Browsing by Author "Turan,M."
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Article Citation Count: 3Bifurcation in a 3D Hybrid system(2010) Turan, Mehmet; 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.Conference Object Citation Count: 2Density-aware outage in clustered Ad Hoc networks(Institute of Electrical and Electronics Engineers Inc., 2018) Turan, Mehmet; 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.Article Citation Count: 1Evaluation and optimization of nonlinear central pattern generators for robotic locomotion(Control Engineering and Applied Informatics Journal, 2018) Turan, Mehmet; Arıkan, Kutluk Bilge; Arikan,K.B.; 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. © 2018 Control Engineering and Applied Informatics Journal.Book Part Citation Count: 0On the orthogonality of the q-derivatives of the discrete q-hermite I polynomials(IGI Global, 2019) Turan, Mehmet; 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: 3On the powers of the Kummer distribution(University of Kuwait, 2017) Ostrovska, Sofiya; Turan, Mehmet; MathematicsThe Kummer distribution is a probability distribution, whose density is given by f(x) = Cxαδx)-γe-βx, x > 0 where α, β, δ > 0, γ ∈ ℝ, and C is a normalizing constant. In this paper, the distributions of random variable Xp, p > 0, where X has the Kummer distribution, are considered with the conditions being IFR/DFR, some properties of moments depending on the parameters and the moment-(in) determinacy. In the case of moment-indeterminacy, exemplary Stieltjes classes are constructed.Article Citation Count: 1Optimization of central patterns generators(Medwell Journals, 2017) Turan, Mehmet; 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: 0Qualitative results on the convergence of the q-bernstein polynomials(North University of Baia Mare, 2015) Ostrovska, Sofiya; Turan, Mehmet; MathematicsDespite many common features, the convergence properties of the Bernstein and the q-Bernstein polynomials are not alike. What is more, the cases 0 < q < 1 and q > 1 are not similar to each other in terms of convergence. In this work, new results demonstrating the striking differences which may occur in those convergence properties are presented. © 2015, North University of Baia Mare. All rights reserved.