Classical Complex Analysis

This book is an innovative historical study of piracy in the Graeco-Roman world from the Archaic period to Late Antiquity. It explores the conditions which allowed piracy to flourish in the ancient Mediterranean, especially the close relationship between warfare and piracy, and examines the impact which pirates had upon ancient society. Particular attention is paid to the numerous states and rulers who claimed to be actively suppressing piracy for the good of all. In many cases these claims turn out to be highly exaggerated ones, intended to enhance the prestige of those on whose behalf they were made. Surprisingly, in view of the prominence of pirates in many works of classical literature, this book is the first to offer detailed analysis of the portrayal of piracy by ancient writers, including Homer, Cicero and the ancient novels, taking account of the political, social and literary contexts which shaped their accounts.

Surveys the complex history of Buddhist dream experience and analysis

This book presents a theory of learning that starts with the assumption that engagement in social practice is the fundamental process by which we get to know what we know and by which we become who we are. The primary unit of analysis of this process is neither the individual nor social institutions, but the informal 'communities of practice' that people form as they pursue shared enterprises over time. To give a social account of learning, the theory explores in a systematic way the intersection of issues of community, social practice, meaning, and identity. The result is a broad framework for thinking about learning as a process of social participation. This ambitious but thoroughly accessible framework has relevance for the practitioner as well as the theoretician, presented with all the breadth, depth, and rigor necessary to address such a complex and yet profoundly human topic.

The question of whether democratization is an elite-led process from above or a popular triumph from below continues to be an area of contention among political scientists. Examining the experiences of countries which have provided the main empirical base for recent theorizing, namely, Western Europe and South America in the 19th and early 20th centuries and again in the 1970s and 1980s, this book delineates a more complex and varied set of patterns. The volume explores the politics of democratization through a comparative analysis that examines the role of labor in relation to elite strategies in both contemporary and historical perspectives. In her detailed analysis, Professor Collier also describes multiple patterns within each historical period, challenges conventional understandings of these events, and recaptures a role for unions and labor-based parties in contemporary processes of democratization.

The question of whether democratization is an elite-led process from above or a popular triumph from below continues to be an area of contention among political scientists. Examining the experiences of countries which have provided the main empirical base for recent theorizing, namely, Western Europe and South America in the 19th and early 20th centuries and again in the 1970s and 1980s, this book delineates a more complex and varied set of patterns. The volume explores the politics of democratization through a comparative analysis that examines the role of labor in relation to elite strategies in both contemporary and historical perspectives. In her detailed analysis, Professor Collier also describes multiple patterns within each historical period, challenges conventional understandings of these events, and recaptures a role for unions and labor-based parties in contemporary processes of democratization.

This book helps explain one of the most intriguing and politically salient puzzles in comparative political economy: why some countries have much higher unemployment rates than others. Contrary to new classical economics the focus is on explaining distribution and equilibrium unemployment, and contrary to neo-corporatist theory the role of monetary policy and rational expectation is integral to the analysis. The book makes two central arguments. The first is that monetary policies affect equilibrium employment whenever wages are set above the firm level. The second argument focuses on the distributive effects of different institutions, and models institutional design as a strategic game between partisan governments and cross-class alliances of unions and employers.

This book helps explain one of the most intriguing and politically salient puzzles in comparative political economy: why some countries have much higher unemployment rates than others. Contrary to new classical economics the focus is on explaining distribution and equilibrium unemployment, and contrary to neo-corporatist theory the role of monetary policy and rational expectation is integral to the analysis. The book makes two central arguments. The first is that monetary policies affect equilibrium employment whenever wages are set above the firm level. The second argument focuses on the distributive effects of different institutions, and models institutional design as a strategic game between partisan governments and cross-class alliances of unions and employers.

This book examines the performance of Greek tragedy in the classical Athenian theatre. Whilst post structuralist criticism of Greek tragedy has tended to focus on the literary text, the analysis of stagecraft and the theatre has been markedly conservative in its methodology. David Wiles corrects that balance, exploring the performance of tragedy as a spatial practice specific to Athenian culture, at once religious and political. Athenian conceptions of space were quite unlike those of the modern world. After reviewing controversies and archaeological data regarding the fifth-century performance space, Wiles turns to the chorus and shows how dance mapped out the space for the purposes of any given play. The book shows how the performance as a whole was organised and, through informative diagrams and accessible analyses, Wiles brings the theatre of Greek tragedy to life.

