We define two classes of rings calling them weakly clean rings and weakly exchange rings both equipped with the strong property. Although the classes of weakly clean rings and weakly exchange rings are different, their two proper subclasses above do coincide. This extends results due to W. Chen (Commun. Algebra, 2006) and Chin-Qua (Acta Math. Hungar., 2011). We also completely characterize stro...

In this paper we give some basic results for interval valued fuzzy ideals and characterize regular and weakly regular hemirings by the properties of their interval valued fuzzy ideals. 2010 AMS Classification: 16Y60, 08A72, 03G25, 03E72

Attested and ‘pathological’ vowel harmony patterns are studied in the context of subclasses of regular functions. The analysis suggests that the computational complexity of phonology can be reduced from regular to weakly deterministic.

All weakly distance-regular digraphs with girth 2 and k − k1,1 = 1 are determined. Moreover, all such digraphs are commutative.

The notion of distance-regularity for undirected graphs can be extended for the directed case in two different ways. Damerell adopted the strongest definition of distanceregularity, which is equivalent to say that the corresponding set of distance matrices {Ai}i=0 constitutes a commutative association scheme. In particular, a (strongly) distance-regular digraph Γ is stable, which means that Ai ...

We show that weakly deterministic regular expressions with counters (WDREs) —as they are used in XML Schema— are at most exponentially larger than equivalent DFAs. As a consequence, the problem, whether a given DFA is equivalent to any WDRE, is decidable in EXPSPACE.

The paper extends quadratic optimal control theory to weakly regular linear systems, a rather broad class of infinite-dimensional systems with unbounded control and observation operators. We assume that the system is stable (in a sense to be defined) and that the associated Popov function is bounded from below. We study the properties of the optimally controlled system, of the optimal cost oper...

We study the Floquet Hamiltonian −i∂t + H + V (ωt), acting in L([ 0, T ],H, dt), as depending on the parameter ω = 2π/T . We assume that the spectrum of H in H is discrete, Spec(H) = {hm}m=1, but possibly degenerate, and that t 7→ V (t) ∈ B(H) is a 2π-periodic function with values in the space of Hermitian operators on H. Let J > 0 and set Ω0 = [ 89J, 98J ]. Suppose that for some σ > 0 it holds...

Spectral properties of the Schrödinger operator Aλ = −∆+λV on regular metric trees are studied. It is shown that as λ goes to zero the behavior of the negative eigenvalues of Aλ depends on the global structure of the tree. Mathematics Subject Classification: 34L40, 34B24, 34B45.

In this paper we introduce intuitionistic fuzzy completely regular weakly generalized continuous mappings and some of their properties are studied.