Fixed Point Theorems on a Non-convex Set

ＦｉｘｅｄＰｏｉｎｔＴｈｅｏｒｅｍｓｏｎａＮｏｎ－ｃｏｎｖｅｘＳｅｔ￥ＺｈａｏＸｉａｏｑｕａｎ（赵晓全）ａｎｄＳｕｎＸｕｅｓｉ（孙学思）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａ，ＨａｒｂｉｎＩｎｓｔｉｔｕｔｅｏｆＥｌｅｃｔｒｉｃａｌＴｅｃｈｎ...     

Combining grey relation and TOPSIS concepts for selecting an expatriate host country

As international corporate activities increase, their staffing involves more strategic concerns. However, foreign assignments have many differences, and dissatisfaction with the host country is a known cause of expatriate failure. From the point of view of an expatriate candidate, the decision of whether to take an expatriate assignment can be regarded as a FMCDM (fuzzy multiple criteria decision making) problem. This paper describes a fuzzy AHP (fuzzy analytic hierarchy process) to determine the weighting of subjective judgments. Using the Sugeno integral for λ-fuzzy measure, and using the nonadditive fuzzy integral technique to evaluate the synthetic utility values of the alternatives and the fuzzy weights, then the best host country alternative can be derived with the grey relation model. The authors further combine the grey relation model based on the concepts of TOPSIS (technique for order preference by similarity to ideal solution) to evaluate and select the best alternative. A real case of expatriate assignment decision-making was used to demonstrate that the grey relation model combined with the ideas of TOPSIS results in a satisfactory and effective evaluation.     

Approximation of the Quadratic Set Covering problem

We study in this article the polynomial approximation properties of the Quadratic Set Covering problem. This problem, which arises in many applications, is a natural generalization of the usual Set Covering problem. We show that this problem is very hard to approximate in the general case, and even in classical subcases (when the size of each set or when the frequency of each element is bounded by a constant). Then we focus on the convex case and give both positive and negative approximation results. Finally, we tackle the unweighted version of this problem.     

Clutter nonidealness

Several key results for set packing problems do not seem to be easily or even possibly transferable to set covering problems, although the symmetry between them. The goal of this paper is to introduce a nonidealness index by transferring the ideas used for the imperfection index defined by Gerke and McDiarmid [Graph imperfection, J. Combin. Theory Ser. B 83 (2001) 58-78]. We found a relationship between the two indices and the strength of facets defined in [M. Goemans, Worst-case comparison of valid inequalities for the TSP, mathematical programming, in: Fifth Integer Programming and Combinatorial Optimization Conference, Lecture Notes in Computer Science, vol. 1084, Vancouver, Canada, 1996, pp. 415-429; M. Goemans, L.A. Hall, The strongest facets of the acyclic subgraph polytope are unknown, in: Integer Programming and Combinatorial Optimization, Lecture Notes in Computer Science, vol. 1084, Springer, Berlin, 1996, pp. 415-429]. We prove that a clutter is as nonideal as its blocker and find some other properties that could be transferred from the imperfection index to the nonidealness index. Finally, we analyze the behavior of the nonidealness index under some clutter operations.     

非线性灰色微分方程(dx)/(dt)+ax~(■a)=b 的拟合

本文给出了拟合非线性灰色微分方程 dx/dt+ax~(■a)=b 的计算方法,并讨论了它的性质及应用.     

基于集值统计的模糊神经网络专家系统及其应用

建立基于集值统计的模糊神经网络专家评审系统，并应用于科研项目评审工作，实际应用表明该系统是可行的。     

自相似曲线与Whitney型临界集

本文讨论一类（包括Ｋｏｃｈ曲线在内的）自相似曲线，证明了其上的简单曲线是Ｗｈｉｔｎｅｙ型临界集，并在微小扰动下仍是简单曲线．     

ITS示范工程对城市交通畅通性的贡献率研究

通过分析城市交通畅通性的影响因素及其与ITS(智能交通系统)的关系,挖掘ITS对城市交通畅通性的贡献率指标.搜集实证研究对象数据,采用灰色预测模型预测贡献率指标的数值,将ITS示范工程实施前后的数值进行对比,计算得到ITS示范工程对城市交通畅通性的贡献率.由贡献率结果判断ITS示范工程对城市交通畅通性的作用及ITS示范工程的实施效果如何,为未来ITS的发展提供相应的参考建议.     

Analysis of a set of nonlinear dynamics trajectories: Stability of difference equations

For a set of difference equations generated by discretization of the set of differential equations with Hukuhara derivative a principle of comparison with matrix Lyapunov function is specified and sufficient stability conditions of certain type are established. The analysis is carried out in terms of a matrix Lyapunov function of special structure. For an essentially nonlinear multiconnected switched difference system, conditions are obtained providing the asymptotic stability of its zero solution for any switching law. An example is presented to demonstrate efficiency of the proposed approaches.     

A new infinite family of minimally nonideal matrices

Minimally nonideal matrices are a key to understanding when the set covering problem can be solved using linear programming. The complete classification of minimally nonideal matrices is an open problem. One of the most important results on these matrices comes from a theorem of Lehman, which gives a property of the core of a minimally nonideal matrix. Cornuéjols and Novick gave a conjecture on the possible cores of minimally nonideal matrices. This paper disproves their conjecture by constructing a new infinite family of square minimally nonideal matrices. In particular, we show that there exists a minimally nonideal matrix with r ones in each row and column for any r?3.