메뉴 건너뛰기




Volumn 35, Issue 2, 1988, Pages 274-291

Convex bodies, economic cap coverings random polytopes

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84971809021     PISSN: 00255793     EISSN: 20417942     Source Type: Journal    
DOI: 10.1112/S0025579300015266     Document Type: Article
Times cited : (153)

References (27)
  • 1
    • 21844440262 scopus 로고
    • Statistics of integral convex polytopes
    • V. I. Arnold. Statistics of integral convex polytopes. Functional Analysis and its Appl., 14 (1980), 1–3.
    • (1980) Functional Analysis and its Appl. , vol.14 , pp. 1-3
    • Arnold, V.I.1
  • 2
    • 0009452589 scopus 로고
    • On the shape of the convex hull of random points
    • I. Bárány and Z. Füredi. On the shape of the convex hull of random points. Probab. Th. Rel. Fields, 77 (1988), 231–240.
    • (1988) Probab. Th. Rel. Fields , vol.77 , pp. 231-240
    • Bárány, I.1    Füredi, Z.2
  • 3
    • 33750448816 scopus 로고
    • Vorlesungen uber Differentialgeometrie II
    • Berlin, Springer
    • W. Blaschke. Vorlesungen uber Differentialgeometrie II. Affine Diffierentialgeometrie (Berlin, Springer, 1923).
    • (1923) Affine Diffierentialgeometrie
    • Blaschke, W.1
  • 6
    • 84971742481 scopus 로고
    • Private communication
    • C. Buchta. Private communication, 1987.
    • (1987)
    • Buchta, C.1
  • 7
    • 0001751998 scopus 로고
    • Helly's theorem and its relatives
    • Convexity (AMS, Providence, RI
    • L. Danzer, B. Grunbaum and V. Klee. Helly's theorem and its relatives. Proc. Symp. Pure Math., vol. VIII, Convexity (AMS, Providence, RI, 1963).
    • (1963) Proc. Symp. Pure Math. , vol.8
    • Danzer, L.1    Grunbaum, B.2    Klee, V.3
  • 8
    • 84971676863 scopus 로고    scopus 로고
    • On the convex hull of random points in a polytope
    • R. A. Dwyer, On the convex hull of random points in a polytope. To appear in J. Applied Prob.
    • J. Applied Prob
    • Dwyer, R.A.1
  • 9
    • 84972015971 scopus 로고
    • The directions of the line segments and of the r-dimensional balls on the boundary of a convex body in Euclidean space
    • G. Ewald, L. G. Larman and C. A. Rogers. The directions of the line segments and of the r-dimensional balls on the boundary of a convex body in Euclidean space. Mathematika, 17 (1970), 1–20.
    • (1970) Mathematika , vol.17 , pp. 1-20
    • Ewald, G.1    Larman, L.G.2    Rogers, C.A.3
  • 10
    • 0040415806 scopus 로고
    • Random polytopes in the d-dimensional cube
    • Z. Furedi. Random polytopes in the d-dimensional cube. Discrete and Comp. Geometry, 1 (1986), 315–319.
    • (1986) Discrete and Comp. Geometry , vol.1 , pp. 315-319
    • Furedi, Z.1
  • 11
    • 0013465628 scopus 로고
    • On the mean value of the volume of a random polytope in a convex set
    • H. Groemer. On the mean value of the volume of a random polytope in a convex set. Arch. Math., 25 (1974), 86–90.
    • (1974) Arch. Math. , vol.25 , pp. 86-90
    • Groemer, H.1
  • 12
    • 0001973248 scopus 로고
    • Approximation of convex bodies, Convexity and its applications
    • ed. P. M. Gruber and J. M. Wills (Basel, Birkhäuser
    • P. M. Gruber. Approximation of convex bodies, Convexity and its applications, ed. P. M. Gruber and J. M. Wills (Basel, Birkhäuser, 1983).
    • (1983)
    • Gruber, P.M.1
  • 13
    • 0011338205 scopus 로고
    • In most cases approximation is irregular
