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2 results

  • When can one domain enclose another in 3?

  • Part of
  • Jiazu zhou
  • Journal:
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 59 / Issue 2 / October 1995
    Published online by Cambridge University Press:
    09 April 2009, pp. 266-272
    Print publication:
    October 1995
    • Article
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  • In this paper, we give a sufficient condition (Theorem) in order that one domain D1 bounded by a C2-smooth boundary can be enclosed in, or enclose, another domain D0 bounded by the same kind of boundary. A same kind of sufficient condition for convex bodies (Corollary) is also obtained.

  • Densities for stationary random sets and point processes

  • Wolfgang Weil, John A. Wieacker
  • Journal:
    Advances in Applied Probability / Volume 16 / Issue 2 / June 1984
    Published online by Cambridge University Press:
    01 July 2016, pp. 324-346
    Print publication:
    June 1984

  • For certain stationary random sets X, densities Dφ (X) of additive functionals φ are defined and formulas for are derived when K is a compact convex set in . In particular, for the quermassintegrals and motioninvariant X, these formulas are in analogy with classical integral geometric formulas. The case where X is the union set of a Poisson process Y of convex particles is considered separately. Here, formulas involving the intensity measure of Y are obtained.