例说解题与美学

在解题过程中正碡运用简洁美、和谐美、奇异美的美学准则,可开阔解题思路,激发解题灵感,起到宏观指导的决策作用.     

Uncertainty principles on two step nilpotent Lie groups

We extend an uncertainty principle due to Cowling and Price to two step nilpotent Lie groups, which generalizes a classical theorem of Hardy. We also prove an analogue of Heisenberg inequality on two step nilpotent Lie groups.     

连续犯罪预测的区域覆盖加权模型(AOWM)

2010年MCM(美国大学生数学建模竞赛)B题-Criminology要求建立连续犯罪的预测模型用于抓捕案犯.利用统计学、犯罪心理学相关知识,建立了区域覆盖加权模型(Area Overlap Weighted Model,简称AOWM).AOWM操作便利,在分析真实案例时的正确率能达到80%以上,因此具有较好的应用前景.     

基于“4S”四共原则的全信息化教学模式实践

疫情期间响应国家“停课不停学”的号召,基于“4S”四共原则对艺术与设计专业基础课程“设计思维与表达”展开了线上信息化教学模式的探索与实践。本文详细介绍了“4S”四共原则的教改思路,从平台、资源、教师、学生四个方面包围式地推进在线教学模式的实施。采用信息化教学手段,从课前、课中、课后三个方面组织在线教学活动。结合“抗疫”主题开展项目式教学,将抗疫精神融入课堂。最终对课程的实施情况展开评价反思与总结,熟悉在线教学模式完整流程,为探索信息化在线教学地顺利实施提供实践基础。     

First-principles study of the electronic structure and transport properties of armchair graphene nanoribbons with adsorbed super-halogen LiF2 and super-alkali Li3 clusters

The electronic structure and quantum transport properties of pristine armchair graphene nanoribbons (AGNRs) and AGNRs adsorbing super-halogen LiF₂ and super-alkaline Li₃ clusters (Li₃/AGNRs/LiF₂) were investigated using density functional theory and non-equilibrium Green's function calculations. It was found that LiF₂ and Li₃ clusters are stably adsorbed on the AGNRs, and the adsorption of Li₃ and LiF₂ endows AGNRs with the characteristics of n-type and p-type semiconductors, respectively. The Li₃/AGNRs/LiF₂ structure reduces the band gap and the turn-on voltage, and improves the transmission coefficient of the ANGRs device. This structure also exhibit the rectification characteristics of a pn junction with the forward bias current greater than the reverse bias current. This shows that adsorption of super-alkali and super-halogen clusters in different regions of AGNRs is a feasible approach for obtaining AGNRs with pn junction characteristics.     

固液界面双电层的理论计算模拟

固液界面双电层在电化学中处于核心地位. 如何发展一个理论方法,在该方法的框架下计算双电层的平衡性质和动力学性质一直以来都是理论研究的难点和热点. 本文总结了最近十几年第一性原理计算方法在计算双电层平衡性质和电催化反应的进展,如热力学方法、反应中心模型以及双参考方法. 并进一步详细地阐述了基于周期性均匀介质溶剂化模型 ( DFT/CM-MPB)对于固液界面双电层的研究,该方法能够计算双电层的平衡性质(零电荷电势和微分电容)和表面相图,在此基础上能深入研究基元反应的电荷转移系数,并结合微观动力学推导出宏观的Tafel(电流-电势)曲线. 并列举了该方法对于重要电化学反应(如氢电极反应)的应用实例.     

Interlayer vibration of twisted bilayer graphene: A first-principles study

Multi-layered structures of graphene and other two dimensional materials are novel organizations with fascinating properties. In this work, we investigate the interlayer lattice dynamics of the Moiré superlattice of twisted bilayer graphene (tBLG) using first-principles calculations. Due to the structural complexity, we calculate the frequencies of the interlayer breathing and shear vibrational modes of the tBLG without exploring all the degree of freedoms of the tBLG. Our calculation shows that the frequencies of breathing and shear modes display pronounced dependence on twisting angle, and compare well with the state of arts experimental measurements. We hint that the strategy employed here paves a route to the study of the interlayer vibrational properties of double layered two dimensional systems.     

化学原理课程小班教学方法的研究与实践

In this paper, the contents and methods of small-class teaching of chemical principles were introduced in detail, including the allocation of teaching time, the allocation of lecturing and self-study contents, organizing seminar and literature reading, as well as the cultivation of students' innovation ability. The reform of teaching content and teaching method in the process of implementing were introduced.