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Quasi-Uniform SPates (Lecture Notes In Pure And Applied Mathematics Ser. #77)
by FletcherSince quasi-uniform spaces were defined in 1948, a diverse and widely dispersed literatureconcerning them has emerged. In Quasi-Uniform Spaces, the authors present a comprehensivestudy of these structures, together with the theory of quasi-proximities. In additionto new results unavailable elsewhere, the volume unites fundamental materialheretofore scattered throughout the literature.Quasi-Uniform Spaces shows by example that these structures provide a natural approachto the study of point-set topology. It is the only source for many results related to completeness,and a primary source for the study of both transitive and quasi-metric spaces.Included are H. Junnila's analogue of Tamano's theorem, J. Kofner's result showing thatevery GO space is transitive, and R. Fox's example of a non-quasi-metrizable r-space. Inaddition to numerous interesting problems mentioned throughout the text , 22 formalresearch problems are featured. The book nurtures a radically different viewpoint oftopology , leading to new insights into purely topological problems.Since every topological space admits a quasi-uniformity, the study of quasi-uniformspaces can be seen as no less general than the study of topological spaces. For such study,Quasi-Uniform Spaces is a necessary, self-contained reference for both researchers andgraduate students of general topology . Information is made particularly accessible withthe inclusion of an extensive index and bibliography .
Quasiconformal Surgery in Holomorphic Dynamics
by Bodil Branner Núria FagellaSince its introduction in the early 1980s quasiconformal surgery has become a major tool in the development of the theory of holomorphic dynamics, and it is essential background knowledge for any researcher in the field. In this comprehensive introduction the authors begin with the foundations and a general description of surgery techniques before turning their attention to a wide variety of applications. They demonstrate the different types of surgeries that lie behind many important results in holomorphic dynamics, dealing in particular with Julia sets and the Mandelbrot set. Two of these surgeries go beyond the classical realm of quasiconformal surgery and use trans-quasiconformal surgery. Another deals with holomorphic correspondences, a natural generalization of holomorphic maps. The book is ideal for graduate students and researchers requiring a self-contained text including a variety of applications. It particularly emphasises the geometrical ideas behind the proofs, with many helpful illustrations seldom found in the literature.
Quaternion Algebras (Graduate Texts in Mathematics #288)
by John VoightThis open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Quaternion and Clifford Fourier Transforms (Trends In Mathematics Ser.)
by Eckhard HitzerQuaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth.The book begins with a historic overview, followed by chapters on Clifford and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and applied mathematicians, physicists, and engineers (signal and color image processing, electrical engineering, computer science, computer graphics, artificial intelligence, geographic information science, aero-space engineering, navigation, etc.).Features Intuitive real geometric approach to higher-dimensional Fourier transformations A comprehensive reference, suitable for graduate students and researchers Includes detailed definitions, properties, and many full step-by-step proofs Many figures and tables, a comprehensive biography, and a detailed index make it easy to locate information
Quaternionic de Branges Spaces and Characteristic Operator Function (SpringerBriefs in Mathematics)
by Daniel Alpay Irene Sabadini Fabrizio ColomboThis work contributes to the study of quaternionic linear operators. This study is a generalization of the complex case, but the noncommutative setting of quaternions shows several interesting new features, see e.g. the so-called S-spectrum and S-resolvent operators. In this work, we study de Branges spaces, namely the quaternionic counterparts of spaces of analytic functions (in a suitable sense) with some specific reproducing kernels, in the unit ball of quaternions or in the half space of quaternions with positive real parts. The spaces under consideration will be Hilbert or Pontryagin or Krein spaces. These spaces are closely related to operator models that are also discussed. The focus of this book is the notion of characteristic operator function of a bounded linear operator A with finite real part, and we address several questions like the study of J-contractive functions, where J is self-adjoint and unitary, and we also treat the inverse problem, namely to characterize which J-contractive functions are characteristic operator functions of an operator. In particular, we prove the counterpart of Potapov's factorization theorem in this framework. Besides other topics, we consider canonical differential equations in the setting of slice hyperholomorphic functions and we define the lossless inverse scattering problem. We also consider the inverse scattering problem associated with canonical differential equations. These equations provide a convenient unifying framework to discuss a number of questions pertaining, for example, to inverse scattering, non-linear partial differential equations and are studied in the last section of this book.
Quaternionic Integral Transforms: A Machine-Generated Literature Overview (Trends in Mathematics)
by Eckhard HitzerThis book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book’s editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.
