id	sid	tid	token	lemma	pos
ejpam-5710	1	1	european	european	PROPN
ejpam-5710	1	2	journal	journal	PROPN
ejpam-5710	1	3	of	of	ADP
ejpam-5710	1	4	pure	pure	ADJ
ejpam-5710	1	5	and	and	CCONJ
ejpam-5710	1	6	applied	applied	ADJ
ejpam-5710	1	7	mathematics	mathematic	NOUN
ejpam-5710	1	8	2025	2025	NUM
ejpam-5710	1	9	,	,	PUNCT
ejpam-5710	1	10	vol	vol	NOUN
ejpam-5710	1	11	.	.	PROPN
ejpam-5710	1	12	18	18	NUM
ejpam-5710	1	13	,	,	PUNCT
ejpam-5710	1	14	issue	issue	NOUN
ejpam-5710	1	15	1	1	NUM
ejpam-5710	1	16	,	,	PUNCT
ejpam-5710	1	17	article	article	NOUN
ejpam-5710	1	18	number	number	NOUN
ejpam-5710	1	19	5710	5710	NUM
ejpam-5710	1	20	issn	issn	PROPN
ejpam-5710	1	21	1307	1307	NUM
ejpam-5710	1	22	-	-	SYM
ejpam-5710	1	23	5543	5543	NUM
ejpam-5710	1	24	–	–	PUNCT
ejpam-5710	1	25	ejpam.com	ejpam.com	X
ejpam-5710	1	26	published	publish	VERB
ejpam-5710	1	27	by	by	ADP
ejpam-5710	1	28	new	new	PROPN
ejpam-5710	1	29	york	york	PROPN
ejpam-5710	1	30	business	business	PROPN
ejpam-5710	1	31	global	global	PROPN
ejpam-5710	1	32	quasi	quasi	NOUN
ejpam-5710	1	33	ruled	rule	VERB
ejpam-5710	1	34	surfaces	surface	NOUN
ejpam-5710	1	35	in	in	ADP
ejpam-5710	1	36	euclidean	euclidean	ADJ
ejpam-5710	1	37	3	3	NUM
ejpam-5710	1	38	-	-	PUNCT
ejpam-5710	1	39	space	space	NOUN
ejpam-5710	1	40	ayman	ayman	NOUN
ejpam-5710	1	41	elsharkawy1,∗	elsharkawy1,∗	PROPN
ejpam-5710	1	42	,	,	PUNCT
ejpam-5710	1	43	hoda	hoda	PROPN
ejpam-5710	1	44	k.	k.	PROPN
ejpam-5710	1	45	elsayied1	elsayied1	PROPN
ejpam-5710	1	46	,	,	PUNCT
ejpam-5710	1	47	aya	aya	PROPN
ejpam-5710	1	48	refaat1	refaat1	PROPN
ejpam-5710	1	49	1	1	NUM
ejpam-5710	1	50	department	department	NOUN
ejpam-5710	1	51	of	of	ADP
ejpam-5710	1	52	mathematics	mathematic	NOUN
ejpam-5710	1	53	,	,	PUNCT
ejpam-5710	1	54	faculty	faculty	NOUN
ejpam-5710	1	55	of	of	ADP
ejpam-5710	1	56	science	science	NOUN
ejpam-5710	1	57	,	,	PUNCT
ejpam-5710	1	58	university	university	PROPN
ejpam-5710	1	59	of	of	ADP
ejpam-5710	1	60	tanta	tanta	PROPN
ejpam-5710	1	61	,	,	PUNCT
ejpam-5710	1	62	tanta	tanta	PROPN
ejpam-5710	1	63	,	,	PUNCT
ejpam-5710	1	64	egypt	egypt	PROPN
ejpam-5710	1	65	abstract	abstract	PROPN
ejpam-5710	1	66	.	.	PUNCT
ejpam-5710	2	1	this	this	DET
ejpam-5710	2	2	paper	paper	NOUN
ejpam-5710	2	3	introduces	introduce	VERB
ejpam-5710	2	4	three	three	NUM
ejpam-5710	2	5	distinct	distinct	ADJ
ejpam-5710	2	6	types	type	NOUN
ejpam-5710	2	7	of	of	ADP
ejpam-5710	2	8	ruled	rule	VERB
ejpam-5710	2	9	surfaces	surface	NOUN
ejpam-5710	2	10	,	,	PUNCT
ejpam-5710	2	11	namely	namely	ADV
ejpam-5710	2	12	,	,	PUNCT
ejpam-5710	2	13	the	the	DET
ejpam-5710	2	14	quasitangent	quasitangent	NOUN
ejpam-5710	2	15	surfaces	surface	NOUN
ejpam-5710	2	16	,	,	PUNCT
ejpam-5710	2	17	the	the	DET
ejpam-5710	2	18	quasi	quasi	ADJ
ejpam-5710	2	19	-	-	ADJ
ejpam-5710	2	20	normal	normal	ADJ
ejpam-5710	2	21	surfaces	surface	NOUN
ejpam-5710	2	22	,	,	PUNCT
ejpam-5710	2	23	and	and	CCONJ
ejpam-5710	2	24	the	the	DET
ejpam-5710	2	25	quasi	quasi	ADJ
ejpam-5710	2	26	-	-	ADJ
ejpam-5710	2	27	binormal	binormal	ADJ
ejpam-5710	2	28	surfaces	surface	NOUN
ejpam-5710	2	29	.	.	PUNCT
ejpam-5710	3	1	these	these	DET
ejpam-5710	3	2	types	type	NOUN
ejpam-5710	3	3	are	be	AUX
ejpam-5710	3	4	determined	determine	VERB
ejpam-5710	3	5	by	by	ADP
ejpam-5710	3	6	the	the	DET
ejpam-5710	3	7	orientation	orientation	NOUN
ejpam-5710	3	8	of	of	ADP
ejpam-5710	3	9	their	their	PRON
ejpam-5710	3	10	direction	direction	NOUN
ejpam-5710	3	11	curves	curve	NOUN
ejpam-5710	3	12	tangent	tangent	NOUN
ejpam-5710	3	13	,	,	PUNCT
ejpam-5710	3	14	normal	normal	ADJ
ejpam-5710	3	15	,	,	PUNCT
ejpam-5710	3	16	and	and	CCONJ
ejpam-5710	3	17	binormal	binormal	NOUN
ejpam-5710	3	18	to	to	ADP
ejpam-5710	3	19	the	the	DET
ejpam-5710	3	20	base	base	NOUN
ejpam-5710	3	21	curve	curve	NOUN
ejpam-5710	3	22	,	,	PUNCT
ejpam-5710	3	23	respectively	respectively	ADV
ejpam-5710	3	24	.	.	PUNCT
ejpam-5710	4	1	this	this	DET
ejpam-5710	4	2	paper	paper	NOUN
ejpam-5710	4	3	does	do	AUX
ejpam-5710	4	4	not	not	PART
ejpam-5710	4	5	only	only	ADV
ejpam-5710	4	6	introduce	introduce	VERB
ejpam-5710	4	7	these	these	DET
ejpam-5710	4	8	surfaces	surface	NOUN
ejpam-5710	4	9	but	but	CCONJ
ejpam-5710	4	10	also	also	ADV
ejpam-5710	4	11	determines	determine	VERB
ejpam-5710	4	12	their	their	PRON
ejpam-5710	4	13	fundamental	fundamental	ADJ
ejpam-5710	4	14	properties	property	NOUN
ejpam-5710	4	15	,	,	PUNCT
ejpam-5710	4	16	including	include	VERB
ejpam-5710	4	17	the	the	DET
ejpam-5710	4	18	first	first	ADJ
ejpam-5710	4	19	,	,	PUNCT
ejpam-5710	4	20	the	the	DET
ejpam-5710	4	21	second	second	ADJ
ejpam-5710	4	22	,	,	PUNCT
ejpam-5710	4	23	and	and	CCONJ
ejpam-5710	4	24	the	the	DET
ejpam-5710	4	25	third	third	ADJ
ejpam-5710	4	26	fundamental	fundamental	ADJ
ejpam-5710	4	27	forms	form	NOUN
ejpam-5710	4	28	,	,	PUNCT
ejpam-5710	4	29	as	as	ADV
ejpam-5710	4	30	well	well	ADV
ejpam-5710	4	31	as	as	ADP
ejpam-5710	4	32	the	the	DET
ejpam-5710	4	33	gaussian	gaussian	NOUN
ejpam-5710	4	34	and	and	CCONJ
ejpam-5710	4	35	the	the	DET
