Expected publication date is November 16, 2002
Description
Phenomena of contact between deformable bodies or between deformable and rigid bodies abound in industry and in everyday life. A few simple examples are brake pads with wheels, tires on roads, and pistons with skirts. Common industrial processes such as metal forming and metal extrusion involve contact evolutions. Because of the importance of contact processes in structural and mechanical systems, considerable effort has been put into modeling and numerical simulations.
This book introduces readers to a mathematical theory of contact problems involving deformable bodies. It covers mechanical modeling, mathematical formulations, variational analysis, and the numerical solution of the associated formulations. The authors give a complete treatment of some contact problems by presenting arguments and results in modeling, analysis, and numerical simulations.
Variational analysis of the models includes existence and uniqueness results of weak solutions, as well as results of continuous dependence of the solution on the data and parameters. Also discussed are links between different mechanical models.
In carrying out the variational analysis, the authors systematically use results on elliptic and evolutionary variational inequalities, convex analysis, nonlinear equations with monotone operators, and fixed points of operators.
Prerequisites include basic functional analysis, variational formulations of partial differential equation problems, and numerical approximations. The text is suitable for graduate students and researchers in applied mathematics, computational mathematics, and computational mechanics.
Contents
・Nonlinear variational problems and numerical approximation Preliminaries of functional analysis Function spaces and their properties Introduction to finite difference and finite element approximations Variational inequalities ・Mathematical modelling in contact mechanics Preliminaries of contact mechanics of continua Constitutive relations in solid mechanics Background on variational and numerical analysis in contact mechanics Contact problems in elasticity ・Contact problems in viscoelasticity A frictionless contact problem Bilateral contact with slip dependent friction Frictional contact with normal compliance Frictional contact with normal damped response Other viscoelastic contact problems ・Contact problems in visocplasticity A Signorini contact problem Frictionless contact with dissipative potential Frictionless contact between two viscoplastic bodies Bilateral contact with Tresca's friction law Other viscoelastic contact problems Bibliography Index
Details:
Series: AMS/IP Studies in Advanced Mathematics, Volume: 30 Publication Year: 2002 ISBN: 0-8218-3192-5 Paging: 442 pp. Binding: Hardcover
Expected publication date is November 21, 2002
Description
"Mean curvature flow" is a term that is used to describe the evolution of a hypersurface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the curve collapses to a point, and if the flow is diluted so that the enclosed area equals pi, the curve tends to the unit circle.
In this book, the author gives a comprehensive account of fundamental results on singularities and the asymptotic behavior of mean curvature flows in higher dimensions. Among other topics, he considers in detail Huisken's theorem (a generalization of Gage-Hamilton's theorem to higher dimension), evolution of non-convex curves and hypersurfaces, and the classification of singularities of the mean curvature flow.
Because of the importance of the mean curvature flow and its numerous applications in differential geometry and partial differential equations, as well as in engineering, chemistry, and biology, this book can be useful to graduate students and researchers working in these areas. The book would also make a nice supplementary text for an advanced course in differential geometry.
Prerequisites include basic differential geometry, partial differential equations, and related applications.
Contents
・The curve shortening flow for convex curves ・The short time existence and the evolution equation of curvatures ・Contraction of convex hypersurfaces ・Monotonicity and self-similar solutions ・Evolution of embedded curves or surfaces (I) ・Evolution of embedded curves and surfaces (II) ・Evolution of embedded curves and surfaces (III) ・Convexity estimates for mean convex surfaces ・Li-Yau estimates and type II singularities ・The mean curvature flow in Riemannian manifolds ・Contracting convex hypersurfaces in Riemannian manifolds ・Definition of center of mass for isolated gravitating systems ・References ・Index
Details:
Series: AMS/IP Studies in Advanced Mathematics, Volume: 32 Publication Year: 2002 ISBN: 0-8218-3311-1 Paging: approximately 160 pp. Binding: Hardcover
Expected publication date is October 11, 2002
Description
This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and very recent developments in operator theory and also draws together results which are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time.
The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere.
The companion volume, Problems in Operator Theory also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory.
The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal.
Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.
Contents
・Odds and ends ・Basic operator theory ・Operators on AL- and AM-spaces ・Special classes of operators ・Integral operators ・Spectral properties ・Some special spectra ・Positive matrices ・Irreducible operators ・Invariant subspaces ・The Daugavet equation ・Bibliography ・Index
Details:
Series: Graduate Studies in Mathematics,Volume: 50 Publication Year: 2002 ISBN: 0-8218-2146-6 Paging: 530 pp. Binding: Hardcover
Expected publication date is November 22, 2002
Description
In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach.
The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective.
The book is suitable for mathematicians and biologists interested in mathematical methods in biology.
Contents
D. Terman -- Dynamics of singularly perturbed neuronal networks D. Tranchina -- Mathematics in visual neuroscience: The retina J. P. Keener -- Arrhythmias by dimension J. Sneyd -- Calcium excitability K. Lange and B. Redelings -- Disease gene dynamics in a population isolate A. S. Perelson and P. W. Nelson -- Modeling viral infections Index
Details:
Series: Proceedings of Symposia in Applied Mathematics, Volume: 59 Publication Year: 2002 ISBN: 0-8218-2816-9 Paging: approximately 192 pp. Binding: Hardcover
ISBN: 0-12-443895-4 Cover: CaseBound Published: May 2002
Database and Data Communication Network Systems examines the utilization of the Internet and Local Area/Wide Area Networks in all areas of human endeavor. This three-volume set covers, among other topics, database systems, data compression, database architecture, data acquisition, asynchronous transfer mode (ATM) and the practical application of these technologies. The international collection of contributors was culled from exhaustive research of over 100,000 related archival and technical journals.
This reference will be indispensable to engineering and computer science libraries, research libraries, and telecommunications, networking, and computer companies. It covers a diverse array of topics, including:
* Techniques in emerging database system architectures * Techniques and applications in data mining * Object-oriented database systems * Data acquisition on the WWW during heavy client/server traffic periods * Information exploration on the WWW * Education and training in multimedia database systems * Data structure techniques in rapid prototyping and manufacturing * Wireless ATM in data networks for mobile systems * Applications in corporate finance * Scientific data visualization * Data compression and information retrieval * Techniques in medical systems, intensive care units