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26 June 1997, Volume 17 Issue 3 Previous Issue    Next Issue

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Strong Approximations for A Smooth Conditional Quantile Process and Its Applications Zhou Yong Acta mathematica scientia,Series A. 1997, 17 (3):  245-254.  Abstract ( 66 )   RICH HTML PDF (560KB) ( 74 )   Save Under some weak conditions,the strong approximations for smooth conditional quantile processes are proved. The wenk convergence and strong uniform convergence of this quantile process are derived by the strong approximations. Related Articles | Metrics

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A General Solution for Trinomial Linear Recurrence with two Indices Yu Changan Acta mathematica scientia,Series A. 1997, 17 (3):  255-260.  Abstract ( 58 )   RICH HTML PDF (319KB) ( 68 )   Save In this paper we consider the following trinomial linear recurrence with two indicis#br#ui,j=f(i,j)ui,j-p+ g(i,j)ui-1,j-p + h(i,j), u1,s=cs(s=1,2,..,p),ui,j=0 (i<1 or j < 1 or j ≤ q(i-1)),#br#where i,j=l, 2,...;p,q ≥ 1;f(i,j),g(i,j) and h(i,j) are variable numbers; c,(s=1, 2,.., p) are constant numbers. Its general solution is given by the formula#br#ui,j={ F(i,j;i-1, θ1, 1) } C(j-q(i-1)-pθ1)+∑l=1i{∑ml=1θl=1{F(i,j;i-l,θl+1-ml,l)}h(l,j-q(i-l)-p(θl+1-ml))}(i,j=1,2...),where θl=[(j-1-q(i-l)/p)(1 ≤ l ≤i). Related Articles | Metrics

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A Representation of Capacity by First Touching Time of m-tight Process on General Topological State Space Dong Zhao Acta mathematica scientia,Series A. 1997, 17 (3):  261-266.  Abstract ( 61 )   RICH HTML PDF (382KB) ( 154 )   Save We prove that the capacity deduced by first-touching time of m-tight process on general topological state space can be expressed throught this first touching time. With this result, we prove several equivalent statements about quasi-continuous functions. Related Articles | Metrics

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On Singular Matrix Liouville Singular Matrix Beta and Singular Matrix Dirichlet Distributions Wang Feixing Acta mathematica scientia,Series A. 1997, 17 (3):  267-273.  Abstract ( 87 )   RICH HTML PDF (385KB) ( 145 )   Save In this paper, we introduce and study the singular matrix Liouville distribution,from which we obtain the singular matrix Beta and the singular matrix Dirichlet distribution,and extend the results of the singular Wishart and the rank-1 singular matrix Betadistributions in[1]. Related Articles | Metrics

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On the Hereditarily Indecomposable and Quotient-Hereditarily Incompound Properties of Banach Spaces Zhong Huaijie Acta mathematica scientia,Series A. 1997, 17 (3):  274-279.  Abstract ( 59 )   RICH HTML PDF (423KB) ( 104 )   Save In this paper, it is shown that the class of Riesz operators on the hereditarily indecomposable space X is the greatest notrivial operator ideal in B(X). The proof about the structure of operators in B(X) by Gowers W. T. and Maurey B. is also simplified. The concept of Quotient-Hereditarily Incompound spaces is introdused by using of the principle of duality. The corresponding results about operators on the Q. H. IC. space are obtained. Related Articles | Metrics

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CHARACTERIZATIONS OF THE PROPERTY (C-K) Wang Jianhua, Zhang Zhihou Acta mathematica scientia,Series A. 1997, 17 (3):  280-284.  Abstract ( 46 )   RICH HTML PDF (323KB) ( 21 )   Save In the theory of the best approximations the properties (C-K),K=Ⅰ,Ⅱ, Ⅲ play a very significant role (see[1]). The purpose of this paper is to give their interesting characterizations. Further we obtain that if a Banach space X has the property (C-Ⅲ) (resp.(C-Ⅱ)) then for any norming set A of X, the σ(X, A) topology and the weak topology (resp.norm topology) coincide on the unit sphere of X and X is nearly very rotund (resp. nealy strongly rotund). Related Articles | Metrics

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The Direct and Inverse Theorems for Multidimensional Bernstein-Kantorovich Operators in C(S) Li Song Acta mathematica scientia,Series A. 1997, 17 (3):  285-293.  Abstract ( 46 )   RICH HTML PDF (440KB) ( 21 )   Save In this paper, a integral estimation and inverse theorem of weak type in continuous spaces are obtained for Bernstein-Kantorovich operator Knf on a simplex. These will imply,for 0< α< 1 and f ∈ C(S),‖Knf-f‖C(S)=O(n-α)⇔ws2(f,t)C(S)=O(t2α),where ws2(f,t)C(S) is Ditzian-Totik modulus of smoothness. Related Articles | Metrics

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Interpolation and Extrapolation Theorems of Regularized Cosine Operator Functions Zhang Jizhou Acta mathematica scientia,Series A. 1997, 17 (3):  294-300.  Abstract ( 66 )   RICH HTML PDF (439KB) ( 79 )   Save In this paper, we study the interpolation and extrapolation theorems of regularized cosine operator funcitons. We show that the linear Operator a generates a exponentially bounded C -regularized cosine function on the Banach space X if and only if there exist a Banach space Y and a linear operator B such that:[R(C]→x→y, where C is a bounded extension of C on Y, B generates a strongly continuous cosine operator funciton and A=B|x. Related Articles | Metrics

