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Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe (Lecture Notes in Mathematics #907)
by Peter Schenzel
Dualities, Helicity Amplitudes, and Little Conformal Symmetry (Springer Theses)
by Kitran Macey ColwellThis book develops two exciting areas of particle physics research. It applies the recent new insights about the usefulness of helicity amplitudes in understanding gauge theory to the long-standing effort to understand theories with both electric and magnetic charges. It is known that for some supersymmetric theories there is an exact duality that relates two descriptions of the physics, one where the electric charges are weakly coupled and another where the electric charges are strongly coupled. The calculations in this thesis suggest that this duality can also hold in the low-energy limit of nonsupersymmetric gauge theories. The idea of addressing the hierarchy problem of the standard model Higgs mechanism using conformal symmetry is also explored. Analogously to “Little Higgs” models, where divergences are cancelled only at one-loop order, models are studied that have infrared conformal fixed points which related gauge and Yukawa couplings, allowing for a cancellation between seemingly unrelated quantum loop diagrams.
Duality for Crossed Products of von Neumann Algebras (Lecture Notes in Mathematics #731)
by Y. Nakagami M. Takesaki
Duality for Nonconvex Approximation and Optimization (CMS Books in Mathematics #Vol. 22)
by Ivan SingerThe theory of convex optimization has been constantly developing over the past 30 years. Most recently, many researchers have been studying more complicated classes of problems that still can be studied by means of convex analysis, so-called "anticonvex" and "convex-anticonvex" optimizaton problems. This manuscript contains an exhaustive presentation of the duality for these classes of problems and some of its generalization in the framework of abstract convexity. This manuscript will be of great interest for experts in this and related fields.
Duality in 19th and 20th Century Mathematical Thinking (Science Networks. Historical Studies #63)
This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.
The Duality of Compact Semigroups and C*-Bigebras (Lecture Notes in Mathematics #129)
by Karl H. Hofmann
Duality Principles in Nonconvex Systems: Theory, Methods and Applications (Nonconvex Optimization and Its Applications #39)
by David Yang GaoMotivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.
Duality System in Applied Mechanics and Optimal Control (Advances in Mechanics and Mathematics #5)
by Wan-Xie ZhongA unified approach is proposed for applied mechanics and optimal control theory. The Hamilton system methodology in analytical mechanics is used for eigenvalue problems, vibration theory, gyroscopic systems, structural mechanics, wave-guide, LQ control, Kalman filter, robust control etc. All aspects are described in the same unified methodology. Numerical methods for all these problems are provided and given in meta-language, which can be implemented easily on the computer. Precise integration methods both for initial value problems and for two-point boundary value problems are proposed, which result in the numerical solutions of computer precision. Key Features of the text include: -Unified approach based on Hamilton duality system theory and symplectic mathematics. -Gyroscopic system vibration, eigenvalue problems. -Canonical transformation applied to non-linear systems. -Pseudo-excitation method for structural random vibrations. -Precise integration of two-point boundary value problems. -Wave propagation along wave-guides, scattering. -Precise solution of Riccati differential equations. -Kalman filtering. -HINFINITY theory of control and filter.
Duality Theories for Boolean Algebras with Operators (Springer Monographs in Mathematics)
by Steven GivantIn this new text, Steven Givant—the author of several acclaimed books, including works co-authored with Paul Halmos and Alfred Tarski—develops three theories of duality for Boolean algebras with operators. Givant addresses the two most recognized dualities (one algebraic and the other topological) and introduces a third duality, best understood as a hybrid of the first two. This text will be of interest to graduate students and researchers in the fields of mathematics, computer science, logic, and philosophy who are interested in exploring special or general classes of Boolean algebras with operators. Readers should be familiar with the basic arithmetic and theory of Boolean algebras, as well as the fundamentals of point-set topology.
Dubbel Mathematik: Eine kompakte Ingenieurmathematik zum Nachschlagen
by U. Jarecki Hans-Joachim SchulzDer Band enthält die gesamte Mathematik für Ingenieure. Behandelt werden die Themen Mengen, Funktionen und Boolesche Algebra; Zahlen; Lineare Algebra; Geometrie; Analytische Geometrie; Differential- und Integralrechnung; Kurven, Flächen und Vektoranalysis; Differentialgleichungen; Auswertung von Beobachtungen und Messungen; praktische Mathematik. Der Anhang enthält Diagramme und Tabellen.
Dude, Can You Count? Stories, Challenges and Adventures in Mathematics
by Christian ConstandaImagine algebra class meets The Hitchhiker’s Guide to the Galaxy… Meet JJ, an unusual character with a unique vantage position from which he can measure and monitor humanity’s progress. Armed with a device that compels all around it to tell the truth, JJ offers a satirical evaluation of our attitudes to numeracy and logic, touching upon several aspects of life on Earth along the way, from the criminal justice system and people’s use of language to highway driving and modern art. A collection of mathematically-flavored stories and jokes, interlaced with puzzles, paradoxes and problems, fuse together in an entertaining, free-flowing narrative that will engage and amuse anyone with an interest in the issues confronting society today. JJ demonstrates how a lack of elementary mathematical knowledge can taint our work and general thinking and reflects upon the importance of what is arguably our most valuable weapon against ignorance: a sound mathematical education.
