Related papers: Survey on perfect isometries
The main purpose of this article is to initiate a systematic study of Semihypergroups, first introduced by C. Dunkl [4], I. Jewett [13] and R. Spector [20] independently around 1972. We introduce and study several natural algebraic and…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
The aim of this survey is to explore complete intersection monomial curves from a contemporary perspective. The main goal is to help readers understand the intricate connections within the field and its potential applications. The…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
Metric spaces satisfying properties stronger than completeness and weaker than compactness have been studied by many authors over the years. One such significant family is that of cofinally complete metric spaces. We discuss the…
The goal of this paper is to make the vertex operator algebra approach to mirror symmetry accessible to algebraic geometers. Compared to better-known approaches using moduli spaces of stable maps and special Lagrangian fibrations, this…
A complete characterisation is given of all the linear isometries of the Fr\'echet space of all holomorphic functions on the unit disc, when it is given one of the two standard metrics: these turn out to be weighted composition operators of…
The inertial measurement unit (IMU) preintegration approach nowadays is widely used in various robotic applications. In this article, we revisit the preintegration theory and propose a novel interpretation to understand it from a nonlinear…
Reparametrization invariant Sobolev metrics on spaces of regular curves have been shown to be of importance in the field of mathematical shape analysis. For practical applications, one usually discretizes the space of smooth curves and…
In the early 80's, Alain Quilliot presented an approach of ordered sets and graphs in terms of metric spaces, where instead of positive real numbers, the values of the distance are elements of an ordered monoid equipped with an involution.…
We solve a long-standing open problem, formulated by Krasner in the 1950's, in the context of Polish (i.e. separable complete) ultrametric spaces by providing a characterization of their isometry groups using suitable forms of generalized…
In 1980, Onishchik introduced the index of a Riemannian symmetric space as the minimal codimension of a (proper) totally geodesic submanifold. He calculated the index for symmetric spaces of rank less than or equal to 2, but for higher rank…
Let $(X,d)$ be a finite ultrametric space. In 1961 E.C. Gomory and T.C. Hu proved the inequality $|Sp(X)|\leqslant |X|$ where $Sp(X)=\{d(x,y)\colon x,y \in X\}$. Using weighted Hamiltonian cycles and weighted Hamiltonian paths we give new…
Moreau's seminal paper, introducing what is now called the Moreau envelope and the proximity operator (also known as the proximal mapping), appeared in 1965. The Moreau envelope of a given convex function provides a regularized version…
K. Mahler introduced the concept of perfect systems in the theory of simultaneous Hermite-Pad\'{e} approximation of analytic functions. Recently, we proved that Nikishin systems, generated by measures with bounded support and…
We present a survey on the recent progress with desingularization of quasi-excellent schemes of characteristic zero. Due to expository goals of the paper we concentrate on giving examples and outlining main ideas, and we refer to other…
According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here,…
The concept of I-statistical convergence of a double sequence was first introduced and study by Das et. el [2]. Here in this paper we discuss some results on rough ideal statistical convergence and also we introduce the notion of rough…
In this paper we discuss the notion of completeness of topologized posets and survey some recent results on closedness properties of complete topologized semilattices.
A broad class of informationally complete symmetric measurements is introduced. It can be understood as a common generalization of symmetric, informationally complete POVMs and mutually unbiased bases. Additionally, it provides a natural…