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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
complex Euclidean space 复欧几里得空间
The names are lended from that of the Euclidean space. 借助这些几何工具对布尔函数与方程式论作了进一步探讨。
Let M be a closed m-dimensional submanifold in the Euclidean space (or sphere Sm+p). 设M是欧几里德空间E~(m+p)或球S~(m+p)中的m维封闭子流形,T_(?)
Standard stochastic gradient algorithm of blind source separation is only adapted to Euclidean space. 盲源分离的常规随机梯度算法只适用于欧氏空间,对于更一般的黎曼空间则必须采用自然梯度算法。
The specular reflection is a very important linear transformation in Euclidean space, and it has a special geometrical explanation in geometrical space. 摘要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。
The above formulae may be applied to the study of the inversion of hypersur-faces in the Euclidean space of N dimensions. 应用上述公式讨论n维欧氏空间的反图法。
The ideal element is a bridge that Euclidean space geometry transits to projection geometry, a cornerstone in project geometry. 摘要理想元素是欧氏几何过渡到射影几何的桥梁，是射影几何的基石。
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.
In this paper the authors generalize 1-independentvariable the integral inequalities by Gronwall and establish the integral inequalities in the n-dimensional Euclidean space R~n. 将一维函数的Gronwall不等式推广到了n维欧几里得空间.
In this paper, we discuss some properties of self-conjugate operator on Euclidean space Rsn and geometry background of generalized real symmtric matrices. 本文探讨了R_s~n上的自共轭变换的性质与广义实对称矩阵的几何背景。
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。
These observations allow one to formalize the definition of reflection: a reflection is an involutive isometry of an Euclidean space whose set of fixed points is an affine subspace of codimension 1. 这些观察允许我们形式化反射的定义: 反射是欧几里得空间的对合等距同构，它的不动点集合是余维度为 1 的仿射子空间。
This thesis investigates seveval problems about discrete fractal indices and their intrinsic relationships in Euclidean lattice and Euclidean space, and some problems in local bifurcation problems of one state variable with Z2 - symmetry. 本文研究欧几里得格和欧几里得空间中有关离散分形指标及其内蕴关系，和Z_2对称分岔理论中的若干问题。
In this paper, the authors show the method for calculating the volume of subregion in Euclidean space, and get calculation formulation for subregion in Euclidean space such as hyper-ellipsoid, simplex of n-dimension and Euclidean polyhedron. 提供了欧氏空间Rn中一些较特殊区域的体积求法,并相应地得到了欧氏空间Rn中椭圆超球体,n维单形,以及n+1面体的体积计算公式。
Instead of directly tackling this tricky problem, this paper converts OTS equivalently into an optimization problem in the Euclidean space, which can be solved by any standard nonlinear programming techniques adopted by OPF (optimal power flow). 将带暂态稳定约束的潮流优化问题等价转换为欧几里德空间的优化问题,然后采用最优潮流(OPF)中常用的标准非线性规划法来解决此问题。经过转换后的OTS,在形式上和OPF有相同的变量,这样即使对于一个存在众多暂态稳定约束和多个扰动的大型电力系统,也变得容易求解。
Aiming at the drawback of this method in dealing with similar targets, this paper looked the multi-evidence set as a multi-evidence space and used Euclidean space distance to improve the algorithm of set-pairs proximity. 文章针对该方法在处理相似目标识别时贴近度相近的缺陷，将多个证据组成的证据集合看作是由多个证据组成的证据空间并在欧氏空间权距离的基础上改进了集对贴近度算法。
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。
Thus it is explained that a vector furc-tion space can be proiected into three uncrossed subspaces not only in Euclidean space but alsoin the subspace of vector wave functipn space. 由此说明了一个矢量函数空间不仅可以通过它在欧氏空间中的射影分解为三个不相交的子空间,同样可以通过它在矢量波函数系上的射影分解为三个不相交的子空间。
Mother and baby interact in a very complex way. 母亲与婴儿以非常复杂的方式相互影响。