Bücher veröffentlicht von Springer New York

Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.

This book contains a unified treatment of a class of problems of signal detection theory. This is the detection of signals in addi- tive noise which is not required to have Gaussian probability den- sity functions in its statistical description. For the most part the material developed here can be classified as belonging to the gen- eral body of results of parametric theory. Thus the probability density functions of the observations are assumed to be known, at least to within a finite number of unknown parameters in a known functional form. Of course the focus is on noise which is not Gaussian; results for Gaussian noise in the problems treated here become special cases. The contents also form a bridge between the classical results of signal detection in Gaussian noise and those of nonparametric and robust signal detection, which are not con- sidered in this book. Three canonical problems of signal detection in additive noise are covered here. These allow between them formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification. The simplest to state and perhaps the most widely studied of all is the problem of detecting a completely known deterministic signal in noise. Also considered here is the detection random non-deterministic signal in noise. Both of these situa- of a tions may arise for observation processes of the low-pass type and also for processes of the band-pass type.

There are a great deal of books on introductory analysis in print today, many written by mathematicians of the first rank. The publication of another such book therefore warrants a defense. I have taught analysis for many years and have used a variety of texts during this time. These books were of excellent quality mathematically but did not satisfy the needs of the students I was teaching. They were written for mathematicians but not for those who were first aspiring to attain that status. The desire to fill this gap gave rise to the writing of this book. This book is intended to serve as a text for an introductory course in analysis. Its readers will most likely be mathematics, science, or engineering majors undertaking the last quarter of their undergraduate education. The aim of a first course in analysis is to provide the student with a sound foundation for analysis, to familiarize him with the kind of careful thinking used in advanced mathematics, and to provide him with tools for further work in it. The typical student we are dealing with has completed a three-semester calculus course and possibly an introductory course in differential equations. He may even have been exposed to a semester or two of modern algebra. All this time his training has most likely been intuitive with heuristics taking the place of proof. This may have been appropriate for that stage of his development.

Textbooks, even excellent ones, are a reflection of their times. Form and content of books depend on what the students know already, what they are expected to learn, how the subject matter is regarded in relation to other divisions of mathematics, and even how fashionable the subject matter is. It is thus not surprising that we no longer use such masterpieces as Hurwitz and Courant's Funktionentheorie or Jordan's Cours d'Analyse in our courses. The last two decades have seen a significant change in the techniques used in the theory of functions of one complex variable. The important role played by the inhomogeneous Cauchy-Riemann equation in the current research has led to the reunification, at least in their spirit, of complex analysis in one and in several variables. We say reunification since we think that Weierstrass, Poincare, and others (in contrast to many of our students) did not consider them to be entirely separate subjects. Indeed, not only complex analysis in several variables, but also number theory, harmonic analysis, and other branches of mathematics, both pure and applied, have required a reconsidera- tion of analytic continuation, ordinary differential equations in the complex domain, asymptotic analysis, iteration of holomorphic functions, and many other subjects from the classic theory of functions of one complex variable. This ongoing reconsideration led us to think that a textbook incorporating some of these new perspectives and techniques had to be written.

The original version of this book, handed out to my students in weekly in- stallments, had a certain rugged charm. Now that it is dressed up as a Springer UTM volume, I feel very much like Alfred Dolittle at Eliza's wedding. I hope the reader will still sense the presence of a young lecturer, enthusiastically urging his audience to enjoy linear algebra. The book is structured in various ways. For example, you will find a test in each chapter; you may consider the material up to the test as basic and the material following the test as supplemental. In principle, it should be possible to go from the test directly to the basic material of the next chapter. Since I had a mixed audience of mathematics and physics students, I tried to give each group some special attention, which in the book results in certain sections being marked* "e;for physicists"e; or "e;for mathematicians. "e; Another structural feature of the text is its division into laconic main text, put in boxes, and more talkative unboxed side text. If you follow just the main text, jumping from box to box, you will find that it makes coherent reading, a real "e;book within the book,"e; presenting all that I want to teach.

This is a systematic exposition of the basic part of the theory of mea- sure and integration. The book is intended to be a usable text for students with no previous knowledge of measure theory or Lebesgue integration, but it is also intended to include the results most com- monly used in functional analysis. Our two intentions are some what conflicting, and we have attempted a resolution as follows. The main body of the text requires only a first course in analysis as background. It is a study of abstract measures and integrals, and comprises a reasonably complete account of Borel measures and in- tegration for R Each chapter is generally followed by one or more supplements. These, comprising over a third of the book, require some- what more mathematical background and maturity than the body of the text (in particular, some knowledge of general topology is assumed) and the presentation is a little more brisk and informal. The material presented includes the theory of Borel measures and integration for ~n, the general theory of integration for locally compact Hausdorff spaces, and the first dozen results about invariant measures for groups. Most of the results expounded here are conventional in general character, if not in detail, but the methods are less so. The following brief overview may clarify this assertion.

