Pure quantitative characterization of finite simple groups

Let G be a finite group, and let π _e (G) be the set of all element orders of G. In this short paper we prove that π _e (B _n (q)) ≠ π _e (C _n (q)) for all odd q.      

Exchange环的K0群的正向凸子群格

本文证明了：(1)Exchange环R的K0群的正向凸子群格同构于R的稳定余有限半本原理想格；(2)稳定有限、半本原的exchange环R是单的当且仅当它是K0-单的并且满足逼近弱s^*—可比性，推广了Goodearl，Ara等人的结果。     

Special representations of the group SP(4,q) with minimal degrees

Let G be a finite group. Let p(G) denote the minimal degree of a faithful permutation representation ofG and let q(G) and c(G) denote the minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers, respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. The purpose of this paper is to calculate p(G), q(G), c(G) and r(G) for the group SP(4,q). This revised version was published online in June 2006 with corrections to the Cover Date.     

On circle diffeomorphisms with discontinuous derivatives and quasi-invariance subgroups of Malliavin-Shavgulidze measures

This note is devoted to construction of the domain of the regular representation of Diff₊(S¹). We consider a subgroup of diffeomorphism group such that the Malliavin-Shavgulidze measure is quasi-invariant with respect to the left action of the subgroup. The measure appears to be quasi-invariant with respect to the left action of diffeomorphisms with discontinuous second derivative. We derive an expression for quasi-invariance density and obtain an additional PSL(2,R) symmetry breaking term.     

On K1 and K2 of Algebraic Surfaces

In this paper we study higher Chow groups of smooth, projective surfaces over a field k of characteristic zero, using some new Hodge theoretic methods which we develop for this purpose. In particular we investigate the subgroup of CH ^r+1 (X,r) with r = 1,2 consisting of cycles that are supported over a normal crossing divisor Z on X. In this case, the Hodge theory of the complement forms an interesting variation of mixed Hodge structures in any geometric deformation of the situation. Our main result is a structure theorem in the case where X is a very general hypersurface of degree d in projective 3-space for d sufficiently large and Z is a union of very general hypersurface sections of X. In this case we show that the subgroup of CH ^r+1 (X,r) we consider is generated by obvious cycles only arising from rational functions on X with poles along Z. This can be seen as a generalization of the Noether–Lefschetz theorem for r = 0. In the case r = 1 there is a similar generalization by Müller-Stach, but our result is more precise than it, since it is geometric and not only cohomological. The case r = 2 is entirely new and original in this paper. For small d, we construct some explicit examples for r = 1 and 2 where the corresponding higher Chow groups are indecomposable, i.e. not the image of certain products of lower order groups. In an appendix Alberto Collino constructs even more indecomposable examples in CH ³ (X,2) which move in a one-dimensional family on the surface X.Contribution to appendix.     

On the isomorphism problem in the class of extensions of a free group by an infinite cyclic group

In the automorphism group of a rank 3 free group we find two nonconjugate automorphisms whose mapping tori are isomorphic groups.     

含语言评价信息的一种模糊多属性群决策方法

对于多属性群决策问题的处理,有时需要采用先决策、后综合的处理方法,而含有语言评价信息的多属性群决策问题,定性目标一般用语言评价信息描述,由决策人给出定性目标和权系数的语言变量评价,用梯形模糊数表示,对定量目标进行无量纲化处理;将决策人对于单一目标的评价指标聚合成多个目标的评价模糊数,采用Bass-Kw akernaak模糊数排序方法对方案进行排序;群体的评价通过Borda函数来集结方案集的群体排序.     

The categoricity of the group of all computable automorphisms of the rational numbers

We prove that there is a first-order sentence ϕ such that the group of all computable automorphisms of the ordering of the rational numbers is its only model among the groups that are embeddable in the group of all computable permutations. Supported by a Scheme 2 grant from the London Mathematical Society. __________ Translated from Algebra i Logika, Vol. 46, No. 5, pp. 649–662, September–October, 2007.     

Tail asymptotics for the fundamental period in the MAP/G/1 queue

This paper studies the tail behavior of the fundamental period in the MAP/G/1 queue. We prove that if the service time distribution has a regularly varying tail, then the fundamental period distribution in the MAP/G/1 queue has also regularly varying tail, and vice versa, by finding an explicit expression for the asymptotics of the tail of the fundamental period in terms of the tail of the service time distribution. Our main result with the matrix analytic proof is a natural extension of the result in (de Meyer and Teugels, J. Appl. Probab. 17: 802–813, 1980) on the M/G/1 queue where techniques rely heavily on analytic expressions of relevant functions. I.-S. Wee’s research was supported by the Korea Research Foundation Grant KRF 2003-070-00008.     

基于2,5-二(4′-甲酰基苯基)苯乙烯的螺旋链光学活性聚合物的合成与表征

通过2,5-二溴苯乙烯与对甲酰基苯硼酸的Suzuki偶联反应得到2,5-二(4′-甲酰基苯基)苯乙烯.在催化剂量的冰乙酸存在下,与光学纯的(S)-(-)-α-甲基苄胺或(R)-(+)-α-甲基苄胺发生缩和反应,得到了一对手性非外消旋单体,(+)-2,5-二{4-′[(N-(S)-α-甲基苄亚胺基)次甲基]苯基}苯乙烯和(-)-2,5-二{4′-[(N-(R)-α-甲基苄亚胺基)次甲基]苯基}苯乙烯.以偶氮二异丁腈(AIBN)或过氧化苯甲酰(BPO)为引发剂,经自由基溶液聚合得到光学活性聚合物.比旋光度、紫外-可见吸收光谱以及圆二色光谱研究表明,聚合物主链可能形成了某一方向占优的稳定螺旋构象,且该螺旋构象的旋光方向与单体的旋光方向相反.聚合条件对聚合物的光学活性有很大影响,在极性较大的芳香族溶剂和较高温度下得到的聚合物具有和单体相差更大的比旋光度.侧基的手性基团脱除后,聚合物仍具有一定的旋光性,说明聚合过程中形成的螺旋手性具有一定的记忆效应.