向量场的向量量

In Riemannian manifolds, one studies Riemannian metric, covariant derivative, Riemannian connection, basic properties of the Riemann curvature tensor, curvature forms etc.

黎曼流形部分主要涉及黎曼度量，黎曼流形的定义，切向量场的协变微分，黎曼联络，黎曼几何的基本定理，曲率张量，曲率形式等概念和理论。

In exterior differentiation, one studies tensors, exterior algebra, tangent bundle, tangent vector fields, one-parameter groups action on a manifold, Frobenius's theorem, tensors fields, exterior differential form, integration on manifolds, Stokes's theorem etc.

外微分部分主要涉及外代数、切丛，光滑切向量场，单参数变换群，光滑张量场，外微分形式，Frobenius定理，外微分形式的积分，Stokes定理及其应用等。

The transient air gap magnetic fields under different conditions are also calculated and analyzed. The novel finite element method directly using magnetic induction as unknown variable has many advantage. It is analyzed theoretically in detail. Nonlinear eddy current field equations and finite element equations using magnetic induction as unknown variable are developed.

直线电机的磁场是一非均匀、非线性的涡流场，文中对非均匀磁场及材料的非线性进行了分析，提出了相应的解决办法，采用以向量磁位为求解量的传统有限元法，对不同合闸角下筒式复合次级圆筒型直线感应电机的瞬态特性进行了计算与试验分析，对不同条件下瞬态气隙磁场进行了研究。

Yano about the harmonic and Killing vector fields in Compact orientable Riemannian spaces with boundary by means of Stokes' and Green's theorem.

Yano 关于具有边界的可定向黎曼流形上的调和和Killing向量场的结果加以推广，显然这个方法也可应用到调和张量场和Killing张量场的情形，这将在另文讨论。

First, we extract the boundaries between two different materials by weighting with gray-level gradient,and only voxels on these boundaries participate in the generation of each image, so it drastically reduces the rendering time. Second. We think the voxels on boundaries as the mixture of different materials,so in every voxel there is a surface. We use the oriented cube-interpolation technique to get the intersection point of viewing orientation and the surface in the voxel, then compute the surface normal of the intersection point. We use the normal to shade the voxel in order to improve the image quality.

首先，采用灰度梯度加权提取出三维数据场中不同物质间的边界，根据显示的需要只对这些边界上的体元赋予相应的阻光度并进行光亮度合成计算，因而可大大减少计算量，提高显示的速度；将边界上的体元作为不同物质的混合体，采用与方向有关的三线性插值来计算视线方向与体素内等值面的交点，根据交点的法向量进行光照效应计算以提高显示图像的质量；最后用投影成像法显示最终的图像。

The topology analysis of vector field around "a singular point" is refered in the study of the topology of three-dimensional symmetric tensor field around a simple degenerated point, which can be classified into three types of hyperstreamline sectors:"hyperbolic sector","parabolic sector" and "elliptic sector".

本文参考矢量场中"奇点"附近的矢量轨迹分布结构，研究了张量场中"退化点"附近的特征向量分布形态。确定了"退化点"附近"超流线体"轨迹的三种形态。"抛物扇区"、"双曲扇区"、"椭圆扇区"及其这些扇区的边界。

Therefore, topology of second-order tensor field around a degenerate point is determined and theoritic foundation of visualization of the second-order tensor field is built.

从而，定性地确定了简单"退化点"附近特征向量轨迹的拓扑结构。为进一步进行二阶张量场的可视化奠定了理论基础。

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。