Methods of Nonlinear Analysis

Increasingly environmental scientists, palaeoceanographers and geologists are collecting quantitative records of environmental changes (time-series) from sediments, ice cores, cave calcite, corals and trees. This book explains how to analyse these records, using straightforward explanations and diagrams rather than formal mathematical derivations. All the main cyclostratigraphic methods are covered including spectral analysis, cross-spectral analysis, filtering, complex demodulation, wavelet and singular spectrum analysis. Practical problems of time-series analysis, including those of distortions of environmental signals during stratigraphic encoding, are considered in detail. Recent research into various types of tidal and climatic cycles is summarised. The book ends with an extensive reference section, and an appendix listing sources of computer algorithms. This book provides the ideal reference for all those using time-series analysis to study the nature and history of climatic and

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

The problem of evaluating integrals is well known to every student who has had a year of calculus. It was an especially important subject in 19th century analysis and it has now been revived with the appearance of symbolic languages. In this book, the authors use the problem of exact evaluation of definite integrals as a starting point for exploring many areas of mathematics. The questions discussed in this book, first published in 2004, are as old as calculus itself. In presenting the combination of methods required for the evaluation of most integrals, the authors take the most interesting, rather than the shortest, path to the results. Along the way, they illuminate connections with many subjects, including analysis, number theory, algebra and combinatorics. This will be a guided tour of exciting discovery for undergraduates and their teachers in mathematics, computer science, physics, and engineering.

This textbook describes polynomial and trigonometric approximation, develops both direct and iterative methods for resolving linear systems, and considers how to approach several nonlinear problems. O

Edward F. Vonesh's Generalized Linear and Nonlinear Models for Correlated Data: Theory and Applications Using SAS is devoted to the analysis of correlated response data using SAS, with special emphasi

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, includi

Stress and accent are central, organizing features of grammar, but their precise nature continues to be a source of mystery and wonder. These issues come to the forefront in the phonetic manifestation of stress and accent, their cross-linguistic variation and the subtle and intricate laws they obey in individual languages. Understanding the nature of stress and accent systems informs all aspects of linguistic theory, methods, typology and especially the grammatical analysis of language data. These themes form the organizational backbone of this book. Bringing together a team of world-renowned phonologists, the volume covers a range of typological and theoretical issues in the study of stress and accent. It will appeal to researchers who value synergistic approaches to the study of stress and accent, careful attention to cross-linguistic variation, and detailed analyzes of both well-studied and understudied languages. The book is a lively testimony of a field of inquiry that shows progr

The recent appearance of wavelets as a new computational tool in applied mathematics has given a new impetus to the field of numerical analysis of Fredholm integral equations. This book gives an account of the state of the art in the study of fast multiscale methods for solving these equations based on wavelets. The authors begin by introducing essential concepts and describing conventional numerical methods. They then develop fast algorithms and apply these to solving linear, nonlinear Fredholm integral equations of the second kind, ill-posed integral equations of the first kind and eigen-problems of compact integral operators. Theorems of functional analysis used throughout the book are summarised in the appendix. The book is an essential reference for practitioners wishing to use the new techniques. It may also be used as a text, with the first five chapters forming the basis of a one-semester course for advanced undergraduates or beginning graduates.

This authored monograph presents key aspects of signal processing analysis in the biomedical arena. Unlike wireless communication systems, biological entities produce signals with underlying nonlinear

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of ma

The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of ma

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. This book details the relatively simple and popular linearization techniqu

This book is focused on the nonlinear theoretical and mathematical problems associated with ultrafast intense laser pulse propagation in gases and in particular, in air. With the aim of understanding

Due to the increase in computational power and new discoveries in propagation phenomena for linear and nonlinear waves, the area of computational wave propagation has become more significant in recent

Multiphase flows are found in all areas of technology, at all length scales and flow regimes and can involve compressible or incompressible linear or nonlinear, fluids. However, although they are ubi

The book presents a range of new developments in the theory and practice of multivariate statistical data analysis. Several contributions illustrate the use of multivariate methods in application fiel

Multivariate methods are employed widely in the analysis of experimental data but are poorly understood by those users who are not statisticians. This is because of the wide divergence between the theory and practice of multivariate methods. This book provides concise yet thorough surveys of developments in multivariate statistical analysis and gives statistically sound coverage of the subject. The contributors are all experienced in the theory and practice of multivariate methods and their aim has been to emphasize the major features from the point of view of applicability and to indicate the limitations and conditions of the techniques. Professional statisticians wanting to improve their background in applicable methods, users of high-level statistical methods wanting to improve their background in fundamentals, and graduate students of statistics will all find this volume of value and use.

