圆环上加权全组合偏差的极值问题  

Extremal problem of weighted total combined energy between annuli

作　　者：钱香燕 冯小高[1] 王朝川 QIAN Xiangyan;FENG Xiaogao;WANG Chaochuan(College of Mathematics and Information,China West Normal University,Nanchong 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《陕西理工大学学报(自然科学版)》2025年第2期101-108,共8页Journal of Shaanxi University of Technology:Natural Science Edition

基　　金：国家自然科学基金项目(11701459)。

摘　　要：依据矩形上的定义,在圆环上给出了关于加权组合偏差、加权组合能量以及加权全组合偏差的新定义,并分别讨论了关于三者在圆环到圆环上保持边界对应的所有保向同胚映射类中的极值问题,运用Eulre-Lagrange方程和均值不等式得到并证明了这三类极值问题的解为径向拉伸映射。According to the definitions on the rectangle,new definitions of the weighted combined distortion,the weighted combined energy and the weighted total combination distortion is given on the annuli.Considering the extremal problems of the set composed of all orientation-preserving homeomorphics with boundary correspondence between annuli under these new definitions,the extremal of the set is obtained by using Euler-Lagrange equation and mean inequality,and the radial mapping is the solution of this kind of extremal problems.

关 键 词：加权组合偏差 加权组合能量 加权全组合偏差 极值问题 

分 类 号：O174.55[理学—数学]