springer new york springer us aug 1983 (5 Ergebnisse)

Buch. Zustand: Neu. Neuware -Proceedings of an American Society Symposium held in Orlando, Florida, August 25-30 1996Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 180 pp. Englisch.

Buch. Zustand: Neu. Neuware -This book discusses some of the first principles of modern analysis. I t can be used for courses at several levels, depending upon the background and ability of the students. It was written on the premise that today's good students have unexpected enthusiasm and nerve. When hard work is put to them, they work harder and ask for more. The honors course (at the University of Wisconsin) which inspired this book was, I think, more fun than the book itself. And better. But then there is acting in teaching, and a typewriter is a poor substitute for an audience. The spontaneous, creative disorder that characterizes an exciting course becomes silly in a book. To write, one must cut and dry. Yet, I hope enough of the spontaneity, enough of the spirit of that course, is left to enable those using the book to create exciting courses of their own. Exercises in this book are not designed for drill. They are designed to clarify the meanings of the theorems, to force an understanding of the proofs, and to call attention to points in a proof that might otherwise be overlooked. The exercises, therefore, are a real part of the theory, not a collection of side issues, and as such nearly all of them are to be done. Some drill is, of course, necessary, particularly in the calculation of integrals.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 468 pp. Englisch.

Buch. Zustand: Neu. Neuware -Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 392 pp. Englisch.

Buch. Zustand: Neu. Neuware -The small book by Shimura-Taniyama on the subject of complex multi is a classic. It gives the results obtained by them (and some by Weil) plication in the higher dimensional case, generalizing in a non-trivial way the method of Deuring for elliptic curves, by reduction mod p. Partly through the work of Shimura himself (cf. [Sh 1] [Sh 2], and [Sh 5]), and some others (Serre, Tate, Kubota, Ribet, Deligne etc.) it is possible today to make a more snappy and extensive presentation of the fundamental results than was possible in 1961. Several persons have found my lecture notes on this subject useful to them, and so I have decided to publish this short book to make them more widely available. Readers acquainted with the standard theory of abelian varieties, and who wish to get rapidly an idea of the fundamental facts of complex multi plication, are advised to look first at the two main theorems, Chapter 3, 6 and Chapter 4, 1, as well as the rest of Chapter 4. The applications of Chapter6 could also be profitably read early. I am much indebted to N. Schappacher for a careful reading of the manu script resulting in a number of useful suggestions. S. LANG Contents CHAPTER 1 Analytic Complex Multiplication 4 I. Positive Definite Involutions . . . 6 2. CM Types and Subfields. . . . . 8 3. Application to Abelian Manifolds. 4. Construction of Abelian Manifolds with CM 14 21 5. Reflex of a CM Type . . . . .Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 196 pp. Englisch.

Buch. Zustand: Neu. Neuware -Atomic transport in solids is a field of growing importance in solid state physics and chemistry, and one which, moreover, has important implications in several areas of materials science. This growth is due first to an increase in the understanding of the fund amentals of transport processes in solids. Of equal importance, however, have been the improvements in the last decade in the experi mental techniques available for the investigation of transport phenomena. The advances in technique have stimulated studies of a wider range of materials; and expansion of the field has been strong ly encouraged by the increasing range of applied areas where transport processes play an essential role. For example, mass transport phenomena play a critical role in the technology of fabrication of components in the electronics industry. Transport processes are involved both during the fabrication and operation of devices and with the growing trend to miniaturisation there are increasing demands on accurate control of diffusion processes. The present book (which is based on a NATO sponsored Advanced Study Institute held in 1981 at Lannion, France) aims to present a general survey of the subject, highlighting those areas where work has been especially active in recent years.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 616 pp. Englisch.