The Sheffer polynomials and the monomiality principle, along with the underlying operational formalism, offer a powerful tool for investigation of the properties of a wide class of polynomials. We present, within such a context, a self-contained theory of such familiar systems of polynomials as the Euler, Bernoulli, Bessel and other clasical polynomials and show how the derivation of some of th...

We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam ...

Non-Gaussian beam profiles such as Bessel or annular beams enable novel approaches to modifying materials through laser-based processing. In this review paper, properties, generation methods and emerging applications for nonconventional beam shapes are discussed, including Bessel, annular, and vortex beams. These intensity profiles have important implications in a number of technologically rele...

We present a method for the realization of radially and azimuthally polarized nonparaxial Bessel beams in a rigorous but simple manner. This result is achieved by using the concept of Hertz vector potential to generate exact vector solutions of Maxwell's equations from scalar Bessel beams. The scalar part of the Hertz potential is built by analogy with the paraxial case as a linear combination ...

Bessel processes play an important role in financial mathematics because of their strong relation to financial processes like geometric Brownian motion or CIR processes. We are interested in the first time Bessel processes and more generally, radial Ornstein–Uhlenbeck processes hit a given barrier. We give explicit expressions of the Laplace transforms of first hitting times by (squared) radial...

In this note, we investigate the performance of the PCM scheme with linear quantization rule for quantizing unit-norm tight frame expansions for R without the White Noise Hypothesis. In [4], Wang and Xu showed that for asymptotically equidistributed unit-norm tight frame the PCM quantization error has an upper bound O(δ(d+1)/2) and they conjecture the upper bound is sharp. In this note, we conf...

introduction: influenza a virus causes unpredictable epidemics and pandemics by creating antigenic variations. with the appearance of each new strain, rapid emergency countermeasures are taken against this new strain. hence, designing an applicable and cross protective strategy to counter this virus is of great importance. to achieve this, choosing conserved antigenic regions in influenza virus...

A point process is said to be rigid if for any bounded domain in the phase space, the number of particles in the domain is almost surely determined by the restriction of the configuration to the complement of our bounded domain. The main result of this paper is that determinantal point processes with the Airy, the Bessel and the Gamma kernels are rigid. The proof follows the scheme of Ghosh [6]...

We present a simple method using an axicon and spatial light modulator to create multiple parallel Bessel beams and precisely control their individual positions in three dimensions. This technique is tested as an alternative to classical holographic beam shaping commonly used now in optical tweezers. Various applications of precise control of multiple Bessel beams are demonstrated within a sing...