Alkan, Akin; Kocayígít, Huseyin; Aydin, Tuba Agirman

In this article, the differential equation characterizations for D-i-Darboux slant helices given with the help of three new orthogonal frames are introduced for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called Osculating Darboux Frame, Normal Darboux Frame, and Rectifying Darboux Frame, respectively.

AtıfWoS1·OpenAlex1

İncele

Ayazoglu, Rabil; Alisoy, Gulizar; Akbulut, Sezgin; Aydin, Tuba Agirman

In this paper, we consider an initial boundary value problem for a class of p(·)-Laplacian parabolic equation with nonstandard nonlinearity in a bounded domain. By using new approach, we obtain the global and decay of existence of the solutions. Moreover, the precise decay estimates of solutions before the occurrence of the extinction are derived.

AtıfScopus1·WoS1·OpenAlex1

İncele

Erpehlivan, Zeliha; Kocayigit, Hüseyin; Aydin, Tuba Agirman

In this study, we examine timelike helices in R-2(4) and some integral characterizations of these curves in terms of Frenet frame. In addition, we study timelike 2B slant helices in R-2(4) and present the differential equations for vector positions.

İncele

Aydin, Tuba Agirman; Ayazoglu, Rabil; Kocayigit, Huseyin

In this paper, we define timelike curves in R-2(4) and characterize such curves in terms of Frenet frame. Also, we examine the timelike helices of R-2(4), taking into account their curvatures. In addition, we study timelike slant helices, timelike B-1-slant helices, timelike B-2-slant helices in four dimensional semi-Euclidean space, R-2(4). And then we obtain an approximate solution for the timelike B-1 slant helix with Taylor matrix collocation method.

AtıfWoS1

İncele

Aydin, Tuba Agirman

In this study, the Bezier curves and surfaces, which have an important place in interactive design applications, are expressed in matrix form using a special matrix that gives the coefficients of the Bernstein base polynomial. The matrix forms of higher order derivatives of the Bezier curves and surfaces are obtained. It is demonstrated by numerical examples that the bidirectional transition between the control points and parametric equations of the Bezier curves and surfaces can be easily achieved using these matrix forms. In addition, it is demonstrated that this type of curve and surface, whose control points are known, its higher order derivatives can be calculated without it's parametric equations. In this study, the Bezier curves and surfaces are presented in a more easily understandable and easy to use format in algebraic form for designers.

AtıfOpenAlex3

İncele

Ayazoglu, Rabil; Akkoyunlu, Ebubekir; Aydin, Tuba Agirman

This paper is concerned with the blow-up of the solutions to a semilinear heat equation with a reaction given by parametric variable sources. Some conditions to parameters and exponents of sources are given to obtain lower–upper bounds for the time of blow-up and some global existence results.

AtıfScopus3·WoS2·OpenAlex2

İncele

Aydin, Tuba Agirman

In this article, the differential equation of lorentzian spherical timelike curves is obtained in E-1(4). It is seen that the differential equation characterizing Lorentzian spherical timelike curves is equivalent to a linear, third order, differential equation with variable coefficients. It is impossible to solve these equations analytically. In this article, a new numerical technique based on hermite polynomials is presented using the initial conditions for the approximate solution. This method is called the modified hermite matrix-collocation method. With this technique, the solution of the problem is reduced to the solution of an algebraic equation system and the approximate solution is obtained. In addition, the validity and applicability of the technique is explained by a sample application.

AtıfWoS1

İncele