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Research in History and Philosophy of Mathematics
by Maria Zack Elaine LandryThis volume contains thirteen papers that were presented at the 2014 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Société Canadienne d'Histoire et de Philosophie des Mathématiques, held on the campus of Brock University in St. Catharines, Ontario, Canada. It contains rigorously reviewed modern scholarship on general topics in the history and philosophy of mathematics, as well as on the meeting's special topic, Early Scientific Computation. These papers cover subjects such as *Physical tools used by mathematicians in the seventeenth century *The first historical appearance of the game-theoretical concept of mixed-strategy equilibrium *George Washington's mathematical cyphering books *The development of the Venn diagram *The role of Euler and other mathematicians in the development of algebraic analysis *Arthur Cayley and Alfred Kempe's influence on Charles Peirce's diagrammatic logic *The influence publishers had on the development of mathematical pedagogy in the nineteenth century *A description of the 1924 International Mathematical Congress held in Toronto, told in the form of a "narrated slide show" Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Research in History and Philosophy of Mathematics
by Maria Zack Elaine LandryThis volume contains seventeen papers that were presented at the 2015 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Soci#65533;t#65533; Canadienne d'Histoire et de Philosophie des Math#65533;matiques, held in Washington, D. C. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of general topics in the history and philosophy of mathematics, this meeting also honored the memories of Jacqueline (Jackie) Stedall and Ivor Grattan-Guinness; celebrated the Centennial of the Mathematical Association of America; and considered the importance of mathematical communities in a special session. These themes and many others are explored in these collected papers, which cover subjects such as New evidence that the Latin translation of Euclid's Elements was based on the Arabic version attributed to al-Ḥajjāj Work done on the arc rampant in the seventeenth century The history of numerical methods for finding roots of nonlinear equations An original play featuring a dialogue between George Boole and Augustus De Morgan that explores the relationship between them Key issues in the digital preservation of mathematical material for future generations A look at the first twenty-five years of The American Mathematical Monthly in the context of the evolving American mathematical community The growth of Math Circles and the unique ways they are being implemented in the United States Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Research in History and Philosophy of Mathematics
by Maria Zack Dirk SchlimmThis volume contains seventeen papers that were presented at the 2015 Annual Meeting of the Canadian Society for History and Philosophy of Mathematics/La Soci#65533;t#65533; Canadienne d'Histoire et de Philosophie des Math#65533;matiques, held in Washington, D. C. In addition to showcasing rigorously reviewed modern scholarship on an interesting variety of general topics in the history and philosophy of mathematics, this meeting also honored the memories of Jacqueline (Jackie) Stedall and Ivor Grattan-Guinness; celebrated the Centennial of the Mathematical Association of America; and considered the importance of mathematical communities in a special session. These themes and many others are explored in these collected papers, which cover subjects such as New evidence that the Latin translation of Euclid's Elements was based on the Arabic version attributed to al-Ḥajjāj Work done on the arc rampant in the seventeenth century The history of numerical methods for finding roots of nonlinear equations An original play featuring a dialogue between George Boole and Augustus De Morgan that explores the relationship between them Key issues in the digital preservation of mathematical material for future generations A look at the first twenty-five years of The American Mathematical Monthly in the context of the evolving American mathematical community The growth of Math Circles and the unique ways they are being implemented in the United States Written by leading scholars in the field, these papers will be accessible to not only mathematicians and students of the history and philosophy of mathematics, but also anyone with a general interest in mathematics.
