Maximal subgroups of direct products

We determine all maximal subgroups of the direct product \sc G^n of \sc n copies of a group~\sc G. If \sc G is finite, we show that the number of maximal subgroups of~\sc G^n is a quadratic function of~\sc n if \sc G is perfect, but grows exponentially otherwise. We~deduce a theorem of Wiegold about the growth behaviour of the number of generators of~\sc G^n.Comment: Plain TeX file, 8 page

Superdeformed Λ\Lambda hypernuclei with antisymmetrized molecular dynamics

The response to the addition of a $\Lambda$ hyperon is investigated for the deformed states such as superdeformation in $^{41}_\Lambda$Ca, $^{46}_\Lambda$Sc and $^{48}_\Lambda$Sc. In the present study, we use the antisymmetrized molecular dynamics (AMD) model. It is pointed out that many kinds of deformed bands appear in $^{45}$Sc and $^{47}$Sc. Especially, it is found that there exists superdeformed states in $^{45}$Sc. By the addition of a $\Lambda$ particle to $^{40}$Ca, $^{45}$Sc and $^{47}$Sc, it is predicted, for the first time, that the superdeformed states exist in the hypernuclei $^{41}_\Lambda$Ca and $^{46}_\Lambda$Sc. The manifestation of the dependence of the $\Lambda$-separation energy on nuclear deformation such as spherical, normal deformation and superdeformation is shown in the energy spectra of $^{41}_\Lambda$Ca, $^{46}_\Lambda$Sc and $^{48}_\Lambda$Sc hypernuclei.Comment: 24 pages, 8 figure

Multi-Dimensional Spatially-Coupled Codes

Spatially-coupled (SC) codes are constructed by coupling many regular low-density parity-check codes in a chain. The decoding chain of SC codes stops when facing burst erasures. This problem can not be overcome by increasing coupling number. In this paper, we introduce multi-dimensional (MD) SC codes. Numerical results show that 2D-SC codes are more robust to the burst erasures than 1D-SC codes. Furthermore, we consider designing MD-SC codes with smaller rateloss