On the Rank of the Semigroup TE(X)

${\cal T}_X $ denotes the full transformation semigroup on a set $ X $. For a nontrivial equivalence $E$ on $X$, let \[ T_E (X) =\{ f\in {\cal T}_X : \forall \, (a,b)\in E,\, (af,bf)\in E \} . \] Then $T_E (X) $ is exactly the semigroup of continuous selfmaps of the topological space $X$ for which the collection of all $E$-classes is a basis. In this paper, we first discuss the rank of the homeomorphism group $G$, and then consider the rank of $T_E (X)$ for a special case that the set $X$ is finite and that each class of the equivalence $E$ has the same cardinality. Finally, the rank of the closed selfmap semigroup $\Gamma(X)$ of the space $X$ is observed. We conclude that the rank of $G$ is no more than 4, the rank of $T_E (X)$ is no more than 6 and the rank of $\Gamma(X)$ is no more than 5.     

The Gain Properties of 1-D Active Photonic Crystal

The terminology ‘ID frequency’(w ID) is proposed after analyzing the 1D active photonic crystal based on the transfer matrix method. The relationship between wID and the structure parameters of the photonic crystal is investigated.     

On Set-Theoretical Solutions to Quantum Yang-Baxter Equation

The problem on the set-theoretical solutions to the quantum Yang-Baxter equation was presented byDrinfel'd as a main unsolved problem in quantum group theory. The set-theoretical solutions are a natural extensionof the usual (linear) solutions. In this paper, we not only give a further study on some known set-theoretical solutions(the Venkov's solutions), but also find a new kind of set-theoretical solutions which have a geometric interpretation.Moreover, the new solutions lead to the metahomomorphisms in group theory.     

取代基效应(SCS)与乙烯-α-烯烃共聚物的序列结构Ⅲ.定量分析

本文在分析乙烯-α-烯烃共聚物序列结构时,把代表共单体反接单元的亚甲基(CH₂)βγ和γδ分别归属给了二元组VV和三元组EEV。与此同时,CH₂-δδ和δδ⁺归属给了二元组EE。表征乙烯长序列的CH₂-δ⁺δ⁺分属二元组EE和三元组EEE,对应峰强度在EE和EEE之间的分配是处理序列分布的关键。在本文中运用序列结构的Bovey关系和Randall统计进行演算,求得了修正值△的数学表达式,严格解和近似解。在规则链条件下得到的近似解与G.J.Ray的结果完全相同。当共单体含量较少时,谱峰强度Iδ⁺δ⁺的分配接近相等。在二元组和三元组的水平上,乙烯-α-稀烃共聚物的¹³C NMR谱中共有十三个峰,属于CH₂的有十个,属于CH的有三个。利用这些谱峰的强度数据可以建立一套计算公式,由此提供共聚物序列结构的全部信息。因此这是一个研究乙烯-α-烯烃共聚物序列结构的普适方法。     

Syntheses,crystal structures and blue emission of three zinc(II) coordination polymers with a 4,4′‐dicarboxybiphenyl sulfone ligand

Three novel zinc complexes [Zn(dbsf)(H₂O)₂] ( 1 ), [Zn(dbsf)(2,2′‐bpy)(H₂O)]·(i‐C₃H₇OH) ( 2 ) and [Zn(dbsf)(DMF)] ( 3 ) (H₂dbsf = 4,4′‐dicarboxybiphenyl sulfone, 2,2′‐bpy = 2,2′‐bipyridine, i‐C₃H₇OH = iso‐propanol, DMF = N,N‐dimethylformamide) were first obtained and characterized by single crystal X‐ray crystallography. Although the results show that all the complexes 1–3 have one‐dimensional chains formed via coordination bonds, unique three‐dimensional supramolecular structures are formed due to different coordination modes and configuration of the dbsf^2? ligand, hydrogen bonds and π–π interactions. Iso‐propanol molecules are in open channels of 2 while larger empty channels are formed in 3 . As compared with emission band of the free H₂dbsf ligand, emission peaks of the complexes 1–3 are red‐shifted, and they show blue emission, which originates from enlarging conjugation upon coordination. Copyright © 2006 John Wiley & Sons, Ltd.     

CH3S CH2SH异化反应的理论研究

利用密度泛函理论(DFT)和从头算(ab initio)研究了CH3S←→CH2SH互异化的反应机理．采用HF、B3LYP、MP2理论水平和中等基组6-31(d)，计算了CH3S、CH2SH及其过渡态的结构参数、谐振频率、零点能(ZPF)、总能量和相对能量，并利用B3LYP／6-31(d)的方法计算了反应的内禀反应坐标(IRC)，给出了分子构型和自旋污染沿反应坐标的变化曲线，以及最小能量曲线(MEP)、绝热能量曲线．此外，利用传统过渡态理论(CTST)研究了该互异化反应的速率常数和平衡常数在200～1000K的变化．     

氯离子柱撑水滑石共沉淀法合成反应动力学

根据氯离子型层状复合氢氧化物(LDH-Cl)制备过程中溶液浓度变化的监测结果和不同反应进程时产物的EDS、IR、XRD、TEM、TG-DTA表征结果,研究了合成LDH-Cl的共沉淀反应动力学特征及机理.实验结果表明, LDH-Cl的生成符合多核层表面反应动力学模型;反应过程中LDH的晶胞参数c从2.421 nm变为2.399 nm,通道高度h由0.3321 nm减小为0.3228 nm,粒子直径Da由6.40 nm增大为15.16 nm, Dc由7.43 nm增大到10.93 nm,纵横比由0.86增大为1.39; IR和TG-DTA特征变化表明了层板对阴离子作用的强度和层板的结构稳定性随反应进程而提高.     

毛细管凝胶电泳的激光光热在线检测

近年来,毛细管电泳已成为一种高效快速的微化学分离分析新技术,在无机、有机及生物化学分析中得到了广泛的应用.但毛细管的内径小,进样量在pg～ng级,给样品的检测带来新的困难.因此,发展高灵敏度的显微在线检测器,已成为毛细管电泳技术发展中的重要环节.基于各种原理的检测器研究已有报道~[1].Dovichi等曾用热透镜技术在线检测了乙腈/