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That interfusion turned out to have great advan tages and gave rise to a vast number of significant results, of which we want to mention especially the classical results on the theory of Fourier series in L2 ( -7r, 7r) and their continual analog - Plancherel's theorem on the Fourier transform in L2 ( -00, +00).

This book deals with asymptotic solutions of linear and nonlinear equa­ tions which decay as h ---+ 0 outside a neighborhood of certain points, curves and surfaces. Such solutions are almost everywhere well approximated by the functions cp(x) exp{iS(x)/h}, x E 1R3, where S(x) is complex, and ImS(x) ~ o. When the phase S(x) is real (ImS(x) = 0), the method for obtaining asymp­ totics of this type is known in quantum mechanics as the WKB-method. We preserve this terminology in the case ImS(x) ~ 0 and develop the method for a wide class of problems in mathematical physics. Asymptotics of this type were constructed recently for many linear prob­ lems of mathematical physics; certain specific formulas were obtained by differ­ ent methods (V. M. Babich [5 -7], V. P. Lazutkin [76], A. A. Sokolov, 1. M. Ter­ nov [113], J. Schwinger [107, 108], E. J. Heller [53], G. A. Hagedorn [50, 51], V. N. Bayer, V. M. Katkov [21], N. A. Chernikov [35] and others). However, a general (Hamiltonian) formalism for obtaining asymptotics of this type is clearly required; this state of affairs is expressed both in recent mathematical and physical literature. For example, the editors of the collected volume [106] write in its preface: "One can hope that in the near future a computational pro­ cedure for fields with complex phase, similar to the usual one for fields with real phase, will be developed.

Massively Parallel Systems (MPSs) with their scalable computation and storage space promises are becoming increasingly important for high-performance computing.

22 papers on control of nonlinear partial differential equations highlight the area from a broad variety of viewpoints. A significant part of the volume is devoted to applications in engineering, continuum mechanics and population biology.

Chapters 1-6 give the function-theoretic background to Hardy Classes and Operator Theory, Oxford Mathematical Monographs, Oxford University Press, New York, 1985. The theory of Hardy and Nevanlinna classes is derived from proper ties of harmonic majorants of subharmonic functions (Chapters 3 and 4).

We have considered writing the present book for a long time, since the lack of a sufficiently complete textbook about complex analysis in infinite dimensional spaces was apparent. There are, however, some separate topics on this subject covered in the mathematical literature. For instance, the elementary theory of holomorphic vector­ functions.and mappings on Banach spaces is presented in the monographs of E. Hille and R. Phillips [1] and L. Schwartz [1], whereas some results on Banach algebras of holomorphic functions and holomorphic operator-functions are discussed in the books of W. Rudin [1] and T. Kato [1]. Apparently, the need to study holomorphic mappings in infinite dimensional spaces arose for the first time in connection with the development of nonlinear anal­ ysis. A systematic study of integral equations with an analytic nonlinear part was started at the end ofthe 19th and the beginning ofthe 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods. The most complete presentation of these methods comes from N. Nazarov. In the forties and fifties the interest in Liapunov's and Schmidt's analytic methods diminished temporarily due to the appearence of variational calculus meth­ ods (M. Golomb, A. Hammerstein and others) and also to the rapid development of the mapping degree theory (J. Leray, J. Schauder, G. Birkhoff, O. Kellog and others).

The school, the book This book is based on lectures given by the authors of the various chapters in a three week long CIMPA summer school, held in Sophia-Antipolis (near Nice) in July 1992. The first week was devoted to the basics of symplectic and Riemannian geometry (Banyaga, Audin, Lafontaine, Gauduchon), the second was the technical one (Pansu, Muller, Duval, Lalonde and Sikorav). The final week saw the conclusion ofthe school (mainly McDuffand Polterovich, with complementary lectures by Lafontaine, Audin and Sikorav). Globally, the chapters here reflect what happened there. Locally, we have tried to reorganise some ofthe material to make the book more coherent. Hence, for instance, the collective (Audin, Lalonde, Polterovich) chapter on Lagrangian submanifolds and the appendices added to some of the chapters. Duval was not able to write up his lectures, so that genuine complex analysis will not appear in the book, although it is a very current tool in symplectic and contact geometry (and conversely). Hamiltonian systems and variational methods were the subject of some of Sikorav's talks, which he also was not able to write up. On the other hand, F. Labourie, who could not be at the school, wrote a chapter on pseudo-holomorphic curves in Riemannian geometry.

