Methods of Nonlinear Analysis

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

Label-free biosensors are devices that use biological or chemical receptors to detect analytes (molecules) in a sample. They give detailed information on the selectivity, affinity, and, in many cases, also the binding kinetics and thermodynamics of an interaction. Although they can be powerful tools in the hands of a skilled user, there is often a lack of knowledge of the best methods for using label-free assays to screen for biologically active molecules and accurately and precisely characterize molecular recognition events. This book reviews both established and newer label-free techniques giving both the expert user and the general reader interested in the technologies and applications behind label-free an insight into the field from expert opinion leaders and practitioners of the technologies. Most importantly, chapters contain worked examples from leaders in the field that take the reader through the basics of experimental design, setup, assay development, and data analysis.

Label-free biosensors are devices that use biological or chemical receptors to detect analytes (molecules) in a sample. They give detailed information on the selectivity, affinity, and, in many cases, also the binding kinetics and thermodynamics of an interaction. Although they can be powerful tools in the hands of a skilled user, there is often a lack of knowledge of the best methods for using label-free assays to screen for biologically active molecules and accurately and precisely characterize molecular recognition events. This book reviews both established and newer label-free techniques giving both the expert user and the general reader interested in the technologies and applications behind label-free an insight into the field from expert opinion leaders and practitioners of the technologies. Most importantly, chapters contain worked examples from leaders in the field that take the reader through the basics of experimental design, setup, assay development, and data analysis.

Interventional radiological techniques are becoming increasingly important in the treatment of both primary and secondary malignant liver tumours. Surgery for liver tumours can be effective but carries considerable risks and new techniques have recently been developed. This volume provides an account of interventional radiological methods by some of the greatest experts in the field. It includes chapters on cryotherapy, chemoembolization and radiofrequency ablation and an extensive chapter on imaging techniques. The scientific background of these techniques, the pathology of the diseases involved and an analysis of more traditional surgical methods are also described. This text brings together the latest advances in this fast-developing field.

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanc

If you're looking to understand photonic crystals, this systematic, rigorous, and pedagogical introduction is a must. Here you'll find intuitive analytical and semi-analytical models applied to complex and practically relevant photonic crystal structures. You will also be shown how to use various analytical methods borrowed from quantum mechanics, such as perturbation theory, asymptotic analysis, and group theory, to investigate many of the limiting properties of photonic crystals which are otherwise difficult to rationalize using only numerical simulations. An introductory review of nonlinear guiding in photonic lattices is also presented, as are the fabrication and application of photonic crystals. In addition, end-of-chapter exercise problems with detailed analytical and numerical solutions allow you to monitor your understanding of the material presented. This accessible text is ideal for researchers and graduate students studying photonic crystals in departments of electrical engi

Incompressible computational fluid dynamics is an emerging and important discipline, with numerous applications in industry and science. Its methods employ rigourous mathematical analysis far beyond what is presently possible for compressible flows. Vortex methods, finite elements, and spectral methods are emphasised. Contributions from leading experts in the various sub-fields portray the wide-ranging nature of the subject. The book provides an entrée into the current research in the field. It can also serve as a source book for researchers and others who require information on methods and techniques.

This book provides an account of developments and applications of social accounts. It concentrates particularly on the methods of social accounting that Richard Stone, Nobel Laureate in Economics, developed and applied during his long and distinguished career. The contributors to the volume examine applications of social accounts in economics and demography, addressing issues of new formulations and specifications at the national and regional levels. Economic structure and issues of structural change are investigated within the context of social accounts matrices, and Linear Expenditure Systems are used to model population change and household consumption. The importance of social accounts matrices (SAM) in generating Computable General Equilibrium (CGE) models and the enormous potential that both SAM and CGE models have for policy analysis are stressed.

The Unprovability of Consistency is concerned with connections between two branches of logic: proof theory and modal logic. Modal logic is the study of the principles that govern the concepts of necessity and possibility; proof theory is, in part, the study of those that govern provability and consistency. In this book, George Boolos looks at the principles of provability from the standpoint of modal logic. In doing so, he provides two perspectives on a debate in modal logic that has persisted for at least thirty years between the followers of C. I. Lewis and W. V. O. Quine. The author employs semantic methods developed by Saul Kripke in his analysis of modal logical systems. The book will be of interest to advanced undergraduate and graduate students in logic, mathematics and philosophy, as well as to specialists in those fields.