Research in History and Philosophy of Mathematics: The CSHPM 2018 Volume (Proceedings of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques)
by Maria Zack Dirk SchlimmThis volume contains ten papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics from the seventeenth century to the modern era.The volume begins with an exposition of the life and work of Professor Bolesław Sobociński. It then moves on to cover a collection of topics about twentieth-century philosophy of mathematics, including Fred Sommers’s creation of Traditional Formal Logic and Alexander Grothendieck’s work as a starting point for discussing analogies between commutative algebra and algebraic geometry. Continuing the focus on the philosophy of mathematics, the next selections discuss the mathematization of biology and address the study of numerical cognition. The volume then moves to discussing various aspects of mathematics education, including Charles Davies’s early book on the teaching of mathematics and the use of Gaussian Lemniscates in the classroom. A collection of papers on the history of mathematics in the nineteenth century closes out the volume, presenting a discussion of Gauss’s “Allgemeine Theorie des Erdmagnetismus” and a comparison of the geometric works of Desargues and La Hire. Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
Research in History and Philosophy of Mathematics: The CSHPM 2019-2020 Volume (Annals of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques)
by Maria Zack Dirk SchlimmThis volume contains eleven papers that have been collected by the Canadian Society for History and Philosophy of Mathematics/Société canadienne d’histoire et de philosophie des mathématiques. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Topics considered includeThe mathematics and astronomy in Nathaniel Torperly’s only published work, Diclides Coelometricae, seu valvae astronomicae universalConnections between the work of Urbain Le Verrier, Carl Gustav Jacob Jacobi, and Augustin-Louis Cauchy on the algebraic eigenvalue problemAn evaluation of Ken Manders’ argument against conceiving of the diagrams in Euclid’s Elements in semantic termsThe development of undergraduate modern algebra courses in the United StatesWays of using the history of mathematics to teach the foundations of mathematical analysisWritten by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
Research in History and Philosophy of Mathematics: The CSHPM 2021 Volume (Annals of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques)
by Maria Zack David WaszekThis volume contains eighteen papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously-reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics, as well as the teaching of the history of mathematics. Some of the topics explored includeArabic editions of Euclid’s Elements from the thirteenth century and their role in the assimilation of Euclidean geometry into the Islamic intellectual traditionPortuguese sixteenth century recreational mathematics as found in the Tratado de Prática Darysmetica A Cambridge correspondence course in arithmetic for women in England in the late nineteenth centuryThe mathematical interests of the famous Egyptologist Thomas Eric (T. E.) Peet The history of Zentralblatt für Mathematik and Mathematical Reviews and their role in creating a publishing infrastructure for a global mathematical literatureThe use of Latin squares for agricultural crop experiments at the Rothamsted Experimental StationThe many contributions of women to the advancement of computing techniques at the Cavendish Laboratory at the University of Cambridge in the 1960sThe volume concludes with two short plays, one set in Ancient Mesopotamia and the other in Ancient Egypt, that are well suited for use in the mathematics classroom.Written by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
Research in History and Philosophy of Mathematics: The CSHPM 2022 Volume (Annals of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques)
by Maria Zack David WaszekThis volume contains 8 papers that have been collected by the Canadian Society for History and Philosophy of Mathematics. It showcases rigorously reviewed contemporary scholarship on an interesting variety of topics in the history and philosophy of mathematics.Some of the topics explored include:A way to rethink how logic is taught to philosophy students by using a rejuvenated version of the Aristotelian idea of an argument schemaA quantitative approach using data from Wikipedia to study collaboration between nineteenth-century British mathematiciansThe depiction and perception of Émilie Du Châtelet’s scientific contributions as viewed through the frontispieces designed for books written by or connected to herA study of the Cambridge Women’s Research Club, a place where British women were able to participate in scholarly scientific discourse in the middle of the twentieth centuryAn examination of the research and writing process of mathematicians by looking at their drafts and other preparatory notesA global history of al-Khwārāzmī’s Kitāb al-jabr wa-l-muqābala as obtained by tracing its reception through numerous translations and commentariesWritten by leading scholars in the field, these papers are accessible not only to mathematicians and students of the history and philosophy of mathematics, but also to anyone with a general interest in mathematics.
The Career of a Research Statistician: From Consulting to Theoretical Development (Statistics for Industry, Technology, and Engineering)
by Shelemyahu ZacksThis monograph highlights the connection between the theoretical work done by research statisticians and the impact that work has on various industries. Drawing on decades of experience as an industry consultant, the author details how his contributions have had a lasting impact on the field of statistics as a whole. Aspiring statisticians and data scientists will be motivated to find practical applications for their knowledge, as they see how such work can yield breakthroughs in their field.Each chapter highlights a consulting position the author held that resulted in a significant contribution to statistical theory. Topics covered include tracking processes with change points, estimating common parameters, crossing fields with absorption points, military operations research, sampling surveys, stochastic visibility in random fields, reliability analysis, applied probability, and more. Notable advancements within each of these topics are presented by analyzing the problems facing various industries, and how solving those problems contributed to the development of the field.The Career of a Research Statistician is ideal for researchers, graduate students, or industry professionals working in statistics. It will be particularly useful for up-and-coming statisticians interested in the promising connection between academia and industry.
