Examining undergraduate student retention in mathematics using network analysis and relative risk

Higher education faces challenges in retaining students who require a command of numeracy in their chosen field of study. This study applies an innovative combination of relative risk and social network analysis to enrolment data of a single cohort of commencing students from an Australian regional university. Relative risk, often used in epidemiology studies, is used to strategically investigate whether first year mathematics subjects at the university demonstrated a higher risk of attrition when compared to other subjects offered in the first year of study. The network analysis is used to illustrate the connections of those mathematics subjects, identifying service subjects through their multiple connections. The analysis revealed that attrition rates for eight of the nine subjects were within acceptable limits, and this included identified service subjects. The exception highlighted the issue of mathematics competencies in this cohort. This combined analytical technique is proposed as appropriate for use when investigating attrition and retention at faculty and institutional levels, including the determination of levels of intervention and support for any subject.     

The external constraint 4 nonempty part sandwich problem

List partitions generalize list colourings. Sandwich problems generalize recognition problems. The polynomial dichotomy (NP-complete versus polynomial) of list partition problems is solved for 4-dimensional partitions with the exception of one problem (the list stubborn problem) for which the complexity is known to be quasipolynomial. Every partition problem for 4 nonempty parts and only external constraints is known to be polynomial with the exception of one problem (the 2K₂-partition problem) for which the complexity of the corresponding list problem is known to be NP-complete. The present paper considers external constraint 4 nonempty part sandwich problems. We extend the tools developed for polynomial solutions of recognition problems obtaining polynomial solutions for most corresponding sandwich versions. We extend the tools developed for NP-complete reductions of sandwich partition problems obtaining the classification into NP-complete for some external constraint 4 nonempty part sandwich problems. On the other hand and additionally, we propose a general strategy for defining polynomial reductions from the 2K₂-partition problem to several external constraint 4 nonempty part sandwich problems, defining a class of 2K₂-hard problems. Finally, we discuss the complexity of the Skew Partition Sandwich Problem.     

Connectivity modeling and optimization of linear consecutively connected systems with repairable connecting elements

Linear consecutively connected systems (LCCSs) are systems containing a linear sequence of ordered nodes. Connection elements (CE) characterized by diverse connection ranges, time-to-failure and time-to-repair distributions are allocated to different nodes to provide the system connectivity, i.e., a connection between the source and sink nodes of the LCCS. Examples of LCCSs abound in practical applications such as flow transmission systems and radio communication systems. Considerable research efforts have been expended in modeling and optimizing LCCSs. However, most of the existing works have assumed that CEs either are non-repairable or undergo a restrictive minimal repair policy with constant repair time. This paper makes new technical contributions by modeling and optimizing LCCSs with CEs under corrective maintenance with random repair time and different repair policies (minimal, perfect, and imperfect). The characteristics of CEs can depend on their location because the distance between adjacent nodes and conditions of CE operation and maintenance at different nodes can be different, which further complicates the problem. We first propose a discrete numerical algorithm to evaluate the instantaneous availability of each CE. A universal generating function based method is then implemented for assessing instantaneous and expected system connectivity for a specific CE allocation. As the CE allocation can have significant impacts on the system connectivity, we further define and solve the optimal CE allocation problem, whose objective is to find the CE allocation among LCCS nodes maximizing the expected system connectivity over a given mission time. Effects of different parameters including repair efficiency, mission time and repair time are investigated. As illustrated through examples, optimization results can facilitate optimal decisions on robust design and effective operation and maintenance managements of LCCSs.     

本科院校"数字媒体技术"专业课程体系改革探讨

"数字媒体技术"是一门新兴的专业,近年来已经有一百多所本科院校申报开办了这门专业.然而各大高校在开设这门专业的同时面临着"专业设置不合理"、"拼盘化"等问题,不能够形成本专业的鲜明特色,满足社会对数字媒体技术类人才的需求,因此,"数字媒体技术"专业的课程体系急需改革.     

高光谱成像仪衍/折射光学系统消二级光谱的设计

采用光学设计的基本原理,结合高光谱成像仪光学系统的特性,详细研究了宽光谱、长焦距衍/折混合光学系统消二级光谱的设计方法、步骤.按照消二级光谱的焦距分配公式,设计了消二级光谱的高光谱成像仪的衍-折混合光学系统,设计的光学系统满足实际使用要求,其二级光谱保持在设计水平以下(≤0.8mm).     

直流电源绝缘检测技术研究

为了保障直流系统的安全可靠运行,绝缘监测装置是必不可少的。对直流系统绝缘检测常用的几种方法进行了分析比较,指出了它们在使用时的优缺点。并在此基础上提出了一种新的改进后的绝缘检测方法。     

面向社会,办好电子信息工程专业

根据我校电子信息工程专业的办学情况,结合参加全国大学生电子设计竞赛的体会,阐述了新时代下如何适应社会发展对高等院校的要求,进行电子信息工程专业教学改革,培养大学生创新意识和创新能力,激发学生学习兴趣和培养学生良好素质.     

电子元器件使用过程中的可靠性试验

本文介绍了影响电子元器件可靠性的因素和可靠性试验的原理,主要阐述在电子产品生产过程中,为确保产品的可靠性,如何对电子元器件进行可靠性试验.     

Characterizing prospective secondary teachers’ foundation and contingency knowledge for definitions of transformations

One promising approach for connecting undergraduate content coursework to secondary teaching is using teacher-created representations of practice. Using these representations effectively requires seeing teachers' use of mathematical knowledge in the work of teaching. We argue that the dimensions of Rowland's (2013) Knowledge Quartet, especially Foundation and Contingency, form a fruitful framework for this purpose. We contribute an analytic framework to characterize the quality of mathematical knowledge observed in the Foundation and Contingency dimensions, developed using a purposive sampling from over 300 representations. These representations all featured geometry teaching. We showcase the framework with examples of "high" and "developing" Foundation and Contingency.Then, we compare our coding along these dimensions with performance on a measure of mathematical knowledge for teaching geometry. Finally, we describe the potential for generalizing this framework to other domains, such as algebra and mathematical modeling.