Statistics – Computation
Scientific paper
Oct 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991azh....68.1036s&link_type=abstract
Astronomicheskii Zhurnal (ISSN 0004-6299), vol. 68, Sept.-Oct. 1991, p. 1036-1045. In Russian.
Statistics
Computation
2
Celestial Mechanics, Differential Geometry, Spatial Distribution, Computational Astrophysics, Functionals, Statistical Distributions
Scientific paper
The qualitative behavior of the functionals A(k)-prime and B(k)-prime is investigated from the standpoint of integral geometry. It is shown that, out of various cases of the arrangement of objects on closed convex curves with a fixed perimeter, the maximum of A(k)-prime is reached on a circle, and the minimum, on a straight chain. The maximum and minimum of B(k)-prime are reached in the opposite way. It is established that the discovered property of A(k)-prime is a necessary but not sufficient sign of ring-shaped configurations. The results are of interest in connection with the investigation of the spatial and apparent distribution of celestial objects.
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