中国科学院数学与系统科学研究院期刊网

15 February 2009, Volume 25 Issue 2
    

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  • Zhe Feng XU
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    Let $q>4$ be an integer. The main purpose of this paper is to study the mean value of Cochrane sum $C(a,q)$ in quarter intervals, and obtain a sharp asymptotic formula for it.
  • Yan Nan LIRui Feng QIUMing Xing ZHANG
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    Let $M$ be a simple manifold, and $F$ be a component of $\partial M$ of genus two. For a slope $\gamma$ on $F$, we denote by $M(\gamma)$ the manifold obtained by attaching a 2-handle to $M$ along a regular neighborhood of $\gamma$ on $F$. In this paper, we shall prove that there is at most one separating slope $\gamma$ on $F$ such that $M(\gamma)$ is $\partial$-reducible.
  • Sh. A. AYUPOVB, A. OMIRO, VKh. KHUDOYBERDIYEV
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    In this work the classification of filiform Leibniz superalgebras of nilindex $n+m,$ where $n$ and $m$ ($m \ne 0$) are dimensions of even and odd parts, respectively, is obtained.
  • Ke Ang FULi Xin ZHANG
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    Let $\{X,X_n;n\geq1\}$ be a sequence of i.i.d. random variables taking values in a real separable Hilbert space $(\textbf{H},\|\cdot\|)$ with covariance operator $\Sigma.$ Set $S_n=X_1+X_2+\cdots+X_n,$ $n\geq1.$ We prove that, for $b>-1$, \begin{eqnarray*} \lim\limits_{\varepsilon\searrow0}\varepsilon^{2(b+1)}\sum\limits_{n=1}^\infty\frac{(\log n)^b}{n^{3/2}}{\textsf{\rm E}}\{\|S_n\|-\sigma\varepsilon\sqrt{n\log n}\}_+=\frac{\sigma^{-2(b+1)}}{(2b+3)(b+1)}{\textsf{\rm E}}\|Y\|^{2b+3} \end{eqnarray*} holds if ${\textsf{\rm E}} X=0,$ and ${\textsf{\rm E}} \|X\|^2(\log\|X\|)^{3b \vee (b+4)}<\infty,$ where $Y$ is a Gaussian random variable taking value in a real separable Hilbert space with mean zero and covariance operator $\Sigma$, and $\sigma^2$ denotes the largest eigenvalue of $\Sigma$.
  • Tao YUShi Yue WU
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    In this paper we characterize commuting dual Toeplitz operators with harmonic symbols on the orthogonal complement of the Dirichlet space in the Sobolev space. We also obtain the sufficient and necessary conditions for the product of two dual Toeplitz operators with harmonic symbols to be a finite rank perturbation of a dual Toeplitz operator.
  • Qiang Chang JU
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    Semiclassical limit to the solution of isentropic quantum drift-diffusion model in semiconductor simulation is discussed. It is proved that the semiclassical limit of this solution satisfies the classical drift-diffusion model. In addition, we also proved the global existence of weak solutions.
  • Gen Sun FANGLi Qin DUAN
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    Temlyakov considered the optimal recovery on the classes of functions with bounded mixed derivative in the $L_p$ metrics and gave the upper estimates of the optimal recovery errors. In this paper, we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information, i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of the optimal recovery.
  • Deng Feng LIWen Chang SUN
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    We show that every Bessel sequence (and therefore every frame) in a separable Hilbert space can be expanded to a tight frame by adding some elements. The proof is based on a recent generalization of the frame concept, the $g$-frame, which illustrates that $g$-frames could be useful in the study of frame theory. As an application, we prove that any Gabor frame can be expanded to a tight frame by adding one window function.
  • Min Zhu ZHANGHuai Hui Chen
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    In this paper we characterize the boundedness and compactness of weighted composition operators of $H^{{\infty}}$ into ${\alpha}$-Bloch spaces on the unit ball in $\mathbb C^n$.
  • Yi Sheng SONG
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    The purpose of this paper is to study the following implicit iteration scheme recently introduced by Xu and Ori [{\it Numer. Funct. Anal. Optim.}, {\bf 22}, (2001) 767--773]: $$ x_{n} = \alpha_{n}x_{n-1}+(1-\alpha_{n})T_{n}x_{n},~~~n\geq 1, $$ and to prove several strongly and weakly convergent theorems of the iteration for a finite family of pseudocontractive mappings under condition $\alpha_n\in(0,b]\subset(0,1)$.
  • Tian Ze WANG
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    A necessary and sufficient solvable condition for diagonal quadratic equation with prime variables in arithmetic progressions is given, and the best qualitative bound for small solutions of the equation is obtained.
  • Fu Qi, YINSheng Fa, n ZHOUZi Gen OUYA, NGCui Hui XIAO
    Acta Mathematica Sinica. 2009, 25(2): 0-0.
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    We consider the asymptotic behavior of solutions of a lattice dynamical system of dissipative Zakharov equation. By introducing a new weight inner product and norm in the space and establishing uniform estimate on `` Tail Ends" of solutions, we successfully overcome some difficulties raised by the lack of Sobolev compact embedding in the case of unbounded domains, and prove the existence of the global attractor; then by using element decomposition and the covering property of a polyhedron in the finite-dimensional space, we obtain the upper bound for the Kolmogorov $\epsilon$-entropy of the global attractor; finally, we consider the upper semicontinuity of the global attractor.