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25 September 1996, Volume 16 Issue 3 Previous Issue    Next Issue

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SOME RESULTS RELATED TO THE SEPARABLE QUOTIENT PROBLEM Zhong Huaijie Acta mathematica scientia,Series B. 1996, 16 (3):  248-256.  Abstract ( 42 )   RICH HTML PDF (530KB) ( 33 )   Save The problem whether every infinite dimensional Banach space has all infinite dimensional separable quotient space has remained unsolved for a long time. In this paper we prove:the Banach space X has an infinite dimensional separable quotient if and only if X has an infinite dimensional separable quasi complemented subspace, also if and only if there exists a Banach space Y and a bounded linear operator T∈ B(Y, X) such that tile range of T is nonclosed and dense in X. Besides, the other relevant questions for such spaces e.g. the question on operator ideals that on H.I.(hereditarily indecomposable) spaces, that on invariant subspaces of operators, etc. are also discussed. Related Articles | Metrics

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ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE ANALYSIS Shi Lei, Wang Xueren Acta mathematica scientia,Series B. 1996, 16 (3):  257-270.  Abstract ( 44 )   RICH HTML PDF (746KB) ( 32 )   Save A recent method for assessing the local influence is introduced by Cook(1986), in which the normal curvature of the influence graph based on the likelihood displace ment is used to monitor the influence of small perturbation. Since then this method has been applied to various kind of models. However, the local influence in multi variate analysis is still an unexplored area because the influence for many statistics in multivariate analysis is not convenient to handle based on the Cook's likelihood displacement. In this papers we suggest a method with a slight modification in Cook's approach to assess the local influence of small perturbation on a certain statistic. The local influence of the perturbation on eigenvalue and eigenvector of variance-covariance matrix in theoretical and sample version is assessed, some results for the other statistics in multivariate analysis such as generalized variance, canonical correlations are studied.Finally, two examples are analysed for illustration. Related Articles | Metrics

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COLLISION AND MEETING OF STABLE PROCESSES Luo Shunlong Acta mathematica scientia,Series B. 1996, 16 (3):  271-278.  Abstract ( 49 )   RICH HTML PDF (446KB) ( 31 )   Save Random path intersections generated by collision and meeting of stable processes in thin time sets are characterized in terms of Hausdorff dimension and capacity. Related Articles | Metrics

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RESAMPLING TESTS OF STATISTICAL HYPOTHESES Shi Jian Acta mathematica scientia,Series B. 1996, 16 (3):  279-286.  Abstract ( 49 )   RICH HTML PDF (465KB) ( 29 )   Save In this paper, large sample properties of resampling tests of hypotheses on the population mean resampled according to the empirical likelihood and the KulbackLeibler criteria are investigated. It is proved that under the null hypothesis both of them are superior to the classical one. Related Articles | Metrics

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ON THE RATES OF CONVERGENCE IN THE CENTRAL LIMIT THEOREM FOR TWO-PARAMETER MARTINGALE DIFFERENCES Long Hongwei Acta mathematica scientia,Series B. 1996, 16 (3):  287-295.  Abstract ( 51 )   RICH HTML PDF (462KB) ( 32 )   Save In this paper we obtain the uniform bounds on the rate of convergence in the central limit theorem (CLT) for a class of two-parameter martingale difference sequences under certain conditions. Related Articles | Metrics

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THE DESIGN AND ANALYSIS OF ALGORITHM OF MINIMUM COST SPANNING TREE Xu Xusong, Liu Dacheng, Wu Lihua Acta mathematica scientia,Series B. 1996, 16 (3):  296-301.  Abstract ( 50 )   RICH HTML PDF (351KB) ( 27 )   Save This paper provides a method of producing a minimum cost spanning tree (MCST) using set operations. It studies the data structure for implementation of set operations and the algorithm to be applied to this structure and proves tile correctness and the complexity of the algorithm. This algorithm uses the FDG (formula to divide elements into groups) to sort (the FDG sorts a sequence of n elements in expected lim O(n)) and uses the method of path compression to find and to unite. Therefore, it produces an MCST of an undirected network having n vertices and e edges in expected time O(eG(n)). Related Articles | Metrics