Bücher veröffentlicht von Springer Basel

The 12th conference on "Variational Calculus, Optimal Control and Applications" took place September 23-27, 1996, in Trassenheide on the Baltic Sea island of Use dom. The conferences were founded, and led ten times, by Professor Bittner (Greifswald) and Professor KlCitzler (Leipzig), who both celebrated their 65th birthdays in 1996.

This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory.

th This volume is dedicated to Carl Pearcy on his 60 birthday. It collects recent contributions to operator theory, nonselfadjoint operator algebras, measure the­ ory, and the theory of moments by several of the lead­ ing specialists in those areas. Many of the contributors are collaborators or former students of Carl Pearcy, and the variety of the topics bears witness to the wide range of his work and interests. The editors were helped by many in the compi­ lation of this volume. Srdjan Petrovic helped com­ pile Carl's list of publications, while Arlen Brown and George Exner helped in writing the biographical and mathematical sketch. The work of many referees, who must remain anonymous, was very valuable. Israel Gohberg suggested that we publish this volume in the distinguished series Operator Theory: Advances and Applications. The whole volume was expertly typeset by Elena Fraboschi. We wish to extend to all of these people our heartfelt thanks. CARL M. PEARCY Carl M. Pearcy: A Biographical Sketch H. BERCOVICI fj C. FOIAS Carl Mark Pearcy, Jr. was born on August 23, 1935 in Beaumont, Texas. He was the eldest of two sons of Carl Mark Pearcy, Sr., and Carrie Edith (Tilbury) Pearcy.

This and the next volume of the OT series contain the proceedings of the Work­ shop on Operator Theory and its Applications, IWOTA 95, which was held at the University of Regensburg, Germany, July 31 to August 4, 1995. It was the eigth workshop of this kind. Following is a list of the seven previous workshops with reference to their proceedings: 1981 Operator Theory (Santa Monica, California, USA) 1983 Applications of Linear Operator Theory to Systems and Networks (Rehovot, Israel), OT 12 1985 Operator Theory and its Applications (Amsterdam, The Netherlands), OT 19 1987 Operator Theory and Functional Analysis (Mesa, Arizona, USA), OT 35 1989 Matrix and Operator Theory (Rotterdam, The Netherlands), OT 50 1991 Operator Theory and Complex Analysis (Sapporo, Japan), OT 59 1993 Operator Theory and Boundary Eigenvalue Problems (Vienna, Austria), OT 80 IWOTA 95 offered a rich programme on a wide range of latest developments in operator theory and its applications. The programme consisted of 6 invited plenary lectures, 54 invited special topic lectures and more than 100 invited session talks. About 180 participants from 25 countries attended the workshop, more than a third came from Eastern Europe. The conference covered different aspects of linear and nonlinear spectral prob­ lems, starting with problems for abstract operators up to spectral theory of ordi­ nary and partial differential operators, pseudodifferential operators, and integral operators. The workshop was also focussed on operator theory in spaces with indefinite metric, operator functions, interpolation and extension problems.

The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests.

Herbert Amann's work is distinguished and marked by great lucidity and deep mathematical understanding. The present collection of 31 research papers, written by highly distinguished and accomplished mathematicians, reflect his interest and lasting influence in various fields of analysis such as degree and fixed point theory, nonlinear elliptic boundary value problems, abstract evolutions equations, quasi-linear parabolic systems, fluid dynamics, Fourier analysis, and the theory of function spaces. Contributors are A. Ambrosetti, S. Angenent, W. Arendt, M. Badiale, T. Bartsch, Ph. Bénilan, Ph. Clément, E. Faöangová, M. Fila, D. de Figueiredo, G. Gripenberg, G. Da Prato, E.N. Dancer, D. Daners, E. DiBenedetto, D.J. Diller, J. Escher, G.P. Galdi, Y. Giga, T. Hagen, D.D. Hai, M. Hieber, H. Hofer, C. Imbusch, K. Ito, P. Krejcí, S.-O. Londen, A. Lunardi, T. Miyakawa, P. Quittner, J. Prüss, V.V. Pukhnachov, P.J. Rabier, P.H. Rabinowitz, M. Renardy, B. Scarpellini, B.J. Schmitt, K. Schmitt, G. Simonett, H. Sohr, V.A. Solonnikov, J. Sprekels, M. Struwe, H. Triebel, W. von Wahl, M. Wiegner, K. Wysocki, E. Zehnder and S. Zheng.

