Let $G$ be a finite group. A subgroup $H$ is called $S$-semipermutable in if $HG_p$ = $G_pH$ for any $G_p\in Syl_p(G)$ with $(|H|, p) 1$, where $p$ prime number divisible $|G|$. Furthermore, said to $NH$-embedded there exists normal $T$ of such that $HT$ Hall and $H \cap T \leq H_{\overline{s}G}$, $H_{\overline{s}G}$ the largest contained $H$, $SS$-quasinormal provided supplement $B$ permutes e...

We investigated the evolution of a scalar field propagating in small Schwarzschild Anti-de Sitter black holes. The imaginary part of the quasinormal frequency decreases with the horizon size and the real part of the quasinormal frequency keeps nearly as a constant. The object-picture clarified the question about on the quasinormal modes for small Anti-de Sitter black holes. Dependence of quasin...

Quasinormal modes have played a prominent role in the discussion of perturbations of black holes, and the question arises whether they are as signiicant as normal modes are for self adjoint systems, such as harmonic oscillators. They can be signiicant in two ways: Individual modes may dominate the time evolution of some perturbation, and a whole set of them could be used to completely describe ...

We perform a quasinormal mode analysis of black-hole configurations in Bose-Einstein condensates (BECs). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BECs with steplike discontinuities. For this case we show that in the hydrodynamic approximation quasinormal modes do n...