The adiabatic‐to‐diabatic transformation angle and topological phases for strongly interacting states: Solution with four states

A few years back T. Vértesi et al. (J Phys Chem A 2005, 109, 3476) gave an elegant procedure to derive the adiabatic‐to‐diabatic transformation angle (ADT‐angle) for lowest two states, γ<sub>12sub>, in presence of their interaction with the higher states. In this article, we explicitly solved the coupled differential equations involving the ADT‐angles describing the mixing of four interacting states for the first time to get all the ADT‐angles, γ<sub>ijsub>'s (including the γ<sub>12sub>) associated with well‐defined topological phases. In application to a suitable configuration space (CS) of a molecular system, we have demonstrated well‐defined Berry phases (Berry M. V., R Soc London Ser A 1984, 45, 392) for an isolated system with as many as four strongly interacting states. © 2012 Wiley Periodicals, Inc.     

蛋白质分子与配体结合过程构象变化的研究

蛋白质分子与配体的作用模式主要有直接的环区结合及铰链式结合两种方式。针对这两种不同的作用方式,我们提出采用不同的策略进行结合过程的构象研究。对于直接的环区结合模式,通过建立环区主链构象库,来实现蛋白质环区与配体的准柔性对接,并以链霉抗生物素蛋白体系为例对构象库建立的可行性进行了验证计算。对铰链结合方式,采用分步对接的方法进行计算,并具体应用于HIV蛋白酶与其小分子配体的结合过程。计算结果表明,这两种处理方法分别能较好地模拟不同类型的蛋白质与配体结合的的构象变化。     

随机次自相似集的表示

本文引进了随机次自相似集与随机推移集的概念,讨论了随机次自相似集的结构,并证明了任一随机集是随机次自相似集的充分必要条件是：该随机集可以表为某一个随机推移集的某个像集。     

二步幂零Lie群上sub-Laplace算子的谱

本文首先研究包括Ｇｒｅｉｎｅｒ算子和二步幂零Ｌｉｅ群上ｓｕｂ Ｌａｐｌａｃｅ算子Ｌ在内的广义齐次线性偏微分算子的谱，然后利用酉表示理论确定了算子Ｌ的谱结构，并深化了Ｋ．Ｆｕｒｕｔａｎｉ，Ｋ．Ｓａｇａｍｉ，Ｎ．Ｏｔｓｕｋｉ关于Ｌａｐｌａｃｅ算子的有关结果．     

The sensitivity of the lehn cryptand—europium and terbium (III) complexes to anions compared to a coordinatively saturated systems

Titrations of the Lehn cryptand [Ln&sub;bpy.bpy.bpy]³⁺ complexes of both europium (III) and terbium (III) with fluoride and phosphate ions indicate that these anions displace water from the solvation sphere. In the case of the europium complex an enhancement of luminescence intensity is observed, whilst with the terbium complex a reduction in the emission intensity occurs. Described are the preparations of analogous, coordinatively saturated complexes that are inert to the influence of these anions.     

Assemblies and Properties of Asymmetric Supercapacitors Based on WO3/Carbon Cloth北大核心CSCD

The demand for a new generation of flexible, portable, and high-capacity power sources increases rapidly with the development of advanced wearable electronic devices. One dimensional (1D) nanowires structures have been demonstrated as one of the most ideal electrode materials in energy storage systems due to their advantages in both micorstructures and their high surface areas. Here we report a simple process for large-scale fabrication of self-standing composite film electrodes composed of WO3nanorods on carbon cloth. In order to improve the energy density of supercapacitor, we assembled an asymmetric supercapacitor using WO3nanorods and activated carbon cloth as positive and negative electrodes, respectively. The scanning electron microscopy (SEM) and X-ray diffraction spectroscopy (XRD) were used to characterize the morphology and structure of the electrode materials, respectively. In addition, cyclic voltammetry (CV), galvanostatic charge-diacharge (GCD) test, and electrochemical impedance spectroscopy (EIS) were employed to study the electrode materials in a three-electrode system. It was found that the WO3nanorods exhibited attractive electrochemical performance as well as remarkable flexibility with the high areal capacitance of 3347 mF·cm-2at 5 mA·cm-2. In addition, to improve the electrochemical performance of activated carbon cloth by introducing function groups onto its surface for producing pseudocapacitance and increasing surface area by electrochemically oxidizing CC in the mixed acid solution, it was also shown the high areal capacitance of 1160 mF·cm-2at 7 mA·cm-2. This method was simpler and more effective compared with the previous strategies for activating carbon materials. The as-fabricated asymmetric supercapacitor based on WO3/carbon cloth exhibited high areal capacitance of 58.96 F·cm-2at 61.9 mA·cm-2, high energy density of 20.36 mWh·cm-2at 0.48 W·cm-2with the operation voltage window expanding to 0 ~ 1.6 V, and excellent lifespan after 3000 cycles. This work opens up a novel, low-cost route to design advanced integrated-array and high performance electrode materials for portable supercapacitor application on a large scale. © Journal of Electrochemistry 2018.     

组稀疏优化问题精确连续Capped-L_(1)松弛北大核心CSCD

本文主要研究损失函数为凸函数且带有约束的组稀疏正则回归问题及组稀疏正则项的精确连续Capped-L_(1)松弛问题.首先对组Capped-L_(1)松弛问题定义了三类稳定点:D(irectional)-稳定点、C(ritical)-稳定点、L(ifted)-稳定点,然后刻画了这三类稳定点之间的关系.进一步,给出了组Capped-L_(1)松弛问题和原始组稀疏正则问题的最优性条件,并从全局解和局部解角度讨论了松弛问题和原问题解的等价关系.     

连续综合控制系统的状态反馈广义H_(2)控制北大核心CSCD

基于Lyapunov稳定性理论、矩阵分析法、线性矩阵不等式等方法,对同时带有控制输入和干扰输入的奇异摄动时变时滞不确定控制系统进行广义H_(2)控制研究.设计一个记忆状态广义H_(2)控制器,给出具体设计方法的判定定理.并对时滞依赖和时滞独立两种情形下采用新的引理,推出保守性相对更小的稳定性判据.对所得结论进行线性化处理,用数值样例验证了该文所得结论的有效性和可行性.指出在零到奇异摄动上界的整个区间范围内,闭环系统渐近稳定,扩大了广义H_(2)稳定空间,缩小了L_(2)-L_(∞)的性能指标.通过与相关文献进行稳定态指标对比,展示出该文所得方法具有一定的优越性和较小的保守性,并且适用于标准和非标准情形.     

Singular nonhomogeneous quasilinear elliptic equations with a convection term

In this work we establish existence results for a class of nonhomogeneous and singular quasilinear elliptic equations involving a convection term. The gradient term makes the problem non variational, and in addition to this difficulty we have to handle the singular term with a sign changing nonlinearity. The proof of the results are made combining the sub‐super solution method, fixed point theorem, Leray–Schauder degree theory and comparison theorems.