β混合随机变量序列加权和的收敛性

本文研究了混合随机变量序列加权和的收敛性.利用Utev, S.和Peligrad, M不等式得到了混合随机变量序列加权和的收敛性定理及Hajeck-Rènyi型不等式,推广和改进了W.F,Stout,吴群英,J.Hajeck和A.Rènyi.的相应结论.     

群的融合自由积的几种广义Fratttini子群

M.K.Azarian将C.Y.Tang的一个引理推广到了下拟Frattini子群的情况,并且还提出了两个公开问题.为了回答这两个问题,进一步研究了群的融合自由积的一些广义Frattini子群,并且得到了一些结果.     

空中加油问题的递推模型与调度策略

首先对空中加油问题进行了分析,提取了相关性质,在此基础上建立了问题的递推模型.根据该模型,提出了一种启发式搜索算法.该算法计算复杂度低,适用性好.对应于辅机是否可以多次起飞,该算法分为两子算法.对这两种不同情况下的具体问题,设计了相关的优化函数.所有算法都在计算机中运行,并得到了相应结果.值得指出的是,提出的启发式搜索算法十分高效.对于问题1和问题2,该算法所得解是约束条件下的最优调度策略.对于问题3,问题4,问题5,该算法所得解逼近最优调度策略.     

具有超抛物型极限方程的非线性奇摄动反应扩散问题

讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.     

一类具有跳跃层的非线性反应扩散系统的渐近行为

讨论了一类具有跳跃层的反应扩散系统.首先,求出了问题的外部解.其次,引入伸长变量,构造了跳跃层校正项.最后,利用微分不等式理论,得到了原问题解的一致有效的渐近展开式.从而研究了相应问题的解的渐近性态.     

关于z.Ditzian定理

1987年Z.Ditzian提出了反映Bernstein算子收敛阶与所逼近函数光滑模之间关系的一个定理,并在α+β≤2情形下给出了这个定理的证明.对于α+β》2情形,Z.Ditzian给出了猜想.1992年周定轩证明了Z.Ditzian的猜想,完成了Z.Ditzian定理的证明.本文对于Z.Ditzian定理给出了一个新的直接证明,这个证明不需要讨论α,β的情况,而且还将Z.Ditzian定理拓广到Bernstein算子线性组合上.     

关于N.A.Menger PN-空间中概率收缩偶与非线性方程组的解的注记

引进了(Φ,Δ)-型概率收缩偶的概念,它简化并减弱了张石生给出的概率收缩偶的定义。在N.A.Menger PN-空间中研究了具有这类概率收缩偶的非线性算子方程组的解的存在性与唯一性问题。改进并推广了M.Altman,A.C.Lee,W.J.Padgett,张石生等人的相应结果。     

多维布朗运动的几个极限定理

本文研究了d(≥3)维布朗运动离开起点a.s.趋向无穷远的速度问题,获得了精密的结果.作为推论,给出了一个有趣的重对数律.同时,我们也给出了布朗运动靠近起点的相应性质.     

不对称柔性壁管道内幂律流体蠕动传输的精确解

在不对称管道内,研究了壁面柔曲性对非Newton流体蠕动流的影响.流变学性质由幂律流体本构方程表征.在数学表达中,采用了长波和低Reynolds数近似.得到了流函数和速度的精确解.给出了流线图及其俘获现象.对所讨论的流动,陈列了关键参数的显著特征,并最后给出了主要结论.     

Maxwell流体在有限长管道中作不稳定的蠕动传输:食道吞咽进程分析

解析地研究了有限长管道中Maxwell流体的不稳定蠕动传输.管壁受到不超过静止边界的收缩波作用.对无量纲形式的方程,应用长波长近似进行分析.导出了轴向速度和径向速度的表达式,评估了沿波长和管道长度方向的压力.讨论了回流现象,确定了回流极限区域.对食道中咀嚼食物(如面包、蛋白等)传输的数学公式给出了物理上的解释.可以看出,与Newton流体相比,Maxwell流体有利于在食道中的流动.与Takahashi等[Rheology,1999,27:169-172]的实验结果相符合.进一步揭示了松弛时间既不影响剪应力,也不影响回流极限.发现了压力的峰值,对整数值波列是相同的,而对非整数值波列是不同的.     

大学生职业生涯发展的决定因素的相关研究

本文利用探索性因素分析方法提出了一个可以用作为甄别大学生涯发展的决定因素的诊断工具,以期帮助职业生涯咨询、指导人员对个体的有关职业生涯态度、职业生涯倾向性有一个基本的了解;同时利用这个工具可以提高个体对职业生涯的认知水平,帮助个体更好地进行职业生涯规划。     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

Strong convergence of weighted sums of random elements through the equivalence of sequences of distributions

The equivalence of sequences of probability measures jointly with the extension of Skorohod's representation theorem due to Blackwell and Dubins is used to obtain strong convergence of weighted sums of random elements in a separable Banach space. Our results include most of the known work on this topic without geometric restrictions on the space. The simple technique developed gives a unified method to extend results on this topic for real random variables to Banach-valued random elements. This technique is also applied to the proof of strong convergence of some statistical functionals.     

Location of courts of justice: The making of the new judiciary map of Portugal

Location modeling techniques have been applied to an extremely wide variety of public facilities. However, their application to one of the most ubiquitous public facilities – courts of justice – has been very rare. In this paper, we describe a study promoted by the Ministry of Justice of Portugal to define a proposal for the country's new judiciary map – that is, the spatial organization of the judicial system. The new map aims to promote the efficiency and specialization of the justice system (leading to better and faster court decisions) and to provide a good level of accessibility to courts. We developed two optimization models addressing those goals – a districting model, to determine the borders of new, large judicial districts; and a court location model, to determine the location, type, size, and coverage area of the courts included in each new district. Both models are discrete facility location models and consider hierarchical facilities – generic courts and specialized courts of multiple types. Our study was publicly acknowledged by the Portuguese government as having contributed to the new judiciary map that has since been approved and implemented.     

A suggestion of a new measure of importance of system components

In this paper we suggest a new measure of the importance of a component in a coherent system and derive some of its properties. The measure is for the case of components not undergoing repair proportional to the expected reduction in the remaining system life-time due to the failure of the component. This measure seems to be a useful guide during the system development phase as to which components should receive the most urgent attention in order to increase the system's expected life-time. The properties of the measure are compared with the ones of a measure suggested by Barlow and Proschan [1].     

确定双指数曲线参数初始值的循环搜索法

提出了在最小二乘意义下用 Gauss-Newton法拟合双指数曲线时 ,充分利用观测值确定参数初始值的一种算法——循环搜索法 .据此可编制一个能自动拟合 2 0种单、双指数曲线中指定曲线的 Qbasic程序 .并成功地以多个模型为例对此进行了验证     

结构方程模型应用陷阱分析

结构方程模型近几年在我国心理学、管理学应用研究领域得到越来越多的应用,但部分应用者因其对其基本原理理解不够透彻导致误用或错用这种重要统计手段。本文通过结合实证研究实例对一些常见应用错误(问题)的分析揭示结构方程模型的原理,以期帮助应用者避免应用陷阱、提高实证研究水平。     

Invertibility of the Difference of Idempotents

We study conditions equivalent to the invertibility of f -g when f and g are idempotents in a unital ring, and give applications to bounded linear operators in Banach and Hilbert spaces. In the setting of rings we are able to show that many conditions previously linked to finite dimensionality, rank equalities, norm topology of bounded linear operators or to properties of C *-algebras can be in fact proved by simple algebraic arguments.     

Categories of models of R-mingle

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic R-mingle to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics.     

Asymptotic behaviour of bounded solutions of a class of higher-order neutral dynamic equations

In this paper, necessary and sufficient conditions for the asymptotic behaviour of all bounded solutions of a class of nonlinear higher-order neutral dynamic equations are stated related to various ranges of the coefficient associated with the neutral part, in one of which the coefficient is allowed to oscillate and not tend to zero asymptotically. The new results improve and generalize the known results stated for difference equations and differential equations, and answer some problems left open for the case for arbitrary time scales. Some certain examples, which the results in the literature fail to deliver an answer to, are given to illustrate the applicability and significance of the new results.