Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective pl...Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective plane this approach leads to elliptic and parabolic problems in the real projective plane. In most previous works these kind of problems have been considered on the unit sphere which is a double cover of the real projective plane. However, numerically this is inefficient because the resulting systems of equations are unnecessarily big. We formulate the problem directly in the real projective plane using a certain parametrization with three coordinate domains. After reducing the computations to the coordinate domains we can then use finite elements almost in a standard way. In particular the standard error estimates with usual Sobolev spaces remain valid in this setting. We consider both elliptic and parabolic cases, and demonstrate the validity of our approach.展开更多
This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-...This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.展开更多
It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.
In civil aviation security screening, laptops, with their intricate structural composition, provide the potential for criminals to conceal dangerous items. Presently, the security process necessitates passengers to in...In civil aviation security screening, laptops, with their intricate structural composition, provide the potential for criminals to conceal dangerous items. Presently, the security process necessitates passengers to individually present their laptops for inspection. The paper introduced a method for laptop removal. By combining projection algorithms with the YOLOv7-Seg model, a laptop’s three views were generated through projection, and instance segmentation of these views was achieved using YOLOv7-Seg. The resulting 2D masks from instance segmentation at different angles were employed to reconstruct a 3D mask through angle restoration. Ultimately, the intersection of this 3D mask with the original 3D data enabled the successful extraction of the laptop’s 3D information. Experimental results demonstrated that the fusion of projection and instance segmentation facilitated the automatic removal of laptops from CT data. Moreover, higher instance segmentation model accuracy leads to more precise removal outcomes. By implementing the laptop removal functionality, the civil aviation security screening process becomes more efficient and convenient. Passengers will no longer be required to individually handle their laptops, effectively enhancing the efficiency and accuracy of security screening.展开更多
文摘Some models dealing with fibers and liquid crystals can be formulated probabilistically in terms of orientation distributions. Since the orientation of a thin object can be specified by a point in a real projective plane this approach leads to elliptic and parabolic problems in the real projective plane. In most previous works these kind of problems have been considered on the unit sphere which is a double cover of the real projective plane. However, numerically this is inefficient because the resulting systems of equations are unnecessarily big. We formulate the problem directly in the real projective plane using a certain parametrization with three coordinate domains. After reducing the computations to the coordinate domains we can then use finite elements almost in a standard way. In particular the standard error estimates with usual Sobolev spaces remain valid in this setting. We consider both elliptic and parabolic cases, and demonstrate the validity of our approach.
基金the Natural Science Foundation of Education Committee of Anhui Province(2004kj166zd)Foundation for Younger Teachers of Anhui Normal University(2005xqn01).
文摘This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.
文摘It has been shown, under certain conditions on the Gauss curvature, every totally real surface of the Cayley projective plane with parallel mean curvature vector is either flat or totally geodesic.
文摘In civil aviation security screening, laptops, with their intricate structural composition, provide the potential for criminals to conceal dangerous items. Presently, the security process necessitates passengers to individually present their laptops for inspection. The paper introduced a method for laptop removal. By combining projection algorithms with the YOLOv7-Seg model, a laptop’s three views were generated through projection, and instance segmentation of these views was achieved using YOLOv7-Seg. The resulting 2D masks from instance segmentation at different angles were employed to reconstruct a 3D mask through angle restoration. Ultimately, the intersection of this 3D mask with the original 3D data enabled the successful extraction of the laptop’s 3D information. Experimental results demonstrated that the fusion of projection and instance segmentation facilitated the automatic removal of laptops from CT data. Moreover, higher instance segmentation model accuracy leads to more precise removal outcomes. By implementing the laptop removal functionality, the civil aviation security screening process becomes more efficient and convenient. Passengers will no longer be required to individually handle their laptops, effectively enhancing the efficiency and accuracy of security screening.
