Related papers: Some study of the approximate orthogonality connec…
We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…
We give a short introduction to Pade approximation (rational approximation to a function with close contact at one point) and to Hermite-Pade approximation (simultaneous rational approximation to several functions with close contact at one…
In this paper we develop a general theory of metric Diophantine approximation for systems of linear forms. A new notion of `weak non-planarity' of manifolds and more generally measures on the space of $m\times n$ matrices over $\Bbb R$ is…
Properties of entangled states based on nonorthogonal states are clarified. Especially, it is shown that they can have complete degree of entanglement.
In this article, we introduce a new type of mapping contracting perimeters of triangles in a complete metric space and present related fixed point theorem. We study the metric completeness property of the underlying space in terms of fixed…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
We introduce the relation ${\rho}_{\lambda}$-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives, and present some of its essential properties. Among other things, we give…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
We combine functional analytic and geometric viewpoints on approximate Birkhoff and isosceles orthogonality in generalized Minkowski spaces which are finite-dimensional vector spaces equipped with a gauge. This is the first approach to…
In this paper I survey some recent results on finite determination, convergence, and approximation of formal mappings between real submanifolds in complex spaces. A number of conjectures are also given.
In this paper we present the novel qualities of entanglement of formation for general (so also infinite dimensional) quantum systems. A major benefit of our presentation is a rigorous description of entanglement of formation. In particular,…
In this article, we present a new characterization of the completeness of a partial metric space--which we call \textit{orbital characterization}-- using fixed point results.
Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…
Using the orthogonal connectedness, we introduce the notion of orthogonal decomposability of convex polytopes and study it in the case of Platonic and Archimedean solids. While doing so, we also encounter polytopes which are not…
In this article we review the Duistermaat-Heckman integration formula and the ensuing equivariant cohomology structure, in the finite dimensional case. In particular, we discuss the connection between equivariant cohomology and classical…
This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of…
The purpose of this paper is to give the flavor of the subject of self-similar tilings in a relatively elementary setting, and to provide a novel method for the construction of such polygonal tilings.
In this paper we consider a new kind of inequality related to fractional integration, motivated by Gressman's paper. Based on it we investigate its multilinear analogue inequalities. Combining with the Gressman's work on multilinear…
In this paper we investigate the monomial ideals which satisfy the copersistence property or nearly copersistence property.