Foata, D., University Louis Pasteur, Strasbourg, France
Han, G.-N., University Louis Pasteur, Strasbourg, France
(Eds.)

The Andrews Festschrift
Seventeen Papers on Classical Number Theory and Combinatorics

2001. X, 426 pp. Softcover
3-540-41491-6

This book contains seventeen contributions made to George Andrews on the occasion of his sixtieth
birthday, ranging from classical number theory (the theory of partitions) to classical and algebraic
combinatorics. Most of the papers were read at the 42nd session of the Seminaire Lotharingien de
Combinatoire that took place at Maratea, Basilicata, in August 1998.
This volume contains a long memoir on Ramanujan's Unpublished Manuscript and the Tau functions
studied with a contemporary eye, together with several papers dealing with the theory of partitions.
There is also a description of a maple package to deal with general q-calculus. More subjects on
algebraic combinatorics are developed, especially the theory of Kostka polynomials, the ice square
model, the combinatorial theory of classical numbers, a new approach to determinant calculus.

Keywords: Partitions, q-calculus, Kostka polynomials, permutations statistics, determinant calculus

Contents: Dominique Foata, Guo-Niu Han Introduction George E. Andrews Some Debts I Owe
Richard Askey The Work of George Andrews: A Madison Perspective Bruce C. Berndt, Ken Ono
Ramanujan Unpublished Manuscript on the Partition and Tau Functions with Proofs and Commentary
Frank Garvan Qseries maple tutorial: A q-product tutorial for a q-series maple package G.-N. Han, A.
Randrianarivony, J. Zeng Un autre q-analogue des nombres d?uler Michael D. Hirschhorn Three
classical results on representations of a number Dongsu Kim, Dennis Stanton Simultaneous maj statistics
David P. Little An extension of Franklin Bijection George E. Andrews, Peter Paule MacMahon Partition
Analysis IV: Hypergeometric Multisums Anatol N. Kirillov, Anne Schilling, Mark Shimozono Various
representations of the generalized Kostka polynomials Herbert S. Wilf The number-theoretic content of
the Jacobi triple product identity Arturo Carpi, Aldo de Luca Words and Repeated Factors Adriano
Garsia, Mark Haiman, Glenn Tesler Explicit Plethystic Formulas for Macdonald q,t-Kostka Coefficients
S. Ole Warnaar Supernomial coefficients, Bailey lemma and Rogers-Ramanujan-type identities. A survey
of results and open problems D. Foata, G.-N. Han The triple, quintuple and septuple product identities
revisited A. Lascoux Square-ice enumeration Christian Krattenthaler Advanced Determinant Calculus

Alefeld, G., University of Karlsruhe, Germany
Rohn, J., University Karlovy, Praha, Czech Republic
Rump, S., Technical University Hamburg-Harburg, Hamburg, Germany
Yamamoto, T., Ehime University, Matsuyama, Japan
(Eds.)

Symbolic Algebraic Methods and Verification Methods

2001. IX, 266 pp. 40 figs. Softcover
3-211-83593-8

The usual "implementation" of real numbers as floating point numbers on existing computers has the
well-known disadvantage that most of the real numbers are not exactly representable in floating point.
Also the four basic arithmetic operations can usually not be performed exactly. During the last years
research in different areas has been intensified in order to overcome these problems. (LEDA-Library by
K. Mehlhorn et al., "Exact arithmetic with real numbers" by A. Edalat et al., Symbolic algebraic
methods, verification methods). The latest development is the combination of symbolic-algebraic
methods and verification methods to so-called hybrid methods.
This book contains a collection of worked out talks on these subjects given during a Dagstuhl seminar at
the Forschungszentrum f?r Informatik, Schlo? Dagstuhl, Germany, presenting the state of the art.

Contents: Introduction (G. Alefeld, J. Rohn, S. Rump, T. Yamamoto).- Topological Concepts for
Hierarchies of Variables, Types and Controls (R. Albrecht).- Modifications of the Oettli-Prager
Theorem with Application to the Eigenvalue Problem (G. Alefeld, V. Kreinovich, G. Mayer).-
Symbolic-Numeric Algorithms for Polynomials: Some Recent Results (R. Corless).- Symbolic-Numeric
QD-Algorithms with Applications in Function Theory and Linear Algebra (A. Cuyt).- On the
Isoefficiency of the Parallel Descartes Method (Th. Decker, W. Krandick).- Matrix Methods for Solving
Algebraic Systems (I. Z. Emiris).- A Feasibility Result for Interval Gaussian Elimination Relying on Graph
Structure (A. Frommer).- Solution of Systems of Polynomial Equations by Using Bernstein Expansion (J.
Garloff, A. P. Smith).- Symbolic-Algebraic Computations in Modeling Language for Mathematical
Programming (D. M. Gay).- Translation of Taylor Series into LFT Expansions (R. Heckmann).- Quasi
Convex-Concave Extensions (Chr. Jansson).- Rewriting, Induction and Decision Procedures: A Case
Study of Presburger Arithmetic (D. Kapur).- Derivative-Based Subdivision in Multi-dimensional Verified
Gaussian Quadrature (B. Lang).- On the Shape of the Fixed Points of ?f?(?x?) = ?A??x? + ?b? (G.
Mayer, I. Warnke).- Exact Computation with leda real - Theory and Geometric Applications (K.
Mehlhorn, St. Schirra).- Numerical Verification Method for Solutions of Nonlinear Hyperbolic Equations
(T. Minamoto).- Geometric Series Bounds for the Local Errors of Taylor Methods for Linear
n-th-Order ODEs (M. Neher).- Save Numerical Error Bounds for Solutions of Nonlinear Elliptic
Boundary Value Problems (M. Plum).- Fast Verification Algorithms in MATLAB (S. Rump).- The Linear
Complementarity Problem with Interval Data (U. Sch?fer).- Some Numerical Methods for Nonlinear
Least Squares Problems (St. Shakhno).- A New Insight of the Shortley-Weller Approximation for
Dirichlet Problems (T. Yamamoto).- How Orthogonality is Lost in Krylov Methods (J. Zemke).

