A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space

We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton-Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton-Kantorovich theorem.     

Time saving fluid dynamic predictions in a wetting-drying process: A hypothesis for vertisols

This paper is aimed at investigating the effect of the initial water content in a vertisol sample on the whole wetting-drying process leading the system to a change in volume. In order to do this, an experimental setup was realized and employed with very thin soil layers wetted from below (“per ascensum”). The results show that the effect of the initial water content on the swelling-shrinkage process is to shift the corresponding curve e-ϑ towards bigger-smaller values of the humidity but does not seem to affect the dynamics of the process. The text was submitted by the authors in English.     

居加猜想的一个等价命题

文章利用数论中的一些简单结果,建立了居加猜想的一个等价命题。     

Norms and perfect graphs

The weak Berge hypothesis states that a graph is perfect if and only if its complement is perfect. Previous proofs of this hypothesis have used combinatorial or polyhedral methods.In this paper, the concept of norms related to graphs is used to provide an alternative proof for the weak Berge hypothesis.This is a written account of an invited lecture delivered by the second author on occasion of the 12. Symposium on Operations Research, Passau, 9.–11. 9. 1987.     

等样本容量的多个正态总体均值相等性的假设检验

本文对多个独立正态总体的均值的相等性的假设检验进行地了探讨，提出用极差统计量进行检验的方法，并以实例说明该检验方法是简单且高效的．     

试论假说方法在进化论研究中的作用

科学研究方法是取得科学研究成果的重要因素之一。生物进化论是一门理论性很强的科学，生物进化论研究成果的取得必需借助假说方法的作用。本文通过对生物进化论学科性质，研究难度、研究问题的抽象程度及研究问题对其它学科的依赖性几个方面对为什么进化论发展需要借助假说方法进行了论证     

中国股市交易量的周内效应

研究了中国股市交易量在一周里面的变化规律,采样时间跨度是从1990-12-19到2002-12-31。以市场换手率度量交易量,采用自回归广义自回归条件异方差(AR-GARCH)模型研究了中国股市交易量的时间系列。研究结果显示沪市和深市的日市场换手率不服从正态分布并且存在着自相关性和ARCH效应;AR-GARCH模型很好地拟合了日市场换手率时间系列,估计出来的参数十分显著;周一到周五的日市场换手率存在显著差异并且周一的市场换手率达到了一周的最大值。利用混合分布假说进行了解释,非交易日的信息积累可能是周一高换手率的原因。结果指出:在该研究的样本范围内,中国股市交易量存在着周内效应。     

关于W.H.Young不等式形式的探讨

通过一个命题的证明，得出关于W．H．Young不等式的另一种形式，并说明这种形式的不必要性，借此来说明W．H．Young不等式形式的内在统一性和数学思维的严密性。     

关于二项式系数的Jones问题

设n是正整数 ,J .P .Jones曾经猜测 :当n >3时 ,如果 2n - 1n ≡ 0 (modn3) ,则n必为奇素数 ,本文中运用初等数论方法证明了 :当n是偶数时 ,2n - 1n 0 (modn2 ) .由此可知Jones猜想在n为偶数时成立