This book provides an elementary introduction to the classical analysis on normed spaces, paying special attention to nonlinear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to get through the basic material as soon as possible and then move on to do their own research immediately. It assumes only general knowledge in finite-dimensional linear algebra, simple calculus and elementary complex analysis. Since the treatment is self-contained with sufficient details, even an undergraduate with mathematical maturity should have no problem working through it alone. Various chapters can be integrated into parts of a Master degree program by course work organized by any regional university. Restricted to finite-dimensional spaces rather than normed spaces, selected chapters can be used for a course in advanced calculus. Engineers and physicists may find this book a handy reference in classical analysis.
Mechanics is the science of studying energy and forces, and their effects on matter. It involves mechanisms, kinematics, cross sections, and transport. Radiation mechanism describes how various types of radiation interact with different targets (atoms and nuclei). The book addresses the above four aspects of radiation mechanics integrating these aspects of radiation behavior in a single treatise under the framework of "radiation mechanics". - Covers all aspects of radiation mechanics - Helps non-nuclear graduates readily familiarize themselves with radiation - Integrates and coordinates mechanisms, kinematics, cross sections and transport in one volume - End of each chapter problems to further assist students in understanding the underlying concepts - Use of computations and Internet resources included in the problems
This book investigates the distributions of functionals defined on the sample paths of stochastic processes. It contains systematic exposition and applications of three general research methods developed by the authors. (i) The method of stratifications is used to study the problem of absolute continuity of distribution for different classes of functionals under very mild smoothness assumptions. It can be used also for evaluation of the distribution density of the functional. (ii) The method of differential operators is based on the abstract formalism of differential calculus and proves to be a powerful tool for the investigation of the smoothness properties of the distributions. (iii) The superstructure method, which is a later modification of the method of stratifications, is used to derive strong limit theorems (in the variation metric) for the distributions of stochastic functionals under weak convergence of the processes. Various application examples concern the functionals of Gaussian, Poisson and diffusion processes as well as partial sum processes from the Donsker-Prokhorov scheme. The research methods and basic results in this book are presented here in monograph form for the first time. The text would be suitable for a graduate course in the theory of stochastic processes and related topics.
This book is an introduction to a comprehensive and unified dynamic transition theory for dissipative systems and to applications of the theory to a range of problems in the nonlinear sciences. The main objectives of this book are to introduce a general principle of dynamic transitions for dissipative systems, to establish a systematic dynamic transition theory, and to explore the physical implications of applications of the theory to a range of problems in the nonlinear sciences. The basic philosophy of the theory is to search for a complete set of transition states, and the general principle states that dynamic transitions of all dissipative systems can be classified into three categories: continuous, catastrophic and random. The audience for this book includes advanced graduate students and researchers in mathematics and physics as well as in other related fields. This second edition introduces a unified theory for topological phase transitions, provides a first-principle approach to statistical and quantum physics, and offers a microscopic mechanism of quantum condensates (Bose-Einstein condensation, superfluidity, and superconductivity). Reviews of first edition: “The goals of this interesting book are to derive a general principle of dynamic transitions for dissipative systems and to establish a systematic dynamic transition theory for a wide range of problems in the nonlinear sciences. ... The intended audience for this book includes students and researchers working on nonlinear problems in physics, meteorology, oceanography, biology, chemistry, and the social sciences.” (Carlo Bianca, Mathematical Reviews, December, 2014) “This is a clearly written book on numerous types of phase transitions taken in a broad sense when a dynamical dissipative system transforms from one physical state into another. ... The book is a very useful literature not only for the professionals in the field of dynamic systems and phase transitions but also for graduate students due to its interdisciplinary coverage and state-of-the-art level.” (Vladimir Čadež, zbMATH, Vol. 1285, 2014)
In an era where there was no saint in the world, a peerless genius had stumbled upon the inheritance of the Stellar Sword Saint and stepped onto the peak of the path of the sword!
The Hauptvermutung is the conjecture that any two triangulations of a poly hedron are combinatorially equivalent. The conjecture was formulated at the turn of the century, and until its resolution was a central problem of topology. Initially, it was verified for low-dimensional polyhedra, and it might have been expected that furt her development of high-dimensional topology would lead to a verification in all dimensions. However, in 1961 Milnor constructed high-dimensional polyhedra with combinatorially inequivalent triangulations, disproving the Hauptvermutung in general. These polyhedra were not manifolds, leaving open the Hauptvermu tung for manifolds. The development of surgery theory led to the disproof of the high-dimensional manifold Hauptvermutung in the late 1960's. Unfortunately, the published record of the manifold Hauptvermutung has been incomplete, as was forcefully pointed out by Novikov in his lecture at the Browder 60th birthday conference held at Princeton in March 1994. This volume brings together the original 1967 papers of Casson and Sulli van, and the 1968/1972 'Princeton notes on the Hauptvermutung' of Armstrong, Rourke and Cooke, making this work physically accessible. These papers include several other results which have become part of the folklore but of which proofs have never been published. My own contribution is intended to serve as an intro duction to the Hauptvermutung, and also to give an account of some more recent developments in the area. In preparing the original papers for publication, only minimal changes of punctuation etc.
