Series: Algorithms and Computation in Mathematics , Vol. 5
3rd ed., 2007, Approx. 665 p., 195 illus., Hardcover
ISBN: 978-3-540-72779-8
Due: August 28, 2007
About this textbook
The third edition of this standard textbook contains additional material: two new application sections (on graphical codes and their decoding) and about two dozen further exercises (with solutions, as throughout the text). Moreover, recent developments have been discussed and referenced, in particular for the travelling salesman problem. The presentation has been improved in many places (for instance, in the chapters on shortest paths and on colorings), and a number of proofs have been reorganized, making them more precise or more transparent.
Table of contents
Prefaces.- Basic Graph Theory.- Algorithms and Complexity.- Shortest Paths.- Spanning Trees.- The Greedy Algorithm.- Flows.- Combinatorial Applications.- Connectivity and Depth First Search.- Colorings.- Circulations.- The Network Simplex Algorithm.- Synthesis of Networks.- Matchings.- Weighted Matchings.- A Hard Problem: The TSP.- Appendix A: Some NP-Complete Problems.- Appendix B: Solutions.- Appendix C: List of Symbols.- References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1915
2007, VIII, 120 p., 35 illus., Softcover
ISBN: 978-3-540-73509-0
Due: August 14, 2007
About this book
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrodinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.
The volume investigates the structure of eigenvectors and looks at the number of their sign graphs ("nodal domains"), Perron components, graphs with extremal properties with respect to eigenvectors. The Rayleigh quotient and rearrangement of graphs form the main methodology.
Table of contents
1.Introduction.- 2.Graph Laplacians.- 3.Eigenfunctions and Nodal Domains.- 4.Nodal Domain Theorems for Special Graph Classes.- 5.Computational Experiments.- 6.Faber-Krahn Type Inequalities.- Appendices: A.Basic Notations.- B.Eigenfunctions Used in Figures.- C.List of Symbols.- References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1918
2007, Approx. 315 p., Softcover
ISBN: 978-3-540-73323-2
Due: August 14, 2007
About this book
Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).
Table of contents
Summary.- Representation Theory.- Paramodular Vectors.- Zeta Integrals.- Non-supercuspidal Representations.- Hecke Operators.- Proofs of the Main Theorems.- Tables for Representations of GSp(4).- References.- Index
Series: Lecture Notes in Mathematics , Vol. 1919
2007, VIII, 213 p., Softcover
ISBN: 978-3-540-73326-3
Due: August 21, 2007
About this book
The Paris-Princeton Lectures in Financial Mathematics, of which this is the third volume, will, on an annual basis, publish cutting-edge research in self-contained, expository articles from outstanding - established or upcoming! - specialists. The aim is to produce a series of articles that can serve as an introductory reference for research in the field. It arises as a result of frequent exchanges between the finance and financial mathematics groups in Paris and Princeton. The present volume sets standards with articles by Rene Carmona, Ivar Ekeland/Erik Taflin, Arturo Kohatsu-Higa, Pierre-Louis Lions/Jean-Michel Lasry, and Hyuen Pham.
Table of contents
R. Carmona: HJM: A Unified Approach to Dynamic Models for Fixed Income, Credit and Equity Markets.- I. Ekeland, Erik Taflin: Optimal Bond Portfolios.- A. Kohatsu-Higa: Models for Insider Trading with Finite Utility.- P.-L. Lions, J.-M. Lasry: Large Investor Trading Impacts on Volatility.- H. Pham: Some Applications and Methods of Large Deviations in Finance and Insurance.
2007, Approx. 550 p., Softcover
ISBN: 978-1-84628-969-9
Due: October 2007
About this textbook
Based on the authorsf classic text, Graph Theory with Applications, this book provides a modern and expanded treatment that takes into account the dramatic developments in the theory over the past 30 years. New features include:
more proofs of theorems; commonly-used proof techniques are also described and illustrated;
a greater emphasis on algorithms;
many new exercises, of varying levels of difficulty.
In addition, a selection of important open problems are highlighted and discussed at length.
The authors provide a coherent introduction suitable as a textbook for advanced undergraduate and graduate students in mathematics and computer scientists, and which also serves as an introduction to research in graph theory suitable for postgraduate students and researchers in mathematics, and also for physicists, chemists and engineers who use graph-theoretic techniques in their work
Table of contents
Graphs.- Subgraphs.- Connected Graphs.- Trees.- Separable and Nonseparable Graphs.- Tree-growing Procedures.- Algorithms and Complexity.- Connectivity.- Planar Graphs.- Stable Sets and Cliques.- Vertex Colourings.- Matchings.- Edge Colourings.- Hamilton Circuits.- Coverings and Packings in Directed Graphs.- Integer Flows and Coverings