单值化点

It is shown that the mechanical properties including Young's modulus, tensile strength, critical strain and stress under buckling can be enhanced with the decreasing of intershell spacing. The shear strength can be enhanced by 2-3 orders of magnitude when the intershell spacing is reduced to 20%, which is also dependent on commensuration. Zigzag-type carbon nanotubes have higher shear strength. The axial stress in tubes when the load transferring from outmost tube to inner tube is observed as well.

研究了单壁纳米管束横截面的六方化失稳现象，给出各种管径的面内压力－应变关系曲线；每条曲线都给出一个明显的拐点而且有很强的非线性；线弹性模量与参考构形有关，也受管直径的影响；分析了管束横截面的晶格不稳定性特征，表明晶格的缺陷能够明显的减小临界值；模拟了在不同应变下纳米管束对静水压的反应，发现不同压力下的截面形态不同，在很高压力下相邻管之间会形成化学键。

The objective of this study is aimed at the implementation of parallelized numerical quadrature routines. The algorithm we choose for numerical quadrature routines is the so called "Adaptive Romberg Tree integration scheme"(abbr."ARTint") proposed by Lin et. al.[1997]. This numerical quadrature scheme can arrange the function evaluation points adaptively in accordance with characteristic of the trend of variation in integrand function values. When the accuracy of the numerical quadrature value is requested to be increased, a newer and larger set of function evaluation points must be incurred. The main advantage of ARTint method is the inclusion of all function evaluation points used in previous stages. It is this feature of ARTint method that makes it a quadratue scheme with prominent computation efficiency.

本研究在探讨数值积分程式之平行化，所使用的演算法为林聪悟与林佳慧[1997]一书所提出的「Romberg树自动布点数值积分」架构，此一数值积分方法能以适应被积函数值变化情形方式自动安排积分点来进行数值求积计算，在提高阶数以获得更高精度积分值的过程中，此一方法只须再计算新增加积分点的函数值，搭配先前已计算过的函数值的重覆运用即可获得更精确的数值积分估计值，如此将能减少升阶过程中函数求值计算的次数，有效率地完成单重积分的数值计算。

A four-point algorithm is presented in this paper for finding the least-squares solution of R and T,which is based on the singular value decomposition of matrix,and the derivation of the algorithm is provided too.

本文提供一种基于矩阵单值分解求解R和T的最小二乘解的四点算法，并对算法进行了推导，该算法与迭代法相比，具有速度快、用点少的优点，尤其适用于实际应用的颅脑手术可视化系统。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。