- Table View
- List View
Rational Bases and Generalized Barycentrics
by Eugene WachspressThis three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation. Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions for a broad class of elements which have widespread graphics and finite element application. Part one is the 1975 book "A Rational Finite Element Basis" (with minor updates and corrections) written by Dr. Wachspress. Part two describes theoretical advances since 1975 and includes analysis of elements not considered previously. Part three consists of annotated MATLAB programs implementing theory presented in Parts one and two.
Rational Decision and Causality
by Ellery EellsFirst published in 1982, Ellery Eells' original work on rational decision making had extensive implications for probability theorists, economists, statisticians and psychologists concerned with decision making and the employment of Bayesian principles. His analysis of the philosophical and psychological significance of Bayesian decision theories, causal decision theories and Newcomb's paradox continues to be influential in philosophy of science. His book is now revived for a new generation of readers and presented in a fresh twenty-first-century series livery, including a specially commissioned preface written by Brian Skyrms, illuminating its continuing importance and relevance to philosophical enquiry.
Rational Decisions (The Gorman Lectures in Economics #4)
by Ken BinmoreIt is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making.
Rational Homotopy Theory and Differential Forms
by Phillip Griffiths John MorganThis completely revised and corrected version of the well-known Florence notes circulated by the authors together with E. Friedlander examines basic topology, emphasizing homotopy theory. Included is a discussion of Postnikov towers and rational homotopy theory. This is then followed by an in-depth look at differential forms and de Tham's theorem on simplicial complexes. In addition, Sullivan's results on computing the rational homotopy type from forms is presented. New to the Second Edition: *Fully-revised appendices including an expanded discussion of the Hirsch lemma *Presentation of a natural proof of a Serre spectral sequence result *Updated content throughout the book, reflecting advances in the area of homotopy theory With its modern approach and timely revisions, this second edition of Rational Homotopy Theory and Differential Forms will be a valuable resource for graduate students and researchers in algebraic topology, differential forms, and homotopy theory.
Rational Number Theory in the 20th Century
by Władysław NarkiewiczThe last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat's problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.
Rational Points and Arithmetic of Fundamental Groups
by Jakob StixThe section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension.
Rational Points on Elliptic Curves
by Joseph H. Silverman John T. TateThe theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. This volume stresses this interplay as it develops the basic theory, thereby providing an opportunity for advanced undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been made to use only methods and results commonly included in the undergraduate curriculum. This accessibility, the informal writing style, and a wealth of exercises make Rational Points on Elliptic Curves an ideal introduction for students at all levels who are interested in learning about Diophantine equations and arithmetic geometry. Most concretely, an elliptic curve is the set of zeroes of a cubic polynomial in two variables. If the polynomial has rational coefficients, then one can ask for a description of those zeroes whose coordinates are either integers or rational numbers. It is this number theoretic question that is the main subject of Rational Points on Elliptic Curves. Topics covered include the geometry and group structure of elliptic curves, the Nagell-Lutz theorem describing points of finite order, the Mordell-Weil theorem on the finite generation of the group of rational points, the Thue-Siegel theorem on the finiteness of the set of integer points, theorems on counting points with coordinates in finite fields, Lenstra's elliptic curve factorization algorithm, and a discussion of complex multiplication and the Galois representations associated to torsion points. Additional topics new to the second edition include an introduction to elliptic curve cryptography and a brief discussion of the stunning proof of Fermat's Last Theorem by Wiles et al. via the use of elliptic curves.
Rational Reconstructions of Modern Physics
by Peter MittelstaedtNewton’s classical physics and its underlying ontology are loaded with several metaphysical hypotheses that cannot be justified by rational reasoning nor by experimental evidence. Furthermore, it is well known that some of these hypotheses are not contained in the great theories of modern physics, such as the theory of relativity and quantum mechanics. This book shows that, on the basis of Newton’s classical physics and by rational reconstruction, the theory of relativity as well as quantum mechanics can be obtained by partly eliminating or attenuating the metaphysical hypotheses. Moreover, it is shown that these reconstructions do not require additional hypotheses or new experimental results.
