This paper introduces a new method for the development of closed-form spatial Green’s functions for electrostatic problems involving layered dielectrics. The new method utilizes a finite-difference approximation of the spectral domain form of the Green’s function to overcome the tedious numerical integration of the Fourier–Bessel inverse transform that is required to generate the Green’s functi...

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible Z-valued functions to continuous R-valued functions over R n. Core contributions include: the definition of the topological Bessel transform; a relationship in terms of the lo...

Abstract. The aim of this paper is to establish an analogue of Logvinenko-Sereda’s theorem for the Fourier-Bessel transform (or Hankel transform) Fα of order α > −1/2. Roughly speaking, if we denote by PWα(b) the Paley-Wiener space of L -functions with FourierBessel transform supported in [0, b], then we show that the restriction map f → f |Ω is essentially invertible on PWα(b) if and only if Ω...

The paper presents calculations for the radiation of a loop antenna wrapped around a metallic cylinder into a conductive medium. The problem has been solved analytically by using Fourier transform and Bessel functions. The evaluation of the analytical solution, involves the use of exponentially scaled Bessel functions, and FFT to evaluate inverse Fourier transform, with all computations done in...

We derive a power series representation of an arbitrary electromagnetic field near some axis through the coaxial components on axis. The obtained equations are compared with Fourier–Bessel approach and verified by several examples. It is shown that for each azimuthal mode we need only two real functions in order to describe source free region it. dipole superconducting radio-frequency gun analy...

A closed integral expression is derived for Neumann series of Bessel functions — a series of Bessel functions of increasing order — over the set of real numbers.

In this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient te...