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17 2 STRESS FIELDS FOR SIMPLE STRUCTURES 2. the plane stress condition with no variation of stress over the thickness of the element) or they are subdivided into several plates. If the lower bound method of the theory of plasticity is employed, then an admissible stress field or any combination of such stress fields may be selected.

The field of neuroscience is experiencing a period of unprecedented growth. The range of ap­ proaches used to investigate the fundamental mechanisms underlying different aspects of somatosen­ sory perception has expanded substantially since the last International Symposium on Informa­ tion Processing in the Somatosensory System. Diversity of approach has become the hallmark of somatosensory research, and I believe that the impact of this diversity continues to be positive. of this symposium with previous symposia will show that researchers are employing Comparison an array of new methods and technologies and that they are offering new insights into old ques­ tions. The techniques range from studies of ionic channels, single unit recordings, functional brain imaging to psychophysics. A careful reading ofthe chapters reveals subtle and, on occasion, also obvious differences of opinion about experimental outcomes, approaches, and views. These differences are healthy signs of venture into new and uncharted territories. It is my hope that read­ ers will appreciate both the diversity of the research addressing somesthesis, and the personal commitment, enthusiasm, and scientific rigor of the participants who made this symposium and volume meaningful for all involved. We all look forward to tracking the progress of somatosensory research at our next Symposium at the turn of the century. OveFranzen November 1995 xv List of Contributors David T. Blake Harold Burton Krieger MindlBrain Institute Department of Anatomy and Neurobiology Department of Neuroscience Washington University The Johns Hopkins University School of Medicine Baltimore, MD 21218, USA St.

Building on the existing titles in the "Airways Smooth Muscle" sub-series, the sixth volume explores physiological and pharmacological processes in the lung in vivo.

thrombospondin-l may be encoded by a tumor suppressor gene. Dr. O'Reilly discusses angiostatin, an exciting recently discovered factor derived from the fibrinolytic proenzyme plasminogen that inhibits tumor angiogenesis, primary tumor growth, and formation of metastases. In addition to the soluble class of angiogenesis-regulatory factors discussed above, interactions of endothelial cells with components of the extracellular matrix and with other cell types are critical for proper formation of vessels. Drs. Grant and Kleinman discuss the role of laminin and other matrix molecules in regulation of capillary formation. Dr. van Hinsbergh and colleagues describe the role of fibrin and the fibrinolytic system in angiogenesis associated with wound repair. Cell surface mole­ cules that interact with the extracellular matrix have been implicated in the regulation of angiogenesis. Dr. Varner discusses some exciting new studies on the roles of specific vascular cell integrins (a /33 and a /3s) in mediating v v tumor angiogenesis and angiogenesis associated with wound healing. The pericyte, a vascular smooth muscle-like cell, exerts a powerful regulatory effect during the later stages of angiogenesis in which mature capillaries are formed. These mechanisms are discussed by Drs. Hirschi and D' Amore. With all the recent progress in the molecular biology of angiogenesis, the contribution of microenvironmental conditions such as hypoxia and pH to angiogenesis is often ignored. Drs. Rockwell and Knisely review this area of investigation and present studies of experimental tumor models.

Volume 46 of "Progress in Drug Research" contains seven reviews and the various indexes which facilitate its use and establish the connection with the previous volumes. The articles in this volume deal with endo­ genous sodium pump inhibition, with neurotransmitters involved in the central regulation of the cardiovascular system, with leukotrienes and development of novel anti-inflammatory agents, with antithrombotic stra­ tegies and drugs affecting the plasma fibrinogen levels, with natural ami­ noglycosides and polyamines and their effects in the mammalian orga­ nism, with the latest developments in antidepressant agents and with immunopharmacological and biochemical bases of Chinese herbal medi­ cine. These reviews provide valuable information on several new deve­ lopments in the complex domain of drug research. In the 37 years that PDR has existed, the Editor has enjoyed the valua­ ble help and advice of many colleagues. Readers, the authors of the reviews and, last but not least, the reviewers have all contributed greatly to the success of this series of monographs. Although the comments received so far have generally been favorable, it is nevertheless necessary to analyze and to reassess the current position and the future direction of such publi­ cations.

Highlighting the current developments and future directions in GABA research, the ambitious aim of this topical volume is to cover GABA from the molecular mechanisms of its transmission to new targets for pharmaceutical research. Distinguished scientists at the forefront of GABA research were invited to contribute reviews on glutamate decarboxylase and autoimmunity, molecular structure and functional regulation of GABA transporters, transmitter release and GABA receptor regulation, GABA receptor subtypes and functional regulation, and GABA receptor ligands and their therapeutic application. Describing the latest advances in what has become a rapidly-evolving field, this volume will prove immensely valuable to neuroscientists, pharmacologists, biochemists, and physiologists working in the field of GABA research.

Periodic differential operators have a rich mathematical theory as well as important physical applications. They have been the subject of intensive development for over a century and remain a fertile research area. This book lays out the theoretical foundations and then moves on to give a coherent account of more recent results, relating in particular to the eigenvalue and spectral theory of the Hill and Dirac equations. The book will be valuable to advanced students and academics both for general reference and as an introduction to active research topics.

