查询词典 Riemannian

The thesis consists of three parts:The first part deals with optimal Sobolev inequalities on compact Riemannian manifolds;the second part is concerned with some variational models in image processing,and we propose variational models as well as experimental results for detection,denoising and mosaicking;the last part deals with inverse differential geometry in 3-D non-local image restoration.

本论文由三个部分组成。第一部分是流形上的非线性分析：第二部分是基于能量极小化方法的图像处理；第三部分是三维非局部图像重建及逆向微分几何。在第一部分中，我们研究了紧致流形上的最优Sobolev不等式，证明了某些不等式虽然就整体而言是不成立的，但总是局部成立的。

The author used this intrinsic connection to give the notion of horizontal mean curvatures of hypersurfaces in sub-Riemannian manifolds.

作者应用这个内在的联络给出了超曲面的水平平均曲率的几何定义。

Gm,np,q-systems and integrable immersions of pseduo-Riemannian space forms

中文题名 Gm，np，q系统与到伪黎曼空间形式的可积浸入

In Chapters3and4, we study the relation between the G〓-systems and integrable immersions of pseduo-Riemannian space forms, where G〓=O /O ×O .

在第三、四章中，利用G〓系统，讨论了与之相关的伪黎曼空间形式中的可积性浸入，其中G〓=O/O×O。

The problem of sub-Riemannian geodesics is a Lagrange problem with constraint. How to describe the constraint condition "γ'∈ D, a. e." is a difficult problem.

次黎曼测地线问题是变分学中的一个有约束的Lagrange问题，但在变分的过程中有个难点―如何推出约束条件&γ'∈D，在上几乎处处成立&的解析式。

It included topics such as Lebesgue integration , matrix theory , numerical analysis , Riemannian geometry , of which I knew nothing...

与此同时，在纯数学的日常应用Cramer的规则来解决偏微分方程导致列入标准的线性代数课程的大学。

Later, Riemann generalized Gauss's theory on surfaces to higher dimensional spaces (called "manifolds") and established Riemannian geometry which constitutes the foundation of Einstein's General Relativity theory.

Riemann将Gauss的理论推广到高维空间而创立了Riemann几何并为Einstein的广义相对论奠定了基础。

It is embodied in the three research programs of modern physics:(1) According to the program of geometrization of physics, the essence of the Curved Space in gravitational field needs to be explicated by Riemannian geometry, differential geometry, tensor analysis;(2)According to the program of quantum field theory, the generation and annihilation operator can represen...

它分别体现在现代物理学的三大研究纲领中：(1)根据物理学的几何化纲领，引力场弯曲空间的奥秘需要通过黎曼几何、微分几何与张量分析来解读；(2)根据量子场论纲领，场理论的&产生和湮灭&算符，能方便而精确地表征和重构相关的微观作用机制；&场的本体论&和&生成辩证法&同时得到体现。

In this paper the writer employs complex Riemannian Geometry and defines the absolute interval between two points as consisting of a real part and an imaginary part. Two postulates and are used: the first may be called law of gravitation and electro-magnetism; the second equation of motion.

在此文内，作者利用复变来曼几何以宇宙间两点之距离为一实数及一虚数部分相构而成，於此并用假说：一可称为吸力及电磁定律，一为物体行动定律，解释吸力及电磁力之各种现象。

DoCarmo, Riemannian Geometry.

标准的黎曼几何教材

"Yes, now you can give yourself airs," she said, you have got what you wanted.

"对了，您现在高兴了，"她说道，这是您所期待的。

Then the LORD said to me: Rebel Israel is inwardly more just than traitorous Judah.

上主于是对我说：＂失节的以色列比失信的犹大，更显得正义。