We use period extension or symmetry extension in image processing. Our arithmetic has perfect properties that validated by numeric experiments in image compression.

图像的边界延拓我们采取周期延拓或对称延拓方式，图像压缩的数字实验验证了算法的优良性。

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General Musharraf's assumption of power was later validated by the supreme court of Pakistan for a period of three years.

BBC: Kargil conflict