微分差分复形及其庞加莱引理

doi:10.13371/j.cnki.chin.q.j.m.2015.01.001

数学季刊 ›› 2015, Vol. 30 ›› Issue (1): 1-11.doi: 10.13371/j.cnki.chin.q.j.m.2015.01.001

• • 下一篇

微分差分复形及其庞加莱引理

1. Institute of Contemporary Mathematics, Henan University 2. School of Mathematics and Statistics, Henan University

收稿日期:2014-09-23 出版日期:2015-03-30 发布日期:2020-11-24
作者简介:BAI Yong-qiang(1975-), male, native of Huxian, Henan, an associate professor of Henan University, Ph.D., engages in mathematical physics.
基金资助:
Supported by the NSFC(10801045)；

Differential-difference Complex and the Poincar\acute{e} Lemma

1. Institute of Contemporary Mathematics, Henan University 2. School of Mathematics and Statistics, Henan University

Received:2014-09-23 Online:2015-03-30 Published:2020-11-24
About author:BAI Yong-qiang(1975-), male, native of Huxian, Henan, an associate professor of Henan University, Ph.D., engages in mathematical physics.
Supported by:
VSupported by the NSFC(10801045)；

摘要/Abstract

摘要： Differential geometry play a fundamental role in discussing partial differential equations（PDEs） in mathematical physics. Recently discrete differential geometry is an active mathematical terrain, which aims at the development and application of discrete equivalents of the geometric notions and methods of differential geometry. In this paper, a discrete theory of exterior differential calculus and the analogue of the Poincar′e lemma for differential-difference complex are proposed. They provide an intrinsic idea for developing the theory to discuss the integrability of difference equations.

关键词: noncommutative differential calculus, differential-difference complex, exact

Abstract: Differential geometry play a fundamental role in discussing partial differential equations（PDEs） in mathematical physics. Recently discrete differential geometry is an active mathematical terrain, which aims at the development and application of discrete equivalents of the geometric notions and methods of differential geometry. In this paper, a discrete theory of exterior differential calculus and the analogue of the Poincar′e lemma for differential-difference complex are proposed. They provide an intrinsic idea for developing the theory to discuss the integrability of difference equations.

Key words: noncommutative differential calculus, differential-difference complex, exact

中图分类号:

O186.1

白永强, 阎国栋. 微分差分复形及其庞加莱引理[J]. 数学季刊, 2015, 30(1): 1-11.

BAI Yong-qiang, YAN Guo-dong. Differential-difference Complex and the Poincar\acute{e} Lemma[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(1): 1-11.

[1]	王珂, 潘盼盼. 一个一维二阶拟线性双曲组的精确边界能控性[J]. 数学季刊, 2023, 38(4): 424-440.
[2]	代兵兵, 张瑞凤. Born-Infeld理论中的多项式函数模型[J]. 数学季刊, 2022, 37(3): 221-236.
[3]	康周正. 应用（G^’/G²）-展开法求解非线性分数阶微分方程[J]. 数学季刊, 2017, 32(3): 261-270.
[4]	刘绍庆, 高国成. Wick-型KdV-Burgcrs方程的精确解[J]. 数学季刊, 2016, 31(2): 139-146.
[5]	王志成. 正合范畴中的Gorenstein性和Tate上同调[J]. 数学季刊, 2015, 30(1): 79-92.
[6]	林浩, 林澜. 图的最小控制树问题[J]. 数学季刊, 2014, 29(1): 1-8.
[7]	许丽萍. 求解非线性微分差分方程精确解的一个算法[J]. 数学季刊, 2012, 27(4): 598-605.
[8]	张颖, 李吉娜, 张江红, 宋晓倩. (2+1)维破裂孤子方程及Kadomtsev-Petviashvili方程的Stable-range解法[J]. 数学季刊, 2012, 27(2): 183-190.
[9]	王秀丽, 周茂袁, 陈志寅. 拟主k-投射半模[J]. 数学季刊, 2011, 26(2): 213-216.
[10]	周慧倩, 刘震, 李起升. 格点空间上的离散水平复形[J]. 数学季刊, 2009, 24(4): 561-567.
[11]	王秀梅, 朱跃峰. 广度kdv方程的精确解:改进的齐次平衡法[J]. 数学季刊, 2008, 23(2): 260-269.
[12]	李怡君, 刘华柯. 一类数论函数的性质(Ⅱ)[J]. 数学季刊, 2007, 22(3): 402-405.
[13]	张令元, 张金良, 王明亮. 一般变系数耗散长水波方程的精确解[J]. 数学季刊, 2006, 21(4): 522-528.
[14]	夏志. 齐次平衡法和浅水波中WBK方程的精确分析解[J]. 数学季刊, 2004, 19(3): 240-246.

微分差分复形及其庞加莱引理

Differential-difference Complex and the Poincar\acute{e} Lemma

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 14

编辑推荐

Metrics

本文评价