Innovative Computing Methods and Their Applications to Engineering Problems

This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and

This two-volume set aims to present as completely as possible the methods of statistical inference with special reference to their economic applications. The reader will find a description not only of the classical concepts and results of mathematical statistics, but also of concepts and methods recently developed for the specific needs of econometrics. The authors have sought to avoid an overly technical presentation and go to some lengths to encourage an intuitive understanding of the results by providing numerous examples throughout. The breadth of approaches and the extensive coverage of the two volumes provide for a thorough and entirely self-contained course in modern econometrics. Volume 1 provides an introduction to general concepts and methods in statistics and econometrics, and goes on to cover estimation and prediction. Volume 2 focuses on testing, confidence regions, model selection, and asymptotic theory.

This two-volume work aims to present as completely as possible the methods of statistical inference with special reference to their economic applications. The reader will find a description not only of the classical concepts and results of mathematical statistics, but also of concepts and methods recently developed for the specific needs of econometrics. The authors have sought to avoid an overly technical presentation and go to some lengths to encourage an intuitive understanding of the results by providing numerous examples throughout. The breadth of approaches and the extensive coverage of the two volumes provide for a thorough and entirely self-contained course in modern econometrics. Volume 1 provides an introduction to general concepts and methods in statistics and econometrics, and goes on to cover estimation and prediction. Volume 2 focuses on testing, confidence regions, model selection, and asymptotic theory.

This two-volume work aims to present as completely as possible the methods of statistical inference with special reference to their economic applications. The reader will find a description not only of the classical concepts and results of mathematical statistics, but also of concepts and methods recently developed for the specific needs of econometrics. The authors have sought to avoid an overly technical presentation and go to some lengths to encourage an intuitive understanding of the results by providing numerous examples throughout. The breadth of approaches and the extensive coverage of the two volumes provide for a thorough and entirely self-contained course in modern econometrics. Volume 1 provides an introduction to general concepts and methods in statistics and econometrics, and goes on to cover estimation and prediction. Volume 2 focuses on testing, confidence regions, model selection, and asymptotic theory.

This book is a self-contained introduction to the theory of distributions, sometimes called generalized functions. Most books on this subject are either intuitive or else rigorous but technically demanding. Here, by concentrating on the essential results, the authors have introduced the subject in a way that will most appeal to non-specialists, yet is still mathematically correct. Topics covered include: the Dirac delta function, generalized functions, dipoles, quadrupoles, pseudofunctions and Fourier transforms. The self-contained treatment does not require any knowledge of functional analysis or topological vector spaces; even measure theory is not needed for most of the book. The book, which can be used either to accompany a course or for self-study, is liberally supplied with exercises. It will be a valuable introduction to the theory of distributions and their applications for students or professionals in statistics, physics, engineering and economics.

Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited review papers, by leaders in their respective fields, allow researchers and graduate students alike quickly to grasp trends and developments. Highlights of the 1995 issue include articles on sequential quadratic programming, mesh adaption, free boundary problems and particle methods in continuum computations.

Drawing on a wide range of mathematical disciplines, including geometry, analysis, applied mathematics and algebra, this book presents an innovative synthesis of methods used to study problems of equivalence and symmetry which arise in a variety of mathematical fields and physical applications. Systematic and constructive methods for solving equivalence problems and calculating symmetries are developed and applied to a wide variety of mathematical systems, including differential equations, variational problems, manifolds, Riemannian metrics, polynomials and differential operators. Particular emphasis is given to the construction and classification of invariants, and to the reductions of complicated objects to simple canonical forms. This book will be a valuable resource for students and researchers in geometry, analysis, algebra, mathematical physics and other related fields.

This is an introduction to nonlinear functional analysis, in particular to those methods based on differential calculus in Banach spaces. It is in two parts; the first deals with the geometry of Banach spaces and includes a discussion of local and global inversion theorems for differentiable mappings. In the second part, the authors are more concerned with bifurcation theory, including the Hopf bifurcation. They include plenty of motivational and illustrative applications, which indeed provide much of the justification of nonlinear analysis. In particular, they discuss bifurcation problems arising from such areas as mechanics and fluid dynamics. The book is intended to accompany upper division courses for students of pure and applied mathematics and physics; exercises are consequently included.

Over the last two years, wavelet methods have shown themselves to be of considerable use to harmonic analysts and, in particular, advances have been made concerning their applications. The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing. Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase.

