Turan, Mehmet

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https://hdl.handle.net/20.500.14411/6771
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.
Job Title
Profesör Doktor
Email Address
mehmet.turan@atilim.edu.tr
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Mathematics
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WoS Researcher ID

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14

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3

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Scholarly Output

55

Articles

44

Views / Downloads

25/0

Supervised MSc Theses

5

Supervised PhD Theses

2

WoS Citation Count

83

Scopus Citation Count

96

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5

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5

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WoS Citations per Publication

1.51

Scopus Citations per Publication

1.75

Open Access Source

13

Supervised Theses

7

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JournalCount
Mathematical Methods in the Applied Sciences3
Numerical Functional Analysis and Optimization2
Quaestiones Mathematicae2
Results in Mathematics2
Mathematica Slovaca2
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Scholarly Output Search Results

Now showing 1 - 10 of 21
  • Thumbnail Image
    Article
    Citation - WoS: 1
    Citation - Scopus: 1
    The Truncated q-bernstein Polynomials in the Case q > 1
    (Hindawi Ltd, 2014) Turan, Mehmet
    The 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.
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    Article
    Fedja’s Proof of Deepti’s Inequality
    (Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet
    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.
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    Article
    Citation - WoS: 4
    Citation - Scopus: 4
    On the Powers of the Kummer Distribution
    (Academic Publication Council, 2017) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
    The Kummer distribution is a probability distribution, whose density is given by f (x) = cx (alpha-1)(1 + delta x)(-gamma) e(-beta x), X > 0, where alpha, beta, delta > 0, gamma is an element of R and C is a normalizing constant. In this paper, the distributions of random variable X-P, 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.
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    Conference Object
    Density-Aware Outage in Clustered Ad Hoc Networks
    (Ieee, 2018) Eroglu, Alperen; Onur, Ertan; Turan, Mehmet
    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.
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    Article
    Citation - Scopus: 3
    Bifurcation in a 3d Hybrid System
    (2010) Akhmet,M.U.; Turan,M.
    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.
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    Article
    Citation - WoS: 3
    Citation - Scopus: 3
    q-stieltjes Classes for Some Families of q-densities
    (Elsevier Science Bv, 2019) Ostrovska, Sofiya; Turan, Mehmet
    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.
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    Article
    Qualitative results on the convergence of the q-Bernstein polynomials
    (North Univ Baia Mare, 2015) Ostrovska, Sofiya; Turan, Mehmet
    Despite 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.
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    Conference Object
    Citation - WoS: 2
    The Limit q-bernstein Operators With Varying q
    (Springer international Publishing Ag, 2019) Almesbahi, Manal Mastafa; Ostrovska, Sofiya; Turan, Mehmet
    [No Abstract Available]
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    Article
    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
    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.
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    Article
    Citation - WoS: 9
    Citation - Scopus: 12
    Bifurcation of Discontinuous Limit Cycles of the Van Der Pol Equation
    (Elsevier, 2014) Akhmet, Marat; Turan, Mehmet
    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.