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The Kolmogorov-Obukhov Theory of Turbulence
by Bjorn BirnirTurbulence is a major problem facing modern societies. It makes airline passengers return to their seats and fasten their seatbelts but it also creates drag on the aircraft that causes it to use more fuel and create more pollution. The same applies to cars, ships and the space shuttle. The mathematical theory of turbulence has been an unsolved problems for 500 years and the development of the statistical theory of the Navier-Stokes equations describes turbulent flow has been an open problem. The Kolmogorov-Obukhov Theory of Turbulence develops a statistical theory of turbulence from the stochastic Navier-Stokes equation and the physical theory, that was proposed by Kolmogorov and Obukhov in 1941. The statistical theory of turbulence shows that the noise in developed turbulence is a general form which can be used to present a mathematical model for the stochastic Navier-Stokes equation. The statistical theory of the stochastic Navier-Stokes equation is developed in a pedagogical manner and shown to imply the Kolmogorov-Obukhov statistical theory. This book looks at a new mathematical theory in turbulence which may lead to many new developments in vorticity and Lagrangian turbulence. But even more importantly it may produce a systematic way of improving direct Navier-Stokes simulations and lead to a major jump in the technology both preventing and utilizing turbulence.
The Koopman Operator in Systems and Control: Concepts, Methodologies, and Applications (Lecture Notes in Control and Information Sciences #484)
by Yoshihiko Susuki Alexandre Mauroy Igor MezićThis book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory.The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts:theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification;data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; andKoopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control.A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.
The Krasnosel'skiĭ-Mann Iterative Method: Recent Progress and Applications (SpringerBriefs in Optimization)
by Panos M. Pardalos Yeol Je Cho Themistocles M. Rassias Qiao-Li Dong Songnian HeThis brief explores the Krasnosel'skiĭ-Man (KM) iterative method, which has been extensively employed to find fixed points of nonlinear methods.
The Krasnoselskii-Mann Method for Common Fixed Point Problems (SpringerBriefs in Optimization)
by Alexander J. ZaslavskiThis book delves into the intricate world of fixed point theory, focusing on the Krasnoselskii-Mann method to tackle common fixed point problems within a finite family of quasi-nonexpansive mappings in hyperbolic metric spaces. By exploring various iterative algorithms, including the Cimmino algorithm and dynamic string-averaging methods, this volume offers a comprehensive study of convergence and approximate solutions amidst computational errors. Key concepts such as W-hyperbolic spaces, convex combinations, and set-valued inclusions are meticulously examined. The author presents a detailed analysis of iterative methods, highlighting their effectiveness in solving complex fixed-point problems. Readers will encounter critical discussions on the behavior of exact and inexact iterates, the role of computational errors, and innovative approaches like remotest set control. This book invites readers to engage with challenging questions about convergence and solution accuracy in mathematical spaces. Ideal for researchers and scholars in mathematics and related fields, this book provides valuable insights into advanced iterative methods for solving fixed-point problems. Whether you are a mathematician specializing in nonlinear analysis or an academic exploring optimization theory, this volume is an essential resource for understanding the latest developments in fixed point theory.
The Kurzweil-Henstock Integral and Its Differential: A Unified Theory of Integration on R and Rn
by Solomon LeaderA comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each sec
The Kurzweil-Henstock Integral for Undergraduates: A Promenade Along the Marvelous Theory of Integration (Compact Textbooks in Mathematics)
by Alessandro FondaThis beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes–Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach–Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.
The Labour Market Impact of the EU Enlargement
by Francesco Pastore Floro Ernesto CaroleoUntil recently, regional labour market imbalances were considered transitory phenomena caused by state failure in yielding distorted investment incentives and by labour market rigidities. Labour mobility and wage flexibility were at the core of the debate over the causes of and cures for regional imbalances. This book bears witness to the changed perspective of research. For instance, in the recent literature, internal migration is depicted as a cause of further geographical divergence. The book contributes to the debate by presenting important new findings on: a) the reasons why structural change in some sectors causes a slump in some regions; b) the extent to which poverty traps explain spatial imbalances; c) the degree of convergence across EU countries and regions; d) the role of labour mobility in Central and Eastern Europe; e) and the role of pro-active employment schemes and child care facilities in alleviating the hardship of the weakest segments of the population.
