This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is to begin with a continuous (in t) and conservative matrix Q(t) = [qij(t)] of nonhomogeneous transition rates qij(t), and use it to construct the transition ...

The problem on the solutions of homogeneous and nonhomogeneous generalized linear vector equations in idempotent algebra is considered. For the study of equations, an idempotent analog of matrix determinant is introduced and its properties are investigated. In the case of irreducible matrix, existence conditions are found and the general solutions of equations are obtained. The results are exte...

We consider denumerable state nonhomogeneous Markov decision processes and extend results from both denumerable state homogeneous and finite state nonhomogeneous problems. We show that, under weak ergodicity, accumulation points of finite horizon optima (termed algorithmic optima) are average cost optimal. We also establish the existence of solution horizons. Finally, an algorithm is presented ...

In this paper, we analyze a recently developed finite volume method for the timedependent Maxwell’s equations in a three-dimensional polyhedral domain composed of two dielectric materials with different parameter values for the electric permittivity and the magnetic permeability. Convergence and error estimates of the numerical scheme are established for general nonuniform tetrahedral triangula...

We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f ∈ Lloc 0, T ;L2 Ω , which is translation compact and φ ∈ C1 b R ;H2 R1 × {±L} asymptotically alm...

Low frequency drift (0.0-0.015 Hz) has often been reported in time series fMRI data. This drift has often been attributed to physiological noise or subject motion, but no studies have been done to test this assumption. Time series T*2-weighted volumes were acquired on two clinical 1.5 T MRI systems using spiral and EPI readout gradients from cadavers, a normal volunteer, and nonhomogeneous and ...

This article is devoted to the study of the nonhomogeneous incompressible Navier-Stokes equations in space dimension three. By making use of the “weakly nonlinear” energy estimate approach introduced by Lei and Zhou in [16], we establish two logarithmically improved blow-up criteria of the strong or smooth solutions subject to vacuum for the 3D nonhomogeneous incompressible Navier-Stokes equati...

The regularized meshless method is a novel boundary-type meshless method but by now has largely been confined to homogeneous problems. In this paper, we apply the regularized meshless method to the nonhomogeneous problems in conjunction with the dual reciprocity technique in the evaluation of the particular solution. Numerical experiments of three benchmark nonhomogeneous problems demonstrate t...

This paper solves analytically and illustrates numerically the full-vector, electromagnetic inverse source problem of synthesizing an unknown source embedded in a given substrate medium of volume V and radiating a prescribed exterior field. The derived formulation and results generalize previous work on the scalar version of the problem, especially the recent “Part I” paper [A.J. Devaney, E.A. ...

This paper series presents a follow-up study of our previous work on the reverse Monte Carlo method solution of transient radiation transport in the homogeneous media. In this study, the method is extended to consider nonhomogeneous media, which exist in many practical problems. The transport process of ultra-short light pulse propagation inside the non-emitting, absorbing, and anisotropically ...