In this thesis, by the existence of the nonholonomic connection of nonintegral distribution, we prove the existence and uniqueness of the sub-Riemannian connection and extend some results of classical transform to notions of sub-Riemannian manifolds.
首先,利用给定流形的向量丛上联络的存在性给出流形上的不可积分布上非完整联络的存在性证明,进而证明了次黎曼联络的存在唯一性,并以此为出发点研究了次黎曼流形中仿射变换、等距变换、共形变换和射影变换下的一些不变性质,给出了相应变换下的一些不变量。
Similarities and Differences between Newton Integral and Riemann Integral;
牛顿积分与黎曼积分之异同
A rigorous coupled wave theory for the Bragg diffraction of a Gaussian beam in the uniaxial crystal is derived and a group of rigorous coupled wave equations and diffraction efficiency formula are obtained in terms of the proper coordinate transformation and Riemann method.
利用适当的坐标变换和黎曼方法建立了高斯光束在单轴晶体中布拉格衍射的严格的耦合波理论 ,获得了一组严格的耦合波方程和衍射效率计算公式 ,讨论了衍射效率随折射率调制量的关系以及波长选择性和角度选择性 ,同时分析了衍射效率对再现光宽度的要求。
The Discrete Definition of "ε-N" of Riemann Integral;
黎曼积分的离散型“ε-N”定义
Advantage of Lebesgue over Riemann integral;
勒贝格积分相对于黎曼积分的优越性
Teaching of Mathematics Short but Reasonable Reasoning for the Riemann Integral;
关于黎曼积分定义教学的新探索