有限个数列相加后盒维数估计及对应级数的敛散性判断  

Estimating the Box Dimension of the Sum of a Finite Number of Sequences and Judging the Convergence or Divergence of the Corresponding Series

作　　者：孙玺轩 梁永顺[1] 

机构地区：[1]南京理工大学数学与统计学院,江苏 南京

出　　处：《理论数学》2024年第12期112-119,共8页Pure Mathematics

基　　金：国家自然科学基金(批准号12071218)。

摘　　要：本文主要讨论两个严格单调正项数列加法运算后盒维数与原先两个数列盒维数的关系,并将其推广到有限个数列进行加法运算的情形。在原先研究基础上,讨论加法运算后数列对应级数的敛散性,并得到了一些初步的研究成果。In this paper, we mainly solve the relationship between the box dimension of two strictly monotone positive series after the addition operation and the box dimension of the original two series. Then extend the conclusion to the addition operation of a finite number of sequences. On the basis of the previous research, the convergence or divergence of the corresponding series of the sequences after the addition operation is discussed. And some preliminary research results are obtained.

关 键 词：盒维数 单调数列 级数敛散性 

分 类 号：G63[文化科学—教育学]