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Rational Points: Seminar Bonn/Wuppertal 1983/84 (Aspects of Mathematics #6)

This book consists of the notes from the seminar Bonn/ Wuppertal 1983/ 84 on Arithmetic Geometry. It contains a proof for the Mordell conjecture and may be useful as an introduction to Arakelov's point of view in diophantine geometry. The third edition includes an appendix in which a detailed survey on the spectacular recent developments in arithmetic algebraic geometry is given. These beautiful new results have their roots in the material covered by this book.

Rational Points on Elliptic Curves (Undergraduate Texts in Mathematics)

The theory of elliptic curves involves a blend of algebra, geometry, analysis, and number theory. This book stresses this interplay as it develops the basic theory, providing an opportunity for readers to appreciate the unity of modern mathematics. The book’s accessibility, the informal writing style, and a wealth of exercises make it an ideal introduction for those interested in learning about Diophantine equations and arithmetic geometry.

Real Algebraic Geometry: Proceedings of the Conference held in Rennes, France, June 24-28, 1991 (Lecture Notes in Mathematics #1524)

Recent Progress in Many-Body Theories: Volume 3

The present volume contains the texts of the invited talks delivered at the Sev­ enth International Conference on Recent Progress in Many-Body Theories held at the University of Minnesota during the period August 26-31, 1991. The proceedings of the Fourth Conference (Oulu, Finland, 1987) and Fifth Conference (Arad, Israel, 1989) have been published by Plenum as the first two volumes of this series. Papers from the First Conference (Trieste, 1978) comprise Nuclear Physics volume A328, Nos. 1, 2. The Second Conference (Oaxtepec, Mexico, 1989) was published by Springer-Verlag as volume 142 of "Lecture Notes in Physics," entitled "Recent Progress in Many­ Body Theories." Volume 198 of the same series contains the papers from the Third Conference (Altenberg, Germany, 1983). These volumes are intended to cover a broad spectrum of current research topics in physics that benefit from the application of many-body theories for their elucidation. At the same time there is a focus on the development and refinement of many-body methods. One of the major aims of the conference series has been to foster the ex­ change of ideas among physicists working in such diverse areas as nucleon-nucleon in­ teractions, nuclear physics, astronomy, atomic and molecular physics, quantum chem­ istry, quantum fluids, and condensed matter physics. The present volume contains contributions from all of these areas.

Recombination of Atomic Ions (Nato Science Series B: #296)

This book is based on contributions to the NATO Advanced Research Workshop on Recombination of Atomic Ions. This was held at the Slieve Donard Hotel in Newcastle, Northern Ireland, between 6 and 9 October 1991 and attracted 35 participants from 5 countries. The book is inter.~ed to serve as an in-depth review of work to this date on the subject of recombination of atomic ions both in collision with free electrons and with atoms. It contains contributions from almost all groups which have made significant contributions in this area during the last decade. In addition, a synopsis of the discussion session following each of the main subject areas is presented. The material is organized into several themes; an overview of the subject area, theoretical aspects of recombination, experimental measurements of electron-ion recombination and experimental measurement.s of recombination in ion-atom collisions. We would like to acknowledge the sponsorship of the NATO Scientific Affairs Division. We would like to thank the Northern Ireland Tourist Board and the Queen's University of Belfast for providing some additional funding. Finally we would like to thank all the contributors to these proceedings for their efforts in preparing the manuscripts and their assistance in the editing process.

Regular and Chaotic Dynamics (Applied Mathematical Sciences #38)

This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects.

Reinforcement Learning (The Springer International Series in Engineering and Computer Science #173)

Reinforcement learning is the learning of a mapping from situations to actions so as to maximize a scalar reward or reinforcement signal. The learner is not told which action to take, as in most forms of machine learning, but instead must discover which actions yield the highest reward by trying them. In the most interesting and challenging cases, actions may affect not only the immediate reward, but also the next situation, and through that all subsequent rewards. These two characteristics -- trial-and-error search and delayed reward -- are the most important distinguishing features of reinforcement learning. Reinforcement learning is both a new and a very old topic in AI. The term appears to have been coined by Minsk (1961), and independently in control theory by Walz and Fu (1965). The earliest machine learning research now viewed as directly relevant was Samuel's (1959) checker player, which used temporal-difference learning to manage delayed reward much as it is used today. Of course learning and reinforcement have been studied in psychology for almost a century, and that work has had a very strong impact on the AI/engineering work. One could in fact consider all of reinforcement learning to be simply the reverse engineering of certain psychological learning processes (e.g. operant conditioning and secondary reinforcement). Reinforcement Learning is an edited volume of original research, comprising seven invited contributions by leading researchers.

