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Constrained Bézier curves' best multi-degree reduction in the L2.norm

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Progress in Natural Science:Materials International 2005年第9期15卷 843-850页

作者： ZHANG Renjiang 1,2.** and WANG Guojin1(1. institute of Computer Images and Graphics, zhejiang university, Hangzhou {2., china 2. china institute of Metrology, zhejiang, Hangzhou 310034, china) institute of Computer Images and Graphics Zhejiang University Hangzhou 310027 China. State Key Laboratory of CAD&CG Zhejiang University Hangzhou 310027 China. china institute of Metrology Zhejiang Hangzhou 310034 China

In computer aided geometric design, the degree reduction of the parameter curve is a key technique in data exchange and data compression. The various existing methods of degree reduction cannot decide whether the degree reduction curve satisfying the given tolerance exists beforehand, cannot give approximation of the best multi-degree reduction, or cannot provide explicit expression and error formula of the degree reduction curve. In this paper, we propose an entirely new method, which can hurdle the above flaws completely. For a given Bézier curve of degree n, we can easily decide whether a Bézier reduction curve of degree m exists, which has equal derivatives with the given curve up to （r-1）-th and （s-1）-th orders （r,s≤m） respectively at the endpoints, so the approximating error is less than the given tolerance ε in the L2.norm. If the curve exists, the explicit expression can be given.

关键词： computer aided design Bézier curve degree reduction L2.norm tolerance.

Synthesis and crystal structure of complex of Ce(NO_3)_3 with N-(3-methyl-pyridin-2.yl)-formimidoyl-(3-methyl-pyridin-2.yl) hydrazone

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Science china Chemistry 2004年第3期47卷 251-256页

作者： JIANG Yinzhi1,2.& HU Weixiao1 1. Department of pharmaceutical Science, zhejiang university of Technology, Hangzhou 310032. {2. 2. Department of Applied Chemistry, zhejiang institute of Science and Technology, Hangzhou 310033, {2. 1. Department of pharmaceutical Science Zhejiang University of Technology 310032 Hangzhou China 2. Department of Applied Chemistry Zhejiang Institute of Science and Technology 310033 Hangzhou China

The reaction of 3,6-di-(3-methyl-pyridin-2.yI)-s-tetrazine (DMPTZ, II) with CeIII salt [Ce(NO3)3 · 6H2.] generates a new ligand, N-(3-methyl-pyridin-2.yl)-formimidoyl-(3-methyl-pyridin-2.yl) hydrazone (L), and forms a new complex: a mononuclear complex [Ce(L)(NO3)2.(H2.)3] · NO3 (III). Crystal data for III: space group P-1, with a = 0.7133(4) nm, b = 1.1139(2. nm, c = 1.4572.3) nm, α= 102.13(2.°, β= 99.81(3)°, γ= 91.10(3)°, Z = 2. V = 1113.6(7) nm3, μ = 2.12. mm?1 and F(000) = 630. L acts as a tri-dentate chelating ligand in III. There are 10 coordination sites around Ce3+ of III, which are respectively occupied by seven oxygen atoms (four from two nitrate anions and three from three H2. molecules) and three nitrogen atoms (all from L). The cerium atom and three chelating nitrogen atoms are coplanar. The mechanism of the metal assisted decomposition is discussed briefly.

关键词： rare earth, complex, crystal structure, synthesize, 3,6-bis (3-methyl-pyridin-2.yl)-s-tetrazine, N-(3-methyl-pyridin- 2.yl)-formimidoyl-(3-methyl-pyridin-2.yl) hydrazone.

A new method for mining deformation monitoring with GPS-RTK

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中国有色金属学会会刊：英文版 2011年第S3期21卷 659-664页

作者： GAO Jing-xiang1, 2. LIU Chao2. WANG Jian1, 2. LI Zeng-ke2. MENG Xiang-chao2.1. Key Laboratory for Land Environment and Disaster Monitoring of State Bureau of Surveying and Mapping, china university of Mining and Technology, Xuzhou 2.1116, china 2. School of Environment and Spatial informatics, china university of Mining and Technology, Xuzhou 2.1116, china [a] Key Laboratory for Land Environment and Disaster Monitoring of State Bureau of Surveying and Mapping China University of Mining and Technology Xuzhou 221116 China [b] School of Environment and Spatial informatics China University of Mining and Technology Xuzhou 221116 China

Based on ranging intersection theory, a new method which is simple and easy to operate was proposed for data collection in the mine surface deformation monitoring with GPS-RTK centering rod measurements. It can fully eliminate the inevitable shaking error and the vertical deflection, and to some extent weaken the multipath effect on the estimates of coordinates in a relatively short period of time, using high-frequency observations. The results show that three-dimensional coordinates with a height accuracy better than 1 cm, horizontal accuracy better than 2.4 cm can be achieved through only 15-30 s continuous observation by 2. Hz high-frequency and effectively improve the measurement accuracy and efficiency of RTK, fully satisfying the high-speed and high-precision data acquisition in mine surface subsidence deformation monitoring.

