Combinatorial Optimization by Dynamic Contraction

A heuristic optimization methodology, Dynamic Contraction (DC), is introduced as an approach for solving a wide variety of hard combinatorial problems. Contraction is an operation that maps an instance of a problem to a smaller instance of the same problem. DC is an iterative improvement strategy that relies on contraction as a mechanism for escaping local minima. As a byproduct of contraction, efficiency is improved due to a reduction of problem size. Effectiveness of DC is shown through simple applications to two classical combinatorial problems: The graph bisection problem and the traveling salesman problem.     

A note on inverses in arithmetic with fuzzy numbers

Algorithms for systematical search of inverse in arithmetic operations with fuzzy numbers are discussed. The fuzzy number derived is considered either in a discrete representation of its support or described by the parameters of the corresponding membership function formula. Both algorithms are easy to be programmed for desk calculators.     

单循环赛赛程安排的一个图论方法

利用图论的边着色理论建立了一个赛程安排的数学模型 .首先建立 n支球队与完全图 Kn的 n个顶点间的一一对应 ,把球队 Ai和 Aj间的比赛关系抽象成 Kn的顶点 i和 j间的边 ( i,j) .然后分别构造出了图K2 m- 1和 K2 m的正常 2 m-1边着色 .从而给出了各球队每两场比赛间得到的休整时间最均等 ,休整的间隔场次数达到上限值 n2 的一个赛程安排方案     

The application of spectral distribution of product of two random matrices in the factor analysis

In the factor analysis model with large cross-section and time-series dimensions,we pro- pose a new method to estimate the number of factors.Specially if the idiosyncratic terms satisfy a linear time series model,the estimators of the parameters can be obtained in the time series model. The theoretical properties of the estimators are also explored.A simulation study and an empirical analysis are conducted.     

逆序数的应用

本文通过“1 4-1 5”智力玩具和最优戴断切割问题两个实例 ,讨论了逆序数在解决实际问题中的应用     

含语言评价信息的一种模糊多属性群决策方法

对于多属性群决策问题的处理,有时需要采用先决策、后综合的处理方法,而含有语言评价信息的多属性群决策问题,定性目标一般用语言评价信息描述,由决策人给出定性目标和权系数的语言变量评价,用梯形模糊数表示,对定量目标进行无量纲化处理;将决策人对于单一目标的评价指标聚合成多个目标的评价模糊数,采用Bass-Kw akernaak模糊数排序方法对方案进行排序;群体的评价通过Borda函数来集结方案集的群体排序.     

一类数论函数的性质(Ⅱ)

For any given positive integer n≥1,the Euler functionφ(n) is defined to be the number of positive integers not exceeding n,which is relatively prime to n.ω(n) is defined to be the number of different prime divisors of n.In order to know the solvability of the function ofφ(φ(φ(n)))=2~(ω(n)),properties of the number theoretical functionφ(φ(n)) is studied in the paper.     

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??In this paper, by applying the moment inequality for asymptotically almost negatively associated (AANA, in short) random sequence and truncated method, the equivalent conditions of complete moment convergence of the maximum partial for weighted sums of AANA random variables are obtained without assumptions of identical distribution, which generalize and improve the corresponding ones of{15},{16} and {17}, respectively.     

Non-linear approximations for natural convection in a horizontal annulus

Two different problems are proposed as approximations of the usual system modelling natural convection under the Oberbeck-Boussinesq assumptions. The error is evaluated by means of the norm of its gradient in the Hilbert space. The average Nusselt number is also estimated.