Relationale Datenbanken: Eine Einführung für die Praxis (Informationstechnik und Datenverarbeitung)

Relative Complexities of First Order Calculi (Künstliche Intelligenz)

Relativistic Dynamics of a Charged Sphere: Updating the Lorentz-Abraham Model (Lecture Notes in Physics Monographs #11)

This is a remarkable book. Arthur Yaghjian is by training and profession an electrical engineer; but he has a deep interest in fundamental questions usually reserved for physicists. Working largely in isolation he has studied the relevant papers of an enormous literature accumulated over a century. The result is a fresh and novel approach to old problems and to their solution. Physicists since Lorentz have looked at the problem of the equations of motion of a charged object primarily as a problem for the description of a fundamental particle, typically an electron. Yaghjian considers a mac- scopic object, a spherical insulator with a surface charge. was therefore not tempted to take the point limit, and he thus avoided the pitfalls that have misguided research in this field since Dirac's famous paper of 1938. Perhaps the author's greatest achievement was the discovery that one does not need to invoke quantum mechanics and the correspondence pr- ciple in order to exclude the unphysical solutions (runaway and pre-acc- eration solutions). Rather, as he discovered, the derivation of the classical equations of motion from the Maxwell-Lorentz equations is invalid when the time rate of change of the dynamical variables too large (even in the relativistic case). Therefore, solutions that show such behavior are inc- sistent consequences. The classical theory thus shown to be physically consistent by itself. It embarrassing--to say the least--that this obs- vation had not been made before.

Relativität, Gruppen, Teilchen: Spezielle Relativitätstheorie als Grundlage der Feld- und Teilchenphysik

Das Thema des Buches ist die spezielle Relativitätstheorie und die Beschreibung der relativistischen Symmetrie in der klassischen und Elementarteilchenphysik. Es werden weniger die Experimente zur Relativitätstheorie diskutiert, als vielmehr deren formale Struktur durchleuchtet, entwickelt und physikalisch gedeutet. Der besondere Reiz dieses Buches besteht in der Balance zwischen physikalischer Diskussion und formaler Struktur. Die Autoren gehen von einer elementaren Präsentation schrittweise zu einer abstrakteren moderneren Darstellung über. Kleinere und auch ausgedehntere historische Noten sowie weiterführende mathematische Bemerkungen sind im Text verstreut. Die vorliegende Neuauflage geht - bei leicht geänderter Stoffanordnung und Einschub zweier Zusatzabschnitte - stärker als bisher ein auf die Rolle der Thomas-Rotation in der Struktur der Lorentzgruppe, auf mehrwertige Darstellungen und Spiegelungen.

Representation of Lie Groups and Special Functions: Volume 3: Classical and Quantum Groups and Special Functions (Mathematics and its Applications #75)

Reviews of Plasma Physics (Reviews of Plasma Physics #17)

''The review articles in this series are invariably of a high standard, and those contained in the most recent volumes to appear (Volumes 14-16), are no exception.'' --- Journal of Plasma Physics, from a review of previous volumes The current volume includes chapters on the generation of noninductive current in a tokamak and resonance effects in oscillations of uneven flows of continuous media.

Riemann Surfaces (Graduate Texts in Mathematics #71)

This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case, while basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the associated Abelian varities. Topics covered include existence of meromorphic functions, the Riemann-Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented, as are alternate proofs for the most important results, showing the diversity of approaches to the subject. Of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics.

Rings and Categories of Modules (Graduate Texts in Mathematics #13)

This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil­ iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de­ composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.

Rings with Morita Duality (Lecture Notes in Mathematics #1523)

Associative rings that possess Morita dualities or self- dualities form the object of this book. They are assumed to have an identity and modules are assumed unitary. The book sets out to give an extensive introduction to thisclass of rings, covering artinian rings, ring extensions, Azuma- ya's exact rings, and more. Among the interesting results presented are a characterization of duality via linear com- pactness, ring extensions with dualities, and exact rings. Some basic knowledge of rings and modules is expected of the reader.

