论文标题
对于某些S-ADIC瓷砖，没有绝对连续的衍射光谱
Absence of absolutely continuous diffraction spectrum for certain S-adic tilings
论文作者
论文摘要
准二元砖通常被认为是准晶体的结构模型。在这种情况下，重要的是要研究砖砌衍射度量的性质。在本文中，我们研究了r^d中的S-ADIC砖块的衍射度量，这些度量是由几何替代规则构建的。特别是，我们首先为衍射度量的绝对连续分量提供足够的条件，以使S-Adic平铺为零。接下来，我们证明了“几乎所有”二元块固定案例的足够条件，因此证明了大多数来自二进制块替代家族的S-ADIC块状都没有绝对连续的衍射光谱。
Quasiperiodic tilings are often considered as structure models of quasicrystals. In this context, it is important to study the nature of the diffraction measures for tilings. In this article, we investigate the diffraction measures for S-adic tilings in R^d, which are constructed from a family of geometric substitution rules. In particular, we firstly give a sufficient condition for the absolutely continuous component of the diffraction measure for an S-adic tiling to be zero. Next, we prove this sufficient condition for "almost all" binary block-substitution cases and thus prove the absence of the absolutely continuous diffraction spectrum for most of the S-adic tilings from a family of binary block substitutions.
