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    • Handbook of Dynamical Systems

      • 1st Edition
      • Volume 1A
      • August 20, 2002
      • B. Hasselblatt + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 8 2 6 6 9 5
      • eBook
        9 7 8 0 0 8 0 5 3 3 4 4 5
      Volumes 1A and 1B.These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys.The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics.Volume 1B will appear 2005.

    • Handbook of Game Theory with Economic Applications

      • 1st Edition
      • Volume 3
      • August 19, 2002
      • R.J. Aumann + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 8 9 4 2 8 1
      • eBook
        9 7 8 0 0 8 0 5 7 4 7 6 9
      This is the third volume of the Handbook of Game Theory with Economic Applications. Since the publication of multi-Volume 1 a decade ago, game theory has continued to develop at a furious pace, and today it is the dominant tool in economic theory. The three volumes together cover the fundamental theoretical aspects, a wide range of applications to economics, several chapters on applications to political science and individual chapters on applications to disciplines as diverse as evolutionary biology, computer science, law, psychology and ethics. The authors are the most eminent practitioners in the field, including three Nobel Prize winners.The topics covered in the present volume include strategic ("Nash") equilibrium; incomplete information; two-person non-zero-sum games; noncooperative games with a continuum of players; stochastic games; industrial organization; bargaining, inspection; economic history; the Shapley value and its applications to perfectly competitive economies, to taxation, to public goods and to fixed prices; political science; law mechanism design; and game experimentation.

    • Handbook of Social Choice and Welfare

      • 1st Edition
      • Volume 19
      • August 15, 2002
      • Kenneth J. Arrow + 2 more
      • English
      • Paperback
        9 7 8 1 4 9 3 3 0 2 5 1 2
      • Hardback
        9 7 8 0 4 4 4 8 2 9 1 4 6
      • eBook
        9 7 8 0 0 8 0 9 3 3 4 8 1
      The Handbook of Social Choice and Welfare presents, in two volumes, essays on past and on-going work in social choice theory and welfare economics. The first volume consists of four parts. In Part 1 (Arrovian Impossibility Theorems), various aspects of Arrovian general impossibility theorems, illustrated by the simple majority cycle first identified by Condorcet, are expounded and evaluated. It also provides a critical survey of the work on different escape routes from impossibility results of this kind. In Part 2 (Voting Schemes and Mechanisms), the operation and performance of voting schemes and cost-sharing mechanisms are examined axiomatically, and some aspects of the modern theory of incentives and mechanism design are expounded and surveyed. In Part 3 (structure of social choice rules), the positional rules of collective decision-making (the origin of which can be traced back to a seminal proposal by Borda), the game-theoretic aspects of voting in committees, and the implications of making use of interpersonal comparisons of welfare (with or without cardinal measurability) are expounded, and the status of utilitarianism as a theory of justice is critically examined. It also provides an analytical survey of the foundations of measurement of inequality and poverty. In order to place these broad issues (as well as further issues to be discussed in the second volume of the Handbook) in perspective, Kotaro Suzumura has written an extensive introduction, discussing the historical background of social choice theory, the vistas opened by Arrow's Social Choice and Individual Values, the famous "socialist planning" controversy, and the theoretical and practical significance of social choice theory. The primary purpose of this Handbook is to provide an accessible introduction to the current state of the art in social choice theory and welfare economics. The expounded theory has a strong and constructive message for pursuing human well-being and facilitating collective decision-making.

    • Handbook of Computer Aided Geometric Design

      • 1st Edition
      • August 13, 2002
      • G. Farin + 2 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 1 0 4 1
      • eBook
        9 7 8 0 0 8 0 5 3 3 4 0 7
      This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include: Historical outline Curve and surface methods Scientific Visualization Implic... methods Reverse engineering.This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposureto this subject.

