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Pappus of Alexandria: Book 4 of the Collection
by Heike Sefrin-WeisAlthough not so well known today, Book 4 of Pappus' Collection is one of the most important and influential mathematical texts from antiquity. The mathematical vignettes form a portrait of mathematics during the Hellenistic "Golden Age", illustrating central problems - for example, squaring the circle; doubling the cube; and trisecting an angle - varying solution strategies, and the different mathematical styles within ancient geometry. This volume provides an English translation of Collection 4, in full, for the first time, including: a new edition of the Greek text, based on a fresh transcription from the main manuscript and offering an alternative to Hultsch's standard edition, notes to facilitate understanding of the steps in the mathematical argument, a commentary highlighting aspects of the work that have so far been neglected, and supporting the reconstruction of a coherent plan and vision within the work, bibliographical references for further study.
Parabolic Equations on an Infinite Strip (Chapman And Hall/crc Pure And Applied Mathematics Ser. #127)
by WatsonThis book focuses on solutions of second order, linear, parabolic, partial differentialequations on an infinite strip-emphasizing their integral representation, their initialvalues in several senses, and the relations between these.Parabolic Equations on an Infinite Strip provides valuable information-previously unavailable in a single volume-on such topics as semigroup property.. . the Cauchy problem ... Gauss-Weierstrass representation . .. initial limits .. .normal limits and related representation theorems ... hyperplane conditions .. .determination of the initial measure .. . and the maximum principle. It also exploresnew, unpublished results on parabolic limits . . . more general limits ... and solutionssatisfying LP conditions.Requiring only a fundamental knowledge of general analysis and measure theory, thisbook serves as an excellent text for graduate students studying partial differentialequations and harmonic analysis, as well as a useful reference for analysts interested inapplied measure theory, and specialists in partial differential equations.
Parabolic Wave Equations with Applications
by Michael D. Collins William L. SiegmannThis book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Paraconsistency: Logic and Applications
by Edwin Mares Francesco Berto Francesco Paoli Koji TanakaA logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.
Paradigms of Combinatorial Optimization: Problems and New Approaches, Volume 2 (Wiley-iste Ser.)
by Vangelis Th. PaschosCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aims to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. “Paradigms of Combinatorial Optimization” is divided in two parts: • Paradigmatic Problems, that handles several famous combinatorial optimization problems as max cut, min coloring, optimal satisfiability tsp, etc., the study of which has largely contributed to both the development, the legitimization and the establishment of the Combinatorial Optimization as one of the most active actual scientific domains; • Classical and New Approaches, that presents the several methodological approaches that fertilize and are fertilized by Combinatorial optimization such as: Polynomial Approximation, Online Computation, Robustness, etc., and, more recently, Algorithmic Game Theory.
Paradigms of Combinatorial Optimization: Problems and New Approaches (Wiley-iste Ser.)
by Vangelis Th. PaschosCombinatorial optimization is a multidisciplinary scientific area, lying in the interface of three major scientific domains: mathematics, theoretical computer science and management. The three volumes of the Combinatorial Optimization series aim to cover a wide range of topics in this area. These topics also deal with fundamental notions and approaches as with several classical applications of combinatorial optimization. Concepts of Combinatorial Optimization, is divided into three parts: - On the complexity of combinatorial optimization problems, presenting basics about worst-case and randomized complexity; - Classical solution methods, presenting the two most-known methods for solving hard combinatorial optimization problems, that are Branch-and-Bound and Dynamic Programming; - Elements from mathematical programming, presenting fundamentals from mathematical programming based methods that are in the heart of Operations Research since the origins of this field.
Paradox
by Jim Al-KhaliliA fun and fascinating look at great scientific paradoxes. Throughout history, scientists have come up with theories and ideas that just don't seem to make sense. These we call paradoxes. The paradoxes Al-Khalili offers are drawn chiefly from physics and astronomy and represent those that have stumped some of the finest minds. For example, how can a cat be both dead and alive at the same time? Why will Achilles never beat a tortoise in a race, no matter how fast he runs? And how can a person be ten years older than his twin? With elegant explanations that bring the reader inside the mind of those who've developed them, Al-Khalili helps us to see that, in fact, paradoxes can be solved if seen from the right angle. Just as surely as Al-Khalili narrates the enduring fascination of these classic paradoxes, he reveals their underlying logic. In doing so, he brings to life a select group of the most exciting concepts in human knowledge. Paradox is mind-expanding fun.
