id	sid	tid	token	lemma	pos
ejpam-1979	1	1	european	european	PROPN
ejpam-1979	1	2	journal	journal	PROPN
ejpam-1979	1	3	of	of	ADP
ejpam-1979	1	4	pure	pure	ADJ
ejpam-1979	1	5	and	and	CCONJ
ejpam-1979	1	6	applied	apply	VERB
ejpam-1979	1	7	mathematics	mathematic	NOUN
ejpam-1979	1	8	vol	vol	NOUN
ejpam-1979	1	9	.	.	PUNCT
ejpam-1979	2	1	7	7	NUM
ejpam-1979	2	2	,	,	PUNCT
ejpam-1979	2	3	no	no	INTJ
ejpam-1979	2	4	.	.	NOUN
ejpam-1979	2	5	1	1	NUM
ejpam-1979	2	6	,	,	PUNCT
ejpam-1979	2	7	2014	2014	NUM
ejpam-1979	2	8	,	,	PUNCT
ejpam-1979	2	9	86	86	NUM
ejpam-1979	2	10	-	-	SYM
ejpam-1979	2	11	96	96	NUM
ejpam-1979	2	12	issn	issn	PROPN
ejpam-1979	2	13	1307	1307	NUM
ejpam-1979	2	14	-	-	SYM
ejpam-1979	2	15	5543	5543	NUM
ejpam-1979	2	16	–	–	PUNCT
ejpam-1979	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1979	2	18	osculating	osculate	VERB
ejpam-1979	2	19	spheres	sphere	NOUN
ejpam-1979	2	20	of	of	ADP
ejpam-1979	2	21	a	a	DET
ejpam-1979	2	22	semi	semi	ADJ
ejpam-1979	2	23	real	real	ADJ
ejpam-1979	2	24	quaternionic	quaternionic	ADJ
ejpam-1979	2	25	curve	curve	NOUN
ejpam-1979	2	26	in	in	ADP
ejpam-1979	2	27	e4	e4	PROPN
ejpam-1979	2	28	2	2	NUM
ejpam-1979	2	29	ö.	ö.	NOUN
ejpam-1979	2	30	bektaş1,∗	bektaş1,∗	NOUN
ejpam-1979	2	31	,	,	PUNCT
ejpam-1979	2	32	n.	n.	PROPN
ejpam-1979	2	33	bayrak	bayrak	PROPN
ejpam-1979	2	34	gürses	gürse	VERB
ejpam-1979	2	35	2	2	NUM
ejpam-1979	2	36	,	,	PUNCT
ejpam-1979	2	37	s.	s.	PROPN
ejpam-1979	2	38	yüce	yüce	PROPN
ejpam-1979	2	39	1	1	NUM
ejpam-1979	2	40	1	1	NUM
ejpam-1979	2	41	department	department	NOUN
ejpam-1979	2	42	of	of	ADP
ejpam-1979	2	43	mathematics	mathematic	NOUN
ejpam-1979	2	44	,	,	PUNCT
ejpam-1979	2	45	faculty	faculty	NOUN
ejpam-1979	2	46	of	of	ADP
ejpam-1979	2	47	arts	art	NOUN
ejpam-1979	2	48	and	and	CCONJ
ejpam-1979	2	49	sciences	science	NOUN
ejpam-1979	2	50	,	,	PUNCT
ejpam-1979	2	51	yıldız	yıldız	PROPN
ejpam-1979	2	52	technical	technical	PROPN
ejpam-1979	2	53	university	university	PROPN
ejpam-1979	2	54	,	,	PUNCT
ejpam-1979	2	55	istanbul	istanbul	PROPN
ejpam-1979	2	56	,	,	PUNCT
ejpam-1979	2	57	turkey	turkey	PROPN
ejpam-1979	2	58	2	2	NUM
ejpam-1979	2	59	department	department	NOUN
ejpam-1979	2	60	of	of	ADP
ejpam-1979	2	61	mathematics	mathematic	NOUN
ejpam-1979	2	62	,	,	PUNCT
ejpam-1979	2	63	graduate	graduate	NOUN
ejpam-1979	2	64	school	school	NOUN
ejpam-1979	2	65	of	of	ADP
ejpam-1979	2	66	natural	natural	ADJ
ejpam-1979	2	67	and	and	CCONJ
ejpam-1979	2	68	applied	applied	ADJ
ejpam-1979	2	69	sciences	science	NOUN
ejpam-1979	2	70	,	,	PUNCT
ejpam-1979	2	71	yıldız	yıldız	PROPN
ejpam-1979	2	72	technical	technical	PROPN
ejpam-1979	2	73	university	university	PROPN
ejpam-1979	2	74	,	,	PUNCT
ejpam-1979	2	75	istanbul	istanbul	PROPN
ejpam-1979	2	76	,	,	PUNCT
ejpam-1979	2	77	turkey	turkey	PROPN
ejpam-1979	2	78	abstract	abstract	NOUN
ejpam-1979	2	79	.	.	PUNCT
ejpam-1979	3	1	in	in	ADP
ejpam-1979	3	2	this	this	DET
ejpam-1979	3	3	study	study	NOUN
ejpam-1979	3	4	,	,	PUNCT
ejpam-1979	3	5	we	we	PRON
ejpam-1979	3	6	define	define	VERB
ejpam-1979	3	7	the	the	DET
ejpam-1979	3	8	osculating	osculating	NOUN
ejpam-1979	3	9	spheres	sphere	NOUN
ejpam-1979	3	10	of	of	ADP
ejpam-1979	3	11	a	a	DET
ejpam-1979	3	12	semi	semi	ADJ
ejpam-1979	3	13	real	real	ADJ
ejpam-1979	3	14	quaternionic	quaternionic	ADJ
ejpam-1979	3	15	curve	curve	NOUN
ejpam-1979	3	16	in	in	ADP
ejpam-1979	3	17	semieuclidean	semieuclidean	ADJ
ejpam-1979	3	18	spaces	space	NOUN
ejpam-1979	3	19	e3	e3	VERB
ejpam-1979	3	20	1	1	NUM
ejpam-1979	3	21	and	and	CCONJ
ejpam-1979	3	22	e4	e4	PROPN
ejpam-1979	3	23	2	2	NUM
ejpam-1979	3	24	.	.	PUNCT
ejpam-1979	4	1	we	we	PRON
ejpam-1979	4	2	give	give	VERB
ejpam-1979	4	3	the	the	DET
ejpam-1979	4	4	equation	equation	NOUN
ejpam-1979	4	5	of	of	ADP
ejpam-1979	4	6	the	the	DET
ejpam-1979	4	7	osculating	osculating	NOUN
ejpam-1979	4	8	spheres	sphere	NOUN
ejpam-1979	4	9	with	with	ADP
ejpam-1979	4	10	respect	respect	NOUN
ejpam-1979	4	11	to	to	ADP
ejpam-1979	4	12	frenet	frenet	NOUN
ejpam-1979	4	13	frames	frame	NOUN
ejpam-1979	4	14	¦	¦	PROPN
ejpam-1979	4	15	t0,n10	t0,n10	PROPN
ejpam-1979	4	16	,	,	PUNCT
ejpam-1979	4	17	n20	n20	NOUN
ejpam-1979	4	18	©	©	PROPN
ejpam-1979	4	19	and	and	CCONJ
ejpam-1979	4	20	¦	¦	PROPN
ejpam-1979	4	21	t0,n10	t0,n10	PROPN
ejpam-1979	4	22	,	,	PUNCT
ejpam-1979	4	23	n20	n20	NOUN
ejpam-1979	4	24	,	,	PUNCT
ejpam-1979	4	25	n30	n30	NOUN
ejpam-1979	4	26	©	©	NOUN
ejpam-1979	4	27	.	.	PUNCT
ejpam-1979	5	1	2010	2010	NUM
ejpam-1979	5	2	mathematics	mathematic	NOUN
ejpam-1979	5	3	subject	subject	NOUN
ejpam-1979	5	4	classifications	classification	NOUN
ejpam-1979	5	5	:	:	PUNCT
ejpam-1979	5	6	14q05	14q05	NUM
ejpam-1979	5	7	,	,	PUNCT
ejpam-1979	5	8	53a17	53a17	NUM
ejpam-1979	5	9	,	,	PUNCT
ejpam-1979	5	10	53c50	53c50	NUM
ejpam-1979	5	11	.	.	PUNCT
ejpam-1979	6	1	key	key	ADJ
ejpam-1979	6	2	words	word	NOUN
ejpam-1979	6	3	and	and	CCONJ
ejpam-1979	6	4	phrases	phrase	NOUN
ejpam-1979	6	5	:	:	PUNCT
ejpam-1979	6	6	osculating	osculate	VERB
ejpam-1979	6	7	sphere	sphere	NOUN
ejpam-1979	6	8	,	,	PUNCT
ejpam-1979	6	9	semi	semi	ADV
ejpam-1979	6	10	real	real	ADJ
ejpam-1979	6	11	quaternionic	quaternionic	ADJ
ejpam-1979	6	12	curve	curve	NOUN
ejpam-1979	6	13	,	,	PUNCT
ejpam-1979	6	14	semi	semi	ADJ
ejpam-1979	6	15	-	-	ADJ
ejpam-1979	6	16	euclidean	euclidean	ADJ
ejpam-1979	6	17	space	space	NOUN
ejpam-1979	6	18	.	.	PUNCT
ejpam-1979	7	1	1	1	X
ejpam-1979	7	2	.	.	X
ejpam-1979	7	3	introduction	introduction	NOUN
ejpam-1979	7	4	quaternion	quaternion	NOUN
ejpam-1979	7	5	algebra	algebra	NOUN
ejpam-1979	7	6	was	be	AUX
ejpam-1979	7	7	introduced	introduce	VERB
ejpam-1979	7	8	by	by	ADP
ejpam-1979	7	9	hamilton	hamilton	PROPN
ejpam-1979	7	10	in	in	ADP
ejpam-1979	7	11	1843	1843	NUM
ejpam-1979	7	12	.	.	PUNCT
ejpam-1979	8	1	important	important	ADJ
ejpam-1979	8	2	precursors	precursor	NOUN
ejpam-1979	8	3	to	to	ADP
ejpam-1979	8	4	this	this	DET
ejpam-1979	8	5	work	work	NOUN
ejpam-1979	8	6	included	include	VERB
ejpam-1979	8	7	euler	euler	PROPN
ejpam-1979	8	8	’s	’s	PART
ejpam-1979	8	9	four	four	NUM
ejpam-1979	8	10	square	square	ADJ
ejpam-1979	8	11	identity	identity	NOUN
ejpam-1979	8	12	and	and	CCONJ
ejpam-1979	8	13	olinde	olinde	ADJ
ejpam-1979	8	14	rodrigues	rodrigue	NOUN
ejpam-1979	8	15	parametrization	parametrization	NOUN
ejpam-1979	8	16	of	of	ADP
ejpam-1979	8	17	general	general	ADJ
ejpam-1979	8	18	rotations	rotation	NOUN
ejpam-1979	8	19	by	by	ADP
ejpam-1979	8	20	four	four	NUM
ejpam-1979	8	21	parameters	parameter	NOUN
ejpam-1979	8	22	,	,	PUNCT
ejpam-1979	8	23	but	but	CCONJ
ejpam-1979	8	24	neither	neither	PRON
ejpam-1979	8	25	of	of	ADP
ejpam-1979	8	26	these	these	DET
ejpam-1979	8	27	writers	writer	NOUN
ejpam-1979	8	28	treated	treat	VERB
ejpam-1979	8	29	the	the	DET
ejpam-1979	8	30	four	four	NUM
ejpam-1979	8	31	parameter	parameter	NOUN
ejpam-1979	8	32	rotations	rotation	NOUN
ejpam-1979	8	33	as	as	ADP
ejpam-1979	8	34	an	an	DET
ejpam-1979	8	35	algebra	algebra	NOUN
ejpam-1979	8	36	.	.	PUNCT
ejpam-1979	9	1	carl	carl	PROPN
ejpam-1979	9	2	friedrich	friedrich	PROPN
ejpam-1979	9	3	gauss	gauss	PROPN
ejpam-1979	9	4	had	have	AUX
ejpam-1979	9	5	also	also	ADV
ejpam-1979	9	6	discovered	discover	VERB
ejpam-1979	9	7	quaternions	quaternion	NOUN
ejpam-1979	9	8	in	in	ADP
ejpam-1979	9	9	1819	1819	NUM
ejpam-1979	9	10	,	,	PUNCT
ejpam-1979	9	11	but	but	CCONJ
ejpam-1979	9	12	this	this	DET
ejpam-1979	9	13	work	work	NOUN
ejpam-1979	9	14	was	be	AUX
ejpam-1979	9	15	not	not	PART
ejpam-1979	9	16	published	publish	VERB
ejpam-1979	9	17	until	until	ADP
ejpam-1979	9	18	1900	1900	NUM
ejpam-1979	9	19	.	.	PUNCT
ejpam-1979	10	1	hamilton	hamilton	PROPN
ejpam-1979	10	2	knew	know	VERB
ejpam-1979	10	3	that	that	SCONJ
ejpam-1979	10	4	the	the	DET
ejpam-1979	10	5	complex	complex	ADJ
ejpam-1979	10	6	numbers	number	NOUN
ejpam-1979	10	7	could	could	AUX
ejpam-1979	10	8	be	be	AUX
ejpam-1979	10	9	interpreted	interpret	VERB
ejpam-1979	10	10	as	as	ADP
ejpam-1979	10	11	points	point	NOUN
ejpam-1979	10	12	in	in	ADP
ejpam-1979	10	13	a	a	DET
ejpam-1979	10	14	plane	plane	NOUN
ejpam-1979	10	15	,	,	PUNCT
ejpam-1979	10	16	and	and	CCONJ
ejpam-1979	10	17	he	he	PRON
ejpam-1979	10	18	was	be	AUX
ejpam-1979	10	19	looking	look	VERB
ejpam-1979	10	20	for	for	ADP
ejpam-1979	10	21	a	a	DET
ejpam-1979	10	22	way	way	NOUN
ejpam-1979	10	23	to	to	PART
ejpam-1979	10	24	do	do	VERB
ejpam-1979	10	25	the	the	DET
ejpam-1979	10	26	same	same	ADJ
ejpam-1979	10	27	for	for	ADP
ejpam-1979	10	28	points	point	NOUN
ejpam-1979	10	29	in	in	ADP
ejpam-1979	10	30	three	three	NUM
ejpam-1979	10	31	-	-	PUNCT
ejpam-1979	10	32	dimensional	dimensional	ADJ
ejpam-1979	10	33	space	space	NOUN
ejpam-1979	10	34	.	.	PUNCT
ejpam-1979	11	1	points	point	NOUN
ejpam-1979	11	2	in	in	ADP
ejpam-1979	11	3	space	space	NOUN
ejpam-1979	11	4	can	can	AUX
ejpam-1979	11	5	be	be	AUX
ejpam-1979	11	6	represented	represent	VERB
ejpam-1979	11	7	by	by	ADP
ejpam-1979	11	8	their	their	PRON
ejpam-1979	11	9	coordinates	coordinate	NOUN
ejpam-1979	11	10	,	,	PUNCT
ejpam-1979	11	11	which	which	PRON
ejpam-1979	11	12	are	be	AUX
ejpam-1979	11	13	triples	triple	NOUN
ejpam-1979	11	14	of	of	ADP
ejpam-1979	11	15	numbers	number	NOUN
ejpam-1979	11	16	,	,	PUNCT
ejpam-1979	11	17	and	and	CCONJ
ejpam-1979	11	18	for	for	ADP
ejpam-1979	11	19	many	many	ADJ
ejpam-1979	11	20	years	year	NOUN
ejpam-1979	11	21	hamilton	hamilton	PROPN
ejpam-1979	11	22	had	have	AUX
ejpam-1979	11	23	known	know	VERB
ejpam-1979	11	24	how	how	SCONJ
ejpam-1979	11	25	to	to	PART
ejpam-1979	11	26	add	add	VERB
ejpam-1979	11	27	and	and	CCONJ
ejpam-1979	11	28	subtract	subtract	VERB
ejpam-1979	11	29	triples	triple	NOUN
ejpam-1979	11	30	of	of	ADP
ejpam-1979	11	31	numbers	number	NOUN
ejpam-1979	11	32	.	.	PUNCT
ejpam-1979	12	1	however	however	ADV
ejpam-1979	12	2	,	,	PUNCT
ejpam-1979	12	3	hamilton	hamilton	PROPN
ejpam-1979	12	4	had	have	AUX
ejpam-1979	12	5	been	be	AUX
ejpam-1979	12	6	stuck	stick	VERB
ejpam-1979	12	7	on	on	ADP
ejpam-1979	12	8	the	the	DET
ejpam-1979	12	9	problem	problem	NOUN
ejpam-1979	12	10	of	of	ADP
ejpam-1979	12	11	multiplication	multiplication	NOUN
ejpam-1979	12	12	and	and	CCONJ
ejpam-1979	12	13	division	division	NOUN
ejpam-1979	12	14	for	for	ADP
ejpam-1979	12	15	a	a	DET
ejpam-1979	12	16	long	long	ADJ
ejpam-1979	12	17	time	time	NOUN
ejpam-1979	12	18	.	.	PUNCT
ejpam-1979	13	1	he	he	PRON
ejpam-1979	13	2	could	could	AUX
ejpam-1979	13	3	not	not	PART
ejpam-1979	13	4	figure	figure	VERB
ejpam-1979	13	5	out	out	ADP
ejpam-1979	13	6	how	how	SCONJ
ejpam-1979	13	7	to	to	PART
ejpam-1979	13	8	calculate	calculate	VERB
ejpam-1979	13	9	the	the	DET
ejpam-1979	13	10	quotient	quotient	NOUN
ejpam-1979	13	11	of	of	ADP
ejpam-1979	13	12	the	the	DET
ejpam-1979	13	13	coordinates	coordinate	NOUN
ejpam-1979	13	14	of	of	ADP
ejpam-1979	13	15	two	two	NUM
ejpam-1979	13	16	points	point	NOUN
ejpam-1979	13	17	in	in	ADP
ejpam-1979	13	18	space	space	NOUN
ejpam-1979	13	19	.	.	PUNCT
ejpam-1979	14	1	the	the	DET
ejpam-1979	14	2	great	great	ADJ
ejpam-1979	14	3	breakthrough	breakthrough	NOUN
ejpam-1979	14	4	in	in	ADP
ejpam-1979	14	5	quaternions	quaternion	NOUN
ejpam-1979	14	6	finally	finally	ADV
ejpam-1979	14	7	came	come	VERB
ejpam-1979	14	8	on	on	ADP
ejpam-1979	14	9	monday	monday	PROPN
ejpam-1979	14	10	16	16	NUM
ejpam-1979	14	11	october	october	PROPN
ejpam-1979	14	12	1843	1843	NUM
ejpam-1979	14	13	in	in	ADP
ejpam-1979	14	14	dublin	dublin	PROPN
ejpam-1979	14	15	,	,	PUNCT
ejpam-1979	14	16	when	when	SCONJ
ejpam-1979	14	17	hamilton	hamilton	PROPN
ejpam-1979	14	18	was	be	AUX
ejpam-1979	14	19	on	on	ADP
ejpam-1979	14	20	his	his	PRON
ejpam-1979	14	21	way	way	NOUN
ejpam-1979	14	22	to	to	ADP
ejpam-1979	14	23	the	the	DET
ejpam-1979	14	24	royal	royal	PROPN
ejpam-1979	14	25	irish	irish	PROPN
ejpam-1979	14	26	academy	academy	PROPN
ejpam-1979	14	27	where	where	SCONJ
ejpam-1979	14	28	he	he	PRON
ejpam-1979	14	29	was	be	AUX
ejpam-1979	14	30	going	go	VERB
ejpam-1979	14	31	to	to	PART
ejpam-1979	14	32	preside	preside	VERB
ejpam-1979	14	33	at	at	ADP
ejpam-1979	14	34	a	a	DET
ejpam-1979	14	35	council	council	NOUN
ejpam-1979	14	36	meeting	meeting	NOUN
ejpam-1979	14	37	.	.	PUNCT
ejpam-1979	15	1	while	while	SCONJ
ejpam-1979	15	2	walking	walk	VERB
ejpam-1979	15	3	along	along	ADP
ejpam-1979	15	4	the	the	DET
ejpam-1979	15	5	towpath	towpath	NOUN
ejpam-1979	15	6	of	of	ADP
ejpam-1979	15	7	the	the	DET
ejpam-1979	15	8	royal	royal	ADJ
ejpam-1979	15	9	canal	canal	NOUN
ejpam-1979	15	10	with	with	ADP
ejpam-1979	15	11	∗corresponding	∗corresponde	VERB
ejpam-1979	15	12	author	author	NOUN
ejpam-1979	15	13	.	.	PUNCT
ejpam-1979	16	1	email	email	NOUN
ejpam-1979	16	2	addresses	address	NOUN
ejpam-1979	16	3	:	:	PUNCT
ejpam-1979	16	4	obektas@yildiz.edu.tr	obektas@yildiz.edu.tr	PROPN
ejpam-1979	16	5	(	(	PUNCT
ejpam-1979	16	6	ö.	ö.	PROPN
ejpam-1979	16	7	bektaş	bektaş	PROPN
ejpam-1979	16	8	)	)	PUNCT
ejpam-1979	16	9	,	,	PUNCT
ejpam-1979	16	10	nbayrak@yildiz.edu.tr	nbayrak@yildiz.edu.tr	PROPN
ejpam-1979	16	11	(	(	PUNCT
ejpam-1979	16	12	n.	n.	NOUN
ejpam-1979	16	13	gürses	gürse	NOUN
ejpam-1979	16	14	)	)	PUNCT
ejpam-1979	16	15	,	,	PUNCT
ejpam-1979	16	16	sayuce@yildiz.edu.tr	sayuce@yildiz.edu.tr	PROPN
ejpam-1979	16	17	(	(	PUNCT
ejpam-1979	16	18	s.	s.	PROPN
ejpam-1979	16	19	yüce	yüce	PROPN
ejpam-1979	16	20	)	)	PUNCT
ejpam-1979	16	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1979	17	1	86	86	NUM
ejpam-1979	18	1	c	c	X
ejpam-1979	18	2	©	©	PROPN
ejpam-1979	18	3	2014	2014	NUM
ejpam-1979	18	4	ejpam	ejpam	NOUN
ejpam-1979	18	5	all	all	DET
ejpam-1979	18	6	rights	right	NOUN
ejpam-1979	18	7	reserved	reserve	VERB
ejpam-1979	18	8	.	.	PUNCT
ejpam-1979	19	1	ö.	ö.	PROPN
ejpam-1979	19	2	bektaş	bektaş	PROPN
ejpam-1979	19	3	,	,	PUNCT
ejpam-1979	19	4	n.	n.	PROPN
ejpam-1979	19	5	gürses	gürse	NOUN
ejpam-1979	19	6	,	,	PUNCT
ejpam-1979	19	7	s.	s.	PROPN
ejpam-1979	19	8	yüce	yüce	PROPN
ejpam-1979	19	9	/	/	SYM
ejpam-1979	19	10	eur	eur	PROPN
ejpam-1979	19	11	.	.	PUNCT
ejpam-1979	20	1	j.	j.	PROPN
ejpam-1979	20	2	pure	pure	PROPN
ejpam-1979	20	3	appl	appl	PROPN
ejpam-1979	20	4	.	.	PROPN
ejpam-1979	20	5	math	math	PROPN
ejpam-1979	20	6	,	,	PUNCT
ejpam-1979	20	7	7	7	NUM
ejpam-1979	20	8	(	(	PUNCT
ejpam-1979	20	9	2014	2014	NUM
ejpam-1979	20	10	)	)	PUNCT
ejpam-1979	20	11	,	,	PUNCT
ejpam-1979	20	12	86	86	NUM
ejpam-1979	20	13	-	-	SYM
ejpam-1979	20	14	96	96	NUM
ejpam-1979	20	15	87	87	NUM
ejpam-1979	20	16	his	his	PRON
ejpam-1979	20	17	wife	wife	NOUN
ejpam-1979	20	18	,	,	PUNCT
ejpam-1979	20	19	the	the	DET
ejpam-1979	20	20	concepts	concept	NOUN
ejpam-1979	20	21	behind	behind	ADP
ejpam-1979	20	22	quaternions	quaternion	NOUN
ejpam-1979	20	23	were	be	AUX
ejpam-1979	20	24	taking	take	VERB
ejpam-1979	20	25	shape	shape	NOUN
ejpam-1979	20	26	in	in	ADP
ejpam-1979	20	27	his	his	PRON
ejpam-1979	20	28	mind	mind	NOUN
ejpam-1979	20	29	.	.	PUNCT
ejpam-1979	21	1	when	when	SCONJ
ejpam-1979	21	2	the	the	DET
ejpam-1979	21	3	answer	answer	NOUN
ejpam-1979	21	4	dawned	dawn	VERB
ejpam-1979	21	5	on	on	ADP
ejpam-1979	21	6	him	he	PRON
ejpam-1979	21	7	,	,	PUNCT
ejpam-1979	21	8	hamilton	hamilton	PROPN
ejpam-1979	21	9	could	could	AUX
ejpam-1979	21	10	not	not	PART
ejpam-1979	21	11	resist	resist	VERB
ejpam-1979	21	12	the	the	DET
ejpam-1979	21	13	urge	urge	NOUN
ejpam-1979	21	14	to	to	PART
ejpam-1979	21	15	carve	carve	VERB
ejpam-1979	21	16	the	the	DET
ejpam-1979	21	17	formula	formula	NOUN
ejpam-1979	21	18	for	for	ADP
ejpam-1979	21	19	the	the	DET
ejpam-1979	21	20	quaternions	quaternion	NOUN
ejpam-1979	21	21	,	,	PUNCT
ejpam-1979	21	22	e1	e1	NOUN
ejpam-1979	21	23	2	2	NUM
ejpam-1979	21	24	=	=	SYM
ejpam-1979	21	25	e2	e2	NOUN
ejpam-1979	21	26	2	2	NUM
ejpam-1979	21	27	=	=	SYM
ejpam-1979	21	28	e3	e3	VERB
ejpam-1979	21	29	2	2	NUM
ejpam-1979	21	30	=	=	SYM
ejpam-1979	21	31	e1e2e3	e1e2e3	NOUN
ejpam-1979	21	32	=	=	NOUN
ejpam-1979	21	33	−1	−1	NOUN
ejpam-1979	21	34	into	into	ADP
ejpam-1979	21	35	the	the	DET
ejpam-1979	21	36	stone	stone	NOUN
ejpam-1979	21	37	of	of	ADP
ejpam-1979	21	38	brougham	brougham	PROPN
ejpam-1979	21	39	bridge	bridge	PROPN
ejpam-1979	21	40	as	as	SCONJ
ejpam-1979	21	41	he	he	PRON
ejpam-1979	21	42	paused	pause	VERB
ejpam-1979	21	43	on	on	ADP
ejpam-1979	21	44	it	it	PRON
ejpam-1979	21	45	.	.	PUNCT
ejpam-1979	22	1	hamilton	hamilton	PROPN
ejpam-1979	22	2	called	call	VERB
ejpam-1979	22	3	a	a	DET
ejpam-1979	22	4	quadruple	quadruple	NOUN
ejpam-1979	22	5	with	with	ADP
ejpam-1979	22	6	these	these	DET
ejpam-1979	22	7	rules	rule	NOUN
ejpam-1979	22	8	of	of	ADP
ejpam-1979	22	9	multiplication	multiplication	NOUN
ejpam-1979	22	10	a	a	DET
ejpam-1979	22	11	quaternion	quaternion	NOUN
ejpam-1979	22	12	,	,	PUNCT
ejpam-1979	22	13	and	and	CCONJ
ejpam-1979	22	14	he	he	PRON
ejpam-1979	22	15	devoted	devote	VERB
ejpam-1979	22	16	most	most	ADJ
ejpam-1979	22	17	of	of	ADP
ejpam-1979	22	18	the	the	DET
ejpam-1979	22	19	remainder	remainder	NOUN
ejpam-1979	22	20	of	of	ADP
ejpam-1979	22	21	his	his	PRON
ejpam-1979	22	22	life	life	NOUN
ejpam-1979	22	23	to	to	ADP
ejpam-1979	22	24	studying	study	VERB
ejpam-1979	22	25	and	and	CCONJ
ejpam-1979	22	26	teaching	teach	VERB
ejpam-1979	22	27	them	they	PRON
ejpam-1979	22	28	.	.	PUNCT
ejpam-1979	23	1	hamilton	hamilton	PROPN
ejpam-1979	23	2	’s	’s	PART
ejpam-1979	23	3	treatment	treatment	NOUN
ejpam-1979	23	4	is	be	AUX
ejpam-1979	23	5	more	more	ADV
ejpam-1979	23	6	geometric	geometric	ADJ
ejpam-1979	23	7	than	than	ADP
ejpam-1979	23	8	the	the	DET
ejpam-1979	23	9	modern	modern	ADJ
ejpam-1979	23	10	approach	approach	NOUN
ejpam-1979	23	11	,	,	PUNCT
ejpam-1979	23	12	which	which	PRON
ejpam-1979	23	13	emphasizes	emphasize	VERB
ejpam-1979	23	14	quaternions	quaternion	NOUN
ejpam-1979	23	15	’	'	PUNCT
ejpam-1979	23	16	algebraic	algebraic	ADJ
ejpam-1979	23	17	properties	property	NOUN
ejpam-1979	23	18	.	.	PUNCT
ejpam-1979	24	1	he	he	PRON
ejpam-1979	24	2	founded	found	VERB
ejpam-1979	24	3	a	a	DET
ejpam-1979	24	4	school	school	NOUN
ejpam-1979	24	5	of	of	ADP
ejpam-1979	24	6	”	"	PUNCT
ejpam-1979	24	7	quaternionists	quaternionist	NOUN
ejpam-1979	24	8	“	"	PUNCT
ejpam-1979	24	9	,	,	PUNCT
ejpam-1979	24	10	and	and	CCONJ
ejpam-1979	24	11	he	he	PRON
ejpam-1979	24	12	tried	try	VERB
ejpam-1979	24	13	to	to	PART
ejpam-1979	24	14	popularize	popularize	VERB
ejpam-1979	24	15	quaternions	quaternion	NOUN
ejpam-1979	24	16	in	in	ADP
ejpam-1979	24	17	several	several	ADJ
ejpam-1979	24	18	books	book	NOUN
ejpam-1979	24	19	.	.	PUNCT
ejpam-1979	25	1	the	the	DET
ejpam-1979	25	2	last	last	ADJ
ejpam-1979	25	3	and	and	CCONJ
ejpam-1979	25	4	longest	long	ADJ
ejpam-1979	25	5	of	of	ADP
ejpam-1979	25	6	his	his	PRON
ejpam-1979	25	7	books	book	NOUN
ejpam-1979	25	8	,	,	PUNCT
ejpam-1979	25	9	elements	element	NOUN
ejpam-1979	25	10	of	of	ADP
ejpam-1979	25	11	quaternions	quaternion	NOUN
ejpam-1979	25	12	,	,	PUNCT
ejpam-1979	25	13	was	be	AUX
ejpam-1979	25	14	800	800	NUM
ejpam-1979	25	15	pages	page	NOUN
ejpam-1979	25	16	long	long	ADV
ejpam-1979	25	17	;	;	PUNCT
ejpam-1979	25	18	it	it	PRON
ejpam-1979	25	19	was	be	AUX
ejpam-1979	25	20	published	publish	VERB
ejpam-1979	25	21	shortly	shortly	ADV
ejpam-1979	25	22	after	after	ADP
ejpam-1979	25	23	his	his	PRON
ejpam-1979	25	24	death	death	NOUN
ejpam-1979	25	25	.	.	PUNCT
ejpam-1979	26	1	after	after	ADP
ejpam-1979	26	2	hamilton	hamilton	PROPN
ejpam-1979	26	3	’s	’s	PART
ejpam-1979	26	4	death	death	NOUN
ejpam-1979	26	5	,	,	PUNCT
ejpam-1979	26	6	his	his	PRON
ejpam-1979	26	7	student	student	NOUN
