Complex Variables

Principles of Measurement and Transduction of Biomedical Variables is a comprehensive text on biomedical transducers covering the principles of functioning, application examples and new technology sol

Presenting the first unified treatment of limit theorems for multiple sums of independent random variables, this volume fills an important gap in the field. Several new results are introduced, even in

Regression Models for Categorical Dependent Variables Using Stata, Third Edition shows how to use Stata to fit and interpret regression models for categorical data. The third edition is a complete rew

This short book provides a unified view of the history and theory of random sets and fuzzy random variables, with special emphasis on its use for representing higher-order non-statistical uncertainty

Assessment of Trauma in Youths: Understanding issues of age, complexity, and associated variables is a collection of articles by well-known specialists in the field of childhood trauma. The articles d

Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayu

Fourier Series in Several Variables with Applications to Partial Differential Equations illustrates the value of Fourier series methods in solving difficult nonlinear partial differential equations (P

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.

This book introduces econometrics at graduate level, and then specializes in micro-econometrics topics such as method of moments, limited and qualitative dependent variables, sample-selection models,

Detailing the main methods in the theory of involutive systems of complex vector fields this book examines the major results from the last twenty five years in the subject. One of the key tools of the subject - the Baouendi-Treves approximation theorem - is proved for many function spaces. This in turn is applied to questions in partial differential equations and several complex variables. Many basic problems such as regularity, unique continuation and boundary behaviour of the solutions are explored. The local solvability of systems of partial differential equations is studied in some detail. The book provides a solid background for others new to the field and also contains a treatment of many recent results which will be of interest to researchers in the subject.

Writing for advanced undergraduates, Cain and Meyer (both mathematics emeriti, Georgia Institute of Technology) introduce a computable separation of variables solutions as an analytic approximate solu

An accessible introduction to the use of regression analysis in the social sciencesRegression with Social Data: Modeling Continuous and Limited Response Variables represents the most complete and full

This mathematical odyssey explains the concepts of variables and constants through the review of how Algebra was invented. Includes a chart of the ancient finger-counting method, various problem-solvi

This mathematical odyssey explains the concepts of variables and constants through the review of how Algebra was invented. Includes a chart of the ancient finger-counting method, various problem-solvi

In response to a growing interest in Total Least Squares (TLS) and Errors-In-Variables (EIV) modeling by researchers and practitioners, well-known experts from several disciplines were invited to prep

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The first part comprises the basic core of a course in complex analysis

The book first discusses in depth various aspects of the well-known inconsistency that arises when explanatory variables in a linear regression model are measured with error. Despite this inconsistenc

This book, first published in 2000, is a comprehensive introduction to holomorphic dynamics, that is the dynamics induced by the iteration of various analytic maps in complex number spaces. This has been the focus of much attention in recent years, with, for example, the discovery of the Mandelbrot set, and work on chaotic behaviour of quadratic maps. The treatment is mathematically unified, emphasizing the substantial role played by classical complex analysis in understanding holomorphic dynamics as well as giving an up-to-date coverage of the modern theory. The authors cover entire functions, Kleinian groups and polynomial automorphisms of several complex variables such as complex Henon maps, as well as the case of rational functions. The book will be welcomed by graduate students and professionals in pure mathematics and science who seek a reasonably self-contained introduction to this exciting area.

The classic text, now completely up to dateThis Second Edition of State Variables for Engineers is completely updated to reflect both the many changes in the field of systems and control and the fact

ABELIAN FUNCTIONS. Power Series in Several Variables. The Preparation Theorem. Regular Functions. Meromorphic Functions. The Theorem of Weierstrass and Cousin. The Period Group. Jacobian Functions. Li

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

The Genetic Analysis of Complex Disease provides a comprehensive introduction to the various strategies, designs, and methods of analysis for the study of human complex genetic disease. Chapt

This book is a guide to doing a new kind of psychological research that focuses on the purposes rather than the causes of behavior. The research methods described here are based on a theory of behaviour called Perceptual Control Theory (PCT) that views organisms as purposeful rather than mechanical systems. According to PCT, purposeful behaviour involves acting to control perceptual input variables. Thus, understanding the purposeful behaviour of living organisms is a matter of determining the perceptual variables they are controlling when they are carrying out various behaviors. This book outlines research methods that determine what perceptual variables an organism is controlling, how it controls those variables, and why. It also describes methods for studying how an organism develops the ability to control different perceptions and how consciousness might be involved in this process.

This book is a guide to doing a new kind of psychological research that focuses on the purposes rather than the causes of behavior. The research methods described here are based on a theory of behaviour called Perceptual Control Theory (PCT) that views organisms as purposeful rather than mechanical systems. According to PCT, purposeful behaviour involves acting to control perceptual input variables. Thus, understanding the purposeful behaviour of living organisms is a matter of determining the perceptual variables they are controlling when they are carrying out various behaviors. This book outlines research methods that determine what perceptual variables an organism is controlling, how it controls those variables, and why. It also describes methods for studying how an organism develops the ability to control different perceptions and how consciousness might be involved in this process.

This book shows how operator theory interacts with function theory in one and several variables. The authors develop the theory in detail, leading the reader to the cutting edge of contemporary research. It starts with a treatment of the theory of bounded holomorphic functions on the unit disc. Model theory and the network realization formula are used to solve Nevanlinna-Pick interpolation problems, and the same techniques are shown to work on the bidisc, the symmetrized bidisc, and other domains. The techniques are powerful enough to prove the Julia-Carathéodory theorem on the bidisc, Lempert's theorem on invariant metrics in convex domains, the Oka extension theorem, and to generalize Loewner's matrix monotonicity results to several variables. In Part II, the book gives an introduction to non-commutative function theory, and shows how model theory and the network realization formula can be used to understand functions of non-commuting matrices.

Unique in its clarity, examples, and range, Physical Mathematics explains simply and succinctly the mathematics that graduate students and professional physicists need to succeed in their courses and research. The book illustrates the mathematics with numerous physical examples drawn from contemporary research. This second edition has new chapters on vector calculus, special relativity and artificial intelligence and many new sections and examples. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations, Bessel functions, and spherical harmonics, the book explains topics such as the singular value decomposition, Lie algebras and group theory, tensors and general relativity, the central limit theorem and Kolmogorov's theorems, Monte Carlo methods of experimental and theoretical physics, Feynman's path integrals, and the standard model of cosmology.

This user-friendly textbook introduces complex analysis at the beginning graduate or advanced undergraduate level. Unlike other textbooks, it follows Weierstrass' approach, stressing the importance of power series expansions instead of starting with the Cauchy integral formula, an approach that illuminates many important concepts. This view allows readers to quickly obtain and understand many fundamental results of complex analysis, such as the maximum principle, Liouville's theorem, and Schwarz's lemma. The book covers all the essential material on complex analysis, and includes several elegant proofs that were recently discovered. It includes the zipper algorithm for computing conformal maps, as well as a constructive proof of the Riemann mapping theorem, and culminates in a complete proof of the uniformization theorem. Aimed at students with some undergraduate background in real analysis, though not Lebesgue integration, this classroom-tested textbook will teach the skills and intui

This title covers key topics and approaches for next generation networks and complex communication systems, and the various aspects of modeling and simulation of these networks from a complex adaptive

Vowel teams can make both long and complex vowel sounds. The special complex vowel teams can be spelled many different ways. They can be used to build common words we use everyday. Let's discover what

This book is a comprehensive introduction to quantitative approaches to complex adaptive systems. Practically all areas of life on this planet are constantly confronted with complex systems, be it eco

This book offers a thorough introduction to the highly promising complex agent-based approach to economics, in which agent-based models (ABMs) are used to represent economic systems as complex and evo

This book presents case-based descriptions of models for the inclusive, multispecialty and multidisciplinary clinical care of complex cases. Cases range from primary care patients with complex system

This book uses a complex systems perspective to describe how a language school in Greece evolved, and at times resisted change. Starting with an accessible introduction to complex systems theory (CST)

Advances in complex networks and graph signal processing have important implications in fields ranging from communications and social networking to big data and biology. In Complex Networks, three pio

Uncertain computation is a system of computation and reasoning in which the objects of computation are not values of variables but restrictions on values of variables. --

Gain a solid understanding of Light-Emitting Diode (LED) Systems Theory with this unique book. Written by a leading expert in LED lighting, it links together the photometric, electrical, thermal and chromatic elements of LED systems into a single, unified framework, and explores their complex interactions with one another. • Get to grips with chromatic, photometric and thermal modelling of LED systems • Discover new techniques for precise dimming and colour control • Learn methods for determining system parameters and internal variables • Gain insight into advanced applications for LED system design and optimization Providing straightforward and intuitive explanations, this is an ideal guide for professional engineers, graduate students and researchers working on solid-state lighting systems and smart lighting, and those taking advanced courses on LED devices and systems.

Complex Housing introduces an architectural type called complex housing, common to the Netherlands and found in other Northern European countries. Eight fully illustrated case studies show successful

This book addresses several important aspects of complex automated negotiations and introduces a number of modern approaches for facilitating agents to conduct complex negotiations. It demonstrates th

This book deals with complex theory of differential equations or more precisely, with the theory of differential equations on complex-analytic manifolds.The theory of differential equations on real ma