Browsing Matematik Bölümü / Department of Mathematics by Title
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An observation on the determinant of a SylvesterKac 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 Binomial Double Sums With Fibonacci And Lucas NumbersII
(Charles Babbage Research Centre, 201904)In this paper, we compute various binomialdoublesums involving the Fibonacci numbers as well as their alternating analogous. It would be interesting that all sums we shall compute are evaluated in nice multiplication ... 
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 ... 
On the number of knormal elements over finite fields
(TÜBİTAK, 2019)In this article we give an explicit formula for the number of kknormal elements, hence answering Problem 6.1. of Huczynska et al. (Existence and properties of kknormal elements over finite fields, Finite Fields Appl 2013; ... 
On the Number of Quadratic Forms Having Codimension 2 Radicals in Characteristic 2 Giving Maximal/Minimal Curves
(Taylor and Francis Inc., 201409)Let Fq be an arbitrary finite field of characteristic 2 and k be an arbitrary even integer. We count the number of quadratic forms having codimension 2 radicals on Fq(k) over Fq such that the corresponding curve is ... 
On a class of nonlocal wave equations from applications
(American Institute of Physics Inc., 201606)We study equations from the area of peridynamics, which is a nonlocal extension of elasticity. The governing equations form asystem of nonlocal wave equations. We take a novel approach by applying operator theory methods ... 
Oscillation criteria for higherorder nonlinear delay dynamic equations on time scales
(De Gruyter Open Ltd, 201606)In this paper, oscillation criteria are obtained for higherorder halflinear delay difference equations involving generalized difference operator of the form Delta(b) (p(n) (Delta(m1)(b) x(n))(alpha)) + q(n)x(nsigma)(beta) ... 
Oscillation Criteriaof impulsive partial difference Equations
(Matematikçiler Derneği, 201301)In this paper, some oscillation criteria of certain impulsive partial difference equations with continuous variables are established. 
Partial sums of the gaussian qbinomial coefficients, their reciprocals, square and squared reciprocals with applications
(University of Miskolc, 2019)In this paper, we shall derive formulæ for partial sums of the Gaussian qbinomial coefficients, their reciprocals, squares and squared reciprocals. To prove the claimed results, we use qcalculus. As applications of our ... 
Poles of LFunctions on Quaternion Groups
(Shanghai Scientific Technology Literature Publishing House, 201408)The author shows that the (partial) standard Langlands Lfunctions on quarternion groups have at most simple poles at certain positive integers. 
Powers Sums of the First and Second Kinds of Chebyshev Polynomials
(Springer, 202004)Odd powers of evenindexed Chebyshev polynomials of the second kind and odd powers of oddindexed Chebyshev polynomials of the first kind were computed. In this paper, we evaluate all of the rest kinds of power sums of the ... 
A proof of a conjecture of Marques and Trojovsky
(University of Miskolc, 2014)In this paper, we consider Marques and Trojovsky's conjecture involving Fibonomial coefficients, Fibonacci and Lucas numbers. After rewriting it in terms of Gaussian qbinomial coefficients and qPochhammer symbols, we ... 
A proof of Clarke's conjecture
(Cambridge University Press, 201907)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 ...