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This book highlights the methods to engineer dissipative and magnetic nonlinear waves propagating in nonlinear systems. In the first part of the book, the authors present methodologically mathematical models of nonlinear waves propagating in one- and two-dimensional nonlinear transmission networks without/with dissipative elements. Based on these models, the authors investigate the generation and the transmission of nonlinear modulated waves, in general, and solitary waves, in particular, in networks under consideration. In the second part of the book, the authors develop basic theoretical results for the dynamics matter-wave and magnetic-wave solitons of nonlinear systems and of Bose–Einstein condensates trapped in external potentials, combined with the time-modulated nonlinearity. The models treated here are based on one-, two-, and three-component non-autonomous Gross–Pitaevskii equations. Based on the Heisenberg model of spin–spin interactions, the authors also investigate thedynamics of magnetization in ferromagnet with or without spin-transfer torque. This research book is suitable for physicists, mathematicians, engineers, and graduate students in physics, mathematics, and network and information engineering.

The Motivation. With intensified use of mathematical ideas, the methods and techniques of the various sciences and those for the solution of practical problems demand of the mathematician not only greater readi­ ness for extra-mathematical applications but also more comprehensive orientations within mathematics. In applications, it is frequently less important to draw the most far-reaching conclusions from a single mathe­ matical idea than to cover a subject or problem area tentatively by a proper'variety'of mathematical theories. To do this the mathematician must be familiar with the shared as weIl as specific features of differ­ ent mathematical approaches, and must have experience with their inter­ connections. The Atiyah-Singer Index Formula,'one of the deepest and hardest results in mathematics','probably has wider ramifications in topology and analysis than any other single result'(F. Hirzebruch) and offers perhaps a particularly fitting example for such an introduction to'Mathematics': In spi te of i ts difficulty and immensely rich interrela­ tions, the realm of the Index Formula can be delimited, and thus its ideas and methods can be made accessible to students in their middle • semesters. In fact, the Atiyah-Singer Index Formula has become progressively'easier'and'more transparent'over the years. The discovery of deeper and more comprehensive applications (see Chapter 111. 4) brought with it, not only a vigorous exploration of its methods particularly in the many­ facetted and always new presentations of the material by M. F.

Boron is a trivalent metalloid element which occurs abundantly in the evaporite ores borax and ulexite. Elemental boron is used as a dopant in the semiconductor industry, while boron compounds play important roles as light structural materials, insecticides and preservatives, and reagents for chemical synthesis. Boron is an essential plant nutrient. Whereas lack of boron results in boron deficiency disorder, high soil concentrations of boron may also be toxic to plants. This book presents current research in the study of boron, including borophosphates; boron in higher plants; thermodynamic stability of boride semiconductor alloys; boron beam interaction with matter; boron processing in the solar cell industry; and treatment of boron-containing water.

This book is an introduction to recent progress in the development and application of glass with special photonics properties. Glass has a number of structural and practical advantages over crystalline materials, including excellent homogeneity, variety of form and size, and the potential for doping with a variety of dopant materials. Glasses with photonic properties have great potential and are expected to play a significant role in the next generation of multimedia systems. Fundamentals of glass materials are explained in the first chapter, and the book then proceeds to a discussion of gradient index glass, laser glasses, nonlinear optical glasses and magneto-optical glasses. Beginning with the basic theory, the book discusses actual problems, performance and applications of glasses. The book will be of value to graduate students, researchers and professional engineers working in materials science, chemistry and physics with an interest in photonics and glass with special properties.

Nanostructured materials is one of the hottest and fastest growing areas in today's materials science field, along with the related field of solid state physics. Nanostructured materials and their based technologies have opened up exciting new possibilites for future applications in a number of areas including aerospace, automotive, x-ray technology, batteries, sensors, color imaging, printing, computer chips, medical implants, pharmacy, and cosmetics. The ability to change properties on the atomic level promises a revolution in many realms of science and technology. Thus, this book details the high level of activity and significant findings are available for those involved in research and development in the field. It also covers industrial findings and corporate support. This five-volume set summarizes fundamentals of nano-science in a comprehensive way. The contributors enlisted by the editor are at elite institutions worldwide.Key Features• Provides comprehensive coverage of the dominant technology of the 21st century• Written by 127 authors from 16 countries, making this truly international• First and only reference to cover all aspects of nanostructured materials and nanotechnology