Rational Reconstructions of Modern Physics, 2nd Enlarged Edition
by Peter MittelstaedtNewton's classical physics and its underlying ontology are loaded with several metaphysical hypotheses that cannot be justified by rational reasoning nor by experimental evidence. Furthermore, it is well known that some of these hypotheses are not contained in the great theories of Modern Physics, such as the theory of Special Relativity and Quantum Mechanics. This book shows that, on the basis of Newton's classical physics and by rational reconstruction, the theory of Special Relativity as well as Quantum Mechanics can be obtained by partly eliminating or attenuating the metaphysical hypotheses. Moreover, it is shown that these reconstructions do not require additional hypotheses or new experimental results. <P><P> In the second edition the rational reconstructions are completed with respect to General Relativity and Cosmology. In addition, the statistics of quantum objects is elaborated in more detail with respect to the rational reconstruction of quantum mechanics. The new material completes the approach of the book as much as it is possible at the present state of knowledge. Presumably, the most important contribution that is added to the second edition refers to the problem of interpretation of the three great theories of Modern Physics. It is shown in detail that in the light of rational reconstructions even realistic interpretations of the three theories of Modern Physics are possible and can easily be achieved.
Rational Ritual: Culture, Coordination, and Common Knowledge
by Michael Suk-Young ChweWhy do Internet, financial service, and beer commercials dominate Super Bowl advertising? How do political ceremonies establish authority? Why does repetition characterize anthems and ritual speech? Why were circular forms favored for public festivals during the French Revolution? This book answers these questions using a single concept: common knowledge. Game theory shows that in order to coordinate its actions, a group of people must form "common knowledge." Each person wants to participate only if others also participate. Members must have knowledge of each other, knowledge of that knowledge, knowledge of the knowledge of that knowledge, and so on. Michael Chwe applies this insight, with striking erudition, to analyze a range of rituals across history and cultures. He shows that public ceremonies are powerful not simply because they transmit meaning from a central source to each audience member but because they let audience members know what other members know. For instance, people watching the Super Bowl know that many others are seeing precisely what they see and that those people know in turn that many others are also watching. This creates common knowledge, and advertisers selling products that depend on consensus are willing to pay large sums to gain access to it. Remarkably, a great variety of rituals and ceremonies, such as formal inaugurations, work in much the same way. By using a rational-choice argument to explain diverse cultural practices, Chwe argues for a close reciprocal relationship between the perspectives of rationality and culture. He illustrates how game theory can be applied to an unexpectedly broad spectrum of problems, while showing in an admirably clear way what game theory might hold for scholars in the social sciences and humanities who are not yet acquainted with it. In a new afterword, Chwe delves into new applications of common knowledge, both in the real world and in experiments, and considers how generating common knowledge has become easier in the digital age.
Rational Sphere Maps (Progress in Mathematics #341)
by John P. D’AngeloThis monograph systematically explores the theory of rational maps between spheres in complex Euclidean spaces and its connections to other areas of mathematics. Synthesizing research from the last forty years, the author aims for accessibility by balancing abstract concepts with concrete examples. Numerous computations are worked out in detail, and more than 100 optional exercises are provided throughout for readers wishing to better understand challenging material.The text begins by presenting core concepts in complex analysis and a wide variety of results about rational sphere maps. The subsequent chapters discuss combinatorial and optimization results about monomial sphere maps, groups associated with rational sphere maps, relevant complex and CR geometry, and some geometric properties of rational sphere maps. Fifteen open problems appear in the final chapter, with references provided to appropriate parts of the text. These problems will encourage readers to apply the material to future research.Rational Sphere Maps will be of interest to researchers and graduate students studying several complex variables and CR geometry. Mathematicians from other areas, such as number theory, optimization, and combinatorics, will also find the material appealing.
Rationality and Operators
by Susumu CatoThis unique book develops an operational approach to preference and rationality as the author employs operators over binary relations to capture the concept of rationality. A preference is a basis of individual behavior and social judgment and is mathematically regarded as a binary relation on the set of alternatives. Traditionally, an individual/social preference is assumed to satisfy completeness and transitivity. However, each of the two conditions is often considered to be too demanding; and then, weaker rationality conditions are introduced by researchers. This book argues that the preference rationality conditions can be captured mathematically by "operators," which are mappings from the set of operators to itself. This operational approach nests traditional concepts in individual/social decision theory and clarifies the underlying formal structure of preference rationality. The author also applies his approach to welfare economics. The core problem of 'new welfare economics,' developed by Kaldor, Hicks, and Samuelson, is the rationality of social preference. In this book the author translates the social criteria proposed by those three economists into operational forms, which provide new insights into welfare economics extending beyond 'new welfare economics. '
Rationality Problems in Algebraic Geometry
by Gian Pietro Pirola Alessandro Verrarita Pardini Alexander Kuznetsov Brendan Hassett Arnaud BeauvilleProviding an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel-Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.
