Applications of the new class of atomic-fractal functions to problems of antenna synthesis

摘要

The new class of fractal functions based on specific properties of atomic functions (AF) y{sub}r and π{sub}m [1-2] is proposed and justified in this work. For the first time, the new types of atomic-fractal functions (AFF) constructed on the base of combinations of Kravchenko AFF with classical nondifferentiable Boltzano (1830), Weierstrass (1872), Besicovitch (1922), Van-der-Waerden (1930), etc. functions [3-5] are obtained. The work consists of two parts. First of them is devoted to foundations of AF and their fractal properties. Here, the construction of AFF is also described. In the second part the applications of AFF for solving some problems of synthesis of discrete and continuous fractal radiating structures are presented. Numerical experiments and their comparison with results obtained by D. Werner et. al. [6] prove the efficiency of the new class of AFF.