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This Volume contains articles covering a broad spectrum of proof theory,
with an emphasis on itsmathematical aspects.
The articles should not only be interesting ti specialists of proof theory,
but should also be accessible to a diverse audience,
including logicians,
mathematicians, computer scientists and philosophers.
Many of the central topics of proof theory have been inclued in
a self-contained expository of articles, covered in great detail and depth.
The chapters are arranged so that the two introductory articles come first;
these are then followed by artcles from core classical areas of proof theory;
the handbook concludes with articles that deal with topics closely related to computer science.
Contents:
First-Order Proof Theory of Arithmetic-
Hierarchies of Provably Recursive Functions-
Subsystems of Set Theory and Second Order Number Theory-
Godel's Functional ("Dialectica") Interpretation-
Realization- The Logic of Provability-
A Proof-Theoretic Framework for Logic Programming-
Dec. 1998 230 pp.
0-444-89840-9
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This book is a comprehensive study of the relationship between a model category and its homotopy category. The author develops the theory of model categories, giving a careful development of the main examples. One highlight of the theory is a proof that the homotopy category of any model category is naturally a closed module over the homotopy category of simplicial sets. Little is required of the reader beyond some category theory and set theory, making the book accessible to graduate students. The book begins with the basic theory of model categories and proceeds to a careful exposition of the main examples, using the theory of cofibrantly generated model categories. It then develops the general theory more fully, showing in particular that the homotopy category of any model category is a module over the homotopy category of simplicial sets, in an appropriate sense. This leads to a simplification and generalization of the loop and suspension functors in the homotopy category of a pointed model category. Nov. 1998 207 pp. 0-8218-1359-5
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This volume is an updated edition of Essays on Mirror Manifolds, the first book of papers published after the phenomenon of mirror symmetry was discovered. The two major groups who made the discovery reported their papers here. Greene, Plesser, and Candelas gave details on their findings; Witten gave his interpretation which was vital for future development. Vafa introduced the concept of quantum cohomology. Several mathematicians, including Katz, Morrison, Wilson, Roan, Tian, Hirsch, Yau, and Borcea discussed current knowledge about Calabi-Yau manifolds. Ferrara and his coauthors addressed special geometry and N=2 supergravity. Rocek proposed possible mirrors for Calabi-Yau manifolds with torsion. This collection continues to be an import-ant book on this spectacular achievement in algebraic geometry and mathematical physics. Oct. 1998 444 pp. 0-8218-0665-3
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Numerical methods for partial differential equations have been the subject of many books in recent times but few have treated the subjects of complex equations. In this important new books, the author introduces the theory of, and approximate methods for, nonlinear elliptic complex equations in multiply connected domains. Constructive methods are systematically applied to proper boundary value problems which include very general boundary conditions. Approximate and numerical methods such as the Newton imbedding method, the continuity method, as well as their applications, are discussed in detail. Dec. 1998 230 pp. 90-5699-135-3
In this extensive work, the authors give a complete self-contained exposition on the subject of classical function theory and the most recent developments in transcendental iteration. They clearly present the theory of iteration of transcendental functions and their analytic and geometric aspects. Attention is concentrated for the first time on the dynamics of transcendental functions to compliment the growing body of work on rational functions. The subjects covered in detail include the fixed point theory, basic properties of Fatou and Julia sets, components of Fatou sets, the geometry of Julia sets and the Hausdorff dimension of the Julia set. Aug. 1998 254 pp. 90-5699-161-2
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This book is written to meet the needs of practitioners and students in applied fields for a single, fairly thin volume covering major, update methods in categorical data analysis. For professional statisticians it offers sufficient details and foundation to provide a better understanding of the various procedures, as well as the relationships, and as a reference book for practicing biomedical research workers, it is very application-oriented. Nov. 1998 312 pp. 0-471-24060-5
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This book the essentials of stochastic dynamic programming (also known as stochastic optimal control, Markov decision processes, or Markov decision chains) with a specific focus on the application of queueing theory. The text integrates both theory and computation in its discussion of stochastic dynamic programming. The theory optimization criterion is first developed and proven before giving the computational methods to determine the numerical policies of the exploration of the application of the outlined principles. Nov. 1998 354 pp. 0-471-16120-9
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Examining a popular method of statistical analysis often used f or analysing multi\stratifird data, this volume takes a balanced view of mixed models by discussing some of the problems in their use and indicaing where more conventional fixed effect models might be preferred. Nov. 1998 0-471-95925-1
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In the book, new methods in the theory of differential equations on manifolds with singularities are presented. The semiclassical theory in quantum mechanics is employed, adapted to operators that are degenerate in a typical way. The degeneracies may be induced by singular geometries, e.g., conical or cuspidal ones. A large variety of non-standard degenerate operators are also discussed. The semiclassical approach yields new results and unexpected effects, also in classical situations. For instance, full asymptotic expansions for cuspidal singularities are constructed, and nonstationary problems on singular manifolds are treated. Moreover, finiteness theorems are obtained by using operator algebra methods in a unified framework. Finally the method of characteristics for general elliptic equations on manifolds with singularities is developed in the book. Nov. 1998 400 pp. 3-527-40086-9
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The central focus of this book is the search for optimal paths in graphs, a simple example being the search for the shortest connection from one place to another in a city. Structural properties of cost measures are studied and many combinatorial results about paths in graphs quoted. Nov. 1998 450 pp. 3-527-40054-0 3
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