After fifty years of development and refinement in Transactional Analysis (TA), the theory of methods and the actual methods have changed considerably from what was originally published by Eric Berne.

This 1996 book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strange attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

This 1996 book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulated as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strange attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.

An authoritative exposition of the methods at the heart of modern non-stationary signal processing from a recognised leader in the field. Offering a global view that favours interpretations and historical perspectives, it explores the basic concepts of time-frequency analysis, and examines the most recent results and developments in the field in the context of existing, lesser-known approaches. Several example waveform families from bioacoustics, mathematics and physics are examined in detail, with the methods for their analysis explained using a wealth of illustrative examples. Methods are discussed in terms of analysis, geometry and statistics. This is an excellent resource for anyone wanting to understand the 'why and how' of important methodological developments in time-frequency analysis, including academics and graduate students in signal processing and applied mathematics, as well as application-oriented scientists.

Quantitative Methods in Archaeology Using R is the first hands-on guide to using the R statistical computing system written specifically for archaeologists. It shows how to use the system to analyze many types of archaeological data. Part I includes tutorials on R, with applications to real archaeological data showing how to compute descriptive statistics, create tables, and produce a wide variety of charts and graphs. Part II addresses the major multivariate approaches used by archaeologists, including multiple regression (and the generalized linear model); multiple analysis of variance and discriminant analysis; principal components analysis; correspondence analysis; distances and scaling; and cluster analysis. Part III covers specialized topics in archaeology, including intra-site spatial analysis, seriation, and assemblage diversity.

Quantitative Methods in Archaeology Using R is the first hands-on guide to using the R statistical computing system written specifically for archaeologists. It shows how to use the system to analyze many types of archaeological data. Part I includes tutorials on R, with applications to real archaeological data showing how to compute descriptive statistics, create tables, and produce a wide variety of charts and graphs. Part II addresses the major multivariate approaches used by archaeologists, including multiple regression (and the generalized linear model); multiple analysis of variance and discriminant analysis; principal components analysis; correspondence analysis; distances and scaling; and cluster analysis. Part III covers specialized topics in archaeology, including intra-site spatial analysis, seriation, and assemblage diversity.

Concise, mathematically clear, and comprehensive treatment of the subject.* Expanded coverage of diagnostics and methods of model fitting.* Requires no specialized knowledge beyond a good grasp of mat

Introduces the methods of synoptic climatology (the spatial analysis of climates) and shows its vital importance in the understanding of environmental systems. Constructed around five environmental sc

Spatial epidemiology is the description and analysis of the geographical distribution of disease. It is more important now than ever, with modern threats such as bio-terrorism making such analysis eve

This introduction to the world of statistics covers exploratory data analysis, methods for collecting data, formal statistical inference, and techniques of regression and analysis of variance. 1983 ed

Sampling-based computational methods have become a fundamental part of the numerical toolset of practitioners and researchers across an enormous number of different applied domains and academic discip

Explaining techniques of multivariate statistical analysis that are widely used in archaeology and archaeological science, Baxter emphasizes the popular methods of principal component analysis, corres

A simple, straightforward presentation of basic statistical methods and experimental designs with emphasis on how to compute essential statistics. Introduces principles of experimentation and explains

This new four-volume major work brings together a wealth of valuable research on the qualitative research methods of grounded theory and its extension, situational analysis.

This volume is a representative selection of current methods of metrical-rhythmical analysis. Leading experts in the field present the latest state of the art in metrical theory, including Generative

This engaging text shows how statistics and methods work together, demonstrating a variety of techniques for evaluating statistical results against the specifics of the methodological design. Richard

The author investigates the Cramer –Lundberg model, collecting the most interesting theorems and methods, which estimate probability of default for a company of insurance business. These offer differe

Modern classrooms face an increasing population of special needs students and “regular” students who have behavioural problems. At the same time, punitive methods of handling misbehaviour are increasi

Modern classrooms face an increasing population of special needs students and “regular” students who have behavioural problems. At the same time, punitive methods of handling misbehaviour are increasi

An outstanding introduction to the fundamentals of regression analysis-updated and expanded The methods of regression analysis are the most widely used statistical tools for discovering the relations

Authored by military and intelligence professionals, this book introduces the new and emerging topic of social network analysis. Focusing on models and methods for the analysis of organizational risk,

Image Analysis in Earth Sciences is a graduate level textbook for researchers and students interested in the quantitative microstructure and texture analysis of earth materials. Methods of analysis an

This brief presents readers with a summary of classic, modern, and state-of-the-art methods for discovering the roles of entities in networks (including social networks) that range from small to large