Basic Methods of Linear Functional Analysis

Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.

Describing two cornerstones of mathematics, this basic textbook presents a unified approach to algebra and geometry. It covers the ideas of complex numbers, scalar and vector products, determinants, linear algebra, group theory, permutation groups, symmetry groups and aspects of geometry including groups of isometries, rotations, and spherical geometry. The book emphasises the interactions between topics, and each topic is constantly illustrated by using it to describe and discuss the others. Many ideas are developed gradually, with each aspect presented at a time when its importance becomes clearer. To aid in this, the text is divided into short chapters, each with exercises at the end. The related website features an HTML version of the book, extra text at higher and lower levels, and more exercises and examples. It also links to an electronic maths thesaurus, giving definitions, examples and links both to the book and to external sources.

Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

Quantile regression is gradually emerging as a unified statistical methodology for estimating models of conditional quantile functions. By complementing the exclusive focus of classical least squares regression on the conditional mean, quantile regression offers a systematic strategy for examining how covariates influence the location, scale and shape of the entire response distribution. This monograph is the first comprehensive treatment of the subject, encompassing models that are linear and nonlinear, parametric and nonparametric. The author has devoted more than 25 years of research to this topic. The methods in the analysis are illustrated with a variety of applications from economics, biology, ecology and finance. The treatment will find its core audiences in econometrics, statistics, and applied mathematics in addition to the disciplines cited above.

Recent advances in computational power are now enabling scientists to consider problems of population dynamics at an advanced level. The small bodies of our solar system, the planets around other stars, dust belts, space debris, etc., need to be understood as a a whole, with their collective dynamical evolution, stability and instability, order and chaos, aggregations and impacts. Important results on specific populations of celestial bodies, in addition to new methods of computation and analysis, have been obtained in the last few years. Scientists from 21 countries convened for the Colloquium "Dynamics of Populations of Planetary Systems", sponsored by the International Astronomical Union, in Belgrade (Serbia and Monte Negro). This proceedings volume reviews current understanding of the field, and is a valuable resource for professional astronomers and planetary scientists.

This introductory 2005 text on air-breathing jet propulsion focuses on the basic operating principles of jet engines and gas turbines. Previous coursework in fluid mechanics and thermodynamics is elucidated and applied to help the student understand and predict the characteristics of engine components and various types of engines and power gas turbines. Numerous examples help the reader appreciate the methods and differing, representative physical parameters. A capstone chapter integrates the text material into a portion of the book devoted to system matching and analysis so that engine performance can be predicted for both on- and off-design conditions. The book is designed for advanced undergraduate and first-year graduate students in aerospace and mechanical engineering. A basic understanding of fluid dynamics and thermodynamics is presumed. Although aircraft propulsion is the focus, the material can also be used to study ground- and marine-based gas turbines and turbomachinery and

This book is targeted to graduate students and researchers at the cutting edge of investigations into the fundamental nature of multiphase flows. It is intended as a reference book for the basic methods used in the treatment of multiphase flows. The subject of multiphase flows encompasses a vast field, a host of different technological contexts, a wide spectrum of different scales, a broad range of engineering disciplines, and a multitude of different analytical approaches. The aim of Fundamentals of Multiphase Flow is to bring much of this fundamental understanding together into one book, presenting a unifying approach to the fundamental ideas of multiphase flows. The book summarizes those fundamental concepts with relevance to a broad spectrum of multiphase flows. It does not pretend to present a comprehensive review of the details of any one multiphase flow or technological context; references to such reviews are included where appropriate.

Health and Long Life: The Chinese Way brings together the wide variety of Chinese medical and spiritual methods in one integrated volume. It provides not only a basic description, but also discusses

This is the 2005 second edition of a highly successful and well-respected textbook on the numerical techniques used to solve partial differential equations arising from mathematical models in science, engineering and other fields. The authors maintain an emphasis on finite difference methods for simple but representative examples of parabolic, hyperbolic and elliptic equations from the first edition. However this is augmented by new sections on finite volume methods, modified equation analysis, symplectic integration schemes, convection-diffusion problems, multigrid, and conjugate gradient methods; and several sections, including that on the energy method of analysis, have been extensively rewritten to reflect modern developments. Already an excellent choice for students and teachers in mathematics, engineering and computer science departments, the revised text includes more latest theoretical and industrial developments.

Written by some of the leading figures in the fields of conversation analysis, discursive psychology and ethnomethodology, this book looks at the challenging implications of discourse-based approaches to the topic of cognition. This volume shows how cognition can be reworked using analyses of engaging examples of real life interaction such as conversations between friends, relationship counselling sessions and legal hearings. It includes an extended introduction that overviews the history and context of cognitive research and its basic assumptions to provide a frame for understanding the specific examples discussed, as well as surveying cutting edge debates about discourse and cognition. This comprehensive and accessible book opens up important ways of understanding the relation between language and cognition.

