Mathematical Aesthetic Principles Nonintegrable Systems

Author : Murray Muraskin
Publisher : World Scientific
Page : 232 pages
File Size : 41,7 Mb
Release : 1995-05-09
Category : Science
ISBN : 9789814500692

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Mathematical Aesthetic Principles/nonintegrable Systems by Murray Muraskin Pdf

Mathematical aesthetics is not discussed as a separate discipline in other books than this, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as “aesthetic” and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, i.e. the results of integration depend on the integration path. The topic of nonintegrable systems has not been given much attention in other books. Hence we discuss techniques for dealing with such systems.

Author : Murray Muraskin
Publisher : World Scientific
Page : 236 pages
File Size : 49,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9810222009

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Mathematical Aesthetic Principles/nonintegrable Systems by Murray Muraskin Pdf

Mathematical aesthetics is not discussed as a separate discipline in other books than this, even though it is reasonable to suppose that the foundations of physics lie in mathematical aesthetics. This book presents a list of mathematical principles that can be classified as ?aesthetic? and shows that these principles can be cast into a nonlinear set of equations. Then, with this minimal input, the book shows that one can obtain lattice solutions, soliton systems, closed strings, instantons and chaotic-looking systems as well as multi-wave-packet solutions as output. These solutions have the common feature of being nonintegrable, i.e. the results of integration depend on the integration path. The topic of nonintegrable systems has not been given much attention in other books. Hence we discuss techniques for dealing with such systems.

Author : Ravi P. Agarwal
Publisher : World Scientific
Page : 720 pages
File Size : 40,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9810223838

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Dynamical Systems and Applications by Ravi P. Agarwal Pdf

World Scientific series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. For the past twenty five years, there has been an explosion of interest in the study of nonlinear dynamical systems. Mathematical techniques developed during this period have been applied to important nonlinear problems ranging from physics and chemistry to ecology and economics. All these developments have made dynamical systems theory an important and attractive branch of mathematics to scientists in many disciplines. This rich mathematical subject has been partially represented in this collection of 45 papers by some of the leading researchers in the area. This volume contains 45 state-of-art articles on the mathematical theory of dynamical systems by leading researchers. It is hoped that this collection will lead new direction in this field.Contributors: B Abraham-Shrauner, V Afraimovich, N U Ahmed, B Aulbach, E J Avila-Vales, F Battelli, J M Blazquez, L Block, T A Burton, R S Cantrell, C Y Chan, P Collet, R Cushman, M Denker, F N Diacu, Y H Ding, N S A El-Sharif, J E Fornaess, M Frankel, R Galeeva, A Galves, V Gershkovich, M Girardi, L Gotusso, J Graczyk, Y Hino, I Hoveijn, V Hutson, P B Kahn, J Kato, J Keesling, S Keras, V Kolmanovskii, N V Minh, V Mioc, K Mischaikow, M Misiurewicz, J W Mooney, M E Muldoon, S Murakami, M Muraskin, A D Myshkis, F Neuman, J C Newby, Y Nishiura, Z Nitecki, M Ohta, G Osipenko, N Ozalp, M Pollicott, Min Qu, Donal O-Regan, E Romanenko, V Roytburd, L Shaikhet, J Shidawara, N Sibony, W-H Steeb, C Stoica, G Swiatek, T Takaishi, N D Thai Son, R Triggiani, A E Tuma, E H Twizell, M Urbanski; T D Van, A Vanderbauwhede, A Veneziani, G Vickers, X Xiang, T Young, Y Zarmi.

Author : H. Pierre Noyes,J. C. van den Berg
Publisher : World Scientific
Page : 1312 pages
File Size : 52,7 Mb
Release : 2001
Category : Science
ISBN : 9812810099

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Bit-string Physics by H. Pierre Noyes,J. C. van den Berg Pdf

We could be on the threshold of a scientific revolution. Quantum mechanics is based on unique, finite, and discrete events. General relativity assumes a continuous, curved space-time. Reconciling the two remains the most fundamental unsolved scientific problem left over from the last century. The papers of H Pierre Noyes collected in this volume reflect one attempt to achieve that unification by replacing the continuum with the bit-string events of computer science. Three principles are used: physics can determine whether two quantities are the same or different; measurement can tell something from nothing; this structure (modeled by binary addition and multiplication) can leave a historical record consisting of a growing universe of bit-strings. This book is specifically addressed to those interested in the foundations of particle physics, relativity, quantum mechanics, physical cosmology and the philosophy of science. Contents: Non-Locality in Particle Physics; On the Physical Interpretation and the Mathematical Structure of the Combinatorial Hierarchy (with T Bastin, J Amson & C W Kilmister); On the Construction of Relativistic Quantum Theory: A Progress Report; Foundations of a Discrete Physics (with D McGoveran); Comment on OC Statistical Mechanical Origin of the Entropy of a Rotating Charged Black HoleOCO Anti-Gravity: The Key to 21st Century Physics; Crossing Symmetry is Incompatible with General Relativity; Operationalism Revisited: Measurement Accuracy, Scale Invariance and the Combinatorial Hierarchy; Discrete Physics and the Derivation of Electromagnetism from the Formalism of Quantum Mechanics (with L H Kauffman); Are Partons Confined Tachyons?; A Short Introduction to Bit-String Physics; Process, System, Causality and Quantum Mechanics: A Psychoanalysis of Animal Faith (with T Etter); and other papers. Readership: Researchers interested in the foundations of particle physics, relativity, quantum mechanics, physical cosmology and the philosophy of science."

Author : Ulianov Montano
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 44,9 Mb
Release : 2013-12-20
Category : Philosophy
ISBN : 9783319034522

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Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics by Ulianov Montano Pdf

This book develops a naturalistic aesthetic theory that accounts for aesthetic phenomena in mathematics in the same terms as it accounts for more traditional aesthetic phenomena. Building upon a view advanced by James McAllister, the assertion is that beauty in science does not confine itself to anecdotes or personal idiosyncrasies, but rather that it had played a role in shaping the development of science. Mathematicians often evaluate certain pieces of mathematics using words like beautiful, elegant, or even ugly. Such evaluations are prevalent, however, rigorous investigation of them, of mathematical beauty, is much less common. The volume integrates the basic elements of aesthetics, as it has been developed over the last 200 years, with recent findings in neuropsychology as well as a good knowledge of mathematics. The volume begins with a discussion of the reasons to interpret mathematical beauty in a literal or non-literal fashion, which also serves to survey historical and contemporary approaches to mathematical beauty. The author concludes that literal approaches are much more coherent and fruitful, however, much is yet to be done. In this respect two chapters are devoted to the revision and improvement of McAllister’s theory of the role of beauty in science. These antecedents are used as a foundation to formulate a naturalistic aesthetic theory. The central idea of the theory is that aesthetic phenomena should be seen as constituting a complex dynamical system which the author calls the aesthetic as process theory. The theory comprises explications of three central topics: aesthetic experience (in mathematics), aesthetic value and aesthetic judgment. The theory is applied in the final part of the volume and is used to account for the three most salient and often used aesthetic terms often used in mathematics: beautiful, elegant and ugly. This application of the theory serves to illustrate the theory in action, but also to further discuss and develop some details and to showcase the theory’s explanatory capabilities.

Author : Anonim
Publisher : Unknown
Page : 672 pages
File Size : 52,7 Mb
Release : 1995
Category : Physics
ISBN : UCSD:31822020189544

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Physics Essays by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 858 pages
File Size : 55,6 Mb
Release : 1993
Category : Mathematics
ISBN : CORNELL:31924074856976

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International Mathematical News by Anonim Pdf

Author : New York Public Library Staff
Publisher : Macmillan Reference USA
Page : 684 pages
File Size : 41,5 Mb
Release : 1996-07
Category : Reference
ISBN : 0783813201

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Bibliographic Guide to East Asian Studies by New York Public Library Staff Pdf

An aid for reseaching non-western cultures, the Bibliographic Guide to East Asian Studies covers Japan, China, North and South Korea, Honk Kong, and Taiwan, with approximately 3,500 listings from LC MARC tapes and the Oriental Division of The New York Public Library. It includes publications about East Asia; materials published in any of the relevant countries; and publications in the Chinese, Japanese and Korean languages. Listings are transcribed into Anglicised characters. Each entry provides complete bibliographic information, along with the NYPL and/or LC call numbers.

Author : Anonim
Publisher : Unknown
Page : 486 pages
File Size : 44,7 Mb
Release : 1999
Category : Electronic
ISBN : NASA:31769000473689

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NASA Breakthrough Propulsion Physics Workshop Proceedings by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 2432 pages
File Size : 46,6 Mb
Release : 1991
Category : American literature
ISBN : STANFORD:36105022609999

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Books in Print by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 1328 pages
File Size : 51,6 Mb
Release : 1996
Category : American literature
ISBN : UOM:39015079622430

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American Book Publishing Record by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 2230 pages
File Size : 50,9 Mb
Release : 1996
Category : American literature
ISBN : UOM:39015058373740

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The Cumulative Book Index by Anonim Pdf

A world list of books in the English language.

Author : Anonim
Publisher : Unknown
Page : 1194 pages
File Size : 46,8 Mb
Release : 1996
Category : Mathematics
ISBN : UOM:39015051367442

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Mathematical Reviews by Anonim Pdf

Author : Ed Bowker Staff,Staff Bowker, Ed
Publisher : R. R. Bowker
Page : 3274 pages
File Size : 49,6 Mb
Release : 2004
Category : Reference
ISBN : 0835246426

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Books In Print 2004-2005 by Ed Bowker Staff,Staff Bowker, Ed Pdf

Author : Ivar Ekeland
Publisher : Springer Science & Business Media
Page : 258 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642743313

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Convexity Methods in Hamiltonian Mechanics by Ivar Ekeland Pdf

In the case of completely integrable systems, periodic solutions are found by inspection. For nonintegrable systems, such as the three-body problem in celestial mechanics, they are found by perturbation theory: there is a small parameter € in the problem, the mass of the perturbing body for instance, and for € = 0 the system becomes completely integrable. One then tries to show that its periodic solutions will subsist for € -# 0 small enough. Poincare also introduced global methods, relying on the topological properties of the flow, and the fact that it preserves the 2-form L~=l dPi 1\ dqi' The most celebrated result he obtained in this direction is his last geometric theorem, which states that an area-preserving map of the annulus which rotates the inner circle and the outer circle in opposite directions must have two fixed points. And now another ancient theme appear: the least action principle. It states that the periodic solutions of a Hamiltonian system are extremals of a suitable integral over closed curves. In other words, the problem is variational. This fact was known to Fermat, and Maupertuis put it in the Hamiltonian formalism. In spite of its great aesthetic appeal, the least action principle has had little impact in Hamiltonian mechanics. There is, of course, one exception, Emmy Noether's theorem, which relates integrals ofthe motion to symmetries of the equations. But until recently, no periodic solution had ever been found by variational methods.