Please use this identifier to cite or link to this item: https://hdl.handle.net/11147/3552
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dc.contributor.advisorPashaev, Oktayen
dc.contributor.authorErkuş, Soner-
dc.date.accessioned2014-07-22T13:51:47Z-
dc.date.available2014-07-22T13:51:47Z-
dc.date.issued2012en
dc.identifier.urihttp://hdl.handle.net/11147/3552-
dc.descriptionThesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2012en
dc.descriptionIncludes bibliographical references (leaves: 92-94)en
dc.descriptionText in English; Abstract: Turkish and Englishen
dc.descriptionviii, 98 leavesen
dc.description.abstractIn 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.isoenen_US
dc.publisherIzmir Institute of Technologyen
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subject.lcshFourier transformationsen
dc.subject.lcshMandelbrot setsen
dc.subject.lcshFractalsen
dc.subject.lcshMellin transformen
dc.titleQ-periodicity, self-similarity and weierstrass-mandelbrot functionen_US
dc.typeMaster Thesisen_US
dc.institutionauthorErkuş, Soner-
dc.departmentIzmir Institute of Technology. Mathematicsen
dc.relation.publicationcategoryTezen_US
item.fulltextWith Fulltext-
item.openairetypeMaster Thesis-
item.cerifentitytypePublications-
item.languageiso639-1en-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.grantfulltextopen-
Appears in Collections:Master Degree / Yüksek Lisans Tezleri
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