Özkan, Engin

We prove some theorems concerning the truncated Lucas sequences. We also state some conjectures concerning the period (mod m) of truncated Lucas sequences, where the integer m is at least 2. In addition, we present some computer-generated results that tend to support these conjectures.

Amiraliyev, G.M.; Amiraliyeva, I.G.; Kudu, Mustafa

We consider a uniform finite difference method on Shishkin mesh for a quasilinear first order singularly perturbed boundary value problem (BVP) with integral boundary condition. We prove that the method is first order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. The parameter uniform convergence is confirmed by numerical computations.

Ugur, Tamer; Kopuzlu, Abdullah; Şimşek, Hakan

The work on torus knots K(p,q) was discussed. Torus knot is a knot which wraps around the standard solid torus T in the longitudinal direction p times and in the meridional direction q times. The (p,q) were relatively prime. A computer program was introduced to plot the curves of regular projection torus knots by computer.

Kopuzlu, Abdullah; Ugur, Tamer

In this paper, we introduce a method finding the matrix of graph of connected sum of torus knot K(2, q) for q = 1, 3, 5,⋯ Then, we show that the dimension of the matrix is (q - 1) k + 1, where k is the number of connected sum. Also, for this method a Maple source code is given.

Ugur, Tamer; Kopuzlu, Abdullah

In this paper we apply computer algebra (Maple) techniques to calculate Jones polynomial of graphs of K(2,q)-Torus knots. For this purpose, a computer program was developed. When a positive integer q is given, the program calculate Jones polynomial of graph of K(2,q)-Torus knots.