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Experimental Computation with Oscillatory Integrals

Experimental Computation with Oscillatory Integrals
Author:
Publisher:
Total Pages: 11
Release: 2009
Genre:
ISBN:

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A previous study by one of the present authors, together with D. Borwein and I. Leonard [8], studied the asymptotic behavior of the p-norm of the sinc function: sinc(x) = (sin x)/x and along the way looked at closed forms for integer values of p. In this study we address these integrals with the tools of experimental mathematics, namely by computing their numerical values to high precision, both as a challenge in itself, and also in an attempt to recognize the numerical values as closed-form constants. With this approach, we are able to reproduce several of the results of [8] and to find new results, both numeric and analytic, that go beyond the previous study.


Gems in Experimental Mathematics

Gems in Experimental Mathematics
Author: Tewodros Amdeberhan
Publisher: American Mathematical Soc.
Total Pages: 426
Release: 2010
Genre: Mathematics
ISBN: 0821848690

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These proceedings reflect the special session on Experimental Mathematics held January 5, 2009, at the Joint Mathematics Meetings in Washington, DC as well as some papers specially solicited for this volume. Experimental Mathematics is a recently structured field of Mathematics that uses the computer and advanced computing technology as a tool to perform experiments. These include the analysis of examples, testing of new ideas, and the search of patterns to suggest results and to complement existing analytical rigor. The development of a broad spectrum of mathematical software products, such as MathematicaR and MapleTM, has allowed mathematicians of diverse backgrounds and interests to use the computer as an essential tool as part of their daily work environment. This volume reflects a wide range of topics related to the young field of Experimental Mathematics. The use of computation varies from aiming to exclude human input in the solution of a problem to traditional mathematical questions for which computation is a prominent tool.


Experimental and Computational Mathematics

Experimental and Computational Mathematics
Author: Jonathan M. Borwein
Publisher: PSIpress
Total Pages: 309
Release: 2010
Genre: Mathematics
ISBN: 193563805X

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A quiet revolution in mathematical computing and scientific visualization took place in the latter half of the 20th century. These developments have dramatically enhanced modes of mathematical insight and opportunities for "exploratory" computational experimentation. This volume collects the experimental and computational contributions of Jonathan and Peter Borwein over the past quarter century.


Computing Highly Oscillatory Integrals

Computing Highly Oscillatory Integrals
Author: Alfredo Deano
Publisher: SIAM
Total Pages: 207
Release: 2018-01-01
Genre: Mathematics
ISBN: 1611975123

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Highly oscillatory phenomena range across numerous areas in science and engineering and their computation represents a difficult challenge. A case in point is integrals of rapidly oscillating functions in one or more variables. The quadrature of such integrals has been historically considered very demanding. Research in the past 15 years (in which the authors played a major role) resulted in a range of very effective and affordable algorithms for highly oscillatory quadrature. This is the only monograph bringing together the new body of ideas in this area in its entirety. The starting point is that approximations need to be analyzed using asymptotic methods rather than by more standard polynomial expansions. As often happens in computational mathematics, once a phenomenon is understood from a mathematical standpoint, effective algorithms follow. As reviewed in this monograph, we now have at our disposal a number of very effective quadrature methods for highly oscillatory integrals--Filon-type and Levin-type methods, methods based on steepest descent, and complex-valued Gaussian quadrature. Their understanding calls for a fairly varied mathematical toolbox--from classical numerical analysis, approximation theory, and theory of orthogonal polynomials all the way to asymptotic analysis--yet this understanding is the cornerstone of efficient algorithms.


Oscillation Theory, Computation, and Methods of Compensated Compactness

Oscillation Theory, Computation, and Methods of Compensated Compactness
Author: C. Dafermos
Publisher: Springer Science & Business Media
Total Pages: 402
Release: 2012-12-06
Genre: Science
ISBN: 1461386896

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This IMA Volume in Mathematics and its Applications Oscillation Theory, Computation, and Methods of Compensated Compactness represents the proceedings of a workshop which was an integral part of the 1984-85 IMA program on CONTINUUM PHYSICS AND PARTIAL DIFFERENTIAL EQUATIONS. We are grateful to the Scientific Committee: J.L. Ericksen D. Kinderlehrer H. Brezis C. Dafermos for their dedication and hard work in developing an imaginative, stimulating, and productive year-long program. George R. Sell Hans Weinberger PREFACE Historically, one of the most important prohlems in continuum mechanics has been the treatment of nonlinear hyperbolic systems of conservation laws. Thp. importance of these systems lies in the fact that the underlyinq equ~tions of mass, momentum, and energy are descrihed by conservation laws. Their nonlinearity and hyperbolicity are consequences of some cornmon constitutive relations, for example, in an ideal gas. The I.M.A. Workshop on "Osci 11 at i on theory. computat i on, and methods of com pensated compactness" brought together scientists from both the analytical and numerical sides of conservation law research. The goal was to examine recent trends in the investigation of systems of conservation laws and in particular to focus on the roles of dispersive and diffusive limits for singularily perturbed conservation laws. Special attention was devoted to the new ideas of compen sated compactness and oscillation theory.


Discovering Biomolecular Mechanisms with Computational Biology

Discovering Biomolecular Mechanisms with Computational Biology
Author: Frank Eisenhaber
Publisher: Springer Science & Business Media
Total Pages: 152
Release: 2007-03-20
Genre: Science
ISBN: 0387367470

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This anthology presents critical reviews of methods and high-impact applications in computational biology that lead to results that non-bioinformaticians must also know to design efficient experimental research plans. Discovering Biomolecular Mechanisms with Computational Biology explores the methodology of translating sequence strings into biological knowledge and considers exemplary groundbreaking results such as unexpected enzyme discoveries. This book also summarizes non-trivial theoretical predictions for regulatory and metabolic networks that have received experimental confirmation.


Computational Science – ICCS 2020

Computational Science – ICCS 2020
Author: Valeria V. Krzhizhanovskaya
Publisher: Springer Nature
Total Pages: 715
Release: 2020-06-18
Genre: Computers
ISBN: 3030504174

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The seven-volume set LNCS 12137, 12138, 12139, 12140, 12141, 12142, and 12143 constitutes the proceedings of the 20th International Conference on Computational Science, ICCS 2020, held in Amsterdam, The Netherlands, in June 2020.* The total of 101 papers and 248 workshop papers presented in this book set were carefully reviewed and selected from 719 submissions (230 submissions to the main track and 489 submissions to the workshops). The papers were organized in topical sections named: Part I: ICCS Main Track Part II: ICCS Main Track Part III: Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Agent-Based Simulations, Adaptive Algorithms and Solvers; Applications of Computational Methods in Artificial Intelligence and Machine Learning; Biomedical and Bioinformatics Challenges for Computer Science Part IV: Classifier Learning from Difficult Data; Complex Social Systems through the Lens of Computational Science; Computational Health; Computational Methods for Emerging Problems in (Dis-)Information Analysis Part V: Computational Optimization, Modelling and Simulation; Computational Science in IoT and Smart Systems; Computer Graphics, Image Processing and Artificial Intelligence Part VI: Data Driven Computational Sciences; Machine Learning and Data Assimilation for Dynamical Systems; Meshfree Methods in Computational Sciences; Multiscale Modelling and Simulation; Quantum Computing Workshop Part VII: Simulations of Flow and Transport: Modeling, Algorithms and Computation; Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Software Engineering for Computational Science; Solving Problems with Uncertainties; Teaching Computational Science; UNcErtainty QUantIficatiOn for ComputationAl modeLs *The conference was canceled due to the COVID-19 pandemic.


Scientific and Technical Aerospace Reports

Scientific and Technical Aerospace Reports
Author:
Publisher:
Total Pages: 652
Release: 1994
Genre: Aeronautics
ISBN:

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Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.


Fundamentals of Seismic Wave Propagation

Fundamentals of Seismic Wave Propagation
Author: Chris Chapman
Publisher: Cambridge University Press
Total Pages: 646
Release: 2004-07-29
Genre: Science
ISBN: 9781139451635

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Fundamentals of Seismic Wave Propagation, published in 2004, presents a comprehensive introduction to the propagation of high-frequency body-waves in elastodynamics. The theory of seismic wave propagation in acoustic, elastic and anisotropic media is developed to allow seismic waves to be modelled in complex, realistic three-dimensional Earth models. This book provides a consistent and thorough development of modelling methods widely used in elastic wave propagation ranging from the whole Earth, through regional and crustal seismology, exploration seismics to borehole seismics, sonics and ultrasonics. Particular emphasis is placed on developing a consistent notation and approach throughout, which highlights similarities and allows more complicated methods and extensions to be developed without difficulty. This book is intended as a text for graduate courses in theoretical seismology, and as a reference for all academic and industrial seismologists using numerical modelling methods. Exercises and suggestions for further reading are included in each chapter.