Mathematics of Discrete Structures for Computer Science

This book provides a background in the mechanics of solids for students of mechanical engineering, while limiting the information on why materials behave as they do. It is assumed that the students have already had courses covering materials science and basic statics. Much of the material is drawn from another book by the author, Mechanical Behavior of Materials. To make the text suitable for mechanical engineers, the chapters on slip, dislocations, twinning, residual stresses, and hardening mechanisms have been eliminated and the treatment of ductility, viscoelasticity, creep, ceramics, and polymers has been simplified.

This book provides a background in the mechanics of solids for students of mechanical engineering, while limiting the information on why materials behave as they do. It is assumed that the students have already had courses covering materials science and basic statics. Much of the material is drawn from another book by the author, Mechanical Behavior of Materials. To make the text suitable for mechanical engineers, the chapters on slip, dislocations, twinning, residual stresses, and hardening mechanisms have been eliminated and the treatment of ductility, viscoelasticity, creep, ceramics, and polymers has been simplified.

This set of four volumes brings together seminal essays spanning the career of Richard Rorty, one of the most creative and influential anglophone philosophers of recent decades. The essays range widely over the concerns of philosophy, politics, science, religion, and culture, engaging with thinkers from Hilary Putnam to Catherine McKinnon and challenging readers to re-examine many traditional tenets in philosophy and elsewhere. They will be essential reading for anyone with a serious interest in contemporary philosophy and what it can do for us in the modern world.

This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.

This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.

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.

Plato stands as the fount of our philosophical tradition, being the first Western thinker to produce a body of writing that touches upon a wide range of topics still discussed by philosophers today. In a sense he invented philosophy as a distinct subject, for although many of these topics were discussed by his intellectual predecessors and contemporaries, he was the first to bring them together by giving them a unitary treatment. This volume contains fourteen essays discussing Plato's views about knowledge, reality, mathematics, politics, ethics, love, poetry, and religion. There are also analyses of the intellectual and social background of his thought, the development of his philosophy throughout his career, the range of alternative approaches to his work, and the stylometry of his writing.

NEW STORIES IN THE GRAND SPACE FANTASY TRADITION!SCIENCE FICTION? FANTASY? SWORDS AND BLASTERS? IS IT TOO MUCH TO ASK FOR BOTH?The distant future—like the distant past—is a place of myths, of legends, and of great heroes. Cyborg knights battle extraterrestrial demons to rescue a peaceful village. A young girl unlocks an ancient power to protect her world from off-world colonists. Here are stories not where magic is science, but with magic and science. Not knights and castles, but knights and starships. Wizards and ray guns. Swords and planets.In D.J. Butler’s “Power and Prestige,” a pair of two-bit mercenaries are hired to solve a murder in a labyrinth beneath a crumbling city at the end of time. A young knight must face down an alien menace and awaken the power within in R.R. Virdi’s “A Knight Luminary,” and in “Saving the Emperor” Simon R. Green takes us deep into the Imperial City of Virimonde . . . and offers a glimpse at how the Deathstalker clan rose to power and fame. Enjo

Discover all there is to know about strong women in fiction: Hermione Granger, Wonder Woman, Princess Leia, and more! A strong woman is not just a badass lady who solves her problems with a high kick and a sassy comeback, all the while looking fabulous in a cape (although the cape is a plus!). A strong woman is a pioneer for bravery, intelligence, determination, and social justice for all. Compelling, humorous and brilliantly illustrated in equal measures, The Science of Strong Women showcases a collection of fifty fantastic fictional feminists we all know and love. Through media analysis and awe-inspiring discoveries, this inspirational guide delves deeper into female-forward fiction and features a truly diverse collection of strong women including: June OsborneStar CarterKatniss EverdeenElizabeth BennetownynJo MarchBuffy SummersAnd many more Here's to strong women. May we know them, may we be them, and may we learn from them with The Science of Strong Women.

Under what conditions is a group of scientists rational? How would rational scientists collectively agree to make their group more effective? What sorts of negotiations would occur among them and under what conditions? What effect would their final agreement have on science and society? These questions have been central to the philosophy of science for the last two decades. In this 2007 book, Husain Sarkar proposes answers to them by building on classical solutions - the skeptical view, two versions of the subjectivist view, the objectivist view, and the view of Hilary Putnam. Although he finds these solutions not completely adequate, Sarkar retrieves what is of value from them and also expropriates the arguments of John Rawls and Amartya Sen, in order to weave a richer, deeper, and more developed theory of group rationality.

