A five facets frame for the design of heuristics

The author suggested to distinguish between the ‘engineering approach’ and the ‘mathematical approach’ in connection with the design of heuristics. Stainton and Papoulias extended the scope by suggesting the ‘relational approach’. Based upon this extension, a five facets frame is presented here which is suggested to precede and accompany the ‘technical’ design of the heuristic. The facets are: coverage by participation, experience by doing, abstraction by structuring, extension by comparison, exploration by creativity.     

Mathematical programming in the Netherlands

Results of an exhaustive survey of mathematical programming in the Netherlands held in 1982 are presented and, where applicable, compared to a survey held in 1976. It appears that the growth rate has levelled off, that about half of the largest one hundred industrial firms in the Netherlands now apply MP and that the users are quite satisfied with LP programs except for input, output and documentation.     

The game for the speed of convergence in repeated games of incomplete information

We consider an infinitely repeated two-person zero-sum game with incomplete information on one side, in which the maximizer is the (more) informed player. Such games have value v _∞ (p) for all 0≤p≤1. The informed player can guarantee that all along the game the average payoff per stage will be greater than or equal to v _∞ (p) (and will converge from above to v _∞ (p) if the minimizer plays optimally). Thus there is a conflict of interest between the two players as to the speed of convergence of the average payoffs-to the value v _∞ (p). In the context of such repeated games, we define a game for the speed of convergence, denoted SG _∞ (p), and a value for this game. We prove that the value exists for games with the highest error term, i.e., games in which v _n (p)− v _∞ (p) is of the order of magnitude of . In that case the value of SG _∞ (p) is of the order of magnitude of . We then show a class of games for which the value does not exist. Given any infinite martingale 𝔛^∞={X _k }^∞ _k=1, one defines for each n : V _n (𝔛^∞) ≔E∑ⁿ _k=1 |X _k+1 − X _k|. For our first result we prove that for a uniformly bounded, infinite martingale 𝔛^∞, V _n (𝔛^∞) can be of the order of magnitude of n ^1/2−ε, for arbitrarily small ε>0. Received January 1999/Final version April 2002     

How do domains of knowledge integrate into mathematics teachers’ practice?

This study is a part of a research project that seeks to characterize the relationship between mathematics teachers’ knowledge and their practice. In this paper, we focus on identifying the characteristics of subject matter knowledge and pedagogical content knowledge that two teachers integrate in decisions they make about the introduction of specific mathematical content. Then, we examine the changes that arise in their classrooms as their plans are put in action. Data were obtained through audiotapes of several semi-structured interviews, through observations, and through videotapes. Although the two teachers in this study had similar backgrounds and experiences, our analysis shows differences in the characteristics of the domains of knowledge they integrated in their planning as well as differences in the adaptations that each made in the classroom. In this sense, this study contributes to better understanding the complexity of teachers’ professional practice.     

Exact tests in simple growth curve models and one-way ANOVA with equicorrelation error structure

We consider exact tests with several equicorrelation error structures and combination of equicorrelation covariance structures in simple growth curve model having single or multiple treatments and in one-way ANOVA model. Exact inferences using generalized p-values are obtained. Tests for equal treatment effects under equal equicorrelation error term and for unequal equicorrelation error terms are also developed. Two examples are given to illustrate the importance of our results. According to our findings, we would be better off dropping the assumption of equal variance when the heteroscedasticity is serious. Therefore, tests based on generalized p-values without the assumption of equal variance are much more powerful than tests with this assumption.     

A note on maximally repeated sub-patterns of a point set

We answer a question raised by Brass on the number of maximally repeated sub-patterns in a set of n points in R^d. We show that this number, which was conjectured to be polynomial, is in fact Θ(2^n/2) in the worst case, regardless of the dimension d.     

分析仪器标本实物学习平台构建及教学实践探索——以分光光度计为例

针对本科生在分析仪器学习中存在的困难,探索构建分析仪器实物学习平台,将抽象的仪器原理和功能学习实物化、具体化;以学习者为主体制作仪器标本和多媒体自学课件,激活了学生自身的学习、创新能力;经过4年的教学实践,说明新模式提高了学习效率和教学效果。     

工科非化学类专业物理化学的教学设计与实践

Based on the situation of China University of Petroleum (East China) and the students' training characteristics, we have explored the reasonable teaching design on the basis of combining the theory and features of physical chemistry course with the practices, to facilitate chemical knowledge acquisition in non-chemical engineering majors. Teaching reforms such as using a variety of teaching methods and evaluation modes were employed in oil & gas storage and transportation engineering major, which has received significant teaching results.     

开放式项目制教学在材料成型专业实践教学中的应用

大学生创新能力、工程意识和团队协作能力的培养是工程训练的重要目标和教学改革的重要内容。“典型生产工艺流程”是湖南大学为化工、材料、环境等专业开设的工程训练项目。结合课程的特点和已存在的问题,课程采用开放式项目制教学的模式,对教学环节进行设计。选取了体现专业特点,并与生活实践、社会热点、科学前沿等结合紧密的案例进行应用。