几何学上

Geometry of classical groups over finite fields and applications Wan Zhexian, 1997

有限域上典型群的几何学及其应用

They include the fundamental concepts of jet bundle geometry needed in describing time-dependent mechanical systems, decomposition of jet bundles into a direct sum according to the constraints, horizontal distributions on constraint mainifolds, the global formulation of D'Alembert-Lagrange's equations and Chaplygin's equations, and nonholonomic mechanics on a Riemann-Cartan manifold. Meanwhile, the geometric significance of Chetaev's conditions and $\rd$-$\delta$ commutation relation are discussed in depth.

本文主要综述非完整约束系统几何动力学的外附型和内禀型Lagrange理论，包括非定常力学系统所需要的射丛几何学的基本概念、射丛按约束的直和分解、约束流形上的水平分布、 D'Alembert-Lagrange方程与Chaplygin方程的整体描述、以及Riemann-Cartan流形上的非完整力学，文中对Chetaev条件和d-δ交换关系的几何意义作了深入讨论。

Geometry of Manifolds analyzes topics such as the differentiable manifolds and vector fields and forms.

流形上的几何学讨论的问题是微分流形，向量场和微分形式。

From these studies I proceeded to elementary geometry, beyond which I never advanced, although I persistently attempted, in some degree, to overcome my weakness of memory by dint of retracing my steps hundreds of times, and by incessantly going over the same ground.

此后，我接着学习基础几何学，这门学科，尽管我尝试过反复地学了N多遍，并且不断从头看起，在一定程度上试图以这种努力，来克服我记忆力低下的问题，但是没有获得进展。

In field Euclidean geometry , the problem of expressing orthogonal transformation as symmetrical product is one of the basic problems in geometry .

域上欧氏几何中，把正交变换表为对称之积的问题，是几何学中基本问题之一。

Rather, we remain within the space, and carry out experiments to see whether the common laws of Euclidean geometry hold or not.

在一定程度上，我们是在空间内部，做一些实验来验证普通的欧几里德几何学是否适用。

Remarkable is that this more than a century ago almost directly with the achievement of modern mathematics, the following methods, the general flow is concepts, algebra to geometry closely linked, he and his successors -- Beiertelami, Christopher Tuofeier, Lee Puxici developed differential Zhang volume analysis has gradually become more research on the flow geometry and analysis of an important tool.

令人赞叹的是，这一个多世纪前的成就几乎直接同现代数学中的拓扑方法、一般流形概念、代数几何学等紧密相连，他和他的接班人——贝尔特拉米、克里斯托费尔、李普希茨所发展的微分张量分析逐渐成为研究流形上几何结构和分析的一个重要工具。

Ah specifically, the angle of the sphere and the relationship side of spherical geometry, spherical trigonometry is a part, mainly in the processing, discovery and interpretation of polygons on the spherical surface contact angle and the edge and relevance.

具体一点啊研究球面上的角与边的关系球面三角学是球面几何学的一部分，主要在处理、发现和解释多边形在球面上的角与边的联系和关联。

Research on cone/bit speed ratio simulation model of tri-cone bit s;2. In this paper, the kinematics simulation model of tri-cone bit s was established according to the roller cone bit geometry and kinematics.

根据钻头几何学和运动学建立起了随钻运动的三牙轮钻头的计算机运动学仿真模型，该仿真模型既表示出了钻头上各牙齿的形状、大小和在钻头上的分布情况，又可真实反映钻头钻进过程中各牙齿的瞬时位置和相互关系。

"As mentioned by Bak in this debate, the SOC hypothesis has been suggested, on the one hand, on the basis of the observation of power law distributions, such as the Gutenberg-Richter law for earthquakes and the fault length distribution, and of the fractal geometry of sets of earthquake epicenters and of fault patterns, and on the other hand on the study of highly simplified models with somewhat similar scale-invariant properties."

&如同Bak在这场辩论中已提到的那样，一方面，在对动力法则分布进行观测的基础上，如用于地震和断层长度分布的Gutenberg-Richter定律，以及对震中的破裂几何学内容的观测和对断层图案的观测，以及另一方面对带有某种程度类似标度不变性质高度简单的模型的观测基础上，提出了SOC〔'自组成危险性'〕假说。&

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。