Under what conditions is a group of scientists rational? How would rational scientists collectively agree to make their group more effective? What sorts of negotiations would occur among them and under what conditions? What effect would their final agreement have on science and society? These questions have been central to the philosophy of science for the last two decades. In this 2007 book, Husain Sarkar proposes answers to them by building on classical solutions - the skeptical view, two versions of the subjectivist view, the objectivist view, and the view of Hilary Putnam. Although he finds these solutions not completely adequate, Sarkar retrieves what is of value from them and also expropriates the arguments of John Rawls and Amartya Sen, in order to weave a richer, deeper, and more developed theory of group rationality.

The discovery of coherent structures in turbulence has fostered the hope that the study of vortices will lead to models and an understanding of turbulent flow, thereby solving or at least making less mysterious one of the great unsolved problems of classical physics. Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. The emphasis in this monograph is on the classical theory of inviscid incompressible fluids containing finite regions of vorticity. The effects of viscosity, compressibility, inhomogeneity and stratification are enormously important in many fields of application, from hypersonic flight to global environmental fluid mechanics. However, this volume focuses on those aspects of fluid motion which are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary.

Hello, World! is a series designed to introduce first nonfiction concepts to babies and toddlers. Told in clear and easy terms and featuring bright, cheerful illustrations, Hello, World! makes learning fun for young children. And each sturdy page offers helpful prompts for engaging with your child. It's a perfect way to bring science and nature into the busy world of a toddler, where learning never stops.

Beautiful science fiction ... The story of an extraterrestrial visitor from another planet is deigned mainly to say something about life on this one. --The New York Times Those who know The Man Who Fell to Earth only from the film version are missing something. This is one of the finest science fiction novels of its period. --J.R. Dunn, author of Full Tide of Night T. J. Newton is an extraterrestrial who goes to Earth on a desperate mission of mercy. But instead of aid, Newton discovers loneliness and despair that ultimately ends in tragedy. Praise for The Man Who Fell to Earth "An utterly realistic novel about an alien human on Earth . . . Realistic enough to become a metaphor for something inside us all, some existential loneliness." --Norman Spinrad"Tevis writes . . . with power and poetry and tension." --The Washington Post Book World"Terrific . . . The Man Who Fell to Earth can be seen as the story of a very hip, space-age Passion--about a savior who comes to Earth not to save us

In response to repeated requests this classic book on space-time structure by Professor Erwin Schrödinger is now available in the Cambridge Science Classics series. First published in 1950, and reprinted in 1954 and 1960, this lucid and profound exposition of Einstein's 1915 theory of gravitation still provides valuable reading for students and research workers in the field.

Fortran is a computer language that has been around for a quarter of a century, and is still much used despite predictions throughout its life that it would be replaced by more elegant languages. But Fortran is still the only language in which it is possible to write truly portable programs. Using his own special formula, Donald Alcock now does for Fortran what he did for BASIC in his earlier book, Illustrating BASIC. The Fortran described and illustrated is that defined by the American National Standards Institute in 1966 but with allusions to the same Institute's standard published in 1978. For both the person who is new to computers and programming, and the person who has met only BASIC before, this book will give an excellent introduction to standard Fortran; it also provides a reference manual for the language.

Hydrocarbon production, gas recovery from shale, CO2 storage and water management have a common scientific underpinning: multiphase flow in porous media. This book provides a fundamental description of multiphase flow through porous rock, with emphasis on the understanding of displacement processes at the pore, or micron, scale. Fundamental equations and principal concepts using energy, momentum, and mass balance are developed, and the latest developments in high-resolution three-dimensional imaging and associated modelling are explored. The treatment is pedagogical, developing sound physical principles to predict flow and recovery through complex rock structures, while providing a review of the recent literature. This systematic approach makes it an excellent reference for those who are new to the field. Inspired by recent research, and based on courses taught to thousands of students and professionals from around the world, it provides the scientific background necessary for a quanti

