özgür keskin - Academia.edu (original) (raw)

Papers by özgür keskin

$Research paper thumbnail of Normal Fermi-Walker Derivative in <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mi>E</mi><mn>1</mn><mn>3</mn></msubsup></mrow><annotation encoding="application/x-tex">E_{1}^{3}</annotation></semantics></math>E13$

In this paper, firstly, in E13E_1^3E13, we defined normal Fermi-Walker derivative and applied for the... more In this paper, firstly, in E13E_1^3E13, we defined normal Fermi-Walker derivative and applied for the adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined for frames throughout spacelike, timelike, lightlike curves. It is shown that the vector field which takes part in [17] is normal Fermi-Walker parallel by the normal Fermi-Walker derivative throughout the spacelike, timelike, and lightlike general helix. Also, we show that the Frenet frame is a normal non-rotating frame using the normal Fermi-Walker derivative. Afterward, we testified that the adapted frame is a normal non-rotating frame throughout the spacelike, timelike, and lightlike general helix.

Mathematical Sciences and Applications E-Notes, 2017

In this paper, first, we defined normal Fermi-Walker derivative and applied for adapted frame. No... more In this paper, first, we defined normal Fermi-Walker derivative and applied for adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame and Darboux vector of normal Fermi-Walker derivative by using normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are researched throughout curve for Frenet frame and Adapted frame. It is shown that vector field which take part in [13] is normal Fermi-Walker parallel in accordance with the normal Fermi-Walker derivative along the general helix. Also, we show that the Frenet frame is normal non-rotating frame in accordance with the normal Fermi-Walker derivative. Afterwards, we testified that the adapted frame is normal non-rotating frame throughout the general helix.

International Journal of Geometric Methods in Modern Physics, 2017

In this paper, we first introduce [Formula: see text]-Bishop frame for a normal direction curve w... more In this paper, we first introduce [Formula: see text]-Bishop frame for a normal direction curve which is defined as an integral curve of the principal normal of a curve. We express this new frame and its properties. Afterwards, we obtain new spherical images by translating [Formula: see text]-Bishop frame vectors to the center of unit sphere [Formula: see text] in [Formula: see text]. Then, these new spherical images are called [Formula: see text]-Bishop spherical images. Additionally, we compute the Frénet–Serret equations of these new spherical images. Moreover, we show that integral curves of [Formula: see text]-Bishop spherical images of slant helices are also slant helices. Finally, we present some illustrated examples.

Journal of Applied Mathematics and Computation, 2021

In this paper, some applications of a Rotation minimizing frame (RMF) are studied in E 1 4 and in... more In this paper, some applications of a Rotation minimizing frame (RMF) are studied in E 1 4 and in E 1 n for timelike, spacelike curves. Firstly, in E 1 4 , a Rotation minimizing frame (RMF) is obtained on the timelike and spacelike direction curves ∫ N(s) ds. The features of this Rotation minimizing frame are expressed. Secondly, it is determined when the timelike and spacelike curves can be rectifying curves. In addition, it has been investigated the conditions under which timelike and spacelike curves can be sphere calcurves. Then, a new characterization of rectifying curves is given, similar to the characterization of spherical curves. Finally, this Rotation minimizing frame is generalized in E 1 n for timelike, spacelike curves. In E 1 n , the conditions being a spherical curve and arectifying curve are given thank to this frame for timelike and spacelike curves. Also, a relationship between the spherical curve and the rectifying curve is stated. It is shown that the coefficients used in obtaining rectifying curves are constant numbers.

Mathematical Methods in The Applied Sciences, 2021

Annals of the Alexandru Ioan Cuza University - Mathematics, 2021

In this paper, certain characterizations of a Rotation minimizing frame (RMF) are studied. An RMF... more In this paper, certain characterizations of a Rotation minimizing frame (RMF) are studied. An RMF is obtained on the direction curve ∫ N(s)ds using a unit quaternionic curve. Some properties of this frame are given. Also, the condition of being a quaternionic rectifying curve and the condition of being a spherical curve is expressed using this frame. Moreover, the characterization of quaternionic rectifying curves is obtained similar to the characterization of spherical curves. Finally, the properties of the quaternionic rectifying curves are given.

In this paper, firstly, in E 1 , we defined normal FermiWalker derivative and applied for the ada... more In this paper, firstly, in E 1 , we defined normal FermiWalker derivative and applied for the adapted frame. Normal FermiWalker parallelism, normal non-rotating frame, and Darboux vector expressions of normal Fermi-Walker derivative by normal FermiWalker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are examined for frames throughout spacelike, timelike, lightlike curves. It is shown that the vector field which takes part in [17] is normal Fermi-Walker parallel by the normal Fermi-Walker derivative throughout the spacelike, timelike, and lightlike general helix. Also, we show that the Frenet frame is a normal non-rotating frame using the normal Fermi-Walker derivative. Afterward, we testified that the adapted frame is a normal non-rotating frame throughout the spacelike, timelike, and lightlike general helix.

$Research paper thumbnail of Rectifying-type curves and rotation minimizing frame <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>R</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">R_{n}</annotation></semantics></math>Rn$

In this paper, we have first given easily the characterization of special curves with the help of... more In this paper, we have first given easily the characterization of special curves with the help of the Rotation minimizing frame (RMF). Also, rectifying-type curves are generalized n-dimensional space RnR_{n}Rn.

First, in Minkowski 3-Space E3 1 , we defined normal Fermi-Walker derivative and applied for adap... more First, in Minkowski 3-Space E3 1 , we defined normal Fermi-Walker derivative and applied for adapted frame. Normal Fermi-Walker parallelism, normal non-rotating frame and normal Fermi-Walker derivative Darboux vector expressions according to normal Fermi-Walker derivative are given for adapted frame. Being conditions of normal Fermi-Walker derivative and normal non-rotating frame are analyzed for frames along spacelike, timelike, lightlike curves. It is shown that vector field which take part in [4] is normal Fermi-Walker parallel according to the normal Fermi-Walker derivative along the spacelike, timelike and lightlike general helix. Also, we show that the Frenet frame is normal nonrotating frame according to the normal Fermi-Walker derivative. Then, we proved that the adapted frame is normal non-rotating frame along the spacelike, timelike and lightlike general helix. Our aim is to show that the Fermi-Walker definitions can be defined by the first vector of other frames.

Applied Mathematics and Nonlinear Sciences

In this paper, we adopt the model of [12] by including fuzzy initial values to study the interact... more In this paper, we adopt the model of [12] by including fuzzy initial values to study the interaction of a monoclonal brain tumor and the macrophages for a condition of extinction of GB(Glioblastoma) by using Allee threshold. Numerical simulations will give detailed information on the behavior of the model at the end of the paper. We perform all the computations in this study with the help of the Maple software.

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