Complex Variables and Applications

Iterative processing is an important technique with numerous applications. Exploiting the power of factor graphs, this detailed survey provides a general framework for systematically developing iterative algorithms for digital receivers, and highlights connections between important algorithms. Starting with basic concepts in digital communications, progressively more complex ideas are presented and integrated resulting in the development of cutting-edge algorithms for iterative receivers. Real-world applications are covered in detail, including decoding for turbo and LDPC codes, and detection for multi-antenna and multi-user systems. This accessible framework will allow the reader to apply factor graphs to practical problems, leading to the design of new algorithms in applications beyond digital receivers. With many examples and algorithms in pseudo-code, this book is an invaluable resource for graduate students and researchers in electrical engineering and computer science, and for pr

It is increasingly apparent that ion-beam-based processing offers unique capabilities for fabrication and complex patterning of 3D, 2D or 1D structures at the few-nanometer scale (e.g., nanowires and quantum dots), and for custom tailoring of nanocomposites, nanoporous materials, catalyst surfaces, optical materials and nanoparticle assemblies. This book addresses achievements, applications and insights into such areas. It also seeks to identify potential dimensional limitations to the future practical implementation of this approach. Topics include: ion-beam nanofab - tools, techniques and applications; patterning, quantum dot synthesis and self assembly; and examples - applications and devices.

The classical fields are the real, rational, complex and p-adic numbers. Each of these fields comprises several intimately interwoven algebraical and topological structures. This comprehensive volume analyzes the interaction and interdependencies of these different aspects. The real and rational numbers are examined additionally with respect to their orderings, and these fields are compared to their non-standard counterparts. Typical substructures and quotients, relevant automorphism groups and many counterexamples are described. Also discussed are completion procedures of chains and of ordered and topological groups, with applications to classical fields. The p-adic numbers are placed in the context of general topological fields: absolute values, valuations and the corresponding topologies are studied, and the classification of all locally compact fields and skew fields is presented. Exercises are provided with hints and solutions at the end of the book. An appendix reviews ordinals a

Sensory scientists are often faced with making business decisions based on the results of complex sensory tests involving a multitude of variables. Multivariate and Probabilistic Analyses of Sensory S

Written by seven internationally known experts, the articles in this book present the fundamentals and practical applications of contemporary wind engineering. It covers complex problems in wind-build

This book presents a model of computing and a measure of computational complexity which are intended to facilitate analysis of computations performed by people, machines, or a mixed system of people and machines. The model is designed to apply directly to models of economic theory, which typically involve continuous variables and smooth functions, without requiring analysis of approximations. The model permits analysis of the feasibility and complexity of the calculations required of economic agents in order for them to arrive at their decisions. The treatment contains applications of the model to game theory and economics, including comparison of the complexities of different solution concepts in certain bargaining games, and the trade-off between communication and computation in an example of an Edgeworth Box economy.

Gain the knowledge and tools to deliver compelling mobile phone applications. Mobile and wireless application design is complex and challenging. Selecting an application technology and designing a mo

Noise pollution around airports, trains, and industries increasingly attracts environmental concern and regulation. Designers and researchers have intensified the use of large-eddy simulation (LES) for noise reduced industrial design and acoustical research. This 2007 book, written by 30 experts, presents the theoretical background of acoustics and of LES, followed by details about numerical methods, e.g. discretization schemes, boundary conditions, coupling aspects. Industrially relevant, hybrid RANS/LES techniques for acoustic source predictions are presented in detail. Many applications are featured ranging from simple geometries for mixing layers and jet flows to complex wing and car geometries. Selected applications include scientific investigations at industrial and university research institutions.

Based on the author's graduate course taught over many years in several physics departments, this 2006 book takes a 'reductionist' view of statistical mechanics, while describing the main ideas and methods underlying its applications. It implicitly assumes that the physics of complex systems as observed is connected to fundamental physical laws represented at the molecular level by Newtonian mechanics or quantum mechanics. Organised into three parts, the first section describes the fundamental principles of equilibrium statistical mechanics. The next section describes applications to phases of increasing density and order: gases, liquids and solids; it also treats phase transitions. The final section deals with dynamics, including a careful account of hydrodynamic theories and linear response theory. This textbook is suitable for a one year graduate course in statistical mechanics for physicists, chemists and chemical engineers. Problems are included following each chapter, with soluti

Published in 2006, Chemical Ecology of Vertebrates was the first book to focus exclusively on the chemically-mediated interactions between vertebrates including fish, amphibians, reptiles, birds and mammals, and other animals and plants. Reviewing research in three core areas - pheromones (where the interactions are between members of the same species), interspecific interactions involving allomones (where the sender benefits) and kairomones (where the receiver benefits), it pulls together information from widely scattered technical literature in many different disciplines into a coherent whole. Chapters on the environment, properties of odour signals, and production and release of chemosignals set the stage for discussion of more complex behavioural topics. While the main focus is ecological, dealing with behaviour and interactions in the field, it also covers chemoreception, orientation and navigation, the development of behaviour and the practical applications of chemosignals.

