ON EVALUATING THE RUN LENGTH PROPERTIES OF X^— CHARTS WITH ESTIMATED CONTROL LIM

X＾－ charts with estimated coutrol limits are commonly used in practice and treated as if the in-control process parameters were known.However,the former can behave quite differently from the latter.To understand the differences,it is necessary to study the run length distribution(RLD),its mean(ARL)and standard deviation(SDRL) of the X^- charts when the control limits are estimated.However,ARL and SDRL are integrals over and infinite region with a boundless integrand,the finiteness has not been proved in literature.In this paper,we show the finiteness and uniform integrability of ARL and SDRL.Furthermore,we numerically evaluate the ARL,SDRL and the RLD using number theory method.A numerical study is conducted to assess the performance of the proposed method and the results are compared with those given by Quesenberry and Chen.     

CONVOLUTION THEOREM AND ASYMPTOTIC EFFICIENCY IN TWO SIDE TRUNCATED DISTRIBUTION FAMILY—THE NORMAL CASE

In the distribution family with common support and the one side truncated distribution family, Bickle, I. A. Ibragimov and R. Z. Hasminskii proved two important convolution theorems. As to the two-side truncated case, we also proved a convolution theorem, which plays an extraordinary role in the efficiency theory. In this paper, we will study another kind of two-side truncated distribution family, and prove a convolution result with normal form. On the basis of this convolution result, a new kind of efficiency concept is given; meanwhile, we will show that MLE is an efficient estimate in this distribution family.     

耦合色散方程的隐对称结构及其可积性

用延拓（Ｐｒｏｌｏｎｇａｔｉｏｎ）方法分析耦合色散方程的隐对称结构，给出了它的无限维李代数表示。并从理论上导出了该系统的线性谱一般形式，从而证明了它是严格可解的。     

积分学的两个定理

给出了（Ｒ）积分的两个定理：正规函数的（Ｒ）可积性；积分号与极限可交换顺序定理。     

广义SRLW方程的Painlevé分析和精确解

证明了SRLW方程及其一些推广形式的方程不具有J .Weiss等人对偏微分方程定义的Painlev啨性质 ,因此可能不是完全可积的 .利用奇异流形方法得到了所论方程的一些显式精确行波解 ,包括显式精确孤立波解、奇异行波解和三角函数状周期波解 .     

一阶非线性常微分方程的新的可积类型

提出一阶非线性常微分方程新的可积型，且给出其通解的参数形式。     

超对称Bullough－Dodd模型的prolongation分析

在扭曲仿射代数A2^(2)上建立了超对称的Bullough-Dodd模型。Prolongation方法的研究表明，该模型承认一个Lax pair，从Lax意义上证明该模型可积。另外，当该超对称模型的所有费米量为零时，该系统就定义了一个新奇的由单标量玻色场指数相互作用构成的可积模型。这个发现还打破了长久以来的一种认识；只有sinh-Gordon和标准Bullough-Dodd模型是Liouville模型。     

两种新矩阵运算及其应用效果的论证

定义了两种新矩阵运算矩阵倒置积与投影 ,论证基本定理 ,论讨了在信息加工与检索中的应用 ,并给出了分析与评价     

SAW卷积器在扩频通讯和其它信号处理中的应用

本文讨论SAW卷积器在通讯和信号处理中的应用,着重介绍它们在扩频通讯中的作用。文中还对卷积器的噪声作了专门分析,以说明内外噪声源。