English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In a previous paper [arXiv:1006.3807], the authors obtained tube formulas forcertain fractals under rather general conditions. Based on these formulas, wegive here a characterization of Minkowski measurability of a certain class ofself-similar tilings and self-similar sets. Under appropriate hypotheses,self-similar tilings with simple generators (more precisely, monophasegenerators) are shown to be Minkowski measurable if and only if the associatedscaling zeta function is of nonlattice type. Under a natural geometriccondition on the tiling, the result is transferred to the associatedself-similar set (i.e., the fractal itself). Also, the latter is shown to beMinkowski measurable if and only if the associated scaling zeta function is ofnonlattice type.

Minkowski measurability results for self-similar tilings and fractals with monophase generators