You all have a sense of what a flat space is, Euclidean space is.
大家都多少知道平面空间是什麽，就是欧几里德空间。
For example, Euclidean space is invariant under rotations and translations.
例如欧氏空间在旋转和平移下都不会改变。
In the third chapter, we discuss the annealing process on the Euclidean space.
第三章，我们考虑了欧氏空间上的退火过程。
The results showed that this method could be used to reconstruct the surgical scene in a close Euclidean space.
实验结果表明此方法可以在近似欧氏空间中从两幅图像重建外科手术场景和手术对象。
The real symmetric matrix, the diagonal matrix and the orthogonal basis of n-dimensional Euclidean space are studied.
研究实对称矩阵、对角矩阵以及欧氏空间的规范正交基。
We prefer the form (5.16.7) since it is in conformity with the definition of scalar product in a complex Euclidean space.
我们愿意用(5.16.7)这种形式，因为它和复欧几里德空间中标积之定义相谐调。
We prefer the form (5. 16. 7) since it is in conformity with the definition of scalar product in a complex Euclidean space.
我们愿意用(5.16.7)这种形式，因为它和复欧几里德空间中标积之定义相谐调。
The essential property and developmental course of Euclidean space, symplectic space and bogus symplectic space are studied.
论述欧氏空间、辛空间、伪辛空间的本质属性及演变过程 。
A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.
利用长度关系给出了欧氏空间的变换为对称变换的若干个充要条件。
A few good necessary and sufficient conditions are given by using length relation for symmetrical transformation on Euclidean space.
借助内积与长度与夹角给出了欧氏空间的变换是反对称变换的若干个充要条件。
In this paper, we make use of the properties of the umbilic to research circle Section question of quadric in 3-dimensional Euclidean space.
文章利用脐点的性质研究了二次曲面的圆截口问题，并给出了与二次曲面交线为圆的圆截口的方程的一种求法。
It has been proved that the nature of independence exists in the axiomatic system of Group, Euclidean space, distance space and topological space.
本文证明了：群、欧几里得空间、距离空间和拓扑空间的公理系统的独立性。
A few good necessary and sufficient conditions are given by using inner product and length relation for antisymmetric transformation on Euclidean space.
借助内积与长度与夹角给出了欧氏空间的变换是反对称变换的若干个充要条件。
The specular reflection is a very important linear transformation in Euclidean space, and it has a special geometrical explanation in geometrical space.
镜面反射是欧氏空间中一类很重要的线性变换，在几何空间中有着极其形象的解释。
Complex network can be tangible objects in the Euclidean space, such as electric power grids, the Internet, highways or subway systems, and the neural network.
在欧氏空间中复杂网络可以是有形物体，如电力网、互联网、高速公路或地铁系统、甚至神经网络等等。
Via an infinitesimal method, the author offers a computing formula for the moment of inertia of mass curves and mass cubes against any straight line in Euclidean space.
应用微元法给出了在三维欧氏空间中质量曲线和质量立体对任意一条直线的转动惯量的计算公式，并给出了对坐标轴的转动惯量的简化计算公式。
Necessary and sufficient conditions are given on the symmetry of points and n-1 dimensional hyperplane of function of many variables in then-dimensional Euclidean space.
在n维欧氏空间内，给出了多元函数分别关于点、n-1维超平面对称的充要条件。
In this paper, we give the sets of radii which make the measures of balls and spheres finite but not infinitesimal respectively, in a Euclidean space of infinite dimension.
本文分别给出了使在无穷维欧氏空间中球体和球面具有有限的，但又不是无穷小的测度的半径集合。
During studying the geometry of normed Spaces, a potential subject is looking for a new concept in more general Spaces to replace the concept of orthogonality in Euclidean space.
在赋范空间几何学的研究中，一个潜在的主题就是在更为一般的空间中寻找一个新的概念来替代欧式空间中的正交性。
In the classical differential geometry which deals with the theory of curves and surfaces of three dimensional Euclidean space, the most distinctive study is the Weingarten surface.
经典微分几何研究三维欧氏空间中曲线曲面理论，其最具有特色的研究是主曲率函数满足某些关系的魏因加吞曲面。
It is revealed that the paradox solution in Euclidean space is just a solution in symplectic space in the Jordan form which can easily be obtained by conventional mathematical means.
本文的工作表明，欧几里得空间下的佯谬解就是辛空间下的约当型解，而且通过标准的数学方法可以直接获得所有佯谬问题的解析解。
In this paper, we make use of the properties of the umbilic to research circle section question of quadric in 3-dimensional Euclidean space. We give the equations of these circle sections.
文章利用脐点的性质研究了二次曲面的圆截口问题，并给出了与二次曲面交线为圆的圆截口的方程的一种求法。
Based on the comparison of fractal geometry and Euclidean geometry, on the basis of geometric from fractal "similar" perspective building space forms of related problems.
本文在比较分形几何和欧氏几何的基础上，试图从分形的“自相似”角度来探究建筑空间形式的相关问题。
We established the local theories of the curves which are in the semi-Euclidean 4-space, especially, we considered some special ones of the timelike curve.
建立了R_2 ~ 4空间中曲线的局部理论，特别地，我们考虑了类时曲线中的一些特殊曲线。
We established the local theories of the curves which are in the semi-Euclidean 4-space, especially, we considered some special ones of the timelike curve.
建立了R_2 ~ 4空间中曲线的局部理论，特别地，我们考虑了类时曲线中的一些特殊曲线。
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