ejpam-5710	4	36	mean	mean	ADJ
ejpam-5710	4	37	curvatures	curvature	NOUN
ejpam-5710	4	38	.	.	PUNCT
ejpam-5710	5	1	also	also	ADV
ejpam-5710	5	2	,	,	PUNCT
ejpam-5710	5	3	the	the	DET
ejpam-5710	5	4	geodesic	geodesic	ADJ
ejpam-5710	5	5	curvature	curvature	NOUN
ejpam-5710	5	6	,	,	PUNCT
ejpam-5710	5	7	the	the	DET
ejpam-5710	5	8	normal	normal	ADJ
ejpam-5710	5	9	curvature	curvature	NOUN
ejpam-5710	5	10	,	,	PUNCT
ejpam-5710	5	11	and	and	CCONJ
ejpam-5710	5	12	the	the	DET
ejpam-5710	5	13	geodesic	geodesic	ADJ
ejpam-5710	5	14	torsion	torsion	NOUN
ejpam-5710	5	15	associated	associate	VERB
ejpam-5710	5	16	with	with	ADP
ejpam-5710	5	17	the	the	DET
ejpam-5710	5	18	base	base	NOUN
ejpam-5710	5	19	curve	curve	NOUN
ejpam-5710	5	20	for	for	ADP
ejpam-5710	5	21	each	each	DET
ejpam-5710	5	22	type	type	NOUN
ejpam-5710	5	23	of	of	ADP
ejpam-5710	5	24	surface	surface	NOUN
ejpam-5710	5	25	are	be	AUX
ejpam-5710	5	26	investigated	investigate	VERB
ejpam-5710	5	27	.	.	PUNCT
ejpam-5710	6	1	furthermore	furthermore	ADV
ejpam-5710	6	2	,	,	PUNCT
ejpam-5710	6	3	the	the	DET
ejpam-5710	6	4	conditions	condition	NOUN
ejpam-5710	6	5	for	for	ADP
ejpam-5710	6	6	the	the	DET
ejpam-5710	6	7	base	base	NOUN
ejpam-5710	6	8	curve	curve	NOUN
ejpam-5710	6	9	to	to	PART
ejpam-5710	6	10	be	be	AUX
ejpam-5710	6	11	as	as	ADP
ejpam-5710	6	12	a	a	DET
ejpam-5710	6	13	geodesic	geodesic	NOUN
ejpam-5710	6	14	,	,	PUNCT
ejpam-5710	6	15	an	an	DET
ejpam-5710	6	16	asymptotic	asymptotic	ADJ
ejpam-5710	6	17	line	line	NOUN
ejpam-5710	6	18	,	,	PUNCT
ejpam-5710	6	19	and	and	CCONJ
ejpam-5710	6	20	a	a	DET
ejpam-5710	6	21	principal	principal	ADJ
ejpam-5710	6	22	line	line	NOUN
ejpam-5710	6	23	for	for	ADP
ejpam-5710	6	24	each	each	DET
ejpam-5710	6	25	type	type	NOUN
ejpam-5710	6	26	of	of	ADP
ejpam-5710	6	27	surface	surface	NOUN
ejpam-5710	6	28	are	be	AUX
ejpam-5710	6	29	provided	provide	VERB
ejpam-5710	6	30	.	.	PUNCT
ejpam-5710	7	1	also	also	ADV
ejpam-5710	7	2	,	,	PUNCT
ejpam-5710	7	3	the	the	DET
ejpam-5710	7	4	conditions	condition	NOUN
ejpam-5710	7	5	for	for	ADP
ejpam-5710	7	6	these	these	DET
ejpam-5710	7	7	curves	curve	NOUN
ejpam-5710	7	8	to	to	PART
ejpam-5710	7	9	be	be	AUX
ejpam-5710	7	10	considered	consider	VERB
ejpam-5710	7	11	developable	developable	ADJ
ejpam-5710	7	12	and	and	CCONJ
ejpam-5710	7	13	minimal	minimal	ADJ
ejpam-5710	7	14	surfaces	surface	NOUN
ejpam-5710	7	15	are	be	AUX
ejpam-5710	7	16	introduced	introduce	VERB
ejpam-5710	7	17	.	.	PUNCT
ejpam-5710	8	1	moreover	moreover	ADV
ejpam-5710	8	2	,	,	PUNCT
ejpam-5710	8	3	two	two	NUM
ejpam-5710	8	4	illustrative	illustrative	ADJ
ejpam-5710	8	5	examples	example	NOUN
ejpam-5710	8	6	are	be	AUX
ejpam-5710	8	7	introduced	introduce	VERB
ejpam-5710	8	8	to	to	PART
ejpam-5710	8	9	obtain	obtain	VERB
ejpam-5710	8	10	our	our	PRON
ejpam-5710	8	11	results	result	NOUN
ejpam-5710	8	12	.	.	PUNCT
ejpam-5710	9	1	2020	2020	NUM
ejpam-5710	9	2	mathematics	mathematic	NOUN
ejpam-5710	9	3	subject	subject	NOUN
ejpam-5710	9	4	classifications	classification	NOUN
ejpam-5710	9	5	:	:	PUNCT
ejpam-5710	9	6	53a05	53a05	NUM
ejpam-5710	9	7	key	key	ADJ
ejpam-5710	9	8	words	word	NOUN
ejpam-5710	9	9	and	and	CCONJ
ejpam-5710	9	10	phrases	phrase	NOUN
ejpam-5710	9	11	:	:	PUNCT
ejpam-5710	9	12	ruled	rule	VERB
ejpam-5710	9	13	surface	surface	NOUN
ejpam-5710	9	14	,	,	PUNCT
ejpam-5710	9	15	euclidean	euclidean	ADJ
ejpam-5710	9	16	space	space	NOUN
ejpam-5710	9	17	,	,	PUNCT
ejpam-5710	9	18	quasi	quasi	NOUN
ejpam-5710	9	19	frame	frame	NOUN
ejpam-5710	9	20	,	,	PUNCT
ejpam-5710	9	21	developable	developable	ADJ
ejpam-5710	9	22	surface	surface	NOUN
ejpam-5710	9	23	,	,	PUNCT
ejpam-5710	9	24	minimal	minimal	ADJ
ejpam-5710	9	25	surface	surface	NOUN
ejpam-5710	9	26	1	1	NUM
ejpam-5710	9	27	.	.	PUNCT
ejpam-5710	9	28	introduction	introduction	NOUN
ejpam-5710	9	29	the	the	DET
ejpam-5710	9	30	study	study	NOUN
ejpam-5710	9	31	of	of	ADP
ejpam-5710	9	32	ruled	rule	VERB
ejpam-5710	9	33	surfaces	surface	NOUN
ejpam-5710	9	34	has	have	AUX
ejpam-5710	9	35	garnered	garner	VERB
ejpam-5710	9	36	significant	significant	ADJ
ejpam-5710	9	37	attention	attention	NOUN
ejpam-5710	9	38	from	from	ADP
ejpam-5710	9	39	researchers	researcher	NOUN
ejpam-5710	9	40	in	in	ADP
ejpam-5710	9	41	recent	recent	ADJ
ejpam-5710	9	42	decades	decade	NOUN
ejpam-5710	9	43	due	due	ADP
ejpam-5710	9	44	to	to	ADP
ejpam-5710	9	45	their	their	PRON
ejpam-5710	9	46	broad	broad	ADJ
ejpam-5710	9	47	applications	application	NOUN
ejpam-5710	9	48	in	in	ADP
ejpam-5710	9	49	various	various	ADJ
ejpam-5710	9	50	fields	field	NOUN
ejpam-5710	9	51	,	,	PUNCT
ejpam-5710	9	52	including	include	VERB
ejpam-5710	9	53	spatial	spatial	ADJ
ejpam-5710	9	54	mechanism	mechanism	NOUN
ejpam-5710	9	55	design	design	NOUN
ejpam-5710	9	56	,	,	PUNCT
ejpam-5710	9	57	computer	computer	NOUN
ejpam-5710	9	58	-	-	PUNCT
ejpam-5710	9	59	aided	aid	VERB
ejpam-5710	9	60	geometric	geometric	ADJ
ejpam-5710	9	61	design	design	NOUN
ejpam-5710	9	62	,	,	PUNCT
ejpam-5710	9	63	architecture	architecture	NOUN
ejpam-5710	9	64	,	,	PUNCT
