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Approximation of functions on the Sobolev space with a Gaussian measure

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Science china Mathematics 2010年第2期53卷 373-384页

作者： WANG HePing 1, ZHANG YanWei 2.& ZHAI XueBo 1 1 school of mathematical {2., capital normal university, Beijing 100048, china 2.Department of Mathematics, Zaozhuang university, Zaozhuang 2.7160, china 1. school of mathematical {2. Capital Normal University Beijing 100048 China2. Department of Mathematics Zaozhuang University Zaozhuang 277160 China

We discuss the best approximation of periodic functions by trigonometric polynomials and the approximation by Fourier partial summation operators, Valle-Poussin operators, Ces`aro operators, Abel opera-tors, and Jackson operators, respectively, on the Sobolev space with a Gaussian measure and obtain the average error estimations. We show that, in the average case setting, the trigonometric polynomial subspaces are the asymptotically optimal subspaces in the L q space for 1≤q < ∞, and the Fourier partial summation operators and the Valle-Poussin operators are the asymptotically optimal linear operators and are as good as optimal nonlinear operators in the L q space for 1≤q < ∞.

关键词： average width best approximation approximation by linear operators Sobolev space Gaussian measure

On the number of B_(π')-characters in a nilpotent π-block

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Science china Mathematics 2008年第1期51卷 1-4页

作者： HAI JinKe~(1+) & ZHU YiXin~2.1 school of mathematical {2., Qingdao university, Qingdao 2.6071, china 2.school of mathematical sciences, capital normal university, Beijing 100037, china school of mathematical {2. Qingdao University Qingdao 266071 China school of mathematical {2. Capital Normal University Beijing 100037 China

Brouéand Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to theπ-block theory of aπ-separable group, defines the nilpotency of aπ-block, and proves that there is a unique B_(π')-character in a nilpotentπ-block.

关键词： π-separable groups π-blocks π-subpairs nilpotentπ-blocks

Efficient estimation for additive hazards regression with bivariate current status data

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Science china Mathematics 2012年第4期55卷 763-774页

作者： TONG XingWei 1,,HU Tao 2.& SUN JianGuo 3,4 1 school of mathematical {2.,Beijing normal university,Beijing 100875,china 2.school of mathematical sciences,capital normal university,Beijing 100048,china 3 school of Mathematics,Jilin university,Changchun 130012.china 4 Department of Statistics,university of Missouri,Columbia,MO 652.1,USA 1. school of mathematical {2. Beijing Normal University Beijing 100875 China2. School of Mathematical Sciences Capital Normal University Beijing 100048 China3. School of Mathematics Jilin University Changchun 130012 China4. Department of Statistics University of Missouri Columbia MO 65211 USA

This paper discusses efficient estimation for the additive hazards regression model when only bivariate current status data are available. Current status data occur in many fields including demographical studies and tumorigenicity experiments （Keiding, 1991; Sun, 2.06） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2.02.. For bivariate data, in addition to facing the same problems as those with univariate data, one needs to deal with the association or correlation between two related failure time variables of interest. For this, we employ the copula model and an efficient estimation procedure is developed for inference. Simulation studies are performed to evaluate the proposed estimates and suggest that the approach works well in practical situations. An illustrative example is provided.

关键词： bivariate current status data copula model counting processes efficient estimation joint survivalfunction

On several families of elliptic curves with arbitrary large Selmer groups

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Science china Mathematics 2010年第9期53卷 2329-2340页

作者： LI Fei & QIU DeRong school of mathematical {2.,Institute of Mathematics and Interdisciplinary Science,capital normal university,Beijing 100048,china 1. school of mathematical {2. Institute of Mathematics and Interdisciplinary Science Capital Normal University Beijing 100048 China

In this paper,we calculate the ()-Selmer groups S()(E/Q) and S()(E/Q) of elliptic curves y2.= x(x + εpD)(x + εqD) via the descent *** particular,we show that the Selmer groups of several families of such ell... 详细信息

关键词： elliptic curve Selmer group Mordell-Weil group

Coexistence of unbounded solutions and periodic solutions of Liénard equations with asymmetric nonlinearities at resonance

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Science china Mathematics 2007年第8期50卷 1205-1216页

