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The p-adic numbers, the earliest of local fields, were introduced by Hensel some 70 years ago as a natural tool in algebra number theory. Today the use of this and other local fields pervades much of mathematics, yet these simple and natural concepts, which often provide remarkably easy solutions to complex problems, are not as familiar as they should be. This book, based on postgraduate lectures at Cambridge, is meant to rectify this situation by providing a fairly elementary and self-contained introduction to local fields. After a general introduction, attention centres on the p-adic numbers and their use in number theory. There follow chapters on algebraic number theory, diophantine equations and on the analysis of a p-adic variable. This book will appeal to undergraduates, and even amateurs, interested in number theory, as well as to graduate students.

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In this book, which was originally published in 1985, Arto Salomaa gives an introduction to certain mathematical topics central to theoretical computer science: computability and recursive functions, formal languages and automata, computational complexity and cryptography. Without sacrificing readability, the presentation is essentially self-contained, with detailed proofs of all statements provided. Professor Salomaa is well known for his books in this area. The present work provides an insight into the basics, together with explanations of some of the more important developments in the field.

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This is a memorial volume to the distinguished Canadian-born mathematician Hugh Dowker, one of the most highly regarded topologists in the United Kingdom and sometime Professor at Birkbeck College, London. The volume comprises specially written articles on various topological topics by experts in many countries who worked with Dowker at one time or another. These include survey, expository and research articles on general topology, algebraic topology and related subjects such as knot theory and graph theory. The volume will be of great interest to graduate students and professional mathematicians whose speciality is topology, in all its aspects.

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The BanachTarski paradox is a most striking mathematical construction: it asserts that a solid ball may be taken apart into finitely many pieces that can be rearranged using rigid motions to form a ball twice as large as the original. This volume explores the consequences of the paradox for measure theory and its connections with group theory, geometry, and logic. It unifies the results of contemporary research on the paradox and presents several new results including some unusual paradoxes in hyperbolic space. It also provides up-to-date proofs and discusses many unsolved problems.

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Introduction to the Science of Medical Imaging

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Revolutionary advances in imaging technology that provide high resolution, 3-D, non-invasive imaging of biological subjects have made biomedical imaging an essential tool in clinical medicine and biomedical research. Key technological advances include MRI, positron emission tomography (PET) and multidetector X-ray CT scanners. Common to all contemporary imaging modalities is the creation of digital data and pictures. The evolution from analog to digital image data is driving the rapidly expanding field of digital image analysis. Scientists from numerous disciplines now require in-depth knowledge of these complex imaging modalities. Introduction to the Science of Medical Imaging presents scientific imaging principles, introduces the major biomedical imaging modalities, reviews the basics of human and computer image analysis and provides examples of major clinical and research applications. Written by one of the world's most innovative and highly respected neuroradiologists, Introduction to the Science of Medical Imaging is a landmark text on image acquisition and interpretation.

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Fluid film bearings are machine elements that should be studied within the broader context of tribology. The three subfields of tribology - friction, lubrication, and wear - are strongly interrelated. The last decade has witnessed significant advances in the area of fluid film lubrication and its applications, and this second edition offers a look at some of these advances. This edition adds to the fundamentals of fluid film lubrication, a discourse on surface effects and the inclusion of treatment of flow with significant inertia within the section on turbulence. Basic ideas of the multigrid method are conveyed along with multilevel multi-integration in the treatment of elastohydrodynamic lubrication. New chapters have been included on ultra-thin films, both liquid and gaseous, and lubrication of articulating joints and their replacement. Some of the most recent literature is discussed.

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Cosmology, Black Holes, and Quantum Gravity

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Canonical methods are a powerful mathematical tool within the field of gravitational research, both theoretical and experimental, and have contributed to a number of recent developments in physics. Providing mathematical foundations as well as physical applications, this is the first systematic explanation of canonical methods in gravity. The book discusses the mathematical and geometrical notions underlying canonical tools, highlighting their applications in all aspects of gravitational research from advanced mathematical foundations to modern applications in cosmology and black hole physics. The main canonical formulations, including the Arnowitt-Deser-Misner (ADM) formalism and Ashtekar variables, are derived and discussed. Ideal for both graduate students and researchers, this book provides a link between standard introductions to general relativity and advanced expositions of black hole physics, theoretical cosmology or quantum gravity.

