Yazar "Karakus, Fatma" seçeneğine göre listele

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    Curvature Control for Plane Curves
    (Mdpi, 2025) Karakus, Fatma; Pripoae, Cristina-Liliana; Pripoae, Gabriel-Teodor
    We define a family of special functions (the CSI ones), which can be used to write any parameterized plane curve with polynomial curvature explicitly. These special functions generalize the Fresnel integrals, and may have an interest in their own right. We prove that any plane curve with polynomial curvature is asymptotically a pseudo-spiral. Using the CSI functions, we can approximate, locally, any plane curve; this approach provides a useful criterion for a (local) classification of plane curves. In addition, we present a new algorithm for finding an arc-length parametrization for any curve, within a prescribed degree of approximation.
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    Generalized Fermi-Walker derivative and non-rotating frame
    (World Scientific Publ Co Pte Ltd, 2017) Ucar, Aysenur; Karakus, Fatma; Yayli, Yusuf
    In this paper, generalized Fermi-Walker derivative, generalized Fermi-Walker parallelism and generalized non-rotating frame concepts are given for Frenet frame, Darboux frame and Bishop frame for any curve in Euclidean space. Being generalized, non-rotating frame conditions are analyzed for each frames along the curve. Then we show that Frenet and Darboux frames are generalized non-rotating frames along all curves and also Bishop frame is generalized non-rotating frame along planar curves in Euclidean space.
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    On the Surface the Fermi-Walker Derivative in Minkowski 3-Space
    (Springer Basel Ag, 2016) Karakus, Fatma; Yayli, Yusuf
    In this paper Fermi-Walker derivative and Fermi-Walker parallelism and non-rotating frame concepts are given along the curve lying on the spacelike surface and the timelike surface in Minkowski 3-space. First, we consider a curve lying on the spacelike surface and investigate the Fermi-Walker derivative along the curve. The concepts which Fermi-Walker derivative and its theorems are analyzed along the curve lying on the spacelike surface in Minkowski 3-space. And then we consider a curve lying on the timelike surface and investigate the Fermi-Walker derivative along the curve.
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    PARALLEL TRANSPORTS WITH RESPECT TO FRENET AND DARBOUX FRAMES IN THE GALILEAN SPACE
    (Editura Bibliotheca-Bibliotheca Publ House, 2020) Sahin, Tevfik; Karakus, Fatma; Orbay, Keziban
    In this paper, we defined Fermi-Walker derivative in Galilean space G(3) Fermi-Walker transport and non-rotating frame by using Fermi-Walker derivative are given in G(3). Being conditions of Fermi-Walker transport and non-rotating frame are investigated along any curve for Frenet frame and Darboux frame.
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    The Fermi derivative in the hypersurfaces
    (World Scientific Publ Co Pte Ltd, 2015) Karakus, Fatma; Yayli, Yusuf
    In this study, Fermi derivative and according to the derivative Fermi parallelism and non-rotating frame concepts are given on any hypersurface in En+1. Initially, Fermi derivative and non-rotating concepts are analyzed on any hypersurface in E-4. As an example, S-3 is taken instead of the hypersurface in E-4. Fermi derivative and non-rotating concepts are examined for S-3. Then a correlation is found between Fermi derivative and Levi-Civita derivative of any vector field in E-4. And then the concepts of Fermi derivative are generalized for n > 4 in En+1.
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    The Fermi-Walker Derivative and Non-rotating Frame in Dual Space
    (Springer Basel Ag, 2018) Sahin, Tevfik; Karakus, Fatma; Yayli, Yusuf
    In this study, we defined Fermi-Walker derivative in dual space D-3. Fermi-Walker transport, non-rotating frame and Fermi-Walker termed Darboux vector by using Fermi-Walker derivative are given in dual space D-3. Being conditions of Fermi-Walker transport and non-rotating frame are investigated along any dual curve for dual Frenet frame, dual Darboux frame and dual Bishop frame.
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    The Fermi-Walker Derivative in Minkowski Space
    (Springer Basel Ag, 2017) Karakus, Fatma; Yayli, Yusuf
    In this study Fermi-Walker derivative, Fermi-Walker parallelism, non-rotating frame, Fermi-Walker terms Darboux vector concepts are given for Minkowski 3-space . First, we get any spacelike curve with a spacelike or timelike principal normal and any vector field along the curve in Minkowski 3-space . Fermi-Walker derivative and Fermi-Walker parallelism are analyzed for any spacelike curve with a spacelike or timelike principal normal in Minkowski 3-space and the necessary conditions to be Fermi-Walker parallel are explained. Then the necessary definitions, concepts and theorems are analyzed about Fermi-Walker derivative for any spacelike curve with a lightlike(null) principal normal. And then, in Minkowski 3-space Fermi-Walker derivative is analyzed for any timelike curves.
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    The Fermi-Walker Derivative on the Spherical Indicatrix of a Space Curve
    (Springer Basel Ag, 2016) Karakus, Fatma; Yayli, Yusuf
    In this paper Fermi-Walker derivative and Fermi-Walker parallelism and non-rotating frame concepts are given along the spherical indicatrix of a curve in E (3). First, we consider a curve in Euclid space and investigate the Fermi-Walker derivative along the tangent. The concepts which Fermi-Walker derivative are analyzed along its tangent. Then, the Fermi-Walker derivative and its theorems are analyzed along the principal normal indicatrix and the binormal indicatrix of any curve in E-3.
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    The Fermi-Walker Derivative on the Spherical Indicatrix of Spacelike Curve in Minkowski 3-Space
    (Springer Basel Ag, 2016) Karakus, Fatma; Yayli, Yusuf
    In this paper Fermi-Walker derivative, Fermi-Walker parallelism, non-rotating frame and Fermi-Walker terms Darboux vector concepts are given along the spherical indicatrix of a spacelike curve with a spacelike or timelike principal normal in . First, we consider a spacelike curve in the Minkowski space and investigate the Fermi-Walker derivative along the tangent. The concepts with the Fermi-Walker derivative are analyzed along its tangent. Then, the Fermi-Walker derivative and its theorems are analyzed along the principal normal indicatrix and the binormal indicatrix of spacelike curve in .
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    The Fermi-Walker Derivative on the Spherical Indicatrix of Timelike Curve in Minkowski 3-Space
    (Springer Basel Ag, 2016) Karakus, Fatma; Yayli, Yusuf
    In this paper Fermi-Walker derivative and Fermi-Walker parallelism and non-rotating frame concepts are given along the spherical indicatrix of a timelike curve in . First, we consider a timelike curve in the Minkowski space and investigate the Fermi-Walker derivative along the tangent. The concepts which Fermi-Walker derivative are analyzed along its tangent. Then, the Fermi-Walker derivative and its theorems are analyzed along the principal normal indicatrix and the binormal indicatrix of timelike curve in E-1(3).