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The interface between a living cell and the surrounding world plays a critical role in numerous complex biological processes. Sperm/egg fusion, virus/cell fusion, exocytosis, endocytosis, and ion permeation are a few examples of processes involving membranes. In recent years, powerful tools such as X-ray crystal­ lography, electron microscopy, nuclear magnetic resonance, and infra-red and Raman spectroscopy have been developed to characterize the structure and dy­ namics of biomembranes. Despite this progress, many of the factors responsible for the function of biomembranes are still not well understood. The membrane is a very complicated supramolecular liquid-crystalline structure that is largely composed of lipids, forming a bilayer, to which proteins and other biomolecules are anchored. Often, the lipid bilayer environment is pictured as a hydropho­ bic structureless slab providing a thermodynamic driving force to partition the amino acids of a membrane protein according to their solubility. However, much of the molecular complexity of the phospholipid bilayer environment is ignored in such a simplified view. It is likely that the atomic details of the polar head­ group region and the transition from the bulk water to the hydrophobic core of the membrane are important. An understanding of the factors responsible for the function of biomembranes thus requires a better characterization at the molec­ ular level of how proteins interact with lipid molecules, of how lipids affect protein structure and of how lipid molecules might regulate protein function.

High blood pressure disease is one of the most prevalent pathological conditions in modem society with potentially serious consequences. During the last two decades major progress has been made in the development of rational approaches to the treatment of high blood pressure. A key factor in this progress has been an increase in our understanding of how the brain controls blood pressure. The chapters in the present book, together with those in a previous volume, provide a broad overview of recent progress in our knowledge of the central neural mechanisms involved in the regulation of the cardiovascular system. It is our hope that these essays by leading experts in the field will not only provide a useful source of information, but will also stimulate inquiry leading to new discoveries in this critically important field of research. George Kunos John Ciriello vii List of Contributors Jeffrey J. Anderson, Department of Pharmacology and Toxicology, Indiana University School of Medicine, Indianapolis, Indiana 46208, USA Katsuyuki Ando, Fourth Department of Internal Medicine, University of Tokyo School of Medicine, Tokyo 112, Japan Jaideep S. Bains, Department of Physiology, Queen's University, Kingston, Ontario, Canada K7L 3N6 Kathleen H. Berecek, Department of Physiology and Biophysics and the Vascular Biology and Hypertension Program, The University of Alabama at Birmingham, Birmingham, Alabama 35294, USA Vernon S. Bishop, Department of Physiology, The University of Texas Health Science Center, San Antonio, Texas 78284-7756, USA P. A.

129 6.2 Representation of hints. 131 6.3 Monotonicity hints .. . 134 6.4 Theory ......... . 139 6.4.1 Capacity results 140 6.4.2 Decision boundaries 144 6.5 Conclusion 145 6.6 References....... ... 146 7 Analysis and Synthesis Tools for Robust SPRness 147 C. Mosquera, J.R. Hernandez, F. Perez-Gonzalez 7.1 Introduction.............. 147 7.2 SPR Analysis of Uncertain Systems. 153 7.2.1 The Poly topic Case . 155 7.2.2 The ZP-Ball Case ...... . 157 7.2.3 The Roots Space Case ... . 159 7.3 Synthesis of LTI Filters for Robust SPR Problems 161 7.3.1 Algebraic Design for Two Plants ..... . 161 7.3.2 Algebraic Design for Three or More Plants 164 7.3.3 Approximate Design Methods. 165 7.4 Experimental results 167 7.5 Conclusions 168 7.6 References ..... . 169 8 Boundary Methods for Distribution Analysis 173 J.L. Sancho et aZ. 8.1 Introduction ............. . 173 8.1.1 Building a Classifier System . 175 8.2 Motivation ............. . 176 8.3 Boundary Methods as Feature-Set Evaluation 177 8.3.1 Results ................ . 179 8.3.2 Feature Set Evaluation using Boundary Methods: S- mary. . . . . . . . . . . . . . . . . . . .. . . 182 . . .

