The transfer operator due to Bogomolny provides a convenient method for obtaining a semiclassical approximation to the energy eigenvalues of a quantum system, no matter what the nature of the analogous classical system. In this paper, the method is applied to integrable systems which are rotationally invariant , in two and three dimensions. In two dimensions, the transfer operator is expanded i...

The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions ...

In order to make the operator freely walk in virtual environment (VE), a new prototype of VE system for assembly is presented in this paper. In this system, a special machine is designed and it enables the operator to walk inside the VE in any directions over a long distance without actually leaving the physical device. Images produced by the computer are projected upon the surface of a large s...

We present an easy-to-use formula for mean (spaceand direction-average) specific intensity of radiation in uniform spherical and cylindrical plasmas, which are not under external irradiation. This formula has high accuracy in any spectral interval dn taken in continuum as well as within a spectral line of any profile, including overlapping lines and lines on a pedestal of intense continuum in a...

Since their introduction, mean value coordinates enjoy ever increasing popularity in computer graphics and computational mathematics because they exhibit a variety of good properties. Most importantly, they are defined in the whole plane which allows interpolation and extrapolation without restrictions. Recently, mean value coordinates were generalized to spheres and to ’3. We show that these s...

The main purpose of this paper is to obtain an explicit expression of a family of matrix valued orthogonal polynomials {Pn}n, with respect to a weight W , that are eigenfunctions of a second order differential operator D. The weight W and the differential operator D were found in [12], using some aspects of the theory of the spherical functions associated to the complex projective spaces. We al...

A semiclassical transport equation for electrons in a semiconductor crystal is considered. It includes a nonlinear scattering operator modelling electron-phonon interaction. A formal macroscopic limit under the assumption of a small phonon energy is carried out, leading to the so called spherical harmonics expansion (SHE-) model for an energy-dependent distribution function with a scattering op...

In this paper, we propose a novel discrete cuckoo search algorithm (DCS) for solving spherical Traveling Salesman Problem (TSP) where all points are on the surface of a sphere. The algorithm is based on the Lévy flight behaviour and brood parasitic behaviour. The proposed algorithm applies study operator, the ”A” operator, and 3-opt operator to solutions in the bulletin board to speed up the co...

The main purpose of this paper is to extend to a situation involving matrix valued orthogonal polynomials and spherical functions, a result that traces its origin and its importance to work of Claude Shannon in laying the mathematical foundations of information theory and to a remarkable series of papers by D. Slepian, H. Landau and H. Pollak. To our knowledge, this is the first example showing...