Quaternions for Computer Graphics
by John VinceIf you have ever wondered what quaternions are — then look no further, John Vince will show you how simple and useful they are. This 2nd edition has been completely revised and includes extra detail on the invention of quaternions, a complete review of the text and equations, all figures are in colour, extra worked examples, an expanded index, and a bibliography arranged for each chapter. Quaternions for Computer Graphics includes chapters on number sets and algebra, imaginary and complex numbers, the complex plane, rotation transforms, and a comprehensive description of quaternions in the context of rotation. The book will appeal to students of computer graphics, computer science and mathematics, as well as programmers, researchers, academics and professional practitioners interested in learning about quaternions. John Vince explains in an easy-to-understand language, with the aid of useful figures, how quaternions emerged, gave birth to modern vector analysis, disappeared, and reemerged to be adopted by the flight simulation industry and computer graphics. This book will give you the confidence to use quaternions within your every-day mathematics, and explore more advanced texts.
Quaternions for Computer Graphics
by John VinceSir William Rowan Hamilton was a genius, and will be remembered for his significant contributions to physics and mathematics. The Hamiltonian, which is used in quantum physics to describe the total energy of a system, would have been a major achievement for anyone, but Hamilton also invented quaternions, which paved the way for modern vector analysis. Quaternions are one of the most documented inventions in the history of mathematics, and this book is about their invention, and how they are used to rotate vectors about an arbitrary axis. Apart from introducing the reader to the features of quaternions and their associated algebra, the book provides valuable historical facts that bring the subject alive. Quaternions for Computer Graphics introduces the reader to quaternion algebra by describing concepts of sets, groups, fields and rings. It also includes chapters on imaginary quantities, complex numbers and the complex plane, which are essential to understanding quaternions. The book contains many illustrations and worked examples, which make it essential reading for students, academics, researchers and professional practitioners.
A Quest Towards a Mathematical Theory of Living Systems (Modeling and Simulation in Science, Engineering and Technology)
by Nicola Bellomo Abdelghani Bellouquid Livio Gibelli Nisrine OutadaThis monograph aims to lay the groundwork for the design of a unified mathematical approach to the modeling and analysis of large, complex systems composed of interacting living things. Drawing on twenty years of research in various scientific fields, it explores how mathematical kinetic theory and evolutionary game theory can be used to understand the complex interplay between mathematical sciences and the dynamics of living systems. The authors hope this will contribute to the development of new tools and strategies, if not a new mathematical theory. The first chapter discusses the main features of living systems and outlines a strategy for their modeling. The following chapters then explore some of the methods needed to potentially achieve this in practice. Chapter Two provides a brief introduction to the mathematical kinetic theory of classical particles, with special emphasis on the Boltzmann equation; the Enskog equation, mean field models, and Monte Carlo methods are also briefly covered. Chapter Three uses concepts from evolutionary game theory to derive mathematical structures that are able to capture the complexity features of interactions within living systems. The book then shifts to exploring the relevant applications of these methods that can potentially be used to derive specific, usable models. The modeling of social systems in various contexts is the subject of Chapter Five, and an overview of modeling crowd dynamics is given in Chapter Six, demonstrating how this approach can be used to model the dynamics of multicellular systems. The final chapter considers some additional applications before presenting an overview of open problems. The authors then offer their own speculations on the conceptual paths that may lead to a mathematical theory of living systems hoping to motivate future research activity in the field. A truly unique contribution to the existing literature, A Quest Toward a Mathematical Theory of Living Systems is an important book that will no doubt have a significant influence on the future directions of the field. It will be of interest to mathematical biologists, systems biologists, biophysicists, and other researchers working on understanding the complexities of living systems.
