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Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets

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Science china mathematics 2007年第11期50卷 1537-1551页

作者： Li-feng XI~(1+) Huo-jun RUAN~2 1 Institute of mathematics,zhejiang Wanli university,Ningbo 315100,china 2 department of mathematics,zhejiang university,hangzhou 310027,china Institute of mathematics Zhejiang Wanli University Ningbo China department of mathematics Zhejiang University Hangzhou China

This paper investigates the Lipschitz equivalence of generalized {1,3,5}-{1,4,5} self-similar sets D=(r_1D)∪(r_2D+(1+r_1-r_2-r_3)/2)∪(r_3D+1+r_3) and E=(r_1E)∪(r_2E+1-r_2- r_3)∪(r_3E+1-r_3),and proves that D and E... 详细信息

关键词： self-similar set overlap Lipschitz equivalence graph-directed construction ergodicity martingale

Biorthogonal multiple wavelets generated by vector refinement equation

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Science china mathematics 2007年第7期50卷 1015-1025页

作者： Song LI~(1+) Jun XIAN~2 1 department of mathematics,zhejiang university,hangzhou 310027,china 2 department of mathematics,Sun Yat-Sen university,Guangzhou 510275,china department of mathematics Zhejiang University Hangzhou China department of mathematics Sun Yat-Sen University Guangzhou China

Biorthogonal multiple wavelets are generated from refinable function vectors by using the multiresolution analysis. In this paper we provide a general method for the construction of compactly supported biorthogonal multiple wavelets by refinable function vectors which are the solutions of vector refinement equations of the form $$\varphi (x) = \sum\limits_{\alpha \in \mathbb{Z}^s } {a(\alpha )\varphi (Mx - \alpha ), x \in \mathbb{R}^s } ,$$ where the vector of functions ? = (? 1, …, ? r)T is in $(L_2 (\mathbb{R}^s ))^r ,a = :(a(\alpha ))_{\alpha \in \mathbb{Z}^s } $ is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix such that lim n→∞ M ?n = 0. Our characterizations are in the general setting and the main results of this paper are the real extensions of some known results.

关键词： refinement equation biorthogonal multiple wavelets refinable function vector 42C40 41A10 41A15 41A25

Interpolating triangular meshes by Loop subdivision scheme

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Science china(Information Sciences) 2010年第9期53卷 1765-1773页

作者： DENG ChongYang1* & WANG GuoZhao2 1Institute of Applied mathematics and Engineering Computations,hangzhou Dianzi university,hangzhou 310018,china 2department of mathematics,zhejiang university,hangzhou 310027,china Institute of Applied mathematics and Engineering Computations Hangzhou Dianzi University Hangzhou China department of mathematics Zhejiang University Hangzhou China

Using the limit point formula of the Loop subdivision scheme,we propose a very simple and efficient method for constructing interpolation surface of triangular meshes by Loop subdivision *** excellent properties of the method are:(1) Locality:the perturbation of a given vertex only influences the surface shape near this vertex.(2) Efficiency:the locations of new points can be computed with explicit formulae.(3) Easiness in implementation:only the geometric rule of the first step should be modified.(4) Freedom:for each edge,there is one degree of freedom to adjust the shape of the interpolation surface.(5) Easiness in generalization:it is easy to generalize our method to other approximation subdivision schemes with explicit formulae to compute limit point.

关键词： computer aided geometric design subdivision surface approximating subdivision scheme Loop surface surface interpolating

Limit theory of restricted range approximations of complex-valued continuous functions

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Science china mathematics 2007年第10期50卷 1427-1440页

作者： Xian-fa LUO~1 Chong LI~(2+) ~1 School of mathematics and Computer Science,Jishou university,Jishou 416000,china ~2 department of mathematics,zhejiang university,hangzhou 310027,china School of mathematics and Computer Science Jishou University Jishou China department of mathematics Zhejiang University Hangzhou China

This paper is concerned with the problem of the best restricted range approximations of complex-valued continuous functions. Several properties for the approximating set PΩ such that the classical characterization results and/or the uniqueness results of the best approximations hold are introduced. Under the very mild conditions, we prove that these properties are equivalent that P is a Haar subspce.

关键词： restricted range approximation, Haar subspace, characterization, uniqueness

The decomposition of K_v into K_2 × K_5's

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Science china mathematics 2007年第10期50卷 1382-1388页

作者： Yang LI~1 Jian-xing YIN~1 Ru-cong ZHANG~2 Gen-nian GE~(2+) ~1 department of mathematics,Suzhou university,Suzhou 215006,china ~2 department of mathematics,zhejiang university,hangzhou 310027,china department of mathematics Suzhou University Suzhou China department of mathematics Zhejiang University Hangzhou China

The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a de... 详细信息

关键词： decomposition, the complete graph Kv, product graph Kr×Kc, DNA library screening

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 310027, 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

Geometric construction of energy-minimizing Bézier curves

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Science china(Information Sciences) 2011年第7期54卷 1395-1406页

作者： XU Gang 1,4,5,WANG GuoZhao 2 & CHEN WenYu 2,3 1 Institute of Graphics and Image,hangzhou Dianzi university,hangzhou 310018,china 2 department of mathematics,zhejiang university,hangzhou 310027,china 3 School of Computer Engineering,Nanyang Technological university,639798,Singapore 4 Galaad,INRIA Sophia-Antipolis,2004 Route des Lucioles,06902,France 5 State Key Lab of CAD & CG,zhejiang university,hangzhou 310027,china Institute of Graphics and Image Hangzhou Dianzi University Hangzhou China Galaad INRIA Sophia-Antipolis Sophia Antipolis France State Key Lab of CAD & CG Zhejiang University Hangzhou China department of mathematics Zhejiang University Hangzhou China School of Computer Engineering Nanyang Technological University Singapore Singapore

Modeling energy-minimizing curves have many applications and are a basic problem of Geometric *** this paper,we propose the method for geometric design of energy-minimizing B′ezier ***,the necessary and sufficient condition on the control points for B′ezier curves to have minimal internal energy is *** on this condition,we propose the geometric constructions of three kinds of B′ezier curves with minimal internal energy including stretch energy,strain energy and jerk *** some control points,the other control points can be determined as the linear combination of the given control *** compare the three kinds of energy-minimizing B′ezier curves via curvature combs and curvature plots,and present the collinear properties of quartic energy-minimizing B′ezier *** also compare the proposed method with previous methods on efficiency and ***,several applications of the curve generation technique,such as curve interpolation with geometric constraints and modeling of circle-like curves are discussed.

关键词： curve design minimal energy geometric construction interpolation with constraints circle-like curves

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. department of mathematics, 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.

Time-periodic solutions of the Einstein's field equations Ⅰ:general framework

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Science china mathematics 2010年第5期53卷 176-193页

作者： KONG DeXing1 & LIU KeFeng2 1department of mathematics,zhejiang university,hangzhou 310027,china 2department of mathematics,university of California at Los Angeles,CA 90095,USA

In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field ***-periodic solutions are constructed by using the new *** singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are *** applications of these solutions in modern cosmology and general relativity are expected.

关键词： Einstein’s field equations time-periodic solution Riemann curvature tensor singularity event horizon