We give a shorter proof of Kanter's (1976) sharp Bessel function bound for concentrations of sums of independent symmetric random vectors. We provide sharp upper bounds for the sum of modified Bessel functions I 0 (x) + I 1 (x), which might be of independent interest. Corollaries improve concentration or smoothness bounds for sums of independent random variables due toČekanavičius

We study the heat equation in n dimensional by Diamond Bessel operator. We find the solution by method of convolution and Fourier transform in distribution theory and also obtain an interesting kernel related to the spectrum and the kernel which is called Bessel heat kernel.

We put forward the concept of reconfigurable structures optically induced by mutually incoherent nondiffracting Bessel beams in Kerr-type nonlinear media. We address collinear couplers and X junctions and show how one can tune the switching properties of such structures by varying the intensity of the Bessel beams.

In this paper we uses an I.I. Hirschman-W. Beckner entropy argument to give an uncertainty inequality for the q-Bessel Fourier transform: Fq,vf(x) = cq,v ∫ ∞ 0 f(t)jv(xt, q 2)t2v+1dqt, where jv(x, q) is the normalized Hahn-Exton q-Bessel function.

The aim of this paper is to generalize the q-Heisenberg uncertainty principles studied by Bettaibi et al. 2007, to state local uncertainty principles for the q-Fourier-cosine, the q-Fourier-sine, and the q-Bessel-Fourier transforms, then to provide an inequality of Heisenberg-Weyl-type for the q-Bessel-Fourier transform.

Named essentially after their close relationship with the modified Bessel function K?(z) of second kind, which is known also as Macdonald (or, a slightly different definition, Basset function), so-called polynomials yn(x) and generalized yn(x;?,?) stemmed naturally in some systematic investigations classical wave equation spherical polar coordinates. Our main purpose this invited survey-cum-exp...

We derive the analytical expression of the M(2) factor of a Bessel-Gauss beam of any order and discuss its behavior for high and low values of the width of the Gaussian profile. The case of unapertured Bessel beams can be treated as a limiting case of our analysis.

We address soliton spiraling in optical lattices induced by multiple coherent Bessel beams and show that the dynamic nature of such lattices makes it possible for them to drag different soliton structures, setting them into rotation. We can control the rotation rate by varying the topological charges of lattice-inducing Bessel beams.

A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.

We demonstrate a simple and compact laser source that directly produces a Bessel–Gauss beam. The laser resonator consists of a diode-end-pumped Nd:YAG crystal, a planar mirror, and a diffractive mirror designed to phase-conjugate only the lowest-order Bessel–Gauss beam. 2004 Elsevier B.V. All rights reserved. PACS: 42.55.Xi; 42.60.Jf; 42.25.Fx