Zhidkov, P.E., Joint Institute for Nuclear Research, Dubna, Russia

Korteweg-de Vries and Nonlinear Schrodinger Equations: Qualitative Theory

2001. VI, 147 pp. Softcover
3-540-41833-4

The emphasis of this book is on questions typical of nonlinear analysis and qualitative theory of PDEs. The selection of the material is related to the author's attempt to illuminate those particularly interesting questions not yet covered in other monographs though they have been the subject of published articles. One chapter, for example, is devoted to the construction of invariant measures for dynamical systems generated by certain equations and a result from a recent paper on basic properties of a system of eigenfunctions of a stationary problem. Also considered is an application of the method of qualitative theory of ODes to proving the existence of radial solutions of stationary problems and stability of solutions of NLSE nonvanishing as the spatial variable tends to infinity. Finally a recent result on the existence of an infinite sequence of invariant measures for the inegrable KdV equation is presented.

Keywords: Well-posedness, stationary solution, stability, invariant measure MSC ( 2000 ): 34B16, 34B40, 35D05, 35J65, 35Q53, 35Q55, 35P30, 37A05, 37K45 .

Contents: Introduction Notation Chapter 1. Evolutionary equations. Results on existance 1.1 The (generalized Korteweg-de Vries equation (KdVE) 1.2 The nonlinear Schro"dinger equation (NLSE) 1.3 On the blowing up of solutions 1.4 Additional remarks Chapter 2. Stationary problems 2.1 Existence of solutions. An ODE approach 2.2 Existence of solutions. A variational method 2.3 The concentration-compactness method of P.L. Lions 2.4 On basis properties of systems of solutions 2.5 Additional remarks Chapter 3. Stability of solutions 3.1 Stability of soliton-like solutions 3.2 Stability of kinks for the KdVE 3.3 Stability of solutions of the NLSE non-vanishing as (x) to infinity 3.4 Additional remarks Chapter 4. Invariant measures 4.1 On Gaussian measures in Hilbert spaces 4.2 An invariant measure for the NLSE 4.3 An infinite series of invariant measures for the KdVE 4.4 Additional remarks Bibliography Index

Series: Lecture Notes in Mathematics.VOL. 1756

Phelps, R.R., University of Washington, Seattle, USA

Lectures on Choquet's Theorem

2nd ed. 2001. VII, 124 pp. Softcover
3-540-41834-2

A well written, readable and easily accessible introduction to "Choquet theory", which treats the representation of elements of a compact convex set as integral averages over extreme points of the set. The interest in this material arises both from its appealing geometrical nature as well as its extraordinarily wide range of application to areas ranging from approximation theory to ergodic theory. Many of these applications are treated in this book. This second edition is an expanded and updated version of what has become a classic basic reference in the subject.

Keywords: Compact convex sets, Choquet ' s Theorem, representing measures MSC ( 2000 ): 46-XX

Contents: Preface 1 Introduction. The Krein-Milman theorem as an integral representation theorem 2 Application of the Krein-Milman theorem to completely monotonic functions 3 Choquet's theorem: The metrizable case 4 The Choquet-Bishop-de Leeuw existence theorem 5 Applications to Rainwater's and Haydon's theorems 6 A new setting: The Choquet boundary 7 Applications of the Choquet boundary to resolvents 8 The Choquet boundary for uniform algebras 9 The Choquet boundary and approximation theory 10 Uniqueness of representing measures 11 Properties of the resultant map 12 Application to invariant and ergodic measures 13 A method for extending the representation theorems: Caps 14 A different method for extending the representation theorems 15 Orderings and dilations of measures 16 Additional Topics References Index of symbols Index

Series: Lecture Notes in Mathematics.VOL. 1757

Gandolfo, G., University of Rome "La Sapienza", Rome, Italy

International Finance and Open-Economy Macroeconomics

2001. XXIV, 613 pp. Hardcover
3-540-41730-3

This book deals with the financial side of international economics and covers all aspects of international finance. "Prof. Gandolfo has written what will be a classic in international finance. His erudition, expository and technical skills are combined to fulfil the needs of undergraduate and graduate students, researchers, and staff members in international economic organisations. The literary part is clear, and the underlying intuition of the arguments is stressed. This is followed by a mathematical analysis, which uses the state of the art techniques. In this manner the reader can go from the intuition-literary argument to the formal derivations and proofs. There are many books and articles by exponents of alternative points of view. I know of no other book that provides the scope, balance, objectivity and rigor of the book." (Professor Jerome L. Stein, Brown University)

Keywords: Open-economy macroeconomics, International finance, International monetary economics, International economics

Contents: The Basics.- Flow Approaches.- Stock and Stock-Flow Approaches.- The Exchange Rate.- The Intertemporal Approach.- International Monetary Integration.- Problems of the International Monetary (Non) System.- Appendices.

