Turan, Mehmet
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Name Variants
T., Mehmet
Turan M.
M.,Turan
Turan,Mehmet
Mehmet, Turan
T.,Mehmet
Turan A.
Mehmet Turan
M., Turan
Turan, Mehmet
Turan,M.
Turan, M.
Turan M.
M.,Turan
Turan,Mehmet
Mehmet, Turan
T.,Mehmet
Turan A.
Mehmet Turan
M., Turan
Turan, Mehmet
Turan,M.
Turan, M.
Job Title
Profesör Doktor
Email Address
mehmet.turan@atilim.edu.tr
Main Affiliation
Mathematics
Status
Website
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Scholarly Output
46
Articles
39
Citation Count
51
Supervised Theses
3
46 results
Scholarly Output Search Results
Now showing 1 - 10 of 46
Article Citation - WoS: 2Citation - Scopus: 2HOW DO SINGULARITIES OF FUNCTIONS AFFECT THE CONVERGENCE OF q-BERNSTEIN POLYNOMIALS?(Element, 2015) Ostrovska, Sofiya; Ozban, Ahmet Yasar; Turan, Mehmet; MathematicsIn this article, the approximation of functions with a singularity at alpha is an element of (0, 1) by the q-Bernstein polynomials for q > 1 has been studied. Unlike the situation when alpha is an element of (0, 1) \ {q(-j)} j is an element of N, in the case when alpha = q(-m), m is an element of N, the type of singularity has a decisive effect on the set where a function can be approximated. In the latter event, depending on the types of singularities, three classes of functions have been examined, and it has been found that the possibility of approximation varies considerably for these classes.Article Citation - WoS: 9Citation - Scopus: 12Bifurcation of Discontinuous Limit Cycles of the Van Der Pol Equation(Elsevier, 2014) Akhmet, Marat; Turan, Mehmet; MathematicsIn this paper, we apply the methods of B-equivalence and psi-substitution to prove the existence of discontinuous limit cycle for the Van der Pol equation with impacts on surfaces. The result is extended through the center manifold theory for coupled oscillators. The main novelty of the result is that the surfaces, where the jumps occur, are not flat. Examples and simulations are provided to demonstrate the theoretical results as well as application opportunities. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.Article Citation - WoS: 0Citation - Scopus: 0On the Lupas q-transform of Unbounded Functions(Walter de Gruyter Gmbh, 2023) Ostrovska, Sofiya; Turan, Mehmet; MathematicsThe Lupa , s q-transform comes out naturally in the study of the Lupa , s q-analogue of the Bernstein operator. It is closely related to the Heine q-distribution which has a numerous application in q-boson operator calculus and to the Valiron method of summation for divergent series. In this paper, the Lupa , s q-transform (lambda(q)f)(z), q is an element of (0, 1), of unbounded functions is considered in distinction to the previous researches, where only the case f is an element of C[0, 1] have been investigated. First, the condition for a function to possess the Lupa , s q-transform is presented. Also, results concerning the connection between growth rate of the function f (t) as t -> 1(-) and the growth of its Lupa , s q-transform (lambda(q)f)(z) as z -> infinity are established. (c) 2023 Mathematical Institute Slovak Academy of SciencesArticle Citation - WoS: 3Citation - Scopus: 3An Unrestricted Arnold's Cat Map Transformation(Springer, 2024) Turan, Mehmet; Goekcay, Erhan; Tora, Hakan; Software Engineering; Mathematics; Airframe and Powerplant MaintenanceThe Arnold's Cat Map (ACM) is one of the chaotic transformations, which is utilized by numerous scrambling and encryption algorithms in Information Security. Traditionally, the ACM is used in image scrambling whereby repeated application of the ACM matrix, any image can be scrambled. The transformation obtained by the ACM matrix is periodic; therefore, the original image can be reconstructed using the scrambled image whenever the elements of the matrix, hence the key, is known. The transformation matrices in all the chaotic maps employing ACM has limitations on the choice of the free parameters which generally require the area-preserving property of the matrix used in transformation, that is, the determinant of the transformation matrix to be +/- 1.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm 1.