Луганський національний університет імені Тараса Шевченка

Branch of the Institute of Applied Mathematics and Mechanics

A branch of the Institute of Applied Mathematics and Mechanics of the NAS of Ukraine (Director – A.V. Zhuchok, Doctor of Physical and Mathematical Sciences, Professor) was established in 2004 with the purpose of organizing complex studies on mathematics problems and their applications.

In 2018, basic research in mathematics and its applications is continued.

Prof. Zhuchko AV studied such algebraic systems as Doppelen semigroups, n-fold semigroups and trioids. He built the free product of arbitrary multiple multiples, introduced the concept of compounds of multiple semigroups, and in terms of this concept described the structure of free products. He constructed a free commutative -fold semigroup of arbitrary rank and characterized single-generated free commutative -fold semigroups. Described the smallest commutative congruence on a free-fold semigroup. He presented new examples of multiple multiple semigroups and calculated the power of a free nilpotent multiple multiple for the finite case. He showed that each Abelian ash subgroup can be constructed from the left and right commutative semigroups, and described a free Abelian ash subgroup. He described the lowest Abelian congruence in the free ash group. He constructed a free commutative trioid of rank 1 and proved that a free commutative trioid of rank is a direct product of a free commutative semigroup of rank and a free commutative trioid of rank 1. The results obtained can be applied to Doppelalgebra and Trialgebra theory.

Prof. Zhuchko Yu.V. The following new theoretical results were obtained: all isomorphisms of free abelian dislocal endomorphisms are found and it is proved that all automorphisms of free abelian disomorphism semigroups are quasi-internal and their automorphism groups are isomorphic to symmetric groups. These descriptions solve BI’s problem. Plotkin on the description of automorphisms of semigroups of free algebra endomorphisms for varieties of Abelian dislocations and are definite analogues of the results of BI Plotkin, G. Mashevitsky, B.M. Shayna, G. Zhytomyrsky, E.B. Plotkin, E. Formanek, A. Kanel-Belova, Y. Katsov, A. Berzins on the description of automorphisms of categories of free groups, semigroups, monoids, associative algebras, modules, semidomodules and Lie algebras.

Prof. Kirichenko V.V. and his co-authors have studied the set of all nonnegative exponential matrices with operations of component maximum and component addition and characterize the automorphisms of the algebra under consideration.

Let X be a random variable with independent triple digits and let {y = F (x)} be a classical singular Cantor function. For the distribution of the random variable {Y = F (X)}, prof. Pratsovytii M.V. with co-authors explores the structure of Lebesgue (ie the content of discrete, completely continuous and singular components).

Prof. Zoltkevich G.M. with co-authors investigated problems caused by nonlinearity of logical time in distributed, especially cyber-physical systems. Two approaches to modeling such systems are considered in the paper. The operating approach is based on a traditional model that defines acceptable system behavior as a set of acceptable system schedules. The denotational approach is presented in the category theory language.

The 2018 branch has published four issues of Algebra and Discrete Mathematics.

As a result of scientific work, 9 articles have been published in the journals included in the Scopus and Web of Science databases, and 5 abstracts.

23.10.2019

© Luhansk Taras Shevchenko National University, 2007-2020