Modulated crystals and quasicrystals can simultaneously be described as modulated quasicrystals, a class of point sets introduced by de Bruijn in 1987. With appropriate modulation functions, modulated quasicrystals themselves constitute a substantial subclass of strongly almost periodic point measures. We re-analyse these structures using methods from modern mathematical diffraction theory, thereby providing a coherent view over that class. Similarly to de Bruijn's analysis, we find stability with respect to almost periodic modulations.

中文翻译：

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调制晶体和几乎周期性的措施

调制晶体和准晶体可以同时被描述为调制准晶体，这是 de Bruijn 在 1987 年引入的一类点集。通过适当的调制函数，调制准晶体本身构成了强几乎周期点测量的一个重要子类。我们使用现代数学衍射理论的方法重新分析这些结构，从而提供对该类的一致看法。与 de Bruijn 的分析类似，我们发现几乎周期性调制的稳定性。