Abelian and Tauberian Theorems on the Bias of the Hill Estimator

The bias of Hill's estimator for the positive extreme value index of a distribution is investigated in relation to the convergence rate in the regular variation property of the tail function of the common distribution of the sample and the corresponding tail quantile function. Based on the theory of generalized regular variation, natural second-order conditions are proposed which both imply and are implied by convergence of the expectation of Hill's estimator to the extreme value index at certain rates. A comparison with second-order conditions encountered in the literature is made.     

正则半群上的极大幂等分离同余

本文利用中间化子的方法给出了一般正则半群上极大幂等分离同余的另一个刻划，从而使其具体化。     

二维LP问题的一个直接算法

针对求解二维线性规划问题的几何算法—图解法,给出了一个二维线性规划问题最优解的性质定理,得到了求解二维线性规划问题的一个直接的代数性算法。利用该算法,可得到一般性规划问题的加速算法,其迭代过程至少是按二维迭代的,迭代速度快于单纯形法。     

A series of group divisible designs

Bose and Shrikhande C19763 proved that if D(m, k, ?) is a Baer subdesign of another SBIBD D₁ (v₁, k₁ ?), k₁>k, then it also contains a complementary subdesign D^* which is symmetric GDD, D^* (v^*, k^*; ?-1, ?; m, n). Utilising this, we give a necessary condition for a SBIBD D to be a Baer subdesign of D₁ and also give the parameters. Some GD designs are constructed.     

李白的货币思想

货币是应人类商品交换的需要而产生的一种工具。人类创造这种工具的目的在用其为自己的利益服务。货币交换也是一种游戏，人们几乎在开展货币交换时，就在制定相应的游戏规则。李白深刻揭示货币运行的规律，并遵循交换的“游戏”规则，从多方面利用货币为人类服务：或充分利用货币的使用价值以福利人；或积极发挥货币交换的职能作用以愉悦人；或努力促进货币循环流通的运动以激励人；或深刻揭示货币充当等价商品的本质以沟通人。     

A condition for best asymptotic normality in a regular family of distributions

A theorem is presented which provides a simple sufficient condition for a weakly consistent estimator of a parameter in a regular family of distributions to be best asymptotically normal (B.A.N.). As a corollary the B.A.N. property of a maximum likelihood estimator is established under weaker conditions than those of Zacks (1971). Two examples are provided to illustrate the technique.     

幂群的正则表示

通过幂群在其自身的左平移作用 ,给出了有限群上幂群的正则表示 ,进而给出了幂群的正则矩阵表示。     

浅析技校教学中平时成绩的评价方法

目前,大部分技术学校均是实行平时成绩和期末成绩相结合的原则,对学生进行期末总评价。而平时成绩是一个模糊化的概念,如何合理给出一个学生的平时成绩,保证每个学生的分数公平公正、合情合理,是一个比较难的事情。文中提出了一种基于模糊数学的评价方法。实践证明该方法能够较好地反应学生的学习过程及学习效果。     

耦合边界条件下Sturm-Liouville问题特征值与特征函数的渐近式

本文利用刘景麟老师《常微分算子谱论》中对分离边界条件下正则Sturm-Liouville问题的研究方法(同阶无穷小的比较),研究了一般耦合边界条件下正则Sturm-Liouville问题,给出了耦合情形下的特征值与特征函数的渐近估计.(比已有的结果更精细)     

A power comparison of three tests for design effects in a random effects covariance model

A preliminary testing procedure for design ettecta in a ran-dom effects covariance model is Compared with the usual procedure to see if the power of the latter can be improved. A procedure which ignores the random covariate effects is included for comparison and for study of misspecification effects. Methodology is based on Roebruck's (1982) results for regular linear models.