DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F24%3APU151701" target="_blank" >RIV/00216305:26210/24:PU151701 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyter.com/document/doi/10.1515/ms-2024-0055/html" target="_blank" >https://www.degruyter.com/document/doi/10.1515/ms-2024-0055/html</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/ms-2024-0055" target="_blank" >10.1515/ms-2024-0055</a>

Result language
angličtina
Original language name
DIGITAL JORDAN SURFACES ARISING FROM TETRAHEDRAL TILING
Original language description
We employ closure operators associated with n-ary relations, n > 1 an integer, to provide the digital space Z^3 with connectedness structures. We show that each of the six inscribed tetrahedra obtained by canonical tessellation of a digital cube in Z^3 with edges consisting of 2n - 1 points is connected. This result is used to prove that certain bounding surfaces of the polyhedra in Z^3 that may be face-to-face tiled with such tetrahedra are digital Jordan surfaces (i.e., separate Z^3 into exactly two connected components). An advantage of these Jordan surfaces over those with respect to the Khalimsky topology is that they may possess acute dihedral angles pi/4 while, in the case of the Khalimsky topology, the dihedral angles may never be less than pi/2.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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