Filling the gap in the literature on low-energy quark models, The Quark Confinement Model of Hadrons investigates confinement effects in the low-energy regions of particle physics using the methods of nonlocal quantum field theory. It also elucidates their role in describing microscopic quantities that characterize hadron-hadron interactions. The authors present a quark confinement model to describe the low-energy physics of light hadrons. Hadrons are treated as collective colorless excitations of quark-gluon interactions while the quark confinement is to be provided by averaging over gluon backgrounds. The model is shown to reproduce the low-energy relations of chiral theory in the case of null momenta and, in addition, allow the researcher to obtain more sophisticated hadron characteristics, such as slope parameters and form factors. Presenting a unified view on a number of low-energy phenomena, The Quark Confinement Model of Hadrons enables an understanding of problems related to the treatment of large distances within quantum chromodynamics.
This book summarizes the proceedings of the 10th international conference on Infonnation Pro cessing in Medical Imaging (IPMI-lO), held in June, 1987, in Zeist, The Netherlands. IPMI is a biennial conference, organized alternately in Europe and North America. The subject of the conference is the use of physics, mathematics, computer science, and engineering in the of medical images. The intent of the conference is to fonnation, processing and interpretation provide a forum where new ideas and results of research in medical imaging can be presented and amply discussed. Accordingly, the programme can comprise only a limited number of papers. The scientific committee of IPMI-lO selected 41 papers for presentation, although a total of 102 extended abstracts of on the average high quality had been submitted. All selected contri butions are included in these proceedings. During of the preparations of the conference the organizers received the tragic news of the death of Francois Erbsmann, the initiator of IPMI, and organizer of the first conference in 1969 in Brussels. Francois always emphasized that the backbone of the IPMI meetings should be promising young and active researchers rather than established scientists in the field. As an appreciation of this idea, and in thankful remembrance of Francois' stimulating work, the IPMI-board has taken the initiative to present the Francois Erbsmann prize for the most significant contribution to the conference by a young investigator.
This book provides a broad introduction to modern asset pricing theory. The theory is self-contained and unified in presentation. Both the no-arbitrage and the general equilibrium approaches of asset pricing theory are treated coherently within the general equilibrium framework. It fills a gap in the body of literature on asset pricing for being both advanced and comprehensive. The absence of arbitrage opportunities represents a necessary condition for equilibrium in the financial markets. However, the absence of arbitrage is not a sufficient condition for establishing equilibrium. These interrelationships are overlooked by the proponents of the no-arbitrage approach to asset pricing.This book also tackles recent advancement on inversion problems raised in asset pricing theory, which include the information role of financial options and the information content of term structure of interest rates and interest rates contingent claims.The inclusion of the proofs and derivations to enhance the transparency of the underlying arguments and conditions for the validity of the economic theory made it an ideal advanced textbook or reference book for graduate students specializing in financial economics and quantitative finance. The detailed explanations will capture the interest of the curious reader, and it is complete enough to provide the necessary background material needed to delve deeper into the subject and explore the research literature.Postgraduate students in economics with a good grasp of calculus, linear algebra, and probability and statistics will find themselves ready to tackle topics covered in this book. They will certainly benefit from the mathematical coverage in stochastic processes and stochastic differential equation with applications in finance. Postgraduate students in financial mathematics and financial engineering will also benefit, not only from the mathematical tools introduced in this book, but also from the economic ideas underpinning the economic modeling of financial markets.Both these groups of postgraduate students will learn the economic issues involved in financial modeling. The book can be used as an advanced text for Masters and PhD students in all subjects of financial economics, financial mathematics, mathematical finance, and financial engineering. It is also an ideal reference for practitioners and researchers in the subjects.
