Results 21 to 30 of about 165,995,511 (248)
Structure of cubic mapping graphs for the ring of Gaussian integers modulo n [PDF]
Czechoslovak Mathematical Journal, 2012 Let \(\mathbb {Z}_n[i]\) be the ring of Gaussian integers modulo \(n\). The authors construct for \(\mathbb {Z}_n[i]\) a cubic iteration digraph \(\Gamma (n)\) whose vertex set consists of all the elements of \(\mathbb {Z}_n[i]\), and for which there is a directed edge from \(a \in \mathbb {Z}_n[i]\) to \(b \in \mathbb {Z}_n[i]\) if \(b = a^3\). Let \(\
Wei, Yangjiang, Nan, Jizhu, Tang, Gaohua
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The Diophantine equation ax2+2bxy−4ay2=±1
International Journal of Mathematics and Mathematical Sciences, 2003 We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy−4ay2=±1, where a and b are nonnegative integers.
Lionel Bapoungué
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Symmetry-Imposed Selection Rules for Excitations of Nontrivial Plasmonic Topologies. [PDF]
Adv Sci (Weinh)A unified group‐theory selection rule governs the excitation of vectorial nearfield topologies across three plasmonic spin states. Derived from first principles, it predicts spin–orbit vortex splitting and multidimensional nested vortices, confirmed by phase‐resolved in situ measurements.
Yang J +14 more
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Torsion-free crystallographic groups with indecomposable holonomy group II. [PDF]
, 2004 Let K be a principal ideal domain, G a finite group, and M a KG-module which is a free K-module of finite rank on which G acts faithfully. A generalized crystallographic group is a non-split extension C of M by G such that conjugation in C induces the G ...
Bódi, Viktor +3 more
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, 2013 This research was presented during the 2012 International Symposium on Information Theory and its Applications (ISITA2012) in Honolulu, USA.Gaussian integer is one of basic algebraic integers.
Mizushima Daichi +7 more
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Mathematics, 2017 In this study, we consider codes over Euclidean domains modulo their ideals. In the first half of the study, we deal with arbitrary Euclidean domains.
Hajime Matsui
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Construction of Period
IEEE Access, 2018 The degree of a perfect Gaussian integer sequence (PGIS) is defined as the number of distinct nonzero Gaussian integers within one period of the sequence. This paper focuses on constructing PGISs with degrees equal to or larger than four and period of N =
Ho-Hsuan Chang +2 more
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An objective representation of the Gaussian integers [PDF]
, 2004 A rig is a riNg without Negatives. We analyse the free rig on a generator x subject to the equivalence x = 1 + x + x<sup>2</sup>, showing that in it the non-constant polynomials form a ring.
Fiore, M. +3 more
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Известия Иркутского государственного университета: Серия "Математика"The results of the paper relate to the following general problem. Find natural finite generating sets of elements of a given linear group over a finitely generated commutative ring.
Ya.N. Nuzhin, T. B. Shaipova
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Complete residue systems in the ring of matrices of rational integers
International Journal of Mathematics and Mathematical Sciences, 1978 This paper deals with the characterizations of the complete residue system mod. G, where G is any n×n matrix, in the ring of n×n matrices.
Jau-Shyong Shiue, Chie-Ping Hwang
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