Das Buch ist ein Leitfaden über die modernen Fertigungsverfahren in der Triebwerktechnik. Besonderer Wert wurde hierbei auf die Darstellung der werkstofftechnischen, metallkundlichen und physikalischen Zusammenhänge gelegt, von denen sich die wesentlichen technischen Maßnahmen der Fertigung ableiten. Die Vertiefung in einzelne Sachgebiete wird mit Hilfe eines umfangreichen Literaturverzeichnisses unterstützt. Das Buch wendet sich mit seiner interdisziplinären Darstellung von Werkstofftechnik, Fertigungstechnik und Funktionalität der Maschinenkomponenten an Ingenieure und Techniker, die an der Entwicklung und Fertigung von Gasturbinen arbeiten. Ebenso sind die Studenten der Werkstofftechnik, der Fertigungstechnik, des Maschinenbaus und der ihm zugeordneten Disziplinen angesprochen. Prof. Dr.-Ing. Peter Adam ist Inhaber des Lehrstuhls für Oberflächentechnik an der Friedrich-Schiller-Universität Jena. Er arbeitete über 20 Jahre als Leiter der Fertigungsverfahrensentwicklung bei der Motoren- und Turbinen-Union München.

Fatty acids play an important role in the barrier function of skin and represent a major source of proinflammatory mediators such as prostaglandins, leukotrienes and other lipids in inflammatory skin disorders.

Pain and inflammation are inextricably linked phenomena. The observation that chemical mediators with combined pro-inflammatory, algesic and/or hyperalgesic activity occur at the site of inflammation is fundamental not only to our present understanding of the inflammatory process but also to our attempts to devise clini­ cally useful anti-inflammatory therapies. Over a hundred years ago it was recognised that primary sensory neurones play a crucially important "dual" role in inflammation. By affecting the transfer of infor­ mation from peripheral nociceptors to the spinal cord, a subpopulation of sensory nerves {"pain fibres"} initiate algesia and hyperalgesia, whose sensations are then modified and fine-tuned in the central nervous system. Equally important is the release from the peripheral terminals of sensory neurones of neuropeptides, the acute effects of which are observed as changes in microvascular tone and perme­ ability leading to neurogenic inflammation. Over the last decade it has become increasingly clear that this view of the func­ tion of sensory nerves is somewhat over-simplified. For example, the mechanisms underlying hyperalgesia may, in certain circumstances, be mimicked in other condi­ tions such as the hypersensivity associated with asthma. Furthermore, it has become increasingly evident that over a longer time period the release of neuropeptides from peripheral sensory nerve endings may also have modulating effects on inmune cells and that this may be relevant to chronic inflammatory disease and possibly also to inflammatory hyperalgesia.

In this volume on valproate emphasis is placed on the scientific back ground leading to the discovery of val pro ate, its subsequent pharmacologi cal and toxicological characterization, and its clinical development into one of the most widely and successfully used anti epileptic drugs, a real mile stone in drug therapy.

For some years, international guidelines on the management of asthma have stressed the importance of early intervention with anti-inflammatory drugs to prevent acute asthma exacerbations and to avert chronic inflammatory damage to the airway.

These chapters provide a unique vantage point from which to examine this question, as the summarized work ranges from evolutionary approaches across diverse species, to the basics of the immune response, to the effect of cytokines on peripheral and central nervous system sites, to therapeutic potential in humans.

At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de­ rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.

This volume will be of great value to all those researchers in the area of the inflam matory response, notably academics, clinicians and members of the pharmaceutical industry.

Claire Detrain, Jean-Louis Deneubourg and Jacques Pasteels Studies on insects have been pioneering in major fields of modern biology. In the same manner, recent studies, which decipher the collective behaviour of insect societies, might be now setting the stage for the elucidation of information processing in animals.

Hypertension is one of the cardiovascular diseases which is most common throughout the world. Such hypertension is termed as essential hypertension. In a few cases (5- 15%), the hypertension is secondary to definable causes, such as renal artery stenosis, a pheochromocytoma, or an endocrine disorder.

A description of the latest and most appropriate mathematical and numerical methods for optimizing soil venting. This book will be of interest to applied mathematicians, geophysicists, geoecologists, soil physicists, and environmental engineers.

Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This monograph, aimed at researchers and students in these fields, explores several aspects of this relationship. The primary focus of the text is the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory. The text first gives the requisite background material from harmonic analysis and discusses known results concerning the nontangential maximal function and area function, as well as the central and essential role these have played in the development of the field.The book next discusses further refinements of traditional results: among these are sharp good-lambda inequalities and laws of the iterated logarithm involving nontangential maximal functions and area functions. Many applications of these results are given. Throughout, the constant interplay between probability and harmonic analysis is emphasized and explained. The text contains some new and many recent results combined in a coherent presentation.