    • Bilingual Sentence Processing

      • 1st Edition
      • Volume 134
      • July 25, 2002
      • Roberto Heredia + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 8 4 7 8
      • eBook
        9 7 8 0 0 8 0 5 0 0 0 9 6

    • Handbook of Mathematical Fluid Dynamics

      • 1st Edition
      • Volume 1
      • July 9, 2002
      • S. Friedlander + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 3 3 0 5
      • eBook
        9 7 8 0 0 8 0 5 3 2 9 2 9
      The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

    • Relation Algebras by Games

      • 1st Edition
      • Volume 147
      • July 1, 2002
      • Robin Hirsch + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 9 3 2 1
      • eBook
        9 7 8 0 0 8 0 5 4 0 4 5 0
      Relation algebras are algebras arising from the study of binary relations.They form a part of the field of algebraic logic, and have applications in proof theory, modal logic, and computer science. This research text uses combinatorial games to study the fundamental notion of representations of relation algebras. Games allow an intuitive and appealing approach to the subject, and permit substantial advances to be made. The book contains many new results and proofs not published elsewhere. It should be invaluable to graduate students and researchers interested in relation algebras and games.After an introduction describing the authors' perspective on the material, the text proper has six parts. The lengthy first part is devoted to background material, including the formal definitions of relation algebras, cylindric algebras, their basic properties, and some connections between them. Examples are given. Part 1 ends with a short survey of other work beyond the scope of the book. In part 2, games are introduced, and used to axiomatise various classes of algebras. Part 3 discusses approximations to representability, using bases, relation algebra reducts, and relativised representations. Part 4 presents some constructions of relation algebras, including Monk algebras and the 'rainbow construction', and uses them to show that various classes of representable algebras are non-finitely axiomatisable or even non-elementary. Part 5 shows that the representability problem for finite relation algebras is undecidable, and then in contrast proves some finite base property results. Part 6 contains a condensed summary of the book, and a list of problems. There are more than 400 exercises.The book is generally self-contained on relation algebras and on games, and introductory text is scattered throughout. Some familiarity with elementary aspects of first-order logic and set theory is assumed, though many of the definitions are given. Chapter 2 introduces the necessary universal algebra and model theory, and more specific model-theoretic ideas are explained as they arise.

    • Elsevier's Dictionary of Geographical Information Systems

      • 1st Edition
      • June 26, 2002
      • B. Delijska
      • English
      • Hardback
        9 7 8 0 4 4 4 5 0 9 9 1 8
      • eBook
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      Elsevier's Dictionary of Geographical Information Systems contains 4,040 terms with about 1,700 cross-references that are commonly used in the theory and practice of geographical information systems. The terms were selected according to their significance or frequency of use. The terminology covers the areas of geoinformatics, geostatistics, computer cartography, geospatial databases, computer graphics, geodesy, photogrammetry, remote sensing, hardware and software for introduction, processing and visualization of geospatial data, etc. Geographical information systems are modern, widely distributed and strategic tools in many human activities (land survey and regulation, ecology, forestry, agronomy, demography, hydrology, urban planning, transport, etc.).Elsevier's Dictionary of Geographical Information Systems will be a valuable tool for specialists, scientists and students and for everyone who is interested in this area.

    • Nonlinear Partial Differential Equations and Their Applications

      • 1st Edition
      • Volume 31
      • June 21, 2002
      • Doina Cioranescu + 1 more
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 1 0 3 4
      • Paperback
        9 7 8 0 4 4 4 5 4 6 8 1 4
      • eBook
        9 7 8 0 0 8 0 5 3 7 6 7 2
      This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

    • Complex Numbers in n Dimensions

      • 1st Edition
      • Volume 190
      • June 20, 2002
      • S. Olariu
      • English
      • Hardback
        9 7 8 0 4 4 4 5 1 1 2 3 2
      • Paperback
        9 7 8 0 4 4 4 5 5 1 8 8 7
      • eBook
        9 7 8 0 0 8 0 5 2 9 5 8 5
      Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functionsof the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

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