Fen Edebiyat Fakültesi / Faculty of Science and Literature http://hdl.handle.net/20.500.11851/246 2020-01-18T03:59:11Z Partial sums of the gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications http://hdl.handle.net/20.500.11851/2955 Partial sums of the gaussian q-binomial coefficients, their reciprocals, square and squared reciprocals with applications Kılıç, Emrah; Akkuş, İlker 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 results, we give some interesting generalized Fibonomial sums formulæ. 2019-01-01T00:00:00Z A nonsymmetrical matrix and its factorizations http://hdl.handle.net/20.500.11851/2956 A nonsymmetrical matrix and its factorizations Arıkan, Talha; Kılıç, Emrah; Prodinger, Helmut 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 come out as consequences of our results for special choices of q and parameters. The approach consists of guessing the relevant quantities and proving them later by traditional means. 2019-08-01T00:00:00Z The concept of Hukuhara derivative and Aumann integral for intuitionistic fuzzy number valued functions http://hdl.handle.net/20.500.11851/2945 The concept of Hukuhara derivative and Aumann integral for intuitionistic fuzzy number valued functions Akın, Ömer; Bayeğ, Selami 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 functions is complete under this metric. Besides, we have studied the concept of Aumann integral for intuitionistic fuzzy number valued functions in terms of ???? and ???? cuts. Finally, we have given the relation between the Hukuhara derivative and Aumann integral for intuitionistic fuzzy valued functions by using the fundamental theorem of calculus 2018-01-01T00:00:00Z A Mathematical Model Of Hepatitis B Transmission In Turkey http://hdl.handle.net/20.500.11851/2948 A Mathematical Model Of Hepatitis B Transmission In Turkey Gölgeli, Meltem 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) transmission is proposed and analyzed. Based on the available data of Republic of Turkey Ministry of Health, associated parameters are estimated and the fitted model is shown by appropriate simulations. The basic reproductive number is obtained by using the estimated parameters. Finally, we discuss the sensitivity of parameters and the effect of changes of parameters in the spread of disease. 2019-01-01T00:00:00Z