Limit points of the branch locus of 𝓜g

Let 𝓜g be the moduli space of compact connected hyperbolic surfaces of genus g ≥ 2, and 𝓑g ⊂ 𝓜g its branch locus. Let $\begin{array}{} \widehat{{\mathcal{M}}_{g}} \end{array} $ be the Deligne–Mumford compactification of the moduli space of smooth, complete, connected surfaces of genus g ≥ 2 over ℂ. The branch locus 𝓑g is stratified by smooth locally closed equisymmetric strata, where a stratum consists of hyperbolic surfaces with equivalent action of their orientation-preserving isometry group. Any stratum can be determined by a certain epimorphism Φ. In this paper, for any of these strata, we describe the topological type of its limits points in 𝓜͡g in terms of Φ. We apply our method to the 2-complex dimensional stratum corresponding to the pyramidal hyperbolic surfaces.

Interaction among n Parallel Dislocations in One-Dimensional Hexagonal Quasicrystals

By means of analytic function theory, the problems of interaction amongparallel dislocations in one-dimensional hexagonal quasicrystals are investigated. The interaction force of parallel dislocations in the material is obtained in forms of complex variable function firstly, which is the versions of well-known Peach-Koehler formula in one-dimensional hexagonal quasicrystals on parallel dislocations. These results are development of the corresponding parts of quasicrystals. Meanwhile, in this paper, we firstly give the equivalent action point of parallel dislocations in one-dimensional hexagonal quasicrystals, which be of important reference value to researching the interaction problems of many dislocations in fracture mechanics of quasicrystals.

Unappealing legislation?

SummaryThe deprivation of liberty safeguards apply to England and Wales. In Scotland, trends and uncertainties in the use of welfare guardianship (the equivalent action under Scottish law) provide a useful comparison. In both jurisdictions, there are risks to the rights of individuals.