Theorems of factorising matrix functions and the operator identity method play an essential role in this book in constructing the spectral theory (direct and inverse problems) of canonical differential systems. Includes many varied applications of the general theory.

The Taylor-Couette system is one of the most studied examples of fluid flow exhibiting the spontaneous formation of dynamical structures. In this book, the variety of time independent solutions with periodic spatial structure is numerically investigated by solution of the Navier-Stokes equations.

This volume, addressed to researchers and postgraduate students, compiles up-to-date research and expository papers on different aspects of complex analysis, including relations to operator theory and hypercomplex analysis. Subjects include the Schroedinger equation, subelliptic operators, Lie algebras and superalgebras, among others.

Many new antileukotriene drugs are now marketed as antiasthma drugs and represent the first new drugs in this field since the 1970s.

Brauer had already introduced the defect of a block and opened the way towards a classification by solving all the problems in defects zero and one, and by providing some evidence for the finiteness of the set of blocks with a given defect.

A collection of contributions on a variety of mathematical, physical and engineering subjects related to turbulence. Topics include mathematical issues, control and related problems, observational aspects, two- and quasi-two-dimensional flows, basic aspects of turbulence modeling, statistical issues and passive scalars.

The application of PDE-based control theory and the corresponding numerical algorithms to industrial problems have become increasingly important in recent years. This volume offers a wide spectrum of aspects of the discipline, and is of interest to mathematicians and scientists working in the field.

This self-contained research monograph focuses on semilinear Dirichlet problems and similar equations involving the p-Laplacian. The author explains new techniques in detail, and derives several numerical methods approximating the concentration point and the free boundary. The corresponding plots are highlights of this book.

A collection of 20 refereed research or review papers presented at a six-day seminar in Switzerland. The contributions focus on stochastic analysis, its applications to the engineering sciences, and stochastic methods in financial models, which was the subject of a minisymposium.

The contributions in this volume are dedicated to Vladimir G. Maz'ya and are par­ tially based on talks given at the conference "Functional Analysis, Partial Differ­ ential Equations, and Applications", which took place at the University of Rostock from August 31 to September 4, 1998, to honour Prof. Maz'ya. This conference (a satellite meeting of the ICM) gave an opportunity to many friends and colleagues from all over the world to honour him. This academic community is very large. The scientific field of Prof. Maz'ya is impressively broad, which is reflected in the variety of contributions included in the volumes. Vladimir Maz'ya is the author and co-author of many publications (see the list of publications at the end of this volume), the topics of which extend from functional analysis, function theory and numerical analysis to partial differential equations and their broad applications. Vladimir G. Maz'ya provided significant contributions, among others to the the­ ory of Sobolev spaces, the capacity theory, boundary integral methods, qualitative and asymptotic methods of analysis of linear and nonlinear elliptic differential equations, the Cauchy problem for elliptic and hyperbolic equations, the theory of multipliers in spaces of differentiable functions, maximum principles for elliptic and parabolic systems, and boundary value problems in domains with piecewise smooth boundaries. Surveys on Maz'ya's work in different fields of mathematics and areas, where he made essential contributions, form a major part of the present first volume of The Maz'ya Anniversary Collection.

The book introduces new techniques which imply rigorous lower bounds on the complexity of some number theoretic and cryptographic problems. These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1.

To attempt to compile a relatively complete bibliography of the theory of functions of a real variable with the requisite bibliographical data, to enumer­ ate the names of the mathematicians who have studied this subject, exhibit their fundamental results, and also include the most essential biographical data about them, to conduct an inventory of the concepts and methods that have been and continue to be applied in the theory of functions of a real variable ... in short, to carry out anyone of these projects with appropriate completeness would require a separate book involving a corresponding amount of work. For that reason the word essays occurs in the title of the present work, allowing some freedom in the selection of material. In justification of this selection, it is reasonable to try to characterize to some degree the subject to whose history these essays are devoted. The truth of the matter is that this is a hopeless enterprise if one requires such a characterization to be exhaustively complete and concise. No living subject can be given a final definition without provoking some objections, usually serious ones. But if we make no such claims, a characterization is possible; and if the first essay of the present book appears unconvincing to anyone, the reason is the personal fault of the author, and not the objective necessity of the attempt.