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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 sciences,Institute of Mathematics and Interdisciplinary Science,capital normal university,beijing 100048,china 1. school of mathematical sciences 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 sciences,capital normal university,beijing 100037,china 1. school of mathematical sciences Capital Normal University Beijing 100037 China

In this paper, we deal with the existence of unbounded orbits of the mapping $$\left\{ \begin{gathered} \theta _1 = \theta + 2n\pi + \frac{1}{\rho }\mu (\theta ) + o(\rho ^{ - 1} ), \hfill \\ \rho _1 = \rho + c - \mu '(\theta ) + o(1), \rho \to \infty \hfill \\ \end{gathered} \right.$$ , where n is a positive integer, c is a constant and μ(θ) is a 2π-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 2π], 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 2π-periodic solutions of this equation.

关键词： Liénard equations unbounded solutions periodic solutions 34C11 34C25

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 sciences,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 65211,USA 1. school of mathematical sciences 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, 2006） and several approaches have been proposed for the additive hazards model with univariate current status data （Linet M., 1998; Martinussen and Scheike, 2002）. 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

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 sciences, capital normal university, beijing 100048, china 2 Department of Mathematics, Zaozhuang university, Zaozhuang 277160, china 1. school of mathematical sciences 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 sciences, Qingdao university, Qingdao 266071, china 2.school of mathematical sciences, capital normal university, beijing 100037, china school of mathematical sciences Qingdao University Qingdao 266071 China school of mathematical sciences 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

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 sciences,beijing normal university,beijing 100875,china 1. school of mathematical sciences Beijing Normal University Beijing 100875 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

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 sciences, beijing normal university, beijing 100875, china 1. school of mathematical sciences Beijing Normal University Beijing 100875 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 42B20 35S05 47G30

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 sciences, beijing normal university, beijing 100875, china 1. school of mathematical sciences Beijing Normal University Beijing 100875 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

On the weak convergence of super-Brownian motion with immigration

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Science china Mathematics 2009年第9期52卷 1875-1886页

作者： ZHANG Mei school of mathematical sciences, beijing normal university, beijing 100875, china school of mathematical sciences Beijing Normal University Beijing 100875 China

We prove fluctuation limit theorems for the occupation times of super-Brownian motion with immigration. The weak convergence of the processes is established, which improves the results in references. The limiting proc... 详细信息

关键词： super-Brownian motion with immigration occupation time process central limit theorem tightness 60J80 60F05