Yazar "Kecilioglu, Osman" seçeneğine göre listele

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    The Fibonacci Octonions
    (Springer Basel Ag, 2015) Kecilioglu, Osman; Akkus, Ilker
    In the present paper, we introduce the Fibonacci and Lucas octonions and give the generating function and Binet formulae for these octionions. In addition, we give some identities and properties of them.
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    Generalized Bertrand Curves with Spacelike (1,3)-Normal Plane in Minkowski Space-Time
    (Scientific Technical Research Council Turkey-Tubitak, 2016) Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim
    In this paper, we reconsider the (1, 3)-Bertrand curves with respect to the casual characters of a (1, 3)-normal plane that is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of (1, 3)-Bertrand curves to the spacelike (1, 3)-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with spacelike (1, 3)-normal plane to be (1, 3)-Bertrand curves and we give the related examples for these curves.
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    Generalized Bertrand curves with timelike (1,3)-normal plane in Minkowski space-time
    (Academic Publication Council, 2015) Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim
    In this paper, we reconsider the (1,3)-Bertrand curves with respect to the casual characters of (1,3)-normal plane which is a plane spanned by the principal normal and the second binormal vector fields of the given curve. Here, we restrict our investigation of (1,3)-Bertrand curves to the timelike (1,3)-normal plane in Minkowski space-time. We obtain the necessary and sufficient conditions for the curves with timelike (1,3)-normal plane to be (1,3)-Bertrand curves and we give the related examples for these curves.
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    GENERALIZED MATRIX MULTIPLICATION AND ITS SOME APPLICATION
    (Univ Nis, 2017) Kecilioglu, Osman; Gundogan, Halit
    In this paper, a generalized matrix multiplication is defined in R-m,R-n x R-n,R-p by using any scalar product in R-n, where R-m,R-n denotes set of matrices of m rows and n columns. With this multiplication it has been shown that R-n,R-n is an algebra with unit. By considering this new multiplication we define eigenvalues and eigenvectors of square n x n matrix A. A special case is considered and generalized diagonalization is also introduced.
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    Generalized pseudo null Bertrand curves in semi-Euclidean 4-space with index 2
    (Springer-Verlag Italia Srl, 2016) Ucum, Ali; Kecilioglu, Osman; Ilarslan, Kazim
    In this paper, we study generalized pseudo null Bertrand curves in semi-Euclidean 4-space E-2(4) with index 2. We get the necessary and sufficient conditions for pseudo null curves to be generalized Bertrand curves and we give some examples.
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    Pseudo Matrix Multiplication
    (Ankara Univ, Fac Sci, 2017) Kecilioglu, Osman; Gundogan, Halit
    In this paper, a new matrix multiplication is defined in R-m,R-n x R-n,R-p by using scalar product in R-n, where R-m,R-n is set of matrices of m rows and n columns. With this multiplication it has been shown that R-n,R-n is an algebra with unit. By considering this new multiplication we define eigenvalues and eigenvectors of square n x n matrix A and also present some applications.
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    Rotations and Screw Motion with Timelike Vector in 3-Dimensional Lorentzian Space
    (Springer Basel Ag, 2012) Kecilioglu, Osman; Ozkaldi, Siddika; Gundogan, Halit
    In the present paper we obtain the timelike Euler parameters of a Lorentzian orthogonal matrix in Lorentz space L-3 = R-2,R-1 by using Lorentzian matrix multiplication. Then, by using the timelike Euler parameters of a given rotation in a split quaternion formulation, we produce split quaternion equation of a rotation motion in L-3. Moreover the components of a dual split quaternion are obtained by replacing the timelike L-Euler parameters with their split dual versions.
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    Split Fibonacci and Lucas Octonions
    (Springer Basel Ag, 2015) Akkus, Ilker; Kecilioglu, Osman
    In this paper, split Fibonacci and Lucas octonions are proposed and their some properties and relations are obtained.
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    Symmetric (f, g) Bi-Derivations Of Lattices
    (Util Math Publ Inc, 2015) Jun, Young Bae; Asci, Mustafa; Kecilioglu, Osman
    In this paper as a generalization of symmetric bi-derivations and symmetric f bi-derivations of a lattice, we introduce the notion of symmetric (f, g) bi-derivations of a lattice. If the function g is equal to the function f then the symmetric (f, g) bi-derivation is the symmetric f bi-derivation defined in [18]. Also if we choose the functions f and g the identity functions both then the derivation we define coincides with the derivation defined in [9].