Browsing by Author "Kazaz M."
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Item Presentations for regular unbranched Cp -coverings of a Klein Bottle(Association for Scientific Research, 2004) Kazaz M.[No abstract available]Item The sine and cosine rules for pure triangles on the dual lorentzian unit sphere S̃12(2005) Kazaz M.The sine and cosine rules for a spherical pure triangle on the dual Lorentzian sphere were proved. On the Lorentzian sphere, there are points, but there are no straight lines, at least not in the usual sense. However, straight timelike, spacelike and lightlike lines in the Lorentzian plane are characterized by the fact that they are the shortest paths between points. The curves on the Lorentzian sphere with the same property are timelike, spacelike and lightlike circles. Thus it is natural to use these circles as replacements for lines.Item Fundamental theorems for the hyperbolic geodesic triangles(2005) Uǧurlu H.H.; Kazaz M.; Özdemir A.In this work, we state and prove the sine, cosine I, cosine II, sine-cosine and cotangent rules for spherical triangles on the hyperbolic unit sphere H02 in the Lorentzian space R13.Item The Cosine Rule II for a spherical triangle on the dual unit sphere S̃2(2005) Kazaz M.; Uǧurlu H.H.; Özdemir A.In this work, we proved the Cosine Rule II for a spherical triangle on the dual unit sphere S̃2. © Association for Scientific Research.Item Hyperbolic sine and cosine rules for geodesic triangles on the hyperbolic unit sphere H02(Association for Scientific Research, 2005) Özdemir A.; Kazaz M.In this work, we proved the sine and cosine rules for a geodesic triangle on the hyperbolic unit sphere H02 by means of timelike unit vectors. We also obtained some useful results.Item Integral characterizations for timelike and spacelike curves on the Lorentzian sphere S13(Shiraz University, 2008) Kazaz M.; Ugurlu H.H.; Ozdemir A.V. Dannon showed that spherical curves in E4 can be given by Frenet-like equations, and he then gave an integral characterization for spherical curves in E4. In this paper, Lorentzian spherical timelike and spacelike curves in the space time R14 are shown to be given by Frenet-like equations of timelike and spacelike curves in the Euclidean space E3 and the Minkowski 3-space R1 3. Thus, finding an integral characterization for a Lorentzian spherical R14 -timelike and spacelike curve is identical to finding it for E3 curves and R13 -timelike and spacelike curves. In the case of E3 curves, the integral characterization coincides with Dannon's. Let {T, N, B} be the moving Frenet frame along the curve α(s) in the Minkowski space R1 3 . Let α(s) be a unit speed C4-timelike (or spacelike) curve in R13 so that α'(s) = T . Then, α(s) is a Frenet curve with curvature κ(S) and torsion τ(S) if and only if there are constant vectors a and b so that (i) T′(s) = κ(s){a cosξ(s)+b sinξ(s) + ∫0s cos[ξ(s)-ξ(δ)]T(δ)κ(δ)doδ}, T is timelike, (ii) T′(s) = κ(S){ aeξ+ ∫0 scosh((ξ(s)-ξ(δ))T(δ)κ(δ)dδ}, N is timelike, where ξ(s)= ∫0s(δ)dδ. © Shiraz University.Item Two-sided Γ-α-derivations in prime and semiprime Γ-near-rings(2008) Kazaz M.; Alkan A.We introduce the notion of two-sided Γ-α-derivation of a Γ-near-ring and give some generalizations of [1,2].© 2008 The Korean Mathematical Society.Item Elliptic motion on dual hyperbolic unit sphere over(H, ∼)02(2009) Kazaz M.; Özdemir A.; Hüseyin Uǧurlu H.Planar and spherical elliptic motions had been introduced by Karger and Novák [A. Karger, J. Novák, Space Kinematics and Lie Groups, Gordon and Breach Science Publishers, New York, London, 1985]. Also, a dual spherical elliptic motion has been defined by Yapar [Z. Yapar, Spatial conchoidal and elliptic motions, Mechanism and Machine Theory 27 (1) (1992) 75-91]. In this paper, we define the elliptic motion on a dual hyperbolic unit sphere over(H, ∼)02 in the dual Lorentzian space D13 with dual signature (+, +, -) and carry the results to the Lorentzian line space