| 若干函数连续性与间断性的理论与应用拓展 |
| |
| 引用本文： | 詹华税,许文彬.若干函数连续性与间断性的理论与应用拓展[J].厦门理工学院学报,2021,29(1):79-84. |
| |
| 作者姓名： | 詹华税 许文彬 |
| |
| 作者单位： | 厦门理工学院应用数学学院,福建 厦门361024;集美大学理学院,福建 厦门361021 |
| |
| 摘 要： | 为进一步充实经典数学分析的理论研究，对变上限积分的连续性与可导性问题展开分析。并利用函数连续性的最值原理，讨论具有连续偏导数的三元函数梯度存在性问题；并基于BV 函数的基本性质，讨论一类金融数学方程BV解的间断点分布的几何性质。结果表明，变上限积分函数是几乎处处可导的函数，比一般的连续函数具有更好的可利用的分析性质；一般可微函数未必存在梯度。文中同时证明了上述金融数学方程BV解的间断点集合是一曲线，而不可能是一曲面。
|
| 关 键 词： | 函数连续性 间断点 变上限积分 金融数学 BV解 |
Some Generalizations of Continuity and Discontinuity of
a Function and Its Applications |
| |
| ZHAN Huashui,XU Wenbin.Some Generalizations of Continuity and Discontinuity of
a Function and Its Applications[J].Journal of Xiamen University of Technology,2021,29(1):79-84. |
| |
| Authors: | ZHAN Huashui XU Wenbin |
| |
| Affiliation: | 1.School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China
2.School of Sciences,Jimei University,Xiamen 361021,China |
| |
| Abstract: | In order to enrich the classical mathematical analysis theory,this paper probes the continuity and derivability of a variable upper bound integral function,uses the maximum principle of the continuity of the function to discuss the existence of the gradient of a three dimensional function which is with continuous partial derivatives,and discusses the distribution of the discontinuous points of the BV solutions to a class of equation arising from mathematical finance by some properties of a BV function.The results show that the variable upper bound integral function is derivative almost everywhere,possessing therefore a better analytic property than that of a continuous function,and that differential function is not necessarily defined as gradient.It is also proved that the discontinuous points of the BV solutions to the studied finance mathematics equation is a curve rather than a surface. |
| |
| Keywords: | function continuitydiscontinuityvariable upper bound integral functionfinance mathematicsBV solution |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
| 点击此处可从《厦门理工学院学报》浏览原始摘要信息 |
|
点击此处可从《厦门理工学院学报》下载全文 |
|
