Quasicrystals and discrete geometry:
Gespeichert in:
| Körperschaft: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[1998]
|
| Schriftenreihe: | Fields Institute monographs
10 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Aus dem Vorwort: "During the second half of 1995 two related events ... The first one was the NATO Advanced Study Institute (21 August - 1 September, 1995. The second event immediately following the first one was a semester programme ... The present volume can be considered as the proceedings of the 1995 fall programme at The Fields Institute." |
| Beschreibung: | xi, 289 Seiten Illustrationen, Diagramme |
| ISBN: | 0821806823 9780821806821 |
Internformat
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| 245 | 1 | 0 | |a Quasicrystals and discrete geometry |c Jiří Patera |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1998] | |
| 264 | 4 | |c © 1998 | |
| 300 | |a xi, 289 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Fields Institute monographs |v 10 | |
| 500 | |a Aus dem Vorwort: "During the second half of 1995 two related events ... The first one was the NATO Advanced Study Institute (21 August - 1 September, 1995. The second event immediately following the first one was a semester programme ... The present volume can be considered as the proceedings of the 1995 fall programme at The Fields Institute." | ||
| 650 | 7 | |a Combinatorische meetkunde |2 gtt | |
| 650 | 7 | |a Cristallographie mathématique |2 ram | |
| 650 | 7 | |a Groepentheorie |2 gtt | |
| 650 | 7 | |a Groupes, Théorie des |2 ram | |
| 650 | 7 | |a Géométrie combinatoire |2 ram | |
| 650 | 7 | |a Quasikristallen |2 gtt | |
| 650 | 4 | |a Crystallography, Mathematical | |
| 650 | 4 | |a Discrete geometry | |
| 650 | 4 | |a Group theory | |
| 650 | 0 | 7 | |a Kristallographie |0 (DE-588)4033217-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |2 gnd |9 rswk-swf |
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| 689 | 1 | 1 | |a Diskrete Mathematik |0 (DE-588)4129143-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Patera, Jiři |d 1936-2022 |0 (DE-588)122701607 |4 edt | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008406652 | |
Datensatz im Suchindex
| _version_ | 1809402892668370944 |
|---|---|
| adam_text |
Contents
Preface xi
Similarity Submodules and Semigroups 1
Michael Baake and Robert V. Moody
1 Introduction 1
2 Definitions and preliminaries 2
3 Examples in one dimension 3
4 Examples in two dimensions 5
5 Examples in three dimensions 7
Pisot Cyclotomic Quasilattices and Their Symmetry 15
Semigroups
Damien Barache, Bernard Champagne and Jean Pierre Gazeau
1 Introduction 15
2 The concept of a quasilattice in Rd 18
3 How to get quasilattices: Windows in conjugate spaces 22
4 How to get quasilattices: Projection from root lattices 26
5 Symmetry semigroups for quasilattices 39
6 Quasilattices based on sets of /^ integers 46
7 How to get quasilattices: 3D icosahedral quasilattices 54
Appendix A Roots of unity and cyclotomic numbers 60
Appendix B Proof of the Proposition 3.1 63
Three Possible Branches of Determinate Modular 67
Generalization of Crystallography
N. A. BULIENKOV
1 Introduction 67
2 Modules of three dimensional structures of crystals 71
and of generalized crystallography
3 Tetrahedral determinate structures for spaces with opposite 73
signs of curvature
4 The modular model of an icosahedral quasicrystal 88
5 Modular hierarchical pentagonal mosaics 104
6 Conclusions 129
vii
viii Contents
Non Crystallographic Root Systems 135
Liang Chen, Robert V. Moody and Jiri Patera
1 Introduction, review of finite root systems 135
2 Z[r] lattices 140
3 Wythoff polytopes 142
4 Root systems of types H2, H3, if4 143
5 iffc invariant lattices 151
6 Star maps 152
7 Meyer sets and quasicrystals 159
8 Amenability and growth 162
9 Examples of amenable regions 166
10 Inflation, quasiaddition, and generation of quasicrystals 172
Upper Bounds for the Lengths of Bridges 179
Based on Delone Sets
Ludwig Danzer
1 Introduction 179
2 Definitions and preliminaries 179
3 Results 183
4 Proofs 184
5 Tables 190
The Local Theorem for Tilings 193
Nikolai Dolbilin and Doris Schattschneider
1 Preliminaries 194
2 The Theorem 196
Uniform Distribution and the Projection Method 201
A. Hof
1 Introduction 201
2 Definitions and notation 202
3 Ergodicity 203
4 Application to the projection method 204
5 Generalization 205
One Corona is enough for the Euclidean Plane 207
Doris Schattschneider and Nikolai Dolbilin
1 Preliminaries 208
2 The one corona theorem for polygonal tilings 210
3 The Escher problem 236
4 Catalog of Monohedral Tilings 237
Contents ix
Cut and Project Sets in Locally Compact 247
Abelian Groups
Martin Schlottmann
1 Introduction 247
2 Density of cut and project sets 248
3 Proof of Proposition 2.1 250
4 The general density formula 253
5 Regular cut and project sets 255
6 Existence of standard projection strips 258
7 Local uniqueness of standard projection strips 260
8 Conclusion 262
Appendix Topological Abelian Groups 263
Spectrum of Dynamical Systems Arising 265
from Delone Sets
Boris Solomyak
1 Introduction 265
2 Delone sets 266
3 Abstract dynamical systems 269
4 Continuous eigenfunctions 270
5 Pure discrete spectrum 271
Non Locality and Aperiodicity of 277
d Dimensional Tilings
Gerrit van Ophuysen
1 Introduction 277
2 Cluster, tiling and species 278
3 Global aspects 279
4 Non locality 282
5 Consequences of locality 283
6 Results and discussion 287
Index 289 |
| any_adam_object | 1 |
| author2 | Patera, Jiři 1936-2022 |
| author2_role | edt |
| author2_variant | j p jp |
| author_GND | (DE-588)122701607 |
| author_corporate | Advanced Study Institute on the Mathematics of Long Range Aperiodic Order Waterloo, Ontario |
| author_corporate_role | aut |
| author_facet | Patera, Jiři 1936-2022 Advanced Study Institute on the Mathematics of Long Range Aperiodic Order Waterloo, Ontario |
| author_sort | Advanced Study Institute on the Mathematics of Long Range Aperiodic Order Waterloo, Ontario |
| building | Verbundindex |
| bvnumber | BV012393171 |
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| ctrlnum | (OCoLC)38557241 (DE-599)BVBBV012393171 |
| dewey-full | 548/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 548 - Crystallography |
| dewey-raw | 548/.7 |
| dewey-search | 548/.7 |
| dewey-sort | 3548 17 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Mathematik |
| format | Book |
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| isbn | 0821806823 9780821806821 |
| language | English |
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| spelling | Quasicrystals and discrete geometry Jiří Patera Providence, Rhode Island American Mathematical Society [1998] © 1998 xi, 289 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Fields Institute monographs 10 Aus dem Vorwort: "During the second half of 1995 two related events ... The first one was the NATO Advanced Study Institute (21 August - 1 September, 1995. The second event immediately following the first one was a semester programme ... The present volume can be considered as the proceedings of the 1995 fall programme at The Fields Institute." Combinatorische meetkunde gtt Cristallographie mathématique ram Groepentheorie gtt Groupes, Théorie des ram Géométrie combinatoire ram Quasikristallen gtt Crystallography, Mathematical Discrete geometry Group theory Kristallographie (DE-588)4033217-2 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Diskrete Mathematik (DE-588)4129143-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Kristallographie (DE-588)4033217-2 s Mathematische Methode (DE-588)4155620-3 s DE-604 Diskrete Mathematik (DE-588)4129143-8 s Patera, Jiři 1936-2022 (DE-588)122701607 edt Erscheint auch als Online-Ausgabe 978-1-4704-3137-2 Fields Institute monographs 10 (DE-604)BV009737926 10 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008406652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Quasicrystals and discrete geometry Fields Institute monographs Combinatorische meetkunde gtt Cristallographie mathématique ram Groepentheorie gtt Groupes, Théorie des ram Géométrie combinatoire ram Quasikristallen gtt Crystallography, Mathematical Discrete geometry Group theory Kristallographie (DE-588)4033217-2 gnd Mathematische Methode (DE-588)4155620-3 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| subject_GND | (DE-588)4033217-2 (DE-588)4155620-3 (DE-588)4129143-8 (DE-588)1071861417 |
| title | Quasicrystals and discrete geometry |
| title_auth | Quasicrystals and discrete geometry |
| title_exact_search | Quasicrystals and discrete geometry |
| title_full | Quasicrystals and discrete geometry Jiří Patera |
| title_fullStr | Quasicrystals and discrete geometry Jiří Patera |
| title_full_unstemmed | Quasicrystals and discrete geometry Jiří Patera |
| title_short | Quasicrystals and discrete geometry |
| title_sort | quasicrystals and discrete geometry |
| topic | Combinatorische meetkunde gtt Cristallographie mathématique ram Groepentheorie gtt Groupes, Théorie des ram Géométrie combinatoire ram Quasikristallen gtt Crystallography, Mathematical Discrete geometry Group theory Kristallographie (DE-588)4033217-2 gnd Mathematische Methode (DE-588)4155620-3 gnd Diskrete Mathematik (DE-588)4129143-8 gnd |
| topic_facet | Combinatorische meetkunde Cristallographie mathématique Groepentheorie Groupes, Théorie des Géométrie combinatoire Quasikristallen Crystallography, Mathematical Discrete geometry Group theory Kristallographie Mathematische Methode Diskrete Mathematik Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008406652&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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