Diagonal uniform association symmetry modelsfor cumulative probabilities in square tables

For the analysis of square contingency tables with ordered categories, Tomizawa (1991) considered the diagonal uniform association symmetry (DUS) model, which has a multiplicative form for cell probabilities and has the structure of uniform association in the tables constructed using two diagonals that are equidistant from the main diagonal. This paper proposes another DUS model which has a similar multiplicative form for cumulative probabilities. The model indicates that the odds that an observation will fall in row category i or below and column category i+k or above, instead of in column category i or below and row category i+k or above, increase (decrease) exponentially as the cutpoint i increases for a fixed k. Examples are given.     

Mkdv方程与对策约束

利用特征值问题得到了Ｍｋｄｖ方程的Ｌａｘ表示，并利用对称约束得到了一个新的可积系，讨论了可积系与特征问题之间的联系，进一步得到了Ｍｋｄｖ方程解的一种表示。     

The Symmetry Rule: A Seven‐Year Study of Symptoms and Explanatory Labels Among Gulf War Veterans

Noticing medical symptoms can cause one to search for explanatory labels such as “ate bad food” or even “exposed to anthrax,” and perhaps these labels may cause new symptom reports. The present study examined whether there is empirical support for this symptom‐label “symmetry rule.” We interviewed veterans (N= 362) from the Gulf War Registry in 1995 and 2002 about their medical symptoms and about their exposure to war‐related hazards and stressors. Health symptom reports were strongly correlated between the two time periods and showed relatively stable mean levels, whereas recall of war‐related exposures was notably unstable. Veterans starting with fewer medical symptoms recalled fewer war‐related exposures seven years later. Initial recollection of chemical and biological warfare exposure (but not other exposures) longitudinally predicted novel medical symptoms. The findings generally support the symmetry rule hypotheses, although the evidence for the label to symptom link was less strong. The findings account for some variability in symptoms and exposure recall over time, but they do not, on their own, account for the Gulf War veterans' elevated number of unexplained medical symptoms.     

对称性性质简化一类定积分计算问题研究

对称性在数学及其更广泛的领域有着重要的意义,在微积分计算中,对称性有着重要的简化运算作用.本文将根据积分区间自身的对称性利用对称性性质对一类定积分计算问题作深入系统的探讨.     

On D-optimal robust designs for lifetime improvement experiments

Locating the optimal operating conditions of the process parameters is critical in a lifetime improvement experiment. For log-normal lifetime distribution with compound error structure (i.e., symmetry, inter-class and intra-class correlation error structures), we have developed methods for construction of D-optimal robust first order designs. It is shown that D-optimal robust first order designs are always robust first order rotatable but the converse is not always true.     

半球延拓的证明方法

本文以半球的稳定场问题为模型,由轴对称问题出发,利用完整球的结果,考虑了勒让德多项式的性质。给出了半球延拓的证明方法。     

对称性在四玻色子系统中的结构效应

本文建立了一个全同四玻色子系统的模型理论，并深入了系统低激发态结构的本质，发现对称性是少体系统结构特征的起源。     

A New Measure of Kurtosis Adjusted for Skewness

Studies of kurtosis often concentrate on only symmetric distributions. This paper identifies a process through which the standardized measure of kurtosis based on the fourth moment about the mean can be written in terms of two parts: (i) an irreducible component, about L₄, which can be seen to occur naturally in the analysis of fourth moments; (ii) terms that depend only on moments of lower order, in particular including the effects of asymmetry attached to the third moment about the mean. This separation of the effect of skewness allows definition of an improved measure of kurtosis. This paper calculates and discusses examples of the new measure of kurtosis for a range of standard distributions.     

汉语四字格成语平仄搭配的对称性与认知

汉语四字格成语的声调搭配形式具有对称性特征,根据现代汉语语音划分平仄的理论可予以分类统计。分类统计表明:平平仄仄和仄仄平平是最主要的声调组合方式,其余多是上述形式的变式,合律型和变式型占绝大多数,拗者仅占少数。实验结果表明:(一)按平仄区别不同声调搭配形式有一定理据性,但同一种平仄搭配形式,具体内容因声调组合而异,所以在随机和分类两种呈现条件下对认知的影响都没有显著差异;(二)分类呈现总的来说对记忆和保持的影响比随机呈现大,说明每一种搭配形式都有规律性;(三)规律和变异乃对立统一体,规律中加上变异才显出语言的节奏,所以完全和谐型成语中镜影型和旋转镜影型以及重复型虽占很大的比例,但仍有很大的变异性。     

Stopping times of one-sample rank order sequential probability ratio tests

Weed, Bradley and Grovindarajulu (1974) propose one-sample probability ratio tests based on Lehmann alternatives. They also study the finite sure termination of the stopping times. Motivated by Stein's proof of (1946) of the termination of a sequential probability ratio test (SPRT) in the case of independent and identically distributed (i.i.d.) random variables and the work of Sethuraman (1970) for the two- sample rank order SPRT, we obtain a very mild condition (namely, that a certain random variable U(Z) is not identically zero) for the finite sure termination of the existence of the moment generating function (m.g.f.) for the stopping time of one- sample rank order SPRT's.