Name
Abstract | ||
|---|---|---|
We extend the definition of the Costas property to functions in the continuum, namely on intervals of the Deals or the rationals, and argue that such functions can be used in the same applications as discrete Costas arrays. We construct Costas bijections in the real continuum within the class of piecewise continuously differentiable functions, but our attempts to construct a fractal-like Costas bijection there are successful only under slight but necessary deviations from the usual arithmetic laws. The situation over the rationals is different: there, we propose a method of great generality and flexibility for the construction of a Costas fractal bijection. Its success, though, relies heavily on the enumerability of the rationals, and therefore it cannot be generalized over the Deals in an obvious way. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.3934/amc.2008.2.113 | ADVANCES IN MATHEMATICS OF COMMUNICATIONS |
Keywords | Field | DocType |
Costas property,continuum,rational continuum,piecewise continuously differentiable bijections,Golomb construction,Welch construction | Discrete mathematics,Rational number,Combinatorics,Bijection,Fractal,Continuum (design consultancy),Pure mathematics,Bijection, injection and surjection,Smoothness,Mathematics,Piecewise,Generality | Journal |
Volume | Issue | ISSN |
2 | 2 | 1930-5346 |
Citations | PageRank | References |
1 | 0.35 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Konstantinos Drakakis | 1 | 78 | 8.09 |
| Scott Rickard | 2 | 149 | 13.09 |