The Metrical Theory Of Continued Fractions To The Nearest Integer
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The Metrical Theory Of Continued Fractions To The Nearest Integer
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Author : Andrew Mansfield Rockett
language : en
Publisher:
Release Date : 1977
The Metrical Theory Of Continued Fractions To The Nearest Integer written by Andrew Mansfield Rockett and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Continued fractions categories.
Metrical Theory Of Continued Fractions
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Author : M. Iosifescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Metrical Theory Of Continued Fractions written by M. Iosifescu 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 2013-06-29 with Mathematics categories.
This monograph is intended to be a complete treatment of the metrical the ory of the (regular) continued fraction expansion and related representations of real numbers. We have attempted to give the best possible results known so far, with proofs which are the simplest and most direct. The book has had a long gestation period because we first decided to write it in March 1994. This gave us the possibility of essentially improving the initial versions of many parts of it. Even if the two authors are different in style and approach, every effort has been made to hide the differences. Let 0 denote the set of irrationals in I = [0,1]. Define the (reg ular) continued fraction transformation T by T (w) = fractional part of n 1/w, w E O. Write T for the nth iterate of T, n E N = {O, 1, ... }, n 1 with TO = identity map. The positive integers an(w) = al(T - (W)), n E N+ = {1,2··· }, where al(w) = integer part of 1/w, w E 0, are called the (regular continued fraction) digits of w. Writing . for arbitrary indeterminates Xi, 1 :::; i :::; n, we have w = lim [al(w),··· , an(w)], w E 0, n--->oo thus explaining the name of T. The above equation will be also written as w = lim [al(w), a2(w),···], w E O.
Mathematical Constants
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Author : Steven R. Finch
language : en
Publisher: Cambridge University Press
Release Date : 2003-08-18
Mathematical Constants written by Steven R. Finch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-18 with Mathematics categories.
Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Doeblin And Modern Probability
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Author : Harry Cohn
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Doeblin And Modern Probability written by Harry Cohn 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 1993 with Mathematics categories.
Wolfgang Doeblin, one of the greatest probabilists of this century, died in action during World War II at the age of twenty-five. He left behind several seminal contributions which have profoundly influenced the field and continue to provide inspiration for current research. This book is based on papers presented at the conference, `Fifty Years after Doeblin: Developments in the Theory of Markov Chains, Markov Processes, and Sums of Random Variables', held at Blaubeuren, Germany, in November 1991. Presented here for the first time is an account of Doeblin's life and work, revealing the circumstances of his tragic death in 1940. Organized into sections according to topic, the papers describe both Doeblin's original contributions as well as current developments. With contributions by top probabilists from sixteen countries, this book will interest both researchers in probability and science historians.
Continued Fractions
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Author : Andrew M Rockett
language : en
Publisher: World Scientific Publishing Company
Release Date : 1992-08-08
Continued Fractions written by Andrew M Rockett and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-08 with Mathematics categories.
This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.
Continued Fractions
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Author : A. M. Rockett
language : en
Publisher: World Scientific
Release Date : 1992-08-01
Continued Fractions written by A. M. Rockett and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-08-01 with Mathematics categories.
This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 2013-12-01 with Mathematics categories.
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathematics. It is a translation with updates and editorial comments of the Soviet Mathematical En cyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977 - 1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivision has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathe matics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, engineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Encyclopaedia Of Mathematics
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Author : M. Hazewinkel
language : en
Publisher: Springer
Release Date : 2013-12-01
Encyclopaedia Of Mathematics written by M. Hazewinkel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Tokyo Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1980
Tokyo Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Cycle Representations Of Markov Processes
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Author : Sophia L. Kalpazidou
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-03-06
Cycle Representations Of Markov Processes written by Sophia L. Kalpazidou 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 2007-03-06 with Mathematics categories.
This book is a prototype providing new insight into Markovian dependence via the cycle decompositions. It presents a systematic account of a class of stochastic processes known as cycle (or circuit) processes - so-called because they may be defined by directed cycles. These processes have special and important properties through the interaction between the geometric properties of the trajectories and the algebraic characterization of the Markov process. An important application of this approach is the insight it provides to electrical networks and the duality principle of networks. In particular, it provides an entirely new approach to infinite electrical networks and their applications in topics as diverse as random walks, the classification of Riemann surfaces, and to operator theory. The second edition of this book adds new advances to many directions, which reveal wide-ranging interpretations of the cycle representations like homologic decompositions, orthogonality equations, Fourier series, semigroup equations, and disintegration of measures. The versatility of these interpretations is consequently motivated by the existence of algebraic-topological principles in the fundamentals of the cycle representations. This book contains chapter summaries as well as a number of detailed illustrations. Review of the earlier edition: "This is a very useful monograph which avoids ready ways and opens new research perspectives. It will certainly stimulate further work, especially on the interplay of algebraic and geometrical aspects of Markovian dependence and its generalizations." Math Reviews