一类高阶泛函微分方程多个周期解的存在性

利用重合度理论,研究一类高阶泛函微分方程周期解存在性的问题,获得了这类方程至少存在两个周期解的结果,并通过两个数值例子表明所获结果的有效性.     

非线性二阶方程周期边值问题解的存在性

在常微分方程理论中,非线性常微分方程周期边值问题是比较重要的数学问题,由于在人们生活中普遍存在着周期现象,所以研究这类问题具有比较重大的理论价值和实际意义.现今,由于科技不断进步,尤其是非线性泛函理论的不断运用,人们开始用它来进行边值问题的研究.在Banach空间中对非线性常微分方程的多解存在性进行研究.     

Emphasis on emotions in student learning: Analyzing relationships between overexcitabilities and the learning approach using Bayesian MIMIC modeling

The aim of this study is to investigate interrelationships between overexcitability and learning patterns from the perspective of personality development according to Dabrowski’s theory of positive disintegration. To this end, Bayesian structural equation modeling (BSEM) is applied which allows for the simultaneous inclusion in the measurement model of all, approximate zero cross-loadings and residual covariances based on zero-mean, small-variance priors, and represents substantive theory better. Our BSEM analysis with a sample of 516 students in higher education yields positive results regarding the validity of the model, in contrast to a frequentist approach to validation, and reveals that overexcitability – the degree and nature of which is characteristic of the potential for advanced personality development, according to Dabrowski’s theory – is substantially related to the way in which information is processed, as well as to the regulation strategies that are used for this purpose and to study motivation. Overexcitability is able to explain variations in learning patterns to varying degrees, ranging from weakly (3.3% for reproduction-directed learning for the female group) to rather strongly (46.1% for meaning-directed learning for males), with intellectual overexcitability representing the strongest indicator of deep learning. This study further argues for the relevance of including emotion dynamics – taking into account their multilevelness – in the study of the learning process.     

基于互联网的常微分方程数值解法的可视化设计

利用Microsoft Visual J＋＋6.0作为实验开发平台,采用Java语言及Applet嵌入网页技术,选择预估-校正法、龙格-库塔相结合的数值算法,实现了基于互联网的常微分方程数值解法的可视化,并通过实例演示该实验设计的各功能,包括用户对相关原理学习、数据的录入、修改、函数识别、常微分方程的求解、绘图及打印等.     

广义变系数Kadomtsev-Petviashvili方程的孤立子解

讨论了广义变系数Kadomtsev-Petviashvili方程.首先假设存在孤波解的形式,然后利用符号计算求得其孤立子解.     

求一类Riccati微分方程通解的分项组合法

讨论了一类Riccati微分方程的通解,得到了它可以使用分项组合法的充要条件,为寻求Riccati微分方程的通解提供了有效的方法,并给出了它的应用.     

固定三角形内插入一点的测边网条件式分析

固定三角形内插入一点的测边网,按条件平差法进行平差计算时,可列出图形条件方程式,也可列出固定角条件方程式,文章分析了两种条件式之间的关系,从理论上证明了不同条件式的替代方法,从而使平差计算更为简单.     

新型城镇化小学生人数变化规律的研究——以上犹县为例

通过建立差分方程模型,研究在新型城镇化快速发展的背景下,小学在校学生人数的变化规律.采用上犹县2003-2008年的相关数据,得到了在校生人数变化规律,并对上犹县后几年的小学学生人数做出了预测,为政府进行城镇新区教育园区的建设提供了一些参考.     

Should Regularization Replace Simple Structure Rotation in Exploratory Factor Analysis?

Exploratory factor analysis (EFA) is an important tool when the measurement structure of psychological constructs is uncertain. Typically, factor rotation is applied to obtain interpretable results resembling a simple structure. However, an overwhelming multitude of rotation techniques is available of which none is unequivocally superior. Recently, regularization has been suggested as an alternative to factor rotation. In two simulation studies, we addressed the question if regularized EFA is a suitable alternative for rotated EFA. We compared their performance in recovering predefined factor loading patterns with varying amounts of cross-loadings. Elastic net regularized EFA yielded estimates comparable to rotated EFA. For complex loading patterns, both rotated and regularized EFA tended to underestimate cross-loadings and inflate factor correlations, but regularized EFA was able to recover loading patterns as long as a subset of items followed a simple structure. We conclude that regularization is a suitable alternative to factor rotation for psychometric applications.     

内河港口基础设施对区域经济增长的影响

为探讨内河港口基础设施对区域经济增长的影响,以我国四大水系28个主要内河港口为研究对象,构建结构方程模型,从港口需求、港口供给和港口价值增值活动等三大因素出发进行分析。实证结果显示:港口需求的不断增长会促进区域经济的发展,同时通过港口价值增值活动可以间接推动区域经济发展。提出我国内河港口发展的对策建议。