The general properties of two-dimensional generalized Bessel functions are discussed. Various asymptotic approximations are derived and applied to analyze the basic structure of the two-dimensional Bessel functions as well as their nodal lines.

Introduction Ultra-short Echo Time (UTE) MRI allows for the detection of short T2 components (T2 of the order of 100 μs) in tissue before they have decayed [1, 2]. This is potentially interesting for a range of applications such as MR imaging of bone, tendons and ligaments, sodium MRI, and other applications such as MR-PET attenuation correction. Until now the UTE method has been based on a Ste...

Bessel beams are of great interest due to their unique non-diffractive properties. Using a conical prism or an objective paired with an annular aperture are two typical approaches to generating zeroth order Bessel beams. However, the former approach has a limited numerical aperture (NA), and the latter suffers from low efficiency since most of the incident light is blocked by the aperture. Furt...

Suppose that d ∈ N and p > 0. In this paper, we study the generalized Bessel functions for the surface {v ∈ Rd : |v|p = 1}, introduced by D.St.P. Richards. We derive a recurrence relation for these functions and utilize a series representation to relate them to the classical symmetric functions. These generalized Bessel functions are symmetric with respect to the action of the hyperoctahedral g...

In this paper we complete and improve the study of the simulation of the hitting times of some given boundaries for Bessel processes. These problems are of great interest in many application fields as finance and neurosciences. In a previous work [9], the authors introduced a new method for the simulation of hitting times for Bessel processes with integer dimension. The method, called walk on m...

Sarcocystis is a genus of cyst-forming parasites infecting both animals and human. This study aimed to isolate coccidian tissue cysts from muscle of infected animals by a simple method in addition to molecular identification of Sarcocystis cruzi from the samples. The samples were obtained from commercial source in Babol, Northern Iran. Five grams of calf muscle was cut into 2-3 pieces in 30 ml ...

The oblique incidence of a Bessel beam on a dielectric slab with refractive index n1 surrounded by a medium of a refractive index n > n1 may be studied simply by expanding the Bessel beam into a set of plane waves forming the same angle θ0 with the axis of the beam. In the present paper we examine a Bessel beam that impinges at oblique incidence onto a layer in such a way that each plane-wave c...

Bessel beam is the important member of the family of non-diffracting beams and has many novel properties which can be used in many areas. However, the source of Bessel beam generated by the existing methods can be used only in a short distance due to its low power. In this paper, based on the coherent combining technology, we have proposed a method which can be used to generate a high-power Bes...

The standard method for computing values of Bessel functions has been to use the well-known ascending series for small argument |z|, and to use an asymptotic series for large |z|. In a recent paper, D. Borwein, J. Borwein, and R. Crandall [1] derived a series for an exp-arc integral which gave rise to an absolutely convergent series for the J and I Bessel functions with integral order. Such ser...