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This is an introduction to geometrical topics that are useful in applied mathematics and theoretical physics, including manifolds, metrics, connections, Lie groups, spinors and bundles, preparing readers for the study of modern treatments of mechanics, gauge fields theories, relativity and gravitation. The order of presentation corresponds to that used for the relevant material in theoretical physics: the geometry of affine spaces, which is appropriate to special relativity theory, as well as to Newtonian mechanics, is developed in the first half of the book, and the geometry of manifolds, which is needed for general relativity and gauge field theory, in the second half. Analysis is included not for its own sake, but only where it illuminates geometrical ideas. The style is informal and clear yet rigorous; each chapter ends with a summary of important concepts and results. In addition there are over 650 exercises, making this a book which is valuable as a text for advanced undergraduate and postgraduate students.

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Hydrodynamics of Pumps is a reference for pump experts and a textbook for advanced students. It examines the fluid dynamics of liquid turbomachines, particularly pumps, focusing on special problems and design issues associated with the flow of liquid through a rotating machine. There are two characteristics of a liquid that lead to problems and cause a significantly different set of concerns than those in gas turbines. These are the potential for cavitation and the high density of liquids, which enhances the possibility of damaging, unsteady flows and forces. The book begins with an introduction to the subject, including cavitation, unsteady flows and turbomachinery, basic pump design and performance principles. Chapter topics include flow features, cavitation parameters and inception, bubble dynamics, cavitation effects on pump performance, and unsteady flows and vibration in pumps - discussed in the three final chapters. The book is richly illustrated and includes many practical examples.

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Filter Bank Transceivers for OFDM and DMT Systems

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Providing key background material together with advanced topics, this self-contained book is written in an easy-to-read style and is ideal for newcomers to multicarrier systems. Early chapters provide a review of basic digital communication, starting from the equivalent discrete time channel and including a detailed review of the MMSE receiver. Later chapters then provide extensive performance analysis of OFDM and DMT systems, with discussions of many practical issues such as implementation and power spectrum considerations. Throughout, theoretical analysis is presented alongside practical design considerations, whilst the filter bank transceiver representation of OFDM and DMT systems opens up possibilities for further optimization such as minimum bit error rate, minimum transmission power, and higher spectral efficiency. With plenty of insightful real-world examples and carefully designed end-of-chapter problems this is an ideal single-semester textbook for senior undergraduate and graduate students, as well as a self-study guide for researchers and professional engineers.

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Yuan-Pei Lin, See-May Phoong, P. P. Vaidyanathan

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Dynamics, Statistics and Projective Geometry of Galois Fields

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V. I. Arnold reveals some unexpected connections between such apparently unrelated theories as Galois fields, dynamical systems, ergodic theory, statistics, chaos and the geometry of projective structures on finite sets. The author blends experimental results with examples and geometrical explorations to make these findings accessible to a broad range of mathematicians, from undergraduate students to experienced researchers.

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Heat Generation and Transport in the Earth

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Heat provides the energy that drives almost all geological phenomena and sets the temperature at which these phenomena operate. This book explains the key physical principles of heat transport with simple physical arguments and scaling laws that allow quantitative evaluation of heat flux and cooling conditions in a variety of geological settings and systems. The thermal structure and evolution of magma reservoirs, the crust, the lithosphere and the mantle of the Earth are reviewed within the context of plate tectonics and mantle convection - illustrating how theoretical arguments can be combined with field and laboratory data to arrive at accurate interpretations of geological observations. Appendices contain data on the thermal properties of rocks, surface heat flux measurements and rates of radiogenic heat production. This book can be used for advanced courses in geophysics, geodynamics and magmatic processes, and is a reference for researchers in geoscience, environmental science, physics, engineering and fluid dynamics.

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This 2004 book is an accessible and comprehensive introduction to machine vision. It provides all the necessary theoretical tools and shows how they are applied in actual image processing and machine vision systems. A key feature is the inclusion of many programming exercises that give insights into the development of practical image processing algorithms. The authors begin with a review of mathematical principles and go on to discuss key issues in image processing such as the description and characterization of images, edge detection, restoration and feature extraction, segmentation, texture and shape. They also discuss image matching, statistical pattern recognition, clustering, and syntactic pattern recognition. Important applications are described, including optical character recognition and automatic target recognition. Software and data used in the book can be found at www.cambridge.org/9780521830461. A useful reference for practitioners, the book is aimed at graduate students in electrical engineering, computer science and mathematics.

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Modern Computer Arithmetic focuses on arbitrary-precision algorithms for efficiently performing arithmetic operations such as addition, multiplication and division, and their connections to topics such as modular arithmetic, greatest common divisors, the Fast Fourier Transform (FFT), and the computation of elementary and special functions. Brent and Zimmermann present algorithms that are ready to implement in your favourite language, while keeping a high-level description and avoiding too low-level or machine-dependent details. The book is intended for anyone interested in the design and implementation of efficient high-precision algorithms for computer arithmetic, and more generally efficient multiple-precision numerical algorithms. It may also be used in a graduate course in mathematics or computer science, for which exercises are included. These vary considerably in difficulty, from easy to small research projects, and expand on topics discussed in the text.  Solutions to selected exercises are available from the authors.

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Spectroscopy enables the precise study of astronomical objects and phenomena. Bridging the gap between physics and astronomy, this is the first integrated graduate-level textbook on atomic astrophysics. It covers the basics of atomic physics and astrophysics, including state-of-the-art research applications, methods and tools. The content is evenly balanced between the physical foundations of spectroscopy and their applications to astronomical objects and cosmology. An undergraduate knowledge of physics is assumed, and relevant basic material is summarized at the beginning of each chapter. The material is completely self-contained and features sufficient background information for self-study. Advanced users will find it handy for spectroscopic studies. A website hosted by the authors contains updates, corrections, exercises and solutions, as well as news items from physics and astronomy related to spectroscopy. A link to this can be found at www.cambridge.org/9780521825368.

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A practical and systematic overview of the design, fabrication and test of MEMS-based inertial sensors, this comprehensive and rigorous guide shows you how to analyze and transform application requirements into practical designs, and helps you to avoid potential pitfalls and to cut design time. With this book you'll soon be up to speed on the relevant basics, including MEMS technologies, packaging, kinematics and mechanics, and transducers. You'll also get a thorough evaluation of different approaches and architectures for design and an overview of key aspects of testing and calibration. Unique insights into the practical difficulties of making sensors for real-world applications make this up-to-date description of the state of the art in inertial MEMS an ideal resource for professional engineers in industry as well as students looking for a complete introduction to the area.

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Written from an engineering standpoint, this book provides the theoretical background and physical insight needed to understand new and future developments in the modeling and design of n- and p-MOS nanoscale transistors. A wealth of applications, illustrations and examples connect the methods described to all the latest issues in nanoscale MOSFET design. Key areas covered include:  Transport in arbitrary crystal orientations and strain conditions, and new channel and gate stack materials  All the relevant transport regimes, ranging from low field mobility to quasi-ballistic transport, described using a single modeling framework  Predictive capabilities of device models, discussed with systematic comparisons to experimental results

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David Esseni, Pierpaolo Palestri, Luca Selmi

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With ever-increasing demands on capacity, quality of service, speed, and reliability, current Internet systems are under strain and under review. Combining contributions from experts in the field, this book captures the most recent and innovative designs, architectures, protocols, and mechanisms that will enable researchers to successfully build the next-generation Internet. A broad perspective is provided, with topics including innovations at the physical/transmission layer in wired and wireless media, as well as the support for new switching and routing paradigms at the device and sub-system layer. The proposed alternatives to TCP and UDP at the data transport layer for emerging environments are also covered, as are the novel models and theoretical foundations proposed for understanding network complexity. Finally, new approaches for pricing and network economics are discussed, making this ideal for students, researchers, and practitioners who need to know about designing, constructing, and operating the next-generation Internet.

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Byrav Ramamurthy, George N. Rouskas, Krishna Moorthy Sivalingam

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Computational semantics is the art and science of computing meaning in natural language. The meaning of a sentence is derived from the meanings of the individual words in it, and this process can be made so precise that it can be implemented on a computer. Designed for students of linguistics, computer science, logic and philosophy, this comprehensive text shows how to compute meaning using the functional programming language Haskell. It deals with both denotational meaning (where meaning comes from knowing the conditions of truth in situations), and operational meaning (where meaning is an instruction for performing cognitive action). Including a discussion of recent developments in logic, it will be invaluable to linguistics students wanting to apply logic to their studies, logic students wishing to learn how their subject can be applied to linguistics, and functional programmers interested in natural language processing as a new application area.

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Complex Webs synthesises modern mathematical developments with a broad range of complex network applications of interest to the engineer and system scientist, presenting the common principles, algorithms, and tools governing network behaviour, dynamics, and complexity. The authors investigate multiple mathematical approaches to inverse power laws and expose the myth of normal statistics to describe natural and man-made networks. Richly illustrated throughout with real-world examples including cell phone use, accessing the Internet, failure of power grids, measures of health and disease, distribution of wealth, and many other familiar phenomena from physiology, bioengineering, biophysics, and informational and social networks, this book makes thought-provoking reading. With explanations of phenomena, diagrams, end-of-chapter problems, and worked examples, it is ideal for advanced undergraduate and graduate students in engineering and the life, social, and physical sciences. It is also a perfect introduction for researchers who are interested in this exciting new way of viewing dynamic networks.