Applied Complex Variables

The late Professor G. N. Watson wrote his monumental 1995 treatise on the theory of Bessel functions with two objects in view. The first was the development of applications of the fundamental processes of the theory of complex variables; and the second was the compilation of a collection of results of value to mathematicians and physicists, who encounter Bessel functions in the course of their researches. The completeness of his theoretical account, combined with the wide scope of the practical examples and the extensive numerical tables, have resulted in a book which is indispensable to pure and applied mathematicians, as well as to physicists.

Ecological data has several special properties: the presence or absence of species on a semi-quantitative abundance scale; non-linear relationships between species and environmental factors; and high inter-correlations among species and among environmental variables. The analysis of such data is important to the interpretation of relationships within plant and animal communities and with their environments. In this corrected version of Data Analysis in Community and Landscape Ecology, without using complex mathematics, the contributors demonstrate the methods that have proven most useful, with examples, exercises and case-studies. Chapters explain in an elementary way powerful data analysis techniques such as logic regression, canonical correspondence analysis, and kriging.

This book offers an extended reinterpretation of English policy in Ireland over the sixteenth century. It seeks to show that the major conflicts between Tudor governors and native lords which characterised the period were not the result of a deliberate Tudor strategy of confrontation, but arose from a failed experiment in legal reform and cultural assimilation which had been applied with remarkable success elsewhere in the Tudor dominions. The book identifies a distinct administrative style which evolved in Irish government in the mid-sixteenth century under a complex set of pressures acting on the would-be reformers both in Ireland and at the Tudor court, and argues that it was this highly centralised and intensely activist mode of government that undermined the aims of reform policy and provoked alienation and hostility.

In Remembering Reconsidered, the new ecologically oriented study of memory makes contact with more traditional approaches. The emerging result may be what several of the authors have begun to call 'functionalism': a concern with the adaptive significance of memory in ordinary life coupled with a careful analysis of the variables on which it depends. In different ways, the chapters reflect this concern. The editors bring together a diverse collection of studies on remembering, using subjects ranging from folk songs to 'crib talk'. Introductory chapters weave these themes together, developing an underlying sense of the project of the volume as a whole. This is the second volume in the Emory Symposia on Cognition. The Emory Cognition Project, directed by Ulric Neisser, emphasizes an ecological approach to problems in theoretical, experimental, and applied cognitive psychology.

This monograph provides an introduction and a survey of recent results in potential theory with respect to the Laplace–Beltrami operator D in several complex variables, with special emphasis on the unit ball in Cn. Topics covered include Poisson–Szegö integrals on the ball, the Green's function for D and the Riesz decomposition theorem for invariant subharmonic functions. The extension to the ball of the classical Fatou theorem on non-tangible limits of Poisson integrals, and Littlewood's theorem on the existence of radial limits of subharmonic functions are covered in detail. The monograph also contains recent results on admissible and tangential boundary limits of Green potentials, and Lp inequalities for the invariant gradient of Green potentials. Applications of some of the results to Hp spaces, and weighted Bergman and Dirichlet spaces of invariant harmonic functions are included. The notes are self-contained, and should be accessible to anyone with some basic knowledge of several

This book describes work, largely that of the author, on the characterization of closed 4-manifolds in terms of familiar invariants such as Euler characteristic, fundamental group, and Stiefel–Whitney classes. Using techniques from homological group theory, the theory of 3-manifolds and topological surgery, infrasolvmanifolds are characterized up to homeomorphism, and surface bundles are characterized up to simple homotopy equivalence. Non-orientable cases are also considered wherever possible, and in the final chapter the results obtained earlier are applied to 2-knots and complex analytic surfaces. This book is essential reading for anyone interested in low-dimensional topology.

This is an updated and expanded second edition of a successful and well-reviewed text presenting a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory. The exposition opens with the theory of analysis over supernumbers (Grassman variables), Berezin integration, supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds, with an account of super-analogs of Lie derivatives, connections, metric, curvature, geodesics, Killing flows, conformal groups, etc. The book goes on to discuss the theory of super Lie groups, super Lie algebras, and invariant geometrical structures on coset spaces. Complete descriptions are given of all the simple super Lie groups. The book then turns to applications. Chapter 5 contains an account of the Peierals bracket for superclassical dynamical systems, super Hilbert spaces, path integration for fe

Provides an introduction to the chemistry of the solid-water interface, progressing from the simple to more complex and applied. Discusses the important interfaces in natural systems, especially geoch

Perturbation methods are one of the fundamental tools used by all applied mathematicians and theoretical physicists. In this book, the author has managed to present the theory and techniques underlying such methods in a manner which will give the text wide appeal to students from a broad range of disciplines. Asymptotic expansions, strained coordinates and multiple scales are illustrated by copious use of examples drawn from all areas of applied mathematics and theoretical physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather to give a physical understanding of the subtle balances in a complex problem.

This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the 'spiral method' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell's equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in

This textbook, available in two volumes, has been developed from a course taught at Harvard over the last decade. The course covers principally the theory and physical applications of linear algebra and of the calculus of several variables, particularly the exterior calculus. The authors adopt the 'spiral method' of teaching, covering the same topic several times at increasing levels of sophistication and range of application. Thus the reader develops a deep, intuitive understanding of the subject as a whole, and an appreciation of the natural progression of ideas. Topics covered include many items previously dealt with at a much more advanced level, such as algebraic topology (introduced via the analysis of electrical networks), exterior calculus, Lie derivatives, and star operators (which are applied to Maxwell's equations and optics). This then is a text which breaks new ground in presenting and applying sophisticated mathematics in an elementary setting. Any student, interpreted in

A great many terrestrial plants live in close association with fungi. The features of this association, which is known as mycorrhiza, are those of a mutualistic symbiosis. Almost all plants from mycorrhizae whereby the fungus provides soil resources to the plant in exchange for energy provided by the plant. The symbiosis means greater productivity under stress for the plant and a steady energy supply for the fungus. This book addresses the diverse and complex ways in which mycorrhizae affect the mechanism for plant survival as individuals and populations, for community structure and functioning. An evolutionary/ecological approach is used to describe how and under what conditions mycorrhizal symbioses range from managing natural and agricultural lands to biotechnological processes that enhance agricultural productivity and sustainability. The Ecology of Mycorrhizae will be an invaluable book, applicable to all levels of theoretical and applied research in agronomy, botany, ecology, env

From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.

Control of office has long been regarded as the key element in understanding power and policy in the Soviet system. What, however, accounts for the control of office and how are individuals recruited into positions of power and responsibility? In An Algebra of Soviet Power, Michael Urban adopts a fresh approach and introduces into the field of political elite studies the sociological technique of vacancy chain analysis. This treats the movements of actors as sequences of complex inter-relations that are structured by the properties and powers of the personnel system rather than by the consequences of individual intentions or characteristics. This algebraic method is applied to a large body of career data of officials from the Soviet Republic of Belorussia for the period 1966–86. The author documents how, despite the formal systems of nomenklatura - central control over personnel placement - the flow of individuals through the hierarchy of offices in Belorussia has not been influenced b

This book is a comprehensive account of the theory and applications of regular variation. It is concerned with the asymptotic behaviour of a real function of a real variable x which is 'close' to a power of x. Such functions are much more than a convenient extension of powers. In many limit theorems regular variation is intrinsic to the result, and exactly characterises the limit behaviour. The book emphasises such characterisations, and gives a comprehensive treatment of those applications where regular variation plays an essential (rather then merely convenient) role. The authors rigorously develop the basic ideas of Karamata theory and de Haan theory including many new results and 'second-order' theorems. They go on to discuss the role of regular variation in Abelian, Tauberian, and Mercerian theorems. These results are then applied in analytic number theory, complex analysis, and probability, with the aim above all of setting the theory in context. A widely scattered literature is

In Remembering Reconsidered, the new ecologically oriented study of memory makes contact with more traditional approaches. The emerging result may be what several of the authors have begun to call 'functionalism': a concern with the adaptive significance of memory in ordinary life coupled with a careful analysis of the variables on which it depends. In different ways, the chapters reflect this concern. The editors bring together a diverse collection of studies on remembering, using subjects ranging from folk songs to 'crib talk'. Introductory chapters weave these themes together, developing an underlying sense of the project of the volume as a whole. This is the second volume in the Emory Symposia on Cognition. The Emory Cognition Project, directed by Ulric Neisser, emphasizes an ecological approach to problems in theoretical, experimental, and applied cognitive psychology.

This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.

In this volume, the author covers the mathematical methods appropriate to both linear-systems theory and signal processing. The text deals with a number of topics usually found in introductory linear-systems courses, such as complex numbers and Laplace transforms, and addresses additional topics such as complex variable theory and Fourier series and transforms. Although the discussion is mathematically self-contained, it assumes that the reader has a firm background in calculus and differential equations. Each chapter contains a number of worked examples plus exercises designed to allow the student to put concepts into practice. The author writes in a mathematically elegant yet relaxed and readable style, and provides interesting historical notes along the way. Undergraduate students of electrical engineering, applied mathematics, and related disciplines - and their teachers - will welcome this book.

This book proposes a fresh approach to sociological analysis and, in particular, to the analysis of scientific culture. It moves away from previous studies, which have tended to focus on scientists' actions and beliefs to show that analysis of scientific discourse can be productive and revealing. The book demonstrates that scientists produce varying accounts of their actions and beliefs in different social situations. Rather than attempting to extract one coherent interpretation from these diverse accounts, the study identifies two basic scientific repertoires and shows how scientists use them to create their discourse. This provides a point of departure for more complex analytical topics. Discourse analysis is applied to show how different degrees of 'consensus' can be ascribed to the same group of scientists at a given moment in time through the application of standard interpretive techniques. Finally, discourse analysis is used to explore scientists' humour, a neglected topic that i

Ecologists are making increasing use of computer methods in analyzing ecological data on plant and animal communities. Ecological problems naturally involve numerous variables and numerous individuals or samples. Multivariate techniques permit the summary of large, complex sets of data and provide the means to tackle many problems that cannot be investigated experimentally because of practical restraints. Ecologists are thus enabled to group similar species and similar sample sites together, and to generate hypotheses about environmental and historical factors that affect the communities. This timely book presents a full critical description of three methodologies - direct gradient analysis, ordination, and classification - from both theoretical and practical viewpoints. Both traditional and new methods are presented. Using a wide range of illustrative examples, Hugh Gauch provides an up-to-date synthesis of this field, which will be of interest to advanced students and ecologists. The

First published in 1981, this book is an introduction to studies of the behaviour of a wide variety of animals including man, farm animals and pest species. The approach is ethological and much reference is made to detailed description of behaviour and to biological function, although there is extensive reference to physiology, brain mechanisms and relevant psychological research. Ideas from sociobiology, motivation and learning studies are emphasised. There is, therefore, very broad coverage of the role of behaviour in all aspects of life. Another novel feature is the extensive reference to applied aspects of behaviour, particularly its importance to the production of farm animals and the control of agricultural and medical pests. The book is intelligible to the educated layman but it deals with some complex ideas. It is an adequate text for all requirements in this area for most undergraduates.

These lecture notes are devoted to an area of current research interest that bridges functional analysis and function theory. The unifying theme is the notion of subharmonicity with respect to a uniform algebra. The topics covered include the rudiments of Choquet theory, various classes of representing measures, the duality between abstract sub-harmonic functions and Jensen measures, applications to problems of approximation of plurisubharmonic functions of several complex variables, and Cole's theory of estimates for conjugate functions. Many of the results are published here for the first time in monograph form.

The study of abelian manifolds forms a natural generalization of the theory of elliptic functions, that is, of doubly periodic functions of one complex variable. When an abelian manifold is embedded in a projective space it is termed an abelian variety in an algebraic geometrical sense. This introduction presupposes little more than a basic course in complex variables. The notes contain all the material on abelian manifolds needed for application to geometry and number theory, although they do not contain an exposition of either application. Some geometrical results are included however.

Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, converge

This well-known little book provides a clear and concise review of general function theory via complex variables. Five main sections offer students valuable background in complex numbers and their geo

Applied Meteorology on the Grid presents state-of-the-art applications and their implementations on the grid infrastructure platform. These include various prediction models and simulations in meteoro

Although state variable concepts are a part of modern control theory, they have not been extensively applied in communication theory. The purpose of this book is to demonstrate how the concepts and me

"This book discusses the best way to promote this approach, when talking about complexity projects. It also proposes a model that will be adding additional important pillars to be applied over the mea

Reservoir engineers today need to acquire more complex reservoir management and modeling skills. Principles of Applied Reservoir Simulation, Fourth Edition, continues to provide the fundamentals on th

Complex-Valued Modeling in Economics and Finance outlines the theory, methodology, and techniques behind modeling economic processes using complex variables theory. The theory of complex variables fu

Designing What Matters significantly expands upon current design knowledge, focussing on the application of design thinking to large scaled complex systems, at the leading edge of cross sector and pub

This handbook collates research evidence and presents the most up-to-date findings on child development in Sub-Saharan Africa. It discusses complex risk factors and medical conditions affecting childh

Data Visualization for Design Thinking helps you make better maps. Treating maps as applied research, you’ll be able to understand how to map sites, places, ideas, and projects, revealing the complex

Data Visualization for Design Thinking helps you make better maps. Treating maps as applied research, you’ll be able to understand how to map sites, places, ideas, and projects, revealing the complex

Sports Law and Society: Rules of the Game, Second Edition stands out for its exceptional depth and practical approach, offering a comprehensive, concise and clear examination of the legal challenges shaping today's sports industry. Designed to engage students, it covers foundational topics like contracts, collective bargaining, and intellectual property in sports while exploring complex, evolving issues such as gender equity, the global sports ecosystem, and data analytics in performance. Each chapter provides real-world examples and cases, giving students an applied understanding of how legal principles operate within professional, college, and youth sports. By balancing established legal doctrines with emerging topics-including artificial intelligence, digital media, athlete mental health, and the future of sports-this book equips readers with both historical context and foresight, making it particularly relevant for a dynamic field.What sets this book apart is its critical focus on

Linear algebra permeates mathematics,perhaps more so than any other single subject.It plays an essential role in pure and applied mathematics,statistics,computer science,and many aspects of physics and engineering.This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst.The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade.In short,this is material that many of us wish we had been taught as graduate students.Roughly the first third of the book covers the basic material of a first course in linear algebra.The remaining chapters are devoted to applications drawn from vector calculus,numerical analysis,control theory,complex analysis,convexity and functional analysis.In particular,fixed point theorems,extremal problems,matrix equations,zero location and eigenvalue location problems,and matrices with nonnegative entries are discussed.App

Science often deals with hard-to-see phenomena, and they only stand out and become real when viewed through the lens of complex statistical tools. This book is not a textbook about statistics applied

This book provides managers, leaders and practitioners with a dynamic framework that links several variables associated with performance management which can be applied across organizations and indust