This book presents a unified approach for solving both stationary and nonstationary interpolation problems, in finite or infinite dimensions, based on the commutant lifting theorem from operator theory and the state space method from mathematical system theory. Initially the authors planned a number of papers treating nonstationary interpolation problems of Nevanlinna-Pick and Nehari type by reducing these nonstationary problems to stationary ones for operator-valued functions with operator arguments and using classical commutant lifting techniques. This reduction method required us to review and further develop the classical results for the stationary problems in this more general framework. Here the system theory turned out to be very useful for setting up the problems and for providing natural state space formulas for describing the solutions. In this way our work involved us in a much wider program than original planned. The final results of our efforts are presented here. The financial support in 1994 from the "NWO-stimulansprogramma" for the Thomas Stieltjes Institute for Mathematics in the Netherlands enabled us to start the research which lead to the present book. We also gratefully acknowledge the support from our home institutions: Indiana University at Bloomington, Purdue University at West Lafayette, Tel-Aviv University, and the Vrije Universiteit at Amsterdam. We warmly thank Dr. A.L. Sakhnovich for his carefully reading of a large part of the manuscript. Finally, Sharon Wise prepared very efficiently and with great care the troff file of this manuscript; we are grateful for her excellent typing.
This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
This book focuses on the design of efficient & dynamic methods to allocate divisible resources under various auction mechanisms, discussing their applications in power & microgrid systems and the V2G & EV charging coordination problems in smart grids. It describes the design of dynamic methods for single-sided and double-sided auction games and presents a number of simulation cases verifying the performances of the proposed algorithms in terms of efficiency, convergence and computational complexity. Further, it explores the performances of certain auction mechanisms in a hierarchical structure and with large-scale agents, as well as the auction mechanisms for the efficient allocation of multi-type resources. Lastly, it generalizes the main and demonstrates their application in smart grids. This book is a valuable resource for researchers, engineers, and graduate students in the fields of optimization, game theory, auction mechanisms and smart grids interested in designing dynamic auction mechanisms to implement optimal allocation of divisible resources, especially electricity and other types of energy in smart grids.
This book provides an introduction to the ideas and methods of linear func tional analysis at a level appropriate to the final year of an undergraduate course at a British university. The prerequisites for reading it are a standard undergraduate knowledge of linear algebra and real analysis (including the the ory of metric spaces). Part of the development of functional analysis can be traced to attempts to find a suitable framework in which to discuss differential and integral equa tions. Often, the appropriate setting turned out to be a vector space of real or complex-valued functions defined on some set. In general, such a vector space is infinite-dimensional. This leads to difficulties in that, although many of the elementary properties of finite-dimensional vector spaces hold in infinite dimensional vector spaces, many others do not. For example, in general infinite dimensional vector spaces there is no framework in which to make sense of an alytic concepts such as convergence and continuity. Nevertheless, on the spaces of most interest to us there is often a norm (which extends the idea of the length of a vector to a somewhat more abstract setting). Since a norm on a vector space gives rise to a metric on the space, it is now possible to do analysis in the space. As real or complex-valued functions are often called functionals, the term functional analysis came to be used for this topic. We now briefly outline the contents of the book.
After her mother was killed by a landmine while fleeing from the soldiers, a Burmese girl joins a Resistance group based on the Burmese-Thai border which employs violence as the chief weapon against tyranny. But the violence is not the same as terrorism, as the group operate by abiding the tough-minded pragmatism of Aung San Suu Kyi, known as ‘the Lady’. Of Crime and Humanity seeks to enlighten readers, through the telling of the adventure of a Burmese girl, of what it is like to be a contemporary of the Lady, and more importantly how Man is held in bitter bondage to his time rigidly and tragically. If there’s an answer to the Lady’s dramatic transformation, it is based on an understanding of compassion and human nature in its complexity and darkness. Based on true events of the Burmese revolutionary days, Of Crime and Humanity describes what it is like being a Burmese girl living under military brutalisation.
One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.
Modern Methods in Analytical Acoustics considers topics fundamental to the understanding of noise, vibration and fluid mechanisms. The series of lectures on which this material is based began by some twenty five years ago and has been developed and expanded ever since. Acknowledged experts in the field have given this course many times in Europe and the USA. Although the scope of the course has widened considerably, the primary aim of teaching analytical techniques of acoustics alongside specific areas of wave motion and unsteady fluid mechanisms remains. The distinguished authors of this volume are drawn from Departments of Acoustics, Engineering of Applied Mathematics in Berlin, Cambridge and London. Their intention is to reach a wider audience of all those concerned with acoustic analysis than has been able to attend the course.
