On ordered categories as a framework for fuzzification of algebraic and topological structures

Using the framework of ordered categories, the paper considers a generalization of the fuzzification machinery of algebraic structures introduced by Rosenfeld as well as provides a new approach to fuzzification of topological structures, which amounts to fuzzifying the underlying “set” of a structure in a suitably compatible way, leaving the structure itself crisp. The latter machinery allows the so-called “double fuzzification”, i.e., a fuzzification of something that is already fuzzified.     

CH3SH…HOO开壳型氢键复合物的结构及其电子密度拓扑性质

在DFT-B3LYP/6-311++G**水平下求得CH3SH…HOO复合物势能面上的稳定构型. 计算结果表明, 在HOO以其O8—H7作为质子供体与CH3SH分子中的S5原子为质子受体形成的氢键复合物1和2中, O8—H7明显被“拉长”, 且其伸缩振动频率发生显著的红移, 红移值分别为330.1和320.4 cm-1; 在CH3SH分子以其S5—H6作为质子供体与HOO的端基O9原子为质子受体形成的氢键复合物3和4中, 也存在类似的情况, 但S5—H6伸缩振动频率红移不大. 经MP2/6-311++G**水平计算的4种复合物含BSSE校正的相互作用能分别为-20.81, -20.10, -4.46和-4.52 kJ/mol. 自然键轨道理论(NBO)分析表明, 在CH3SH…HOO复合物1和2中, 引起H7—O8键长增加的因素包括两种电荷转移, 即孤对电子n1(S5)→σ*(H7—O8)和孤对电子n2(S5)→σ*(H7—O8), 其中后者为主要作用. 在复合物3和4中也有相似的电荷转移情况, 但轨道间的相互作用要弱一些. AIM理论分析结果表明, 4个复合物中的S5…H7间和O9…H6间都存在键鞍点, 且其Laplacian量▽2ρ(r)都是很小的正值, 说明这种相互作用介于共价键和离子键之间, 偏静电作用为主.     

乙醛二聚体内蓝移型氢键的理论研究

利用理论方法研究了乙醛二聚体内的氢键. 在MP2/6-31＋G(d), B3LYP/6-31＋G(d), B3LYP/6-311＋＋G(d,p)和B3LYP/6-311＋＋G(3df,2p)水平上, 利用常规方法和均衡校正方法对3种稳定的乙醛二聚体进行了几何优化和振动频率计算. 计算结果表明: 在二聚体A和C中乙醛中C—H键强烈收缩, 存在显著的C—H…O蓝移型氢键. 自然键轨道(NBO)分析表明, 电子供体轨道和电子受体轨道之间相互作用的稳定化能、分子内电子密度重排、轨道再杂化和结构重组是决定氢键红移和蓝移的主要因素. 其中, 轨道间稳定化能属于键伸长效应, 分子内电子密度重排、轨道再杂化和电子受体内部结构重组属于键收缩效应. 在二聚体A和C中, 由于键收缩效应处于优势地位导致C—H…O蓝移氢键存在.     

Z—P—S空间中一类新的不动点定理

利用概率度量空间中A—proper映射拓扑度的基本性质,在投影完备的Z—P—S空间中研究了非线性映射的不动点问题,得到了一些新的结果．     

Closedness of the solution map for parametric weak vector equilibrium problems

In this paper we introduced a new definition of vector topological pseudomonotonicity to study the parametric weak vector equilibrium problems. The main result gives sufficient conditions for closedness of the solution map defined on the set of parameters.     

关于拓扑对策中的I2(κ)(∈)I(κ)问题

证明了如果空间类K为D-空间类或闭遗传不可约空间类,则I（K）包含K.这一结果对于K为D空间类和闭遗传不可约空间类,肯定地回答了I（K）是否包含I^2（K）问题.     

Static reanalysis for topological modifications of structures

A procedure for reanalysis of various structures subjected to various topological modifications is presented. The procedure is based on the results of a single exact analysis and the factorization of the stiffness matrix of initial structures. It is suitable for the case of addition of joints, where the number of the degrees of freedom is increased. The method deals with the stiffness matrix of structures directly, so it can be used with a general finite element system. It is shown that the proposed approximation method is most effective in terms of accuracy, efficiency, and ease of implementation.     

Influence of pressure on electron spectra of metals and semiconductors

Abstract

We have already reported the results of direct observations of electron-topological phase transition (ETT) in cadmium'. The appearance of new dHvA-frequencies corresponding to the Fermi surface (FS) change, i.e. restoring of folding of hole “monster” and electron “needle” appearance is observed under pressure. In t h i s report we are going to enlarge on the ETT consequences study in cadmium-on the advent of anomalous electronic features in transverse magnetoresistance and thermoelectric power.