In this note, we first derive an exponential generating function of the alternating run polynomials. We then deduce an explicit formula of the alternating run polynomials in terms of the partial Bell polynomials.
文摘In this note, we first derive an exponential generating function of the alternating run polynomials. We then deduce an explicit formula of the alternating run polynomials in terms of the partial Bell polynomials.
基金supported by the National Key Research and Development Program of China(2021YFA1501500)the National Natural Science Foundation of China(22033008,22220102005,and 22171265)Fujian Science&Technology Innovation Laboratory for Optoelectronic Information of China(2021ZZ103).
文摘催化剂与助催化剂之间的低电荷分离效率严重限制了光催化性能.催化剂与助催化剂之间的强界面相互作用可以提高电荷分离效率.通过引入界面化学键增强组分间的界面相互作用是提高光催化性能的有效手段之一.本文合成了ZnIn_(2)S_(4)(ZIS)/Sv-MoS_(2)光催化剂,ZIS中的S原子与Sv-MoS_(2)中未配位Mo原子之间的键合作用形成了界面Mo–S键,这极大地提高了ZIS的光催化活性.采用不同的NaBH4蚀刻时间制备了MoS_(2-x)h.优化后的Z I S/MoS_(2)-4 h复合材料的产氢速率为7.6 mmol g^(−1)h^(−1),是原ZIS(1.6 mmol g^(−1)h^(−1))的4.75倍,是ZIS/MoS_(2)(3.7 mmol g^(−1)h^(−1))的2.05倍.非凡的光催化活性可归因于光生电子在Mo–S键的作用下更容易从ZIS转移到MoS_(2).光电测量表明,ZIS/MoS_(2)-4h具有有效的电荷转移.本工作揭示了引入界面化学键对ZIS/MoS_(2)光催化活性的影响,为通过界面工程设计优良的助催化剂提供了一种简单有效的方法.
