The Experts below are selected from a list of 45936 Experts worldwide ranked by ideXlab platform
Yasin Altun - One of the best experts on this subject based on the ideXlab platform.
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On the Smarandache Curves of Spatial Quaternionic Involute Curve
Proceedings of the National Academy of Sciences India Section A: Physical Sciences, 2019Co-Authors: Suleyman Senyurt, Ceyda Cevahir, Yasin AltunAbstract:In this study, the spatial quaternionic curve and the relationship between Frenet frames of involute curve of spatial quaternionic curve are expressed by using the angle between the Darboux Vector and binormal Vector of the basic curve. Secondly, the Frenet Vectors of involute curve are taken as Position Vector and curvature and torsion of obtained Smarandache curves are calculated. The calculated curvatures and torsions are given depending on Frenet apparatus of basic curve. Finally, an example is given and the shapes of these curves are drawn by using Mapple program.
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On Spatial Quaternionic Involute Curve A New View
Advances in Applied Clifford Algebras, 2017Co-Authors: Suleyman Senyurt, Ceyda Cevahir, Yasin AltunAbstract:In this study, the normal Vector and the unit Darboux Vector of spatial involute curve of the spatial quaternionic curve are taken as the Position Vector, the curvature and torsion of obtained smarandahce curve were calculeted.
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On The Darboux Vector Belonging To Involute Curve A Different View
Mathematical Sciences and Applications E-Notes, 2016Co-Authors: Suleyman Senyurt, Yasin Altun, Ceyda CevahirAbstract:In this paper, we investigated special Smarandache curves in terms of Sabban frame drawn on the surface of the sphere by the unit Darboux Vector of involute curve. We created Sabban frame belonging to this curve. It was explained Smarandache curves Position Vector is composed by Sabban Vectors belonging to this curve. Then, we calculated geodesic curvatures of this Smarandache curves. Found results were expressed depending on the base curve. We also gave example belonging to the results found.
Essin Turhan - One of the best experts on this subject based on the ideXlab platform.
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Evolute Curves of Timelike Biharmonic Curves According to Flat Metric in Lorentzian Heisenberg Group Heis 3
2011Co-Authors: Talat Körpinar, Essin Turhan, Vedat AsilAbstract:In this paper, we study evolute curves of timelike biharmonic curves according to flat metric in the Lorentzian Heisenberg group Heis 3 . We characterize evolute curves of timelike biharmonic curves in terms of their curvature and torsion. Finally, we find Position Vector of evolute curves of timelike biharmonic curves according to flat metric in the Lorentzian Heisenberg group Heis 3 .
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Position Vector of spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3
2011Co-Authors: Essin TurhanAbstract:In this paper, we study spacelike biharmonic curves in the Lorentzian Heisenberg group Heis 3 . We show that spacelike biharmonic curves are general helices. We characterize Position Vector of spacelike biharmonic general helices in terms of their curvature and torsion.
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Position Vector of spacelike biharmonic slant helices with timelike principal normal according to Bishop frame in Minkowski 3-space
International Journal of Physical Sciences, 2010Co-Authors: Essin Turhan, Talat Kouml, RpinarAbstract:In this paper, we study spacelike biharmonic curves with timelike principal normal according to Bishop frame in Minkowski 3-space and give some characterizations for curvature and torsion of a biharmonic curve in Minkowski 3-space . Moreover, the Position Vectors of spacelike biharmonic slant helices were obtained in Minkowski 3-space Key words: Energy, bienergy, biharmonic curve, Minkowski 3-space.
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Position Vectors of timelike biharmonic Legendre curves in the Lorentzian Heisenberg group Heis 3
2010Co-Authors: Essin TurhanAbstract:In this paper, we study timelike biharmonic Legendre curves in the Lorentzian Heisenberg group Heis 3 . We characterize the biharmonic curves in terms of their curvature and torsion. We prove that all of timelike biharmonic curves are helices. Moreover, we obtain the Position Vectors of timelike biharmonic Legendre curves in the Lorentzian Heisenberg group Heis 3 . Also, by using the Position Vector, we give some characterizations for timelike biharmonic Legendre curves.
Suleyman Senyurt - One of the best experts on this subject based on the ideXlab platform.
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On the Smarandache Curves of Spatial Quaternionic Involute Curve
Proceedings of the National Academy of Sciences India Section A: Physical Sciences, 2019Co-Authors: Suleyman Senyurt, Ceyda Cevahir, Yasin AltunAbstract:In this study, the spatial quaternionic curve and the relationship between Frenet frames of involute curve of spatial quaternionic curve are expressed by using the angle between the Darboux Vector and binormal Vector of the basic curve. Secondly, the Frenet Vectors of involute curve are taken as Position Vector and curvature and torsion of obtained Smarandache curves are calculated. The calculated curvatures and torsions are given depending on Frenet apparatus of basic curve. Finally, an example is given and the shapes of these curves are drawn by using Mapple program.
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On Spatial Quaternionic Involute Curve A New View
Advances in Applied Clifford Algebras, 2017Co-Authors: Suleyman Senyurt, Ceyda Cevahir, Yasin AltunAbstract:In this study, the normal Vector and the unit Darboux Vector of spatial involute curve of the spatial quaternionic curve are taken as the Position Vector, the curvature and torsion of obtained smarandahce curve were calculeted.
