CHARACTERIZATION AND GENERATION OF ALPHA-DENSE CURVES

If a curve ranges through a cube H = Pi(i=1)(n)[a(i),b(i)] so that, fo r every point x is an element of H, there is at least a point in the c urve at a distance not greater than a positive number alpha, the curve is called alpha-dense in H. It is very important in the construction of such curves to find algorithms of approximation for global optimiza tion and, in fact, there are several methods to do it, e.g., [1-3]. In this paper, we give a characterization of such curves in terms of gam ma-stochastically independent functions, as well as a constructive met hod to generate them by means of only one function rho called gamma-un iformly distributed. Finally, in the above class, i.e., in the set of the gamma-uniformly distributed functions, we will choose one of them, will construct the corresponding curve, and will compute its theoreti c calculation time.