Martingale Limit Theory and Its Application discusses the asymptotic properties of martingales, particularly as regards key prototype of probabilistic behavior that has wide applications. The book explains the thesis that martingale theory is central to probability theory, and also examines the relationships between martingales and processes embeddable in or approximated by Brownian motion. The text reviews the martingale convergence theorem, the classical limit theory and analogs, and the martingale limit theorems viewed as the rate of convergence results in the martingale convergence theorem. The book explains the square function inequalities, weak law of large numbers, as well as the strong law of large numbers. The text discusses the reverse martingales, martingale tail sums, the invariance principles in the central limit theorem, and also the law of the iterated logarithm. The book investigates the limit theory for stationary processes via corresponding results for approximating martingales and the estimation of parameters from stochastic processes. The text can be profitably used as a reference for mathematicians, advanced students, and professors of higher mathematics or statistics.
This book considers various spaces and algebras made up of functions, measures, and other objects-situated always on one or another locally compact abelian group, and studied in the light of the Fourier transform. The emphasis is on the objects themselves, and on the structure-in-detail of the spaces and algebras. A mathematician needs to know only a little about Fourier analysis on the commutative groups, and then may go many ways within the large subject of harmonic analysis-into the beautiful theory of Lie group representations, for example. But this book represents the tendency to linger on the line, and the other abelian groups, and to keep asking questions about the structures thereupon. That tendency, pursued since the early days of analysis, has defined a field of study that can boast of some impressive results, and in which there still remain unanswered questions of compelling interest. We were influenced early in our careers by the mathematicians Jean-Pierre Kahane, Yitzhak Katznelson, Paul Malliavin, Yves Meyer, Joseph Taylor, and Nicholas Varopoulos. They are among the many who have made the field a productive meeting ground of probabilistic methods, number theory, diophantine approximation, and functional analysis. Since the academic year 1967-1968, when we were visitors in Paris and Orsay, the field has continued to see interesting developments. Let us name a few. Sam Drury and Nicholas Varopoulos solved the union problem for Helson sets, by proving a remarkable theorem (2.1.3) which has surely not seen its last use.
This book gives a self-contained fundamental study of the subject. Besides the following special features it contains the author's detailed solution to the long-standing unsolved problem in the theory of complex manifolds: Does there exist a complex structure on the six-sphere? The special features of the book are: a classification of almost complex (and similarly, almost Hermitian) structures together with inclusion relations; discussions about various known almost Hermitian structures; a necessary and sufficient condition for a general almost Hermitian manifold to have constant holomorphic sectional (or bisectional) curvature and similar conditions for various special almost Hermitian manifolds; some complex Laplacians together with some of their relationships with the real Laplacian; the spectral geometry of Riemannian manifolds and some general almost Hermitian manifolds including Khlerian manifolds as a special case; conditions for an almost complex structure to be a complex structure; some vanishing theorems for Riemannian and almost Hermitian manifolds.
The authors examine several topical subjects, commencing with a general introduction to path integrals in quantum mechanics and the group theoretical backgrounds for path integrals. Applications of harmonic analysis, polar coordinate formulation, various techniques and path integrals on SU(2) and SU(1, 1) are discussed. Soluble examples presented include particle-flux system, a pulsed oscillator, magnetic monopole, the Coulomb problem in curved space and others.The second part deals with the SU(2) coherent states and their applications. Construction and generalization of the SU(2) coherent states, formulation of coherent path integrals for spin and unitary spin, and semiclassical quantization are presented. Applications are made to the study of quantum fluctuation, the nonlinear field model and phase holonomy.The final chapters present the theory of the SU(1, 1) coherent states and their applications. The radial coulomb problem, the Morse oscillator, and the large-N approximation are discussed. Applications to problems in quantum optics such as squeezed states, interaction with the squeezed vacuum states, and phase operator formalism are also included.This book will be useful as an introduction to the subject as well as a valuable work of reference.
This new book demonstrates the usefulness of the switching function in analyzing power electronic circuits in the steady state. A procedure is suggested for the effective application of this method for the analysis of all types of power electronic circuits."--BOOK JACKET.
