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MGM is introduced to solve field distributions in 3-D electron optical systems. The difference equation, the discrete form of Laplace's equation, is deduced in 3-D Cartesian coordinates. In view of the smooth effect, MGM combines Gauss-Seidel iteration with a technique known as coarse grid correction. Formulae for restriction and prolongation are deduced and expressed in terms of tensors.

将多重网格法引入电子光学系统中三维静电场的计算，对三维笛卡尔坐标系中的差分方程，采用高斯-赛德尔迭代法求解差分方程组，并结合迭代过程讨论了粗网格的误差校正技术；在不同网格层之间进行场值的限制和延拓，推导了三维静电场中的限制、延拓公式并以张量的形式表示。

Since Descarted, there has appeared in the western philosophy a new trend: to secure self - evidence in the inner consciousness and make it the " Archimedean Point" for philosophical construction.

自笛卡尔以来，西方哲学兴起了在内知觉中寻求自明性，并以内知觉的自明性为哲学建构的"阿基米德点"的思潮，胡塞尔的现象学可谓是这一思潮的集大成。

As to the complexity of lake's geometry boundary, Cartesian cut cell method based on finite volume method is adopted to solve the flow field efficiently and accurately.

针对湖泊几何边界复杂的特点，为了高效并准确地计算流场，采用了基于有限体积法的笛卡尔切割单元法。

Introduced the locally Cartesian coordinate system and discussed the inclusion of the curvature terms.

介绍局笛卡儿坐标系并讨论曲率项的内容。

At first,cartesian product provided us with a method for constructing information granularity in fuzzy relation.

首先利用笛卡尔积，构建了模糊关系下的信息粒；然后给出不同粒度下模糊粗糙算子的表示方法，进而形成一个分层递阶结构；最后考虑了对于模糊信息系统粒度粗细的选择问题，并给出一个实例，从而为粒度计算提供一个具体而实用的框架。

In this chapter, we give out the definitionsof Cartesian product, composition, union and join for two L-graphs, which aregeneralization of the corresponding operations in graph, and the necessary conditionsthat a partial L-subgraph of these operations can be obtained by the same operationfor some partial L-subgraph of the given two L-graphs are investigated.

本章定义了两个L-图的笛卡尔积运算、合成运算、并运算和联运算(它们是图中相应运算的推广)，并研究了这些运算的部分L-子图可以由这两个L-图的部分L-子图通过相应的运算生成所需要的条件。

A database engine can make very strong assumptions about first constrain ing the heavily indexed dimension tables, and then attacking the fact table all at once with the Cartesian product of the dimension table keys satisfying the user's constraints.

数据库引擎会对具有约束并大量索引的维度表做假设，然后使用满足用户条件的维度表的主键与事实表做笛卡尔积。

In spite of their Unitarian proclivities and their masks of conservative broadmindedness, they were two generations behind interpretative science: their mental processes were mediaeval, while their thinking on the ultimate data of existence and of the universe struck him as the same metaphysical method that was as young as the youngest race, as old as the cave-man, and older - the same that moved the first Pleistocene ape-man to fear the dark; that moved the first hasty Hebrew savage to incarnate Eve from Adam's rib; that moved Descartes to build an idealistic system of the universe out of the projections of his own puny ego; and that moved the famous British ecclesiastic to denounce evolution in satire so scathing as to win immediate applause and leave his name a notorious scrawl on the page of history.

同时，他也感到，他们看待生命和宇宙的终极事实的方法还是形而上学的，那种看法阻地球上最年轻的种族的看法一样幼稚；也跟穴居人的看法一样古老，甚至更古老--那看法使第一个更新世的猿人害怕黑暗；使第一个匆促的希伯来野蛮人用亚当的肋骨造成了夏娃；使笛卡尔通过反射渺小的自我建立了唯心主义的宇宙体系；使那有名的英格兰传教士用尖刻的讽刺来谴责进化论，并立即博得了喝彩，从而在历史的篇章里草草留下了一个臭名。

In the part of introduction, it presents Defoe's status in the history of English literatu...

引言部分主要介绍笛福在英国文学史上的地位、研究现状以及叙述学对叙事作品描述层次的划分的相关理论，并提出本文所要探讨的论题。

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

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。