The importance of concrete as a structural material is undeniable. The key indicator of concrete as a construction material is strength. Creating and solving a concrete strength mathematical model will allow optimizing raw material costs, increasing the financial result of concrete production, and managing the concrete strength at the stage of its production. The authors reviewed existing concrete strength mathematical models. In the considered models, the concrete strength was influenced by various factors – water-cement ratio, C3S hardness, etc. The authors used the kinetic theory of solid destruction as the basis for their mathematical model of concrete strength. The process of destruction of the sample is considered without deformation. Applying the concept of strained and broken bonds, the authors constructed and solved a concrete strength mathematical model. The main parameters of the model are the speed formation coefficient of the stressed bonds and the speed formation coefficient of destroyed bonds. The model allows estimating the time required for sample destruction at a given load. This is a non-trivial conclusion.

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The authors reviewed the statistics of winter diesel fuel consumption in the Russian Federation for 2000–2017, revealed a positive growth rate. On this fact, the relevance of the study was substantiated. The complexity and importance of the refining process leads to the need for digitalization of oil refineries. The object of the study is obtaining winter diesel fuel, taking into account transport costs. The subject of the study is digitalization of the oil refining process on the base of constructing the mathematical model for obtaining winter diesel fuel, taking into account delivery costs. Main research methods: retrospective data analysis, synthesis, comparison, linear programming methods. The authors considered two stages of winter diesel fuel production: dewaxing a mixture of stages of hydrocarbon raw materials on zeolite and subsequent compounding. For each stage, the authors compiled a system of equations describing the process. The authors also compiled a target function for obtaining winter diesel fuel, taking into account the costs of receiving and delivering. The obtained mathematical model can be used to ensure the required quality of winter diesel fuel (in terms of sulfur content, density and flash point).

The research objective is to simplify the method for estimating the density of straight-run hydrotreated winter diesel fuel (HTDFWs). The density of straight-run hydrotreated winter diesel fuel is one of the quality indicators ultimately determining the density of winter diesel fuel and therefore, the quality of winter diesel fuel in terms of density. Problems: to describe the current methodology for estimating the HTDFWs’ density, isolate the cycles, and express the cycles by formulas. Research methods – analysis, synthesis, comparison, mathematical analysis. As a result, simplified density calculation with expressing cycles by formulas has been proposed. A mathematical model has been obtained to estimate the density of straight-run hydrotreated winter diesel fuel.

The research subject is a mathematical model of municipal solid waste management (hereinafter – MMMSWM). Relevance: the growth of the world’s population and its consumption (primarily, in the Golden Billion countries) leads to a corresponding increase in the amount of solid municipal waste (hereinafter – SMW). This increase is an additional global warming factor. Also, growing SMW requires additional land areas. Since the time of Galileo, science has been the application of mathematics to study any object. In the case of SMW, building and solving a mathematical model of SMW management will reduce the anthropogenic load on Earth. The research objective is to build a mathematical model of municipal solid waste management and propose ways to solve it. The research goal is to perform a literature review of existing mathematical models of municipal solid waste management and suggest a new MMMSWM. The research techniques include retrospective analysis, synthesis, comparison, and methods of the theory of differential equations. The research result is building a new mathematical model of solid municipal waste management, which ensures an acceptable control over the filtrate concentration.