中国科学院数学与系统科学研究院期刊网

15 April 1998, Volume 14 Issue 2
    

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  • You Jiangsheng
    Acta Mathematica Sinica. 1998, 14(2): 145-160. https://doi.org/10.1007/BF02560201
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    By the use of Moser iteration and Campanato space estimate, the L and Cα regularity estimate of the gradient of solutions of nonlinear parabolic system ∂ui/∂t-▽·(g|▽u|▽ui)=0 with nonstandard growth conditions are obtained under the natural structure constraints.
  • Fang Ainong
    Acta Mathematica Sinica. 1998, 14(2): 161-168. https://doi.org/10.1007/BF02560202
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    In this paper, a distortion theorem and some equicontinuity and compactness theorems are obtained for the homeomorphism f with the sphere dilatation H(x,f)Lloc(D).
  • Xiong Hongyun, Rong Ximin
    Acta Mathematica Sinica. 1998, 14(2): 169-174. https://doi.org/10.1007/BF02560203
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    Let {Ei:i∈I} be a family of Archimedean Riesz spaces. The Riesz product space is denoted by ∏i∈I Ei. The main result in this paper is the following conclusion: There exists a completely regular Hausdorff space X such that ∏i∈I Ei is Riesz isomorphic to C(X) if and only if for everyemI there exists a completely regular Hausdorff space Xi such that Ei is Riesz isomorphic to C(Xi).
  • Todd Cochrane, Zheng Zhiyong
    Acta Mathematica Sinica. 1998, 14(2): 175-182. https://doi.org/10.1007/BF02560204
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    For any integers a1,a2,a3,a4 and c with a1a2a3a40(modp), this paper shows that there exists a solution X=(x1,x2,x3,x4)∈Z4 of the congruence a1x12+a2x22+a3x32+a4x42c(modp) such that
  • Gao Hongjun, Guo Boling
    Acta Mathematica Sinica. 1998, 14(2): 183-190. https://doi.org/10.1007/BF02560205
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    A nonlinear hinged extensible elastic body equation with strong structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures of higher dimensions. In this paper, the absorbing sets and flat inertial manifold are obtained for this nonlinear body equation. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite dimensional feedback, control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to the uncertainty in structural parameters.
  • Wang Qihua
    Acta Mathematica Sinica. 1998, 14(2): 191-200. https://doi.org/10.1007/BF02560206
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    In this paper, a class of functionals of Kaplan-Meier estimator is investigated. Counting process martingale methods are used to show the asymptotic normality, and we establish a mean square error inequality and a probability inequality of them without the assumption that F, G are continuous, where,F, G are survival time distribution and censoring time distribution respectively.
  • Cao Guangfu, N. Elias, P. Ghatage, Yu Dahai
    Acta Mathematica Sinica. 1998, 14(2): 201-208. https://doi.org/10.1007/BF02560207
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    In this paper, we study composition operators on a Banach space of analytic functions, denoted by X, which includes the Bloch space. This space arises naturally as the dual space of analytic functions in the Bergman space Lα1(D) which admit an atomic decomposition. We characterize the functions which induce compact composition operators and those which induce Fredholm operatorson this space. We also investigate when a composition operator has a closed range.
  • Shi Shuzhong, Wang Bingwu
    Acta Mathematica Sinica. 1998, 14(2): 209-222. https://doi.org/10.1007/BF02560208
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    The differentiability of a norm of a Banach space may be characterized by its unit sphere. This paper generalizes these geometric conditions of norm's differentiability to the case of a regular locally Lipschitz function.
  • Claus Bauer
    Acta Mathematica Sinica. 1998, 14(2): 223-234. https://doi.org/10.1007/BF02560209
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    Let E(X)=|{NX;Np12+p23+p34+p45 for any primespi}|. It is proved in this paper that there exists a positive constant δ>0 such that which improves a result of prachar.
  • Fan Dashan, Lu Shanzhen, Pan Yibiao
    Acta Mathematica Sinica. 1998, 14(2): 235-244. https://doi.org/10.1007/BF02560210
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    Suppose that {αk}k=-∞ is a Lacunary sequance of positive numbers satisfying inf and that Ω(y') is a function in the Besov space B10,1 (Sn-1) where Sn-1 is the unit sphere on Rn(n≥2). We prove that if ∫Sn-1Ω(y')dσ(y') then the discrete singular integral operator

    and the associated maximal operator

    are both bounded in the space L2(Rn)

    The theorems in this paper improve a result by Duoandikoetxea and Rubio de Francia[1] in the L2 case.

  • Guo Zongming, Yang Zuodong
    Acta Mathematica Sinica. 1998, 14(2): 245-260. https://doi.org/10.1007/BF02560211
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    Existence and uniqueness results are obtained for positive radial solutions of a class of quasilinear elliptic equations in aN-ball or an annulus without monotone assumptions on the nonlinear term f. It is also proved that there is no non-radial positive solution.
  • Chen Hua, Brian D. Sleeman
    Acta Mathematica Sinica. 1998, 14(2): 261-276. https://doi.org/10.1007/BF02560212
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    In this paper, we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture. We prove, for some special connected fractal domains, the sharp estimate for second term of counting function asymptotics, which implies that the weak form of the Weyl-Berry conjecture holds for the case. Finally, we also study a naturally connected fractal domain, and we prove, in this case, the weak Weyl-Berry conjecture holds as well.
  • Luo Libo
    Acta Mathematica Sinica. 1998, 14(2): 277-284. https://doi.org/10.1007/BF02560213
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    We confirm the Vaught's conjecture and obtain a complete classification for the theories of unitary relations.
  • Li Haizhong, Chen Weihuan
    Acta Mathematica Sinica. 1998, 14(2): 285-288. https://doi.org/10.1007/BF02560214
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    We establish integral formulas of Minkowski's type for compact spacelike hypersurfaces in de sitter space S1n+1 (1) and give their applications to the case of constant r-th mean curvature (r=1,2,…,n-1). When r=1 we recover Montiel's result.