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Can discover immediately, do not know to be kicked to go up by the child of whose home archness on the gate a lot of small footmark, he is forced to whitewash the gate afresh, but very fast, be kicked to go up again a few new black track.

可很快地发现，大门上不知道被谁家调皮的孩子踢上去很多小脚印，他只好将大门重新粉刷一遍，可很快，又被踢上去一些新的黑脚印。

What is the area of a circle whose diameter is 4 inches?

一个直径是4英寸的园，它的面积是多少？

This is the argument of central bankers whose function is reduced to financial centre lobbyists.

这是那些职能被弱化为金融中心游说者的央行行长们的观点。

In Chapter 2, one kind of rational cubic spline interpolation with linear denominator has been proposed, whose derivatives are replaced with accurate derivative values, difference quotient and arithmetic average difference quotientrespectively.

第二章给出了一类分母为线性的有理三次插值函数，当其导数值分别取为导数的精确值，一阶差商，以及算术均差商时，便得到三种插值格式，分别为给定导数值的有理三次插值函数，基于函数值的有理三次插值函数，以及基于算数均差商的有理三次插值函数。

First the math theory of machining simulation is studied, and the set structure of NC machining simulation system whose components, including time, input, output and so on, are defined. Hereby we set up the hierarchy structure, the logical structure, the static model and the dynamic model of simulation system. The construction method of sweep entity of cutter and rotation parts is researched, and their differential geometry invariants are calculated. NC code is unscrambled, and the recursion division arithmetic of time segment is put forward, which is the driven data of the movement or rotation parts. The CLDATA should be interference-free. To examine if there is interference between cutter flank and the work piece, an arithmetic that discussed the existence of intersecting curve between them is put forward. To examine if there is interference between two turrets, an arithmetic that discussed the existence of intersection set between two polygons is put forward.

首先研究加工过程仿真的数学基础，然后定义数控加工仿真系统的集合结构及时间集、输入集、输出集等概念，建立加工仿真的层次结构和逻辑结构，阐述双刀车削仿真系统的静态模型和动态模型建立方法，分析刀具扫描体和旋转部件扫描体的建立方法及其微分几何性质；研究NC代码解读技术和双刀加工时间段递归子分划技术，为驱动各仿真单元作数据准备；通过讨论后刀面和工件表面交线的存在性判断刀具后刀面与工件间是否干涉，通过求多边形的交集判断刀架与刀架是否干涉。

In the second chapter, elementary theories and ideas of one step forming inverse approach were described and warped modification method, implemented by Cook, was introduced into one step forming simulation and based on idea of surface spreading; new quadrilateral element modification arithmetic was put forward. By spreading warped quadrilateral onto plane in local coordinate system, a plane quadrilateral element whose shape and area were equal to original warped quadrilateral element was gotten and internal force vectors of four nodes and stiffness matrix of elements were improved to increase precision of simulations on this plane element.

第二章从一步成形逆有限元法的基本理论和思想出发，将Cook基于弹性理论的四边形单元的翘曲修正算法引入基于塑性的一步成形，并且基于曲面展开的思想，本文提出一种新的四节点单元翘曲修正方案，通过把翘曲的单元展开的方法在局部参考系中得到一个与实际翘曲单元的形状与面积非常接近的平面单元，在该平面单元中进行单元刚度及内力向量的计算，进一步改善模拟结果的精度。

In an arithmetic operation,a result whose absolute value is too small to be represented within the range of the numeration system in use.

在算术运算中，运算结果的绝对值太小，以致不能在所用数制的范围内表示。

Math a progression of terms whose reciprocals form an arithmetic progression.

其倒数构成一个等差级数的级数术语。

It shows that the reservoir rock consists of fine arkose and litharenite lithic feldspar, whose elastic granule appears subangular, compositional maturity is low and textural maturity is medium; the clastic rocks had experienced a series of complex diagenesis as compaction, cementation, pressure solution and dissolution; and the sandstones are of low porosity and low permeability.

结果表明，该储集岩为细粒的长石砂岩和岩屑长石砂岩，颗粒呈次棱角状，成分成熟度普遍较低，结构成熟度中等－较好；经历了压实、胶结、压溶和溶解等一系列成岩作用；储集岩具有低孔、低渗的特点。

Furthermore, in their Remonstrance of 1610 and afterward the Arminian party, whose proponents then came to be called "Remonstrants," was unwilling to say that man is totally unable to save himself; it held rather that, while human nature has been impaired by sin, the will is still free and able to respond to the grace of God.

此外，在他们的谏的1610年和以后的arminian党的倡议者，后来被称为" remonstrants "，也不愿说，该名男子是完全无法拯救自己；举行，而不是说，虽然人类的本质已经受损的罪过，将仍是免费的，并能够回应天主的恩典。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。