多维对称随机变量分布函数的充要条件

讨论了多维对称随机变量的若干性质,阐明其分量仍是对称随机变量,在此基础上,进一步给出多维对称随机变量分布函数的一个充分必要条件.     

离散型随机变量密度函数的定义与探讨

使用“δ函数”定义离散型随机变量的密度函数，寻求离散型随机变量与连续型随机变量的统一处理方法．基于离散型随机变量密度函数的定义．其一维随机变量函数的密度函数以及多维随机变量的边缘密度等，均可直接利用连续型随机变量的相关结论．     

一类由一维概率密度函数构造多维概率密度函数的方法

将文献[1]给出的由一维连续型随机变量的概率密度函数构造二维连续型随机变量的概率密度函数的方法,推广为由一维连续型随机变量的概率密度函数构造三维连续型随机变量的概率密度函数的情况,并作出了证明和举例说明.说明利用本文的方法构造多维概率密度函数,其方法简单易行.     

基于主成分分析的水质评价方法

主成分分析法能够在保证原始数据信息损失最小的情况下,以少数的综合变量取代原有的多维变量,使数据结构大为简化,并且客观地确定变量权数,避免了主观随意性.应用主成分分析法对长春市地面水环境进行评价,且与其它评价方法相比较,结果显示主成分分析法更客观且指导性较强,是一种行之有效的水质评价方法.通过主成分分析进行水质评价,可为水资源规划、利用、开发和环境系统优化提供更为客观的参考依据.     

多维指数分布

本文讨论了服从多维指数分布的随机向量的各分量间的独立性与相关性，证明了诸分量相互独立的充分必要条件是它们两两无关；并证明了多维指数分布类在弱收敛下的封闭性．     

在《概率论与数理统计》教学实践中反思《高等数学》教学

通过对概率论与数理统计课程的教学实践进行深入挖掘,从内容和思想方法两个方面探索了《高等数学》与《概率论与数理统计》课程之间的关系.内容方面主要体现在离散型随机变量与无穷级数、连续型随机变量和积分、最大似然估计和最值理论等方面,而思想方法方面主要体现在利用微积分的重要思想建立概率统计中的相关概念和相关理论.通过对两门课程的关系进行梳理,一方面可以更好的进行概率统计课程的教学,同时也可以为高等数学教学提供有益的借鉴.     

电视广告效果预测模型

本文通过引入电视广告影响力指数 ,利用主成分分析和多维偏好线性规划方法 ,结合广告理论 ,构建了电视广告效果的预测模型 ;对模型的基本原理和求解方法作了分析和讨论 ,并通过一真实的广告案例对模型进行了检验 .     

基于Adaptive-Lasso的本科成绩统计分析

本文主要研究了合肥工业大学数学学院数学专业学生的本科成绩状况,应用多元线性统计方法,探讨了前期所有课程成绩对后期成绩的影响.首先对前期课程进行主成分分析,并采用逐步回归方法建立了后期成绩与主成分之间的回归模型.其次,采用Adaptive-Lasso方法建立后期成绩与前期课程成绩间的Adaptive-Lasso回归模型.最后,对以上模型进行对比分析.研究表明,基于Adaptive-Lasso方法的主成分回归模型能很好地拟合后期成绩,并对后期成绩情况给出合理的解释.     

主分量回归在骨龄系数测定中的应用

运用主成分分析法提取了十二种足骨发育等级的主分量,接着进行主分量回归,然后再进行分年龄段回归,可得用于年龄鉴定的骨龄系数表。     

阵列代数与高阶矩

阵列代数与高阶矩李作发，罗玉芳（武汉测绘科技大学，武汉４３００７０）在概率中，ｎ维随机变量的协方差阵表达了各分量围绕它们的数学期望的疏散程度，以及各分量间相关程度的一组数字特征．我们将利用阵列代数引进ｔ个ｎ维随机向量的各分量间相关程度的ｔ阶相关中心矩...     

The Largest Class of Closed Convex Valued Multifunctions for which Effros Measurability and Scalar Measurability Coincide

This paper deals with the comparison of Effros measurability and scalar measurability for multifunctions whose values lie in C(X), the set of closed convex subsets of a normed linear space X. An introductory counter-example shows that, on C(X), the Effros measurability is strictly stronger than the scalar measurability. Then, we introduce the notion of countably supported subspace of C(X). After some preparatory results and examples about this class of convex subsets, we show that on an analytic countably supported subspace of C(X), the Effros and the scalar -fields coincide. Conversely, we show that, if on a subspace of C(X), nonnecessarily analytic, the Effros and scalar -fields are identical, then is countably supported. This leads us to exhibit and study a wide class of subspaces of C(X) both countably supported and analytic. At last, we compare our results with the already existing ones and we briefly show how our main results can be extended to the case where X is a locally convex vector space.     

