We study carefully the problem of bootstrap on half line. show why one needs full set constraints derived from Stieltjes theorem moment by reexamining previous results hydrogen atom. also atom at continuous angular momentum. that alone do not fix boundary conditions in all cases and least positive matrices to be slightly enlarged remove unphysical branches. explain how solve more general for Ro...

For a plane wave incident on either a Luneburg lens or a modified Luneburg lens, the magnitude and phase of the transmitted electric field are calculated as a function of the scattering angle in the context of ray theory. It is found that the ray trajectory and the scattered intensity are not uniformly convergent in the vicinity of edge ray incidence on a Luneburg lens, which corresponds to the...

Integral representations are onsidered of solutions of the Airy di erential equation w z w = 0 for omputing Airy fun tions for omplex values of z. In a rst method ontour integral representations of the Airy fun tions are written as non-os illating integrals for obtaining stable representations, whi h are evaluated by the trapezoidal rule. In a se ond method an integral representation is evaluat...

We establish the universal edge scaling limit of random partitions with infinite-parameter distribution called Schur measure. explore asymptotic behavior wave function, which is a building block corresponding kernel, based on Schrödinger-type differential equation. show that function in general to Airy and its higher-order analogs limit. construct kernel Tracy–Widom from discuss implication mul...

objective: dietary changes playmajor risk roles in oxidative stress andcardiovascular disease and modulate normal metabolic function. the present study was designed to investigate the ameliorative potential of different extracts of hemidesmus indicus to experimental high-fat diet in wistar rats, and their possible mechanism of action.  materials and methods: male wistar rats were divided into 6...

We establish that the static height fluctuations of a particular growth model, the PNG droplet, converges upon proper rescaling to a limit process, which we call the Airy process A(y). The Airy process is stationary, it has continuous sample paths, its single “time” (fixed y) distribution is the Tracy-Widom distribution of the largest eigenvalue of a GUE random matrix, and the Airy process has ...

We show both experimentally and numerically, control over the acceleration of two-dimensional Airy beam propagating in optically induced photonic lattice. Varying the lattice strength and including various defects we can reach a state, where the acceleration is completely stopped. We find an additional class of discrete lattice beams, localized and defect modes observed with Airy beams propagat...

We investigate the acceleration dynamics of quasi-diffraction-free Airy beams in both one- and two-dimensional configurations. We show that this class of finite energy waves can retain their intensity features over several diffraction lengths. The possibility of other physical realizations involving spatiotemporal Airy wave packets is also considered.

In this paper, we consider the discrete Laguerre polynomials [Formula: see text] orthogonal with respect to weight function supported on infinite nodes text]. We focus “band-saturated region” situation when parameter As text], uniform expansions for are achieved in different regions complex plane. Typically, Airy-function and Gamma-function derived near endpoints of band origin, respectively. T...