本研究采用水热-冷冻干燥-煅烧的方法成功制备了铜掺杂硫化锡负载氧化石墨烯气凝胶(Cu x SnSO@GO),并采用X射线衍射仪(XRD)、扫描电子显微镜(SEM)、透射电子显微镜(TEM)和紫外-可见光反射分析(UV-vis DRS)对材料进行表征,研究了不同Cu...本研究采用水热-冷冻干燥-煅烧的方法成功制备了铜掺杂硫化锡负载氧化石墨烯气凝胶(Cu x SnSO@GO),并采用X射线衍射仪(XRD)、扫描电子显微镜(SEM)、透射电子显微镜(TEM)和紫外-可见光反射分析(UV-vis DRS)对材料进行表征,研究了不同Cu掺杂量和不同反应时间对光催重整纤维素酶解液产乳酸的影响。结果表明,铜成功的掺入到SnS_(2)结构中,产生表面硫缺陷,改变了SnS_(2)的带隙,提高了SnS_(2)的光催属性。此外,煅烧工艺制备的Cu x SnSO@GO改善了光生电子和空穴的分离效率,显著提高了光催化效率。Cu x SnSO@GO在可见光照射下能够高效的光催重整纤维素酶解液产乳酸,当Cu掺杂量x=0.06反应时间为4 h时,Cu x SnSO@GO具有38.8%的最佳产率。Cu x SnSO@GO形成的表面硫空位、高吸收性、可调节的能带结构以及煅烧后形成的Cu x SnS_(2)-SnO 2异质结都有利于乳酸的选择性转化,这为研究生物质光催化重整的机理提供了一种新的途径。展开更多
A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G.The acyclic edge chromatic number of G,denoted byχ′a(G),is the smallest number of colors in an acyclic edge coloring of G...A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G.The acyclic edge chromatic number of G,denoted byχ′a(G),is the smallest number of colors in an acyclic edge coloring of G.Let G be a planar graph with maximum degree.In this paper,we show thatχ′a(G)+2,if G has no adjacent i-and j-cycles for any i,j∈{3,4,5},which implies a result of Hou,Liu and Wu(2012);andχ′a(G)+3,if G has no adjacent i-and j-cycles for any i,j∈{3,4,6}.展开更多
A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest num...A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we give some upper bounds on linear chromatic number for plane graphs with respect to their girth, that improve some results of Raspaud and Wang (2009).展开更多
We consider the design of semidefinite programming(SDP) based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance(MHC-LU): Find a partition of the vertices of a weighted hypergraph H =(V,...We consider the design of semidefinite programming(SDP) based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance(MHC-LU): Find a partition of the vertices of a weighted hypergraph H =(V, E) into two subsets V1, V2 with ‖V2|- |V1‖ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance(MC-LU), Max Set Splitting,Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/|V|. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko(2000) on Max Hypergraph Bisection(MHC-LU with u = 0), and results of Andersson and Engebretsen(1999), Gaur and Krishnamurti(2001) and Zhang et al.(2004) on Max Set Splitting(MHC-LU with u = |V|). Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli(2007) is responsible for the improvement of a result of Galbiati and Maffioli(2007) on MC-LU for some range of τ.展开更多
Let G be a graph, let s be a positive integer, and let X be a subset of V(G). Denote δ(X) to be the minimum degree of the subgraph G[X] induced by X. A partition(X, Y) of V(G) is called s-good if min{δ(X), δ(Y)} s....Let G be a graph, let s be a positive integer, and let X be a subset of V(G). Denote δ(X) to be the minimum degree of the subgraph G[X] induced by X. A partition(X, Y) of V(G) is called s-good if min{δ(X), δ(Y)} s. In this paper, we strengthen a result of Maurer and a result of Arkin and Hassin, and prove that for any positive integer k with 2 k |V(G)|- 2, every connected graph G with δ(G) 2 admits a1-good partition(X, Y) such that |X| = k and |Y| = |V(G)|- k, and δ(X) + δ(Y) δ(G)- 1.展开更多
文摘本研究采用水热-冷冻干燥-煅烧的方法成功制备了铜掺杂硫化锡负载氧化石墨烯气凝胶(Cu x SnSO@GO),并采用X射线衍射仪(XRD)、扫描电子显微镜(SEM)、透射电子显微镜(TEM)和紫外-可见光反射分析(UV-vis DRS)对材料进行表征,研究了不同Cu掺杂量和不同反应时间对光催重整纤维素酶解液产乳酸的影响。结果表明,铜成功的掺入到SnS_(2)结构中,产生表面硫缺陷,改变了SnS_(2)的带隙,提高了SnS_(2)的光催属性。此外,煅烧工艺制备的Cu x SnSO@GO改善了光生电子和空穴的分离效率,显著提高了光催化效率。Cu x SnSO@GO在可见光照射下能够高效的光催重整纤维素酶解液产乳酸,当Cu掺杂量x=0.06反应时间为4 h时,Cu x SnSO@GO具有38.8%的最佳产率。Cu x SnSO@GO形成的表面硫空位、高吸收性、可调节的能带结构以及煅烧后形成的Cu x SnS_(2)-SnO 2异质结都有利于乳酸的选择性转化,这为研究生物质光催化重整的机理提供了一种新的途径。
基金supported by National Natural Science Foundation of China(Grant Nos.10931003 and 11171160)by Doctoral Fund of Ministry of Education of China(Grant No.10871011)
