二阶延迟微分方程单支θ-方法的渐近稳定性

考虑二阶微分方程单支θ-方法的稳定性质,证明当θ=1时数值方法将保持此时滞系统解析解的稳定性。     

一阶线性偏微分方程求解的教学方法新探

通过常微分方程与偏微分方程之间的关系我们寻找到一种特殊的规范变换,通过此变换将复杂的偏微分方程的求解转化为可积分的偏微分方程(含参数的常微分方程)的求解.     

Lambert W函数性质及其应用

介绍了Lambert W函数的代数及图像性质,如该函数的级数展开式、微分及函数在复平面的图像等。总结了其在数学、物理、化学和生物等领域的应用情况。     

一类奇异半线性椭圆型方程的Dirichlet问题

本文研究了如下方程解的存在性{-Δu-uu/|x2|=λ|u|q-1+f(x,u),x∈Ω;u=0,x∈Ω.其中ΩRN(N≥3)是包含原点的有界区域,λ>0,2相似文献   

基于劳伦兹系统的交通模型近似解

通过代换,将基于劳伦兹系统构建的交通流方程组转换成非线性方程,分别利用匹配渐近法和同伦分析法研究非线性交通模型,讨论当参数σ= t n/t v ?1时的新情况,得到非线性方程的两种解析近似解,为分析车头变化情况提供理论依据。     

关于柯西方程的一点注记

若函数f在一点连续,则柯西方程的解是唯一的.在此假设下,要求函数f的一部分点满足柯西方程,证明了解的唯一性,并推广已知的结论.     

广义Boussinesq方程的KAM环面(英文)

考虑周期边界下具有非线性项f(u)=u3的一维广义Boussinesq方程u tt-u xx+(f(u)+u xx)xx=0.首先,将上述方程转化为一个哈密顿系统,并将该系统在线性算子的特征基上展开得到坐标形式下的哈密顿系统.鉴于切频与法频之间复杂的共振关系,考虑一类具有特殊结构的拟周期解.其次,验证了哈密顿向量场的正则性,并对四次项进行规范化,从规范形中可以得到无穷维KAM定理所要求的非退化和非共振条件.利用一个KAM定理证明与方程等价的无穷维哈密顿系统存在许多有限维不变环面,故原方程有许多小振幅的拟周期解.     

Cognitive load in algebra: element interactivity in solving equations

Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side only. In an experiment, middle school students (N?=?71) were randomly assigned to the balance and inverse methods to complete a pre-test, an acquisition phase and a post-test. Pre-test and post-test comparisons found that the inverse group outperformed the balance group for those equations that involved high element interactivity. Instructional efficiency measures further confirmed that the balance method imposed higher cognitive load. The inverse method was capable of reducing cognitive load due to the interacting elements.     

Revisiting Zhang’s scale of transactional distance: refinement and validation using structural equation modeling

Transactional distance has been defined as barriers to students’ engagement with learning in the online environment. This research updates Zhang’s (2003) scale of transactional distance, which quantified the extent of the barriers, in light of the massive changes in today’s web-based learning environment. The resulting revised scale of transactional distance (RSTD) is a parsimonious version with 12 elements (compared to 31 original) that measure the transactional distance between student and teacher, student and student, and student and content. The RSTD has excellent factorial validity and reliability, yields better fit statistics, and is easier and less time-consuming to apply. The transactional distance values are unique predictors of student satisfaction, which is correlated to learning and persistence (a major concern with massive open online courses). This information can form the basis for a systematic approach to improving the design of today’s contemporary open, flexible, distance education courses and thus serve as a valuable tool for researchers and educators alike.     

Teacher change beliefs: validating a scale with structural equation modelling

The objectives of the study were to validate a substantiated Teacher Change Beliefs Model (TCBM) and an instrument to identify critical components of teacher change beliefs (TCB) in Malaysian secondary schools. Five different pilot test approaches were applied to ensure the validity and reliability of the instrument. A total of 936 teachers from 47 high-performing secondary schools completed the survey. Structural equation modelling was applied to test the models. Exploratory factor analysis was employed to identify the underlying factors, whereas confirmatory factor analysis was applied to test the measurement models. The analysis yielded a three-factor TCBM: (1) discrepancy, (2) efficacy and (3) principal support. The results demonstrated a good fit of the model: normed χ² = 3.156, Tucker-Lewis Fix Index = .987, Comparative Fix Index = .991 and Root Mean Square Error of Approximation = .048. The results also provided evidence for convergent validity, discriminant validity and construct reliability. The TCBM is an empirically tested model derived in a local Malaysian cultural education setting. It provides direction for practitioners in planning and designing training programmes of change management for school principals in the enhancement of TCB among teachers in schools. Besides, Teacher Change Beliefs Scale is a promising and welcome tool for both practitioners and researchers. With only nine items, it is easy to administer and not time-consuming.