关键词： GPS rover pole multipath delay deformation monitoring

Linguistic granular model: design and realization

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Progress in Natural Science:Materials International 2005年第8期15卷 749-756页

作者： YUE Shihong 1,2., LI Ping2.and SONG Zhihuan2.1. institute of Industrial Process Control, zhejiang university, Hangzhou {2., china 2. School of Electric Engineering and Atomization, Tianjin university, Tianjin 300072. china) institute of Industrial Process Control Zhejiang University Hangzhou 310027 China. School of Electric Engineering and Atomization Tianjin University Tianjin 300072 China

A new linguistic granular model is proposed and the effect of its parameters on the output is analyzed. The design of the model consists of two stages: using conditional fuzzy clustering for information granular, and integrating all information granules to final output. The integrating tool is fuzzy integral based on fuzzy measure, and the generalization of fuzzy integral increases flexibility of the linguistic granular model greatly. A heuristic algorithm to determine the parameters in the fuzzy integral is used to realize the linguistic model. Two experiments verify the feasibility of the proposed model.

关键词： linguistic model granular fuzzy clustering fuzzy integral.

Shape blending of artistic brushstroke represented by disk B-spline curves

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Progress in Natural Science:Materials International 2007年第12期17卷 1501-1507页

作者： Cheng Min1,2.and Wang Guojin1(1. Department of Mathematics, zhejiang university, Hangzhou 31002., {2. 2. Department of Mathematics, zhejiang university of Technology, Hangzhou 310032. {2.) Department of Mathematics Zhejiang University Hangzhou 310027 China 2. Department of Mathematics Zhejiang University of Technology Hangzhou 310032 China

This paper presents an algorithm for automatically generating in-between frames of two artistic brushstrokes. The basic idea of the algorithm is to represent the two key frames of artistic brushstrokes in disk B-spline curves, and then make blending of their geometric intrinsic variables. Given two key frames of artistic brushstrokes, the skeleton curves can be obtained by certain skeleton-based techniques. After disk B-spline representation of the key frames is generated, interpolation of the intrinsic variables of the initial and the target disk B-spline curves is carried out. Examples show that this method can efficiently create in-between frames of artistic brushstrokes.

关键词： computer aided calligraphy shape blending brushstroke disk B-spline curve skeleton.

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 {2., 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

Perturbations of the radical of nest algebras

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Chinese Science Bulletin 1998年第7期43卷 556-560页

作者： LU Fangyan 1 and LU Shijie 2.1. Department of Mathematics, Suzhou university, Suzhou 2.5006, china 2. Department of Mathematics, {2., Hangzhou 31002., china Department of Mathematics Suzhou University Suzhou China Department of Mathematics Zhejiang University Hangzhou China

Let R N and K-N be the radical ideal and the compact operator ideal of nest algebra T(N) respectively. It is proved thatR-N+K-N=span{T∈T(N)∶TT(N)NCT}=span{T∈T(N): #σ′(ST)≤1, S∈T(N)}.

关键词： nest algebras radical perturbation.

Electro-mechanical response of functionally graded beams with imperfectly integrated surface piezoelectric layers

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Science china(Physics,Mechanics & Astronomy) 2006年第5期49卷 513-525页

作者： YAN Wei1 & CHEN Weiqiu1,2.1. Department of Civil Engineering, zhejiang university, Hangzhou 31002., {2. 2. State Key Lab of CAD & CG, zhejiang university, Hangzhou 31002., {2. 1. Department of Civil Engineering Zhejiang University Hangzhou 310027 China 2. State Key Lab of CAD & CG Zhejiang University Hangzhou 310027 China

The time-dependent behavior of a simply-supported functionally graded beam bonded with piezoelectric sensors and actuators is studied using the state-space method. The creep behavior of bonding adhesives between piezoelectric layers and beam is characterized by a Kelvin-Voigt viscoelastic model, which is practical in a high temperature circumstance. Both the host elastic functionally graded beam and the piezoelectric layers are orthotropic and in a state of plane stress, with the former being inhomogeneous along the thickness direction. A laminate model is employed to approximate the host beam. Moreover, the coupling effect between the elastic deformation and electric field in piezoelectric layers is considered. Results indicate that the viscoelastic property of interfacial adhesives has a significant effect on the function of bonded actuators and sensors with time elapsing.

关键词： functionally graded beam piezoelectric layers Kelvin-Voigt model state-space method

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., {2. 2. Department of Mathematics, Hangzhou university, Hangzhou 31002., {2. 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.