Bücher veröffentlicht von Birkhauser Boston

Dedicated to Anthony Joseph, this volume contains surveys and invited articles by leading specialists in representation theory. The focus here is on semisimple Lie algebras and quantum groups, where the impact of Joseph's work has been seminal and has changed the face of the subject.Two introductory biographical overviews of Joseph's contributions in classical representation theory (the theory of primitive ideals in semisimple Lie algebras) and quantized representation theory (the study of the quantized enveloping algebra) are followed by 16 research articles covering a number of varied and interesting topics in representation theory.Contributors: J. Alev; A. Beilinson; A. Braverman; I. Cherednik; J. Dixmier; F. Dumas; P. Etingof; D. Farkas; D. Gaitsgory; F. Ivorra; A. Joseph; D. Joseph; M. Kashiwara; D. Kazhdan; A.A. Kirillov; B. Kostant; S. Kumar; G. Letzter; T. Levasseur; G. Lusztig; L. Makar-Limanov; W. McGovern; M. Nazarov; K-H. Neeb; L.G. Rybnikov; P. Schapira; V. Schechtman; A. Sergeev; J.T. Stafford; Ya. Varshavsky; N. Wallach; and I. Waschkies.

For more than two decades percolation theory, random walks, interacting parti- cle systems and topics related to statistical mechanics have experienced inten- sive growth. In the last several years, especially remarkable progress has been made in a number of directions, such as: Wulff constructions above two dimen- sions for percolation, Potts and Ising models, classification of random walks in random environments, better understanding of fluctuations in two dimen- sional growth processes, the introduction and remarkable uses of the Stochastic Loewner Equation, the rigorous derivation of exact intersection exponents for planar Brownian motion, and finally, the proof of conformal invariance for crit- ical percolation scaling limits on the triangular lattice. It was thus a fortuitous time to bring together researchers, including many personally responsible for these advances, in the framework of the IVth Brazilian School of Probability, held at Mambucaba on August 14-19,2000. This School, first envisioned and organized by IMPA's probability group in 1997, has since developed into an annual meeting with an almost constant format: it usually offers three advanced courses delivered by prominent scientists, combined with a high-level conference. This volume contains invited articles associated with that meeting, and we hope it will provide the reader with an accurate impression regarding the current state of affairs in these important fields of probability theory.

Linear algebra is one of the most important subjects in the study of science and engineering because of its widespread applications in social or natural science, computer science, physics, or economics. As one of the most useful courses in undergraduate mathematics, it has provided essential tools for industrial scientists. The basic concepts of linear algebra are vector spaces, linear transformations, matrices and determinants, and they serve as an abstract language for stating ideas and solving problems. This book is based on the lectures delivered several years in a sophomore- level linear algebra course designed for science and engineering students. The primary purpose of this book is to give a careful presentation of the basic concepts of linear algebra as a coherent part of mathematics, and to illustrate its power and usefulness through applications to other disciplines. We have tried to emphasize the computational skills along with the mathematical abstractions, which have also an integrity and beauty of their own. The book includes a variety of interesting applications with many examples not only to help students understand new concepts but also to practice wide applications of the subject to such areas as differential equations, statistics, geometry, and physics. Some of those applications may not be central to the mathematical development and may be omitted or selected in a syllabus at the discretion of the instructor.

* Contains research and survey articles by well known and respected mathematicians on recent developments and research trends in differential geometry and topology* Dedicated in honor of Lieven Vanhecke, as a tribute to his many fruitful and inspiring contributions to these fields* Papers include all necessary introductory and contextual material to appeal to non-specialists, as well as researchers and differential geometers

S. Panchapakesan has made significant contributions to ranking and selection and has published in many other areas of statistics, including order statistics, reliability theory, stochastic inequalities, and inference. Written in his honor, the twenty invited articles in this volume reflect recent advances in these fields and form a tribute to Panchapakesan's influence and impact on these areas. Thematically organized, the chapters cover a broad range of topics from:* Inference* Ranking and Selection* Multiple Comparisons and Tests * Agreement Assessment * Reliability * Biostatistics Featuring theory, methods, applications, and extensive bibliographies with special emphasis on recent literature, this comprehensive reference work will serve researchers, practitioners, and graduate students in the statistical and applied mathematics communities.

