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Fractional Order Analysis: Theory, Methods and Applications
by Hemen DuttaA guide to the new research in the field of fractional order analysis Fractional Order Analysis contains the most recent research findings in fractional order analysis and its applications. The authors—noted experts on the topic—offer an examination of the theory, methods, applications, and the modern tools and techniques in the field of fractional order analysis. The information, tools, and applications presented can help develop mathematical methods and models with better accuracy. Comprehensive in scope, the book covers a range of topics including: new fractional operators, fractional derivatives, fractional differential equations, inequalities for different fractional derivatives and fractional integrals, fractional modeling related to transmission of Malaria, and dynamics of Zika virus with various fractional derivatives, and more. Designed to be an accessible text, several useful, relevant and connected topics can be found in one place, which is crucial for an understanding of the research problems of an applied nature. This book: Contains recent development in fractional calculus Offers a balance of theory, methods, and applications Puts the focus on fractional analysis and its interdisciplinary applications, such as fractional models for biological models Helps make research more relevant to real-life applications Written for researchers, professionals and practitioners, Fractional Order Analysis offers a comprehensive resource to fractional analysis and its many applications as well as information on the newest research.
Fractional Order Darwinian Particle Swarm Optimization
by Micael Couceiro Pedram GhamisiThis book examines the bottom-up applicability of swarm intelligence to solving multiple problems, such as curve fitting, image segmentation, and swarm robotics. It compares the capabilities of some of the better-known bio-inspired optimization approaches, especially Particle Swarm Optimization (PSO), Darwinian Particle Swarm Optimization (DPSO) and the recently proposed Fractional Order Darwinian Particle Swarm Optimization (FODPSO), and comprehensively discusses their advantages and disadvantages. Further, it demonstrates the superiority and key advantages of using the FODPSO algorithm, such as its ability to provide an improved convergence towards a solution, while avoiding sub-optimality. This book offers a valuable resource for researchers in the fields of robotics, sports science, pattern recognition and machine learning, as well as for students of electrical engineering and computer science.
Fractional Order Signal Processing
by Indranil Pan Saptarshi DasThe book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, biomedical signal processing, electrochemical applications and many more. Adequate references are provided in each category so that the researchers can delve deeper into each area and broaden their horizon of understanding. Available MATLAB tools to simulate FOSP theories are also introduced so that the readers can apply the theoretical concepts right-away and gain practical insight in the specific domain.
Fractional Processes and Fractional-Order Signal Processing
by Hu Sheng Yangquan Chen Tianshuang QiuFractional processes are widely found in science, technology and engineering systems. In Fractional Processes and Fractional-order Signal Processing, some complex random signals, characterized by the presence of a heavy-tailed distribution or non-negligible dependence between distant observations (local and long memory), are introduced and examined from the 'fractional' perspective using simulation, fractional-order modeling and filtering and realization of fractional-order systems. These fractional-order signal processing (FOSP) techniques are based on fractional calculus, the fractional Fourier transform and fractional lower-order moments. Fractional Processes and Fractional-order Signal Processing: presents fractional processes of fixed, variable and distributed order studied as the output of fractional-order differential systems; introduces FOSP techniques and the fractional signals and fractional systems point of view; details real-world-application examples of FOSP techniques to demonstrate their utility; and provides important background material on Mittag-Leffler functions, the use of numerical inverse Laplace transform algorithms and supporting MATLAB® codes together with a helpful survey of relevant webpages. Readers will be able to use the techniques presented to re-examine their signals and signal-processing methods. This text offers an extended toolbox for complex signals from diverse fields in science and engineering. It will give academic researchers and practitioners a novel insight into the complex random signals characterized by fractional properties, and some powerful tools to analyze those signals.
