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Browsing Matematik / Mathematics by Author "Tosun, Murat"

Browsing Matematik / Mathematics by Author "Tosun, Murat"

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  • A New Generalization of the Steiner Formula and the Holditch Theorem 
    Tulay Erisir; Güngör, Mehmet Ali; Tosun, Murat (SPRINGER BASEL AG, 2016)
    In this study, we first obtained the Steiner area formula in the generalized complex plane. Then, with the aid of this formula, we determined a new approach for the Holditch theorem giving the relationship between the areas ...
  • A Note on Evolution of Curves in the Minkowski Spaces 
    Onder Gokmen Yildiz; Tosun, Murat (SPRINGER BASEL AG, 2017)
    In this paper, we study the evolution of non-null curve in n-dimensional Minkowski Space. We express evolution equation of the Frenet frame by matrix equation. We obtain integrability conditions for the evolutions. Finally, ...
  • A Study on Dual Hyperbolic Fibonacci and Lucas Numbers 
    Arzu Cihan; Azak, Ayşe Zeynep; Güngör, Mehmet Ali; Tosun, Murat (OVIDIUS UNIV PRESS, 2019)
    In this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers. Additionally, we give the identities regarding negadual-hyperbolic ...
  • A study on time-like complementary ruled surfaces in the Minkowski n-space 
    Tosun, Murat; Güngör, Mehmet Ali (SHIRAZ UNIV, 2005)
    For the first time in the Minkowski space, an R-1(n) time-like complementary ruled surface is described and relations are given connected with an asymptotic and tangential bundle of the time-like complementary ruled surface. ...
  • Beltrami-Meusnier formulas of generalized semi ruled surfaces in semi Euclidean space 
    Akyiğit, Mahmut; Ersoy, Soley; Tosun, Murat (ACADEMIC PUBLICATION COUNCIL, 2014)
    In this paper, we study the sectional curvatures of the generalized semi ruled surfaces in semi Euclidean space E-v(n+1). The first fundamental form and the metric coefficients of the generalized semi ruled surfaces are ...
  • Commutative Quaternion Matrices 
    Kösal, Hidayet Hüda; Tosun, Murat (SPRINGER BASEL AG, 2014)
    In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their fundamental matrices. After that we investigate ...
  • Dual Lorentzian spherical motions and dual Euler-Savary formula 
    Güngör, Mehmet Ali; Ersoy, Soley; Tosun, Murat (GAUTHIER-VILLARS/EDITIONS ELSEVIER, 2009)
    In this paper, defining one-parameter dual Lorentzian motion in three-dimensional dual Lorentzian space D(1)(3) and we have obtained the relations between the absolute, relative and sliding velocities of these motions. In ...
  • Euler savary formula for the one parameter motions in the complex plane C 
    Masal, Melek; Tosun, Murat; Azak, Ayşe Zeynep (ACADEMIC JOURNALS, 2010)
    Muller (1978), in the Euclidean plane E-2 introduced the one parameter planar motions and obtained the relation between absolute, relative, sliding velocities (and accelerations). During one parameter planar motion in the ...
  • Fibonacci Generalized Quaternions 
    Akyiğit, Mahmut; Kösal, Hidayet Hüda; Tosun, Murat (SPRINGER BASEL AG, 2014)
    In this paper, the Fibonacci generalized quaternions are introduced. We use the well-known identities related to the Fibonacci and Lucas numbers to obtain the relations regarding these quaternions. Furthermore, the Fibonacci ...
  • Generalized Timelike Mannheim Curves in Minkowski Space-Time E-1(4) 
    Özgür, İbrahim; Akyiğit, Mahmut; Ersoy, Soley; Tosun, Murat (HINDAWI PUBLISHING CORPORATION, 2011)
    We give the definition of generalized timelike Mannheim curve in Minkowski space-time E-1(4). The necessary and sufficient conditions for the generalized timelike Mannheim curve are obtained. We show some characterizations ...