This book is concerned with the bifurcation theory, the study of the changes in the structures of the solution of ordinary differential equations as parameters of the model vary. The theory has developed rapidly over the past two decades. Chapters 1 and 2 of the book introduce two systematic methods of simplifying equations: centre manifold theory and normal form theory, by which the dimension of equations may be reduced and the forms changed so that they are as simple as possible. Chapters 3–5 of the book study in considerable detail the bifurcation of those one- or two-dimensional equations with one, two or several parameters. This book is aimed at mathematicians and graduate students interested in dynamical systems, ordinary differential equations and/or bifurcation theory. The basic knowledge required by this book is advanced calculus, functional analysis and qualitative theory of ordinary differential equations.

This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The applications,

本書從爆破震動信號的產生與傳播、爆破震動監測、爆破震動預測、爆破震動信號分析技術、爆破震動作用下結構體的動態響應特征、爆破震動危害機制與主動控制、爆破震動安全判據等方面，對爆破震動效應進行了較為全面且深入的研究和總結，系統介紹了爆破震動效應分析中的理論和研究方法，特別是應用爆破震動信號分析理論與技術解決實際問題的途徑。本書可作為高等院校礦業工程、土木工程等專業研究生的教材，還可作為相關領域的工程技

This text emphasizes contemporary research problems to better illustrate the relevance of statistical analysis in scientific research. All statistical methods are introduced in the context of a realis

This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis.

Written to complement the second edition of best-selling textbook Introductory Econometrics for Finance, this book provides a comprehensive introduction to the use of the Regression Analysis of Time Series (RATS) software for modelling in finance and beyond. It provides numerous worked examples with carefully annotated code and detailed explanations of the outputs, giving readers the knowledge and confidence to use the software for their own research and to interpret their own results. A wide variety of important modelling approaches are covered, including such topics as time-series analysis and forecasting, volatility modelling, limited dependent variable and panel methods, switching models and simulations methods. The book is supported by an accompanying website containing freely downloadable data and RATS instructions.

Written to complement the second edition of best-selling textbook Introductory Econometrics for Finance, this book provides a comprehensive introduction to the use of the Regression Analysis of Time Series (RATS) software for modelling in finance and beyond. It provides numerous worked examples with carefully annotated code and detailed explanations of the outputs, giving readers the knowledge and confidence to use the software for their own research and to interpret their own results. A wide variety of important modelling approaches are covered, including such topics as time-series analysis and forecasting, volatility modelling, limited dependent variable and panel methods, switching models and simulations methods. The book is supported by an accompanying website containing freely downloadable data and RATS instructions.

The core methods in today's econometric toolkit are linear regression for statistical control, instrumental variables methods for the analysis of natural experiments, and differences-in-differences m

The text here provides the reader with an in-depth overview and analysis of the fundamental methods and techniques developed following G. Voronoi’s ground-breaking ideas, in the context of the vast an

This book and companion DVD provide a comprehensive set of modeling methods for data and uncertainty analysis, taking readers beyond mainstream methods described in standard texts. The emphasis throu

Advances in Quantitative Analysis of Finance and Accounting (New Series) is an annual publication designed to disseminate developments in the quantitative analysis of finance and accounting. The publication is a forum for statistical and quantitative analyses of issues in finance and accounting as well as applications of quantitative methods to problems in financial management, financial accounting, and business management. The objective is to promote interaction between academic research in finance and accounting and applied research in the financial community and the accounting profession. The papers in this volume cover a wide range of topics including corporate finance and debt management, earnings management, equity market, auditing, option pricing theory, and interest rate theory. In this volume there are eleven chapters, five of them are corporate finance and debt management: 1. Liquidity and Adverse Selection: Evidence from the Five-or-Fewer Rule Change; 2. Changing Busin

These two volumes provide a comprehensive guide and source book on the marine use of composite materials. The first volume, Fundamental Aspects, provides a rigourous development of theory. Areas covered include materials science, environmental aspects, production technology, structural analysis, finite-element methods, materials failure mechanisms and the role of standard test procedures. An appendix gives tables of the mechanical properties of common polymeric composites and laminates in marine use. The second volume, Practical Considerations, examines how the theory can be used in the design and construction of marine structures, including boats, submersibles, offshore structures and other deep-ocean installations. These volumes will provide an up-to-date comprehensive introduction and reference to this important and fast-growing area.

