In 1997 the National Institute of Mental Health assembled a working group of international experts to address the mental health consequences of torture and related violence and trauma; report on the status of scientific knowledge; and include research recommendations with implications for treatment, services, and policy development. This book, dedicated to those who experience the horrors of torture and those who work to end it, is based on that report.
The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.
In 1996, representatives from 27 different countries met in Jerusalem to share ideas about traumatic stress and its impact. For many, this represented the first dialogue that they had ever had with a mental health professional from another country. Many of the attendees had themselves been exposed to either personal trauma or traumatizing stories involving their patients, and represented countries that were embroiled in conflicts with each other. Listening to one another became possible because of the humbling humanity of each participant, and the accuracy and objectivity of the data presented. Understanding human traumatization had thus become a common denomi nator, binding together all attendees. This book tries to capture the spirit of the Jerusalem World Conference on Traumatic Stress, bringing forward the diversities and commonalties of its constructive discourse. In trying to structure the various themes that arose, it was all too obvious that paradigms of different ways of conceiving of traumatic stress should be addressed first. In fact, the very idea that psychological trauma can result in mental health symptoms that should be treated has not yet gained universal acceptability. Even within medicine and mental health, competing approaches about the impact of trauma and the origins of symptoms abound. Part I discusses how the current paradigm of traumatic stress disorder developed within the historical, social, and process contexts. It also grapples with some of the difficulties that are presented by this paradigm from anthropologic, ethical, and scientific perspectives.
This little book is conceived as a service to mathematicians attending the 1998 International Congress of Mathematicians in Berlin. It presents a comprehensive, condensed overview of mathematical activity in Berlin, from Leibniz almost to the present day (without, however, including biographies of living mathematicians). Since many towering figures in mathematical history worked in Berlin, most of the chapters of this book are concise biographies. These are held together by a few survey articles presenting the overall development of entire periods of scientific life at Berlin. Overlaps between various chapters and differences in style between the chap ters were inevitable, but sometimes this provided opportunities to show different aspects of a single historical event - for instance, the Kronecker-Weierstrass con troversy. The book aims at readability rather than scholarly completeness. There are no footnotes, only references to the individual bibliographies of each chapter. Still, we do hope that the texts brought together here, and written by the various authors for this volume, constitute a solid introduction to the history of Berlin mathematics.
This book covers Lebesgue integration and its generalizations from Daniell's point of view, modified by the use of seminorms. Integrating functions rather than measuring sets is posited as the main purpose of measure theory. From this point of view Lebesgue's integral can be had as a rather straightforward, even simplistic, extension of Riemann's integral; and its aims, definitions, and procedures can be motivated at an elementary level. The notion of measurability, for example, is suggested by Littlewood's observations rather than being conveyed authoritatively through definitions of (sigma)-algebras and good-cut-conditions, the latter of which are hard to justify and thus appear mysterious, even nettlesome, to the beginner. The approach taken provides the additional benefit of cutting the labor in half. The use of seminorms, ubiquitous in modern analysis, speeds things up even further. The book is intended for the reader who has some experience with proofs, a beginning graduate student for example. It might even be useful to the advanced mathematician who is confronted with situations - such as stochastic integration - where the set-measuring approach to integration does not work.
