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AKPINAR, ATİLLA

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AKPINAR

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ATİLLA

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2019 - 201912020 - 20212
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    N-spaces
    (Ankara Üniversitesi, 2020-01-01) Akpınar, Atilla; AKPINAR, ATİLLA; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7612-2448; ABB-9790-2020
    In this paper, we introduce n-spaces constructed over an local ring with the maximal ideal (of non-unit elements). So, we give the example of an octonion n-space. Finally, we give two collineations of quaternion n-space.
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    On distance in some finite planes and graphs arising from those planes
    (Hindawi, 2021-01-28) Doğan, İsa; Akpınar, Atilla; Doğan, İsa; AKPINAR, ATİLLA; Bursa Uludağ Üniversitesi/Fen Bilimleri Enstitüsü/Matematik Bölümü; Bursa Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; 0000-0002-7612-2448; ABB-9790-2020; CNU-8477-2022
    In this paper, affine and projective graphs are obtained from affine and projective planes of order p(r) by accepting a line as a path. Some properties of these affine and projective graphs are investigated. Moreover, a definition of distance is given in the affine and projective planes of order p(r) and, with the help of this distance definition, the point or points having the most advantageous (central) position in the corresponding graphs are determined, with some examples being given. In addition, the concepts of a circle, ellipse, hyperbola, and parabola, which are well known for the Euclidean plane, are carried over to these finite planes. Finally, the roles of finite affine and projective Klingenberg planes in all the results obtained are considered and their equivalences in graph applications are discussed.
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    Projective coordinate spaces over modules
    (Hacettepe Universitesi, 2019-01-01) Erdoğan, Fatma Özen; ÖZEN ERDOĞAN, FATMA; Akpınar, Atilla; AKPINAR, ATİLLA; Bursa Uludağ Üniversitesi/Fen Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-7612-2448; ABB-9790-2020; AAG-8274-2021
    In this paper, we investigate some properties of the (right) modules constructed over the local ring and also construct a projective coordinate space over the (right) module. Finally, in a 3-dimensional projective coordinate space, the incidence matrix for a line that combines the certain two points and also all points of a line given with the incidence matrix are found by the help of Maple programme.