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A problem of cable force optimization of cable-stayed bridge is equated as a nonlinear implicit optimization model. In the mathematical model, the object function is minimizing summation of bending strain energy and axial strain energy, and the constrain conditions are nonlinear and related to reasonable finished dead state. The optimization model is solved by projection gradient method, fully considering all kinds geometric nonlinearity.

把超千米级斜拉桥的索力优化问题归结为非线性隐式优化的数学模型，以系统最小弯压应变能为目标，根据合理成桥状态指定各种非线性约束条件，利用投影梯度法进行优化问题的求解，求解过程中充分考虑了各种几何非线性的影响。

In this paper, We only analyse the projective transformation in3- Dimension space, explain the geometric significance of its column and row's correlation coefficient and give the method of changing the non-full rank projective transformation of3- Dimension to2- Dimension.

对三维空间中的射影变换加以分析，说明其行、相关系数的几何意义及将三维非满秩射影变换改为二维满秩射影变换的处理方法进行探索，这对计算机辅助设计中的图形处理和建立图形数据库是有利的。

Because projective invariance between 3D object and its 2D image could overcome the problem caused by viewpoint, calibration and feature correspondence effectively, it has been attracting more and more attention and research efforts over the last 20 years. For more comprehension to this field, firstly, the main research contents of the invariance-based 3D object recognition is discussed, including geometry frames and their invariance, as well as the way to apply the geometric invariance.

为使人们了解该领域的研究现状，以对该领域的研究有所启发，首先讨论了基于几何不变性的3D物体识别方法的研究内容，包括研究的几何框架和其不变性以及几何不变性在3D物体识别中的主要应用；其次，总结性地评述了该领域的研究现状；最后，提出了研究的发展方向。

The line pencil equation for geometric elements in En is studied. From the direction number in the equation, the relative position between the elements and the projective space anp that between any two elements are analyzed.

本文系统地研究了E~n中几何元素的线束方程，由方程中的方向数分析几何元素对投影空间的相对位置和几何元素间的相对位置，规律性强。

Several essential problems about the mechanism, such as the relations between cam angles and geometric parameters, the allowable values of some angular parameters, the equations of cam prole and the return motion of rocker AC, are solved.

关于这种机构的几个基本问题得到解决，如凸轮角度和几何参数的关系，一些角参数的允许值，凸轮的轮廓线和摇杆的回行运动的方程。

So, based on previous experience with geometric dissection problems, I have decided to do a research on regular triangle dissection extending from Pythagorean theorem.

因此，承袭著之前处理几何问题的经验，决定挑战毕氏定理演译的正三角形分割研究。

The circle is today the geometric matrix that answers more than others to the need of who loves pure and regular shapes not exclusively quadrangular shapes.

圆形石今天几何形体中可以满足那些喜欢纯粹和规则外形而不是四边形的人的口味。

The concept of exponential transformations of rectangular Cartesiancoordinates is introduced, showing that a plane curve is more frequently expressed by a unionof four or fewer quadrantal equations defined uniquely in the respective quadrants whichthe curve covers and are therefore quadrant invariant, then the Fermat curve s with someof their geometric properties are formulated.

引入直角笛卡儿坐标幂变换的概念，说明一平面曲线是较经常地用4个或更少的象限方程的并集来表示的；这些象限方程是在曲线所在的各个象限中惟一定义的，因而是象限不变的。然后列出费马曲线的方程，并简述了费马曲线的一些几何性质

Of or relating to geometric surfaces that are defined by quadratic equations.

二次曲面的由二次方程式所定义的几何平面的，或与其有关的

Classifying and computing a QSIC (quadric surface intersection curve) are important operations in computing the boundary representation of a solid in solid modeling system, and also are applied in other geometric processing.

对两二次曲面交线(QSIC-Quadric SurfaceIntersection Curve)的拓扑分类和计算是立体造型系统计算三维物体边界表示的一个非常重要的操作，同时还可应用在其它的几何处理算法中。

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。