SCIENTIFIC RESEARCH OF MASTER’S STUDENTS AND THEIR RESULTS

On April 17, 2026, a regular scientific seminar was held at the Research Institute “Fundamental, Applied Research and Innovative Technologies” of the Scientific-Educational Production Complex “Jalal-Abad State University named after B. Osmonov”. The event was organized on the basis of the laboratory “Asymptotic, Computational, Topological Methods and Technologies of Teaching Mathematics”. Representatives of the scientific community, laboratory members, and young researchers took part in the seminar. Within the framework of the seminar, master’s students presented reports substantiating the relevance and scientific novelty of their research. 1. Guliza Dzhumalieva, Topic: “Singularly Perturbed Equations with Zeros and Poles” The speaker analyzed the behavior of solutions to singularly perturbed equations in three main directions: – features in the case of only poles; – mathematical modeling in the presence of multiple poles; – complex-structured problems where zeros and poles occur simultaneously. 2. Aisara Keneshbekova, Topic: “Singularly Perturbed Equations with Analytic Functions of Certain Classes” The study focused on the following aspects: – determination of boundary layer lines; – classification of singular and regular regions; – the phenomenon of solution “capture”; – the influence of zeros and poles of eigenvalues on the asymptotic behavior of solutions. The presentations were followed by a Q&A session and an active discussion. The head of the laboratory, Doctor of Physical and Mathematical Sciences, Professor K.S. Alybaev, noted: “The presented studies address complex problems of modern differential equations. Clarifying the role of zeros and poles in the study of asymptotic behavior is a particularly promising research direction.” The professor also provided valuable recommendations on further deepening the research, publishing results in international scientific databases, and developing their practical applications. The purpose of the seminar is to enhance the scientific potential of young researchers and to facilitate the exchange of experience in the field of fundamental mathematics.