This study developed models to solve problems of optimisation, production, and consumption in waste management based on methods of system analysis. Mathematical models of the problems of optimisation and sustainable waste management in deterministic conditions and in a fuzzy environment were formulated. The income from production was maximised considering environmental standards that apply to the field of macroeconomics and microeconomics. The proposed approach used MANAGER software to formalise and solve the problem of revenue optimisation with production waste management to optimise the production of oil products with waste management at a specific technological facility of the Atyrau oil refinery in Kazakhstan. Based on the combined application of the principles of maximin and Pareto optimality, a formulation of the problem of production optimisation with waste management was obtained and a heuristic algorithm for solving the formulated fuzzy optimisation problem with waste management was developed.

Sustainable management issues of waste during drilling oil wells in marine conditions, the process of disposal of drill cuttings in the conditions of deficiency, and fuzzy initial information using fuzzy inference system are investigated. Based on the conducted system analysis, the main criteria for controlling the process of re-injection of suspended drill cuttings were analyzed and selected. We described the technology of preparation and injection of drill cuttings slurry into the underground horizon. The method of modeling and management of the process of disposal of drilling cuttings in the marine environment in a fuzzy environment with the use of fuzzy inference system, which helps to overcome the problems of scarcity and fuzziness of the original information due to the knowledge and experience of experts are proposed. The scheme and structure of the elements of the fuzzy inference system based on the Mamdani algorithm are given. The implementation of the fuzzy output system procedure was carried out in MatLab using Fuzzy Logic Toolbox. For the purpose of sustainable waste management in the process of oil production of marine fields, waste management tasks are formulated as a fuzzy mathematical programming problem, which takes into account economic and environmental criteria and many production constraints that may be fuzzy. Since the vector of such criteria is characterized by inconsistency, the developed methods for solving the set tasks of sustainable management are based on various tradeoff schemes modified to work in a fuzzy environment. The novelty and originality of the developed methods lies in the fact that, unlike the well-known methods of similar methods for solving fuzzy problems, they are set and solved without conversion to a system of equivalent deterministic problems, with-out losing the main part of the collected fuzzy information. This allows, through the full use of the original fuzzy information, to obtain a more adequate solution to the fuzzy problem of the real problem under production conditions.

The Sulfur Production Unit with Hydrogen Extraction (SPUHE) plays a critical role in oil refineries by converting hydrogen sulfide into high-quality sulfur and hydrogen. However, optimizing SPUHE operations is challenging due to the uncertainty in process parameters and qualitative assessments of sulfur properties. This study proposes a systematic modeling approach that integrates deterministic, statistical, and fuzzy logic methods to enhance process efficiency and accuracy. Mathematical models were developed for key SPUHE units, including the thermoreactor, Claus reactor, and Cold Bed Absorption reactors. The inclusion of fuzzy logic allows the incorporation of expert knowledge, enabling the assessment of non-measurable sulfur characteristics and improving model reliability. The proposed system accounts for interdependencies between process units, ensuring a comprehensive optimization framework. A comparative analysis with traditional deterministic models demonstrates that the proposed approach improves sulfur recovery efficiency by 11.94%, enhances hydrogen extraction, and reduces operational costs through energy-efficient process adjustments. The developed system provides a robust decision-support tool for refineries, contributing to environmental sustainability and energy optimization. This research offers significant implications for oil refining, hydrogen energy, and industrial process control, demonstrating the advantages of hybrid modeling in managing complex refinery operations under uncertain conditions.

Sequence recognition is a critical task across numerous disciplines. While traditional methods utilizing Finite State Machines (FSMs) offer a structured data representation and high interpretability, their flexibility is limited. Contemporary Machine Learning (ML) algorithms exhibit high accuracy but demand substantial computational resources. Combining these paradigms can enhance the effectiveness of complex sequence recognition. This study explores the integration of FSMs with ML techniques to address sequence analysis problems. Three distinct applications are examined: text classification (spam detection), recognition of genetic sequences related to Alzheimer's disease, and image-based gesture identification. For each, hybrid models were developed and tested, combining Deterministic Finite Automata (DFA), Non-deterministic Finite Automata (NFA), and ML algorithms such as Random Forest, Gradient Boosting, and Multilayer Perceptrons (MLP). Experimental results indicate that these hybrid models achieve performance comparable to traditional ML methods, and in some instances, yield more accurate predictions. In spam classification, neural network models demonstrated the best results, with FSM-neural network combinations providing similar effectiveness. For genetic sequence analysis, gradient boosting-based models exhibited the highest accuracy, with the inclusion of FSMs maintaining performance while enhancing interpretability. In gesture recognition, neural network approaches proved most effective, but integrating FSMs with ensemble methods achieved a high level of predictive capability, surpassing conventional ML models. In conclusion, the integration of FSMs and ML presents a promising avenue in sequence analysis. Future research could focus on optimizing model architectures and applying them to other domains requiring high-precision recognition of intricate structures.

The relevance of the research is determined by the need to simulate wave propagation in heterogeneous media based on phononic crystals. These studies are necessary for the tasks of flaw detection, the development of non-destructive testing methods, geophysics, engineering geophysics and other methods of acoustic research. During the study, it was determined that the fragmentation of the components of two-component phononic crystals into 2, 3, … N equal parts in the unit cell leads to a catastrophic rearrangement of the dispersion relations and the appearance of new elementary wave packets for acoustic waves. Using numerical-analytical methods, it is shown that in two-component phononic crystals, the polydispersity of the components can significantly affect the average characteristics of the propagation of long acoustic waves when the polydisperse crystal is close to monodisperse with a smaller unit cell size. For polydisperse crystals close to monodisperse with the same period (unit cell size), their averaged characteristics for long waves coincide.