Crossed Modules and Quantum Groups in Braided Categories

Let A be a Hopf algebra in a braided category . Crossed modules over A are introduced and studied as objects with both module and comodule structures satisfying a compatibility condition. The category of crossed modules is braided and is a concrete realization of a known general construction of a double or center of a monoidal category. For a quantum braided group the corresponding braided category of modules is identified with a full subcategory in . The connection with cross products is discussed and a suitable cross product in the class of quantum braided groups is built. Majid–Radford theorem, which gives equivalent conditions for an ordinary Hopf algebra to be such a cross product, is generalized to the braided category. Majid's bosonization theorem is also generalized.     

Development of Methods for the Synthesis of Neopentyl Glycol by Hydrogenation of Hydroxypivaldehyde

Neopentyl glycol (NPG) is a precursor for the manufacture of many valuable products of industrial importance such as polyester, polyurethane and alkyd resins, synthetic lubricants, hydraulic fluids, drugs, etc. The structure of NPG provides the resins with excellent hydrolytic stability, resistance to weather conditions, good flexibility-hardness balance, and outstanding functional properties. The paper presents a literature review on the development of methods for NPG preparation, focusing primarily on the synthesis of NPG by hydrogenation of hydroxypivaldehyde, which is obtained by the crossed aldol condensation of isobutyraldehyde and formaldehyde. Preparation of the substrates, catalysts, technical and apparatus solutions, and NPG purification were discussed.     

Photofragment translational spectroscopy of iodobenzene at 266 nm

The photofragmentation of C_6 H_5I at 266 nm is investigated on the nuiversal crossed molecular beam machine, and the translational spectroseopy as well as the angular distribution of I atom is measured. The results reveal that under the laser intensity of 10~8 W/cm~2 the single-phuton dissociation competes with multi-photon processes. In singlephoton dissociation the anisotropy parameter β is 0.4 and the average translational energy is only 1.04 keal/mol, which indicates that this process is a slow predissociation. In two-photon phutofragmentation the average translational energy is 51.64 kcal/mol, which accounts for about 35% of the available energy. Another photofragmentation channel is even more faster, whose peak in time-of-flight spectra corresponds to four or five photon absorptions. The branching ratio of these three channels is determined to be about 3: 3: 4.     

关于余模余代数的L-R smash余积和L-R扭曲余积

由一种新方法给出了L-R smash余积的Mashke定理,并研究了L-R扭曲余积与左(右)扭曲偶的关系.     

Weak crossed biproducts and weak projections

In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization.     

Negative differential resistance behaviour in N-doped crossed graphene nanoribbons

By using first-principles calculations and nonequilibrium Green’s function technique, we study elastic transport properties of crossed graphene nanoribbons. The results show that the electronic transport properties of molecular junctions can be modulated by doped atoms. Negative differential resistance (NDR) behaviour can be observed in a certain bias region, when crossed graphene nanoribbons are doped with nitrogen atoms at the shoulder, but it cannot be observed for pristine crossed graphene nanoribbons at low biases. A mechanism for the negative differential resistance behaviour is suggested.     

玉米kn-1同源盒的高效表达

同源盒基因(homeoboxgenes)在植物,动物,真菌的广泛存在说明这种结构在真核生物进化过程中高度保守,并暗示其具有重要功能.本文将玉米kn-1同源盒插入表达载体pGEM△XbaI,并将形成的重组克隆pGEM△MK转化BL21(DE3)而获得高效表达;表达产物的分子量为29×103,并主要以可溶性蛋白形式存在.Kn-1,Quox-1,OSIH-1间的交叉免疫反应证实三者在蛋白质水平具同源性.而Kn-1同源结构域(Homeodomain)高效表达有助于进一步寻找其靶基因.     

偶交叉双积Hopf代数B RH的构造

本文给出了Doi Y.构造的偶交叉积B H的代数结构与Reshetikhim～N.构造的双代数BRH的余代数结构在张量空间B H上构成双代数(记为BRH)的充要条件,利用此结论具体构造了一个有趣的例子H4 KZ2,证明了当B,H均为Hopf.代数时BRH也为Hopf代数,最后给出这类双代数的映射刻划.     

扭曲余积和广义相关Hopf模

本文在学习［1,2］之后,首先给出了扭曲余积关于量子余交换的一个重要性质;在学习［3］之后,又证明了广义相关Hopf模的对偶模仍是广义相关Hopf模,从而推广了［3］中的相关结论.     

Compatible actions of Lie algebras

Abstract

We study compatible actions (introduced by Brown and Loday in their work on the non-abelian tensor product of groups) in the category of Lie algebras over a fixed ring. We describe the Peiffer product via a new diagrammatic approach, which specializes to the known definitions both in the case of groups and of Lie algebras. We then use this approach to transfer a result linking compatible actions and pairs of crossed modules over a common base object L from groups to Lie algebras. Finally, we show that the Peiffer product, naturally endowed with a crossed module structure, has the universal property of the coproduct in XMod_L(Lie_R).