This paper presents the selected materials from the preprint of Vladimir Vdovitsyn’s Report at the Meeting of the Academic Council of the Department of Mathematical Methods of Scientific Research and Design Automation (MMSRDA Department), Karelian Branch of the USSR Academy of Sciences on May 4, 1990.

After 26 years, it appears that the Report had a great influence on the formation of the main research and development areas of the present Institute of Applied Mathematical Research of the Karelian Research Centre, Russian Academy of Sciences, which is the successor to the MMSRDA Department.