Q-periodicity, self-similarity and weierstrass-mandelbrot function için kapak resmi
Q-periodicity, self-similarity and weierstrass-mandelbrot function
Başlık:
Q-periodicity, self-similarity and weierstrass-mandelbrot function
Yazar:
Erkuş, Soner.
Yazar Ek Girişi:
Yayın Bilgileri:
[s.l.]: [s.n.], 2012.
Fiziksel Tanımlama:
viii, 98leaves.: ill.+ 1 computer laser optical disc.
Özet:
In the present thesis we study self-similar objects by method’s of the q-calculus. This calculus is based on q-rescaled finite differences and introduces the q-numbers, the qderivative and the q-integral. Main object of consideration is the Weierstrass-Mandelbrot functions, continuous but nowhere differentiable functions. We consider these functions in connection with the q-periodic functions. We show that any q-periodic function is connected with standard periodic functions by the logarithmic scale, so that q-periodicity becomes the standard periodicity. We introduce self-similarity in terms of homogeneous functions and study properties of these functions with some applications. Then we introduce the dimension of self-similar objects as fractals in terms of scaling transformation. We show that q-calculus is proper mathematical tools to study the self-similarity. By using asymptotic formulas and expansions we apply our method to Weierstrass-Mandelbrot function, convergency of this function and relation with chirp decomposition.
Yazar Ek Girişi:
Tek Biçim Eser Adı:
Thesis (Master)--İzmir Institute of Technology:Mathematics.

İzmir Institute of Technology:Mathematics--Thesis (Master).
Elektronik Erişim:
Access to Electronic Versiyon.
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