收敛性

From 1978 to 2000, there was not σ-convergence of the PGDP growth in Jiangsu province; From 1984 to 1993 and since 1999, there was not σ-convergence of the per capital net income of rural households growth, but from 1993 to 1999, there was a -convergence; From 1978 to 2000, there was not absolute β-convergence of the PGDP growth in Jiangsu province, but there was conditional β-convergence and the convergence intensity was feeble, half-lifecycle is comparative long, the least half -time of the undeveloped region will catch up with the developed region was 115 years; From 1994 to 2000, there was club-convergence hi the northern Jiangsu and the Middle Jiangsu, but there was not club-convergence in the northern Jiangsu.

第四，基于经济增长收敛的理论与方法，对江苏省区域经济发展的收敛性进行了研究。1978一2000年，江苏省人均GDP总体上不存在u一收敛；农民人均纯收入增长在1 984一1993年及1999年以后不存在a一收敛、在1993一1999期间存在a一收敛；1978-2 000年，人均GDP增长总体上不存在绝对p一收敛，但存在条件p一收敛，收敛的程度较弱，半生命周期比较长，落后区域要缩小与发达区域经济差异的一半最少也需要115年；1 994一2000年，在经济比较发达的苏南和苏中内部存在俱乐部收敛，在苏北内部不存在俱乐部收敛趋势。

Convergence of the test results shows that the economy does not have absolute convergence of the economic characteristics, but this shows the characteristics of condition convergence; Human capital investment rate in the regional economic model have shown significant positive effects that is a notable convergence of factors of affecting the regional economy. On the three core areas of the club convergence test shows that within the three core areas still exist absolute convergence trend, but including human capital expansion of the Solow model the test results have all shown significant convergence of the regional club.

3收敛性的计量检验结果说明，浙江区域经济不存在绝对收敛的经济特征，但表现出显著的条件收敛性特征；人力资本投资、教育和健康形式的人力资本积累均有利于提高区域经济增长，且对区域经济收敛性具有促进作用，这种效应在浙江区域经济中已表现出显著性效应，是影响区域经济收敛的一个显著因素；对三大核心区的俱乐部收敛性检验说明，三大核心区内部仍不存在绝对收敛趋势，但包括人力资本的扩展Solow模型的检验结果却均表现出显著的地区俱乐部收敛性。

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 this paper, the relevant definitions and theorems of function series continuity and function of the carried out a detailed convergence analysis, so that readers of their intrinsic relationship between the more detailed understanding.

本文通过相关定义与定理对函数的连续性及函数项级数的收敛性进行了详细的分析，使读者对它们之间存在的内在关系有更详细的认识。关键词：函数列；函数项级数；连续性；收敛性；一致收敛性

Furthermore, the first-order optimality condition and its equivalent reformulations for generalized semi-infinite max-min programming with a non-compact set are presented using the lower-Hadamard directional derivative and subdifferential.2. Chapter 3 studies the gradient-type methods for unconstrained optimization problems. Section 1 proposes a new class of three-term memory gradient methods. The global convergence property of the method is established. Furthermore, in order to improve the convergence property of the method, a new class of memory gradient projection methods is presented with the property that the whole sequence of iterates converges to a solution to the problem under the conditions such as pseudo-convexity and continuous differentiability of objective function. In section 2, two new classes of methods, called gradient-type method with perturbations and hybrid projection method with perturbations, are proposed. In these methods, non-monotone line search technique is employed, which makes them easily executed in computer.

第3章研究了无约束优化问题的梯度型算法，第1节提出了一类新的三项记忆梯度算法，讨论了算法的全局收敛性，进一步提出了一类新的具有更好收敛性质的记忆梯度投影算法，并证明了该算法在函数伪凸的情况下具有整体收敛性，第2节在非单调步长搜索下提出了带扰动项的梯度型算法及其混合投影算法，这两类算法的一个重要特征就是步长采用线搜索确定而不象许多文献中那样要求步长趋于零，这样更容易在计算机上实现，在较弱的条件下证明了这些算法的全局收敛性，数值算例表明了算法的有效性。

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence. Second, the relations among some types of convergence are studied. Finally, we design some algorithms about fuzzy random simulations to compute the mean chance of fuzzy random event, find the optimistic value of a return function, and evaluate the expected value of a fuzzy random variable.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

First, we present various new convergence concepts for sequence of fuzzy random variables, including convergence sure, convergence almost sure, uniform convergence, uniform convergence almost sure, almost uniform convergence, convergence in chance measure, and their corresponding weak convergence.

首先，提出了几类模糊随机变量序列的收敛性概念，包括：必然收敛、几乎必然收敛、一致收敛、几乎必然一致收敛、近一致收敛、依机会测度收敛以及与以上概念相对应的弱收敛；其次，讨论了收敛性之间的关系；最后我们设计了模糊随机模拟算法，用于计算模糊随机事件的平均机会，寻找收益函数的乐观值，以及估计模糊随机变量的期望值。

In Chapter 3,we discuss theconvergence of Newton's method for nonlinear inclusion problems with values in aclosed convex cone,using the new theory developed by Wang Xinghua,we generalizeRobinson's Kantorovich theorem for this problem to a more widely function classes,inthe same time our results take Smale theorem as a special case.

在第三章，我们利用王兴华最近提出的理论框架研究在闭凸锥中取值的非线性包含问题的Newton方法，将Robinson在特殊Lipshitz条件下建立的Kantorovich型收敛性定理推广至满足中心Lipshitz条件的函数类，我们建立的一般的收敛性定理同时将Smale型收敛性定理包容其中。

Under weaker conditions without the strict com-plementarity,the new algorithm still possesses global convergence,strong convergence,superlinearconvergence and quadratic convergence rate.

在无严格互补的条件下，仍获得算法的全局收敛性、强收敛性、超线性收敛性及二次收敛速度。

An explicit definition of local peak is shown, and the existence condition of local peak is given. It is proved that the GA is constringent at the neighbor of its local peak. The theoretical evidences of some improvements on GA are given, which points out the way forward for improving GAs performance.

关于遗传算法的收敛性研究的一些典型结果包括：文献 [2 ]分析了在种群规模无穷的情况下典型遗传算法的收敛性；文献 [3]证明了典型遗传算法不收敛，而如果对算法采取记录每一代中最佳个体的策略，则改进的算法收敛；文献 [4]提出了一种等价的遗传算法，并给出了收敛条件与收敛速度；文献 [5 ]研

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。