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/

Zendy Plus

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

Zendy Tools

Zendy Open

We provide two methods to characterize the connectedness of all$d$-dimensional generalized Sierpi\'nski sponges whose corresponding IFSs areallowed to have rotational and reflectional components. Our approach is toreduce it to an intersection problem between the coordinates of graph-directedattractors. More precisely, let $(K_1,\ldots,K_n)$ be a Cantor-typegraph-directed attractor in $\mathbb{R}^d$. By creating an auxiliary graph, weprovide an effective criterion for whether $K_i\cap K_j$ is empty for everypair of $1\leq i,j\leq n$. Moreover, the emptiness can be checked by examiningonly a finite number of geometric approximations of the attractor. The approachis also applicable to more general graph-directed systems.

The connectedness of Sierpi\'nski sponges with rotational and reflectional components and associated graph-directed systems