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    Öğe
    DUAL QUATERNION FRAMES
    (Ankara Univ, Fac Sci, 2010) Ozturk, Ufuk; Hacisalihoglu, H. H.; Yayli, Yusuf; Ozturk, E. Betul Koc
    Serret-Frenet and Parallel-Transport frame are produced with the help of reel quaternions again by Andrew J. Hanson [7]. In this study, calculations mentioned above are applied for dual quaternion and Serret-Frenet and Parallel-Transport frame are obtained by the aid of dual quarternions.
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    A New Polar Representation for Split and Dual Split Quaternions
    (Springer Basel Ag, 2017) Atasoy, Ali; Ata, Erhan; Yayli, Yusuf; Kemer, Yasemin
    We present a new different polar representation of split and dual split quaternions inspired by the Cayley-Dickson representation. In this new polar form representation, a split quaternion is represented by a pair of complex numbers, and a dual split quaternion is represented by a pair of dual complex numbers as in the Cayley-Dickson form. Here, in a split quaternion these two complex numbers are a complex modulus and a complex argument while in a dual split quaternion two dual complex numbers are a dual complex modulus and a dual complex argument. The modulus and argument are calculated from an arbitrary split quaternion in Cayley-Dickson form. Also, the dual modulus and dual argument are calculated from an arbitrary dual split quaternion in Cayley-Dickson form. By the help of polar representation for a dual split quaternion, we show that a Lorentzian screw operator can be written as product of two Lorentzian screw operators. One of these operators is in the two-dimensional space produced by 1 and i vectors. The other is in the three-dimensional space generated by 1, j and k vectors. Thus, an operator in a four-dimensional space is expressed by means of two operators in two and three-dimensional spaces. Here, vector 1 is in the intersection of these spaces.
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    On Mannheim partner curves in dual Lorentzian space
    (Hacettepe Univ, Fac Sci, 2011) Ozkaldi, Siddika; Ilarslan, Kazim; Yayli, Yusuf
    In this paper we define non-null Mannheim partner curves in three dimensional dual Lorentzian space D(1)(3), and obtain necessary and sufficient conditions for the existence of non-null Mannheim partner curves in dual Lorentzian space D(1)(3).