收敛

The major subjects in the approximation of operators are to study the convergent property of a sequence of linear operators, the quantization of its convergence rate and the saturation results in the theory of approximations.

算子逼近论主要是研究线性算子列的收敛性质，收敛速度的量化以及逼近论中的饱和现象。

If the Landweber method and pre-iteration method were convergent, the residue sequence would be monotone decreasing. By analyzing the convergence, the fact is demonstrated that for the severe ill-conditioned matrix of sensitivity coefficient, because of the limitation of the precision of the computer, the residue sequence is not monotone decreasing; thereby the reconstruction images diverge from the true distribution of the conductivity. So the generalized inverse method with threshold is established and the selection way of the regularization parameter is presented, by which the better images are reconstructed.

Landweber法和预迭代法收敛，则其残差序列单调递减，通过对它们的收敛性进行分析，证实对于病态性严重的灵敏度系数矩阵，由于受计算精度的限制，迭代过程中的残差序列不再单调递减，从而导致重建图象偏离实际电导率分布，因此作者建立了带阈值的广义逆算法，提出了规则化参数选择方法，获得了较好的图象重建质量。

Then we detailed proved the EM algorithm is convergent and the series generated by the EM algorithm is also convergent.

然后详细证明了本模型中EM算法是收敛的，并且产生的序列也是收敛的。

Theorem 8 If the series converges absolutely, the series must be convergent.

定理8 如果级数绝对收敛，则级数必定收敛。

Then the Fourier series of is convergent, and the sum function is if is continuous at ;If is the discontinuity point of , the sum function is

当是的连续点时，级数收敛于；当是的间断点时，级数收敛于

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。

Compared with standard genetic algorithm, it has the better convergent ability and speed.

与标准遗传算法相比，它具有更好的全局收敛能力与收敛速度。

Under some reasonable conditions, it is proved that the algorithm is locally and globally convergent.

在合适的条件下，证明了算法的全局收敛性和局部二次收敛性。

Experimental results show that new algorithm is characterized by higher convergent probability and convergent speed.

新方法具有更高的收敛概率和收敛速度。

However, the smoothness and convergence of these methods are not satisfactory. Because cubic spline function can be a piecewise, and its second order derivative is continuous, it is smooth and convergent.

但以上算法的光滑性和收敛性不好，而三次样条函数具有连续的二阶导数，且可采用分段函数的形式，具有很好的光滑性和收敛性。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