一般洛伦兹变换的推导

本文根据相对性原理和间隔不变性,并借助Maple数学软件给出了一般洛伦兹变换的推导.     

Testing Factorial Invariance in Multilevel Data: A Monte Carlo Study

Testing factorial invariance has recently gained more attention in different social science disciplines. Nevertheless, when examining factorial invariance, it is generally assumed that the observations are independent of each other, which might not be always true. In this study, we examined the impact of testing factorial invariance in multilevel data, especially when the dependency issue is not taken into account. We considered a set of design factors, including number of clusters, cluster size, and intraclass correlation (ICC) at different levels. The simulation results showed that the test of factorial invariance became more liberal (or had inflated Type I error rate) in terms of rejecting the null hypothesis of invariance held between groups when the dependency was not considered in the analysis. Additionally, the magnitude of the inflation in the Type I error rate was a function of both ICC and cluster size. Implications of the findings and limitations are discussed.     

教育技术学实验研究工具的跨时测量恒等检测

基于跨时测量恒等视角与知识图谱分析,文章对我国教育技术学较常探讨的变量"自我效能"量表进行了工具检测,并以四川省某小学三年级的197名学生为被试,前后测时间间隔为6个月。文章采用结构方程模型的跨时测量恒等检验程序,依序针对不同恒等程度的模型进行比较,结果发现:数学自我效能量表不符合完全的度量恒等,放宽两道题项的参数限制后可达到部分的纯量恒等,但仍不及严格恒等的要求;跨时测量恒等性的结果会影响配对样本t检验的结论。基于此,文章提出建议:为了提升实验的内在效度,较长时间的实验研究应纳入工具的跨时测量恒等性检验。     

量子场论中的时空特性分析

经典量子力学中粒子的基态场值,对应于量子场论中的真空期待值,场值的非零和零值,直接与背景空间的平坦性有关.当我们把坐标系建于运动的微观粒子之上时,坐标系的运动状态,又刚好与时空的平坦性相联系.匀速动的坐标系时空均匀而对称,加速运动的坐标系时空不均匀、不对称,有了这种联系,我们对量子场论中规范不变化的时空特征和真空对称性破缺机制就可做出合理的解释.     

关于力学系统的对称性

力学系统有各种对称性。该文就完整力学系统举例说明各种对称性之间的关系。     

Mathematical equivalence assessment: Measurement invariance across six countries

Within mathematics education research, there has been a strong focus on students’ understanding of mathematical equivalence because of its key role in the development of mathematics skills. One of the most frequently used tools to assess students’ understanding of equivalence has been the Mathematical Equivalence Assessment (MEA) (Rittle-Johnson et al., 2011). In this study, we investigate for the first time the cross-cultural measurement invariance of an adaptation of the MEA. This included a sample (N = 2760) of students aged 8–12 years old from China, England, New Zealand, South Korea, Turkey, and US to examine whether the same construct is being measured across all countries. Configural and partial scalar invariance was established for a two-factor, 11-item version of the adapted MEA. There were significant mean differences across countries, with students from China performing better and students from New Zealand performing worse than the rest of the sample.     

Teachers' attitudes and self-efficacy on implementing inclusive education in Japan and Finland: A comparative study using multi-group structural equation modelling

This study aims to explore relationships between teachers' attitudes, self-efficacy, and background variables regarding inclusive education by using a sample of 359 Japanese and 872 Finnish teachers. A multi-group structural equation modelling was conducted to find similarities and differences in how the background variables predict teachers' attitudes and self-efficacy. Experience in teaching students with disabilities had a positive effect on teachers' attitudes and self-efficacy in both countries. However, teachers' teaching career and the amount of inclusive education training affected them differently in Japan and Finland. The findings could be used to improve inclusive education training for pre- and in-service teachers.     

物理规律(方程)的对称性、协变性、规范不变性

较为详细地论述了物理规律的对称性、协变性、规范不变性三之间的关系及其应用，揭示了物理规律的对称性在科研中所具有的重要作用。     

Rasch模型项目参数不变性的验证研究

Rasch模型具有被试参数和项目参数相互独立的性质,即被试能力与项目难度无关。本研究以某年度大学入学考试数学学科的实测成绩数据为例,在随机抽样、不同性别抽样、不同水平群体抽样等条件下,对Rasch模型项目参数不变性进行了验证研究。研究表明:Rasch模型项目参数不变性验证的前提条件较为严格,需要排除诸多干扰因素的影响;Rasch模型项目参数不变性的验证存在一定的误差,无法实现与理论一致的"不变性";Rasch模型项目参数不变性没有统一的标准,需依据实际问题确定。     

相空间中Hamilton系统的Noether对称性、Lie对称性和形式不变性

For the non-conservative holonomic Hamiltonian systems in phase space, the definition and criteria of the form invariance of the generalized Hamilton canonical equations were given. The relations among the form invariance, Noether symmetry and Lie symmetry were studied. The theory of the form invariance for the conservative holonomical systems was worked out. An example was given to illustrate the results.