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WEAK CHEBYSHEV SPACES ON LOCALLY ORDERED TOPOLOGY SPACE AND THE RELATED CONTINUOUS METRIC SELECTIONS

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Chinese Annals of mathematics 1987年第4期8卷 420-427页

作者：李武 department of mathematics{2. China.

Let C(X)be the space of all continuous real-valued functions on a compact Hausdorffspace X under the uniform norm:‖f‖=max{|f(x)|:x∈X}.For G(?)C(X),defineP_G(f)={g∈G:‖f-g‖=inf{‖f-p‖:p∈G}}.If there exists a continuous mapping S from C(X)to G such that S(f)∈P_G(f)for everyf in C(X),then S is called a continuous selection of the metric projection P_*** G is called a Z-subspace of C(X),if,for every nonzero g in G,g does not vanishon any open subset of *** this paper,the author gives several characterizations of Z-subspaces G whose metricprojections P_G have continuous *** following results are obtained:If X is locally connected and G is an n-dimensional Z-subspace of C(X),then P_G hasa continuous selection if and only if every nonzero g in G has at most n zeros and has atmost n-1 zeros with sign changes.

关键词：一夕 WEAK CHEBYSHEV SPACES ON LOCALLY ORDERED TOPOLOGY SPACE AND THE RELATED CONTINUOUS METRIC SELECTIONS De 一刁

Estimation for nearly unit root processes with GARCH errors

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Applied mathematics(A Journal of Chinese Universities) 2010年第3期25卷 297-306页

作者： YUAN Yu-ze ZHANG Rong-mao department of mathematics, Zhejiang{2., hangzhou 31002., China department of mathematics Zhejiang University Hangzhou China

In this paper the limiting distribution of the least square estimate for the autoregressive coefficient of a nearly unit root model with GARCH errors is derived. Since the limiting distribution depends on the unknown variance of the errors, an empirical likelihood ratio statistic is proposed from which confidence intervals can be constructed for the nearly unit root model without knowing the variance. To gain an intuitive sense for the empirical likelihood ratio, a small simulation for the asymptotic distribution is given.

关键词： Nearly unit root GARCH error least square estimation Ornstein-Uhlenbeck process empirical likelihood.

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 31002.,China 3 School of Computer Engineering,Nanyang Technological university,639798,Singapore 4 Galaad,INRIA Sophia-Antipolis,2.04 Route des Lucioles,06902.France 5 State Key Lab of CAD & CG,Zhejiang university,hangzhou 31002.,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

Piecewise-Koszul algebras

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Science China mathematics 2007年第12期50卷 1795-1804页

作者： Jia-feng L■~1 Ji-wei HE~2.Di-ming LU~(1+) ~1 department of mathematics,Zhejiang{2.,hangzhou 31002.,China ~2.department of mathematics,Shaoxing College of Arts and Sciences,Shaoxing 312.00,China department of mathematics Zhejiang University Hangzhou 310027 China department of mathematics Shaoxing College of Arts Sciences Shaoxing 312000 China

It is a small step toward the Koszul-type *** piecewise-Koszul algebras are, in general,a new class of quadratic algebras but not the classical Koszul ones,simultaneously they agree with both the classical Koszul and higher Koszul algebras in special *** give a criteria theorem for a graded algebra A to be piecewise-Koszul in terms of its Yoneda-Ext algebra E(A),and show an A_∞-structure on E(A).Relations between Koszul algebras and piecewise-Koszul algebras are *** particular,our results are related to the third question of Green-Marcos.

关键词： (d-)Koszul algebras A_∞-algebras Yoneda-Ext algebras

A new method for adaptive color image filtering

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Chinese Science Bulletin 2000年第13期45卷 1230-1235页

作者： JIANG Gangyi, YU Mei & YU Bokang1. department, of Information & Electronic Engineering, Hang/hou university of Commerce,{2. 310035, China 2. department, of Electronic Engineering,{2. institute of Electronics Engineering,{2. 310037, China 3. State Key Laboratory on Machine Perception, Peking university, Beijing 100871, China Correspondence should be addressed to Yu Mei department of Information & Electronic Engineering Hangzhou University of Commerce Hangzhou China State Key Laboratory on Machine Perception Peking University Beijing China department of Electronic Engineering Hangzhou Institute of Electronics Engineering Hangzhou China

An adaptive color image filter (ACIF) is proposed in this note. Through analyzing noise corruption of color image, efficient locally adaptive filters are chosen for image enhancement. The proposed adaptive color image filter combines advantages of both nonlinear vector filters and linear filters, it attenuates noise and preserves edges and details very well. Experimental results show that the proposed filter performs better than vector median filter, directional-distance filter, directional-magnitude vector filter, adaptive nearest-neighbor filter, and α-trimmed mean filter.

关键词： color image noise analysis locally adaptive filters adaptive color image filter (ACIF).

The cohomology group of weak entwining structure

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Science China mathematics 2007年第5期50卷 665-674页

作者： Ling JIA & Fang LI department of mathematics, Ludong{2., Yantai 2.402., China department of mathematics, Zhejiang{2., hangzhou 31002., China 1. department of mathematics Ludong University Yantai 264025 China 2. department of mathematics Zhejiang University Hangzhou 310027 China

In this paper, we reveal that a weak entwining structure admits a rich cohomology theory. As an application we compute the cohomology of a weak entwining structure associated to a weak coalgebra-Galois extension.

关键词： weak entwining structure cohomology group 16W80 16W99

Sufficient and Necessary Conditions for Limit Laws on Lag Sums of I. I. D. R. V. S

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Acta Mathematica Sinica,English Series 1998年第1期14卷 113-124页

作者： Zhang Lixin department of mathematics,{2., hangzhou 31002., China

Let {X, Xn;n≥1} be a sequence of i.i.d.r.v.s with EX=0 and EX2.σ2.0n=sum from i=1 to n Xl We obtain some sufficient and necessary conditions for lim sup max max |SN-SN-j|/{2.2.（log N/k+log logk）}1/2.1 a,s to hol... 详细信息

Let {X, Xn;n≥1} be a sequence of i.i.d.r.v.s with EX=0 and EX2./sup>=σ2./sup>（0n=sum from i=1 to n Xl We obtain some sufficient and necessary conditions for lim sup max max |SN-SN-j|/{2.2./sup>k（log N/k+log logk）}1/2./sup>=1 a,s to hold, get the widest range of k’s and answer a question of Hanson and Russo（1983）.

关键词： Strong approximation Wiener process Lag sums of i.i.d.r.v.s Chernoff function

ON COMPLETE CONVERGENCE OF NONPARAMETRIC REGRESSION M-QUANTILES

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Systems Science and Mathematical Sciences 1992年第3期5卷 227-232页

作者： CAI Zongwu (department of mathematics,{2. university,{2. 31002.,China) 杭州大学浙江杭州

Consider the nonparametric regression model Y_i=m(x_i)+ε_i,i=1,…,n,where m(?)is an unknown function,and the design points x_i are knownand *** robust nonparametric estimators were introduced by H(?)rdleand Gasser in *** estimators can be viewed as regression *** then establish complete convergence for such quantiles under only the finitemoment condition.

关键词： Nonparametric kernel type estimator M-smoother quantile complete convergence

High-resolution dating of Co-rich crusts: A comparative study using the methods of orbital pacing and ^(2.0)Th_(ex)/^(2.2.Th dating

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Science China Earth Sciences 2009年第4期52卷 484-488页

作者： HAN XiQiu1,2. QIU ZhongYan1,2.3, MA WeiLin1,2.& QIAN JiangChu1,2.1 Key Laboratory of Submarine Geosciences, State Oceanic Administration, hangzhou 310012. China 2.Second Institute of Oceanography, State Oceanic Administration, hangzhou 310012. China 3{2. of Earth Sciences, Zhejiang university, hangzhou 31002., China Key Laboratory of Submarine Geosciences State Oceanic Administration Hangzhou 310012 China Second Institute of Oceanography State Oceanic Administration Hangzhou 310012 China department of Earth Sciences Zhejiang University Hangzhou

Due to their slow growth rates, seamount Co-rich crusts are very difficult to date with high resolution and precision. This paper is to test the use of orbital pacing on the growth profile of crusts to determine high-resolution age and growth rate. Crust CB14 from the central Pacific Ocean was selected for this study. We first examined the growth pattern in detail under a reflected-light microscope and ascertained that the growth environment was stable for the sub-layer 1 (0-3 mm). We then used electron micro-probe line-scanning to obtain elemental profiles. The pattern of the power spectrum analysis of the Al-profile revealed that there are significant cycles of 113.9, 87.8, 51.5, 42.2.and 2..8 μm. These cycles correspond to the Milankovitch cycles of 53.1, 41, 2., 19.7 and 12.ka, respectively, and yield the growth rate of about 2.14 mm/Ma and an age of about 1.40 Ma for the boundary between the sub-layer 1 and sub-layer 2. We also used a drilling machine with a numerically controlled drive to obtain high-resolution samples at 0.1mm intervals, and used the 2.0Thex/2.2.h method to date the samples. For the uppermost 1.3 mm, the growth rate was about 2.15 mm/Ma, and the age for the layer at the depth of 3 mm was about 1.40 Ma, which coincides perfectly with the results obtained from orbital pacing. Thus, it is considered that orbital pacing is a new and effective method to determine the growth rate of the seamount Co-rich crust. This method is applicable for establishing a high-resolution age frame for the crusts of the world's oceans.

关键词： seamount Co-rich crust Milankovitch cycles 2.0Thex/2.2.h dating growth rates of Mn-crusts central Pacific Ocean