The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century
by David SalsburgThis author brilliantly relates the history of statistics with colorful stories and intriguing details concerning the pioneers in the field.
The Lambert W Function: Its Generalizations and Applications (Discrete Mathematics and Its Applications)
by Istvan MezoThis book is the very first one in the English language entirely dedicated to the Lambert W function, its generalizations, and its applications. One goal is to promote future research on the topic. The book contains all the information one needs when trying to find a result. The most important formulas and results are framed. The Lambert W function is a multi-valued inverse function with plenty of applications in areas like molecular physics, relativity theory, fuel consumption models, plasma physics, analysis of epidemics, bacterial growth models, delay differential equations, fluid mechanics, game theory, statistics, study of magnetic materials, and so on. The first part of the book gives a full treatise of the W function from theoretical point of view. The second part presents generalizations of this function which have been introduced by the need of applications where the classical W function is insufficient. The third part presents a large number of applications from physics, biology, game theory, bacterial cell growth models, and so on. The second part presents the generalized Lambert functions based on the tools we had developed in the first part. In the third part familiarity with Newtonian physics will be useful. The text is written to be accessible for everyone with only basic knowledge on calculus and complex numbers. Additional features include the Further Notes sections offering interesting research problems and information for further studies. Mathematica codes are included. The Lambert function is arguably the simplest non-elementary transcendental function out of the standard set of sin, cos, log, etc., therefore students who would like to deepen their understanding of real and complex analysis can see a new “almost elementary” function on which they can practice their knowledge.
The Language Lover's Puzzle Book: A World Tour Of Languages And Alphabets In 100 Amazing Puzzles (Alex Bellos Puzzle Books #0)
by Alex Bellos100 wonder-filled word puzzles that thrill and tantalize with the beauty, magic, and weirdness of world language Whether you’re a crossword solver, cryptogram fan, Scrabble addict, or Sudoku savant, The Language Lover’s Puzzle Book is guaranteed to tease your brain and twist your tongue. Puzzle master Alex Bellos begins in Japan, where we can observe some curious counting: boru niko = two balls tsuna nihon = two ropes uma nito = two horses kami nimai = two sheets of paper ashi gohon = five legs ringo goko = five apples sara gomai = five plates kaba goto = five hippos Now, how do the Japanese say “nine cucumbers”?* a) kyuri kyuhon b) kyuri kyuko c) kyuri kyuhiki d) kyuri kyuto Bellos finds the intrigue—and the human element—in a dizzying array of ancient, modern, and even invented tongues, from hieroglyphs to Blissymbolics, Danish to Dothraki. Filled with unusual alphabets, fascinating characters, and intriguing local customs for time-telling, naming children, and more, this is a bravura book of brainteasers and beyond—it’s a globe-trotting, time-traveling celebration of language. *The word endings depend on shape: Flat things end in -mai and spherical things end in -ko. Cucumbers are long things (like ropes and legs), so they end in -hon. The answer is (a)!
The Language Phenomenon
by K. Smith P. M. BinderThis volume contains a contemporary, integrated description of the processes of language. These range from fast scales (fractions of a second) to slow ones (over a million years). The contributors, all experts in their fields, address language in the brain, production of sentences and dialogues, language learning, transmission and evolutionary processes that happen over centuries or millenia, the relation between language and genes, the origins of language, self-organization, and language competition and death. The book as a whole will help to show how processes at different scales affect each other, thus presenting language as a dynamic, complex and profoundly human phenomenon.