In his new undergraduate textbook, Harold M. Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra. Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century.Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience.Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject. Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject.

* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow.* Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics. 

Parametric and semiparametric models are tools with a wide range of applications to reliability, survival analysis, and quality of life. This self-contained volume examines these tools in survey articles written by experts currently working on the development and evaluation of models and methods. While a number of chapters deal with general theory, several explore more specific connections and recent results in "real-world" reliability theory, survival analysis, and related fields.

The book deals with several closely related topics concerning approxima- tions and perturbations of random processes and their applications to some important and fascinating classes of problems in the analysis and design of stochastic control systems and nonlinear filters. The basic mathematical methods which are used and developed are those of the theory of weak con- vergence. The techniques are quite powerful for getting weak convergence or functional limit theorems for broad classes of problems and many of the techniques are new. The original need for some of the techniques which are developed here arose in connection with our study of the particular applica- tions in this book, and related problems of approximation in control theory, but it will be clear that they have numerous applications elsewhere in weak convergence and process approximation theory. The book is a continuation of the author's long term interest in problems of the approximation of stochastic processes and its applications to problems arising in control and communication theory and related areas. In fact, the techniques used here can be fruitfully applied to many other areas. The basic random processes of interest can be described by solutions to either (multiple time scale) Ito differential equations driven by wide band or state dependent wide band noise or which are singularly perturbed. They might be controlled or not, and their state values might be fully observable or not (e. g. , as in the nonlinear filtering problem).

This volume! aims at introducing some basic ideas for studying approxima- tion processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calcu- lus, has become more and more relevant with the use of computers. The volume is suitably divided in two parts. In the first part we illustrate the numerical systems of reals, of integers as a subset of the reals, and of complex numbers. In this context we intro- duce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and continuity2 in terms of discrete processes; then, in Chapter 3, we discuss some elements of combinatorial calculus and the mathematical notion of infinity. In Chapter 4 we introduce complex num- bers and illustrate some of their applications to elementary geometry; in Chapter 5 we prove the fundamental theorem of algebra and present some of the elementary properties of polynomials and rational functions, and of finite sums of harmonic motions. In the second part we deal with discrete processes, first with the process of infinite summation, in the numerical case, i.e., in the case of numerical series in Chapter 6, and in the case of power series in Chapter 7. The last chapter provides an introduction to discrete dynamical systems; it should be regarded as an invitation to further study.

This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France};' It is intended to serve as an intro- duction to the stability analysis of noncharacteristic multidimensional small viscosity boundary layers developed in (MZl]. We consider parabolic singular perturbations of hyperbolic systems L(u) - GBPP(u) = 0, where L is a nonlinear hyperbolic first order system and P a nonlinear spatially elliptic term. The parameter e measures the strength of the diffusive effects. With obvious reference to fluid mechanics, it is referred to as a "e;viscosity."e; The equation holds on a domain n and is supplemented by boundary conditions on an.The main goal of this book is to studythe behavior of solutions as etends to O. In the interior of the domain, the diffusive effects are negligible and the nondiffusive or inviscid equations (s = 0) are good approximations. However, the diffusive effects remain important in a small vicinity of the boundary where they induce rapid fluctuations of the solution, called layers. Boundary layers occur in many problems in physics and mechanics. They also occur in free boundary value problems, and in particular in the analysis of shock waves. Indeed, our study of noncharacteristic boundary layers is strongly motivated by the analysis of multidimensional shock waves. At the least, it is a necessary preliminary and important step. We also recall the importance of the viscous approach in the theoretical analysis ofconservation laws (see, e.g., [Lax], (Kru], (Bi-Br]).

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples.* Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications.* Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