ejpam-5710	9	65	civil	civil	ADJ
ejpam-5710	9	66	engineering	engineering	NOUN
ejpam-5710	9	67	,	,	PUNCT
ejpam-5710	9	68	and	and	CCONJ
ejpam-5710	9	69	solid	solid	ADJ
ejpam-5710	9	70	modeling	modeling	NOUN
ejpam-5710	9	71	[	[	X
ejpam-5710	9	72	5–7	5–7	NUM
ejpam-5710	9	73	,	,	PUNCT
ejpam-5710	9	74	23	23	NUM
ejpam-5710	9	75	,	,	PUNCT
ejpam-5710	9	76	24	24	NUM
ejpam-5710	9	77	,	,	PUNCT
ejpam-5710	9	78	31	31	NUM
ejpam-5710	9	79	]	]	PUNCT
ejpam-5710	9	80	.	.	PUNCT
ejpam-5710	10	1	in	in	ADP
ejpam-5710	10	2	differential	differential	ADJ
ejpam-5710	10	3	geometry	geometry	NOUN
ejpam-5710	10	4	,	,	PUNCT
ejpam-5710	10	5	ruled	rule	VERB
ejpam-5710	10	6	surfaces	surface	NOUN
ejpam-5710	10	7	are	be	AUX
ejpam-5710	10	8	generated	generate	VERB
ejpam-5710	10	9	by	by	ADP
ejpam-5710	10	10	the	the	DET
ejpam-5710	10	11	motion	motion	NOUN
ejpam-5710	10	12	of	of	ADP
ejpam-5710	10	13	a	a	DET
ejpam-5710	10	14	straight	straight	ADJ
ejpam-5710	10	15	line	line	NOUN
ejpam-5710	10	16	,	,	PUNCT
ejpam-5710	10	17	called	call	VERB
ejpam-5710	10	18	a	a	DET
ejpam-5710	10	19	ruling	ruling	NOUN
ejpam-5710	10	20	,	,	PUNCT
ejpam-5710	10	21	along	along	ADP
ejpam-5710	10	22	a	a	DET
ejpam-5710	10	23	base	base	NOUN
ejpam-5710	10	24	curve	curve	NOUN
ejpam-5710	10	25	in	in	ADP
ejpam-5710	10	26	space	space	NOUN
ejpam-5710	10	27	.	.	PUNCT
ejpam-5710	11	1	these	these	DET
ejpam-5710	11	2	surfaces	surface	NOUN
ejpam-5710	11	3	are	be	AUX
ejpam-5710	11	4	central	central	ADJ
ejpam-5710	11	5	to	to	ADP
ejpam-5710	11	6	many	many	ADJ
ejpam-5710	11	7	theoretical	theoretical	ADJ
ejpam-5710	11	8	and	and	CCONJ
ejpam-5710	11	9	practical	practical	ADJ
ejpam-5710	11	10	advancements	advancement	NOUN
ejpam-5710	11	11	,	,	PUNCT
ejpam-5710	11	12	including	include	VERB
ejpam-5710	11	13	the	the	DET
ejpam-5710	11	14	study	study	NOUN
ejpam-5710	11	15	of	of	ADP
ejpam-5710	11	16	developable	developable	ADJ
ejpam-5710	11	17	ruled	rule	VERB
ejpam-5710	11	18	surfaces	surface	NOUN
ejpam-5710	11	19	,	,	PUNCT
ejpam-5710	11	20	which	which	PRON
ejpam-5710	11	21	are	be	AUX
ejpam-5710	11	22	characterized	characterize	VERB
ejpam-5710	11	23	by	by	ADP
ejpam-5710	11	24	zero	zero	NUM
ejpam-5710	11	25	gaussian	gaussian	ADJ
ejpam-5710	11	26	curvature	curvature	NOUN
ejpam-5710	11	27	and	and	CCONJ
ejpam-5710	11	28	can	can	AUX
ejpam-5710	11	29	be	be	AUX
ejpam-5710	11	30	unfolded	unfold	VERB
ejpam-5710	11	31	onto	onto	ADP
ejpam-5710	11	32	a	a	DET
ejpam-5710	11	33	plane	plane	NOUN
ejpam-5710	11	34	without	without	ADP
ejpam-5710	11	35	distortion	distortion	NOUN
ejpam-5710	11	36	[	[	X
ejpam-5710	11	37	8	8	NUM
ejpam-5710	11	38	,	,	PUNCT
ejpam-5710	11	39	26	26	NUM
ejpam-5710	11	40	]	]	PUNCT
ejpam-5710	11	41	,	,	PUNCT
ejpam-5710	11	42	and	and	CCONJ
ejpam-5710	11	43	minimal	minimal	ADJ
ejpam-5710	11	44	ruled	rule	VERB
ejpam-5710	11	45	surfaces	surface	NOUN
ejpam-5710	11	46	,	,	PUNCT
ejpam-5710	11	47	which	which	PRON
ejpam-5710	11	48	minimize	minimize	VERB
ejpam-5710	11	49	surface	surface	NOUN
ejpam-5710	11	50	area	area	NOUN
ejpam-5710	11	51	and	and	CCONJ
ejpam-5710	11	52	are	be	AUX
ejpam-5710	11	53	characterized	characterize	VERB
ejpam-5710	11	54	by	by	ADP
ejpam-5710	11	55	vanishing	vanish	VERB
ejpam-5710	11	56	mean	mean	ADJ
ejpam-5710	11	57	curvature	curvature	NOUN
ejpam-5710	11	58	[	[	X
ejpam-5710	11	59	29	29	NUM
ejpam-5710	11	60	]	]	PUNCT
ejpam-5710	11	61	.	.	PUNCT
ejpam-5710	12	1	a	a	DET
ejpam-5710	12	2	significant	significant	ADJ
ejpam-5710	12	3	body	body	NOUN
ejpam-5710	12	4	of	of	ADP
ejpam-5710	12	5	work	work	NOUN
ejpam-5710	12	6	has	have	AUX
ejpam-5710	12	7	explored	explore	VERB
ejpam-5710	12	8	the	the	DET
ejpam-5710	12	9	relationship	relationship	NOUN
ejpam-5710	12	10	between	between	ADP
ejpam-5710	12	11	ruled	rule	VERB
ejpam-5710	12	12	surfaces	surface	NOUN
ejpam-5710	12	13	and	and	CCONJ
ejpam-5710	12	14	helical	helical	ADJ
ejpam-5710	12	15	curves	curve	NOUN
ejpam-5710	12	16	within	within	ADP
ejpam-5710	12	17	the	the	DET
ejpam-5710	12	18	framework	framework	NOUN
ejpam-5710	12	19	of	of	ADP
ejpam-5710	12	20	the	the	DET
ejpam-5710	12	21	frenet	frenet	ADJ
ejpam-5710	12	22	frame	frame	NOUN
ejpam-5710	12	23	in	in	ADP
ejpam-5710	12	24	three	three	NUM
ejpam-5710	12	25	-	-	PUNCT
ejpam-5710	12	26	dimensional	dimensional	ADJ
ejpam-5710	12	27	euclidean	euclidean	ADJ
ejpam-5710	12	28	space	space	NOUN
ejpam-5710	12	29	[	[	X
ejpam-5710	12	30	2	2	NUM
ejpam-5710	12	31	,	,	PUNCT
ejpam-5710	12	32	3	3	NUM
ejpam-5710	12	33	,	,	PUNCT
ejpam-5710	12	34	26	26	NUM
ejpam-5710	12	35	,	,	PUNCT
ejpam-5710	12	36	32	32	NUM
ejpam-5710	12	37	]	]	PUNCT
ejpam-5710	12	38	.	.	PUNCT
ejpam-5710	13	1	historical	historical	ADJ
ejpam-5710	13	2	contributions	contribution	NOUN
ejpam-5710	13	3	include	include	VERB
ejpam-5710	13	4	the	the	DET
ejpam-5710	13	5	foundational	foundational	ADJ
ejpam-5710	13	6	work	work	NOUN
ejpam-5710	13	7	of	of	ADP
ejpam-5710	13	8	karger	karger	NOUN
ejpam-5710	13	9	∗corresponding	∗corresponde	VERB
ejpam-5710	13	10	author	author	NOUN
