Cilt:70 Sayı:01 (2021)
http://hdl.handle.net/20.500.12575/76441
2024-02-24T00:18:11ZAn approach for designing a surface pencil through a given geodesic curve
http://hdl.handle.net/20.500.12575/76504
An approach for designing a surface pencil through a given geodesic curve
Atalay, Günnur Şaffak; Güler, Fatma; Bayram, Ergin; Kasap, Emin
In the present paper, we propose a new method to construct a surface interpolating a given curve as the geodesic curve of it. Also, we analyze the conditions when the resulting surface is a ruled surface. In addition, developablity along the common geodesic of the members of surface family are discussed. Finally, we illustrate this method by presenting some examples.
2021-06-30T00:00:00ZBivariate Bernstein polynomials that reproduce exponential functions
http://hdl.handle.net/20.500.12575/76503
Bivariate Bernstein polynomials that reproduce exponential functions
Bozkurt, Kenan; Özsaraç, Fırat; Aral, Ali
In this paper, we construct Bernstein type operators that reproduce exponential functions on simplex with one moved curved side. The operator interpolates the function at the corner points of the simplex. Used function sequence with parameters α and β not only are gained more modeling flexibility to operator but also satisfied to preserve some exponential functions. We examine the convergence properties of the new approximation processes. Later, we also state its shape preserving properties by considering classical convexity. Finally, a Voronovskaya-type theorem is given and our results are supported by graphics.
2021-06-30T00:00:00ZNatural and conjugate mates of Frenet curves in three-dimensional Lie group
http://hdl.handle.net/20.500.12575/76502
Natural and conjugate mates of Frenet curves in three-dimensional Lie group
Mak, Mahmut
In this study, we introduce the natural mate and conjugate mate of a Frenet curve in a three dimensional Lie group
G
with bi-invariant metric. Also, we give some relationships between a Frenet curve and its natural mate or its conjugate mate in
G
. Especially, we obtain some results for the natural mate and the conjugate mate of a Frenet curve in
G
when the Frenet curve is a general helix, a slant helix, a spherical curve, a rectifying curve, a Salkowski (constant curvature and non-constant torsion), anti-Salkowski (non-constant curvature and constant torsion), Bertrand curve. Finally, we give nice graphics with numeric solution in Euclidean 3-space as a commutative Lie group.
2021-06-30T00:00:00ZDifferential geometric aspects of nonlinear Schrödinger equation
http://hdl.handle.net/20.500.12575/76500
Differential geometric aspects of nonlinear Schrödinger equation
Erdoğdu, Melek; Yavuz, Ayşe
The main scope of this paper is to examine the smoke ring (or vortex filament) equation which can be viewed as a dynamical system on the space curve in E³. The differential geometric properties the soliton surface accociated with Nonlinear Schrödinger (NLS) equation, which is called NLS surface or Hasimoto surface, are investigated by using Darboux frame. Moreover, Gaussian and mean curvature of Hasimoto surface are found in terms of Darboux curvatures k_{n}, k_{g} and τ_{g.}. Then, we give a different proof of that the s- parameter curves of NLS surface are the geodesics of the soliton surface. As applications we examine two NLS surfaces with Darboux Frame.
2021-06-30T00:00:00Z