以下为句子列表：
英文: By the mean's inequality and truncated method, the upper bound of the distribution of the partial sums is given.
中文: 利用矩不等式和截尾方法，得到了部分和分布函数的上界。
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英文: Degenerate slice indices are handled gracefully: an index that is too large is replaced by the string size, an upper bound smaller than the lower bound returns an empty string.
中文: 退化的切片索引处理方式很优美：过大的索引代替为字符串大小，下界比上界大的返回空字符串。
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英文: Next, the lower and upper bound expressions are evaluated, insofar they are present; defaults are zero and the sequence's length.
中文: 下一步，在它们所出现的范围内，对上下限表达式求值；缺省值是零和序列长度。
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英文: The paper discuss the upper bound of the distribution of the partial sums of identically distributed mixing random variables.
中文: 摘要本文讨论了同分布混合序列部分和分布函数的上界及其应用。
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英文: Using matrix theory, we present a sharp upper bound on the spectral radius of digraphs and strongly connected diagraphs.
中文: 摘要利用矩阵理论，给出了简单有向图的谱半径可达上界和强连通有向图的谱半径上界。
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