材料化学课程线上教学初探

2020新年伊始,新冠肺炎突然来袭,为了防止聚集性感染,教育部提出了"停课不停教、停课不停学"的要求。地方普通高校学生的自律性、自觉性及能动性差别十分明显,这样的学情对如何有效开展化学专业的线上教学工作提出了更大的挑战。本文以材料化学课程线上教学为例,介绍地方普通高校化学专业线上教学工作的开展情况。针对教学过程中遇到的各种问题和采用的应对方案,探讨线上教学过程中的注意事项。希望本文能为地方普通高校化学专业线上教学工作提供有益的参考。     

Prime Submodules and a Sheaf on the Prime Spectra of Modules

We define and investigate a sheaf of modules on the prime spectra of modules, and it is shown that there is an isomorphism between the sections of this sheaf and the ideal transform module.     

Extension of the 2-p-opt and 1-shift algorithms to the heterogeneous probabilistic traveling salesman problem

The probabilistic traveling salesman problem is a well known problem that is quite challenging to solve. It involves finding the tour with the lowest expected cost for customers that will require a visit with a given probability. There are several proposed algorithms for the homogeneous version of the problem, where all customers have identical probability of being realized. From the literature, the most successful approaches involve local search procedures, with the most famous being the 2-p-opt and 1-shift procedures proposed by Bertsimas [D.J. Bertsimas, L. Howell, Further results on the probabilistic traveling salesman problem, European Journal of Operational Research 65 (1) (1993) 68–95]. Recently, however, evidence has emerged that indicates the equations offered for these procedures are not correct, and even when corrected, the translation to the heterogeneous version of the problem is not simple. In this paper we extend the analysis and correction to the heterogeneous case. We derive new expressions for computing the cost of 2-p-opt and 1-shift local search moves, and we show that the neighborhood of a solution may be explored in O(n²) time, the same as for the homogeneous case, instead of O(n³) as first reported in the literature.     

基于统计窗的恒星连续谱自动拟合方法

提出一种基于统计窗的恒星连续谱拟合方法。该方法将恒星光谱划分为若干个统计窗,在每个窗口内根据信噪比选取一定比例的流量点,然后对选出来的流量点进行低阶多项式迭代拟合,从而得到连续谱。实验表明,与其他方法相比,该方法得到的连续谱更接近于实际连续谱。该方法对SDSS中除M外的各种光谱型连续谱的拟合均具有很高的实用性和鲁棒性,对于郭守敬望远镜(LAMOST)先导巡天恒星光谱的连续谱拟合同样具有非常好的效果。     

Chaos and reproduction in sea level

Prediction of sea-level is an important task for navigation, coastal engineering and geodetic applications, as well as recreational activities. This study presents a comparison of Chaos theory and Auto-Regressive Integrated Moving Average (ARIMA) techniques for sea level modelling for daily, weekly, 10-day and monthly time scale at the Cocos (Keeling) islands from 1992 to 2001. The state space reconstruction of the unknown underlying process is directly employed from time series data, through Takens delay embedding method: optimal embedding dimension and delay time are obtained from false nearest neighbours and average mutual information techniques, respectively. Optimal values are then used for the estimation of the correlation dimension and the largest Lyapunov exponent, for inspecting possible signatures of chaotic dynamics. We find a positive Lyapunov exponent an evident feature of chaos. Indeed, the nonlinear prediction of sea level, in the period ranging from January 2001 to December 2001, is in an excellent agreement with the data for the same period, evidencing the nonlinear nature of the process. ARIMA method is also used for sea level modelling, for the same time scales; the performances of the two models are compared using such statistical indices as the root mean square error (RMSE) and correlation coefficient (CC). The comparative analyses show that the chaos theory model has a slight edge over ARIMA while both models are in principal acceptable.     

激光诱导击穿空气等离子体光谱及半经验理论模拟

利用Nd∶YAG激光器输出的1 064 nm激光进行了激光诱导击穿空气光谱实验,测量了空气等离子体的时间分辨光谱。基于局域热动力学平衡模型,建立了模拟激光诱导击穿光谱的方法。对700~900 nm波段的空气等离子体光谱进行了模拟。通过模拟结果与实验结果的比较,进一步估算出了空气中氮、氧和氩的相对含量。     

场发射栅孔阵列的制备

 采用硅的局部氧化技术以及湿法刻蚀技术,利用2.6 μm的光刻掩模板在n型硅片上形成了栅极孔径为1 μm的场发射阴极的栅极空腔阵列,实现了用大阵点尺寸的栅极掩模板制备较小尺寸栅孔阵列。硅的湿法刻蚀溶液采用各向同性的硝酸和氢氟酸混合溶液,刻蚀后空腔的深度和宽度均随刻蚀时间线性增加。同时,由于刻蚀溶液具有较高的Si/SiO₂ 刻蚀选择比,栅极孔径随刻蚀时间增大的速度远低于深度和宽度增大的速度,栅极孔径主要取决于掩模的尺寸和氧化层的厚度。通过选择掩模板的尺寸以及氧化层的厚度,采用局部氧化技术和湿法刻蚀技术能够制备出微米或亚微米的场发射阴极的栅极空腔阵列。     

Fitting models to correlated data III: A comparison between residual analysis and other methods

Applications of the χ² test, the F test, the Durbin-Watson d test, and the f (or Sign) test, to examples of correlated data treatment, show important drawbacks with the d test and (apparently) with the f test. An analytical approach based on residual analysis suggests an improvement in their use that leads to better results at lowest order; it also points out a distinction between goodness-of-fit tests, as the f test, and goodness-of-modeling tests, as the χ² and F tests. The residual analysis method is applied to the same examples; it looks faster, simpler, and often more accurate than the classical ones.     

Local time-stepping procedures for the space-time conservation element and solution element method

A local time-stepping procedure for the space-time conservation element and solution element (CESE) method has been developed. This new procedure allows for variation of time-step size in both space and time, and can also be extended to become multi-dimensional solvers with structured/unstructured spatial grids. Moreover, it differs substantially in concept and methodology from the existing approaches. By taking full advantage of key concepts of the CESE method, in a simple and efficient manner it can enforce flux conservation across an interface separating grid zones of different time-step sizes. In particular, no correction pass is needed. Numerical experiments show that, for a variety of flow problems involving moving shock and flame discontinuities, accurate and robust numerical simulations can be achieved even with a reduction in time-step size on the order of 10 or higher for grids across a single interface.     

The partial inverse minimum spanning tree problem when weight increase is forbidden

In a partial inverse optimization problem there is an underlying optimization problem with a partially given solution. The objective is to find a minimal perturbation of some of the problem’s parameter values, in such a way that the partial solution becomes a part of the optimal solution.