Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time. Presentation of many new results in one place for the first time First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals Fredholm determinants and Painlevé equations The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities Fredholm determinants and inverse scattering theory Probability densities of random determinants
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper on a multiple integral also gave rise to hundreds of recent publications. This book presents a coherent and detailed analytical treatment of random matrices, leading in particular to the calculation of n-point correlations, of spacing probabilities, and of a number of statistical quantities. The results are used in describing the statistical properties of nuclear excitations, the energies of chaotic systems, the ultrasonic frequencies of structural materials, the zeros of the Riemann zeta function, and in general the characteristic energies of any sufficiently complicated system. Of special interest to physicists and mathematicians, the book is self-contained and the reader need know mathematics only at the undergraduate level.Key Features* The three Gaussian ensembles, unitary, orthogonal, and symplectic; their n-point correlations and spacing probabilities* The three circular ensembles: unitary, orthogonal, and symplectic; their equivalence to the Gaussian* Matrices with quaternion elements* Integration over alternate and mixed variables* Fredholm determinants and inverse scattering theory* A Brownian motion model of the matrices* Computation of the mean and of the variance of a number of statistical quantities* Selberg's integral and its consequences
Random Matrices gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time. Presentation of many new results in one place for the first time First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals Fredholm determinants and Painlevé equations The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities Fredholm determinants and inverse scattering theory Probability densities of random determinants
“I located and dissected the testes in that massive tumour. It was like hunting and searching a needle in a desert.” “Dear, what is LBW?” asked my wife Kamal. I replied, “It is one way a batman is out in cricket. It is not libido below waist!” I teased her. “Shut up!” She rebuked. “You, dirty old man!” Events that make you smile and laugh, even in solitude. You just won’t be able to put the book down.
This volume is a part of the comprehensive study about social problems that India is facing at present. The whole study is divided into five volumes. This Volume Two deals with various fields of social work in India and is the Fifth revised edition of the earlier volume published in 1967. The fields covered have been discussed under five heads. Part One deals with concept and scope of social work as well as history of social work in U.K., U.S.A. and India. Part Two examines the social welfare services being provided for children, women, youth, labour and backward classes; urban and rural welfare; family welfare and housing. Part Three deals with social security measures and services for the handicapped. Part Four is concerned with social administration and legislation. Part Five deals with international welfare agencies and examines critically the state of welfare services being provided in India. Part Six deals with developments which have taken place in this field since 1973 when the second edition was brought out.
“You have to do it, Damn’it…” roared the boss… I held the scalpel with trembling hands… I moved forward after dropping the scalpel on the floor, looking stupid and clumsy. “Sister give him another knife…” - My maiden attempt to cut open a live human… a surgeon was born. It has taken 80 years of perspicacity to be able to pen a literary vision of my life - The life of a boy born in 1939 rising from a self-effacing family and his journey of becoming a successful surgeon ahead surviving the challenging generational ideologies. This classic collection of true life stories is a real flight of struggle and love of 3 generations with humorous anecdotes in school and medical college representing spectacular scene in real life. It is a true extraordinary account of a doctor’s life and each page will make you smile, cry or think!
Taking a long view of the three-party relationship, and its future prospects In this Asian century, scholars, officials and journalists are increasingly focused on the fate of the rivalry between China and India. They see the U.S. relationships with the two Asian giants as now intertwined, after having followed separate paths during the Cold War. In Fateful Triangle, Tanvi Madan argues that China's influence on the U.S.-India relationship is neither a recent nor a momentary phenomenon. Drawing on documents from India and the United States, she shows that American and Indian perceptions of and policy toward China significantly shaped U.S.-India relations in three crucial decades, from 1949 to 1979. Fateful Triangle updates our understanding of the diplomatic history of U.S.-India relations, highlighting China's central role in it, reassesses the origins and practice of Indian foreign policy and nonalignment, and provides historical context for the interactions between the three countries. Madan's assessment of this formative period in the triangular relationship is of more than historic interest. A key question today is whether the United States and India can, or should develop ever-closer ties as a way of countering China's desire to be the dominant power in the broader Asian region. Fateful Triangle argues that history shows such a partnership is neither inevitable nor impossible. A desire to offset China brought the two countries closer together in the past, and could do so again. A look to history, however, also shows that shared perceptions of an external threat from China are necessary, but insufficient, to bring India and the United States into a close and sustained alignment: that requires agreement on the nature and urgency of the threat, as well as how to approach the threat strategically, economically, and ideologically. With its long view, Fateful Triangle offers insights for both present and future policymakers as they tackle a fateful, and evolving, triangle that has regional and global implications.
