Basic Methods of Linear Functional Analysis

Between 1814 and 1831, the great French mathematician A. L. Cauchy created practically single-handedly a new branch of pure mathematics. Complex function theory was and remains of central importance, and its creation marked the start of one of the most exciting periods in the development of mathematics. In this book Dr Smithies analyses the process whereby Cauchy created the basic structure of complex analysis, describing first the eighteenth-century background before proceeding to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem and his work on expansions in power series. Smithies describes how Cauchy overcame difficulties including false starts and contradictions brought about by over-ambitious assumptions, as well as the improvements that came about as the subject developed in Cauchy's hands. Controversies associated with the birth of complex function theory are described in detail. Throughout, new light is thrown on Cauchy's thinking during t

The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.

The book is an overview of the research on minimal surfaces of the last few years written by several renowned researchers. The methods used are taken from differential geometry, complex analysis, calc

Cell culture techniques are invaluable to the modern researcher but difficult to carry out successfully. As part of the series of Handbooks in Practical Animal Cell Biology, this volume offers a concise practical guide to the basic essentials of the technique. Researchers new to cell culture will find a clear explanation of the essential equipment of a tissue culture facility, including tissue culture media and sera. It describes methods for growing suspension and adhesion cultures, including how to store cells and prepare primary cultures from cells. For those already culturing cells, the handbook will act as a handy reference to the basic techniques. The essence of the book is to deal with the generalities of cell culture to give a grasp of the basic concepts before involvement in more specialized work in the field. Ideal for anyone moving into tissue cell culture techniques or looking for a concise reference book.

Cell culture techniques are invaluable to the modern researcher but difficult to carry out successfully. As part of the series of Handbooks in Practical Animal Cell Biology, this volume offers a concise practical guide to the basic essentials of the technique. Researchers new to cell culture will find a clear explanation of the essential equipment of a tissue culture facility, including tissue culture media and sera. It describes methods for growing suspension and adhesion cultures, including how to store cells and prepare primary cultures from cells. For those already culturing cells, the handbook will act as a handy reference to the basic techniques. The essence of the book is to deal with the generalities of cell culture to give a grasp of the basic concepts before involvement in more specialized work in the field. Ideal for anyone moving into tissue cell culture techniques or looking for a concise reference book.

This volume is a fascinating introduction to the core themes and basic methods of aesthetics and the philosophy of art. Providing an analytic and historical treatment of the issues, and including many

This volume is a fascinating introduction to the core themes and basic methods of aesthetics and the philosophy of art. Providing an analytic and historical treatment of the issues, and including many

In the late 1960s, Berlin and Kay argued that there are commonalities of basic colour term use that extend across languages and cultures, and probably express universal features of perception and cognition. In 1992, at the Asilomar Conference Centre, visual scientists and psychologists met with linguists and anthropologists for the first time to examine how these claims have fared in the light of current knowledge. To what extent can cross-cultural regularities be explained by the operation of the human visual system? What can the study of colour categorisation tell us about concept formation? Are the Berlin-Kay results an artifact of their methods? What tools have been and should be used to probe the structure of human colour categories? In this volume, which arose from that conference but also incorporates new work, a distinguished team of contributors survey key ideas, results and techniques from the study of human colour vision, as well as field methods and theoretical interpretati

Choice, Welfare and Measurement contains many of Amartya Sen's most important contributions to economic analysis and methods, including papers on individual and social choice, preference and rational

The twelve essays in this volume propose new directions in the analysis of class. John R. Hall argues that recent historical and intellectual developments require reworking basic assumptions about cl

This book provides an introduction to some aspects of the analytic theory of automorphic forms on G=SL2(R) or the upper-half plane X, with respect to a discrete subgroup G of G of finite covolume. The point of view is inspired by the theory of infinite dimensional unitary representations of G; this is introduced in the last sections, making this connection explicit. The topics treated include the construction of fundamental domains, the notion of automorphic form on G\G and its relationship with the classical automorphic forms on X, Poincare series, constant terms, cusp forms, finite dimensionality of the space of automorphic forms of a given type, compactness of certain convolution operators, Eisenstein series, unitary representations of G, and the spectral decomposition of L2 (G\G). The main prerequisites are some results in functional analysis (reviewed, with references) and some familiarity with the elementary theory of Lie groups and Lie algebras. Graduate students and researcher