Question Evaluation Methods
by Aaron Maitland Jennifer Madans Kristen Miller Gordon WillisInsightful observations on common question evaluation methods and best practices for data collection in survey researchFeaturing contributions from leading researchers and academicians in the field of survey research, Question Evaluation Methods: Contributing to the Science of Data Quality sheds light on question response error and introduces an interdisciplinary, cross-method approach that is essential for advancing knowledge about data quality and ensuring the credibility of conclusions drawn from surveys and censuses. Offering a variety of expert analyses of question evaluation methods, the book provides recommendations and best practices for researchers working with data in the health and social sciences.Based on a workshop held at the National Center for Health Statistics (NCHS), this book presents and compares various question evaluation methods that are used in modern-day data collection and analysis. Each section includes an introduction to a method by a leading authority in the field, followed by responses from other experts that outline related strengths, weaknesses, and underlying assumptions. Topics covered include:Behavior codingCognitive interviewingItem response theoryLatent class analysisSplit-sample experimentsMultitrait-multimethod experimentsField-based data methodsA concluding discussion identifies common themes across the presented material and their relevance to the future of survey methods, data analysis, and the production of Federal statistics. Together, the methods presented in this book offer researchers various scientific approaches to evaluating survey quality to ensure that the responses to these questions result in reliable, high-quality data.Question Evaluation Methods is a valuable supplement for courses on questionnaire design, survey methods, and evaluation methods at the upper-undergraduate and graduate levels. it also serves as a reference for government statisticians, survey methodologists, and researchers and practitioners who carry out survey research in the areas of the social and health sciences.
Questions in Dataviz: A Design-Driven Process for Data Visualisation (AK Peters Visualization Series)
by Neil RichardsThis book takes the reader through the process of learning and creating data visualisation, following a unique journey with questions every step of the way, ultimately discussing how and when to bend and break the "rules" to come up with creative, unique, and sometimes unconventional ideas. Each easy-to-follow chapter poses one key question and provides a selection of discussion points and relevant data visualisation examples throughout. Structured in three parts: Section I poses questions around some fundamental data visualisation principles, while Section II introduces more advanced questions, challenging perceived best practices and suggesting when rules are open to interpretation or there to be broken. The questions in Section III introduce further themes leading on to specific ideas and visualisation projects in more detail. Questions in Dataviz: A Design-Driven Process for Data Visualisation will appeal to any reader with an interest in creative or unconventional data visualisation and will be especially useful for those at a beginner or intermediate level looking for inspiration and alternative ways to deploy their data visualisation skills outside of conventional business charts.
Queueing Theory 1: Advanced Trends
by Vladimir Anisimov Nikolaos LimniosThe aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This first volume includes ten chapters written by experts well-known in their areas. The book studies the analysis of queues with interdependent arrival and service times, characteristics of fluid queues, modifications of retrial queueing systems and finite-source retrial queues with random breakdowns, repairs and customers’ collisions. Some recent tendencies in the asymptotic analysis include the average and diffusion approximation of Markov queueing systems and networks, the diffusion and Gaussian limits of multi-channel queueing networks with rather general input flow, and the analysis of two-time-scale nonhomogenous Markov chains using the large deviations principle. The book also analyzes transient behavior of infinite-server queueing models with a mixed arrival process, the strong stability of queueing systems and networks, and applications of fast simulation methods for solving high-dimension combinatorial problems.
Queueing Theory 2: Advanced Trends
by Vladimir Anisimov Nikolaos LimniosThe aim of this book is to reflect the current cutting-edge thinking and established practices in the investigation of queueing systems and networks. This second volume includes eight chapters written by experts wellknown in their areas. The book conducts a stability analysis of certain types of multiserver regenerative queueing systems; a transient evaluation of Markovian queueing systems, focusing on closed-form distributions and numerical techniques; analysis of queueing models in service sectors using analytical and simulation approaches; plus an investigation of probability distributions in queueing models and their use in economics, industry, demography and environmental studies. This book also considers techniques for the control of information in queueing systems and their impact on strategic customer behavior, social welfare and the revenue of monopolists. In addition, applications of maximum entropy methods of inference for the analysis of a stable M/G/1 queue with heavy tails, and inventory models with positive service time - including perishable items and stock supplied using various algorithmic control policies ((s; S); (r;Q), etc.).
Queueing Theory and Network Applications: 14th International Conference, QTNA 2019, Ghent, Belgium, August 27–29, 2019, Proceedings (Lecture Notes in Computer Science #11688)
by Tuan Phung-Duc Shoji Kasahara Sabine WittevrongelThis book constitutes the proceedings of the 14th International Conference on Queueing Theory and Network Applications, QTNA 2019, held in Ghent, Belgium, in August 2019.The 23 full papers included in this volume were carefully reviewed and selected from 49 initial submissions. The papers are organized in topical sections on Retrial Queues; Controllable Queues; Strategic Queues; Queueing Networks; Scheduling Policies; Multidimensional Systems; and Queueing Models in Applications.
Queues
by D.R. CoxThis is a classic book on Queues. First published in 1961 it is clearly and concisely introduces the theory of queueing systems and is still just as relevant today. The monograph is aimed at both students and operational research workers concerned with the practical investigations of queueing, although almost every statistician will find its contents of interest.
