Ravi P. Agarwal, Maria Meehan, Donal O'Regan
Fixed Point Theory and Applications
(Cambridge Tracts in Mathematics vol.141)
Description
This book provides a clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, among others. Starting from the basics of Banach's contraction theorem, most of the main results and techniques are developed: fixed point results are
established for several classes of maps and the three main approaches to establishing continuation principles are presented. The theory is applied to many areas of current interest in analysis, with topological considerations playing a crucial role, including a final chapter on the relationship with degree theory.
Researchers and graduate students in applicable analysis will find this to be a useful survey of the fundamental principles of the subject. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type.
Chapter Contents
Preface; 1. Contraction; 2. Nonexpansive maps; 3. Continuation methods for contractive nonexpansive maps; 4. The theorems of Brouwer, Schauder and Mvnch; 5. Nonlinear alternatives of Leray-Schauder type; 6. Continuation principles for condensing maps; 7. Fixed point theorems in conical shells; 8. Fixed point
theory in Hausdorff locally convex linear topological spaces; 9. Contractive and nonexpansive multivalued mappings; 10. Multivalued maps with continuous selection; 11. Multivalued maps with closed graph; 12. Degree theory; 13. References; Index.
ISBN: 0-521-80250-4
Binding: Hardback
Pages: 181
Figures: 95 exercises
Published: 22 March 2001
George E. Andrews, Richard Askey, Ranjan Roy
Special Functions, paperback edition
(Encyclopedia of Mathematics and its Applications)
Description
Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric
series, including Bessel functions and classical orthogonal polynomials, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included.
Other topics includeq-extensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics.
ISBN: 0-521-78988-5
Binding: Paperback
Pages: 680
Published: 12 April 2001
Ross Honsberger
Mathematical Chestnuts from Around the World
(Dolciani Mathematical Expositions Series)
Description
Ross Honsberger has compiled another collection of miscellaneous gems from elementary mathematics, this time from sources the world over, and ranging from the latest International Olympiads all the way back to Euclid. Each one casts light on a striking result or a brilliant device and any reader with only a modest
mathematical background will appreciate the ingenious solutions that are also presented.
Chapter Contents
1. Problems from Ireland; 2. Three solutions to an old chestnut; 3. Problems from Eotvos-Kurschak competitions; 4. Polish math olympiads; 5. East German olympiads; 6. Problems from Pi Mu
Epsilon Journal; 7. Austrian-Polish math olympiads; 8. Problems from Quantum; 9. Bulgarian problems for 11-14 year olds; 10. Cusumano's challenge; 11. Five easy problems from Leningrad; 12. An arithmetic puzzle; 13. Gleanings from the Mathematical Gazette; 14. Problems from the Putnam contest; 15. A second
look at a problem from Romania; 16. 32 miscellaneous problems; 17. Two problems in combinatorics; 18. An unused problem from the 1988 International Olympiad; 19. Four problems from the 1995 International Olympiad; 20. Two geometry problems; 21. An unlikely perfect square; 22. The nine-point circle and Coolidge's
theorem, the De Longchamps point of a triangle, Cantor's theorem, and Napoleon's theorem; 23. A problem from the Philippines; 24. Four solutions by George Evagelopoulos; 25. A Canadian problem; 26. A function of exponential order; Solutions.
ISBN: 0-883-85330-2
Binding: Paperback
Size: 228 x 154 mm
Pages: 220
Published: 29 March 2001
John P. Mayberry
The Foundations of Mathematics in the Theory of Sets
(Encyclopedia of Mathematics and its Applications , vol.82)
Description
This book presents a unified approach to the foundations of mathematics in the theory of sets, covering both conventional and finitary (constructive) mathematics. It is based on a philosophical, historical and mathematical analysis of the relation between the concepts of Natural number・and 壮et・ This leads
to an investigation of the logic of quantification over the universe of sets and a discussion of its role in second order logic, as well as in the analysis of proof by induction and definition by recursion.
