中国科学院数学与系统科学研究院期刊网

1992年, 第5卷, 第3期 刊出日期:1992-08-15

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  • LI Shujie
    Journal of Systems Science and Complexity. 1992, 5(3): 193-204.
    摘要 ( 1564 ) PDF全文 ( 661 )   可视化   收藏
    In references, some authors have succeeded in obtaining existence results of the superlinear wave equation without the assumption of monotonicity for the nonlinear term. In this paper, we present existence results for this problem byusing local linking idea and improve some previous results.
  • YANG Xuefeng
    Journal of Systems Science and Complexity. 1992, 5(3): 205-212.
    摘要 ( 1550 ) PDF全文 ( 650 )   可视化   收藏
    In this paper,we study the existence and regularity of G-equivariant harmonic maps between surfaces with a finite group G\subset O(3)action. We discoverthat the energy level of compactness in the G-equivariant perturbed problems is higher than that in general case. This implies the multiplicity of harmonic mapsfor some examples.
  • GAO Aijun;CHEN Hanfu(H.F.Chen)
    Journal of Systems Science and Complexity. 1992, 5(3): 213-226.
    摘要 ( 1585 ) PDF全文 ( 569 )   可视化   收藏
    A multidimensional adaptive stochastic approximation procedure truncated at randomly varying bounds is studied for the regression function observed with correlated noise. The algorithm is proved to be asymptotically efficient. The result of the paper generalizes the one shown in[1] for the observation noise being i.i.d. random vectors and under other restrictive conditions imposed on the regression function.
  • CAI Zongwu
    Journal of Systems Science and Complexity. 1992, 5(3): 227-232.
    摘要 ( 1452 ) PDF全文 ( 571 )   可视化   收藏
    Consider the nonparametric regression model Y_i=m(x_i)+ε_i,i=1,…,n,where m(.) is an unknown function, and the design points x_i are knownand nonrandom. The robust nonparametric estimators were introduced by Hardleand Gasser in 1984. These estimators can be viewed as regression M-quantiles. We then establish complete convergence for such quantiles under only the finite moment condition.
  • LI Ronglu;CHARLES Swartz;CHO Minhyung
    Journal of Systems Science and Complexity. 1992, 5(3): 233-238.
    摘要 ( 1541 ) PDF全文 ( 806 )   可视化   收藏
    Every complete metric linear space is a K-space. A non-complete normed space can be a K-space. And non-metrizable K-spaces exist. A series of basic results on complete metric linear spaces Can be generalized to K-spaces. Forexample, every bounded linear operator from a K-space into a locally convex spaceis sequentially continuous; every bounded semi-norm on a K-space is sequentially continuous and, therefore, piecewise separable; a. C-sequeatial K-space is both barrelled and bornological; the family of sequentially continuous linear functionals ona K-space is weak sequentially complete.
  • ZHENG Zhongguo
    Journal of Systems Science and Complexity. 1992, 5(3): 239-250.
    摘要 ( 1496 ) PDF全文 ( 594 )   可视化   收藏
    Let (Y,X) be a random vector with its value in R~1×R~d,d\le 1. Let \Theta be the collection of real valued functions θ(x) on R~d which is p times differ-entiable at x=0 and p-1 times differentiable on an open neighborhood U of the origin of R~d. The conditional distribution of Y is assumed to be of the form of f(y|x,θ(x))dy where θ(x)∈\Theta is called the parameter of the family. (Y,X) is called a nonparametric median model if furthermore the conditional median of Y given X=x is θ(x). In this paper, the optimal rate of convergence for estimators of T(θ)=θ(0)is discussed. Under certain conditions, it is proved that for the nonparametric median model the optimal rate of convergence is r=p/(2p+d). A sequence of estimators, which is asymptotically normal with the optimal rate of covergence, is constructed.
  • JIN Mingzhong;CHEN Xiru
    Journal of Systems Science and Complexity. 1992, 5(3): 251-259.
    摘要 ( 1614 ) PDF全文 ( 964 )   可视化   收藏
    Consider the linear regression model Y_i=x_i′β+σ_ie_i,i=1,…,n,…, where E(e_i)=0, E(e_ie_j)=δ_(ij), 0<σ_1~2\le σ_2~2\le … and {x_i} satisfies A_1\le sum from i=1 to n x_ix_i′/n\le A_2, for n large, A_1>0,A_2>0. This paper shows that (i) if σ_i~2,i=1,2…, are known, then the necessary and sufficient condition for the consistency of the best unbiased linear estimate of β is sum from i=1 to ∞ σ_i~(-2)=∞;(ii) if {σ_i~2} is only known to belong to the set {(h_1,h_2,…)∶ 0
  • GAO Xiaoshan
    Journal of Systems Science and Complexity. 1992, 5(3): 260-273.
    摘要 ( 1876 ) PDF全文 ( 768 )   可视化   收藏
    A theorem of transformation between two geometries is proved on the basis of Wu's method of mechanical theorem proving. By using this theorem for Cayley-Klein geometries of dimension two, we prove that the nine Cayley-Klein geometries can be divided into three groups within which the geometries are mutually equivalent in the sense that certain geometry statements are correct inone geometry if and only if they are correct in the other geometries of the same group. This means that for each group we only need to choose a model geometry to study and the theorems of other geometries in the same group can be obtained from the model geometry automatically. The three model geometries chosen forthe nine Cayley-Klein geometries are: Euclidean geometry, Riemann geometry, and Galilean geometry.
  • ZHANG Jian
    Journal of Systems Science and Complexity. 1992, 5(3): 274-286.
    摘要 ( 1516 ) PDF全文 ( 568 )   可视化   收藏
    Let X_1,X_2,… be a sequence of independent random vectors which take values in IR~2 and X_i~P. By the projection pursuit (PP) method, we canconstruct PP type Kolmogrov-Smirnov statistics: K_n=\sup_{\|a\|=1,z\in R}\sup_{|t<+\infty|}1/\sqre{n} | \sum_{i=1}^{n} (I_[a~rX_i\leq t]-P(a~rX_j\leq t))|, where I_[·] is the indicator function of the set [·] and P is a probability distribution. The limit distribution of K_n is the distribution for the suprema of a P-bridgewhose index is the set of all half spaces in IR~2. Let{W_p([0,Extra close brace or missing open brace])∶Extra close brace or missing open brace∈[0,1]~2} be a two parameter Brownish bridge. The main result of this paper is P(?)for all λ, provided P is the uniform distribution on [0,k_1]×[0,k_2], 0
  • LIN Qun;ZHOU Aihui
    Journal of Systems Science and Complexity. 1992, 5(3): 287-288.
    摘要 ( 1455 ) PDF全文 ( 478 )   可视化   收藏
    A defect correction scheme of fourth order accuracy for linear finiteelement gradient is proposed in this note.This extends the Rannacher's scheme forfinite element solution to gradient and can compete with superconvergence fromquadratic elements.