Die Entstehung des chemischen Verbindungsbegriffs, ein Fundamentalbegriff der neuzeitlichen Chemie, ist kaum untersucht, weil er für eine blosse Präzisierung des naturphilosophischen Atomkonzepts gehalten wurde. Das Buch widerlegt diese Ansicht als ideengeschichtliches Vorurteil und weist minutiös nach, dass der Verbindungsbegriff als Resultat der begrifflichen Strukturierung des empirischen Wissens entstand, das aus der gewerblichen chemischen Praxis des 16. und 17. Jahrhunderts stammte. Damit rekonstruiert die Autorin nicht allein den Beginn der wissenschaftlichen Chemie in einer grundlegend neuen historischen, begrifflichen und methodischen Ordnung. Sie zeigt darüber hinaus, wie diese "chemische Revolution" in den Kontext der wissenschaftlichen Revolution des 17. Jahrhunderts einzuordnen ist, nämlich als die einer "baconischen Wissenschaft" (Kuhn), die das Erfahrungswissen einer neuartigen gewerblichen Praxis ohne Rückgriffsmöglichkeiten auf brauchbare Theorietraditionen in eine wissenschaftliche Theorie überführte. Das Buch ist so zugleich ein substanzieller Beitrag zum Verständnis wissenschaftlicher Revolutionen, der insbesondere zum Überdenken der wissenschaftstheoretischen Annahme einer Theoriedominanz bei der Entstehung und Entwicklung der Wissenschaften nötigt. Es ist deswegen nicht nur für Chemiehistoriker, für die es zum neuen Standardwerk über die Chemie des 17. Jahr- hunderts werden dürfte, von Interesse, sondern ebenso für Wissenschaftshistoriker allgemein sowie für Wissenschaftstheoretiker, Philosophen und Kulturhistoriker.

Everybody having even the slightest interest in analytical mechanics remembers having met there the Poisson bracket of two functions of 2n variables (pi, qi) f g ~(8f8g 8 8 ) (0.1) {f,g} = L... ~[ji - [ji~ , ;=1 p, q q p, and the fundamental role it plays in that field. In modern works, this bracket is derived from a symplectic structure, and it appears as one of the main in­ gredients of symplectic manifolds. In fact, it can even be taken as the defining clement of the structure (e.g., [TIl]). But, the study of some mechanical sys­ tems, particularly systems with symmetry groups or constraints, may lead to more general Poisson brackets. Therefore, it was natural to define a mathematical structure where the notion of a Poisson bracket would be the primary notion of the theory, and, from this viewpoint, such a theory has been developed since the early 19708, by A. Lichnerowicz, A. Weinstein, and many other authors (see the references at the end of the book). But, it has been remarked by Weinstein [We3] that, in fact, the theory can be traced back to S. Lie himself [Lie].

Many advances have been made in the field of thermoregulation in the past few years. These include our understanding of Fever, which is now considered not simply a rise in deep body temperature foHowing infection, but just one aspect, though perhaps the most easily measured, of the Acute Phase of the Immune Response. Classification and identification of the Cytokines and the availability of recombinant material has greatly aided this research. Similarly, our understanding of the Hypothalamo-Pituitary Adrenal Axis has altered our way of thinking about temperature regulation. Of importance are the problems associated with adverse climatic conditions and survival, and the problems encountered by the neonate and the hibernator. At the biochemical level, our knowledge of the control of heat production and the role of brown adipose tissue is rapidly advancing. All these issues and many others were discussed at a Symposium 'Thermal Physiology 1993' held in Aberdeen, Scotland in August 1993 under the auspices of the Thermal Physiology Commission of the International Union of Physiological Sciences. Six main aspects of the subject of temperature regulation are included in this book, namely, Fever (including the Acute Phase of the Immune Response and Thermoregulatory Peptides), Neurophysiology of Thermoregulation, Neonatal Thermoregulation, Mechanisms of Heat Production, Ecological and Behavioural Thermoregulation, and Emerging Themes in Thermoregulation.