The subject matter of the book falls on the borderline between philosophy and mathematics, and should appeal to both philosophers and mathematicians with an interest in the foundations of mathematics.
Chapter Contents
Preface; Part I. Preliminaries: 1. The idea of foundations of mathematics; 2. Simple arithmetic; Part II. Basic Set Theory: 3. Semantics, ontology and logic; 4. The principal axioms and definitions of set theory; Part III. Cantorian Set Theory: 5. Cantorian finitism; 6. The axiomatic method; 7. Axiomatic set theory; Part IV. Euclidean Set Theory: 8. Euclidian finitism; 9. The Euclidean theory of cardinality; 10. The theory of simply
infinite systems; 11. Euclidean set theory from the Cantorian standpoint; 12. Envoi; Appendices; Bibliography; Index.
ISBN: 0-521-77034-3
Binding: Hardback
Pages: 456
Published: 22 March 2001
M. Osborne
Simplicial Algorithms for Minimizing Polyhedral Functions
Description
This book provides the first general account of the development of simplicial algorithms. These include the ubiquitous simplex method of linear programming, widely used in industrial optimization and strategic decision making. They also include methods important in data analysis, such as problems involving very large data sets. The theoretical development is based on a new way of representing the underlying geometry of polyhedra
functions (functions whose graphs are made up of plane faces), and is capable of resolving problems which occur when combinatorially large numbers of faces intersect at each vertex.
Chapter Contents
1. Some basic convex analysis; 2. Introduction to Polyhedra functions; 3. Linear programming algorithms; 4. Piecewise linear separable problems; 5. Rank regression problems; 6. Polyhedral
SBN: 0-521-79133-2
Binding: Hardback
Size: 236 x 162 mm
Pages: 272
Figures: 13 line diagrams 38 tables
Published: 15 March 2001
Edited by S. Roberts, R. Everson
Independent Component Analysis
Contributors
Stephen Roberts, Richard Everson, Aapo Hyvdrinen, Hagai Attias, Juha Karhunen, Lucas Parra, Clay Spence, Jean-Frangois Cardoso, Dinh-Tuan Pham, Michael Zibulevsky, Barak Pearlmutter, Pau Bofill, Pavel Kisilev, James Miskin, David MacKay, Te-Won Lee, Michael S. Lewicki, Mark Girolami, William Penny
Description
Independent Component Analysis (ICA) has recently become an important tool for modelling and understanding empirical datasets. It is a method of separating out independent sources from linearly mixed data, and belongs to the class of general linear models. ICA provides a better decomposition than other
well-known models such as principal component analysis. This self-contained book contains a structured series of edited papers by leading researchers in the field, including an extensive introduction to ICA. The major theoretical bases are reviewed from a modern perspective, current developments are surveyed
and many case studies of applications are described in detail. The latter include biomedical examples, signal and image denoising and mobile communications. ICA is discussed in the framework of general linear models, but also in comparison with other paradigms such as neural network and graphical modelling methods. The book is ideal for researchers and graduate students in the field.
SBN: 0-521-79298-3
Binding: Hardback
Size: 236 x 160 mm
Pages: 352
Figures: 99 figures
Published: 1 March 2001
G. Sapiro
Geometric Partial Differential Equations and Image Analysis
Description
This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. State-of-the-art practical results in a large number
of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practitioners. It is intened to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.
Chapter Contents
1. Basic mathematical background; 2. Geometric curve and surface evolution; 3. Geodesic curves and minimal surfaces; 4. Geometric diffusion of scalar images; 5. Geometric diffusion of vector valued images; 6. Diffusion on non-flat manifolds; 7. Contrast enhancement; 8. Additional theories and applications
SBN: 0-521-79075-1
Binding: Hardback
Size: 236 x 162 mm
Pages: 440
Weight: 0.677kg
Figures: 38 line diagrams 43 half-tones 26 colour plates
Published: 5 April 2001