Overview Many problems in mathematical physics and applied mathematics can be reduced to boundary value problems for differential, and in some cases, inte- grodifferential equations. These equations are solved by using methods from the theory of ordinary and partial differential equations, variational calculus, operational calculus, function theory, functional analysis, probability theory, numerical analysis and computational techniques. Mathematical models of quantum physics require new areas such as generalized functions, theory of distributions, functions of several complex variables, and topological and al- gebraic methods. The main purpose of this book is to provide a self contained and system- atic introduction to just one aspect of analysis which deals with the theory of fundamental solutions for differential operators and their applications to boundary value problems of mathematical physics, applied mathematics, and engineering, with the related applicable and computational features. The sub- ject matter of this book has its own deep rooted theoretical importance since it is related to Green's functions which are associated with most boundary value problems. The application of fundamental solutions to a recently devel- oped area of boundary element methods has provided a distinct advantage in that an integral equation representation of a boundary value problem is often x PREFACE more easily solved by numerical methods than a differential equation with specified boundary and initial conditions. This situation makes the subject more attractive to those whose interest is primarily in numerical methods.

It is a great pleasure to write the foreword to this important volume for several reasons. First: As far as we know, already primitive societies had to cope with environmental toxins of many kinds and set up regulations to limit their effects on food and drug use. Modem science, synthesizing tens of millions of new compounds has incredibly magnified this challenge. Today, xenobiotic metabolism has become a crucial task for humans and many other species alike. Second: When reading this book, one is impressed by the extraordinary speed at which neurotoxicology has advanced. Obviously, processing (and endogenous formation) oftox­ ins has become an extremely relevant topic. When I had the chance, almost three decades ago, to work in chemical pharmacology with Bernard B. Brodie at NIH, the drug metabo­ lizing system of the liver had just been recognized and characterized. We had just started to work on the biogenic amines, newly discovered cyclic nucleotides in rat brain, human cere­ brospinal fluid, and on the effects of toxic drugs like amphetamines. Today, biochemical neuropharmacology is a mature field of neuroscience.

By a Hilbert-space operator we mean a bounded linear transformation be­ tween separable complex Hilbert spaces. Decompositions and models for Hilbert-space operators have been very active research topics in operator theory over the past three decades. The main motivation behind them is the in­ variant subspace problem: does every Hilbert-space operator have a nontrivial invariant subspace? This is perhaps the most celebrated open question in op­ erator theory. Its relevance is easy to explain: normal operators have invariant subspaces (witness: the Spectral Theorem), as well as operators on finite­ dimensional Hilbert spaces (witness: canonical Jordan form). If one agrees that each of these (i. e. the Spectral Theorem and canonical Jordan form) is important enough an achievement to dismiss any further justification, then the search for nontrivial invariant subspaces is a natural one; and a recalcitrant one at that. Subnormal operators have nontrivial invariant subspaces (extending the normal branch), as well as compact operators (extending the finite-dimensional branch), but the question remains unanswered even for equally simple (i. e. simple to define) particular classes of Hilbert-space operators (examples: hyponormal and quasinilpotent operators). Yet the invariant subspace quest has certainly not been a failure at all, even though far from being settled. The search for nontrivial invariant subspaces has undoubtly yielded a lot of nice results in operator theory, among them, those concerning decompositions and models for Hilbert-space operators. This book contains nine chapters.

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi- neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati- cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high- quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil- ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu- ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in- vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work- shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe- matics and the Departments of Informatics and Mathematics at the Uni- versity of Oslo.

The purpose of this annual series, Applied and Computational Control, Signals, and Circuits, is to keep abreast of the fast-paced developments in computational mathematics and scientific computing and their increasing use by researchers and engineers in control, signals, and circuits. The series is dedicated to fostering effective communication between mathematicians, computer scientists, computational scientists, software engineers, theorists, and practicing engineers. This interdisciplinary scope is meant to blend areas of mathematics (such as linear algebra, operator theory, and certain branches of analysis) and computational mathematics (numerical linear algebra, numerical differential equations, large scale and parallel matrix computations, numerical optimization) with control and systems theory, signal and image processing, and circuit analysis and design. The disciplines mentioned above have long enjoyed a natural synergy. There are distinguished journals in the fields of control and systems the- ory, as well as signal processing and circuit theory, which publish high quality papers on mathematical and engineering aspects of these areas; however, articles on their computational and applications aspects appear only sporadically. At the same time, there has been tremendous recent growth and development of computational mathematics, scientific comput- ing, and mathematical software, and the resulting sophisticated techniques are being gradually adapted by engineers, software designers, and other scientists to the needs of those applied disciplines.

