Basic Methods of Linear Functional Analysis

A comprehensive survey of all the mathematical methods that should be available to graduate students in physics. In addition to the usual topics of analysis, such as infinite series, functions of a co

An analysis of what many considered to be FDR's failure to rescue imperiled Jewish Europeans during World War II challenges beliefs that depict the president as anti-Semitic, drawing on extensive rese

This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral eq

This work deals with basic theory for design and analysis of low-probability-of-intercept radar systems. Drawing on research he conducted at the International Research Center for Telecommunications an

The theory of elliptic complexes of linear partial differential operators is closely interwoven with complex analysis. In particular, the Dolbeault complex is at the same time an important example of

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,

Spline functions are universally recognized as highly effective tools in approximation theory, computer-aided geometric design, image analysis, and numerical analysis. The theory of univariate splines is well known but this text is the first comprehensive treatment of the analogous bivariate theory. A detailed mathematical treatment of polynomial splines on triangulations is outlined, providing a basis for developing practical methods for using splines in numerous application areas. The detailed treatment of the Bernstein-Bézier representation of polynomials will provide a valuable source for researchers and students in CAGD. Chapters on smooth macro-element spaces will allow engineers and scientists using the FEM method to solve partial differential equations numerically with new tools. Workers in the geosciences will find new tools for approximation and data fitting on the sphere. Ideal as a graduate text in approximation theory, and as a source book for courses in computer-aided geo

Over the last thirty years there has been extensive use of continuous time econometric methods in macroeconomic modelling. This monograph presents a continuous time macroeconometric model of the United Kingdom incorporating stochastic trends. Its development represents a major step forward in continuous time macroeconomic modelling. The book describes the model in detail and, like earlier models, it is designed in such a way as to permit a rigorous mathematical analysis of its steady-state and stability properties, thus providing a valuable check on the capacity of the model to generate plausible long-run behaviour. The model is estimated using newly developed exact Gaussian estimation methods for continuous time econometric models incorporating unobservable stochastic trends. The book also includes discussion of the application of the model to dynamic analysis and forecasting.

This book examines the economic bases of regional sovereignty movements in the Russian Federation from 1990–1993. The analysis is based on an original data set of Russian regional sovereignty movements and the author employs a variety of methods including quantitative statistical analysis, as well as qualitative case studies of Sverdlovsk and Samara oblasts using systematic content analysis of local newspaper articles. The central finding of the book is that variation in Russian regional activism is explained not by differences in economic conditions but by differences in the construction or imagination of economic interests; to put it in the language of other contemporary debates, economic advantage and disadvantage are as imagined as nations. In arguing that regional economic interests are inter-subjective, contingent, and institutionally specific, the book addresses a major question in political economy, namely the origin of economic interests. In addition, by engaging the national

First published in 2007, this second edition describes the computational methods used in theoretical physics. New sections were added to cover finite element methods and lattice Boltzmann simulation, density functional theory, quantum molecular dynamics, Monte Carlo simulation, and diagonalisation of one-dimensional quantum systems. It covers many different areas of physics research and different computational methodologies, including computational methods such as Monte Carlo and molecular dynamics, various electronic structure methodologies, methods for solving partial differential equations, and lattice gauge theory. Throughout the book the relations between the methods used in different fields of physics are emphasised. Several new programs are described and can be downloaded from www.cambridge.org/9781107677135. The book requires a background in elementary programming, numerical analysis, and field theory, as well as undergraduate knowledge of condensed matter theory and statistica

A self-contained, contemporary treatment of the analysis of long-range dependent data Long-Memory Time Series: Theory and Methods provides an overview of the theory and methods developed to deal with

The modelling of ocean circulation is important not only for its own sake, but also in terms of the prediction of weather patterns and the effects of climate change. This 2007 book introduces the basic computational techniques necessary for all models of the ocean and atmosphere, and the conditions they must satisfy. It describes the workings of ocean models, the problems that must be solved in their construction, and how to evaluate computational results. Major emphasis is placed on examining ocean models critically, and determining what they do well and what they do poorly. Numerical analysis is introduced as needed, and exercises are included to illustrate major points. Developed from notes for a course taught in physical oceanography at the College of Oceanic and Atmospheric Sciences at Oregon State University, this book is ideal for graduate students of oceanography, geophysics, climatology and atmospheric science, and researchers in oceanography and atmospheric science.

