X with respect to the counting measure on a Cayley graph of G. Our techniques allow us to remove the usual assumptions of properness and smoothness of the…

A numerical method, based on the discrete lattice Boltzmann equation, is presented for solving the volume-averaged Navier-Stokes equations. With a modified equilibrium distribution and an additional forcing term, the volume-averaged…

We study an optimal stretching problem, which is a variant lattice point problem, for convex domains in $\mathbb{R}^d$ ($d\geq 2$) with smooth boundary of finite type that are symmetric with respect to each coordinate hyperplane/axis. We…

We use Lyapunov type functions to find conditions of finite shadowing in a neighborhood of a nonhyperbolic fixed point of a one-dimensional or two-dimensional homeomorphism or diffeomorphism. A new concept of shadowing in which we control…

In the framework laid down by Matveev and Shevchishin, superintegrability is achieved with one integral linear in the momenta (a Killing vector) and two extra integrals of of any degree above two in the momenta. However these extra…

We derive the Enskog equation utilizing orthonormal vielbein fields, enabling the utilization of arbitrary coordinate systems to characterize spatial geometry. Additionally, we employ an adapted coordinate system in the momentum space,…

A point is called generic for a flow preserving an infinite ergodic invariant Radon measure, if its orbit satisfies the conclusion of the ratio ergodic theorem for every pair of continuous functions with compact support and non-zero…