Digital Jordan surfaces arising from tetrahedral tiling
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Josef Šlapal
Abstract
We employ closure operators associated with n-ary relations, n > 1 an integer, to provide the digital space ℤ3 with connectedness structures. We show that each of the six inscribed tetrahedra obtained by canonical tessellation of a digital cube in ℤ3 with edges consisting of 2n − 1 points is connected. This result is used to prove that certain bounding surfaces of the polyhedra in ℤ3 that may be face-to-face tiled with such tetrahedra are digital Jordan surfaces (i.e., separate ℤ3 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
The work was supported by the Brno University of Technology under the Specific Research Project no. FSI-S-23-8161.
Communicated by Tibor Macko
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- Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
- A general formula in composition theory
- A nonlinear Filbert-like matrix with three free parameters: From linearity to nonlinearity
- On universality in short intervals for zeta-functions of certain cusp forms
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- Kneser-type oscillation theorems for second-order functional differential equations with unbounded neutral coefficients
- Approximation theorems via Pp-statistical convergence on weighted spaces
- Global existence and multiplicity of positive solutions for anisotropic eigenvalue problems
- Theoretical analysis of higher-order system of difference equations with generalized balancing numbers
- On a solvable difference equations system of second order its solutions are related to a generalized Mersenne sequence
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- Digital Jordan surfaces arising from tetrahedral tiling
- Influence of ideals in compactifications
- On the functions ωf and Ωf
- On the 𝓐-generators of the polynomial algebra as a module over the Steenrod algebra, I
- A bivariate distribution with generalized exponential conditionals
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