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Crowd forecasting is a relatively new task in predicting the future. Today, the crowd studied by classical social psychology has undergone significant changes, which has led to the emergence of such a concept as "Internet crowd". Internet crowd technology is now used to create "dead souls", i.e. fake accounts, using fake names and addresses to form, disseminate opinions and/or impose opinions on real users. The aim of the work is to develop a mathematical model of a virtual crowd to predict its behavior and calculate the probability of transition of a virtual crowd to a real one. The paper highlights the most important factors influencing the emergence of protest movements through the formation of a virtual crowd. It is shown that a person living in a country with a high level of economic development, it is easier to decide to participate in the protest because of confidence in the further stable development of the state. The importance of Internet censorship in the modern world and the possibility of the influence of this factor on the formation of primary groups of protesters in a virtual environment are demonstrated. The methods of mathematical modeling used in the work make it possible to obtain scientifically substantiated variants of development and the probability of changes that the virtual crowd undergoes in time, until its rebirth into real motion. Thus, the assessment of the probability of the transition of the crowd from the virtual to the real state, is important and relevant both in terms of security of the individual citizen and society, and in terms of security of the state as a whole. The proposed model will allow to develop recommendations for specialists who help to ensure a high level of safety in ordinary and extreme situations, to optimize urban development in terms of efficiency of human traffic flow, as well as to effectively manage traffic flow. [ABSTRACT FROM AUTHOR]

In present paper the applied (one-dimensional) model of micropolar elastic thin beam with a circular axis is constructed including the variation principles, on the basis of the two-dimensional equations of micropolar theory of elasticity with constrained rotation written in the polar coordinate system and previously developed hypotheses for thin bodies. Within the framework of this mathematical model, boundary problems with applied values are formulated, which are solved in the final form. Further, the scheme of application of finite element method (FEM) is developed for the boundary problems of micropolar elastic beam with a circular axis with constrained rotation. The boundary problems stated above are solved by using the FEM and on the basis of an analysis obtained through the numerical results, the specific property of micropolarity of the material is established, that it raises the rigidity of the beam as compared with the classical theory. [ABSTRACT FROM AUTHOR]

The key features of the concept of Industry 4.0 development at the enterprises of machinebuilding industry were singled out. The analysis of mathematical models on classes of typical tasks for use at the construction of smart enterprises in the machine-building industry were carried out. It was determined, that in the process of ensuring the innovative development of machinebuilding enterprises within the Industry 4.0 framework it is necessary to use mathematical models, appropriate to machine vision technologies, robotic equipment, automated and intelligent production and control systems within the framework of enterprises’ cyberphysical systems. Such cyberphysical systems should be connected to the outside world through sensors and actuators, receiving data streams from the physical world, establishing and continuously updating the virtual twin of the physical world and including the possibility of interaction in reality according to instructions from the virtual sphere. This will allow ensuring the possibility of joint work, adaptation and development of all enterprise’s systems to improve working conditions, product quality, reduce labour requirements and increase the efficiency of manufacturing process of machine- building enterprises. The introduction of the above classes of mathematical models within the framework of cyberphysical systems must be carried out according to innovations in machinebuilding enterprises, which will ensure the automation of manual labour, the renewal of the already used innovative technologies and their unification in a single information space. The resulted models demand adaptation and the further development according to those innovative decisions, which will define a management of specific machine-building enterprises, depending on the specificity of the enterprise. Recommendations were given to the heads of machine-building enterprises on the use of mathematical models in the process of introducing the concept of smart-enterprises in the Ukrainian machine-building industry. Prospective directions of research were outlined in the paper. [ABSTRACT FROM AUTHOR]

The paper presents the results of theoretical investigations dissipation fertilizer centrifugal working organs machines of their introduction, as well as confirmation of the basic theoretical principles experimentally. Research includes the study of the application process for sowing fertilizer bodies of interaction of working with fertilizers for their capture, acceleration fertilizer centrifugal method, movement of fertilizers from dissipates in the air with the wind and the accompanying air flow to the surface of the soil, as well as the distribution of fertilizers in the soil within the machine width. [ABSTRACT FROM AUTHOR]

The paper deals with the classification system model information space systems, air traffic control for a set of three criteria that allow the simulation of its operation, but the choice of modeling methods necessary to assess the level of possible relationships between the elements of the system. [ABSTRACT FROM AUTHOR]

The mathematical model for a conditioned premise with non-stationary heatmoist loadings is presented in the paper. This model allows to analyze the work of SLE depending on the intensity of changes of heat and moisture receipts indoors. [ABSTRACT FROM AUTHOR]

Important nuclear power safety problem in touch with modeling of melted corium jet spreading inside the coolant pool is considered in the paper. It appears by development of the passive protection systems against severe accidents. The non-linear mathematical developed model is presented for the jet under reactor vessel pool for one of the perspective passive protection systems and the results of its analysis and studies are given. The performed analysis and the results of the numerical simulation done on the base of the model have allowed establishing the interesting behaviors of the system, which may be useful for the scientists, as well as the engineers-constructors of the passive protection systems against severe accidents. [ABSTRACT FROM AUTHOR]

On the basis of the constructed mathematical model of the motion of the new separator cleaning element topper on the head of sugar beet roots and solutions to these expressions PEOM analytical dependence efforts in the point of contact. Constructed image changes depending on the components of efforts at the point of contact with the head of the working element root. Values of the components of of efforts was used in the future for the power analysis of this interaction. [ABSTRACT FROM AUTHOR]

On the basis of the constructed mathematical model of copying parts cleaning element of the new trap with a head topper sugar beet roots and solutions to these expressions PC analytical efforts of this interaction depends on the design parameters of the cleaning element copying. The values obtained were used in the effort to further analysis of the power of this dynamic interaction with the head cleaning element root. [ABSTRACT FROM AUTHOR]