奇 $Hamiltonian$ 超代数偶部的负 $\mathbb{Z}$-齐次导子

本文主要研究了特征 $p>3$ 的域上的有限维奇 $Hamiltonian$ 李超代数 $HO$ 的偶部到广义 $Witt$李超代数 $W$ 的奇部的负$\mathbb{Z}$-齐次导子. 我们利用 $\mathcal{HO}$ 的生成元集, 通过计算导子在其生成元集上的作用的方法, 首先计算了$\mathbb{Z}$-次数为 $-1$ 的导子, 然后决定了 $\mathbb{Z}$-次数小于 $-1$ 的导子.     

Polyhedra associated with identifying codes

The identifying code problem is a newly emerging search problem, challenging both from a theoretical and a computational point of view, even for special graphs like bipartite graphs. Hence, a typical line of attack for this problem is to determine minimum identifying codes of special graphs or to provide bounds for their size. In this work we study the associated polyhedra and present some general results on their combinatorial structure. We demonstrate how the polyhedral approach can be applied to find minimum identifying codes for special bipartite graphs, and discuss further lines of research in order to obtain strong lower bounds stemming from linear relaxations of the identifying code polyhedron, enhanced by suitable cutting planes to be used in a B&C framework.     

Dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate liquid crystal

The dielectric and elastic properties of liquid crystals (LCs) generally depend on the molecule structure, such as polar group and carbon chain length. For further investigation of the influence of molecular structure on the dielectric and elastic properties of fluorine-containing tricyclic isothiocyanate LC, the experimental temperature was controlled at 25°C by precision hot stage, and a precision LCR meter was used to measure the capacitance of six LC cells under the voltage from 0.1 to 20 V at 1 kHz. An LC cell capacitance model and a dual-cell model were adopted to obtain the dielectric anisotropy, and the capacitance–voltage curves of six LC materials were plotted. The threshold voltage of Fréedericksz transition was analysed, and a finite difference iterative method was used to attain specific values of three elastic constants. The influence of molecular structure on the dielectric and elastic constants was finally analysed. Experimental results showed that the introduction of meta-difluoro group would increase the dielectric anisotropy and reduce the threshold voltage of LC. As the length of the alkyl carbon chain increased, the dielectric anisotropy would have an odd–even alternation effect, which would lead to changes in the elastic constants of LC.     

奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

Elucidating the mass spectrum of the retronecine alkaloid using DFT calculations

Pyrrolizidine alkaloids are natural molecules playing important roles in different biochemical processes in nature and in humans. In this work, the electron ionization mass spectrum of retronecine, an alkaloid molecule found in plants, was investigated computationally. Its mass spectrum can be characterized by three main fragment ions having the following m/z ratios: 111, 94, and 80. In order to rationalize the mass spectrum, minima and transition state geometries were computed using density functional theory. It was showed that the dissociation process includes an aromatization of the originally five‐membered ring of retronecine converted into a six‐membered ring compound. A fragmentation pathway mechanism involving dissociation activation barriers that are easily overcome by the initial ionization energy was found. From the computed quantum chemical geometric, atomic charges, and energetic parameters, the abundance of each ion in the mass spectrum of retronecine was discussed.     

光子晶体光纤耦合器中的标量调制不稳定性

从光纤耦合器的耦合模方程出发,用偶奇超模对其进行重写,讨论了当输入条件使奇偶超模其中之一被单独激发时,在光子晶体光纤耦合器中的调制不稳定性.结果表明：光子晶体光纤耦合器中在正常和反常色散区均存在调制不稳定性,并且调制不稳定性与三阶色散项无关、与四阶色散项有关,给出了增益谱在不同色散区随输入功率的变化关系;当满足一定条件时,在光子晶体光纤耦合器中传播的准连续波可以分解成脉冲序列,由此可以分离和提取超短脉冲. 关键词： 光子晶体光纤耦合器 偶次超模 奇次超模 标量调制不稳定性     

双曲正弦、余弦算符与奇偶相干态

利用Fock空间的平移算符引入了双曲正弦和余弦算符,该算符作用在真空态上给出奇相干态和偶相干态的一种新表示形式,并讨论了奇、偶相干态的准概率分布函数和非经典特性．