Related papers: Numerical Methods for the Discrete Map $Z^a$
In two-dimensional statistical models possessing a discretely holomorphic parafermion, we introduce a modified discrete Cauchy-Riemann equation on the boundary of the domain, and we show that the solution of this equation yields integrable…
In this paper, we introduce three new iterative methods for finding a common point of the set of fixed points of a symmetric generalized hybrid mapping and the set of solutions of an equilibrium problem in a real Hilbert space. Each method…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
We study the Dirichlet problem for p-harmonic functions on metric spaces with respect to arbitrary compactifications. A particular focus is on the Perron method, and as a new approach to the invariance problem we introduce Sobolev-Perron…
Two discrete dynamical systems are discussed and analyzed whose trajectories encode significant explicit information about a number of problems in combinatorial probability, including graphical enumeration on Riemann surfaces and random…
To a pair (X,f), X compact ANR and f a continuous angle valued map defined on X, a fixed field and a nonnegative integer one assigns a finite configuration of complex numbers with multiplicities located in the punctured complex plane and a…
In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…
The discrete Painlev\'e property is precisely defined, and basic discretization rules to preserve it are stated. The discrete Painlev\'e test is enriched with a new method which perturbs the continuum limit and generates infinitely many…
We discuss a method to construct Dirac-harmonic maps developed by J.~Jost, X.~Mo and M.~Zhu in J.~Jost, X.~Mo, M.~Zhu, \emph{Some explicit constructions of Dirac-harmonic maps}, J. Geom. Phys. \textbf{59} (2009), no. 11, 1512--1527.The…
In this note we discuss the geometry of Riemannian surfaces having a discrete set of singular points. We assume the conformal structure extends through the singularities and the curvature is integrable. Such points are called \emph{simple…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends the corresponding result of Guo and Wenger [Comm. Anal. Geom. 2020]. The main new ingredient in our proofs is a suitable extension of…
In this work, we consider the Dirichlet boundary value problem for nonlinear triharmonic equation. Due to the reduction of the nonlinear boundary value problem to operator equation for the nonlinear term and the unknown second normal…
Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann-Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their…
This paper develops a method for solving Einstein's equation numerically on multi-cube representations of manifolds with arbitrary spatial topologies. This method is designed to provide a set of flexible, easy to use computational…
In topological data analysis (TDA), persistence diagrams have been a succesful tool. To compare them, Wasserstein and Bottleneck distances are commonly used. We address the shortcomings of these metrics and show a way to investigate them in…
We study whether in the setting of the Deift-Zhou nonlinear steepest descent method one can avoid solving local parametrix problems explicitly, while still obtaining asymptotic results. We show that this can be done, provided an a priori…
We study the asymptotic behavior of the Ablowitz-Segur solutions for the second Painlev\'e equation using the Riemann-Hilbert approach and methods based on asymptotic expansions of classical special functions. Recent results show that the…
In 2012, Barbulescu, Detrey, Estibals and Zimmermann proposed a new framework to exhaustively search for optimal formulae for evaluating bilinear maps, such as Strassen or Karatsuba formulae. The main contribution of this work is a new…
Motivated by geometry processing for surfaces with non-trivial topology, we study discrete harmonic maps between closed surfaces of genus at least two. Harmonic maps provide a natural framework for comparing surfaces by minimizing…