ejpam-1979	26	8	peter	peter	PROPN
ejpam-1979	26	9	tait	tait	PROPN
ejpam-1979	26	10	continued	continue	VERB
ejpam-1979	26	11	promoting	promote	VERB
ejpam-1979	26	12	quaternions	quaternion	NOUN
ejpam-1979	26	13	.	.	PUNCT
ejpam-1979	27	1	at	at	ADP
ejpam-1979	27	2	this	this	DET
ejpam-1979	27	3	time	time	NOUN
ejpam-1979	27	4	,	,	PUNCT
ejpam-1979	27	5	quaternions	quaternion	NOUN
ejpam-1979	27	6	were	be	AUX
ejpam-1979	27	7	a	a	DET
ejpam-1979	27	8	mandatory	mandatory	ADJ
ejpam-1979	27	9	examination	examination	NOUN
ejpam-1979	27	10	topic	topic	NOUN
ejpam-1979	27	11	in	in	ADP
ejpam-1979	27	12	dublin	dublin	PROPN
ejpam-1979	27	13	.	.	PUNCT
ejpam-1979	28	1	topics	topic	NOUN
ejpam-1979	28	2	in	in	ADP
ejpam-1979	28	3	physics	physics	NOUN
ejpam-1979	28	4	and	and	CCONJ
ejpam-1979	28	5	geometry	geometry	NOUN
ejpam-1979	28	6	that	that	PRON
ejpam-1979	28	7	would	would	AUX
ejpam-1979	28	8	now	now	ADV
ejpam-1979	28	9	be	be	AUX
ejpam-1979	28	10	described	describe	VERB
ejpam-1979	28	11	using	use	VERB
ejpam-1979	28	12	vectors	vector	NOUN
ejpam-1979	28	13	,	,	PUNCT
ejpam-1979	28	14	such	such	ADJ
ejpam-1979	28	15	as	as	ADP
ejpam-1979	28	16	kinematics	kinematic	NOUN
ejpam-1979	28	17	in	in	ADP
ejpam-1979	28	18	space	space	NOUN
ejpam-1979	28	19	and	and	CCONJ
ejpam-1979	28	20	maxwell	maxwell	PROPN
ejpam-1979	28	21	’s	’s	PART
ejpam-1979	28	22	equations	equation	NOUN
ejpam-1979	28	23	,	,	PUNCT
ejpam-1979	28	24	were	be	AUX
ejpam-1979	28	25	described	describe	VERB
ejpam-1979	28	26	entirely	entirely	ADV
ejpam-1979	28	27	in	in	ADP
ejpam-1979	28	28	terms	term	NOUN
ejpam-1979	28	29	of	of	ADP
ejpam-1979	28	30	quaternions	quaternion	NOUN
ejpam-1979	28	31	.	.	PUNCT
ejpam-1979	29	1	there	there	PRON
ejpam-1979	29	2	was	be	VERB
ejpam-1979	29	3	even	even	ADV
ejpam-1979	29	4	a	a	DET
ejpam-1979	29	5	professional	professional	ADJ
ejpam-1979	29	6	research	research	NOUN
ejpam-1979	29	7	association	association	NOUN
ejpam-1979	29	8	,	,	PUNCT
ejpam-1979	29	9	the	the	DET
ejpam-1979	29	10	quaternion	quaternion	NOUN
ejpam-1979	29	11	society	society	NOUN
ejpam-1979	29	12	,	,	PUNCT
ejpam-1979	29	13	devoted	devote	VERB
ejpam-1979	29	14	to	to	ADP
ejpam-1979	29	15	the	the	DET
ejpam-1979	29	16	study	study	NOUN
ejpam-1979	29	17	of	of	ADP
ejpam-1979	29	18	quaternions	quaternion	NOUN
ejpam-1979	29	19	and	and	CCONJ
ejpam-1979	29	20	other	other	ADJ
ejpam-1979	29	21	hypercomplex	hypercomplex	NOUN
ejpam-1979	29	22	number	number	NOUN
ejpam-1979	29	23	systems	system	NOUN
ejpam-1979	29	24	.	.	PUNCT
ejpam-1979	30	1	from	from	ADP
ejpam-1979	30	2	the	the	DET
ejpam-1979	30	3	mid-1880s	mid-1880	NOUN
ejpam-1979	30	4	,	,	PUNCT
ejpam-1979	30	5	quaternions	quaternion	NOUN
ejpam-1979	30	6	began	begin	VERB
ejpam-1979	30	7	to	to	PART
ejpam-1979	30	8	be	be	AUX
ejpam-1979	30	9	displaced	displace	VERB
ejpam-1979	30	10	by	by	ADP
ejpam-1979	30	11	vector	vector	NOUN
ejpam-1979	30	12	analysis	analysis	NOUN
ejpam-1979	30	13	,	,	PUNCT
ejpam-1979	30	14	which	which	PRON
ejpam-1979	30	15	had	have	AUX
ejpam-1979	30	16	been	be	AUX
ejpam-1979	30	17	developed	develop	VERB
ejpam-1979	30	18	by	by	ADP
ejpam-1979	30	19	josiah	josiah	PROPN
ejpam-1979	30	20	willard	willard	PROPN
ejpam-1979	30	21	gibbs	gibbs	PROPN
ejpam-1979	30	22	,	,	PUNCT
ejpam-1979	30	23	oliver	oliver	PROPN
ejpam-1979	30	24	heaviside	heaviside	PROPN
ejpam-1979	30	25	,	,	PUNCT
ejpam-1979	30	26	and	and	CCONJ
ejpam-1979	30	27	hermann	hermann	PROPN
ejpam-1979	30	28	von	von	PROPN
ejpam-1979	30	29	helmholtz	helmholtz	PROPN
ejpam-1979	30	30	.	.	PUNCT
ejpam-1979	31	1	vector	vector	NOUN
ejpam-1979	31	2	analysis	analysis	NOUN
ejpam-1979	31	3	described	describe	VERB
ejpam-1979	31	4	the	the	DET
ejpam-1979	31	5	same	same	ADJ
ejpam-1979	31	6	phenomena	phenomena	NOUN
ejpam-1979	31	7	as	as	ADP
ejpam-1979	31	8	quaternions	quaternion	NOUN
ejpam-1979	31	9	,	,	PUNCT
ejpam-1979	31	10	so	so	CCONJ
ejpam-1979	31	11	it	it	PRON
ejpam-1979	31	12	borrowed	borrow	VERB
ejpam-1979	31	13	some	some	DET
ejpam-1979	31	14	ideas	idea	NOUN
ejpam-1979	31	15	and	and	CCONJ
ejpam-1979	31	16	terminology	terminology	NOUN
ejpam-1979	31	17	liberally	liberally	ADV
ejpam-1979	31	18	from	from	ADP
ejpam-1979	31	19	the	the	DET
ejpam-1979	31	20	literature	literature	NOUN
ejpam-1979	31	21	of	of	ADP
ejpam-1979	31	22	quaternions	quaternion	NOUN
ejpam-1979	31	23	.	.	PUNCT
ejpam-1979	32	1	however	however	ADV
ejpam-1979	32	2	,	,	PUNCT
ejpam-1979	32	3	vector	vector	NOUN
ejpam-1979	32	4	analysis	analysis	NOUN
ejpam-1979	32	5	was	be	AUX
ejpam-1979	32	6	conceptually	conceptually	ADV
ejpam-1979	32	7	simpler	simple	ADJ
ejpam-1979	32	8	and	and	CCONJ
ejpam-1979	32	9	notationally	notationally	ADV
ejpam-1979	32	10	cleaner	clean	ADJ
ejpam-1979	32	11	,	,	PUNCT
ejpam-1979	32	12	and	and	CCONJ
ejpam-1979	32	13	eventually	eventually	ADV
ejpam-1979	32	14	quaternions	quaternion	NOUN
ejpam-1979	32	15	were	be	AUX
ejpam-1979	32	16	relegated	relegate	VERB
ejpam-1979	32	17	to	to	ADP
ejpam-1979	32	18	a	a	DET
ejpam-1979	32	19	minor	minor	ADJ
ejpam-1979	32	20	role	role	NOUN
ejpam-1979	32	21	in	in	ADP
ejpam-1979	32	22	mathematics	mathematic	NOUN
ejpam-1979	32	23	and	and	CCONJ
ejpam-1979	32	24	physics	physics	NOUN
ejpam-1979	32	25	.	.	PUNCT
ejpam-1979	33	1	a	a	DET
ejpam-1979	33	2	side	side	ADJ
ejpam-1979	33	3	effect	effect	NOUN
ejpam-1979	33	4	of	of	ADP
ejpam-1979	33	5	this	this	DET
ejpam-1979	33	6	transition	transition	NOUN
ejpam-1979	33	7	is	be	AUX
ejpam-1979	33	8	that	that	SCONJ
ejpam-1979	33	9	hamilton	hamilton	PROPN
ejpam-1979	33	10	’s	’s	PART
ejpam-1979	33	11	work	work	NOUN
ejpam-1979	33	12	is	be	AUX
ejpam-1979	33	13	difficult	difficult	ADJ
ejpam-1979	33	14	to	to	PART
ejpam-1979	33	15	comprehend	comprehend	VERB
ejpam-1979	33	16	for	for	ADP
ejpam-1979	33	17	many	many	ADJ
ejpam-1979	33	18	modern	modern	ADJ
ejpam-1979	33	19	readers	reader	NOUN
ejpam-1979	33	20	.	.	PUNCT
ejpam-1979	34	1	hamilton	hamilton	PROPN
ejpam-1979	34	2	’s	’s	PART
ejpam-1979	34	3	original	original	ADJ
ejpam-1979	34	4	definitions	definition	NOUN
ejpam-1979	34	5	are	be	AUX
ejpam-1979	34	6	unfamiliar	unfamiliar	ADJ
ejpam-1979	34	7	and	and	CCONJ
ejpam-1979	34	8	his	his	PRON
ejpam-1979	34	9	writing	writing	NOUN
ejpam-1979	34	10	style	style	NOUN
ejpam-1979	34	11	was	be	AUX
ejpam-1979	34	12	wordy	wordy	ADJ
ejpam-1979	34	13	and	and	CCONJ
ejpam-1979	34	14	difficult	difficult	ADJ
ejpam-1979	34	15	to	to	PART
ejpam-1979	34	16	understand	understand	VERB
ejpam-1979	34	17	.	.	PUNCT
ejpam-1979	35	1	however	however	ADV
ejpam-1979	35	2	,	,	PUNCT
ejpam-1979	35	3	quaternions	quaternion	NOUN
ejpam-1979	35	4	have	have	AUX
ejpam-1979	35	5	had	have	VERB
ejpam-1979	35	6	a	a	DET
ejpam-1979	35	7	revival	revival	NOUN
ejpam-1979	35	8	since	since	SCONJ
ejpam-1979	35	9	the	the	DET
ejpam-1979	35	10	late	late	ADJ
ejpam-1979	35	11	20th	20th	ADJ
ejpam-1979	35	12	century	century	NOUN
ejpam-1979	35	13	,	,	PUNCT
ejpam-1979	35	14	primarily	primarily	ADV
ejpam-1979	35	15	due	due	ADP
ejpam-1979	35	16	to	to	ADP
ejpam-1979	35	17	their	their	PRON
ejpam-1979	35	18	utility	utility	NOUN
ejpam-1979	35	19	in	in	ADP
ejpam-1979	35	20	describing	describe	VERB
ejpam-1979	35	21	spatial	spatial	ADJ
ejpam-1979	35	22	rotations	rotation	NOUN
ejpam-1979	35	23	.	.	PUNCT
ejpam-1979	36	1	the	the	DET
ejpam-1979	36	2	representations	representation	NOUN
ejpam-1979	36	3	of	of	ADP
ejpam-1979	36	4	rotations	rotation	NOUN
ejpam-1979	36	5	by	by	ADP
ejpam-1979	36	6	quaternions	quaternion	NOUN
ejpam-1979	36	7	are	be	AUX
ejpam-1979	36	8	more	more	ADV
ejpam-1979	36	9	compact	compact	ADJ
ejpam-1979	36	10	and	and	CCONJ
ejpam-1979	36	11	quicker	quick	ADJ
ejpam-1979	36	12	to	to	PART
ejpam-1979	36	13	compute	compute	VERB
ejpam-1979	36	14	than	than	ADP
ejpam-1979	36	15	the	the	DET
ejpam-1979	36	16	representations	representation	NOUN
ejpam-1979	36	17	by	by	ADP
ejpam-1979	36	18	matrices	matrix	NOUN
ejpam-1979	36	19	.	.	PUNCT
ejpam-1979	37	1	in	in	ADP
ejpam-1979	37	2	addition	addition	NOUN
ejpam-1979	37	3	,	,	PUNCT
ejpam-1979	37	4	unlike	unlike	ADP
ejpam-1979	37	5	euler	euler	NOUN
ejpam-1979	37	6	angles	angle	NOUN
ejpam-1979	37	7	they	they	PRON
ejpam-1979	37	8	are	be	AUX
ejpam-1979	37	9	not	not	PART
ejpam-1979	37	10	susceptible	susceptible	ADJ
ejpam-1979	37	11	to	to	ADP
ejpam-1979	37	12	gimbal	gimbal	ADJ
ejpam-1979	37	13	lock	lock	NOUN
ejpam-1979	37	14	.	.	PUNCT
ejpam-1979	38	1	for	for	ADP
ejpam-1979	38	2	this	this	DET
ejpam-1979	38	3	reason	reason	NOUN
ejpam-1979	38	4	,	,	PUNCT
ejpam-1979	38	5	quaternions	quaternion	NOUN
ejpam-1979	38	6	are	be	AUX
ejpam-1979	38	7	used	use	VERB
ejpam-1979	38	8	in	in	ADP
ejpam-1979	38	9	computer	computer	NOUN
ejpam-1979	38	10	graphics	graphic	NOUN
ejpam-1979	38	11	,	,	PUNCT
ejpam-1979	38	12	computer	computer	NOUN
ejpam-1979	38	13	vision	vision	NOUN
ejpam-1979	38	14	,	,	PUNCT
ejpam-1979	38	15	robotics	robotic	NOUN
ejpam-1979	38	16	,	,	PUNCT
ejpam-1979	38	17	control	control	NOUN
ejpam-1979	38	18	theory	theory	NOUN
ejpam-1979	38	19	,	,	PUNCT
ejpam-1979	38	20	signal	signal	ADJ
ejpam-1979	38	21	processing	processing	NOUN
ejpam-1979	38	22	,	,	PUNCT
ejpam-1979	38	23	attitude	attitude	NOUN
ejpam-1979	38	24	control	control	NOUN
ejpam-1979	38	25	,	,	PUNCT
ejpam-1979	38	26	physics	physics	NOUN
ejpam-1979	38	27	,	,	PUNCT
ejpam-1979	38	28	bioinformatics	bioinformatic	NOUN
ejpam-1979	38	29	,	,	PUNCT
ejpam-1979	38	30	molecular	molecular	ADJ
ejpam-1979	38	31	dynamics	dynamic	NOUN
ejpam-1979	38	32	,	,	PUNCT
ejpam-1979	38	33	computer	computer	NOUN
ejpam-1979	38	34	simulations	simulation	NOUN
ejpam-1979	38	35	,	,	PUNCT
ejpam-1979	38	36	and	and	CCONJ
ejpam-1979	38	37	orbital	orbital	ADJ
ejpam-1979	38	38	mechanics	mechanic	NOUN
ejpam-1979	38	39	.	.	PUNCT
ejpam-1979	39	1	for	for	ADP
ejpam-1979	39	2	example	example	NOUN
ejpam-1979	39	3	,	,	PUNCT
ejpam-1979	39	4	it	it	PRON
ejpam-1979	39	5	is	be	AUX
ejpam-1979	39	6	common	common	ADJ
ejpam-1979	39	7	for	for	SCONJ
ejpam-1979	39	8	the	the	DET
ejpam-1979	39	9	attitude	attitude	NOUN
ejpam-1979	39	10	-	-	PUNCT
ejpam-1979	39	11	control	control	NOUN
ejpam-1979	39	12	systems	system	NOUN
ejpam-1979	39	13	of	of	ADP
ejpam-1979	39	14	spacecraft	spacecraft	NOUN
ejpam-1979	39	15	to	to	PART
ejpam-1979	39	16	be	be	AUX
ejpam-1979	39	17	commanded	command	VERB
ejpam-1979	39	18	in	in	ADP
ejpam-1979	39	19	terms	term	NOUN
ejpam-1979	39	20	of	of	ADP
ejpam-1979	39	21	quaternions	quaternion	NOUN
ejpam-1979	39	22	.	.	PUNCT
ejpam-1979	40	1	quaternions	quaternion	NOUN
ejpam-1979	40	2	have	have	AUX
ejpam-1979	40	3	received	receive	VERB
ejpam-1979	40	4	another	another	DET
ejpam-1979	40	5	boost	boost	NOUN
ejpam-1979	40	6	from	from	ADP
ejpam-1979	40	7	number	number	NOUN
ejpam-1979	40	8	theory	theory	NOUN
ejpam-1979	40	9	because	because	SCONJ
ejpam-1979	40	10	of	of	ADP
ejpam-1979	40	11	their	their	PRON
ejpam-1979	40	12	relationships	relationship	NOUN
ejpam-1979	40	13	with	with	ADP
ejpam-1979	40	14	the	the	DET
ejpam-1979	40	15	quadratic	quadratic	ADJ
ejpam-1979	40	16	forms	form	NOUN
ejpam-1979	40	17	[	[	X
ejpam-1979	40	18	1	1	NUM
ejpam-1979	40	19	]	]	PUNCT
ejpam-1979	40	20	.	.	PUNCT
ejpam-1979	41	1	the	the	DET
ejpam-1979	41	2	set	set	NOUN
ejpam-1979	41	3	of	of	ADP
ejpam-1979	41	4	quaternions	quaternion	NOUN
ejpam-1979	41	5	is	be	AUX
ejpam-1979	41	6	denoted	denote	VERB
ejpam-1979	41	7	byh	byh	ADV
ejpam-1979	41	8	.	.	PUNCT
ejpam-1979	42	1	while	while	SCONJ
ejpam-1979	42	2	the	the	DET
ejpam-1979	42	3	quaternions	quaternion	NOUN
ejpam-1979	42	4	are	be	AUX
ejpam-1979	42	5	not	not	PART
ejpam-1979	42	6	commutative	commutative	ADJ
ejpam-1979	42	7	,	,	PUNCT
ejpam-1979	42	8	they	they	PRON
ejpam-1979	42	9	are	be	AUX
ejpam-1979	42	10	associative	associative	ADJ
ejpam-1979	42	11	,	,	PUNCT
ejpam-1979	42	12	and	and	CCONJ
ejpam-1979	42	13	they	they	PRON
ejpam-1979	42	14	form	form	VERB
ejpam-1979	42	15	a	a	DET
ejpam-1979	42	16	group	group	NOUN
ejpam-1979	42	17	known	know	VERB
ejpam-1979	42	18	as	as	ADP
ejpam-1979	42	19	the	the	DET
ejpam-1979	42	20	quaternion	quaternion	NOUN
ejpam-1979	42	21	group	group	NOUN
ejpam-1979	42	22	.	.	PUNCT
ejpam-1979	43	1	by	by	ADP
ejpam-1979	43	2	analogy	analogy	NOUN
ejpam-1979	43	3	with	with	ADP
ejpam-1979	43	4	the	the	DET
ejpam-1979	43	5	complex	complex	ADJ
ejpam-1979	43	6	numbers	number	NOUN
ejpam-1979	43	7	being	be	AUX
ejpam-1979	43	8	representable	representable	ADJ
ejpam-1979	43	9	as	as	ADP
ejpam-1979	43	10	a	a	DET
ejpam-1979	43	11	sum	sum	NOUN
ejpam-1979	43	12	of	of	ADP
ejpam-1979	43	13	real	real	ADJ
ejpam-1979	43	14	and	and	CCONJ
ejpam-1979	43	15	imaginary	imaginary	ADJ
ejpam-1979	43	16	parts	part	NOUN
ejpam-1979	43	17	,	,	PUNCT
ejpam-1979	43	18	a01	a01	NOUN
ejpam-1979	43	19	+	+	CCONJ
ejpam-1979	43	20	a1e1	a1e1	NOUN
ejpam-1979	43	21	,	,	PUNCT
ejpam-1979	43	22	a	a	DET
ejpam-1979	43	23	quaternion	quaternion	NOUN
ejpam-1979	43	24	can	can	AUX
ejpam-1979	43	25	also	also	ADV
ejpam-1979	43	26	be	be	AUX
ejpam-1979	43	27	written	write	VERB
ejpam-1979	43	28	as	as	ADP
ejpam-1979	43	29	a	a	DET
ejpam-1979	43	30	linear	linear	ADJ
ejpam-1979	43	31	combination	combination	NOUN
ejpam-1979	43	32	a01	a01	NOUN
ejpam-1979	43	33	+	+	CCONJ
ejpam-1979	43	34	a1e1	a1e1	PROPN
ejpam-1979	43	35	+	+	ADJ
ejpam-1979	43	36	a2e2	a2e2	PROPN
ejpam-1979	43	37	+	+	ADJ
ejpam-1979	43	38	a3e3	a3e3	PROPN
ejpam-1979	43	39	.	.	PROPN
ejpam-1979	43	40	as	as	ADP
ejpam-1979	43	41	a	a	DET
ejpam-1979	43	42	set	set	NOUN
ejpam-1979	43	43	,	,	PUNCT
ejpam-1979	43	44	the	the	DET
ejpam-1979	43	45	quaternions	quaternions	ADJ
ejpam-1979	43	46	h	h	NOUN
ejpam-1979	43	47	are	be	AUX
ejpam-1979	43	48	equal	equal	ADJ
ejpam-1979	43	49	to	to	ADP
ejpam-1979	43	50	e4	e4	PROPN
ejpam-1979	43	51	,	,	PUNCT
ejpam-1979	43	52	a	a	DET
ejpam-1979	43	53	four	four	NUM
ejpam-1979	43	54	dimensional	dimensional	ADJ
ejpam-1979	43	55	vector	vector	NOUN
ejpam-1979	43	56	space	space	NOUN
ejpam-1979	43	57	over	over	ADP
ejpam-1979	43	58	the	the	DET
ejpam-1979	43	59	real	real	ADJ
ejpam-1979	43	60	numbers	number	NOUN
ejpam-1979	43	61	.	.	PUNCT
ejpam-1979	44	1	h	h	PROPN
ejpam-1979	44	2	has	have	VERB
ejpam-1979	44	3	three	three	NUM
ejpam-1979	44	4	operations	operation	NOUN
ejpam-1979	44	5	:	:	PUNCT
ejpam-1979	44	6	addition	addition	NOUN
ejpam-1979	44	7	,	,	PUNCT
ejpam-1979	44	8	scalar	scalar	ADJ
ejpam-1979	44	9	multiplication	multiplication	NOUN
ejpam-1979	44	10	and	and	CCONJ
ejpam-1979	44	11	quaternion	quaternion	NOUN
ejpam-1979	44	12	multiplication	multiplication	NOUN
ejpam-1979	44	13	.	.	PUNCT
ejpam-1979	45	1	the	the	DET
ejpam-1979	45	2	sum	sum	NOUN
ejpam-1979	45	3	of	of	ADP
ejpam-1979	45	4	two	two	NUM
ejpam-1979	45	5	elements	element	NOUN
ejpam-1979	45	6	of	of	ADP
ejpam-1979	45	7	h	h	NOUN
ejpam-1979	45	8	is	be	AUX
ejpam-1979	45	9	defined	define	VERB
ejpam-1979	45	10	to	to	PART
ejpam-1979	45	11	be	be	AUX
ejpam-1979	45	12	their	their	PRON
ejpam-1979	45	13	sum	sum	NOUN
ejpam-1979	45	14	as	as	ADP
ejpam-1979	45	15	elements	element	NOUN
ejpam-1979	45	16	of	of	ADP
ejpam-1979	45	17	e4	e4	PROPN
ejpam-1979	45	18	.	.	PUNCT
ejpam-1979	46	1	similarly	similarly	ADV
ejpam-1979	46	2	ö.	ö.	VERB
ejpam-1979	46	3	bektaş	bektaş	PROPN
ejpam-1979	46	4	,	,	PUNCT
ejpam-1979	46	5	n.	n.	PROPN
ejpam-1979	46	6	gürses	gürse	NOUN
ejpam-1979	46	7	,	,	PUNCT
ejpam-1979	46	8	s.	s.	PROPN
ejpam-1979	46	9	yüce	yüce	PROPN
ejpam-1979	46	10	/	/	SYM
ejpam-1979	46	11	eur	eur	PROPN
ejpam-1979	46	12	.	.	PUNCT
ejpam-1979	47	1	j.	j.	PROPN
ejpam-1979	47	2	pure	pure	PROPN
ejpam-1979	47	3	appl	appl	PROPN
ejpam-1979	47	4	.	.	PROPN
ejpam-1979	47	5	math	math	PROPN
ejpam-1979	47	6	,	,	PUNCT
ejpam-1979	47	7	7	7	NUM
ejpam-1979	47	8	(	(	PUNCT
ejpam-1979	47	9	2014	2014	NUM
ejpam-1979	47	10	)	)	PUNCT
ejpam-1979	47	11	,	,	PUNCT
ejpam-1979	47	12	86	86	NUM
ejpam-1979	47	13	-	-	SYM
ejpam-1979	47	14	96	96	NUM
ejpam-1979	47	15	88	88	NUM
ejpam-1979	47	16	the	the	DET
ejpam-1979	47	17	product	product	NOUN
ejpam-1979	47	18	of	of	ADP
ejpam-1979	47	19	an	an	DET
ejpam-1979	47	20	element	element	NOUN
ejpam-1979	47	21	of	of	ADP
ejpam-1979	47	22	h	h	NOUN
ejpam-1979	47	23	by	by	ADP
ejpam-1979	47	24	a	a	DET
ejpam-1979	47	25	real	real	ADJ
ejpam-1979	47	26	number	number	NOUN
ejpam-1979	47	27	is	be	AUX
ejpam-1979	47	28	defined	define	VERB
ejpam-1979	47	29	to	to	PART
ejpam-1979	47	30	be	be	AUX
ejpam-1979	47	31	same	same	ADJ
ejpam-1979	47	32	as	as	SCONJ
ejpam-1979	47	33	the	the	DET
ejpam-1979	47	34	product	product	NOUN
ejpam-1979	47	35	in	in	ADP
ejpam-1979	47	36	e4.to	e4.to	NOUN
ejpam-1979	47	37	define	define	VERB
ejpam-1979	47	38	the	the	DET
ejpam-1979	47	39	product	product	NOUN
ejpam-1979	47	40	of	of	ADP
ejpam-1979	47	41	two	two	NUM
ejpam-1979	47	42	elements	element	NOUN
ejpam-1979	47	43	inh	inh	PROPN
ejpam-1979	47	44	requires	require	VERB
ejpam-1979	47	45	a	a	DET
ejpam-1979	47	46	choice	choice	NOUN
ejpam-1979	47	47	of	of	ADP
ejpam-1979	47	48	basis	basis	NOUN
ejpam-1979	47	49	for	for	ADP
ejpam-1979	47	50	e4	e4	PROPN
ejpam-1979	47	51	.	.	PUNCT
ejpam-1979	48	1	the	the	DET
ejpam-1979	48	2	elements	element	NOUN
ejpam-1979	48	3	of	of	ADP
ejpam-1979	48	4	this	this	DET
ejpam-1979	48	5	basis	basis	NOUN
ejpam-1979	48	6	are	be	AUX
ejpam-1979	48	7	customarily	customarily	ADV
ejpam-1979	48	8	denoted	denote	VERB
ejpam-1979	48	9	as	as	ADP
ejpam-1979	48	10	1	1	NUM
ejpam-1979	48	11	,	,	PUNCT
ejpam-1979	48	12	i	i	PRON
ejpam-1979	48	13	,	,	PUNCT
ejpam-1979	48	14	j	j	PROPN
ejpam-1979	48	15	,	,	PUNCT
ejpam-1979	48	16	and	and	CCONJ
ejpam-1979	48	17	k.	k.	NOUN
ejpam-1979	49	1	every	every	DET
ejpam-1979	49	2	element	element	NOUN
ejpam-1979	49	3	of	of	ADP
ejpam-1979	49	4	h	h	NOUN
ejpam-1979	49	5	can	can	AUX
ejpam-1979	49	6	be	be	AUX
ejpam-1979	49	7	uniquely	uniquely	ADV
ejpam-1979	49	8	written	write	VERB
ejpam-1979	49	9	as	as	ADP
ejpam-1979	49	10	a	a	DET
ejpam-1979	49	11	linear	linear	ADJ
ejpam-1979	49	12	combination	combination	NOUN
ejpam-1979	49	13	of	of	ADP
ejpam-1979	49	14	these	these	DET
ejpam-1979	49	15	basis	basis	NOUN
ejpam-1979	49	16	elements	element	NOUN
ejpam-1979	49	17	,	,	PUNCT
ejpam-1979	49	18	that	that	ADV
ejpam-1979	49	19	is	is	ADV
ejpam-1979	49	20	,	,	PUNCT
ejpam-1979	49	21	as	as	ADP
ejpam-1979	49	22	a01	a01	NOUN
ejpam-1979	49	23	+	+	CCONJ
ejpam-1979	49	24	a1e1	a1e1	PROPN
ejpam-1979	49	25	+	+	CCONJ
ejpam-1979	49	26	a2e2	a2e2	PROPN
ejpam-1979	49	27	+	+	NUM
ejpam-1979	49	28	a3e3	a3e3	PROPN
ejpam-1979	49	29	,	,	PUNCT
ejpam-1979	49	30	where	where	SCONJ
ejpam-1979	49	31	a0	a0	PROPN
ejpam-1979	49	32	,	,	PUNCT
ejpam-1979	49	33	a1	a1	PROPN
ejpam-1979	49	34	,	,	PUNCT
ejpam-1979	49	35	a2	a2	PROPN
ejpam-1979	49	36	,	,	PUNCT
ejpam-1979	49	37	and	and	CCONJ
ejpam-1979	49	38	a3	a3	NOUN
ejpam-1979	49	39	are	be	AUX
ejpam-1979	49	40	real	real	ADJ
ejpam-1979	49	41	numbers	number	NOUN
ejpam-1979	49	42	.	.	PUNCT
ejpam-1979	50	1	the	the	DET
ejpam-1979	50	2	basis	basis	NOUN
ejpam-1979	50	3	element	element	NOUN
ejpam-1979	50	4	1	1	NUM
ejpam-1979	50	5	will	will	AUX
ejpam-1979	50	6	be	be	AUX
ejpam-1979	50	7	the	the	DET
ejpam-1979	50	8	identity	identity	NOUN
ejpam-1979	50	9	element	element	NOUN
ejpam-1979	50	10	ofh	ofh	PROPN
ejpam-1979	50	11	,	,	PUNCT
ejpam-1979	50	12	meaning	mean	VERB
ejpam-1979	50	13	that	that	SCONJ
ejpam-1979	50	14	multiplication	multiplication	NOUN
ejpam-1979	50	15	by	by	ADP
ejpam-1979	50	16	1	1	NUM
ejpam-1979	50	17	does	do	VERB
ejpam-1979	50	18	nothing	nothing	PRON
ejpam-1979	50	19	,	,	PUNCT
ejpam-1979	50	20	and	and	CCONJ
