The main objective of this work is to develop a pair of Lommel matrix functions suggested by the hypergeometric matrix functions and some of their properties are studied. Some properties of the hypergeometric and Bessel matrix functions are obtained.

We evaluate the eigenfields of an unstable Bessel-Gauss resonator (UBGR) by use of the transfer-matrix method in which the transverse profiles and their corresponding losses of the UBGR are considered as the eigenvectors and eigenvalues of a transfer matrix so that the dominant mode fields and their losses of the UBGR can be readily extracted in terms of the matrix eigenvalue algorithm. Moreove...

Relativistic electrons counterpropagating through the center of a radially polarized J_{1} optical Bessel beam in vacuum will emit radiation in a manner analogous to the channeling radiation that occurs when charged particles traverse through a crystal lattice. However, since this interaction occurs in vacuum, problems with scattering of the electrons by the lattice atoms are eliminated. Contra...

e review a recent result in modeling lower order (univariate and bivariate) probability densities of pixel values resulting from bandpass filtering of images. Assuming an object-based model for images, a parametric family of probabilities, called Bessel K forms, has been derived [1]. This parametric family matches well with the observed histograms for a large variety of images (video, range, in...

1 Abstract — It is shown that the limited-diffraction Bessel beam of order zero can be generated by a transducer with equal-area division of elements and with a fixed prefocus, i.e. conventional transducers used in medical imaging equipment. The element division implies that the scaling parameter must be chosen to contain the first lobe of the Bessel function in the first element. In addition t...

Ordinary Bessel beams are described in terms of the generalized Lorenz-Mie theory (GLMT) by adopting, for what is to our knowledge the first time in the literature, the integral localized approximation for computing their beam shape coefficients (BSCs) in the expansion of the electromagnetic fields. Numerical results reveal that the beam shape coefficients calculated in this way can adequately ...

This paper introduces the concept of Bessel multipliers. These operators are defined by a fixed multiplication pattern, which is inserted between the analysis and synthesis operators. The proposed concept unifies the approach used for Gabor multipliers for arbitrary analysis/synthesis systems, which form Bessel sequences, like wavelet or irregular Gabor frames. The basic properties of this clas...

USFKAD is an encoded expert system for the eigenfunction expansion of solutions to the wave, diffusion, and Laplace equations: both homogeneous and nonhomogenous; one, two, or three dimensions; Cartesian, cylindrical, or spherical coordinates; Dirichlet, Neumann, Robin, or singular boundary conditions; in time, frequency, or Laplace domain. The user follows a menu to enter his/her choices and t...

Seeking universal probability models for image representations, we employ a spectral approach where the images are decomposed using several bandpass lters, and probability models on the lter outputs (or spectral components) are imposed. We apply a (two-parameter) analytical form, introduced in [9] and called a Bessel K form, for modeling the marginal probabilities of these spectral components, ...

This principal result in this article is that every Poisson-Dirichlet distribution PD(0, θ) is an asymptotically invariant distribution for a growing collection of independent Bessel square processes of dimension zero divided by their total sum, under the condition that the sum total of their initial values grows to infinity in probability. Implications in several areas of Probability theory ha...