    • P. M. Gruber. In most cases approximation is irregular. Rendiconti Sem. Mat. Torino, 41 (1983), 19–33.
    • (1983) Rendiconti Sem. Mat. Torino , vol.41 , pp. 19-33
    • Gruber, P.M.1
  • 14
    • 84971747825 scopus 로고
    • Private communication
    • R. Kannan. Private communication, 1987.
    • (1987)
    • Kannan, R.1
  • 15
    • 84959745161 scopus 로고
    • A lower bound for Heilbronn's problem
    • J. Komlos, J. Pintz and E. Szemeredi. A lower bound for Heilbronn's problem. J. London Math. Soc. (2), 25 (1982), 13–24.
    • (1982) J. London Math. Soc. , vol.25 , Issue.2 , pp. 13-24
    • Komlos, J.1    Pintz, J.2    Szemeredi, E.3
  • 16
    • 0039940455 scopus 로고
    • Estimation of the number of vertices of a convex integral polyhedron in terms of its volume
    • S. B. Konyagin and K. A. Sevastyanov. Estimation of the number of vertices of a convex integral polyhedron in terms of its volume. Functional Analysis and its Appl., 18 (1984), 13–15.
    • (1984) Functional Analysis and its Appl. , vol.18 , pp. 13-15
    • Konyagin, S.B.1    Sevastyanov, K.A.2
  • 17
    • 0002420944 scopus 로고
    • A theorem on non-homogeneous lattices
    • A. M. Macbeath. A theorem on non-homogeneous lattices. Annals of Math. (2), 56 (1952), 269–293.
    • (1952) Annals of Math. , vol.56 , Issue.2 , pp. 269-293
    • Macbeath, A.M.1
  • 20
    • 0012882958 scopus 로고
    • On a problem of Heilbronn, III
    • K. F. Roth. On a problem of Heilbronn, III. Proc. London Math. Soc. (3), 25 (1972), 543–549.
    • (1972) Proc. London Math. Soc. , vol.25 , Issue.3 , pp. 543-549
    • Roth, K.F.1
  • 22
    • 33646777279 scopus 로고
    • Approximation of convex bodies by random polytopes
    • R. Schneider. Approximation of convex bodies by random polytopes. Aequationes Math., 32 (1987), 304–310.
    • (1987) Aequationes Math. , vol.32 , pp. 304-310
    • Schneider, R.1
  • 23
    • 0000623082 scopus 로고
    • A problem in geometric probability
    • J. G. Wendel. A problem in geometric probability. Math. Scand., 11 (1962), 109–111.
    • (1962) Math. Scand. , vol.11 , pp. 109-111
    • Wendel, J.G.1
  • 24
    • 84971689598 scopus 로고
    • Einige Probleme der polyedrischen Approximation
    • Frieburg i. Br.
    • J. A. Wieacker. Einige Probleme der polyedrischen Approximation. Diplomarbeit (Frieburg i. Br., 1987).
    • (1987) Diplomarbeit
    • Wieacker, J.A.1
  • 25
    • 0001432978 scopus 로고
    • A lower bound for the volumes of strictly convex bodies with many boundary points
    • G. E. Andrews. A lower bound for the volumes of strictly convex bodies with many boundary points. Trans. Amer. Math. Soc., 106 (1965), 270–279.
    • (1965) Trans. Amer. Math. Soc. , vol.106 , pp. 270-279
    • Andrews, G.E.1
  • 26
    • 0002273065 scopus 로고
    • Uber eine Formel Blaschkes zur Affinoberflache
    • K. Leichtweiss. Uber eine Formel Blaschkes zur Affinoberflache. Studia Math. Hung., 21 (1986), 453–474.
    • (1986) Studia Math. Hung. , vol.21 , pp. 453-474
    • Leichtweiss, K.1
  • 27
    • 0002171401 scopus 로고
    • Boundary structure and curvature of convex bodies
    • Birkhäuser, Basel
    • R. Schneider. Boundary structure and curvature of convex bodies. Proc. Geom. Symp., Siegen, 1978 (Birkhäuser, Basel, 1979), 13–59.
    • (1979) Proc. Geom. Symp., Siegen, 1978 , pp. 13-59
    • Schneider, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.