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Fast Multipole Boundary Element Method
by Yijun LiuThe fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged, as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. This book will help students, researchers, and engineers to learn the BEM and fast multipole method from a single source.
Fast Sequential Monte Carlo Methods for Counting and Optimization
by Reuven Y. Rubinstein Radislav Vaisman Ad RidderA comprehensive account of the theory and application of Monte Carlo methodsBased on years of research in efficient Monte Carlo methods for estimation of rare-event probabilities, counting problems, and combinatorial optimization, Fast Sequential Monte Carlo Methods for Counting and Optimization is a complete illustration of fast sequential Monte Carlo techniques. The book provides an accessible overview of current work in the field of Monte Carlo methods, specifically sequential Monte Carlo techniques, for solving abstract counting and optimization problems.Written by authorities in the field, the book places emphasis on cross-entropy, minimum cross-entropy, splitting, and stochastic enumeration. Focusing on the concepts and application of Monte Carlo techniques, Fast Sequential Monte Carlo Methods for Counting and Optimization includes:Detailed algorithms needed to practice solving real-world problemsNumerous examples with Monte Carlo method produced solutions within the 1-2% limit of relative errorA new generic sequential importance sampling algorithm alongside extensive numerical resultsAn appendix focused on review material to provide additional background informationFast Sequential Monte Carlo Methods for Counting and Optimization is an excellent resource for engineers, computer scientists, mathematicians, statisticians, and readers interested in efficient simulation techniques. The book is also useful for upper-undergraduate and graduate-level courses on Monte Carlo methods.
Fast Solar Sailing
by Giovanni VulpettiThe range of solar sailing is very vast; it is a fully in-space means of propulsion that should allow us to accomplish various mission classes that are literally impossible using rocket propulsion, no matter if nuclear or electric. Fast and very fast solar sailings are special classes of sailcraft missions, initially developed only in the first half of the 1990s and still evolving, especially after the latest advances in nanotechnology. This book describes how to plan, compute and optimize the trajectories of sailcraft with speeds considerably higher than 100 km/s; such sailcraft would be able to explore the outer heliosphere, the near interstellar medium and the solar gravitational lens (550-800 astronomical units) in times significantly shorter than the span of an average career (~ 35 years), just to cite a few examples. The scientific interest in this type of exploration is huge.
Fast Solvers for Mesh-Based Computations (Advances in Applied Mathematics)
by Maciej PaszynskiFast Solvers for Mesh-Based Computations presents an alternative way of constructing multi-frontal direct solver algorithms for mesh-based computations. It also describes how to design and implement those algorithms.The book's structure follows those of the matrices, starting from tri-diagonal matrices resulting from one-dimensional mesh-based meth
Fast Track to Differential Equations: Applications-Oriented – Comprehensible – Compact
by Albert FässlerThis compact introduction to the ordinary differential equations and their applications is aimed at anyone who, in their studies, is confronted voluntarily or involuntarily with this versatile subject. Numerous examples from physics, technology, biomathematics, cosmology, economy and optimization allow a quick and motivating approach - abstract proofs and unnecessary formalism are avoided as far as possible. In the foreground is the modelling of ordinary differential equations of the 1st and 2nd order as well as their analytical and numerical solution methods, in which the theory is briefly dealt with before the application examples. In addition, codes show exemplarily how even more demanding questions can be answered and meaningfully represented with the help of a computer algebra system. In the first chapter the necessary previous knowledge from integral and differential calculus is treated. A large number of exercises including solutions round off the work.
Fast Track: Essential Review for AP, Honors, and Other Advanced Study (High School Subject Review)
by The Princeton ReviewGET UP TO SPEED WITH FAST TRACK: GEOMETRY! Covering the most important material taught in high school geometry classes, this essential review book gets readers on the fast track to class success, with critical information presented in an easy-to-follow quick-study format!Inside this book, you'll find:• Clear, concise summaries of the most important concepts, formulas, and geometric skills• Diagrams, charts, and graphs for quick visual reference• Easy-to-follow content organization and illustrationsWith its friendly, straightforward approach and a clean, colorful modern design crafted to appeal to visual learners, this guidebook is perfect for catching up in class or getting ahead on exam review.Topics covered in Fast Track: Geometry include:• Key terms• Angles• Polygons• Circles• Congruence and similarity• Constructions• Transformations• Trigonometry• Three-dimensional figures• Reasoning and proofs• Perimeter, area, and volume... and more!
