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Author : Michael Baake,Uwe Grimm
Publisher : Cambridge University Press
Page : 548 pages
File Size : 52,5 Mb
Release : 2013-08-22
Category : Mathematics
ISBN : 9780521869911
A comprehensive introductory monograph on the theory of aperiodic order, with numerous illustrations and examples.
Author : Johannes Kellendonk,Daniel Lenz,Jean Savinien
Publisher : Birkhäuser
Page : 428 pages
File Size : 40,8 Mb
Release : 2015-06-05
Category : Mathematics
ISBN : 9783034809030
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.
Author : Michael Baake,Uwe Grimm
Publisher : Cambridge University Press
Page : 407 pages
File Size : 53,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9780521869928
The second volume in a series exploring the mathematics of aperiodic order. Covers various aspects of crystallography.
Author : Michael Baake,Uwe Grimm
Publisher : Cambridge University Press
Page : 548 pages
File Size : 46,6 Mb
Release : 2013-08-22
Category : Mathematics
ISBN : 9781316184387
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics.
Author : R.V. Moody
Publisher : Springer
Page : 0 pages
File Size : 43,8 Mb
Release : 2010-12-15
Category : Mathematics
ISBN : 9048148324
THEOREM: Rotational symmetries of order greater than six, and also five-fold rotational symmetry, are impossible for a periodic pattern in the plane or in three-dimensional space. The discovery of quasicrystals shattered this fundamental 'law', not by showing it to be logically false but by showing that periodicity was not synonymous with long-range order, if by 'long-range order' we mean whatever order is necessary for a crystal to produce a diffraction pat tern with sharp bright spots. It suggested that we may not know what 'long-range order' means, nor what a 'crystal' is, nor how 'symmetry' should be defined. Since 1984, solid state science has been under going a veritable K uhnian revolution. -M. SENECHAL, Quasicrystals and Geometry Between total order and total disorder He the vast majority of physical structures and processes that we see around us in the natural world. On the whole our mathematics is well developed for describing the totally ordered or totally disordered worlds. But in reality the two are rarely separated and the mathematical tools required to investigate these in-between states in depth are in their infancy.
Author : Michael Baake,Uwe Grimm
Publisher : Cambridge University Press
Page : 408 pages
File Size : 50,9 Mb
Release : 2017-11-02
Category : Mathematics
ISBN : 9781108514491
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field.
Author : Gheorghe Paun
Publisher : World Scientific
Page : 500 pages
File Size : 55,9 Mb
Release : 1994-10-25
Category : Computers
ISBN : 9789814518154
This book contains original reviews by well-known workers in the field of mathematical linguistics and formal language theory, written in honour of Professor Solomon Marcus on the occasion of his 70th birthday. Some of the papers deal with contextual grammars, a class of generative devices introduced by Marcus, motivated by descriptive linguistics. Others are devoted to grammar systems, a very modern branch of formal language theory. Automata theory and the algebraic approach to computer science are other well-represented areas. While the contributions are mathematically oriented, practical issues such as cryptography, grammatical inference and natural language processing are also discussed. Contents:Substitutions on Words and LanguagesApplications to Cryptography (A Atanasiu)Grammar Systems: A Multi-Agent Framework for Natural Language Generation (E Csuhaj-Varjú)Normal Forms for Contextual Grammars (A Ehrenfeucht et al.)Control Mechanisms on #-Context-Free Array Grammars (R Freund)On Transitive Cofinal Automata (M Ito & M Katsura)Algebraic Foundations for Montague Grammars (H Jürgensen & K Tent)A Periodic Languages and Generalizations (J Kari & G Thierrin)Matrix Grammars Versus Parallel Communicating Grammar Systems (V Mihalache)Reducts Versus Reducing Operators (M Novotný)On Conditional Grammars and Conditional Petri Nets (F-L Tiplea)and other papers Readership: Computer scientists. keywords:Algebra;Array Grammar;Automaton;Chomsky Grammar;Combinatorics on Words;Cryptography;Grammar System;Marcus Grammar;Mereology;Montague Grammar;Natural Language;Petri Net
Author : Michael Baake,Uwe Grimm
Publisher : Cambridge University Press
Page : 407 pages
File Size : 50,5 Mb
Release : 2017-11-02
Category : Mathematics
ISBN : 9781108505550
Quasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The mathematics that underlies this discovery or that proceeded from it, known as the theory of Aperiodic Order, is the subject of this comprehensive multi-volume series. This second volume begins to develop the theory in more depth. A collection of leading experts, among them Robert V. Moody, cover various aspects of crystallography, generalising appropriately from the classical case to the setting of aperiodically ordered structures. A strong focus is placed upon almost periodicity, a central concept of crystallography that captures the coherent repetition of local motifs or patterns, and its close links to Fourier analysis. The book opens with a foreword by Jeffrey C. Lagarias on the wider mathematical perspective and closes with an epilogue on the emergence of quasicrystals, written by Peter Kramer, one of the founders of the field.
Author : Francoise Axel,Denis Gratias
Publisher : Springer Science & Business Media
Page : 624 pages
File Size : 48,8 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783662031308
This book is the collection of most of the written versions of the Courses given at the Winter School "Beyond Quasicrystals" in Les Houches (March 7-18, 1994). The School gathered lecturers and participants from all over the world and was prepared in the spirit of a general effort to promote theoretical and experimental interdisciplinary communication between mathematicians, theoretical and experimental physicists on the topic of the nature of geometric order in solids beyond standard periodicity and quasi periodicity. The overall structure of the book reflects the wish of the editors to pose this fundamental question of geometric order in solids from both the experimental and theoretical point of view. The first part is devoted more specifically to quasicrystals. These materials were the common starting point of most of the audience and present a first concrete example of a non-trivial geometric order. We chose to focus on a few fundamental aspects of quasicrystals related to hidden symmetries in solids which are not easily found in standard textbooks on the topic, not to reach an exhaustive survey which is already available elsewhere.
Author : F. Bertola,U. Curi
Publisher : Cambridge University Press
Page : 196 pages
File Size : 46,9 Mb
Release : 1993-07-30
Category : Science
ISBN : 0521382033
Long awaited proceedings of an important conference on the anthropic prininciple.
Author : Douglas Bridges,Hajime Ishihara,Michael Rathjen,Helmut Schwichtenberg
Publisher : Cambridge University Press
Page : 864 pages
File Size : 41,8 Mb
Release : 2023-03-31
Category : Mathematics
ISBN : 9781009041416
Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches.
Author : Artur Avila,Michael Th. Rassias,Yakov Sinai
Publisher : Springer Nature
Page : 388 pages
File Size : 45,6 Mb
Release : 2022-11-01
Category : Mathematics
ISBN : 9783031053313
Analysis at Large is dedicated to Jean Bourgain whose research has deeply influenced the mathematics discipline, particularly in analysis and its interconnections with other fields. In this volume, the contributions made by renowned experts present both research and surveys on a wide spectrum of subjects, each of which pay tribute to a true mathematical pioneer. Examples of topics discussed in this book include Bourgain’s discretized sum-product theorem, his work in nonlinear dispersive equations, the slicing problem by Bourgain, harmonious sets, the joint spectral radius, equidistribution of affine random walks, Cartan covers and doubling Bernstein type inequalities, a weighted Prékopa-Leindler inequality and sumsets with quasicubes, the fractal uncertainty principle for the Walsh-Fourier transform, the continuous formulation of shallow neural networks as Wasserstein-type gradient flows, logarithmic quantum dynamical bounds for arithmetically defined ergodic Schrödinger operators, polynomial equations in subgroups, trace sets of restricted continued fraction semigroups, exponential sums, twisted multiplicativity and moments, the ternary Goldbach problem, as well as the multiplicative group generated by two primes in Z/QZ. It is hoped that this volume will inspire further research in the areas of analysis treated in this book and also provide direction and guidance for upcoming developments in this essential subject of mathematics.
Author : Ted Janssen,Gervais Chapuis,Marc de Boissieu
Publisher : Oxford University Press, USA
Page : 481 pages
File Size : 46,5 Mb
Release : 2007-05-24
Category : Science
ISBN : 9780198567776
Most materials and crystals have an atomic structure which is described by a regular stacking of a microscopic fundamental unit, the unit cell. However, there are also many well ordered materials without such a unit cell. This book deals with the structure determination and a discussion of the main special properties of these materials.
Author : Anonim
Publisher : Unknown
Page : 480 pages
File Size : 49,6 Mb
Release : 1978
Category : Biology
ISBN : UOM:39015000416746
Author : Masaki Kashiwara,Tetsuji Miwa
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200871
'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.
