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In Chapter two, based on the result of Wang, we elaborate properties of boundary of interval Bézier curves and interval Bézier surfaces.

在第二章里，基于王国瑾([50])一文的结论，对区间Bézier曲线和曲面的边界进行了更细致的刻划。

We analyze the boundary structure of interval Bézier curves in detail. Efficient and reliable algorithms for evaluating the boundaries of the interval Bézier curve in 2D and 3D are presented.

作者对区间Bézier曲线的边界结构作了精细的分析，详细地给出了计算平面区间Bézier曲线边界的编程算法，并将边界曲线表示为B样条。

Of or relating to a surface having no boundary curves.

闭合曲面的：无边界曲线的面的，或与之相关的

. In this thesis, a common mathematical model of the interpolating surface of boundary curves to be given is introduced.

本文还介绍了一个构造给定边界线的插值曲面的一般数学模型，并将工程中常用的几种特殊插值曲面的描述方法统一于这个数学模型之中。

At first, it may be a good idea to select the numbers of control points from the boundary curves. If the surface is not adequate, this number can be increased.

起初，从边界曲线上选择控制点可能是个比较好的主意，但如果曲面不够的话，这个数量可能会增加。

1Algorithm of approximating to a domain bounded by multiple curves anddistinguishing different material regions and inheriting of stresses ispresented.

提出了对多种曲线构成区域的网格逼近和材料分区识别、应力继承的算法，实现了四边形单元弹塑性自适应有限元计算程序。

2Algorithm of approximating to the domain bounded by multiple curves anddistinguishing different material regions is programmed.

研究了对多种曲线组成区域的网格逼近、不同材料区域的识别算法，提出并改进多条曲线交界处网格逼近的算法。

A quantitative analysis using computer simulation based on the modified Bragg's law and the optical multilayer theory was used to reproduce the diffraction rocking curves which fitted very well with the experimental ones, and a method to measure the structural parameters of Ge〓Si〓/Si superlattices was set up.

用光学多层膜理论对谱线作计算模拟的结果和实验非常一致，并在此基础上建立了一套同小角衍射测量Ge〓Si〓/Si超晶格结构参数的方法。

We describe the algebraic characteristic of the public-key cryptosystems based on algebraic structures such as elliptic curves,bilinear pairings,as well as braid group s,with the emphasis on the difficulties of constructing public-key cryptosystems based on non-commutative algebraic structures.

通过分析基于椭圆曲线、双线性对以及基于辫子群的公钥密码体制的代数学特征，着重讨论了构建基于非交换代数的公钥密码体制所面临的困难。

The conclusions show that with γP0 increasing the nonlinear dispersion curves shift to the negative region of δ,the upper branch of the curve will form a ring when γP0 exceeds a critical value,while the anomalous dispersion region of group velocity dispersion induced by fiber Bragg grating vanishes,group velocity dispersion becomes only one normal dispersion region.

结果表明：随着βg2的增加，非线性色散曲线的上、下两支向δ的负值区移动，当超过某一临界值时，曲线上支开始形成环，这时光纤光栅引起的群速度色散中的反常色散区消失，全部变成正常色散。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。