Engineers and applied geophysicists routinely encounter interpolation and estimation problems when analysing data from field observations. Introduction to Geostatistics presents practical techniques for the estimation of spatial functions from sparse data. The author's unique approach is a synthesis of classic and geostatistical methods with a focus on the most practical linear minimum-variance estimation methods, and includes suggestions on how to test and extend the applicability of such methods. The author includes many useful methods (often not covered in other geostatistics books) such as estimating variogram parameters, evaluating the need for a variable mean, parameter estimation and model testing in complex cases (e.g. anisotropy, variable mean, and multiple variables), and using information from deterministic mathematical models. Well illustrated with exercises and worked examples taken from hydrogeology, Introduction to Geostatistics assumes no background in statistics and

In this volume, Charles Kindleberger makes a powerful case against the idea that any one model could be used to unlock the basic secret of economic history. It is essentially an exercise in methodology, addressed to economists and economic historians alike. He argues that too many economists discover a relationship or a uniformity in economic behaviour, develop a model, and use it to explain more than it is capable of, including, on occasion, all economic behaviour. These lectures discuss four 'laws' in economics to show how uniformities can illuminate economic history in particular aspects. They illustrate the view that the economist or economic historian seeking to test analysis against historical data should have a variety of different models, and not just one. The implication is that however scientific and technical the tools, choosing them carefully to fit particular circumstances is itself an art.

A self-contained introduction to magnetohydrodynamics (MHD), with emphasis on nonlinear processes. Chapters 2 to 4 outline the conventional aspects of MHD theory, magnetostatic equilibrium and linear stability theory, which form a natural basis for the topics in the subsequent chapters. The main part, chapters 5 to 7, presents nonlinear theory, starting with the evolutions and saturations of individual ideas and resistive instabilities, continuing with a detailed analysis of magnetic reconnection, and concluding with the most complex nonlinear behaviour, that of MHD turbulence. The last chapters describe three important applications of the theory: disruptive processes in tokamaks, MHD effects in reversed-field pinches, and solar flares. In the presentation the focus is more on physical mechanisms than on special formalisms. The book is essential reading for researchers and graduate students interested in MHD processes both in laboratory and in astrophysical plasmas.

The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.

The aim of this book is to provide the reader with a basic understanding of Fourier series, Fourier transforms and Laplace transforms. The book is an expanded and polished version of the authors' notes for a one semester course, for students of mathematics, electrical engineering, physics and computer science. Prerequisites for readers of this book are a basic course in both calculus and linear algebra. Otherwise the material is self-contained with numerous exercises and various examples of applications.

This book will show you the technique of star-hopping, or using the brighter stars and asterisms as guideposts on celestial paths to fainter stars or celestial objects. Twelve monthly star-hops form the heart of the book. Two or more tours are given for each month of the year. Each main hop is a step-by-step trip for you to follow. Taking these exciting tours reinforces the lessons of the methods of star-hopping. These celestial tours can be taken any time during the year. One chapter is devoted to the popular Messier Marathon. The book covers such techniques as reading star charts, finding celestial directions, telescopic types, and selecting and using light pollution reduction filters. Basic information is also given about what we know about the universe and the people who have made the discoveries, and the ancient mythology of the sky.

Stimulating, thought-provoking analysis of a number of the most interesting intellectual inconsistencies in mathematics, physics, and language. Delightful elucidations of methods for misunderstanding

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

Edited by two of the world's leading analysts of post communist politics, this book brings together distinguished specialists on Bosnia-Hercegovina, Croatia, Macedonia, Slovenia, Serbia/Montenegro, Albania, Bulgaria, and Romania. The authors analyse the challenge of building democracy in the countries of the former Yugoslavia riven by conflict, and in neighboring states. They focus on oppositional activity, political cultures that often favour strong presidentialism, the role of nationalism, and basic socioeconomic trends. Karen Dawisha and Bruce Parrott provide theoretical and comparative chapters on post communist political development across the region. This book will provide students and scholars with detailed analysis by leading authorities, plus the latest research data on recent political and economic developments in each country.

