Abstract We consider properties of semi-classical orthogonal polynomials with respect to the generalised Airy weight ω <mml:mo stret...

Purpose To demonstrate the viability of improving transverse image resolution in reflectance scanning adaptive optics ophthalmoscopy using sub-Airy disk confocal detection. Methods The foveal cone mosaic was imaged in five human subjects free of known eye disease using two custom adaptive optics scanning light ophthalmoscopes (AOSLOs) in reflectance with 7.75 and 4.30 mm pupil diameters. Conf...

We demonstrate how the complex integral formula for the Airy functions arises from Penrose’s twistor contour integral formula. We then use the Lax formulation of the isomonodromy problem with one irregular singularity of order four to show that the Airy equation arises from the anti-self-duality equations for conformal structures of neutral signature invariant under the isometric action of the ...

We consider several aspects of the scaling limit of percolation on random planar triangulations, both finite and infinite. The equivalents for random maps of Cardy’s formula for the limit under scaling of various crossing probabilities are given. The limit probabilities are expressed in terms of simple events regarding Airy-Lévy processes. Some explicit formulas for limit probabilities follow f...

A 30-year-old man presented with headache, vomiting, altered sensorium and seizures. There was no history of trauma or surgery. On examination, he was unconscious with signs of meningeal irritation and asymmetrical pupils. Computed tomography (CT) scan of brain revealed pneumocephalus. He died immediately after the CT scan. He was later found to be immunocompetent. Computed tomography scan (fig...

We demonstrate both theoretically and experimentally the generation of a tunable two-dimensional superoscillating optical field through the interference of multiple Airy beams. The resulting pattern exhibits self-healing properties for a set of sub-Fourier diffraction spots with decreasing dimensions. Such spatial optical fields might find applications in microscopy, particle manipulation, and ...

in this article using the inverse laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. these transfers have been expressed as the couette flow with the fractional derivative of the caputo sense. also, using the hankel contour for the bromwich's integral, the solutions are given in terms of the generalized airy functions.

The extended Airy kernel describes the space-time correlation functions for the Airy process, which is the limiting process for a polynuclear growth model. The Airy functions themselves are given by integrals in which the exponents have a cubic singularity, arising from the coalescence of two saddle points in an asymptotic analysis. Pearcey functions are given by integrals in which the exponent...

We demonstrate a new type of soliton formation arising from the interaction of multiple two-dimensional Airy beams in a nonlinear medium. While in linear regime, interference effects of two or four spatially displaced Airy beams lead to accelerated intensity structures that can be used for optical induction of novel light guiding refractive index structures, the nonlinear cross-interaction betw...

In general, there is an inverse relation between the degree of localization of a wave function of a certain class and its transform representation dictated by the scaling property of the Fourier transform. We report that in the case of finite energy Airy wave packets a simultaneous increase in their localization in the direct and transform domains can be obtained as the apodization parameter is...