The recognition of bounded convex bodies D by means of random k-flats (k-dimensional planes) intersecting D is one of the interesting problems of Stochastic Geometry. In particular, the problem of recognition of bounded convex domains D by chord length distribution function is of much interest. One can consider the case when the orientation and the length of the chords are observed. We refer this case as the orientation-dependent chord length distribution. All these problems are the problems of geometric tomography, since orientation-dependent chord length distribution function at point y is the probability that parallel X-ray in a fixed direction is less than or equal to y. Investigation of convex bodies by orientation-dependent chord length distribution is equivalent to the investigation of their covariograms. The present note considers some problems and recent results related to covariograms, and their applications to various problems of tomography.
The combinatorial junctions in fuzzy discrete initial sets of elements and the junctions with fuzzy number of elements are analyzed. The examples of calculation of a number of the fuzzy combinatorial junctions are presented. The peculiarities of event fuzzy probabilities due to fuzzy combinatorics are considered. It is shown that during probability problem solving upon Bernoulli conditions scheme account must be taken of the fuzzy variables interaction (dependence). The permutations in the presence of fuzzy number of indistinguishable elements that unified into respective clusters are investigated separately.
We consider the least studied queuing system - model GI | G | s | ∞. In the case of the Poisson distribution for the incoming flow of the system is sufficiently studied in the works of classical queuing theory. The absence of this assumption complicates the study of the model, so we were limited to the results of the existence of limiting stationary distribution for the main characteristics and the rate of convergence to limit processes.
The article discusses the single-channel queuing system with waiting. The basic assumption - the incoming flow of events is a Poisson distribution. A class of limit distributions for the basic functions of discrete and continuous performance under different constraints on the system load.
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