IR13 by means of Study's mapping. © 2008 Elsevier Ltd. All rights reserved.Item Elementary abelian coverings of regular hypermaps of types (5, 5, 5) and (5, 2, 10) of genus 2(2009) Kazaz M.In this paper, we find elementary abelian coverings of the regular hyper- maps H1 of type {5, 5, 5} and M1 of type {5, 2, 10} of genus 2 corresponding to the orientation-preserving automorphism groups C 5, the cyclic group of order 5, and C10, the cyclic group of order 10, respectively. We also determine the reflexibility of these coverings.Item Spacelike helices in Minkowski 4-space E 1 4(Springer-Verlag Italia s.r.l., 2010) Önder M.; Kocayiğit H.; Kazaz M.In this paper, we give some characterizations for spacelike helices in Minkowski space-time E 1 4 . We find the differential equations characterizing the spacelike helices and also give the integral characterizations for these curves in Minkowski space-time E 1 4 . © 2010 Università degli Studi di Ferrara.Item Spacelike B2-slant helix in Minkowski 4-space E41(2010) Önder M.; Kocayǐit H.; Kazaz M.In this paper, we give the characterizations of spacelike B2 -slant helix by means of curvatures of the spacelike curve in Minkowski 4 - space. Furthermore, we give the integral characterization of the spacelike B2 - slant helix. © 2010 Academic Journals.Item Some characterizations of Mannheim partner curves in the minkowski 3-space E 3 1 ; [Mannheimi partnerkõverate iseloomustus Minkowski 3-ruumis E 3 1 ](2011) Kahraman T.; Önder M.; Kazaz M.; Hüseyin Uǧurlu H.In this paper, we give some characterizations of Mannheim partner curves in the Minkowski 3-space E 3 1. Firstly, we classify these curves in E 3 1. Next, we give some relationships characterizing these curves and we show that the Mannheim theorem is not valid for the Mannheim partner curves in E 3 1. Moreover, by considering the spherical indicatrix of the Frenet vectors of those curves, we obtain some new relationships between the curvatures and torsions of the Mannheim partner curves in E 3 1.Item A study on motion of a robot end-effector using the curvature theory of dual unit hyperbolic spherical curves(University of Nis, 2016) Sahiner B.; Kazaz M.; Ugurlu H.H.In this paper we study the motion of a robot end-effector by using the curvature theory of a dual unit hyperbolic spherical curve which corresponds to a timelike ruled surface with timelike ruling generated by a line fixed in the end-effector. In this way, the linear and angular differential properties of the motion of a robot end-effector such as velocities and accelerations which are important information in robot trajectory planning are determined. Moreover, the motion of a robot end-effector which moves on the surface of a right circular hyperboloid of one sheet is examined as a practical example. © 2016, University of Nis. All rights reserved.Item Characterizations for slant ruled surfaces in dual space(Shiraz University, 2017) Oral S.; Kazaz M.In this paper, we study slant ruled surfaces in dual space by considering E. Study’s mapping. We consider ruled surfaces as spherical curves lying on dual unit sphere and study the notion of ‘‘slant ruled surface’’ by means of dual Darboux frame and obtain some dual characterizations for which the real parts of them coincide with results given by Önder (Slant ruled surfaces in Euclidean 3-space E3, arXiv:1311.0627v1 [math.DG], 2013). © Shiraz University 2017.Item GEOMETRIC INEQUALITIES FOR STATISTICAL SUBMANIFOLDS IN COSYMPLECTIC STATISTICAL MANIFOLDS(University of Kragujevac, Faculty of Science, 2024) Kazaz M.; Aslam M.; Aquib M.In this paper, we obtain two important geometric inequalities namely, Euler’s inequality and Chen’s inequality for statistical submanifolds in cosymplectic statistical manifolds with constant curvature, and discuss the equality case of the inequalities. We also give some applications of the inequalities obtained. © (2024), (Kragujevac Journal of Mathematics). All rights reserved.