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Author: Mark Braverman
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
ISBN: 9780612952645
Category :
Languages : en
Pages : 180
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Book Description
We apply the concepts developed to show that hyperbolic Julia sets are polynomial time computable. This result is a significant generalization of the result in [RW03], where polynomial time computability has been shown for a restricted type of hyperbolic Julia sets. We investigate different definitions of the computability and complexity of sets in Rk, and establish new connections between these definitions. This allows us to connect the computability of real functions and real sets in a new way. We show that equivalence of some of the definitions corresponds to equivalence between famous complexity classes. The model we use is mostly consistent with [Wei00].
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Author: Mark Braverman
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
ISBN: 9780612952645
Category :
Languages : en
Pages : 180
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Book Description
We apply the concepts developed to show that hyperbolic Julia sets are polynomial time computable. This result is a significant generalization of the result in [RW03], where polynomial time computability has been shown for a restricted type of hyperbolic Julia sets. We investigate different definitions of the computability and complexity of sets in Rk, and establish new connections between these definitions. This allows us to connect the computability of real functions and real sets in a new way. We show that equivalence of some of the definitions corresponds to equivalence between famous complexity classes. The model we use is mostly consistent with [Wei00].
Author: Mark Braverman
Publisher:
ISBN: 9780494447024
Category : Computer science
Languages : en
Pages : 390
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Book Description
The field of study in the thesis is Real Computation, and Computability and Complexity in Dynamical Systems. The thesis consists of two parts. The first part is devoted to results on general computation of functions and sets over the reals, while in the second part results about computability and complexity in Complex Dynamics are presented. Studying computability and complexity over the reals is important for understanding the relationship between nature and computing, and for providing theoretical backing to fundamental problems in Numerical Analysis. In the first part of the thesis results unifying two most commonly used models of computation are presented. One is the model of Computable Analysis that is based on rational approximations of continuous objects, such as real functions and sets [Grz55, Ko91, Wei00]. The other is the Blum-Shub-Smale (BSS) model that is based on precise algebraic operations [BCSS98]. Insights obtained through this connection are then used to extend the computational complexity notion to some discontinuous functions. In the second part of the thesis, results on the computability and complexity of Julia sets are presented. Julia sets arise in one-dimensional complex dynamics. They have been intensely studied in the past 100 years, and since the 1980s numerous programs have been written to produce images of the sets, both for research and for their aesthetic value. We have studied computational properties of Julia sets, obtaining a virtually complete classification of the computational properties of Julia sets as well as complexity results, that complement the previous empirical work on producing their images.
Author: Paul Nevai
Publisher: Springer Science & Business Media
ISBN: 9400905017
Category : Mathematics
Languages : en
Pages : 472
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Book Description
This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.
Author: Hans-Dietrich Gronau
Publisher: Springer Science & Business Media
ISBN: 3642145655
Category : Mathematics
Languages : en
Pages : 298
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Book Description
In July 2009 Germany hosted the 50th International Mathematical Olympiad (IMO). For the very first time the number of participating countries exceeded 100, with 104 countries from all continents. Celebrating the 50th anniversary of the IMO provides an ideal opportunity to look back over the past five decades and to review its development to become a worldwide event. This book is a report about the 50th IMO as well as the IMO history. A lot of data about all the 50 IMOs are included. We list the most successful contestants, the results of the 50 Olympiads and the 112 countries that have ever taken part. It is impressive to see that many of the world’s leading research mathematicians were among the most successful IMO participants in their youth. Six of them gave presentations at a special celebration: Bollobás, Gowers, Lovász, Smirnov, Tao and Yoccoz. This book is aimed at students in the IMO age group and all those who have interest in this worldwide leading competition for highschool students.
Author: Walter Gautschi
Publisher: Birkhäuser
ISBN: 3034886853
Category : Technology & Engineering
Languages : en
Pages : 275
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Book Description
This volume contains a collection of papers dealing with applications of orthogonal polynomials and methods for their computation, of interest to a wide audience of numerical analysts, engineers, and scientists. The applications address problems in applied mathematics as well as problems in engineering and the sciences.
Author: Klaus Weihrauch
Publisher: Springer Science & Business Media
ISBN: 9783540668176
Category : Computers
Languages : en
Pages : 312
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Book Description
Merging fundamental concepts of analysis and recursion theory to a new exciting theory, this book provides a solid fundament for studying various aspects of computability and complexity in analysis. It is the result of an introductory course given for several years and is written in a style suitable for graduate-level and senior students in computer science and mathematics. Many examples illustrate the new concepts while numerous exercises of varying difficulty extend the material and stimulate readers to work actively on the text.
Author: Peter Erdi
Publisher: Springer Science & Business Media
ISBN: 3540357785
Category : Technology & Engineering
Languages : en
Pages : 400
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Book Description
This book explains why complex systems research is important in understanding the structure, function and dynamics of complex natural and social phenomena. It illuminates how complex collective behavior emerges from the parts of a system, due to the interaction between the system and its environment. Readers will learn the basic concepts and methods of complex system research. The book is not highly technical mathematically, but teaches and uses the basic mathematical notions of dynamical system theory, making the book useful for students of science majors and graduate courses.
Author: Rudy Rucker
Publisher: Princeton University Press
ISBN: 0691191255
Category : Mathematics
Languages : en
Pages :
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Book Description
A dynamic exploration of infinity In Infinity and the Mind, Rudy Rucker leads an excursion to that stretch of the universe he calls the “Mindscape,” where he explores infinity in all its forms: potential and actual, mathematical and physical, theological and mundane. Using cartoons, puzzles, and quotations to enliven his text, Rucker acquaints us with staggeringly advanced levels of infinity, delves into the depths beneath daily awareness, and explains Kurt Gödel’s belief in the possibility of robot consciousness. In the realm of infinity, mathematics, science, and logic merge with the fantastic. By closely examining the paradoxes that arise, we gain profound insights into the human mind, its powers, and its limitations. This Princeton Science Library edition includes a new preface by the author.
Author: Willi Jäger
Publisher: Springer Science & Business Media
ISBN: 3642557538
Category : Computers
Languages : en
Pages : 733
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Book Description
Efficient transfer between science and society is crucial for their future development. The rapid progress of information technology and computer systems offers a large potential and new perspectives for solving complex problems. Mathematical modelling and simulation have become important tools not only in scientific investigations but also in analysing, planning and controlling technological and economic processes. Mathematics, imbedded in an interdisciplinary concept, has become a key technology. The book covers the results of a variety of major projects in industrial mathematics following an initiative of the German Federal Ministry of Education and Research. All projects are collaborations of industrial companies and university-based researchers, and range from automotive industry to computer technology and medical visualisation. In general, the projects presented in this volume prove that new mathematical ideas and methods can be decisive for the solution of industrial and economic problems.
Author: Bloomsbury Publishing
Publisher: Bloomsbury Publishing
ISBN: 1408102579
Category : Games & Activities
Languages : en
Pages : 719
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Book Description
Anagram Solver is the essential guide to cracking all types of quiz and crossword featuring anagrams. Containing over 200,000 words and phrases, Anagram Solver includes plural noun forms, palindromes, idioms, first names and all parts of speech. Anagrams are grouped by the number of letters they contain with the letters set out in alphabetical order so that once the letters of an anagram are arranged alphabetically, finding the solution is as easy as locating the word in a dictionary.