The purpose of this book is to provide a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis

Late Nineteenth-Century American Development is an economist's attempt to interpret a critical period of US history, from Civil War to World War I. The questions raised have always been at the heart of American historiography. What accounts for the retardation up to the turn of the century? How did capital markets operate and what was their influence on the pace and pattern of our growth? What determined farm performance and what impact did that performance have on the economy as a whole? Yet while the questions raised in this book are familiar, the methods are not. This book blends traditional historical analysis with general equilibrium theory, modern macroeconomics and simulation analysis. The result is a provocative book of remarkable scope which offers a fresh interpretation of late nineteenth-century American growth.

This book provides a comprehensive review of optical pattern recognition, covering theoretical aspects as well as details of practical implementations and signal processing techniques. The first chapter is devoted to pattern recognition performed with optical correlators. Later chapters discuss approaches based on neural networks, wavelet transforms and the fractional Fourier transform. The book also covers nonlinear filter methods and optical-electronic hybrid systems. The final part of the book deals with the devices and materials employed in modern systems, such as photorefractive crystals, microlasers, and liquid crystal spatial light modulators. The book gives many examples of working systems that integrate optics, electronics and computers, and it covers a range of developments from mathematical theories to novel optical materials. It will be of great interest to graduate students and researchers in optical engineering and machine vision.

Providing thorough coverage of the methods and tools required in studying historical and contemporary theatre, this Introduction examines the complexities of a rapidly changing and dynamic discipline. Following a cross-cultural perspective, the book surveys the ways theatre and performance are studied by looking initially at key elements such as performers, spectators and space. The central focus is on methodology, which is divided into sections covering theatre theory, historiography and textual and performance analysis. The book covers all the main theatrical genres - drama, opera and dance - providing students with a comparative, integrated perspective. Designed to guide students through the academic dimension of the discipline, the volume emphasizes questions of methodology, research techniques and approaches, and will therefore be relevant for a wide variety of theatre studies courses. Informative textboxes provide background on key topics, and suggestions for further reading are

Providing thorough coverage of the methods and tools required in studying historical and contemporary theatre, this Introduction examines the complexities of a rapidly changing and dynamic discipline. Following a cross-cultural perspective, the book surveys the ways theatre and performance are studied by looking initially at key elements such as performers, spectators and space. The central focus is on methodology, which is divided into sections covering theatre theory, historiography and textual and performance analysis. The book covers all the main theatrical genres - drama, opera and dance - providing students with a comparative, integrated perspective. Designed to guide students through the academic dimension of the discipline, the volume emphasizes questions of methodology, research techniques and approaches, and will therefore be relevant for a wide variety of theatre studies courses. Informative textboxes provide background on key topics, and suggestions for further reading are

As a partner to Volume 1: Dimensional Continuous Models, this monograph provides a self-contained introduction to algebro-geometric solutions of completely integrable, nonlinear, partial differential-difference equations, also known as soliton equations. The systems studied in this volume include the Toda lattice hierarchy, the Kac-van Moerbeke hierarchy, and the Ablowitz-Ladik hierarchy. An extensive treatment of the class of algebro-geometric solutions in the stationary as well as time-dependent contexts is provided. The theory presented includes trace formulas, algebro-geometric initial value problems, Baker-Akhiezer functions, and theta function representations of all relevant quantities involved. The book uses basic techniques from the theory of difference equations and spectral analysis, some elements of algebraic geometry and especially, the theory of compact Riemann surfaces. The presentation is constructive and rigorous, with ample background material provided in various appen

'Metaphor' is the phenomenon whereby we talk and, potentially, think about something in terms of something else. In this book Elena Semino discusses metaphor as a common linguistic occurrence, which is varied in its textual appearance, versatile in the functions it may perform, and central to many different types of communication, from informal interaction to political speeches. She discusses the use of metaphor across a variety of texts and genres from literature, politics, science, education, advertising and the discourse of mental illness. Each chapter includes detailed case studies focusing on specific texts, from election leaflets to specialist scientific articles. Also included is a detailed consideration of corpus (computer-based) methods of analysis. Wide-ranging and informative, this book will be invaluable to those interested in metaphor from a range of disciplines.

