Absence of absolutely continuous diffraction spectrum for certain S-adic tilings

Quasiperiodic tilings are often considered as structure models of quasicrystals. In this context, it is important to study the nature diffraction measures for tilings. article, we investigate S-adic in R^d, which constructed from a family geometric substitution rules. particular, firstly give sufficient condition absolutely continuous component measure an tiling be zero. Next, prove "almost all" binary block-substitution cases and thus absence spectrum most block substitutions.