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Boundary value problems on a manifold with smooth boundary are closely related to the edge calculus where the boundary plays the role of an edge. The problem of expressing parametrices of Shapiro-Lopatinskij elliptic boundary value problems for differential operators gives rise to pseudo-differential operators with the transmission property at the boundary. However, there are interesting pseudo-differential operators without the transmission property, for instance, the Dirichlet-to-Neumann operator. In this case the symbols become edge-degenerate under a suitable quantisation, cf. Chang et al. (J Pseudo-Differ Oper Appl 5(2014):69-155, 2014). If the boundary itself has singularities, e.g., conical points or edges, then the symbols are corner-degenerate. In the present paper we study elements of the corresponding corner pseudo-differential calculus.
By edge algebra we understand a pseudo-differential calculus on a manifold with edge. The operators have a two-component principal symbolic hierarchy which determines operators up to lower order terms. Those belong to a filtration of the corresponding operator spaces. We give a new characterisation of this structure, based on an alternative representation of edge amplitude functions only containing holomorphic edge-degenerate Mellin symbols.
In this study, we reassessed the taxonomic position of Typhlomys (Rodentia: Platacanthomyidae) from Huangshan, Anhui, China, based on morphological and molecular evidence. Results suggested that Typhlomys is comprised of up to six species, including four currently recognized species ( Typhlomys cinereus, T. chapensis, T. daloushanensis, and T. nanus), one unconfirmed candidate species, and one new species ( Typhlomys huangshanensis sp. nov.). Morphological analyses further supported the designation of the Huangshan specimens found at mid-elevations in the southern Huangshan Mountains (600 m to 1 200 m a.s.l.) as a new species.