Series: London Mathematical Society Lecture Note Series (No. 392)
ISBN: 9781107601093 Paperback
45 b/w illus. 12 tables
Dimensions: 228 x 152 mm
available from July 2011
This volume contains nine survey articles based on the invited lectures given at the 23rd British Combinatorial Conference, held at Exeter in July 2011. This biennial conference is a well-established international event, with speakers from all over the world. By its nature, this volume provides an up-to-date overview of current research activity in several areas of combinatorics, including extremal graph theory, the cyclic sieving phenomenon and transversals in Latin squares. Each article is clearly written and assumes little prior knowledge on the part of the reader. The authors are some of the world's foremost researchers in their fields, and here they summarise existing results and give a unique preview of the most recent developments. The book provides a valuable survey of the present state of knowledge in combinatorics. It will be useful to research workers and advanced graduate students, primarily in mathematics but also in computer science and statistics.
Preface
1. Counting planar maps, coloured or uncoloured Mireille Bousquet-Melou
2. A survey of PPAD-completeness for computing Nash equilibria Paul W. Goldberg
3. Hypergraph Turan problems Peter Keevash
4. Some new results in extremal graph theory V. Nikiforov
5. The cyclic sieving phenomenon: a survey Bruce Sagan
6. Order in building theory Koen Thas
7. Graphs, colours, weights and hereditary properties Andrew Thomason
8. Random geometric graphs Mark Walters
9. Transversals in Latin squares: a survey Ian Wanless.
Series: London Mathematical Society Lecture Note Series (No. 391)
ISBN: 9781107601000 Paperback
Dimensions: 228 x 152 mm
available from August 2011
Introduction
1. Introduction to fusion systems
2. The local theory of fusion systems
3. Fusion and homotopy theory
4. Fusion and representation theory
Appendix. Background facts about groups
References
List of notation
Index.
Series: London Mathematical Society Lecture Note Series (No. 390)
ISBN: 9781107621541 Paperback
35 b/w illus. 165 exercises
Dimensions: 228 x 152 mm
available from October 2011
This book provides a comprehensive treatment of the Gross-Pitaevskii equation with a periodic potential; in particular, the localized modes supported by the periodic potential. It takes the mean-field model of the Bose?Einstein condensation as the starting point of analysis and addresses the existence and stability of localized modes. The mean-field model is simplified further to the coupled nonlinear Schrodinger equations, the nonlinear Dirac equations, and the discrete nonlinear Schrodinger equations. One of the important features of such systems is the existence of band gaps in the wave transmission spectra, which support stationary localized modes known as the gap solitons. These localized modes realise a balance between periodicity, dispersion and nonlinearity of the physical system. Written for researchers in applied mathematics, this book mainly focuses on the mathematical properties of the Gross?Pitaevskii equation. It also serves as a reference for theoretical physicists interested in localization in periodic potentials
Preface
1. Formalism of the nonlinear Schrodinger equations
2. Justification of the nonlinear Schrodinger equations
3. Existence of localized modes in periodic potentials
4. Stability of localized modes
5. Traveling localized modes in lattices
Appendix A. Mathematical notations
Appendix B. Selected topics of applied analysis
References
Index.
Series: Cambridge Tracts in Mathematics (No. 189)
ISBN: 9780521898812 Hardback
15 b/w illus.
Dimensions: 228 x 152 mm
available from January 2012
In the past several decades the classical Perron-Frobenius theory for nonnegative matrices has been extended to obtain remarkably precise and beautiful results for classes of nonlinear maps. This nonlinear Perron?Frobenius theory has found significant uses in computer science, mathematical biology, game theory and the study of dynamical systems. This is the first comprehensive and unified introduction to nonlinear Perron?Frobenius theory suitable for graduate students and researchers entering the field for the first time. It acquaints the reader with recent developments and provides a guide to challenging open problems. To enhance accessibility, the focus is on finite dimensional nonlinear Perron-Frobenius theory, but pointers are provided to infinite dimensional results. Prerequisites are little more than basic real analysis and topology.
Preface
1. What is nonlinear Perron-Frobenius theory?
2. Non-expansiveness and nonlinear Perron?Frobenius theory
3. Dynamics of non-expansive maps
4. Sup-norm non-expansive maps
5. Eigenvectors and eigenvalues of nonlinear cone maps
6. Eigenvectors in the interior of the cone
7. Applications to matrix scaling problems
8. Dynamics of subhomogeneous maps
9. Dynamics of integral-preserving maps
Appendix A. The Birkhoff?Hopf theorem
Appendix B. Classical Perron?Frobenius theory
References
Index.
Series: Classics in Applied Mathematics
ISBN: 9780898719994 Paperback
Dimensions: 247 x 174 mm
available from January 2012
This classic textbook provides a unified treatment of spectral approximation for closed or bounded operators, as well as for matrices. Despite significant changes and advances in the field since it was first published in 1983, the book continues to form the theoretical bedrock for any computational approach to spectral theory over matrices or linear operators. This coverage of classical results is not readily available elsewhere. Spectral Approximation of Linear Operators offers in-depth coverage of properties of various types of operator convergence, the spectral approximation of non-self-adjoint operators, a generalization of classical perturbation theory, and computable error bounds and iterative refinement techniques, along with many exercises (with solutions), making it a valuable textbook for graduate students and reference manual for self-study.
Preface to the Classics Edition
Foreword
Preface
Notation
List of errata
1. The matrix eigenvalue problem
2. Elements of functional analysis: basic concepts
3. Elements of functional analysis: convergence and perturbation theory
4. Numerical approximation methods for integral and differential operators
5. Spectral approximation of a closed linear operator
6. Error bounds and localization results for the eigenelements
7. Some examples of applications
Appendix: discrete approximation theory
References
Solutions to exercises
Notation index
Subject index.