Using intersection matrices to identify graphical structure

Intersection matrices help identify the common graphical structure of two or more objects. They arise naturally in a variety of settings. Several examples of their use in a computer algebra environment are given. These include: simplifying an expression involving array products, automating cumulant calculations, determining the behaviour of an expected value operator and identifying model hierarchy in a factorial experiment. The emphasis is placed on the graphical structure, and the symmetry of arrays help reduce the complexity of the graphical problem.     

Between stability and higher-order asymptotics

We discuss the effects of model misspecifications on higher-order asymptotic approximations of the distribution of estimators and test statistics. In particular we show that small deviations from the model can wipe out the nominal improvements of the accuracy obtained at the model by second-order approximations of the distribution of classical statistics. Although there is no guarantee that the first-order robustness properties of robust estimators and tests will carry over to second-order in a neighbourhood of the model, the behaviour of robust procedures in terms of second-order accuracy is generally more stable and reliable than that of their classical counterparts. Finally, we discuss some related work on robust adjustments of the profile likelihood and outline the role of computer algebra in this type of research.     

Bounding convergence rates for Markov chains: An example of the use of computer algebra

Kolassa and Tanner (J. Am. Stat. Assoc. (1994) 89, 697–702) present the Gibbs-Skovgaard algorithm for approximate conditional inference. Kolassa (Ann Statist. (1999), 27, 129–142) gives conditions under which their Markov chain is known to converge. This paper calculates explicity bounds on convergence rates in terms calculable directly from chain transition operators. These results are useful in cases like those considered by Kolassa (1999).     

Symbolic computation for approximating distributions of some families of one and two-sample nonparametric test statistics

A conditional saddlepoint approximation was provided by Gatto and Jammalamadaka (1999) for computing the distribution function of many test statistics based on dependent quantities like multinomial frequencies, spacing frequencies, etc. The considerable complexity of the formulas involved can be bypassed by symbolic computation. This article illustrates the effectiveness of symbolic computation to evaluate the saddlepoint approximation for the likelihood ratio, the exponential score, and the Wald-Wolfowitz test statistics. The case of composite hypotheses is also discussed.     

拉格朗日在高次代数方程解法探索中的贡献

本文回顾了高次代数方程解法探索的历程，分析了拉格朗日为问题最终解决所起的作用．     

某些特殊矩阵方程组的解及其有关结论

本文给出了域K上全矩阵代数M_n(k)中几类特殊矩阵方程组的解以及它们与代数M_n(K)的自同构或反自同构之间的密切关系     

中小学数学教学衔接问题的探讨

本文从九年义务教育中小学教学教材的知识结构出发，阐述了中小学数学概念教学、数运算与式运算教学、应用题教学、思维方法的培养与几何知识教学等方面的衔接问题，探讨了衔接的途径与作法．     

一类自反代数的单元和自同构

讨论了Ｂａｎａｃｈ空间Ｘ中自反代数　的一些性质。指出了在　中非零单元与一秩算子是等价的．特别证明了　的每一自同构都是自动连续的，此外，若Ｘ还是自反的，则　的自同构必是空间的。     

The score function and a comparison of various adjustments of the profile likelihood

Several adjustments of the profile likelihood have the common effect of reducing the bias of the associated score function. Hence expansions for the adjusted score functions differ by a term, D_ξ, that has small asymptotic order (n ^?½). The effect of D_ξ on other quantities of interest is studied. In particular, we find the bias and variance of the adjusted maximum-likelihood estimate to be relatively unaffected, while differences in the Bartlett correction depend on D_ξ in a simple way.     

半素路代数的有向图特征及其应用

用图论的方法讨论有向图Δ的几何性质及其路代数k(Δ)的代数性质.论图Δ不是有向环线弧点图,则Δ是双侧连接图■k(Δ)是素代数,给出了无限和有限竞赛图Hamilton圈存在的路代数条件;给出了半素路代数的有向图特征.