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In an exploration paper, {\it L. Chen, Algorithms for Deforming and Contracting Simply Connected Discrete Closed Manifolds (I)}, we designed algorithms for deforming and contracting a simply connected discrete closed manifold to a discrete…
For the solution of 2D exterior Dirichlet Poisson problems we propose the coupling of a Curved Virtual Element Method (CVEM) with a Boundary Element Method (BEM), by using decoupled approximation orders. We provide optimal convergence error…
In this paper we present a novel approach for the prescription of high order boundary conditions when approximating the solution of the Euler equations for compressible gas dynamics on curved moving domains. When dealing with curved…
We present an interpretation of Deepcode, a learned feedback code that showcases higher-order error correction relative to an earlier interpretable model. By interpretation, we mean succinct analytical encoder and decoder expressions…
Biharmonic maps between surfaces are studied in this paper. We compute the bitension field of a map between surfaces with conformal metrics in complex coordinates. As applications, we show that a linear map from Euclidean plane into…
This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion…
Closed meanders are planar configurations of one or several disjoint closed Jordan curves intersecting a given line or curve transversely. They arise as shooting curves of parabolic PDEs in one space dimension, as trajectories of Cartesian…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
The development of higher order finite elements methods has become an active research area. The deformation method for mesh generation has achieved a prescribed positive Jacobian determinant constraint and it has been a useful method for…
Bi-modal (respectively, multi-modal) constrained coding refers to an encoding model whereby a user input block can be mapped to two (respectively, multiple) codewords. In current storage applications, such as optical disks, multi-modal…
We present an algorithm for computing a separating linear form of a system of bivariate polynomials with integer coefficients, that is a linear combination of the variables that takes different values when evaluated at distinct (complex)…
The development of scalable and wavenumber-robust iterative solvers for Helmholtz problems is challenging but also relevant for various application fields. In this work, two-level Schwarz domain decomposition preconditioners are enhanced by…
The goal of combining beamforming and space-time coding in this work is to obtain full-diversity order and to provide additional received power (array gain) compared to conventional space-time codes. In our system, we consider a…
We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast…
This paper introduces an extension of the Morley element for approximating solutions to biharmonic equations. Traditionally limited to piecewise quadratic polynomials on triangular elements, the extension leverages weak Galerkin finite…
We study a class of bivariate deformed Hermite polynomials and some of their properties using classical analytic techniques and the Wigner map. We also prove the positivity of certain determinants formed by the deformed polynomials. Along…
Nowadays, high-speed machining is usually used for production of hardened material parts with complex shapes such as dies and molds. In such parts, tool paths generated for bottom machining feature with the conventional parallel plane…
A general action is proposed for the fields of $q$-dimensional differential form over the compact Riemannian manifold of arbitrary dimensions. Mathematical tools are based on the well-known de Rham-Kodaira decomposing theorem on harmonic…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
A two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion…