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.     

基于特征建模的TDD系统大气波导干扰控制体系研究

大气波导干扰是特定气象条件下发生的时分双工（time-division duplex，TDD）系统内干扰，是TDD移动通信系统大规模组网面临的顽疾。在总结分析大气波导干扰成因和分类等的基础上，对大气波导干扰进行建模和表征，验证了海量干扰源在时域和频域的功率集总特征，并结合大量4G/5G现网实测数据给出了典型条件下内陆波导和海面波导的量化干扰信号传播模型，对于干扰的预测和预防具有重要意义。基于干扰特征，给出了TDD系统预防大气波导干扰的帧结构与组网的4项设计原则，5G现网数据表明干扰控制方案有效，上行干扰下降10 dB以上，相关原则对于6G系统的设计也具有指导意义。     

Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

Context-free grammars to detect straight segments and a novel polygonal approximation method

A new method for the polygonal approximation is presented. The method is based on the search for break points through a context-free grammar, that accepts digital straight segments with loss of information, as well as the decrease in the error committed employing the comparison of a tolerable error. We present an application of our method to different sets of objects widely used, as well as a comparison of our results with the best results reported in the literature, proving that our method achieves better values of error criteria. Besides, a new way to find polygonal approximations, with context-free grammars to recognize digital straight segments without loss of pixels, it is also addressed.     

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.     

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

A DFT study on mechanisms of CO2 coupling with propargylic alcohols using alkali carbonates

The mechanisms of CO₂ coupling with the propargylic alcohol using alkali carbonates M₂CO₃ (M = Li, Na, K, Cs) have been investigated by means of density functional theory calculations. The calculations reveal that the target product tetronic acid (TA) is yielded through two stages: (a) the formation of the α-alkylidene cyclic carbonate (αACC) intermediate via Cs₂CO₃-mediated carboxylative cyclization of the propargylic alcohol with CO₂, and (b) the conversion of the αACC intermediate with Cs₂CO₃ to produce the cesium salt of the TA. Since the overall kinetic barriers for the two stages are comparable and affordable, the excellent chemoselectivity to the TA should be primarily originated from the high thermodynamic stability of the cesium salt of the TA. Moreover, relative to the TA, the possibility to yield the by-product acyclic carbonate can be excluded due to the both kinetics and thermodynamic inferiority. This result is different from the organic base-mediated reaction. Alternatively, our calculations predict that CsHCO₃ together generated with the cesium salt of the TA might also be an available mediating reagent for the incorporation of CO₂ with the propargylic alcohol. Compared to other alkali carbonates M₂CO₃ (M = Li, Na, K), the stronger basicity of Cs₂CO₃ and the lower ionic potential of cesium ion can raise the effective concentration of the αACC intermediate, and thus the conversion of the αACC intermediate into the cesium salt of the TA can be achieved with high yield.