Approximations of doubly substochastic operators.

Doubly-finite Volterra-series Approximations

We consider causal time-invariant nonlinear inputoutput maps that take a set of bounded functions into a set of real-valued functions, and we give criteria under which these maps can be uniformly approximated arbitrarily well using a certain structure consisting of a notnecessarily linear dynamic part followed by a nonlinear memoryless section that may contain sigmoids or radial basis functions...

Doubly Invariant Subspaces of Annulus Operators

Decompositions of Substochastic Transition Functions

Three decompositions of a substochastic transition function are shown to yield substochastic parts. These are the Lebesgue decomposition with respect to a finite measure, the decomposition into completely atomic and continuous parts, and on Rn, a decomposition giving a part with continuous distribution function and a part with discontinuous distribution function. Introduction. The present paper...

Consistent Approximations of Some Geometric Differential Operators

The numerical integration of many geometric partial differential equations involve discrete approximations of some differential geometric operators. In this paper, we consider consistent discretized approximations of these operators based on a quadratic fitting scheme. Asymptotic error analysis on the quadratic fitting are conducted. The experiments show that the proposed approach is effective.

Approximations to wave propagation through doubly-periodic arrays of scatterers

The propagation of waves through a doubly-periodic array of identical rigid scatterers is considered in the case that the field equation is the two-dimensional Helmholtz equation. The method of matched asymptotic expansions is used to obtain the dispersion relation corresponding to wave propagation through an array of scatterers of arbitrary shape that are each small relative to both the wave l...