Lβ集合套与La集合套理论及应用

本文在Ｌ是完全分配格时，借助极小集与极大集概念引入了Ｌβ集合套与Ｌａ集合套，它们是集合套概念的推广，但不同于Ｌ集合套。得到了一般Ｌ－ｆｕｚｚｙ集的若干新的分解定理与表现定理，进一步又给出了它们在Ｌ－ｆｕｚｚｙ代数，Ｌ－ｆｕｚｚｙ拓扑等方面的若干应用。     

对偶导集及其应用

借助对偶范畴的思想和方法在点集拓扑学中引入了对偶导集概念,讨论了对偶导集和对偶导集运算的相关性质.并以此为基础引入了对偶连通空间的概念,讨论了对偶连通空间和连通空间之间的关系,借此给出了不连通空间的几个等价刻画.为拓扑空间的研究提供了新的途径.     

HNO二聚体蓝移氢键的理论研究

利用分子轨道从头算理论和密度泛函理论结合不同理论基组对于N-H…O蓝移氢键进行了详细的研究.利用标准方法和均衡校正方法对二聚体进行了几何优化,振动频率和相互作用能的计算.拓扑学和自然键轨道理论对于蓝移氢键的本质进行分析.自然键轨道(NBO)分析表明,σ*(N-H)轨道上电子密度降低是电子密度重排效应的结果.分子内电子重排、轨道再杂化和电子受体内部结构重组共同作用结果导致了N-H的振动频率大幅蓝移现象的出现.     

Topological Vortices in a Spin-Triplet Superconductor

Based on the complex three-component order parameter model of a spin-triplet superconductor, by using the C-mapping theory, we derive a new equation describing the distribution of the magnetic field for vortices, which can be reduced to the modified London equation in the case of ｜ψ^2｜^2 ~- ｜ψ^3｜^2 = 0 and Wl^1= 1. A magnetic flux quantization condition for vortices in a spin-triplet superconductor is also derived, which is topological-invariant. Fhrthermore, the branch processes during the evolution of the vortices in a spin-triplet superconductor are discussed. We also point out that the sum of the magnetic flux quantization that those vortices carried is 2nФo （Фo is the unit magnetic flux）, that is to say, the sum of winding number is even, which needs to be proved by experiment.     

Topological Aspects of Solitons in Ferromagnets

Two kinds of topological soliton （skyrmion and magnetic vortex ring） in ferromagnets are studied. They have the common topological origin, a tensor Hαβ = n→·（δαn→×βδn→）, which describes the non-trivial distribution of local orientation of magnetization n→ at large distances in space. The topological stability of skyrmion is protected by the winding number. Knot-like topological defect as magnetic vortex rings is also studied. On the assumption that magnetic vortex rings are geometric lines, we present their δ-function distribution in ferromagnetic materials. Furthermore, it is briefly shown that Hopf invariant is a proper topological invariant to describe the topology of magnetic vortex rings.     

A Novel （4,6）-Connected Net Based on Dysprosium Benzenedicarboxylate, [Dy（OAc）（BDC）]n

A new lanthanide coordination polymer, [Dy（OAc）（BDC）]n 1 （OAc = acetate, BDC = 1,4-benzenediacarboxylate）, has been synthesized under hydrothermal conditions. Single-crystal X-ray diffraction analysis reveals that complex 1 has infinite zigzag Dy-OAc chains, which are further connected by BDC to form a 3D metal-organic framework. According to topology analysis, this framework can be characterized as （4,6）-connected （3.4.54）（32.4.56.66） net that has never been reported before. Crystal structure for 1： space group Pbca, a = 13.314（3）, b = 8.0269（18）, c = 20.275（5）A, V= 2166.8（9）A3, C10H7O6Dy, Mr = 385.66, Z= 8, Dc = 2.364 g/cm^3, μ= 6.910 mm^-1, F（000） = 1448, the final R = 0.0181 and wR = 0.0520.     

晶粒棱长、尺寸与拓扑学特征之间关系的Monte Carlo仿真研究

采用Potts模型Monte Carlo方法研究了晶粒棱长、尺寸与拓扑学特征之间的统计关系.结果表明,晶粒棱长与晶粒面数之间呈线性统计关系,并且平均N面体晶粒模型和Poisson-Voronoi组织均支持该结论.不同时刻的晶粒长大仿真数据表明,在准稳态晶粒长大阶段晶粒棱长的分布具有自相似性.个体晶粒的平均棱长随晶粒面数（或晶粒尺寸）的增加而逐渐增大,这说明一些理论模型中采用的“不同面数的晶粒平均棱长均相等”的假设具有局限性.仿真数据和纯铁实验数据均表明,晶粒尺寸与晶粒面数之间的统计关系表现为一条单调递增的凸曲线. 关键词： 晶粒棱长 晶粒尺寸 拓扑学 Monte Carlo仿真     

L-fuzzy层次拓扑空间的I_r-可数性

在L-fuzzy层次拓扑空间中,引入了第一Ir-可数空间和第二Ir-可数空间等概念,分别给出了第一Ir-可数空间和第二Ir-可数空间的基本性质.讨论了这两种可数性之间的关系以及它们的应用.证明了这两种可数性都是可遗传的、可数可乘的、而且在Dα-同胚序同态下都保持不变等性质.     

生成映射的若干性质

在LF拓扑空间中,讨论了生成映射ι的若干性质,并推广了现有的相应结果.