We derive completeness criteria for sequences of functions of the form f(xλn), where λn is the nth zero of a suitably chosen entire function. Using these criteria, we construct systems of nonorthogonal Fourier-Bessel functions and their q-analogues, as well as other complete sets of q-special functions. The completeness of certain sets of q-Bessel functions is then used to prove that, if a func...

In this article, we studied the necessary conditions for univalence of integral operators that involve two functions: generalized Bessel function and a from well-known class normalized analytic functions in open unit disk. The main tools our discussions were Kudriasov univalency functions, as well functional inequalities functions. We included Bessel, modified spherical special cases. Furthermo...

An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...

The aim of the present work is to study the  $F$-transform over a generalized residuated lattice.  We discuss the properties that are common with the $F$-transform over a residuated lattice. We show that the $F^{uparrow}$-transform can be used in establishing a fuzzy (pre)order on the set of fuzzy sets.

In this paper, we consider the normalized Bessel function of index ?>?12, find an integral representation term xnj?+n(x)j?(y). This allows us to establish a product formula for generalized Hankel B??,n on R. is kernel transform F?,n arising from Dunkl theory. Indeed show that B??,n(x)B??,n(y) can be expressed as in terms B??,n(z) with explicit invoking Gegenbauer polynomials all n?N?. The obtai...

We report the first experimental realization of all-optical trapping and manipulation of plasmonic nanowires in three dimensions. The optical beam used for trapping is the Fourier transform of a linearly polarized Bessel beam (termed FT-Bessel). The extended depth of focus of this beam enables the use of a retroreflection geometry to cancel radiation pressure in the beam propagation direction, ...

Final Project Report Jungwoo Lee (610-21-4670) Reference : An Improved Gridding Method for Spiral MRI Using Nonuniform Fast Fourier Transform Authors: Liewei Sha, Hua Guo, and Allen W.Song Introduction The objective of this project is to develop improved reconstruction algorithm using nonuniform fast Fourier transform(NUFFT) for spiral MRI. In conventional gridding methods, while explicit forms...

Yor’s generalized meander is a temporally inhomogeneous modification of the 2(ν+1)-dimensional Bessel process with ν > −1, in which the inhomogeneity is indexed by κ ∈ [0, 2(ν + 1)). We introduce the non-colliding particle systems of the generalized meanders and prove that they are the Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infini...

using a generalized spherical mean operator, we obtain the generalizationof titchmarsh's theorem for the dunkl transform for functions satisfyingthe lipschitz condition in l2(rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.

the video quality assessment must be adapted to the human visual system, which is why researchers have performed subjective viewing experiments in order to obtain the conditions of encoding of video systems to provide the best quality to the user. the objective of this study is to assess the video quality using image features extraction without using reference video. rmse values and processing ...