Fast Transverse Beam Instability Caused by Electron Cloud Trapped in Combined Function Magnets (Springer Theses)
by Sergey A. AntipovThis thesis presents profound insights into the origins and dynamics of beam instabilities using both experimental observations and numerical simulations. When the Recycler Ring, a high-intensity proton beam accelerator at Fermi National Accelerator Laboratory, was commissioned, it became evident that the Recycler beam experiences a very fast instability of unknown nature. This instability was so fast that the existing dampers were ineffective at suppressing it. The nature of this phenomenon, alongside several other poorly understood features of the beam, became one of the biggest puzzles in the accelerator community. The author investigated a hypothesis that the instability arises from an interaction with a dense cloud of electrons accompanying the proton beam. He studied the phenomena experimentally by comparing the dynamics of stable and unstable beams, by numerically simulating the build-up of the electron cloud and its interaction with the beam, and by constructing an analytical model of an electron cloud-driven instability with the electrons trapped in combined-function dipole magnets. He has devised a method to stabilize the beam by a clearing bunch, which conclusively revealed that the instability is caused by the electron cloud, trapped in a strong magnetic field. Finally, he conducted measurements of the microwave propagation through a single dipole magnet. These measurements have confirmed the presence of the electron cloud in combined-function magnets.
Fast Variables in Stochastic Population Dynamics
by George William Albert ConstableIn this thesis two variants of the fast variable elimination method are developed. They are intuitive, simple to implement and give results which are in very good agreement with those found from numerical simulations. The relative simplicity of the techniques makes them ideal for applying to problems featuring demographic stochasticity, for experts and non-experts alike. Within the context of mathematical modelling, fast variable elimination is one of the central tools with which one can simplify a multivariate problem. When used in the context of of deterministic systems, the theory is quite standard, but when stochastic effects are present, it becomes less straightforward to apply. While the introductory and background chapters form an excellent primer to the theory of stochastic population dynamics, the techniques developed can be applied to systems exhibiting a separation of timescales in a variety of fields including population genetics, ecology and epidemiology.
Faster Isn't Smarter: Messages about Math, Teaching, and Learning in the 21st Century
by Cathy L. SeeleyFeaturing 41 entirely updated messages and four new ones, this second edition continues to offer straight talk and common sense about some of today's most important, thought-provoking issues in education. With themes ranging from equity, intelligence, and the incredible potential of all students to challenging students to think with a problem-centered approach focused on student engagement and classroom discourse, the book provides a base for lively discussion among elementary, middle, and high school teachers; leaders; policymakers; and families. Entirely updated, including new messages.
Faszinierende Geometrie: Mathematische Zusammenhänge und ihre Anschauung – in der Ebene, im Raum und auf der Kugel
by Sergei KovalenkoIn diesem Buch findest du eine detaillierte und zugleich sehr anschauliche Darstellung ausgewählter Inhalte aus der elementaren Geometrie, untermauert mit historischem Kontext und geschichtlichen Erzählungen. Neben den klassischen Sätzen und Ergebnissen der ebenen und räumlichen Geometrie und Trigonometrie werden auch speziellere Themen behandelt – etwa die sphärische Geometrie oder die theoretischen Grundlagen der Konstruktion geometrischer Objekte mit Hilfe von Lineal und Zirkel. Das Buch richtet sich an alle, die sich für Geometrie, ihre theoretischen Aspekte und deren Zusammenhänge sowie für ihre vielfältigen Anwendungen interessieren; es setzt nur mathematische Grundkenntnisse wie Term- und Äquivalenzumformungen voraus. Insbesondere Lehramtsstudierenden sowie Lehrerinnen und Lehrern kann es neue kreative Impulse zur Weitergabe an jüngere Generationen liefern.
Fat Chance: Probability from 0 to 1
by Emily Riehl Joe Harris Benedict GrossIn a world where we are constantly being asked to make decisions based on incomplete information, facility with basic probability is an essential skill. This book provides a solid foundation in basic probability theory designed for intellectually curious readers and those new to the subject. Through its conversational tone and careful pacing of mathematical development, the book balances a charming style with informative discussion. This text will immerse the reader in a mathematical view of the world, giving them a glimpse into what attracts mathematicians to the subject in the first place. Rather than simply writing out and memorizing formulas, the reader will come out with an understanding of what those formulas mean, and how and when to use them. Readers will also encounter settings where probabilistic reasoning does not apply or where intuition can be misleading. This book establishes simple principles of counting collections and sequences of alternatives, and elaborates on these techniques to solve real world problems both inside and outside the casino. Pair this book with the HarvardX online course for great videos and interactive learning: https://harvardx.link/fat-chance.
