Hardback
ISBN:9780521517188
Publication date:November 2011
202pages
64 b/w illus. 10 tables
Dimensions: 228 x 152 mm
Weight: 0.41kg
himon Even's Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the field. This thoroughly revised second edition, with a foreword by Richard M. Karp and notes by Andrew V. Goldberg, continues the exceptional presentation from the first edition and explains algorithms in a formal but simple language with a direct and intuitive presentation. The book begins by covering basic material, including graphs and shortest paths, trees, depth-first-search and breadth-first search. The main part of the book is devoted to network flows and applications of network flows, and it ends with chapters on planar graphs and testing graph planarity.
* Classic text with revisions by the author offers an attractive choice of topics with simple yet precise explanations
* Foreword by Richard M. Karp
1. Paths in graphs
2. Trees
3. Depth-first search
4. Ordered trees
5. Flow in networks
6. Applications of network flow techniques
7. Planar graphs
8. Testing graph planarity.
Hardback
Series: Cambridge Studies in Advanced Mathematics(No. 134)
ISBN:9781107020641
Dimensions: 228 x 152 mm
available from May 2012
Introduction
1. First and second variational formulas for area
2. Volume comparison theorem
3. Bochner?Weitzenbock formulas
4. Laplacian comparison theorem
5. Poincare inequality and the first eigenvalue
6. Gradient estimate and Harnack inequality
7. Mean value inequality
8. Reilly's formula and applications
9. Isoperimetric inequalities and Sobolev inequalities
10. The heat equation
11. Properties and estimates of the heat kernel
12. Gradient estimate and Harnack inequality for the heat equation
13. Upper and lower bounds for the heat kernel
14. Sobolev inequality, Poincare inequality and parabolic mean value inequality
15. Uniqueness and maximum principle for the heat equation
16. Large time behavior of the heat kernel
17. Green's function
18. Measured Neumann?Poincare inequality and measured Sobolev inequality
19. Parabolic Harnack inequality and regularity theory
20. Parabolicity
21. Harmonic functions and ends
22. Manifolds with positive spectrum
23. Manifolds with Ricci curvature bounded from below
24. Manifolds with finite volume
25. Stability of minimal hypersurfaces in a 3-manifold
26. Stability of minimal hypersurfaces in a higher dimensional manifold
27. Linear growth harmonic functions
28. Polynomial growth harmonic functions
29. Lq harmonic functions
30. Mean value constant, Liouville property, and minimal submanifolds
31. Massive sets
32. The structure of harmonic maps into a Cartan?Hadamard manifold
Appendix A. Computation of warped product metrics
Appendix B. Polynomial growth harmonic functions on Euclidean space
References
Index.
Hardback
Series: Encyclopedia of Mathematics and its Applications(No. 146)
ISBN:9780521113090
32 b/w illus.
Dimensions: 234 x 156 mm
available from June 2012
The sphere is what might be called a perfect shape. Unfortunately nature is imperfect and many bodies are better represented by an ellipsoid. The theory of ellipsoidal harmonics, originated in the nineteenth century, could only be seriously applied with the kind of computational power available in recent years. This, therefore, is the first book devoted to ellipsoidal harmonics. Topics are drawn from geometry, physics, biosciences and inverse problems. It contains classical results as well as new material, including ellipsoidal bi-harmonic functions, the theory of images in ellipsoidal geometry and vector surface ellipsoidal harmonics, which exhibit an interesting analytical structure. Extended appendices provide everything one needs to solve formally boundary value problems. End-of-chapter problems complement the theory and test the reader's understanding. The book serves as a comprehensive reference for applied mathematicians, physicists, engineers and for anyone who needs to know the current state of the art in this fascinating subject.
Prologue
1. The ellipsoidal system and its geometry
2. Differential operators in ellipsoidal geometry
3. Lame functions
4. Ellipsoidal harmonics
5. The theory of Niven and Cartesian harmonics
6. Integration techniques
7. Boundary value problems in ellipsoidal geometry
8. Connection between sphero-conal and ellipsoidal harmonics
9. The elliptic functions approach
10. Ellipsoidal bi-harmonic functions
11. Vector ellipsoidal harmonics
12. Applications to geometry
13. Applications to physics
14. Applications to low-frequency scattering theory
15. Applications to bioscience
16. Applications to inverse problems
Epilogue
Appendix A. Background material
Appendix B. Elements of dyadic analysis
Appendix C. Legendre functions and spherical harmonics
Appendix D. The fundamental polyadic integral
Appendix E. Forms of the Lame equation
Appendix F. Table of formulae
Appendix G. Miscellaneous relations
Bibliography
Index.
Hardback
ISBN:9780521767248
260 b/w illus. 10 colour illus. 50 tables 300 exercises
Dimensions: 247 x 174 mm
available from July 2012
1. A tour of matroids
2. Cryptomorphisms
3. New matroids from old
4. Graphic matroids
5. Finite geometry
6. Representable matroids
7. Other matroids
8. Matroid minors
9. The Tutte polynomial
Appendix: projects
Index.
EMS Tracts in Mathematics Vol. 17
ISBN 978-3-03719-099-9
DOI 10.4171/099
November 2011, 415 pages, hardcover, 17 x 24 cm.
The p-Laplace equation is the main prototype for nonlinear elliptic problems and forms a basis for various applications, such as injection moulding of plastics, nonlinear elasticity theory and image processing. Its solutions, called p-harmonic functions, have been studied in various contexts since the 1960s, first on Euclidean spaces and later on Riemannian manifolds, graphs and Heisenberg groups. Nonlinear potential theory of p-harmonic functions on metric spaces has been developing since the 1990s and generalizes and unites these earlier theories.
This monograph gives a unified treatment of the subject and covers most of the available results in the field, so far scattered over a large number of research papers. The aim is to serve both as an introduction to the area for an interested reader and as a reference text for an active researcher. The presentation is rather self-contained, but the reader is assumed to know measure theory and functional analysis.
The first half of the book deals with Sobolev type spaces, so-called Newtonian spaces, based on upper gradients on general metric spaces. In the second half, these spaces are used to study p-harmonic functions on metric spaces and a nonlinear potential theory is developed under some additional, but natural, assumptions on the underlying metric space.
Each chapter contains historical notes with relevant references and an extensive index is provided at the end of the book.