Bücher veröffentlicht von Birkhauser Boston

This volume contains a selection of papers by the participants of the 6. International Conference on Probability in Banach Spaces, Sand- bjerg, Denmark, June 16-D1, 1986. The conference was attended by 45 participants from several countries. One thing makes this conference completely different from the previous five ones, namely that it was ar- ranged jointly in Probability in Banach spaces and Banach space theory with almost equal representation of scientists in the two fields. Though these fields are closely related it seems that direct collaboration between researchers in the two groups has been seldom. It is our feeling that the conference, where the participants were together for five days taking part in lectures and intense discussions of mutual problems, has contributed to a better understanding and closer collaboration in the two fields. The papers in the present volume do not cover all the material pre- sented in the lectures; several results covered have been published else- where. The sponsors of the conference are: The Carlsberg Foundation, The Danish Natural Science Research Council, The Danish Department of Education, The Department of Mathematics, Odense University, The Department of Mathematics, Aarhus University, The Knudsen Foundation, Odense, Odense University, The Research Foundation of Aarhus University, The Thborg Foundation. The participants and the organizers would like to thank these institu- tions for their support. The Organizers. Contents A. de Acosta and M. Ledoux, On the identification of the limits in the law of the iterated logarithm in Banach spaces. . . . .

The Workshop on Stable Processes and Related Topics took place at Cor- nell University in January 9-13, 1990, under the sponsorship of the Mathemat- ical Sciences Institute. It attracted an international roster of probabilists from Brazil, Japan, Korea, Poland, Germany, Holland and France as well as the U. S. This volume contains a sample of the papers presented at the Workshop. All the papers have been refereed. Gaussian processes have been studied extensively over the last fifty years and form the bedrock of stochastic modeling. Their importance stems from the Central Limit Theorem. They share a number of special properties which facilitates their analysis and makes them particularly suitable to statistical inference. The many properties they share, however, is also the seed of their limitations. What happens in the real world away from the ideal Gaussian model? The non-Gaussian world may contain random processes that are close to the Gaussian. What are appropriate classes of nearly Gaussian models and how typical or robust is the Gaussian model amongst them? Moving further away from normality, what are appropriate non-Gaussian models that are sufficiently different to encompass distinct behavior, yet sufficiently simple to be amenable to efficient statistical inference? The very Central Limit Theorem which provides the fundamental justifi- cation for approximate normality, points to stable and other infinitely divisible models. Some of these may be close to and others very different from Gaussian models.

Animal models represent experimental investigations developed in one species for the purpose of studying phenomena in another species and provide numerous advantages for preclinical research. They allow scientists greater control and isolation of important experimental variables. Animal models are safe, reproducible strategies by which to evaluate and design new pharma- cological treatment strategies, while also allowing direct central nervous system intervention to alter the course of the aberrant behavior. Animal models have been developed for a number of mental illnesses; in this particular domain, they hold the promise to shed light on the still obscure etiologies of these illnesses and ultimately to facilitate the development and testing of "e;cures. "e; Yet, true models of mental illness are difficult to develop, because mental illness may be a uniquely human phenomenon. It was based on these considerations that the MacArthur Foundation Research Network on the Psychobiology of Depression set out to sponsor a conference to review the status, problems, promises, and relevance of animal models to the clinical conditions of affective disorders. The conference was held in September 1986 and included participants from both within the Network as well as scientists and scholars from various disciplines relevant to the concerns of the conference. After the conference was held, it became clear to the organizers that the material presented could be helpful to a broader field of investigators, since a significant portion of the information has not been presented elsewhere or in the unified context of a monograph.

This volume consists of about half of the papers presented during a three-day seminar on stochastic processes held at Northwestern U- versity, Evanston. The seminar was the fourth of such yearly seminars aimed at bringing together a small group of researchers to discuss their current work in an informal atmosphere. The invited participants in the seminar were B.W. ATKINSON, R.M. BLUMENTHAL, K. BURDZY, D. BURKHOLDER, M. CRANSTON, C. DOLEANS"e;'DADE, J.L. DOOB, N. FALKNER, P. FITZSIMMONS, J. GLOVER, F. KNIGHT, T. McCONNELL, J.B. MITRO, S. OREY, J. PITMAN, A.O. PITTENGER, Z. POP- STOJANOVIC, P. PROTTER, T. SALISBURY, M. SHARPE, C.T. SHIH, A. SZNITMAN, S.J. TAYLOR, J. WALSH, and R. WILLIAMS. We thank them and the other partiCipants for the lively seminar they created. The seminar was made possible through the partial support of the Air Force Office of Scientific Research via their Grant No. 82-0109 to Northwestern University. E.

