The aim of this paper is to characterize the formal power series which have purely periodic β-expansions in Pisot or Salem unit base under some condition. Furthermore, we will prove that if β is a quadratic Pisot unit base, then every rational f in the unit disk has a purely periodic β-expansion and discuss their periods. [ABSTRACT FROM AUTHOR]
GRISHKOV, ALEXANDER, LOGINOV, EUGENE, and Kharlampovich, Olga
Subjects
GROUP theory, GENERALIZATION, PROBLEM solving, MATHEMATICAL analysis, NUMERICAL analysis, MATHEMATICS, ALGEBRA
Abstract
In the present paper we generalize the concept of groups with triality and apply it to the theory of the Moufang, Bol and Bruck loops. Such generalizations allow us to reduce certain problems from the loop theory to problems in the theory of groups. [ABSTRACT FROM AUTHOR]
We determine the integers a, b ≥ 1 and the prime powers q for which the word map w(x, y) = xayb is surjective on the group PSL(2, q) (and SL(2, q)). We moreover show that this map is almost equidistributed for the family of groups PSL(2, q) (and SL(2, q)). Our proof is based on the investigation of the trace map of positive words. [ABSTRACT FROM AUTHOR]
FINITE element method, NUMERICAL analysis, DUALITY theory (Mathematics), MATHEMATICAL analysis, ALGEBRA, MATHEMATICS
Abstract
We show that, within the class of three-element unary algebras, there is a tight connection between a finitely based quasi-equational theory, finite rank, enough algebraic operations (from natural duality theory) and a special injectivity condition. [ABSTRACT FROM AUTHOR]