Within the model of social dynamics determined by collective decisions in a stochastic environment (ViSE model), we consider the case of a homogeneous society consisting of classically rational economic agents (or homines economici, or egoists). We present expressions for the optimal majority threshold and the maximum expected capital increment as functions of the parameters of the environment. An estimate of the rate of change of the optimal threshold at zero is given, which is an absolute constant.

A class of optimization control problems is considered in social networks under certain constraints imposed on opinions of agents. Well-known solution methods are discussed. The corresponding mathematical models are proposed and their specific features are identified. Finally, the directions and restrictions on their possible application in practice are analyzed.

Currently, tender procedures occupy an important place in the work of the procurement department of any company. Most of the modern recommendation services operate on web-platforms. Implementation of a tendering system in a company can increase the level of maturity of the procurement process and will not require serious changes in the structure of the processes. This article is devoted to the study of the structure of an integrated tender recommendation system. The integrated tender recommendation system is based on procedures prescribed by federal laws, aggregated tenders from different e-trade sites (presenting state and commercial platforms); it offers to its users additional services. The main purpose of the study is to develop an effective model of an integrated tender recommendation system. In the description part of this article, we present information on peculiarities of the tender procedure in the Russian Federation and modern advisory services are considered. The functional advantages of an integrated system in comparison with the web platform are set out. The structure of the system is designed using several approaches. Using the IDEF0 methodology, a functional model of the system that reflects the work of processes has been developed and described. The operation of the main system and subsystems has been analyzed using the projected diagrams of the DFD methodology. A mathematical model of dynamic filtering of tenders for creating recommendations to users is described. Relying on the basic principles of collaborative filtering and, with the help of appropriate algorithms, the integrated system gives recommendations to users and determines the probability of success in a particular tender. Application of such technology of tenders is possible in companies of different scale. The developed structure of the integrated system and filtering methods for recommendations are based on the basic principles of a new international trend – e-tendering.

The report is devoted to the systematization of large terminological texts on the basis of a hierarchical representation of definitions of concepts. By integration, such models form a semantic network of terms. Thanks to the binary, homogeneous and oriented nature of this network, it is possible to obtain a hierarchical representation model and quantitative indices indicators for evaluating the integrity of the terminological text.

The proposed model is intended to assessment of company's operation effectiveness, which is an important factor at investment decisions making. There are compared indicators of the growth rate, profitability and risk for shares placed on various stock exchanges with an assessment of the intrinsic value and management efficiency of company. The information received is useful for investors and company managers for operating on stock markets.