Zobrazit minimální záznam



dc.contributor.authorMasáková , Zuzana
dc.contributor.authorMazáč , Jan
dc.date.accessioned2018-01-18T08:11:22Z
dc.date.available2018-01-18T08:11:22Z
dc.date.issued2017
dc.identifier.citationActa Polytechnica. 2017, vol. 57, no. 6, p. 430-445.
dc.identifier.issn1210-2709 (print)
dc.identifier.issn1805-2363 (online)
dc.identifier.urihttp://hdl.handle.net/10467/73719
dc.description.abstractAmong the commonly used mathematical models of quasicrystals are Delone sets constructed using a cut-and-project scheme, the so-called cut-and-project sets. A cut-and-project scheme (L,π1, π2) is given by a lattice L in Rs and projections π1, π2 to suitable subspaces V1, V2. In this paper we derive several statements describing the connection between self-similarity transformations of the lattice L and transformations of its projections π1(L), π2(L). For a self-similarity of a set Σ we take any linear mapping A such that AΣ ⊂ Σ, which generalizes the notion of self-similarity usually restricted to scaled rotations. We describe a method of construction of cut-and-project scheme such that π1(L) ⊂ R2 is invariant under an isometry of order 5. We describe all linear self-similarities of the scheme thus constructed and show that they form an 8-dimensional associative algebra over the ring Z. We perform an example of a cut-and-project set with linear self-similarity which is not a scaled rotation.en
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherČeské vysoké učení technické v Prazecs
dc.publisherCzech Technical University in Pragueen
dc.relation.ispartofseriesActa Polytechnica
dc.relation.urihttps://ojs.cvut.cz/ojs/index.php/ap/article/view/4587
dc.rightsCreative Commons Attribution 4.0 International Licenseen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subjectself-similarityen
dc.subjectquasicrystalen
dc.subjectcut-and-project schemeen
dc.titleON SELF-SIMILARITIES OF CUT-AND-PROJECT SETS
dc.typearticleen
dc.date.updated2018-01-18T08:11:22Z
dc.identifier.doi10.14311/AP.2017.57.0430
dc.rights.accessopenAccess
dc.type.statusPeer-reviewed
dc.type.versionpublishedVersion


Soubory tohoto záznamu



Tento záznam se objevuje v následujících kolekcích

Zobrazit minimální záznam

Creative Commons Attribution 4.0 International License
Kromě případů, kde je uvedeno jinak, licence tohoto záznamu je Creative Commons Attribution 4.0 International License