A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras.As of yet,algebras verified to satisfy the Connes's embedding pr...A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras.As of yet,algebras verified to satisfy the Connes's embedding property belong to just a few special classes (e.g.,amenable algebras and free group factors).In this article,we prove that von Neumann algebras satisfying Popa's co-amenability have Connes's embedding property.展开更多
A novel polarization splitter based on octagonal dual-core photonic crystal fiber(O-D-PCF) is proposed. The impacts of several fiber parameters on the coupling characteristics of the polarization splitter are investig...A novel polarization splitter based on octagonal dual-core photonic crystal fiber(O-D-PCF) is proposed. The impacts of several fiber parameters on the coupling characteristics of the polarization splitter are investigated by full-vectorial finite element method(FV-FEM) in detail. Through optimizing the fiber configuration, a 4.267-mm-long polarization splitter with a bandwidth of 37 nm is achieved, and its extinction ratio(ER) is as high as 81.2 d B at the wavelength of 1.55 μm. Compared with the hexagonal dual-core photonic crystal fiber(H-D-PCF) based polarization splitter, both ER and bandwidth of the O-D-PCF based one are effectively improved.展开更多
文摘A longstanding open question of Connes asks whether any finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras.As of yet,algebras verified to satisfy the Connes's embedding property belong to just a few special classes (e.g.,amenable algebras and free group factors).In this article,we prove that von Neumann algebras satisfying Popa's co-amenability have Connes's embedding property.
基金supported by the National Natural Science Foundation of China(No.61405096)
文摘A novel polarization splitter based on octagonal dual-core photonic crystal fiber(O-D-PCF) is proposed. The impacts of several fiber parameters on the coupling characteristics of the polarization splitter are investigated by full-vectorial finite element method(FV-FEM) in detail. Through optimizing the fiber configuration, a 4.267-mm-long polarization splitter with a bandwidth of 37 nm is achieved, and its extinction ratio(ER) is as high as 81.2 d B at the wavelength of 1.55 μm. Compared with the hexagonal dual-core photonic crystal fiber(H-D-PCF) based polarization splitter, both ER and bandwidth of the O-D-PCF based one are effectively improved.
