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Online uniform machine covering with the known largest size

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Progress in Natural Science:Materials International 2007年第11期17卷 1271-1278页

作者： Cao Shunjuan1,2.and Tan Zhiyi1,3(1. department of mathematics, Zhejiang {2., Hangzhou 31002., china 2. department of mathematics, Zhejiang Forestry {2., Hangzhou 311300, china 3. State Key Laboratory of CAD & CG, Zhejiang {2., Hangzhou 31002., china) department of mathematics Zhejiang University Hangzhou 310027 China department of mathematics Zhejiang Forestry University Hangzhou 311300 China State Key Laboratory of CAD and CG Zhejiang University Hangzhou 310027 China

This paper investigates the semi-online scheduling problem with the known largest size on two uniform machines. The objective is to maximize the minimum machine completion time. Both lower bounds and algorithms are given. Algorithms are optimal for the majority values of s≥1, where s is the speed ratio of the two machines. The largest gap between the competitive ratio and the lower bound is about 0.064. Moreover, the overall competitive ratio 2.matches the overall lower bound.

关键词： scheduling and covering uniform machine design and analysis of algorithm online competitive ratio

Lipschitz continuity of best approximations and Chebyshev centers

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Chinese Science Bulletin 1998年第3期43卷 185-188页

作者： LI Chong 1 and WANG Xinghua 2.1. Center for Mathematical Sciences, Zhejiang university, Hangzhou 31002., china {2., Hangzhou university, Hangzhou 31002., china Center for Mathematical Sciences Zhejiang University Hangzhou China department of mathematics Hangzhou University Hangzhou China

The Lipschitz continuity results are given for best approximations and Chebyshev centers. Consequently, the open problem presented by Septycki and Vleck is solved completely.

关键词： best approximation Chebyshev center uniform convexity.

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2. WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics, Nanjing {2., Nanjing 2.0093, china 2. department of mathematics, Henan {2., Kaifeng 475001, china 3. department of Applied mathematics, Southeast {2., department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.

On the classification of compact quantum groups Uθ（2.

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Science china mathematics 2010年第5期 256-269页

作者： ZHANG XiaoXia department of mathematics,{2.,yantai 2.4005,china

In this paper,we show that the corepresentation of compact group Uθ(2. on the vector space is determined by its infinitesimal generators B0,B2.A0,A1 and A2.where θ is an irrational *** also show that B0 and B2.commute with Aj,j = 0,1,2.so B0,A0,A1 and A2.are sl(2.C) loop *** we exhibit all irreducible representations of Uθ(2.,which are different from those of group U(2.,and use above results to give the classification of quantum groups Uθ(2.,which is analogous to that of irrational algebra Aθ.At the same time,we also give all the forms of automorphisms on quantum group Uθ(2..

关键词： compact quantum group comultiplication irreducible representation

Dimension and measure theoretic entropy of a subshift in symbolic space

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Chinese Science Bulletin 1997年第14期42卷 1193-1196页

作者： CHEN Ercai and XIONG Jincheng1. department of Astronomy, Nanjing university, Nangjing 2.0093, {2. 2. department of mathematics, South {2. Normal university, Guangzhou 510631, {2. department of Astronomy Nanjing University Nangjing China department of mathematics South China Normal University Guangzhou China

1 Definitions and resultsWITH the development of the theory of dynamical systems and fractal geometry, one provedthat symbolic dynamics is a powerful tool to study chaos and fractals. It is useful to study thefractal characteristics of symbolic dynamics. In the present note we shall point out the relationbetween the dimension and measure theoretic entropy of any subshift in symbolic space. Weprove here that the Bowen’s formula for Hausdorff dimension holds without Markov struc-ture. A variational principle for dimension is obtained.

关键词： symbolic space subshift measure theoretic entropy dimension.

On the Cayley-Bacharach property and the construction of vector bundles

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Science china mathematics 2011年第9期54卷 1891-1898页

作者： SUN Hao 1,2.1 department of mathematics and Statistics,Huazhong Normal {2.,Wuhan 430079,china 2.department of mathematics,East china Normal {2.,Shanghai 2.02.1,china department of mathematics and Statistics Huazhong Normal University Wuhan China department of mathematics East China Normal University Shanghai China

We study the Cayley-Bacharach property on complex projective smooth varieties of dimension n≥2.for zero dimensional subscheme defined by the zero set of the wedge of r-n + 1 global sections of a rank r≥n vector bund... 详细信息

关键词： Cayley-Bacharach property vector bundle reflexive sheaf k-very ample

Empirical likelihood confidence regions of the parameters in a partially linear single-index model

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Science china mathematics 2005年第10期48卷 1333-1348页

作者： XUE Liugen~1 & ZHU Lixing~2.1. College of Applied Sciences,Beijing university of Technology,Beijing 10002.,china {2.,Hong Kong Baptist university,Hong Kong,china College of Applied Sciences Beijing University of Technology Beijing China department of mathematics Hong Kong Baptist University Hong Kong China

In this paper, a partially linear single-index model is investigated, and three empirical log-likelihood ratio statistics for the unknown parameters in the model are suggested. It is proved that the proposed statistics are asymptotically standard chi-square under some suitable conditions, and hence can be used to construct the confidence regions of the parameters. Our methods can also deal with the confidence region construction for the index in the pure single-index model. A simulation study indicates that, in terms of coverage probabilities and average areas of the confidence regions, the proposed methods perform better than the least-squares method.

关键词： partially linear single-index model, empirical likelihood, confidence region, chi-square distribution, coverage probability.

On the periodic solutions of a type of differential-iterative equations

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Chinese Science Bulletin 1998年第3期43卷 204-206页

作者： GE Weigao 1, LIU Zhengrong 2.and YU Yuanhong 3 1. department of Applied mathematics, Beijing Institute of Technology, Beijing 100081, {2. 2. department of mathematics, Yunnan university, Kunming 650091, {2. 3. Institute of Applied mathematics, C department of Applied mathematics Beijing Institute of Technology Beijing China department of mathematics Yunnan University Kunming China Institute of Applied mathematics Chinese Academy of Sciences Beijing China

Sufficient conditions for the existence of periodic solutions to a type of nonautonomous differential_iterative equations are given.

关键词： differential_iterative equation periodic solution fixed point.

Two-dimensional Riemann problems of simplified Euler equation

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Chinese Science Bulletin 1998年第6期43卷 441-444页

作者： YANG Xiaozhou 1,2.and HUANG Feimin+1 1. Institute of Applied mathematics, Chinese Academy of Sciences, Beijing 100080, china {2., Shantou university, Guangdong 515063, china Institute of Applied mathematics Chinese Academy of Sciences Beijing China department of mathematics Shantou University Guangdong China

The two-dimensional Riemann problem of simplifed Euler equation is discussed, in which initial value contains two different constant states that are separated by a smooth curve. This problem is a natural description of realistic phenomena, but it is hard to study by conventional idea. So a new approach is proposed. Some new properties about two-dimensional rarefaction wave, shock wave and intermediate state of solutions are disclosed.

关键词： D Riemann problem implicit functions cylindrical surface pencil of cylindrical surface.