Many dynamical systems in physics, chemistry and biology exhibit complex be haviour. The apparently random motion of a fluid is the best known example. How ever also vibrating structures, electronic oscillators, magnetic devices,lasers, chemical oscillators, and population kinetics can behave in a complicated manner. One can find irregular oscillations, which is now known as chaotic behaviour. The research field of nonlinear dynamical systems and especially the study of chaotic systems has been hailed as one of the important breaktroughs in science this century. The sim plest realization of a system with chaotic behaviour is an electronic oscillator. The purpose of this book is to provide a comprehensive introduction to the application of chaos theory to electronic systems. The book provides both the theoretical and experimental foundations of this research field. Each electronic circuit is described in detail together with its mathematical model. Controlling chaos of electronic oscilla tors is also included. End of proofs and examples are indicated by •. Inside examples the end of proofs are indicated with O. We wish to express our gratitude to Catharine Thompson for a critical reading of the manuscript. Any useful suggestions and comments are welcome. Email address of the first author: MVANWYK@TSAMAIL. TRSA. AC. ZA Email address of the first author: WHS@RAU3. RAU. AC. ZA Home page of the authors: http://zeus. rau. ac. za/steeb/steeb. html xi Chapter 1 Introduction 1.
This book, originally published in 1966, deals mainly with morphemes and with grammatical and syntactic behaviour. Although some vocabulary material is contained in this volume, and some more in the Linguistic Survey of the Northern Bantu Borderland, vocabulary comparison itself plays little part. The volume presents an overall picture of the working of representative languages from each section of the Handbook and provides grammatical material which will help future students in classifying the languages to their typological as apart from their lexical features.
Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.
This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Calculation methods in the context of physics are emphasized. New materials drawn from the teaching and research experience of the author are included. The generalized Gel'fand's method is presented to calculate the matrices of irreducible representations of the simple Lie algebra and its Clebsch-Gordan coefficients. This book is for graduate students and young researchers in physics, especially theoretical physics. It is also for graduate students in theoretical chemistry.
Public performance-accountability nexus is a hot topic in recent research, but we know little about its antecedents and consequences in developing countries and transition economies. Are top-down appointed political elites taken accountable for public service performance in authoritarian nations like China? The question is theoretically and empirically examined in the book. I argue that government cadres are appropriately appraised and promoted even with the lame democracy. Using a novel dataset and event history analysis method, I test the performance-based political promotion tournament theory and its contingent features. I find that career advancement of provincial leading officials is positively influenced by public service performance but not by economic performance. The effect is stronger for Party secretaries than governors, for central connected officials than local officials, for younger than older, and for short tenure in office than long serving. The performance-promotion nexus in relatively weak and contingent on contextual attributes, suggesting performance-based reform should be deepened to make local agents accountable for public service delivery and responsiveness.
This two-volume work presents state-of-the-art mathematical theories and results on infinite-dimensional dynamical systems. Inertial manifolds, approximate inertial manifolds, discrete attractors and the dynamics of small dissipation are discussed in detail. The unique combination of mathematical rigor and physical background makes this work an essential reference for researchers and graduate students in applied mathematics and physics. The main emphasis in the first volume is on the mathematical analysis of attractors and inertial manifolds. This volume deals with the existence of global attractors, inertial manifolds and with the estimation of Hausdorff fractal dimension for some dissipative nonlinear evolution equations in modern physics. Known as well as many new results about the existence, regularity and properties of inertial manifolds and approximate inertial manifolds are also presented in the first volume. The second volume will be devoted to modern analytical tools and methods in infinite-dimensional dynamical systems. Contents Attractor and its dimension estimation Inertial manifold The approximate inertial manifold
What would you like to obtain from your research and practice of an Okinawan martial art? For an academic, it would be to obtain historical and cultural facts and details. For a practitioner, it would be to gain expertise in the combative skills. If you’re interested in both, this first of a three-volume anthology is assembled for your convenience to facilitate your endeavors. These volumes assemble a wealth of material originally published during the two decades when the Journal of Asian Martial Arts was in print. Hundreds of pages and photographs present the richness of Okinawan martial traditions, from the original combatives to those influenced by Chinese and mainland Japanese martial art styles. The variety of topics shown in the table of contents indicate the depth and breath in the chapters, along with the authors who are well-known for their meticulous research and practical skills in specific arts. These three volumes dive deep into the history and culture of Okinawan martial arts. You’ll find coverage of the actual artifacts—the material culture related to weaponry and training methods. Instructions from the masters details both open-hand techniques as well as with weapons. The chapters offer insights into “the lives of many masters over the past few centuries, giving the raison d’être for these unique fighting arts—their reason for being. Many streams of arts have contributed to the martial traditions found on the small island: Naha-te, Shuri-te, Fukien White Crane, Shorin, Goju, Motobu, Shotokan, Isshin, Kyokushin, Pwang Gai Noon, Shito, Uechi, and the list continues … Along with the various styles come the associated training methods, such as conditioning exercises with weights and creatively designed apparatus, such as the punching post (makiwara), or stone lever and stone padlockshaped weights. Some become battle-hardened by active and passive breaking of objects (tameshiwari), including wooden boards, baseball bats, rocks, and ice. The extensive use of weaponry is found in many Okinawan styles, often associated with their farming and fishing occupations. Such a blend of history and culture make the Okinawan fighting traditions a fascinating field of study. Besides being such vital sources of information, these three volumes will prove enjoyable reading and permanent at-hand reference sources in your library.
