Basic Methods of Linear Functional Analysis

Andrew Russell Forsyth (1858–1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1900, this book constitutes the third of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on ordinary equations which are not linear. The text contains detailed information on the development of this area and substantial contributions made to it. All sources are quoted in their proper connection and a few fresh investigations are added. Examples are given, where necessary, in order to provide illustrations of various methods. This book will be of value to anyone with an interest in differential equations and the history of mathematics.

Filtering and system identification are powerful techniques for building models of complex systems. This 2007 book discusses the design of reliable numerical methods to retrieve missing information in models derived using these techniques. Emphasis is on the least squares approach as applied to the linear state-space model, and problems of increasing complexity are analyzed and solved within this framework, starting with the Kalman filter and concluding with the estimation of a full model, noise statistics and state estimator directly from the data. Key background topics, including linear matrix algebra and linear system theory, are covered, followed by different estimation and identification methods in the state-space model. With end-of-chapter exercises, MATLAB simulations and numerous illustrations, this book will appeal to graduate students and researchers in electrical, mechanical and aerospace engineering. It is also useful for practitioners. Additional resources for this title,

In a number of famous works, M. Kac showed that various methods of probability theory can be fruitfully applied to important problems of analysis. The interconnection between probability and analysis

This book applies philosophical hermeneutics to biblical studies. Whereas traditional studies of the Bible limit their analysis to the exploration of the texts' original historical sense, this book discusses how to move beyond these issues to a consideration of biblical texts' existential significance for the present. In response to the rejection of biblical significance in the late nineteenth century and the accompanying crisis of nihilism, B. H. McLean argues that the philosophical thought of Heidegger, Bultmann, Gadamer, Habermas, Ricoeur, Levinas, Deleuze and Guattari provides an alternative to historically oriented approaches to biblical interpretation. He uses basic principles drawn from these philosophers' writings to create a framework for a new 'post-historical' mode of hermeneutic inquiry that transcends the subject-based epistemological structure of historical positivism.

This book applies philosophical hermeneutics to biblical studies. Whereas traditional studies of the Bible limit their analysis to the exploration of the texts' original historical sense, this book discusses how to move beyond these issues to a consideration of biblical texts' existential significance for the present. In response to the rejection of biblical significance in the late nineteenth century and the accompanying crisis of nihilism, B. H. McLean argues that the philosophical thought of Heidegger, Bultmann, Gadamer, Habermas, Ricoeur, Levinas, Deleuze and Guattari provides an alternative to historically oriented approaches to biblical interpretation. He uses basic principles drawn from these philosophers' writings to create a framework for a new 'post-historical' mode of hermeneutic inquiry that transcends the subject-based epistemological structure of historical positivism.

This book deals with electromagnetic theory and its applications at the level of a senior-level undergraduate course for science and engineering. The basic concepts and mathematical analysis are clear

Focusing on what actuaries need in practice, this introductory account provides readers with essential tools for handling complex problems and explains how simulation models can be created, used and re-used (with modifications) in related situations. The book begins by outlining the basic tools of modelling and simulation, including a discussion of the Monte Carlo method and its use. Part II deals with general insurance and Part III with life insurance and financial risk. Algorithms that can be implemented on any programming platform are spread throughout and a program library written in R is included. Numerous figures and experiments with R-code illustrate the text. The author's non-technical approach is ideal for graduate students, the only prerequisites being introductory courses in calculus and linear algebra, probability and statistics. The book will also be of value to actuaries and other analysts in the industry looking to update their skills.

Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on compu

The state of migration research has undergone rapid change since methods of analysis involving stable and radiogen isotopes and molecular genetics have been started to be applied. At a conference held

Fuzzy classi?ers are important tools in exploratory data analysis, which is a vital set of methods used in various engineering, scienti?c and business applications. Fuzzy classi?ers use fuzzy rules an

Tobias Nau addresses initial boundary value problems in cylindrical space domains with the aid of modern techniques from functional analysis and operator theory. In particular, the author uses concept

Although formal analysis programming techniques may be quite old, the introduction of formal methods only dates from the 1980s. These techniques enable us to analyze the behavior of a software applica

