O přesnosti hodnot nabytých průkladem praktických tabulek mathematických
On a Conjecture of R. E. Miles About the Convex Hull of Random Points.
On a geometrical interpretation of a sampling.
On a sphere of influence graph in a one-dimensional space
A sphere of influence graph generated by a finite population of generated points on the real line by a Poisson process is considered. We determine the expected number and variance of societies formed by population of n points in a one-dimensional space.
On a variational problem for an infinite particle system in a random medium.
On an interval-partitioning scheme
In a recent paper, Neuts, Rauschenberg and Li [10] examined, by computer experimentation, four different procedures to randomly partition the interval [0,1] into m intervals. The present paper presents some new theoretical results on one of the partitioning schemes. That scheme is called Random Interval (RI); it starts with a first random point in [0,1] and places the kth point at random in a subinterval randomly picked from the current k subintervals (1
On Buffon's problem for a lattice and its deformations.
On calculation of zeta function of integral matrix
Values of the Epstein zeta function of a positive definite matrix and the knowledge of matrices with minimal values of the Epstein zeta function are important in various mathematical disciplines. Analytic expressions for the matrix theta functions of integral matrices can be used for evaluation of the Epstein zeta function of matrices. As an example, principal coefficients in asymptotic expansions of variance of the lattice point count in the random ball are calculated for some lattices.
On certain random polygons of large areas.
On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane
A method of estimation of intrinsic volume densities for stationary random closed sets in based on estimating volumes of tiny collars has been introduced in T. Mrkvička and J. Rataj, On estimation of intrinsic volume densities of stationary random closed sets, Stoch. Proc. Appl. 118 (2008), 2, 213-231. In this note, a stronger asymptotic consistency is proved in dimension 2. The implementation of the method is discussed in detail. An important step is the determination of dilation radii in the...
On geometric-optical projection of spatial particle size distribution
On invariants of random planar endomorphisms
We estimate the expected value of the gradient degree of certain Gaussian random polynomials in two variables and discuss its relations with some other numerical invariants of random polynomials
On mean value theorems for small geodesic spheres in Riemannian manifolds
On random convex hulls
On random fractals with infinite branching: definition, measurability, dimensions
We investigate the definition and measurability questions of random fractals with infinite branching, and find, under certain conditions, a formula for the upper and lower Minkowski dimensions. For the case of a random self-similar set we obtain the packing dimension.
On random subsets of projective spaces
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 estimation variances in spatial statistics
On some random convex sets
On testing of general random closed set model hypothesis
A new method of testing the random closed set model hypothesis (for example: the Boolean model hypothesis) for a stationary random closed set with values in the extended convex ring is introduced. The method is based on the summary statistics – normalized intrinsic volumes densities of the -parallel sets to . The estimated summary statistics are compared with theirs envelopes produced from simulations of the model given by the tested hypothesis. The p-level of the test is then computed via approximation...