The educational optimization process is widely researched in the theoretical aspect. Analyzing existing sources made it possible to highlight the research issues: the need to create an optimizing distance studying model, in which work with weaker students becomes possible both within the educational process and in individual or group independent work. The study aims to develop an information-logical model for optimizing distance studying. This model should provide for the learning process organization in such a way as to strengthen the weaknesses of students, reveal their potential and focus on the comprehensive development of knowledge and skills. The task formalization is carried out using the Hungarian algorithm and Boolean variables. The main work limitation is the operation with integers. Discreteness manifests itself already at the modelling stages in many problems, for example, when working with Boolean variables. An example with the most straightforward information model construction using the logical functions "true/false" with the transition to a chain of matrices is given. It demonstrates the studying optimization algorithm and presents an expanded information-logical model. The presented model was preliminary tested in one of the academic groups of the S. Seifullin Kazakh Agro Technical Research University. Students' knowledge inspections were carried out at the approbation beginning. Then a student group working on a student project was divided into subgroups according to the algorithm. The knowledge inspection showed an 11.3% improvement in results at the work's end. Further research on this topic may consist of expanding the presented model's capabilities and developing appropriate modules for knowledge control and algorithmization of related tasks.

The importance of this research topic lies in the need to gather, store, analyze and disseminate accurate information on the management status of educational institutions to guarantee the provision of quality educational services. This is particularly crucial in the current trend towards digitalizing educational work and utilizing the internet to facilitate practical management tasks. The study aims to construct a case method model to supervise educational process management outcomes. For that purpose, the study scrutinises the implementation methodologies of existing case models to monitor and analyse the situation without human intervention. Also, the investigation entails creating an implementation algorithm and a simulation model of an interactive case method to monitor educational activities. The formalized logical-semantic apparatus is used to address the research problems. The algorithm development and simulation modeling enabled correlation of the obtained answer with the assigned task, automating the results output. Generating answers in the case method involves considering rules based on the base word, answer keywords, and constraints (true/false). These elements are part of the thesaurus specific to the survey domain and are included in the test's base vocabulary. To test an answer against a question, each inductive step is viewed through a logical formula. Logical statements such as conjunction, disjunction, logical negation, implication, and equivalence are represented by formulas. This method enables the evaluation of the respondent's answer based on the nodes within the statement tree integrated into the test. The progression from the initial word to the node-connection generates an automated assessment of individual educational process management standards. This study enables the enhancement of automated monitoring capabilities for the University's educational process results. The research suggests the potential for developing models and algorithms to form question sets and enable individualized assessments based on the respondent's performance. As a consequence, the devised algorithm and simulation model for the interactive case approach are showcased. During the testing, the key words and example words were compared with the responses of the participants and specific results were obtained. Additional case vocabulary terms need to be added to address the limitations encountered during the model testing and the testing period.

This study presents PAGER-Life, an adaptive hybrid framework for the early prediction of lithium-ion battery service life under heterogeneous operating conditions. The system integrates physically interpretable degradation features and standardized charge–discharge curves using linear regression, decision tree-based models, and neural networks. An error-aware routing mechanism combines expert predictions based on out-of-fold errors, while conformal prediction enables uncertainty quantification. The framework was evaluated using the MATR and HUST datasets with observation horizons of 20, 50, and 100 cycles, following a protocol that accounts for the grouped data structure and prevents information leakage. A comparative analysis involving 114 physical cells and 14 alternative methods demonstrated the following performance metrics for PAGER-Life: Mean Absolute Percentage Error (MAPE) of 12.827%, Mean Absolute Error (MAE) of 166.766 cycles, Root Mean Square Error (RMSE) of 210.715 cycles, and a macro-averaged coefficient of determination (R²) of 0.495. Ablation studies indicated that removing the physically grounded degradation features substantially degraded predictive performance. The results indicate that the adaptive integration of complementary prognostic models offers a promising approach for the early estimation of battery service life under heterogeneous operating conditions.