Bücher veröffentlicht von Springer Berlin Heidelberg

The Bachelier Society for Mathematical Finance held its first World Congress in Paris last year, and coincided with the centenary of Louis Bacheliers thesis defence. In his thesis Bachelier introduces Brownian motion as a tool for the analysis of financial markets as well as the exact definition of options. The thesis is viewed by many the key event that marked the emergence of mathematical finance as a scientific discipline. The prestigious list of plenary speakers in Paris included two Nobel laureates, Paul Samuelson and Robert Merton, and the mathematicians Henry McKean and S.R.S. Varadhan. Over 130 further selected talks were given in three parallel sessions. .

The present book contains fourteen expository contributions on various topics connected to Number Theory, or Arithmetics, and its relationships to Theoreti- cal Physics. The first part is mathematically oriented; it deals mostly with ellip- tic curves, modular forms, zeta functions, Galois theory, Riemann surfaces, and p-adic analysis. The second part reports on matters with more direct physical interest, such as periodic and quasiperiodic lattices, or classical and quantum dynamical systems. The contribution of each author represents a short self-contained course on a specific subject. With very few prerequisites, the reader is offered a didactic exposition, which follows the author's original viewpoints, and often incorpo- rates the most recent developments. As we shall explain below, there are strong relationships between the different chapters, even though every single contri- bution can be read independently of the others. This volume originates in a meeting entitled Number Theory and Physics, which took place at the Centre de Physique, Les Houches (Haute-Savoie, France), on March 7 - 16, 1989. The aim of this interdisciplinary meeting was to gather physicists and mathematicians, and to give to members of both com- munities the opportunity of exchanging ideas, and to benefit from each other's specific knowledge, in the area of Number Theory, and of its applications to the physical sciences. Physicists have been given, mostly through the program of lectures, an exposition of some of the basic methods and results of Num- ber Theory which are the most actively used in their branch.

The author of this book, Prof. Vadim Vasilievich Schmidt, was known in the West as 'Russian Schmidt'. Being a talented theoretician and at the same time heading an experimentallaboratory in Chernogolovka, Vadim Schmidt had a unique talent for explaining complicated physical models and ideas in a simple way. One of his favorite sayings was 'physics is a verbal science'. The book is based on his introductory course on superconductivity. It was published in Russian in 1982 and very soon became undoubtedly the most popular Russian textbook on the physics of superconductors. Without losing its generality and depth, the book presents key aspects of superconductivity in a very clear and logically structured form. As the author said in his pref­ ace to the Russian edition, he tried to 'avoid situations when the words "it is easy to show" conceal tedious and bulky computations'. In spite of its rel­ atively small volume, the book gives a broad overview and covers the major topics of superconductivity. Well-selected examples are clearly described and help the re ader to understand the ideas presented. The book even allows an inexperienced reader to quickly get a grasp of a topic. Vadim Schmidt was born in 1927 in Moscow. His father was a well-known politician and the family did not escape the purges of Stalin's time.

Ex situ preservation of germplasm for higher plant species has been accom­ plished using either seeds or clones, but storage of these under typical condi­ tions does not provide the extreme longevities that are needed to minimize risk of loss. Costs of maintenance and regeneration of stocks are also high. Systems that provide virtually indefinite storage should supplement existing methods and it is within this context that cryopreservation is presented. The use of low temperature preservation was initially more a concern of medicine and animal breeding, and was expanded to plants in the 1970s. Sur­ vival after cryogenic exposure has now been demonstrated for diverse plant groups including algae, bryophytes, fungi and higher plants. If survival is com­ monplace, then the eventual application is a cryopreservation system, whereby cells, tissues and organs are held indefinitely for use, often in the unforeseen future. The increasing interest and capabilities for application could not haveoccurred at a more opportune time since expanding human populations have placed unprecedented pressures on plant diversity. This book emphasizes cry­ opreservation of higher plants and was initially driven by the concern for loss of diversity in crops and the recognized need that this diversity would be essential for continued improvement of the many plants used by society for food, health and shelter. The interest in cryopreservation has been expanded by conservationists and their concerns for retaining, as much as possible, the diversity of natural populations. The need for cryopreservation, thus, is well established.

This book is concerned with a number of theories that can be used for describ­ ing and analyzing systems of interacting components in case it is desirable or necessary to regard their time-dependent behavior. Society is becoming increasingly more dependent on complex computer­ based systems that are composed of several components that act concurrently and interact - to synchronize and communicate with each other. The com­ plexity of these systems arises to a great extent from the many ways in which their components can interact. The need that these components act and in­ teract on time as well adds considerably to the complexity. In developing such a system, it is important to be able to acquire a better understanding of the relevant issues at the conceptual level, to describe the system in a precise way at various levels of detail, and to analyze it on the basis of the descriptions. When the early algebraic theories about processes, such as ACP [16, 17, 20], CCS [49, 50] and CSP [27, 39], were developed for that purpose, the established opinion was still that timing is a concern that can more often than not be treated independently. It is therefore not surprising that timing is deliberately ignored in those theories. They have now all been extended to deal with timing.

This book, now in its ninth edition, still has the character of a textbook with the emphasis on "e;Physics"e;. The volume has increased somewhat because several improvements have been made and some new items have been included. In Sect. 13. 2 the new Quantum Cascade Laser which covers the far in- frared spectral range has been added. In Sect. 14. 4 the theory of the quantum Hall effect is now based on ballistic transport which in a more general respect without referring to the then still unknown quantum Hall effect was consid- ered already by Rudolf Peierls. In the same chapter, the recent discovery of a low-temperature resistance oscillation in a very pure semiconductor under the influence of combined dc and ac electric fields in addition to a magnetic field is presented. Furthermore, quantum Hall effect observations with an unprece- dented high precision are remarkable and may give a new impetus to theory. A new Sect. 15. 5 presents information about coaxial carbon tubes of nanometer size diameter and how they are integrated as the current transporting element in a field effect transistor. In another new addition Sect. 15. 6 with the title Molecular Electronics, the current-voltage rectifying characteristics of an or- ganic Langmuir-Blodgett film of nanometer thickness is shown. These efforts serve to demonstrate where the ever decreasing size of electronic circuits may come to its natural limits. The system of units preferred here is the SI system.

In inverse problems, the aim is to obtain, via a mathematical model, information on quantities that are not directly observable but rather depend on other observable quantities. Inverse problems are encountered in such diverse areas of application as medical imaging, remote sensing, material testing, geosciences and financing. It has become evident that new ideas coming from differential geometry and modern analysis are needed to tackle even some of the most classical inverse problems. This book contains a collection of presentations, written by leading specialists, aiming to give the reader up-to-date tools for understanding the current developments in the field.

In this book the process of decoherence is reviewed from both the theoretical and the experimental physicist's point of view. Implications of this important concept for fundamental problems of quantum theory and for chemistry and biology are also given. This broad review of decoherence addresses researchers and graduate students. It could also be used in seminar work.