The Metrical Theory of Jacobi-Perron Algorithm
Author : F. Schweiger
Publisher : Springer
Page : 117 pages
File Size : 39,12 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540470107
Mathematical Constants II
Author : Steven R. Finch
Publisher : Cambridge University Press
Page : 783 pages
File Size : 26,61 MB
Release : 2018-12-06
Category : Mathematics
ISBN : 110860403X
Book Description
Famous mathematical constants include the ratio of circular circumference to diameter, π = 3.14 ..., and the natural logarithm base, e = 2.718 .... Students and professionals can often name a few others, but there are many more buried in the literature and awaiting discovery. How do such constants arise, and why are they important? Here the author renews the search he began in his book Mathematical Constants, adding another 133 essays that broaden the landscape. Topics include the minimality of soap film surfaces, prime numbers, elliptic curves and modular forms, Poisson–Voronoi tessellations, random triangles, Brownian motion, uncertainty inequalities, Prandtl–Blasius flow (from fluid dynamics), Lyapunov exponents, knots and tangles, continued fractions, Galton–Watson trees, electrical capacitance (from potential theory), Zermelo's navigation problem, and the optimal control of a pendulum. Unsolved problems appear virtually everywhere as well. This volume continues an outstanding scholarly attempt to bring together all significant mathematical constants in one place.
Women in Numbers Europe IV
Author : Ramla Abdellatif
Publisher : Springer Nature
Page : 378 pages
File Size : 24,24 MB
Release :
Category :
ISBN : 3031521633
Book Description
Substitutions in Dynamics, Arithmetics and Combinatorics
Author : N. Pytheas Fogg
Publisher : Springer
Page : 411 pages
File Size : 18,35 MB
Release : 2003-10-24
Category : Mathematics
ISBN : 3540457143
Book Description
A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.
Multidimensional Continued Fractions
Author : Fritz Schweiger
Publisher : Oxford University Press, USA
Page : 250 pages
File Size : 13,99 MB
Release : 2000
Category : Mathematics
ISBN : 9780198506867
Book Description
Mathematician Fritz Schweiger, whose academic affiliation is not provided, provides an introduction to a field of research that has seen remarkable progress in recent decades, concentrating on multidimensional continued fractions which can be described by fractional linear maps or equivalently by a set of (n + 1) x (n + 1) matrices. Addressing the question of periodicity, he refines the problem of convergence to the question of whether these algorithms give "good" simultaneous Diophantine approximations. He notes that these algorithms are not likely to provide such "good" approximations which satisfy the n-dimensional Dirichlet property. Also studied are the ergodic properties of these maps. Annotation copyrighted by Book News Inc., Portland, OR
Dynamical Systems and Statistical Mechanics
Author : I͡Akov Grigorʹevich Sinaĭ
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 45,86 MB
Release : 1991
Category : Mathematics
ISBN : 9780821841020
Book Description
Dynamical systems and statistical mechanics have been developing in close interaction during the past decade, and the papers in this book attest to the productiveness of this interaction. The first paper in the collection contains a new result in the theory of quantum chaos, a burgeoning line of inquiry which combines mathematics and physics and which is likely in time to produce many new connections and applications. Another paper, related to the renormalization group method for the study of maps of the circle with singularities due to a jump in the derivative, demonstrates that the fixed point of the renormgroup can in this case be sufficiently described. In certain situations, the renormgroup methods work better than the traditional KAM method. Other topics covered include: thermodynamic formalism for certain infinite-dimensional dynamical systems, numerical simulation of dynamical systems with hyperbolic behaviour, periodic points of holomorphic maps, the theory of random media, statistical properties of the leading eigenvalue in matrix ensembles of large dimension, spectral properties of the one-dimensional Schrodinger operator. This volume will appeal to many readers, as it covers a broad range of topics and presents a view of some of the frontier research in the Soviet Union today.
Geometry of Continued Fractions
Author : Oleg N. Karpenkov
Publisher : Springer Nature
Page : 462 pages
File Size : 30,18 MB
Release : 2022-05-28
Category : Mathematics
ISBN : 3662652773
Book Description
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.
Progress in Cryptology -- AFRICACRYPT 2011
Author : Abderrahmane Nitaj
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 38,79 MB
Release : 2011-06-22
Category : Business & Economics
ISBN : 3642219683
Book Description
This book constitutes the refereed proceedings of the 4th International Conference on the Theory and Application of Cryptographic Techniques in Africa, AFRICACRYPT 2011, held in Dakar, Senegal, in July 2011. The 23 papers presented together with abstracts of 3 invited talks were carefully reviewed and selected from 76 submissions. They are organized in topical sections on protocols, cryptanalysis, secret-key cryptography, efficient implementations, cryptographic schemes, algorithmic problems, elliptic curves, fault analysis, and security proofs.
Theory of Linear and Integer Programming
Author : Alexander Schrijver
Publisher : John Wiley & Sons
Page : 488 pages
File Size : 48,52 MB
Release : 1998-06-11
Category : Mathematics
ISBN : 9780471982326
Book Description
Theory of Linear and Integer Programming Alexander Schrijver Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands This book describes the theory of linear and integer programming and surveys the algorithms for linear and integer programming problems, focusing on complexity analysis. It aims at complementing the more practically oriented books in this field. A special feature is the author's coverage of important recent developments in linear and integer programming. Applications to combinatorial optimization are given, and the author also includes extensive historical surveys and bibliographies. The book is intended for graduate students and researchers in operations research, mathematics and computer science. It will also be of interest to mathematical historians. Contents 1 Introduction and preliminaries; 2 Problems, algorithms, and complexity; 3 Linear algebra and complexity; 4 Theory of lattices and linear diophantine equations; 5 Algorithms for linear diophantine equations; 6 Diophantine approximation and basis reduction; 7 Fundamental concepts and results on polyhedra, linear inequalities, and linear programming; 8 The structure of polyhedra; 9 Polarity, and blocking and anti-blocking polyhedra; 10 Sizes and the theoretical complexity of linear inequalities and linear programming; 11 The simplex method; 12 Primal-dual, elimination, and relaxation methods; 13 Khachiyan's method for linear programming; 14 The ellipsoid method for polyhedra more generally; 15 Further polynomiality results in linear programming; 16 Introduction to integer linear programming; 17 Estimates in integer linear programming; 18 The complexity of integer linear programming; 19 Totally unimodular matrices: fundamental properties and examples; 20 Recognizing total unimodularity; 21 Further theory related to total unimodularity; 22 Integral polyhedra and total dual integrality; 23 Cutting planes; 24 Further methods in integer linear programming; Historical and further notes on integer linear programming; References; Notation index; Author index; Subject index
Geometry of Continued Fractions
Author : Oleg Karpenkov
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 14,38 MB
Release : 2013-08-15
Category : Mathematics
ISBN : 3642393683
Book Description
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.
