牛顿

By using standard ideas from Lie groups and Lie algebra, the recursive formulation and the Lagrangian formulation were presented.

采用李群和李代数的方法来描述牛顿—欧拉方程和拉格朗日方程，得到机器人动力学在关节空间和操作空间内单个连杆的递推公式以及整个系统动力学方程的矩阵表达式。

Newton was born on Christmas Day 1642, in the rural English county of Lincolnshire.

凡是上过学的人大概都知道这个典故：艾萨克·牛顿在看到从树上掉下的苹果后，就创立了著名的万有引力学说。

In 1666,Isaac newton was struggled overhead by a fallen apple as it shown in the garden of Lincolnshire.

中文是：接下来这篇文章是亨利报道的。1966年，牛顿在林肯郡的一个花园中被一个苹果砸中头部。

In 1666,Isaac newton was struggled with the head by a fallen apple as it grown in the garden of Lincolnshire.

在1666年，牛顿被一个林肯郡花园里长熟的掉下来的苹果砸到了。

In Chapter 4, using the formula A_k(2) given by Wei, we propose a new A_k(2)-SQP method, which develepments the using of the quasi-Newton formula BFGS, and combines with SQP method to solve constrained optimization problems, the corresponding algorithm possesses global convergence and supei linear convergence property.

第四章，利用韦提出的A_κ(2)公式，我们给出了一种A_κ(2)-SQP方法，该方法把拟牛顿修正公式BFGS进行了推广，并结合SQP方法去解约束优化问题，相应的算法具有全局收敛性和超线性收敛性。

For the original infinite dimensional problem, if the inexact quasi-newton method with Broyden updating can not converge quickly , for example, it can not attain super linear convergence rate , then when the discretization is becoming finer and finer , we can not get fast convergence rate for the corresponding finite dimensional problem.

对于原来的无限维问题，如果使用不精确Broyden方法不能得到较快的收敛速度，比如超线性收敛性，那么当离散化逐渐加细的时候，对于所得的有限维问题使用不精确Broyden方法也不可能得到较快的收敛速度，所以有必要在无穷维空间上对收敛性问题加以分析，从而为不精确拟牛顿法结合投影法求解算子方程做好准备。

The forth algorithm is the same as the third one with an addition of finite termination criteria. Although the latter two algorithms have only linear rate of convergence, they are especially suitable for large-scale and sparse problems, with features of simple formula, small storage, sparsity preservation and easy implementation.

前者借助NCP函数把互补问题转化为等价的非光滑方程组，再用带参数的光滑方程组近似这些非光滑方程组，最后用牛顿型方法求解所得到的光滑方程组，希望通过光滑参数趋于零得到原来互补问题的解；后者基于等价不动点格式，构造了一个光滑迭代算法和一个具有有限终止性质的算法，虽然这种迭代算法仅有线性收敛速度，但由于其格式简单、存储量小、保稀疏性、非常易于计算机实现等特点，故较适用于求解大规模稀疏问题。

We derive the local values of parameters of this barrier function and obtain the complexity bound of a full-Newton step interior-point algorithm based on this local self-concordant function for linear optimization problem.

通过求解此障碍函数的局部参数值，我们得到了求解线性规划问题的基于此局部Self-Concordant障碍函数的纯牛顿步内点算法的理论迭代界。

The linear regression of experimental data to Power-Law has been made.

并在改进的MPV-1500试验机上进行了这种非牛顿流体的流变性能试验。

According to the linear search technique, the Quasi-Newton algorithm can be divided into monotone algorithm and non-monotone algorithm.

根据所采用的搜索准则，拟牛顿算法可以分为单调的算法和非单调的算法。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。