In this paper, we introduce and investigate new concepts of L-weakly M-weakly demicompact operators. Let E be a Banach lattice. An operator T : ? is called demicompact, if for every norm bounded sequence (xn) in BE such that {xn Txn, n N} an compact subset E, have {xn, E. Additionally, disjoint ?xn ?Txn? 0, ?xn? 0. (resp. M-weakly) operators generalize known classes which are We also elaborate ...

We have investigated theoretically the formation of a coherent population trapping resonance in a finite-size vapour cell without a buffer gas. We have demonstrated the novel mechanisms of the resonance narrowing: an analogue of the Dicke effect and light-induced narrowing. In the light-induced narrowing regime the parameters of the coherent population trapping resonance weakly depend on the ce...

The production of o(1 g 2) particles in a weakly-coupled theory is believed to be non-perturbatively suppressed. I comment on the prospects of (a) establishing this rigorously, and (b) estimating the effect to exponential accuracy semiclassically, by discussing two closely-related problems: the large-order behaviour of few-point Green functions, and induced excitation in quantum mechanics. Indu...