The partial inverse minimum spanning tree problem when weight increase is forbidden

In a partial inverse optimization problem there is an underlying optimization problem with a partially given solution. The objective is to find a minimal perturbation of some of the problem’s parameter values, in such a way that the partial solution becomes a part of the optimal solution.     

Estimation of the order of a group generated by a twisted subset

We prove that a group generated by a twisted subset is finite and its order is bounded by some function depending only on the order of the twisted subset.     

Effective Relaxations and Partitioning Schemes for Solving Water Distribution Network Design Problems to Global Optimality

In this paper, we address the development of a global optimization procedure for the problem of designing a water distribution network, including the case of expanding an already existing system, that satisfies specified flow demands at stated pressure head requirements. The proposed approach significantly improves upon a previous method of Sherali et al. (1998) by way of adopting tighter polyhedral relaxations, and more effective partitioning strategies in concert with a maximal spanning tree-based branching variable selection procedure. Computational experience on three standard test problems from the literature is provided to evaluate the proposed procedure. For all these problems, proven global optimal solutions within a tolerance of 10^–4% and/or within 1$ of optimality are obtained. In particular, the two larger instances of the Hanoi and the New York test networks are solved to global optimality for the very first time in the literature. A new real network design test problem based on the Town of Blacksburg Water Distribution System is also offered to be included in the available library of test cases, and related computational results are presented.     

Intuitionistic notions of boundedness in ℕ

We consider notions of boundedness of subsets of the natural numbers ? that occur when doing mathematics in the context of intuitionistic logic. We obtain a new characterization of the notion of a pseudobounded subset and we formulate the closely related notion of a detachably finite subset. We establish metric equivalents for a subset of ? to be detachably finite and to satisfy the ascending chain condition. Following Ishihara, we spell out the relationship between detachable finiteness and sequential continuity. Most of the results do not require countable choice. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

非紧超凸度量空间中的一个新的极大元定理及其对抽象经济的应用

在非紧超凸度量空间中建立了一个新的极大元定理.作为应用，获得了连续选择及其不动点定理和一个Browder-Fan不动点定理.最后，新建了非紧超凸度量空间中的定性对策和抽象经济的平衡点存在定理.     

Undirected simple connected graphs with minimum number of spanning trees

We show that for positive integers n, m with n(n−1)/2≥m≥n−1, the graph L_n,m having n vertices and m edges that consists of an (n−k)-clique and k−1 vertices of degree 1 has the fewest spanning trees among all connected graphs on n vertices and m edges. This proves Boesch’s conjecture [F.T. Boesch, A. Satyanarayana, C.L. Suffel, Least reliable networks and reliability domination, IEEE Trans. Commun. 38 (1990) 2004-2009].     

Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems

The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.     

一个Erdis问题在二次曲线下的推广

著名数学家Paul Erd■s曾提出过这样一个有趣的问题:"设U为平面上一些单位圆所成之集,如果平面上任一条直线总和U中至少一个圆相交或相切,那么是否可以肯定:对任给的自然数m,总能找到一条直线,它至少和U中的m个圆相交或相切?"张景中,杨路等人解决了这个问题.本文探讨了该问题在二次曲线下的推广,得到了和原Erd■s问题相似的结论.     

The non-approximability of bicriteria network design problems

Let G be an undirected graph with two edge costs (c-cost and d-cost). We want to minimize the diameter of a spanning subgraph S (under d-cost) subject to the constraint that the total cost of the edges in S (with respect to c) does not exceed a given budget. We prove that this problem is non-approximable, even in some special cases. Similar results are proved if the stretch factor or the root stretch factor is considered instead of the diameter.     

路或圈的笛卡尔乘积图的支撑树数

设G是路或圈的笛卡尔乘积图，t(G)表示G的支撑树数.该文借助于第二类Chebyshev多项式给出t(G)的公式，并考虑了t(G)的线性递归关系及渐近性态.