Some perturbation results for exponentially dichotomous operators are applied to prove the existence of stable and anti-stable solutions of Riccati equations associated to block operators on generalâ€¦ (More)

Simple eigenvalue tests are given to ascertain that a given real 4X 4 matrix transforms the four-vector of Stokes parameters of a beam of light into the four-vector of Stokes parameters of anotherâ€¦ (More)

In this paper, we derive a class of explicit solutions, global in (x, t) âˆˆ R, of the focusing matrix nonlinear SchrÃ¶dinger equation using straightforward linear algebra. We obtain both the usual andâ€¦ (More)

The one-dimensional Schrodinger equation and two of its generalizations are considered, as they arise in quantum mechanics, wave propagation in a nonhomogeneous medium, and wave propagation in aâ€¦ (More)

In this article the existence and uniqueness theory of time dependent kinetic equations is developed for collision terms dominated in the norm by the collision frequency, thus generalizing prior workâ€¦ (More)

This paper is dgdicated to K.M. Case on thg occasion of his sixtieth birthday We study the abstract differential equation T~ + Af = O on a Hilbert space H, which represents a variety of differentâ€¦ (More)

For diffusion equations of indefinite Sturm-Liouville type, we develop two equivalent methods of constructing explicit representations for the solutions. The lirst method is based on an eigenfunctionâ€¦ (More)

0. INTRODUCTION In this article a study is made of the integro-differential equation d_~(x,~) + ~(x,~) = dx +I 2~-1 0 (-1~+1, O<x<~g+~) where T is either finite or infinite. In astrophysics thisâ€¦ (More)

This paper deals with two interrelated issues. One is an invariant subspace approach to finding solutions for the algebraic Riccati equation for a class of infinite dimensional systems. The second isâ€¦ (More)

A mathematical justification ls given for the multiple interface reflection expansion arising when using the adding method for solving numerically the equation of transfer of polarized light in aâ€¦ (More)