Bücher veröffentlicht von Springer New York

Subject Matter The original title of this book was Tractatus Classico-Quantummechanicus, but it was pointed out to the author that this was rather grandiloquent. In any case, the book discusses certain topics in the interface between classical and quantum mechanics. Mathematically, one looks for similarities between Poisson algebras and symplectic geometry on the classical side, and operator algebras and Hilbert spaces on the quantum side. Physically, one tries to understand how a given quan- tum system is related to its alleged classical counterpart (the classical limit), and vice versa (quantization). This monograph draws on two traditions: The algebraic formulation of quan- tum mechanics and quantum field theory, and the geometric theory of classical mechanics. Since the former includes the geometry of state spaces, and even at the operator-algebraic level more and more submerges itself into noncommutative geometry, while the latter is formally part of the theory of Poisson algebras, one should take the words "e;algebraic"e; and "e;geometric"e; with a grain of salt! There are three central themes. The first is the relation between constructions involving observables on one side, and pure states on the other. Thus the reader will find a unified treatment of certain aspects of the theory of Poisson algebras, oper- ator algebras, and their state spaces, which is based on this relationship.

Carbohydrates are the most widely distributed naturally-occurring organic compounds on Earth. They make up much of our food, clothing and shelter, and are as vital to national economies as they are to our diet. This book is the first broad treatment of carbohydrate chemistry in many years, and presents the structures, reactions, modifications, and properties of carbohydrates. Woven throughout the text are discussions of biological properties of carbohydrates, their industrial applications, and the history of the field of carbohydrate chemistry. Written for students as well as practicing scientists, this text/reference will be of interest to a wide range of disciplines influenced by carbohydrates: biochemistry, chemistry, food and nutrition, microbiology, pharmacology, and medicine.

Dynamic Modeling of Environmental Systems is a primer on using models to understand environmental problems. With their many natural, economic, political, and technical aspects, environmental problems require a systems approach. This book provides an introduction to modeling concepts and applications that is specifically geared toward the environmental field. Sections on modeling terminology, the uses of models, the model-building process, and the interpretation of output provide the foundation for detailed applications. After an introduction to the basics of dynamic modeling, the book leads students through an analysis of several environmental problems, including surface-water pollution, matter-cycling disruptions, and global warming. The scientific and technical context is provided for each problem, and the methods for analyzing and designing appropriate modeling approaches is provided. While the mathematical content does not exceed the level of a first-semester Calculus course, the book gives students all of the background, examples, and practice exercises needed both to use and understand environmental modeling. It is suitable for upper-level undergraduate and beginning-graduate-level environmental science courses. The text is also useful for environmental professionals seeking an introduction to modeling in their field. About the Series: The availability of powerful, intuitive software for developing and running simulation models of real-world phenomena promises a revolution in studying, teaching, and thinking about complex problems that range from the functioning of a cell to that of an ecosystem to that of a national economy. The books in the series Modeling Dynamic Systems will promote the spread of "e;systems thinking"e; by integrating state-of-the-art modeling techniques with the theories and concepts of specific disciplines or interdisciplinary topics. The unifying theme of the series is the ease, power, and transparency of model-building.

The study of the development of flowering plants may be said to be in the throes of a revolution. The literature on the subject is extensive and continues to grow rapidly as new discoveries pile one on top of the other; moreover, these striking advances in our knowledge have put plant developmental biology well ahead of other aspects of the study of plants. This has come about after a period of neglect and stagnation in the field and has been triggered by the power of recombinant DNA technology to analyze genetic information and by a fruitful cross-fertilization between physiology, genetics, and molecular biology. Whereas considerations of developmental phenomena were at one time largely restricted to the structure and physiology of a wide selection of plants, recent molecular and genetic approaches are focused on one or two model systems. Notwithstanding the difficulty of having to relate developmental mechanisms in a few experimentally attractive models to the enormous range of plants, the use of model systems has gained wide accep- tance. This book is intended to meet the need for a unified account of the general principles of development of flowering plants representing structural, physiolog- ical, biochemical, genetic, and molecular perspectives. It arose out of the revision and upgrading of an undergraduate course in plant development that I have taught here at The Ohio State University for more than 20 years.

Mathematics students generally meet the Riemann integral early in their undergraduate studies, then at advanced undergraduate or graduate level they receive a course on measure and integration dealing with the Lebesgue theory. However, those whose interests lie more in the direction of applied mathematics will in all probability find themselves needing to use the Lebesgue or Lebesgue-Stieltjes Integral without having the necessary theoretical background. It is to such readers that this book is addressed. The authors aim to introduce the Lebesgue-Stieltjes integral on the real line in a natural way as an extension of the Riemann integral. They have tried to make the treatment as practical as possible. The evaluation of Lebesgue-Stieltjes integrals is discussed in detail, as are the key theorems of integral calculus as well as the standard convergence theorems. The book then concludes with a brief discussion of multivariate integrals and surveys ok L^p spaces and some applications. Exercises, which extend and illustrate the theory, and provide practice in techniques, are included. Michael Carter and Bruce van Brunt are senior lecturers in mathematics at Massey University, Palmerston North, New Zealand. Michael Carter obtained his Ph.D. at Massey University in 1976. He has research interests in control theory and differential equations, and has many years of experience in teaching analysis. Bruce van Brunt obtained his D.Phil. at the University of Oxford in 1989. His research interests include differential geometry, differential equations, and analysis. His publications include

