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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 {2., Suzhou 2.5006, China 2. department of mathematics, zhejiang university, 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.

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

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. {2. 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.

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, {2., 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

A note on certain square functions on product spaces

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Science China mathematics 2006年第1期49卷 98-108页

作者： WANG Meng, CHEN Jiecheng2.& FAN Dashan department of mathematics, {2. (at Yuquan campus), hangzhou 31002., China department of mathematics, {2. (at Xixi campus), hangzhou 31002., China department of mathematics, university of Wisconsin-Milwaukee, Milwaukee, WI532.1, USA department of mathematics Zhejiang University [at Yuquan campus] Hangzhou 310027 China department of mathematics Zhejiang University [at Xixi campus] Hangzhou 310028 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI53201 USA

We study certain square functions on product spaces Rn × Rm, whose integral kernels are obtained from kernels which are homogeneous in each factor Rn and Rm and locally in L(log+ L) away from Rn × {0} and {0} × Rm by means of polynomial distortions in the radial variable. As a model case, we obtain that the Marcinkiewicz integral operator is bounded on Lp(Rn × Rm)(P > 1) for Ω∈ e Llog+ L(Sn-1 × Sm-1) satisfying the cancellation condition.

关键词： square function, Marcinkiewicz integral, product space.

THE CONVERGENCE ON A FAMILY OF ITERATIONS WITH CUBIC ORDER

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Journal of Computational mathematics 2001年第5期19卷 467-474页

作者： Dan-fu Han (department of mathematics, {2., hangzhou 31002., China) 浙江大学浙江杭州 310028

Establishes a convergent theorem for a family of iterations with cubic order by using general convergence hypotheses. Disadvantage of using the cubic majorizing function; Convergence of the majorizing sequence; Overvi... 详细信息

关键词： convergence majorizing method gamma-condition error estimate

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 {2.,Ningbo 315100,China 2.department of mathematics,zhejiang university,hangzhou 31002.,China Institute of mathematics Zhejiang Wanli University Ningbo 315100 China department of mathematics Zhejiang University Hangzhou 310027 China

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

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, {2., China 2. State Key Lab of CAD & CG, zhejiang university, {2., 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

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,{2.,hangzhou 31002.,China 2.department of mathematics,Sun Yat-Sen university,Guangzhou 5102.5,China 1. department of mathematics Zhejiang University Hangzhou 310027 China 2. department of mathematics Sun Yat-Sen University Guangzhou 510275 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 42.40 41A10 41A15 41A2.