Browsing by Author "Turan, Mehmet"

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Citation - Scopus: 3
Bifurcation in a 3d Hybrid System
(2010) Akhmet,M.U.; Turan,M.; Mathematics
In 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.
Citation - WoS: 9
Citation - Scopus: 12
Bifurcation of Discontinuous Limit Cycles of the Van Der Pol Equation
(Elsevier, 2014) Akhmet, Marat; Turan, Mehmet; Mathematics
In 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.
Citation - WoS: 5
Citation - Scopus: 6
Bifurcation of Three-Dimensional Discontinuous Cycles
(Pergamon-elsevier Science Ltd, 2009) Akhmet, M. U.; Turan, M.; Mathematics
We consider three-dimensional discontinuous dynamical systems with non-fixed moments of impacts. Existence of the center manifold is proved for the system. The result is applied for the extension of the planar Hopf bifurcation theorem [M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163-178]. Illustrative examples are constructed for the theory. (C) 2009 Elsevier Ltd. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 1
The Continuity in Q of the Lupaş Q-Analogues of the Bernstein Operators
(Academic Press inc Elsevier Science, 2024) Yilmaz, Ovgue Gurel; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Mathematics; Mathematics
The Lupas q-analogue Rn,q of the Bernstein operator is the first known q-version of the Bernstein polynomials. It had been proposed by A. Lupas in 1987, but gained the popularity only 20 years later, when q-analogues of classical operators pertinent to the approximation theory became an area of intensive research. In this work, the continuity of operators Rn,q with respect to parameter q in the strong operator topology and in the uniform operator topology has been investigated. The cases when n is fixed and n -> infinity have been considered. (c) 2022 Elsevier Inc. All rights reserved.
Citation - WoS: 0
Density-Aware Outage in Clustered Ad Hoc Networks
(Ieee, 2018) Eroglu, Alperen; Onur, Ertan; Turan, Mehmet; Mathematics
Density 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.
Citation - Scopus: 2
Density-Aware Outage in Clustered Ad Hoc Networks
(Institute of Electrical and Electronics Engineers Inc., 2018) Eroǧlu,A.; Onur,E.; Turan,M.; Mathematics
Density 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.
Citation - WoS: 1
Citation - Scopus: 1
The Distance Between Two Limit q-bernstein Operators
(Rocky Mt Math Consortium, 2020) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
For q is an element of (0, 1), let B-q denote the limit q-Bernstein operator. The distance between B-q and B-r for distinct q and r in the operator norm on C[0, 1] is estimated, and it is proved that 1 <= parallel to B-q - B-r parallel to <= 2, where both of the equalities can be attained. Furthermore, the distance depends on whether or not r and q are rational powers of each other. For example, if r(j) not equal q(m) for all j, m is an element of N, then parallel to B-q - B-r parallel to = 2, and if r = q(m) for some m is an element of N, then parallel to B-q - B-r parallel to = 2(m - 1)/m.
Citation - WoS: 1
Citation - Scopus: 1
Evaluation 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; Mathematics; Department of Mechatronics Engineering; Mathematics
With 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.
Citation - WoS: 0
Citation - Scopus: 0
Fedja’s Proof of Deepti’s Inequality
(Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
The 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.
Citation - WoS: 10
Citation - Scopus: 12
A Generalized Arnold's Cat Map Transformation for Image Scrambling
(Springer, 2022) Tora, Hakan; Gokcay, Erhan; Turan, Mehmet; Buker, Mohamed; Mathematics; Software Engineering; Airframe and Powerplant Maintenance
This study presents a new approach to generate the transformation matrix for Arnold's Cat Map (ACM). Matrices of standard and modified ACM are well known by many users. Since the structure of the possible matrices is known, one can easily select one of them and use it to recover the image with several trials. However, the proposed method generates a larger set of transform matrices. Thus, one will have difficulty in estimating the transform matrix used for scrambling. There is no fixed structure for our matrix as in standard or modified ACM, making it much harder for the transform matrix to be discovered. It is possible to use different type, order and number of operations to generate the transform matrix. The quality of the shuffling process and the strength against brute-force attacks of the proposed method is tested on several benchmark images.
Citation - WoS: 2
Citation - Scopus: 2
HOW DO SINGULARITIES OF FUNCTIONS AFFECT THE CONVERGENCE OF q-BERNSTEIN POLYNOMIALS?
(Element, 2015) Ostrovska, Sofiya; Ozban, Ahmet Yasar; Turan, Mehmet; Mathematics
In 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.
Citation - WoS: 3
Citation - Scopus: 3
q-stieltjes Classes for Some Families of q-densities
(Elsevier Science Bv, 2019) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly infinite families of probability densities with the same sequence of moments. In this paper, the notion of q-moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either q-moment determinate or indeterminate in terms of its q-density have been obtained. Also, a q-analogue of Stieltjes classes is defined for q-distributions and q-Stieltjes classes have been constructed for a family of q-densities of q-moment indeterminate distributions. (C) 2018 Elsevier B.V. All rights reserved.
