Browsing Matematik Bölümü / Department of Mathematics by Title
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LPolynomials of the Curve
(Springer Verlag, 2015)Let chi be a smooth, geometrically irreducible and projective curve over a finite field Fq of odd characteristic. The Lpolynomial Lchi(t) of chi determines the number of rational points of chi not only over Fq but also ... 
A Mathematical Model Of Hepatitis B Transmission In Turkey
(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) ... 
The Matrix of Super Patalan Numbers and its Factorizations
(University of Nis, 2017)Matrices related to Patalan and superPatalan numbers are factored according to the LUdecomposition. Results are obtained via inspired guessings and later proved using methods from Computer Algebra. 
New analogues of the Filbert and Lilbert matrices via products of two ktuples asymmetric entries
(Hacettepe University, 20200402)In this paper, we present new analogues of the Filbert and Lilbert matrices via products of two ktuples asymmetric entries consist of the Fibonacci and Lucas numbers. We shall derive explicit formulæ for their LUdecompositions ... 
New asymmetric generalizations of the Filbert and Lilbert matrices
(Springer Netherlands, 201906)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 ... 
New binomial double sums with products of Fibonacci and Lucas numbers
(Utilitas Mathematica Publisher Inc., 2019)In this paper, we consider and compute various interesting families of binomial double sums including products of the Fibonacci and Lucas numbers. These sums have nice representations in terms of again the Fibonacci and ... 
New Sums Identities In Weighted Catalan Triangle With The Powers Of Generalized Fibonacci And Lucas Numbers
(Charles Babbage Research Centre, 201407)In this paper, we consider a generalized Catalan triangle defined by k(m)/n(2n n  k) for positive integer m. Then we compute the weighted half binomial sums with the certain powers of generalized Fibonacci and Lucas numbers ... 
Nonlinear Approximation: qBernstein Operators of MaxProduct Kind
(Springer Verlag, 2016)In this paper, we construct a certain family of nonlinear operators in order to approximate a function by these nonlinear operators. For construction, we use the linear qBernstein polynomials and also the maxproduct algebra. 
Nonlinear BernsteinType operators providing a better error estimation
(University of Miskolc, 2014)In this paper, when approximating a continuos nonnegative function on the unit interval, we present an alternative way to the classical Bernstein polynomials. Our new operators become nonlinear, however, for some classes ... 
A nonsymmetrical matrix and its factorizations
(De Gruyter, 201908)We introduce a nonsymmetric matrix defined by qintegers. Explicit formul ae are derived for its LUdecomposition, the inverse matrices L1 and U1 and its inverse. Nonsymmetric variants of the Filbert and Lilbert matrices ... 
A note on the conjecture of Ramirez and Sirvent
(University of Waterloo, 201402)We give a proof of a recent conjecture of Ramirez and Sirvent on the generating function of the incomplete Tribonacci numbers. 
An observation on the determinant of aSylvesterKac type matrix
(sciendo, 20200409)Based on a lessknown result, we prove a recent conjecture concerning the determinant of a certain SylvesterKac type matrix related tosome Lie Algebras. The determinant of an extension of that matrix ispresented. 
On Alternating Weighted Binomıal Sums With Falling Factorıals
(Int Center Scientific Research & Studies, 2017)In this paper, by inspiring from earlier recent works on weighted binomial sums, we introduce and compute new kinds of binomial sums including rising factorial of the summation indices. 
On Binomial Double Sums with Fibonacci and Lucas numbersI
(Charles Babbage Research Centre, 201904)In this paper, we compute various binomial double sums involving the generalized Fibonacci and Lucas numbers as well as their alternating analogous. 
On Fibonomial sums identities with special sign functions: analytically qcalculus approach
(De Gruyter Open Ltd, 20180626)Recently Marques and Trojovsky [On some new identities for the Fibonomial coefficients, Math. Slovaca 64 (2014), 809818] presented interesting two sum identities including the Fibonomial coefficients and Fibonacci numbers. ... 
On solutions of the recursive equations x_{n+1}=x_{n1}^{p}/x_{n}^{p} (p>0) via Fibonaccitype sequences
(201901)Abstract. In this paper, by using the classical Fibonacci sequence and the golden ratio, we ﬁrst give the exact solution of the nonlinear recursive equation xn+1 = xn−1/xn with respect to certain powers of the initial ... 
On sums of squares of Fibonomial coefficients by qcalculus
(World Scientific Publishing Co. Pte Ltd, 201609)We present some new kinds of sums of squares of Fibonomial coefficients with finite products of generalized Fibonacci and Lucas numbers as coefficients. As proof method, we will follow the method given in [E. Kili, c and ... 
On the correlation of the supremum and the infimum and of maximum gain and maximum loss of Brownian motion with drift
(Elsevier Science Bv, 201308)Investors are naturally interested in the supremum and the infimum of stock prices, also in the maximum gain and the maximum loss over a time period. To shed light on these relatively complicated aspects of sample paths, ... 
On the exact number of solutions of certain linearized equations
(Springer, 201411)In this note we have revisited some of the results of Trachtenberg (On the crosscorrelation functions of maximal linear sequences, Ph.D. thesis, University of Southern California, Los Angeles, 1970), which are directly ... 
On the Number of Irreducible Polynomials over GF(2) with Some Prescribed Coefficients
(Longdom Publishing, 201709)In this paper we evaluate the number of monic irreducible polynomials in ??2[??] of even degree ?? whose first four coefficients have prescribed values. This problem first studied in [7] and some approximate results are ...