Applied Complex Variables

Quantum mesoscopic physics covers a whole class in interference effects related to the propagation of waves in complex and random media. These effects are ubiquitous in physics, from the behaviour of electrons in metals and semiconductors to the propagation of electromagnetic waves in suspensions such as colloids, and quantum systems like cold atomic gases. A solid introduction to quantum mesoscopic physics, this book is a modern account of the problem of coherent wave propagation in random media. It provides a unified account of the basic theoretical tools and methods, highlighting the common aspects of the various optical and electronic phenomena involved and presenting a large number of experimental results. With over 200 figures, and exercises throughout, the book was originally published in 2007 and is ideal for graduate students in physics, electrical engineering, applied physics, acoustics and astrophysics. It will also be an interesting reference for researchers.

This 1961 book presents a concise and systematic treatment of two-dimensional subsonic, inviscid fluid motion and its aeronautical applications. Part I surveys the relevant fluid dynamics, assuming only a basic knowledge of the topic. In Part II, the methods of conformal mapping and Cauchy integrals are developed, on the assumption that the reader has only an elementary understanding of complex variable theory; this will be of interest to a wide range of applied mathematicians and engineers. In Part III, the methods are applied to several problems in fluid mechanics and aero dynamics. The text provides an extensive account of mixed boundary-value problems and treats such examples of these problems as occur in ventilated wind-tunnel theory, jet-flap theory and unsteady Hemholtz motions.

This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials,

Low-temperature radio frequency plasmas are essential in various sectors of advanced technology, from micro-engineering to spacecraft propulsion systems and efficient sources of light. The subject lies at the complex interfaces between physics, chemistry and engineering. Focusing mostly on physics, this book will interest graduate students and researchers in applied physics and electrical engineering. The book incorporates a cutting-edge perspective on RF plasmas. It also covers basic plasma physics including transport in bounded plasmas and electrical diagnostics. Its pedagogic style engages readers, helping them to develop physical arguments and mathematical analyses. Worked examples apply the theories covered to realistic scenarios, and over 100 in-text questions let readers put their newly acquired knowledge to use and gain confidence in applying physics to real laboratory situations.

Modeling atmospheric processes in order to forecast the weather or future climate change is an extremely complex and computationally intensive undertaking. One of the main difficulties is that there are a huge number of factors that need to be taken into account, some of which are still poorly understood. The Factor Separation (FS) method is a computational procedure that helps deal with these nonlinear factors. In recent years many scientists have applied FS methodology to a range of modeling problems, including paleoclimatology, limnology, regional climate change, rainfall analysis, cloud modeling, pollution, crop growth, and other forecasting applications. This book is the first to describe the fundamentals of the method, and to bring together its many applications in the atmospheric sciences. The main audience is researchers and graduate students using the FS method, but it is also of interest to advanced students, researchers, and professionals across the atmospheric sciences.

Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts

Complex Systems in Finance and Econometrics is an authoritative reference to the basic tools and concepts of complexity and systems theory as applied to an understanding of complex, financial-based bu

Bioinspired computation methods such as evolutionary algorithms and ant colony optimization are being applied successfully to complex engineering problems and to problems from combinatorial optimizati

Bayesian decision analysis supports principled decision making in complex domains. This textbook takes the reader from a formal analysis of simple decision problems to a careful analysis of the sometimes very complex and data rich structures confronted by practitioners. The book contains basic material on subjective probability theory and multi-attribute utility theory, event and decision trees, Bayesian networks, influence diagrams and causal Bayesian networks. The author demonstrates when and how the theory can be successfully applied to a given decision problem, how data can be sampled and expert judgements elicited to support this analysis, and when and how an effective Bayesian decision analysis can be implemented. Evolving from a third-year undergraduate course taught by the author over many years, all of the material in this book will be accessible to a student who has completed introductory courses in probability and mathematical statistics.

Thanks to new tools of research and the heightened scientific rigor with which they are applied, medical science has reached a far more heightened understanding of nutrition’s complex relation with di

Methods for more planet-friendly process engineering Our earth is just one big, complex Process Facility with limited air, water, and mineral resources. It responds to a number of process variables—a

Are all film stars linked to Kevin Bacon? Why do the stock markets rise and fall sharply on the strength of a vague rumour? How does gossip spread so quickly? Are we all related through six degrees of separation? There is a growing awareness of the complex networks that pervade modern society. We see them in the rapid growth of the internet, the ease of global communication, the swift spread of news and information, and in the way epidemics and financial crises develop with startling speed and intensity. This introductory book on the new science of networks takes an interdisciplinary approach, using economics, sociology, computing, information science and applied mathematics to address fundamental questions about the links that connect us, and the ways that our decisions can have consequences for others.

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

Discover what you can do with R! Introducing the R system, covering standard regression methods, then tackling more advanced topics, this book guides users through the practical, powerful tools that the R system provides. The emphasis is on hands-on analysis, graphical display, and interpretation of data. The many worked examples, from real-world research, are accompanied by commentary on what is done and why. The companion website has code and datasets, allowing readers to reproduce all analyses, along with solutions to selected exercises and updates. Assuming basic statistical knowledge and some experience with data analysis (but not R), the book is ideal for research scientists, final-year undergraduate or graduate-level students of applied statistics, and practising statisticians. It is both for learning and for reference. This third edition expands upon topics such as Bayesian inference for regression, errors in variables, generalized linear mixed models, and random forests.

To the new student of international law, the subject can appear extremely complex: a system of laws created by states, international courts and tribunals operating at the national and global level. A clear guide to the subject is essential to ensure understanding. This handbook provides exactly that: written by an expert who both teaches and practises in the field, it focuses on what the law is; how it is created; and how it is applied to solve day-to-day problems. It offers a practical approach to the subject, giving it relevance and immediacy. The new edition retains a concise, user-friendly format allowing central principles such as jurisdiction and the law of treaties to be understood. In addition, it explores more specialised topics such as human rights, terrorism and the environment. This handbook is the ideal introduction for students new to international law.

To the new student of international law, the subject can appear extremely complex: a system of laws created by states, international courts and tribunals operating at the national and global level. A clear guide to the subject is essential to ensure understanding. This handbook provides exactly that: written by an expert who both teaches and practises in the field, it focuses on what the law is; how it is created; and how it is applied to solve day-to-day problems. It offers a practical approach to the subject, giving it relevance and immediacy. The new edition retains a concise, user-friendly format allowing central principles such as jurisdiction and the law of treaties to be understood. In addition, it explores more specialised topics such as human rights, terrorism and the environment. This handbook is the ideal introduction for students new to international law.

Engineers and other applied scientists are frequently faced with models of complex systems for which no rigorous mathematical solution can be calculated. Numerical approximations are thus frequently u

Because networks not only help visualize highly interdependent data, but also allow stringent mathematical and statistical analysis, the approach is often being applied to the massive and complex data

This important collection brings together leading econometricians to discuss advances in the areas of the econometrics of panel data. The papers in this collection can be grouped into two categories. The first, which includes chapters by Amemiya, Baltagi, Arellano, Bover and Labeaga, primarily deal with different aspects of limited dependent variables and sample selectivity. The second group of papers, including those by Nerlove, Schmidt and Ahn, Kiviet, Davies and Lahiri, consider issues that arise in the estimation of dyanamic (possibly) heterogeneous panel data models. Overall, the contributors focus on the issues of simplifying complex real-world phenomena into easily generalisable inferences from individual outcomes. As the contributions of G. S. Maddala in the fields of limited dependent variables and panel data were particularly influential, it is a fitting tribute that this volume is dedicated to him.

Engineers and scientists need powerful formalisms to make conceptual models of systems in order to analyse and design them. These models can be used to verify the behaviour of the systems, or as an executable specification of them. In this textbook, Professor van Hee concentrates on discrete dynamic systems, e.g. computer hardware, and information and logistical systems. He develops an integrated formalism which can be used as a prototyping language. It has three components: Petri nets, extended with time, token values and hierarchy; a specification language that is a subset of Z; and a binary data model, extended with complex objects. Much attention is paid to methods for constructing models of systems and analysing their behaviour, i.e. putting the theory into practice. The text is designed for use by advanced undergraduate and beginning graduate students, in computer science, electrical and industrial engineering, or applied mathematics; indeed, it is based on courses taught by the

Using fundamental physics, the theory of stellar structure and evolution can predict how stars are born, how their complex internal structure changes, what nuclear fuel they burn, and their ultimate fate. This textbook is a stimulating introduction for undergraduates in astronomy, physics and applied mathematics, taking a course on the physics of stars. It uniquely emphasises the basic physical principles governing stellar structure and evolution. This second edition contains two new chapters on mass loss from stars and interacting binary stars, and new exercises. Clear and methodical, it explains the processes in simple terms, while maintaining mathematical rigour. Starting from general principles, this textbook leads students step-by-step to a global, comprehensive understanding of the subject. Fifty exercises and full solutions allow students to test their understanding. No prior knowledge of astronomy is required, and only a basic background in physics and mathematics is necessary.

