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Introduction. The application of a systematic approach to business process modeling is an effective solution for finding options for optimizing the organization’s activities, forecasting and minimizing potential risks. The correct construction of the model allows to systematize each individual process, and all business processes of the enterprise simultaneously. It is important to take into account the peculiarities of the functioning of individual enterprises and to construct business processes in accordance with them.

The comparative analysis of the most common systems of computer mathematics is made and their structure is described. The main functions of the systems of computer mathematics are determined and benefits and disadvantages of using the systems Derive, Mathematika, Matlab, Mathcad, Maple, MuPad, Gran, GeoGebra are directed. The Ukrainian software tool Gran is described which is used for graphical analysis of functions (Gran1), the systems of geometrical objects on the plane (Gran-2D) and objects in space (Gran-3D).

Aim. The simulation of forming process for tooth flanks of worm gears for globoid worm gears by continuous forming method using disk milling cutters for development scientific well-founded recommendations about technological ensuring for manufacture of globoid worm-wheels. Method. The researches are based on kinematic analysis methods of classical mechanics, differential and analytic geometry, theory of gear wheels, theory of forming surfaces of parts by cutting.

The article describes the methodological bases of calculation of multiphase transmission lines with distributed parameters of the type of cable lines of high voltage for the analysis of electromagnetic and transient processes in three-phase cable lines. Methods of constructing mathematical model, choice of their structure and calculation of model parameters are shown. An example of the use and research of mathematical model data in the Matlab system.

The results of theoretical studies on the correspondence of the numerical value of the critical density of internal energy to the value of the enthalpy of melting and the structural-energy analogy between the processes of mechanical destruction and melting  are  analyzed. The  physical  picture  of  the  distribution  of  temperature  field  formed  at  the  time  of  the  birth  defect, assuming considered previously investigated defect-free matter and assuming that the temperature redistribution in volume and at the surface  is uniform.

Extraction of glucomannan from crude porang flour by acid hydrolysis and ethanol precipitation was studied. Effects of acid concentration, temperatures and time were investigated, kinetics model of the process was developed and the parameters were evaluated based on experimental data. New data on yield and purity of glucomannan under various conditions were obtained.

Being an objective element of the global economic system, international migration produces a significant impact on the performance of individual countries nowadays. The economic impact of international migration is driven by various factors, primarily the type of international migration (labour migration, refugee migration, family migration, or student migration) and the legislation of a receiving country which determines the ability of international migrants to interact with the host country’s economy and to produce the respective impact.

A comparative analysis of existing approaches to Cyber-Physical Systems simulation has been conducted. The intrinsic peculiarities of Cyber-Physical Systems have been reasoned and generalized. Thelimitations of available simulation tools have been pointed out. The approach to Cyber-Physical Systems design solutions checking on the basis of timed automata, UPPAAL integrated tool environment and Temporal Logic of Actions usage has been proposed.

Розглянуто найпотужніші та найпоширеніші засоби моделювання та прогнозування поширення вірусних захворювань, проаналізовано можливість їх застосування в умовах України та визначено напрям досліджень у галузі прогнозування та аналізу розвитку епідемій.