Recent achievements in sunlight concentration techniques have increased the potential of solar power as a viable source of renewable energy. Through its critical analysis of current methods, Photovolt

The Art and Science of Optical Design is a comprehensive introduction to lens design, covering the fundamental physical principles and key engineering issues. Several practical examples of modern computer-aided lens design are worked out in detail from start to finish. The basic theory and results of optics are presented early on in the book, along with a discussion of optical materials. Aberrations, and their correction, and image analysis are then covered in great detail. Subsequent chapters deal with design optimisation and tolerance analysis. Several design examples are then given, beginning with basic lens design forms, and progressing to advanced systems, such as gradient index and diffractive optical components. In covering all aspects of optical design, including the use of modern lens design software, this book will be invaluable to students of optical engineering as well as to anyone engaged in optical design at any stage.

The Art and Science of Optical Design is a comprehensive introduction to lens design, covering the fundamental physical principles and key engineering issues. Several practical examples of modern computer-aided lens design are worked out in detail from start to finish. The basic theory and results of optics are presented early on in the book, along with a discussion of optical materials. Aberrations, and their correction, and image analysis are then covered in great detail. Subsequent chapters deal with design optimisation and tolerance analysis. Several design examples are then given, beginning with basic lens design forms, and progressing to advanced systems, such as gradient index and diffractive optical components. In covering all aspects of optical design, including the use of modern lens design software, this book will be invaluable to students of optical engineering as well as to anyone engaged in optical design at any stage.

Lets you target the specific information you need quickly and easily -so you can stay in the lab and out of the library.This invaluable database -available in print and electronic form -gives you fast

Morphometrics is the statistical study of biological shape and shape change. Its richest data are landmarks, points such as 'the bridge of the nose' that have biological names as well as geometric locations. This book is the first systematic survey of morphometric methods for landmark data. The methods presented here combine conventional multivariate statistical analysis with themes from plane and solid geometry and from biomathematics to support biological insights into the features of many different organs and organisms. This book will be of value to applied statisticians and geometers, as well as to all biological and biomedical researchers who need quantitative analyses of information from biomedical images.

This book gives an introduction to theories of computability from a mathematically sophisticated point of view. It treats not only 'the' theory of computability (created by Alan Turing and others in the 1930s), but also a variety of other theories (of Boolean functions, automata and formal languages). These are addressed from the classical perspective of their generation by grammars and from the modern perspective as rational cones. The treatment of the classical theory of computable functions and relations takes the form of a tour through basic recursive function theory, starting with an axiomatic foundation and developing the essential methods in order to survey the most memorable results of the field. This authoritative account by one of the leading lights of the subject will prove exceptionally useful reading for graduate students, and researchers in theoretical computer science and mathematics.

This book is an introductory text on the combinatorial theory of finite geometry. It assumes only a basic knowledge of set theory and analysis, but soon leads the student to results at the frontiers of research. It begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes. The next part deals with polar spaces, partial geometries, and generalised quadrangles. The revised edition contains an entirely new chapter on blocking sets in linear spaces, which highlights some of the most important applications of blocking sets from the initial game-theoretic setting to their recent use in cryptography. Extensive exercises at the end of each chapter ensure the usefulness of this book for senior undergraduate and beginning graduate students.

This book is an introductory text on the combinatorial theory of finite geometry. It assumes only a basic knowledge of set theory and analysis, but soon leads the student to results at the frontiers of research. It begins with an elementary combinatorial approach to finite geometries based on finite sets of points and lines, and moves into the classical work on affine and projective planes. The next part deals with polar spaces, partial geometries, and generalised quadrangles. The revised edition contains an entirely new chapter on blocking sets in linear spaces, which highlights some of the most important applications of blocking sets from the initial game-theoretic setting to their recent use in cryptography. Extensive exercises at the end of each chapter ensure the usefulness of this book for senior undergraduate and beginning graduate students.

