In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating fun...In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.展开更多
Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigi...Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.展开更多
饮用水水源地水质演变趋势研究对水源地的保护具有重要意义。以中国某城市6个市级水源地为研究对象,采用水质指数法进行水质评价,在此基础上结合Pettitt Mann Whitney变异点分析法、Mann-Kendall趋势检验法和线性回归法,深入分析了各水...饮用水水源地水质演变趋势研究对水源地的保护具有重要意义。以中国某城市6个市级水源地为研究对象,采用水质指数法进行水质评价,在此基础上结合Pettitt Mann Whitney变异点分析法、Mann-Kendall趋势检验法和线性回归法,深入分析了各水源地水质突变时间及演变趋势,并结合该市近年来的管理政策分析了水质变化的原因。2020年-2022年各水源地水质现状整体较好,4个水源地水质评价结果为优良,其余为良好。变异点和演变趋势分析结果表明,各水源地均存在突变时间,水质指数突变时间主要集中在2021年2月-2022年4月,突变后2个水源地水质变差,其余水源地水质变好,仅1个水源地变异显著。该市水源地整体上2022年水质状况优于往年,主要得益于流域整体水环境质量改善和水源地特殊保护的加强。展开更多
文摘In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.
基金supported by the National Natural Science Foundation of China(No.12271069)the Natural Science Foundation of Chongqing(No.cstc2021jcyj-msxm X0443)+1 种基金the Chongqing“Zhitongche”foundation for doctors(No.CSTB2022BSXM-JCX0101)the Scientific and Technological Research Program of Chongqing Municipal Education Commission(No.KJQN202201138)。
文摘Zhang(2021),Luo and Yin(2022)initiated the study of Lagrangian submanifolds satisfying▽*T=0 or▽*T=0 in C^(n) or CP^(n),where T=▽*h and h is the Lagrangian trace-free second fundamental form.They proved several rigidity theorems for Lagrangian surfaces satisfying▽*T=0 or▽*▽*T=0 in C2 under proper small energy assumption and gave new characterization of the Whitney spheres in C2.In this paper,the authors extend these results to Lagrangian submanifolds in Cn of dimension n≥3 and to Lagrangian submanifolds in CPn.
文摘饮用水水源地水质演变趋势研究对水源地的保护具有重要意义。以中国某城市6个市级水源地为研究对象,采用水质指数法进行水质评价,在此基础上结合Pettitt Mann Whitney变异点分析法、Mann-Kendall趋势检验法和线性回归法,深入分析了各水源地水质突变时间及演变趋势,并结合该市近年来的管理政策分析了水质变化的原因。2020年-2022年各水源地水质现状整体较好,4个水源地水质评价结果为优良,其余为良好。变异点和演变趋势分析结果表明,各水源地均存在突变时间,水质指数突变时间主要集中在2021年2月-2022年4月,突变后2个水源地水质变差,其余水源地水质变好,仅1个水源地变异显著。该市水源地整体上2022年水质状况优于往年,主要得益于流域整体水环境质量改善和水源地特殊保护的加强。
