The $L(3, 2, 1)$-Labeling on Bipartite Graphs

An $L(3, 2, 1)$-labeling of a graph $G$ is a function from the vertex set $V(G)$ to the set of all nonnegative integers such that $|f(u)−f(v)|≥3$ if $d_G(u, v)=1$, $|f(u)−f(v)|≥2$ if $d_G(u, v)=2$, and $|f(u)−f(v)|≥1$ if $d_G(u, v)=3$. The $L(3, 2, 1)$-labeling problem is to find the smallest number $λ_3(G)$ such that there exists an $L(3, 2, 1)$-labeling function with no label greater than it. This paper studies the problem for bipartite graphs. We obtain some bounds of $λ_3$ for bipartite graphs and its subclasses. Moreover, we provide a best possible condition for a tree $T$ such that $λ_3(T)$ attains the minimum value.     

果树种植最佳土地租赁期的数学模型建构

以种植果树为例,根据果树种植的客观规律,引进折扣因子δ=U-α,给出了通过确定投资合同期使利润达到最大的数学模型,并进行了讨论和推广.     

Path Decomposition of Graphs with Given Path Length

A path decomposition of a graph G is a list of paths such that each edge appears in exactly onepath in the list.G is said to admit a {P_l}-decomposition if G can be decomposed into some copies of P_l,whereP_l is a path of length l-1.Similarly,G is said to admit a {P_l,P_k}=decomposition if G can be decomposed intosome copies of P_l or P_k.An k-cycle,denoted by C_k,is a cycle with k vertices.An odd tree is a tree of which allvertices have odd degree.In this paper,it is shown that a connected graph G admits a {P_3,P_4}-decompositionif and only if G is neither a 3-cycle nor an odd tree.This result includes the related result of Yan,Xu andMutu.Moreover,two polynomial algorithms are given to find {P_3}-decomposition and {P_3,P_4}-decompositionof graphs,respectively.Hence,{P_3}-decomposition problem and {P_3,P_4}-decomposition problem of graphs aresolved completely.     

2IV^m-p设计的弱最小低阶混杂与纯净效应准则等价的条件

该文给出了2IVm-p设计包含最多纯净两因子交互效应与该设计具有弱最小低阶混杂等价的几个条件．并在文章的末尾给出了一组既具有弱最小低阶混杂又包含最多纯净两因子交互效应的2IVm-p设计．     

A Necessary and Sufficient Condition for the Existence of a Heterochromatic Spanning Tree in a Graph

We prove the following theorem. An edge-colored (not necessary to be proper) connected graph G of order n has a heterochromatic spanning tree if and only if for any r colors (1≤r≤n−2), the removal of all the edges colored with these r colors from G results in a graph having at most r+1 components, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors.     

The Two-Point Codes with the Designed Distance on a Hermitian Curve in Even Characteristic

In Homma M and Kim SJ [2], the authors considered two-point codes on a Hermitian curve defined over fields of odd characteristic. In this paper, we study the geometry of a Hermitian curve over fields of even characteristic and classify the two-point codes whose minimum distances agree with the designed ones.     

Partitioning complete graphs by heterochromatic trees

A heterochromatic tree is an edge-colored tree in which any two edges have different colors. The heterochromatic tree partition number of an r-edge-colored graph G, denoted by t _r (G), is the minimum positive integer p such that whenever the edges of the graph G are colored with r colors, the vertices of G can be covered by at most p vertex-disjoint heterochromatic trees. In this paper we determine the heterochromatic tree partition number of r-edge-colored complete graphs. We also find at most t _r (K _n ) vertex-disjoint heterochromatic trees to cover all the vertices in polynomial time for a given r-edge-coloring of K _n .     

求解最小Steiner树的蚁群优化算法及其收敛性

最小Steiner树问题是NP难问题,它在通信网络等许多实际问题中有着广泛的应用．蚁群优化算法是最近提出的求解复杂组合优化问题的启发式算法．本文以无线传感器网络中的核心问题之一,路由问题为例,给出了求解最小Steiner树的蚁群优化算法的框架．把算法的迭代过程看作是离散时间的马尔科夫过程,证明了在一定的条件下,该算法所产生的解能以任意接近于1的概率收敛到路由问题的最优解．     

Time optimality and the maximum principle in infinite dimension

We present three counterexamples related to the maximum principle for the time optimal problem. The system is linear, infinite dimensional, with point target and “full” control     

关于树指标马氏链的若干强偏差定理

树指标随机过程已成为近年来发展起来的概率论的研究方向之一.强偏差定理一直是国际概率论界研究的中心课题之一.通过构造适当的非负鞅,将Doob鞅收敛定理应用于几乎处处收敛的研究,研究给出了一类非齐次树上连续状态马氏链滑动平均的若干强偏差定理.