id	sid	tid	token	lemma	pos
ejpam-2382	1	1	compile	compile	NOUN
ejpam-2382	1	2	/	/	SYM
ejpam-2382	1	3	output.dvi	output.dvi	NOUN
ejpam-2382	1	4	european	european	ADJ
ejpam-2382	1	5	journal	journal	NOUN
ejpam-2382	1	6	of	of	ADP
ejpam-2382	1	7	pure	pure	ADJ
ejpam-2382	1	8	and	and	CCONJ
ejpam-2382	1	9	applied	apply	VERB
ejpam-2382	1	10	mathematics	mathematic	NOUN
ejpam-2382	1	11	vol	vol	NOUN
ejpam-2382	1	12	.	.	PROPN
ejpam-2382	1	13	8	8	NUM
ejpam-2382	1	14	,	,	PUNCT
ejpam-2382	1	15	no	no	INTJ
ejpam-2382	1	16	.	.	NOUN
ejpam-2382	1	17	2	2	NUM
ejpam-2382	1	18	,	,	PUNCT
ejpam-2382	1	19	2015	2015	NUM
ejpam-2382	1	20	,	,	PUNCT
ejpam-2382	1	21	255	255	NUM
ejpam-2382	1	22	-	-	SYM
ejpam-2382	1	23	270	270	NUM
ejpam-2382	1	24	issn	issn	PROPN
ejpam-2382	1	25	1307	1307	NUM
ejpam-2382	1	26	-	-	SYM
ejpam-2382	1	27	5543	5543	NUM
ejpam-2382	1	28	–	–	PUNCT
ejpam-2382	1	29	www.ejpam.com	www.ejpam.com	X
ejpam-2382	1	30	frenet	frenet	NOUN
ejpam-2382	1	31	apparatus	apparatus	NOUN
ejpam-2382	1	32	of	of	ADP
ejpam-2382	1	33	the	the	DET
ejpam-2382	1	34	curves	curve	NOUN
ejpam-2382	1	35	and	and	CCONJ
ejpam-2382	1	36	some	some	DET
ejpam-2382	1	37	special	special	ADJ
ejpam-2382	1	38	curves	curve	NOUN
ejpam-2382	1	39	in	in	ADP
ejpam-2382	1	40	the	the	DET
ejpam-2382	1	41	euclidean	euclidean	ADJ
ejpam-2382	1	42	5	5	NUM
ejpam-2382	1	43	-	-	PUNCT
ejpam-2382	1	44	space	space	NOUN
ejpam-2382	1	45	e5	e5	NOUN
ejpam-2382	1	46	melek	melek	NOUN
ejpam-2382	1	47	masal	masal	PROPN
ejpam-2382	1	48	,	,	PUNCT
ejpam-2382	1	49	a.	a.	NOUN
ejpam-2382	1	50	zeynep	zeynep	PROPN
ejpam-2382	1	51	azak∗	azak∗	PROPN
ejpam-2382	1	52	department	department	PROPN
ejpam-2382	1	53	of	of	ADP
ejpam-2382	1	54	elementary	elementary	ADJ
ejpam-2382	1	55	education	education	NOUN
ejpam-2382	1	56	,	,	PUNCT
ejpam-2382	1	57	faculty	faculty	NOUN
ejpam-2382	1	58	of	of	ADP
ejpam-2382	1	59	education	education	NOUN
ejpam-2382	1	60	,	,	PUNCT
ejpam-2382	1	61	sakarya	sakarya	NOUN
ejpam-2382	1	62	university	university	NOUN
ejpam-2382	1	63	,	,	PUNCT
ejpam-2382	1	64	sakarya	sakarya	NOUN
ejpam-2382	1	65	,	,	PUNCT
ejpam-2382	1	66	turkey	turkey	NOUN
ejpam-2382	1	67	abstract	abstract	NOUN
ejpam-2382	1	68	.	.	PUNCT
ejpam-2382	2	1	in	in	ADP
ejpam-2382	2	2	this	this	DET
ejpam-2382	2	3	study	study	NOUN
ejpam-2382	2	4	,	,	PUNCT
ejpam-2382	2	5	initially	initially	ADV
ejpam-2382	2	6	the	the	DET
ejpam-2382	2	7	geometric	geometric	ADJ
ejpam-2382	2	8	meanings	meaning	NOUN
ejpam-2382	2	9	of	of	ADP
ejpam-2382	2	10	the	the	DET
ejpam-2382	2	11	curvatures	curvature	NOUN
ejpam-2382	2	12	of	of	ADP
ejpam-2382	2	13	the	the	DET
ejpam-2382	2	14	curves	curve	NOUN
ejpam-2382	2	15	parametrized	parametrized	ADJ
ejpam-2382	2	16	with	with	ADP
ejpam-2382	2	17	the	the	DET
ejpam-2382	2	18	arc	arc	NOUN
ejpam-2382	2	19	length	length	NOUN
ejpam-2382	2	20	are	be	AUX
ejpam-2382	2	21	given	give	VERB
ejpam-2382	2	22	in	in	ADP
ejpam-2382	2	23	e5	e5	PROPN
ejpam-2382	2	24	.	.	PUNCT
ejpam-2382	3	1	this	this	PRON
ejpam-2382	3	2	is	be	AUX
ejpam-2382	3	3	followed	follow	VERB
ejpam-2382	3	4	by	by	ADP
ejpam-2382	3	5	the	the	DET
ejpam-2382	3	6	calculation	calculation	NOUN
ejpam-2382	3	7	of	of	ADP
ejpam-2382	3	8	the	the	DET
ejpam-2382	3	9	frenet	frenet	ADJ
ejpam-2382	3	10	vectors	vector	NOUN
ejpam-2382	3	11	and	and	CCONJ
ejpam-2382	3	12	curvatures	curvature	NOUN
ejpam-2382	3	13	of	of	ADP
ejpam-2382	3	14	any	any	DET
ejpam-2382	3	15	curve	curve	NOUN
ejpam-2382	3	16	.	.	PUNCT
ejpam-2382	4	1	after	after	ADP
ejpam-2382	4	2	these	these	PRON
ejpam-2382	4	3	,	,	PUNCT
ejpam-2382	4	4	some	some	DET
ejpam-2382	4	5	results	result	NOUN
ejpam-2382	4	6	have	have	AUX
ejpam-2382	4	7	been	be	AUX
ejpam-2382	4	8	given	give	VERB
ejpam-2382	4	9	for	for	ADP
ejpam-2382	4	10	the	the	DET
ejpam-2382	4	11	state	state	NOUN
ejpam-2382	4	12	of	of	ADP
ejpam-2382	4	13	evolute	evolute	PROPN
ejpam-2382	4	14	curve	curve	PROPN
ejpam-2382	4	15	x	x	PUNCT
ejpam-2382	4	16	being	be	AUX
ejpam-2382	4	17	a	a	DET
ejpam-2382	4	18	w	w	NOUN
ejpam-2382	4	19	-	-	PUNCT
ejpam-2382	4	20	curve	curve	NOUN
ejpam-2382	4	21	and	and	CCONJ
ejpam-2382	4	22	the	the	DET
ejpam-2382	4	23	frenet	frenet	ADJ
ejpam-2382	4	24	vectors	vector	NOUN
ejpam-2382	4	25	and	and	CCONJ
ejpam-2382	4	26	curvatures	curvature	NOUN
ejpam-2382	4	27	of	of	ADP
ejpam-2382	4	28	involute	involute	ADJ
ejpam-2382	4	29	curve	curve	NOUN
ejpam-2382	4	30	y	y	PROPN
ejpam-2382	4	31	have	have	AUX
ejpam-2382	4	32	been	be	AUX
ejpam-2382	4	33	calculated	calculate	VERB
ejpam-2382	4	34	in	in	ADP
ejpam-2382	4	35	terms	term	NOUN
ejpam-2382	4	36	of	of	ADP
ejpam-2382	4	37	frenet	frenet	ADJ
ejpam-2382	4	38	vectors	vector	NOUN
ejpam-2382	4	39	and	and	CCONJ
ejpam-2382	4	40	curvatures	curvature	NOUN
ejpam-2382	4	41	of	of	ADP
ejpam-2382	4	42	the	the	DET
ejpam-2382	4	43	curve	curve	NOUN
ejpam-2382	4	44	x.	x.	NOUN
ejpam-2382	4	45	at	at	ADP
ejpam-2382	4	46	last	last	ADJ
ejpam-2382	4	47	,	,	PUNCT
ejpam-2382	4	48	the	the	DET
ejpam-2382	4	49	differential	differential	ADJ
ejpam-2382	4	50	equation	equation	NOUN
ejpam-2382	4	51	of	of	ADP
ejpam-2382	4	52	the	the	DET
ejpam-2382	4	53	spherical	spherical	ADJ
ejpam-2382	4	54	curves	curve	NOUN
ejpam-2382	4	55	,	,	PUNCT
ejpam-2382	4	56	the	the	DET
ejpam-2382	4	57	equation	equation	NOUN
ejpam-2382	4	58	of	of	ADP
ejpam-2382	4	59	the	the	DET
ejpam-2382	4	60	radius	radius	NOUN
ejpam-2382	4	61	and	and	CCONJ
ejpam-2382	4	62	the	the	DET
ejpam-2382	4	63	center	center	NOUN
ejpam-2382	4	64	of	of	ADP
ejpam-2382	4	65	the	the	DET
ejpam-2382	4	66	osculating	osculating	NOUN
ejpam-2382	4	67	hyperspheres	hypersphere	NOUN
ejpam-2382	4	68	have	have	AUX
ejpam-2382	4	69	been	be	AUX
ejpam-2382	4	70	achieved	achieve	VERB
ejpam-2382	4	71	in	in	ADP
ejpam-2382	4	72	e5	e5	PROPN
ejpam-2382	4	73	.	.	PUNCT
ejpam-2382	5	1	2010	2010	NUM
ejpam-2382	5	2	mathematics	mathematic	NOUN
ejpam-2382	5	3	subject	subject	NOUN
ejpam-2382	5	4	classifications	classification	NOUN
ejpam-2382	5	5	:	:	PUNCT
ejpam-2382	5	6	53a04	53a04	NUM
ejpam-2382	5	7	,	,	PUNCT
ejpam-2382	5	8	14h50	14h50	NUM
ejpam-2382	5	9	key	key	ADJ
ejpam-2382	5	10	words	word	NOUN
ejpam-2382	5	11	and	and	CCONJ
ejpam-2382	5	12	phrases	phrase	NOUN
ejpam-2382	5	13	:	:	PUNCT
ejpam-2382	5	14	euclidean	euclidean	ADJ
ejpam-2382	5	15	5	5	NUM
ejpam-2382	5	16	-	-	PUNCT
ejpam-2382	5	17	space	space	NOUN
ejpam-2382	5	18	,	,	PUNCT
ejpam-2382	5	19	involute	involute	ADJ
ejpam-2382	5	20	-	-	PUNCT
ejpam-2382	5	21	evolute	evolute	NOUN
ejpam-2382	5	22	curves	curve	NOUN
ejpam-2382	5	23	,	,	PUNCT
ejpam-2382	5	24	curvatures	curvature	NOUN
ejpam-2382	5	25	,	,	PUNCT
ejpam-2382	5	26	frenet	frenet	NOUN
ejpam-2382	5	27	apparatus	apparatus	NOUN
ejpam-2382	5	28	,	,	PUNCT
ejpam-2382	5	29	spherical	spherical	ADJ
ejpam-2382	5	30	curves	curve	NOUN
ejpam-2382	5	31	1	1	NUM
ejpam-2382	5	32	.	.	PUNCT
ejpam-2382	5	33	introduction	introduction	NOUN
ejpam-2382	5	34	the	the	DET
ejpam-2382	5	35	involute	involute	NOUN
ejpam-2382	5	36	-	-	PUNCT
ejpam-2382	5	37	evolute	evolute	NOUN
ejpam-2382	5	38	curves	curve	NOUN
ejpam-2382	5	39	and	and	CCONJ
ejpam-2382	5	40	helices	helix	NOUN
ejpam-2382	5	41	can	can	AUX
ejpam-2382	5	42	often	often	ADV
ejpam-2382	5	43	be	be	AUX
ejpam-2382	5	44	seen	see	VERB
ejpam-2382	5	45	in	in	ADP
ejpam-2382	5	46	our	our	PRON
ejpam-2382	5	47	daily	daily	ADJ
ejpam-2382	5	48	lives	life	NOUN
ejpam-2382	5	49	.	.	PUNCT
ejpam-2382	6	1	for	for	ADP
ejpam-2382	6	2	example	example	NOUN
ejpam-2382	6	3	,	,	PUNCT
ejpam-2382	6	4	the	the	DET
ejpam-2382	6	5	idea	idea	NOUN
ejpam-2382	6	6	of	of	ADP
ejpam-2382	6	7	a	a	DET
ejpam-2382	6	8	string	string	NOUN
ejpam-2382	6	9	involute	involute	NOUN
ejpam-2382	6	10	is	be	AUX
ejpam-2382	6	11	due	due	ADJ
ejpam-2382	6	12	to	to	ADP
ejpam-2382	6	13	c.	c.	PROPN
ejpam-2382	6	14	huygens	huygens	PROPN
ejpam-2382	6	15	,	,	PUNCT
ejpam-2382	6	16	who	who	PRON
ejpam-2382	6	17	is	be	AUX
ejpam-2382	6	18	also	also	ADV
ejpam-2382	6	19	known	know	VERB
ejpam-2382	6	20	for	for	ADP
ejpam-2382	6	21	his	his	PRON
ejpam-2382	6	22	works	work	NOUN
ejpam-2382	6	23	in	in	ADP
ejpam-2382	6	24	optics	optic	NOUN
ejpam-2382	6	25	.	.	PUNCT
ejpam-2382	7	1	he	he	PRON
ejpam-2382	7	2	discovered	discover	VERB
ejpam-2382	7	3	involutes	involute	NOUN
ejpam-2382	7	4	while	while	SCONJ
ejpam-2382	7	5	trying	try	VERB
ejpam-2382	7	6	to	to	PART
ejpam-2382	7	7	build	build	VERB
ejpam-2382	7	8	a	a	DET
ejpam-2382	7	9	more	more	ADV
ejpam-2382	7	10	accurate	accurate	ADJ
ejpam-2382	7	11	clock	clock	NOUN
ejpam-2382	7	12	[	[	X
ejpam-2382	7	13	2	2	NUM
ejpam-2382	7	14	,	,	PUNCT
ejpam-2382	7	15	7	7	NUM
ejpam-2382	7	16	]	]	PUNCT
ejpam-2382	7	17	.	.	PUNCT
ejpam-2382	8	1	in	in	ADP
ejpam-2382	8	2	addition	addition	NOUN
ejpam-2382	8	3	to	to	ADP
ejpam-2382	8	4	this	this	PRON
ejpam-2382	8	5	,	,	PUNCT
ejpam-2382	8	6	standard	standard	ADJ
ejpam-2382	8	7	screws	screw	NOUN
ejpam-2382	8	8	,	,	PUNCT
ejpam-2382	8	9	bolts	bolt	NOUN
ejpam-2382	8	10	and	and	CCONJ
ejpam-2382	8	11	a	a	DET
ejpam-2382	8	12	double	double	ADJ
ejpam-2382	8	13	-	-	PUNCT
ejpam-2382	8	14	stranded	strand	VERB
ejpam-2382	8	15	molecule	molecule	NOUN
ejpam-2382	8	16	of	of	ADP
ejpam-2382	8	17	dna	dna	PROPN
ejpam-2382	8	18	are	be	AUX
ejpam-2382	8	19	the	the	DET
ejpam-2382	8	20	most	most	ADV
ejpam-2382	8	21	common	common	ADJ
ejpam-2382	8	22	examples	example	NOUN
ejpam-2382	8	23	for	for	ADP
ejpam-2382	8	24	helices	helix	NOUN
ejpam-2382	8	25	in	in	ADP
ejpam-2382	8	26	the	the	DET
ejpam-2382	8	27	nature	nature	NOUN
ejpam-2382	8	28	and	and	CCONJ
ejpam-2382	8	29	structures	structure	NOUN
ejpam-2382	8	30	[	[	X
ejpam-2382	8	31	11	11	NUM
ejpam-2382	8	32	]	]	PUNCT
ejpam-2382	8	33	.	.	PUNCT
ejpam-2382	9	1	a.	a.	PROPN
ejpam-2382	9	2	r.	r.	PROPN
ejpam-2382	9	3	forsyth	forsyth	PROPN
ejpam-2382	9	4	(	(	PUNCT
ejpam-2382	9	5	1930	1930	NUM
ejpam-2382	9	6	)	)	PUNCT
ejpam-2382	10	1	[	[	X
ejpam-2382	10	2	4	4	X
ejpam-2382	10	3	]	]	PUNCT
ejpam-2382	10	4	has	have	AUX
ejpam-2382	10	5	took	take	VERB
ejpam-2382	10	6	the	the	DET
ejpam-2382	10	7	hypothesis	hypothesis	NOUN
ejpam-2382	10	8	of	of	ADP
ejpam-2382	10	9	curves	curve	NOUN
ejpam-2382	10	10	and	and	CCONJ
ejpam-2382	10	11	surfaces	surface	NOUN
ejpam-2382	10	12	in	in	ADP
ejpam-2382	10	13	the	the	DET
ejpam-2382	10	14	four	four	NUM
ejpam-2382	10	15	-	-	PUNCT
ejpam-2382	10	16	dimensional	dimensional	ADJ
ejpam-2382	10	17	euclidean	euclidean	ADJ
ejpam-2382	10	18	space	space	NOUN
ejpam-2382	10	19	e4	e4	PROPN
ejpam-2382	10	20	[	[	X
ejpam-2382	10	21	4	4	NUM
ejpam-2382	10	22	]	]	PUNCT
ejpam-2382	10	23	,	,	PUNCT
ejpam-2382	10	24	while	while	SCONJ
ejpam-2382	10	25	h.	h.	PROPN
ejpam-2382	10	26	gluck	gluck	PROPN
ejpam-2382	10	27	(	(	PUNCT
ejpam-2382	10	28	1966	1966	NUM
ejpam-2382	10	29	)	)	PUNCT
ejpam-2382	11	1	[	[	X
ejpam-2382	11	2	5	5	NUM
ejpam-2382	11	3	]	]	PUNCT
ejpam-2382	11	4	examined	examine	VERB
ejpam-2382	11	5	the	the	DET
ejpam-2382	11	6	curvatures	curvature	NOUN
ejpam-2382	11	7	of	of	ADP
ejpam-2382	11	8	the	the	DET
ejpam-2382	11	9	curve	curve	NOUN
ejpam-2382	11	10	in	in	ADP
ejpam-2382	11	11	the	the	DET
ejpam-2382	11	12	n	n	ADV
ejpam-2382	11	13	-	-	PUNCT
ejpam-2382	11	14	dimensional	dimensional	ADJ
ejpam-2382	11	15	euclidean	euclidean	ADJ
ejpam-2382	11	16	space	space	NOUN
ejpam-2382	11	17	en	en	PROPN
ejpam-2382	11	18	.	.	PUNCT
ejpam-2382	12	1	lately	lately	ADV
ejpam-2382	12	2	the	the	DET
ejpam-2382	12	3	studies	study	NOUN
ejpam-2382	12	4	in	in	ADP
ejpam-2382	12	5	the	the	DET
ejpam-2382	12	6	four	four	NUM
ejpam-2382	12	7	and	and	CCONJ
ejpam-2382	12	8	five	five	NUM
ejpam-2382	12	9	-	-	PUNCT
ejpam-2382	12	10	dimensional	dimensional	ADJ
ejpam-2382	12	11	spaces	space	NOUN
ejpam-2382	12	12	have	have	AUX
ejpam-2382	12	13	been	be	AUX
ejpam-2382	12	14	accelerated	accelerate	VERB
ejpam-2382	12	15	.	.	PUNCT
ejpam-2382	13	1	for	for	ADP
ejpam-2382	13	2	example	example	NOUN
ejpam-2382	13	3	,	,	PUNCT
ejpam-2382	13	4	some	some	DET
ejpam-2382	13	5	characterizations	characterization	NOUN
ejpam-2382	13	6	for	for	ADP
ejpam-2382	13	7	the	the	DET
ejpam-2382	13	8	spherical	spherical	ADJ
ejpam-2382	13	9	curves	curve	NOUN
ejpam-2382	13	10	and	and	CCONJ
ejpam-2382	13	11	helices	helix	NOUN
ejpam-2382	13	12	have	have	AUX
ejpam-2382	13	13	been	be	AUX
ejpam-2382	13	14	obtained	obtain	VERB
ejpam-2382	13	15	in	in	ADP
ejpam-2382	13	16	the	the	DET
ejpam-2382	13	17	four	four	NUM
ejpam-2382	13	18	-	-	PUNCT
ejpam-2382	13	19	dimensional	dimensional	ADJ
ejpam-2382	13	20	euclidean	euclidean	ADJ
ejpam-2382	13	21	space	space	NOUN
ejpam-2382	13	22	e4	e4	PROPN
ejpam-2382	13	23	,	,	PUNCT
ejpam-2382	13	24	[	[	X
ejpam-2382	13	25	8	8	NUM
ejpam-2382	13	26	,	,	PUNCT
ejpam-2382	13	27	10	10	NUM
ejpam-2382	13	28	,	,	PUNCT
ejpam-2382	13	29	13	13	NUM
ejpam-2382	13	30	]	]	PUNCT
ejpam-2382	13	31	.	.	PUNCT
ejpam-2382	14	1	also	also	ADV
ejpam-2382	14	2	some	some	DET
ejpam-2382	14	3	characterizations	characterization	NOUN
ejpam-2382	14	4	related	relate	VERB
ejpam-2382	14	5	to	to	ADP
ejpam-2382	14	6	the	the	DET
ejpam-2382	14	7	inclined	inclined	ADJ
ejpam-2382	14	8	curves	curve	NOUN
ejpam-2382	14	9	have	have	AUX
ejpam-2382	14	10	been	be	AUX
ejpam-2382	14	11	defined	define	VERB
ejpam-2382	14	12	in	in	ADP
ejpam-2382	14	13	the	the	DET
ejpam-2382	14	14	5	5	NUM
ejpam-2382	14	15	-	-	PUNCT
ejpam-2382	14	16	dimensional	dimensional	ADJ
ejpam-2382	14	17	euclidean	euclidean	ADJ
ejpam-2382	14	18	space	space	NOUN
ejpam-2382	14	19	e5	e5	PROPN
ejpam-2382	14	20	and	and	CCONJ
ejpam-2382	14	21	5	5	NUM
ejpam-2382	14	22	-	-	PUNCT
ejpam-2382	14	23	dimensional	dimensional	ADJ
ejpam-2382	14	24	lorentzian	lorentzian	ADJ
ejpam-2382	14	25	space	space	NOUN
ejpam-2382	14	26	l5	l5	NOUN
ejpam-2382	14	27	,	,	PUNCT
ejpam-2382	14	28	[	[	X
ejpam-2382	14	29	1	1	NUM
ejpam-2382	14	30	,	,	PUNCT
ejpam-2382	14	31	11	11	NUM
ejpam-2382	14	32	]	]	PUNCT
ejpam-2382	14	33	.	.	PUNCT
ejpam-2382	15	1	the	the	DET
ejpam-2382	15	2	frenet	frenet	ADJ
ejpam-2382	15	3	vectors	vector	NOUN
ejpam-2382	15	4	of	of	ADP
ejpam-2382	15	5	any	any	DET
ejpam-2382	15	6	curve	curve	NOUN
ejpam-2382	15	7	and	and	CCONJ
ejpam-2382	15	8	involute	involute	ADJ
ejpam-2382	15	9	-	-	PUNCT
ejpam-2382	15	10	evolute	evolute	NOUN
ejpam-2382	15	11	curves	curve	NOUN
ejpam-2382	15	12	in	in	ADP
ejpam-2382	15	13	e4	e4	PROPN
ejpam-2382	15	14	and	and	CCONJ
ejpam-2382	15	15	e4	e4	PROPN
ejpam-2382	15	16	1	1	NUM
ejpam-2382	15	17	have	have	AUX
ejpam-2382	15	18	been	be	AUX
ejpam-2382	15	19	given	give	VERB
ejpam-2382	15	20	by	by	ADP
ejpam-2382	15	21	[	[	X
ejpam-2382	15	22	12	12	NUM
ejpam-2382	15	23	,	,	PUNCT
ejpam-2382	15	24	15	15	NUM
ejpam-2382	15	25	]	]	PUNCT
ejpam-2382	15	26	.	.	PUNCT
ejpam-2382	16	1	in	in	ADP
ejpam-2382	16	2	addition	addition	NOUN
ejpam-2382	16	3	∗corresponding	∗corresponde	VERB
ejpam-2382	16	4	author	author	NOUN
ejpam-2382	16	5	.	.	PUNCT
ejpam-2382	17	1	email	email	NOUN
ejpam-2382	17	2	addresses	address	NOUN
ejpam-2382	17	3	:	:	PUNCT
ejpam-2382	17	4	mmasal@sakarya.edu.tr	mmasal@sakarya.edu.tr	PROPN
ejpam-2382	17	5	(	(	PUNCT
ejpam-2382	17	6	m.	m.	NOUN
ejpam-2382	17	7	masal	masal	PROPN
ejpam-2382	17	8	)	)	PUNCT
ejpam-2382	17	9	,	,	PUNCT
ejpam-2382	17	10	apirdal@sakarya.edu.tr	apirdal@sakarya.edu.tr	PROPN
ejpam-2382	17	11	(	(	PUNCT
ejpam-2382	17	12	a.	a.	NOUN
ejpam-2382	17	13	azak	azak	PROPN
ejpam-2382	17	14	)	)	PUNCT
ejpam-2382	17	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2382	18	1	255	255	NUM
ejpam-2382	18	2	c	c	X
ejpam-2382	18	3	©	©	PROPN
ejpam-2382	18	4	2015	2015	NUM
ejpam-2382	18	5	ejpam	ejpam	NOUN
ejpam-2382	18	6	all	all	DET
ejpam-2382	18	7	rights	right	NOUN
ejpam-2382	18	8	reserved	reserve	VERB
ejpam-2382	18	9	.	.	PUNCT
ejpam-2382	19	1	m.	m.	NOUN
ejpam-2382	19	2	masal	masal	PROPN
ejpam-2382	19	3	,	,	PUNCT
ejpam-2382	19	4	a.	a.	PROPN
ejpam-2382	19	5	azak	azak	PROPN
ejpam-2382	19	6	/	/	SYM
ejpam-2382	19	7	eur	eur	PROPN
ejpam-2382	19	8	.	.	PUNCT
ejpam-2382	20	1	j.	j.	PROPN
ejpam-2382	20	2	pure	pure	PROPN
ejpam-2382	20	3	appl	appl	PROPN
ejpam-2382	20	4	.	.	PROPN
ejpam-2382	20	5	math	math	PROPN
ejpam-2382	20	6	,	,	PUNCT
ejpam-2382	20	7	8	8	NUM
ejpam-2382	20	8	(	(	PUNCT
ejpam-2382	20	9	2015	2015	NUM
ejpam-2382	20	10	)	)	PUNCT
ejpam-2382	20	11	,	,	PUNCT
ejpam-2382	20	12	255	255	NUM
ejpam-2382	20	13	-	-	SYM
ejpam-2382	20	14	270	270	NUM
ejpam-2382	20	15	256	256	NUM
ejpam-2382	20	16	to	to	ADP
ejpam-2382	20	17	this	this	PRON
ejpam-2382	20	18	,	,	PUNCT
ejpam-2382	20	19	the	the	DET
ejpam-2382	20	20	curvatures	curvature	NOUN
ejpam-2382	20	21	and	and	CCONJ
ejpam-2382	20	22	frenet	frenet	ADJ
ejpam-2382	20	23	vectors	vector	NOUN
ejpam-2382	20	24	of	of	ADP
ejpam-2382	20	25	the	the	DET
ejpam-2382	20	26	curves	curve	NOUN
ejpam-2382	20	27	parametrized	parametrized	ADJ
ejpam-2382	20	28	with	with	ADP
ejpam-2382	20	29	the	the	DET
ejpam-2382	20	30	arc	arc	NOUN
ejpam-2382	20	31	length	length	NOUN
ejpam-2382	20	32	in	in	ADP
ejpam-2382	20	33	e5	e5	PROPN
ejpam-2382	20	34	and	and	CCONJ
ejpam-2382	20	35	l5	l5	PROPN
ejpam-2382	20	36	have	have	AUX
ejpam-2382	20	37	been	be	AUX
ejpam-2382	20	38	determined	determine	VERB
ejpam-2382	20	39	,	,	PUNCT
ejpam-2382	20	40	[	[	X
ejpam-2382	20	41	14	14	NUM
ejpam-2382	20	42	,	,	PUNCT
ejpam-2382	20	43	16	16	NUM
ejpam-2382	20	44	]	]	PUNCT
ejpam-2382	20	45	.	.	PUNCT
ejpam-2382	21	1	at	at	ADP
ejpam-2382	21	2	last	last	ADJ
ejpam-2382	21	3	,	,	PUNCT
ejpam-2382	21	4	bertrand	bertrand	PROPN
ejpam-2382	21	5	curves	curve	VERB
ejpam-2382	21	6	in	in	ADP
ejpam-2382	21	7	e5	e5	PROPN
ejpam-2382	21	8	and	and	CCONJ
ejpam-2382	21	9	l5	l5	PROPN
ejpam-2382	21	10	have	have	AUX
ejpam-2382	21	11	been	be	AUX
ejpam-2382	21	12	defined	define	VERB
ejpam-2382	21	13	,	,	PUNCT
ejpam-2382	21	14	[	[	X
ejpam-2382	21	15	3	3	NUM
ejpam-2382	21	16	,	,	PUNCT
ejpam-2382	21	17	8	8	NUM
ejpam-2382	21	18	]	]	PUNCT
ejpam-2382	21	19	.	.	PUNCT
ejpam-2382	22	1	in	in	ADP
ejpam-2382	22	2	this	this	DET
ejpam-2382	22	3	study	study	NOUN
ejpam-2382	22	4	,	,	PUNCT
ejpam-2382	22	5	initially	initially	ADV
ejpam-2382	22	6	we	we	PRON
ejpam-2382	22	7	have	have	AUX
ejpam-2382	22	8	given	give	VERB
ejpam-2382	22	9	the	the	DET
ejpam-2382	22	10	geometrical	geometrical	ADJ
ejpam-2382	22	11	meanings	meaning	NOUN
ejpam-2382	22	12	of	of	ADP
ejpam-2382	22	13	the	the	DET
ejpam-2382	22	14	curvatures	curvature	NOUN
ejpam-2382	22	15	of	of	ADP
ejpam-2382	22	16	curves	curve	NOUN
ejpam-2382	22	17	parametrized	parametrize	VERB
ejpam-2382	22	18	with	with	ADP
ejpam-2382	22	19	arc	arc	NOUN
ejpam-2382	22	20	length	length	NOUN
ejpam-2382	22	21	in	in	ADP
ejpam-2382	22	22	the	the	DET
ejpam-2382	22	23	euclidean	euclidean	ADJ
ejpam-2382	22	24	5	5	NUM
ejpam-2382	22	25	-	-	PUNCT
ejpam-2382	22	26	space	space	NOUN
ejpam-2382	22	27	.	.	PUNCT
ejpam-2382	23	1	afterwards	afterwards	ADV
ejpam-2382	23	2	,	,	PUNCT
ejpam-2382	23	3	we	we	PRON
ejpam-2382	23	4	have	have	AUX
ejpam-2382	23	5	calculated	calculate	VERB
ejpam-2382	23	6	the	the	DET
ejpam-2382	23	7	frenet	frenet	ADJ
ejpam-2382	23	8	vectors	vector	NOUN
ejpam-2382	23	9	and	and	CCONJ
ejpam-2382	23	10	curvatures	curvature	NOUN
ejpam-2382	23	11	of	of	ADP
ejpam-2382	23	12	an	an	DET
ejpam-2382	23	13	arbitrary	arbitrary	ADJ
ejpam-2382	23	14	curve	curve	NOUN
ejpam-2382	23	15	in	in	ADP
ejpam-2382	23	16	e5	e5	PROPN
ejpam-2382	23	17	.	.	PUNCT
ejpam-2382	24	1	moreover	moreover	ADV
ejpam-2382	24	2	,	,	PUNCT
ejpam-2382	24	3	we	we	PRON
ejpam-2382	24	4	have	have	AUX
ejpam-2382	24	5	given	give	VERB
ejpam-2382	24	6	the	the	DET
ejpam-2382	24	7	frenet	frenet	ADJ
ejpam-2382	24	8	vectors	vector	NOUN
ejpam-2382	24	9	and	and	CCONJ
ejpam-2382	24	10	curvatures	curvature	NOUN
ejpam-2382	24	11	of	of	ADP
ejpam-2382	24	12	the	the	DET
ejpam-2382	24	13	involute	involute	ADJ
ejpam-2382	24	14	curve	curve	NOUN
ejpam-2382	24	15	y	y	PROPN
ejpam-2382	24	16	in	in	ADP
ejpam-2382	24	17	the	the	DET
ejpam-2382	24	18	state	state	NOUN
ejpam-2382	24	19	of	of	ADP
ejpam-2382	24	20	the	the	DET
ejpam-2382	24	21	evolute	evolute	PROPN
ejpam-2382	24	22	curve	curve	NOUN
ejpam-2382	24	23	x	x	PUNCT
ejpam-2382	24	24	as	as	ADP
ejpam-2382	24	25	the	the	DET
ejpam-2382	24	26	wcurve	wcurve	NOUN
ejpam-2382	24	27	.	.	PUNCT
ejpam-2382	25	1	finally	finally	ADV
ejpam-2382	25	2	,	,	PUNCT
ejpam-2382	25	3	we	we	PRON
ejpam-2382	25	4	have	have	AUX
ejpam-2382	25	5	defined	define	VERB
ejpam-2382	25	6	the	the	DET
ejpam-2382	25	7	differential	differential	ADJ
ejpam-2382	25	8	equation	equation	NOUN
ejpam-2382	25	9	of	of	ADP
ejpam-2382	25	10	the	the	DET
ejpam-2382	25	11	spherical	spherical	ADJ
ejpam-2382	25	12	curves	curve	NOUN
ejpam-2382	25	13	,	,	PUNCT
ejpam-2382	25	14	the	the	DET
ejpam-2382	25	15	equation	equation	NOUN
ejpam-2382	25	16	of	of	ADP
ejpam-2382	25	17	the	the	DET
ejpam-2382	25	18	center	center	NOUN
ejpam-2382	25	19	of	of	ADP
ejpam-2382	25	20	osculating	osculating	NOUN
ejpam-2382	25	21	hyperspheres	hypersphere	NOUN
ejpam-2382	25	22	and	and	CCONJ
ejpam-2382	25	23	the	the	DET
ejpam-2382	25	24	equation	equation	NOUN
ejpam-2382	25	25	of	of	ADP
ejpam-2382	25	26	their	their	PRON
ejpam-2382	25	27	radius	radius	NOUN
ejpam-2382	25	28	in	in	ADP
ejpam-2382	25	29	e5	e5	PROPN
ejpam-2382	25	30	.	.	PUNCT
ejpam-2382	26	1	2	2	X
ejpam-2382	26	2	.	.	X
ejpam-2382	26	3	preliminaries	preliminary	NOUN
ejpam-2382	26	4	in	in	ADP
ejpam-2382	26	5	this	this	DET
ejpam-2382	26	6	section	section	NOUN
ejpam-2382	26	7	,	,	PUNCT
ejpam-2382	26	8	we	we	PRON
ejpam-2382	26	9	recall	recall	VERB
ejpam-2382	26	10	some	some	DET
ejpam-2382	26	11	basic	basic	ADJ
ejpam-2382	26	12	concepts	concept	NOUN
ejpam-2382	26	13	on	on	ADP
ejpam-2382	26	14	classical	classical	ADJ
ejpam-2382	26	15	differential	differential	NOUN
ejpam-2382	26	16	geometry	geometry	NOUN
ejpam-2382	26	17	of	of	ADP
ejpam-2382	26	18	space	space	NOUN
ejpam-2382	26	19	curve	curve	NOUN
ejpam-2382	26	20	in	in	ADP
ejpam-2382	26	21	the	the	DET
ejpam-2382	26	22	euclidean	euclidean	ADJ
ejpam-2382	26	23	5	5	NUM
ejpam-2382	26	24	-	-	PUNCT
ejpam-2382	26	25	space	space	NOUN
ejpam-2382	26	26	and	and	CCONJ
ejpam-2382	26	27	the	the	DET
ejpam-2382	26	28	definitions	definition	NOUN
ejpam-2382	26	29	of	of	ADP
ejpam-2382	26	30	special	special	ADJ
ejpam-2382	26	31	curves	curve	NOUN
ejpam-2382	26	32	.	.	PUNCT
ejpam-2382	27	1	let	let	VERB
ejpam-2382	27	2	x	x	PRON
ejpam-2382	27	3	:	:	PUNCT
ejpam-2382	27	4	i	i	PRON
ejpam-2382	27	5	⊂	⊂	PROPN
ejpam-2382	27	6	r	r	X
ejpam-2382	27	7	→	→	SYM
ejpam-2382	27	8	e5	e5	PROPN
ejpam-2382	27	9	be	be	AUX
ejpam-2382	27	10	an	an	DET
ejpam-2382	27	11	arbitrary	arbitrary	ADJ
ejpam-2382	27	12	curve	curve	NOUN
ejpam-2382	27	13	in	in	ADP
ejpam-2382	27	14	the	the	DET
ejpam-2382	27	15	euclidean	euclidean	ADJ
ejpam-2382	27	16	5	5	NUM
ejpam-2382	27	17	-	-	PUNCT
ejpam-2382	27	18	space	space	NOUN
ejpam-2382	27	19	.	.	PUNCT
ejpam-2382	28	1	we	we	PRON
ejpam-2382	28	2	call	call	VERB
ejpam-2382	28	3	the	the	DET
ejpam-2382	28	4	curve	curve	NOUN
ejpam-2382	28	5	x	x	PUNCT
ejpam-2382	28	6	as	as	ADP
ejpam-2382	28	7	unit	unit	NOUN
ejpam-2382	28	8	speed	speed	NOUN
ejpam-2382	28	9	curve	curve	NOUN
ejpam-2382	28	10	if	if	SCONJ
ejpam-2382	28	11	〈	〈	PROPN
ejpam-2382	28	12	x	x	PROPN
ejpam-2382	28	13	′(s	′(s	NOUN
ejpam-2382	28	14	)	)	PUNCT
ejpam-2382	28	15	,	,	PUNCT
ejpam-2382	28	16	x	x	X
ejpam-2382	28	17	′(s)〉=	′(s)〉=	PUNCT
ejpam-2382	28	18	1	1	NUM
ejpam-2382	28	19	,	,	PUNCT
ejpam-2382	28	20	where	where	SCONJ
ejpam-2382	28	21	〈	〈	NOUN
ejpam-2382	28	22	,	,	PUNCT
ejpam-2382	28	23	〉	〉	NOUN
ejpam-2382	28	24	is	be	AUX
ejpam-2382	28	25	the	the	DET
ejpam-2382	28	26	standard	standard	ADJ
ejpam-2382	28	27	scalar	scalar	ADJ
ejpam-2382	28	28	product	product	NOUN
ejpam-2382	28	29	of	of	ADP
ejpam-2382	28	30	e5	e5	PROPN
ejpam-2382	28	31	given	give	VERB
ejpam-2382	28	32	by	by	ADP
ejpam-2382	28	33	〈	〈	PROPN
ejpam-2382	28	34	a	a	PRON
ejpam-2382	28	35	,	,	PUNCT
ejpam-2382	28	36	b〉=	b〉=	NOUN
ejpam-2382	28	37	a1	a1	NOUN
ejpam-2382	28	38	b1	b1	NOUN
ejpam-2382	28	39	+	+	CCONJ
ejpam-2382	28	40	a2	a2	PROPN
ejpam-2382	28	41	b2	b2	NOUN
ejpam-2382	28	42	+	+	CCONJ
ejpam-2382	28	43	a3	a3	NOUN
ejpam-2382	28	44	b3	b3	PROPN
ejpam-2382	28	45	+	+	CCONJ
ejpam-2382	28	46	a4	a4	NOUN
ejpam-2382	28	47	b4	b4	NOUN
ejpam-2382	28	48	+	+	CCONJ
ejpam-2382	28	49	a5	a5	PROPN
ejpam-2382	28	50	b5	b5	PROPN
ejpam-2382	28	51	,	,	PUNCT
ejpam-2382	28	52	for	for	ADP
ejpam-2382	28	53	each	each	DET
ejpam-2382	28	54	vectors	vector	NOUN
ejpam-2382	28	55	a	a	DET
ejpam-2382	28	56	=	=	SYM
ejpam-2382	28	57	(	(	PUNCT
ejpam-2382	28	58	a1	a1	PROPN
ejpam-2382	28	59	,	,	PUNCT
ejpam-2382	28	60	a2	a2	PROPN
ejpam-2382	28	61	,	,	PUNCT
ejpam-2382	28	62	a3	a3	NOUN
ejpam-2382	28	63	,	,	PUNCT
ejpam-2382	28	64	a4	a4	NOUN
ejpam-2382	28	65	,	,	PUNCT
ejpam-2382	28	66	a5	a5	PROPN
ejpam-2382	28	67	)	)	PUNCT
ejpam-2382	28	68	and	and	CCONJ
ejpam-2382	28	69	b	b	X
ejpam-2382	28	70	=	=	SYM
ejpam-2382	28	71	(	(	PUNCT
ejpam-2382	28	72	b1	b1	PROPN
ejpam-2382	28	73	,	,	PUNCT
ejpam-2382	28	74	b2	b2	NOUN
ejpam-2382	28	75	,	,	PUNCT
ejpam-2382	28	76	b3	b3	PROPN
ejpam-2382	28	77	,	,	PUNCT
ejpam-2382	28	78	b4	b4	NOUN
ejpam-2382	28	79	,	,	PUNCT
ejpam-2382	28	80	b5	b5	PROPN
ejpam-2382	28	81	)	)	PUNCT
ejpam-2382	28	82	of	of	ADP
ejpam-2382	28	83	e5	e5	PROPN
ejpam-2382	28	84	,	,	PUNCT
ejpam-2382	28	85	[	[	X
ejpam-2382	28	86	6	6	NUM
ejpam-2382	28	87	]	]	PUNCT
ejpam-2382	28	88	.	.	PUNCT
ejpam-2382	29	1	the	the	DET
ejpam-2382	29	2	norm	norm	NOUN
ejpam-2382	29	3	of	of	ADP
ejpam-2382	29	4	a	a	DET
ejpam-2382	29	5	vector	vector	NOUN
ejpam-2382	29	6	a	a	PRON
ejpam-2382	29	7	of	of	ADP
ejpam-2382	29	8	e5	e5	PROPN
ejpam-2382	29	9	is	be	AUX
ejpam-2382	29	10	given	give	VERB
ejpam-2382	29	11	by	by	ADP
ejpam-2382	29	12	‖a‖=	‖a‖=	PROPN
ejpam-2382	29	13	p	p	X
ejpam-2382	29	14	〈	〈	PROPN
ejpam-2382	29	15	a	a	NOUN
ejpam-2382	29	16	,	,	PUNCT
ejpam-2382	29	17	a	a	DET
ejpam-2382	29	18	〉	〉	NOUN
ejpam-2382	29	19	,	,	PUNCT
ejpam-2382	29	20	[	[	X
ejpam-2382	29	21	6	6	NUM
ejpam-2382	29	22	]	]	PUNCT
ejpam-2382	29	23	.	.	PUNCT
ejpam-2382	30	1	let	let	VERB
ejpam-2382	30	2	a	a	DET
ejpam-2382	30	3	=	=	SYM
ejpam-2382	30	4	(	(	PUNCT
ejpam-2382	30	5	a1	a1	PROPN
ejpam-2382	30	6	,	,	PUNCT
ejpam-2382	30	7	a2	a2	PROPN
ejpam-2382	30	8	,	,	PUNCT
ejpam-2382	30	9	a3	a3	NOUN
ejpam-2382	30	10	,	,	PUNCT
ejpam-2382	30	11	a4	a4	PROPN
ejpam-2382	30	12	,	,	PUNCT
ejpam-2382	30	13	a5	a5	PROPN
ejpam-2382	30	14	)	)	PUNCT
ejpam-2382	30	15	,	,	PUNCT
ejpam-2382	30	16	b	b	X
ejpam-2382	30	17	=	=	SYM
ejpam-2382	30	18	(	(	PUNCT
ejpam-2382	30	19	b1	b1	PROPN
ejpam-2382	30	20	,	,	PUNCT
ejpam-2382	30	21	b2	b2	NOUN
ejpam-2382	30	22	,	,	PUNCT
ejpam-2382	30	23	b3	b3	PROPN
ejpam-2382	30	24	,	,	PUNCT
ejpam-2382	30	25	b4	b4	NOUN
ejpam-2382	30	26	,	,	PUNCT
ejpam-2382	30	27	b5	b5	PROPN
ejpam-2382	30	28	)	)	PUNCT
ejpam-2382	30	29	,	,	PUNCT
ejpam-2382	30	30	c	c	X
ejpam-2382	30	31	=	=	SYM
ejpam-2382	30	32	(	(	PUNCT
ejpam-2382	30	33	c1	c1	PROPN
ejpam-2382	30	34	,	,	PUNCT
ejpam-2382	30	35	c2	c2	PROPN
ejpam-2382	30	36	,	,	PUNCT
ejpam-2382	30	37	c3	c3	PROPN
ejpam-2382	30	38	,	,	PUNCT
ejpam-2382	30	39	c4	c4	NOUN
ejpam-2382	30	40	,	,	PUNCT
ejpam-2382	30	41	c5	c5	PROPN
ejpam-2382	30	42	)	)	PUNCT
ejpam-2382	30	43	and	and	CCONJ
ejpam-2382	30	44	d	d	NOUN
ejpam-2382	30	45	=	=	SYM
ejpam-2382	30	46	(	(	PUNCT
ejpam-2382	30	47	d1	d1	PROPN
ejpam-2382	30	48	,	,	PUNCT
ejpam-2382	30	49	d2	d2	PROPN
ejpam-2382	30	50	,	,	PUNCT
ejpam-2382	30	51	d3	d3	PROPN
ejpam-2382	30	52	,	,	PUNCT
ejpam-2382	30	53	d4	d4	PROPN
ejpam-2382	30	54	,	,	PUNCT
ejpam-2382	30	55	d5	d5	NOUN
ejpam-2382	30	56	)	)	PUNCT
ejpam-2382	30	57	be	be	VERB
ejpam-2382	30	58	vectors	vector	NOUN
ejpam-2382	30	59	in	in	ADP
ejpam-2382	30	60	e5	e5	PROPN
ejpam-2382	30	61	.	.	PUNCT
ejpam-2382	31	1	the	the	DET
ejpam-2382	31	2	vectorial	vectorial	ADJ
ejpam-2382	31	3	product	product	NOUN
ejpam-2382	31	4	of	of	ADP
ejpam-2382	31	5	these	these	DET
ejpam-2382	31	6	vectors	vector	NOUN
ejpam-2382	31	7	is	be	AUX
ejpam-2382	31	8	defined	define	VERB
ejpam-2382	31	9	by	by	ADP
ejpam-2382	31	10	the	the	DET
ejpam-2382	31	11	determinant,[6	determinant,[6	NOUN
ejpam-2382	31	12	]	]	X
ejpam-2382	31	13	a	a	DET
ejpam-2382	31	14	∧	∧	PROPN
ejpam-2382	31	15	b	b	PROPN
ejpam-2382	31	16	∧	∧	PROPN
ejpam-2382	31	17	c	c	NOUN
ejpam-2382	31	18	∧	∧	PROPN
ejpam-2382	31	19	d	d	PROPN
ejpam-2382	31	20	=	=	SYM
ejpam-2382	31	21	�	�	PROPN
ejpam-2382	31	22	�	�	PROPN
ejpam-2382	31	23	�	�	PROPN
ejpam-2382	31	24	�	�	PROPN
ejpam-2382	31	25	�	�	PROPN
ejpam-2382	31	26	�	�	PROPN
ejpam-2382	31	27	�	�	PROPN
ejpam-2382	31	28	�	�	PROPN
ejpam-2382	31	29	�	�	PROPN
ejpam-2382	31	30	�	�	PROPN
ejpam-2382	31	31	e1	e1	PROPN
ejpam-2382	31	32	e2	e2	PROPN
ejpam-2382	31	33	e3	e3	NOUN
ejpam-2382	31	34	e4	e4	PROPN
ejpam-2382	31	35	e5	e5	PROPN
ejpam-2382	31	36	a1	a1	PROPN
ejpam-2382	31	37	a2	a2	PROPN
ejpam-2382	31	38	a3	a3	PROPN
ejpam-2382	31	39	a4	a4	PROPN
ejpam-2382	31	40	a5	a5	PROPN
ejpam-2382	31	41	b1	b1	PROPN
ejpam-2382	31	42	b2	b2	NOUN
ejpam-2382	31	43	b3	b3	PROPN
ejpam-2382	31	44	b4	b4	PROPN
ejpam-2382	31	45	b5	b5	PROPN
ejpam-2382	31	46	c1	c1	PROPN
ejpam-2382	31	47	c2	c2	PROPN
ejpam-2382	31	48	c3	c3	PROPN
ejpam-2382	31	49	c4	c4	PROPN
ejpam-2382	31	50	c5	c5	PROPN
ejpam-2382	31	51	d1	d1	PROPN
ejpam-2382	31	52	d2	d2	PROPN
ejpam-2382	31	53	d3	d3	PROPN
ejpam-2382	31	54	d4	d4	PROPN
ejpam-2382	31	55	d5	d5	PROPN
ejpam-2382	31	56	�	�	PROPN
ejpam-2382	31	57	�	�	PROPN
ejpam-2382	31	58	�	�	PROPN
ejpam-2382	31	59	�	�	PROPN
ejpam-2382	31	60	�	�	PROPN
ejpam-2382	31	61	�	�	PROPN
ejpam-2382	31	62	�	�	PROPN
ejpam-2382	31	63	�	�	PROPN
ejpam-2382	31	64	�	�	PROPN
ejpam-2382	31	65	�	�	PROPN
ejpam-2382	31	66	where	where	SCONJ
ejpam-2382	31	67	ei	ei	X
ejpam-2382	31	68	for	for	ADP
ejpam-2382	31	69	1≤	1≤	NUM
ejpam-2382	31	70	i	i	PRON
ejpam-2382	31	71	≤	≤	ADV
ejpam-2382	31	72	5	5	NUM
ejpam-2382	31	73	are	be	AUX
ejpam-2382	31	74	the	the	DET
ejpam-2382	31	75	standard	standard	ADJ
ejpam-2382	31	76	basis	basis	NOUN
ejpam-2382	31	77	vectors	vector	NOUN
ejpam-2382	31	78	of	of	ADP
ejpam-2382	31	79	e5	e5	PROPN
ejpam-2382	31	80	which	which	PRON
ejpam-2382	31	81	satisfies	satisfy	VERB
ejpam-2382	31	82	e1∧	e1∧	PROPN
ejpam-2382	31	83	e2∧	e2∧	PROPN
ejpam-2382	31	84	e3∧	e3∧	PROPN
ejpam-2382	31	85	e4	e4	PROPN
ejpam-2382	31	86	=	=	SYM
ejpam-2382	31	87	e5	e5	PROPN
ejpam-2382	31	88	,	,	PUNCT
ejpam-2382	31	89	e2	e2	PROPN
ejpam-2382	31	90	∧	∧	PROPN
ejpam-2382	31	91	e3	e3	NOUN
ejpam-2382	31	92	∧	∧	PROPN
ejpam-2382	31	93	e4	e4	PROPN
ejpam-2382	31	94	∧	∧	PROPN
ejpam-2382	31	95	e5	e5	PROPN
ejpam-2382	31	96	=	=	PROPN
ejpam-2382	31	97	e1	e1	PROPN
ejpam-2382	31	98	,	,	PUNCT
ejpam-2382	31	99	e3	e3	NOUN
ejpam-2382	31	100	∧	∧	PROPN
ejpam-2382	31	101	e4	e4	PROPN
ejpam-2382	31	102	∧	∧	PROPN
ejpam-2382	31	103	e5	e5	PROPN
ejpam-2382	31	104	∧	∧	PROPN
ejpam-2382	31	105	e1	e1	PROPN
ejpam-2382	31	106	=	=	PROPN
ejpam-2382	31	107	e2	e2	PROPN
ejpam-2382	31	108	,	,	PUNCT
ejpam-2382	31	109	e4	e4	PROPN
ejpam-2382	31	110	∧	∧	PROPN
ejpam-2382	31	111	e5	e5	PROPN
ejpam-2382	31	112	∧	∧	PROPN
ejpam-2382	31	113	e1	e1	NOUN
ejpam-2382	31	114	∧	∧	PROPN
ejpam-2382	31	115	e2	e2	NOUN
ejpam-2382	31	116	=	=	PUNCT
ejpam-2382	31	117	e3	e3	PROPN
ejpam-2382	31	118	,	,	PUNCT
ejpam-2382	31	119	e5	e5	PROPN
ejpam-2382	31	120	∧	∧	PROPN
ejpam-2382	31	121	e1	e1	PROPN
ejpam-2382	31	122	∧	∧	PROPN
ejpam-2382	31	123	e2	e2	NOUN
ejpam-2382	31	124	∧	∧	PROPN
ejpam-2382	31	125	e3	e3	NOUN
ejpam-2382	31	126	=	=	PROPN
ejpam-2382	31	127	e4	e4	PROPN
ejpam-2382	31	128	.	.	PUNCT
ejpam-2382	32	1	let	let	VERB
ejpam-2382	32	2	�	�	PROPN
ejpam-2382	32	3	v1	v1	PROPN
ejpam-2382	32	4	,	,	PUNCT
ejpam-2382	32	5	v2	v2	PROPN
ejpam-2382	32	6	,	,	PUNCT
ejpam-2382	32	7	v3	v3	PROPN
ejpam-2382	32	8	,	,	PUNCT
ejpam-2382	32	9	v4	v4	PROPN
ejpam-2382	32	10	,	,	PUNCT
ejpam-2382	32	11	v5	v5	PROPN
ejpam-2382	32	12	denotes	denote	VERB
ejpam-2382	32	13	the	the	DET
ejpam-2382	32	14	moving	move	VERB
ejpam-2382	32	15	frenet	frenet	ADJ
ejpam-2382	32	16	frame	frame	NOUN
ejpam-2382	32	17	of	of	ADP
ejpam-2382	32	18	the	the	DET
ejpam-2382	32	19	unit	unit	NOUN
ejpam-2382	32	20	speed	speed	NOUN
ejpam-2382	32	21	curve	curve	NOUN
ejpam-2382	32	22	x	x	X
ejpam-2382	32	23	.	.	PUNCT
ejpam-2382	33	1	then	then	ADV
ejpam-2382	33	2	the	the	DET
ejpam-2382	33	3	frenet	frenet	ADJ
ejpam-2382	33	4	formulas	formula	NOUN
ejpam-2382	33	5	are	be	AUX
ejpam-2382	33	6	given	give	VERB
ejpam-2382	33	7	by	by	ADP
ejpam-2382	33	8			NOUN
ejpam-2382	33	9			ADJ
ejpam-2382	33	10			ADJ
ejpam-2382	33	11			ADJ
ejpam-2382	33	12			ADJ
ejpam-2382	33	13			NUM
ejpam-2382	33	14	v	v	ADP
ejpam-2382	33	15	′1	′1	NOUN
ejpam-2382	33	16	v	v	NOUN
ejpam-2382	33	17	′2	′2	NOUN
ejpam-2382	33	18	v	v	ADP
ejpam-2382	33	19	′3	′3	NUM
ejpam-2382	33	20	v	v	NUM
ejpam-2382	33	21	′4	′4	PROPN
ejpam-2382	33	22	v	v	NUM
ejpam-2382	33	23	′5	′5	NOUN
ejpam-2382	33	24			PROPN
ejpam-2382	33	25			PROPN
ejpam-2382	33	26			PROPN
ejpam-2382	33	27			PROPN
ejpam-2382	34	1			PROPN
ejpam-2382	34	2			PROPN
ejpam-2382	34	3	=	=	PUNCT
ejpam-2382	34	4			NOUN
ejpam-2382	34	5			ADJ
ejpam-2382	34	6			ADJ
ejpam-2382	34	7			ADJ
ejpam-2382	34	8			ADJ
ejpam-2382	34	9			NOUN
ejpam-2382	34	10	0	0	NUM
ejpam-2382	34	11	k1	k1	NOUN
ejpam-2382	34	12	0	0	NUM
ejpam-2382	34	13	0	0	SYM
ejpam-2382	34	14	0	0	NUM
ejpam-2382	34	15	−k1	−k1	NOUN
ejpam-2382	34	16	0	0	PUNCT
ejpam-2382	34	17	k2	k2	NOUN
ejpam-2382	34	18	0	0	NUM
ejpam-2382	34	19	0	0	NUM
ejpam-2382	34	20	0	0	NUM
ejpam-2382	34	21	−k2	−k2	NOUN
ejpam-2382	34	22	0	0	PUNCT
ejpam-2382	35	1	k3	k3	VERB
ejpam-2382	35	2	0	0	NUM
ejpam-2382	35	3	0	0	NUM
ejpam-2382	35	4	0	0	NUM
ejpam-2382	36	1	−k3	−k3	NOUN
ejpam-2382	36	2	0	0	NUM
ejpam-2382	37	1	k4	k4	NOUN
ejpam-2382	37	2	0	0	NUM
ejpam-2382	37	3	0	0	NUM
ejpam-2382	37	4	0	0	PUNCT
ejpam-2382	38	1	−k4	−k4	NOUN
ejpam-2382	38	2	0	0	PUNCT
ejpam-2382	38	3			PROPN
ejpam-2382	38	4			PROPN
ejpam-2382	38	5			PROPN
ejpam-2382	38	6			PROPN
ejpam-2382	38	7			PROPN
ejpam-2382	38	8			PROPN
ejpam-2382	38	9			NOUN
ejpam-2382	38	10			ADJ
ejpam-2382	38	11			ADJ
ejpam-2382	38	12			ADJ
ejpam-2382	38	13			ADJ
ejpam-2382	38	14			NUM
ejpam-2382	38	15	v1	v1	PROPN
ejpam-2382	38	16	v2	v2	PROPN
ejpam-2382	38	17	v3	v3	PROPN
ejpam-2382	38	18	v4	v4	PROPN
ejpam-2382	38	19	v5	v5	PROPN
ejpam-2382	38	20			PROPN
ejpam-2382	38	21			PROPN
ejpam-2382	38	22			PROPN
ejpam-2382	38	23			PROPN
ejpam-2382	38	24			PROPN
ejpam-2382	38	25			PROPN
ejpam-2382	38	26	where	where	SCONJ
ejpam-2382	38	27	vi	vi	NOUN
ejpam-2382	38	28	,	,	PUNCT
ejpam-2382	38	29	i	i	PRON
ejpam-2382	38	30	=	=	NOUN
ejpam-2382	39	1	1,2,3,4,5	1,2,3,4,5	NOUN
ejpam-2382	39	2	are	be	AUX
ejpam-2382	39	3	called	call	VERB
ejpam-2382	39	4	the	the	DET
ejpam-2382	39	5	i	i	PROPN
ejpam-2382	39	6	th	th	PUNCT
ejpam-2382	39	7	frenet	frenet	ADJ
ejpam-2382	39	8	vectors	vector	NOUN
ejpam-2382	39	9	of	of	ADP
ejpam-2382	39	10	the	the	DET
ejpam-2382	39	11	curve	curve	NOUN
ejpam-2382	39	12	x	x	PUNCT
ejpam-2382	39	13	and	and	CCONJ
ejpam-2382	39	14	the	the	DET
ejpam-2382	39	15	functions	function	NOUN
ejpam-2382	39	16	ki	ki	PROPN
ejpam-2382	39	17	,	,	PUNCT
ejpam-2382	39	18	i	i	PRON
ejpam-2382	39	19	=	=	NOUN
ejpam-2382	39	20	1,2,3,4	1,2,3,4	NUM
ejpam-2382	39	21	are	be	AUX
ejpam-2382	39	22	called	call	VERB
ejpam-2382	39	23	the	the	DET
ejpam-2382	39	24	i	i	NOUN
ejpam-2382	39	25	th	th	X
ejpam-2382	39	26	curvatures	curvature	NOUN
ejpam-2382	39	27	of	of	ADP
ejpam-2382	39	28	the	the	DET
ejpam-2382	39	29	curve	curve	NOUN
ejpam-2382	39	30	x	x	X
ejpam-2382	39	31	,	,	PUNCT
ejpam-2382	39	32	[	[	X
ejpam-2382	39	33	6	6	NUM
ejpam-2382	39	34	]	]	PUNCT
ejpam-2382	39	35	.	.	PUNCT
ejpam-2382	40	1	the	the	DET
ejpam-2382	40	2	set	set	NOUN
ejpam-2382	40	3	,	,	PUNCT
ejpam-2382	40	4	whose	whose	DET
ejpam-2382	40	5	elements	element	NOUN
ejpam-2382	40	6	are	be	AUX
ejpam-2382	40	7	frame	frame	NOUN
ejpam-2382	40	8	vectors	vector	NOUN
ejpam-2382	40	9	and	and	CCONJ
ejpam-2382	40	10	curvatures	curvature	NOUN
ejpam-2382	40	11	of	of	ADP
ejpam-2382	40	12	a	a	DET
ejpam-2382	40	13	curve	curve	NOUN
ejpam-2382	40	14	,	,	PUNCT
ejpam-2382	40	15	is	be	AUX
ejpam-2382	40	16	called	call	VERB
ejpam-2382	40	17	frenet	frenet	NOUN
ejpam-2382	40	18	apparatus	apparatus	NOUN
ejpam-2382	40	19	of	of	ADP
ejpam-2382	40	20	the	the	DET
ejpam-2382	40	21	curve	curve	NOUN
ejpam-2382	40	22	.	.	PUNCT
ejpam-2382	41	1	a	a	DET
ejpam-2382	41	2	regular	regular	ADJ
ejpam-2382	41	3	curve	curve	NOUN
ejpam-2382	41	4	is	be	AUX
ejpam-2382	41	5	m.	m.	NOUN
ejpam-2382	41	6	masal	masal	NOUN
ejpam-2382	41	7	,	,	PUNCT
ejpam-2382	41	8	a.	a.	PROPN
ejpam-2382	41	9	azak	azak	PROPN
ejpam-2382	41	10	/	/	SYM
ejpam-2382	41	11	eur	eur	PROPN
ejpam-2382	41	12	.	.	PUNCT
ejpam-2382	42	1	j.	j.	PROPN
ejpam-2382	42	2	pure	pure	PROPN
ejpam-2382	42	3	appl	appl	PROPN
ejpam-2382	42	4	.	.	PROPN
ejpam-2382	42	5	math	math	PROPN
ejpam-2382	42	6	,	,	PUNCT
ejpam-2382	42	7	8	8	NUM
ejpam-2382	42	8	(	(	PUNCT
ejpam-2382	42	9	2015	2015	NUM
ejpam-2382	42	10	)	)	PUNCT
ejpam-2382	42	11	,	,	PUNCT
ejpam-2382	42	12	255	255	NUM
ejpam-2382	42	13	-	-	SYM
ejpam-2382	42	14	270	270	NUM
ejpam-2382	42	15	257	257	NUM
ejpam-2382	42	16	called	call	VERB
ejpam-2382	42	17	a	a	DET
ejpam-2382	42	18	w	w	NOUN
ejpam-2382	42	19	-	-	PUNCT
ejpam-2382	42	20	curve	curve	NOUN
ejpam-2382	42	21	if	if	SCONJ
ejpam-2382	42	22	it	it	PRON
ejpam-2382	42	23	has	have	VERB
ejpam-2382	42	24	constant	constant	ADJ
ejpam-2382	42	25	frenet	frenet	ADJ
ejpam-2382	42	26	curvatures	curvature	NOUN
ejpam-2382	42	27	.	.	PUNCT
ejpam-2382	43	1	a	a	DET
ejpam-2382	43	2	unit	unit	NOUN
ejpam-2382	43	3	speed	speed	NOUN
ejpam-2382	43	4	curve	curve	NOUN
ejpam-2382	43	5	x	x	VERB
ejpam-2382	43	6	is	be	AUX
ejpam-2382	43	7	called	call	VERB
ejpam-2382	43	8	inclined	inclined	ADJ
ejpam-2382	43	9	curve	curve	NOUN
ejpam-2382	43	10	in	in	ADP
ejpam-2382	43	11	e5	e5	PROPN
ejpam-2382	43	12	if	if	SCONJ
ejpam-2382	43	13	its	its	PRON
ejpam-2382	43	14	tangent	tangent	NOUN
ejpam-2382	43	15	vector	vector	NOUN
ejpam-2382	43	16	v1	v1	NOUN
ejpam-2382	43	17	makes	make	VERB
ejpam-2382	43	18	a	a	DET
ejpam-2382	43	19	constant	constant	ADJ
ejpam-2382	43	20	angle	angle	NOUN
ejpam-2382	43	21	with	with	ADP
ejpam-2382	43	22	a	a	DET
ejpam-2382	43	23	unit	unit	NOUN
ejpam-2382	43	24	fixed	fix	VERB
ejpam-2382	43	25	direction	direction	NOUN
ejpam-2382	43	26	u	u	NOUN
ejpam-2382	43	27	.	.	PUNCT
ejpam-2382	44	1	let	let	VERB
ejpam-2382	44	2	x	x	PRON
ejpam-2382	44	3	and	and	CCONJ
ejpam-2382	44	4	y	y	PROPN
ejpam-2382	44	5	be	be	AUX
ejpam-2382	44	6	unit	unit	NOUN
ejpam-2382	44	7	speed	speed	NOUN
ejpam-2382	44	8	curves	curve	NOUN
ejpam-2382	44	9	in	in	ADP
ejpam-2382	44	10	e5	e5	PROPN
ejpam-2382	44	11	.	.	PUNCT
ejpam-2382	45	1	y	y	PROPN
ejpam-2382	45	2	is	be	AUX
ejpam-2382	45	3	an	an	DET
ejpam-2382	45	4	involute	involute	NOUN
ejpam-2382	45	5	of	of	ADP
ejpam-2382	45	6	x	x	PRON
ejpam-2382	45	7	if	if	SCONJ
ejpam-2382	45	8	the	the	DET
ejpam-2382	45	9	tangent	tangent	NOUN
ejpam-2382	45	10	line	line	NOUN
ejpam-2382	45	11	v1	v1	NOUN
ejpam-2382	45	12	at	at	ADP
ejpam-2382	45	13	x	x	X
ejpam-2382	45	14	(	(	PUNCT
ejpam-2382	45	15	s	s	NOUN
ejpam-2382	45	16	)	)	PUNCT
ejpam-2382	45	17	and	and	CCONJ
ejpam-2382	45	18	the	the	DET
ejpam-2382	45	19	tangent	tangent	NOUN
ejpam-2382	45	20	line	line	NOUN
ejpam-2382	45	21	v	v	ADP
ejpam-2382	45	22	∗1	∗1	PROPN
ejpam-2382	45	23	at	at	ADP
ejpam-2382	45	24	y	y	PROPN
ejpam-2382	45	25	(	(	PUNCT
ejpam-2382	45	26	s	s	X
ejpam-2382	45	27	)	)	PUNCT
ejpam-2382	45	28	are	be	AUX
ejpam-2382	45	29	perpendicular	perpendicular	ADJ
ejpam-2382	45	30	for	for	ADP
ejpam-2382	45	31	each	each	DET
ejpam-2382	45	32	s.	s.	PROPN
ejpam-2382	45	33	x	x	PRON
ejpam-2382	45	34	is	be	AUX
ejpam-2382	45	35	an	an	DET
ejpam-2382	45	36	evolute	evolute	NOUN
ejpam-2382	45	37	of	of	ADP
ejpam-2382	45	38	y	y	PROPN
ejpam-2382	45	39	if	if	SCONJ
ejpam-2382	45	40	y	y	PROPN
ejpam-2382	45	41	is	be	AUX
ejpam-2382	45	42	an	an	DET
ejpam-2382	45	43	involute	involute	NOUN
ejpam-2382	45	44	of	of	ADP
ejpam-2382	45	45	x	x	X
ejpam-2382	45	46	.	.	PUNCT
ejpam-2382	46	1	this	this	DET
ejpam-2382	46	2	curve	curve	NOUN
ejpam-2382	46	3	couple	couple	NOUN
ejpam-2382	46	4	is	be	AUX
ejpam-2382	46	5	defined	define	VERB
ejpam-2382	46	6	by	by	ADP
ejpam-2382	46	7	[	[	X
ejpam-2382	46	8	12	12	NUM
ejpam-2382	46	9	]	]	X
ejpam-2382	46	10	y	y	NOUN
ejpam-2382	46	11	=	=	PUNCT
ejpam-2382	46	12	x	x	PUNCT
ejpam-2382	47	1	+	+	NOUN
ejpam-2382	47	2	µv1	µv1	NOUN
ejpam-2382	47	3	.	.	PUNCT
ejpam-2382	48	1	the	the	DET
ejpam-2382	48	2	euclidean	euclidean	PROPN
ejpam-2382	48	3	hypersphere	hypersphere	PROPN
ejpam-2382	48	4	with	with	ADP
ejpam-2382	48	5	the	the	DET
ejpam-2382	48	6	center	center	NOUN
ejpam-2382	48	7	c	c	NOUN
ejpam-2382	48	8	and	and	CCONJ
ejpam-2382	48	9	radius	radius	NOUN
ejpam-2382	48	10	r	r	PROPN
ejpam-2382	48	11	∈	∈	PROPN
ejpam-2382	48	12	r+	r+	NOUN
ejpam-2382	48	13	in	in	ADP
ejpam-2382	48	14	euclidean	euclidean	ADJ
ejpam-2382	48	15	5	5	NUM
ejpam-2382	48	16	-	-	PUNCT
ejpam-2382	48	17	space	space	NOUN
ejpam-2382	48	18	e5	e5	PROPN
ejpam-2382	48	19	is	be	AUX
ejpam-2382	48	20	defined	define	VERB
ejpam-2382	48	21	by	by	ADP
ejpam-2382	48	22	[	[	X
ejpam-2382	48	23	6	6	NUM
ejpam-2382	48	24	]	]	X
ejpam-2382	48	25	s4	s4	PROPN
ejpam-2382	48	26	=	=	SYM
ejpam-2382	48	27	�	�	PROPN
ejpam-2382	48	28	x	x	SYM
ejpam-2382	48	29	∈	∈	PROPN
ejpam-2382	48	30	e5|〈x	e5|〈x	NOUN
ejpam-2382	48	31	−	−	NOUN
ejpam-2382	48	32	c	c	NOUN
ejpam-2382	48	33	,	,	PUNCT
ejpam-2382	48	34	x	x	PUNCT
ejpam-2382	48	35	−	−	NOUN
ejpam-2382	48	36	c〉=	c〉=	ADJ
ejpam-2382	48	37	r2	r2	NOUN
ejpam-2382	48	38	if	if	SCONJ
ejpam-2382	48	39	x	x	PRON
ejpam-2382	48	40	⊂	⊂	PROPN
ejpam-2382	48	41	s4	s4	PROPN
ejpam-2382	48	42	is	be	AUX
ejpam-2382	48	43	a	a	DET
ejpam-2382	48	44	regular	regular	ADJ
ejpam-2382	48	45	curve	curve	NOUN
ejpam-2382	48	46	in	in	ADP
ejpam-2382	48	47	e5	e5	PROPN
ejpam-2382	48	48	,	,	PUNCT
ejpam-2382	48	49	then	then	ADV
ejpam-2382	48	50	the	the	DET
ejpam-2382	48	51	curve	curve	NOUN
ejpam-2382	48	52	x	x	PUNCT
ejpam-2382	48	53	is	be	AUX
ejpam-2382	48	54	called	call	VERB
ejpam-2382	48	55	as	as	ADP
ejpam-2382	48	56	a	a	DET
ejpam-2382	48	57	spherical	spherical	ADJ
ejpam-2382	48	58	curve	curve	NOUN
ejpam-2382	48	59	in	in	ADP
ejpam-2382	48	60	e5	e5	PROPN
ejpam-2382	48	61	.	.	PUNCT
ejpam-2382	49	1	the	the	DET
ejpam-2382	49	2	hypersphere	hypersphere	NOUN
ejpam-2382	49	3	is	be	AUX
ejpam-2382	49	4	called	call	VERB
ejpam-2382	49	5	as	as	ADP
ejpam-2382	49	6	osculating	osculate	VERB
ejpam-2382	49	7	hypersphere	hypersphere	ADV
ejpam-2382	49	8	if	if	SCONJ
ejpam-2382	49	9	it	it	PRON
ejpam-2382	49	10	has	have	VERB
ejpam-2382	49	11	six	six	NUM
ejpam-2382	49	12	common	common	ADJ
ejpam-2382	49	13	points	point	NOUN
ejpam-2382	49	14	with	with	ADP
ejpam-2382	49	15	the	the	DET
ejpam-2382	49	16	curve	curve	NOUN
ejpam-2382	49	17	x	x	PUNCT
ejpam-2382	49	18	at	at	ADP
ejpam-2382	49	19	the	the	DET
ejpam-2382	49	20	point	point	NOUN
ejpam-2382	49	21	x	x	X
ejpam-2382	49	22	(	(	PUNCT
ejpam-2382	49	23	s),[6	s),[6	VERB
ejpam-2382	49	24	]	]	X
ejpam-2382	49	25	3	3	X
ejpam-2382	49	26	.	.	PUNCT
ejpam-2382	49	27	geometric	geometric	ADJ
ejpam-2382	49	28	meanings	meaning	NOUN
ejpam-2382	49	29	of	of	ADP
ejpam-2382	49	30	the	the	DET
ejpam-2382	49	31	curvatures	curvature	NOUN
ejpam-2382	49	32	in	in	ADP
ejpam-2382	49	33	euclidean	euclidean	ADJ
ejpam-2382	49	34	5	5	NUM
ejpam-2382	49	35	-	-	PUNCT
ejpam-2382	49	36	space	space	NOUN
ejpam-2382	49	37	let	let	VERB
ejpam-2382	49	38	x	x	PUNCT
ejpam-2382	49	39	=	=	SYM
ejpam-2382	49	40	x	x	X
ejpam-2382	49	41	(	(	PUNCT
ejpam-2382	49	42	s	s	X
ejpam-2382	49	43	)	)	PUNCT
ejpam-2382	49	44	be	be	AUX
ejpam-2382	49	45	a	a	DET
ejpam-2382	49	46	unit	unit	NOUN
ejpam-2382	49	47	speed	speed	NOUN
ejpam-2382	49	48	curve	curve	NOUN
ejpam-2382	49	49	in	in	ADP
ejpam-2382	49	50	euclidean	euclidean	ADJ
ejpam-2382	49	51	5	5	NUM
ejpam-2382	49	52	-	-	PUNCT
ejpam-2382	49	53	space	space	NOUN
ejpam-2382	49	54	.	.	PUNCT
ejpam-2382	50	1	the	the	DET
ejpam-2382	50	2	frenet	frenet	ADJ
ejpam-2382	50	3	vectors	vector	NOUN
ejpam-2382	50	4	and	and	CCONJ
ejpam-2382	50	5	curvatures	curvature	NOUN
ejpam-2382	50	6	of	of	ADP
ejpam-2382	50	7	x	x	PRON
ejpam-2382	50	8	,	,	PUNCT
ejpam-2382	50	9	are	be	AUX
ejpam-2382	50	10	given	give	VERB
ejpam-2382	50	11	by	by	ADP
ejpam-2382	50	12	v1	v1	NOUN
ejpam-2382	50	13	=	=	SYM
ejpam-2382	50	14	x	x	SYM
ejpam-2382	50	15	′	′	NOUN
ejpam-2382	50	16	,	,	PUNCT
ejpam-2382	50	17	v2	v2	NOUN
ejpam-2382	50	18	=	=	PUNCT
ejpam-2382	50	19	x	x	SYM
ejpam-2382	50	20	′′	′′	PROPN
ejpam-2382	50	21	k1	k1	NOUN
ejpam-2382	50	22	,	,	PUNCT
ejpam-2382	50	23	v3	v3	PROPN
ejpam-2382	50	24	=	=	PUNCT
ejpam-2382	50	25	x	x	SYM
ejpam-2382	50	26	′′	′′	NOUN
ejpam-2382	50	27	2	2	NUM
ejpam-2382	50	28	(	(	PUNCT
ejpam-2382	50	29	x	x	SYM
ejpam-2382	50	30	′′′	′′′	PROPN
ejpam-2382	51	1	+	+	CCONJ
ejpam-2382	51	2	x	x	PART
ejpam-2382	51	3	′′	′′	NOUN
ejpam-2382	51	4	2	2	NUM
ejpam-2382	51	5	x	x	SYM
ejpam-2382	51	6	′)−	′)−	ADP
ejpam-2382	51	7	〈	〈	PROPN
ejpam-2382	51	8	x	x	SYM
ejpam-2382	51	9	′′	′′	PROPN
ejpam-2382	51	10	,	,	PUNCT
ejpam-2382	51	11	x	x	PUNCT
ejpam-2382	51	12	′′′〉x	′′′〉x	NOUN
ejpam-2382	51	13	′′	′′	PROPN
ejpam-2382	51	14	‖x	‖x	NOUN
ejpam-2382	51	15	′′‖2	′′‖2	PROPN
ejpam-2382	51	16	(	(	PUNCT
ejpam-2382	51	17	x	x	SYM
ejpam-2382	51	18	′′′	′′′	PROPN
ejpam-2382	51	19	+	+	NUM
ejpam-2382	51	20	‖x	‖x	NOUN
ejpam-2382	51	21	′′‖2	′′‖2	NOUN
ejpam-2382	51	22	x	x	X
ejpam-2382	51	23	′)−	′)−	ADJ
ejpam-2382	51	24	〈	〈	PROPN
ejpam-2382	51	25	x	x	SYM
ejpam-2382	51	26	′′	′′	PROPN
ejpam-2382	51	27	,	,	PUNCT
ejpam-2382	51	28	x	x	PUNCT
ejpam-2382	51	29	′′′〉x	′′′〉x	NOUN
ejpam-2382	51	30	′′	′′	PROPN
ejpam-2382	51	31	,	,	PUNCT
ejpam-2382	51	32	v4	v4	PROPN
ejpam-2382	51	33	=	=	SYM
ejpam-2382	51	34	ηv3	ηv3	PROPN
ejpam-2382	51	35	∧	∧	PROPN
ejpam-2382	51	36	v2	v2	NOUN
ejpam-2382	51	37	∧	∧	PROPN
ejpam-2382	51	38	v1	v1	NOUN
ejpam-2382	51	39	∧	∧	PROPN
ejpam-2382	51	40	v5	v5	NOUN
ejpam-2382	51	41	,	,	PUNCT
ejpam-2382	51	42	v5	v5	PROPN
ejpam-2382	51	43	=	=	SYM
ejpam-2382	51	44	η	η	X
ejpam-2382	51	45	v1	v1	PROPN
ejpam-2382	51	46	∧	∧	PROPN
ejpam-2382	51	47	v2	v2	PROPN
ejpam-2382	51	48	∧	∧	NOUN
ejpam-2382	51	49	x	x	X
ejpam-2382	51	50	′′′	′′′	PROPN
ejpam-2382	51	51	∧	∧	PROPN
ejpam-2382	51	52	x	x	X
ejpam-2382	51	53	(	(	PUNCT
ejpam-2382	51	54	4	4	X
ejpam-2382	51	55	)	)	PUNCT
ejpam-2382	51	56	v1	v1	NOUN
ejpam-2382	51	57	∧	∧	NOUN
ejpam-2382	51	58	v2	v2	PROPN
ejpam-2382	51	59	∧	∧	NOUN
ejpam-2382	51	60	x	x	X
ejpam-2382	51	61	′′′	′′′	PROPN
ejpam-2382	51	62	∧	∧	PROPN
ejpam-2382	51	63	x	x	X
ejpam-2382	51	64	(	(	PUNCT
ejpam-2382	51	65	4	4	NUM
ejpam-2382	51	66	)	)	PUNCT
ejpam-2382	51	67	,	,	PUNCT
ejpam-2382	51	68	k1	k1	NOUN
ejpam-2382	51	69	=	=	PUNCT
ejpam-2382	51	70	x	x	SYM
ejpam-2382	51	71	′′	′′	PROPN
ejpam-2382	51	72	,	,	PUNCT
ejpam-2382	51	73	k2	k2	NOUN
ejpam-2382	51	74	=	=	SYM
ejpam-2382	51	75	〈	〈	PROPN
ejpam-2382	51	76	x	x	PROPN
ejpam-2382	51	77	′′′	′′′	PROPN
ejpam-2382	51	78	,	,	PUNCT
ejpam-2382	51	79	v3	v3	PROPN
ejpam-2382	51	80	〉	〉	NOUN
ejpam-2382	51	81	‖x	‖x	NOUN
ejpam-2382	51	82	′′‖	′′‖	PROPN
ejpam-2382	51	83	,	,	PUNCT
ejpam-2382	51	84	k3	k3	PROPN
ejpam-2382	51	85	=	=	NOUN
ejpam-2382	51	86	v1	v1	NOUN
ejpam-2382	51	87	∧	∧	PROPN
ejpam-2382	51	88	v2	v2	PROPN
ejpam-2382	51	89	∧	∧	NOUN
ejpam-2382	51	90	x	x	X
ejpam-2382	51	91	′′′	′′′	PROPN
ejpam-2382	51	92	∧	∧	PROPN
ejpam-2382	51	93	x	x	X
ejpam-2382	51	94	(	(	PUNCT
ejpam-2382	51	95	4	4	NUM
ejpam-2382	51	96	)	)	PUNCT
ejpam-2382	51	97	�	�	PROPN
ejpam-2382	51	98	〈	〈	PROPN
ejpam-2382	51	99	x	x	PROPN
ejpam-2382	51	100	′′′	′′′	PROPN
ejpam-2382	51	101	,	,	PUNCT
ejpam-2382	51	102	v3	v3	PROPN
ejpam-2382	51	103	〉	〉	NOUN
ejpam-2382	51	104	�	�	NOUN
ejpam-2382	51	105	2	2	NUM
ejpam-2382	51	106	,	,	PUNCT
ejpam-2382	51	107	k4	k4	NOUN
ejpam-2382	51	108	=	=	PUNCT
ejpam-2382	51	109	〈	〈	PROPN
ejpam-2382	51	110	x	x	SYM
ejpam-2382	51	111	(	(	PUNCT
ejpam-2382	51	112	4	4	NUM
ejpam-2382	51	113	)	)	PUNCT
ejpam-2382	51	114	,	,	PUNCT
ejpam-2382	51	115	v5	v5	PROPN
ejpam-2382	51	116	〉	〉	NOUN
ejpam-2382	51	117	�	�	PROPN
ejpam-2382	51	118	〈	〈	PROPN
ejpam-2382	51	119	x	x	PROPN
ejpam-2382	51	120	′′′	′′′	PROPN
ejpam-2382	51	121	,	,	PUNCT
ejpam-2382	51	122	v3	v3	PROPN
ejpam-2382	51	123	〉	〉	NOUN
ejpam-2382	51	124	�	�	PROPN
ejpam-2382	51	125	2	2	NUM
ejpam-2382	51	126	v1	v1	NOUN
ejpam-2382	51	127	∧	∧	NOUN
ejpam-2382	51	128	v2	v2	PROPN
ejpam-2382	51	129	∧	∧	NOUN
ejpam-2382	51	130	x	x	X
ejpam-2382	51	131	′′′	′′′	PROPN
ejpam-2382	51	132	∧	∧	PROPN
ejpam-2382	51	133	x	x	X
ejpam-2382	51	134	(	(	PUNCT
ejpam-2382	51	135	4	4	NUM
ejpam-2382	51	136	)	)	PUNCT
ejpam-2382	51	137	.	.	PUNCT
ejpam-2382	52	1	where	where	SCONJ
ejpam-2382	52	2	v1	v1	NOUN
ejpam-2382	52	3	,	,	PUNCT
ejpam-2382	52	4	v2	v2	PROPN
ejpam-2382	52	5	,	,	PUNCT
ejpam-2382	52	6	v3	v3	PROPN
ejpam-2382	52	7	,	,	PUNCT
ejpam-2382	52	8	v4	v4	PROPN
ejpam-2382	52	9	,	,	PUNCT
ejpam-2382	52	10	v5	v5	NOUN
ejpam-2382	52	11	and	and	CCONJ
ejpam-2382	52	12	k1	k1	NOUN
ejpam-2382	52	13	,	,	PUNCT
ejpam-2382	52	14	k2	k2	PROPN
ejpam-2382	52	15	,	,	PUNCT
ejpam-2382	52	16	k3	k3	PROPN
ejpam-2382	52	17	,	,	PUNCT
ejpam-2382	52	18	k4	k4	PROPN
ejpam-2382	52	19	denote	denote	VERB
ejpam-2382	52	20	the	the	DET
ejpam-2382	52	21	frenet	frenet	ADJ
ejpam-2382	52	22	vectors	vector	NOUN
ejpam-2382	52	23	and	and	CCONJ
ejpam-2382	52	24	frenet	frenet	ADJ
ejpam-2382	52	25	curvatures	curvature	NOUN
ejpam-2382	52	26	of	of	ADP
ejpam-2382	52	27	the	the	DET
ejpam-2382	52	28	curve	curve	NOUN
ejpam-2382	52	29	x	x	X
ejpam-2382	52	30	,	,	PUNCT
ejpam-2382	52	31	respectively	respectively	ADV
ejpam-2382	52	32	.	.	PUNCT
ejpam-2382	53	1	also	also	ADV
ejpam-2382	53	2	,	,	PUNCT
ejpam-2382	53	3	η	η	PROPN
ejpam-2382	53	4	number	number	NOUN
ejpam-2382	53	5	is	be	AUX
ejpam-2382	53	6	selected	select	VERB
ejpam-2382	53	7	as+1	as+1	PROPN
ejpam-2382	53	8	or	or	CCONJ
ejpam-2382	53	9	-1	-1	ADP
ejpam-2382	53	10	,	,	PUNCT
ejpam-2382	53	11	in	in	ADP
ejpam-2382	53	12	order	order	NOUN
ejpam-2382	53	13	to	to	PART
ejpam-2382	53	14	make	make	VERB
ejpam-2382	53	15	the	the	DET
ejpam-2382	53	16	determinant	determinant	NOUN
ejpam-2382	53	17	of	of	ADP
ejpam-2382	53	18	�	�	PROPN
ejpam-2382	53	19	v1	v1	PROPN
ejpam-2382	53	20	,	,	PUNCT
ejpam-2382	53	21	v2	v2	PROPN
ejpam-2382	53	22	,	,	PUNCT
ejpam-2382	53	23	v3	v3	PROPN
ejpam-2382	53	24	,	,	PUNCT
ejpam-2382	53	25	v4	v4	PROPN
ejpam-2382	53	26	,	,	PUNCT
ejpam-2382	53	27	v5	v5	PROPN
ejpam-2382	53	28	�	�	PROPN
ejpam-2382	53	29	matrix	matrix	NOUN
ejpam-2382	53	30	+1	+1	PROPN
ejpam-2382	53	31	.	.	PUNCT
ejpam-2382	54	1	thus	thus	ADV
ejpam-2382	54	2	,	,	PUNCT
ejpam-2382	54	3	the	the	DET
ejpam-2382	54	4	frenet	frenet	ADJ
ejpam-2382	54	5	frame	frame	NOUN
ejpam-2382	54	6	will	will	AUX
ejpam-2382	54	7	be	be	AUX
ejpam-2382	54	8	directed	direct	VERB
ejpam-2382	54	9	positively	positively	ADV
ejpam-2382	54	10	,	,	PUNCT
ejpam-2382	54	11	[	[	X
ejpam-2382	54	12	16	16	NUM
ejpam-2382	54	13	]	]	PUNCT
ejpam-2382	54	14	.	.	PUNCT
ejpam-2382	55	1	m.	m.	NOUN
ejpam-2382	55	2	masal	masal	PROPN
ejpam-2382	55	3	,	,	PUNCT
ejpam-2382	55	4	a.	a.	PROPN
ejpam-2382	55	5	azak	azak	PROPN
ejpam-2382	55	6	/	/	SYM
ejpam-2382	55	7	eur	eur	PROPN
ejpam-2382	55	8	.	.	PUNCT
ejpam-2382	56	1	j.	j.	PROPN
ejpam-2382	56	2	pure	pure	PROPN
ejpam-2382	56	3	appl	appl	PROPN
ejpam-2382	56	4	.	.	PROPN
ejpam-2382	56	5	math	math	PROPN
ejpam-2382	56	6	,	,	PUNCT
ejpam-2382	56	7	8	8	NUM
ejpam-2382	56	8	(	(	PUNCT
ejpam-2382	56	9	2015	2015	NUM
ejpam-2382	56	10	)	)	PUNCT
ejpam-2382	56	11	,	,	PUNCT
ejpam-2382	56	12	255	255	NUM
ejpam-2382	56	13	-	-	SYM
ejpam-2382	56	14	270	270	NUM
ejpam-2382	56	15	258	258	NUM
ejpam-2382	56	16	the	the	DET
ejpam-2382	56	17	geometric	geometric	ADJ
ejpam-2382	56	18	meanings	meaning	NOUN
ejpam-2382	56	19	of	of	ADP
ejpam-2382	56	20	the	the	DET
ejpam-2382	56	21	curvatures	curvature	NOUN
ejpam-2382	56	22	at	at	ADP
ejpam-2382	56	23	the	the	DET
ejpam-2382	56	24	initial	initial	ADJ
ejpam-2382	56	25	point	point	NOUN
ejpam-2382	56	26	x	x	X
ejpam-2382	56	27	(	(	PUNCT
ejpam-2382	56	28	0	0	NUM
ejpam-2382	56	29	)	)	PUNCT
ejpam-2382	56	30	of	of	ADP
ejpam-2382	56	31	the	the	DET
ejpam-2382	56	32	curve	curve	NOUN
ejpam-2382	56	33	x	x	PUNCT
ejpam-2382	56	34	can	can	AUX
ejpam-2382	56	35	be	be	AUX
ejpam-2382	56	36	given	give	VERB
ejpam-2382	56	37	with	with	ADP
ejpam-2382	56	38	respect	respect	NOUN
ejpam-2382	56	39	to	to	ADP
ejpam-2382	56	40	the	the	DET
ejpam-2382	56	41	taylor	taylor	PROPN
ejpam-2382	56	42	expansion	expansion	NOUN
ejpam-2382	56	43	of	of	ADP
ejpam-2382	56	44	the	the	DET
ejpam-2382	56	45	curve	curve	NOUN
ejpam-2382	56	46	x	x	PUNCT
ejpam-2382	56	47	at	at	ADP
ejpam-2382	56	48	this	this	DET
ejpam-2382	56	49	point	point	NOUN
ejpam-2382	56	50	in	in	ADP
ejpam-2382	56	51	the	the	DET
ejpam-2382	56	52	euclidean	euclidean	ADJ
ejpam-2382	56	53	5	5	NUM
ejpam-2382	56	54	-	-	PUNCT
ejpam-2382	56	55	space	space	NOUN
ejpam-2382	56	56	e5	e5	NOUN
ejpam-2382	56	57	as	as	SCONJ
ejpam-2382	56	58	if	if	SCONJ
ejpam-2382	56	59	in	in	ADP
ejpam-2382	56	60	the	the	DET
ejpam-2382	56	61	euclidean	euclidean	ADJ
ejpam-2382	56	62	3	3	NUM
ejpam-2382	56	63	-	-	PUNCT
ejpam-2382	56	64	space	space	NOUN
ejpam-2382	56	65	e3	e3	NOUN
ejpam-2382	56	66	.	.	PUNCT
ejpam-2382	57	1	firstly	firstly	ADV
ejpam-2382	57	2	,	,	PUNCT
ejpam-2382	57	3	let	let	VERB
ejpam-2382	57	4	us	we	PRON
ejpam-2382	57	5	write	write	VERB
ejpam-2382	57	6	taylor	taylor	PROPN
ejpam-2382	57	7	expansion	expansion	NOUN
ejpam-2382	57	8	about	about	ADP
ejpam-2382	57	9	the	the	DET
ejpam-2382	57	10	point	point	NOUN
ejpam-2382	57	11	x	x	SYM
ejpam-2382	57	12	(	(	PUNCT
ejpam-2382	57	13	0	0	NUM
ejpam-2382	57	14	)	)	PUNCT
ejpam-2382	57	15	up	up	ADP
ejpam-2382	57	16	to	to	PART
ejpam-2382	57	17	fifth	fifth	ADJ
ejpam-2382	57	18	order	order	NOUN
ejpam-2382	57	19	and	and	CCONJ
ejpam-2382	57	20	take	take	VERB
ejpam-2382	57	21	the	the	DET
ejpam-2382	57	22	terms	term	NOUN
ejpam-2382	57	23	including	include	VERB
ejpam-2382	57	24	the	the	DET
ejpam-2382	57	25	lowest	low	ADJ
ejpam-2382	57	26	powers	power	NOUN
ejpam-2382	57	27	of	of	ADP
ejpam-2382	57	28	s	s	PRON
ejpam-2382	57	29	in	in	ADP
ejpam-2382	57	30	every	every	DET
ejpam-2382	57	31	component	component	NOUN
ejpam-2382	57	32	.	.	PUNCT
ejpam-2382	58	1	thus	thus	ADV
ejpam-2382	58	2	the	the	DET
ejpam-2382	58	3	taylor	taylor	PROPN
ejpam-2382	58	4	expansion	expansion	NOUN
ejpam-2382	58	5	can	can	AUX
ejpam-2382	58	6	be	be	AUX
ejpam-2382	58	7	given	give	VERB
ejpam-2382	58	8	by	by	ADP
ejpam-2382	58	9	x	x	SYM
ejpam-2382	58	10	(	(	PUNCT
ejpam-2382	58	11	s)∼=	s)∼=	NOUN
ejpam-2382	58	12	x	x	SYM
ejpam-2382	58	13	(	(	PUNCT
ejpam-2382	58	14	0	0	NUM
ejpam-2382	58	15	)	)	PUNCT
ejpam-2382	58	16	+	+	PRON
ejpam-2382	58	17	s	s	X
ejpam-2382	58	18	x	x	SYM
ejpam-2382	58	19	′(0	′(0	PROPN
ejpam-2382	58	20	)	)	PUNCT
ejpam-2382	59	1	+	+	CCONJ
ejpam-2382	59	2	s2	s2	VERB
ejpam-2382	59	3	2	2	NUM
ejpam-2382	59	4	x	x	SYM
ejpam-2382	59	5	′′(0	′′(0	X
ejpam-2382	59	6	)	)	PUNCT
ejpam-2382	59	7	+	+	CCONJ
ejpam-2382	59	8	s3	s3	PROPN
ejpam-2382	59	9	6	6	NUM
ejpam-2382	59	10	x	x	SYM
ejpam-2382	59	11	′′′(0	′′′(0	PROPN
ejpam-2382	59	12	)	)	PUNCT
ejpam-2382	59	13	+	+	CCONJ
ejpam-2382	59	14	s4	s4	PROPN
ejpam-2382	59	15	4	4	NUM
ejpam-2382	59	16	!	!	NOUN
ejpam-2382	59	17	x	x	SYM
ejpam-2382	59	18	(	(	PUNCT
ejpam-2382	59	19	4)(0	4)(0	NUM
ejpam-2382	59	20	)	)	PUNCT
ejpam-2382	59	21	+	+	CCONJ
ejpam-2382	59	22	s5	s5	PROPN
ejpam-2382	59	23	5	5	NUM
ejpam-2382	59	24	!	!	PUNCT
ejpam-2382	59	25	x	x	PUNCT
ejpam-2382	59	26	(	(	PUNCT
ejpam-2382	59	27	5)(0	5)(0	NUM
ejpam-2382	59	28	)	)	PUNCT
ejpam-2382	59	29	.	.	PUNCT
ejpam-2382	60	1	and	and	CCONJ
ejpam-2382	60	2	considering	consider	VERB
ejpam-2382	60	3	the	the	DET
ejpam-2382	60	4	frenet	frenet	NOUN
ejpam-2382	60	5	formulas	formula	NOUN
ejpam-2382	60	6	,	,	PUNCT
ejpam-2382	60	7	we	we	PRON
ejpam-2382	60	8	obtain	obtain	VERB
ejpam-2382	60	9	x	x	PUNCT
ejpam-2382	60	10	(	(	PUNCT
ejpam-2382	60	11	s)∼=x	s)∼=x	NOUN
ejpam-2382	60	12	(	(	PUNCT
ejpam-2382	60	13	0	0	NUM
ejpam-2382	60	14	)	)	PUNCT
ejpam-2382	60	15	+	+	NUM
ejpam-2382	60	16	sv1(0	sv1(0	NOUN
ejpam-2382	60	17	)	)	PUNCT
ejpam-2382	61	1	+	+	CCONJ
ejpam-2382	61	2	s2	s2	VERB
ejpam-2382	61	3	2	2	NUM
ejpam-2382	61	4	k1(0)v2(0	k1(0)v2(0	NOUN
ejpam-2382	61	5	)	)	PUNCT
ejpam-2382	61	6	+	+	CCONJ
ejpam-2382	61	7	s3	s3	PROPN
ejpam-2382	61	8	3	3	NUM
ejpam-2382	61	9	!	!	PUNCT
ejpam-2382	61	10	k1(0)k2(0)v3(0	k1(0)k2(0)v3(0	NOUN
ejpam-2382	61	11	)	)	PUNCT
ejpam-2382	62	1	+	+	CCONJ
ejpam-2382	62	2	s4	s4	PROPN
ejpam-2382	62	3	4	4	NUM
ejpam-2382	62	4	!	!	PUNCT
ejpam-2382	62	5	k1(0)k2(0)k3(0)v4(0	k1(0)k2(0)k3(0)v4(0	NOUN
ejpam-2382	62	6	)	)	PUNCT
ejpam-2382	62	7	+	+	NUM
ejpam-2382	62	8	s5	s5	PROPN
ejpam-2382	62	9	5	5	NUM
ejpam-2382	62	10	!	!	PUNCT
ejpam-2382	62	11	k1(0)k2(0)k3(0)k4(0)v5(0	k1(0)k2(0)k3(0)k4(0)v5(0	NOUN
ejpam-2382	62	12	)	)	PUNCT
ejpam-2382	62	13	.	.	PUNCT
ejpam-2382	63	1	(	(	PUNCT
ejpam-2382	63	2	1	1	X
ejpam-2382	63	3	)	)	PUNCT
ejpam-2382	63	4	the	the	DET
ejpam-2382	63	5	first	first	ADJ
ejpam-2382	63	6	two	two	NUM
ejpam-2382	63	7	terms	term	NOUN
ejpam-2382	63	8	of	of	ADP
ejpam-2382	63	9	the	the	DET
ejpam-2382	63	10	equation	equation	NOUN
ejpam-2382	63	11	(	(	PUNCT
ejpam-2382	63	12	1	1	X
ejpam-2382	63	13	)	)	PUNCT
ejpam-2382	63	14	x1	x1	NOUN
ejpam-2382	63	15	(	(	PUNCT
ejpam-2382	63	16	s	s	NOUN
ejpam-2382	63	17	)	)	PUNCT
ejpam-2382	63	18	=	=	SYM
ejpam-2382	64	1	x	x	SYM
ejpam-2382	64	2	(	(	PUNCT
ejpam-2382	64	3	0	0	NUM
ejpam-2382	64	4	)	)	PUNCT
ejpam-2382	64	5	+	+	NUM
ejpam-2382	64	6	sv1(0	sv1(0	NOUN
ejpam-2382	64	7	)	)	PUNCT
ejpam-2382	64	8	gives	give	VERB
ejpam-2382	64	9	us	we	PRON
ejpam-2382	64	10	a	a	DET
ejpam-2382	64	11	tangent	tangent	ADJ
ejpam-2382	64	12	line	line	NOUN
ejpam-2382	64	13	which	which	PRON
ejpam-2382	64	14	is	be	AUX
ejpam-2382	64	15	the	the	DET
ejpam-2382	64	16	best	good	ADJ
ejpam-2382	64	17	linear	linear	ADJ
ejpam-2382	64	18	approach	approach	NOUN
ejpam-2382	64	19	of	of	ADP
ejpam-2382	64	20	the	the	DET
ejpam-2382	64	21	curve	curve	NOUN
ejpam-2382	64	22	x	x	PUNCT
ejpam-2382	64	23	in	in	ADP
ejpam-2382	64	24	the	the	DET
ejpam-2382	64	25	neighborhood	neighborhood	NOUN
ejpam-2382	64	26	of	of	ADP
ejpam-2382	64	27	x	x	X
ejpam-2382	64	28	(	(	PUNCT
ejpam-2382	64	29	0	0	NUM
ejpam-2382	64	30	)	)	PUNCT
ejpam-2382	64	31	.	.	PUNCT
ejpam-2382	65	1	the	the	DET
ejpam-2382	65	2	first	first	ADJ
ejpam-2382	65	3	three	three	NUM
ejpam-2382	65	4	terms	term	NOUN
ejpam-2382	65	5	of	of	ADP
ejpam-2382	65	6	the	the	DET
ejpam-2382	65	7	equation	equation	NOUN
ejpam-2382	65	8	(	(	PUNCT
ejpam-2382	65	9	1	1	X
ejpam-2382	65	10	)	)	PUNCT
ejpam-2382	65	11	x2	x2	NOUN
ejpam-2382	65	12	(	(	PUNCT
ejpam-2382	65	13	s	s	NOUN
ejpam-2382	65	14	)	)	PUNCT
ejpam-2382	65	15	=	=	SYM
ejpam-2382	65	16	x	x	SYM
ejpam-2382	65	17	(	(	PUNCT
ejpam-2382	65	18	0	0	NUM
ejpam-2382	65	19	)	)	PUNCT
ejpam-2382	65	20	+	+	NUM
ejpam-2382	65	21	sv1(0	sv1(0	NOUN
ejpam-2382	65	22	)	)	PUNCT
ejpam-2382	65	23	+	+	CCONJ
ejpam-2382	65	24	s2	s2	VERB
ejpam-2382	65	25	2	2	NUM
ejpam-2382	65	26	k1(0)v2(0	k1(0)v2(0	NOUN
ejpam-2382	65	27	)	)	PUNCT
ejpam-2382	65	28	is	be	AUX
ejpam-2382	65	29	a	a	DET
ejpam-2382	65	30	parabola	parabola	NOUN
ejpam-2382	65	31	which	which	PRON
ejpam-2382	65	32	is	be	AUX
ejpam-2382	65	33	the	the	DET
ejpam-2382	65	34	best	good	ADJ
ejpam-2382	65	35	quadratic	quadratic	ADJ
ejpam-2382	65	36	approach	approach	NOUN
ejpam-2382	65	37	of	of	ADP
ejpam-2382	65	38	the	the	DET
ejpam-2382	65	39	curve	curve	NOUN
ejpam-2382	65	40	x	x	PUNCT
ejpam-2382	65	41	in	in	ADP
ejpam-2382	65	42	the	the	DET
ejpam-2382	65	43	neighborhood	neighborhood	NOUN
ejpam-2382	65	44	of	of	ADP
ejpam-2382	65	45	x	x	X
ejpam-2382	65	46	(	(	PUNCT
ejpam-2382	65	47	0	0	NUM
ejpam-2382	65	48	)	)	PUNCT
ejpam-2382	65	49	.	.	PUNCT
ejpam-2382	66	1	thus	thus	ADV
ejpam-2382	66	2	parabola	parabola	PROPN
ejpam-2382	66	3	lies	lie	VERB
ejpam-2382	66	4	on	on	ADP
ejpam-2382	66	5	the	the	DET
ejpam-2382	66	6	plane	plane	NOUN
ejpam-2382	66	7	spanned	span	VERB
ejpam-2382	66	8	by	by	ADP
ejpam-2382	66	9	the	the	DET
ejpam-2382	66	10	vectors	vector	NOUN
ejpam-2382	66	11	v1	v1	VERB
ejpam-2382	66	12	and	and	CCONJ
ejpam-2382	66	13	v2	v2	NOUN
ejpam-2382	66	14	.	.	PUNCT
ejpam-2382	67	1	thus	thus	ADV
ejpam-2382	67	2	the	the	DET
ejpam-2382	67	3	curvature	curvature	NOUN
ejpam-2382	67	4	k1(0	k1(0	PROPN
ejpam-2382	67	5	)	)	PUNCT
ejpam-2382	67	6	indicates	indicate	VERB
ejpam-2382	67	7	how	how	SCONJ
ejpam-2382	67	8	much	much	ADJ
ejpam-2382	67	9	v2	v2	NOUN
ejpam-2382	67	10	changes	change	NOUN
ejpam-2382	67	11	in	in	ADP
ejpam-2382	67	12	the	the	DET
ejpam-2382	67	13	direction	direction	NOUN
ejpam-2382	67	14	that	that	PRON
ejpam-2382	67	15	is	be	AUX
ejpam-2382	67	16	tangent	tangent	NOUN
ejpam-2382	67	17	to	to	ADP
ejpam-2382	67	18	the	the	DET
ejpam-2382	67	19	curve	curve	NOUN
ejpam-2382	67	20	.	.	PUNCT
ejpam-2382	68	1	the	the	DET
ejpam-2382	68	2	first	first	ADJ
ejpam-2382	68	3	four	four	NUM
ejpam-2382	68	4	terms	term	NOUN
ejpam-2382	68	5	of	of	ADP
ejpam-2382	68	6	the	the	DET
ejpam-2382	68	7	equation	equation	NOUN
ejpam-2382	68	8	(	(	PUNCT
ejpam-2382	68	9	1	1	X
ejpam-2382	68	10	)	)	PUNCT
ejpam-2382	68	11	x3	x3	NOUN
ejpam-2382	68	12	(	(	PUNCT
ejpam-2382	68	13	s	s	NOUN
ejpam-2382	68	14	)	)	PUNCT
ejpam-2382	68	15	=	=	SYM
ejpam-2382	68	16	x	x	SYM
ejpam-2382	68	17	(	(	PUNCT
ejpam-2382	68	18	0	0	NUM
ejpam-2382	68	19	)	)	PUNCT
ejpam-2382	68	20	+	+	NUM
ejpam-2382	68	21	sv1(0	sv1(0	NOUN
ejpam-2382	68	22	)	)	PUNCT
ejpam-2382	68	23	+	+	CCONJ
ejpam-2382	68	24	s2	s2	VERB
ejpam-2382	68	25	2	2	NUM
ejpam-2382	68	26	k1(0)v2(0	k1(0)v2(0	NOUN
ejpam-2382	68	27	)	)	PUNCT
ejpam-2382	68	28	+	+	CCONJ
ejpam-2382	68	29	s3	s3	PROPN
ejpam-2382	68	30	3	3	NUM
ejpam-2382	68	31	!	!	PUNCT
ejpam-2382	68	32	k1(0)k2(0)v3(0	k1(0)k2(0)v3(0	NOUN
ejpam-2382	68	33	)	)	PUNCT
ejpam-2382	68	34	is	be	AUX
ejpam-2382	68	35	cubic	cubic	ADJ
ejpam-2382	68	36	which	which	PRON
ejpam-2382	68	37	is	be	AUX
ejpam-2382	68	38	the	the	DET
ejpam-2382	68	39	best	good	ADJ
ejpam-2382	68	40	cubic	cubic	ADJ
ejpam-2382	68	41	approach	approach	NOUN
ejpam-2382	68	42	of	of	ADP
ejpam-2382	68	43	the	the	DET
ejpam-2382	68	44	curve	curve	NOUN
ejpam-2382	68	45	x	x	PUNCT
ejpam-2382	68	46	in	in	ADP
ejpam-2382	68	47	the	the	DET
ejpam-2382	68	48	neighborhood	neighborhood	NOUN
ejpam-2382	68	49	of	of	ADP
ejpam-2382	68	50	x	x	X
ejpam-2382	68	51	(	(	PUNCT
ejpam-2382	68	52	0	0	NUM
ejpam-2382	68	53	)	)	PUNCT
ejpam-2382	68	54	.	.	PUNCT
ejpam-2382	69	1	this	this	DET
ejpam-2382	69	2	curve	curve	NOUN
ejpam-2382	69	3	lies	lie	VERB
ejpam-2382	69	4	on	on	ADP
ejpam-2382	69	5	sp	sp	ADP
ejpam-2382	69	6	�	�	PROPN
ejpam-2382	69	7	v1	v1	PROPN
ejpam-2382	69	8	,	,	PUNCT
ejpam-2382	69	9	v2	v2	PROPN
ejpam-2382	69	10	,	,	PUNCT
ejpam-2382	69	11	v3	v3	PROPN
ejpam-2382	69	12	-subspace	-subspace	NOUN
ejpam-2382	69	13	.	.	PUNCT
ejpam-2382	70	1	the	the	DET
ejpam-2382	70	2	torsion	torsion	NOUN
ejpam-2382	70	3	k2(0	k2(0	NOUN
ejpam-2382	70	4	)	)	PUNCT
ejpam-2382	70	5	indicates	indicate	VERB
ejpam-2382	70	6	how	how	SCONJ
ejpam-2382	70	7	much	much	ADJ
ejpam-2382	70	8	v3	v3	ADJ
ejpam-2382	70	9	changes	change	NOUN
ejpam-2382	70	10	in	in	ADP
ejpam-2382	70	11	the	the	DET
ejpam-2382	70	12	direction	direction	NOUN
ejpam-2382	70	13	orthogonal	orthogonal	NOUN
ejpam-2382	70	14	to	to	ADP
ejpam-2382	70	15	the	the	DET
ejpam-2382	70	16	v1	v1	NOUN
ejpam-2382	70	17	,	,	PUNCT
ejpam-2382	70	18	v2	v2	NOUN
ejpam-2382	70	19	-	-	PUNCT
ejpam-2382	70	20	plane	plane	NOUN
ejpam-2382	70	21	of	of	ADP
ejpam-2382	70	22	the	the	DET
ejpam-2382	70	23	curve	curve	NOUN
ejpam-2382	70	24	.	.	PUNCT
ejpam-2382	71	1	if	if	SCONJ
ejpam-2382	71	2	k2(0	k2(0	PROPN
ejpam-2382	71	3	)	)	PUNCT
ejpam-2382	71	4	is	be	AUX
ejpam-2382	71	5	zero	zero	NUM
ejpam-2382	71	6	,	,	PUNCT
ejpam-2382	71	7	then	then	ADV
ejpam-2382	71	8	the	the	DET
ejpam-2382	71	9	curve	curve	NOUN
ejpam-2382	71	10	x	x	PUNCT
ejpam-2382	71	11	lies	lie	VERB
ejpam-2382	71	12	on	on	ADP
ejpam-2382	71	13	the	the	DET
ejpam-2382	71	14	sp	sp	ADP
ejpam-2382	71	15	�	�	PROPN
ejpam-2382	71	16	v1	v1	PROPN
ejpam-2382	71	17	,	,	PUNCT
ejpam-2382	71	18	v2	v2	NOUN
ejpam-2382	71	19	-plane	-plane	NOUN
ejpam-2382	71	20	.	.	PUNCT
ejpam-2382	72	1	the	the	DET
ejpam-2382	72	2	first	first	ADJ
ejpam-2382	72	3	five	five	NUM
ejpam-2382	72	4	terms	term	NOUN
ejpam-2382	72	5	of	of	ADP
ejpam-2382	72	6	the	the	DET
ejpam-2382	72	7	equation	equation	NOUN
ejpam-2382	72	8	(	(	PUNCT
ejpam-2382	72	9	1	1	X
ejpam-2382	72	10	)	)	PUNCT
ejpam-2382	72	11	x4	x4	PROPN
ejpam-2382	72	12	(	(	PUNCT
ejpam-2382	72	13	s	s	NOUN
ejpam-2382	72	14	)	)	PUNCT
ejpam-2382	72	15	=	=	SYM
ejpam-2382	72	16	x	x	SYM
ejpam-2382	72	17	(	(	PUNCT
ejpam-2382	72	18	0	0	NUM
ejpam-2382	72	19	)	)	PUNCT
ejpam-2382	72	20	+	+	NUM
ejpam-2382	72	21	sv1(0	sv1(0	NOUN
ejpam-2382	72	22	)	)	PUNCT
ejpam-2382	72	23	+	+	CCONJ
ejpam-2382	72	24	s2	s2	VERB
ejpam-2382	72	25	2	2	NUM
ejpam-2382	72	26	k1(0)v2(0	k1(0)v2(0	NOUN
ejpam-2382	72	27	)	)	PUNCT
ejpam-2382	72	28	+	+	CCONJ
ejpam-2382	72	29	s3	s3	PROPN
ejpam-2382	72	30	3	3	NUM
ejpam-2382	72	31	!	!	PUNCT
ejpam-2382	72	32	k1(0)k2(0)v3(0	k1(0)k2(0)v3(0	NOUN
ejpam-2382	72	33	)	)	PUNCT
ejpam-2382	73	1	+	+	CCONJ
ejpam-2382	73	2	s4	s4	PROPN
ejpam-2382	73	3	4	4	NUM
ejpam-2382	73	4	!	!	PUNCT
ejpam-2382	73	5	k1(0)k2(0)k3(0)v4(0	k1(0)k2(0)k3(0)v4(0	NOUN
ejpam-2382	73	6	)	)	PUNCT
ejpam-2382	73	7	is	be	AUX
ejpam-2382	73	8	a	a	DET
ejpam-2382	73	9	curve	curve	NOUN
ejpam-2382	73	10	which	which	PRON
ejpam-2382	73	11	is	be	AUX
ejpam-2382	73	12	the	the	DET
ejpam-2382	73	13	best	well	ADV
ejpam-2382	73	14	quartic	quartic	ADJ
ejpam-2382	73	15	approach	approach	NOUN
ejpam-2382	73	16	of	of	ADP
ejpam-2382	73	17	the	the	DET
ejpam-2382	73	18	curve	curve	NOUN
ejpam-2382	73	19	x	x	PUNCT
ejpam-2382	73	20	in	in	ADP
ejpam-2382	73	21	the	the	DET
ejpam-2382	73	22	neighborhood	neighborhood	NOUN
ejpam-2382	73	23	of	of	ADP
ejpam-2382	73	24	x	x	X
ejpam-2382	73	25	(	(	PUNCT
ejpam-2382	73	26	0	0	NUM
ejpam-2382	73	27	)	)	PUNCT
ejpam-2382	73	28	.	.	PUNCT
ejpam-2382	74	1	this	this	DET
ejpam-2382	74	2	curve	curve	NOUN
ejpam-2382	74	3	lies	lie	VERB
ejpam-2382	74	4	on	on	ADP
ejpam-2382	74	5	the	the	DET
ejpam-2382	74	6	sp	sp	ADP
ejpam-2382	74	7	�	�	PROPN
ejpam-2382	74	8	v1	v1	PROPN
ejpam-2382	74	9	,	,	PUNCT
ejpam-2382	74	10	v2	v2	PROPN
ejpam-2382	74	11	,	,	PUNCT
ejpam-2382	74	12	v3	v3	PROPN
ejpam-2382	74	13	,	,	PUNCT
ejpam-2382	74	14	v4	v4	NOUN
ejpam-2382	74	15	-subspace	-subspace	NOUN
ejpam-2382	74	16	.	.	PUNCT
ejpam-2382	75	1	the	the	DET
ejpam-2382	75	2	curvature	curvature	PROPN
ejpam-2382	75	3	k3(0	k3(0	PROPN
ejpam-2382	75	4	)	)	PUNCT
ejpam-2382	75	5	is	be	AUX
ejpam-2382	75	6	the	the	DET
ejpam-2382	75	7	scale	scale	NOUN
ejpam-2382	75	8	of	of	ADP
ejpam-2382	75	9	the	the	DET
ejpam-2382	75	10	curve	curve	NOUN
ejpam-2382	75	11	m.	m.	NOUN
ejpam-2382	75	12	masal	masal	PROPN
ejpam-2382	75	13	,	,	PUNCT
ejpam-2382	75	14	a.	a.	PROPN
ejpam-2382	75	15	azak	azak	PROPN
ejpam-2382	75	16	/	/	SYM
ejpam-2382	75	17	eur	eur	PROPN
ejpam-2382	75	18	.	.	PUNCT
ejpam-2382	76	1	j.	j.	PROPN
ejpam-2382	76	2	pure	pure	PROPN
ejpam-2382	76	3	appl	appl	PROPN
ejpam-2382	76	4	.	.	PROPN
ejpam-2382	76	5	math	math	PROPN
ejpam-2382	76	6	,	,	PUNCT
ejpam-2382	76	7	8	8	NUM
ejpam-2382	76	8	(	(	PUNCT
ejpam-2382	76	9	2015	2015	NUM
ejpam-2382	76	10	)	)	PUNCT
ejpam-2382	76	11	,	,	PUNCT
ejpam-2382	76	12	255	255	NUM
ejpam-2382	76	13	-	-	SYM
ejpam-2382	76	14	270	270	NUM
ejpam-2382	76	15	259	259	NUM
ejpam-2382	76	16	x	x	SYM
ejpam-2382	76	17	separating	separate	VERB
ejpam-2382	76	18	from	from	ADP
ejpam-2382	76	19	the	the	DET
ejpam-2382	76	20	sp	sp	ADP
ejpam-2382	76	21	�	�	PROPN
ejpam-2382	76	22	v1	v1	PROPN
ejpam-2382	76	23	,	,	PUNCT
ejpam-2382	76	24	v2	v2	PROPN
ejpam-2382	76	25	,	,	PUNCT
ejpam-2382	76	26	v3	v3	PROPN
ejpam-2382	76	27	-subspace	-subspace	NOUN
ejpam-2382	76	28	.	.	PUNCT
ejpam-2382	77	1	if	if	SCONJ
ejpam-2382	77	2	k3(0	k3(0	PROPN
ejpam-2382	77	3	)	)	PUNCT
ejpam-2382	77	4	is	be	AUX
ejpam-2382	77	5	zero	zero	NUM
ejpam-2382	77	6	,	,	PUNCT
ejpam-2382	77	7	then	then	ADV
ejpam-2382	77	8	the	the	DET
ejpam-2382	77	9	curve	curve	NOUN
ejpam-2382	77	10	x	x	PUNCT
ejpam-2382	77	11	lies	lie	VERB
ejpam-2382	77	12	on	on	ADP
ejpam-2382	77	13	the	the	DET
ejpam-2382	77	14	sp	sp	ADP
ejpam-2382	77	15	�	�	PROPN
ejpam-2382	77	16	v1	v1	PROPN
ejpam-2382	77	17	,	,	PUNCT
ejpam-2382	77	18	v2	v2	PROPN
ejpam-2382	77	19	,	,	PUNCT
ejpam-2382	77	20	v3	v3	PROPN
ejpam-2382	77	21	-subspace	-subspace	NOUN
ejpam-2382	77	22	.	.	PUNCT
ejpam-2382	78	1	the	the	DET
ejpam-2382	78	2	first	first	ADJ
ejpam-2382	78	3	six	six	NUM
ejpam-2382	78	4	terms	term	NOUN
ejpam-2382	78	5	of	of	ADP
ejpam-2382	78	6	the	the	DET
ejpam-2382	78	7	equation	equation	NOUN
ejpam-2382	78	8	(	(	PUNCT
ejpam-2382	78	9	1	1	X
ejpam-2382	78	10	)	)	PUNCT
ejpam-2382	78	11	x5	x5	NOUN
ejpam-2382	78	12	(	(	PUNCT
ejpam-2382	78	13	s	s	NOUN
ejpam-2382	78	14	)	)	PUNCT
ejpam-2382	78	15	=	=	NOUN
ejpam-2382	78	16	x	x	X
ejpam-2382	78	17	(	(	PUNCT
ejpam-2382	78	18	0	0	NUM
ejpam-2382	78	19	)	)	PUNCT
ejpam-2382	78	20	+	+	NUM
ejpam-2382	78	21	sv1(0	sv1(0	NOUN
ejpam-2382	78	22	)	)	PUNCT
ejpam-2382	78	23	+	+	CCONJ
ejpam-2382	78	24	s2	s2	VERB
ejpam-2382	78	25	2	2	NUM
ejpam-2382	78	26	k1(0)v2(0	k1(0)v2(0	NOUN
ejpam-2382	78	27	)	)	PUNCT
ejpam-2382	78	28	+	+	CCONJ
ejpam-2382	78	29	s3	s3	PROPN
ejpam-2382	78	30	3	3	NUM
ejpam-2382	78	31	!	!	PUNCT
ejpam-2382	78	32	k1(0)k2(0)v3(0	k1(0)k2(0)v3(0	NOUN
ejpam-2382	78	33	)	)	PUNCT
ejpam-2382	79	1	+	+	CCONJ
ejpam-2382	79	2	s4	s4	PROPN
ejpam-2382	79	3	4	4	NUM
ejpam-2382	79	4	!	!	PUNCT
ejpam-2382	79	5	k1(0)k2(0)k3(0)v4(0	k1(0)k2(0)k3(0)v4(0	NOUN
ejpam-2382	79	6	)	)	PUNCT
ejpam-2382	79	7	+	+	NUM
ejpam-2382	79	8	s5	s5	PROPN
ejpam-2382	79	9	5	5	NUM
ejpam-2382	79	10	!	!	PUNCT
ejpam-2382	79	11	k1(0)k2(0)k3(0)k4(0)v5(0	k1(0)k2(0)k3(0)k4(0)v5(0	NOUN
ejpam-2382	79	12	)	)	PUNCT
ejpam-2382	79	13	is	be	AUX
ejpam-2382	79	14	a	a	DET
ejpam-2382	79	15	curve	curve	NOUN
ejpam-2382	79	16	which	which	PRON
ejpam-2382	79	17	is	be	AUX
ejpam-2382	79	18	the	the	DET
ejpam-2382	79	19	best	good	ADJ
ejpam-2382	79	20	quintic	quintic	ADJ
ejpam-2382	79	21	approach	approach	NOUN
ejpam-2382	79	22	of	of	ADP
ejpam-2382	79	23	the	the	DET
ejpam-2382	79	24	curve	curve	NOUN
ejpam-2382	79	25	x	x	PUNCT
ejpam-2382	79	26	in	in	ADP
ejpam-2382	79	27	the	the	DET
ejpam-2382	79	28	neighborhood	neighborhood	NOUN
ejpam-2382	79	29	of	of	ADP
ejpam-2382	79	30	x	x	X
ejpam-2382	79	31	(	(	PUNCT
ejpam-2382	79	32	0	0	NUM
ejpam-2382	79	33	)	)	PUNCT
ejpam-2382	79	34	.	.	PUNCT
ejpam-2382	80	1	this	this	DET
ejpam-2382	80	2	curve	curve	NOUN
ejpam-2382	80	3	lies	lie	VERB
ejpam-2382	80	4	on	on	ADP
ejpam-2382	80	5	the	the	DET
ejpam-2382	80	6	sp	sp	ADP
ejpam-2382	80	7	�	�	PROPN
ejpam-2382	80	8	v1	v1	PROPN
ejpam-2382	80	9	,	,	PUNCT
ejpam-2382	80	10	v2	v2	PROPN
ejpam-2382	80	11	,	,	PUNCT
ejpam-2382	80	12	v3	v3	PROPN
ejpam-2382	80	13	,	,	PUNCT
ejpam-2382	80	14	v4	v4	PROPN
ejpam-2382	80	15	,	,	PUNCT
ejpam-2382	80	16	v5	v5	PROPN
ejpam-2382	80	17	-subspace	-subspace	NOUN
ejpam-2382	80	18	.	.	PUNCT
ejpam-2382	81	1	the	the	DET
ejpam-2382	81	2	curvature	curvature	NOUN
ejpam-2382	81	3	k4(0	k4(0	NOUN
ejpam-2382	81	4	)	)	PUNCT
ejpam-2382	81	5	is	be	AUX
ejpam-2382	81	6	the	the	DET
ejpam-2382	81	7	scale	scale	NOUN
ejpam-2382	81	8	of	of	ADP
ejpam-2382	81	9	the	the	DET
ejpam-2382	81	10	curve	curve	NOUN
ejpam-2382	81	11	x	x	PUNCT
ejpam-2382	81	12	separating	separate	VERB
ejpam-2382	81	13	from	from	ADP
ejpam-2382	81	14	the	the	DET
ejpam-2382	81	15	sp	sp	ADP
ejpam-2382	81	16	�	�	PROPN
ejpam-2382	81	17	v1	v1	PROPN
ejpam-2382	81	18	,	,	PUNCT
ejpam-2382	81	19	v2	v2	PROPN
ejpam-2382	81	20	,	,	PUNCT
ejpam-2382	81	21	v3	v3	PROPN
ejpam-2382	81	22	,	,	PUNCT
ejpam-2382	81	23	v4	v4	NOUN
ejpam-2382	81	24	-subspace	-subspace	NOUN
ejpam-2382	81	25	.	.	PUNCT
ejpam-2382	82	1	if	if	SCONJ
ejpam-2382	82	2	k4(0	k4(0	PROPN
ejpam-2382	82	3	)	)	PUNCT
ejpam-2382	82	4	is	be	AUX
ejpam-2382	82	5	zero	zero	NUM
ejpam-2382	82	6	,	,	PUNCT
ejpam-2382	82	7	then	then	ADV
ejpam-2382	82	8	the	the	DET
ejpam-2382	82	9	curve	curve	NOUN
ejpam-2382	82	10	x	x	PUNCT
ejpam-2382	82	11	lies	lie	VERB
ejpam-2382	82	12	on	on	ADP
ejpam-2382	82	13	the	the	DET
ejpam-2382	82	14	sp	sp	ADP
ejpam-2382	82	15	�	�	PROPN
ejpam-2382	82	16	v1	v1	PROPN
ejpam-2382	82	17	,	,	PUNCT
ejpam-2382	82	18	v2	v2	PROPN
ejpam-2382	82	19	,	,	PUNCT
ejpam-2382	82	20	v3	v3	PROPN
ejpam-2382	82	21	,	,	PUNCT
ejpam-2382	82	22	v4	v4	NOUN
ejpam-2382	82	23	-subspace	-subspace	NOUN
ejpam-2382	82	24	.	.	PUNCT
ejpam-2382	83	1	therefore	therefore	ADV
ejpam-2382	83	2	,	,	PUNCT
ejpam-2382	83	3	the	the	DET
ejpam-2382	83	4	following	follow	VERB
ejpam-2382	83	5	theorem	theorem	NOUN
ejpam-2382	83	6	can	can	AUX
ejpam-2382	83	7	be	be	AUX
ejpam-2382	83	8	given	give	VERB
ejpam-2382	83	9	.	.	PUNCT
ejpam-2382	84	1	theorem	theorem	NOUN
ejpam-2382	84	2	1	1	NUM
ejpam-2382	84	3	.	.	PUNCT
ejpam-2382	85	1	(	(	PUNCT
ejpam-2382	85	2	i	i	NOUN
ejpam-2382	85	3	)	)	PUNCT
ejpam-2382	85	4	a	a	DET
ejpam-2382	85	5	unit	unit	NOUN
ejpam-2382	85	6	speed	speed	NOUN
ejpam-2382	85	7	curve	curve	NOUN
ejpam-2382	85	8	is	be	AUX
ejpam-2382	85	9	a	a	DET
ejpam-2382	85	10	line	line	NOUN
ejpam-2382	85	11	if	if	SCONJ
ejpam-2382	86	1	and	and	CCONJ
ejpam-2382	86	2	only	only	ADV
ejpam-2382	86	3	if	if	SCONJ
ejpam-2382	86	4	the	the	DET
ejpam-2382	86	5	first	first	ADJ
ejpam-2382	86	6	curvature	curvature	NOUN
ejpam-2382	86	7	is	be	AUX
ejpam-2382	86	8	zero	zero	NUM
ejpam-2382	86	9	.	.	PUNCT
ejpam-2382	87	1	(	(	PUNCT
ejpam-2382	87	2	ii	ii	NOUN
ejpam-2382	87	3	)	)	PUNCT
ejpam-2382	87	4	a	a	DET
ejpam-2382	87	5	unit	unit	NOUN
ejpam-2382	87	6	speed	speed	NOUN
ejpam-2382	87	7	curve	curve	NOUN
ejpam-2382	87	8	is	be	AUX
ejpam-2382	87	9	a	a	DET
ejpam-2382	87	10	quadratic	quadratic	ADJ
ejpam-2382	87	11	(	(	PUNCT
ejpam-2382	87	12	to	to	PART
ejpam-2382	87	13	be	be	AUX
ejpam-2382	87	14	on	on	ADP
ejpam-2382	87	15	the	the	DET
ejpam-2382	87	16	sp	sp	ADP
ejpam-2382	87	17	�	�	PROPN
ejpam-2382	87	18	v1	v1	PROPN
ejpam-2382	87	19	,	,	PUNCT
ejpam-2382	87	20	v2	v2	NOUN
ejpam-2382	87	21	-plane	-plane	NOUN
ejpam-2382	87	22	)	)	PUNCT
ejpam-2382	87	23	if	if	SCONJ
ejpam-2382	87	24	and	and	CCONJ
ejpam-2382	87	25	only	only	ADV
ejpam-2382	87	26	if	if	SCONJ
ejpam-2382	87	27	the	the	DET
ejpam-2382	87	28	second	second	ADJ
ejpam-2382	87	29	curvature	curvature	NOUN
ejpam-2382	87	30	is	be	AUX
ejpam-2382	87	31	zero	zero	NUM
ejpam-2382	87	32	.	.	PUNCT
ejpam-2382	88	1	(	(	PUNCT
ejpam-2382	88	2	iii	iii	X
ejpam-2382	88	3	)	)	PUNCT
ejpam-2382	88	4	a	a	DET
ejpam-2382	88	5	unit	unit	NOUN
ejpam-2382	88	6	speed	speed	NOUN
ejpam-2382	88	7	curve	curve	NOUN
ejpam-2382	88	8	is	be	AUX
ejpam-2382	88	9	a	a	DET
ejpam-2382	88	10	cubic	cubic	ADJ
ejpam-2382	88	11	(	(	PUNCT
ejpam-2382	88	12	to	to	PART
ejpam-2382	88	13	be	be	AUX
ejpam-2382	88	14	on	on	ADP
ejpam-2382	88	15	the	the	DET
ejpam-2382	88	16	sp	sp	ADP
ejpam-2382	88	17	�	�	PROPN
ejpam-2382	88	18	v1	v1	PROPN
ejpam-2382	88	19	,	,	PUNCT
ejpam-2382	88	20	v2	v2	PROPN
ejpam-2382	88	21	,	,	PUNCT
ejpam-2382	88	22	v3	v3	PROPN
ejpam-2382	88	23	-subspace	-subspace	NOUN
ejpam-2382	88	24	)	)	PUNCT
ejpam-2382	88	25	if	if	SCONJ
ejpam-2382	88	26	and	and	CCONJ
ejpam-2382	88	27	only	only	ADV
ejpam-2382	88	28	if	if	SCONJ
ejpam-2382	88	29	the	the	DET
ejpam-2382	88	30	third	third	ADJ
ejpam-2382	88	31	curvature	curvature	NOUN
ejpam-2382	88	32	is	be	AUX
ejpam-2382	88	33	zero	zero	NUM
ejpam-2382	88	34	.	.	PUNCT
ejpam-2382	89	1	(	(	PUNCT
ejpam-2382	89	2	iv	iv	X
ejpam-2382	89	3	)	)	PUNCT
ejpam-2382	89	4	a	a	DET
ejpam-2382	89	5	unit	unit	NOUN
ejpam-2382	89	6	speed	speed	NOUN
ejpam-2382	89	7	curve	curve	NOUN
ejpam-2382	89	8	is	be	AUX
ejpam-2382	89	9	a	a	DET
ejpam-2382	89	10	quartic	quartic	ADJ
ejpam-2382	89	11	(	(	PUNCT
ejpam-2382	89	12	to	to	PART
ejpam-2382	89	13	be	be	AUX
ejpam-2382	89	14	on	on	ADP
ejpam-2382	89	15	the	the	DET
ejpam-2382	89	16	sp	sp	ADP
ejpam-2382	89	17	�	�	PROPN
ejpam-2382	89	18	v1	v1	PROPN
ejpam-2382	89	19	,	,	PUNCT
ejpam-2382	89	20	v2	v2	PROPN
ejpam-2382	89	21	,	,	PUNCT
ejpam-2382	89	22	v3	v3	PROPN
ejpam-2382	89	23	,	,	PUNCT
ejpam-2382	89	24	v4	v4	NOUN
ejpam-2382	89	25	-subspace	-subspace	NOUN
ejpam-2382	89	26	)	)	PUNCT
ejpam-2382	89	27	if	if	SCONJ
ejpam-2382	89	28	and	and	CCONJ
ejpam-2382	89	29	only	only	ADV
ejpam-2382	89	30	if	if	SCONJ
ejpam-2382	89	31	the	the	DET
ejpam-2382	89	32	fourth	fourth	ADJ
ejpam-2382	89	33	curvature	curvature	NOUN
ejpam-2382	89	34	is	be	AUX
ejpam-2382	89	35	zero	zero	NUM
ejpam-2382	89	36	.	.	PUNCT
ejpam-2382	90	1	(	(	PUNCT
ejpam-2382	90	2	v	v	NOUN
ejpam-2382	90	3	)	)	PUNCT
ejpam-2382	90	4	a	a	DET
ejpam-2382	90	5	unit	unit	NOUN
ejpam-2382	90	6	speed	speed	NOUN
ejpam-2382	90	7	curve	curve	NOUN
ejpam-2382	90	8	is	be	AUX
ejpam-2382	90	9	a	a	DET
ejpam-2382	90	10	quintic	quintic	ADJ
ejpam-2382	90	11	(	(	PUNCT
ejpam-2382	90	12	to	to	PART
ejpam-2382	90	13	be	be	AUX
ejpam-2382	90	14	on	on	ADP
ejpam-2382	90	15	the	the	DET
ejpam-2382	90	16	sp	sp	ADP
ejpam-2382	90	17	�	�	PROPN
ejpam-2382	90	18	v1	v1	PROPN
ejpam-2382	90	19	,	,	PUNCT
ejpam-2382	90	20	v2	v2	PROPN
ejpam-2382	90	21	,	,	PUNCT
ejpam-2382	90	22	v3	v3	PROPN
ejpam-2382	90	23	,	,	PUNCT
ejpam-2382	90	24	v4	v4	PROPN
ejpam-2382	90	25	,	,	PUNCT
ejpam-2382	90	26	v5	v5	NOUN
ejpam-2382	90	27	-subspace	-subspace	NOUN
ejpam-2382	90	28	)	)	PUNCT
ejpam-2382	90	29	if	if	SCONJ
ejpam-2382	90	30	and	and	CCONJ
ejpam-2382	90	31	only	only	ADV
ejpam-2382	90	32	if	if	SCONJ
ejpam-2382	90	33	the	the	DET
ejpam-2382	90	34	all	all	DET
ejpam-2382	90	35	curvatures	curvature	NOUN
ejpam-2382	90	36	are	be	AUX
ejpam-2382	90	37	different	different	ADJ
ejpam-2382	90	38	from	from	ADP
ejpam-2382	90	39	zero	zero	NUM
ejpam-2382	90	40	.	.	PUNCT
ejpam-2382	91	1	4	4	X
ejpam-2382	91	2	.	.	X
ejpam-2382	91	3	calculation	calculation	NOUN
ejpam-2382	91	4	of	of	ADP
ejpam-2382	91	5	the	the	DET
ejpam-2382	91	6	frenet	frenet	NOUN
ejpam-2382	91	7	apparatus	apparatus	NOUN
ejpam-2382	91	8	of	of	ADP
ejpam-2382	91	9	the	the	DET
ejpam-2382	91	10	curves	curve	NOUN
ejpam-2382	91	11	in	in	ADP
ejpam-2382	91	12	the	the	DET
ejpam-2382	91	13	euclidean	euclidean	ADJ
ejpam-2382	91	14	5	5	NUM
ejpam-2382	91	15	-	-	PUNCT
ejpam-2382	91	16	space	space	NOUN
ejpam-2382	91	17	the	the	DET
ejpam-2382	91	18	frenet	frenet	NOUN
ejpam-2382	91	19	apparatus	apparatus	NOUN
ejpam-2382	91	20	of	of	ADP
ejpam-2382	91	21	a	a	DET
ejpam-2382	91	22	curve	curve	NOUN
ejpam-2382	91	23	with	with	ADP
ejpam-2382	91	24	respect	respect	NOUN
ejpam-2382	91	25	to	to	ADP
ejpam-2382	91	26	any	any	DET
ejpam-2382	91	27	parameter	parameter	NOUN
ejpam-2382	91	28	in	in	ADP
ejpam-2382	91	29	the	the	DET
ejpam-2382	91	30	euclidean	euclidean	ADJ
ejpam-2382	91	31	5	5	NUM
ejpam-2382	91	32	-	-	PUNCT
ejpam-2382	91	33	space	space	NOUN
ejpam-2382	91	34	can	can	AUX
ejpam-2382	91	35	be	be	AUX
ejpam-2382	91	36	calculated	calculate	VERB
ejpam-2382	91	37	via	via	ADP
ejpam-2382	91	38	the	the	DET
ejpam-2382	91	39	same	same	ADJ
ejpam-2382	91	40	method	method	NOUN
ejpam-2382	91	41	in	in	ADP
ejpam-2382	91	42	the	the	DET
ejpam-2382	91	43	euclidean	euclidean	ADJ
ejpam-2382	91	44	3	3	NUM
ejpam-2382	91	45	-	-	PUNCT
ejpam-2382	91	46	space	space	NOUN
ejpam-2382	91	47	.	.	PUNCT
ejpam-2382	92	1	let	let	VERB
ejpam-2382	92	2	x	x	PRON
ejpam-2382	92	3	be	be	AUX
ejpam-2382	92	4	an	an	DET
ejpam-2382	92	5	arbitrary	arbitrary	ADJ
ejpam-2382	92	6	curve	curve	NOUN
ejpam-2382	92	7	and	and	CCONJ
ejpam-2382	92	8	a	a	DET
ejpam-2382	92	9	function	function	NOUN
ejpam-2382	92	10	is	be	AUX
ejpam-2382	92	11	of	of	ADP
ejpam-2382	92	12	class	class	NOUN
ejpam-2382	92	13	c5	c5	PROPN
ejpam-2382	92	14	in	in	ADP
ejpam-2382	92	15	e5	e5	PROPN
ejpam-2382	92	16	.	.	PUNCT
ejpam-2382	93	1	if	if	SCONJ
ejpam-2382	93	2	the	the	DET
ejpam-2382	93	3	derivatives	derivative	NOUN
ejpam-2382	93	4	of	of	ADP
ejpam-2382	93	5	the	the	DET
ejpam-2382	93	6	curve	curve	NOUN
ejpam-2382	93	7	x	x	PUNCT
ejpam-2382	93	8	up	up	ADP
ejpam-2382	93	9	to	to	ADP
ejpam-2382	93	10	the	the	DET
ejpam-2382	93	11	fifth	fifth	ADJ
ejpam-2382	93	12	order	order	NOUN
ejpam-2382	93	13	are	be	AUX
ejpam-2382	93	14	calculated	calculate	VERB
ejpam-2382	93	15	with	with	ADP
ejpam-2382	93	16	respect	respect	NOUN
ejpam-2382	93	17	to	to	ADP
ejpam-2382	93	18	parameter	parameter	PROPN
ejpam-2382	93	19	t	t	PROPN
ejpam-2382	93	20	in	in	ADP
ejpam-2382	93	21	terms	term	NOUN
ejpam-2382	93	22	of	of	ADP
ejpam-2382	93	23	the	the	DET
ejpam-2382	93	24	parameter	parameter	NOUN
ejpam-2382	93	25	s	s	PROPN
ejpam-2382	93	26	,	,	PUNCT
ejpam-2382	93	27	the	the	DET
ejpam-2382	93	28	following	follow	VERB
ejpam-2382	93	29	equations	equation	NOUN
ejpam-2382	93	30	are	be	AUX
ejpam-2382	93	31	obtained	obtain	VERB
ejpam-2382	93	32	ẋ	ẋ	PROPN
ejpam-2382	94	1	=	=	PUNCT
ejpam-2382	94	2	v	v	ADP
ejpam-2382	94	3	v1	v1	NOUN
ejpam-2382	94	4	,	,	PUNCT
ejpam-2382	94	5	v	v	NOUN
ejpam-2382	94	6	=	=	X
ejpam-2382	94	7	ds	ds	PROPN
ejpam-2382	94	8	d	d	PROPN
ejpam-2382	94	9	t	t	PROPN
ejpam-2382	94	10	6=	6=	ADP
ejpam-2382	94	11	0	0	NUM
ejpam-2382	94	12	(	(	PUNCT
ejpam-2382	94	13	2	2	NUM
ejpam-2382	94	14	)	)	PUNCT
ejpam-2382	94	15	ẍ	ẍ	X
ejpam-2382	95	1	=	=	NOUN
ejpam-2382	95	2	v̇	v̇	NOUN
ejpam-2382	95	3	v1	v1	NOUN
ejpam-2382	95	4	+	+	CCONJ
ejpam-2382	95	5	v2	v2	NOUN
ejpam-2382	95	6	k1	k1	NOUN
ejpam-2382	95	7	v2	v2	NOUN
ejpam-2382	95	8	(	(	PUNCT
ejpam-2382	95	9	3	3	NUM
ejpam-2382	95	10	)	)	PUNCT
ejpam-2382	95	11	...	...	PUNCT
ejpam-2382	96	1	x	x	X
ejpam-2382	96	2	=(	=(	NOUN
ejpam-2382	96	3	v̈	v̈	PRON
ejpam-2382	96	4	−	−	ADP
ejpam-2382	96	5	v3k2	v3k2	NOUN
ejpam-2382	96	6	1)v1	1)v1	NUM
ejpam-2382	96	7	+	+	CCONJ
ejpam-2382	96	8	(	(	PUNCT
ejpam-2382	96	9	3vv̇k1	3vv̇k1	NUM
ejpam-2382	96	10	+	+	CCONJ
ejpam-2382	96	11	v2k̇1)v2	v2k̇1)v2	NOUN
ejpam-2382	96	12	+	+	CCONJ
ejpam-2382	96	13	(	(	PUNCT
ejpam-2382	96	14	v	v	NUM
ejpam-2382	96	15	3k1k2)v3	3k1k2)v3	NUM
ejpam-2382	96	16	(	(	PUNCT
ejpam-2382	96	17	4	4	NUM
ejpam-2382	96	18	)	)	PUNCT
ejpam-2382	96	19	x	x	X
ejpam-2382	96	20	(	(	PUNCT
ejpam-2382	96	21	4	4	X
ejpam-2382	96	22	)	)	PUNCT
ejpam-2382	96	23	=(	=(	NOUN
ejpam-2382	96	24	...	...	PUNCT
ejpam-2382	97	1	v	v	X
ejpam-2382	97	2	−	−	NOUN
ejpam-2382	97	3	6v2	6v2	NUM
ejpam-2382	97	4	v̇k2	v̇k2	NOUN
ejpam-2382	97	5	1	1	NUM
ejpam-2382	97	6	−	−	NOUN
ejpam-2382	97	7	3v3k1k̇1)v1	3v3k1k̇1)v1	NUM
ejpam-2382	97	8	+	+	CCONJ
ejpam-2382	97	9	(	(	PUNCT
ejpam-2382	97	10	4vv̈k1	4vv̈k1	NUM
ejpam-2382	97	11	−	−	PROPN
ejpam-2382	97	12	v4k3	v4k3	CCONJ
ejpam-2382	97	13	1	1	NUM
ejpam-2382	97	14	+	+	SYM
ejpam-2382	97	15	3v̇2k1	3v̇2k1	PROPN
ejpam-2382	97	16	+	+	NUM
ejpam-2382	97	17	5vv̇k̇1	5vv̇k̇1	NUM
ejpam-2382	97	18	+	+	CCONJ
ejpam-2382	97	19	v2k̈1	v2k̈1	PROPN
ejpam-2382	97	20	−	−	PROPN
ejpam-2382	97	21	v4k1k2	v4k1k2	VERB
ejpam-2382	97	22	2)v2	2)v2	PROPN
ejpam-2382	97	23	+	+	NUM
ejpam-2382	97	24	(	(	PUNCT
ejpam-2382	97	25	6v2	6v2	NUM
ejpam-2382	97	26	v̇k1k2	v̇k1k2	PROPN
ejpam-2382	97	27	+	+	CCONJ
ejpam-2382	97	28	2v3k̇1k2	2v3k̇1k2	NUM
ejpam-2382	97	29	+	+	CCONJ
ejpam-2382	97	30	v3k1k̇2)v3	v3k1k̇2)v3	PROPN
ejpam-2382	97	31	+	+	CCONJ
ejpam-2382	97	32	(	(	PUNCT
ejpam-2382	97	33	v	v	NUM
ejpam-2382	97	34	4k1k2k3)v4	4k1k2k3)v4	NOUN
ejpam-2382	97	35	(	(	PUNCT
ejpam-2382	97	36	5	5	NUM
ejpam-2382	97	37	)	)	PUNCT
ejpam-2382	97	38	m.	m.	NOUN
ejpam-2382	97	39	masal	masal	NOUN
ejpam-2382	97	40	,	,	PUNCT
ejpam-2382	97	41	a.	a.	PROPN
ejpam-2382	97	42	azak	azak	PROPN
ejpam-2382	97	43	/	/	SYM
ejpam-2382	97	44	eur	eur	PROPN
ejpam-2382	97	45	.	.	PUNCT
ejpam-2382	98	1	j.	j.	PROPN
ejpam-2382	98	2	pure	pure	PROPN
ejpam-2382	98	3	appl	appl	PROPN
ejpam-2382	98	4	.	.	PROPN
ejpam-2382	98	5	math	math	PROPN
ejpam-2382	98	6	,	,	PUNCT
ejpam-2382	98	7	8	8	NUM
ejpam-2382	98	8	(	(	PUNCT
ejpam-2382	98	9	2015	2015	NUM
ejpam-2382	98	10	)	)	PUNCT
ejpam-2382	98	11	,	,	PUNCT
ejpam-2382	98	12	255	255	NUM
ejpam-2382	98	13	-	-	SYM
ejpam-2382	98	14	270	270	NUM
ejpam-2382	98	15	260	260	NUM
ejpam-2382	98	16	x	x	SYM
ejpam-2382	98	17	(	(	PUNCT
ejpam-2382	98	18	5	5	NUM
ejpam-2382	98	19	)	)	PUNCT
ejpam-2382	98	20	=(	=(	NOUN
ejpam-2382	98	21	v(4	v(4	NOUN
ejpam-2382	98	22	)	)	PUNCT
ejpam-2382	99	1	−	−	PROPN
ejpam-2382	99	2	15vv̇2k2	15vv̇2k2	NUM
ejpam-2382	99	3	1	1	NUM
ejpam-2382	99	4	−	−	PROPN
ejpam-2382	99	5	10v2	10v2	NUM
ejpam-2382	99	6	v̈k2	v̈k2	PROPN
ejpam-2382	99	7	1	1	NUM
ejpam-2382	99	8	−	−	PROPN
ejpam-2382	99	9	26v2	26v2	NUM
ejpam-2382	99	10	v̇k1k̇1	v̇k1k̇1	NOUN
ejpam-2382	99	11	−	−	PROPN
ejpam-2382	99	12	3v3k̇2	3v3k̇2	NUM
ejpam-2382	99	13	1	1	NUM
ejpam-2382	99	14	−	−	PROPN
ejpam-2382	99	15	4v3k1k̈1	4v3k1k̈1	PROPN
ejpam-2382	99	16	+	+	CCONJ
ejpam-2382	99	17	v5k4	v5k4	X
ejpam-2382	99	18	1	1	NUM
ejpam-2382	99	19	+	+	CCONJ
ejpam-2382	99	20	v5k2	v5k2	PROPN
ejpam-2382	99	21	1k2	1k2	NUM
ejpam-2382	99	22	2)v1	2)v1	NUM
ejpam-2382	99	23	+	+	CCONJ
ejpam-2382	99	24	(	(	PUNCT
ejpam-2382	99	25	5	5	NUM
ejpam-2382	99	26	...	...	SYM
ejpam-2382	99	27	v	v	X
ejpam-2382	99	28	vk1	vk1	NOUN
ejpam-2382	99	29	−	−	PROPN
ejpam-2382	99	30	10v3	10v3	NUM
ejpam-2382	99	31	v̇k3	v̇k3	ADP
ejpam-2382	99	32	1	1	NUM
ejpam-2382	99	33	−	−	NOUN
ejpam-2382	99	34	6v4k2	6v4k2	NUM
ejpam-2382	99	35	1	1	NUM
ejpam-2382	99	36	k̇1	k̇1	PROPN
ejpam-2382	99	37	+	+	CCONJ
ejpam-2382	99	38	10v̇	10v̇	NUM
ejpam-2382	99	39	v̈k1	v̈k1	NOUN
ejpam-2382	99	40	+	+	CCONJ
ejpam-2382	99	41	9vv̈k̇1	9vv̈k̇1	NUM
ejpam-2382	100	1	+	+	CCONJ
ejpam-2382	100	2	8v̇2k̇1	8v̇2k̇1	PROPN
ejpam-2382	100	3	+	+	CCONJ
ejpam-2382	100	4	7vv̇k̈1	7vv̇k̈1	NUM
ejpam-2382	100	5	+	+	CCONJ
ejpam-2382	100	6	v2	v2	NOUN
ejpam-2382	100	7	...	...	PUNCT
ejpam-2382	100	8	k1	k1	NOUN
ejpam-2382	100	9	−	−	PROPN
ejpam-2382	100	10	10v3	10v3	NUM
ejpam-2382	100	11	v̇k1k2	v̇k1k2	PROPN
ejpam-2382	100	12	2	2	NUM
ejpam-2382	100	13	−	−	PROPN
ejpam-2382	100	14	3v4k̇1k2	3v4k̇1k2	NUM
ejpam-2382	100	15	2	2	NUM
ejpam-2382	100	16	−	−	PROPN
ejpam-2382	100	17	3v4k1k2k̇2)v2	3v4k1k2k̇2)v2	PROPN
ejpam-2382	100	18	+	+	CCONJ
ejpam-2382	100	19	(	(	PUNCT
ejpam-2382	100	20	10v2	10v2	NUM
ejpam-2382	100	21	v̈k1k2	v̈k1k2	NUM
ejpam-2382	100	22	−	−	PROPN
ejpam-2382	100	23	v5k3	v5k3	ADP
ejpam-2382	100	24	1k2	1k2	NUM
ejpam-2382	100	25	+	+	CCONJ
ejpam-2382	100	26	15vv̇2k1k2	15vv̇2k1k2	NUM
ejpam-2382	100	27	+	+	CCONJ
ejpam-2382	100	28	17v2	17v2	NUM
ejpam-2382	100	29	v̇	v̇	NOUN
ejpam-2382	100	30	k̇1k2	k̇1k2	NOUN
ejpam-2382	101	1	+	+	CCONJ
ejpam-2382	101	2	3v3k̈1k2	3v3k̈1k2	NUM
ejpam-2382	101	3	−	−	PROPN
ejpam-2382	101	4	v5k1k3	v5k1k3	NOUN
ejpam-2382	101	5	2	2	NUM
ejpam-2382	101	6	+	+	CCONJ
ejpam-2382	101	7	9v2	9v2	NUM
ejpam-2382	101	8	v̇k1k̇2	v̇k1k̇2	NOUN
ejpam-2382	101	9	+	+	CCONJ
ejpam-2382	101	10	3v3k̇1k̇2	3v3k̇1k̇2	NUM
ejpam-2382	101	11	+	+	CCONJ
ejpam-2382	101	12	v3k1k̈2	v3k1k̈2	PROPN
ejpam-2382	101	13	−	−	PROPN
ejpam-2382	101	14	v5k1k2k2	v5k1k2k2	PROPN
ejpam-2382	101	15	3)v3	3)v3	PROPN
ejpam-2382	101	16	+	+	CCONJ
ejpam-2382	101	17	(	(	PUNCT
ejpam-2382	101	18	10v3	10v3	NUM
ejpam-2382	101	19	v̇k1k2k3	v̇k1k2k3	PROPN
ejpam-2382	101	20	+	+	CCONJ
ejpam-2382	101	21	3v4k̇1k2k3	3v4k̇1k2k3	NUM
ejpam-2382	101	22	+	+	CCONJ
ejpam-2382	101	23	2v4k1k̇2k3	2v4k1k̇2k3	PROPN
ejpam-2382	101	24	+	+	NUM
ejpam-2382	101	25	v4k1k2k̇3)v4	v4k1k2k̇3)v4	NOUN
ejpam-2382	101	26	+	+	CCONJ
ejpam-2382	101	27	(	(	PUNCT
ejpam-2382	101	28	v5k1k2k3k4)v5	v5k1k2k3k4)v5	X
ejpam-2382	101	29	(	(	PUNCT
ejpam-2382	101	30	6	6	NUM
ejpam-2382	101	31	)	)	PUNCT
ejpam-2382	101	32	where	where	SCONJ
ejpam-2382	101	33	"	"	PUNCT
ejpam-2382	101	34	·	·	PUNCT
ejpam-2382	101	35	"	"	PUNCT
ejpam-2382	101	36	denotes	denote	VERB
ejpam-2382	101	37	the	the	DET
ejpam-2382	101	38	derivative	derivative	NOUN
ejpam-2382	101	39	with	with	ADP
ejpam-2382	101	40	respect	respect	NOUN
ejpam-2382	101	41	to	to	ADP
ejpam-2382	101	42	t.	t.	NOUN
ejpam-2382	101	43	from	from	ADP
ejpam-2382	101	44	the	the	DET
ejpam-2382	101	45	equation	equation	NOUN
ejpam-2382	101	46	(	(	PUNCT
ejpam-2382	101	47	2	2	NUM
ejpam-2382	101	48	)	)	PUNCT
ejpam-2382	101	49	,	,	PUNCT
ejpam-2382	101	50	we	we	PRON
ejpam-2382	101	51	find	find	VERB
ejpam-2382	101	52	v	v	NOUN
ejpam-2382	101	53	=	=	SYM
ejpam-2382	101	54	ẋ	ẋ	PROPN
ejpam-2382	101	55	(	(	PUNCT
ejpam-2382	101	56	7	7	NUM
ejpam-2382	101	57	)	)	PUNCT
ejpam-2382	101	58	and	and	CCONJ
ejpam-2382	101	59	v1	v1	PROPN
ejpam-2382	101	60	=	=	SYM
ejpam-2382	101	61	ẋ	ẋ	PROPN
ejpam-2382	101	62	ẋ	ẋ	PROPN
ejpam-2382	101	63	.	.	PUNCT
ejpam-2382	102	1	(	(	PUNCT
ejpam-2382	102	2	8)	8)	NUM
ejpam-2382	102	3	since	since	SCONJ
ejpam-2382	102	4	v2	v2	PROPN
ejpam-2382	102	5	=	=	SYM
ejpam-2382	102	6	ẋ	ẋ	PROPN
ejpam-2382	102	7	,	,	PUNCT
ejpam-2382	102	8	ẋ	ẋ	PROPN
ejpam-2382	102	9	�	�	PROPN
ejpam-2382	102	10	,	,	PUNCT
ejpam-2382	102	11	if	if	SCONJ
ejpam-2382	102	12	the	the	DET
ejpam-2382	102	13	derivative	derivative	NOUN
ejpam-2382	102	14	of	of	ADP
ejpam-2382	102	15	this	this	DET
ejpam-2382	102	16	term	term	NOUN
ejpam-2382	102	17	is	be	AUX
ejpam-2382	102	18	taken	take	VERB
ejpam-2382	102	19	consecutively	consecutively	ADV
ejpam-2382	102	20	,	,	PUNCT
ejpam-2382	102	21	we	we	PRON
ejpam-2382	102	22	have	have	VERB
ejpam-2382	102	23	v̇	v̇	NOUN
ejpam-2382	102	24	=	=	SYM
ejpam-2382	102	25	ẋ	ẋ	PROPN
ejpam-2382	102	26	,	,	PUNCT
ejpam-2382	102	27	ẍ	ẍ	PROPN
ejpam-2382	102	28	�	�	PROPN
ejpam-2382	102	29	ẋ	ẋ	PROPN
ejpam-2382	102	30	(	(	PUNCT
ejpam-2382	102	31	9	9	NUM
ejpam-2382	102	32	)	)	PUNCT
ejpam-2382	102	33	and	and	CCONJ
ejpam-2382	102	34	v̈	v̈	X
ejpam-2382	103	1	=	=	PUNCT
ejpam-2382	103	2	ẍ	ẍ	PROPN
ejpam-2382	103	3	2	2	NUM
ejpam-2382	103	4	ẋ	ẋ	PROPN
ejpam-2382	103	5	2	2	NUM
ejpam-2382	103	6	+	+	CCONJ
ejpam-2382	103	7	ẋ	ẋ	PROPN
ejpam-2382	103	8	,	,	PUNCT
ejpam-2382	103	9	...	...	PUNCT
ejpam-2382	104	1	x	x	X
ejpam-2382	104	2	�	�	PROPN
ejpam-2382	104	3	ẋ	ẋ	PROPN
ejpam-2382	104	4	2	2	NUM
ejpam-2382	104	5	−	−	PROPN
ejpam-2382	104	6	ẋ	ẋ	PROPN
ejpam-2382	104	7	,	,	PUNCT
ejpam-2382	104	8	ẍ	ẍ	PROPN
ejpam-2382	104	9	�	�	PROPN
ejpam-2382	104	10	2	2	NUM
ejpam-2382	104	11	ẋ	ẋ	PROPN
ejpam-2382	104	12	3	3	NUM
ejpam-2382	104	13	(	(	PUNCT
ejpam-2382	104	14	10	10	NUM
ejpam-2382	104	15	)	)	PUNCT
ejpam-2382	104	16	if	if	SCONJ
ejpam-2382	104	17	the	the	DET
ejpam-2382	104	18	first	first	ADJ
ejpam-2382	104	19	curvature	curvature	NOUN
ejpam-2382	104	20	is	be	AUX
ejpam-2382	104	21	calculated	calculate	VERB
ejpam-2382	104	22	from	from	ADP
ejpam-2382	104	23	the	the	DET
ejpam-2382	104	24	equation	equation	NOUN
ejpam-2382	104	25	(	(	PUNCT
ejpam-2382	104	26	3	3	NUM
ejpam-2382	104	27	)	)	PUNCT
ejpam-2382	104	28	,	,	PUNCT
ejpam-2382	104	29	the	the	DET
ejpam-2382	104	30	following	follow	VERB
ejpam-2382	104	31	equations	equation	NOUN
ejpam-2382	104	32	are	be	AUX
ejpam-2382	104	33	obtained	obtain	VERB
ejpam-2382	104	34	k1	k1	PROPN
ejpam-2382	104	35	=	=	SYM
ejpam-2382	104	36	ẋ	ẋ	PROPN
ejpam-2382	104	37	2	2	NUM
ejpam-2382	104	38	ẍ	ẍ	NOUN
ejpam-2382	105	1	−	−	PROPN
ejpam-2382	106	1	〈	〈	PROPN
ejpam-2382	106	2	ẋ	ẋ	PROPN
ejpam-2382	106	3	,	,	PUNCT
ejpam-2382	106	4	ẍ	ẍ	PROPN
ejpam-2382	106	5	〉	〉	PROPN
ejpam-2382	106	6	ẋ	ẋ	PROPN
ejpam-2382	106	7	ẋ	ẋ	PROPN
ejpam-2382	106	8	4	4	NUM
ejpam-2382	106	9	(	(	PUNCT
ejpam-2382	106	10	11	11	NUM
ejpam-2382	106	11	)	)	PUNCT
ejpam-2382	106	12	and	and	CCONJ
ejpam-2382	106	13	k2	k2	PROPN
ejpam-2382	106	14	1	1	NUM
ejpam-2382	106	15	=	=	SYM
ejpam-2382	106	16	ẍ	ẍ	PROPN
ejpam-2382	106	17	2	2	NUM
ejpam-2382	106	18	ẋ	ẋ	PROPN
ejpam-2382	106	19	2	2	NUM
ejpam-2382	106	20	−	−	NOUN
ejpam-2382	106	21	〈	〈	PROPN
ejpam-2382	106	22	ẋ	ẋ	PROPN
ejpam-2382	106	23	,	,	PUNCT
ejpam-2382	106	24	ẍ	ẍ	PROPN
ejpam-2382	106	25	〉	〉	PROPN
ejpam-2382	106	26	2	2	NUM
ejpam-2382	106	27	ẋ	ẋ	PROPN
ejpam-2382	106	28	6	6	NUM
ejpam-2382	106	29	(	(	PUNCT
ejpam-2382	106	30	12	12	NUM
ejpam-2382	106	31	)	)	PUNCT
ejpam-2382	106	32	if	if	SCONJ
ejpam-2382	106	33	we	we	PRON
ejpam-2382	106	34	take	take	VERB
ejpam-2382	106	35	the	the	DET
ejpam-2382	106	36	derivative	derivative	NOUN
ejpam-2382	106	37	of	of	ADP
ejpam-2382	106	38	both	both	DET
ejpam-2382	106	39	sides	side	NOUN
ejpam-2382	106	40	of	of	ADP
ejpam-2382	106	41	the	the	DET
ejpam-2382	106	42	equation	equation	NOUN
ejpam-2382	106	43	(	(	PUNCT
ejpam-2382	106	44	11	11	NUM
ejpam-2382	106	45	)	)	PUNCT
ejpam-2382	106	46	with	with	ADP
ejpam-2382	106	47	respect	respect	NOUN
ejpam-2382	106	48	to	to	ADP
ejpam-2382	106	49	t	t	PROPN
ejpam-2382	106	50	,	,	PUNCT
ejpam-2382	106	51	we	we	PRON
ejpam-2382	106	52	get	get	VERB
ejpam-2382	106	53	k̇1	k̇1	PROPN
ejpam-2382	106	54	=	=	SYM
ejpam-2382	106	55	ẋ	ẋ	PROPN
ejpam-2382	106	56	4	4	NUM
ejpam-2382	106	57	〈	〈	PROPN
ejpam-2382	106	58	ẍ	ẍ	PROPN
ejpam-2382	106	59	,	,	PUNCT
ejpam-2382	106	60	...	...	PUNCT
ejpam-2382	107	1	x	x	PUNCT
ejpam-2382	107	2	〉	〉	NOUN
ejpam-2382	107	3	+	+	X
ejpam-2382	107	4	3〈ẋ	3〈ẋ	NUM
ejpam-2382	107	5	,	,	PUNCT
ejpam-2382	107	6	ẍ	ẍ	X
ejpam-2382	107	7	〉	〉	PROPN
ejpam-2382	107	8	3	3	NUM
ejpam-2382	107	9	−	−	PROPN
ejpam-2382	107	10	ẋ	ẋ	PROPN
ejpam-2382	107	11	2	2	NUM
ejpam-2382	107	12	〈	〈	PROPN
ejpam-2382	107	13	ẋ	ẋ	PROPN
ejpam-2382	107	14	,	,	PUNCT
ejpam-2382	107	15	ẍ	ẍ	PROPN
ejpam-2382	107	16	〉	〉	PROPN
ejpam-2382	107	17	〈	〈	PROPN
ejpam-2382	107	18	ẋ	ẋ	PROPN
ejpam-2382	107	19	,	,	PUNCT
ejpam-2382	107	20	...	...	PUNCT
ejpam-2382	108	1	x	x	X
ejpam-2382	108	2	〉	〉	NOUN
ejpam-2382	108	3	−	−	PROPN
ejpam-2382	108	4	3	3	NUM
ejpam-2382	108	5	ẋ	ẋ	PROPN
ejpam-2382	108	6	2	2	NUM
ejpam-2382	108	7	ẍ	ẍ	NOUN
ejpam-2382	108	8	2	2	NUM
ejpam-2382	108	9	〈	〈	PROPN
ejpam-2382	108	10	ẋ	ẋ	PROPN
ejpam-2382	108	11	,	,	PUNCT
ejpam-2382	108	12	ẍ	ẍ	PROPN
ejpam-2382	108	13	〉	〉	NOUN
ejpam-2382	108	14	ẋ	ẋ	PROPN
ejpam-2382	108	15	4	4	NUM
ejpam-2382	108	16	ẋ	ẋ	NOUN
ejpam-2382	108	17	2	2	NUM
ejpam-2382	108	18	ẍ	ẍ	NOUN
ejpam-2382	108	19	−	−	PROPN
ejpam-2382	109	1	〈	〈	PROPN
ejpam-2382	109	2	ẋ	ẋ	PROPN
ejpam-2382	109	3	,	,	PUNCT
ejpam-2382	109	4	ẍ	ẍ	PROPN
ejpam-2382	109	5	〉	〉	PROPN
ejpam-2382	109	6	ẋ	ẋ	PROPN
ejpam-2382	109	7	(	(	PUNCT
ejpam-2382	109	8	13	13	NUM
ejpam-2382	109	9	)	)	PUNCT
ejpam-2382	109	10	in	in	ADP
ejpam-2382	109	11	addition	addition	NOUN
ejpam-2382	109	12	to	to	ADP
ejpam-2382	109	13	this	this	PRON
ejpam-2382	109	14	,	,	PUNCT
ejpam-2382	109	15	the	the	DET
ejpam-2382	109	16	second	second	ADJ
ejpam-2382	109	17	frenet	frenet	NOUN
ejpam-2382	109	18	vector	vector	NOUN
ejpam-2382	109	19	from	from	ADP
ejpam-2382	109	20	the	the	DET
ejpam-2382	109	21	equation	equation	NOUN
ejpam-2382	109	22	(	(	PUNCT
ejpam-2382	109	23	3	3	X
ejpam-2382	109	24	)	)	PUNCT
ejpam-2382	109	25	is	be	AUX
ejpam-2382	109	26	v2	v2	PROPN
ejpam-2382	109	27	=	=	PUNCT
ejpam-2382	109	28	ẍ	ẍ	PROPN
ejpam-2382	109	29	ẋ	ẋ	PROPN
ejpam-2382	110	1	2	2	NUM
ejpam-2382	110	2	−	−	DET
ejpam-2382	110	3	〈	〈	PROPN
ejpam-2382	110	4	ẋ	ẋ	PROPN
ejpam-2382	110	5	,	,	PUNCT
ejpam-2382	110	6	ẍ	ẍ	PROPN
ejpam-2382	110	7	〉	〉	PROPN
ejpam-2382	110	8	ẋ	ẋ	PROPN
ejpam-2382	110	9	ẋ	ẋ	PROPN
ejpam-2382	110	10	2	2	NUM
ejpam-2382	110	11	ẍ	ẍ	NOUN
ejpam-2382	110	12	−	−	PROPN
ejpam-2382	111	1	〈	〈	PROPN
ejpam-2382	111	2	ẋ	ẋ	PROPN
ejpam-2382	111	3	,	,	PUNCT
ejpam-2382	111	4	ẍ	ẍ	PROPN
ejpam-2382	111	5	〉	〉	PROPN
ejpam-2382	111	6	ẋ	ẋ	PROPN
ejpam-2382	111	7	.	.	PUNCT
ejpam-2382	112	1	(	(	PUNCT
ejpam-2382	112	2	14	14	NUM
ejpam-2382	112	3	)	)	PUNCT
ejpam-2382	112	4	m.	m.	NOUN
ejpam-2382	112	5	masal	masal	NOUN
ejpam-2382	112	6	,	,	PUNCT
ejpam-2382	112	7	a.	a.	PROPN
ejpam-2382	112	8	azak	azak	PROPN
ejpam-2382	112	9	/	/	SYM
ejpam-2382	112	10	eur	eur	PROPN
ejpam-2382	112	11	.	.	PUNCT
ejpam-2382	113	1	j.	j.	PROPN
ejpam-2382	113	2	pure	pure	PROPN
ejpam-2382	113	3	appl	appl	PROPN
ejpam-2382	113	4	.	.	PROPN
ejpam-2382	113	5	math	math	PROPN
ejpam-2382	113	6	,	,	PUNCT
ejpam-2382	113	7	8	8	NUM
ejpam-2382	113	8	(	(	PUNCT
ejpam-2382	113	9	2015	2015	NUM
ejpam-2382	113	10	)	)	PUNCT
ejpam-2382	113	11	,	,	PUNCT
ejpam-2382	113	12	255	255	NUM
ejpam-2382	113	13	-	-	SYM
ejpam-2382	113	14	270	270	NUM
ejpam-2382	113	15	261	261	NUM
ejpam-2382	113	16	by	by	ADP
ejpam-2382	113	17	using	use	VERB
ejpam-2382	113	18	the	the	DET
ejpam-2382	113	19	equation	equation	NOUN
ejpam-2382	113	20	(	(	PUNCT
ejpam-2382	113	21	4	4	NUM
ejpam-2382	113	22	)	)	PUNCT
ejpam-2382	113	23	,	,	PUNCT
ejpam-2382	113	24	we	we	PRON
ejpam-2382	113	25	can	can	AUX
ejpam-2382	113	26	write	write	VERB
ejpam-2382	113	27	〈	〈	PROPN
ejpam-2382	113	28	...	...	PUNCT
ejpam-2382	113	29	x	x	X
ejpam-2382	113	30	,	,	PUNCT
ejpam-2382	113	31	v3〉=	v3〉=	PROPN
ejpam-2382	113	32	v3k1k2	v3k1k2	PROPN
ejpam-2382	113	33	.	.	PUNCT
ejpam-2382	114	1	substituting	substitute	VERB
ejpam-2382	114	2	the	the	DET
ejpam-2382	114	3	equations	equation	NOUN
ejpam-2382	114	4	(	(	PUNCT
ejpam-2382	114	5	7	7	NUM
ejpam-2382	114	6	)	)	PUNCT
ejpam-2382	114	7	and	and	CCONJ
ejpam-2382	114	8	(	(	PUNCT
ejpam-2382	114	9	11	11	NUM
ejpam-2382	114	10	)	)	PUNCT
ejpam-2382	114	11	in	in	ADP
ejpam-2382	114	12	the	the	DET
ejpam-2382	114	13	above	above	ADJ
ejpam-2382	114	14	equation	equation	NOUN
ejpam-2382	114	15	,	,	PUNCT
ejpam-2382	114	16	we	we	PRON
ejpam-2382	114	17	obtain	obtain	VERB
ejpam-2382	114	18	the	the	DET
ejpam-2382	114	19	second	second	ADJ
ejpam-2382	114	20	curvature	curvature	NOUN
ejpam-2382	114	21	k2	k2	PROPN
ejpam-2382	114	22	as	as	SCONJ
ejpam-2382	114	23	follows	follow	VERB
ejpam-2382	114	24	k2	k2	PROPN
ejpam-2382	114	25	=	=	SYM
ejpam-2382	114	26	〈	〈	PROPN
ejpam-2382	114	27	...	...	PUNCT
ejpam-2382	114	28	x	x	X
ejpam-2382	114	29	,	,	PUNCT
ejpam-2382	114	30	v3	v3	PROPN
ejpam-2382	114	31	〉	〉	NOUN
ejpam-2382	114	32	ẋ	ẋ	PROPN
ejpam-2382	115	1	ẋ	ẋ	PROPN
ejpam-2382	115	2	2	2	NUM
ejpam-2382	116	1	ẍ	ẍ	NOUN
ejpam-2382	116	2	−	−	PROPN
ejpam-2382	117	1	〈	〈	PROPN
ejpam-2382	117	2	ẋ	ẋ	PROPN
ejpam-2382	117	3	,	,	PUNCT
ejpam-2382	117	4	ẍ	ẍ	PROPN
ejpam-2382	117	5	〉	〉	PROPN
ejpam-2382	117	6	ẋ	ẋ	PROPN
ejpam-2382	117	7	.	.	PUNCT
ejpam-2382	118	1	(	(	PUNCT
ejpam-2382	118	2	15	15	NUM
ejpam-2382	118	3	)	)	PUNCT
ejpam-2382	118	4	again	again	ADV
ejpam-2382	118	5	,	,	PUNCT
ejpam-2382	118	6	considering	consider	VERB
ejpam-2382	118	7	the	the	DET
ejpam-2382	118	8	equation	equation	NOUN
ejpam-2382	118	9	(	(	PUNCT
ejpam-2382	118	10	4	4	NUM
ejpam-2382	118	11	)	)	PUNCT
ejpam-2382	118	12	,	,	PUNCT
ejpam-2382	118	13	the	the	DET
ejpam-2382	118	14	third	third	ADJ
ejpam-2382	118	15	frenet	frenet	NOUN
ejpam-2382	118	16	vector	vector	NOUN
ejpam-2382	118	17	v3	v3	PROPN
ejpam-2382	118	18	of	of	ADP
ejpam-2382	118	19	x	x	PROPN
ejpam-2382	118	20	is	be	AUX
ejpam-2382	118	21	given	give	VERB
ejpam-2382	118	22	by	by	ADP
ejpam-2382	118	23	v3	v3	PROPN
ejpam-2382	118	24	=	=	PUNCT
ejpam-2382	118	25	...	...	PUNCT
ejpam-2382	119	1	x	x	X
ejpam-2382	119	2	−	−	NOUN
ejpam-2382	119	3	av1	av1	NOUN
ejpam-2382	119	4	−	−	PROPN
ejpam-2382	119	5	bv2	bv2	NOUN
ejpam-2382	119	6	...	...	PUNCT
ejpam-2382	120	1	x	x	X
ejpam-2382	120	2	−	−	NOUN
ejpam-2382	120	3	av1	av1	NOUN
ejpam-2382	120	4	−	−	NOUN
ejpam-2382	120	5	bv2	bv2	NOUN
ejpam-2382	120	6	such	such	ADJ
ejpam-2382	120	7	that	that	SCONJ
ejpam-2382	120	8	a	a	DET
ejpam-2382	120	9	=	=	NOUN
ejpam-2382	120	10	v̈	v̈	NOUN
ejpam-2382	120	11	−	−	ADJ
ejpam-2382	120	12	v3k2	v3k2	NOUN
ejpam-2382	120	13	1	1	NUM
ejpam-2382	120	14	b	b	X
ejpam-2382	120	15	=	=	SYM
ejpam-2382	120	16	3vv̇k1	3vv̇k1	PROPN
ejpam-2382	120	17	+	+	X
ejpam-2382	120	18	v2k̇1	v2k̇1	PROPN
ejpam-2382	120	19	.	.	PUNCT
ejpam-2382	121	1	(	(	PUNCT
ejpam-2382	121	2	16	16	NUM
ejpam-2382	121	3	)	)	PUNCT
ejpam-2382	121	4	substituting	substitute	VERB
ejpam-2382	121	5	the	the	DET
ejpam-2382	121	6	equations	equation	NOUN
ejpam-2382	121	7	(	(	PUNCT
ejpam-2382	121	8	7	7	NUM
ejpam-2382	121	9	)	)	PUNCT
ejpam-2382	121	10	,	,	PUNCT
ejpam-2382	121	11	(	(	PUNCT
ejpam-2382	121	12	9	9	NUM
ejpam-2382	121	13	)	)	PUNCT
ejpam-2382	121	14	,	,	PUNCT
ejpam-2382	121	15	(	(	PUNCT
ejpam-2382	121	16	10	10	NUM
ejpam-2382	121	17	)	)	PUNCT
ejpam-2382	121	18	,	,	PUNCT
ejpam-2382	121	19	(	(	PUNCT
ejpam-2382	121	20	11	11	NUM
ejpam-2382	121	21	)	)	PUNCT
ejpam-2382	121	22	and	and	CCONJ
ejpam-2382	121	23	(	(	PUNCT
ejpam-2382	121	24	13	13	NUM
ejpam-2382	121	25	)	)	PUNCT
ejpam-2382	121	26	in	in	ADP
ejpam-2382	121	27	the	the	DET
ejpam-2382	121	28	equation	equation	NOUN
ejpam-2382	121	29	(	(	PUNCT
ejpam-2382	121	30	16	16	NUM
ejpam-2382	121	31	)	)	PUNCT
ejpam-2382	121	32	,	,	PUNCT
ejpam-2382	121	33	we	we	PRON
ejpam-2382	121	34	have	have	VERB
ejpam-2382	121	35	a	a	DET
ejpam-2382	121	36	=	=	SYM
ejpam-2382	121	37	〈	〈	PROPN
ejpam-2382	121	38	ẋ	ẋ	PROPN
ejpam-2382	121	39	,	,	PUNCT
ejpam-2382	121	40	...	...	PUNCT
ejpam-2382	122	1	x	x	X
ejpam-2382	122	2	〉	〉	NOUN
ejpam-2382	122	3	ẋ	ẋ	PROPN
ejpam-2382	122	4	.	.	PUNCT
ejpam-2382	123	1	and	and	CCONJ
ejpam-2382	123	2	b	b	X
ejpam-2382	123	3	=	=	SYM
ejpam-2382	123	4	ẋ	ẋ	PROPN
ejpam-2382	123	5	2	2	NUM
ejpam-2382	123	6	〈	〈	PROPN
ejpam-2382	123	7	ẍ	ẍ	PROPN
ejpam-2382	123	8	,	,	PUNCT
ejpam-2382	123	9	...	...	PUNCT
ejpam-2382	124	1	x	x	PUNCT
ejpam-2382	124	2	〉	〉	NOUN
ejpam-2382	124	3	−	−	NOUN
ejpam-2382	124	4	〈	〈	PROPN
ejpam-2382	124	5	ẋ	ẋ	PROPN
ejpam-2382	124	6	,	,	PUNCT
ejpam-2382	124	7	ẍ	ẍ	PROPN
ejpam-2382	124	8	〉	〉	PROPN
ejpam-2382	124	9	〈	〈	PROPN
ejpam-2382	124	10	ẋ	ẋ	PROPN
ejpam-2382	124	11	,	,	PUNCT
ejpam-2382	124	12	...	...	PUNCT
ejpam-2382	124	13	x	x	X
ejpam-2382	124	14	〉	〉	NOUN
ejpam-2382	124	15	ẋ	ẋ	PROPN
ejpam-2382	124	16	2	2	NUM
ejpam-2382	124	17	ẍ	ẍ	NOUN
ejpam-2382	124	18	−	−	PROPN
ejpam-2382	125	1	〈	〈	PROPN
ejpam-2382	125	2	ẋ	ẋ	PROPN
ejpam-2382	125	3	,	,	PUNCT
ejpam-2382	125	4	ẍ	ẍ	PROPN
ejpam-2382	125	5	〉	〉	PROPN
ejpam-2382	125	6	ẋ	ẋ	PROPN
ejpam-2382	125	7	.	.	PUNCT
ejpam-2382	126	1	now	now	ADV
ejpam-2382	126	2	,	,	PUNCT
ejpam-2382	126	3	we	we	PRON
ejpam-2382	126	4	can	can	AUX
ejpam-2382	126	5	compute	compute	VERB
ejpam-2382	126	6	the	the	DET
ejpam-2382	126	7	vector	vector	NOUN
ejpam-2382	126	8	form	form	NOUN
ejpam-2382	126	9	v1	v1	NOUN
ejpam-2382	126	10	∧	∧	PROPN
ejpam-2382	126	11	v2	v2	PROPN
ejpam-2382	126	12	∧	∧	NOUN
ejpam-2382	126	13	...	...	PUNCT
ejpam-2382	127	1	x	x	PUNCT
ejpam-2382	127	2	∧	∧	NOUN
ejpam-2382	127	3	x	x	SYM
ejpam-2382	127	4	(	(	PUNCT
ejpam-2382	127	5	4	4	NUM
ejpam-2382	127	6	)	)	PUNCT
ejpam-2382	127	7	as	as	ADP
ejpam-2382	127	8	the	the	DET
ejpam-2382	127	9	follows	follow	NOUN
ejpam-2382	127	10	;	;	PUNCT
ejpam-2382	127	11	v1	v1	VERB
ejpam-2382	127	12	∧	∧	PROPN
ejpam-2382	127	13	v2	v2	PROPN
ejpam-2382	127	14	∧	∧	NOUN
ejpam-2382	127	15	...	...	PUNCT
ejpam-2382	128	1	x	x	PUNCT
ejpam-2382	128	2	∧	∧	NOUN
ejpam-2382	128	3	x	x	SYM
ejpam-2382	128	4	(	(	PUNCT
ejpam-2382	128	5	4	4	NUM
ejpam-2382	128	6	)	)	PUNCT
ejpam-2382	128	7	=	=	NOUN
ejpam-2382	129	1	v7k2	v7k2	ADP
ejpam-2382	129	2	1k2	1k2	NUM
ejpam-2382	129	3	2k3v5	2k3v5	NUM
ejpam-2382	129	4	.	.	PUNCT
ejpam-2382	130	1	(	(	PUNCT
ejpam-2382	130	2	17	17	NUM
ejpam-2382	130	3	)	)	PUNCT
ejpam-2382	130	4	then	then	ADV
ejpam-2382	130	5	from	from	ADP
ejpam-2382	130	6	the	the	DET
ejpam-2382	130	7	above	above	ADJ
ejpam-2382	130	8	equation	equation	NOUN
ejpam-2382	130	9	v5	v5	PROPN
ejpam-2382	130	10	=	=	SYM
ejpam-2382	130	11	η	η	PROPN
ejpam-2382	130	12	v1	v1	PROPN
ejpam-2382	130	13	∧	∧	PROPN
ejpam-2382	130	14	v2	v2	PROPN
ejpam-2382	130	15	∧	∧	NOUN
ejpam-2382	130	16	...	...	PUNCT
ejpam-2382	131	1	x	x	PUNCT
ejpam-2382	131	2	∧	∧	NOUN
ejpam-2382	131	3	x	x	SYM
ejpam-2382	131	4	(	(	PUNCT
ejpam-2382	131	5	4	4	X
ejpam-2382	131	6	)	)	PUNCT
ejpam-2382	131	7	v1	v1	NOUN
ejpam-2382	131	8	∧	∧	NOUN
ejpam-2382	131	9	v2	v2	PROPN
ejpam-2382	131	10	∧	∧	NOUN
ejpam-2382	131	11	...	...	PUNCT
ejpam-2382	132	1	x	x	PUNCT
ejpam-2382	132	2	∧	∧	NOUN
ejpam-2382	132	3	x	x	SYM
ejpam-2382	132	4	(	(	PUNCT
ejpam-2382	132	5	4	4	NUM
ejpam-2382	132	6	)	)	PUNCT
ejpam-2382	132	7	.	.	PUNCT
ejpam-2382	133	1	(	(	PUNCT
ejpam-2382	133	2	18	18	NUM
ejpam-2382	133	3	)	)	PUNCT
ejpam-2382	133	4	and	and	CCONJ
ejpam-2382	133	5	η	η	PROPN
ejpam-2382	133	6	is	be	AUX
ejpam-2382	133	7	taken	take	VERB
ejpam-2382	133	8	±1	±1	VERB
ejpam-2382	133	9	to	to	PART
ejpam-2382	133	10	make	make	VERB
ejpam-2382	133	11	det(v1	det(v1	NOUN
ejpam-2382	133	12	,	,	PUNCT
ejpam-2382	133	13	v2	v2	PROPN
ejpam-2382	133	14	,	,	PUNCT
ejpam-2382	133	15	v3	v3	PROPN
ejpam-2382	133	16	,	,	PUNCT
ejpam-2382	133	17	v4	v4	PROPN
ejpam-2382	133	18	,	,	PUNCT
ejpam-2382	133	19	v5	v5	PROPN
ejpam-2382	133	20	)	)	PUNCT
ejpam-2382	133	21	=	=	SYM
ejpam-2382	133	22	+1	+1	PROPN
ejpam-2382	133	23	.	.	PUNCT
ejpam-2382	134	1	substituting	substitute	VERB
ejpam-2382	134	2	the	the	DET
ejpam-2382	134	3	equations	equation	NOUN
ejpam-2382	134	4	(	(	PUNCT
ejpam-2382	134	5	7	7	NUM
ejpam-2382	134	6	)	)	PUNCT
ejpam-2382	134	7	,	,	PUNCT
ejpam-2382	134	8	(	(	PUNCT
ejpam-2382	134	9	12	12	NUM
ejpam-2382	134	10	)	)	PUNCT
ejpam-2382	134	11	and	and	CCONJ
ejpam-2382	134	12	(	(	PUNCT
ejpam-2382	134	13	15	15	NUM
ejpam-2382	134	14	)	)	PUNCT
ejpam-2382	134	15	in	in	ADP
ejpam-2382	134	16	the	the	DET
ejpam-2382	134	17	equation	equation	NOUN
ejpam-2382	134	18	(	(	PUNCT
ejpam-2382	134	19	17	17	NUM
ejpam-2382	134	20	)	)	PUNCT
ejpam-2382	134	21	,	,	PUNCT
ejpam-2382	134	22	the	the	DET
ejpam-2382	134	23	third	third	ADJ
ejpam-2382	134	24	curvature	curvature	NOUN
ejpam-2382	134	25	is	be	AUX
ejpam-2382	134	26	found	find	VERB
ejpam-2382	134	27	k3	k3	ADJ
ejpam-2382	134	28	=	=	SYM
ejpam-2382	134	29	v1	v1	NOUN
ejpam-2382	134	30	∧	∧	PROPN
ejpam-2382	134	31	v2	v2	PROPN
ejpam-2382	134	32	∧	∧	NOUN
ejpam-2382	134	33	...	...	PUNCT
ejpam-2382	135	1	x	x	PUNCT
ejpam-2382	135	2	∧	∧	NOUN
ejpam-2382	135	3	x	x	SYM
ejpam-2382	135	4	(	(	PUNCT
ejpam-2382	135	5	4	4	NUM
ejpam-2382	135	6	)	)	PUNCT
ejpam-2382	135	7	〈	〈	NOUN
ejpam-2382	135	8	...	...	PUNCT
ejpam-2382	135	9	x	x	X
ejpam-2382	135	10	,	,	PUNCT
ejpam-2382	135	11	v3〉2	v3〉2	PROPN
ejpam-2382	135	12	ẋ	ẋ	PROPN
ejpam-2382	135	13	.	.	PUNCT
ejpam-2382	136	1	(	(	PUNCT
ejpam-2382	136	2	19	19	NUM
ejpam-2382	136	3	)	)	PUNCT
ejpam-2382	136	4	the	the	DET
ejpam-2382	136	5	inner	inner	ADJ
ejpam-2382	136	6	product	product	NOUN
ejpam-2382	136	7	〈	〈	NOUN
ejpam-2382	136	8	x	x	SYM
ejpam-2382	136	9	(	(	PUNCT
ejpam-2382	136	10	5	5	NUM
ejpam-2382	136	11	)	)	PUNCT
ejpam-2382	136	12	,	,	PUNCT
ejpam-2382	136	13	v5	v5	PROPN
ejpam-2382	136	14	〉	〉	NOUN
ejpam-2382	136	15	gives	give	VERB
ejpam-2382	136	16	us	we	PRON
ejpam-2382	136	17	the	the	DET
ejpam-2382	136	18	fourth	fourth	ADJ
ejpam-2382	136	19	curvature	curvature	NOUN
ejpam-2382	136	20	k4	k4	NOUN
ejpam-2382	136	21	as	as	ADP
ejpam-2382	136	22	k4	k4	NOUN
ejpam-2382	136	23	=	=	PUNCT
ejpam-2382	136	24	〈	〈	NOUN
ejpam-2382	136	25	x	x	SYM
ejpam-2382	136	26	(	(	PUNCT
ejpam-2382	136	27	5	5	NUM
ejpam-2382	136	28	)	)	PUNCT
ejpam-2382	136	29	,	,	PUNCT
ejpam-2382	136	30	v5	v5	NOUN
ejpam-2382	136	31	〉	〉	ADJ
ejpam-2382	136	32	v5k1k2k3	v5k1k2k3	NOUN
ejpam-2382	136	33	.	.	PUNCT
ejpam-2382	137	1	(	(	PUNCT
ejpam-2382	137	2	20	20	NUM
ejpam-2382	137	3	)	)	PUNCT
ejpam-2382	137	4	m.	m.	NOUN
ejpam-2382	137	5	masal	masal	NOUN
ejpam-2382	137	6	,	,	PUNCT
ejpam-2382	137	7	a.	a.	PROPN
ejpam-2382	137	8	azak	azak	PROPN
ejpam-2382	137	9	/	/	SYM
ejpam-2382	137	10	eur	eur	PROPN
ejpam-2382	137	11	.	.	PUNCT
ejpam-2382	138	1	j.	j.	PROPN
ejpam-2382	138	2	pure	pure	PROPN
ejpam-2382	138	3	appl	appl	PROPN
ejpam-2382	138	4	.	.	PROPN
ejpam-2382	138	5	math	math	PROPN
ejpam-2382	138	6	,	,	PUNCT
ejpam-2382	138	7	8	8	NUM
ejpam-2382	138	8	(	(	PUNCT
ejpam-2382	138	9	2015	2015	NUM
ejpam-2382	138	10	)	)	PUNCT
ejpam-2382	138	11	,	,	PUNCT
ejpam-2382	138	12	255	255	NUM
ejpam-2382	138	13	-	-	SYM
ejpam-2382	138	14	270	270	NUM
ejpam-2382	138	15	262	262	NUM
ejpam-2382	138	16	then	then	ADV
ejpam-2382	138	17	,	,	PUNCT
ejpam-2382	138	18	if	if	SCONJ
ejpam-2382	138	19	we	we	PRON
ejpam-2382	138	20	substitute	substitute	VERB
ejpam-2382	138	21	the	the	DET
ejpam-2382	138	22	equations	equation	NOUN
ejpam-2382	138	23	(	(	PUNCT
ejpam-2382	138	24	7	7	NUM
ejpam-2382	138	25	)	)	PUNCT
ejpam-2382	138	26	,	,	PUNCT
ejpam-2382	138	27	(	(	PUNCT
ejpam-2382	138	28	11	11	NUM
ejpam-2382	138	29	)	)	PUNCT
ejpam-2382	138	30	,	,	PUNCT
ejpam-2382	138	31	(	(	PUNCT
ejpam-2382	138	32	15	15	NUM
ejpam-2382	138	33	)	)	PUNCT
ejpam-2382	138	34	and	and	CCONJ
ejpam-2382	138	35	(	(	PUNCT
ejpam-2382	138	36	19	19	NUM
ejpam-2382	138	37	)	)	PUNCT
ejpam-2382	138	38	in	in	ADP
ejpam-2382	138	39	the	the	DET
ejpam-2382	138	40	above	above	ADJ
ejpam-2382	138	41	equation	equation	NOUN
ejpam-2382	138	42	,	,	PUNCT
ejpam-2382	138	43	we	we	PRON
ejpam-2382	138	44	immediately	immediately	ADV
ejpam-2382	138	45	arrive	arrive	VERB
ejpam-2382	138	46	to	to	ADP
ejpam-2382	138	47	k4	k4	NOUN
ejpam-2382	138	48	=	=	PUNCT
ejpam-2382	138	49	〈	〈	NOUN
ejpam-2382	138	50	x	x	SYM
ejpam-2382	138	51	(	(	PUNCT
ejpam-2382	138	52	5	5	NUM
ejpam-2382	138	53	)	)	PUNCT
ejpam-2382	138	54	,	,	PUNCT
ejpam-2382	138	55	v5	v5	PROPN
ejpam-2382	138	56	〉	〉	NOUN
ejpam-2382	138	57	〈	〈	NOUN
ejpam-2382	138	58	...	...	PUNCT
ejpam-2382	138	59	x	x	X
ejpam-2382	138	60	,	,	PUNCT
ejpam-2382	138	61	v3	v3	PROPN
ejpam-2382	138	62	〉	〉	NOUN
ejpam-2382	138	63	v1	v1	NOUN
ejpam-2382	138	64	∧	∧	PROPN
ejpam-2382	138	65	v2	v2	PROPN
ejpam-2382	138	66	∧	∧	NOUN
ejpam-2382	138	67	...	...	PUNCT
ejpam-2382	139	1	x	x	PUNCT
ejpam-2382	139	2	∧	∧	NOUN
ejpam-2382	139	3	x	x	SYM
ejpam-2382	139	4	(	(	PUNCT
ejpam-2382	139	5	4	4	NUM
ejpam-2382	139	6	)	)	PUNCT
ejpam-2382	139	7	ẋ	ẋ	PROPN
ejpam-2382	139	8	.	.	PUNCT
ejpam-2382	140	1	(	(	PUNCT
ejpam-2382	140	2	21	21	NUM
ejpam-2382	140	3	)	)	PUNCT
ejpam-2382	140	4	finally	finally	ADV
ejpam-2382	140	5	,	,	PUNCT
ejpam-2382	140	6	the	the	DET
ejpam-2382	140	7	fourth	fourth	ADJ
ejpam-2382	140	8	frenet	frenet	NOUN
ejpam-2382	140	9	vector	vector	NOUN
ejpam-2382	140	10	is	be	AUX
ejpam-2382	140	11	v3	v3	PROPN
ejpam-2382	140	12	∧	∧	PROPN
ejpam-2382	140	13	v2	v2	PROPN
ejpam-2382	140	14	∧	∧	PROPN
ejpam-2382	140	15	v1	v1	NOUN
ejpam-2382	140	16	∧	∧	NOUN
ejpam-2382	140	17	v5	v5	PROPN
ejpam-2382	140	18	=	=	SYM
ejpam-2382	140	19	v4	v4	PROPN
ejpam-2382	140	20	(	(	PUNCT
ejpam-2382	140	21	22	22	NUM
ejpam-2382	140	22	)	)	PUNCT
ejpam-2382	140	23	therefore	therefore	ADV
ejpam-2382	140	24	,	,	PUNCT
ejpam-2382	140	25	the	the	DET
ejpam-2382	140	26	following	follow	VERB
ejpam-2382	140	27	theorem	theorem	NOUN
ejpam-2382	140	28	can	can	AUX
ejpam-2382	140	29	be	be	AUX
ejpam-2382	140	30	given	give	VERB
ejpam-2382	140	31	.	.	PUNCT
ejpam-2382	141	1	theorem	theorem	NOUN
ejpam-2382	141	2	2	2	NUM
ejpam-2382	141	3	.	.	PUNCT
ejpam-2382	142	1	let	let	VERB
ejpam-2382	142	2	x	x	PRON
ejpam-2382	142	3	be	be	AUX
ejpam-2382	142	4	an	an	DET
ejpam-2382	142	5	arbitrary	arbitrary	ADJ
ejpam-2382	142	6	curve	curve	NOUN
ejpam-2382	142	7	of	of	ADP
ejpam-2382	142	8	class	class	NOUN
ejpam-2382	142	9	c5	c5	PROPN
ejpam-2382	142	10	in	in	ADP
ejpam-2382	142	11	the	the	DET
ejpam-2382	142	12	euclidean	euclidean	ADJ
ejpam-2382	142	13	5	5	NUM
ejpam-2382	142	14	-	-	PUNCT
ejpam-2382	142	15	space	space	NOUN
ejpam-2382	142	16	e5	e5	NOUN
ejpam-2382	142	17	.	.	PUNCT
ejpam-2382	143	1	in	in	ADP
ejpam-2382	143	2	this	this	DET
ejpam-2382	143	3	regard	regard	NOUN
ejpam-2382	143	4	,	,	PUNCT
ejpam-2382	143	5	the	the	DET
ejpam-2382	143	6	frenet	frenet	ADJ
ejpam-2382	143	7	vectors	vector	NOUN
ejpam-2382	143	8	and	and	CCONJ
ejpam-2382	143	9	curvatures	curvature	NOUN
ejpam-2382	143	10	of	of	ADP
ejpam-2382	143	11	the	the	DET
ejpam-2382	143	12	curve	curve	NOUN
ejpam-2382	143	13	x	x	PUNCT
ejpam-2382	143	14	are	be	AUX
ejpam-2382	143	15	v1	v1	PROPN
ejpam-2382	143	16	=	=	SYM
ejpam-2382	143	17	ẋ	ẋ	PROPN
ejpam-2382	144	1	ẋ	ẋ	PROPN
ejpam-2382	144	2	,	,	PUNCT
ejpam-2382	145	1	v2	v2	PROPN
ejpam-2382	145	2	=	=	PUNCT
ejpam-2382	145	3	ẍ	ẍ	X
ejpam-2382	145	4	ẋ	ẋ	PROPN
ejpam-2382	145	5	2	2	NUM
ejpam-2382	145	6	−	−	PROPN
ejpam-2382	145	7	ẋ	ẋ	PROPN
ejpam-2382	146	1	ẋ	ẋ	PROPN
ejpam-2382	146	2	,	,	PUNCT
ejpam-2382	146	3	ẍ	ẍ	PROPN
ejpam-2382	146	4	�	�	PROPN
ejpam-2382	146	5	ẋ	ẋ	PROPN
ejpam-2382	146	6	2	2	NUM
ejpam-2382	146	7	ẍ	ẍ	NOUN
ejpam-2382	147	1	−	−	PROPN
ejpam-2382	147	2	ẋ	ẋ	PROPN
ejpam-2382	148	1	ẋ	ẋ	PROPN
ejpam-2382	148	2	,	,	PUNCT
ejpam-2382	148	3	ẍ	ẍ	PROPN
ejpam-2382	148	4	�	�	PROPN
ejpam-2382	148	5	,	,	PUNCT
ejpam-2382	148	6	v3	v3	PROPN
ejpam-2382	148	7	=	=	PUNCT
ejpam-2382	148	8	...	...	PUNCT
ejpam-2382	149	1	x	x	X
ejpam-2382	149	2	−	−	NOUN
ejpam-2382	149	3	av1	av1	NOUN
ejpam-2382	149	4	−	−	PROPN
ejpam-2382	149	5	bv2	bv2	NOUN
ejpam-2382	149	6	...	...	PUNCT
ejpam-2382	150	1	x	x	X
ejpam-2382	150	2	−	−	NOUN
ejpam-2382	150	3	av1	av1	NOUN
ejpam-2382	150	4	−	−	PROPN
ejpam-2382	150	5	bv2	bv2	NOUN
ejpam-2382	150	6	,	,	PUNCT
ejpam-2382	150	7	a	a	DET
ejpam-2382	150	8	=	=	X
ejpam-2382	150	9	ẋ	ẋ	PROPN
ejpam-2382	150	10	,	,	PUNCT
ejpam-2382	150	11	...	...	PUNCT
ejpam-2382	150	12	x	x	X
ejpam-2382	150	13	〉	〉	NOUN
ejpam-2382	150	14	ẋ	ẋ	PROPN
ejpam-2382	150	15	,	,	PUNCT
ejpam-2382	150	16	b	b	X
ejpam-2382	150	17	=	=	SYM
ejpam-2382	150	18	ẋ	ẋ	PROPN
ejpam-2382	150	19	2	2	NUM
ejpam-2382	150	20	ẍ	ẍ	NOUN
ejpam-2382	150	21	,	,	PUNCT
ejpam-2382	150	22	...	...	PUNCT
ejpam-2382	150	23	x	x	PUNCT
ejpam-2382	150	24	〉	〉	NOUN
ejpam-2382	150	25	−	−	PROPN
ejpam-2382	150	26	ẋ	ẋ	PROPN
ejpam-2382	150	27	,	,	PUNCT
ejpam-2382	150	28	ẍ	ẍ	PROPN
ejpam-2382	150	29	�	�	PROPN
ejpam-2382	150	30	ẋ	ẋ	PROPN
ejpam-2382	150	31	,	,	PUNCT
ejpam-2382	150	32	...	...	PUNCT
ejpam-2382	151	1	x	x	X
ejpam-2382	151	2	〉	〉	NOUN
ejpam-2382	151	3	ẋ	ẋ	PROPN
ejpam-2382	151	4	2	2	NUM
ejpam-2382	151	5	ẍ	ẍ	NOUN
ejpam-2382	151	6	−	−	PROPN
ejpam-2382	151	7	ẋ	ẋ	PROPN
ejpam-2382	151	8	,	,	PUNCT
ejpam-2382	151	9	ẍ	ẍ	PROPN
ejpam-2382	151	10	�	�	PROPN
ejpam-2382	151	11	ẋ	ẋ	PROPN
ejpam-2382	151	12	,	,	PUNCT
ejpam-2382	151	13	v4	v4	PROPN
ejpam-2382	151	14	=	=	SYM
ejpam-2382	151	15	ηv3	ηv3	PROPN
ejpam-2382	151	16	∧	∧	PROPN
ejpam-2382	151	17	v2	v2	NOUN
ejpam-2382	151	18	∧	∧	PROPN
ejpam-2382	151	19	v1	v1	NOUN
ejpam-2382	151	20	∧	∧	PROPN
ejpam-2382	151	21	v5	v5	NOUN
ejpam-2382	151	22	,	,	PUNCT
ejpam-2382	151	23	v5	v5	PROPN
ejpam-2382	151	24	=	=	SYM
ejpam-2382	151	25	η	η	X
ejpam-2382	151	26	v1	v1	PROPN
ejpam-2382	151	27	∧	∧	PROPN
ejpam-2382	151	28	v2	v2	PROPN
ejpam-2382	151	29	∧	∧	NOUN
ejpam-2382	151	30	...	...	PUNCT
ejpam-2382	151	31	x	x	PUNCT
ejpam-2382	152	1	∧	∧	NOUN
ejpam-2382	152	2	x	x	SYM
ejpam-2382	152	3	(	(	PUNCT
ejpam-2382	152	4	4	4	X
ejpam-2382	152	5	)	)	PUNCT
ejpam-2382	152	6	v1	v1	NOUN
ejpam-2382	152	7	∧	∧	NOUN
ejpam-2382	152	8	v2	v2	PROPN
ejpam-2382	152	9	∧	∧	NOUN
ejpam-2382	152	10	...	...	PUNCT
ejpam-2382	152	11	x	x	PUNCT
ejpam-2382	153	1	∧	∧	NOUN
ejpam-2382	153	2	x	x	SYM
ejpam-2382	153	3	(	(	PUNCT
ejpam-2382	153	4	4	4	NUM
ejpam-2382	153	5	)	)	PUNCT
ejpam-2382	153	6	,	,	PUNCT
ejpam-2382	153	7	k1	k1	NOUN
ejpam-2382	153	8	=	=	SYM
ejpam-2382	153	9	ẋ	ẋ	PROPN
ejpam-2382	153	10	2	2	NUM
ejpam-2382	153	11	ẍ	ẍ	X
ejpam-2382	153	12	−	−	PROPN
ejpam-2382	153	13	ẋ	ẋ	PROPN
ejpam-2382	153	14	,	,	PUNCT
ejpam-2382	153	15	ẍ	ẍ	PROPN
ejpam-2382	153	16	�	�	PROPN
ejpam-2382	153	17	ẋ	ẋ	PROPN
ejpam-2382	153	18	ẋ	ẋ	PROPN
ejpam-2382	153	19	4	4	NUM
ejpam-2382	153	20	,	,	PUNCT
ejpam-2382	153	21	k2	k2	NOUN
ejpam-2382	153	22	=	=	SYM
ejpam-2382	153	23	...	...	PUNCT
ejpam-2382	154	1	x	x	X
ejpam-2382	154	2	,	,	PUNCT
ejpam-2382	154	3	v3	v3	PROPN
ejpam-2382	154	4	�	�	PROPN
ejpam-2382	154	5	ẋ	ẋ	PROPN
ejpam-2382	154	6	ẋ	ẋ	PROPN
ejpam-2382	155	1	2	2	NUM
ejpam-2382	155	2	ẍ	ẍ	X
ejpam-2382	156	1	−	−	PROPN
ejpam-2382	156	2	ẋ	ẋ	PROPN
ejpam-2382	156	3	,	,	PUNCT
ejpam-2382	156	4	ẍ	ẍ	PROPN
ejpam-2382	156	5	�	�	PROPN
ejpam-2382	156	6	ẋ	ẋ	PROPN
ejpam-2382	156	7	,	,	PUNCT
ejpam-2382	156	8	k3	k3	PROPN
ejpam-2382	156	9	=	=	SYM
ejpam-2382	156	10	v1	v1	NOUN
ejpam-2382	156	11	∧	∧	PROPN
ejpam-2382	156	12	v2	v2	PROPN
ejpam-2382	156	13	∧	∧	NOUN
ejpam-2382	156	14	...	...	PUNCT
ejpam-2382	157	1	x	x	PUNCT
ejpam-2382	157	2	∧	∧	NOUN
ejpam-2382	157	3	x	x	SYM
ejpam-2382	157	4	(	(	PUNCT
ejpam-2382	157	5	4	4	NUM
ejpam-2382	157	6	)	)	PUNCT
ejpam-2382	157	7	...	...	PUNCT
ejpam-2382	158	1	x	x	X
ejpam-2382	158	2	,	,	PUNCT
ejpam-2382	158	3	v3	v3	PROPN
ejpam-2382	158	4	�	�	PROPN
ejpam-2382	158	5	ẋ	ẋ	PROPN
ejpam-2382	158	6	,	,	PUNCT
ejpam-2382	158	7	k4	k4	NOUN
ejpam-2382	158	8	=	=	PUNCT
ejpam-2382	158	9	x	x	SYM
ejpam-2382	158	10	(	(	PUNCT
ejpam-2382	158	11	5	5	NUM
ejpam-2382	158	12	)	)	PUNCT
ejpam-2382	158	13	,	,	PUNCT
ejpam-2382	158	14	v5	v5	PROPN
ejpam-2382	158	15	�	�	PROPN
ejpam-2382	158	16	...	...	PUNCT
ejpam-2382	158	17	x	x	X
ejpam-2382	158	18	,	,	PUNCT
ejpam-2382	158	19	v3	v3	PROPN
ejpam-2382	158	20	�	�	PROPN
ejpam-2382	158	21	v1	v1	PROPN
ejpam-2382	158	22	∧	∧	PROPN
ejpam-2382	158	23	v2	v2	PROPN
ejpam-2382	158	24	∧	∧	NOUN
ejpam-2382	158	25	...	...	PUNCT
ejpam-2382	158	26	x	x	PUNCT
ejpam-2382	159	1	∧	∧	NOUN
ejpam-2382	159	2	x	x	SYM
ejpam-2382	159	3	(	(	PUNCT
ejpam-2382	159	4	4	4	NUM
ejpam-2382	159	5	)	)	PUNCT
ejpam-2382	159	6	ẋ	ẋ	PROPN
ejpam-2382	159	7	,	,	PUNCT
ejpam-2382	159	8	respectively	respectively	ADV
ejpam-2382	159	9	.	.	PUNCT
ejpam-2382	160	1	5	5	X
ejpam-2382	160	2	.	.	X
ejpam-2382	160	3	involute	involute	ADJ
ejpam-2382	160	4	-	-	PUNCT
ejpam-2382	160	5	evolute	evolute	NOUN
ejpam-2382	160	6	curve	curve	NOUN
ejpam-2382	160	7	couples	couple	NOUN
ejpam-2382	160	8	in	in	ADP
ejpam-2382	160	9	the	the	DET
ejpam-2382	160	10	euclidean	euclidean	ADJ
ejpam-2382	160	11	5	5	NUM
ejpam-2382	160	12	-	-	PUNCT
ejpam-2382	160	13	space	space	NOUN
ejpam-2382	160	14	let	let	VERB
ejpam-2382	160	15	x	x	PRON
ejpam-2382	160	16	be	be	AUX
ejpam-2382	160	17	a	a	DET
ejpam-2382	160	18	w	w	NOUN
ejpam-2382	160	19	-	-	PUNCT
ejpam-2382	160	20	curve	curve	NOUN
ejpam-2382	160	21	and	and	CCONJ
ejpam-2382	160	22	y	y	PROPN
ejpam-2382	160	23	be	be	AUX
ejpam-2382	160	24	the	the	DET
ejpam-2382	160	25	involute	involute	NOUN
ejpam-2382	160	26	of	of	ADP
ejpam-2382	160	27	x	x	PUNCT
ejpam-2382	160	28	in	in	ADP
ejpam-2382	160	29	e5	e5	PROPN
ejpam-2382	160	30	.	.	PUNCT
ejpam-2382	161	1	while	while	SCONJ
ejpam-2382	161	2	the	the	DET
ejpam-2382	161	3	frenet	frenet	NOUN
ejpam-2382	161	4	apparatus	apparatus	NOUN
ejpam-2382	161	5	of	of	ADP
ejpam-2382	161	6	x	x	PROPN
ejpam-2382	161	7	is	be	AUX
ejpam-2382	161	8	�	�	PROPN
ejpam-2382	161	9	v1	v1	NOUN
ejpam-2382	161	10	,	,	PUNCT
ejpam-2382	161	11	v2	v2	PROPN
ejpam-2382	161	12	,	,	PUNCT
ejpam-2382	161	13	v3	v3	PROPN
ejpam-2382	161	14	,	,	PUNCT
ejpam-2382	161	15	v4	v4	PROPN
ejpam-2382	161	16	,	,	PUNCT
ejpam-2382	161	17	v5	v5	NOUN
ejpam-2382	161	18	,	,	PUNCT
ejpam-2382	161	19	k1	k1	NOUN
ejpam-2382	161	20	,	,	PUNCT
ejpam-2382	161	21	k2	k2	NOUN
ejpam-2382	161	22	,	,	PUNCT
ejpam-2382	161	23	k3	k3	PROPN
ejpam-2382	161	24	,	,	PUNCT
ejpam-2382	161	25	k4	k4	PROPN
ejpam-2382	161	26	,	,	PUNCT
ejpam-2382	161	27	we	we	PRON
ejpam-2382	161	28	will	will	AUX
ejpam-2382	161	29	denote	denote	VERB
ejpam-2382	161	30	the	the	DET
ejpam-2382	161	31	frenet	frenet	NOUN
ejpam-2382	161	32	apparatus	apparatus	NOUN
ejpam-2382	161	33	of	of	ADP
ejpam-2382	161	34	y	y	PROPN
ejpam-2382	161	35	with	with	ADP
ejpam-2382	161	36	m.	m.	NOUN
ejpam-2382	161	37	masal	masal	PROPN
ejpam-2382	161	38	,	,	PUNCT
ejpam-2382	161	39	a.	a.	PROPN
ejpam-2382	161	40	azak	azak	PROPN
ejpam-2382	161	41	/	/	SYM
ejpam-2382	161	42	eur	eur	PROPN
ejpam-2382	161	43	.	.	PUNCT
ejpam-2382	162	1	j.	j.	PROPN
ejpam-2382	162	2	pure	pure	PROPN
ejpam-2382	162	3	appl	appl	PROPN
ejpam-2382	162	4	.	.	PROPN
ejpam-2382	162	5	math	math	PROPN
ejpam-2382	162	6	,	,	PUNCT
ejpam-2382	162	7	8	8	NUM
ejpam-2382	162	8	(	(	PUNCT
ejpam-2382	162	9	2015	2015	NUM
ejpam-2382	162	10	)	)	PUNCT
ejpam-2382	162	11	,	,	PUNCT
ejpam-2382	162	12	255	255	NUM
ejpam-2382	162	13	-	-	SYM
ejpam-2382	162	14	270	270	NUM
ejpam-2382	162	15	263	263	NUM
ejpam-2382	162	16	�	�	PROPN
ejpam-2382	162	17	v	v	ADP
ejpam-2382	162	18	y	y	PROPN
ejpam-2382	162	19	1	1	NUM
ejpam-2382	162	20	,	,	PUNCT
ejpam-2382	162	21	v	v	NOUN
ejpam-2382	162	22	y	y	PROPN
ejpam-2382	162	23	2	2	NUM
ejpam-2382	162	24	,	,	PUNCT
ejpam-2382	162	25	v	v	NOUN
ejpam-2382	162	26	y	y	PROPN
ejpam-2382	162	27	3	3	NUM
ejpam-2382	162	28	,	,	PUNCT
ejpam-2382	162	29	v	v	NOUN
ejpam-2382	162	30	y	y	PROPN
ejpam-2382	162	31	4	4	NUM
ejpam-2382	162	32	,	,	PUNCT
ejpam-2382	162	33	v	v	NOUN
ejpam-2382	162	34	y	y	PROPN
ejpam-2382	162	35	5	5	NUM
ejpam-2382	162	36	,	,	PUNCT
ejpam-2382	162	37	ky	ky	PROPN
ejpam-2382	162	38	1	1	NUM
ejpam-2382	162	39	,	,	PUNCT
ejpam-2382	162	40	ky	ky	PROPN
ejpam-2382	162	41	2	2	NUM
ejpam-2382	162	42	,	,	PUNCT
ejpam-2382	162	43	ky	ky	PROPN
ejpam-2382	162	44	3	3	NUM
ejpam-2382	162	45	,	,	PUNCT
ejpam-2382	162	46	ky	ky	PROPN
ejpam-2382	162	47	4	4	NUM
ejpam-2382	162	48	.	.	PUNCT
ejpam-2382	163	1	so	so	ADV
ejpam-2382	163	2	,	,	PUNCT
ejpam-2382	163	3	from	from	ADP
ejpam-2382	163	4	the	the	DET
ejpam-2382	163	5	definition	definition	NOUN
ejpam-2382	163	6	of	of	ADP
ejpam-2382	163	7	involute	involute	ADJ
ejpam-2382	163	8	-	-	PUNCT
ejpam-2382	163	9	evolute	evolute	NOUN
ejpam-2382	163	10	curve	curve	NOUN
ejpam-2382	163	11	,	,	PUNCT
ejpam-2382	163	12	we	we	PRON
ejpam-2382	163	13	may	may	AUX
ejpam-2382	163	14	express	express	VERB
ejpam-2382	163	15	y	y	NOUN
ejpam-2382	163	16	=	=	PUNCT
ejpam-2382	163	17	x	x	PUNCT
ejpam-2382	164	1	+	+	ADJ
ejpam-2382	164	2	µv1	µv1	NOUN
ejpam-2382	164	3	(	(	PUNCT
ejpam-2382	164	4	23	23	NUM
ejpam-2382	164	5	)	)	PUNCT
ejpam-2382	164	6	where	where	SCONJ
ejpam-2382	164	7	s	s	PRON
ejpam-2382	164	8	and	and	CCONJ
ejpam-2382	164	9	sy	sy	PROPN
ejpam-2382	164	10	denote	denote	VERB
ejpam-2382	164	11	the	the	DET
ejpam-2382	164	12	arc	arc	NOUN
ejpam-2382	164	13	-	-	PUNCT
ejpam-2382	164	14	parameters	parameter	NOUN
ejpam-2382	164	15	of	of	ADP
ejpam-2382	164	16	the	the	DET
ejpam-2382	164	17	curves	curve	NOUN
ejpam-2382	164	18	x	x	PUNCT
ejpam-2382	164	19	and	and	CCONJ
ejpam-2382	164	20	y	y	PROPN
ejpam-2382	164	21	,	,	PUNCT
ejpam-2382	164	22	respectively	respectively	ADV
ejpam-2382	164	23	.	.	PUNCT
ejpam-2382	165	1	differentiating	differentiate	VERB
ejpam-2382	165	2	the	the	DET
ejpam-2382	165	3	both	both	DET
ejpam-2382	165	4	sides	side	NOUN
ejpam-2382	165	5	of	of	ADP
ejpam-2382	165	6	the	the	DET
ejpam-2382	165	7	equation	equation	NOUN
ejpam-2382	165	8	(	(	PUNCT
ejpam-2382	165	9	23	23	NUM
ejpam-2382	165	10	)	)	PUNCT
ejpam-2382	165	11	with	with	ADP
ejpam-2382	165	12	respect	respect	NOUN
ejpam-2382	165	13	to	to	ADP
ejpam-2382	165	14	s	s	PRON
ejpam-2382	165	15	,	,	PUNCT
ejpam-2382	165	16	one	one	PRON
ejpam-2382	165	17	can	can	AUX
ejpam-2382	165	18	obtain	obtain	VERB
ejpam-2382	165	19	dy	dy	X
ejpam-2382	165	20	dsy	dsy	PROPN
ejpam-2382	165	21	dsy	dsy	NOUN
ejpam-2382	165	22	ds	ds	PROPN
ejpam-2382	165	23	=	=	SYM
ejpam-2382	165	24	dx	dx	X
ejpam-2382	165	25	ds	ds	PROPN
ejpam-2382	165	26	+	+	CCONJ
ejpam-2382	165	27	dµ	dµ	DET
ejpam-2382	165	28	ds	ds	ADJ
ejpam-2382	165	29	v1	v1	NOUN
ejpam-2382	165	30	+	+	NOUN
ejpam-2382	165	31	µk1v2	µk1v2	X
ejpam-2382	165	32	.	.	PUNCT
ejpam-2382	166	1	(	(	PUNCT
ejpam-2382	166	2	24	24	NUM
ejpam-2382	166	3	)	)	PUNCT
ejpam-2382	166	4	since	since	SCONJ
ejpam-2382	166	5	the	the	DET
ejpam-2382	166	6	tangent	tangent	NOUN
ejpam-2382	166	7	vector	vector	NOUN
ejpam-2382	166	8	v1	v1	NOUN
ejpam-2382	166	9	of	of	ADP
ejpam-2382	166	10	the	the	DET
ejpam-2382	166	11	curve	curve	NOUN
ejpam-2382	166	12	x	x	PUNCT
ejpam-2382	166	13	orthogonal	orthogonal	ADJ
ejpam-2382	166	14	to	to	ADP
ejpam-2382	166	15	the	the	DET
ejpam-2382	166	16	tangent	tangent	NOUN
ejpam-2382	166	17	vector	vector	NOUN
ejpam-2382	166	18	v	v	PROPN
ejpam-2382	166	19	y	y	PROPN
ejpam-2382	166	20	1	1	NUM
ejpam-2382	166	21	of	of	ADP
ejpam-2382	166	22	the	the	DET
ejpam-2382	166	23	curve	curve	NOUN
ejpam-2382	166	24	y	y	PROPN
ejpam-2382	166	25	,	,	PUNCT
ejpam-2382	166	26	it	it	PRON
ejpam-2382	166	27	is	be	AUX
ejpam-2382	166	28	easily	easily	ADV
ejpam-2382	166	29	seen	see	VERB
ejpam-2382	166	30	that	that	SCONJ
ejpam-2382	166	31	1	1	NUM
ejpam-2382	166	32	+	+	NUM
ejpam-2382	166	33	dµ	dµ	ADJ
ejpam-2382	166	34	ds	ds	ADJ
ejpam-2382	166	35	=	=	NOUN
ejpam-2382	166	36	0	0	NUM
ejpam-2382	166	37	.	.	PUNCT
ejpam-2382	167	1	(	(	PUNCT
ejpam-2382	167	2	25	25	NUM
ejpam-2382	167	3	)	)	PUNCT
ejpam-2382	167	4	we	we	PRON
ejpam-2382	167	5	know	know	VERB
ejpam-2382	167	6	that	that	DET
ejpam-2382	167	7	µ=	µ=	VERB
ejpam-2382	168	1	c	c	NOUN
ejpam-2382	169	1	−	−	NOUN
ejpam-2382	169	2	s	s	VERB
ejpam-2382	169	3	from	from	ADP
ejpam-2382	169	4	the	the	DET
ejpam-2382	169	5	equation	equation	NOUN
ejpam-2382	169	6	(	(	PUNCT
ejpam-2382	169	7	25	25	NUM
ejpam-2382	169	8	)	)	PUNCT
ejpam-2382	169	9	.	.	PUNCT
ejpam-2382	170	1	so	so	ADV
ejpam-2382	170	2	,	,	PUNCT
ejpam-2382	170	3	we	we	PRON
ejpam-2382	170	4	can	can	AUX
ejpam-2382	170	5	write	write	VERB
ejpam-2382	170	6	y	y	PROPN
ejpam-2382	170	7	=	=	PUNCT
ejpam-2382	170	8	x	x	PUNCT
ejpam-2382	171	1	+	+	PUNCT
ejpam-2382	171	2	(	(	PUNCT
ejpam-2382	171	3	c	c	NOUN
ejpam-2382	171	4	−	−	NOUN
ejpam-2382	172	1	s)v1	s)v1	NOUN
ejpam-2382	172	2	(	(	PUNCT
ejpam-2382	172	3	26	26	NUM
ejpam-2382	172	4	)	)	PUNCT
ejpam-2382	172	5	and	and	CCONJ
ejpam-2382	172	6	v	v	ADP
ejpam-2382	172	7	y	y	PROPN
ejpam-2382	172	8	1	1	NUM
ejpam-2382	172	9	dsy	dsy	NOUN
ejpam-2382	172	10	ds	ds	NOUN
ejpam-2382	172	11	=	=	SYM
ejpam-2382	172	12	(	(	PUNCT
ejpam-2382	172	13	c	c	X
ejpam-2382	172	14	−	−	NOUN
ejpam-2382	172	15	s)k1v2	s)k1v2	ADJ
ejpam-2382	172	16	.	.	PUNCT
ejpam-2382	173	1	(	(	PUNCT
ejpam-2382	173	2	27	27	NUM
ejpam-2382	173	3	)	)	PUNCT
ejpam-2382	173	4	also	also	ADV
ejpam-2382	173	5	the	the	DET
ejpam-2382	173	6	equation	equation	NOUN
ejpam-2382	173	7	(	(	PUNCT
ejpam-2382	173	8	27	27	NUM
ejpam-2382	173	9	)	)	PUNCT
ejpam-2382	173	10	yields	yield	VERB
ejpam-2382	173	11	ẏ	ẏ	NOUN
ejpam-2382	173	12	=	=	SYM
ejpam-2382	173	13	(	(	PUNCT
ejpam-2382	173	14	c	c	X
ejpam-2382	173	15	−	−	NOUN
ejpam-2382	173	16	s)k1v2	s)k1v2	ADJ
ejpam-2382	173	17	.	.	PUNCT
ejpam-2382	174	1	(	(	PUNCT
ejpam-2382	174	2	28	28	NUM
ejpam-2382	174	3	)	)	PUNCT
ejpam-2382	174	4	if	if	SCONJ
ejpam-2382	174	5	we	we	PRON
ejpam-2382	174	6	take	take	VERB
ejpam-2382	174	7	the	the	DET
ejpam-2382	174	8	norm	norm	NOUN
ejpam-2382	174	9	of	of	ADP
ejpam-2382	174	10	ẏ	ẏ	PROPN
ejpam-2382	174	11	,	,	PUNCT
ejpam-2382	174	12	we	we	PRON
ejpam-2382	174	13	have	have	VERB
ejpam-2382	174	14	ẏ	ẏ	PROPN
ejpam-2382	174	15	=	=	SYM
ejpam-2382	174	16	(	(	PUNCT
ejpam-2382	174	17	c	c	NOUN
ejpam-2382	174	18	−	−	PROPN
ejpam-2382	174	19	s)k1	s)k1	PROPN
ejpam-2382	174	20	.	.	PUNCT
ejpam-2382	175	1	(	(	PUNCT
ejpam-2382	175	2	29	29	NUM
ejpam-2382	175	3	)	)	PUNCT
ejpam-2382	175	4	where	where	SCONJ
ejpam-2382	175	5	the	the	DET
ejpam-2382	175	6	subscript	subscript	NOUN
ejpam-2382	175	7	dot	dot	NOUN
ejpam-2382	175	8	"	"	PUNCT
ejpam-2382	175	9	·	·	PUNCT
ejpam-2382	175	10	"	"	PUNCT
ejpam-2382	175	11	denotes	denote	VERB
ejpam-2382	175	12	the	the	DET
ejpam-2382	175	13	derivative	derivative	NOUN
ejpam-2382	175	14	of	of	ADP
ejpam-2382	175	15	y	y	PROPN
ejpam-2382	175	16	with	with	ADP
ejpam-2382	175	17	respect	respect	NOUN
ejpam-2382	175	18	to	to	ADP
ejpam-2382	175	19	s.	s.	PROPN
ejpam-2382	175	20	moreover	moreover	PROPN
ejpam-2382	175	21	,	,	PUNCT
ejpam-2382	175	22	the	the	DET
ejpam-2382	175	23	derivatives	derivative	NOUN
ejpam-2382	175	24	of	of	ADP
ejpam-2382	175	25	the	the	DET
ejpam-2382	175	26	curve	curve	NOUN
ejpam-2382	175	27	y	y	PROPN
ejpam-2382	175	28	up	up	ADP
ejpam-2382	175	29	to	to	ADP
ejpam-2382	175	30	the	the	DET
ejpam-2382	175	31	fifth	fifth	ADJ
ejpam-2382	175	32	order	order	NOUN
ejpam-2382	175	33	are	be	AUX
ejpam-2382	175	34	given	give	VERB
ejpam-2382	175	35	by	by	ADP
ejpam-2382	175	36	ÿ	ÿ	NOUN
ejpam-2382	176	1	=	=	NOUN
ejpam-2382	176	2	−	−	PROPN
ejpam-2382	176	3	(	(	PUNCT
ejpam-2382	176	4	c	c	NOUN
ejpam-2382	176	5	−	−	PROPN
ejpam-2382	176	6	s)k2	s)k2	PROPN
ejpam-2382	176	7	1v1	1v1	NUM
ejpam-2382	176	8	−	−	PROPN
ejpam-2382	177	1	k1v2	k1v2	X
ejpam-2382	177	2	+	+	CCONJ
ejpam-2382	177	3	(	(	PUNCT
ejpam-2382	177	4	c	c	NOUN
ejpam-2382	177	5	−	−	PROPN
ejpam-2382	177	6	s)k1k2v3	s)k1k2v3	PROPN
ejpam-2382	177	7	,	,	PUNCT
ejpam-2382	177	8	(	(	PUNCT
ejpam-2382	177	9	30	30	NUM
ejpam-2382	177	10	)	)	PUNCT
ejpam-2382	177	11	...	...	PUNCT
ejpam-2382	178	1	y	y	PROPN
ejpam-2382	178	2	=	=	PROPN
ejpam-2382	178	3	2k2	2k2	NUM
ejpam-2382	178	4	1v1	1v1	NUM
ejpam-2382	178	5	−	−	PROPN
ejpam-2382	178	6	(	(	PUNCT
ejpam-2382	178	7	c	c	NOUN
ejpam-2382	178	8	−	−	NOUN
ejpam-2382	178	9	s)k1(k	s)k1(k	NOUN
ejpam-2382	178	10	2	2	NUM
ejpam-2382	178	11	1	1	NUM
ejpam-2382	178	12	+	+	CCONJ
ejpam-2382	178	13	k2	k2	ADJ
ejpam-2382	178	14	2)v2	2)v2	PROPN
ejpam-2382	178	15	−	−	NOUN
ejpam-2382	178	16	2k1k2v3	2k1k2v3	NUM
ejpam-2382	178	17	+	+	CCONJ
ejpam-2382	178	18	(	(	PUNCT
ejpam-2382	178	19	c	c	PROPN
ejpam-2382	178	20	−	−	PROPN
ejpam-2382	178	21	s)k1k2k3v4	s)k1k2k3v4	PROPN
ejpam-2382	178	22	,	,	PUNCT
ejpam-2382	178	23	(	(	PUNCT
ejpam-2382	178	24	31	31	NUM
ejpam-2382	178	25	)	)	PUNCT
ejpam-2382	178	26	y	y	NOUN
ejpam-2382	178	27	(	(	PUNCT
ejpam-2382	178	28	4	4	NUM
ejpam-2382	178	29	)	)	PUNCT
ejpam-2382	178	30	=(	=(	NOUN
ejpam-2382	178	31	c	c	NOUN
ejpam-2382	178	32	−	−	PROPN
ejpam-2382	178	33	s)k2	s)k2	NOUN
ejpam-2382	178	34	1(k	1(k	NUM
ejpam-2382	178	35	2	2	NUM
ejpam-2382	178	36	1	1	NUM
ejpam-2382	178	37	+	+	CCONJ
ejpam-2382	178	38	k2	k2	PROPN
ejpam-2382	178	39	2)v1	2)v1	NOUN
ejpam-2382	178	40	+	+	CCONJ
ejpam-2382	178	41	3k1(k	3k1(k	NUM
ejpam-2382	178	42	2	2	NUM
ejpam-2382	178	43	1	1	NUM
ejpam-2382	178	44	+	+	CCONJ
ejpam-2382	178	45	k2	k2	ADJ
ejpam-2382	178	46	2)v2	2)v2	PROPN
ejpam-2382	178	47	−	−	PROPN
ejpam-2382	178	48	(	(	PUNCT
ejpam-2382	178	49	c	c	NOUN
ejpam-2382	178	50	−	−	NOUN
ejpam-2382	178	51	s)k1k2(k	s)k1k2(k	NOUN
ejpam-2382	178	52	2	2	NUM
ejpam-2382	178	53	1	1	NUM
ejpam-2382	178	54	+	+	CCONJ
ejpam-2382	178	55	k2	k2	ADJ
ejpam-2382	178	56	2	2	NUM
ejpam-2382	178	57	+	+	SYM
ejpam-2382	178	58	k2	k2	PROPN
ejpam-2382	178	59	3)v3	3)v3	PROPN
ejpam-2382	178	60	−	−	PROPN
ejpam-2382	178	61	3k1k2k3v4	3k1k2k3v4	NUM
ejpam-2382	178	62	+	+	CCONJ
ejpam-2382	178	63	(	(	PUNCT
ejpam-2382	178	64	c	c	PROPN
ejpam-2382	178	65	−	−	PROPN
ejpam-2382	178	66	s)k1k2k3k4v5	s)k1k2k3k4v5	PROPN
ejpam-2382	178	67	,	,	PUNCT
ejpam-2382	178	68	(	(	PUNCT
ejpam-2382	178	69	32	32	NUM
ejpam-2382	178	70	)	)	PUNCT
ejpam-2382	178	71	y	y	PROPN
ejpam-2382	178	72	(	(	PUNCT
ejpam-2382	178	73	5	5	NUM
ejpam-2382	178	74	)	)	PUNCT
ejpam-2382	178	75	=	=	NOUN
ejpam-2382	178	76	−	−	NOUN
ejpam-2382	178	77	4k2	4k2	NUM
ejpam-2382	178	78	1(k	1(k	NUM
ejpam-2382	178	79	2	2	NUM
ejpam-2382	178	80	1	1	NUM
ejpam-2382	178	81	+	+	CCONJ
ejpam-2382	178	82	k2	k2	PROPN
ejpam-2382	178	83	2)v1	2)v1	PROPN
ejpam-2382	178	84	+	+	CCONJ
ejpam-2382	178	85	(	(	PUNCT
ejpam-2382	178	86	c	c	NOUN
ejpam-2382	178	87	−	−	PROPN
ejpam-2382	178	88	s)k1	s)k1	PROPN
ejpam-2382	178	89	�	�	PROPN
ejpam-2382	178	90	k2	k2	NOUN
ejpam-2382	178	91	1(k	1(k	NUM
ejpam-2382	178	92	2	2	NUM
ejpam-2382	178	93	1	1	NUM
ejpam-2382	178	94	+	+	CCONJ
ejpam-2382	178	95	k2	k2	ADJ
ejpam-2382	178	96	2	2	NUM
ejpam-2382	178	97	)	)	PUNCT
ejpam-2382	178	98	+	+	CCONJ
ejpam-2382	178	99	k2	k2	ADJ
ejpam-2382	178	100	2(k	2(k	NUM
ejpam-2382	178	101	2	2	NUM
ejpam-2382	178	102	1	1	NUM
ejpam-2382	178	103	+	+	CCONJ
ejpam-2382	178	104	k2	k2	ADJ
ejpam-2382	178	105	2	2	NUM
ejpam-2382	178	106	+	+	SYM
ejpam-2382	178	107	k2	k2	ADJ
ejpam-2382	178	108	3	3	NUM
ejpam-2382	178	109	)	)	PUNCT
ejpam-2382	178	110	�	�	PROPN
ejpam-2382	178	111	v2	v2	PROPN
ejpam-2382	179	1	+	+	CCONJ
ejpam-2382	179	2	4k1k2(k	4k1k2(k	NOUN
ejpam-2382	179	3	2	2	NUM
ejpam-2382	179	4	1	1	NUM
ejpam-2382	179	5	+	+	CCONJ
ejpam-2382	179	6	k2	k2	ADJ
ejpam-2382	179	7	2	2	NUM
ejpam-2382	179	8	+	+	SYM
ejpam-2382	179	9	k2	k2	PROPN
ejpam-2382	179	10	3)v3	3)v3	PROPN
ejpam-2382	179	11	−	−	PROPN
ejpam-2382	180	1	(	(	PUNCT
ejpam-2382	180	2	c	c	NOUN
ejpam-2382	180	3	−	−	PROPN
ejpam-2382	180	4	s)k1k2k3(k	s)k1k2k3(k	NOUN
ejpam-2382	180	5	2	2	NUM
ejpam-2382	180	6	1	1	NUM
ejpam-2382	180	7	+	+	CCONJ
ejpam-2382	180	8	k2	k2	ADJ
ejpam-2382	180	9	2	2	NUM
ejpam-2382	180	10	+	+	SYM
ejpam-2382	180	11	k2	k2	ADJ
ejpam-2382	180	12	3	3	NUM
ejpam-2382	180	13	+	+	CCONJ
ejpam-2382	180	14	k2	k2	ADJ
ejpam-2382	180	15	4)v4	4)v4	PROPN
ejpam-2382	180	16	−	−	PROPN
ejpam-2382	180	17	4k1k2k3k4v5	4k1k2k3k4v5	PROPN
ejpam-2382	180	18	.	.	PUNCT
ejpam-2382	181	1	(	(	PUNCT
ejpam-2382	181	2	33	33	NUM
ejpam-2382	181	3	)	)	PUNCT
ejpam-2382	181	4	from	from	ADP
ejpam-2382	181	5	the	the	DET
ejpam-2382	181	6	equation	equation	NOUN
ejpam-2382	181	7	(	(	PUNCT
ejpam-2382	181	8	8)	8)	NUM
ejpam-2382	181	9	,	,	PUNCT
ejpam-2382	181	10	the	the	DET
ejpam-2382	181	11	first	first	ADJ
ejpam-2382	181	12	frenet	frenet	ADJ
ejpam-2382	181	13	vector	vector	NOUN
ejpam-2382	181	14	of	of	ADP
ejpam-2382	181	15	the	the	DET
ejpam-2382	181	16	curve	curve	NOUN
ejpam-2382	181	17	y	y	PROPN
ejpam-2382	181	18	can	can	AUX
ejpam-2382	181	19	be	be	AUX
ejpam-2382	181	20	written	write	VERB
ejpam-2382	181	21	as	as	ADP
ejpam-2382	181	22	v	v	NOUN
ejpam-2382	181	23	y	y	PROPN
ejpam-2382	181	24	1	1	NUM
ejpam-2382	181	25	=	=	NOUN
ejpam-2382	181	26	ẏ	ẏ	PROPN
ejpam-2382	181	27	ẏ	ẏ	PROPN
ejpam-2382	181	28	.	.	PUNCT
ejpam-2382	182	1	m.	m.	NOUN
ejpam-2382	182	2	masal	masal	PROPN
ejpam-2382	182	3	,	,	PUNCT
ejpam-2382	182	4	a.	a.	PROPN
ejpam-2382	182	5	azak	azak	PROPN
ejpam-2382	182	6	/	/	SYM
ejpam-2382	182	7	eur	eur	PROPN
ejpam-2382	182	8	.	.	PUNCT
ejpam-2382	183	1	j.	j.	PROPN
ejpam-2382	183	2	pure	pure	PROPN
ejpam-2382	183	3	appl	appl	PROPN
ejpam-2382	183	4	.	.	PROPN
ejpam-2382	183	5	math	math	PROPN
ejpam-2382	183	6	,	,	PUNCT
ejpam-2382	183	7	8	8	NUM
ejpam-2382	183	8	(	(	PUNCT
ejpam-2382	183	9	2015	2015	NUM
ejpam-2382	183	10	)	)	PUNCT
ejpam-2382	183	11	,	,	PUNCT
ejpam-2382	183	12	255	255	NUM
ejpam-2382	183	13	-	-	SYM
ejpam-2382	183	14	270	270	NUM
ejpam-2382	183	15	264	264	NUM
ejpam-2382	183	16	considering	consider	VERB
ejpam-2382	183	17	the	the	DET
ejpam-2382	183	18	equations	equation	NOUN
ejpam-2382	183	19	(	(	PUNCT
ejpam-2382	183	20	28	28	NUM
ejpam-2382	183	21	)	)	PUNCT
ejpam-2382	183	22	and	and	CCONJ
ejpam-2382	183	23	(	(	PUNCT
ejpam-2382	183	24	29	29	NUM
ejpam-2382	183	25	)	)	PUNCT
ejpam-2382	183	26	,	,	PUNCT
ejpam-2382	183	27	we	we	PRON
ejpam-2382	183	28	find	find	VERB
ejpam-2382	183	29	v	v	ADP
ejpam-2382	183	30	y	y	PROPN
ejpam-2382	183	31	1	1	NUM
ejpam-2382	183	32	=	=	SYM
ejpam-2382	183	33	v2	v2	PROPN
ejpam-2382	183	34	.	.	PUNCT
ejpam-2382	184	1	(	(	PUNCT
ejpam-2382	184	2	34	34	NUM
ejpam-2382	184	3	)	)	PUNCT
ejpam-2382	184	4	from	from	ADP
ejpam-2382	184	5	the	the	DET
ejpam-2382	184	6	equations	equation	NOUN
ejpam-2382	184	7	(	(	PUNCT
ejpam-2382	184	8	28	28	NUM
ejpam-2382	184	9	)	)	PUNCT
ejpam-2382	184	10	and	and	CCONJ
ejpam-2382	184	11	(	(	PUNCT
ejpam-2382	184	12	30	30	NUM
ejpam-2382	184	13	)	)	PUNCT
ejpam-2382	184	14	,	,	PUNCT
ejpam-2382	184	15	we	we	PRON
ejpam-2382	184	16	get	get	VERB
ejpam-2382	184	17	ẏ	ẏ	PROPN
ejpam-2382	184	18	2	2	NUM
ejpam-2382	184	19	ÿ	ÿ	NOUN
ejpam-2382	184	20	−	−	NOUN
ejpam-2382	184	21	ẏ	ẏ	PROPN
ejpam-2382	184	22	,	,	PUNCT
ejpam-2382	184	23	ÿ	ÿ	PROPN
ejpam-2382	184	24	�	�	PROPN
ejpam-2382	184	25	ẏ	ẏ	PROPN
ejpam-2382	184	26	=	=	PUNCT
ejpam-2382	184	27	−(c	−(c	NOUN
ejpam-2382	185	1	−	−	PROPN
ejpam-2382	185	2	s)3k4	s)3k4	PROPN
ejpam-2382	185	3	1v1	1v1	NUM
ejpam-2382	186	1	+	+	CCONJ
ejpam-2382	187	1	(	(	PUNCT
ejpam-2382	187	2	c	c	X
ejpam-2382	187	3	−	−	PROPN
ejpam-2382	187	4	s)3k3	s)3k3	PROPN
ejpam-2382	187	5	1k2v3	1k2v3	NUM
ejpam-2382	187	6	(	(	PUNCT
ejpam-2382	187	7	35	35	NUM
ejpam-2382	187	8	)	)	PUNCT
ejpam-2382	187	9	and	and	CCONJ
ejpam-2382	187	10	ẏ	ẏ	PROPN
ejpam-2382	187	11	2	2	NUM
ejpam-2382	187	12	ÿ	ÿ	NUM
ejpam-2382	187	13	−	−	NOUN
ejpam-2382	187	14	ẏ	ẏ	PROPN
ejpam-2382	187	15	,	,	PUNCT
ejpam-2382	187	16	ÿ	ÿ	PROPN
ejpam-2382	187	17	�	�	PROPN
ejpam-2382	187	18	ẏ	ẏ	PROPN
ejpam-2382	187	19	=	=	SYM
ejpam-2382	187	20	(	(	PUNCT
ejpam-2382	187	21	c	c	X
ejpam-2382	187	22	−	−	PROPN
ejpam-2382	187	23	s)3k3	s)3k3	PROPN
ejpam-2382	187	24	1	1	NUM
ejpam-2382	187	25	q	q	NOUN
ejpam-2382	187	26	k2	k2	PROPN
ejpam-2382	187	27	1	1	NUM
ejpam-2382	187	28	+	+	SYM
ejpam-2382	187	29	k2	k2	PROPN
ejpam-2382	187	30	2	2	NUM
ejpam-2382	187	31	.	.	PUNCT
ejpam-2382	187	32	(	(	PUNCT
ejpam-2382	187	33	36	36	NUM
ejpam-2382	187	34	)	)	PUNCT
ejpam-2382	187	35	if	if	SCONJ
ejpam-2382	187	36	we	we	PRON
ejpam-2382	187	37	use	use	VERB
ejpam-2382	187	38	the	the	DET
ejpam-2382	187	39	equations	equation	NOUN
ejpam-2382	187	40	(	(	PUNCT
ejpam-2382	187	41	11	11	NUM
ejpam-2382	187	42	)	)	PUNCT
ejpam-2382	187	43	and	and	CCONJ
ejpam-2382	187	44	(	(	PUNCT
ejpam-2382	187	45	14	14	NUM
ejpam-2382	187	46	)	)	PUNCT
ejpam-2382	187	47	,	,	PUNCT
ejpam-2382	187	48	then	then	ADV
ejpam-2382	187	49	we	we	PRON
ejpam-2382	187	50	will	will	AUX
ejpam-2382	187	51	obtain	obtain	VERB
ejpam-2382	187	52	the	the	DET
ejpam-2382	187	53	second	second	ADJ
ejpam-2382	187	54	frenet	frenet	NOUN
ejpam-2382	187	55	vector	vector	NOUN
ejpam-2382	187	56	and	and	CCONJ
ejpam-2382	187	57	the	the	DET
ejpam-2382	187	58	first	first	ADJ
ejpam-2382	187	59	curvature	curvature	NOUN
ejpam-2382	187	60	of	of	ADP
ejpam-2382	187	61	curve	curve	NOUN
ejpam-2382	187	62	y	y	PROPN
ejpam-2382	187	63	as	as	SCONJ
ejpam-2382	187	64	follows	follow	VERB
ejpam-2382	187	65	;	;	PUNCT
ejpam-2382	187	66	v	v	X
ejpam-2382	187	67	y	y	PROPN
ejpam-2382	187	68	2	2	NUM
ejpam-2382	187	69	=	=	SYM
ejpam-2382	187	70	−	−	PROPN
ejpam-2382	187	71	k1	k1	PROPN
ejpam-2382	187	72	q	q	PROPN
ejpam-2382	187	73	k2	k2	PROPN
ejpam-2382	187	74	1	1	NUM
ejpam-2382	187	75	+	+	SYM
ejpam-2382	187	76	k2	k2	ADJ
ejpam-2382	187	77	2	2	NUM
ejpam-2382	187	78	v1	v1	NOUN
ejpam-2382	187	79	+	+	CCONJ
ejpam-2382	187	80	k2	k2	PROPN
ejpam-2382	187	81	q	q	PROPN
ejpam-2382	187	82	k2	k2	PROPN
ejpam-2382	187	83	1	1	NUM
ejpam-2382	187	84	+	+	SYM
ejpam-2382	187	85	k2	k2	PROPN
ejpam-2382	187	86	2	2	NUM
ejpam-2382	187	87	v3	v3	PROPN
ejpam-2382	187	88	(	(	PUNCT
ejpam-2382	187	89	37	37	NUM
ejpam-2382	187	90	)	)	PUNCT
ejpam-2382	187	91	and	and	CCONJ
ejpam-2382	187	92	ky	ky	PROPN
ejpam-2382	187	93	1	1	NUM
ejpam-2382	187	94	=	=	SYM
ejpam-2382	187	95	q	q	PROPN
ejpam-2382	187	96	k2	k2	PROPN
ejpam-2382	187	97	1	1	NUM
ejpam-2382	187	98	+	+	SYM
ejpam-2382	187	99	k2	k2	ADJ
ejpam-2382	187	100	2	2	NUM
ejpam-2382	187	101	(	(	PUNCT
ejpam-2382	187	102	c	c	NOUN
ejpam-2382	187	103	−	−	PROPN
ejpam-2382	188	1	s)k1	s)k1	PROPN
ejpam-2382	188	2	(	(	PUNCT
ejpam-2382	188	3	38	38	NUM
ejpam-2382	188	4	)	)	PUNCT
ejpam-2382	188	5	respectively	respectively	ADV
ejpam-2382	188	6	.	.	PUNCT
ejpam-2382	189	1	besides	besides	SCONJ
ejpam-2382	189	2	,	,	PUNCT
ejpam-2382	189	3	considering	consider	VERB
ejpam-2382	189	4	the	the	DET
ejpam-2382	189	5	equations	equation	NOUN
ejpam-2382	189	6	(	(	PUNCT
ejpam-2382	189	7	28	28	NUM
ejpam-2382	189	8	)	)	PUNCT
ejpam-2382	189	9	,	,	PUNCT
ejpam-2382	189	10	(	(	PUNCT
ejpam-2382	189	11	29	29	NUM
ejpam-2382	189	12	)	)	PUNCT
ejpam-2382	189	13	,	,	PUNCT
ejpam-2382	189	14	(	(	PUNCT
ejpam-2382	189	15	30	30	NUM
ejpam-2382	189	16	)	)	PUNCT
ejpam-2382	189	17	,	,	PUNCT
ejpam-2382	189	18	(	(	PUNCT
ejpam-2382	189	19	31	31	NUM
ejpam-2382	189	20	)	)	PUNCT
ejpam-2382	189	21	and	and	CCONJ
ejpam-2382	189	22	(	(	PUNCT
ejpam-2382	189	23	36	36	NUM
ejpam-2382	189	24	)	)	PUNCT
ejpam-2382	189	25	,	,	PUNCT
ejpam-2382	189	26	one	one	PRON
ejpam-2382	189	27	can	can	AUX
ejpam-2382	189	28	calculate	calculate	VERB
ejpam-2382	189	29	...	...	PUNCT
ejpam-2382	190	1	y	y	PRON
ejpam-2382	190	2	−	−	NOUN
ejpam-2382	190	3	ẏ	ẏ	PROPN
ejpam-2382	190	4	,	,	PUNCT
ejpam-2382	190	5	...	...	PUNCT
ejpam-2382	191	1	y	y	X
ejpam-2382	191	2	〉	〉	NOUN
ejpam-2382	191	3	ẏ	ẏ	NOUN
ejpam-2382	191	4	v	v	VERB
ejpam-2382	191	5	y	y	PROPN
ejpam-2382	191	6	1	1	NUM
ejpam-2382	191	7	−	−	NOUN
ejpam-2382	191	8	ẏ	ẏ	PROPN
ejpam-2382	191	9	2	2	NUM
ejpam-2382	191	10	ÿ	ÿ	PROPN
ejpam-2382	191	11	,	,	PUNCT
ejpam-2382	191	12	...	...	PUNCT
ejpam-2382	192	1	y	y	X
ejpam-2382	192	2	〉	〉	NOUN
ejpam-2382	192	3	−	−	VERB
ejpam-2382	192	4	ẏ	ẏ	PROPN
ejpam-2382	192	5	,	,	PUNCT
ejpam-2382	192	6	ÿ	ÿ	PROPN
ejpam-2382	192	7	�	�	PROPN
ejpam-2382	192	8	ẏ	ẏ	PROPN
ejpam-2382	192	9	,	,	PUNCT
ejpam-2382	192	10	...	...	PUNCT
ejpam-2382	193	1	y	y	X
ejpam-2382	193	2	〉	〉	NOUN
ejpam-2382	193	3	ẏ	ẏ	PROPN
ejpam-2382	193	4	2	2	NUM
ejpam-2382	193	5	ÿ	ÿ	NOUN
ejpam-2382	193	6	−	−	NOUN
ejpam-2382	193	7	ẏ	ẏ	PROPN
ejpam-2382	193	8	,	,	PUNCT
ejpam-2382	193	9	ÿ	ÿ	PROPN
ejpam-2382	193	10	�	�	PROPN
ejpam-2382	193	11	ẏ	ẏ	VERB
ejpam-2382	193	12	v	v	ADP
ejpam-2382	193	13	y	y	PROPN
ejpam-2382	193	14	2	2	NUM
ejpam-2382	193	15	=	=	SYM
ejpam-2382	193	16	(	(	PUNCT
ejpam-2382	193	17	c	c	NOUN
ejpam-2382	193	18	−	−	PROPN
ejpam-2382	193	19	s)k1k2k3v4	s)k1k2k3v4	PROPN
ejpam-2382	193	20	.	.	PUNCT
ejpam-2382	194	1	(	(	PUNCT
ejpam-2382	194	2	39	39	NUM
ejpam-2382	194	3	)	)	PUNCT
ejpam-2382	194	4	the	the	DET
ejpam-2382	194	5	third	third	ADJ
ejpam-2382	194	6	frenet	frenet	NOUN
ejpam-2382	194	7	vector	vector	NOUN
ejpam-2382	194	8	of	of	ADP
ejpam-2382	194	9	y	y	PROPN
ejpam-2382	194	10	is	be	AUX
ejpam-2382	194	11	obtained	obtain	VERB
ejpam-2382	194	12	from	from	ADP
ejpam-2382	194	13	the	the	DET
ejpam-2382	194	14	equation	equation	NOUN
ejpam-2382	194	15	(	(	PUNCT
ejpam-2382	194	16	16	16	NUM
ejpam-2382	194	17	)	)	PUNCT
ejpam-2382	194	18	as	as	ADP
ejpam-2382	194	19	v	v	NUM
ejpam-2382	194	20	y	y	PROPN
ejpam-2382	194	21	3	3	NUM
ejpam-2382	194	22	=	=	SYM
ejpam-2382	194	23	v4	v4	NOUN
ejpam-2382	194	24	.	.	PUNCT
ejpam-2382	195	1	(	(	PUNCT
ejpam-2382	195	2	40	40	NUM
ejpam-2382	195	3	)	)	PUNCT
ejpam-2382	195	4	if	if	SCONJ
ejpam-2382	195	5	the	the	DET
ejpam-2382	195	6	equations	equation	NOUN
ejpam-2382	195	7	(	(	PUNCT
ejpam-2382	195	8	31	31	NUM
ejpam-2382	195	9	)	)	PUNCT
ejpam-2382	195	10	and	and	CCONJ
ejpam-2382	195	11	(	(	PUNCT
ejpam-2382	195	12	40	40	NUM
ejpam-2382	195	13	)	)	PUNCT
ejpam-2382	195	14	are	be	AUX
ejpam-2382	195	15	taken	take	VERB
ejpam-2382	195	16	into	into	ADP
ejpam-2382	195	17	consideration	consideration	NOUN
ejpam-2382	195	18	,	,	PUNCT
ejpam-2382	195	19	we	we	PRON
ejpam-2382	195	20	get	get	VERB
ejpam-2382	195	21	...	...	PUNCT
ejpam-2382	196	1	y	y	PROPN
ejpam-2382	196	2	,	,	PUNCT
ejpam-2382	196	3	v	v	PROPN
ejpam-2382	196	4	y	y	PROPN
ejpam-2382	196	5	3	3	NUM
ejpam-2382	196	6	�	�	PROPN
ejpam-2382	196	7	=	=	SYM
ejpam-2382	196	8	(	(	PUNCT
ejpam-2382	196	9	c	c	X
ejpam-2382	196	10	−	−	PROPN
ejpam-2382	196	11	s)k1k2k3	s)k1k2k3	PROPN
ejpam-2382	196	12	.	.	PUNCT
ejpam-2382	197	1	(	(	PUNCT
ejpam-2382	197	2	41	41	NUM
ejpam-2382	197	3	)	)	PUNCT
ejpam-2382	197	4	from	from	ADP
ejpam-2382	197	5	the	the	DET
ejpam-2382	197	6	equations	equation	NOUN
ejpam-2382	197	7	(	(	PUNCT
ejpam-2382	197	8	15	15	NUM
ejpam-2382	197	9	)	)	PUNCT
ejpam-2382	197	10	,	,	PUNCT
ejpam-2382	197	11	(	(	PUNCT
ejpam-2382	197	12	36	36	NUM
ejpam-2382	197	13	)	)	PUNCT
ejpam-2382	197	14	and	and	CCONJ
ejpam-2382	197	15	(	(	PUNCT
ejpam-2382	197	16	41	41	NUM
ejpam-2382	197	17	)	)	PUNCT
ejpam-2382	197	18	,	,	PUNCT
ejpam-2382	197	19	the	the	DET
ejpam-2382	197	20	second	second	ADJ
ejpam-2382	197	21	curvature	curvature	NOUN
ejpam-2382	197	22	of	of	ADP
ejpam-2382	197	23	y	y	PROPN
ejpam-2382	197	24	is	be	AUX
ejpam-2382	197	25	found	find	VERB
ejpam-2382	197	26	as	as	ADP
ejpam-2382	197	27	ky	ky	PROPN
ejpam-2382	197	28	2	2	NUM
ejpam-2382	197	29	=	=	SYM
ejpam-2382	197	30	k2k3	k2k3	X
ejpam-2382	197	31	(	(	PUNCT
ejpam-2382	197	32	c	c	NOUN
ejpam-2382	197	33	−	−	PROPN
ejpam-2382	198	1	s)k1	s)k1	PROPN
ejpam-2382	198	2	q	q	PROPN
ejpam-2382	198	3	k2	k2	ADJ
ejpam-2382	198	4	1	1	NUM
ejpam-2382	198	5	+	+	SYM
ejpam-2382	198	6	k2	k2	ADJ
ejpam-2382	198	7	2	2	NUM
ejpam-2382	198	8	.	.	PUNCT
ejpam-2382	199	1	(	(	PUNCT
ejpam-2382	199	2	42	42	NUM
ejpam-2382	199	3	)	)	PUNCT
ejpam-2382	199	4	moreover	moreover	ADV
ejpam-2382	199	5	,	,	PUNCT
ejpam-2382	199	6	from	from	ADP
ejpam-2382	199	7	the	the	DET
ejpam-2382	199	8	equations	equation	NOUN
ejpam-2382	199	9	(	(	PUNCT
ejpam-2382	199	10	31	31	NUM
ejpam-2382	199	11	)	)	PUNCT
ejpam-2382	199	12	,	,	PUNCT
ejpam-2382	199	13	(	(	PUNCT
ejpam-2382	199	14	32	32	NUM
ejpam-2382	199	15	)	)	PUNCT
ejpam-2382	199	16	,	,	PUNCT
ejpam-2382	199	17	(	(	PUNCT
ejpam-2382	199	18	34	34	NUM
ejpam-2382	199	19	)	)	PUNCT
ejpam-2382	199	20	and	and	CCONJ
ejpam-2382	199	21	(	(	PUNCT
ejpam-2382	199	22	37	37	NUM
ejpam-2382	199	23	)	)	PUNCT
ejpam-2382	199	24	,	,	PUNCT
ejpam-2382	199	25	we	we	PRON
ejpam-2382	199	26	have	have	VERB
ejpam-2382	199	27	v	v	NUM
ejpam-2382	199	28	y	y	PROPN
ejpam-2382	199	29	1	1	NUM
ejpam-2382	199	30	∧	∧	PROPN
ejpam-2382	199	31	v	v	ADP
ejpam-2382	199	32	y	y	PROPN
ejpam-2382	199	33	2	2	NUM
ejpam-2382	199	34	∧	∧	PROPN
ejpam-2382	199	35	...	...	PUNCT
ejpam-2382	200	1	y	y	PROPN
ejpam-2382	200	2	∧	∧	PROPN
ejpam-2382	200	3	y	y	PROPN
ejpam-2382	200	4	(	(	PUNCT
ejpam-2382	200	5	4	4	NUM
ejpam-2382	200	6	)	)	PUNCT
ejpam-2382	200	7	=	=	SYM
ejpam-2382	200	8	(	(	PUNCT
ejpam-2382	200	9	c	c	X
ejpam-2382	200	10	−	−	NOUN
ejpam-2382	200	11	s)2k2	s)2k2	PROPN
ejpam-2382	200	12	1k3	1k3	NUM
ejpam-2382	200	13	2k2	2k2	NUM
ejpam-2382	200	14	3k4	3k4	NUM
ejpam-2382	200	15	q	q	PROPN
ejpam-2382	200	16	k2	k2	PROPN
ejpam-2382	200	17	1	1	NUM
ejpam-2382	200	18	+	+	CCONJ
ejpam-2382	200	19	k2	k2	ADJ
ejpam-2382	200	20	2	2	NUM
ejpam-2382	200	21	v1	v1	NOUN
ejpam-2382	200	22	+	+	CCONJ
ejpam-2382	200	23	(	(	PUNCT
ejpam-2382	200	24	c	c	NOUN
ejpam-2382	200	25	−	−	PROPN
ejpam-2382	200	26	s)2k3	s)2k3	PROPN
ejpam-2382	200	27	1k2	1k2	NUM
ejpam-2382	200	28	2k2	2k2	NUM
ejpam-2382	200	29	3k4	3k4	NUM
ejpam-2382	200	30	q	q	PROPN
ejpam-2382	200	31	k2	k2	PROPN
ejpam-2382	200	32	1	1	NUM
ejpam-2382	200	33	+	+	SYM
ejpam-2382	200	34	k2	k2	ADJ
ejpam-2382	200	35	2	2	NUM
ejpam-2382	200	36	v3	v3	PROPN
ejpam-2382	200	37	+	+	CCONJ
ejpam-2382	200	38	(	(	PUNCT
ejpam-2382	200	39	c	c	NOUN
ejpam-2382	200	40	−	−	PROPN
ejpam-2382	200	41	s)2k3	s)2k3	PROPN
ejpam-2382	200	42	1k2	1k2	NUM
ejpam-2382	200	43	2k3	2k3	NUM
ejpam-2382	200	44	3	3	NUM
ejpam-2382	200	45	q	q	PROPN
ejpam-2382	200	46	k2	k2	PROPN
ejpam-2382	200	47	1	1	NUM
ejpam-2382	200	48	+	+	SYM
ejpam-2382	200	49	k2	k2	ADJ
ejpam-2382	200	50	2	2	NUM
ejpam-2382	200	51	v5	v5	PROPN
ejpam-2382	200	52	(	(	PUNCT
ejpam-2382	200	53	43	43	NUM
ejpam-2382	200	54	)	)	PUNCT
ejpam-2382	200	55	and	and	CCONJ
ejpam-2382	200	56	v	v	ADP
ejpam-2382	200	57	y	y	PROPN
ejpam-2382	200	58	1	1	NUM
ejpam-2382	200	59	∧	∧	PROPN
ejpam-2382	200	60	v	v	ADP
ejpam-2382	200	61	y	y	PROPN
ejpam-2382	200	62	2	2	NUM
ejpam-2382	200	63	∧	∧	PROPN
ejpam-2382	200	64	...	...	PUNCT
ejpam-2382	201	1	y	y	PROPN
ejpam-2382	201	2	∧	∧	PROPN
ejpam-2382	201	3	y	y	PROPN
ejpam-2382	201	4	(	(	PUNCT
ejpam-2382	201	5	4	4	NUM
ejpam-2382	201	6	)	)	PUNCT
ejpam-2382	201	7	=	=	SYM
ejpam-2382	201	8	(	(	PUNCT
ejpam-2382	201	9	c	c	X
ejpam-2382	201	10	−	−	NOUN
ejpam-2382	201	11	s)2k2	s)2k2	PROPN
ejpam-2382	201	12	1k2	1k2	NUM
ejpam-2382	201	13	2k2	2k2	NUM
ejpam-2382	201	14	3	3	NUM
ejpam-2382	201	15	q	q	PROPN
ejpam-2382	201	16	k2	k2	PROPN
ejpam-2382	201	17	1	1	NUM
ejpam-2382	201	18	+	+	SYM
ejpam-2382	201	19	k2	k2	ADJ
ejpam-2382	201	20	2	2	NUM
ejpam-2382	201	21	q	q	PROPN
ejpam-2382	201	22	k2	k2	NOUN
ejpam-2382	201	23	1k2	1k2	NUM
ejpam-2382	201	24	3	3	NUM
ejpam-2382	201	25	+	+	SYM
ejpam-2382	201	26	k2	k2	NOUN
ejpam-2382	201	27	2k2	2k2	NUM
ejpam-2382	201	28	4	4	NUM
ejpam-2382	201	29	+	+	SYM
ejpam-2382	201	30	k2	k2	X
ejpam-2382	201	31	1k2	1k2	NUM
ejpam-2382	201	32	4	4	NUM
ejpam-2382	201	33	.	.	PUNCT
ejpam-2382	202	1	(	(	PUNCT
ejpam-2382	202	2	44	44	NUM
ejpam-2382	202	3	)	)	PUNCT
ejpam-2382	202	4	m.	m.	NOUN
ejpam-2382	202	5	masal	masal	NOUN
ejpam-2382	202	6	,	,	PUNCT
ejpam-2382	202	7	a.	a.	PROPN
ejpam-2382	202	8	azak	azak	PROPN
ejpam-2382	202	9	/	/	SYM
ejpam-2382	202	10	eur	eur	PROPN
ejpam-2382	202	11	.	.	PUNCT
ejpam-2382	203	1	j.	j.	PROPN
ejpam-2382	203	2	pure	pure	PROPN
ejpam-2382	203	3	appl	appl	PROPN
ejpam-2382	203	4	.	.	PROPN
ejpam-2382	203	5	math	math	PROPN
ejpam-2382	203	6	,	,	PUNCT
ejpam-2382	203	7	8	8	NUM
ejpam-2382	203	8	(	(	PUNCT
ejpam-2382	203	9	2015	2015	NUM
ejpam-2382	203	10	)	)	PUNCT
ejpam-2382	203	11	,	,	PUNCT
ejpam-2382	203	12	255	255	NUM
ejpam-2382	203	13	-	-	SYM
ejpam-2382	203	14	270	270	NUM
ejpam-2382	203	15	265	265	NUM
ejpam-2382	203	16	thus	thus	ADV
ejpam-2382	203	17	,	,	PUNCT
ejpam-2382	203	18	if	if	SCONJ
ejpam-2382	203	19	we	we	PRON
ejpam-2382	203	20	take	take	VERB
ejpam-2382	203	21	the	the	DET
ejpam-2382	203	22	equations	equation	NOUN
ejpam-2382	203	23	(	(	PUNCT
ejpam-2382	203	24	18	18	NUM
ejpam-2382	203	25	)	)	PUNCT
ejpam-2382	203	26	,	,	PUNCT
ejpam-2382	203	27	(	(	PUNCT
ejpam-2382	203	28	43	43	NUM
ejpam-2382	203	29	)	)	PUNCT
ejpam-2382	203	30	and	and	CCONJ
ejpam-2382	203	31	(	(	PUNCT
ejpam-2382	203	32	44	44	NUM
ejpam-2382	203	33	)	)	PUNCT
ejpam-2382	203	34	,	,	PUNCT
ejpam-2382	203	35	the	the	DET
ejpam-2382	203	36	fifth	fifth	ADJ
ejpam-2382	203	37	frenet	frenet	NOUN
ejpam-2382	203	38	vector	vector	NOUN
ejpam-2382	203	39	of	of	ADP
ejpam-2382	203	40	the	the	DET
ejpam-2382	203	41	curve	curve	NOUN
ejpam-2382	203	42	y	y	PROPN
ejpam-2382	203	43	is	be	AUX
ejpam-2382	203	44	v	v	ADP
ejpam-2382	203	45	y	y	PROPN
ejpam-2382	203	46	5	5	NUM
ejpam-2382	203	47	=	=	SYM
ejpam-2382	203	48	k2k4	k2k4	PROPN
ejpam-2382	203	49	q	q	PROPN
ejpam-2382	203	50	k2	k2	NOUN
ejpam-2382	203	51	1k2	1k2	NUM
ejpam-2382	203	52	3	3	NUM
ejpam-2382	203	53	+	+	SYM
ejpam-2382	203	54	k2	k2	NOUN
ejpam-2382	203	55	2k2	2k2	NUM
ejpam-2382	203	56	4	4	NUM
ejpam-2382	203	57	+	+	SYM
ejpam-2382	203	58	k2	k2	X
ejpam-2382	203	59	1k2	1k2	NUM
ejpam-2382	203	60	4v1	4v1	NUM
ejpam-2382	204	1	+	+	CCONJ
ejpam-2382	204	2	k1k4	k1k4	PROPN
ejpam-2382	204	3	q	q	PROPN
ejpam-2382	204	4	k2	k2	PROPN
ejpam-2382	204	5	1k2	1k2	NUM
ejpam-2382	204	6	3	3	NUM
ejpam-2382	204	7	+	+	SYM
ejpam-2382	204	8	k2	k2	NOUN
ejpam-2382	204	9	2k2	2k2	NUM
ejpam-2382	204	10	4	4	NUM
ejpam-2382	204	11	+	+	SYM
ejpam-2382	204	12	k2	k2	ADJ
ejpam-2382	204	13	1k2	1k2	NUM
ejpam-2382	204	14	4v3	4v3	NUM
ejpam-2382	205	1	+	+	CCONJ
ejpam-2382	205	2	k1k3	k1k3	PROPN
ejpam-2382	205	3	q	q	PROPN
ejpam-2382	205	4	k2	k2	PROPN
ejpam-2382	205	5	1k2	1k2	NUM
ejpam-2382	205	6	3	3	NUM
ejpam-2382	205	7	+	+	SYM
ejpam-2382	205	8	k2	k2	NOUN
ejpam-2382	205	9	2k2	2k2	NUM
ejpam-2382	205	10	4	4	NUM
ejpam-2382	205	11	+	+	SYM
ejpam-2382	205	12	k2	k2	PROPN
ejpam-2382	205	13	1k2	1k2	PROPN
ejpam-2382	205	14	4v5	4v5	PROPN
ejpam-2382	205	15	.	.	PUNCT
ejpam-2382	206	1	(	(	PUNCT
ejpam-2382	206	2	45	45	NUM
ejpam-2382	206	3	)	)	PUNCT
ejpam-2382	206	4	by	by	ADP
ejpam-2382	206	5	(	(	PUNCT
ejpam-2382	206	6	41	41	NUM
ejpam-2382	206	7	)	)	PUNCT
ejpam-2382	206	8	and	and	CCONJ
ejpam-2382	206	9	(	(	PUNCT
ejpam-2382	206	10	44	44	NUM
ejpam-2382	206	11	)	)	PUNCT
ejpam-2382	206	12	,	,	PUNCT
ejpam-2382	206	13	we	we	PRON
ejpam-2382	206	14	obtain	obtain	VERB
ejpam-2382	206	15	v	v	PROPN
ejpam-2382	206	16	y	y	PROPN
ejpam-2382	206	17	1	1	NUM
ejpam-2382	206	18	∧	∧	PROPN
ejpam-2382	206	19	v	v	ADP
ejpam-2382	206	20	y	y	PROPN
ejpam-2382	206	21	2	2	NUM
ejpam-2382	206	22	∧	∧	PROPN
ejpam-2382	206	23	...	...	PUNCT
ejpam-2382	207	1	y	y	PROPN
ejpam-2382	207	2	∧	∧	PROPN
ejpam-2382	207	3	y	y	PROPN
ejpam-2382	207	4	(	(	PUNCT
ejpam-2382	207	5	4	4	NUM
ejpam-2382	207	6	)	)	PUNCT
ejpam-2382	207	7	�	�	PROPN
ejpam-2382	207	8	...	...	PUNCT
ejpam-2382	208	1	y	y	PROPN
ejpam-2382	208	2	,	,	PUNCT
ejpam-2382	208	3	v	v	PROPN
ejpam-2382	208	4	y	y	PROPN
ejpam-2382	208	5	3	3	NUM
ejpam-2382	208	6	�	�	PROPN
ejpam-2382	208	7	�	�	NOUN
ejpam-2382	208	8	2	2	NUM
ejpam-2382	208	9	ẏ	ẏ	NOUN
ejpam-2382	208	10	=	=	PUNCT
ejpam-2382	208	11	q	q	PROPN
ejpam-2382	208	12	k2	k2	PROPN
ejpam-2382	208	13	1k2	1k2	NUM
ejpam-2382	208	14	3	3	NUM
ejpam-2382	208	15	+	+	SYM
ejpam-2382	208	16	k2	k2	NOUN
ejpam-2382	208	17	2k2	2k2	NUM
ejpam-2382	208	18	4	4	NUM
ejpam-2382	208	19	+	+	SYM
ejpam-2382	208	20	k2	k2	X
ejpam-2382	208	21	1k2	1k2	NUM
ejpam-2382	208	22	4	4	NUM
ejpam-2382	208	23	(	(	PUNCT
ejpam-2382	208	24	c	c	NOUN
ejpam-2382	208	25	−	−	PROPN
ejpam-2382	208	26	s)k1	s)k1	PROPN
ejpam-2382	208	27	q	q	PROPN
ejpam-2382	208	28	k2	k2	ADJ
ejpam-2382	208	29	1	1	NUM
ejpam-2382	208	30	+	+	SYM
ejpam-2382	208	31	k2	k2	ADJ
ejpam-2382	208	32	2	2	NUM
ejpam-2382	208	33	.	.	PUNCT
ejpam-2382	209	1	therefore	therefore	ADV
ejpam-2382	209	2	,	,	PUNCT
ejpam-2382	209	3	from	from	ADP
ejpam-2382	209	4	the	the	DET
ejpam-2382	209	5	equation	equation	NOUN
ejpam-2382	209	6	(	(	PUNCT
ejpam-2382	209	7	19	19	NUM
ejpam-2382	209	8	)	)	PUNCT
ejpam-2382	209	9	the	the	DET
ejpam-2382	209	10	third	third	ADJ
ejpam-2382	209	11	curvature	curvature	NOUN
ejpam-2382	209	12	of	of	ADP
ejpam-2382	209	13	the	the	DET
ejpam-2382	209	14	curve	curve	NOUN
ejpam-2382	209	15	y	y	PROPN
ejpam-2382	209	16	can	can	AUX
ejpam-2382	209	17	be	be	AUX
ejpam-2382	209	18	found	find	VERB
ejpam-2382	209	19	as	as	SCONJ
ejpam-2382	209	20	follows	follow	VERB
ejpam-2382	209	21	ky	ky	PROPN
ejpam-2382	209	22	3	3	NUM
ejpam-2382	209	23	=	=	SYM
ejpam-2382	209	24	q	q	PROPN
ejpam-2382	209	25	k2	k2	NOUN
ejpam-2382	209	26	1k2	1k2	NUM
ejpam-2382	209	27	3	3	NUM
ejpam-2382	209	28	+	+	SYM
ejpam-2382	209	29	k2	k2	NOUN
ejpam-2382	209	30	2k2	2k2	NUM
ejpam-2382	209	31	4	4	NUM
ejpam-2382	209	32	+	+	SYM
ejpam-2382	209	33	k2	k2	X
ejpam-2382	209	34	1k2	1k2	NUM
ejpam-2382	209	35	4	4	NUM
ejpam-2382	209	36	(	(	PUNCT
ejpam-2382	209	37	c	c	NOUN
ejpam-2382	209	38	−	−	PROPN
ejpam-2382	209	39	s)k1	s)k1	PROPN
ejpam-2382	209	40	q	q	PROPN
ejpam-2382	209	41	k2	k2	ADJ
ejpam-2382	209	42	1	1	NUM
ejpam-2382	209	43	+	+	SYM
ejpam-2382	209	44	k2	k2	ADJ
ejpam-2382	209	45	2	2	NUM
ejpam-2382	209	46	.	.	PUNCT
ejpam-2382	210	1	(	(	PUNCT
ejpam-2382	210	2	46	46	NUM
ejpam-2382	210	3	)	)	PUNCT
ejpam-2382	210	4	if	if	SCONJ
ejpam-2382	210	5	the	the	DET
ejpam-2382	210	6	vectorial	vectorial	ADJ
ejpam-2382	210	7	product	product	NOUN
ejpam-2382	210	8	v	v	ADP
ejpam-2382	210	9	y	y	PROPN
ejpam-2382	210	10	3	3	NUM
ejpam-2382	210	11	∧	∧	PROPN
ejpam-2382	210	12	v	v	ADP
ejpam-2382	210	13	y	y	PROPN
ejpam-2382	210	14	2	2	NUM
ejpam-2382	210	15	∧	∧	PROPN
ejpam-2382	210	16	v	v	ADP
ejpam-2382	210	17	y	y	PROPN
ejpam-2382	210	18	1	1	NUM
ejpam-2382	210	19	∧	∧	PROPN
ejpam-2382	210	20	v	v	ADP
ejpam-2382	210	21	y	y	PROPN
ejpam-2382	210	22	5	5	NUM
ejpam-2382	210	23	is	be	AUX
ejpam-2382	210	24	calculated	calculate	VERB
ejpam-2382	210	25	by	by	ADP
ejpam-2382	210	26	using	use	VERB
ejpam-2382	210	27	the	the	DET
ejpam-2382	210	28	equations	equation	NOUN
ejpam-2382	210	29	(	(	PUNCT
ejpam-2382	210	30	34	34	NUM
ejpam-2382	210	31	)	)	PUNCT
ejpam-2382	210	32	,	,	PUNCT
ejpam-2382	210	33	(	(	PUNCT
ejpam-2382	210	34	37	37	NUM
ejpam-2382	210	35	)	)	PUNCT
ejpam-2382	210	36	,	,	PUNCT
ejpam-2382	210	37	(	(	PUNCT
ejpam-2382	210	38	40	40	NUM
ejpam-2382	210	39	)	)	PUNCT
ejpam-2382	210	40	and	and	CCONJ
ejpam-2382	210	41	(	(	PUNCT
ejpam-2382	210	42	45	45	NUM
ejpam-2382	210	43	)	)	PUNCT
ejpam-2382	210	44	,	,	PUNCT
ejpam-2382	210	45	we	we	PRON
ejpam-2382	210	46	find	find	VERB
ejpam-2382	210	47	the	the	DET
ejpam-2382	210	48	fourth	fourth	ADJ
ejpam-2382	210	49	frenet	frenet	ADJ
ejpam-2382	210	50	vector	vector	NOUN
ejpam-2382	210	51	of	of	ADP
ejpam-2382	210	52	the	the	DET
ejpam-2382	210	53	curve	curve	NOUN
ejpam-2382	210	54	y	y	PROPN
ejpam-2382	210	55	,	,	PUNCT
ejpam-2382	210	56	considering	consider	VERB
ejpam-2382	210	57	the	the	DET
ejpam-2382	210	58	equation	equation	NOUN
ejpam-2382	210	59	(	(	PUNCT
ejpam-2382	210	60	22	22	NUM
ejpam-2382	210	61	)	)	PUNCT
ejpam-2382	210	62	as	as	SCONJ
ejpam-2382	210	63	follows	follow	VERB
ejpam-2382	210	64	:	:	PUNCT
ejpam-2382	210	65	v	v	NUM
ejpam-2382	210	66	y	y	PROPN
ejpam-2382	210	67	4	4	NUM
ejpam-2382	210	68	=	=	SYM
ejpam-2382	210	69	−k1k2k3	−k1k2k3	PROPN
ejpam-2382	210	70	q	q	PROPN
ejpam-2382	210	71	k2	k2	PROPN
ejpam-2382	210	72	1	1	NUM
ejpam-2382	210	73	+	+	CCONJ
ejpam-2382	210	74	k2	k2	ADJ
ejpam-2382	210	75	2	2	NUM
ejpam-2382	210	76	q	q	PROPN
ejpam-2382	210	77	k2	k2	NOUN
ejpam-2382	210	78	1k2	1k2	NUM
ejpam-2382	210	79	3	3	NUM
ejpam-2382	210	80	+	+	SYM
ejpam-2382	210	81	k2	k2	NOUN
ejpam-2382	210	82	2k2	2k2	NUM
ejpam-2382	210	83	4	4	NUM
ejpam-2382	210	84	+	+	SYM
ejpam-2382	210	85	k2	k2	ADJ
ejpam-2382	210	86	1k2	1k2	NUM
ejpam-2382	210	87	4	4	NUM
ejpam-2382	210	88	v1	v1	PROPN
ejpam-2382	210	89	−	−	PROPN
ejpam-2382	210	90	k2	k2	PROPN
ejpam-2382	210	91	1k3	1k3	PROPN
ejpam-2382	210	92	q	q	PROPN
ejpam-2382	210	93	k2	k2	PROPN
ejpam-2382	210	94	1	1	NUM
ejpam-2382	210	95	+	+	SYM
ejpam-2382	210	96	k2	k2	ADJ
ejpam-2382	210	97	2	2	NUM
ejpam-2382	210	98	q	q	PROPN
ejpam-2382	210	99	k2	k2	NOUN
ejpam-2382	210	100	1k2	1k2	NUM
ejpam-2382	210	101	3	3	NUM
ejpam-2382	211	1	+	+	SYM
ejpam-2382	211	2	k2	k2	NOUN
ejpam-2382	211	3	2k2	2k2	NUM
ejpam-2382	211	4	4	4	NUM
ejpam-2382	211	5	+	+	SYM
ejpam-2382	211	6	k2	k2	X
ejpam-2382	211	7	1k2	1k2	NUM
ejpam-2382	211	8	4	4	NUM
ejpam-2382	211	9	v3	v3	PROPN
ejpam-2382	211	10	+	+	CCONJ
ejpam-2382	211	11	k4(k	k4(k	PROPN
ejpam-2382	211	12	2	2	NUM
ejpam-2382	211	13	1	1	NUM
ejpam-2382	211	14	+	+	CCONJ
ejpam-2382	211	15	k2	k2	ADJ
ejpam-2382	211	16	2	2	NUM
ejpam-2382	211	17	)	)	PUNCT
ejpam-2382	211	18	q	q	PROPN
ejpam-2382	211	19	k2	k2	PROPN
ejpam-2382	211	20	1	1	NUM
ejpam-2382	211	21	+	+	SYM
ejpam-2382	211	22	k2	k2	ADJ
ejpam-2382	211	23	2	2	NUM
ejpam-2382	211	24	q	q	PROPN
ejpam-2382	211	25	k2	k2	NOUN
ejpam-2382	211	26	1k2	1k2	NUM
ejpam-2382	211	27	3	3	NUM
ejpam-2382	211	28	+	+	SYM
ejpam-2382	211	29	k2	k2	NOUN
ejpam-2382	211	30	2k2	2k2	NUM
ejpam-2382	211	31	4	4	NUM
ejpam-2382	211	32	+	+	SYM
ejpam-2382	211	33	k2	k2	X
ejpam-2382	211	34	1k2	1k2	NUM
ejpam-2382	211	35	4	4	NUM
ejpam-2382	211	36	v5	v5	PROPN
ejpam-2382	211	37	(	(	PUNCT
ejpam-2382	211	38	47	47	NUM
ejpam-2382	211	39	)	)	PUNCT
ejpam-2382	211	40	from	from	ADP
ejpam-2382	211	41	the	the	DET
ejpam-2382	211	42	equations	equation	NOUN
ejpam-2382	211	43	(	(	PUNCT
ejpam-2382	211	44	33	33	NUM
ejpam-2382	211	45	)	)	PUNCT
ejpam-2382	211	46	and	and	CCONJ
ejpam-2382	211	47	(	(	PUNCT
ejpam-2382	211	48	45	45	NUM
ejpam-2382	211	49	)	)	PUNCT
ejpam-2382	211	50	,	,	PUNCT
ejpam-2382	211	51	the	the	DET
ejpam-2382	211	52	inner	inner	ADJ
ejpam-2382	211	53	product	product	NOUN
ejpam-2382	211	54	of	of	ADP
ejpam-2382	211	55	the	the	DET
ejpam-2382	211	56	vectors	vector	NOUN
ejpam-2382	211	57	y	y	PROPN
ejpam-2382	211	58	(	(	PUNCT
ejpam-2382	211	59	5	5	NUM
ejpam-2382	211	60	)	)	PUNCT
ejpam-2382	211	61	and	and	CCONJ
ejpam-2382	211	62	v	v	ADP
ejpam-2382	211	63	y	y	PROPN
ejpam-2382	211	64	5	5	NUM
ejpam-2382	211	65	is	be	AUX
ejpam-2382	211	66	y	y	PROPN
ejpam-2382	211	67	(	(	PUNCT
ejpam-2382	211	68	5	5	NUM
ejpam-2382	211	69	)	)	PUNCT
ejpam-2382	211	70	,	,	PUNCT
ejpam-2382	211	71	v	v	NOUN
ejpam-2382	211	72	y	y	PROPN
ejpam-2382	211	73	5	5	NUM
ejpam-2382	211	74	�	�	PROPN
ejpam-2382	211	75	=	=	SYM
ejpam-2382	211	76	4k2	4k2	NUM
ejpam-2382	211	77	1k2	1k2	NUM
ejpam-2382	211	78	2k4(1−	2k4(1−	NUM
ejpam-2382	211	79	k2	k2	NOUN
ejpam-2382	211	80	)	)	PUNCT
ejpam-2382	211	81	q	q	PROPN
ejpam-2382	211	82	k2	k2	PROPN
ejpam-2382	211	83	1k2	1k2	NUM
ejpam-2382	211	84	3	3	NUM
ejpam-2382	211	85	+	+	SYM
ejpam-2382	211	86	k2	k2	NOUN
ejpam-2382	211	87	2k2	2k2	NUM
ejpam-2382	211	88	4	4	NUM
ejpam-2382	211	89	+	+	SYM
ejpam-2382	211	90	k2	k2	X
ejpam-2382	211	91	1k2	1k2	NUM
ejpam-2382	211	92	4	4	NUM
ejpam-2382	211	93	.	.	PUNCT
ejpam-2382	212	1	(	(	PUNCT
ejpam-2382	212	2	48	48	NUM
ejpam-2382	212	3	)	)	PUNCT
ejpam-2382	212	4	finally	finally	ADV
ejpam-2382	212	5	,	,	PUNCT
ejpam-2382	212	6	considering	consider	VERB
ejpam-2382	212	7	the	the	DET
ejpam-2382	212	8	equations	equation	NOUN
ejpam-2382	212	9	(	(	PUNCT
ejpam-2382	212	10	21	21	NUM
ejpam-2382	212	11	)	)	PUNCT
ejpam-2382	212	12	,	,	PUNCT
ejpam-2382	212	13	(	(	PUNCT
ejpam-2382	212	14	41	41	NUM
ejpam-2382	212	15	)	)	PUNCT
ejpam-2382	212	16	,	,	PUNCT
ejpam-2382	212	17	(	(	PUNCT
ejpam-2382	212	18	44	44	NUM
ejpam-2382	212	19	)	)	PUNCT
ejpam-2382	212	20	and	and	CCONJ
ejpam-2382	212	21	(	(	PUNCT
ejpam-2382	212	22	48	48	NUM
ejpam-2382	212	23	)	)	PUNCT
ejpam-2382	212	24	the	the	DET
ejpam-2382	212	25	fourth	fourth	ADJ
ejpam-2382	212	26	curvature	curvature	NOUN
ejpam-2382	212	27	of	of	ADP
ejpam-2382	212	28	y	y	PROPN
ejpam-2382	212	29	is	be	AUX
ejpam-2382	212	30	found	find	VERB
ejpam-2382	212	31	as	as	ADP
ejpam-2382	212	32	ky	ky	PROPN
ejpam-2382	212	33	4	4	NUM
ejpam-2382	212	34	=	=	SYM
ejpam-2382	212	35	4k2k4(1−	4k2k4(1−	NUM
ejpam-2382	212	36	k2	k2	NOUN
ejpam-2382	212	37	)	)	PUNCT
ejpam-2382	212	38	q	q	PROPN
ejpam-2382	212	39	k2	k2	PROPN
ejpam-2382	212	40	1	1	NUM
ejpam-2382	212	41	+	+	SYM
ejpam-2382	212	42	k2	k2	ADJ
ejpam-2382	212	43	2	2	NUM
ejpam-2382	212	44	k3(c	k3(c	ADP
ejpam-2382	212	45	−	−	PROPN
ejpam-2382	212	46	s)2(k2	s)2(k2	NOUN
ejpam-2382	212	47	1k2	1k2	NUM
ejpam-2382	212	48	3	3	NUM
ejpam-2382	212	49	+	+	CCONJ
ejpam-2382	212	50	k2	k2	NOUN
ejpam-2382	212	51	2k2	2k2	NUM
ejpam-2382	212	52	4	4	NUM
ejpam-2382	212	53	+	+	SYM
ejpam-2382	212	54	k2	k2	X
ejpam-2382	212	55	1k2	1k2	NUM
ejpam-2382	212	56	4	4	NUM
ejpam-2382	212	57	)	)	PUNCT
ejpam-2382	212	58	.	.	PUNCT
ejpam-2382	213	1	(	(	PUNCT
ejpam-2382	213	2	49	49	NUM
ejpam-2382	213	3	)	)	PUNCT
ejpam-2382	213	4	therefore	therefore	ADV
ejpam-2382	213	5	,	,	PUNCT
ejpam-2382	213	6	the	the	DET
ejpam-2382	213	7	following	follow	VERB
ejpam-2382	213	8	theorem	theorem	NOUN
ejpam-2382	213	9	and	and	CCONJ
ejpam-2382	213	10	results	result	NOUN
ejpam-2382	213	11	can	can	AUX
ejpam-2382	213	12	be	be	AUX
ejpam-2382	213	13	given	give	VERB
ejpam-2382	213	14	theorem	theorem	VERB
ejpam-2382	213	15	3	3	X
ejpam-2382	213	16	.	.	PUNCT
ejpam-2382	214	1	let	let	VERB
ejpam-2382	214	2	x	x	PRON
ejpam-2382	214	3	be	be	AUX
ejpam-2382	214	4	a	a	DET
ejpam-2382	214	5	w	w	NOUN
ejpam-2382	214	6	-	-	PUNCT
ejpam-2382	214	7	curve	curve	NOUN
ejpam-2382	214	8	and	and	CCONJ
ejpam-2382	214	9	y	y	PROPN
ejpam-2382	214	10	be	be	AUX
ejpam-2382	214	11	the	the	DET
ejpam-2382	214	12	involute	involute	NOUN
ejpam-2382	214	13	of	of	ADP
ejpam-2382	214	14	x	x	PUNCT
ejpam-2382	214	15	in	in	ADP
ejpam-2382	214	16	e5	e5	PROPN
ejpam-2382	214	17	.	.	PUNCT
ejpam-2382	215	1	�	�	PROPN
ejpam-2382	215	2	v1	v1	PROPN
ejpam-2382	215	3	,	,	PUNCT
ejpam-2382	215	4	v2	v2	PROPN
ejpam-2382	215	5	,	,	PUNCT
ejpam-2382	215	6	v3	v3	PROPN
ejpam-2382	215	7	,	,	PUNCT
ejpam-2382	215	8	v4	v4	PROPN
ejpam-2382	215	9	,	,	PUNCT
ejpam-2382	215	10	v5	v5	NOUN
ejpam-2382	215	11	,	,	PUNCT
ejpam-2382	215	12	k1	k1	NOUN
ejpam-2382	215	13	,	,	PUNCT
ejpam-2382	215	14	k2	k2	NOUN
ejpam-2382	215	15	,	,	PUNCT
ejpam-2382	215	16	k3	k3	PROPN
ejpam-2382	215	17	,	,	PUNCT
ejpam-2382	215	18	k4	k4	NOUN
ejpam-2382	215	19	and	and	CCONJ
ejpam-2382	215	20	�	�	PROPN
ejpam-2382	215	21	v	v	PROPN
ejpam-2382	215	22	y	y	PROPN
ejpam-2382	215	23	1	1	NUM
ejpam-2382	215	24	,	,	PUNCT
ejpam-2382	215	25	v	v	NOUN
ejpam-2382	215	26	y	y	PROPN
ejpam-2382	215	27	2	2	NUM
ejpam-2382	215	28	,	,	PUNCT
ejpam-2382	215	29	v	v	NOUN
ejpam-2382	215	30	y	y	PROPN
ejpam-2382	215	31	3	3	NUM
ejpam-2382	215	32	,	,	PUNCT
ejpam-2382	215	33	v	v	NOUN
ejpam-2382	215	34	y	y	PROPN
ejpam-2382	215	35	4	4	NUM
ejpam-2382	215	36	,	,	PUNCT
ejpam-2382	215	37	v	v	NOUN
ejpam-2382	215	38	y	y	PROPN
ejpam-2382	215	39	5	5	NUM
ejpam-2382	215	40	,	,	PUNCT
ejpam-2382	215	41	ky	ky	PROPN
ejpam-2382	215	42	1	1	NUM
ejpam-2382	215	43	,	,	PUNCT
ejpam-2382	215	44	ky	ky	PROPN
ejpam-2382	215	45	2	2	NUM
ejpam-2382	215	46	,	,	PUNCT
ejpam-2382	215	47	ky	ky	PROPN
ejpam-2382	215	48	3	3	NUM
ejpam-2382	215	49	,	,	PUNCT
ejpam-2382	215	50	ky	ky	PROPN
ejpam-2382	215	51	4	4	NUM
ejpam-2382	215	52	denote	denote	VERB
ejpam-2382	215	53	the	the	DET
ejpam-2382	215	54	frenet	frenet	NOUN
ejpam-2382	215	55	apparatus	apparatus	NOUN
ejpam-2382	215	56	of	of	ADP
ejpam-2382	215	57	the	the	DET
ejpam-2382	215	58	curves	curve	NOUN
ejpam-2382	215	59	x	x	PUNCT
ejpam-2382	215	60	and	and	CCONJ
ejpam-2382	215	61	y	y	PROPN
ejpam-2382	215	62	,	,	PUNCT
ejpam-2382	215	63	respectively	respectively	ADV
ejpam-2382	215	64	.	.	PUNCT
ejpam-2382	216	1	the	the	DET
ejpam-2382	216	2	relation	relation	NOUN
ejpam-2382	216	3	can	can	AUX
ejpam-2382	216	4	be	be	AUX
ejpam-2382	216	5	expressed	express	VERB
ejpam-2382	216	6	as	as	ADP
ejpam-2382	216	7	v	v	NOUN
ejpam-2382	216	8	y	y	PROPN
ejpam-2382	216	9	1	1	NUM
ejpam-2382	216	10	=	=	SYM
ejpam-2382	216	11	v2	v2	PROPN
ejpam-2382	216	12	,	,	PUNCT
ejpam-2382	216	13	m.	m.	NOUN
ejpam-2382	216	14	masal	masal	NOUN
ejpam-2382	216	15	,	,	PUNCT
ejpam-2382	216	16	a.	a.	PROPN
ejpam-2382	216	17	azak	azak	PROPN
ejpam-2382	216	18	/	/	SYM
ejpam-2382	216	19	eur	eur	PROPN
ejpam-2382	216	20	.	.	PUNCT
ejpam-2382	217	1	j.	j.	PROPN
ejpam-2382	217	2	pure	pure	PROPN
ejpam-2382	217	3	appl	appl	PROPN
ejpam-2382	217	4	.	.	PROPN
ejpam-2382	217	5	math	math	PROPN
ejpam-2382	217	6	,	,	PUNCT
ejpam-2382	217	7	8	8	NUM
ejpam-2382	217	8	(	(	PUNCT
ejpam-2382	217	9	2015	2015	NUM
ejpam-2382	217	10	)	)	PUNCT
ejpam-2382	217	11	,	,	PUNCT
ejpam-2382	217	12	255	255	NUM
ejpam-2382	217	13	-	-	SYM
ejpam-2382	217	14	270	270	NUM
ejpam-2382	217	15	266	266	NUM
ejpam-2382	217	16	v	v	NOUN
ejpam-2382	217	17	y	y	PROPN
ejpam-2382	217	18	2	2	NUM
ejpam-2382	217	19	=	=	NOUN
ejpam-2382	217	20	−	−	PROPN
ejpam-2382	217	21	k1	k1	PROPN
ejpam-2382	217	22	q	q	PROPN
ejpam-2382	217	23	k2	k2	PROPN
ejpam-2382	217	24	1	1	NUM
ejpam-2382	217	25	+	+	SYM
ejpam-2382	217	26	k2	k2	ADJ
ejpam-2382	217	27	2	2	NUM
ejpam-2382	217	28	v1	v1	NOUN
ejpam-2382	217	29	+	+	CCONJ
ejpam-2382	217	30	k2	k2	PROPN
ejpam-2382	217	31	q	q	PROPN
ejpam-2382	217	32	k2	k2	PROPN
ejpam-2382	217	33	1	1	NUM
ejpam-2382	217	34	+	+	CCONJ
ejpam-2382	217	35	k2	k2	PROPN
ejpam-2382	217	36	2	2	NUM
ejpam-2382	217	37	v3	v3	PROPN
ejpam-2382	217	38	,	,	PUNCT
ejpam-2382	217	39	v	v	NOUN
ejpam-2382	217	40	y	y	PROPN
ejpam-2382	217	41	3	3	NUM
ejpam-2382	217	42	=	=	SYM
ejpam-2382	217	43	v4	v4	NOUN
ejpam-2382	217	44	,	,	PUNCT
ejpam-2382	217	45	v	v	NOUN
ejpam-2382	217	46	y	y	PROPN
ejpam-2382	217	47	4	4	NUM
ejpam-2382	217	48	=	=	SYM
ejpam-2382	217	49	−	−	PROPN
ejpam-2382	217	50	k1k2k3	k1k2k3	PROPN
ejpam-2382	217	51	q	q	PROPN
ejpam-2382	217	52	k2	k2	PROPN
ejpam-2382	217	53	1	1	NUM
ejpam-2382	217	54	+	+	SYM
ejpam-2382	217	55	k2	k2	ADJ
ejpam-2382	217	56	2	2	NUM
ejpam-2382	217	57	q	q	PROPN
ejpam-2382	217	58	k2	k2	NOUN
ejpam-2382	217	59	1k2	1k2	NUM
ejpam-2382	217	60	3	3	NUM
ejpam-2382	217	61	+	+	SYM
ejpam-2382	217	62	k2	k2	NOUN
ejpam-2382	217	63	2k2	2k2	NUM
ejpam-2382	217	64	4	4	NUM
ejpam-2382	217	65	+	+	SYM
ejpam-2382	217	66	k2	k2	ADJ
ejpam-2382	217	67	1k2	1k2	NUM
ejpam-2382	217	68	4	4	NUM
ejpam-2382	217	69	v1	v1	PROPN
ejpam-2382	217	70	−	−	PROPN
ejpam-2382	217	71	k2	k2	PROPN
ejpam-2382	217	72	1k3	1k3	PROPN
ejpam-2382	217	73	q	q	PROPN
ejpam-2382	217	74	k2	k2	PROPN
ejpam-2382	217	75	1	1	NUM
ejpam-2382	217	76	+	+	SYM
ejpam-2382	217	77	k2	k2	ADJ
ejpam-2382	217	78	2	2	NUM
ejpam-2382	217	79	q	q	PROPN
ejpam-2382	217	80	k2	k2	NOUN
ejpam-2382	217	81	1k2	1k2	NUM
ejpam-2382	217	82	3	3	NUM
ejpam-2382	218	1	+	+	SYM
ejpam-2382	218	2	k2	k2	NOUN
ejpam-2382	218	3	2k2	2k2	NUM
ejpam-2382	218	4	4	4	NUM
ejpam-2382	218	5	+	+	SYM
ejpam-2382	218	6	k2	k2	X
ejpam-2382	218	7	1k2	1k2	NUM
ejpam-2382	218	8	4	4	NUM
ejpam-2382	218	9	v3	v3	PROPN
ejpam-2382	218	10	+	+	CCONJ
ejpam-2382	218	11	k4	k4	PROPN
ejpam-2382	218	12	�	�	PROPN
ejpam-2382	218	13	k2	k2	PROPN
ejpam-2382	218	14	1	1	NUM
ejpam-2382	218	15	+	+	CCONJ
ejpam-2382	218	16	k2	k2	ADJ
ejpam-2382	218	17	2	2	NUM
ejpam-2382	218	18	�	�	PROPN
ejpam-2382	218	19	q	q	PROPN
ejpam-2382	218	20	k2	k2	PROPN
ejpam-2382	218	21	1	1	NUM
ejpam-2382	218	22	+	+	SYM
ejpam-2382	218	23	k2	k2	ADJ
ejpam-2382	218	24	2	2	NUM
ejpam-2382	218	25	q	q	PROPN
ejpam-2382	218	26	k2	k2	NOUN
ejpam-2382	218	27	1k2	1k2	NUM
ejpam-2382	218	28	3	3	NUM
ejpam-2382	218	29	+	+	SYM
ejpam-2382	218	30	k2	k2	NOUN
ejpam-2382	218	31	2k2	2k2	NUM
ejpam-2382	218	32	4	4	NUM
ejpam-2382	218	33	+	+	SYM
ejpam-2382	218	34	k2	k2	ADJ
ejpam-2382	218	35	1k2	1k2	NUM
ejpam-2382	218	36	4	4	NUM
ejpam-2382	218	37	v5	v5	PROPN
ejpam-2382	218	38	,	,	PUNCT
ejpam-2382	218	39	v	v	NOUN
ejpam-2382	218	40	y	y	PROPN
ejpam-2382	218	41	5	5	NUM
ejpam-2382	218	42	=	=	SYM
ejpam-2382	218	43	k2k4	k2k4	PROPN
ejpam-2382	218	44	q	q	PROPN
ejpam-2382	218	45	k2	k2	NOUN
ejpam-2382	218	46	1k2	1k2	NUM
ejpam-2382	218	47	3	3	NUM
ejpam-2382	218	48	+	+	SYM
ejpam-2382	218	49	k2	k2	NOUN
ejpam-2382	218	50	2k2	2k2	NUM
ejpam-2382	218	51	4	4	NUM
ejpam-2382	218	52	+	+	SYM
ejpam-2382	218	53	k2	k2	X
ejpam-2382	218	54	1k2	1k2	NUM
ejpam-2382	218	55	4v1	4v1	NUM
ejpam-2382	219	1	+	+	CCONJ
ejpam-2382	219	2	k1k4	k1k4	PROPN
ejpam-2382	219	3	q	q	PROPN
ejpam-2382	219	4	k2	k2	PROPN
ejpam-2382	219	5	1k2	1k2	NUM
ejpam-2382	219	6	3	3	NUM
ejpam-2382	219	7	+	+	SYM
ejpam-2382	219	8	k2	k2	NOUN
ejpam-2382	219	9	2k2	2k2	NUM
ejpam-2382	219	10	4	4	NUM
ejpam-2382	219	11	+	+	SYM
ejpam-2382	219	12	k2	k2	ADJ
ejpam-2382	219	13	1k2	1k2	NUM
ejpam-2382	219	14	4v3	4v3	NUM
ejpam-2382	220	1	+	+	CCONJ
ejpam-2382	220	2	k1k3	k1k3	PROPN
ejpam-2382	220	3	q	q	PROPN
ejpam-2382	220	4	k2	k2	PROPN
ejpam-2382	220	5	1k2	1k2	NUM
ejpam-2382	220	6	3	3	NUM
ejpam-2382	220	7	+	+	SYM
ejpam-2382	220	8	k2	k2	NOUN
ejpam-2382	220	9	2k2	2k2	NUM
ejpam-2382	220	10	4	4	NUM
ejpam-2382	220	11	+	+	SYM
ejpam-2382	220	12	k2	k2	PROPN
ejpam-2382	220	13	1k2	1k2	PROPN
ejpam-2382	220	14	4v5	4v5	PROPN
ejpam-2382	220	15	,	,	PUNCT
ejpam-2382	220	16	ky	ky	PROPN
ejpam-2382	220	17	1	1	NUM
ejpam-2382	220	18	=	=	SYM
ejpam-2382	220	19	q	q	PROPN
ejpam-2382	220	20	k2	k2	PROPN
ejpam-2382	220	21	1	1	NUM
ejpam-2382	220	22	+	+	SYM
ejpam-2382	220	23	k2	k2	ADJ
ejpam-2382	220	24	2	2	NUM
ejpam-2382	220	25	(	(	PUNCT
ejpam-2382	220	26	c	c	NOUN
ejpam-2382	220	27	−	−	PROPN
ejpam-2382	220	28	s	s	NOUN
ejpam-2382	220	29	)	)	PUNCT
ejpam-2382	220	30	k1	k1	NOUN
ejpam-2382	220	31	,	,	PUNCT
ejpam-2382	220	32	ky	ky	PROPN
ejpam-2382	220	33	2	2	NUM
ejpam-2382	220	34	=	=	SYM
ejpam-2382	220	35	k2k3	k2k3	X
ejpam-2382	220	36	(	(	PUNCT
ejpam-2382	220	37	c	c	X
ejpam-2382	220	38	−	−	PROPN
ejpam-2382	220	39	s	s	NOUN
ejpam-2382	220	40	)	)	PUNCT
ejpam-2382	220	41	k1	k1	PROPN
ejpam-2382	220	42	q	q	PROPN
ejpam-2382	220	43	k2	k2	PROPN
ejpam-2382	220	44	1	1	NUM
ejpam-2382	220	45	+	+	SYM
ejpam-2382	220	46	k2	k2	PROPN
ejpam-2382	220	47	2	2	NUM
ejpam-2382	220	48	,	,	PUNCT
ejpam-2382	220	49	ky	ky	PROPN
ejpam-2382	220	50	3	3	NUM
ejpam-2382	220	51	=	=	SYM
ejpam-2382	220	52	q	q	PROPN
ejpam-2382	220	53	k2	k2	NOUN
ejpam-2382	220	54	1k2	1k2	NUM
ejpam-2382	220	55	3	3	NUM
ejpam-2382	220	56	+	+	SYM
ejpam-2382	220	57	k2	k2	NOUN
ejpam-2382	220	58	2k2	2k2	NUM
ejpam-2382	220	59	4	4	NUM
ejpam-2382	220	60	+	+	SYM
ejpam-2382	220	61	k2	k2	X
ejpam-2382	220	62	1k2	1k2	NUM
ejpam-2382	220	63	4	4	NUM
ejpam-2382	220	64	(	(	PUNCT
ejpam-2382	220	65	c	c	NOUN
ejpam-2382	220	66	−	−	PROPN
ejpam-2382	220	67	s	s	NOUN
ejpam-2382	220	68	)	)	PUNCT
ejpam-2382	220	69	k1	k1	PROPN
ejpam-2382	220	70	q	q	PROPN
ejpam-2382	220	71	k2	k2	PROPN
ejpam-2382	220	72	1	1	NUM
ejpam-2382	220	73	+	+	SYM
ejpam-2382	220	74	k2	k2	PROPN
ejpam-2382	220	75	2	2	NUM
ejpam-2382	220	76	,	,	PUNCT
ejpam-2382	220	77	ky	ky	PROPN
ejpam-2382	220	78	4	4	NUM
ejpam-2382	220	79	=	=	SYM
ejpam-2382	220	80	4k2k4	4k2k4	NUM
ejpam-2382	220	81	�	�	PROPN
ejpam-2382	220	82	1−	1−	NUM
ejpam-2382	220	83	k2	k2	PROPN
ejpam-2382	220	84	�	�	PROPN
ejpam-2382	220	85	q	q	PROPN
ejpam-2382	220	86	k2	k2	PROPN
ejpam-2382	220	87	1	1	NUM
ejpam-2382	220	88	+	+	SYM
ejpam-2382	220	89	k2	k2	ADJ
ejpam-2382	220	90	2	2	NUM
ejpam-2382	220	91	(	(	PUNCT
ejpam-2382	220	92	c	c	NOUN
ejpam-2382	220	93	−	−	PROPN
ejpam-2382	220	94	s)2	s)2	NOUN
ejpam-2382	220	95	k3	k3	PROPN
ejpam-2382	220	96	�	�	PROPN
ejpam-2382	220	97	k2	k2	PROPN
ejpam-2382	220	98	1k2	1k2	NUM
ejpam-2382	220	99	3	3	NUM
ejpam-2382	220	100	+	+	SYM
ejpam-2382	220	101	k2	k2	NOUN
ejpam-2382	220	102	2k2	2k2	NUM
ejpam-2382	220	103	4	4	NUM
ejpam-2382	220	104	+	+	SYM
ejpam-2382	220	105	k2	k2	ADJ
ejpam-2382	220	106	1k2	1k2	NUM
ejpam-2382	220	107	4	4	NUM
ejpam-2382	220	108	�	�	PROPN
ejpam-2382	220	109	.	.	PUNCT
ejpam-2382	221	1	corollary	corollary	ADJ
ejpam-2382	221	2	1	1	NUM
ejpam-2382	221	3	.	.	PUNCT
ejpam-2382	221	4	�	�	PROPN
ejpam-2382	221	5	v	v	ADP
ejpam-2382	221	6	y	y	PROPN
ejpam-2382	221	7	1	1	NUM
ejpam-2382	221	8	,	,	PUNCT
ejpam-2382	221	9	v	v	NOUN
ejpam-2382	221	10	y	y	PROPN
ejpam-2382	221	11	2	2	NUM
ejpam-2382	221	12	,	,	PUNCT
ejpam-2382	221	13	v	v	NOUN
ejpam-2382	221	14	y	y	PROPN
ejpam-2382	221	15	3	3	NUM
ejpam-2382	221	16	,	,	PUNCT
ejpam-2382	221	17	v	v	NOUN
ejpam-2382	221	18	y	y	PROPN
ejpam-2382	221	19	4	4	NUM
ejpam-2382	221	20	,	,	PUNCT
ejpam-2382	221	21	v	v	NOUN
ejpam-2382	221	22	y	y	PROPN
ejpam-2382	221	23	5	5	NUM
ejpam-2382	221	24	is	be	AUX
ejpam-2382	221	25	an	an	DET
ejpam-2382	221	26	orthonormal	orthonormal	ADJ
ejpam-2382	221	27	frame	frame	NOUN
ejpam-2382	221	28	in	in	ADP
ejpam-2382	221	29	e5	e5	PROPN
ejpam-2382	221	30	.	.	PUNCT
ejpam-2382	222	1	corollary	corollary	ADJ
ejpam-2382	222	2	2	2	NUM
ejpam-2382	222	3	.	.	PUNCT
ejpam-2382	223	1	while	while	SCONJ
ejpam-2382	223	2	x	x	PRON
ejpam-2382	223	3	is	be	AUX
ejpam-2382	223	4	a	a	DET
ejpam-2382	223	5	w	w	NOUN
ejpam-2382	223	6	-	-	PUNCT
ejpam-2382	223	7	curve	curve	NOUN
ejpam-2382	223	8	,	,	PUNCT
ejpam-2382	223	9	y	y	PROPN
ejpam-2382	223	10	can	can	AUX
ejpam-2382	223	11	not	not	PART
ejpam-2382	223	12	be	be	AUX
ejpam-2382	223	13	a	a	DET
ejpam-2382	223	14	w	w	NOUN
ejpam-2382	223	15	-	-	PUNCT
ejpam-2382	223	16	curve	curve	NOUN
ejpam-2382	223	17	.	.	PUNCT
ejpam-2382	224	1	corollary	corollary	ADJ
ejpam-2382	224	2	3	3	NUM
ejpam-2382	224	3	.	.	PUNCT
ejpam-2382	225	1	the	the	DET
ejpam-2382	225	2	involute	involute	ADJ
ejpam-2382	225	3	curve	curve	NOUN
ejpam-2382	225	4	y	y	PROPN
ejpam-2382	225	5	ca	can	AUX
ejpam-2382	225	6	n’t	not	PART
ejpam-2382	225	7	be	be	AUX
ejpam-2382	225	8	an	an	DET
ejpam-2382	225	9	inclined	inclined	ADJ
ejpam-2382	225	10	curve	curve	NOUN
ejpam-2382	225	11	.	.	PUNCT
ejpam-2382	226	1	6	6	X
ejpam-2382	226	2	.	.	PUNCT
ejpam-2382	226	3	the	the	DET
ejpam-2382	226	4	spherical	spherical	ADJ
ejpam-2382	226	5	curves	curve	NOUN
ejpam-2382	226	6	in	in	ADP
ejpam-2382	226	7	euclidean	euclidean	ADJ
ejpam-2382	226	8	5	5	NUM
ejpam-2382	226	9	-	-	PUNCT
ejpam-2382	226	10	space	space	NOUN
ejpam-2382	226	11	let	let	VERB
ejpam-2382	226	12	x	x	PROPN
ejpam-2382	226	13	⊂	⊂	PROPN
ejpam-2382	226	14	r5	r5	PROPN
ejpam-2382	226	15	curve	curve	NOUN
ejpam-2382	226	16	be	be	AUX
ejpam-2382	226	17	given	give	VERB
ejpam-2382	226	18	with	with	ADP
ejpam-2382	226	19	coordinate	coordinate	ADJ
ejpam-2382	226	20	neighborhood	neighborhood	NOUN
ejpam-2382	226	21	(	(	PUNCT
ejpam-2382	226	22	i	i	NOUN
ejpam-2382	226	23	,	,	PUNCT
ejpam-2382	226	24	x	x	PROPN
ejpam-2382	226	25	)	)	PUNCT
ejpam-2382	226	26	and	and	CCONJ
ejpam-2382	226	27	s	s	NOUN
ejpam-2382	226	28	∈	∈	NOUN
ejpam-2382	226	29	i	i	PRON
ejpam-2382	226	30	be	be	VERB
ejpam-2382	226	31	arc	arc	NOUN
ejpam-2382	226	32	-	-	PUNCT
ejpam-2382	226	33	length	length	NOUN
ejpam-2382	226	34	parameter	parameter	NOUN
ejpam-2382	226	35	of	of	ADP
ejpam-2382	226	36	x	x	X
ejpam-2382	226	37	.	.	PUNCT
ejpam-2382	227	1	also	also	ADV
ejpam-2382	227	2	,	,	PUNCT
ejpam-2382	227	3	assume	assume	VERB
ejpam-2382	227	4	that	that	SCONJ
ejpam-2382	227	5	s4	s4	PROPN
ejpam-2382	227	6	is	be	AUX
ejpam-2382	227	7	a	a	DET
ejpam-2382	227	8	hypersphere	hypersphere	NOUN
ejpam-2382	227	9	which	which	PRON
ejpam-2382	227	10	has	have	VERB
ejpam-2382	227	11	six	six	NUM
ejpam-2382	227	12	common	common	ADJ
ejpam-2382	227	13	coalescent	coalescent	NOUN
ejpam-2382	227	14	points	point	NOUN
ejpam-2382	227	15	with	with	ADP
ejpam-2382	227	16	the	the	DET
ejpam-2382	227	17	curve	curve	NOUN
ejpam-2382	227	18	x	x	X
ejpam-2382	227	19	.	.	PUNCT
ejpam-2382	228	1	if	if	SCONJ
ejpam-2382	228	2	x	x	X
ejpam-2382	228	3	(	(	PUNCT
ejpam-2382	228	4	s	s	X
ejpam-2382	228	5	)	)	PUNCT
ejpam-2382	228	6	is	be	AUX
ejpam-2382	228	7	a	a	DET
ejpam-2382	228	8	point	point	NOUN
ejpam-2382	228	9	on	on	ADP
ejpam-2382	228	10	this	this	DET
ejpam-2382	228	11	hypersphere	hypersphere	NOUN
ejpam-2382	228	12	,	,	PUNCT
ejpam-2382	228	13	c	c	PROPN
ejpam-2382	228	14	is	be	AUX
ejpam-2382	228	15	the	the	DET
ejpam-2382	228	16	center	center	NOUN
ejpam-2382	228	17	of	of	ADP
ejpam-2382	228	18	this	this	DET
ejpam-2382	228	19	hypersphere	hypersphere	NOUN
ejpam-2382	228	20	and	and	CCONJ
ejpam-2382	228	21	r	r	NOUN
ejpam-2382	228	22	is	be	AUX
ejpam-2382	228	23	the	the	DET
ejpam-2382	228	24	radius	radius	NOUN
ejpam-2382	228	25	of	of	ADP
ejpam-2382	228	26	it	it	PRON
ejpam-2382	228	27	,	,	PUNCT
ejpam-2382	228	28	then	then	ADV
ejpam-2382	228	29	the	the	DET
ejpam-2382	228	30	equation	equation	NOUN
ejpam-2382	228	31	of	of	ADP
ejpam-2382	228	32	the	the	DET
ejpam-2382	228	33	hypersphere	hypersphere	PROPN
ejpam-2382	228	34	s4	s4	PROPN
ejpam-2382	228	35	is	be	AUX
ejpam-2382	228	36	〈	〈	NOUN
ejpam-2382	228	37	x	x	X
ejpam-2382	228	38	(	(	PUNCT
ejpam-2382	228	39	s)−	s)−	PROPN
ejpam-2382	228	40	c	c	PROPN
ejpam-2382	228	41	,	,	PUNCT
ejpam-2382	228	42	x	x	X
ejpam-2382	228	43	(	(	PUNCT
ejpam-2382	228	44	s)−	s)−	PROPN
ejpam-2382	228	45	c	c	NOUN
ejpam-2382	228	46	〉	〉	NOUN
ejpam-2382	228	47	=	=	SYM
ejpam-2382	228	48	r2	r2	NOUN
ejpam-2382	228	49	.	.	PUNCT
ejpam-2382	229	1	(	(	PUNCT
ejpam-2382	229	2	50	50	NUM
ejpam-2382	229	3	)	)	PUNCT
ejpam-2382	229	4	on	on	ADP
ejpam-2382	229	5	the	the	DET
ejpam-2382	229	6	other	other	ADJ
ejpam-2382	229	7	hand	hand	NOUN
ejpam-2382	229	8	,	,	PUNCT
ejpam-2382	229	9	for	for	ADP
ejpam-2382	229	10	the	the	DET
ejpam-2382	229	11	base	base	PROPN
ejpam-2382	229	12	�	�	PROPN
ejpam-2382	229	13	v1	v1	PROPN
ejpam-2382	229	14	,	,	PUNCT
ejpam-2382	229	15	v2	v2	PROPN
ejpam-2382	229	16	,	,	PUNCT
ejpam-2382	229	17	v3	v3	PROPN
ejpam-2382	229	18	,	,	PUNCT
ejpam-2382	229	19	v4	v4	PROPN
ejpam-2382	229	20	,	,	PUNCT
ejpam-2382	229	21	v5	v5	PROPN
ejpam-2382	229	22	and	and	CCONJ
ejpam-2382	229	23	mi(s	mi(s	NUM
ejpam-2382	229	24	)	)	PUNCT
ejpam-2382	229	25	∈	∈	PROPN
ejpam-2382	229	26	r	r	NOUN
ejpam-2382	229	27	c	c	NOUN
ejpam-2382	229	28	−	−	NOUN
ejpam-2382	229	29	x	x	SYM
ejpam-2382	229	30	(	(	PUNCT
ejpam-2382	229	31	s	s	NOUN
ejpam-2382	229	32	)	)	PUNCT
ejpam-2382	229	33	=	=	SYM
ejpam-2382	229	34	m1(s)v1(s	m1(s)v1(	NOUN
ejpam-2382	229	35	)	)	PUNCT
ejpam-2382	229	36	+	+	NOUN
ejpam-2382	229	37	m2(s)v2(s	m2(s)v2(s	NOUN
ejpam-2382	229	38	)	)	PUNCT
ejpam-2382	229	39	+	+	NOUN
ejpam-2382	229	40	m3(s)v3(s	m3(s)v3(	NOUN
ejpam-2382	229	41	)	)	PUNCT
ejpam-2382	229	42	+	+	NOUN
ejpam-2382	229	43	m4(s)v4(s	m4(s)v4(s	NOUN
ejpam-2382	229	44	)	)	PUNCT
ejpam-2382	229	45	+	+	NOUN
ejpam-2382	229	46	m5(s)v5(s	m5(s)v5(s	X
ejpam-2382	229	47	)	)	PUNCT
ejpam-2382	229	48	,	,	PUNCT
ejpam-2382	229	49	(	(	PUNCT
ejpam-2382	229	50	51	51	NUM
ejpam-2382	229	51	)	)	PUNCT
ejpam-2382	229	52	can	can	AUX
ejpam-2382	229	53	be	be	AUX
ejpam-2382	229	54	written	write	VERB
ejpam-2382	229	55	.	.	PUNCT
ejpam-2382	230	1	hence	hence	ADV
ejpam-2382	230	2	,	,	PUNCT
ejpam-2382	230	3	mi(s	mi(s	ADV
ejpam-2382	230	4	)	)	PUNCT
ejpam-2382	231	1	=	=	PUNCT
ejpam-2382	231	2	c	c	NOUN
ejpam-2382	231	3	−	−	NOUN
ejpam-2382	231	4	x	x	SYM
ejpam-2382	231	5	(	(	PUNCT
ejpam-2382	231	6	s	s	NOUN
ejpam-2382	231	7	)	)	PUNCT
ejpam-2382	231	8	,	,	PUNCT
ejpam-2382	231	9	vi(s	vi(s	NUM
ejpam-2382	231	10	)	)	PUNCT
ejpam-2382	231	11	�	�	PROPN
ejpam-2382	231	12	,	,	PUNCT
ejpam-2382	231	13	1≤	1≤	NUM
ejpam-2382	232	1	i	i	X
ejpam-2382	232	2	≤	≤	ADV
ejpam-2382	232	3	5	5	NUM
ejpam-2382	232	4	(	(	PUNCT
ejpam-2382	232	5	52	52	NUM
ejpam-2382	232	6	)	)	PUNCT
ejpam-2382	232	7	m.	m.	NOUN
ejpam-2382	232	8	masal	masal	NOUN
ejpam-2382	232	9	,	,	PUNCT
ejpam-2382	232	10	a.	a.	PROPN
ejpam-2382	232	11	azak	azak	PROPN
ejpam-2382	232	12	/	/	SYM
ejpam-2382	232	13	eur	eur	PROPN
ejpam-2382	232	14	.	.	PUNCT
ejpam-2382	233	1	j.	j.	PROPN
ejpam-2382	233	2	pure	pure	PROPN
ejpam-2382	233	3	appl	appl	PROPN
ejpam-2382	233	4	.	.	PROPN
ejpam-2382	233	5	math	math	PROPN
ejpam-2382	233	6	,	,	PUNCT
ejpam-2382	233	7	8	8	NUM
ejpam-2382	233	8	(	(	PUNCT
ejpam-2382	233	9	2015	2015	NUM
ejpam-2382	233	10	)	)	PUNCT
ejpam-2382	233	11	,	,	PUNCT
ejpam-2382	233	12	255	255	NUM
ejpam-2382	233	13	-	-	SYM
ejpam-2382	233	14	270	270	NUM
ejpam-2382	233	15	267	267	NUM
ejpam-2382	233	16	in	in	ADP
ejpam-2382	233	17	accordance	accordance	NOUN
ejpam-2382	233	18	with	with	ADP
ejpam-2382	233	19	this	this	PRON
ejpam-2382	233	20	,	,	PUNCT
ejpam-2382	233	21	let	let	VERB
ejpam-2382	233	22	us	we	PRON
ejpam-2382	233	23	consider	consider	VERB
ejpam-2382	233	24	f	f	X
ejpam-2382	234	1	:	:	PUNCT
ejpam-2382	234	2	i	i	PRON
ejpam-2382	234	3	→	→	SYM
ejpam-2382	234	4	r	r	NOUN
ejpam-2382	234	5	s→	s→	SYM
ejpam-2382	234	6	f	f	X
ejpam-2382	234	7	(	(	PUNCT
ejpam-2382	234	8	s	s	NOUN
ejpam-2382	234	9	)	)	PUNCT
ejpam-2382	234	10	=	=	PUNCT
ejpam-2382	235	1	〈	〈	PROPN
ejpam-2382	235	2	x	x	SYM
ejpam-2382	235	3	−	−	PROPN
ejpam-2382	235	4	c	c	NOUN
ejpam-2382	235	5	,	,	PUNCT
ejpam-2382	235	6	x	x	X
ejpam-2382	235	7	−	−	NOUN
ejpam-2382	235	8	c	c	X
ejpam-2382	235	9	〉	〉	NOUN
ejpam-2382	235	10	−	−	NOUN
ejpam-2382	235	11	r2	r2	NOUN
ejpam-2382	235	12	.	.	PUNCT
ejpam-2382	236	1	if	if	SCONJ
ejpam-2382	236	2	we	we	PRON
ejpam-2382	236	3	have	have	VERB
ejpam-2382	236	4	the	the	DET
ejpam-2382	236	5	following	follow	VERB
ejpam-2382	236	6	equations	equation	NOUN
ejpam-2382	236	7	f	f	X
ejpam-2382	236	8	(	(	PUNCT
ejpam-2382	236	9	s	s	X
ejpam-2382	236	10	)	)	PUNCT
ejpam-2382	236	11	=	=	SYM
ejpam-2382	236	12	f	f	X
ejpam-2382	236	13	′(s	′(s	NOUN
ejpam-2382	236	14	)	)	PUNCT
ejpam-2382	237	1	=	=	SYM
ejpam-2382	238	1	f	f	X
ejpam-2382	238	2	′′	′′	PROPN
ejpam-2382	238	3	(	(	PUNCT
ejpam-2382	238	4	s	s	X
ejpam-2382	238	5	)	)	PUNCT
ejpam-2382	238	6	=	=	SYM
ejpam-2382	238	7	f	f	X
ejpam-2382	238	8	′′′	′′′	PROPN
ejpam-2382	238	9	(	(	PUNCT
ejpam-2382	238	10	s	s	X
ejpam-2382	238	11	)	)	PUNCT
ejpam-2382	238	12	=	=	SYM
ejpam-2382	238	13	f	f	PROPN
ejpam-2382	238	14	(	(	PUNCT
ejpam-2382	238	15	4	4	NUM
ejpam-2382	238	16	)	)	PUNCT
ejpam-2382	238	17	(	(	PUNCT
ejpam-2382	238	18	s	s	X
ejpam-2382	238	19	)	)	PUNCT
ejpam-2382	238	20	=	=	SYM
ejpam-2382	238	21	f	f	PROPN
ejpam-2382	238	22	(	(	PUNCT
ejpam-2382	238	23	5)(s	5)(s	NUM
ejpam-2382	238	24	)	)	PUNCT
ejpam-2382	238	25	=	=	SYM
ejpam-2382	238	26	0	0	NUM
ejpam-2382	238	27	then	then	ADV
ejpam-2382	238	28	we	we	PRON
ejpam-2382	238	29	say	say	VERB
ejpam-2382	238	30	that	that	SCONJ
ejpam-2382	238	31	the	the	DET
ejpam-2382	238	32	hypersphere	hypersphere	NOUN
ejpam-2382	238	33	touches	touch	VERB
ejpam-2382	238	34	to	to	ADP
ejpam-2382	238	35	x	x	PUNCT
ejpam-2382	238	36	at	at	ADP
ejpam-2382	238	37	the	the	DET
ejpam-2382	238	38	fifth	fifth	ADJ
ejpam-2382	238	39	order	order	NOUN
ejpam-2382	238	40	to	to	ADP
ejpam-2382	238	41	the	the	DET
ejpam-2382	238	42	curve	curve	NOUN
ejpam-2382	238	43	at	at	ADP
ejpam-2382	238	44	x	x	X
ejpam-2382	238	45	(	(	PUNCT
ejpam-2382	238	46	s	s	NOUN
ejpam-2382	238	47	)	)	PUNCT
ejpam-2382	238	48	.	.	PUNCT
ejpam-2382	239	1	therefore	therefore	ADV
ejpam-2382	239	2	,	,	PUNCT
ejpam-2382	239	3	f	f	PROPN
ejpam-2382	239	4	(	(	PUNCT
ejpam-2382	239	5	s	s	NOUN
ejpam-2382	239	6	)	)	PUNCT
ejpam-2382	239	7	=	=	PUNCT
ejpam-2382	239	8	〈	〈	PROPN
ejpam-2382	239	9	x	x	SYM
ejpam-2382	239	10	−	−	PROPN
ejpam-2382	239	11	c	c	NOUN
ejpam-2382	239	12	,	,	PUNCT
ejpam-2382	239	13	x	x	X
ejpam-2382	239	14	−	−	NOUN
ejpam-2382	239	15	c	c	X
ejpam-2382	239	16	〉	〉	NOUN
ejpam-2382	239	17	−	−	NOUN
ejpam-2382	239	18	r2	r2	NOUN
ejpam-2382	239	19	=	=	SYM
ejpam-2382	239	20	0	0	NUM
ejpam-2382	239	21	,	,	PUNCT
ejpam-2382	239	22	(	(	PUNCT
ejpam-2382	239	23	53	53	NUM
ejpam-2382	239	24	)	)	PUNCT
ejpam-2382	239	25	f	f	NOUN
ejpam-2382	239	26	′(s	′(s	NOUN
ejpam-2382	239	27	)	)	PUNCT
ejpam-2382	239	28	=	=	SYM
ejpam-2382	239	29	v1	v1	NOUN
ejpam-2382	239	30	,	,	PUNCT
ejpam-2382	239	31	x	x	PUNCT
ejpam-2382	239	32	−	−	PROPN
ejpam-2382	239	33	c	c	PROPN
ejpam-2382	239	34	�	�	PROPN
ejpam-2382	239	35	=	=	SYM
ejpam-2382	239	36	0⇒	0⇒	PROPN
ejpam-2382	239	37	m1	m1	NOUN
ejpam-2382	239	38	=	=	SYM
ejpam-2382	239	39	0	0	PROPN
ejpam-2382	239	40	,	,	PUNCT
ejpam-2382	239	41	(	(	PUNCT
ejpam-2382	239	42	54	54	NUM
ejpam-2382	239	43	)	)	PUNCT
ejpam-2382	239	44	f	f	PROPN
ejpam-2382	239	45	′′(s	′′(s	PROPN
ejpam-2382	239	46	)	)	PUNCT
ejpam-2382	240	1	=	=	NOUN
ejpam-2382	240	2	0⇒	0⇒	NOUN
ejpam-2382	240	3	v2	v2	NOUN
ejpam-2382	240	4	,	,	PUNCT
ejpam-2382	240	5	x	x	NOUN
ejpam-2382	240	6	−	−	PROPN
ejpam-2382	240	7	c	c	PROPN
ejpam-2382	240	8	�	�	PROPN
ejpam-2382	240	9	=	=	SYM
ejpam-2382	240	10	1	1	NUM
ejpam-2382	240	11	k1	k1	NOUN
ejpam-2382	240	12	⇒	⇒	NOUN
ejpam-2382	240	13	m2	m2	PROPN
ejpam-2382	240	14	=	=	SYM
ejpam-2382	240	15	1	1	NUM
ejpam-2382	240	16	k1	k1	NOUN
ejpam-2382	240	17	,	,	PUNCT
ejpam-2382	240	18	(	(	PUNCT
ejpam-2382	240	19	55	55	NUM
ejpam-2382	240	20	)	)	PUNCT
ejpam-2382	240	21	f	f	PROPN
ejpam-2382	241	1	′′′(s	′′′(s	PROPN
ejpam-2382	241	2	)	)	PUNCT
ejpam-2382	241	3	=	=	NOUN
ejpam-2382	241	4	0⇒	0⇒	NOUN
ejpam-2382	241	5	v3	v3	PROPN
ejpam-2382	241	6	,	,	PUNCT
ejpam-2382	241	7	x	x	PROPN
ejpam-2382	241	8	−	−	PROPN
ejpam-2382	241	9	c	c	PROPN
ejpam-2382	241	10	�	�	PROPN
ejpam-2382	241	11	=	=	PUNCT
ejpam-2382	241	12	m′2	m′2	NOUN
ejpam-2382	241	13	k2	k2	PROPN
ejpam-2382	241	14	⇒	⇒	PROPN
ejpam-2382	241	15	m3	m3	PROPN
ejpam-2382	241	16	=	=	PUNCT
ejpam-2382	241	17	m′2	m′2	PROPN
ejpam-2382	241	18	k2	k2	PROPN
ejpam-2382	241	19	,	,	PUNCT
ejpam-2382	241	20	(	(	PUNCT
ejpam-2382	241	21	56	56	NUM
ejpam-2382	241	22	)	)	PUNCT
ejpam-2382	241	23	f	f	NOUN
ejpam-2382	241	24	(	(	PUNCT
ejpam-2382	241	25	4)(s	4)(s	NOUN
ejpam-2382	241	26	)	)	PUNCT
ejpam-2382	242	1	=	=	NOUN
ejpam-2382	242	2	0⇒	0⇒	NUM
ejpam-2382	242	3	v4	v4	NOUN
ejpam-2382	242	4	,	,	PUNCT
ejpam-2382	242	5	x	x	PUNCT
ejpam-2382	242	6	−	−	PROPN
ejpam-2382	242	7	c	c	PROPN
ejpam-2382	242	8	�	�	PROPN
ejpam-2382	242	9	=	=	NOUN
ejpam-2382	242	10	m′3	m′3	NOUN
ejpam-2382	242	11	+	+	CCONJ
ejpam-2382	242	12	k2m2	k2m2	X
ejpam-2382	242	13	k3	k3	ADJ
ejpam-2382	242	14	⇒	⇒	PROPN
ejpam-2382	242	15	m4	m4	PROPN
ejpam-2382	242	16	=	=	SYM
ejpam-2382	242	17	m′3	m′3	NOUN
ejpam-2382	242	18	+	+	CCONJ
ejpam-2382	242	19	k2m2	k2m2	X
ejpam-2382	242	20	k3	k3	ADJ
ejpam-2382	242	21	,	,	PUNCT
ejpam-2382	242	22	(	(	PUNCT
ejpam-2382	242	23	57	57	NUM
ejpam-2382	242	24	)	)	PUNCT
ejpam-2382	242	25	f	f	NOUN
ejpam-2382	242	26	(	(	PUNCT
ejpam-2382	242	27	5)(s	5)(s	NUM
ejpam-2382	242	28	)	)	PUNCT
ejpam-2382	243	1	=	=	NOUN
ejpam-2382	243	2	0⇒	0⇒	NOUN
ejpam-2382	243	3	v5	v5	NOUN
ejpam-2382	243	4	,	,	PUNCT
ejpam-2382	243	5	x	x	PROPN
ejpam-2382	243	6	−	−	PROPN
ejpam-2382	243	7	c	c	PROPN
ejpam-2382	243	8	�	�	PROPN
ejpam-2382	244	1	=	=	PUNCT
ejpam-2382	245	1	m′4	m′4	NOUN
ejpam-2382	246	1	+	+	CCONJ
ejpam-2382	247	1	k3m3	k3m3	X
ejpam-2382	247	2	k4	k4	ADJ
ejpam-2382	247	3	⇒	⇒	NOUN
ejpam-2382	247	4	m5	m5	PROPN
ejpam-2382	247	5	=	=	SYM
ejpam-2382	247	6	m′4	m′4	NOUN
ejpam-2382	248	1	+	+	CCONJ
ejpam-2382	248	2	k3m3	k3m3	PROPN
ejpam-2382	248	3	k4	k4	NOUN
ejpam-2382	248	4	.	.	PUNCT
ejpam-2382	249	1	(	(	PUNCT
ejpam-2382	249	2	58	58	NUM
ejpam-2382	249	3	)	)	PUNCT
ejpam-2382	249	4	are	be	AUX
ejpam-2382	249	5	obtained	obtain	VERB
ejpam-2382	249	6	.	.	PUNCT
ejpam-2382	250	1	thus	thus	ADV
ejpam-2382	250	2	,	,	PUNCT
ejpam-2382	250	3	the	the	DET
ejpam-2382	250	4	center	center	NOUN
ejpam-2382	250	5	of	of	ADP
ejpam-2382	250	6	the	the	DET
ejpam-2382	250	7	hypersphere	hypersphere	NOUN
ejpam-2382	250	8	is	be	AUX
ejpam-2382	250	9	c	c	NOUN
ejpam-2382	250	10	=	=	PUNCT
ejpam-2382	250	11	x	x	PUNCT
ejpam-2382	251	1	+	+	PUNCT
ejpam-2382	251	2	m2v2	m2v2	ADJ
ejpam-2382	251	3	+	+	CCONJ
ejpam-2382	251	4	�	�	PROPN
ejpam-2382	251	5	m′2	m′2	PROPN
ejpam-2382	251	6	k2	k2	PROPN
ejpam-2382	251	7	�	�	PROPN
ejpam-2382	251	8	v3	v3	PROPN
ejpam-2382	251	9	+	+	CCONJ
ejpam-2382	251	10			PROPN
ejpam-2382	251	11			NOUN
ejpam-2382	251	12			PROPN
ejpam-2382	251	13	�	�	PROPN
ejpam-2382	251	14	m′2	m′2	PROPN
ejpam-2382	251	15	k2	k2	PROPN
ejpam-2382	251	16	�	�	PROPN
ejpam-2382	251	17	′	′	PROPN
ejpam-2382	252	1	+	+	CCONJ
ejpam-2382	252	2	k2m2	k2m2	X
ejpam-2382	252	3	k3	k3	ADJ
ejpam-2382	252	4			NOUN
ejpam-2382	252	5			NOUN
ejpam-2382	252	6	v4	v4	DET
ejpam-2382	252	7	+	+	NUM
ejpam-2382	252	8			NOUN
ejpam-2382	252	9			NOUN
ejpam-2382	252	10			NOUN
ejpam-2382	252	11			NOUN
ejpam-2382	252	12			NOUN
ejpam-2382	252	13			NOUN
ejpam-2382	252	14			PROPN
ejpam-2382	252	15	�	�	PROPN
ejpam-2382	252	16	m′2	m′2	PROPN
ejpam-2382	252	17	k2	k2	PROPN
ejpam-2382	252	18	�	�	PROPN
ejpam-2382	252	19	′	′	PROPN
ejpam-2382	253	1	+	+	CCONJ
ejpam-2382	253	2	k2m2	k2m2	X
ejpam-2382	253	3	k3	k3	ADJ
ejpam-2382	253	4			NOUN
ejpam-2382	253	5			NOUN
ejpam-2382	253	6			PUNCT
ejpam-2382	254	1	′	′	NOUN
ejpam-2382	255	1	+	+	CCONJ
ejpam-2382	255	2	k3	k3	ADJ
ejpam-2382	255	3	�	�	PROPN
ejpam-2382	255	4	m′2	m′2	PROPN
ejpam-2382	255	5	k2	k2	PROPN
ejpam-2382	255	6	�	�	PROPN
ejpam-2382	255	7			PROPN
ejpam-2382	255	8			PROPN
ejpam-2382	255	9			NOUN
ejpam-2382	255	10			PUNCT
ejpam-2382	256	1	1	1	NUM
ejpam-2382	256	2	k4	k4	NOUN
ejpam-2382	256	3	v5	v5	PROPN
ejpam-2382	256	4	(	(	PUNCT
ejpam-2382	256	5	59	59	NUM
ejpam-2382	256	6	)	)	PUNCT
ejpam-2382	256	7	and	and	CCONJ
ejpam-2382	256	8	for	for	ADP
ejpam-2382	256	9	the	the	DET
ejpam-2382	256	10	square	square	NOUN
ejpam-2382	256	11	of	of	ADP
ejpam-2382	256	12	the	the	DET
ejpam-2382	256	13	radius	radius	NOUN
ejpam-2382	256	14	r2	r2	PROPN
ejpam-2382	256	15	=	=	SYM
ejpam-2382	256	16	m2	m2	PROPN
ejpam-2382	256	17	2	2	PROPN
ejpam-2382	256	18	+	+	CCONJ
ejpam-2382	256	19	�	�	PROPN
ejpam-2382	256	20	m′2	m′2	NOUN
ejpam-2382	256	21	k2	k2	PROPN
ejpam-2382	256	22	�	�	PROPN
ejpam-2382	256	23	2	2	NUM
ejpam-2382	256	24	+	+	NUM
ejpam-2382	256	25			NOUN
ejpam-2382	256	26			NOUN
ejpam-2382	256	27			PROPN
ejpam-2382	256	28	�	�	PROPN
ejpam-2382	256	29	m′2	m′2	PROPN
ejpam-2382	256	30	k2	k2	PROPN
ejpam-2382	256	31	�	�	PROPN
ejpam-2382	256	32	′	′	PROPN
ejpam-2382	257	1	+	+	CCONJ
ejpam-2382	257	2	k2m2	k2m2	X
ejpam-2382	257	3	k3	k3	ADJ
ejpam-2382	257	4			PROPN
ejpam-2382	257	5			NOUN
ejpam-2382	257	6			PUNCT
ejpam-2382	258	1	2	2	NUM
ejpam-2382	258	2	+	+	NUM
ejpam-2382	258	3			NOUN
ejpam-2382	258	4			NOUN
ejpam-2382	258	5			NOUN
ejpam-2382	258	6			NOUN
ejpam-2382	258	7			NOUN
ejpam-2382	258	8			NOUN
ejpam-2382	258	9			PROPN
ejpam-2382	258	10	�	�	PROPN
ejpam-2382	258	11	m′2	m′2	PROPN
ejpam-2382	258	12	k2	k2	PROPN
ejpam-2382	258	13	�	�	PROPN
ejpam-2382	258	14	′	′	PROPN
ejpam-2382	259	1	+	+	CCONJ
ejpam-2382	259	2	k2m2	k2m2	X
ejpam-2382	259	3	k3	k3	ADJ
ejpam-2382	259	4	+	+	CCONJ
ejpam-2382	259	5	k3	k3	PROPN
ejpam-2382	259	6	�	�	PROPN
ejpam-2382	259	7	m′2	m′2	PROPN
ejpam-2382	259	8	k2	k2	PROPN
ejpam-2382	259	9	�	�	PROPN
ejpam-2382	259	10			PROPN
ejpam-2382	259	11			NOUN
ejpam-2382	259	12			PUNCT
ejpam-2382	260	1	′	′	NUM
ejpam-2382	260	2			NOUN
ejpam-2382	260	3			NOUN
ejpam-2382	260	4			VERB
ejpam-2382	260	5			PUNCT
ejpam-2382	261	1	2	2	NUM
ejpam-2382	261	2	1	1	NUM
ejpam-2382	261	3	k2	k2	NOUN
ejpam-2382	261	4	4	4	NUM
ejpam-2382	261	5	(	(	PUNCT
ejpam-2382	261	6	60	60	NUM
ejpam-2382	261	7	)	)	PUNCT
ejpam-2382	261	8	is	be	AUX
ejpam-2382	261	9	attained	attain	VERB
ejpam-2382	261	10	.	.	PUNCT
ejpam-2382	262	1	differentiating	differentiate	VERB
ejpam-2382	262	2	the	the	DET
ejpam-2382	262	3	equation	equation	NOUN
ejpam-2382	262	4	(	(	PUNCT
ejpam-2382	262	5	59	59	NUM
ejpam-2382	262	6	)	)	PUNCT
ejpam-2382	262	7	,	,	PUNCT
ejpam-2382	262	8	we	we	PRON
ejpam-2382	262	9	obtain	obtain	VERB
ejpam-2382	262	10	the	the	DET
ejpam-2382	262	11	derivative	derivative	NOUN
ejpam-2382	262	12	of	of	ADP
ejpam-2382	262	13	the	the	DET
ejpam-2382	262	14	center	center	NOUN
ejpam-2382	262	15	as	as	SCONJ
ejpam-2382	262	16	follows	follow	VERB
ejpam-2382	262	17	c	c	NOUN
ejpam-2382	262	18	′	′	NUM
ejpam-2382	263	1	=	=	PUNCT
ejpam-2382	264	1	(	(	PUNCT
ejpam-2382	264	2	m4k4	m4k4	INTJ
ejpam-2382	264	3	+	+	NOUN
ejpam-2382	264	4	m′5)v5	m′5)v5	PROPN
ejpam-2382	264	5	.	.	PUNCT
ejpam-2382	265	1	(	(	PUNCT
ejpam-2382	265	2	61	61	NUM
ejpam-2382	265	3	)	)	PUNCT
ejpam-2382	265	4	considering	consider	VERB
ejpam-2382	265	5	the	the	DET
ejpam-2382	265	6	equality	equality	NOUN
ejpam-2382	265	7	(	(	PUNCT
ejpam-2382	265	8	61	61	NUM
ejpam-2382	265	9	)	)	PUNCT
ejpam-2382	265	10	,	,	PUNCT
ejpam-2382	265	11	it	it	PRON
ejpam-2382	265	12	can	can	AUX
ejpam-2382	265	13	be	be	AUX
ejpam-2382	265	14	said	say	VERB
ejpam-2382	265	15	that	that	SCONJ
ejpam-2382	265	16	the	the	DET
ejpam-2382	265	17	centers	center	NOUN
ejpam-2382	265	18	of	of	ADP
ejpam-2382	265	19	the	the	DET
ejpam-2382	265	20	osculating	osculate	VERB
ejpam-2382	265	21	hyperspheres	hypersphere	NOUN
ejpam-2382	265	22	of	of	ADP
ejpam-2382	265	23	a	a	DET
ejpam-2382	265	24	spherical	spherical	ADJ
ejpam-2382	265	25	curve	curve	NOUN
ejpam-2382	265	26	are	be	AUX
ejpam-2382	265	27	in	in	ADP
ejpam-2382	265	28	the	the	DET
ejpam-2382	265	29	direction	direction	NOUN
ejpam-2382	265	30	of	of	ADP
ejpam-2382	265	31	v5	v5	PROPN
ejpam-2382	265	32	.	.	PUNCT
ejpam-2382	266	1	in	in	ADP
ejpam-2382	266	2	addition	addition	NOUN
ejpam-2382	266	3	,	,	PUNCT
ejpam-2382	266	4	all	all	DET
ejpam-2382	266	5	spherical	spherical	ADJ
ejpam-2382	266	6	curves	curve	NOUN
ejpam-2382	266	7	satisfy	satisfy	VERB
ejpam-2382	266	8	the	the	DET
ejpam-2382	266	9	following	follow	VERB
ejpam-2382	266	10	m.	m.	NOUN
ejpam-2382	266	11	masal	masal	PROPN
ejpam-2382	266	12	,	,	PUNCT
ejpam-2382	266	13	a.	a.	PROPN
ejpam-2382	266	14	azak	azak	PROPN
ejpam-2382	266	15	/	/	SYM
ejpam-2382	266	16	eur	eur	PROPN
ejpam-2382	266	17	.	.	PUNCT
ejpam-2382	267	1	j.	j.	PROPN
ejpam-2382	267	2	pure	pure	PROPN
ejpam-2382	267	3	appl	appl	PROPN
ejpam-2382	267	4	.	.	PROPN
ejpam-2382	267	5	math	math	PROPN
ejpam-2382	267	6	,	,	PUNCT
ejpam-2382	267	7	8	8	NUM
ejpam-2382	267	8	(	(	PUNCT
ejpam-2382	267	9	2015	2015	NUM
ejpam-2382	267	10	)	)	PUNCT
ejpam-2382	267	11	,	,	PUNCT
ejpam-2382	267	12	255	255	NUM
ejpam-2382	267	13	-	-	SYM
ejpam-2382	267	14	270	270	NUM
ejpam-2382	267	15	268	268	NUM
ejpam-2382	267	16	differential	differential	ADJ
ejpam-2382	267	17	equation	equation	NOUN
ejpam-2382	267	18	:	:	PUNCT
ejpam-2382	267	19	m2	m2	PROPN
ejpam-2382	267	20	2	2	PROPN
ejpam-2382	267	21	+	+	CCONJ
ejpam-2382	267	22	�	�	PROPN
ejpam-2382	267	23	m′2	m′2	NOUN
ejpam-2382	267	24	k2	k2	PROPN
ejpam-2382	267	25	�	�	PROPN
ejpam-2382	267	26	2	2	NUM
ejpam-2382	267	27	+	+	NUM
ejpam-2382	267	28	�	�	PROPN
ejpam-2382	267	29	�	�	PROPN
ejpam-2382	267	30	m′2	m′2	PROPN
ejpam-2382	267	31	k2	k2	PROPN
ejpam-2382	267	32	�	�	PROPN
ejpam-2382	267	33	′	′	PROPN
ejpam-2382	267	34	+	+	CCONJ
ejpam-2382	267	35	k2m2	k2m2	X
ejpam-2382	267	36	�	�	SYM
ejpam-2382	267	37	2	2	NUM
ejpam-2382	267	38	1	1	NUM
ejpam-2382	267	39	k2	k2	NOUN
ejpam-2382	267	40	3	3	NUM
ejpam-2382	267	41	+	+	NUM
ejpam-2382	267	42			NOUN
ejpam-2382	267	43			NOUN
ejpam-2382	267	44			NOUN
ejpam-2382	267	45			NOUN
ejpam-2382	267	46			NOUN
ejpam-2382	267	47			NOUN
ejpam-2382	267	48			PROPN
ejpam-2382	267	49	�	�	PROPN
ejpam-2382	267	50	m′2	m′2	PROPN
ejpam-2382	267	51	k2	k2	PROPN
ejpam-2382	267	52	�	�	PROPN
ejpam-2382	267	53	′	′	PROPN
ejpam-2382	268	1	+	+	CCONJ
ejpam-2382	268	2	k2m2	k2m2	X
ejpam-2382	268	3	k3	k3	ADJ
ejpam-2382	268	4	+	+	CCONJ
ejpam-2382	268	5	k3	k3	PROPN
ejpam-2382	268	6	�	�	PROPN
ejpam-2382	268	7	m′2	m′2	PROPN
ejpam-2382	268	8	k2	k2	PROPN
ejpam-2382	268	9	�	�	PROPN
ejpam-2382	268	10			PROPN
ejpam-2382	268	11			NOUN
ejpam-2382	268	12			PUNCT
ejpam-2382	269	1	′	′	NUM
ejpam-2382	269	2			NOUN
ejpam-2382	269	3			NOUN
ejpam-2382	269	4			VERB
ejpam-2382	269	5			PUNCT
ejpam-2382	270	1	2	2	NUM
ejpam-2382	270	2	1	1	NUM
ejpam-2382	270	3	k2	k2	ADJ
ejpam-2382	270	4	4	4	NUM
ejpam-2382	270	5	=	=	SYM
ejpam-2382	270	6	a2	a2	PROPN
ejpam-2382	270	7	.	.	PUNCT
ejpam-2382	271	1	(	(	PUNCT
ejpam-2382	271	2	62	62	NUM
ejpam-2382	271	3	)	)	PUNCT
ejpam-2382	271	4	if	if	SCONJ
ejpam-2382	271	5	the	the	DET
ejpam-2382	271	6	curve	curve	NOUN
ejpam-2382	271	7	is	be	AUX
ejpam-2382	271	8	spherical	spherical	ADJ
ejpam-2382	271	9	,	,	PUNCT
ejpam-2382	271	10	then	then	ADV
ejpam-2382	271	11	the	the	DET
ejpam-2382	271	12	hypersphere	hypersphere	NOUN
ejpam-2382	271	13	is	be	AUX
ejpam-2382	271	14	also	also	ADV
ejpam-2382	271	15	an	an	DET
ejpam-2382	271	16	osculating	osculating	NOUN
ejpam-2382	271	17	hypersphere	hypersphere	X
ejpam-2382	271	18	.	.	PUNCT
ejpam-2382	272	1	here	here	ADV
ejpam-2382	272	2	a	a	PRON
ejpam-2382	272	3	will	will	AUX
ejpam-2382	272	4	be	be	AUX
ejpam-2382	272	5	the	the	DET
ejpam-2382	272	6	radius	radius	NOUN
ejpam-2382	272	7	of	of	ADP
ejpam-2382	272	8	the	the	DET
ejpam-2382	272	9	hypersphere	hypersphere	NOUN
ejpam-2382	272	10	.	.	PUNCT
ejpam-2382	273	1	conversely	conversely	ADV
ejpam-2382	273	2	,	,	PUNCT
ejpam-2382	273	3	if	if	SCONJ
ejpam-2382	273	4	the	the	DET
ejpam-2382	273	5	equation	equation	NOUN
ejpam-2382	273	6	(	(	PUNCT
ejpam-2382	273	7	62	62	NUM
ejpam-2382	273	8	)	)	PUNCT
ejpam-2382	273	9	is	be	AUX
ejpam-2382	273	10	provided	provide	VERB
ejpam-2382	273	11	,	,	PUNCT
ejpam-2382	273	12	the	the	DET
ejpam-2382	273	13	radius	radius	NOUN
ejpam-2382	273	14	of	of	ADP
ejpam-2382	273	15	the	the	DET
ejpam-2382	273	16	osculating	osculating	NOUN
ejpam-2382	273	17	hypersphere	hypersphere	NOUN
ejpam-2382	273	18	is	be	AUX
ejpam-2382	273	19	constant	constant	ADJ
ejpam-2382	273	20	.	.	PUNCT
ejpam-2382	274	1	if	if	SCONJ
ejpam-2382	274	2	the	the	DET
ejpam-2382	274	3	derivative	derivative	NOUN
ejpam-2382	274	4	of	of	ADP
ejpam-2382	274	5	the	the	DET
ejpam-2382	274	6	equation	equation	NOUN
ejpam-2382	274	7	(	(	PUNCT
ejpam-2382	274	8	62	62	NUM
ejpam-2382	274	9	)	)	PUNCT
ejpam-2382	274	10	is	be	AUX
ejpam-2382	274	11	taken	take	VERB
ejpam-2382	274	12	,	,	PUNCT
ejpam-2382	274	13	m5(m4k4	m5(m4k4	NOUN
ejpam-2382	274	14	+	+	PROPN
ejpam-2382	274	15	m′5	m′5	NOUN
ejpam-2382	274	16	)	)	PUNCT
ejpam-2382	274	17	=	=	SYM
ejpam-2382	274	18	0	0	NUM
ejpam-2382	274	19	(	(	PUNCT
ejpam-2382	274	20	63	63	NUM
ejpam-2382	274	21	)	)	PUNCT
ejpam-2382	274	22	is	be	AUX
ejpam-2382	274	23	found	find	VERB
ejpam-2382	274	24	.	.	PUNCT
ejpam-2382	275	1	therefore	therefore	ADV
ejpam-2382	275	2	,	,	PUNCT
ejpam-2382	275	3	if	if	SCONJ
ejpam-2382	275	4	we	we	PRON
ejpam-2382	275	5	consider	consider	VERB
ejpam-2382	275	6	the	the	DET
ejpam-2382	275	7	equation	equation	NOUN
ejpam-2382	275	8	(	(	PUNCT
ejpam-2382	275	9	63	63	NUM
ejpam-2382	275	10	)	)	PUNCT
ejpam-2382	275	11	with	with	ADP
ejpam-2382	275	12	(	(	PUNCT
ejpam-2382	275	13	61	61	NUM
ejpam-2382	275	14	)	)	PUNCT
ejpam-2382	275	15	,	,	PUNCT
ejpam-2382	275	16	then	then	ADV
ejpam-2382	275	17	c	c	NOUN
ejpam-2382	275	18	′	′	NUM
ejpam-2382	276	1	=	=	NOUN
ejpam-2382	277	1	0	0	X
ejpam-2382	277	2	.	.	PUNCT
ejpam-2382	278	1	this	this	PRON
ejpam-2382	278	2	means	mean	VERB
ejpam-2382	278	3	that	that	SCONJ
ejpam-2382	278	4	the	the	DET
ejpam-2382	278	5	center	center	NOUN
ejpam-2382	278	6	of	of	ADP
ejpam-2382	278	7	the	the	DET
ejpam-2382	278	8	osculating	osculating	NOUN
ejpam-2382	278	9	hypersphere	hypersphere	NOUN
ejpam-2382	278	10	is	be	AUX
ejpam-2382	278	11	constant	constant	ADJ
ejpam-2382	278	12	.	.	PUNCT
ejpam-2382	279	1	from	from	ADP
ejpam-2382	279	2	the	the	DET
ejpam-2382	279	3	equation	equation	NOUN
ejpam-2382	279	4	(	(	PUNCT
ejpam-2382	279	5	63	63	NUM
ejpam-2382	279	6	)	)	PUNCT
ejpam-2382	279	7	,	,	PUNCT
ejpam-2382	279	8	all	all	PRON
ejpam-2382	279	9	of	of	ADP
ejpam-2382	279	10	the	the	DET
ejpam-2382	279	11	differential	differential	ADJ
ejpam-2382	279	12	equations	equation	NOUN
ejpam-2382	279	13	of	of	ADP
ejpam-2382	279	14	the	the	DET
ejpam-2382	279	15	spherical	spherical	ADJ
ejpam-2382	279	16	curves	curve	NOUN
ejpam-2382	279	17	are	be	AUX
ejpam-2382	279	18	m4k4	m4k4	ADJ
ejpam-2382	279	19	+	+	NOUN
ejpam-2382	279	20	m′5	m′5	NOUN
ejpam-2382	279	21	=	=	SYM
ejpam-2382	279	22	0	0	NUM
ejpam-2382	279	23	(	(	PUNCT
ejpam-2382	279	24	64	64	NUM
ejpam-2382	279	25	)	)	PUNCT
ejpam-2382	279	26	or	or	CCONJ
ejpam-2382	279	27	�	�	PROPN
ejpam-2382	279	28	�	�	PROPN
ejpam-2382	279	29	m′2	m′2	PROPN
ejpam-2382	279	30	k2	k2	PROPN
ejpam-2382	279	31	�	�	PROPN
ejpam-2382	279	32	′	′	PROPN
ejpam-2382	280	1	+	+	CCONJ
ejpam-2382	281	1	k2m2	k2m2	PROPN
ejpam-2382	281	2	�	�	PROPN
ejpam-2382	281	3	k4	k4	NOUN
ejpam-2382	281	4	k3	k3	VERB
ejpam-2382	281	5	+	+	CCONJ
ejpam-2382	281	6			NOUN
ejpam-2382	281	7			NOUN
ejpam-2382	281	8			NOUN
ejpam-2382	281	9			NOUN
ejpam-2382	281	10			VERB
ejpam-2382	281	11			NOUN
ejpam-2382	281	12			NOUN
ejpam-2382	281	13			NOUN
ejpam-2382	281	14			NOUN
ejpam-2382	281	15			NOUN
ejpam-2382	281	16			PROPN
ejpam-2382	281	17	�	�	PROPN
ejpam-2382	281	18	m′2	m′2	PROPN
ejpam-2382	281	19	k2	k2	PROPN
ejpam-2382	281	20	�	�	PROPN
ejpam-2382	281	21	′	′	PROPN
ejpam-2382	282	1	+	+	CCONJ
ejpam-2382	282	2	k2m2	k2m2	X
ejpam-2382	282	3	k3	k3	ADJ
ejpam-2382	282	4			NOUN
ejpam-2382	282	5			NOUN
ejpam-2382	282	6			PUNCT
ejpam-2382	283	1	′	′	NOUN
ejpam-2382	284	1	+	+	CCONJ
ejpam-2382	284	2	k3	k3	ADJ
ejpam-2382	284	3	�	�	PROPN
ejpam-2382	284	4	m′2	m′2	PROPN
ejpam-2382	284	5	k2	k2	PROPN
ejpam-2382	284	6	�	�	PROPN
ejpam-2382	284	7			PROPN
ejpam-2382	284	8			PROPN
ejpam-2382	284	9			VERB
ejpam-2382	284	10			PUNCT
ejpam-2382	285	1	1	1	NUM
ejpam-2382	285	2	k4	k4	PROPN
ejpam-2382	285	3			PROPN
ejpam-2382	285	4			NOUN
ejpam-2382	285	5			VERB
ejpam-2382	285	6			PUNCT
ejpam-2382	286	1	′	′	NUM
ejpam-2382	286	2	=	=	NOUN
ejpam-2382	286	3	0	0	X
ejpam-2382	286	4	.	.	PUNCT
ejpam-2382	287	1	however	however	ADV
ejpam-2382	287	2	,	,	PUNCT
ejpam-2382	287	3	the	the	DET
ejpam-2382	287	4	following	follow	VERB
ejpam-2382	287	5	theorem	theorem	NOUN
ejpam-2382	287	6	can	can	AUX
ejpam-2382	287	7	be	be	AUX
ejpam-2382	287	8	given	give	VERB
ejpam-2382	287	9	:	:	PUNCT
ejpam-2382	287	10	theorem	theorem	NOUN
ejpam-2382	287	11	4	4	NUM
ejpam-2382	287	12	.	.	PUNCT
ejpam-2382	288	1	let	let	VERB
ejpam-2382	288	2	x	x	PRON
ejpam-2382	288	3	be	be	AUX
ejpam-2382	288	4	a	a	DET
ejpam-2382	288	5	unit	unit	NOUN
ejpam-2382	288	6	speed	speed	NOUN
ejpam-2382	288	7	curve	curve	NOUN
ejpam-2382	288	8	in	in	ADP
ejpam-2382	288	9	e5	e5	PROPN
ejpam-2382	288	10	.	.	PUNCT
ejpam-2382	289	1	(	(	PUNCT
ejpam-2382	289	2	i	i	NOUN
ejpam-2382	289	3	)	)	PUNCT
ejpam-2382	289	4	the	the	DET
ejpam-2382	289	5	curve	curve	NOUN
ejpam-2382	289	6	x	x	PUNCT
ejpam-2382	289	7	is	be	AUX
ejpam-2382	289	8	a	a	DET
ejpam-2382	289	9	spherical	spherical	ADJ
ejpam-2382	289	10	curve	curve	NOUN
ejpam-2382	289	11	if	if	SCONJ
ejpam-2382	289	12	and	and	CCONJ
ejpam-2382	289	13	only	only	ADV
ejpam-2382	289	14	if	if	SCONJ
ejpam-2382	289	15	the	the	DET
ejpam-2382	289	16	differential	differential	ADJ
ejpam-2382	289	17	equation	equation	NOUN
ejpam-2382	289	18	m4k4	m4k4	PROPN
ejpam-2382	289	19	+	+	NOUN
ejpam-2382	289	20	m′5	m′5	NOUN
ejpam-2382	289	21	=	=	SYM
ejpam-2382	289	22	0	0	NUM
ejpam-2382	289	23	is	be	AUX
ejpam-2382	289	24	satisfied	satisfied	ADJ
ejpam-2382	289	25	.	.	PUNCT
ejpam-2382	290	1	(	(	PUNCT
ejpam-2382	290	2	ii	ii	NOUN
ejpam-2382	290	3	)	)	PUNCT
ejpam-2382	290	4	if	if	SCONJ
ejpam-2382	290	5	x	x	PRON
ejpam-2382	290	6	is	be	AUX
ejpam-2382	290	7	a	a	DET
ejpam-2382	290	8	spherical	spherical	ADJ
ejpam-2382	290	9	curve	curve	NOUN
ejpam-2382	290	10	,	,	PUNCT
ejpam-2382	290	11	then	then	ADV
ejpam-2382	290	12	the	the	DET
ejpam-2382	290	13	center	center	NOUN
ejpam-2382	290	14	of	of	ADP
ejpam-2382	290	15	the	the	DET
ejpam-2382	290	16	hypersphere	hypersphere	NOUN
ejpam-2382	290	17	is	be	AUX
ejpam-2382	290	18	c	c	NOUN
ejpam-2382	290	19	=	=	PUNCT
ejpam-2382	290	20	x	x	PUNCT
ejpam-2382	291	1	+	+	PUNCT
ejpam-2382	291	2	m2v2	m2v2	ADJ
ejpam-2382	291	3	+	+	ADJ
ejpam-2382	291	4	m3v3	m3v3	NOUN
ejpam-2382	291	5	+	+	NOUN
ejpam-2382	291	6	m4v4	m4v4	ADJ
ejpam-2382	291	7	+	+	ADJ
ejpam-2382	291	8	m5v5	m5v5	PROPN
ejpam-2382	291	9	and	and	CCONJ
ejpam-2382	291	10	the	the	DET
ejpam-2382	291	11	radius	radius	NOUN
ejpam-2382	291	12	is	be	AUX
ejpam-2382	291	13	r	r	NOUN
ejpam-2382	291	14	=	=	PUNCT
ejpam-2382	291	15	q	q	NOUN
ejpam-2382	291	16	m2	m2	PROPN
ejpam-2382	291	17	2	2	NUM
ejpam-2382	291	18	+	+	NOUN
ejpam-2382	291	19	m2	m2	PROPN
ejpam-2382	291	20	3	3	NUM
ejpam-2382	291	21	+	+	NOUN
ejpam-2382	291	22	m2	m2	PROPN
ejpam-2382	291	23	4	4	NUM
ejpam-2382	291	24	+	+	NOUN
ejpam-2382	291	25	m2	m2	PROPN
ejpam-2382	291	26	5	5	NUM
ejpam-2382	291	27	such	such	ADJ
ejpam-2382	291	28	that	that	SCONJ
ejpam-2382	291	29	m2	m2	PROPN
ejpam-2382	291	30	=	=	SYM
ejpam-2382	291	31	1	1	NUM
ejpam-2382	291	32	k1	k1	NOUN
ejpam-2382	291	33	,	,	PUNCT
ejpam-2382	291	34	m3	m3	PROPN
ejpam-2382	291	35	=	=	PUNCT
ejpam-2382	291	36	m′2	m′2	PROPN
ejpam-2382	291	37	k2	k2	PROPN
ejpam-2382	291	38	,	,	PUNCT
ejpam-2382	291	39	m4	m4	PROPN
ejpam-2382	291	40	=	=	SYM
ejpam-2382	291	41	m′3	m′3	NOUN
ejpam-2382	291	42	+	+	CCONJ
ejpam-2382	291	43	k2m2	k2m2	X
ejpam-2382	291	44	k3	k3	ADJ
ejpam-2382	291	45	,	,	PUNCT
ejpam-2382	291	46	m5	m5	NOUN
ejpam-2382	291	47	=	=	SYM
ejpam-2382	291	48	m′4	m′4	NOUN
ejpam-2382	292	1	+	+	CCONJ
ejpam-2382	292	2	k3m3	k3m3	PROPN
ejpam-2382	292	3	k4	k4	NOUN
ejpam-2382	292	4	.	.	PUNCT
ejpam-2382	293	1	(	(	PUNCT
ejpam-2382	293	2	iii	iii	X
ejpam-2382	293	3	)	)	PUNCT
ejpam-2382	293	4	the	the	DET
ejpam-2382	293	5	radius	radius	NOUN
ejpam-2382	293	6	of	of	ADP
ejpam-2382	293	7	the	the	DET
ejpam-2382	293	8	osculating	osculating	NOUN
ejpam-2382	293	9	hypersphere	hypersphere	NOUN
ejpam-2382	293	10	is	be	AUX
ejpam-2382	293	11	constant	constant	ADJ
ejpam-2382	293	12	at	at	ADP
ejpam-2382	293	13	the	the	DET
ejpam-2382	293	14	point	point	NOUN
ejpam-2382	293	15	x	x	X
ejpam-2382	293	16	(	(	PUNCT
ejpam-2382	293	17	s	s	NOUN
ejpam-2382	293	18	)	)	PUNCT
ejpam-2382	293	19	if	if	SCONJ
ejpam-2382	293	20	and	and	CCONJ
ejpam-2382	293	21	only	only	ADV
ejpam-2382	293	22	if	if	SCONJ
ejpam-2382	293	23	the	the	DET
ejpam-2382	293	24	centers	center	NOUN
ejpam-2382	293	25	of	of	ADP
ejpam-2382	293	26	the	the	DET
ejpam-2382	293	27	osculating	osculating	NOUN
ejpam-2382	293	28	hyperspheres	hypersphere	NOUN
ejpam-2382	293	29	are	be	AUX
ejpam-2382	293	30	the	the	DET
ejpam-2382	293	31	same[9	same[9	NOUN
ejpam-2382	293	32	]	]	PUNCT
ejpam-2382	293	33	.	.	PUNCT
ejpam-2382	294	1	references	reference	NOUN
ejpam-2382	294	2	269	269	NUM
ejpam-2382	294	3	acknowledgements	acknowledgement	NOUN
ejpam-2382	294	4	the	the	DET
ejpam-2382	294	5	authors	author	NOUN
ejpam-2382	294	6	thank	thank	VERB
ejpam-2382	294	7	to	to	ADP
ejpam-2382	294	8	referees	referee	NOUN
ejpam-2382	294	9	.	.	PUNCT
ejpam-2382	295	1	references	reference	NOUN
ejpam-2382	295	2	[	[	X
ejpam-2382	295	3	1	1	NUM
ejpam-2382	295	4	]	]	X
ejpam-2382	295	5	a.t	a.t	PROPN
ejpam-2382	295	6	.	.	PROPN
ejpam-2382	295	7	ali	ali	PROPN
ejpam-2382	295	8	.	.	PROPN
ejpam-2382	296	1	inclined	inclined	ADJ
ejpam-2382	296	2	curves	curve	NOUN
ejpam-2382	296	3	in	in	ADP
ejpam-2382	296	4	the	the	DET
ejpam-2382	296	5	euclidean	euclidean	ADJ
ejpam-2382	296	6	5	5	NUM
ejpam-2382	296	7	-	-	PUNCT
ejpam-2382	296	8	space	space	NOUN
ejpam-2382	296	9	e5	e5	PROPN
ejpam-2382	296	10	.	.	PUNCT
ejpam-2382	297	1	journal	journal	PROPN
ejpam-2382	297	2	of	of	ADP
ejpam-2382	297	3	advanced	advanced	ADJ
ejpam-2382	297	4	research	research	NOUN
ejpam-2382	297	5	in	in	ADP
ejpam-2382	297	6	pure	pure	ADJ
ejpam-2382	297	7	mathematics	mathematic	NOUN
ejpam-2382	297	8	,	,	PUNCT
ejpam-2382	297	9	1:15–22	1:15–22	NUM
ejpam-2382	297	10	,	,	PUNCT
ejpam-2382	297	11	2009	2009	NUM
ejpam-2382	297	12	.	.	PUNCT
ejpam-2382	298	1	[	[	X
ejpam-2382	298	2	2	2	NUM
ejpam-2382	298	3	]	]	PUNCT
ejpam-2382	298	4	c.	c.	PROPN
ejpam-2382	298	5	boyer	boyer	PROPN
ejpam-2382	298	6	.	.	PUNCT
ejpam-2382	299	1	a	a	DET
ejpam-2382	299	2	history	history	NOUN
ejpam-2382	299	3	of	of	ADP
ejpam-2382	299	4	mathematics	mathematic	NOUN
ejpam-2382	299	5	.	.	PUNCT
ejpam-2382	300	1	wiley	wiley	PROPN
ejpam-2382	300	2	press	press	PROPN
ejpam-2382	300	3	,	,	PUNCT
ejpam-2382	300	4	new	new	PROPN
ejpam-2382	300	5	york	york	PROPN
ejpam-2382	300	6	,	,	PUNCT
ejpam-2382	300	7	1968	1968	NUM
ejpam-2382	300	8	.	.	PUNCT
ejpam-2382	301	1	[	[	X
ejpam-2382	301	2	3	3	X
ejpam-2382	301	3	]	]	X
ejpam-2382	301	4	s.	s.	PROPN
ejpam-2382	301	5	ersoy	ersoy	PROPN
ejpam-2382	301	6	and	and	CCONJ
ejpam-2382	301	7	a.	a.	NOUN
ejpam-2382	301	8	inalcık	inalcık	PROPN
ejpam-2382	301	9	.	.	PUNCT
ejpam-2382	302	1	on	on	ADP
ejpam-2382	302	2	the	the	DET
ejpam-2382	302	3	genaralized	genaralize	VERB
ejpam-2382	302	4	timelike	timelike	PROPN
ejpam-2382	302	5	bertrand	bertrand	PROPN
ejpam-2382	302	6	curves	curve	NOUN
ejpam-2382	302	7	in	in	ADP
ejpam-2382	302	8	5	5	NUM
ejpam-2382	302	9	-	-	PUNCT
ejpam-2382	302	10	dimensional	dimensional	ADJ
ejpam-2382	302	11	lorentzian	lorentzian	ADJ
ejpam-2382	302	12	space	space	NOUN
ejpam-2382	302	13	.	.	PUNCT
ejpam-2382	303	1	differential	differential	ADJ
ejpam-2382	303	2	geometry	geometry	NOUN
ejpam-2382	303	3	-	-	PUNCT
ejpam-2382	303	4	dynamical	dynamical	ADJ
ejpam-2382	303	5	systems	system	NOUN
ejpam-2382	303	6	,	,	PUNCT
ejpam-2382	303	7	13:78–88	13:78–88	NUM
ejpam-2382	303	8	,	,	PUNCT
ejpam-2382	303	9	2011	2011	NUM
ejpam-2382	303	10	.	.	PUNCT
ejpam-2382	304	1	[	[	X
ejpam-2382	304	2	4	4	NUM
ejpam-2382	304	3	]	]	X
ejpam-2382	304	4	a.r	a.r	PROPN
ejpam-2382	304	5	.	.	PROPN
ejpam-2382	304	6	forsyth	forsyth	PROPN
ejpam-2382	304	7	.	.	PUNCT
ejpam-2382	304	8	geometry	geometry	NOUN
ejpam-2382	304	9	of	of	ADP
ejpam-2382	304	10	four	four	NUM
ejpam-2382	304	11	dimensions	dimension	NOUN
ejpam-2382	304	12	.	.	PUNCT
ejpam-2382	305	1	cambridge	cambridge	PROPN
ejpam-2382	305	2	university	university	PROPN
ejpam-2382	305	3	press	press	PROPN
ejpam-2382	305	4	,	,	PUNCT
ejpam-2382	305	5	london	london	PROPN
ejpam-2382	305	6	,	,	PUNCT
ejpam-2382	305	7	1930	1930	NUM
ejpam-2382	305	8	.	.	PUNCT
ejpam-2382	306	1	[	[	X
ejpam-2382	306	2	5	5	X
ejpam-2382	306	3	]	]	PUNCT
ejpam-2382	306	4	h.	h.	PROPN
ejpam-2382	306	5	gluck	gluck	PROPN
ejpam-2382	306	6	.	.	PUNCT
ejpam-2382	307	1	higher	high	ADJ
ejpam-2382	307	2	curvatures	curvature	NOUN
ejpam-2382	307	3	of	of	ADP
ejpam-2382	307	4	curves	curve	NOUN
ejpam-2382	307	5	in	in	ADP
ejpam-2382	307	6	euclidean	euclidean	ADJ
ejpam-2382	307	7	space	space	NOUN
ejpam-2382	307	8	.	.	PUNCT
ejpam-2382	308	1	the	the	DET
ejpam-2382	308	2	american	american	PROPN
ejpam-2382	308	3	mathematical	mathematical	PROPN
ejpam-2382	308	4	monthly	monthly	ADV
ejpam-2382	308	5	,	,	PUNCT
ejpam-2382	308	6	73(7):699–704	73(7):699–704	NOUN
ejpam-2382	308	7	,	,	PUNCT
ejpam-2382	308	8	1966	1966	NUM
ejpam-2382	308	9	.	.	PUNCT
ejpam-2382	309	1	[	[	X
ejpam-2382	309	2	6	6	NUM
ejpam-2382	309	3	]	]	X
ejpam-2382	309	4	h.h	h.h	PROPN
ejpam-2382	309	5	.	.	PROPN
ejpam-2382	309	6	hacısalihoğlu	hacısalihoğlu	PROPN
ejpam-2382	309	7	.	.	PUNCT
ejpam-2382	310	1	differential	differential	PROPN
ejpam-2382	310	2	geometry	geometry	NOUN
ejpam-2382	310	3	.	.	PUNCT
ejpam-2382	311	1	ankara	ankara	PROPN
ejpam-2382	311	2	university	university	PROPN
ejpam-2382	311	3	faculty	faculty	NOUN
ejpam-2382	311	4	of	of	ADP
ejpam-2382	311	5	science	science	PROPN
ejpam-2382	311	6	press	press	NOUN
ejpam-2382	311	7	,	,	PUNCT
ejpam-2382	311	8	ankara	ankara	PROPN
ejpam-2382	311	9	,	,	PUNCT
ejpam-2382	311	10	2000	2000	NUM
ejpam-2382	311	11	.	.	PUNCT
ejpam-2382	312	1	[	[	X
ejpam-2382	312	2	7	7	X
ejpam-2382	312	3	]	]	X
ejpam-2382	312	4	c.	c.	PROPN
ejpam-2382	312	5	huygens	huygens	PROPN
ejpam-2382	312	6	.	.	PROPN
ejpam-2382	313	1	oeuvres	oeuvre	NOUN
ejpam-2382	313	2	completes	complete	VERB
ejpam-2382	313	3	.	.	PUNCT
ejpam-2382	314	1	martinus	martinus	PROPN
ejpam-2382	314	2	nijhoff	nijhoff	PROPN
ejpam-2382	314	3	,	,	PUNCT
ejpam-2382	314	4	den	den	PROPN
ejpam-2382	314	5	haag	haag	PROPN
ejpam-2382	314	6	,	,	PUNCT
ejpam-2382	314	7	1895	1895	NUM
ejpam-2382	314	8	.	.	PUNCT
ejpam-2382	315	1	[	[	X
ejpam-2382	315	2	8	8	NUM
ejpam-2382	315	3	]	]	PUNCT
ejpam-2382	315	4	a.	a.	NOUN
ejpam-2382	315	5	mağden	mağden	PROPN
ejpam-2382	315	6	.	.	PUNCT
ejpam-2382	316	1	characterizations	characterization	NOUN
ejpam-2382	316	2	of	of	ADP
ejpam-2382	316	3	some	some	DET
ejpam-2382	316	4	special	special	ADJ
ejpam-2382	316	5	curves	curve	NOUN
ejpam-2382	316	6	in	in	ADP
ejpam-2382	316	7	e4	e4	PROPN
ejpam-2382	316	8	.	.	PUNCT
ejpam-2382	317	1	phd	phd	NOUN
ejpam-2382	317	2	thesis	thesis	PROPN
ejpam-2382	317	3	,	,	PUNCT
ejpam-2382	317	4	atatürk	atatürk	PROPN
ejpam-2382	317	5	university	university	NOUN
ejpam-2382	317	6	,	,	PUNCT
ejpam-2382	317	7	1990	1990	NUM
ejpam-2382	317	8	.	.	PUNCT
ejpam-2382	318	1	[	[	X
ejpam-2382	318	2	9	9	NUM
ejpam-2382	318	3	]	]	PUNCT
ejpam-2382	318	4	z.	z.	PROPN
ejpam-2382	318	5	nadenik	nadenik	PROPN
ejpam-2382	318	6	.	.	PUNCT
ejpam-2382	319	1	bertrand	bertrand	PROPN
ejpam-2382	319	2	curves	curve	VERB
ejpam-2382	319	3	in	in	ADP
ejpam-2382	319	4	five	five	NUM
ejpam-2382	319	5	dimensional	dimensional	ADJ
ejpam-2382	319	6	space	space	NOUN
ejpam-2382	319	7	(	(	PUNCT
ejpam-2382	319	8	in	in	ADP
ejpam-2382	319	9	russian	russian	NOUN
ejpam-2382	319	10	)	)	PUNCT
ejpam-2382	319	11	.	.	PUNCT
ejpam-2382	320	1	czechoslovak	czechoslovak	ADJ
ejpam-2382	320	2	mathematical	mathematical	PROPN
ejpam-2382	320	3	journal	journal	NOUN
ejpam-2382	320	4	,	,	PUNCT
ejpam-2382	320	5	2(1):57–87	2(1):57–87	NUM
ejpam-2382	320	6	,	,	PUNCT
ejpam-2382	320	7	1952	1952	NUM
ejpam-2382	320	8	.	.	PUNCT
ejpam-2382	321	1	[	[	X
ejpam-2382	321	2	10	10	NUM
ejpam-2382	321	3	]	]	X
ejpam-2382	321	4	m.	m.	NOUN
ejpam-2382	321	5	önder	önder	NOUN
ejpam-2382	321	6	,	,	PUNCT
ejpam-2382	321	7	h.	h.	PROPN
ejpam-2382	321	8	kocayiğit	kocayiğit	PROPN
ejpam-2382	321	9	m.	m.	PROPN
ejpam-2382	321	10	kazaz	kazaz	PROPN
ejpam-2382	321	11	,	,	PUNCT
ejpam-2382	321	12	and	and	CCONJ
ejpam-2382	321	13	o.	o.	PROPN
ejpam-2382	321	14	kılıç	kılıç	PROPN
ejpam-2382	321	15	.	.	PUNCT
ejpam-2382	321	16	b2	b2	NOUN
ejpam-2382	321	17	-	-	PUNCT
ejpam-2382	321	18	slant	slant	NOUN
ejpam-2382	321	19	helix	helix	NOUN
ejpam-2382	321	20	in	in	ADP
ejpam-2382	321	21	euclidean	euclidean	ADJ
ejpam-2382	321	22	4	4	NUM
ejpam-2382	321	23	-	-	PUNCT
ejpam-2382	321	24	space	space	NOUN
ejpam-2382	321	25	e4	e4	PROPN
ejpam-2382	321	26	.	.	PUNCT
ejpam-2382	322	1	international	international	ADJ
ejpam-2382	322	2	journal	journal	PROPN
ejpam-2382	322	3	of	of	ADP
ejpam-2382	322	4	contemporary	contemporary	PROPN
ejpam-2382	322	5	mathematical	mathematical	PROPN
ejpam-2382	322	6	sciences	sciences	PROPN
ejpam-2382	322	7	,	,	PUNCT
ejpam-2382	322	8	3(29	3(29	NUM
ejpam-2382	322	9	)	)	PUNCT
ejpam-2382	322	10	,	,	PUNCT
ejpam-2382	322	11	2008	2008	NUM
ejpam-2382	322	12	.	.	PUNCT
ejpam-2382	323	1	[	[	X
ejpam-2382	323	2	11	11	NUM
ejpam-2382	323	3	]	]	X
ejpam-2382	323	4	h.	h.	PROPN
ejpam-2382	323	5	b.	b.	PROPN
ejpam-2382	323	6	öztekin	öztekin	PROPN
ejpam-2382	323	7	and	and	CCONJ
ejpam-2382	323	8	s.	s.	PROPN
ejpam-2382	323	9	tatlıpınar	tatlıpınar	PROPN
ejpam-2382	323	10	.	.	PUNCT
ejpam-2382	324	1	the	the	DET
ejpam-2382	324	2	characterizations	characterization	NOUN
ejpam-2382	324	3	of	of	ADP
ejpam-2382	324	4	nonnull	nonnull	ADJ
ejpam-2382	324	5	inclined	incline	VERB
ejpam-2382	324	6	curves	curve	NOUN
ejpam-2382	324	7	in	in	ADP
ejpam-2382	324	8	lorentzian	lorentzian	ADJ
ejpam-2382	324	9	space	space	NOUN
ejpam-2382	324	10	l5	l5	PROPN
ejpam-2382	324	11	.	.	PUNCT
ejpam-2382	325	1	international	international	ADJ
ejpam-2382	325	2	journal	journal	PROPN
ejpam-2382	325	3	of	of	ADP
ejpam-2382	325	4	mathematical	mathematical	ADJ
ejpam-2382	325	5	combinatorics	combinatoric	NOUN
ejpam-2382	325	6	,	,	PUNCT
ejpam-2382	325	7	4:09–16	4:09–16	PROPN
ejpam-2382	325	8	,	,	PUNCT
ejpam-2382	325	9	2012	2012	NUM
ejpam-2382	325	10	.	.	PUNCT
ejpam-2382	326	1	[	[	X
ejpam-2382	326	2	12	12	NUM
ejpam-2382	326	3	]	]	X
ejpam-2382	326	4	e.	e.	PROPN
ejpam-2382	326	5	özyılmaz	özyılmaz	PROPN
ejpam-2382	326	6	and	and	CCONJ
ejpam-2382	326	7	s.	s.	PROPN
ejpam-2382	326	8	yılmaz	yılmaz	PROPN
ejpam-2382	326	9	.	.	PUNCT
ejpam-2382	327	1	involute	involute	PROPN
ejpam-2382	327	2	-	-	PUNCT
ejpam-2382	327	3	evolute	evolute	NOUN
ejpam-2382	327	4	curve	curve	NOUN
ejpam-2382	327	5	couples	couple	NOUN
ejpam-2382	327	6	in	in	ADP
ejpam-2382	327	7	the	the	DET
ejpam-2382	327	8	euclidean	euclidean	ADJ
ejpam-2382	327	9	4	4	NUM
ejpam-2382	327	10	-	-	PUNCT
ejpam-2382	327	11	space	space	NOUN
ejpam-2382	327	12	.	.	PUNCT
ejpam-2382	328	1	international	international	ADJ
ejpam-2382	328	2	journal	journal	NOUN
ejpam-2382	328	3	of	of	ADP
ejpam-2382	328	4	open	open	ADJ
ejpam-2382	328	5	problems	problem	NOUN
ejpam-2382	328	6	in	in	ADP
ejpam-2382	328	7	computer	computer	NOUN
ejpam-2382	328	8	science	science	NOUN
ejpam-2382	328	9	and	and	CCONJ
ejpam-2382	328	10	mathematics	mathematic	NOUN
ejpam-2382	328	11	,	,	PUNCT
ejpam-2382	328	12	2(2):168	2(2):168	NUM
ejpam-2382	328	13	–	–	PUNCT
ejpam-2382	328	14	174	174	NUM
ejpam-2382	328	15	,	,	PUNCT
ejpam-2382	328	16	2009	2009	NUM
ejpam-2382	328	17	.	.	PUNCT
ejpam-2382	329	1	[	[	X
ejpam-2382	329	2	13	13	NUM
ejpam-2382	329	3	]	]	PUNCT
ejpam-2382	329	4	m.	m.	NOUN
ejpam-2382	329	5	turgut	turgut	PROPN
ejpam-2382	329	6	and	and	CCONJ
ejpam-2382	329	7	a.t	a.t	PROPN
ejpam-2382	329	8	.	.	PROPN
ejpam-2382	329	9	ali	ali	PROPN
ejpam-2382	329	10	.	.	PUNCT
ejpam-2382	330	1	some	some	DET
ejpam-2382	330	2	characterizations	characterization	NOUN
ejpam-2382	330	3	of	of	ADP
ejpam-2382	330	4	special	special	ADJ
ejpam-2382	330	5	curves	curve	NOUN
ejpam-2382	330	6	in	in	ADP
ejpam-2382	330	7	the	the	DET
ejpam-2382	330	8	euclidean	euclidean	ADJ
ejpam-2382	330	9	space	space	NOUN
ejpam-2382	330	10	e4	e4	PROPN
ejpam-2382	330	11	.	.	PUNCT
ejpam-2382	331	1	acta	acta	PROPN
ejpam-2382	331	2	universitatis	universitatis	PROPN
ejpam-2382	331	3	sapientiae	sapientiae	PROPN
ejpam-2382	331	4	mathematica	mathematica	PROPN
ejpam-2382	331	5	,	,	PUNCT
ejpam-2382	331	6	2(1):111–122	2(1):111–122	NUM
ejpam-2382	331	7	,	,	PUNCT
ejpam-2382	331	8	2010	2010	NUM
ejpam-2382	331	9	.	.	PUNCT
ejpam-2382	332	1	[	[	X
ejpam-2382	332	2	14	14	NUM
ejpam-2382	332	3	]	]	PUNCT
ejpam-2382	332	4	m.	m.	NOUN
ejpam-2382	332	5	turgut	turgut	PROPN
ejpam-2382	332	6	,	,	PUNCT
ejpam-2382	332	7	l.	l.	PROPN
ejpam-2382	332	8	lopez	lopez	PROPN
ejpam-2382	332	9	-	-	PUNCT
ejpam-2382	332	10	bonilla	bonilla	NOUN
ejpam-2382	332	11	,	,	PUNCT
ejpam-2382	332	12	and	and	CCONJ
ejpam-2382	332	13	s.	s.	PROPN
ejpam-2382	332	14	yılmaz	yılmaz	PROPN
ejpam-2382	332	15	.	.	PUNCT
ejpam-2382	333	1	on	on	ADP
ejpam-2382	333	2	frenet	frenet	NOUN
ejpam-2382	333	3	-	-	PUNCT
ejpam-2382	333	4	serret	serret	NOUN
ejpam-2382	333	5	invariants	invariant	NOUN
ejpam-2382	333	6	of	of	ADP
ejpam-2382	333	7	non	non	ADJ
ejpam-2382	333	8	-	-	ADJ
ejpam-2382	333	9	null	null	ADJ
ejpam-2382	333	10	curves	curve	NOUN
ejpam-2382	333	11	in	in	ADP
ejpam-2382	333	12	lorentzian	lorentzian	ADJ
ejpam-2382	333	13	space	space	NOUN
ejpam-2382	333	14	l5	l5	PROPN
ejpam-2382	333	15	.	.	PUNCT
ejpam-2382	334	1	world	world	PROPN
ejpam-2382	334	2	academy	academy	PROPN
ejpam-2382	334	3	of	of	ADP
ejpam-2382	334	4	science	science	PROPN
ejpam-2382	334	5	,	,	PUNCT
ejpam-2382	334	6	engineering	engineering	NOUN
ejpam-2382	334	7	and	and	CCONJ
ejpam-2382	334	8	technology	technology	NOUN
ejpam-2382	334	9	,	,	PUNCT
ejpam-2382	334	10	3:7–27	3:7–27	NUM
ejpam-2382	334	11	,	,	PUNCT
ejpam-2382	334	12	2009	2009	NUM
ejpam-2382	334	13	.	.	PUNCT
ejpam-2382	335	1	[	[	X
ejpam-2382	335	2	15	15	NUM
ejpam-2382	335	3	]	]	X
ejpam-2382	335	4	m.	m.	NOUN
ejpam-2382	335	5	turgut	turgut	PROPN
ejpam-2382	335	6	and	and	CCONJ
ejpam-2382	335	7	s.	s.	PROPN
ejpam-2382	335	8	yılmaz	yılmaz	PROPN
ejpam-2382	335	9	.	.	PUNCT
ejpam-2382	336	1	on	on	ADP
ejpam-2382	336	2	the	the	DET
ejpam-2382	336	3	frenet	frenet	ADJ
ejpam-2382	336	4	frame	frame	NOUN
ejpam-2382	336	5	and	and	CCONJ
ejpam-2382	336	6	a	a	DET
ejpam-2382	336	7	characterization	characterization	NOUN
ejpam-2382	336	8	of	of	ADP
ejpam-2382	336	9	spacelike	spacelike	ADJ
ejpam-2382	336	10	involute	involute	NOUN
ejpam-2382	336	11	-	-	PUNCT
ejpam-2382	336	12	evolute	evolute	NOUN
ejpam-2382	336	13	curve	curve	NOUN
ejpam-2382	336	14	couple	couple	NOUN
ejpam-2382	336	15	in	in	ADP
ejpam-2382	336	16	minkowski	minkowski	ADJ
ejpam-2382	336	17	space	space	NOUN
ejpam-2382	336	18	-	-	PUNCT
ejpam-2382	336	19	time	time	NOUN
ejpam-2382	336	20	.	.	PUNCT
ejpam-2382	337	1	international	international	ADJ
ejpam-2382	337	2	mathematical	mathematical	PROPN
ejpam-2382	337	3	forum	forum	PROPN
ejpam-2382	337	4	,	,	PUNCT
ejpam-2382	337	5	3(16):793–801	3(16):793–801	NUM
ejpam-2382	337	6	,	,	PUNCT
ejpam-2382	337	7	2008	2008	NUM
ejpam-2382	337	8	.	.	PUNCT
ejpam-2382	338	1	references	reference	NOUN
ejpam-2382	338	2	270	270	NUM
ejpam-2382	339	1	[	[	X
ejpam-2382	339	2	16	16	NUM
ejpam-2382	339	3	]	]	PUNCT
ejpam-2382	339	4	s.	s.	PROPN
ejpam-2382	339	5	yılmaz	yılmaz	PROPN
ejpam-2382	339	6	and	and	CCONJ
ejpam-2382	339	7	m.	m.	NOUN
ejpam-2382	339	8	turgut	turgut	PROPN
ejpam-2382	339	9	.	.	PUNCT
ejpam-2382	340	1	a	a	DET
ejpam-2382	340	2	method	method	NOUN
ejpam-2382	340	3	to	to	PART
ejpam-2382	340	4	calculate	calculate	VERB
ejpam-2382	340	5	frenet	frenet	NOUN
ejpam-2382	340	6	apparatus	apparatus	NOUN
ejpam-2382	340	7	of	of	ADP
ejpam-2382	340	8	the	the	DET
ejpam-2382	340	9	curves	curve	NOUN
ejpam-2382	340	10	in	in	ADP
ejpam-2382	340	11	euclidean	euclidean	ADJ
ejpam-2382	340	12	5	5	NUM
ejpam-2382	340	13	-	-	PUNCT
ejpam-2382	340	14	space	space	NOUN
ejpam-2382	340	15	.	.	PUNCT
ejpam-2382	341	1	international	international	ADJ
ejpam-2382	341	2	journal	journal	PROPN
ejpam-2382	341	3	of	of	ADP
ejpam-2382	341	4	computational	computational	ADJ
ejpam-2382	341	5	and	and	CCONJ
ejpam-2382	341	6	mathematics	mathematic	NOUN
ejpam-2382	341	7	sciences	science	NOUN
ejpam-2382	341	8	,	,	PUNCT
ejpam-2382	341	9	2(2):101–103	2(2):101–103	NUM
ejpam-2382	341	10	,	,	PUNCT
ejpam-2382	341	11	2008	2008	NUM
ejpam-2382	341	12	.	.	PUNCT