一个特殊6点图Q与nK_1,P_n及C_n的联图交叉数

图的交叉数是图的一个重要参数,研究图的交叉数问题是拓扑图论中的前沿难题.确定图的交叉数是NP-难问题,因为其难度,能够确定交叉数的图类很少.通过圆盘画法途径,确定了一个特殊6点图与n个孤立点nK_1,路P_n及圈C_n的联图的交叉数分别是cr(Q+nK_1)=Z(6,n)+2[n/2],cr(Q+P_n)=Z(6,n)+2[n/2]+1及cr(Q+C_n)=Z(6,n)+2[n/2]+3.     

基于网格化管理视角下灾后应急物流决策模型与算法研究

灾害发生后,应急资源的需求预测与应急配送中心的合理选址是实现高效救援的关键。本文通过在网格化管理视角下的信息更新将应急救援过程划分为多个阶段,在开展救援的过程中实现救援信息收集和救援预测的同步开展,建立一种多阶段带时间约束的应急救援物资配送响应-时效性的选址模型。借助遗传算法(NSGA-II),实现了基于编码结构独立、路径相互关联基础上的多目标规划求解。本研究的决策模型及算法有着较好的搜索与寻优能力,对实际救援开展具有指导意义。     

White and some colored marbles as alternative radiation shielding materials for applications

ABSTRACT

In this paper, the radiation shielding parameters such as linear attenuation coefficients (LAC, µ), mass attenuation coefficients (MAC, µ/ρ), effective atomic numbers (Z_eff), effective electron densities (N_eff), half value of layers (HVL), mean free paths (MFP) and buildup factors (exposure (EBF) and energy absorption (EABF)) were investigated for cream (M1), pink (M2), white (M3), maroon (M4) and green (M5) marbles. Attenuation coefficients were measured in the energy region 31.18–661.66 keV photon energies. The values of Z_eff and N_eff were then calculated using these coefficients with logarithmic interpolation method, and HVLs and MFPs were calculated using the values of LAC of marble samples at the same photon energies. The experimental results were compared with the theoretical values obtained from WinXCom program, and good agreements were observed between the experimental and theoretical results. HVLs and MFPs of all marble samples were compared with those of some concretes, glasses and commercial radiation shielding glasses (SCHOTT Co.). The studied marbles were better radiation shielding materials than standard shielding concretes due to lower HVL and MFP values lower than the ordinary concrete. Finally, EBFs and EABFs of the marbles were calculated in the energy region 0.015–1?MeV up to penetration depths of 40 mfps by Geometric Progression method (G-P), and the results were discussed in terms of photon energies and chemical compositions of the marbles.     

利用有限域上非零向量的道路图结构与内积构作结合方案

Um（n,R）表示域F上n元非零向量之集．本文先确定了有限域上n≥5维非零向量的道路图结构,然后利用有限域Fq上Um（n,R）／EnR中具有相同范数的向量的道路图结构与内积构作了具有多个结合的结合方案,并计算出相应的参数．     

Finding the shortest paths by node combination

By repeatedly combining the source node’s nearest neighbor, we propose a node combination (NC) method to implement the Dijkstra’s algorithm. The NC algorithm finds the shortest paths with three simple iterative steps: find the nearest neighbor of the source node, combine that node with the source node, and modify the weights on edges that connect to the nearest neighbor. The NC algorithm is more comprehensible and convenient for programming as there is no need to maintain a set with the nodes’ distances. Experimental evaluations on various networks reveal that the NC algorithm is as efficient as Dijkstra’s algorithm. As the whole process of the NC algorithm can be implemented with vectors, we also show how to find the shortest paths on a weight matrix.     

Hamiltonian and long paths in bipartite graphs with connectivity

Let G be a graph, $\nu (G)$ the order of G, $\kappa (G)$ the connectivity of G and k a positive integer such that $k\le (\nu (G)?2)/2$. Then G is said to be k-extendable if it has a matching of size k and every matching of size k extends to a perfect matching of G. A Hamiltonian path of a graph G is a spanning path of G. A bipartite graph G with vertex sets $V_1$ and $V_2$ is defined to be Hamiltonian-laceable if such that $|V_1|=|V_2|$ and for every pair of vertices $p\in V_1$ and $q\in V_2$, there exists a Hamiltonian path in G with endpoints p and q, or $|V_1|=|V_2|+1$ and for every pair of vertices $p,q\in V_1,p\ne q$, there exists a Hamiltonian path in G with endpoints p and q. Let G be a bipartite graph with bipartition $(X,Y)$. Define $bn(G)$ to be a maximum integer such that $0\le bn(G)<min\{|X|,|Y|\}$ and (1) for each non-empty subset S of X, if $|S|\le |X|?bn(G)$, then $|N(S)|\ge |S|+bn(G)$, and if $|X|?bn(G)<|S|\le |X|$, then $N(S)=Y$; and (2) for each non-empty subset S of Y, if $|S|\le |Y|?bn(G)$, then $|N(S)|\ge |S|+bn(G)$, and if $|Y|?bn(G)<|S|\le |Y|$, then $N(S)=X$; and (3) $bn(G)=0$ if there is no non-negative integer satisfying (1) and (2).Let G be a bipartite graph with bipartition $(X,Y)$ such that $|X|=|Y|$ and $bn(G)>0$. In this paper, we show that if $\nu (G)\le 2\kappa (G)+4bn(G)?4$, then G is Hamiltonian-laceable; or if $\nu (G)>6bn(G)?2$, then for every pair of vertices $x\in X$ and $y\in Y$, there is an $(x,y)$-path P in G with $|V(P)|\ge 6bn(G)?2$. We show some of its corollaries in k-extendable, bipartite graphs and a conjecture in k-extendable graphs.     

A decomposition-related throughput property of tandem queueing networks with blocking

A general throughput property of tandem queueing networks with blocking that relates existing decomposition methods to throughput bounds is discussed using the sample path approach.     

部分相干光在大气湍流中斜程传输路径上的展宽与漂移

基于Andrews和Philips经典漂移方差模型,利用部分相干高斯-谢尔光束在大气湍流中斜程传输的光束扩展半径,推导出考虑外尺度情况时部分相干高斯-谢尔光束斜程情况下的漂移方差表达式,应用随高度变化的大气结构常量模型进行数值计算,对比分析了部分相干光和完全相干光在大气湍流中的展宽和漂移特性.结果表明:相同的传输条件下,部分相干光比完全相干光的光束扩展更迅速,受湍流的影响也更小;初始半径越大,接收机高度越高,光束的扩展效应越小;随着传输距离的增大,光束的质心漂移方差随光束初始半径的增大而减小,不同相干性的光束漂移方差变化很小;完全相干光的光束漂移受波长的影响较小,而部分相干光的波长越长,漂移越明显.     

光程差计算中的近似问题

指出某些教材在计算相干光的光程差时，存在不妥当的近似。