关于可达矩阵的求法探讨

在《离散数学》、《图论》课程中 ,用矩阵表示图时 ,涉及到一类重要的矩阵——可达矩阵 ,它是判别图中任意两点是否有通路的重要手段 ,也是求强分图的重要方法 ,但是可达矩阵的求法比较复杂 .本文针对这一问题 ,对可达矩阵的求法进行了改进 ,提出了一种简单可行的算法 .     

A comparison of two algorithms for the assignment problem

State-of-the-art computational results have shown that the shortest augmenting path (SAP) methods are more efficient than other primal-dual and primal-simplex based methods for solving the linear assignment problem on uniprocessor computers. There is, however, some controversy concerning their merits when compared with Bertsekas' auction algorithm on multiprocessor computers. In this study we investigate the performance of these competing methods on the Alliant FX/8. For each method, theoretical motivation, sources of parallelism and computational results are presented.     

Combinatorics of normal sequences of braids

Many natural counting problems arise in connection with the normal form of braids—and seem to have not been much considered so far. Here we solve some of them. One of the noteworthy points is that a number of different induction schemes appear. The key technical ingredient is an analysis of the normality condition in terms of permutations and their descents, in the vein of the Solomon algebra. As was perfectly summarized by a referee, the main result asserts that the size of the automaton involved in the automatic structure of Bn associated with the normal form can be lowered from n! to p(n), the number of partitions of n.     

一类特殊二维0-1规划的广义指派模型求解

二维0-1整数规划模型应用广泛,对广义指派问题的研究,解决了一些二维0-1整数规划问题.但有些实际问题具有特殊上限约束,目前还没有对应的方法.针对该实际情形,本文建立了相应的数学模型,利用对指派模型的推广,求得问题最优解,从理论上解决了这一类特殊约束二维0-1整数规划的最优解求取问题.并通过算例说明了方法的使用.     

Solving a multiobjective location routing problem with a metaheuristic based on tabu search. Application to a real case in Andalusia

In this work we present a multiobjective location routing problem and solve it with a multiobjective metaheuristic procedure. In this type of problem, we have to locate some plants within a set of possible locations to meet the demands of a number of clients with multiple objectives. This type of model is used to solve a problem with real data in the region of Andalusia (Spain). Thus, we study the location of two incineration plants for the disposal of solid animal waste from some preestablished locations in Andalusia, and design the routes to serve the different slaughterhouses in this region. This must be done while taking into account certain economic objectives (start-up, maintenance, and transport costs) and social objectives (social rejection by towns on the truck routes, maximum risk as an equity criterion, and the negative implications for towns close to the plant).     

具常数存放的非线性功能反应捕食模型的定性分析

研究一类食饵具常数存放且功能反应函数为次线性函数的食饵-捕食者模型,获得了一些平衡点全局渐近稳定,极限环存在惟一的充分条件.利用数值仿真检验了我们的结论.     

求解P0函数互补问题的一种微分方程方法

本针对P0函数互补问题，给出了一种微方程方法，并且证明了P0函数互补问题的解是微分方程系统的渐进稳定平衡点。在适当的假设条件下，证明了所给出的算法具有二次收敛速度。几个数值例子表明了该算法的有效性。     

全纯函数族的正规定则

Let f be a holomorphic function on a domain D Lontaiu in C, and let a be a finite complex number. We denote by -↑Ef/(a) = {z ∈ D : f(z) = a, ignoring multiplicity} the set of all distinct α-points of f. Let F be a family of holomorphic functions on D. If there exist three finite values a, b(≠ O,α) and c(≠ O) such that for every f ∈F, -↑Ef′/(0) Lontain in -↑Ef(α） and -↑Ef′ (b) Lontain in -↑Ef(c), then F is a normal family on D.     

等式与界约束非线性优化信赖域算法的全局收敛

§ 1　ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｉｄｅｒｔｈｅｆｏｌｌｏｗｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉｚａｔｉｏｎｐｒｏｂｌｅｍ :ｍｉｎｉｍｉｚｅｆ(ｘ)ｓｕｂｊｅｃｔｔｏＣ(ｘ) =0 ,　ａ≤ｘ≤ｂ ,( 1 .1 )ｗｈｅｒｅｆ(ｘ) :Ｒｎ→Ｒ ,Ｃ(ｘ) =(ｃ1(ｘ) ,ｃ2 (ｘ) ,...,ｃｍ(ｘ) ) Ｔ:Ｒｎ→Ｒｍ ａｒｅｔｗｉｃｅｃｏｎｔｉｎｕｏｕｓｌｙｄｉｆｆｅｒｅｎｔｉａｂｌｅ,ｍ≤ｎ ,ａ ,ｂ∈Ｒｎ.Ｔｒｕｓｔｒｅｇｉｏｎａｌｇｏｒｉｔｈｍｓａｒｅｖｅｒｙｅｆｆｅｃｔｉｖｅｆｏｒｓｏｌｖｉｎｇｎｏｎｌｉｎｅａｒｏｐｔｉｍｉ…     

A closed-form representation of mixed-integer program value functions

We identify a class of formulas computable in polynomial time such that the functions defined by these formulas are precisely the value functions of mixed-integer programs with rational constraint coefficients.