Related papers: Complete confined bases for beam propagation in Ca…
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type, in the class of metrics yielding an infinite deficiency…
We conducted a comprehensive study on the robust propagation of the same spot-size Gaussian beam (SSGB), same envelope Gaussian beam (SEGB), Circular Airy beam (CAB) and Circular Pearcey beam (CPB) in complex environments. Our findings…
We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…
We consider bivariate piecewise polynomial finite element spaces for curved domains bounded by piecewise conics satisfying homogeneous boundary conditions, construct stable local bases for them using Bernstein-B\'ezier techniques, prove…
We consider Friedlander's wave equation in two space dimensions in the half-space x > 0 with the boundary condition u(x,y,t)=0 when x=0. For a Gaussian beam w(x,y,t;k) concentrated on a ray path that is tangent to x=0 at (x,y,t)=(0,0,0) we…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
The transport equations for polarized radiation transfer in non-Riemannian, Weyl-Cartan type space-times are derived, with the effects of both torsion and non-metricity included. To obtain the basic propagation equations we use the tangent…
We describe a new class of propagation-invariant light beams with Fourier transform given by an eigenfunction of the quantum mechanical pendulum. These beams, whose spectra (restricted to a circle) are doubly-periodic Mathieu functions in…
It is shown how unbound electron wave functions can be expanded in a suitably chosen localized basis sets for any desired range of energies. In particular, we focus on the use of gaussian basis sets, commonly used in first-principles codes.…
We introduce a new class of optical beams, which feature a spatial profile akin to an ``inverted pin''. In particular, we asymptotically find that close to the axis the transverse amplitude profile of such beams takes the form of a Bessel…
Gaussian scale spaces are a cornerstone of signal representation and processing, with applications in filtering, multiscale analysis, anti-aliasing, and many more. However, obtaining such a scale space is costly and cumbersome, in…
While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic…
The quotient bases for zero-dimensional ideals are often of interest in the investigation of multivariate polynomial interpolation, algebraic coding theory, and computational molecular biology, etc. In this paper, we discuss the properties…
With the proliferation of modern high-resolution measuring instruments mounted on satellites, planes, ground-based vehicles and monitoring stations, a need has arisen for statistical methods suitable for the analysis of large spatial…
We solve the problem of best approximation by Parseval frames to an arbitrary frame in a subspace of an infinite dimensional Hilbert space. We explicitly describe all the solutions and we give a criterion for uniqueness. This best…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
We derive simple formulae for the transmittance $T$ and reflectance $R$ of Gaussian-Schell beams incident upon any stratified dielectric structure by using second-order classical coherence theory in the space-frequency picture. The…
A Green's function formalism to analyze the scattering properties in confined geometries is developed. This includes scattering from a central field inside the guide created e.g. by impurities. For atomic collisions our approach applies to…
The exact evolution in time and space of a distribution of the temperature (or density of diffusing matter) in an isotropic homogeneous medium is determined where the initial distribution is described by a piecewise polynomial. In two…
Some properties of generalized convexity for sets and for functions are identified in case of the reliability polynomials of two dual minimal networks. A method of approximating the reliability polynomials of two dual minimal network is…