Fat-Tailed Distributions: Data, Diagnostics and Dependence
by Daan Nieboer Roger M. Cooke Jolanta MisiewiczThis title is written for the numerate nonspecialist, and hopes to serve three purposes. First it gathers mathematical material from diverse but related fields of order statistics, records, extreme value theory, majorization, regular variation and subexponentiality. All of these are relevant for understanding fat tails, but they are not, to our knowledge, brought together in a single source for the target readership. Proofs that give insight are included, but for most fussy calculations the reader is referred to the excellent sources referenced in the text. Multivariate extremes are not treated. This allows us to present material spread over hundreds of pages in specialist texts in twenty pages. Chapter 5 develops new material on heavy tail diagnostics and gives more mathematical detail. Since variances and covariances may not exist for heavy tailed joint distributions, Chapter 6 reviews dependence concepts for certain classes of heavy tailed joint distributions, with a view to regressing heavy tailed variables. Second, it presents a new measure of obesity. The most popular definitions in terms of regular variation and subexponentiality invoke putative properties that hold at infinity, and this complicates any empirical estimate. Each definition captures some but not all of the intuitions associated with tail heaviness. Chapter 5 studies two candidate indices of tail heaviness based on the tendency of the mean excess plot to collapse as data are aggregated. The probability that the largest value is more than twice the second largest has intuitive appeal but its estimator has very poor accuracy. The Obesity index is defined for a positive random variable X as: Ob(X) = P (X1 +X4 > X2 +X3|X1 1 then Ob(X) Third and most important, we hope to convince the reader that fat tail phenomena pose real problems; they are really out there and they seriously challenge our usual ways of thinking about historical averages, outliers, trends, regression coefficients and confidence bounds among many other things. Data on flood insurance claims, crop loss claims, hospital discharge bills, precipitation and damages and fatalities from natural catastrophes drive this point home. While most fat tailed distributions are "bad", research in fat tails is one distribution whose tail will hopefully get fatter.
Fatal Misconception: The Struggle to Control World Population
by Matthew ConnellyListen to a short interview with Matthew Connelly Host: Chris Gondek | Producer: Heron & Crane Fatal Misconception is the disturbing story of our quest to remake humanity by policing national borders and breeding better people. As the population of the world doubled once, and then again, well-meaning people concluded that only population control could preserve the "quality of life." This movement eventually spanned the globe and carried out a series of astonishing experiments, from banning Asian immigration to paying poor people to be sterilized. Supported by affluent countries, foundations, and non-governmental organizations, the population control movement experimented with ways to limit population growth. But it had to contend with the Catholic Church's ban on contraception and nationalist leaders who warned of "race suicide." The ensuing struggle caused untold suffering for those caught in the middle--particularly women and children. It culminated in the horrors of sterilization camps in India and the one-child policy in China. Matthew Connelly offers the first global history of a movement that changed how people regard their children and ultimately the face of humankind. It was the most ambitious social engineering project of the twentieth century, one that continues to alarm the global community. Though promoted as a way to lift people out of poverty--perhaps even to save the earth--family planning became a means to plan other people‘s families. With its transnational scope and exhaustive research into such archives as Planned Parenthood and the newly opened Vatican Secret Archives, Connelly's withering critique uncovers the cost inflicted by a humanitarian movement gone terribly awry and urges renewed commitment to the reproductive rights of all people.