This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert s

Understanding damage and failure of composite materials is critical for reliable and cost-effective engineering design. Bringing together materials mechanics and modeling, this book provides a complete guide to damage, fatigue and failure of composite materials. Early chapters focus on the underlying principles governing composite damage, reviewing basic equations and mechanics theory, before describing mechanisms of damage such as cracking, breakage and buckling. In subsequent chapters, the physical mechanisms underlying the formation and progression of damage under mechanical loads are described with ample experimental data, and micro- and macro-level damage models are combined. Finally, fatigue of composite materials is discussed using fatigue-life diagrams. While there is a special emphasis on polymer matrix composites, metal and ceramic matrix composites are also described. Outlining methods for more reliable design of composite structures, this is a valuable resource for engineer

Since the advent of the nuclear reactor, thermal neutron scattering has proved a valuable tool for studying many properties of solids and liquids, and research workers are active in the field at reactor centres and universities throughout the world. This classic text provides the basic quantum theory of thermal neutron scattering and applies the concepts to scattering by crystals, liquids and magnetic systems. Other topics discussed are the relation of the scattering to correlation functions in the scattering system, the dynamical theory of scattering and polarisation analysis. No previous knowledge of the theory of thermal neutron scattering is assumed, but basic knowledge of quantum mechanics and solid state physics is required. The book is intended for experimenters rather than theoreticians, and the discussion is kept as informal as possible. A number of examples, with worked solutions, are included as an aid to the understanding of the text.

For graduate students and researchers with a basic knowledge of general topology, functional analysis, and Lebesgue integration, Florescu ("Alexandru Ioan Cuza" U., Romania) and Godet-Thobie (U. de Br

Over the past decade, computer supported data analysis by statistical methods has been one of the fastest growth areas in chemometrics, biometrics and other related branches of natural, technical and

This book introduces in a systematic manner a general nonparametric theory of statistics on manifolds, with emphasis on manifolds of shapes. The theory has important and varied applications in medical diagnostics, image analysis, and machine vision. An early chapter of examples establishes the effectiveness of the new methods and demonstrates how they outperform their parametric counterparts. Inference is developed for both intrinsic and extrinsic Fréchet means of probability distributions on manifolds, then applied to shape spaces defined as orbits of landmarks under a Lie group of transformations - in particular, similarity, reflection similarity, affine and projective transformations. In addition, nonparametric Bayesian theory is adapted and extended to manifolds for the purposes of density estimation, regression and classification. Ideal for statisticians who analyze manifold data and wish to develop their own methodology, this book is also of interest to probabilists, mathematicia

Self-sufficient and user-friendly, this book provides a complete introduction to the anisotropic elasticity theory necessary to model a wide range of crystal defects. Assuming little prior knowledge of the subject, the reader is first walked through the required basic mathematical techniques and methods. This is followed by treatments of point, line, planar and volume type defects such as vacancies, dislocations, grain boundaries, inhomogeneities and inclusions. Included are analyses of their elastic fields, interactions with imposed stresses and image stresses, and interactions with other defects, all employing the basic methods introduced earlier. This step by step approach, aided by numerous exercises with solutions provided, strengthens the reader's understanding of the principles involved, extending it well beyond the immediate scope of the book. As the first comprehensive review of anisotropic elasticity theory for crystal defects, this text is ideal for both graduate students an

A seminal text in European studies, which addresses issues of research design and causal analysis. The chapters draw on different methodological traditions, notions of causality, and methods and use s

Astronomy needs statistical methods to interpret data, but statistics is a many-faceted subject that is difficult for non-specialists to access. This handbook helps astronomers analyze the complex data and models of modern astronomy. This second edition has been revised to feature many more examples using Monte Carlo simulations, and now also includes Bayesian inference, Bayes factors and Markov chain Monte Carlo integration. Chapters cover basic probability, correlation analysis, hypothesis testing, Bayesian modelling, time series analysis, luminosity functions and clustering. Exercises at the end of each chapter guide readers through the techniques and tests necessary for most observational investigations. The data tables, solutions to problems, and other resources are available online at www.cambridge.org/9780521732499. Bringing together the most relevant statistical and probabilistic techniques for use in observational astronomy, this handbook is a practical manual for advanced und

