LEADER 05905nam 22007332 450 001 9910828054403321 005 20240405100410.0 010 $a1-316-18318-1 010 $a1-316-18367-X 010 $a1-316-18377-7 010 $a1-316-18448-X 010 $a1-316-18473-0 010 $a1-316-18403-X 010 $a1-139-02525-2 035 $a(CKB)3720000000033886 035 $a(EBL)1823053 035 $a(SSID)ssj0001425989 035 $a(PQKBManifestationID)11840121 035 $a(PQKBTitleCode)TC0001425989 035 $a(PQKBWorkID)11381214 035 $a(PQKB)10850748 035 $a(UkCbUP)CR9781139025256 035 $a(Au-PeEL)EBL1823053 035 $a(CaPaEBR)ebr11017189 035 $a(CaONFJC)MIL733769 035 $a(OCoLC)904404337 035 $a(MiAaPQ)EBC1823053 035 $a(PPN)261331957 035 $a(EXLCZ)993720000000033886 100 $a20110218d2013|||| uy| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAperiodic order$hVolume 1$iA mathematical invitation /$fMichael Baake, Uwe Grimm$b[electronic resource] 205 $a1st ed. 210 1$aCambridge :$cCambridge University Press,$d2013. 215 $a1 online resource (xvi, 531 pages) $cdigital, PDF file(s) 225 1 $aEncyclopedia of mathematics and its applications ;$vvolume 149 300 $aTitle from publisher's bibliographic system (viewed on 05 Oct 2015). 311 $a1-336-02483-6 311 $a0-521-86991-9 320 $aIncludes bibliographical references and index. 327 $aCover; Half-title; Series information; Title page; Copyright information; Table of contents; Foreword; Preface; Chapter 1 Introduction; Chapter 2 Preliminaries; 2.1. Point sets; 2.2. Voronoi and Delone cells; 2.3. Groups; 2.4. Perron-Frobenius theory; 2.5. Number-theoretic tools; Chapter 3 Lattices and Crystals; 3.1. Periodicity and lattices; 3.2. The crystallographic restriction; 3.3. Root lattices; 3.4. Minkowski embedding; Chapter 4 Symbolic Substitutions and Inflations; 4.1. Substitution rules; 4.2. Hulls and their properties; 4.3. Symmetries, invariant measures and ergodicity 327 $a4.4. Metallic means sequences4.5. Period doubling and paper folding; 4.6. Thue-Morse substitution; 4.7. Rudin-Shapiro and Kolakoski sequences; 4.8. Complexity and further directions; 4.9. Block substitutions; Chapter 5 Patterns and Tilings; 5.1. Patterns and local indistinguishability; 5.2. Local derivability; 5.3. Repetitivity and finite local complexity; 5.4. Geometric hull; 5.5. Proximality; 5.6. Symmetry and inflation; 5.7. Local rules; Chapter 6 Inflation Tilings; 6.1. Ammann-Beenker tilings; 6.2. Penrose tilings and their relatives; 6.3. Square triangle and shield tilings 327 $a6.4. Planar tilings with integer inflation multiplier6.5. Examples of non-Pisot tilings; 6.6. Pinwheel tilings; 6.7. Tilings in higher dimensions; 6.8. Colourful examples; Chapter 7 Projection Method and Model Sets; 7.1. Silver mean chain via projection; 7.2. Cut and project schemes and model sets; 7.3. Cyclotomic model sets; 7.4. Icosahedral model sets and beyond; 7.5. Alternative constructions; Chapter 8 Fourier Analysis and Measures; 8.1. Fourier series; 8.2. Almost periodic functions; 8.3. Fourier transform of functions; 8.4. Fourier transform of distributions 327 $a8.5. Measures and their decomposition8.6. Fourier transform of measures; 8.7. Fourier-Stieltjes coefficients of measures on S1; 8.8. Volume averaged convolutions; Chapter 9 Diffraction; 9.1. Mathematical diffraction theory; 9.2. Poisson's summation formula and perfect crystals; 9.3. Autocorrelation and diffraction of the silver mean chain; 9.4. Autocorrelation and diffraction of regular model sets; 9.5. Pure point diffraction of weighted Dirac combs; 9.6. Homometric point sets; Chapter 10 Beyond Model Sets; 10.1. Diffraction of the Thue-Morse chain 327 $a10.2. Diffraction of the Rudin-Shapiro chain10.3. Diffraction of lattice subsets; 10.4. Visible lattice points; 10.5. Extension to Meyer sets; Chapter 11 Random Structures; 11.1. Probabilistic preliminaries; 11.2. Bernoulli systems; 11.3. Renewal processes on the line; 11.4. Point processes from random matrix theory; 11.5. Lattice systems with interaction; 11.6. Random tilings; Appendix A The Icosahedral Group; Appendix B The Dynamical Spectrum; References; List of Definitions; List of Examples; List of Remarks; Index 330 $aQuasicrystals are non-periodic solids that were discovered in 1982 by Dan Shechtman, Nobel Prize Laureate in Chemistry 2011. The underlying mathematics, known as the theory of aperiodic order, is the subject of this comprehensive multi-volume series. This first volume provides a graduate-level introduction to the many facets of this relatively new area of mathematics. Special attention is given to methods from algebra, discrete geometry and harmonic analysis, while the main focus is on topics motivated by physics and crystallography. In particular, the authors provide a systematic exposition of the mathematical theory of kinematic diffraction. Numerous illustrations and worked-out examples help the reader to bridge the gap between theory and application. The authors also point to more advanced topics to show how the theory interacts with other areas of pure and applied mathematics. 410 0$aEncyclopedia of mathematics and its applications ;$vv. 149. 606 $aAperiodic tilings 606 $aQuasicrystals$xMathematics 615 0$aAperiodic tilings. 615 0$aQuasicrystals$xMathematics. 676 $a548.7 700 $aBaake$b Michael$01596714 702 $aGrimm$b Uwe 801 0$bUkCbUP 801 1$bUkCbUP 906 $aBOOK 912 $a9910828054403321 996 $aAperiodic order$93918190 997 $aUNINA