The improved LaSalle-type theorems for stochastic functional differential equations

The main aim of this paper is to improve some results obtained by Mao [X. Mao, The LaSalle-type theorems for stochastic functional differential equations, Nonlinear Stud. 7 (2000) 307-328]. Our new theorems give better results while conditions imposed are much weaker than in the paper mentioned above. For example, we need only the local Lipschitz condition but neither the linear growth condition nor the bounded moment condition on the solutions. To guarantee the existence and uniqueness of the global solution to the underlying stochastic functional differential equation (SFDE) under the weaker conditions imposed in this paper, we establish a generalised existence-and-uniqueness theorem which covers a wider class of nonlinear SFDEs as demonstrated by the examples discussed in this paper. Moreover, from our improved results follow some new criteria on the stochastic asymptotic stability for SFDEs.     

方差分量谱分解估计的几个性质

对于线性混合模型中方差分量的估计，虽有多种方法，但一般情况下只有方差分析估计和谱分解估计有显式解，本文就线性混合模型中含两个方差分量的情形，对方差分析估计和谱分解估计进行了比较，证明了在一些条件下两个估计的方差相等，由此推出谱分解估计也具有方差分析估计的某些优良性．文末用实例进一步说明了文中的结果．     

关于凸子集和（绝对）收缩核

讨论了线性度量空间中凸子集在什么情况下为该空间的收缩核，以及在什么情况下为绝对收缩核。     

����Adaptive-Lasso�ı��Ƴɼ�ͳ�Ʒ���

??In this paper, the multivariate linear statistical method is applied to research the undergraduate grades of students from the school of mathematics in Hefei University of Technology, and explore the impact on the later achievement by the early stage of achievement from all undergraduate courses. First, we get the main components from the previous courses by principal component analysis, then construct a linear regression model between the later achievement and main components by the stepwise regression method. Next, a linear regression model between the later achievement and the early stage of achievement from all undergraduate courses is constructed by Adaptive-Lasso method. Finally, comparative analysis is performed for the result of the above models. The research shows that the principal component regression model based on the Adaptive-Lasso method can well fit the later achievement, and give a reasonable explanation for the later academic performance.     

A characterization of constant-time linear control systems satisfying the Pontryagin maximum principle

Using the subdifferential, we extend the main characterization of Banach linear systems satisfying the Pontryagin maximum principle, given in our previous paper (Ref. 1), to the case whenF andX are locally convex spaces and the norm ofF is replaced by an arbitrary continuous convex functionalh onF.     

Complete spaces and zero-one measures

It is the purpose of this paper to characterize the complete spaces in the sense of [6] by measure-theoretic properties. Let (X,) be a measurable space and let be a subpaving of satisfying certain closure properties, then X is-complete iff every 0,1-valued-regular measure on is a Dirac measure. In particular, we obtain Hewitt's well-known theorem that a completely regular space X is realcompact iff every 0,1-valued Baire measure on X is a Dirac measure. The main tool for our investigations is an extension theorem for measures due to Topsoe [10].     

Linear Invariance of Locally Biholomorphic Mappings in Hilbert Spaces

We study the notion of linear invariance on the unit ball of a complex Hilbert space X and we obtain some connections between the norm-order of a linear invariant family (L.I.F.) and the quasi-convexity. Also, we give some results concerning the radius of univalence of some linear invariant families. Finally we find the norm-order of normalized convex mappings in the unit ball of X and some lower bounds for the radius of convexity and the radius of starlikeness for a certain L.I.F. in X .     

An asymptotic formula for the number of prime solutions for multivariate linear equations

In this paper, we study the multivariate linear equations with arbitrary positive integral coefficients. Under the Generalized Riemann Hypothesis, we obtained the asymptotic formula for the linear equations with more than five prime variables. This asymptotic formula is composed of three parts, that is, the first main term, the explicit second main term and the error term. Among them, the first main term is similar with the former one, the explicit second main term is relative to the non-trivial zeros of Dirichlet L-functions, and our error term improves the former one.     

基于主成分回归的杭州市PM2.5含量的综合分析

为探究杭州市PM2.5含量与其他指标之间的关系,搜集杭州市2019年的AQI指数和AQI 6项指标进行分析.首先通过相关分析揭示PM2.5与其余5项指标的相关性,发现各指标与PM2.5均呈线性关系,又因为其余5项指标之间存在显著的线性相关性,故自变量之间存在多重共线性.为了消除多重共线性的影响,对这5项指标提取主成分,再基于主成分分析做回归分析.最后对模型进行统计诊断,按照一定标准筛选出原始数据中的强影响点,删除强影响点后得到最终模型.