Combining discourse and comparative historical methods of analysis, this book explores how colonialists and anti-colonialists renegotiated transnational power relationships within the debates on decol

The emergence of satellite technology has changed the lives of millions of people. In particular, GPS has brought an unprecedented level of accuracy to the field of geodesy. This text is a guide to the algorithms and mathematical principles that account for the success of GPS technology and replaces the authors' previous work, Linear Algebra, Geodesy, and GPS (1997). An initial discussion of the basic concepts, characteristics and technical aspects of different satellite systems is followed by the necessary mathematical content which is presented in a detailed and self-contained fashion. At the heart of the matter are the positioning algorithms on which GPS technology relies, the discussion of which will affirm the mathematical contents of the previous chapters. Numerous ready-to-use MATLAB codes are included for the reader. This comprehensive guide will be invaluable for engineers and academic researchers who wish to master the theory and practical application of GPS technology.

This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it readily accessible to people whose background is probability theory. Many results are given new proofs designed for readers with limited expertise in analysis. The author covers the theory of linear, second order, partial differential equations of parabolic and elliptic types. Many of the techniques have antecedents in probability theory, although the book also covers a few purely analytic techniques. In particular, a chapter is devoted to the De Giorgi–Moser–Nash estimates, and the concluding chapter gives an introduction to the theory of pseudodifferential operators and their application to hypoellipticity, including the famous theorem of Lars Hormander.

Advances in morphological and molecular methods continue to uncover new information on the origin and evolution of bats. Presenting some of the most remarkable discoveries and research involving living and fossil bats, this book explores their evolutionary history from a range of perspectives. Phylogenetic studies based on both molecular and morphological data have established a framework of evolutionary relationships that provides a context for understanding many aspects of bat biology and diversification. In addition to detailed studies of the relationships and diversification of bats, the topics covered include the mechanisms and evolution of powered flight, evolution and enhancement of echolocation, feeding ecology, population genetic structure, ontogeny and growth of facial form, functional morphology and evolution of body size. The book also examines the fossil history of bats from their beginnings over 50 million years ago to their diversification into one of the most globally w

Biological Anthropology is a concise introduction to the basic themes, theories, methods and facts of bioanthropology. The scientific method provides a framework that brings accessibility and context

The interdisciplinary nature of bioinformatics presents a research challenge in integrating concepts, methods, software and multiplatform data. Although there have been rapid developments in new technology and an inundation of statistical methods for addressing other types of high-throughput data, such as proteomic profiles that arise from mass spectrometry experiments. This book discusses the development and application of Bayesian methods in the analysis of high-throughput bioinformatics data that arise from medical, in particular, cancer research, as well as molecular and structural biology. The Bayesian approach has the advantage that evidence can be easily and flexibly incorporated into statistical methods. A basic overview of the biological and technical principles behind multi-platform high-throughput experimentation is followed by expert reviews of Bayesian methodology, tools and software for single group inference, group comparisons, classification and clustering, motif discov

This book of general analytical chemistry – as opposed to instrumental analysis or separation methods – in aqueous solutions is focuses on fundamentals, which is an area too often overlooked in the li

Anthropology as a discipline is rapidly becoming more quantitative, and anthropology students are now required to develop sophisticated statistical skills. This book provides students of anthropology with a clear, step-by-step guide to univariate statistical methods, demystifying the aspects that are often seen as difficult or impenetrable. Explaining the central role of statistical methods in anthropology and using only anthropological examples, the book provides a solid footing in statistical techniques. Beginning with basic descriptive statistics, this new edition also covers more advanced methods such as analyses of frequencies and variance, simple and multiple regression analysis with dummy and continuous variables. It addresses commonly encountered problems such as small samples and non-normality. Each statistical technique is accompanied by clearly worked examples and the chapters end with practice problem sets. Many of the datasets are available for download at www.cambridge.or

Based on the ideas of Russian psychologists Lev Vygotsky and Alexander Luria, this book explores methods of preventing or overcoming learning disabilities. Tatiana V. Akhutina and Natalia M. Pylaeva build on Vygotsky and Luria's sociocultural theory and their principle of a systemic structure and dynamic organization of higher mental functions. They focus on the interactive scaffolding of the weak components of the child's functional systems, the transition from joint child-adult co-actions, and the emotional involvement of the child. The authors discuss effective ways to remediate issues with attention, executive functions (working memory and cognitive control) and spatial and visual-verbal functions. Overcoming Learning Disabilities translates complex problems into easily understandable concepts useful to school psychologists, special and general education teachers, and parents of children with learning disabilities.

