DEA的交形式生产可能集及其应用

DEA理论、模型及方法可用以评价给定决策单元之间的相对有效性,其在经济学中的应用体现在经验生产可能集的构造上.DEA的生产可能集有两种等价形式—和形式及交形式.相比较而言,交形式更具几何直观性及计算便利性.     

值得引入物理化学教材的重要内容:势能面交叉

势能面交叉既是内转换和系间窜越的实际通道,也是联系光化学和热化学的重要桥梁。势能面交叉引起的非绝热过程广泛存在于各种生物、化学和材料的体系当中。笔者建议将势能面交叉的相关内容引入物理化学课程的教材中,因为这不但会使教材内容更加丰富和成体系,而且有利于学生了解科技发展前沿,激发他们探索未知的兴趣。     

Spin-flip approach within time-dependent density functional tight-binding method: Theory and applications

A spin-flip time-dependent density functional tight-binding (SF-TDDFTB) method is developed that describes target states as spin-flipping excitation from a high-spin reference state obtained by the spin-restricted open shell treatment. Furthermore, the SF-TDDFTB formulation is extended to long-range correction (LC), denoted as SF-TDLCDFTB. The LC technique corrects the overdelocalization of electron density in systems such as charge-transfer systems, which is typically found in conventional DFTB calculations as well as density functional theory calculations using pure functionals. The numerical assessment of the SF-TDDFTB method shows smooth potential curves for the bond dissociation of hydrogen fluoride and the double-bond rotation of ethylene and the double-cone shape of H₃ as the simplest degenerate systems. In addition, numerical assessments of SF-TDDFTB and SF-TDLCDFTB for 39 S₀/S₁ minimum energy conical intersection (MECI) structures are performed. The SF-TDDFTB and SF-TDLCDFTB methods drastically reduce the computational cost with accuracy for MECI structures compared with SF-TDDFT.     

Dependency of the Dimethyldihydropyrene Photochromic Properties on the Number of Pyridinium Electron-Withdrawing Groups

Photochromic dimethyldihydropyrenes substituted with electron-withdrawing pyridinium groups have shown an increase of photo-induced ring-opening efficiency and a light sensitivity that is red shifted relative to the unsubstituted compound. However, a recently synthesized tetrapyridinium derivative showed a considerable decrease of the photo-isomerization quantum yield relative to the monopyridinium and bispyridinium derivatives. We provide a rationale for this unexpected photochemical behavior based on the comparative theoretical investigations of the relevant excited states of these systems. In particular, we found that the nature and order of the lowest two excited states depend on the number of pyridinium groups and on the symmetry of the system. While the lowest S₁ excited state is photo-active in the monopyridinium and bispyridinium derivatives, the photo-isomerizing state is S₂ in the reference unsubstituted compound and both S₁ and S₂ lead to isomerization in the tetrapyridinium derivative, albeit with a low efficiency. In the latter derivative, the photo-isomerization is hindered by the particular S₁/S₂ conical intersection topology.     

Section theorems,coincidence theorems and intersection theorems on H-spaces with applications

The purpose of this paper is to study the section theorems, coincidence theorems and intersection theorems on H-spaces. As a way of application, we use these results to study the existence problems of solutions for minimax inequalities and variational inequalities. The results presented in this paper improve and extend the corresponding results in [1, 3, 5, 6, 8, 9, 12, 14,15, 17]     

3-二甲氨基-2-甲基丙烯醛S2激发态结构动力学 (cited: 3)

采用共振拉曼光谱和完全活性自洽场理论计算研究了3-二甲氨基-2-甲基丙烯醛(DMAMP)光激发到S₂(ππ^*)态后的光物理性能．在B3LYP/6-311++G(d,p)水平计算确定了DMAMP与其三种异构体之间的基态异构化能垒,指认了振动光谱．采用涵盖紫外强吸收带的激光波长,获得了DMAMP在环己烷、乙腈和甲醇溶剂中的A-带共振拉曼光谱,含时密度泛函方法计算确定了该光谱中基频的相对强度,发现振动-电子耦合发生在S₂(ππ^*)态的Franck-Condon区域．CASSCF计算方法确定低单重和三重激发态、势能面锥形交叉点和系间窜跃点的激发能．共振拉曼光谱强度模式分析和CASSCF计算获得了DMAMP的A-带短时结构动力学和其后的衰变动力学表明,C1=O6和C2=C3之间的瞬时去共轭效应发生在S₂(ππ^*)态的Franck-Condon区域,激发态电荷重分布机制表明,C3和二甲氨基之间以及C1和C2之间的共轭增强效应发生在波包离开Franck-Condon区域后．C1=O6和C2=C3之间的去共轭效应使得-C3=N(CH₃)₂沿着C2-C3键旋转更加容易,C1-C2之间以及C3和N(CH₃)的共轭增强效应使得绕C1-C2和C3-N5旋转变得比较困难．这些表明DMAMP初始结构动力学沿着CI-1(S₂/S₀)交叉点展开,而沿CI-2(S₂/S₀)和CI-3(S₂/S₀)交叉点展开的几率可以忽略．提出了DMAMP分子受光激发从S_2,FC(ππ^*)经由各锥形交叉点和各系间窜跃点回到S₀或T_1,min的两个衰变通道.     

Multipermutation-Based Intersection Theorem and Its Applications

In this paper, we introduce a multipermutation-based intersection theorem on the product space of several unit simplices, called the simplotope. This theorem gives a substantial generalization of an intersection result of Scarf on the unit simplex (Ref. 1). By using this new result, we also obtain a multipermutation-based generalization of the Brouwer fixed-point theorem on the simplotope. Furthermore, we apply this new result to an economic equilibrium model with indivisibilities and obtain an equilibrium existence theorem.     

Cycles on Arithmetic Surfaces

We develop a localized intersection theory for arithmetic schemes on the model of Fulton's intersection theory. We prove a Lefschetz fixed point formula for arithmetic surfaces, and give an application to a conjecture of Serre on the existence of Artin's representations for regular local rings of dimension 2 and unequal characteristic.     

平面上Brown运动的重正化自交局部时的光滑性

本文运用实插值理论中的K-方法证明了平面上Brown运动自交局部时属于分数次Sob0lev空间Dpa,其中p＞1及α＜1/3.     

基于元胞自动机的交叉口混合交通模型研究

在我国很多中小城市普遍存在着摩托车与小汽车混行的现象,摩托车既有类似自行车横向移动灵活、启动速度快的特点,又有类似小汽车纵向移动速度快的特点,特别是在城市交叉口附近范围内,摩托车与小汽车几乎速度相当.根据交叉口红灯起亮时,摩托车会灵活穿插,充分利用车道空间,绿灯起亮时,由于摩托车的启动速度比小汽车快,产生侧向膨胀效应,挤压小汽车行驶空间,从而使其速度减慢等现象,结合我国中小城市交叉口小汽车及摩托车的行驶特性,利用元胞自动机模型,建立信号交叉口小汽车与摩托车的混合交通模型.