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.     

类比法讨论旋转带电体的磁矩

由刚体转动惯量计算法则类比推导出旋转带电体磁矩的平行轴定理、垂直轴定理及中心矩定理,并举例说明其应用。     

虚时间步长法的狄拉克海难

通过用虚时间步长法(ITS)演化由Dirac方程导出的Schrdinger-like方程得到了Fermi海和Dirac海中12C分离的单粒子能谱,避免了出现狄拉克海难。将ITS方法直接用于求解Dirac方程,会导致单粒子能谱只能演化到狄拉克海中。研究发现,通过将Dirac方程转化为等效的Schrdinger-like方程,从正无穷延伸到负无穷的单粒子能谱可以分别在Fermi海或Dirac海中通过ITS演化而获得。利用ITS方法演化等效的Schrdinger-like方程得到了与常规Shooting方法相同的结果,此事实证明了该算法的可行性、实用性及可靠性,同时消除了能否将ITS方法应用于描述相对论系统的质疑。     

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.     

利用差分方程巧解高等代数中的一些问题

主要利用差分方程巧妙的解决了高等代数中矩阵的乘方与行列式的计算.     

A Systematic Evaluation and Comparison Between Exploratory Structural Equation Modeling and Bayesian Structural Equation Modeling

In this study, we contrast two competing approaches, not previously compared, that balance the rigor of CFA/SEM with the flexibility to fit realistically complex data. Exploratory SEM (ESEM) is claimed to provide an optimal compromise between EFA and CFA/SEM. Alternatively, a family of three Bayesian SEMs (BSEMs) replace fixed-zero estimates with informative, small-variance priors for different subsets of parameters: cross-loadings (CL), residual covariances (RC), or CLs and RCs (CLRC). In Study 1, using three simulation studies, results showed that (1) BSEM-CL performed more closely to ESEM; (2) BSEM-CLRC did not provide more accurate model estimation compared with BSEM-CL; (3) BSEM-RC provided unstable estimation; and (4) different specifications of targeted values in ESEM and informative priors in BSEM have significant impacts on model estimation. The real data analysis (Study 2) showed that the differences in estimation between different models were largely consistent with those in Study1 but somewhat smaller.     

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.