Recent years have seen a rapid development of neural network control tech niques and their successful applications. Numerous simulation studies and actual industrial implementations show that artificial neural network is a good candidate for function approximation and control system design in solving the control problems of complex nonlinear systems in the presence of different kinds of uncertainties. Many control approaches/methods, reporting inventions and control applications within the fields of adaptive control, neural control and fuzzy systems, have been published in various books, journals and conference proceedings. In spite of these remarkable advances in neural control field, due to the complexity of nonlinear systems, the present research on adaptive neural control is still focused on the development of fundamental methodologies. From a theoretical viewpoint, there is, in general, lack of a firmly mathematical basis in stability, robustness, and performance analysis of neural network adaptive control systems. This book is motivated by the need for systematic design approaches for stable adaptive control using approximation-based techniques. The main objec tives of the book are to develop stable adaptive neural control strategies, and to perform transient performance analysis of the resulted neural control systems analytically. Other linear-in-the-parameter function approximators can replace the linear-in-the-parameter neural networks in the controllers presented in the book without any difficulty, which include polynomials, splines, fuzzy systems, wavelet networks, among others. Stability is one of the most important issues being concerned if an adaptive neural network controller is to be used in practical applications.
Because of the high symmetry involved, the Jahn-Teller effect is the natural starting point for considering electron-phonon (or vibronic) interactions in icosahedral molecules. This work is the first comprehensive theoretical analysis of the Jahn-Teller interaction in C60 and other icosahedral complexes. The importance of this research derives in part from the increasing, widespread interest in C60 and other molecular clusters and their application in science and industry. The electrical and spectroscopic properties of fullerene and fulleride compounds depend intimately on the coupling between the electronic and vibrational modes of these systems, and this book addresses the fundamental theoretical questions. In particular, a chapter is devoted to the connection between the theory and experimental observations, such as ESR (electron spin resonance) effects and molecular spectra. Earlier books have discussed the theory of Jahn-Teller interactions in lower symmetry structures (cubic, tetrahedral, tetragonal, trigonal,...); this is the first that focuses on the new icosahedral systems, whose most famous example is Buckminsterfullerene, C60. The book's authors have over fifty years of combined research experience into the theoretical aspects of the Jahn-Teller effect.
Continue to follow the adventures of Cyprien on Kadelka as he builds a dynasty. Cyprien: Kadelka is a thrilling science fiction novel where, after a terrifying cosmic event, Cyprien finds himself separated from his ship, Beatrice, and on an alien planet with amnesia. He washes up on the beach of a medieval world where enormous monsters roam and is thrust into a political challenge to save a royal house and his life. He must follow the twists and turns of his guided fate as he struggles to cope with the strange society living in castle cities. He then finds another alien being from an ancient race and together they build an incredible dynasty against all odds.
The interplay between the external world (ching) and the poet’s inner world (ch’ing) lies at the heart of Chinese poetry, and understanding the interaction of the two is crucial to understanding this work from within its own tradition. Closely coordinating her discussions of poetry and criticism so that practice and theory become mutually enriching and illuminating, Sun offers sensitive and original readings of poems and a wealth of insights into Chinese poetics.
This volume presents a collection of contributions to an international conference on complex analysis and its applications held at the newly founded Hong Kong University of Science and Technology in January 1993. The aim of the conference was to advance the theoretical aspects of complex analysis and to explore the application of its techniques to physical and engineering problems. Three main areas were emphasised: Value distribution theory; Complex dynamical system and geometric function theory; and the Application of complex analysis to differential quations and physical engineering problems.
A comprehensive and up-to-date reference book on modern electric vehicle technology, which covers the engineering philosophy, state-of-the-art technology, and commercialisation of electrical vehicles.
