最优无线电信道分配

本文讨论 2 0 0 0年 MCM— B题的扩展 ,给出了无线电信道配置模型 ( k,l)全部的最优解及部分证明 .     

三层干扰下的最优无线电信道问题的研究

研究了 2 0 0 0年 MCM— B题 ,将问题推广到有三层干扰的复杂情况 ,给出并严格证明了 ( k,1,1)问题的最优解     

关于“截断切割”的最优设计

针对 1 997年全国大学生数学建模竟赛 B题 ,对于换刀费用 e=0的情况 ,本文设计了一种异常简捷的切割厚度排序法来寻找最优切割方案 ,同时在数学上给出了严格的证明 .对于换刀费用 e≠ 0的情况 ,以 e=0时得到的最优切割方案为基础 ,先通过简单的调整原则寻找出限定不同换刀次数时各自的最优切割方案 ,再通过费用比较便可简捷地得到随 e值的大小而变化的最优切割方案 .本文构造的模型在求解时无须用计算机编程 ,只用手算即可简捷地得到答案     

陈省身杯一赛题的另解

<正>题目如图1,已知锐角△ABC满足AB>AC,O、H分别为△ABC的外心、垂心,直线BH与AC交于点B1,直线CH与AB交于点C1.若OH∥B1C1,证明:cos2B+cos2C+1=0.此题是第五届(2014年)陈省身杯全国高中数学奥林匹克第1题,这是一道不落俗套,内涵丰富,解法多样的好题.文[1]中给出了组委会所提供的参考答案,经笔者探究,再给出下面有别于参考答案的新证法.     

GSOR方法最优迭代参数的简化推导

对于增广线性系统,Bai等研究了广义SOR方法（Bai Z Z,Parlett B,Wang Z Q.On generaliged successive overrelaxation methods for augmented linear systems.Numerische Mathematik,2005,102（1）：1-38）,并得到其最优迭代参数.给出了另外一种推导最优迭代参数的简化方法,这种方法对于求解其他参数加速定常迭代方法的最优迭代参数非常有意义.     

图的min-max型最优消去顺序问题

文[1]从算法复杂性的估计中提出一个图的最优标号(排序)问题-顶点的最优消去问题.本文将给出若干基本的理论结果,其中包含NP-完全性、上下界、与其它目论参数的关系及特殊图结果等.     

突发事件中对嫌疑犯有效封堵的模型与算法

基于CUMCM-2011 B题中关于嫌疑犯的封堵问题的研究.通过建立描述市区交通网络图的权矩阵,采用求最短路的Dijstra算法求出市区任意两节点的最短路径及路长,构作最佳路径阵和距离矩阵,以此为基点建立封堵路口的最优调度方案模型,再在此基础上建立封堵住嫌疑犯的最优模型,并设计了模型求解的算法.将算法应用于CUMCM-2011 B题中关于嫌疑犯的封堵问题,获得最优封堵方案.     

等周四边形问题

<正>"等周四边形中,正方形面积最大",是一个广为人知的结论,而且出现在了人教社B版新教材的课后题中,但教参中没有给出证明,能查到的方法几乎都是分好多步一点点证明的,非常繁琐,本文提供了这个问题的两种简要证明.1问题与简要分析(人教社B版必修一第78页习题2G2C组第6题)设桌面上有一个由铁丝围成的封闭曲线,周长是2L.     

一道例题的多种解法

<正>《中学生数学》2015年6月(上)刊发的《一题多解案例》一文给出了一道题的4种解法,读后受益匪浅.继承与发展(创新)是最好的学习,本文在原文解法的基础上再给出4种解法,以飨读者.     

货郎担问题的对角线生成和2—最优改进回路解法

第Ⅰ部分以十个城市的货郎担题为例,提出了一个快速求得较好的初始可行解的启发式方法——对角线生成法。该方法可以与解货郎担题的任何一种改进回路的方法结合使用。从而求得货郎担题的最优或接近最优的解。第Ⅱ部分将以上的方法与2-最优改进回路的方法相结合,计算了十个文献中报导的货郎担题,其规模从十个城市到318个城市。计算结果表明该方法相对于别的方法而言,其主要优点是:它的计算时间随着城市个数的增加而增加的速度较慢,因而适用于解几百个城市的大规模的货郎担题。结论本文所介绍的方法是一种解货郎担题,尤其是大规模货郎担题的快速而有效的计算机算法。     

