不可测集的性质

研究了不可测集的性质:如果一列互不相交的集合并集的外测度小于外测度的和,则其中至少有两个是不可测集。通过具体例子说明:存在一列互不相交的不可测集使得它们并集的外测度小于外测度的和。     

风车的δ-最优性

给出了关于风车的一组标号,证明了风车wm^n（m≥3,m≠4,5）是δ-最优的．     

级数求和的一个定理

建立了由函数恒等式所导出的函数项级数的求和定理，并给出了具体应用的实例。     

Exponential smoothing: Behavior of the ex-post sum of squares near 0 and 1

When using simple exponential smoothing on a given time series the nature of the relationship between the optimal smoothing constant and the autocorrelation structure of the series remains an unresolved question. Although numerical search routines can easily be used to find optimal values of the smoothing constant, they offer little insight into the nature of the relationship between the estimated smoothing constant and the structure of the underlying time series. We suggest that renewed investigations of the ex-post sum of squares function may prove helpful in this pursuit. Results are presented that illustrate how the optimal smoothing constant depends upon the value used to initialize the smoothing and upon the sample autocorrelation coefficients of the observed series. These results are based on a new formula for the derivative of the ex-post sum of squares function. In particular, the derivative is examined near 0 and 1, where great simplifications occur in its form, thereby facilitating investigations near these points. A necessary and sufficient condition is stated for when the ex-post sum of squares must have a positive derivative at 0 and the autocorrelation coefficients of the differenced series are shown to affect the sign of the derivative near 1. Based on these results, a general algorithm is presented as an alternative to grid search routines for minimizing the ex-post sum of squares.     

幂级数的和及其求法

本文通过具体实例给出求幂级数和函数的若干种方法。     

计算f（k）的一个初等方法

本文利用二项式定理推出前ｎ个自然数的各次方和的公式，进而将写成从而进行有关的计算。     

线性循环细胞自动机的动态分析

本文利用线性循环细胞自动机的线性循环特性,把自动机问题归结为有限环R=F_■[x]/(x~■-1)中的一些纯粹代数问题.即用中国剩余定理,把环R 分解成一些子环的直和.然后将与这些子环相对应的小自动机的功态特性合成为原来自动机的动态特性.     

M-环之BM-结构

本文试图讨论环中某种特殊根可以从某类特殊环中分裂出来的问题。文中先引入M-环之概念,利用它可完全刻划能表成有单位元的单环之直和的环,由此得知任何一个M-环皆可表成其BM-根与一个BM-半单理想的直和。     

多元累积和控制图

讨论了两种多元累积和图.第1种是利用 Hotelling 统计量进行累积和,形成多元累积和控制图,并讨论了它的平均游程长度(ARL);第2种是在已知偏移状态下,用序贯概率比检验法将多元累积和问题转化为一元累积和问题.这两种方法的前提都是随机变量服从正态分布.     

N＝2的Krichever－Novikov超代数的基本超场表示

利用算符乘积展开方法，通过在Ｎ＝２的超空间引入基本超场建立了高亏格Ｒｉｅｍａｎｎ面上Ｎ＝２的Ｋｒｉｃｈｅｖｅｒ－Ｎｏｖｉｋｏｖ代数的基本超场表示，并且给出了这种表示的分量形式。