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[1]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.[doi:1019697/jcnki16734432202101012]
 ZHAN Huashui,XU Wenbin.Some Generalizations of Continuity and Discontinuity ofa Function and Its Applications[J].Journal of JOURNAL OF XIAMEN,2021,29(1):79-84.[doi:1019697/jcnki16734432202101012]
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若干函数连续性与间断性的理论与应用拓展(PDF/HTML)
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《厦门理工学院学报》[ISSN:1673-4432/CN:35-1289/Z]

卷:
29
期数:
2021年第1期
页码:
79-84
栏目:
应用数理科学
出版日期:
2021-02-28

文章信息/Info

Title:
Some Generalizations of Continuity and Discontinuity of a Function and Its Applications
文章编号:
16734432(2021)01007906
作者:
詹华税1许文彬2
1厦门理工学院应用数学学院,福建 厦门 361024; 2集美大学理学院,福建 厦门 361021
Author(s):
ZHAN Huashui1XU Wenbin2
1.School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China 2.School of Sciences,Jimei University,Xiamen 361021,China
关键词:
函数连续性间断点变上限积分金融数学BV解
Keywords:
function continuitydiscontinuityvariable upper bound integral functionfinance mathematicsBV solution
分类号:
O1722O17529
DOI:
1019697/jcnki16734432202101012
文献标志码:
A
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。
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.

参考文献/References:

[1] 上海交通大学, 集美大学.高等数学[M].北京:科学出版社,2010. [2] 菲赫金哥尔茨.微积分学教程:第二卷 第一分册[M].北京大学高等数学教研室,译.北京:人民教育出版社,1956. [3] 许晓婕,费祥历,孙清滢.连续函数的概念和性质剖析及其拓展教学研究[J].高等数学研究,2017,20(5):3034. [4] 黄娟霞.关于函数连续性的研究[J].通化师范学院学报,2019,40(10):2729. [5] 吴伟志,刘志松,徐优红.用二元关系刻画极限存在性和函数连续性[J].湖州师范学院学报,2016,38(8):3944. [6] 李娜.高等代数与数学分析在某些方面的互通性[J].科技视界,2014(33):30,48. [7] 鲍丽娟.“函数连续性与间断点”的对分课堂教学设计与实践[J].高等数学研究,2019,22(5):6164. [8] 陈吉象.代数拓扑基础讲义[M].北京:高等教育出版社,1987. [9] ANTONELLI F,BATRUCCI E,MANCINO M E.A comparison result for BFSDE’s and applications to decisions theory [J].Math Methods Opwer Res,2001,54:407423. [10] CRANDALL M G,ISHII H,LIONS P L.User’s guide to viscosity solutions of second order partial differential equations [J].Bull Amer Math Soc (N.S.),1992,27(1):167. [11] 詹华税.关于一类拟线性退化抛物方程[J].数学年刊,2006,27(6):731740. [12] ZHAN H S,ZHAO J N.Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations in multispace variables[J].Chinese J of Contem Math,2006,26:303312. [13] 詹华税,赵俊宁.二阶拟线性退化抛物方程Cauchy问题解的稳定性[J].数学学报,2007,50(3):615628. [14] WU Z Q,ZHAO J N,LI H L,et al.Nonlinear diffusion equations[M].Singapore:Word Scientific Publishing,2001. [15] ZHAN H S.The stability of an equation from mathematics finance without the boundary value condition[J].Boundary Value Problems,2019,95:117. [16] CITTI G,PASCUCCI A,POLIDORO S.Regularity properties of viscosity solutions of a nonHormander degenerate equation [J].J Math Pures Appl,2001,80:901918. [17] OLEINIK O A,SAMOKHIN V N.Mathematical models in boundary layer theorem[M].Boca Raton:Chapman and Hall/CRC,1999.

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备注/Memo

备注/Memo:
收稿日期:20201218修回日期:20210224 基金项目:福建省自然科学基金项目(2019J01858) 通信作者:许文彬,男,副教授,研究方向为微分几何与偏微分方程,Email:wbxu@jmu.edu.cn。
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