由普通导算子诱导的F导算子及由F导算子诱导的F拓扑

本文扩展了普通集X的导算子d的定义，诱导出了X的fuzzy导算子d，进而由~^d诱导出了X的一个fuzzy拓扑T，证明了fuzzy拓扑空间（X，T）愉是由d诱导的分明拓扑空间（X，π）拓扑生成的，对X的每个fuzzy导算子d，存在X唯一拓扑T，使得对X的每个fuzzy子集A，其在（X，T）中的导集A^d恰是它在fuzzy导算子~^d下的象~^d（A）。     

M_2(R)上的非线性Lie导子

设R是一个含有单位元的2无扰的交换环,M_2(R)是定义在R上的全矩阵代数,证明了M_2(R)上的每一个非线性Lie导子都可以表示成一个内导子,一个可加诱导导子和一个映所有二次换位子为零的中心映射的和.     

不可解Lie代数完备的等价条件

目的是给出特征零域上的有限维不可解L ie代数L完备的等价条件.主要是讨论L的所有导子都是内导子的充要条件.根据L的L ev i分解式(即L分解成它的根基R和另一个半单子代数S的空间直和),先在一定条件下将根基R上的导子扩充为L上的导子,给出了L完备的一个必要条件,然后又将L上的导子诱导到半单子代数S上,利用半单子代数S的完备性,证明了上述必要条件也是L完备的充分条件.     

自由电子激光诱导Hg1-xCdxTe中双光子光电导

应用北京自由电子激光（BFEL）对典型的红外光电子材料Hg_1-xCd_xTe进行了非线性光电导特性研究. 利用自由电子激光的高光子密度特性,采用光电导实验构型研究了Hg_1-xCd_xTe材料中双光子吸收诱导光电导特性,观测到了随激发光强度增大而出现的饱和效应,并比较了不同偏压下双光子光电导的特性.     

JBW-代数上的局部导子

本文证明了JBW-代数上的局部导子是导子,举反例说明了JBW-代数上的局部内导子未必是内导子,并且给出了JBW-代数的一个充要条件使得它上的局部内导子是内导子,     

三角代数上的广义Jordan导子

主要研究了三角代数上的广义Jordan导子．利用三角代数上广义Jordan导子和广义内导子的联系．证明了作用在一个含单位元的可交换环上的三角代数到其自身上的环线性广义Jordan导子是一个广义导子．     

李超三系的广义导子

给出了李超三系上(广义)(θ,φ)-导子和(广义)Jordan(θ,φ)-导子的定义,得到了李超三系上Jordan(θ,φ)-导子是(θ,φ)-导子,以及广义Jordan(θ,φ)-导子是广义(θ,φ)-导子的充分条件,并证明了李超三系的Jordanθ-导子就是θ-导子.     

4维幂零李代数的导子与triple导子

利用导子和triple导子的定义,刻画了特征不等于2的代数闭域上4维幂零李代数的导子和triple导子.     

数学教学中“导”的思考

“导”是引导、诱导,教学中的“导”,其本质和核心是导学．它充分体现了课堂教学活动中师与生、生与生、教与学的辨证关系,把“教”变为“导”,以导促学,以导达思．“导”的目的就是激发学生自身的兴趣和天赋,召唤参与动机,激发参与意识,促进学生可持续发展．发挥教师的“导”,是促进学生“学”的关键,因此“教”必须致力于“导”,服务于“学”．     

内导集与内导集运算

给出了内导集的定义,证明了其性质,并且讨论了内导集与导集之间的关系.随之定义了内导集运算,利用内导集运算定义了拓扑,并讨论了内导集运算条件之间的独立性.     

导集运算及其条件的独立性

对点集拓扑学中由导集运算决定拓扑的方法进行了讨论,给出了导集运算的定义,导集运算决定拓扑定理,并讨论了导集运算中条件的相互独立性.进一步完善了点集拓扑学中有关导集概念的内容.     

L─fts中的导集和导算子

本文首先讨论了Ｌ─ｆｔｓ中ＬＦ集的聚点的分布；其次讨论了ＬＦ集的导集的一些性质，并给出了一般的Ｌ─ｆｔｓ中类似于杨忠道定理的结果；本文最后引进了导算子的概念，并用其刻划一般的Ｌ─ｆｔｓ．     

On the resolvent arising in a parameter‐elliptic multi‐order boundary problem

In this paper we consider a boundary problem for a parameter‐elliptic, multi‐order system of differential equations defined over a bounded region in $\mathbb {R}^n$ and under limited smoothness assumptions as well as under boundary conditions which include those of Dirichlet. Information is then derived concerning the asymptotic behaviour of the trace of a power of the resolvent of the Hilbert space operator, in general non‐selfadjoint, induced by the boundary problem under null boundary conditions. This information will then be used in a subsequent work to derive various results pertaining to the asymptotic behaviour of the eigenvalues of this operator.     

Relative derived equivalences and relative homological dimensions

Let A be a small abelian category. For a closed subbifunctor F of Ext_A¹(-,-), Buan has generalized the construction of Verdier's quotient category to get a relative derived category, where he localized with respect to F-acyclic complexes. In this paper, the homological properties of relative derived categories are discussed, and the relation with derived categories is given. For Artin algebras, using relative derived categories, we give a relative version on derived equivalences induced by F-tilting complexes. We discuss the relationships between relative homological dimensions and relative derived equivalences.     

Lie Derived Lengths of Group Algebras of Groups with Cyclic Derived Subgroup

In this article the Lie derived length and the strong Lie derived length of group algebras are determined in the case when the derived subgroup of the basic group is cyclic of odd order. As a consequence, we have the characterization of the group algebras of minimal strong Lie derived length.     

On a p-adic Hilbert-type integral operator and its applications

In this note, we deal with a $p$-adic Hilbert-type integral operator induced by a symmetric homogeneous kernel of degree $-1$ and obtain the expression of the norm of this operator. As applications, we establish some new $p$-adic Hilbert-type inequalities with best constant factors.     

换位子群为P 阶群的有限P- 群的自同构群(Ⅱ)

本文给出了换位子群为p 阶群的有限p-群的自同构群的结构定理的两点应用: 其一, 直接导出某些有限p-群的自同构群的结构; 其二, 对换位子群为p 阶群的有限p-群, 确定了其自同构群的阶何时达到最大值和最小值.     

A graph-theoretic version of the union-closed sets conjecture

An induced subgraph S of a graph G is called a derived subgraph of G if S contains no isolated vertices. An edge e of G is said to be residual if e occurs in more than half of the derived subgraphs of G. We introduce the conjecture: Every non-empty graph contains a non-residual edge. This conjecture is implied by, but weaker than, the union-closed sets conjecture. We prove that a graph G of order n satisfies this conjecture whenever G satisfies any one of the conditions: δ(G) ≤ 2, log₂ n ≤ δ(G), n ≤ 10, or the girth of G is at least 6. Finally, we show that the union-closed sets conjecture, in its full generality, is equivalent to a similar conjecture about hypergraphs. © 1997 John Wiley & Sons, Inc. J Graph Theory 26: 155–163, 1997     

Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.