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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., China 2. Department of Mathematics, zhejiang university of Technology, hangzhou 310032. China) 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.

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 31002., China 2. China Institute of Metrology, {2., 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.

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., China 2. State Key Lab of CAD & CG, zhejiang university, hangzhou 31002., China 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., China 2. Department of Mathematics, 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.

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 university, hangzhou 31002., China 2. Department of Mathematics, {2. Forestry university, hangzhou 311300, China 3. State Key Laboratory of CAD & CG, zhejiang university, 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 & 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

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, zhejiang university, {2. 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.

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. China 2. Department of Applied Chemistry, {2. Institute of Science and Technology, hangzhou 310033, China 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.

Dynamic behavior of polymer surface and the time dependence of contact angle

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Science China Chemistry 2005年第6期48卷 553-559页

作者： WANG Xinping1, CHEN Zhifang1 & SHEN Zhiquan2.1. Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry, Department of Applied Chemistry, zhejiang Institute of Science and Technology, hangzhou 310033, China 2. Department of Polymer Science and Engineering,{2., hangzhou 31002., China 1. Department of Applied Chemistry Zhejiang Institute of Science and Technology Key Laboratory of Advanced Textile Materials and Manufacturing Technology of Education Ministry 310033 Hangzhou China 2. Department of Polymer Science and Engineering Zhejiang University 310027 Hangzhou China

Time-dependent contact angles were measured by depositing sessile drops of wa-ter on the polymer surfaces and monitoring the drop shape as a function of time. It was found that contact angles decreased sharply with contact time and the equilibrium contact angle was finally attained after a certain time. Values of starting (θ s) and equilibrium contact angles (θ e) obtained by the sessile drop method depend on polymer properties. The Wilhelmy plate technique was used to measure advancing and receding contact angles. The variations of starting (θ s) and equilibrium contact angles (θ e), advancing (θ a) and receding contact angles (θ r) have been studied on the oxidized surface of polymers containing polybutadiene block to explore the cause of time-dependence in contact angle measurement and the meaning of θ s and θ e. The results showed the linear relationships between starting (θ s) and advancing contact angles (θ a), the equilibrium (θ e) and receding contact angles (θ r). The similar relationship was also established between the contact angle hysteresis (θ a?θ r) and differences (θ s ?θ e) in starting contact angles and equilibrium contact angles. Therefore, time-dependence in contact angle measurement was mainly attributed to the surface reconstruction when water drops were deposited on polymer surfaces. The starting contact angle was contributed by the hydrophobic component on polymer surface and the equilibrium contact angle mainly by the hydrophilic component of polymer. These results not only demonstrated the interdependency between two contact angle measurements, the sessile drop method and the Wilhelmy plate technique, but also provided the experimental evidence to explain the cause of time-dependent contact angle. This may also provide a new method to study dynamic behavior of polymer surface.

关键词： contact angle, surface dynamic behavior, polymer surface, dynamic contact angle, time-dependence.

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 31002., 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