Basic Methods of Linear Functional Analysis

Since the 1970s social scientists and scientists in a variety of fields - psychology, sociology, education, psychiatry, economics and engineering - have been interested in problems that require the statistical analysis of data over time and there has been in effect a conceptual revolution in ways of thinking about pattern and regularity. This book is a comprehensive introduction to all the major time-series techniques, both time-domain and frequency-domain. It includes work on linear models that simplify the solution of univariate and multivariate problems. The author begins with a non-mathematical overview: throughout, he provides easy-to-understand, fully worked examples drawn from real studies in psychology and sociology. Other, less comprehensive, books on time-series analysis require calculus: this presupposes only a standard introductory statistics course covering analysis of variance and regression. The chapters are short, designed to build concepts (and the reader's confidence)

There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, or

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

Concrete Vaulted Construction in Imperial Rome examines methods and techniques that enabled builders to construct some of the most imposing monuments of ancient Rome. Focusing on structurally innovative vaulting and the factors that influenced its advancement, Lynne Lancaster also explores a range of related practices, including lightweight pumice as aggregate, amphoras in vaults, vaulting ribs, metal tie bars, and various techniques of buttressing. She provides the geological background of the local building stones and applies mineralogical analysis to determine material provenance, which in turn suggests trading patterns and land use. Lancaster also examines construction techniques in relation to the social, economic, and political contexts of Rome, in an effort to draw connections between changes in the building industry and the events that shaped Roman society from the early empire to late antiquity. This book was awarded the James R. Wiseman Book Award from the Archaeological Inst

Damages Under the Convention on Contracts for the International Sale of Goods, Second Edition presents a practical and detailed analysis of the methods used to determine and calculate damages under th

Risk control and derivative pricing have become of major concern to financial institutions, and there is a real need for adequate statistical tools to measure and anticipate the amplitude of the potential moves of the financial markets. Summarising theoretical developments in the field, this 2003 second edition has been substantially expanded. Additional chapters now cover stochastic processes, Monte-Carlo methods, Black-Scholes theory, the theory of the yield curve, and Minority Game. There are discussions on aspects of data analysis, financial products, non-linear correlations, and herding, feedback and agent based models. This book has become a classic reference for graduate students and researchers working in econophysics and mathematical finance, and for quantitative analysts working on risk management, derivative pricing and quantitative trading strategies.

This exciting revision of Communication Systems, a classic text in the communications field, presents an introduction to electrical communication systems, including analysis methods, design principles

For nearly nineteen hundred years, few have questioned the single authorship of Luke and Acts. A careful reassessment of the internal and external evidence, however, reveals this assumption to be built on a shakier foundation than was previously thought. Patricia Walters's innovative study offers a statistical analysis of Luke and Acts, pointing to the existence of highly significant differences in their prose style. In particular, a comprehensive survey and re-examination of the two books' least contested authorial stratum - their seams and summaries - brings to light ancient prose compositional patterns that distinguish Luke and Acts beyond a reasonable doubt. Walters's application of statistical analysis is unique in biblical scholarship, and will provide impetus for using similar methods in other areas of the field. This book will therefore be of great interest to academic researchers and students of early Christianity, classical literature and rhetoric, and New Testament studies.

This volume of the Animas–La Plata series (SWCA Anthropological Research Paper No. 10) presents flaked stone and ground stone assemblage data and analysis methods and results. Patterning in Archaic, B

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.

Spaces of holomorphic functions have been a prominent theme in analysis since early in the twentieth century. Of interest to complex analysts, functional analysts, operator theorists and systems theorists, their study is now flourishing. This volume, an outgrowth of a 1995 program at the Mathematical Sciences Research Institute, contains expository articles by programme participants. Here researchers and graduate students will encounter Hardy spaces, Bergman spaces, Dirichlet spaces, Hankel and Toeplitz operators, and a sampling of the role these objects play in modern analysis.

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.

