We propose a high order positivity-preserving conservative remapping method on three-dimensional (3D) tetrahedral meshes , based the weighted essentially non-oscillatory (WENO) reconstruction method. By precisely computing overlaps between before and after rezoning step in arbitrary Lagrangian–Eulerian (ALE) framework, our does not limit range of mesh movements has wider applications. This also...

Entrywise powers of matrices have been well-studied in the literature, and have recently received renewed attention due to their application in the regularization of highdimensional correlation matrices. In this paper, we study powers of positive semidefinite block matrices (Hst) n s,t=1 where each block Hst is a complex m × m matrix. We first characterize the powers α ∈ R such that the blockwi...

Abstract In this article, one standard and four nonstandard finite difference methods are used to solve a cross-diffusion malignant invasion model. The model consists of system nonlinear coupled partial differential equations (PDEs) subject specified initial boundary conditions, no exact solution is known for problem. It difficult obtain theoretically the stability region classical scheme set P...

Weconstruct a nonlinear finite volume (FV) scheme for diffusion equationon star-shapedpolygonalmeshes andprove that the scheme ismonotone, i.e., it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients. Our scheme has only cell-centered unknowns, and it treats material discontinuities rigorously and offers an explicit expression for the...

We give a useful new characterization of the set of all completely positive, trace-preserving maps Φ : M2 → M2. This allows us to determine explicitly all extreme points of this set, and to easily check any tracepreserving map for complete positivity. We also find an interesting class of extreme channels which appear to be new.

We discuss the problem of constrained approximation and interpolation of scattered data by using compactly supported radial basis functions, subjected to the constraint of preserving positivity. The approaches are presented to compute positive approximation and interpolation by solving the two corresponding optimization problems. Numerical experiments are provided to illustrate that the propose...

Computational methods are developed for generating Gauss-type quadrature formulae having nodes of arbitrary multiplicity at one or both end points of the interval of integration. Positivity properties of the boundary weights are investigated numerically, and related conjectures are formulated. Applications are made to moment-preserving spline approximation. AMS subject classification: 65D30.

A new formalism and tools are proposed to characterize high-order reconstructions in the finite volume method context. We introduce the notion of admissible reconstruction and investigate the maximum principle and positivity preserving properties for scalar hyperbolic problem using the new formalism. We show that the traditional limiting strategies cast in out formalism and provide new proves o...

We show that all quantum states that do not have a positive partial transpose are distillable via channels, which preserve the positivity of the partial transpose. The question whether bound entangled states with non-positive partial transpose exist is therefore closely related to the connection between the set of separable superoperators and positive partial transpose-preserving maps.

The main objective of the present work is to study contraction semigroups generated by Laplace operators on metric graphs, which are not necessarily self-adjoint. We prove criteria for such semigroups to be continuity and positivity preserving. Also we provide a characterization of generators of Feller semi-groups on metric graphs.