These three volumes entitled Advances in Hypersonics contain the Proceedings of the Second and Third Joint US/Europe Short Course in Hypersonics which took place in Colorado Springs and Aachen. The Second Course was organized at the US Air Force Academy, USA in January 1989 and the Third Course at Aachen, Germany in October 1990. The main idea of these Courses was to present to chemists, com- puter scientists, engineers, experimentalists, mathematicians, and physicists state of the art lectures in scientific and technical dis- ciplines including mathematical modeling, computational methods, and experimental measurements necessary to define the aerothermo- dynamic environments for space vehicles such as the US Orbiter or the European Hermes flying at hypersonic speeds. The subjects can be grouped into the following areas: Phys- ical environments, configuration requirements, propulsion systems (including airbreathing systems), experimental methods for external and internal flow, theoretical and numerical methods. Since hyper- sonic flight requires highly integrated systems, the Short Courses not only aimed to give in-depth analysis of hypersonic research and technology but also tried to broaden the view of attendees to give them the ability to understand the complex problem of hypersonic flight. Most of the participants in the Short Courses prepared a docu- ment based on their presentation for reproduction in the three vol- umes. Some authors spent considerable time and energy going well beyond their oral presentation to provide a quality assessment of the state of the art in their area of expertise as of 1989 and 1991.

The theory of operators stands at the intersection of the frontiers of modern analysis and its classical counterparts; of algebra and quantum mechanics; of spectral theory and partial differential equations; of the modern global approach to topology and geometry; of representation theory and harmonic analysis; and of dynamical systems and mathematical physics. The present collection of papers represents contributions to a conference, and they have been carefully selected with a view to bridging different but related areas of mathematics which have only recently displayed an unexpected network of interconnections, as well as new and exciting cross-fertilizations. Our unify- ing theme is the algebraic view and approach to the study of operators and their applications. The complementarity between the diversity of topics on the one hand and the unity of ideas on the other has been stressed. Some of the longer contributions represent material from lectures (in expanded form and with proofs for the most part). However, the shorter papers, as well as the longer ones, are an integral part of the picture; they have all been carefully refereed and revised with a view to a unity of purpose, timeliness, readability, and broad appeal. Raul Curto and Paile E. T.

This book deals with estimating and testing the probability of an event. It aims at providing practitioners with refined and easy to use techniques as well as initiating a new field of research in theoretical statistics. Practical, comprehensive tables for data analysis of the experimental state of investigations are included. Statisticians and practitioners will find this book an essential reference.

All models are lies. "e;The Earth orbits the sun in an ellipse with the sun at one focus"e; is false, but accurate enough for almost all purposes. This book describes the current state of the art of telling useful lies about time-varying systems in the real world. Specifically, it is about trying to "e;understand"e; (that is, tell useful lies about) dynamical systems directly from observa- tions, either because they are too complex to model in the conventional way or because they are simply ill-understood. B(:cause it overlaps with conventional time-series analysis, building mod- els of nonlinear dynamical systems directly from data has been seen by some observers as a somewhat ill-informed attempt to reinvent time-series analysis. The truth is distinctly less trivial. It is surely impossible, except in a few special cases, to re-create Newton's astonishing feat of writing a short equation that is an excellent description of real-world phenomena. Real systems are connected to the rest of the world; they are noisy, non- stationary, and have high-dimensional dynamics; even when the dynamics contains lower-dimensional attractors there is almost never a coordinate system available in which these at tractors have a conventionally simple description.

