We prove uniqueness and give precise criteria for existence of split and non-split Bessel models for a class of lowest and highest weight representations of the groups GSp(4,R) and Sp(4,R) including all holomorphic and anti-holomorphic discrete series representations. Explicit formulas for the resulting Bessel functions are obtained by solving systems of differential equations. The formulas are...

We introduce integral transforms to study problems for the singular Bessel differential operators B−γ with negative parameter −γ < 0. A solution equation B−γu+u = 0 is a function u

A few transformations are presented for reducing certain cases of Meijer’s Gfunction to a G-function of lower order. Their applications to the integration of a product of Bessel functions are given. The algorithm has been implemented within Mathematica 3.0.

the current study presents a new analytical method for buckling analysis of circular plates with constant thickness and poisson’s ratio, made of functionally graded material subjected to radial load. governing equations are based on energy method for thin plates. the boundary conditions of the plate are assumed to be simply supported and clamped. the stability equations were obtained by using c...

It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed...

An alternative method to generate J(0) Bessel beams with controlled spatial partial coherence properties is introduced. Far field diffraction from a discrete number of source points on an annular region is calculated. The average for different diffracted fields produced at several rotation angles is numerically calculated and experimentally detected. Theoretical and experimental results show th...

A higher-order oscillator, including a nonlinear unit and an 8th-order low-pass active Bessel ̄lter is described. The Bessel unit plays the role of \three-in-one": a delay line, an ampli ̄er and a ̄lter. Results of hardware experiments and numerical simulation are presented. Depending on the parameters of the nonlinear unit the oscillator operates either in a one-scroll or two-scroll mode. Two pos...

We prove sharp power-weighted L, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic analysis related to Bessel operators.

In this paper, transient solution of two dimensional asymmetric thermal and mechanical stresses for a hollow cylinder made of piezoelectric material is developed. Transient temperature distribution, as function of radial and circumferential directions and time with general thermal boundary-conditions, is analytically obtained, using the method of separation of variables and<br...

In this paper, we introduce and investigate a new extension of the beta function by means an integral operator involving product Bessel-Struve kernel functions. We also define well-known distribution, Gauss hypergeometric confluent in terms our extended function. addition, some useful properties these functions are indicated systematic way.