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Cartesian closedness of categories of completely distributive lattices

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Chinese Science Bulletin 1998年第24期43卷 2059-2063页

作者： ZHANG Dexue 1.and YANG Zhongqiang 2.1. {1. of mathematics, Sichuan University, Chengdu 61.064,{2. 2. department of mathematics, Shaanxi Normal University, Xi’an 71.062.{2. department of {1. Sichuan University Chengdu China department of {1. Shaanxi Normal University Xi’an China

The category of completely distributive lattices with Scott continuous functions is cartesian closed. Neither the category of completely distributive lattices with arbitrary union preserving mappings nor the category ... 详细信息

关键词： completely distributive lattice continuous lattice cartesian closedness.

CMC surfaces in the hyperbolic 3-space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1. 2.and LI Zhenqi 1. 3 1. Institute of {1., Fudan University, Shanghai 2.0433, china {2.,Sichuan Union University, Chengdu 61.064, china 3. department of {1., Nanchang University, Nanchang 33 nstitute of Mathemalics Fudan University Shanghai China department of {1. Sichuan Union University Chengdu China department of {1. Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1.are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

Mathematical stencil and its application in finite difference approximation to the Poisson equation

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Science china {1. 2005年第10期48卷 1421-1429页

作者： FENG Hui~1.ZHANG Baolin~(1.2. & LIU Yang~1.1. {1. of mathematics,Wuhan University,Wuhan 430072.{2. 2. Laboratory of Computational Physics,Institute of Applied Physics and Computational mathematics,Beijing 1.0088. china 1. department of {1. Wuhan University 430072 Wuhan China 2. Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics 100088 Beijing China

The concept of mathematical stencil and the strategy of stencil elimination for solving the finite difference equation is presented, and then a new type of the iteration algorithm is established for the Poisson equation. The new algorithm has not only the obvious property of parallelism, but also faster convergence rate than that of the classical Jacobi iteration. Numerical experiments show that the time for the new algorithm is less than that of Jacobi and Gauss-Seidel methods to obtain the same precision, and the computational velocity increases obviously when the new iterative method, instead of Jacobi method, is applied to polish operation in multi-grid method, furthermore, the polynomial acceleration method is still applicable to the new iterative method.

关键词： mathematical stencil, stencil elimination, Poisson equation, finite difference, iterative algorithm,parallelism.

Characteristic analysis for a polynomial-like iterative equation

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Chinese Science Bulletin 1998年第3期43卷 192-196页

作者： Janusz Matkowski 1.and ZHANG Weinian 2.1. {1. of mathematics, Technical University, 43_300 Bielsko_Biala, Poland {2., Sichuan Union University, Chengdu 61.064, china department of {1. Technical University Bielsko-Biala Poland department of {1. Sichuan Union University Chengdu China

In the light of Euler’s idea for differential equations,a polynomial_like n _order iterative equation is discussed through analyzing its characteristic polynomial. An unproved result is verified rigorously for the fi... 详细信息

关键词： iterative dynamics functional equation characteristic.

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 31.02., china 2. department of mathematics, Hangzhou University, Hangzhou 31.02., china Center for Mathematical Sciences Zhejiang University Hangzhou China department of {1. 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.

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. {1. of Applied mathematics, Beijing Institute of Technology, Beijing 1.0081.{2. 2. department of mathematics, Yunnan University, Kunming 650091.{2. 3. Institute of Applied mathematics, C department of Applied {1. Beijing Institute of Technology Beijing China department of {1. 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.

Planar cubic hybrid hyperbolic polynomial curve and its shape classification

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Progress in Natural Science:Materials International 2004年第1期14卷 42-47页

作者： WANG Guozhao 1.2. * and YANG Qinmin 1.2. (1. Institute of Computer Graphics and Image Processing, 2. department of mathematics, Zhejiang University, Hangzhou 31.02., china) Zhejiang Univ Inst Comp Graph & Image Proc Hangzhou 310027 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China

The planar cubic hybrid hyperbolic polynomial curves and cubic H Bézier curves are presented. The conditions leading to inflection points and singularities (cusps and loops) are investigated and the shape of these curves is classified. The conclusions enable us to detect inflection points and singularities and get an idea of how to preserve the fair shape when designing such curves.

关键词： hybrid hyperbolic polynomial curve H-Bézier curve shape classification inflection points singularities

Fredholm operators in Toeplitz algebras associated with discrete abelian groups

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Chinese Science Bulletin 1998年第14期43卷 1175-1179页

作者： XU Qingxiang 1.and CHEN Xiaoman 2.1. {1. of mathematics, Shanghai Normal University, Shanghai 2.02.4,{2. 2. Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics, Fudan University, Shanghai 2.0433,{2. department of {1. Shanghai Normal University Shanghai China Laboratory of mathematics for Nonlinear Sciences and Institute of mathematics Fudan University Shanghai China

The locally finite below sets are introduced and the Fredholm operators in Toeplitz algebras associated with discrete abelian groups are studied.

关键词： discrete abelian group quasi_ordered group Toeplitz operator Fredholm operator.

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

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Science china {1. 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 1.002.,china 2. department of mathematics,Hong Kong Baptist University,Hong Kong,china 1. College of Applied Sciences Beijing University of Technology 100022 Beijing China 2. 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.