Fluid flows that transfer heat and mass often involve drops and bubbles, particularly if there are changes of phase in the fluid in the formation or condensation of steam, for example. Such flows pose problems for the chemical and mechanical engineer significantly different from those posed by single-phase flows. This book reviews the current state of the field and will serve as a reference for researchers, engineers, teachers, and students concerned with transport phenomena. It begins with a review of the basics of fluid flow and a discussion of the shapes and sizes of fluid particles and the factors that determine these. The discussion then turns to flows at low Reynolds numbers, including effects due to phase changes or to large radial inertia. Flows at intermediate and high Reynolds numbers are treated from a numerical perspective, with reference to experimental results. The next chapter considers the effects of solid walls on fluid particles, treating both the statics and dynamics of the particle-wall interaction and the effects of phase changes at a solid wall. This is followed by a discussion of the formation and breakup of drops and bubbles, both with and without phase changes. The last two chapters discuss compound drops and bubbles, primarily in three-phase systems, and special topics, such as transport in an electric field.

This book contains an introduction to the theory of functions, with emphasis on functions of several variables. The central topics are the differentiation and integration of such functions. Although many of the topics are familiar, the treatment is new; the book developed from a new approach to the theory of differentiation. Iff is a function of two real variables x and y, its deriva- tives at a point Po can be approximated and found as follows. Let PI' P2 be two points near Po such that Po, PI, P2 are not on a straight line. The linear function of x and y whose values at Po, PI' P2 are equal to those off at these points approximates f near Po; determinants can be used to find an explicit representation of this linear function (think of the equation of the plane through three points in three-dimensional space). The (partial) derivatives of this linear function are approximations to the derivatives of f at Po ; each of these (partial) derivatives of the linear function is the ratio of two determinants. The derivatives off at Po are defined to be the limits of these ratios as PI and P2 approach Po (subject to an important regularity condition). This simple example is only the beginning, but it hints at a m theory of differentiation for functions which map sets in IRn into IR which is both general and powerful, and which reduces to the standard theory of differentiation in the one-dimensional case.

This atlas is a comprehensive compendium of congeni- and two-dimensional echocardiographic examples. The tal cardiac morphology as depicted by tomographic two- examples and experience span all ages and may be used dimensional echocardiography. Anatomic specimens by both pediatric and adult cardiologists. The intended cut in planes of section corresponding to the echocar- emphasis is on tomographic morphology and not on diographic views help in the understanding of the echo- specialty applications such as fetal, contrast, or Dop- cardiographic sections. Composite photographs relate pler echocardiography. different planes of section or cardiac events. Still-frame The tomographic approach to congenital anomalies is photography cannot always adequately relate real-time the imaging modality of the 80s and is applicable to echocardiography, computerized tomography, and imaging events. However, the emphasis of this text is to demonstrate the tomographic morphology and no at- magnetic resonance imaging. It is the building block tempt is made to discuss in detail functional or physio- from which the expected three-dimensional imaging logic events. techniques of the 1990s will be developed. The wide- spread clinical application of these imaging modalities Those performing two-dimensional echocardiography should have a working knowledge of cardiac anatomy has rekindled interest in cardiac anatomy and pathol- and common congenital aberrations. This is an in-depth ogy, particularly in the evaluation of patients with con- tomographic atlas not only of the common congenital genital heart disease.

Hungry Hollow is simply an ordinary creek winding through about a mile of ordinary forest and meadow somewhere east of the Rocky Mountains. But like all such places, it is also a vast and intricate web of life with extensions that reach around the planet, back into prehistoric time, and within to a teeming, bizarre microscopic world. In dozens of short, wonderfully imaginative chapters, A.K. Dewdney introduces us to the denizens of this world. We encounter a hackberry tree whose branches perfectly reproduce the taxonomic Tree of Life, learn how it would look and feel to shrink by stages to the size of an amoeba while swimming in a river, watch a toad win the lottery, and see the world of Hungry Hollow from the viewpoint of bears, earthworms, and even stones. This is an excursion into natural history like no other.

How can an airplane weighing many tons stay aloft for many hours, flying so smoothly that the passengers may feel less like they are moving than they would in a car? The answer, of course, lies in the wings and the air they are moving through, and the study of the flow of air around airplane wings is part of the science of aerodynamics. This book is about aerodynamics in the broadest sense. In addition to airplanes, it discusses the aerodynamics of cars and birds, and the motion of diverse object thorugh air and water. The fundamental notions of mechanics and fluid dynamics -- that is, the basic physics underlying aerodynamics -- are clearly explained. The underlying science is discussed rigorously, but only elementary mathematics is used, and only occasionally. To put the science into its human context, the author describes (with many illustrations) the history of human attempts to fly and discusses the social impact of commercial aviation as well as the outlook for future developments. This book is addressed primarily to readers whose background is not in physics or engineering. It will deepen their knowledge of these fields and add to their appreciation of some exciting recent developements in technology. This new edition has been brought up to date throughout; solutions to selected exercises have been added, as well as new problems and other study aids.

From the editors of the wildly successful Beyond Calculation comes another exploration of the overwhelming impact of computers on our future. This time, the essays focus on the human impact of computer technology and culture: how computers will affect the ways we teach, learn, communicate, relate to each other, and live in the coming decades. The contributors, representing the best of many fields, include Secretary of Defense William Perry on how computers will affect warfare; Brian Ferrin on technology and storytelling; Patti Maes on intelligent agents; Nobel Laureate Murray Gell-Mann on the quality of information; Eliot Soloway on the impact of computers on education; and many more. Like Beyond Calculation, praised by the New York Times for its "astonishing intellectual reach," this sequel engages readers with some of the most compelling and important issues of our time.