空间性

Chapter 3 discusses the algebraic and spectral properties of dual Toeplitz operators on the orthogonal complement of the Bergman space, such as boundedness, compactness, spectral properties and so on.

第三章研究了多圆盘Bergman空间的正交补空间L_a~2(D~n~⊥上对偶Toeplitz算子的代数性质，比如：有界性、紧性和谱性质等。

In this paper, some decision theorems are suggested about the matrix orthogonal problem on the subspace of the finite dimensional Euclidan subspace. In addition, some concise results are obtained by matrix representation of the orthogonal complement and injection of vectors on the subspace.

利用向量组的Gram矩阵和向量的坐标矩阵对有限维欧氏空间中子空间的正交性给出了矩阵判定条件，对子空间的正交补及向量在子空间上的内射影给出了矩阵表示，获得了一些简捷有用的结果。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

The problem is researched that under what conditions the - resolvent operator of - subdifferential mapping of a proper functional is aLipschitz continuous single-valued mapping on whole space.

利用冲一预解算子分析了有限维欧氏空间中的广义参数集值变分包含问题唯一解的灵敏性；利用预解算子分析了有限维欧氏空间中的一般参数集值变分包含问题解集的灵敏性。

First of all, retreat of glaciers and shrink of perennial snowbank induced by climate warming provide parent materials and spatial room for soil formation and development in the maritime Antarctica. Meanwhile, melt water originating from glaciers and snow-ice covers enhances temporal and spatial availability of free water, which plays all-important roles both in periglacial processes and the processes within soil profiles, thus influencing soil genesis and evolution to a great degree.

首先，南极海洋性气候区日益加速的气候变暖现象导致冰川消退、地表积雪融化，为土壤形成与分布提供了母质与空间基础；同时，气候变暖导致自由水活动在时间和空间上的加强促进了以自由水为基础的土壤过程和冰缘地貌过程，对南极海洋性气候区土壤发生、发育产生深刻影响。

Spatial query language ; topological relationship ; complex spatial feature ; completeness ; exclusiveness

空间查询语言；拓扑关系；复杂空间对象；完备性；互斥性

In 1936, J.Clarkson first introduced the concept of uniformly convex Banach spaces ,initiated from geometric structure of the unit sphere of Banach spaces to research the properties of Banach spaces, began to research convex theory of Banach spaces. The same year, J.

Clarkson首先引入了一致凸Banach空间的概念，开创了从Banach空间单位球的几何结构出发来研究Banach空间性质的方法，开始了Banach空间凸性理论的研究。

The characteristics of online trade, such as its anonymity of subject, virtuality of space, and delay of accomplishment, which greatly attack the law system when it applying in the cyberspace.

网络交易的主体匿名性、空间的虚拟性、完成的非及时性，使现有的法律体系在网络空间的适用受到了极大的冲击。

On the Hardy space and Bergman space with parameter 1, we find that the weighted composition operators are compact if and only if they are weakly compact.

对于参数为1的Hardy空间H〓和Bergman空间L〓，证明了其上定义的加权复合算子的紧性与弱紧性是等价的。

This thesis focuses on studying the matrix equa-tion problem systematically, and proposed an abstract algorithm of solving the matrixequation with constraints, and established a strict convergence theory. Using this algo-rithm, we can solve the sets of matrix equation satisfying some constraint conditions,such as symmetric, antisymmetric, centrosymmetric, centroskew symmetric, re?exive,antire?exive, bisymmetric, symmetric and antipersymmetric, symmetric orthogonalsymmetric, symmetric orthogonal antisymmetric, Hermite generalized Hamilton ma-trix;So we can solve the problem with this algorithm, if the set of constrain matrixcan make a subspace in matrix space, and this algorithm also can solve the optimalapproximation and least squares problem. So this abstract algorithm has universal andimportant practical value.

本篇硕士论文系统地研究了此类问题，并找到了求解约束矩阵问题的抽象算法，并建立严格的收敛性理论，利用这一算法可求解约束条件为对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵，对称正交对称矩阵、对称正交反对称矩阵、双中心矩阵、Hermite广义Hamilton矩阵等；可以说只要约束矩阵集合在矩阵空间中构成子空间，都可以考虑用此算法求解，而且这一算法还能把矩阵方程解及其最佳逼近，最小二乘解及其最佳逼近统一处理，因此本文算法有普适性和重要的实用价值。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。