Related papers: Alexandrov's Approach to the Minkowski Problem
The subject of this paper is the history of the Minkowski-Funk Transform. After introducing the Minkowski-Funk Transform as well as its dual transform and a generalization of both, we will present an inversion formula of the Minkowski-Funk…
In this paper, we discuss the basic properties of Alexandroff spaces. Several examples of Alexandroff spaces are given. We show how to construct new Alexandroff spaces from given ones. Finally, two invariants for compact Alexandroff spaces…
Minkowski sums are of theoretical interest and have applications in fields related to industrial backgrounds. In this paper we focus on the specific case of summing polytopes as we want to solve the tolerance analysis problem described in…
This is an English translation of the following paper, published several years ago: Nikonorov Yu.G., Nikonorova Yu.V. Generalized Popoviciu's problem (Russian), Tr. Rubtsovsk. Ind. Inst., 7, 229-232 (2000), Zbl. 0958.51021. All inserted…
Many scientific and engineering applications are formulated as inverse problems associated with stochastic models. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their…
Various Alexandrov-Fenchel type inequalities have appeared and played important roles in convex geometry, matrix theory and complex algebraic geometry. It has been noticed for some time that they share some striking analogies and have…
Given a real number $q$ and a star body in the $n$-dimensional Euclidean space, the generalized dual curvature measure of a convex body was introduced by Lutwak-Yang-Zhang [43]. The corresponding generalized dual Minkowski problem is…
We clarify and discuss a misunderstanding between uniform completeness and metric completeness, that has appeared in the literature in a study on the Alexandrov topology for a spacetime.
A brief presentation of basics of the theory of Tchebycheff and Markov systems of functions and its applications to extremal problems for integrals of such functions is given. The results, as well as all the necessary definitions, are…
The review presents rigorous results of the theory of fundamental equations of evolution of many-particle systems with collisions and also considers their connection with nonlinear kinetic equations describing the collective behavior of…
We overview the main ideas and techniques of the functional-analytical approach to some extremal problems of convex geometry that stem from the Queen Dido problem.
We discuss, in the context of inverse linear problems in Hilbert space, the notion of the associated infinite-dimensional Krylov subspace and we produce necessary and sufficient conditions for the Krylov-solvability of a given inverse…
This paper presents a brief account of the important milestones in the historical development of the theory of differential equations. The paper begins with a discussion on the date of birth of differential equations and then touches upon…
Contents: Introduction(3).The method of Ermakov(4).The method of Milne(7). Pinney's result(8).Lewis' results(8). The interpretation of Eliezer and Gray(14). The connection of the Ermakov invariant with N\"other's theorem(17). Possible…
The purpose of this paper is to show that in a finite dimensional metric space with Alexandrov's curvature bounded below, Monge's transport problem for the quadratic cost admits a unique solution.
In this paper, we study $C^{1, 1}$ regularity for solutions to the degenerate $L_p$ Dual Minkowski problem. Our proof is motivated by the idea of Guan and Li's work on $C^{1,1}$ estimates for solutions to the Aleksandrov problem.
We study two extremal problems of geometric function theory introduced by A. A. Goldberg in 1973. For one problem we find the exact solution, and for the second one we obtain partial results. In the process we study the lengths of…
Dedication to my untimely departed friends, Dmitry Igorevich Diakonov, Viktor Yur'evich Petrov and Maxim Vladimirovich Polyakov.
Most of the literature on the solution of linear ill-posed operator equations, or their discretization, focuses only on the infinite-dimensional setting or only on the solution of the algebraic linear system of equations obtained by…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…