C_（60）~（2－）单态的Jahn－Teller畸变和光谱性质

用ＩＮＤＯ系列方法，对Ｃ单态进行几何构型优化，得到３种不同对称性的构型：Ｄ５ｄ、Ｄ３ｄ、Ｄ２ｈ。表明Ｃ已发生Ｊａｈｎ－Ｔｅｌｌｅｒ畸变，Ｄ５ｄ有４种原子７种键；Ｄ３ｄ有６种原子１０种键；Ｄ２ｈ有９种原子１５种键。额外负电荷主要分布在赤道附近。以这３种构型为基础分别计算了Ｃ单态的电子光谱，说明Ｃ的基态应该是三态。     

On Mixed Pressure-Velocity Regularity Criteria to the Navier-stokes Equations in Lorentz Spaces,Part Ⅱ:The Non-slip Boundary Value Problem

This paper is a continuation of the authors recent work [Beir?o da Veiga, H.and Yang, J., On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces, Chin. Ann. Math., 42(1), 2021, 1–16], in which mixed pressure-velocity criteria in Lorentz spaces for Leray-Hopf weak solutions of the three-dimensional NavierStokes equations, in the whole space R~3 and in the periodic torus T~3, are established. The purpose of the present work is to extend the result of mentio...     

The residual symmetry,B?cklund transformations,CRE integrability and interaction solutions:(2+1)-dimensional Chaffee-Infante equation

In this paper, we consider the(2+1)-dimensional Chaffee–Infante equation, which occurs in the fields of fluid dynamics, high-energy physics, electronic science etc. We build B?cklund transformations and residual symmetries in nonlocal structure using the Painlevé truncated expansion approach. We use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation group. In this transformation group, we deliver new exact solution profiles via the combi...     

Operations on 3-Dimensional Small Covers

The purpose of this paper is to study relations among equivariant operations on 3-dimensional small covers. The author gets three formulas for these operations. As an application, the Nishimura＇s theorem on the construction of oriented 3-dimensional small covers and the Lu-Yu＇s theorem on the construction of all 3-dimensional small covers are improved. Moreover, for a construction of 3-dimensional 2-torus manifolds, it is shown that all operations can be obtained by using the equivariant surgeries.     

Asymptotics of Stationary Navier Stokes Equations in Higher Dimensions

We show that the asymptotics of solutions to stationary Navier Stokes equations in 4, 5 or 6 dimensions in the whole space with a smooth compactly supported forcing are given by the linear Stokes equation. We do not need to assume any smallness condition. The result is in contrast to three dimensions, where the asymptotics for steady states are different from the linear Stokes equation, even for small data, while the large data case presents an open problem. The case of dimension n = 2 is still harder.     

The Picard Theorem on S-metric spaces

Recently, the notion of an S-metric space is defined and extensively studied as a generalization of a metric space. In this paper, we define the notion of the S∞-space and prove its completeness. We obtain a new generalization of the classical "Picard Theorem".     

C60的理论研究—Jahn—Teller变形,电子结构和光谱性质

本文用ＩＮＤＯ系列方法对Ｃ６０进行了几何构型优化，得到Ｄ５ｄ对称性的构型，表明Ｃ６０确实发生了Ｊａｈｎ－Ｔｅｌｌｅｒ畸变，导致原Ｃ６０Ｉｈ对称性的球体沿五重轴拉长而单键变短双键变长。其额外负电荷主要分布在赤道附近，以此构型为基础，计算了Ｃ６０的电子光谱，与实验值吻合，在对光谱进行理论指认的同时讨论了光谱红移的原因。     

关于确定“规定非比例伸长应力”的探索

关于确定“规定非比例伸长应力”的探索黄帆，刘承安（北京联合大学自动化工程学院北京１０００８３）（北京科技大学北京１０００８３）１引言高精度电子万能试验机采用两点法求弹性模量Ｅ，出现与传统值差别较大的问题［’］，已为用户所公认．但是，求得合适的Ｅ以后，...     

C76及Cn76离子的电子结构和单态的电子光谱

KxC76不同于K3C60的半导体行为[1]引起了我们对Cn-76的研究兴趣. 自Ettl[2]分离表征C76以来, 相应的实验及理论研究已经开始[3,4], 但对C-76以外其它离子的电子结构和光谱的理论研究尚未见报道. 本文用INDO系列方法对Cn76进行系统研究, 考察其是否发生Jahn-Teller畸变, 首次计算了Cn76单态离子的电子光谱, 对电子跃迁进行理论指认, 讨论了Cn76光谱的特征吸收与C76相比发生红移的原因.     

苝二酸酐与嘧啶衍生物的氢键组装

Semi-empirical AM1 method was used to study 1:1 and 1:2 hydrogen bond complexes formed with perylene dianhydride and pyridine derivatives. The weak interaction energy become bigger as the number of hydrogen bonds increases. The donor groups on the host and electron-withdrawing groups on the guest molecules favor hydrogen bonding interactions, and the formation of hydrogen bonding leads to electron density flow from the host to the guest molecules. Electronic spectra of these complexes were computed using INDO/SCI method. Blue-shift of the electronic absorption spectra for the complexes, comparing that of the host,takes place, and the first peaks for different complexes changed slightly. These are in agreement with the experimental results. The cause of blue-shift was discussed, and the electronic transitions were assigned based on theoretical calculations. The potential curve of double proton transfer in the complex was calculated, and the transition state and activated energy relative to the N-H bond were obtained.