Scaling up the extrinsic curvature in gravitational initial data

Vacuum solutions to the Einstein equations can be viewed as the interplay between the geometry and the gravitational wave energy content. The constraints on initial data reflect this interaction. We assume we are looking at cosmological solutions to the Einstein equations so we assume that the 3-space is compact, without boundary. In this article we investigate, using both analytic and numerical techniques, what happens when the extrinsic curvature is increased while the background geometry is held fixed. This is equivalent to trying to magnify the local gravitational wave kinetic energy on an unchanged background. We find that the physical intrinsic curvature does not blow up. Rather the local volume of space expands to accommodate this attempt to increase the kinetic energy.Comment: 9 pages, 8 figure

A Rough-Set-basedClustering Algorithm for Multi-stream

AbstractThe paper propose a rough-set-based clustering algorithm for multiple data stream, which solve the problem that existing clustering algorithm for multiple data streams can not take into account conflicts between clustering quality and efficiency. Firstly, the algorithm calculates the distance between data stream to determine the initial equivalence relations, and calculates the similarity between the initial equivalence relation to determine the initial cluster. In the second place, the similarity between the initial clusters is used to merge the initial clusters. Finally, k-means clustering algorithm is called to dynamically adjust the clustering results, and then real-time clustering structure is obtained. In conclusion Experimental results demonstrated that the algorithm has higher efficiency and clustering quality

A distributed system structure for modular product architecture development and variation.

Customer need is variable and unstable. It confronts the manufacturing industry with increasing demand for needed variety with limited product design budget. A successful way to offer the needed variety while reducing the product design cost is to launch modular product families. Determining and controlling product architecture is one of the key activities during product family design or redesign. This research will present a systematic method for developing product architecture and configuring varieties, in which two linear programming models will be introduced to identify feasible sub-functions and configure product varieties. Then, a simple example is given to demonstrate the method. Based on the methodology, a structure of distributed design support system will be formulated using Object-Oriented technology with Unified Modeling Language (UML). This structure will enable the automation of modular product family development and variant configuration in enterprise level.Dept. of Industrial and Manufacturing Systems Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2001 .B35. Source: Masters Abstracts International, Volume: 40-03, page: 0763. Adviser: Michael H. Wang. Thesis (M.A.Sc.)--University of Windsor (Canada), 2001