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.

We consider a class of functions, defined on a locally compact abelian group by letting a class of modulation operators act on a countable collection of functions. We derive sufficient conditions for such a class of functions to form a Bessel sequence or a frame and for two such systems to be dual frames. Explicit constructions are obtained via various generalizations of the classical B-splines...

Detailed understanding of the complexities of flow and in biological materials is essential for the design, development, and optimization of MRI protocols for medical and biomedical applications. However, the design of such processes resort to trial and error, because the mathematics and physics of most experimental techniques are fundamentally limited. In this study, we develop a new magnetic ...

The theory of Generalized Bessel Functions is reviewed and their application to various problems in the study electro-magnetic processes presented. We consider cases emission bremsstrahlung radiation by ultra-relativistic electrons linearly polarized undulators, including also exotic configurations, aimed at enhancing harmonic content emitted radiation. analysis eventually extended generalizati...

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...

The concept of pseudo-Bessel correlated beams is introduced, and their scintillation properties on propagation through turbulence are investigated. By using the Rytov approximation, the scintillation index of pseudo-Bessel correlated beams is formulated in weak turbulence. The study of scintillation is extended into strong turbulence by numeric simulations. It is shown that by choosing an appro...

For automorphic representations in the nontempered cuspidal spectrum of SO5, we establish a precise Bessel period formula, in which the square of the global Bessel period is decomposed as an Euler product of regularized local Bessel period integrals of matrix coefficients.

In this paper, we discuss efficient exact random variate generation for the Bessel distribution. The expected time of the algorithm is uniformly bounded over all choices of the parameters, and the algorithm avoids any computation of Bessel functions or Bessel ratios.

In this paper, we introduce $(mathcal{C},mathcal{C}')$-controlled continuous $g$-Bessel families and their multipliers in Hilbert spaces and investigate some of their properties. We show that under some conditions sum of two $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frames is a $(mathcal{C},mathcal{C}')$-controlled continuous $g$-frame. Also, we investigate when a $(mathcal{C},mathca...

We show that in addition to well-known Bessel, Hermite–Gauss and Laguerre– Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of ρ. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, ...