Integrated optical phased arrays for generating quasi-Bessel beams are proposed and experimentally demonstrated in a CMOS-compatible platform. Owing to their elongated central beams, Bessel beams have applications in a range of fields, including multiparticle trapping and laser lithography. In this Letter, continuous Bessel theory is manipulated to formulate the phase and amplitude conditions n...

In this paper, we study a family of analytical probability models for images within the spectral representation framework. First the input image is decomposed using a bank of filters, and probability models are imposed on the filter outputs (or spectral components). A two-parameter analytical form, called a Bessel K form, derived based on a generator model, is used to model the marginal probabi...

Basic math constants Derived from the basic ones ... from 0 and 1 ... from i ... from 1 and i ... from π ... from e ... from e and π ... from γ ... from Φ Named real math constants Other notable real constants Notable integer numbers Named/notable functions on N Named/notable integer sequences Related to Factorials Related to Hamming weight Related to Powers Related to Divisors Related to Aliqu...

In this paper, we define fractal bases and frames of L2(I×J), where I J are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification L2(I×J) with tensor product space L2(I)⨂L2(J). First, recall procedure constructing perturbation continuous or integrable function. Then, composed such functions. We also obtain we...

We prove that every irreducible, admissible representation π of GSp(4, F ), where F is a non-archimedean local field of characteristic zero, admits a Bessel functional, provided π is not onedimensional. If π is not supercuspidal, we explicitly determine the set of all Bessel functionals admitted by π, and prove that Bessel functionals of a fixed type are unique. If π is supercuspidal, we do the...

In this paper, we extend some known elementary trigonometric inequalities, and their hyperbolic analogues to Bessel and modified Bessel functions of the first kind. In order to prove our main results, we present some monotonicity and convexity properties of some functions involving Bessel and modified Bessel functions of the first kind. We also deduce some Turán and Lazarević-type inequalities ...

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 ...