Comparative study on diameter distribution of single-walled carbon nanotubes using growth templates with different pore sizes: Zeolite-L,ZSM-5, and MCM-41

We report a comparative study on diameter distribution of single-walled carbon nanotubes (SWNTs) grown using nanoporous templates having different pore sizes, namely, zeolite-L, ZSM-5, and MCM-41. The change in the tube diameter based on catalytic film thickness and growth temperature was systematically investigated. We prepared very thin Fe catalyst films with nominal thicknesses of 0.5, 0.7, 1, and 2 Å, and the growth temperature was varied from 850 to 925 °C. We found that the SWNT mean diameter and size distribution width decreased with decreasing catalyst film thickness, growth temperature, and pore sizes of the templates. In addition, all SWNTs grown from the nanoporous templates have narrower diameter distribution compared to the SWNTs grown from SiO₂ planar surface. The obtained results are straightforward and suggest that the template growth has potential for SWNT growth with very narrow diameter distribution.     

The commutation graph for the longest signed permutation

Using the standard Coxeter presentation for the signed symmetric group ${\mathfrak{S}}_{n+1}^B$ on $n+1$ letters, two reduced expressions for a given signed permutation are in the same commutation class if one expression can be obtained from the other one by applying a finite sequence of commutations. The commutative classes of a given signed permutation can be seen as the vertices of a graph, called the commutation graph, where two classes are connected by an edge if there are elements in those classes that differ by a long braid relation. We define a rank function for the commutation graph for the longest signed permutation, and use this function to compute the diameter and the radius of the graph. We also prove that the commutation graph for the longest signed permutation is not planar for $n>2$, and identify the classes with a single element.     

重组竹横纹销槽承压强度试验研究

设计4组仅销槽直径不同的试件来分析螺杆直径对重组竹横纹销槽承压强度的影响,根据试验结果评价美国木结构设计规范和欧洲木结构设计规范推荐的理论计算公式对重组竹的适应性。采用1mm/min的速度加载至试件破坏,根据试验结果,得到了所有试件的荷载-位移曲线和极限强度值,并且得到基于美国规范5%d偏移法的屈服强度试验值,结果表明采用5%d偏移法得到的重组横纹竹销槽承压屈服强度值比较均匀,变异系数13.36%之内,并且其平均值随螺杆直径增大而减小,大于理论公式的计算结果,因此采用规范推荐的理论计算公式具有较高的可靠性。     

The Complement Graph for Gaussian Integers Modulo n

This article is a continuation for the work done in [1 Abu Osba , E. , Al-Addasi , S. , Abu Jaradeh , N. ( 2008 ). Zero divisor graph for the ring of Gaussian integers modulo . n. Comm. Algebra 36 ( 10 ): 3865 – 3877 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar], 2 Abu Osba , E. , Al-Addasi , S. , Al-Khamaiseh , B. ( 2011 ). Some properties of the zero divisor graph for the ring of gaussian integers modulo . n. Glasgow Journal of Mathematics 53 : 391 – 399 .[Crossref], [Web of Science ®] , [Google Scholar]] on the zero divisor graph for the ring of Gaussian integers modulo n. It investigates when the complement graph of the zero divisor graph for the Gaussian integers modulo n connected, planar, regular, or Eulerian. The girth and diameter were also studied.     

On the eccentric connectivity index of a graph

If G is a connected graph with vertex set V, then the eccentric connectivity index of G, ξ^C(G), is defined as where is the degree of a vertex v and is its eccentricity. We obtain an exact lower bound on ξ^C(G) in terms of order, and show that this bound is sharp. An asymptotically sharp upper bound is also derived. In addition, for trees of given order, when the diameter is also prescribed, precise upper and lower bounds are provided.     

The Randi? index and the diameter of graphs

The Randi? indexR(G) of a graph G is defined as the sum of over all edges uv of G, where d_u and d_v are the degrees of vertices u and v, respectively. Let D(G) be the diameter of G when G is connected. Aouchiche et al. (2007) [1] conjectured that among all connected graphs G on n vertices the path P_n achieves the minimum values for both R(G)/D(G) and R(G)−D(G). We prove this conjecture completely. In fact, we prove a stronger theorem: If G is a connected graph, then , with equality if and only if G is a path with at least three vertices.     

Diameter bounds for planar graphs

The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a crucial surgery method, we begin by proving the simpler related upper bounds (4(|V|−1)−|E|)/3 and 4|V|²/3|E| on the diameter (for connected planar graphs), which are also tight.     

Diameter, connectivity, and phase transition of the uniform random intersection graph

We study properties of the uniform random intersection graph model G(n,m,d). We find asymptotic estimates on the diameter of the largest connected component of the graph near the phase transition and connectivity thresholds. Moreover we manage to prove an asymptotically tight bound for the connectivity and phase transition thresholds for all possible ranges of d, which has not been obtained before. The main motivation of our research is the usage of the random intersection graph model in the studies of wireless sensor networks.     

在水热条件下利用微胶束对TiO2纳米线阵列直径的精细调控

通过探讨氧化钛纳米线阵列反应机制,建立了在水热条件下,氧化钛纳米线阵列在亲水掺铟氧化锡表面上由极性/非极性溶剂体系中形成的胶束内反应并生长的模型.并由此利用微胶束的尺寸限制作用,通过温度对微胶束尺寸进行调节,以及Cl^-离子的晶面限制效应,实现了在较大范围内对纳米线直径的调控.另外反应体系中极性与非极性溶液的比例的变化对纳米阵列的直径影响不大,因此可以认为在此反应体系中,氧化钛纳米线的直径主要受到微胶束的限域效应以及Cl^-离子的晶面限制效应影响.此方法可应用于其他相关氧化物纳米材料的尺寸控制合成中.