This book introduces the use of Lie algebra and differential geometry methods to study nonlinear integrable systems of Toda type. Many challenging problems in theoretical physics are related to the solution of nonlinear systems of partial differential equations. One of the most fruitful approaches in recent years has resulted from a merging of group algebraic and geometric techniques. The book gives a comprehensive introduction to this exciting branch of science. Chapters 1 and 2 review basic notions of Lie algebras and differential geometry with an emphasis on further applications to integrable nonlinear systems. Chapter 3 contains a derivation of Toda type systems and their general solutions based on Lie algebra and differential geometry methods. The last chapter examines explicit solutions of the corresponding equations. The book is written in an accessible 'lecture note' style with many examples and exercises to illustrate key points and to reinforce understanding.

Optical devices are employed in an ever-increasing range of applications, from simple lenses to complex fibre-optic communication networks. This book provides a detailed introduction to modern optical engineering, covering the fundamental concepts as well as practical techniques and applications. Basic optical principles are presented, particularly reflection, refraction, aberrations, diffraction and interference. Building on this foundation, a wide variety of optical devices and processes are then discussed, including simple optical instruments, photodetectors, spatial light modulators, holography and lasers. Two chapters are devoted to linear system transforms and signal processing, and the book concludes with a chapter on fibre optics. The book contains many worked examples and over 250 problems (solutions manual for instructors available from the publishers). It will be invaluable to electrical engineering and physics undergraduates taking courses in optical engineering, photonics,

The purpose of this book is to introduce Fourier descriptors as a method for measuring the shape of whole or parts of organisms. Fourier descriptors refer to the utilization of Fourier analysis, primarily the Fourier series as a curve-fitting technique, that can numerically describe the outline (shape) of irregular structures such as are commonly found in living organisms. The quantitative characterization of irregular forms is often a first step towards elucidation of the underlying biological processes, whether they be genetic, evolutionary, or functional. The first five chapters discuss the theory behind the use of Fourier descriptors and the remaining chapters show case studies of how they can be used in various fields of biology such as anatomy, cell biology, medicine and dentistry. This book is solely devoted to this subject and will be of interest to all those interested in biological morphometrics.

This book challenges standard accounts of early Christian exegesis of the Bible. Professor Young sets the interpretation of the Bible in the context of the Graeco-Roman world - the dissemination of books and learning, the way texts were received and read, the function of literature in shaping not only a culture but a moral universe. For the earliest Christians, the adoption of the Jewish scriptures constituted a supersessionary claim in relation to Hellenism as well as Judaism. Yet the debt owed to the practice of exegesis in the grammatical and rhetorical schools is of overriding significance. Methods were philological and deductive, and the usual analysis according to 'literal', 'typological' and 'allegorical' is inadequate to describe questions of reference and issues of religious language. The biblical texts shaped a 'totalizing discourse' which by the fifth century was giving identity, morality and meaning to a new Christian culture.

Mendelssohn's Philosophical Writings, published in 1761, bring the metaphysical tradition to bear on the topic of 'sentiments' (defined as knowledge or awareness by way of the senses). Mendelssohn offers a nuanced defence of Leibniz's theodicy and conception of freedom, an examination of the ethics of suicide, an account of the 'mixed sentiments' so central to the tragic genre, a hypothesis about weakness of will, an elaboration of the main principles and types of art, a definition of sublimity and analysis of its basic forms, and, lastly, a brief tract on probability theory, aimed at rebutting Hume's scepticism. This volume also includes the essay 'On Evidence in Metaphysical Sciences', selected in 1763 by the Berlin Royal Academy of Sciences over all other submitted essays, including one by Kant, as the best answer to the question of whether metaphysical sciences are capable of the same sort and degree of evidence as mathematics.

