The discrete Painlevé III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel function. Moreover, based on the observation that these discrete Bessel functions are transformed to the q-Bessel functions by a simple variable transformation, we present a q-difference ...

In this paper we study spaces of Bessel potentials in n-dimensional Euclidean spaces. They are constructed on the basis of a rearrangement-invariant space (RIS) by using convolutions with Bessel-MacDonald kernels. Specifically, the treatment covers spaces of classical Bessel potentials. We establish two-sided estimates for the corresponding modulus of smoothness of order k ∈ N, ωk(f ; t), and d...

BACKGROUND: Ov-CHI-1 is a chitinase specifically expressed in the infective stage larvae of the human filarial parasite Onchocerca volvulus. Evidence has show that it could be a vaccine candidate, however, there is no data available regarding the immunological status of people naturally exposed to infective stage larvae and thus provoked by this antigen. METHOD: We analysed the Ov-CHI-1-specifi...

Photoelectrochemical (PEC) water splitting is a promising approach for renewable solar light conversion. However, surface Fermi level pinning (FLP), caused by trap states, severely restricts the PEC activities. Theoretical calculations indicate subsurface oxygen vacancy (sub-Ov) could release FLP and retain active structure. A series of metal oxide semiconductors with sub-Ov were prepared throu...

The normalization of energy divergent Weber waves and finite energy Weber-Gauss beams is reported. The well-known Bessel and Mathieu waves are used to derive the integral relations between circular, elliptic, and parabolic waves and to present the Bessel and Mathieu wave decomposition of the Weber waves. The efficiency to approximate a Weber-Gauss beam as a finite superposition of Bessel-Gauss ...

We theoretically investigate the use of Bessel light beams generated using axicons for creating optical dipole traps for cold atoms and atomic waveguiding. Zeroth-order Bessel beams can be used to produce highly elongated dipole traps allowing for the study of one-dimensional trapped gases and realization of a Tonks gas of impentrable bosons. First-order Bessel beams are shown to be able to pro...

Abstract. The series expansion of a power of the modified Bessel function of the first kind is studied. This expansion involves a family of polynomials introduced by C. Bender et al. New results on these polynomials established here include recurrences in terms of Bell polynomials evaluated at values of the Bessel zeta function. A probabilistic version of an identity of Euler yields additional ...

X iv :0 90 5. 40 67 v1 [ m at h. FA ] 2 5 M ay 2 00 9 BESSEL TYPE INEQUALITIES IN HILBERT C-MODULES S. S. DRAGOMIR, M. KHOSRAVI AND M. S. MOSLEHIAN Abstract. Regarding the generalizations of the Bessel inequality in Hilbert spaces which are due to Bombiari and Boas–Bellman, we obtain a version of the Bessel inequality and some generalizations of this inequality in the framework of Hilbert C∗-mo...

Background: Insulin resistance (IR) is frequently associated with hepatitis C virus (HCV) infection, and development of IR can occur early in the course of HCV infection and promote hepatic fibrosis. Aim of the Study: We aimed to assess the impact of IR on the development of oesophageal varices (OV) in HCV-related liver cirrhosis. Subjects and Methods: We enrolled 80 HCV-related liver cirrhosis...

Infinite integrals involving Bessel functions are recast, by means of an Abel transform, in terms of Fourier integrals. As there are many efficient numerical methods for computing Fourier integrals, this leads to a convenient way of approximating Bessel function integrals.