Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions
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Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions
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Author : Gregory R. Maloney
language : en
Publisher:
Release Date : 2009
Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions written by Gregory R. Maloney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Thirty years ago, Effros and Shen classified the simple dimension groups with rank two. Every such group is parametrized by an irrational number, and can be constructed as an inductive limit using that number's continued fraction expansion. There is a natural generalization of continued fractions to higher dimensions, and this invites the following question: What dimension groups correspond to multidimensional continued fractions? We describe this class of groups and show how some properties of a continued fraction are reflected in the structure of its dimension group. We also consider a related issue: an Effros-Shen group has been shown to arise in a natural way from the tail equivalence relation on a certain sequence space. We describe a more general class of sequence spaces to which this construction can be applied to obtain other dimension groups, including dimension groups corresponding to multidimensional continued fractions.
Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions
DOWNLOAD
Author : Gregory R. Maloney
language : en
Publisher:
Release Date : 2009
Dimension Groups And C Algebras Associated To Multidimensional Continued Fractions written by Gregory R. Maloney and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Thirty years ago, Effros and Shen classified the simple dimension groups with rank two. Every such group is parametrized by an irrational number, and can be constructed as an inductive limit using that number's continued fraction expansion.There is a natural generalization of continued fractions to higher dimensions, and this invites the following question: What dimension groups correspond to multidimensional continued fractions? We describe this class of groups and show how some properties of a continued fraction are reflected in the structure of its dimension group.We also consider a related issue: an Effros-Shen group has been shown to arise in a natural way from the tail equivalence relation on a certain sequence space. We describe a more general class of sequence spaces to which this construction can be applied to obtain other dimension groups, including dimension groups corresponding to multidimensional continued fractions.
Trends In Logic
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Author : Vincent F. Hendricks
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Trends In Logic written by Vincent F. Hendricks and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
In 1953, exactly 50 years ago to this day, the first volume of Studia Logica appeared under the auspices of The Philosophical Committee of The Polish Academy of Sciences. Now, five decades later the present volume is dedicated to a celebration of this 50th Anniversary of Studia Logica. The volume features a series of papers by distinguished scholars reflecting both the aim and scope of this journal for symbolic logic.
Geometry Of Continued Fractions
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Author : Oleg Karpenkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-08-15
Geometry Of Continued Fractions written by Oleg Karpenkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-15 with Mathematics categories.
Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
The Legacy Of Niels Henrik Abel
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Author : Olav Arnfinn Laudal
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28
The Legacy Of Niels Henrik Abel written by Olav Arnfinn Laudal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.
This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century. It is accompanied by a CD-ROM with a large amount of information related to Niels Henrik Abel, such as on the Abel Centennial in 1902 and the Abel Bicentennial Conference in 2002, the launching of the Abel Prize, Abel monuments, and stamps, banknotes, coins etc. issued in honour of Niels Henrik Abel.
Reviews In Number Theory 1984 96
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Author :
language : en
Publisher:
Release Date : 1997
Reviews In Number Theory 1984 96 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Number theory categories.
Geometry Of Continued Fractions
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Author : Oleg N. Karpenkov
language : en
Publisher: Springer Nature
Release Date : 2022-05-28
Geometry Of Continued Fractions written by Oleg N. Karpenkov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-28 with Mathematics categories.
This book introduces a new geometric vision of continued fractions. It covers several applications to questions related to such areas as Diophantine approximation, algebraic number theory, and toric geometry. The second edition now includes a geometric approach to Gauss Reduction Theory, classification of integer regular polygons and some further new subjects. Traditionally a subject of number theory, continued fractions appear in dynamical systems, algebraic geometry, topology, and even celestial mechanics. The rise of computational geometry has resulted in renewed interest in multidimensional generalizations of continued fractions. Numerous classical theorems have been extended to the multidimensional case, casting light on phenomena in diverse areas of mathematics. The reader will find an overview of current progress in the geometric theory of multidimensional continued fractions accompanied by currently open problems. Whenever possible, we illustrate geometric constructions with figures and examples. Each chapter has exercises useful for undergraduate or graduate courses.
Machines Computations And Universality
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Author : Jerome Durand-Lose
language : en
Publisher: Springer
Release Date : 2015-08-29
Machines Computations And Universality written by Jerome Durand-Lose and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-29 with Computers categories.
This book constitutes the refereed proceedings of the 7th International Conference on Machines, Computations, and Universality, MCU 2015, held in Famagusta, North Cyprus, in September 2015. The 10 revised full papers presented together with 4 invited talks were carefully reviewed and selected from 23 submissions. MCU explores computation in the setting of various discrete models (Turing machines, register machines, cellular automata, tile assembly systems, rewriting systems, molecular computing models, neural models, etc.) and analog and hybrid models (BSS machines, infinite time cellular automata, real machines, quantum computing, etc.).
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2005
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
Pseudoperiodic Topology
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Author : Maxim Kontsevich
language : en
Publisher: American Mathematical Soc.
Release Date : 1999
Pseudoperiodic Topology written by Maxim Kontsevich and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
Moscow mathematicians offer researchers and graduate students working in dynamical systems, topology, and number theory an account of the current status of a young branch of mathematics, born at the boundary between those three disciplines. The theory is related to the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. They discuss the topology of quasiperiodic functions, statistics of Klein polyhedra and multidimensional continued fractions, pseudoperiodic mappings, how leaves of a closed one-form wind around a surface, and other topics. They do not provide an index. Annotation copyrighted by Book News, Inc., Portland, OR