定理

And to prove several complete theorems in the two-dimensional space with the complete covering theorem.

利用完全覆盖定理证明二维空间的几个完备性定理。

Part four will prove the following 4 theorems : theorem 1 :the curvature and torsion of the locus of foot point of the perpendicular line between the origin and the tangent line of the cylindrical spiral remains to be function t , but not trigonometric function t .

第四部分证明四个定理分别为定理1 由坐标系原点至圆柱螺线的切线所引垂线的垂足的轨迹曲率和挠率仍为t的函数，但不是t的三角函数。

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

Aiming at bottom roof caving and support impact problems induced with abrupt large scale caving upper roof in face 21303 of Daliuta mine, this paper put forward the motion parameter at roof caving and calculation formula of roof shear breaking force with the help of theorem of momentum, theorem of moment of momentum and D' Alembert principle. Roof caving process was simulated by Ansys Ls-DYNA program, and maxim impact force was got. The theoretical research outcomes in the paper were applied in face 21303 of Daliuta mine, and were accordant with actual observing status of roof caving process.

针对神东煤炭公司大柳塔煤矿活井21303综采工作面，上层采空区顶板突然大规模垮落对下层顶板及支架的突然冲击问题，文章采用动量定理、动量矩定理、达朗伯原理推出了顶板垮落瞬间的运动量及顶板切顶垮落所需要的剪力值计算公式，用ANSYS LS-DYNA程序对顶板垮落过程进行了数值计算，得到了最大冲击力，在大柳塔煤矿活井21303综采工作面对顶板垮落特征进行了实际观测和理论成果验证。

A necessary and sufficient exponential stability theorem with respect to a constant decay degree for general nonlinear dynamical systems is presented.

首先给出了一般非线性动态系统的关于常衰减度的指数稳定性充分必要定理，接着探讨了新型指数稳定性定理在线性系统稳定性分析中的应用。

This paper presents another direction of generalization that if S is a minimal vertex cut of G and G-S has at least |S| components, then G is decomposable by S. Some applications of this theorem are also discussed.

本文首先给出基本分解定理的另外一个推广：如果S是G的一个极小点割集且G-S含有至少|S|个分支，则G经由S是可分解的；其次，给出了这个新推广定理的一些应用。

Properties of cut sets, decomposition theorem, representation theorem of intuitionistic fuzzy sets are discussed.

在此基础上，给出了直觉模糊集的分解定理和表现定理。

This theory can also have relativistic kinematics. The CPT theorem and cluster decomposition are still hold for free fields.

虽然可以证明这一理论满足CPT定理以及团簇分解定理等相对论性理论的要求，但仍然存在两个关键性问题。

In this paper a modified centroid coincidence theorem and a motion parameter decomposition theorem are introduced,which degenerate it into a pure rotation problem with only 3 degrees of freedom.

最优运动估计本质上是6自由度的非线性问题，本文提出推广的质心重合定理和运动参数分解定理，将其简化成3自由度的纯旋转问题。

Accordingly,they can result in the celebrated Jordan theorem and the third decomposition theorem of space directly and, moreover,they can give a new deep insight into the exquisite and subtle structure of the Jordan ...

因而，它们能够直接导致著名的Jordan定理及空间的第三分解定理，且能给出对Jordan形精致微妙结构的新的深刻洞察。后者表明，复线性变换的Jordan标准形是一种在双重任意选择下具有不变性的结构。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。