Abstract Inverse medium problems involve the reconstruction of a spatially varying unknown from available observations by exploring restricted search space possible solutions. Standard grid-based representations are very general but all too often computationally prohibitive due to high dimension space. Adaptive spectral decompositions instead expand in basis eigenfunctions judicious elliptic op...

In this paper, we consider the numerical approximation of Steklov eigenvalue problem that arises in inverse acoustic scattering. The underlying scattering is for an inhomogeneous isotropic medium. These eigenvalues have been proposed to be used as a target signature since they can recovered from data. A Galerkin method studied where basis functions are Neumann eigenfunctions Laplacian. Error es...

The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to change the additional fundamental spectral parameter, the degree of exponential solution growth, at arbitrary given energy points inside the forbidden zones...

We analyze the achievable communication rates of a generalized soliton-based transmission system for the optical fiber channel. This method is based on modulation of parameters of the scattering domain, via the inverse scattering transform, by the information bits. The decoder uses the direct spectral transform to estimate these parameters and decode the information message. Unlike ordinary On-...

A problem of first-order bandpass sampling is that the indifferent disposition of the baseband spectrum may cause inconvenience in practical applications. To overcome it, we modify the first-order bandpass sampling theory according to the spectral arrangement of the sampled signal. We consider two situations on the arrangement of the shifted replicas of the bandpass signal spectrum: the normal ...

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...