Empirical process techniques for independent data have been used for many years in statistics and probability theory. These techniques have proved very useful for studying asymptotic properties of parametric as well as non-parametric statistical procedures. Recently, the need to model the dependence structure in data sets from many different subject areas such as finance, insurance, and telecommunications has led to new developments concerning the empirical distribution function and the empirical process for dependent, mostly stationary sequences. This work gives an introduction to this new theory of empirical process techniques, which has so far been scattered in the statistical and probabilistic literature, and surveys the most recent developments in various related fields. Key features: A thorough and comprehensive introduction to the existing theory of empirical process techniques for dependent data * Accessible surveys by leading experts of the most recent developments in various related fields * Examines empirical process techniques for dependent data, useful for studying parametric and non-parametric statistical procedures * Comprehensive bibliographies * An overview of applications in various fields related to empirical processes: e.g., spectral analysis of time-series, the bootstrap for stationary sequences, extreme value theory, and the empirical process for mixing dependent observations, including the case of strong dependence. To date this book is the only comprehensive treatment of the topic in book literature. It is an ideal introductory text that will serve as a reference or resource for classroom use in the areas of statistics, time-series analysis, extreme value theory, point process theory, and applied probability theory. Contributors: P. Ango Nze, M.A. Arcones, I. Berkes, R. Dahlhaus, J. Dedecker, H.G. Dehling,

This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self­ preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con­ tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com­ pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso­ ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.

Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed.

Loosely speaking, adaptive systems are designed to deal with, to adapt to, chang- ing environmental conditions whilst maintaining performance objectives. Over the years, the theory of adaptive systems evolved from relatively simple and intuitive concepts to a complex multifaceted theory dealing with stochastic, nonlinear and infinite dimensional systems. This book provides a first introduction to the theory of adaptive systems. The book grew out of a graduate course that the authors taught several times in Australia, Belgium, and The Netherlands for students with an engineering and/or mathemat- ics background. When we taught the course for the first time, we felt that there was a need for a textbook that would introduce the reader to the main aspects of adaptation with emphasis on clarity of presentation and precision rather than on comprehensiveness. The present book tries to serve this need. We expect that the reader will have taken a basic course in linear algebra and mul- tivariable calculus. Apart from the basic concepts borrowed from these areas of mathematics, the book is intended to be self contained.

This monograph isdevoted to a special area ofBanach space theory-the Kothe- Bochner function space. Two typical questions in this area are: Question 1. Let E be a Kothe function space and X a Banach space. Does the Kothe-Bochner function space E(X) have the Dunford-Pettis property if both E and X have the same property? If the answer is negative, can we find some extra conditions on E and (or) X such that E(X) has the Dunford-Pettis property? Question 2. Let 1~ p~ 00, E a Kothe function space, and X a Banach space. Does either E or X contain an lp-sequence ifthe Kothe-Bochner function space E(X) has an lp-sequence? To solve the above two questions will not only give us a better understanding of the structure of the Kothe-Bochner function spaces but it will also develop some useful techniques that can be applied to other fields, such as harmonic analysis, probability theory, and operator theory. Let us outline the contents of the book. In the first two chapters we provide some some basic results forthose students who do not have any background in Banach space theory. We present proofs of Rosenthal's l1-theorem, James's theorem (when X is separable), Kolmos's theorem, N. Randrianantoanina's theorem that property (V*) is a separably determined property, and Odell-Schlumprecht's theorem that every separable reflexive Banach space has an equivalent 2R norm.

Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. In this self-contained textbook, algebraic graph theory is used to introduce groups; topological graph theory is used to explore surfaces; and geometric graph theory is implemented to analyze incidence geometries.After a preview of configurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5 introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied. Geometric aspects, some historical remarks, references, and applications of classical configurations appear in the last chapter.With over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint is well suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicians and researchers.

Unifying two decades of research, this book is the first to establish a comprehensive foundation for a systematic analysis and design of linear systems with general state and input constraints. For such systems, which can be used as models for most nonlinear systems, the issues of stability, controller design, additonal constraints, and satisfactory performance are addressed.The book is an excellent reference for practicing engineers, graduate students, and researchers in control systems theory and design. It may also serve as an advanced graduate text for a course or a seminar in nonlinear control systems theory and design in applied mathematics or engineering departments. Minimal prerequisites include a first graduate course in state-space methods as well as a first course in control systems design.

