Download or read book Experimental Computation with Oscillatory Integrals written by and published by . This book was released on 2009 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Gems in Experimental Mathematics written by Tewodros Amdeberhan and published by American Mathematical Soc.. This book was released on 2010 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Experimental and Computational Mathematics written by Jonathan M. Borwein and published by PSIpress. This book was released on 2010 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Computing Highly Oscillatory Integrals written by Alfredo Deano and published by SIAM. This book was released on 2018-01-01 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Extrapolation Experiments with a Class of Infinite Oscillatory Integrals written by U. T. Ehrenmark and published by . This book was released on 1988 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Oscillation Theory Computation and Methods of Compensated Compactness written by C. Dafermos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Discovering Biomolecular Mechanisms with Computational Biology written by Frank Eisenhaber and published by Springer Science & Business Media. This book was released on 2007-03-20 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Mathematical Tables and Other Aids to Computation written by and published by . This book was released on 1955 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Results in Numerical and Experimental Fluid Mechanics VI written by Cameron Tropea and published by Springer Science & Business Media. This book was released on 2007-10-26 with total page 973 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features the contributions to the 15th Symposium of the STAB (German Aerospace Aerodynamics Association). Papers provide a broad overview of ongoing work in Germany, including high aspect ratio wings, low aspect ratio wings, bluff bodies, laminar flow control and transition, active flow control, hypersonic flows, aeroelasticity, aeroacoustics, mathematical fundamentals, numerical simulations, physical fundamentals, and facilities.
Download or read book Computational Techniques And Applications Ctac 97 Proceedings Of The Eight Biennial Conference written by John Noye and published by World Scientific. This book was released on 1998-08-08 with total page 818 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume contains three invited papers and 93 contributed papers. The topics covered range from studies of theoretical aspects of computational methods to simulation of industrial processes, with an emphasis on the efficient use of computers to solve practical problems. Developers and users of computational techniques who wish to keep up with recent developments in the application of modern computational technology to problems in science and engineering will have much interest in this volume.
Download or read book Mathematical Modeling and Computational Science written by Gheorghe Adam and published by Springer Science & Business Media. This book was released on 2012-02-17 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed post-proceedings of the International Conference on Mathematical Modeling and Computational Physics, MMCP 2011, held in Stará Lesná, Slovakia, in July 2011. The 41 revised papers presented were carefully reviewed and selected from numerous submissions. They are organized in topical sections on mathematical modeling and methods, numerical modeling and methods, computational support of the experiments, computing tools, and optimization and simulation.
Download or read book Contemporary Computational Mathematics A Celebration of the 80th Birthday of Ian Sloan written by Josef Dick and published by Springer. This book was released on 2018-05-23 with total page 1330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.
Download or read book Integral Transforms and Operational Calculus written by H. M. Srivastava and published by MDPI. This book was released on 2019-11-20 with total page 510 pages. Available in PDF, EPUB and Kindle. Book excerpt: Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably wide-spread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. This Special Issue contains a total of 36 carefully-selected and peer-reviewed articles which are authored by established researchers from many countries. Included in this Special Issue are review, expository and original research articles dealing with the recent advances on the topics of integral transforms and operational calculus as well as their multidisciplinary applications
Download or read book Progress in Underwater Acoustics written by Harold Merklinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: IMAGE TRACKS AT HALIFAX by L.B. Felsen All living kind much effort spend Some model modes, some model rays, To cope with their environment Some feel that spectra all portrays. Some use their eyes, some use their nose Then there are those who with despatch, To sense where other things repose. Take refuge in the ocean wedge. For one group, nothing's more profound Than to explore the world with sound. If things get messy, randomize. These audio diagnosticians What's partly smooth, determinize. You ponder, is it this or that? Go by the name of acousticians. And wish you were a lowly bat They regularly meet to check Whether their sonogram's on track. The meeting's hosts did treat us well. With images stored in their packs, They let the climate cast its spell. This year they came to Halifax. No weath'ry hope was placed in vain. There they combined with ocean types We were exposed to wind and rain, And each could hear the other's gripes. We glimpsed blue sky through clouds dispersed. A meeting naturally does start But rainy sequence was reversed: Reviewing present state of art. The ocean types would like it wet What we found out is where it's at: Yet they got stuck with sun instead. We cannot hope to match the bat Each confrence has the same refrain: Computer printouts by the reams It has been fun to meet again.
Download or read book Highly Oscillatory Problems written by Bjorn Engquist and published by Cambridge University Press. This book was released on 2009-07-02 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Review papers from experts in areas of active research into highly oscillatory problems, with an emphasis on computation.
Download or read book Recent Trends in Theory of Physical Phenomena in High Magnetic Fields written by Israel D. Vagner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive collection of papers on theoretical aspects of electronic processes in simple and synthetic metals, superconductors, bulk and low-dimensional semiconductors under extreme conditions, such as high magnetic and electric fields, low and ultra-low temperatures. The main emphasis is on low-dimensional conductors and superconductors, where correlated electrons, interacting with magnetic or nonmagnetic impurities, phonons, photons, or nuclear spins, result in a variety of new physical phenomena, such as quantum oscillations in the superconducting state, Condon instability, Skyrmions and composite fermions in quantum Hall effect systems, and hyperfine field-induced mesoscopic and nanoscopic phenomena. Several new experimental achievements are reported that promise to delineate future trends in low temperature and high magnetic field physics, including the experimental observation of the interplay between superconductivity and nuclear spin ordering at ultra-low temperatures, new observations of Condon domains in normal metals, and an experimental proposal for the realisation of isotopically engineered, semiconductor-based spin-qubit elements for future quantum computation and communication technology.