ejpam-1979	50	21	for	for	ADP
ejpam-1979	50	22	this	this	DET
ejpam-1979	50	23	reason	reason	NOUN
ejpam-1979	50	24	,	,	PUNCT
ejpam-1979	50	25	elements	element	NOUN
ejpam-1979	50	26	ofh	ofh	PROPN
ejpam-1979	50	27	are	be	AUX
ejpam-1979	50	28	usually	usually	ADV
ejpam-1979	50	29	written	write	VERB
ejpam-1979	50	30	a01	a01	NOUN
ejpam-1979	50	31	+	+	CCONJ
ejpam-1979	50	32	a1e1	a1e1	PROPN
ejpam-1979	50	33	+	+	CCONJ
ejpam-1979	50	34	a2e2	a2e2	PROPN
ejpam-1979	50	35	+	+	NUM
ejpam-1979	50	36	a3e3	a3e3	PROPN
ejpam-1979	50	37	,	,	PUNCT
ejpam-1979	50	38	suppressing	suppress	VERB
ejpam-1979	50	39	the	the	DET
ejpam-1979	50	40	basis	basis	NOUN
ejpam-1979	50	41	element	element	NOUN
ejpam-1979	50	42	1	1	NUM
ejpam-1979	50	43	.	.	PUNCT
ejpam-1979	51	1	given	give	VERB
ejpam-1979	51	2	this	this	DET
ejpam-1979	51	3	basis	basis	NOUN
ejpam-1979	51	4	,	,	PUNCT
ejpam-1979	51	5	associative	associative	ADJ
ejpam-1979	51	6	quaternion	quaternion	NOUN
ejpam-1979	51	7	multiplication	multiplication	NOUN
ejpam-1979	51	8	is	be	AUX
ejpam-1979	51	9	defined	define	VERB
ejpam-1979	51	10	by	by	ADP
ejpam-1979	51	11	first	first	ADV
ejpam-1979	51	12	defining	define	VERB
ejpam-1979	51	13	the	the	DET
ejpam-1979	51	14	products	product	NOUN
ejpam-1979	51	15	of	of	ADP
ejpam-1979	51	16	basis	basis	NOUN
ejpam-1979	51	17	elements	element	NOUN
ejpam-1979	51	18	and	and	CCONJ
ejpam-1979	51	19	then	then	ADV
ejpam-1979	51	20	defining	define	VERB
ejpam-1979	51	21	all	all	DET
ejpam-1979	51	22	other	other	ADJ
ejpam-1979	51	23	products	product	NOUN
ejpam-1979	51	24	using	use	VERB
ejpam-1979	51	25	the	the	DET
ejpam-1979	51	26	distributive	distributive	ADJ
ejpam-1979	51	27	law	law	NOUN
ejpam-1979	51	28	,	,	PUNCT
ejpam-1979	51	29	[	[	X
ejpam-1979	51	30	2–4	2–4	NUM
ejpam-1979	51	31	]	]	PUNCT
ejpam-1979	51	32	.	.	PUNCT
ejpam-1979	52	1	in	in	ADP
ejpam-1979	52	2	[	[	X
ejpam-1979	52	3	5	5	NUM
ejpam-1979	52	4	]	]	PUNCT
ejpam-1979	52	5	,	,	PUNCT
ejpam-1979	52	6	baharathi	baharathi	PROPN
ejpam-1979	52	7	and	and	CCONJ
ejpam-1979	52	8	nagaraj	nagaraj	PROPN
ejpam-1979	52	9	studied	study	VERB
ejpam-1979	52	10	the	the	DET
ejpam-1979	52	11	differential	differential	ADJ
ejpam-1979	52	12	geometry	geometry	NOUN
ejpam-1979	52	13	of	of	ADP
ejpam-1979	52	14	a	a	DET
ejpam-1979	52	15	smooth	smooth	ADJ
ejpam-1979	52	16	quaternionic	quaternionic	ADJ
ejpam-1979	52	17	curve	curve	NOUN
ejpam-1979	52	18	in	in	ADP
ejpam-1979	52	19	e3	e3	NOUN
ejpam-1979	52	20	and	and	CCONJ
ejpam-1979	52	21	e4	e4	PROPN
ejpam-1979	52	22	.	.	PUNCT
ejpam-1979	53	1	elements	element	NOUN
ejpam-1979	53	2	of	of	ADP
ejpam-1979	53	3	e4	e4	PROPN
ejpam-1979	53	4	were	be	AUX
ejpam-1979	53	5	identified	identify	VERB
ejpam-1979	53	6	with	with	ADP
ejpam-1979	53	7	quaternions	quaternion	NOUN
ejpam-1979	53	8	in	in	ADP
ejpam-1979	53	9	a	a	DET
ejpam-1979	53	10	natural	natural	ADJ
ejpam-1979	53	11	way	way	NOUN
ejpam-1979	53	12	.	.	PUNCT
ejpam-1979	54	1	the	the	DET
ejpam-1979	54	2	serret	serret	ADJ
ejpam-1979	54	3	-	-	PUNCT
ejpam-1979	54	4	frenet	frenet	NOUN
ejpam-1979	54	5	formulae	formulae	NOUN
ejpam-1979	54	6	for	for	ADP
ejpam-1979	54	7	a	a	DET
ejpam-1979	54	8	quaternionic	quaternionic	ADJ
ejpam-1979	54	9	curves	curve	NOUN
ejpam-1979	54	10	in	in	ADP
ejpam-1979	54	11	e3	e3	NOUN
ejpam-1979	54	12	and	and	CCONJ
ejpam-1979	54	13	e4	e4	PROPN
ejpam-1979	54	14	were	be	AUX
ejpam-1979	54	15	given	give	VERB
ejpam-1979	54	16	by	by	ADP
ejpam-1979	54	17	them	they	PRON
ejpam-1979	54	18	.	.	PUNCT
ejpam-1979	55	1	then	then	ADV
ejpam-1979	55	2	serret	serret	VERB
ejpam-1979	55	3	frenet	frenet	PROPN
ejpam-1979	55	4	formulae	formulae	NOUN
ejpam-1979	55	5	for	for	ADP
ejpam-1979	55	6	quaternionic	quaternionic	ADJ
ejpam-1979	55	7	curves	curve	NOUN
ejpam-1979	55	8	in	in	ADP
ejpam-1979	55	9	semi	semi	ADJ
ejpam-1979	55	10	-	-	ADJ
ejpam-1979	55	11	euclidean	euclidean	ADJ
ejpam-1979	55	12	space	space	NOUN
ejpam-1979	55	13	are	be	AUX
ejpam-1979	55	14	given	give	VERB
ejpam-1979	55	15	by	by	ADP
ejpam-1979	55	16	[	[	X
ejpam-1979	55	17	6	6	NUM
ejpam-1979	55	18	]	]	PUNCT
ejpam-1979	55	19	.	.	PUNCT
ejpam-1979	56	1	by	by	ADP
ejpam-1979	56	2	using	use	VERB
ejpam-1979	56	3	of	of	ADP
ejpam-1979	56	4	these	these	DET
ejpam-1979	56	5	formulas	formula	NOUN
ejpam-1979	56	6	,	,	PUNCT
ejpam-1979	56	7	new	new	ADJ
ejpam-1979	56	8	definitions	definition	NOUN
ejpam-1979	56	9	and	and	CCONJ
ejpam-1979	56	10	new	new	ADJ
ejpam-1979	56	11	characterizations	characterization	NOUN
ejpam-1979	56	12	of	of	ADP
ejpam-1979	56	13	quaternionic	quaternionic	ADJ
ejpam-1979	56	14	curves	curve	NOUN
ejpam-1979	56	15	are	be	AUX
ejpam-1979	56	16	studied	study	VERB
ejpam-1979	56	17	in	in	ADP
ejpam-1979	56	18	[	[	X
ejpam-1979	56	19	2	2	NUM
ejpam-1979	56	20	,	,	PUNCT
ejpam-1979	56	21	3	3	NUM
ejpam-1979	56	22	]	]	PUNCT
ejpam-1979	56	23	.	.	PUNCT
ejpam-1979	57	1	in	in	ADP
ejpam-1979	57	2	euclidean	euclidean	ADJ
ejpam-1979	57	3	space	space	NOUN
ejpam-1979	57	4	e3	e3	NOUN
ejpam-1979	57	5	,	,	PUNCT
ejpam-1979	57	6	there	there	PRON
ejpam-1979	57	7	is	be	VERB
ejpam-1979	57	8	a	a	DET
ejpam-1979	57	9	unique	unique	ADJ
ejpam-1979	57	10	sphere	sphere	NOUN
ejpam-1979	57	11	for	for	ADP
ejpam-1979	57	12	a	a	DET
ejpam-1979	57	13	curve	curve	NOUN
ejpam-1979	57	14	α	α	NOUN
ejpam-1979	57	15	which	which	PRON
ejpam-1979	57	16	contacts	contact	NOUN
ejpam-1979	57	17	α	α	NOUN
ejpam-1979	57	18	at	at	ADP
ejpam-1979	57	19	the	the	DET
ejpam-1979	57	20	third	third	ADJ
ejpam-1979	57	21	order	order	NOUN
ejpam-1979	57	22	at	at	ADP
ejpam-1979	57	23	α(0	α(0	PROPN
ejpam-1979	57	24	)	)	PUNCT
ejpam-1979	57	25	.	.	PUNCT
ejpam-1979	58	1	the	the	DET
ejpam-1979	58	2	intersection	intersection	NOUN
ejpam-1979	58	3	of	of	ADP
ejpam-1979	58	4	the	the	DET
ejpam-1979	58	5	sphere	sphere	NOUN
ejpam-1979	58	6	with	with	ADP
ejpam-1979	58	7	the	the	DET
ejpam-1979	58	8	osculating	osculating	NOUN
ejpam-1979	58	9	plane	plane	NOUN
ejpam-1979	58	10	is	be	AUX
ejpam-1979	58	11	a	a	DET
ejpam-1979	58	12	circle	circle	NOUN
ejpam-1979	58	13	which	which	PRON
ejpam-1979	58	14	contacts	contact	NOUN
ejpam-1979	58	15	at	at	ADP
ejpam-1979	58	16	the	the	DET
ejpam-1979	58	17	second	second	ADJ
ejpam-1979	58	18	order	order	NOUN
ejpam-1979	58	19	at	at	ADP
ejpam-1979	58	20	α(0	α(0	PROPN
ejpam-1979	58	21	)	)	PUNCT
ejpam-1979	58	22	,	,	PUNCT
ejpam-1979	59	1	[	[	X
ejpam-1979	59	2	7–9	7–9	X
ejpam-1979	59	3	]	]	X
ejpam-1979	59	4	.	.	PUNCT
ejpam-1979	60	1	this	this	DET
ejpam-1979	60	2	concept	concept	NOUN
ejpam-1979	60	3	studied	study	VERB
ejpam-1979	60	4	in	in	ADP
ejpam-1979	60	5	[	[	X
ejpam-1979	60	6	10	10	NUM
ejpam-1979	60	7	]	]	PUNCT
ejpam-1979	60	8	in	in	ADP
ejpam-1979	60	9	terms	term	NOUN
ejpam-1979	60	10	of	of	ADP
ejpam-1979	60	11	quaternionic	quaternionic	ADJ
ejpam-1979	60	12	curves	curve	NOUN
ejpam-1979	60	13	in	in	ADP
ejpam-1979	60	14	e4	e4	PROPN
ejpam-1979	60	15	.	.	PUNCT
ejpam-1979	61	1	in	in	ADP
ejpam-1979	61	2	[	[	X
ejpam-1979	61	3	11	11	NUM
ejpam-1979	61	4	]	]	PUNCT
ejpam-1979	61	5	,	,	PUNCT
ejpam-1979	61	6	the	the	DET
ejpam-1979	61	7	osculating	osculating	NOUN
ejpam-1979	61	8	sphere	sphere	NOUN
ejpam-1979	61	9	and	and	CCONJ
ejpam-1979	61	10	the	the	DET
ejpam-1979	61	11	osculating	osculating	NOUN
ejpam-1979	61	12	circle	circle	NOUN
ejpam-1979	61	13	of	of	ADP
ejpam-1979	61	14	the	the	DET
ejpam-1979	61	15	curve	curve	NOUN
ejpam-1979	61	16	are	be	AUX
ejpam-1979	61	17	investigated	investigate	VERB
ejpam-1979	61	18	in	in	ADP
ejpam-1979	61	19	semi	semi	ADJ
ejpam-1979	61	20	-	-	ADJ
ejpam-1979	61	21	euclidean	euclidean	ADJ
ejpam-1979	61	22	spaces	space	NOUN
ejpam-1979	61	23	e3	e3	VERB
ejpam-1979	61	24	1	1	NUM
ejpam-1979	61	25	,	,	PUNCT
ejpam-1979	61	26	e4	e4	PROPN
ejpam-1979	61	27	1	1	NUM
ejpam-1979	61	28	,	,	PUNCT
ejpam-1979	61	29	and	and	CCONJ
ejpam-1979	61	30	e4	e4	PROPN
ejpam-1979	61	31	2	2	NUM
ejpam-1979	61	32	.	.	PUNCT
ejpam-1979	62	1	in	in	ADP
ejpam-1979	62	2	this	this	DET
ejpam-1979	62	3	study	study	NOUN
ejpam-1979	62	4	,	,	PUNCT
ejpam-1979	62	5	we	we	PRON
ejpam-1979	62	6	give	give	VERB
ejpam-1979	62	7	definition	definition	NOUN
ejpam-1979	62	8	of	of	ADP
ejpam-1979	62	9	the	the	DET
ejpam-1979	62	10	osculating	osculating	NOUN
ejpam-1979	62	11	spheres	sphere	NOUN
ejpam-1979	62	12	for	for	ADP
ejpam-1979	62	13	semi	semi	ADJ
ejpam-1979	62	14	quaternionic	quaternionic	ADJ
ejpam-1979	62	15	curve	curve	NOUN
ejpam-1979	62	16	in	in	ADP
ejpam-1979	62	17	semi	semi	ADJ
ejpam-1979	62	18	-	-	ADJ
ejpam-1979	62	19	euclidean	euclidean	ADJ
ejpam-1979	62	20	spaces	space	NOUN
ejpam-1979	62	21	e3	e3	VERB
ejpam-1979	62	22	1	1	NUM
ejpam-1979	62	23	and	and	CCONJ
ejpam-1979	62	24	e4	e4	PROPN
ejpam-1979	62	25	2	2	NUM
ejpam-1979	62	26	with	with	ADP
ejpam-1979	62	27	respect	respect	NOUN
ejpam-1979	62	28	to	to	ADP
ejpam-1979	62	29	frenet	frenet	NOUN
ejpam-1979	62	30	frames	frame	NOUN
ejpam-1979	62	31	¦	¦	PROPN
ejpam-1979	62	32	t0,n10	t0,n10	PROPN
ejpam-1979	62	33	,	,	PUNCT
ejpam-1979	62	34	n20	n20	NOUN
ejpam-1979	62	35	©	©	PROPN
ejpam-1979	62	36	and	and	CCONJ
ejpam-1979	62	37	¦	¦	PROPN
ejpam-1979	62	38	t0,n10	t0,n10	PROPN
ejpam-1979	62	39	,	,	PUNCT
ejpam-1979	62	40	n20	n20	NOUN
ejpam-1979	62	41	,	,	PUNCT
ejpam-1979	62	42	n30	n30	PROPN
ejpam-1979	62	43	©	©	PROPN
ejpam-1979	62	44	,	,	PUNCT
ejpam-1979	62	45	respectively	respectively	ADV
ejpam-1979	62	46	.	.	PUNCT
ejpam-1979	63	1	2	2	X
ejpam-1979	63	2	.	.	NUM
ejpam-1979	63	3	preliminaries	preliminary	NOUN
ejpam-1979	63	4	a	a	DET
ejpam-1979	63	5	semi	semi	ADJ
ejpam-1979	63	6	real	real	ADJ
ejpam-1979	63	7	quaternion	quaternion	NOUN
ejpam-1979	63	8	is	be	AUX
ejpam-1979	63	9	defined	define	VERB
ejpam-1979	63	10	by	by	ADP
ejpam-1979	63	11	q	q	NOUN
ejpam-1979	63	12	=	=	NOUN
ejpam-1979	63	13	ae1+be2+ce3	ae1+be2+ce3	PROPN
ejpam-1979	63	14	+	+	CCONJ
ejpam-1979	63	15	de4	de4	NOUN
ejpam-1979	63	16	such	such	ADJ
ejpam-1979	63	17	that	that	DET
ejpam-1979	63	18	ei	ei	NOUN
ejpam-1979	63	19	×	×	NOUN
ejpam-1979	63	20	ei	ei	NOUN
ejpam-1979	63	21	=	=	NOUN
ejpam-1979	63	22	−	−	NOUN
ejpam-1979	63	23	εei	εei	NOUN
ejpam-1979	63	24	,	,	PUNCT
ejpam-1979	64	1	1≤	1≤	INTJ
ejpam-1979	64	2	i	i	X
ejpam-1979	64	3	≤	≤	ADV
ejpam-1979	64	4	3	3	NUM
ejpam-1979	64	5	ei	ei	NOUN
ejpam-1979	64	6	×	×	PROPN
ejpam-1979	64	7	e	e	X
ejpam-1979	64	8	j	j	PROPN
ejpam-1979	64	9	=	=	NOUN
ejpam-1979	64	10	εei	εei	NOUN
ejpam-1979	64	11	εe	εe	ADP
ejpam-1979	64	12	j	j	PROPN
ejpam-1979	64	13	ek	ek	PROPN
ejpam-1979	64	14	,	,	PUNCT
ejpam-1979	64	15	in	in	ADP
ejpam-1979	64	16	e3	e3	NOUN
ejpam-1979	64	17	1	1	NUM
ejpam-1979	64	18	ei	ei	NOUN
ejpam-1979	64	19	×	×	PROPN
ejpam-1979	64	20	e	e	X
ejpam-1979	64	21	j	j	PROPN
ejpam-1979	64	22	=	=	NOUN
ejpam-1979	64	23	−	−	PROPN
ejpam-1979	64	24	εei	εei	NOUN
ejpam-1979	64	25	εe	εe	ADP
ejpam-1979	64	26	j	j	PROPN
ejpam-1979	64	27	ek	ek	PROPN
ejpam-1979	64	28	,	,	PUNCT
ejpam-1979	64	29	in	in	ADP
ejpam-1979	64	30	e4	e4	PROPN
ejpam-1979	64	31	2	2	NUM
ejpam-1979	64	32	,	,	PUNCT
ejpam-1979	64	33	where	where	SCONJ
ejpam-1979	64	34	(	(	PUNCT
ejpam-1979	64	35	i	i	NOUN
ejpam-1979	64	36	jk	jk	PROPN
ejpam-1979	64	37	)	)	PUNCT
ejpam-1979	64	38	is	be	AUX
ejpam-1979	64	39	an	an	DET
ejpam-1979	64	40	even	even	ADJ
ejpam-1979	64	41	permutation	permutation	NOUN
ejpam-1979	64	42	of	of	ADP
ejpam-1979	64	43	(	(	PUNCT
ejpam-1979	64	44	123	123	NUM
ejpam-1979	64	45	)	)	PUNCT
ejpam-1979	64	46	.	.	PUNCT
ejpam-1979	65	1	notice	notice	NOUN
ejpam-1979	65	2	here	here	ADV
ejpam-1979	65	3	that	that	SCONJ
ejpam-1979	65	4	we	we	PRON
ejpam-1979	65	5	denote	denote	VERB
ejpam-1979	65	6	the	the	DET
ejpam-1979	65	7	set	set	NOUN
ejpam-1979	65	8	of	of	ADP
ejpam-1979	65	9	all	all	DET
ejpam-1979	65	10	spatial	spatial	ADJ
ejpam-1979	65	11	semi	semi	ADJ
ejpam-1979	65	12	real	real	ADJ
ejpam-1979	65	13	quaternions	quaternions	ADJ
ejpam-1979	65	14	byhp	byhp	NOUN
ejpam-1979	65	15	and	and	CCONJ
ejpam-1979	65	16	all	all	DET
ejpam-1979	65	17	semi	semi	ADJ
ejpam-1979	65	18	real	real	ADJ
ejpam-1979	65	19	quaternions	quaternion	NOUN
ejpam-1979	65	20	byh	byh	VERB
ejpam-1979	65	21	.	.	PUNCT
ejpam-1979	66	1	it	it	PRON
ejpam-1979	66	2	is	be	AUX
ejpam-1979	66	3	defined	define	VERB
ejpam-1979	66	4	by	by	ADP
ejpam-1979	66	5	h	h	NOUN
ejpam-1979	66	6	=	=	SYM
ejpam-1979	66	7	¦	¦	PROPN
ejpam-1979	66	8	q	q	PROPN
ejpam-1979	66	9	=	=	PUNCT
ejpam-1979	66	10	ae1	ae1	PROPN
ejpam-1979	66	11	+	+	SYM
ejpam-1979	66	12	be2	be2	PROPN
ejpam-1979	66	13	+	+	SYM
ejpam-1979	66	14	ce3	ce3	PROPN
ejpam-1979	66	15	+	+	X
ejpam-1979	66	16	de4	de4	NOUN
ejpam-1979	66	17	:	:	PUNCT
ejpam-1979	66	18	a	a	DET
ejpam-1979	66	19	,	,	PUNCT
ejpam-1979	66	20	b	b	NOUN
ejpam-1979	66	21	,	,	PUNCT
ejpam-1979	66	22	c	c	NOUN
ejpam-1979	66	23	,	,	PUNCT
ejpam-1979	66	24	d	d	PROPN
ejpam-1979	66	25	∈	∈	PROPN
ejpam-1979	66	26	r	r	NOUN
ejpam-1979	66	27	,	,	PUNCT
ejpam-1979	66	28	e1	e1	PROPN
ejpam-1979	66	29	,	,	PUNCT
ejpam-1979	66	30	e2	e2	PROPN
ejpam-1979	66	31	,	,	PUNCT
ejpam-1979	66	32	e3	e3	VERB
ejpam-1979	66	33	in	in	ADP
ejpam-1979	66	34	e3	e3	NOUN
ejpam-1979	66	35	1	1	NUM
ejpam-1979	66	36	,	,	PUNCT
ejpam-1979	66	37	ei	ei	NOUN
ejpam-1979	66	38	,	,	PUNCT
ejpam-1979	66	39	ei	ei	X
ejpam-1979	66	40	�	�	PROPN
ejpam-1979	66	41	=	=	SYM
ejpam-1979	66	42	εei	εei	NOUN
ejpam-1979	66	43	,	,	PUNCT
ejpam-1979	66	44	1≤	1≤	INTJ
ejpam-1979	66	45	i	i	PRON
ejpam-1979	66	46	≤	≤	ADV
ejpam-1979	66	47	3	3	NUM
ejpam-1979	67	1	©	©	PROPN
ejpam-1979	67	2	where	where	SCONJ
ejpam-1979	67	3	index	index	NOUN
ejpam-1979	67	4	=	=	NOUN
ejpam-1979	67	5	1,2	1,2	NUM
ejpam-1979	67	6	.	.	PUNCT
ejpam-1979	68	1	if	if	SCONJ
ejpam-1979	68	2	ei	ei	NOUN
ejpam-1979	68	3	is	be	AUX
ejpam-1979	68	4	a	a	DET
ejpam-1979	68	5	spacelike	spacelike	ADJ
ejpam-1979	68	6	or	or	CCONJ
ejpam-1979	68	7	timelike	timelike	PROPN
ejpam-1979	68	8	vector	vector	NOUN
ejpam-1979	68	9	,	,	PUNCT
ejpam-1979	68	10	then	then	ADV
ejpam-1979	68	11	εei	εei	VERB
ejpam-1979	68	12	=	=	SYM
ejpam-1979	68	13	+1	+1	PROPN
ejpam-1979	68	14	or	or	CCONJ
ejpam-1979	68	15	−1	−1	NOUN
ejpam-1979	68	16	,	,	PUNCT
ejpam-1979	68	17	respectively	respectively	ADV
ejpam-1979	68	18	.	.	PUNCT
ejpam-1979	69	1	for	for	ADP
ejpam-1979	69	2	p	p	NOUN
ejpam-1979	69	3	=	=	SYM
ejpam-1979	69	4	sp	sp	ADP
ejpam-1979	69	5	+	+	X
ejpam-1979	69	6	vp	vp	PROPN
ejpam-1979	69	7	and	and	CCONJ
ejpam-1979	69	8	q	q	NOUN
ejpam-1979	69	9	=	=	PUNCT
ejpam-1979	69	10	sq	sq	PROPN
ejpam-1979	69	11	+	+	PROPN
ejpam-1979	69	12	vq	vq	PROPN
ejpam-1979	69	13	,	,	PUNCT
ejpam-1979	69	14	the	the	DET
ejpam-1979	69	15	multiplication	multiplication	NOUN
ejpam-1979	69	16	of	of	ADP
ejpam-1979	69	17	two	two	NUM
ejpam-1979	69	18	semi	semi	ADJ
ejpam-1979	69	19	real	real	ADJ
ejpam-1979	69	20	quaternions	quaternion	NOUN
ejpam-1979	69	21	p	p	NOUN
ejpam-1979	69	22	and	and	CCONJ
ejpam-1979	69	23	q	q	NOUN
ejpam-1979	69	24	is	be	AUX
ejpam-1979	69	25	defined	define	VERB
ejpam-1979	69	26	as	as	SCONJ
ejpam-1979	69	27	follows	follow	VERB
ejpam-1979	69	28	:	:	PUNCT
ejpam-1979	69	29	p×	p×	NOUN
ejpam-1979	69	30	q	q	NOUN
ejpam-1979	69	31	=	=	PUNCT
ejpam-1979	69	32	spsq	spsq	NOUN
ejpam-1979	69	33	−	−	PROPN
ejpam-1979	69	34	¬	¬	PROPN
ejpam-1979	69	35	vp	vp	PROPN
ejpam-1979	69	36	,	,	PUNCT
ejpam-1979	69	37	vq	vq	PROPN
ejpam-1979	69	38	¶	¶	PROPN
ejpam-1979	69	39	+	+	CCONJ
ejpam-1979	69	40	spvq	spvq	NOUN
ejpam-1979	69	41	+	+	CCONJ
ejpam-1979	69	42	sqvp	sqvp	NOUN
ejpam-1979	70	1	+	+	PROPN
ejpam-1979	70	2	vp	vp	PROPN
ejpam-1979	70	3	∧vq	∧vq	PROPN
ejpam-1979	70	4	,	,	PUNCT
ejpam-1979	70	5	∀p	∀p	AUX
ejpam-1979	70	6	,	,	PUNCT
ejpam-1979	70	7	q	q	X
ejpam-1979	70	8	∈h	∈h	NOUN
ejpam-1979	70	9	,	,	PUNCT
ejpam-1979	70	10	ö.	ö.	PROPN
ejpam-1979	70	11	bektaş	bektaş	PROPN
ejpam-1979	70	12	,	,	PUNCT
ejpam-1979	70	13	n.	n.	PROPN
ejpam-1979	70	14	gürses	gürse	NOUN
ejpam-1979	70	15	,	,	PUNCT
ejpam-1979	70	16	s.	s.	PROPN
ejpam-1979	70	17	yüce	yüce	PROPN
ejpam-1979	70	18	/	/	SYM
ejpam-1979	70	19	eur	eur	PROPN
ejpam-1979	70	20	.	.	PUNCT
ejpam-1979	71	1	j.	j.	PROPN
ejpam-1979	71	2	pure	pure	PROPN
ejpam-1979	71	3	appl	appl	PROPN
ejpam-1979	71	4	.	.	PROPN
ejpam-1979	71	5	math	math	PROPN
ejpam-1979	71	6	,	,	PUNCT
ejpam-1979	71	7	7	7	NUM
ejpam-1979	71	8	(	(	PUNCT
ejpam-1979	71	9	2014	2014	NUM
ejpam-1979	71	10	)	)	PUNCT
ejpam-1979	71	11	,	,	PUNCT
ejpam-1979	71	12	86	86	NUM
ejpam-1979	71	13	-	-	SYM
ejpam-1979	71	14	96	96	NUM
ejpam-1979	71	15	89	89	NUM
ejpam-1979	71	16	where	where	SCONJ
ejpam-1979	71	17	we	we	PRON
ejpam-1979	71	18	have	have	AUX
ejpam-1979	71	19	used	use	VERB
ejpam-1979	71	20	the	the	DET
ejpam-1979	71	21	scalar	scalar	ADJ
ejpam-1979	71	22	and	and	CCONJ
ejpam-1979	71	23	cross	cross	NOUN
ejpam-1979	71	24	products	product	NOUN
ejpam-1979	71	25	in	in	ADP
ejpam-1979	71	26	e3	e3	NOUN
ejpam-1979	71	27	1	1	NUM
ejpam-1979	71	28	.	.	PUNCT
ejpam-1979	72	1	let	let	VERB
ejpam-1979	72	2	q	q	PROPN
ejpam-1979	72	3	denotes	denote	VERB
ejpam-1979	72	4	the	the	DET
ejpam-1979	72	5	conjugate	conjugate	NOUN
ejpam-1979	72	6	of	of	ADP
ejpam-1979	72	7	a	a	DET
ejpam-1979	72	8	quaternion	quaternion	NOUN
ejpam-1979	72	9	,	,	PUNCT
ejpam-1979	72	10	q	q	NOUN
ejpam-1979	72	11	=	=	PUNCT
ejpam-1979	72	12	−ae1	−ae1	NOUN
ejpam-1979	72	13	−	−	NOUN
ejpam-1979	72	14	be2	be2	NOUN
ejpam-1979	72	15	−	−	NOUN
ejpam-1979	73	1	ce3	ce3	NOUN
ejpam-1979	74	1	+	+	CCONJ
ejpam-1979	74	2	d	d	NOUN
ejpam-1979	74	3	for	for	ADP
ejpam-1979	74	4	every	every	DET
ejpam-1979	74	5	q	q	PROPN
ejpam-1979	74	6	∈	∈	PROPN
ejpam-1979	74	7	h	h	NOUN
ejpam-1979	74	8	.	.	PUNCT
ejpam-1979	75	1	this	this	PRON
ejpam-1979	75	2	helps	help	VERB
ejpam-1979	75	3	to	to	PART
ejpam-1979	75	4	define	define	VERB
ejpam-1979	75	5	the	the	DET
ejpam-1979	75	6	symmetric	symmetric	ADJ
ejpam-1979	75	7	,	,	PUNCT
ejpam-1979	75	8	non	non	ADJ
ejpam-1979	75	9	-	-	ADJ
ejpam-1979	75	10	degenerate	degenerate	ADJ
ejpam-1979	75	11	,	,	PUNCT
ejpam-1979	75	12	bilinear	bilinear	NOUN
ejpam-1979	75	13	form	form	NOUN
ejpam-1979	75	14	as	as	SCONJ
ejpam-1979	75	15	follows	follow	VERB
ejpam-1979	75	16	:	:	PUNCT
ejpam-1979	75	17	〈	〈	NOUN
ejpam-1979	75	18	,	,	PUNCT
ejpam-1979	75	19	〉	〉	NOUN
ejpam-1979	75	20	:	:	PUNCT
ejpam-1979	75	21	h	h	NOUN
ejpam-1979	75	22	×h	×h	PROPN
ejpam-1979	76	1	→r	→r	NOUN
ejpam-1979	76	2	,	,	PUNCT
ejpam-1979	76	3	(	(	PUNCT
ejpam-1979	76	4	p	p	X
ejpam-1979	76	5	,	,	PUNCT
ejpam-1979	76	6	q)→	q)→	PROPN
ejpam-1979	76	7	p	p	X
ejpam-1979	76	8	,	,	PUNCT
ejpam-1979	76	9	q	q	PROPN
ejpam-1979	76	10	�	�	PROPN
ejpam-1979	76	11	p	p	NOUN
ejpam-1979	76	12	=	=	NOUN
ejpam-1979	76	13	1	1	NUM
ejpam-1979	76	14	2	2	NUM
ejpam-1979	76	15	�	�	PROPN
ejpam-1979	76	16	εpεq	εpεq	PROPN
ejpam-1979	76	17	�	�	PROPN
ejpam-1979	76	18	p×	p×	PROPN
ejpam-1979	76	19	q	q	PROPN
ejpam-1979	76	20	�	�	PROPN
ejpam-1979	76	21	+	+	CCONJ
ejpam-1979	76	22	εqεp	εqεp	ADJ
ejpam-1979	76	23	�	�	PROPN
ejpam-1979	76	24	q×	q×	PUNCT
ejpam-1979	76	25	p	p	PROPN
ejpam-1979	76	26	�	�	PROPN
ejpam-1979	76	27	�	�	PROPN
ejpam-1979	76	28	for	for	ADP
ejpam-1979	76	29	e3	e3	NOUN
ejpam-1979	76	30	1	1	NUM
ejpam-1979	76	31	(	(	PUNCT
ejpam-1979	76	32	p	p	NOUN
ejpam-1979	76	33	,	,	PUNCT
ejpam-1979	76	34	q)→	q)→	PROPN
ejpam-1979	76	35	p	p	X
ejpam-1979	76	36	,	,	PUNCT
ejpam-1979	76	37	q	q	PROPN
ejpam-1979	76	38	�	�	PROPN
ejpam-1979	76	39	=	=	NOUN
ejpam-1979	76	40	−	−	PROPN
ejpam-1979	76	41	1	1	NUM
ejpam-1979	76	42	2	2	NUM
ejpam-1979	76	43	�	�	PROPN
ejpam-1979	76	44	εpεq	εpεq	PROPN
ejpam-1979	76	45	�	�	PROPN
ejpam-1979	76	46	p×	p×	PROPN
ejpam-1979	76	47	q	q	PROPN
ejpam-1979	76	48	�	�	PROPN
ejpam-1979	76	49	+	+	CCONJ
ejpam-1979	76	50	εqεp	εqεp	ADJ
ejpam-1979	76	51	�	�	PROPN
ejpam-1979	76	52	q×	q×	PUNCT
ejpam-1979	76	53	p	p	PROPN
ejpam-1979	76	54	�	�	PROPN
ejpam-1979	76	55	�	�	PROPN
ejpam-1979	76	56	for	for	ADP
ejpam-1979	76	57	e4	e4	PROPN
ejpam-1979	76	58	2	2	NUM
ejpam-1979	76	59	.	.	PUNCT
ejpam-1979	77	1	the	the	DET
ejpam-1979	77	2	norm	norm	NOUN
ejpam-1979	77	3	of	of	ADP
ejpam-1979	77	4	semi	semi	ADJ
ejpam-1979	77	5	real	real	ADJ
ejpam-1979	77	6	quaternion	quaternion	NOUN
ejpam-1979	77	7	q	q	NOUN
ejpam-1979	77	8	is	be	AUX
ejpam-1979	77	9	denoted	denote	VERB
ejpam-1979	77	10	by	by	ADP
ejpam-1979	77	11	q	q	NOUN
ejpam-1979	77	12	=	=	SYM
ejpam-1979	77	13	�	�	PROPN
ejpam-1979	77	14	�	�	PROPN
ejpam-1979	77	15	q	q	PROPN
ejpam-1979	77	16	,	,	PUNCT
ejpam-1979	77	17	q	q	PROPN
ejpam-1979	77	18	�	�	PROPN
ejpam-1979	77	19	�	�	PROPN
ejpam-1979	77	20	�	�	PROPN
ejpam-1979	77	21	=	=	SYM
ejpam-1979	77	22	�	�	PROPN
ejpam-1979	77	23	�	�	PROPN
ejpam-1979	77	24	p	p	PROPN
ejpam-1979	77	25	�	�	PROPN
ejpam-1979	77	26	q×	q×	PROPN
ejpam-1979	77	27	q	q	PROPN
ejpam-1979	77	28	�	�	PROPN
ejpam-1979	77	29	�	�	PROPN
ejpam-1979	77	30	�	�	PROPN
ejpam-1979	77	31	=	=	SYM
ejpam-1979	77	32	�	�	PROPN
ejpam-1979	77	33	�	�	PROPN
ejpam-1979	77	34	−a2−	−a2−	NUM
ejpam-1979	77	35	b2	b2	NOUN
ejpam-1979	77	36	+	+	CCONJ
ejpam-1979	77	37	c2	c2	PROPN
ejpam-1979	77	38	+	+	CCONJ
ejpam-1979	77	39	d2	d2	PROPN
ejpam-1979	77	40	�	�	PROPN
ejpam-1979	77	41	�	�	PROPN
ejpam-1979	77	42	for	for	ADP
ejpam-1979	77	43	p	p	NOUN
ejpam-1979	77	44	,	,	PUNCT
ejpam-1979	77	45	q	q	PROPN
ejpam-1979	77	46	∈	∈	PROPN
ejpam-1979	77	47	h	h	NOUN
ejpam-1979	77	48	.	.	PUNCT
ejpam-1979	78	1	if	if	SCONJ
ejpam-1979	78	2	p	p	X
ejpam-1979	78	3	,	,	PUNCT
ejpam-1979	78	4	q	q	PROPN
ejpam-1979	78	5	�	�	PROPN
ejpam-1979	78	6	=	=	SYM
ejpam-1979	78	7	0	0	NUM
ejpam-1979	78	8	,	,	PUNCT
ejpam-1979	78	9	then	then	ADV
ejpam-1979	78	10	p	p	NOUN
ejpam-1979	78	11	and	and	CCONJ
ejpam-1979	78	12	q	q	NOUN
ejpam-1979	78	13	are	be	AUX
ejpam-1979	78	14	called	call	VERB
ejpam-1979	78	15	orthogonal	orthogonal	ADJ
ejpam-1979	78	16	.	.	PUNCT
ejpam-1979	79	1	q	q	PUNCT
ejpam-1979	79	2	is	be	AUX
ejpam-1979	79	3	called	call	VERB
ejpam-1979	79	4	a	a	DET
ejpam-1979	79	5	spatial	spatial	ADJ
ejpam-1979	79	6	semi	semi	ADV
ejpam-1979	79	7	quaternion	quaternion	NOUN
ejpam-1979	79	8	whenever	whenever	SCONJ
ejpam-1979	79	9	q	q	NOUN
ejpam-1979	80	1	+	+	NUM
ejpam-1979	80	2	q	q	NOUN
ejpam-1979	80	3	=	=	SYM
ejpam-1979	80	4	0	0	PUNCT
ejpam-1979	81	1	[	[	X
ejpam-1979	81	2	6	6	NUM
ejpam-1979	81	3	]	]	PUNCT
ejpam-1979	81	4	.	.	PUNCT
ejpam-1979	82	1	the	the	DET
ejpam-1979	82	2	serret	serret	ADJ
ejpam-1979	82	3	frenet	frenet	NOUN
ejpam-1979	82	4	formulae	formulae	NOUN
ejpam-1979	82	5	for	for	ADP
ejpam-1979	82	6	semi	semi	ADJ
ejpam-1979	82	7	-	-	ADJ
ejpam-1979	82	8	real	real	ADJ
ejpam-1979	82	9	quaternionic	quaternionic	ADJ
ejpam-1979	82	10	curves	curve	NOUN
ejpam-1979	82	11	in	in	ADP
ejpam-1979	82	12	e3	e3	NOUN
ejpam-1979	82	13	1	1	NUM
ejpam-1979	82	14	and	and	CCONJ
ejpam-1979	82	15	e4	e4	PROPN
ejpam-1979	82	16	2	2	NUM
ejpam-1979	82	17	are	be	AUX
ejpam-1979	82	18	as	as	SCONJ
ejpam-1979	82	19	follows	follow	VERB
ejpam-1979	82	20	:	:	PUNCT
ejpam-1979	82	21	the	the	DET
ejpam-1979	82	22	three	three	NUM
ejpam-1979	82	23	-	-	PUNCT
ejpam-1979	82	24	dimensional	dimensional	ADJ
ejpam-1979	82	25	semi	semi	ADJ
ejpam-1979	82	26	-	-	ADJ
ejpam-1979	82	27	euclidean	euclidean	ADJ
ejpam-1979	82	28	space	space	NOUN
ejpam-1979	82	29	e3	e3	NOUN
ejpam-1979	82	30	1	1	NUM
ejpam-1979	82	31	is	be	AUX
ejpam-1979	82	32	identified	identify	VERB
ejpam-1979	82	33	with	with	ADP
ejpam-1979	82	34	the	the	DET
ejpam-1979	82	35	space	space	NOUN
ejpam-1979	82	36	of	of	ADP
ejpam-1979	82	37	spatial	spatial	ADJ
ejpam-1979	82	38	quaternions	quaternion	NOUN
ejpam-1979	82	39	hp	hp	NOUN
ejpam-1979	82	40	=	=	SYM
ejpam-1979	82	41	¦	¦	PROPN
ejpam-1979	82	42	γ	γ	PROPN
ejpam-1979	82	43	∈h	∈h	PROPN
ejpam-1979	82	44	�	�	PROPN
ejpam-1979	82	45	�	�	PROPN
ejpam-1979	82	46	γ+	γ+	X
ejpam-1979	82	47	γ=	γ=	PROPN
ejpam-1979	82	48	0	0	PUNCT
ejpam-1979	83	1	©	©	PROPN
ejpam-1979	83	2	in	in	ADP
ejpam-1979	83	3	an	an	DET
ejpam-1979	83	4	obvious	obvious	ADJ
ejpam-1979	83	5	manner	manner	NOUN
ejpam-1979	83	6	.	.	PUNCT
ejpam-1979	84	1	let	let	VERB
ejpam-1979	84	2	i	i	PRON
ejpam-1979	84	3	=	=	PUNCT
ejpam-1979	85	1	[	[	X
ejpam-1979	85	2	0,1	0,1	NUM
ejpam-1979	85	3	]	]	PUNCT
ejpam-1979	85	4	be	be	AUX
ejpam-1979	85	5	an	an	DET
ejpam-1979	85	6	interval	interval	NOUN
ejpam-1979	85	7	in	in	ADP
ejpam-1979	85	8	the	the	DET
ejpam-1979	85	9	real	real	ADJ
ejpam-1979	85	10	line	line	NOUN
ejpam-1979	85	11	r	r	NOUN
ejpam-1979	85	12	and	and	CCONJ
ejpam-1979	85	13	γ	γ	NOUN
ejpam-1979	85	14	:	:	PUNCT
ejpam-1979	85	15	i	i	PRON
ejpam-1979	85	16	⊂	⊂	PROPN
ejpam-1979	85	17	r→hp	r→hp	VERB
ejpam-1979	85	18	s→	s→	X
ejpam-1979	85	19	γ	γ	X
ejpam-1979	85	20	(	(	PUNCT
ejpam-1979	85	21	s	s	NOUN
ejpam-1979	85	22	)	)	PUNCT
ejpam-1979	85	23	=	=	SYM
ejpam-1979	85	24	3	3	NUM
ejpam-1979	85	25	∑	∑	NOUN
ejpam-1979	85	26	i=1	i=1	PROPN
ejpam-1979	85	27	γi	γi	X
ejpam-1979	85	28	(	(	PUNCT
ejpam-1979	85	29	s	s	NOUN
ejpam-1979	85	30	)	)	PUNCT
ejpam-1979	85	31	ei	ei	NOUN
ejpam-1979	85	32	,	,	PUNCT
ejpam-1979	85	33	(	(	PUNCT
ejpam-1979	85	34	1≤	1≤	INTJ
ejpam-1979	85	35	i	i	PRON
ejpam-1979	85	36	≤	≤	ADJ
ejpam-1979	85	37	3	3	X
ejpam-1979	85	38	)	)	PUNCT
ejpam-1979	85	39	be	be	AUX
ejpam-1979	85	40	an	an	DET
ejpam-1979	85	41	arc	arc	NOUN
ejpam-1979	85	42	length	length	NOUN
ejpam-1979	85	43	curve	curve	NOUN
ejpam-1979	85	44	with	with	ADP
ejpam-1979	85	45	nonzero	nonzero	PROPN
ejpam-1979	85	46	curvatures	curvature	NOUN
ejpam-1979	85	47	{	{	PUNCT
ejpam-1979	85	48	k	k	NOUN
ejpam-1979	85	49	,	,	PUNCT
ejpam-1979	85	50	r	r	NOUN
ejpam-1979	85	51	}	}	PUNCT
ejpam-1979	85	52	.	.	PUNCT
ejpam-1979	86	1	let	let	VERB
ejpam-1979	86	2	�	�	PROPN
ejpam-1979	86	3	t	t	PROPN
ejpam-1979	86	4	,	,	PUNCT
ejpam-1979	86	5	n1,n2	n1,n2	PROPN
ejpam-1979	86	6	denote	denote	VERB
ejpam-1979	86	7	the	the	DET
ejpam-1979	86	8	frenet	frenet	ADJ
ejpam-1979	86	9	frame	frame	NOUN
ejpam-1979	86	10	of	of	ADP
ejpam-1979	86	11	the	the	DET
ejpam-1979	86	12	curve	curve	NOUN
ejpam-1979	86	13	γ	γ	PROPN
ejpam-1979	86	14	.	.	PROPN
ejpam-1979	87	1	then	then	ADV
ejpam-1979	87	2	frenet	frenet	NOUN
ejpam-1979	87	3	formulae	formulae	NOUN
ejpam-1979	87	4	are	be	AUX
ejpam-1979	87	5	given	give	VERB
ejpam-1979	87	6	by	by	ADP
ejpam-1979	87	7	t	t	PROPN
ejpam-1979	87	8	′	′	NUM
ejpam-1979	87	9	(	(	PUNCT
ejpam-1979	87	10	s	s	X
ejpam-1979	87	11	)	)	PUNCT
ejpam-1979	87	12	=	=	NOUN
ejpam-1979	87	13	εn1	εn1	NOUN
ejpam-1979	87	14	kn1	kn1	NOUN
ejpam-1979	87	15	(	(	PUNCT
ejpam-1979	87	16	s	s	NOUN
ejpam-1979	87	17	)	)	PUNCT
ejpam-1979	87	18	n	n	NOUN
ejpam-1979	87	19	′	′	NUM
ejpam-1979	87	20	1	1	NUM
ejpam-1979	87	21	(	(	PUNCT
ejpam-1979	87	22	s	s	NOUN
ejpam-1979	87	23	)	)	PUNCT
ejpam-1979	87	24	=	=	NOUN
ejpam-1979	87	25	−	−	PROPN
ejpam-1979	87	26	εtkt	εtkt	NOUN
ejpam-1979	87	27	(	(	PUNCT
ejpam-1979	87	28	s	s	NOUN
ejpam-1979	87	29	)	)	PUNCT
ejpam-1979	87	30	+	+	NUM
ejpam-1979	87	31	εn1	εn1	NOUN
ejpam-1979	87	32	rn2	rn2	PROPN
ejpam-1979	87	33	(	(	PUNCT
ejpam-1979	87	34	s	s	NOUN
ejpam-1979	87	35	)	)	PUNCT
ejpam-1979	87	36	n	n	NOUN
ejpam-1979	87	37	′	′	NUM
ejpam-1979	87	38	2	2	NUM
ejpam-1979	87	39	(	(	PUNCT
ejpam-1979	87	40	s	s	NOUN
ejpam-1979	87	41	)	)	PUNCT
ejpam-1979	87	42	=	=	NOUN
ejpam-1979	87	43	−	−	PROPN
ejpam-1979	87	44	εn2	εn2	PROPN
ejpam-1979	87	45	rn1	rn1	PROPN
ejpam-1979	87	46	(	(	PUNCT
ejpam-1979	87	47	s	s	PROPN
ejpam-1979	87	48	)	)	PUNCT
ejpam-1979	87	49	,	,	PUNCT
ejpam-1979	87	50	(	(	PUNCT
ejpam-1979	87	51	1	1	X
ejpam-1979	87	52	)	)	PUNCT
ejpam-1979	87	53	where	where	SCONJ
ejpam-1979	87	54	〈	〈	NOUN
ejpam-1979	87	55	t	t	PROPN
ejpam-1979	87	56	,	,	PUNCT
ejpam-1979	87	57	t〉p	t〉p	PROPN
ejpam-1979	87	58	=	=	PUNCT
ejpam-1979	87	59	εt	εt	PROPN
ejpam-1979	87	60	,	,	PUNCT
ejpam-1979	87	61	n1,n1	n1,n1	PROPN
ejpam-1979	87	62	�	�	PROPN
ejpam-1979	87	63	p	p	NOUN
ejpam-1979	87	64	=	=	NOUN
ejpam-1979	87	65	εn1	εn1	NOUN
ejpam-1979	87	66	,	,	PUNCT
ejpam-1979	87	67	n2,n2	n2,n2	PROPN
ejpam-1979	87	68	�	�	PROPN
ejpam-1979	88	1	p	p	NOUN
ejpam-1979	88	2	=	=	PUNCT
ejpam-1979	88	3	εn2	εn2	PROPN
ejpam-1979	89	1	[	[	X
ejpam-1979	89	2	6	6	NUM
ejpam-1979	89	3	]	]	PUNCT
ejpam-1979	89	4	.	.	PUNCT
ejpam-1979	90	1	the	the	DET
ejpam-1979	90	2	four	four	NUM
ejpam-1979	90	3	dimensional	dimensional	ADJ
ejpam-1979	90	4	semi	semi	ADJ
ejpam-1979	90	5	-	-	ADJ
ejpam-1979	90	6	euclidean	euclidean	ADJ
ejpam-1979	90	7	space	space	NOUN
ejpam-1979	90	8	e4	e4	PROPN
ejpam-1979	90	9	2	2	NUM
ejpam-1979	90	10	is	be	AUX
ejpam-1979	90	11	identified	identify	VERB
ejpam-1979	90	12	with	with	ADP
ejpam-1979	90	13	the	the	DET
ejpam-1979	90	14	space	space	NOUN
ejpam-1979	90	15	of	of	ADP
ejpam-1979	90	16	unit	unit	NOUN
ejpam-1979	90	17	quaternionsh	quaternionsh	PROPN
ejpam-1979	90	18	.	.	PUNCT
ejpam-1979	91	1	let	let	VERB
ejpam-1979	91	2	i	i	PRON
ejpam-1979	91	3	=	=	PUNCT
ejpam-1979	92	1	[	[	X
ejpam-1979	92	2	0,1	0,1	NUM
ejpam-1979	92	3	]	]	PUNCT
ejpam-1979	92	4	be	be	VERB
ejpam-1979	92	5	an	an	DET
ejpam-1979	92	6	unit	unit	NOUN
ejpam-1979	92	7	interval	interval	NOUN
ejpam-1979	92	8	in	in	ADP
ejpam-1979	92	9	the	the	DET
ejpam-1979	92	10	real	real	ADJ
ejpam-1979	92	11	line	line	NOUN
ejpam-1979	92	12	r	r	NOUN
ejpam-1979	92	13	and	and	CCONJ
ejpam-1979	92	14	β	β	X
ejpam-1979	92	15	:	:	PUNCT
ejpam-1979	93	1	i	i	PRON
ejpam-1979	93	2	⊂	⊂	PROPN
ejpam-1979	93	3	r→h	r→h	PROPN
ejpam-1979	93	4	s→	s→	X
ejpam-1979	93	5	β	β	X
ejpam-1979	93	6	(	(	PUNCT
ejpam-1979	93	7	s	s	X
ejpam-1979	93	8	)	)	PUNCT
ejpam-1979	93	9	=	=	SYM
ejpam-1979	93	10	4	4	NUM
ejpam-1979	93	11	∑	∑	NOUN
ejpam-1979	93	12	i=1	i=1	PROPN
ejpam-1979	93	13	γi	γi	X
ejpam-1979	93	14	(	(	PUNCT
ejpam-1979	93	15	s	s	NOUN
ejpam-1979	93	16	)	)	PUNCT
ejpam-1979	93	17	ei	ei	NOUN
ejpam-1979	93	18	,	,	PUNCT
ejpam-1979	93	19	e4	e4	PROPN
ejpam-1979	93	20	=	=	PROPN
ejpam-1979	93	21	+1	+1	PROPN
ejpam-1979	93	22	ö.	ö.	PROPN
ejpam-1979	93	23	bektaş	bektaş	PROPN
ejpam-1979	93	24	,	,	PUNCT
ejpam-1979	93	25	n.	n.	PROPN
ejpam-1979	93	26	gürses	gürse	NOUN
ejpam-1979	93	27	,	,	PUNCT
ejpam-1979	93	28	s.	s.	PROPN
ejpam-1979	93	29	yüce	yüce	PROPN
ejpam-1979	93	30	/	/	SYM
ejpam-1979	93	31	eur	eur	PROPN
ejpam-1979	93	32	.	.	PUNCT
ejpam-1979	94	1	j.	j.	PROPN
ejpam-1979	94	2	pure	pure	PROPN
ejpam-1979	94	3	appl	appl	PROPN
ejpam-1979	94	4	.	.	PROPN
ejpam-1979	94	5	math	math	PROPN
ejpam-1979	94	6	,	,	PUNCT
ejpam-1979	94	7	7	7	NUM
ejpam-1979	94	8	(	(	PUNCT
ejpam-1979	94	9	2014	2014	NUM
ejpam-1979	94	10	)	)	PUNCT
ejpam-1979	94	11	,	,	PUNCT
ejpam-1979	94	12	86	86	NUM
ejpam-1979	94	13	-	-	SYM
ejpam-1979	94	14	96	96	NUM
ejpam-1979	94	15	90	90	NUM
ejpam-1979	94	16	be	be	AUX
ejpam-1979	94	17	a	a	DET
ejpam-1979	94	18	smooth	smooth	ADJ
ejpam-1979	94	19	curve	curve	NOUN
ejpam-1979	94	20	in	in	ADP
ejpam-1979	94	21	e4	e4	PROPN
ejpam-1979	94	22	2	2	NUM
ejpam-1979	94	23	with	with	ADP
ejpam-1979	94	24	nonzero	nonzero	ADJ
ejpam-1979	94	25	curvatures	curvature	NOUN
ejpam-1979	94	26	{	{	PUNCT
ejpam-1979	94	27	k	k	X
ejpam-1979	94	28	,	,	PUNCT
ejpam-1979	94	29	k	k	PROPN
ejpam-1979	94	30	,	,	PUNCT
ejpam-1979	94	31	r	r	NOUN
ejpam-1979	94	32	−	−	NOUN
ejpam-1979	94	33	k	k	NOUN
ejpam-1979	94	34	}	}	PUNCT
ejpam-1979	94	35	.	.	PUNCT
ejpam-1979	95	1	let	let	VERB
ejpam-1979	95	2	�	�	PROPN
ejpam-1979	95	3	t	t	PROPN
ejpam-1979	95	4	,	,	PUNCT
ejpam-1979	95	5	n1,n2,n3	n1,n2,n3	NOUN
ejpam-1979	95	6	be	be	AUX
ejpam-1979	95	7	frenet	frenet	ADJ
ejpam-1979	95	8	frame	frame	NOUN
ejpam-1979	95	9	of	of	ADP
ejpam-1979	95	10	β	β	PROPN
ejpam-1979	95	11	.	.	PUNCT
ejpam-1979	96	1	then	then	ADV
ejpam-1979	96	2	frenet	frenet	NOUN
ejpam-1979	96	3	formulae	formulae	NOUN
ejpam-1979	96	4	are	be	AUX
ejpam-1979	96	5	given	give	VERB
ejpam-1979	96	6	by	by	ADP
ejpam-1979	96	7	t	t	PROPN
ejpam-1979	96	8	′	′	NUM
ejpam-1979	96	9	(	(	PUNCT
ejpam-1979	96	10	s	s	X
ejpam-1979	96	11	)	)	PUNCT
ejpam-1979	96	12	=	=	NOUN
ejpam-1979	96	13	εn1	εn1	NOUN
ejpam-1979	96	14	kn1	kn1	NOUN
ejpam-1979	96	15	(	(	PUNCT
ejpam-1979	96	16	s	s	NOUN
ejpam-1979	96	17	)	)	PUNCT
ejpam-1979	96	18	n	n	NOUN
ejpam-1979	96	19	′	′	NUM
ejpam-1979	96	20	1	1	NUM
ejpam-1979	96	21	(	(	PUNCT
ejpam-1979	96	22	s	s	NOUN
ejpam-1979	96	23	)	)	PUNCT
ejpam-1979	96	24	=	=	NOUN
ejpam-1979	96	25	−	−	NOUN
ejpam-1979	96	26	εn1	εn1	NOUN
ejpam-1979	96	27	εtkt	εtkt	NOUN
ejpam-1979	96	28	(	(	PUNCT
ejpam-1979	96	29	s	s	NOUN
ejpam-1979	96	30	)	)	PUNCT
ejpam-1979	96	31	+	+	NUM
ejpam-1979	96	32	εn1	εn1	NOUN
ejpam-1979	96	33	kn2	kn2	NOUN
ejpam-1979	96	34	(	(	PUNCT
ejpam-1979	96	35	s	s	X
ejpam-1979	96	36	)	)	PUNCT
ejpam-1979	96	37	n	n	NOUN
ejpam-1979	96	38	′	′	NUM
ejpam-1979	96	39	2	2	NUM
ejpam-1979	96	40	(	(	PUNCT
ejpam-1979	96	41	s	s	NOUN
ejpam-1979	96	42	)	)	PUNCT
ejpam-1979	96	43	=	=	NOUN
ejpam-1979	96	44	−	−	NOUN
ejpam-1979	96	45	εtkn1	εtkn1	NOUN
ejpam-1979	96	46	(	(	PUNCT
ejpam-1979	96	47	s	s	NOUN
ejpam-1979	96	48	)	)	PUNCT
ejpam-1979	96	49	+	+	NUM
ejpam-1979	96	50	εn1	εn1	NOUN
ejpam-1979	96	51	�	�	NOUN
ejpam-1979	96	52	r	r	NOUN
ejpam-1979	96	53	−	−	PROPN
ejpam-1979	96	54	kεtεtεn1	kεtεtεn1	PROPN
ejpam-1979	96	55	�	�	PROPN
ejpam-1979	96	56	n3	n3	PROPN
ejpam-1979	96	57	(	(	PUNCT
ejpam-1979	96	58	s	s	NOUN
ejpam-1979	96	59	)	)	PUNCT
ejpam-1979	96	60	n	n	NOUN
ejpam-1979	96	61	′	′	NUM
ejpam-1979	96	62	3	3	NUM
ejpam-1979	96	63	(	(	PUNCT
ejpam-1979	96	64	s	s	NOUN
ejpam-1979	96	65	)	)	PUNCT
ejpam-1979	96	66	=	=	NOUN
ejpam-1979	96	67	−	−	PROPN
ejpam-1979	96	68	εn2	εn2	NOUN
ejpam-1979	96	69	�	�	PROPN
ejpam-1979	96	70	r	r	NOUN
ejpam-1979	96	71	−	−	PROPN
ejpam-1979	96	72	kεtεtεn1	kεtεtεn1	PROPN
ejpam-1979	96	73	�	�	PROPN
ejpam-1979	96	74	n2	n2	PROPN
ejpam-1979	96	75	(	(	PUNCT
ejpam-1979	96	76	s	s	NOUN
ejpam-1979	96	77	)	)	PUNCT
ejpam-1979	96	78	,	,	PUNCT
ejpam-1979	96	79	(	(	PUNCT
ejpam-1979	96	80	2	2	X
ejpam-1979	96	81	)	)	PUNCT
ejpam-1979	96	82	where	where	SCONJ
ejpam-1979	96	83	〈	〈	NOUN
ejpam-1979	96	84	t	t	PROPN
ejpam-1979	96	85	,	,	PUNCT
ejpam-1979	96	86	t〉=	t〉=	NOUN
ejpam-1979	96	87	εt	εt	PROPN
ejpam-1979	96	88	,	,	PUNCT
ejpam-1979	96	89	n1,n1	n1,n1	PROPN
ejpam-1979	96	90	�	�	PROPN
ejpam-1979	96	91	=	=	SYM
ejpam-1979	96	92	εn1	εn1	NOUN
ejpam-1979	96	93	,	,	PUNCT
ejpam-1979	96	94	n2,n2	n2,n2	PROPN
ejpam-1979	96	95	�	�	PROPN
ejpam-1979	96	96	=	=	SYM
ejpam-1979	96	97	εn2	εn2	PROPN
ejpam-1979	96	98	and	and	CCONJ
ejpam-1979	96	99	k	k	NOUN
ejpam-1979	96	100	=	=	PUNCT
ejpam-1979	96	101	εn1	εn1	NOUN
ejpam-1979	96	102	t	t	NOUN
ejpam-1979	96	103	′	′	NUM
ejpam-1979	96	104	(	(	PUNCT
ejpam-1979	96	105	s	s	X
ejpam-1979	96	106	)	)	PUNCT
ejpam-1979	96	107	,	,	PUNCT
ejpam-1979	97	1	[	[	X
ejpam-1979	97	2	6	6	NUM
ejpam-1979	97	3	]	]	PUNCT
ejpam-1979	97	4	.	.	PUNCT
ejpam-1979	98	1	3	3	X
ejpam-1979	98	2	.	.	X
ejpam-1979	98	3	spatial	spatial	ADJ
ejpam-1979	98	4	semi	semi	ADJ
ejpam-1979	98	5	quaternionic	quaternionic	ADJ
ejpam-1979	98	6	osculating	osculating	NOUN
ejpam-1979	98	7	spheres	sphere	NOUN
ejpam-1979	98	8	of	of	ADP
ejpam-1979	98	9	a	a	DET
ejpam-1979	98	10	spatial	spatial	ADJ
ejpam-1979	98	11	semi	semi	ADJ
ejpam-1979	98	12	quaternionic	quaternionic	ADJ
ejpam-1979	98	13	curve	curve	NOUN
ejpam-1979	98	14	in	in	ADP
ejpam-1979	98	15	e3	e3	NOUN
ejpam-1979	98	16	1	1	NUM
ejpam-1979	98	17	definition	definition	NOUN
ejpam-1979	98	18	1	1	NUM
ejpam-1979	98	19	.	.	PUNCT
ejpam-1979	99	1	let	let	VERB
ejpam-1979	99	2	γ	γ	NOUN
ejpam-1979	99	3	:	:	PUNCT
ejpam-1979	99	4	i	i	PRON
ejpam-1979	99	5	⊂	⊂	PROPN
ejpam-1979	99	6	r→hp	r→hp	VERB
ejpam-1979	99	7	s→	s→	X
ejpam-1979	99	8	γ	γ	X
ejpam-1979	99	9	(	(	PUNCT
ejpam-1979	99	10	s	s	NOUN
ejpam-1979	99	11	)	)	PUNCT
ejpam-1979	99	12	=	=	SYM
ejpam-1979	99	13	3	3	NUM
ejpam-1979	99	14	∑	∑	NOUN
ejpam-1979	99	15	i=1	i=1	PROPN
ejpam-1979	99	16	γi	γi	X
ejpam-1979	99	17	(	(	PUNCT
ejpam-1979	99	18	s	s	NOUN
ejpam-1979	99	19	)	)	PUNCT
ejpam-1979	99	20	ei	ei	NOUN
ejpam-1979	99	21	,	,	PUNCT
ejpam-1979	99	22	be	be	AUX
ejpam-1979	99	23	a	a	DET
ejpam-1979	99	24	spatial	spatial	ADJ
ejpam-1979	99	25	semi	semi	ADJ
ejpam-1979	99	26	quaternionic	quaternionic	ADJ
ejpam-1979	99	27	curve	curve	NOUN
ejpam-1979	99	28	in	in	ADP
ejpam-1979	99	29	e3	e3	NOUN
ejpam-1979	99	30	1	1	NUM
ejpam-1979	99	31	identified	identify	VERB
ejpam-1979	99	32	withhp	withhp	NOUN
ejpam-1979	99	33	in	in	ADP
ejpam-1979	99	34	an	an	DET
ejpam-1979	99	35	obvious	obvious	ADJ
ejpam-1979	99	36	manner	manner	NOUN
ejpam-1979	99	37	.	.	PUNCT
ejpam-1979	100	1	let	let	VERB
ejpam-1979	100	2	i	i	PRON
ejpam-1979	100	3	=	=	PUNCT
ejpam-1979	101	1	[	[	X
ejpam-1979	101	2	0,1	0,1	NUM
ejpam-1979	101	3	]	]	PUNCT
ejpam-1979	101	4	be	be	AUX
ejpam-1979	101	5	an	an	DET
ejpam-1979	101	6	interval	interval	NOUN
ejpam-1979	101	7	in	in	ADP
ejpam-1979	101	8	the	the	DET
ejpam-1979	101	9	real	real	ADJ
ejpam-1979	101	10	line	line	NOUN
ejpam-1979	101	11	r	r	NOUN
ejpam-1979	101	12	and	and	CCONJ
ejpam-1979	101	13	s	s	AUX
ejpam-1979	101	14	be	be	AUX
ejpam-1979	101	15	an	an	DET
ejpam-1979	101	16	arc	arc	NOUN
ejpam-1979	101	17	-	-	PUNCT
ejpam-1979	101	18	length	length	NOUN
ejpam-1979	101	19	parameter	parameter	NOUN
ejpam-1979	101	20	.	.	PUNCT
ejpam-1979	102	1	so	so	ADV
ejpam-1979	102	2	we	we	PRON
ejpam-1979	102	3	say	say	VERB
ejpam-1979	102	4	that	that	SCONJ
ejpam-1979	102	5	γ	γ	PROPN
ejpam-1979	102	6	′	′	NUM
ejpam-1979	102	7	(	(	PUNCT
ejpam-1979	102	8	s	s	NOUN
ejpam-1979	102	9	)	)	PUNCT
ejpam-1979	102	10	p	p	NOUN
ejpam-1979	102	11	=	=	PROPN
ejpam-1979	102	12	‖t	‖t	NOUN
ejpam-1979	102	13	(	(	PUNCT
ejpam-1979	102	14	s)‖p	s)‖p	VERB
ejpam-1979	102	15	=	=	SYM
ejpam-1979	102	16	1	1	X
ejpam-1979	102	17	.	.	X
ejpam-1979	103	1	we	we	PRON
ejpam-1979	103	2	assume	assume	VERB
ejpam-1979	103	3	that	that	SCONJ
ejpam-1979	103	4	l	l	NOUN
ejpam-1979	103	5	=	=	SYM
ejpam-1979	103	6	�	�	PROPN
ejpam-1979	103	7	l1	l1	PROPN
ejpam-1979	103	8	,	,	PUNCT
ejpam-1979	103	9	l2	l2	NOUN
ejpam-1979	103	10	,	,	PUNCT
ejpam-1979	103	11	l3	l3	PROPN
ejpam-1979	103	12	�	�	PROPN
ejpam-1979	103	13	be	be	AUX
ejpam-1979	103	14	a	a	DET
ejpam-1979	103	15	rectangular	rectangular	ADJ
ejpam-1979	103	16	coordinate	coordinate	NOUN
ejpam-1979	103	17	system	system	NOUN
ejpam-1979	103	18	of	of	ADP
ejpam-1979	103	19	e3	e3	NOUN
ejpam-1979	103	20	1	1	NUM
ejpam-1979	103	21	.	.	PUNCT
ejpam-1979	104	1	we	we	PRON
ejpam-1979	104	2	take	take	VERB
ejpam-1979	104	3	a	a	DET
ejpam-1979	104	4	sphere	sphere	NOUN
ejpam-1979	104	5	〈	〈	PROPN
ejpam-1979	104	6	l	l	NOUN
ejpam-1979	104	7	−m	−m	NOUN
ejpam-1979	104	8	,	,	PUNCT
ejpam-1979	104	9	l	l	NOUN
ejpam-1979	105	1	−m〉p	−m〉p	NOUN
ejpam-1979	105	2	=	=	SYM
ejpam-1979	105	3	r2	r2	PROPN
ejpam-1979	105	4	with	with	ADP
ejpam-1979	105	5	origin	origin	NOUN
ejpam-1979	105	6	m	m	PROPN
ejpam-1979	105	7	and	and	CCONJ
ejpam-1979	105	8	radius	radius	PROPN
ejpam-1979	105	9	r.	r.	PROPN
ejpam-1979	105	10	we	we	PRON
ejpam-1979	105	11	define	define	VERB
ejpam-1979	105	12	a	a	DET
ejpam-1979	105	13	function	function	NOUN
ejpam-1979	105	14	f	f	X
ejpam-1979	105	15	(	(	PUNCT
ejpam-1979	105	16	s	s	X
ejpam-1979	105	17	)	)	PUNCT
ejpam-1979	105	18	=	=	SYM
ejpam-1979	105	19	γ	γ	X
ejpam-1979	105	20	(	(	PUNCT
ejpam-1979	105	21	s)−m	s)−m	PROPN
ejpam-1979	105	22	,	,	PUNCT
ejpam-1979	105	23	γ	γ	X
ejpam-1979	105	24	(	(	PUNCT
