Methods of Nonlinear Analysis

For graduate students looking for an introduction to this area of nonlinear analysis, Liu (mathematics, Stanford U.) offers a self-contained study of shock waves explaining the new wave interactions f

This concise guide covers the fundamental aspects of the numerical analysis, basing upon it the construction of its routines for solving nonlinear equations, linear and nonlinear systems of equations,

Proven statistical reliability analysis methods-available for the first time to engineers in the West While probabilistic methods of system reliability analysis have reached an unparalleled degree of

This volume brings together leading European scholars and policy-makers to address the determinants of foreign direct investment (FDI) and its effects on globalisation, growth and European integration since 1945. The main focus of the study is foreign direct investment by German multinational companies. A range of methods, including econometric studies, survey-based analysis, and detailed discussions of published statistics are used to assess the implications for the German economy and the results in host countries of foreign investment. Consideration is also given to FDI by Swedish multinational corporations, as well as to the role national and supranational institutions can play in stimulating FDI. Although FDI often raises fears for employment and growth, it is an effective way of transferring techniques, processes and products into new markets. Firm-specific assets transferred in this way can raise productivity in the host country without sacrificing jobs in the home country.

Time series analysis has undergone many changes in recent years with the advent of unit roots and cointegration. Maddala and Kim present a comprehensive review of these important developments and examine structural change. The volume provides an analysis of unit root tests, problems with unit root testing, estimation of cointegration systems, cointegration tests, and econometric estimation with integrated regressors. The authors also present the Bayesian approach to these problems and bootstrap methods for small-sample inference. The chapters on structural change discuss the problems of unit root tests and cointegration under structural change, outliers and robust methods, the Markov-switching model and Harvey's structural time series model. Unit Roots, Cointegration and Structural Change is a major contribution to Themes in Modern Econometrics, of interest both to specialists and graduate and upper-undergraduate students.

Integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems, offering

By looking at the processes of change over time - by carrying out longitudinal studies - researchers answer questions about learning, development, educational growth, social change and medical outcom

Presenting innovative, promising and unconventional techniques, Post-modern Electromagnetics outlines the essential tools for the creation of numerical methods. Hafner offers a comparative analysis of

Ragnar Frisch (1895–1973) received the first Nobel Memorial Prize in Economic Science together with Jan Tinbergen in 1969 for having played an important role in ensuring that mathematical techniques figure prominently in modern economic analysis. Frisch was also a co-founder of the Econometric Society in 1930, the inaugural editor of its journal Econometrica for over 20 years, and a major figure in Norwegian academic life. This collection of essays derived from the centennial symposium which marked Frisch's birth explores his contributions to econometrics and other key fields in the discipline as well as the results of new research. Contributors include eminent scholars from Europe, the United Kingdom and North America who investigate themes in utility measurement, production theory, microeconomic policy, econometric methods, macrodynamics, and macroeconomic planning.

The middle-class condition, seen during the twentieth century as both the symbol of progress and order and the means to achieve it, has largely evaded historical analysis. Blending historical methods

On-line learning is one of the most powerful and commonly used techniques for training large layered networks and has been used successfully in many real-world applications. Traditional analytical methods have been recently complemented by ones from statistical physics and Bayesian statistics. This powerful combination of analytical methods provides more insight and deeper understanding of existing algorithms and leads to novel and principled proposals for their improvement. This book presents a coherent picture of the state-of-the-art in the theoretical analysis of on-line learning. An introduction relates the subject to other developments in neural networks and explains the overall picture. Surveys by leading experts in the field combine new and established material and enable non-experts to learn more about the techniques and methods used. This book, the first in the area, provides a comprehensive view of the subject and will be welcomed by mathematicians, scientists and engineers,

Ragnar Frisch (1895–1973) received the first Nobel Memorial Prize in Economic Science together with Jan Tinbergen in 1969 for having played an important role in ensuring that mathematical techniques figure prominently in modern economic analysis. Frisch was also a co-founder of the Econometric Society in 1930, the inaugural editor of its journal Econometrica for over 20 years, and a major figure in Norwegian academic life. This collection of essays derived from the centennial symposium which marked Frisch's birth explores his contributions to econometrics and other key fields in the discipline as well as the results of new research. Contributors include eminent scholars from Europe, the United Kingdom and North America who investigate themes in utility measurement, production theory, microeconomic policy, econometric methods, macrodynamics, and macroeconomic planning.

