For totally positive algebraic integers α 6= 0, 1 of degree d(α), we consider the set L of values of M(α) 1 d(α) = Ω(α), where M(α) is the Mahler measure of α. C. J. Smyth has found the four smallest values of L and conjectured that the fifth point is Ω((2 cos 2π 60 )2). We prove that this is so and, moreover, we give the sixth point of L.

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

The aim of this paper is to propose a soft consensus model based on interpolative Boolean algebra for group decision making problems. Consensus degrees are calculated on three levels (on pairs of alternatives, alternatives, collective level) by means of pseudo-logical aggregation. The relation of equivalence is employed as a similarity measure among experts' opinions. In fact real-valued realiz...