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Complete families of linearly independent solutions to the scalar Helmholtz equation introduced and studied in detail by a number of authors provide a unified view over a class of direct and inverse scattering problems and have an impact over solution algorithms. In this paper, they are shown to improve the understanding of two known direct scattering algorithms and to suggest a new solution method for an imaging problem: the reconstruction of an impenetrable obstacle in the resonance region from the knowledge of the incident field and the scattering amplitude and from prior information.

An analysis of the propagation of electromagnetic waves along a perfectly conducting wire parallel to a plane interface between dissimilar materials is presented. Particular emphasis is placed on determination of the significance of the first order Fourier components of current on the wire compared with the zero order current which has no azimuthal dependence around the wire. (Author)

The behavior of arrays of coupled oscillators has been previously studied by computatinal solution of a set of non-linear differential equations describing the time dependence of each oscillator in the presence of signals coupled from neighboring oscillators.