The Dynamical System Generated By The 3n 1 Function
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The Dynamical System Generated By The 3n 1 Function
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Author : Günther J. Wirsching
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1998-02-19
The Dynamical System Generated By The 3n 1 Function written by Günther J. Wirsching and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-02-19 with Computers categories.
The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.
The Dynamical System Generated By The 3n 1 Function
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Author : Gunther J. Wirsching
language : en
Publisher:
Release Date : 2014-01-15
The Dynamical System Generated By The 3n 1 Function written by Gunther J. Wirsching and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
The Dynamical System Generated By The 3n 1 Function
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Author : Günther J. Wirsching
language : en
Publisher: Springer
Release Date : 2006-11-14
The Dynamical System Generated By The 3n 1 Function written by Günther J. Wirsching and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The 3n+1 function T is defined by T(n)=n/2 for n even, and T(n)=(3n+1)/2 for n odd. The famous 3n+1 conjecture, which remains open, states that, for any starting number n>0, iterated application of T to n eventually produces 1. After a survey of theorems concerning the 3n+1 problem, the main focus of the book are 3n+1 predecessor sets. These are analyzed using, e.g., elementary number theory, combinatorics, asymptotic analysis, and abstract measure theory. The book is written for any mathematician interested in the 3n+1 problem, and in the wealth of mathematical ideas employed to attack it.
The Dynamical System On The Natural Numbers Generated By The 3n 1 Function
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Author : Günther Wirsching
language : en
Publisher:
Release Date : 1996
The Dynamical System On The Natural Numbers Generated By The 3n 1 Function written by Günther Wirsching and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Seminaire De Probabilites Xxxv
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Author : J. Azema
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-04-10
Seminaire De Probabilites Xxxv written by J. Azema 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 2001-04-10 with Mathematics categories.
Researchers and graduate students in the theory of stochastic processes will find in this 35th volume some thirty articles on martingale theory, martingales and finance, analytical inequalities and semigroups, stochastic differential equations, functionals of Brownian motion and of Lévy processes. Ledoux's article contains a self-contained introduction to the use of semigroups in spectral gaps and logarithmic Sobolev inequalities; the contribution by Emery and Schachermayer includes an exposition for probabilists of Vershik's theory of backward discrete filtrations.
Biscuits Of Number Theory
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Author : Arthur T. Benjamin
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-29
Biscuits Of Number Theory written by Arthur T. Benjamin 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 2020-07-29 with Mathematics categories.
Geometric Aspects Of Functional Analysis
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Author : V.D. Milman
language : en
Publisher: Springer
Release Date : 2007-05-09
Geometric Aspects Of Functional Analysis written by V.D. Milman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-09 with Mathematics categories.
This volume of original research papers from the Israeli GAFA seminar during the years 1996-2000 not only reports on more traditional directions of Geometric Functional Analysis, but also reflects on some of the recent new trends in Banach Space Theory and related topics. These include the tighter connection with convexity and the resulting added emphasis on convex bodies that are not necessarily centrally symmetric, and the treatment of bodies which have only very weak convex-like structure. Another topic represented here is the use of new probabilistic tools; in particular transportation of measure methods and new inequalities emerging from Poincaré-like inequalities.
Differentiability Of Six Operators On Nonsmooth Functions And P Variation
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Author : R. M. Dudley
language : en
Publisher: Springer Science & Business
Release Date : 1999-06-21
Differentiability Of Six Operators On Nonsmooth Functions And P Variation written by R. M. Dudley and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-21 with Mathematics categories.
The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function. The operators are differentiable with respect to p-variation norms with optimal remainder bounds. Thus the functions as arguments of the operators can be nonsmooth, possibly discontinuous, but four of the six operators turn out to be analytic (holomorphic) for some p-variation norms. The reader will need to know basic real analysis, including Riemann and Lebesgue integration. The book is intended for analysts, statisticians and probabilists. Analysts and statisticians have each studied the differentiability of some of the operators from different viewpoints, and this volume seeks to unify and expand their results.
Diffraction By An Immersed Elastic Wedge
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Author : Jean-Pierre Croisille
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-12-15
Diffraction By An Immersed Elastic Wedge written by Jean-Pierre Croisille 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 1999-12-15 with Mathematics categories.
This series reports on new developments in mathematical research and teaching - quickly, informally and at a high level. The type of material considered for publication includes 1. Research monographs 2. Lectures on a new field or presentations of a new angle in a classical field 3. Summer schools and intensive courses on topics of current research. Texts which are out of print but still in demand may also be considered. The timeliness of a manuscript is sometimes more important than its form, which might be preliminary or tentative. Details of the editorial policy can be found on the inside front-cover of a current volume. Manuscripts should be submitted in camera-ready form according to Springer-Verlag's specification: technical instructions will be sent on request. TEX macros may be found at: http://www.springer.de/math/authors/b- tex.html Select the version of TEX you use and then click on "Monographs". A subject index should be included. We recommend contacting the publisher or the series editors at an early stage of your project. Addresses are given on the inside back-cover.
The Ultimate Challenge
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Author : Jeffrey C. Lagarias
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-19
The Ultimate Challenge written by Jeffrey C. Lagarias and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-19 with Mathematics categories.
The $3x+1$ problem, or Collatz problem, concerns the following seemingly innocent arithmetic procedure applied to integers: If an integer $x$ is odd then “multiply by three and add one”, while if it is even then “divide by two”. The $3x+1$ problem asks whether, starting from any positive integer, repeating this procedure over and over will eventually reach the number 1. Despite its simple appearance, this problem is unsolved. Generalizations of the problem are known to be undecidable, and the problem itself is believed to be extraordinarily difficult. This book reports on what is known on this problem. It consists of a collection of papers, which can be read independently of each other. The book begins with two introductory papers, one giving an overview and current status, and the second giving history and basic results on the problem. These are followed by three survey papers on the problem, relating it to number theory and dynamical systems, to Markov chains and ergodic theory, and to logic and the theory of computation. The next paper presents results on probabilistic models for behavior of the iteration. This is followed by a paper giving the latest computational results on the problem, which verify its truth for $x < 5.4 cdot 10^{18}$. The book also reprints six early papers on the problem and related questions, by L. Collatz, J. H. Conway, H. S. M. Coxeter, C. J. Everett, and R. K. Guy, each with editorial commentary. The book concludes with an annotated bibliography of work on the problem up to the year 2000.