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.
The Pushtimarg, a Hindu sect established in India in the fifteenth century, possesses a unique culture--reaching back centuries and still vital today--in which art and devotion are deeply intertwined. This important volume, illustrated with more than one hundred vivid images, offers a new, in-depth look at the Pushtimarg and its rich aesthetic traditions, which are largely unknown outside of South Asia. Original essays by eminent scholars of Indian art focus on the style of worship, patterns of patronage, and artistic heritage that generated pichvais, large paintings on cloth designed to hang in temples, as well as other paintings for the Pushtimarg. In this expansive study, the authors deftly examine how pichvais were and still are used in the seasonal and daily veneration of Shrinathji, an aspect of Krishna as a child who is the chief deity of the temple town of Nathdwara in Rajasthan. Gates of the Lord introduces readers not only to the visual world of the Pushtimarg, but also to the spirit of Nathdwara.
Is God good? Or is He a manipulative villain who plays with the lives of his creations in the name of karma? As far as Mohan Mishra is concerned, God is a villain. Mohan is God’s soft target, for He ‘blesses’ him with a strange mental problem and kills his support system when he needed it the most. The Soft Target is the story of a boy’s journey into manhood, as he takes on God with his mental prowess, defeating Him at every stage, thus making God his soft target. Supported by great friends and a loving wife, Mohan fights an epic battle against the murderous society, the conniving legal system and ultimately God himself, with remarkable courage and spirit.
The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in each chapter, partly to initiate and motivate the theory developed and partly to underscore the applications. The choice of topics in this vastly developed book is a difficult one, and the authors have made an effort to stay closer to applications instead of bringing in too many abstract concepts.
This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab initio exposition of the basic results concerning the topology of metric spaces, particularly of normed linear spaces.The last chapter deals with miscellaneous applications of the Differential Calculus including an introduction to the Calculus of Variations. As a corollary to this, there is a brief discussion of geodesics in Euclidean and hyperbolic planes and non-Euclidean geometry.
This book discusses in detail the basic algorithms of video compression that are widely used in modern video codec. The authors dissect complicated specifications and present material in a way that gets readers quickly up to speed by describing video compression algorithms succinctly, without going to the mathematical details and technical specifications. For accelerated learning, hybrid codec structure, inter- and intra- prediction techniques in MPEG-4, H.264/AVC, and HEVC are discussed together. In addition, the latest research in the fast encoder design for the HEVC and H.264/AVC is also included.
This volume of Progress in Clinical Neurosciences comprises review articles on various aspects of movement disorders and cerebrovascular diseases in Neurology, and vascular surgery and neuro-oncology in Neurosurgery. Besides these, there are chapters on the Consumer Protection Act, normal pressure hydro-cephalus and miscellaneous topics. The authors of these chapters are well recognized for their work and the exhaustive review of the literature contained in the chapters will benefit not only postgraduate students but will also update the knowledge of practising clinicians.
Guru Charitra is one of the most revered scriptural texts of Hinduism. Containing the biographies of Lord Dattatreya, (Lord Bramha, Vishnu and Mahesh) and his subsequent incarnations Sripada Sri Vallabha and Sri Narasimha Saraswati, it clarifies several doubts on religious dogmas, rituals and doctrines through a conversation between the master and his disciple. This book, steeped in lofty Hindu philosophical ideas also portrays a picture of the social and economic condition of the medieval times in India, and the message conveyed by the numerous teachings of the Guru needs to be understood in the context of those days. Reading of this interactive account, written in simple and lucid language will give strength and encouragement to spiritual aspirants to continue with their sadhana (spiritual pursuit), enable them to overcome the various problems of modern day living and fulfil their inherent wishes.
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