Russian Journal of Mathematical Research. Series A

4-8

Authors: Oleg V. Grober, Tatyana A. Grober, Andrey B. Bychkov

The paper studies the separable Banach spaces of the functions, which satisfy the generalized intensified integral Hölder conditions on the whole real line for the modules of continuity of a broad class, and locally convex spaces , which are the projective limits of the spaces. The paper studies the properties of the Hilbert transformations in the mentioned spaces. The invariance of the "reinforced" spaces regarding the Hilbert operator was obtained under certain restrictions on the modulus of continuity.

15-22

Authors: Irina L. Makarova, Victor I. Samarin, Natalya F. Yakunina

Change of the fuzziness boundaries of the partial solutions feasible region for difference and differential equations is analyzed. It is shown that space-time effect of the dependent variable fuzziness reduction («clutch-effect») is possible. In particular, the focusing of fuzzy variable at the specified equations solving may be controlled by corresponding fuzzy initial and boundary conditions assignment.

38-42

Authors: Arsen R. Simonyan, Elena I. Ulitina, Simon Zh. Simavoryan

The article investigates the multidimensional laws limiting waiting times for virtual models Prabhu. It assumes that the system load is greater than unity. Thus, the system is in a transient mode. For non-stationary mode to obtain accurate results is not easy, so the asymptotic results were obtained under certain restrictions on the admission process.

40-44

Authors: Victor K. Ohanyan

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.

58-61

Authors: Arsen R. Simonyan

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.

4-8

Authors: Narine G. Aharonyan

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.

14-19

Authors: Hakop Kechejian, Victor Ohanyan, Vardan Bardakhchyan

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.

31-36

Authors: Arsen R. Simonyan

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.