Bücher veröffentlicht von Birkhauser Boston

This volume brings together some of the best recent scholarship on what might be termed Einstein's formative period, that is, the thirty years before he obtained his first academic position in 1909. Topics covered include Einstein's early reading and his university education, his early views on scientific method and some of the crucial philosophical influences shaping those views, his early work on statistical mechanics, Brownian motion, quantum theory, relativity theory, and his youthful vision of a unified foundation for physics. Seven of the eight papers appear here in print for the first time. The contributors draw extensively upon much of the interesting new documentation, such as personal letters, including love letters to his fiancee, and unpublished manuscripts, that has come to light in the course of work on the first several volumes of {\it The Collected Papers of Albert Einstein}. This engaging book examining the young Einstein from a variety of perspectives---personal, scientific, historical, and philosophical--- will be accessible to a broad general readership.

This volume contains the original lecture notes presented by A. Weil in which the concept of adeles was first introduced, in conjunction with various aspects of C.L. Siegel's work on quadratic forms. Serving as an introduction to the subject, these notes may also provide stimulation for further research.

The design of nonlinear controllers for mechanical systems has been an ex- tremely active area of research in the last two decades. From a theoretical point of view, this attention can be attributed to their interesting dynamic behavior, which makes them suitable benchmarks for nonlinear control the- oreticians. On the other hand, recent technological advances have produced many real-world engineering applications that require the automatic con- trol of mechanical systems. the mechanism for de- Often, Lyapunov-based techniques are utilized as veloping different nonlinear control structures for mechanical systems. The allure of the Lyapunov-based framework for mechanical system control de- sign can most likely be assigned to the fact that Lyapunov function candi- dates can often be crafted from physical insight into the mechanics of the system. That is, despite the nonlinearities, couplings, and/or the flexible effects associated with the system, Lyapunov-based techniques can often be used to analyze the stability of the closed-loop system by using an energy- like function as the Lyapunov function candidate. In practice, the design procedure often tends to be an iterative process that results in the death of many trees. That is, the controller and energy-like function are often constructed in concert to foster an advantageous stability property and/or robustness property. Fortunately, over the last 15 years, many system the- ory and control researchers have labored in this area to produce various design tools that can be applied in a variety of situations.

In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non- associative algebras generalize C*-algebras and von Neumann algebras re- spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character- ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained.

Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.

This study began as an attempt to understand mechanics in the nineteenth century. The terms mechanics and mechanical world view were being used as general descriptions of nineteenth-century physicists' assumptions and interpretations of nature. However, there were no studies of the particulars of these assumptions or the range and content of these interpretations. Rene Dugas' work on classical mechanics focused on France. The search for the particulars of these forms of "mechanics" led me to explore precisely what mechanics meant to physicists of a century and more ago. However, none of Lagrange's, Hamilton's, or Jacobi's "mechanics," while ele­ gant, fits easily within the history of physics. Lagrange reduced mechanics to an exercise in analysis; Hamilton and Jacobi used mechanics to explore solutions to partial differential equations. They were mathematicians doing mathematics. As I went deeper into the matter it became obvious that, in the nineteenth century, there were two kinds of mechanics, each containing a variety of forms, one physical, the other mathematical. There were a group of men using mechanics to understand nature and another group using the equations of mechanics to explore the calcu­ lus. However, when tracing these two traditions back into the eighteenth century, physics disappeared altogether.

The aim of this monograph is quite modest: It attempts to be a systematic exposition of all that appeared in the literature and was known to us by the end of the 20th century about the Laplace distribution and its numerous generalizations and extensions. We have tried to cover both theoretical developments and applications. There were two main reasons for writing this book. The first was our conviction that the areas and situations where the Laplace distribution naturally occurs is so extensive that tracking the original sources is unfeasible. The second was our observation of the growing demand for statistical distributions having properties tangent to those exhibited by the Laplace laws. These two "necessary" conditions justified our efforts that led to this book. Many details are arranged primarily for reference, such as inclusion of the most commonly used terminology and notation. In several cases, we have proposed unification to overcome the ambiguity of notions so often present in this area. Personal taste may have done some injustice to the subject matter by omitting or emphasizing certain topics due to space limitations. We trust that this feature does not constitute a serious drawback-in our literature search we tried to leave no stone unturned (we collected over 400 references).

