• Partial sums of the gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications 

  Kılıç, Emrah; Akkuş, İlker (University of Miskolc, 2019)

  In this paper, we shall derive formulæ for partial sums of the Gaussian q-binomial coefficients, their reciprocals, squares and squared reciprocals. To prove the claimed results, we use q-calculus. As applications of our ...
• A nonsymmetrical matrix and its factorizations 

  Arıkan, Talha; Kılıç, Emrah; Prodinger, Helmut (De Gruyter, 2019-08)

  We introduce a nonsymmetric matrix defined by q-integers. Explicit formul ae are derived for its LU-decomposition, the inverse matrices L-1 and U-1 and its inverse. Nonsymmetric variants of the Filbert and Lilbert matrices ...
• The discreteness of the spectrum of the Schrödinger operator equation and some properties of the s-numbers of the inverse Schrödinger operator 

  Hashimoglu, Ilyas; Akın, Ömer; Mamedov, Khanlar R. (John Wiley and Sons Ltd, 2019-05)

  In this article, we investigate the discreteness and some other properties of the spectrum for the Schrödinger operator L defined by the formula LY=-d 2 y/dx 2 +A(A+I)/x 2 y+Q(x)y on the space L 2 (H, [0, ?)), where H is ...
• On solutions of the recursive equations x_{n+1}=x_{n-1}^{p}/x_{n}^{p} (p>0) via Fibonacci-type sequences 

  Öcalan, Özkan; Duman, Oktay (2019-01)

  In this paper, by using the classical Fibonacci sequence and the golden ratio, we ?rst give the exact solution of the nonlinear recursive equation xn+1 = xn?1/xn with respect to certain powers of the initial values x?1 and ...
• New asymmetric generalizations of the Filbert and Lilbert matrices 

  Kılıç, Emrah; Koparal, Sibel; Ömür, Neşe (Springer Netherlands, 2019-06)

  Two new asymmetric generalizations of the Filbert and Lilbert matrices constructed by the products of two Fibonacci and Lucas numbers are considered, with additional parameter settings. Explicit formulæ are derived for ...
• Evaluation of sums involving products of Gaussian q-binomial coefficients with applications 

  Kılıç, Emrah; Prodinger, Helmut (De Gruyter, 2019-04)

  Sums of products of two Gaussian q-binomial coefficients, are investigated, one of which includes two additional parameters, with a parametric rational weight function. By means of partial fraction decomposition, first the ...
• Explicit spectrum of a circulant-tridiagonal matrix with applications 

  Kılıç, Emreah; Yalciner, Aynur (American Institute of Physics Inc., 2019-07)

  We consider a circulant-tridiagonal matrix and compute its determinant by using generating function method. Then we explicitly determine its spectrum. Finally we present applications of our results for trigonometric ...
• A Mathematical Model Of Hepatitis B Transmission In Turkey 

  Gölgeli, Meltem (Ankara UniversityAnkara Üniversitesi, 2019)

  Hepatitis B infection is one of the serious viral infections that is treating the global health. Turkey has an intermediate endemicity for hepatitis B. In this study, a classical SIR model for hepatitis B virus (HBV) ...
• A nonlinear generalization of the Filbert matrix and its Lucas analogue 

  Kılıç, Emrah; Arıkan, Talha (Taylor and Francis Ltd., 2019-01)

  In this paper, we present both a new generalization and an analogue of the Filbert matrix (Formula presented.) by the means of the Fibonacci and Lucas numbers whose indices are in nonlinear form (Formula presented.) for ...
• Studying new generalizations of Max-Min matrices with a novel approach 

  Kılıç, Emrah; Arıkan, Talha (TÜBİTAK, 2019)

  We consider new kinds of max and min matrices, [amax(i,j)]i,j?1 and [amin(i,j)]i,j?1, as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence {an} have been ...
• On the number of k-normal elements over finite fields 

