弱收敛

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。

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。

It investigates mainly the dualinvariant of λ- multiplier convergent series, the full invariant ofλ-multiplier convergent series, the λ- multiplier convergent series in spaceswith a basis, the compact sets in the infinite matrix topological algebras, thecharacteristics of have the same compact sets in different topologies,the weak sequentially completeness of , the characteristics ofSchur-matrices, the characteristics of p- uniform Toeplitz matrices and theEberlein-Smulian theorem in the locally convex spaces, etc.

主要研究了〓数乘收敛级数的对偶不变性，〓数乘收敛级数的全程不变性，有基空间中的〓数乘收敛级数，无穷矩阵拓扑代数〓中的紧集，〓在不同拓扑下具有相同紧集的刻划，〓的弱序列完备性，Schur—矩阵的刻划，p-一致Toeplitz矩阵的刻划以及局部凸空间上的Eberlein—Smulian定理等。

With four continuity of non-additive set function and the relation of four convergences of the measurable function sequence,four forms Lebesgue theorem about measurable closed-valued functions on monotone measure space are discussed,respectively.

在经典测度论中，Lebesgue定理刻画了实值可测函数序列几乎处处收敛和依测度收敛之间的关系。1984~1986年，王震源[9]先后提出了较弱的"自连续"、"零可加"、"伪自连续"、"伪零可加"等重要概念，讨论了模糊测度空间上单值可测函数序列各种收敛之间的关系，推广了经典测度论中著名的Lebesgue定理以及其他定理。

For the linear problem, the linearity of the problem is also well preserved in the merit functions. The global convergence, local superlinear or quadratic convergence and finite convergence for linear problems of the proposed algorithms are also obtained under conditions as above or even weaker.

基此构造的互补和混合互补问题的算法，均具备在前述条件或比其更弱条件下的全局收敛性、局部超线性或二次收敛率以及在线性情形下的有限步收敛性。

Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs.

基于此给出了求解箱约束变分不等式的一种阻尼牛顿算法，在较弱的条件下，证明了算法的全局收敛性和局部超线性收敛率，以及对线性箱约束变分不等式的有限步收敛性。

A damped Newton type method was presented based on it.Global and local superlinear/quadratic convergence results were obtained under mild conditions, and the finite termination property was also shown for the linear BVIs.

基于此给出了求解箱约束变分不等式的一种阻尼牛顿算法，在较弱的条件下，证明了算法的全局收敛性和局部超线性收敛率，以及对线性箱约束变分不等式的有限步收敛性。

We show that the solutions for the HARA utility are stable in the sense of weak convergence when the parameters vary in a suitable way.

当效用函数为HARA、指数和对数型时，我们分别得到了最优投资的显式解，并且证明了当HARA效用函数中的参数变化时所对应的最优策略在弱收敛意义下的稳定性。

In an appropriate condition,the βn,σn of their asymptotic normalities and the gn of optimal weak convergence rate were obtained.

在适当的条件下，得到^βn，^nσ的渐近正态性和^gn最优弱收敛速度

Course topics will be selected from: the general theory of processes, sample function properties, weak convergence, Brownian motion, diffusions, Levy processes, Markov processes, martingales, Gaussian processes and further topics.

课程论题将从以下选择：过程的一般理论，样本函数的特性，弱收敛，布朗运动，扩散，Levy过程，马氏过程，鞅，高斯过程及更深的论题。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。