The aim of this book is to present graduate students with a thorough survey of reference probability models and their applications to optimal estimation and control. These new and powerful methods are

There has been an explosion of interest in the study of molecular crystals, and their applications in optics and electronics. This advanced 1994 textbook describes their chemical and physical structure, their optical and electronic properties and the reactions between neighbouring molecules in crystals. The author has taken into account research areas which have undergone extremely rapid development since the first edition was published in 1987. For instance, this edition features the applications of molecular materials in high-technology devices. There is also an additional chapter on C60 and organic non-linear optic materials. The level of treatment is aimed at first-year postgraduates or workers in industrial research laboratories wishing to gain insights into organic solid state materials. Molecular Crystals is also suitable for special topics in final year undergraduate courses in chemistry, physics and electronic engineering.

There has been an explosion of interest in the study of molecular crystals, and their applications in optics and electronics. This advanced 1994 textbook describes their chemical and physical structure, their optical and electronic properties and the reactions between neighbouring molecules in crystals. The author has taken into account research areas which have undergone extremely rapid development since the first edition was published in 1987. For instance, this edition features the applications of molecular materials in high-technology devices. There is also an additional chapter on C60 and organic non-linear optic materials. The level of treatment is aimed at first-year postgraduates or workers in industrial research laboratories wishing to gain insights into organic solid state materials. Molecular Crystals is also suitable for special topics in final year undergraduate courses in chemistry, physics and electronic engineering.

The study of the Earth and the environment requires an understanding of the physical processes within and at the surface of the Earth. This book allows the student to develop a broad working knowledge of mechanics and its application to the earth and environmental sciences - providing the background necessary to study the professional literature. The mathematical background required is a first-year course in calculus - more advanced topics are introduced in the context of their applications. The book aims to develop an understanding of the physics for each topic in mechanics, to provide insight into a wide range of natural phenomena. The breadth of application, and the many worked examples and problems will lead both students and professionals to a better understanding of the physical systems at work in the Earth's crust and at its surface.

The exploration and colonisation of the Pacific is a remarkable episode of human prehistory. Early sea-going explorers had no prior knowledge of Pacific geography, no documents to record their route, no metal, no instruments for measuring time and none for exploration. Forty years of modern archaeology, experimental voyages in rafts, and computer simulations of voyages have produced an enormous range of literature on this controversial and mysterious subject. This book represents a major advance in knowledge of the settlement of the Pacific by suggesting that exploration was rapid and purposeful, undertaken systematically, and that navigation methods progressively improved. Using an innovative model to establish a detailed theory of navigation, Geoffrey Irwin claims that rather than sailing randomly downwind in search of the unknown, Pacific Islanders expanded settlement by the cautious strategy of exploring upwind, so as to ease their safe return. The author has tested this hypothesis

This comprehensive text is a revised and greatly expanded second edition of a book first published in 1987, and provides a thorough introduction to the complex fields of signal coding and signal processing. Among the key topics covered are: the fundamentals of pulse code modulation; modern data compression techniques; block and convolutional error control codes; transmission coding techniques; digital filters; infinite and finite impulse response filters; adaptive filters; and fast Fourier transform theory, implementation and applications. Complete with problems and solutions, and containing over 230 diagrams, this textbook will be invaluable to third and fourth year undergraduates in electronic, electrical or communication engineering. It will also act as a useful reference for anyone working in this technologically important field.

The definition and solution of engineering problems relies on the ability to represent systems and their behaviour in mathematical terms.Mathematics for Electrical Technicians 4/5 provides a simple an

Comparative research is exploding with alternative methodological and theoretical approaches. In this book, experts in each one of these methods provide a comprehensive explanation and application of time-series, pooled, event history and Boolean methods to substantive problems of the welfare state. Each section of the book focuses on a different method with a general introduction to the methods and then two papers using the method to deal with analysis concerning welfare state problems in a political economy perspective. Scholars concerned with methodology in this area cannot afford to overlook this book because it will help them keep up on proliferating methodologies. Graduate students in political science and sociology will find this book extremely useful in their careers.

