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By using the properties of part matrix elements in N1 , and by looking for positive diagonal matrix factors, we present some new sufficient conditions of generalized strictly diagonally dominant matrix and improve the recent results.

第二章在行非严格对角占优集N_1划分为N_1~(1)与N_1~(2)的直和N_1~(1)⊕N_1~(2)的条件下，利用下标在N_1上部分矩阵元素的性质，寻求正对角矩阵因子，给出了广义严格对角占优矩阵的几个新的充分条件，同时改进了近期的一些结果。

In chapter four, by defining and studying a type of local doublediagonally dominant matrix, we give some new criteria foridentifying generalized strictly diagonally dominant matrix, andextend some existing results.

第四章定义了一种局部双对角占优矩阵，给出了广义严格对角占优矩阵的几个新判别法，推广了已有的一些结果。

In chapter three, we divide the rows of matrix into types finer than those in chapter one. Again by looking for positive diagonal matrix factors, we obtain several new criteria for identifying generalized strictly diagonally dominant matrix, improving some existing criteria.

第三章在下标集N 递进式划分的条件下，根据递进后，某些下标集上部分矩阵元素的性质，寻求正对角矩阵因子，获得了广义严格对角占优矩阵的几个新判别法，同时改进了一些已有结果。

Moreover, when the normalized damping matrix is diagonally dominant, it is strictly shown that decoupling the modal equations by neglecting the off-diagonal elements indeed minimizes the error upper bound.

同时，还严格地证明了，当正则化的模态阻尼矩阵是对角占优时，由忽略其非对角线元素使模态方程解耦的方法所引起的误差的上限的确能达到最小。

In this paper, we give the upper bounds for inverse elements of strictly diagonally dominant periodic tridiagonal matrices.

本文给出了严格对角占优的周期三角矩阵逆元素的上界估计。

In our results, we do not require activation functions to be bounded,differentiable or strictly increasing.

同已有的结果相比，我们不要求函数有界，可微或严格增加等条件。

Therefore, it s very important to control the content of dimethyallylamine and dimethylamine, strictly in the polymerization.

因此，在DMDAAC的合成中应严格控制二甲胺、叔胺含量；对于氯化钠、叔胺盐酸盐、二甲胺盐酸盐可以考虑控制在1000mg·kg~(-1)之内以降低精制成本。

However, Diophantus\' solution is strictly algebraic, unlike the quasigeometric Babylonian solution.

但是，丢番图的解是严格代数的，而不像巴比伦人的解是拟几何的。

Company will strictly of the direct examination scoops out in the production, sale, each link in etc.

公司将严格的监督检验挖掘在生产、销售、售后服务等各个环节，同时，一批高素质的技术人员和职工队伍，兢兢业业的工作，使产品不断更新。

Since the B-spline is a locally supported function, the smoothing formula can be strictly limited in a neighborhood of each point. The smoothing surface defined by the smoothing formula has the same convexity as that of the original image. Secondly, the edge points are detected by either computing the local extremum points of the directional derivative or computing zero-crossing of the second-order directional derivative of the smoothing surface. Finally, an example of an edge detector is given.

针对反卷积视觉模型的病态性，增加了适当的约束，给出了基于低松弛迭代格式的快速自适应滤波算法，对于一个N×N输入图象，由于变换核的局部支撑性质以及低松弛迭代格式的引入，使得快速自适应滤波算法的计算复杂度降为象素个数N〓的线性量阶N〓，就最小二乘算法的复杂性而言，优于不动点迭代算法的O以及基于FFT的预处理共轭梯度算法的O。

It's bell can reach over a meter in diameter.

它的身体最大可以达到直径1米多。

Now they are overdue and I shall have to pay a fine.

现在他们过期了，我不得不付罚款。