A relaxed extragradient-like method for a generalized mixed equilibrium problem,a general system of generalized equilibria and a fixed point problem

Very recently, Takahashi and Takahashi [S. Takahashi, W. Takahashi, Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space, Nonlinear Anal. 69 (2008) 1025–1033] suggested and analyzed an iterative method for finding a common solution of a generalized equilibrium problem and a fixed point problem of a nonexpansive mapping in a Hilbert space. In this paper, based on Takahashi–Takahashi’s iterative method and well-known extragradient method we introduce a relaxed extragradient-like method for finding a common solution of a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem of a strictly pseudocontractive mapping in a Hilbert space and then obtain a strong convergence theorem. Utilizing this theorem, we establish some new strong convergence results in fixed point problems, variational inequalities, mixed equilibrium problems and systems of generalized equilibria.     

A Priori and A Posteriori: A Bootstrapping Relationship

The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning, and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification.     

Topological representation of posets

There is a canonical imbedding of a poset into a complete Boolean lattice and hence into a Boolean lattice. This gives it a representation as a collection of clopen sets of a Boolean space. There are reflective functions from a category of distributive posets to the subcategories of distributive and Boolean lattices and consequently a topological dual equivalence that extends the Stone duality of Boolean lattices.Presented by B. Jonsson.     

若干笛卡尔积图的邻点可区别关联染色

An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors.We obtain the adjacent vertex distinguishing incidence chromatic number of the Cartesian product of a path and a path,a path and a wheel,a path and a fan,and a path and a star.     

A Characterization of Semirings Which Are Subdirect Products of a Distributive Lattice and a Ring

E -inversive semiring and a Clifford semiring and show that a semiring S is a subdirect product of a distributive lattice and a ring if and only if S is an E-inversive strong distributive lattice of halfrings. Further a Clifford semiring which is, in fact, an inversive subdirect product of a distributive lattice and a ring, is characterized as a strong distributive lattice of rings. Finally, as a consequence of these results we extend a result of Galbiati and Veronesi [2] in the case of Boolean semirings.     

Scalarization of Henig Proper Efficient Points in a Normed Space

In a general normed space equipped with the order induced by a closed convex cone with a base, using a family of continuous monotone Minkowski functionals and a family of continuous norms, we obtain scalar characterizations of Henig proper efficient points of a general set and a bounded set, respectively. Moreover, we give a scalar characterization of a superefficient point of a set in a normed space equipped with the order induced by a closed convex cone with a bounded base.     

New parameters of subsets in polynomial association schemes

We define new parameters, a zero interval and a dual zero interval, of subsets in P- or Q-polynomial association schemes. A zero interval of a subset in a P-polynomial association scheme is a successive interval index for which the inner distribution vanishes, and a dual zero interval of a subset in a Q-polynomial association scheme is a successive interval index for which the dual inner distribution vanishes. We derive bounds of the lengths of a zero interval and a dual zero interval using the degree and dual degree respectively, and show that a subset in a P-polynomial association scheme (resp. a Q-polynomial association scheme) having a large length of a zero interval (resp. a dual zero interval) induces a completely regular code (resp. a Q-polynomial association scheme). Moreover, we consider the spherical analogue of a dual zero interval.     

Cayley hypergraphs and Cayley hypermaps

In this paper, we introduce a Cayley hypergraph which is a generalization of a Cayley graph, and a Cayley hypermap which is a generalization of a Cayley map. We investigate some properties of Cayley hypergraphs and Cayley hypermaps, describe the automorphism group of a Cayley hypermap and determine when a Cayley hypermap is regular.     

On Right Hereditary Rings and Dedekind Domains

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Remarks on pseudo-valuation rings

A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable for all a,b ε A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal of A is a strongly prime ideal. We show that if A is a PVR with maximal ideal M, then every overring of A is a PVR if and only if M is a maximal ideal of every overring of M that does not contain the reciprocal’of any element of M.We show that if R is an atomic domain and a PVD, then dim(R) ≤ 1. We show that if R is a PVD and a prime ideal of R is finitely generated, then every overring of R is a PVD. We give a characterization of an atomic PVD in terms of the concept of half-factorial domain.