In this book a general topological construction of extension is proposed for problems of attainability in topological spaces under perturbation of a system of constraints. This construction is realized in a special class of generalized elements defined as finitely additive measures. A version of the method of programmed iterations is constructed. This version realizes multi-valued control quasistrategies, which guarantees the solution of the control problem that consists in guidance to a given set under observation of phase constraints.
Audience: The book will be of...
In this book a general topological construction of extension is proposed for problems of attainability in topological spaces under perturbation of ...
The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness...
The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both...
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents. Resurrected by A. Robinson in the early 1960's with the epithet 'nonstandard', infinitesimal analysis not only has revived the methods of infinitely small and infinitely large quantities, which go back to the very beginning of calculus, but also has suggested many powerful tools for research in every branch of modern mathematics.
The book sets forth the basics of the...
Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object b...
This is the first monograph on rings closed to von Neumann regular rings. The following classes of rings are considered: exchange rings, pi-regular rings, weakly regular rings, rings with comparability, V-rings, and max rings. Every Artinian or von Neumann regular ring A is an exchange ring (this means that for every one of its elements a, there exists an idempotent e of A such that aA contains eA and (1-a)A contains (1-e)A). Exchange rings are very useful in the study of direct decompositions of modules, and have many applications to theory of Banach algebras, ring theory, and K-theory....
This is the first monograph on rings closed to von Neumann regular rings. The following classes of rings are considered: exchange rings, pi-regular...
Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non stationary problems of mathematical physics. In the theoretical analysis of difference schemes our basic attention is paid to the problem of sta bility of a difference solution (or well posedness of a difference scheme) with respect to small perturbations of the initial conditions and the right hand side. The theory of stability of difference schemes develops in various di...
Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect...
This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0...
This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representation...
The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants of a pair of nonempty compact convex subsets of a locally convex vector space in the sense of the Radstrom-Hormander Theory. Minimal pairs of compact convex sets arise naturally in different fields of mathematics, as for instance in non-smooth analysis, set-valued analysis and in the field of combinatorial convexity. In the first three chapters of the book the basic facts about convexity, mixed volumes and the Radstrom-Hormander lattice are...
The book is devoted to the theory of pairs of compact convex sets and in particular to the problem of finding different types of minimal representants...
This book concentrates on the branching solutions of nonlinear operator equations and the theory of degenerate operator-differential equations especially applicable to algorithmic analysis and nonlinear PDE's in mechanics and mathematical physics. The authors expound the recent result on the generalized eigen-value problem, the perturbation method, Schmidt's pseudo-inversion for regularization of linear and nonlinear problems in the branching theory and group methods in bifurcation theory. The book covers regular iterative methods in a neighborhood of branch points and the theory of...
This book concentrates on the branching solutions of nonlinear operator equations and the theory of degenerate operator-differential equations especia...
This introductory book, which grew out of lectures given at the Mathematics Institute of Wurzburg University, proposes a combination of coding theory and number theory. Chapter 1 gives a standard course of linear codes. The next two chapters treat a link between coding theory and number theory. Chapter 4 is a systematic study of algebraic-geometric codes and in Chapter 5 a connection between binary linear codes and theta functions is discussed.
The book is designed to teach undergraduates and graduates the basic ideas and techniques of coding theory and number theory."
This introductory book, which grew out of lectures given at the Mathematics Institute of Wurzburg University, proposes a combination of coding theo...
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on...
Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathem...
