覆盖空间及粗糙集与拓扑的统一

引入覆盖空间,定义了其邻域、内部、闭包、测度等概念,研究了它们的性质.得出了粗糙集近似空间和拓扑空间都是具体覆盖空间的重要结论,从而用覆盖空间统一了粗糙集和拓扑.利用覆盖空间,得到了粗糙集和拓扑中更深刻的性质,从算子论和集合论的角度丰富和深化了粗糙集与拓扑的内容.     

Combination of MCDM and covering techniques in a hierarchical model for facility location: A case study

In this paper, locating some warehouses as distribution centers (DCs) in a real-world military logistics system will be investigated. There are two objectives: finding the least number of DCs and locating them in the best possible locations. The first objective implies the minimum cost of locating the facilities and the latter expresses the quality of the DCs locations, which is evaluated by studying the value of appropriate attributes affecting the quality of a location. Quality of a location depends on a number of attributes; so the value of each location is determined by using Multi Attribute Decision Making models, by considering the feasible alternatives, the related attributes and their weights according to decision maker’s (DM) point of view. Then, regarding the obtained values and the minimum number of DCs, the two objective functions are formed. Constraints imposed on these two objectives cover all centers, which must be supported by the DCs. Using Multiple Objective Decision Making techniques, the locations of DCs are determined. In the final phase, we use a simple set partitioning model to assign each supported center to only one of the located DCs.     

关于格点覆盖的一个注记

对于一个给定椭球,本文给出了它的任一全等椭球都包含一个整点的一个充分必要条件.     

T‐joins intersecting small edge‐cuts in graphs

In an earlier paper 3 , we studied cycles in graphs that intersect all edge‐cuts of prescribed sizes. Passing to a more general setting, we examine the existence of T‐joins in grafts that intersect all edge‐cuts whose size is in a given set A ?{1,2,3}. In particular, we characterize all the contraction‐minimal grafts admitting no T‐joins that intersect all edge‐cuts of size 1 and 2. We also show that every 3‐edge‐connected graft admits a T‐join intersecting all 3‐edge‐cuts. © 2007 Wiley Periodicals, Inc. J Graph Theory 56: 64–71, 2007     

An effective and simple heuristic for the set covering problem

This paper investigates the development of an effective heuristic to solve the set covering problem (SCP) by applying the meta-heuristic Meta-RaPS (Meta-heuristic for Randomized Priority Search). In Meta-RaPS, a feasible solution is generated by introducing random factors into a construction method. Then the feasible solutions can be improved by an improvement heuristic. In addition to applying the basic Meta-RaPS, the heuristic developed herein integrates the elements of randomizing the selection of priority rules, penalizing the worst columns when the searching space is highly condensed, and defining the core problem to speedup the algorithm. This heuristic has been tested on 80 SCP instances from the OR-Library. The sizes of the problems are up to 1000 rows × 10,000 columns for non-unicost SCP, and 28,160 rows × 11,264 columns for the unicost SCP. This heuristic is only one of two known SCP heuristics to find all optimal/best known solutions for those non-unicost instances. In addition, this heuristic is the best for unicost problems among the heuristics in terms of solution quality. Furthermore, evolving from a simple greedy heuristic, it is simple and easy to code. This heuristic enriches the options of practitioners in the optimization area.     

Weak Covering at Large Cardinals

We show that weakly compact cardinals are the smallest large cardinals k where k⁺ < k⁺ is impossible provided 0^# does not exist. We also show that if k^+Kc < k⁺ for some k being weakly compact (where K^c is the countably complete core model below one strong cardinal), then there is a transitive set M with M ? ZFC + “there is a strong cardinal”.     

Asymmetric Binary Covering Codes

An asymmetric binary covering code of length n and radius R is a subset of the n-cube Q_n such that every vector xQ_n can be obtained from some vector c by changing at most R 1's of c to 0's, where R is as small as possible. K⁺(n,R) is defined as the smallest size of such a code. We show K⁺(n,R)Θ(2ⁿ/n^R) for constant R, using an asymmetric sphere-covering bound and probabilistic methods. We show K⁺(n,n− )= +1 for constant coradius iff n ( +1)/2. These two results are extended to near-constant R and , respectively. Various bounds on K⁺ are given in terms of the total number of 0's or 1's in a minimal code. The dimension of a minimal asymmetric linear binary code ([n,R]⁺-code) is determined to be min{0,n−R}. We conclude by discussing open problems and techniques to compute explicit values for K⁺, giving a table of best-known bounds.     

具有广义分解态射的广义(i,…,j)逆

本文研究范畴中态射的广义(i，…，j)逆，利用态射广义分解的性质给出了态射广义(i，…，j)逆存在的一些充要条件，导出了态射的广义Moore-Penrose逆的表达式，推广了态射(i，…，j)逆的相应结果．     

On semisymmetric cubic graphs of order 6p~2

A graph r is said to be G-semisymmetric if it is regular and there exists a subgroup G of A := Aut(Г) acting transitively on its edge set but not on its vertex set. In the case of G. = A, we call r a semisymmetric graph. The aim of this paper is to investigate (G-)semisymmetric graphs of prime degree. We give a group-theoretical construction of such graphs, and give a classification of semisymmetric cubic graphs of order 6p2 for an odd prime p.