Branch of the Institute of Applied Mathematics and Mechanics
The branch of the Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine (Director – Zhuchok A. V., Doctor of Physical and Mathematical Sciences, Professor) was established in 2004 to organize comprehensive research on mathematics and their applications.
In 2019 the implementation of basic research in mathematics and its applications continued.
The research of prof. Zhuchok A. V. is devoted to the study of such algebraic systems as dopelna semigroups, n-fold semigroups and trioids. He solved the problem of describing a free n-fold semigroup of arbitrary rank. He built some relatively free dopelna semigroups, in particular, free Abelian dopelna semigroups. The design of a free commutative trioid is presented. The problem of characterizing groups of automorphisms constructed by relatively free algebras is solved. He described a number of the smallest congruences on constructed free n-fold semigroups, trioids, and dopelna semigroups.
The results of prof. Zhuchok Yu. V. have theoretical significance as such, which are a contribution to the further development of the theory of ordered dopelna semigroups and trioids.
Prof. Pratsiovytyi M. V. and co-authors studied continuous, strictly monotonic functions that preserve some properties of images of real numbers. With these functions, they build continuous transformations; determine the probability distributions in this interval. It is proved that the set of all transformations is infinite and forms a noncommutative group with respect to the composition (superposition). Thus, the probability distribution group is based on an interval. These distributions have non-trivial local properties (self-similar structure).
Prof. Zholtkevych H. M. and co-authors continue to develop categorical-theoretical methods of concretization and analysis of logical time models in distributed systems, including cyberphysical systems. Another area of research is the study of the method of machine learning for the synthesis of regular image detectors proposed by the authors. This method can be used in event handling systems. The main result is the proof of theorems that substantiate that the method sometimes leads to the desired result.
On the basis of the branch in 2019, four issues of the journal “Algebra and Discrete Mathematics” were published.
In 2019, the employees of the branch took part in 4 international conferences and seminars.
As a result of scientific work, 11 articles were published in journals included in the scientometric databases Scopus and Web of Science and 5 theses.