A path decomposition of a graph G is a list of paths such that each edge appears in exactly one path in the list. G is said to admit a {Pl }-decomposition if G can be decomposed into some copies of Pl, where Pl is a p...A path decomposition of a graph G is a list of paths such that each edge appears in exactly one path in the list. G is said to admit a {Pl }-decomposition if G can be decomposed into some copies of Pl, where Pl is a path of length l - 1. Similarly, G is said to admit a {Pl, Pk}-decomposition if G can be decomposed into some copies of Pl or Pk. An k-cycle, denoted by Ck, is a cycle with k vertices. An odd tree is a tree of which all vertices have odd degree. In this paper, it is shown that a connected graph G admits a {P3, P4}-decomposition if and only if G is neither a 3-cycle nor an odd tree. This result includes the related result of Yan, Xu and Mutu. Moreover, two polynomial algorithms are given to find {P3}-decomposition and {P3, P4}-decomposition of graphs, respectively. Hence, {P3}-decomposition problem and {P3, P4}-decomposition problem of graphs are solved completely.展开更多
Thermal decomposition behaviors of TiH_2 powder under a flowing helium atmosphere and in a low vacuum condition have been studied using an in situ EXAFS technique.By an EXAFS analysis containing the multiple scatterin...Thermal decomposition behaviors of TiH_2 powder under a flowing helium atmosphere and in a low vacuum condition have been studied using an in situ EXAFS technique.By an EXAFS analysis containing the multiple scattering paths including H atoms,the changes of the hydrogen stoichiometric ratio and the phase transformation sequence are obtained.The results demonstrate that the initial decomposition temperature is dependent on experimental conditions,which occurs,respectively,at about 300 and 400℃ in a low vacuum condition and under a flowing helium atmosphere.During the decomposition process of TiH_2 in a low vacuum condition,the sample experiences a phase change process：δ（TiH_2）→δ（TiH_x）→δ（TiH_1）＋β（TiH_x）→δ（TiH_x）＋β（TiH_x）＋α（Ti）→β（TiH_x）＋α（Ti）→α（Ti）＋β（Ti）.This study offers a way to detect the structural information of hydrogen.A detailed discussion about the decomposition process of TiH_2 is given in this paper.展开更多
基金Supported by the National Natural Science Foundation of China(No.10301010)Science and Technology Commission of Shanghai Municipality(No.04JC14031)Natural Science Project of Chuzhou University(No.2006kyy017)
文摘A path decomposition of a graph G is a list of paths such that each edge appears in exactly one path in the list. G is said to admit a {Pl }-decomposition if G can be decomposed into some copies of Pl, where Pl is a path of length l - 1. Similarly, G is said to admit a {Pl, Pk}-decomposition if G can be decomposed into some copies of Pl or Pk. An k-cycle, denoted by Ck, is a cycle with k vertices. An odd tree is a tree of which all vertices have odd degree. In this paper, it is shown that a connected graph G admits a {P3, P4}-decomposition if and only if G is neither a 3-cycle nor an odd tree. This result includes the related result of Yan, Xu and Mutu. Moreover, two polynomial algorithms are given to find {P3}-decomposition and {P3, P4}-decomposition of graphs, respectively. Hence, {P3}-decomposition problem and {P3, P4}-decomposition problem of graphs are solved completely.
基金Supported by National Natural Science Foundation of China(10875143)
文摘Thermal decomposition behaviors of TiH_2 powder under a flowing helium atmosphere and in a low vacuum condition have been studied using an in situ EXAFS technique.By an EXAFS analysis containing the multiple scattering paths including H atoms,the changes of the hydrogen stoichiometric ratio and the phase transformation sequence are obtained.The results demonstrate that the initial decomposition temperature is dependent on experimental conditions,which occurs,respectively,at about 300 and 400℃ in a low vacuum condition and under a flowing helium atmosphere.During the decomposition process of TiH_2 in a low vacuum condition,the sample experiences a phase change process：δ（TiH_2）→δ（TiH_x）→δ（TiH_1）＋β（TiH_x）→δ（TiH_x）＋β（TiH_x）＋α（Ti）→β（TiH_x）＋α（Ti）→α（Ti）＋β（Ti）.This study offers a way to detect the structural information of hydrogen.A detailed discussion about the decomposition process of TiH_2 is given in this paper.
