关于(QU)型模糊拓扑群的直积

研究(QU)型模糊拓扑群族直积,证明了任意(QU)型模糊拓扑群族的直积仍是(QU)型模糊拓扑群;研究了(QU)型模糊拓扑群族直积的模糊单位元之重域基的结构,得到了(QU)型模糊拓扑群族直积的一些重要性质.     

布里渊区内能带E(k)=E(-k)的对称性

说明了布里渊区内能带Ｅ（ｋ）＝Ｅ（－ｋ）的对称性是时间反演对称性的结果，而与晶体的空间对称性无关．并且证明了当晶体具有中心反演对称性时，布里渊区内能带是二重简并的．     

Synthesis of new thermosetting poly(2,6‐dimethyl‐1,4‐phenylene oxide)s containing epoxide pendant groups

A new class of thermosetting poly(2,6‐dimethyl‐1,4‐phenylene oxide)s containing pendant epoxide groups were synthesized and characterized. These new epoxy polymers were prepared through the bromination of poly(2,6‐dimethyl‐1,4‐phenylene oxide) in halogenated aromatic hydrocarbons followed by a Wittig reaction to yield vinyl‐substituted polymer derivatives. The treatment of the vinyl‐substituted polymers with m‐chloroperbenzoic acid led to the formation of epoxidized poly(2,6‐dimethyl‐1,4‐phenylene oxide) with variable pendant ratios, and the structures and properties were studied with nuclear magnetic resonance spectroscopy, Fourier transform infrared spectroscopy, differential scanning calorimetry, thermogravimetric analysis, and gel permeation chromatography. The ratios of pendant functional groups were tailored for the polymer properties, and the results showed that the glass‐transition temperatures increased as the benzylic protons were replaced by bromo‐, vinyl‐, or epoxide‐functional groups, whereas the thermal stability decreased in comparison with the original polymer. Within a molar fraction of 20–50%, the degree of functionalization had little effect on the glass‐transition temperature; however, it correlated inversely with the thermal stability of each functionalized polymer. The thermal curing behavior of the epoxide‐functionalized polymer was enhanced by the increment of the pendant functionality, which resulted in a significant increase in the glass‐transition temperature as well as the thermal stability after the curing reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5875–5886, 2006     

Innately transitive subgroups of wreath products in product action

A permutation group is innately transitive if it has a transitive minimal normal subgroup, which is referred to as a plinth. We study the class of finite, innately transitive permutation groups that can be embedded into wreath products in product action. This investigation is carried out by observing that such a wreath product preserves a natural Cartesian decomposition of the underlying set. Previously we classified the possible embeddings in the case where the plinth is simple. Here we extend that classification and identify several different types of Cartesian decompositions that can be preserved by an innately transitive group with a non-abelian plinth. These different types of decompositions lead to different types of embeddings of the acting group into wreath products in product action. We also obtain a full characterisation of embeddings of innately transitive groups with diagonal type into such wreath products.

     

Some refinements of Dade's projective conjecture

In this paper a further refinement of Dade's projective conjecture, due to Boltje, is presented. This new statement includes ideas first published by Isaacs and Navarro as well as the recent contractibility version of Alperin's conjecture introduced by Boltje. Leaning heavily on the work of Robinson, weaker forms of the conjecture are proved in the case of p-solvable groups.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Lefschetz Formulae for p-Adic Groups

In this paper,Lefschetz formulae for torus actions on p-adic groups are proven. These are similar to comparable formulae for real Lie groups.Applications lie in the realm of dynamical zeta functions.     

Trace Equivalence in SU(2, 1)

In this paper it is shown that one can choose an arbitrarily large number of inconjugate elements of the group Z/2Z*Z/2Z*Z/2Z which have the property that, under all representations of the group in SU(2,1) as a discrete complex hyperbolic ideal triangle group, the elements are hyperbolic and correspond to closed geodesics of equal length on the associated complex hyperbolic surface. This is an analogue of the geometric fact that the multiplicity of the length spectrum of a Riemann surface is never bounded or the equivalent algebraic phenomenon that an arbitrarily large number of conjugacy classes in a free group can have the same trace under all representations in SL(2,R ).     

SO(n,1) Wigner rotation as an SL(2,R) problem

We show that the composition of not only two SO(3,1) boosts, but also that of two SO(n,1) boosts for anyn 2, is basically an SO(2,1) problem and hence can be analysed completely using SL(2,R) matrices. By computing the expression for the Thomas/Wigner angle directly using SL(2,R) matrices we show that this approach results in considerable economy of algebra.