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1. Three classes of curves in Descartes'Geometry | |||
SHI Xianghui | |||
Mathematics 15 May 2012 | |||
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Abstract:Descartes' three volume Geometry discuss three classes of curves: (1) curves generated by regulated continuous motions, (2) curves generated by (uniform) pointwise construction, and (3) curves given by an algebraic equation. It's widely hold that Descartes considers the three classes essentially the same class of curves. But one can barely find an argument for this in the literature. In this paper an argument for the view is presented. The discussion is carried out from both technical and philosophical points of view. The situation here is quite similar to that of Church's Thesis in recursion theory regarding computable functions. | |||
TO cite this article:SHI Xianghui. Three classes of curves in Descartes'Geometry[OL].[15 May 2012] http://en.paper.edu.cn/en_releasepaper/content/4478590 |
2. Online scheduling on unbounded parallel-batch machines to minimize maximum flow-time | |||
Li Wenhua,Yuan Jinjiang | |||
Mathematics 04 January 2011 | |||
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Abstract:This paper considers online scheduling on m unbounded parallel-batch machines to minimize maximum flow-time of the jobs. The research shows that no online algorithm can have a competitive ratio less than, where is the positive root of, and this lower bound is still valid even when all jobs have the same processing times. An online algorithm of competitive ratio 1+1/m is presented in the paper. When the jobs have the same processing times, a best possible online algorithm of competitive ratio is established. | |||
TO cite this article:Li Wenhua,Yuan Jinjiang. Online scheduling on unbounded parallel-batch machines to minimize maximum flow-time[OL].[ 4 January 2011] http://en.paper.edu.cn/en_releasepaper/content/4403852 |
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