ejpam-1979	105	25	s)−m	s)−m	X
ejpam-1979	105	26	�	�	PROPN
ejpam-1979	105	27	p	p	NOUN
ejpam-1979	105	28	−	−	PROPN
ejpam-1979	105	29	r2	r2	PROPN
ejpam-1979	105	30	holds	hold	VERB
ejpam-1979	105	31	the	the	DET
ejpam-1979	105	32	following	follow	VERB
ejpam-1979	105	33	equations	equation	NOUN
ejpam-1979	105	34	f	f	X
ejpam-1979	105	35	(	(	PUNCT
ejpam-1979	105	36	0	0	NUM
ejpam-1979	105	37	)	)	PUNCT
ejpam-1979	105	38	=	=	SYM
ejpam-1979	106	1	f	f	X
ejpam-1979	106	2	′	′	NUM
ejpam-1979	107	1	(	(	PUNCT
ejpam-1979	107	2	0	0	NUM
ejpam-1979	107	3	)	)	PUNCT
ejpam-1979	107	4	=	=	SYM
ejpam-1979	108	1	f	f	X
ejpam-1979	108	2	′′	′′	PROPN
ejpam-1979	108	3	(	(	PUNCT
ejpam-1979	108	4	0	0	NUM
ejpam-1979	108	5	)	)	PUNCT
ejpam-1979	108	6	=	=	SYM
ejpam-1979	109	1	f	f	X
ejpam-1979	109	2	′′′	′′′	PROPN
ejpam-1979	109	3	(	(	PUNCT
ejpam-1979	109	4	0	0	NUM
ejpam-1979	109	5	)	)	PUNCT
ejpam-1979	109	6	=	=	SYM
ejpam-1979	109	7	0	0	NUM
ejpam-1979	109	8	,	,	PUNCT
ejpam-1979	109	9	f	f	X
ejpam-1979	109	10	(	(	PUNCT
ejpam-1979	109	11	4	4	NUM
ejpam-1979	109	12	)	)	PUNCT
ejpam-1979	109	13	6=	6=	ADP
ejpam-1979	109	14	0	0	X
ejpam-1979	109	15	.	.	PUNCT
ejpam-1979	110	1	then	then	ADV
ejpam-1979	110	2	we	we	PRON
ejpam-1979	110	3	called	call	VERB
ejpam-1979	110	4	that	that	SCONJ
ejpam-1979	110	5	the	the	DET
ejpam-1979	110	6	sphere	sphere	NOUN
ejpam-1979	110	7	contacts	contact	NOUN
ejpam-1979	110	8	at	at	ADP
ejpam-1979	110	9	third	third	ADJ
ejpam-1979	110	10	order	order	NOUN
ejpam-1979	110	11	to	to	ADP
ejpam-1979	110	12	the	the	DET
ejpam-1979	110	13	curve	curve	NOUN
ejpam-1979	110	14	γ	γ	NOUN
ejpam-1979	110	15	at	at	ADP
ejpam-1979	110	16	γ	γ	X
ejpam-1979	110	17	(	(	PUNCT
ejpam-1979	110	18	0	0	NUM
ejpam-1979	110	19	)	)	PUNCT
ejpam-1979	110	20	.	.	PUNCT
ejpam-1979	111	1	the	the	DET
ejpam-1979	111	2	sphere	sphere	NOUN
ejpam-1979	111	3	is	be	AUX
ejpam-1979	111	4	called	call	VERB
ejpam-1979	111	5	spatial	spatial	ADJ
ejpam-1979	111	6	semi	semi	ADJ
ejpam-1979	111	7	real	real	ADJ
ejpam-1979	111	8	quaternionic	quaternionic	ADJ
ejpam-1979	111	9	osculating	osculating	NOUN
ejpam-1979	111	10	sphere	sphere	NOUN
ejpam-1979	111	11	for	for	ADP
ejpam-1979	111	12	spatial	spatial	ADJ
ejpam-1979	111	13	semi	semi	ADJ
ejpam-1979	111	14	quaternionic	quaternionic	ADJ
ejpam-1979	111	15	curves	curve	NOUN
ejpam-1979	111	16	in	in	ADP
ejpam-1979	111	17	e3	e3	NOUN
ejpam-1979	111	18	1	1	NUM
ejpam-1979	111	19	.	.	PUNCT
ejpam-1979	111	20	theorem	theorem	NOUN
ejpam-1979	111	21	1	1	NUM
ejpam-1979	111	22	.	.	PUNCT
ejpam-1979	112	1	let	let	VERB
ejpam-1979	112	2	γ	γ	NOUN
ejpam-1979	112	3	:	:	PUNCT
ejpam-1979	112	4	i	i	PRON
ejpam-1979	112	5	⊂	⊂	PROPN
ejpam-1979	112	6	r→hp	r→hp	VERB
ejpam-1979	112	7	be	be	AUX
ejpam-1979	112	8	a	a	DET
ejpam-1979	112	9	spatial	spatial	ADJ
ejpam-1979	112	10	semi	semi	ADJ
ejpam-1979	112	11	quaternionic	quaternionic	ADJ
ejpam-1979	112	12	curve	curve	NOUN
ejpam-1979	112	13	with	with	ADP
ejpam-1979	112	14	nonzero	nonzero	PROPN
ejpam-1979	112	15	curvatures	curvature	NOUN
ejpam-1979	112	16	k	k	PROPN
ejpam-1979	112	17	(	(	PUNCT
ejpam-1979	112	18	0	0	NUM
ejpam-1979	112	19	)	)	PUNCT
ejpam-1979	112	20	and	and	CCONJ
ejpam-1979	112	21	r	r	NOUN
ejpam-1979	112	22	(	(	PUNCT
ejpam-1979	112	23	0	0	NUM
ejpam-1979	112	24	)	)	PUNCT
ejpam-1979	112	25	at	at	ADP
ejpam-1979	112	26	γ	γ	X
ejpam-1979	112	27	(	(	PUNCT
ejpam-1979	112	28	0	0	NUM
ejpam-1979	112	29	)	)	PUNCT
ejpam-1979	112	30	.	.	PUNCT
ejpam-1979	113	1	then	then	ADV
ejpam-1979	113	2	there	there	PRON
ejpam-1979	113	3	exists	exist	VERB
ejpam-1979	113	4	a	a	DET
ejpam-1979	113	5	sphere	sphere	NOUN
ejpam-1979	113	6	which	which	DET
ejpam-1979	113	7	contacts	contact	NOUN
ejpam-1979	113	8	at	at	ADP
ejpam-1979	113	9	the	the	DET
ejpam-1979	113	10	third	third	ADJ
ejpam-1979	113	11	order	order	NOUN
ejpam-1979	113	12	to	to	ADP
ejpam-1979	113	13	the	the	DET
ejpam-1979	113	14	curve	curve	NOUN
ejpam-1979	113	15	γ	γ	NOUN
ejpam-1979	113	16	at	at	ADP
ejpam-1979	113	17	γ	γ	X
ejpam-1979	113	18	(	(	PUNCT
ejpam-1979	113	19	0	0	NUM
ejpam-1979	113	20	)	)	PUNCT
ejpam-1979	113	21	and	and	CCONJ
ejpam-1979	113	22	the	the	DET
ejpam-1979	113	23	equation	equation	NOUN
ejpam-1979	113	24	of	of	ADP
ejpam-1979	113	25	the	the	DET
ejpam-1979	113	26	spatial	spatial	ADJ
ejpam-1979	113	27	semi	semi	ADJ
ejpam-1979	113	28	quaternionic	quaternionic	ADJ
ejpam-1979	113	29	osculating	osculating	NOUN
ejpam-1979	113	30	sphere	sphere	ADV
ejpam-1979	113	31	according	accord	VERB
ejpam-1979	113	32	to	to	ADP
ejpam-1979	113	33	the	the	DET
ejpam-1979	113	34	frenet	frenet	ADJ
ejpam-1979	113	35	frame	frame	NOUN
ejpam-1979	113	36	¦	¦	PROPN
ejpam-1979	113	37	t0,n10	t0,n10	PROPN
ejpam-1979	113	38	,	,	PUNCT
ejpam-1979	113	39	n20	n20	NOUN
ejpam-1979	113	40	©	©	PROPN
ejpam-1979	113	41	as	as	SCONJ
ejpam-1979	113	42	follows	follow	VERB
ejpam-1979	113	43	:	:	PUNCT
ejpam-1979	113	44	εt0	εt0	NOUN
ejpam-1979	113	45	x2	x2	NOUN
ejpam-1979	113	46	1	1	NUM
ejpam-1979	113	47	+	+	CCONJ
ejpam-1979	114	1	εn10	εn10	PROPN
ejpam-1979	114	2	�	�	PROPN
ejpam-1979	114	3	x2−	x2−	PROPN
ejpam-1979	114	4	εt0	εt0	NOUN
ejpam-1979	114	5	ρ0	ρ0	PROPN
ejpam-1979	114	6	�	�	PROPN
ejpam-1979	114	7	2	2	NUM
ejpam-1979	114	8	+	+	CCONJ
ejpam-1979	114	9	εn20	εn20	PROPN
ejpam-1979	114	10	x3−	x3−	PROPN
ejpam-1979	114	11	εt0	εt0	NOUN
ejpam-1979	114	12	εn20	εn20	PROPN
ejpam-1979	114	13	ρ′0σ0	ρ′0σ0	PROPN
ejpam-1979	114	14	!	!	PUNCT
ejpam-1979	115	1	2	2	X
ejpam-1979	115	2	=	=	SYM
ejpam-1979	115	3	εn10	εn10	PROPN
ejpam-1979	115	4	ρ2	ρ2	PROPN
ejpam-1979	115	5	0	0	PUNCT
ejpam-1979	116	1	+	+	CCONJ
ejpam-1979	116	2	εn20	εn20	PROPN
ejpam-1979	116	3	�	�	PROPN
ejpam-1979	116	4	ρ′0σ0	ρ′0σ0	PROPN
ejpam-1979	116	5	�	�	PROPN
ejpam-1979	116	6	2	2	NUM
ejpam-1979	116	7	where	where	SCONJ
ejpam-1979	116	8	ρ0	ρ0	PROPN
ejpam-1979	116	9	=	=	SYM
ejpam-1979	116	10	1	1	NUM
ejpam-1979	116	11	k0	k0	PROPN
ejpam-1979	116	12	and	and	CCONJ
ejpam-1979	116	13	σ0	σ0	PROPN
ejpam-1979	116	14	=	=	SYM
ejpam-1979	116	15	1	1	NUM
ejpam-1979	116	16	r0	r0	NOUN
ejpam-1979	116	17	ö.	ö.	PROPN
ejpam-1979	116	18	bektaş	bektaş	PROPN
ejpam-1979	116	19	,	,	PUNCT
ejpam-1979	116	20	n.	n.	PROPN
ejpam-1979	116	21	gürses	gürse	NOUN
ejpam-1979	116	22	,	,	PUNCT
ejpam-1979	116	23	s.	s.	PROPN
ejpam-1979	116	24	yüce	yüce	PROPN
ejpam-1979	116	25	/	/	SYM
ejpam-1979	116	26	eur	eur	PROPN
ejpam-1979	116	27	.	.	PUNCT
ejpam-1979	117	1	j.	j.	PROPN
ejpam-1979	117	2	pure	pure	PROPN
ejpam-1979	117	3	appl	appl	PROPN
ejpam-1979	117	4	.	.	PROPN
ejpam-1979	117	5	math	math	PROPN
ejpam-1979	117	6	,	,	PUNCT
ejpam-1979	117	7	7	7	NUM
ejpam-1979	117	8	(	(	PUNCT
ejpam-1979	117	9	2014	2014	NUM
ejpam-1979	117	10	)	)	PUNCT
ejpam-1979	117	11	,	,	PUNCT
ejpam-1979	117	12	86	86	NUM
ejpam-1979	117	13	-	-	SYM
ejpam-1979	117	14	96	96	NUM
ejpam-1979	117	15	91	91	NUM
ejpam-1979	117	16	proof	proof	NOUN
ejpam-1979	117	17	.	.	PUNCT
ejpam-1979	118	1	if	if	SCONJ
ejpam-1979	118	2	f	f	PROPN
ejpam-1979	118	3	(	(	PUNCT
ejpam-1979	118	4	0	0	NUM
ejpam-1979	118	5	)	)	PUNCT
ejpam-1979	118	6	=	=	SYM
ejpam-1979	118	7	0	0	PUNCT
ejpam-1979	119	1	then	then	ADV
ejpam-1979	119	2	γ	γ	X
ejpam-1979	119	3	(	(	PUNCT
ejpam-1979	119	4	0)−m	0)−m	NUM
ejpam-1979	119	5	,	,	PUNCT
ejpam-1979	119	6	γ	γ	X
ejpam-1979	119	7	(	(	PUNCT
ejpam-1979	119	8	0)−m	0)−m	NUM
ejpam-1979	119	9	�	�	PROPN
ejpam-1979	119	10	p	p	NOUN
ejpam-1979	119	11	=	=	PROPN
ejpam-1979	119	12	r2	r2	PROPN
ejpam-1979	119	13	.	.	PUNCT
ejpam-1979	120	1	by	by	ADP
ejpam-1979	120	2	differentiating	differentiate	VERB
ejpam-1979	120	3	this	this	DET
ejpam-1979	120	4	equation	equation	NOUN
ejpam-1979	120	5	,	,	PUNCT
ejpam-1979	120	6	we	we	PRON
ejpam-1979	120	7	get	get	VERB
ejpam-1979	120	8	f	f	PROPN
ejpam-1979	120	9	′	′	NUM
ejpam-1979	120	10	(	(	PUNCT
ejpam-1979	120	11	0	0	NUM
ejpam-1979	120	12	)	)	PUNCT
ejpam-1979	120	13	=	=	SYM
ejpam-1979	120	14	0	0	NUM
ejpam-1979	121	1	and	and	CCONJ
ejpam-1979	121	2	f	f	PROPN
ejpam-1979	121	3	′	′	NUM
ejpam-1979	122	1	=	=	SYM
ejpam-1979	122	2	2	2	NUM
ejpam-1979	122	3	γ′,γ−m	γ′,γ−m	PROPN
ejpam-1979	122	4	�	�	PROPN
ejpam-1979	122	5	p	p	X
ejpam-1979	122	6	=	=	PROPN
ejpam-1979	122	7	0	0	NUM
ejpam-1979	122	8	.	.	PUNCT
ejpam-1979	123	1	because	because	SCONJ
ejpam-1979	123	2	of	of	ADP
ejpam-1979	123	3	this	this	PRON
ejpam-1979	123	4	,	,	PUNCT
ejpam-1979	123	5	we	we	PRON
ejpam-1979	123	6	can	can	AUX
ejpam-1979	123	7	write	write	VERB
ejpam-1979	123	8	t0,γ	t0,γ	PROPN
ejpam-1979	123	9	(	(	PUNCT
ejpam-1979	123	10	0)−m	0)−m	NUM
ejpam-1979	123	11	�	�	PROPN
ejpam-1979	124	1	p	p	X
ejpam-1979	124	2	=	=	NOUN
ejpam-1979	124	3	0	0	PROPN
ejpam-1979	124	4	.	.	PUNCT
ejpam-1979	125	1	(	(	PUNCT
ejpam-1979	125	2	3	3	X
ejpam-1979	125	3	)	)	PUNCT
ejpam-1979	125	4	in	in	ADP
ejpam-1979	125	5	a	a	DET
ejpam-1979	125	6	similar	similar	ADJ
ejpam-1979	125	7	way	way	NOUN
ejpam-1979	125	8	we	we	PRON
ejpam-1979	125	9	can	can	AUX
ejpam-1979	125	10	get	get	VERB
ejpam-1979	125	11	f	f	NOUN
ejpam-1979	125	12	′′	′′	PROPN
ejpam-1979	125	13	=	=	PROPN
ejpam-1979	125	14	2	2	NUM
ejpam-1979	125	15	�	�	PROPN
ejpam-1979	125	16	γ′′,γ−m	γ′′,γ−m	PROPN
ejpam-1979	125	17	�	�	PROPN
ejpam-1979	126	1	p	p	NOUN
ejpam-1979	126	2	+	+	CCONJ
ejpam-1979	126	3	γ′,γ′	γ′,γ′	PROPN
ejpam-1979	126	4	�	�	PROPN
ejpam-1979	126	5	p	p	PROPN
ejpam-1979	126	6	�	�	PROPN
ejpam-1979	126	7	=	=	SYM
ejpam-1979	126	8	0	0	NUM
ejpam-1979	126	9	and	and	CCONJ
ejpam-1979	126	10	f	f	PROPN
ejpam-1979	126	11	′′	′′	PROPN
ejpam-1979	126	12	(	(	PUNCT
ejpam-1979	126	13	0	0	NUM
ejpam-1979	126	14	)	)	PUNCT
ejpam-1979	126	15	=	=	NOUN
ejpam-1979	127	1	0	0	X
ejpam-1979	127	2	.	.	PUNCT
ejpam-1979	128	1	if	if	SCONJ
ejpam-1979	128	2	we	we	PRON
ejpam-1979	128	3	use	use	VERB
ejpam-1979	128	4	the	the	DET
ejpam-1979	128	5	equation	equation	NOUN
ejpam-1979	128	6	(	(	PUNCT
ejpam-1979	128	7	1	1	X
ejpam-1979	128	8	)	)	PUNCT
ejpam-1979	128	9	we	we	PRON
ejpam-1979	128	10	have	have	VERB
ejpam-1979	128	11	d	d	PROPN
ejpam-1979	128	12	εn10	εn10	PROPN
ejpam-1979	128	13	k0n10	k0n10	X
ejpam-1979	128	14	(	(	PUNCT
ejpam-1979	128	15	s	s	PROPN
ejpam-1979	128	16	)	)	PUNCT
ejpam-1979	128	17	,	,	PUNCT
ejpam-1979	128	18	γ	γ	X
ejpam-1979	128	19	(	(	PUNCT
ejpam-1979	128	20	0)−m	0)−m	NUM
ejpam-1979	128	21	e	e	X
ejpam-1979	128	22	p	p	X
ejpam-1979	128	23	+	+	CCONJ
ejpam-1979	128	24	t0	t0	PROPN
ejpam-1979	128	25	,	,	PUNCT
ejpam-1979	128	26	t0	t0	PROPN
ejpam-1979	128	27	�	�	PROPN
ejpam-1979	129	1	p	p	NOUN
ejpam-1979	129	2	=	=	NOUN
ejpam-1979	129	3	0	0	NUM
ejpam-1979	129	4	and	and	CCONJ
ejpam-1979	129	5	¬	¬	PROPN
ejpam-1979	129	6	n10	n10	X
ejpam-1979	129	7	(	(	PUNCT
ejpam-1979	129	8	s	s	NOUN
ejpam-1979	129	9	)	)	PUNCT
ejpam-1979	129	10	,	,	PUNCT
ejpam-1979	129	11	γ	γ	X
ejpam-1979	129	12	(	(	PUNCT
ejpam-1979	129	13	0)−m	0)−m	NUM
ejpam-1979	129	14	¶	¶	PROPN
ejpam-1979	129	15	p	p	NOUN
ejpam-1979	130	1	=	=	NOUN
ejpam-1979	130	2	−	−	X
ejpam-1979	130	3	εt0	εt0	NOUN
ejpam-1979	131	1	εn10	εn10	PROPN
ejpam-1979	131	2	k0	k0	PROPN
ejpam-1979	131	3	=	=	PROPN
ejpam-1979	131	4	−	−	PROPN
ejpam-1979	131	5	εt0	εt0	NOUN
ejpam-1979	132	1	εn10	εn10	PROPN
ejpam-1979	132	2	ρ0	ρ0	PROPN
ejpam-1979	132	3	(	(	PUNCT
ejpam-1979	132	4	4	4	NUM
ejpam-1979	132	5	)	)	PUNCT
ejpam-1979	132	6	where	where	SCONJ
ejpam-1979	132	7	1	1	NUM
ejpam-1979	132	8	k0	k0	PROPN
ejpam-1979	132	9	=	=	PROPN
ejpam-1979	132	10	ρ0	ρ0	PROPN
ejpam-1979	132	11	.	.	PUNCT
ejpam-1979	133	1	by	by	ADP
ejpam-1979	133	2	considering	consider	VERB
ejpam-1979	133	3	f	f	X
ejpam-1979	133	4	′′′	′′′	PROPN
ejpam-1979	133	5	=	=	SYM
ejpam-1979	133	6	2	2	NUM
ejpam-1979	133	7	�	�	PROPN
ejpam-1979	133	8	γ′′′,γ−m	γ′′′,γ−m	X
ejpam-1979	133	9	�	�	PROPN
ejpam-1979	133	10	p	p	PROPN
ejpam-1979	133	11	+	+	CCONJ
ejpam-1979	133	12	3	3	NUM
ejpam-1979	133	13	γ′′,γ′	γ′′,γ′	PROPN
ejpam-1979	133	14	�	�	PROPN
ejpam-1979	133	15	p	p	PROPN
ejpam-1979	133	16	�	�	PROPN
ejpam-1979	133	17	=	=	SYM
ejpam-1979	133	18	0	0	NUM
ejpam-1979	133	19	and	and	CCONJ
ejpam-1979	133	20	f	f	PROPN
ejpam-1979	133	21	′′′	′′′	PROPN
ejpam-1979	133	22	(	(	PUNCT
ejpam-1979	133	23	0	0	NUM
ejpam-1979	133	24	)	)	PUNCT
ejpam-1979	133	25	=	=	SYM
ejpam-1979	133	26	0	0	PUNCT
ejpam-1979	133	27	and	and	CCONJ
ejpam-1979	133	28	using	use	VERB
ejpam-1979	133	29	the	the	DET
ejpam-1979	133	30	equations	equation	NOUN
ejpam-1979	133	31	(	(	PUNCT
ejpam-1979	133	32	3	3	NUM
ejpam-1979	133	33	)	)	PUNCT
ejpam-1979	133	34	and	and	CCONJ
ejpam-1979	133	35	(	(	PUNCT
ejpam-1979	133	36	4	4	NUM
ejpam-1979	133	37	)	)	PUNCT
ejpam-1979	133	38	,	,	PUNCT
ejpam-1979	133	39	we	we	PRON
ejpam-1979	133	40	have	have	VERB
ejpam-1979	133	41	¬	¬	PROPN
ejpam-1979	133	42	n20	n20	NOUN
ejpam-1979	133	43	(	(	PUNCT
ejpam-1979	133	44	s	s	NOUN
ejpam-1979	133	45	)	)	PUNCT
ejpam-1979	133	46	,	,	PUNCT
ejpam-1979	133	47	γ	γ	X
ejpam-1979	133	48	(	(	PUNCT
ejpam-1979	133	49	0)−m	0)−m	NUM
ejpam-1979	133	50	¶	¶	NOUN
ejpam-1979	133	51	p	p	PROPN
ejpam-1979	134	1	=	=	NOUN
ejpam-1979	134	2	−εt0	−εt0	NOUN
ejpam-1979	134	3	k′0	k′0	VERB
ejpam-1979	134	4	k2	k2	PROPN
ejpam-1979	134	5	0	0	NUM
ejpam-1979	134	6	r0	r0	NOUN
ejpam-1979	134	7	=	=	NOUN
ejpam-1979	134	8	−εt0	−εt0	PROPN
ejpam-1979	134	9	ρ′0σ0	ρ′0σ0	PROPN
ejpam-1979	134	10	.	.	PUNCT
ejpam-1979	135	1	(	(	PUNCT
ejpam-1979	135	2	5	5	NUM
ejpam-1979	135	3	)	)	PUNCT
ejpam-1979	135	4	when	when	SCONJ
ejpam-1979	135	5	all	all	PRON
ejpam-1979	135	6	is	be	AUX
ejpam-1979	135	7	said	say	VERB
ejpam-1979	135	8	and	and	CCONJ
ejpam-1979	135	9	done	do	VERB
ejpam-1979	135	10	,	,	PUNCT
ejpam-1979	135	11	presently	presently	ADV
ejpam-1979	135	12	we	we	PRON
ejpam-1979	135	13	study	study	VERB
ejpam-1979	135	14	to	to	PART
ejpam-1979	135	15	find	find	VERB
ejpam-1979	135	16	the	the	DET
ejpam-1979	135	17	numbers	number	NOUN
ejpam-1979	135	18	ϑ1	ϑ1	NOUN
ejpam-1979	135	19	,	,	PUNCT
ejpam-1979	135	20	ϑ2	ϑ2	NOUN
ejpam-1979	135	21	,	,	PUNCT
ejpam-1979	135	22	and	and	CCONJ
ejpam-1979	135	23	ϑ3	ϑ3	NOUN
ejpam-1979	135	24	such	such	ADJ
ejpam-1979	135	25	that	that	SCONJ
ejpam-1979	135	26	γ	γ	X
ejpam-1979	135	27	(	(	PUNCT
ejpam-1979	135	28	0)−m=	0)−m=	X
ejpam-1979	135	29	ϑ1t0	ϑ1t0	PROPN
ejpam-1979	135	30	+	+	NUM
ejpam-1979	135	31	ϑ2n10	ϑ2n10	NOUN
ejpam-1979	135	32	+	+	CCONJ
ejpam-1979	135	33	ϑ3n20	ϑ3n20	ADJ
ejpam-1979	135	34	.	.	PUNCT
ejpam-1979	136	1	(	(	PUNCT
ejpam-1979	136	2	6	6	NUM
ejpam-1979	136	3	)	)	PUNCT
ejpam-1979	136	4	from	from	ADP
ejpam-1979	136	5	t0,γ	t0,γ	PROPN
ejpam-1979	136	6	(	(	PUNCT
ejpam-1979	136	7	0)−m	0)−m	NUM
ejpam-1979	136	8	�	�	PROPN
ejpam-1979	136	9	p	p	NOUN
ejpam-1979	136	10	=	=	PROPN
ejpam-1979	136	11	ϑ1	ϑ1	NOUN
ejpam-1979	136	12	and	and	CCONJ
ejpam-1979	136	13	by	by	ADP
ejpam-1979	136	14	using	use	VERB
ejpam-1979	136	15	the	the	DET
ejpam-1979	136	16	equation	equation	NOUN
ejpam-1979	136	17	(	(	PUNCT
ejpam-1979	136	18	3	3	X
ejpam-1979	136	19	)	)	PUNCT
ejpam-1979	136	20	we	we	PRON
ejpam-1979	136	21	obtain	obtain	VERB
ejpam-1979	136	22	ϑ1	ϑ1	NOUN
ejpam-1979	136	23	=	=	NOUN
ejpam-1979	136	24	0	0	NUM
ejpam-1979	136	25	.	.	PUNCT
ejpam-1979	137	1	in	in	ADP
ejpam-1979	137	2	the	the	DET
ejpam-1979	137	3	same	same	ADJ
ejpam-1979	137	4	vein	vein	NOUN
ejpam-1979	137	5	,	,	PUNCT
ejpam-1979	137	6	by	by	ADP
ejpam-1979	137	7	using	use	VERB
ejpam-1979	137	8	the	the	DET
ejpam-1979	137	9	equations	equation	NOUN
ejpam-1979	137	10	(	(	PUNCT
ejpam-1979	137	11	4	4	NUM
ejpam-1979	137	12	)	)	PUNCT
ejpam-1979	137	13	and	and	CCONJ
ejpam-1979	137	14	(	(	PUNCT
ejpam-1979	137	15	5	5	NUM
ejpam-1979	137	16	)	)	PUNCT
ejpam-1979	137	17	,	,	PUNCT
ejpam-1979	137	18	we	we	PRON
ejpam-1979	137	19	get	get	VERB
ejpam-1979	137	20	ϑ2	ϑ2	NOUN
ejpam-1979	138	1	=	=	PUNCT
ejpam-1979	138	2	−εt0	−εt0	NUM
ejpam-1979	138	3	ρ0	ρ0	PROPN
ejpam-1979	138	4	and	and	CCONJ
ejpam-1979	138	5	ϑ3	ϑ3	NOUN
ejpam-1979	138	6	=	=	PUNCT
ejpam-1979	139	1	−	−	PROPN
ejpam-1979	139	2	εt0	εt0	X
ejpam-1979	139	3	εn20	εn20	PROPN
ejpam-1979	139	4	ρ′0σ0	ρ′0σ0	PROPN
ejpam-1979	139	5	.	.	PUNCT
ejpam-1979	140	1	also	also	ADV
ejpam-1979	140	2	the	the	DET
ejpam-1979	140	3	origin	origin	NOUN
ejpam-1979	140	4	of	of	ADP
ejpam-1979	140	5	the	the	DET
ejpam-1979	140	6	sphere	sphere	NOUN
ejpam-1979	140	7	that	that	SCONJ
ejpam-1979	140	8	contacts	contact	NOUN
ejpam-1979	140	9	at	at	ADP
ejpam-1979	140	10	the	the	DET
ejpam-1979	140	11	third	third	ADJ
ejpam-1979	140	12	order	order	NOUN
ejpam-1979	140	13	to	to	ADP
ejpam-1979	140	14	the	the	DET
ejpam-1979	140	15	curve	curve	NOUN
ejpam-1979	140	16	at	at	ADP
ejpam-1979	140	17	the	the	DET
ejpam-1979	140	18	point	point	NOUN
ejpam-1979	140	19	γ	γ	X
ejpam-1979	140	20	(	(	PUNCT
ejpam-1979	140	21	0	0	NUM
ejpam-1979	140	22	)	)	PUNCT
ejpam-1979	140	23	is	be	AUX
ejpam-1979	140	24	m=	m=	X
ejpam-1979	140	25	γ	γ	X
ejpam-1979	140	26	(	(	PUNCT
ejpam-1979	140	27	0)−	0)−	PROPN
ejpam-1979	140	28	ϑ1t0−	ϑ1t0−	PROPN
ejpam-1979	140	29	ϑ2n10	ϑ2n10	NOUN
ejpam-1979	141	1	−	−	PROPN
ejpam-1979	141	2	ϑ3n20	ϑ3n20	PROPN
ejpam-1979	141	3	.	.	PUNCT
ejpam-1979	142	1	let	let	VERB
ejpam-1979	142	2	q	q	PART
ejpam-1979	142	3	be	be	AUX
ejpam-1979	142	4	a	a	DET
ejpam-1979	142	5	spatial	spatial	ADJ
ejpam-1979	142	6	semi	semi	ADJ
ejpam-1979	142	7	quaternionic	quaternionic	ADJ
ejpam-1979	142	8	variable	variable	NOUN
ejpam-1979	142	9	on	on	ADP
ejpam-1979	142	10	spatial	spatial	ADJ
ejpam-1979	142	11	semi	semi	ADJ
ejpam-1979	142	12	quaternionic	quaternionic	ADJ
ejpam-1979	142	13	osculating	osculating	NOUN
ejpam-1979	142	14	sphere	sphere	NOUN
ejpam-1979	142	15	,	,	PUNCT
ejpam-1979	142	16	assume	assume	VERB
ejpam-1979	142	17	q	q	X
ejpam-1979	142	18	=	=	VERB
ejpam-1979	142	19	γ	γ	X
ejpam-1979	142	20	(	(	PUNCT
ejpam-1979	142	21	0	0	NUM
ejpam-1979	142	22	)	)	PUNCT
ejpam-1979	142	23	+	+	NOUN
ejpam-1979	143	1	x1t0	x1t0	PUNCT
ejpam-1979	143	2	+	+	NOUN
ejpam-1979	143	3	x2n10	x2n10	X
ejpam-1979	144	1	+	+	CCONJ
ejpam-1979	144	2	x3n20	x3n20	PROPN
ejpam-1979	144	3	.	.	PUNCT
ejpam-1979	145	1	from	from	ADP
ejpam-1979	145	2	the	the	DET
ejpam-1979	145	3	above	above	ADJ
ejpam-1979	145	4	discussions	discussion	NOUN
ejpam-1979	145	5	,	,	PUNCT
ejpam-1979	145	6	we	we	PRON
ejpam-1979	145	7	have	have	VERB
ejpam-1979	145	8	the	the	DET
ejpam-1979	145	9	following	follow	VERB
ejpam-1979	145	10	statement	statement	NOUN
ejpam-1979	145	11	q−m=	q−m=	NOUN
ejpam-1979	145	12	x1t0	x1t0	PROPN
ejpam-1979	145	13	+	+	PROPN
ejpam-1979	145	14	�	�	PROPN
ejpam-1979	145	15	x2−	x2−	PROPN
ejpam-1979	145	16	εt0	εt0	NOUN
ejpam-1979	145	17	ρ0	ρ0	PROPN
ejpam-1979	145	18	�	�	PROPN
ejpam-1979	145	19	n10	n10	X
ejpam-1979	146	1	+	+	CCONJ
ejpam-1979	146	2	x3−	x3−	PROPN
ejpam-1979	146	3	εt0	εt0	NOUN
ejpam-1979	146	4	εn20	εn20	PROPN
ejpam-1979	146	5	ρ′0σ0	ρ′0σ0	PROPN
ejpam-1979	146	6	!	!	PUNCT
ejpam-1979	147	1	n20	n20	PROPN
ejpam-1979	147	2	ö.	ö.	PROPN
ejpam-1979	147	3	bektaş	bektaş	PROPN
ejpam-1979	147	4	,	,	PUNCT
ejpam-1979	147	5	n.	n.	PROPN
ejpam-1979	147	6	gürses	gürse	NOUN
ejpam-1979	147	7	,	,	PUNCT
ejpam-1979	147	8	s.	s.	PROPN
ejpam-1979	147	9	yüce	yüce	PROPN
ejpam-1979	147	10	/	/	SYM
ejpam-1979	147	11	eur	eur	PROPN
ejpam-1979	147	12	.	.	PUNCT
ejpam-1979	148	1	j.	j.	PROPN
ejpam-1979	148	2	pure	pure	PROPN
ejpam-1979	148	3	appl	appl	PROPN
ejpam-1979	148	4	.	.	PROPN
ejpam-1979	148	5	math	math	PROPN
ejpam-1979	148	6	,	,	PUNCT
ejpam-1979	148	7	7	7	NUM
ejpam-1979	148	8	(	(	PUNCT
ejpam-1979	148	9	2014	2014	NUM
ejpam-1979	148	10	)	)	PUNCT
ejpam-1979	148	11	,	,	PUNCT
ejpam-1979	148	12	86	86	NUM
ejpam-1979	148	13	-	-	SYM
ejpam-1979	148	14	96	96	NUM
