Download or read book The Center and Cyclicity Problems written by Valery Romanovski and published by Springer Science & Business Media. This book was released on 2009-04-29 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a computational algebra approach, this comprehensive text addresses the center and cyclicity problems as behaviors of dynamical systems and families of polynomial systems. The book gives the main properties of ideals in polynomial rings and their affine varieties followed by a discussion on the theory of normal forms and stability of differential equations. It contains numerous examples, pseudocode displays of all the computational algorithms, historical notes, nearly two hundred exercises, and an extensive bibliography, making it a suitable graduate textbook as well as research reference.
Download or read book Computer Algebra in Scientific Computing written by Vladimir P. Gerdt and published by Springer. This book was released on 2017-09-07 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, held in Beijing, China, in September 2017. The 28 full papers presented in this volume were carefully reviewed and selected from 33 submissions. They deal with cutting-edge research in all major disciplines of Computer Algebra.
Download or read book Global Bifurcation Theory and Hilbert s Sixteenth Problem written by V. Gaiko and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the 8th of August 1900 outstanding German mathematician David Hilbert delivered a talk "Mathematical problems" at the Second Interna tional Congress of Mathematicians in Paris. The talk covered practically all directions of mathematical thought of that time and contained a list of 23 problems which determined the further development of mathema tics in many respects (1, 119]. Hilbert's Sixteenth Problem (the second part) was stated as follows: Problem. To find the maximum number and to determine the relative position of limit cycles of the equation dy Qn(X, y) -= dx Pn(x, y)' where Pn and Qn are polynomials of real variables x, y with real coeffi cients and not greater than n degree. The study of limit cycles is an interesting and very difficult problem of the qualitative theory of differential equations. This theory was origi nated at the end of the nineteenth century in the works of two geniuses of the world science: of the Russian mathematician A. M. Lyapunov and of the French mathematician Henri Poincare. A. M. Lyapunov set forth and solved completely in the very wide class of cases a special problem of the qualitative theory: the problem of motion stability (154]. In turn, H. Poincare stated a general problem of the qualitative analysis which was formulated as follows: not integrating the differential equation and using only the properties of its right-hand sides, to give as more as possi ble complete information on the qualitative behaviour of integral curves defined by this equation (176].
Download or read book Planar Dynamical Systems written by Yirong Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-10-29 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 2008, November 23-28, the workshop of ”Classical Problems on Planar Polynomial Vector Fields ” was held in the Banff International Research Station, Canada. Called "classical problems", it was concerned with the following: (1) Problems on integrability of planar polynomial vector fields. (2) The problem of the center stated by Poincaré for real polynomial differential systems, which asks us to recognize when a planar vector field defined by polynomials of degree at most n possesses a singularity which is a center. (3) Global geometry of specific classes of planar polynomial vector fields. (4) Hilbert’s 16th problem. These problems had been posed more than 110 years ago. Therefore, they are called "classical problems" in the studies of the theory of dynamical systems. The qualitative theory and stability theory of differential equations, created by Poincaré and Lyapunov at the end of the 19th century, had major developments as two branches of the theory of dynamical systems during the 20th century. As a part of the basic theory of nonlinear science, it is one of the very active areas in the new millennium. This book presents in an elementary way the recent significant developments in the qualitative theory of planar dynamical systems. The subjects are covered as follows: the studies of center and isochronous center problems, multiple Hopf bifurcations and local and global bifurcations of the equivariant planar vector fields which concern with Hilbert’s 16th problem. The book is intended for graduate students, post-doctors and researchers in dynamical systems. For all engineers who are interested in the theory of dynamical systems, it is also a reasonable reference. It requires a minimum background of a one-year course on nonlinear differential equations.
Download or read book Computation and Applied Mathematics written by and published by . This book was released on 2001 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bifurcations and Periodic Orbits of Vector Fields written by Dana Schlomiuk and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 483 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last thirty years were a period of continuous and intense growth in the subject of dynamical systems. New concepts and techniques and at the same time new areas of applications of the theory were found. The 31st session of the Seminaire de Mathematiques Superieures (SMS) held at the Universite de Montreal in July 1992 was on dynamical systems having as its center theme "Bifurcations and periodic orbits of vector fields". This session of the SMS was a NATO Advanced Study Institute (ASI). This ASI had the purpose of acquainting the participants with some of the most recent developments and of stimulating new research around the chosen center theme. These developments include the major tools of the new resummation techniques with applications, in particular to the proof of the non-accumulation of limit-cycles for real-analytic plane vector fields. One of the aims of the ASI was to bring together methods from real and complex dy namical systems. There is a growing awareness that an interplay between real and complex methods is both useful and necessary for the solution of some of the problems. Complex techniques become powerful tools which yield valuable information when applied to the study of the dynamics of real vector fields. The recent developments show that no rigid frontiers between disciplines exist and that interesting new developments occur when ideas and techniques from diverse disciplines are married. One of the aims of the ASI was to show these multiple interactions at work.
Download or read book Differential Equations with Symbolic Computation written by Dongming Wang and published by Springer Science & Business Media. This book was released on 2006-03-16 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in tackling differential equations using advanced methods and software tools of symbolic computation. It focuses on the symbolic-computational aspects of three kinds of fundamental problems in differential equations: transforming the equations, solving the equations, and studying the structure and properties of their solutions.
Download or read book Ring Theory 1989 written by Shimshon A. Amitsur and published by . This book was released on 1989 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Israel Mathematical Conference Proceedings written by and published by . This book was released on 1989 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cycles of Time written by Roger Penrose and published by Vintage. This book was released on 2011-09-06 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: From Nobel prize-winner Roger Penrose, this groundbreaking book is for anyone "who is interested in the world, how it works, and how it got here" (New York Journal of Books). Penrose presents a new perspective on three of cosmology’s essential questions: What came before the Big Bang? What is the source of order in our universe? And what cosmic future awaits us? He shows how the expected fate of our ever-accelerating and expanding universe—heat death or ultimate entropy—can actually be reinterpreted as the conditions that will begin a new “Big Bang.” He details the basic principles beneath our universe, explaining various standard and non-standard cosmological models, the fundamental role of the cosmic microwave background, the paramount significance of black holes, and other basic building blocks of contemporary physics. Intellectually thrilling and widely accessible, Cycles of Time is a welcome new contribution to our understanding of the universe from one of our greatest mathematicians and thinkers.
Download or read book Normal Forms Bifurcations and Finiteness Problems in Differential Equations written by Christiane Rousseau and published by Springer Science & Business Media. This book was released on 2004-02-29 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the Nato Advanced Study Institute, held in Montreal, Canada, from 8 to 19 July 2002
Download or read book A3 His Algebra written by Nancy E. Albert and published by iUniverse. This book was released on 2005 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: A3 & HIS ALGEBRA is the true story of a struggling young boy from Chicago's west side who grew to become a force in American mathematics. For nearly 50 years, A. A. Albert thrived at the University of Chicago, one of the world's top centers for algebra. His "pure research" in algebra found its way into modern computers, rocket guidance systems, cryptology, and quantum mechanics, the basic theory behind atomic energy calculations. This first-hand account of the life of a world-renowned American mathematician is written by Albert's daughter. Her memoir, which favors a general audience, offers a personal and revealing look at the multidimensional life of an academic who had a lasting impact on his profession. SOME QUOTATIONS FROM PROFESSOR ALBERT: "There are really few bad students of mathematics. There are, instead, many bad teachers and bad curricula..." "The difficulty of learning mathematics is increased by the fact that in so many high schools this very difficult subject is considered to be teachable by those whose major subject is language, botany, or even physical education." "It is still true that in a majority of American universities the way to find the Department of Mathematics is to ask for the location of the oldest and most decrepit building on campus." "The production of a single scientist of first magnitude will have a greater impact on our civilization than the production of fifty mediocre Ph.D.'s." "Freedom is having the time to do research...Even in mathematics there are 'fashions'. This doesn't mean that the researcher is controlled by them. Many go their own way, ignoring the fashionable. That's part of the strength of a great university."
Download or read book Dynamic Systems and Applications written by and published by . This book was released on 1998 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Issues in General and Specialized Mathematics Research 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.
Download or read book A Hilbert Space Problem Book written by P.R. Halmos and published by Springer Science & Business Media. This book was released on 1982-11-08 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written for the active reader with some background in the topic, this book presents problems in Hilbert space theory, with definitions, corollaries and historical remarks, hints, proofs, answers and constructions.
Download or read book Bifurcations of Planar Vector Fields and Hilbert s Sixteenth Problem written by Robert Roussarie and published by Springer Science & Business Media. This book was released on 1998-05-19 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in the recently developed methods. The book, reflecting the current state of the art, can also be used for teaching special courses. (Mathematical Reviews)
Download or read book Near Rings and Near Fields written by Yuen Fong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Near-Rings and Near-Fields opens with three invited lectures on different aspects of the history of near-ring theory. These are followed by 26 papers reflecting the diversity of the subject in regard to geometry, topological groups, automata, coding theory and probability, as well as the purely algebraic structure theory of near-rings. Audience: Graduate students of mathematics and algebraists interested in near-ring theory.