  Saygı, Zülfükar; Tilenbaev, Ernist; Ürtiş, Çetin (TÜBİTAK, 2019)

  In this article we give an explicit formula for the number of kk-normal elements, hence answering Problem 6.1. of Huczynska et al. (Existence and properties of kk-normal elements over finite fields, Finite Fields Appl 2013; ...
• Intuitionistic Fuzzy Initial Value Problems - An Application 

  Akın, Ömer; Bayeğ, Selami (Hacettepe UniversityHacettpe Üniversitesi, 2019)

  In this paper, by using the properties of ?\alpha? and ?\beta? cuts of intuitionistic fuzzy numbers, we have firstly proposed a method to find the general solution of the second order initial value problem with intuitionistic ...
• System of intuitionistic fuzzy differential equations with intuitionistic fuzzy initial values 

  Akın, Ömer; Bayeğ, Selami (Biophysics and Biomedical Engineering of the Bulgarian Academy of Sciences, 2018)

  In this paper, we have studied the system of differential equations with intuitionistic fuzzy initial values under the interpretation of (i,ii)-GH differentiability concepts and Zadeh's extension principle interpretation. ...
• The concept of Hukuhara derivative and Aumann integral for intuitionistic fuzzy number valued functions 

  Akın, Ömer; Bayeğ, Selami (Kyrgyz Turkish Manas UniversityKırgızistan Türkiye Manas Üniversitesi, 2018)

  In this paper we have rstly dened a metric based on the Hausdor metric in intuitionistic fuzzy environment and studied its properties. Then we have proved that the metric space of intuitionistic fuzzy number valued ...
• Global Stability Analysis of a General Scalar Difference Equation 

  Merdan, Hüseyin; Gumus, Ozlem Ak; Karahisarli, Gamzegul (L and H Scientific Publishing, LLC, 2018)

  We consider a general ?rst-order scalar difference equation with and without Allee effect. The model without Allee effect represents asexual reproduction of a species while the model including Allee effect represents sexual ...
• A proof of Clarke's conjecture 

  Kılıç, Emrah; Arıkan, Talha (Cambridge University Press, 2019-07)

  We consider new kinds of max and min matrices, [amax(i,j)]i,j?1 and [amin(i,j)]i,j?1, as generalizations of the classical max and min matrices. Moreover, their reciprocal analogues for a given sequence {an} have been ...
• Asset price dynamics for a two-asset market system 

  Bulut, H.; Merdan, Hüseyin; Swigon, D. (American Institute of Physics Inc., 2019-02)

  We present a mathematical model for a market involving two stocks which are traded within a single homogeneous group of investors who have similar motivations and strategies for trading. It is assumed that the market ...
• Summability on Mellin-type nonlinear integral operators 

  Aslan, İsmail; Duman, Oktay (Taylor and Francis Ltd., 2019-06)

  In this study, approximation properties of the Mellin-type nonlinear integral operators defined on multivariate functions are investigated. In order to get more general results than the classical aspects, we mainly use the ...
• UAV coverage using hexagonal tessellation 

  Kadıoğlu Ürtiş, Esra; Ürtiş, Çetin; Papanikolopoulos, Nikolaos (IEEE, 2019-07)

  Unmanned aerial vehicles (UAVs) are increasingly being used for coverage applications. Some common examples include inspecting agricultural fields for certain plant diseases, tracking wildfire, photogrammetry, flying over ...
• Obstrüktif Uyku Apnesi Hastalarında Zihinsel Yorgunluk ve Dikkat Kontrolü De?işiminin İncelenmesi 

  Nassehi, Farhad; Özdemir, Galip; Eroğul, Osman; Atalay, Nart Bedin; Yuceege, Melike; Fırat, Hikmet (IEEE, 2019-04)

  Obstructive sleep apnea (OSA) is the most common respiratory sleep disorder. Mental fatigue and attention control difficulties during the day have been reported in several studies for patients who are diagnosed with OSA. ...

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