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.
A formula for calculation of the density function of the distance between two independent points randomly and uniformly chosen in a bounded convex domain D is given. The obtained formula permits to find an explicit form of the density function for the domains D with known chord length distributions. In particular, an application of the formula gives explicit expressions for in the cases of a disc, a regular triangle, a rectangle and a regular pentagon.
In this paper, we will discuss a newly constructed subclass of analytic starlike functions by which we will be obtaining sharp upper bounds of the functional for the analytic function belonging to this subclasses.
The power plant tolling contract is one of most complicated derivative instruments among energy derivatives. The paper continues the investigations begun in [1]. Some papers introduce more complicated switching strategies. However, we deal with much simpler dispatch structures, to introduce a new method of evaluation.
In the paper we investigate the multidimensional inverse problem for the system of parabolic equations in an unbounded domain. The proposed problem is reduced to a boundary value problem of infinite elliptic equations and the method of successive approximations allows one to prove the existence and uniqueness theorems for solutions of systems of these elliptic.
The article focuses on the criteria of convergence of series of independent random variables and regularly varying functions. The author examines the convergence of sums of independent random variables in many of the classical limit theorems of probability theory. Limit laws are derived using characteristic functions (or integral Laplace transform). That is, in the transition to the characteristic functions, the transition from a group with addition (and subtraction) to a group with multiplication (and division). This factor is the basis for the research of measurable Cantor groups.
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