Vol 10, No 4 (2016)

Under study is the influence of external and internal random noises on the behavior of concentrations of the components of chemical reactions. We investigate the use of statistical modeling for solving the relevant stochastic differential equations (SDEs). Some results of numerical experiments are presented. To analyze numerical solutions, we use the frequency characteristics that generalize the integral curve and the phase portrait. Numerical experiments show that the random noise even with low intensity causes all kinds of transitions from one oscillation mode to another in the solutions of SDEs.

Analytical expressions are obtained for calculating the stresses in a coal seam in presence of gas diffusion. The solution is given as a sum whose four terms are convergent series. All functions in the relevant expressions can easily be computed either separately or successively; i.e., it is not required to solve infinite systems of equations.

Within the framework of the theory of large deformations, we consider deformation of some material with nonlinear elastic and viscous properties that is located in the gap between two rigid coaxial cylindrical surfaces when the inner surface moves rectilinearly. We study the uniformly acceleratedmotion of the inner cylinder, its subsequentmotion with a constant speed, and further deceleration till the full stop. We calculate stresses, reversible and irreversible deformations, displacements and study the stress relaxation after the full stop of the cylinder.

Under study is some mathematical model for quantitative evaluation of investment projects for development of oil fields at the stage of conceptual design. As the basis of such a model we suggest that the field is considered as a cluster of equitype elements of area pattern of oil wells. The model operates with the net present value as a continuous function of the process parameters and enables us to analyze a broad spectrum of possible options in implementing the investment project. Some important ratios between the technical and economic parameters are obtained in concise and practically suitable forms by application of operational calculus and the Laplace transform.

Under study is a dynamic mixed problem concerning the impact on a circular cylinder and its subsequent movement with a constant speed in an ideal incompressible liquid. The influence is investigated of the physical and geometrical parameters of the problem on the cavity form and the configuration of the external free surface of the liquid for small times. An asymptotic analysis is carried out for the inner free boundary of liquid taking into account the dynamics of separation points. The reaction force of the medium on the cylinder is determined. The necessity is substantiated of introducing additional cavitation zones in the dynamic problem of impact.

We show that each q-ary constant-weight code of weight 3, minimum distance 4, and length m embeds in a q-ary 1-perfect code of length n = (q^m − 1)/(q − 1).

The permanent of a multidimensional matrix is the sum of the products of entries over all diagonals. In this survey, we consider the basic properties of the multidimensional permanent, sufficient conditions for its positivity, available upper bounds, and the specifics of the permanents of polystochasticmatrices.We prove that the number of various combinatorial objects can be expressed via multidimensional permanents. Special attention is paid to the number of 1-factors of uniform hypergraphs and the number of transversals in Latin hypercubes.