Aydın, Tuba Ağırman; Kocayiğit, Hüseyin; Kara, Meryem

In this paper, we obtain some characterizations for a Frenet curve with the help of an alternative frame different from the Frenet frame. Also, in the present study, we consider weak biharmonic and harmonic 1-type curves by using the mean curvature vector field of the curve. We also study 1-type and biharmonic curves whose mean curvature vector field is in the kernel of Laplacian. We give some theorems for such curves in the Euclidean 3-space. Moreover, we give the classifications of these types of curves.

İncele

Aydın, Tuba Ağırman; Sezer, Mehmet; (Mashiyev), Rabil Ayazoglu; Çayan, Seda

The fixed-width curves, which have a very special place in many fields such as kinematics, engineering, art, cam design and geometry, are specially discussed under this title. In this study, three differential equations obtained by means of a system of differential equations characterizing fixed-width curves are examined. These differential equations are third order, variable coefficient, homogeneous, linear differential equations based on different variables. Approximate solutions of these equations are calculated with two different polynomial approximations and error analysis is made for the solutions. Thus, the best approach method is determined for the most accurate result. Also, these equations can constitute a characterization for different types of curves according to different frames in different spaces. Therefore, this study is important not only for this curve type but also for the geometry of all curves that can be expressed with similar equations.

İncele

Aydın, Tuba Ağırman; Kocayigit, Hüseyin

In this study, a kind of generalized involute and evolute curve pair is considered in 4 dimensional semi Euclidean space with 2 index. The curvatures and the associated Frenet Frame of this kind of generalized involute-evolute curve pair are presented.

AtıfOpenAlex1

İncele

Ayazoglu, Rabil; Şule Şener, Sidika; Aydın, Tuba Ağırman

The present paper is concerned with the resonant problem −div (a (x, ∇u)) = λ1|u|p −2 u + f (x, u) − g(x) in Ω, where Ω is a bounded domain with smooth boundary in RN (N ≥ 2), p ∈ (1, ∞) and div(a (x, ∇u)) is a general elliptic operators in divergence form. By assuming a Landesman-Lazer type condition and using a variational method based on the Minimum Principle, we show the existence of a weak solution in the Sobolev space W0 1,p (Ω).

İncele

Aydın, Tuba Ağırman; Sezer, Mehmet

In this study, we considered an n th order linear differential equation with variable coefficients characterizing spherical curves according to Frenet frame in Euclidean n-Space E n . This equation whose coefficients are related to special function, curvature and torsion, is satisfied by the position vector of any regular unit velocity spherical curve. These type equations are generally impossible to solve analytically and so, for approximate solution we presented a numerical method based on Taylor polynomials and collocations points by using initial conditions. Our method reduces the solution of problem to the solution of a system of algebraic equations and the approximate solution is obtained in terms of Taylor polynomials.

İncele

Aydın, Tuba Ağırman; Sezer, Mehmet

In this study we consider a third order linear differential equation with variable coefficients characterizingspherical curves according to Frenet frame in Euclidean 4-Space E 4 . This equation whose coefficients arerelated to special function, curvature and torsion, is satisfied by the position vector of any regular unitvelocity spherical curve. These type equations are generally impossible to solve analytically and so, forapproximate solution we present a numerical method based on Taylor polynomials and collocations pointsby using initial conditions. Our method reduces the solution of problem to the solution of a system ofalgebraic equations and the approximate solution is obtained in terms of Taylor polynomials.

AtıfOpenAlex1·TR Dizin1

İncele