This book provides an introduction to biodeterioration - the attack on man-made materials by living organisms. The authors outline the principles involved, as well as the ways in which such damage can be controlled and prevented. A wide range of organisms are covered (including bacteria, fungi, algae, lichens, insects and other invertebrates, birds, mammals and plants) and the types of biodeterioration discussed include: • natural materials such as foodstuffs, wood, metal, stone, cellulose and leather • synthetic products such as paint, adhesives and plastics • structures and systems such as buildings, monuments, transport systems and vehicles. In this updated and expanded second edition, new molecular and genetic techniques are included, and regulatory, environmental and safety issues are emphasised. This book is suitable not only for biologists, but also for those in industry, commerce and local government who are concerned with the preservation and conservation of a wide range of m

This book provides an introduction to biodeterioration - the attack on man-made materials by living organisms. The authors outline the principles involved, as well as the ways in which such damage can be controlled and prevented. A wide range of organisms are covered (including bacteria, fungi, algae, lichens, insects and other invertebrates, birds, mammals and plants) and the types of biodeterioration discussed include: • natural materials such as foodstuffs, wood, metal, stone, cellulose and leather • synthetic products such as paint, adhesives and plastics • structures and systems such as buildings, monuments, transport systems and vehicles. In this updated and expanded second edition, new molecular and genetic techniques are included, and regulatory, environmental and safety issues are emphasised. This book is suitable not only for biologists, but also for those in industry, commerce and local government who are concerned with the preservation and conservation of a wide range of m

This textbook covers all the theoretical aspects of real variable analysis which undergraduates reading mathematics are likely to require during the first two or three years of their course. It is based on lecture courses which the author has given in the universities of Wales, Cambridge and London. The subject is presented rigorously and without padding. Definitions are stated explicitly and the whole development of the subject is logical and self-contained. Complex numbers are used but the complex variable calculus is not. 'Applied analysis', such as differential equations and Fourier series, is not dealt with. A large number of examples is included, with hints for the solution of many of them. These will be of particular value to students working on their own.

The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron - an electrically active nerve cell - and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two, some familiarity with differ

The human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron - an electrically active nerve cell - and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principal mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two, some familiarity with differ

This book, first published in 2000, is a pioneering study of politics and society in the early Middle Ages. Whereas it is widely believed that the source materials for early medieval Europe are too sparse to allow sustained study of the workings of social and political relationships on the ground, this book focuses on a uniquely well-documented area to investigate the basis of power. Topics covered include the foundation of monasteries, their relationship with the laity, and their role as social centres; the significance of urbanism; the control of land, the development of property rights and the organization of states; community, kinship and lordship; justice and dispute settlement; the uses of the written word; violence and the feud; and the development of political structures from the Roman empire to the high Middle Ages.

This is the first textbook to integrates both general and specific topics, theoretical background and biomedical engineering applications, as well as analytical and numerical approaches. This quantitative approach integrates the classical concepts of mechanics and computational modelling techniques, in a logical progression through a wide range of fundamental biomechanics principles. Online MATLAB-based software along with examples and problems using biomedical applications will motivate undergraduate biomedical engineering students to practise and test their skills. The book covers topics such as kinematics, equilibrium, stresses and strains, and also focuses on large deformations and rotations and non-linear constitutive equations, including visco-elastic behaviour and the behaviour of long slender fibre-like structures. This is the definitive textbook for students.

The conceptual changes brought by modern physics are important, radical and fascinating, yet they are only vaguely understood by people working outside the field. Exploring the four pillars of modern physics – relativity, quantum mechanics, elementary particles and cosmology – this clear and lively account will interest anyone who has wondered what Einstein, Bohr, Schrödinger and Heisenberg were really talking about. The book discusses quarks and leptons, antiparticles and Feynman diagrams, curved space-time, the Big Bang and the expanding Universe. Suitable for undergraduate students in non-science as well as science subjects, it uses problems and worked examples to help readers develop an understanding of what recent advances in physics actually mean.

This volume details preparations, separations, identification, analysis of postbiotics types and mechanism, uses of postbiotics in health, pharma, aquacultures, and the food industry. Divided into five sections chapters provide methods on antimicrobials, antibiofilm, anti-inflammatory, antiallergies, antiobesity, meurotransmitter activity, dietary supplementation and Immunomodulatory activity of postbiotics, postbiotics as biopreservatives, and as well as food packing material. . Written in the format of the Methods and Protocols in Food Science series, chapters list necessary materials and methods for readily reproducible protocols. Authoritative and cutting-edge, Postbiotics aims to be a foundation for future studies and to be a source of inspiration for new investigations in the field.

