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Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Interpolation Functors and Interpolation Spaces

    • 1st Edition
    • Volume 47
    • March 18, 1991
    • English
    The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the results of that solution, as well as drawing heavily on a classic paper by Aronszajn and Gagliardo, which appeared in 1965 but whose real importance was not realized until a decade later. This includes a systematic use of the language, if not the theory, of categories. In this way the book also opens up many new vistas which still have to be explored. This volume is the first of three planned books. Volume II will deal with the complex method, while Volume III will deal with applications.

  • Ring Theory, 83

    Student Edition
    • 1st Edition
    • February 5, 1991
    • Louis H. Rowen
    • English
    This is an abridged edition of the author's previous two-volume work, Ring Theory, which concentrates on essential material for a general ring theory course while ommitting much of the material intended for ring theory specialists. It has been praised by reviewers:**"As a textbook for graduate students, Ring Theory joins the best....The experts will find several attractive and pleasant features in Ring Theory. The most noteworthy is the inclusion, usually in supplements and appendices, of many useful constructions which are hard to locate outside of the original sources....The audience of nonexperts, mathematicians whose speciality is not ring theory, will find Ring Theory ideally suited to their needs....They, as well as students, will be well served by the many examples of rings and the glossary of major results."**--NOTICES OF THE AMS

  • Topics on Domination

    • 1st Edition
    • February 1, 1991
    • S.T. Hedetniemi + 1 more
    • English
    The contributions in this volume are divided into three sections: theoretical, new models and algorithmic. The first section focuses on properties of the standard domination number &ggr;(G), the second section is concerned with new variations on the domination theme, and the third is primarily concerned with finding classes of graphs for which the domination number (and several other domination-related parameters) can be computed in polynomial time.

  • Submodular Functions and Optimization

    • 1st Edition
    • Volume 47
    • January 24, 1991
    • S. Fujishige
    • English
    The importance of submodular functions has been widely recognized in recent years in combinatorial optimization. This is the first book devoted to the exposition of the theory of submodular functions from an elementary technical level to an advanced one. A unifying view of the theory is shown by means of base polyhedra and duality for submodular and supermodular systems. Among the subjects treated are: neoflows (submodular flows, independent flows, polymatroidal flows), submodular analysis (submodular programs, duality, Lagrangian functions, principal partitions), nonlinear optimization with submodular constraints (lexicographically optimal bases, fair resource allocation). Special emphasis is placed on the constructive aspects of the theory, which lead to practical, efficient algorithms.

  • Latin Squares

    New Developments in the Theory and Applications
    • 1st Edition
    • January 24, 1991
    • József Dénes + 1 more
    • English
    In 1974 the editors of the present volume published a well-received book entitled ``Latin Squares and their Applications''. It included a list of 73 unsolved problems of which about 20 have been completely solved in the intervening period and about 10 more have been partially solved. The present work comprises six contributed chapters and also six further chapters written by the editors themselves. As well as discussing the advances which have been made in the subject matter of most of the chapters of the earlier book, this new book contains one chapter which deals with a subject (r-orthogonal latin squares) which did not exist when the earlier book was written.The success of the former book is shown by the two or three hundred published papers which deal with questions raised by it.

  • Quasihomogeneous Distributions

    • 1st Edition
    • Volume 165
    • January 24, 1991
    • O. von Grudzinski
    • English
    This is a systematic exposition of the basics of the theory of quasihomogeneous (in particular, homogeneous) functions and distributions (generalized functions). A major theme is the method of taking quasihomogeneous averages. It serves as the central tool for the study of the solvability of quasihomogeneous multiplication equations and of quasihomogeneous partial differential equations with constant coefficients. Necessary and sufficient conditions for solvability are given. Several examples are treated in detail, among them the heat and the Schrödinger equation. The final chapter is devoted to quasihomogeneous wave front sets and their application to the description of singularities of quasihomogeneous distributions, in particular to quasihomogeneous fundamental solutions of the heat and of the Schrödinger equation.

  • Algebraic and Structural Automata Theory

    • 1st Edition
    • Volume 44
    • January 14, 1991
    • B. Mikolajczak
    • English
    Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development.The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups.Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

  • Stochastic Models in Queuing Theory

    • 1st Edition
    • January 1, 1991
    • J. Medhi
    • English

  • The Mathematics of Finite Elements and Applications VII

    MAFELAP 1990
    • 1st Edition
    • January 1, 1991
    • J. R. Whiteman
    • English

  • Digital Systems Reference Book

    • 1st Edition
    • January 1, 1991
    • Brian Holdsworth + 1 more
    • English

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