Raum für Inklusion: Schule als Lernort für Alle gestalten und nutzen (Forschungsreihe der FH Münster)
by Jeanne Lengersdorf Anna HagemannDer Raum gewinnt zunehmend an Bedeutung. Gerade in Zeiten des pädagogischen Wandels und mit der Unterzeichnung der UN-Konvention über die Rechte von Menschen mit Behinderung rückt konstruktivistisch, inklusiv ausgelegte Didaktik in den Vordergrund schulischer Entwicklungen. Dieses Buch geht der Frage nach, wie sich Schule als Lernort für Alle gestalten und nutzen lässt. Dazu wird unter den Schwerpunkten Beziehungsebene, Multiprofessionelle Teamarbeit, individualisiertes Lernen und Ort des Lernens anhand einer Triangulation von empirischen Forschungsmethoden eine inklusive berufliche Schule in Hamburg beleuchtet. Im Mittelpunkt der Arbeit steht das Zusammenspiel von Raum und Pädagogik unter dem Leitgedanken der Inklusion.Die AutorinnenAnna Hagemann, M. Ed., Lehramt an Berufskollegs in der beruflichen Fachrichtung Mediendesign und Designtechnik und dem allgemeinbilden Fach EnglischJeanne Lengersdorf, M. Ed., Lehramt an Berufskollegs in der beruflichen Fachrichtung Mediendesign und Designtechnik und dem allgemeinbilden Fach Sport, seit 2019 wissenschaftliche Mitarbeiterin an der FH Münster am Institut für Berufliche Lehrerbildung (abgeordnet von der WWU Münster)
The Raven's Hat: Fallen Pictures, Rising Sequences, and Other Mathematical Games
by Jonas Peters Nicolai MeinshausenGames that show how mathematics can solve the apparently unsolvable.This book presents a series of engaging games that seem unsolvable--but can be solved when they are translated into mathematical terms. How can players find their ID cards when the cards are distributed randomly among twenty boxes? By applying the theory of permutations. How can a player guess the color of her own hat when she can only see other players' hats? Hamming codes, which are used in communication technologies. Like magic, mathematics solves the apparently unsolvable. The games allow readers, including university students or anyone with high school-level math, to experience the joy of mathematical discovery.
Ray Methods for Nonlinear Waves in Fluids and Plasmas (Monographs And Surveys In Pure And Applied Mathematics Ser.)
by Marcelo Anile P Pantano G Russo J HunterPresents in a systematic and unified manner the ray method, in its various forms, for studying nonlinear wave propagation in situations of physical interest, essentially fluid dynamics and plasma physics.
Ray Tracing and Beyond
by E. R. Tracy Aptara. IncThis complete introduction to the use of modern ray tracing techniques in plasma physics describes the powerful mathematical methods generally applicable to vector wave equations in non-uniform media, and clearly demonstrates the application of these methods to simplify and solve important problems in plasma wave theory. Key analytical concepts are carefully introduced as needed, encouraging the development of a visual intuition for the underlying methodology, with more advanced mathematical concepts succinctly explained in the appendices, and supporting Matlab and Raycon code available online. Covering variational principles, covariant formulations, caustics, tunnelling, mode conversion, weak dissipation, wave emission from coherent sources, incoherent wave fields, and collective wave absorption and emission, all within an accessible framework using standard plasma physics notation, this is an invaluable resource for graduate students and researchers in plasma physics.
Re-Examining the History of the Russian Economy: A New Analytic Tool from Field Theory
by Jeffrey K. HassThis book explores the application of field theory (patterns of interaction) to Russian economic history, and how social and political fields mediate the influences of institutions, structures, discourses and ideologies in the creation and dissemination of economic thinking, theory and practice. Using focused cases on Russia's economy from the mid-nineteenth century to the present, Hass and co-authors expand the empirical basis of field studies to provide new material on Russian economic history. The cases are divided into two complementary halves: i) The role of fields of institutions, discourses, and structures in the development of Russian economic thought, especially economic theories and discourses; and ii) The role of fields in the real adoption and implementation of policies in Soviet and Russian economic history. With developed discussion of fields and field theory, this book moves beyond sociology to demonstrate to other disciplines the relation of fields and field theory to other frameworks and methodological considerations for field analysis, as well as providing new empirical insights and narratives not as well-known abroad.
