Bücher veröffentlicht von Springer New York

This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite- difference methods and of projection methods for approximating their variational formulations.

Naked-eye comets are far from uncommon. As a rough average, one appears every 18 months or thereabouts, and it is not very unusual to see more than two in a single year. The record so far seems to have been 2004, with a total of five comets visible without optical aid. But 2006, 1970, and 1911 were not far behind with a total of four apiece. Yet, the majority of these pass unnoticed by the general public. Most simply look like fuzzy stars with tails that are either faint or below the naked-eye threshold. The ¿classical¿ comet ¿ a bright star-like object with a long flowing tail ¿ is a sight that graces our skies about once per decade, on average. These ¿great comets¿ are surely among the most beautiful objects that we can see in the heavens, and it is no wonder that they created such fear in earlier times. Just what makes a comet ¿¿great¿¿ is not easy to define. It is neither just about brightness nor only a matter of size. Some comets can sport prodigiously long tails and yet not be regarded as great. Others can become very bright, but hardly anyone other than a handful of enthusiastic astronomers will ever see them. Much depends on their separation from the Sun, the intensity of the tail, and so forth.

This is a textbook on Galois theory. Galois theory has a well-deserved re- tation as one of the most beautiful subjects in mathematics. I was seduced by its beauty into writing this book. I hope you will be seduced by its beauty in reading it. This book begins at the beginning. Indeed (and perhaps a little unusually for a mathematics text), it begins with an informal introductory chapter, Ch- ter 1. In this chapter we give a number of examples in Galois theory, even before our terms have been properly de?ned. (Needless to say, even though we proceed informally here, everything we say is absolutely correct.) These examples are sort of an airport beacon, shining a clear light at our destination as we navigate a course through the mathematical skies to get there. Then we start with our proper development of the subject, in Chapter 2. We assume no prior knowledge of ?eld theory on the part of the reader. We develop ?eld theory, with our goal being the Fundamental Theorem of Galois Theory (the FTGT). On the way, we consider extension ?elds, and deal with the notions of normal, separable, and Galois extensions. Then, in the penul- mate section of this chapter, we reach our main goal, the FTGT.

In the Victorian era - or for non-British readers, the mid-to-late nineteenth century - amateur astronomy tended to center on Solar System objects. The Moon and planets, as well as bright comets, were the key objects of interest. The brighter variable stars were monitored, but photography was in its infancy and digital imaging lay a century in the future. Today, at the start of the twenty-first century, amateurs are better equipped than any professionals of the mid-twentieth century, let alone the nineteenth. An amateur equipped with a 30-cm telescope and a CCD camera can easily image objects below magnitude 20 and, from very dark sites, 22 or 23. Such limits would have been within the realm of the 100- and 200-inch reflectors on Mount Wilson and Mount Palomar in the 1950s, but no other observatories. However, even those telescopes took hours to reach such limits, and then the photographic plates had to be developed, fixed, and examined by eye. In the modern era digital images can be obtained in minutes and analyzed 'on the fly' while more images are being downloaded. Developments can be e-mailed to other interested amateurs in real time, during an observing session, so that when a cataclysmic event takes place amateurs worldwide know about it. As recently as the 1980s, even professional astronomers could only dream of such instantaneous communication and proc- sing ability.

Many books have already been written about the perturbation theory of differential equations with a small parameter. Therefore, we would like to give some reasons why the reader should bother with still another book on this topic. Speaking for the present only about ordinary differential equations and their applications, we notice that methods of solutions are so numerous and diverse that this part of applied mathematics appears as an aggregate of poorly connected methods. The majority of these methods require some previous guessing of a structure of the desired asymptotics. The Poincare method of normal forms and the Bogolyubov-Krylov­ Mitropolsky averaging methods, well known in the literature, should be mentioned specifically in connection with what will follow. These methods do not assume an immediate search for solutions in some special form, but make use of changes of variables close to the identity transformation which bring the initial system to a certain normal form. Applicability of these methods is restricted by special forms of the initial systems.