This major survey features the work of 18 outstanding mathematicians. Primary subjects include analytic geometry, algebra, ordinary and partial differential equations, the calculus of variations, functions of a complex variable, prime numbers, and theories of probability and functions. Other topics include linear and non-Euclidean geometry, topology, functional analysis, more. 1963 edition.

Industrial Environmental Performance Metrics is a corporate-focused analysis that brings clarity and practicality to the complex issues of environmental metrics in industry. The book examines the metr

The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area o

This 1999 book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package MATLAB. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with MATLAB, no starting knowledge of the package being assumed. The range of material is wide: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations form the basic mathematics. This is applied to a large number of investigations and modelling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web.

This 1999 book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package MATLAB. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with MATLAB, no starting knowledge of the package being assumed. The range of material is wide: matrices, whole numbers, complex numbers, geometry of curves and families of lines, data analysis, random numbers and simulations, and differential equations form the basic mathematics. This is applied to a large number of investigations and modelling problems, from sequences of real numbers to cafeteria queues, from card shuffling to models of fish growth. All extras to the standard MATLAB package are supplied on the World Wide Web.

In this 1999 study, Beat Wyss provides a critical analysis of Hegel's theories of art history. Analogous to his philosophy of history, Hegel viewed the history of art in dialectical terms: with its origins in the Ancient Near East, Western art culminated in Classical Greece, but began its decline already in the Hellenistic period. Yet, as Wyss posits, art refuses its programmed demise. He highlights the political dimension of this contradiction, showing the implication of theories which subordinate art to the will of absolute rule. Wyss follows his analysis of Hegel's theories with a discussion of the work of four modern successors - Nordau, Spengler, Sedlmayr and Lukacs - all of whom adapted Hegel's dialectical model, in an effort to demonstrate the central contradictions of twentieth-century aesthetics.

Now in paperback, the main theme of this book is the study of geometric properties of general sets and measures in euclidean spaces. Applications of this theory include fractal-type objects such as strange attractors for dynamical systems and those fractals used as models in the sciences. The author provides a firm and unified foundation and develops all the necessary main tools, such as covering theorems, Hausdorff measures and their relations to Riesz capacities and Fourier transforms. The last third of the book is devoted to the Beisovich-Federer theory of rectifiable sets, which form in a sense the largest class of subsets of euclidean space posessing many of the properties of smooth surfaces. These sets have wide application including the higher-dimensional calculus of variations. Their relations to complex analysis and singular integrals are also studied. Essentially self-contained, this book is suitable for graduate students and researchers in mathematics.

This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.

The theory of distributions is an extension of classical analysis which has acquired a particular importance in the field of linear partial differential equations, as well as having many other applications, for example in harmonic analysis. Underlying it is the theory of topological vector spaces, but it is possible to give a systematic presentation without presupposing a knowledge, or using more than a bare minimum, of this. This book, first published in 1999, adopts this course and is based on graduate lectures given over a number of years. The prerequisites are few, but a reasonable degree of mathematical maturity is expected of the reader, as the treatment is rigorous throughout. From the outset the theory is developed in several variables, unlike most elementary texts; it is taken as far as such important topics as Schwartz kernels, the Paley-Wiener-Schwartz theorem and Sobolev spaces.

