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Furthermore, it is proved that convex combination of judgment matrix addition and convex combination of Hadamard multiplication in group AHP can remove the influence of subjective factors, and keep and improve the consistency of judgment matrix.

文中定义了具有实际意义的矩阵"加法"、"乘法"、"指数"运算，指出了这些运算的性质；给出了判断矩阵"加法"凸组合及Hadamard"乘法"凸组合的概念，并证明了在群体AHP中判断矩阵的"加法"凸组合及Hadamard"乘法"凸组合不仅能消除主观因素的影响，而且还能保持和改善判断矩阵的一致性。

In 1985,Guo Dajun proved that an increasing and α concave operator is of cone contraction,however,is an increasing and α convex operator of cone expansion ?

5年 ，郭大钧证明了增的α-凹算子是锥压缩的，那么增的α-凸算子是否是锥拉伸的呢？

It is proved that strictly efficient point set of the objective space is connected when objective function is cone convex－like,and that if objective function is cone convex set－valued mapping,then strictly efficient solution set is also connected.

证明了当目标函数为锥类凸的集值映射时，其目标空间里的严有效点集是连通的；若目标函数为锥凸的集值映射时，其严有效解集也是连通的。

It also provided the conditions for the existence of large cores of symmetric games. It proved the equivalence relation of convex games and monotonic symmetric games.

本章还给出了对称对策的广义核心存在的条件，证明了凸对策与单调对称对策的等价关系。

In this paper, we use the convex function to form the order statistic and the linear rank statistic, and the asymptotic normality of the statistics are proved.

本文用凸函数构造了线性次序统计量和线性秩统计量，并证明了它们的渐近正态性。

In view of that conventional algorithms of collision detection spend a lot of detection time on complex polyhedrons, an algorithm to divide a convex polyhedron was presented and proved.

针对传统的碰撞检测算法对于复杂多面体之间的碰撞检测时间过长的缺陷，提出并证明了一种凸多面体的剖分算法，该算法能将复杂的凸多面体剖分为简单四面体，利用基于MPI(Mes-sagePassingInterface)并行处理的方法来提高碰撞检测的实时性。

In this paper the topological properties of solution set of non-autonomous differential inclusions are discussed,and the fact that the mild solution set of Cauchy is a retract of a convex subset of a Banach space is proved.

讨论了半线性微分包含解的拓扑性质，证明了非自治情况下其适度解集是一Banach空间的凸子集的收缩核，且收缩映射连续依赖于初值。

Xu and Noor had proved the theorem on convergence of three-step iterations for asymptotically nonexpansive mapping on nonempty closed, bounded, and convex subset of uniformly convex Banach space.

王娴 ，何震Xu和Norr已经证明了建立在一致凸Banach空间的一个非空有界闭凸子集上的渐进非扩张映射的三步迭代的收敛定理问题。

A Lipschitz strictly pseudocontractive map from a nonempty closed convex subset of a Hilbert space into itself was showed to have fixed points, Ishikawa and Mann iterative sequences with errors of a Lipschitz strictly pseudocontractive map was introduced and the iteration processes strongly converges to a fixed point was proved.

证明了在Hilbert空间中的非空闭凸集上Lipschitz严格伪压缩映象有不动点，介绍了Lips-chitz严格伪压缩映像下的的具误差的 Ishikawa和Mann迭代序列并证明了其强收敛性于不动点，其结果把非扩张映像推广到Lipschitz严格伪压缩映象上，改进了一些相关结果。

For strictly convex problems, it is proved that the decomposed two-level problem is equivalent to the original one.

对于严格凸问题，证明了分解问题与原问题的等价性。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失