Semen Kutateladze
Novosibirsk State University, Mechanics and Mathematics, Faculty Member
- A mathematician by call and tradeedit
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1. Discretization is approximation of arbitrary function spaces and operators by their analogs in finite dimensions. Discretization matches the marvelous universal understanding of computational mathematics as the science of finite... more
1. Discretization is approximation of arbitrary function spaces and operators by their analogs in finite dimensions. Discretization matches the marvelous universal understanding of computational mathematics as the science of finite approximations to general (not necessarily metrizable) compacta. This revolutionary and challenging definition was given in the joint talk submitted by S. L. Sobolev, L. A. Lyuster-nik, and L. V. Kantorovich at the Third All-Union Mathematical Congress in 1956. Infinitesimal methods suggest a background, providing new schemes for discretiza-tion of general compact spaces. As an approximation to a compact space we may take an arbitrary internal subset containing all standard elements of the space under approximation. 2. Hypodiscretization of the equation Tx = y, with T: X → Y a bounded linear operator between some Banach spaces X and Y, consists in choosing finite-dimensional vector spaces XN and YN, the corresponding embeddings ıN and N, and some operator...
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This talk overviews the life and mathematical legacy of L. V. Kantorovich (1912–1986). The Appendix contains details on intraction between K-space and the real
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The book treats Boolean valued analysis. This term signifies the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose... more
The book treats Boolean valued analysis. This term signifies the technique of studying properties of an arbitrary mathematical object by means of comparison between its representations in two different set-theoretic models whose construction utilizes principally distinct Boolean algebras. As these models, we usually take the classical Cantorian paradise in the shape of the von Neumann universe and a specially-trimmed Boolean valued universe in which the conventional set-theoretic concepts and propositions acquire bizarre interpretations. Exposition focuses on the fundamental properties of order bounded operators in vector lattices. This volume is intended for the classical analyst seeking new powerful tools and for the model theorist in search of challenging applications of nonstandard models of set theory.
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This is a collection of a few generalities and conjectures that mostly concern the nature of science and its place in life.
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This is a survey of some recent applications of Boolean valued analysis to operator theory and harmonic analysis. Under consideration are pseudoembedding operators, the noncommutative Wickstead problem, the Radon-Nikodym Theorem for... more
This is a survey of some recent applications of Boolean valued analysis to operator theory and harmonic analysis. Under consideration are pseudoembedding operators, the noncommutative Wickstead problem, the Radon-Nikodym Theorem for JB-algebras, and the Bochner Theorem for lattice-valued positive definite mappings on locally compact groups.
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A dependence of the relative friction coefficient on the form parameter of the aerodynamic curvature is proposed on the basis of measurements of the tangential stress on the wall during the flow of a liquid in a diffusor using the... more
A dependence of the relative friction coefficient on the form parameter of the aerodynamic curvature is proposed on the basis of measurements of the tangential stress on the wall during the flow of a liquid in a diffusor using the electrodiffusion method. The intensity of fluctuations of the tangential stress at the wall and the instant of appearance of reverse
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Boolean models are applied to deriving operator versions of the classical Farkas Lemma in the theory of simultaneous linear inequalities.
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This is a short overview of some recent tendencies in the theory of linear inequalities that are evoked by Boolean valued analysis.
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This collection of articles and essays of the last decade is devoted to science and its place in the modern society. Most attention is paid to the people of science. Several articles reflect the life and contributions of A.D. Alexandrov,... more
This collection of articles and essays of the last decade is devoted to science and its place in the modern society. Most attention is paid to the people of science. Several articles reflect the life and contributions of A.D. Alexandrov, L.V., Kantorovich, N.N. Luzin, S. Mac Lane, S.L. Sobolev, L. Schwartz, and other contemporary scientists. Some room is allotted to the classics of science: Newton, Leibniz, and Euclid. A few articles touch on the history of mathematics, the problems of teaching in higher education, and the criticism of pseudoscience. The book is intended for the wide readership of those interested in science and its people.
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Page 1. CHOQUET BOUNDARIES IN K-SPACES This article has been downloaded from IOPscience. Please scroll down to see the full text article. 1975 Russ. Math. Surv. 30 115 (http://iopscience.iop.org/0036-0279/30/4/R03) ...