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Some necesarry and sufficient coditions for generalized diagonal dominance for matrices are discussed by using the determinant and the closed convex cone generated by matrices column vectors. This paper, thus provides some new methoods for determining the generalized diagonal dominance in matrices.

利用矩阵的列向量所生成的闭凸锥及矩阵的行列式来讨论其行广义对角占优的若干充要条件，为判别矩阵是否为广义对角占优提供若干新方法。

Then, through quadratic separators, the sufficient condition of the fault tolerant controller existence can be transformed into the problem of solving some limited number of linear matrix inequalities, including each vertex of the convex polyhedron.

然后，通过二次可分原理，求解只包含关于凸多面体各顶点的有限个线性矩阵不等式，给出了容错控制器存在的充分条件。

Necessary and sufficient conditions of the robust positively invariant sets are established for the linear discrete-time system family specified by matrix convex polyhedron and additive interval disturbances.

对由矩阵凸多面体和加性区间扰动描述的线性时变离散系统族，得到了鲁棒正不变集的充分必要条件；对非线性系统族则得到有关充分条件。

For linear time-delay systems with norm-bounded uncertainties or convex polyhedron uncertainties, a sufficient and necessary delay independent condition of quadratic stabilizability under certain robust H~?

讨论了具有范数有界不确定参数线性不确定时滞系统的指定衰减度鲁棒稳定的一个充分性判据以及设计状态反馈控制器使得闭环系统具有指定鲁棒衰减度的方法。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

In the second we give the necessary and sufficient conditions for strict convexity of power function of exponential family in the discrete case.

在第二个问题中，我们给出了在离散的情形下，指数族势函数严凸的充分必要条件。

By weakening the premise of the convexity of the objective function required in paper[7], we prove the sufficient desent property and the global convergence with the strong Wolfe line search.

在第二章中，我们参照文献[7]中的方法，提出了一类与HS算法相关的共轭梯度算法，并减弱了文[7]中要求目标函数二阶连续可微且为凸的前提条件，采用强Wolfe线搜索，在较弱的条件下证明了这一类算法具有充分下降性和全局收敛性。

We have sufficient evidence to convict him.

我们有充分的证据证明他有罪。

And afterwards I was very glad that the coolie had been killed; it put me legally in the right and it gave me a sufficient pretext for shooting the elephant.

然后我非常高兴的小工身亡，它把我的合法的权利和它的给我一个足够的借口射击的大象。

This department with excellent products, reasonable price and perfect service, will become your cooperator that you can sufficient trust.

本部将以优质的产品、合理的价格、完善的服务，成为您足以信赖的合作伙伴

I can not negligent, he should do what?

我不能不在意了，他要做什么呢？

It is very dangerous to swim in the river alone.

一个人到河里游泳是很危险的。