This paper analyses the influence of scale factor on moment invariant features in discrete, constructs a new moment invariant with both scale, translation and rotating invariance.

分析了在离散状态下比例因子对不变矩特征的影响，构造了一种新的不变矩，使其具有平移、旋转和比例因子的不变性。

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By using this new expression, we derive a perturbation bound for the subunitary polar factor for any unitarily invariant norm.

本文证明了此方程存在唯一的正定解，并推导出此正定解的扰动边界和条件数的显式表达式。

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Some applications, including the Aharonov-Bohm effect, are considered for the special case of adiabatic evolution, this phase factor is a gauge-invariant generalization of the one found by Berry.

一些应用，包括AB效应，被认为是绝热演化，即由Berry发现的、作为一个规范不变量的推广的相因子的特殊情况。

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