Some problems connect ed with production of new light-weight filler type are considered for sandwich layers. Constructively, the filler is the folded structure that can be developed on a plane. This feature makes it...Some problems connect ed with production of new light-weight filler type are considered for sandwich layers. Constructively, the filler is the folded structure that can be developed on a plane. This feature makes it possible to produce the filler by isometric t ransformation of thin sheet through local bending without material stretching.Th e main difficulty is that the bending must be carried out along all lines of com plex-shaped marking-out at a time. The problem of shaping can be solved by use of the original shaping device that can be transformed in operation. The herein -presented technology of production makes it possible to fabricate parts with d eep relief using a wide gamut of different materials even as the thin-sheet met al alloys and paper.展开更多
Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(...Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.展开更多
文摘Some problems connect ed with production of new light-weight filler type are considered for sandwich layers. Constructively, the filler is the folded structure that can be developed on a plane. This feature makes it possible to produce the filler by isometric t ransformation of thin sheet through local bending without material stretching.Th e main difficulty is that the bending must be carried out along all lines of com plex-shaped marking-out at a time. The problem of shaping can be solved by use of the original shaping device that can be transformed in operation. The herein -presented technology of production makes it possible to fabricate parts with d eep relief using a wide gamut of different materials even as the thin-sheet met al alloys and paper.
基金Project supported by the National Natural Science Foundation of China (No.10271107) the 973 Project of the Ministry of Science and Technology of China (No.G1999075105) the Zhejiang Provincial Natural Science Foundation of China (No.RC97017).
文摘Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.
