浅谈射影几何的优越性

从三个方面阐述了运用射影几何学中有关原理解决问题具有一定的优越性:可使证明过程简化;揭示内在联系;发现新结论,并举例说明该观点.     

Validity and reliability of the Very Short form of the Physical Self-Inventory among Turkish adolescents

The study aimed to test the validity and reliability of the Very Short form of the Physical Self-Inventory (PSI-VS) among a sample of 635 Turkish adolescents. These adolescents have completed the 12 original items of the PSI-VS, plus a positively worded reformulation of the single reverse-keyed item of the physical attractiveness subscale. A series of confirmatory factor analyses was used to examine the psychometric properties of the original and modified versions of the PSI-VS. Findings revealed superior psychometric properties with the modified version than with the original set of items. The modified version was thus subsequently used to examine its factor structure invariance across sexes, age groups and sport practice involvement. Results not only report that this version was fully invariant across, but also that latent means were significantly different across sexes and sport practice involvement. In sum, the Turkish modified version of the PSI-VS presents acceptable psychometric properties and may be used to repeatedly and/or intensively assess participants’ physical self-perceptions in the context of sport and exercise interventions.     

What are the Conditions Associated with Subscore Added Value Noninvariance? Implications for Improving Subscore Interpretation Fairness

Subscore added value analyses assume invariance across test taking populations; however, this assumption may be untenable in practice as differential subdomain relationships may be present among subgroups. The purpose of this simulation study was to understand the conditions associated with subscore added value noninvariance when manipulating: (a) subdomain test length, (b) differences in subgroup mean ability, and (c) subgroup differences in intersubdomain correlations. Results demonstrated that subscore added value was noninvariant for 24–100% of replications (depending on subdomain test length) when the subgroup difference in intersubdomain correlation was equal to .30. To examine if this condition was met in practice, applied invariance analyses of three operational testing programs were conducted. Across these datasets, noninvariant subscore added value was present for some subdomains across sex and ethnic subgroups. Overall, these results indicate that subscore added value noninvariance is largely driven by differential intersubdomain correlations among subgroups, which may be present in some operational testing programs.     

一阶微分形式不变性在课堂教学中的妙用

通过举例说明使用一阶微分形式不变性对帮助学生理解凑微分积分法、多元复合函数求导、求多元复合函数的高阶偏导等内容,简化解题过程具有良好的作用     

用光子模型讨论多普勒效应

本文用光子模型来讨论多普勒效应及相位不变性,与波动法有殊途同归的效果.     

Cross-Level Invariance in Multilevel Factor Models

When modeling latent variables at multiple levels, it is important to consider the meaning of the latent variables at the different levels. If a higher-level common factor represents the aggregated version of a lower-level factor, the associated factor loadings will be equal across levels. However, many researchers do not consider cross-level invariance constraints in their research. Not applying these constraints when in fact they are appropriate leads to overparameterized models, and associated convergence and estimation problems. This simulation study used a two-level mediation model on common factors to show that when factor loadings are equal in the population, not applying cross-level invariance constraints leads to more estimation problems and smaller true positive rates. Some directions for future research on cross-level invariance in MLSEM are discussed.     

Testing measurement invariance of PISA 2015 mathematics,science, and ICT scales using the alignment method

This study investigates measurement invariance of the mathematics, science, and ICT scales across the 47 countries that participated in the PISA 2015 ICT Familiarity Questionnaire. Knowing whether the same constructs and measurements can be reliably compared across countries constitutes an important goal. The Alignment method is employed to test the measurement invariance of the three scales. The results show that mathematics and science scores are highly invariant and can be used to compare countries, whereas the ICT scale is mostly non-invariant and cannot be used to reliably compare ICT means across all participating countries. Implications and limitations are discussed.     

C_q(D)上扩展型广义块Pick矩阵的秩不变性

利用块Toeplitz向量方法,证明同一个矩阵值Carathéodory函数的扩展型广义块Pick矩阵的秩重合于具有秩不变性的块Toeplitz矩阵的秩,从而证明了该类型的广义块Pick矩阵的秩不变性.     

Development and validation of scales to measure environmental responsibility,character development,and attitudes toward school

This investigation examines the use of structural equation modeling (SEM) procedures to develop and validate scales to measure environmental responsibility, character development and leadership, and attitudes toward school for environmental education programs servicing middle school children. The scales represent outcomes commonly of interest to environmental education programs and also to after‐school and positive youth development activities. First, we developed the scales using confirmatory factor analysis (CFA) and then we used multi‐group longitudinal CFA to cross‐validate the model with data collected before participation in the environmental education program, immediately after the program, and three months later. The results support a three‐factor model, producing three scales that appear to be valid and reliable.     

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.