A beam that resembles a Bessel beam on two scales is generated using a tunable acoustic gradient index of refraction (TAG) lens. The minor scale of the TAG-generated Bessel beam is nondiffracting and self-healing. The major scale of the beam diffracts while still forming a Bessel pattern due to the specific geometry of the TAG lens. The acoustic and optical theory behind the TAG lens is outline...

We consider the exact path sampling of the squared Bessel process and some other continuous-time Markov processes, such as the CIR model, constant elasticity of variance diffusion model, and hypergeometric diffusions, which can all be obtained from a squared Bessel process by using a change of variable, time and scale transformation, and/or change of measure. All these diffusions are broadly us...

n this article, we prove An Lp-Lq-version of Morgan’s theorem for the generalized Bessel transform.

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 paper, we introduce and study the concepts of $mathcal{i}_2$-convergence, $mathcal{i}_2^{*}$-convergence for double sequences of fuzzy real numbers, where $mathcal{i}_2$ denotes the ideal of subsets of $mathbb n times mathbb n$. also, we study some properties and relations of them.

Let Π n d denote the space of spherical polynomials degree at most on unit sphere S ⊂ R + 1 that is equipped with surface Lebesgue measure σ normalized by ∫ ( x ) = . This paper establishes a close connection between asymptotic Nikolskii constant, L ∗ ≔ lim → ∞ dim sup f ∈ ‖ , and following extremal problem: I α inf k j t − ∑ q ∕ infimum being taken over all sequences { } such infinite series c...