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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,{2., 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.

Transitional function of DG to CA3 in the hippocampus

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Progress in Natural Science:Materials International 2007年第12期17卷 1436-1444页

作者： Yan Chuankui1 and Liu Shenquan2.1. Department of mathematics, hangzhou Normal {2., hangzhou 310036, china 2. Department of Applied mathematics, School of Mathematical Sciences, South china {2. of Technology, Guangzhou 510640, china) Department of mathematics Hangzhou Normal University Hangzhou 310036 China Department of Applied mathematics School of Mathematical Sciences South China University of Technology Guangzhou 510640 China

Using single cell channel model, the transmission features of CA3-DG network in the hippocampus are investigated. The influence of the stimulation on discharge pattern of pyramidal neurons is analyzed, which shows that it starts with period spiking discharges, followed by period-doubling bifurcation to chaos, and period 3 discharge evolving into chaos, and ultimately a period of bursting discharges. By the synaptic model, the CA3-DG network model is constructed, which analyzes the summation of postsynaptic currents in the network, the influence of postsynaptic current on discharge rhythm as well as the mechanism of bursting discharges. The strong capacity of spatiotemporal encoding in the network indicates the features of CA3 network during the information transmission process in the hippocampus. The modeling result with time delay of the synaptic transmission is in accordance with the experimental phenomena of action potential in the hippocampus.

关键词： hippocampus CA3-DG period-doubling bifurcation chaos.

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,{2. 2. Department of mathematics, Zhejiang university, hangzhou 31002.,{2. 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.

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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 university,{2., china 2. Department of mathematics, Zhejiang Forestry university, hangzhou 311300, china 3. State Key Laboratory of CAD & CG, Zhejiang university,{2., 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

Weighted composition operators between μ-Bloch spaces on the unit ball

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Science china mathematics 2005年第10期48卷 1349-1368页

作者： ZHANG Xuejun~1 & XIAO Jianbin~2.1. College of mathematics and Computer Science,Hunan Normal university,Changsha 410006,{2.(email:xuejunttt@2.3. net) 2. The School of Science,hangzhou Dianzi university,hangzhou 310037,{2. 1. College of mathematics and Computer Science Hunan Normal University 410006 Changsha China 2. The School of Science Hangzhou Dianzi University 310037 Hangzhou China

In this paper,necessary and sufficient conditions are given for the weighted composition operator T_(ψ,ψ) to be bounded or compact from the space β_μ to β_ν (or β_(μ,0) to β_(ν,0) ) on the unit ball of C^***... 详细信息

关键词： μ-Bloch space, weighted composition operator, boundedness, compactness.

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Numerical research on the 3D fiber orientation distribution in arbitrary planar flows

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Progress in Natural Science:Materials International 2007年第11期17卷 1357-1362页

作者： Zhou Kun1 and Lin Jianzhong1,2.1. State Key Laboratory of Fluid Power Transmission and Control, Zhejiang university, hangzhou 31002.,{2. 2.{2. Jiliang university, hangzhou 310018,{2.) State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China china Jiliang university Hangzhou 310018 China

The fiber orientation distribution in a fiber suspension flow was investigated by a finite difference scheme in spherical coordinates. The diffusivity was transformed between Cartesian and spherical coordinates through tensor analysis to obtain efficiency. It is found that under simple shear flow condition the diffusivity in the azimuthal direction, Dr, has greater effect on the orientation distribution than that in the colatitude direction, Drθθ.

关键词： fiber suspension flow orientation distribution diffusivity

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.,{2. 2.{2. Institute of Metrology, Zhejiang, hangzhou 310034,{2.) 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.

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,{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

Numerical simulation of the efficiency of mixing in heterogeneous microchannels with patterned surface potentials

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Progress in Natural Science:Materials International 2006年第12期16卷 1322-1328页

作者： ZHANG Kai~1, LIN Jianzhong~ 1,2.** and LI Huijun~1(1. State Key Laboratory of Fluid Power Transmission and Control, Zhejiang university, hangzhou 31002.,{2. 2.{2. Jiliang university, hangzhou 310018,{2.) [a]State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hanghou China [b]china Jiliang university Hangzhou China

The mixing of samples in heterogeneous microchannels with a periodically stepwise surface potential was analyzed numerically using the control volume method. The equations describing the wall potential and external potential were solved first to get the distribution of wall potential and external potential, respectively, then the momentum equation was solved to get the developed flow field. Finally, the mass transport equation was solved to get the concentration field. The simulation results show that the distribution of samples at the inlet of the microchannel determines its theoretical value of concentration, therefore, the pattern of the distribution of samples at the inlet and its corresponding velocity can be changed to get the desirable concentration of solute. The heterogeneous wall potential almost has no effect on the mixing of samples in two-inlet microfluidic devices. For three-inlet microfluidic devices, the comprehensive ability of transportation and mixing has an optimization when the ratio of periodic length of wall potential to the height of the microchannel is about 4.88. The above conclusions are helpful to the optimization of the design of microfluidic devices.

关键词： microchannel mixing efficiency electroosmosis numerical simulation.