Mathematical calculations for subsynchronous system modeling Subsynchronous Resonance in Power Systems provides in-depth guidance toward the parameters, modeling, and analysis of this complex subclass

An integral part of engineering design is the development of models that describe physical behavior or phenomena in mathematical terms. As engineering systems have become more complex, classic linear methods of modeling and analysis have proved inadequate, creating a need for nonlinear models to solve design problems. This 1999 text provides an introduction to mathematical modeling of linear and nonlinear systems, with an emphasis on the solution of nonlinear design problems. While encouraging the use of the computer as a tool for modeling and analysis, the aim is to discuss the basic concepts underlying computer techniques and to seek analytical solutions. Among topics covered are exact solution, numerical solution, graphical solution, and approximate solution methods; and the stability of nonlinear systems. Numerous examples show how to apply modeling methods to real engineering systems. The book also includes end-of-chapter problems and case studies of challenging design problems. I

The first edition of this well known book was noted for its clear and accessible exposition of the basic theory of Hardy spaces from the concrete point of view (in the unit circle and the half plane). The intention was to give the reader, assumed to know basic real and complex variable theory and a little functional analysis, a secure foothold in the basic theory, and to understand its applications in other areas. For this reason, emphasis is placed on methods and the ideas behind them rather than on the accumulation of as many results as possible. The second edition retains that intention, but the coverage has been extended. The author has included two appendices by V. P. Havin, on Peter Jones' interpolation formula, and Havin's own proof of the weak sequential completeness of L1/H1(0); in addition, numerous amendments, additions and corrections have been made throughout.

Tackles the complex problem of the law relating to marine pollution and collisions. This work provides a detailed analysis of the legal framework relating to oil pollution and collisions, including th

The theme of this unique work, the logarithmic integral, lies athwart much of twentieth century analysis. It is a thread connecting many apparently separate parts of the subject, and so is a natural point at which to begin a serious study of real and complex analysis. Professor Koosis' aim is to show how, from simple ideas, one can build up an investigation which explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows. The presentation is straightforward, so this, the first of two volumes, is self-contained, but more importantly, by following the theme, Professor Koosis has produced a work that can be read as a whole. He has brought together here many results, some unpublished, some new, and some available only in inaccessible journals.

With the advent of the Human Genome Project there have been many claims for the genetic origins of complex human behavior including insanity, criminality, and intelligence. But what does it really mean to call something 'genetic'? This is the fundamental question that Sahotra Sarkar's book addresses. The author analyses the nature of reductionism in classical and molecular genetics. He shows that there are two radically different kinds of reductionist explanation: genetic reduction (as found in classical genetics) and physical reduction (found in molecular genetics). This important book clarifies the meaning of the term 'genetic', shows how molecular studies have affected genetics, and provides the philosophical background necessary to understand the debates over the Human Genome Project. It will be of particular interest to professionals and students in the philosophy of science, the history of science, and the social studies of science, medicine, and technology.

The Bayeux Tapestry has long been recognized as one of the most problematical historical documents of the Norman Conquest of England in 1066. More than a reinterpretation of the historical evidence, Suzanne Lewis's study explores the visual and textual strategies that have made the Bayeux Tapestry's narrative such a powerful experience for audiences over the centuries. The Rhetoric of Power focuses on how the Tapestry tells its story and how it shapes the responses of reader-viewers. This involves a detailed analysis of the way the visual narrative draws on diverse literary genres to establish the cultural resonance of the story it tells. The material is organized into self-contained yet cross-referencing episodes that not only portray the events of the Conquest but locate those events within the ideological codes of Norman feudalism. Lewis's analysis conveys how the whole 232-foot tapestry would have operated as a complex cultural 'fiction' comparable to modern cinema.

Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, proba

Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the bas

Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior and graduate level students, especially in aerospace engineering, as well as researchers and practising engineers, will find a wealth of invaluable information on high-speed gas flows in this text.

Numerical methods are indispensable tools in the analysis of complex fluid flows. This book focuses on computational techniques for high-speed gas flows, especially gas flows containing shocks and other steep gradients. The book decomposes complicated numerical methods into simple modular parts, showing how each part fits and how each method relates to or differs from others. The text begins with a review of gasdynamics and computational techniques. Next come basic principles of computational gasdynamics. The last two parts cover basic techniques and advanced techniques. Senior and graduate level students, especially in aerospace engineering, as well as researchers and practising engineers, will find a wealth of invaluable information on high-speed gas flows in this text.

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.

