抽象空间

Vector spaces are a central theme in modern mathematics ; thus, linear algebra is widely used in both abstract algebra and functional analysis .

向量空间的一个中心主题在现代数学，因此，线性代数被广泛使用在抽象代数和功能分析。

Three dimensions are weakened in the work by the method of semi abstract expressionism.

作品减弱三度空间等特征，用半抽象手法，抽离了真实形象中具体细节，强化外形和构成元素。

This kind of works are vested with strong expression_r_rism on the part of image-making and painting skills, and also they are constitutionally narrative by pictorial space and figure relation; other group is that abstract paintings made of oil, pastel, and water color, which should be taken as another world created by Huan Xun artistically, a world of more freedom, relaxation, and openness.

这类作品在形象的塑造和绘画的手段上，带有很强的表现性，同时具有由画面空间和人物关系构成的故事性；另一类是完全抽象的作品，分别用油彩、油画棒和水质颜料画成，这部分作品可以说是幻循在艺术创造上的另一个世界，也是一个极为自由、放松、开阔的世界。

Although the resulting mathematics is rather abstract, it nevertheless captures the essential nature of the Euclidean spaces we are all familiar with.

尽管结果的数学非常抽象，它却捕获了我们熟悉的欧几里德空间的根本本质。

The success of Indian mathematics was mainly due to the fact that Indians had a clear conception of the abstract number as distinct from the numerical quantity of objects or spatial extension.

印度数学的成功主要归功于印度人对物体的数量或空间的扩展抽象成清晰化的数字的观念。

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。

The social level structure is defined from its basic conception, in-depth meaning and characteristics. The term refers to a functional being and social reality, a unity of physical space and value space as well as connectional and theoretical existence. Viewed from the perspective of political philosophy, the social level structure is a political sovereignty grading or ladder in a state who values the supremacy of sovereignty, penetrating into economic, cultural and social fields, universally forming social relationship. Based on general social structure, social system and political sovereignty, the social level structure is an abstractly summary of social hierarchy which is neither a copy of political structure nor simply addition of economic, cultural and social structure. The social level structure is long hidden but universally existing, deeply affecting and shaping social system, people's life and thinking. Based on the above, the thesis probes the social foundation, evolutional law, fundamental quality, running mechanism, historical function, current significant and the reform necessity.

从社会层级结构概念的基本规定、深层意蕴和性状表现三个方面界定社会层级结构概念，认为社会层级结构既是一种实体性存在和社会现实，也是一种观念性存在和理论构造，是物理空间和意义空间的统一；从政治哲学视野，社会层级结构是在政治国家内部按照权力至上的方式形成的权力级别或权力阶梯，并渗透到经济、文化、社会领域，形成具有普遍性的社会关系体系；它以总体社会结构为依托，以社会制度为外化，以政治权力为中轴；它既不是政治结构的翻版，不是社会阶层结构的别名，也不是经济、文化、社会结构的简单叠加，而是对它们层级性的一种抽象和概括；这种结构长期隐而不显，但却无处不在、无时不有，深深地影响和牢牢地控制着社会制度、人的生活和人的思维方式。

By analyzing the cognitive motivation of prepositional spatial metaphor, we can safely conclude that prepositions have produced numerous different meanings and developed colorful metaphorical connotations, and the polysemantic network is thus formed.

空间隐喻是有理据的，而不是任意和约定俗成的，介词在其空间概念的基础上通过从具体到抽象的隐喻投射产生了大量不同的义项，发展了丰富多彩的隐喻含义，并最终形成了介词的多义性网络。

By analyzing the cognitive motivation of prepositional spatial metaphor, we can safely conclude that prepositions have produced numerous different meanings and developed colorful metaphorical connotations, and the polysemantic network is thus formed.

空间隐喻是有理据的，而不是任意和约定俗成的，介词在其空间概念的基础上通过从具体到抽象的隐喻投射产生了大量不同的义项，发展了丰富多彩的隐喻含义，并最终形成了介词的多义性网络。介词at-on-in构成了一个&点面体三位一体&的微观系统，它们 www。

With the abstract theory for parabolic differential equations in Banach spaces, the free boundary problem is locally well-posed in little Hlder spaces is proved.

利用Banach空间中抛物方程的抽象理论证明此问题在little Hlder空间是局部适定的。

If you are unfortunate enough to the lovelorn, please tell me, I will help you out, really, please contact me!

如果你不幸失恋了，请告诉我，我会帮助你摆脱困境，真的，请联系我啦！

China's plan to cut energy intensity by 20 percent and pollutant discharges by 10 percent between 2006 and 2010 is a case in point.

中国计划在2006年到2010间降低20%的能源强度和减少10%的主要污染物排放，就是一个这样的例子。