粘合、倾斜同调维数与高维Auslander-Reiten理论

本文主要研究阿贝尔范畴粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中$\mathscr{A}$, $\mathscr{B}$与$\mathscr{C}$之间的倾斜同调维数关系. 特别地,对遗传的阿贝尔范畴$\mathscr{B}$,给出了粘合$(\mathscr{A}, \mathscr{B}, \mathscr{C})$中的范畴之间的$n$-几乎可裂序列间的联系.     

Algebraic techniques for least squares problem over generalized quaternion algebras: A unified approach in quaternionic and split quaternionic theory

This paper aims to present, in a unified manner, algebraic techniques for least squares problem in quaternionic and split quaternionic mechanics. This paper, by means of a complex representation and a real representation of a generalized quaternion matrix, studies generalized quaternion least squares (GQLS) problem, and derives two algebraic methods for solving the GQLS problem. This paper gives not only algebraic techniques for least squares problem over generalized quaternion algebras, but also a unification of algebraic techniques for least squares problem in quaternionic and split quaternionic theory.     

微分学中构造函数的新方法

结合实例将常微分方程中的首次积分和特征方程理论应用于微分学中函数的构造,从而使之有章可循.     

Laplacian differential reconstruction of one in-line digital hologram

We introduced an easy approach to realize the Laplacian first-order and second-order differential of the object wave in transverse direction by use of one in-line digital hologram. It can be used for pinpoint the position of the objects.     

DFT-BS study on the magnetic coupling interaction in a series of (R-Bpmp)Mn2(μ-OAc)2 complexes

The magnetic properties of a series of dinuclear Mn^II systems are investigated by the calculations based on density functional theory combined with broken-symmetry approach (DEF-BS). It is found that there are weak antiferromagnetic interactions in these systems with different bridging ligands. The changing trend of the magnetic coupling constants J indicates that with the electronegativity of the increasing bridging ligands, the antiferromagnetic coupling interaction is weakened. The analyses of the magnetic orbitals and the spin densities show that the weakly antiferromagnetic couplings in these systems are due to the vertical magnetic d orbitals and the weak spin delocalization. These results should be instructive for the design of new molecular magnetic materials.     

Interaction between adrenaline and dibenzo-18-crown-6: Electrochemical,nuclear magnetic resonance,and theoretical study

The interaction between adrenaline (Ad) and dibenzo-18-crown-6 (DB18C6) was studied by cyclic voltammetry, nuclear magnetic resonance spectroscopy, and the theoretical calculations, respectively. The results show that DB18C6 will affect the electron transfer properties of Ad. DB18C6 can form stable supramolecular complexes with Ad through ion-dipole and hydrogen bond interactions.     

Theoretical Studies on the Reactions of 1,1,2,2,3,3,4‐Heptafluorocyclopentane with Hydroxyl and Hydrogen Free Radicals

1,1,2,2,3,3,4‐Heptafluorocyclopentane (F7A) has considerable potential to be a new halon replacement due to its environmental friendliness and low‐toxicity. However, the reaction processes of F7A with hydroxyl and hydrogen free radicals, which are of great importance for investigating its fire suppression mechanisms, are still unclear. In this paper, ab inito and density functional theory are used to deduce the possible reaction pathways for the reactions of F7A with hydroxyl and hydrogen free radicals at the CCSD/cc‐pVDZ//B3LYP/6‐311++G (d,p) level of theory. Two distinct reaction pathways including ten elementary reaction channels for F7A with hydroxyl free radical, and five distinct reaction pathways including twenty elementary reaction channels for F7A with hydrogen free radical are investigated. The geometries, vibrational frequencies and reaction energy barriers are also determined. Based on the calculated results, the possible reaction mechanisms are proposed and discussed. The most feasible reaction channel for F7A with hydroxyl free radical is that leads to CH(OH)CH₂(CF₂)₃+·F, and the most feasible reaction channel for F7A with hydrogen free radical is that leads to (CF₂)₃CH₂CH·+HF. The study is helpful to further study its fire suppression mechanisms and promote it to be a new generation of halon replacement.     

保等价部分变换半群的变种半群上的正则元

在现有的保等价部分变换半群的基础上,引入了一个新的运算,得出保等价部分变换半群的变种半群的概念,利用格林关系及幂等元的正则性,讨论了这类半群中元素的正则性,给出了保等价部分变换半群的变种半群中一个元是正则元的充要条件     

研究宇称算符的一种新方法

在量子力学中,宇称算符P^的3种表象积分分别表示为∫d2zπ|z〉〈-z|、∫dq|q〉〈-q|和∫dp|p〉〈-p|.借助Dirac符号法和量子力学表象的完备性,找到了一种非常新颖的方法,给出了宇称算符的积分显式.