Methods of Nonlinear Analysis

Offers methods and approaches that are applicable in a wide range of disciplines: politics, sociology, anthropology, history, economics, and more. This book covers approaches to analysis ranging from

This book is concerned with partial differential equations applied to fluids problems in science and engineering and is designed for two potential audiences. First, this book can function as a text for a course in mathematical methods in fluid mechanics in non-mathematics departments or in mathematics service courses. The authors have taught both. Second, this book is designed to help provide serious readers of journals (professionals, researchers, and graduate students) in analytical science and engineering with tools to explore and extend the missing steps in an analysis. The topics chosen for the book are those that the authors have found to be of considerable use in their own research careers. These topics are applicable in many areas, such as aeronautics and astronautics; biomechanics; chemical, civil, and mechanical engineering; fluid mechanics; and geophysical flows. Continuum ideas arise in other contexts, and the techniques included have applications there as well.

Among the modern methods used to study prime numbers, the 'sieve' has been one of the most efficient. Originally conceived by Linnik in 1941, the 'large sieve' has developed extensively since the 1960s, with a recent realisation that the underlying principles were capable of applications going well beyond prime number theory. This book develops a general form of sieve inequality, and describes its varied applications, including the study of families of zeta functions of algebraic curves over finite fields; arithmetic properties of characteristic polynomials of random unimodular matrices; homological properties of random 3-manifolds; and the average number of primes dividing the denominators of rational points on elliptic curves. Also covered in detail are the tools of harmonic analysis used to implement the forms of the large sieve inequality, including the Riemann Hypothesis over finite fields, and Property (T) or Property (tau) for discrete groups.

Developments in trade marks law have called into question a variety of basic features, as well as bolder extensions, of legal protection. Other disciplines can help us think about fundamental issues such as: what is a trade mark? What does it do? What should be the scope of its protection? This volume assembles essays examining trade marks and brands from a multiplicity of fields: from business history, marketing, linguistics, legal history, philosophy, sociology and geography. Each chapter pairs lawyers' and non-lawyers' perspectives, so that each commentator addresses and critiques his or her counterpart's analysis. The perspectives of non-legal fields are intended to enrich legal academics' and practitioners' reflections about trade marks, and to expose lawyers, judges and policy-makers to ideas, concepts and methods that could prove to be of particular importance in the development of positive law.

This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretic

A lot of recent developments have been made about adhesively bonded joints modeling using various methods of analysis. The increasing application of adhesives in industry is partly due to the increase

Space-time coding is a technique that promises greatly improved performance in wireless networks by using multiple antennas at the transmitter and receiver. Space-Time Block Coding for Wireless Communications, first published in 2003, is an introduction to the theory of this technology. The authors develop the topic using a unified framework and cover a variety of topics ranging from information theory to performance analysis and space-time coding methods for both flat and frequency-selective fading multiple-antenna channels. The authors concentrate on key principles rather than specific practical applications, and present the material in a concise and accessible manner. Their treatment reviews the fundamental aspects of multiple-input, multiple-output communication theory, and guides the reader through a number of topics at the forefront of research and development. The book includes homework exercises and is aimed at graduate students and researchers working on wireless communication

This book is an introduction to the study of mathematical models of electrically active cells, which play an essential role in, for example, nerve conduction and cardiac functions. This is an important and vigorously researched field. In the book, Dr Cronin synthesizes and reviews this material and provides a detailed discussion of the Hodgkin-Huxley model for nerve conduction, which forms the cornerstone of this body of work. Her treatment includes a derivation of the Hodgkin-Huxley model, which is a system of four nonlinear differential equations; a discussion of the validity of this model; and a summary of some of the mathematical analysis carried out on this model. Special emphasis is placed on singular perturbation theory, and arguments, both mathematical and physiological, for using the perturbation viewpoint are presented.

Markov chains are an important idea, related to random walks, which crops up widely in applied stochastic analysis. They are used, for example, in performance modelling and evaluation of computer networks, queuing networks, and telecommunication systems. The main point of the present book is to provide methods, based on the construction of Lyapunov functions, of determining when a Markov chain is ergodic, null recurrent, or transient. These methods can also be extended to the study of questions of stability. Of particular concern are reflected random walks and reflected Brownian motion. The authors provide not only a self-contained introduction to the theory but also details of how the required Lyapunov functions are constructed in various situations.

How do scientists use analogies and other processes to break away from old theories and generate new ones? This book documents such methods through the analysis of video tapes of scientifically train

This book studies the struggle to enforce international human rights law in federal courts. In 1980, a federal appeals court ruled that a Paraguayan family could sue a Paraguayan official under the Alien Tort Statute – a dormant provision of the 1789 Judiciary Act – for torture committed in Paraguay. Since then, courts have been wrestling with this step toward a universal approach to human rights law. Davis examines attempts by human rights groups to use the law to enforce human rights norms. He explains the separation of powers issues arising when victims sue the United States or when the United States intervenes to urge dismissal of a claim and analyses the controversies arising from attempts to hold foreign nations, foreign officials, and corporations liable under international human rights law. While Davis's analysis is driven by social science methods, its foundation is the dramatic human story from which these cases arise.

In recent years the interaction between dynamical systems theory and non-equilibrium statistical mechanics has been enormous. The discovery of fluctuation theorems as a fundamental structure common to almost all non-equilibrium systems, and the connections with the free energy calculation methods of Jarzynski and Crooks, have excited both theorists and experimentalists. This graduate-level book charts the development and theoretical analysis of molecular dynamics as applied to equilibrium and non-equilibrium systems. Designed for both researchers in the field and graduate students of physics, it connects molecular dynamics simulation with the mathematical theory to understand non-equilibrium steady states. It also provides a link between the atomic, nano, and macro worlds. The book ends with an introduction to the use of non-equilibrium statistical mechanics to justify a thermodynamic treatment of non-equilibrium steady states, and gives a direction to further avenues of exploration.

This book studies the struggle to enforce international human rights law in federal courts. In 1980, a federal appeals court ruled that a Paraguayan family could sue a Paraguayan official under the Alien Tort Statute – a dormant provision of the 1789 Judiciary Act – for torture committed in Paraguay. Since then, courts have been wrestling with this step toward a universal approach to human rights law. Davis examines attempts by human rights groups to use the law to enforce human rights norms. He explains the separation of powers issues arising when victims sue the United States or when the United States intervenes to urge dismissal of a claim and analyses the controversies arising from attempts to hold foreign nations, foreign officials, and corporations liable under international human rights law. While Davis's analysis is driven by social science methods, its foundation is the dramatic human story from which these cases arise.

Information systems development is not merely a technical intervention but involves social and ethical dilemmas that affect the human, social and organizational domains. To demonstrate this point, the authors conduct a thorough and substantive description and analysis of the conceptual and philosophical underpinnings of systems development. In particular they analyse a number of systems development methodologies including structured methods, prototyping, ETHICS and Soft Systems Methodology to reveal the underlying conceptual and philosophical foundations. The book provides an in-depth analysis of data modelling theory and its links with theories of language and cognition. It offers a framework to describe and analyse different systems development approaches and to explain their strengths and weaknesses. The book is aimed at graduate students taking courses in information systems and data modelling, but will also appeal to information systems managers and professionals for whom the summ

This book presents the salient features of the general theory of infinite electrical networks in a coherent exposition. Using the basic tools of functional analysis and graph theory, the author examines the fundamental developments in the field and discusses applications to other areas of mathematics. The first half of the book presents existence and uniqueness theorems for both infinite-power and finite-power voltage-current regimes, and the second half discusses methods for solving problems in infinite cascades and grids. A notable feature is the invention of transfinite networks, roughly analogous to Cantor's extension of the natural numbers to the transfinite ordinals. The last chapter is a survey of application to exterior problems of partial differential equations, random walks on infinite graphs, and networks of operators on Hilbert spaces.

If you need a book that relates the core principles of quantum mechanics to modern applications in engineering, physics, and nanotechnology, this is it. Students will appreciate the book's applied emphasis, which illustrates theoretical concepts with examples of nanostructured materials, optics, and semiconductor devices. The many worked examples and more than 160 homework problems help students to problem solve and to practise applications of theory. Without assuming a prior knowledge of high-level physics or classical mechanics, the text introduces Schrödinger's equation, operators, and approximation methods. Systems, including the hydrogen atom and crystalline materials, are analyzed in detail. More advanced subjects, such as density matrices, quantum optics, and quantum information, are also covered. Practical applications and algorithms for the computational analysis of simple structures make this an ideal introduction to quantum mechanics for students of engineering, physics, nan

This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate-level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.

This book presents and analyses vortex methods as a tool for the direct numerical simulation of incompressible viscous flows. Vortex methods have matured, offering an interesting alternative to finite difference and spectral methods for high-resolution numerical solutions of the Navier–Stokes equations. Research in the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character that was the motivation for their introduction. Scientists working in the areas of numerical analysis and fluid mechanics will benefit from this book, which may serve both communities as both a reference monograph and a textbook for computational fluid dynamics courses.