文摘A proper edge coloring of a graph G is said to be acyclic if there is no bicolored cycle in G.The acyclic edge chromatic number of G,denoted byχ′a(G),is the smallest number of colors in an acyclic edge coloring of G.Let G be a planar graph with maximum degree.In this paper,we show thatχ′a(G)+2,if G has no adjacent i-and j-cycles for any i,j∈{3,4,5},which implies a result of Hou,Liu and Wu(2012);andχ′a(G)+3,if G has no adjacent i-and j-cycles for any i,j∈{3,4,6}.
基金supported by National Natural Science Foundation of China (Grant Nos. 10931003, 10801077)the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 08KJB110008).
文摘A proper vertex coloring of a graph G is linear if the graph induced by the vertices of any two color classes is the union of vertex-disjoint paths. The linear chromatic number lc(G) of the graph G is the smallest number of colors in a linear coloring of G. In this paper, we give some upper bounds on linear chromatic number for plane graphs with respect to their girth, that improve some results of Raspaud and Wang (2009).
基金supported by National Natural Science Foundation of China(Grant Nos.11171160,11331003 and 11471003)the Priority Academic Program Development of Jiangsu Higher Education Institutions+2 种基金the Natural Science Foundation of the Jiangsu Higher Education Institutions of China(Grant No.13KJB1100188)Natural Science Foundation of Guangdong Province(Grant No.S2012040007521)Sienceand Technology Planning Project in Guangzhou(Grant No.2013J4100077)
文摘We consider the design of semidefinite programming(SDP) based approximation algorithm for the problem Max Hypergraph Cut with Limited Unbalance(MHC-LU): Find a partition of the vertices of a weighted hypergraph H =(V, E) into two subsets V1, V2 with ‖V2|- |V1‖ u for some given u and maximizing the total weight of the edges meeting both V1 and V2. The problem MHC-LU generalizes several other combinatorial optimization problems including Max Cut, Max Cut with Limited Unbalance(MC-LU), Max Set Splitting,Max Ek-Set Splitting and Max Hypergraph Bisection. By generalizing several earlier ideas, we present an SDP randomized approximation algorithm for MHC-LU with guaranteed worst-case performance ratios for various unbalance parameters τ = u/|V|. We also give the worst-case performance ratio of the SDP-algorithm for approximating MHC-LU regardless of the value of τ. Our strengthened SDP relaxation and rounding method improve a result of Ageev and Sviridenko(2000) on Max Hypergraph Bisection(MHC-LU with u = 0), and results of Andersson and Engebretsen(1999), Gaur and Krishnamurti(2001) and Zhang et al.(2004) on Max Set Splitting(MHC-LU with u = |V|). Furthermore, our new formula for the performance ratio by a tighter analysis compared with that in Galbiati and Maffioli(2007) is responsible for the improvement of a result of Galbiati and Maffioli(2007) on MC-LU for some range of τ.
基金supported by National Natural Science Foundation of China(Grant Nos.11201156,11331003 and 11171160)Natural Science Foundation of Jiangsu Province(Grant No.BK20131357)+1 种基金the Doctoral Fund of Ministry of Education of Chinaa project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Let G be a graph, let s be a positive integer, and let X be a subset of V(G). Denote δ(X) to be the minimum degree of the subgraph G[X] induced by X. A partition(X, Y) of V(G) is called s-good if min{δ(X), δ(Y)} s. In this paper, we strengthen a result of Maurer and a result of Arkin and Hassin, and prove that for any positive integer k with 2 k |V(G)|- 2, every connected graph G with δ(G) 2 admits a1-good partition(X, Y) such that |X| = k and |Y| = |V(G)|- k, and δ(X) + δ(Y) δ(G)- 1.
