Brown, R.F.; Furi, M.; Gorniewicz, L.; Jiang, B. (Eds.)

Handbook of Topological Fixed Point Theory

2005, IX, 971 p., Hardcover
ISBN: 1-4020-3221-8

About this book

This book is the first in the world literature presenting all new trends in topological fixed point theory. Until now all books connected to the topological fixed point theory were devoted only to some parts of this theory.

This book will be especially useful for post-graduate students and researchers interested in the fixed point theory, particularly in topological methods in nonlinear analysis, differential equations and dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

Table of contents

Preface.
I. Homological Methods in Fixed Point Theory.
1. Coincidence theory. 2. On the Lefschetz fixed point theorem. 3. Linearizations for maps of nilmanifolds and solvmanifolds. 4. Homotopy minimal periods. 5. Perodic points and braid theory. 6. Fixed point theory of multivalued weighted maps. 7. Fixed point theory for homogeneous spaces ? a brief survey.
II. Equivariant Fixed Point Theory.
8. A note on equivariant fixed point theory. 9. Equivariant degree. 10. Bifurcations of solutions of SO (2)-symmetric nonlinear problems with variational structure.
III. Nielsen Theory.
11. Nielsen root theory. 12. More about Nielsen theories and their applications. 13. Algebraic techniques for calculating the Nielsen number on hyperbolic surfaces. 14. Fibre techniques in Nielsen theory calculations. 15. Wecken theorem for fixed and periodic points. 16. A primer of Nielsen fixed point theory. 17. Nielsen fixed point theory on surfaces. 18. Relative Nielsen theory.
IV. Applications.
19. Applicable fixed point principles. 20. The fixed point index of the Poincare translation. 21. On the existence of equilibria and fixed points of maps under constraints. 22. Topological fixed point theory and nonlinear differential equations. 23. Fixed point results based on the Wazeski method.

N. Balakrishnan McMaster University, Ontario, Canada
I. G Bairamov Izmir University of Economics, Ismir, Balcova, Turkey
O. L Gebizlioglu Ankara University, Ankara, Tandogan, Turkey

Advances on Models, Characterizations and Applications

Series: Statistics: Textbooks and Monographs Volume: 180
ISBN: 0-8247-4022-X
Publication Date: 5/31/2005
Number of Pages: 256

Comprises self-contained chapters contributed by world-renowned authorities
Presents an up-to-date exposition of the recent developments in important properties of statistical distributions
Covers advances on inferential procedures for several distributions and models
Relates these advances to real-world applications and problems

Statistical distributions are one of the most important applied mathematical tools across a wide spectrum of disciplines, including engineering, biological sciences, and health and social sciences. Since they are used to model observed data and ultimately to develop inferential procedures, understanding the properties of statistical distributions is critical to developing optimal inferential methods and validating the resulting model assumptions. Advances on Models, Characterizations and Applications offers up-to-date information on many recent developments in the field.

Comprising fourteen self-contained chapters contributed by internationally renowned experts, this book delineates recent developments on characterizations and other important properties of several distributions, inferential issues related to these models, and several applications of the models to real-world problems. Each chapter is rich with references for further study or more in-depth information on each topic and reflects work presented at the International Conference on Advances on Characterizations, Models, and Applications held in Antalya, Turkey in December 2001.

Advances on Models, Characterizations and Applications provides an updated account of important properties of statistical distributions that reflects their deep importance and broad application and is a welcome addition to the literature.

Table of Contents

Richard A Mollin Calgary, Alberta, Canada

Codes: The Guide to Secrecy From Ancient to Modern Times

Series: Discrete Mathematics and Its Applications Volume: 33
ISBN: 1-58488-470-3
Publication Date: 5/24/2005
Number of Pages: 704

Presents self-contained, thorough, and vibrantly illustrated coverage accessible to both professionals and laypersons
Provides an intuitive approach with illustrations to provide an overview of the topics for the general reader that does not require a mathematical approach
Incorporates more than 200 footnotes and 300 references for access to more in-depth information and further reading
Contains all necessary mathematics, requisite probability theory, and exercises organized by chapter in the appendices

From the Rosetta Stone to public-key cryptography, the art and science of cryptology has been used to unlock the vivid history of ancient cultures, to turn the tide of warfare, and to thwart potential hackers from attacking computer systems. Codes: The Guide to Secrecy from Ancient to Modern Times explores the depth and breadth of the field, remaining accessible to the uninitiated while retaining enough rigor for the seasoned cryptologist.

The book begins by tracing the development of cryptology from that of an arcane practice used, for example, to conceal alchemic recipes, to the modern scientific method that is studied and employed today. The remainder of the book explores the modern aspects and applications of cryptography, covering symmetric- and public-key cryptography, cryptographic protocols, key management, message authentication, e-mail and Internet security, and advanced applications such as wireless security, smart cards, biometrics, and quantum cryptography. The author also includes non-cryptographic security issues and a chapter devoted to information theory and coding. Nearly 200 diagrams, examples, figures, and tables along with abundant references and exercises complement the discussion.

