非线性复合介质电导的有效介质近似

在强外场作用下,复合介质的电输运性能服从非线性的本构关系。复合介质非线性电导率的计算相当复要,在线性复合介质的理论框架内,已发展了多种有效介质近似方法。利用有效介质近似,可以导出计算有效输运系数的简洁的解析公式。只要颗粒浓度在逾渗临界点以外以及颗粒和杂质的输运系数之比为有限的情况下,有效介质近似的计算都可以给出相当可靠的理论结果,因此,对于工程应用来说,有效介质近似是十分有的工具。本文在非线性复合     

复杂网络链路预测

网络中的链路预测是指如何通过已知的网络结构等信息预测网络中尚未产生连边的两个节点之间产生连接的可能性。预测那些已经存在但尚未被发现的连接实际上是一种数据挖掘的过程,而对于未来可能产生的连边的预测则与网络的演化相关。传统的方法是基于马尔科夫链或者机器学习的,往往考虑节点的属性特征。该类方法虽然能够得到较高的预测精度,但是由于计算的复杂度以及非普适性的参数使其应用范围受到限制。另一类方法是基于网络结构的最大似然估计,该类方法也有计算复杂度高的问题。相比上述两种方法,基于网络结构相似性的方法更加简单。通过在多个实际网络中的实验发现,基于相似性的方法能够得到很好的预测效果,并且网络的拓扑结构性质能够帮助选择合适的相似性指标。该文综述并比较了若干有代表性的链路预测方法,展望了若干重要的开放性问题。     

Sikkema-Bézier型算子对有界变差函数的点态逼近度

构造了两种Sikkema -B啨ｚｉｅｒ型算子Ｓｎ,a(f,x) ,S n ,a(f,x) (它们是Sikkema算子的两种推广 ) ,并研究了它们对有界变差函数的点态逼近 ,得到它们对这类函数点态逼近的最优估计式     

Using a correlated probit model approximation to estimate the variance for binary matched pairs

A correlated probit model approximation for conditional probabilities (Mendell and Elston 1974) is used to estimate the variance for binary matched pairs data by maximum likelihood. Using asymptotic data, the bias of the estimates is shown to be small for a wide range of intra-class correlations and incidences. This approximation is also compared with other recently published, or implemented, improved approximations. For the small sample examples presented, it shows a substantial advantage over other approximations. The method is extended to allow covariates for each observation, and fitting by iteratively reweighted least squares.     

On some formulas for weighted sum of invariant polynomials of two matrix arguments

Some properties of the generalized binomial coefficients and new coefficients related to symmetric functions are discussed. Several formulas of the weighted sum of invariant polynomials of two matrix arguments which are useful in multivariate distribution theory are presented.     

一道IMO试题的推广及证明

将 4 2届国际数学奥林匹克竞赛 (IMO)中的一个不等式问题加以推广 ,并给出其证明     

Sequential Estimation of Expectations in the Presence of Trend2

A sequence of independent random variables {Z_n:n≥ 1} with unknown probability distributions is considered and the problem of estimating their expectations {M_n+1: n≥ 1} is examined. The estimation of M_n+1 is based on a finite set {z_k:1≤k≤n}, each z_k being an observed value of Z_k, 1 ≤k≤n, and also based on the assumption that {M_n:n≥ 1} follows an unknown trend of a specified form.     

Simultaneous tolerance intervals in the random one-way model with covariates

Simultaneous tolerance intervals developed by Limam and Thomas (19881, for the normal regression model, are generalized to the random one-way model with covariates. Simultaneous tolerance intervals for unit means are developed for the balanced model. A simulation study is used to estimate the exact confidence of the tolerance intervals for models with one covariate.     

A confidence interval for the scale parameter based on sukhtmes two-sample statistic

Sukhatme (1957) introduced a statistic which may be used to test the equality of variances in two independent samples from continuous distributions, centered at zero. It has become evident that this statistic cound be used to construct, analytically, a confidence interval for the scale parameter relating the two random variables(of.Laubscher (1968) and Noether (1967, pp. 66-69 and 1972)). In view of this additional use of the statistic, and since no tables of critical values exist, we provide such a table which makes the application of the statistic a practical proposition. In addition, a normal approximation is suggested for the use outside the range of Table III and the accuracy of this approximation is investigated. The Sukhatme test applied to sample values reduced by t n e i r medians i s studied in a small simulation exercise. It appears that this test when used in conjunction with the critical values of Sukhatme's statistic, is a very conservative one and that it is probably fairly robust with respect to the underlying population distribution.     

Comments on zacks' recent paper on one-sided cusum procedures

The goal of this paper is to propose approximations for the cdf and the inverse cdf of the normal sample median. The presented methodology, which seems to not have been investigated before, suggests to fit the normal sample median distribution with a symmetrical Johnson S_U: distribution having ap-proximatively the same second and fourth moments. The results obtained with this approach, compared with the normal approximation, are very impressive, especially for the inverse cdf. One important application of the inverse cdf approximation of the normal sample median is the computation of accurate α‐level median/range control limits for any value of α (and not only for the popular value α = 0.0027). This paper can be also viewed as an homage to Professor N.L. Johnson's works by making a link between two of his major papers.