The 1 1 Nonlinear Universe Of The Parabolic Map And Combinatorics

Author : James D Louck
Publisher : World Scientific
ISBN 13 : 9814632430
Total Pages : 192 pages
Book Rating : 4.30/5 ( download)

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Download or read book The (1+1)-Nonlinear Universe of the Parabolic Map and Combinatorics written by James D Louck and published by World Scientific. This book was released on 2014-12-30 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops chaos theory from properties of the graphs inverse to the parabolic map of the interval [0, 2], where the height at the midpoint x = 1 may be viewed as a time-like parameter, which together with the x-coordinate, provide the two parameters that uniquely characterize the parabola, and which are used throughout the monograph. There is only one basic mathematical operation used: function composition. The functions studied are the n-fold composition of the basic parabola with itself. However, it is the properties of the graph inverse to this n-fold composition that are the objects whose properties are developed. The reflection symmetry of the basic parabola through the vertical line x = 1 gives rise to two symmetry classes of inverse graphs: the inverse graphs and their conjugates. Quite remarkably, it turns out that there exists, among all the inverse graphs and their conjugates, a completely deterministic class of inverse graphs and their conjugates. Deterministic in the sense that this class is uniquely determined for all values of the time-like parameter and the x-coordinate, the entire theory, of course, being highly nonlinear — it is polynomial in the time-like parameter and in the x-coordinate. The deterministic property and its implementation are key to the argument that the system is a complex adaptive system in the sense that a few axioms lead to structures of unexpected richness. This monograph is about working out the many details that advance the notion that deterministic chaos theory, as realized by a complex adaptive system, is indeed a new body of mathematics that enriches our understanding of the world around us. But now the imagination is also opened to the possibility that the real universe is a complex adaptive system. * deceased Contents:Introduction and Point of ViewRecursive ConstructionDescription of Events in the Inverse GraphThe (1+1)-Dimensional Nonlinear UniverseThe Creation TableGraphical Presentation of MSS RootsGraphical Presentation of Inverse Graphs Readership: Post-graduates from mathematics and physics backgrounds, mathematics and physics professionals with an interest in astrophysics. Key Features:There exists a unique inverse graph. This unique graph can be constructed from a simple algorithmThe concept of a deterministic inverse graph and its relationship to complex adaptive systems is newThis monograph is of general value to readers because it illustrates nicely that research in new methodologies in Mathematics can lead to new insights in PhysicsKeywords:Mathematical Models;Inverse Graph;Chaos Theory;Function Composition;Creation of Fixed Points;Creation Diagram;Unique Theory;Complex Adaptive Systems;Context and Models;Applications to Weather Patterns;Potential Application to General RelativityReviews: “It is intended for readers with a perchance for the unusual and unexpected.” Zentralblatt MATH

Author : Mauricio Matos Peixoto
Publisher : Springer Science & Business Media
ISBN 13 : 3642114563
Total Pages : 812 pages
Book Rating : 4.64/5 ( download)

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Download or read book Dynamics, Games and Science I written by Mauricio Matos Peixoto and published by Springer Science & Business Media. This book was released on 2011-03-29 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamics, Games and Science I and II are a selection of surveys and research articles written by leading researchers in mathematics. The majority of the contributions are on dynamical systems and game theory, focusing either on fundamental and theoretical developments or on applications to modeling in biology, ecomonics, engineering, finances and psychology. The papers are based on talks given at the International Conference DYNA 2008, held in honor of Mauricio Peixoto and David Rand at the University of Braga, Portugal, on September 8-12, 2008. The aim of these volumes is to present cutting-edge research in these areas to encourage graduate students and researchers in mathematics and other fields to develop them further.

Author : Mikl¢s B¢na
Publisher : World Scientific
ISBN 13 : 9812568859
Total Pages : 492 pages
Book Rating : 4.54/5 ( download)

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Download or read book A Walk Through Combinatorics written by Mikl¢s B¢na and published by World Scientific. This book was released on 2006 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for an introductory combinatorics course that can take up one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first edition, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible for the talented and hard-working undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings and Eulerian and Hamiltonian cycles. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

Author :
Publisher :
ISBN 13 :
Total Pages : 1574 pages
Book Rating : 4.26/5 ( download)

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Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1574 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Edward B Curtis
Publisher : World Scientific
ISBN 13 : 9814493821
Total Pages : 196 pages
Book Rating : 4.26/5 ( download)

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Download or read book Inverse Problems for Electrical Networks written by Edward B Curtis and published by World Scientific. This book was released on 2000-03-02 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a very timely exposition of part of an important subject which goes under the general name of “inverse problems”. The analogous problem for continuous media has been very much studied, with a great deal of difficult mathematics involved, especially partial differential equations. Some of the researchers working on the inverse conductivity problem for continuous media (the problem of recovering the conductivity inside from measurements on the outside) have taken an interest in the authors' analysis of this similar problem for resistor networks. The authors' treatment of inverse problems for electrical networks is at a fairly elementary level. It is accessible to advanced undergraduates, and mathematics students at the graduate level. The topics are of interest to mathematicians working on inverse problems, and possibly to electrical engineers. A few techniques from other areas of mathematics have been brought together in the treatment. It is this amalgamation of such topics as graph theory, medial graphs and matrix algebra, as well as the analogy to inverse problems for partial differential equations, that makes the book both original and interesting. Contents:Circular Planar GraphsResistor NetworksHarmonic FunctionsCharacterization IAdjoining EdgesCharacterization IIMedial GraphsRecovering a GraphLayered Networks Readership: Graduate students and researchers in applied mathematics and electrical and electronic engineering. Keywords:Inverse Problems;Resistor Network;Schur Complement;Medial Graph;Circular Planar Graph;Kirchhoff Matrix;Response Matrix;“Y-Delta” Transformation;Gamma-Harmonic Function;Connections;Dirichlet Problem

Author : Steven H. Strogatz
Publisher : CRC Press
ISBN 13 : 0429961111
Total Pages : 532 pages
Book Rating : 4.13/5 ( download)

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Download or read book Nonlinear Dynamics and Chaos written by Steven H. Strogatz and published by CRC Press. This book was released on 2018-05-04 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

Author : Robert Vichnevetsky
Publisher :
ISBN 13 :
Total Pages : 998 pages
Book Rating : 4.81/5 ( download)

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Download or read book IMACS '91, 13th World Congress on Computation and Applied Mathematics written by Robert Vichnevetsky and published by . This book was released on 1991 with total page 998 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings -- Computer Arithmetic, Algebra, OOP.

Author : Staples George Stacey
Publisher : World Scientific
ISBN 13 : 1908977574
Total Pages : 428 pages
Book Rating : 4.71/5 ( download)

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Download or read book Operator Calculus On Graphs: Theory And Applications In Computer Science written by Staples George Stacey and published by World Scientific. This book was released on 2012-02-23 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science.Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations.

Author : Martin W. Liebeck
Publisher : Cambridge University Press
ISBN 13 : 0521406854
Total Pages : 505 pages
Book Rating : 4.57/5 ( download)

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Download or read book Groups, Combinatorics and Geometry written by Martin W. Liebeck and published by Cambridge University Press. This book was released on 1992-09-10 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers on the subject of the classification of finite simple groups.

Author : Panos M Pardalos
Publisher : World Scientific
ISBN 13 : 9814489654
Total Pages : 372 pages
Book Rating : 4.52/5 ( download)

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Download or read book Combinatorial and Global Optimization written by Panos M Pardalos and published by World Scientific. This book was released on 2002-04-05 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans–Williamson relaxation of the maximum cut problem, and the Du–Hwang solution of the Gilbert–Pollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on “Combinatorial and Global Optimization” held at Crete, Greece. Contents:A Forest Exterior Point Algorithm for Assignment Problems (H Achatz et al.)Location/Allocation of Queuing Facilities in Continuous Space Using Minsum and Minimax Criteria (J Brimberg et al.)Algorithms for the Consistency Analysis in Scenario Projects (R Feldmann et al.)Solving Quadratic Knapsack Problems by Reformulation and Tabu Search. Single Constraint Case (F Glover et al.)Global Optimization Using Dynamic Search Trajectories (A A Groenwold & J A Snyman)On Pareto Efficiency. A General Constructive Existence Principle (G Isac)Piecewise Linear Network Flow Problems (D Kim & P M Pardalos)Semidefinite Programming Approaches for MAX-2-SAT and MAX-3-SAT: Computational Perspectives (E de Klerk & J P Warners)Heuristic Solutions of Vehicle Routing Problems in Supply Chain Management (Y Marinakis & A Migdalas)A New Finite Cone Covering Algorithm for Concave Minimization (C Meyer & B Jaumard)Frequency Assignment for Very Large, Sparse Networks (R Murphey)GPS Network Design: An Application of the Simulated Annealing Heuristic Technique (H A Saleh & P J Dare)Normal Branch and Bound Algorithms for General Nonconvex Quadratic Programming (H Tuy)and other papers Readership: Researchers in numerical & computational mathematics, optimization, combinatorics & graph theory, networking and materials engineering. Keywords:Combinatorial Optimization;Global Optimization