Costas Stefanis MD

Costas Stefanis MD

On Costas Sets and Costas Clouds

and Applied Analysis 3 2. Basics—The Costas Property 2.1. Notation We denote the set of the first n integers {1, 2, . . . , n} by n , and more generally the set {α β, α 2β, . . . , α nβ} by α β n ; in particular, n −1 {0, 1, . . . , n−1}. The set of algebraic real numbers, namely, those real numbers that can be solutions of polynomials with rational or, equivalently, integer coefficients, is de...

A Review of Costas Arrays

Costas arrays are not only useful in radar engineering, but they also present many interesting, and still open, mathematical problems. This work collects in it all important knowledge about them available today: some history of the subjects, density results, construction methods, construction algorithms with full proofs, and open questions. At the same time all the necessary mathematical backgr...

Open problems in Costas arrays

A collection of open problems in Costas arrays is presented, classified into several categories, along with the context in which they arise.

Algebraic Constructions for Costas Arrays

Thus, if ai,,j, = ail,il= ajl,j, = aiJqj4 = 1 in the matrix, we must not have ii2 1 il 3jjL;$) = (i4 4 ,.i, -jd, nor may we have (iz i,,j, -j,)= . ,. . 13 ‘2, 3 Such matri& have been called either Costas Arrays or constellations in Ref. [2], which explores constructions as well as applications for these patterns. It is convenient to represent these arrays on an n X n grid, using dots for the l’...