We determine the class of entire functions for which the Airy kernel (of random matrix theory) is a reproducing kernel. We deduce an Airy sampling series and quadrature formula. Our results are analogues of well known ones for the Bessel kernel. The need for these arises in investigating universality limits for random matrices at the soft edge of the spectrum. 1. Introduction Universality limit...

Riesz fractional derivatives of a function, Dα xf(x) (also called Riesz potentials), are defined as fractional powers of the Laplacian. Asymptotic expansions for large x are computed for the Riesz fractional derivatives of the Airy function of the first kind, Ai(x), and the Scorer function, Gi(x). Reduction formulas are provided that allow one to express Riesz potentials of products of Airy fun...

The physical properties of granular materials have been extensively studied in recent years. So far, however, there exists no theoretical framework which can explain the observations in a unified manner beyond the phenomenological jamming diagram [1]. This work focuses on the case of static granular matter, where we have constructed a statistical ensemble [2] which mirrors equilibrium statistic...

We derive integral formulas, involving the Airy function, for moments of the time a two-sided Brownian motion with parabolic drift attains its maximum.

This paper presents a novel formulation for static limit analysis of structures, which the Airy stress function is approximated using stabilized Radial Point Interpolation Mesh-free method (RPIM). The field determined as second-order derivatives function, and equilibrium equations are automatically satisfied priori. so-called Stabilized Conforming Nodal Integration (SCNI) employed to ensure pre...

We have theoretically and numerically investigated the self-healing peculiarity of Airy beams truncated by different decay factors. The self-healing dynamic processes of truncated Airy beams are different from that of blocked Airy beams. The wing with large truncation of Airy beam can propagate much longer distance than that of small truncated wing. When one of the wings is complete truncated, ...

This paper studies the pure bending and bending-induced local buckling of a nanocomposite beam reinforced by a single-walled carbon nanotube (SWNT). The Airy stress-function method was employed to analyse the deformation of the matrix, and the cross-sectional change of the SWNT in bending was taken into account. A particular consideration was given to the effect of the SWNT s radial flexibility...

In this article we propose and analyze a Virtual Element Method (VEM) to approximate the isolated solutions of von Kármán equations, which describe deformation very thin elastic plates. We consider variational formulation in terms two variables: transverse displacement plate Airy stress function. The VEM scheme is conforming H 2 for both variables has advantages supporting general polygonal mes...