The Paradox of Diversity
by Wahideh AchbariThis book is about ethnic diversity in voluntary organizations and seeks to explain whether intergroup contact contributes to the development of generalized trust. It relies on a novel multilevel design and data from Amsterdam in which 40 voluntary organizations and 463 participants have been sampled. Contrary to conventional wisdom, this book argues that cognitive processes are contributing more toward the evaluation of strangers or generalized trust than interethnic contact. Since trusting unknown people is essentially a risky endeavor, this suggests that participants of both association types who report trusting strangers can afford to do so, because they are better educated, have a more positive worldview, and have had fewer negative life experiences. That is to say, they are socially more successful and view their future as more promising. Previous findings are inconclusive since most studies that conclude diversity has led to less generalized trust do not include interethnic contact directly in their analyses. These studies also downplay the importance of cognitive processes, which may shape generalized trust. What is more, people join ethnically diverse civic groups, because they already have more trustful attitudes, rather than learning to trust through interethnic contact. Despite the recent multiculturalist backlash, this book demonstrates that participation in ethno-national organizations does not pose a threat to social cohesion. The analysis in this book serves to build a general theory of trust that moves beyond emphasizing interaction between people who are different from each other, but one that includes the importance of cognition.
Paradoxes and Inconsistent Mathematics
by Zach WeberLogical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses “dialetheic paraconsistency” – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.
Paradoxes in Mathematics (Dover Books on Mathematics)
by Stanley J. FarlowThere's more than one way to define a paradox, and this intriguing book offers examples of every kind. Stanley J. Farlow, a prominent educator and author, presents a captivating mix of mathematical paradoxes: the kind with surprising, nonintuitive outcomes; the variety that rely on mathematical sleight-of-hand to impress the unwary observer; and the baffling type with a solution that passes all understanding.Students and puzzle enthusiasts will find plenty of thought-provoking enjoyment mixed with a bit of painless mathematical instruction among these twenty-eight conundrums. Some of them involve counting, some deal with infinity, and others draw on principles of geometry and arithmetic. None requires an extensive background in higher mathematics. Challenges include The Curve That Shook the World, a variation on the famous Monty Hall Problem, Space Travel in a Wineglass, Through Cantor's Looking Glass, and other fun-to-ponder paradoxes.
Paradoxes in Probability Theory
by William EckhardtParadoxes provide a vehicle for exposing misinterpretations and misapplications of accepted principles. This book discusses seven paradoxes surrounding probability theory. Some remain the focus of controversy; others have allegedly been solved, however the accepted solutions are demonstrably incorrect. Each paradox is shown to rest on one or more fallacies. Instead of the esoteric, idiosyncratic, and untested methods that have been brought to bear on these problems, the book invokes uncontroversial probability principles, acceptable both to frequentists and subjectivists. The philosophical disputation inspired by these paradoxes is shown to be misguided and unnecessary; for instance, startling claims concerning human destiny and the nature of reality are directly related to fallacious reasoning in a betting paradox, and a problem analyzed in philosophy journals is resolved by means of a computer program.
Paradoxes of the Infinite (Routledge Revivals)
by Bernard BolzanoParadoxes of the Infinite presents one of the most insightful, yet strangely unacknowledged, mathematical treatises of the 19th century: Dr Bernard Bolzano’s Paradoxien. This volume contains an adept translation of the work itself by Donald A. Steele S.J., and in addition an historical introduction, which includes a brief biography as well as an evaluation of Bolzano the mathematician, logician and physicist.
