Applied Complex Variables

This volume provides readers with a simple, non-technical introduction to correspondence analysis (CA), a technique for summarily describing the relationships among categorical variables in large tab

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This permits a simpler treatment than other books, yet is still sufficient for a wide range of applications to complex analysis; these include Picard's theorem, the Phragmén–Lindelöf principle, the Koebe one-quarter mapping theorem and a sharp quantitative form of Runge's theorem. In addition there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics, and gives a flavour of some recent research. Exercises are provided throughout, enabling the book to be used with advanced courses on complex analysis or potential theory.

Potential theory is the broad area of mathematical analysis encompassing such topics as harmonic and subharmonic functions, the Dirichlet problem, harmonic measure, Green's functions, potentials and capacity. This is an introduction to the subject suitable for beginning graduate students, concentrating on the important case of two dimensions. This permits a simpler treatment than other books, yet is still sufficient for a wide range of applications to complex analysis; these include Picard's theorem, the Phragmén–Lindelöf principle, the Koebe one-quarter mapping theorem and a sharp quantitative form of Runge's theorem. In addition there is a chapter on connections with functional analysis and dynamical systems, which shows how the theory can be applied to other parts of mathematics, and gives a flavour of some recent research. Exercises are provided throughout, enabling the book to be used with advanced courses on complex analysis or potential theory.

Graphical models--a subset of log-linear models--reveal the interrelationships between multiple variables and features of the underlying conditional independence. Following the theorem-proof-remarks

This text is part of the International Series in Pure and Applied Mathematics. It is designed for junior, senior, and first-year graduate students in mathematics and engineering. This edition preserve

This cross-disciplinary volume provides an overview of how complexity theory and the tools of statistical mechanics can be applied to linguistic problems to help reveal language groups, and to model the evolution and competition of languages in space and time. Illustrated with a series of case studies and worked examples, it presents an interdisciplinary framework to enable researchers from the mathematical, physical and social sciences to collaborate on linguistic problems. It demonstrates the complexity of linguistic databases and provides a mathematical toolkit for analyzing and extracting useful information from them - helping to conceptualize empirical facts better than a mere ethnographic view. Providing an important bridge to facilitate collaboration between linguists and mathematical modelers, this book will stimulate new ideas and avenues for research, and will form a valuable resource for advanced students and academics working across complex systems, sociolinguistics, and la

The upheavals of recent decades show us that traditional models of understanding processes of social and economic change are failing to capture real-world risk and volatility. This has resulted in flawed policy that seeks to capture change in terms of the rise or decline of regimes or regions. In order to comprehend current events, understand future risks and decide how to prepare for them, we need to consider economies and social orders as open, complex networks. This highly original work uses the tools of network analysis to understand great transitions in history, particularly those concerning economic development and globalisation. Hilton L. Root shifts attention away from particular agents – whether individuals, groups, nations or policy interventions – and toward their dynamic interactions. Applying insights from complexity science to often overlooked variables across European and Chinese history, he explores the implications of China's unique trajectory and ascendency, as a comp

This book provides practical guidance on research methods and designs that can be applied to Complex Dynamic Systems Theory (CDST) research. It discusses the contribution of CDST to the field of appli

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

This practical book is designed for applied researchers who want to use mixed models with their data. It discusses the basic principles of mixed model analysis, including two-level and three-level structures, and covers continuous outcome variables, dichotomous outcome variables, and categorical and survival outcome variables. Emphasizing interpretation of results, the book develops the most important applications of mixed models, such as the study of group differences, longitudinal data analysis, multivariate mixed model analysis, IPD meta-analysis, and mixed model predictions. All examples are analyzed with STATA, and an extensive overview and comparison of alternative software packages is provided. All datasets used in the book are available for download, so readers can re-analyze the examples to gain a strong understanding of the methods. Although most examples are taken from epidemiological and clinical studies, this book is also highly recommended for researchers working in other

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 essential book describes the mathematical formulations and subsequent computer simulations required to accurately project the trajectory of spacecraft and rockets in space, using the formalism of optimal control for minimum-time transfer in general elliptic orbit. The material will aid research students in aerospace engineering, as well as practitioners in the field of spaceflight dynamics, in developing simulation software to carry out trade studies useful in vehicle and mission design. It will teach readers to develop flight software for operational applications in autonomous mode, so to actually transfer space vehicles from one orbit to another. The practical, real-life applications discussed will give readers a clear understanding of the mathematics of orbit transfer, allow them to develop their own operational software to fly missions, and to use the contents as a research tool to carry out even more complex analyses.

