Related papers: Linear Programming and Kantorovich Spaces
A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to…
Georgy Theodosiyovych Voronoi (1868-1908) is famous for his seminal contributions to number theory,perhaps mostly those involving quadratic forms and Voronoi tessellations. He was born and grew up in the town of Zhuravka in the Ukraine, at…
Linear Programming is now included in Algorithm undergraduate and postgraduate courses for Computer Science majors. It is possible to teach interior-point methods directly with just minimal knowledge of Algebra and Matrices.
We prove some properties of positive polynomial mappings between Riesz spaces, using finite difference calculus. We establish the polynomial analogue of the classical result that positive, additive mappings are linear. And we prove a…
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
The main solutions in sense of Kantorovich of nonlinear Volterra operator-integral equations are constructed. Convergence of the successive approximations is established through studies of majorant integral and majorant algebraic equations.…
In the present article, we analyse the behaviour of a new family of Kantorovich type sampling operators $(K_w^{\varphi}f)_{w>0}.$ First, we give a Voronovskaya type theorem for these Kantorovich generalized sampling series and a…
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career…
The paper is dedicated to the memory of prominent theoretical physicist and mathematician Dr. Vadim Kuznetsov who worked, in particular, in the fields of the nonlinear dynamics, separation of variables, integrability theory, special…
In this paper, ellipsoid method for linear programming is derived using only minimal knowledge of algebra and matrices. Unfortunately, most authors first describe the algorithm, then later prove its correctness, which requires a good…
In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by…
Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.
In the context of partially ordered vector spaces one encounters different sorts of order convergence and order topologies. This article will investigate these notions and their relations. In particular we study and relate the order…
In the present paper, an inverse result of approximation, i.e., a saturation theorem for the sampling Kantorovich operators is derived, in the case of uniform approximation for uniformly continuous and bounded functions on the whole real…
We show the following result: Let $A,B\in \mathbb{B}\left( \mathcal{H} \right)$ be two strictly positive operators such that $A\le B$ and $m{{\mathbf{1}}_{\mathcal{H}}}\le B\le M{{\mathbf{1}}_{\mathcal{H}}}$ for some scalars $0<m<M$. Then…
Latroids were introduced by Vertigan, who associated a latroid to a linear block code and showed that its Tutte polynomial determines the weight enumerator of the code. We associate a latroid to a code over a ring or a field endowed with a…
The purpose of this paper is two-fold. The first is to give a tutorial introduction to the Sarkisov program, a 3-dimensional generalization of Castelnuovo-N\"other Theorem ``untwisting" birational maps between Mori fiber spaces, which was…
We introduce a new class of optimization problems called integer Minkowski programs. The formulation of such problems involves finitely many integer variables and nonlinear constraints involving functionals defined on families of discrete…
Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its…