Yazar "Kilic, Nayil" seçeneğine göre listele

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    All rank 2 primitive geometries of the Mathieu group M11
    (Hikari Ltd., 2014) Kilic, Nayil
    In this paper, we determine all rank 2 primitive geometries for the Mathieu group M11 for which object stabilizers are maximal subgroups. © Nayil Kilic.
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    ON HORADAM OCTONIONS
    (Util Math Publ Inc, 2019) Kilic, Nayil
    In this paper, we introduce the Horadam octonions, we give the Binet formula, generating function and exponential generating function of these octonions. Also, we obtain some identities for Horadam octonions including Catalan, Cassini and d'Ocagne identities. By using these results, we have the Binet formula, generating function, summation formula, Catalan and d'Ocagne identities for Fibonacci, Lucas, Jacobsthal, Jacobsthal- Lucas, Pell and Pell- Lucas octonions. Finally, we introduce the matrix generator for Horadam octonions and this generator gives the Cassini formula for the Horadam octonions.
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    ON SPLIT k- JACOBSTHAL AND k- JACOBSTHAL-LUCAS QUATERNIONS
    (Charles Babbage Res Ctr, 2019) Kilic, Nayil
    In this paper, we investigate the split k- Jacobsthal and k- Jacobsthal-Lucas quaternions, we give the Binet formulas, generating functions and exponential generating functions of these quaternions. Also, we obtain the Catalan, Cassini and d'Ocagne identities for the split k- Jacobsthal and k- Jacobsthal-Lucas quaternions.
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    ON TERMS OF THE SEQUENCE {un}
    (Charles Babbage Res Ctr, 2019) Kilic, Nayil
    In this paper, we consider the generalized Fibonacci sequence {u(n)}. We derive a generating matrix for both the sums of squares of the form Sigma(n)(k=0) q(n-k)u(k)(2) (q not equal 0) and the products of the form qu(n)u(n+2) (q not equal 0). Also, we give a matrix method to generate the sums of product of two consecutive terms u(n)n(n+1), as well as the product qu(n)u(n+2) (q not equal 0). Furthermore we obtain generating functions and combinatorial representations of u(n)u(n+1) and u(n-1)u(n+1).
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    The h(x)-Lucas quaternion polynomials
    (E K F Liceum Kiado, 2017) Kilic, Nayil
    In this paper, we study h(x)-Lucas quaternion polynomials considering several properties involving these polynomials and we present the exponential generating functions and the Poisson generating functions of the h(x)-Lucas quaternion polynomials. Also, by using Binet's formula we give the Cassini's identity, Catalan's identity and d'Ocagne's identity of the h(x)-Lucas quaternion polynomials.