  • Geometry of the Hyperbolic Spinors Corresponding to Alternative Frame 
    Erişir, Tülay; Güngör, Mehmet Ali; Tosun, Murat (SPRINGER BASEL AG, 2015)
    In this paper, we study to express the theory of curves including a wide section of Lorentzian geometry in terms of spinors with two hyperbolic components which has an important place in the Clifford algebra. In other ...
  • Homothetic Cayley Formula and its Applications 
    Dogan Unal; Güngör, Mehmet Ali; Tosun, Murat (SPRINGER BASEL AG, 2016)
    In this study the homothetic Cayley Formula has been defined for an antisymmetric matrix and the relation between an antisymmetric matrix and a vector has been given. Hence Rodrigues and Euler parameters have been obtained ...
  • Lamarle formula in 3-dimensional Lorentz space 
    Ersoy, Soley; Tosun, Murat (UNIV OSIJEK, DEPT MATHEMATICS, 2011)
    The Lamarle Formula is known as a relationship between the Gaussian curvature and the distribution parameter (Drall) of a ruled surface in the surface theory, [12]. In R-1(3), the non-null ruled surfaces were investigated ...
  • On sectional curvatures of the generalized surfaces correspond to each other under symmetric helical motion of order k in the euclidean space E(n) 
    Tosun, Murat (NORTH UNIV BAIA MARE, 2008)
    The purpose of the paper is to present a summary of known results and to discuss sectional curvatures of fixed and moving axoids corresponding to each other under helical motion of order k in E(n) and study some of their ...
  • On the Consimilarity of Split Quaternions and Split Quaternion Matrices 
    Kösal, Hidayet Hüda; Akyiğit, Mahmut; Tosun, Murat (OVIDIUS UNIV PRESS, 2016)
    In this paper, we introduce the concept of consimilarity of split quaternions and split quaternion matrices. In this regard, we examine the solvability conditions and general solutions of the equations a (x) over tilde= ...
  • On the one-parameter Lorentzian spherical motions and Euler-Savary formula 
    Tosun, Murat; Güngör, Mehmet Ali; Okur, İbrahim (ASME, 2007)
    In this paper we have introduced one-parameter Lorentzian spherical motion. In addition to that, we have given the relations between the absolute, relative, and sliding velocities of these motions. Furthermore, the relations ...
  • On the Semisimilarity and Consemisimilarity of Split Quaternions 
    Onder Gokmen Yildiz; Hidayet Huda Kosal; Tosun, Murat (SPRINGER BASEL AG, 2016)
    In this study, we introduce the concept of semisimilarity and consemisimilarity of split quaternions. Moreover, we examine the solvability conditions and general solutions of systems in split quaternions. If there exist x ...
  • p-Trigonometric Approach to Elliptic Biquaternions 
    Kahraman Esen Ozen; Tosun, Murat (SPRINGER BASEL AG, 2018)
    In this paper, we obtain the p-trigonometric functions of an elliptical complex variable and express the elliptic biquaternions in the p-trigonometric form by means of these functions. Additionally, De-Moivre's and Euler ...
  • SECTIONAL CURVATURE OF TIMELIKE RULED SURFACE PART I: LORENTZIAN BELTRAMI-EULER FORMULA 
    Ersoy, Soley; Tosun, Murat (SHIRAZ UNIV, 2010)
    In this paper, the Lorentzian version of Beltrami-Euler formula is investigated in R(1)(n). Initially, the first fundamental form and the metric coefficients of generalized timelike ruled surface are calculated and by the ...
  • Siacci's Theorem According to Darboux Frame 
    Tosun, Murat; Akyiğit, Mahmut (OVIDIUS UNIV PRESS, 2017)
    The resolution of the acceleration vector of rigid body moving along a space curve is well known thanks to Siacci [1]. In this resolution,the acceleration vector is stated as the sum of two special oblique components in ...