Approach your problems from the It isn't that they can't see the end and begin with the answers. solution. It is that they can't Then one day, perhaps you will see the problem. find the final question. G.K. Chesterton. The Scandal of 'The Hermit Clad in Crane Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of mono graphs and textbooks on increasingly topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electric engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "complete integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifica tion schemes. The draw upon widely different sections of mathematics.

In the twenty years since Zabusky and Kruskal coined the term ``soliton'', this concept changed the outlook on certain types of nonlinear phenomena and found its way into all branches of physics. The present volume deals with a great variety of applications of the new concept in condensed-matter physics, which is particularly reached in experimentally observable occurrences. The presentation is not centred around the mathematical aspects; the emphasis is on the physical nature of the nonlinear phenomena occurring in particular situations.With its emphasis on concrete, mostly experimentally verifiable cases, ``Solitons'' constitutes a very readable and instructive introduction to the subject as well as an up-to-date account of current developments in a field of research reaching maturity.

This book addresses the issue of non-linear problems that have dominated the forefront of physics. To analyse these problems, it is necessary to develop mathematical methods to match new concepts. In this connection, for the first time in a long time, the same key notions have attracted the attention of physicists and mathematicians. This book discusses how the role of such excitations in essentially non-linear systems is similar to that of harmonic oscillations and waves in linear physical models.

Synergetics is the quantitative study of multicomponent systems that exhibit nonlinear dynamics and cooperativity. This book specifically considers basic models of the nonlinear dynamics of molecular systems and discusses relevant applications in biological physics and the polymer sciences. Emphasis is placed on specific solutions to the dynamical equations that correspond to the coherent formation of spatial-temporal structures, such as solitons, kinks and breathers, in particular. The emergence of these patterns in molecular structures provides a variety of information on their structural properties and plays a significant part in energy transfer processes, topological defects, dislocations, and related structure transitions. Real media, in which solitons take the form of solitary waves, are also considered. In this context, the formation of nonlinear waves in a continuous medium described by nonlinear equations is associated with spontaneous breaking of the local symmetry of the homogeneous system, which produces a range of interesting phenomena. A particular feature of this text is its combination of analytic and computational strategies to tackle difficult nonlinear problems at the molecular level of matter.

Proceedings of the NATO Advanced Research Workshop on Molecular Self-Organization: From Molecules to Water, to Nanoparticles, to DNA and Proteins Kyiv, Ukraine 8-12 June 2008

Proceedings of a NATO ARW held in Thisted, Denmark, July 30-August 5, 1989

Molecular Electronics and Molecular Electronic Devices is a book that provides a comprehensive review of current problems and information regarding aspects of molecular electronics and molecular electronic devices. Experimental and theoretical aspects of molecular electronics and molecular electronic devices are reviewed by distinguished researchers working in chemistry, physics, computer science, and various areas of biology. These books will be an excellent reference for physicists, chemists, electronics engineers and researchers interested in molecular electronics and molecular electronic devices.

This book presents the current knowledge about nonlinear localized travelling excitations in crystals. Excitations can be vibrational, electronic, magnetic or of many other types, in many different types of crystals, as silicates, semiconductors and metals. The book is dedicated to the British scientist FM Russell, recently turned 80. He found 50 years ago that a mineral mica muscovite was able to record elementary charged particles and much later that also some kind of localized excitations, he called them quodons, was also recorded. The tracks, therefore, provide a striking experimental evidence of quodons existence. The first chapter by him presents the state of knowledge in this topic. It is followed by about 18 chapters from world leaders in the field, reviewing different aspects, materials and methods including experiments, molecular dynamics and theory and also presenting the latest results. The last part includes a personal narration of FM Russell of the deciphering of the marks in mica. It provides a unique way to present the science in an accessible way and also illustrates the process of discovery in a scientist's mind.

Even though there is no generally accepted definition of nanotechnologies to be defined as distinct discipline there is an emerging consensus that their advent and development is a growing in importance factor of the contemporary and future technological civilization. One of these most fundamental issues we are confronted with is the compatibility with life itself. From single cell organisms to humans, carbon is a key building block of all molecular structures of life. In contrast the man created electronic industry to build on other elements, of which silicon is the most common. Both carbon and silicon create molecular chains, although different in their internal structure. All life is built from carbon-based chains. As long as the man built technological products do not directly interfere with the physiology of life the associated risks from them are relatively easy to identify. They are primarily in the environmental pollution and the possibility of upsetting the natural balance of biocoenosis, on a planetary scale. The basic life functions are still not directly subverted. We can use TV, computers, drive cars and use other technological utilities without fear of direct interference with our cellular functions. This is in particular because all these technological utilities are many orders of magnitude larger than typical scales of biological activity. Most of biological activity, from fermentative catalysis to DNA replication takes place on nanoscale. The situation is radically different when the technological goals are building nanoscale size products. All biological processes take place on nanoscale.

At first glance, the articles in this book may appear to have nothing in common. They cover such seemingly disparate subjects as the properties of small metallic clusters and the behavior of superfluid He3, nuclear physics and organic materials, copper oxides and mag netic resonance. Why have they been brought together, particUlarly in our time of narrow spe cialization? In fact, the properties and effects described in this book touch upon one and the same fundamental phenomenon: pair correlation. Introduced in the theory of superconductivity by J. Bardeen, L. Cooper, and J. Schrieffer (BCS), this effect plays a key role in various Fermi systems. The book consists of several sections. The first chapter is concerned with conven tional and high Tc superconductors. The second chapter describes two relatively young fami lies of superconductors: organics and fullerenes. Chapter III addresses the superfluidity of 3 He • The discovery of this phenomenon in 1971 was a big event in physics and last year was acknowledged by a Nobel prize. This book contains the text of the Nobel lecture. Chapters IV and V are devoted to correlations in finite Fermi systems such as small metallic clusters, C 60 anions, and atomic nuclei. The book thus covers a broad range of problems, illuminating the close ties between various areas of physics.