The behaviour of systems occurring in real life is often modelled by partial differential equations. This book investigates how a user or observer can influence the behaviour of such systems mathematically and computationally. A thorough mathematical analysis of controllability problems is combined with a detailed investigation of methods used to solve them numerically, these methods being validated by the results of numerical experiments. In Part I of the book the authors discuss the mathematics and numerics relating to the controllability of systems modelled by linear and non-linear diffusion equations; Part II is dedicated to the controllability of vibrating systems, typical ones being those modelled by linear wave equations; finally, Part III covers flow control for systems governed by the Navier-Stokes equations modelling incompressible viscous flow. The book is accessible to graduate students in applied and computational mathematics, engineering and physics; it will also be of us

Terence Mills' best-selling graduate textbook provides detailed coverage of research techniques and findings relating to the empirical analysis of financial markets. In its previous editions it has become required reading for many graduate courses on the econometrics of financial modelling. This third edition, co-authored with Raphael Markellos, contains a wealth of material reflecting the developments of the last decade. Particular attention is paid to the wide range of nonlinear models that are used to analyse financial data observed at high frequencies and to the long memory characteristics found in financial time series. The central material on unit root processes and the modelling of trends and structural breaks has been substantially expanded into a chapter of its own. There is also an extended discussion of the treatment of volatility, accompanied by a new chapter on nonlinearity and its testing.

The first edition of this well known book was noted for its clear and accessible exposition of the basic theory of Hardy spaces from the concrete point of view (in the unit circle and the half plane). The intention was to give the reader, assumed to know basic real and complex variable theory and a little functional analysis, a secure foothold in the basic theory, and to understand its applications in other areas. For this reason, emphasis is placed on methods and the ideas behind them rather than on the accumulation of as many results as possible. The second edition retains that intention, but the coverage has been extended. The author has included two appendices by V. P. Havin, on Peter Jones' interpolation formula, and Havin's own proof of the weak sequential completeness of L1/H1(0); in addition, numerous amendments, additions and corrections have been made throughout.

This volume presents state-of-the-art papers on important topics and methods in the analysis of vertebrate microfossil assemblages. The minute remains of animals and plants have proven very useful to

This updated edition on evaluating the effectiveness of school programs provides an expanded needs-assessment section, additional methods for data analysis, and tools for communicating program results

This updated edition on evaluating the effectiveness of school programs provides an expanded needs-assessment section, additional methods for data analysis, and tools for communicating program result

In early modern England, boys and girls learned to be masculine or feminine as they learned to read and write. This 1999 book explores how gender differences, instilled through specific methods of instruction in literacy, were scrutinised in the English public theatre. Close readings of plays from Shakespeare's Love's Labour's Lost to Thomas Dekker's Whore of Babylon, and of poems, didactic treatises and autobiographical writings from the same period, offer a richly textured analysis of the interaction between didactic precepts, literary models, and historical men and women. At the cross-roads between literary studies and social and cultural history, Eve Sanders' research offers insights into poems, plays, and first-person narratives (including works by women writers, such as Mary Sidney and Anne Clifford) and into the social conflicts that shaped individuals as the writers and readers of such texts.

This book presents the nonlinear theory of continuum mechanics and demonstrates its use in developing nonlinear computer formulations for large displacement dynamic analysis. Basic concepts used in continuum mechanics are presented and used to develop nonlinear general finite element formulations that can be effectively used in large displacement analysis. The book considers two nonlinear finite element dynamic formulations: a general large deformation finite element formulation and a formulation that can efficiently solve small deformation problems that characterize very stiff structures. The book presents material clearly and systematically, assuming the reader has only basic knowledge in matrix and vector algebra and dynamics. The book is designed for use by advanced undergraduates and first-year graduate students. It is also a reference for researchers, practising engineers, and scientists working in computational mechanics, bio-mechanics, computational biology, multibody system dy

Newton's mathematical researches during the last five years of his stay in Cambridge before leaving in April 1696 to take up his duties at the Mint in London have three main centres of interest: methods of fluxions and series, classical pure geometry, and Cartesian analytical geometry. Part 1 reproduces Newton's advances at this time in further extending the techniques of his combined calculus of fluxions and fluent, and of expansion into infinite series. Part 2 gives publication of Newton's lengthy excursions in the early 1690s into the modes of geometrical analysis used by the 'ancient' geometers, based – by way of Commandino's Latin translation – on the account of this little understood field of the Greek 'topos analuomenos' which was given by Pappus in the prolegomenon to the seventh book of his Mathematical Collection. Part 3 gives prominence to the final text of the Enumeratio Linearum Tertii Ordinis which Newton put together in June 1695.

The guerrilla fighter is a defining image of Latin America. This book reviews recent guerrilla movements across the continent, providing a perceptive analysis of their methods and motivations. Alberto

This book is on the analysis and design of nonlinear analog integrated circuits that form the basis of present-day communication systems. The material is intended to be a textbook for class use but s

This text demonstrates the roles of statistical methods, coordinate transformations, and mathematical analysis in mapping complex, unpredictable dynamical systems. Written by a well-known authority in

Growth, Maturation and Body Composition documents one of the most remarkable and significant studies in the field of human biology. The Fels Longitudinal Study is the longest, largest and most productive serial study of human growth, maturation and body composition. This book shows how data collected from more than 1000 participants during the past 60 years have been analysed to test a wide range of hypotheses, and describes how the findings have led to the development of improved research methods. Topics covered include the management and analysis of data, prenatal, familial and genetic studies, physical growth, development and maturation, bones and teeth, body composition, and risk factors for cardiovascular disease. With more than 1000 specialized publications of Fels data, the present book provides a unique overview of this fascinating research programme, which will be of interest to a wide range of researchers, including those in the fields of physical anthropology, nutrition scie

Certain nonlinear optimization problems arising in such disparate areas as the theory of computation, pure and applied probability and mathematical physics, can be solved by linear methods, provided one replaces the usual number system with one in which addition satisfies the idempotent law. This systematic study of the subject has emerged, triggered in part by a workshop organized by Hewlett-Packard's Basic Research Institute in the Mathematical Sciences (BRIMS), which brought together many leading researchers in the area. This volume is a record of that workshop, but it also includes other invited contributions, a broad Introduction to Idempotency, written specially for the book, and a bibliography of the subject. In sum, the articles cover both practical and more theoretical considerations, making it essential reading for all workers in the area.

This is an introductory text for students interested in identification and analysis of animal remains from archaeological sites. The emphasis is on animals whose remains inform us about the relationship between humans and their natural and social environments, especially site formation processes, subsistence strategies, the processes of domestication, and paleoenvironments. Examining examples from all over the world, from the Pleistocene period up to the present, this volume is organized in a way that is parallel to faunal study, beginning with background information, bias in a faunal assemblage, and basic zooarchaeological methods. This revised edition reflects developments in zooarchaeology during the past decade. It includes sections on enamel ultrastructure and incremental analysis, stable isotyopes and trace elements, ancient genetics and enzymes, environmental reconstruction, people as agents of environmental change, applications of zooarchaeology in animal conservation and herit

This is an introductory text for students interested in identification and analysis of animal remains from archaeological sites. The emphasis is on animals whose remains inform us about the relationship between humans and their natural and social environments, especially site formation processes, subsistence strategies, the processes of domestication, and paleoenvironments. Examining examples from all over the world, from the Pleistocene period up to the present, this volume is organized in a way that is parallel to faunal study, beginning with background information, bias in a faunal assemblage, and basic zooarchaeological methods. This revised edition reflects developments in zooarchaeology during the past decade. It includes sections on enamel ultrastructure and incremental analysis, stable isotyopes and trace elements, ancient genetics and enzymes, environmental reconstruction, people as agents of environmental change, applications of zooarchaeology in animal conservation and herit

Written for maximum flexibility, this best-selling junior level mechanics text is easily adaptable to any length--one- or two-semester--or focus of course.LAGRANGIAN and HAMILTONIAN DYNAMICS are introduced early in the text.This text has an entire chapter on NONLINEAR METHODS.NUMERICAL METHODS PROBLEMS are included for students to solve using a computer.

Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions. Core chapters assume only exposure to stochastic processes and linear algebra at undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model at the heart of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation

This is the first book-length treatment of statistical surveillance methods used in financial analysis. It contains carefully selected chapters written by specialists from both fields and strikes a ba

This book challenges standard accounts of early Christian exegesis of the Bible. Professor Young sets the interpretation of the Bible in the context of the Graeco-Roman world - the dissemination of books and learning, the way texts were received and read, the function of literature in shaping not only a culture but a moral universe. For the earliest Christians, the adoption of the Jewish scriptures constituted a supersessionary claim in relation to Hellenism as well as Judaism. Yet the debt owed to the practice of exegesis in the grammatical and rhetorical schools is of overriding significance. Methods were philological and deductive, and the usual analysis according to 'literal', 'typological' and 'allegorical' is inadequate to describe questions of reference and issues of religious language. The biblical texts shaped a 'totalizing discourse' which by the fifth century was giving identity, morality and meaning to a new Christian culture.

This second volume of a two-volume work discusses systematically the complete theory of space beam-columns. It presents principles and methods of analysis for beam-columns in space which should be the

Recent work in artificial intelligence has increasingly turned to argumentation as a rich, interdisciplinary area of research that can provide new methods related to evidence and reasoning in the area of law. Douglas Walton provides an introduction to basic concepts, tools and methods in argumentation theory and artificial intelligence as applied to the analysis and evaluation of witness testimony. He shows how witness testimony is by its nature inherently fallible and sometimes subject to disastrous failures. At the same time such testimony can provide evidence that is not only necessary but inherently reasonable for logically guiding legal experts to accept or reject a claim. Walton shows how to overcome the traditional disdain for witness testimony as a type of evidence shown by logical positivists, and the views of trial sceptics who doubt that trial rules deal with witness testimony in a way that yields a rational decision-making process.