Engineers face numerous uncertainties in the design and development of products and processes. To deal with the uncertainties inherent in measured information, they make use of a variety of statistical techniques. This 1999 book presents single-variable statistical distributions that are useful in engineering design and analysis. It lists significant properties of these distributions and describes methods for estimating parameters and their standard errors, constructing confidence intervals, testing hypotheses, and plotting data. Figures are used extensively to clarify concepts. Methods are illustrated by numerous fully worked examples in the form of Mathcad documents that readers can use as templates for their own data, eliminating the need for programming. Intended as both a text and reference, the book assumes an elementary knowledge of calculus and probability. Graduate and advanced undergraduate students, as well as practising engineers and scientists, will be able to use this bo

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.

String Theory comprises two volumes which give a comprehensive and pedagogic account of the subject. Volume 1, first published in 1998, provides a thorough introduction to the bosonic string. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory and of the Polyakov path integral, and the covariant quantization of the string. The next three chapters treat string interactions: the general formalism, and detailed treatments of the tree level and one loop amplitudes. Chapter eight covers toroidal compactification and many important aspects of string physics, such as T-duality and D-branes. Chapter nine treats higher-order amplitudes, including an analysis of their finiteness and unitarity, and various nonperturbative ideas. An appendix giving a short course on path integral methods is included. This is an essential text and reference for graduate students and researchers interested in modern superstring theory.

This book deals with the application of fractal and nonlinear time-series analysis to seismicity and earthquakes within the framework of earthquake prediction research. Emphasis is on theoretical foun

Advances in the study of dynamical systems have revolutionized the way that classical mechanics is taught and understood. Classical Dynamics, first published in 1998, is a comprehensive textbook that provides a complete description of this fundamental branch of physics. The authors cover all the material that one would expect to find in a standard graduate course: Lagrangian and Hamiltonian dynamics, canonical transformations, the Hamilton-Jacobi equation, perturbation methods, and rigid bodies. They also deal with more advanced topics such as the relativistic Kepler problem, Liouville and Darboux theorems, and inverse and chaotic scattering. A key feature of the book is the early introduction of geometric (differential manifold) ideas, as well as detailed treatment of topics in nonlinear dynamics (such as the KAM theorem) and continuum dynamics (including solitons). The book contains many worked examples and over 200 homework exercises. It will be an ideal textbook for graduate studen

Many geological features of the Earth's lithosphere create variations in the Earth's magnetic field that can be detected by satellites. The resulting magnetic anomaly maps can provide insights into the tectonic features and broad structures of the lithosphere. This book, which was originally published in 1998, documents the acquisition, reduction and analysis of satellite magnetic field data in the study of the Earth's lithosphere. The text considers issues of interpreting data, summarises various interpretation methods, considers rock magnetism concepts and sources of variation in magnetism, and provides a summary of published maps and the various methods used to create them. Mapping and interpreting lithospheric fields from satellite magnetic data has resulted in the sub-discipline of geomagnetism. Advanced students and researchers will find this book to be of interest.

This long awaited third edition of Phytochemical Methods is, as its predecessors, a key tool for undergraduates, research workers in plant biochemistry, plant taxonomists and any researchers in rel

Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior and graduate level students, especially in aerospace engineering, as well as researchers and practising engineers, will find a wealth of invaluable information on high-speed gas flows in this text.

This is the first book devoted to the Queen's Men, one of the major acting companies of the age of Shakespeare. In describing the troupe's position in the general political situation and the London theatre scene of the 1580s, the authors break new ground by showing how Elizabethan theatre history can be refocused by concentrating on the company which produced the plays rather than on the authors who wrote them. The book combines a thorough examination of documentary evidence with textual and critical analysis, to provide a full account of the characteristics which gave the company its identity: its acting style, staging methods, touring patterns and repertoire. The conclusions will interest Elizabethan historians as well as students and scholars of early modern theatre.

Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior and graduate level students, especially in aerospace engineering, as well as researchers and practising engineers, will find a wealth of invaluable information on high-speed gas flows in this text.

Leading forensic experts from around the world describe in detail their time-proven methods for identity testing through DNA analysis. Their state-of-the-art collection of easily reproducible methods

This volume provides a concise, historical review of the methods of structural analysis and design - from Galileo in the seventeenth century, to the present day. Through it, students in structural engineering and professional engineers will gain a deeper understanding of the theory behind the modern software packages they use daily in structural design. This book also offers the reader a lucid examination of the process of structural analysis and how it relates to modern design. The first three chapters cover questions about the strength of materials, and how to calculate local effects. An account is then given of the development of the equations of elastic flexure and buckling, followed by a separate chapter on masonry arches. Three chapters on the overall behaviour of elastic structures lead to a discussion of plastic behaviour, and a final chapter indicates that there are still problems needing solution.