“This may capture the experience of children of divorce better than any book out there and deserves readership beyond a middle-grade audience. A winner!”–San Francisco City Book Review C. C. Payne intertwines heartache with humor and hope in a novel about navigating divorce and blended families, following your passion, and celebrating who you are. Fizzy is a good Southern girl who just wants to be perfect. And win the Southern Living cook-off. The being perfect part is hard though, since her parents’ divorced and everything in her life has changed. Wary of her too-perfect stepmom and her mom’s neat-freak, dismissive boyfriend, she’s often angry or upset and feels like a guest in both homes. She tells herself to face facts: She’s a “leftover” kid from a marriage that her parents want to forget. But she has to keep all of that to herself, because a good Southern girl never yells, or throws fits, or says anything that might hurt other people’s feelings—instead she throws her shoulders back, says yes ma’am, and tries to do better. So Fizzy tries her best, but it’s hard to stay quiet when her family keeps getting more complicated. Fortunately, the Southern Living cook-off gives her a welcome distraction, as do her new friends Miyoko and Zach, who have parent issues of their own. With the poignancy and humor of Joan Bauer and Lynda Mullaly Hunt, this poignant story reminds readers that they have a right to a voice, that it is okay to say how you feel, and that some leftovers are absolutely delicious!
Risk Management for Geotechnical Engineering: Hazard, Risks and Consequences covers the application of risk management for soil and rock engineering projects, and the preparation of reliable designs that account for uncertainty. The book discusses qualitative risk assessments based on experience and judgement, as well as quantitative risk analysis using probabilistic methods and decision analysis to optimize designs. Many examples are included of how risk management can be applied to geotechnical engineering, with case studies presented for debris flows, rock falls, tunnel stability, and dam foundations. Also discussed are issues of liability insurance and contract law related to geotechnical engineering. This comprehensive book is ideal for practicing geotechnical engineers, addressing the challenges of making decisions in circumstances where uncertainties exist in site conditions, material properties and analysis methods.
Specialist Periodical Reports provide systematic and detailed review coverage of progress in the major areas of chemical research. Written by experts in their specialist fields the series creates a unique service for the active research chemist, supplying regular critical in-depth accounts of progress in particular areas of chemistry. For over 80 years the Royal Society of Chemistry and its predecessor, the Chemical Society, have been publishing reports charting developments in chemistry, which originally took the form of Annual Reports. However, by 1967 the whole spectrum of chemistry could no longer be contained within one volume and the series Specialist Periodical Reports was born. The Annual Reports themselves still existed but were divided into two, and subsequently three, volumes covering Inorganic, Organic and Physical Chemistry. For more general coverage of the highlights in chemistry they remain a 'must'. Since that time the SPR series has altered according to the fluctuating degree of activity in various fields of chemistry. Some titles have remained unchanged, while others have altered their emphasis along with their titles; some have been combined under a new name whereas others have had to be discontinued. The current list of Specialist Periodical Reports can be seen on the inside flap of this volume.
This bestselling textbook for higher-level courses was extensively revised in 1990 to accommodate developments in model theoretic methods. Topics include models constructed from constants, ultraproducts, and saturated and special models. 1990 edition.
The first account in book form of all the essential features of the quasi-likelihood methodology, stressing its value as a general purpose inferential tool. The treatment is rather informal, emphasizing essential principles rather than detailed proofs, and readers are assumed to have a firm grounding in probability and statistics at the graduate level. Many examples of the use of the methods in both classical statistical and stochastic process contexts are provided.
In the last few years the study of germinal centers of the lymphoid tissue has progressed at an accelerated pace. Questions about their role and their significance in immune responses that could not be answered, mainly because of tedmicallimitations, are presently approached experimentally from many different directions. Hypotheses, some more than half a century old, receive renewed attention. At this time, members of the Biology Division, Oak Ridge National Laboratory, U.S.A., and of the Institute of Pathology, University of Bern, Switzerland, decided to bring together workers interested in the field. The Conference was held in Bern, June 22-24, 1966, and included fifty-seven contributions which were discussed at length. The range of interest extended from phylogenesis and anatomy to studies on cell proliferation, immunohistochemistry, cancer research and radiobiology. The aim of this broad coverage was to combine all available information on the role of germinal centers in immune responses in a single package, instead of leaving it scattered around in reports dealing with divergent immunological problems. This attempt is reflected in the present book. A rather large space has been devoted to the lively discussions which followed the reports, the volume of most of which had been voluntarily limited. The discussions are not reported verbatim but care has been taken to insure neutrality and objectivity in the necessary adaptation of the shortened transcription. We have been very fortunate indeed, to have Drs.
