Sphere packings:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1999
|
| Schriftenreihe: | Universitext
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 219 - 236 |
| Beschreibung: | XIII, 241 S. graph. Darst. |
| ISBN: | 0387987940 |
Internformat
MARC
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| 100 | 1 | |a Zong, Chuanming |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Sphere packings |c Chuanming Zong. Ed. by John Talbot |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1999 | |
| 300 | |a XIII, 241 S. |b graph. Darst. | ||
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| 490 | 0 | |a Universitext | |
| 500 | |a Literaturverz. S. 219 - 236 | ||
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Datensatz im Suchindex
| _version_ | 1804127566702837760 |
|---|---|
| adam_text | Contents
Preface vii
Basic Notation ix
1. The Gregory Newton Problem
and Kepler s Conjecture 1
1.1. Introduction 1
1.2. Packings of Circular Disks 7
1.3. The Gregory Newton Problem 10
1.4. Kepler s Conjecture 13
1.5. Some General Remarks 18
2. Positive Definite Quadratic Forms
and Lattice Sphere Packings 23
2.1. Introduction 23
2.2. The Lagrange Seeber Minkowski Reduction
and a Theorem of Gauss 25
2.3. Mordell s Inequality on Hermite s Constants
and a Theorem of Korkin and Zolotarev 31
2.4. Perfect Forms, Voronoi s Method, and a Theorem
of Korkin and Zolotarev 33
2.5. The Korkin Zolotarev Reduction and Theorems
of Blichfeldt, Barnes, and Vetcinkin 36
2.6. Perfect Forms, the Lattice Kissing Numbers
of Spheres, and Watson s Theorem 41
xii Contents
2.7. Three Mathematical Geniuses: Zolotarev,
Minkowski, and Voronoi 42
3. Lower Bounds for the Packing Densities of Spheres 47
3.1. The Minkowski Hlawka Theorem 47
3.2. Siegel s Mean Value Formula 51
3.3. Sphere Coverings and the Coxeter Few Rogers
Lower Bound for 5(Sn) 55
3.4. Edmund Hlawka 62
4. Lower Bounds for the Blocking Numbers
and the Kissing Numbers of Spheres 65
4.1. The Blocking Numbers of S3 and S4 65
4.2. The Shannon Wyner Lower Bound for Both
b(Sn) and k{Sn) 71
4.3. A Theorem of Swinnerton Dyer 72
4.4. A Lower Bound for the Translative Kissing Numbers
of Superspheres 74
5. Sphere Packings Constructed from Codes 79
5.1. Codes 79
5.2. Construction A 82
5.3. Construction B 84
5.4. Construction C 85
5.5. Some General Remarks 89
6. Upper Bounds for the Packing Densities
and the Kissing Numbers of Spheres I 91
6.1. Blichfeldt s Upper Bound for the Packing Densities
of Spheres 91
6.2. Rankin s Upper Bound for the Kissing Numbers
of Spheres 95
6.3. An Upper Bound for the Packing Densities
of Superspheres 99
6.4. Hans Frederik Blichfeldt 101
7. Upper Bounds for the Packing Densities
and the Kissing Numbers of Spheres II 103
7.1. Rogers Upper Bound for the Packing Densities
of Spheres 103
7.2. Schlafli s Function 107
7.3. The Coxeter Boroczky Upper Bound
for the Kissing Numbers of Spheres Ill
7.4. Claude Ambrose Rogers 122
Contents xiii
8. Upper Bounds for the Packing Densities
and the Kissing Numbers of Spheres III 125
8.1. Jacobi Polynomials 125
8.2. Delsarte s Lemma 127
8.3. The Kabatjanski Levenstein Upper Bounds
for the Packing Densities and the Kissing Numbers
of Spheres 132
9. The Kissing Numbers of Spheres in Eight
and Twenty—Four Dimensions 139
9.1. Some Special Lattices 139
9.2. Two Theorems of Levenstein, Odlyzko, and Sloane 141
9.3. Two Principles of Linear Programming 142
9.4. Two Theorems of Bannai and Sloane 143
10. Multiple Sphere Packings 153
10.1. Introduction 153
10.2. A Basic Theorem of Asymptotic Type 154
10.3. A Theorem of Few and Kanagasahapathy 157
10.4. Remarks on Multiple Circle Packings 162
11. Holes in Sphere Packings 165
11.1. Spherical Holes in Sphere Packings 165
11.2. Spherical Holes in Lattice Sphere Packings 176
11.3. Cylindrical Holes in Lattice Sphere Packings 178
12. Problems of Blocking Light Rays 183
12.1. Introduction 183
12.2. Hornich s Problem 185
12.3. L. Fejes Toth s Problem 189
12.4. Laszlo Fejes Toth 198
13. Finite Sphere Packings 199
13.1. Introduction 199
13.2. The Spherical Conjecture 200
13.3. The Sausage Conjecture 204
13.4. The Sausage Catastrophe 214
Bibliography 219
Index 237
|
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| dewey-full | 511.6 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.6 |
| dewey-search | 511.6 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV012880511 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:35:23Z |
| institution | BVB |
| isbn | 0387987940 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008767636 |
| oclc_num | 245924864 |
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| owner_facet | DE-29T DE-20 DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-824 DE-634 DE-83 DE-11 DE-188 |
| physical | XIII, 241 S. graph. Darst. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Zong, Chuanming Verfasser aut Sphere packings Chuanming Zong. Ed. by John Talbot New York [u.a.] Springer 1999 XIII, 241 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Literaturverz. S. 219 - 236 Kugelpackung Sphere packings Kugelpackung (DE-588)4165929-6 gnd rswk-swf Kugelpackung (DE-588)4165929-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008767636&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zong, Chuanming Sphere packings Kugelpackung Sphere packings Kugelpackung (DE-588)4165929-6 gnd |
| subject_GND | (DE-588)4165929-6 |
| title | Sphere packings |
| title_auth | Sphere packings |
| title_exact_search | Sphere packings |
| title_full | Sphere packings Chuanming Zong. Ed. by John Talbot |
| title_fullStr | Sphere packings Chuanming Zong. Ed. by John Talbot |
| title_full_unstemmed | Sphere packings Chuanming Zong. Ed. by John Talbot |
| title_short | Sphere packings |
| title_sort | sphere packings |
| topic | Kugelpackung Sphere packings Kugelpackung (DE-588)4165929-6 gnd |
| topic_facet | Kugelpackung Sphere packings |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008767636&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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