Fractional Thermoelasticity
by Yuriy PovstenkoThis book is devoted to fractional thermoelasticity, i. e. thermoelasticity based on the heat conduction equation with differential operators of fractional order. Readers will discover how time-fractional differential operators describe memory effects and space-fractional differential operators deal with the long-range interaction. Fractional calculus, generalized Fourier law, axisymmetric and central symmetric problems and many relevant equations are featured in the book. The latest developments in the field are included and the reader is brought up to date with current research. The book contains a large number of figures, to show the characteristic features of temperature and stress distributions and to represent the whole spectrum of order of fractional operators. This work presents a picture of the state-of-the-art of fractional thermoelasticity and is suitable for specialists in applied mathematics, physics, geophysics, elasticity, thermoelasticity and engineering sciences. Corresponding sections of the book may also be used as additional reading material for courses on heat and mass transfer, continuum mechanics, thermal stresses as well as in fractional calculus and its applications for graduate and postgraduate students. Extensive references are included in order to stimulate further studies.
Fractional Thermoelasticity (Solid Mechanics and Its Applications #278)
by Yuriy PovstenkoThis new edition offers expanded coverage of fractional calculus, including Riemann–Liouville fractional integrals, Riemann–Liouville and Caputo fractional derivatives, Riesz fractional operators, and Mittag-Leffler and Wright functions. Additionally, it provides a comprehensive examination of fractional heat conduction and related theories of thermoelasticity. Readers will gain insights into the concepts of time and space nonlocality and their impact on the generalizations of Fourier's law in thermoelasticity. This edition presents a detailed formulation of the problem of heat conduction in different domains and the associated thermal stresses, covering topics such as the fundamental solution to the Dirichlet problem, constant boundary conditions for temperature, and the fundamental solution to the physical Neumann problem. New insights into time-harmonic heat impact on the boundary have also been added. Cracks in the framework of fractional thermoelasticity are also considered.
The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science
by Tom T. Hartley Carl F. LorenzoAddresses the rapidly growing field of fractional calculus and provides simplified solutions for linear commensurate-order fractional differential equations The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science is the result of the authors' work in fractional calculus, and more particularly, in functions for the solutions of fractional differential equations, which is fostered in the behavior of generalized exponential functions. The authors discuss how fractional trigonometry plays a role analogous to the classical trigonometry for the fractional calculus by providing solutions to linear fractional differential equations. The book begins with an introductory chapter that offers insight into the fundamentals of fractional calculus, and topical coverage is then organized in two main parts. Part One develops the definitions and theories of fractional exponentials and fractional trigonometry. Part Two provides insight into various areas of potential application within the sciences. The fractional exponential function via the fundamental fractional differential equation, the generalized exponential function, and R-function relationships are discussed in addition to the fractional hyperboletry, the R1-fractional trigonometry, the R2-fractional trigonometry, and the R3-trigonometric functions. The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science also: Presents fractional trigonometry as a tool for scientists and engineers and discusses how to apply fractional-order methods to the current toolbox of mathematical modelers Employs a mathematically clear presentation in an e ort to make the topic broadly accessible Includes solutions to linear fractional differential equations and generously features graphical forms of functions to help readers visualize the presented concepts Provides effective and efficient methods to describe complex structures The Fractional Trigonometry: With Applications to Fractional Differential Equations and Science is an ideal reference for academic researchers, research engineers, research scientists, mathematicians, physicists, biologists, and chemists who need to apply new fractional calculus methods to a variety of disciplines. The book is also appropriate as a textbook for graduate- and PhD-level courses in fractional calculus. Carl F. Lorenzo is Distinguished Research Associate at the NASA Glenn Research Center in Cleveland, Ohio. His past positions include chief engineer of the Instrumentation and Controls Division and chief of the Advanced Controls Technology and Systems Dynamics branches at NASA. He is internationally recognized for his work in the development and application of the fractional calculus and fractional trigonometry. Tom T. Hartley, PhD, is Emeritus Professor in the Department of Electrical and Computer Engineering at The University of Akron. Dr Hartley is a recognized expert in fractional-order systems, and together with Carl Lorenzo, has solved fundamental problems in the area including Riemann's complementary-function initialization function problem. He received his PhD in Electrical Engineering from Vanderbilt University.
Fractions, Decimals & Percents: GRE Math Preparation Guide
by The Editors at the Manhattan GREThis book provides an in-depth look at the array of GRE questions that test knowledge of Fractions, Decimals, and Percents. Learn to see the connections among these part-whole relationships and practice implementing strategic shortcuts.
