A number of new definite integrals involving Bessel functions are presented. These have been derived by finding new integral representations for the product of two Bessel functions of different order and argument in terms of the generalized hypergeometric function with subsequent reduction to special cases. Connection is made with Weber's second exponential integral and Laplace transforms of pr...

An overview of two types of beam solutions is presented, Gaussian beams and Bessel beams. Gaussian beams are examples of non-localized or diffracting beam solutions, and Bessel beams are example of localized, non-diffracting beam solutions. Gaussian beams stay bounded over a certain propagation range after which they diverge. Bessel beams are among a class of solutions to the wave equation that...

Abstract We study optional projections of ${\mathbb{G}}$ G -adapted strict local martingales on a smaller filtration ${\mathbb{F}}$ F under changes equivalent martingale measures. General results are provided as well detailed analysis two specific examples given by the inverse Bessel process ...

Introduction. Whittaker models have been crucial in the development of the theory of automorphic forms. Within the Langlands-Shahidi method, Whittaker models give rise to the definition of local coefficients [Sh1,Sh2], which proved critical in establishing the proof of Langlands’s conjecture relating local L–functions to Plancherel measures for generic representations [Sh3]. This, in turn, led ...

Light scattered by turbid tissue is known to degrade optical coherence tomography (OCT) image contrast progressively with depth. Bessel beams have been proposed as an alternative to Gaussian beams to image deeper into turbid tissue. However, studies of turbid tissue comparing the image quality for different beam types are lacking. We present such a study, using numerically simulated beams and e...

We study the existence and uniqueness of solutions of SDEs describing squared Bessel particle systems in full generality. We define non-negative and non-colliding squared Bessel particle systems and we study their properties. Particle systems dissatisfying noncolliding and unicity properties are pointed out. The structure of squared Bessel particle systems is described.

Orthogonal Frequency Division Multiplexing (OFDM) is a hotly researched topic, due to its high data rate and robustness to multi-path fading. As such, it has been widely adopted in wireless standards, e.g., IEEE 802.11a/g, digital audio/video broadcasting and Integrated Services Digital Broadcasting (ISDB). In the presence of doubly-selectivity in fading channels, OFDM suffers from intercarrier...

The lost of nonentun and stiffness due to ablation nay significantly influence the vibrations of a solid propellant grain. This paper presents an analytical study of the axial shear vibrations of a long hollow cylinder that is subjected to tine dependent body forces in the axial direction. The outer surface of the cylinder is bonded to a rigid case, and the inner radius increases monotonically ...

We report on a novel pumping scheme for stimulated Raman scattering (SRS) that uses a Bessel beam. We have used this scheme for SRS from molecular vibrations in acetone and from a polariton mode in a LiIO(3) crystal. A nearly diffraction-limited Stokes beam was observed along the cone axis of the Bessel beam. The generation mechanism of the Stokes beam is identified as being due to noncollinear...