Q-periodicity, self-similarity and weierstrass-mandelbrot function
by
Erkuş, Soner.
Title
:
Q-periodicity, self-similarity and weierstrass-mandelbrot function
Author
:
Erkuş, Soner.
Personal Author
:
Erkuş, Soner.
Publication Information
:
[s.l.]: [s.n.], 2012.
Physical Description
:
viii, 98leaves.: ill.+ 1 computer laser optical disc.
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.
Subject Term
:
Fourier transformations.
Mandelbrot sets.
Fractals.
Mellin transform.
Added Author
:
Pashaev, Oktay.
Added Corporate Author
:
İzmir Institute of Technology. Mathematics.
Added Uniform Title
:
Thesis (Master)--İzmir Institute of Technology:Mathematics.
İzmir Institute of Technology:Mathematics--Thesis (Master).
Electronic Access
:
Library | Material Type | Item Barcode | Shelf Number | Status |
---|
IYTE Library | Thesis | T001084 | QA432 .E68 2012 | Tez Koleksiyonu |
IYTE Library | Supplementary CD-ROM | ROM2033 | QA432 .E68 2012 EK.1 | Tez Koleksiyonu |