Examples and Problems in Mathematical Statistics
by Shelemyahu ZacksProvides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercises With a clear and detailed approach to the fundamentals of statistical theory, "Examples and Problems in Mathematical Statistics "uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results. Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, "Examples and Problems in Mathematical Statistics "features: Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solving More than 430 unique exercises with select solutions Key statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysis Recommended for graduate-level courses in probability and statistical inference, "Examples and Problems in Mathematical Statistics "is also an ideal reference for applied statisticians and researchers.
Examples and Problems in Mathematical Statistics
by Shelemyahu ZacksProvides the necessary skills to solve problems in mathematical statistics through theory, concrete examples, and exercisesWith a clear and detailed approach to the fundamentals of statistical theory, Examples and Problems in Mathematical Statistics uniquely bridges the gap between theory andapplication and presents numerous problem-solving examples that illustrate the relatednotations and proven results.Written by an established authority in probability and mathematical statistics, each chapter begins with a theoretical presentation to introduce both the topic and the important results in an effort to aid in overall comprehension. Examples are then provided, followed by problems, and finally, solutions to some of the earlier problems. In addition, Examples and Problems in Mathematical Statistics features:Over 160 practical and interesting real-world examples from a variety of fields including engineering, mathematics, and statistics to help readers become proficient in theoretical problem solvingMore than 430 unique exercises with select solutionsKey statistical inference topics, such as probability theory, statistical distributions, sufficient statistics, information in samples, testing statistical hypotheses, statistical estimation, confidence and tolerance intervals, large sample theory, and Bayesian analysisRecommended for graduate-level courses in probability and statistical inference, Examples and Problems in Mathematical Statistics is also an ideal reference for applied statisticians and researchers.
Industrial Statistics: A Computer-Based Approach with Python (Statistics for Industry, Technology, and Engineering)
by Shelemyahu Zacks Ron S. Kenett Peter GedeckThis innovative textbook presents material for a course on industrial statistics that incorporates Python as a pedagogical and practical resource. Drawing on many years of teaching and conducting research in various applied and industrial settings, the authors have carefully tailored the text to provide an ideal balance of theory and practical applications. Numerous examples and case studies are incorporated throughout, and comprehensive Python applications are illustrated in detail. A custom Python package is available for download, allowing students to reproduce these examples and explore others.The first chapters of the text focus on the basic tools and principles of process control, methods of statistical process control (SPC), and multivariate SPC. Next, the authors explore the design and analysis of experiments, quality control and the Quality by Design approach, computer experiments, and cybermanufacturing and digital twins. The text then goes on to cover reliability analysis, accelerated life testing, and Bayesian reliability estimation and prediction. A final chapter considers sampling techniques and measures of inspection effectiveness. Each chapter includes exercises, data sets, and applications to supplement learning.Industrial Statistics: A Computer-Based Approach with Python is intended for a one- or two-semester advanced undergraduate or graduate course. In addition, it can be used in focused workshops combining theory, applications, and Python implementations. Researchers, practitioners, and data scientists will also find it to be a useful resource with the numerous applications and case studies that are included. A second, closely related textbook is titled Modern Statistics: A Computer-Based Approach with Python. It covers topics such as probability models and distribution functions, statistical inference and bootstrapping, time series analysis and predictions, and supervised and unsupervised learning. These texts can be used independently or for consecutive courses.This book is part of an impressive and extensive write up enterprise (roughly 1,000 pages!) which led to two books published by Birkhäuser. This book is on Industrial Statistics, an area in which the authors are recognized as major experts. The book combines classical methods (never to be forgotten!) and “hot topics” like cyber manufacturing, digital twins, A/B testing and Bayesian reliability. It is written in a very accessible style, focusing not only on HOW the methods are used, but also on WHY. In particular, the use of Python, throughout the book is highly appreciated. Python is probably the most important programming language used in modern analytics. The authors are warmly thanked for providing such a state-of-the-art book. It provides a comprehensive illustration of methods and examples based on the authors longstanding experience, and accessible code for learning and reusing in classrooms and on-site applicationsProfessor Fabrizio RuggeriResearch Director at the National Research Council, ItalyPresident of the International Society for Business and Industrial Statistics (ISBIS)Editor-in-Chief of Applied Stochastic Models in Business and Industry (ASMBI)
Recent Developments and the New Direction in Soft-Computing Foundations and Applications: Selected Papers From The 6th World Conference On Soft Computing, May 22-25, 2016, Berkeley, Usa (Studies in Fuzziness and Soft Computing #361)
by Lotfi A. Zadeh Ronald R. Yager Shahnaz N. Shahbazova Marek Z. Reformat Vladik KreinovichThis book is an authoritative collection of contributions in the field of soft-computing. Based on selected works presented at the 6th World Conference on Soft Computing, held on May 22-25, 2016, in Berkeley, USA, it describes new theoretical advances, as well as cutting-edge methods and applications. Theories cover a wealth of topics, such as fuzzy logic, cognitive modeling, Bayesian and probabilistic methods, multi-criteria decision making, utility theory, approximate reasoning, human-centric computing and many others. Applications concerns a number of fields, such as internet and semantic web, social networks and trust, control and robotics, computer vision, medicine and bioinformatics, as well as finance, security and e-Commerce, among others. Dedicated to the 50th Anniversary of Fuzzy Logic and to the 95th Birthday Anniversary of Lotfi A. Zadeh, the book not only offers a timely view on the field, yet it also discusses thought-provoking developments and challenges, thus fostering new research directions in the diverse areas of soft computing.
