Author

# Zubeyir Cinkir

Other affiliations: Middle East Technical University, University of Georgia, Abant Izzet Baysal University ...read more

Bio: Zubeyir Cinkir is an academic researcher from Zirve University. The author has contributed to research in topics: Laplacian matrix & Toeplitz matrix. The author has an hindex of 11, co-authored 32 publications receiving 312 citations. Previous affiliations of Zubeyir Cinkir include Middle East Technical University & University of Georgia.

##### Papers

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Zirve University

^{1}TL;DR: In this article, the Effective Bogomolov Conjecture was proved over a function field of characteristic 0 by proving Zhang's Conjectures about certain invariants of metrized graphs, which were previously known to be true only for curves of good reduction, for curve of genus at most 4 and a few other special cases.

Abstract: We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang’s Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures were previously known to be true only for curves of good reduction, for curves of genus at most 4 and a few other special cases. We also either verify or improve the previous results. We relate the invariants involved in Zhang’s Conjecture to the tau constant of metrized graphs. Then we use and extend our previous results on the tau constant. By proving another Conjecture of Zhang, we obtain a new proof of the slope inequality for Faltings heights on moduli space of curves.

45 citations

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Zirve University

^{1}TL;DR: In this paper, the Effective Bogomolov Conjecture over a function field of characteristic 0 was shown to be true for curves of genus at most 4 and a few other special cases.

Abstract: We prove the Effective Bogomolov Conjecture, and so the Bogomolov Conjecture, over a function field of characteristic 0 by proving Zhang's Conjecture about certain invariants of metrized graphs. In the function field case, these conjectures were previously known to be true only for curves of genus at most 4 and a few other special cases. We also either verify or improve the previous results. We relate the invariants involved in Zhang's Conjecture to the tau constant of metrized graphs. Then we use and extend our previous results on the tau constant. By proving another Conjecture of Zhang, we obtain a new proof of the slope inequality for Faltings heights on moduli space of curves.

40 citations

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TL;DR: It is shown that the reversibility problem can be reduced to solving a recurrence relation depending on the number of cells and the coefficients of the local rules defining the one-dimensional linear cellular automata.

Abstract: The reversibility problem for linear cellular automata with null boundary defined by a rule matrix in the form of a pentadiagonal matrix was studied recently over the binary field ℤ2 (del Rey and Rodriguez Sanchez in Appl Math Comput, 2011, doi:101016/jamc201103033) In this paper, we study one-dimensional linear cellular automata with periodic boundary conditions over any finite field ℤp For any given p≥2, we show that the reversibility problem can be reduced to solving a recurrence relation depending on the number of cells and the coefficients of the local rules defining the one-dimensional linear cellular automata More specifically, for any given values (from any fixed field ℤp) of the coefficients of the local rules, we outline a computer algorithm determining the recurrence relation which can be solved by testing reversibility of the cellular automaton for some finite number of cells As an example, we give the full criteria for the reversibility of the one-dimensional linear cellular automata over the fields ℤ2 and ℤ3

33 citations

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Zirve University

^{1}TL;DR: A new kind of elementary algorithm requiring [email protected]?+30k+O(logn) operations, where k>=4 is an integer that needs to be chosen freely at the beginning of the algorithm.

29 citations

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TL;DR: In this article, the effective resistances between any two vertices of a ladder graph were explicitly computed by using circuit reductions, and an explicit sum formula involving trigonometric functions was obtained.

Abstract: We explicitly compute the effective resistances between any two vertices of a ladder graph by using circuit reductions. Using our findings, we obtain explicit formulas for Kirchhoff index of a ladder graph. Comparing our formula for Kirchhoff index and previous results in the literature, we obtain an explicit sum formula involving trigonometric functions. We also expressed our formulas in terms of certain generalized Fibonacci numbers that are the values of the Chebyshev polynomials of the second kind at 2.

24 citations

##### Cited by

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TL;DR: The Matrices: Methods and Applications as mentioned in this paper is a collection of matrix-based methods and applications for the analysis of operational R-matrices and its application in the field of network engineering.

Abstract: (1992). Matrices: Methods and Applications. Journal of the Operational Research Society: Vol. 43, No. 12, pp. 1185-1185.

275 citations

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TL;DR: In this paper, a survey of cellular automata is presented, focusing on non-uniformity in CAs and especially on elementary CAs, which have been very useful in solving several real-life problems.

Abstract: Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of several researchers over various backgrounds and fields for modeling different physical, natural as well as real-life phenomena. Classically, CAs are uniform. However, non-uniformity has also been introduced in update pattern, lattice structure, neighborhood dependency and local rule. In this survey, we tour to the various types of CAs introduced till date, the different characterization tools, the global behavior of CAs, like universality, reversibility, dynamics etc. Special attention is given to non-uniformity in CAs and especially to non-uniform elementary CAs, which have been very useful in solving several real-life problems.

53 citations

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TL;DR: In this article, the authors present measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications, as well as their applications.

Abstract: This paper has two goals. The first is to present the construction, due to the author, of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add remarks, examples and mention related results.

48 citations

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TL;DR: In this paper, an explicit closed-form formula for degree-Kirchhoff index and the number of spanning trees of generalized phenylenes are obtained based on the normalized Laplacian spectrum.

48 citations