Person: AKPINAR, ATİLLA
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AKPINAR
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ATİLLA
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Publication On some projective planes of finite order(Gazi Üniversitesi, 2005-01-01) Akpınar, Atilla; AKPINAR, ATİLLA; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-7612-2448; ABB-9790-2020In this work, construction methods of projective planes of order 2, 3, 4, 5, 7 and 8 are examined. Informations about the obtaining of known four different planes of order 9 and non-existence of a projective plane of order 10 which is obtained according to computer based calculations are collected.Publication On distance in some finite planes and graphs arising from those planes(Hindawi, 2021-01-28) Doğan, İsa; Akpınar, Atilla; Doğan, İsa; AKPINAR, ATİLLA; Fen Bilimleri Enstitüsü; Matematik Bölümü; 0000-0002-7612-2448; ABB-9790-2020; CNU-8477-2022In 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.Publication N-spaces(Ankara Üniversitesi, 2020-01-01) Akpınar, Atilla; AKPINAR, ATİLLA; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-7612-2448; ABB-9790-2020In 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.Publication N-spaces(Ankara Üniversitesi, 2020-01-01) Akpınar, Atilla; AKPINAR, ATİLLA; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-7612-2448; ABB-9790-2020In 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.Publication On a new class of moufang-klingenberg planes(World Scientific Publ, 2021-07-01) Doğan, İsa; Akpınar, Atilla; Doğan, İsa; AKPINAR, ATİLLA; Fen Edebiyat Fakültesi; Matematik Bölümü; 0000-0002-7612-2448; ABB-9790-2020; CNU-8477-2022In this paper, we deal with a new class of Moufang-Klingenberg planes and study with the concepts of 4-transitivity and 6-figures on the class of planes. So, we reach some algebraic and geometric results related on the concepts. For instance, we show that the group of collineations of these planes acts transitively on 4-gons. Finally, we obtain some properties of 6-figures.Publication Projective coordinate spaces over modules(Hacettepe Universitesi, 2019-01-01) Erdoğan, Fatma Özen; ÖZEN ERDOĞAN, FATMA; Akpınar, Atilla; AKPINAR, ATİLLA; Fen Edebiyat Fakültesi; Matematik Ana Bilim Dalı; 0000-0002-7612-2448; ABB-9790-2020; AAG-8274-2021In 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.