At first glance, studying behavior is easy, but as every budding ethologist quickly realises, there are a host of complex practical, methodological and analytical problems to solve before designing and conducting the study. How do you choose which species or which behavior to study? What equipment will you need to observe and record behavior successfully? How do you record data in the dark, in the wet, or without missing part of the action? How do you analyse and interpret the data to yield meaningful information? This new expanded edition of the Handbook of Ethological Methods provides a complete step-by-step introduction to ethological methods from topic choice and behavioral description to data collection and statistical analysis. This book will be a must for beginning students and experienced researchers studying animal behavior in the field or laboratory.

Blood Road is a complex mix of social history, literary analysis, political biography, and murder mystery. It explores and analyzes the social and cultural dynamics of the Chinese revolution of the 19

This new critique of Aquinas's theory of natural law presents an incisive, new analysis of the central themes and relevant texts in the Summa Theologiae which became the classical canon for natural la

Edouard Manet's controversial painting 'Le Déjeuner sur l'herbe' is one of the best-known images in French art. The subject of critical analysis for more than a century, it still defies singular interpretation. This book offers six different readings of the painting. Based on new ideas about its context, production, meaning, and reception, these essays, written specially for this volume by the leading scholars of French modern art, incorporate close examinations of its radical style and novel subject, relevant historical developments and archival material, as well as biographical evidence that prompts psychological inquiries. Shedding new light on the artist and the touchstone work of modernism, this title also introduces readers to current methodologies in art history and to the multiple ways that this complex painting can be framed.

In this innovative introduction, Robert Layton reviews the ideas that have inspired anthropologists in their studies of societies around the world. An Introduction to Theory in Anthropology provides a clear and concise analysis of the theories, and traces the way in which they have been translated into anthropological debates. The opening chapter sets out the classical theoretical issues formulated by Hobbes, Rousseau, Marx and Durkheim. Successive chapters discuss Functionalism, Structuralism, Interactionist theories, and Marxist anthropology, while the final chapters address the competing paradigms of Socioecology and Postmodernism. Using detailed case studies, Professor Layton illustrates the way in which various theoretical perspectives have shaped competing, or complementary, accounts of specific human societies.

Turgenev's novel about conflicting ideas, social classes and generations questions human nature and man's place in the universe. This is one in a series offering a critical analysis of Russian texts a

Mathematical modelling is the basis of almost all applied mathematics. A 'real-world' problem is dissected and phrased in a mathematical setting, allowing it to be simplified and ultimately solved. This book presents a thorough grounding in the techniques of modelling, and proceeds to explore a range of classical and continuum models from an impressive array of disciplines, including: biology, chemical engineering, fluid and solid mechanics, geophysics, medicine, and physics. It assumes only a basic mathematical grounding in calculus and analysis and will provide a wealth of examples for students of mathematics, engineering, and the range of applied sciences.

Why is the relationship between inequality and democracy so compelling to the contemporary social scientist? This 1997 volume addresses questions that were raised as early as the time of Aristotle and through Marx to the present. Theoretical lacunae are explored, as are major current policy concerns. The book focuses on the sources of democracy, the relationship between economic development and thresholds of democracy, and finally on responses to democratization. Of course, definitions of democracy have varied over an extraordinarily wide range, as have conceptions of inequality, and the reader will find such variations reflected in the contributions to this volume. Descriptions of democracy vary from an emphasis on equality of participation for all citizens in decision making, to more complex indices emphasizing competitiveness and civil liberties. The contributors to this volume provide the kind of multidimensional analysis which is essential to a comprehensive treatment of the relat

Why is the relationship between inequality and democracy so compelling to the contemporary social scientist? This 1997 volume addresses questions that were raised as early as the time of Aristotle and through Marx to the present. Theoretical lacunae are explored, as are major current policy concerns. The book focuses on the sources of democracy, the relationship between economic development and thresholds of democracy, and finally on responses to democratization. Of course, definitions of democracy have varied over an extraordinarily wide range, as have conceptions of inequality, and the reader will find such variations reflected in the contributions to this volume. Descriptions of democracy vary from an emphasis on equality of participation for all citizens in decision making, to more complex indices emphasizing competitiveness and civil liberties. The contributors to this volume provide the kind of multidimensional analysis which is essential to a comprehensive treatment of the relat

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