An embedding of a digraph in an orientable surface is an embedding as the underlying graph and arcs in each region force a directed cycle. The directed genus is the minimum genus of surfaces in which the digraph can b...An embedding of a digraph in an orientable surface is an embedding as the underlying graph and arcs in each region force a directed cycle. The directed genus is the minimum genus of surfaces in which the digraph can be directed embedded. Bonnington, Conder, Morton and McKenna [J. Cornbin. Theory Ser. B,85（2002） 1-20] gave the problem that which tournaments on n vertices have the directed genus [（n-3）（n-4）/12]the genus of Kn. In this paper, we use the current graph method to show that there exists a tournament, whichhas the directed genus[（n-3）（n-4）/12], on n vertices if and only if n = 3 or 7 （mod 12）.展开更多
Constructing a photoanode with both high dark-state protection performance and high stability remains a top priority for photoelectrochemical cathodic protection technology,especially in a marine environment(dark-stat...Constructing a photoanode with both high dark-state protection performance and high stability remains a top priority for photoelectrochemical cathodic protection technology,especially in a marine environment(dark-state or rainy conditions)without hole scavenging agents.In this work,we developed a class of energy-storage quasi-planar heterojunctions(WO_(3)-Nb_(2)O_(5)-ZnIn_(2)S_(4))with directional paths(low onset potential and well-matched energy band)and embedded morphology.The co-design of embedded and directional paths reduces the carrier transport energy barrier at the composite interface,and increases the interface contact area,thereby achieving highly stable and sensitive dark-state energy storage and photoelectrochemical cathodic protection performance in 3.5 wt.%NaCl solution without hole scavenging agent(Dark-state energy storage efficiency increased by 43%.For carbon steel,the performance retention rate is 99.6%after 500 cycles,the performance retention rate is 89%after 5000 s).展开更多
基金Supported by the National Natural Science Foundation of China(No.11731002)the Fundamental Research Funds for the Central Universities(Nos.2016JBM071,2016JBZ012)
文摘An embedding of a digraph in an orientable surface is an embedding as the underlying graph and arcs in each region force a directed cycle. The directed genus is the minimum genus of surfaces in which the digraph can be directed embedded. Bonnington, Conder, Morton and McKenna [J. Cornbin. Theory Ser. B,85（2002） 1-20] gave the problem that which tournaments on n vertices have the directed genus [（n-3）（n-4）/12]the genus of Kn. In this paper, we use the current graph method to show that there exists a tournament, whichhas the directed genus[（n-3）（n-4）/12], on n vertices if and only if n = 3 or 7 （mod 12）.
基金financially supported by the Henan Province Key R&D and Promotion Project(Technology Research)(NO.232102230011)the Fundamental Research Fund of Henan Academy of Sciences(NO.230618026)+1 种基金Joint Fund of Henan Province Science and Technology R&D Program(NO.225200810120)High-level Talent Research Start-up Project Funding of Henan Academy of Sciences(NOs.231818022 and 232018001).
文摘Constructing a photoanode with both high dark-state protection performance and high stability remains a top priority for photoelectrochemical cathodic protection technology,especially in a marine environment(dark-state or rainy conditions)without hole scavenging agents.In this work,we developed a class of energy-storage quasi-planar heterojunctions(WO_(3)-Nb_(2)O_(5)-ZnIn_(2)S_(4))with directional paths(low onset potential and well-matched energy band)and embedded morphology.The co-design of embedded and directional paths reduces the carrier transport energy barrier at the composite interface,and increases the interface contact area,thereby achieving highly stable and sensitive dark-state energy storage and photoelectrochemical cathodic protection performance in 3.5 wt.%NaCl solution without hole scavenging agent(Dark-state energy storage efficiency increased by 43%.For carbon steel,the performance retention rate is 99.6%after 500 cycles,the performance retention rate is 89%after 5000 s).