作者： Zai-hong WANG school of mathematical {2.,capital normal university,Beijing 100037,china 1. school of mathematical {2. Capital Normal University Beijing 100037 China

In this paper, we deal with the existence of unbounded orbits of the mapping $$\left\{ \begin{gathered} \theta _1 = \theta + 2.\pi + \frac{1}{\rho }\mu (\theta ) + o(\rho ^{ - 1} ), \hfill \\ \rho _1 = \rho + c - \mu ... 详细信息

In this paper, we deal with the existence of unbounded orbits of the mapping $$\left\{ \begin{gathered} \theta _1 = \theta + 2.\pi + \frac2.{\rho }\mu (\theta ) + o(\rho ^{ - 1} ), \hfill \\ \rho _1 = \rho + c - \mu '(\theta ) + o(1), \rho \to \infty \hfill \\ \end{gathered} \right.$$ , where n is a positive integer, c is a constant and μ(θ) is a 2.-periodic function. We prove that if c > 0 and μ(θ) ≠ 0, θ, ∈ [0, 2.], then every orbit of the given mapping goes to infinity in the future for ρ large enough; if c 2.], then every orbit of the given mapping goes to infinity in the past for ρ large enough. By using this result, we prove that the equation x″+f(x)x′+ax +?bx ?+?(x)=p(t) has unbounded solutions provided that a, b satisfy $1/\sqrt a + 1/\sqrt b = 2.n$ and ?(x) satisfies some limit conditions. At the same time, we obtain the existence of 2.-periodic solutions of this equation.

关键词： Liénard equations unbounded solutions periodic solutions 34C11 34C2.

Local 3-cocycles of von Neumann algebras

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Science china Mathematics 2007年第9期50卷 1240-1250页

作者： Cheng-jun HOU~(1+) Ben-yin FU~2.1 school of mathematical {2.,Qufu normal university,Qufu 2.3165,china 2.school of mathematical sciences,Fudan university,Shanghai 2.0433,china 1. school of mathematical {2. Qufu Normal University Qufu 273165 China 2. school of mathematical {2. Fudan University Shanghai 200433 China

We show that every local 3-cocycle of a von Neumann algebra $\mathcal{R}$ into an arbitrary unital dual $\mathcal{R}$ -bimodule $\mathcal{S}$ is a 3-cocycle.

关键词： von Neumann algebra dual bimodule local 3-cocycle 3-cocycle 46L10

Hereditary C~*-subalgebras and comparison of positive elements

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Science china Mathematics 2010年第6期53卷 1565-1570页

作者： WEI ChangGuo1,& WANG LiGuang2.1school of mathematical {2.,Ocean university of china,Qingdao 2.6071,china 2.0} of mathematical {2.,Qufu normal university,Qufu 2.3165,china 1. school of mathematical {2. Ocean University of China Qingdao 266071 China2. School of Mathematical Sciences Qufu Normal University Qufu 273165 China

Characterizations of hereditary subalgebras generated by subsets of a C*-algebra are given through open *** these results,we give some equivalent conditions of comparison of positive elements.

关键词： hereditary subalgebra open projection positive element

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, Hangzhou normal university, Hangzhou 310036, {2. 2. Department of Applied Mathematics, school of mathematical sciences, South {2. university of Technology, Guangzhou 510640, {2.) 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.

Split-plot designs with general minimum lower-order confounding

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Science china Mathematics 2010年第4期53卷 939-952页

作者： WEI JiaLin 1,4,YANG JianFeng 1,LI Peng 3 & ZHANG RunChu 1,2.1 school of mathematical {2. and LPMC,Nankai university,Tianjin 300071,china 2.KLAS and school of Mathematics and Statistics,Northeast normal university,Changchun 13002.,china 3 school of mathematical {2.,{12.,Beijing 100037,china 4 school of {2.,Tianjin university of Commerce,Tianjin 300134,china 1. school of mathematical {2. and LPMC Nankai University Tianjin 300071 China4. School of Sciences Tianjin University of Commerce Tianjin 300134 China3. School of Mathematical Sciences Capital Normal University Beijing 100037 China2. KLAS and School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

Split-plot designs have been widely used in industrial *** to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) ***,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et *** a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) *** is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal *** this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot *** comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32.run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

关键词： fractional factorial design GMC criterion minimum aberration split-plot