Due Date-Related Scheduling with Two Agents: Models and Algorithms (Uncertainty and Operations Research)
by Yunqiang Yin Dujuan Wang T.C.E. ChengThis book provides an introduction to the models, methods, and results of some due date-related scheduling problems in the field of multiagent scheduling. In multiagent scheduling, two or more agents share a common processing resource and each agent wants to optimize its own objective function with respect to its own set of jobs. Since the agents have conflicting objective functions, they have to negotiate among themselves with regard to sharing the common resource to optimize their own objective functions. A key feature of due date-related scheduling concerns the way in which due dates are considered: they can be given parameters or decision variables. For the former case, the motivation stems from the need to improve inventory and production management. For the latter case, due date assignment becomes a challenging issue since the decision-maker has to balance inventory holding costs against the benefits of fulfifilling orders in time.As for due dates, this book addresses the following three different scenarios: (i) The due dates of the jobs from either one or both of the two agents are decision variables, which are determined using some due date assignment models; (ii) The due dates of jobs in each job set are considered as given parameters, whereas which due date corresponds to a given job needs to determine; and (iii) The due date of each job is exogenously given. When the last case is involved, the objective function of each agent is related to the number of just-in-time jobs that are completed exactly on their due dates.For each considered scenario, depending on the model settings, and on the objective function of each agent, this book addresses the complexity, and the design of efficient exact or approximated algorithms.This book aims at introducing the author's research achievements in due date-related scheduling with two agents. It is written for researchers and Ph.D. students working in scheduling theory and other members of scientific community who are interested in recent scheduling models. Our goal is to enable the reader to know about some new achievements on this topic.
Duelling Idiots and Other Probability Puzzlers
by Paul J. NahinWhat are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds. If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly," for example, is a clever variation of a "random walk" problem, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions. Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.
Duelling Idiots and Other Probability Puzzlers (PDF)
by Paul J. NahinWhat are your chances of dying on your next flight, being called for jury duty, or winning the lottery? We all encounter probability problems in our everyday lives. In this collection of twenty-one puzzles, Paul Nahin challenges us to think creatively about the laws of probability as they apply in playful, sometimes deceptive, ways to a fascinating array of speculative situations. Games of Russian roulette, problems involving the accumulation of insects on flypaper, and strategies for determining the odds of the underdog winning the World Series all reveal intriguing dimensions to the workings of probability. Over the years, Nahin, a veteran writer and teacher of the subject, has collected these and other favorite puzzles designed to instruct and entertain math enthusiasts of all backgrounds. If idiots A and B alternately take aim at each other with a six-shot revolver containing one bullet, what is the probability idiot A will win? What are the chances it will snow on your birthday in any given year? How can researchers use coin flipping and the laws of probability to obtain honest answers to embarrassing survey questions? The solutions are presented here in detail, and many contain a profound element of surprise. And some puzzles are beautiful illustrations of basic mathematical concepts: "The Blind Spider and the Fly," for example, is a clever variation of a "random walk" problem, and "Duelling Idiots" and "The Underdog and the World Series" are straightforward introductions to binomial distributions. Written in an informal way and containing a plethora of interesting historical material, Duelling Idiots is ideal for those who are fascinated by mathematics and the role it plays in everyday life and in our imaginations.
Dummett on Analytical Philosophy (Philosophers in Depth)
by Bernhard WeissDummett argues that the aim of philosophy is the analysis of thought and that, with Frege, analytical philosophy learned that the route to the analysis of thought is the analysis of language. Here are bold and deep readings of the subject's history and character, which form the topic of this volume.
DUNE — The Distributed and Unified Numerics Environment (Lecture Notes in Computational Science and Engineering #140)
by Oliver SanderThe Distributed and Unified Numerics Environment (Dune) is a set of open-source C++ libraries for the implementation of finite element and finite volume methods. Over the last 15 years it has become one of the most commonly used libraries for the implementation of new, efficient simulation methods in science and engineering. Describing the main Dune libraries in detail, this book covers access to core features like grids, shape functions, and linear algebra, but also higher-level topics like function space bases and assemblers. It includes extensive information on programmer interfaces, together with a wealth of completed examples that illustrate how these interfaces are used in practice. After having read the book, readers will be prepared to write their own advanced finite element simulators, tapping the power of Dune to do so.