The 1986 Seminar on Stochastic Processes was held at the University of Virginia, Charlottesville, in March. It was the sixth seminar in a continuing series of meetings which provide opportunities for researchers to discuss current work in stochastic processes in an informal atmosphere. Previous seminars were held at Northwestern University, Evanston and the University of Florida, Gainesville. The participants' enthusiasm and interest have resulted in stimulating and successful seminars. We thank them for it, and we also thank those participants who have permitted us to publish their research here. The seminar was made possible through the generous support of the Office of Naval Research (Contract # A86-4633-P) and the University of Virginia. We are grateful for their support. The participants were welcomed to Virginia by S. J. Taylor, whose store of energy and organizing talent resulted in a wonderful reunion of researchers. We extend to him our warmest appreciation for his efforts; his hospitality makes us hope that we can someday return to Virginia for another conference. J. ~. ~aineauille, ISBn TABLE OF CONTENTS K. L. CHUNG Green's Function for a Ball 1 P. J. FITZSIMMONS On the Identification of Markov Processes by the Distribution of Hitting Times 15 P. FITZSIMMONS On Two Results in the Potential Theory of J.

These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979. The main topic is the Hermitian classgroup of orders, and in particular of group rings. Most of this work is published here for the first time. The primary motivation came from the connection with the Galois module structure of rings of algebraic integers. The principal aim was to lay the theoretical basis for attacking what may be called the "e;converse problem"e; of Galois module structure theory: to express the symplectic local and global root numbers and conductors as algebraic invariants. A previous edition of these notes was circulated privately among a few collaborators. Based on this, and following a partial solution of the problem by the author, Ph. Cassou-Nogues and M. Taylor succeeded in obtaining a complete solution. In a different direction J. Ritter published a paper, answering certain character theoretic questions raised in the earlier version. I myself disapprove of "e;secret circulation"e;, but the pressure of other work led to a delay in publication; I hope this volume will make amends. One advantage of the delay is that the relevant recent work can be included. In a sense this is a companion volume to my recent Springer-Ergebnisse-Bericht, where the Hermitian theory was not dealt with. Our approach is via "e;Hom-groups"e;, analogous to that followed in recent work on locally free classgroups.

The first international conference on Probability in Banach Spaces was held at Oberwolfach, West Germany, in 1975. It brought together European researchers who, under the inspiration of the Schwartz Seminar in Paris, were using probabi- listic methods in the study of the geometry of Banach spaces, a rather small number of probabilists who were already studying classical limit laws on Banach spaces, and a larger number of probabilists, specialists in various aspects of the study of Gaussian processes, whose results and techniques were of interest to the members of the first two groups. This first conference was very fruitful. It fos- tered a continuing relationship among 50 to 75 probabilists and analysts working on probability on infinite-dimensional spaces, the geometry of Banach spaces, and the use of random methods in harmonic analysis. Six more international conferences were held since the 1975 meeting. Two of the meetings were held at Tufts University, one at Snderborg, Denmark, and the others at Oberwolfach. This volume contains a selection of papers by the partici- pants of the Seventh International Conference held at Oberwolfach, West Ger- many, June 26-July 2, 1988. This exciting and provocative conference was at- tended by more than 50 mathematicians from many countries. These papers demonstrate the range of interests of the conference participants. In addition to the ongoing study of classical and modern limit theorems in Banach spaces, a branching out has occurred among the members of this group.

