We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we pr...

In this paper, we give a detailed proof to result of Gabber (unpublished) on the lifting problem quasi-excellent rings, extending previous work Nishimura-Nishimura. As corollary, establish that an ideal-adic completion excellent (resp. quasi-excellent) ring is quasi-excellent).

The concept of quasi-threshold multipartite access structures for secret sharing schemes is introduced. These access structures allow one distinguished class of participants to retain control over the reconstruction of the secret, while allowing flexibility over the quorum of participants from other classes. While ideal bipartite access structures have been classified, the case for multipartite...

On the basis of the concept of grades of a fuzzy point to belongingness (∈) or quasi-coincident (q) or belongingness and quasi-coincident (∈ ∧q) or belongingness or quasi-coincident (∈ ∨q) in an intuitionistic fuzzy set of a ring, the notion of a (α,β )intuitionistic fuzzy subring and ideal is introduced by applying the Lukasiewicz 3-valued implication operator. Using the notion of fuzzy cut se...

The notions of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are introduced, and related properties are investigated. Characterizations of uni-soft semigroups, uni-soft left (right) ideals and uni-soft quasi ideals are discussed. A regular semigroup is characterized by the notion of a uni-soft quasi ideal.