A very general beam solution of the paraxial wave equation in elliptic cylindrical coordinates is presented. We call such a field an elliptic beam (EB). The complex amplitude of the EB is described by either the generalized Ince functions or the Whittaker-Hill functions and is characterized by four parameters that are complex in the most general situation. The propagation through complex ABCD o...

It is a fact of experience from the study of higher type computability that a wide range of approaches to defining a class of (hereditarily) total functionals over N leads in practice to a relatively small handful of distinct type structures. Among these are the type structure C of Kleene-Kreisel continuous functionals, its effective substructure C, and the type structure HEO of the hereditaril...

In this computational study the buckling analysis of symmetrically laminated elliptical and super-elliptical thin plates was carried out. The were considered as clamped or simply supported at boundary. minimum load determined using Rayleigh-Ritz method Galerkin Method based on Classical Laminated Plate Theory (CLPT). influence solution methods, shape functions, boundary conditions, power, lamin...

The four largest well-preserved impact basins in the solar system, Borealis, Hellas, and Utopia on Mars, and South Pole–Aitken on the Moon, are all signifi cantly elongated, with aspect ratios >1.2. This population stands in contrast to experimental studies of impact cratering that predict <1% of craters should be elliptical, and the observation that ~5% of the small crater population on the te...

The asymmetric, elliptical shape of a transcatheter aortic valve (TAV), after implantation into a calcified aortic root, has been clinically observed. However, the impact of elliptical TAV configuration on TAV leaflet stress and strain distribution and valve regurgitation is largely unknown. In this study, we developed computational models of elliptical TAVs based on a thin pericardial bioprost...

We present new data on the globular cluster system of the elliptical galaxy NGC 3923 which show that it has the most globular clusters per unit luminosity of any noncluster elliptical yet observed, with SN = 6:4 1:4. NGC 3923 is also among the brightest ellipticals outside of a galaxy cluster for which the number of globular clusters has been determined. Our observation of a large number of clu...

Electromagnetic beams in a uniaxial crystal are treated with emphasis on the extraordinary mode. A virtual source that generates a basic elliptical Gaussian wave propagating obliquely to the optic axis is identified. An exact expression is obtained for this basic elliptical Gaussian wave that simplifies to the corresponding basic elliptical Gaussian beam in the appropriate limit. In the directi...

A high-speed method for elliptical object location is proposed. Through the use of the geometric symmetry, it first locates the centers of elliptical objects and classifies the boundary points. Then, each point possible on an elliptical object boundary is used to obtain the remaining three parameters of the elliptical object. Since each boundary point is at most transformed to one point on the ...

A new elliptical invisible cloak is proposed using a coordinate transformation in the elliptical-cylindrical coordinate system, which crushes the cloaked object to a line segment instead of a point. The elliptical cloak is reduced to a nearly-circular cloak if the elliptical focus becomes very small. The advantage of the proposed invisible cloak is that none of the parameters is singular and th...