ejpam-1979	148	15	92	92	NUM
ejpam-1979	148	16	and	and	CCONJ
ejpam-1979	148	17	〈	〈	NOUN
ejpam-1979	148	18	q−m	q−m	PROPN
ejpam-1979	148	19	,	,	PUNCT
ejpam-1979	148	20	q−m〉p	q−m〉p	NOUN
ejpam-1979	148	21	=	=	SYM
ejpam-1979	148	22	εt0	εt0	NOUN
ejpam-1979	148	23	x2	x2	NOUN
ejpam-1979	148	24	1	1	NUM
ejpam-1979	148	25	+	+	CCONJ
ejpam-1979	149	1	εn10	εn10	PROPN
ejpam-1979	149	2	�	�	PROPN
ejpam-1979	149	3	x2−	x2−	PROPN
ejpam-1979	149	4	εt0	εt0	NOUN
ejpam-1979	149	5	ρ0	ρ0	PROPN
ejpam-1979	149	6	�	�	PROPN
ejpam-1979	149	7	2	2	NUM
ejpam-1979	149	8	+	+	CCONJ
ejpam-1979	149	9	εn20	εn20	PROPN
ejpam-1979	149	10	x3−	x3−	PROPN
ejpam-1979	149	11	εt0	εt0	NOUN
ejpam-1979	149	12	εn20	εn20	PROPN
ejpam-1979	149	13	ρ′0σ0	ρ′0σ0	PROPN
ejpam-1979	149	14	!	!	PUNCT
ejpam-1979	150	1	2	2	X
ejpam-1979	150	2	.	.	PUNCT
ejpam-1979	151	1	finally	finally	ADV
ejpam-1979	151	2	,	,	PUNCT
ejpam-1979	151	3	with	with	ADP
ejpam-1979	151	4	the	the	DET
ejpam-1979	151	5	aim	aim	NOUN
ejpam-1979	151	6	of	of	ADP
ejpam-1979	151	7	the	the	DET
ejpam-1979	151	8	equation	equation	NOUN
ejpam-1979	151	9	(	(	PUNCT
ejpam-1979	151	10	6	6	NUM
ejpam-1979	151	11	)	)	PUNCT
ejpam-1979	151	12	we	we	PRON
ejpam-1979	151	13	get	get	VERB
ejpam-1979	151	14	r2	r2	NOUN
ejpam-1979	151	15	=	=	SYM
ejpam-1979	151	16	γ	γ	X
ejpam-1979	151	17	(	(	PUNCT
ejpam-1979	151	18	0)−m	0)−m	NUM
ejpam-1979	151	19	,	,	PUNCT
ejpam-1979	151	20	γ	γ	X
ejpam-1979	151	21	(	(	PUNCT
ejpam-1979	151	22	0)−m	0)−m	NUM
ejpam-1979	151	23	�	�	PROPN
ejpam-1979	151	24	p	p	X
ejpam-1979	151	25	=	=	PUNCT
ejpam-1979	151	26	εn10	εn10	PROPN
ejpam-1979	151	27	ρ2	ρ2	PROPN
ejpam-1979	151	28	0	0	PUNCT
ejpam-1979	152	1	+	+	CCONJ
ejpam-1979	152	2	εn20	εn20	PROPN
ejpam-1979	152	3	�	�	PROPN
ejpam-1979	152	4	ρ′0σ0	ρ′0σ0	PROPN
ejpam-1979	152	5	�	�	PROPN
ejpam-1979	152	6	2	2	NUM
ejpam-1979	152	7	which	which	PRON
ejpam-1979	152	8	is	be	AUX
ejpam-1979	152	9	the	the	DET
ejpam-1979	152	10	equation	equation	NOUN
ejpam-1979	152	11	of	of	ADP
ejpam-1979	152	12	the	the	DET
ejpam-1979	152	13	spatial	spatial	ADJ
ejpam-1979	152	14	semi	semi	ADJ
ejpam-1979	152	15	quaternionic	quaternionic	ADJ
ejpam-1979	152	16	osculating	osculating	NOUN
ejpam-1979	152	17	sphere	sphere	ADV
ejpam-1979	152	18	in	in	ADP
ejpam-1979	152	19	e3	e3	NOUN
ejpam-1979	152	20	1	1	NUM
ejpam-1979	152	21	.	.	PUNCT
ejpam-1979	153	1	this	this	PRON
ejpam-1979	153	2	completes	complete	VERB
ejpam-1979	153	3	proof	proof	NOUN
ejpam-1979	153	4	.	.	PUNCT
ejpam-1979	154	1	4	4	X
ejpam-1979	154	2	.	.	X
ejpam-1979	154	3	semi	semi	ADJ
ejpam-1979	154	4	quaternionic	quaternionic	ADJ
ejpam-1979	154	5	osculating	osculating	NOUN
ejpam-1979	154	6	spheres	sphere	NOUN
ejpam-1979	154	7	of	of	ADP
ejpam-1979	154	8	a	a	DET
ejpam-1979	154	9	semi	semi	ADJ
ejpam-1979	154	10	quaternionic	quaternionic	ADJ
ejpam-1979	154	11	curve	curve	NOUN
ejpam-1979	154	12	in	in	ADP
ejpam-1979	154	13	e4	e4	PROPN
ejpam-1979	154	14	2	2	NUM
ejpam-1979	154	15	definition	definition	NOUN
ejpam-1979	154	16	2	2	NUM
ejpam-1979	154	17	.	.	PUNCT
ejpam-1979	155	1	β	β	NOUN
ejpam-1979	155	2	:	:	PUNCT
ejpam-1979	156	1	i	i	PRON
ejpam-1979	156	2	⊂	⊂	PROPN
ejpam-1979	156	3	r→h	r→h	PROPN
ejpam-1979	156	4	s→	s→	X
ejpam-1979	156	5	β	β	X
ejpam-1979	156	6	(	(	PUNCT
ejpam-1979	156	7	s	s	X
ejpam-1979	156	8	)	)	PUNCT
ejpam-1979	156	9	=	=	SYM
ejpam-1979	156	10	3	3	NUM
ejpam-1979	156	11	∑	∑	PUNCT
ejpam-1979	156	12	i=0	i=0	PROPN
ejpam-1979	156	13	γi	γi	X
ejpam-1979	156	14	(	(	PUNCT
ejpam-1979	156	15	s	s	NOUN
ejpam-1979	156	16	)	)	PUNCT
ejpam-1979	156	17	ei	ei	NOUN
ejpam-1979	156	18	,	,	PUNCT
ejpam-1979	156	19	be	be	AUX
ejpam-1979	156	20	a	a	DET
ejpam-1979	156	21	semi	semi	ADJ
ejpam-1979	156	22	quaternionic	quaternionic	ADJ
ejpam-1979	156	23	curve	curve	NOUN
ejpam-1979	156	24	in	in	ADP
ejpam-1979	156	25	e4	e4	PROPN
ejpam-1979	156	26	2	2	NUM
ejpam-1979	156	27	identified	identify	VERB
ejpam-1979	156	28	with	with	ADP
ejpam-1979	156	29	the	the	DET
ejpam-1979	156	30	space	space	NOUN
ejpam-1979	156	31	of	of	ADP
ejpam-1979	156	32	semi	semi	ADJ
ejpam-1979	156	33	quaternionsh	quaternionsh	PROPN
ejpam-1979	156	34	.	.	PUNCT
ejpam-1979	157	1	let	let	VERB
ejpam-1979	157	2	i	i	PRON
ejpam-1979	157	3	=	=	PUNCT
ejpam-1979	158	1	[	[	X
ejpam-1979	158	2	0	0	NUM
ejpam-1979	158	3	,	,	PUNCT
ejpam-1979	158	4	1	1	NUM
ejpam-1979	158	5	]	]	PUNCT
ejpam-1979	158	6	be	be	AUX
ejpam-1979	158	7	an	an	DET
ejpam-1979	158	8	interval	interval	NOUN
ejpam-1979	158	9	in	in	ADP
ejpam-1979	158	10	the	the	DET
ejpam-1979	158	11	real	real	ADJ
ejpam-1979	158	12	line	line	NOUN
ejpam-1979	158	13	r	r	NOUN
ejpam-1979	158	14	and	and	CCONJ
ejpam-1979	158	15	s	s	AUX
ejpam-1979	158	16	be	be	AUX
ejpam-1979	158	17	an	an	DET
ejpam-1979	158	18	arc	arc	NOUN
ejpam-1979	158	19	-	-	PUNCT
ejpam-1979	158	20	length	length	NOUN
ejpam-1979	158	21	parameter	parameter	NOUN
ejpam-1979	158	22	.	.	PUNCT
ejpam-1979	159	1	in	in	ADP
ejpam-1979	159	2	this	this	DET
ejpam-1979	159	3	position	position	NOUN
ejpam-1979	159	4	we	we	PRON
ejpam-1979	159	5	say	say	VERB
ejpam-1979	159	6	that	that	SCONJ
ejpam-1979	159	7	β	β	PRON
ejpam-1979	159	8	′	′	NUM
ejpam-1979	159	9	(	(	PUNCT
ejpam-1979	159	10	s	s	X
ejpam-1979	159	11	)	)	PUNCT
ejpam-1979	159	12	=	=	NOUN
ejpam-1979	159	13	‖t	‖t	NOUN
ejpam-1979	159	14	(	(	PUNCT
ejpam-1979	159	15	s)‖	s)‖	NOUN
ejpam-1979	159	16	=	=	SYM
ejpam-1979	159	17	1	1	X
ejpam-1979	159	18	.	.	X
ejpam-1979	160	1	we	we	PRON
ejpam-1979	160	2	assume	assume	VERB
ejpam-1979	160	3	that	that	SCONJ
ejpam-1979	160	4	l	l	NOUN
ejpam-1979	160	5	=	=	SYM
ejpam-1979	160	6	�	�	PROPN
ejpam-1979	160	7	l1	l1	PROPN
ejpam-1979	160	8	,	,	PUNCT
ejpam-1979	160	9	l2	l2	NOUN
ejpam-1979	160	10	,	,	PUNCT
ejpam-1979	160	11	l3	l3	PROPN
ejpam-1979	160	12	,	,	PUNCT
ejpam-1979	160	13	l4	l4	PROPN
ejpam-1979	160	14	�	�	PROPN
ejpam-1979	160	15	be	be	AUX
ejpam-1979	160	16	a	a	DET
ejpam-1979	160	17	rectangular	rectangular	ADJ
ejpam-1979	160	18	coordinate	coordinate	NOUN
ejpam-1979	160	19	system	system	NOUN
ejpam-1979	160	20	of	of	ADP
ejpam-1979	160	21	e4	e4	PROPN
ejpam-1979	160	22	2	2	NUM
ejpam-1979	160	23	.	.	PUNCT
ejpam-1979	161	1	we	we	PRON
ejpam-1979	161	2	take	take	VERB
ejpam-1979	161	3	a	a	DET
ejpam-1979	161	4	sphere〈l−m	sphere〈l−m	NOUN
ejpam-1979	161	5	,	,	PUNCT
ejpam-1979	161	6	l−m	l−m	NOUN
ejpam-1979	161	7	〉	〉	NOUN
ejpam-1979	161	8	=	=	PUNCT
ejpam-1979	161	9	r2	r2	PROPN
ejpam-1979	161	10	with	with	ADP
ejpam-1979	161	11	origin	origin	NOUN
ejpam-1979	161	12	m	m	PROPN
ejpam-1979	161	13	and	and	CCONJ
ejpam-1979	161	14	radius	radius	PROPN
ejpam-1979	161	15	r.	r.	PROPN
ejpam-1979	161	16	we	we	PRON
ejpam-1979	161	17	define	define	VERB
ejpam-1979	161	18	a	a	DET
ejpam-1979	161	19	function	function	NOUN
ejpam-1979	161	20	g	g	NOUN
ejpam-1979	161	21	(	(	PUNCT
ejpam-1979	161	22	s	s	NOUN
ejpam-1979	161	23	)	)	PUNCT
ejpam-1979	161	24	=	=	SYM
ejpam-1979	161	25	β	β	X
ejpam-1979	161	26	(	(	PUNCT
ejpam-1979	161	27	s)−m	s)−m	X
ejpam-1979	161	28	,	,	PUNCT
ejpam-1979	161	29	β	β	X
ejpam-1979	161	30	(	(	PUNCT
ejpam-1979	161	31	s)−m	s)−m	X
ejpam-1979	161	32	�	�	PROPN
ejpam-1979	161	33	−	−	PROPN
ejpam-1979	161	34	r2	r2	PROPN
ejpam-1979	161	35	satisfies	satisfy	VERB
ejpam-1979	161	36	the	the	DET
ejpam-1979	161	37	following	follow	VERB
ejpam-1979	161	38	equations	equation	NOUN
ejpam-1979	161	39	g	g	PROPN
ejpam-1979	161	40	(	(	PUNCT
ejpam-1979	161	41	0	0	NUM
ejpam-1979	161	42	)	)	PUNCT
ejpam-1979	161	43	=	=	SYM
ejpam-1979	162	1	g	g	NOUN
ejpam-1979	162	2	′	′	NUM
ejpam-1979	163	1	(	(	PUNCT
ejpam-1979	163	2	0	0	NUM
ejpam-1979	163	3	)	)	PUNCT
ejpam-1979	163	4	=	=	SYM
ejpam-1979	164	1	g	g	PROPN
ejpam-1979	164	2	′′	′′	PROPN
ejpam-1979	164	3	(	(	PUNCT
ejpam-1979	164	4	0	0	NUM
ejpam-1979	164	5	)	)	PUNCT
ejpam-1979	164	6	=	=	NOUN
ejpam-1979	164	7	g	g	PROPN
ejpam-1979	164	8	′′′	′′′	PROPN
ejpam-1979	164	9	(	(	PUNCT
ejpam-1979	164	10	0	0	NUM
ejpam-1979	164	11	)	)	PUNCT
ejpam-1979	164	12	=	=	SYM
ejpam-1979	164	13	g(4	g(4	PROPN
ejpam-1979	164	14	)	)	PUNCT
ejpam-1979	164	15	=	=	SYM
ejpam-1979	164	16	0	0	NUM
ejpam-1979	164	17	,	,	PUNCT
ejpam-1979	164	18	g(5	g(5	PROPN
ejpam-1979	164	19	)	)	PUNCT
ejpam-1979	164	20	6=	6=	ADP
ejpam-1979	164	21	0	0	X
ejpam-1979	164	22	.	.	PUNCT
ejpam-1979	165	1	then	then	ADV
ejpam-1979	165	2	we	we	PRON
ejpam-1979	165	3	called	call	VERB
ejpam-1979	165	4	that	that	SCONJ
ejpam-1979	165	5	the	the	DET
ejpam-1979	165	6	sphere	sphere	NOUN
ejpam-1979	165	7	contacts	contact	NOUN
ejpam-1979	165	8	at	at	ADP
ejpam-1979	165	9	fourth	fourth	ADJ
ejpam-1979	165	10	order	order	NOUN
ejpam-1979	165	11	to	to	ADP
ejpam-1979	165	12	the	the	DET
ejpam-1979	165	13	curve	curve	NOUN
ejpam-1979	165	14	β	β	PROPN
ejpam-1979	165	15	at	at	ADP
ejpam-1979	165	16	β	β	X
ejpam-1979	165	17	(	(	PUNCT
ejpam-1979	165	18	0	0	NUM
ejpam-1979	165	19	)	)	PUNCT
ejpam-1979	165	20	.	.	PUNCT
ejpam-1979	166	1	the	the	DET
ejpam-1979	166	2	sphere	sphere	NOUN
ejpam-1979	166	3	is	be	AUX
ejpam-1979	166	4	called	call	VERB
ejpam-1979	166	5	semi	semi	ADV
ejpam-1979	166	6	real	real	ADJ
ejpam-1979	166	7	quaternionic	quaternionic	ADJ
ejpam-1979	166	8	osculating	osculating	NOUN
ejpam-1979	166	9	sphere	sphere	NOUN
ejpam-1979	166	10	for	for	ADP
ejpam-1979	166	11	semi	semi	ADJ
ejpam-1979	166	12	quaternionic	quaternionic	ADJ
ejpam-1979	166	13	curves	curve	NOUN
ejpam-1979	166	14	in	in	ADP
ejpam-1979	166	15	e4	e4	PROPN
ejpam-1979	166	16	2	2	NUM
ejpam-1979	166	17	.	.	PUNCT
ejpam-1979	166	18	theorem	theorem	NOUN
ejpam-1979	166	19	2	2	NUM
ejpam-1979	166	20	.	.	PUNCT
ejpam-1979	167	1	let	let	VERB
ejpam-1979	167	2	β	β	NOUN
ejpam-1979	167	3	:	:	PUNCT
ejpam-1979	167	4	i	i	PRON
ejpam-1979	167	5	⊂	⊂	PROPN
ejpam-1979	167	6	r	r	NOUN
ejpam-1979	167	7	→	→	SYM
ejpam-1979	167	8	h	h	NOUN
ejpam-1979	167	9	be	be	AUX
ejpam-1979	167	10	a	a	DET
ejpam-1979	167	11	semi	semi	ADJ
ejpam-1979	167	12	quaternionic	quaternionic	ADJ
ejpam-1979	167	13	curve	curve	NOUN
ejpam-1979	167	14	with	with	ADP
ejpam-1979	167	15	nonzero	nonzero	PROPN
ejpam-1979	167	16	curvatures	curvature	NOUN
ejpam-1979	167	17	k	k	PROPN
ejpam-1979	167	18	(	(	PUNCT
ejpam-1979	167	19	0	0	NUM
ejpam-1979	167	20	)	)	PUNCT
ejpam-1979	167	21	,	,	PUNCT
ejpam-1979	167	22	r	r	NOUN
ejpam-1979	167	23	(	(	PUNCT
ejpam-1979	167	24	0	0	NUM
ejpam-1979	167	25	)	)	PUNCT
ejpam-1979	167	26	,	,	PUNCT
ejpam-1979	167	27	and	and	CCONJ
ejpam-1979	167	28	(	(	PUNCT
ejpam-1979	167	29	r	r	NOUN
ejpam-1979	167	30	−	−	PROPN
ejpam-1979	167	31	k	k	NOUN
ejpam-1979	167	32	)	)	PUNCT
ejpam-1979	167	33	(	(	PUNCT
ejpam-1979	167	34	0	0	NUM
ejpam-1979	167	35	)	)	PUNCT
ejpam-1979	167	36	at	at	ADP
ejpam-1979	167	37	β	β	X
ejpam-1979	167	38	(	(	PUNCT
ejpam-1979	167	39	0	0	NUM
ejpam-1979	167	40	)	)	PUNCT
ejpam-1979	167	41	.	.	PUNCT
ejpam-1979	168	1	then	then	ADV
ejpam-1979	168	2	there	there	PRON
ejpam-1979	168	3	exists	exist	VERB
ejpam-1979	168	4	a	a	DET
ejpam-1979	168	5	sphere	sphere	NOUN
ejpam-1979	168	6	which	which	DET
ejpam-1979	168	7	contacts	contact	NOUN
ejpam-1979	168	8	at	at	ADP
ejpam-1979	168	9	the	the	DET
ejpam-1979	168	10	fourth	fourth	ADJ
ejpam-1979	168	11	order	order	NOUN
ejpam-1979	168	12	to	to	ADP
ejpam-1979	168	13	the	the	DET
ejpam-1979	168	14	curve	curve	NOUN
ejpam-1979	168	15	β	β	PROPN
ejpam-1979	168	16	at	at	ADP
ejpam-1979	168	17	β	β	X
ejpam-1979	168	18	(	(	PUNCT
ejpam-1979	168	19	0	0	NUM
ejpam-1979	168	20	)	)	PUNCT
ejpam-1979	168	21	and	and	CCONJ
ejpam-1979	168	22	the	the	DET
ejpam-1979	168	23	equation	equation	NOUN
ejpam-1979	168	24	of	of	ADP
ejpam-1979	168	25	the	the	DET
ejpam-1979	168	26	semi	semi	ADJ
ejpam-1979	168	27	quaternionic	quaternionic	ADJ
ejpam-1979	168	28	osculating	osculating	NOUN
ejpam-1979	168	29	sphere	sphere	ADV
ejpam-1979	168	30	according	accord	VERB
ejpam-1979	168	31	to	to	ADP
ejpam-1979	168	32	the	the	DET
ejpam-1979	168	33	frenet	frenet	ADJ
ejpam-1979	168	34	frame	frame	NOUN
ejpam-1979	168	35	¦	¦	PROPN
ejpam-1979	168	36	t0,n10	t0,n10	PROPN
ejpam-1979	168	37	,	,	PUNCT
ejpam-1979	168	38	n20	n20	NOUN
ejpam-1979	168	39	,	,	PUNCT
ejpam-1979	168	40	n30	n30	PROPN
ejpam-1979	168	41	©	©	PROPN
ejpam-1979	168	42	such	such	ADJ
ejpam-1979	168	43	that	that	DET
ejpam-1979	168	44	εt0	εt0	NOUN
ejpam-1979	168	45	x	x	SYM
ejpam-1979	168	46	2	2	NUM
ejpam-1979	168	47	1	1	NUM
ejpam-1979	168	48	+	+	CCONJ
ejpam-1979	168	49	εn10	εn10	PROPN
ejpam-1979	168	50	x2−	x2−	PROPN
ejpam-1979	168	51	εt0	εt0	NOUN
ejpam-1979	168	52	εn10	εn10	PROPN
ejpam-1979	168	53	ς0	ς0	PROPN
ejpam-1979	168	54	!	!	PUNCT
ejpam-1979	168	55	2	2	NUM
ejpam-1979	169	1	+	+	CCONJ
ejpam-1979	169	2	εn20	εn20	PROPN
ejpam-1979	169	3	x3−	x3−	PROPN
ejpam-1979	169	4	εt0	εt0	NOUN
ejpam-1979	169	5	εn10	εn10	PROPN
ejpam-1979	169	6	εn10	εn10	PROPN
ejpam-1979	169	7	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	169	8	!	!	PUNCT
ejpam-1979	169	9	2	2	NUM
ejpam-1979	170	1	+	+	CCONJ
ejpam-1979	170	2	εn30	εn30	PROPN
ejpam-1979	170	3	�	�	PROPN
ejpam-1979	170	4	x4−ω0	x4−ω0	X
ejpam-1979	170	5	�	�	PROPN
ejpam-1979	170	6	εt0	εt0	NOUN
ejpam-1979	170	7	εn10	εn10	PROPN
ejpam-1979	170	8	�	�	PROPN
ejpam-1979	170	9	�	�	PROPN
ejpam-1979	170	10	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	170	11	�	�	PROPN
ejpam-1979	170	12	′	′	PROPN
ejpam-1979	171	1	+	+	CCONJ
ejpam-1979	171	2	εt0	εt0	X
ejpam-1979	171	3	�	�	NOUN
ejpam-1979	171	4	εn10	εn10	PROPN
ejpam-1979	171	5	�	�	PROPN
ejpam-1979	171	6	ς0	ς0	VERB
ejpam-1979	171	7	ρ0	ρ0	PROPN
ejpam-1979	171	8	�	�	PROPN
ejpam-1979	172	1	−	−	PROPN
ejpam-1979	173	1	εn10	εn10	PROPN
ejpam-1979	173	2	ρ0	ρ0	PROPN
ejpam-1979	173	3	−	−	PROPN
ejpam-1979	173	4	4	4	NUM
ejpam-1979	173	5	�	�	NOUN
ejpam-1979	173	6	ρ0	ρ0	PROPN
ejpam-1979	173	7	ς0	ς0	PROPN
ejpam-1979	173	8	�	�	PROPN
ejpam-1979	173	9	�	�	PROPN
ejpam-1979	173	10	+	+	CCONJ
ejpam-1979	173	11	3	3	NUM
ejpam-1979	173	12	εt0	εt0	NOUN
ejpam-1979	173	13	εn10	εn10	PROPN
ejpam-1979	173	14	�	�	PROPN
ejpam-1979	173	15	ρ0	ρ0	PROPN
ejpam-1979	173	16	ς0	ς0	PROPN
ejpam-1979	173	17	�	�	PROPN
ejpam-1979	173	18	�	�	PROPN
ejpam-1979	173	19	�	�	PROPN
ejpam-1979	173	20	�	�	PROPN
ejpam-1979	173	21	2	2	NUM
ejpam-1979	173	22	ö.	ö.	NOUN
ejpam-1979	173	23	bektaş	bektaş	PROPN
ejpam-1979	173	24	,	,	PUNCT
ejpam-1979	173	25	n.	n.	PROPN
ejpam-1979	173	26	gürses	gürse	NOUN
ejpam-1979	173	27	,	,	PUNCT
ejpam-1979	173	28	s.	s.	PROPN
ejpam-1979	173	29	yüce	yüce	PROPN
ejpam-1979	173	30	/	/	SYM
ejpam-1979	173	31	eur	eur	PROPN
ejpam-1979	173	32	.	.	PUNCT
ejpam-1979	174	1	j.	j.	PROPN
ejpam-1979	174	2	pure	pure	PROPN
ejpam-1979	174	3	appl	appl	PROPN
ejpam-1979	174	4	.	.	PROPN
ejpam-1979	174	5	math	math	PROPN
ejpam-1979	174	6	,	,	PUNCT
ejpam-1979	174	7	7	7	NUM
ejpam-1979	174	8	(	(	PUNCT
ejpam-1979	174	9	2014	2014	NUM
ejpam-1979	174	10	)	)	PUNCT
ejpam-1979	174	11	,	,	PUNCT
ejpam-1979	174	12	86	86	NUM
ejpam-1979	174	13	-	-	SYM
ejpam-1979	174	14	96	96	NUM
ejpam-1979	174	15	93	93	NUM
ejpam-1979	175	1	=	=	NUM
ejpam-1979	175	2	εn10	εn10	PROPN
ejpam-1979	175	3	ς2	ς2	PROPN
ejpam-1979	175	4	0	0	NUM
ejpam-1979	175	5	+	+	NUM
ejpam-1979	175	6	εn20	εn20	PROPN
ejpam-1979	175	7	�	�	PROPN
ejpam-1979	175	8	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	175	9	�	�	PROPN
ejpam-1979	175	10	2	2	NUM
ejpam-1979	175	11	+	+	CCONJ
ejpam-1979	175	12	εn30	εn30	PROPN
ejpam-1979	175	13	�	�	PROPN
ejpam-1979	175	14	ω2	ω2	NOUN
ejpam-1979	175	15	0	0	NUM
ejpam-1979	175	16	�	�	PROPN
ejpam-1979	175	17	�	�	PROPN
ejpam-1979	175	18	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	175	19	�	�	PROPN
ejpam-1979	175	20	′	′	PROPN
ejpam-1979	176	1	+	+	CCONJ
ejpam-1979	176	2	εt0	εt0	X
ejpam-1979	176	3	�	�	NOUN
ejpam-1979	176	4	εn10	εn10	PROPN
ejpam-1979	176	5	�	�	PROPN
ejpam-1979	176	6	ς0	ς0	VERB
ejpam-1979	176	7	ρ0	ρ0	PROPN
ejpam-1979	176	8	�	�	PROPN
ejpam-1979	177	1	−	−	PROPN
ejpam-1979	178	1	εn10	εn10	PROPN
ejpam-1979	178	2	ρ0	ρ0	PROPN
ejpam-1979	178	3	−	−	PROPN
ejpam-1979	178	4	4	4	NUM
ejpam-1979	178	5	�	�	NOUN
ejpam-1979	178	6	ρ0	ρ0	PROPN
ejpam-1979	178	7	ς0	ς0	PROPN
ejpam-1979	178	8	�	�	PROPN
ejpam-1979	178	9	�	�	PROPN
ejpam-1979	178	10	+	+	CCONJ
ejpam-1979	178	11	3	3	NUM
ejpam-1979	178	12	εt0	εt0	NOUN
ejpam-1979	178	13	εn10	εn10	PROPN
ejpam-1979	178	14	�	�	PROPN
ejpam-1979	178	15	ρ0	ρ0	PROPN
ejpam-1979	178	16	ς0	ς0	PROPN
ejpam-1979	178	17	�	�	PROPN
ejpam-1979	178	18	�	�	PROPN
ejpam-1979	178	19	�	�	PROPN
ejpam-1979	178	20	where	where	SCONJ
ejpam-1979	178	21	ς0	ς0	PROPN
ejpam-1979	178	22	=	=	SYM
ejpam-1979	178	23	1	1	NUM
ejpam-1979	178	24	k0	k0	PROPN
ejpam-1979	178	25	,	,	PUNCT
ejpam-1979	178	26	ρ0	ρ0	PROPN
ejpam-1979	178	27	=	=	SYM
ejpam-1979	178	28	1	1	NUM
ejpam-1979	178	29	k0	k0	PROPN
ejpam-1979	178	30	,	,	PUNCT
ejpam-1979	178	31	and	and	CCONJ
ejpam-1979	178	32	ω0	ω0	ADV
ejpam-1979	178	33	=	=	SYM
ejpam-1979	178	34	1	1	NUM
ejpam-1979	178	35	r0−εt0	r0−εt0	NOUN
ejpam-1979	178	36	εt0εn10	εt0εn10	PROPN
ejpam-1979	178	37	k0	k0	PROPN
ejpam-1979	178	38	.	.	PUNCT
ejpam-1979	179	1	proof	proof	NOUN
ejpam-1979	179	2	.	.	PUNCT
ejpam-1979	180	1	if	if	SCONJ
ejpam-1979	180	2	g	g	PROPN
ejpam-1979	180	3	(	(	PUNCT
ejpam-1979	180	4	0	0	NUM
ejpam-1979	180	5	)	)	PUNCT
ejpam-1979	180	6	=	=	SYM
ejpam-1979	180	7	0	0	PUNCT
ejpam-1979	181	1	then	then	ADV
ejpam-1979	181	2	β	β	X
ejpam-1979	181	3	(	(	PUNCT
ejpam-1979	181	4	0)−m	0)−m	NUM
ejpam-1979	181	5	,	,	PUNCT
ejpam-1979	181	6	β	β	X
ejpam-1979	181	7	(	(	PUNCT
ejpam-1979	181	8	0)−m	0)−m	NUM
ejpam-1979	181	9	�	�	PROPN
ejpam-1979	181	10	=	=	SYM
ejpam-1979	181	11	r2	r2	PROPN
ejpam-1979	181	12	.	.	PUNCT
ejpam-1979	182	1	by	by	ADP
ejpam-1979	182	2	differentiating	differentiate	VERB
ejpam-1979	182	3	this	this	DET
ejpam-1979	182	4	equation	equation	NOUN
ejpam-1979	182	5	,	,	PUNCT
ejpam-1979	182	6	we	we	PRON
ejpam-1979	182	7	get	get	VERB
ejpam-1979	182	8	g	g	NOUN
ejpam-1979	182	9	′	′	NUM
ejpam-1979	182	10	(	(	PUNCT
ejpam-1979	182	11	0	0	NUM
ejpam-1979	182	12	)	)	PUNCT
ejpam-1979	182	13	=	=	SYM
ejpam-1979	182	14	0	0	NUM
ejpam-1979	182	15	and	and	CCONJ
ejpam-1979	182	16	g	g	NOUN
ejpam-1979	182	17	′	′	NOUN
ejpam-1979	182	18	=	=	SYM
ejpam-1979	182	19	2	2	NUM
ejpam-1979	182	20	�	�	PROPN
ejpam-1979	182	21	β	β	X
ejpam-1979	182	22	′	′	NUM
ejpam-1979	182	23	(	(	PUNCT
ejpam-1979	182	24	0	0	NUM
ejpam-1979	182	25	)	)	PUNCT
ejpam-1979	182	26	,	,	PUNCT
ejpam-1979	182	27	β	β	X
ejpam-1979	182	28	(	(	PUNCT
ejpam-1979	182	29	0)−m	0)−m	NUM
ejpam-1979	182	30	�	�	PROPN
ejpam-1979	182	31	�	�	PROPN
ejpam-1979	182	32	=	=	SYM
ejpam-1979	182	33	0	0	PROPN
ejpam-1979	182	34	.	.	PUNCT
ejpam-1979	183	1	because	because	SCONJ
ejpam-1979	183	2	of	of	ADP
ejpam-1979	183	3	this	this	PRON
ejpam-1979	183	4	,	,	PUNCT
ejpam-1979	183	5	we	we	PRON
ejpam-1979	183	6	can	can	AUX
ejpam-1979	183	7	write	write	VERB
ejpam-1979	183	8	t0,β	t0,β	PROPN
ejpam-1979	183	9	(	(	PUNCT
ejpam-1979	183	10	0)−m	0)−m	NUM
ejpam-1979	183	11	�	�	PROPN
ejpam-1979	183	12	=	=	SYM
ejpam-1979	183	13	0	0	PROPN
ejpam-1979	183	14	.	.	PUNCT
ejpam-1979	184	1	(	(	PUNCT
ejpam-1979	184	2	7	7	X
ejpam-1979	184	3	)	)	PUNCT
ejpam-1979	184	4	similarly	similarly	ADV
ejpam-1979	184	5	we	we	PRON
ejpam-1979	184	6	can	can	AUX
ejpam-1979	184	7	get	get	VERB
ejpam-1979	184	8	g	g	NOUN
ejpam-1979	184	9	′′	′′	PROPN
ejpam-1979	184	10	(	(	PUNCT
ejpam-1979	184	11	0	0	NUM
ejpam-1979	184	12	)	)	PUNCT
ejpam-1979	184	13	=	=	SYM
ejpam-1979	184	14	2	2	NUM
ejpam-1979	184	15	�	�	PROPN
ejpam-1979	184	16	β	β	X
ejpam-1979	184	17	′′	′′	PROPN
ejpam-1979	184	18	(	(	PUNCT
ejpam-1979	184	19	0	0	NUM
