渐近鞅差序列的大数定律

研究渐近鞅的收敛性及渐近鞅的 Doob分解 ,证明了渐近鞅差序列服从大数定律     

First-principles calculations for transition phase and thermodynamic properties of GaAs

The transition phase of GaAs from the zincblende (ZB) structure to the rocksalt (RS) structure is investigated by ab initio plane-wave pseudopotential density functional theory method, and the thermodynamic properties of the ZB and RS structures are obtained through the quasi-harmonic Debye model. It is found that the transition from the ZB structure to the RS structure occurs at the pressure of about 16.3\,GPa, this fact is well consistent with the experimental data and other theoretical results. The dependences of the relative volume V/V₀ on the pressure P, the Debye temperature \Th and specific heat C_V on the pressure P, as well as the specific heat C_V on the temperature T are also obtained successfully.     

Paraelectric--ferroelectric interface dynamics induced by latent heat transfer and irreversibility of ferroelectric phase transitions

The temperature gradients that arise in the paraelectric--ferroelectric interface dynamics induced by the latent heat transfer are studied from the point of view that a ferroelectric phase transition is a stationary, thermal-electric coupled transport process. The local entropy production is derived for a ferroelectric phase transition system from the Gibbs equation. Three types of regions in the system are described well by using the Onsager relations and the principle of minimum entropy production. The theoretical results coincides with the experimental ones.     

蒽醌及其羟基衍生物的密度泛函理论研究

运用密度泛函理论, 在B3LYP/6-31G*水平上, 对蒽醌及其羟基取代衍生物进行理论计算. 几何全优化的结果表明, 标题化合物均取平面构型, 分子内氢键对几何构型和电子结构影响很大. 基于简谐振动分析求得IR谱频率和强度, 并作了对称性分类和指认, 计算值与实验值良好相符. 运用含时密度泛函理论方法在相同水平上计算了标题物的电子吸收光谱, 发现蒽醌芳环取代衍生物的最低激发单重态均源自HOMO-LUMO(π→π*)跃迁. 基于振动分析, 由统计热力学求得了标题物的热力学性质.     

新型吡啶基修饰的尾式卟啉的合成及性质

报道了一种新型尾式锌卟啉(o-PyOC₆H₁₂OTPPZn)的合成及表征, 采用紫外-可见光谱滴定法对该化合物与5种吡啶类小分子间的轴向配位反应的热力学性质进行了研究. 轴配体系的热力学数据显示, 5种吡啶类配体的平衡常数按K(4-MePy)>K(Py)>K(3-MePy)>K(2,4,6-triMePy)>K(2-MePy)依次减小, 吡啶类小分子对主体的配位能力按4-MePy>Py>3-MePy>2,4,6-triMePy>2-MePy依次减弱, 同时分子模拟的理论研究得到了与实验完全一致的结果. 通过Z-扫描实验对该化合物的非线性光学性质的研究表明, 该样品具有较强的反饱和吸收特征.     

流动相组成和温度对衍生化b-环糊精键合固定相拆 分四种仲醇消旋体的影响

采用3,5-二甲苯基异氰酸酯衍生化β-环糊精键合固定相, 以正己烷-脂肪醇为流动相, 研究了脂肪醇结构及其浓度、柱温对2-苯基环己醇、2-萘基环己醇、4-三氟甲基-2-苯基环己醇以及3-(1-羟乙基)香豆素等四种仲醇手性拆分行为的影响. 当流动相中醇的摩尔浓度相同时, 异构体容量因子随脂肪醇碳链的增长而减小; 柱温升高, 异构体容量因子减小, 而分离因子增大. 用溶质的计量置换保留模型(SDM-R)和热力学理论对此现象进行了解释.     

多溴吩噻嗪系列化合物的稳定性和热力学性质的密度泛函理论研究

用Gaussian 03程序, 在B3LYP/6-31G*水平上全优化计算了吩噻嗪和135个多溴吩噻嗪系列化合物(PBPTHs)在298.15 K和101.3 kPa状态时的热力学参数. 设计等键反应, 计算了PBPTHs系列化合物的标准生成热( )和标准生成自由能( ). 同时研究了这些参数与溴原子的取代位置及取代数目(NPBS)之间的关系. 结果表明: 多溴吩噻嗪的热能校正值(Eth)、恒容热容( )、标准熵( )、标准焓( )以及标准自由能( )与NPBS之间有很强的相关性(r2≥0.998). 在相关方程中, 溴原子的取代个数对多溴代吩噻嗪热力学数值的大小有很大影响. 根据 的相对大小, 从理论上求得异构体的相对稳定性顺序.     

Fermionic Zero Modes in Self-dual Vortex Background on a Torus

We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in （5＋1） dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.     

Impulsive control of chaotic systems with exogenous perturbations

The impulsive control of chaotic systems, which are subjected to unbounded exogenous perturbations, is considered. By using the theory of impulsive differential equation together with the fuzzy control technique, the authors propose an impulsive robust chaos controlling criterion expressed as linear matrix inequalities (LMIs). Based on the proposed control criterion, the procedure for designing impulsive controllers of common (perturbed) chaotic systems is provided. Finally, a numerical example is given to demonstrate the obtained theoretical result.     

Coupled viscoplasticity damage constitutive model for concrete materials

A coupled viscoplasticity damage constitutive model for concrete materials is developed within the framework of irreversible thermodynamics.Simultaneously the Helmholtz free energy function and a non-associated flow potential function are given, which include the internal variables of kinematic hardening,isotropic hardening and dam- age.Results from the numerical simulation show that the model presented can describe the deformation properties of the concrete without the formal hypotheses of yield criterion and failure criteria,such as the volume dilatancy under the compression,strain-rate sen- sitivity,stiffness degradation and stress-softening behavior beyond the peak stress which are brought by damages and fractures.Moreover,we could benefit from the application of the finite element method based on this model under complex loading because of not having to choose different constitutive models based on the deformation level.