Analysis of variance (ANOVA) models have become widely used tools and play a fundamental role in much of the application of statistics today. In particular, ANOVA models involving random effects have found widespread application to experimental design in a variety of fields requiring measurements of variance, including agriculture, biology, animal breeding, applied genetics, econometrics, quality control, medicine, engineering, and social sciences. This two-volume work is a comprehensive presentation of different methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Both Bayesian and repeated sampling procedures are considered. Volume I examines models with balanced data (orthogonal models); Volume II studies models with unbalanced data (nonorthogonal models). Features and Topics: * Systematic treatment of the commonly employed crossed and nested classification models used in analysis of variance designs* Detailed and thorough discussion of certain random effects models not commonly found in texts at the introductory or intermediate level* Numerical examples to analyze data from a wide variety of disciplines* Many worked examples containing computer outputs from standard software packages such as SAS, SPSS, and BMDP for each numerical example* Extensive exercise sets at the end of each chapter* Numerous appendices with background reference concepts, terms, and results* Balanced coverage of theory, methods, and practical applications* Complete citations of important and related works at the end of each chapter, as well as an extensive general bibliographyAccessible to readers with only a modest mathematical and statistical background, the work will appeal to a broad audience of students, researchers, and practitioners in the mathematical, life, social, and engineering sciences. It may be used as a textbook in upper-level undergraduate and graduate courses, or as a reference for readers interested in the use of random effects models for data analysis.

Advances in technology over the last 25 years have created a situation in which workers in diverse areas of computerscience and engineering have found it neces- sary to increase their knowledge of related fields in order to make further progress. Clifford (geometric) algebra offers a unified algebraic framework for the direct expression of the geometric ideas underlying the great mathematical theories of linear and multilinear algebra, projective and affine geometries, and differential geometry. Indeed, for many people working in this area, geometric algebra is the natural extension of the real number system to include the concept of direction. The familiar complex numbers of the plane and the quaternions of four dimen- sions are examples of lower-dimensional geometric algebras. During "e;The 6th International Conference on Clifford Algebras and their Ap- plications in Mathematical Physics"e; held May 20--25, 2002, at Tennessee Tech- nological University in Cookeville, Tennessee, a Lecture Series on Clifford Ge- ometric Algebras was presented. Its goal was to to provide beginning graduate students in mathematics and physics and other newcomers to the field with no prior knowledge of Clifford algebras with a bird's eye view of Clifford geometric algebras and their applications. The lectures were given by some of the field's most recognized experts. The enthusiastic response of the more than 80 partici- pants in the Lecture Series, many of whom were graduate students or postdocs, encouraged us to publish the expanded lectures as chapters in book form.

It is with great pleasure that I offer my reflections on Professor Anthony N. Michel's retirement from the University of Notre Dame. I have known Tony since 1984 when he joined the University of Notre Dame's faculty as Chair of the Depart- ment of Electrical Engineering. Tony has had a long and outstanding career. As a researcher, he has made im- portant contributions in several areas of systems theory and control theory, espe- cially stability analysis of large-scale dynamical systems. The numerous awards he received from the professional societies, particularly the Institute of Electrical and Electronics Engineers (IEEE), are a testament to his accomplishments in research. He received the IEEE Control Systems Society's Best Transactions Paper Award (1978), and the IEEE Circuits and Systems Society's Guillemin-Cauer Prize Paper Award (1984) and Myril B. Reed Outstanding Paper Award (1993), among others. In addition, he was a Fulbright Scholar (1992) and received the Alexander von Hum- boldt Forschungspreis (Alexander von Humboldt Research Award for Senior U.S. Scientists) from the German government (1997). To date, he has written eight books and published over 150 archival journal papers. Tony is also an effective administrator who inspires high academic standards.

Rigid (analytic) spaces were invented to describe degenerations, reductions, and moduli of algebraic curves and abelian varieties. This work, a revised and greatly expanded new English edition of an earlier French text by the same authors, presents important new developments and applications of the theory of rigid analytic spaces to abelian varieties, "e;points of rigid spaces,"e; etale cohomology, Drinfeld modular curves, and Monsky-Washnitzer cohomology. The exposition is concise, self-contained, rich in examples and exercises, and will serve as an excellent graduate-level text for the classroom or for self-study.

Analysis on Lie Groups with Polynomial Growth is the first book to present a method for examining the surprising connection between invariant differential operators and almost periodic operators on a suitable nilpotent Lie group. It deals with the theory of second-order, right invariant, elliptic operators on a large class of manifolds: Lie groups with polynomial growth. In systematically developing the analytic and algebraic background on Lie groups with polynomial growth, it is possible to describe the large time behavior for the semigroup generated by a complex second-order operator with the aid of homogenization theory and to present an asymptotic expansion. Further, the text goes beyond the classical homogenization theory by converting an analytical problem into an algebraic one.This work is aimed at graduate students as well as researchers in the above areas. Prerequisites include knowledge of basic results from semigroup theory and Lie group theory.