| 2010 | Hardcover | * ISBN 978-3-11-021808-4
Series: de Gruyter Studies in Mathematics 19
* This book contains an introductory and comprehensive account of the theory of (symmetric) Dirichlet forms. Moreover this analytic theory is unified with the probabilistic potential theory based on symmetric Markov processes and developed further in conjunction with the stochastic analysis based on additive functional.
Since the publication of the first edition in 1994, this book has attracted constant interests from readers and is by now regarded as a standard reference for the theory of Dirichlet forms.
For the present second edition, the authors not only revised the existing text, but also added sections on capacities and Sobolev type inequalities, irreducible recurrence and ergodicity, recurrence and Poincare type inequalities, the Donsker-Varadhan type large deviation principle, as well as several new exercises with solutions.
The book addresses to researchers and graduate students who wish to comprehend the area of Dirichlet forms and symmetric Markov processes.
ISBN: 978-0-470-17793-8
Hardcover
768 pages
March 2011
The purpose of this handbook is to provide an accessible and comprehensive compendium of Monte Carlo techniques and related topics. It contains a mix of theory (summarized), algorithms (pseudo and actual), and applications. Since the audience is broad, the theory is kept to a minimum, this without sacrificing rigor.
The book is intended to be used as an essential guide to Monte Carlo methods to quickly look up ideas, procedures, formulas, pictures, etc., rather than purely a monograph for researchers or a textbook for students.
As the popularity of these methods continues to grow, and new methods are developed in rapid succession, the staggering number of related techniques, ideas, concepts and algorithms makes it difficult to maintain an overall picture of the Monte Carlo approach. This book attempts to encapsulate the emerging dynamics of this field of study.
ISBN: 978-0-470-69750-4
Hardcover
264 pages
March 2011
Most books in reliability theory are dealing with a description of component and system states as binary: functioning or failed. However, many systems are composed of multi-state components with different performance levels and several failure modes. There is a great need in a series of applications to have a more refined description of these states, for instance, the amount of power generated by an electrical power generation system or the amount of gas that can be delivered through an offshore gas pipeline network.
This book provides a descriptive account of various types of multistate system, bound-for multistate systems, probabilistic modeling of monitoring and maintenance of multistate systems with components along with examples of applications.
* Looks at modern multistate reliability theory with applications covering a refined description of components and system states.
* Presents new research, such as Bayesian assessment of system availabilities and measures of component importance.
* Complements the methodological description with two substantial case studies.
Reliability engineers and students involved in the field of reliability, applied mathematics and probability theory will benefit from this book.
Oxford Graduate Texts in Mathematics 21
704 pages | 266 illustrations | 234x156mm
978-0-19-856694-6 | Hardback | February 2011 (estimated)
978-0-19-960339-8 | Paperback
A major revision of a classic text, with more than 30% new material
Careful, lucid exposition from an author at the forefront of research
Contains over 700 exercises at section ends
Every relevant major proof is given in full
Lists unsolved problems and describes progress towards their solutions
More than 200 new exercises
New chapter covering and proving Seymour's Decomposition Theorem
New chapter on research in representability and structure
Coverage of Dowling matroids
Inclusion of Tutte's Linking Theorem
Addition of proofs of the excluded-minor theorems for regular, ternary and graphic matrices
Updated and enlarged discussion of unsolved problems
* What is the essence of the similarity between linearly independent sets of columns of a matrix and forests in a graph*
* Why does the greedy algorithm produce a spanning tree of minimum weight in a connected graph*
* Can we test in polynomial time whether a matrix is totally unimodular*
Matroid theory examines and answers questions like these. Seventy-five years of study of matroids has seen the development of a rich theory with links to graphs, lattices, codes, transversals, and projective geometries. Matroids are of fundamental importance in combinatorial optimization and their applications extend into electrical and structural engineering.
This book falls into two parts: the first provides a comprehensive introduction to the basics of matroid theory, while the second treats more advanced topics. The book contains over seven hundred exercises and includes, for the first time in one place, proofs of all of the major theorems in the subject. The last two chapters review current research and list more than eighty unsolved problems along with a description of the progress towards their solutions.
Readership: Mathematicians, computer scientists and engineers with interests in combinatorics and combinatorial optimization, graph theory, lattice theory or projective geometry.
1: Basic definitions and examples
2: Duality
3: Minors
4: Connectivity
5: Graphic matroids
6: Representable matroids
7: Constructions
8: Higher connectivity
9: Binary matroids
10: Excluded-minor theorems
11: Submodular functions and matroid union
12: The Splitter Theorem
13: Seymour's Decomposition Theorem
14: Research in representability and structure
15: Unsolved problems
Some interesting matroids
References
Notation
Index