Now showing items 97-116 of 135

    • 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 ...
    • Poles of L-Functions on Quaternion Groups 

      Ürtiş, Çetin (Shanghai Scientific Technology Literature Publishing House, 2014-08)
      The author shows that the (partial) standard Langlands L-functions on quarternion groups have at most simple poles at certain positive integers.
    • Powers Sums of the First and Second Kinds of Chebyshev Polynomials 

      Kılıç, Emrah; Koparal, Sibel; Ömür, Neşe (Springer, 2020-04)
      Odd powers of even-indexed Chebyshev polynomials of the second kind and odd powers of odd-indexed 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 

      Kılıç, Emrah (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 q-binomial coefficients and q-Pochhammer symbols, we ...
    • 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 ...
    • Quadratic sums of Gaussian q-binomial coefficients and Fibonomial coefficients 

      Kılıç, Emrah; Chu, Wenchang (Springer, 2020)
      In this paper we evaluate quadratic sums of Gaussian q-binomial coefficients with two additional parameters. We obtain a general summation theorem using a combination of Heine’s transformation, the q-Pfaff–Saalschutz theorem ...
    • Rational points of the curve over 

      Özbudak, Ferruh; Saygı, Zülfükar (Cambridge University Press, 2014-01)
      Let q be a power of an odd prime. For arbitrary positive integers h, n, m with n dividing m and arbitrary with ? ? 0 we determine the number of -rational points of the curve in many cases.
    • Robust preconditioners for the high-contrast Stokes equation 

      Aksoylu, Burak (Elsevier Science Bv, 2014-03)
      We consider the Stokes equation with high-contrast viscosity coefficients. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by ...
    • Ruehr's identities with two additional parameters 

      Kılıç, Emrah; Arıkan, Talha (Integers, 2016-03)
      We present generalizations of Ruehr’s identities with two additional parameters. We prove the claimed results by two di?erent proof methods, namely combinatorially and mechanically. Further, we derive recurrence relations ...
    • Singular approximation in polydiscs by summability process 

      Duman, Oktay (Springer, 2016-09)
      In this paper, we approximate a continuous function in a polydisc by means of multivariate complex singular operators which preserve the analytic functions. In this singular approximation, we mainly use a regular summability ...
    • Smoothness Properties of Modified Bernstein-Kantorovich Operators 

      Ozarslan, Mehmet Ali; Duman, Oktay (Taylor and Francis Inc., 2016-01)
      In this article, we consider modified Bernstein-Kantorovich operators and investigate their approximation properties. We show that the order of approximation to a function by these operators is at least as good as that of ...
    • Solving a Second Order Fuzzy Initial Value Problem Using The Heaviside Function 

      Akın, Ömer; Khaniyev, Tahir; Bayeğ, Selami; Türkşen, İ. B. (Matematikçiler Derneği, 2016-06)
      In this paper, we reformulate the algorithm in [7] to find an analytical expression for ?-cuts of the solution of the second order nonhomogeneous fuzzy initial value problem with fuzzy initial values and fuzzy forcing ...
    • Some classes of alternating weighted binomial sums 

      Kılıç, Emrah (2016-09)
      In this paper, we consider three classes of generalized alternating weighted binomial sums of the form where f (n, i, k, t) will be chosen as UktiVkn?k(t+2)i, UktiVkn?kti and UtkiV(k+1)tn?(k+2)ti. We use the Binet formula ...
    • Some Double binomial sums related to Fibonacci, Pell and generalized order-k Fibonacci numbers 

      Kılıç, Emrah; Prodinger, Helmut (Rocky Mt Math Consortium, 2013-10)
      We consider some double binomial sums related to the Fibonacci and Pell numbers and a multiple binomial sum related to the generalized order-k Fibonaccinumbers. The Lagrange-Burmann formula and other well-known techniques ...
    • Some Gaussian binomial sum formulæ with applications 

      Kılıç, Emrah; Prodinger, Helmut (Indian National Science Academy, 2016-09)
      We introduce and compute some Gaussian q-binomial sums formul ae. In order to prove these sums, our approach is to use q-analysis, in particular a formula of Rothe, and computer algebra. We present some applications of our ...
    • Some possible fuzzy solutions for second order fuzzy initial value problems involving forcing terms 

      Akın, Ömer; Khaniyev, Tahir; Oruc, O.; Turksen, I. B. (Azerbaijan National Academy of Sciences, 2014)
      In this paper, we state a fuzzy initial value problem of the second order fuzzy differential equations. Here, we investigate problems with fuzzy coefficients, fuzzy initial values, and fuzzy forcing functions where fuzzy ...
    • Some Results On Hausdorff Metric For Intuitionistic Fuzzy Sets 

      Akın, Ömer; Bayeğ, Selami (Matematikçiler Derneği, 2018)
      Fuzzy set theory was frstly introduced by L. A. Zadeh in 1965 [1]. In fuzzy sets, every element in the set is accompanied with a function μ(x): X → [0, 1], called membership function. The membership function may have ...
    • Some Results on the Fundamental Concepts of Fuzzy Set Theory in Intuitionistic Fuzzy Environment by Using α and β cuts 

      Akın, Ömer; Bayeğ, Selami (University of Nis, 2019)
      In this paper we have frstly examined the properties of α and β cuts of intuitionistic fuzzy numbers in Rn with the help of well-known Stacking and Characterization theorems in fuzzy set theory. Then, we have studied the ...
    • Some Subsequences of the Generalized Fibonacci and Lucas Sequences 

      Kılıç, Emrah; Kılıç, Elif Tan (Utilitas Mathematica Publishing Inc., 2015-07)
      We derive first-order nonlinear homogeneous recurrence relations for certain subsequences of generalized Fibonacci and Lucas sequences. We also present a polynomial representation for the terms of Lucas subsequence.
    • Some weighted sums of products of Lucas sequences 

      Kılıç, Emrah; Ömür, Neşe (Integers, 2013-11)
      In this paper, we consider the weighted sums of products of Lucas sequences of the form (Formula Presented) where rn and sn are the terms of Lucas sequences {Un} and {Vn} for some positive integers t and m. By using ...