This issue (Volume 266, issue 1) is the first in a series of direct submissions (Series A) making the Journal of Mathematical Sciences an excellent new platform for the publication of high-quality papers submitted by scientists from all over the world. The link is here https://link.springer.com/journal/10958/volumes-and-issues/266-1 .The present issue is dedicated to the memory of Professor N. Karapetiants (1942-2005) on the occasion of 80th anniversary from the date of his birthday. It appeared on the basis of the editorial activities of the OTHA-2022 conference. Professor Nikolai Karapetiants (1942–2005) was born on January 22, 1942, in Rostov-on-Don. In 1959, he graduated from high school and entered the Faculty of Physics and Mathematics of the Rostov State University. His first paper (1965) was dedicated to the theory of boundary value problems for analytic functions in spaces of generalized functions. In 1969, he defended his Ph.D. thesis and began working at the Chair of Differential Equations of the Rostov State University, first as an assistant, and later he took the position of professor, and was the head of the Chair from 1998. In 1989, in Tbilisi, Georgia, Nikolai Karapetiants defended his doctoral (Doctor of Sciences, second degree) dissertation “Integral convolution operators and with homogeneous kernels with variable coefficients” at Andrea Razmadze Mathematical Institute. Nikolai Karapetiants was one of the first scientists who started research in the field of normalization of normally unsolvable operators. His scientific interests were very broad. He was a world-class expert in the field of integral operators and related areas of analysis. He made a great contribution to the development of the theory of singular integral operators, convolution-type operators in the discrete and continuous cases, integral operators with homogeneous and quasi-homogeneous kernels, integral equations with a shift, fractional integro-differentiation, and some other areas of mathematics. Professor N. Karapetiants published more than 100 scientific papers, as well as two monographs, the last of which was Equations with Involutive Operators (together with S. Samko) published by Birkhäuser Boston, MA in 2001. This Special Issue consists of ten research articles and one review (bibliographical) article written by O.Avsyankin and S.Samko. The contributing authors are from Belarus, Georgia, Israel, Mexico, Russian Federation, the USA, the UK, and the United Arab Emirates There is also Preface (Editorial) to the Special Issue available at https://link.springer.com/article/10.1007/s10958-022-06025-1