Methods of Nonlinear Analysis

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral

Cross-cultural research is now an undeniable part of mainstream psychology and has had a major impact on conceptual models of human behavior. Although it is true that the basic principles of social psychological methodology and data analysis are applicable to cross-cultural research, there are a number of issues that are distinct to it, including managing incongruities of language and quantifying cultural response sets in the use of scales. Cross-Cultural Research Methods in Psychology provides state-of-the-art knowledge about the methodological problems that need to be addressed if a researcher is to conduct valid and reliable cross-cultural research. It also offers practical advice and examples of solutions to those problems and is a must-read for any student of culture.

Cross-cultural research is now an undeniable part of mainstream psychology and has had a major impact on conceptual models of human behavior. Although it is true that the basic principles of social psychological methodology and data analysis are applicable to cross-cultural research, there are a number of issues that are distinct to it, including managing incongruities of language and quantifying cultural response sets in the use of scales. Cross-Cultural Research Methods in Psychology provides state-of-the-art knowledge about the methodological problems that need to be addressed if a researcher is to conduct valid and reliable cross-cultural research. It also offers practical advice and examples of solutions to those problems and is a must-read for any student of culture.

Analysing language data systematically and looking closely at how people formulate their thoughts can reveal astonishing insights about the human mind. Without presupposing specific subject knowledge, this book gently introduces its readers to theoretical insights as well as practical principles for systematic linguistic analysis from a cognitive perspective. Drawing on Thora Tenbrink's twenty years' experience in both linguistics and cognitive science, this book offers theoretical guidance and practical advice for doing cognitive discourse analysis. It covers areas of analysis as diverse as attention, perspective, granularity, certainty, inference, transformation, communication, and cognitive strategies, using inspiring examples from many different projects. Simple techniques and tools are used to allow readers new to the subject easy ways to apply the methods, without the need for complex technologies, whilst the cross-disciplinary approach can be applied to a diverse range of resear

Analysing language data systematically and looking closely at how people formulate their thoughts can reveal astonishing insights about the human mind. Without presupposing specific subject knowledge, this book gently introduces its readers to theoretical insights as well as practical principles for systematic linguistic analysis from a cognitive perspective. Drawing on Thora Tenbrink's twenty years' experience in both linguistics and cognitive science, this book offers theoretical guidance and practical advice for doing cognitive discourse analysis. It covers areas of analysis as diverse as attention, perspective, granularity, certainty, inference, transformation, communication, and cognitive strategies, using inspiring examples from many different projects. Simple techniques and tools are used to allow readers new to the subject easy ways to apply the methods, without the need for complex technologies, whilst the cross-disciplinary approach can be applied to a diverse range of resear

This volume discusses protocols for key laboratory techniques used to study Duchenne and Becker muscular dystrophies. The chapters in this book cover a wide array of topics such as biochemical assays, quantification of dystrophin and related proteins, and measurements of muscle physiology. The chapters also cover methods of DMD sequence analysis; processing and isolation of cells from muscle tissue; culture and study of patient-derived cells; and work with animal models of DMD. Written in the highly successful Methods in Molecular Biology series format, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step, readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls. Comprehensive and authoritative, Duchenne Muscular Dystrophy: Methods and Protocols is a valuable resource that will contribute to the standardization of practices in the study of dystrophin and dystrophin-related diseas

The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical but have little to do with what is described these days as real analysis. Most of the results described in this book have a dual formulation; they have a 'discrete version' related to a finitely generated discrete group, and a continuous version related to a Lie group. The authors chose to centre this book around Lie groups but could quite easily have pushed it in several other directions as it interacts with opetators, and probability theory, as well as with group theory. This book will serve as an excellent basis for graduate courses in Lie groups, Markov chains or potential theory.

The geometry and analysis that is discussed in this book extends to classical results for general discrete or Lie groups, and the methods used are analytical but have little to do with what is described these days as real analysis. Most of the results described in this book have a dual formulation; they have a 'discrete version' related to a finitely generated discrete group, and a continuous version related to a Lie group. The authors chose to centre this book around Lie groups but could quite easily have pushed it in several other directions as it interacts with opetators, and probability theory, as well as with group theory. This book will serve as an excellent basis for graduate courses in Lie groups, Markov chains or potential theory.

