收敛性

The merits of RGA consist in the efficiency, stability and controllability of local convergence.

RGA的价值体现在局部收敛的高效性、稳定性和可控制性。

First,we consider the lower semicontinuity property fora functional with linear growth in LDΩthe second, in the SBD space,we discussthe lower semicontinuity of an integral functional that the integrand is a Carathéodoryfunction and that satisfies a symmetric quasi-convex assumption, by the compactnesstheorem of the SBD space,blow-up method and Morrey theorem,prove that integral functional is lower semicontinuous with respect to L~1- convergence;then by using theone-dimentional sections method and the structure theorem of the BD functions, dis-cuss the lower semicontinuity of the integral functional in the whole BD space.

首先我们考虑LD空间满足线性增长的积分泛函的下半连续性；其次在SBD函数空间讨论了被积函数为Carathéodory函数时的积分泛函在满足对称拟凸条件时的下半连续性，主要利用SBD函数空间的紧性定理和blow-up方法以及Morrey定理等给出了积分泛函关于L~1-强收敛的下半连续性；然后利用BD函数的一维截断方法和结构定理，讨论了在BD全空间上的积分泛函的下半连续性。

Then we prove a nonsmooth minimax theorem by usingsome relative results about multi-valued maximal monotone mappings. Finally, we construct a nonsmooth minimax network to search for thesaddle points of the saddle functional. We have also proved that thetrajectory of the network is asymptotically convergent to thesaddle point of the saddle functional by usying Lyapunov function.

我们先介绍有关Clarke的广义梯度，次梯度及鞍泛函的有关结论；然后利用多值极大单调映象的满射性结果证明了一个非光滑的minimax定理；最后建立了一个非光滑的minimax神经网络来求解泛函的鞍点，并在一定的条件下构造出LYAPUNOV函数来证明网络的轨道渐近收敛于鞍泛函的鞍点。

To enhance the robustness of DTS, the solution with the minimum error is taken as the result when convergence cannot be found.

算法在不收敛情况下以误差最小解为计算结果，提高了DTS的鲁棒性。

Due to the fact that the method based on local linearization is usually lost in local minimum values and the optimization solution is dependent on the selection of initial solution,the standard genetic algorithm has po...

该算法利用拟网格法初始种群和综合交叉策略，克服了早熟收敛现象，从而提高了遗传寻优的效率。理论模型反演与其它方法比较，结果说明遗传算法具有不依赖初始模型，不容易陷入局部极小，多点多路径概率搜索，以及隐含并行性等优点。

In the third chapter,we study the rate of convergence of nonhomogeneous Markov chains and the absolute average strong ergodic.

第三章研究一类非齐次马氏链的收敛速度及绝对平均强遍历性。

The experimental results show that this method has the advantages of robustness,global optimality and high convergent speed and it is feasible for optical flow estimation of nonrigid body.

实验结果表明：本方法具有鲁棒性好、全局搜索能力强、收敛速度快和可用于非刚性体运动估计等优点。

According to theoretical analysis, it is convergent and has good convergence if the coefficient matrix is a nonsingular matrix. Moreover, examples have been implemented on HP rx2600 cluster, and the data verify that the numerical results of this algorithm coincide with its theoretics.

在理论上，算法只要系数矩阵A是非奇异矩阵就能够收敛，而且有较好的并行性，在HPrx2600集群上进行数值试验，验证了算法的计算结果与理论相一致。

The idea is to add some lower degree terms in the remainder of orthogonal expansion in an element so that the remainder satisfies more orthogonality conditions in the element, and get a desired superclose funtion uI to finite element solution uh.

简述了有限元超收敛研究的一种新想法，即在单元正交展开的余项中添加若干待定低次项，使此余项在一个单元上满足更多的正交性条件，并得到所需的超接近于有限元解uh的逼近函数uI。

The new algorithm effectively combines the advantages of ACO and PSO. It adopts the grid method for environment modeling and makes use of the efficiency and succinctness of PSO to obtain the initial distribution of pheromone, reducing the number of iterations and accelerating the convergence. At the same time, by using the parallelizability of ants and distributed parallelized-searching technology, the performance of the algorithm is effectively improved.

该方法有效地结合了粒子群算法和蚁群算法的优点，采用栅格法进行环境建模，利用粒子群算法的快速简洁等特点得到蚁群算法初始信息素分布，以减少迭代次数，加快算法的收敛速度；同时利用蚁群算法之间的可并行性，采用分布式技术实现蚂蚁之间的并行搜索，求解精度高等优点，求精确解。

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。