Related papers: Orthogonal basis with a conicoid first mode for sh…
A perfect focus telescope is one in which all rays parallel to the axis meet at a point and give equal magnification there. It is shown that these two conditions define the shapes of both primary and secondary mirrors. Apart from scale, the…
We study the orthospectrum and the simple orthospectrum of compact hyperbolic surfaces with geodesic boundary. We show that there are finitely many hyperbolic surfaces sharing the same simple orthospectrum and finitely many hyperbolic…
We present a new method for the analysis of images, a fundamental task in observational astronomy. It is based on the linear decomposition of each object in the image into a series of localised basis functions of different shapes, which we…
Isotropic functions of positions $\hat{\bf r}_1, \hat{\bf r}_2,\ldots, \hat{\bf r}_N$, i.e. functions invariant under simultaneous rotations of all the coordinates, are conveniently formed using spherical harmonics and Clebsch-Gordan…
A surface is considered flexible if it allows a continuous deformation that preserves both metric and smoothness. We introduce a novel construction method, called 'base + crinkle,' for generating a broad class of non-self-intersecting…
In this paper, we present a new polygonal finite element method, called the Zipped Finite Element Method, for star-shaped polygons. The proposed approach constructs high-order shape functions as linear combinations of standard finite…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Notions of the orthogonality and convolution orthogonality are explored with the use of the Kontorovich-Lebedev transform and its convolution. New classes of the corresponding orthogonal polynomials and functions are investigated. Integral…
Generalizing both hyperbolic framed surfaces and one-parameter families of hyperbolic framed curves, we introduce the concept of hyperbolic generalized framed surfaces and establish their relations in hyperbolic 3-space. We provide the…
We analyze the approximation by radial basis functions of a hypersingular integral equation on an open surface. In order to accommodate the homogeneous essential boundary condition along the surface boundary, scaled radial basis functions…
We present a new type of basis set which is local, compact, and orthogonal. The basis functions, called orthlets, are centered at the sites of a lattice and are specifically adapted to represent the system being studied. The adaptability…
There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…
A new method of composition orthogonality is introduced. It is applied to generate new sequences of orthogonal polynomials and functions. In particular, classical orthogonal polynomials are interpreted in the sense of composition…
The aim of this paper is to study finite orthogonal polynomials on a cone of revolution and its surface. We define two classes of finite orthogonal polynomials on the solid cone and derive their corresponding differential equations and…
Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton…
Cosmologists are taking a renewed interest in multiconnected spherical 3-manifolds (spherical spaceforms) as possible models for the physical universe. To understand the formation of large scale structures in such a universe, cosmologists…
To encode an important property of the "no broken circuit bases" of the Orlik-Solomon-Terao algebras, Andras Szenes has introduced a particular type of bases, the so called "diagonal basis". We prove that this definition extends naturally…
We give a general expression of spherical functions on $p$-adic homogeneous spaces of $G$, based on data of $G$ and functional equations of spherical functions. Then, we show a unified method to obtain functional equations of spherical…
In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part,…
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…