Since the baseball statistics revolution began in the 1970s, no one had written the book that reveals, across every area of strategy and management, how the best practitioners of statistical analysis

This book offers a major reassessment of Leibniz's metaphysics. Christia Mercer has exposed the underlying doctrines of Leibniz's philosophy. By analysing Leibniz's early works she demonstrates that the metaphysics of pre-established harmony developed many years earlier than previously believed and for reasons which have not been understood. As a result of this analysis she has unearthed a philosophical school that Leibniz scholars have not recognized. A much deeper understanding of some of Leibniz's key doctrines emerges. Moreover, since the Leibniz that is revealed here does not fit neatly into the standard accounts of the history of philosophy and science, Christia Mercer's study will prompt scholars to reconsider their basic assumptions about early modern philosophy and science.

The book introduces most of the basic tools of chemometrics including experimental design, signal analysis, statistical methods for analytical chemistry and multivariate methods. It then discusses a n

The statistical bootstrap is one of the methods that can be used to calculate estimates of a certain number of unknown parameters of a random process or a signal observed in noise, based on a random sample. Such situations are common in signal processing and the bootstrap is especially useful when only a small sample is available or an analytical analysis is too cumbersome or even impossible. This book covers the foundations of the bootstrap, its properties, its strengths and its limitations. The authors focus on bootstrap signal detection in Gaussian and non-Gaussian interference as well as bootstrap model selection. The theory developed in the book is supported by a number of useful practical examples written in MATLAB. The book is aimed at graduate students and engineers, and includes applications to real-world problems in areas such as radar and sonar, biomedical engineering and automotive engineering.

This book was first published in 2007, a time of enormous change in the field of optical spectrometry. Although the basic optical principles remained unchanged, the design considerations were very different and, in many cases, more demanding. Developments in computer ray-tracing and computer-aided design coped with the extra impositions and allowed the construction of a new generation of spectrographs. The book covers the general principles of spectrographic design at the time, and the practical and engineering aspects of a broad range of spectrographs and spectrometers. The book deals with materials and methods of construction and includes suggestions for the choice of optical table, the design of slit mechanisms, and adjustable mirror, grating and lens mounts, with suggestions for the alignment and calibration of the finished instrument.

There are forty-one problematic play texts, variously classified as 'bad quartos' or 'memorial reconstructions', from Shakespeare's time. Textual criticism of these quartos has been fraught with assumption and contradiction. Laurie Maguire examines all the texts in detail. She deconstructs the theories of W. W. Greg and his followers, scrutinizing the methods by which critics diagnose texts as 'bad', and examines the historical evidence for the concept of memorial reconstruction (compilation from the recollection of actors or spectators). The valuable contextual material includes fresh analysis of the New Bibliographers, the rise of English studies, Renaissance oral culture and textual problems in non-suspect texts. The assembly of textual information about all the suspect texts in tabular form makes the book an essential reference work. The result is a study which covers a vast textual subject without sacrificing detail.

The study of vibration in physical systems is central to almost all fields in physics and engineering. This work, originally published in two volumes, examines the classical aspects in Part I and the quantum oscillator in Part II. The classical linear vibrator is treated first and the underlying unity of all linear oscillations in electrical, mechanical and acoustic systems is emphasized. The treatment of nonlinear vibrations, a field with which engineers and physicists are generally less familiar, is then examined. Part II then concentrates on quantum systems, looking at the vibrations in atoms and molecules and their interaction with electromagnetic radiation. The similarities of classical and quantum methods are stressed and the limits of the classical treatment are examined. Throughout the book, each phenomenon discussed is well illustrated with many examples; and theory and experiment are compared. This is a useful introduction to the more advanced mathematical treatment of vibrat