Fractions For Dummies
by Mark ZegarelliAn easy, straightforward, and fun guide for learning fractions and its counterparts Fractions For Dummies is the perfect strategy guide for both understanding and using one of math's most common (and most challenging) topic areas. You'll explore current solving strategies for fraction-related problems, and you'll also discover how to solve problems involving fractions' closely related cousins, decimals and percentages. Dive deep into the basics of these topics before moving on to more advanced uses, such as word problems, with the help of author and experienced math teacher Mark Zegarelli. This straightforward and intuitive book also includes: Techniques for working with mixed numbers (numbers that include whole amounts and fractions) and more Ways to add, subtract, multiply, and divide fractions with whole numbers and with each other Strategies for helping and supporting the young student in your life who's struggling with fractions, decimals, and/or percentages It's time you showed these math areas who's boss. Fractions For Dummies shows you just how easy fractions and the like can be!
Fractions in Disguise: A Math Adventure (Charlesbridge Math Adventures)
by Edward Einhorn&“No question—a large fraction of parents and teachers will be reaching for this&” entertaining math adventure that introduces simplified and reduced fractions with intrigue and humor (Kirkus) When a valuable fraction goes missing, George Cornelius Factor (a.k.a. GCF) vows to track it down. Knowing that the villainous Dr. Brok likes to disguise his ill-gotten fractions, G.C.F. invents a Reducer—half ray gun, half calculator— that strips away the disguise, reducing the fraction to its lowest common denominator and revealing its true form. With the Reducer in hand, George seeks out Dr. Brok in hopes of retrieving the missing fraction. Equal parts action and humor add up to a wholly entertaining introduction to simplifying fractions. David Clark&’s illustrations are packed with humorous details as well as clearly defined fractions and their corresponding reduction equations.
Fractions In Disguise: A Math Adventure (Charlesbridge Math Adventures Ser.)
by Edward Einhorn David Clark
Fractions, Ratios, and Roots: Rediscover the Basics and Learn About Interesting Applications (essentials)
by Renate MotzerRenate Motzer introduces the world of fractions and connects them with decimal numbers. She clearly shows that fractions can be understood as parts of a whole, but also as ratios of two quantities. The author clearly shows why roots cannot be exactly indicated by fractions, how to find good approximations and why an unusual addition of fractions can lead to paradoxical results. Furthermore, she explains the use of fractions in percentage and probability calculations in a practical way and finally discusses different ways of forming mean values.This Springer essential is a translation of the original German 1st edition essentials, Brüche, Verhältnisse und Wurzeln by Renate Motzer, published by Springer Fachmedien Wiesbaden GmbH, part of Springer Nature in 2018. The translation was done with the help of artificial intelligence (machine translation by the service DeepL.com). A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation. Springer Nature works continuously to further the development of tools for the production of books and on the related technologies to support the authors.
Fracture Mechanics
by Alan T. ZehnderFracture mechanics is a vast and growing field. This book develops the basic elements needed for both fracture research and engineering practice. The emphasis is on continuum mechanics models for energy flows and crack-tip stress- and deformation fields in elastic and elastic-plastic materials. In addition to a brief discussion of computational fracture methods, the text includes practical sections on fracture criteria, fracture toughness testing, and methods for measuring stress intensity factors and energy release rates. Class-tested at Cornell, this book is designed for students, researchers and practitioners interested in understanding and contributing to a diverse and vital field of knowledge.
