空间

We found , however, that the concept of hyper-operator itself is very important for quantum physics , group representation and Lie algebras.

本文内容的具体安排如下：第一章介绍了线性空间，赋范线性空间，Banach 空间，内积空间和Hilbert 空间的概念。

An iterative factorization method based on linear subspace for projective reconstruction is presented in the paper. It relies on the facts that the rows in the matrix including all the image points span the same linear subspace as the rows in the matrix including space points and the fact that any basis of the subspace can be regarded as projective reconstruction. The projective reconstruction and the depth factors are obtained based on linear iteration.

摘要该文提出了一种基于子空间线性迭代的射影重建方法，该方法利用所有的图像序列构成的行向量生成的线性子空间之和与射影重建结构点构成的行向量生成的子空间是同一线性子空间及在该子空间中任何一个基底都可以作为射影重建的特性，线性迭代地求取射影重建及图像深度因子。

The method relies on the facts that the row vectors composed of all the image points span, the same linear subspace as the row vectors composed of 3D space points span and that a basis of the subspace can consist of two row vectors composed of all the image points and one row vector in 3D space that is orthogonal to the former. The row vector can be determined, and the 3D reconstruction is accomplished. The novelty lies in the fact that the method can treat all the image points uniformly.

利用所有图像序列构成的行向量生成的子空间之和与三维空间点构成的行向量生成的子空间是同一线性子空间、同时由所有图像点构成的2个行向量外加一个行向量就可以组成该子空间的一个基底的特性，线性地求取子空间中的行向量，最后完成三维重建。

In chapter 2, we prove that sn—first countable spaces are preserved by the finite subsequence-covering mappings.By this result, we prove that the finite subsequence-covering, quotient mappings preserve g—metrizable spaces, also prove that the finite subsequence-covering, closed mappings preserve sn—metrizable spaces, g-metrizable spaces, metrizable spaces, point-countable bases.

在第二章中，我们主要证明了有限子序列覆盖映射保持sn-第一可数空间，作为它的应用，又证明了有限子序列覆盖、商映射保持g-第一可数空间，也证明了有限子序列覆盖闭映射保持sn-度量空间，g-度量空间，度量空间，点可数基。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

And also,the Holder"s, Minkowski"s,Young-type inequalities and four interpolation theorems,which are hold on the Lebesgue spaces,are established on the homogeneous Morrey-Herz spaces MK_~ and the weak homogeneous Morrey-Herz spaces WMK_~.These results on the cor-responding homogeneous Herz space K_q~and the weak homogeneous Herz spaces WK_q~are also new.

同时把Lebesgue空间上成立的Holder、Minkowski、Young不等式以及四个插值定理推广到了齐次Morrey-Herz空间及弱Morrey-Herz空间WMK_~上，而这些结果在相应的齐次Herz空间K_q~和弱齐次Herz空间WK_q~上也是新的。

The nonstandard anslysis theory is used in the κ-saturated nonstandard model, the definition of the quasi-near-standard points in a metric space is given and it is proved that a point in nonstandard metric space is quasi-near-standard point if and only if its monad contained in every *-open ball of some standard point.

在κ-饱和的非标准模型下，采用非标准分析方法，提出了度量空间中的拟近标准点的定义，得到了非标准度量空间中的点是拟近标准点的充要条件是它属于某一个标准点的每一个*-开球，证明了度量空间的非标准完备化恰是该空间的非标准扩张中拟近标准点集的商空间。

Since convergencehas a close relationship with normed space itself, the definition which is normedspace (Y_1) stronger than normed space (Y_2), and normed space is presented innormed space for further research.

由于收敛性与赋范线性空间Y本身关系密切，文中引入了赋范线性空间Y_1强于赋范线性空间Y_2的定义，并将赋范线性空间Y具体到赋范线性空间l_p中进行研究。

The local decision space partitioning is given in the sense of maximum Bhattacharyya distance criterion. The optimality and the non-triviality of the partitioning scheme are proved. The reasonability of using Bhattacharyya distance as partitioning criterion is analyzed. The simulation results show that the partitioning method based on Bhattacharyya distance criterion is superior to that based on J-diversity criterion.

研究了基于 Bhattacharyya 距离准则的决策空间优化划分问题，求出了在 Bhattacharyya 距离最大意义下的决策空间划分方法，证明了这种决策空间划分方法的最优性和非退化性，分析了选择 Bhattacharyya 距离作为划分准则的合理性，并进行了计算机仿真比较，结果表明基于 Bhattacharyya 距离准则的决策空间优化划分优于基于最大 J-散度准则的决策空间划分。

Several strategies including strategy of difference space, strategy of group which is discussed in detail, strategy of backdating, strategy of convergence, are used synthetically to implement the packing algorithm and to realize the continuous orthogonal decomposition of the packing space.

其后论述了实现算法的各种策略，包括差空间(第一差空间、第二差空间)策略、群组策略、回溯策略、收敛空间策略等，并详细阐述了群组的定义、方式、约束及算法等；各种布局策略的综合运用，使布局能按空间正交分解的方式持续进行。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了