The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probability and mathematical physics.
This volume contains current work at the frontiers of research in infinite dimensional stochastic analysis. It presents a carefully chosen collection of articles by experts to highlight the latest developments in white noise theory, infinite dimensional transforms, quantum probability, stochastic partial differential equations, and applications to mathematical finance. Included in this volume are expository papers which will help increase communication between researchers working in these areas. The tools and techniques presented here will be of great value to research mathematicians, graduate students and applied mathematicians.
This comprehensive review of cinchona-based chiralilty inducers and their applications covers every topic, including ligands, immobilization and organocatalysis. Each chapter summarizes the scope and limitations of the new methods and technologies, while the final chapter contains carefully selected working procedures of cinchona alkaloid-promoted reactions organized according to reaction type. Invaluable reading for anyone wanting to learn about the current state of this hot topic.
This book represents the first synthesis of the considerable body of new research into positive definite matrices. These matrices play the same role in noncommutative analysis as positive real numbers do in classical analysis. They have theoretical and computational uses across a broad spectrum of disciplines, including calculus, electrical engineering, statistics, physics, numerical analysis, quantum information theory, and geometry. Through detailed explanations and an authoritative and inspiring writing style, Rajendra Bhatia carefully develops general techniques that have wide applications in the study of such matrices. Bhatia introduces several key topics in functional analysis, operato...
"The book presents a compendium of knowledge on general environment and acrobiology having 29 research articles classified under five sections, i.e., General Aerobiology having five papers, Aeropalynology having four papers, Aeromycology having seven papers, Epidemiology and Forecast having six papers and Allergy and Immunology having seven papers. These articles have been contributed by over 50 research workers."