The Language of Algebra: Equations, Tables, and Graphs, Student Guide
by McGraw-HillMathScape(TM): Seeing and Thinking Mathematically is an NSF funded standards based program. This unique comprehensive curriculum encourages students to learn mathematics by doing mathematics, by using and connecting mathematical ideas, and by actively increasing their understanding. MathScape(TM): Seeing and Thinking Mathematically is one of four middle school programs to receive a satisfactory rating from the American Association for the Advancement of Science (AAAS).
The Language of Mathematics
by Robert L. BaberA new and unique way of understanding the translation of concepts and natural language into mathematical expressionsTransforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process--not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and improve their ability to apply mathematics more efficiently and effectively to practical problems in their own work.Using parts of speech to identify variables and functions in a mathematical model is a new approach, as is the insight that examining aspects of grammar is highly useful when formulating a corresponding mathematical model. This book identifies the basic elements of the language of mathematics, such as values, variables, and functions, while presenting the grammatical rules for combining them into expressions and other structures. The author describes and defines different notational forms for expressions, and also identifies the relationships between parts of speech and other grammatical elements in English and components of expressions in the language of mathematics. Extensive examples are used throughout that cover a wide range of real-world problems and feature diagrams and tables to facilitate understanding.The Language of Mathematics is a thought-provoking book of interest for readers who would like to learn more about the linguistic nature and aspects of mathematical notation. The book also serves as a valuable supplement for engineers, technicians, managers, and consultants who would like to improve their ability to apply mathematics effectively, systematically, and efficiently to practical problems.
The Language of Mathematics: The Stories behind the Symbols
by Raúl RojasA marvelous compendium of mathematical symbols and their fascinating historiesGalileo famously wrote that the book of nature is written in mathematical language. The Language of Mathematics is a wide-ranging and beautifully illustrated collection of short, colorful histories of the most commonly used symbols in mathematics, providing readers with an engaging introduction to the origins, evolution, and conceptual meaning of each one.In dozens of lively and informative entries, Raúl Rojas shows how today&’s mathematics stands on the shoulders of giants, mathematicians from around the world who developed mathematical notation through centuries of collective effort. He tells the stories of such figures as al-Khwārizmī, René Descartes, Joseph-Louis Lagrange, Carl Friedrich Gauss, Augustin-Louis Cauchy, Karl Weierstrass, Sofia Kovalevskaya, David Hilbert, and Kenneth Iverson. Topics range from numbers and variables to sets and functions, constants, and combinatorics. Rojas describes the mathematical problems associated with different symbols and reveals how mathematical notation has sometimes been an accidental process. The entries are self-contained and can be read in any order, each one examining one or two symbols, their history, and the variants they may have had over time.An essential companion for math enthusiasts, The Language of Mathematics shows how mathematics is a living and evolving entity, forever searching for the best symbolism to express relationships between abstract concepts and to convey meaning.
The Laplace Equation
by Dagmar MedkováThis book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the Neumann problem, the Robin problem, the derivative oblique problem, the transmission problem, the skip problem and mixed problems. It also examines different solutions - classical, in Sobolev spaces, in Besov spaces, in homogeneous Sobolev spaces and in the sense of non-tangential limit. It also explains relations between different solutions. The book has been written in a way that makes it as readable as possible for a wide mathematical audience, and includes all the fundamental definitions and propositions from other fields of mathematics. This book is of interest to research students, as well as experts in partial differential equations and numerical analysis.
The Large Flux Problem to the Navier-Stokes Equations: Global Strong Solutions in Cylindrical Domains (Advances in Mathematical Fluid Mechanics)
by Joanna Rencławowicz Wojciech M. ZajączkowskiThis monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux. To accomplish this, some assumptions are necessary: The flux is close to homogeneous, and the initial velocity and the external force do not change too much along the axis of the cylinder. This is achieved by utilizing a sophisticated method of deriving energy type estimates for weak solutions and global estimates for regular solutions—an approach that is wholly unique within the existing literature on the Navier-Stokes equations. To demonstrate these results, three main steps are followed: first, the existence of weak solutions is shown; next, the conditions guaranteeing the regularity of weak solutions are presented; and, lastly, global regular solutions are proven. This volume is ideal for mathematicians whose work involves the Navier-Stokes equations, and, more broadly, researchers studying fluid mechanics.