Discover the science behind wild and wonderful weather in this fact-packed book!From heatwaves and big freezes to tornadoes and fog, this science book gives your budding meteorologist a glimpse into all the action that happens in the sky. Learn about all kinds of weather and marvel at how powerful it can be!At a time when extreme weather is becoming more and more common, this eco-focused book is perfect for getting your little one clued up about the environment. Throughout the pages of this colorful and energetic STEM book, your child will discover fun facts about the weather. They will also gain insight into serious topics such as global warming and how our climate is changing.Inside the pages of this beautifully illustrated children's science book, you'll learn all about the weather, and discover:- Fascinating illustrations that introduce scientific topics in a simple and accessible way- Stand out facts, presented clearly on each spread- Easy to understand text that teach children ab

Meet Bibsy Cross, the precocious eight-year-old heroine of this charming chapter book series, as she navigates a relationship with a teacher who thinks that Bibsy is justtoo much.Most things are easy-peasy, regular-pegular for Bibsy Cross. She loves her parents, her cat, her best friend, Natia. And shelovesgoing to school. She might just love that most of all!This year, Bibsy has Mrs. Stumper for a teacher... and Mrs. Stumper doesn't seem too keen on Bibsy. She thinks Bibsy talks too much--especially about her science fair project.But one day, when Bibsy talks a littletoomuch, and goes a stonetoofar, Mrs. Stumper punishes her by punching a hole in her paper apple that hangs in the classroom. And Bibsy is devastated.How can she make the best science fair project when she feels so rotten?

The essential guide for anyone wanting a quick introduction to the fundamental ideas underlying photonics. The author uses his forty years of experience in photonics research and teaching to provide intuitive explanations of key concepts, and demonstrates how these relate to the operation of photonic devices and systems. Readers will gain insight into the nature of light and the ways in which it interacts with materials and structures, and learn how these basic ideas are applied in areas such as optical systems, 3D imaging and astronomy. Carefully designed worked examples and end-of-chapter problems enable students to check their understanding, with full solutions available online. Mathematical treatments are kept as simple as possible, allowing readers to grasp even the most complex of concepts. Clear, concise and accessible, this is the perfect guide for undergraduate students taking a first course in photonics, and anyone in academia or industry wanting to review the fundamentals.

The essential guide for anyone wanting a quick introduction to the fundamental ideas underlying photonics. The author uses his forty years of experience in photonics research and teaching to provide intuitive explanations of key concepts, and demonstrates how these relate to the operation of photonic devices and systems. Readers will gain insight into the nature of light and the ways in which it interacts with materials and structures, and learn how these basic ideas are applied in areas such as optical systems, 3D imaging and astronomy. Carefully designed worked examples and end-of-chapter problems enable students to check their understanding, with full solutions available online. Mathematical treatments are kept as simple as possible, allowing readers to grasp even the most complex of concepts. Clear, concise and accessible, this is the perfect guide for undergraduate students taking a first course in photonics, and anyone in academia or industry wanting to review the fundamentals.

This book is concerned with the relationship between semantics and surface structure and in particular with the way in which each is mapped into the other. Jim Miller argues that semantic and syntactic structure require different representations and that semantic structure is far more complex than many analysts realise. He argues further that semantic structure should be based on notions of location and movement. The need for a semantic component of greater complexity is demonstrated by an examination of prepositions, particles, adverbs and verb-prefixes, and is shown to accord with cross-language and historical facts. The volume goes on to consider the sort of rules that are required to map semantic structures onto syntax. Semantics and Syntax tackles fundamental issues and draws together many of the key concepts of traditional grammar and formal linguistics. The general framework for handling syntax, semantics and morphology that it outlines is perhaps a controversial one, but it wil

Reversibility is a thread woven through many branches of mathematics. It arises in dynamics, in systems that admit a time-reversal symmetry, and in group theory where the reversible group elements are those that are conjugate to their inverses. However, the lack of a lingua franca for discussing reversibility means that researchers who encounter the concept may be unaware of related work in other fields. This text is the first to make reversibility the focus of attention. The authors fix standard notation and terminology, establish the basic common principles, and illustrate the impact of reversibility in such diverse areas as group theory, differential and analytic geometry, number theory, complex analysis and approximation theory. As well as showing connections between different fields, the authors' viewpoint reveals many open questions, making this book ideal for graduate students and researchers. The exposition is accessible to readers at the advanced undergraduate level and above.

