弱收敛

In Part two, it is proved that, the evolution strategy of uniform distribution for continuous functions, asymptotically converges to the global optimal solutions in probability, by using central limit theorem, under suitable conditions. Then a new kind of evolution strategies is proposed.

第二部分，针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的进化策略是依概率收敛的，然后给出了采用一般连续型随机变量作为变异算子的进化策略依概率收敛的证明。

In view of continuous function problems,it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem.Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收敛，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收敛的证明。

The main results areas follows: On the invariants of λ-multiplier convergent series, first, it proves that ifλ- has the signed weak gliding hump property, the λ-multiplier convergentseries has the dual invariant.

获得了如下研究成果：在〓数乘收敛级数的不变性方面，首先证明了若〓具有弱滑脊性，那么〓数乘收敛级数具有对偶不变性。

By using modified conditions for dominant function,we establish extended dominated convergence theorem and obtain an application to integral operators with weak singularity , which simplifies the proof of the classical conclusion.

本文研究了一类推广的控制收敛定理及其应用，利用对控制函数满足条件的修改，建立了推广的控制收敛定理，获得其在弱奇异性积分算子中的应用，简化了经典结论的证明。

Its global convergence and linear convergence rate were proved under some mild conditions.

提出一类新的求解无约束优化问题的记忆梯度法，在较弱条件下证明了算法具有全局收敛性和线性收敛速率。

The variational convergence of real function sequence is extended to vector function sequence and the lower semicontinuity of approximating set of weak Pareto solutions of a given multiobjective decision making problem with general constraint set is obtained by using the variational convergence.

本文将函数序列的v－收敛性推广到向量值函数，在v－收敛性的条件下得到了给定的多目标决策问题的近似弱有效解集的下半连续性并给出了若干容易验证的充分条件。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

Under mild conditions, we prove the global and superlinear convergence of the method.

在较弱的条件下，得到了算法的全局收敛性及其超线性收敛性。

Under weaker conditions, we show that this method converges quadratically.

最后，在比广义互补问题其他算法收敛条件弱的情况下，我们证明了该算法二次收敛。

It is proved that Newton iteration method is still quadratically convergent under a weak condition, and a new point is added to Newton s method , i.

本文讨论求解非线性方程的牛顿法，证明牛顿法在一个弱条件下仍保持局部二阶收敛性，给出牛顿法的一点改进，即一个不带导数的单参数的二阶收敛的迭代法，而且分别得到这两种迭代法的收敛因子，最后进行数值实验

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。