some estimates are proved for the generalized fourier-bessel transform in the space (l^2) (alpha,n)-index certain classes of functions characterized by the generalized continuity modulus.

In this paper, we study Bessel processes of dimension δ ≡ 2(1 − μ), with 0 < δ < 2, and some related martingales and random times. Our approach is based on martingale techniques and the general theory of stochastic processes (unlike the usual approach based on excursion theory), although for 0 < δ < 1, these processes are even not semimartingales. The last time before 1 when a Bessel process hi...

Title of dissertation: HOLLOW BESSEL TUNNEL GUIDE: THEORY AND EXPERIMENT Narupon Chattrapiban Doctor of Philosophy, 2012 Dissertation directed by: Professor Wendell T. Hill, III Department of Physics The main objectives of this thesis were to create and investigate properties and applications of all-optical atomic guides, which are potential building blocks for atom optics experiments. Specific...

Diffraction is a cornerstone of optical physics and has implications for the design of all optical systems. The paper discusses the so-called ‘non-diffracting’ light field, commonly known as the Bessel beam. Approximations to such beams can be experimentally realized using a range of different means. The theoretical foundation of these beams is described and then various experiments that make u...

Recently, harmonic imaging has been shown to increase image quality in medical imaging. This is believed to be caused by decreased sidelobes. It is also due to a decreased sensitivity to near-field aberrations owing to the lower transmission frequency, and the lower relative amplitude of the second harmonic in the near-field. One of the problems of limited diffraction beams has been the sidelob...

Title of Dissertation: Two Experiments with Cold Atoms: I. Application of Bessel Beams for Atom Optics, and II. Spectroscopic Measurements of Rydberg Blockade Effect Ilya Arakelyan, Doctor of Philosophy, 2010 Dissertation directed by: Prof. Wendell Hill, III Department of Physics In this dissertation we report the results of two experimental projects with lasercooled rubidium atoms: I. Applicat...

In this letter, we explore the possibilities of generating diffraction-free caustics over a predetermined range. For the first time we demonstrate the possibility to generate diffraction-free caustic beams. Caustic beams are a topic of increased interest over the past few years. Diffraction-free caustics may find applications in situations where large depth of field and uniform axial energy dis...

A recurrence, a determinant formula, and generating functions are presented for enumerating words with restricted letters by adjacencies. The main theorem leads to re nements (with up to two additional parameters) of known results on compositions, polyominoes, and permutations. Among the examples considered are (1) the introduction of the ascent variation on compositions, (2) the enumeration of...

The m m determinant of hyperbolic Bessel functions det jI a i ?b j (2x)j can be factored into two smaller determinants by elementary operations if a i = ?a m+1?i and b i = ?b m+1?i. We give combinatorial interpretations for these determinants as exponential generating functions for walks which stay within Weyl chambers. We then use these to provide a combinatorial proof of the formulas by nding...