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https://hdl.handle.net/11147/3552
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DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Pashaev, Oktay | en |
dc.contributor.author | Erkuş, Soner | - |
dc.date.accessioned | 2014-07-22T13:51:47Z | - |
dc.date.available | 2014-07-22T13:51:47Z | - |
dc.date.issued | 2012 | en |
dc.identifier.uri | http://hdl.handle.net/11147/3552 | - |
dc.description | Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2012 | en |
dc.description | Includes bibliographical references (leaves: 92-94) | en |
dc.description | Text in English; Abstract: Turkish and English | en |
dc.description | viii, 98 leaves | en |
dc.description.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. | en |
dc.language.iso | en | en_US |
dc.publisher | Izmir Institute of Technology | en |
dc.rights | info:eu-repo/semantics/openAccess | en_US |
dc.subject.lcsh | Fourier transformations | en |
dc.subject.lcsh | Mandelbrot sets | en |
dc.subject.lcsh | Fractals | en |
dc.subject.lcsh | Mellin transform | en |
dc.title | Q-periodicity, self-similarity and weierstrass-mandelbrot function | en_US |
dc.type | Master Thesis | en_US |
dc.institutionauthor | Erkuş, Soner | - |
dc.department | Thesis (Master)--İzmir Institute of Technology, Mathematics | en_US |
dc.relation.publicationcategory | Tez | en_US |
item.languageiso639-1 | en | - |
item.grantfulltext | open | - |
item.openairetype | Master Thesis | - |
item.cerifentitytype | Publications | - |
item.fulltext | With Fulltext | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
Appears in Collections: | Master Degree / Yüksek Lisans Tezleri |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
T001084.pdf | MasterThesis | 774.27 kB | Adobe PDF | View/Open |
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