Yazar "Ayyildiz, Nihat" seçeneğine göre listele

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    Characterization of integral curves of a linear vector field in Lorentz 3-space
    (World Scientific Publ Co Pte Ltd, 2016) Turhan, Tunahan; Ayyildiz, Nihat
    We propose a detail study of integral curves or flow lines of a linear vector field in Lorentz 3-space. We construct the matrix A depending on the causal characters of the vector x by analyzing the non-zero solutions of the equation A(x) = 0, x is an element of E-1(3), in such a space, where A is the skew-symmetric matrix corresponding to the linear map A. Considering the structure of a linear vector field, we obtain the linear first-order system of differential equations. The solutions of this system of equations give rise to integral curves of linear vector fields from which we provide a classification of such curves.
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    INTEGRAL CURVES OF A LINEAR VECTOR FIELD IN SEMI-EUCLIDEAN SPACES
    (Dynamic Publishers, Inc, 2015) Turhan, Tunahan; Ayyildiz, Nihat
    In this paper, we study integral curves or flow lines of a linear vector field in (2n+1)-dimensional semi-Euclidean space E-v(2n+1). The skew symmetric matrix has been found depending on the number of timelike vectors are odd or even. Taking into consideration of the structure, we obtained the linear first order system of differential equations. This system gives rise to integral curves of linear vector fields. Meanwhile solution of the system has also been presented and discussed. Keywords. Integral curve, linear vector field, semi-Euclidean space, skew-symmetric matrix.
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    Skew-symmetric matrices and integral curves in Lorentzian spaces
    (Academic Publication Council, 2016) Turhan, Tunahan; Ayyildiz, Nihat
    We provide some existence results about integral curves of a linear vector field on 3-dimensional Lorentzian space E-1(3). Moreover we have a classification of integral curves (flow lines) of a linear vector field and the normal forms of the matrix corresponding to a mapping A in Lorentzian spaces E-1(3) and E-1(2n+1).