Zobrazeno 1 - 10
of 17
pro vyhledávání: '"Manuel Joseph C. Loquias"'
Autor:
Manuel Joseph C. Loquias
Publikováno v:
2019-20 MATRIX Annals ISBN: 9783030624965
A lattice \(\Gamma\) (of rank and dimension d) is a discrete subset of ℝd that is the \(\mathbb{Z}\)-span of d linearly independent vectors v1, . . . ,vd \(\in\) ℝd over ℝ. The set {v1, . . . ,vd} is called a basis for \(\Gamma\) , and \(\Gamma
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7590e89b579d16b6aa5bc12417e6fbd5
https://doi.org/10.1007/978-3-030-62497-2_51
https://doi.org/10.1007/978-3-030-62497-2_51
A linear isometry $R$ of $\mathbb{R}^d$ is called a similarity isometry of a lattice $\Gamma \subseteq \mathbb{R}^d$ if there exists a positive real number $\beta$ such that $\beta R\Gamma$ is a sublattice of (finite index in) $\Gamma$. The set $\bet
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f81d2346cd94bf6d7c59036af495d1a9
http://arxiv.org/abs/2002.07460
http://arxiv.org/abs/2002.07460
Publikováno v:
Journal of Number Theory. 171:358-390
Let $P, Q\in \mathbb{F}_q[X]\setminus\{0\}$ be two coprime polynomials over the finite field $\mathbb{F}_q$ with $\operatorname{deg}{P} > \operatorname{deg}{Q}$. We represent each polynomial $w$ over $\mathbb{F}_q$ by \[w=\sum_{i=0}^k\frac{s_i}{Q}{\l
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb12d610f8da556902afe1fa1d611c67
https://doi.org/10.1016/j.jnt.2016.07.021
https://doi.org/10.1016/j.jnt.2016.07.021
We show by construction that every rhombic lattice $\Gamma$ in $\mathbb{R}^{2}$ has a fundamental domain whose symmetry group contains the point group of $\Gamma$ as a subgroup of index $2$. This solves the last open case of a question raised in [3]
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2a69e6c3a99f4258404ff80633276afc
Publikováno v:
Aperiodic 2018 ("9th Conference on Aperiodic Crystals").
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::60a8aa3aef2f3242a54a2166aba59a44
https://doi.org/10.31274/aperiodic2018-180810-22
https://doi.org/10.31274/aperiodic2018-180810-22
A submodule of a $\mathbb{Z}$-module determines a coloring of the module where each coset of the submodule is associated to a unique color. Given a submodule coloring of a $\mathbb{Z}$-module, the group formed by the symmetries of the module that ind
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ef7fc2bc0240896186a0b964b21c8289
Publikováno v:
Zeitschrift für Kristallographie - Crystalline Materials. 223:483-491
If $G$ is the symmetry group of an uncolored pattern then a coloring of the pattern is semiperfect if the associated color group $H$ is a subgroup of $G$ of index 2. We give results on how to identify and enumerate all inequivalent semiperfect colori
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4458779316ec138053d8ec41a9839c0d
https://doi.org/10.1524/zkri.2008.0053
https://doi.org/10.1524/zkri.2008.0053
Autor:
Manuel Joseph C. Loquias, Peter Zeiner
Even though a lattice and its sublattices have the same group of coincidence isometries, the coincidence index of a coincidence isometry with respect to a lattice $\Lambda_1$ and to a sublattice $\Lambda_2$ may differ. Here, we examine the coloring o
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::246b2051ffbbcdce422ee0d1985587f3
We obtain tilings with a singular point by applying conformal maps on regular tilings of the Euclidean plane, and determine its symmetries. The resulting tilings are then symmetrically colored by applying the same conformal maps on colorings of regul
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::325bd3a2514d3c7a17d5f2f28e7512bd
Publikováno v:
Acta Crystallographica Section A Foundations and Advances. 73:C289-C289
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c3d9aa335084cb1ef8a01546b596d11d
https://doi.org/10.1107/s2053273317092841
https://doi.org/10.1107/s2053273317092841