Photocatalytic performance of Cu2O and Ag/Cu2O composite octahedra prepared by a propanetriol-reduced process

Cu₂O and Ag/Cu₂O composite octahedra were synthesized via a hydrothermal reaction of CuAc₂ with urea in H₂O–propanetriol binary solution by adjusting the quantity of AgNO₃ at 180 °C for 10 h. The influence of reaction temperature and time on the morphology and phase of the products was investigated, and a possible growth mechanism of Cu₂O octahedron was also proposed. The photocatalytic activities of the as-prepared Cu₂O and Ag/Cu₂O octahedra for the degradation of methyl orange aqueous solution were studied. The results show that they are effective photocatalysts for the degradation of methyl orange, and the photocatalytic ability of Ag/Cu₂O composite is stronger than that of Cu₂O octahedra, which are expected to be useful in the treatment of wastewaters.     

圈的中间图pebbling数和Graham猜想

图G的一个pebbling移动是从一个顶点移走2个pebble, 而把其中的1个pebble移到与其相邻的一个顶点上. 图G 的pebbling数f(G)是最小的正整数n, 使得不论n个pebble 如何放置在G的顶点上, 总可以通过一系列的pebbling移动, 把1个pebble移到图G的任意一个顶点上. 图G 的中间图M(G) 就是在G 的每一条边上插入一个新点, 再把G 上相邻边上的新点用一条边连接起来的图. 对于任意两个连通图G和H, Graham猜测f(G\times H)\leq f(G)f(H). 首先研究了圈的中间图的pebbling 数, 然后讨论了一些圈的中间图满足Graham猜想.     

Minimizing the least eigenvalue of unicyclic graphs with fixed diameter

Let U(n,d) be the set of unicyclic graphs on n vertices with diameter d. In this article, we determine the unique graph with minimal least eigenvalue among all graphs in U(n,d). It is found that the extremal graph is different from that for the corresponding problem on maximal eigenvalue as done by Liu et al. [H.Q. Liu, M. Lu, F. Tian, On the spectral radius of unicyclic graphs with fixed diameter, Linear Algebra Appl. 420 (2007) 449-457].     

An extremal problem on non-full colorable graphs

For a given graph G of order n, a k-L(2,1)-labelling is defined as a function f:V(G)→{0,1,2,…k} such that |f(u)-f(v)|?2 when d_G(u,v)=1 and |f(u)-f(v)|?1 when d_G(u,v)=2. The L(2,1)-labelling number of G, denoted by λ(G), is the smallest number k such that G has a k-L(2,1)-labelling. The hole index ρ(G) of G is the minimum number of integers not used in a λ(G)-L(2,1)-labelling of G. We say G is full-colorable if ρ(G)=0; otherwise, it will be called non-full colorable. In this paper, we consider the graphs with λ(G)=2m and ρ(G)=m, where m is a positive integer. Our main work generalized a result by Fishburn and Roberts [No-hole L(2,1)-colorings, Discrete Appl. Math. 130 (2003) 513-519].     

MKdV方程和SG方程的可积曲面的构造

给出Modified Korteweg-de Vries方程(MKdV)and Sine-Gordon(SG)方程n重达布交换后的孤子解和孤子曲面的表达式.进一步,分析了孤子曲线和曲面在达布变换下的性质和变化规律.     

3, 4-吡啶二酸钡配合物的合成、结构、荧光和热稳定性研究

BaCl₂·2H₂O和配体3,4-吡啶二酸在溶剂热条件下反应生成了配合物[Ba₂(pdc)₂(H₂O)₃] _n (1)(H₂pdc=3, 4-吡啶二酸), 用单晶X-射线、元素分析和FT-IR对生成的晶体进行了表征。Ba1和Ba2分别采取了八配位扭曲四方反棱柱和十配位的双帽四棱柱几何构型, 整个pdc^2-作为四齿桥联配体连结4个不同的Ba(Ⅱ)原子形成二维网结构, O-H…N氢键将二维网结合在一起形成三维结构。还研究了配合物1的荧光和热重性质。     

Sharp upper bounds on the second largest eigenvalues of connected graphs

Let ${\lambda }_2$ be the second largest eigenvalue of a graph. Powers (1988) [4] gave some upper bounds of ${\lambda }_2$ for general graphs and bipartite graphs, respectively. Considering that these bounds are not always attainable for connected graphs, we present sharp upper bounds of ${\lambda }_2$ for connected graphs and connected bipartite graphs in this paper. Moreover, the extremal graphs are completely characterized.