The article has been devoted to the problem of improvement real numerical modeling accuracy for the viscous fluid flow between two coaxial half-cylinders on rectangular grids taking into account the filling of cells are used to solve this problem. Approximation of the problem with respect to time is performed on the basis of splitting schemes for physical processes. Difference schemes for solving the hydrodynamic problem are proposed. Analytic solution describing the Taylor-Couette flow is used as a standard to evaluate the numerical solution accuracy of hydrodynamics problems. The simulation was performed on a sequence of condensing computed grids of sizes 11 × 21, 21 × 41, 41 × 81, and 81 × 161 nodes for the areas of smooth and piecewise rectangular boundaries. The grids taking into account the filling of cells are used to improve the smoothness of the solution. In the case of piecewise rectangular approximation the numerical solution error reaches 70%. The grids taking into account the filling of cells reduce the numerical solution error to 6% for the test problem. The test problem shows that using the grid condenced in each spatial direction by 8 times does not lead to increasing the accuracy solutions whereas the solutions accuracy obtained on the basis proposed approach has significant advantage in accuracy.

This paper considers the case of online flashmob 63230522231643, which was intended to show the indignation of Russian opposition to the contested parliamentary elections in 2011. The expression of indignation lasted for 47 days. The organizers called on all who believed that the elections had been rigged to enter the aforementioned number anywhere on the internet so that it could be indexed by search engines. The assumption was that the number could hardly be expected to appear in any context other than the flashmob. Thus, using the Google search engine and counting its appearances, anyone would be able to estimate the extent or severity of indignation, which was the political opposition members thought was as very widespread. However, the flashmob mobilized only a small number of participants and failed to achieve its political goals. At the same time, it turned out to be a rare example of the spread of information in a world that was sparse, that is, considering only those individuals whose political attitudes and dispositions to online activity made them available for participation, we get a social network with relatively few edges, which is a sub-network of a denser and larger network of users.
Methods. The paper presents empirical data on the daily number of flashmob-related tweets and presents a mathematical model to describe the dynamics of a flashmob on Twitter and compare the results of modeling with empirical data for flashmob 63230522231643.
Results. The model correctly represents and explains some important features of the dynamics of a flashmob. To explain the other features would require more a more complex model and building and verifying such a model would call for more abundant empirical data.

Polymerase chain reaction (PCR) is one of the most common experimental methods for solving DNA analysis problems. The possibility of PCR experiment conduction and its success are vastly depend on oligonucleotide structures. Oligonucleotide primers are important component of any PCR, and therefore, there are a number of requirements for their design. In this regard, it is essential to provide computer analysis for the primer selection. In current paper a new approach is proposed for a specific primer design which is based on Boyer-Moore search algorithm. Computer software is developed for computer-aided primer design, which noticeably simplifies the pre-experiment phase and improves PCR results.

The paper covers the research and parameterization of the delay effect in regulation of biological kinetics processes for interacting populations, including the modification of the mathematical model to describe the development of population fluctuations. Numerical implementation of the modified Conway algorithm for a cellular automaton with a ternary state of cells was developed for analysis the model scenarios of dynamics of nonlinear interacting biological populations, taking into account factors that have a significant influence on the nature of researched processes. The transformation conditions of the cells’ state show that the formalized delay can refer to the dynamics of interaction of species and supporting the living conditions of the environment. A numerical implementation of a fundamentally different version of the cellular automaton was proposed. The cellular automaton allow modeling the processes of population dynamics regulation taking into account the delay effect on the basis of three dynamically interacting factors: ontogenetic delay, the necessary to restore resources, and diffusion component depending on the development rate of individuals in the population.

The application of graph theory to describe the various processes of oil refining is an urgent problem. This facilitates the development, analysis and design of production data. In the future, it is possible to obtain qualitative and quantitative characteristics of these processes. This article presents a description using the theory of graph processes for the oxidative regeneration of catalysts of dehydrogenation of butane and catalytic cracking. The obtained regularities using graphs can be used to optimize these processes.

The article is devoted to the development of a sprinkling process model that is in relation to the probabilistic similarity to the simulated process, the numerical implementation of which allows to calculate the matrix of irrigation doses in the sprinkling area, or at the test site. The study was performed using system analysis and probabilistic modeling. The uniform distribution of fluid over the area until 2004 was estimated by the RD 10.11.1–9-89 by the effective irrigation coefficient, in-sufficient irrigation coefficient, and excessive irrigation coefficient. After the introduction of the interstate standard ISO 7749-2-2004 it is estimated by the Christiansen coefficient. New mathematical models and software were designed for probabilistic modeling of the sprinkling process. In constructing the model, the event combining theorem and the Lyapunov theorem were used. As the example, analysis of the operation of twelve sprinklers was carried out. The presented computational experiment was performed to optimize the positioning of the apparatuses according to the criteria of irrigation uniformity and the coefficient of ac-counting completeness of water, which falls on the test site. The obtained results can be used in the process of optimizing the placement of vehicles on «Volzhanka» and «Dnepr» machines. Probabilistic mathematical models of the sprinkling process make it possible to optimize the positioning of apparatuses according to the criteria of uniform irrigation. The programs for modeling water distribution by devices from four positions are applicable only when the distance between the positions is greater than the radius of the sprinkling zone. Irrigation uniformity indicators do not meet agrotechnical requirements. Optimization of the positioning of the apparatus in twelve positions provides excellent indicators for irrigation uniformity. The optimization programs and techniques that were used in the study are applicable to optimize the distribution of other liquids in agricultural technologies, for example, for the distribution of pesticides.