EDITED BY MARC BEZEM
Universitetet i Bergen, Norway
Term Rewriting Systems
Description: Term rewriting systems developed out of mathematical logic and are an important part of theoretical computer science. They consist of sequences of discrete transformation steps where one term is replaced with another and have applications in many areas, from functional programming to automatic theorem proving and computer algebra. This book starts at an elementary level with the earlier chapters providing a foundation for the rest of the work. Much of the advanced material appears here for the first time in book form. Subjects treated include orthogonality, termination, completion, lambda calculus, higher-order rewriting, infinitary rewriting and term graph rewriting. Many exercises are included with selected solutions provided on the web. A comprehensive bibliography makes this book ideal both for teaching and research. A chapter is included presenting applications of term rewriting systems, with many pointers to actual implementations.
Contents: 1. Abstract reduction systems; 2. First-order term rewriting systems; 3. Examples of TRSs and special rewriting formats; 4. Orthogonality; 5. Properties of rewriting: decidability and modularity; 6. Termination; 7. Completion of equational specifications; 8. Equivalence of reductions; 9. Strategies; 10. Lambda calculus; 11. Higher order rewriting; 12. Infinitary rewriting; 13. Term graph rewriting; 14. Advanced ARS theory; 15. Rewriting based languages and systems; 16. Mathematical background.
Essential Information
ISBN, Binding, : 0-521-39115-6 Hardback
Pages: 890
Approximate Publication Date: c.01/08/2002
Main Subject Category: Theory of computation, data
Series: Cambridge Tracts in Theoretical Computer Science, No. 25
Market (Subject)
theoretical computer science, logic
Level
academic researchers, graduate students
Bibliographic Details
273 line diagrams
Comparable titles: BAADER and NIPKOW/Term Rewriting and All That/1998/0521 455200 REYNOLDS/Theory of Programming Languages/1998/0521 594146
FREDERIC HELEIN
Ecole Normale Superieure de Cachan
Harmonic Maps, Conservation Laws and Moving Frames
Description: The author presents an accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. The reader is then presented with a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A self-contained presentation of 'exotic' functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a ‘Coulomb moving frame’ is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces.
Contents: Preface; Introduction; Acknowledgements; Notations; 1. Geometric and analytic setting; 2. Harmonic maps with symmetries; 3. Compensations and exotic function spaces; 4. Harmonic maps without symmetries; 5. Surfaces with mean curvature in L2; References.
Essential Information
ISBN, Binding, : 0-521-81160-0 Hardback
Pages: 288
Approximate Publication Date: c.01/06/2002
Main Subject Category: Mathematics - analysis, probability
Series: Cambridge Tracts in Mathematics, No. 150
Market (Subject)
geometry, analysis, partial differential equations, mathematical physics
Level
academic researchers, graduate students
Comparable titles: EELLS and FUGLEDE/Harmonic Maps and Riemannian Polyhedra/2001/0521 773113 SERRE/Systems of Conservation Laws/Volume 1: 1999/0521582334/Volume 2: 2000/0521 633303 GUEST/Harmonic Maps, Loop Groups, and Integrable Systems/1997/0521 580854
CLAUS HERTLING
Max Planck Institut fur Mathematik, Bonn
Frobenius Manifolds and Moduli Spaces for Singularities
Description: The relations between Frobenius manifolds and singularity theory are treated here in a rigorous yet accessible manner. For those working in singularity theory or other areas of complex geometry, this book will open the door to the study of Frobenius manifolds. This class of manifolds are now known to be relevant for the study of singularity theory, quantum cohomology, mirror symmetry, symplectic geometry and integrable systems. The first part of the book explains the theory of manifolds with a multiplication on the tangent bundle. The second presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will find here a careful and sound study of the fundamental structures and results in this exciting branch of maths. This book will serve as an excellent resource for researchers and graduate students who wish to work in this area.
Contents: Part I. Multiplication on the Tangent Bundle: 1. Introduction to part 1; 2. Definition and first properties of F-manifolds; 3. Massive F-manifolds and Lagrange maps; 4. Discriminants and modality of F-manifolds; 5. Singularities and Coxeter groups; Part II. Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities: 6. Introduction to part 2; 7. Connections on the punctured plane; 8. Meromorphic connections; 9. Frobenius manifolds ad second structure connections; 10. Gauss-Manin connections for hypersurface singularities; 11. Frobenius manifolds for hypersurface singularities; 12. \mu-constant stratum; 13. Moduli spaces for singularities; 14. Variance of the spectral numbers.
Essential Information
ISBN, Binding, : 0-521-81296-8 Hardback
Pages: 272
Approximate Publication Date: c.01/07/2002
Main Subject Category: Geometry, topology
Series: Cambridge Tracts in Mathematics, No. 151
Market (Subject)
singularity theory, geometry
Level
academic researchers, graduate students
Bibliographic Details
7 line diagrams
Comparable titles: KULIKOV/Mixed Hodge Structures and Singularities/1998/0521 620600 LOOIJENGA/Isolated Singular Points on Complete Intersections/1984/0521 286743
CLAIRE VOISIN
Hodge Theory and Complex Algebraic Geometry I
Description: This is a modern introduction to Kaehlerian geometry and Hodge structure. It starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The book culminates with the Hodge decomposition theorem. In between, the author proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The second part of the book investigates the meaning of these results in several directions. The book is is completely self-contained and can be used by students, while its content gives an up-to-date account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.
Contents: Introduction; Part I. Preliminaries: 1. Holomorphic functions of many variables; 2. Complex manifolds; 3. Kahler metrics; 4. Sheaves and cohomology; Part II. The Hodge Decomposition: 5. Harmonic forms and cohomology; 6. The case of Kahler manifolds; 7. Hodge structures and polarisations; 8. Holomorphic de Rham complexes; Part III. Variations of Hodge Structure: 9. Families and deformations; 10. Variations of Hodge structure; Part IV. Cycles and Cycle Classes: 11. Hodge classes; 12. The Abel-Jacobi map; Bibliography; Index.
Essential Information
ISBN, Binding, : 0-521-80260-1 Hardback
Pages: 250
Approximate Publication Date: c.01/09/2002
Main Subject Category: Geometry, topology
Series: Cambridge Studies in Advanced Mathematics, No. 76
Market (Subject)
mathematics, complex algebraic geometry
Level
academic researchers, graduate students
Bibliographic Details
30 exercises
Comparable titles: BEAUVILLE/Complex Algebraic Surfaces/1996/0521 498422 KIRWAN/Complex Algebraic Curves/1992/0521 423538