THIS VOLUME, LIKE THOSE PRIOR TO IT, FEATURES CHAPTERS BY EXPERTS IN VARIOUS FIELDS OF COMPUTATIONAL CHEMISTRY. Volume 23 COVERS LINEAR SCALING METHODS FOR QUANTUM CHEMISTRY, VARIATIONAL TRANSITION ST

The classical theory of stochastic processes has important applications arising from the need to describe irreversible evolutions in classical mechanics; analogously quantum stochastic processes can be used to model the dynamics of irreversible quantum systems. Noncommutative, i.e. quantum, geometry provides a framework in which quantum stochastic structures can be explored. This book is the first to describe how these two mathematical constructions are related. In particular, key ideas of semigroups and complete positivity are combined to yield quantum dynamical semigroups (QDS). Sinha and Goswami also develop a general theory of Evans-Hudson dilation for both bounded and unbounded coefficients. The unique features of the book, including the interaction of QDS and quantum stochastic calculus with noncommutative geometry and a thorough discussion of this calculus with unbounded coefficients, will make it of interest to graduate students and researchers in functional analysis, probabili

Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturer

This book is an introductory manual that explains the basic concepts of chemistry behind scientific analytical techniques and that reviews their application to archaeology. It explains key terminology, outlines the procedures to be followed in order to produce good data, and describes the function of the basic instrumentation required to carry out those procedures. The manual contains chapters on the basic chemistry and physics necessary to understand the techniques used in analytical chemistry, with more detailed chapters on Atomic Absorption, Inductively Coupled Plasma Emission Spectroscopy, Neutron Activation Analysis, X-ray Flourescence, Electron Microscopy, Infra-red and Raman Spectroscopy, and Mass Spectrometry. Each chapter describes the operation of the instruments, some hints on the practicalities, and a review of the application of the technique to archaeology, including some case studies. With guides to further reading on the topic, it is an essential tool for practitioners

This book is an introductory manual that explains the basic concepts of chemistry behind scientific analytical techniques and that reviews their application to archaeology. It explains key terminology, outlines the procedures to be followed in order to produce good data, and describes the function of the basic instrumentation required to carry out those procedures. The manual contains chapters on the basic chemistry and physics necessary to understand the techniques used in analytical chemistry, with more detailed chapters on Atomic Absorption, Inductively Coupled Plasma Emission Spectroscopy, Neutron Activation Analysis, X-ray Flourescence, Electron Microscopy, Infra-red and Raman Spectroscopy, and Mass Spectrometry. Each chapter describes the operation of the instruments, some hints on the practicalities, and a review of the application of the technique to archaeology, including some case studies. With guides to further reading on the topic, it is an essential tool for practitioners

Virginia Woolf, the Intellectual, and the Public Sphere relates Woolf's literary reviews and essays to early twentieth-century debates about the value of 'highbrow' culture, the methods of instruction in universities and adult education, and the importance of an educated public for the realization of democratic goals. By focusing on Woolf's theories and practice of reading, Melba Cuddy-Keane refutes assumptions about Woolf's modernist elitism, revealing instead a writer who was pedagogically oriented, publicly engaged and committed to the ideal of classless intellectuals working together in reciprocal exchange. Woolf emerges as a stimulating theorist of the unconscious, of dialogic reading, of historicist criticism and of value judgments, while her theoretically informed but accessible prose challenges us to reflect on academic writing today. Combining a wealth of historical detail with a penetrating analysis of Woolf's essays, this 2003 study will alter our views of Woolf, of modernis

This concise text introduces students to the elements of analytical geometry, covering basic ideas and methods. Topics include transformation of axes, the line at infinity, conics and pencils of conic

The world's marine fisheries are in trouble, as a direct result of overfishing and the overcapacity of fishing fleets. Despite intensive management efforts, the problems still persist in many areas, resulting in many fisheries being neither sustainable nor profitable. Using bio-economic models of commercial fisheries, this book demonstrates that new management methods, based on individual or community catch quotas, are required to resolve the overfishing problem. Uncertainty about marine systems may be another factor contributing to overfishing. Methods of decision analysis and Bayesian inference are used to discuss risk management and the precautionary principle, arguing that extensive marine reserves may be the best way to protect fisheries, alongside a controlled catch quota system. This book will be of interest to environmental scientists, economists and fisheries managers, providing novel insights into many well-known but poorly understood aspects of fisheries management.

