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In order to construct a class of new Turaev-braided group category with nontrivial associativity, the concept of a quasitriangular quasi-Turaev group coalgebras was recently introduced. Inside the definition, the conditions of invertibility of the R-matrix R and bijectivity of the antipode S are required. In this article, we prove that the antipode of a quasitriangular quasi-Turaev group coalgebra without the assumptions about invertibility of the antipode and R-matrix is inner, and a fortiori, bijective. As an application, we prove that for a quasitriangular quasi-Turaev group coalgebra, two conditions mentioned above are unnecessary. 相似文献
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Bradley Currey Hartmut Führ Vignon Oussa 《Applied and Computational Harmonic Analysis》2019,46(3):500-543
This paper presents a full catalogue, up to conjugacy and subgroups of finite index, of all matrix groups that give rise to a continuous wavelet transform with associated irreducible quasi-regular representation. For each group in this class, coorbit theory allows to consistently define spaces of sparse signals, and to construct atomic decompositions converging simultaneously in a whole range of these spaces. As an application of the classification, we investigate the existence of compactly supported admissible vectors and atoms for the groups. 相似文献
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John Asplund Gregory Clark Garner Cochran va Czabarka Arran Hamm Gwen Spencer Lszl Szkely Libby Taylor Zhiyu Wang 《组合设计杂志》2019,27(10):586-597
The crossing number of a graph is the smallest number of edge crossings over all drawings of in the plane. For any , the ‐planar crossing number of , is defined as the minimum of over all graphs with . Pach et al [Comput. Geom.: Theory Appl. 68 (2018), pp. 2–6] showed that for every , we have and that this bound does not remain true if we replace the constant by any number smaller than . We improve the upper bound to as . For the class of bipartite graphs, we show that the best constant is exactly for every . The results extend to the rectilinear variant of the ‐planar crossing number. 相似文献
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X-ray Photoelectron Spectroscopy was used to study a ferroan platinum crystal from the Kondyor Massif, Russian Far East. Prior to the X-ray Photoelectron Spectroscopic analyses, the nature of the crystal was confirmed by X-ray diffraction. The survey scan showed mainly the presence of Pt and Fe, with smaller amounts of O and Si. The high resolutions spectra of the Pt 4f and Fe 2p showed 18.3 atom% Fe in the crystal, which puts the composition on the lower boundary for ferroan platinum and confirms earlier analyses using other methods such as Scanning Electron Microscopy-Energy Dispersive X-ray analysis/microprobe. The binding energy of the Pt 4f5/2 was 74.0?eV and Pt 4f7/2 70.5?eV, while the Fe 2p3/2 for metallic Fe was observed at 707.2?eV. The Fe 2p3/2 for metallic Fe was significantly sharper than that of Fe 2p3/2 at 710.7?eV associated with surface material. The Raman spectrum was dominated by the Pt–Pt stretching mode at 253?cm?1. Changed orientation resulted in the observation of two bands at 127 and 139?cm?1, interpreted as being due to stretching modes of two Pt–Pt bonds with the third bond to Fe and Pt fixed. The presence of Ca-Fe-Al-Mg-Si-O on the surface was probably associated with the presence of a clinopyroxene. These minerals can be expected since the crystal came originally from a clinopyroxenite-dunite matrix. The spectra showed a variety of interferences, e.g. Al 2p with Pt 4f, Mg 2p with Fe 3p, and Ca 2p1/2 with Mg Auger, making exact determinations of the ratios of these elements difficult. 相似文献
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