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Arnold's Problems
Vladimir Arnold is one of the most outstanding mathematicians of our time Many of these problems are at the front line of current research
Differential and Symplectic Topology of Knots and Curves
This book presents a collection of papers on two related topics: topology of knots and knot-like objects (such as curves on surfaces) and topology of Legendrian knots and links in 3-dimensional contact manifolds. Featured is the work of international experts in knot theory ("quantum" knot invariants, knot invariants of finite type), in symplectic and contact topology, and in singularity theory. The interplay of diverse methods from these fields makes this volume unique in the study of Legendrian knots and knot-like objects such as wave fronts. A particularly enticing feature of the volume is its international significance. The volume successfully embodies a fine collaborative effort by worldwide experts from Belgium, France, Germany, Israel, Japan, Poland, Russia, Sweden, the UK, and the US.
Differential Geometry of Varieties with Degenerate Gauss Maps
This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.
New Developments in Singularity Theory
Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions. The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters. The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.
Nanoscale Phenomena
The main intention of the editors of the book is the demonstration of the intrinsic correlation and mutual influence of three important components of nanoscience: new phenomena – nanomaterials – nanodevices. This is the organizing concept of the book. To discover new phenomena it is necessary to develop novel nanotechnological processes for fabrication of nanomaterials. Nanostructures and new phenomena serve as the base for the development of novel nanoelectronic devices and systems. The articles selected for the book illustrate this interrelation.
Transition Metal Arene π-Complexes in Organic Synthesis and Catalysis
Metal-arene pi-complexes show a rich and varied chemistry. The metal adds a third dimension to the planar aromatic compounds and coordination of a metal to an arene thus not only altering the reactivity of ring-carbons and substituents but also makes possible reactions that lead to chiral non-racemic products. This book, organized in nine chapters and written by leading scientists in the field provides the reader with an up-to-date treatise on the subject organized according to reaction type and use. It covers the wide spectrum of arene activation: from the electrophilic activation of h6-bound arene by pi-Lewis acid metal complex fragments, to reactions of nucleophilic h2-coordinated arene c...
Nanostructured Magnetic Materials and their Applications
Interest in research on nanoscale materials is steadily increasing: nano-structured magnetic materials exhibit new and interesting physical properties, which cannot be found in the bulk. Many of these unique properties have great potential for technical applications in magneto-sensors, bio-sensors, magneto-electronics, data storage, magnetic heads of computer hard disks, single-electron devises, microwave electronic devices, etc. Current research concentrates on device design, synthesis and the characterization of nanostructured materials. The contributions to this book concentrate on magnetic properties of nanoscale magnetic materials, especially on fabrication and characterization, and the physics underlying the unique properties of these structures and devices.
Mathematical Feynman Path Integrals And Their Applications (Second Edition)
Feynman path integrals are ubiquitous in quantum physics, even if a large part of the scientific community still considers them as a heuristic tool that lacks a sound mathematical definition. Our book aims to refute this prejudice, providing an extensive and self-contained description of the mathematical theory of Feynman path integration, from the earlier attempts to the latest developments, as well as its applications to quantum mechanics.This second edition presents a detailed discussion of the general theory of complex integration on infinite dimensional spaces, providing on one hand a unified view of the various existing approaches to the mathematical construction of Feynman path integrals and on the other hand a connection with the classical theory of stochastic processes. Moreover, new chapters containing recent applications to several dynamical systems have been added.This book bridges between the realms of stochastic analysis and the theory of Feynman path integration. It is accessible to both mathematicians and physicists.
Real and Complex Singularities
This volume collects papers presented at the eighth São Carlos Workshop on Real and Complex Singularities, held at the IML, Marseille, July 2004. Like the workshop, this collection establishes the state of the art and presents new trends, new ideas and new results in all of the branches of singularities. Real and Complex Singularities offers a useful summary of leading ideas in singularity theory, and inspiration for future research.
