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Öğe Characterization of integral curves of a linear vector field in Lorentz 3-space(World Scientific Publ Co Pte Ltd, 2016) Turhan, Tunahan; Ayyildiz, NihatWe 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.Öğe INTEGRAL CURVES OF A LINEAR VECTOR FIELD IN SEMI-EUCLIDEAN SPACES(Dynamic Publishers, Inc, 2015) Turhan, Tunahan; Ayyildiz, NihatIn 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.Öğe Matlab Applications for Skew-Symmetric Matrices and Integral Curves in Lorentzian Spaces(2017) Turhan, Tunahan; Göktepe, Yunus Emre; Ayyıldız, Nihat[8] de, yazarlar (2n1) boyutlu Lorentz uzayında, A matrisi A lineer dönüşümüne karşılık gelen anti-simetrik matris olmak üzere, A(x)0 denkleminin sıfırdan farklı çözümlerini ve x vektörünün kosul karakterlerine göre A anti-simetrik matrisinin normal formlarını elde ettiler. Bu çalışmada, A matrisinin yapısı göz önüne alınarak, antisimetrik matrislerin normal formları için bazı Matlab uygulamaları ve Matlab kodları üretildi. Ayrıca bu uzayda çözümleri lineer vektör alanlarının integral eğrilerine karşılık gelen birinci mertebeden lineer diferansiyel denklem sistemleri için Matlab kodları verildi. Dahası özel durumlar ve x vektörünün kosul karakterlerine göre Matlab uygulamaları yapıldı.Öğe On pseudohyperbolic space motions(2015) Turhan, Tunahan; Yüksel, Nural; Ayyıldız, NihatIn the present paper, the geometrical instantaneous invariants of the motion Hm/Hf in dual Lorentzian 3 -space are determined. Depending on this, the dual Lorentzian instantaneous screw axis of the motion of Km with respect to the dual pseudohyperbolic space Km is constructed. On the other hand, we show that, in each position of Hm , the fixed and moving axodes have the instantaneous screw axis of this position in common. We also give relations between the geodetic curvature and the curvature of the polodes.Öğe Skew-symmetric matrices and integral curves in Lorentzian spaces(Academic Publication Council, 2016) Turhan, Tunahan; Ayyildiz, NihatWe 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).
