Regioselective alkali metal reduction of dibenzocyclooctadiene lignan derivatives,demethoxylation followed by dehalogenation

The regioselective demethoxylation and dehalogenation of dihalogenated dibenzocyclooctadiene lignans derivatives were realized in a one-step reaction with excellent yields in the sodium and t-butanol reaction system.     

Low-Storage Runge-Kutta Method for Simulating Time-Dependent Quantum Dynamics

A wide range of quantum systems are time-invariant and the corresponding dynamics is dictated by linear differential equations with constant coefficients.Although simple in mathematical concept,the integration of these equations is usually complicated in practice for complex systems,where both the computational time and the memory storage become limiting factors.For this reason,low-storage Runge-Kutta methods become increasingly popular for the time integration.This work suggests a series of s-stage sth-order explicit RungeKutta methods specific for autonomous linear equations,which only requires two times of the memory storage for the state vector.We also introduce a 13-stage eighth-order scheme for autonomous linear equations,which has optimized stability region and is reduced to a fifth-order method for general equations.These methods exhibit significant performance improvements over the previous general-purpose low-stage schemes.As an example,we apply the integrator to simulate the non-Markovian exciton dynamics in a 15-site linear chain consisting of perylene-bisimide derivatives.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.     

具有时滞的比率型三种群捕食模型的分支分析

本文研究了一类具有时滞的比率型三种群捕食模型.通过分析该模型的特征方程,证明了该模型在正平衡点的稳定性.通过选择时滞τ为分支参数,得到了当时滞τ通过一系列的临界值时,Hopf分支产生.应用中心流形和规范型理论,得到了关于确定Hopf分支特性的计算公式.最后进行数值模拟验证了我们所得结果的正确性.所得结果是对前人工作的补充.     

复线性微分方程解的增长性的几个结果

本文研究了复线性微分方程解的增长性问题.利用两类具有某种渐进增长性质的函数作为线性微分方程的系数,讨论了两类二阶线性微分方程解的增长性,获得了方程解为无穷级.这些结果推广了先前的一些结果.     

可行策略对应的图像拓扑下广义博弈Nash平衡的稳定性

以往关于广义博弈Nash平衡的稳定性的研究,均利用可行策略映射之间的一致度量.现考虑在更弱的度量下,利用可行策略映射图像之间的Hausdorff距离定义度量.在此弱图像拓扑下,证明了广义博弈空间的完备性,以及Nash平衡映射的上半连续性和紧性,进而得到广义博弈Nash平衡的通有稳定性.即在Baire分类的意义下,大多数的广义博弈都是本质的.     

Finite time stability analysis of systems based on delayed exponential matrix

In this paper, we analyze finite time stability for a class of differential equations with finite delay. Some sufficient conditions for the finite time stability results are derived based on delayed matrix exponential approach and Jensen’s and Coppel’s inequalities. Finally, we demonstrate the validity of designed method and make some discussions by using a numerical example.     

Aryldiazonium salts can serve as nitrogen-based Lewis acid catalysts and their applications in the formation of photoactive charge transfer complexes

We report the Lewis acid catalysis of aryldiazonium salts, and their Lewis acidity applications in photogeneration of aryl radicals under additive-, photocatalyst- and transition metal-free conditions. In this visible light-mediated transformation, the Lewis acidic character of aryldiazonium salts enables access to the photoactive charge transfer complex with dichalcogenides. The usefulness and versatility of this new protocol are demonstrated through the chalcogenation of a variety of aryldiazonium salts.     

Bidirectionally polarizing surface chemistry of heteroatom-doped carbon matrix towards fast and longevous lithium-sulfur batteries

Herein, a bidirectional polarization strategy is proposed for hosting efficient and durable lithium-sulfur battery (Li-S) electrochemistry. By co-doping electronegative N and electropositive B in graphene matrix (BNrGO), the bidirectional electron redistribution enables a higher polysulfide affinity over its mono-doped counterparts, contributing to strong sulfur immobilization and fast conversion kinetics. As a result, BNrGO as the cathode host matrix realizes excellent cycling stability over 1000 cycles with a minimum capacity fading of 0.027% per cycle, and superb rate capability up to 10 C. Meanwhile, decent areal capacity (6.46 mAh/cm²) and cyclability (300 cycles) are also achievable under high sulfur loading and limited electrolyte. This work provides instructive insights into the interaction between doping engineering and sulfur electrochemistry for pursuing superior Li-S batteries.