in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

The inverse scattering transform for an integrable discretization of the defocusing nonlinear Schrodinger equation with nonvanishing boundary values at infinity is constructed. This problem had been previously studied, and many key results had been established. Here, a suitable transformation of the scattering problem is introduced in order to address the open issue of analyticity of eigenfunct...

This paper is concerned with the inverse medium scattering problem with a stochastic source, the reconstruction of the refractive index of an inhomogeneous medium from the boundary measurements of the scattered field. As an inverse problem, there are two major difficulties in addition to being highly nonlinear: the ill-posedness and the presence of many local minima. To overcome the difficultie...

We formulate and present algorithms and applications for the inverse scattering problem for a one-dimensional layered medium whose reflection coefficients vary with time. We show that given the reflection responses to impulsive plane waves incident on the medium at different times, this problem can be solved either by solving a series of nested non-Toeplitz systems of equations, or by propagati...

We consider the inverse scattering problem of determining the shape of a partially coated obstacle in R 3 from a knowledge of the incident time harmonic electromagnetic plane wave and the electric far field pattern of the scattered wave. A justification is given of the linear sampling method in this case and numerical examples are provided showing the practicality of our method. 1. Introduction...

Direct inversion of acoustic scattering problems is nonlinear. One way to treat the inverse scattering problem is based on the reversion of the Born–Neumann series solution of the Lippmann–Schwinger equation. An important issue for this approach is the radius of convergence of the Born–Neumann series for the forward problem. However, this issue can be tackled by employing a renormalization tech...

A multilayered particle is illuminated by plane acoustic or electromagnetic waves of one or several frequencies. We consider the inverse scattering problem for the identification of the layers and of the refraction coefficients of the scatterer in a non-Born region of scattering. Local de-terministic and global probabilistic minimization methods are studied. A special Reduction Procedure is int...

We consider an inverse scattering problem and its near-field approximation at high frequencies. We first prove, for both problems, Lipschitz stability results for determining the low-frequency component of the potential. Then we show that, in the case of a radial potential supported sufficiently near the boundary, infinite resolution can be achieved from measurements of the near-field operator ...