A study is made of the excitation of electromagnetic waves by spatially bounded, arbitrary sources in the presence of a cylindrical guiding structure immersed in an infinitely extended, homogeneous gyrotropic medium whose permittivity and permeability are both describable by tensors with nonzero off-diagonal elements. The axis of symmetry of the considered cylindrical structure is assumed to co...

Integral equation formulation and magnetic potential Green’s dyadics for multilayered rectangular waveguide are presented for modeling interacting printed antenna arrays used in waveguidebased spatial power combiners. Dyadic Green’s functions are obtained as a partial eigenfunction expansion in the form of a double series over the complete system of eigenfunctions of transverse Laplacian operat...

The wave equation occurs in many branches of physics, in applied mathematics as well as in engineering, and it is also considered as one of the three fundamental equations in mathematical physics. The homogenous wave equation with constant coefficient can be solved by many ways such as separation of variables [1], the methods of characteristics [2, 3], and Laplace transform and Fourier transfor...

Abstract The paper suggests a new technique for solution of the inverse problem for Maxwell’s equations in a dissipating medium. Being non-self-adjoint, the problem generally requires computing an adjoint operator on each step of gradient descent minimization procedure. The suggested approach introduces a conjugation operator and develops a representation of the system of Maxwell’s equations ba...

The Fredholm integral equations of the first kind are a classical example of ill-posed problem in the sense of Hadamard. If the integral operator is self-adjoint and admits a set of eigenfunctions, then a formal solution can be written in terms of eigenfunction expansions. One of the possible methods of regularization consists in truncating this formal expansion after restricting the class of a...

The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach metastable vacuum states, both the case when potential is bounded from below, and it unbounded below therefore no stable state exists. In cases, decay rate of given by lowest nonzero eigenvalue associated Fokker--Planck equation. corresponding eigenfunctio...

Abstract: In this paper, a perturbing nonlinear homogeneous Schrodinger equation is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation and Picard approximation methods together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a...

In recent years several new inverse scattering techniques have been developed that determine the boundary of an unknown obstacle by reconstructing the surrounding scattered field. In the case of sound soft obstacles, the boundary is usually found as the minimum contour of the total field. In this note we derive a different approach for imaging the boundary from the reconstructed fields based on...

In this work decay estimates are derived for the solutions of 1-D linear parabolic PDEs with disturbances at both boundaries and distributed disturbances. The decay estimates are given in the 2 L and 1 H norms of the solution and discontinuous disturbances are allowed. Although an eigenfunction expansion for the solution is exploited for the proof of the decay estimates, the estimates do not re...

For 1-D parabolic PDEs with disturbances at both boundaries and distributed disturbances we provide ISS estimates in various norms. Due to the lack of an ISS Lyapunov functional for boundary disturbances, the proof methodology uses (i) an eigenfunction expansion of the solution, and (ii) a finite-difference scheme. The ISS estimate for the sup-norm leads to a refinement of the well-known maximu...