Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscrib...Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.展开更多
This paper proposes an adaptive localization approach for wireless sensor networks based on Gauss-Markov mobility model. In the approach,the perpendicular bisector strategy,the virtual repulsive strategy,and the veloc...This paper proposes an adaptive localization approach for wireless sensor networks based on Gauss-Markov mobility model. In the approach,the perpendicular bisector strategy,the virtual repulsive strategy,and the velocity adjustment strategy are properly combined to enhance localization effciency. The velocity adjustment strategy causes that the mobile anchor node automatically tunes its velocity. The perpendicular bisector strategy locally adjusts trajectory for the mobile anchor node,which ensures that unknown nodes obtain enough non-collinear anchor coordinates as soon as possible. The virtual repulsive strategy impels that the mobile anchor node rapidly leaves the communication range of location-aware nodes or returns to the surveillance region after the mobile anchor node was out of the boundary. Both theoretical analysis and simulation studies show that this approach can increase localization accuracy,consume less energy,and cover more surveillance region during the same period than virtual beacons-energy ratios localization scheme using the Gauss-Markov mobility model.展开更多
文摘Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.
基金Supported by National Natural Science Foundation of China(60776834, 60870010)
文摘This paper proposes an adaptive localization approach for wireless sensor networks based on Gauss-Markov mobility model. In the approach,the perpendicular bisector strategy,the virtual repulsive strategy,and the velocity adjustment strategy are properly combined to enhance localization effciency. The velocity adjustment strategy causes that the mobile anchor node automatically tunes its velocity. The perpendicular bisector strategy locally adjusts trajectory for the mobile anchor node,which ensures that unknown nodes obtain enough non-collinear anchor coordinates as soon as possible. The virtual repulsive strategy impels that the mobile anchor node rapidly leaves the communication range of location-aware nodes or returns to the surveillance region after the mobile anchor node was out of the boundary. Both theoretical analysis and simulation studies show that this approach can increase localization accuracy,consume less energy,and cover more surveillance region during the same period than virtual beacons-energy ratios localization scheme using the Gauss-Markov mobility model.