ejpam-5710	13	11	.	.	PUNCT
ejpam-5710	14	1	doi	doi	NOUN
ejpam-5710	14	2	:	:	PUNCT
ejpam-5710	14	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5710	https://doi.org/10.29020/nybg.ejpam.v18i1.5710	ADJ
ejpam-5710	14	4	email	email	NOUN
ejpam-5710	14	5	addresses	address	NOUN
ejpam-5710	14	6	:	:	PUNCT
ejpam-5710	14	7	ayman_ramadan@science.tanta.edu.eg	ayman_ramadan@science.tanta.edu.eg	PROPN
ejpam-5710	14	8	(	(	PUNCT
ejpam-5710	14	9	a.	a.	NOUN
ejpam-5710	14	10	elsharkawy	elsharkawy	PROPN
ejpam-5710	14	11	)	)	PUNCT
ejpam-5710	14	12	hkelsayied1989@yahoo.com	hkelsayied1989@yahoo.com	X
ejpam-5710	15	1	(	(	PUNCT
ejpam-5710	15	2	h.	h.	PROPN
ejpam-5710	15	3	k.	k.	PROPN
ejpam-5710	15	4	elsayied	elsayied	PROPN
ejpam-5710	15	5	)	)	PUNCT
ejpam-5710	15	6	,	,	PUNCT
ejpam-5710	15	7	aya30899252@science.tanta.edu.eg	aya30899252@science.tanta.edu.eg	CCONJ
ejpam-5710	15	8	(	(	PUNCT
ejpam-5710	15	9	a.	a.	NOUN
ejpam-5710	15	10	refaat	refaat	PROPN
ejpam-5710	15	11	)	)	PUNCT
ejpam-5710	15	12	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5710	16	1	1	1	NUM
ejpam-5710	16	2	copyright	copyright	NOUN
ejpam-5710	16	3	:	:	PUNCT
ejpam-5710	16	4	©	©	PROPN
ejpam-5710	16	5	2025	2025	NUM
ejpam-5710	16	6	the	the	DET
ejpam-5710	16	7	author(s	author(s	NOUN
ejpam-5710	16	8	)	)	PUNCT
ejpam-5710	16	9	.	.	PUNCT
ejpam-5710	17	1	(	(	PUNCT
ejpam-5710	17	2	cc	cc	NOUN
ejpam-5710	17	3	by	by	ADP
ejpam-5710	17	4	-	-	PUNCT
ejpam-5710	17	5	nc	nc	PROPN
ejpam-5710	17	6	4.0	4.0	NUM
ejpam-5710	17	7	)	)	PUNCT
ejpam-5710	17	8	a.	a.	NOUN
ejpam-5710	17	9	elsharkawy	elsharkawy	PROPN
ejpam-5710	17	10	,	,	PUNCT
ejpam-5710	17	11	h.	h.	PROPN
ejpam-5710	17	12	k.	k.	PROPN
ejpam-5710	17	13	elsayied	elsayied	PROPN
ejpam-5710	17	14	,	,	PUNCT
ejpam-5710	17	15	a.	a.	NOUN
ejpam-5710	17	16	refaat	refaat	PROPN
ejpam-5710	17	17	/	/	SYM
ejpam-5710	17	18	eur	eur	PROPN
ejpam-5710	17	19	.	.	PUNCT
ejpam-5710	18	1	j.	j.	PROPN
ejpam-5710	18	2	pure	pure	PROPN
ejpam-5710	18	3	appl	appl	PROPN
ejpam-5710	18	4	.	.	PROPN
ejpam-5710	18	5	math	math	PROPN
ejpam-5710	18	6	,	,	PUNCT
ejpam-5710	18	7	18	18	NUM
ejpam-5710	18	8	(	(	PUNCT
ejpam-5710	18	9	1	1	NUM
ejpam-5710	18	10	)	)	PUNCT
ejpam-5710	18	11	(	(	PUNCT
ejpam-5710	18	12	2025	2025	NUM
ejpam-5710	18	13	)	)	PUNCT
ejpam-5710	18	14	,	,	PUNCT
ejpam-5710	18	15	5710	5710	NUM
ejpam-5710	18	16	2	2	NUM
ejpam-5710	18	17	of	of	ADP
ejpam-5710	18	18	18	18	NUM
ejpam-5710	18	19	and	and	CCONJ
ejpam-5710	18	20	novak	novak	NOUN
ejpam-5710	18	21	in	in	ADP
ejpam-5710	18	22	1978	1978	NUM
ejpam-5710	18	23	,	,	PUNCT
ejpam-5710	18	24	introducing	introduce	VERB
ejpam-5710	18	25	frenet	frenet	NOUN
ejpam-5710	18	26	frames	frame	NOUN
ejpam-5710	18	27	and	and	CCONJ
ejpam-5710	18	28	invariants	invariant	NOUN
ejpam-5710	18	29	for	for	ADP
ejpam-5710	18	30	ruled	rule	VERB
ejpam-5710	18	31	surfaces	surface	NOUN
ejpam-5710	18	32	[	[	X
ejpam-5710	18	33	27	27	NUM
ejpam-5710	18	34	]	]	PUNCT
ejpam-5710	18	35	,	,	PUNCT
ejpam-5710	18	36	and	and	CCONJ
ejpam-5710	18	37	pottmann	pottmann	PROPN
ejpam-5710	18	38	et	et	PROPN
ejpam-5710	18	39	.	.	PUNCT
ejpam-5710	19	1	al	al	PROPN
ejpam-5710	19	2	.	.	PROPN
ejpam-5710	19	3	exploration	exploration	NOUN
ejpam-5710	19	4	of	of	ADP
ejpam-5710	19	5	rational	rational	ADJ
ejpam-5710	19	6	ruled	rule	VERB
ejpam-5710	19	7	surfaces	surface	NOUN
ejpam-5710	19	8	and	and	CCONJ
ejpam-5710	19	9	their	their	PRON
ejpam-5710	19	10	offsets	offset	NOUN
ejpam-5710	19	11	in	in	ADP
ejpam-5710	19	12	1996	1996	NUM
ejpam-5710	19	13	[	[	X
ejpam-5710	19	14	34	34	NUM
ejpam-5710	19	15	]	]	PUNCT
ejpam-5710	19	16	.	.	PUNCT
ejpam-5710	20	1	later	later	ADV
ejpam-5710	20	2	,	,	PUNCT
ejpam-5710	20	3	peternel	peternel	PROPN
ejpam-5710	20	4	et	et	PROPN
ejpam-5710	20	5	al	al	PROPN
ejpam-5710	20	6	.	.	PROPN
ejpam-5710	20	7	addressed	address	VERB
ejpam-5710	20	8	computational	computational	ADJ
ejpam-5710	20	9	aspects	aspect	NOUN
ejpam-5710	20	10	of	of	ADP
ejpam-5710	20	11	ruled	rule	VERB
ejpam-5710	20	12	surfaces	surface	NOUN
ejpam-5710	20	13	in	in	ADP
ejpam-5710	20	14	1999	1999	NUM
ejpam-5710	20	15	[	[	X
ejpam-5710	20	16	33	33	NUM
ejpam-5710	20	17	]	]	PUNCT
ejpam-5710	20	18	,	,	PUNCT
ejpam-5710	20	19	while	while	SCONJ
ejpam-5710	20	20	recent	recent	ADJ
ejpam-5710	20	21	research	research	NOUN
ejpam-5710	20	22	has	have	AUX
ejpam-5710	20	23	extended	extend	VERB
ejpam-5710	20	24	these	these	DET
ejpam-5710	20	25	investigations	investigation	NOUN
ejpam-5710	20	26	to	to	ADP
ejpam-5710	20	27	the	the	DET
ejpam-5710	20	28	differential	differential	ADJ
ejpam-5710	20	29	geometry	geometry	NOUN
ejpam-5710	20	30	of	of	ADP
ejpam-5710	20	31	ruled	rule	VERB
ejpam-5710	20	32	surfaces	surface	NOUN
ejpam-5710	20	33	in	in	ADP
ejpam-5710	20	34	minkowski	minkowski	ADJ
ejpam-5710	20	35	space	space	NOUN
ejpam-5710	21	1	[	[	X
ejpam-5710	21	2	1	1	NUM
ejpam-5710	21	3	,	,	PUNCT
ejpam-5710	21	4	4	4	NUM
ejpam-5710	21	5	,	,	PUNCT
ejpam-5710	21	6	9	9	NUM
ejpam-5710	21	7	,	,	PUNCT
ejpam-5710	21	8	28	28	NUM
ejpam-5710	21	9	,	,	PUNCT
ejpam-5710	21	10	30	30	NUM
ejpam-5710	21	11	,	,	PUNCT
ejpam-5710	21	12	35	35	NUM
ejpam-5710	21	13	,	,	PUNCT
ejpam-5710	21	14	36	36	NUM
ejpam-5710	21	15	,	,	PUNCT
ejpam-5710	21	16	39	39	NUM
ejpam-5710	21	17	]	]	PUNCT
ejpam-5710	21	18	.	.	PUNCT
ejpam-5710	22	1	the	the	DET
ejpam-5710	22	2	quasi	quasi	NOUN
ejpam-5710	22	3	-	-	NOUN
ejpam-5710	22	4	frame	frame	NOUN
ejpam-5710	22	5	has	have	AUX
ejpam-5710	22	6	emerged	emerge	VERB
ejpam-5710	22	7	as	as	ADP
ejpam-5710	22	8	an	an	DET
ejpam-5710	22	9	alternative	alternative	NOUN
ejpam-5710	22	10	to	to	ADP
ejpam-5710	22	11	the	the	DET
ejpam-5710	22	12	frenet	frenet	ADJ
ejpam-5710	22	13	frame	frame	NOUN
ejpam-5710	22	14	for	for	ADP
ejpam-5710	22	15	studying	study	VERB
ejpam-5710	22	16	curves	curve	NOUN
ejpam-5710	22	17	and	and	CCONJ
ejpam-5710	22	18	surfaces	surface	NOUN
ejpam-5710	22	19	.	.	PUNCT
ejpam-5710	23	1	defined	define	VERB
ejpam-5710	23	2	by	by	ADP
ejpam-5710	23	3	a	a	DET
ejpam-5710	23	4	fixed	fix	VERB
ejpam-5710	23	5	projection	projection	NOUN
ejpam-5710	23	6	vector	vector	NOUN
ejpam-5710	23	7	and	and	CCONJ
ejpam-5710	23	8	the	the	DET
ejpam-5710	23	9	angle	angle	NOUN
ejpam-5710	23	10	between	between	ADP
ejpam-5710	23	11	the	the	DET
ejpam-5710	23	12	principal	principal	NOUN
ejpam-5710	23	13	normal	normal	ADJ
ejpam-5710	23	14	and	and	CCONJ
ejpam-5710	23	15	the	the	DET
ejpam-5710	23	16	quasi	quasi	ADJ
ejpam-5710	23	17	-	-	ADJ
ejpam-5710	23	18	normal	normal	ADJ
ejpam-5710	23	19	vector	vector	NOUN
ejpam-5710	23	20	field	field	NOUN
ejpam-5710	23	21	,	,	PUNCT
ejpam-5710	23	22	the	the	DET
ejpam-5710	23	23	quasi	quasi	ADJ
ejpam-5710	23	24	-	-	ADJ
ejpam-5710	23	25	frame	frame	ADJ
ejpam-5710	23	26	simplifies	simplifie	NOUN
ejpam-5710	23	27	computations	computation	NOUN
ejpam-5710	23	28	compared	compare	VERB
ejpam-5710	23	29	to	to	ADP
ejpam-5710	23	30	the	the	DET
ejpam-5710	23	31	frenet	frenet	NOUN
ejpam-5710	23	32	and	and	CCONJ
ejpam-5710	23	33	bishop	bishop	PROPN
ejpam-5710	23	34	frames	frame	NOUN
ejpam-5710	23	35	.	.	PUNCT
ejpam-5710	24	1	this	this	DET
ejpam-5710	24	2	simplicity	simplicity	NOUN
ejpam-5710	24	3	has	have	AUX
ejpam-5710	24	4	made	make	VERB
ejpam-5710	24	5	the	the	DET
ejpam-5710	24	6	quasiframe	quasiframe	NOUN
ejpam-5710	24	7	a	a	DET
ejpam-5710	24	8	valuable	valuable	ADJ
ejpam-5710	24	9	tool	tool	NOUN
ejpam-5710	24	10	in	in	ADP
ejpam-5710	24	11	exploring	explore	VERB
ejpam-5710	24	12	geometrical	geometrical	ADJ
ejpam-5710	24	13	properties	property	NOUN
ejpam-5710	24	14	and	and	CCONJ
ejpam-5710	24	15	applications	application	NOUN
ejpam-5710	24	16	in	in	ADP
ejpam-5710	24	17	euclidean	euclidean	ADJ
ejpam-5710	24	18	,	,	PUNCT
ejpam-5710	24	19	minkowski	minkowski	ADJ
ejpam-5710	24	20	,	,	PUNCT
ejpam-5710	24	21	and	and	CCONJ
ejpam-5710	24	22	galilean	galilean	PROPN
ejpam-5710	24	23	spaces	space	VERB
ejpam-5710	24	24	[	[	X
ejpam-5710	24	25	13	13	NUM
ejpam-5710	24	26	,	,	PUNCT
ejpam-5710	24	27	14	14	NUM
ejpam-5710	24	28	,	,	PUNCT
ejpam-5710	24	29	18	18	NUM
ejpam-5710	24	30	,	,	PUNCT
ejpam-5710	24	31	22	22	NUM
ejpam-5710	24	32	,	,	PUNCT
ejpam-5710	24	33	25	25	NUM
ejpam-5710	24	34	]	]	PUNCT
ejpam-5710	24	35	.	.	PUNCT
ejpam-5710	25	1	furthermore	furthermore	ADV
ejpam-5710	25	2	,	,	PUNCT
ejpam-5710	25	3	variants	variant	NOUN
ejpam-5710	25	4	of	of	ADP
ejpam-5710	25	5	quasiframes	quasiframe	NOUN
ejpam-5710	25	6	,	,	PUNCT
ejpam-5710	25	7	such	such	ADJ
ejpam-5710	25	8	as	as	ADP
ejpam-5710	25	9	equiform	equiform	NOUN
ejpam-5710	25	10	and	and	CCONJ
ejpam-5710	25	11	modified	modify	VERB
ejpam-5710	25	12	frames	frame	NOUN
ejpam-5710	25	13	,	,	PUNCT
ejpam-5710	25	14	have	have	AUX
ejpam-5710	25	15	been	be	AUX
ejpam-5710	25	16	utilized	utilize	VERB
ejpam-5710	25	17	in	in	ADP
ejpam-5710	25	18	diverse	diverse	ADJ
ejpam-5710	25	19	contexts	context	NOUN
ejpam-5710	25	20	[	[	X
ejpam-5710	25	21	10–12	10–12	NUM
ejpam-5710	25	22	,	,	PUNCT
ejpam-5710	25	23	15	15	NUM
ejpam-5710	25	24	,	,	PUNCT
ejpam-5710	25	25	17	17	NUM
ejpam-5710	25	26	,	,	PUNCT
ejpam-5710	25	27	19–21	19–21	NUM
ejpam-5710	25	28	,	,	PUNCT
ejpam-5710	25	29	24	24	NUM
ejpam-5710	25	30	,	,	PUNCT
ejpam-5710	25	31	37	37	NUM
ejpam-5710	25	32	,	,	PUNCT
ejpam-5710	25	33	38	38	NUM
ejpam-5710	25	34	]	]	PUNCT
ejpam-5710	25	35	.	.	PUNCT
ejpam-5710	26	1	this	this	DET
ejpam-5710	26	2	paper	paper	NOUN
ejpam-5710	26	3	is	be	AUX
ejpam-5710	26	4	organized	organize	VERB
ejpam-5710	26	5	as	as	SCONJ
ejpam-5710	26	6	follows	follow	VERB
ejpam-5710	26	7	.	.	PUNCT
ejpam-5710	27	1	in	in	ADP
ejpam-5710	27	2	section	section	NOUN
ejpam-5710	27	3	2	2	NUM
ejpam-5710	27	4	,	,	PUNCT
ejpam-5710	27	5	we	we	PRON
ejpam-5710	27	6	provide	provide	VERB
ejpam-5710	27	7	fundamental	fundamental	ADJ
ejpam-5710	27	8	definitions	definition	NOUN
ejpam-5710	27	9	and	and	CCONJ
ejpam-5710	27	10	concepts	concept	NOUN
ejpam-5710	27	11	used	use	VERB
ejpam-5710	27	12	throughout	throughout	ADP
ejpam-5710	27	13	the	the	DET
ejpam-5710	27	14	paper	paper	NOUN
ejpam-5710	27	15	.	.	PUNCT
ejpam-5710	28	1	section	section	NOUN
ejpam-5710	28	2	3	3	NUM
ejpam-5710	28	3	introduces	introduce	NOUN
ejpam-5710	28	4	three	three	NUM
ejpam-5710	28	5	new	new	ADJ
ejpam-5710	28	6	types	type	NOUN
ejpam-5710	28	7	of	of	ADP
ejpam-5710	28	8	ruled	rule	VERB
ejpam-5710	28	9	surfaces	surface	NOUN
ejpam-5710	28	10	based	base	VERB
ejpam-5710	28	11	on	on	ADP
ejpam-5710	28	12	the	the	DET
ejpam-5710	28	13	quasi	quasi	NOUN
ejpam-5710	28	14	-	-	NOUN
ejpam-5710	28	15	frame	frame	NOUN
ejpam-5710	28	16	:	:	PUNCT
ejpam-5710	28	17	qrt	qrt	NOUN
ejpam-5710	28	18	-	-	PUNCT
ejpam-5710	28	19	surfaces	surface	NOUN
ejpam-5710	28	20	,	,	PUNCT
ejpam-5710	28	21	qrn	qrn	NOUN
ejpam-5710	28	22	-	-	PUNCT
ejpam-5710	28	23	surfaces	surface	NOUN
ejpam-5710	28	24	,	,	PUNCT
ejpam-5710	28	25	and	and	CCONJ
ejpam-5710	28	26	qrb	qrb	NOUN
ejpam-5710	28	27	-	-	PUNCT
ejpam-5710	28	28	surfaces	surface	NOUN
ejpam-5710	28	29	.	.	PUNCT
ejpam-5710	29	1	for	for	ADP
ejpam-5710	29	2	each	each	DET
ejpam-5710	29	3	surface	surface	NOUN
ejpam-5710	29	4	type	type	NOUN
ejpam-5710	29	5	,	,	PUNCT
ejpam-5710	29	6	we	we	PRON
ejpam-5710	29	7	discuss	discuss	VERB
ejpam-5710	29	8	their	their	PRON
ejpam-5710	29	9	fundamental	fundamental	ADJ
ejpam-5710	29	10	properties	property	NOUN
ejpam-5710	29	11	and	and	CCONJ
ejpam-5710	29	12	provide	provide	VERB
ejpam-5710	29	13	a	a	DET
ejpam-5710	29	14	detailed	detailed	ADJ
ejpam-5710	29	15	analysis	analysis	NOUN
ejpam-5710	29	16	.	.	PUNCT
ejpam-5710	30	1	finally	finally	ADV
ejpam-5710	30	2	,	,	PUNCT
ejpam-5710	30	3	we	we	PRON
ejpam-5710	30	4	present	present	VERB
ejpam-5710	30	5	two	two	NUM
ejpam-5710	30	6	illustrative	illustrative	ADJ
ejpam-5710	30	7	examples	example	NOUN
ejpam-5710	30	8	in	in	ADP
ejpam-5710	30	9	section	section	NOUN
ejpam-5710	30	10	4	4	NUM
ejpam-5710	30	11	to	to	PART
ejpam-5710	30	12	validate	validate	VERB
ejpam-5710	30	13	the	the	DET
ejpam-5710	30	14	theoretical	theoretical	ADJ
ejpam-5710	30	15	results	result	NOUN
ejpam-5710	30	16	and	and	CCONJ
ejpam-5710	30	17	demonstrate	demonstrate	VERB
ejpam-5710	30	18	their	their	PRON
ejpam-5710	30	19	practical	practical	ADJ
ejpam-5710	30	20	relevance	relevance	NOUN
ejpam-5710	30	21	.	.	PUNCT
ejpam-5710	31	1	2	2	X
ejpam-5710	31	2	.	.	X
ejpam-5710	31	3	preliminaries	preliminary	NOUN
ejpam-5710	31	4	let	let	VERB
ejpam-5710	31	5	e3	e3	NOUN
ejpam-5710	31	6	be	be	AUX
ejpam-5710	31	7	an	an	DET
ejpam-5710	31	8	euclidean	euclidean	ADJ
ejpam-5710	31	9	3	3	NUM
ejpam-5710	31	10	-	-	PUNCT
ejpam-5710	31	11	space	space	NOUN
ejpam-5710	31	12	equipped	equip	VERB
ejpam-5710	31	13	with	with	ADP
ejpam-5710	31	14	the	the	DET
ejpam-5710	31	15	metric	metric	NOUN
ejpam-5710	31	16	<	<	X
ejpam-5710	31	17	,	,	PUNCT
ejpam-5710	31	18	>	>	PUNCT
ejpam-5710	31	19	given	give	VERB
ejpam-5710	31	20	by	by	ADP
ejpam-5710	31	21	<	<	X
ejpam-5710	31	22	,	,	PUNCT
ejpam-5710	31	23	>	>	PUNCT
ejpam-5710	31	24	=	=	SYM
ejpam-5710	31	25	du2	du2	NOUN
ejpam-5710	31	26	+	+	CCONJ
ejpam-5710	31	27	dv2	dv2	NOUN
ejpam-5710	31	28	+	+	CCONJ
ejpam-5710	31	29	dw2	dw2	NOUN
ejpam-5710	31	30	,	,	PUNCT
ejpam-5710	31	31	where	where	SCONJ
ejpam-5710	31	32	(	(	PUNCT
ejpam-5710	31	33	u	u	NOUN
ejpam-5710	31	34	,	,	PUNCT
ejpam-5710	31	35	v	v	NOUN
ejpam-5710	31	36	,	,	PUNCT
ejpam-5710	31	37	w	w	NOUN
ejpam-5710	31	38	)	)	PUNCT
ejpam-5710	31	39	is	be	AUX
ejpam-5710	31	40	a	a	DET
ejpam-5710	31	41	coordinate	coordinate	NOUN
ejpam-5710	31	42	system	system	NOUN
ejpam-5710	31	43	of	of	ADP
ejpam-5710	31	44	e3	e3	NOUN
ejpam-5710	31	45	.	.	PUNCT
ejpam-5710	32	1	for	for	ADP
ejpam-5710	32	2	a	a	DET
ejpam-5710	32	3	space	space	NOUN
ejpam-5710	32	4	curve	curve	NOUN
ejpam-5710	32	5	α(s	α(s	PROPN
ejpam-5710	32	6	)	)	PUNCT
ejpam-5710	32	7	:	:	PUNCT
ejpam-5710	32	8	(	(	PUNCT
ejpam-5710	32	9	a	a	PRON
ejpam-5710	32	10	,	,	PUNCT
ejpam-5710	32	11	b	b	NOUN
ejpam-5710	32	12	)	)	PUNCT
ejpam-5710	32	13	∈	∈	PROPN
ejpam-5710	32	14	i	i	PRON
ejpam-5710	32	15	→	→	SYM
ejpam-5710	32	16	r3	r3	PROPN
ejpam-5710	32	17	represented	represent	VERB
ejpam-5710	32	18	by	by	ADP
ejpam-5710	32	19	its	its	PRON
ejpam-5710	32	20	arc	arc	NOUN
ejpam-5710	32	21	-	-	PUNCT
ejpam-5710	32	22	length	length	NOUN
ejpam-5710	32	23	s	s	VERB
ejpam-5710	32	24	let	let	VERB
ejpam-5710	32	25	{	{	PUNCT
ejpam-5710	32	26	tq(s	tq(s	NUM
ejpam-5710	32	27	)	)	PUNCT
ejpam-5710	32	28	,	,	PUNCT
ejpam-5710	32	29	nq(s	nq(s	NUM
ejpam-5710	32	30	)	)	PUNCT
ejpam-5710	32	31	,	,	PUNCT
ejpam-5710	32	32	bq(s	bq(s	PROPN
ejpam-5710	32	33	)	)	PUNCT
ejpam-5710	32	34	}	}	PUNCT
ejpam-5710	32	35	be	be	AUX
ejpam-5710	32	36	the	the	DET
ejpam-5710	32	37	quasi	quasi	ADJ
ejpam-5710	32	38	frame	frame	NOUN
ejpam-5710	32	39	along	along	ADP
ejpam-5710	32	40	α(s	α(s	PROPN
ejpam-5710	32	41	)	)	PUNCT
ejpam-5710	33	1	in	in	ADP
ejpam-5710	33	2	which	which	PRON
ejpam-5710	33	3	tq(s	tq(s	NUM
ejpam-5710	33	4	)	)	PUNCT
ejpam-5710	33	5	,	,	PUNCT
ejpam-5710	33	6	nq(s	nq(s	NUM
ejpam-5710	33	7	)	)	PUNCT
ejpam-5710	33	8	and	and	CCONJ
ejpam-5710	33	9	bq(s	bq(s	NUM
ejpam-5710	33	10	)	)	PUNCT
ejpam-5710	33	11	are	be	AUX
ejpam-5710	33	12	the	the	DET
ejpam-5710	33	13	quasi	quasi	NOUN
ejpam-5710	33	14	-	-	NOUN
ejpam-5710	33	15	tangent	tangent	ADJ
ejpam-5710	33	16	,	,	PUNCT
ejpam-5710	33	17	quasi	quasi	ADJ
ejpam-5710	33	18	-	-	ADJ
ejpam-5710	33	19	normal	normal	ADJ
ejpam-5710	33	20	and	and	CCONJ
ejpam-5710	33	21	quasi	quasi	ADJ
ejpam-5710	33	22	-	-	ADJ
ejpam-5710	33	23	binormal	binormal	ADJ
ejpam-5710	33	24	vectors	vector	NOUN
ejpam-5710	33	25	,	,	PUNCT
ejpam-5710	33	26	respectively	respectively	ADV
ejpam-5710	33	27	,	,	PUNCT
ejpam-5710	33	28	given	give	VERB
ejpam-5710	33	29	in	in	ADP
ejpam-5710	33	30	[	[	NOUN
ejpam-5710	33	31	22	22	NUM
ejpam-5710	33	32	]	]	PUNCT
ejpam-5710	33	33	by	by	ADP
ejpam-5710	33	34	tq(s	tq(s	NUM
ejpam-5710	33	35	)	)	PUNCT
ejpam-5710	33	36	=	=	SYM
ejpam-5710	34	1	α′(s	α′(s	X
ejpam-5710	34	2	)	)	PUNCT
ejpam-5710	34	3	∥	∥	PUNCT
ejpam-5710	34	4	α′(s	α′(s	X
ejpam-5710	34	5	)	)	PUNCT
ejpam-5710	34	6	∥	∥	PUNCT
ejpam-5710	34	7	,	,	PUNCT
ejpam-5710	34	8	nq(s	nq(s	NUM
ejpam-5710	34	9	)	)	PUNCT
ejpam-5710	34	10	=	=	PUNCT
ejpam-5710	35	1	tq	tq	ADP
ejpam-5710	35	2	×m	×m	NOUN
ejpam-5710	35	3	∥	∥	PUNCT
ejpam-5710	35	4	tq	tq	ADP
ejpam-5710	35	5	×m	×m	NOUN
ejpam-5710	35	6	∥	∥	PUNCT
ejpam-5710	35	7	,	,	PUNCT
ejpam-5710	35	8	bq(s	bq(s	NOUN
ejpam-5710	35	9	)	)	PUNCT
ejpam-5710	35	10	=	=	PUNCT
ejpam-5710	36	1	tq	tq	ADP
ejpam-5710	36	2	×	×	PROPN
ejpam-5710	36	3	nq	nq	PROPN
ejpam-5710	36	4	,	,	PUNCT
ejpam-5710	36	5	(	(	PUNCT
ejpam-5710	36	6	2.1	2.1	NUM
ejpam-5710	36	7	)	)	PUNCT
ejpam-5710	36	8	where	where	SCONJ
ejpam-5710	36	9	′	′	PRON
ejpam-5710	36	10	is	be	AUX
ejpam-5710	36	11	the	the	DET
ejpam-5710	36	12	derivative	derivative	NOUN
ejpam-5710	36	13	with	with	ADP
ejpam-5710	36	14	respect	respect	NOUN
ejpam-5710	36	15	to	to	ADP
ejpam-5710	36	16	s	s	PRON
ejpam-5710	36	17	and	and	CCONJ
ejpam-5710	36	18	m	m	PROPN
ejpam-5710	36	19	is	be	AUX
ejpam-5710	36	20	the	the	DET
ejpam-5710	36	21	projection	projection	NOUN
ejpam-5710	36	22	vector	vector	NOUN
ejpam-5710	36	23	which	which	PRON
ejpam-5710	36	24	we	we	PRON
ejpam-5710	36	25	could	could	AUX
ejpam-5710	36	26	choose	choose	VERB
ejpam-5710	36	27	m	m	NOUN
ejpam-5710	36	28	=	=	SYM
ejpam-5710	36	29	(	(	PUNCT
ejpam-5710	36	30	0	0	NUM
ejpam-5710	36	31	,	,	PUNCT
ejpam-5710	36	32	1	1	NUM
ejpam-5710	36	33	,	,	PUNCT
ejpam-5710	36	34	0	0	NUM
ejpam-5710	36	35	)	)	PUNCT
ejpam-5710	36	36	,	,	PUNCT
ejpam-5710	36	37	(	(	PUNCT
ejpam-5710	36	38	1	1	NUM
ejpam-5710	36	39	,	,	PUNCT
ejpam-5710	36	40	0	0	NUM
ejpam-5710	36	41	,	,	PUNCT
ejpam-5710	36	42	0	0	NUM
ejpam-5710	36	43	)	)	PUNCT
ejpam-5710	36	44	or	or	CCONJ
ejpam-5710	36	45	(	(	PUNCT
ejpam-5710	36	46	0	0	NUM
ejpam-5710	36	47	,	,	PUNCT
ejpam-5710	36	48	0	0	NUM
ejpam-5710	36	49	,	,	PUNCT
ejpam-5710	36	50	1	1	NUM
ejpam-5710	36	51	)	)	PUNCT
ejpam-5710	36	52	.	.	PUNCT
ejpam-5710	37	1	the	the	DET
ejpam-5710	37	2	quasi	quasi	NOUN
ejpam-5710	37	3	-	-	NOUN
ejpam-5710	37	4	frame	frame	NOUN
ejpam-5710	37	5	becomes	become	VERB
ejpam-5710	37	6	singular	singular	ADJ
ejpam-5710	37	7	in	in	ADP
ejpam-5710	37	8	all	all	DET
ejpam-5710	37	9	cases	case	NOUN
ejpam-5710	37	10	where	where	SCONJ
ejpam-5710	37	11	t	t	NOUN
ejpam-5710	37	12	and	and	CCONJ
ejpam-5710	37	13	m	m	PROPN
ejpam-5710	37	14	are	be	AUX
ejpam-5710	37	15	parallel	parallel	ADJ
ejpam-5710	37	16	and	and	CCONJ
ejpam-5710	37	17	in	in	ADP
ejpam-5710	37	18	these	these	DET
ejpam-5710	37	19	cases	case	NOUN
ejpam-5710	37	20	we	we	PRON
ejpam-5710	37	21	change	change	VERB
ejpam-5710	37	22	the	the	DET
ejpam-5710	37	23	projection	projection	NOUN
ejpam-5710	37	24	.	.	PUNCT
ejpam-5710	38	1	the	the	DET
ejpam-5710	38	2	quasi	quasi	PROPN
ejpam-5710	38	3	formulae	formulae	NOUN
ejpam-5710	38	4	are	be	AUX
ejpam-5710	38	5	given	give	VERB
ejpam-5710	38	6	in	in	ADP
ejpam-5710	38	7	[	[	X
ejpam-5710	38	8	25	25	NUM
ejpam-5710	38	9	]	]	PUNCT
ejpam-5710	38	10	by	by	ADP
ejpam-5710	38	11	d	d	PROPN
ejpam-5710	38	12	ds	ds	X
ejpam-5710	38	13			NOUN
ejpam-5710	38	14	tq(s	tq(s	NUM
ejpam-5710	38	15	)	)	PUNCT
ejpam-5710	38	16	nq(s	nq(s	NUM
ejpam-5710	38	17	)	)	PUNCT
ejpam-5710	38	18	bq(s	bq(s	NOUN
ejpam-5710	38	19	)	)	PUNCT
ejpam-5710	38	20			NOUN
ejpam-5710	38	21	=	=	PUNCT
ejpam-5710	38	22			PROPN
ejpam-5710	38	23	0	0	NUM
ejpam-5710	38	24	κ1	κ1	PROPN
ejpam-5710	38	25	κ2	κ2	PROPN
ejpam-5710	38	26	−κ1	−κ1	PROPN
ejpam-5710	38	27	0	0	NUM
ejpam-5710	39	1	κ3	κ3	PROPN
ejpam-5710	39	2	−κ2	−κ2	PROPN
ejpam-5710	39	3	−κ3	−κ3	PROPN
ejpam-5710	39	4	0	0	PUNCT
ejpam-5710	39	5			NOUN
ejpam-5710	39	6	tq(s	tq(s	NUM
ejpam-5710	39	7	)	)	PUNCT
ejpam-5710	39	8	nq(s	nq(s	NUM
ejpam-5710	39	9	)	)	PUNCT
ejpam-5710	39	10	bq(s	bq(s	NOUN
ejpam-5710	39	11	)	)	PUNCT
ejpam-5710	39	12			NOUN
ejpam-5710	39	13	,	,	PUNCT
ejpam-5710	39	14	(	(	PUNCT
ejpam-5710	39	15	2.2	2.2	NUM
ejpam-5710	39	16	)	)	PUNCT
ejpam-5710	39	17	where	where	SCONJ
ejpam-5710	39	18	the	the	DET
ejpam-5710	39	19	functions	function	NOUN
ejpam-5710	39	20	κ1	κ1	NOUN
ejpam-5710	39	21	,	,	PUNCT
ejpam-5710	39	22	κ2	κ2	NOUN
ejpam-5710	39	23	and	and	CCONJ
