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Theorem The arc length of a plane curve which is smooth can be calculated.

定理 光滑曲线弧是可以求长的。

Theresistance to a rising object is one order magnitude greater than that to a settling object. The efficient buoy-ancy on a flaky object, which lies flat on the gas distributor, is much less than that calculated according tothe Archimedes' principle.

物体上浮时受到的阻力要比下落时大一个数量级，平躺在气体分布板上的扁平状物体受到的浮力比理论计算值小得多。

Calculating the area of a circle; calculated their probable time of arrival.

计算圆的面积；计算他们可能的抵达时间

Calculated area of circle, a numerical input, press the button will get a corresponding area of circle.

详细说明：计算圆面积，输入一个数值，按按钮就会得到相应的圆面积。

On the basis of OCM, segmentation based on curvature radium is presented in the paper, in which curvature radium is calculated using parametric-surface fitting, and detecting edge points is realized from orthogonal direction, which ensure the integrality of edge points. Since the data is organized by cross-line in OCM, a new arithmetic, Double-direction Angle Difference arithmetic, is brought forward, which can pick up edge points more quickly.

物体的表面一般由多个曲面相交组成，要建立完整的几何模型，需要对测量数据进行区域分割——区分不同曲面的数据，现有的区域分割大多是对单视图的图像式测量数据进行的，但完整的CAD模型需要联合多个视图产生，本文在上面提出的三维正交模型的基础上，提出了三种区域分割方法：第一种方法是基于曲率半径的数据分区方法，通过二次参数曲面拟合计算局部曲率半径，从正交的多个方向进行检测，保证了边点提取的完整性。

By applying the difference arithmetic to solve the differential vibration model of the single-degree-of-freedom,the acceleration responses of the vibrated bevel wheel was calculated.The bevel wheel contact fault was simulated by taking it as the impulsion loading in local point.By using techniques of wavelet de-noising and demodulated resonance,gear contact character information was picked up successfully.

从齿轮的单自由度振动模型出发，运用差分算法对模型进行求解，得到斜齿轮的振动加速度响应，将齿面接触型故障等效为在局部点突加一个冲击载荷，对齿轮齿面接触型故障进行了仿真，利用小波降噪和共振解调技术分别对仿真的染噪振动加速度信号进行处理，成功地提取了轮齿接触故障的信息。

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。

It is indicated that the arithmetic mean value can be used to substitute for that calculated with the theore tieal formula,while the required relative erroris no larger than 1

结果表明，用较简单的算术平均值代替较繁复的理论计算值，其相对误差不超过1％。

The definition and properties of line segment arithmetic are given,which is a special situation of point set arithmetic,but easily calculated.

文章给出了线段算术的定义和性质，它是点集算术的特殊情况，但更便于计算；提出了线段Bézier曲线的概念，就是把区间Bézier曲线中的长方形换成满足一定条件的线段，这里的线段是指该线段上所有点的集合；给出了线段Bézier曲线的性质及其细分算法。

Minimum spanning network of the 18 non-coding haplotypes was made using ARLEQUIN 2.0 and genetic distance was calculated based on COII gene sequences. The analysis showed that the population was interrelated and the Apis cerana population of China had expanded in history.v.

对mtDNA的18种非编码区单倍型利用ARLEQUIN 2.0进行最小跨度网络分析以及对COⅡ基因的遗传距离计算显示，中华蜜蜂种群内部关系密切，在历史上曾发生过群体扩张； 5。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。