Biological O2 sensing probes and measurement techniques were first introduced in the late 80s. In the last 3-5 years they have undergone major development that have made them available and affordable for a broad range of applications in various disciplines of the life and biomedical sciences. These new chemistries and technologies, which are significantly different from the majority of other fluorescence-based probes and detection techniques, have already demonstrated their high utility. This book will provide a systematic overview of the existing and emerging O2 sensing technologies in their different modifications, a practical guide to their rational selection and use, and examples of biological applications/case studies, including details on how to set up and conduct such experiments, troubleshoot and interpret the data.

Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few.

This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook. The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems. ------The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (...) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world.(Mathematical Reviews)

This volume comprises the proceedings of the Conference on Operator Theory and its Applications held in Gothenburg, Sweden, April 26-29, 2011.

Galileo Galilei said he was "e;reading the book of nature"e; as he observed pendulums swinging, but he might also simply have tried to draw the numbers themselves as they fall into networks of permutations or form loops that synchronize at different speeds, or attach themselves to balls passing in and out of the hands of good jugglers. Numbers are, after all, a part of nature. As such, looking at and thinking about them is a way of understanding our relationship to nature. But when we do so in a technical, professional way, we tend to overlook their basic attributes, the things we can understand by simply "e;looking at numbers."e; Tom Johnson is a composer who uses logic and mathematical models, such as combinatorics of numbers, in his music. The patterns he finds while "e;looking at numbers"e; can also be explored in drawings. This book focuses on such drawings, their beauty and their mathematical meaning. The accompanying comments were written in collaboration with the mathematician Franck Jedrzejewski.

The Indian National. Science Academy has planned to bring out monographs on special topics with the aim of providing acce~sible surveys/reviews of topics of current research in various fields. Prof. S. K. Malik, FNA, Editor of Publications INSA asked me in October 1997 to edit a volume on algebra in this series. I invited a number of algebraists, several of them working in group rings, and it is with great satisfaction and sincere thanks to the authors that I present here in Algebra: Some Recent Advances the sixteen contributions received in response to my invitations. I. B. S. Passi On Abelian Difference Sets K. r Arasu* and Surinder K. Sehgal 1. Introduction We review some existence and nonexistence results - new and old - on abelian difference sets. Recent surveys on difference sets can be found in Arasu (1990), Jungnickel (1992a, b), Pott (1995), Jungnickel and Schmidt (1997), and Davis and Jedwab (1996). Standard references for difference sets are Baumert (1971), Beth et al. (1998), and Lander (1983). This article presents a flavour of the subject, by discussing some selected topics. Difference sets are very important in combinatorial design theory and in commu­ nication engineering while designing sequences with good correlation properties. Our extended bibliography covers a wide variety of papers written in the area of difference sets and related topics.

Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations. Readers of this exposition will be advanced students and researchers in mathematics, physics and other.

Kurt Goedel, together with Bertrand Russell, is the most important name in logic, and in the foundations and philosophy of mathematics of this century.

In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads.

4 Hardy-Toeplitz Operators Over Tubular Domains 267 4.

Advancements in digital sensor technology, digital image analysis techniques, as well as computer software and hardware have brought together the fields of computer vision and photogrammetry, which are now converging towards sharing, to a great extent, objectives and algorithms.

This book shows how the abstract methods of analytic semigroups and evolution equations in Banach spaces can be applied to the study of parabolic problems. It presents known theorems from a novel perspective and teaches how to exploit basic techniques.

Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.

This distinguishes it from the theory of nonlinear contraction semigroups whose basis is a nonlinear version of the Hille Yosida theorem: the Crandall-Liggett theorem. Thus the theory of nonlinear contraction semigroups does not apply to systems, in general, since they do not allow for a maximum principle.

Andreas Floer died on May 15, 1991 an untimely and tragic death. His visions and far-reaching contributions have significantly influenced the developments of mathematics. His main interests centered on the fields of dynamical systems, symplectic geometry, Yang-Mills theory and low dimensional topology. Motivated by the global existence problem of periodic solutions for Hamiltonian systems and starting from ideas of Conley, Gromov and Witten, he developed his Floer homology, providing new, powerful methods which can be applied to problems inaccessible only a few years ago. This volume opens with a short biography and three hitherto unpublished papers of Andreas Floer. It then presents a collection of invited contributions, and survey articles as well as research papers on his fields of interest, bearing testimony of the high esteem and appreciation this brilliant mathematician enjoyed among his colleagues. Authors include: A. Floer, V.I. Arnold, M. Atiyah, M. Audin, D.M. Austin, S.M. Bates, P.J. Braam, M. Chaperon, R.L. Cohen, G. Dell' Antonio, S.K. Donaldson, B. D'Onofrio, I. Ekeland, Y. Eliashberg, K.D. Ernst, R. Finthushel, A.B. Givental, H. Hofer, J.D.S. Jones, I. McAllister, D. McDuff, Y.-G. Oh, L. Polterovich, D.A. Salamon, G.B. Segal, R. Stern, C.H. Taubes, C. Viterbo, A. Weinstein, E. Witten, E. Zehnder

The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis.

