条件收敛的

We obtain that if any 〓 is discrete or elementaryand 〓 satisfies Condition A,then the algebraic limit G of group sequence 〓is discrete or elementary.

首先，我们不再仅仅考虑离散非初等群集〓的代数极限G，而是离散群或初等群群集〓的代数极限G，我们对〓上〓变换群中斜驶元及其不动点进行了细致研究，注意到任意一个斜驶元存在一个仅仅含有斜驶元的领域，从而证明了初等群群集〓的代数极限G仍然是初等群，进而我们得到了一个代数收敛定理：如果任一〓是离散群或者初等群并且〓满足条件A，那么，群列〓的代数极限G一定是离散群或者初等群。

An extended hyperbolic mild-slope equation, which can take such terms as wind input, bottom friction and nonlinearity of wave into account, here has been deduced into a parabolic one in the form of a series of governing equations described with complex amplitude. It became a complete wave model when integrated with corresponding physical and imaginary boundaries, and can be solved through the improved Crank-Nicholson or the well known Alternating Direction Implicit difference method, both of which can accelerate the convergent speed , expand limitation of the mathematical method and improve the quality of the solution.

本文基于综合考虑底摩阻、风能输入及非线性影响的推广双曲型缓坡方程，将其进行转换，产生一个演变方程，其复振幅控制方程为抛物线性，并采用ADI差分格式、改进的Crank-Nicholson格式及相应的物理和虚拟边界条件进行求解，以提高数值模拟的适用性、数值计算的稳定性、收敛速度及精度。

By using the sliding mode approach and a multi-step control strategy, a new controller is presented, which can not only satisfy the control constraints but also stabilize the system to an arbitrarily small ε-neighborhood about its equilibrium in a finite time.

利用滑动模态的思想和多步控制策略，设计了不连续反馈镇定律，该镇定律一方面满足控制受限条件，另一方面使得闭环系统的状态收敛到预先给定的原点的任意小的ε邻域中。

By giving the example, explains that theorem 4 in the refuted paper is not the necessary condition of the continued fraction convergences, by discussing the indeterminacy of the lever function and citing the counterexamples, expounds that the theorem 4 is not sufficient condition of the parameters W and W -1 neutralizing each other, and so shows algorithm 1 and 2 in the refuted paper to be incorrect.

通过举例说明了"攻文"定理4不是连分式收敛项的必要条件，并通过对杠杆函数不确定性的讨论和反例的举证说明了"攻文"定理4不是W与W –1相互抵消的充分条件，从而证明了"攻文"算法1和2及其衍生方法是错误的。

Under suit upper and lower solution, iteration sequences were constructed, and existence and unique of solutions of linear boundary value problems on second order nonlinear Hammerstein type integro-differential-difference equation were obtained by means of applying the Arzela-Ascoli theorem Lebesque control convergence theorem and disproof method.

在上下解存在的条件下，构造迭代序列，由Arzea-Ascoli定理和Lebesque控制收敛定理得到了二阶非线性Hammerstein型积分微分差分方程的线性边值问题的解的存在性。再利用反证法获得了解的唯一性。

By using Lebesgue s dominated convergence theorem,several new comparison theorems for the oscillations of the difference equations with continuous arguments were established.

利用Lebesgue控制收敛定理，建立了具连续变量差分方程振动性的几个新的比较定理，给出了具连续变量差分方程强迫振动性的充分条件，并举例说明了强迫项对方程解的振动性的影响

Because of the complexity of the terms in the expansions, many turned to the research of the second-order (also called one-term) Edgeworth expansions, and the rate of convergence of the distributions of the standard...

最近，在更弱的矩的条件下，关于单样本学生化U统计量的Edgeworth展开的收敛速度问题有了更进一步的结果。

The paper proves that the search process of the non-crossover genetic algorithm is an ergodic homogeneous Markov Chain. The proof of global convergence of NCGA is presented is this paper. The upper bound of convergence speed of the NCGA is the same as the CGA. The possibly of retain the promising genes of NCGA is larger than CGA.

对于本人可以找到的32种典型的非线性优化测试函数，应用无交叉算子遗传算法，与基于经典遗传算法相比，在相同的进化代数的条件下，NCGA同样取得了略优的收敛速度，在相同CPU计算时间上NCGA也取得略优的结果； 3 提出了复合算子遗传算法。

In Chapter 6, based on discretization technique an implementable algorithm for nonconvex generalized semi-infinite minimax problems is presented and, utilizing properties of generalized quasi-directional derivative, its global convergence is proven under weak conditions.

对于广义极大极小问题，本文第六章在较弱的条件下，利用广义伪方向导数的性质，用离散化的技巧给出了非凸广义半无限极大极小问题的一种可实现的全局收敛算法。

Consistency of change-point estimator is proved and its rate of convergence is established under weak assumptions. To construct confidence interval, the limiting distribution of change-point estimator is obtained.

在较弱的条件下证明了变点估计的一致性，并得到了佑计的收敛率；为构造变点的置信区间给出了变点的极限分布。

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。