Two scientific results achieved by a group of the faculty of Azerbaijan University were included by decision of the Presidium of ANAS in the report of the Departments of Physical, Mathematical&Technical Sciences and Social Sciences of the Academy on essential results of research conducted in 2022. 

Success achieved by the University teams consisting of  Vice-rector for Scientific Affairs, Doctor of Sciences in Mathematics Yusif Gasimov, Doctor of Sciences in Mathematics Agil Khanmammadov, Head of the Science Department, Doctor of Philosophy in Mathematics Latifa Agamaliyeva; Doctor of Sciences in History, Professor Gabil Aliyev, lecturer of the Department of Social Sciences Aliya Hajiyeva is an important component and logical continuation of purposeful and consistent work towards increasing the scientific authority of the University, as well as an important step in meeting modern challenges. This success is also important in terms of the fact that Azerbaijan University is included in report for the second time and at the same time Azerbaijan University is the only private university in report. 8 articles related to the results of the conducted scientific research were published in magazines with the highest impact factor.

The topics of research papers contained in report of the organization coordinating scientific activities in Azerbaijan are “Construction of mathematical models describing various physical processes, verification of their adequacy, development of numerical and analytical methods for solving” and “Economic and cultural development of Azerbaijan and the Caucasus”. 

Summary of the scientific results obtained

In the first research paper (Construction of mathematical models describing various physical processes, verification of their adequacy, development of numerical and analytical methods for solving), direct and inverse spectral analysis problems for a one-dimensional Schrodinger equation with potentials of a special type were investigated. Indications of Yost-type solutions for such equations were obtained, direct and inverse problems of spectral analysis in various applications were solved. Algorithms for solving inverse problems are given. The problem that remains open until now on the scattering theory of the Schrodinger equation with additional periodic potential has been solved. For matrix factorization of the helmholst equation in a multidimensional bounded domain, the problem of continuation of solution of ill-posed Cauchy problem was considered, an explicit formula for the continuation of the solution was obtained. Stability for the Cauchy problem was evaluated for solution of the Cauchy problem in the classical sense. Variational and non-variational approaches with Li algebra were applied to solve the generalized (3+1) dimensional nonlinear potential Yu-Toda-Sasa-Fukuyama equation and appropriate solutions of the problem were found.

And in the second research paper (Economic and cultural development of Azerbaijan and the Caucasus), success in the field of economy and education in the Caucasus region was investigated as the first direction of research. The study proves with concrete facts the railway construction project in Karabakh in the last decades of the XIX – first decades of the XX century, and that the graduates of the Iravan Teachers' Seminary had a significant impact on public, social and cultural life in Azerbaijan and throughout the Caucasus. Another direction in scientific research was related to the development of culture in Azerbaijan. According to the results of research, influence of the Muslim Renaissance on Azerbaijan in the IX-early XIII centuries, successes in humanitarian relations with neighboring countries were brought to the attention of scientific community.  

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