非退化扩散过程的水平集和极集

设X(t)(t∈R )是一个d维非退化扩散过程．本文得到了比原有结果更一般的非退化扩散过程极性的充分条件,证明了对任意u∈Rd,紧集E(0, ∞),有若d=1,则对任意紧集F(?)R, 若d≥2,则对任意紧集E ∈(0, ∞), 其中B(Rd)为Rd上的Borel σ-代数,dim和Dim分别表示Hausdorff维数和Packing 维数．     

图的下测地数和上测地数

对于图G(或有向图D)内的任意两点u和v,u—v测地线是指在u和v之间(或从u到v)的最短路．I(u,v)表示位于u—v测地线上所有点的集合,对于S(?)V(G)(或V(D)),I(S)表示所有I(u,v)的并,这里u,v∈S．G(或D)的测地数g(G)(或g(D))是使I(S)=V(G)(或I(S)=V(D))的点集S的最小基数．G的下测地数g~-(G)=min{g(D)：D是G的定向图},G的上测地数g~ (G)=max{g(D)：D是G的定向图}．对于u∈V(G)和v∈V(H),G_u H_v表示在u和v之间加一条边所得的图．本文主要研究图G_u H_v的测地数和上(下)测地数．     

Topological structure of solution sets in Fréchet spaces: The projective limit approach

In this paper we show that the solution set of certain Volterra inclusions defined between Fréchet spaces is a continuum. The proof relies on results in Banach spaces and on viewing a Fréchet space as a projective limit of a sequence of Banach spaces.     

置换空间中的最佳逼近

我们首次得到了置换空间PXXn中的点到太阳集的最佳逼近特征定理.     

The Hausdorff dimension of a class of recurrent sets

In this paper we obtain a lower bound for the Hausdorff dimension of recurrent sets and, in a general setting, we show that a conjecture of Dekking [F.M. Dekking, Recurrent sets: A fractal formalism, Report 82-32, Technische Hogeschool, Delft, 1982] holds.     

广义幂级数环的Morita对偶

设A,B是有单位元的环, (S,≤)是有限生成的Artin的严格全序幺半群, AMB是双模.本文证明了双模[[AS,≤]][MS,≤][[BS,≤]]定义一个Morita对偶当且仅当 AMB定义一个Morita对偶且A是左noether的,B是右noether的.因此A上的广 义幂级数环[[AS,≤]]具有Morita对偶当且仅当A是左noether的且具有由双模AMB 诱导的Morita对偶,使得B是右noether的.     

分次反单本原根

本文给出分次情形的反单本原根SJGG,当群G满足|G|<∞,证明了SJG=SJref=SJG,其中SJref和SJG分别表示反射反单本原根和限制反单本原根.而且讨论了SJG的分次补根.     

On the Derivations of Filiform Leibniz Algebras

The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov.     

Cover and Bounded Parallel Faces

We use the cover or the closure of the cover in order to determine when two disjoint closed convex sets have parallel faces, one of them being bounded. Moreover, we show that the study of the closure of the cover gives interesting results about the cover itself.     

一类独立随机变量均值中参数的估计

本文给出了独立随机变量均值中参数ａ＝（ａ１，…，ａｐ）′的估计量（ａ１Ｘ１，…，ａｐＸｐ）′在加权平方和损失下为可容许估计的充要条件及在一般损失Ｌｖ下为可容许估计的充分条件（在线性估计类中）。