二元函数重极限存在与否的降维证明  

Dimensionality Reduction Proof of the Existence or Non Existence of Double Limit for Binary Functions

作　　者：陈楠楠 陆万春 贺妤函 CHEN Nannan;LU Wanchun;HE Yuhan(College of Engineering and Management,Pingxiang University,Pingxiang,Jiangxi 337000,China)

机构地区：[1]萍乡学院工程与管理学院,江西萍乡337000

出　　处：《萍乡学院学报》2024年第6期1-4,共4页Journal of Pingxiang University

基　　金：江西省教育厅科技项目“基于EMD-NLM的遥感图像条带去除方法研究”(GJJ18112);萍乡学院青年基金项目“基于EMD的遥感影像滤波方法研究”(2018D0218)。

摘　　要：为了研究“0/0”型的二元分式函数重极限存在与否,课题组先将二元分式函数f(x,y)化简降维为三类含未定式类型的函数,再根据未定式选择路径或根据已定式确定数值,讨论它们在(x,y)→(0,0)时的重极限。对三类含未定式类型的函数极限课题组给出了定理及相关证明,并用多个实例验证了降维证明法,阐释了降维证明的缘由与本质。In order to investigate the existence or absence of the double limit of binary fractional functions of the"0/0"type,the research team first simplifies and reduces the binary fractional functions into three types of functions with indeterminate forms.Then,based on the indeterminate form,the path is selected or the value is determined according to the definite form,and their double limits at time are discussed.The research group provided theorems and related proofs for three types of function limits containing indefinite forms,and verified the dimensionality reduction proof method with multiple examples,explaining the reasons and essence of dimensionality reduction proof.

关 键 词：二元函数 重极限 降维证明 未定式 

分 类 号：O13[理学—数学]