Risk Assessment of Prenatally-Induced Adverse Health Effects

Since the thalidomide (Contergan) tragedy about 30 years ago the induction of prenatally-induced morphological or functional defects has been an area of extensive research. Risk assessment of prenatally-induced adverse health effects is still a difficult task from both experimental data as well asfrom observations in humans. In the contributions to this book three major aspects are dealt with: - Quantitative extrapolations of experimental data to the situation possibly relevant for man. - The significance for a risk assessment with respect to man of minor or rare structural abnormalities observed in experimental studies - The future need to assess congenital dysfunctions (e.g. of the hormone or the immune system) beside the present evaulation of structural defects. Limitations as well as gaps of the present knowledge in this area of basic and applied research are pointed out. Since the results of prenatally-induced lesions may manifest themselves not only pre- but often not before late postnatally, numerous aspects of structural and functional abnormaldevelopment must be studied in experimental and clinical investigations.

A Road to Randomness in Physical Systems (Lecture Notes in Statistics #71)

There are many ways of introducing the concept of probability in classical, i. e, deter­ ministic, physics. This work is concerned with one approach, known as "the method of arbitrary funetionJ. " It was put forward by Poincare in 1896 and developed by Hopf in the 1930's. The idea is the following. There is always some uncertainty in our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. A probability density may be used to describe this uncertainty. For many physical systems, dependence on the initial density washes away with time. Inthese cases, the system's position eventually converges to the same random variable, no matter what density is used to describe initial uncertainty. Hopf's results for the method of arbitrary functions are derived and extended in a unified fashion in these lecture notes. They include his work on dissipative systems subject to weak frictional forces. Most prominent among the problems he considers is his carnival wheel example, which is the first case where a probability distribution cannot be guessed from symmetry or other plausibility considerations, but has to be derived combining the actual physics with the method of arbitrary functions. Examples due to other authors, such as Poincare's law of small planets, Borel's billiards problem and Keller's coin tossing analysis are also studied using this framework. Finally, many new applications are presented.

Robustness of Dynamic Systems with Parameter Uncertainties (Monte Verita)

Robust Control is one of the fastest growing and promising areas of research today. In many practical systems there exist uncertainties which have to be considered in the analysis and design of control systems. In the last decade methods were developed for dealing with dynamic systems with unstructured uncertainties such as HOO_ and £I-optimal control. For systems with parameter uncertainties, the seminal paper of V. L. Kharitonov has triggered a large amount of very promising research. An international workshop dealing with all aspects of robust control was successfully organized by S. P. Bhattacharyya and L. H. Keel in San Antonio, Texas, USA in March 1991. We organized the second international workshop in this area in Ascona, Switzer­ land in April 1992. However, this second workshop was restricted to robust control of dynamic systems with parameter uncertainties with the objective to concentrate on some aspects of robust control. This book contains a collection of papers presented at the International Workshop on Robust Control held at the Centro Stefano Franscini, Monte Verita, Ascona, Switzer­ land on April 12-17, 1992 as well as a list of open problems presented during a dis­ cussion session at the workshop. Thirtyfive leading researchers from all over the world working in the area of robust control of dynamic systems with parameter uncertainties were invited to present their recent results and to discuss with their colleagues the recent advances in this field.

The Role of Topology in Classical and Quantum Physics (Lecture Notes in Physics Monographs #7)

Rotating Fluids in Geophysical and Industrial Applications (CISM International Centre for Mechanical Sciences #329)

The volume presents a comprehensive overview of rotation effects on fluid behavior, emphasizing non-linear processes. The subject is introduced by giving a range of examples of rotating fluids encountered in geophysics and engineering. This is then followed by a discussion of the relevant scales and parameters of rotating flow, and an introduction to geostrophic balance and vorticity concepts. There are few books on rotating fluids and this volume is, therefore, a welcome addition. It is the first volume which contains a unified view of turbulence in rotating fluids, instability and vortex dynamics. Some aspects of wave motions covered here are not found elsewhere.

