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On Costas Sets and Costas Clouds
Author
Source
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-11-23
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Drakakis, Konstantinos. 2009. On Costas Sets and Costas Clouds. Abstract and Applied Analysis،Vol. 2009, no. 2009, pp.1-23.
https://search.emarefa.net/detail/BIM-473810
Modern Language Association (MLA)
Drakakis, Konstantinos. On Costas Sets and Costas Clouds. Abstract and Applied Analysis No. 2009 (2009), pp.1-23.
https://search.emarefa.net/detail/BIM-473810
American Medical Association (AMA)
Drakakis, Konstantinos. On Costas Sets and Costas Clouds. Abstract and Applied Analysis. 2009. Vol. 2009, no. 2009, pp.1-23.
https://search.emarefa.net/detail/BIM-473810
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-473810