On Buffon's problem for a lattice and its deformations.
On certain random polygons of large areas.
On set covariance and three-point test sets
The information contained in the measure of all shifts of two or three given points contained in an observed compact subset of is studied. In particular, the connection of the first order directional derivatives of the described characteristic with the oriented and the unoriented normal measure of a set representable as a finite union of sets with positive reach is established. For smooth convex bodies with positive curvatures, the second and the third order directional derivatives of the characteristic...
On some random convex sets
On the Busemann area in Minkowski spaces.
On the Convex Hull of Uniform Random Points in a Simple d-Polytope.
On the Expected Number of k-Sets.
On the measurability of sets of pairs of intersecting nonisotropic straight lines of type beta in the simply isotropic space
The measurable sets of pairs of intersecting non-isotropic straight lines of type and the corresponding densities with respect to the group of general similitudes and some its subgroups are described. Also some Crofton-type formulas are presented.
On the measurability of sets of pairs of straight lines in the simply isotropic space
We study the measurability of sets of pairs of straight lines with respect to the group of motions in the simply isotropic space by solving PDEs. Also some Crofton type formulas are obtained for the corresponding densities.
On the Modality of Convex Polygons.
On the speed of a planar random walk avoiding its past convex hull
On the volume of the double stochastic matrices.
Planar anisotropy revisited
The paper concerns estimation of anisotropy of planar fibre systems using the relation between the rose of directions and the rose of intersections. The discussion about the properties of the Steiner compact estimator is based on both theoretical and simulation results. The approach based on the distribution of the Prokhorov distance between the estimated and true rose of directions is developed. Finally the curved test systems are investigated in both Fourier and Steiner compact analysis of anisotropy....
Quelques considérations concernant le problème de l'aguille de Buffon dans l'espace euclidien En.
Random fixed point theorems for multivalued nonexpansive non-self-random operators.
Random polytopes and the volume-product of symmetric convex bodies.
Random polytopes in a convex polytope, independence of shape, and concentration of vertices.
Random Polytopes in the d- Dimensional Cube.
Random Projections of Regular Simplices.
Random system of lines in the Euclidean plane .