条件收敛的

It is less known that the method used in this proof was mentioned for the first time at a conference of the Academy of Natural Sciences of the Serbian Royal Academy of Sciences in Belgrade in 1929, where Karamata introduced the notion of majorizability as a new condition of convergence for Abel summable series.

这是非常少有人知道，该方法在这方面的证据使用的，以及在一个自然的塞尔维亚皇家科学院在贝尔格莱德科学院于1929年，中国科学院会议首次提出在Karamata的一项新条件的majorizability概念收敛阿贝尔summable系列。

For solving the boundary case of 〓 interpolation subdivision given in forth chapter, we give convergence and smoothing conditions and a C〓 continuous four point interpolation scheme using the curve triple subdivision methods from chapter three.

另外本文在第三章给出了曲线三分法细分算法的收敛和光滑条件，并给出了C〓连续的三分法四点插值算法，它解决了我们第四章给出的〓插值算法在边界上会遇到的问题。

The objective of Chapter 2 is to give the weak convergence theorem of S ={T1 :t E G of asymptotically nonexpansive mappings in a uniformly convex Banach space without assuming that X has a Frechet differentiable norm.

本文第二章在G仅要求是一个定向网，X为不具有范数Frechet可微条件的一致凸Banach空间的情况下，给出了一族渐近非扩张映射的弱收敛定理。

A class of modified BFGS algorithm which satisfies the new quasi-Newton equation is proposed in the paper[1],and the global convergence of the algorithm is proved under the condition that the objective function is uniformly convex.

文献[1]曾在已建立的一类新拟牛顿方程 Bk+1sk=yk-=yk+kγskTsksk的基础上，证明了满足新拟牛顿方程的一类改进BFGS算法在目标函数为一致凸的条件下，具有全局收敛性。

Some sufficient conditions are presented, which all solutions of the proposed neural network are globally exponentially convergent to the unique solution of the linear variational inequality problem.

得到了一些保证该神经网络的所有解全局指数地收敛到线性变分不等式问题的解的充分条件。

Chapter 3: Using spectral projected gradient method and a new nonmonotone line search technique, we propose a algorithm for solving the trust region subproblem. Under weak conditions, the global convergence is established.

第三章：利用谱投影梯度方法与一个新的非单调线搜索技术给出了求解信赖域子问题的一个方法，在一般的假设条件下获得了方法的全局收敛性。

But the weak law of large numbers and the complete convergence for arrays of rowwiseρ*-mixing random variables have not been reported.

但是关于它所生成的随机变量组列的弱大数定律及完全收敛性还未见报道，本章讨论这方面的内容，仅在条件ρ~*(1)＜1，而对混合速度不作任何限制下，得到了：定理0.1.1设{X_；1≤k≤n，n≥1}是行内随机变量为ρ~*混合且ρ~*(1)＜1的随机变量组列。

Giving the more explicit boundary conditions and using Biconjugate gradients stabilized method to solve the linear algebra equation with large coefficient matrix, we get a fast algorithm of highprecision to calculate effectively electrical and magnetic fields in the whole space.

由于提出了简洁的边界条件，采用了解大型系数矩阵方程组的双共轭梯度稳定解法，所实现的三维交错采样有限差分数值模拟算法具有迭代收敛稳定、计算精度高、速度快等特点。

This thesis focuses on studying the matrix equa-tion problem systematically, and proposed an abstract algorithm of solving the matrixequation with constraints, and established a strict convergence theory. Using this algo-rithm, we can solve the sets of matrix equation satisfying some constraint conditions,such as symmetric, antisymmetric, centrosymmetric, centroskew symmetric, re?exive,antire?exive, bisymmetric, symmetric and antipersymmetric, symmetric orthogonalsymmetric, symmetric orthogonal antisymmetric, Hermite generalized Hamilton ma-trix;So we can solve the problem with this algorithm, if the set of constrain matrixcan make a subspace in matrix space, and this algorithm also can solve the optimalapproximation and least squares problem. So this abstract algorithm has universal andimportant practical value.

本篇硕士论文系统地研究了此类问题，并找到了求解约束矩阵问题的抽象算法，并建立严格的收敛性理论，利用这一算法可求解约束条件为对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵，对称正交对称矩阵、对称正交反对称矩阵、双中心矩阵、Hermite广义Hamilton矩阵等；可以说只要约束矩阵集合在矩阵空间中构成子空间，都可以考虑用此算法求解，而且这一算法还能把矩阵方程解及其最佳逼近，最小二乘解及其最佳逼近统一处理，因此本文算法有普适性和重要的实用价值。

By using truncation methods of random variables and Doob martingale convergence theorem,the properties of sequence of arbitrary random variables are studied,a class of strong limit theorems for sequences of arbitrary random variables is obtained under moment conditions, and some conclusions corresponded to these are generalized.

利用随机变量的截尾方法和Doob鞅收敛定理，研究了任意随机变量序列的性质，得到了一类矩条件下任意随机变量序列的强极限定理，推广了与此相应的一些结果

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。