Howie, J.M., Mathematical Institute, St. Andrews, UK

Real Analysis

2001. X, 276 pp. 35 figs. Softcover
1-85233-314-6

Understanding the concepts and methods of real analysis is an essential skill for every undergraduate mathematics student. Written in an easy-to-read style, Real Analysis is a comprehensive introduction to this core subject and is ideal for self-study or as a course textbook for first and second-year undergraduates. Combining an informal style with precision mathematics, Real Analysis covers all the key topics with fully worked examples and exercises with solutions.
Featuring: Sequences and series - considering the central notion of a limit; Continuous functions; Differentiation; Integration; Logarithmic and exponential functions; Uniform convergence; Circular functions.
All these concepts and techniques are deployed in examples in the final chapter to provide the student with a thorough understanding of this challenging subject.

Contents: Introductory Ideas.- Sequences and Series.- Functions and Continuity.- Differentiation.- Integration.- The Logarithmic and Exponential Functions.- Sequences and Series of Functions.- The Circular Functions.- Miscellaneous Examples Solutions to Exercises.- Appendix: The Greek Alphabet.- Bibliography.- Index.

Series: Springer Undergraduate Mathematics Series.

Kalikmanov, V.I., University of Delft, The Netherlands

Statistical Physics of Fluids
Basic Concepts and Applications

2001. XII, 257 pp. 52 figs., 5 tabs. Hardcover
3-540-41747-8

The book focuses on the main physical ideas and mathematical methods of the microscopic theory of fluids, starting with the basic principles of statistical mechanics. The detailed derivation of results is accompanied by explanation of their physical meaning. The same approach refers to several specialized topics of the liquid state, most of which are recent developments, such as: a perturbation approach to the surface tension, an algebraic perturbation theory of polar nonpolarizable fluids and ferrocolloids, a semi-phenomenological theory of the Tolman length and some others. The book addresses researchers as well as graduate students in physics and chemistry with research interests in the statistical physics of fluids.

Keywords: Statistical Mechanics, Perturbation Approach, Equation of State, Surface Tension, Density Functional Theory .

Contents: Ensembles in Statistical Mechanics.- Method of Correllation Functions.- Equations of State.- Liquid--Vapor Interface.- Perturbation Approach.- Equilibrium Phase Transitions.- Monte Carlo Methods.- Theories of Correlation Functions.- Density Functional Theory.- Real Gases.- Surface Tension of a Curved Interface.- Polar Fluids.- Mixtures.- Ferrofluids.- Empirical Correlations for Macroscopic Properties of Argon, Benzene and n-Nonane.- Angular Dipole Integrals.- De Gennes--Pincus Integral.- Calculation of gamma D and gamma Delta in the Algebraic Perturbation Theory for Polar Fluids.- Mixtures of Hard Spheres.- References.- Index.

Series: Texts and Monographs in Physics.

Schanz, M., Technical University of Braunschweig, Germany

Wave Propagation in Viscoelastic and Poroelastic Continua
A Boundary Element Approach

2001. Approx. 180 pp. 78 figs. Hardcover
3-540-41632-3

Wave propagation in poroelastic and viscoelastic solids treated by the Boundary Element method in time domain is the topic of this research book. A novel boundary element formulation has been presented based on the Convolution Quadrature Method. Because in this time-stepping formulation only Laplace domain fundamental solutions are needed this method can be effectively applied to a plenty of problems, e.g., anisotropic or transversely isotropic continua. So, this method combines the advantage of the Laplace domain with the advantage of a time domain calculation. Here, wave propagation phenomenon in viscoelastic as well as poroelastic half spaces are considered. The Rayleigh wave as well as the slow compressional wave in the poroelastic solid is discussed.

Keywords: Waves, vibrations, elasticity, viscoelasticity, porous me- dia, poroelasticity, numerical methods, computational me- thods, boundary element methods, BEM, soil mechanics .

Contents: Introduction.- Convolution quadrature method.- Viscoelastically supported Euler-Bernoulli beam.- Time domain boundary element formulation.- Viscoelastodynamic boundary element formulation.- Poroelastodynamic boundary element formulation.- Wave propagation.- Conclusions and Applications.- Appendices: Mathematical preliminaries; BEM details.

Series: Lecture Notes in Applied Mechanics.VOL. 2