Zubeyir Cinkir
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Zubeyir Cinkir has a total of 2 co-authors. Here are the top co-authors by number of shared publications:
- Hasan Akin
Harran University
1 shared publication - Irfan Siap
Department of Mathematics, Yildiz Technical University, Istanbul, Turkey
1 shared publication
Latest Publications
- Open Access
Admissible Invariants of genus 3 Curves
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we explicitly calculated these admissible invariants for all curves of genus $3$. We find the sharp lower bound for the invariants $\varphi$, $\lambda$ and $\epsilon$ for all polarized metrized graphs of genus $3$. This improves the lower bound given for Effective Bogomolov Conjecture for such curves.Open AccessAdmissible Invariants of genus 3 Curves
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we explicitly calculated these admissible invariants for all curves of genus $3$. We find the sharp lower bound for the invariants $\varphi$, $\lambda$ and $\epsilon$ for all polarized metrized graphs of genus $3$. This improves the lower bound given for Effective Bogomolov Conjecture for such curves. - Open Access
- 18 October 2012
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 19 (4) , P46
The Tau Constant and the Edge Connectivity of a Metrized Graph
The tau constant is an important invariant of a metrized graph. It has connections to other graph invariants such as Kirchhoff index, and it has applications to arithmetic properties of algebraic curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We prove identities which we call "contraction", "deletion", and "contraction-deletion" identities on a metrized graph. By establishing a lower bound for the tau constant in terms of the edge connectivity, we prove that Baker and Rumely's lower bound conjecture on the tau constant holds for metrized graphs with edge connectivity 5 or more. We show that proving this conjecture for 3-regular graphs is enough to prove it for all graphs.
- 18 October 2012
- Published by The Electronic Journal of Combinatorics in The Electronic Journal of Combinatorics
- Vol. 19 (4) , P46
Open AccessThe Tau Constant and the Edge Connectivity of a Metrized Graph
The tau constant is an important invariant of a metrized graph. It has connections to other graph invariants such as Kirchhoff index, and it has applications to arithmetic properties of algebraic curves. We show how the tau constant of a metrized graph changes under successive edge contractions and deletions. We prove identities which we call "contraction", "deletion", and "contraction-deletion" identities on a metrized graph. By establishing a lower bound for the tau constant in terms of the edge connectivity, we prove that Baker and Rumely's lower bound conjecture on the tau constant holds for metrized graphs with edge connectivity 5 or more. We show that proving this conjecture for 3-regular graphs is enough to prove it for all graphs.
- Open Access
A fast elementary algorithm for computing the determinant of toeplitz matrices
In recent years, a number of fast algorithms for computing the determinant of a Toeplitz matrix were developed. The fastest algorithm we know so far is of order $k^2\log{n}+k^3$, where $n$ is the number of rows of the Toeplitz matrix and $k$ is the bandwidth size. This is possible because such a determinant can be expressed as the determinant of certain parts of $n$-th power of a related $k \times k$ companion matrix. In this paper, we give a new elementary proof of this fact, and provide various examples. We give symbolic formulas for the determinants of Toeplitz matrices in terms of the eigenvalues of the corresponding companion matrices when $k$ is small.Open AccessA fast elementary algorithm for computing the determinant of toeplitz matrices
In recent years, a number of fast algorithms for computing the determinant of a Toeplitz matrix were developed. The fastest algorithm we know so far is of order $k^2\log{n}+k^3$, where $n$ is the number of rows of the Toeplitz matrix and $k$ is the bandwidth size. This is possible because such a determinant can be expressed as the determinant of certain parts of $n$-th power of a related $k \times k$ companion matrix. In this paper, we give a new elementary proof of this fact, and provide various examples. We give symbolic formulas for the determinants of Toeplitz matrices in terms of the eigenvalues of the corresponding companion matrices when $k$ is small. - Open Access
Computation of Polarized Metrized Graph Invariants By Using Discrete Laplacian Matrix
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian matrix and its pseudo inverse. Algorithms we give can be used for both symbolic and numerical computations. We present various examples to illustrate the implementation of these algorithms.
Open AccessComputation of Polarized Metrized Graph Invariants By Using Discrete Laplacian Matrix
Several invariants of polarized metrized graphs and their applications in Arithmetic Geometry are studied recently. In this paper, we give fast algorithms to compute these invariants by expressing them in terms of the discrete Laplacian matrix and its pseudo inverse. Algorithms we give can be used for both symbolic and numerical computations. We present various examples to illustrate the implementation of these algorithms.
- 31 May 2011
- Published by Elsevier in European Journal of Combinatorics
- Vol. 32 (4) , 639-655
The tau constant and the discrete Laplacian matrix of a metrized graph
- 31 May 2011
- Published by Elsevier in European Journal of Combinatorics
- Vol. 32 (4) , 639-655
The tau constant and the discrete Laplacian matrix of a metrized graph
- 27 April 2011
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 143 (4) , 807-823
Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$- 27 April 2011
- Published by Springer Nature in Journal of Statistical Physics
- Vol. 143 (4) , 807-823
Reversibility of 1D Cellular Automata with Periodic Boundary over Finite Fields $\pmb{ {\mathbb{Z}}}_{p}$- 23 November 2010
- Published by Wiley in International Journal of Quantum Chemistry
- Vol. 111 (15) , 4030-4041
Deletion and contraction identities for the resistance values and the Kirchhoff index
- 23 November 2010
- Published by Wiley in International Journal of Quantum Chemistry
- Vol. 111 (15) , 4030-4041
Deletion and contraction identities for the resistance values and the Kirchhoff index