Fatigue and Corrosion in Metals
by Pietro Paolo MilellaThis textbook, suitable for students, researchers and engineers, gathers the experience of more than 20 years of teaching fracture mechanics, fatigue and corrosion to professional engineers and running experimental tests and verifications to solve practical problems in engineering applications. As such, it is a comprehensive blend of fundamental knowledge and technical tools to address the issues of fatigue and corrosion. The book initiates with a systematic description of fatigue from a phenomenological point of view, since the early signs of submicroscopic damage in few surface grains and continues describing, step by step, how these precursors develop to become mechanically small cracks and, eventually, macrocracks whose growth is governed by fracture mechanics. But fracture mechanics is also introduced to analyze stress corrosion and corrosion assisted fatigue in a rather advanced fashion. The author dedicates a particular attention to corrosion starting with an electrochemical treatment that mechanical engineers with a rather limited knowledge of electrochemistry will well digest without any pain. The electrochemical introduction is considered an essential requirement to the full understanding of corrosion that is essentially an electrochemical process. All stress corrosion aspects are treated, from the generalized film rupture-anodic dissolution process that is the base of any corrosion mechanism to the aggression occurring in either mechanically or thermally sensitized alloys up to the universe of hydrogen embrittlement, which is described in all its possible modes of appearance. Multiaxial fatigue and out-of-phase loading conditions are treated in a rather comprehensive manner together with damage progression and accumulation that are not linear processes. Load spectra are analyzed also in the frequency domain using the Fourier transform in a rather elegant fashion full of applications that are generally not considered at all in fatigue textbooks, yet they deserve a special place and attention. The issue of fatigue cannot be treated without a probabilistic approach unless the designer accepts the shame of one-out-of-two pieces failure. The reader is fully introduced to the most promising and advanced analytical tools that do not require a normal or lognormal distribution of the experimental data, which is the most common case in fatigue. But the probabilistic approach is also used to introduce the fundamental issue of process volume that is the base of any engineering application of fatigue, from the probability of failure to the notch effect, from the metallurgical variability and size effect to the load type effect. Fractography plays a fundamental role in the post mortem analysis of fatigue and corrosion failures since it can unveil the mystery encrypted in any failure.
Fatigue and Fracture Reliability Engineering
by J. J. Xiong R. A. ShenoiFatigue and Fracture Reliability Engineering is an attempt to present an integrated and unified approach to reliability determination of fatigue and fracture behaviour, incorporating probability, statistics and other related areas. A series of original and practical approaches, are suggested in Fatigue and Fracture Reliability Engineering, including new techniques in determining fatigue and fracture performances. It also carries out an investigation into static and fatigue properties, and into the failure mechanisms of unnotched and notched CFR composite laminates with different lay-ups to optimize the stacking sequence effect. Further benefits include: a novel convergence-divergence counting procedure to extract all load cycles from a load history of divergence-convergence waves;practical scatter factor formulae to determine the safe fatigue crack initiation and propagation lives from the results of a single full-scale test of a complete structure; anda nonlinear differential kinetic model for describing the dynamical behaviour of an atom at a fatigue crack tip.Fatigue and Fracture Reliability Engineering is intended for practising engineers in marine, civil construction, aerospace, offshore, automotive and chemical industries. It is also useful reading for researchers on doctoral programmes, and is appropriate for advanced undergraduate and postgraduate programmes in any mechanically-oriented engineering discipline.
Fault Diagnosis Inverse Problems: Solution with Metaheuristics (Studies in Computational Intelligence #763)
by Orestes Llanes Santiago Lídice Camps Echevarría Haroldo Fraga Campos Velho Antônio José Silva NetoThis book presents a methodology based on inverse problems for use in solutions for fault diagnosis in control systems, combining tools from mathematics, physics, computational and mathematical modeling, optimization and computational intelligence. This methodology, known as fault diagnosis – inverse problem methodology or FD-IPM, unifies the results of several years of work of the authors in the fields of fault detection and isolation (FDI), inverse problems and optimization. The book clearly and systematically presents the main ideas, concepts and results obtained in recent years. By formulating fault diagnosis as an inverse problem, and by solving it using metaheuristics, the authors offer researchers and students a fresh, interdisciplinary perspective for problem solving in these fields. Graduate courses in engineering, applied mathematics and computing also benefit from this work.
Fault-tolerant Control and Diagnosis for Integer and Fractional-order Systems: Fundamentals of Fractional Calculus and Differential Algebra with Real-Time Applications (Studies in Systems, Decision and Control #328)
by Rafael Martínez-Guerra Fidel Meléndez-Vázquez Iván Trejo-ZúñigaThis book is about algebraic and differential methods, as well as fractional calculus, applied to diagnose and reject faults in nonlinear systems, which are of integer or fractional order. This represents an extension of a very important and widely studied problem in control theory, namely fault diagnosis and rejection (using differential algebraic approaches), to systems presenting fractional dynamics, i.e. systems whose dynamics are represented by derivatives and integrals of non-integer order. The authors offer a thorough overview devoted to fault diagnosis and fault-tolerant control applied to fractional-order and integer-order dynamical systems, and they introduce new methodologies for control and observation described by fractional and integer models, together with successful simulations and real-time applications. The basic concepts and tools of mathematics required to understand the methodologies proposed are all clearly introduced and explained. Consequently, the book is useful as supplementary reading in courses of applied mathematics and nonlinear control theory. This book is meant for engineers, mathematicians, physicists and, in general, to researchers and postgraduate students in diverse areas who have a minimum knowledge of calculus. It also contains advanced topics for researchers and professionals interested in the area of states and faults estimation.
