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Often decisions in social groups are made by consensus. This applies, for example, to the examination in the technical committee for standardization (TC) before the approval of the national standard by Rosstandart. The standard is approved if and only if the secured consensus in the TC. The same approach to standards development was adopted in almost all countries and at the regional and international level. Previously published works of authors dedicated to the construction of a mathematical model of time to reach consensus in technical committees for standardization in terms of variation in the number of TC members and their level of authoritarianism. The present study is a continuation of these works for the case of the formation of coalitions that are often formed during the consideration of the draft standard to the TC. In the article the mathematical model is constructed to ensure consensus on the work of technical standardization committees in terms of coalitions. In the framework of the model it is shown that in the presence of coalitions consensus is not achievable. However, the coalition, as a rule, are overcome during the negotiation process, otherwise the number of the adopted standards would be extremely small. This paper analyzes the factors that influence the bridging coalitions: the value of the assignment and an index of the effect of the coalition. On the basis of statistical modelling of regular Markov chains is investigated their effects on the time to ensure consensus in the technical Committee. It is proved that the time to reach consensus significantly depends on the value of unilateral concessions coalition and weakly depends on the size of coalitions. Built regression model of dependence of the average number of approvals from the value of the assignment. It was revealed that even a small concession leads to the onset of consensus, increasing the size of the assignment results (with other factors being equal) to a sharp decline in time before the consensus. It is shown that the assignment of a larger coalition against small coalitions takes on average more time before consensus. The result has practical value for all organizational structures, where the emergence of coalitions entails the inability of decision-making in the framework of consensus and requires the consideration of various methods for reaching a consensus decision.

The mathematical estimation model for employee labor process, built on the basis of Bayesian network is presented in the article. The great attention is given to the estimation of qualitative characteristics of labor product. Usage of described model is supposed in the companies with the management employee workflows system.

This work is devoted to molecular dynamic modeling of the thermal impact processes on the metal sample consisting of nickel atoms. For the solution of this problem, a continuous mathematical model on the basis of the classical Newton mechanics equations has been used; a numerical method based on the Verlet scheme has been chosen; a parallel algorithm has been offered, and its realization within the MPI and OpenMP technologies has been executed. By means of the developed parallel program, the investigation of thermodynamic equilibrium of nickel atoms’ system under the conditions of heating a sample to desired temperature has been executed. In numerical experiments both optimum parameters of calculation procedure and physical parameters of analyzed process have been defined. The obtained numerical results are well corresponding to known theoretical and experimental data.

Efficiency and completeness of the numerical simulation in oceanography and hydrometeorology are entirely determined by algorithmic features of the construction of an interactive computer simulations in the scale of the oceans with adaptive coated closed seas and coastal waters refined mathematical models, with the possibility of specifying software parallelization calculations near the concrete — the protected areas of the sea coast. An important component of the research is continuous graphical visualization techniques in the course of calculations, including those undertaken in parallel processes with shared RAM or test points on the external media. The results of computational experiments are used in the description of hydrodynamic processes near the coast, which is important in keeping the organization of sea control services and forecasting marine hazards.

Object of research: The creation of algorithm for mass computations of options‘ price for formation of a riskless portfolio. The method is based on the generalization of the Black–Scholes method. The task is the modeling of behavior of all options and tools for their insurance. This task is characterized by large volume of realtime complex computations that should be executed concurrently The problem of the research: depending on conditions approaches to the solution should be various. There are three methods which can be used with different conditions: the finite difference method, the path-integral approach and methods which work in conditions of trade stop. Distributed computating in these three cases is organized differently and it is necessary to involve various approaches. In addition to complexity the mathematical formulation of the problem in literature is not quite correct. There is no complete description of boundary and initial conditions and also several hypotheses of the model do not correspond to real market. It is necessary to give mathematically correct formulation of the task, and to neutralize a difference between hypotheses of the model and their prototypes in the market. For this purpose it is necessary to expand standard formulation by additional methods and develop methods of realization for each of solution branches.

The paper discusses the design and verification stages in the development of complex numerical algorithms to create direct computational experiments in fluid mechanics. The modeling of physical fields and nonstationary processes of continuum mechanics, it is desirable to rely on strict rules of construction the numerical objects and related computational algorithms. Synthesis of adaptive the numerical objects and effective arithmetic- logic operations can serve to optimize the whole computing tasks, provided strict following and compliance with the original of the laws of fluid mechanics. The possibility of using ternary logic enables to resolve some contradictions of functional and declarative programming in the implementation of purely applied problems of mechanics. Similar design decisions lead to new numerical schemes tensor mathematics to help optimize effectiveness and validate correctness the simulation results. The most important consequence is the possibility of using interactive graphical techniques for the visualization of intermediate results of modeling, as well as managed to influence the course of computing experiment under the supervision of engineers aerohydrodynamics– researchers.

Course “Natural models of parallel computing”, given for senior students of the Faculty of Computational Mathematics and Cybernetics, Moscow State University, is devoted to the issues of supercomputer implementation of natural computational models and is, in fact, an introduction to the theory of natural computing, a relatively new branch of science, formed at the intersection of mathematics, computer science and natural sciences (especially biology). Topics of the natural computing include both already classic subjects such as cellular automata, and relatively new, introduced in the last 10–20 years, such as swarm intelligence. Despite its biological origin, all these models are widely applied in the fields related to computer data processing. Research in the field of natural computing is closely related to issues and technology of parallel computing. Presentation of theoretical material of the course is accompanied by a consideration of the possible schemes for parallel computing, in the practical part of the course it is supposed to perform by the students a software implementation using MPI technology and numerical experiments to investigate the effectiveness of the chosen schemes of parallel computing.

This paper is devoted to the analysis of the partial mathematical model describing the process of growth and spread of malignant and normal cells under the influence of chemotherapy. We found the periodic therapy regime, conditions the existence of this regime and suggest the search algorithm of this regime. This paper also includes the examples of simulation and the set of parameter values.