This research paper proposes an innovative approach to urban waste management using intelligent methods of classification, clustering, and forecasting. The application of this approach allows for more efficient waste management and contributes to the sustainable development of the urban environment. The aim of this research is to develop an intelligent method for urban waste management, which includes clustering of waste sources, accurate forecasting of waste volumes, and evaluation of forecast results. To achieve this goal, a real dataset with city characteristics and waste data was used. On account of the war in Ukraine, the authors faced the problem of obtaining open data on waste in Ukraine, so it was decided to use data from another city (Singapore). The results show the high efficiency of the developed method. Comparison of the obtained results with the results of the nearest similar works shows that the main feature of this study is the high accuracy of waste-volume forecasting using the XGBoost model, which reached a level of up to 98%.

Aims: The aim of this study was to develop the mathematical models of the linear elasticity theory of biomaterials by taking into account their fractal structure. This study further aimed to construct a variational formulation of the problem, obtain the main relationships of the finite element method to calculate the rheological characteristics of a biomaterial with a fractal structure, and develop application software for calculating the components of the stress-strain state of biomaterials while considering their fractal structure. The obtained results were analyzed. Background: The development of adequate mathematical models of the linear elasticity theory for biomaterials with a fractal structure is an urgent scientific task. Finding its solution will make it possible to analyze the rheological behavior of biomaterials exposed to external loads by taking into account the existing effects of memory, spatial non-locality, self-organization, and deterministic chaos in the material. Objective: The objective of this study was the deformation process of biomaterials with a fractal structure under external load. Methods: The equations of the linear elasticity theory for the construction of the mathematical models of the deformation process of biomaterials under external load were used. Mathematical apparatus of integro-differentiation of fractional order to take into account the fractal structure of the biomaterial was used. A variational formulation of the linear elasticity problem while taking into account the fractal structure of the biomaterial was formulated. The finite element method with a piecewise linear basis for finding an approximate solution to the problem was used. Results: The main relations of the linear elasticity problem, which takes into account the fractal structure of the biomaterial, were obtained. A variational formulation of the problem was constructed. The main relations of the finite-element calculation of the linear elasticity problem of a biomaterial with a fractal structure using a piecewise-linear basis are found. The main components of the stress-strain state of the biomaterial exposed to external loads are found. Conclusion: Using the mathematical apparatus of integro-differentiation of fractional order in the construction of the mathematical models of the deformation process of biomaterials with a fractal structure makes it possible to take into account the existing effects of memory, spatial non-locality, self-organization, and deterministic chaos in the material. Also, this approach makes it possible to determine the residual stresses in the biomaterial, which play an important role in the appearance of stresses during repeated loads.

Mathematical model of the linear elasticity problem for capillary-porous materials with fractal structure is constructed. The basic physical and geometric relationships of the stress-strain state of the considered material are obtained. Integro-differentiation apparatus of fractional order to account the fractal structure of the material in the ratios of linear elasticity was used. A variational formulation of the linear elasticity problem for capillary-porous materials with fractal structure is obtained. A method for getting an approximate solution for the considered problem is proposed. For partial cases the results obtained are analyzed.

Mathematical model of heat and moisture transfer in the materials with fractal structure considering the effects of memory and spatial correlation are synthesized. Explicit and implicit difference schemes for related equations are built. A numerical method predictor-corrector for the implementation of the mathematical model of heat and moisture transfer in materials with fractal structure was introduced. The parallelization of algorithm of implementation this numerical method was proposed.

The two-dimensional mathematical model of rheological behavior of wood in non-isothermal moisture transfer conditions which consider the medium fractal structure, available memory and spatial correlation effects was synthesized. Difference schemes of differential equations of heat and moisture transfer and visco-elastic deformation in the two-dimensional area with appropriate boundary conditions was constructed. The algorithmic and software aspects for implementing the mathematical models using predictor-corrector method was obtained.