Mathematical Aesthetic Principles Nonintegrable Systems

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Mathematical Aesthetic Principles/nonintegrable Systems

Author : Murray Muraskin
Publisher : World Scientific
ISBN 13 : 9814500690
Total Pages : 232 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Mathematical Aesthetic Principles/nonintegrable Systems by : Murray Muraskin

Download or read book Mathematical Aesthetic Principles/nonintegrable Systems written by Murray Muraskin and published by World Scientific. This book was released on 1995-05-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Aesthetic Principles/nonintegrable Systems

Author : Murray Muraskin
Publisher : World Scientific
ISBN 13 : 9789810222000
Total Pages : 236 pages
Book Rating : 4.2/5 (22 download)

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Book Synopsis Mathematical Aesthetic Principles/nonintegrable Systems by : Murray Muraskin

Download or read book Mathematical Aesthetic Principles/nonintegrable Systems written by Murray Muraskin and published by World Scientific. This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Dynamical Systems and Applications

Author : Ravi P. Agarwal
Publisher : World Scientific
ISBN 13 : 9789810223830
Total Pages : 720 pages
Book Rating : 4.2/5 (238 download)

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Book Synopsis Dynamical Systems and Applications by : Ravi P. Agarwal

Download or read book Dynamical Systems and Applications written by Ravi P. Agarwal and published by World Scientific. This book was released on 1995 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Bit-string Physics

Author : H. Pierre Noyes
Publisher : World Scientific
ISBN 13 : 9789812810090
Total Pages : 1312 pages
Book Rating : 4.8/5 (1 download)

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Book Synopsis Bit-string Physics by : H. Pierre Noyes

Download or read book Bit-string Physics written by H. Pierre Noyes and published by World Scientific. This book was released on 2001 with total page 1312 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics

Author : Ulianov Montano
Publisher : Springer Science & Business Media
ISBN 13 : 3319034529
Total Pages : 224 pages
Book Rating : 4.3/5 (19 download)

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

Download or read book Explaining Beauty in Mathematics: An Aesthetic Theory of Mathematics written by Ulianov Montano and published by Springer Science & Business Media. This book was released on 2013-12-20 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gravitation and Cosmology: From the Hubble Radius to the Planck Scale

Author : Richard L. Amoroso
Publisher : Springer Science & Business Media
ISBN 13 : 1402008856
Total Pages : 556 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Gravitation and Cosmology: From the Hubble Radius to the Planck Scale by : Richard L. Amoroso

Download or read book Gravitation and Cosmology: From the Hubble Radius to the Planck Scale written by Richard L. Amoroso and published by Springer Science & Business Media. This book was released on 2002-10-31 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jean-Pierre Vigier continually labeled one of les heretiques de la science, l’eternel resistant et le patriarche is yet a pillar of modern physics and mathematics, with one leg firmly planted in theory and the other in empiricism spanning a career of nearly 60 years with a publication vitae quickly approaching 400! He wrote of his mentor Louis de Broglie “Great physicists fight great battles”, which perhaps applies even more so to 1 Jean-Pierre Vigier himself . If fortune allows a visit to Paris, reported to be the city of love, and certainly one of the most beautiful and interesting cities in the world; one has been treated to a visual and cultural feast. For example a leisurely stroll from the Musee du Louvre along the Champs-Elysees to the Arc de Triomphe would instill even the least creative soul with the entelechies of a poets muse. It is perhaps open to theoretical interpretation, but if causal conditions have allowed one to be a physicist, visiting Paris, one may have taken opportunity to visit the portion of the old Latin quarter in place Jussieu where Pierre et Marie Curie Universite, reported to be ‘the best university in France’, is stationed.

Mathematics and the Aesthetic

Author : Nathalie Sinclair
Publisher : Springer Science & Business Media
ISBN 13 : 0387381457
Total Pages : 288 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Mathematics and the Aesthetic by : Nathalie Sinclair

Download or read book Mathematics and the Aesthetic written by Nathalie Sinclair and published by Springer Science & Business Media. This book was released on 2007-12-28 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection of essays explores the ancient affinity between the mathematical and the aesthetic, focusing on fundamental connections between these two modes of reasoning and communicating. From historical, philosophical and psychological perspectives, with particular attention to certain mathematical areas such as geometry and analysis, the authors examine ways in which the aesthetic is ever-present in mathematical thinking and contributes to the growth and value of mathematical knowledge.

Physics Essays

Author :
Publisher :
ISBN 13 :
Total Pages : 672 pages
Book Rating : 4.:/5 (318 download)

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Book Synopsis Physics Essays by :

Download or read book Physics Essays written by and published by . This book was released on 1995 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Bibliographic Guide to East Asian Studies

Author : New York Public Library Staff
Publisher : Macmillan Reference USA
ISBN 13 : 9780783813202
Total Pages : 684 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Bibliographic Guide to East Asian Studies by : New York Public Library Staff

Download or read book Bibliographic Guide to East Asian Studies written by New York Public Library Staff and published by Macmillan Reference USA. This book was released on 1996-07 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

NASA Breakthrough Propulsion Physics Workshop Proceedings

Author :
Publisher :
ISBN 13 :
Total Pages : 486 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis NASA Breakthrough Propulsion Physics Workshop Proceedings by :

Download or read book NASA Breakthrough Propulsion Physics Workshop Proceedings written by and published by . This book was released on 1999 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Books in Print

Author :
Publisher :
ISBN 13 :
Total Pages : 2432 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Books in Print by :

Download or read book Books in Print written by and published by . This book was released on 1991 with total page 2432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Cumulative Book Index

Author :
Publisher :
ISBN 13 :
Total Pages : 2230 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Cumulative Book Index by :

Download or read book The Cumulative Book Index written by and published by . This book was released on 1996 with total page 2230 pages. Available in PDF, EPUB and Kindle. Book excerpt: A world list of books in the English language.

American Book Publishing Record

Author :
Publisher :
ISBN 13 :
Total Pages : 1328 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis American Book Publishing Record by :

Download or read book American Book Publishing Record written by and published by . This book was released on 1996 with total page 1328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Mathematical Reviews

Author :
Publisher :
ISBN 13 :
Total Pages : 1194 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Mathematical Reviews by :

Download or read book Mathematical Reviews written by and published by . This book was released on 1996 with total page 1194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Books In Print 2004-2005

Author : Ed Bowker Staff
Publisher : R. R. Bowker
ISBN 13 : 9780835246422
Total Pages : 3274 pages
Book Rating : 4.2/5 (464 download)

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Book Synopsis Books In Print 2004-2005 by : Ed Bowker Staff

Download or read book Books In Print 2004-2005 written by Ed Bowker Staff and published by R. R. Bowker. This book was released on 2004 with total page 3274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Convexity Methods in Hamiltonian Mechanics

Author : Ivar Ekeland
Publisher : Springer Science & Business Media
ISBN 13 : 3642743315
Total Pages : 258 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Convexity Methods in Hamiltonian Mechanics by : Ivar Ekeland

Download or read book Convexity Methods in Hamiltonian Mechanics written by Ivar Ekeland and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

How Chinese Learn Mathematics

Author : Lianghuo Fan
Publisher : World Scientific
ISBN 13 : 9789812562241
Total Pages : 594 pages
Book Rating : 4.5/5 (622 download)

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Book Synopsis How Chinese Learn Mathematics by : Lianghuo Fan

Download or read book How Chinese Learn Mathematics written by Lianghuo Fan and published by World Scientific. This book was released on 2004 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book has been written by an international group of very activeresearchers and scholars who have a passion for the study of Chinesemathematics education. It aims to provide readers with a comprehensiveand updated picture of the teaching and learning of mathematicsinvolving Chinese students from various perspectives, including theways in which Chinese students learn mathematics in classrooms, schools and homes, the influence of the cultural and socialenvironment on Chinese students'' mathematics learning, and thestrengths and weaknesses of the ways in which Chinese learnmathematics