Scalar Wave Theory: Green’s Functions and Applications (Springer Series on Wave Phenomena #12)

This book comprises some of the lecture notes I developed for various one-or two-semester courses I taught at the Colorado School of Mines. The main objective of all the courses was to introduce students to the mathematical aspects of wave theory with a focus on the solution of some specific fundamental problems. These fundamental solutions would then serve as a basis for more complex wave propagation and scattering problems. Although the courses were taught in the mathematics department, the audience was mainly not mathematicians. It consisted of gradu­ ate science and engineering majors with a varied background in both mathematics and wave theory in general. I believed it was necessary to start from fundamental principles of both advanced applied math­ ematics as well as wave theory and to develop them both in some detail. The notes reflect this type of development, and I have kept this detail in the text. I believe it essential in technical careers to see this detailed development at least once. This volume consists of five chapters. The first two on Scalar Wave Theory (Chapter 1) and Green's Functions (Chapter 2) are mainly mathematical although in Chapter 1 the wave equation is derived from fundamental physical principles. More complicated problems involving spatially and even temporally varying media are briefly introduced.

Schrödinger Operators The Quantum Mechanical Many-Body Problem: Proceedings of a Workshop Held at Aarhus, Denmark 15 May - 1 August 1991 (Lecture Notes in Physics #403)

In these proceedings basic questions regarding n-body Schr|dinger operators are dealt with, such as asymptotic completeness of systems with long-range potentials (including Coulomb), a new proof of completeness for short-range potentials, energy asymptotics of large Coulomb systems,asymptotic neutrality of polyatomic molecules. Other contributions deal withdifferent types of problems, such as quantum stability, Schr|dinger operators on a torus and KAM theory, semiclassical theory, time delay, radiation conditions, magnetic Stark resonances, random Schr|dinger operators and stochastic spectral analysis. The volume presents the results in such detail that it could well serve as basic literature for seminar work.

Scientific Computing on Supercomputers III

The International Workshop on "The Use of Supercomputers in Theoretical Science" took place on January 24 and 25, 1991, at the University of Antwerp (UIA), Antwerpen, Belgium. It was the sixth in a series of workshops, the fIrst of which took place in 1984. The principal aim of these workshops is to present the state of the art in scientific large-scale and high speed-computation. Computational science has developed into a third methodology equally important now as its theoretical and experimental companions. Gradually academic researchers acquired access to a variety of supercomputers and as a consequence computational science has become a major tool for their work. It is a pleasure to thank the Belgian National Science Foundation (NFWO-FNRS) and the Ministry of ScientifIc Affairs for sponsoring the workshop. It was organized both in the framework of the Third Cycle "Vectorization, Parallel Processing and Supercomputers" and the "Governemental Program in Information Technology". We also very much would like to thank the University of Antwerp (Universitaire Instelling Antwerpen -VIA) for fInancial and material support. Special thanks are due to Mrs. H. Evans for the typing and editing of the manuscripts and for the preparation of the author and subject indexes. J.T. Devreese P.E. Van Camp University of Antwerp July 1991 v CONlENTS High Perfonnance Numerically Intensive Applications on Distributed Memory Parallel Computers .................... . F.W. Wray Abstract ......................................... .

The Selberg-Arthur Trace Formula: Based on Lectures by James Arthur (Lecture Notes in Mathematics #1503)

This book based on lectures given by James Arthur discusses the trace formula of Selberg and Arthur. The emphasis is laid on Arthur's trace formula for GL(r), with several examples in order to illustrate the basic concepts. The book will be useful and stimulating reading for graduate students in automorphic forms, analytic number theory, and non-commutative harmonic analysis, as well as researchers in these fields. Contents: I. Number Theory and Automorphic Representations.1.1. Some problems in classical number theory, 1.2. Modular forms and automorphic representations; II. Selberg's Trace Formula 2.1. Historical Remarks, 2.2. Orbital integrals and Selberg's trace formula, 2.3.Three examples, 2.4. A necessary condition, 2.5. Generalizations and applications; III. Kernel Functions and the Convergence Theorem, 3.1. Preliminaries on GL(r), 3.2. Combinatorics and reduction theory, 3.3. The convergence theorem; IV. The Ad lic Theory, 4.1. Basic facts; V. The Geometric Theory, 5.1. The JTO(f) and JT(f) distributions, 5.2. A geometric I-function, 5.3. The weight functions; VI. The Geometric Expansionof the Trace Formula, 6.1. Weighted orbital integrals, 6.2. The unipotent distribution; VII. The Spectral Theory, 7.1. A review of the Eisenstein series, 7.2. Cusp forms, truncation, the trace formula; VIII.The Invariant Trace Formula and its Applications, 8.1. The invariant trace formula for GL(r), 8.2. Applications and remarks