'Metaphor' is the phenomenon whereby we talk and, potentially, think about something in terms of something else. In this book Elena Semino discusses metaphor as a common linguistic occurrence, which is varied in its textual appearance, versatile in the functions it may perform, and central to many different types of communication, from informal interaction to political speeches. She discusses the use of metaphor across a variety of texts and genres from literature, politics, science, education, advertising and the discourse of mental illness. Each chapter includes detailed case studies focusing on specific texts, from election leaflets to specialist scientific articles. Also included is a detailed consideration of corpus (computer-based) methods of analysis. Wide-ranging and informative, this book will be invaluable to those interested in metaphor from a range of disciplines.

This textbook introduces the principles and methods for the analysis and design of non-linear texts, from websites to CD-ROMs.

This textbook introduces the principles and methods for the analysis and design of non-linear texts, from websites to CD-ROMs.

This book attempts an interpretation of Revolutionary American culture. It argues that the cultural identity of the United States, like its political identity, emerged from a quarrel with the Old World. Europeans believed that the Revolution had 'turned the world upside down'. American intellectuals tried to construct a republic which refuted European criticism. They failed, but in failing they created an attitude to the terrain which became a central theme in American culture. The book employs the methods of perceptual geography and close textual analysis to examine images of the terrain and to propose close links between imaginative literature and a wide range of non-literary writing.

Laser Induced Breakdown Spectroscopy (LIBS) is an emerging technique for determining elemental composition. With the ability to analyse solids, liquids and gases with little or no sample preparation, it is more versatile than conventional methods and is ideal for on-site analysis. This is a comprehensive reference explaining the fundamentals of the LIBS phenomenon, its history and its fascinating applications across eighteen chapters written by recognized leaders in the field. Over 300 illustrations aid understanding. This book will be of significant interest to researchers in chemical and materials analysis within academia and industry.

The aim of this book is to demonstrate both the difficulties and the opportunities which the accumulation of statistical information in economically advanced countries offers for studying nineteenth-century society in depth. The chief emphasis is upon quantitative methods of analysis. The main focus of the attention is the census – what information was required on census night; how the information was collected; how accurately and completely population characteristics were recorded, the problems which arise in attempting to use either the published census volumes or the enumerators' books; and the techniques which have proved useful in analysis. Related topics covered include the study of family structure, the use of information about occupation, the measurement of migration, criminal statistics, educational provision and sampling in historical research.

Matters of Opinion offers an interesting insight into 'public opinion' as reported in the media, asking where these opinions actually come from, and how they have their effects. Drawing on the analysis of conversations from focus groups, phone-ins and broadcast interviews with members of the public, Greg Myers argues that we must go back to these encounters, asking questions such as what members of the public thought they were being asked, who they were talking as, and whom they were talking to. He reveals that people don't carry a store of opinions, ready to tell strangers; they use opinions in order to get along with other people, and how they say things is as important as what they say. Engaging and informative, this book illuminates debates on research methods, the public sphere and deliberative democracy, on broadcast talk, and on what it means to participate in public life.

This 2004 book in English integrates detailed literary criticism of the exorcism stories in Luke-Acts with wide-ranging comparative study of ancient sources on demonology, spirit affliction and exorcistic healing. Methods from systemic functional linguistics and critical theory are explained and then applied to each story. Careful focus is placed on each narrative's linguistic functions and also on relevant aspects of its literary co-text and the wider context of culture. Implications of the analysis for the new perspective on Luke-Acts, especially the implied author's relationship with Judaism, are explored in relation to the Lukan stories' original context of reception. Largely neglected interfaces between Luke's narrative representation of exorcism and emerging academic discourse about religious experience, shamanism, health care in antiquity, ritual performance and ancient Jewish systems of impurity are probed in ways that shed fresh light on this supremely alien part of the Lukan

This volumes comes out of a symposium, sponsored by the Society for Risk Analysis and the National Science Foundation, which explored practical methods and robust theories of risk communication arisin

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