Beginning in 1983, the Swedish Council for Planning and Coordination of Research has organized an annual workshop devoted to some aspect of the behavior and modeling of complex systems. These workshops have been held at the Abisko Research Station of the Swedish Academy of Sciences, a remote location far above the Arctic Circle in northern Sweden. During the period of the midnight sun, from May 4-8, 1987 this exotic venue served as the gathering place for a small group of scientists, scholars, and other connoisseurs of the unknown to ponder the problem of how to model "e;living systems,"e; a term singling out those systems whose principal components are living agents. The 1987 Abisko Workshop focused primarily upon the general system-theoretic concepts of process, function, and form. In particular, a main theme of the Workshop was to examine how these concepts are actually realized in biological, economic, and linguistic situations. As the Workshop unfolded, it became increasingly evident that the central concern of the participants was directed to the matter of how those quintessential aspects of living systems-metabolism, self-repair, and replication-might be brought into contact with the long-established modeling paradigms employed in physics, chemistry, and engineering.

N 1964 at the World's Fair in New York I City one room was dedicated solely to mathematics. The display included a very at- tractive and informative mural, about 13 feet long, sponsored by one of the largest com- puter manufacturing companies and present- ing a brief survey of the history of mathemat- ics. Entitled, "e;Men of Modern Mathematics,"e; it gives an outline of the development of that science from approximately 1000 B. C. to the year of the exhibition. The first centuries of this time span are illustrated by pictures from the history of art and, in particular, architec- ture; the period since 1500 is illuminated by portraits of mathematicians, including brief descriptions of their lives and professional achievements. Close to eighty portraits are crowded into a space of about fourteen square feet; among them, only one is of a woman. Her face-mature, intelligent, neither pretty nor handsome-may suggest her love of sci- 1 Emmy Noether ence and creative gift, but certainly reveals a likeable personality and a genuine kindness of heart. It is the portrait of Emmy Noether ( 1882 - 1935), surrounded by the likenesses of such famous men as Joseph Liouville (1809-1882), Georg Cantor (1845-1918), and David Hilbert (1862 -1943). It is accom- panied by the following text: Emmy Noether, daughter of the mathemati- cian Max, was often called "e;Der Noether,"e; as if she were a man.

JAMES L. MCGAUGH Understanding of the nature and functions of neurotransmitter systems in the brain has increased enormously in recent decades. Lack of knowledge required us, not too long ago, to use the adjective "e;putative"e; when discussing transmitters. Such caution is no longer essential (at least for a number of transmitters). Impressive progress has been achieved in understanding the pharmacology, biochemistry and anatomy of transmitter systems. There has, however, been relatively less progress in understanding the functioning of brain transmitters in regulating and mediating behavior. A simple and certainly correct explanation for this is, of course, that understanding of neurotransmitter functions requires prior detailed knowledge of basic pharmacology, biochemistry and anatomy. Beyond that, it now seems likely that progress in understanding the functions of brain neurotransmitters will proceed only as we examine the interactions of neurotransmitter systems in regulating behavioral functions. This premise is, of course, suggested by the findings of studies of the chemical neuroanatomy of the brain: Neurotransmitter systems are influenced by other neurotransmitter systems and, in tum, influence the same as well as other systems. No system works alone. The chapters in this book explicitly examine the interactions of neurotransmitter systems involved in the regulation of cognitive processes. The facts and interpretations offered provide compelling support for the premise that cognitive processes are orchestrated by interactions among neurotransmitter systems. And, they offer promise that understanding of such interactions will be of critical importance in the develop- ment of treatments for brain diseases affecting cognitive functioning.

A successful seientific career requires constant effort on the part of the seientist. If such a career is to be achieved by seientists in developing countries where the faeilities are not easily available, even more dedication is required. Dr. K. M. Sivanandaiah, having completed a successful career in the field of peptide chemistry, is such a seientist. Being weIl aware of the limited research facilities available in India, we are extraordinarily appreciative of Professor Sivanandaiah's dedication to the advancement of science. As a Professor of Chemistry and, until his retirement in 1992, the Head of the Department of Studies in Chemistry at Bangalore University, India, he not only devoted much of his time to his students, teaching basic organic chemistry, but was also able to contribute to the field of peptide chemistry. After completing 25 years of service at Central College, Bangalore, where he was admired as an outstanding teacher, Professor Sivanandaiah is still active in research. He is now Professor Emeritus and continues to contribute to the field of peptides. As former students of Professor Sivanandaiah, we felt that publishing a book containing articles related to the design, synthesis, conformation, and biological activity of peptides and written by eminent scientists in the field of peptide research would be a fitting tribute to his role in the field of bioorganic chemistry.