This modem introduction to the foundations of logic, mathematics, and computer science answers frequent questions that mysteriously remain mostly unanswered in other texts: * Why is the truth table for the logical implication so unintuitive? * Why are there no recipes to design proofs? * Where do these numerous mathematical rules come from? * What are the applications of formal logic and abstract mathematics? * What issues in logic, mathematics, and computer science still remain unresolved? Answers to such questions must necessarily present both theory and significant applica- tions, which explains the length of the book. The text first shows how real life provides some guidance for the selection of axioms for the basis of a logical system, for instance, Boolean, classical, intuitionistic, or minimalistic logic. From such axioms, the text then derives de- tailed explanations of the elements of modem logic and mathematics: set theory, arithmetic, number theory, combinatorics, probability, and graph theory, with applications to computer science. The motivation for such detail, and for the organization of the material, lies in a continuous thread from logic and mathematics to their uses in everyday life.

This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's and Hashimoto's Theorems to more recent results such as the Li--Milner Structure Theorem. Major topics covered include: chains and antichains, lowest upper and greatest lower bounds, retractions, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, algorithmic approaches and the role of algebraic topology. Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory class. After working through a comparatively lean core, the reader can choose from a diverse range of topics such as structure theory, enumeration or algorithmic aspects. Also presented are some key topics less customary to discrete mathematics/graph theory, including a concise introduction to homology for graphs, and the presentation of forward checking as a more efficient alternative to the standard backtracking algorithm. The coverage throughout provides a solid foundation upon which research can be started by a mathematically mature reader. Rich in exercises, illustrations, and open problems, Ordered Sets: An Introduction is an excellent text for undergraduate and graduate students and a good resource for the interested researcher. Readers will discover order theory's role in discrete mathematics as a supplier of ideas as well as an attractive source of applications.

Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author's lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets.Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth's or the brain's interior. Specific topics covered include:* the advantages and disadvantages of Fourier, spline, and wavelet methods* theory and numerics of orthogonal polynomials on intervals, spheres, and balls* cubic splines and splines based on reproducing kernels* multiresolution analysis using wavelets and scaling functionsThis textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

This comprehensive textbook is intended for a two-semester sequence in analysis. The first four chapters present a practical introduction to analysis by using the tools and concepts of calculus. The last five chapters present a first course in analysis. The presentation is clear and concise, allowing students to master the calculus tools that are crucial in understanding analysis. From Calculus to Analysis prepares readers for their first analysis course-important because many undergraduate programs traditionally require such a course. Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide. The only prerequisite is a standard calculus course.

The second of two volumes presenting papers from an international conference on analytic number theory. The two volumes contain 50 papers, with an emphasis on topics such as sieves, related combinatorial aspects, multiplicative number theory, additive number theory, and Riemann zeta-function.

Equations occur in many computer applications, such as symbolic compu- tation, functional programming, abstract data type specifications, program verification, program synthesis, and automated theorem proving. Rewrite systems are directed equations used to compute by replacing subterms in a given formula by equal terms until a simplest form possible, called a normal form, is obtained. The theory of rewriting is concerned with the compu- tation of normal forms. We shall study the use of rewrite techniques for reasoning about equations. Reasoning about equations may, for instance, involve deciding whether an equation is a logical consequence of a given set of equational axioms. Convergent rewrite systems are those for which the rewriting process de- fines unique normal forms. They can be thought of as non-deterministic functional programs and provide reasonably efficient decision procedures for the underlying equational theories. The Knuth-Bendix completion method provides a means of testing for convergence and can often be used to con- struct convergent rewrite systems from non-convergent ones. We develop a proof-theoretic framework for studying completion and related rewrite- based proof procedures. We shall view theorem provers as proof transformation procedures, so as to express their essential properties as proof normalization theorems.

