Let be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer copies of H<sub>i</sub>, where . Let C<sub>k</sub>, P<sub>k...Let be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer copies of H<sub>i</sub>, where . Let C<sub>k</sub>, P<sub>k</sub> and S<sub>k</sub> denote a cycle, a path and a star with k edges, respectively. For an integer , we prove that a balanced complete bipartite multigraph has a -decomposition if and only if k is even, and .展开更多
Pure phase star-shaped hydrogarnet Sr3Fe2（OH）12 assemblies were synthesized by a mild hydrothermal method （210℃, 12 h）, and the effects of the preparation conditions on the phase composition of the product were i...Pure phase star-shaped hydrogarnet Sr3Fe2（OH）12 assemblies were synthesized by a mild hydrothermal method （210℃, 12 h）, and the effects of the preparation conditions on the phase composition of the product were investigated. It was found that the impurity phases could be decreased or eliminated by increasing the molar ratio of Sr2＋ to Fe3＋, and that high temperatures favored the formation of Sr3 Fe2（OH）12 and reduced the concentration of CO32- -containing byproducts. The thermal decomposition of the star-shaped Sr3Fe2（OH）12 assemblies was examined, and the results showed that the dehydration process at higher temperatures is accompanied by the formation of SrFeO3-δ. Above 655 ℃, a solid state reaction between the SrFeO3-δ and Sr（OH）2 or SrCO3 results in the formation of Sr4Fe3O10-δ.The mag- netic properties of the as-synthesized Sr3Fe2（OH）12 and of samples calcined at different temperatures were assessed. A sample calcined at 575 ℃ exhibited greatly enhanced ferromagnetic properties, with a remanent magnetization of 1.28 emu/g and a coercivity of 4522.1 Oe at room temperature.展开更多
文摘Let be a family of subgraphs of a graph G. An L-decomposition of G is an edge-disjoint decomposition of G into positive integer copies of H<sub>i</sub>, where . Let C<sub>k</sub>, P<sub>k</sub> and S<sub>k</sub> denote a cycle, a path and a star with k edges, respectively. For an integer , we prove that a balanced complete bipartite multigraph has a -decomposition if and only if k is even, and .
文摘Pure phase star-shaped hydrogarnet Sr3Fe2（OH）12 assemblies were synthesized by a mild hydrothermal method （210℃, 12 h）, and the effects of the preparation conditions on the phase composition of the product were investigated. It was found that the impurity phases could be decreased or eliminated by increasing the molar ratio of Sr2＋ to Fe3＋, and that high temperatures favored the formation of Sr3 Fe2（OH）12 and reduced the concentration of CO32- -containing byproducts. The thermal decomposition of the star-shaped Sr3Fe2（OH）12 assemblies was examined, and the results showed that the dehydration process at higher temperatures is accompanied by the formation of SrFeO3-δ. Above 655 ℃, a solid state reaction between the SrFeO3-δ and Sr（OH）2 or SrCO3 results in the formation of Sr4Fe3O10-δ.The mag- netic properties of the as-synthesized Sr3Fe2（OH）12 and of samples calcined at different temperatures were assessed. A sample calcined at 575 ℃ exhibited greatly enhanced ferromagnetic properties, with a remanent magnetization of 1.28 emu/g and a coercivity of 4522.1 Oe at room temperature.