William Q. Meeker has made pioneering and phenomenal contributions to the general areaofreliabilityand,inparticular,tothetopicsofdegradationandacceleratedtesting. Hisresearchpublicationsandthenumerouscitationshehasreceivedoverthepastthree decades provide an ample testimony to this fact. Statistical methods have become critical in analyzing reliability and survival data. Highly reliable products have necessitated the development of accelerated testing and degradation models and their analyses. This volume has been put together in order to (i) review some of the recent advances on accelerated testing and degradation, (ii) highlight some new results and discuss their applications, and (iii) suggest possible directions for future research in these topics. With these speci?c goals in mind, many authors were invited to write a chapter for this volume. These authors are not only experts in lifetime data analysis, but also form a representative group from former students, colleagues, and other close professional associates of William Meeker. All contributions have been peer reviewed and organized into 26 chapters. For the convenience of readers, the volume has been divided into the following six parts: ¿ Review, Tutorials, and Perspective ¿ Shock Models ¿ Degradation Models ¿ Reliability Estimation and ALT ¿ Survival Function Estimation ¿ Competing Risk and Chaotic Systems Itneedstobeemphasizedherethatthisvolumeisnotaproceedings,butacarefully anddeliberatelyplannedvolumecomprisingchaptersconsistentwiththeeditorialgoals and purposes mentioned above. Our thanks go to all the authors who have contributed to this volume. Thanks are also due to Mrs. Debbie Iscoe for the excellent typesetting of the entire volume.SpecialthanksgotoMs.ReginaGorenshteynandMr.TomGrasso(Editor,Birkh¿ auser, Boston) for their interest and support for this project.

The 1991 Seminar on Stochastic Processes was held at the University of California, Los Angeles, from March 23 through March 25, 1991. This was the eleventh in a series of annual meetings which provide researchers with the opportunity to discuss current work on stochastic processes in an informal and enjoyable atmosphere. Previous seminars were held at Northwestern University, Princeton University, the University of Florida, the University of Virginia, the University of California, San Diego, and the University of British Columbia. Following the successful format of previous years there were five invited lectures. These were given by M. Barlow, G. Lawler, P. March, D. Stroock, M. Talagrand. The enthusiasm and interest of the participants created a lively and stimulating atmosphere for the seminar. Some of the topics discussed are represented by the articles in this volume. P. J. Fitzsimmons T. M. Liggett S. C. Port Los Angeles, 1991 In Memory of Steven Orey M. CRANSTON The mathematical community has lost a cherished colleague with the passing of Steven Orey. This unique and thoughtful man has left those who knew him with many pleasant memories. He has also left us with important contributions in the development of the theory of Markov processes. As a friend and former student, I wish to take this chance to recall to those who know and introduce to those who do not a portion of his lifework.

by Ivor Grattan-Guinness One of the distortions in most kinds of history is an imbalance between the study devoted to major figures and to lesser ones, concerning both achievements and influence: the Great Ones may be studied to death while the others are overly ignored and thereby remain underrated. In my own work in the history of mathematics I have noted at least a score of outstanding candidates for neglect, of whom Mario Pieri (1860¿1913) is one. A most able contributor to geometry, arithmetic and mathematical analysis, and mat- matical logic during his rather short life, his work and its legacy are not well known. The main reason is that Pieri worked ¿in the shadow of giants,¿ to quote one of the authors 1 of this volume. Born into a scholarly family in Lucca, Pieri was educated briefly at the University of Bologna and principally at the prestigious Scuola Normale Superiore, in Pisa; under the influence of Luigi Bianchi (1856¿1928) he wrote there his doctoral dissertations on al-braic and differential geometry. During his twenties came appointments in Turin, first at the military academy and then also at the university, where he fell under the sway of Corrado Segre (1863¿1924) in algebraic geometry, and Giuseppe Peano (1858¿1932) in the foundations of arithmetic, mathematical analysis, and mathematical logic. From 1900 to 1908 he held a chair at the University of Catania before moving to Parma, where he died from cancer.A list of errata can be found on the author Smith¿s personal webpage.

Devoted to the application of neural networks to the concrete problem of time series of sea dataGood reference for a diverse audience of grad students, researchers, and practitioners in applied mathematics, data analysis, meteorlogy, hydraulic, civil and marine engineeringMethods, models and alogrithms developed in the work are useful for the construction of sea structures, ports, and marine experiments