id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-1979	Bektas, O.; Bayrak Gurses, N.; Yuce, S.	Osculating Spheres of a Semi Real Quaternionic Curve in E_2^4	2014	11	.pdf	application/pdf	4068	196	78	Then there exists a sphere which contacts at the fourth order to the curve β at β (0) and the equation of the semi quaternionic osculating sphere according to the Frenet frame ¦ T0,N10 ,N20 ,N30 © such that εT0 X 2 1 + εN10 X2− εT0 εN10 ς0 !2 + εN20 X3− εT0 εN10 εn10 ς′0ρ0 !2 + εN30 � X4−Ω0 � εT0 εN10 � � ς′0ρ0 �′ + εt0 � εn10 � ς0 ρ0 � − εN10 ρ0 − 4 � ρ0 ς0 � � + 3 εT0 εN10 � ρ0 ς0 ����2 Ö. Bektaş, N. Gürses, S. Yüce / Eur. = 2 � β ′′ (0) ,β (0)−M � + β ′ (0) ,β ′ (0) �� = 0 and g ′′ (0) .	cache/ejpam-1979.pdf	txt/ejpam-1979.txt