Experts translate the latest findings on embodied cognition from neuroscience, psychology, and cognitive science to inform teaching and learning pedagogy.Embodied cognition represents a radical shift in conceptualizing cognitive processes, in which cognition develops through mind-body environmental interaction. If this supposition is correct, then the conventional style of instruction―in which students sit at desks, passively receiving information―needs rethinking. Movement Matters considers the educational implications of an embodied account of cognition, describing the latest research applications from neuroscience, psychology, and cognitive science and demonstrating their relevance for teaching and learning pedagogy. The contributors cover a range of content areas, explaining how the principles of embodied cognition can be applied in classroom settings. After a discussion of the philosophical and theoretical underpinnings of embodied cognition, contributors describe its applications

Imitation guides the behaviour of a range of species. Scientific advances in the study of imitation at multiple levels from neurons to behaviour have far-reaching implications for cognitive science, neuroscience, and evolutionary and developmental psychology. This volume, first published in 2002, provides a summary of the research on imitation in both Europe and America, including work on infants, adults, and nonhuman primates, with speculations about robotics. A special feature of the book is that it provides a concrete instance of the links between developmental psychology, neuroscience, and cognitive science. It showcases how an interdisciplinary approach to imitation can illuminate long-standing problems in the brain sciences, including consciousness, self, perception-action coding, theory of mind, and intersubjectivity. The book addresses what it means to be human and how we get that way.

Imitation guides the behaviour of a range of species. Scientific advances in the study of imitation at multiple levels from neurons to behaviour have far-reaching implications for cognitive science, neuroscience, and evolutionary and developmental psychology. This volume, first published in 2002, provides a summary of the research on imitation in both Europe and America, including work on infants, adults, and nonhuman primates, with speculations about robotics. A special feature of the book is that it provides a concrete instance of the links between developmental psychology, neuroscience, and cognitive science. It showcases how an interdisciplinary approach to imitation can illuminate long-standing problems in the brain sciences, including consciousness, self, perception-action coding, theory of mind, and intersubjectivity. The book addresses what it means to be human and how we get that way.

Fundamental arithmetic operations support virtually all of the engineering, scientific, and financial computations required for practical applications, from cryptography, to financial planning, to rocket science. This comprehensive reference provides researchers with the thorough understanding of number representations that is a necessary foundation for designing efficient arithmetic algorithms. Using the elementary foundations of radix number systems as a basis for arithmetic, the authors develop and compare alternative algorithms for the fundamental operations of addition, multiplication, division, and square root with precisely defined roundings. Various finite precision number systems are investigated, with the focus on comparative analysis of practically efficient algorithms for closed arithmetic operations over these systems. Each chapter begins with an introduction to its contents and ends with bibliographic notes and an extensive bibliography. The book may also be used for grad

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Climate change and variability has become the primary environmental concern of the 21st Century. The potential impacts and mitigation of climate change need to be analyzed within the context of sustainable development. Primer on Climate Change and Sustainable Development presents a condensed and accessible review of the latest state-of-the-art assessments of the Intergovernmental Panel on Climate Change. The book begins with a foreword from the chair of the IPCC. Our current knowledge of the basic science of climate change is described, before moving on to future scenarios of development within the context of climate change. Possible adaptation and mitigation measures, including cost and benefit analysis, are discussed. The book will be an invaluable textbook for students of environmental science and policy, and researchers and policy makers involved in all aspects of climate change.

The modern understanding of turbulence is that it is a collection of weakly correlated vortical motions, which, despite their intermittent and chaotic distribution over a wide range of space and time scales, actually consist of local characteristic 'eddy' patterns that persist as they move around under the influences of their own and other eddies' vorticity fields. Numerical simulations and experimental observations have now identified some forms and elements of 'life-cycles' of some of these structures. The articles in this volume, first published in 2000, examine a number of key questions that have engaged turbulence researchers for many years. Most involve mathematical analysis, but some describe numerical simulations and experimental results that focus on these questions. However, all are addressed to a wide cross-section of the turbulence community, namely mathematicians, engineers and scientists.