疫情下电磁场理论课程的网络教学

本文主要总结了新冠疫情期间作者的电磁场理论课程在线教学经验。对比分析了录播和直播的优缺点后,选择录播教学方式。基于超星网络教学平台,展示了录播网络教学的具体措施,包括网上答疑和学习效果检查以及在线批改作业等。给出了网络教学可以为线下教学继续使用的方法和手段,为疫情结束后的正常教学提供了新的网络教学补充措施。     

The Role of Radical Bridges in Polynuclear Single-Molecule Magnets

Employing radical bridges between anisotropic metal ions has been a viable route to achieve high-performance single-molecule magnets (SMMs). While the bridges have been mainly considered for their ability to promote exchange interactions, the crystal-field effect arising from them has not been taken into account explicitly. This lack of consideration may distort the understanding and limit the development of the entire family. To shed light on this aspect, herein we report a theoretical investigation of a series of N -radical-bridged diterbium complexes. It is found that while promoting strong exchange coupling between the terbium ions, the N -radical induces a crystal field that interferes destructively with that of the outer ligands, and thus reduces the overall SMM behavior. Based on the theoretical results, we conclude that the SMM behavior in this series could be further maximized if the crystal field of the outer ligands is designed to be collinear with that of the radical bridge. This conclusion can be generalized to all exchange-coupled SMMs.     

What is the optimal cutoff surface for ore bodies with more than one mineral?

In mine planning problems, cutoff grade optimization defines a threshold at every time period such that material above this value is processed, and the rest is considered waste. In orebodies with multiple minerals, which occur in practice, the natural extension is to consider a cutoff surface. We show that in two dimensions the optimal solution is a line, and in n dimensions it is a hyperplane.     

The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics

This paper infers from a generalized Picone identity the uniqueness of the stable positive solution for a class of semilinear equations of superlinear indefinite type, as well as the uniqueness and global attractivity of the coexistence state in two generalized diffusive prototypes of the symbiotic and competing species models of Lotka–Volterra. The optimality of these uniqueness theorems reveals the tremendous strength of the Picone identity.     

Cyberbullying: Effect of emergency perception on the helping tendencies of bystanders

The effect of the emergency perception of bystanders of cyberbullying victims on helping behaviors is often neglected in research on cyberbullying. In this study, we explored the influence of this cognitive factor on cyber-bystanders’ helping tendencies as well as elucidated possible underlying processes. The results of two studies were reported. In Study 1, 150 undergraduates read a true case of a girl experiencing cyberbullying. The results indicated that when the participants perceived the victim’s situation to be more critical (i.e., higher emergency perception), their helping tendencies were stronger, partly through increased state empathy followed by feelings of responsibility to help. In Study 2, we randomly assigned 300 undergraduates to two groups. The low emergency group read the same cyberbullying case as Study 1, whereas the cyberbullying case read by the high emergency group contained additional emergency information of the victim. The results indicated that the high emergency group expressed stronger helping tendencies than did the low emergency group. This effect was caused by a stronger perception that the victim was in an emergency situation, which not only strengthened the participants’ helping tendencies directly but also indirectly through increasing their state empathy and feelings of responsibility to help.     

Lithiation MXene Derivative Skeletons for Wide-Temperature Lithium Metal Anodes

Lithium (Li) metal, as an appealing candidate for the next-generation of high-energy-density batteries, is plagued by its safety issue mainly caused by uncontrolled dendrite growth and infinite volume expansion. Developing new materials that can improve the performance of Li-metal anode is one of the urgent tasks. Herein, a new MXene derivative containing pure rutile TiO₂ and N-doped carbon prepared by heat-treating MXene under a mixing gas, exhibiting high chemical activity in molten Li, is reported. The lithiation MXene derivative with a hybrid of LiTiO₂-Li₃N-C and Li offers outstanding electrochemical properties. The symmetrical cell assembling lithiation MXene derivative hybrid anode exhibits an ultra-long cycle lifespan of 2000 h with an overpotential of ≈30 mV at 1 mA cm⁻², which overwhelms Li-based anodes reported so far. Additionally, long-term operations of 34, 350, and 500 h at 10 mA cm⁻² can be achieved in symmetrical cells at temperatures of −10, 25, and 50 °C, respectively. Both experimental tests and density functional theory calculations confirm that the LiTiO₂-Li₃N-C skeleton serves as a promising host for Li infusion by alleviating volume variation. Simultaneously, the superlithiophilic interphase of Li₃N guides Li deposition along the LiTiO₂-Li₃N-C skeleton to avoid dendrite growth.     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.