The Large Hadron Collider
by Martin BeechIt may at first seem that the world of subatomic physics is far removed from our every day lives. Isn't it all just a waste of time and taxpayers' money? Hopefully, all who read this book will come to a different conclusion. Collider physics is all about our origins, and this aspect alone makes it worthy of our very best attention. The experiments conducted within the vast collider chambers are at the forefront of humanity's quest to unweave the great tapestry that is the universe. Everything is connected. Within the macrocosm is the microcosm. By knowing how matter is structured, how atoms and elementary particles interact, and what forces control the interactions between the particles, we discover further clues as to why the universe is the way it is, and we uncover glimpses of how everything came into being. The Large Hadron Collider (LHC), in the process of coming online at CERN, is the world's largest and most complex machine. It represents the pinnacle of human ingenuity, and its physical characteristics, costs, and workings astound us at every turn. We are literally humbled by the machine that has been produced through a grand international collaboration of scientists. This book is about what those scientists hope to discover with the LHC, for hopes do run high, and there is much at stake. Careers, reputations and prestigious science prizes will be realized, and possibly lost, in the wake of the results that the LHC will produce. And there are risks, real and imagined. The LHC will probe the very fabric of matter and it will help us understand the very weft and the weave of the universe.
The Last Man in Russia: The Struggle to Save a Dying Nation
by Oliver BulloughRussia is dying from within. Oligarchs and oil barons may still dominate international news coverage, but their prosperity masks a deep-rooted demographic tragedy. Faced with staggering population decline--and near-certain economic collapse--driven by toxic levels of alcohol abuse, Russia is also battling a deeper sickness: a spiritual one, born out of the country’s long totalitarian experiment. In The Last Man in Russia, award-winning journalist Oliver Bullough uses the tale of a lone priest to give life to this national crisis. Father Dmitry Dudko, a dissident Orthodox Christian, was thrown into a Stalinist labor camp for writing poetry. Undaunted, on his release in the mid-1950s he began to preach to congregations across Russia with little concern for his own safety. At a time when the Soviet government denied its subjects the prospect of advancement, and turned friend against friend and brother against brother, Dudko urged his followers to cling to hope. He maintained a circle of sacred trust at the heart of one of history’s most deceitful systems. But as Bullough reveals, this courageous group of believers was eventually shattered by a terrible act of betrayal--one that exposes the full extent of the Communist tragedy. Still, Dudko’s dream endures. Although most Russians have forgotten the man himself, the embers of hope that survived the darkness are once more beginning to burn. Leading readers from a churchyard in Moscow to the snow-blanketed ghost towns of rural Russia, and from the forgotten graves of Stalin’s victims to a rock festival in an old gulag camp, The Last Man in Russia is at once a travelogue, a sociological study, a biography, and a cri de coeur for a dying nation--one that, Bullough shows, might yet be saved.
The Lattice Boltzmann Method
by Timm Krüger Halim Kusumaatmaja Alexandr Kuzmin Orest Shardt Goncalo Silva Erlend Magnus ViggenThis book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.
The Lattice of Subquasivarieties of a Locally Finite Quasivariety (CMS Books in Mathematics)
by Jennifer Hyndman J. B. NationThis book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout.