ejpam-1979	184	20	)	)	PUNCT
ejpam-1979	184	21	,	,	PUNCT
ejpam-1979	184	22	β	β	X
ejpam-1979	184	23	(	(	PUNCT
ejpam-1979	184	24	0)−m	0)−m	NUM
ejpam-1979	184	25	�	�	PROPN
ejpam-1979	184	26	+	+	NUM
ejpam-1979	184	27	β	β	X
ejpam-1979	184	28	′	′	NUM
ejpam-1979	184	29	(	(	PUNCT
ejpam-1979	184	30	0	0	NUM
ejpam-1979	184	31	)	)	PUNCT
ejpam-1979	184	32	,	,	PUNCT
ejpam-1979	184	33	β	β	X
ejpam-1979	184	34	′	′	NUM
ejpam-1979	184	35	(	(	PUNCT
ejpam-1979	184	36	0	0	NUM
ejpam-1979	184	37	)	)	PUNCT
ejpam-1979	184	38	�	�	PROPN
ejpam-1979	184	39	�	�	PROPN
ejpam-1979	184	40	=	=	SYM
ejpam-1979	184	41	0	0	NUM
ejpam-1979	184	42	and	and	CCONJ
ejpam-1979	184	43	g	g	PROPN
ejpam-1979	184	44	′′	′′	PROPN
ejpam-1979	184	45	(	(	PUNCT
ejpam-1979	184	46	0	0	NUM
ejpam-1979	184	47	)	)	PUNCT
ejpam-1979	184	48	.	.	PUNCT
ejpam-1979	185	1	by	by	ADP
ejpam-1979	185	2	taking	take	VERB
ejpam-1979	185	3	into	into	ADP
ejpam-1979	185	4	account	account	NOUN
ejpam-1979	185	5	the	the	DET
ejpam-1979	185	6	equations	equation	NOUN
ejpam-1979	185	7	(	(	PUNCT
ejpam-1979	185	8	2	2	NUM
ejpam-1979	185	9	)	)	PUNCT
ejpam-1979	185	10	and	and	CCONJ
ejpam-1979	185	11	using	use	VERB
ejpam-1979	185	12	the	the	DET
ejpam-1979	185	13	last	last	ADJ
ejpam-1979	185	14	equation	equation	NOUN
ejpam-1979	185	15	we	we	PRON
ejpam-1979	185	16	have	have	VERB
ejpam-1979	185	17	d	d	PROPN
ejpam-1979	185	18	εn10	εn10	PROPN
ejpam-1979	185	19	k0n10	k0n10	PROPN
ejpam-1979	185	20	,	,	PUNCT
ejpam-1979	185	21	β	β	X
ejpam-1979	185	22	(	(	PUNCT
ejpam-1979	185	23	0)−m	0)−m	NUM
ejpam-1979	185	24	e	e	PROPN
ejpam-1979	185	25	+	+	CCONJ
ejpam-1979	185	26	t0,t0	t0,t0	PROPN
ejpam-1979	185	27	�	�	PROPN
ejpam-1979	185	28	=	=	SYM
ejpam-1979	185	29	0	0	NUM
ejpam-1979	185	30	¬	¬	PROPN
ejpam-1979	185	31	n10	n10	PROPN
ejpam-1979	185	32	,	,	PUNCT
ejpam-1979	185	33	β	β	X
ejpam-1979	185	34	(	(	PUNCT
ejpam-1979	185	35	0)−m	0)−m	NUM
ejpam-1979	185	36	¶	¶	PROPN
ejpam-1979	185	37	=	=	NOUN
ejpam-1979	185	38	−	−	NOUN
ejpam-1979	185	39	εt0	εt0	NOUN
ejpam-1979	185	40	εn10	εn10	PROPN
ejpam-1979	185	41	k0	k0	PROPN
ejpam-1979	185	42	=	=	PROPN
ejpam-1979	185	43	−	−	PROPN
ejpam-1979	185	44	εt0	εt0	NOUN
ejpam-1979	185	45	εn10	εn10	PROPN
ejpam-1979	185	46	ς0	ς0	PROPN
ejpam-1979	185	47	(	(	PUNCT
ejpam-1979	185	48	8)	8)	NUM
ejpam-1979	185	49	by	by	ADP
ejpam-1979	185	50	considering	consider	VERB
ejpam-1979	185	51	g	g	PROPN
ejpam-1979	185	52	′′′	′′′	PROPN
ejpam-1979	185	53	(	(	PUNCT
ejpam-1979	185	54	0	0	NUM
ejpam-1979	185	55	)	)	PUNCT
ejpam-1979	185	56	=	=	SYM
ejpam-1979	185	57	2	2	NUM
ejpam-1979	185	58	�	�	PROPN
ejpam-1979	185	59	β	β	X
ejpam-1979	185	60	′′′	′′′	PROPN
ejpam-1979	185	61	(	(	PUNCT
ejpam-1979	185	62	0	0	NUM
ejpam-1979	185	63	)	)	PUNCT
ejpam-1979	185	64	,	,	PUNCT
ejpam-1979	185	65	β	β	X
ejpam-1979	185	66	(	(	PUNCT
ejpam-1979	185	67	0)−m	0)−m	NUM
ejpam-1979	185	68	�	�	PROPN
ejpam-1979	185	69	+	+	CCONJ
ejpam-1979	185	70	3	3	NUM
ejpam-1979	185	71	β	β	X
ejpam-1979	185	72	′′	′′	PROPN
ejpam-1979	185	73	(	(	PUNCT
ejpam-1979	185	74	0	0	NUM
ejpam-1979	185	75	)	)	PUNCT
ejpam-1979	185	76	,	,	PUNCT
ejpam-1979	185	77	β	β	X
ejpam-1979	185	78	′	′	NUM
ejpam-1979	185	79	(	(	PUNCT
ejpam-1979	185	80	0	0	NUM
ejpam-1979	185	81	)	)	PUNCT
ejpam-1979	185	82	�	�	PROPN
ejpam-1979	185	83	�	�	PROPN
ejpam-1979	185	84	=	=	SYM
ejpam-1979	185	85	0	0	NUM
ejpam-1979	185	86	and	and	CCONJ
ejpam-1979	185	87	g	g	PROPN
ejpam-1979	185	88	′′′	′′′	PROPN
ejpam-1979	185	89	(	(	PUNCT
ejpam-1979	185	90	0	0	NUM
ejpam-1979	185	91	)	)	PUNCT
ejpam-1979	185	92	=	=	SYM
ejpam-1979	185	93	0	0	NUM
ejpam-1979	185	94	and	and	CCONJ
ejpam-1979	185	95	from	from	ADP
ejpam-1979	185	96	equations	equation	NOUN
ejpam-1979	185	97	(	(	PUNCT
ejpam-1979	185	98	7	7	NUM
ejpam-1979	185	99	)	)	PUNCT
ejpam-1979	185	100	and	and	CCONJ
ejpam-1979	185	101	(	(	PUNCT
ejpam-1979	185	102	8)	8)	NUM
ejpam-1979	185	103	,	,	PUNCT
ejpam-1979	185	104	we	we	PRON
ejpam-1979	185	105	get	get	VERB
ejpam-1979	185	106	¬	¬	PROPN
ejpam-1979	185	107	n20	n20	NOUN
ejpam-1979	185	108	(	(	PUNCT
ejpam-1979	185	109	s	s	NOUN
ejpam-1979	185	110	)	)	PUNCT
ejpam-1979	185	111	,	,	PUNCT
ejpam-1979	185	112	β	β	X
ejpam-1979	185	113	(	(	PUNCT
ejpam-1979	185	114	0)−m	0)−m	NUM
ejpam-1979	185	115	¶	¶	PROPN
ejpam-1979	185	116	=	=	SYM
ejpam-1979	186	1	εt0	εt0	X
ejpam-1979	186	2	k	k	NOUN
ejpam-1979	186	3	′0	′0	VERB
ejpam-1979	186	4	εn10	εn10	PROPN
ejpam-1979	186	5	εn10	εn10	PROPN
ejpam-1979	186	6	k0k2	k0k2	PROPN
ejpam-1979	186	7	0	0	NUM
ejpam-1979	187	1	=	=	NOUN
ejpam-1979	187	2	−	−	NOUN
ejpam-1979	187	3	εt0	εt0	NOUN
ejpam-1979	187	4	εn10	εn10	PROPN
ejpam-1979	187	5	εn10	εn10	PROPN
ejpam-1979	187	6	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	187	7	.	.	PUNCT
ejpam-1979	188	1	(	(	PUNCT
ejpam-1979	188	2	9	9	NUM
ejpam-1979	188	3	)	)	PUNCT
ejpam-1979	188	4	additionally	additionally	ADV
ejpam-1979	188	5	,	,	PUNCT
ejpam-1979	188	6	we	we	PRON
ejpam-1979	188	7	obtain	obtain	VERB
ejpam-1979	188	8	g(4	g(4	NOUN
ejpam-1979	188	9	)	)	PUNCT
ejpam-1979	188	10	(	(	PUNCT
ejpam-1979	188	11	0	0	NUM
ejpam-1979	188	12	)	)	PUNCT
ejpam-1979	188	13	=	=	SYM
ejpam-1979	188	14	2	2	NUM
ejpam-1979	188	15	�	�	PROPN
ejpam-1979	188	16	¬	¬	PROPN
ejpam-1979	188	17	β	β	X
ejpam-1979	188	18	(	(	PUNCT
ejpam-1979	188	19	4	4	NUM
ejpam-1979	188	20	)	)	PUNCT
ejpam-1979	188	21	(	(	PUNCT
ejpam-1979	188	22	0	0	NUM
ejpam-1979	188	23	)	)	PUNCT
ejpam-1979	188	24	,	,	PUNCT
ejpam-1979	188	25	β	β	X
ejpam-1979	188	26	(	(	PUNCT
ejpam-1979	188	27	0)−m	0)−m	NUM
ejpam-1979	188	28	¶	¶	NOUN
ejpam-1979	188	29	+	+	CCONJ
ejpam-1979	188	30	4	4	NUM
ejpam-1979	188	31	¬	¬	PROPN
ejpam-1979	188	32	β	β	X
ejpam-1979	188	33	′′′	′′′	NOUN
ejpam-1979	188	34	(	(	PUNCT
ejpam-1979	188	35	0	0	NUM
ejpam-1979	188	36	)	)	PUNCT
ejpam-1979	188	37	,	,	PUNCT
ejpam-1979	188	38	β	β	X
ejpam-1979	188	39	′	′	NUM
ejpam-1979	188	40	(	(	PUNCT
ejpam-1979	188	41	0	0	NUM
ejpam-1979	188	42	)	)	PUNCT
ejpam-1979	188	43	¶	¶	NOUN
ejpam-1979	189	1	+	+	CCONJ
ejpam-1979	189	2	3	3	NUM
ejpam-1979	189	3	β	β	X
ejpam-1979	189	4	′′	′′	PROPN
ejpam-1979	189	5	(	(	PUNCT
ejpam-1979	189	6	0	0	NUM
ejpam-1979	189	7	)	)	PUNCT
ejpam-1979	189	8	,	,	PUNCT
ejpam-1979	189	9	β	β	X
ejpam-1979	189	10	′′	′′	PROPN
ejpam-1979	189	11	(	(	PUNCT
ejpam-1979	189	12	0	0	NUM
ejpam-1979	189	13	)	)	PUNCT
ejpam-1979	189	14	�	�	PROPN
ejpam-1979	189	15	�	�	PROPN
ejpam-1979	189	16	=	=	SYM
ejpam-1979	189	17	0	0	NUM
ejpam-1979	189	18	and	and	CCONJ
ejpam-1979	189	19	g(4	g(4	PROPN
ejpam-1979	189	20	)	)	PUNCT
ejpam-1979	189	21	(	(	PUNCT
ejpam-1979	189	22	0	0	NUM
ejpam-1979	189	23	)	)	PUNCT
ejpam-1979	189	24	=	=	SYM
ejpam-1979	189	25	0	0	NUM
ejpam-1979	189	26	where	where	SCONJ
ejpam-1979	189	27	¬	¬	PROPN
ejpam-1979	189	28	β	β	PROPN
ejpam-1979	189	29	′′′	′′′	PROPN
ejpam-1979	189	30	(	(	PUNCT
ejpam-1979	189	31	0	0	NUM
ejpam-1979	189	32	)	)	PUNCT
ejpam-1979	189	33	,	,	PUNCT
ejpam-1979	189	34	β	β	X
ejpam-1979	189	35	′	′	NUM
ejpam-1979	189	36	(	(	PUNCT
ejpam-1979	189	37	0	0	NUM
ejpam-1979	189	38	)	)	PUNCT
ejpam-1979	189	39	¶	¶	NOUN
ejpam-1979	190	1	=	=	NOUN
ejpam-1979	190	2	−εt0	−εt0	NOUN
ejpam-1979	190	3	εt0	εt0	X
ejpam-1979	190	4	k2	k2	PROPN
ejpam-1979	190	5	0	0	NUM
ejpam-1979	190	6	,	,	PUNCT
ejpam-1979	190	7	β	β	X
ejpam-1979	190	8	′′	′′	PROPN
ejpam-1979	190	9	(	(	PUNCT
ejpam-1979	190	10	0	0	NUM
ejpam-1979	190	11	)	)	PUNCT
ejpam-1979	190	12	,	,	PUNCT
ejpam-1979	190	13	β	β	X
ejpam-1979	190	14	′′	′′	PROPN
ejpam-1979	190	15	(	(	PUNCT
ejpam-1979	190	16	0	0	NUM
ejpam-1979	190	17	)	)	PUNCT
ejpam-1979	190	18	�	�	NOUN
ejpam-1979	190	19	=	=	SYM
ejpam-1979	190	20	εn10	εn10	PROPN
ejpam-1979	190	21	k2	k2	PROPN
ejpam-1979	190	22	0	0	NUM
ejpam-1979	190	23	.	.	PUNCT
ejpam-1979	191	1	so	so	ADV
ejpam-1979	191	2	we	we	PRON
ejpam-1979	191	3	have	have	VERB
ejpam-1979	191	4	¬	¬	PROPN
ejpam-1979	191	5	n30	n30	PROPN
ejpam-1979	191	6	(	(	PUNCT
ejpam-1979	191	7	s	s	NOUN
ejpam-1979	191	8	)	)	PUNCT
ejpam-1979	191	9	,	,	PUNCT
ejpam-1979	191	10	β	β	X
ejpam-1979	191	11	(	(	PUNCT
ejpam-1979	191	12	0)−m	0)−m	NUM
ejpam-1979	191	13	¶	¶	PROPN
ejpam-1979	192	1	=	=	PROPN
ejpam-1979	192	2	−ω0	−ω0	PROPN
ejpam-1979	192	3			PROPN
ejpam-1979	192	4			PROPN
ejpam-1979	192	5			NOUN
ejpam-1979	192	6	−	−	PROPN
ejpam-1979	192	7	εt0	εt0	NOUN
ejpam-1979	193	1	εn10	εn10	PROPN
ejpam-1979	193	2			AUX
ejpam-1979	193	3			ADJ
ejpam-1979	193	4			NOUN
ejpam-1979	193	5	k	k	X
ejpam-1979	193	6	′′0	′′0	VERB
ejpam-1979	193	7	ς	ς	PROPN
ejpam-1979	193	8	2	2	NUM
ejpam-1979	193	9	0ρ0−	0ρ0−	NUM
ejpam-1979	193	10	εt0	εt0	NOUN
ejpam-1979	193	11	εn10	εn10	PROPN
ejpam-1979	193	12	�	�	PROPN
ejpam-1979	193	13	ς0	ς0	VERB
ejpam-1979	193	14	ρ0	ρ0	PROPN
ejpam-1979	193	15	�	�	PROPN
ejpam-1979	193	16	−	−	PUNCT
ejpam-1979	193	17	εt0	εt0	NOUN
ejpam-1979	194	1	εn10	εn10	PROPN
ejpam-1979	194	2	ρ0	ρ0	PROPN
ejpam-1979	194	3	+2k	+2k	PRON
ejpam-1979	194	4	′0ς	′0ς	ADJ
ejpam-1979	194	5	′	′	NUM
ejpam-1979	194	6	0ρ0ς0	0ρ0ς0	NOUN
ejpam-1979	194	7	+	+	X
ejpam-1979	194	8	k′0ς	k′0ς	NOUN
ejpam-1979	194	9	′	′	NOUN
ejpam-1979	194	10	0ρ	0ρ	NOUN
ejpam-1979	194	11	2	2	NUM
ejpam-1979	194	12	0	0	NUM
ejpam-1979	195	1	+	+	CCONJ
ejpam-1979	195	2	4εt0	4εt0	NUM
ejpam-1979	195	3	�	�	NOUN
ejpam-1979	195	4	ρ0	ρ0	PROPN
ejpam-1979	195	5	ς0	ς0	PROPN
ejpam-1979	195	6	�	�	PROPN
ejpam-1979	195	7			PROPN
ejpam-1979	195	8			PROPN
ejpam-1979	195	9			PROPN
ejpam-1979	195	10	+	+	NUM
ejpam-1979	195	11	3	3	NUM
ejpam-1979	195	12	ρ0	ρ0	NOUN
ejpam-1979	195	13	ς0	ς0	PROPN
ejpam-1979	195	14			PROPN
ejpam-1979	195	15			PROPN
ejpam-1979	195	16			NOUN
ejpam-1979	195	17	.	.	PUNCT
ejpam-1979	196	1	ö.	ö.	PROPN
ejpam-1979	196	2	bektaş	bektaş	PROPN
ejpam-1979	196	3	,	,	PUNCT
ejpam-1979	196	4	n.	n.	PROPN
ejpam-1979	196	5	gürses	gürse	NOUN
ejpam-1979	196	6	,	,	PUNCT
ejpam-1979	196	7	s.	s.	PROPN
ejpam-1979	196	8	yüce	yüce	PROPN
ejpam-1979	196	9	/	/	SYM
ejpam-1979	196	10	eur	eur	PROPN
ejpam-1979	196	11	.	.	PUNCT
ejpam-1979	197	1	j.	j.	PROPN
ejpam-1979	197	2	pure	pure	PROPN
ejpam-1979	197	3	appl	appl	PROPN
ejpam-1979	197	4	.	.	PROPN
ejpam-1979	197	5	math	math	PROPN
ejpam-1979	197	6	,	,	PUNCT
ejpam-1979	197	7	7	7	NUM
ejpam-1979	197	8	(	(	PUNCT
ejpam-1979	197	9	2014	2014	NUM
ejpam-1979	197	10	)	)	PUNCT
ejpam-1979	197	11	,	,	PUNCT
ejpam-1979	197	12	86	86	NUM
ejpam-1979	197	13	-	-	SYM
ejpam-1979	197	14	96	96	NUM
ejpam-1979	197	15	94	94	NUM
ejpam-1979	197	16	the	the	DET
ejpam-1979	197	17	following	follow	VERB
ejpam-1979	197	18	two	two	NUM
ejpam-1979	197	19	statements	statement	NOUN
ejpam-1979	197	20	are	be	AUX
ejpam-1979	197	21	found	find	VERB
ejpam-1979	197	22	such	such	ADJ
ejpam-1979	197	23	that	that	PRON
ejpam-1979	197	24	¬	¬	PROPN
ejpam-1979	197	25	n30	n30	PROPN
ejpam-1979	197	26	(	(	PUNCT
ejpam-1979	197	27	s	s	NOUN
ejpam-1979	197	28	)	)	PUNCT
ejpam-1979	197	29	,	,	PUNCT
ejpam-1979	197	30	β	β	X
ejpam-1979	197	31	(	(	PUNCT
ejpam-1979	197	32	0)−m	0)−m	NUM
ejpam-1979	197	33	¶	¶	PROPN
ejpam-1979	197	34	=	=	PROPN
ejpam-1979	197	35	−ω0	−ω0	PROPN
ejpam-1979	197	36	�	�	PROPN
ejpam-1979	197	37	−	−	X
ejpam-1979	197	38	εt0	εt0	NOUN
ejpam-1979	198	1	εn10	εn10	PROPN
ejpam-1979	198	2			VERB
ejpam-1979	198	3			ADJ
ejpam-1979	198	4			NUM
ejpam-1979	198	5	2	2	NUM
ejpam-1979	198	6	�	�	PROPN
ejpam-1979	198	7	ς′0	ς′0	PROPN
ejpam-1979	198	8	�	�	PROPN
ejpam-1979	198	9	2	2	NUM
ejpam-1979	198	10	ρ0	ρ0	PROPN
ejpam-1979	198	11	ς0	ς0	PROPN
ejpam-1979	198	12	−	−	PROPN
ejpam-1979	198	13	ς′′0ρ0−	ς′′0ρ0−	NOUN
ejpam-1979	198	14	εt0	εt0	NOUN
ejpam-1979	198	15	εn10	εn10	PROPN
ejpam-1979	198	16	�	�	PROPN
ejpam-1979	198	17	ς0	ς0	VERB
ejpam-1979	198	18	ρ0	ρ0	PROPN
ejpam-1979	198	19	�	�	PROPN
ejpam-1979	199	1	−	−	PUNCT
ejpam-1979	200	1	εt0	εt0	NOUN
ejpam-1979	201	1	εn10	εn10	PROPN
ejpam-1979	201	2	ρ0	ρ0	PROPN
ejpam-1979	201	3	−2	−2	PROPN
ejpam-1979	201	4	�	�	PROPN
ejpam-1979	201	5	ς′0	ς′0	PROPN
ejpam-1979	201	6	�	�	PROPN
ejpam-1979	201	7	2	2	NUM
ejpam-1979	201	8	ρ0	ρ0	PROPN
ejpam-1979	201	9	ς0	ς0	PROPN
ejpam-1979	201	10	−	−	PROPN
ejpam-1979	201	11	ς′0ρ	ς′0ρ	PROPN
ejpam-1979	201	12	′	′	NUM
ejpam-1979	201	13	0	0	NUM
ejpam-1979	202	1	+	+	NUM
ejpam-1979	202	2	4εt0	4εt0	NUM
ejpam-1979	202	3	�	�	NOUN
ejpam-1979	202	4	ρ0	ρ0	PROPN
ejpam-1979	202	5	ς0	ς0	PROPN
ejpam-1979	202	6	�	�	PROPN
ejpam-1979	202	7			PROPN
ejpam-1979	202	8			PROPN
ejpam-1979	202	9			PROPN
ejpam-1979	202	10	+	+	NUM
ejpam-1979	202	11	3	3	NUM
ejpam-1979	202	12	ρ0	ρ0	PROPN
ejpam-1979	202	13	ς0	ς0	PROPN
ejpam-1979	202	14	�	�	PROPN
ejpam-1979	202	15	and	and	CCONJ
ejpam-1979	202	16	¬	¬	PROPN
ejpam-1979	202	17	n30	n30	PROPN
ejpam-1979	202	18	(	(	PUNCT
ejpam-1979	202	19	s	s	NOUN
ejpam-1979	202	20	)	)	PUNCT
ejpam-1979	202	21	,	,	PUNCT
ejpam-1979	202	22	β	β	X
ejpam-1979	202	23	(	(	PUNCT
ejpam-1979	202	24	0)−m	0)−m	NUM
ejpam-1979	202	25	¶	¶	PROPN
ejpam-1979	202	26	=	=	PROPN
ejpam-1979	202	27	−ω0	−ω0	PROPN
ejpam-1979	202	28	�	�	PROPN
ejpam-1979	202	29	εt0	εt0	NOUN
ejpam-1979	202	30	εn10	εn10	PROPN
ejpam-1979	202	31	�	�	PROPN
ejpam-1979	202	32	�	�	PROPN
ejpam-1979	202	33	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	202	34	�	�	PROPN
ejpam-1979	202	35	′	′	PROPN
ejpam-1979	202	36	+	+	CCONJ
ejpam-1979	202	37	εt0	εt0	X
ejpam-1979	202	38	�	�	NOUN
ejpam-1979	202	39	εn10	εn10	PROPN
ejpam-1979	202	40	�	�	PROPN
ejpam-1979	202	41	ς0	ς0	VERB
ejpam-1979	202	42	ρ0	ρ0	PROPN
ejpam-1979	202	43	�	�	PROPN
ejpam-1979	203	1	−	−	PROPN
ejpam-1979	204	1	εn10	εn10	PROPN
ejpam-1979	204	2	ρ0−	ρ0−	PROPN
ejpam-1979	204	3	4	4	NUM
ejpam-1979	204	4	�	�	PROPN
ejpam-1979	204	5	ρ0	ρ0	PROPN
ejpam-1979	204	6	ς0	ς0	PROPN
ejpam-1979	204	7	�	�	PROPN
ejpam-1979	204	8	�	�	PROPN
ejpam-1979	204	9	+	+	CCONJ
ejpam-1979	204	10	3	3	NUM
ejpam-1979	204	11	εt0	εt0	NOUN
ejpam-1979	204	12	εn10	εn10	PROPN
ejpam-1979	204	13	�	�	PROPN
ejpam-1979	205	1	ρ0	ρ0	PROPN
ejpam-1979	205	2	ς0	ς0	PROPN
ejpam-1979	205	3	�	�	PROPN
ejpam-1979	205	4	�	�	PROPN
ejpam-1979	205	5	�	�	PROPN
ejpam-1979	205	6	(	(	PUNCT
ejpam-1979	205	7	10	10	NUM
ejpam-1979	205	8	)	)	PUNCT
ejpam-1979	205	9	furthermore	furthermore	ADV
ejpam-1979	205	10	,	,	PUNCT
ejpam-1979	205	11	let	let	VERB
ejpam-1979	205	12	take	take	VERB
ejpam-1979	205	13	the	the	DET
ejpam-1979	205	14	numbers	number	NOUN
ejpam-1979	205	15	ω1	ω1	PROPN
ejpam-1979	205	16	,	,	PUNCT
ejpam-1979	205	17	ω2	ω2	ADJ
ejpam-1979	205	18	,	,	PUNCT
ejpam-1979	205	19	ω3	ω3	NOUN
ejpam-1979	205	20	and	and	CCONJ
ejpam-1979	205	21	ω4	ω4	NUM
ejpam-1979	205	22	such	such	ADJ
ejpam-1979	205	23	that	that	SCONJ
ejpam-1979	205	24	β	β	X
ejpam-1979	205	25	(	(	PUNCT
ejpam-1979	205	26	0)−m	0)−m	NUM
ejpam-1979	205	27	=	=	X
ejpam-1979	205	28	ω1t0+ω2n10	ω1t0+ω2n10	X
ejpam-1979	205	29	+	+	ADJ
ejpam-1979	205	30	ω3n20	ω3n20	ADJ
ejpam-1979	205	31	+	+	ADJ
ejpam-1979	205	32	ω4n30	ω4n30	NOUN
ejpam-1979	205	33	.	.	PUNCT
ejpam-1979	206	1	from	from	ADP
ejpam-1979	206	2	t0,β	t0,β	PROPN
ejpam-1979	206	3	(	(	PUNCT
ejpam-1979	206	4	0)−m	0)−m	NUM
ejpam-1979	206	5	�	�	PROPN
ejpam-1979	206	6	=	=	SYM
ejpam-1979	206	7	ω1	ω1	PROPN
ejpam-1979	206	8	and	and	CCONJ
ejpam-1979	206	9	by	by	ADP
ejpam-1979	206	10	using	use	VERB
ejpam-1979	206	11	the	the	DET
ejpam-1979	206	12	equation	equation	NOUN
ejpam-1979	206	13	(	(	PUNCT
ejpam-1979	206	14	7	7	X
ejpam-1979	206	15	)	)	PUNCT
ejpam-1979	206	16	we	we	PRON
ejpam-1979	206	17	obtain	obtain	VERB
ejpam-1979	206	18	ω1	ω1	PROPN
ejpam-1979	206	19	=	=	SYM
ejpam-1979	206	20	0	0	NUM
ejpam-1979	206	21	.	.	PUNCT
ejpam-1979	207	1	similarly	similarly	ADV
ejpam-1979	207	2	,	,	PUNCT
ejpam-1979	207	3	using	use	VERB
ejpam-1979	207	4	the	the	DET
ejpam-1979	207	5	equations	equation	NOUN
ejpam-1979	207	6	(	(	PUNCT
ejpam-1979	207	7	8)	8)	NUM
ejpam-1979	207	8	,	,	PUNCT
ejpam-1979	207	9	(	(	PUNCT
ejpam-1979	207	10	9	9	NUM
ejpam-1979	207	11	)	)	PUNCT
ejpam-1979	207	12	,	,	PUNCT
ejpam-1979	207	13	and	and	CCONJ
ejpam-1979	207	14	(	(	PUNCT
ejpam-1979	207	15	10	10	NUM
ejpam-1979	207	16	)	)	PUNCT
ejpam-1979	207	17	we	we	PRON
ejpam-1979	207	18	get	get	VERB
ejpam-1979	207	19	ω2	ω2	ADJ
ejpam-1979	208	1	=	=	NOUN
ejpam-1979	208	2	−	−	NOUN
ejpam-1979	209	1	εt0	εt0	NOUN
ejpam-1979	209	2	εn10	εn10	PROPN
ejpam-1979	209	3	ς0	ς0	PROPN
ejpam-1979	209	4	,	,	PUNCT
ejpam-1979	209	5	ω3	ω3	NOUN
ejpam-1979	209	6	=	=	NOUN
ejpam-1979	209	7	−	−	X
ejpam-1979	209	8	εt0	εt0	NOUN
ejpam-1979	209	9	εn10	εn10	PROPN
ejpam-1979	209	10	εn10	εn10	PROPN
ejpam-1979	209	11	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	209	12	,	,	PUNCT
ejpam-1979	209	13	and	and	CCONJ
ejpam-1979	209	14	ω4	ω4	NUM
ejpam-1979	209	15	=	=	SYM
ejpam-1979	209	16	−ω0	−ω0	PROPN
ejpam-1979	209	17	�	�	PROPN
ejpam-1979	209	18	εt0	εt0	NOUN
ejpam-1979	209	19	εn10	εn10	PROPN
ejpam-1979	209	20	�	�	PROPN
ejpam-1979	209	21	�	�	PROPN
ejpam-1979	209	22	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	209	23	�	�	PROPN
ejpam-1979	209	24	′	′	PROPN
ejpam-1979	210	1	+	+	CCONJ
ejpam-1979	210	2	εt0	εt0	X
ejpam-1979	210	3	�	�	NOUN
ejpam-1979	210	4	εn10	εn10	PROPN
ejpam-1979	210	5	�	�	PROPN
ejpam-1979	210	6	ς0	ς0	VERB
ejpam-1979	210	7	ρ0	ρ0	PROPN
ejpam-1979	210	8	�	�	PROPN
ejpam-1979	211	1	−	−	PROPN
ejpam-1979	212	1	εn10	εn10	PROPN
ejpam-1979	212	2	ρ0−	ρ0−	PROPN
ejpam-1979	212	3	4	4	NUM
ejpam-1979	212	4	�	�	PROPN
ejpam-1979	212	5	ρ0	ρ0	PROPN
ejpam-1979	212	6	ς0	ς0	PROPN
ejpam-1979	212	7	�	�	PROPN
ejpam-1979	212	8	�	�	PROPN
ejpam-1979	212	9	+	+	CCONJ
ejpam-1979	212	10	3	3	NUM
ejpam-1979	212	11	εt0	εt0	NOUN
ejpam-1979	212	12	εn10	εn10	PROPN
ejpam-1979	212	13	�	�	PROPN
ejpam-1979	213	1	ρ0	ρ0	PROPN
ejpam-1979	213	2	ς0	ς0	PROPN
ejpam-1979	213	3	�	�	PROPN
ejpam-1979	213	4	�	�	PROPN
ejpam-1979	213	5	�	�	PROPN
ejpam-1979	213	6	.	.	PUNCT
ejpam-1979	214	1	also	also	ADV
ejpam-1979	214	2	the	the	DET
ejpam-1979	214	3	origin	origin	NOUN
ejpam-1979	214	4	of	of	ADP
ejpam-1979	214	5	the	the	DET
ejpam-1979	214	6	sphere	sphere	NOUN
ejpam-1979	214	7	that	that	SCONJ
ejpam-1979	214	8	contacts	contact	NOUN
ejpam-1979	214	9	at	at	ADP
ejpam-1979	214	10	the	the	DET
ejpam-1979	214	11	fourth	fourth	ADJ
ejpam-1979	214	12	order	order	NOUN
ejpam-1979	214	13	to	to	ADP
ejpam-1979	214	14	the	the	DET
ejpam-1979	214	15	curve	curve	NOUN
ejpam-1979	214	16	at	at	ADP
ejpam-1979	214	17	the	the	DET
ejpam-1979	214	18	point	point	NOUN
ejpam-1979	214	19	β	β	X
ejpam-1979	214	20	(	(	PUNCT
ejpam-1979	214	21	0	0	NUM
ejpam-1979	214	22	)	)	PUNCT
ejpam-1979	214	23	is	be	AUX
ejpam-1979	214	24	m	m	NOUN
ejpam-1979	214	25	=	=	ADJ
ejpam-1979	214	26	β	β	X
ejpam-1979	214	27	(	(	PUNCT
ejpam-1979	214	28	0)−ω1t0−ω2n10	0)−ω1t0−ω2n10	NUM
ejpam-1979	214	29	−ω3n20	−ω3n20	PROPN
ejpam-1979	214	30	−ω4n30	−ω4n30	PROPN
ejpam-1979	214	31	.	.	PUNCT
ejpam-1979	215	1	let	let	VERB
ejpam-1979	215	2	p	p	PRON
ejpam-1979	215	3	be	be	AUX
ejpam-1979	215	4	a	a	DET
ejpam-1979	215	5	semi	semi	ADJ
ejpam-1979	215	6	quaternionic	quaternionic	ADJ
ejpam-1979	215	7	variable	variable	NOUN
ejpam-1979	215	8	on	on	ADP
ejpam-1979	215	9	semi	semi	ADJ
ejpam-1979	215	10	quaternionic	quaternionic	ADJ
ejpam-1979	215	11	osculating	osculating	NOUN
ejpam-1979	215	12	sphere	sphere	NOUN
ejpam-1979	215	13	,	,	PUNCT
ejpam-1979	215	14	assume	assume	VERB
ejpam-1979	215	15	p	p	X
ejpam-1979	215	16	=	=	PUNCT
ejpam-1979	215	17	β	β	X
ejpam-1979	215	18	(	(	PUNCT
ejpam-1979	215	19	0	0	NUM
ejpam-1979	215	20	)	)	PUNCT
ejpam-1979	216	1	+	+	NOUN
ejpam-1979	217	1	x1t0	x1t0	PUNCT
ejpam-1979	217	2	+	+	NOUN
ejpam-1979	217	3	x2n10	x2n10	X
ejpam-1979	218	1	+	+	CCONJ
ejpam-1979	218	2	x3n20	x3n20	PROPN
