Turan, Mehmet
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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
ORCID ID
Scopus Author ID
Turkish CoHE Profile ID
Google Scholar ID
WoS Researcher ID
Scholarly Output
48
Articles
41
Citation Count
51
Supervised Theses
3
47 results
Scholarly Output Search Results
Now showing 1 - 10 of 47
Article Citation Count: 0Stieltjes Classes for Discrete Distributions of Logarithmic Type(Univ Nis, Fac Sci Math, 2020) Ostrovska, Sofiya; Turan, Mehmet; MathematicsStieltjes classes play a significant role in the moment problem since they permit to expose explicitly an infinite family of probability distributions all having equal moments of all orders. Mostly, the Stieltjes classes have been considered for absolutely continuous distributions. In this work, they have been considered for discrete distributions. New results on their existence in the discrete case are presented.Conference Object Citation Count: 2Density-aware outage in clustered Ad Hoc networks(Institute of Electrical and Electronics Engineers Inc., 2018) Eroǧlu,A.; Onur,E.; Turan,M.; 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 in addition to comparison with two different estimators. The accuracy of the estimator is impressive even under a high amount of distance measurement errors. We also demonstrate impact of density on network outage and transmission power adaption via proposing 2-D analytic models based on density and validating these models with the proposed density estimator. © 2018 IEEE.Book Part Citation Count: 0On the orthogonality of the q-derivatives of the discrete q-hermite I polynomials(IGI Global, 2019) Alwhishi,S.; Adigüzel,R.S.; Turan,M.; MathematicsDiscrete q-Hermite I polynomials are a member of the q-polynomials of the Hahn class. They are the polynomial solutions of a second order difference equation of hypergeometric type. These polynomials are one of the q-analogous of the Hermite polynomials. It is well known that the q-Hermite I polynomials approach the Hermite polynomials as q tends to 1. In this chapter, the orthogonality property of the discrete q-Hermite I polynomials is considered. Moreover, the orthogonality relation for the k-th order q-derivatives of the discrete q-Hermite I polynomials is obtained. Finally, it is shown that, under a suitable transformation, these relations give the corresponding relations for the Hermite polynomials in the limiting case as q goes to 1. © 2020, IGI Global.Article Citation Count: 8Bifurcation 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 Count: 1Optimization of central patterns generators(Medwell Journals, 2017) Elbori,A.; Turan,M.; Ankan,K.B.; MathematicsThe issue of how best to optimize Central Patterns Generators (CPG) for locomotion to generate motion for one leg with two degrees of freedom has inspired many researchers to explore the ways in which rhythmic patterns obtained by genetic algorithms may be utilized in uncoupled, unidirectional and bidirectional two CPGs. This study takes as its assumption that the focus on stability analysis to decrease variation between steps brings about better results with respect to the gait locomotion and argues that controlling the amplitude and frequency may lead to more robust results viz., stimulation for movement. © Medwell Journals, 2017.Article Citation Count: 0ON THE LIMIT OF DISCRETE q-HERMITE I POLYNOMIALS(Ankara Univ, Fac Sci, 2019) Alwhishi, Sakina; Adıgüzel, Rezan Sevinik; Turan, Mehmet; MathematicsThe main purpose of this paper is to introduce the limit relationsbetween the discrete q-Hermite I and Hermite polynomials such that the orthogonality property and the three-terms recurrence relations remain valid.The discrete q-Hermite I polynomials are the q-analogues of the Hermite polynomials which form an important class of the classical orthogonal polynomials.The q-di§erence equation of hypergeometric type, Rodrigues formula and generating function are also considered in the limiting case.Article Citation Count: 1Evaluation and Optimization of Nonlinear Central Pattern Generators for Robotic Locomotion(Romanian Soc Control Tech informatics, 2018) Elbori, Abdalftah; Turan, Mehmet; Arikan, Kutluk Bilge; Department of Mechatronics Engineering; MathematicsWith regard to the optimization of Central Pattern Generators (CPGs) for bipedal locomotion in robots, this paper investigates how the different cases of CPGs such as uncoupled, unidirectional, bidirectional two CPGs are used to produce rhythmic patterns for one leg with two degrees of freedom (DOF). This paper also discusses the stability analysis of CPGs and attempts to utilize genetic algorithms with the hybrid function and adapts the CPGs to robotic systems that perform one-leg movement, by utilizing the bidirectional two CPGs. The results show far greater improvement than in the other cases. CPGs not only enhance movement but also control locomotion without any sensory feedback.Article Citation Count: 0UNCORRELATEDNESS SETS OF DISCRETE RANDOM VARIABLES VIA VANDERMONDE-TYPE DETERMINANTS(Walter de Gruyter Gmbh, 2019) Turan, Mehmet; Ostrovska, Sofiya; Ozban, Ahmet Yasar; MathematicsGiven random variables X and Y having finite moments of all orders, their uncorrelatedness set is defined as the set of all pairs (j, k) is an element of N-2; for which X-j and Y-kappa are uncorrelated. It is known that, broadly put, any subset of N-2 can serve as an uncorrelatedness set. This claim is no longer valid for random variables with prescribed distributions, in which case the need arises so as to identify the possible uncorrelatedness sets. This paper studies the uncorrelatedness sets for positive random variables uniformly distributed on three points. Some general features of these sets are derived. Two related Vandermonde-type determinants are examined and applied to describe uncorrelatedness sets in some special cases. (C) 2019 Mathematical Institute Slovak Academy of SciencesArticle Citation Count: 8On the eigenvectors of the q-Bernstein operators(Wiley, 2014) Ostrovska, S.; Turan, M.; MathematicsIn this article, both the eigenvectors and the eigenvalues of the q-Bernstein operators have been studied. Explicit formulae are presented for the eigenvectors, whose limit behavior is determined both in the case 01. Because the classical case, where q=1, was investigated exhaustively by S. Cooper and S. Waldron back in 2000, the present article also discusses the related similarities and distinctions with the results in the classical case. Copyright (c) 2013 John Wiley & Sons, Ltd.Article Citation Count: 0On the Eigenstructure of the Modified Bernstein Operators(Taylor & Francis inc, 2022) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet; MathematicsStarting from the well-known work of Cooper and Waldron published in 2000, the eigenstructure of various Bernstein-type operators has been investigated by many researchers. In this work, the eigenvalues and eigenvectors of the modified Bernstein operators Q(n) have been studied. These operators were introduced by S. N. Bernstein himself, in 1932, for the purpose of accelerating the approximation rate for smooth functions. Here, the explicit formulae for the eigenvalues and corresponding eigenpolynomials together with their limiting behavior are established. The results show that although some outcomes are similar to those for the Bernstein operators, there are essentially different ones as well.
