具有渐近平均跟踪性质的系统

简记渐近平均跟踪性质为AASP.对于紧致度量空间上的连续映射f,证明了:(1)f有AASP当且仅当其逆极限空间上的移位映射有AASP;(2)若f有AASP且是等度连续的,则f是极小同胚.此外,讨论了AASP的拓扑共轭不变性.     

How useful are closed captions for learning mathematics via online video?

Closed captioning of instructional videos is a topic that has not seen much discussion despite its importance for hearing-impaired students and recent legal ramifications if videos are not appropriately captioned. In particular, it is unclear what best practice in captioning videos should be to benefit all learners in disciplines such as mathematics with a reliance on the development of visual explanation while providing audio narration. In this paper, we report on a study undertaken at an Australian university, to investigate the perceived level of usefulness of captions and their automatic translations in a mathematics course. We discovered that students broadly agreed that captions are a useful learning feature: to allow flexibility of where and when a video is watched, but also to help understand speaker accents, and clarify explanations that are difficult to hear in the recording. Due to the high levels of use and perceived educational benefits of closed captions in online video but limited literature, there is a significant need for new research in this area. An urgent discussion is needed to explore how students engage with closed captions, how they may support learning, and to investigate implications on instructional design of mathematical videos.     

Investigating undergraduate mathematics learners’ cognitive engagement with recorded lecture videos

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, although it is unclear whether this is because regular users are generally weaker mathematics students or because RLV use is somehow depressing student learning. Through the lens of cognitive engagement, a quasi-experimental pre- and post-test design study was conducted to investigate the latter possibility.

Cognitive engagement was operationalized using the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F), which measures learning approaches on two major scales: surface and deep. In two mathematics courses at two universities, in Australia and the UK, participants were administered the questionnaire near the course start and finish. Overall findings were similar in both contexts: a reduction in live lecture attendance coupled with a dependence on RLVs was associated with an increase in surface approaches to learning.

This study has important implications for future pedagogical development and adds to the sense of urgency regarding research into best practices using RLVs in mathematics.     

Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

GRIN光学中光线追迹的一种新方法

由哈密顿光学中的拉格朗日方程推出光线方程，用Runge—Kutta方法求解光线方程，给出光线追迹的新方法。     

一种结合Mean—shift和粒子滤波的视频跟踪算法

提出一种结合均值偏移算法和粒子滤波理论的视频跟踪算法,解决了目标旋转、部分遮挡和运动速度过快的问题．通过均值偏移对粒子滤波中的粒子集进行进一步寻优,增加了粒子的有效性,极大减少了粒子采样的数量,且解决了经过多次重采样后粒子多样性降低的问题．新的粒子通过与观测值之间的巴氏系数来决定重要性权重．实验证明：本算法可以完成实时地对视频目标进行部分遮挡以及目标旋转下的跟踪,具有较强的鲁棒性．     

基于感知的右视点质量可分级编码算法

为了减少立体视频传输如此庞大的数据量,根据人眼的立体掩蔽效应,提出了基于感知的右视点质量可分级编码算法．该算法将宏块分为3类：平坦块、纹理块和边缘块,通过不同的量化步长使得右视点图像块的质量可分级．实验证明根据左视点的图像质量,右视点在人眼感知范围内码率减少25％～37％．该算法能在人眼主观察觉范围内很好地提高码率,进一步消除人眼立体视觉冗余．     

土地利用现状变更记录存储方式的研究与应用

在频繁的土地变更过程中产生的大量历史数据对于数据挖掘分析、政府决策支持具有重要的价值.文章在传统的全状态记录模式基础上提出了更加简洁的特殊状态记录模式,减少了冗余数据的产生,简化了变更记录,同时优化了历史回溯等功能.     

具有跟踪性可扩流的周期轨的双曲性

证明了具有跟踪性的可扩流在其周期轨附近的拓扑动力性质与双曲周期轨相同.     

线激光束均匀化整形方法研究

为解决核物理工程、表面热处理、激光加工、激光通信中传输激光束的均匀性问题,提出采用三角楔柱透镜改善线激光均匀性的新方法,并在ZEMAX开发环境下建立了整形光路系统的理论模型。利用所建立的模型,分析了整形柱透镜在不同半径、斜面夹角、透镜介质折射率等参数下光束的均匀性。研究表明：在远场条件下,通过改变整形柱透镜的参数,能够得到能量分布均匀的线激光。在实际应用中,可以采用1个半圆柱和2个相同三角楔胶合成型的简单工艺。进一步模拟发现,两种整形系统所得到的均匀度和线宽一致。