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These curves contain a shape parameter which can adjust the softness of curve and have the same continuity with the original B-spline. In succession, using the positive conditions of Bernstein polynomial to find a range in which the shape parameter takes its value so as to make the corresponding interpolating curves monotonicity-preserving and C~2 continuous.

利用奇异混合的思想构造出一类带有形状参数的多项式样条曲线，即均匀α-B样条曲线，在无需反求方程组、迭代过程和最值求解的情况下就能轻松做到插值给定的点列；它含有形状参数α，这就增加了曲线的柔性，同时又和原B样条曲线具有相同的参数连续性。

The basic idea is as follows: first, a kind of plane α-B-spline interpolation curve with a shape control parameter a is constructed; then, by converting the first derivatives of the curve into Bernstein polynomial, the positive conditions of Bernstein polynomial can be used to get the necessary and sufficie nt conditions for the monotonicity of α-B-spline interpolation curves, i.e., the range of the parameter a. Therefore, monotone-preserving interpolating curves can be obtained succinctly.

其基本思想是：首先构造带有形状可调参数的一类平面(-B样条插值曲线，再把其一阶导矢的两个分量分别转化为Bernstein多项式，从而利用Bernstein多项式的正性条件，得到此曲线为单调的充要条件，即形状参数的取值范围，简单、快捷地实现此参数样条曲线的保单调插值。

In this paper,singularity is used to study the classification of singularities of the binormal curves and focal surfaces of a spacelike in Minkowski 3-space,and also establish the relationships between singularities of these and geometric invariants of curves under the action of Lorentzian group.

应用奇点理论方法对三维Minkowski空间内由空间型曲线生成的副法线标型和可展焦曲面的奇点进行了分类，并且研究了在Lorenzian群作用下的空间型曲线的几何学不变量同这些奇点之间的关系。

The boundary of interval Ball curves of degree n is discussed and two algorithms for the degree reduction of interval Ball curves are given by means of linear programming and best approximation respectively.

讨论了n次区间Ball曲线的边界的构成；同时通过讨论区间多项式的降阶，利用线性规划法及最佳一致逼近法，给出了区间Ball曲线的的降阶算法。

With scheduling algorithms FIFO,the communication model is set up and network elements' arrive curves and service curves are derived for a switched industrial Ethernet model with two levels' tree topology.Then,analytic expressions of the worst case end-to-end delay,buffer size and output burstiness are presented,the maximum network delays of real-time data are calculated based on derived results.

针对FIFO调度算法，对两级树型拓扑结构的交换式以太网系统建立了通信模型，推导出各网络元素的到达曲线和服务曲线，由此得到了最大时延、所需缓冲区大小、输出突发量等实时业务流的主要参数解析表达式；利用推导所得结论计算了实时业务流的最大网络时延。

Secondly, an adaptive real-time interpolation algorithm for B-spline curves is proposed combined with the chord error control and the largest centripetal acceleration control based on the differential geometry and the properties of B-spline curves.

其次，根据B样条曲线的特性以及微分几何原理，实现了一种带弦高误差控制和法向最大加速度控制的进给步长自适应B样条曲线实时插补算法。

On the basis of Aumann,Meng Ya-qin and Ye Zheng-lin[13],Cuan-ying and Xue Ji-jun[16] have gained some conditions about characteristic polygon of the ruled surface,they used two Bezier curves in paralled plane as boundary curves to get ruled surface.

国内孟雅琴、叶正麟、爨莹、薛继军等人在Anmann方法的基础上，用位于两平行平面上的两条Bézier曲线作边界曲线，形成直纹面，并得到了它们可展时特征多边形顶点应该满足的条件。

The segment arrangement on circular curves has proven theoretical support;the segment arrangement on transition curves,however,has no theoretical support and is usually executed by means of VMT systems equipped on shield machines.

对于圆曲线的管片排版已有了相对较为成熟的理论，而缓和曲线上的管片排版以往通常是根据盾构机VMT来选择，没有成型的理论支持，为此，结合测量理论和弯环管片的实际，探索出在缓和曲线上准确选择弯环管片理论排版的方法。

By utilizing the complex multiplication property of the curves and using a modulo reduction and Frobenius expansion technique, it is shown that there is a fast point multiplication method without precomputation on the curves, which is 6 times faster than the ordinary repeated-double-add method.

结果显示，利用这类曲线的复乘性质，使用模约减和Frobenius展开技巧，这类曲线上存在一种不带预计算的快速点乘算法，其运算速度是通常的重复加倍-点加算法的6倍。

Utilizing the complex multiplication property of the curves and using a modulo reduction and Frobenius expansion technique, Bring forward that there is a fast point multiplication method without precomputation on the curves, which is 6 times fast than the ordinary repeated-double-add method.

针对一类特征3的Koblitz椭圆曲线的点乘算法，利用这类曲线的复乘性质，使用模约减和Frobenius展开技巧，提出一种不带预计算的快速点乘算法。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