To commemorate properly the 70th birthday of a man who, by his very nature, is too busy to pause for any kind of ceremonial event unless it has a concomitant functional output was a difficult problem for the Staff and Associates of the Neurosciences Research Program. Frank (F. O. S. ) has always dreaded the prospect that sometime it might be appropriate for his colleagues to present him a Fest­ schrift. In fact, "Fest me no Schriften" became his battle cry, expressing his feeling that the idea of testimonials clustered into a book was anathema. So the "break­ through" idea for the planners was to organize a symposium around the theme of discovery in neuroscience that would be valuable scientifically and, in its demon­ stration of interdisciplinary interaction, would support that emphasis in Frank's career. After much planning a program was developed, beginning with a birthday party the evening before, followed by the two-day symposium, and closing with the first F. O. Schmitt Lecture in Neuroscience. We hope that publication of the scientific proceedings in this volume will be of interest not only to the neuroscience community, but also to a broad general readership interested in discovery, under­ standing, and the creative processes in scientific work. An organizing committee, chaired by Fred Worden, collected advice and guidance leading to the selection of speakers whose scientific careers have played an important part in the recent history of modern neuroscience.

The 1990 Seminar on Stochastic Processes was held at the University of British Columbia from May 10 through May 12, 1990. This was the tenth 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 Univer- sity of Florida, the University of Virginia and the University of California, San Diego. Following the successful format of previous years, there were five invited lectures, delivered by M. Marcus, M. Vor, D. Nualart, M. Freidlin and L. C. G. Rogers, with the remainder of the time being devoted to informal communications and workshops on current work and problems. The enthusiasm and interest of the participants created a lively and stimulating atmosphere for the seminar. A sample of the research discussed there is contained in this volume. The 1990 Seminar was made possible by the support of the Natural Sciences and Engin~ring Research Council of Canada, the Southwest University Mathematics Society of British Columbia, and the University of British Columbia. To these entities and the organizers of this year's conference, Ed Perkins and John Walsh, we extend oul' thanks. Finally, we acknowledge the support and assistance of the staff at Birkhauser Boston.

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions of complexity classes, on finite model theory, on models of feasible computation for real numbers, on vector spaces and on recursion theory. The vVorkshop on Feasible Mathematics was sponsored by the Mathematical Sciences Institute and was held at Cornell University, June 26-28, 1989.

1. 1 The problem and the approach The model developed here, which is actually more a collection of com- ponents than a single monolithic structure, traces a path from relatively low-level neural/connectionistic structures and processes to relatively high-level animal/artificial intelligence behaviors. Incremental extension of this initial path permits increasingly sophisticated representation and processing strategies, and consequently increasingly sophisticated behavior. The initial chapters develop the basic components of the sys- tem at the node and network level, with the general goal of efficient category learning and representation. The later chapters are more con- cerned with the problems of assembling sequences of actions in order to achieve a given goal state. The model is referred to as connectionistic rather than neural, be- cause, while the basic components are neuron-like, there is only limited commitment to physiological realism. Consequently the neuron-like ele- ments are referred to as "e;nodes"e; rather than "e;neurons"e;. The model is directed more at the behavioral level, and at that level, numerous con- cepts from animal learning theory are directly applicable to connectionis- tic modeling. An attempt to actually implement these behavioral theories in a computer simulation can be quite informative, as most are only partially specified, and the gaps may be apparent only when actual- ly building a functioning system. In addition, a computer implementa- tion provides an improved capability to explore the strengths and limita- tions of the different approaches as well as their various interactions.

