收敛

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

In general,the convergent sequence and bounded set are concepts only in topological spaces.

收敛序列和有界集一般是拓扑空间中的概念，文章首先引入序列收敛C和L-空间(给出某种序列收敛关系的向量空间)，然后在其中定义有界集。

Cauchy convergence criteria is proved the convergence and spread the basic method and through this method also launched many simple method, thus the important position of cauchy criterion, this kind of method is obvious superiority of the characteristics of itself, through to judge whether to prove the convergence, and this will bring convenience to the standards for the following summary, and probes into some of the relationship between them.

柯西收敛准则是证明收敛与发散的基本方法，并且通过此种方法还推出了非常多简单的方法，由此可见柯西准则的重要地位，此种方法的优越性也是显而易见的，就是通过本身的特征来判断是不是收敛，这就给证明带来了方便，本文将这几种准则作了以下总结，并且探讨了它们之间的一些关系。

In view of crosswell and 3D VSP layout, we use high resolution Radon transform based on Cauchy distribution to perform Radon transform for hole data. In this process, we study discrete dip overlay operator, improve damping factor that affects Radon energy convergence in order to let Radon energy converge, 6 resolve leggy in Radon data, and decouple smoothing effect among each energy group, we use Cauchy distribution to regularize data, let energy focus on one point, and improve Radon resolution. All these work well in wavefield separation. Finally, by inversion results and model trial, we verify the feasibility and stability of this method.

在Radon变换原理分析基础上，采用基于柯西分布的高分辨率线性Radon变换对井孔数据进行Radon变换，其间通过对离散倾角叠加算子求取的研究，及对影响Radon能量收敛的重要参数阻尼因子算法的改进，使数据在Radon域以能量团的形式呈现，得到很好的收敛效果，基本解决了Radon域数据的一定程度的拖尾现象，消除了各能量团之间的平滑效应，采用柯西分布来规则化数据，提高了Radon域的分辨率，Radon域能量也收敛到一个点上，有利于上下行波或纵横波波场分离。

In view of crosswell and 3D VSP layout, we use high resolution Radon transform based on Cauchy distribution to perform Radon transform for hole data. In this process, we study discrete dip overlay operator, improve damping factor that affects Radon energy convergence in order to let Radon energy converge, 6 resolve leggy in Radon data, and decouple smoothing effect among each energy group, we use Cauchy distribution to regularize data, let energy focus on one point, and improve Radon resolution. All these work well in wavefield separation.

在Radon变换原理分析基础上，采用基于柯西分布的高分辨率线性Radon变换对井孔数据进行Radon变换，其间通过对离散倾角叠加算子求取的研究，及对影响Radon能量收敛的重要参数阻尼因子算法的改进，使数据在Radon域以能量团的形式呈现，得到很好的收敛效果，基本解决了Radon域数据的一定程度的拖尾现象，消除了各能量团之间的平滑效应，采用柯西分布来规则化数据，提高了Radon域的分辨率，Radon域能量也收敛到一个点上，有利于上下行波或纵横波波场分离。

I. d. Bernoulli random variables. First, we can get the upper bound with order from Chebyshev inequality. Second, a better upper bound was gotten with the new inequalities, which can fasten the convergence rate.

并对服从两点分布的独立随机变量X1，X2，…，X进行研究，首先利用Chebyshev不等式得到随机变量偏离方差ES的上界，但它只有阶的收敛速度，然后利用新的不等式得到一个新的上界，它有更快的收敛速度，这在探讨收敛速度时有着重要的理论意义。

The experimental results prove that the convergence speed of the proposed method is non-linear and the use of convergence points can lower the complicacy of process of iteration.

实验结果表明，改进后的高斯核均值漂移算法以超线性的速度收敛，收敛点的应用降低了收敛过程中的计算量。

Our results show that there is no obvious conditional convergence in china, that is, given the same level of human capital, market openness and other factors the economic provinces have demonstrated an unconspicuous growth convergence.

本文研究得出，中国地区间的经济增长，存在不明显的条件收敛的特征，即在具有相同的人力资本、市场开放度等结构特征的经济地区间不存在明显的增长收敛趋势，但是存在着很显著的"俱乐部收敛"特征，即按东中西划分的区域内部人均经济产出具有明显的聚集现象。

Our results show that not only the club convergence has been obviously exhibited, that is, the output per capita congregates within the east, middle and west districts respectively; but also the conditional convergence has been identified, that is, given the same level of human capital, market openness and other factors the economic provinces have demonstrated a certain growth convergence.

本文认为中国地区间的经济增长，不仅存在着显著的"俱乐部收敛"特征，即按东中西划分的区域内部人均产出具有明显的聚集现象；而且存在着条件收敛的特征，即在具有相同的人力资本、市场开放度等结构特征的经济地区间存在着一定的增长收敛趋势。

We prove that the economic growth mode will be nonlinear in a region restricted by Minimum Government Scale, conditional convergence and club convergence would be found and the regional gap would reduce the first, then enlarge and reduce in the last.

我们证明，存在最小政府规模的经济其增长是非线性的，经济收敛性在短期表现为条件收敛与俱乐部收敛的双重特征，并且地区差距的变化将呈现出缩小-扩大-再缩小的动态特征。

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。