数的几何

In this paper, mathematical analysis, linear algebra is more material as the foundation, on the basis of previous studies, will solve a number of the function extreme value methods, such as distribution method, elimination method, the discriminant method, mean inequality method, the geometric method, vector method and derivative method, and so to summarize, and on this basis is given for each method the corresponding examples to illustrate for readers to reference and understanding.

本文以数学分析、线性代数更教材为基础，在前人研究的基础上，将求解函数极值的若干方法，如配方法、消元法、判别式法、均值不等式法、几何法、向量法和导数法等等进行归纳总结，并在此基础上针对每一种方法给出相应的例子加以说明，以便读者参考和理解。

A geometric structure representation of images based on the angle between spectral coefficient vectors of Laplacian graph was proposed. Graph clustering of spectral features was also investigated.

提出一种用拉普拉斯图的谱系数夹角谱特征来描述图像几何结构的方法，同时研究了基于图的谱聚类系统。

The relations between the numbers of measured points and measuring error are found based on least-square method in calculating the geometric paramteters of circle, sphere, plane etc. Furthermore the choice of the number of measured point and their distribution have been recomended instructively.

为了减小偶然误差或消除零件表面形状误差对测量结果的影响，往往多测数点或数十点，本文推导出了使用最小二乘法计算几何参数时，如圆、球、平面等，测量点数与测量误差的关系，对测量点数及测点位置的选择提出了指导性意见。

The property of the invariant set and measures dimension of the IFS are main objects in the studying of fractal geometry.

完备度量空间上迭代函数系统的不变集性质及测度的维数是分形几何研究的主要对象。

The study of operator algebra theory began in 30s of the 20th century: With thefast development of the theory, now it has become a hot branch playing the role ofan initiator in modern mathematics. It has unexpected relations and inter infiltrationswith quantum mechanics, noncommutative geometry, linear system and control theory,number theory as well as some other important branches of mathematics.

算子代数理论产生于20世纪30年代，随着这一理论的迅速发展，它已成为现代数学的一个热门分支，它与量子力学，非交换几何，线性系统和控制理论，数论以及其它一些数学分支有着出人意料的联系和相互渗透。

The saw-toothed geometric boundary of Cartesian Grid has bad influences to the simulation convergence. However, under the circumstances that grid is smooth (i.e. without the saw-tooth boundary), the simulation converges better as the grid level increases.

卡氏网格在几何边界所形成之锯齿状边界对於模拟计算之收敛性有不良的影响，然而，在边界平滑无锯齿状的情形下，卡氏网格层数越多，程式收敛情形越佳。

Examples include a Jersey cow, a hamburger, a paper bag, geometric objects such as triangles, arrays of objects such as the dots on a domino, the drawing of a graph of a function, a Venn diagram, and so on.

例子包括泽牛，一个汉堡，一纸袋子、几何对象如三角形，数组的物体例如点多米诺、图纸的功能图，范恩图，等等。

Along with operations of the turning, sharpping, drilling, milling and grinding, some new methods, technologies and processings such as overlap workpieces, improved cutting tool formes, workpiece charmfer, adjustment of cutting parameters and others to restrain and decrease burrs in size are developed, which have noticeable theoretical significance and wide practical value in the precision cutting, FMS and automatic machining.

结合车削、刨削、钻削、铣削和磨削等加工，开发出了斜置工件法，双主偏角刀具切削法、切削用量选择法、刀具几何参数调整法、工件叠加切削法、工件终端部材料脆化法、工件终端部倒角法、挡板切削法、刀具结构改进法和切削方式选择法等十数种抑制或减小切削毛刺的技术、工艺和方法，在精密加工、柔性制造系统和其它自动化加工中有较大的实际应用价值。

Geometric continuity is less strict than mathematical continuity. G0 and C0 are equivalent, that is, the segments are positionally continuous. G1 implies that the tangent vectors are equal in direction, but not magnitude. G2 implies the curvature is the same, but the second derivatives are not.

几何连续性没有数学连续性严格。G0 和 C0 的意思相同，即段在位置上连续。G1 意味着切向矢量的方向相同，但模量不同。G2 意味着曲率相同，但二阶导数不同。

Geometric continuity is less strict than mathematical continuity. G0 and C0 are equialent, that is, the segments are positionally continuous. G1 implies that the tangent ectors are equal in direction, but not magnitude. G2 implies the curature is the same, but the second deriaties are not.

几何连续性没有数学连续性严格。G0 和 C0 的意思相同，即段在位置上连续。G1 意味着切向矢量的方向相同，但模量不同。G2 意味着曲率相同，但二阶导数不同。

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。