DOI: 10.25136/2409-8647.2021.1.27680

Abstract: The subject of this research is the processes of price formation for raw materials depending on the demand for end consumer products. The article reviews a mathematical model that is based on the principle of maximum utility. The proposed model is founded on the stage-by-stage determination of the production output and consumption of end products, as well as corresponding prices depending on the prices of used raw materials and semi-finished products. The prices for intermediate products and raw materials are formed depending on the need for end products output with their optimization by demand. The article provides the basic mathematical ration with regards to using principle of maximum utility applicable to the demand-supply model and its implementation in multi-stage production. The acquired results indicate weak dependence of production output and prices for end products on the cost of raw material in terms of advanced refining. With limited production capacity of raw materials, the dynamics of prices is well predicted. The results of modeling, compared to the available statistical data, indicate the adequacy of the proposed model to the unfolding economic processes. It is determined that the accuracy of price prediction for raw products with a significant volume of its subsequent processing is limited.

DOI: 10.25136/2409-8647.2020.1.29404

Abstract: The subject of this research is the model of business development that describes the dependence of ongoing volume of production from previous investments and intensity of wear of production capacities. The investment process is characterized by a delay between the moment of investment, actual return and its continuation, gradual decrease in the level of return, and discreetness of investments. In the process of modeling, discrete investment were replaced by an integral, which leads to integral-differential equation, and in terms of facile assumption to the linear standard differential equation of second order or their system, solved by the disharmonious fluctuations on the background of an aperiodic trend. As the method of analysis of correspondence of the model data with the actual dynamics of business development, the research utilizes computational solution of the emerging differential equations. Comparison of the model data with the known statistics reveals their adequacy to the current economic processes. Statistical data contains noise component, which consists of various economic and political factors and principally limits the precision of forecasting. Differences in the length of fluctuation periods by industries impedes analysis of the economic behavior as a whole. At the same time, forecast of crisis phenomena that emerge in superposition of the phases of industry fluctuations can be executed with sufficient level of precision.

DOI: 10.25136/2644-5522.2019.1.27031

Abstract: The article discusses the methodology for estimating the noise component in time series with variable pitch, its justification, and suggests an algorithm for removing noise from data. The analysis is based on the requirement of smoothness of a function representing the original data and having continuous derivatives up to the third order. The proposed method and algorithms for estimating and eliminating noise in the data under the assumption of smoothness, the function they represent, allow reasonably determining both absolute and relative noise in the data, regardless of the uniformity of the measurement step in the source data, the noise level in the data, remove the noise component from the data . The algorithm for solving the problem is based on minimizing the deviations of the calculated values from the smooth function, provided that the deviations from the source data correspond to the noise level. The proposed method and algorithms for estimating and eliminating noise in the data under the assumption of smoothness, the function they represent, allow reasonably determining both absolute and relative noise in the data, regardless of the uniformity of the measurement step in the source data and their noise, and remove the noise component from the data. Considering the smoothness of the data obtained as a result of noise elimination, the data obtained by noise elimination are suitable for detecting both analytical and differential dependencies in them.