Queues
by Moshe HavivQueueing theory (the mathematical theory of waiting lines in all its configurations) continues to be a standard major area of operations research on the stochastic side. Therefore, universities with an active program in operations research sometimes will have an entire course devoted mainly or entirely to queueing theory, and the course is also taught in computer science, electrical engineering, mathematics, and industrial engineering programs. The basic course in queueing theory is often taught at first year graduate level, though can be taught at senior level undergraduate as well. This text evolved from the author's preferred syllabus for teaching the course, presenting the material in a more logical order than other texts and so being more effective in teaching the basics of queueing theory. The first three chapters focus on the needed preliminaries, including exposition distributions, Poisson processes and generating functions, renewal theory, and Markov chains, Then, rather than switching to first-come first-served memoryless queues here as most texts do, Haviv discusses the M/G/1 model instead of the M/M/1, and then covers priority queues. Later chapters cover the G/M/1 model, thirteen examples of continuous-time Markov processes, open networks of memoryless queues and closed networks, queueing regimes with insensitive parameters, and then concludes with two-dimensional queueing models which are quasi birth and death processes. Each chapter ends with exercises.
Queues and Lévy Fluctuation Theory
by Krzysztof Dębicki Michel MandjesThe book provides an extensive introduction to queueing models driven by Lévy-processes as well as a systematic account of the literature on Lévy-driven queues. The objective is to make the reader familiar with the wide set of probabilistic techniques that have been developed over the past decades, including transform-based techniques, martingales, rate-conservation arguments, change-of-measure, importance sampling, and large deviations. On the application side, it demonstrates how Lévy traffic models arise when modelling current queueing-type systems (as communication networks) and includes applications to finance. Queues and Lévy Fluctuation Theory will appeal to postgraduate students and researchers in mathematics, computer science, and electrical engineering. Basic prerequisites are probability theory and stochastic processes.
Queuing Theory and Telecommunications
by Giovanni GiambeneThis book is aimed to provide a basic description of current networking technologies and protocols as well as to provide important tools for network performance analysis based on queuing theory. The second edition adds selected contents in the first part of the book for what concerns: (i) the token bucket regulator and traffic shaping issues; (ii) the TCP protocol congestion control that has a significant part in current networking; (iii) basic satellite networking issues; (iv) adding details on QoS support in IP networks. The book is organized so that we have first networking technologies and protocols (Part I) and then theory and exercises with applications to the different technologies and protocols (Part II). This book is intended as a textbook for master level courses in networking and telecommunications sectors.
Quick Calculus: A Self-Teaching Guide (Wiley Self-Teaching Guides)
by Daniel Kleppner Peter Dourmashkin Norman RamseyDiscover an accessible and easy-to-use guide to calculus fundamentals In Quick Calculus: A Self-Teaching Guide, 3rd Edition, a team of expert MIT educators delivers a hands-on and practical handbook to essential calculus concepts and terms. The author explores calculus techniques and applications, showing readers how to immediately implement the concepts discussed within to help solve real-world problems. In the book, readers will find: An accessible introduction to the basics of differential and integral calculus An interactive self-teaching guide that offers frequent questions and practice problems with solutions. A format that enables them to monitor their progress and gauge their knowledge This latest edition provides new sections, rewritten introductions, and worked examples that demonstrate how to apply calculus concepts to problems in physics, health sciences, engineering, statistics, and other core sciences. Quick Calculus: A Self-Teaching Guide, 3rd Edition is an invaluable resource for students and lifelong learners hoping to strengthen their foundations in calculus.
Quick Review Math Handbook Book 1
by Mcgraw-Hill StaffA handbook used to refresh your memory of mathematics concepts and skills.
¿Quién salta más? / Who Jumps More? (Storytelling Math)
by Grace Lin¡Libro de cartón grueso ahora disponible en español-inglés bilingüe! La ganadora del Honor de Caldecott, Grace Lin, celebra las matemáticas para todos los niños, ¡en todas partes!Board book now available in bilingual Spanish-English! Caldecott Honor winner Grace Lin celebrates math for every kid, everywhere!Olivia y Mei saltan en la nieve hasta llegar al árbol alto. Mei da unos saltos grandes como un reno. Olivia da muchos saltitos más pequeños como un conejo. Cada una salta "más" de manera diferente. Una exploración juguetona de la medición, la proporción y la amistad.Storytelling Math celebra a los niños usando las matemáticas en sus aventuras diarias mientras juegan, construyen y descubren el mundo que les rodea. Historias alegres y actividades manuales hacen que sea fácil para los niños y sus adultos explorar las matemáticas cotidianas juntos. Desarrollado en colaboración con expertos en matemáticas de TERC, una organización educativa con enfoque en ciencia, tecnología, ingeniería y matemáticas (STEM, por sus siglas en inglés), bajo una subvención de la Fundación Heising-Simons.Olivia and Mei jump in the snow all the way to the tall tree. Mei takes a few big leaps like a deer. Olivia makes lots of smaller hops like a bunny. Each jumps &“more&” in a different way. A playful exploration of measurement, proportion, and friendship.Storytelling Math celebrates children using math in their daily adventures as they play, build, and discover the world around them. Joyful stories and hands-on activities make it easy for kids and their grown-ups to explore everyday math together. Developed in collaboration with math experts at STEM education nonprofit TERC, under a grant from the Heising-Simons Foundation.
Quirky Quantum Concepts
by Eric L. MichelsenQuirky Quantum Concepts explains the more important and more difficult concepts in theoretical quantum mechanics, especially those which are consistently neglected or confusing in many common expositions. The emphasis is on physical understanding, which is necessary for the development of new, cutting edge science. In particular, this book explains the basis for many standard quantum methods, which are too often presented without sufficient motivation or interpretation. The book is not a simplification or popularization: it is real science for real scientists. Physics includes math, and this book does not shy away from it, but neither does it hide behind it. Without conceptual understanding, math is gibberish. The discussions here provide the experimental and theoretical reasoning behind some of the great discoveries, so the reader may see how discoveries arise from a rational process of thinking, a process which Quirky Quantum Concepts makes accessible to its readers. Quirky Quantum Concepts is therefore a supplement to almost any existing quantum mechanics text. Students and scientists will appreciate the combination of conversational style, which promotes understanding, with thorough scientific accuracy.
Quiver Representations
by Ralf SchifflerThis book is intended to serve as a textbook for a course in Representation Theory of Algebras at the beginning graduate level. The text has two parts. In Part I, the theory is studied in an elementary way using quivers and their representations. This is a very hands-on approach and requires only basic knowledge of linear algebra. The main tool for describing the representation theory of a finite-dimensional algebra is its Auslander-Reiten quiver, and the text introduces these quivers as early as possible. Part II then uses the language of algebras and modules to build on the material developed before. The equivalence of the two approaches is proved in the text. The last chapter gives a proof of Gabriel's Theorem. The language of category theory is developed along the way as needed.
R 4 Quick Syntax Reference: A Pocket Guide to the Language, API's and Library
by Margot TollefsonThis handy reference book detailing the intricacies of R covers version 4.x features, including numerous and significant changes to syntax, strings, reference counting, grid units, and more.Starting with the basic structure of R, the book takes you on a journey through the terminology used in R and the syntax required to make R work. You will find looking up the correct form for an expression quick and easy. Some of the new material includes information on RStudio, S4 syntax, working with character strings, and an example using the Twitter API.With a copy of the R 4 Quick Syntax Reference in hand, you will find that you are able to use the multitude of functions available in R and are even able to write your own functions to explore and analyze data.What You Will LearnDiscover the modes and classes of R objects and how to use themUse both packaged and user-created functions in R Import/export data and create new data objects in RCreate descriptive functions and manipulate objects in RTake advantage of flow control and conditional statementsWork with packages such as base, stats, and graphicsWho This Book Is ForThose with programming experience, either new to R, or those with at least some exposure to R but who are new to the latest version.
R Alles-in-einem-Band für Dummies (Für Dummies)
by Joseph SchmullerWenn Sie R von Grund auf kennenlernen und auch die fortgeschrittenen Techniken zur Lösung gängiger Aufgaben bei der Datenanalyse mit R beherrschen möchten, dann liegen Sie mit diesem Buch goldrichtig. Es bietet Ihnen nicht nur einen Überblick über die Programmierung in R und die Arbeit mit der Sprache, sondern geht auch auf die Arten von Projekten und Anwendungen ein, die R-Entwicklerinnen und -Entwickler häufig in Angriff nehmen müssen. Statistische Analysen, Datenvisualisierungen, maschinelles Lernen und Datenmanagement mit R: All das lernen Sie mit diesem Buch intensiv kennen.