Reachability Problems: 17th International Conference, RP 2023, Nice, France, October 11–13, 2023, Proceedings (Lecture Notes in Computer Science #14235)
by Olivier Bournez Enrico Formenti Igor PotapovThis book constitutes the refereed proceedings of the 17th International Conference on Reachability Problems, RP 2023, held in Nice, France, during October 11–13, 2023.The 13 full papers included in this book were carefully reviewed and selected from 19 submissions. They present recent research on reachability problems to promote the exploration of new approaches for the modeling and analysis of computational processes by combining mathematical, algorithmic, and computational techniques.
Reachability Problems: 12th International Conference, RP 2018, Marseille, France, September 24-26, 2018, Proceedings (Lecture Notes in Computer Science #11123)
by Igor Potapov Pierre-Alain ReynierThis book constitutes the refereed proceedings of the 12th International Conference on Reachability Problems, RP 2018, held in Marseille, France, in September 2018.The 11 full papers presented were carefully reviewed and selected from 21 submissions. The papers cover topics such as reachability for infinite state systems; rewriting systems; reachability analysis in counter/timed/cellular/communicating automata; Petri nets; computational aspects of semigroups, groups, and rings; reachability in dynamical and hybrid systems; frontiers between decidable and undecidable reachability problems; complexity and decidability aspects; predictability in iterative maps, and new computational paradigms.
Reachability Problems: 18th International Conference, RP 2024, Vienna, Austria, September 25–27, 2024, Proceedings (Lecture Notes in Computer Science #15050)
by Ana Sokolova Laura KovácsThis book constitutes the proceedings of the 18th International Conference on Reachability Problems, RP 2024, which took place in Vienna, Austria, during September 25–27, 2024. The 13 full papers included in these proceedings were carefully reviewed and selected from 37 submissions. The book also contains two invited talks in full paper length. The contributions in these proceedings cover topics from computability and reachability; automata and complexity; linear systems and recurrences; and games and abstractions.
Reaching and Teaching Neurodivergent Learners in STEM: Strategies for Embracing Uniquely Talented Problem Solvers
by Jodi Asbell-ClarkeProviding salient stories and practical strategies, this book empowers educators to embrace the unique talents of neurodivergent learners in science, technology, engineering, and mathematics (STEM). An exploration of the exciting opportunities neurodiversity presents to build an innovative workforce is grounded in a large body of research from psychology, neuroscience, and education. Author Jodi Asbell-Clarke presents individual examples of neurodivergent journeys in STEM to establish evidence-based connections between neurodiversity and the types of innovative problem-solving skills needed in today’s workforce. The featured stories come directly from the author’s many years in inclusive classrooms with STEM teachers along with interviews from many neurodivergent professionals in STEM. Teachers will learn how to embrace the unique brilliance and potential of the neurodivergent learners in their classroom, working against historic marginalization and deficit-based perspectives of neurodiversity within the education system. Featuring illustrations of classroom-designed tools and materials alongside basic strategies to support executive function and emotion in learning, this book will help you nurture the talents of your neurodivergent learners and recognize their unique potential within STEM. Ideal for K-12 classroom teachers, special educators, learning specialists, psychologists, and school administrators.
Reaction Diffusion Systems
by Gabriella Caristi; Enzo Mitidieri"Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."
Reaction Kinetics: Mathematica for Deterministic and Stochastic Kinetics
by János Tóth Attila László Nagy Dávid PappFifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.
A Readable Introduction to Real Mathematics (Undergraduate Texts in Mathematics)
by Daniel Rosenthal David Rosenthal Peter RosenthalDesigned for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to teach mathematical thinking while conveying the beauty and elegance of mathematics. The book contains a large number of exercises of varying difficulty, some of which are designed to help reinforce basic concepts and others of which will challenge virtually all readers. The sole prerequisite for reading this text is high school algebra. Topics covered include: * mathematical induction * modular arithmetic * the Fundamental Theorem of Arithmetic * Fermat's Little Theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean plane geometry * constructibility (including a proof that an angle of 60 degrees cannot be trisected with a straightedge and compass)* infinite series * higher dimensional spaces. <P><P> This textbook is suitable for a wide variety of courses and for a broad range of students of mathematics and other subjects. Mathematically inclined senior high school students will also be able to read this book.