In this paper, we use the averaging method to find an approximate solution in the optimal control problem of a parabolic system with non-linearity of the form $f(t/\epsilon ,y)$ on an infinite time interval.

In 2020, due to the COVID-19 pandemic, university funding in Ukraine suffered significant losses due to unprecedented quarantine measures. The challenge for universities is to diversify funding sources, develop effective approaches to minimize existing and prevent future threats to ensure their financial stabilization (sustainability) in the post-pandemic period. The paper aims to consider financial sustainability of a university (the case of Taras Shevchenko National University of Kyiv) due to COVID-19 using the objective calculative approach on the statistical sample of data for 2011–2020. The tasks for achieving the aim are seen in determining, using regression methods, the number of lost receipts from general and special funds in the short and medium term, which will maintain a constant value of receipts at constant assets. The main idea of the paper is that financial sustainability is considered as a condition, and stabilization is considered as a process towards stability/sustainability. The modeling approach reveals a fragile list of factors for the future preventing measures of the University to sustain. It is estimated that the University’s top management should consider financial strategy in dollar terms only. The challenge is that funding in hryvnia seems to be quite increasing and linear, but indeed, funding of the University is non-linear and has a quite intensive downward trend. Thus, for the financial sustainability strategy, this fact should be crucial.The results indicate the need for a significant increase in university funding to mitigate the impact of macroeconomic instability due to various crises, including the COVID-19 pandemic. AcknowledgmentThe study is carried out under the grant funded from the National Research Fund of Ukraine within the competition Science for Human Security and Society, topic 2020.01/0265.

Military training programs have been developed to enhance soldier resilience competencies, which are necessary for soldiers to perform their duties effectively under stress. The ongoing military conflict in Ukraine and the experience of previous military missions abroad emphasize the need for effective training that helps soldiers recover quickly and continue their missions. However, selecting the most suitable resilience training program is challenging and the selection criteria need to be optimized to ensure the most needed competencies are considered. This study aimed to utilize a fuzzy MCDM method to establish the priority weight of decision-making criteria, identifying the core competencies necessary for soldier resilience training, and utilizing the fuzzy TOPSIS method to rank and select the most appropriate training program. The evaluation results were calculated using the MATLAB (R2020b) mathematical package developed by MathWorks. The application of the hierarchical MCDA model based on fuzzy sets theory indicated that mental agility is the most important competence in high-stress environments. The study found that the Mindfulness-Based Mind Fitness Training (MMFT) program, which is intended to regulate soldiers’ emotions, had the highest rank among evaluated options according to the combined FAHP sub-factor fuzzy weights and alternatives evaluation conducted using FTOPSIS. The study provides valuable information on the selection of military resilience training programs.

This paper describes the system of intellectual analysis and prediction of reactions to the news based on data from Telegram channels In particular, the features of collecting and pre-processing datasets for the intelligence systems, the methodology of thematic analysis of the received data, and the model used to obtain predictions of reactions to Telegram messages depending on their text are described We show the work of this system in the example of the Ukrainian news Telegram channel The results are estimations of probability of emojis for the news from the testing dataset Also, we give F-measures for our approaches to precise input data and models.