Provides an excellent introductory text for students on the principles and methods of statistical analysis in the life sciences, helping them choose and analyse statistical tests for their own problem

Powerful techniques have been developed in recent years for the analysis of digital data, especially the manipulation of images. This book provides an in-depth introduction to a range of these innovative, avante-garde data-processing techniques. It develops the reader's understanding of each technique and then shows with practical examples how they can be applied to improve the skills of graduate students and researchers in astronomy, electrical engineering, physics, geophysics and medical imaging. What sets this book apart from others on the subject is the complementary blend of theory and practical application. Throughout, it is copiously illustrated with real-world examples from astronomy, electrical engineering, remote sensing and medicine. It also shows how many, more traditional, methods can be enhanced by incorporating the new wavelet and multiscale methods into the processing. For graduate students and researchers already experienced in image processing and data analysis, this

Covers recent advances in pressure-volume-temperature (PVT) analysis of petroleum reservoir fluids, explains fundamentals, and presents conventional and new methods of determining fluid properties for

In this collection, archaeologists, historians, geographers and language specialists re-examine the structure and political development of Celtic states scattered across present-day Europe. The main theoretical focus is on whether and when state-level complexity was attained in the different Celtic settlements. The contributors also discuss and evaluate the various methods for studying Celtic social systems: the historical textual studies, as opposed to the analysis of the archaeological record, and the use of regional comparisons. Interweaving archaeological and textual evidence, the result is an interdisciplinary study of state formation never before attempted on such a wide scale which contributes to our understanding of social complexity in Celtic Europe, and, more generally, to the processes underlying social transformation.

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.

"With a focus on providing a working knowledge of optical systems and their principles of operation, this book employs today's most important methods for optical analysis: geometrical ray optics, ract

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of 'modern' set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.

The book is an overview of the research on minimal surfaces of the last few years written by several renowned researchers. The methods used are taken from differential geometry, complex analysis, calc

How well can we reconstruct the appearance, movements and behavior of extinct vertebrates from studies of their bones and other, more rarely preserved parts? Where is the boundary between the scientific evidence for reconstruction and the need to resort to imagination? In this book, sixteen paleontologists and biologists discuss these questions, review the status of functional studies of extinct vertebrates in the context of similar work on living animals, and present a broad philosophical view of the subject's development within the framework of phylogenetic analysis. The authors describe and debate methods for making robust inferences of function in fossil vertebrates, and present examples where we may be confident that our reconstructions are both detailed and accurate. The detailed studies are placed in the context of their contribution to the understanding of evolutionary processes and will be valuable reading for vertebrate paleontologists, comparative anatomists and evolutionary

Choice, Welfare and Measurement contains many of Amartya Sen's most important contributions to economic analysis and methods, including papers on individual and social choice, preference and rational

This book presents the most recent progress of fundamental nature made in the new developed field of micromechanics: transformation field analysis, variational bounds for nonlinear composites, higher-

Stimulating, thought-provoking analysis of a number of the most interesting intellectual inconsistencies in mathematics, physics, and language. Delightful elucidations of methods for misunderstanding

This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life scie

This book provides an extensive introduction to the numerical solution of a large class of integral equations. The initial chapters provide a general framework for the numerical analysis of Fredholm integral equations of the second kind, covering degenerate kernel, projection and Nystrom methods. Additional discussions of multivariable integral equations and iteration methods update the reader on the present state of the art in this area. The final chapters focus on the numerical solution of boundary integral equation (BIE) reformulations of Laplace's equation, in both two and three dimensions. Two chapters are devoted to planar BIE problems, which include both existing methods and remaining questions. Practical problems for BIE such as the set up and solution of the discretised BIE are also discussed. Each chapter concludes with a discussion of the literature and a large bibliography serves as an extended resource for students and researchers needing more information on solving partic

This book describes the signal processing aspects of neural networks. It begins with a presentation of the necessary background material in electronic circuits, mathematical modeling and analysis, signal processing, and neurosciences, and then proceeds to applications. These applications include small networks of neurons, such as those used in control of warm-up and flight in moths and control of respiration during exercise in humans. Next, a theory of mnemonic surfaces is developed and studied and material on pattern formation and cellular automata is presented. Finally, large networks are studied, such as the thalamus-reticular complex circuit, believed to be involved in focusing attention, and the development of connections in the visual cortex. Additional material is also provided about nonlinear wave propagation in networks. This book will serve as an excellent text for advanced undergraduates and graduates in the physical sciences, mathematics, engineering, medicine and life scie