Durable-Strategies Dynamic Games: Theory, Solution Techniques and Applications (Theory and Decision Library C #50)
by David W. Yeung Leon A. PetrosyanDurable strategies that have prolonged effects are prevalent in real-world situations. Revenue-generating investments, toxic waste disposal, long-lived goods, regulatory measures, coalition agreements, diffusion of knowledge, advertisement and investments to accumulate physical capital are concrete and common examples of durable strategies. This book provides an augmentation of dynamic game theory and advances a new game paradigm with durable strategies in decision-making schemes. It covers theories, solution techniques, and the applications of a general class of dynamic games with multiple durable strategies. Non-cooperative equilibria and cooperative solutions are derived, along with advanced topics including random termination, asynchronous game horizons, and stochastic analysis. The techniques presented here will enable readers to solve numerous practical dynamic interactive problems with durable strategies. This book not only expands the scope of applied dynamic game theory, but also provides a solid foundation for further theoretical and technical advancements. As such, it will appeal to scholars and students of quantitative economics, game theory, operations research, and computational mathematics."Not too many new concepts have been introduced in dynamic games since their inception. The introduction of the concept of durable strategies changes this trend and yields important contributions to environmental and business applications." Dušan M Stipanović, Professor, University of Illinois at Urbana-Champaign "Before this book, the field simply did not realize that most of our strategies are durable and entail profound effects in the future. Putting them into the mathematical framework of dynamic games is a great innovative effort." Vladimir Turetsky, Professor, Ort Braude College “Durable-strategies Dynamic Games is truly a world-leading addition to the field of dynamic games. It is a much needed publication to tackle increasingly crucial problems under the reality of durable strategies.” Vladimir Mazalov, Director of Mathematical Research, Russian Academy of Sciences & President of the International Society of Dynamic Games
Duration and Bandwidth Limiting: Prolate Functions, Sampling, and Applications (Applied and Numerical Harmonic Analysis)
by Jeffrey A. Hogan Joseph D. LakeyIncreasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals. This concise but comprehensive monograph is the first to be devoted specifically to this subdiscipline, providing a thorough investigation of its theory and applications. Through cutting-edge numerical methods, it develops the tools for applications not only to communications engineering, but also to optical engineering, geosciences, planetary sciences, and biomedicine. With broad coverage and a careful balance between rigor and readability, Duration and Bandwidth Limiting is a particularly original and valuable resource both for mathematicians interested in the field and for professional engineers with an interest in theory. While its main target audience is practicing scientists, the book may also serve as useful supplemental reading material for mathematically-based graduate courses in communications and signal processing.
Duration and Change: Fifty Years at Oberwolfach
by Michael Artin Hanspeter Kraft Reinhold RemmertA volume containing original essays from quite diverse fields in mathematics is something of a rarity, especially if renowned scientists show the width of their discipline to the reader. This book is just such a rarity - a veritable gem. It was written to celebrate the 50th anniversary of the mathematical research institute at Oberwolfach. The articles span a range of topics from general reflections on the place of mathematics in contemporary culture to essays dealing with aspects of algebra, analysis, geometry, coding theory, scientific computing and topology. All essays are interrelated, proving the old rule that you can divide and still conquer. A book in which every mathematician or scientist interested in mathematics will find something to take their fancy.
Duration Calculus: A Formal Approach to Real-Time Systems (Monographs in Theoretical Computer Science. An EATCS Series)
by Chaochen Zhou Michael R. HansenA comprehensive introduction to interval logic and duration calculus for modelling, analysing and verifying real-time systems. The Duration Calculus (DC) represents a logical approach to formal design of real-time systems. In DC real numbers are used to model time and Boolean-valued (i.e. {0,1}-valued) functions over time to model states of real-time systems. The duration of a state in a time interval is the accumulated presence time of the state in the interval. DC extends interval logic to a calculus to specify and reason about properties of state durations. The text covers theory (completeness, decidability, undecidability, model-checking), results, as well as case studies (Deadline Driven Scheduler).
Durch Symmetrie die moderne Physik verstehen: Ein neuer Zugang zu den fundamentalen Theorien
by Jakob SchwichtenbergAuf der Basis von Symmetrie-Überlegungen bietet dieses Buch eine einzigartige Herleitung der fundamentalen Theorien der Physik. Dafür werden zunächst alle mathematische Werkzeuge eingeführt, die der Leser benötigt, um mit Symmetrien in der Physik zu arbeiten. Hierbei wird jedoch nur gewöhnliche Schulmathematik vorausgesetzt. Anschließend werden diese Werkzeuge benutzt, um durch Symmetrie-Überlegungen die fundamentalen Gleichungen der Quantenmechanik, Quantenfeldtheorie, Elektrodynamik und Klassischen Mechanik herzuleiten. So ist der Leser in der Lage, die Basis-Annahmen hinter und die Verbindungen zwischen den modernen Theorien der Physik zu verstehen. Im letzten Teil des Buches werden dann Anwendungen der zuvor hergeleiteten Gleichungen besprochen. Das Buch richtet sich an alle, die sich ein tieferes Verständnis der modernen Physik wünschen. Anfänger und Selbstlerner erhalten durch die "Symmetrie-Perspektive" einen schnellen, aber tiefen Überblick über die moderne Physik. Erfahrene Studierende können durch den unkonventionellen Blickwinkel ihr Verständnis vertiefen und Wissenslücken füllen.Nachdem das Buch "Physics From Symmetry" Leser in aller Welt begeisterte, erscheint nun mit "Physik und Symmetrie" eine verbesserte deutsche Version.
Dusk of Dawn!: An Essay Toward an Autobiography of Race Concept
by W. E. DuBoisIn her perceptive introduction to this edition, Irene Diggs sets this classic autobiography against its broad historical context and critically analyzes its theoretical and methodological significance.