The world's marine fisheries are in trouble, as a direct result of overfishing and the overcapacity of fishing fleets. Despite intensive management efforts, the problems still persist in many areas, resulting in many fisheries being neither sustainable nor profitable. Using bio-economic models of commercial fisheries, this book demonstrates that new management methods, based on individual or community catch quotas, are required to resolve the overfishing problem. Uncertainty about marine systems may be another factor contributing to overfishing. Methods of decision analysis and Bayesian inference are used to discuss risk management and the precautionary principle, arguing that extensive marine reserves may be the best way to protect fisheries, alongside a controlled catch quota system. This book will be of interest to environmental scientists, economists and fisheries managers, providing novel insights into many well-known but poorly understood aspects of fisheries management.

Political Game Theory is a self-contained introduction to game theory and its applications to political science. The book presents choice theory, social choice theory, static and dynamic games of complete information, static and dynamic games of incomplete information, repeated games, bargaining theory, mechanism design and a mathematical appendix covering, logic, real analysis, calculus and probability theory. The methods employed have many applications in various disciplines including comparative politics, international relations and American politics. Political Game Theory is tailored to students without extensive backgrounds in mathematics, and traditional economics, however there are also many special sections that present technical material that will appeal to more advanced students. A large number of exercises are also provided to practice the skills and techniques discussed.

Aimed at an audience of researchers and graduate students in computational geometry and algorithm design, this book uses the Geometric Spanner Network Problem to showcase a number of useful algorithmic techniques, data structure strategies, and geometric analysis techniques with many applications, practical and theoretical. The authors present rigorous descriptions of the main algorithms and their analyses for different variations of the Geometric Spanner Network Problem. Though the basic ideas behind most of these algorithms are intuitive, very few are easy to describe and analyze. For most of the algorithms, nontrivial data structures need to be designed, and nontrivial techniques need to be developed in order for analysis to take place. Still, there are several basic principles and results that are used throughout the book. One of the most important is the powerful well-separated pair decomposition. This decomposition is used as a starting point for several of the spanner constructi

This 2007 book provides a systematic and self-contained account of the fast-developing theory of complex social networks. Social networks are central to the understanding of most socio-economic phenomena in the modern world. The classical approach to studying them relies on a methodology that abstracts from their size and complexity. In contrast, the approach taken in this book keeps complexity at the core, whilst integrating it with the incentive considerations that are preeminent in traditional economic analysis. The treatment starts with a detailed discussion of the basic models that act as 'benchmarks' for the complex-network literature: random networks, small worlds, and scale-free networks, before studying three different forces that underlie almost all network phenomena in social contexts: diffusion, search, and play. Finally, these forces are combined into a unified framework that is brought to bear on the issue of network formation and the coevolution of agents' behaviour and

Peak signal power is an important factor in the implementation of multicarrier (MC) modulation schemes, like OFDM, in wireless and wireline communication systems. This 2007 book describes tools necessary for analyzing and controlling the peak-to-average power ratio in MC systems, and how these techniques are applied in practical designs. The author starts with an overview of multicarrier signals and basic tools and algorithms, before discussing properties of MC signals in detail: discrete and continuous maxima; statistical distribution of peak power; codes with constant peak-to-average power ratio are all covered, concluding with methods to decrease peak power in MC systems. Current knowledge, problems, methods and definitions are summarized using rigorous mathematics, with an overview of the tools for the engineer. The book is aimed at graduate students and researchers in electrical engineering, computer science and applied mathematics, and practitioners in the telecommunications indu

Methods from contact and symplectic geometry can be used to solve highly non-trivial nonlinear partial and ordinary differential equations without resorting to approximate numerical methods or algebraic computing software. This book explains how it's done. It combines the clarity and accessibility of an advanced textbook with the completeness of an encyclopedia. The basic ideas that Lie and Cartan developed at the end of the nineteenth century to transform solving a differential equation into a problem in geometry or algebra are here reworked in a novel and modern way. Differential equations are considered as a part of contact and symplectic geometry, so that all the machinery of Hodge-deRham calculus can be applied. In this way a wide class of equations can be tackled, including quasi-linear equations and Monge-Ampere equations (which play an important role in modern theoretical physics and meteorology).