Building on the success of the first edition and bringing together contributions from a range of experts in the field, the second edition of this guide to research on wild primates covers the latest advances in the field, including new information on field experiments and measuring behaviour. It provides essential information and advice on the technical and practical aspects of both field and laboratory methods, covering topics such as ethnoprimatology; remote sensing; GPS and radio-tracking; trapping and handling; dietary ecology; and non-invasive genetics and endocrinology. This integrated approach opens up new opportunities to study the behavioural ecology of some of the most endangered primates and to collect information on previously studied populations. Chapters include methodological techniques; instructions on collecting, processing and preserving samples/data for later analysis; ethical considerations; comparative costs; and further reading, making this an invaluable tool for

Building on the success of the first edition and bringing together contributions from a range of experts in the field, the second edition of this guide to research on wild primates covers the latest advances in the field, including new information on field experiments and measuring behaviour. It provides essential information and advice on the technical and practical aspects of both field and laboratory methods, covering topics such as ethnoprimatology; remote sensing; GPS and radio-tracking; trapping and handling; dietary ecology; and non-invasive genetics and endocrinology. This integrated approach opens up new opportunities to study the behavioural ecology of some of the most endangered primates and to collect information on previously studied populations. Chapters include methodological techniques; instructions on collecting, processing and preserving samples/data for later analysis; ethical considerations; comparative costs; and further reading, making this an invaluable tool for

Physical labels such as stable nitroxide radicals, luminescent and photochromic chromophores, so-called Mössbauer atoms and electron-dense assemblies of heavy atoms have proved to be effective tools in solving many problems at the molecular level in biological systems. These physical labels are used as 'molecular rulers' to measure the distances between chosen groups and to measure the size, form and microrelief of objects. By providing information about these factors, the label provides information that can help the scientist to understand the structure of membranes, nucleic acids, enzymes and proteins and how they function. This 1993 volume covers all aspects of this field: the theoretical bases, the experimental techniques, and it also shows how to interpret the resulting data. It also critically discusses some recent results obtained with these techniques and gives an analysis of likely developments in the future.

Physical labels such as stable nitroxide radicals, luminescent and photochromic chromophores, so-called Mössbauer atoms and electron-dense assemblies of heavy atoms have proved to be effective tools in solving many problems at the molecular level in biological systems. These physical labels are used as 'molecular rulers' to measure the distances between chosen groups and to measure the size, form and microrelief of objects. By providing information about these factors, the label provides information that can help the scientist to understand the structure of membranes, nucleic acids, enzymes and proteins and how they function. This 1993 volume covers all aspects of this field: the theoretical bases, the experimental techniques, and it also shows how to interpret the resulting data. It also critically discusses some recent results obtained with these techniques and gives an analysis of likely developments in the future.

Mixed effects models, including linear mixed models, generalized linear mixed models, nonlinear mixed effects models, and non-parametric mixed effects models, are complex models by nature; yet, these

Learn about the state-of-the-art at the interface between information theory and data science with this first unified treatment of the subject. Written by leading experts in a clear, tutorial style, and using consistent notation and definitions throughout, it shows how information-theoretic methods are being used in data acquisition, data representation, data analysis, and statistics and machine learning. Coverage is broad, with chapters on signal acquisition, data compression, compressive sensing, data communication, representation learning, emerging topics in statistics, and much more. Each chapter includes a topic overview, definition of the key problems, emerging and open problems, and an extensive reference list, allowing readers to develop in-depth knowledge and understanding. Providing a thorough survey of the current research area and cutting-edge trends, this is essential reading for graduate students and researchers working in information theory, signal processing, machine le

The goal of this Third Edition is the same as previous editions: to provide a good foundation - and a joyful experience! - for anyone who'd like to learn about nonlinear dynamics and chaos from an applied perspective.The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, strange attractors, and synchronization.The prerequisites are comfort with multivariable calculus and linear algebra, as well as a first course in physics.Changes to this edition include substantial exercises about conceptual models of climate change, an updated treatment of the SIR model of epidemics, and amendments (based on recent research) about the Selkov model of oscillatory glycolysis. Equa

First published in 1965, this book was written in response to the considerable changes that had taken place in shipbuilding techniques since 1945 and to the new scientific methods that were being increasingly adopted in a strongly competitive market. It describes the advances which had been made in one field of the design of ship structures, a field also of importance in the design of bridges and other rigid structures on land. A grillage is a structure of intersecting beams, usually attached to one side of a continuous plate panel, which is loaded normal to its surface. The decks, bottoms and bulkheads (vertical divisions) of ships are usually flat grillages, and this form of construction is also commonly used in the decks of bridges. The methods of plastic analysis are not directly applicable to plated grillage structures and Mr Clarkson has therefore discussed only elastic methods of design.

