网络最小割计算的一点注记

给出了具有单一源和单一汇网络割的数目,完善了一些文献中的不完整之处.     

网络割的计数

指出了文献[1],[2]所出现的欠妥处,给出了网络割的计数.     

紧急网络中的最小饱和流问题

网络N中的一个流,如果沿前向已无法再增流,则称为饱和流,在交通拥挤或紧急疏散时,网络往往被一饱和流所堵塞。显然,这饱和流的值越小,网络的性能就越差。于是从网络分析的观点就提出最小饱和流问题。本文首先证明此问题NP－困难的。然后给出关于最小饱和流与最大流的关系及算法方面的结果。     

网络最小覆盖流问题

网络流理论中最基本的模型是最大流及最小费用流问题. 为研 究堵塞现象, 文献中出现了最小饱和流问题, 但它是NP-难的. 研究类似的最小覆盖流问题, 即求一流, 使每一条弧的流量达到一定的额定量, 而流的值为最小. 主要结果是给出多项式时间算法, 并应用于最小饱和流问题.     

有上下界网络最大流与最小截问题

为了便于建立与有上下界网络最大流与最小截问题有关的决策支持系统，本文给出一个求有上下界网络最大流与最小截的数值算法，证明了算法的理论依据，并举例说明了算法在堵塞流理论中的应用。该算法能判定问题是否有可行解，在问题有可行解的情况下能求得问题的最优解。该算法具有易于编程实现、收敛性好等优点。数值实验表明该算法有较高的计算效率，可用于求解最小饱和流问题。     

关于有能力限制的指派问题的一点注记

首先讨论了有能力限制的不平衡指派问题的转化和最优性,并提出了采用最小费用最大流的方法求解该问题.     

带有模糊容量限制的网络中的最佳最小费用量大流

本文主要讨论当网络中弧容量限制和最大流目标要求带有模糊性时的最小费最大流问题，通过构造带费用的增量网络并设法寻找其中的最佳最小费用路，给出了求解这类模糊网络流问题的算法。     

会计数据的网络流分析

学者已证明一个会计主体如一家企业、其复式簿记中一级账户记录的数据组成一个矩阵;继而提出了会计回路概念,并认识到会计回路符合网络的某些规律.提出复式簿记系统的矩阵对应于1个网络,该网络存在着网络流.图论中的最大流最小割定理在该网络中同样有效,可以对之求解最大流最小割.最小割的集合是网络中的"瓶颈",直接影响着总的通过流量.计算出最小割的值,找出它由哪些会计分录组成、关联到哪些会计科目、流量是多少,这正是该会计主体运营中的薄弱环节.这是会计史上第一种整体地、定量地分析会计主体运营状况的数学方法.     

运输网络中求最小费用最大流的一个算法

给出一个求动输网络中的最小费用最大流的数值算法,证明了算法的理论依据,并举例说明算法的应用。     

带有模糊容量限制的网络中的最佳最小费用最大流

本文主要讨论当网络中的弧容量限制和最大流目标要求带有模糊性时的最小费用最大流问题，通过构造带费用的增量网络并设法寻找其中的最佳最小费用路，给出了求解这类模糊网络流问题的算法。     

Maximal and Minimal Semilattices on Ordered Sets

The map which takes an element of an ordered set to its principal ideal is a natural embedding of that ordered set into its powerset, a semilattice. If attention is restricted to all finite intersections of the principal ideals of the original ordered set, then an embedding into a much smaller semilattice is obtained. In this paper the question is answered of when this construction is, in a certain arrow-theoretic sense, minimal. Specifically, a characterisation is given, in terms of ideals and filters, of those ordered sets which admit a so-called minimal embedding into a semilattice. Similarly, a candidate maximal semilattice on an ordered set can be constructed from the principal filters of its elements. A characterisation of those ordered sets that extend to a maximal semilattice is given. Finally, the notion of a free semilattice on an ordered set is given, and it is shown that the candidate maximal semilattice in the embedding-theoretic sense is the free object.     

The Maximal and Minimal Ranks of Some Expressions of Generalized Inverses of Matrices

In this paper, we first determine the maximal and minimal ranks of A — BXC with respect to X. Using those results, we then find the maximal and minimal ranks of the expressions AA^– — A^– A — BB^– A — AC^– C and B^– BA — ACC^– with respect to the choice of generalized inverses A^–, B^– and C^–. In particular, we consider the commutativity of A and A^–, A^k and A^–.The research of the author was supported in part by the Natural Sciences and Engineering Research Council of Canada.     

乘积空间中非线性算子的极大极小不动点定理及迭代法*

本文研究了乘积空间中非线性算子的极大极小不动点和迭代法.作为我们结果的推论,一些耦合不动点定理被获得、它们推广了由郭大钧和Lankshmikantham获得的耦合不动点定理.(见Nonlinear Anal、11(1986),623-632)和由兰在[4]、[6]中获得的结果.     

Minimal Networks on the Regular n-Dimensional Simplex

The paper gives the proof of the following fact: all simple, i.e., having no nodes of degree 2, trees that span the vertices of the regular n-dimensional simplex can be realized as nondegenerate minimal parametric networks.     

Minimal and maximal unconditional bases with respect to framings

This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if （xi, fi） is a framing of a Banach space X, and （eimin） and （eimax） are the minimal unconditional basis and the maximal unconditional basis with respect to （xi, fi）, respectively, then for any unconditional basis （ei） associated with （xi, fi）, there are A,B 〉 0 such that A｜｜i=1∑∞aieimin｜｜≤｜｜i=1∑∞aiei｜｜≤B｜｜i=1∑∞aieimax｜｜ for all （ai） ∈ c00.
It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.     

Minimal Hypersurfaces in Hyperbolic Spaces

In this paper, we reprove a theorem of M. Anderson [Invent. Math., 69 （1982）, pp. 477-494] which established the existence of a minimal hypersurface in the hyperbolic space with prescribed asymptotic boundary with non-negative mean curvature in the non-parametric case. We use the mean curvature flow method.     

Height Preserving Minimal Interval Extensions

We consider minimal interval extensions of a partial order which preserve the height of each vertex. We show that minimal interval extensions having this property bijectively correspond to the maximal chains of a sublattice of the lattice of maximal antichains of the given order. We show that they also correspond to the set of minimal interval extensions of a certain extension of this order.