Statistical Analysis in Forensic Science
by Grzegorz Zadora Daniel Ramos Colin Aitken Agnieszka MartynaA practical guide for determining the evidential value of physicochemical dataMicrotraces of various materials (e.g. glass, paint, fibres, and petroleum products) are routinely subjected to physicochemical examination by forensic experts, whose role is to evaluate such physicochemical data in the context of the prosecution and defence propositions. Such examinations return various kinds of information, including quantitative data. From the forensic point of view, the most suitable way to evaluate evidence is the likelihood ratio. This book provides a collection of recent approaches to the determination of likelihood ratios and describes suitable software, with documentation and examples of their use in practice. The statistical computing and graphics software environment R, pre-computed Bayesian networks using Hugin Researcher and a new package, calcuLatoR, for the computation of likelihood ratios are all explored.Statistical Analysis in Forensic Science will provide an invaluable practical guide for forensic experts and practitioners, forensic statisticians, analytical chemists, and chemometricians.Key features include:Description of the physicochemical analysis of forensic trace evidence.Detailed description of likelihood ratio models for determining the evidential value of multivariate physicochemical data.Detailed description of methods, such as empirical cross-entropy plots, for assessing the performance of likelihood ratio-based methods for evidence evaluation.Routines written using the open-source R software, as well as Hugin Researcher and calcuLatoR.Practical examples and recommendations for the use of all these methods in practice.
Population Studies in the Western Balkans (European Studies of Population #26)
by Konstantinos N. Zafeiris Byron Kotzamanis Christos SkiadasThis book is a collection of scientific studies regarding the biological, economic, historical, health, social, and other aspects of the populations of the western Balkans, a geographic area with distinct as well as diverse socioeconomic backgrounds, political systems, ethnic characteristics, development, and history. Through providing data analyses, statistical methodologies, and important applications, the book addresses and explores topics such as temporary migration and human resource availability, depopulation, and the immigration future, returning migrants, poverty, population dynamics and birth rate trends, reproduction and family creation, aging, mortality and health developments, and much more. As such, this book is of great importance in understanding the mechanisms of population change and dynamics in an European area and provides a valuable guide for researchers, policy makers, and practitioners from various disciplines.
A Comparative Analysis of European Time Transfers between Generations and Genders (SpringerBriefs in Population Studies)
by Emilio Zagheni Marina Zannella Gabriel Movsesyan Brittney WagnerThis comparative study of European time transfers reveals the full extent of transfers in the form of unpaid work and highlights the existence of important gender differences in household time production. A large quantity of goods and services are produced by household members for their own consumption, without involving market transactions. Despite the economic and social importance of unpaid work, these productive activities are largely invisible to traditional national economic accounts. As a consequence, standard measures of intergenerational transfers typically ignore household production, and thus underestimate the overall value of goods and services produced over the life cycle; in particular, the economic contribution of females. The book uses a life course approach to offer policy-relevant insights into the effect of demographic and social change on intergenerational ties and gender inequality in household production.
