Demuth, M., TU Clausthal-Zellerfeld, Germany,
Schulze, B.-W., University of Potsdam, Germany (Eds.)

Partial Differential Equations and Spectral Theory

2001. 364 pages. Hardcover
ISBN 3-7643-6219-7
English

Operator Theory : Advances and Applications vol.126

The intention of the international conference PDE2000 was to bring together specialists from different areas of modern analysis, mathematical physics and geometry, to discuss not only the recent progress in their own fields but also the interaction between these fields. The special topics of the conference were spectral and scattering theory, semiclassical and asymptotic analysis, pseudodifferential operators and their relation to geometry, as well as partial differential operators and their connection to stochastic analysis and to the theory of semigroups.
The scientific advisory board of the conference in Clausthal consisted of M. Ben-Artzi (Jerusalem), Chen Hua (Peking), M. Demuth (Clausthal), T. Ichinose (Kanazawa), L. Rodino (Turin), B.-W. Schulze (Potsdam) and J. Sjostrand (Paris).
The book is aimed at researchers in mathematics and mathematical physics with interests in partial differential equations and all its related fields.

Kopachevsky, N.D., Taurida National V. Vernadsky University, Simferopol, Ukraine, Krein, S.G.

Operator Approach to Linear Problems of Hydrodynamics
Volume 1: Self-adjoint Problems for an Ideal Fluid

2001. 408 pages. Hardcover

ISBN 3-7643-5406-2
English

Due in August 2001

Operator Theory : Advances and Applications vol.128

This is the first volume of a set of two devoted to the operator approach to linear problems in hydrodynamics. It presents functional analytical methods applied to the study of small movements and
normal oscillations of hydromechanical systems having cavities filled with either ideal or viscous fluids. The work is a sequel to and at the same time substantially extends the volume Operator Methods in Linear Hydrodynamics: Evolution and Spectral Problems by N.D. Kopachevsky, S.G. Krein and Ngo Zuy Kan, published in 1989 by Nauka in Moscow. It includes several new problems on the oscillations of partially dissipative hydrosystems and the oscillations of visco-elastic or relaxing fluids. The work relies on the authors' and their students’ works of the last 30-40 years.
The readers are not supposed to be familiar with the methods of functional analysis. In the first part of the present volume, the main facts of linear operator theory relevant to linearized problems of hydrodynamics are summarized, including elements of the theories of distributions, self-adjoint operators in Hilbert spaces and in spaces with an indefinite metric, evolution equations and asymptotic methods for their solutions, the spectral theory of operator pencils.
The book is particularly useful for researchers, engineers and students in fluid mechanics and mathematics interested in operator theoretical methods for the analysis of hydrodynamical problems.

Mikusinski, P., University of Central Florida, Orlando, USA,
Taylor, M.D., University of Central Florida, Orlando, USA

An Introduction to Multivariable Analysis
From Vector to Manifold

2001. Approx. 320 pages. Hardcover
ISBN 0-8176-4234-X
English

Due in September 2001

The subject of multivariable analysis is of interest to pure and applied mathematicians, physicists, electrical, mechanical and systems engineers, mathematical economists, biologists, and statisticians. This introductory text provides graduate students and researchers in the above fields with various ways of handling some of the useful but difficult concepts encountered in dealing with the machinery of differential forms on manifolds. The approach here is to make such concepts as concrete as possible.
Highlights and key features:
* systematic exposition, supported by numerous examples and exercises from the computational to the theoretical * brief development of linear algebra in R((bold))((superscript N)), presenting concepts that figure prominently later in the book * review of the elements of metric space theory * treatment of standard multivariable material: differentials as linear transformations, the inverse and implicit function theorems, Taylor's theorem, the change of variables for multiple integrals (the most complex proof in the book) * Lebesgue integration introduced in a concrete way rather than via measure theory. This involves certain series 'expansions' of functions, reduces the theory of integration to that of absolutely convergent series, which in the latter chapters serves to simplify the definition of integration of real-valued functions on manifolds * latter chapters move beyond R((bold))((superscript N)) to manifolds and analysis on manifolds, covering the wedge product, differential forms, and the generalized S tokes' theorem * bibliography and comprehensive index
This book takes the reader on a journey through the core topics in multivariable analysis that are basic for senior undergraduate and graduate studies in differential geometry, and for analysis in N-dimensions and on manifolds. The book may be used for self-study to anyone working in the areas of dynamical systems, control theory and optimization, general relativity and electromagnetic phenomena. Aside from mathematical maturity, prerequisites are a one-semester undergraduate course in advanced calculus or analysis, and linear algebra.

Preface * Vectors and Volumes * Metric Spaces * Differentiation * The Lebesgue Integral * Integrals on Manifolds * K-Vectors and Wedge Products * Vector Analysis on Manifolds * Bibliography * Index

Sobczyk, K., Institute of Fundamental Technological Research, Warsaw, Poland,
Kirkner, D.J., University of Notre Dame, USA

Stochastic Modeling of Microstructures

2001. Approx. 296 pages. Hardcover
ISBN 0-8176-4233-1
English

Due in September 2001

This book presents the language of random field theory and the principles of stochastic geometry in order to give the systematic and concise knowledge necessary for modeling real random heterogeneous media. This book is ideal for a general scientific audience needing an in-depth guide to current ideas, methods and models for the stochastic modeling of microstructures. It is an essential reference for practitioners, researchers and professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.

Introduction, 1. Probability and Random Variables, 2. Continuous Random Fields, 3. Random Point Fields, 4. Statistical Inference, 5. Material Media Microstructure: Modeling Issues, 6. Physical Phenomena in Random Microstructures: Selected applications, References, Index

Storer, J.A., Brandeis University, Waltham, USA

Data Structures and Algorithms

2001. Approx. 500 pages. Hardcover
ISBN 0-8176-4253-6

Due in September 2001

PCS - Progress in Computer Science and Applied Logic

Data structures and algorithms are presented at the college level in a way that is unique in content and presentation from current available texts. A highly a highly accessible format presents algorithms with one page displays that will appeal to both students and teachers of computer science. The thirteen chapters systematically and comprehensively cover Models of Computation, Lists, Induction and Recursion, Trees, Algorithms Design, Hashing, Heaps, Balanced Trees, Sets Over a Small Universe, Discrete Fourier Transform, Strings, Graphs, Parallel Models of Computation.

Data structures and algorithms are presented at the college level in a way that is unique in content and presentation from current available texts. A highly accessible format that presents algorithms with one-page displays will appeal to students and teachers of computer science. The thirteen chapters systematically and comprehensively cover: Models of Computation, Lists, Induction and Recursion, Trees, Algorithms Design, Hashing, Heaps, Balanced Trees, Sets Over a Small Universe, Discrete Fourier Transform, Strings, Graphs, Parallel Models of Computation.

Contents:

1. RAM Model * 2. Lists * 3. Induction and Recursion * 4. Trees * 5. Algorithms Design Techniques * 6. Hashing * 7. Heaps * 8. Balanced Trees * 9. Sets Over a Small Universe * 10. Discrete Fourier Transform (DFT) * 11. Strings * 12. Graphs * 13. Parallel Models of Computation * Appendix of Common Sums * Bibliography * Notation * Index