矢量法判定分子极性在中学化学中的应用

给出了一种通过不同类型分子的空间结构求算分子中键长的矢量和进而得到一个判断分子极性新判据的方法     

关于环上矩阵的平行和

本文研究了环上矩阵的平行和性质，并将文[1]中若干结果推广到一类特殊的环中。     

关于级数Sum from i=1 to n () i~k的求和及其贝努里数的计算

本文从有限差理论出发，给出了■的求和方面递推公式，定理的证明比前人简捷，并顺便导出贝努里的递推公式。     

Effect on probabilities and quantiles of adding a quantity with small variance

This paper gives simple approximations for the distribution function and quantiles of the sum X + Y when X is a continuous variable and Y is an independent variable with variance small compared to that of X . The approximations are based around the distribution function or quantiles of X and require only the first two or three moments of Y to be known. Example evaluations with X having a normal, Student's t or chi-squared distribution suggest that the approximations are good in unbounded tail regions when the ratio of variances is less than 0.2.     

求sum from k=1 to n(k~m)之和的一种新方法

本文提出了一种以多项式函数为主要工具去求前n个正整数的方幂之和的新方法。     

用行等和矩阵构造2~n阶全对称雪花幻方

本文利用行等和矩阵的概念,构造2~n 阶全对称雪花幻方,然后给出此类全对称雪花幻方的三条性质。     

矩阵直接和的｛1,2｝-逆

本文给出了任意矩阵为｛1，2｝一道的结构，进而得到了矩阵直接和的｛1，2｝-逆的表示式．     

任意除环上的矩阵直接和的g-逆

本文给出了任者除环上矩阵直接和的定义，得到了矩阵直接和的g一逆的表达式．     

Goodness-of-fit Tests for GEE with Correlated Binary Data

The marginal logistic regression, in combination with GEE, is an increasingly important method in dealing with correlated binary data. As for independent binary data, when the number of possible combinations of the covariate values in a logistic regression model is much larger than the sample size, such as when the logistic model contains at least one continuous covariate, many existing chi-square goodness-of-fit tests either are not applicable or have some serious drawbacks. In this paper two residual based normal goodness-of-fit test statistics are proposed: the Pearson chi-square and an unweighted sum of residual squares. Easy-to-calculate approximations to the mean and variance of either statistic are also given. Their performance, in terms of both size and power, was satisfactory in our simulation studies. For illustration we apply them to a real data set.     

关于自然数的方幂和

设,借助于母函数与微积分的方法,获得了S_r(n)的一些重要性质,从这些性质出发给出了求S_r(n)与Bernolli数的新方法.