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2002. The subject of this book is the study of automorphic distributions, by which is meant distributions on R2 invariant under the linear action of SL(2,Z), and of the operators associated with such distributions under the Weyl rule of symbolic calculus. Researchers and postgraduates interested in pseudodifferential analyis, the theory of non-holomorphic modular forms, and symbolic calculi will benefit from the clear exposition and new results and insights.

This book expresses the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Historical notes and Mathematica drawings have been added to this revised second edition. From the reviews:"Will do much to make Weyl's tube formula more accessible to modern readers....

This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion.

The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces.

The book presents state-of-the-art results on the analysis of the Einstein equations and the large scale structure of their solutions.

M. LUCERTINI, A. MILLAN GASCA, AND F. NICOLO 1 Technology as Knowledge: The Case of Modern Engineering Systems In recent years scholars coming from the fields of history and philosophy of sci­ ence and technology have devoted much attention to the problem of "technology as knowledge" and to the emergence of an autonomous engineering science in the Industrial Agel. This interest echoes a growing awareness among engineers of the independence of their conceptual approach with respect to other forms of knowl­ edge, linked to the consolidation of autonomous academic engineering research in th the 20 century. A careful examination of the nature of technological knowledge appears particularly valuable in view of the pervasive presence of technology in contemporary life and culture, not only as a result of its impressive achievements, but through the less obvious influence of its concepts and viewpoints as well. The activity of engineers and technicians has been traditionally based on the practical ability to cope with specific situations and to attain the corresponding specific goal by means of the design and realization of an artifact or structure, on the basis of past experience handed down by tradition and applied by means of trial-and-error and rule-of-thumb procedures. But the existence of a theoreti­ cal background and of principles underpinning this activity can be traced back to classical antiquity.

This book presents recent results in the following areas: spectral analysis of one-dimensional Schroedinger and Jacobi operators, discrete WKB analysis of solutions of second order difference equations, and applications of functional models of non-selfadjoint operators.

This drug is a landmark discovery, which consequently has become the definitive therapy for the treatment of erectile dysfunction (ED). Following the major breakthrough in the field of nitric oxide (NO)-physiology and pharmacology leading to sildenafil being marketed, the most current information is presented in this reference book, including ongoing research from several disparate groups about NO as endothelium-derived relaxing factor (EDRF) and also as a neurotransmitter for nerves innervating erectile tissue in mammals.The development of sildenafil as an oral phosphodiesterase-5 (PDE5) inhibitor drug for the treatment of ED resulted in one of the first products, which made its way successfully from basic NO research to routine clinical therapy.This volume addresses all fields of sildenafil application in both men and women. In a highly competitive research environment with a critical medical need for drug improvements the reader will learn more about clinical resistance to sildenafil treatment and the modalities to overcome the failure rates. The individual chapters cover clinical use, pharmacokinetics, pharmacodynamics, biochemistry, and cultural aspects. They are written by leading experts in their respective fields. Therefore, readers ¿ whether professionals in the pharmaceutical industry, physicians treating ED, biochemists, chemists or pharmacologists ¿ will find a detailed and up-to-date knowledge base about current research activities and an excellent overview for further research on this compound class and its cultural impact.

This book covers facts and methods for the reconstruction of a function in a real affine or projective space from data of integrals, particularly over lines, planes, and spheres. The first half of the book includes the ray, the spherical mean transforms in the plane or in 3-space, and inversion from incomplete data.

The aim of this monograph is to introduce the reader to modern methods of projective geometry involving certain techniques of formal geometry.

Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2003.This book contains a detailed mathematical analysis of the variational approach to image restoration based on the minimization of the total variation submitted to the constraints given by the image acquisition model. This model, initially introduced by Rudin, Osher, and Fatemi, had a strong influence in the development of variational methods for image denoising and restoration, and pioneered the use of the BV model in image processing. After a full analysis of the model, the minimizing total variation flow is studied under different boundary conditions, and its main qualitative properties are exhibited. In particular, several explicit solutions of the denoising problem are computed.

This volume is devoted to the life and work of the applied mathematician Professor Erhard Meister (1930-2001). He was a member of the editorial boards of this book series Operator The ory: Advances and Applications as well as of the journal Integral Equations and Operator Theory, both published by Birkhauser (now part of Springer-Verlag).

This book explores new difference schemes for approximating the solutions of regular and singular perturbation boundary-value problems for PDEs.

Chronic viral hepatitis has emerged as one of the most common causes of disease and death worldwide. Because of their unique modes of replication and intimate association with the host immune system, hepatitis B virus (HBV) and hepatitis C virus (HCV) pose challenging problems to scientists in basic and applied research as well as to clinicians engaged in disease management. Although approved antiviral therapy is available for chronic HBV, the emergence of viral resistance provides a rationale for the development of novel chemotherapeutic agents. The lack of a robust cell culture system for HCV replication and a readily accessible small-animal model of HCV infection have hampered the development of antiviral agents for HCV. Neverthe-less, new antiviral agents targeting HCV are now in preclinical and clinical development.This monograph, providing an up-to-date overview of the field of Hepatitis Prevention and Treatment, includes contributions from internationally recognized experts in the field of viral hepatitis, and covers the current state of knowledge and practice regarding the molecular biology, immunology, biochemistry, pharmacology and clinical aspects of chronic HBV and HCV infection. The volume includes salient topics such as: the history and epidemiology of HBV and HCV; recent insights into the molecular mechanisms of viral replication; the host immune response to infection and a discussion of the use (HBV) or potential development (HCV) of vaccines; the current standard of care for chronically-infected patients; and emerging therapies and issues associated with current antiviral treatments. The latest information to researchers and clinicians actively engaged in viral hepatitis research is provided, but also sufficient background and discussion of the literature to benefit the newcomer to the field.

This is the first monograph devoted to a fairly wide class of operators, namely band and band-dominated operators and their Fredholm theory. Applications are presented to several important classes of such operators: convolution type operators and pseudo-differential operators on bad domains and with bad coefficients.

Die Erforschung des Baugrundes als wichtiger Bestandteil einer Baumaßnahme ist eine relativ junge Wissenschaft. Falsche Einschätzung der Baugrundverhältnisse und hieraus resultierende, zum Teil erhebliche Haftungsrisiken haben es notwendig werden lassen, der Einstufung der Bodenverhältnisse, der Methodik der Baugrunderkundung und der Berechnung der Gründungsart ein Regelwerk voranzustellen. Für den Bauherrn ist wichtig, dass nur ausreichende und regelgerechte Baugrunduntersuchung ihm die gewünschte Planungssicherheit, Kostensicherheit und Schadensfreiheit bietet. Das Buch informiert über die Verfahren der Baugrund- und Bauwerksanalysen, Instandsetzungsverfahren von Gründungen und die Schadensbeseitigung durch Verpresstechniken. Zahlreiche Beispiele aus der Praxis dokumentieren Sanierungsleistungen an historischen Gebäuden, Stützmauern und Brücken.

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary".

Fractal geometry is used to model complicated natural and technical phenomena in various disciplines like physics, biology, finance, and medicine. Since most convincing models contain an element of randomness, stochastics enters the area in a natural way. This book documents the establishment of fractal geometry as a substantial mathematical theory. As in the previous volumes, which appeared in 1998 and 2000, leading experts known for clear exposition were selected as authors. They survey their field of expertise, emphasizing recent developments and open problems. Main topics include multifractal measures, dynamical systems, stochastic processes and random fractals, harmonic analysis on fractals.

This book deals with the dynamics of general systems such as foliations, groups and pseudogroups, systems which are closely related via the notion of holonomy. It concentrates on notions and results related to different ways of measuring complexity of systems under consideration.