The perturbation method in supersymmetric quantum mechanics (SUSYQM) is used to study the spheroidal wave functions’ eigenvalue problem. Expanded by the parameter α, the first order term of ground eigen-value and the eigen-function are gotten. In virtue of the good form of the first term in the superpotential and its shape-invariant property in the first order, we also obtain the eigenvalues an...

This work initiates the study of orthogonal symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were construct...

The problem of robust feedback control of spatially distributed processes described by dissipative partial differential equations (PDEs) is considered. Typically, this problem is addressed through model reduction where finite dimensional approximations to the original PDE system are derived. A common approach to this task is the Karhunen-Loève expansion combined with the method of snapshots. To...

The linear force-free field of a plasma in between spherical shells is found allowing for inhomogeneous boundary conditions. A three-dimensional solution is found by analysis and used as a benchmark to test a solution in terms of an expansion of eigenfunctions where the coefficients are determined by a new method. Alternative methods are also applied in the context of the spherical shell exampl...

In this section we will consider the general properties of the solution p(r, t) of the Smoluchowski equation in the case that the force field is derived from a potential, i.e., F (r) = −∇U(r) and that the potential is finite everywhere in the diffusion doamain Ω. We will demonstrate first that the solutions, in case of reaction-free boundary conditions, obey an extremum principle, namely, that ...

By means of the two-scale convergence method, we investigate the asymptotic behavior of eigenvalues and eigenfunctions of Stekloff eigenvalue problems in perforated domains. We prove a concise and precise homogenization result including convergence of gradients of eigenfunctions which improves the understanding of the asymptotic behavior of eigenfunctions. It is also justified that the natural ...

We present the Quantum Section Method as a quantization technique to compute the eigenvalues and the eigenfunctions of quantum systems. As an instructive example we apply this procedure to quantize the annular billiard. The method uses the symmetry of the system to determine an auxiliary section separating the system into partial regions and computes the Green's functions for Schroedinger's equ...

The method of Λ-operators developed by S. Derkachov, G. Korchemsky, A. Ma-nashov is applied to a derivation of eigenfunctions for the open Toda chain. The Sklyanin measure is reproduced using diagram technique developed for these Λ-operators. The properties of the Λ-operators are studied. This approach to the open Toda chain eigenfunctions reproduces Gauss-Givental representation for these eige...

In this paper, the asymptotic representation of the corresponding eigenfunctions of the eigenvalues has been investigated. Furthermore, we obtain the zeros of eigenfunctions.

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...