Mendelssohn's Philosophical Writings, published in 1761, bring the metaphysical tradition to bear on the topic of 'sentiments' (defined as knowledge or awareness by way of the senses). Mendelssohn offers a nuanced defence of Leibniz's theodicy and conception of freedom, an examination of the ethics of suicide, an account of the 'mixed sentiments' so central to the tragic genre, a hypothesis about weakness of will, an elaboration of the main principles and types of art, a definition of sublimity and analysis of its basic forms, and, lastly, a brief tract on probability theory, aimed at rebutting Hume's scepticism. This volume also includes the essay 'On Evidence in Metaphysical Sciences', selected in 1763 by the Berlin Royal Academy of Sciences over all other submitted essays, including one by Kant, as the best answer to the question of whether metaphysical sciences are capable of the same sort and degree of evidence as mathematics.

Successful traders know that before stepping into the wilderness of the speculative markets, you need a solid understanding of basic market behavior. But the conventional methods often fall short of p

Acquaints graduate students with basic ideas and methods of modern differential geometry and their applications in physics. Half of the chapters focus on local analysis, useful for graduate students o

The aim of this book is to develop the combinatorics of Young tableaux and to show them in action in the algebra of symmetric functions, representations of the symmetric and general linear groups, and the geometry of flag varieties. The first part of the book is a self-contained presentation of the basic combinatorics of Young tableaux, including the remarkable constructions of 'bumping' and 'sliding', and several interesting correspondences. In Part II these results are used to study representations with geometry on Grassmannians and flag manifolds, including their Schubert subvarieties, and the related Schubert polynomials. Much of this material has never appeared in book form.There are numerous exercises throughout, with hints or answers provided. Researchers in representation theory and algebraic geometry as well as in combinatorics will find Young Tableaux interesting and useful; students will find the intuitive presentation easy to follow.

This book reviews one-dimensional reactions, dynamics, diffusion and adsorption. In studies of complex systems in biology, chemistry and physics, understanding can be gained by analytical and numerical analyses of simple models. This book presents review articles at an advanced research level, describing results for one-dimensional models of dynamical processes such as chemical reactions and catalysis, kinetic ising models, phase separation and cluster growth, monolayer and multilayer adsorption with added relaxation, surface and hard-core particle dynamics, diffusional transport, random systems and experimental results. It also covers experimental results for systems ranging from chemical reactions to adsorption and reactions on polymer chains, steps on crystalline surfaces, and DNA. All chapters are written by leading scientists in the field. They present a self-contained review of this subject that will guide a reader from basic concepts, ideas, methods and models to the forefront o

In this stimulating book, aimed at researchers both established and budding, Peter Elliott demonstrates a method and a motivating philosophy that combine to cohere a large part of analytic number theory, including the hitherto nebulous study of arithmetic functions. Besides its application, the book also illustrates a way of thinking mathematically: historical background is woven into the narrative, variant proofs illustrate obstructions, false steps and the development of insight, in a manner reminiscent of Euler. It is shown how to formulate theorems as well as how to construct their proofs. Elementary notions from functional analysis, Fourier analysis, functional equations and stability in mechanics are controlled by a geometric view and synthesized to provide an arithmetical analogue of classical harmonic analysis that is powerful enough to establish arithmetic propositions until now beyond reach. Connections with other branches of analysis are illustrated by over 250 exercises, st

The starting point of this book is Sperner's theorem, which answers the question: What is the maximum possible size of a family of pairwise (with respect to inclusion) subsets of a finite set? This theorem stimulated the development of a fast growing theory dealing with external problems on finite sets and, more generally, on finite partially ordered sets. This book presents Sperner theory from a unified point of view, bringing combinatorial techniques together with methods from programming, linear algebra, Lie-algebra representations and eigenvalue methods, probability theory, and enumerative combinatorics. Researchers and graduate students in discrete mathematics, optimisation, algebra, probability theory, number theory, and geometry will find many powerful new methods arising from Sperner theory.