On Costas Sets and Costas Clouds
We abstract the definition of the Costas property in the context of a group and study specifically dense Costas sets (named Costas clouds) in groups with the topological property that they are dense in themselves: as a result, we prove the existence of nowhere continuous dense bijections that satisf...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/467342 |
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| _version_ | 1832545384030797824 |
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| author | Konstantinos Drakakis |
| author_facet | Konstantinos Drakakis |
| author_sort | Konstantinos Drakakis |
| collection | DOAJ |
| description | We abstract the definition of the Costas property in the context of a group and study specifically dense
Costas sets (named Costas clouds) in groups with the topological property that they are dense in themselves:
as a result, we prove the existence of nowhere continuous dense bijections that satisfy the Costas property on ℚ2, ℝ2, and ℂ2, the latter two being based on nonlinear solutions of Cauchy's functional equation, as well as on
ℚ, ℝ, and ℂ, which are, in effect, generalized Golomb rulers. We generalize the Welch and Golomb construction
methods for Costas arrays to apply on ℝ and ℂ, and we prove that group isomorphisms on and tensor products of Costas sets result to new Costas sets with respect to an appropriate set of distance vectors. We also give two constructive examples of a nowhere continuous function that satisfies a constrained form of the Costas property (over rational or algebraic displacements only, i.e.), based on the indicator function of a dense subset of ℝ. |
| format | Article |
| id | doaj-art-904b580805f040bfa6da146dd1321dea |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-904b580805f040bfa6da146dd1321dea2025-02-03T07:26:00ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/467342467342On Costas Sets and Costas CloudsKonstantinos Drakakis0UCD CASL, University College Dublin, Belfield, Dublin 4, IrelandWe abstract the definition of the Costas property in the context of a group and study specifically dense Costas sets (named Costas clouds) in groups with the topological property that they are dense in themselves: as a result, we prove the existence of nowhere continuous dense bijections that satisfy the Costas property on ℚ2, ℝ2, and ℂ2, the latter two being based on nonlinear solutions of Cauchy's functional equation, as well as on ℚ, ℝ, and ℂ, which are, in effect, generalized Golomb rulers. We generalize the Welch and Golomb construction methods for Costas arrays to apply on ℝ and ℂ, and we prove that group isomorphisms on and tensor products of Costas sets result to new Costas sets with respect to an appropriate set of distance vectors. We also give two constructive examples of a nowhere continuous function that satisfies a constrained form of the Costas property (over rational or algebraic displacements only, i.e.), based on the indicator function of a dense subset of ℝ.http://dx.doi.org/10.1155/2009/467342 |
| spellingShingle | Konstantinos Drakakis On Costas Sets and Costas Clouds Abstract and Applied Analysis |
| title | On Costas Sets and Costas Clouds |
| title_full | On Costas Sets and Costas Clouds |
| title_fullStr | On Costas Sets and Costas Clouds |
| title_full_unstemmed | On Costas Sets and Costas Clouds |
| title_short | On Costas Sets and Costas Clouds |
| title_sort | on costas sets and costas clouds |
| url | http://dx.doi.org/10.1155/2009/467342 |
| work_keys_str_mv | AT konstantinosdrakakis oncostassetsandcostasclouds |