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• MakaleYayıncıda açık erişim2026/r/bayburt/14434
  Yİ-DARBOUX SLANT HELICES ON SURFACES

  Tosun, Ceyda; Kocayigit, Huseyin; Aydin, Tuba agirman

  In this study, a new class of surface curves, namely Yi-Darboux slant helices, is investigated. The conditions under which a surface curve is a iY-Darboux slant helix with respect to the Osculating Darboux (OD), Normal Darboux (ND), and Rectifying Darboux (RD) frames are established, and several characterizations are obtained. In particular, necessary and sufficient conditions are derived in terms of the curvature functions associated with these frames. Furthermore, relationships between iY-Darboux slant helices and classical helices and slant helices are established for special surface curves, including geodesics, asymptotic curves, and lines of curvature. Concrete examples on conical and cylindrical surfaces are also presented to illustrate the theoretical results.

  İncele
• MakaleYalnız künye2026Scopus SJRQ1/r/bayburt/10935
  Problem posing on vectors in space: preservice teachers’ perspectives

  Ergin, Ayda Nur; Öztürk, Mesut; Aydin, Tuba Ağirman

  This 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.

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  İncele
• MakaleAçık Erişim2025/r/bayburt/14448
  DIFFERENTIAL EQUATIONS CHARACTERIZATION FOR Di-DARBOUX SLANT HELICES

  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
• MakaleAçık Erişim2024Scopus SJRQ4/r/bayburt/13149
  New moving frames for the curves lying on a surface

  Alkan, Akın; Hüseyin, Kocayi̇Ği̇T; Ağirman Aydin, Tuba

  In this article, three new orthogonal frames are defined for the curves lying on a surface. These moving frames, obtained based on the Darboux frame, are called “Osculator Darboux Frame”, “Normal Darboux Frame” and “Rectifying Darboux Frame”, respectively. Also, the Osculator Darboux Frame components and curvatures are calculated for a presented example. Cite this article as: Alkan A, Kocayiğit H, Ağırman Aydın T. New moving frames for the curves lying on a surface. Sigma J Eng Nat Sci 2024;42(4):1023−1029. Copyright 2021, Yıldız Technical University.

  AtıfScopus2·WoS4·OpenAlex2

  İncele
• MakaleAçık Erişim2024Scopus SJRQ3/r/bayburt/12954
  Existence and extinction of solutions for parabolic equations with nonstandard growth nonlinearity

  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
• MakaleAçık Erişim2024Scopus SJRQ4/r/bayburt/12880
  Di-Darboux Slant Helices on Surface

  Alkan, Akın; Kocayiğit, Hüseyin; Ağırman Aydın, Tuba

  In this study, we consider Di-Darboux slant helices which are new surface curves on an oriented surface. We give some characterizations for such curves according to the Darboux frame, OD-frame, ND-frame, RD-frame, and obtain axes of the Di-Darboux slant helices. Moreover, the position vectors of the Di-Darboux slant helices are obtained.

  AtıfOpenAlex2

  İncele
• MakaleAçık Erişim2023/r/bayburt/13027
  A New Approach on Some Special Curves

  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
• MakaleYalnız künye2022/r/bayburt/14452
  TIMELIKE HELICES IN THE SEMI-EUCLIDEAN SPACE E24

  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
• MakaleAçık Erişim2022/r/bayburt/14465
  SOME INTEGRAL CHARACTERIZATIONS OF TIMELIKE HELICES IN R42

  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
• MakaleAçık Erişim2021/r/bayburt/14753
  A Study on a Curve and Three Equations

  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