收敛

Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space.

王娴 ，何震Xu和Norr已经证明了建立在一致凸Banach空间的一个非空有界闭凸子集上的渐进非扩张映射的三步迭代的收敛定理问题。

A Lipschitz strictly pseudocontractive map from a nonempty closed convex subset of a Hilbert space into itself was showed to have fixed points, Ishikawa and Mann iterative sequences with errors of a Lipschitz strictly pseudocontractive map was introduced and the iteration processes strongly converges to a fixed point was proved.

证明了在Hilbert空间中的非空闭凸集上Lipschitz严格伪压缩映象有不动点，介绍了Lips-chitz严格伪压缩映像下的的具误差的 Ishikawa和Mann迭代序列并证明了其强收敛性于不动点，其结果把非扩张映像推广到Lipschitz严格伪压缩映象上，改进了一些相关结果。

By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.

在第二章中，我们参照文献[7]中的方法，提出了一类与HS算法相关的共轭梯度算法，并减弱了文[7]中要求目标函数二阶连续可微且为凸的前提条件，采用强Wolfe线搜索，在较弱的条件下证明了这一类算法具有充分下降性和全局收敛性。

The PSE in the curve coordinate systems are solved by the numerical techniques developed efficiently in this paper. A normal transform is introduced, and there are enough much grids in the region between the critical layer and the wall, where the variation of the disturbance is the quickest. The finite-difference of governing equations with fourth-order accuracy in the normal direction is utilized in full regions including points close the wall, and is very important for accurately discreting equations.

对于曲线坐标系下的抛物化稳定性方程，文中发展了求解的高效数值方法：引进法向变换，使得在临界层与壁面之间的扰动量变化最快的区域有更多的法向网格点；导出包含边界邻域在内的完全四阶精度的法向有限差分格式，这对方程精确离散至关重要；采用全局法和局部法相结合的方法及其新的迭代公式，大大加速收敛并得到更精确的特征值。

The essence of design is to ensure trajectories of states ultimately entering into some neighborhood of the coordinate origin, and the convergence of states is evident later on.

设计的本质在于保证系统的状态最终进入坐标系原点的小邻域，而其后状态的收敛性是明显的。

The final experimental results on the Corel database show that the proposed approach greatly improves the retrieval performance.

在Corel通用图像测试库上的实验表明，本文算法可以明显提高检索的准确率和收敛的速度。

This new method reduces the computational complexity by using the block tridiagonal structure of the input sample correlation matrix, and at the same time keeps the advantage of fast convergence.

在保持了该算法快速收敛优点的同时，利用相关矩阵块三对角的特殊结构，降低了该算法的计算复杂度。

In chapter 2, using the favorable characters of the function Q = ch{x - 1, we construct the hyperbolic cosine penalty function and algorithms and proved its convergence .

在第二章中，我们利用函数Q=ch-1良好的性质，提出一种用双曲余弦函数作罚项的双曲余弦罚函数及算法，证明了该罚函数和算法的合理性及迭代点列的收敛性。

A costate prediction method based on bilinear model is presented. Using simple general model, two implemental DISOPElike algorithms based on Hopfield network and on temporal decomposition method are proposed respectively.

同时对于具有终端状态等式约束问题，建立了基于时变线性模型的递推DISOPE算法；对于非齐次双线性二次型问题提出了一个迭代算法，并且给出了该算法收敛的充分条件；给出了基于双线性模型的协状态预测算法；利用一般模型，分别提出了基于Hopfield网络和时间分解方法的DISOPE算法。

Several forms of Coulomb's Law are studied in detail when the foundation surface is rough and friction exists.

由于使用了统一的位移增量收敛判据，所得数值解具有很好的精度和可靠性。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。