During the last ten years a powerful technique for the study of partial differential equations with regular singularities has developed using the theory of hyperfunctions. The technique has had several important applications in harmonic analysis for symmetric spaces.This book gives an introductory exposition of the theory of hyperfunctions and regular singularities, and on this basis it treats two major applications to harmonic analysis. The first is to the proof of Helgason's conjecture, due to Kashiwara et al., which represents eigenfunctions on Riemannian symmetric spaces as Poisson integrals of their hyperfunction boundary values.A generalization of this result involving the full boundary of the space is also given. The second topic is the construction of discrete series for semisimple symmetric spaces, with an unpublished proof, due to Oshima, of a conjecture of Flensted-Jensen.This first English introduction to hyperfunctions brings readers to the forefront of research in the theory of harmonic analysis on symmetric spaces. A substantial bibliography is also included. This volume is based on a paper which was awarded the 1983 University of Copenhagen Gold Medal Prize.

The primary mission of the medical school is to create new doctors. Once the medical student has received his or her doctorate, the medical school's interest in, and acceptance of, responsibility for the continued professional development of the physician ceases almost entirely. Yet, with scientific advances in medicine increasing exponentially and the inevitable erosion of memory with time, teachings from our schools of medicine become increasingly irrelevant, forgotten, or both. To maintain competence, the physician must continuously re-educate him- or herself. CME-Continuing Medical Education-will probably never attain the status of the medical school's degree-granting undergraduate program, but medical schools and their faculties must recognize their responsibility, not creating competent physicians but also for maintaining that com- only for petence. is the product of a Continuing Medical Education program This volume initiated by the Department of Anesthesiology at the Albert Einstein Col- lege of Medicine/Montefiore Medical Center. Our Department of Anes- thesiology has historically been, and continues to be, unusually active in post-doctoral education through regional and national conferences and symposia. We recognized, however, that programs that bring physicians together in one location for a limited menu of lectures, questions, and discussion reach only a fraction of the potential audience of anesthesiolo- gists. Such programs, as valuable as they are, by their very structure exclude more anesthesiologists than they include.

A mathematically precise definition of the intuitive notion of "e;algorithm"e; was implicit in Kurt Godel's [1931] paper on formally undecidable propo- sitions of arithmetic. During the 1930s, in the work of such mathemati- cians as Alonzo Church, Stephen Kleene, Barkley Rosser and Alfred Tarski, Godel's idea evolved into the concept of a recursive function. Church pro- posed the thesis, generally accepted today, that an effective algorithm is the same thing as a procedure whose output is a recursive function of the input (suitably coded as an integer). With these concepts, it became possible to prove that many familiar theories are undecidable (or non-recursive)-i. e. , that there does not exist an effective algorithm (recursive function) which would allow one to determine which sentences belong to the theory. It was clear from the beginning that any theory with a rich enough mathematical content must be undecidable. On the other hand, some theories with a substantial content are decidable. Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930). The de- termination of precise lines of division between the classes of decidable and undecidable theories became an important goal of research in this area. algebra we mean simply any structure (A, h(i E I)} consisting of By an a nonvoid set A and a system of finitary operations Ii over A.

Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten- dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un- derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: * A proof of localization at all energies is still missing for two dimen- sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro- cedure necessary to reach the full two-dimensional lattice has never been controlled. * The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.

This is the first of two volumes representing the current state of knowledge about Enriques surfaces which occupy one of the classes in the classification of algebraic surfaces. Recent improvements in our understanding of algebraic surfaces over fields of positive characteristic allowed us to approach the subject from a completely geometric point of view although heavily relying on algebraic methods. Some of the techniques presented in this book can be applied to the study of algebraic surfaces of other types. We hope that it will make this book of particular interest to a wider range of research mathematicians and graduate students. Acknowledgements. The undertaking of this project was made possible by the support of several institutions. Our mutual cooperation began at the University of Warwick and the Max Planck Institute of Mathematics in 1982/83. Most of the work in this volume was done during the visit of the first author at the University of Michigan in 1984-1986. The second author was supported during all these years by grants from the National Science Foundation.