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On The Darboux Vector Belonging To Involute Curve A Different View
Mathematical Sciences and Applications E-Notes, 2016Co-Authors: Suleyman Senyurt, Yasin Altun, Ceyda CevahirAbstract:In this paper, we investigated special Smarandache curves in terms of Sabban frame drawn on the surface of the sphere by the unit Darboux Vector of involute curve. We created Sabban frame belonging to this curve. It was explained Smarandache curves Position Vector is composed by Sabban Vectors belonging to this curve. Then, we calculated geodesic curvatures of this Smarandache curves. Found results were expressed depending on the base curve. We also gave example belonging to the results found.
Süha Yilmaz - One of the best experts on this subject based on the ideXlab platform.
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A New Special Helices in the Galilean Space G4
Prespacetime Journal, 2018Co-Authors: Süha Yilmaz, Umit Ziya SavciAbstract:In this work, we characterize certain special curves in the four-dimensional Galilean space in terms of Frenet-Serret Vector fields. We investigate an explicit characterization of general helices of the Galilean space G4. We express Position Vector of an arbitrary helix and, introduce type-1, type-2 and type-3 slant helices by aid of the second, third and fourth Vector fields of the Frenet-Serret tetrad. A number of differential and integral characterizations of the mentioned curves are expressed using classical differential geometry methods.
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Minkowski 3-uzayda 2. tip Bishop çatısına göre null olmayan eğrilerin karakterizasyonlarına dair bir inceleme
SAÜ Fen Bilimleri Enstitüsü Dergisi, 2016Co-Authors: Süha Yilmaz, Yasin Ünlütürk, Abdullah MagdenAbstract:In this work, we study classical differential geometry of non-null curves according to the new version of Bishop frame in which we call it along the work as “the Bishop frame of type-2”. First, we investigate Position Vector of a regular non-null curve by obtaining a system of ordinary differential equations. The solution of the system gives the components of the Position Vector with respect to the Bishop frame of type-2 in . Moreover, we define the first, second and third order Bishop planes according to this new frame, and also, regardig to these planes, we characterize Position Vectors in .
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Contributions to differential geometry of isotropic curves in the complex space
Journal of Mathematical Analysis and Applications, 2011Co-Authors: Süha YilmazAbstract:AbstractThis work deals with classical differential geometry of isotropic curves in the complex space C4. First, we study spherical isotropic curves and pseudo helices. Besides, in this section we introduce some special isotropic helices (type-1, type-2 and type-3 isotropic slant helices) and express some characterizations of them in terms of É. Cartan equations. Thereafter, we prove that Position Vector of an isotropic curve satisfies a Vector differential equation of fourth order. Finally, we investigate Position Vector of an arbitrary curve with respect to É. Cartan frame by a system of complex differential equations whose solution gives components of the Position Vector. Solutions of the mentioned system and Vector differential equation have not yet been found. Therefore, in terms of special cases, we present some special characterizations
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Contributions to differential geometry of isotropic curves in the complex space
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Süha YilmazAbstract:Abstract This work deals with classical differential geometry of isotropic curves in the complex space C 4 . First, we study spherical isotropic curves and pseudo helices. Besides, in this section we introduce some special isotropic helices (type-1, type-2 and type-3 isotropic slant helices) and express some characterizations of them in terms of E. Cartan equations. Thereafter, we prove that Position Vector of an isotropic curve satisfies a Vector differential equation of fourth order. Finally, we investigate Position Vector of an arbitrary curve with respect to E. Cartan frame by a system of complex differential equations whose solution gives components of the Position Vector. Solutions of the mentioned system and Vector differential equation have not yet been found. Therefore, in terms of special cases, we present some special characterizations.
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Position Vector of a Partially Null Curve Derived from a Vector Differential Equation
World Academy of Science Engineering and Technology International Journal of Mathematical Computational Physical Electrical and Computer Engineering, 2009Co-Authors: Süha Yilmaz, Emin Özyilmaz, Melih Turgut, Şuur NizamoğluAbstract:In this paper, Position Vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that Position Vector of every partially null unit speed curve satisfies a Vector differential equation of fourth order. In terms of solution of the differential equation, Position Vector of a partially null unit speed curve is expressed.
Yun-hui Liu - One of the best experts on this subject based on the ideXlab platform.
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IROS - Lyapunov-stable Eye-in-hand Kinematic Visual Servoing with Unstructured Static Feature Points
2014 IEEE RSJ International Conference on Intelligent Robots and Systems, 2014Co-Authors: David Navarro-alarcon, Yun-hui LiuAbstract:In this paper, we address the visual servoing problem of robot manipulators with eye-in-hand cameras. To servo-control the image Position of a feature point, traditional image-based controllers require the computation of the point's Position Vector with respect to the camera's frame. However, when the point's location is uncertain, the stability of traditional visual servoing controllers can not be rigorously guaranteed. To contribute to this problem, in this paper we present two new kinematic image-based controllers that do not require the exact location of static features. The first controller is a depth-free method that uses the camera's calibration matrix and visual feedback to compute a quasi-Position Vector of the feature point. The second controller uses adaptive control techniques to iteratively estimate the calibration matrix and the point's Position Vector. We prove the stability of both servo-controllers using Lyapunov theory, and present experimental results to evaluate its performance.