Dr. A. D. Morris had a long interest in, and great familiarity with, the life and times of James Parkinson (1755-1824). He was an avid collector of material related to Parkinson, some of which he communicated to medi· cal and historical groups, and which he also incorporated into publica· tions, especially his admirable work, The Hoxton Madhouses. When Dr. Morris died, in 1980, he left behind a large typescript devoted to Parkinson's life. It was single·minded in its dedication to primary texts, quoting liberally from the whole range of Parkinson's writings. This was particularly valuable since so many of Parkinson's publications were tracts, pamphlets, or occasional pieces which are now very scarce. A copy of the entire manuscript has been deposited in the Library of the Well· come Institute for the History of Medicine in London, where it may be consulted. The length of the manuscript made publication of the whole impossible, especially since it would have had to include the facsimile reproduction of Morris's The Hoxton Madhouses.

The five stories in this book are tales about human beings and the human condition in which they find themselves. They are stories of scientists - but not of white-coated laboratory figures, happy to leave to others the practical application of their discoveries. In the circumstances I recount, the scientists were brought face to face, sometimes in dramatic confrontations, with the very people whose problems their work might help solve. As I came to realize, there now exists an international network of unusual scientists whose members are concerned individuals, deter- mined that their scientific work should help alleviate the human condition. This book was conceived as an account of some exciting epi- sodes in contemporary biomedicine. But during the four years it took to complete, several other themes emerged. First, each story illustrates aspects of the relation between Western science and technology and those major health problems which are often of dreadful significance for the Third World. In this relation the fruits of Western research are not simply applied to global health problems. Rather the relation is reciprocal, for scientific research, whether prompted by the medical problems of the Third World or actually conducted there, is yielding vital clues to many fundamental aspects of human biology, as well as pointing toward possible therapies for the serious diseases of Western society, such as cancer or the dementi as of old age. After I had written the first draft a second theme emerged.

. . . And indeed, these latest centuries merit praise because it is during them that the arts and sciences, discovered Iry the ancients, have been reduced to so great and constantlY increasing perfec­ tion through the investigations and experiments of clear-seeing minds. This development is particularlY evident in the case of the mathematical sciences. Here, without mentioning various men who have achieved success, we must without hesitation and with the unanimous approval of scholars assign the first place to Gali­ leo Galilei, Member of the Acadmry of the Lincei. This he de­ serves not onlY because he has effectivelY demonstrated faUacies in many of our current conclusions, as is amplY shown Iry his published works, but also Iry means of the telescope (invented in this country but greatlY perfected Iry him) he has discovered the four sateOites of Jupiter, has shown us the true character of the Milky wa~ and has made us acquainted with spots on the Sun, with the rough and cloudy portions of the lunar surface, with the threefold nature of Saturn, with the phases of Venus and with the physical character of comets. These matters were entirelY unknown to the ancient astronomers and philosophers; so that we may trulY say that he has restored to the world the science of astronomy and has presented it in a new light.

STANISLAW MARCIN ULAM, or Stan as his friends called him, was one of those great creative mathematicians whose interests ranged not only over all fields of mathematics, but over the physical and biological sciences as well. Like his good friend "e;Johnny"e; von Neumann, and unlike so many of his peers, Ulam is unclassifiable as a pure or applied mathematician. He never ceased to find as much beauty and excitement in the applications of mathematics as in working in those rarefied regions where there is a total un- concern with practical problems. In his Adventures of a Mathematician Ulam recalls playing on an oriental carpet when he was four. The curious patterns fascinated him. When his father smiled, Ulam remembers thinking: "e;He smiles because he thinks I am childish, but I know these are curious patterns. I know something my father does not know."e; The incident goes to the heart of Ulam's genius. He could see quickly, in flashes of brilliant insight, curious patterns that other mathematicians could not see. "e;I am the type that likes to start new things rather than improve or elaborate,"e; he wrote. "e;I cannot claim that I know much of the technical material of mathematics.