Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

A new quantum group associated with a ‘nonstandard’ braid group representation

A new quantum group is derived from a nonstandard braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x ²–y ²=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.     

Extraction Equilibria between Benzene and Water of Uni- and Bivalent Metal Picrates with Lariat 16-Crown-5: Effect of the Side Arms on the Extraction Ability and Selectivity

The overall extraction constants (K_ex) of uni- andbivalent metal picrates with 15-(2,5-dioxahexyl)-15-methyl-16-crown-5(L16C5) were determined between benzene and water at 25°C. TheK_ex values were analyzed into the constituent equilibriumconstants, i.e., the extraction constant of picric acid, the distributionconstant of the crown ether, the stability constant of the metalion–crown ether complex in water, and the ion-pair extraction constantof the complex cation with the picrate anion. The K_ex valuedecreases in the orders Ag⁺ > Na⁺ >Tl⁺ > K⁺ > Li⁺ andPb²⁺ > Ba²⁺ > Sr²⁺ for theuni- and bivalent metals, respectively, which are the same as those observedfor 16C5. The extraction selectivity was found to be governed by theselectivity of the ion-pair extraction of the L16C5–metal picratecomplex rather than by that of the complex formation in water. Theextraction ability of L16C5 is smaller for all the metals than that of 16C5,which is mostly attributed to the higher lipophilicity of L16C5. Differencesin the extraction selectivity between L16C5 and 16C5 were observed for thebivalent metals but little for the univalent metals. The side-arm effect onthe extraction selectivity was interpreted on the basis of the negativecorrelation between the effect on the complex stability constant in waterand that on the ion-pair extraction constant.     

On the homogeneity of additive mappings

LetK be a ring with an identity 1 0 andM, L two unitaryK-modules. Then, for any additive mappingf:M L, the setH _f :={ K f(x)=f(x) for allx M} forms a subring ofK, the homogeneity ring off. It is shown that, forM {0},L {0} and any subringS ofK for whichM is a freeS-module, there exists an additive mappingf:ML such thatH _f =S. This result is applied to the four Cauchy functional equations, and it leads also to an answer to the question as to whether it is possible to introduce onM a multiplication ·:M × M M makingM into a ring but not into aK-algebra.     

以聚乙二醇-b-聚四乙烯基吡啶为模板制备聚联苯胺微/纳米颗粒及其电容特性

以两亲性嵌段共聚物聚乙二醇-b-聚四乙烯基吡啶(PEO-b-P4VP)为模板制备聚联苯胺微/纳米颗粒,调节模板剂胶束溶液pH,得到了一系列形貌和尺寸可控的聚联苯胺微/纳米颗粒。利用红外光谱、核磁共振、透射电镜、循环伏安、恒电流放电、交流阻抗等测试对材料的结构和性能进行了表征。模板法合成的聚联苯胺为平均直径小于200nm的亚微米至纳米级棒状颗粒,其直径随着模板剂胶束溶液pH的降低而增加。所得聚联苯胺颗粒均显示了一定的电化学活性,当电流密度为1A/g时,聚联苯胺的比电容量达到306.3F/g,经过长时间的充放电测试,不同条件下合成的聚联苯胺的容量衰减率均很小,表现出良好的循环稳定性且各样品电化学性能呈现出随着直径的减小而增强的趋势。     

Lifting via cocycle deformation

We develop a strategy to compute all liftings of a Nichols algebra over a finite dimensional cosemisimple Hopf algebra. We produce them as cocycle deformations of the bosonization of these two. In parallel, we study the shape of any such lifting.     

Characterization of embeddings of Sobolev-type spaces into generalized Hölder spaces defined by Lp-modulus of smoothness

We prove a sharp estimate for the k-modulus of smoothness, modelled upon a $L^p$-Lebesgue space, of a function f in $W^k{L}^{\frac{pn}{n+kp},p}(\mathrm{\Omega })$, where Ω is a domain with minimally smooth boundary and finite Lebesgue measure, $k,n\in \mathbb{N}$, $k<n$ and $\frac{n}{n?k}<p<+\infty$. This sharp estimate is used to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces into generalized Hölder spaces defined by means of the k-modulus of smoothness. General results are illustrated with examples. In particular, we obtain a generalization of the classical Jawerth embeddings.     

PRME AND k-PRIME IDEALS IN Ω-GROUPS

Abstract

In this paper we define two concepts of prime ideals for Ω-groups. The first generalizes the definitions of prime ideal in rings, nearrings, Γ-rings, associative algebras and Lie algebras. The second generalizes a concept defined for groups by ??ukin ([21]). We show that both lead to radicals in the sense of Hoehnke ([10]). Furthermore in the case of rings, Γ-rings, abelian zero-symmetric nearrings and cubic rings these two definitions coincide, thus obtaining a new characterization for the prime ideal. Zero-symmetric Ω-groups are defined analogously to the nearring case and a new characterization in term of ideals is given.