This book examines the issues relevant to the design of vector and pipelined computer systems using the Cray X-MP/24. The purpose of the book is to help the readers arrive at a deep understanding of how vector processing systems really work. These insights will be useful to the scientist who would like to obtain maximum performance from a vector machine, to the computer science student, and to the compiler writer. The book can also be used to supplement a regular textbook in a graduate or senior level course in computer architecture. The book looks at the overall design of the Cray X-MP and then explores the operation of the machine by looking at detailed timings of various instructions and code segments. It examines such issues as instruction issues and buffering, handling of jump instructions, use of registers to hold intermediate results, memory conflicts resulting from vectorization, optimal vectorization of multiple statement loops, and synchronization problems with multi-tasking.Detailed Gantt charts are provided to guide the reader through the timing issues.

From Math Reviews: This is Volume II of a two-volume introductory text in classical algebra. The text moves carefully with many details so that readers with some basic knowledge of algebra can read it without difficulty. The book can be recommended either as a textbook for some particular algebraic topic or as a reference book for consultations in a selected fundamental branch of algebra. The book contains a wealth of material. Amongst the topics covered in Volume II the reader can find: the theory of ordered fields (e.g., with reformulation of the fundamental theorem of algebra in terms of ordered fields, with Sylvester's theorem on the number of real roots), Nullstellen-theorems (e.g., with Artin's solution of Hilbert's 17th problem and Dubois' theorem), fundamentals of the theory of quadratic forms, of valuations, local fields and modules. The book also contains some lesser known or nontraditional results; for instance, Tsen's results on solubility of systems of polynomial equations with a sufficiently large number of indeterminates. These two volumes constitute a very good, readable and comprehensive survey of classical algebra and present a valuable contribution to the literature on this subject.

In an easy to use dictionary style of A¿Z presentation, this volume lists the taxonomy and medicinal usage of Indian plants. Also given are both traditional Indian and international synonyms along with details of the habitats of the plants.Indian Medicinal Plants. An Illustrated Dictionary is aimed at bringing out an updated Acute Study Dictionary of plant sources of Indian medicine.The text is based on authentic treatises which are the outcome of scientific screening and critical evaluation by eminent scholars. Readers, if they so desire, can always refer back to a particular research paper cited in the original source.The text is illustrated by over 550 full-color figures.

It has been my good fortune to meet and get to know many remarkable people, mostly statisticians and mathematicians, and to derive much pleasure and benefit from these contacts. They were teachers, colleagues and students, and the following pages sketch their careers and our interactions. Also included are a few persons with whom I had little or no direct contact but whose ideas had a decisive influence on my work. To provide some coherence, the account is largely chronological and follows the steps of my own career. Taken together, these sketches provide a very personal picture of the dev- opment of statistical theory from the 1930s to the 1970s. It is the period between two revolutions: that of Fisher, Neyman, and Pearson, which laid the foundations for the classical statistical theory of that period; and the second revolution, forty years later, brought about by the advent of the computer, which turned statistics in new directions. The present account of this history is a highly selective one, which emphasizes the persons, institutions, and statistical topics that were close to my interests. One narrowing effect of this perspective stems from the fact that my career took place in the United States. As a consequence, the book focuses on American statisticians and institutions. Only the last two ch- ters discuss, briefly and very incompletely, developments in some other countries.

This Student Guide is exceptional, maybe even unique, among such guides in that its author, Fred Soon, was actually a student user of the textbook during one of the years we were writing and debugging the book. (He was one of the best students that year, by the way. ) Because of his background, Fred has taken, in the Guide, the point of view of an experienced student tutor helping you to learn calculus. \~ile we do not always think Fred's jokes are as funny as he does, we appreciate his enthusiasm and his desire to enter into communication with his readers; since we nearly always agree with the mathe- matical judgements he has made in explaining the material, we believe that this Guide can serve you as a valuable supplement to our text. To get maximum benefit from this Guide, you should begin by spending a few moments to acquaint yourself with its structure. Once you get started in the course, take advantage of the many opportunities which the text and Student Guide together provide for learning calculus in the only way that any mathe- matical subject can truly be mastered - through attempting to solve problems on your own. As you read the text, try doing each example and exercise your- self before reading the solution; do the same with the quiz problems provided by Fred.