$$\end{document} This reduces the number of possible set of keys which leads to discovering the ACM matrix in encryption algorithms using the brute-force method. Additionally, the period obtained is small which also causes the faster discovery of the original image by repeated application of the matrix. These two parameters are important in a brute-force attack to find out the original image from a scrambled one. The objective of the present study is to increase the key space of the ACM matrix, hence increase the security of the scrambling process and make a brute-force attack more difficult. It is proved mathematically that area-preserving property of the traditional matrix is not required for the matrix to be used in scrambling process. Removing the restriction enlarges the maximum possible key space and, in many cases, increases the period as well. Additionally, it is supplied experimentally that, in scrambling images, the new ACM matrix is equivalent or better compared to the traditional one with longer periods. Consequently, the encryption techniques with ACM become more robust compared to the traditional ones. The new ACM matrix is compatible with all algorithms that utilized the original matrix. In this novel contribution, we proved that the traditional enforcement of the determinant of the ACM matrix to be one is redundant and can be removed.Article Citation - WoS: 1Citation - Scopus: 1The Truncated q-bernstein Polynomials in the Case q > 1(Hindawi Ltd, 2014) Turan, Mehmet; MathematicsThe truncated q-Bernstein polynomials B-n,B-m,B-q (f; x), n is an element of N, and m is an element of N-0 emerge naturally when the q-Bernstein polynomials of functions vanishing in some neighbourhood of 0 are considered. In this paper, the convergence of the truncated q-polynomials on [0, 1] is studied. To support the theoretical results, some numerical examples are provided.Conference Object Citation - WoS: 2The Limit q-bernstein Operators With Varying q(Springer international Publishing Ag, 2019) Almesbahi, Manal Mastafa; Ostrovska, Sofiya; Turan, Mehmet; Mathematics[No Abstract Available]Conference Object Citation - WoS: 0Density-Aware Outage in Clustered Ad Hoc Networks(Ieee, 2018) Eroglu, Alperen; Onur, Ertan; Turan, Mehmet; MathematicsDensity of ad hoc networks may vary in time and space because of mobile stations, sleep scheduling or failure of nodes. Resources such as spectrum will be wasted if the network is not density-aware and -adaptive. Towards this aim, distributed and robust network density estimators are required. In this paper, we propose a novel cluster density estimator in random ad hoc networks by employing distance matrix. Monte-Carlo simulation results validate the proposed estimator. The accuracy of the estimator is impressive even under a high amount of distance measurement errors. We also propose a network outage model and a transmit power adaption technique that are density-aware. The results indicate the necessity of the density-aware solutions for making network performance better from capacity, coverage and energy conservation viewpoints.Article Citation - Scopus: 3Bifurcation in a 3d Hybrid System(2010) Akhmet,M.U.; Turan,M.; MathematicsIn this paper, we study a 3 dimensional Hybrid system which involves a switching mechanism such that at the moment of switching the differential equation that governs the mode] is changing. We first show that there is a center manifold and based on the results in [2] we show that the system under investigation has a Hopf bifurcation. An appropriate example is constructed to illustrate the theory. © Dynamic Publishers, Inc.Master Thesis Q-bernstein Polinomlarının Özellikleri Üzerine(2017) Almesbahı, Manal Mastafa; Turan, Mehmet; Ostrovska, Sofıya; MathematicsBu tezin amacı Bernstein polinomları teorisini ve son genişletmesi olan q-kalkülüsü çalışmaktır. Bu çalışmanın temel odak noktası 20 yıl önce ortaya çıkan ve kısa sürede birçok araştırmacının dikkatini çeken q-Bernstein polinomlarıdır. Bu tez Bernstein polinomlarına dair bilinen bazı sonuçların derlemesinden, q-Bernstein polinomları teorisine kısa bir giriş ve bazı yeni gelişmelerden oluşmaktadır. Yeni gelişmeler kısmında; limit q-Bernstein operatör dizisinin kuvvetli operatör limiti ve q-Bernstein operatörlerinin zayıf Picard operatörler oldukları ifade edilmiştir.Article Citation - WoS: 0Citation - Scopus: 0Fedja’s Proof of Deepti’s Inequality(Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet; MathematicsThe paper aims to present, in a systematic way, an elegant proof of Deepti’s inequality. Both the inequalityand various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none haveappeared in the literature thus far. In this work, suggestions pertaining to users ‘Deepti’ and ‘fedja’ are traced, whencethe title. The results or the paper are new, and the proof is divided into a series of statements, many of which are ofinterest in themselves.
