Related papers: Alexandrov's Approach to the Minkowski Problem
Yuri L'vovich Klimontovich (28.09.1924--26.10.2002) was an outstanding theoretical physicist who made major contributions to kinetic theory. On the occasion of his 100th birthday we recall his main scientific achievements.
The topic of this paper is, on the one hand to introduce algebraic analysis results of \'Etienne B\'ezout (1730- 1783) not as we know them today but as he found them in his time, and on the other hand to emphasize his innovating viewpoints.…
The Minkowski problem for electrostatic capacity characterizes measures generated by electrostatic capacity, which is a well-known variant of the Minkowski problem. This problem has been generalized to $L_p$ Minkowski problem for…
Alexander Andreevich Andrianov was a remarkable personality in Russian physics during the last decades. A member of th prestigious school of theoretical physics in Saint Petersburg, he made relevant contributions to a number of topics along…
Paul Chernoff in 1968 proposed his approach to approximations of one-parameter operator semigroups while trying to give a rigorous mathematical meaning to Feynman's path integral formulation of quantum mechanics. In early 2000's Oleg…
In the "6D treatment of Special Relativity" proposed by Igor A. Urusovskii one deals with universal light-like motion of matter pre-elements in the extended (3+3) space and with their regular rotation in the additional 3-space. On the other…
In this paper we continue the analysis of the two-scale method for the Monge-Amp\`ere equation for dimension $d \geq 2$ introduced in [10]. We prove continuous dependence of discrete solutions on data that in turn hinges on a discrete…
The Alexander polynomial (1928) is the first polynomial invariant of links devised to help distinguish links up to isotopy. Fox's conjecture (1962) -- stating that the absolute values of the coefficients of the Alexander polynomial for any…
Necessary and sufficient conditions are given for the existence of solutions to the discrete Lp Minkowski problem for the critical case where 0 < p < 1.
Recently, the horospherical $p$-Minkowski problem in hyperbolic space was proposed as a counterpart of $L_p$ Minkowski problem in Euclidean space. Through designing a new volume preserving curvature flow, the existence of normalized even…
This short note gives an elementary alternative proof for a theorem of Danilov and Koshevoy on Minkowski summation and unimodularity in discrete convex analysis. It is intended to disseminate this fundamental theorem and make its proof…
In this paper, we present the solution to Kolmogorov's problem for the classes of multiply monotone and completely monotone functions together with its connections to the Markov moment problem, Hermite-Birkhoff interpolation problem, and…
We present numerical results concerning the solution of the time-harmonic Maxwell's equations discretized by discontinuous Galerkin methods. In particular, a numerical study of the convergence, which compares different strategies proposed…
In this paper, we deal with the torsion log-Minkowski problem without symmetry assumptions via an approximation argument.
In this short note, we prove the existence of solutions to a Monge-Amp\`ere equation of entire type derived by a weighted version of the classical Minkowski problem.
This presentation goes beyond celebratory narration of the life and scientific achievements of Russia's first modern scientist Mikhail Vasilievich Lomonosov (1711-1765). Coming from the notion of complexity of sciences, we introduce "a…
In this work we establish eigenvalue inequalities for elliptic differential operators either for Dirichlet or for Robin eigenvalue problems, by using the technique introduced by Alexandroff, Bakelman and Pucci. These inequalities can be…
In the article we give an appreciation of Edward Nelson's multifaceted contribution to mathematics, and particularly to foundational theories of infinitesimals.
The initial motivation of this text was to provide an up to date translation of the monograph [45] written in french by the first author, taking account of more recent developments of infinite dimensional dynamics based on the…
This chapter is mainly a tutorial introduction to methods recently developed in order to find all (as opposed to some) meromorphic particular solutions of given nonintegrable, autonomous, algebraic ordinary differential equations of any…