In this paper, we introduce the concept of N -fuzzy quasi-ideals in ordered semigroups and investigate the basic theorem of quasi-ideals of ordered semigroups in terms of N -fuzzy quasi-ideals. We characterize left (resp. right) regular and completely regular ordered semigroups in terms of N -fuzzy quasi-ideals. We de ne semiprime N fuzzy quasi-ideals and characterize completely regular ordered...

A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a simple proof for this fact that yields the better upper bound of 8n edges for n vertices. Our best construction with 7n−O(1) edges comes very close to this bound. Moreover, we show matching upper and lower bounds for seve...

We show that the problem whether a given simple graph G admits a quasi-covering to a fixed connected graph H is solvable in polynomial time if H has at most two vertices and that it is NP-complete otherwise. As a byproduct we show constructions of regular quasi-covers and of multi-quasi-covers that might be of independent interest.

The validity of a widely used simple closed-form expression for the recombination associated with dangling bonds in hydrogenated amorphous silicon a-Si:H is linked to the relative position of the distribution of the dangling bond states with respect to the quasi-Fermi levels for trapped electrons and holes. However, these quasi-Fermi levels for traps have not been derived before. In this work, ...