This book provides the basic models and methods for the profitable use and marketing of advanced technology. It provides a guide to developing and administering marketing plans, conducting market rese

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

The Schur algebra is an algebraic system providing a link between the representation theory of the symmetric and general linear groups (both finite and infinite). In the text Dr Martin gives a full, self-contained account of this algebra and these links, covering both the basic theory of Schur algebras and related areas. He discusses the usual representation-theoretic topics such as constructions of irreducible modules, the blocks containing them, their modular characters and the problem of computing decomposition numbers; moreover deeper properties such as the quasi-hereditariness of the Schur algebra are discussed. The opportunity is taken to give an account of quantum versions of Schur algebras and their relations with certain q-deformations of the coordinate rings of the general linear group. The approach is combinatorial where possible, making the presentation accessible to graduate students. This is the first comprehensive text in this important and active area of research; it wi

This tract is devoted to the theory of linear equations, mainly of the second kind, associated with the names of Volterra, Fredholm, Hilbert and Schmidt. The treatment has been modernised by the systematic use of the Lebesgue integral, which considerably widens the range of applicability of the theory. Special attention is paid to the singular functions of non-symmetric kernels and to obtaining as strong results as possible for the convergence of the expansions in infinite series. References are given to work on numerical methods of solution. Individual chapters deal with the resolvent kernel and the Neumann series, the Fredholm theorems, orthonormal systems of functions, the classical Fredholm theory, the Fred-holm formulae for ß2 kernels, Hermitian kernels, singular functions and singular values.

Dependence with complete connections is a more general type of stochastic process than the well-known Markovian dependence, accounting for a complete history of a stochastic evolution. This book is an authoritative survey of knowledge of the subject, dealing with the basic theoretical understanding and also with applications. These arise in a variety of situations as diverse as stochastic models of learning, branching processes in random environments, continued fractions and dynamical systems. Thus the book will appeal to mathematicians working in probability theory, ergodic theory and number theory, as well as applied mathematicians, engineers, biologists and social scientists interested in applications of stochastic methods.

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.

This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students.

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.

The theory of Lie groups rests on three pillars: analysis, topology and algebra. Correspondingly it is possible to distinguish several phases, overlapping in some degree, in its development. It also allows one to regard the subject from different points of view, and it is the algebraic standpoint which has been chosen in this tract as the most suitable one for a first introduction to the subject. The aim has been to develop the beginnings of the theory of Lie groups, especially the fundamental theorems of Lie relating the group to its infinitesimal generators (the Lie algebra); this account occupies the first five chapters. Next to Lie's theorems in importance come the basic properties of subgroups and homomorphisms, and they form the content of Chapter VI. The final chapter, on the universal covering group, could perhaps be most easily dispensed with, but, it is hoped, justifies its existence by bringing back into circulation Schreier's elegant method of constructing covering groups.

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.

The Overcoming Series offers step-by-step guides to self-improvement based on the methods of cognitive behavioral therapy. The series aims to help readers conquer a broad range of disabling condition

The Overcoming Series offers step-by-step guides to self-improvement based on the methods of cognitive behavioral therapy. The series aims to help readers conquer a broad range of disabling condition

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

The art of bending wood confounds most woodworkers, yet it is surprisingly easy to do with the four basic methods in this complete guide. The techniques are presented in step-by-step photo sequences t

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

The Overcoming Series offers step-by-step guides to self-improvement based on the methods of cognitive behavioral therapy. The series aims to help readers conquer a broad range of disabling condition

The Overcoming Series offers step-by-step guides to self-improvement based on the methods of cognitive behavioral therapy. The series aims to help readers conquer a broad range of disabling condition

The problem of detecting abrupt changes in the behavior of an observed signal or time series arises in a variety of fields, including climate modeling, finance, image analysis, and security. Quickest detection refers to real-time detection of such changes as quickly as possible after they occur. Using the framework of optimal stopping theory, this book describes the fundamentals underpinning the field, providing the background necessary to design, analyze, and understand quickest detection algorithms. For the first time the authors bring together results which were previously scattered across disparate disciplines, and provide a unified treatment of several different approaches to the quickest detection problem. This book is essential reading for anyone who wants to understand the basic statistical procedures for change detection from a fundamental viewpoint, and for those interested in theoretical questions of change detection. It is ideal for graduate students and researchers of engi

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.

A truly interdisciplinary clinical text, Clinical Neuroradiology investigates the structure-function relationship for major CNS diseases, illustrated by considering actual clinical cases. Authored by a leading neuroradiologist, this landmark publication provides neuroradiologists with clinical neurological correlates and neurologists with imaging correlates for all key neurological conditions. Organised by brain region, each chapter contains an introductory section of clinically relevant neuroanatomy followed by a series of case studies giving: • Brief history and summary of findings • Differential diagnosis • Imaging findings, related to clinical deficits • Pertinent neuronal circuits, neurochemistry and neurogenetics • Basic therapeutic approaches to each syndrome Due to its utility in demonstrating structural-functional correlates, a separate chapter on stroke is included. Lavishly illustrated with images from all modalities and outstanding anatomical diagrams rendered in true radi

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.