The term "dislocation" is used in several different senses in the literature of mechanics. In the elassic work of VOLTERRA, WEINGARTEN, and SOMIGLIANA, it refers to particular solutions of the equations of linear elasticity, in which a con tinuous field of strain does not correspond, globally, to a continuous field of dis placement. The configuration of the body so obtained, even when that body is free of all load, is subject to interior stress that does not vanish, and in general no deformation of the body as a wh oIe can bring it into a stress-free configuration. Nevertheless, if any sufficiently sm all part of the body is considered by itself, a configuration for it in which the stress is everywhere zero may be found at once. In this work constitutiL"e assumptions provide the basic data. These consist in prescribed stress-free configurations for each material point and in prescribed elastic moduli governing the response to deformation from the stress-free configuration at each material point. Everything follows from these data, ineluding the dislocations present, if any. In particular, the common boundary-value problems of linear elasticity may be set and solved for the dislocated body.
The second edition of The Biomarker Guide is a fully updated and expanded version of this essential reference. Now in two volumes, it provides a comprehensive account of the role that biomarker technology plays both in petroleum exploration and in understanding Earth history and processes. Biomarkers and Isotopes in Petroleum Exploration and Earth History itemizes parameters used to genetically correlate petroleum and interpret thermal maturity and extent of biodegradation. It documents most known petroleum systems by geologic age throughout Earth history. The Biomarker Guide is an invaluable resource for geologists, petroleum geochemists, biogeochemists, and environmental scientists.
This book addresses the construction, analysis, and intepretation of mathematical models that shed light on significant problems in the physical sciences, with exercises that reinforce, test and extend the reader's understanding. It may be used as an upper level undergraduate or graduate textbook as well as a reference for researchers.
A theoretical framework aiming to facilitate study of development economics. The author presents his theory in three sections: how advanced nations developed; a proposed third dimension, in addition to labour and capital; and why capital accumulation is unnecessary, even potentially harmful.
The Mah&_ratnak&_ta S&_tra is one of the five major sutra groups in the Mah&_y&_na canon. Of the two great schools of Buddhism, Mah&_y&_na has the greatest number of adherents worldwide&—it prevails among the Chinese, Japanese, Koreans, Tibetans, and Vietnamese&—and contains within it a number of movements, notably Zen, which have been of growing interest in the West in recent decades. Yet despite this increased attention and enormous following, translations of Mah&_y&_na scriptures have been scarce and fragmentary; clearly, a comprehensive translation of a major work within the canon was called for. This volume addresses that need. It contains 22 of the 49 S&_tras of the Mah&_ratnak&_ta (or &"Treasury&") S&_tra, many translated for the first time in a Western language, selected and arranged to give the modern reader a progressive introduction to one of the world's major religious traditions. Subjects covered include M&_y&_ and miracles, the teachings on Consciousness, Emptiness, and monastic discipline, the Mystical Light of the Tath&_gata, and the devotional practice of Pure Land, making this a comprehensive source book of Mah&_y&_na Buddhism hitherto unavailable in English. The book also includes an introduction to provide historical and interpretive guidance, annotations that assist in the comprehension of difficult passages, and an extensive glossary that will be valuable to specialist and layman alike. A team of scholars, working in Taiwan, spent eight years translating the Treasury's million words from Chinese, using Tibetan texts for comparison and checking each S&_tra with an international board of scholars. In the course of translating from the original, special effort was made to retain both the devotional style appropriate for religious reading and the precision required by the scholar, while presenting the material with a clarity and flow that would make it accessible to the Western layman. The editors then selected, arranged, and annotated the 22 S&_tras presented here. Published in cooperation with The Institute for Advanced Studies of World Religions.
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