Related papers: Alexandrov's Approach to the Minkowski Problem
We find a semi-algebraic description of the Minkowski sum $\mathcal{A}_{3,n}$ of $n$ copies of the bounded twisted cubic $\{(t,t^2,t^3)\mid -1\leq t\leq 1\}$ for each integer $n\geq3$. These descriptions provide efficient membership tests…
This is a short survey article written for the Erd\H{o}s centennial conference in Budapest in 2013. The main two topics covered are Szemer\'edi's theorem and its ramifications, and the Erd\H{o}s discrepancy problem. There is an emphasis on…
In this paper we will study the numerical solution of a discontinuous differential system by a Rosenbrock method. We will also focus on one-sided approach in the context of Rosenbrock schemes, and we will suggest a technique based on the…
The Pomeransky-Sen'kov solution is well known to describe an asymptotically flat doubly rotating black ring in five dimensions, whose self-gravity is exactly balanced by the centrifugal force arising from the rotation in the ring direction.…
We study Alexandrov curvature in the tropical projective torus with respect to the tropical metric, which has been useful in various statistical analyses, particularly in phylogenomics. Alexandrov curvature is a generalization of classical…
The aim of this paper is to review how some approximation results in commutative algebra are being used to construct equisingular deformations of singularities. The first example of such an approximation result appeared for the first time…
Analytical solutions are presented for eigenvalues, eigenfunctions of {\color{red} D-dimensional Schrodinger equation having Eckart potential} within Nikiforov-Uvarov method. This uses a new, improved approximation for centrifugal term,…
Certain excess versions of the Minkowski and H\"older inequalities are given. These new results generalize and improve the Minkowski and H\"older inequalities.
The method proposed by the present authors to deal analytically with the problem of Anderson localization via disorder [J.Phys.: Condens. Matter {\bf 14} (2002) 13777] is generalized for higher spatial dimensions D. In this way the…
This paper proposes an inexact Aleksandrov-solution-based iteration method, formulated by adapting the convergent Rayleigh inverse iterative scheme introduced by Abedin and Kitagawa, to solve real Monge-Amp{\`e}re eigenvalue (MAE) problems.…
We approximate the solution to some linear and degenerate quasi-linear problem involving a linear elliptic operator (like the semi-discrete in time implicit Euler approximation of Richards and Stefan equations) with measure right-hand side…
Under the definition of Ricci curvature bounded below for Alexandrov spaces introduced by Zhang-Zhu, we generalize a result by Colding that an n dimentional manifold with Ricci curvature greater or equal to n minus 1 and volume close to…
In the article we have obtained some estimates of the rate of convergence for the recently proposed by Yu.E. Nesterov method of minimization of a convex Lipschitz-continuous function of two variables on a square with a fixed side. The…
In the Euclidean setting, the well-known Alexandrov theorem states that convex functions are twice differentiable almost everywhere. In this note, we extend this theorem to rank-one convex functions. Our approach is novel in that it draws…
In \cite{LX}, the first author and Xu introduced and studied the horospherical $p$-Minkowski problem in hyperbolic space $\mathbb{H}^{n+1}$. In particular, they established the uniqueness result for solutions to this problem when the…
This collection presents a selected set of unsolved problems in semigroup theory, a fundamental branch of modern algebra. The publication is dedicated to the 110th anniversary of the birth of E. S. Lyapin, one of the founders of the field…
This is an English translation of "The Problem of Resolvents and Critical Manifolds" by Tschebotarow/Chebotarev. In this article, Chebotarev explains his work on resolvent problems using critical manifolds. The current ideas of resolvent…
We consider various inequalities for polynomials, with an emphasis on the most fundamental inequalities of approximation theory. In the sequel a key role is played by the generalized Minkowski functional \alpha(K,x), already being used by…
Boris Venkov passed away on November 10 2011 just 5 days before his 77th birthday. This article gives a short survey of the mathematical work of Boris Venkov in this direction.
This article provides a historical overview of Geometry of Numbers. 1. Figures, 2. The circuit problem and its relatives, 3. Minkowski lattice point set, 4. The young Hermann Minkowski, 5. The geometry of numbers develops, 6. Minkowski…