Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

Self-diffusion of multiarm star polymers in solution far from and near the ordering transition

The self-diffusion of three 128-arm polybutadiene star solutions in toluene was investigated over a broad concentration range from dilute to the ordering region with pulsed field gradient NMR (PFG-NMR). The strong concentration dependence of the self-diffusion coefficient in the fluid state is distinguished clearly from that of linear chains and can be described by a non-Arrhenius VFT-like equation with the concentration playing the role of inverse temperature. In the concentrated regime, the observation of two dynamic phases reflects the coexistence of crystalline and liquid phases over a limited concentration region. The concentration dependences of both the ordinary (fluid-like) diffusion and the completely restricted in-cage motion of these hyper stars are in agreement with the behavior of concentrated colloidal suspensions.     

图的Hyper-Wiener指数的综述(英文)

设G是一个图.G的顶点u和v的距离是u和v之间最短路的长度.Wiener指数是G中所有无序顶点对之间距离之和,而Hyper-Wiener指数定义为WW(G)=?∑u,v∈V(G)d(u,v)+?∑u,v∈V(G)d2(u,v),式中的和取遍G的所有顶点对.本文总结了图的Hyper-Wiener指数的最近结论.     

ON A HYPER HILBERT TRANSFORM＊＊＊＊

The authors define the directional hyper Hilbert transform and give ita mixed norm estimate. The similar conclusions for the directional fractional integral of one dimension are also obtained in this paper. As an application of the above results, the authors give the Lp-boundedness for a class of the hyper singular integrals and the fractional integrals with variable kernel. Moreover, as another application of the above results, the authors prove the dimension free estimate for the hyper Riesz transform. This is an extension of the related result obtained by Stein.     

非齐次线性微分方程解的增长性

研究了非齐次线性微分方程f^{(k)}+A_{k-1}(z)f^{(k-1)}+...+A_{s}(z)f^{(s)}+...+A_{0}(z)f=F(z) 解的增长性,其中A_{j}(j=0,1,\cdots,k-1)及F是整函数. 在A_{s}比其他系数有较快增 长的情况下,得到了上述非齐次微分方程在一定条件下的超越整函数解的超级的精确估计.     

亚纯系数的高阶线性微分方程的解的增长性

本文研究亚纯系数的高阶线性微分方程,当方程系数满足一定条件时,得到方程的每一非零亚纯解具有无穷级且超级为n.此外,还研究了非齐次线性微分方程的亚纯解.     

Stochastic Models for the Amount of Overflow in a Finite Dam with Random Inputs,Random Outputs,and Exponential Release Policy

In this article, we discuss finite dam models to study the expected amount of overflow in a given time. The inputs into the dam are taken as random and there are two types of outputs—one is random and the other is deterministic which is proportional to the content of the dam. The master equation for the expected amount of overflow is an one dimensional equation with separable kernel. For this class of master equation, the integral equation for the expected amount of overflow has been transformed exactly into ordinary differential equation with variable coefficients. The imbedding method is used to study the expected amount of overflow in a given time without emptiness in this period. We also consider the model for the expected amount of overflow in a given time with any number of emptiness of the dam in this period. The results are derived in the form of a third order differential Equation for the Laplace transformation function for the expected overflow. The closed form analytical solutions are obtained in terms of beta functions and degenerate hyper-geometric functions of two variables.     

A Hyper‐conjugated Structure: The Research into the Picryl Chloride Functionalized 1‐Picrylamino‐tetrazol‐5‐one

A hyper conjugated structure, picryl chloride functionalized 1‐picrylamino‐tetrazol‐5‐one, was synthesized by a nucleophilic substitution reaction. The single crystals of 1‐picrylamino‐tetrazol‐5‐one were cultured and determined by X‐ray single‐crystal diffractometer. The thermal behavior was investigated by differential scanning calorimetry (DSC) and thermogravimetry‐derivative thermogravimetry (TG‐DTG) technologies. Additionally, the sensitivities towards friction and impact were tested. The results show that the hyper conjugated structure adopts a π–π stacking, besides, many strong interactions such as nitro–π and hydrogen bonding interactions were observed. All of them together make a contribution to its enhanced thermal stability and reduced sensitivities. 1‐Picrylamino‐tetrazol‐5‐one turns out to be a representative of hyper conjugated structures in energetic materials, and may further strengthen the functionalization of picryl chloride with energetic tetrazoles.     

分层关联表中伞形序对无约束问题的检验

概率分布间的随机序是应用概率论与统计推断中的一个重要概念. 基于交叉分类数据的趋势检验问题已被广泛地研究, 并且分层关联表广泛存在于实践中. 似然比检验方法常用于涉及随机序约束问题的检验. 对带序约束的分层关联表, 该文介绍了一种不基于模型假定的似然比检验方法, 并且给出了检验统计量的极限分布.     

二阶微分方程解的零点分布

应用角域Nevanlinna理论和Ahlfors覆盖曲面理论, 研究了二阶微分方程f’’+A(z)f=0的解的零点分布. 证明了在复平面上至少存在一条半直线, 使得二阶微分方程解在该直线上的零点的径向收敛指数为无穷. 用新的方法证明了伍胜健在文献[5]中的一个定理.