Bøger i Applied Mathematical Sciences serien

The scattering of acoustic and electromagnetic waves by periodic sur faces plays a role in many areas of applied physics and engineering. Trains of surface waves on the oceans are natural diffraction gratings which influence the scattering of electromagnetic waves and underwater sound.

Stratified fluids whose densities, sound speeds and other parameters are functions of a single depth coordinate occur widely in nature. The purpose of this monograph is to develop from first principles a theory of sound propagation in stratified fluids whose densities and sound speeds are essentially arbitrary functions of the depth.

I was guided by the desire to prove, as simply as possible, that, like systems of n linear algebraic equations in n unknowns, the solvability of basic boundary value (and initial-boundary value) problems for partial differential equations is a consequence of the uniqueness theorems in a "sufficiently large" function space.

They are mainly concerned with regularity theory for obstacle problems, and with the dam problem, which, in the rectangular case, is one of the most in teresting applications of Variational Inequalities with an obstacle.

The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. This book serves as an entree for scholars beginning their journey into the world of dynamical systems, especially infinite dimensional spaces. The main approach involves the theory of evolutionary equations.

My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.

We concentrate our efforts on this method, not because we underrate those which appear more powerful in some circumstances, but because it is important enough, along with its modern developments, to justify the writing of an up-to-date monograph.

This book is the result of lectures which I gave dur ing the academic year 1972-73 to third-year students a~ Aarhus University in Denmark. The purpose of the book, as of the lectures, is to survey some of the main themes in the modern theory of stochastic processes.

This research project has been supported by the Division of Mathematical and Computer Sciences of the National Science Foundation and (the work on language abduction, pattern processors, and patterns in program behavior) by the Information Systems Program of the Office of Naval Research.

The book deals with a powerful and convenient approach to a great variety of types of problems of the recursive monte-carlo or stochastic approximation type. The approach, relating algorithm behavior to qualitative properties of deterministic or stochastic differ ential equations, has advantages in algorithm conceptualiza tion and design.

This approach makes it possible to treat a seemingly broad range of equations from nonautonomous ordinary differential equa tions and partial differential equations to stochastic differ ential equations. This space serves as the phase space for the semidynamical system.

The aim of the seminars was to present geometric quantization from the point of view* of its applica tions to quantum mechanics, and to introduce the quantum dynamics of various physical systems as the result of the geometric quantization of the classical dynamics of these systems.

The first to examine topological, group-theoretic and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified viewpoint, this book describes preliminary notions in hydrodynamics and pure mathematics with numerous examples and figures.

The idea for this book was conceived by the authors some time in 1988, and a first outline of the manuscript was drawn up during a summer school on mathematical physics held in Ravello in September 1988, where all three of us were present as lecturers or organizers.

The author presents the basic facts of functional analysis in a form suitable for engineers, scientists, and applied mathematicians. Although the Definition-Theorem-Proof format of mathematics is used, careful attention is given to motivation of the material covered and many illustrative examples are presented.

An exposition of the derivation and use of equations of motion for two-phase flow. The work focuses on the fundamental aspects of two-phase flow, and is intended to give the reader a background for understanding the dynamics as well as a system of equations that can be used in predictions of the behavior of dispersed two-phase flows.

For the most part, derivations are based on perturbation methods, and the majority of the text is devoted to careful derivations of implicit function theorems, the method of averaging, and quasi-static state approximation methods.

By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.

The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications.

Ludwig Prandtl has been called the father of modern fluid mechanics, and this updated and extended edition of his classic text on the field is based on the 12th German edition with additional material included.

Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more.

Dynamical Systems and Chaos provides an overview of the field that bridges the gap between abstract and applied areas of study. Exercises included at the end of each chapter illustrate the concepts discussed, and are appropriate for undergraduate and graduate courses, alike.

This illustrated book provides a modern investigation into the bifurcation phenomena of physical and engineering problems. Systematic methods are used to examine experimental and computational data from numerous examples (soil, sand, kaolin, concrete, domes).

The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry.

This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. The book also develops basic differential geometrical concepts centred about curvature.

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic.