Literatur

Aufwärts: Gleichmäßige Verteilung von Punkten Vorherige Seite: Approximation durch Zonotope Inhalt

Literatur

1: Alexander, J.R.
On the sums of distances between points on a sphere
Acta Math Acad Sci Hung 23 (1972) 443 - 448
2: Beck, J.
Sums of Distances between Points on a Sphere - an Application of the Theory of Irregularities of Distribution to Discrete Geometry
Mathematika 31 (1984) no 1, 33 - 41
3: Beck, J.; Chen, W.W.L.
Irregularities of Distribution
Cambridge, 1987
4: Bezdek, K.; Conelly, R.; Kertész, G.
On the Average Number of Neighbors in a Spherical
Packing : Intuitive Geometry, 1985
5: Bezdek, A.; Bezdek, K.
On the Second Smallest Distance between Points on the Sphere
Geometriae dedicata 29 (1989) no 2, 141 - 152
6: Betke, U.; McMullen, P.
Estimating the Sizes of Convex Bodies from Projektions
J London Math Soc (2) 27 (1983) no 3, 525 - 538
7: Blümlinger, M.
Slice Discrepancy and Irregularities of Distribution on Spheres
Mathematika 38, nr. 1 (1991), 105 - 116
8: Böröczky, K.
Packing of Spheres in Spaces of Constant Curvatures
Acta Math Acad Sci Hungar 32 (1978) no 3-4 , 243 - 269
9: Böröczky, K.
The Problem of Tammes for n = 11
Studia Sci Math Hungar 18 (1983) no 2 - 4, 165 - 171
10: Bourgain, J.; Lindenstrauß, J.
Projektion Bodies
Lecture Notes in Math 1317 (1986/87), 250 - 270
11: Bourgain, J.; Lindenstrauß, J.
Distribution of Points on Spheres and Approximation by Zonotopes
Israel J Math 64 (1988) no 1, 25 - 31
12: Bourgain, J.; Lindenstrauß, J.
Nouveau resultats sur les zonoïds et les corps de projection
Compte Rendus Acad Sci Paris Ser I Math 306 (1988) no 8, 377 - 380
13: Bourgain, J.; Lindenstrauß, J.
Approximation of Zonoids by Zonotopes
Acta Math 162 (1989) no 1-2, 72 - 141
14: Buchta, C.
Zufällige Polytope - eine Übersicht
in : Lecture Notes 1114 (1983), 1 - 13
15: Buchta, C.; Müller, J.; Tichy, R.F.
Stochastic approximation of convex bodies
Math Ann 271 (1985) no 2, 225 - 235
16: Chakerian, G.D.; Filliman, P.
The Measures of the Projektions of a Cube
Studia Sci Math Hung 21 (1986) no 1-2, 103 - 110
17: Clare, B.W.; Kepert, D.L.
The Closest Packing of Equal Circles on a Sphere
Proc Roy Soc London Ser A 405 (1986) no 1829, 329 ff.
18: Gruber, P.M. ; Wills, J.M. (Herausgeber)
Convexity and its Applications
Basel : Birkhäuser 1983
19: Cover, T.M.; Efron, B.
Geometrical Probability and Random Points on a Hypersphere
Ann Math Stat 38 (1967), 213 - 220
20: Coxeter, H.S.M.
Arrangements of Equal Spheres in Non-Euclidean Space
Acta Math Acad Sci Hungar 4 (1954), 263 - 274
21: Coxeter, H.S.M.
Regular Polytopes
Dover Publication, New York, 1973
22: Coxeter, H.S.M.
A Packing of 840 Balls of Radius $9^\circ0'19''$ on the 3-Sphere
in : Intuitive Geometry, 1985
23: Delsarte, P.; Goethals, J.M.; Seidel, J.J.
Spherical Codes and Designs
Geometriae dedicata 6 (1977) no 3, 363 - 388
24: Danzer, L.
Finite Point Sets on with Minimum Distance as large as possible
Discrete Math 60 (1986), 3 - 66
(Habilschrift 1963, Göttingen)
25: Erdös, P.; Hickerson, D.; Pack, J.
A Problem of Leo Moser about Repeated Distances on the Sphere
Amer Math Monthly 96 (1989) no 7, 569 - 575
26: Fejes-Tóth,Gábor
Kreisüberdeckungen der Sphäre
Studia Sci Math Hungar 4 (1969), 225 - 247
27: Fejes-Tóth,Gábor
Packungs- und Überdeckungsprobleme auf der Sphäre
in : 12-tes Steirisches Mathematik Symposium, Graz 1980
28: Fejes-Tóth,Gábor
New Results of Packing and Covering
in : Convexity and its Applications, 1985
29: Fejes-Tóth,Lászlo
Lagerungen in der Ebene auf der Kugel und im Raum
Grundlehren der Mathematischen Wissenschaft, Bd 65
Springer-Verlag, Berlin-New York, 1957, 1972
30: Fejes-Tóth,Lászlo
Reguläre Figuren
Akademiai Kiado, Budapest, 1965
31: Fejes-Tóth,Lászlo; Fejes-Tóth,Gábor
Dictatores on a Planet
Studia Sci Math Hungar 15 (1980), no 1 - 3, 313 - 316
32: Filliman, P.
Extremum Properties for Zonotopes
Geometriae dedicata 27 (1988) no 3, 251 - 262
33: Goethals, J.-M.; Seidel, J.-J.
Cubature formulae, Polytopes and Spherical Designs
in : The Geometric Vein; Springer 1981
34: Goethals, J.-M.; Seidel, J.-J.
The Football
Nieuw Arch Wisk (3) 29 (1981/82) no 1, 50 - 58
35: Groemer, H.
Über die Lagerung von Punkten auf der Kugel
Elemente der Mathematik 15 (1960), 133 - 134
36: Groemer, H.
On the Average Size of Polytopes in a Convex Set
Geometriae dedicata 13 (1982) no 1, 37 - 62
37: Gruber, P.M.
Approximation of Convex Bodies by Polytopes
Rendiconti Circolo Matematiko Palermo (2), 31 (1982) no 2, 195 - 225
38: Gruber, P.M.
Approximation of Convex Bodies
in : Convexity and its Applications, 131 - 162
39: Habicht, W.; v.d. Waerden, B.L.
Lagerungen von Punkten auf der Kugel
Math Ann 123 (1951), 223 - 234
40: Hadwiger, H.
Vorlesungen über Inhalt, Oberfläche und Isoperimetrie
Berlin/Göttingen/Heidelberg : Springer 1957
41: Hars, L.
The Tammes - Problem for n = 10
Studia Sci Math Hung 21 (1986) no 3-4, 439- 451
42: Intuitiv Geometry (Siófok 1985)
Colloq Math Soc János Bolyai, 48
North-Holland-Company; Amsterdam-New York, 1985
43: Kabatjanskijm, G.A.
Bounds for Packings on the Sphere and in Space
Problems of Information Transmission 14 (1978) no 1, 3 - 25
44: Karabinta,A.; Székely, E.
Sur les Empilements Optimaux de Cercles Congruents sur la Sphère.
Ann. Univ. Budapest. Sect Math 16 (1973), 143 - 154
45: Kelly, D.G.; Tolle, J.W.
Expected Number of Vertices of a Random Convex Polyhedron
SIAM J Algebraic Discrete Methods 2 (1981) no 4, 441 - 451
46: Kesten, H.
Symmetric Random Walks on Groups
Transactions of the Amer. Math. Soc. 92 (1959), 336 - 354
47: Kottwitz, D.A.
The Densest Packing of Equal Circles on a Sphere
Acta Cryst. A47 (1991) 158 - 165
48: Kuipers, L.; Niederreiter, H.
Uniform Distribution of Sequences
Wiley & Sons, New York, 1974
49: Leech, J.
Equilibrium of Sets of Particles on a Sphere
Math. Gaz. 41 (1957), 81 - 90
50: Leech, J.
Arrangements of 22 Circles on a Sphere
Ann Univ Budapest Eötvös, Sect Math 31 (1988) pp 27 - 37 (1989)
51: Leichtweiß, K.
Konvexe Mengen
Hochschultext zur Mathematik, Springer, 1980
52: Linhart, J.
An Upper Bound for Equilateral Zonotopes
in : Intuitive Geometry
53: Linhart, J.
Extremaleigenschaften der Regulären 3-Zonotope
Studia Sci Math Hung 21 (1986) no 1-2, 181 - 188
54: Linhart, J.
Über die Varianz der Breite von Zonotopen
Beiträge Algebra Geom 27 (1988), 55 - 62
55: Linhart, J.
Approximation of a Ball using Zonotopes
Arch Math (Basel) 53 (1989) no 1, 82 - 86
56: Linhart, J.; Österreicher, F.
Gleichmäßige Verteilung von Punkten in gewissen metrischen Räumen, speziell auf der Kugel
Monatshefte der Mathematik 89 (1980), 111 - 120
57: Lubotzsky, A.; Phillips, R.; Sarnak, P.
Hecke Operators and Distributing Points on a Sphere I
Comm. on Pure and Appl. Math., Vol XXXIX, (1986), nr Supplement, S. 149 - 186
58: Lubotzsky, A.; Phillips, R.; Sarnak, P.
Hecke Operators and Distributing Points on II
Comm. on Pure and Appl. Math., Vol XXXX, nr 4 (1987), 401 - 420
59: Mackay, A.L.; Finney, J.L.; Gotoh, K.
The Closest Packing of Equal Spheres on a Spherical Surface
Acta Cryst. A33, (1977), 98 - 100
60: Mackay, A.L.
The Packing of Three Dimensional Spheres on the Surface of a Four-Dimensional Hypersphere
J Phys 13 (1980) no 11, 3373 - 3379
61: Martini, Horst
Some Results and Problems around Zonotops
in : Intuitive Geometry, 1985
62: Melnyk, T.W.; Knop, O.; Smith, W.R.
Extremal Arrangements of Points and Unit Charges on a Sphere: Equilibrium Configurations Revisited
Canadian Journal of Chemistry 55 (1977), 1745 - 1761
63: Meschkowski, H.
Ungelöste und unlösbare Probleme der Geometrie
Braunschweig, Bibliographisches Institut, 1960
64: Miles, R.E.
Isotropic Random Simplizes
Adv. Appl. Prob 3, (1971), 353 - 382
65: Molnár, J.
Kreislagerungen auf einer Kugel
Mat Lapok 4 (1953), 113 - 123
66: Molnár, J.
Sur les Empilements Optimaux des Sphères dans une Sphère de l'Espace à courbure costante à n Dimensions
Ann Univ Sci Budapest 18 (1974), 87 - 99
67: Müller, C.
Spherical Harmonics
Lecture Notes in Mathematics, 17; Springer, 1967
68: Neumaier, A.
Discrete Measures for Spherical Design
Nederl Akad Wetensch Indeg Math 50 (1988) no 3, 321 - 334
69: Neutsch, W.
Optimal Spherical Designs and Numerical Integration on the Sphere
J Comput Phys 51 (1983) no 2, 313 - 325
70: Robinson, R.M.
Arrangement of 24 Circles on a Sphere
Math Ann 144 (1961), 17 - 48
71: Robinson, R.M.
Finite Sets of Points on a Sphere with Each Nearest to Five Others
Math Ann 179 (1969), 296 - 318
72: Rogers, C.A.
Packing and Covering
Cambridge University Press 1964
73: Schneider, R.
Zur optimalen Approximation konvexer Hyperflächen durch Polyeder
Math Ann 256 (1981), 289 - 301
74: Schneider, R.; Weil, W.
Zonoids and related topics
in : Convexity and its Applications
75: Schütte, K.
Überdeckung der Kugel mit höchstens acht Kreisen
Math Ann 129 (1955), 181 - 186
76: Schütte, K.; v.d. Waerden, B.L.
Auf welcher Kugel haben 5,6,7,8 oder 9 Punkte mit Mindestabstand Eins Platz ?
Math. Ann. 123 (1951), 96 - 124
77: Seymour, P.D.; Zaslavsky, T.
Averaging Sets
Adv. of Math. 52 (1984), 213 - 240
78: Stolarsky, K.B.
Sums of distances between points on a sphere II
Proc Amer Math Soc 41 (1973), 572 - 582
79: Stolarsky, K.B.
An extremal Characterisation of regular Simplizes via Gegenbauer Polynomials.
Geometriae dedicata 5 (1976) no 2, 229 - 238
80: Strohmajer, J.
Über die Verteilung von Punkten auf der Kugel
Ann Univ Sci Budapest Eötvös Sect Math 6 (1963), 49 - 53
81: Szabó, J.; Roller, B.
Anwendung der Matrizenrechnung auf Stabwerke
Akademiai Kiado, Budapest, 1978
82: Székely, E.
Sur le problème de Tammes
Ann Univ Sci Budapest Eötvös Sect Math 17 (1974) pp 157 - 175
83: Tammes, R.M.L.
On the Origin Number and Arrangement of the Places of Exits on the Surface of Pollengrains.
Rec.Trv.Bot.Neerl. 27 (1930), 1 - 84
84: Tarnai, T.
Note on the Packing of 19 Equal Circles on a Sphere
Elem Math 22 (1967) 108 - 110
Elem Math 39 (1984) no 2, 25 - 27
85: Tarnai, T.
Packing of 180 Equal Circles on a Sphere
Elem Math 38 (1983), no 5, 199 - 122
86: Tarnai, T.
Multisymmetric Packing of Equal Circles on a Sphere
Ann Univ Sci Budapest Eötvös Sect Math 27 (1984), pp 199 - 204
87: Tarnai, T.
Spherical Circle-Packing in Nature, Practise and Theory
Structural Topology 1984 no 9 , 39 - 58
88: Tarnai, T.; Gáspár, Zs.
Improved Packing of Equal Circles on a Sphere and Rigidity of its Graph
Math Proc Cambridge Philos Soc 93 (1983) no 2, 191 - 218
89: Tarnai, T.; Gáspár, Zs.
Rigidity of the Graphs of the Spherical Circle Packings
Z Angew Math Mech 63 (1983) no 5, T 333 - T 334
90: Tarnai, T.; Gáspár, Zs.
Covering the Sphere with Equal Non-Overlapping Circles
in : Intuitive Geometry , 1985
91: Tarnai, T.; Gáspár, Zs.
Covering the Sphere with 11 Equal Circles
Elem Math 41 (1986), no 2, 35 - 38
92: Tarnai, T.; Gáspár, Zs.
Multisymmetric Close Packings of Equal Spheres on the Spherical Surface
Acta Cryst Sect A 43 (1987) no 5, 612 - 616
93: Tarnai, T.; Gáspár, Zs.
Covering a Sphere by Equal Circles and the Rigidity of its Graph
Math Proc Cambridge Phil Soc, Vol 110, no 1 (1991),pp 71 - 90
94: v.d.Waerden, B.L.
Punkte auf der Kugel. Drei Zusätze
Math Ann 125 (1952), 213 - 222
95: v.d.Waerden, B.L.
Pollenkörner, Punktverteilungen auf der Kugel und Informationstheorie
Die Naturwissenschaft 48 (1961), 189 - 192
96: Wagner, G.
On Means of Distances on the Surface of a Sphere
J Austral Math Soc Ser A 47 (1989) no 3, 466 - 482
97: Wagner, G.
On the product of distances to a Point Set on a Sphere
Pacific J Math 144 (1990) no 2, 389 - 398
98: Wagner, G.
On Averaging Sets
Monatshefte der Mathematik 111 (1991) no 1, 69 - 79
99: Wagner, G.
On a New Method for Constructing Good Point Sets on Spheres
Preprint
100: Wendel, J.G.
A Problem in Geometric Probability
Math Scand 11, (1962), 109 - 111
101: Whyte, L.L.
Unique Arrangement of Points on a Sphere
Amer Math Monthly 59 (1952), 606 - 611
102: Zhou, J.N.
An Inequality Involving the Distances between Points on a Sphere
Kexue Tongbao 33 (1988) no 14, 1045 - 1047
103: Zhou, J.N.
An Inequality of Distances between Points on a Hypersphere
Chinese Sci Bull 34 (1989) no 18, 1514 - 1518
104: Zhou, J.N.
An Inequality of Distances between Points on a Hypersphere
J of Math Research Exposition, 10 (1990), no 1, 65 - 68

2004-03-25