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Öğe AN APPROXIMATE SOLUTION FOR LORENTZIAN SPHERICAL TIMELIKE CURVES(Editura Bibliotheca-Bibliotheca Publ House, 2020) Aydin, Tuba AgirmanIn 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.Öğe Bernsteinn polynomials approach to determine timelike curves of constant breadth in Minkowski 3-space(Mustafa BAYRAM, 0208) Aydin, Tuba Agirman; Sezer, Mehmet; Kocayigit, HuseyinKredinin geri ödenmeme riskine karşı alacaklıyı koruma altına alan kredi türev enstrümanı şeklinde tanımlanan, kredi risk primleri (CDS) özellikle kredi derecelendirme kuruluşları tarafından belirlenen ülke kredi notlarının yoğun eleştirilere maruz kaldığı bu dönemde piyasa aktörleri tarafından yakından takip edilen önemli bir risk göstergesi niteliğindedir. CDS primlerinin ülkelerin kredibilitesi hakkında önemli ipuçları sunuyor olması yatırımcıların kararlarını da önemli ölçüde etkileyebilmektedir. Bu yönüyle CDS’ler özellikle yatırım kanalıyla ekonomilerde üretim düzeyini etkileyebilmektedirler. Bu da CDS’ler ve ekonomik büyüme arasında bir nedensellik ilişkisinin olabileceğini göstermektedir. Bu çalışmada da Türkiye’ye ait kredi risk primleri (CDS) ile ekonomik büyüme arasında bir nedensellik ilişkisinin olup olmadığı ve bu ilişkinin zamanla değişip değişmediğinin belirlenmesi amaçlanmaktadır. Bu amaca yönelik olarak çalışmada 2012M01-2016M12 dönemi için CDS’lerdeki değişim ile ekonomik büyümeyi temsilen sanayi üretim endeksindeki değişim (IPI) arasındaki zamanla değişen nedensellik ilişkileri incelenmiştir. Çalışmada öncelikle ilgili dönemin tamamı için nedensellik ilişkisi olup olmadığı Hacker ve Hatemi-j (2006) tarafından geliştirilmiş olan nedensellik analizi yöntemiyle araştırılmıştır. Sonrasında ise incelen dönem içinde istikrarsız ilişkilerin olabileceği düşüncesiyle, Hacker ve Hatemi-j (2006) yöntemine dayalı zamanla değişen nedensellik yöntemi kullanılarak değişkenler arasındaki nedensellik ilişkileri alt dönemler için analiz edilmiştir. Çalışmanın sonucunda incelenen dönemin tamamı için ekonomik büyüme ve CDS’ler arasında herhangi bir nedensellik ilişkisi olmamasına rağmen, alt dönemlerde değişkenler arasında farklı nedensellik ilişkilerinin varlığı tespit edilmiştir.Öğe DIFFERENTIAL EQUATIONS CHARACTERIZATION FOR Di-DARBOUX SLANT HELICES(Editura Bibliotheca-Bibliotheca Publ House, 2025) Alkan, Akin; Kocayigit, Huseyin; Aydin, Tuba AgirmanIn 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.Öğe Existence and extinction of solutions for parabolic equations with nonstandard growth nonlinearity(Hacettepe Univ, Fac Sci, 2024) Ayazoglu (Mashiyev), Rabil; Alisoy, Gulizar; Akbulut, Sezgin; Aydin, Tuba AgirmanIn 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.Öğe Legendre Matrix Method for Legendre Curve in Sasakian 3-Manifold(Walter De Gruyter Gmbh, 2021) Aydin, Tuba Agirman; Sezer, Mehmet; Kocayigit, HuseyinIn this study, unit-speed the Legendre curves are studied in Sasakian 3-manifold. Firstly, differential equations characterizing the Legendre curves are obtained and the method used for the approximate solution is explained. Then, the approximate solution is found for one of the characterizations of the Legendre curve with the Legendre matrix collocation method. In addition, a sample application is made to make the method more understandable. And finally, with the help of these equations and the approximate solution, the geometric properties of this curve type are examined.Öğe A MATRIX PRESENTATION OF HIGHER ORDER DERIVATIVES OF BEZIER CURVE AND SURFACE(Editura Bibliotheca-Bibliotheca Publ House, 2021) Aydin, Tuba AgirmanIn 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.Öğe Morgan-Voyce Polynomial Approach for Quaternionic Space Curves of Constant Width(Walter De Gruyter Gmbh, 2021) Aydin, Tuba Agirman; Ayazoglu, Rabil; Kocayigit, HuseyinThe curves of constant width are special curves used in engineering, architecture and technology. In the literature, these curves are considered according to different roofs in different spaces and some integral characterizations of these curves are obtained. However, in order to examine the geometric properties of curves of constant width, more than characterization is required. In this study, firstly differential equations characterizing quaternionic space curves of constant width are obtained. Then, the approximate solutions of the differential equations obtained are calculated by the Morgan-Voyce polynomial approach. The geometric properties of this curve type are examined with the help of these solutions.Öğe On global existence and bounds for the blow-up time in a semilinear heat equation involving parametric variable sources(Acad Sciences, 2021) Ayazoglu (Mashiyev), Rabil; Akkoyunlu, Ebubekir; Aydin, Tuba AgirmanThis 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.Öğe Problem posing on vectors in space: preservice teachers' perspectives(Springer, 2026) Ergin, Ayda Nur; Ozturk, Mesut; Aydin, Tuba AgirmanThis study examines preservice elementary mathematics teachers' problem-posing processes related to vectors in space. Adopting a qualitative case study design, the problem-posing process was analyzed by treating the phases of orientation, connection, generation, and reflection as analytic units, focusing on the cognitive, linguistic, and reasoning-based actions exhibited at each phase. The findings reveal that preservice teachers experience considerable difficulties in establishing meaningful connections between mathematical structures and real-life contexts, particularly when posing vector problems in three-dimensional environments. In addition, causal attribution processes became salient during the reflection phase, with participants frequently explaining their successes and difficulties by referring to their conceptual understanding, prior experiences, and perceived competence. The results offer implications for the design of theory-based learning environments that support problem-posing processes in mathematics teacher education, particularly for advanced mathematical topics.Öğe SOME INTEGRAL CHARACTERIZATIONS OF TIMELIKE HELICES IN R42(Editura Bibliotheca-Bibliotheca Publ House, 2022) Erpehlivan, Zeliha; Kocayigit, Hüseyin; Aydin, Tuba AgirmanIn 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.Öğe TIMELIKE HELICES IN THE SEMI-EUCLIDEAN SPACE E24(Honam Mathematical Soc, 2022) Aydin, Tuba Agirman; Ayazoglu, Rabil; Kocayigit, HuseyinIn 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.
