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Title: | Q-periodicity, self-similarity and weierstrass-mandelbrot function | Authors: | Erkuş, Soner | Advisors: | Pashaev, Oktay | Publisher: | Izmir Institute of Technology | Abstract: | 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. | Description: | Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2012 Includes bibliographical references (leaves: 92-94) Text in English; Abstract: Turkish and English viii, 98 leaves |
URI: | http://hdl.handle.net/11147/3552 |
Appears in Collections: | Master Degree / Yüksek Lisans Tezleri |
Files in This Item:
File | Description | Size | Format | |
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T001084.pdf | MasterThesis | 774.27 kB | Adobe PDF | View/Open |
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