ejpam-1979	218	3	+	+	CCONJ
ejpam-1979	218	4	x4n30	x4n30	PROPN
ejpam-1979	218	5	.	.	PUNCT
ejpam-1979	219	1	then	then	ADV
ejpam-1979	219	2	we	we	PRON
ejpam-1979	219	3	can	can	AUX
ejpam-1979	219	4	write	write	VERB
ejpam-1979	219	5	p	p	PRON
ejpam-1979	219	6	−m	−m	NOUN
ejpam-1979	219	7	=	=	SYM
ejpam-1979	219	8	x1t0	x1t0	PROPN
ejpam-1979	219	9	+	+	NOUN
ejpam-1979	219	10	x2−	x2−	PROPN
ejpam-1979	219	11	εt0	εt0	NOUN
ejpam-1979	220	1	εn10	εn10	PROPN
ejpam-1979	220	2	ς0	ς0	PROPN
ejpam-1979	220	3	!	!	PUNCT
ejpam-1979	221	1	n10	n10	PROPN
ejpam-1979	222	1	+	+	CCONJ
ejpam-1979	222	2	x3−	x3−	PROPN
ejpam-1979	222	3	εt0	εt0	NOUN
ejpam-1979	222	4	εn10	εn10	PROPN
ejpam-1979	222	5	εn10	εn10	PROPN
ejpam-1979	222	6	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	222	7	!	!	PUNCT
ejpam-1979	223	1	n20	n20	NOUN
ejpam-1979	223	2	+	+	CCONJ
ejpam-1979	223	3	�	�	PROPN
ejpam-1979	223	4	x4−ω0	x4−ω0	SYM
ejpam-1979	223	5	�	�	PROPN
ejpam-1979	223	6	εt0	εt0	NOUN
ejpam-1979	223	7	εn10	εn10	PROPN
ejpam-1979	223	8	�	�	PROPN
ejpam-1979	223	9	�	�	PROPN
ejpam-1979	223	10	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	223	11	�	�	PROPN
ejpam-1979	223	12	′	′	PROPN
ejpam-1979	224	1	+	+	CCONJ
ejpam-1979	224	2	εt0	εt0	X
ejpam-1979	224	3	�	�	NOUN
ejpam-1979	224	4	εn10	εn10	PROPN
ejpam-1979	224	5	�	�	PROPN
ejpam-1979	224	6	ς0	ς0	VERB
ejpam-1979	224	7	ρ0	ρ0	PROPN
ejpam-1979	224	8	�	�	PROPN
ejpam-1979	225	1	−	−	PROPN
ejpam-1979	226	1	εn10	εn10	PROPN
ejpam-1979	226	2	ρ0	ρ0	PROPN
ejpam-1979	226	3	−	−	PROPN
ejpam-1979	226	4	4	4	NUM
ejpam-1979	226	5	�	�	NOUN
ejpam-1979	226	6	ρ0	ρ0	PROPN
ejpam-1979	226	7	ς0	ς0	PROPN
ejpam-1979	226	8	�	�	PROPN
ejpam-1979	226	9	�	�	PROPN
ejpam-1979	226	10	+	+	CCONJ
ejpam-1979	226	11	3	3	NUM
ejpam-1979	226	12	εt0	εt0	NOUN
ejpam-1979	226	13	εn10	εn10	PROPN
ejpam-1979	226	14	�	�	PROPN
ejpam-1979	226	15	ρ0	ρ0	PROPN
ejpam-1979	226	16	ς0	ς0	PROPN
ejpam-1979	226	17	�	�	PROPN
ejpam-1979	226	18	�	�	PROPN
ejpam-1979	226	19	�	�	PROPN
ejpam-1979	226	20	�	�	PROPN
ejpam-1979	226	21	n30	n30	PROPN
ejpam-1979	226	22	.	.	PUNCT
ejpam-1979	227	1	from	from	ADP
ejpam-1979	227	2	the	the	DET
ejpam-1979	227	3	last	last	ADJ
ejpam-1979	227	4	equation	equation	NOUN
ejpam-1979	227	5	,	,	PUNCT
ejpam-1979	227	6	we	we	PRON
ejpam-1979	227	7	get	get	VERB
ejpam-1979	227	8	〈	〈	PROPN
ejpam-1979	227	9	p	p	NOUN
ejpam-1979	227	10	−m	−m	NOUN
ejpam-1979	227	11	,	,	PUNCT
ejpam-1979	227	12	p	p	NOUN
ejpam-1979	227	13	−m〉=εt0	−m〉=εt0	NOUN
ejpam-1979	227	14	x	x	SYM
ejpam-1979	227	15	2	2	NUM
ejpam-1979	227	16	1	1	NUM
ejpam-1979	227	17	+	+	CCONJ
ejpam-1979	228	1	εn10	εn10	PROPN
ejpam-1979	228	2	x2−	x2−	PROPN
ejpam-1979	228	3	εt0	εt0	NOUN
ejpam-1979	228	4	εn10	εn10	PROPN
ejpam-1979	228	5	ς0	ς0	PROPN
ejpam-1979	228	6	!	!	PUNCT
ejpam-1979	228	7	2	2	NUM
ejpam-1979	229	1	+	+	CCONJ
ejpam-1979	229	2	εn20	εn20	PROPN
ejpam-1979	229	3	x3−	x3−	PROPN
ejpam-1979	229	4	εt0	εt0	NOUN
ejpam-1979	229	5	εn10	εn10	PROPN
ejpam-1979	229	6	εn10	εn10	PROPN
ejpam-1979	229	7	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	229	8	!	!	PUNCT
ejpam-1979	230	1	2	2	NUM
ejpam-1979	230	2	references	reference	NOUN
ejpam-1979	230	3	95	95	NUM
ejpam-1979	230	4	+	+	NUM
ejpam-1979	230	5	εn30	εn30	PROPN
ejpam-1979	230	6	�	�	PROPN
ejpam-1979	230	7	x4−ω0	x4−ω0	X
ejpam-1979	230	8	�	�	PROPN
ejpam-1979	230	9	εt0	εt0	NOUN
ejpam-1979	230	10	εn10	εn10	PROPN
ejpam-1979	230	11	�	�	PROPN
ejpam-1979	230	12	�	�	PROPN
ejpam-1979	230	13	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	230	14	�	�	PROPN
ejpam-1979	230	15	′	′	PROPN
ejpam-1979	230	16	+	+	CCONJ
ejpam-1979	230	17	εt0	εt0	X
ejpam-1979	230	18	�	�	NOUN
ejpam-1979	230	19	εn10	εn10	PROPN
ejpam-1979	230	20	�	�	PROPN
ejpam-1979	230	21	ς0	ς0	VERB
ejpam-1979	230	22	ρ0	ρ0	PROPN
ejpam-1979	230	23	�	�	PROPN
ejpam-1979	231	1	−	−	PROPN
ejpam-1979	232	1	εn10	εn10	PROPN
ejpam-1979	232	2	ρ0	ρ0	PROPN
ejpam-1979	232	3	−	−	PROPN
ejpam-1979	232	4	4	4	NUM
ejpam-1979	232	5	�	�	NOUN
ejpam-1979	232	6	ρ0	ρ0	PROPN
ejpam-1979	232	7	ς0	ς0	PROPN
ejpam-1979	232	8	�	�	PROPN
ejpam-1979	232	9	�	�	PROPN
ejpam-1979	232	10	+	+	CCONJ
ejpam-1979	232	11	3	3	NUM
ejpam-1979	232	12	εt0	εt0	NOUN
ejpam-1979	232	13	εn10	εn10	PROPN
ejpam-1979	232	14	�	�	PROPN
ejpam-1979	232	15	ρ0	ρ0	PROPN
ejpam-1979	232	16	ς0	ς0	PROPN
ejpam-1979	232	17	�	�	PROPN
ejpam-1979	232	18	�	�	PROPN
ejpam-1979	232	19	�	�	PROPN
ejpam-1979	232	20	�	�	NOUN
ejpam-1979	232	21	2	2	NUM
ejpam-1979	232	22	and	and	CCONJ
ejpam-1979	232	23	from	from	ADP
ejpam-1979	232	24	the	the	DET
ejpam-1979	232	25	equation	equation	NOUN
ejpam-1979	232	26	(	(	PUNCT
ejpam-1979	232	27	10	10	NUM
ejpam-1979	232	28	)	)	PUNCT
ejpam-1979	232	29	we	we	PRON
ejpam-1979	232	30	finally	finally	ADV
ejpam-1979	232	31	calculate	calculate	VERB
ejpam-1979	232	32	the	the	DET
ejpam-1979	232	33	equation	equation	NOUN
ejpam-1979	232	34	of	of	ADP
ejpam-1979	232	35	the	the	DET
ejpam-1979	232	36	semi	semi	ADJ
ejpam-1979	232	37	real	real	ADJ
ejpam-1979	232	38	quaternionic	quaternionic	ADJ
ejpam-1979	232	39	osculating	osculating	NOUN
ejpam-1979	232	40	sphere	sphere	NOUN
ejpam-1979	232	41	in	in	ADP
ejpam-1979	232	42	e4	e4	PROPN
ejpam-1979	232	43	2	2	NUM
ejpam-1979	232	44	such	such	ADJ
ejpam-1979	232	45	that	that	DET
ejpam-1979	232	46	r2	r2	NOUN
ejpam-1979	232	47	=	=	PUNCT
ejpam-1979	232	48	β	β	X
ejpam-1979	232	49	(	(	PUNCT
ejpam-1979	232	50	0)−m	0)−m	NUM
ejpam-1979	232	51	,	,	PUNCT
ejpam-1979	233	1	β	β	X
ejpam-1979	233	2	(	(	PUNCT
ejpam-1979	233	3	0)−m	0)−m	NUM
ejpam-1979	233	4	�	�	PROPN
ejpam-1979	233	5	=	=	SYM
ejpam-1979	234	1	εn10	εn10	PROPN
ejpam-1979	234	2	ς2	ς2	PROPN
ejpam-1979	234	3	0	0	NUM
ejpam-1979	235	1	+	+	NUM
ejpam-1979	235	2	εn20	εn20	PROPN
ejpam-1979	235	3	�	�	PROPN
ejpam-1979	235	4	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	235	5	�	�	PROPN
ejpam-1979	235	6	2	2	NUM
ejpam-1979	235	7	+	+	CCONJ
ejpam-1979	235	8	εn30	εn30	PROPN
ejpam-1979	235	9	(	(	PUNCT
ejpam-1979	235	10	ω2	ω2	ADJ
ejpam-1979	235	11	0	0	NUM
ejpam-1979	235	12			PROPN
ejpam-1979	235	13			NUM
ejpam-1979	235	14	�	�	PROPN
ejpam-1979	235	15	ς′0ρ0	ς′0ρ0	PROPN
ejpam-1979	235	16	�	�	PROPN
ejpam-1979	235	17	′	′	PROPN
ejpam-1979	236	1	+	+	CCONJ
ejpam-1979	236	2	εt0	εt0	X
ejpam-1979	236	3	�	�	NOUN
ejpam-1979	236	4	εn10	εn10	PROPN
ejpam-1979	236	5	�	�	PROPN
ejpam-1979	236	6	ς0	ς0	VERB
ejpam-1979	236	7	ρ0	ρ0	PROPN
ejpam-1979	236	8	�	�	PROPN
ejpam-1979	237	1	−	−	PROPN
ejpam-1979	238	1	εn10	εn10	PROPN
ejpam-1979	238	2	ρ0−	ρ0−	PROPN
ejpam-1979	238	3	4	4	NUM
ejpam-1979	238	4	�	�	PROPN
ejpam-1979	238	5	ρ0	ρ0	PROPN
ejpam-1979	238	6	ς0	ς0	PROPN
ejpam-1979	238	7	�	�	PROPN
ejpam-1979	238	8	�	�	PROPN
ejpam-1979	238	9	+	+	CCONJ
ejpam-1979	238	10	3	3	NUM
ejpam-1979	238	11	εt0	εt0	NOUN
ejpam-1979	238	12	εn10	εn10	PROPN
ejpam-1979	238	13	�	�	PROPN
ejpam-1979	239	1	ρ0	ρ0	PROPN
ejpam-1979	239	2	ς0	ς0	PROPN
ejpam-1979	239	3	�	�	PROPN
ejpam-1979	239	4			PROPN
ejpam-1979	239	5			PROPN
ejpam-1979	239	6	)	)	PUNCT
ejpam-1979	239	7	.	.	PUNCT
ejpam-1979	240	1	this	this	PRON
ejpam-1979	240	2	completes	complete	VERB
ejpam-1979	240	3	proof	proof	NOUN
ejpam-1979	240	4	.	.	PUNCT
ejpam-1979	241	1	acknowledgements	acknowledgement	NOUN
ejpam-1979	241	2	the	the	DET
ejpam-1979	241	3	authors	author	NOUN
ejpam-1979	241	4	thank	thank	VERB
ejpam-1979	241	5	the	the	DET
ejpam-1979	241	6	readers	reader	NOUN
ejpam-1979	241	7	of	of	ADP
ejpam-1979	241	8	european	european	PROPN
ejpam-1979	241	9	journal	journal	PROPN
ejpam-1979	241	10	of	of	ADP
ejpam-1979	241	11	pure	pure	ADJ
ejpam-1979	241	12	and	and	CCONJ
ejpam-1979	241	13	applied	applied	ADJ
ejpam-1979	241	14	mathematics	mathematic	NOUN
ejpam-1979	241	15	,	,	PUNCT
ejpam-1979	241	16	for	for	ADP
ejpam-1979	241	17	making	make	VERB
ejpam-1979	241	18	our	our	PRON
ejpam-1979	241	19	journal	journal	NOUN
ejpam-1979	241	20	successful	successful	ADJ
ejpam-1979	241	21	.	.	PUNCT
ejpam-1979	242	1	references	reference	NOUN
ejpam-1979	242	2	[	[	X
ejpam-1979	242	3	1	1	NUM
ejpam-1979	242	4	]	]	PUNCT
ejpam-1979	242	5	w.	w.	PROPN
ejpam-1979	242	6	k.	k.	PROPN
ejpam-1979	242	7	clifford	clifford	PROPN
ejpam-1979	242	8	.	.	PUNCT
ejpam-1979	243	1	preliminary	preliminary	ADJ
ejpam-1979	243	2	sketch	sketch	NOUN
ejpam-1979	243	3	of	of	ADP
ejpam-1979	243	4	biquaternions	biquaternion	NOUN
ejpam-1979	243	5	,	,	PUNCT
ejpam-1979	243	6	proceedings	proceeding	NOUN
ejpam-1979	243	7	of	of	ADP
ejpam-1979	243	8	the	the	DET
ejpam-1979	243	9	london	london	PROPN
ejpam-1979	243	10	mathematical	mathematical	ADJ
ejpam-1979	243	11	society	society	NOUN
ejpam-1979	243	12	,	,	PUNCT
ejpam-1979	243	13	4	4	NUM
ejpam-1979	243	14	,	,	PUNCT
ejpam-1979	243	15	361	361	NUM
ejpam-1979	243	16	-	-	SYM
ejpam-1979	243	17	395	395	NUM
ejpam-1979	243	18	,	,	PUNCT
ejpam-1979	243	19	1873	1873	NUM
ejpam-1979	243	20	.	.	PUNCT
ejpam-1979	244	1	[	[	X
ejpam-1979	244	2	2	2	NUM
ejpam-1979	244	3	]	]	PUNCT
ejpam-1979	244	4	a.	a.	NOUN
ejpam-1979	244	5	c.	c.	PROPN
ejpam-1979	244	6	çöken	çöken	VERB
ejpam-1979	244	7	and	and	CCONJ
ejpam-1979	244	8	a.	a.	NOUN
ejpam-1979	244	9	tuna	tuna	PROPN
ejpam-1979	244	10	.	.	PUNCT
ejpam-1979	245	1	on	on	ADP
ejpam-1979	245	2	the	the	DET
ejpam-1979	245	3	quaternionic	quaternionic	ADJ
ejpam-1979	245	4	inclined	inclined	ADJ
ejpam-1979	245	5	curves	curve	NOUN
ejpam-1979	245	6	in	in	ADP
ejpam-1979	245	7	the	the	DET
ejpam-1979	245	8	semi	semi	ADJ
ejpam-1979	245	9	-	-	ADJ
ejpam-1979	245	10	euclidean	euclidean	ADJ
ejpam-1979	245	11	space	space	NOUN
ejpam-1979	245	12	e4	e4	PROPN
ejpam-1979	245	13	2	2	NUM
ejpam-1979	245	14	,	,	PUNCT
ejpam-1979	245	15	appl	appl	PROPN
ejpam-1979	245	16	.	.	PROPN
ejpam-1979	245	17	math	math	NOUN
ejpam-1979	245	18	.	.	PUNCT
ejpam-1979	246	1	comput	comput	NOUN
ejpam-1979	246	2	.	.	PUNCT
ejpam-1979	247	1	155	155	NUM
ejpam-1979	247	2	,	,	PUNCT
ejpam-1979	247	3	373–389	373–389	NUM
ejpam-1979	247	4	,	,	PUNCT
ejpam-1979	247	5	2004	2004	NUM
ejpam-1979	247	6	.	.	PUNCT
ejpam-1979	248	1	[	[	X
ejpam-1979	248	2	3	3	NUM
ejpam-1979	248	3	]	]	X
ejpam-1979	248	4	f.	f.	PROPN
ejpam-1979	248	5	kahraman	kahraman	PROPN
ejpam-1979	248	6	,	,	PUNCT
ejpam-1979	248	7	i̇.	i̇.	VERB
ejpam-1979	248	8	gök	gök	ADV
ejpam-1979	248	9	,	,	PUNCT
ejpam-1979	248	10	and	and	CCONJ
ejpam-1979	248	11	h.	h.	PROPN
ejpam-1979	248	12	h.	h.	PROPN
ejpam-1979	248	13	hacısalihoğlu	hacısalihoğlu	PROPN
ejpam-1979	248	14	.	.	PUNCT
ejpam-1979	249	1	on	on	ADP
ejpam-1979	249	2	the	the	DET
ejpam-1979	249	3	quaternionic	quaternionic	ADJ
ejpam-1979	249	4	b2	b2	NOUN
ejpam-1979	249	5	slant	slant	ADJ
ejpam-1979	249	6	helices	helix	NOUN
ejpam-1979	249	7	in	in	ADP
ejpam-1979	249	8	the	the	DET
ejpam-1979	249	9	semieuclidean	semieuclidean	ADJ
ejpam-1979	249	10	space	space	NOUN
ejpam-1979	249	11	e4	e4	PROPN
ejpam-1979	249	12	2	2	NUM
ejpam-1979	249	13	,	,	PUNCT
ejpam-1979	249	14	applied	apply	VERB
ejpam-1979	249	15	mathematics	mathematic	NOUN
ejpam-1979	249	16	and	and	CCONJ
ejpam-1979	249	17	computation	computation	NOUN
ejpam-1979	249	18	,	,	PUNCT
ejpam-1979	249	19	218,6391	218,6391	NUM
ejpam-1979	249	20	-	-	SYM
ejpam-1979	249	21	6400	6400	NUM
ejpam-1979	249	22	,	,	PUNCT
ejpam-1979	249	23	2012	2012	NUM
ejpam-1979	249	24	.	.	PUNCT
ejpam-1979	250	1	[	[	X
ejpam-1979	250	2	4	4	X
ejpam-1979	250	3	]	]	PUNCT
ejpam-1979	250	4	j.	j.	PROPN
ejpam-1979	250	5	p.	p.	PROPN
ejpam-1979	250	6	ward	ward	PROPN
ejpam-1979	250	7	.	.	PUNCT
ejpam-1979	251	1	quaternions	quaternion	NOUN
ejpam-1979	251	2	and	and	CCONJ
ejpam-1979	251	3	cayley	cayley	ADJ
ejpam-1979	251	4	numbers	number	NOUN
ejpam-1979	251	5	,	,	PUNCT
ejpam-1979	251	6	kluwer	kluwer	NOUN
ejpam-1979	251	7	academic	academic	ADJ
ejpam-1979	251	8	publishers	publisher	NOUN
ejpam-1979	251	9	,	,	PUNCT
ejpam-1979	251	10	boston	boston	PROPN
ejpam-1979	251	11	/	/	SYM
ejpam-1979	251	12	london	london	PROPN
ejpam-1979	251	13	,	,	PUNCT
ejpam-1979	251	14	1997	1997	NUM
ejpam-1979	251	15	.	.	PUNCT
ejpam-1979	252	1	[	[	X
ejpam-1979	252	2	5	5	X
ejpam-1979	252	3	]	]	PUNCT
ejpam-1979	252	4	k.	k.	PROPN
ejpam-1979	252	5	bharathi	bharathi	PROPN
ejpam-1979	252	6	and	and	CCONJ
ejpam-1979	252	7	m.	m.	PROPN
ejpam-1979	252	8	nagaraj	nagaraj	PROPN
ejpam-1979	252	9	.	.	PUNCT
ejpam-1979	253	1	quaternion	quaternion	PROPN
ejpam-1979	253	2	valued	value	VERB
ejpam-1979	253	3	function	function	NOUN
ejpam-1979	253	4	of	of	ADP
ejpam-1979	253	5	a	a	DET
ejpam-1979	253	6	real	real	ADJ
ejpam-1979	253	7	variable	variable	ADJ
ejpam-1979	253	8	serret	serret	ADJ
ejpam-1979	253	9	-	-	PUNCT
ejpam-1979	253	10	frenet	frenet	NOUN
ejpam-1979	253	11	formulae	formulae	NOUN
ejpam-1979	253	12	,	,	PUNCT
ejpam-1979	253	13	indian	indian	ADJ
ejpam-1979	253	14	journal	journal	NOUN
ejpam-1979	253	15	of	of	ADP
ejpam-1979	253	16	pure	pure	ADJ
ejpam-1979	253	17	and	and	CCONJ
ejpam-1979	253	18	applied	applied	ADJ
ejpam-1979	253	19	mathematics	mathematic	NOUN
ejpam-1979	253	20	,	,	PUNCT
ejpam-1979	253	21	18(6	18(6	NOUN
ejpam-1979	253	22	)	)	PUNCT
ejpam-1979	253	23	,	,	PUNCT
ejpam-1979	253	24	507	507	NUM
ejpam-1979	253	25	-	-	SYM
ejpam-1979	253	26	511	511	NUM
ejpam-1979	253	27	,	,	PUNCT
ejpam-1979	253	28	1987	1987	NUM
ejpam-1979	253	29	.	.	PUNCT
ejpam-1979	254	1	[	[	X
ejpam-1979	254	2	6	6	NUM
ejpam-1979	254	3	]	]	PUNCT
ejpam-1979	254	4	a.	a.	NOUN
ejpam-1979	254	5	tuna	tuna	PROPN
ejpam-1979	254	6	.	.	PUNCT
ejpam-1979	255	1	serret	serret	ADJ
ejpam-1979	255	2	frenet	frenet	PROPN
ejpam-1979	255	3	formulae	formulae	NOUN
ejpam-1979	255	4	for	for	ADP
ejpam-1979	255	5	quaternionic	quaternionic	ADJ
ejpam-1979	255	6	curves	curve	NOUN
ejpam-1979	255	7	in	in	ADP
ejpam-1979	255	8	semi	semi	ADJ
ejpam-1979	255	9	-	-	ADJ
ejpam-1979	255	10	euclidean	euclidean	ADJ
ejpam-1979	255	11	space	space	NOUN
ejpam-1979	255	12	,	,	PUNCT
ejpam-1979	255	13	master	master	NOUN
ejpam-1979	255	14	thesis	thesis	NOUN
ejpam-1979	255	15	,	,	PUNCT
ejpam-1979	255	16	süleyman	süleyman	NOUN
ejpam-1979	255	17	demirel	demirel	PROPN
ejpam-1979	255	18	university	university	NOUN
ejpam-1979	255	19	,	,	PUNCT
ejpam-1979	255	20	graduate	graduate	NOUN
ejpam-1979	255	21	school	school	NOUN
ejpam-1979	255	22	of	of	ADP
ejpam-1979	255	23	natural	natural	ADJ
ejpam-1979	255	24	and	and	CCONJ
ejpam-1979	255	25	applied	applied	ADJ
ejpam-1979	255	26	science	science	NOUN
ejpam-1979	255	27	,	,	PUNCT
ejpam-1979	255	28	department	department	NOUN
ejpam-1979	255	29	of	of	ADP
ejpam-1979	255	30	mathematics	mathematic	NOUN
ejpam-1979	255	31	,	,	PUNCT
ejpam-1979	255	32	isparta	isparta	NOUN
ejpam-1979	255	33	,	,	PUNCT
ejpam-1979	255	34	turkey	turkey	NOUN
ejpam-1979	255	35	,	,	PUNCT
ejpam-1979	255	36	2002	2002	NUM
ejpam-1979	255	37	.	.	PUNCT
ejpam-1979	256	1	[	[	X
ejpam-1979	256	2	7	7	X
ejpam-1979	256	3	]	]	X
ejpam-1979	256	4	h.	h.	PROPN
ejpam-1979	256	5	h.	h.	PROPN
ejpam-1979	256	6	hacısalihoğlu	hacısalihoğlu	PROPN
ejpam-1979	256	7	.	.	PUNCT
ejpam-1979	257	1	diferensiyel	diferensiyel	PROPN
ejpam-1979	257	2	geometri	geometri	PROPN
ejpam-1979	257	3	,	,	PUNCT
ejpam-1979	257	4	faculty	faculty	NOUN
ejpam-1979	257	5	of	of	ADP
ejpam-1979	257	6	sciences	science	NOUN
ejpam-1979	257	7	,	,	PUNCT
ejpam-1979	257	8	university	university	NOUN
ejpam-1979	257	9	of	of	ADP
ejpam-1979	257	10	ankara	ankara	PROPN
ejpam-1979	257	11	press	press	PROPN
ejpam-1979	257	12	,	,	PUNCT
ejpam-1979	257	13	1993	1993	NUM
ejpam-1979	257	14	.	.	PUNCT
ejpam-1979	258	1	[	[	X
ejpam-1979	258	2	8	8	NUM
ejpam-1979	258	3	]	]	PUNCT
ejpam-1979	258	4	a.	a.	NOUN
ejpam-1979	258	5	sabuncuoğlu	sabuncuoğlu	PROPN
ejpam-1979	258	6	.	.	PUNCT
ejpam-1979	259	1	diferensiyel	diferensiyel	PROPN
ejpam-1979	259	2	geometri	geometri	PROPN
ejpam-1979	259	3	,	,	PUNCT
ejpam-1979	259	4	nobel	nobel	PROPN
ejpam-1979	259	5	press	press	PROPN
ejpam-1979	259	6	,	,	PUNCT
ejpam-1979	259	7	2010	2010	NUM
ejpam-1979	259	8	.	.	PUNCT
ejpam-1979	260	1	references	reference	NOUN
ejpam-1979	260	2	96	96	NUM
ejpam-1979	261	1	[	[	X
ejpam-1979	261	2	9	9	NUM
ejpam-1979	261	3	]	]	X
ejpam-1979	261	4	d.	d.	PROPN
ejpam-1979	261	5	j.	j.	PROPN
ejpam-1979	261	6	struik	struik	PROPN
ejpam-1979	261	7	.	.	PUNCT
ejpam-1979	262	1	differential	differential	PROPN
ejpam-1979	262	2	geometry	geometry	NOUN
ejpam-1979	262	3	,	,	PUNCT
ejpam-1979	262	4	second	second	ADJ
ejpam-1979	262	5	ed	ed	NOUN
ejpam-1979	262	6	.	.	PROPN
ejpam-1979	262	7	,	,	PUNCT
ejpam-1979	262	8	addison	addison	PROPN
ejpam-1979	262	9	-	-	PUNCT
ejpam-1979	262	10	wesley	wesley	PROPN
ejpam-1979	262	11	,	,	PUNCT
ejpam-1979	262	12	reading	reading	NOUN
ejpam-1979	262	13	,	,	PUNCT
ejpam-1979	262	14	massachusetts	massachusetts	PROPN
ejpam-1979	262	15	.	.	PROPN
ejpam-1979	262	16	1961	1961	NUM
ejpam-1979	262	17	.	.	PUNCT
ejpam-1979	263	1	[	[	X
ejpam-1979	263	2	10	10	NUM
ejpam-1979	263	3	]	]	X
ejpam-1979	263	4	d.	d.	PROPN
ejpam-1979	263	5	sağlam	sağlam	PROPN
ejpam-1979	263	6	.	.	PUNCT
ejpam-1979	264	1	on	on	ADP
ejpam-1979	264	2	the	the	DET
ejpam-1979	264	3	osculating	osculating	NOUN
ejpam-1979	264	4	spheres	sphere	NOUN
ejpam-1979	264	5	of	of	ADP
ejpam-1979	264	6	a	a	DET
ejpam-1979	264	7	real	real	ADJ
ejpam-1979	264	8	quaternionic	quaternionic	ADJ
ejpam-1979	264	9	curve	curve	NOUN
ejpam-1979	264	10	in	in	ADP
ejpam-1979	264	11	the	the	DET
ejpam-1979	264	12	euclidean	euclidean	ADJ
ejpam-1979	264	13	space	space	NOUN
ejpam-1979	264	14	e4	e4	PROPN
ejpam-1979	264	15	,	,	PUNCT
ejpam-1979	264	16	international	international	ADJ
ejpam-1979	264	17	journal	journal	NOUN
ejpam-1979	264	18	of	of	ADP
ejpam-1979	264	19	mathematical	mathematical	ADJ
ejpam-1979	264	20	combinatorics	combinatoric	NOUN
ejpam-1979	264	21	,	,	PUNCT
ejpam-1979	264	22	3	3	NUM
ejpam-1979	264	23	,	,	PUNCT
ejpam-1979	264	24	46	46	NUM
ejpam-1979	264	25	-	-	SYM
ejpam-1979	264	26	53	53	NUM
ejpam-1979	264	27	,	,	PUNCT
ejpam-1979	264	28	2012	2012	NUM
ejpam-1979	264	29	.	.	PUNCT
ejpam-1979	265	1	[	[	X
ejpam-1979	265	2	11	11	NUM
ejpam-1979	265	3	]	]	X
ejpam-1979	265	4	e.	e.	PROPN
ejpam-1979	265	5	soytürk	soytürk	PROPN
ejpam-1979	265	6	,	,	PUNCT
ejpam-1979	265	7	k.	k.	PROPN
ejpam-1979	265	8	i̇larslan	i̇larslan	PROPN
ejpam-1979	265	9	,	,	PUNCT
ejpam-1979	265	10	and	and	CCONJ
ejpam-1979	265	11	d.	d.	PROPN
ejpam-1979	265	12	sağlam	sağlam	PROPN
ejpam-1979	265	13	.	.	PUNCT
ejpam-1979	266	1	osculating	osculate	VERB
ejpam-1979	266	2	spheres	sphere	NOUN
ejpam-1979	266	3	and	and	CCONJ
ejpam-1979	266	4	osculating	osculating	NOUN
ejpam-1979	266	5	circles	circle	NOUN
ejpam-1979	266	6	of	of	ADP
ejpam-1979	266	7	a	a	DET
ejpam-1979	266	8	curve	curve	NOUN
ejpam-1979	266	9	in	in	ADP
ejpam-1979	266	10	semi	semi	ADJ
ejpam-1979	266	11	-	-	ADJ
ejpam-1979	266	12	reimannian	reimannian	ADJ
ejpam-1979	266	13	space	space	NOUN
ejpam-1979	266	14	,	,	PUNCT
ejpam-1979	266	15	communications	communication	NOUN
ejpam-1979	266	16	,	,	PUNCT
ejpam-1979	266	17	faculty	faculty	NOUN
ejpam-1979	266	18	of	of	ADP
ejpam-1979	266	19	science	science	NOUN
ejpam-1979	266	20	,	,	PUNCT
ejpam-1979	266	21	university	university	PROPN
ejpam-1979	266	22	of	of	ADP
ejpam-1979	266	23	ankara	ankara	PROPN
ejpam-1979	266	24	series	series	PROPN
ejpam-1979	266	25	a1	a1	PROPN
ejpam-1979	266	26	,	,	PUNCT
ejpam-1979	266	27	54	54	NUM
ejpam-1979	266	28	(	(	PUNCT
ejpam-1979	266	29	2	2	NUM
ejpam-1979	266	30	)	)	PUNCT
ejpam-1979	266	31	,	,	PUNCT
ejpam-1979	266	32	39	39	NUM
ejpam-1979	266	33	-	-	SYM
ejpam-1979	266	34	48	48	NUM
ejpam-1979	266	35	,	,	PUNCT
ejpam-1979	266	36	2005	2005	NUM
ejpam-1979	266	37	.	.	PUNCT