This book presents correct-by-design control techniques for switching systems, using different methods of stability analysis. Switching systems are increasingly used in the electronics and mechanical

This volume presents theoretical developments, applications and computational methods for the analysis and modeling in behavioral and social sciences where data are usually complex to explore and inve

This practice-oriented guidebook collects nearly all methods published since 1975 on the chemical analysis of seawaters. Detailed descriptions of both classical and most advanced physico-chemical and

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 book approaches the analysis of forensic contact traces from a polymer science perspective. The development of characterization methods of new or unusual traces and the improvement of existing pr

Providing an introduction to isogeometric methods with a focus on their mathematical foundations, this book is composed of four chapters, each devoted to a topic of special interests for isogeometric

Over the past 15 years, the availability of cheap and convenient microcomputers has changed the collection methods and analysis of household survey data in developing countries, making the data availa

This text on the different methods of analysis and modeling is broken into three parts: a summary of the transdisciplinary fundamentals; a discussion detailing case studies from various fields; and a

This work takes financial ratios, a popular tool for analyzing firms and their performance, and describes the methods that can be used for comparing these ratios across a large number of industries.

Drug safety has always been important, but it’s taken on increasing criticality and scrutiny in recent years. This book covers the most state-of-the-art methods in drug safety assessment. In addition,

This book is divided in two parts. Part I provides a brief but accurate summary of all the basic ideas, theories, methods, and conspicuous results of structure analysis and molecular modelling of the

The book juxtaposes economic analysis with moral philosophy, political theory, egalitarianism, and other methodological principles.

Multi-scale systems, involving complex interacting processes that occur over a range of temporal and spatial scales, are present in a broad range of disciplines. Several methodologies exist to retrieve this multi-scale information from a given time series; however, each method has its own limitations. This book presents the mathematical theory behind the stochastic analysis of scaling time series, including a general historical introduction to the problem of intermittency in turbulence, as well as how to implement this analysis for a range of different applications. Covering a variety of statistical methods, such as Fourier analysis and wavelet transforms, it provides readers with a thorough understanding of the techniques and when to apply them. New techniques to analyse stochastic processes, including empirical mode decomposition, are also explored. Case studies, in turbulence and ocean sciences, are used to demonstrate how these statistical methods can be applied in practice, for st

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic an

Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a

The first extended analysis of the relationship between Italian criminology and crime fiction in English, Methods of Murder examines works by major authors both popular, such as Gianrico Carofiglio, a

This book covers the fundamental principles of measuring oceans from space, and also contains state-of-the-art developments in data analysis and interpretation and in sensors. Completely new will be m

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasises applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal co-ordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange–Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis,

How to spot patterns, identify opportunities, and grow your technical analysis skillsThe Trading Methodologies of W.D. Gann, Second Edition is a detailed yet accessible guide for trading, forecasting, and investing—using the principles of technical analysis to identify opportunities for profit. Beginning in the early 20th century, W.D. Gann developed pioneering methods of technical analysis that continue to hold value for modern traders. Gann’s insights on interpreting market conditions and recognizing patterns are a valuable addition to any trader’s strategy. The often cryptic nature of Gann’s original publications, however, prove challenging to modern readers. This valuable guide demystifies Gann’s techniques, providing clear and concise explanations and easy-to-follow instructions for today’s traders and investors. Expert trader and technical analyst Hima Reddy draws from her extensive experience to provide a systematic approach to Gann’s methodologies. This revised second edition i

Ecological theories and hypotheses are usually complex because of natural variability in space and time, which often makes the design of experiments difficult. The statistical tests we use require data to be collected carefully and with proper regard to the needs of these tests. This book, first published in 1996, describes how to design ecological experiments from a statistical basis using analysis of variance, so that we can draw reliable conclusions. The logical procedures that lead to a need for experiments are described, followed by an introduction to simple statistical tests. This leads to a detailed account of analysis of variance, looking at procedures, assumptions and problems. One-factor analysis is extended to nested (hierarchical) designs and factorial analysis. Finally, some regression methods for examining relationships between variables are covered. Examples of ecological experiments are used throughout to illustrate the procedures and examine problems. This book will be

Ecological theories and hypotheses are usually complex because of natural variability in space and time, which often makes the design of experiments difficult. The statistical tests we use require data to be collected carefully and with proper regard to the needs of these tests. This book, first published in 1996, describes how to design ecological experiments from a statistical basis using analysis of variance, so that we can draw reliable conclusions. The logical procedures that lead to a need for experiments are described, followed by an introduction to simple statistical tests. This leads to a detailed account of analysis of variance, looking at procedures, assumptions and problems. One-factor analysis is extended to nested (hierarchical) designs and factorial analysis. Finally, some regression methods for examining relationships between variables are covered. Examples of ecological experiments are used throughout to illustrate the procedures and examine problems. This book will be

This book summarizes the main methods of experimental stress analysis and examines their application to various states of stress of major technical interest, highlighting aspects not always covered in

Three engineering professors lay down the foundation of singular perturbation theory for linear and nonlinear systems, and illustrate the theory with solved examples and applications. This reprint of

This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on problems