İkinci Mertebeden Lineer Olmayan Bir Fark Denkleminin Dinamikleri Üzerine
(2014) Aksoy, Aycan; Turan, Mehmet; Mathematics
Bu tezde iki keyfi parametre içeren ikinci dereceden özel bir rasyonel fark denklemi ele alınmıştır. Bu denklem bazı dinamik yapıları incelenmiştir: pozitif çözümlerin kararlılık ve yarı döngü analizleri; periyodik çözümlerin varlığı; denge noktasının yerel ve global kararlılık analizleri yapılmıştır. Bu tez dört bölümden oluşmaktadır. İlk bölümde fark denklemleri hakkında tarihsel bilgi, bunların bazı modellemeleri, ve yakın zamanda yapılmış bazı çalışmalar verilmiştir. İkinci bölümde, diziler ve fark denklemleriyle ilgili bilinen tanımlar ve sonuçlar gösterilmiştir. Asıl sonuçlar Bölüm 3'te sunulmuştur. Son bölümde kısa bir sonuç yazılmıştır.
Citation - WoS: 2
Citation - Scopus: 2
The Impact of the Limit q-durrmeyer Operator on Continuous Functions
(Springer Heidelberg, 2024) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet; Mathematics
The limit q-Durrmeyer operator, D-infinity,D-q, was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172-178, 2008) during a study of q-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of D-infinity,D-q. The interrelation between the analytic properties of a function f and the rate of growth for D(infinity,q)f are established, and the sharpness of the obtained results are demonstrated.
Citation - WoS: 2
The Limit q-bernstein Operators With Varying q
(Springer international Publishing Ag, 2019) Almesbahi, Manal Mastafa; Ostrovska, Sofiya; Turan, Mehmet; Mathematics
[No Abstract Available]
Merkezi Örüntü Üreteçlerin Optimizasyonu
(2018) Elborı, Alftah; Turan, Mehmet; Arıkan, Kutluk Bilge; Mathematics
Günümüzde insanlar gibi dinamik ve sağlam hareket edebilen insan robotunu bulmak en zor görevlerden biridir. İki ayaklı hareketi araştıran birçok araştırma olmasına rağmen, günümüzde insan yetenekleri olan robot bulunmamaktadır. Bu tezde robotlarda iki ayaklı hareket için Merkezi Örüntü Üreteçlerin (CPG) optimizasyonu ile ilgili olarak, üç matematiksel yapı tartışılmıştır. Ayrıca, bu tezde iki serbestlik dereceli bir bacakta ritmik hareket elde etmek için CPG'lerin, bağlantısız, tek yönlü veya çift yönlü bağlantılı gibi farklı şekillerde eşleşmeleri incelenmiştir. CPG'lerin üç matematiksel yapısı için de kararlılık analizi yapılmıştır. Bu tezde ele alınan farklı yapılardaki farklı eşleştirmeler arasından üçüncü yapıda çift yönlü eşleştirme en iyi sonucu vermiştir. Yapılardaki parametreler kararlılık bölgesinden seçildiği zaman, herhangi bir duyusal geribildirim olmaksızın önemli sonuçların elde edildiği gözlemlenmiştir.
Citation - WoS: 0
Citation - Scopus: 0
Moment Determinacy Versus q-moment Determinacy of Probability Distributions
(Springer Basel Ag, 2021) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
Since the classical moment problem is an important issue deeply connected to various mathematical disciplines, its q-analogue based on the notion of q-moments has emerged in the study of q-distributions. For a wide class of probability distributions, both of these problems can be considered. The aim of this work is to establish a connection between the two moment problems. In this paper, the class A of probability distributions possessing finite moments of all orders and support on (0, infinity) is examined. For each q is an element of(0,1), a distribution P is an element of A can be characterized with respect to moment-determinacy as well as q-moment determinacy. It is proved that the properties of P regarding these characterizations may differ, and that the q-moment determinacy of P may depend on the value of q.
Citation - WoS: 1
Citation - Scopus: 1
On the q-moment Determinacy of Probability Distributions
(Malaysian Mathematical Sciences Soc, 2020) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
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Citation - WoS: 5
Citation - Scopus: 4
On the Block Functions Generating the Limit q-lupas Operator
(Taylor & Francis Ltd, 2023) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
The limit q-Lupas operator emerged in the study of the Lupas q-analogue of the Bernstein operator. Afterward, it has been found that it is connected to numerical analysis, computer aided geometric design, probability theory and other areas. In this paper, properties of block functions generating the limit q-Lupas operator have been investigated.
Citation - WoS: 0
Citation - Scopus: 0
On the Continuity in q of the Family of the Limit q-durrmeyer Operators
(de Gruyter Poland Sp Z O O, 2024) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet; Mathematics
This study deals with the one-parameter family {D-q}(q is an element of[0,1]) of Bernstein-type operators introduced by Gupta and called the limit q-Durrmeyer operators. The continuity of this family with respect to the parameter q is examined in two most important topologies of the operator theory, namely, the strong and uniform operator topologies. It is proved that {D-q}(q is an element of[0,1]) is continuous in the strong operator topology for all q is an element of [0, 1]. When it comes to the uniform operator topology, the continuity is preserved solely at q = 0 and fails at all q is an element of (0, 1]. In addition, a few estimates for the distance between two limit q-Durrmeyer operators have been derived in the operator norm on C[0, 1].