超晶格界面的电子反射与干涉

从电子波动的观点出发，考虑电子波在超晶格阱层／势垒层界面的反射与干涉，讨论超晶格的电子态. 提出一种计算超晶格电子态的新方法. 理论计算出的电子能态与实验结果一致.     

格蕴涵代数的LI-理想空间

In this paper,a topological space based on LI-ideals of a lattice implication algebra is constructed,and its topological properties,such as separability,compactness and connectedness are discussed.     

半导体与超晶格的数学模型及其分析Ⅰ:模型

本文论及半导体与超晶格的数学模型方法的一些新近发展动态。介绍了半导体与超晶格的一些背景材料并给出了半导体宏观模型间的层次框架。超晶格中载流子传输的SHE扩散模型也被观察。     

关于某些拟一致空间的超空间拓扑

设(X,τ)是一个拓扑空间。在本文中,我们证明了在超空间2^X上局部有限拓扑e^τ与局部有限覆盖拟一致u_LF所导出的超拓扑|2^u_LF|是相同的。我们还证明了下面条件是等价的:(1)(X,τ)是仿紧的;(2)(X,τ)是orth紧的,且e^τ=|2^u_FT|;(3)存在一个Lebes-yue拟一致u_L,使e^τ<     

关于Lasnev空间的超空间

讨论了Ｌａｓｎｅｖ空间的超空间的某些性质．文中构造一反例，证明存在可数Ｌａｓｎｅｖ空间，其紧子集超空间不是层型空间．并指出文［６］中关于上述结果的证明中有一关键性失误，故［６］中的反例尚不能说明上述结论成立．本文还对具有σ－ＣＦ拟基的ｋ′空间给出一个刻画定理     

超紧空间和收敛序列

Ｈａｕｓｄｏｒｆｆ拓扑空间Ｘ被称为超紧的，如果存在Ｘ的子基Ｓ，使得由φ中的元素组成的Ｘ的覆盖存在由两个元素组成的子覆盖，超紧空间中的每个可数子集的每一聚点都是非平凡的序列的极限。     

超积空间及其性质

引进了和内积空间没有相互包含关系的一类新空间:超积空间,进而研究了超积空间的性质.这类新的线性空间具有许多内积空间的重要性质,从而得到了线性空间一类新的度量刻画.     

关于超空间连通性的一个注记

本文回答了由E.Klein与A.C.Thompson在其著作《Thery of Correspondences》中提出的一个问题。主要结果是:若X是一度量空间,且在X中存在一条弧,则在P(X)中有一条序弧α,满足条件i)α(0)是连通子集;ii) (?)α(t)是不连通的。     

关于子空间的超空间拓扑

For a topological space X we denote by CL(X) the collection of all nonempty closed subsets of X. Suppose we have a map T which assigns in some coherent way to every topological space X some topology T(X) on CL(X). In this paper we study continuity and inverse continuity of the map iA,X : (CL(A), T(A))→(CL(X),T(X)) defined by iA,x(F) = ^-F whenever F ∈ CL(A), for various assignment T; in particular, for locally finite topology, upper Kuratowski topology, and Attouch-Wets topology, etc.     

超sober空间的若干基本性质

本文主要讨论超sober空间的一些基本性质，对三类特殊空间的超sober性进行了讨论，并对T₀空间X的超sober性与其Smyth幂空间、Hoare幂空间的超sober性之间的关系进行了讨论；用反例说明了可数无限多个超sober空间的乘积一般不是超sober的；证明了若T₀空间X不是超sober的，则其超sober化不存在。     

The lattice of closure operators on a subgroup lattice

We say a lattice L is a subgroup lattice if there exists a group G such that Sub(G)?L, where Sub(G) is the lattice of subgroups of G, ordered by inclusion. We prove that the lattice of closure operators which act on the subgroup lattice of a finite group G is itself a subgroup lattice if and only if G is cyclic of prime power order.     

Notes on sectionally complemented lattices. IV How far does the Atom Lemma go?

There are two results in the literature that prove that the ideal lattice of a finite, sectionally complemented, chopped lattice is again sectionally complemented. The first is in the 1962 paper of G. Grätzer and E. T. Schmidt, where the ideal lattice is viewed as a closure space to prove that it is sectionally complemented; we call the sectional complement constructed then the 1960 sectional complement. The second is the Atom Lemma from a 1999 paper of the same authors that states that if a finite, sectionally complemented, chopped lattice is made up of two lattices overlapping in an atom and a zero, then the ideal lattice is sectionally complemented. In this paper, we show that the method of proving the Atom Lemma also applies to the 1962 result. In fact, we get a stronger statement, in that we get many sectional complements and they are rather close to the componentwise sectional complement.     

Subalgebras and Homomorphic Images of Algebras Having the CEP and the WCIP

In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.     

On a discrete version of alexandrov’s projection theorem

In this paper, we consider a discrete version of Aleksandrov＇s projection theorem. We prove that an origin-symmetric convex lattice set, whose lattice＇s y-coordinates＇ absolute values are not bigger than 2, can be uniquely determined by its lattice projection counts if its cardinality is not 11. This partly answers a question on the discrete version of Aleksandrov＇s projection theorem which was proposed by Gardner, Gronchi and Zong in 2005.     

分配伪补格的主理想

本文给出了分配伪补格 ( L;∧ ,∨ ,* ,0 ,1 )中的主理想 I=( d]成为同余理想的充分必要条件 .当 L是局部有限时 (即 d∈ S( L) ,Fd={x|x* * =d}有限 ) ,对骨架 S( L)中的每个元素 d,我们找到了以 I=( d]为核心的最小同余关系 ,利用以上结果我们得到一个 Stone代数是布尔代数的一些等价条件 .     

Consistent lattices and Steinitz spaces

It is well-known that a finite lattice L is isomorphic to the lattice of flats of a matroid if and only if L is geometric. A result due to Edelman (see [1], Theorem 3.3) states that a lattice is meet-distributive if and only if it is isomorphic to the lattice of all closed sets of a convex geometry. In this note we prove that a finite lattice is the lattice of closed sets of a closure space with the Steinitz exchange property if and only if it is a consistent lattice. Received February 28, 1997; accepted in final form February 2, 1998.     

分子格上伪补的构造

本文给出了分子格上伪补的构造定理，并证明了当一个非平凡分子格上有伪补，其既约因子上并不一定存在伪补，但其准既约因子上一定存在伪补，且任一分子格上的伪补都可表为其准既约因子上伪补的直积．     

Congruence-preserving extensions of finite lattices to sectionally complemented lattices

In 1962, the authors proved that every finite distributive lattice can be represented as the congruence lattice of a finite sectionally complemented lattice. In 1992, M. Tischendorf verified that every finite lattice has a congruence-preserving extension to an atomistic lattice. In this paper, we bring these two results together. We prove that every finite lattice has a congruence-preserving extension to a finite sectionally complemented lattice.