High-Dimensional Covariance Matrix Estimation: An Introduction to Random Matrix Theory (SpringerBriefs in Applied Statistics and Econometrics)
by Aygul ZagidullinaThis book presents covariance matrix estimation and related aspects of random matrix theory. It focuses on the sample covariance matrix estimator and provides a holistic description of its properties under two asymptotic regimes: the traditional one, and the high-dimensional regime that better fits the big data context. It draws attention to the deficiencies of standard statistical tools when used in the high-dimensional setting, and introduces the basic concepts and major results related to spectral statistics and random matrix theory under high-dimensional asymptotics in an understandable and reader-friendly way. The aim of this book is to inspire applied statisticians, econometricians, and machine learning practitioners who analyze high-dimensional data to apply the recent developments in their work.
Trotter-Kato Product Formulæ (Operator Theory: Advances and Applications #296)
by Valentin A. Zagrebnov Hagen Neidhardt Takashi IchinoseThe book captures a fascinating snapshot of the current state of results about the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces. It also includes results on the operator-norm convergent product formulæ for solution operators of the non-autonomous Cauchy problems as well as similar results on the unitary and Zeno product formulæ.After the Sophus Lie product formula for matrices was established in 1875, it was generalised to Hilbert and Banach spaces for convergence in the strong operator topology by H. Trotter (1959) and then in an extended form by T. Kato (1978). In 1993 Dzh. L. Rogava discovered that convergence of the Trotter product formula takes place in the operator-norm topology. The latter is the main subject of this book, which is dedicated essentially to the operator-norm convergent Trotter-Kato Product Formulæ on Hilbert and Banach spaces, but also to related results on the time-dependent, unitary and Zeno product formulæ. The book yields a detailed up-to-date introduction into the subject that will appeal to any reader with a basic knowledge of functional analysis and operator theory. It also provides references to the rich literature and historical remarks.
Invariant Probabilities of Transition Functions
by Radu ZaharopolThe structure of the set of all the invariant probabilities and the structure of various types of individual invariant probabilities of a transition function are two topics of significant interest in the theory of transition functions, and are studied in this book. The results obtained are useful in ergodic theory and the theory of dynamical systems, which, in turn, can be applied in various other areas (like number theory). They are illustrated using transition functions defined by flows, semiflows, and one-parameter convolution semigroups of probability measures. In this book, all results on transition probabilities that have been published by the author between 2004 and 2008 are extended to transition functions. The proofs of the results obtained are new. For transition functions that satisfy very general conditions the book describes an ergodic decomposition that provides relevant information on the structure of the corresponding set of invariant probabilities. Ergodic decomposition means a splitting of the state space, where the invariant ergodic probability measures play a significant role. Other topics covered include: characterizations of the supports of various types of invariant probability measures and the use of these to obtain criteria for unique ergodicity, and the proofs of two mean ergodic theorems for a certain type of transition functions. The book will be of interest to mathematicians working in ergodic theory, dynamical systems, or the theory of Markov processes. Biologists, physicists and economists interested in interacting particle systems and rigorous mathematics will also find this book a valuable resource. Parts of it are suitable for advanced graduate courses. Prerequisites are basic notions and results on functional analysis, general topology, measure theory, the Bochner integral and some of its applications.
Rethinking the Individualism-Holism Debate: Essays in the Philosophy of Social Science (Synthese Library #372)
by Julie Zahle Finn CollinThis collection of papers investigates the most recent debates about individualism and holism in the philosophy of social science. The debates revolve mainly around two issues: firstly, whether social phenomena exist sui generis and how they relate to individuals. This is the focus of discussions between ontological individualists and ontological holists. Secondly, to what extent social scientific explanations may and should, focus on individuals and social phenomena respectively. This issue is debated amongst methodological holists and methodological individualists.In social science and philosophy, both issues have been intensively discussed and new versions of the dispute have appeared just as new arguments have been advanced. At present, the individualism/holism debate is extremely lively and this book reflects the major positions and perspectives within the debate. This volume is also relevant to debates about two closely related issues in social science: the micro-macro debate and the agency-structure debate.This book presents contributions from key figures in both social science and philosophy, in the first such collection on this topic to be published since the 1970s.
McGraw-Hill Education TASC - Test Accessing Secondary Completion
by Kathy A. ZahlerIt's packed with everything you need to succeed on the test---and get the high school credential you want. Only this guide can show you exactly what to expect on the test, tell you how the test is scored, and give you authentic TASC questions for practice. That makes this bestselling guide your most reliable and accurate source for everything you need to know about the TASC.
