In this paper we study the pointed representations of the Virasoro algebra.We show that unitary irreducible pointed representations of the Virasoro algebra are Harish-Chandra repre- sentations,thus they either are of ...In this paper we study the pointed representations of the Virasoro algebra.We show that unitary irreducible pointed representations of the Virasoro algebra are Harish-Chandra repre- sentations,thus they either are of highest or lowest weights or have all weight spaces of dimension 1.Further,we prove that unitary irreducible weight representations of Virasoro superalgebras are either of highest weights or of lowest weights,hence they are also Harish-Chandra representations.展开更多
A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a qu...A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a quotient of some Verma-like poillted module; moreover if it is irreduciblethen it is a quotieDt of the Vermarlike poiDted module by the left kernel of some bilinearpairing K. In case the mass fUnction is symmetric, there exists a bilinear form on M(ρ). It isproved that unitals pointed modules are integrable. In addition, a characterization of the massfunctions of Kac-Moody algebras is given, which is a generalization of the finite dimensionalLie algebras case.展开更多
Background Despite the recent progress in 3D point cloud processing using deep convolutional neural networks,the inability to extract local features remains a challenging problem.In addition,existing methods consider ...Background Despite the recent progress in 3D point cloud processing using deep convolutional neural networks,the inability to extract local features remains a challenging problem.In addition,existing methods consider only the spatial domain in the feature extraction process.Methods In this paper,we propose a spectral and spatial aggregation convolutional network(S^(2)ANet),which combines spectral and spatial features for point cloud processing.First,we calculate the local frequency of the point cloud in the spectral domain.Then,we use the local frequency to group points and provide a spectral aggregation convolution module to extract the features of the points grouped by the local frequency.We simultaneously extract the local features in the spatial domain to supplement the final features.Results S^(2)ANet was applied in several point cloud analysis tasks;it achieved stateof-the-art classification accuracies of 93.8%,88.0%,and 83.1%on the ModelNet40,ShapeNetCore,and ScanObjectNN datasets,respectively.For indoor scene segmentation,training and testing were performed on the S3DIS dataset,and the mean intersection over union was 62.4%.Conclusions The proposed S^(2)ANet can effectively capture the local geometric information of point clouds,thereby improving accuracy on various tasks.展开更多
文摘In this paper we study the pointed representations of the Virasoro algebra.We show that unitary irreducible pointed representations of the Virasoro algebra are Harish-Chandra repre- sentations,thus they either are of highest or lowest weights or have all weight spaces of dimension 1.Further,we prove that unitary irreducible weight representations of Virasoro superalgebras are either of highest weights or of lowest weights,hence they are also Harish-Chandra representations.
文摘A contravaried bilinear pairing X on every M(ρ) × M(ρθ) is determined and it is provedthat M(ρ)is irreducible if and only if K is left nondegellerate. It is also proved that every cyclicpointed module is a quotient of some Verma-like poillted module; moreover if it is irreduciblethen it is a quotieDt of the Vermarlike poiDted module by the left kernel of some bilinearpairing K. In case the mass fUnction is symmetric, there exists a bilinear form on M(ρ). It isproved that unitals pointed modules are integrable. In addition, a characterization of the massfunctions of Kac-Moody algebras is given, which is a generalization of the finite dimensionalLie algebras case.
文摘Background Despite the recent progress in 3D point cloud processing using deep convolutional neural networks,the inability to extract local features remains a challenging problem.In addition,existing methods consider only the spatial domain in the feature extraction process.Methods In this paper,we propose a spectral and spatial aggregation convolutional network(S^(2)ANet),which combines spectral and spatial features for point cloud processing.First,we calculate the local frequency of the point cloud in the spectral domain.Then,we use the local frequency to group points and provide a spectral aggregation convolution module to extract the features of the points grouped by the local frequency.We simultaneously extract the local features in the spatial domain to supplement the final features.Results S^(2)ANet was applied in several point cloud analysis tasks;it achieved stateof-the-art classification accuracies of 93.8%,88.0%,and 83.1%on the ModelNet40,ShapeNetCore,and ScanObjectNN datasets,respectively.For indoor scene segmentation,training and testing were performed on the S3DIS dataset,and the mean intersection over union was 62.4%.Conclusions The proposed S^(2)ANet can effectively capture the local geometric information of point clouds,thereby improving accuracy on various tasks.
