Çelik, Songül; Durukan, İnan; Özkan, Engin

In this study, the Pell numbers are placed clockwise on the vertices of the polygons with a number corresponding to each vertex. Then, a relation among the numbers corresponding to a vertex is given. Furthermore, we obtain a formula which gives the mth term of the sequence formed at the kth vertex in an n-gon. The same procedure is repeated with Pell-Lucas, Jacobsthal and Jacobsthal-Lucas numbers.

Özkan, Engin; Kuloǧlu, Bahar; Peters, James F.

This paper introduces self-similarity inherent in planar Milich-Jennings centered flip graphs derived from the Narayana sequence. We show that self-similarity found in a Narayana sequence yields a connected spanning subgraph with a centered flip. This paper has several main results (1) Every Narayana sequence constructs a flip graph, (2) Every Narayana sequence is self-similar and (3) Every Pascal 3-triangle has a free group presentation.

Yapman, Ömer; Amiraliyev, Gabil M.

A linear Volterra delay-integro-differential equation with a singular perturbation parameter ε is considered. The problem is discretized using exponentially fitted schemes on the Shishkin type meshes. It is proved that the numerical approximations generated by this method are O(N−2lnN) convergent in the discrete maximum norm, where N is the mesh parameter. Numerical results show a good agreement with the theoretical analysis.