8 articles in this issue
V.F. Babenko,V.V. Babenko,O.V. Kovalenko,N.V. Parfinovych
In this article we prove sharp Landau-Kolmogorov type inequalities on a class of charges defined on Lebesgue measurable subsets of a cone in Rd\mathbb{R}^d, d?1d\geqslant 1, that are absolutely continuous with respect to the Lebesgue measure. In addition ... see more
R. Bilichenko,S. Zhir
We give specific examples of the spectral decomposition of self-adjoint operators in application to establish sharp inequalities for their powers.
M.R. Dixon,L.A. Kurdachenko
We prove a criteria for nilpotency of left braces in terms of the ?\star-central series and also discuss Noetherian braces, obtaining some of their elementary properties. We also show that if a finitely generated brace AA is Smoktunowicz-nilpotent, then t... see more
V.A. Kofanov,A.V. Zhuravel
For odd r?Nr\in \mathbb{N}; a,ß>0\alpha, \beta >0; p?[1,8]p\in [1, \infty]; d?(0,2p)\delta \in (0, 2 \pi), any 2p2\pi-periodic function x?Lr8(I2p)x\in L^r_{\infty}(I_{2\pi}), I2p:=[0,2p]I_{2\pi}:=[0, 2\pi], and arbitrary measurable set B?I2p,B \subset ... see more
L.A. Kurdachenko,O.O. Pypka,M.M. Semko
Let LL be an algebra over a field FF with the binary operations ++ and [,][,]. Then LL is called a left Leibniz algebra if it satisfies the left Leibniz identity: [[a,b],c]=[a,[b,c]]-[b,[a,c]][[a,b],c]=[a,[b,c]]-[b,[a,c]] for all elements a,b,c?La,b,c\in ... see more
L.A. Kurdachenko,M.M. Semko,V.S. Yashchuk
We describe the algebra of derivations of some nilpotent Leibniz algebra, having dimensionality 3.
A.V. Tushev
In the paper we study structure of soluble-by-finite groups of finite torsion-free rank which admit faithful modules with conditions of primitivity. In particular, we prove that under some additional conditions if an infinite finitely generated linear gro... see more