A D. Alexandrov

Kutateladze, S.S.

Chapman & Hall/CRC

This monograph presents the most important results of a new branch of functional analysis: subdifferential calculus and its applications. New tools and techniques of convex and nonsmooth analysis are presented, such as Kantorovich spaces, vector duality, Boolean-valued and infinitesimal versions of nonstandard analysis, etc., covering a wide range of topics. This volume fills the gap between the theoretical core of modern functional analysis and its applicable sections, such as optimization, optimal control, mathematical programming, economics and related subjects. The material in this book will be of interest to theoretical mathematicians looking for possible new applications and applied mathematicians seeking powerful contemporary theoretical methods.

Subdifferentials: Theory and Applications (Mathematics and Its Applications)

Science & Math

Kusraev, A.G.

Mathematics

Springer

Boolean valued analysis is a technique for studying properties of an arbitrary mathematical object by comparing its representations in two different set-theoretic models whose construction utilises principally distinct Boolean algebras. The use of two models for studying a single object is a characteristic of the so-called non-standard methods of analysis. Application of Boolean valued models to problems of analysis rests ultimately on the procedures of ascending and descending, the two natural functors acting between a new Boolean valued universe and the von Neumann universe. This book demonstrates the main advantages of Boolean valued analysis which provides the tools for transforming, for example, function spaces to subsets of the reals, operators to functionals, and vector-functions to numerical mappings. Boolean valued representations of algebraic systems, Banach spaces, and involutive algebras are examined thoroughly.  Audience: This volume is intended for classical analysts seeking powerful new tools, and for model theorists in search of challenging applications of nonstandard models.

Boolean Valued Analysis (Mathematics and Its Applications)

This book contains papers presented at the Second International Conference on Algebra, held in Barnaul in August 1991 in honor of the memory of A. I. Shirshov (1921--1981). Many of the results presented here have not been published elsewhere in the literature. The collection provides a panorama of current research in PI-, associative, Lie, and Jordan algebras and discusses the interrelations of these areas with geometry and physics. Other topics in group theory and homological algebra are also covered.

Second International Conference on Algebra: Dedicated to the Memory of A.I. Shirshov : Proceedings of the Second International Conference on Algebra, ... Barnaul, Russua (Contemporary Mathematics)

Bokut, L. A.

International Conference on Algebra (2nd : 1991 : Barnaul, Altaiskii Krai, Russia)

Amer Mathematical Society

Kantorovich, the late Nobel Laureate, was a respected mathematical economist, and one of the founding fathers of linear programming. Part I begins with chapters on the theory of sets and real functions. Topics treated include universal functions, W.H. Young's classification, generalized derivatives of continuous functions and the H. Steinhaus problem. The book also includes papers on the theory of projective sets, general and particular methods of the extension of Hilbert space, and linear semi-ordered spaces. The author deals with a number of approximate calculations and solutions including a discussion of an approximate calculation of certain types of definite integrals, and also a method for the approximate solution of partial differential equations. In addition to this, the author looks at various other methods, including the Ritz method, the Galerkin method in relation to the reduction of differential equations and the Newton methods for functional equations. Towards the end of the book there are several chapters on computers.

Applied Functional Analysis. Approximation Methods and Computers: Applied Functional Analysis, Approximation Methods and Computers (Classics of Soviet Mathematics,)

CRC-Press

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