Fracture Mechanics of Electrically Passive and Active Composites with Periodic Cracking along the Interface (Springer Tracts in Mechanical Engineering)
by Volodymyr Loboda Sergey KozinovThis book offers a comprehensive and timely review of the fracture behavior of bimaterial composites consisting of periodically connected components, i.e. of bimaterial composites possessing periodical cracks along the interface. It first presents an overview of the literature, and then analyzes the isotropic, anisotropic and piezoelectric/dielectric properties of bimaterial components, gradually increasing the difficulty of the solutions discussed up to the coupled electromechanical problems. While in the case of isotropic and anisotropic materials it covers the problems generated by an arbitrary set of cracks, for the piezoelectric materials it focuses on studying the influence of the electric permittivity of the crack’s filler, using not only a simple, fully electrically permeable model, but also a physically realistic, semi-permeable model. Throughout the analyses, the effects of the contact of the crack faces are taken into account so as to exclude the physically unrealistic interpenetration of the composite components that are typical of the classical open model. Further, the book derives and examines the mechanical and electromechanical fields, stress and electric intensity factors in detail. Providing extensive information on the fracture processes taking place in composite materials, the book helps readers become familiar with mathematical methods of complex function theory for obtaining exact analytical solutions.
Fractured Vuggy Carbonate Reservoir Simulation (Springer Mineralogy)
by Jun Yao Zhao-Qin HuangThis book solves the open problems in fluid flow modeling through the fractured vuggy carbonate reservoirs. Fractured vuggy carbonate reservoirs usually have complex pore structures, which contain not only matrix and fractures but also the vugs and cavities. Since the vugs and cavities are irregular in shape and vary in diameter from millimeters to meters, modeling fluid flow through fractured vuggy porous media is still a challenge. The existing modeling theory and methods are not suitable for such reservoir. It starts from the concept of discrete fracture and fracture-vug networks model, and then develops the corresponding mathematical models and numerical methods, including discrete fracture model, discrete fracture-vug model, hybrid model and multiscale models. Based on these discrete porous media models, some equivalent medium models and methods are also discussed. All the modeling and methods shared in this book offer the key recent solutions into this area.
Fraenkel: Mengen bilden
by Matthias WilleErleben Sie das Wiedererwachen des universitären Lebens nach 1918 aus der Sicht eines Betroffenen. Tauchen Sie ein in die Erziehungs- und Sozialgeschichte der Mathematik zur Zeit der Weimarer Republik und erfahren aus der Perspektive eines jungen Autors das Aufstreben der Firma von Julius Springer zum führenden Mathematikverlag. Dank der Verwendung einer Vielzahl von unveröffentlichten Quellen erhalten Sie einen überaus facettenreichen Eindruck des zeitgenössischen akademischen Milieus. In dieser weltweit ersten umfassenden Studie zu Abraham Adolf Fraenkel werden Ihnen bis dato vollkommen unbekannte Einblicke in die Werkstatt seiner mathematischen Gedanken geboten, die verständlich machen, wie innerhalb kürzester Zeit aus einem Laien ein international renommierter Experte für Mengenlehre wurde. Minutiös wird rekonstruiert, wie er vor exakt 100 Jahren zu seinen wegweisenden Resultaten gelangte, die schließlich zum unaufhaltsamen Aufstieg des modernen mengentheoretischen Paradigmas führten.
Fragebögen: Fundierte Konstruktion, sachgerechte Anwendung und aussagekräftige Auswertung (essentials)
by Stefan HollenbergStefan Hollenberg stellt in diesem essential wichtige Hinweise aus über 40 einschlägigen Fachtexten zur Entwicklung, Konstruktion, Durchführung und Auswertung von schriftlichen Fragebögen zusammen. Es eignet sich besonders gut als Leitfaden für die praktische Anwendung in Studium und Praxis.
Frailty Models in Survival Analysis (Chapman & Hall/CRC Biostatistics Series)
by Andreas WienkeThe concept of frailty offers a convenient way to introduce unobserved heterogeneity and associations into models for survival data. In its simplest form, frailty is an unobserved random proportionality factor that modifies the hazard function of an individual or a group of related individuals. Frailty Models in Survival Analysis presents a compreh
Frame Theory in Data Science (Advances in Science, Technology & Innovation)
by Zhihua Zhang Palle E. JorgensenThis book establishes brand-new frame theory and technical implementation in data science, with a special focus on spatial-scale feature extraction, network dynamics, object-oriented analysis, data-driven environmental prediction, and climate diagnosis. Given that data science is unanimously recognized as a core driver for achieving Sustainable Development Goals of the United Nations, these frame techniques bring fundamental changes to multi-channel data mining systems and support the development of digital Earth platforms. This book integrates the authors' frame research in the past twenty years and provides cutting-edge techniques and depth for scientists, professionals, and graduate students in data science, applied mathematics, environmental science, and geoscience.
Frames and Other Bases in Abstract and Function Spaces
by Isaac Pesenson Quoc Thong Le Gia Azita Mayeli Hrushikesh Mhaskar Ding-Xuan ZhouThe first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.
A Franchise on the Rise: The First Twenty Years of the New York Yankees
by Dom Amore John Sterling2018 marks 115 years since the inception of the New York Yankees--and what a 115-year period it's been! But how did the team that has since won a league-leading 27 world championships get started? In A Franchise on the Rise, veteran sportswriter Dom Amore takes readers back in time to the first twenty years of the team's existence, from 1903 to 1923, focusing on all the major players and events, including their first ten years as the Highlanders, their move to Yankee Stadium, and their subsequent first World Series in 1923. In doing so, Amore successfully finds the characters' own voices and thereby vividly reconstructs events of more than a century ago. He recounts the snowy night Honus Wagner was offered twenty crisp $1,000 bills to join the new franchise in New York; the story behind the holes punched in the outfield fence that facilitated the stealing of signs in 1909; and why the team thought it may have had the next big superstar in a college football end named George Halas. This is a tale about the business of baseball as it was done at the time and, in many ways, as it still must be done. There was no secret to building a winning organization. It took money and luck, but it also took a group of people working as a team, each allowed to do his job and each doing it superbly.
Frank Ramsey and the Realistic Spirit (History of Analytic Philosophy)
by Steven MethvenThis book attempts to explicate and expand upon Frank Ramsey's notion of the realistic spirit. In so doing, it provides a systematic reading of his work, and demonstrates the extent of Ramsey's genius as evinced by both his responses to the Tractatus Logico-Philosophicus, and the impact he had on Wittgenstein's later philosophical insights.
Freakonomics
by Stephen J. Dubner Steven D. LevittThrough forceful storytelling and wry insight, Levitt and co-author Stephen J. Dubner show that economics is, at root, the study of incentives--how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they set out to explore the hidden side of ... well, everything.
Freakonomics Rev Ed: A Rogue Economist Explores the Hidden Side of Everything
by Stephen J. Dubner Steven D. LevittWhich is more dangerous, a gun or a swimming pool? What do schoolteachers and sumo wrestlers have in common? Why do drug dealers still live with their moms? How much do parents really matter? How did the legalization of abortion affect the rate of violent crime? These may not sound like typical questions for an econo-mist to ask. But Steven D. Levitt is not a typical economist. He is a much-heralded scholar who studies the riddles of everyday life-from cheating and crime to sports and child-rearing-and whose conclusions turn conventional wisdom on its head. Freakonomics is a groundbreaking collaboration between Levitt and Stephen J. Dubner, an award-winning author and journalist. They usually begin with a mountain of data and a simple question. Some of these questions concern life-and-death issues; others have an admittedly freakish quality. Thus the new field of study contained in this book: freakonomics. Through forceful storytelling and wry insight, Levitt and Dubner show that economics is, at root, the study of incentives-how people get what they want, or need, especially when other people want or need the same thing. In Freakonomics, they explore the hidden side of . . . well, everything. The inner workings of a crack gang. The truth about real-estate agents. The myths of campaign finance. The telltale marks of a cheating schoolteacher. The secrets of the Klu Klux Klan. What unites all these stories is a belief that the modern world, despite a great deal of complexity and downright deceit, is not impenetrable, is not unknowable, and-if the right questions are asked-is even more intriguing than we think. All it takes is a new way of looking. Freakonomics establishes this unconventional premise: If morality represents how we would like the world to work, then economics represents how it actually does work. It is true that readers of this book will be armed with enough riddles and stories to last a thousand cocktail parties. But Freakonomics can provide more than that. It will literally redefine the way we view the modern world.
Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (Annals of Mathematics Studies #179)
by Joram Lindenstrauss David Preiss Jaroslav TišerThis book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis. The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics.