id	sid	tid	token	lemma	pos
ejpam-1551	1	1	3_bektas.dvi	3_bektas.dvi	NUM
ejpam-1551	1	2	european	european	PROPN
ejpam-1551	1	3	journal	journal	PROPN
ejpam-1551	1	4	of	of	ADP
ejpam-1551	1	5	pure	pure	ADJ
ejpam-1551	1	6	and	and	CCONJ
ejpam-1551	1	7	applied	apply	VERB
ejpam-1551	1	8	mathematics	mathematic	NOUN
ejpam-1551	1	9	vol	vol	NOUN
ejpam-1551	1	10	.	.	PROPN
ejpam-1551	2	1	6	6	NUM
ejpam-1551	2	2	,	,	PUNCT
ejpam-1551	2	3	no	no	INTJ
ejpam-1551	2	4	.	.	NOUN
ejpam-1551	2	5	1	1	NUM
ejpam-1551	2	6	,	,	PUNCT
ejpam-1551	2	7	2013	2013	NUM
ejpam-1551	2	8	,	,	PUNCT
ejpam-1551	2	9	20	20	NUM
ejpam-1551	2	10	-	-	SYM
ejpam-1551	2	11	29	29	NUM
ejpam-1551	2	12	issn	issn	PROPN
ejpam-1551	2	13	1307	1307	NUM
ejpam-1551	2	14	-	-	SYM
ejpam-1551	2	15	5543	5543	NUM
ejpam-1551	2	16	–	–	PUNCT
ejpam-1551	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1551	2	18	special	special	ADJ
ejpam-1551	2	19	involute	involute	NOUN
ejpam-1551	2	20	-	-	PUNCT
ejpam-1551	2	21	evolute	evolute	NOUN
ejpam-1551	2	22	partner	partner	NOUN
ejpam-1551	2	23	d	d	NOUN
ejpam-1551	2	24	-	-	PUNCT
ejpam-1551	2	25	curves	curve	NOUN
ejpam-1551	2	26	in	in	ADP
ejpam-1551	2	27	e3	e3	NOUN
ejpam-1551	2	28	özcan	özcan	PROPN
ejpam-1551	2	29	bektaş∗	bektaş∗	NOUN
ejpam-1551	2	30	,	,	PUNCT
ejpam-1551	2	31	salim	salim	PROPN
ejpam-1551	2	32	yüce	yüce	PROPN
ejpam-1551	2	33	yıldız	yıldız	PROPN
ejpam-1551	2	34	technical	technical	PROPN
ejpam-1551	2	35	university	university	PROPN
ejpam-1551	2	36	,	,	PUNCT
ejpam-1551	2	37	faculty	faculty	NOUN
ejpam-1551	2	38	of	of	ADP
ejpam-1551	2	39	arts	art	NOUN
ejpam-1551	2	40	and	and	CCONJ
ejpam-1551	2	41	sciences	science	NOUN
ejpam-1551	2	42	,	,	PUNCT
ejpam-1551	2	43	department	department	NOUN
ejpam-1551	2	44	of	of	ADP
ejpam-1551	2	45	mathematics	mathematic	NOUN
ejpam-1551	2	46	,	,	PUNCT
ejpam-1551	2	47	34210	34210	NUM
ejpam-1551	2	48	,	,	PUNCT
ejpam-1551	2	49	esenler	esenler	NOUN
ejpam-1551	2	50	,	,	PUNCT
ejpam-1551	2	51	istanbul	istanbul	PROPN
ejpam-1551	2	52	,	,	PUNCT
ejpam-1551	2	53	turkey	turkey	PROPN
ejpam-1551	2	54	abstract	abstract	NOUN
ejpam-1551	2	55	.	.	PUNCT
ejpam-1551	3	1	in	in	ADP
ejpam-1551	3	2	this	this	DET
ejpam-1551	3	3	paper	paper	NOUN
ejpam-1551	3	4	,	,	PUNCT
ejpam-1551	3	5	we	we	PRON
ejpam-1551	3	6	take	take	VERB
ejpam-1551	3	7	into	into	ADP
ejpam-1551	3	8	account	account	NOUN
ejpam-1551	3	9	the	the	DET
ejpam-1551	3	10	opinion	opinion	NOUN
ejpam-1551	3	11	of	of	ADP
ejpam-1551	3	12	involute	involute	ADJ
ejpam-1551	3	13	-	-	PUNCT
ejpam-1551	3	14	evolute	evolute	NOUN
ejpam-1551	3	15	curves	curve	NOUN
ejpam-1551	3	16	which	which	PRON
ejpam-1551	3	17	lie	lie	VERB
ejpam-1551	3	18	on	on	ADP
ejpam-1551	3	19	fully	fully	ADV
ejpam-1551	3	20	surfaces	surface	NOUN
ejpam-1551	3	21	and	and	CCONJ
ejpam-1551	3	22	by	by	ADP
ejpam-1551	3	23	taking	take	VERB
ejpam-1551	3	24	into	into	ADP
ejpam-1551	3	25	account	account	NOUN
ejpam-1551	3	26	the	the	DET
ejpam-1551	3	27	darboux	darboux	NOUN
ejpam-1551	3	28	frames	frame	NOUN
ejpam-1551	3	29	of	of	ADP
ejpam-1551	3	30	them	they	PRON
ejpam-1551	3	31	we	we	PRON
ejpam-1551	3	32	illustrate	illustrate	VERB
ejpam-1551	3	33	these	these	DET
ejpam-1551	3	34	curves	curve	NOUN
ejpam-1551	3	35	as	as	ADP
ejpam-1551	3	36	special	special	ADJ
ejpam-1551	3	37	involute	involute	NOUN
ejpam-1551	3	38	-	-	PUNCT
ejpam-1551	3	39	evolute	evolute	NOUN
ejpam-1551	3	40	partner	partner	NOUN
ejpam-1551	3	41	d	d	NOUN
ejpam-1551	3	42	-	-	PUNCT
ejpam-1551	3	43	curves	curve	NOUN
ejpam-1551	3	44	in	in	ADP
ejpam-1551	3	45	e3	e3	NOUN
ejpam-1551	3	46	.	.	PUNCT
ejpam-1551	4	1	besides	besides	SCONJ
ejpam-1551	4	2	,	,	PUNCT
ejpam-1551	4	3	we	we	PRON
ejpam-1551	4	4	find	find	VERB
ejpam-1551	4	5	the	the	DET
ejpam-1551	4	6	relations	relation	NOUN
ejpam-1551	4	7	between	between	ADP
ejpam-1551	4	8	the	the	DET
ejpam-1551	4	9	normal	normal	ADJ
ejpam-1551	4	10	curvatures	curvature	NOUN
ejpam-1551	4	11	,	,	PUNCT
ejpam-1551	4	12	the	the	DET
ejpam-1551	4	13	geodesic	geodesic	ADJ
ejpam-1551	4	14	curvatures	curvature	NOUN
ejpam-1551	4	15	and	and	CCONJ
ejpam-1551	4	16	the	the	DET
ejpam-1551	4	17	geodesic	geodesic	ADJ
ejpam-1551	4	18	torsions	torsion	NOUN
ejpam-1551	4	19	of	of	ADP
ejpam-1551	4	20	these	these	DET
ejpam-1551	4	21	curves	curve	NOUN
ejpam-1551	4	22	.	.	PUNCT
ejpam-1551	5	1	finally	finally	ADV
ejpam-1551	5	2	,	,	PUNCT
ejpam-1551	5	3	some	some	DET
ejpam-1551	5	4	consequences	consequence	NOUN
ejpam-1551	5	5	and	and	CCONJ
ejpam-1551	5	6	examples	example	NOUN
ejpam-1551	5	7	are	be	AUX
ejpam-1551	5	8	given	give	VERB
ejpam-1551	5	9	.	.	PUNCT
ejpam-1551	6	1	2010	2010	NUM
ejpam-1551	6	2	mathematics	mathematic	NOUN
ejpam-1551	6	3	subject	subject	NOUN
ejpam-1551	6	4	classifications	classification	NOUN
ejpam-1551	6	5	:	:	PUNCT
ejpam-1551	6	6	53a04	53a04	NUM
ejpam-1551	6	7	key	key	ADJ
ejpam-1551	6	8	words	word	NOUN
ejpam-1551	6	9	and	and	CCONJ
ejpam-1551	6	10	phrases	phrase	NOUN
ejpam-1551	6	11	:	:	PUNCT
ejpam-1551	6	12	involute	involute	ADJ
ejpam-1551	6	13	-	-	PUNCT
ejpam-1551	6	14	evolute	evolute	NOUN
ejpam-1551	6	15	curve	curve	NOUN
ejpam-1551	6	16	,	,	PUNCT
ejpam-1551	6	17	darboux	darboux	VERB
ejpam-1551	6	18	frame	frame	NOUN
ejpam-1551	6	19	,	,	PUNCT
ejpam-1551	6	20	normal	normal	ADJ
ejpam-1551	6	21	curvature	curvature	NOUN
ejpam-1551	6	22	,	,	PUNCT
ejpam-1551	6	23	geodesic	geodesic	ADJ
ejpam-1551	6	24	curvature	curvature	NOUN
ejpam-1551	6	25	,	,	PUNCT
ejpam-1551	6	26	geodesic	geodesic	ADJ
ejpam-1551	6	27	torsion	torsion	NOUN
ejpam-1551	6	28	1	1	NUM
ejpam-1551	6	29	.	.	PUNCT
ejpam-1551	6	30	introduction	introduction	NOUN
ejpam-1551	6	31	in	in	ADP
ejpam-1551	6	32	differential	differential	ADJ
ejpam-1551	6	33	geometry	geometry	NOUN
ejpam-1551	7	1	,	,	PUNCT
ejpam-1551	7	2	there	there	PRON
ejpam-1551	7	3	are	be	VERB
ejpam-1551	7	4	many	many	ADJ
ejpam-1551	7	5	important	important	ADJ
ejpam-1551	7	6	consequences	consequence	NOUN
ejpam-1551	7	7	and	and	CCONJ
ejpam-1551	7	8	properties	property	NOUN
ejpam-1551	7	9	of	of	ADP
ejpam-1551	7	10	curves	curve	NOUN
ejpam-1551	7	11	.	.	PUNCT
ejpam-1551	8	1	researchers	researcher	NOUN
ejpam-1551	8	2	follow	follow	VERB
ejpam-1551	8	3	labours	labour	NOUN
ejpam-1551	8	4	about	about	ADP
ejpam-1551	8	5	the	the	DET
ejpam-1551	8	6	curves	curve	NOUN
ejpam-1551	8	7	.	.	PUNCT
ejpam-1551	9	1	in	in	ADP
ejpam-1551	9	2	the	the	DET
ejpam-1551	9	3	light	light	NOUN
ejpam-1551	9	4	of	of	ADP
ejpam-1551	9	5	the	the	DET
ejpam-1551	9	6	existing	exist	VERB
ejpam-1551	9	7	studies	study	NOUN
ejpam-1551	9	8	,	,	PUNCT
ejpam-1551	9	9	authors	author	NOUN
ejpam-1551	9	10	always	always	ADV
ejpam-1551	9	11	introduce	introduce	VERB
ejpam-1551	9	12	new	new	ADJ
ejpam-1551	9	13	curves	curve	NOUN
ejpam-1551	9	14	.	.	PUNCT
ejpam-1551	10	1	involute	involute	ADJ
ejpam-1551	10	2	-	-	PUNCT
ejpam-1551	10	3	evolute	evolute	NOUN
ejpam-1551	10	4	curves	curve	NOUN
ejpam-1551	10	5	are	be	AUX
ejpam-1551	10	6	one	one	NUM
ejpam-1551	10	7	of	of	ADP
ejpam-1551	10	8	them	they	PRON
ejpam-1551	10	9	.	.	PUNCT
ejpam-1551	11	1	c.	c.	PROPN
ejpam-1551	11	2	huggens	huggens	PROPN
ejpam-1551	11	3	discovered	discover	VERB
ejpam-1551	11	4	involutes	involute	NOUN
ejpam-1551	11	5	while	while	SCONJ
ejpam-1551	11	6	trying	try	VERB
ejpam-1551	11	7	to	to	PART
ejpam-1551	11	8	build	build	VERB
ejpam-1551	11	9	a	a	DET
ejpam-1551	11	10	more	more	ADV
ejpam-1551	11	11	accurate	accurate	ADJ
ejpam-1551	11	12	clock	clock	NOUN
ejpam-1551	11	13	,	,	PUNCT
ejpam-1551	11	14	[	[	X
ejpam-1551	11	15	1	1	NUM
ejpam-1551	11	16	]	]	PUNCT
ejpam-1551	11	17	.	.	PUNCT
ejpam-1551	12	1	later	later	ADV
ejpam-1551	12	2	,	,	PUNCT
ejpam-1551	12	3	the	the	DET
ejpam-1551	12	4	relations	relation	NOUN
ejpam-1551	12	5	frenet	frenet	NOUN
ejpam-1551	12	6	apparatus	apparatus	NOUN
ejpam-1551	12	7	of	of	ADP
ejpam-1551	12	8	involute	involute	NOUN
ejpam-1551	12	9	-	-	PUNCT
ejpam-1551	12	10	evolute	evolute	NOUN
ejpam-1551	12	11	curve	curve	NOUN
ejpam-1551	12	12	couple	couple	NOUN
ejpam-1551	12	13	in	in	ADP
ejpam-1551	12	14	the	the	DET
ejpam-1551	12	15	space	space	NOUN
ejpam-1551	12	16	e3	e3	NOUN
ejpam-1551	12	17	were	be	AUX
ejpam-1551	12	18	given	give	VERB
ejpam-1551	12	19	in	in	ADP
ejpam-1551	12	20	[	[	X
ejpam-1551	12	21	2	2	NUM
ejpam-1551	12	22	]	]	PUNCT
ejpam-1551	12	23	.	.	PUNCT
ejpam-1551	13	1	a.	a.	PROPN
ejpam-1551	13	2	turgut	turgut	PROPN
ejpam-1551	13	3	examined	examine	VERB
ejpam-1551	13	4	involute	involute	NOUN
ejpam-1551	13	5	-	-	PUNCT
ejpam-1551	13	6	evolute	evolute	NOUN
ejpam-1551	13	7	curve	curve	NOUN
ejpam-1551	13	8	couple	couple	NOUN
ejpam-1551	13	9	in	in	ADP
ejpam-1551	13	10	en	en	ADP
ejpam-1551	13	11	,	,	PUNCT
ejpam-1551	13	12	[	[	X
ejpam-1551	13	13	5	5	NUM
ejpam-1551	13	14	]	]	PUNCT
ejpam-1551	13	15	.	.	PUNCT
ejpam-1551	14	1	mannheim	mannheim	PROPN
ejpam-1551	14	2	partner	partner	NOUN
ejpam-1551	14	3	dcurves	dcurve	VERB
ejpam-1551	14	4	in	in	ADP
ejpam-1551	14	5	euclidean	euclidean	ADJ
ejpam-1551	14	6	space	space	NOUN
ejpam-1551	14	7	were	be	AUX
ejpam-1551	14	8	studied	study	VERB
ejpam-1551	14	9	by	by	ADP
ejpam-1551	14	10	kazaz	kazaz	PROPN
ejpam-1551	14	11	and	and	CCONJ
ejpam-1551	14	12	others	other	NOUN
ejpam-1551	14	13	[	[	X
ejpam-1551	14	14	3	3	NUM
ejpam-1551	14	15	]	]	PUNCT
ejpam-1551	14	16	.	.	PUNCT
ejpam-1551	15	1	in	in	ADP
ejpam-1551	15	2	this	this	DET
ejpam-1551	15	3	study	study	NOUN
ejpam-1551	15	4	,	,	PUNCT
ejpam-1551	15	5	we	we	PRON
ejpam-1551	15	6	consider	consider	VERB
ejpam-1551	15	7	the	the	DET
ejpam-1551	15	8	notion	notion	NOUN
ejpam-1551	15	9	of	of	ADP
ejpam-1551	15	10	the	the	DET
ejpam-1551	15	11	involute	involute	NOUN
ejpam-1551	15	12	-	-	PUNCT
ejpam-1551	15	13	evolute	evolute	NOUN
ejpam-1551	15	14	curves	curve	NOUN
ejpam-1551	15	15	lying	lie	VERB
ejpam-1551	15	16	on	on	ADP
ejpam-1551	15	17	the	the	DET
ejpam-1551	15	18	surfaces	surface	NOUN
ejpam-1551	15	19	for	for	ADP
ejpam-1551	15	20	a	a	DET
ejpam-1551	15	21	special	special	ADJ
ejpam-1551	15	22	situation	situation	NOUN
ejpam-1551	15	23	.	.	PUNCT
ejpam-1551	16	1	we	we	PRON
ejpam-1551	16	2	determine	determine	VERB
ejpam-1551	16	3	the	the	DET
ejpam-1551	16	4	special	special	ADJ
ejpam-1551	16	5	involute	involute	NOUN
ejpam-1551	16	6	-	-	PUNCT
ejpam-1551	16	7	evolute	evolute	NOUN
ejpam-1551	16	8	partner	partner	NOUN
ejpam-1551	16	9	d	d	NOUN
ejpam-1551	16	10	-	-	PUNCT
ejpam-1551	16	11	curves	curve	NOUN
ejpam-1551	16	12	in	in	ADP
ejpam-1551	16	13	e3	e3	NOUN
ejpam-1551	16	14	.	.	PUNCT
ejpam-1551	17	1	by	by	ADP
ejpam-1551	17	2	using	use	VERB
ejpam-1551	17	3	the	the	DET
ejpam-1551	17	4	darboux	darboux	VERB
ejpam-1551	17	5	frame	frame	NOUN
ejpam-1551	17	6	of	of	ADP
ejpam-1551	17	7	the	the	DET
ejpam-1551	17	8	curves	curve	NOUN
ejpam-1551	17	9	we	we	PRON
ejpam-1551	17	10	obtain	obtain	VERB
ejpam-1551	17	11	the	the	DET
ejpam-1551	17	12	necessary	necessary	ADJ
ejpam-1551	17	13	and	and	CCONJ
ejpam-1551	17	14	sufficient	sufficient	ADJ
ejpam-1551	17	15	conditions	condition	NOUN
ejpam-1551	17	16	between	between	ADP
ejpam-1551	17	17	κg	κg	PROPN
ejpam-1551	17	18	,	,	PUNCT
ejpam-1551	17	19	τg	τg	PROPN
ejpam-1551	17	20	,	,	PUNCT
ejpam-1551	17	21	κn	κn	NOUN
ejpam-1551	17	22	and	and	CCONJ
ejpam-1551	17	23	κ∗n	κ∗n	PUNCT
ejpam-1551	17	24	for	for	ADP
ejpam-1551	17	25	a	a	DET
ejpam-1551	17	26	curve	curve	NOUN
ejpam-1551	17	27	to	to	PART
ejpam-1551	17	28	be	be	AUX
ejpam-1551	17	29	the	the	DET
ejpam-1551	17	30	special	special	ADJ
ejpam-1551	17	31	involute	involute	ADJ
ejpam-1551	17	32	partner	partner	NOUN
ejpam-1551	17	33	d	d	NOUN
ejpam-1551	17	34	-	-	PUNCT
ejpam-1551	17	35	curve	curve	NOUN
ejpam-1551	17	36	.	.	PUNCT
ejpam-1551	18	1	κ∗g	κ∗g	VERB
ejpam-1551	18	2	and	and	CCONJ
ejpam-1551	18	3	τ∗g	τ∗g	NUM
ejpam-1551	18	4	of	of	ADP
ejpam-1551	18	5	this	this	DET
ejpam-1551	18	6	special	special	ADJ
ejpam-1551	18	7	involute	involute	ADJ
ejpam-1551	18	8	partner	partner	NOUN
ejpam-1551	18	9	d	d	NOUN
ejpam-1551	18	10	-	-	PUNCT
ejpam-1551	18	11	curve	curve	NOUN
ejpam-1551	18	12	are	be	AUX
ejpam-1551	18	13	found	find	VERB
ejpam-1551	18	14	.	.	PUNCT
ejpam-1551	19	1	finally	finally	ADV
ejpam-1551	19	2	,	,	PUNCT
ejpam-1551	19	3	some	some	DET
ejpam-1551	19	4	special	special	ADJ
ejpam-1551	19	5	case	case	NOUN
ejpam-1551	19	6	and	and	CCONJ
ejpam-1551	19	7	examples	example	NOUN
ejpam-1551	19	8	are	be	AUX
ejpam-1551	19	9	given	give	VERB
ejpam-1551	19	10	.	.	PUNCT
ejpam-1551	20	1	∗corresponding	∗corresponde	VERB
ejpam-1551	20	2	author	author	NOUN
ejpam-1551	20	3	.	.	PUNCT
ejpam-1551	21	1	email	email	NOUN
ejpam-1551	21	2	addresses	address	NOUN
ejpam-1551	21	3	:	:	PUNCT
ejpam-1551	21	4	obektas�yildiz.edu.tr	obektas�yildiz.edu.tr	PROPN
ejpam-1551	21	5	(	(	PUNCT
ejpam-1551	21	6	ö.	ö.	PROPN
ejpam-1551	21	7	bektaş	bektaş	PROPN
ejpam-1551	21	8	)	)	PUNCT
ejpam-1551	21	9	,	,	PUNCT
ejpam-1551	21	10	sayu	sayu	PROPN
ejpam-1551	21	11	e�yildiz.edu.tr	e�yildiz.edu.tr	PROPN
ejpam-1551	21	12	(	(	PUNCT
ejpam-1551	21	13	s.	s.	PROPN
ejpam-1551	21	14	yüce	yüce	PROPN
ejpam-1551	21	15	)	)	PUNCT
ejpam-1551	21	16	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1551	22	1	20	20	NUM
ejpam-1551	22	2	c	c	X
ejpam-1551	22	3	©	©	PROPN
ejpam-1551	22	4	2013	2013	NUM
ejpam-1551	22	5	ejpam	ejpam	NOUN
ejpam-1551	22	6	all	all	DET
ejpam-1551	22	7	rights	right	NOUN
ejpam-1551	22	8	reserved	reserve	VERB
ejpam-1551	22	9	.	.	PUNCT
ejpam-1551	23	1	ö.	ö.	PROPN
ejpam-1551	23	2	bektaş	bektaş	PROPN
ejpam-1551	23	3	,	,	PUNCT
ejpam-1551	23	4	s.	s.	PROPN
ejpam-1551	23	5	yüce	yüce	PROPN
ejpam-1551	23	6	/	/	SYM
ejpam-1551	23	7	eur	eur	PROPN
ejpam-1551	23	8	.	.	PUNCT
ejpam-1551	24	1	j.	j.	PROPN
ejpam-1551	24	2	pure	pure	PROPN
ejpam-1551	24	3	appl	appl	PROPN
ejpam-1551	24	4	.	.	PROPN
ejpam-1551	24	5	math	math	PROPN
ejpam-1551	24	6	,	,	PUNCT
ejpam-1551	24	7	6	6	NUM
ejpam-1551	24	8	(	(	PUNCT
ejpam-1551	24	9	2013	2013	NUM
ejpam-1551	24	10	)	)	PUNCT
ejpam-1551	24	11	,	,	PUNCT
ejpam-1551	24	12	20	20	NUM
ejpam-1551	24	13	-	-	SYM
ejpam-1551	24	14	29	29	NUM
ejpam-1551	24	15	21	21	NUM
ejpam-1551	24	16	2	2	NUM
ejpam-1551	24	17	.	.	PUNCT
ejpam-1551	24	18	preliminaries	preliminary	NOUN
ejpam-1551	24	19	in	in	ADP
ejpam-1551	24	20	this	this	DET
ejpam-1551	24	21	section	section	NOUN
ejpam-1551	25	1	,	,	PUNCT
ejpam-1551	25	2	we	we	PRON
ejpam-1551	25	3	give	give	VERB
ejpam-1551	25	4	information	information	NOUN
ejpam-1551	25	5	about	about	ADP
ejpam-1551	25	6	involute	involute	ADJ
ejpam-1551	25	7	-	-	PUNCT
ejpam-1551	25	8	evolute	evolute	NOUN
ejpam-1551	25	9	curves	curve	NOUN
ejpam-1551	25	10	and	and	CCONJ
ejpam-1551	25	11	darboux	darboux	ADJ
ejpam-1551	25	12	frame	frame	NOUN
ejpam-1551	25	13	.	.	PUNCT
ejpam-1551	26	1	let	let	VERB
ejpam-1551	26	2	α	α	PRON
ejpam-1551	26	3	(	(	PUNCT
ejpam-1551	26	4	s	s	X
ejpam-1551	26	5	)	)	PUNCT
ejpam-1551	26	6	be	be	AUX
ejpam-1551	26	7	a	a	DET
ejpam-1551	26	8	curve	curve	NOUN
ejpam-1551	26	9	on	on	ADP
ejpam-1551	26	10	an	an	DET
ejpam-1551	26	11	oriented	orient	VERB
ejpam-1551	26	12	surface	surface	NOUN
ejpam-1551	26	13	m	m	NOUN
ejpam-1551	26	14	.	.	PUNCT
ejpam-1551	27	1	since	since	SCONJ
ejpam-1551	27	2	the	the	DET
ejpam-1551	27	3	curve	curve	NOUN
ejpam-1551	27	4	α	α	X
ejpam-1551	27	5	(	(	PUNCT
ejpam-1551	27	6	s	s	X
ejpam-1551	27	7	)	)	PUNCT
ejpam-1551	27	8	is	be	AUX
ejpam-1551	27	9	also	also	ADV
ejpam-1551	27	10	in	in	ADP
ejpam-1551	27	11	space	space	NOUN
ejpam-1551	27	12	,	,	PUNCT
ejpam-1551	27	13	there	there	PRON
ejpam-1551	27	14	exists	exist	VERB
ejpam-1551	27	15	frenet	frenet	ADJ
ejpam-1551	27	16	frame	frame	NOUN
ejpam-1551	27	17	{	{	PUNCT
ejpam-1551	27	18	t	t	PROPN
ejpam-1551	27	19	,	,	PUNCT
ejpam-1551	27	20	n	n	CCONJ
ejpam-1551	27	21	,	,	PUNCT
ejpam-1551	27	22	b	b	NOUN
ejpam-1551	27	23	}	}	PUNCT
ejpam-1551	27	24	at	at	ADP
ejpam-1551	27	25	each	each	DET
ejpam-1551	27	26	points	point	NOUN
ejpam-1551	27	27	of	of	ADP
ejpam-1551	27	28	the	the	DET
ejpam-1551	27	29	curve	curve	NOUN
ejpam-1551	27	30	where	where	SCONJ
ejpam-1551	27	31	t	t	PROPN
ejpam-1551	27	32	is	be	AUX
ejpam-1551	27	33	unit	unit	NOUN
ejpam-1551	27	34	tangent	tangent	PROPN
ejpam-1551	27	35	vector	vector	PROPN
ejpam-1551	27	36	,	,	PUNCT
ejpam-1551	27	37	n	n	PRON
ejpam-1551	27	38	is	be	AUX
ejpam-1551	27	39	principal	principal	ADJ
ejpam-1551	27	40	normal	normal	ADJ
ejpam-1551	27	41	vector	vector	NOUN
ejpam-1551	27	42	and	and	CCONJ
ejpam-1551	27	43	b	b	NOUN
ejpam-1551	27	44	is	be	AUX
ejpam-1551	27	45	binormal	binormal	ADJ
ejpam-1551	27	46	vector	vector	NOUN
ejpam-1551	27	47	,	,	PUNCT
ejpam-1551	27	48	respectively	respectively	ADV
ejpam-1551	27	49	.	.	PUNCT
ejpam-1551	28	1	the	the	DET
ejpam-1551	28	2	frenet	frenet	ADJ
ejpam-1551	28	3	equations	equation	NOUN
ejpam-1551	28	4	of	of	ADP
ejpam-1551	28	5	the	the	DET
ejpam-1551	28	6	curve	curve	NOUN
ejpam-1551	28	7	α	α	PROPN
ejpam-1551	28	8	(	(	PUNCT
ejpam-1551	28	9	s	s	X
ejpam-1551	28	10	)	)	PUNCT
ejpam-1551	28	11	is	be	AUX
ejpam-1551	28	12	given	give	VERB
ejpam-1551	28	13	by	by	ADP
ejpam-1551	28	14			PROPN
ejpam-1551	28	15			NOUN
ejpam-1551	28	16			NOUN
ejpam-1551	28	17	t	t	PROPN
ejpam-1551	28	18	′	′	NOUN
ejpam-1551	28	19	=	=	PUNCT
ejpam-1551	28	20	κn	κn	NOUN
ejpam-1551	28	21	n	n	NOUN
ejpam-1551	28	22	′	′	NUM
ejpam-1551	29	1	=	=	PUNCT
ejpam-1551	29	2	−κt+τb	−κt+τb	PROPN
ejpam-1551	29	3	b	b	NOUN
ejpam-1551	29	4	′	′	NOUN
ejpam-1551	29	5	=	=	SYM
ejpam-1551	29	6	−τn	−τn	NOUN
ejpam-1551	29	7	where	where	SCONJ
ejpam-1551	29	8	κ	κ	PROPN
ejpam-1551	29	9	and	and	CCONJ
ejpam-1551	29	10	τ	τ	PROPN
ejpam-1551	29	11	are	be	AUX
ejpam-1551	29	12	curvature	curvature	NOUN
ejpam-1551	29	13	and	and	CCONJ
ejpam-1551	29	14	torsion	torsion	NOUN
ejpam-1551	29	15	of	of	ADP
ejpam-1551	29	16	the	the	DET
ejpam-1551	29	17	curve	curve	NOUN
ejpam-1551	29	18	α	α	PROPN
ejpam-1551	29	19	(	(	PUNCT
ejpam-1551	29	20	s	s	NOUN
ejpam-1551	29	21	)	)	PUNCT
ejpam-1551	29	22	,	,	PUNCT
ejpam-1551	29	23	respectively	respectively	ADV
ejpam-1551	29	24	.	.	PUNCT
ejpam-1551	30	1	since	since	SCONJ
ejpam-1551	30	2	the	the	DET
ejpam-1551	30	3	curve	curve	NOUN
ejpam-1551	30	4	α	α	X
ejpam-1551	30	5	(	(	PUNCT
ejpam-1551	30	6	s	s	NOUN
ejpam-1551	30	7	)	)	PUNCT
ejpam-1551	30	8	lies	lie	VERB
ejpam-1551	30	9	on	on	ADP
ejpam-1551	30	10	the	the	DET
ejpam-1551	30	11	surface	surface	NOUN
ejpam-1551	30	12	m	m	VERB
ejpam-1551	30	13	there	there	ADV
ejpam-1551	30	14	exists	exist	VERB
ejpam-1551	30	15	another	another	DET
ejpam-1551	30	16	frame	frame	NOUN
ejpam-1551	30	17	of	of	ADP
ejpam-1551	30	18	the	the	DET
ejpam-1551	30	19	curve	curve	NOUN
ejpam-1551	30	20	α	α	PROPN
ejpam-1551	30	21	(	(	PUNCT
ejpam-1551	30	22	s	s	NOUN
ejpam-1551	30	23	)	)	PUNCT
ejpam-1551	30	24	which	which	PRON
ejpam-1551	30	25	is	be	AUX
ejpam-1551	30	26	called	call	VERB
ejpam-1551	30	27	darboux	darboux	ADJ
ejpam-1551	30	28	frame	frame	NOUN
ejpam-1551	30	29	and	and	CCONJ
ejpam-1551	30	30	denoted	denote	VERB
ejpam-1551	30	31	by	by	ADP
ejpam-1551	30	32	�	�	PROPN
ejpam-1551	30	33	t	t	PROPN
ejpam-1551	30	34	,	,	PUNCT
ejpam-1551	30	35	g	g	NOUN
ejpam-1551	30	36	,	,	PUNCT
ejpam-1551	30	37	n	n	NOUN
ejpam-1551	30	38	.	.	PUNCT
ejpam-1551	31	1	in	in	ADP
ejpam-1551	31	2	this	this	DET
ejpam-1551	31	3	frame	frame	NOUN
ejpam-1551	31	4	t	t	NOUN
ejpam-1551	31	5	is	be	AUX
ejpam-1551	31	6	the	the	DET
ejpam-1551	31	7	unit	unit	NOUN
ejpam-1551	31	8	tangent	tangent	NOUN
ejpam-1551	31	9	of	of	ADP
ejpam-1551	31	10	the	the	DET
ejpam-1551	31	11	curve	curve	NOUN
ejpam-1551	31	12	,	,	PUNCT
ejpam-1551	31	13	n	n	X
ejpam-1551	31	14	is	be	AUX
ejpam-1551	31	15	the	the	DET
ejpam-1551	31	16	unit	unit	NOUN
ejpam-1551	31	17	normal	normal	ADJ
ejpam-1551	31	18	of	of	ADP
ejpam-1551	31	19	the	the	DET
ejpam-1551	31	20	surface	surface	NOUN
ejpam-1551	31	21	m	m	PROPN
ejpam-1551	31	22	and	and	CCONJ
ejpam-1551	31	23	g	g	PROPN
ejpam-1551	31	24	is	be	AUX
ejpam-1551	31	25	a	a	DET
ejpam-1551	31	26	unit	unit	NOUN
ejpam-1551	31	27	vector	vector	NOUN
ejpam-1551	31	28	given	give	VERB
ejpam-1551	31	29	by	by	ADP
ejpam-1551	31	30	g=	g=	PROPN
ejpam-1551	31	31	n×t	n×t	PROPN
ejpam-1551	31	32	.	.	PROPN
ejpam-1551	32	1	since	since	SCONJ
ejpam-1551	32	2	the	the	DET
ejpam-1551	32	3	unit	unit	NOUN
ejpam-1551	32	4	tangent	tangent	PROPN
ejpam-1551	32	5	t	t	PROPN
ejpam-1551	32	6	is	be	AUX
ejpam-1551	32	7	common	common	ADJ
ejpam-1551	32	8	in	in	ADP
ejpam-1551	32	9	both	both	PRON
ejpam-1551	32	10	frenet	frenet	ADJ
ejpam-1551	32	11	frame	frame	NOUN
ejpam-1551	32	12	and	and	CCONJ
ejpam-1551	32	13	darboux	darboux	ADJ
ejpam-1551	32	14	frame	frame	NOUN
ejpam-1551	32	15	,	,	PUNCT
ejpam-1551	32	16	the	the	DET
ejpam-1551	32	17	vectors	vector	NOUN
ejpam-1551	32	18	n	n	CCONJ
ejpam-1551	32	19	,	,	PUNCT
ejpam-1551	32	20	b	b	PROPN
ejpam-1551	32	21	,	,	PUNCT
ejpam-1551	32	22	g	g	PROPN
ejpam-1551	32	23	,	,	PUNCT
ejpam-1551	32	24	n	n	PRON
ejpam-1551	32	25	lie	lie	VERB
ejpam-1551	32	26	on	on	ADP
ejpam-1551	32	27	the	the	DET
ejpam-1551	32	28	same	same	ADJ
ejpam-1551	32	29	plane	plane	NOUN
ejpam-1551	32	30	.	.	PUNCT
ejpam-1551	33	1	so	so	SCONJ
ejpam-1551	33	2	that	that	SCONJ
ejpam-1551	33	3	the	the	DET
ejpam-1551	33	4	relations	relation	NOUN
ejpam-1551	33	5	between	between	ADP
ejpam-1551	33	6	these	these	DET
ejpam-1551	33	7	frames	frame	NOUN
ejpam-1551	33	8	can	can	AUX
ejpam-1551	33	9	be	be	AUX
ejpam-1551	33	10	given	give	VERB
ejpam-1551	33	11	as	as	SCONJ
ejpam-1551	33	12	follows	follow	VERB
ejpam-1551	33	13			NOUN
ejpam-1551	33	14			NOUN
ejpam-1551	33	15			NUM
ejpam-1551	34	1	t	t	X
ejpam-1551	34	2	g	g	PROPN
ejpam-1551	34	3	n	n	PROPN
ejpam-1551	34	4			PROPN
ejpam-1551	34	5			PROPN
ejpam-1551	34	6	=	=	NOUN
ejpam-1551	34	7			VERB
ejpam-1551	34	8			ADJ
ejpam-1551	34	9			NUM
ejpam-1551	34	10	1	1	NUM
ejpam-1551	34	11	0	0	NUM
ejpam-1551	34	12	0	0	NUM
ejpam-1551	34	13	0	0	NUM
ejpam-1551	34	14	cosϕ	cosϕ	NOUN
ejpam-1551	34	15	sinϕ	sinϕ	NOUN
ejpam-1551	34	16	0	0	NUM
ejpam-1551	35	1	−	−	PRON
ejpam-1551	35	2	sinϕ	sinϕ	NOUN
ejpam-1551	35	3	cosϕ	cosϕ	NOUN
ejpam-1551	35	4			PROPN
ejpam-1551	35	5			PROPN
ejpam-1551	35	6			PROPN
ejpam-1551	35	7	·	·	PUNCT
ejpam-1551	35	8			NOUN
ejpam-1551	35	9			NOUN
ejpam-1551	35	10			NUM
ejpam-1551	35	11	t	t	PROPN
ejpam-1551	35	12	n	n	CCONJ
ejpam-1551	35	13	b	b	PROPN
ejpam-1551	35	14			PROPN
ejpam-1551	35	15			PROPN
ejpam-1551	35	16			PROPN
ejpam-1551	35	17	(	(	PUNCT
ejpam-1551	35	18	1	1	NUM
ejpam-1551	35	19	)	)	PUNCT
ejpam-1551	35	20	where	where	SCONJ
ejpam-1551	35	21	ϕ	ϕ	NOUN
ejpam-1551	35	22	is	be	AUX
ejpam-1551	35	23	the	the	DET
ejpam-1551	35	24	angle	angle	NOUN
ejpam-1551	35	25	between	between	ADP
ejpam-1551	35	26	the	the	DET
ejpam-1551	35	27	vectors	vector	NOUN
ejpam-1551	35	28	g	g	NOUN
ejpam-1551	35	29	and	and	CCONJ
ejpam-1551	35	30	n.	n.	VERB
ejpam-1551	35	31	the	the	DET
ejpam-1551	35	32	derivative	derivative	ADJ
ejpam-1551	35	33	formulae	formulae	NOUN
ejpam-1551	35	34	of	of	ADP
ejpam-1551	35	35	the	the	DET
ejpam-1551	35	36	darboux	darboux	VERB
ejpam-1551	35	37	frame	frame	NOUN
ejpam-1551	35	38	is	be	AUX
ejpam-1551	35	39			NOUN
ejpam-1551	35	40			ADJ
ejpam-1551	35	41			ADJ
ejpam-1551	35	42			NOUN
ejpam-1551	35	43	·	·	PUNCT
ejpam-1551	36	1	t	t	X
ejpam-1551	36	2	·	·	PUNCT
ejpam-1551	36	3	g	g	NOUN
ejpam-1551	36	4	·	·	PUNCT
ejpam-1551	36	5	n	n	CCONJ
ejpam-1551	36	6			PROPN
ejpam-1551	36	7			PROPN
ejpam-1551	36	8			PROPN
ejpam-1551	36	9			PROPN
ejpam-1551	36	10	=	=	NOUN
ejpam-1551	36	11			NOUN
ejpam-1551	36	12			ADJ
ejpam-1551	36	13			NOUN
ejpam-1551	36	14	0	0	PUNCT
ejpam-1551	37	1	κg	κg	ADP
ejpam-1551	37	2	κn	κn	NOUN
ejpam-1551	37	3	−κg	−κg	PROPN
ejpam-1551	37	4	0	0	NUM
ejpam-1551	37	5	τg	τg	NUM
ejpam-1551	37	6	−κn	−κn	PROPN
ejpam-1551	37	7	−τg	−τg	PROPN
ejpam-1551	37	8	0	0	PUNCT
ejpam-1551	38	1			PROPN
ejpam-1551	39	1			PROPN
ejpam-1551	39	2			PROPN
ejpam-1551	39	3	·	·	PUNCT
ejpam-1551	39	4			NOUN
ejpam-1551	39	5			NOUN
ejpam-1551	39	6			NOUN
ejpam-1551	39	7	t	t	X
ejpam-1551	39	8	g	g	PROPN
ejpam-1551	39	9	n	n	PROPN
ejpam-1551	39	10			PROPN
ejpam-1551	39	11			PROPN
ejpam-1551	39	12			PROPN
ejpam-1551	39	13	(	(	PUNCT
ejpam-1551	39	14	2	2	NUM
ejpam-1551	39	15	)	)	PUNCT
ejpam-1551	39	16	where	where	SCONJ
ejpam-1551	39	17	,	,	PUNCT
ejpam-1551	39	18	κg	κg	PROPN
ejpam-1551	39	19	is	be	AUX
ejpam-1551	39	20	the	the	DET
ejpam-1551	39	21	geodesic	geodesic	ADJ
ejpam-1551	39	22	curvature	curvature	NOUN
ejpam-1551	39	23	,	,	PUNCT
ejpam-1551	39	24	κn	κn	NOUN
ejpam-1551	39	25	is	be	AUX
ejpam-1551	39	26	the	the	DET
ejpam-1551	39	27	normal	normal	ADJ
ejpam-1551	39	28	curvature	curvature	NOUN
ejpam-1551	39	29	and	and	CCONJ
ejpam-1551	39	30	τg	τg	NOUN
ejpam-1551	39	31	is	be	AUX
ejpam-1551	39	32	the	the	DET
ejpam-1551	39	33	geodesic	geodesic	ADJ
ejpam-1551	39	34	torsion	torsion	NOUN
ejpam-1551	39	35	of	of	ADP
ejpam-1551	39	36	α	α	PROPN
ejpam-1551	39	37	(	(	PUNCT
ejpam-1551	39	38	s	s	NOUN
ejpam-1551	39	39	)	)	PUNCT
ejpam-1551	39	40	.	.	PUNCT
ejpam-1551	40	1	here	here	ADV
ejpam-1551	40	2	and	and	CCONJ
ejpam-1551	40	3	in	in	ADP
ejpam-1551	40	4	the	the	DET
ejpam-1551	40	5	following	following	NOUN
ejpam-1551	40	6	,	,	PUNCT
ejpam-1551	40	7	we	we	PRON
ejpam-1551	40	8	use	use	VERB
ejpam-1551	40	9	“	"	PUNCT
ejpam-1551	40	10	dot	dot	NOUN
ejpam-1551	40	11	”	"	PUNCT
ejpam-1551	40	12	(	(	PUNCT
ejpam-1551	40	13	·	·	PUNCT
ejpam-1551	40	14	)	)	PUNCT
ejpam-1551	40	15	to	to	PART
ejpam-1551	40	16	denote	denote	VERB
ejpam-1551	40	17	the	the	DET
ejpam-1551	40	18	derivative	derivative	NOUN
ejpam-1551	40	19	with	with	ADP
ejpam-1551	40	20	respect	respect	NOUN
ejpam-1551	40	21	to	to	ADP
ejpam-1551	40	22	the	the	DET
ejpam-1551	40	23	arc	arc	NOUN
ejpam-1551	40	24	length	length	NOUN
ejpam-1551	40	25	parameter	parameter	NOUN
ejpam-1551	40	26	of	of	ADP
ejpam-1551	40	27	a	a	DET
ejpam-1551	40	28	curve	curve	NOUN
ejpam-1551	40	29	.	.	PUNCT
ejpam-1551	41	1	the	the	DET
ejpam-1551	41	2	relations	relation	NOUN
ejpam-1551	41	3	between	between	ADP
ejpam-1551	41	4	κg	κg	PROPN
ejpam-1551	41	5	,	,	PUNCT
ejpam-1551	41	6	κn	κn	NOUN
ejpam-1551	41	7	,	,	PUNCT
ejpam-1551	41	8	τg	τg	PROPN
ejpam-1551	41	9	and	and	CCONJ
ejpam-1551	41	10	κ	κ	PROPN
ejpam-1551	41	11	,	,	PUNCT
ejpam-1551	41	12	τ	τ	PROPN
ejpam-1551	41	13	are	be	AUX
ejpam-1551	41	14	given	give	VERB
ejpam-1551	41	15	as	as	SCONJ
ejpam-1551	41	16	follows	follow	VERB
ejpam-1551	41	17	κg	κg	ADP
ejpam-1551	41	18	=	=	SYM
ejpam-1551	41	19	κ	κ	NOUN
ejpam-1551	41	20	cosϕ	cosϕ	NOUN
ejpam-1551	41	21	,	,	PUNCT
ejpam-1551	41	22	κn	κn	NOUN
ejpam-1551	41	23	=	=	PUNCT
ejpam-1551	41	24	κ	κ	PROPN
ejpam-1551	41	25	sinϕ	sinϕ	NOUN
ejpam-1551	41	26	,	,	PUNCT
ejpam-1551	41	27	τg	τg	PROPN
ejpam-1551	41	28	=	=	NOUN
ejpam-1551	41	29	τ+	τ+	PUNCT
ejpam-1551	41	30	dϕ	dϕ	NOUN
ejpam-1551	41	31	ds	ds	ADJ
ejpam-1551	41	32	.	.	PUNCT
ejpam-1551	42	1	(	(	PUNCT
ejpam-1551	42	2	3	3	X
ejpam-1551	42	3	)	)	PUNCT
ejpam-1551	42	4	furthermore	furthermore	ADV
ejpam-1551	42	5	,	,	PUNCT
ejpam-1551	42	6	the	the	DET
ejpam-1551	42	7	geodesic	geodesic	ADJ
ejpam-1551	42	8	curvature	curvature	NOUN
ejpam-1551	42	9	κg	κg	NOUN
ejpam-1551	42	10	and	and	CCONJ
ejpam-1551	42	11	geodesic	geodesic	ADJ
ejpam-1551	42	12	torsion	torsion	NOUN
ejpam-1551	42	13	τg	τg	NUM
ejpam-1551	42	14	of	of	ADP
ejpam-1551	42	15	the	the	DET
ejpam-1551	42	16	curve	curve	NOUN
ejpam-1551	42	17	α	α	PROPN
ejpam-1551	42	18	(	(	PUNCT
ejpam-1551	42	19	s	s	X
ejpam-1551	42	20	)	)	PUNCT
ejpam-1551	42	21	can	can	AUX
ejpam-1551	42	22	be	be	AUX
ejpam-1551	42	23	calculated	calculate	VERB
ejpam-1551	42	24	as	as	SCONJ
ejpam-1551	42	25	follows	follow	VERB
ejpam-1551	42	26	κg	κg	ADP
ejpam-1551	42	27	=	=	SYM
ejpam-1551	43	1	®	®	NOUN
ejpam-1551	43	2	dα	dα	NOUN
ejpam-1551	43	3	ds	ds	ADJ
ejpam-1551	43	4	,	,	PUNCT
ejpam-1551	43	5	d2α	d2α	PROPN
ejpam-1551	43	6	ds2	ds2	PROPN
ejpam-1551	43	7	×	×	PROPN
ejpam-1551	43	8	n	n	X
ejpam-1551	43	9	¸	¸	X
ejpam-1551	43	10	,	,	PUNCT
ejpam-1551	43	11	τg	τg	NUM
ejpam-1551	43	12	=	=	SYM
ejpam-1551	43	13	�	�	PROPN
ejpam-1551	44	1	dα	dα	NOUN
ejpam-1551	44	2	ds	ds	PROPN
ejpam-1551	44	3	,	,	PUNCT
ejpam-1551	44	4	n×	n×	PROPN
ejpam-1551	44	5	dn	dn	PROPN
ejpam-1551	44	6	ds	ds	PRON
ejpam-1551	44	7	�	�	PROPN
ejpam-1551	44	8	(	(	PUNCT
ejpam-1551	44	9	4	4	NUM
ejpam-1551	44	10	)	)	PUNCT
ejpam-1551	44	11	in	in	ADP
ejpam-1551	44	12	the	the	DET
ejpam-1551	44	13	differential	differential	ADJ
ejpam-1551	44	14	geometry	geometry	NOUN
ejpam-1551	44	15	of	of	ADP
ejpam-1551	44	16	surfaces	surface	NOUN
ejpam-1551	44	17	,	,	PUNCT
ejpam-1551	44	18	for	for	ADP
ejpam-1551	44	19	a	a	DET
ejpam-1551	44	20	curve	curve	NOUN
ejpam-1551	44	21	α	α	X
ejpam-1551	44	22	(	(	PUNCT
ejpam-1551	44	23	s	s	NOUN
ejpam-1551	44	24	)	)	PUNCT
ejpam-1551	44	25	lying	lie	VERB
ejpam-1551	44	26	on	on	ADP
ejpam-1551	44	27	a	a	DET
ejpam-1551	44	28	surface	surface	NOUN
ejpam-1551	44	29	m	m	VERB
ejpam-1551	44	30	the	the	DET
ejpam-1551	44	31	followings	following	NOUN
ejpam-1551	44	32	are	be	AUX
ejpam-1551	44	33	well	well	ADV
ejpam-1551	44	34	-	-	PUNCT
ejpam-1551	44	35	known	know	VERB
ejpam-1551	44	36	i	i	NOUN
ejpam-1551	44	37	)	)	PUNCT
ejpam-1551	44	38	α	α	PROPN
ejpam-1551	44	39	(	(	PUNCT
ejpam-1551	44	40	s	s	X
ejpam-1551	44	41	)	)	PUNCT
ejpam-1551	44	42	is	be	AUX
ejpam-1551	44	43	a	a	DET
ejpam-1551	44	44	geodesic	geodesic	NOUN
ejpam-1551	44	45	curve⇔	curve⇔	NOUN
ejpam-1551	44	46	κg	κg	ADP
ejpam-1551	44	47	=	=	SYM
ejpam-1551	44	48	0	0	PROPN
ejpam-1551	44	49	,	,	PUNCT
ejpam-1551	44	50	ö.	ö.	PROPN
ejpam-1551	44	51	bektaş	bektaş	PROPN
ejpam-1551	44	52	,	,	PUNCT
ejpam-1551	44	53	s.	s.	PROPN
ejpam-1551	44	54	yüce	yüce	PROPN
ejpam-1551	44	55	/	/	SYM
ejpam-1551	44	56	eur	eur	PROPN
ejpam-1551	44	57	.	.	PUNCT
ejpam-1551	45	1	j.	j.	PROPN
ejpam-1551	45	2	pure	pure	PROPN
ejpam-1551	45	3	appl	appl	PROPN
ejpam-1551	45	4	.	.	PROPN
ejpam-1551	45	5	math	math	PROPN
ejpam-1551	45	6	,	,	PUNCT
ejpam-1551	45	7	6	6	NUM
ejpam-1551	45	8	(	(	PUNCT
ejpam-1551	45	9	2013	2013	NUM
ejpam-1551	45	10	)	)	PUNCT
ejpam-1551	45	11	,	,	PUNCT
ejpam-1551	45	12	20	20	NUM
ejpam-1551	45	13	-	-	SYM
ejpam-1551	45	14	29	29	NUM
ejpam-1551	45	15	22	22	NUM
ejpam-1551	45	16	ii	ii	NOUN
ejpam-1551	45	17	)	)	PUNCT
ejpam-1551	45	18	α	α	PROPN
ejpam-1551	45	19	(	(	PUNCT
ejpam-1551	45	20	s	s	NOUN
ejpam-1551	45	21	)	)	PUNCT
ejpam-1551	45	22	is	be	AUX
ejpam-1551	45	23	an	an	DET
ejpam-1551	45	24	asymptotic	asymptotic	ADJ
ejpam-1551	45	25	line⇔	line⇔	ADJ
ejpam-1551	45	26	κn	κn	NOUN
ejpam-1551	45	27	=	=	SYM
ejpam-1551	45	28	0	0	NUM
ejpam-1551	45	29	,	,	PUNCT
ejpam-1551	45	30	iii	iii	X
ejpam-1551	45	31	)	)	PUNCT
ejpam-1551	45	32	α	α	NOUN
ejpam-1551	45	33	(	(	PUNCT
ejpam-1551	45	34	s	s	X
ejpam-1551	45	35	)	)	PUNCT
ejpam-1551	45	36	is	be	AUX
ejpam-1551	45	37	a	a	DET
ejpam-1551	45	38	principal	principal	ADJ
ejpam-1551	45	39	line⇔	line⇔	NOUN
ejpam-1551	45	40	τg	τg	NUM
ejpam-1551	46	1	=	=	NOUN
ejpam-1551	46	2	0	0	PROPN
ejpam-1551	46	3	,	,	PUNCT
ejpam-1551	46	4	[	[	X
ejpam-1551	46	5	4	4	NUM
ejpam-1551	46	6	]	]	PUNCT
ejpam-1551	46	7	.	.	PUNCT
ejpam-1551	47	1	let	let	VERB
ejpam-1551	47	2	α	α	PRON
ejpam-1551	47	3	and	and	CCONJ
ejpam-1551	47	4	β	β	X
ejpam-1551	47	5	be	be	AUX
ejpam-1551	47	6	two	two	NUM
ejpam-1551	47	7	curves	curve	NOUN
ejpam-1551	47	8	in	in	ADP
ejpam-1551	47	9	the	the	DET
ejpam-1551	47	10	euclidean	euclidean	ADJ
ejpam-1551	47	11	space	space	NOUN
ejpam-1551	47	12	e3	e3	NOUN
ejpam-1551	47	13	.	.	PUNCT
ejpam-1551	48	1	let	let	VERB
ejpam-1551	48	2	{	{	PUNCT
ejpam-1551	48	3	t	t	PROPN
ejpam-1551	48	4	,	,	PUNCT
ejpam-1551	48	5	n	n	CCONJ
ejpam-1551	48	6	,	,	PUNCT
ejpam-1551	48	7	b	b	NOUN
ejpam-1551	48	8	}	}	PUNCT
ejpam-1551	48	9	and	and	CCONJ
ejpam-1551	48	10	{	{	PUNCT
ejpam-1551	48	11	t∗,n∗,b∗	t∗,n∗,b∗	NOUN
ejpam-1551	48	12	}	}	PUNCT
ejpam-1551	48	13	be	be	AUX
ejpam-1551	48	14	frenet	frenet	NOUN
ejpam-1551	48	15	frames	frame	NOUN
ejpam-1551	48	16	of	of	ADP
ejpam-1551	48	17	α	α	PROPN
ejpam-1551	48	18	and	and	CCONJ
ejpam-1551	48	19	β	β	X
ejpam-1551	48	20	,	,	PUNCT
ejpam-1551	48	21	respectively	respectively	ADV
ejpam-1551	48	22	.	.	PUNCT
ejpam-1551	49	1	then	then	ADV
ejpam-1551	49	2	the	the	DET
ejpam-1551	49	3	curve	curve	NOUN
ejpam-1551	49	4	β	β	X
ejpam-1551	49	5	is	be	AUX
ejpam-1551	49	6	called	call	VERB
ejpam-1551	49	7	the	the	DET
ejpam-1551	49	8	involute	involute	NOUN
ejpam-1551	49	9	of	of	ADP
ejpam-1551	49	10	the	the	DET
ejpam-1551	49	11	curve	curve	NOUN
ejpam-1551	49	12	α	α	NOUN
ejpam-1551	49	13	,	,	PUNCT
ejpam-1551	49	14	if	if	SCONJ
ejpam-1551	49	15	the	the	DET
ejpam-1551	49	16	tangent	tangent	NOUN
ejpam-1551	49	17	vector	vector	NOUN
ejpam-1551	49	18	of	of	ADP
ejpam-1551	49	19	the	the	DET
ejpam-1551	49	20	curve	curve	NOUN
ejpam-1551	49	21	α	α	NOUN
ejpam-1551	49	22	at	at	ADP
ejpam-1551	49	23	the	the	DET
ejpam-1551	49	24	points	point	NOUN
ejpam-1551	49	25	α	α	X
ejpam-1551	49	26	(	(	PUNCT
ejpam-1551	49	27	s	s	NOUN
ejpam-1551	49	28	)	)	PUNCT
ejpam-1551	49	29	passes	pass	VERB
ejpam-1551	49	30	through	through	ADP
ejpam-1551	49	31	the	the	DET
ejpam-1551	49	32	tangent	tangent	ADJ
ejpam-1551	49	33	vector	vector	NOUN
ejpam-1551	49	34	of	of	ADP
ejpam-1551	49	35	the	the	DET
ejpam-1551	49	36	curve	curve	NOUN
ejpam-1551	49	37	β	β	PROPN
ejpam-1551	49	38	at	at	ADP
ejpam-1551	49	39	the	the	DET
ejpam-1551	49	40	point	point	NOUN
ejpam-1551	49	41	β	β	X
ejpam-1551	49	42	(	(	PUNCT
ejpam-1551	49	43	s	s	NOUN
ejpam-1551	49	44	)	)	PUNCT
ejpam-1551	49	45	and	and	CCONJ
ejpam-1551	49	46	t	t	PROPN
ejpam-1551	49	47	,	,	PUNCT
ejpam-1551	49	48	t∗	t∗	PROPN
ejpam-1551	49	49	�	�	PROPN
ejpam-1551	49	50	=	=	SYM
ejpam-1551	49	51	0	0	NUM
ejpam-1551	49	52	,	,	PUNCT
ejpam-1551	49	53	also	also	ADV
ejpam-1551	49	54	,	,	PUNCT
ejpam-1551	49	55	the	the	DET
ejpam-1551	49	56	curve	curve	NOUN
ejpam-1551	49	57	α	α	PROPN
ejpam-1551	49	58	is	be	AUX
ejpam-1551	49	59	called	call	VERB
ejpam-1551	49	60	the	the	DET
ejpam-1551	49	61	evolute	evolute	NOUN
ejpam-1551	49	62	of	of	ADP
ejpam-1551	49	63	the	the	DET
ejpam-1551	49	64	curve	curve	NOUN
ejpam-1551	49	65	β	β	X
ejpam-1551	49	66	.	.	PUNCT
ejpam-1551	50	1	3	3	X
ejpam-1551	50	2	.	.	X
ejpam-1551	50	3	special	special	ADJ
ejpam-1551	50	4	involute	involute	NOUN
ejpam-1551	50	5	-	-	PUNCT
ejpam-1551	50	6	evolute	evolute	NOUN
ejpam-1551	50	7	partner	partner	NOUN
ejpam-1551	50	8	d	d	NOUN
ejpam-1551	50	9	-	-	PUNCT
ejpam-1551	50	10	curves	curve	NOUN
ejpam-1551	50	11	in	in	ADP
ejpam-1551	50	12	e3	e3	NOUN
ejpam-1551	50	13	in	in	ADP
ejpam-1551	50	14	this	this	DET
ejpam-1551	50	15	section	section	NOUN
ejpam-1551	50	16	,	,	PUNCT
ejpam-1551	50	17	by	by	ADP
ejpam-1551	50	18	considering	consider	VERB
ejpam-1551	50	19	the	the	DET
ejpam-1551	50	20	darboux	darboux	VERB
ejpam-1551	50	21	frame	frame	NOUN
ejpam-1551	50	22	,	,	PUNCT
ejpam-1551	50	23	we	we	PRON
ejpam-1551	50	24	define	define	VERB
ejpam-1551	50	25	involute	involute	ADJ
ejpam-1551	50	26	evolute	evolute	PROPN
ejpam-1551	50	27	partner	partner	NOUN
ejpam-1551	50	28	d	d	PROPN
ejpam-1551	50	29	-	-	PUNCT
ejpam-1551	50	30	curves	curve	NOUN
ejpam-1551	50	31	and	and	CCONJ
ejpam-1551	50	32	give	give	VERB
ejpam-1551	50	33	the	the	DET
ejpam-1551	50	34	characterizations	characterization	NOUN
ejpam-1551	50	35	of	of	ADP
ejpam-1551	50	36	these	these	DET
ejpam-1551	50	37	curves	curve	NOUN
ejpam-1551	50	38	.	.	PUNCT
ejpam-1551	51	1	definition	definition	NOUN
ejpam-1551	51	2	1	1	NUM
ejpam-1551	51	3	.	.	PUNCT
ejpam-1551	52	1	let	let	AUX
ejpam-1551	52	2	m	m	PRON
ejpam-1551	52	3	and	and	CCONJ
ejpam-1551	52	4	n	n	CCONJ
ejpam-1551	52	5	be	be	AUX
ejpam-1551	52	6	oriented	orient	VERB
ejpam-1551	52	7	surfaces	surface	NOUN
ejpam-1551	52	8	in	in	ADP
ejpam-1551	52	9	three	three	NUM
ejpam-1551	52	10	dimensional	dimensional	ADJ
ejpam-1551	52	11	euclidean	euclidean	ADJ
ejpam-1551	52	12	space	space	NOUN
ejpam-1551	52	13	e3	e3	NOUN
ejpam-1551	52	14	and	and	CCONJ
ejpam-1551	52	15	the	the	DET
ejpam-1551	52	16	arc	arc	NOUN
ejpam-1551	52	17	length	length	NOUN
ejpam-1551	52	18	parameter	parameter	PROPN
ejpam-1551	52	19	curves	curve	NOUN
ejpam-1551	52	20	α	α	PROPN
ejpam-1551	52	21	(	(	PUNCT
ejpam-1551	52	22	s	s	NOUN
ejpam-1551	52	23	)	)	PUNCT
ejpam-1551	52	24	and	and	CCONJ
ejpam-1551	52	25	β	β	X
ejpam-1551	52	26	(	(	PUNCT
ejpam-1551	52	27	s∗	s∗	PROPN
ejpam-1551	52	28	)	)	PUNCT
ejpam-1551	52	29	lying	lie	VERB
ejpam-1551	52	30	fully	fully	ADV
ejpam-1551	52	31	on	on	ADP
ejpam-1551	52	32	m	m	PROPN
ejpam-1551	52	33	and	and	CCONJ
ejpam-1551	52	34	n	n	CCONJ
ejpam-1551	52	35	,	,	PUNCT
ejpam-1551	52	36	respectively	respectively	ADV
ejpam-1551	52	37	.	.	PUNCT
ejpam-1551	53	1	denote	denote	VERB
ejpam-1551	53	2	the	the	DET
ejpam-1551	53	3	darboux	darboux	NOUN
ejpam-1551	53	4	frames	frame	NOUN
ejpam-1551	53	5	of	of	ADP
ejpam-1551	53	6	α	α	PROPN
ejpam-1551	53	7	(	(	PUNCT
ejpam-1551	53	8	s	s	NOUN
ejpam-1551	53	9	)	)	PUNCT
ejpam-1551	53	10	and	and	CCONJ
ejpam-1551	53	11	β	β	X
ejpam-1551	53	12	(	(	PUNCT
ejpam-1551	53	13	s∗	s∗	PROPN
ejpam-1551	53	14	)	)	PUNCT
ejpam-1551	53	15	by	by	ADP
ejpam-1551	53	16	�	�	PROPN
ejpam-1551	53	17	t	t	PROPN
ejpam-1551	53	18	,	,	PUNCT
ejpam-1551	53	19	g	g	NOUN
ejpam-1551	53	20	,	,	PUNCT
ejpam-1551	53	21	n	n	PROPN
ejpam-1551	53	22	and	and	CCONJ
ejpam-1551	53	23	�	�	PROPN
ejpam-1551	53	24	t∗,g∗,n∗	t∗,g∗,n∗	NUM
ejpam-1551	53	25	,	,	PUNCT
ejpam-1551	53	26	respectively	respectively	ADV
ejpam-1551	53	27	.	.	PUNCT
ejpam-1551	54	1	if	if	SCONJ
ejpam-1551	54	2	there	there	PRON
ejpam-1551	54	3	exists	exist	VERB
ejpam-1551	54	4	a	a	DET
ejpam-1551	54	5	corresponding	correspond	VERB
ejpam-1551	54	6	relationship	relationship	NOUN
ejpam-1551	54	7	between	between	ADP
ejpam-1551	54	8	the	the	DET
ejpam-1551	54	9	curves	curve	NOUN
ejpam-1551	54	10	α	α	NOUN
ejpam-1551	54	11	and	and	CCONJ
ejpam-1551	54	12	β	β	PRON
ejpam-1551	54	13	such	such	ADJ
ejpam-1551	54	14	that	that	SCONJ
ejpam-1551	54	15	,	,	PUNCT
ejpam-1551	54	16	at	at	ADP
ejpam-1551	54	17	the	the	DET
ejpam-1551	54	18	corresponding	corresponding	ADJ
ejpam-1551	54	19	points	point	NOUN
ejpam-1551	54	20	of	of	ADP
ejpam-1551	54	21	the	the	DET
ejpam-1551	54	22	curves	curve	NOUN
ejpam-1551	54	23	,	,	PUNCT
ejpam-1551	54	24	the	the	DET
ejpam-1551	54	25	darboux	darboux	VERB
ejpam-1551	54	26	frame	frame	NOUN
ejpam-1551	54	27	element	element	NOUN
ejpam-1551	54	28	t	t	PROPN
ejpam-1551	54	29	of	of	ADP
ejpam-1551	54	30	α	α	PROPN
ejpam-1551	54	31	coincides	coincide	VERB
ejpam-1551	54	32	with	with	ADP
ejpam-1551	54	33	the	the	DET
ejpam-1551	54	34	darboux	darboux	VERB
ejpam-1551	54	35	frame	frame	NOUN
ejpam-1551	54	36	element	element	NOUN
ejpam-1551	54	37	g∗	g∗	NOUN
ejpam-1551	54	38	of	of	ADP
ejpam-1551	54	39	β	β	PRON
ejpam-1551	54	40	,	,	PUNCT
ejpam-1551	54	41	then	then	ADV
ejpam-1551	54	42	α	α	PROPN
ejpam-1551	54	43	is	be	AUX
ejpam-1551	54	44	called	call	VERB
ejpam-1551	54	45	a	a	DET
ejpam-1551	54	46	special	special	ADJ
ejpam-1551	54	47	evolute	evolute	NOUN
ejpam-1551	54	48	d	d	NOUN
ejpam-1551	54	49	-	-	PUNCT
ejpam-1551	54	50	curve	curve	NOUN
ejpam-1551	54	51	of	of	ADP
ejpam-1551	54	52	β	β	PROPN
ejpam-1551	54	53	and	and	CCONJ
ejpam-1551	54	54	β	β	X
ejpam-1551	54	55	is	be	AUX
ejpam-1551	54	56	a	a	DET
ejpam-1551	54	57	special	special	ADJ
ejpam-1551	54	58	involute	involute	ADJ
ejpam-1551	54	59	d	d	NOUN
ejpam-1551	54	60	-	-	NOUN
ejpam-1551	54	61	curve	curve	NOUN
ejpam-1551	54	62	of	of	ADP
ejpam-1551	54	63	α	α	NOUN
ejpam-1551	54	64	.	.	PUNCT
ejpam-1551	55	1	then	then	ADV
ejpam-1551	55	2	,	,	PUNCT
ejpam-1551	55	3	the	the	DET
ejpam-1551	55	4	pair	pair	NOUN
ejpam-1551	55	5	�	�	PROPN
ejpam-1551	55	6	α	α	PROPN
ejpam-1551	55	7	,	,	PUNCT
ejpam-1551	55	8	β	β	X
ejpam-1551	55	9	is	be	AUX
ejpam-1551	55	10	said	say	VERB
ejpam-1551	55	11	to	to	PART
ejpam-1551	55	12	be	be	AUX
ejpam-1551	55	13	a	a	DET
ejpam-1551	55	14	special	special	ADJ
ejpam-1551	55	15	involute	involute	NOUN
ejpam-1551	55	16	evolute	evolute	NOUN
ejpam-1551	55	17	d	d	X
ejpam-1551	55	18	-	-	PUNCT
ejpam-1551	55	19	pair	pair	NOUN
ejpam-1551	55	20	.	.	PUNCT
ejpam-1551	56	1	theorem	theorem	NOUN
ejpam-1551	56	2	1	1	NUM
ejpam-1551	56	3	.	.	PUNCT
ejpam-1551	57	1	let	let	VERB
ejpam-1551	57	2	α	α	PROPN
ejpam-1551	57	3	(	(	PUNCT
ejpam-1551	57	4	s	s	NOUN
ejpam-1551	57	5	)	)	PUNCT
ejpam-1551	57	6	and	and	CCONJ
ejpam-1551	57	7	β	β	X
ejpam-1551	57	8	(	(	PUNCT
ejpam-1551	57	9	s∗	s∗	PROPN
ejpam-1551	57	10	)	)	PUNCT
ejpam-1551	57	11	be	be	VERB
ejpam-1551	57	12	two	two	NUM
ejpam-1551	57	13	curves	curve	NOUN
ejpam-1551	57	14	in	in	ADP
ejpam-1551	57	15	the	the	DET
ejpam-1551	57	16	euclidean	euclidean	ADJ
ejpam-1551	57	17	space	space	NOUN
ejpam-1551	57	18	e3	e3	NOUN
ejpam-1551	57	19	.	.	PUNCT
ejpam-1551	58	1	if	if	SCONJ
ejpam-1551	58	2	the	the	DET
ejpam-1551	58	3	pair	pair	NOUN
ejpam-1551	58	4	�	�	PROPN
ejpam-1551	58	5	α	α	PROPN
ejpam-1551	58	6	,	,	PUNCT
ejpam-1551	58	7	β	β	X
ejpam-1551	58	8	is	be	AUX
ejpam-1551	58	9	a	a	DET
ejpam-1551	58	10	special	special	ADJ
ejpam-1551	58	11	involute	involute	NOUN
ejpam-1551	58	12	evolute	evolute	NOUN
ejpam-1551	58	13	d	d	X
ejpam-1551	58	14	-	-	PUNCT
ejpam-1551	58	15	pair	pair	NOUN
ejpam-1551	58	16	,	,	PUNCT
ejpam-1551	58	17	then	then	ADV
ejpam-1551	58	18	β	β	X
ejpam-1551	58	19	(	(	PUNCT
ejpam-1551	58	20	s	s	X
ejpam-1551	58	21	)	)	PUNCT
ejpam-1551	58	22	=	=	SYM
ejpam-1551	58	23	α	α	PROPN
ejpam-1551	58	24	(	(	PUNCT
ejpam-1551	58	25	s	s	NOUN
ejpam-1551	58	26	)	)	PUNCT
ejpam-1551	58	27	+	+	CCONJ
ejpam-1551	58	28	(	(	PUNCT
ejpam-1551	58	29	c	c	X
ejpam-1551	58	30	−	−	PROPN
ejpam-1551	58	31	s)t	s)t	X
ejpam-1551	58	32	(	(	PUNCT
ejpam-1551	58	33	s	s	NOUN
ejpam-1551	58	34	)	)	PUNCT
ejpam-1551	58	35	proof	proof	NOUN
ejpam-1551	58	36	.	.	PUNCT
ejpam-1551	58	37	suppose	suppose	VERB
ejpam-1551	58	38	that	that	SCONJ
ejpam-1551	58	39	the	the	DET
ejpam-1551	58	40	pair	pair	NOUN
ejpam-1551	58	41	�	�	PROPN
ejpam-1551	58	42	α	α	PROPN
ejpam-1551	58	43	,	,	PUNCT
ejpam-1551	58	44	β	β	X
ejpam-1551	58	45	is	be	AUX
ejpam-1551	58	46	a	a	DET
ejpam-1551	58	47	special	special	ADJ
ejpam-1551	58	48	involute	involute	NOUN
ejpam-1551	58	49	evolute	evolute	NOUN
ejpam-1551	58	50	d	d	X
ejpam-1551	58	51	-	-	PUNCT
ejpam-1551	58	52	pair	pair	NOUN
ejpam-1551	58	53	.	.	PUNCT
ejpam-1551	59	1	from	from	ADP
ejpam-1551	59	2	definition	definition	NOUN
ejpam-1551	59	3	of	of	ADP
ejpam-1551	59	4	special	special	ADJ
ejpam-1551	59	5	involute	involute	NOUN
ejpam-1551	59	6	-	-	PUNCT
ejpam-1551	59	7	evolute	evolute	NOUN
ejpam-1551	59	8	d	d	NOUN
ejpam-1551	59	9	-	-	PUNCT
ejpam-1551	59	10	pair	pair	NOUN
ejpam-1551	59	11	,	,	PUNCT
ejpam-1551	59	12	we	we	PRON
ejpam-1551	59	13	know	know	VERB
ejpam-1551	59	14	β	β	X
ejpam-1551	59	15	(	(	PUNCT
ejpam-1551	59	16	s	s	X
ejpam-1551	59	17	)	)	PUNCT
ejpam-1551	59	18	=	=	SYM
ejpam-1551	59	19	α	α	PROPN
ejpam-1551	59	20	(	(	PUNCT
ejpam-1551	59	21	s	s	NOUN
ejpam-1551	59	22	)	)	PUNCT
ejpam-1551	60	1	+	+	NOUN
ejpam-1551	60	2	λ	λ	X
ejpam-1551	60	3	(	(	PUNCT
ejpam-1551	60	4	s)t	s)t	X
ejpam-1551	60	5	(	(	PUNCT
ejpam-1551	60	6	s	s	NOUN
ejpam-1551	60	7	)	)	PUNCT
ejpam-1551	60	8	.	.	PUNCT
ejpam-1551	61	1	(	(	PUNCT
ejpam-1551	61	2	5	5	X
ejpam-1551	61	3	)	)	PUNCT
ejpam-1551	61	4	differentiating	differentiate	VERB
ejpam-1551	61	5	both	both	DET
ejpam-1551	61	6	sides	side	NOUN
ejpam-1551	61	7	of	of	ADP
ejpam-1551	61	8	the	the	DET
ejpam-1551	61	9	equation	equation	NOUN
ejpam-1551	61	10	(	(	PUNCT
ejpam-1551	61	11	5	5	NUM
ejpam-1551	61	12	)	)	PUNCT
ejpam-1551	61	13	with	with	ADP
ejpam-1551	61	14	respect	respect	NOUN
ejpam-1551	61	15	to	to	ADP
ejpam-1551	61	16	s	s	PRON
ejpam-1551	61	17	and	and	CCONJ
ejpam-1551	61	18	use	use	VERB
ejpam-1551	61	19	the	the	DET
ejpam-1551	61	20	darboux	darboux	VERB
ejpam-1551	61	21	formulas	formula	NOUN
ejpam-1551	61	22	,	,	PUNCT
ejpam-1551	61	23	we	we	PRON
ejpam-1551	61	24	obtain	obtain	VERB
ejpam-1551	61	25	t∗	t∗	PROPN
ejpam-1551	61	26	�	�	PROPN
ejpam-1551	61	27	s∗	s∗	PROPN
ejpam-1551	61	28	�	�	PROPN
ejpam-1551	61	29	ds∗	ds∗	PROPN
ejpam-1551	61	30	ds	ds	PROPN
ejpam-1551	61	31	=	=	SYM
ejpam-1551	61	32	t	t	PROPN
ejpam-1551	61	33	(	(	PUNCT
ejpam-1551	61	34	s	s	NOUN
ejpam-1551	61	35	)	)	PUNCT
ejpam-1551	61	36	+	+	CCONJ
ejpam-1551	61	37	·	·	PUNCT
ejpam-1551	61	38	λ	λ	NOUN
ejpam-1551	61	39	(	(	PUNCT
ejpam-1551	61	40	s)t	s)t	X
ejpam-1551	61	41	(	(	PUNCT
ejpam-1551	61	42	s	s	X
ejpam-1551	61	43	)	)	PUNCT
ejpam-1551	62	1	+	+	CCONJ
ejpam-1551	62	2	κg	κg	PROPN
ejpam-1551	62	3	(	(	PUNCT
ejpam-1551	62	4	s)λ	s)λ	NOUN
ejpam-1551	62	5	(	(	PUNCT
ejpam-1551	62	6	s)g	s)g	X
ejpam-1551	62	7	(	(	PUNCT
ejpam-1551	62	8	s	s	NOUN
ejpam-1551	62	9	)	)	PUNCT
ejpam-1551	62	10	+	+	CCONJ
ejpam-1551	62	11	κn	κn	NOUN
ejpam-1551	62	12	(	(	PUNCT
ejpam-1551	62	13	s)λ	s)λ	NOUN
ejpam-1551	62	14	(	(	PUNCT
ejpam-1551	62	15	s)n	s)n	NOUN
ejpam-1551	62	16	(	(	PUNCT
ejpam-1551	62	17	s	s	NOUN
ejpam-1551	62	18	)	)	PUNCT
ejpam-1551	62	19	since	since	SCONJ
ejpam-1551	62	20	the	the	DET
ejpam-1551	62	21	direction	direction	NOUN
ejpam-1551	62	22	of	of	ADP
ejpam-1551	62	23	t	t	PROPN
ejpam-1551	62	24	coincides	coincide	VERB
ejpam-1551	62	25	with	with	ADP
ejpam-1551	62	26	the	the	DET
ejpam-1551	62	27	direction	direction	NOUN
ejpam-1551	62	28	of	of	ADP
ejpam-1551	62	29	g∗	g∗	PROPN
ejpam-1551	62	30	,	,	PUNCT
ejpam-1551	62	31	we	we	PRON
ejpam-1551	62	32	get	get	VERB
ejpam-1551	62	33	·	·	PUNCT
ejpam-1551	62	34	λ	λ	X
ejpam-1551	62	35	(	(	PUNCT
ejpam-1551	62	36	s	s	NOUN
ejpam-1551	62	37	)	)	PUNCT
ejpam-1551	62	38	=	=	SYM
ejpam-1551	62	39	−1	−1	NOUN
ejpam-1551	62	40	(	(	PUNCT
ejpam-1551	62	41	6	6	NUM
ejpam-1551	62	42	)	)	PUNCT
ejpam-1551	62	43	and	and	CCONJ
ejpam-1551	62	44	λ	λ	X
ejpam-1551	62	45	(	(	PUNCT
ejpam-1551	62	46	s	s	NOUN
ejpam-1551	62	47	)	)	PUNCT
ejpam-1551	63	1	=	=	SYM
ejpam-1551	63	2	c	c	PROPN
ejpam-1551	63	3	−	−	NOUN
ejpam-1551	63	4	s	s	X
ejpam-1551	63	5	(	(	PUNCT
ejpam-1551	63	6	7	7	NUM
ejpam-1551	63	7	)	)	PUNCT
ejpam-1551	63	8	ö.	ö.	NOUN
ejpam-1551	63	9	bektaş	bektaş	PROPN
ejpam-1551	63	10	,	,	PUNCT
ejpam-1551	63	11	s.	s.	PROPN
ejpam-1551	63	12	yüce	yüce	PROPN
ejpam-1551	63	13	/	/	SYM
ejpam-1551	63	14	eur	eur	PROPN
ejpam-1551	63	15	.	.	PUNCT
ejpam-1551	64	1	j.	j.	PROPN
ejpam-1551	64	2	pure	pure	PROPN
ejpam-1551	64	3	appl	appl	PROPN
ejpam-1551	64	4	.	.	PROPN
ejpam-1551	64	5	math	math	PROPN
ejpam-1551	64	6	,	,	PUNCT
ejpam-1551	64	7	6	6	NUM
ejpam-1551	64	8	(	(	PUNCT
ejpam-1551	64	9	2013	2013	NUM
ejpam-1551	64	10	)	)	PUNCT
ejpam-1551	64	11	,	,	PUNCT
ejpam-1551	64	12	20	20	NUM
ejpam-1551	64	13	-	-	SYM
ejpam-1551	64	14	29	29	NUM
ejpam-1551	64	15	23	23	NUM
ejpam-1551	64	16	where	where	SCONJ
ejpam-1551	64	17	c	c	NOUN
ejpam-1551	64	18	is	be	AUX
ejpam-1551	64	19	constant	constant	ADJ
ejpam-1551	64	20	.	.	PUNCT
ejpam-1551	65	1	thus	thus	ADV
ejpam-1551	65	2	,	,	PUNCT
ejpam-1551	65	3	the	the	DET
ejpam-1551	65	4	equality	equality	NOUN
ejpam-1551	65	5	(	(	PUNCT
ejpam-1551	65	6	5	5	NUM
ejpam-1551	65	7	)	)	PUNCT
ejpam-1551	65	8	can	can	AUX
ejpam-1551	65	9	be	be	AUX
ejpam-1551	65	10	written	write	VERB
ejpam-1551	65	11	as	as	SCONJ
ejpam-1551	65	12	follows	follow	VERB
ejpam-1551	65	13	β	β	X
ejpam-1551	65	14	(	(	PUNCT
ejpam-1551	65	15	s	s	X
ejpam-1551	65	16	)	)	PUNCT
ejpam-1551	65	17	=	=	SYM
ejpam-1551	65	18	α	α	PROPN
ejpam-1551	65	19	(	(	PUNCT
ejpam-1551	65	20	s	s	NOUN
ejpam-1551	65	21	)	)	PUNCT
ejpam-1551	65	22	+	+	CCONJ
ejpam-1551	65	23	(	(	PUNCT
ejpam-1551	65	24	c	c	X
ejpam-1551	65	25	−	−	PROPN
ejpam-1551	65	26	s)t	s)t	X
ejpam-1551	65	27	(	(	PUNCT
ejpam-1551	65	28	s	s	NOUN
ejpam-1551	65	29	)	)	PUNCT
ejpam-1551	65	30	.	.	PUNCT
ejpam-1551	66	1	(	(	PUNCT
ejpam-1551	66	2	8)	8)	NUM
ejpam-1551	66	3	corollary	corollary	NOUN
ejpam-1551	66	4	1	1	NUM
ejpam-1551	66	5	.	.	PUNCT
ejpam-1551	67	1	let	let	VERB
ejpam-1551	67	2	α	α	PROPN
ejpam-1551	67	3	(	(	PUNCT
ejpam-1551	67	4	s	s	NOUN
ejpam-1551	67	5	)	)	PUNCT
ejpam-1551	67	6	and	and	CCONJ
ejpam-1551	67	7	β	β	X
ejpam-1551	67	8	(	(	PUNCT
ejpam-1551	67	9	s∗	s∗	PROPN
ejpam-1551	67	10	)	)	PUNCT
ejpam-1551	67	11	be	be	VERB
ejpam-1551	67	12	two	two	NUM
ejpam-1551	67	13	curves	curve	NOUN
ejpam-1551	67	14	in	in	ADP
ejpam-1551	67	15	the	the	DET
ejpam-1551	67	16	euclidean	euclidean	ADJ
ejpam-1551	67	17	space	space	NOUN
ejpam-1551	67	18	e3	e3	NOUN
ejpam-1551	67	19	.	.	PUNCT
ejpam-1551	68	1	if	if	SCONJ
ejpam-1551	68	2	the	the	DET
ejpam-1551	68	3	pair	pair	NOUN
ejpam-1551	68	4	�	�	PROPN
ejpam-1551	68	5	α	α	PROPN
ejpam-1551	68	6	,	,	PUNCT
ejpam-1551	68	7	β	β	X
ejpam-1551	68	8	is	be	AUX
ejpam-1551	68	9	a	a	DET
ejpam-1551	68	10	special	special	ADJ
ejpam-1551	68	11	involute	involute	NOUN
ejpam-1551	68	12	evolute	evolute	NOUN
ejpam-1551	68	13	d	d	X
ejpam-1551	68	14	-	-	PUNCT
ejpam-1551	68	15	pair	pair	NOUN
ejpam-1551	68	16	,	,	PUNCT
ejpam-1551	68	17	then	then	ADV
ejpam-1551	68	18	the	the	DET
ejpam-1551	68	19	distance	distance	NOUN
ejpam-1551	68	20	between	between	ADP
ejpam-1551	68	21	the	the	DET
ejpam-1551	68	22	curves	curve	NOUN
ejpam-1551	68	23	α	α	X
ejpam-1551	68	24	(	(	PUNCT
ejpam-1551	68	25	s	s	NOUN
ejpam-1551	68	26	)	)	PUNCT
ejpam-1551	68	27	and	and	CCONJ
ejpam-1551	68	28	β	β	X
ejpam-1551	68	29	(	(	PUNCT
ejpam-1551	68	30	s∗	s∗	PROPN
ejpam-1551	68	31	)	)	PUNCT
ejpam-1551	68	32	is	be	AUX
ejpam-1551	68	33	constant	constant	ADJ
ejpam-1551	68	34	.	.	PUNCT
ejpam-1551	69	1	theorem	theorem	NOUN
ejpam-1551	69	2	2	2	NUM
ejpam-1551	69	3	.	.	PUNCT
ejpam-1551	70	1	let	let	AUX
ejpam-1551	70	2	m	m	PRON
ejpam-1551	70	3	and	and	CCONJ
ejpam-1551	70	4	n	n	CCONJ
ejpam-1551	70	5	be	be	AUX
ejpam-1551	70	6	oriented	orient	VERB
ejpam-1551	70	7	surfaces	surface	NOUN
ejpam-1551	70	8	in	in	ADP
ejpam-1551	70	9	three	three	NUM
ejpam-1551	70	10	dimensional	dimensional	ADJ
ejpam-1551	70	11	euclidean	euclidean	ADJ
ejpam-1551	70	12	space	space	NOUN
ejpam-1551	70	13	e3	e3	NOUN
ejpam-1551	70	14	and	and	CCONJ
ejpam-1551	70	15	the	the	DET
ejpam-1551	70	16	arc	arc	NOUN
ejpam-1551	70	17	length	length	NOUN
ejpam-1551	70	18	parameter	parameter	PROPN
ejpam-1551	70	19	curves	curve	NOUN
ejpam-1551	70	20	α	α	PROPN
ejpam-1551	70	21	(	(	PUNCT
ejpam-1551	70	22	s	s	NOUN
ejpam-1551	70	23	)	)	PUNCT
ejpam-1551	70	24	and	and	CCONJ
ejpam-1551	70	25	β	β	X
ejpam-1551	70	26	(	(	PUNCT
ejpam-1551	70	27	s∗	s∗	PROPN
ejpam-1551	70	28	)	)	PUNCT
ejpam-1551	70	29	lying	lie	VERB
ejpam-1551	70	30	fully	fully	ADV
ejpam-1551	70	31	on	on	ADP
ejpam-1551	70	32	m	m	PROPN
ejpam-1551	70	33	and	and	CCONJ
ejpam-1551	70	34	n	n	CCONJ
ejpam-1551	70	35	,	,	PUNCT
ejpam-1551	70	36	respectively	respectively	ADV
ejpam-1551	70	37	.	.	PUNCT
ejpam-1551	71	1	β	β	X
ejpam-1551	71	2	(	(	PUNCT
ejpam-1551	71	3	s∗	s∗	PROPN
ejpam-1551	71	4	)	)	PUNCT
ejpam-1551	71	5	is	be	AUX
ejpam-1551	71	6	special	special	ADJ
ejpam-1551	71	7	involute	involute	ADJ
ejpam-1551	71	8	d	d	NOUN
ejpam-1551	71	9	-	-	NOUN
ejpam-1551	71	10	curve	curve	NOUN
ejpam-1551	71	11	of	of	ADP
ejpam-1551	71	12	α	α	PROPN
ejpam-1551	71	13	(	(	PUNCT
ejpam-1551	71	14	s	s	NOUN
ejpam-1551	71	15	)	)	PUNCT
ejpam-1551	71	16	if	if	SCONJ
ejpam-1551	71	17	and	and	CCONJ
ejpam-1551	71	18	only	only	ADV
ejpam-1551	71	19	if	if	SCONJ
ejpam-1551	71	20	the	the	DET
ejpam-1551	71	21	normal	normal	ADJ
ejpam-1551	71	22	curvature	curvature	NOUN
ejpam-1551	71	23	κ∗n	κ∗n	PUNCT
ejpam-1551	71	24	of	of	ADP
ejpam-1551	71	25	β	β	X
ejpam-1551	71	26	(	(	PUNCT
ejpam-1551	71	27	s∗	s∗	PROPN
ejpam-1551	71	28	)	)	PUNCT
ejpam-1551	71	29	and	and	CCONJ
ejpam-1551	71	30	the	the	DET
ejpam-1551	71	31	geodesic	geodesic	ADJ
ejpam-1551	71	32	curvature	curvature	NOUN
ejpam-1551	71	33	κg	κg	ADP
ejpam-1551	71	34	,	,	PUNCT
ejpam-1551	71	35	the	the	DET
ejpam-1551	71	36	normal	normal	ADJ
ejpam-1551	71	37	curvature	curvature	NOUN
ejpam-1551	71	38	κn	κn	NOUN
ejpam-1551	71	39	and	and	CCONJ
ejpam-1551	71	40	the	the	DET
ejpam-1551	71	41	geodesic	geodesic	ADJ
ejpam-1551	71	42	torsion	torsion	NOUN
ejpam-1551	71	43	τg	τg	PROPN
ejpam-1551	71	44	of	of	ADP
ejpam-1551	71	45	α	α	PROPN
ejpam-1551	71	46	(	(	PUNCT
ejpam-1551	71	47	s	s	NOUN
ejpam-1551	71	48	)	)	PUNCT
ejpam-1551	71	49	satisfy	satisfy	VERB
ejpam-1551	71	50	the	the	DET
ejpam-1551	71	51	following	follow	VERB
ejpam-1551	71	52	equation	equation	NOUN
ejpam-1551	71	53	·	·	PUNCT
ejpam-1551	71	54	κn	κn	NOUN
ejpam-1551	71	55	=	=	PUNCT
ejpam-1551	71	56	κ2	κ2	PROPN
ejpam-1551	71	57	n	n	PROPN
ejpam-1551	71	58	+	+	CCONJ
ejpam-1551	71	59	κ	κ	PROPN
ejpam-1551	71	60	2	2	NUM
ejpam-1551	71	61	g	g	NOUN
ejpam-1551	71	62	κg	κg	PROPN
ejpam-1551	71	63	!	!	PUNCT
ejpam-1551	72	1	�	�	PROPN
ejpam-1551	72	2	λκ∗nκg	λκ∗nκg	PROPN
ejpam-1551	72	3	cosθ	cosθ	PROPN
ejpam-1551	72	4	−τg	−τg	PROPN
ejpam-1551	72	5	�	�	PROPN
ejpam-1551	72	6	+	+	CCONJ
ejpam-1551	72	7	·	·	PUNCT
ejpam-1551	72	8	κgκn	κgκn	ADJ
ejpam-1551	72	9	κg	κg	ADP
ejpam-1551	72	10	for	for	ADP
ejpam-1551	72	11	some	some	DET
ejpam-1551	72	12	nonzero	nonzero	PROPN
ejpam-1551	72	13	constants	constant	NOUN
ejpam-1551	72	14	λ	λ	PROPN
ejpam-1551	72	15	,	,	PUNCT
ejpam-1551	72	16	where	where	SCONJ
ejpam-1551	72	17	θ	θ	PROPN
ejpam-1551	72	18	is	be	AUX
ejpam-1551	72	19	the	the	DET
ejpam-1551	72	20	angle	angle	NOUN
ejpam-1551	72	21	between	between	ADP
ejpam-1551	72	22	the	the	DET
ejpam-1551	72	23	vectors	vector	NOUN
ejpam-1551	72	24	n	n	CCONJ
ejpam-1551	72	25	and	and	CCONJ
ejpam-1551	72	26	n∗	n∗	PROPN
ejpam-1551	72	27	at	at	ADP
ejpam-1551	72	28	the	the	DET
ejpam-1551	72	29	corresponding	corresponding	ADJ
ejpam-1551	72	30	points	point	NOUN
ejpam-1551	72	31	of	of	ADP
ejpam-1551	72	32	α	α	PROPN
ejpam-1551	72	33	(	(	PUNCT
ejpam-1551	72	34	s	s	NOUN
ejpam-1551	72	35	)	)	PUNCT
ejpam-1551	72	36	and	and	CCONJ
ejpam-1551	72	37	β	β	X
ejpam-1551	72	38	(	(	PUNCT
ejpam-1551	72	39	s∗	s∗	PROPN
ejpam-1551	72	40	)	)	PUNCT
ejpam-1551	72	41	.	.	PUNCT
ejpam-1551	73	1	proof	proof	NOUN
ejpam-1551	73	2	.	.	PUNCT
ejpam-1551	74	1	suppose	suppose	VERB
ejpam-1551	74	2	that	that	SCONJ
ejpam-1551	74	3	m	m	PROPN
ejpam-1551	74	4	and	and	CCONJ
ejpam-1551	74	5	n	n	PRON
ejpam-1551	74	6	are	be	AUX
ejpam-1551	74	7	oriented	orient	VERB
ejpam-1551	74	8	surfaces	surface	NOUN
ejpam-1551	74	9	in	in	ADP
ejpam-1551	74	10	three	three	NUM
ejpam-1551	74	11	dimensional	dimensional	ADJ
ejpam-1551	74	12	euclidean	euclidean	ADJ
ejpam-1551	74	13	space	space	NOUN
ejpam-1551	74	14	e3	e3	NOUN
ejpam-1551	74	15	and	and	CCONJ
ejpam-1551	74	16	the	the	DET
ejpam-1551	74	17	arc	arc	NOUN
ejpam-1551	74	18	length	length	NOUN
ejpam-1551	74	19	parameter	parameter	PROPN
ejpam-1551	74	20	curves	curve	NOUN
ejpam-1551	74	21	α	α	PROPN
ejpam-1551	74	22	(	(	PUNCT
ejpam-1551	74	23	s	s	NOUN
ejpam-1551	74	24	)	)	PUNCT
ejpam-1551	74	25	and	and	CCONJ
ejpam-1551	74	26	β	β	X
ejpam-1551	74	27	(	(	PUNCT
ejpam-1551	74	28	s∗	s∗	PROPN
ejpam-1551	74	29	)	)	PUNCT
ejpam-1551	74	30	lying	lie	VERB
ejpam-1551	74	31	fully	fully	ADV
ejpam-1551	74	32	on	on	ADP
ejpam-1551	74	33	m	m	PROPN
ejpam-1551	74	34	and	and	CCONJ
ejpam-1551	74	35	n	n	CCONJ
ejpam-1551	74	36	,	,	PUNCT
ejpam-1551	74	37	respectively	respectively	ADV
ejpam-1551	74	38	.	.	PUNCT
ejpam-1551	75	1	denote	denote	VERB
ejpam-1551	75	2	the	the	DET
ejpam-1551	75	3	darboux	darboux	NOUN
ejpam-1551	75	4	frames	frame	NOUN
ejpam-1551	75	5	of	of	ADP
ejpam-1551	75	6	α	α	PROPN
ejpam-1551	75	7	(	(	PUNCT
ejpam-1551	75	8	s	s	NOUN
ejpam-1551	75	9	)	)	PUNCT
ejpam-1551	75	10	and	and	CCONJ
ejpam-1551	75	11	β	β	X
ejpam-1551	75	12	(	(	PUNCT
ejpam-1551	75	13	s∗	s∗	PROPN
ejpam-1551	75	14	)	)	PUNCT
ejpam-1551	75	15	by	by	ADP
ejpam-1551	75	16	�	�	PROPN
ejpam-1551	75	17	t	t	PROPN
ejpam-1551	75	18	,	,	PUNCT
ejpam-1551	75	19	g	g	NOUN
ejpam-1551	75	20	,	,	PUNCT
ejpam-1551	75	21	n	n	PROPN
ejpam-1551	75	22	and	and	CCONJ
ejpam-1551	75	23	�	�	PROPN
ejpam-1551	75	24	t∗,g∗,n∗	t∗,g∗,n∗	NUM
ejpam-1551	75	25	,	,	PUNCT
ejpam-1551	75	26	respectively	respectively	ADV
ejpam-1551	75	27	.	.	PUNCT
ejpam-1551	76	1	then	then	ADV
ejpam-1551	76	2	by	by	ADP
ejpam-1551	76	3	the	the	DET
ejpam-1551	76	4	definition	definition	NOUN
ejpam-1551	76	5	we	we	PRON
ejpam-1551	76	6	can	can	AUX
ejpam-1551	76	7	assume	assume	VERB
ejpam-1551	76	8	that	that	SCONJ
ejpam-1551	76	9	β	β	PROPN
ejpam-1551	76	10	(	(	PUNCT
ejpam-1551	76	11	s	s	X
ejpam-1551	76	12	)	)	PUNCT
ejpam-1551	76	13	=	=	SYM
ejpam-1551	76	14	α	α	PROPN
ejpam-1551	76	15	(	(	PUNCT
ejpam-1551	76	16	s	s	NOUN
ejpam-1551	76	17	)	)	PUNCT
ejpam-1551	76	18	+	+	NOUN
ejpam-1551	76	19	λ	λ	X
ejpam-1551	76	20	(	(	PUNCT
ejpam-1551	76	21	s)t	s)t	X
ejpam-1551	76	22	(	(	PUNCT
ejpam-1551	76	23	s	s	X
ejpam-1551	76	24	)	)	PUNCT
ejpam-1551	76	25	(	(	PUNCT
ejpam-1551	76	26	9	9	NUM
ejpam-1551	76	27	)	)	PUNCT
ejpam-1551	76	28	for	for	ADP
ejpam-1551	76	29	some	some	DET
ejpam-1551	76	30	function	function	NOUN
ejpam-1551	76	31	λ	λ	X
ejpam-1551	76	32	(	(	PUNCT
ejpam-1551	76	33	s	s	NOUN
ejpam-1551	76	34	)	)	PUNCT
ejpam-1551	76	35	.	.	PUNCT
ejpam-1551	77	1	by	by	ADP
ejpam-1551	77	2	taking	take	VERB
ejpam-1551	77	3	derivative	derivative	NOUN
ejpam-1551	77	4	of	of	ADP
ejpam-1551	77	5	(	(	PUNCT
ejpam-1551	77	6	9	9	NUM
ejpam-1551	77	7	)	)	PUNCT
ejpam-1551	77	8	with	with	ADP
ejpam-1551	77	9	respect	respect	NOUN
ejpam-1551	77	10	to	to	ADP
ejpam-1551	77	11	s	s	PRON
ejpam-1551	77	12	and	and	CCONJ
ejpam-1551	77	13	applying	apply	VERB
ejpam-1551	77	14	the	the	DET
ejpam-1551	77	15	darboux	darboux	VERB
ejpam-1551	77	16	formulas	formula	NOUN
ejpam-1551	77	17	(	(	PUNCT
ejpam-1551	77	18	2	2	X
ejpam-1551	77	19	)	)	PUNCT
ejpam-1551	77	20	we	we	PRON
ejpam-1551	77	21	have	have	VERB
ejpam-1551	77	22	t∗	t∗	NOUN
ejpam-1551	77	23	ds∗	ds∗	NOUN
ejpam-1551	77	24	ds	ds	NOUN
ejpam-1551	77	25	=	=	SYM
ejpam-1551	77	26	�	�	PROPN
ejpam-1551	77	27	1	1	NUM
ejpam-1551	77	28	+	+	CCONJ
ejpam-1551	77	29	·	·	PUNCT
ejpam-1551	77	30	λ	λ	PROPN
ejpam-1551	77	31	�	�	PROPN
ejpam-1551	77	32	t+λκgg+λκnn	t+λκgg+λκnn	PROPN
ejpam-1551	77	33	(	(	PUNCT
ejpam-1551	77	34	10	10	NUM
ejpam-1551	77	35	)	)	PUNCT
ejpam-1551	77	36	from	from	ADP
ejpam-1551	77	37	(	(	PUNCT
ejpam-1551	77	38	6	6	NUM
ejpam-1551	77	39	)	)	PUNCT
ejpam-1551	77	40	we	we	PRON
ejpam-1551	77	41	get	get	VERB
ejpam-1551	77	42	t∗	t∗	NOUN
ejpam-1551	77	43	ds∗	ds∗	NOUN
ejpam-1551	77	44	ds	ds	X
ejpam-1551	77	45	=	=	SYM
ejpam-1551	77	46	λκgg+λκnn	λκgg+λκnn	PROPN
ejpam-1551	77	47	.	.	PUNCT
ejpam-1551	78	1	(	(	PUNCT
ejpam-1551	78	2	11	11	NUM
ejpam-1551	78	3	)	)	PUNCT
ejpam-1551	78	4	on	on	ADP
ejpam-1551	78	5	the	the	DET
ejpam-1551	78	6	other	other	ADJ
ejpam-1551	78	7	hand	hand	NOUN
ejpam-1551	78	8	we	we	PRON
ejpam-1551	78	9	have	have	VERB
ejpam-1551	78	10	t∗	t∗	NOUN
ejpam-1551	78	11	=	=	SYM
ejpam-1551	78	12	cosθg−	cosθg−	NOUN
ejpam-1551	78	13	sinθn	sinθn	NOUN
ejpam-1551	78	14	.	.	PUNCT
ejpam-1551	79	1	(	(	PUNCT
ejpam-1551	79	2	12	12	NUM
ejpam-1551	79	3	)	)	PUNCT
ejpam-1551	79	4	differentiating	differentiate	VERB
ejpam-1551	79	5	(	(	PUNCT
ejpam-1551	79	6	12	12	NUM
ejpam-1551	79	7	)	)	PUNCT
ejpam-1551	79	8	with	with	ADP
ejpam-1551	79	9	respect	respect	NOUN
ejpam-1551	79	10	to	to	ADP
ejpam-1551	79	11	s	s	PRON
ejpam-1551	79	12	,	,	PUNCT
ejpam-1551	79	13	we	we	PRON
ejpam-1551	79	14	obtain	obtain	VERB
ejpam-1551	79	15	�	�	PROPN
ejpam-1551	79	16	κ∗gg	κ∗gg	NOUN
ejpam-1551	79	17	∗	∗	NOUN
ejpam-1551	79	18	+	+	CCONJ
ejpam-1551	79	19	κ∗nn∗	κ∗nn∗	PROPN
ejpam-1551	79	20	�	�	PROPN
ejpam-1551	79	21	ds∗	ds∗	NOUN
ejpam-1551	79	22	ds	ds	PROPN
ejpam-1551	79	23	=	=	SYM
ejpam-1551	79	24	�	�	PROPN
ejpam-1551	79	25	κg	κg	PROPN
ejpam-1551	79	26	cosθ−κn	cosθ−κn	PROPN
ejpam-1551	79	27	sinθ	sinθ	PROPN
ejpam-1551	79	28	�	�	PROPN
ejpam-1551	79	29	t+	t+	PUNCT
ejpam-1551	79	30	�	�	PROPN
ejpam-1551	79	31	τg	τg	NUM
ejpam-1551	79	32	−	−	PROPN
ejpam-1551	79	33	·	·	PUNCT
ejpam-1551	79	34	θ	θ	X
ejpam-1551	79	35	�	�	PROPN
ejpam-1551	79	36	sinθg+	sinθg+	PUNCT
ejpam-1551	79	37	�	�	PROPN
ejpam-1551	79	38	τg	τg	NUM
ejpam-1551	79	39	−	−	PROPN
ejpam-1551	79	40	·	·	PUNCT
ejpam-1551	79	41	θ	θ	PROPN
ejpam-1551	79	42	�	�	PROPN
ejpam-1551	79	43	cosθn	cosθn	PROPN
ejpam-1551	79	44	from	from	ADP
ejpam-1551	79	45	the	the	DET
ejpam-1551	79	46	last	last	ADJ
ejpam-1551	79	47	equation	equation	NOUN
ejpam-1551	79	48	and	and	CCONJ
ejpam-1551	79	49	the	the	DET
ejpam-1551	79	50	fact	fact	NOUN
ejpam-1551	79	51	that	that	SCONJ
ejpam-1551	79	52	n∗	n∗	VERB
ejpam-1551	80	1	=	=	PRON
ejpam-1551	80	2	sinθg+	sinθg+	X
ejpam-1551	80	3	cosθn	cosθn	NOUN
ejpam-1551	80	4	we	we	PRON
ejpam-1551	80	5	have	have	VERB
ejpam-1551	80	6	�	�	PROPN
ejpam-1551	80	7	κ∗gg	κ∗gg	NOUN
ejpam-1551	80	8	∗	∗	NOUN
ejpam-1551	80	9	+	+	CCONJ
ejpam-1551	80	10	κ∗nsinθg+	κ∗nsinθg+	PROPN
ejpam-1551	80	11	κ∗n	κ∗n	PUNCT
ejpam-1551	80	12	cosθn	cosθn	PROPN
ejpam-1551	80	13	�	�	PROPN
ejpam-1551	80	14	ds∗	ds∗	PROPN
ejpam-1551	80	15	ds	ds	PROPN
ejpam-1551	80	16	=	=	SYM
ejpam-1551	80	17	�	�	PROPN
ejpam-1551	80	18	κn	κn	PROPN
ejpam-1551	80	19	sinθ	sinθ	PROPN
ejpam-1551	80	20	−	−	PROPN
ejpam-1551	80	21	κg	κg	PROPN
ejpam-1551	80	22	cosθ	cosθ	PROPN
ejpam-1551	80	23	�	�	PROPN
ejpam-1551	80	24	t+	t+	PUNCT
ejpam-1551	80	25	�	�	PROPN
ejpam-1551	80	26	τg	τg	NUM
ejpam-1551	80	27	−	−	PROPN
ejpam-1551	80	28	·	·	PUNCT
ejpam-1551	80	29	θ	θ	PROPN
ejpam-1551	80	30	�	�	PROPN
ejpam-1551	80	31	sinθg	sinθg	PROPN
ejpam-1551	80	32	ö.	ö.	PROPN
ejpam-1551	80	33	bektaş	bektaş	PROPN
ejpam-1551	80	34	,	,	PUNCT
ejpam-1551	80	35	s.	s.	PROPN
ejpam-1551	80	36	yüce	yüce	PROPN
ejpam-1551	80	37	/	/	SYM
ejpam-1551	80	38	eur	eur	PROPN
ejpam-1551	80	39	.	.	PUNCT
ejpam-1551	81	1	j.	j.	PROPN
ejpam-1551	81	2	pure	pure	PROPN
ejpam-1551	81	3	appl	appl	PROPN
ejpam-1551	81	4	.	.	PROPN
ejpam-1551	81	5	math	math	PROPN
ejpam-1551	81	6	,	,	PUNCT
ejpam-1551	81	7	6	6	NUM
ejpam-1551	81	8	(	(	PUNCT
ejpam-1551	81	9	2013	2013	NUM
ejpam-1551	81	10	)	)	PUNCT
ejpam-1551	81	11	,	,	PUNCT
ejpam-1551	81	12	20	20	NUM
ejpam-1551	81	13	-	-	SYM
ejpam-1551	81	14	29	29	NUM
ejpam-1551	81	15	24	24	NUM
ejpam-1551	81	16	+	+	NUM
ejpam-1551	81	17	�	�	PROPN
ejpam-1551	81	18	τg	τg	PRON
ejpam-1551	81	19	−	−	PROPN
ejpam-1551	81	20	·	·	PUNCT
ejpam-1551	81	21	θ	θ	PROPN
ejpam-1551	81	22	�	�	PROPN
ejpam-1551	81	23	cosθn	cosθn	PROPN
ejpam-1551	81	24	.	.	PUNCT
ejpam-1551	82	1	since	since	SCONJ
ejpam-1551	82	2	the	the	DET
ejpam-1551	82	3	direction	direction	NOUN
ejpam-1551	82	4	of	of	ADP
ejpam-1551	82	5	t	t	PROPN
ejpam-1551	82	6	is	be	AUX
ejpam-1551	82	7	coincident	coincident	ADJ
ejpam-1551	82	8	with	with	ADP
ejpam-1551	82	9	g∗	g∗	NOUN
ejpam-1551	82	10	we	we	PRON
ejpam-1551	82	11	have	have	VERB
ejpam-1551	83	1	·	·	PUNCT
ejpam-1551	83	2	θ	θ	X
ejpam-1551	83	3	=	=	SYM
ejpam-1551	83	4	τg	τg	PROPN
ejpam-1551	84	1	−	−	PROPN
ejpam-1551	84	2	κ	κ	PROPN
ejpam-1551	84	3	∗	∗	X
ejpam-1551	84	4	n	n	CCONJ
ejpam-1551	84	5	ds∗	ds∗	ADJ
ejpam-1551	84	6	ds	ds	X
ejpam-1551	84	7	.	.	PUNCT
ejpam-1551	85	1	(	(	PUNCT
ejpam-1551	85	2	13	13	NUM
ejpam-1551	85	3	)	)	PUNCT
ejpam-1551	85	4	from	from	ADP
ejpam-1551	85	5	(	(	PUNCT
ejpam-1551	85	6	10	10	NUM
ejpam-1551	85	7	)	)	PUNCT
ejpam-1551	85	8	and	and	CCONJ
ejpam-1551	85	9	(	(	PUNCT
ejpam-1551	85	10	12	12	NUM
ejpam-1551	85	11	)	)	PUNCT
ejpam-1551	85	12	we	we	PRON
ejpam-1551	85	13	obtain	obtain	VERB
ejpam-1551	85	14	ds∗	ds∗	NOUN
ejpam-1551	85	15	ds	ds	NOUN
ejpam-1551	85	16	=	=	PUNCT
ejpam-1551	85	17	λκg	λκg	NOUN
ejpam-1551	85	18	cosθ	cosθ	X
ejpam-1551	85	19	=	=	SYM
ejpam-1551	86	1	−	−	PROPN
ejpam-1551	86	2	λκn	λκn	X
ejpam-1551	86	3	sinθ	sinθ	X
ejpam-1551	86	4	(	(	PUNCT
ejpam-1551	86	5	14	14	NUM
ejpam-1551	86	6	)	)	PUNCT
ejpam-1551	86	7	and	and	CCONJ
ejpam-1551	86	8	−λκn	−λκn	X
ejpam-1551	86	9	=	=	PUNCT
ejpam-1551	86	10	λκg	λκg	NOUN
ejpam-1551	86	11	tanθ	tanθ	NOUN
ejpam-1551	86	12	(	(	PUNCT
ejpam-1551	86	13	15	15	NUM
ejpam-1551	86	14	)	)	PUNCT
ejpam-1551	86	15	by	by	ADP
ejpam-1551	86	16	taking	take	VERB
ejpam-1551	86	17	the	the	DET
ejpam-1551	86	18	derivative	derivative	NOUN
ejpam-1551	86	19	of	of	ADP
ejpam-1551	86	20	this	this	DET
ejpam-1551	86	21	equation	equation	NOUN
ejpam-1551	86	22	and	and	CCONJ
ejpam-1551	86	23	applying	apply	VERB
ejpam-1551	86	24	(	(	PUNCT
ejpam-1551	86	25	13	13	NUM
ejpam-1551	86	26	)	)	PUNCT
ejpam-1551	86	27	we	we	PRON
ejpam-1551	86	28	get	get	VERB
ejpam-1551	86	29	·	·	PUNCT
ejpam-1551	86	30	κn	κn	NOUN
ejpam-1551	86	31	=	=	PUNCT
ejpam-1551	86	32	κ2	κ2	PROPN
ejpam-1551	86	33	n	n	PROPN
ejpam-1551	86	34	+	+	CCONJ
ejpam-1551	86	35	κ	κ	PROPN
ejpam-1551	86	36	2	2	NUM
ejpam-1551	86	37	g	g	NOUN
ejpam-1551	86	38	κg	κg	PROPN
ejpam-1551	86	39	!	!	PUNCT
ejpam-1551	87	1	�	�	PROPN
ejpam-1551	87	2	λκ∗nκg	λκ∗nκg	PROPN
ejpam-1551	87	3	cosθ	cosθ	PROPN
ejpam-1551	87	4	−τg	−τg	PROPN
ejpam-1551	87	5	�	�	PROPN
ejpam-1551	87	6	+	+	CCONJ
ejpam-1551	87	7	·	·	PUNCT
ejpam-1551	87	8	κgκn	κgκn	ADJ
ejpam-1551	87	9	κg	κg	PROPN
ejpam-1551	87	10	.	.	PUNCT
ejpam-1551	88	1	(	(	PUNCT
ejpam-1551	88	2	16	16	NUM
ejpam-1551	88	3	)	)	PUNCT
ejpam-1551	88	4	that	that	PRON
ejpam-1551	88	5	is	be	AUX
ejpam-1551	88	6	desired	desire	VERB
ejpam-1551	88	7	.	.	PUNCT
ejpam-1551	89	1	conversely	conversely	ADV
ejpam-1551	89	2	,	,	PUNCT
ejpam-1551	89	3	assume	assume	VERB
ejpam-1551	89	4	that	that	SCONJ
ejpam-1551	89	5	the	the	DET
ejpam-1551	89	6	equation	equation	NOUN
ejpam-1551	89	7	(	(	PUNCT
ejpam-1551	89	8	16	16	NUM
ejpam-1551	89	9	)	)	PUNCT
ejpam-1551	89	10	holds	hold	VERB
ejpam-1551	89	11	for	for	ADP
ejpam-1551	89	12	some	some	DET
ejpam-1551	89	13	nonzero	nonzero	PROPN
ejpam-1551	89	14	constants	constant	NOUN
ejpam-1551	89	15	λ	λ	PROPN
ejpam-1551	89	16	.	.	PUNCT
ejpam-1551	89	17	then	then	ADV
ejpam-1551	89	18	by	by	ADP
ejpam-1551	89	19	using	use	VERB
ejpam-1551	89	20	(	(	PUNCT
ejpam-1551	89	21	14	14	NUM
ejpam-1551	89	22	)	)	PUNCT
ejpam-1551	89	23	,	,	PUNCT
ejpam-1551	89	24	(	(	PUNCT
ejpam-1551	89	25	15	15	NUM
ejpam-1551	89	26	)	)	PUNCT
ejpam-1551	89	27	and	and	CCONJ
ejpam-1551	89	28	(	(	PUNCT
ejpam-1551	89	29	16	16	NUM
ejpam-1551	89	30	)	)	PUNCT
ejpam-1551	89	31	gives	give	VERB
ejpam-1551	89	32	us	we	PRON
ejpam-1551	89	33	κ∗n	κ∗n	PUNCT
ejpam-1551	89	34	�	�	PROPN
ejpam-1551	89	35	ds∗	ds∗	ADJ
ejpam-1551	89	36	ds	ds	PROPN
ejpam-1551	89	37	�	�	PROPN
ejpam-1551	89	38	3	3	NUM
ejpam-1551	89	39	=	=	SYM
ejpam-1551	89	40	λ2	λ2	NOUN
ejpam-1551	89	41	·	·	PUNCT
ejpam-1551	89	42	κnκg−λ	κnκg−λ	NUM
ejpam-1551	89	43	2	2	NUM
ejpam-1551	89	44	·	·	SYM
ejpam-1551	89	45	κgκn+λ	κgκn+λ	NOUN
ejpam-1551	89	46	2	2	NUM
ejpam-1551	89	47	�	�	PROPN
ejpam-1551	89	48	κ2	κ2	PROPN
ejpam-1551	89	49	n+	n+	ADP
ejpam-1551	89	50	κ	κ	PROPN
ejpam-1551	89	51	2	2	NUM
ejpam-1551	89	52	g	g	PROPN
ejpam-1551	89	53	�	�	PROPN
ejpam-1551	89	54	τg	τg	PROPN
ejpam-1551	89	55	(	(	PUNCT
ejpam-1551	89	56	17	17	NUM
ejpam-1551	89	57	)	)	PUNCT
ejpam-1551	89	58	let	let	AUX
ejpam-1551	89	59	define	define	VERB
ejpam-1551	89	60	a	a	DET
ejpam-1551	89	61	curve	curve	NOUN
ejpam-1551	89	62	β	β	X
ejpam-1551	89	63	(	(	PUNCT
ejpam-1551	89	64	s	s	X
ejpam-1551	89	65	)	)	PUNCT
ejpam-1551	89	66	=	=	SYM
ejpam-1551	89	67	α	α	PROPN
ejpam-1551	89	68	(	(	PUNCT
ejpam-1551	89	69	s	s	NOUN
ejpam-1551	89	70	)	)	PUNCT
ejpam-1551	90	1	+	+	NOUN
ejpam-1551	90	2	λ	λ	X
ejpam-1551	90	3	(	(	PUNCT
ejpam-1551	90	4	s)t	s)t	X
ejpam-1551	90	5	(	(	PUNCT
ejpam-1551	90	6	s	s	X
ejpam-1551	90	7	)	)	PUNCT
ejpam-1551	90	8	by	by	ADP
ejpam-1551	90	9	taking	take	VERB
ejpam-1551	90	10	the	the	DET
ejpam-1551	90	11	derivative	derivative	NOUN
ejpam-1551	90	12	of	of	ADP
ejpam-1551	90	13	the	the	DET
ejpam-1551	90	14	last	last	ADJ
ejpam-1551	90	15	equation	equation	NOUN
ejpam-1551	90	16	with	with	ADP
ejpam-1551	90	17	respect	respect	NOUN
ejpam-1551	90	18	to	to	ADP
ejpam-1551	90	19	s	s	NOUN
ejpam-1551	90	20	twice	twice	ADV
ejpam-1551	90	21	,	,	PUNCT
ejpam-1551	90	22	we	we	PRON
ejpam-1551	90	23	get	get	VERB
ejpam-1551	90	24	t∗	t∗	NOUN
ejpam-1551	90	25	ds∗	ds∗	NOUN
ejpam-1551	90	26	ds	ds	NOUN
ejpam-1551	90	27	=	=	SYM
ejpam-1551	90	28	λκgg+λκnn	λκgg+λκnn	PROPN
ejpam-1551	90	29	(	(	PUNCT
ejpam-1551	90	30	18	18	NUM
ejpam-1551	90	31	)	)	PUNCT
ejpam-1551	90	32	and	and	CCONJ
ejpam-1551	90	33	�	�	PROPN
ejpam-1551	90	34	κ∗gg∗+κ∗nn	κ∗gg∗+κ∗nn	PROPN
ejpam-1551	90	35	∗	∗	PROPN
ejpam-1551	90	36	�	�	PROPN
ejpam-1551	90	37	�	�	PROPN
ejpam-1551	90	38	ds∗	ds∗	PROPN
ejpam-1551	90	39	ds	ds	PROPN
ejpam-1551	90	40	�	�	PROPN
ejpam-1551	90	41	2	2	NUM
ejpam-1551	90	42	+	+	NOUN
ejpam-1551	90	43	t∗	t∗	ADJ
ejpam-1551	90	44	d2s∗	d2s∗	PROPN
ejpam-1551	90	45	ds2	ds2	PROPN
ejpam-1551	90	46	=	=	ADJ
ejpam-1551	90	47	−λ	−λ	PROPN
ejpam-1551	90	48	�	�	PROPN
ejpam-1551	90	49	κ2	κ2	PROPN
ejpam-1551	90	50	n	n	PROPN
ejpam-1551	90	51	+	+	CCONJ
ejpam-1551	90	52	κ	κ	PROPN
ejpam-1551	90	53	2	2	NUM
ejpam-1551	90	54	g	g	PROPN
ejpam-1551	90	55	�	�	PROPN
ejpam-1551	90	56	t+	t+	PUNCT
ejpam-1551	90	57	�	�	PROPN
ejpam-1551	90	58	λ	λ	PROPN
ejpam-1551	90	59	·	·	PUNCT
ejpam-1551	90	60	κg	κg	ADP
ejpam-1551	90	61	−	−	PROPN
ejpam-1551	90	62	κg−λκnτg	κg−λκnτg	VERB
ejpam-1551	90	63	�	�	PROPN
ejpam-1551	90	64	g	g	PROPN
ejpam-1551	90	65	+	+	PROPN
ejpam-1551	90	66	�	�	PROPN
ejpam-1551	90	67	λ	λ	PROPN
ejpam-1551	90	68	·	·	PUNCT
ejpam-1551	90	69	κn	κn	ADP
ejpam-1551	90	70	−	−	PROPN
ejpam-1551	90	71	κn−λκgτg	κn−λκgτg	NOUN
ejpam-1551	90	72	�	�	PROPN
ejpam-1551	90	73	n	n	CCONJ
ejpam-1551	90	74	(	(	PUNCT
ejpam-1551	90	75	19	19	NUM
ejpam-1551	90	76	)	)	PUNCT
ejpam-1551	90	77	respectively	respectively	ADV
ejpam-1551	90	78	.	.	PUNCT
ejpam-1551	91	1	taking	take	VERB
ejpam-1551	91	2	the	the	DET
ejpam-1551	91	3	cross	cross	NOUN
ejpam-1551	91	4	product	product	NOUN
ejpam-1551	91	5	of	of	ADP
ejpam-1551	91	6	(	(	PUNCT
ejpam-1551	91	7	18	18	NUM
ejpam-1551	91	8	)	)	PUNCT
ejpam-1551	91	9	with	with	ADP
ejpam-1551	91	10	(	(	PUNCT
ejpam-1551	91	11	19	19	NUM
ejpam-1551	91	12	)	)	PUNCT
ejpam-1551	91	13	we	we	PRON
ejpam-1551	91	14	have	have	AUX
ejpam-1551	91	15	�	�	PROPN
ejpam-1551	91	16	κ∗gn∗−κ∗ng∗	κ∗gn∗−κ∗ng∗	PROPN
ejpam-1551	91	17	�	�	PROPN
ejpam-1551	91	18	�	�	PROPN
ejpam-1551	91	19	ds∗	ds∗	PROPN
ejpam-1551	91	20	ds	ds	PROPN
ejpam-1551	91	21	�	�	PROPN
ejpam-1551	91	22	2	2	NUM
ejpam-1551	91	23	=	=	SYM
ejpam-1551	91	24	h	h	NOUN
ejpam-1551	91	25	λ2	λ2	PROPN
ejpam-1551	91	26	�	�	PROPN
ejpam-1551	91	27	κg	κg	PROPN
ejpam-1551	91	28	·	·	PUNCT
ejpam-1551	91	29	κn	κn	ADP
ejpam-1551	91	30	−	−	PROPN
ejpam-1551	91	31	κn	κn	NOUN
ejpam-1551	91	32	·	·	PUNCT
ejpam-1551	91	33	κg	κg	ADP
ejpam-1551	92	1	+	+	CCONJ
ejpam-1551	92	2	κ	κ	PROPN
ejpam-1551	92	3	2	2	NUM
ejpam-1551	92	4	gτg	gτg	NOUN
ejpam-1551	92	5	+	+	CCONJ
ejpam-1551	92	6	κ	κ	PROPN
ejpam-1551	92	7	2	2	NUM
ejpam-1551	92	8	nτg	nτg	NUM
ejpam-1551	92	9	�	�	NOUN
ejpam-1551	92	10	i	i	PROPN
ejpam-1551	92	11	t−λ2	t−λ2	PART
ejpam-1551	92	12	�	�	PROPN
ejpam-1551	92	13	κ3	κ3	PROPN
ejpam-1551	92	14	n	n	PROPN
ejpam-1551	92	15	+	+	CCONJ
ejpam-1551	92	16	κnκ	κnκ	PROPN
ejpam-1551	92	17	2	2	NUM
ejpam-1551	92	18	g	g	ADP
ejpam-1551	92	19	�	�	PROPN
ejpam-1551	92	20	g	g	PROPN
ejpam-1551	92	21	+	+	PROPN
ejpam-1551	92	22	λ2	λ2	PROPN
ejpam-1551	92	23	�	�	PROPN
ejpam-1551	92	24	κ3	κ3	PROPN
ejpam-1551	92	25	g	g	PROPN
ejpam-1551	92	26	+	+	CCONJ
ejpam-1551	92	27	κgκ	κgκ	PROPN
ejpam-1551	92	28	2	2	NUM
ejpam-1551	92	29	n	n	PRON
ejpam-1551	92	30	�	�	PROPN
ejpam-1551	92	31	n.	n.	NOUN
ejpam-1551	92	32	(	(	PUNCT
ejpam-1551	92	33	20	20	NUM
ejpam-1551	92	34	)	)	PUNCT
ejpam-1551	93	1	ö.	ö.	PROPN
ejpam-1551	93	2	bektaş	bektaş	PROPN
ejpam-1551	93	3	,	,	PUNCT
ejpam-1551	93	4	s.	s.	PROPN
ejpam-1551	93	5	yüce	yüce	PROPN
ejpam-1551	93	6	/	/	SYM
ejpam-1551	93	7	eur	eur	PROPN
ejpam-1551	93	8	.	.	PUNCT
ejpam-1551	94	1	j.	j.	PROPN
ejpam-1551	94	2	pure	pure	PROPN
ejpam-1551	94	3	appl	appl	PROPN
ejpam-1551	94	4	.	.	PROPN
ejpam-1551	94	5	math	math	PROPN
ejpam-1551	94	6	,	,	PUNCT
ejpam-1551	94	7	6	6	NUM
ejpam-1551	94	8	(	(	PUNCT
ejpam-1551	94	9	2013	2013	NUM
ejpam-1551	94	10	)	)	PUNCT
ejpam-1551	94	11	,	,	PUNCT
ejpam-1551	94	12	20	20	NUM
ejpam-1551	94	13	-	-	SYM
ejpam-1551	94	14	29	29	NUM
ejpam-1551	94	15	25	25	NUM
ejpam-1551	94	16	by	by	ADP
ejpam-1551	94	17	substituting	substitute	VERB
ejpam-1551	94	18	(	(	PUNCT
ejpam-1551	94	19	17	17	NUM
ejpam-1551	94	20	)	)	PUNCT
ejpam-1551	94	21	in	in	ADP
ejpam-1551	94	22	(	(	PUNCT
ejpam-1551	94	23	20	20	X
ejpam-1551	94	24	)	)	PUNCT
ejpam-1551	94	25	we	we	PRON
ejpam-1551	94	26	get	get	VERB
ejpam-1551	95	1	�	�	PROPN
ejpam-1551	95	2	κ∗gn∗−κ∗ng	κ∗gn∗−κ∗ng	PROPN
ejpam-1551	95	3	∗	∗	NUM
ejpam-1551	95	4	�	�	PROPN
ejpam-1551	95	5	�	�	PROPN
ejpam-1551	95	6	ds∗	ds∗	PROPN
ejpam-1551	95	7	ds	ds	PROPN
ejpam-1551	95	8	�	�	PROPN
ejpam-1551	95	9	3	3	NUM
ejpam-1551	95	10	=	=	SYM
ejpam-1551	95	11	−κ∗n	−κ∗n	X
ejpam-1551	95	12	�	�	PROPN
ejpam-1551	95	13	ds∗	ds∗	PROPN
ejpam-1551	95	14	ds	ds	PROPN
ejpam-1551	95	15	�	�	PROPN
ejpam-1551	95	16	3	3	NUM
ejpam-1551	95	17	t−λ2	t−λ2	PART
ejpam-1551	95	18	�	�	PROPN
ejpam-1551	95	19	κ3	κ3	PROPN
ejpam-1551	95	20	n	n	PROPN
ejpam-1551	95	21	+	+	CCONJ
ejpam-1551	95	22	κnκ	κnκ	PROPN
ejpam-1551	95	23	2	2	NUM
ejpam-1551	95	24	g	g	NOUN
ejpam-1551	95	25	�	�	PROPN
ejpam-1551	95	26	g+λ2	g+λ2	PROPN
ejpam-1551	95	27	�	�	PROPN
ejpam-1551	95	28	κ3	κ3	PROPN
ejpam-1551	95	29	g	g	PROPN
ejpam-1551	95	30	+	+	CCONJ
ejpam-1551	95	31	κgκ	κgκ	PROPN
ejpam-1551	95	32	2	2	NUM
ejpam-1551	95	33	n	n	PRON
ejpam-1551	95	34	�	�	PROPN
ejpam-1551	95	35	n.	n.	NOUN
ejpam-1551	95	36	(	(	PUNCT
ejpam-1551	95	37	21	21	NUM
ejpam-1551	95	38	)	)	PUNCT
ejpam-1551	95	39	taking	take	VERB
ejpam-1551	95	40	the	the	DET
ejpam-1551	95	41	cross	cross	NOUN
ejpam-1551	95	42	product	product	NOUN
ejpam-1551	95	43	of	of	ADP
ejpam-1551	95	44	(	(	PUNCT
ejpam-1551	95	45	18	18	NUM
ejpam-1551	95	46	)	)	PUNCT
ejpam-1551	95	47	with	with	ADP
ejpam-1551	95	48	(	(	PUNCT
ejpam-1551	95	49	21	21	NUM
ejpam-1551	95	50	)	)	PUNCT
ejpam-1551	95	51	we	we	PRON
ejpam-1551	95	52	have	have	AUX
ejpam-1551	95	53	�	�	PROPN
ejpam-1551	95	54	−κ∗nn∗−κ∗gg	−κ∗nn∗−κ∗gg	NOUN
ejpam-1551	95	55	∗	∗	NOUN
ejpam-1551	95	56	�	�	PROPN
ejpam-1551	95	57	�	�	PROPN
ejpam-1551	95	58	ds∗	ds∗	PROPN
ejpam-1551	95	59	ds	ds	PROPN
ejpam-1551	95	60	�	�	PROPN
ejpam-1551	95	61	4	4	NUM
ejpam-1551	95	62	=	=	SYM
ejpam-1551	95	63	−λ3	−λ3	PROPN
ejpam-1551	95	64	�	�	PROPN
ejpam-1551	95	65	κ2	κ2	PROPN
ejpam-1551	95	66	n+	n+	ADP
ejpam-1551	95	67	κ	κ	PROPN
ejpam-1551	95	68	2	2	NUM
ejpam-1551	95	69	g	g	PROPN
ejpam-1551	95	70	�	�	PROPN
ejpam-1551	95	71	t+λκnκ	t+λκnκ	PROPN
ejpam-1551	95	72	∗	∗	NOUN
ejpam-1551	95	73	n	n	CCONJ
ejpam-1551	95	74	�	�	PROPN
ejpam-1551	95	75	ds∗	ds∗	PROPN
ejpam-1551	95	76	ds	ds	PROPN
ejpam-1551	95	77	�	�	NOUN
ejpam-1551	95	78	3	3	NUM
ejpam-1551	95	79	g−λκgκ	g−λκgκ	NOUN
ejpam-1551	95	80	∗	∗	NOUN
ejpam-1551	95	81	n	n	CCONJ
ejpam-1551	95	82	�	�	PROPN
ejpam-1551	95	83	ds∗	ds∗	NOUN
ejpam-1551	95	84	ds	ds	PROPN
ejpam-1551	95	85	�	�	PROPN
ejpam-1551	95	86	3	3	NUM
ejpam-1551	95	87	n	n	PROPN
ejpam-1551	95	88	(	(	PUNCT
ejpam-1551	95	89	22	22	NUM
ejpam-1551	95	90	)	)	PUNCT
ejpam-1551	95	91	from	from	ADP
ejpam-1551	95	92	(	(	PUNCT
ejpam-1551	95	93	21	21	NUM
ejpam-1551	95	94	)	)	PUNCT
ejpam-1551	95	95	and	and	CCONJ
ejpam-1551	95	96	(	(	PUNCT
ejpam-1551	95	97	22	22	NUM
ejpam-1551	95	98	)	)	PUNCT
ejpam-1551	95	99	we	we	PRON
ejpam-1551	95	100	have	have	VERB
ejpam-1551	95	101	−	−	PROPN
ejpam-1551	95	102	�	�	PROPN
ejpam-1551	95	103	κ∗	κ∗	PROPN
ejpam-1551	95	104	2	2	NUM
ejpam-1551	95	105	n	n	NOUN
ejpam-1551	95	106	+	+	NOUN
ejpam-1551	95	107	κ	κ	PROPN
ejpam-1551	95	108	∗2	∗2	PROPN
ejpam-1551	95	109	g	g	PROPN
ejpam-1551	95	110	�	�	PROPN
ejpam-1551	95	111	�	�	PROPN
ejpam-1551	95	112	ds∗	ds∗	PROPN
ejpam-1551	95	113	ds	ds	PROPN
ejpam-1551	95	114	�	�	PROPN
ejpam-1551	95	115	4	4	NUM
ejpam-1551	95	116	n∗	n∗	NOUN
ejpam-1551	95	117	=	=	PUNCT
ejpam-1551	96	1			PROPN
ejpam-1551	96	2	−κ∗nκ	−κ∗nκ	NOUN
ejpam-1551	96	3	∗	∗	PROPN
ejpam-1551	96	4	g	g	PROPN
ejpam-1551	96	5	�	�	PROPN
ejpam-1551	96	6	ds∗	ds∗	PROPN
ejpam-1551	96	7	ds	ds	PROPN
ejpam-1551	96	8	�	�	PROPN
ejpam-1551	96	9	4	4	NUM
ejpam-1551	96	10	+	+	ADJ
ejpam-1551	96	11	λ3κ∗n	λ3κ∗n	PROPN
ejpam-1551	96	12	�	�	PROPN
ejpam-1551	96	13	κ2	κ2	PROPN
ejpam-1551	96	14	n	n	PROPN
ejpam-1551	96	15	+	+	CCONJ
ejpam-1551	96	16	κ	κ	PROPN
ejpam-1551	96	17	2	2	NUM
ejpam-1551	96	18	g	g	NOUN
ejpam-1551	96	19	�	�	PROPN
ejpam-1551	96	20	2	2	NUM
ejpam-1551	96	21			PROPN
ejpam-1551	96	22	t	t	PROPN
ejpam-1551	96	23	+	+	CCONJ
ejpam-1551	96	24	κn	κn	NOUN
ejpam-1551	96	25	(	(	PUNCT
ejpam-1551	96	26	h	h	NOUN
ejpam-1551	96	27	λ2κ∗g	λ2κ∗g	PROPN
ejpam-1551	96	28	�	�	PROPN
ejpam-1551	96	29	κ2	κ2	PROPN
ejpam-1551	96	30	n	n	PROPN
ejpam-1551	96	31	+	+	CCONJ
ejpam-1551	96	32	κ	κ	PROPN
ejpam-1551	96	33	2	2	NUM
ejpam-1551	96	34	g	g	NOUN
ejpam-1551	96	35	�	�	PROPN
ejpam-1551	96	36	i	i	PRON
ejpam-1551	96	37	�	�	PROPN
ejpam-1551	96	38	ds∗	ds∗	PROPN
ejpam-1551	96	39	ds	ds	PROPN
ejpam-1551	96	40	�	�	PROPN
ejpam-1551	96	41	+	+	PROPN
ejpam-1551	96	42	λκ∗	λκ∗	NOUN
ejpam-1551	96	43	2	2	NUM
ejpam-1551	96	44	n	n	PRON
ejpam-1551	96	45	�	�	PROPN
ejpam-1551	96	46	ds∗	ds∗	NOUN
ejpam-1551	96	47	ds	ds	PROPN
ejpam-1551	96	48	�	�	PROPN
ejpam-1551	96	49	3	3	NUM
ejpam-1551	96	50	)	)	PUNCT
ejpam-1551	96	51	g	g	NOUN
ejpam-1551	96	52	−	−	PROPN
ejpam-1551	96	53	κg	κg	PROPN
ejpam-1551	96	54	(	(	PUNCT
ejpam-1551	96	55	h	h	NOUN
ejpam-1551	96	56	λ2κ∗g	λ2κ∗g	PROPN
ejpam-1551	96	57	�	�	PROPN
ejpam-1551	96	58	κ2	κ2	PROPN
ejpam-1551	96	59	n	n	PROPN
ejpam-1551	96	60	+	+	CCONJ
ejpam-1551	96	61	κ	κ	PROPN
ejpam-1551	96	62	2	2	NUM
ejpam-1551	96	63	g	g	NOUN
ejpam-1551	96	64	�	�	PROPN
ejpam-1551	96	65	i	i	PRON
ejpam-1551	96	66	�	�	PROPN
ejpam-1551	96	67	ds∗	ds∗	PROPN
ejpam-1551	96	68	ds	ds	PROPN
ejpam-1551	96	69	�	�	PROPN
ejpam-1551	96	70	+	+	PROPN
ejpam-1551	96	71	λκ∗	λκ∗	NOUN
ejpam-1551	96	72	2	2	NUM
ejpam-1551	96	73	n	n	PRON
ejpam-1551	96	74	�	�	PROPN
ejpam-1551	96	75	ds∗	ds∗	NOUN
ejpam-1551	96	76	ds	ds	PROPN
ejpam-1551	96	77	�	�	PROPN
ejpam-1551	96	78	3	3	NUM
ejpam-1551	96	79	)	)	PUNCT
ejpam-1551	96	80	n	n	CCONJ
ejpam-1551	96	81	(	(	PUNCT
ejpam-1551	96	82	23	23	NUM
ejpam-1551	96	83	)	)	PUNCT
ejpam-1551	96	84	furthermore	furthermore	ADV
ejpam-1551	96	85	,	,	PUNCT
ejpam-1551	96	86	from	from	ADP
ejpam-1551	96	87	(	(	PUNCT
ejpam-1551	96	88	18	18	NUM
ejpam-1551	96	89	)	)	PUNCT
ejpam-1551	96	90	and	and	CCONJ
ejpam-1551	96	91	(	(	PUNCT
ejpam-1551	96	92	21	21	NUM
ejpam-1551	96	93	)	)	PUNCT
ejpam-1551	96	94	we	we	PRON
ejpam-1551	96	95	get	get	VERB
ejpam-1551	96	96			PROPN
ejpam-1551	96	97			ADP
ejpam-1551	96	98			ADJ
ejpam-1551	96	99	�	�	PROPN
ejpam-1551	96	100	ds∗	ds∗	PROPN
ejpam-1551	96	101	ds	ds	PROPN
ejpam-1551	96	102	�	�	PROPN
ejpam-1551	96	103	2	2	NUM
ejpam-1551	96	104	=	=	SYM
ejpam-1551	96	105	λ2	λ2	PROPN
ejpam-1551	96	106	�	�	PROPN
ejpam-1551	96	107	κ2	κ2	PROPN
ejpam-1551	96	108	n+	n+	ADP
ejpam-1551	96	109	κ	κ	PROPN
ejpam-1551	96	110	2	2	NUM
ejpam-1551	96	111	g	g	PROPN
ejpam-1551	96	112	�	�	PROPN
ejpam-1551	96	113	κ∗	κ∗	PROPN
ejpam-1551	96	114	2	2	NUM
ejpam-1551	96	115	g	g	NOUN
ejpam-1551	96	116	�	�	PROPN
ejpam-1551	96	117	ds∗	ds∗	PROPN
ejpam-1551	96	118	ds	ds	PROPN
ejpam-1551	96	119	�	�	PROPN
ejpam-1551	96	120	2	2	NUM
ejpam-1551	96	121	=	=	SYM
ejpam-1551	96	122	�	�	PROPN
ejpam-1551	96	123	κ2	κ2	PROPN
ejpam-1551	96	124	n+	n+	ADP
ejpam-1551	96	125	κ	κ	PROPN
ejpam-1551	96	126	2	2	NUM
ejpam-1551	96	127	g	g	PROPN
ejpam-1551	96	128	�	�	PROPN
ejpam-1551	96	129	(	(	PUNCT
ejpam-1551	96	130	24	24	NUM
ejpam-1551	96	131	)	)	PUNCT
ejpam-1551	96	132	respectively	respectively	ADV
ejpam-1551	96	133	.	.	PUNCT
ejpam-1551	97	1	substituting	substitute	VERB
ejpam-1551	97	2	(	(	PUNCT
ejpam-1551	97	3	24	24	NUM
ejpam-1551	97	4	)	)	PUNCT
ejpam-1551	97	5	in	in	ADP
ejpam-1551	97	6	(	(	PUNCT
ejpam-1551	97	7	23	23	NUM
ejpam-1551	97	8	)	)	PUNCT
ejpam-1551	97	9	we	we	PRON
ejpam-1551	97	10	obtain	obtain	VERB
ejpam-1551	97	11	−	−	PROPN
ejpam-1551	97	12	�	�	PROPN
ejpam-1551	97	13	κ∗	κ∗	PROPN
ejpam-1551	97	14	2	2	NUM
ejpam-1551	97	15	n	n	NOUN
ejpam-1551	97	16	+	+	NOUN
ejpam-1551	97	17	κ	κ	PROPN
ejpam-1551	97	18	∗2	∗2	PROPN
ejpam-1551	97	19	g	g	PROPN
ejpam-1551	97	20	�	�	PROPN
ejpam-1551	97	21	�	�	PROPN
ejpam-1551	97	22	ds∗	ds∗	PROPN
ejpam-1551	97	23	ds	ds	PROPN
ejpam-1551	97	24	�	�	PROPN
ejpam-1551	97	25	4	4	NUM
ejpam-1551	97	26	n∗	n∗	NOUN
ejpam-1551	97	27	=	=	NOUN
ejpam-1551	97	28	κn	κn	NOUN
ejpam-1551	97	29	(	(	PUNCT
ejpam-1551	97	30	h	h	NOUN
ejpam-1551	97	31	λ2κ∗g	λ2κ∗g	PROPN
ejpam-1551	97	32	�	�	PROPN
ejpam-1551	97	33	κ2	κ2	PROPN
ejpam-1551	97	34	n+	n+	ADP
ejpam-1551	98	1	κ	κ	PROPN
ejpam-1551	98	2	2	2	NUM
ejpam-1551	98	3	g	g	PROPN
ejpam-1551	98	4	�	�	PROPN
ejpam-1551	98	5	i	i	PRON
ejpam-1551	98	6	�	�	PROPN
ejpam-1551	98	7	ds∗	ds∗	PROPN
ejpam-1551	98	8	ds	ds	PROPN
ejpam-1551	98	9	�	�	PROPN
ejpam-1551	98	10	+	+	PROPN
ejpam-1551	98	11	λκ∗	λκ∗	NOUN
ejpam-1551	98	12	2	2	NUM
ejpam-1551	98	13	n	n	PRON
ejpam-1551	98	14	�	�	PROPN
ejpam-1551	98	15	ds∗	ds∗	NOUN
ejpam-1551	98	16	ds	ds	PROPN
ejpam-1551	98	17	�	�	PROPN
ejpam-1551	98	18	3	3	NUM
ejpam-1551	98	19	)	)	PUNCT
ejpam-1551	98	20	g	g	PROPN
ejpam-1551	98	21	+	+	CCONJ
ejpam-1551	98	22	κg	κg	PROPN
ejpam-1551	98	23	(	(	PUNCT
ejpam-1551	98	24	h	h	NOUN
ejpam-1551	98	25	λ2κ∗g	λ2κ∗g	PROPN
ejpam-1551	98	26	�	�	PROPN
ejpam-1551	98	27	κ2	κ2	PROPN
ejpam-1551	98	28	n	n	PROPN
ejpam-1551	98	29	+	+	CCONJ
ejpam-1551	98	30	κ	κ	PROPN
ejpam-1551	98	31	2	2	NUM
ejpam-1551	98	32	g	g	NOUN
ejpam-1551	98	33	�	�	PROPN
ejpam-1551	98	34	i	i	PRON
ejpam-1551	98	35	�	�	PROPN
ejpam-1551	98	36	ds∗	ds∗	PROPN
ejpam-1551	98	37	ds	ds	PROPN
ejpam-1551	98	38	�	�	PROPN
ejpam-1551	98	39	+	+	PROPN
ejpam-1551	98	40	λκ∗	λκ∗	NOUN
ejpam-1551	98	41	2	2	NUM
ejpam-1551	98	42	n	n	PRON
ejpam-1551	98	43	�	�	PROPN
ejpam-1551	98	44	ds∗	ds∗	NOUN
ejpam-1551	98	45	ds	ds	PROPN
ejpam-1551	98	46	�	�	PROPN
ejpam-1551	98	47	3	3	NUM
ejpam-1551	98	48	)	)	PUNCT
ejpam-1551	98	49	n.	n.	NOUN
ejpam-1551	98	50	(	(	PUNCT
ejpam-1551	98	51	25	25	NUM
ejpam-1551	98	52	)	)	PUNCT
ejpam-1551	98	53	equality	equality	NOUN
ejpam-1551	98	54	(	(	PUNCT
ejpam-1551	98	55	18	18	NUM
ejpam-1551	98	56	)	)	PUNCT
ejpam-1551	98	57	and	and	CCONJ
ejpam-1551	98	58	(	(	PUNCT
ejpam-1551	98	59	25	25	NUM
ejpam-1551	98	60	)	)	PUNCT
ejpam-1551	98	61	shows	show	VERB
ejpam-1551	98	62	that	that	SCONJ
ejpam-1551	98	63	the	the	DET
ejpam-1551	98	64	vectors	vector	NOUN
ejpam-1551	98	65	t∗	t∗	VERB
ejpam-1551	98	66	and	and	CCONJ
ejpam-1551	98	67	n∗	n∗	NOUN
ejpam-1551	98	68	lie	lie	VERB
ejpam-1551	98	69	on	on	ADP
ejpam-1551	98	70	the	the	DET
ejpam-1551	98	71	plane	plane	NOUN
ejpam-1551	98	72	sp	sp	ADP
ejpam-1551	98	73	�	�	PROPN
ejpam-1551	98	74	g	g	PROPN
ejpam-1551	98	75	,	,	PUNCT
ejpam-1551	98	76	n	n	PROPN
ejpam-1551	98	77	.	.	PUNCT
ejpam-1551	99	1	so	so	ADV
ejpam-1551	99	2	,	,	PUNCT
ejpam-1551	99	3	at	at	ADP
ejpam-1551	99	4	the	the	DET
ejpam-1551	99	5	corresponding	corresponding	ADJ
ejpam-1551	99	6	points	point	NOUN
ejpam-1551	99	7	of	of	ADP
ejpam-1551	99	8	the	the	DET
ejpam-1551	99	9	curves	curve	NOUN
ejpam-1551	99	10	,	,	PUNCT
ejpam-1551	99	11	the	the	DET
ejpam-1551	99	12	darboux	darboux	VERB
ejpam-1551	99	13	frame	frame	NOUN
ejpam-1551	99	14	element	element	NOUN
ejpam-1551	99	15	t	t	PROPN
ejpam-1551	99	16	of	of	ADP
ejpam-1551	99	17	α	α	PROPN
ejpam-1551	99	18	coincides	coincide	VERB
ejpam-1551	99	19	with	with	ADP
ejpam-1551	99	20	the	the	DET
ejpam-1551	99	21	darboux	darboux	VERB
ejpam-1551	99	22	frame	frame	NOUN
ejpam-1551	99	23	element	element	NOUN
ejpam-1551	99	24	g∗	g∗	NOUN
ejpam-1551	99	25	of	of	ADP
ejpam-1551	99	26	β	β	PROPN
ejpam-1551	99	27	.	.	PUNCT
ejpam-1551	100	1	thus	thus	ADV
ejpam-1551	100	2	,	,	PUNCT
ejpam-1551	100	3	the	the	DET
ejpam-1551	100	4	proof	proof	NOUN
ejpam-1551	100	5	is	be	AUX
ejpam-1551	100	6	completed	complete	VERB
ejpam-1551	100	7	.	.	PUNCT
ejpam-1551	101	1	special	special	ADJ
ejpam-1551	101	2	case	case	NOUN
ejpam-1551	101	3	1	1	X
ejpam-1551	101	4	.	.	PUNCT
ejpam-1551	102	1	let	let	VERB
ejpam-1551	102	2	β	β	X
ejpam-1551	102	3	(	(	PUNCT
ejpam-1551	102	4	s∗	s∗	PROPN
ejpam-1551	102	5	)	)	PUNCT
ejpam-1551	102	6	be	be	AUX
ejpam-1551	102	7	an	an	DET
ejpam-1551	102	8	asymptotic	asymptotic	ADJ
ejpam-1551	102	9	special	special	ADJ
ejpam-1551	102	10	involute	involute	ADJ
ejpam-1551	102	11	d	d	NOUN
ejpam-1551	102	12	-	-	NOUN
ejpam-1551	102	13	curve	curve	NOUN
ejpam-1551	102	14	of	of	ADP
ejpam-1551	102	15	α	α	NOUN
ejpam-1551	102	16	.	.	PUNCT
ejpam-1551	103	1	i	i	PRON
ejpam-1551	103	2	)	)	PUNCT
ejpam-1551	103	3	consider	consider	VERB
ejpam-1551	103	4	that	that	SCONJ
ejpam-1551	103	5	α	α	PROPN
ejpam-1551	103	6	(	(	PUNCT
ejpam-1551	103	7	s	s	X
ejpam-1551	103	8	)	)	PUNCT
ejpam-1551	103	9	is	be	AUX
ejpam-1551	103	10	an	an	DET
ejpam-1551	103	11	asymptotic	asymptotic	ADJ
ejpam-1551	103	12	line	line	NOUN
ejpam-1551	103	13	.	.	PUNCT
ejpam-1551	104	1	then	then	ADV
ejpam-1551	104	2	α	α	X
ejpam-1551	104	3	(	(	PUNCT
ejpam-1551	104	4	s	s	X
ejpam-1551	104	5	)	)	PUNCT
ejpam-1551	104	6	is	be	AUX
ejpam-1551	104	7	special	special	ADJ
ejpam-1551	104	8	evolute	evolute	NOUN
ejpam-1551	104	9	d	d	X
ejpam-1551	104	10	-	-	PUNCT
ejpam-1551	104	11	curve	curve	NOUN
ejpam-1551	104	12	of	of	ADP
ejpam-1551	104	13	β	β	PROPN
ejpam-1551	104	14	(	(	PUNCT
ejpam-1551	104	15	s∗	s∗	PROPN
ejpam-1551	104	16	)	)	PUNCT
ejpam-1551	105	1	if	if	SCONJ
ejpam-1551	105	2	and	and	CCONJ
ejpam-1551	105	3	only	only	ADV
ejpam-1551	105	4	if	if	SCONJ
ejpam-1551	105	5	the	the	DET
ejpam-1551	105	6	geodesic	geodesic	ADJ
ejpam-1551	105	7	curvature	curvature	NOUN
ejpam-1551	105	8	κg	κg	ADP
ejpam-1551	105	9	,	,	PUNCT
ejpam-1551	105	10	the	the	DET
ejpam-1551	105	11	geodesic	geodesic	ADJ
ejpam-1551	105	12	normal	normal	ADJ
ejpam-1551	105	13	κn	κn	NOUN
ejpam-1551	105	14	and	and	CCONJ
ejpam-1551	105	15	the	the	DET
ejpam-1551	105	16	geodesic	geodesic	ADJ
ejpam-1551	105	17	torsion	torsion	NOUN
ejpam-1551	105	18	τg	τg	PROPN
ejpam-1551	105	19	of	of	ADP
ejpam-1551	105	20	α	α	PROPN
ejpam-1551	105	21	(	(	PUNCT
ejpam-1551	105	22	s	s	NOUN
ejpam-1551	105	23	)	)	PUNCT
ejpam-1551	105	24	satisfy	satisfy	VERB
ejpam-1551	105	25	the	the	DET
ejpam-1551	105	26	following	follow	VERB
ejpam-1551	105	27	equation	equation	NOUN
ejpam-1551	105	28	,	,	PUNCT
ejpam-1551	105	29	·	·	PUNCT
ejpam-1551	105	30	κn	κn	NOUN
ejpam-1551	105	31	=	=	PUNCT
ejpam-1551	105	32	−τgκg	−τgκg	PROPN
ejpam-1551	105	33	.	.	PUNCT
ejpam-1551	106	1	ö.	ö.	PROPN
ejpam-1551	106	2	bektaş	bektaş	PROPN
ejpam-1551	106	3	,	,	PUNCT
ejpam-1551	106	4	s.	s.	PROPN
ejpam-1551	106	5	yüce	yüce	PROPN
ejpam-1551	106	6	/	/	SYM
ejpam-1551	106	7	eur	eur	PROPN
ejpam-1551	106	8	.	.	PUNCT
ejpam-1551	107	1	j.	j.	PROPN
ejpam-1551	107	2	pure	pure	PROPN
ejpam-1551	107	3	appl	appl	PROPN
ejpam-1551	107	4	.	.	PROPN
ejpam-1551	107	5	math	math	PROPN
ejpam-1551	107	6	,	,	PUNCT
ejpam-1551	107	7	6	6	NUM
ejpam-1551	107	8	(	(	PUNCT
ejpam-1551	107	9	2013	2013	NUM
ejpam-1551	107	10	)	)	PUNCT
ejpam-1551	107	11	,	,	PUNCT
ejpam-1551	107	12	20	20	NUM
ejpam-1551	107	13	-	-	SYM
ejpam-1551	107	14	29	29	NUM
ejpam-1551	107	15	26	26	NUM
ejpam-1551	107	16	ii	ii	NOUN
ejpam-1551	107	17	)	)	PUNCT
ejpam-1551	107	18	consider	consider	VERB
ejpam-1551	107	19	that	that	SCONJ
ejpam-1551	107	20	α	α	PROPN
ejpam-1551	107	21	(	(	PUNCT
ejpam-1551	107	22	s	s	X
ejpam-1551	107	23	)	)	PUNCT
ejpam-1551	107	24	is	be	AUX
ejpam-1551	107	25	a	a	DET
ejpam-1551	107	26	principal	principal	ADJ
ejpam-1551	107	27	line	line	NOUN
ejpam-1551	107	28	.	.	PUNCT
ejpam-1551	108	1	then	then	ADV
ejpam-1551	108	2	α	α	X
ejpam-1551	108	3	(	(	PUNCT
ejpam-1551	108	4	s	s	X
ejpam-1551	108	5	)	)	PUNCT
ejpam-1551	108	6	is	be	AUX
ejpam-1551	108	7	special	special	ADJ
ejpam-1551	108	8	evolute	evolute	NOUN
ejpam-1551	108	9	d	d	X
ejpam-1551	108	10	-	-	PUNCT
ejpam-1551	108	11	curve	curve	NOUN
ejpam-1551	108	12	of	of	ADP
ejpam-1551	108	13	β	β	X
ejpam-1551	108	14	(	(	PUNCT
ejpam-1551	108	15	s∗)if	s∗)if	NOUN
ejpam-1551	108	16	and	and	CCONJ
ejpam-1551	108	17	only	only	ADV
ejpam-1551	108	18	if	if	SCONJ
ejpam-1551	108	19	the	the	DET
ejpam-1551	108	20	geodesic	geodesic	ADJ
ejpam-1551	108	21	curvature	curvature	NOUN
ejpam-1551	108	22	κg	κg	PROPN
ejpam-1551	108	23	and	and	CCONJ
ejpam-1551	108	24	the	the	DET
ejpam-1551	108	25	geodesic	geodesic	ADJ
ejpam-1551	108	26	normal	normal	ADJ
ejpam-1551	108	27	κn	κn	NOUN
ejpam-1551	108	28	of	of	ADP
ejpam-1551	108	29	α	α	PROPN
ejpam-1551	108	30	(	(	PUNCT
ejpam-1551	108	31	s	s	NOUN
ejpam-1551	108	32	)	)	PUNCT
ejpam-1551	108	33	satisfy	satisfy	VERB
ejpam-1551	108	34	the	the	DET
ejpam-1551	108	35	following	follow	VERB
ejpam-1551	108	36	equation	equation	NOUN
ejpam-1551	108	37	,	,	PUNCT
ejpam-1551	108	38	·	·	PUNCT
ejpam-1551	108	39	κn	κn	NOUN
ejpam-1551	108	40	=	=	SYM
ejpam-1551	108	41	κn	κn	NOUN
ejpam-1551	108	42	·	·	PUNCT
ejpam-1551	108	43	κg	κg	ADP
ejpam-1551	108	44	κg	κg	PROPN
ejpam-1551	108	45	.	.	PUNCT
ejpam-1551	109	1	theorem	theorem	VERB
ejpam-1551	109	2	3	3	X
ejpam-1551	109	3	.	.	PUNCT
ejpam-1551	110	1	let	let	VERB
ejpam-1551	110	2	the	the	DET
ejpam-1551	110	3	pair	pair	NOUN
ejpam-1551	110	4	�	�	PROPN
ejpam-1551	110	5	α	α	PROPN
ejpam-1551	110	6	,	,	PUNCT
ejpam-1551	110	7	β	β	X
ejpam-1551	110	8	be	be	AUX
ejpam-1551	110	9	a	a	DET
ejpam-1551	110	10	special	special	ADJ
ejpam-1551	110	11	involute	involute	NOUN
ejpam-1551	110	12	evolute	evolute	NOUN
ejpam-1551	111	1	d	d	X
ejpam-1551	111	2	-	-	PUNCT
ejpam-1551	111	3	pair	pair	NOUN
ejpam-1551	111	4	in	in	ADP
ejpam-1551	111	5	the	the	DET
ejpam-1551	111	6	euclidean	euclidean	ADJ
ejpam-1551	111	7	space	space	NOUN
ejpam-1551	111	8	e3	e3	NOUN
ejpam-1551	111	9	then	then	ADV
ejpam-1551	111	10	the	the	DET
ejpam-1551	111	11	relation	relation	NOUN
ejpam-1551	111	12	between	between	ADP
ejpam-1551	111	13	the	the	DET
ejpam-1551	111	14	geodesic	geodesic	ADJ
ejpam-1551	111	15	curvature	curvature	NOUN
ejpam-1551	111	16	κ∗g	κ∗g	X
ejpam-1551	111	17	and	and	CCONJ
ejpam-1551	111	18	the	the	DET
ejpam-1551	111	19	geodesic	geodesic	ADJ
ejpam-1551	111	20	torsion	torsion	NOUN
ejpam-1551	111	21	τ∗g	τ∗g	NUM
ejpam-1551	111	22	of	of	ADP
ejpam-1551	111	23	β	β	X
ejpam-1551	111	24	(	(	PUNCT
ejpam-1551	111	25	s∗	s∗	PROPN
ejpam-1551	111	26	)	)	PUNCT
ejpam-1551	111	27	is	be	AUX
ejpam-1551	111	28	given	give	VERB
ejpam-1551	111	29	as	as	SCONJ
ejpam-1551	111	30	follows	follow	VERB
ejpam-1551	111	31	κ∗g	κ∗g	AUX
ejpam-1551	111	32	+	+	ADV
ejpam-1551	111	33	τ	τ	PROPN
ejpam-1551	111	34	∗	∗	NOUN
ejpam-1551	111	35	g	g	NOUN
ejpam-1551	111	36	=	=	SYM
ejpam-1551	111	37	−	−	PROPN
ejpam-1551	111	38	1	1	NUM
ejpam-1551	111	39	λ	λ	NOUN
ejpam-1551	111	40	for	for	ADP
ejpam-1551	111	41	some	some	DET
ejpam-1551	111	42	nonzero	nonzero	PROPN
ejpam-1551	111	43	constants	constant	NOUN
ejpam-1551	111	44	λ	λ	PROPN
ejpam-1551	111	45	,	,	PUNCT
ejpam-1551	111	46	where	where	SCONJ
ejpam-1551	111	47	θ	θ	PROPN
ejpam-1551	111	48	is	be	AUX
ejpam-1551	111	49	the	the	DET
ejpam-1551	111	50	angle	angle	NOUN
ejpam-1551	111	51	between	between	ADP
ejpam-1551	111	52	the	the	DET
ejpam-1551	111	53	vectors	vector	NOUN
ejpam-1551	111	54	n	n	CCONJ
ejpam-1551	111	55	and	and	CCONJ
ejpam-1551	111	56	n∗	n∗	PROPN
ejpam-1551	111	57	at	at	ADP
ejpam-1551	111	58	the	the	DET
ejpam-1551	111	59	corresponding	corresponding	ADJ
ejpam-1551	111	60	points	point	NOUN
ejpam-1551	111	61	of	of	ADP
ejpam-1551	111	62	α	α	PROPN
ejpam-1551	111	63	(	(	PUNCT
ejpam-1551	111	64	s	s	NOUN
ejpam-1551	111	65	)	)	PUNCT
ejpam-1551	111	66	and	and	CCONJ
ejpam-1551	111	67	β	β	X
ejpam-1551	111	68	(	(	PUNCT
ejpam-1551	111	69	s∗	s∗	PROPN
ejpam-1551	111	70	)	)	PUNCT
ejpam-1551	111	71	.	.	PUNCT
ejpam-1551	112	1	proof	proof	NOUN
ejpam-1551	112	2	.	.	PUNCT
ejpam-1551	113	1	let	let	VERB
ejpam-1551	113	2	the	the	DET
ejpam-1551	113	3	pair	pair	NOUN
ejpam-1551	113	4	�	�	PROPN
ejpam-1551	113	5	α	α	PROPN
ejpam-1551	113	6	,	,	PUNCT
ejpam-1551	113	7	β	β	X
ejpam-1551	113	8	be	be	AUX
ejpam-1551	113	9	a	a	DET
ejpam-1551	113	10	special	special	ADJ
ejpam-1551	113	11	involute	involute	NOUN
ejpam-1551	113	12	evolute	evolute	NOUN
ejpam-1551	114	1	d	d	X
ejpam-1551	114	2	-	-	PUNCT
ejpam-1551	114	3	pair	pair	NOUN
ejpam-1551	114	4	in	in	ADP
ejpam-1551	114	5	the	the	DET
ejpam-1551	114	6	euclidean	euclidean	ADJ
ejpam-1551	114	7	space	space	NOUN
ejpam-1551	114	8	e3	e3	NOUN
ejpam-1551	114	9	.	.	PUNCT
ejpam-1551	115	1	then	then	ADV
ejpam-1551	115	2	from	from	ADP
ejpam-1551	115	3	(	(	PUNCT
ejpam-1551	115	4	9	9	X
ejpam-1551	115	5	)	)	PUNCT
ejpam-1551	115	6	we	we	PRON
ejpam-1551	115	7	can	can	AUX
ejpam-1551	115	8	write	write	VERB
ejpam-1551	115	9	β	β	X
ejpam-1551	115	10	(	(	PUNCT
ejpam-1551	115	11	s	s	X
ejpam-1551	115	12	)	)	PUNCT
ejpam-1551	116	1	=	=	SYM
ejpam-1551	116	2	α	α	PROPN
ejpam-1551	116	3	(	(	PUNCT
ejpam-1551	116	4	s	s	NOUN
ejpam-1551	116	5	)	)	PUNCT
ejpam-1551	117	1	+	+	NOUN
ejpam-1551	117	2	λ	λ	X
ejpam-1551	117	3	(	(	PUNCT
ejpam-1551	117	4	s)t	s)t	X
ejpam-1551	117	5	(	(	PUNCT
ejpam-1551	117	6	s	s	X
ejpam-1551	117	7	)	)	PUNCT
ejpam-1551	117	8	for	for	ADP
ejpam-1551	117	9	some	some	DET
ejpam-1551	117	10	constants	constant	NOUN
ejpam-1551	117	11	λ	λ	NOUN
ejpam-1551	117	12	.	.	PUNCT
ejpam-1551	118	1	the	the	DET
ejpam-1551	118	2	last	last	ADJ
ejpam-1551	118	3	equation	equation	NOUN
ejpam-1551	118	4	is	be	AUX
ejpam-1551	118	5	written	write	VERB
ejpam-1551	118	6	as	as	SCONJ
ejpam-1551	118	7	follows	follow	VERB
ejpam-1551	118	8	α	α	PROPN
ejpam-1551	118	9	(	(	PUNCT
ejpam-1551	118	10	s	s	NOUN
ejpam-1551	118	11	)	)	PUNCT
ejpam-1551	118	12	=	=	SYM
ejpam-1551	118	13	β	β	X
ejpam-1551	118	14	(	(	PUNCT
ejpam-1551	118	15	s)−λ	s)−λ	X
ejpam-1551	118	16	(	(	PUNCT
ejpam-1551	118	17	s)t	s)t	X
ejpam-1551	118	18	(	(	PUNCT
ejpam-1551	118	19	s	s	X
ejpam-1551	118	20	)	)	PUNCT
ejpam-1551	118	21	since	since	SCONJ
ejpam-1551	118	22	the	the	DET
ejpam-1551	118	23	direction	direction	NOUN
ejpam-1551	118	24	of	of	ADP
ejpam-1551	118	25	t	t	PROPN
ejpam-1551	118	26	is	be	AUX
ejpam-1551	118	27	coincident	coincident	ADJ
ejpam-1551	118	28	with	with	ADP
ejpam-1551	118	29	g∗	g∗	NOUN
ejpam-1551	118	30	we	we	PRON
ejpam-1551	118	31	have	have	VERB
ejpam-1551	118	32	α	α	X
ejpam-1551	118	33	(	(	PUNCT
ejpam-1551	118	34	s	s	NOUN
ejpam-1551	118	35	)	)	PUNCT
ejpam-1551	119	1	=	=	SYM
ejpam-1551	119	2	β	β	X
ejpam-1551	119	3	(	(	PUNCT
ejpam-1551	119	4	s)−λ	s)−λ	X
ejpam-1551	119	5	(	(	PUNCT
ejpam-1551	119	6	s)g∗	s)g∗	X
ejpam-1551	119	7	(	(	PUNCT
ejpam-1551	119	8	s	s	NOUN
ejpam-1551	119	9	)	)	PUNCT
ejpam-1551	119	10	(	(	PUNCT
ejpam-1551	119	11	26	26	NUM
ejpam-1551	119	12	)	)	PUNCT
ejpam-1551	119	13	by	by	ADP
ejpam-1551	119	14	differentiating	differentiate	VERB
ejpam-1551	119	15	(	(	PUNCT
ejpam-1551	119	16	26	26	NUM
ejpam-1551	119	17	)	)	PUNCT
ejpam-1551	119	18	with	with	ADP
ejpam-1551	119	19	respect	respect	NOUN
ejpam-1551	119	20	to	to	ADP
ejpam-1551	119	21	s	s	PRON
ejpam-1551	119	22	and	and	CCONJ
ejpam-1551	119	23	since	since	SCONJ
ejpam-1551	119	24	the	the	DET
ejpam-1551	119	25	direction	direction	NOUN
ejpam-1551	119	26	of	of	ADP
ejpam-1551	119	27	t	t	PROPN
ejpam-1551	119	28	is	be	AUX
ejpam-1551	119	29	coincident	coincident	ADJ
ejpam-1551	119	30	with	with	ADP
ejpam-1551	119	31	g∗	g∗	NOUN
ejpam-1551	119	32	we	we	PRON
ejpam-1551	119	33	have	have	VERB
ejpam-1551	119	34	κ∗g	κ∗g	VERB
ejpam-1551	120	1	+	+	ADJ
ejpam-1551	120	2	τ	τ	PROPN
ejpam-1551	120	3	∗	∗	NOUN
ejpam-1551	120	4	g	g	NOUN
ejpam-1551	120	5	=	=	SYM
ejpam-1551	120	6	−	−	PROPN
ejpam-1551	120	7	1	1	NUM
ejpam-1551	120	8	λ	λ	PROPN
ejpam-1551	120	9	.	.	PUNCT
ejpam-1551	121	1	special	special	ADJ
ejpam-1551	121	2	case	case	NOUN
ejpam-1551	121	3	2	2	X
ejpam-1551	121	4	.	.	PUNCT
ejpam-1551	121	5	let	let	VERB
ejpam-1551	121	6	the	the	DET
ejpam-1551	121	7	pair	pair	NOUN
ejpam-1551	121	8	�	�	PROPN
ejpam-1551	121	9	α	α	PROPN
ejpam-1551	121	10	,	,	PUNCT
ejpam-1551	121	11	β	β	X
ejpam-1551	121	12	be	be	AUX
ejpam-1551	121	13	a	a	DET
ejpam-1551	121	14	special	special	ADJ
ejpam-1551	121	15	involute	involute	NOUN
ejpam-1551	121	16	evolute	evolute	NOUN
ejpam-1551	121	17	d	d	X
ejpam-1551	121	18	-	-	PUNCT
ejpam-1551	121	19	pair	pair	NOUN
ejpam-1551	121	20	in	in	ADP
ejpam-1551	121	21	the	the	DET
ejpam-1551	121	22	euclidean	euclidean	ADJ
ejpam-1551	121	23	space	space	NOUN
ejpam-1551	121	24	e3	e3	NOUN
ejpam-1551	121	25	.	.	PUNCT
ejpam-1551	122	1	i	i	PRON
ejpam-1551	122	2	)	)	PUNCT
ejpam-1551	122	3	if	if	SCONJ
ejpam-1551	122	4	β	β	X
ejpam-1551	122	5	is	be	AUX
ejpam-1551	122	6	geodesic	geodesic	ADJ
ejpam-1551	122	7	curve	curve	NOUN
ejpam-1551	122	8	,	,	PUNCT
ejpam-1551	122	9	then	then	ADV
ejpam-1551	122	10	τ∗g	τ∗g	PUNCT
ejpam-1551	122	11	=	=	SYM
ejpam-1551	122	12	−	−	PROPN
ejpam-1551	122	13	1	1	NUM
ejpam-1551	122	14	λ	λ	PROPN
ejpam-1551	122	15	.	.	PUNCT
ejpam-1551	123	1	ii	ii	X
ejpam-1551	123	2	)	)	PUNCT
ejpam-1551	123	3	if	if	SCONJ
ejpam-1551	123	4	β	β	X
ejpam-1551	123	5	is	be	AUX
ejpam-1551	123	6	a	a	DET
ejpam-1551	123	7	principal	principal	ADJ
ejpam-1551	123	8	line	line	NOUN
ejpam-1551	123	9	,	,	PUNCT
ejpam-1551	123	10	then	then	ADV
ejpam-1551	123	11	κ∗g	κ∗g	PROPN
ejpam-1551	123	12	=	=	SYM
ejpam-1551	123	13	−	−	PROPN
ejpam-1551	123	14	1	1	NUM
ejpam-1551	123	15	λ	λ	X
ejpam-1551	123	16	.	.	PUNCT
ejpam-1551	124	1	theorem	theorem	ADJ
ejpam-1551	124	2	4	4	NUM
ejpam-1551	124	3	.	.	PUNCT
ejpam-1551	125	1	let	let	VERB
ejpam-1551	125	2	the	the	DET
ejpam-1551	125	3	pair	pair	NOUN
ejpam-1551	125	4	�	�	PROPN
ejpam-1551	125	5	α	α	PROPN
ejpam-1551	125	6	,	,	PUNCT
ejpam-1551	125	7	β	β	X
ejpam-1551	125	8	be	be	AUX
ejpam-1551	125	9	a	a	DET
ejpam-1551	125	10	special	special	ADJ
ejpam-1551	125	11	involute	involute	NOUN
ejpam-1551	125	12	evolute	evolute	NOUN
ejpam-1551	126	1	d	d	X
ejpam-1551	126	2	-	-	PUNCT
ejpam-1551	126	3	pair	pair	NOUN
ejpam-1551	126	4	in	in	ADP
ejpam-1551	126	5	the	the	DET
ejpam-1551	126	6	euclidean	euclidean	ADJ
ejpam-1551	126	7	space	space	NOUN
ejpam-1551	126	8	e3	e3	NOUN
ejpam-1551	126	9	.	.	PUNCT
ejpam-1551	127	1	then	then	ADV
ejpam-1551	127	2	the	the	DET
ejpam-1551	127	3	following	follow	VERB
ejpam-1551	127	4	relations	relation	NOUN
ejpam-1551	127	5	hold	hold	VERB
ejpam-1551	127	6	:	:	PUNCT
ejpam-1551	127	7	•	•	NOUN
ejpam-1551	127	8	κ∗n	κ∗n	PUNCT
ejpam-1551	127	9	=	=	NOUN
ejpam-1551	127	10	τg	τg	ADP
ejpam-1551	127	11	ds	ds	ADJ
ejpam-1551	127	12	ds∗	ds∗	NOUN
ejpam-1551	127	13	−	−	PROPN
ejpam-1551	127	14	dθ	dθ	PROPN
ejpam-1551	127	15	ds∗	ds∗	PROPN
ejpam-1551	127	16	ö.	ö.	PROPN
ejpam-1551	127	17	bektaş	bektaş	PROPN
ejpam-1551	127	18	,	,	PUNCT
ejpam-1551	127	19	s.	s.	PROPN
ejpam-1551	127	20	yüce	yüce	PROPN
ejpam-1551	127	21	/	/	SYM
ejpam-1551	127	22	eur	eur	PROPN
ejpam-1551	127	23	.	.	PUNCT
ejpam-1551	128	1	j.	j.	PROPN
ejpam-1551	128	2	pure	pure	PROPN
ejpam-1551	128	3	appl	appl	PROPN
ejpam-1551	128	4	.	.	PROPN
ejpam-1551	128	5	math	math	PROPN
ejpam-1551	128	6	,	,	PUNCT
ejpam-1551	128	7	6	6	NUM
ejpam-1551	128	8	(	(	PUNCT
ejpam-1551	128	9	2013	2013	NUM
ejpam-1551	128	10	)	)	PUNCT
ejpam-1551	128	11	,	,	PUNCT
ejpam-1551	128	12	20	20	NUM
ejpam-1551	128	13	-	-	SYM
ejpam-1551	128	14	29	29	NUM
ejpam-1551	128	15	27	27	NUM
ejpam-1551	128	16	•	•	NOUN
ejpam-1551	128	17	κg	κg	ADP
ejpam-1551	128	18	ds	ds	ADJ
ejpam-1551	128	19	ds∗	ds∗	NOUN
ejpam-1551	128	20	=	=	SYM
ejpam-1551	128	21	−κ∗g	−κ∗g	X
ejpam-1551	129	1	cosθ	cosθ	PROPN
ejpam-1551	129	2	+	+	PROPN
ejpam-1551	129	3	τ∗g	τ∗g	X
ejpam-1551	129	4	sinθ	sinθ	PROPN
ejpam-1551	129	5	•	•	NUM
ejpam-1551	129	6	κn	κn	NOUN
ejpam-1551	129	7	ds	ds	ADJ
ejpam-1551	129	8	ds∗	ds∗	NOUN
ejpam-1551	129	9	=	=	SYM
ejpam-1551	129	10	κ∗g	κ∗g	PROPN
ejpam-1551	129	11	sinθ	sinθ	PROPN
ejpam-1551	129	12	+	+	PROPN
ejpam-1551	129	13	τ∗g	τ∗g	X
ejpam-1551	129	14	cosθ	cosθ	X
ejpam-1551	129	15	•	•	PRON
ejpam-1551	129	16	κ∗g	κ∗g	PROPN
ejpam-1551	129	17	=	=	SYM
ejpam-1551	129	18	�	�	PROPN
ejpam-1551	129	19	κn	κn	PROPN
ejpam-1551	129	20	sinθ	sinθ	PROPN
ejpam-1551	129	21	−	−	PROPN
ejpam-1551	129	22	κgcosθ	κgcosθ	ADJ
ejpam-1551	129	23	�	�	NOUN
ejpam-1551	129	24	ds	ds	ADJ
ejpam-1551	129	25	ds∗	ds∗	NOUN
ejpam-1551	129	26	proof	proof	NOUN
ejpam-1551	129	27	.	.	PUNCT
ejpam-1551	130	1	•	•	NUM
ejpam-1551	130	2	by	by	ADP
ejpam-1551	130	3	differentiating	differentiate	VERB
ejpam-1551	130	4	the	the	DET
ejpam-1551	130	5	equation	equation	NOUN
ejpam-1551	130	6	〈	〈	NOUN
ejpam-1551	130	7	n	n	CCONJ
ejpam-1551	130	8	,	,	PUNCT
ejpam-1551	130	9	n∗〉=	n∗〉=	NOUN
ejpam-1551	130	10	cosθ	cosθ	X
ejpam-1551	130	11	with	with	ADP
ejpam-1551	130	12	respect	respect	NOUN
ejpam-1551	130	13	to	to	ADP
ejpam-1551	130	14	s∗	s∗	PROPN
ejpam-1551	130	15	we	we	PRON
ejpam-1551	130	16	have	have	VERB
ejpam-1551	130	17	�	�	PROPN
ejpam-1551	130	18	�	�	PROPN
ejpam-1551	130	19	−κnt−τgg	−κnt−τgg	ADJ
ejpam-1551	130	20	�	�	PROPN
ejpam-1551	130	21	ds	ds	ADJ
ejpam-1551	130	22	ds∗	ds∗	NOUN
ejpam-1551	130	23	,	,	PUNCT
ejpam-1551	130	24	n∗	n∗	PROPN
ejpam-1551	130	25	�	�	PROPN
ejpam-1551	131	1	+	+	CCONJ
ejpam-1551	131	2	d	d	PROPN
ejpam-1551	131	3	n,−κ∗nt	n,−κ∗nt	NUM
ejpam-1551	131	4	∗−τ∗gg	∗−τ∗gg	NOUN
ejpam-1551	131	5	∗	∗	NOUN
ejpam-1551	131	6	e	e	NOUN
ejpam-1551	132	1	=	=	PUNCT
ejpam-1551	132	2	−	−	PROPN
ejpam-1551	132	3	sinθ	sinθ	PROPN
ejpam-1551	132	4	dθ	dθ	PROPN
ejpam-1551	132	5	ds∗	ds∗	PROPN
ejpam-1551	132	6	using	use	VERB
ejpam-1551	132	7	the	the	DET
ejpam-1551	132	8	fact	fact	NOUN
ejpam-1551	132	9	that	that	SCONJ
ejpam-1551	132	10	the	the	DET
ejpam-1551	132	11	direction	direction	NOUN
ejpam-1551	132	12	of	of	ADP
ejpam-1551	132	13	t	t	PROPN
ejpam-1551	132	14	coincides	coincide	VERB
ejpam-1551	132	15	with	with	ADP
ejpam-1551	132	16	the	the	DET
ejpam-1551	132	17	direction	direction	NOUN
ejpam-1551	132	18	of	of	ADP
ejpam-1551	132	19	g∗	g∗	PROPN
ejpam-1551	132	20	and	and	CCONJ
ejpam-1551	132	21	t∗	t∗	NOUN
ejpam-1551	132	22	=	=	SYM
ejpam-1551	132	23	cosθg−	cosθg−	NOUN
ejpam-1551	132	24	sinθn	sinθn	NOUN
ejpam-1551	132	25	g∗	g∗	PROPN
ejpam-1551	132	26	=	=	PUNCT
ejpam-1551	132	27	sinθg+	sinθg+	X
ejpam-1551	132	28	cosθn	cosθn	NOUN
ejpam-1551	132	29	we	we	PRON
ejpam-1551	132	30	easily	easily	ADV
ejpam-1551	132	31	get	get	VERB
ejpam-1551	132	32	that	that	DET
ejpam-1551	132	33	κ∗n	κ∗n	ADJ
ejpam-1551	132	34	=	=	NOUN
ejpam-1551	132	35	τg	τg	ADP
ejpam-1551	132	36	ds	ds	ADJ
ejpam-1551	132	37	ds∗	ds∗	NOUN
ejpam-1551	132	38	−	−	PROPN
ejpam-1551	132	39	dθ	dθ	PROPN
ejpam-1551	132	40	ds∗	ds∗	PROPN
ejpam-1551	132	41	similarly	similarly	ADV
ejpam-1551	132	42	other	other	ADJ
ejpam-1551	132	43	choices	choice	NOUN
ejpam-1551	132	44	are	be	AUX
ejpam-1551	132	45	testified	testify	VERB
ejpam-1551	132	46	.	.	PUNCT
ejpam-1551	133	1	theorem	theorem	ADJ
ejpam-1551	133	2	5	5	NUM
ejpam-1551	133	3	.	.	PUNCT
ejpam-1551	134	1	let	let	VERB
ejpam-1551	134	2	the	the	DET
ejpam-1551	134	3	pair	pair	NOUN
ejpam-1551	134	4	�	�	PROPN
ejpam-1551	134	5	α	α	PROPN
ejpam-1551	134	6	,	,	PUNCT
ejpam-1551	134	7	β	β	X
ejpam-1551	134	8	be	be	AUX
ejpam-1551	134	9	a	a	DET
ejpam-1551	134	10	special	special	ADJ
ejpam-1551	134	11	involute	involute	NOUN
ejpam-1551	134	12	evolute	evolute	NOUN
ejpam-1551	135	1	d	d	X
ejpam-1551	135	2	-	-	PUNCT
ejpam-1551	135	3	pair	pair	NOUN
ejpam-1551	135	4	in	in	ADP
ejpam-1551	135	5	the	the	DET
ejpam-1551	135	6	euclidean	euclidean	ADJ
ejpam-1551	135	7	space	space	NOUN
ejpam-1551	135	8	e3	e3	NOUN
ejpam-1551	135	9	.	.	PUNCT
ejpam-1551	136	1	then	then	ADV
ejpam-1551	136	2	geodesic	geodesic	ADJ
ejpam-1551	136	3	curvature	curvature	NOUN
ejpam-1551	136	4	κ∗g	κ∗g	PROPN
ejpam-1551	136	5	of	of	ADP
ejpam-1551	136	6	β	β	X
ejpam-1551	136	7	(	(	PUNCT
ejpam-1551	136	8	s∗	s∗	PROPN
ejpam-1551	136	9	)	)	PUNCT
ejpam-1551	136	10	is	be	AUX
ejpam-1551	136	11	κ∗g	κ∗g	PRON
ejpam-1551	136	12	=	=	SYM
ejpam-1551	136	13	λ	λ	PROPN
ejpam-1551	136	14	2	2	NUM
ejpam-1551	136	15	�	�	PROPN
ejpam-1551	136	16	κ2	κ2	NOUN
ejpam-1551	136	17	n−κ	n−κ	VERB
ejpam-1551	136	18	2	2	NUM
ejpam-1551	136	19	g	g	PROPN
ejpam-1551	136	20	�	�	PROPN
ejpam-1551	136	21	�	�	PROPN
ejpam-1551	136	22	ds	ds	PROPN
ejpam-1551	136	23	ds∗	ds∗	PROPN
ejpam-1551	136	24	�	�	PROPN
ejpam-1551	136	25	3	3	NUM
ejpam-1551	136	26	�	�	PROPN
ejpam-1551	136	27	κg	κg	ADP
ejpam-1551	136	28	cosθ	cosθ	PROPN
ejpam-1551	136	29	+	+	PROPN
ejpam-1551	136	30	κn	κn	PROPN
ejpam-1551	136	31	sinθ	sinθ	PROPN
ejpam-1551	136	32	�	�	PROPN
ejpam-1551	136	33	where	where	SCONJ
ejpam-1551	136	34	θ	θ	PROPN
ejpam-1551	136	35	is	be	AUX
ejpam-1551	136	36	the	the	DET
ejpam-1551	136	37	angle	angle	NOUN
ejpam-1551	136	38	between	between	ADP
ejpam-1551	136	39	the	the	DET
ejpam-1551	136	40	vectors	vector	NOUN
ejpam-1551	136	41	n	n	CCONJ
ejpam-1551	136	42	and	and	CCONJ
ejpam-1551	136	43	n∗	n∗	PROPN
ejpam-1551	136	44	at	at	ADP
ejpam-1551	136	45	the	the	DET
ejpam-1551	136	46	corresponding	corresponding	ADJ
ejpam-1551	136	47	points	point	NOUN
ejpam-1551	136	48	of	of	ADP
ejpam-1551	136	49	α	α	PROPN
ejpam-1551	136	50	(	(	PUNCT
ejpam-1551	136	51	s	s	NOUN
ejpam-1551	136	52	)	)	PUNCT
ejpam-1551	136	53	and	and	CCONJ
ejpam-1551	136	54	β	β	X
ejpam-1551	136	55	(	(	PUNCT
ejpam-1551	136	56	s∗	s∗	PROPN
ejpam-1551	136	57	)	)	PUNCT
ejpam-1551	136	58	.	.	PUNCT
ejpam-1551	137	1	proof	proof	NOUN
ejpam-1551	137	2	.	.	PUNCT
ejpam-1551	138	1	suppose	suppose	VERB
ejpam-1551	138	2	that	that	SCONJ
ejpam-1551	138	3	the	the	DET
ejpam-1551	138	4	pair	pair	NOUN
ejpam-1551	138	5	�	�	PROPN
ejpam-1551	138	6	α	α	PROPN
ejpam-1551	138	7	,	,	PUNCT
ejpam-1551	138	8	β	β	X
ejpam-1551	138	9	is	be	AUX
ejpam-1551	138	10	a	a	DET
ejpam-1551	138	11	special	special	ADJ
ejpam-1551	138	12	involute	involute	NOUN
ejpam-1551	138	13	evolute	evolute	NOUN
ejpam-1551	138	14	d	d	X
ejpam-1551	138	15	-	-	PUNCT
ejpam-1551	138	16	pair	pair	NOUN
ejpam-1551	138	17	in	in	ADP
ejpam-1551	138	18	the	the	DET
ejpam-1551	138	19	euclidean	euclidean	ADJ
ejpam-1551	138	20	3	3	NUM
ejpam-1551	138	21	space	space	NOUN
ejpam-1551	138	22	e3	e3	NOUN
ejpam-1551	138	23	.	.	PUNCT
ejpam-1551	139	1	from	from	ADP
ejpam-1551	139	2	the	the	DET
ejpam-1551	139	3	first	first	ADJ
ejpam-1551	139	4	equation	equation	NOUN
ejpam-1551	139	5	of	of	ADP
ejpam-1551	139	6	(	(	PUNCT
ejpam-1551	139	7	4	4	NUM
ejpam-1551	139	8	)	)	PUNCT
ejpam-1551	139	9	and	and	CCONJ
ejpam-1551	139	10	by	by	ADP
ejpam-1551	139	11	using	use	VERB
ejpam-1551	139	12	the	the	DET
ejpam-1551	139	13	fact	fact	NOUN
ejpam-1551	139	14	that	that	SCONJ
ejpam-1551	139	15	t	t	PROPN
ejpam-1551	139	16	is	be	AUX
ejpam-1551	139	17	coincident	coincident	ADJ
ejpam-1551	139	18	with	with	ADP
ejpam-1551	139	19	g∗	g∗	NOUN
ejpam-1551	139	20	we	we	PRON
ejpam-1551	139	21	have	have	VERB
ejpam-1551	139	22	κ∗g	κ∗g	VERB
ejpam-1551	139	23	=	=	SYM
ejpam-1551	139	24	®	®	NOUN
ejpam-1551	139	25	dβ	dβ	ADJ
ejpam-1551	139	26	ds∗	ds∗	NOUN
ejpam-1551	139	27	,	,	PUNCT
ejpam-1551	139	28	d2β	d2β	VERB
ejpam-1551	139	29	ds∗2	ds∗2	NOUN
ejpam-1551	139	30	×n∗	×n∗	NOUN
ejpam-1551	139	31	¸	¸	X
ejpam-1551	139	32	=	=	SYM
ejpam-1551	139	33	λ2	λ2	PROPN
ejpam-1551	139	34	�	�	PROPN
ejpam-1551	139	35	κ2	κ2	PROPN
ejpam-1551	139	36	n−κ	n−κ	VERB
ejpam-1551	139	37	2	2	NUM
ejpam-1551	139	38	g	g	PROPN
ejpam-1551	139	39	�	�	PROPN
ejpam-1551	139	40	�	�	PROPN
ejpam-1551	139	41	ds	ds	PROPN
ejpam-1551	139	42	ds∗	ds∗	PROPN
ejpam-1551	139	43	�	�	PROPN
ejpam-1551	139	44	3	3	NUM
ejpam-1551	139	45	�	�	PROPN
ejpam-1551	139	46	κg	κg	ADP
ejpam-1551	139	47	cosθ	cosθ	PROPN
ejpam-1551	139	48	+	+	PROPN
ejpam-1551	139	49	κn	κn	PROPN
ejpam-1551	139	50	sinθ	sinθ	PROPN
ejpam-1551	139	51	�	�	PROPN
ejpam-1551	139	52	special	special	ADJ
ejpam-1551	139	53	case	case	NOUN
ejpam-1551	139	54	3	3	X
ejpam-1551	139	55	.	.	PUNCT
ejpam-1551	140	1	let	let	VERB
ejpam-1551	140	2	the	the	DET
ejpam-1551	140	3	pair	pair	NOUN
ejpam-1551	140	4	�	�	PROPN
ejpam-1551	140	5	α	α	PROPN
ejpam-1551	140	6	,	,	PUNCT
ejpam-1551	140	7	β	β	X
ejpam-1551	140	8	be	be	AUX
ejpam-1551	140	9	a	a	DET
ejpam-1551	140	10	special	special	ADJ
ejpam-1551	140	11	involute	involute	NOUN
ejpam-1551	140	12	evolute	evolute	NOUN
ejpam-1551	141	1	d	d	X
ejpam-1551	141	2	-	-	PUNCT
ejpam-1551	141	3	pair	pair	NOUN
ejpam-1551	141	4	in	in	ADP
ejpam-1551	141	5	the	the	DET
ejpam-1551	141	6	euclidean	euclidean	ADJ
ejpam-1551	141	7	space	space	NOUN
ejpam-1551	141	8	e3	e3	NOUN
ejpam-1551	141	9	.	.	PUNCT
ejpam-1551	142	1	ö.	ö.	PROPN
ejpam-1551	142	2	bektaş	bektaş	PROPN
ejpam-1551	142	3	,	,	PUNCT
ejpam-1551	142	4	s.	s.	PROPN
ejpam-1551	142	5	yüce	yüce	PROPN
ejpam-1551	142	6	/	/	SYM
ejpam-1551	142	7	eur	eur	PROPN
ejpam-1551	142	8	.	.	PUNCT
ejpam-1551	143	1	j.	j.	PROPN
ejpam-1551	143	2	pure	pure	PROPN
ejpam-1551	143	3	appl	appl	PROPN
ejpam-1551	143	4	.	.	PROPN
ejpam-1551	143	5	math	math	PROPN
ejpam-1551	143	6	,	,	PUNCT
ejpam-1551	143	7	6	6	NUM
ejpam-1551	143	8	(	(	PUNCT
ejpam-1551	143	9	2013	2013	NUM
ejpam-1551	143	10	)	)	PUNCT
ejpam-1551	143	11	,	,	PUNCT
ejpam-1551	143	12	20	20	NUM
ejpam-1551	143	13	-	-	SYM
ejpam-1551	143	14	29	29	NUM
ejpam-1551	143	15	28	28	NUM
ejpam-1551	143	16	i	i	NOUN
ejpam-1551	143	17	)	)	PUNCT
ejpam-1551	143	18	if	if	SCONJ
ejpam-1551	143	19	α	α	PRON
ejpam-1551	143	20	is	be	AUX
ejpam-1551	143	21	a	a	DET
ejpam-1551	143	22	geodesic	geodesic	ADJ
ejpam-1551	143	23	curve	curve	NOUN
ejpam-1551	143	24	,	,	PUNCT
ejpam-1551	143	25	then	then	ADV
ejpam-1551	143	26	the	the	DET
ejpam-1551	143	27	geodesic	geodesic	ADJ
ejpam-1551	143	28	curvature	curvature	NOUN
ejpam-1551	143	29	κ∗g	κ∗g	PROPN
ejpam-1551	143	30	of	of	ADP
ejpam-1551	143	31	β	β	X
ejpam-1551	143	32	(	(	PUNCT
ejpam-1551	143	33	s∗	s∗	PROPN
ejpam-1551	143	34	)	)	PUNCT
ejpam-1551	143	35	is	be	AUX
ejpam-1551	143	36	κ∗g	κ∗g	PROPN
ejpam-1551	143	37	=	=	SYM
ejpam-1551	143	38	λ	λ	PROPN
ejpam-1551	143	39	2κ3	2κ3	NUM
ejpam-1551	143	40	n	n	PRON
ejpam-1551	143	41	�	�	PROPN
ejpam-1551	143	42	ds	ds	PROPN
ejpam-1551	143	43	ds∗	ds∗	PROPN
ejpam-1551	143	44	�	�	PROPN
ejpam-1551	143	45	3	3	NUM
ejpam-1551	143	46	sinθ	sinθ	PROPN
ejpam-1551	143	47	ii	ii	PROPN
ejpam-1551	143	48	)	)	PUNCT
ejpam-1551	143	49	if	if	SCONJ
ejpam-1551	143	50	α	α	PRON
ejpam-1551	143	51	is	be	AUX
ejpam-1551	143	52	an	an	DET
ejpam-1551	143	53	asymptotic	asymptotic	ADJ
ejpam-1551	143	54	line	line	NOUN
ejpam-1551	143	55	,	,	PUNCT
ejpam-1551	143	56	then	then	ADV
ejpam-1551	143	57	the	the	DET
ejpam-1551	143	58	geodesic	geodesic	ADJ
ejpam-1551	143	59	curvature	curvature	NOUN
ejpam-1551	143	60	κ∗g	κ∗g	PROPN
ejpam-1551	143	61	of	of	ADP
ejpam-1551	143	62	β	β	X
ejpam-1551	143	63	(	(	PUNCT
ejpam-1551	143	64	s∗	s∗	PROPN
ejpam-1551	143	65	)	)	PUNCT
ejpam-1551	143	66	is	be	AUX
ejpam-1551	143	67	κ∗g	κ∗g	PROPN
ejpam-1551	143	68	=	=	SYM
ejpam-1551	143	69	λ	λ	PROPN
ejpam-1551	143	70	2κ3	2κ3	NUM
ejpam-1551	143	71	g	g	NOUN
ejpam-1551	143	72	�	�	X
ejpam-1551	143	73	ds	ds	PROPN
ejpam-1551	143	74	ds∗	ds∗	PROPN
ejpam-1551	143	75	�	�	PROPN
ejpam-1551	143	76	3	3	NUM
ejpam-1551	143	77	cosθ	cosθ	NOUN
ejpam-1551	143	78	theorem	theorem	NOUN
ejpam-1551	143	79	6	6	NUM
ejpam-1551	143	80	.	.	PUNCT
ejpam-1551	144	1	let	let	VERB
ejpam-1551	144	2	the	the	DET
ejpam-1551	144	3	pair	pair	NOUN
ejpam-1551	144	4	�	�	PROPN
ejpam-1551	144	5	α	α	PROPN
ejpam-1551	144	6	,	,	PUNCT
ejpam-1551	144	7	β	β	X
ejpam-1551	144	8	be	be	AUX
ejpam-1551	144	9	a	a	DET
ejpam-1551	144	10	special	special	ADJ
ejpam-1551	144	11	involute	involute	NOUN
ejpam-1551	144	12	evolute	evolute	NOUN
ejpam-1551	145	1	d	d	X
ejpam-1551	145	2	-	-	PUNCT
ejpam-1551	145	3	pair	pair	NOUN
ejpam-1551	145	4	in	in	ADP
ejpam-1551	145	5	the	the	DET
ejpam-1551	145	6	euclidean	euclidean	ADJ
ejpam-1551	145	7	space	space	NOUN
ejpam-1551	145	8	e3	e3	NOUN
ejpam-1551	145	9	.	.	PUNCT
ejpam-1551	146	1	then	then	ADV
ejpam-1551	146	2	geodesic	geodesic	ADJ
ejpam-1551	146	3	curvature	curvature	NOUN
ejpam-1551	146	4	τ∗g	τ∗g	NUM
ejpam-1551	146	5	of	of	ADP
ejpam-1551	146	6	β	β	X
ejpam-1551	146	7	(	(	PUNCT
ejpam-1551	146	8	s∗	s∗	PROPN
ejpam-1551	146	9	)	)	PUNCT
ejpam-1551	146	10	is	be	AUX
ejpam-1551	146	11	τ∗g	τ∗g	X
ejpam-1551	146	12	=	=	SYM
ejpam-1551	146	13	−λ	−λ	PROPN
ejpam-1551	146	14	sinθ	sinθ	PROPN
ejpam-1551	146	15	cosθ	cosθ	PROPN
ejpam-1551	146	16	�	�	PROPN
ejpam-1551	146	17	κ2	κ2	PROPN
ejpam-1551	146	18	n+κ	n+κ	PROPN
ejpam-1551	146	19	2	2	NUM
ejpam-1551	146	20	g	g	PROPN
ejpam-1551	146	21	�	�	PROPN
ejpam-1551	146	22	�	�	PROPN
ejpam-1551	146	23	ds	ds	PROPN
ejpam-1551	146	24	ds∗	ds∗	PROPN
ejpam-1551	146	25	�	�	PROPN
ejpam-1551	146	26	2	2	NUM
ejpam-1551	146	27	−λκnκg	−λκnκg	NOUN
ejpam-1551	146	28	�	�	PROPN
ejpam-1551	146	29	ds	ds	PROPN
ejpam-1551	146	30	ds∗	ds∗	PROPN
ejpam-1551	146	31	�	�	PROPN
ejpam-1551	146	32	2	2	NUM
ejpam-1551	146	33	where	where	SCONJ
ejpam-1551	146	34	θ	θ	PROPN
ejpam-1551	146	35	is	be	AUX
ejpam-1551	146	36	the	the	DET
ejpam-1551	146	37	angle	angle	NOUN
ejpam-1551	146	38	between	between	ADP
ejpam-1551	146	39	the	the	DET
ejpam-1551	146	40	vectors	vector	NOUN
ejpam-1551	146	41	n	n	CCONJ
ejpam-1551	146	42	and	and	CCONJ
ejpam-1551	146	43	n∗	n∗	PROPN
ejpam-1551	146	44	at	at	ADP
ejpam-1551	146	45	the	the	DET
ejpam-1551	146	46	corresponding	corresponding	ADJ
ejpam-1551	146	47	points	point	NOUN
ejpam-1551	146	48	of	of	ADP
ejpam-1551	146	49	α	α	PROPN
ejpam-1551	146	50	(	(	PUNCT
ejpam-1551	146	51	s	s	NOUN
ejpam-1551	146	52	)	)	PUNCT
ejpam-1551	146	53	and	and	CCONJ
ejpam-1551	146	54	β	β	X
ejpam-1551	146	55	(	(	PUNCT
ejpam-1551	146	56	s∗	s∗	PROPN
ejpam-1551	146	57	)	)	PUNCT
ejpam-1551	146	58	.	.	PUNCT
ejpam-1551	147	1	proof	proof	NOUN
ejpam-1551	147	2	.	.	PUNCT
ejpam-1551	148	1	suppose	suppose	VERB
ejpam-1551	148	2	that	that	SCONJ
ejpam-1551	148	3	the	the	DET
ejpam-1551	148	4	pair	pair	NOUN
ejpam-1551	148	5	�	�	PROPN
ejpam-1551	148	6	α	α	PROPN
ejpam-1551	148	7	,	,	PUNCT
ejpam-1551	148	8	β	β	X
ejpam-1551	148	9	is	be	AUX
ejpam-1551	148	10	a	a	DET
ejpam-1551	148	11	special	special	ADJ
ejpam-1551	148	12	involute	involute	NOUN
ejpam-1551	148	13	evolute	evolute	NOUN
ejpam-1551	148	14	d	d	X
ejpam-1551	148	15	-	-	PUNCT
ejpam-1551	148	16	pair	pair	NOUN
ejpam-1551	148	17	in	in	ADP
ejpam-1551	148	18	the	the	DET
ejpam-1551	148	19	euclidean	euclidean	ADJ
ejpam-1551	148	20	space	space	NOUN
ejpam-1551	148	21	e3	e3	NOUN
ejpam-1551	148	22	.	.	PUNCT
ejpam-1551	149	1	from	from	ADP
ejpam-1551	149	2	the	the	DET
ejpam-1551	149	3	first	first	ADJ
ejpam-1551	149	4	equation	equation	NOUN
ejpam-1551	149	5	of	of	ADP
ejpam-1551	149	6	(	(	PUNCT
ejpam-1551	149	7	4	4	NUM
ejpam-1551	149	8	)	)	PUNCT
ejpam-1551	149	9	and	and	CCONJ
ejpam-1551	149	10	by	by	ADP
ejpam-1551	149	11	using	use	VERB
ejpam-1551	149	12	the	the	DET
ejpam-1551	149	13	fact	fact	NOUN
ejpam-1551	149	14	that	that	SCONJ
ejpam-1551	149	15	t	t	PROPN
ejpam-1551	149	16	is	be	AUX
ejpam-1551	149	17	coincident	coincident	ADJ
ejpam-1551	149	18	with	with	ADP
ejpam-1551	149	19	g∗	g∗	NOUN
ejpam-1551	149	20	we	we	PRON
ejpam-1551	149	21	have	have	VERB
ejpam-1551	149	22	τ∗g	τ∗g	NUM
ejpam-1551	149	23	=	=	SYM
ejpam-1551	149	24	®	®	NOUN
ejpam-1551	149	25	dβ	dβ	ADJ
ejpam-1551	149	26	ds∗	ds∗	NOUN
ejpam-1551	149	27	,	,	PUNCT
ejpam-1551	149	28	n∗×	n∗×	ADJ
ejpam-1551	149	29	dn∗	dn∗	NOUN
ejpam-1551	149	30	ds∗	ds∗	NOUN
ejpam-1551	149	31	¸	¸	X
ejpam-1551	150	1	=	=	PUNCT
ejpam-1551	150	2	−λ	−λ	PROPN
ejpam-1551	150	3	sinθ	sinθ	PROPN
ejpam-1551	150	4	cosθ	cosθ	PROPN
ejpam-1551	150	5	�	�	PROPN
ejpam-1551	150	6	κ2	κ2	PROPN
ejpam-1551	150	7	n+κ	n+κ	PROPN
ejpam-1551	150	8	2	2	NUM
ejpam-1551	150	9	g	g	PROPN
ejpam-1551	150	10	�	�	PROPN
ejpam-1551	150	11	�	�	PROPN
ejpam-1551	150	12	ds	ds	PROPN
ejpam-1551	150	13	ds∗	ds∗	PROPN
ejpam-1551	150	14	�	�	PROPN
ejpam-1551	150	15	2	2	NUM
ejpam-1551	150	16	−λκnκg	−λκnκg	NOUN
ejpam-1551	150	17	�	�	PROPN
ejpam-1551	150	18	ds	ds	PROPN
ejpam-1551	150	19	ds∗	ds∗	PROPN
ejpam-1551	150	20	�	�	PROPN
ejpam-1551	150	21	2	2	NUM
ejpam-1551	150	22	corollary	corollary	NOUN
ejpam-1551	150	23	2	2	NUM
ejpam-1551	150	24	.	.	PUNCT
ejpam-1551	150	25	let	let	VERB
ejpam-1551	150	26	the	the	DET
ejpam-1551	150	27	pair	pair	NOUN
ejpam-1551	150	28	�	�	PROPN
ejpam-1551	150	29	α	α	PROPN
ejpam-1551	150	30	,	,	PUNCT
ejpam-1551	150	31	β	β	X
ejpam-1551	150	32	be	be	AUX
ejpam-1551	150	33	a	a	DET
ejpam-1551	150	34	special	special	ADJ
ejpam-1551	150	35	involute	involute	NOUN
ejpam-1551	150	36	evolute	evolute	NOUN
ejpam-1551	151	1	d	d	X
ejpam-1551	151	2	-	-	PUNCT
ejpam-1551	151	3	pair	pair	NOUN
ejpam-1551	151	4	in	in	ADP
ejpam-1551	151	5	the	the	DET
ejpam-1551	151	6	euclidean	euclidean	ADJ
ejpam-1551	151	7	space	space	NOUN
ejpam-1551	151	8	e3	e3	NOUN
ejpam-1551	151	9	.	.	PUNCT
ejpam-1551	152	1	i	i	PRON
ejpam-1551	152	2	)	)	PUNCT
ejpam-1551	152	3	if	if	SCONJ
ejpam-1551	152	4	α	α	PRON
ejpam-1551	152	5	is	be	AUX
ejpam-1551	152	6	a	a	DET
ejpam-1551	152	7	geodesic	geodesic	ADJ
ejpam-1551	152	8	curve	curve	NOUN
ejpam-1551	152	9	,	,	PUNCT
ejpam-1551	152	10	then	then	ADV
ejpam-1551	152	11	the	the	DET
ejpam-1551	152	12	geodesic	geodesic	ADJ
ejpam-1551	152	13	curvature	curvature	NOUN
ejpam-1551	152	14	τ∗g	τ∗g	NUM
ejpam-1551	152	15	of	of	ADP
ejpam-1551	152	16	β	β	X
ejpam-1551	152	17	(	(	PUNCT
ejpam-1551	152	18	s∗	s∗	PROPN
ejpam-1551	152	19	)	)	PUNCT
ejpam-1551	152	20	is	be	AUX
ejpam-1551	152	21	τ∗g	τ∗g	X
ejpam-1551	152	22	=	=	SYM
ejpam-1551	152	23	−λ	−λ	PROPN
ejpam-1551	152	24	sinθ	sinθ	PROPN
ejpam-1551	152	25	cosθκ2	cosθκ2	PROPN
ejpam-1551	152	26	n	n	CCONJ
ejpam-1551	152	27	�	�	PROPN
ejpam-1551	152	28	ds	ds	PROPN
ejpam-1551	152	29	ds∗	ds∗	PROPN
ejpam-1551	152	30	�	�	PROPN
ejpam-1551	152	31	2	2	NUM
ejpam-1551	152	32	ii	ii	NOUN
ejpam-1551	152	33	)	)	PUNCT
ejpam-1551	152	34	if	if	SCONJ
ejpam-1551	152	35	α	α	PRON
ejpam-1551	152	36	is	be	AUX
ejpam-1551	152	37	an	an	DET
ejpam-1551	152	38	asymptotic	asymptotic	ADJ
ejpam-1551	152	39	line	line	NOUN
ejpam-1551	152	40	,	,	PUNCT
ejpam-1551	152	41	then	then	ADV
ejpam-1551	152	42	the	the	DET
ejpam-1551	152	43	geodesic	geodesic	ADJ
ejpam-1551	152	44	curvature	curvature	NOUN
ejpam-1551	152	45	τ∗g	τ∗g	NUM
ejpam-1551	152	46	of	of	ADP
ejpam-1551	152	47	β	β	X
ejpam-1551	152	48	(	(	PUNCT
ejpam-1551	152	49	s∗	s∗	PROPN
ejpam-1551	152	50	)	)	PUNCT
ejpam-1551	152	51	is	be	AUX
ejpam-1551	152	52	τ∗g	τ∗g	X
ejpam-1551	152	53	=	=	SYM
ejpam-1551	152	54	−λ	−λ	PROPN
ejpam-1551	152	55	sinθ	sinθ	PROPN
ejpam-1551	152	56	cosθκ2	cosθκ2	PROPN
ejpam-1551	152	57	g	g	PROPN
ejpam-1551	152	58	�	�	PROPN
ejpam-1551	152	59	ds	ds	PROPN
ejpam-1551	152	60	ds∗	ds∗	PROPN
ejpam-1551	152	61	�	�	PROPN
ejpam-1551	152	62	2	2	NUM
ejpam-1551	152	63	example	example	NOUN
ejpam-1551	152	64	1	1	NUM
ejpam-1551	152	65	.	.	PUNCT
ejpam-1551	153	1	let	let	VERB
ejpam-1551	153	2	α	α	PROPN
ejpam-1551	153	3	(	(	PUNCT
ejpam-1551	153	4	s	s	NOUN
ejpam-1551	153	5	)	)	PUNCT
ejpam-1551	153	6	=	=	SYM
ejpam-1551	153	7	�	�	PROPN
ejpam-1551	153	8	sin	sin	NOUN
ejpam-1551	153	9	s	s	PROPN
ejpam-1551	153	10	,	,	PUNCT
ejpam-1551	153	11	cos	cos	PROPN
ejpam-1551	153	12	s	s	PROPN
ejpam-1551	153	13	,	,	PUNCT
ejpam-1551	153	14	sin3	sin3	PROPN
ejpam-1551	153	15	s−	s−	PROPN
ejpam-1551	153	16	3	3	NUM
ejpam-1551	153	17	sin	sin	NOUN
ejpam-1551	153	18	s	s	PART
ejpam-1551	153	19	cos2	cos2	PROPN
ejpam-1551	153	20	s	s	PART
ejpam-1551	153	21	�	�	PROPN
ejpam-1551	153	22	be	be	AUX
ejpam-1551	153	23	a	a	DET
ejpam-1551	153	24	curve	curve	NOUN
ejpam-1551	153	25	.	.	PUNCT
ejpam-1551	154	1	this	this	DET
ejpam-1551	154	2	curve	curve	NOUN
ejpam-1551	154	3	lies	lie	VERB
ejpam-1551	154	4	on	on	ADP
ejpam-1551	154	5	the	the	DET
ejpam-1551	154	6	surface	surface	NOUN
ejpam-1551	154	7	z	z	NOUN
ejpam-1551	155	1	=	=	PUNCT
ejpam-1551	155	2	x3	x3	ADJ
ejpam-1551	155	3	−	−	PROPN
ejpam-1551	156	1	3x	3x	NUM
ejpam-1551	156	2	y2	y2	PROPN
ejpam-1551	156	3	(	(	PUNCT
ejpam-1551	156	4	monkey	monkey	NOUN
ejpam-1551	156	5	saddle	saddle	NOUN
ejpam-1551	156	6	)	)	PUNCT
ejpam-1551	156	7	.	.	PUNCT
ejpam-1551	157	1	the	the	DET
ejpam-1551	157	2	special	special	ADJ
ejpam-1551	157	3	involute	involute	ADJ
ejpam-1551	157	4	d	d	NOUN
ejpam-1551	157	5	-	-	NOUN
ejpam-1551	157	6	curve	curve	NOUN
ejpam-1551	157	7	of	of	ADP
ejpam-1551	157	8	the	the	DET
ejpam-1551	157	9	curve	curve	NOUN
ejpam-1551	157	10	α	α	PROPN
ejpam-1551	157	11	(	(	PUNCT
ejpam-1551	157	12	s	s	X
ejpam-1551	157	13	)	)	PUNCT
ejpam-1551	157	14	can	can	AUX
ejpam-1551	157	15	be	be	AUX
ejpam-1551	157	16	given	give	VERB
ejpam-1551	157	17	below	below	ADP
ejpam-1551	157	18	β	β	X
ejpam-1551	157	19	(	(	PUNCT
ejpam-1551	157	20	s	s	X
ejpam-1551	157	21	)	)	PUNCT
ejpam-1551	157	22	=	=	SYM
ejpam-1551	157	23	�	�	PROPN
ejpam-1551	157	24	sin	sin	NOUN
ejpam-1551	157	25	s+	s+	PUNCT
ejpam-1551	157	26	(	(	PUNCT
ejpam-1551	157	27	c	c	X
ejpam-1551	157	28	−	−	PROPN
ejpam-1551	157	29	s	s	PART
ejpam-1551	157	30	)	)	PUNCT
ejpam-1551	157	31	cos	cos	PROPN
ejpam-1551	157	32	s	s	PROPN
ejpam-1551	157	33	,	,	PUNCT
ejpam-1551	157	34	cos	cos	PROPN
ejpam-1551	157	35	s+	s+	ADV
ejpam-1551	157	36	(	(	PUNCT
ejpam-1551	157	37	s−	s−	PROPN
ejpam-1551	157	38	c	c	NOUN
ejpam-1551	157	39	)	)	PUNCT
ejpam-1551	157	40	sin	sin	NOUN
ejpam-1551	157	41	s	s	PROPN
ejpam-1551	157	42	,	,	PUNCT
ejpam-1551	157	43	sin3	sin3	PROPN
ejpam-1551	157	44	s−	s−	PROPN
ejpam-1551	157	45	3	3	NUM
ejpam-1551	157	46	sin	sin	NOUN
ejpam-1551	157	47	s	s	PART
ejpam-1551	157	48	cos2	cos2	NOUN
ejpam-1551	157	49	s	s	PART
ejpam-1551	157	50	+	+	NOUN
ejpam-1551	157	51	(	(	PUNCT
ejpam-1551	157	52	1−	1−	NUM
ejpam-1551	157	53	s)(9	s)(9	NUM
ejpam-1551	157	54	sin2	sin2	PROPN
ejpam-1551	157	55	s	s	PART
ejpam-1551	157	56	cos	cos	ADP
ejpam-1551	157	57	s−	s−	PROPN
ejpam-1551	157	58	3	3	NUM
ejpam-1551	157	59	cos3	cos3	PROPN
ejpam-1551	157	60	s	s	PART
ejpam-1551	157	61	)	)	PUNCT
ejpam-1551	157	62	�	�	PROPN
ejpam-1551	157	63	,	,	PUNCT
ejpam-1551	157	64	c	c	PROPN
ejpam-1551	157	65	∈	∈	PROPN
ejpam-1551	157	66	r	r	NOUN
ejpam-1551	157	67	,	,	PUNCT
ejpam-1551	157	68	c	c	PROPN
ejpam-1551	157	69	is	be	AUX
ejpam-1551	157	70	a	a	DET
ejpam-1551	157	71	constant	constant	ADJ
ejpam-1551	157	72	for	for	ADP
ejpam-1551	157	73	specially	specially	ADV
ejpam-1551	157	74	,	,	PUNCT
ejpam-1551	157	75	c	c	NOUN
ejpam-1551	157	76	=	=	SYM
ejpam-1551	157	77	1	1	NUM
ejpam-1551	157	78	and	and	CCONJ
ejpam-1551	157	79	s	s	NOUN
ejpam-1551	157	80	∈	∈	NOUN
ejpam-1551	158	1	[	[	X
ejpam-1551	158	2	0,2π	0,2π	NOUN
ejpam-1551	158	3	]	]	PUNCT
ejpam-1551	158	4	,	,	PUNCT
ejpam-1551	158	5	we	we	PRON
ejpam-1551	158	6	can	can	AUX
ejpam-1551	158	7	draw	draw	VERB
ejpam-1551	158	8	special	special	ADJ
ejpam-1551	158	9	involute	involute	ADJ
ejpam-1551	158	10	evolute	evolute	NOUN
ejpam-1551	158	11	d	d	X
ejpam-1551	158	12	-	-	PUNCT
ejpam-1551	158	13	pair	pair	NOUN
ejpam-1551	158	14	�	�	PROPN
ejpam-1551	158	15	α	α	PROPN
ejpam-1551	158	16	,	,	PUNCT
ejpam-1551	158	17	β	β	X
ejpam-1551	158	18	using	use	VERB
ejpam-1551	158	19	maple	maple	NOUN
ejpam-1551	158	20	12	12	NUM
ejpam-1551	158	21	as	as	SCONJ
ejpam-1551	158	22	shown	show	VERB
ejpam-1551	158	23	in	in	ADP
ejpam-1551	158	24	figure	figure	NOUN
ejpam-1551	158	25	1a	1a	NOUN
ejpam-1551	158	26	.	.	PUNCT
ejpam-1551	159	1	references	reference	NOUN
ejpam-1551	159	2	29	29	NUM
ejpam-1551	159	3	example	example	NOUN
ejpam-1551	159	4	2	2	NUM
ejpam-1551	159	5	.	.	PUNCT
ejpam-1551	160	1	let	let	VERB
ejpam-1551	160	2	α	α	PROPN
ejpam-1551	160	3	(	(	PUNCT
ejpam-1551	160	4	s	s	NOUN
ejpam-1551	160	5	)	)	PUNCT
ejpam-1551	160	6	=	=	SYM
ejpam-1551	160	7	�	�	PROPN
ejpam-1551	160	8	s	s	PART
ejpam-1551	160	9	sin	sin	NOUN
ejpam-1551	160	10	s	s	PROPN
ejpam-1551	160	11	,	,	PUNCT
ejpam-1551	160	12	s	s	X
ejpam-1551	160	13	cos	cos	PROPN
ejpam-1551	160	14	s	s	PROPN
ejpam-1551	160	15	,	,	PUNCT
ejpam-1551	160	16	s2	s2	PROPN
ejpam-1551	160	17	�	�	PROPN
ejpam-1551	160	18	be	be	AUX
ejpam-1551	160	19	a	a	DET
ejpam-1551	160	20	curve	curve	NOUN
ejpam-1551	160	21	.	.	PUNCT
ejpam-1551	161	1	this	this	DET
ejpam-1551	161	2	curve	curve	NOUN
ejpam-1551	161	3	lies	lie	VERB
ejpam-1551	161	4	on	on	ADP
ejpam-1551	161	5	the	the	DET
ejpam-1551	161	6	surface	surface	NOUN
ejpam-1551	161	7	z	z	NOUN
ejpam-1551	161	8	=	=	SYM
ejpam-1551	161	9	x2	x2	PROPN
ejpam-1551	161	10	+	+	CCONJ
ejpam-1551	161	11	y2	y2	NOUN
ejpam-1551	161	12	.	.	PUNCT
ejpam-1551	162	1	the	the	DET
ejpam-1551	162	2	special	special	ADJ
ejpam-1551	162	3	involute	involute	ADJ
ejpam-1551	162	4	d	d	NOUN
ejpam-1551	162	5	-	-	NOUN
ejpam-1551	162	6	curve	curve	NOUN
ejpam-1551	162	7	of	of	ADP
ejpam-1551	162	8	the	the	DET
ejpam-1551	162	9	curve	curve	NOUN
ejpam-1551	162	10	α	α	PROPN
ejpam-1551	162	11	(	(	PUNCT
ejpam-1551	162	12	s	s	X
ejpam-1551	162	13	)	)	PUNCT
ejpam-1551	162	14	can	can	AUX
ejpam-1551	162	15	be	be	AUX
ejpam-1551	162	16	given	give	VERB
ejpam-1551	162	17	below	below	ADP
ejpam-1551	162	18	β	β	X
ejpam-1551	162	19	(	(	PUNCT
ejpam-1551	162	20	s	s	X
ejpam-1551	162	21	)	)	PUNCT
ejpam-1551	162	22	=	=	SYM
ejpam-1551	162	23	�	�	PROPN
ejpam-1551	162	24	s	s	PART
ejpam-1551	162	25	sin	sin	NOUN
ejpam-1551	162	26	s+	s+	PUNCT
ejpam-1551	162	27	(	(	PUNCT
ejpam-1551	162	28	c	c	NOUN
ejpam-1551	162	29	−	−	PROPN
ejpam-1551	162	30	s)(sin	s)(sin	NOUN
ejpam-1551	162	31	s+	s+	ADP
ejpam-1551	162	32	s	s	PART
ejpam-1551	162	33	cos	cos	PROPN
ejpam-1551	162	34	s	s	PROPN
ejpam-1551	162	35	)	)	PUNCT
ejpam-1551	162	36	,	,	PUNCT
ejpam-1551	162	37	s	s	PROPN
ejpam-1551	162	38	cos	cos	PROPN
ejpam-1551	162	39	s+	s+	X
ejpam-1551	162	40	(	(	PUNCT
ejpam-1551	162	41	c	c	X
ejpam-1551	162	42	−	−	PROPN
ejpam-1551	162	43	s)(cos	s)(cos	PROPN
ejpam-1551	162	44	s−	s−	PROPN
ejpam-1551	162	45	s	s	PART
ejpam-1551	162	46	sin	sin	NOUN
ejpam-1551	162	47	s	s	NOUN
ejpam-1551	162	48	)	)	PUNCT
ejpam-1551	162	49	,	,	PUNCT
ejpam-1551	162	50	s2	s2	VERB
ejpam-1551	162	51	+	+	CCONJ
ejpam-1551	162	52	2(c	2(c	NUM
ejpam-1551	162	53	−	−	PROPN
ejpam-1551	162	54	s)s	s)s	X
ejpam-1551	162	55	�	�	PROPN
ejpam-1551	162	56	,	,	PUNCT
ejpam-1551	163	1	c	c	PROPN
ejpam-1551	163	2	∈	∈	PROPN
ejpam-1551	163	3	r	r	NOUN
ejpam-1551	163	4	,	,	PUNCT
ejpam-1551	163	5	c	c	PROPN
ejpam-1551	163	6	is	be	AUX
ejpam-1551	163	7	a	a	DET
ejpam-1551	163	8	constant	constant	ADJ
ejpam-1551	163	9	this	this	DET
ejpam-1551	163	10	curve	curve	NOUN
ejpam-1551	163	11	lies	lie	VERB
ejpam-1551	163	12	on	on	ADP
ejpam-1551	163	13	the	the	DET
ejpam-1551	163	14	surface	surface	NOUN
ejpam-1551	163	15	z	z	NOUN
ejpam-1551	163	16	=	=	PUNCT
ejpam-1551	163	17	−	−	PROPN
ejpam-1551	163	18	p	p	PROPN
ejpam-1551	163	19	x2	x2	PROPN
ejpam-1551	163	20	+	+	CCONJ
ejpam-1551	163	21	y2	y2	NOUN
ejpam-1551	163	22	.	.	PUNCT
ejpam-1551	164	1	for	for	ADP
ejpam-1551	164	2	specially	specially	ADV
ejpam-1551	164	3	,	,	PUNCT
ejpam-1551	164	4	c	c	NOUN
ejpam-1551	164	5	=	=	SYM
ejpam-1551	164	6	0	0	NUM
ejpam-1551	164	7	and	and	CCONJ
ejpam-1551	164	8	s	s	PROPN
ejpam-1551	164	9	∈	∈	PROPN
ejpam-1551	164	10	[	[	X
ejpam-1551	164	11	0	0	NUM
ejpam-1551	164	12	,	,	PUNCT
ejpam-1551	164	13	3	3	NUM
ejpam-1551	164	14	2	2	NUM
ejpam-1551	164	15	π	π	NOUN
ejpam-1551	164	16	]	]	X
ejpam-1551	164	17	we	we	PRON
ejpam-1551	164	18	can	can	AUX
ejpam-1551	164	19	draw	draw	VERB
ejpam-1551	164	20	special	special	ADJ
ejpam-1551	164	21	involute	involute	ADJ
ejpam-1551	164	22	evolute	evolute	NOUN
ejpam-1551	164	23	d	d	X
ejpam-1551	164	24	-	-	PUNCT
ejpam-1551	164	25	pair	pair	NOUN
ejpam-1551	164	26	�	�	PROPN
ejpam-1551	164	27	α	α	PROPN
ejpam-1551	164	28	,	,	PUNCT
ejpam-1551	164	29	β	β	X
ejpam-1551	164	30	using	use	VERB
ejpam-1551	164	31	maple	maple	NOUN
ejpam-1551	164	32	12	12	NUM
ejpam-1551	164	33	as	as	SCONJ
ejpam-1551	164	34	shown	show	VERB
ejpam-1551	164	35	in	in	ADP
ejpam-1551	164	36	figure	figure	NOUN
ejpam-1551	164	37	1b	1b	NUM
ejpam-1551	164	38	.	.	PUNCT
ejpam-1551	165	1	(	(	PUNCT
ejpam-1551	165	2	a	a	X
ejpam-1551	165	3	)	)	PUNCT
ejpam-1551	165	4	example	example	NOUN
ejpam-1551	165	5	1	1	NUM
ejpam-1551	165	6	(	(	PUNCT
ejpam-1551	165	7	b	b	NOUN
ejpam-1551	165	8	)	)	PUNCT
ejpam-1551	165	9	example	example	NOUN
ejpam-1551	165	10	2	2	NUM
ejpam-1551	165	11	figure	figure	NOUN
ejpam-1551	165	12	1	1	NUM
ejpam-1551	165	13	:	:	PUNCT
ejpam-1551	165	14	special	special	ADJ
ejpam-1551	165	15	involute	involute	NOUN
ejpam-1551	165	16	-	-	PUNCT
ejpam-1551	165	17	evolute	evolute	NOUN
ejpam-1551	165	18	partner	partner	NOUN
ejpam-1551	165	19	d	d	NOUN
ejpam-1551	165	20	-	-	NOUN
ejpam-1551	165	21	curves	curve	NOUN
ejpam-1551	165	22	.	.	PUNCT
ejpam-1551	166	1	references	reference	NOUN
ejpam-1551	166	2	[	[	X
ejpam-1551	166	3	1	1	NUM
ejpam-1551	166	4	]	]	PUNCT
ejpam-1551	166	5	c.	c.	PROPN
ejpam-1551	166	6	boyer	boyer	PROPN
ejpam-1551	166	7	,	,	PUNCT
ejpam-1551	166	8	c.	c.	PROPN
ejpam-1551	166	9	a	a	DET
ejpam-1551	166	10	history	history	NOUN
ejpam-1551	166	11	of	of	ADP
ejpam-1551	166	12	mathematics	mathematic	NOUN
ejpam-1551	166	13	,	,	PUNCT
ejpam-1551	166	14	new	new	PROPN
ejpam-1551	166	15	york	york	PROPN
ejpam-1551	166	16	:	:	PUNCT
ejpam-1551	166	17	wiley	wiley	PROPN
ejpam-1551	166	18	.	.	PUNCT
ejpam-1551	167	1	1968	1968	NUM
ejpam-1551	167	2	.	.	PUNCT
ejpam-1551	168	1	[	[	X
ejpam-1551	168	2	2	2	X
ejpam-1551	168	3	]	]	PUNCT
ejpam-1551	168	4	h.	h.	PROPN
ejpam-1551	168	5	h.	h.	PROPN
ejpam-1551	168	6	hacısalihoğlu	hacısalihoğlu	PROPN
ejpam-1551	168	7	.	.	PUNCT
ejpam-1551	169	1	diferensiyel	diferensiyel	PROPN
ejpam-1551	169	2	geometri	geometri	PROPN
ejpam-1551	169	3	,	,	PUNCT
ejpam-1551	169	4	inönö	inönö	PROPN
ejpam-1551	169	5	üniversitesi	üniversitesi	PROPN
ejpam-1551	169	6	fen	fen	PROPN
ejpam-1551	169	7	-	-	PUNCT
ejpam-1551	169	8	edebiyat	edebiyat	PROPN
ejpam-1551	169	9	fakültesi	fakültesi	NOUN
ejpam-1551	169	10	.	.	PUNCT
ejpam-1551	170	1	yayınları	yayınları	PROPN
ejpam-1551	170	2	mat	mat	PROPN
ejpam-1551	170	3	.	.	PUNCT
ejpam-1551	170	4	no:2	no:2	PROPN
ejpam-1551	170	5	,	,	PUNCT
ejpam-1551	170	6	1983	1983	NUM
ejpam-1551	170	7	.	.	PUNCT
ejpam-1551	171	1	[	[	X
ejpam-1551	171	2	3	3	NUM
ejpam-1551	171	3	]	]	X
ejpam-1551	171	4	m.	m.	NOUN
ejpam-1551	171	5	kazaz	kazaz	PROPN
ejpam-1551	171	6	,	,	PUNCT
ejpam-1551	171	7	h.	h.	PROPN
ejpam-1551	171	8	h.	h.	PROPN
ejpam-1551	171	9	uğurlu	uğurlu	PROPN
ejpam-1551	171	10	,	,	PUNCT
ejpam-1551	171	11	m.	m.	NOUN
ejpam-1551	171	12	önder	önder	NOUN
ejpam-1551	171	13	,	,	PUNCT
ejpam-1551	171	14	and	and	CCONJ
ejpam-1551	171	15	t.	t.	PROPN
ejpam-1551	171	16	kahraman	kahraman	NOUN
ejpam-1551	171	17	.	.	PUNCT
ejpam-1551	172	1	“	"	PUNCT
ejpam-1551	172	2	mannheim	mannheim	PROPN
ejpam-1551	172	3	partner	partner	NOUN
ejpam-1551	172	4	d	d	NOUN
ejpam-1551	172	5	curves	curve	NOUN
ejpam-1551	172	6	in	in	ADP
ejpam-1551	172	7	euclidean	euclidean	ADJ
ejpam-1551	172	8	3	3	NUM
ejpam-1551	172	9	-	-	PUNCT
ejpam-1551	172	10	space	space	NOUN
ejpam-1551	172	11	”	"	PUNCT
ejpam-1551	172	12	,	,	PUNCT
ejpam-1551	172	13	arxiv:1003.2042	arxiv:1003.2042	PROPN
ejpam-1551	172	14	math.dg	math.dg	NUM
ejpam-1551	172	15	.	.	PUNCT
ejpam-1551	173	1	[	[	X
ejpam-1551	173	2	4	4	X
ejpam-1551	173	3	]	]	PUNCT
ejpam-1551	173	4	b.	b.	PROPN
ejpam-1551	173	5	o’neill	o’neill	PROPN
ejpam-1551	173	6	.	.	PUNCT
ejpam-1551	174	1	“	"	PUNCT
ejpam-1551	174	2	elementary	elementary	ADJ
ejpam-1551	174	3	differential	differential	PROPN
ejpam-1551	174	4	geometry	geometry	NOUN
ejpam-1551	174	5	”	"	PUNCT
ejpam-1551	174	6	academic	academic	PROPN
ejpam-1551	174	7	press	press	PROPN
ejpam-1551	174	8	inc	inc	PROPN
ejpam-1551	174	9	.	.	PROPN
ejpam-1551	174	10	new	new	PROPN
ejpam-1551	174	11	york	york	PROPN
ejpam-1551	174	12	,	,	PUNCT
ejpam-1551	174	13	1966	1966	NUM
ejpam-1551	174	14	.	.	PUNCT
ejpam-1551	175	1	[	[	X
ejpam-1551	175	2	5	5	NUM
ejpam-1551	175	3	]	]	PUNCT
ejpam-1551	175	4	a.	a.	NOUN
ejpam-1551	175	5	turgut	turgut	PROPN
ejpam-1551	175	6	,	,	PUNCT
ejpam-1551	175	7	and	and	CCONJ
ejpam-1551	175	8	e.	e.	PROPN
ejpam-1551	175	9	erdoğan	erdoğan	PROPN
ejpam-1551	175	10	.	.	PUNCT
ejpam-1551	176	1	involute	involute	PROPN
ejpam-1551	176	2	evolute	evolute	PROPN
ejpam-1551	176	3	curve	curve	NOUN
ejpam-1551	176	4	couples	couple	NOUN
ejpam-1551	176	5	of	of	ADP
ejpam-1551	176	6	higher	high	ADJ
ejpam-1551	176	7	order	order	NOUN
ejpam-1551	176	8	in	in	ADP
ejpam-1551	176	9	rn	rn	PROPN
ejpam-1551	176	10	and	and	CCONJ
ejpam-1551	176	11	their	their	PRON
ejpam-1551	176	12	horizontal	horizontal	ADJ
ejpam-1551	176	13	lifts	lift	NOUN
ejpam-1551	176	14	in	in	ADP
ejpam-1551	176	15	rn	rn	PROPN
ejpam-1551	176	16	,	,	PUNCT
ejpam-1551	176	17	communications	communication	NOUN
ejpam-1551	176	18	of	of	ADP
ejpam-1551	176	19	the	the	DET
ejpam-1551	176	20	faculty	faculty	NOUN
ejpam-1551	176	21	of	of	ADP
ejpam-1551	176	22	sciences	science	NOUN
ejpam-1551	176	23	of	of	ADP
ejpam-1551	176	24	the	the	DET
ejpam-1551	176	25	university	university	NOUN
ejpam-1551	176	26	of	of	ADP
ejpam-1551	176	27	ankara	ankara	PROPN
ejpam-1551	176	28	,	,	PUNCT
ejpam-1551	176	29	series	series	PROPN
ejpam-1551	176	30	a	a	PROPN
ejpam-1551	176	31	,	,	PUNCT
ejpam-1551	176	32	41	41	NUM
ejpam-1551	176	33	(	(	PUNCT
ejpam-1551	176	34	3	3	NUM
ejpam-1551	176	35	)	)	PUNCT
ejpam-1551	176	36	,	,	PUNCT
ejpam-1551	176	37	125	125	NUM
ejpam-1551	176	38	-	-	SYM
ejpam-1551	176	39	130	130	NUM
ejpam-1551	176	40	.	.	PUNCT
ejpam-1551	176	41	1992	1992	NUM
ejpam-1551	176	42	.	.	PUNCT