Graham Priest

An Introduction to Non-Classical Logic

This book is an introduction to non-classical propositional logics. It brings together for the first time in a textbook a range of topics in logic, many of them of relatively recent origin, including modal, conditional, intuitionist, many-valued, paraconsistent, relevant and fuzzy logics. Students with a basic understanding of classical logic will find this an invaluable introduction to an area that has become of central importance in both logic and philosophy. It will be of interest to readers studying logic, and, more widely, to readers working in mathematics and computer science.

Introduction; 1. Classical logic and the material conditional; 2. Basic modal logic; 3. Normal modal logics; 4. Non-normal worlds; strict conditionals; 5. Conditional logics; 6. Intuitionist logic; 7. Many-valued logics; 8. First degree entailment; 9. Basic relevant logic; 10. Mainstream relevant logics; 11. Fuzzy logic; 12. Conclusion: a historical perspective.

0 521 79098 0 Hardcover 200pp
0 521 79434 X Papaerback 200pp

Feb. 2001

W. Noel Cottingham and Derek A. Greenwood

An Introduction to Nuclear Physics

This clear and concise introduction to nuclear physics provides an excellent basis for a core undergraduate course in this area. The book opens by setting nuclear physics in the context of elementary particle physics and then shows how simple models can provide an understanding of the properties of nuclei, both in their ground states and excited states, and also of the nature of nuclear reactions. The book also includes chapters on nuclear fission, its application in nuclear power reactors, the role of nuclear physics in energy production and nucleosynthesis in stars. This new edition contains several additional topics: muon-catalysed fusion, the nuclear and neutrino physics of supernovae, neutrino mass and neutrino oscillations, and the biological effects of radiation. A knowledge of basic quantum mechanics and special relativity is assumed. Appendices deal with other more specialized topics. Each chapter ends with a set of problems for which outline solutions are provided.

1. Prologue; 2. Leptons and the electromagnetic and weak interactions; 3. Nucleons and the strong interaction; 4. Nuclear sizes and nuclear masses; 5. Ground state properties of nuclei; the shell model; 6. Alpha decay and spontaneous fission; 7. Excited states of nuclei; 8. Nuclear reactions; 9. Power from nuclear fission; 10. Nuclear fission; 11. Nucleosynthesis in stars; 12. Beta decay and gamma decay; 13. The passage of energetic particles through matter; Appendices: A. Cross-sections; B. Density of states; C. Angular momentum; D. Unstable states and resonances; E. Radioactivity and radiological units.

0 521 65733 4 Paperback Feb.2001 296pp
0 521 65149 2 Hardcover Feb.2001 296pp

Jun Kigami

Analysis on Fractals

This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.

Introduction; 1. Geometry of self-similar sets; 2. Analysis on limits of networks; 3. Construction of Laplacians on P. C. F. self-similar structures; 4. Eigenvalues and eigenfunctions of Laplacians; 5. Heat kernels; Appendix A: Additional fact; Appendix B: Mathematical backgrounds; Bibliography; List of notations; Index.

Cambridge Tracts in Mathematics, 143

0 521 79321 1 Hardcover May2001 216pp

B. Bollobas

Random Graphs 2nd editon

This is a new edition of the now classic text. The already extensive treatment given in the first edition has been heavily revised by the author. The addition of two new sections, numerous new results and 150 references means that this represents an up to date and comprehensive account of random graph theory. The theory (founded by Erd�s and R駭yi in the late fifties) aims to estimate the number of graphs of a given degree that exhibit certain properties. It not only has numerous combinatorial applications, but also serves as a model for the probabilistic treatment of more complicated random structures. This book, written by an acknowledged expert in the field, can be used by mathematicians, computer scientists and electrical engineers, as well as people working in biomathematics. It is self-contained, and with numerous exercises in each chapter, is ideal for advanced courses or self study.

1. Probability theoretic preliminaries; 2. Models of random graphs; 3. The degree sequence; 4. Small subgraphs; 5. The evolution of random graphs - sparse components; 6. The evolution of random graphs-the giant component; 7. Connectivity and components; 8. Long paths and cycles; 9. The automorphism group; 10. The diameter; 11. Cliques, independent sets and colouring; 12. Ramsey theory; 13. Explicit constructions; 14. Sequences, matrices and permutations; 15. Sorting algorithms; 16. Random graphs of small order.

0 521 79722 5 Paperback Aug.2001 50pp