提出一种基于齐次模型的信赖域算法，传统的基于二次模型的信赖域算法只是它的一个特例。

This paper presents a trust region algorithm based upon the homogeneous model. The traditional trust region algorithm based on the quadratic model is one of its special cases.

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利用齐次离散时间马尔可夫链模型描述了大地震沿一条活动断裂带的迁移过程。

A homogeneous discrete-time Markov chains model is used to characterize migration of large earthquakes along an active fault zone.

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然后，我们证明：在较弱的条件下，从决定性的初始产综出发，齐次的随机模型必定走向崩溃。

Then, we prove that under some weaker assumptions, the homogeneous Stochastic models starting from a deterministic initial vector should go to collapse with probability one.

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