Written by some of the leading figures in the fields of conversation analysis, discursive psychology and ethnomethodology, this book looks at the challenging implications of discourse-based approaches to the topic of cognition. This volume shows how cognition can be reworked using analyses of engaging examples of real life interaction such as conversations between friends, relationship counselling sessions and legal hearings. It includes an extended introduction that overviews the history and context of cognitive research and its basic assumptions to provide a frame for understanding the specific examples discussed, as well as surveying cutting edge debates about discourse and cognition. This comprehensive and accessible book opens up important ways of understanding the relation between language and cognition.

A new and incisive analysis of the political viability of human rights, with an in-depth investigation of its largest violation: world hunger. Gonzalez-Pelaez develops John Vincent's theory of basic h

Hands-on researchers describe in step-by-step detail 73 proven laboratory methods and bioinformatics tools essential for analysis of the proteome. These cutting-edge techniques address such important

This practical handbook guides readers through the various tools, methods of analysis and research skills needed for studying local churches. It is aimed at final year undergraduates, Masters level st

This book covers the all-important basic rules of grammar. The correct methods ofgrammar are shown, and common errors are explored in a very approachable way. A lively cast of cartoon character

An Introduction to Glass Science and Technology presents the fundamental topics in glass science and technology including glass formation, crystallisation and phase separation. A detailed discussion of glass structure models with emphasis on the oxygen balance model is also presented. This expanded second edition also includes new chapters on the compositions and properties of commercial glasses and thermal analysis of glasses and melts. Exercises are included at the end of the chapters.This introductory text is ideal for undergraduates in materials science, ceramics or inorganic chemistry. It will also be useful to the engineer or scientist seeking basic knowledge of the formation, properties and production of glass.

This engaging 2005 introduction offers a critical approach to discourse, written by an expert uniquely placed to cover the subject for a variety of disciplines. Organised along thematic lines, the book begins with an outline of the basic principles, moving on to examine the methods and theory of CDA (critical discourse analysis). It covers topics such as text and context, language and inequality, choice and determination, history and process, ideology and identity. Blommaert focuses on how language can offer a crucial understanding of wider aspects of power relations, arguing that critical discourse analysis should specifically be an analysis of the 'effects' of power, what power does to people, groups and societies, and how this impact comes about. Clearly argued, this concise introduction will be welcomed by students and researchers in a variety of disciplines involved in the study of discourse, including linguistics, linguistic anthropology and the sociology of language.

What does Google's management of billions of Web pages have in common with analysis of a genome with billions of nucleotides? Both apply methods that coordinate many processors to accomplish a single

The Metaphysics of Apes, first published in 2005, traces the discovery and interpretation of the human-like great apes and the ape-like earliest ancestors of present-day humans. It shows how, from the days of Linnaeus to recent research, the sacred and taboo-ridden animal-human boundary was time and again challenged and adjusted. The unique dignity of humans, a central idea and value in the West, was, and to some extent still is, centrally on the minds of taxonomists, ethnologists, primatologists, and archaeologists. It has guided their research to a considerable extent. The basic presupposition was that humans are not entirely part of nature but, as symbolizing minds and as moral persons, transcend nature. This book was the first to offer an anthropological analysis of the burgeoning anthropological disciplines in terms of their own cultural taboos and philosophical preconceptions.

The Metaphysics of Apes, first published in 2005, traces the discovery and interpretation of the human-like great apes and the ape-like earliest ancestors of present-day humans. It shows how, from the days of Linnaeus to recent research, the sacred and taboo-ridden animal-human boundary was time and again challenged and adjusted. The unique dignity of humans, a central idea and value in the West, was, and to some extent still is, centrally on the minds of taxonomists, ethnologists, primatologists, and archaeologists. It has guided their research to a considerable extent. The basic presupposition was that humans are not entirely part of nature but, as symbolizing minds and as moral persons, transcend nature. This book was the first to offer an anthropological analysis of the burgeoning anthropological disciplines in terms of their own cultural taboos and philosophical preconceptions.

Organized thematically, this introduction outlines the basic principles and moves on to examine the methods and theory of CDA (critical discourse analysis). Topics covered include text and context, la

Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of

The description of solids at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. It is impossible to solve the corresponding many-body problems analytically or numerically, although much insight can be gained from the analysis of simplified models. An important example is the Hubbard model, which describes interacting electrons in narrow energy bands, and which has been applied to problems as diverse as high-Tc superconductivity, band magnetism, and the metal-insulator transition. This book presents a coherent, self-contained account of the exact solution of the Hubbard model in one dimension. The early chapters will be accessible to beginning graduate students with a basic knowledge of quantum mechanics and statistical mechanics. The later chapters address more advanced topics, and are intended as a guide for researchers to some of the more topical results in the field of integrable models.