book and to the publisher NOORDHOFF who made possible the appearance of the second edition and enabled the author to introduce the above-mentioned modifi cations and additions. Moscow M. A. NAIMARK August 1963 FOREWORD TO THE SECOND SOVIET EDITION In this second edition the initial text has been worked over again and improved, certain portions have been completely rewritten; in particular, Chapter VIII has been rewritten in a more accessible form. The changes and extensions made by the author in the Japanese, German, first and second (= first revised) American, and also in the Romanian (lithographed) editions, were hereby taken into account. Appendices II and III, which are necessary for understanding Chapter VIII, have been included for the convenience of the reader. The book discusses many new theoretical results which have been developing in tensively during the decade after the publication of the first edition. Of course, lim itations on the volume of the book obliged the author to make a tough selection and in many cases to limit himself to simply a formulation of the new results or to pointing out the literature. The author was also compelled to make a choice of the exceptionally extensive collection of new works in extending the literature list. Monographs and survey articles on special topics of the theory which have been published during the past decade have been included in this list and in the litera ture pointed out in the individual chapters.
This book offers a fundamental and practical introduction to the use of computational methods. A thorough discussion of practical aspects of the subject is presented in a consistent manner, and the level of treatment is rigorous without being unnecessarily abstract. Each chapter ends with bibliographic information and exercises.
Advanced Theory of Constraint and Motion Analysis for Robot Mechanisms provides a complete analytical approach to the invention of new robot mechanisms and the analysis of existing designs based on a unified mathematical description of the kinematic and geometric constraints of mechanisms. Beginning with a high level introduction to mechanisms and components, the book moves on to present a new analytical theory of terminal constraints for use in the development of new spatial mechanisms and structures. It clearly describes the application of screw theory to kinematic problems and provides tools that students, engineers and researchers can use for investigation of critical factors such as workspace, dexterity and singularity. - Combines constraint and free motion analysis and design, offering a new approach to robot mechanism innovation and improvement - Clearly describes the use of screw theory in robot kinematic analysis, allowing for concise representation of motion and static forces when compared to conventional analysis methods - Includes worked examples to translate theory into practice and demonstrate the application of new analytical methods to critical robotics problems
This authored monograph presents a study on fundamental limits and robustness of stability and stabilization of time-delay systems, with an emphasis on time-varying delay, robust stabilization, and newly emerged areas such as networked control and multi-agent systems. The authors systematically develop an operator-theoretic approach that departs from both the traditional algebraic approach and the currently pervasive LMI solution methods. This approach is built on the classical small-gain theorem, which enables the author to draw upon powerful tools and techniques from robust control theory. The book contains motivating examples and presents mathematical key facts that are required in the subsequent sections. The target audience primarily comprises researchers and professionals in the field of control theory, but the book may also be beneficial for graduate students alike.
The Lahu, with a population of around 470,000, inhabit the mountainous country in Yunnan Province bordering on Burma, Laos and northern Thailand. Buddhists, with a long history of resistance to the Chinese Han majority, the Lahu are currently facing a serious collapse of their traditional social system, with the highest suicide rate in the world, large scale human trafficking of their women, alcoholism and poverty. This book, based on extensive original research including long-term anthropological research among the Lahu, provides an overview of the traditional way of life of the Lahu, their social system, culture and beliefs, and discusses the ways in which these are changing. It shows how the Lahu are especially vulnerable because of their lack of political representatives and a state educated elite which can engage with, and be part of, the government administrative system. The Lahu are one of many relatively small ethnic minorities in China – overall the book provides an example of how the Chinese government approaches these relatively small ethnic minorities.
This monograph proposes how to manage complexity by organizing the system as a State Tree Structure (STS). Based on STS, which is an adaptation of statecharts to Supervisory Control Theory, an efficient recursive symbolic algorithm is presented that can perform nonblocking supervisory control design in reasonable time and memory for complex systems. Nonblocking Supervisory Control of State Tree Structures presents how this results in tractable and highly comprehensible controllers, especially to users who are not specialists in Discrete - Event Systems.
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