Atomic-fractal Functions in Problems of Antenna Synthesis

Кравченко, В. Ф.; Potapov, Aleksander Alekseevich; Masyuk, V. M.

doi:10.1615/telecomradeng.v56.i6-7.20

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-The Family Of Aff Y R and ( ) M X π1

-Synthesis Of Atomic-fractal Radiation Patterns1

-Introduction1

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“…Taking into account ideas and results presented in [5] and according to [9], we can construct the new class of AFF by multiplying distributions by another fractal function (Weierstrass, Cantor, Besicovitch, Van-der-Waerden, etc. ).…”

Section: -The Family Of Aff Y R and ( ) M X πmentioning

confidence: 99%

“…A family of functions, called the generalized Weierstrass functions [5] are known to play a pivotal role in the theory of fractal radiation pattern synthesis. These functions are everywhere continuous but nowhere differentiable and exhibit fractal behavior at all scales.…”

Section: -Synthesis Of Atomic-fractal Radiation Patternsmentioning

confidence: 99%

“…The new class of fractal functions based on specific properties of atomic functions (AF) y r and π m [1][2][3][4][5][6][7] 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.…”

Section: -Introductionmentioning

confidence: 99%

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