Bücher veröffentlicht von Springer Berlin Heidelberg

The contributions to this volume are based on selected lectures from the first international workshop on decoherence, information, complexity and entropy (DICE). The aim of this volume is to reflect the growing importance ot common concepts behind seemingly different fields such as quantum mechanics, general relativity and statistical physics in a form accessible to nonspecialist researchers. Many presentations include original results which are published here for the first time.

Mathematicians do not study objects, but relations among objectsj they are indifferent to the replacement of objects by others as long as relations do not change. Matter is not important, only form interests them. HENRI POINCARE (1854-1912) Computer scientists working on algorithms for factorization would be well advised to brush up on their number theory. IAN STEWART [219] The theory of numbers, in mathematics, is primarily the theory of the prop- erties of integers (i.e., the whole numbers), particularly the positive integers. For example, Euclid proved 2000 years aga in his Elements that there exist infinitely many prime numbers. The subject has long been considered as the purest branch of mathematics, with very few applications to other areas. How- ever, recent years have seen considerable increase in interest in several central topics of number theory, precisely because of their importance and applica- tions in other areas, particularly in computing and information technology.

Diagnostically illustrated with light and scanning electron micrographs, Comparative Wood Anatomy lucidly introduces dicotyledon wood in terms of cell types and their variations, pertinent literature, taxonomic distribution of features, terminology, and methods for preparation. Two final chapters present syntheses: taxonomic achievements of wood studies; and the evolutionary relationship between structure, physiological function, and ecology. This detailed survey serves a wide range of interests: identification, systematics, evolution and physiology.

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "e;Higher Dimensional Varieties and Rational Points"e; held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

More than half of all stars in the universe formed and evolved as binary systems and their study is essential for understanding stellar and galactic evolution. The six lectures in this book give both a readable introduction and an up-to-date review of nearly all aspects of  research into binary stars, including the range from common binaries to more exotic systems composed of white dwarfs, neutron stars and black holes.

Evanescent waves play a growing role in many different areas such as guided optics, optical-fiber couplers, integrated optical elements, internal reflection spectroscopy, atom optics, dark-field microscopy, scanning tunneling optical microscopy, microaperture microscopy, and apertureless microscopies. This book describes the near field of an object through the role of the evanescent field in these areas of research. It is intended as a reference for scientists and as an introduction at the graduate level.

The original version of this article was written more than fiveyears ago with S. Z. Shefel',a profound and original mathematician who died in 1984. Sincethen the geometry of surfaces has continued to be enriched with ideas and results. This has required changes and additions, but has not influenced the character of the article, the design ofwhich originated with Shefel'. Without knowing to what extent Shefel' would have approved the changes, I should nevertheless like to dedicate this article to his memory. (Yu. D. Burago) We are trying to state the qualitative questions of the theory of surfaces in Euclidean spaces in the form in which they appear to the authors at present. This description does not entirely correspond to the historical development of the subject. The theory of surfaces was developed in the first place mainly as the 3 theory of surfaces in three-dimensional Euclidean space E ; however, it makes sense to begin by considering surfaces F in Euclidean spaces of any dimension n~ 3. This approach enables us, in particular, to put in a new light some 3 unsolved problems of this developed (and in the case of surfaces in E fairly complete) theory, and in many cases to refer to the connections with the present stage ofdevelopment of the theory of multidimensional submanifolds. The leading question of the article is the problem of the connection between classes of metrics and classes of surfaces in En.