以下为句子列表：
英文: A partitioned optimal filtering algorithm for multi-channel systems with multiplicative noise among observation channels is proposed.
中文: 摘要针对多通道观测环境下带乘性噪声系统的最优滤波问题，提出了1种状态最优滤波的分部算法。
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英文: Abstract: Using the notion of fuzzy point, the concept of weak implicative ideal is introduced, and the equivalence between fuzzy implicative ideal and weak implicative ideal, weak ideal and weak implicative ideal are also given.
中文: 文摘:运用模糊点的概念,引入了弱关联理想的概念,给出了模糊关联理想与弱关联理想、弱理想与弱关联理想的等价关系.
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英文: Another way for enlarging sentence type is to increase modifiers and use subordinate clauses. i.e.to make the thought complicative by using subordinate clauses.
中文: 句型扩大的另一种方法是增加修饰语和使用从属分句。也就是说，利用从属分句来使思想表达复杂化。
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英文: At the same time, for the process additive and multiplicative uncertainties mostly encountered in practice, the sufficient and necessary conditions for holding the control system robust stability are analyzed, and thus, an intuitive determination method i
中文: 同时，对于实际中最常见的被控过程的加性和乘性不确定性，分析了控制系统保证鲁棒稳定性的充要条件，由此给出了基于谱半径判据的直观判定方法。
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英文: Based on the article [1], we discuss and prove two sufficient and necessary conditions of multiplicative convex functions. We also prove the other two theorems about multiplicative convex functions.
中文: 摘要在文献[1]的基础上，讨论并证明了积性凸函数的两个充分必要条件，同时证明了积性凸函数的另外两个定理。
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