1. Regular antilatticesKarin Cvetko-Vah, Michael Kinyon, Jonathan Leech, Tomaž Pisanski, 2019, original scientific article Abstract: Antilattices ▫$(S; \vee, \wedge)$▫ for which the Green's equivalences ▫$\mathcal{L}_{(\vee)}$▫, ▫$\mathcal{R}_{(\vee)}$▫, ▫$\mathcal{L}_{(\wedge)}$▫ and ▫$\mathcal{R}_{(\wedge)}$▫ are all congruences of the entire antilattice are studied and enumerated.
Keywords: noncommutative lattice, antilattice, Green's equivalences, lattice of subvarieties, enumeration, partition, composition
Published in RUP: 03.01.2022; Views: 1076; Downloads: 16
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5. Three-pencil lattice on triangulationsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2007, published scientific conference contribution Abstract: In this paper, three-pencil lattices on triangulations are studied. The explicit representation of a lattice, based upon barycentric coordinates, enables us to construct lattice points in a simple and numerically stable way. Further, this representation carries over to triangulations in a natural way. The construction is based upon group action of S 3 on triangle vertices, and it is shown that the number of degrees of freedom is equal to the number of vertices of the triangulation.
Keywords: numerical analysis, lattice, barycentric coordinates, triangulations, interpolation
Published in RUP: 03.04.2017; Views: 2123; Downloads: 84
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6. Barycentric coordinates for Lagrange interpolation over lattices on a simplexGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2008, published scientific conference contribution Abstract: In this paper, a ▫$(d+1)$▫-pencil lattice on a simplex in ▫${\mathbb{R}}^d$▫ is studied. The lattice points are explicitly given in barycentric coordinates. This enables the construction and the efficient evaluation of the Lagrange interpolating polynomial over a lattice on a simplex. Also, the barycentric representation, based on shape parameters, turns out to be appropriate for the lattice extension from a simplex to a simplicial partition.
Keywords: numerical analysis, lattice, barycentric coordinates, simplex, interpolation
Published in RUP: 03.04.2017; Views: 2234; Downloads: 139
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7. Lattices on simplicial partitionsGašper Jaklič, Jernej Kozak, Marjetka Knez, Vito Vitrih, Emil Žagar, 2010, published scientific conference contribution Abstract: In this paper, a ▫$(d+1)$▫-pencil lattices on a simplex in ▫${\mathbb{R}}^d$▫ are studied. The barycentric approach naturally extends the lattice from a simplex to a simplicial partition, providing a continuous piecewise polynomial interpolant over the extended lattice. The number of degrees of freedom is equal to the number of vertices of the simplicial partition. The constructive proof of thisfact leads to an efficient computer algorithm for the design of a lattice.
Keywords: numerical analysis, lattice, barycentric coordinates, simplicial partition
Published in RUP: 03.04.2017; Views: 2143; Downloads: 135
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