Comparative research is exploding with alternative methodological and theoretical approaches. In this book, experts in each one of these methods provide a comprehensive explanation and application of time-series, pooled, event history and Boolean methods to substantive problems of the welfare state. Each section of the book focuses on a different method with a general introduction to the methods and then two papers using the method to deal with analysis concerning welfare state problems in a political economy perspective. Scholars concerned with methodology in this area cannot afford to overlook this book because it will help them keep up on proliferating methodologies. Graduate students in political science and sociology will find this book extremely useful in their careers.

In 1985, Buckminsterfullerene (fullerene-60) C60 was discovered serendipitously during graphite laser vaporisation experiments designed to simulate the chemistry in a red giant carbon star. The molecule was isolated for the first time in macroscopic amounts in 1990, a breakthrough which triggered an explosion of research into its chemical and physical properties. The fullerenes hold great potential for material science applications, such as semiconductors and microscopic engineering, and as new compounds for pharmaceuticals, polymers and the chemical industry. In October 1992, a Discussion Meeting of the Royal Society entitled A Post-Buckminsterfullerene View of the Chemistry, Physics and Astrophysics of Carbon, organised by H. W. Kroto, A. L. Makay, G. Turner and D. R. M. Walton, was held to celebrate this exciting advance. The scientists who played key roles in the discovery and who are currently uncovering fascinating problems and the implications of this elegant molecule presented

Numbers are part of our everyday experience and their properties have fascinated mankind since ancient times. Deciding whether a number is prime and if not, what its factors are, are both fundamental problems. In recent years analysis and solution of these problems have assumed commercial significance since large primes are an essential feature of secure methods of information transmission. The purely mathematical fascination that led to the development of methods for primality testing has been supplemented by the need to test within reasonable timescales, and computational methods have entered at all levels of number theory. In this book, Peter Giblin describes, in the context of an introduction to the theory of numbers, some of the more elementary methods for factorization and primality testing; that is, methods independent of a knowledge of other areas of mathematics. Indeed everything is developed from scratch so the mathematical prerequisites are minimal. An essential feature of t

Within both the social and environmental sciences, much of the data collected is within a spatial context and requires statistical analysis for interpretation. The purpose of this book is to describe current methods for the analysis of spatial data. Methods described include data description, map interpolation, and exploratory and explanatory analyses. The book also examines spatial referencing, and methods for detecting problems, assessing their seriousness and taking appropriate action are discussed. This is an important text for any discipline requiring a broad overview of current theoretical and applied work for the analysis of spatial data sets. It will be of particular use to research workers and final year undergraduates in the fields of geography, environmental sciences and social sciences.

For the third edition of this successful undergraduate text, the author has made a number of changes to improve the presentation and clarify some of the arguments, and has also brought several of the applications up to date. The new material includes an elementary, descriptive introduction to the ideas behind the new science of chaos. The overall objectives of the book are unchanged: to lead the student to a thorough understanding of the basic concepts of vibrations and waves, to show how these concepts unify a wide variety of familiar physics, and to open doors to advanced topics which they illuminate. Each section of the book contains a brief summary of its salient contents. There are approximately 180 problems to which all numerical answers are provided, together with hints for their solution. This book is designed both for use as a text for an initial undergraduate course on vibrations and waves, and for a reference at later stages when more advanced topics or applications are met.

The Science and Practice of Welding, now in its tenth edition and published in two volumes, is an introduction to the theory and practice of welding processes and their applications. Volume 2, The Practice of Welding, is a comprehensive survey of the welding methods in use today and gives up-to-date information on all types of welding methods and tools. Processes described include manual metal arc welding (MMA or SMAW); gas shielded metal arc welding (MIG, MAG or GMAW); tungsten inert gas shielded welding (TIG or GTAW) and plasma arc (PA) and cutting. Resistance, flash butt and oxy-acetylene welding are also included. Cutting processes are given a separate chapter. This new edition has been brought right up-to-date with a new chapter on the welding of plastics, and new sections on the welding of duplex stainless steel and air plasma cutting. The text is illustrated by up-to-date photographs of plant and equipment. As in previous editions, the appendices bring together a wealth of essen

The Science and Practice of Welding, now in its tenth edition and published in two volumes, is an introduction to the theory and practice of welding processes and their applications. Volume 2, The Practice of Welding, is a comprehensive survey of the welding methods in use today and gives up-to-date information on all types of welding methods and tools. Processes described include manual metal arc welding (MMA or SMAW); gas shielded metal arc welding (MIG, MAG or GMAW); tungsten inert gas shielded welding (TIG or GTAW) and plasma arc (PA) and cutting. Resistance, flash butt and oxy-acetylene welding are also included. Cutting processes are given a separate chapter. This new edition has been brought right up-to-date with a new chapter on the welding of plastics, and new sections on the welding of duplex stainless steel and air plasma cutting. The text is illustrated by up-to-date photographs of plant and equipment. As in previous editions, the appendices bring together a wealth of essen