Written by leading authority and best-selling author on the subject Richard A. Mollin, Codes: The Guide to Secrecy from Ancient to Modern Times is the essential reference for anyone interested in this exciting and fascinating field, from novice to veteran practitioner.

Table of contents

Oleg Emanouvilov Iowa State University, Ames, USA
Guenter Leugering Tech Universitat Darmstadt, Germany
Roberto Triggiani University of Virginia, Charlottesville, USA
Bing-Yu Zhang University of Cincinnati, Ohio, USA

Control Theory of Partial Differential Equations

Series: Lecture Notes in Pure and Applied Mathematics Volume: 242
ISBN: 0-8247-2546-8
Publication Date: 5/27/2005
Number of Pages: 416
Availability: In Stock

Presents the state-of-the-art in control theory for partial differential equations
Combines contributions from international leaders in the field
Covers recent developments, new discoveries and tools, and challenging open problems
Contains modeling and analysis of applied mathematics topics, such as networks of canals, aircraft wing modeling, poro-elastic filtration coupled to Stokes flows, and axially moving tapes

The field of control theory in PDEs has broadened considerably as more realistic models have been introduced and investigated. This book presents a broad range of recent developments, new discoveries, and mathematical tools in the field. The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a manifold. This is a valuable tool authored by international specialists in the field.

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Fionn Murtagh Royal Holloway University of London, UK

Correspondence Analysis and Data Coding with Java and R

Series: Chapman & Hall/CRC Computer Science & Data Analysis Volume: 4
ISBN: 1-58488-528-9
Publication Date: 5/26/2005
Number of Pages: 256

Introduces the theory, methods, and applications of correspondence analysis, with an emphasis on data coding
Exemplifies the importance of correspondence analysis in areas such as the analysis of time-evolving data and the analysis of text
Includes applications to financial and other time series analysis
Offers full discussion of software code in both Java and R
Provides software and data sets used in the book on a supporting web site: www.correspondances.info

Developed by Jean-Paul Benzerci more than 30 years ago, correspondence analysis as a framework for analyzing data quickly found widespread popularity in Europe. The topicality and importance of correspondence analysis continue, and with the tremendous computing power now available and new fields of application emerging, its significance is greater than ever.

Correspondence Analysis and Data Coding with Java and R clearly demonstrates why this technique remains important and in the eyes of many, unsurpassed as an analysis framework. After presenting some historical background, the author presents a theoretical overview of the mathematics and underlying algorithms of correspondence analysis and hierarchical clustering. The focus then shifts to data coding, with a survey of the widely varied possibilities correspondence analysis offers and introduction of the Java software for correspondence analysis, clustering, and interpretation tools. A chapter of case studies follows, wherein the author explores applications to areas such as shape analysis and time-evolving data. The final chapter reviews the wealth of studies on textual content as well as textual form, carried out by Benzecri and his research lab. These discussions show the importance of correspondence analysis to artificial intelligence as well as to stylometry and other fields.

This book not only shows why correspondence analysis is important, but with a clear presentation replete with advice and guidance, also shows how to put this technique into practice. Downloadable software and data sets allow quick, hands-on exploration of innovative correspondence analysis applications.

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SANZ-SOLE,M.

Malliavin Calculus with Applications to Stochastic Partial Differential Equations

ISBN: 0-8493-4030-6
Publication Date: 6/30/2005
Number of Pages: 150

Presents applications of Malliavin calculus to the analysis of probability laws of solutions of stochastic partial differential equations
Introduces this type of calculus based on Gaussian space
Includes finite-dimensional and infinite-dimensional settings
Addresses applications based on recent research

Presented in a comprehensive way, A Course on Malliavin Calculus with Applications to Stochastic Partial Differential Equations describes applications of Malliavin calculus to the analysis of probability laws of solutions of stochastic partial differential equations, driven by Gaussian noises that are white in time and colored in space. The text begins with an introduction to this type of calculus based on a general Gaussian space, from finite-dimensional to infinite-dimensional settings. The book later presents applications to stochastic partial differential equations based on current research, supplemented by comments concerning the origin of the work developed within and its references.

Table of Contents

Introduction. Integration by Parts and Absolute Continuity of Probability Laws. Finite Dimensional Malliavin Calculus. The Basic Operators of Malliavin Calculus. Representation of Wiener Functionals. Criteria for Absolute Continuity and Smoothness of Probability Laws. Stochastic Partial Differential Equations driven by Spatially Homogenous Gaussian Noise. Malliavin Regularity of Solutions of SPDEs. Analysis of the Malliavin Matrix of Solutions of SPDEs. Definition of Spaces Used Throughout the Course.