The development of advanced optical structures has enabled tremendous control over the propagation and manipulation of light waves. At the forefront of these advances is the development of micro- and nanostructured optical devices that have dimensions smaller than the wavelength of light. In particular, the engineering of light localization, optical dispersion and plasmonic fields in complex optical media has the potential to boost the scaling of optical technologies below the diffraction limit, opening unprecedented opportunities for basic and applied research. This book bridges three closely related research fields of nanoplasmonics, metamaterials and light localization in complex media. The goal is to share recent progress, identify critical problems and provide promising solutions for the next generation of photonic functionality. Topics include: metamaterials and superlenses; metamaterials; and optical nanoantennas and decay engineering.

Exact statistical inference may be employed in diverse fields of science and technology. As problems become more complex and sample sizes become larger, mathematical and computational difficulties can arise that require the use of approximate statistical methods. Such methods are justified by asymptotic arguments but are still based on the concepts and principles that underlie exact statistical inference. With this in perspective, this book presents a broad view of exact statistical inference and the development of asymptotic statistical inference, providing a justification for the use of asymptotic methods for large samples. Methodological results are developed on a concrete and yet rigorous mathematical level and are applied to a variety of problems that include categorical data, regression, and survival analyses. This book is designed as a textbook for advanced undergraduate or beginning graduate students in statistics, biostatistics, or applied statistics but may also be used as a

This book tackles the question: how can an engineer with a powerful finite element program but modest background knowledge of mechanics solve unfamiliar problems? Engineering educators will find this book to be a new and exciting approach to helping students engage with complex ideas. Practising engineers who use finite element methods to solve problems in solids and structures will extend the range of problems they can solve as well as accelerate their learning on new problems. This book's special strengths include: • A thoroughly modern approach to learning and understanding mechanics problems • Comprehensive coverage of a large collection of problems ranging from static to dynamic and from linear to nonlinear, applied to a variety of structures and components • Accompanying software that is sophisticated and versatile and is available for free from the book's website • Ability to complement any standard finite element textbook.

This book is devoted to the study of classical combinatorial structures such as random graphs, permutations, and systems of random linear equations in finite fields. The author shows how the application of the generalized scheme of allocation in the study of random graphs and permutations reduces the combinatorial problems to classical problems of probability theory on the summation of independent random variables. He concentrates on research by Russian mathematicians, including a discussion of equations containing an unknown permutation and a presentation of techniques for solving systems of random linear equations in finite fields. These results will interest specialists in combinatorics and probability theory and will also be useful in applied areas of probabilistic combinatorics such as communication theory, cryptology, and mathematical genetics.

Planning is a critical stage of radiotherapy. Careful consideration of the complex variables involved and critical assessment of the techniques available are fundamental to good and effective practic

First published in 1989, this book contained the first systematic account of magnetoresistance in metals, the study of which has provided solid-state physicists with much valuable information about electron motion in metals. The electrical resistance of a metal is usually changed when a magnetic field is applied to it; at low temperatures the change may be very large indeed and when magnetic breakdown is involved, very complex. Every metal behaves differently, and the effect is highly dependent on the direction of the field relative to the crystal axes. Quite apart from its usefulness for determining the Ferni surfaces of individual metals, the phenomenon presents many interesting problems in its own right; it is the phenomenon, rather than its applications, that Professor Pippard concentrates on in this book. The level of treatment is aimed at readers with a basic knowledge of undergraduate solid-state physics, and makes no great demand on mathematical ability. The text is copiously i

Why is it necessary to strike while the iron is hot? What makes a good liquid crystal display? Why is rubber so elastic? These questions can be answered through rheophysics, using the mechanics of continuous media at the macroscopic scale, and statistical mechanics and the physics of defects at the microscopic level. This book addresses problems involving the flow of matter, covering the main aspects of the mechanical response of fluids and solids to applied stress or strain. It includes the hydrodynamics of ordinary liquids, the elasticity and plasticity of solids, and the rheology of complex fluids such as suspensions, polymers and liquid crystals. Dislocations are described thoroughly, and special attention is given to instabilities. Concepts and physical properties are illustrated by numerous experiments, historical anecdotes, and applications to aeronautics, metallurgy, and geophysics, making this a valuable reference for researchers and graduate students in physics, engineering,

Decision making is a critical element in the field of medicine that can lead to life-or-death outcomes, yet it is an element fraught with complex and conflicting variables, diagnostic and therapeutic

Sure to be influential, this book lays the foundations for the use of algebraic geometry in statistical learning theory. Many widely used statistical models and learning machines applied to information science have a parameter space that is singular: mixture models, neural networks, HMMs, Bayesian networks, and stochastic context-free grammars are major examples. Algebraic geometry and singularity theory provide the necessary tools for studying such non-smooth models. Four main formulas are established: 1. the log likelihood function can be given a common standard form using resolution of singularities, even applied to more complex models; 2. the asymptotic behaviour of the marginal likelihood or 'the evidence' is derived based on zeta function theory; 3. new methods are derived to estimate the generalization errors in Bayes and Gibbs estimations from training errors; 4. the generalization errors of maximum likelihood and a posteriori methods are clarified by empirical process theory o

An engagingly-written account of mathematical tools and ideas, this book provides a graduate-level introduction to the mathematics used in research in physics. The first half of the book focuses on the traditional mathematical methods of physics – differential and integral equations, Fourier series and the calculus of variations. The second half contains an introduction to more advanced subjects, including differential geometry, topology and complex variables. The authors' exposition avoids excess rigor whilst explaining subtle but important points often glossed over in more elementary texts. The topics are illustrated at every stage by carefully chosen examples, exercises and problems drawn from realistic physics settings. These make it useful both as a textbook in advanced courses and for self-study. Password-protected solutions to the exercises are available to instructors at www.cambridge.org/9780521854030.

Comparative Physiology: Primitive Mammals attempts to dispel the widely held notion that 'primitive' animals are less advanced or less complex than the 'non-primitive'. The term 'primitive', or more accurately 'conservative', refers to the fact that these animals have retained many of the characteristics of their evolutionary ancestors. Because they have been able to adapt to a variety of environmental conditions, these so-called primitive animals should be considered highly successful evolutionary solutions. The papers contained in this volume are the result of the Fourth International Conference on Comparative Physiology held at Crans-sur-Sierre in 1978. The conference, which was sponsored by the Interunion Commission on Comparative Physiology representing the International Unions of Biological Sciences, Physiological Sciences, and Pure and Applied Biophysics, brought together scientists from various fields to discuss the widely scattered information on primitive mammals from the per

This graduate-level treatment of aerodynamic theory opens with a survey of vector analysis and complex variables that presents readers with the basic tools for handling subsequent chapters. Topics inc

This important contribution to scholarship in social science history examines the development of public education in nineteenth-century Massachusetts. Until the 1950s educational historians emphasized the relationship of schooling to the political system and the development of a common American culture. In recent years a social history perspective has emerged that stresses the socioeconomic influences that tie education to other institutions and processes in society rather than to political ideals. Carl Kaestle's and Maris Vinovskis's study is firmly grounded in this newer perspective. However, their work questions the adequacy of any single-factor explanation of the broad educational changes that occurred during this period - whether it be the emergence of factory production or the broader concept of modernization. They argue that these educational changes were the result of the complex interaction of cultural, demographic and economic variables operating in varying ways in different

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanc

If you're looking to understand photonic crystals, this systematic, rigorous, and pedagogical introduction is a must. Here you'll find intuitive analytical and semi-analytical models applied to complex and practically relevant photonic crystal structures. You will also be shown how to use various analytical methods borrowed from quantum mechanics, such as perturbation theory, asymptotic analysis, and group theory, to investigate many of the limiting properties of photonic crystals which are otherwise difficult to rationalize using only numerical simulations. An introductory review of nonlinear guiding in photonic lattices is also presented, as are the fabrication and application of photonic crystals. In addition, end-of-chapter exercise problems with detailed analytical and numerical solutions allow you to monitor your understanding of the material presented. This accessible text is ideal for researchers and graduate students studying photonic crystals in departments of electrical engi

This textbook provides engineers with the capability, tools and confidence to solve real-world heat transfer problems. It includes many advanced topics, such as Bessel functions, Laplace transforms, separation of variables, Duhamel's theorem and complex combination, as well as high order explicit and implicit numerical integration algorithms. These analytical and numerical solution methods are applied to topics not considered in most textbooks. Examples include heat exchangers involving fluids with varying specific heats or phase changes; heat exchangers in which axial conduction is a concern; and regenerators. Derivations of important results are presented completely, without skipping steps, which reduces student frustration and improves readability and retention. The examples are not trivial 'textbook' exercises; they are rather complex and timely real-world problems that are inherently interesting. This book integrates the computational software packages Maple, MATLAB®, FEHT and Eng

This textbook covers all the theoretical aspects of real variable analysis which undergraduates reading mathematics are likely to require during the first two or three years of their course. It is based on lecture courses which the author has given in the universities of Wales, Cambridge and London. The subject is presented rigorously and without padding. Definitions are stated explicitly and the whole development of the subject is logical and self-contained. Complex numbers are used but the complex variable calculus is not. 'Applied analysis', such as differential equations and Fourier series, is not dealt with. A large number of examples is included, with hints for the solution of many of them. These will be of particular value to students working on their own.

Ecological and environmental research has increased in scope and complexity in the last few decades, from simple systems with a few managed variables to complex ecosystems with many uncontrolled vari

Ecological and environmental research has increased in scope and complexity in the last few decades, from simple systems with a few managed variables to complex ecosystems with many uncontrolled vari