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A number of properties of countable topological space were given systematically, such as its countability, separability, compactness and connectedness, including their proofs on the basis of the nature of topological space, real number space and corresponding theorems.

摘要在可数补拓扑空间的拓扑性质的研究基础上，系统的给出了可数补拓扑空间的可数性，分离性，紧致性，连通性等性质，并给予证明。

In the thesis, the author firstly clears up some basic theories of wavelet analysis, revises some formulae and proves and deduces some theorems and formulae in detail and gives a counter example and paradox.

本文首先对小波分析的理论部分进行整理，对部分公式进行修正，同时给出了部分定理和公式详细的推导和证明，并且给出无穷区间积分的一个反例和悖论。

Physics concepts, theorems as well as principles are primary content of physics learning, those knowledge take on the forms by proposition . In chapter 3, the study revealed that physics proposition are mainly obtained by reasoning (inductive reasoning such as tallying method, differentiation method and covariant method, deductive reasoning such as negative expression of hypothetical inference, affirmative expression of hypothetical inference ).Then by the means of experiment, the different condition needed when applying those reasoning was explored.

由于定义性概念、定理和定律等命题知识是物理教学的主要内容，所以在第三章中首先通过研究，表明物理命题主要是运用推理策略获得的(归纳推理策略中的求同策略、差异策略和共变策略，演绎推理策略)；然后通过实验等方法研究使用策略需要的条件；最后依据前面的研究提出适合物理命题学习的任务分析方法。

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。

There are fourteen chapters, including introduction, plane stress and plane strain, two-dimensional problems in rectangular coordinates, two-dimensional problems in polar coordinates, photoelastic and moire experimental methods, two-dimensional problems in curvilinear coordinates, analysis of stress and strain in three dimensions, general theorems, torsion, bending of bars, axisymmetric stress and deformation in a solid of revolution, thermal stress, the propagation of waves in elastic solid media, at last there is an appendix on the application of finite-difference equations in elasticity.

全书共十四章，包括绪论、平面应力和平面应变、直角坐标中的二维问题、极坐标中的二维问题、光弹性与云纹实验方法、曲线坐标中的二维问题、三维应力和应变问题、一般定理、简单的三维弹性问题、扭转、杆的弯曲、回转体中的轴对称应力和变形、热应力、弹性固体介质中波的传播，最后有一附录，讲述差分方程在弹性理论中的应用。

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。

However ,the reader should realize that all properties of real numbers that are to be accepted as theorems must be deducible froom the axioms without any reference to geometry.

然而，读者应该认识到，拟被采用作为定理的所有关于实数的性质都必须不借助于几何就能从公理推出。

The definitions of local basis, dense set, character and density on continuous Domains are given first, and then some characteristic theorems are obtained.

从 2 0世纪 70年代D 。S 。Scott的开创性工作以来，Domain理论一直受到计算机科学和数学领域诸多学者的关注。

In this paper, we mainly disscuss derivable mappings at zero point, Jordan derivations and 2-local derivations on some operator algebras. The details as following:In chapter 1, some notations, definitions are introduced and some theorems are given.

本文主要对几类算子代数上的在零点可导映射和Jordan导子以及2-局部导子进行了研究，具体内容如下：第一章主要介绍了本文中要用到的一些符号，定义以及本文要用到的一些已知结论和定理。

The paper gives several theorems for derivate of the function with finite limit at the infinite point and its strict proof.

给出了在无穷远处具有有穷极限的函数的有关导数的几个定理及其严格证明。

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