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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., 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.

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{2., 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.

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,{2. Normal university,{2. 310036, China 2. department of Applied mathematics, School of Mathematical Sciences, South China university 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.

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

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

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

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,China(email:xuejunttt@2.3. net) 2. The School of Science,{2. Dianzi university,{2. 310037,China 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.

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,{2. 310032. China 2. department of Applied Chemistry, Zhejiang Institute of Science and Technology,{2. 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.

Ordinal scheduling problem and its asymptotically optimal algorithms on parallel machine system

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Science in China(Series F) 2004年第2期47卷 161-169页

作者： TAN Zhiyi1,2.& HE Yong1 1. department of mathematics, Zhejiang{2., hangzhou 31002., China (email: tanzy@math.zju. *** heyong@math.zju.***) 2. State Key Laboratory of CAD & CG, Zhejiang{2., hangzhou 31002., China 1. department of mathematics Zhejiang University 310027 Hangzhou China 2. State Key Laboratory of CAD & CG Zhejiang University 310027 Hangzhou China

Focusing on the ordinal scheduling problem on a parallel machine system, we discuss the background of ordinal scheduling and the motivation of ordinal algorithms. In addition, for the ordinal scheduling problem on identical parallel machines with the objective to maximize the minimum machine load, we then give two asymptotically optimal algorithm classes which have worst-case ratios very close to the upper bound of the problem for any given m. These results greatly improve the results proposed by He Yong and Tan Zhiyi in 2.02.

关键词： scheduling design and analysis of algorithm worst-case ratio.