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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 school of mathematical {2. Capital Normal University Beijing 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.

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 {2., capital normal university, beijing 100037, China school of mathematical {2. Qingdao University Qingdao China school of mathematical {2. Capital Normal University Beijing 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

The localization of 1-cohomology of transitive Lie algebroids

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Science China Mathematics 2006年第2期49卷 277-288页

作者： CHEN Zhuo & LIU Zhangju Department of Mathematics, capital normal university, beijing 100037, China {2. of mathematical Science, Peking university, beijing 100871, China Department of Mathematics Capital Normal University Beijing China school of mathematical Science Peking University Beijing China

For a transitive Lie algebroid A on a connected manifold M and its representation on a vector bundle F, we define a morphism of cohomology groups rk: Hk(A,F) → Hk(Lx,Fx), called the localization map, where Lx is the adjoint algebra at x ∈ M. The main result in this paper is that if M is simply connected, or H (LX,FX) is trivial, then T is injective. This means that the Lie algebroid 1-cohomology is totally determined by the 1-cohomology of its adjoint Lie algebra in the above two cases.

关键词： transitive Lie algebroid representation cohomology localization.

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 {2.,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 school of mathematical {2. Beijing Normal University Beijing China school of mathematical {2. Capital Normal University Beijing China school of Mathematics Jilin University Changchun China Department of Statistics University of Missouri Columbia 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

Sieve M-estimation for semiparametric varying-coefficient partially linear regression model

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Science China Mathematics 2010年第8期53卷 1995-2010页

作者： HU Tao 1,2.& CUI HengJian 1,2.1 school of mathematical {2.,beijing normal university,Laboratory of Mathematics and Complex Systems,Ministry of Education,beijing 100875,China 2.school of mathematical {2.,capital normal university,beijing 100048,China school of mathematical {2. Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education school of mathematical {2. Capital Normal University

This article considers a semiparametric varying-coefficient partially linear regression *** semiparametric varying-coefficient partially linear regression model which is a generalization of the partially linear regression model and varying-coefficient regression model that allows one to explore the possibly nonlinear effect of a certain covariate on the response variable.A sieve M-estimation method is proposed and the asymptotic properties of the proposed estimators are *** main object is to estimate the nonparametric component and the unknown parameters *** is easier to compute and the required computation burden is much less than the existing two-stage estimation ***,the sieve M-estimation is robust in the presence of outliers if we choose appropriate ρ(·).Under some mild conditions,the estimators are shown to be strongly consistent;the convergence rate of the estimator for the unknown nonparametric component is obtained and the estimator for the unknown parameter is shown to be asymptotically normally *** experiments are carried out to investigate the performance of the proposed method.

关键词： partly linear model varying-coefficient robustness optimal convergence rate asymptotic normality

RESEARCH　ANNOUNCEMENTS　The　Comparison　Theorem　for　the　Bergman　and　Kobayashi　Metrics　on　a　Class　of　Pseudoconvex　Domains

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数学进展 1996年第3期 277-278页

作者： Yin Weiping(mathematical sciences Research Institute, {2., beijing, 100037)

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＴｈｅＣｏｍｐａｒｉｓｏｎＴｈｅｏｒｅｍｆｏｒｔｈｅＢｅｒｇｍａｎａｎｄＫｏｂａｙａｓｈｉＭｅｔｒｉｃｓｏｎａＣｌａｓｓｏｆＰｓｅｕｄｏｃｏｎｖｅｘＤｏｍａｉｎｓ￥ＹｉｎＷｅ... 详细信息

ＲＥＳＥＡＲＣＨＡＮＮＯＵＮＣＥＭＥＮＴＳＴｈｅＣｏｍｐａｒｉｓｏｎＴｈｅｏｒｅｍｆｏｒｔｈｅＢｅｒｇｍａｎａｎｄＫｏｂａｙａｓｈｉＭｅｔｒｉｃｓｏｎａＣｌａｓｓｏｆＰｓｅｕｄｏｃｏｎｖｅｘＤｏｍａｉｎｓ￥ＹｉｎＷｅｉｐｉｎｇ（Ｍａｔｈｅｍａｔｉｃａ...

关键词： Theorem the Bergman ANNOUNCEMENTS Comparison

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 sciences,capital normal university,beijing 100037,China 4 school of {2.,Tianjin university of Commerce,Tianjin 300134,China school of mathematical {2. and LPMC Nankai University school of sciences Tianjin University of Commerce school of mathematical {2. Capital Normal University

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

Commutators of pseudo-differential operators

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Science China Mathematics 2008年第3期51卷 453-460页

作者： LIN Yan school of mathematical {2., beijing normal university, beijing 100875, China school of mathematical {2. Beijing Normal University Beijing China

In this paper, the boundedness of commutators generated by pseudo-differential operators and BMO functions is discussed on Lebesgue spaces.

关键词： pseudo-differential operator BMO function commutator Lebesgue space 42.2. 35S05 47G30

Some scaled limit theorems for an immigration super-Brownian motion

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Science China Mathematics 2008年第2期51卷 203-214页

作者： ZHANG Mei school of mathematical {2.,beijing normal university,beijing 100875,China school of mathematical {2. Beijing Normal University Beijing China

In this paper,the small time limit behaviors for an immigration super-Brownian motion are studied,where the immigration is determined by Lebesgue *** first prove a functional central limit theorem,and then study the l... 详细信息

关键词： super-Brownian motion with immigration functional central limit theorem large deviation moderate deviation 60J80 60F05

Infinitely many radial solutions to elliptic prob-lems with critical Sobolev and Hardy terms

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Science China Mathematics 2008年第9期51卷 1609-1618页

作者： TANG ZhongWei school of mathematical {2., beijing normal university, beijing 100875, China school of mathematical {2. Beijing Normal University Beijing China

Let Ω ? ? N be a ball centered at the origin with radius R > 0 and N ? 7, 2* = $ \frac{{2N}} {{N - 2}} $ . We obtain the existence of infinitely many radial solutions for the Dirichlet problem ?Δu = $ \frac{\mu } {{|x|^2 }}u + |u|^{2^* - 2} u + \lambda u $ in Ω, u = 0 on ?Ω for suitable positive numbers μ and λ. Such solutions are characterized by the number of their nodes.

关键词： nodal solutions compactness critical Sobolev and Hardy terms 35J60 35B33