The book is an outgrowth of the international conference "Centennial Hurwitz on Stability Theory" which was held to honor Adolf Hurwitz, whose arti cle on the location of roots of a polynomial was published one hundred years ago.

Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely:¿ control theory ¿ classical mechanics ¿ Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) ¿ diffusion on manifolds ¿ analysis of hypoelliptic operators ¿ Cauchy-Riemann (or CR) geometry.Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists:¿ André Bellaïche: The tangent space in sub-Riemannian geometry ¿ Mikhael Gromov: Carnot-Carathéodory spaces seen from within ¿ Richard Montgomery: Survey of singular geodesics ¿ Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers ¿ Jean-Michel Coron: Stabilization of controllable systems

Over the past ten years, the asymptotic theory of one-parameter semigroups of operators has witnessed an explosive development. A number oflong-standing open problems have recently been solved and the theory seems to have obtained a certain degree of maturity. These notes, based on a course delivered at the University of Tiibingen in the academic year 1994-1995, represent a first attempt to organize the available material, most of which exists only in the form of research papers. If A is a bounded linear operator on a complex Banach space X, then it is an easy consequence of the spectral mapping theorem exp(tO"(A)) = O"(exp(tA)), t E JR, and Gelfand's formula for the spectral radius that the uniform growth bound of the wt family {exp(tA)h~o, i. e. the infimum of all wE JR such that II exp(tA)II :::: Me for some constant M and all t 2: 0, is equal to the spectral bound s(A) = sup{Re A : A E O"(A)} of A. This fact is known as Lyapunov's theorem. Its importance resides in the fact that the solutions of the initial value problem du(t) =A () dt u t , u(O) = x, are given by u(t) = exp(tA)x. Thus, Lyapunov's theorem implies that the expo­ nential growth of the solutions of the initial value problem associated to a bounded operator A is determined by the location of the spectrum of A.

Die Akustik ist ein Gebiet, das erstaunlicherweise in der wissenschaftshistorischen Literatur nur relativ selten zu finden ist. Darstellungen langerer Epochen in der Entwicklung dieses Fachgebietes haben noch groBeren Seltenheitswert. Nach dem Zweiten Weltkrieg erschien bisher lediglich F.V. HUNTS "Origins in acoustics", das im wesentlichen die Zeitepoche von der Antike bis NEWTON beschreibt. Ein Buch, das in gewisser Weise aIs eine Fortsetzung betrachtet werden kann, ist CANNON/DoSTROVSKYS "The evolution of dynamics: Vibration theory from 1687 to 1742". Es setzt jedoch gemlill seinem Titel ganz bestimmte Akzente. Mit NEWTONS "Principia" von 1687 beginnt eine Periode ausgesprochen theoretischer Forschung auf dem Gebiet der Akustik, fUr die Namen wie z.B. TAYLOR, SAUVEUR, EULER, D'ALEMBERT, JOHANN und DANIEL BERNOULLI Zeugnis ablegen. Dieses Uberwiegen der Theorie wird 1787 mit dem Auftreten CHLADNIS wieder zugunsten des Experiments verschoben. Da es tiber die Tatigkeit der eben genannten Forscher bereits einige ausfUhrliche DarsteIlungen gibt, beginnt die detaillierte Betrachtung in diesem Buch erst im Erscheinungsjahr von CHLADNIS Erstlingswerk. Ziel dieses Buches ist es, nicht nur die akustischen Arbeiten CHLADNIS zu beschreiben, sondem auch seinen Einflull auf die Forschung bis in die Mitte des 19.

Incomplete second order linear differential equations in Banach spaces as well as first order equations have become a classical part of functional analysis. Special emphasis is placed on new surprising effects arising for complete second order equations which do not take place for first order and incomplete second order equations.

"Functional Analysis" is a comprehensive, 2-volume treatment of a subject lying at the core of modern analysis and mathematical physics. Volume II moves on to more advanced topics including unbounded operators, spectral decomposition, expansion in generalized eigenvectors, rigged spaces, and partial differential operators.

In 1992, a group of scientists including molecular biologists, microbiologists, population biolo­ gists, ecologists, human geneticists, moral philosophers and others met discussing the state of affairs regarding the deliberate or unintentional release of genetically modified organisms. The proceedings of this meeting were subsequently published by Birkhauser Verlag as Transgenic Organisms: Risk Assessment of Deliberate Release (K. Wohrmann and J. Tomiuk). Since then we have gained many new insights that are also worthy of discussion. And although other equally important scientific views on the release of genetically modified organisms exist, we have mainly concentrated on aspects of population biology and evolution. The results of a second meeting in 1995 are summarized here. We are grateful to colleagues and friends for their help in the translation, correction and review of the authors' contributions. We especially want to thank Jutta Bachmann, Donna Devine, Diana von Finck, Friedrich Laplace, Volker Loeschcke, Rolf Lorenz, Dave Parker and Trevor Petney. A grant (BMFT N' 0311035) from the Ministerium fUr Forschung und Technologie der Bundesrepublik Deutschland again made possible the continuation of this cooperative endeavour.