杜布瓦雷蒙分型工作的初衷  

On the Original Intention of Du Bois-Reymond’s Classification

作　　者：杨浩菊[1] 任辛喜[1] YANG Haoju;REN Xinxi(School of Mathematics and Computer Science,Shanxi Normal University,Linfen,Shanxi,041004)

机构地区：[1]山西师范大学数学与计算机科学学院,山西临汾041004

出　　处：《自然辩证法通讯》2021年第6期16-23,共8页Journal of Dialectics of Nature

基　　金：国家自然科学基金资助项目“全球背景下的近代东亚数学知识交流图谱的构建”(项目编号:11971380)。

摘　　要：分型与黎曼函数是杜布瓦雷蒙对线性偏微分方程理论的独特贡献。本文就杜布瓦雷蒙的思想渊源和此二项工作的逻辑关系对原文进行了详细的考查,指出,分型目的在于推广黎曼方法,也是将该方法一般化的必要前提。比起黎曼方法,分型本身在原文作者心目中是次要的。杜布瓦雷蒙之所以能完成分型,一个决定因素是他早年研究过的特征理论。无论偏微分方程理论的发展如何改变分型和黎曼函数的份量,搞清楚杜布瓦雷蒙分型的初衷对于客观评价他的贡献都是必要的。The classification and Riemann Function are the unique contributions of Du Bois-Reymond to the theory of linear partial differential equations.A detailed examination of the original text and the logical relationship between the two works are made.It is pointed out that the purpose of the classification is to generalize Riemann’s method and the classification is also a necessary precondition for generalizing this method.Compared with Riemann’s method,the classification itself was secondary in Du Bois-Reymond’s view.One of the decisive factors that Du Bois-Reymond was able to complete the classification was the theory of characteristics he had studied in his early years.No matter how the development of the theory of partial differential equation changes the weight of classification and Riemann function,it is necessary to make clear the original intention of Du Bois-Reymond’s classification for objective evaluating of his contribution objectively.

关 键 词：偏微分方程分类 杜布瓦雷蒙 黎曼函数 特征曲线 

分 类 号：NO[理学—数学] O175.2[理学—基础数学]