Assuming only basic knowledge of probability theory and functional analysis, this book provides a self-contained introduction to Malliavin calculus and infinite-dimensional Brownian motion. In an effort to demystify a subject thought to be difficult, it exploits the framework of nonstandard analysis, which allows infinite-dimensional problems to be treated as finite-dimensional. The result is an intuitive, indeed enjoyable, development of both Malliavin calculus and nonstandard analysis. The main aspects of stochastic analysis and Malliavin calculus are incorporated into this simplifying framework. Topics covered include Brownian motion, Ornstein–Uhlenbeck processes both with values in abstract Wiener spaces, Lévy processes, multiple stochastic integrals, chaos decomposition, Malliavin derivative, Clark–Ocone formula, Skorohod integral processes and Girsanov transformations. The careful exposition, which is neither too abstract nor too theoretical, makes this book accessible to graduat

• This new edition gives students valuable practice in reading and evaluating research. All major methods of research are illustrated, including qualitative research, content/document analysis, survey

This book focuses on the basic electrochemical applications of DNA in various areas, from basic principles to the most recent discoveries. The book comprises theoretical and experimental analysis of v

Advances in morphological and molecular methods continue to uncover new information on the origin and evolution of bats. Presenting some of the most remarkable discoveries and research involving living and fossil bats, this book explores their evolutionary history from a range of perspectives. Phylogenetic studies based on both molecular and morphological data have established a framework of evolutionary relationships that provides a context for understanding many aspects of bat biology and diversification. In addition to detailed studies of the relationships and diversification of bats, the topics covered include the mechanisms and evolution of powered flight, evolution and enhancement of echolocation, feeding ecology, population genetic structure, ontogeny and growth of facial form, functional morphology and evolution of body size. The book also examines the fossil history of bats from their beginnings over 50 million years ago to their diversification into one of the most globally w

This volume provides an overview of the occurrence and fate of emerging contaminants, discusses advanced chemical analysis methods, toxicological and ecotoxicological effects as well as human exposure

These lectures in functional analysis cover several aspects of Banach spaces, a conceptualization of complete normed linear spaces developed by Stefan Banach in 1932, and include a number of topics wh

This comprehensive text brings together in one volume the range of methods available for undertaking qualitative data collection and analysis. Qualitative Organizational Research contains 27 chapters

A systematic, unified treatment of orthogonal transform methods for signal processing, data analysis and communications, this book guides the reader from mathematical theory to problem solving in practice. It examines each transform method in depth, emphasizing the common mathematical principles and essential properties of each method in terms of signal decorrelation and energy compaction. The different forms of Fourier transform, as well as the Laplace, Z-, Walsh–Hadamard, Slant, Haar, Karhunen–Loève and wavelet transforms, are all covered, with discussion of how each transform method can be applied to real-world experimental problems. Numerous practical examples and end-of-chapter problems, supported by online Matlab and C code and an instructor-only solutions manual, make this an ideal resource for students and practitioners alike.

This book was first published in 1977. It deals with the importance of weed seed and grain-eating birds in natural and agricultural environments. These birds are to be found worldwide and are a component of man-made ecosystems where they are associated with man's main food crops. An analysis is made of their evolution and genetics, population dynamics, energy and food requirements, impact on ecosystems and control. Principles, procedures and basic data are presented that can be applied to the evaluation and control of pest species anywhere in the world. In this synthesis volume full use is made of the systems approach, the ecological and evolutionary aspects of the study are integrated. In linking the studies with fundamental work on bioenergetics, new insights are provided into the behavioural and applied aspects of granivory. Studies which encompass archaeological and anthropological investigations form a backcloth for the detailed interpretation of the population biology and bioener

This text provides a basic treatment of modern electric machine analysis that gives readers the necessary background for comprehending the traditional applications and operating characteristics of ele