Linear algebra is the branch of mathematics that has grown from a care- ful study of the problem of solving systems of linear equations. The ideas that developed in this way have become part of the language of much of higher mathematics. They also provide a framework for appli- cations of linear algebra to many problems in mathematics, the natural sciences, economics, and computer science. This book is the revised fourth edition of a textbook designed for upper division courses in linear algebra. While it does not presuppose an earlier course, many connections between linear algebra and under- graduate analysis are worked into the discussion, making it best suited for students who have completed the calculus sequence. For many students, this may be the first course in which proofs of the main results are presented on an equal footing with methods for solving numerical problems. The concepts needed to understand the proofs are shown to emerge naturally from attempts to solve concrete problems. This connection is illustrated by worked examples in almost every section. Many numerical exercises are included, which use all the ideas, and develop important techniques for problem-solving. There are also theoretical exercises, which provide opportunities for students to discover interesting things for themselves, and to write mathematical explanations in a convincing way. Answers and hints for many of the problems are given in the back. Not all answers are given, however, to encourage students to learn how to check their work.

This is the first half of a text for a two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the second. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "e;interesting but not essential"e; (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "e;INE"e;. We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.

This book is based on a course I have given five times at the University of Michigan, beginning in 1973. The aim is to present an introduction to a sampling of ideas, phenomena, and methods from the subject of partial differential equations that can be presented in one semester and requires no previous knowledge of differential equations. The problems, with hints and discussion, form an important and integral part of the course. In our department, students with a variety of specialties-notably differen- tial geometry, numerical analysis, mathematical physics, complex analysis, physics, and partial differential equations-have a need for such a course. The goal of a one-term course forces the omission of many topics. Everyone, including me, can find fault with the selections that I have made. One of the things that makes partial differential equations difficult to learn is that it uses a wide variety of tools. In a short course, there is no time for the leisurely development of background material. Consequently, I suppose that the reader is trained in advanced calculus, real analysis, the rudiments of complex analysis, and the language offunctional analysis. Such a background is not unusual for the students mentioned above. Students missing one of the "e;essentials"e; can usually catch up simultaneously. A more difficult problem is what to do about the Theory of Distributions.

Computational complexity theory provides a framework for understanding the cost of solving computational problems, as measured by the requirement for resources such as time and space. The objects of study are algorithms defined within a formal model of computation. Upper bounds on the computational complexity of a problem are usually derived by constructing and analyzing specific algorithms. Meaningful lower bounds on computational complexity are harder to come by, and are not available for most problems of interest. The dominant approach in complexity theory is to consider algorithms as oper- ating on finite strings of symbols from a finite alphabet. Such strings may represent various discrete objects such as integers or algebraic expressions, but cannot rep- resent real or complex numbers, unless the numbers are rounded to approximate values from a discrete set. A major concern of the theory is the number of com- putation steps required to solve a problem, as a function of the length of the input string.

Intended for undergraduate students of electrical engineering, this introduction to electromagnetic fields emphasizes the computation of fields as well as the development of theoretical relations. The first part thus presents the electromagnetic field and Maxwell's equations with a view toward connecting the disparate applications to the underlying relations, while the second part presents computational methods of solving the equations - which for most practical calses cannot be solved analytically.

Intended for graduate students in physics and related fields, this text is a self contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green's functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero- temperature perturbation theory, and the Matsubara, Keldysh, and Nambu -Gor'kov formalisms. The aim is not to be exhaustive, but to present just enough detail to enable the student to follow the current research literature or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum coherence is maintained throughout their volume, and which therefore provides an ideal testing ground for many-body theories. The book begins by introducing the Green's function for one-particle systems (using Feynman path integrals), general perturbation theory, and second quantization. It then turns to the usual zero-temperature formalism, discussing the properties and physical meaning of the Green's function for many-body systems and then developing the diagram techniques of perturbation theory. The theory is extended to finite temperatures, including a discussion of the Matsubara formalism as well as the Keldysh technique for essentially nonequilibrium systems. The final chapter is devoted to applications of the techniques to superconductivity, incuding discussions of the superconducting phase transition, elementary excitations, transport, Andreev reflections, and Josephson junctions. Problems at the end of each chapter help to guide learning an to

This IMA Volume in Mathematics and its Applications COMPUTATIONAL MODELING IN BIOLOGICAL FLUID DYNAMICS is based on the proceedings of a very successful workshop with the same title. The workshop was an integral part of the September 1998 to June 1999 IMA program on "e;MATHEMATICS IN BIOLOGY."e; I would like to thank the organizing committee: Lisa J. Fauci of Tulane University and Shay Gueron of Technion - Israel Institute of Technology for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Founda- tion (NSF), whose financial support of the IMA made the Mathematics in Biology program possible. Willard Miller, Jr., Professor and Director Institute for Mathematics and its Applications University of Minnesota 400 Lind Hall, 207 Church St. SE Minneapolis, MN 55455-0436 612-624-6066, FAX 612-626-7370 miller@ima.umn.edu World Wide Web: http://www.ima.umn.edu v PREFACE A unifying theme in biological fluid dynamics is the interaction of moving, elastic boundaries with a surrounding fluid. A complex dynami- cal system describes the motion of red blood cells through the circulatory system, the movement of spermatazoa in the reproductive tract, cilia of microorganisms, or a heart pumping blood. The revolution in computa- tional technology has allowed tremendous progress in the study of these previously intractable fluid-structure interaction problems.