arXiv subjects
Publications and source records attributed to N. A. Ismailov.
An algebra is said to be a unary Leibniz algebra if every one-generated subalgebra is a Leibniz algebra. An algebra is said to be a binary Leibniz algebra if every two-generated subalgebra is a Leibniz algebra. We give characterizations of unary and binary Leibniz algebras in terms of identities.
A mathematical model of oscillatory systems control with liquid dampers is considered which differs from the classical ones by replacing the first derivative of such a fractional derivative that is between numbers 0 and 2 other than unity. Using the methods of constructing Letov controllers, a control law is constructed that ensures the asymptotic stability of the closed system and minimizes the quadratic functional. The results are illustrated by a specific numerical example.
An algebra with identities $a(bc)=b(ac),$ $(ab)c=(ac)b$ is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bicommutative algebra. We give criterions for elements of a free bicommutative algebra to be Lie or Jordan.