The years 2021 to 2030 have been designated as "The United Nations Decade on Ecosystem Restoration". Ecological restoration and biodiversity conservation efforts face unprecedented challenges, especially in developing countries and areas, such as the Hindu Kush-Himalayan (HKH) region. This huge HKH region, which includes areas in eight separate countries (Afghanistan, Pakistan, Nepal, India, China, Bangladesh, Myanmar and Bhutan), is a biodiversity hotspot with a vast array of ecosystems, landscapes, peoples and cultures. It is known as one of 'the pulses of the world'. However, the HKH is also the world's largest and poorest mountain region, where landscapes and environments have been severely damaged as a result of climate change and human activities. Coordinating conservation and restoration policies, sharing knowledge and funds, and maintaining livelihoods are major challenges and are in urgent need of improvement. This book details the past and current ecological problems in the HKH region, and the threats and challenges that ecosystems and local people face. It pays special attention to developments of transformative adaptations and presents examples of sustainable conservation and ecological restoration management practices. This book is essential reading for ecologists and conservation biologists involved in large-scale ecological restoration projects, along with practitioners, graduate students, policy makers and international development workers.
This work is a comprehensive study of the social problems facing India at present. It is the first study of its kind and provides a coordinated picture of social problems confronted by India particularly after Independence. The revised editions now divided into five volumes. Volume One presents an analysis of the causes of Social and Personal Disorganization and deals with the problems of crime and juvenile delinquency, major social vices, maladjustment in institutions resulting in poverty and unemployment, population explosion, undernutrition, mass illiteracy, students’ indiscipline, moral degeneration, misuse of leisure, corruption, family disintegration and community conflicts in the form of casteism, provincialism, lingualism and communalism.
What makes some experiences more memorable than others? How can you better remember specific information later? Memories That Matter addresses these questions and more. The book is divided into three main parts, with each part focusing on a different aspect of memory. After the introductory first part, Part II discusses everyday uses of memory and why we remember, establishing a foundation for how memory is structured and stored in the brain. Part III dives into what makes us remember. Emotional and rewarding experiences are both more memorable than mundane experiences but are often studied using different approaches. Self-relevance and objects we can interact with are remembered better than less relevant information. The author explores these motivation-related influences on memory and considers whether a common mechanism underlies them all. Part IV changes the focus, discussing how we sometimes want to remember specific information that does not automatically capture our attention. The book considers evidence-based learning strategies and memory strategies, whilst also exploring real-world applications, with discussion of professions that accomplish amazing memory feats daily. The book concludes with a reflection on how the role of memory is changing as our world makes information increasingly accessible, particularly with the ever-expanding influence of the internet. Drawing from a variety of literatures and perspectives, this important book will be relevant for all students of memory from psychology, cognitive neuroscience, and related health backgrounds.
Prof. V L Mote was an extraordinary academician, who left a lasting impression on generations of participants of the Indian Institute of Management, Ahmedabad, Post Graduate Programme and Management Development Programme. He is also remembered by executives in several organizations that benefitted from his consulting assistance. With an M.Sc. degree in Mathematics from Bombay University and a PhD in Statistics from the University of North Carolina, USA, he began his academic career as Assistant Professor at the University of Florida, USA. This was followed by a position at Calico Mills, after which he was invited by Dr Vikram Sarabhai to join IIMA in 1962 where he became the first Chairman of the PGP, where he remained till his retirement in 1993. This book is a tribute to Professor VL Mote, with a collection of articles, messages and eulogies from his peers, colleagues, students and family members.
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