Parallel Algorithms in Computational Science and Engineering (Modeling and Simulation in Science, Engineering and Technology)
by Ananth Grama Ahmed H. SamehThis contributed volume highlights two areas of fundamental interest in high-performance computing: core algorithms for important kernels and computationally demanding applications. The first few chapters explore algorithms, numerical techniques, and their parallel formulations for a variety of kernels that arise in applications. The rest of the volume focuses on state-of-the-art applications from diverse domains. By structuring the volume around these two areas, it presents a comprehensive view of the application landscape for high-performance computing, while also enabling readers to develop new applications using the kernels. Readers will learn how to choose the most suitable parallel algorithms for any given application, ensuring that theory and practicality are clearly connected. Applications using these techniques are illustrated in detail, including:Computational materials science and engineeringComputational cardiovascular analysisMultiscale analysis of wind turbines and turbomachineryWeather forecastingMachine learning techniquesParallel Algorithms in Computational Science and Engineering will be an ideal reference for applied mathematicians, engineers, computer scientists, and other researchers who utilize high-performance computing in their work.
Parallel Computers 2: Architecture, Programming and Algorithms
by R.W Hockney C.R JesshopeSince the publication of the first edition, parallel computing technology has gained considerable momentum. A large proportion of this has come from the improvement in VLSI techniques, offering one to two orders of magnitude more devices than previously possible. A second contributing factor in the fast development of the subject is commercialization. The supercomputer is no longer restricted to a few well-established research institutions and large companies. A new computer breed combining the architectural advantages of the supercomputer with the advance of VLSI technology is now available at very attractive prices. A pioneering device in this development is the transputer, a VLSI processor specifically designed to operate in large concurrent systems. Parallel Computers 2: Architecture, Programming and Algorithms reflects the shift in emphasis of parallel computing and tracks the development of supercomputers in the years since the first edition was published. It looks at large-scale parallelism as found in transputer ensembles. This extensively rewritten second edition includes major new sections on the transputer and the OCCAM language. The book contains specific information on the various types of machines available, details of computer architecture and technologies, and descriptions of programming languages and algorithms. Aimed at an advanced undergraduate and postgraduate level, this handbook is also useful for research workers, machine designers, and programmers concerned with parallel computers. In addition, it will serve as a guide for potential parallel computer users, especially in disciplines where large amounts of computer time are regularly used.
Parallel Computing: Methods, Algorithms and Applications
by David J Evans; C SuttiParallel Computing: Methods, Algorithms and Applications presents a collection of original papers presented at the international meeting on parallel processing, methods, algorithms, and applications at Verona, Italy in September 1989.
Parallel Computing Technologies: 17th International Conference, PaCT 2023, Astana, Kazakhstan, August 21–25, 2023, Proceedings (Lecture Notes in Computer Science #14098)
by Victor MalyshkinThis book constitutes the refereed proceedings of the 17th International Conference on Parallel Computing Technologies, PaCT 2023, held in Astana, Kazakhstan, during August 21-25, 2023. The 15 full papers included in this book were carefully reviewed and selected from 23 submissions. They were organized in topical sections as follows: automatic programming and program tuning; frameworks and services; algorithms; and distributed systems management.
Parallel Curriculum Units for Mathematics, Grades 6–12
by Dr Jann H. Leppien Dr Jeanne H. PurcellMaximize your mathematics curriculum to challenge all students This collection of lessons from experienced teachers provides multifaceted examples of rigorous learning opportunities for mathematics students in Grades 6–12. The four sample units focus on fractions, linear programming, geometry, and quadratic relationships. The authors provide user-friendly methods for instruction and demonstrate how to differentiate the lessons for the benefit of all students. Included are standards-based strategies that guide students through: Understanding secondary mathematics concepts Discovering connections between mathematics and other subjects Developing critical thinking skills Connecting mathematics learning to society through the study of real-world data, proportional reasoning, and problem solving
Parallel Finite Volume Computation on General Meshes
by Yuri Vassilevski Kirill Terekhov Kirill Nikitin Ivan KapyrinThis book presents a systematic methodology for the development of parallel multi-physics models and its implementation in geophysical and biomedical applications. The methodology includes conservative discretization methods for partial differential equations on general meshes, as well as data structures and algorithms for organizing parallel simulations on general meshes. The structures and algorithms form the core of the INMOST (Integrated Numerical Modelling Object-oriented Supercomputing Technologies) platform for the development of parallel models on general meshes. The authors consider applications for addressing specific geophysical and biomedical challenges, including radioactive contaminant propagation with subsurface waters, reservoir simulation, and clot formation in blood flows. The book gathers all the components of this methodology, from algorithms and numerical methods to the open-source software, as well as examples of practical applications, in a single source, making it a valuable asset for applied mathematicians, computer scientists, and engineers alike.
Parallel-in-Time Integration Methods: 9th Parallel-in-Time Workshop, June 8–12, 2020 (Springer Proceedings in Mathematics & Statistics #356)
by Benjamin Ong Jacob Schroder Jemma Shipton Stephanie FriedhoffThis volume includes contributions from the 9th Parallel-in-Time (PinT) workshop, an annual gathering devoted to the field of time-parallel methods, aiming to adapt existing computer models to next-generation machines by adding a new dimension of scalability. As the latest supercomputers advance in microprocessing ability, they require new mathematical algorithms in order to fully realize their potential for complex systems. The use of parallel-in-time methods will provide dramatically faster simulations in many important areas, including biomedical (e.g., heart modeling), computational fluid dynamics (e.g., aerodynamics and weather prediction), and machine learning applications. Computational and applied mathematics is crucial to this progress, as it requires advanced methodologies from the theory of partial differential equations in a functional analytic setting, numerical discretization and integration, convergence analyses of iterative methods, and the development and implementation of new parallel algorithms. Therefore, the workshop seeks to bring together an interdisciplinary group of experts across these fields to disseminate cutting-edge research and facilitate discussions on parallel time integration methods.
Parallel Problem Solving from Nature – PPSN XV: 15th International Conference, Coimbra, Portugal, September 8–12, 2018, Proceedings, Part I (Lecture Notes in Computer Science #11101)
by Anne Auger Carlos M. Fonseca Nuno Lourenço Penousal Machado Luís Paquete Darrell WhitleyThis two-volume set LNCS 11101 and 11102 constitutes the refereed proceedings of the 15th International Conference on Parallel Problem Solving from Nature, PPSN 2018, held in Coimbra, Portugal, in September 2018. The 79 revised full papers were carefully reviewed and selected from 205 submissions. The papers cover a wide range of topics in natural computing including evolutionary computation, artificial neural networks, artificial life, swarm intelligence, artificial immune systems, self-organizing systems, emergent behavior, molecular computing, evolutionary robotics, evolvable hardware, parallel implementations and applications to real-world problems. The papers are organized in the following topical sections: numerical optimization; combinatorial optimization; genetic programming; multi-objective optimization; parallel and distributed frameworks; runtime analysis and approximation results; fitness landscape modeling and analysis; algorithm configuration, selection, and benchmarking; machine learning and evolutionary algorithms; and applications. Also included are the descriptions of 23 tutorials and 6 workshops which took place in the framework of PPSN XV.
Parallel Problem Solving from Nature – PPSN XV: 15th International Conference, Coimbra, Portugal, September 8–12, 2018, Proceedings, Part II (Lecture Notes in Computer Science #11102)
by Anne Auger Carlos M. Fonseca Nuno Lourenço Penousal Machado Luís Paquete Darrell WhitleyThis two-volume set LNCS 11101 and 11102 constitutes the refereed proceedings of the 15th International Conference on Parallel Problem Solving from Nature, PPSN 2018, held in Coimbra, Portugal, in September 2018. The 79 revised full papers were carefully reviewed and selected from 205 submissions. The papers cover a wide range of topics in natural computing including evolutionary computation, artificial neural networks, artificial life, swarm intelligence, artificial immune systems, self-organizing systems, emergent behavior, molecular computing, evolutionary robotics, evolvable hardware, parallel implementations and applications to real-world problems. The papers are organized in the following topical sections: numerical optimization; combinatorial optimization; genetic programming; multi-objective optimization; parallel and distributed frameworks; runtime analysis and approximation results; fitness landscape modeling and analysis; algorithm configuration, selection, and benchmarking; machine learning and evolutionary algorithms; and applications. Also included are the descriptions of 23 tutorials and 6 workshops which took place in the framework of PPSN XV.
Parallel Problem Solving from Nature – PPSN XVI: 16th International Conference, PPSN 2020, Leiden, The Netherlands, September 5-9, 2020, Proceedings, Part II (Lecture Notes in Computer Science #12270)
by Thomas Bäck Mike Preuss André Deutz Hao Wang Carola Doerr Michael Emmerich Heike TrautmannThis two-volume set LNCS 12269 and LNCS 12270 constitutes the refereed proceedings of the 16th International Conference on Parallel Problem Solving from Nature, PPSN 2020, held in Leiden, The Netherlands, in September 2020. The 99 revised full papers were carefully reviewed and selected from 268 submissions. The topics cover classical subjects such as automated algorithm selection and configuration; Bayesian- and surrogate-assisted optimization; benchmarking and performance measures; combinatorial optimization; connection between nature-inspired optimization and artificial intelligence; genetic and evolutionary algorithms; genetic programming; landscape analysis; multiobjective optimization; real-world applications; reinforcement learning; and theoretical aspects of nature-inspired optimization.
Parallel Problem Solving from Nature – PPSN XVI: 16th International Conference, PPSN 2020, Leiden, The Netherlands, September 5-9, 2020, Proceedings, Part I (Lecture Notes in Computer Science #12269)
by Thomas Bäck Mike Preuss André Deutz Hao Wang Carola Doerr Michael Emmerich Heike TrautmannThis two-volume set LNCS 12269 and LNCS 12270 constitutes the refereed proceedings of the 16th International Conference on Parallel Problem Solving from Nature, PPSN 2020, held in Leiden, The Netherlands, in September 2020. The 99 revised full papers were carefully reviewed and selected from 268 submissions. The topics cover classical subjects such as automated algorithm selection and configuration; Bayesian- and surrogate-assisted optimization; benchmarking and performance measures; combinatorial optimization; connection between nature-inspired optimization and artificial intelligence; genetic and evolutionary algorithms; genetic programming; landscape analysis; multiobjective optimization; real-world applications; reinforcement learning; and theoretical aspects of nature-inspired optimization.
Parallel Processing and Applied Mathematics: 4th International Conference, Ppam 2001, Naleczow, Poland, September 9-12, 2001, Revised Papers (Lecture Notes in Computer Science #2328)
by Konrad Karczewski Ewa Deelman Jack Dongarra Roman WyrzykowskiThe two-volume set LNCS 10777 and 10778 constitutes revised selected papers from the 12th International Conference on Parallel Processing and Applied Mathematics, PPAM 2017, held in Lublin, Poland, in September 2017.The 49 regular papers presented in this volume were selected from 98 submissions. For the workshops and special sessions, that were held as integral parts of the PPAM 2017 conference, a total of 51 papers was accepted from 75 submissions. The papers were organized in topical sections named as follows:Part I: numerical algorithms and parallel scientific computing; particle methods in simulations; task-based paradigm of parallel computing; GPU computing; parallel non-numerical algorithms; performance evaluation of parallel algorithms and applications; environments and frameworks for parallel/distributed/cloud computing; applications of parallel computing; soft computing with applications; and special session on parallel matrix factorizations. Part II: workshop on models, algorithms and methodologies for hybrid parallelism in new HPC systems; workshop power and energy aspects of computations (PEAC 2017); workshop on scheduling for parallel computing (SPC 2017); workshop on language-based parallel programming models (WLPP 2017); workshop on PGAS programming; minisymposium on HPC applications in physical sciences; minisymposium on high performance computing interval methods; workshop on complex collective systems.
Parallel Processing and Applied Mathematics
by Kazimierz Wiatr Jacek Kitowski Konrad Karczewski Jack Dongarra Ewa Deelman Roman WyrzykowskiThis two-volume set LNCS 9573 and LNCS 9574 constitutes the refereed proceedings of the 11th International Conference of Parallel Processing and Applied Mathematics, PPAM 2015, held in Krakow, Poland, in September 2015. The 111 revised full papers presented in both volumes were carefully reviewed and selected from 196 submissions. The focus of PPAM 2015 was on models, algorithms, and software tools which facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications, including big data problems.