This book presents state-of-the-art analytical methods from statistics and data mining for the analysis of high-throughput data from genomics and proteomics. It adopts an approach focusing on concept

A good grasp of the theory of structures - the theoretical basis by which the strength, stiffness and stability of a building can be understood - is fundamental to structural engineers and architects. Yet most modern structural analysis and design is carried out by computer, with the user isolated from the processes in action. This book provides a broad introduction to the mathematics behind a range of structural processes. The basic structural equations have been known for at least 150 years, but modern plastic theory has opened up a fundamentally new way of advancing structural theory. Paradoxically, the powerful plastic theorems can be used to examine 'classic' elastic design activity, and strong mathematical relationships exist between these two approaches. Some of the techniques used in this book may be familiar to the reader, and some may not, but each of the topics examined will give the structural engineer valuable insight into the basis of the subject. This lucid volume provid

Where did SARS come from? Have we inherited genes from Neanderthals? How do plants use their internal clock? The genomic revolution in biology enables us to answer such questions. But the revolution would have been impossible without the support of powerful computational and statistical methods that enable us to exploit genomic data. Many universities are introducing courses to train the next generation of bioinformaticians: biologists fluent in mathematics and computer science, and data analysts familiar with biology. This readable and entertaining book, based on successful taught courses, provides a roadmap to navigate entry to this field. It guides the reader through key achievements of bioinformatics, using a hands-on approach. Statistical sequence analysis, sequence alignment, hidden Markov models, gene and motif finding and more, are introduced in a rigorous yet accessible way. A companion website provides the reader with Matlab-related software tools for reproducing the steps de

Advances in experimental methods have resulted in the generation of enormous volumes of data across the life sciences. Hence clustering and classification techniques that were once predominantly the domain of ecologists are now being used more widely. This 2006 book provides an overview of these important data analysis methods, from long-established statistical methods to more recent machine learning techniques. It aims to provide a framework that will enable the reader to recognise the assumptions and constraints that are implicit in all such techniques. Important generic issues are discussed first and then the major families of algorithms are described. Throughout the focus is on explanation and understanding and readers are directed to other resources that provide additional mathematical rigour when it is required. Examples taken from across the whole of biology, including bioinformatics, are provided throughout the book to illustrate the key concepts and each technique's potential.

This second volume of essays in Chopin Studies contains Chopin research by twelve leading scholars. Three main topics are addressed: reception history, aesthetics and criticism, and performance studies. The first four chapters investigate certain images associated with Chopin during his lifetime and after his death: Chopin as classical composer, as salon composer, as modernist, as 'otherwordly', as androgyne. The next four essays contextualize and define aspects of his musical language, including narrative stuctures, baroque affinities, progressive tendencies and functional ambiguity. The last four deal with analysis and source study as related to performance, structure and expression, tempo rubato and 'authentic' interpretation. The book ends with a thumbnail sketch of Chopin as revealed in a recently discovered diary for 1847–8.

The characteristics of the basic elements and the cardiac functions will be highlighted in this volume. In their contributions, the authors concentrate on the analysis and integration of the interacti

In this sophisticated yet accessible analysis of the open economies of Sub-Saharan Africa, Jean-Paul Azam analyses international trade, exchange rate issues, and longer-term growth, taking due account of the distinctive features of African economies. In particular, he examines the informal as well as the formal institutional frameworks which prevail in different African countries and which affect their macroeconomic behaviour. Key issues explored include tariffs and quotas, membership of the CFA Zone, and currency convertibility or inconvertibility, as well as smuggling, corruption, parallel markets in goods and currencies, ethnic diversity and redistribution. Case studies of important macroeconomic events are used to establish basic stylized facts from which the theory emerges, and special attention is paid to the consequences of macroeconomic events for the poor, via the food market or traditional redistribution mechanisms.