Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide ...Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.展开更多
In this work, we prepared three simple arylamine-based hole transporting materials from commercially available starting materials. The effect of extending z-conjugation length or increasing the number of side groups c...In this work, we prepared three simple arylamine-based hole transporting materials from commercially available starting materials. The effect of extending z-conjugation length or increasing the number of side groups compared with reference compound on the photophysical, electrochemical, hole mobility properties and performance in perovskite solar cells were further studied. It is noted that these two kinds of molecular modifications can significantly lower the HOMO level and improve the hole mobility, thus improving the hole injection from valence band of perovskite. On the other hand, the compound with more side groups showed higher hole injection efficiency due to lower HOMO level and higher hole mo- bility compared with the compound with extending π-conjugation length. The perovskite solar cells with the modified molecules as hole transporting materials showed a higher efficiency of 15.40% and 16.95%, respectively, which is better than that of the reference compound （13.18%）. Moreover, the compound with increasing number of side groups based devices showed comparable photovoltaic performance with that of conventional spiro-OMeTAD （16.87%）.展开更多
Let G be aπ-separable group for a set of primes, let N be a normal subgroup of G, and letθbe an Iπ-character （i.e., irreducibleπ-partial character） of N . We obtain a necessary and sufficient condition for the n...Let G be aπ-separable group for a set of primes, let N be a normal subgroup of G, and letθbe an Iπ-character （i.e., irreducibleπ-partial character） of N . We obtain a necessary and sufficient condition for the number of Iπ-characters of G overθ to take the possible maximum ｜G：N｜π. Some applications are given.展开更多
基金Supported by NSF of China(1117116911071155)the B.S.Foundation of Shandong Province(BS2012SF003)
文摘Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.
基金supported by the National Basic Research Program of China (No. 2015CB932200)the CAS-Iranian Vice Presidency for Science and Technology Joint Research Project (No. 116134KYSB20160130)+2 种基金the Natural Science Foundation of Anhui Province (No. 1508085SMF224)the National Natural Science Foundation of China (No. 51474201)the External Cooperation Program of BIC, Chinese Academy of Sciences (No. GJHZ1607)
文摘In this work, we prepared three simple arylamine-based hole transporting materials from commercially available starting materials. The effect of extending z-conjugation length or increasing the number of side groups compared with reference compound on the photophysical, electrochemical, hole mobility properties and performance in perovskite solar cells were further studied. It is noted that these two kinds of molecular modifications can significantly lower the HOMO level and improve the hole mobility, thus improving the hole injection from valence band of perovskite. On the other hand, the compound with more side groups showed higher hole injection efficiency due to lower HOMO level and higher hole mo- bility compared with the compound with extending π-conjugation length. The perovskite solar cells with the modified molecules as hole transporting materials showed a higher efficiency of 15.40% and 16.95%, respectively, which is better than that of the reference compound （13.18%）. Moreover, the compound with increasing number of side groups based devices showed comparable photovoltaic performance with that of conventional spiro-OMeTAD （16.87%）.
基金Supported by the NSF of Shanxi Province(2013011001-3)
文摘Let G be aπ-separable group for a set of primes, let N be a normal subgroup of G, and letθbe an Iπ-character （i.e., irreducibleπ-partial character） of N . We obtain a necessary and sufficient condition for the number of Iπ-characters of G overθ to take the possible maximum ｜G：N｜π. Some applications are given.
