The article presents a mathematical model for assessing the applicability of intelligent chatbots in the context of studying dialects of foreign languages. The model is based on the analysis of key parameters and characteristics of chatbots, as well as their ability to adapt to various dialects. The model's parameters include questions, answers, evaluation criteria, types, and costs of errors. The quality of the chatbot's responses is evaluated both according to individual criteria and overall. To test the effectiveness of the proposed method, an experimental study was conducted using the dialects of the German language as examples. During the research, such intelligent chatbots as ChatGPT-3.5, GPT-4, YouChat, Bard, DeepSeek, and Chatsonic were evaluated. The analysis of the results of applying the developed mathematical model showed that at present, the models by OpenAI (ChatGPT-3.5 and GPT-4) offer the broadest range of possibilities. ChatGPT-3.5 demonstrated the best results in communication in Bavarian and Austrian dialects, while YouChat excelled in the Swiss dialect. The obtained results allow for important practical recommendations to be made for selecting intelligent chatbots in the field of studying dialects of foreign languages and serve as a basis for further research in the area of evaluating the effectiveness of educational technologies based on artificial intelligence.

Keywords: large language model, chatbot, quality assessment, foreign language learning, artificial intelligence technology in education

The article considers the problem of optimizing the scheme of portages in a cutting area. The mathematical model of the cutting area is a polygon - a bounded closed broken part of the plane. The portage scheme corresponds to a root graph (forest, tree) of a special type. We have introduced the concept of covering a polygon with a rooted forest. The cover is interpreted as the possibility of cutting and collecting all the trees in the cutting area while moving the harvester and forwarder along the trails. The trails are laid according to the found covering root forest. Two variants of the algorithm for solving the problem are proposed, which are a modification of the local search. The first algorithm uses the greedy method we described earlier[18] to find the underlying solution. The second algorithm uses the branch and bound method to find the basic solution. Comparative experiments were carried out on polygons sized 12x12 and 18x18. Experimental results show that both modifications of the algorithm improve the basic solution. The first algorithm improves the solution by an average of 11% for a 12x12 polygon and by 24% for a 18x18 polygon.

Keywords: portage schemes, cutting area, polygon covering the root forest, local search, coverage