Fluid flow turbulence is a phenomenon of great importance in many fields of engineering and science. Turbulence and related areas have continued to be subjects of intensive research over the last century. In this second edition of their successful textbook Professors Landahl and Mollo-Christensen have taken the opportunity to include recent developments in the field of chaos and its applications to turbulent flow. This timely update continues the original theme of the book: presenting the fundamental concepts and basic methods of fluid flow turbulence which enable the reader to follow the literature and understand current research. The emphasis upon the dynamic processes that create and maintain turbulent flows gives this book an original approach. This book should be useful to graduate students and researchers in fluid dynamics and, in particular, turbulence and related fields.

This text is a beginning graduate-level introduction to neural networks, focussing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final part reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual ne

This text is a beginning graduate-level introduction to neural networks, focussing on current theoretical models, examining what these models can reveal about how the brain functions, and discussing the ramifications for psychology, artificial intelligence and the construction of a new generation of intelligent computers. The book is divided into four parts. The first part gives an account of the anatomy of the central nervous system, followed by a brief introduction to neurophysiology. The second part is devoted to the dynamics of neuronal states, and demonstrates how very simple models may stimulate associative memory. The third part of the book discusses models of learning, including detailed discussions on the limits of memory storage, methods of learning and their associated models, associativity, and error correction. The final part reviews possible applications of neural networks in artificial intelligence, expert systems, optimization problems, and the construction of actual ne

This book, the first in the Cambridge Nonlinear Science Series, presents the fundamentals of chaos theory in conservative systems, providing a systematic study of the theory of transitional states of physical systems which lie between deterministic and chaotic behaviour. The authors' treatment of transitions to chaos, the theory of stochastic layers and webs, and the numerous applications of this theory, particularly to pattern symmetry, will make the book of importance to scientists from many disciplines.The authors have been meticulous in providing a detailed presentation of the material, enabling the reader to learn the necessary computational methods and to apply them in other problems. The inclusion of a significant amount of computer graphics is also an important aid to understanding. The final section of the book contains a fascinating collection of patterns in art and living nature. The book will be of interest to graduate students and researchers in physics and mathematics who

Algebraic geometers have renewed their interest in the interplay between algebraic vector bundles and projective embeddings. New methods have been developed for questions such as: what is the geometric content of syzygies and of bundles derived from them? how can they be used for giving good compactifications of natural families? which differential techniques are needed for the study of families of projective varieties? Such problems have often been reformulated over the last decade; often the need for a deeper analysis of the works of classical algebraic geometers was recognised. These questions were addressed at successive conferences held in Trieste and Bergen. New results, work in progress, conjectures and modern accounts of classical ideas were presented. This collection represents a development of the work conducted at the conferences; the Editors have taken the opportunity to mould the papers into a cohesive volume.

In this treatise, the authors present the general theory of orthogonal polynomials on the complex plane and several of its applications. The assumptions on the measure of orthogonality are general, the only restriction is that it has compact support on the complex plane. In the development of the theory the main emphasis is on asymptotic behaviour and the distribution of zeros. In the following chapters, the author explores the exact upper and lower bounds are given for the orthonormal polynomials and for the location of their zeros; regular n-th root asymptotic behaviour; and applications of the theory, including exact rates for convergence of rational interpolants, best rational approximants and non-diagonal Pade approximants to Markov functions (Cauchy transforms of measures). The results are based on potential theoretic methods, so both the methods and the results can be extended to extremal polynomials in norms other than L2 norms. A sketch of the theory of logarithmic potentials

Provides a firm theoretical grounding for the increasing movement of cognitive psychologists, neuropsychologists and their students beyond the laboratory, in an attempt to understand human cognitive abilities as they are manifested in natural contexts. The pros and cons of the laboratory and the real world - the problems of generalizability versus rigor - are thoroughly analyzed, and practical escapes from what has become a false dichotomy are suggested. The authors present relevant data that open up new directions for those studying cognitive aging. Finally, they consider the applications of the new knowledge for clinicians and educators.

Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purp

Optimal control theory is a technique being used increasingly by academic economists to study problems involving optimal decisions in a multi-period framework. This textbook is designed to make the difficult subject of optimal control theory easily accessible to economists while at the same time maintaining rigour. Economic intuitions are emphasized, and examples and problem sets covering a wide range of applications in economics are provided to assist in the learning process. Theorems are clearly stated and their proofs are carefully explained. The development of the text is gradual and fully integrated, beginning with simple formulations and progressing to advanced topics such as control parameters, jumps in state variables, and bounded state space. For greater economy and elegance, optimal control theory is introduced directly, without recourse to the calculus of variations. The connection with the latter and with dynamic programming is explained in a separate chapter. A second purp

The dynamics of physical, chemical, biological or fluid systems generally must be described by nonlinear models, whose detailed mathematical solutions are not obtainable. To understand some aspects of such dynamics, various complementary methods and viewpoints are of crucial importance. In this book and its companion volume, Perspectives of nonlinear dynamics, volume 1, the perspectives generated by analytical, topological and computational methods, and interplays between them, are developed in a variety of contexts. The presentation and style is intended to stimulate the reader's imagination to apply these methods to a host of problems and situations. The text is complemented by copious references, extensive historical and bibliographical notes, exercises and examples, and appendices giving more details of some mathematical ideas. Each chapter includes an extensive section commentary on the exercises and their solution. Graduate students and research workers in physics, applied mathem

Applied Nonparametric Regression is the first book to bring together in one place the techniques for regression curve smoothing involving more than one variable. The computer and the development of interactive graphics programs have made curve estimation possible. This volume focuses on the applications and practical problems of two central aspects of curve smoothing: the choice of smoothing parameters and the construction of confidence bounds. Härdle argues that all smoothing methods are based on a local averaging mechanism and can be seen as essentially equivalent to kernel smoothing. To simplify the exposition, kernel smoothers are introduced and discussed in great detail. Building on this exposition, various other smoothing methods (among them splines and orthogonal polynomials) are presented and their merits discussed. All the methods presented can be understood on an intuitive level; however, exercises and supplemental materials are provided for those readers desiring a deeper un

This 1992 book provides a comprehensive introduction to the theory of electrical circuits for students in the physical sciences taking a first course in electronics. The methods of circuit analysis are clearly explained and illustrated with the aid of numerous worked examples. Applications of the theory relevant to the fields of electronics, telecommunications and power systems are treated throughout. These sections will prepare students for more advanced courses. The text is written for first and second year undergraduate courses in electronics for science and engineering students. The more specialised sections also provide some advanced material which is covered in third year courses.

This 1992 book provides a comprehensive introduction to the theory of electrical circuits for students in the physical sciences taking a first course in electronics. The methods of circuit analysis are clearly explained and illustrated with the aid of numerous worked examples. Applications of the theory relevant to the fields of electronics, telecommunications and power systems are treated throughout. These sections will prepare students for more advanced courses. The text is written for first and second year undergraduate courses in electronics for science and engineering students. The more specialised sections also provide some advanced material which is covered in third year courses.

This book is an undergraduate textbook for students of electrical and electronic engineering. It is written at an intermediate level, with second year students particularly in mind, and discusses analogue circuits used in various fields. Basic electronics has been omitted so that appropriate emphasis can be given to the design of the most popular and useful circuits. The contents of chapters 3, 5, 7 and 8 are not covered together by any other single textbook available on the market. Each chapter also contains a significant number of worked examples and several carefully chosen problems at various levels of difficulty. Each topic has been carefully selected, and the author concentrates on the practical details and applications of the material he covers. Both students and practising engineers alike will therefore find this book extremely useful and informative.

This book is an undergraduate textbook for students of electrical and electronic engineering. It is written at an intermediate level, with second year students particularly in mind, and discusses analogue circuits used in various fields. Basic electronics has been omitted so that appropriate emphasis can be given to the design of the most popular and useful circuits. The contents of chapters 3, 5, 7 and 8 are not covered together by any other single textbook available on the market. Each chapter also contains a significant number of worked examples and several carefully chosen problems at various levels of difficulty. Each topic has been carefully selected, and the author concentrates on the practical details and applications of the material he covers. Both students and practising engineers alike will therefore find this book extremely useful and informative.