Hilbert空间中一类强伪压缩映射的不动点定理与路径收敛

研究了Hilbert空间中一类强伪压缩映射的不动点问题,提出了一个新的路径公式,得到了一个新的不动点存在定理和路径收敛性结果.给出了所得结果在变分不等式解存在性研究中的应用.     

数学分析中Jensen不等式由浅入深进行教学

不等式的证明一直是数学分析教学的重点和难点,运用Jensen不等式能使不等式的证明变得清晰明了.目前大多数学分析教材对Jensen不等式叙述零散且证明复杂繁琐不统一.在数学分析中由浅入深的系统学习离散型和积分型Jensen不等式,并利用凸函数的性质给出了这几种类型Jensen不等式的简单统一证明尤为重要.     

关于曲线凹凸性的讨论

函数曲线凹凸性定义不同形式,不仅是证明曲线凹凸性判定定理的理论依据,亦是导入凹凸函数性质所必须,借助定义一般及特殊形式,得到凹凸函数的重要性质,解决了有关著名不等式的证明问题．     

Reliability analysis of a two-dependent-unit parallel system with a standby unit

A parallel system with two active components and a cold standby unit is studied in this paper. The two simultaneously working components are dependent and the copula function is used to model their dependence. An explicit expression is obtained for the mean time to failure of the system in terms of the copula function and marginal lifetime distributions in two different cases As an application, numerical calculations are presented corresponding to two different copula functions and marginal lifetime distributions.     

探讨石油价格、粮食价格及汇率难经济成长率的影响分析

粮食与石油是人类生存与发展的基本资源,粮食危机与能源危机都将对经济成长有相当的影响。汇率升贬值亦面临物价稳定与经济成长之抉择。不同于过去文献大多探讨单一因素对经济成长率的影响,同时探讨实质油价、粮食价格及汇率对经济成长率的关系,分别探讨对于高收入与低收入不同经济结构的国家是否会有不同的影响。由实证结果得知,较多的分析采用PMG估计法较为有效。实质油价、汇率、粮食价格对经济成长率存在长期关系,且长期、短期的结果在影响的方向上有差异。若未同时考虑油价、粮食价格及汇率对经济成长率的影响,其所得到的结果将会产生偏差;且不同的经济体结构其实质油价、粮食价格与汇率对经济成长率的反应亦有所差异。故在探讨此议题时应同时考虑实质油价、粮食价格及汇率对经济成长率的影响,亦应对不同经济结构分别探讨其间的关系,始能得到更正确的分析。     

Euler函数性质在Mizar系统下的实现

在计算机上利用有限序列的理论性质给出了Euler函数在Mizar系统下的定义．给出了与Euler函数有关的一些定理和性质的证明。并实现了算术基本定理在Mizar系统下的实现．     

Detecting Misspecification in Mean Structures for Growth Curve Models: Performance of Pseudo R 2s and Concordance Correlation Coefficients

This study examined the performance of 4 correlation-based fit indexes (marginal and conditional pseudo R ²s; average and conditional concordance correlations) in detecting misspecification in mean structures in growth curve models. Their performance was also compared to that of 4 traditional SEM fit indexes. We found that the marginal pseudo R ² and average concordance correlation were able to detect misspecification in the marginal mean structure (average change trajectory). The conditional pseudo R ² and concordance correlation could detect misspecification when it occurred in the conditional mean structure (individual change trajectory) or in both mean structures. Compared to the SEM fit indexes, the correlation-based fit indexes were more robust to sample size but were less robust to data properties such as magnitude of population mean and measurement error. Theoretical and practical implications of the results and directions for future research are discussed.     

残差性质的探究

残差是回归分析中的重要概念。本文对残差的分布、性质做了一定研究,得出了其期望和方差,并否定了一种关于残差的分布的假定。     

有限群全形的计算

根据群的全形的定义及相关理论,设计出计算有限群全形的算法及程序,给出了剩余类加群全形的特殊算法及程序。     

一个有最佳常数因子的-3μ齐次半离散Hilbert型不等式

应用权函数,给出一个有最佳常数因子的-3μ齐次半离散Hilbert型不等式.同时给出它的等价式.