Bücher veröffentlicht von Birkhauser Boston

This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "e;diagonal-type"e; Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe- cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "e;cul- ture"e; that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal- type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many in- stances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and suffi- cient stability conditions for some classes of nonlinear dynamical systems.

The goal of this is book to give a detailed presentation of multicomponent flow models and to investigate the mathematical structure and properties of the resulting system of partial differential equations. These developments are also illustrated by simulating numerically a typical laminar flame. Our aim in the chapters is to treat the general situation of multicomponent flows, taking into account complex chemistry and detailed transport phe- nomena. In this book, we have adopted an interdisciplinary approach that en- compasses a physical, mathematical, and numerical point of view. In par- ticular, the links between molecular models, macroscopic models, mathe- matical structure, and mathematical properties are emphasized. We also often mention flame models since combustion is an excellent prototype of multicomponent flow. This book still does not pretend to be a complete survey of existing models and related mathematical results. In particular, many subjects like multi phase-flows , turbulence modeling, specific applications, porous me- dia, biological models, or magneto-hydrodynamics are not covered. We rather emphasize the fundamental modeling of multicomponent gaseous flows and the qualitative properties of the resulting systems of partial dif- ferential equations. Part of this book was taught at the post-graduate level at the Uni- versity of Paris, the University of Versailles, and at Ecole Poly technique in 1998-1999 to students of applied mathematics.

Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon- structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial CT (for the purpose of nonde- structive testing or reverse engineering) are made of a single material and so the ideal reconstruction should contain only two values: zero for air and the value associated with the material composing the object. Similar as- sumptions may even be made for some specific medical applications; for example, in angiography ofthe heart chambers the value is either zero (in- dicating the absence of dye) or the value associated with the dye in the chamber. Another example arises in the electron microscopy of biological macromolecules, where we may assume that the object to be reconstructed is composed of ice, protein, and RNA. One can also apply electron mi- croscopy to determine the presenceor absence ofatoms in crystallinestruc- tures, which is again a two-valued situation.

¿The authors have backgrounds which are ideally suited for writing this book. ...They have produced a compact, moderately general book which encompasses many fluid models of current interest¿The book is written very clearly and contains a large number of exercises and their solutions. The level of mathematics is that commonly taught to undergraduates in mathematics departments. This is an excellent book which is highly recommended to students and researchers in fluid mechanics.¿ (Mathematical Reviews)¿The writing style is quintessential Truesdellania: purely mathematical, breathtaking, irrepressible, irreverent, uncompromising, taking no prisoners...The book is filled with historical nuggets¿Its pure, exact mathematics will baptize, enlighten and exhilarate.¿ (Applied Mechanics Review)¿The most positive aspect of this book is its brevity; a large number of topics are covered within the space of a little more than 250 pages.¿ (Current Science)¿This advanced monograph presents one of the best new views on the subject for those who like relative simplicity and certain abstractness combined with mathematical rigor and elegance¿The book should be useful for graduates and researchers not only in applied mathematics and mechanical engineering but also in advanced materials science and technology¿Each public scientific library as well as hydrodynamics hand libraries should own this timeless book¿Everyone who decides to buy this book can be sure to have bought a classic of science and the heritage of an outstanding scientist.¿ (Silikáty)¿All applied mathematicians, mechanical engineers, aerospace engineers, and engineering mechanics graduates and researchers will find the book an essential reading resource for fluids.¿ (Simulation News Europe)

This edition develops the basic theory of Fourier transform. Stroock's approach is the one taken originally by Norbert Wiener and the Parseval's formula, as well as the Fourier inversion formula via Hermite functions. New exercises and solutions have been added for this edition.

There are two main fields of application of pulse-modulated sys- tems, communications and control. Communication is not a subject of our concern in this book. Controlling by a pulse-modulated feed- attracted our efforts. The peculiarity of this book is that all back the sampled-data systems are considered in continuous time, so no discrete time schemes are presented. And finally, we pay a little at- tention to pulse-amplitude modulation which was treated in a vast number of publications. The primary fields of our interest are pulse- width, pulse-frequency, and pulse-phase modulated control systems. The study of such systems meets with substantial difficulties. An engineer, who embarks on theoretical investigations of a pulse-mo- dulated control, is often embarrassed by the sophisticated mathe- matical tools he needs to know. When a mathematician, who looks for practical applications of his mathematical machinery, meets with these systems, he faces a lot of of complicated technical schemes and terms. Probably this is the reason why publications on pulse modu- lation are seldom in scientific journals. As for books on this subject (save on amplitude modulation), the significant part of them is in Russian and hardly available for a non-Russian reader.

This body of work represents the first volume of a book series covering the field of tissue engineering. Tissue engineering, which refers to a category of therapeutic or diagnostic products and processes which are based upon a combination of living cells and biomaterials, was defined as a field only a few years ago (1988). Tissue engineering is an inherently interdisciplinary field, combining bioengineering, life sciences and clinical sciences. The definition of this area of work as the field of tissue engineering brought together scientists from multiple backgrounds who already were working toward the achievement of similar goals. Why a book series exclusively devoted to tissue engineering? The field of tissue engineering is heterogeneous. The cells involved in tissue engineering can be autologous, allogeneic or xenogeneic. The biomaterials utilized can be either naturally occurring, synthetic or a combination of both. The appli- cation of the technology can be either for acute or permanent purposes. An attempt to cover the field of tissue engineering in a single volume, with the degree of detail necessary for individuals with different scientific back- grounds and disciplines, would be a difficult task to accomplish, particularly when this field is just emerging and changing rapidly. Therefore, addressing different technologies within the field of tissue engineering, in a comprehen- sive manner, is the main mission of this series of volumes. A stellar group of scientists has been brought together to form the editorial board of the series.

The hypermedia authoring process has been vividly described in a special issue of the Economist as a combination of writing a book, a play, a film, and a radio or television show: A hypermedia document combines all these elements and adds some of its own. The author' s first job is to structure and explain all of the infor- mation. The author then must distill the information into brief, descriptive nodes. Each node has to contain a Iist of the ingredients, and instructions on how the ingredients are mixed together to the greatest advantage. The structure of the material provided is translated into an architectural metaphor of some kind; much of the designer' s work is the creation of this imaginary space. Then, the designers must chart the details of what to animate, what to film, who to inter- view, and how to arrange the information in the space tobe built [Eco95a]. This book presents guidelines, tools, and techniques for prospective authors such that they can design better hypermedia documents and applications. lt surveys the different techniques used to organize, search, and structure infor- mation in a large information system. It then describes the algorithms used to locate, reorganize, and link data to enable navigation and retrieval. It Iooks in detail at the creation and presentation of certain types of visual information, namely algorithm animations. It introduces new mechanisms for editing audio and video data streams.