Hopf代数上的扭曲模和(斜)余配对Hopf模

本文第一部分主要把扭曲的方法运用到模上,从而得到扭曲模．作为特例,我们构造了H  M的Smaush模和量子模．当K是有限维Hopf代数,证明K*  M是一个右D(K)-Hopf模,因此得到了一个基本同构定理．第二部分主要把斜余配对双代数进行推广,得到了斜余配对Hopf模,并且给出判断斜余配对Hopf模的一个充要条件．     

New (1R,4R)-2-arylidene-p-menthan-3-ones with a bridging ester group in the arylidene fragment. Synthesis and behavior in liquid-crystalline systems

(1R,4R)-2-(4-Hydroxybenzylidene)- and (1R,4R)-2-(4"-hydroxybiphenyl-4-yl)methylene-p-menthan-3-ones were synthesized by condensation of (–)-menthone with O-tetrahydropyran-2-yl derivatives of 4-hydroxybenzaldehyde and 4"-hydroxy-4-formylbiphenyl, respectively, in a DMSO—base medium followed by the removal of the protective group. The reactions of these hydroxy derivatives with 4-alkylbenzoic, 4-alkyloxybenzoic, trans-4-alkylcyclohexane-4-carboxylic, and 4"-alkylbiphenyl-4-carboxylic acids afforded three series of new chiral esters. Compounds containing the arylidene moiety with three benzene rings were found to exhibit liquid-crystalline properties. The characteristic features of these compounds are discussed based on the results of studies by polarizing microscopy, differential scanning calorimetry, and small-angle X-ray scattering. It was found that the mesomorphic compounds under study can form a smectic A mesophase, twist grain boundary mesophases (TGBA), and blue phases in a wide temperature range. Upon dissolution of certain of chiral compounds in 4"-cyano-4-pentylbiphenyl, a rather high twisting power and the thermal stabilizing effect on mesophases were observed.     

Cholesteric induction power of β-galactose derivatives

Galactose derivatives were explored as chiral dopants, effective for inducing chiral nematic liquid crystal (LC) phases. Galactose bearing O-isopropylidene substituents at the C3 and C4 and butoxybiphenyl substituents at the C2 and C6 positions exhibits a high helical twisting power (HTP) value of ?74.4 μm^?1. Such a high HTP value for the galactose derivative is attributed to (1) linkage of the C3 and C4 carbons with the O-isopropylidene substituent, which places the C2 and C6 substitutes in a skew arrangement at a large angle and (2) enhancement of the affinity with the host nematic LCs by incorporating aromatic substituents at the C2 and C6 positions that are similar to those in the host.     

A field-reversal method for measuring the parameters of a ferroelectric liquid crystal

A method for measuring the spontaneous polarization P _s, the switching time, the rotational viscosity γ_φ, and the d.c. conductivity σ is presented. The possibilities of estimating the azimuthal angle φ₀, the dielectric anisotropy δε and the dielectric permittivity ε_⊥ in the same experiment are also discussed. It is explicitly shown that the switching delay, though primarily dependent on the material and the applied field, is also dependent on the geometry of the cell.     

Numerical analysis of nematic liquid crystal alignment on asymmetric surface grating structures

The influence of an asymmetric periodic grooved cell surface on the 2D static director configuration of a nematic liquid crystal has been investigated. The minimum in the Frank-Oseen free energy was solved numerically with the Rapini-Papoular form of the surface anchoring energy at the nematic-grating interface. Results are presented for the variation of pretilt angle in the tilted bulk director field as a function of the surface groove depth, pitch and asymmetry and the bulk parameters. The simulations demonstrate the existence of two energetically degenerate high and low pretilted bulk alignment configurations. The pretilt values in these two regimes and also for the low tilt regime with finite surface anchoring are consistent with experimental results. An effective increase in the resolution of the model is obtained by using an irregular grid to describe the surface profile.     

具扰动项的L—R型迁移方程的谱问题

本文在Lp（1≤P〈＋∞）空间上,研究了种群细胞增生中一类具扰动项的L—R模型,证明了这类模型相应的迁移算子生成半群的Dyson—Phillips展式的9阶余项R9（t）在L1空间上是弱紧和在Lp（1〈P〈＋∞）空间上是紧的,从而获得了该迁移算子的谱在右半平面上仅由有限个具有限代数重数的离散本征值组成及该迁移方程解的渐近稳定性等结果．     

相关扭曲Hopf模的基本同构定理与相关Yetter-Drinfel'd模

扭曲的方法在构造新的代数结构与余代数结构中起了重要的作用.本文首先把扭曲的方法运用到模与余模的构造中,得到扭曲模和扭曲余模;其次在更加一般的情形下给出相关扭曲Hopf模的基本同构定理;最后考虑在HopfYD模中如何使扭曲模构成相关Yetter-Drinfel'd模和相关Hopf模.     

基于Bonissone近似算法的群决策方法

把模糊数学理论应用到群决策领域是解决不确定问题的有效方法 .介绍了定性语言描述转化成定量模糊序关系的方法 ;采用 Bonissone的 L-R梯形模糊数近似算法 ,提出了基数型和序数型决策问题的群决策程序 ;用实例说明了这种群决策方法的使用步骤 .