How to Solve Real-world Optimization Problems: From Theory to Practice (SpringerBriefs in Operations Research)
by Eugene J. ZakWritten by an experienced operations research practitioner with a strong applied mathematics background, this book offers practical insights into how to approach optimization problems, how to develop intelligent and efficient mathematical models and algorithms, and how to implement and deliver software products to customers. With a focus on revealing the similarities and differences between academia and industry in mathematical modeling, the book provides useful tips and advice based on the author’s extensive experience as a principal developer working to solve real-world optimization problems for several major high-tech companies.The book offers valuable food for thought for researchers and practical guidance for graduate students preparing for their future projects in the industry. It is also an essential resource for practitioners working in the industrial, business, and service sectors.
Rotation Sets and Complex Dynamics (Lecture Notes in Mathematics #2214)
by Saeed ZakeriThis monograph examines rotation sets under the multiplication by d (mod 1) map and their relation to degree d polynomial maps of the complex plane. These sets are higher-degree analogs of the corresponding sets under the angle-doubling map of the circle, which played a key role in Douady and Hubbard's work on the quadratic family and the Mandelbrot set. Presenting the first systematic study of rotation sets, treating both rational and irrational cases in a unified fashion, the text includes several new results on their structure, their gap dynamics, maximal and minimal sets, rigidity, and continuous dependence on parameters. This abstract material is supplemented by concrete examples which explain how rotation sets arise in the dynamical plane of complex polynomial maps and how suitable parameter spaces of such polynomials provide a complete catalog of all such sets of a given degree. As a main illustration, the link between rotation sets of degree 3 and one-dimensional families of cubic polynomials with a persistent indifferent fixed point is outlined. The monograph will benefit graduate students as well as researchers in the area of holomorphic dynamics and related fields.
Chimera Patterns in Networks: Interplay between Dynamics, Structure, Noise, and Delay (Understanding Complex Systems)
by Anna ZakharovaThis is the first book devoted to chimera states - peculiar partial synchronization patterns in networks. Providing an overview of the state of the art in research on this topic, it explores how these hybrid states, which are composed of spatially separated domains of synchronized and desynchronized behavior, arise surprisingly in networks of identical units and symmetric coupling topologies. The book not only describes various types of chimeras, but also discusses the role of time delay, stochasticity, and network topology for these synchronization-desynchronization patterns. Moreover, it addresses the question of robustness and control of chimera states, which have various applications in physics, biology, chemistry, and engineering.This book is intended for researchers with a background in physics, applied mathematics, or engineering. Of great interest to specialists working on related problems, it is also a valuable resource for newcomers to the field and other scientists working on the control of spatio-temporal patterns.
GARCH Models
by Jean-Michel Zakoian Christian FrancqThis book provides a comprehensive and systematic approach to understanding GARCH time series models and their applications whilst presenting the most advanced results concerning the theory and practical aspects of GARCH. The probability structure of standard GARCH models is studied in detail as well as statistical inference such as identification, estimation and tests. The book also provides coverage of several extensions such as asymmetric and multivariate models and looks at financial applications.Key features:Provides up-to-date coverage of the current research in the probability, statistics and econometric theory of GARCH models.Numerous illustrations and applications to real financial series are provided.Supporting website featuring R codes, Fortran programs and data sets.Presents a large collection of problems and exercises.This authoritative, state-of-the-art reference is ideal for graduate students, researchers and practitioners in business and finance seeking to broaden their skills of understanding of econometric time series models.
Complex Analysis and Dynamical Systems: New Trends and Open Problems (Trends in Mathematics #553)
by Lawrence Zalcman Mark Agranovsky Anatoly Golberg Fiana Jacobzon David ShoikhetThis book focuses on developments in complex dynamical systems and geometric function theory over the past decade, showing strong links with other areas of mathematics and the natural sciences. Traditional methods and approaches surface in physics and in the life and engineering sciences with increasing frequency - the Schramm‐Loewner evolution, Laplacian growth, and quadratic differentials are just a few typical examples. This book provides a representative overview of these processes and collects open problems in the various areas, while at the same time showing where and how each particular topic evolves. This volume is dedicated to the memory of Alexander Vasiliev.