Applied Complex Variables

Quantitative research in social science research is changing rapidly. Researchers have vast and complex arrays of data with which to work: we have incredible tools to sift through the data and recognize patterns in that data; there are now many sophisticated models that we can use to make sense of those patterns; and we have extremely powerful computational systems that help us accomplish these tasks quickly. This book focuses on some of the extraordinary work being conducted in computational social science - in academia, government, and the private sector - while highlighting current trends, challenges, and new directions. Thus, Computational Social Science showcases the innovative methodological tools being developed and applied by leading researchers in this new field. The book shows how academics and the private sector are using many of these tools to solve problems in social science and public policy.

Quantitative research in social science research is changing rapidly. Researchers have vast and complex arrays of data with which to work: we have incredible tools to sift through the data and recognize patterns in that data; there are now many sophisticated models that we can use to make sense of those patterns; and we have extremely powerful computational systems that help us accomplish these tasks quickly. This book focuses on some of the extraordinary work being conducted in computational social science - in academia, government, and the private sector - while highlighting current trends, challenges, and new directions. Thus, Computational Social Science showcases the innovative methodological tools being developed and applied by leading researchers in this new field. The book shows how academics and the private sector are using many of these tools to solve problems in social science and public policy.

The first study of its kind, Regional Variation in Written American English takes a corpus-based approach to map over one hundred grammatical alternation variables across the United States. A multivariate spatial analysis of these maps shows that grammatical alternation variables follow a relatively small number of common regional patterns in American English, which can be explained based on both linguistic and extra-linguistic factors. Based on this rigorous analysis of extensive data, Grieve identifies five primary modern American dialect regions, demonstrating that regional variation is far more pervasive and complex in natural language than is generally assumed. The wealth of maps and data, and the groundbreaking implications of this volume, make it essential reading for students and researchers in linguistics, English language, geography, computer science, sociology and communication studies.

As most econometricians will readily agree, the data used in applied econometrics seldom provide accurate measurements for the pertinent theory's variables. Here, Bernt Stigum offers the first systema

Over the last twenty years, genome-wide association studies (GWAS) have revealed a great deal about the genetic basis of a wide range of complex diseases and they will undoubtedly continue to have a broad impact as we move to an era of personalised medicine. This authoritative text, written by leaders and innovators from both academia and industry, covers the basic science as well as the clinical, biotechnological and pharmaceutical potential of these methods. With special emphasis given to highlighting pharmacogenomics and population genomics studies using next-generation technology approaches, this is the first book devoted to combining association studies with single nucleotide polymorphisms, copy number variants, haplotypes and expressed quantitative trait loci. A reliable guide for newcomers to the field as well as for experienced scientists, this is a unique resource for anyone interested in how the revolutionary power of genomics can be applied to solve problems in complex disea

From social networks such as Facebook, the World Wide Web and the Internet, to the complex interactions between proteins in the cells of our bodies, we constantly face the challenge of understanding the structure and development of networks. The theory of random graphs provides a framework for this understanding, and in this book the authors give a gentle introduction to the basic tools for understanding and applying the theory. Part I includes sufficient material, including exercises, for a one semester course at the advanced undergraduate or beginning graduate level. The reader is then well prepared for the more advanced topics in Parts II and III. A final part provides a quick introduction to the background material needed. All those interested in discrete mathematics, computer science or applied probability and their applications will find this an ideal introduction to the subject.

Exploring Language and Linguistics considers the key concepts of linguistics and the application of these concepts to real-world settings. The first eight chapters cover the standard topics of introduction to linguistics courses, while subsequent chapters introduce students to applied topics such as media discourse, literary linguistics and psycholinguistics. Each chapter has been written by a subject expert and experienced teacher, ensuring that the text is both up-to-date and clearly presented. Numerous learning features provide extensive student support: exercises allow students to review their understanding of key topics; summaries encourage students to reflect on the main points of each chapter; figures, photos, tables and charts clarify complex topics; and annotated suggestions for further reading point students to resources for self-study. A companion website, with 170 self-test questions, suggested group exercises, audio files and links to additional web resources, completes th

Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.

Exploring Language and Linguistics considers the key concepts of linguistics and the application of these concepts to real-world settings. The first eight chapters cover the standard topics of introduction to linguistics courses, while subsequent chapters introduce students to applied topics such as media discourse, literary linguistics and psycholinguistics. Each chapter has been written by a subject expert and experienced teacher, ensuring that the text is both up-to-date and clearly presented. Numerous learning features provide extensive student support: exercises allow students to review their understanding of key topics; summaries encourage students to reflect on the main points of each chapter; figures, photos, tables and charts clarify complex topics; and annotated suggestions for further reading point students to resources for self-study. A companion website, with 170 self-test questions, suggested group exercises, audio files and links to additional web resources, completes th

This authoritative treatment covers theory, optimal estimation and a range of practical applications. The first book on the subject, and written by leading researchers, this clear and rigorous work presents a comprehensive theory for both the stability boundary and the stability regions of a range of nonlinear dynamical systems including continuous, discrete, complex, two-time-scale and non-hyperbolic systems, illustrated with numerical examples. The authors also propose new concepts of quasi-stability region and of relevant stability regions and their complete characterisations. Optimal schemes for estimating stability regions of general nonlinear dynamical systems are also covered, and finally the authors describe and explain how the theory is applied in applications including direct methods for power system transient stability analysis, nonlinear optimisation for finding a set of high-quality optimal solutions, stabilisation of nonlinear systems, ecosystem dynamics, and immunisation

A comprehensive exposition of the theory and techniques of fault identification and decision theory when applied to complex systems‧ shows how modern computer analysis and diagnostic methods might be

The monograph is devoted to integral representations for holomorphic functions in several complex variables, such as Bochner-Martinelli, Cauchy-Fantappie, Koppelman, multidimensional logarithmic resid

Hans Grauert was one of the world's leading mathematicians in the field of Several Complex Variables; he not only shaped the development of this area decisively but was also responsible for some of it

Dynamical models on graphs or random graphs are increasingly used in applied sciences as mathematical tools to study complex systems whose exact structure is too complicated to be known in detail. Bes

The mathematical theory of stochastic dynamics has become an important tool in the modeling of uncertainty in many complex biological, physical, and chemical systems and in engineering applications - for example, gene regulation systems, neuronal networks, geophysical flows, climate dynamics, chemical reaction systems, nanocomposites, and communication systems. It is now understood that these systems are often subject to random influences, which can significantly impact their evolution. This book serves as a concise introductory text on stochastic dynamics for applied mathematicians and scientists. Starting from the knowledge base typical for beginning graduate students in applied mathematics, it introduces the basic tools from probability and analysis and then develops for stochastic systems the properties traditionally calculated for deterministic systems. The book's final chapter opens the door to modeling in non-Gaussian situations, typical of many real-world applications. Rich wit

The mathematical theory of stochastic dynamics has become an important tool in the modeling of uncertainty in many complex biological, physical, and chemical systems and in engineering applications - for example, gene regulation systems, neuronal networks, geophysical flows, climate dynamics, chemical reaction systems, nanocomposites, and communication systems. It is now understood that these systems are often subject to random influences, which can significantly impact their evolution. This book serves as a concise introductory text on stochastic dynamics for applied mathematicians and scientists. Starting from the knowledge base typical for beginning graduate students in applied mathematics, it introduces the basic tools from probability and analysis and then develops for stochastic systems the properties traditionally calculated for deterministic systems. The book's final chapter opens the door to modeling in non-Gaussian situations, typical of many real-world applications. Rich wit

As both the societies and the world in which we live face increasingly rapid and turbulent changes, the concept of resilience has become an active and important research area. Reflecting the very latest research, this book provides a critical review of the ways in which resilience of social-ecological systems, and the ecosystem services they provide, can be enhanced. With contributions from leaders in the field, the chapters are structured around seven key principles for building resilience: maintain diversity and redundancy; manage connectivity; manage slow variables and feedbacks; foster complex adaptive systems thinking; encourage learning; broaden participation; and promote polycentric governance. The authors assess the evidence in support of these principles, discussing their practical application and outlining further research needs. Intended for researchers, practitioners and graduate students, this is an ideal resource for anyone working in resilience science and for those in t

Focusing on deterministic models in discrete time, this concise yet rigorous textbook provides a clear and systematic introduction to the theory and application of dynamic economic models. It guides students through the most popular model structures and solution concepts, from the simplest dynamic economic models through to complex problems of optimal policy design in dynamic general equilibrium frameworks. Chapters feature theorems and practical hints, and seventy-five worked examples highlight the various methods and results that can be applied in dynamic economic models. Notation and formulation is uniform throughout, so students can easily discern the similarities and differences between various model classes. Chapters include more than sixty exercises for students to self-test their analytical skills, and password-protected solutions are available for instructors on the companion website. Assuming no prior knowledge of dynamic economic analysis or dynamic optimization, this textbo

Bringing together basic ideas, classical theories, recent experimental and theoretical aspects, this book explains desiccation cracks from simple, easily-comprehensible cases to more complex, applied

Quick solutions to complex numerical problems in physics, applied mathematics, and science with SciPy About This BookUse different modules and routines from the SciPy library quickly and efficientlyCr

Ruel V. Churchill 撰寫的複變函數與應用，理論與應用並重，出版以來，風行全球將近半個世紀，深受各界喜愛。本書第九版仍由第八版的作者，美國密西根大學數學系教授James Ward Brown 執筆，他根據多年的教學經驗，擷取各界人士的建議，做了大幅度的修正，使本書除了可當做教科書，也適合參考與自修之用。 本書有兩個主要的目標•首先詳述有關複變函數應用方面的理論。•其次是介紹留數與保角

Focusing on simplified models of physical flow processes, this book develops a series of quantitative models to describe the recovery of oil and gas from hydrocarbon reservoirs (including fracking), the physics of geo-sequestration of CO2, geothermal power production, and the potential for underground contaminant dispersal in the long-term storage of nuclear waste. The author approaches these problems by developing simplified mathematical models and identifying the key dimensionless variables that control the processes. This analysis is then used to demonstrate the challenges and constraints of modelling flow in complex and heterogeneous rocks, which often have uncertain flow properties. Analytical solutions for flows are provided where possible, and analogue laboratory experiments are also presented to help illustrate and provide a different perspective on the flows. Incorporating end-of-chapter exercises, this is an important introduction to the different controls on flow in porous r

Applied econometrics, known to aficionados as 'metrics, encompasses the statistical methods economists use to untangle cause and effect in human affairs. Through accessible discussion and with a dose of kung fu-themed humor, Mastering 'Metrics presents the essential tools of econometric research and demonstrates why econometrics is exciting and useful.The five most valuable econometric methods, or what the authors call the Furious Five--random assignment, regression, instrumental variables, regression discontinuity designs, and differences in differences--are illustrated through well-crafted real-world examples (vetted for awesomeness by Kung Fu Panda's Jade Palace). Does health insurance make you healthier? Randomized experiments provide answers. Are expensive private colleges and selective public high schools better than more pedestrian institutions? Regression analysis and a regression discontinuity design reveal the surprising truth. When private banks teeter, and depositors take t

Hans Grauert was one of the world's leading mathematicians in the field of Several Complex Variables; he not only shaped the development of this area decisively but was also responsible for some of it

Many social work students find studying the law a complex and challenging process. This book helps students gain a strong foothold in understanding aspects of law as applied to social work practice.

"This book highlights analytical chemistry instrumentation and practices applied to the analysis of natural products and their complex mixtures, describing techniques for isolating and characterizing

Drawing on extensive corpus-based research, this book explores the nature and behavior of coordinate constructions in three case studies, covering order in copulative compounds, binomials (bare phrases), and more complex phrases. Historically, research on order in coordination has concentrated on so-called irreversible binomials, but Lohmann's research places significant focus on reversible ad hoc coordination and also presents a detailed comparison between irreversible and reversible binomials. This book uses empirical analyses to explore a wide range of factors, ranging from pragmatic to phonetic influences on the ordering process. It also offers readers a processing perspective on the results obtained, and puts forth a processing explanation for the characteristics of irreversible binomials. The book is ideal for researchers and advanced students working in English linguistics, syntax and psycholinguistics, and due to the multifactorial methodology applied it will be of particular i

Fourier Analysis with Complex Variables explains transform methods and their application to electrical systems from circuits, antennas, and signal processors—ably guiding readers from vector space con

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,

The purpose of the corona workshop was to consider the corona problem in both one and several complex variables, both in the context of function theory and harmonic analysis as well as the context of

Many of the operators one meets in several complex variables, such as the famous Lewy operator, are not locally solvable. Nevertheless, such an operator L can be thoroughly studied if one can find a s

From the German preface of R. Remmert: “When kings build their kingdom, there is work for the draymen. Kiyoshi Oka was a king. His kingdom was the function theory of several complex variables. He solv

Ben Hogan made hitting a golf ball look easy, and the results spoke for themselves. But Hogan’s ?swing system” is as complex as a spider’s web; the variables and connections are never-ending. In Ben H

Modern Administrative Law in Australia provides an authoritative overview of administrative law in Australia. It clarifies and enlivens this crucial but complex area of law, with erudite analysis and modern perspectives. The contributors - including highly respected academics from eleven Australian law schools, as well as eminent practitioners including Chief Justice Robert French AC and Justice Stephen Gageler of the High Court of Australia - are at the forefront of current research, debate and decision making, and infuse the book with unique insight. The book examines the structure and themes of administrative law, the theory and practice of judicial review, and the workings of administrative law beyond the courts. Administrative law affects innumerable aspects of political, commercial and private life, and yet is often considered difficult to understand. Modern Administrative Law unravels the intricacies and reveals how they are applied in real cases. It is an essential reference fo

Reviewing macroscopic quantum phenomena and quantum dissipation, from the phenomenology of magnetism and superconductivity to the presentation of alternative models for quantum dissipation, this book develops the basic material necessary to understand the quantum dynamics of macroscopic variables. Macroscopic quantum phenomena are presented through several examples in magnetism and superconductivity, developed from general phenomenological approaches to each area. Dissipation naturally plays an important role in these phenomena, and therefore semi-empirical models for quantum dissipation are introduced and applied to the study of a few important quantum mechanical effects. The book also discusses the relevance of macroscopic quantum phenomena to the control of meso- or nanoscopic devices, particularly those with potential applications in quantum computation or quantum information. It is ideal for graduate students and researchers.

At the heart of Houston stands the Texas Medical Center. This dense complex of educational, clinical, and hospital facilities offers state-of-the-art patient care, basic science, and applied research

On one hand, marginals are complex organizational systems. On the other hand, they are an example of elegant, applied organizational operations. In The Marginal Organization, Tafoya focuses on organiz

This definitive textbook provides a solid introduction to discrete and continuous stochastic processes, tackling a complex field in a way that instils a deep understanding of the relevant mathematical principles, and develops an intuitive grasp of the way these principles can be applied to modelling real-world systems. It includes a careful review of elementary probability and detailed coverage of Poisson, Gaussian and Markov processes with richly varied queuing applications. The theory and applications of inference, hypothesis testing, estimation, random walks, large deviations, martingales and investments are developed. Written by one of the world's leading information theorists, evolving over twenty years of graduate classroom teaching and enriched by over 300 exercises, this is an exceptional resource for anyone looking to develop their understanding of stochastic processes.

The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and teachers. Volume 1 focuses on the analysis of real-valued functions of a real variable. This second volume goes on to consider metric and topological spaces. Topics such as completeness, compactness and connectedness are developed, with emphasis on their applications to analysis. This leads to the theory of functions of several variables. Differential manifolds in Euclidean space are introduced in a final chapter, which includes an account of Lagrange multipliers and a detailed proof of the divergence theorem. Volume 3 covers complex analysis and the theory of measure and integration.