Bücher der Reihe Mathematics and its Applications

This is a monograph on geometrical and topological features which arise in various quantization procedures. When this internal space variable is considered as a direc tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field.

Offers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.

The main tools of the theory of autowave processes are various methods used for investigating nonlinear discrete or distributed oscillating systems, the mathe matical theory of nonlinear parabolic differential equations, and methods of the theory of finite automata.

Presents the advanced theory and practice of fractional programming. This title provides possible fields of application for fractional programming methods. It describes the convex, quasi-convex, pseudo-convex, and log-convex functions.

In particular, linear dynamic control systems iJ = Ay + Bu, y E M C ]Rn, U E ]RT, (1) where A and B are constants, are often abandoned in favor of nonlinear dynamic control systems (2) which, in addition, contain a large number of equations.

This volume provides a study of some of the well-known inequalities in classical mathematical analysis. Subjects dealt with include: Hardy-Littlewood-type inequalities, Hardy's and Carleman's inequalities, Lyapunov inequalities, and generalized Shannon functional inequality.

This book attempts to give a presentation of the advance of our knowledge of phase portraits of quadratic systems, paying special attention to the historical development of the subject. This the only book that organizes the portraits into classes, using the notions of finite and infinite multiplicity and finite and infinite index.

'Et moi ¿...¿ si j'avait su comment en revenir. One service mathematics has rendered the je n'y serais point aile: human race. It has put common sense back where it belongs. on the topmost shelf next Jules Verne (0 the dusty canister labelled 'discarded non­ sense'. The series is divergent; therefore we may be able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non­ linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com­ puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes.

Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics;

The Feynman integral is considered as an intuitive representation of quantum mechanics showing the complex quantum phenomena in a language comprehensible at a classical level.

Research in the theory of trigonometric series has been carried out for over two centuries. The achievements in the theory of multiple trigonometric series look rather modest as compared to those in the one-dimensional case though multiple trigonometric series seem to be a natural, interesting and promising object of investigation.

As soon as the problem without considering the symmetry is solved for one kind of map, the general problem with symmetry can always, in principle, be solved from what we have known about the automorphism of a polyhedron, a synonym for a map, which can be determined efficiently according to another monograph of the present author [Liu58].

Since about 1915 integration theory has consisted of two separate branches: the abstract theory required by probabilists and the theory, preferred by analysts, that combines integration and topology.

This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

This book is the first to systematically explore the classification and function theory of complex homogeneous bounded domains. Using the normal Siegel domains to realize the homogeneous bounded domains, we can obtain more property of the geometry and the function theory on homogeneous bounded domains.

This book covers the latest achievements of the Theory of Classes of Finite Groups. By gathering the research of many authors scattered in hundreds of papers the book contributes to the understanding of the structure of finite groups by adapting and extending the successful techniques of the Theory of Finite Soluble Groups.

'Et moi, ... , so j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point al!e.' human race. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics ... 'One service category theory has rendered mathematics ...

The aim of this book is to give the reader an insight into the mathematical methods which can be used in queueing theory and to present examples of solving problems with the help of these methods.

The analytical basis of Navier-Stokes Equations in Irregular Domains is formed by coercive estimates, which enable proofs to be given of the solvability of the boundary value problems for Stokes and Navier-Stokes equations in weighted Sobolev and Hoelder spaces, and the investigation of the smoothness of their solutions.

This volume presents a unified approach to the mathematical theory of a wide class of non-additive set functions, the so called null-additive set functions, which also includes classical measure theory.

(In certain cases, such as that of semigroups, in order to have the right always to say that SubA is a lattice, we have to treat the empty set as a subsystem.) The study of various inter-relationships between systems and their subsystem lattices is a rather large field of investigation developed over many years.

At the first stage, until the middle of the 1970s, pattern recogni tion theory was replenished mainly from adjacent mathematical disciplines: mathe matical statistics, functional analysis, discrete mathematics, and information theory.

The other restricts its area of interest to certain families of equations and studies in maximal details phenomena which characterize only those equations. Among them we find third and fourth order equations, self adjoint equations, etc.

This monograph covers one of the divisions of mathematical theory of control which examines moving objects functionating under conflict and uncertainty conditions. The contents of the monograph is confined to studying classical pursuit-evasion problems which are central to the theory of conflict controlled processes.

As such, it tries to find a unified way of dealing with diverse topics in mathematics and theoretical com puter science as formal language theory, the theory of fuzzy algebraic structures, models of optimal control, and many others. to what extent basic fields of mathematics like algebra and topology are dependent on the underlying set theory?"

Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems.