Complex Variables

This book introduces the reader to the vast area of research focusing on quantum mechanical systems described by continuous variables, such as positions and momenta of particles, which provide the the

What Makes Variables Random: Probability for the Applied Researcher provides an introduction to the foundations of probability that underlie the statistical analyses used in applied research. By expla

This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.

This valuable compendium provides an overview of the variables and consequences of oceanic carbon cycling in the context of climate change. The chapters highlight the importance of marine plankton in

Seven of the eleven papers in this collection explain how to estimate discrete dependent variables with spatial dependence using maximum likelihood and how to estimate binary and count dependent va

Predictive modeling uses data to forecast future events. It exploits relationships between explanatory variables and the predicted variables from past occurrences to predict future outcomes. Forecasting financial events is a core skill that actuaries routinely apply in insurance and other risk-management applications. Predictive Modeling Applications in Actuarial Science emphasizes life-long learning by developing tools in an insurance context, providing the relevant actuarial applications, and introducing advanced statistical techniques that can be used to gain a competitive advantage in situations with complex data. Volume 2 examines applications of predictive modeling. Where Volume 1 developed the foundations of predictive modeling, Volume 2 explores practical uses for techniques, focusing on property and casualty insurance. Readers are exposed to a variety of techniques in concrete, real-life contexts that demonstrate their value and the overall value of predictive modeling, for se

This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical syst

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.

Measuring Non Cognitive Variables: Improving Admissions and Post Enrollment Services in Higher Education is written for admissions professionals, counselors, faculty and advisors who admit, teach, or

Measuring Non Cognitive Variables: Improving Admissions and Post Enrollment Services in Higher Education is written for admissions professionals, counselors, faculty and advisors who admit, teach, or

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

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,

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

Logistic Regression Models for Ordinal Response Variables provides applied researchers in the social, educational, and behavioral sciences with an accessible and comprehensive coverage of analyses fo

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 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.

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 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