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Firstly, the development of the spherical robot is introduced and according to the knowledge of the research forepassed, the nonholonomy and the nonlinear controllability for a spherical robot based on the principle of angular momentum conservation are discussed with the differential geometric control theory.

首先介绍了球形机器人的发展状况，在了解前人研究领域的基础上，应用微分几何控制理论，对此角动量守恒的球形机器人的非完整性和非线性可控性进行了研究。

Furthermore, we define a convolution multiplication between characteristic functions of constructible subsets by using push-forward functor from the category of algebraic varieties over C to the category of spaces of constructible functions. We construct geometric model for "intrinsic symmetry" of the octahedral axiom in a triangulated category. Using it, we deduce the multiplication satisfies the Jacobi identity of Lie algebra and then realize infinite dimensional Lie algebras.

进一步，我们使用复代数簇范畴到可构函数空间范畴的pushforward函子，给出了可构集上特征函数的卷积乘法，并构造了三角范畴八面体公理的内蕴对称性的几何模型，最终证明了对于不可分解支撑有界可构集的特征函数，乘法满足李代数定义的Jacobi恒等式，从而给出了无限维李代数的实现。

Now we have a similar geometric construction problem but with the following

现在我们也有类似的几何构造问题，但以下

Then an n-th order balance geometric continuity condition and...

此方法适用于计算机动画和工业造型设计

For combined Bezier curves case, after we strictly analyze the shape blending process, we introduce the balance geometric continuity condition to ensure the shape feature and give a set of logical solutions.

作者进一步分析了基于参数曲面片拼接技术的形状调配过程的困难性，从而引出随后的细分方法研究。

On the basis of analysis and comparison of their strengths and weaknesses, each method can find its applied occasion. With energy method, we can conveniently control the precision of the objective surface and add boundary constraints for preserving the models global geometric continuity, but this method is very time-consuming.

其中基于能量原理的光顺方法能够方便地控制目标曲面的精度和边界条件，从而能够实现曲面模型的全局连续性，但是能量法的运算速度还有待提高；刚度调整法实现简单，但是生成的曲面的可编辑性较差；小波分解方法计算速度很快，能够有效地实现数据压缩，但是其逼近误差和边界条件却难于控制。

Based on the geometric nonlinear and material nonlinear of structure, the three dimension stability analysis of long span curve continuous rigid frame is performed on the base of the numerical analysis, and comparison of the linear and the non-linear is also done.

本文分别考虑结构的几何非线性和材料非线性力学特征，对高墩大跨弯连续刚构桥梁的结构稳定性进行详细的数值分析，并与线弹性的计算结果进行对比。

We also develope the corresponding rational composite Bezier curve with geometric continuous design facility.

本文还将这一方法推广到有理情形，提出了有理组合Bezier曲线的几何连续设计方法。

The analysis results show that the stability of long span curve continuous rigid frame is actually the ultimate load carry capacity considering the yield strength of material and the effect of the geometric nonlinear effect to structure can not be ignored.

结果表明：弯连续刚构桥梁的稳定问题已经转化为考虑结构材料屈服强度的极限承载力问题，同时几何非线性对稳定的影响亦不能忽略。

In this paper presents a new geometric active contour scheme for medical image segmentation.

提出一种新的几何活动轮廊模型对医学图像进行分割。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。