取代基及共轭链长对共轭多烯二阶线性光学系数影响的量子化学研究

本文采用引入外场微扰的CNDO/S-CI方法, 计算了一系列取代共轭多烯分子的二阶非线性光学系数β~vec, 探讨了 取代基及共轭链长与分子微观非线性光学效应的关系和规律。结构表明:吸电子或供电子基团的引入, 有利于增强分子的微观非线性光学效应, 但该效应随取代基数目增多有减缓的趋势, "饱和"取代时由于"饱和效应"而使β~vec值降低; 取代基间的距离增大, 分子的β~vec值提高, 端基代时β~vec值最大; 取代共轭多烯的lnβ~vec与分子中所含双键数n之间具有线性关系。本文还对上述结论给出了理论解释。     

双核V配合物中金属-金属键的INDO定域化方法研究

本文利用INDO和E_R定域化方法,对Ⅴ~2(μ-η^2-S~2)~2(SCCH~2)~4和[V~2O~2Cl~6]^2-双核配合物进行了量子化学计算研究,讨论了它们的电子结构和化学键性质,并讨论了利用mulliken键序判别金属原子间成键的可靠.进而基于过渡金属原子主要是以d亚层轨道参与成键,建议用金属原子d亚层的键序讨论键强度的新方法.     

(CH3)2N(C6H4)nCN系列分子二阶非线性光学系数的理论研究

在AM1和INDO/CI方法的基础上, 用自编程序计算了(CH3)2N(C6H4)nCN(n=1→6)系列分子的二阶非线性光学系数β~i~j~k和β~μ并系统地研究了共轭链长对分子二阶非线性光学系统的影响及β~μ对激光场频率的依赖关系(色散效应)     

炼铝用碳阳极中碱金属氧化物作用机理的量子化学研究

本文应用CNDO/2法研究了炼铝用碳阳极中添加碱金属氧化物的吸附行为, 通过优化得到了吸附的最佳模型, 考察了吸附结合能随分子间距的变化, 进而给出了碱金属氧化物在碳阳极中作用的机理。量子化学计算结果表明: 碱金属氧化物添加到炼铝用碳阳极中起传输电子的电桥作用, 是碳阳极在空气中氧化反应以及铝电解时生成氧气的氧化反应的催化剂; 理论计算和实验结果二者吻合较好, 可以用来解释若干实验结果。     

集值映射的(C,ε)-超次微分和集值优化问题的最优性条件北大核心CSCD

本文研究了集值映射的(C,ε)-超次微分.首先,引进了集合的(C,ε)-超有效点,呈现了(C,ε)-超有效点的一些性质和等价刻画,在(C,ε)-超有效性意义下,获得了集值优化问题的标量化定理.其次,定义了集值映射的(C,ε)-超次微分,研究了(C,ε)-超次微分的存在条件,建立了用(C,ε)-超次微分刻画的Moreau-Rockafellar定理.最后,作为应用,建立了涉及(C,ε)-超次微分的集值优化问题的最优性条件.本文获得的结果统一和推广了一些文献中用超次微分或ε-超次微分刻画的结果.     

The Discrete Approximation of Continuous-state Nonlinear Branching Processes in Lévy Random Environments北大核心CSCD

In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

一般Brown桥的解析解、数值解及仿真

对任意区间[t₀,t₁]任意初值为x₀和终值为x₁的Brown桥,即随机微分方程dx=(x₁-x)/(t₁-t)dt+dB(t) x(t₀)=x₀,给出其解析解(包括随机积分解和Fourier级数解),及Milstein数值解并进行期望和方差分析,求得期望函数、期望±标准差曲线和95%置信区间边界曲线.并对不同Brown运动对应的不同轨线实现进行仿真模拟.对一个非真实的近似解加以辨别.     

5-取代丙二酸亚异丙酯的结构研究 II: 5-(α-异丙基)-2,2-二甲基-1,3-二氧杂环乙烷-4,6-二酮的晶体结构及量子化学计算

5-(α-异丙基)-2,2-二甲基-1,3-二氧杂环己烷-4,6-二酮C9H14O4, MT=186.21, 正交晶系, 空间群为P212121, 晶胞参数为: a=5.228(1), b=11.079(4), c=16.955埃.V=892.1(5)埃^3, Dc=1.286g.cm^-^3. Z=4, μ(MoKa)=0.92cm^-^1. 用直接法解出结构, 经最小二乘法修正, 最后的偏离因子R=0.062. 结构 测定表明, 分子内六元环具有扭曲船式结构. 对5-(α-苯乙基)-2,2-二甲基-1,3-二氧杂环己烷-4,6-二酮的CNDO/2计算表明, 最稳定构型是扭曲船式结构, 与X射线晶体分析 结果相一致.     

Huckel-hubbard相关图

Huckel模型和Heisnberg-Dirac模型考虑了两种不同的相互作用,前者为单电子作用,而后者仅考虑了电子相关作用,它们是 Hubbard 模型的两种极限情形.本文以四轨道四电子体系为例讨论了三种模型,所得到的Huckel-Hubbard相关图展示了它们的适用范围及其相互关系,这样处理具有代表性,可以推广到较大的共轭体系.