Fear of a Black Universe: An Outsider's Guide to the Future of Physics
by Stephon AlexanderIn this important guide to science and society, a cosmologist argues that physics must embrace the excluded, listen to the unheard, and be unafraid of being wrong. Years ago, cosmologist Stephon Alexander received life-changing advice: to discover real physics, he needed to stop memorizing and start taking risks. In Fear of a Black Universe, Alexander shows that great physics requires us to think outside the mainstream -- to improvise and rely on intuition. His approach leads him to three principles that shape all theories of the universe: the principle of invariance, the quantum principle, and the principle of emergence. Alexander uses them to explore some of physics' greatest mysteries, from what happened before the big bang to how the universe makes consciousness possible. Drawing on his experience as a Black physicist, he makes a powerful case for diversifying our scientific communities. Compelling and empowering, Fear of a Black Universe offers remarkable insight into the art of physics.
Feast For 10
by Cathryn FalwellA counting book that features an African-American family shopping for food, preparing dinner, and sitting down to eat. Lively read-aloud text paired with bright collage illustrations.
Feature Engineering and Selection: A Practical Approach for Predictive Models (Chapman & Hall/CRC Data Science Series)
by Max Kuhn Kjell JohnsonThe process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.
Feature Engineering for Machine Learning and Data Analytics (Chapman & Hall/CRC Data Mining and Knowledge Discovery Series)
by Huan Liu Guozhu DongFeature engineering plays a vital role in big data analytics. Machine learning and data mining algorithms cannot work without data. Little can be achieved if there are few features to represent the underlying data objects, and the quality of results of those algorithms largely depends on the quality of the available features. Feature Engineering for Machine Learning and Data Analytics provides a comprehensive introduction to feature engineering, including feature generation, feature extraction, feature transformation, feature selection, and feature analysis and evaluation. The book presents key concepts, methods, examples, and applications, as well as chapters on feature engineering for major data types such as texts, images, sequences, time series, graphs, streaming data, software engineering data, Twitter data, and social media data. It also contains generic feature generation approaches, as well as methods for generating tried-and-tested, hand-crafted, domain-specific features. The first chapter defines the concepts of features and feature engineering, offers an overview of the book, and provides pointers to topics not covered in this book. The next six chapters are devoted to feature engineering, including feature generation for specific data types. The subsequent four chapters cover generic approaches for feature engineering, namely feature selection, feature transformation based feature engineering, deep learning based feature engineering, and pattern based feature generation and engineering. The last three chapters discuss feature engineering for social bot detection, software management, and Twitter-based applications respectively. This book can be used as a reference for data analysts, big data scientists, data preprocessing workers, project managers, project developers, prediction modelers, professors, researchers, graduate students, and upper level undergraduate students. It can also be used as the primary text for courses on feature engineering, or as a supplement for courses on machine learning, data mining, and big data analytics.
Feedback Arc Set: A History of the Problem and Algorithms (SpringerBriefs in Computer Science)
by Robert KudelićThe main aim of the book is to give a review of all relevant information regarding a well-known and important problem of Feedback Arc Set (FAS). This review naturally also includes a history of the problem, as well as specific algorithms. To this point such a work does not exist: There are sources where one can find incomplete and perhaps untrustworthy information. With this book, information about FAS can be found easily in one place: formulation, description, theoretical background, applications, algorithms etc. Such a compendium will be of help to people involved in research, but also to people that want to quickly acquaint themselves with the problem and need reliable information. Thus research, professional work and learning can proceed in a more streamlined and faster way.
Feedback Control in Systems Biology
by Carlo Cosentino Declan BatesLike engineering systems, biological systems must also operate effectively in the presence of internal and external uncertainty-such as genetic mutations or temperature changes, for example. It is not surprising, then, that evolution has resulted in the widespread use of feedback, and research in systems biology over the past decade has shown that
Feedback Systems: An Introduction for Scientists and Engineers
by Richard M. Murray Karl Johan Aström<p>This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. <p>Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. They provide exercises at the end of every chapter, and an accompanying electronic solutions manual is available. Feedback Systems is a complete one-volume resource for students and researchers in mathematics, engineering, and the sciences. <p> <li>Covers the mathematics needed to model, analyze, and design feedback systems <li>Serves as an introductory textbook for students and a self-contained resource for researchers <li>Includes exercises at the end of every chapter <li>Features an electronic solutions manual <li>Offers techniques applicable across a range of disciplines</li>