Practical applications and examples highlight this treatment of computational modeling for handling complex flowfields. A reference for researchers and graduate students of many different backgrounds,

SuperFractals, first published in 2006, is the successor to Fractals Everywhere, in which the power and beauty of Iterated Function Systems were introduced and applied to producing startling and original images that reflect complex structures found for example in nature. This provoked the question of whether there is a deeper connection between topology, geometry, IFS and codes on the one hand and biology, DNA and protein development on the other. Now, 20 years later, Barnsley explains how IFS have developed in order to address this issue. Ideas such as fractal tops and superIFS are introduced, and the classical deterministic approach is combined with probabilistic ideas to produce new mathematics and algorithms that open a whole theory that could have applications in computer graphics, bioinformatics, economics, signal processing and beyond. For the first time these ideas are explained in book form, and illustrated with breathtaking pictures.

This set consists of the third edition of this highly acclaimed undergraduate textbook and its solutions manual containing complete worked solutions to half of the problems. Suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences, the text provides lucid descriptions of all the topics, many worked examples, and over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, the remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

In the past few decades we have come to understand that even motions in simple systems can have complex and surprising properties. Chaotic Dynamics provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior in-depth scientific and mathematical knowledge. Richly illustrated throughout, examples are taken from classical mechanics whose elementary laws are familiar to the reader. In order to emphasize the general features of chaos, the most important relations are also given in simple mathematical forms, independent of any mechanical interpretation. A broad range of potential applications are presented, ranging from everyday phenomena through engineering and environmental problems to astronomical aspects. Chaos occurs in a variety of scientific disciplines, and proves to be the rule, not the exception. This book is primarily intended for undergraduate students in science, engineering, and mathematics.

The theory of probability is a powerful tool that helps electrical and computer engineers to explain, model, analyze, and design the technology they develop. The text begins at the advanced undergraduate level, assuming only a modest knowledge of probability, and progresses through more complex topics mastered at graduate level. The first five chapters cover the basics of probability and both discrete and continuous random variables. The later chapters have a more specialized coverage, including random vectors, Gaussian random vectors, random processes, Markov Chains, and convergence. Describing tools and results that are used extensively in the field, this is more than a textbook; it is also a reference for researchers working in communications, signal processing, and computer network traffic analysis. With over 300 worked examples, some 800 homework problems, and sections for exam preparation, this is an essential companion for advanced undergraduate and graduate students. Further re

Intended for Java developers, this guide shows how to use the IDEA Java development environment to build complex Java applications, analyze them with the symbolic debugger, and test them with JUnit. T

Critical effects in semiclassical scattering, in which the standard approximations break down, are associated with forward peaking, rainbows, glories, orbiting and resonances. Besides giving rise to beautiful optical effects in the atmosphere, critical effects have important applications in many areas of physics. However, their interpretation and accurate treatment is difficult. This book, based on the Elliott Montroll Lectures, given at the University of Rochester, deals with the theory of these critical effects. After a preliminary chapter in which the problem of critical effects is posed, the next three chapters on coronae, rainbows and glories are written so as to be accessible to a broader audience. The main part of the book then describes the results obtained from the application of complex angular momentum techniques to scattering by homogeneous spheres. These techniques lead to practically usable asymptotic approximations, and to new physical insights into critical effects. A n

Discover how to streamline complex bioinformatics applications with parallel computingThis publication enables readers to handle more complex bioinformatics applications and larger and richer data set

Mathematical Methods for Physics and Engineering, Third Edition is a highly acclaimed undergraduate textbook that teaches all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. This solutions manual accompanies the third edition of Mathematical Methods for Physics and Engineering. It contains complete worked solutions to over 400 exercises in the main textbook, the odd-numbered exercises, that are provided with hints and answers. The even-numbered exercises have no hints, answers or worked solutions and are intended for unaided homework problems; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9

The interest in climbing and walking robots (CLAWAR) has intensified in recent years, and novel solutions for complex and very diverse applications have been anticipated by means of significant progre

This is the first book to give a complete overview of the properties of deep-level, localized defects in semiconductors. Such comparatively long-lived (or metastable) defects exhibit complex interactions with the surrounding material, and can significantly affect the performance and stability of certain semiconductor devices. After an introductory discussion of metastable defects, the properties of DX and EL2 centres in III–V compounds are presented. Additional crystalline materials are also dealt with, before a detailed description is given of the properties and kinetics of photo-induced defects in amorphous semiconductors. The book closes with an examination of the effects of photo-induced defects in a range of practical applications. Throughout, unifying concepts and models are stressed, and the book will be of great use to graduate students and researchers interested in the physics and materials science of semiconductors.

Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and

Classic?three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and

Foliated spaces look locally like products, but their global structure is generally not a product, and tangential differential operators are correspondingly more complex. In the 1980s, Alain Connes founded what is now known as noncommutative geometry and topology. One of the first results was his generalization of the Atiyah-Singer index theorem to compute the analytic index associated with a tangential (pseudo) - differential operator and an invariant transverse measure on a foliated manifold, in terms of topological data on the manifold and the operator. This second edition presents a complete proof of this beautiful result, generalized to foliated spaces (not just manifolds). It includes the necessary background from analysis, geometry, and topology. The present edition has improved exposition, an updated bibliography, an index, and additional material covering developments and applications since the first edition came out, including the confirmation of the Gap Labeling Conjecture

Lexical semantics has become a major research area within computational linguistics, drawing from psycholinguistics, knowledge representation, computer algorithms and architecture. Research programmes whose goal is the definition of large lexicons are asking what the appropriate representation structure is for different facets of lexical information. Among these facets, semantic information is probably the most complex and the least explored. Computational Lexical Semantics is one of the first volumes to provide models for the creation of various kinds of computerized lexicons for the automatic treatment of natural language, with applications to machine translation, automatic indexing, and database front-ends, knowledge extraction, among other things. It focuses on semantic issues, as seen by linguists, psychologists and computer scientists. Besides describing academic research, it also covers ongoing industrial projects.

Correlation is a robust and general technique for pattern recognition and is used in many applications, such as automatic target recognition, biometric recognition and optical character recognition. The design, analysis and use of correlation pattern recognition algorithms requires background information, including linear systems theory, random variables and processes, matrix/vector methods, detection and estimation theory, digital signal processing and optical processing. This book provides a needed review of this diverse background material and develops the signal processing theory, the pattern recognition metrics, and the practical application know-how from basic premises. It shows both digital and optical implementations. It also contains technology presented by the team that developed it and includes case studies of significant interest, such as face and fingerprint recognition. Suitable for graduate students taking courses in pattern recognition theory, whilst reaching technical

In this book, Professor McGarity reveals the complex and problematic relationship between the 'regulatory reform' movements initiated in the early l970s and the United States' federal bureaucracy. Examining both the theory and application of 'regulatory reform' under the Reagan administration, the author succeeds in offering both a relevant analysis and critique of 'regulatory reform' and its implementation through bureaucratic channels. Using several case studies from the early Reagan years, this book describes the clash of regulatory cultures resulting from the President's attempt to incorporate 'regulatory analysis' into the bureaucratic decision-making process. Yet while McGarity recognizes the limitations of regulatory analysis, he concludes with suggestions for enhancing its effectiveness. This book could be used not only as a textbook for political science and government courses but also for graduate applications in public policy and public administration.

The interacting boson-fermion model has become in recent years the standard model for the description of atomic nuclei with an odd number of protons and/or neutrons. This book describes the mathematical framework on which the interacting boson-fermion model is built and presents applications to a variety of situations encountered in nuclei. The book addresses both the analytical and the numerical aspects of the problem. The analytical aspect requires the introduction of rather complex group theoretic methods, including the use of graded (or super) Lie algebras. The first (and so far only) example of supersymmetry occurring in nature is also discussed. The book is the first comprehensive treatment of the subject and will appeal to both theoretical and experimental physicists. The large number of explicit formulas for level energies, electromagnetic transition rates and intensities of transfer reactions presented in the book provide a simple but detailed way to analyse experimental data.

The major histocompatibility complex (MHC) genes are involved in the immune system's response to tumour and infected cells and in generating an immune response. This book brings together basic aspects of the regulation of MHC antigens with important clinical applications (in viral infection, viral oncology, cancer biology and autoimmunity). There is a strong emphasis on situations where MHC expression is modulated (either stimulated or repressed). The book's major themes are: the mechanisms of MHC expression explored at several levels including the transcription and translation of MHC genes and the insertion of MHC protein molecules into plasma membranes; the effect of cytokines on MHC expression both in the aetiology of certain diseases and in possible immunotherapeutic approaches to disease; and the use of gene therapy to modify MHC expression in cancer cells, and thereby cause tumour rejection.

Because of its versatility in analyzing a broad range of applications, multibody dynamics has grown in the past two decades to be an important tool for designing, prototyping, and simulating complex a

Studying the dynamics of a large number of particles interacting through long-range forces, commonly referred to as the 'N-body problem', is a central aspect of many different branches of physics. In recent years, significant advances have been made in the development of fast N-body algorithms to deal efficiently with such complex problems. This book is the first to give a thorough introduction to these so-called 'tree methods', setting out the basic principles and giving many practical examples of their use. No prior specialist knowledge is assumed, and the techniques are illustrated throughout with reference to a broad range of applications. The book will be of great interest to graduate students and researchers working on the modelling of systems in astrophysics, plasma physics, nuclear and particle physics, condensed matter physics and materials science.

Plasticity theory is widely used to describe the behaviour of soil and rock in many engineering situations. Plasticity and Geomechanics presents a concise introduction to the general subject of plasticity with a particular emphasis on applications in geomechanics. Derived from the authors' own lecture notes, this book is written with students firmly in mind. Excessive use of mathematical methods is avoided in the main body of the text and, where possible, physical interpretations are given for important concepts. In this way the authors present a clear introduction to the complex ideas and concepts of plasticity as well as demonstrating how this developing subject is of critical importance to geomechanics and geotechnical engineering. This book therefore complements Elasticity and Geomechanics by the same authors and will appeal to graduate students and researchers in the fields of soil mechanics, foundation engineering, and geomechanics.

Rapid advances in complex macromolecular synthesis and the fabrication of nanostructures have provided expansive opportunities for the development of new materials with unique optical and nonlinear optical properties. Key to continual progress is the establishment of robust structure-property-processing relationships that will provide a framework to evaluate ultimate potential, articulate relevant figures of merit, and engineer materials systems for specific applications. Success necessitates interactions across diverse disciplines spanning theory, synthesis, fabrication, characterization and device evaluation for photonic applications. This book addresses the challenges associated with the synthesis, theory and characterization of new compounds and nanostructured materials that exhibit, or are formed, using unique photophysics. Topics include: nonlinear optical properties materials; nonlinear optical materials; organometallic optical materials; plasmonics; electro-optical and electron

The topic of 'circle packing' was born of the computer age but takes its inspiration and themes from core areas of classical mathematics. A circle packing is a configuration of circles having a specified pattern of tangencies, as introduced by William Thurston in 1985. This book, first published in 2005, lays out their study, from first definitions to latest theory, computations, and applications. The topic can be enjoyed for the visual appeal of the packing images - over 200 in the book - and the elegance of circle geometry, for the clean line of theory, for the deep connections to classical topics, or for the emerging applications. Circle packing has an experimental and visual character which is unique in pure mathematics, and the book exploits that to carry the reader from the very beginnings to links with complex analysis and Riemann surfaces. There are intriguing, often very accessible, open problems throughout the book and seven Appendices on subtopics of independent interest. Th

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful and theoretically complex analytical tool. Basic 1H- and 13C-NMR Spectroscopy provides an introduction to the principles and applications of

The digital divide and the inequalities of the availability and deployment of Information and Communication Technologies (ICTs) between developed and developing countries have long been a source of concern. Global institutions such as the United Nations, the International Telecommunications Union (ITU) and the World Bank, as well as regional and national level agencies, have set up task forces to investigate how ICTs can be enacted most effectively in developing countries. How this shared vision should be put into practice is a complex undertaking, but it is already taking place. In this volume, we go beyond the theoretical, the polemical and the philosophical to consider practical issues as they are encountered by stakeholders in the developing country context. 15 author teams explore key issues organized into four sections: (1) Theoretical Background and Culture; (2) Telecentres; (3) Applications; and (4) Key Concepts with Country Specific Studies. Examples of these applications are

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

Making the specifics of a complex concern accessible and its handling quite manageable, this fourth edition of the Project and Cost Engineers' Handbook examines the variables associated with internati

This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and comprehensive account of the rapidly growing field of basic hypergeometric series, or q-series. Simplicity, clarity, deductive proofs, thoughtfully designed exercises, and useful appendices are among its strengths. The first five chapters cover basic hypergeometric series and integrals, whilst the next five are devoted to applications in various areas including Askey-Wilson integrals and orthogonal polynomials, partitions in number theory, multiple series, orthogonal polynomials in several variables, and generating functions. Chapters 9-11 are new for the second edition, the final chapter containing a simplified version of the main elements of the theta and elliptic hypergeometric series as a natural extension of the single-base q-series. Some sections and exercises have been added to reflect recent developments, and the Bibliography has been revised to maintain i

Combining a concrete perspective with an exploration-based approach, Exploratory Galois Theory develops Galois theory at an entirely undergraduate level. The text grounds the presentation in the concept of algebraic numbers with complex approximations and assumes of its readers only a first course in abstract algebra. The author organizes the theory around natural questions about algebraic numbers, and exercises with hints and proof sketches encourage students' participation in the development. For readers with Maple or Mathematica, the text introduces tools for hands-on experimentation with finite extensions of the rational numbers, enabling a familiarity never before available to students of the subject. Exploratory Galois Theory includes classical applications, from ruler-and-compass constructions to solvability by radicals, and also outlines the generalization from subfields of the complex numbers to arbitrary fields. The text is appropriate for traditional lecture courses, for sem