Series: Encyclopedia of Mathematics and its Applications (No. 64)
Paperback (ISBN-13: 9780521118668)
This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.
* Multidisciplinary applications from game theory, optimisation, mathematical
programming, economics and statistics * Many results, most of them completely
proved * Minimal prerequisites: each section of the book is self-contained
and can be read independently
Preface; 1. Perron-Frobenius theory and matrix games; 2. Doubly stochastic matrices; 3. Inequalities; 4. Conditionally positive definite matrices; 5. Topics in combinatorial theory; 6. Scaling problems and their applications; 7. Special matrices in economic models; References; Index; Author index.
Hardback (ISBN-13: 9780521768481)
Dealing with all aspects of Monte Carlo simulation of complex physical systems encountered in condensed-matter physics and statistical mechanics, this book provides an introduction to computer simulations in physics. This edition now contains material describing powerful new algorithms that have appeared since the previous edition was published, and highlights recent technical advances and key applications that these algorithms now make possible. Updates also include several new sections and a chapter on the use of Monte Carlo simulations of biological molecules. Throughout the book there are many applications, examples, recipes, case studies, and exercises to help the reader understand the material. It is ideal for graduate students and researchers, both in academia and industry, who want to learn techniques that have become a third tool of physical science, complementing experiment and analytical theory.
* Contains material describing powerful new algorithms, recent technical
advances and key applications * Deals with all aspects of Monte Carlo simulation
encountered in condensed-matter physics and statistical mechanics * Includes
many applications, examples, recipes, case studies, and exercises to help
the reader understand the material
Preface; 1. Introduction; 2. Some necessary background; 3. Simple sampling Monte Carlo methods; 4. Importance sampling Monte Carlo methods; 5. More on importance sampling Monte Carlo methods of lattice systems; 6. Off-lattice models; 7. Reweighting methods; 8. Quantum Monte Carlo methods; 9. Monte Carlo renormalization group methods; 10. Non-equilibrium and irreversible processes; 11. Lattice gauge models: a brief introduction; 12. A brief review of other methods of computer simulation; 13. Monte Carlo simulations at the periphery of physics and beyond; 14. Monte Carlo studies of biological molecules; 15. Outlook; Appendix; Index.
Series: Cambridge Tracts in Theoretical Computer Science (No. 49)
Paperback (ISBN-13: 9780521106597)
First published in 1999, this book combines traditional graph theory with the matroidal view of graphs and throws light on mathematical aspects of network analysis. This approach is called here hybrid graph theory. This is essentially a vertex-independent view of graphs naturally leading into the domain of graphoids, a generalisation of graphs. This enables the authors to combine the advantages of both the intuitive view from graph theory and the formal mathematical tools from the theory of matroids. A large proportion of the material is either new or is interpreted from a fresh viewpoint. Hybrid graph theory has particular relevance to electrical network analysis, which was one of the earliest areas of application of graph theory. It was essentially out of developments in this area that hybrid graph theory evolved.
* Includes new results as well as synthesising and reworking last 30 years
of research * Forms a bridge between traditional graph theory and the matroidal
view of graphs, with applications in the hybrid analysis of networks *
First book with this view of subject
Preface; 1. Two dual structures of a graph; 2. Independence structures; 3. Basoids; 4. Pairs of trees; 5. Maximally distant pairs of trees; Bibliography; Index.
Series: Encyclopedia of Mathematics and its Applications (No. 73)
Paperback (ISBN-13: 9780521118842)
In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff’s concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are ‘close’ to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.
* Introduces the theory of semimodular lattices as a far-reaching generalization
of Boolean algebras * Examines the interdependence of related concepts
such as M-symmetry and conditions of MacLane and Dilworth * Has applications
to discrete mathematics, combinatorics, group theory and universal algebra
Preface; 1. From Boolean algebras to semimodular lattices; 2. M-symmetric lattices; 3. Conditions related to semimodularity, 0-conditions and disjointness properties; 4. Supersolvable and admissible lattices, consistent and strong lattices; 5. The covering graph; 6. Semimodular lattices of finite length; 7. Local distributivity; 8. Local modularity; 9. Congruence semimodularity; Master reference list; Table of notation; Index.
Hardback (ISBN-13: 9780521889445)
Paperback (ISBN-13: 9780521717939)
Richly illustrated with the images from observatories on the ground and in space, and computer simulations, this book shows how black holes were discovered, and discusses our current understanding of their role in cosmic evolution. This second edition covers new discoveries made in the past decade, including definitive proof of a black hole at the center of the Milky Way, evidence that the expansion of the Universe is accelerating, and the new appreciation of the connection between black holes and galaxy formation. There are entirely new chapters on gamma-ray bursts and cosmic feedback. Begelman and Rees blend theoretical arguments with observational results to demonstrate how both approaches contributed to this subject. Clear illustrations and photographs reveal the strange and amazing workings of our universe. The engaging style makes this book suitable for introductory undergraduate courses, amateur astronomers, and all readers interested in astronomy and physics.
* Covers new discoveries made in the past decade, with two entirely new
chapters on gamma-ray bursts and cosmic feedback * Richly illustrated with
clear, explanatory images revealing the strange and amazing workings of
our universe * Engaging style makes it suitable for introductory undergraduate
courses, amateur astronomers, and all readers interested in astronomy and
physics
1. Gravity triumphant; 2. Stars and their fates; 3. Black holes in our backyard; 4. Galaxies and their nuclei; 5. Quasars and kin; 6. Jets; 7. Blasts from the past; 8. Black holes in hibernation; 9. Cosmic feedback; 10. Checking up on Einstein; 11. Through the horizon; Appendix: Gravity and cosmic dimensions; Index.