Economic forecasting is a key ingredient of decision making both in the public and in the private sector. Because economic outcomes are the result of a vast, complex, dynamic and stochastic system, fo

This volume sheds light on the current state of complex networks and nonlinear dynamics applied to the understanding of economic and social phenomena ranging from geographical economics to macroeco

This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading exper

This volume includes 28 chapters by authors who are leading researchers of the world describing many of the up-to-date aspects in the field of several complex variables (SCV). These contributions are

Ivancevic and Reid present a graduate level textbook on modern complexity theory to be used in a one-semester course for students of engineering, applied and pure mathematics, theoretical and experime

This book explains and examines the theoretical underpinnings of the Complex Variable Boundary Element Method (CVBEM) as applied to higher dimensions, providing the reader with the tools for extending

Written in a unique style, this book is a valuable resource for faculty, graduate students, and researchers in the communications and networking area whose work interfaces with optimization. It teaches you how various optimization methods can be applied to solve complex problems in wireless networks. Each chapter reviews a specific optimization method and then demonstrates how to apply the theory in practice through a detailed case study taken from state-of-the-art research. You will learn various tips and step-by-step instructions for developing optimization models, reformulations, and transformations, particularly in the context of cross-layer optimization problems in wireless networks involving flow routing (network layer), scheduling (link layer), and power control (physical layer). Throughout, a combination of techniques from both operations research and computer science disciplines provides a holistic treatment of optimization methods and their applications. Each chapter includes

This book links the emerging concepts of complexity, complex adaptive systems (CAS) and resilience to forest ecology and management. It explores how these concepts can be applied in various forest bio

Have you ever solved problems which then recur again and again? Have you ever thought about the benefits you may have from learning a practical approach to clarify complex scenarios? Do you know the r

In this thesis, novel Monte Carlo methods for precisely calculating the critical phenomena of the effectively frustrated quantum spin system are developed and applied to the critical phenomena of the

The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phe

Based on course notes from over twenty years of teaching engineering and physical sciences at Michigan Technological University, Tomas Co's engineering mathematics textbook is rich with examples, applications and exercises. Professor Co uses analytical approaches to solve smaller problems to provide mathematical insight and understanding, and numerical methods for large and complex problems. The book emphasises applying matrices with strong attention to matrix structure and computational issues such as sparsity and efficiency. Chapters on vector calculus and integral theorems are used to build coordinate-free physical models with special emphasis on orthogonal co-ordinates. Chapters on ODEs and PDEs cover both analytical and numerical approaches. Topics on analytical solutions include similarity transform methods, direct formulas for series solutions, bifurcation analysis, Lagrange–Charpit formulas, shocks/rarefaction and others. Topics on numerical methods include stability analysis,

Addressing a hugely diverse range of topics, both fundamental and applied, this anthology of papers from leading researchers in non-linear and complex dynamics honors the seminal contributions to the

To say that complex data analyses are ubiquitous in the education and social sciences might be an understatement. Funding agencies and peer-review journals alike require that researchers use the most

To say that complex data analyses are ubiquitous in the education and social sciences might be an understatement. Funding agencies and peer-review journals alike require that researchers use the most

This book links the emerging concepts of complexity, complex adaptive system (CAS) and resilience to forest ecology and management. It explores how these concepts can be applied in various forest biom

Increasingly powerful and diverse computing technologies have the potential to tackle ever greater and more complex problems and dilemmas in engineering and science disciplines. Principal Concepts in

The book reviews recent research activities in applied mechanics and applied mathematics such as the fields of solid & fluid constitutive modeling for coupled fields, applications of geophysical &

The purpose of this book, first published in 1939, updated in 1953, is to give a treatment of the so-called operational method and to illustrate its application to problems in various branches of technology. It is written primarily for technologists who use mathematics in solving technical problems in industrial and applied research work, and the treatment is sufficiently rigorous for their needs. The theory of the complex variable and of transform calculus occupy the first half of the book. A further third of the book describes the application of this theory to problems arising in electrical circuits; vibrational systems; aeroplane dynamics; the deflexion of beams; radio and television receivers; the solution of partial differential equations; electrical transmission limes; electrical wave filters; solenoids with metal cores; condenser microphones; loud speaker horns and the absorption of moisture. The final part contains over 100 problems - many with hints for their solution - append