The Leading Indicators: A Short History of the Numbers That Rule Our World
by Zachary KarabellHow did we come by the "leading indicators" we place such stock in? We allocate trillions of dollars and make public policy and personal decisions based upon them, but what do they really tell us?"The leading indicators" shape our lives intimately, but few of us know where these numbers come from, what they mean, or why they rule the world. GDP, inflation, unemployment, trade, and a host of averages determine whether we feel optimistic or pessimistic about the country's future and our own. They dictate whether businesses hire and invest, or fire and hunker down, whether governments spend trillions or try to reduce debt, whether individuals marry, buy a car, get a mortgage, or look for a job.Zachary Karabell tackles the history and the limitations of each of our leading indicators. The solution is not to invent new indicators, but to become less dependent on a few simple figures and tap into the data revolution. We have unparalleled power to find the information we need, but only if we let go of the outdated indicators that lead and mislead us.
The Learning Framework in Number: Pedagogical Tools for Assessment and Instruction (Math Recovery)
by Robert J Wright David Ellemor-CollinsThis book is borne out of a collaborative research project (2004-8) between Math Recovery and CEM (Catholic Education Melbourne) funded by the Australian Research Council focusing on intervention in the number learning of low-attaining students in the first five years of school. This has involved developing new pedagogical tools (PTs) for assessment, instruction and intervention including a coherent, research-based framework for understanding the key aspects of students’ developing number knowledge. It also offers guidance on innovative video-based assessment and an overview of principles of intervention instruction. This book will be a useful guide for all primary and elementary school classroom teachers and assistants, and specialist teachers, including experienced Mathematics Recovery instructors. It will also be of significant interest to teacher educators and researchers.
The Learning Framework in Number: Pedagogical Tools for Assessment and Instruction (Math Recovery)
by Robert J Wright David Ellemor-CollinsThis book is borne out of a collaborative research project (2004-8) between Math Recovery and CEM (Catholic Education Melbourne) funded by the Australian Research Council focusing on intervention in the number learning of low-attaining students in the first five years of school. This has involved developing new pedagogical tools (PTs) for assessment, instruction and intervention including a coherent, research-based framework for understanding the key aspects of students’ developing number knowledge. It also offers guidance on innovative video-based assessment and an overview of principles of intervention instruction. This book will be a useful guide for all primary and elementary school classroom teachers and assistants, and specialist teachers, including experienced Mathematics Recovery instructors. It will also be of significant interest to teacher educators and researchers.
The Learning and Development of Mathematics Teacher Educators: International Perspectives and Challenges (Research in Mathematics Education)
by Merrilyn Goos Kim BeswickResearch in mathematics teacher education as a distinctive field of inquiry has grown substantially over the past 10-15 years. Within this field there is emerging interest in how mathematics teacher educators (MTEs) themselves learn and develop. Until recently there were few published studies on this topic, and the processes by which mathematics teacher educators learn, and the forms of knowledge they require for effective practice, had not been systematically investigated. However, researchers in mathematics education are now beginning to investigate the development of MTE expertise and associated issues. This volume draws on the latest research and thinking in this area is therefore timely to stimulate future development and directions. It will survey the emerging field of inquiry in mathematics education, combining the work of established scholars with perspectives of newcomers to the field, with the aim of influencing development of the field, invite cross-cultural comparisons in becoming a mathematics teacher educator by highlighting issues in the development of MTEs in different countries, and examine the roles of both mathematics educators and mathematicians in preparing future teachers of mathematics. The primary audience will be university-based mathematics teacher educators and MTE researchers, and postgraduate research students who are seeking academic careers as MTEs. Additional interest may come from teacher educators in disciplines other than mathematics, and education policy makers responsible for accreditation and quality control of initial teacher education programs.
The Learning and Teaching of Algebra: Ideas, Insights and Activities (IMPACT: Interweaving Mathematics Pedagogy and Content for Teaching #8)
by Kaye Stacey Paul Drijvers Abraham ArcaviIMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include: • Algebra: Setting the Scene • Some Lessons From History • Seeing Algebra Through the Eyes of a Learner • Emphases in Algebra Teaching • Algebra Education in the Digital Era This guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides.