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Fixed Point Theory in Distance Spaces
by William Kirk Naseer ShahzadThis is a monograph on fixed point theory, covering the purely metric aspects of the theory-particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler's well known set-valued extension of that theorem, the extension of Banach's theorem to nonexpansive mappings, and Caristi's theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi's theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain results in hyperconvex metric spaces and ultrametric spaces. Part II treats fixed point theory in classes of spaces which, in addition to having a metric structure, also have geometric structure. These specifically include the geodesic spaces, length spaces and CAT(0) spaces. Part III focuses on distance spaces that are not necessarily metric. These include certain distance spaces which lie strictly between the class of semimetric spaces and the class of metric spaces, in that they satisfy relaxed versions of the triangle inequality, as well as other spaces whose distance properties do not fully satisfy the metric axioms.
Fixed Point Theory in Metric Spaces: Recent Advances and Applications
by Praveen Agarwal Mohamed Jleli Bessem SametThis book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of α-ψ contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials.The book is a valuable resource for a wide audience, including graduate students and researchers.
Fixed Point Theory in Metric Type Spaces
by Ravi P. Agarwal Erdal Karapınar Donal O'Regan Antonio Francisco Roldán-López-de-HierroWritten by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research.
Fixed Point Theory in Modular Function Spaces
by Mohamed A. Khamsi Wojciech M. KozlowskiThis monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, Calderon-Lozanovskii spaces, and others. In most cases, particularly in applications to integral operators, approximation and fixed point results, modular type conditions are much more natural and can be more easily verified than their metric or norm counterparts. There are also important results that can be proved only using the apparatus of modular function spaces. The material is presented in a systematic and rigorous manner that allows readers to grasp the key ideas and to gain a working knowledge of the theory. Despite the fact that the work is largely self-contained, extensive bibliographic references are included, and open problems and further development directions are suggested when applicable. The monograph is targeted mainly at the mathematical research community but it is also accessible to graduate students interested in functional analysis and its applications. It could also serve as a text for an advanced course in fixed point theory of mappings acting in modular function spaces.
Fixed Point Theory, Variational Analysis, and Optimization
by Saleh A. R. Al-Mezel Falleh R. M. Al-Solamy Qamrul H. AnsariFixed Point Theory, Variational Analysis, and Optimization not only covers three vital branches of nonlinear analysis-fixed point theory, variational inequalities, and vector optimization-but also explains the connections between them, enabling the study of a general form of variational inequality problems related to the optimality conditions invol
Fixed-Time Cooperative Control of Multi-Agent Systems
by Zongyu Zuo Qing-Long Han Boda NingThis monograph presents new theories and methods for fixed-time cooperative control of multi-agent systems. Fundamental concepts of fixed-time stability and stabilization are introduced with insightful understanding. This book presents solutions for several problems of fixed-time cooperative control using systematic design methods. The book compares fixed-time cooperative control with asymptotic cooperative control, demonstrating how the former can achieve better closed-loop performance and disturbance rejection properties. It also discusses the differences from finite-time control, and shows how fixed-time cooperative control can produce the faster rate of convergence and provide an explicit estimate of the settling time independent of initial conditions. This monograph presents multiple applications of fixed-time control schemes, including to distributed optimization of multi-agent systems, making it useful to students, researchers and engineers alike.
Fixpunkte und Nullstellen: Klartext für Nichtmathematiker (essentials)
by Guido WalzDieses Buch vermittelt in leicht zugänglicher Sprache Methoden zur numerischen Berechnung von Fixpunkten und Nullstellen reeller Funktionen mithilfe von Iterationsverfahren. Insbesondere das Banach-Verfahren zur Fixpunktbestimmung sowie das Newton-Verfahren, eines der besten numerischen Verfahren zur Nullstellenberechnung von Funktionen, werden ausführlich dargestellt. In einem abschließenden Kapitel werden Anwendungen dieser Verfahren behandelt. Unter anderen geht es dabei um die beliebig genaue Berechnung von Wurzeln jeder Ordnung. Da sich der Text ausdrücklich (auch) an Nichtmathematiker und Nichtmathematikerinnen wendet, ist er bewusst in allgemein verständlicher Sprache gehalten, um die Leser nicht durch übertriebene Fachsprache abzuschrecken; schließlich soll es sich ebenfalls laut Untertitel um „Klartext“ handeln. Zahlreiche Beispiele machen die einzelnen Themen leicht verständlich.
Flash Computation and EoS Modelling for Compositional Thermal Simulation of Flow in Porous Media (Springer Theses)
by Duncan PatersonThis book investigates a wide range of phase equilibrium modelling and calculation problems for compositional thermal simulation. Further, it provides an effective solution for multiphase isenthalpic flash under the classical framework, and it also presents a new flash calculation framework for multiphase systems, which can handle phase equilibrium and chemical reaction equilibrium simultaneously. The framework is particularly suitable for systems with many phases and reactions. In this book, the author shows how the new framework can be generalised for different flash specifications and different independent variables. Since the flash calculation is at the heart of various types of compositional simulation, the findings presented here will promote the combination of phase equilibrium and chemical equilibrium calculations in future simulators, aiming at improving their robustness and efficiency.
Flatland: A Romance of Many Dimensions (Dover Thrift Editions: Classic Novels)
by Edwin A. AbbottThis masterpiece of science (and mathematical) fiction is a delightfully unique and highly entertaining satire that has charmed readers for more than 100 years. The work of English clergyman, educator and Shakespearean scholar Edwin A. Abbott (1838-1926), it describes the journeys of A. Square, a mathematician and resident of the two-dimensional Flatland, where women-thin, straight lines-are the lowliest of shapes, and where men may have any number of sides, depending on their social status.Through strange occurrences that bring him into contact with a host of geometric forms, Square has adventures in Spaceland (three dimensions), Lineland (one dimension) and Pointland (no dimensions) and ultimately entertains thoughts of visiting a land of four dimensions—a revolutionary idea for which he is returned to his two-dimensional world. Charmingly illustrated by the author, Flatland is not only fascinating reading, it is still a first-rate fictional introduction to the concept of the multiple dimensions of space. "Instructive, entertaining, and stimulating to the imagination." — Mathematics Teacher.
Flatland: A Romance of Many Dimensions
by Edwin Abbott Abbott Thomas BanchoffIn 1884, Edwin Abbott Abbott wrote a mathematical adventure set in a two-dimensional plane world, populated by a hierarchical society of regular geometrical figures-who think and speak and have all too human emotions. Since then Flatland has fascinated generations of readers, becoming a perennial science-fiction favorite. By imagining the contact of beings from different dimensions, the author fully exploited the power of the analogy between the limitations of humans and those of his two-dimensional characters. A first-rate fictional guide to the concept of multiple dimensions of space, the book will also appeal to those who are interested in computer graphics. This field, which literally makes higher dimensions seeable, has aroused a new interest in visualization. We can now manipulate objects in four dimensions and observe their three-dimensional slices tumbling on the computer screen. But how do we interpret these images? In his introduction, Thomas Banchoff points out that there is no better way to begin exploring the problem of understanding higher-dimensional slicing phenomena than reading this classic novel of the Victorian era.
Flatland
by by Edwin A. Abbott William F. Lindgren Thomas F. Banchoff by Edwin A. Abbott William F. Lindgren Thomas F. BanchoffFlatland, Edwin Abbott's story of a two-dimensional universe, as told by one of its inhabitants who is introduced to the mysteries of three-dimensional space, has enjoyed an enduring popularity from the time of its publication in 1884. This fully annotated edition enables the modern-day reader to understand and appreciate the many 'dimensions' of this classic satire. Mathematical notes and illustrations enhance the usefulness of Flatland as an elementary introduction to higher-dimensional geometry. Historical notes show connections to late-Victorian England and to classical Greece. Citations from Abbott's other writings as well as the works of Plato and Aristotle serve to interpret the text. Commentary on language and literary style includes numerous definitions of obscure words. An appendix gives a comprehensive account of the life and work of Flatland's remarkable author.
The Flawed Genius of William Playfair: The Story of the Father of Statistical Graphics
by David R. BellhouseA product of the Scottish Enlightenment, William Playfair (1759–1823) worked as a statistician, economist, engineer, banker, land speculator, scam artist, and political propagandist. It has been claimed – erroneously – that Playfair was a spy for the British government and ran a forging operation to print the paper money of the French Revolution. The Flawed Genius of William Playfair offers a complete account of Playfair’s life, richly contextualized in the economic, political, and cultural history of the French Revolution and Napoleonic Wars. The book explores the many peaks and troughs of Playfair’s career, ranging from moderate prosperity to bankruptcy and imprisonment. Through careful analysis, David R. Bellhouse shows that Playfair was neither a spy nor a forger, but perhaps briefly a one-time courier for a government minister. Bellhouse pieces together as complete a picture as possible of the forging operations supported by the British government and illuminates Playfair’s lasting contributions in economics and statistics, where he is known as the father of statistical graphics. Disputing the misinformation about the man, The Flawed Genius of William Playfair highlights that the truth about Playfair’s life is often more intriguing than the fictions that surround him.
Flaws and Fallacies in Statistical Thinking
by Stephen K. CampbellThis book was written with a dual purpose: first, the author was motivated to relieve his distress over the faulty conclusions drawn from the frequent misuse of relatively simple statistical tools such as percents, graphs, and averages. Second, his objective was to create a nontechnical book that would help people make better-informed decisions by increasing their ability to judge the quality of statistical evidence. This volume achieves both, serving as a supplemental text for students taking their first course in statistics, and as a self-help guide for anyone wishing to evaluate statistical evidence more judiciously.The sequence of topics corresponds with that of many beginning textbooks in statistics, and the terminology and treatment of subjects are based on the assumption that readers have had little or no prior exposure to statistics or formal mathematics. The author examines the perils of statistical ignorance, some problems in basic measurement and definition, and the prevalence of meaningless statistics, far-fetched estimates, cheating charts, and accommodating averages. He explains common pitfalls of statistical thinking such as ignoring dispersion, inflating percentages, drawing improper comparisons, jumping to conclusions, and making errors of probability and induction. Playful in tone but scrupulously accurate in nature, this text is equally valuable in and out of the classroom.
Flexibility of Group Actions on the Circle (Lecture Notes in Mathematics #2231)
by Sang-Hyun Kim Thomas Koberda Mahan MjIn this partly expository work, a framework is developed for building exotic circle actions of certain classical groups. The authors give general combination theorems for indiscrete isometry groups of hyperbolic space which apply to Fuchsian and limit groups. An abundance of integer-valued subadditive defect-one quasimorphisms on these groups follow as a corollary. The main classes of groups considered are limit and Fuchsian groups. Limit groups are shown to admit large collections of faithful actions on the circle with disjoint rotation spectra. For Fuchsian groups, further flexibility results are proved and the existence of non-geometric actions of free and surface groups is established. An account is given of the extant notions of semi-conjugacy, showing they are equivalent. This book is suitable for experts interested in flexibility of representations, and for non-experts wanting an introduction to group representations into circle homeomorphism groups.
Flexible and Generalized Uncertainty Optimization: Theory and Approaches (Studies in Computational Intelligence #696)
by Weldon A. Lodwick Luiz L. Salles-NetoThis book presents the theory and methods of flexible and generalized uncertainty optimization. Particularly, it describes the theory of generalized uncertainty in the context of optimization modeling. The book starts with an overview of flexible and generalized uncertainty optimization. It covers uncertainties that are both associated with lack of information and are more general than stochastic theory, where well-defined distributions are assumed. Starting from families of distributions that are enclosed by upper and lower functions, the book presents construction methods for obtaining flexible and generalized uncertainty input data that can be used in a flexible and generalized uncertainty optimization model. It then describes the development of the associated optimization model in detail. Written for graduate students and professionals in the broad field of optimization and operations research, this second edition has been revised and extended to include more worked examples and a section on interval multi-objective mini-max regret theory along with its solution method.
Flexible Approaches in Data, Information and Knowledge Management
by Olivier Pivert Sławomir ZadrożnyThis volume showcases contributions from internationally-known researchers in the field of information management. Most of the approaches presented here make use of fuzzy logic, introduced by L. A. Zadeh almost 50 years ago, which constitute a powerful tool to model and handle gradual concepts. What all of these contributions have in common is placing the user at the center of the information system, be it for helping him/her to query a data set, to handle imperfect information, or to discover useful knowledge from a massive collection of data. Researchers working in data and knowledge management will greatly benefit from this collection of up-to-date studies. This may be also an invaluable source of information for postgraduate students interested in advanced information management techniques.
Flexible Imputation of Missing Data (Chapman & Hall/CRC Interdisciplinary Statistics)
by Stef Van BuurenMissing data pose challenges to real-life data analysis. Simple ad-hoc fixes, like deletion or mean imputation, only work under highly restrictive conditions, which are often not met in practice. Multiple imputation replaces each missing value by multiple plausible values. The variability between these replacements reflects our ignorance of the true (but missing) value. Each of the completed data set is then analyzed by standard methods, and the results are pooled to obtain unbiased estimates with correct confidence intervals. Multiple imputation is a general approach that also inspires novel solutions to old problems by reformulating the task at hand as a missing-data problem. This is the second edition of a popular book on multiple imputation, focused on explaining the application of methods through detailed worked examples using the MICE package as developed by the author. This new edition incorporates the recent developments in this fast-moving field. This class-tested book avoids mathematical and technical details as much as possible: formulas are accompanied by verbal statements that explain the formula in accessible terms. The book sharpens the reader’s intuition on how to think about missing data, and provides all the tools needed to execute a well-grounded quantitative analysis in the presence of missing data.
Flexible Nonparametric Curve Estimation
by Hassan DoostiThis book delves into the realm of nonparametric estimations, offering insights into essential notions such as probability density, regression, Tsallis Entropy, Residual Tsallis Entropy, and intensity functions. Through a series of carefully crafted chapters, the theoretical foundations of flexible nonparametric estimators are examined, complemented by comprehensive numerical studies. From theorem elucidation to practical applications, the text provides a deep dive into the intricacies of nonparametric curve estimation. Tailored for postgraduate students and researchers seeking to expand their understanding of nonparametric statistics, this book will serve as a valuable resource for anyone who wishes to explore the applications of flexible nonparametric techniques.
Flexible Query Answering Systems: 14th International Conference, FQAS 2021, Bratislava, Slovakia, September 19–24, 2021, Proceedings (Lecture Notes in Computer Science #12871)
by Troels Andreasen Guy De Tré Janusz Kacprzyk Henrik Legind Larsen Gloria Bordogna Sławomir ZadrożnyThis book constitutes the refereed proceedings of the 14th International Conference on Flexible Query Answering Systems, FQAS 2021, held virtually and in Bratislava, Slovakia, in September 2021.The 16 full papers and 1 perspective papers presented were carefully reviewed and selected from 17 submissions. They are organized in the following topical sections: model-based flexible query answering approaches and data-driven approaches.
Flexible Query Answering Systems: 13th International Conference, FQAS 2019, Amantea, Italy, July 2–5, 2019, Proceedings (Lecture Notes in Computer Science #11529)
by Alfredo Cuzzocrea Sergio Greco Henrik Legind Larsen Domenico Saccà Troels Andreasen Henning ChristiansenThis book constitutes the refereed proceedings of the 13th International Conference on Flexible Query Answering Systems, FQAS 2019, held in Amantea, Italy, in July 2019.The 27 full papers and 10 short papers presented were carefully reviewed and selected from 43 submissions. The papers present emerging research trends with a special focus on flexible querying and analytics for smart cities and smart societies in the age of big data. They are organized in the following topical sections: flexible database management and querying; ontologies and knowledge bases; social networks and social media; argumentation-based query answering; data mining and knowledge discovery; advanced flexible query answering methodologies and techniques; flexible query answering methods and techniques; flexible intelligent information-oriented and network-oriented approaches; big data veracity and soft computing; flexibility in tools; and systems and miscellanea.
Flexible Query Answering Systems: 15th International Conference, FQAS 2023, Mallorca, Spain, September 5–7, 2023, Proceedings (Lecture Notes in Computer Science #14113)
by Henrik Legind Larsen Maria J. Martin-Bautista M. Dolores Ruiz Troels Andreasen Gloria Bordogna Guy De TréThis book constitutes the refereed proceedings of the 15th International Conference on Flexible Query Answering Systems, FQAS 2023, held in September 2023 in Palma de Mallorca, Spain. The 24 full papers presented were carefully reviewed and selected from numerous submissions. They are organized in the following topical sections: Flexible Queries over Semantic Systems; Advanced Methods and Applications in Natural Language; Processing (NLP); New Advances in Disinformation Detection; Data and Text Mining; Applying AI to Social Science and Social Science to AI; Artificial Intelligence Law and Regulation.
Flexible Regression and Smoothing: Using GAMLSS in R (Chapman & Hall/CRC The R Series)
by Gillian Heller Mikis Stasinopoulos Robert Rigby Fernanda De Bastiani Vlasios VoudourisThis book is about learning from data using the Generalized Additive Models for Location, Scale and Shape (GAMLSS). GAMLSS extends the Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) to accommodate large complex datasets, which are increasingly prevalent. GAMLSS allows any parametric distribution for the response variable and modelling all the parameters (location, scale and shape) of the distribution as linear or smooth functions of explanatory variables. This book provides a broad overview of GAMLSS methodology and how it is implemented in R. It includes a comprehensive collection of real data examples, integrated code, and figures to illustrate the methods, and is supplemented by a website with code, data and additional materials.
Flexible, Reliable Software: Using Patterns and Agile Development (Chapman & Hall/CRC Textbooks in Computing)
by null Henrik B. ChristensenFlexible, Reliable Software: Using Patterns and Agile Development guides students through the software development process. By describing practical stories, explaining the design and programming process in detail, and using projects as a learning context, the text helps readers understand why a given technique is required and why techniqu
Flexibles Rechnen im Grundschulverlauf: Eine Längsschnittstudie zur Förderung und Entwicklung flexibler Vorgehensweisen beim Addieren und Subtrahieren (Mathematikdidaktik im Fokus)
by Anna KörnerDie Entwicklung von Flexibilität beim Rechnen gilt seit vielen Jahren als zentrales Ziel des Arithmetikunterrichts der Grundschule. Dennoch belegen die Ergebnisse empirischer Studien zu Vorgehensweisen von Kindern, dass viele Schüler*innen einen Hauptrechenweg bevorzugen und selten flexibel agieren. Flexibilität scheint sich also nicht automatisch zu entwickeln, sondern muss gezielt gefördert werden. Aufbauend auf Ergebnissen anderer Studien wurde für die vorliegende Untersuchung eine Unterrichtskonzeption zur kontinuierlichen Förderung von Flexibilität vom ersten bis zum vierten Schuljahr entwickelt und umgesetzt. Im Rahmen dieser längsschnittlichen Studie wurden die Vorgehensweisen der Schüler*innen beim Addieren und Subtrahieren sieben Mal im Projektzeitraum in leitfadengestützten Einzelinterviews erfasst, um anhand qualitativer Inhaltsanalyse mit darauf folgender Fallkontrastierung und Typenbildung charakteristische Entwicklungen im Grundschulverlauf rekonstruieren zu können. Alszentrales Ergebnis wird eine Typologie zur Einordnung der Vorgehensweisen beim Lösen von Additions- und Subtraktionsaufgaben vorgestellt, anhand derer Fort- und Rückschritte im Entwicklungsverlauf dokumentiert werden können.
Flight Safety Management: Quantitative and AI Approaches (Studies in Systems, Decision and Control #228)
by Chi-Bin Cheng Huan-Jyh ShyurThis book offers a comprehensive overview of using artificial intelligence and quantitative approaches in many phases of flight safety management, from proactive assessment of potential risks of flights before taking-off to automatic analysis of occurred flight events, for commercial airlines. Flight safety is commonly the core values of airlines. Serious flight disasters always bring tremendous impacts and losses to the industry and the society; thus, airlines and the authorities always treat the issues of flight safety management as the first priority. It presents the information systems that assist the safety staff and managers to adopt preventive operations or to analyze the critical factors or operations that cause a flight event. Such information systems were developed based on artificial intelligence and quantitative approaches, including fuzzy logic, expert systems, deep learning, decision-making methods, reliability theory, and data mining. After introducing the flight safety management practice and common programs, as well as basic artificial intelligence and quantitative approaches, the book describes in detail the information systems we have developed and provides instructions for flight safety practitioners to implement such information systems in their organizations. Case studies collected from the cooperated airline are also presented.