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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

Homoclinic orbits of the doubly periodic Davey-Stewartson equation

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Progress in Natural Science:Materials International 2004年第11期 95-96页

作者： ZHANG Jun 1*, GUO Boling 1 and SHEN Shoufeng 2.1. Institute of Applied Physics and Computational mathematics, Beijing 100088, china {2., zhejiang university, hangzhou 310027, china) InstituteofAppliedPhysicsandComputationalmathematics Beijing100088China departmentofmathematics ZhejiangUniversityHangzhou310027China

Chaos is closely associated with homoclinic orbits in deterministic nonlinear dynamics. In this note, the homoclinic orbits of the doubly periodic Davey-Stewartson equation are obtained by using the Hirota's bilinear ... 详细信息

关键词： homoclinic orbit Hirota’s bilinear method Davey-Stewartson equation.

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,{2., hangzhou 310027, china 2. department of mathematics,{2. of Technology, hangzhou 310032. china) department of mathematics Zhejiang University Hangzhou 310027 China 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.

ON MULTIPLE POSITIVE SOLUTIONS FOR A NONLINEAR ELLIPTIC PROBLEM IN R^N

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Chinese Annals of mathematics,Series B 2000年第3期21卷 351-358页

作者： YANG HAITAO(department of mathematics,{2., hangzhou 310027, china.) WU SHAOPING(department of mathematics,{2., hangzhou 310027, china.) department of mathematics Zhejiang University Hangzhou 310027 China

By making use of Variational method, the authors obtain some results about existence of multiple positive solutions and their asymptotic behavior as the parameter →＋∞ for a semilinear elliptic problem in RN.

关键词： Critical point Asymptotic behavior Concentration

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,{2., hangzhou 310027, china 2. department of mathematics, zhejiang Forestry university, hangzhou 311300, china 3. State Key Laboratory of CAD & CG,{2., hangzhou 310027, 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

REMARKS ON h-TRANSFORM AND DRIFT

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Chinese Annals of mathematics,Series B 1998年第4期19卷 473-478页

作者： YING JIANGANG (department of mathematics,{2., hangzhou 310027, china.) department of mathematics Zhejiang University Hangzhou 310027 China

The author studies the h-transforms of symmetric Markov processes and corresponding Dirichlet spaces, and also discusses the drift transformation of Fukushima and Takeda’s type[2. and improves their result by a diffe... 详细信息

关键词： Right processes Revuz measures h-transform

Circular β ensembles,CMV representation,characteristic polynomials

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Science china mathematics 2009年第7期52卷 1467-1477页

作者： SU ZhongGen department of mathematics,{2. university,hangzhou 310027,china department of mathematics Zhejiang University Hangzhou China

In this note we first briefly review some recent progress in the study of the circular β ensemble on the unit circle,where β > 0 is a model *** the special cases β = 1,2.and 4,this ensemble describes the joint probability density of eigenvalues of random orthogonal,unitary and sympletic matrices,*** general β,Killip and Nenciu discovered a five-diagonal sparse matrix model,the CMV *** representation is new even in the case β = 2.and it has become a powerful tool for studying the circular β *** then give an elegant derivation for the moment identities of characteristic polynomials via the link with orthogonal polynomials on the unit circle.

关键词： characteristic polynomials circular β ensembles CMV representation moment identity 15A52

Mean size formula of wavelet subdivision tree on Heisenberg group

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Applied mathematics(A Journal of Chinese Universities) 2008年第3期23卷 303-312页

作者： WANG Guo-mao department of mathematics,{2. university,hangzhou 310027,china department of mathematics,hangzhou Dianzi university,hangzhou 310018,china. department of mathematics Zhejiang University Hangzhou China department of mathematics Hangzhou Dianzi University Hangzhou China

The purpose of this paper is to investigate the mean size formula of wavelet packets （wavelet subdivision tree） on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree.

关键词： Heisenberg group wavelet packets subdivision tree joint spectral radius stability

Rigidity for rational maps with Cantor Julia sets

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Science china mathematics 2008年第1期51卷 79-92页

作者： ZHAI Yu department of mathematics,{2., hangzhou 310027, china department of mathematics Zhejiang University Hangzhou China

In this paper, we prove that two rational maps with the Cantor Julia sets are quasicon- formally conjugate if they are topologically conjugate.

关键词： Cantor Julia set rigidity puzzle piece bounded shape quasiconformally conjugate 37F12