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Nonnegative Unbiased Estimation of Variance for Systematic Sampling with Supplementary Observations Zou Guohua, Feng Shiyong Acta mathematica scientia,Series A. 1997, 17 (3):  301-307.  Abstract ( 72 )   RICH HTML PDF (410KB) ( 141 )   Save The main objective is to consider nonnegative unbiased estimation of variance for systematic sampling when supplementary sample is drawn by arbitrary sampling design. Our result unifies the relevant ones in the literature. Related Articles | Metrics

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Existence and Uniqueness Theorems of Solutions for Nonlinear Operator Equations and Applications Lou Bendong, Song Guangxing Acta mathematica scientia,Series A. 1997, 17 (3):  308-313.  Abstract ( 55 )   RICH HTML PDF (314KB) ( 154 )   Save In this paper, we investigate the existence and uniqueness of solutions for a class of nonlinear operator equations in abstract functional spaces by means of iterative technique and apply our main results to integral equations in Banach spaces. Related Articles | Metrics

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The Pure-Gauge Potentials Under Time-Scale Transformation in Vaidya-Schwarzschild-de Sittet Space-Time Ma Yong, Zhao Zheng Acta mathematica scientia,Series A. 1997, 17 (3):  314-319.  Abstract ( 96 )   RICH HTML PDF (300KB) ( 27 )   Save Like a stationary space-time, the Hawking effect can be regarded as a compensate effect of the scale transformation of coordinate time in the non-stationary Vaidya-Schwarzschild-de sitter space-time-One of the pure-gauge potentials represents the Hawking temperature and the other the change rate of the temperature. Related Articles | Metrics

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Discussion of General Properties of Soliton Solutions of KdV Equation by Using Darboux Transformation Li Jinping, Yan Mulin, Yuan Zhihua Acta mathematica scientia,Series A. 1997, 17 (3):  320-329.  Abstract ( 62 )   RICH HTML PDF (560KB) ( 143 )   Save We point out that, by making use of Darboux trans formation, the analytical form of one-and two-soliton solutions of KdV equation not only can be obtained concisely,but also the properties of any soliton solutions of KdV equation can be discussed easily.Through the detailed discussion of three-soliton solution and the analytical analysis of multisoliton solutions of KdV equation, we obtain some general and interesting conclusions about properties for all soliton solutions of KdV equation. The conclusions would play an important role in the deep understanding of the law for interaction between solitons. Related Articles | Metrics

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Compactness Related to the Transport Operator of the Relativistic Boltzmann Equation Jiang Zhenglu Acta mathematica scientia,Series A. 1997, 17 (3):  330-335.  Abstract ( 92 )   RICH HTML PDF (358KB) ( 160 )   Save This paper shows the result about compactness related to the transport operator of the relativistic Boltzmann equation. This result is a generalization of that of DiPerna and Lions in the nonrelativistic case, and plays a very important role in the study of the relativistic Boltzmann equation. Related Articles | Metrics

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The Minimum L∞-norm Method of the Nonlinear Parameter Estimation Qi Huan, Fei Qi Acta mathematica scientia,Series A. 1997, 17 (3):  336-340.  Abstract ( 104 )   RICH HTML PDF (296KB) ( 194 )   Save The quasi -convex properties of L∞ -norm has been studied in this paper. Q-algrithm of minimum L∞-norm has been made with maximum Entropy method. This is a metric method with the open formula of searching direction, suits for the nonlinear parameter estimation. Related Articles | Metrics

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Some Results of Multivariate Polynomial Approximation on C([-π,π]n) Liu Yingfan Acta mathematica scientia,Series A. 1997, 17 (3):  341-347.  Abstract ( 50 )   RICH HTML PDF (397KB) ( 138 )   Save This paper constracts some n dimensional nonpositive Rogosinski-type kernal on Rn and some relative nonpositive polynomial approximation operators on the periodic continu ous function space C([-π,π]n), and has obtained certain higher dimensional Rogosinskitype approximation theorem under the approximate error described by the second order continuous module on this function space. Related Articles | Metrics

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Indirect Approximate Solution With Complex Splines for Singular Integral Equations on A Closed Contour Wang Xiaolin Acta mathematica scientia,Series A. 1997, 17 (3):  348-355.  Abstract ( 53 )   RICH HTML PDF (461KB) ( 73 )   Save In this paper, using the interpolating complex cubic splines, we give a method of indirect approximate solution for singular integral eguations of normal type defined on a smooth closed contour, discuss the property of uniform convergence. We also estimate the errors for a kind of singular integral equations. Related Articles | Metrics

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Cyclic Vectors in the BMOA Space Ye Shanli Acta mathematica scientia,Series A. 1997, 17 (3):  356-360.  Abstract ( 87 )   RICH HTML PDF (292KB) ( 87 )   Save In this paper we try to identify the funciton whose polynomial multiples are weak* dense in thc BMOA space. Wc obtain that if|f(z)| ≥ |g(z)|at all points and if g is cyclic, then f is cyclic, Theorem 2 gives a sufficient and nccessary condition for a function to be cyclic is that f is an outer function. Related Articles | Metrics