Morphometrics has undergone a revolutionary transformation in the past two decades as new methods have been developed to address shortcomings in the traditional multivirate analysis of linear distance

This book focuses on developments in experimental methods, theory, modeling and HV technology through the past decade. The coverage includes advances in basic understanding and capability, for instan

This book covers both basic elements and the state-of-the-art in applications of proteomics. The first section gives an introduction to the field, from differential approaches to functional proteomics

In recent years the subtlety and complexity of Apollonius' Argonautica have been better appreciated, but in Dr Hunter's view the purposes and aesthetic of the epic are still not readily understood and much basic analysis remains to be done. The present book seeks to offer some of that analysis and to place the Argonautica within its social and intellectual context. A series of studies deal with notions of heroism; with eros and the suffering of Medea; the role of the divine; poetic voice and literary self-consciousness; and the Ptolemaic context of the poem. A pervasive theme of the book is Apollonius' creative engagement with Homer, and a final chapter sketches out an approach to Virgil's use of Apollonius in the Aeneid. The Argonautica emerges as a brilliant and original experiment. This book is the only advanced study of the Argonautica currently available. All Greek is translated.

This is the second volume of a two-volume translation of Heinrich Schenker's Der Tonwille (1921-24). Among the foremost music theorists of the twentieth century, Schenker's methods of analysis continu

Many practical applications require the reconstruction of a multivariate function from discrete, unstructured data. This book gives a self-contained, complete introduction into this subject. It concentrates on truly meshless methods such as radial basis functions, moving least squares, and partitions of unity. The book starts with an overview on typical applications of scattered data approximation, coming from surface reconstruction, fluid-structure interaction, and the numerical solution of partial differential equations. It then leads the reader from basic properties to the current state of research, addressing all important issues, such as existence, uniqueness, approximation properties, numerical stability, and efficient implementation. Each chapter ends with a section giving information on the historical background and hints for further reading. Complete proofs are included, making this perfectly suited for graduate courses on multivariate approximation and it can be used to suppo

A state-of-the-art collection of readily reproducible laboratory methods for DNA identity analysis, including Y chromosome haplotyping, mtDNA, and SNP typing. The book offers well-tested protocols fo

Modeling and Control of Dynamic Systems teaches the basic concepts of control systems analysis and design. The book first focuses on understanding the basic building blocks of the dynamic systems surr

This volume offers a new view of Joseph Haydn's instrumental music. It argues that many of Haydn's greatest and most characteristic instrumental works are 'through-composed' in the sense that their several movements are bound together into a cycle. This cyclic integration is articulated, among other ways, by the 'progressive' form of individual movements, structural and gestural links between the movements, and extramusical associations. Central to the study is a detailed and comprehensive analysis of the 'Farewell' Symphony, No. 45 in F sharp minor (1772). The analysis is distinguished by its systematic use of different methods (Toveyan formalism, Schenkerian voice leading, Schoenbergian developing variation) to elucidate the work's overall coherence. The work's unique musical processes, in turn, suggest an interpretation of the entire piece (not merely the famous 'farewell' finale) in terms of the familiar programmatic story of the musicians' wish to leave Castle Eszterhaza. In a boo

This book teaches basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Cov

Crowley's pragmatic analysis has three basic purposes: to show why theory developed in academia is too little used off campus; to explore why it's in the interests of library faculty members, consulta

The Economics of Information Technology is a concise and accessible review of some of the important economic factors affecting information technology industries. These industries are characterized by high fixed costs and low marginal costs of production, large switching costs for users, and strong network effects. These factors combine to produce some unique behavior. The book consists of two parts. In the first part, Professor Varian outlines the basic economics of these industries. In the second part, Professors Farrell and Shapiro describe the impact of these factors on competition policy. The clarity of the analysis and exposition makes this an ideal introduction for undergraduate and graduate students in economics, business strategy, law and related areas.

The Economics of Information Technology is a concise and accessible review of some of the important economic factors affecting information technology industries. These industries are characterized by high fixed costs and low marginal costs of production, large switching costs for users, and strong network effects. These factors combine to produce some unique behavior. The book consists of two parts. In the first part, Professor Varian outlines the basic economics of these industries. In the second part, Professors Farrell and Shapiro describe the impact of these factors on competition policy. The clarity of the analysis and exposition makes this an ideal introduction for undergraduate and graduate students in economics, business strategy, law and related areas.

In 1989, Michael Rabin proposed a fundamentally new approach to the problems of fault-tolerant routing and memory management in parallel computation, based on the idea of information dispersal. Yuh-Dauh Lyuu developed this idea in a number of new and exciting ways in his PhD thesis. Further work has led to extensions of these methods to other applications such as shared memory emulations. This volume presents an extended and updated printing of Lyuu's thesis. It gives a detailed treatment of the information dispersal approach to the problems of fault-tolerance and distributed representations of information which have resisted rigorous analysis by previous methods.

This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-conta

Take an in-depth, how-to look at Forex trading using the methods, analysis, and insights of a renowned trader, Raghee Horner. As the fate of the dollar against foreign currency generates both anxiety

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.