On equivelar triangulations of surfaces

Adıgüzel, Ebru
Persistent homology is an algebraic method for understanding topological features of discrete objects or data (finite set of points with metric defined on it). In algebraic topology, the Mayer Vietoris sequence is a powerful tool which allows one to study the homology groups of a given space in terms of simpler homology groups of its subspaces. In this thesis, we study to what extent does persistent homology benefit from Mayer Vietoris sequence.


On endomorphisms of surface mapping class groups
Korkmaz, Mustafa (Elsevier BV, 2001-05-01)
In this paper, we prove that every endomorphism of the mapping class group of an orientable surface onto a subgroup of finite index is in fact an automorphism.
On maximal curves and linearized permutation polynomials over finite fields
Özbudak, Ferruh (Elsevier BV, 2001-08-08)
The purpose of this paper is to construct maximal curves over large finite fields using linearized permutation polynomials. We also study linearized permutation polynomials under finite field extensions.
On multiplication in finite fields
Cenk, Murat; Özbudak, Ferruh (2010-04-01)
We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite ...
Shape models based on elliptic PDES, associated energies, and their applications in 2D and 3D
Gençtav, Aslı; Tarı, Zehra Sibel; Can, Tolga; Department of Computer Engineering (2018)
By using an elliptic PDE or its modifications, we develop implicit shape representations and demonstrate their two- and three-dimensional applications. In the first part of the thesis, we present a novel shape characterization field that provides a local measure of roundness at each shape point. The field is computed by comparing the solution of the elliptic PDE on the shape domain and the solution of the same PDE on the reference disk. We demonstrate its potential via illustrative applications including gl...
Fixed-frequency slice computation of discrete Cohen's bilinear class of time-frequency representations
Ozgen, MT (2000-02-01)
This communication derives DFT-sample-based discrete formulas directly in the spectral-correlation domain for computing fixed-frequency slices of discrete Cohen's class members with reduced computational cost, both for one-dimensional and multidimensional (specifically two-dimensional (2-D)) finite-extent sequence cases. Frequency domain integral expressions that define discrete representations are discretized to obtain these discrete implementation formulas. 2-D ambiguity function domain kernels are chosen...
Citation Formats
E. Adıgüzel, “On equivelar triangulations of surfaces,” M.S. - Master of Science, Middle East Technical University, 2018.