On the Stieltjes moment problem on semigroups

We characterize finitely generated abelian semigroups such that every completely positive definite function (a function all of whose shifts are positive definite) is an integral of nonnegative miltiplicative real-valued functions (called nonnegative characters).     

Singular Supports for Character Sheaves on a Group Compactification

Let G be a semisimple adjoint group over C and Ḡ be the De Concini–Procesi completion of G. In this paper, we define a Lagrangian subvariety Λ of the cotangent bundle of Ḡ such that the singular support of any character sheaf on Ḡ is contained in Λ. Received: May 2006, Accepted: November 2006     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O ^p (G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.     

Hopf algebras of primitive Lie pseudogroups and Hopf cyclic cohomology

We associate to each infinite primitive Lie pseudogroup a Hopf algebra of ‘transverse symmetries,’ by refining a procedure due to Connes and the first author in the case of the general pseudogroup. The affiliated Hopf algebra can be viewed as a ‘quantum group’ counterpart of the infinite-dimensional primitive Lie algebra of the pseudogroup. It is first constructed via its action on the étale groupoid associated to the pseudogroup, and then realized as a bicrossed product of a universal enveloping algebra by a Hopf algebra of regular functions on a formal group. The bicrossed product structure allows to express its Hopf cyclic cohomology in terms of a bicocyclic bicomplex analogous to the Chevalley-Eilenberg complex. As an application, we compute the relative Hopf cyclic cohomology modulo the linear isotropy for the Hopf algebra of the general pseudogroup, and find explicit cocycle representatives for the universal Chern classes in Hopf cyclic cohomology. As another application, we determine all Hopf cyclic cohomology groups for the Hopf algebra associated to the pseudogroup of local diffeomorphisms of the line.     

Parameter Inequalities for Orthogonal Arrays with Mixed Levels

An important question in the construction of orthogonal arrays is what the minimal size of an array is when all other parameters are fixed. In this paper, we will provide a generalization of an inequality developed by Bierbrauer for symmetric orthogonal arrays. We will utilize his algebraic approach to provide an analogous inequality for orthogonal arrays having mixed levels and show that the bound obtained in this fashion is often sharper than Raos bounds. We will also provide a new proof of Raos inequalities for arbitrary orthogonal arrays with mixed levels based on the same method.     

特征标次数图是一种连通图的单群

对有限单群G,假设其不可约特征标次数图Δ(G)连通,且图顶点集ρ(G)=π_1∪π_2∪{p},其中|π_1|,|π_2|≥1,π_1∩π_2=θ,且π_1与π_2中顶点不相邻.证明了Δ(G)满足上面的假设的有限单群G只有4种:M_(11),J_1,PSL_3(4)或²B_2(q2B_2(q²),其中q2),其中q²一1是Mersenne素数.     

马林果砖红色素的提取及理化性质研究

以马林果为原料,30%乙醇作溶剂提取砖红色素并研究该色索的理化性质．通过实验证明该色索耐热。耐光．在食品工业和医药方面有一定的利用价值．     

Curvature of curvilinear 4-webs and pencils of one forms: Variation on a theorem of Poincaré, Mayrhofer and Reidemeister

A curvilinear d-web W = (F ₁ , . . . , F _d ) is a configuration of d curvilinear foliations F _i on a surface. When d = 3, Bott connections of the normal bundles of F _i extend naturally to equal affine connection, which is called Chern connection. For 3 < d, this is the case if and only if the modulus of tangents to the leaves of F _i at a point is constant. A d-web is associative if the modulus is constant and weakly associative if Chern connections of all 3-subwebs have equal curvature form. We give a geometric interpretation of the curvature form in terms of fake billiard in §2, and prove that a weakly associative d-web is associative if Chern connections of triples of the members are non flat, and then the foliations are defined by members of a pencil (projective linear family of dim 1) of 1-forms. This result completes the classification of weakly associative 4-webs initiated by Poincaré, Mayrhofer and Reidemeister for the flat case. In §4, we generalize the result for n + 2-webs of n-spaces. Received: September 23, 1996     

Brauer第24问题的推广

本文对Ｂｒａｕｅｒ第２４问题［１］作了推广．利用Ｄａｄｅ关于循环块的理论得到如下结果：设Ｇ是有限群，Ｐ是Ｇ的循环Ｓｙｌｏｗｐ子群．设｜Ｐ｜＝ｐａ，ａ为正整数．令Ｐｉ为Ｐ中唯一的ｐｉ阶子群，１ｉａ．则｜Ｃｌ（Ｇ）｜＝｜Ｃｌ（ＮＧ（Ｐｉ））｜的充分必要条件为ＰｉＧ．