Complex Variables

Pain is a complex experience, influenced by many variables. There is currently growing interest in the influence of sex and gender on the experience of pain. The fact that there are sex differences in

Due to the countless variables that affect revenue and cost, the hospital reimbursement process is by far the most complex of any industry. Requiring only a basic financial background and a working kn

The sheer number of variables of complex dynamic systems do not allow their workings or failures to be understood by linear thinking or standard analytical methods. Hollnagel (U. of Southern Denmark)

Numerical and statistical methods have rapidly become part of a palaeolimnologist’s tool-kit. They are used to explore and summarise complex data, reconstruct past environmental variables from fossil

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,

This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, d

This Book begins with the basics of geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, diffe

Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.

Study faster, learn better, and get top grades Modified to conform to the current curriculum, Schaum's Outline of Probability, Random Variables, and Random Processes complements these courses in scop

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

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

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

In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cart

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

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

The first of two volumes offering a modern introduction to Kaehlerian geometry and Hodge structure. The book starts with basic material on complex variables, complex manifolds, holomorphic vector bundles, sheaves and cohomology theory, the latter being treated in a more theoretical way than is usual in geometry. The author then proves the Kaehler identities, which leads to the hard Lefschetz theorem and the Hodge index theorem. The book culminates with the Hodge decomposition theorem. The meanings of these results are investigated in several directions. Completely self-contained, the book is ideal for students, while its content gives an account of Hodge theory and complex algebraic geometry as has been developed by P. Griffiths and his school, by P. Deligne, and by S. Bloch. The text is complemented by exercises which provide useful results in complex algebraic geometry.

Sensory scientists are often faced with making business decisions based on the results of complex sensory tests involving a multitude of variables. Multivariate and Probabilistic Analyses of Sensory S

Introduces the algebraic equation and variables using examples relating to flight.

Although regression models for categorical dependent variables are common, few texts explain how to interpret such models. Regression Models for Categorical Dependent Variables Using Stata, Second Edi

Making the specifics of a complex concern accessible and its handling quite manageable, this fourth edition of the Project and Cost Engineers' Handbook examines the variables associated with internati

Products of Random Variables explores the theory of products of random variables through from distributions and limit theorems, to characterizations, to applications in physics, order statistics, and

A textbook for a year-long graduate course for students at least somewhat familiar with mathematical methods, Fourier series and Fourier integrals, elementary complex variables, elementary ordinary an

Governed by strict regulations and the intricate balance of complex interactions among variables, the application of mechanics to vehicle crashworthiness is not a simple task. It demands a solid under

Multivariate analysis plays an important role in the understanding of complex data sets requiring simultaneous examination of all variables. Breaking through the apparent disorder of the information,

This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book prese

The task of management has become increasingly complex in recent years. Chief executives and senior managers are confronted with the daunting challenge of making sense of a myriad of variables that

In this introduction to commutative algebra, the author leads the beginning student through the essential ideas, without getting embroiled in technicalities. The route chosen takes the reader quickly to the fundamental concepts for understanding complex projective geometry, the only prerequisites being a basic knowledge of linear and multilinear algebra and some elementary group theory. In the first part, the general theory of Noetherian rings and modules is developed. A certain amount of homological algebra is included, and rings and modules of fractions are emphasised, as preparation for working with sheaves. In the second part, the central objects are polynomial rings in several variables with coefficients in the field of complex numbers. After Noether's normalisation lemma and Hilbert's Nullstellensatz, affine complex schemes and their morphisms are introduced; Zariski's main theorem and Chevalley's semi-continuity theorem are then proved. Finally, a detailed study of Weil and Cart

This book presents the econometric analysis of single-equation and simultaneous-equation models in which the jointly dependent variables can be continuous, categorical, or truncated. Despite the traditional emphasis on continuous variables in econometrics, many of the economic variables encountered in practice are categorical (those for which a suitable category can be found but where no actual measurement exists) or truncated (those that can be observed only in certain ranges). Such variables are involved, for example, in models of occupational choice, choice of tenure in housing, and choice of type of schooling. Models with regulated prices and rationing, and models for program evaluation, also represent areas of application for the techniques presented by the author.

Originally published in 1977, this volume is concerned with the relationship between symmetries of a linear second-order partial differential equation of mathematical physics, the coordinate systems in which the equation admits solutions via separation of variables, and the properties of the special functions that arise in this manner. Some group-theoretic twists in the ancient method of separation of variables that can be used to provide a foundation for much of special function theory are shown. In particular, it is shown explicitly that all special functions that arise via separation of variables in the equations of mathematical physics can be studied using group theory.

Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, converge

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This pioneering study combines insights from philosophy and linguistics to develop a novel framework for theorizing about linguistic meaning and the role of context in interpretation. A key innovation is to introduce explicit representations of context - assignment variables - in the syntax and semantics of natural language. The proposed theory systematizes a spectrum of 'shifting' phenomena in which the context relevant for interpreting certain expressions depends on features of the linguistic environment. Central applications include local and non-local contextual dependencies with quantifiers, attitude ascriptions, conditionals, questions, and relativization. The result is an innovative philosophically informed compositional semantics compatible with the truth-conditional paradigm. At the forefront of contemporary interdisciplinary research into meaning and communication, Semantics with Assignment Variables is essential reading for researchers and students in a diverse range of fiel

This book introduces the reader to a wide range of topics in the theory of holomorphic functions of several variables, with fairly complete proofs. It reviews the relevant properties of subharmonic fu

Production of world food supplies is related to more complicated socioeconomic variables than have previously been analyzed. Besides traditional inputs of land, labor, and fertilizer, the technologica

Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications is a comprehensive undergraduate-level textbook. With its excellent topical coverage, the focus of this

Separation of variables methods for solving partial differential equations are of immense theoretical and practical importance in mathematical physics. They are the most powerful tool known for obtain

This book presents an overview of the different errors-in-variables (EIV) methods that can be used for system identification. Readers will explore the properties of an EIV problem. Such problems play

A concise monograph by two Russian experts provides an account of the operational calculus in two variables based on the two-dimensional Laplace transform. Suitable for advanced undergraduates and gra

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