矩阵秩求解方法的推广

矩阵的秩的概念及有关理论是高等代数、线性代数课程中十分重要的教学内容。本文通过引入三个相关引理,推导出矩阵秩的一个新的判别方法。     

中国宏观外债适度规模研究

本文通过将BP网络和非线性方程组求解结合起来，提出了一种求解一般抽象非线性方程组的算法，并将其应用于中国宏观外债模型。     

浅谈对修正牛顿法的一点改进

为进一步拓展修正牛顿法在求解非线性方程组的适用范围,引入阻尼因子以克服雅克矩阵的奇异性。本文先简要介绍修正牛顿牛顿法的基本原理,再给出改进算法,并通过实验实例说明其有效性。     

拉格朗日乘数法中方程组的解法

拉格朗日乘数法依极值必要条件得到的方程组一般都是非线性的。本文主要介绍此类方程组的解法。     

Excel在求解方程组中的应用

Excel具有强大的计算和分析数据能力,在求解线性方程组、非线性方程组方面起着积极的作用。     

加深对麦克斯韦方程组的理解

麦克斯韦方程组是电磁理论的核心方程组，通过对麦克斯韦方程组的建立、麦克斯韦方程组的形式即微分形式、积分形势以及麦克斯韦方程组所蕴涵的物理的美即简单美、和谐美、对称美和统一美进行简要介绍，从各个角度加深对麦克斯韦方程组的理解。     

二维随机变量的分布函数

概率论与数理统计是学习现代科学技术的重要理论基础,同时它也是考研必考科目之一,在教学过程中,我遇到了这样一道题目,本文由这道概率习题联想到了几个问题:二维随机变量的分布函数是否唯一;三元三次方程组解的唯一性.     

创新性线性代数课程的教学探究

针对线性代数教学现状,构建了以线性方程组为主线的、各章节紧密相关的创新性理论体系,并以行列式为案例,讲述了行列式的产生的知识背景、行列式的性质的几何解释,并以前后呼应的方式导出了Cramer法则,并把计算机软引入到实例分析当中,整个章节融合了创新思维和创新能力的培养,遵从了从理论到实践再到理论辩证规律。     

环域上的二阶椭圆型方程组的正径向解

基于乘积锥上不动点指数的乘积公式以及经典的不动点指数理论,我们获得了一类二阶椭圆型方程组正径向解的存在性。     

交通网络中动态OD矩阵反推算法研究

文章根据极大熵基本原理并运用排列组合理论推导出OD矩阵反推的极大熵模型;然后用拉格朗日乘子法求得该模型的非线性方程组,并运用Newton算法对此非线性方程组求解,得到动态OD估计矩阵。最后,在实例应用中,应用此模型和文章给出的模型解法取得了令人满意的结果。     

ON ERROR CORRECTION MODELS: SPECIFICATION, INTERPRETATION, ESTIMATION

Abstract. Error Correction Models (ECMs) have proved a popular organising principle in applied econometrics, despite the lack of consensus as to exactly what constitutes their defining characteristic, and the rather limited role that has been given to economic theory by their proponents. This paper uses a historical survey of the evolution of ECMs to explain the alternative specifications and interpretations and proceeds to examine their implications for estimation. The various approaches are illustrated for wage equations by application to UK labour market data 1855–1987. We demonstrate that error correction models impose strong and testable non-linear restrictions on dynamic econometric equations, and that they do not obviate the need for modelling the process of expectations formation. With the exception of a few special cases, both the non-linear restrictions and the modelling of expectations have been ignored by those who have treated ECMs as merely reparameterisations of dynamic linear regression models or vector autoregressions.     

Multiple solutions in systems of functional differential equations

This paper proposes conditions for the existence and uniqueness of solutions to systems of linear differential or algebraic equations with delays or advances, in which some variables may be non-predetermined. These conditions represent the counterpart to the Blanchard and Kahn conditions for the functional equations under consideration. To illustrate the mathematical results, applications to an overlapping generations model and a time-to-build model are developed.     

浅谈《高等代数》中的问题探究

任何一门学科的教学都有其具体的教学目标,而现代大学教育更多地强调学生的综合素质的发展。如何将大学教学的基本原则贯穿于高等代数的教学中,使学生在获取专业理论知识的同时,又得到多种能力的提高,实现真正意义上的素质教育目标,在《高等代数》课程的教学中作了一些尝试。     

关于常微分方程教学探索

常微分方程是高等教育的核心基础课程的一部分重要内容,是进一步学习泛函分析,偏微分方程,稳定性理论和控制论等方向的入门学科,具有很强的理论性与应用性的背景,因此,对该部分的教学的教师有责任进行教学设计与探索,以期取得令人满意的教学效果。     

一类非单调二元算子方程解的存在唯一性

利用锥理论和非对称迭代方法,讨论了一类非单调二元算子方程解的存在唯一性,给出了迭代序列收敛于解的误差估计,所得结果是某些已知结果的改进和推广。     

Consumer credit and consumption forecasts

Recent advances in the theory of consumer behavior indicate that consumption may exhibit non-linear dynamics characterized by occasional surges. Building upon them, and taking explicitly into account the forward-looking nature of consumption, this paper argues that rising consumer debt can signal such surges, as well as the consumption underprediction which will occur if they are not taken sufficiently into account in forecasting. This insight is tested with and strongly confirmed by the Organization of Economic Cooperation and Developments forecasts for the USA. The results should be of interest not only to professional forecasters and policy-makers, but also to theoretical economists and econometricians who study non-linear dynamic models.     

A short history of algebraic statistics

In algebraic statistics, computational techniques from algebraic geometry become tools to address statistical problems. This, in turn, may prompt research in algebraic geometry. The basic ideas at the core of algebraic statistics will be presented. In particular, we shall consider application to contingency tables and to design of experiments.     

sk−p Fractional factorial designs in sb blocks

Draper and Guttman (1997) shows that for basic 2^k−p designs, p≥0, k − p replicates of blocks designs of size two are needed to estimate all the usual (estimable) effects. In this work, we provide an algebraic formal proof for the two-level blocks designs results and present results applicable to the general case; that is, for the case of s ^k factorial (p=0) or s ^k−p fractional factorial (p >0) designs in s ^b blocks, where 0<b<k− p, at least replicates are needed to clear up all possible effects. Through the theoretical development presented in this work, it can provide a clearer view on why those results would hold. We will also discuss the estimation equations given in Draper and Guttman (1997).  Research supported in part by the National Science Council of Taiwan, R.O.C., Grant No. NSC 89-2118-M110-010. Acknowledgement. The authors would like to thank the referee for very helpful comments.     

复变函数课程的对比教学法研究

复变函数主要研究复数域上的函数,是高等数学课程的延伸。本文阐述了复变函数和高等数学在理论体系上的异同,并强调其差异性。在复变函数的授课中,采用对比教学法,以加深学生对知识的理解,提高分析和解决问题的能力。     

On MLEs in an extended multivariate linear growth curve model

In this paper the extended growth curve model is considered. The literature comprises two versions of the model. These models can be connected by one-to-one reparameterizations but since estimators are non-linear it is not obvious how to transmit properties of estimators from one model to another. Since it is only for one of the models where detailed knowledge concerning estimators is available (Kollo and von Rosen, Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005) the object in this paper is therefore to present uniqueness properties and moment relations for the estimators of the second model. One aim of the paper is also to complete the results for the model presented in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005). The presented proofs of uniqueness for linear combinations of estimators are valid for both models and are simplifications of proofs given in Kollo and von Rosen (Advanced multivariate statistics with matrices. Springer, Dordrecht, 2005).