ejpam-5710	39	24	κ3	κ3	PROPN
ejpam-5710	39	25	are	be	AUX
ejpam-5710	39	26	the	the	DET
ejpam-5710	39	27	first	first	ADJ
ejpam-5710	39	28	,	,	PUNCT
ejpam-5710	39	29	second	second	ADJ
ejpam-5710	39	30	,	,	PUNCT
ejpam-5710	39	31	and	and	CCONJ
ejpam-5710	39	32	third	third	ADJ
ejpam-5710	39	33	quasi	quasi	NOUN
ejpam-5710	39	34	-	-	NOUN
ejpam-5710	39	35	curvatures	curvature	NOUN
ejpam-5710	39	36	of	of	ADP
ejpam-5710	39	37	the	the	DET
ejpam-5710	39	38	curve	curve	NOUN
ejpam-5710	39	39	,	,	PUNCT
ejpam-5710	39	40	respectively	respectively	ADV
ejpam-5710	39	41	,	,	PUNCT
ejpam-5710	39	42	given	give	VERB
ejpam-5710	39	43	by	by	ADP
ejpam-5710	39	44	κ1	κ1	PROPN
ejpam-5710	39	45	=	=	SYM
ejpam-5710	39	46	κ(s	κ(s	PROPN
ejpam-5710	39	47	)	)	PUNCT
ejpam-5710	39	48	cos(ϕ	cos(ϕ	PROPN
ejpam-5710	39	49	)	)	PUNCT
ejpam-5710	39	50	,	,	PUNCT
ejpam-5710	39	51	(	(	PUNCT
ejpam-5710	39	52	2.3	2.3	NUM
ejpam-5710	39	53	)	)	PUNCT
ejpam-5710	39	54	a.	a.	NOUN
ejpam-5710	39	55	elsharkawy	elsharkawy	PROPN
ejpam-5710	39	56	,	,	PUNCT
ejpam-5710	39	57	h.	h.	PROPN
ejpam-5710	39	58	k.	k.	PROPN
ejpam-5710	39	59	elsayied	elsayied	PROPN
ejpam-5710	39	60	,	,	PUNCT
ejpam-5710	39	61	a.	a.	NOUN
ejpam-5710	39	62	refaat	refaat	PROPN
ejpam-5710	39	63	/	/	SYM
ejpam-5710	39	64	eur	eur	PROPN
ejpam-5710	39	65	.	.	PUNCT
ejpam-5710	40	1	j.	j.	PROPN
ejpam-5710	40	2	pure	pure	PROPN
ejpam-5710	40	3	appl	appl	PROPN
ejpam-5710	40	4	.	.	PROPN
ejpam-5710	40	5	math	math	PROPN
ejpam-5710	40	6	,	,	PUNCT
ejpam-5710	40	7	18	18	NUM
ejpam-5710	40	8	(	(	PUNCT
ejpam-5710	40	9	1	1	NUM
ejpam-5710	40	10	)	)	PUNCT
ejpam-5710	40	11	(	(	PUNCT
ejpam-5710	40	12	2025	2025	NUM
ejpam-5710	40	13	)	)	PUNCT
ejpam-5710	40	14	,	,	PUNCT
ejpam-5710	40	15	5710	5710	NUM
ejpam-5710	40	16	3	3	NUM
ejpam-5710	40	17	of	of	ADP
ejpam-5710	40	18	18	18	NUM
ejpam-5710	40	19	κ2	κ2	NOUN
ejpam-5710	40	20	=	=	SYM
ejpam-5710	40	21	−	−	PROPN
ejpam-5710	40	22	κ(s	κ(s	PROPN
ejpam-5710	40	23	)	)	PUNCT
ejpam-5710	40	24	sin(ϕ	sin(ϕ	PROPN
ejpam-5710	40	25	)	)	PUNCT
ejpam-5710	40	26	,	,	PUNCT
ejpam-5710	40	27	(	(	PUNCT
ejpam-5710	40	28	2.4	2.4	NUM
ejpam-5710	40	29	)	)	PUNCT
ejpam-5710	40	30	κ3	κ3	PROPN
ejpam-5710	40	31	=	=	PUNCT
ejpam-5710	40	32	dϕ	dϕ	NOUN
ejpam-5710	40	33	ds	ds	X
ejpam-5710	40	34	+	+	ADV
ejpam-5710	40	35	τ(s	τ(s	NOUN
ejpam-5710	40	36	)	)	PUNCT
ejpam-5710	40	37	,	,	PUNCT
ejpam-5710	40	38	(	(	PUNCT
ejpam-5710	40	39	2.5	2.5	NUM
ejpam-5710	40	40	)	)	PUNCT
ejpam-5710	40	41	where	where	SCONJ
ejpam-5710	40	42	κ(s	κ(s	NOUN
ejpam-5710	40	43	)	)	PUNCT
ejpam-5710	40	44	and	and	CCONJ
ejpam-5710	40	45	τ(s	τ(s	NOUN
ejpam-5710	40	46	)	)	PUNCT
ejpam-5710	40	47	are	be	AUX
ejpam-5710	40	48	the	the	DET
ejpam-5710	40	49	frenet	frenet	ADJ
ejpam-5710	40	50	curvature	curvature	NOUN
ejpam-5710	40	51	and	and	CCONJ
ejpam-5710	40	52	frenet	frenet	NOUN
ejpam-5710	40	53	torsion	torsion	NOUN
ejpam-5710	40	54	,	,	PUNCT
ejpam-5710	40	55	respectively	respectively	ADV
ejpam-5710	40	56	[	[	X
ejpam-5710	40	57	13	13	NUM
ejpam-5710	40	58	,	,	PUNCT
ejpam-5710	40	59	14	14	NUM
ejpam-5710	40	60	,	,	PUNCT
ejpam-5710	40	61	22	22	NUM
ejpam-5710	40	62	,	,	PUNCT
ejpam-5710	40	63	25	25	NUM
ejpam-5710	40	64	]	]	PUNCT
ejpam-5710	40	65	.	.	PUNCT
ejpam-5710	41	1	if	if	SCONJ
ejpam-5710	41	2	ϕ	ϕ	NOUN
ejpam-5710	41	3	is	be	AUX
ejpam-5710	41	4	the	the	DET
ejpam-5710	41	5	angle	angle	NOUN
ejpam-5710	41	6	between	between	ADP
ejpam-5710	41	7	the	the	DET
ejpam-5710	41	8	frenet	frenet	NOUN
ejpam-5710	41	9	normal	normal	ADJ
ejpam-5710	41	10	n	n	NOUN
ejpam-5710	41	11	and	and	CCONJ
ejpam-5710	41	12	the	the	DET
ejpam-5710	41	13	quasi	quasi	NOUN
ejpam-5710	41	14	normal	normal	ADJ
ejpam-5710	41	15	nq	nq	PROPN
ejpam-5710	41	16	and	and	CCONJ
ejpam-5710	41	17	the	the	DET
ejpam-5710	41	18	relation	relation	NOUN
ejpam-5710	41	19	between	between	ADP
ejpam-5710	41	20	the	the	DET
ejpam-5710	41	21	quasi	quasi	ADJ
ejpam-5710	41	22	frame	frame	NOUN
ejpam-5710	41	23	and	and	CCONJ
ejpam-5710	41	24	usual	usual	ADJ
ejpam-5710	41	25	orthonormal	orthonormal	ADJ
ejpam-5710	41	26	frenet	frenet	NOUN
ejpam-5710	41	27	frame	frame	NOUN
ejpam-5710	41	28	{	{	PUNCT
ejpam-5710	41	29	t	t	PROPN
ejpam-5710	41	30	,	,	PUNCT
ejpam-5710	41	31	n	n	CCONJ
ejpam-5710	41	32	,	,	PUNCT
ejpam-5710	41	33	b	b	NOUN
ejpam-5710	41	34	}	}	PUNCT
ejpam-5710	41	35	given	give	VERB
ejpam-5710	41	36	by	by	ADP
ejpam-5710	41	37	tq(s	tq(s	NUM
ejpam-5710	41	38	)	)	PUNCT
ejpam-5710	41	39	=	=	SYM
ejpam-5710	41	40	t(s	t(s	PROPN
ejpam-5710	41	41	)	)	PUNCT
ejpam-5710	41	42	,	,	PUNCT
ejpam-5710	41	43	(	(	PUNCT
ejpam-5710	41	44	2.6	2.6	NUM
ejpam-5710	41	45	)	)	PUNCT
ejpam-5710	41	46	nq(s	nq(s	NUM
ejpam-5710	41	47	)	)	PUNCT
ejpam-5710	41	48	=	=	PUNCT
ejpam-5710	41	49	cos(ϕ)n(s	cos(ϕ)n(s	NOUN
ejpam-5710	41	50	)	)	PUNCT
ejpam-5710	41	51	+	+	NUM
ejpam-5710	41	52	sin(ϕ)b(s	sin(ϕ)b(	NOUN
ejpam-5710	41	53	)	)	PUNCT
ejpam-5710	41	54	,	,	PUNCT
ejpam-5710	41	55	(	(	PUNCT
ejpam-5710	41	56	2.7	2.7	NUM
ejpam-5710	41	57	)	)	PUNCT
ejpam-5710	41	58	bq(s	bq(s	NOUN
ejpam-5710	41	59	)	)	PUNCT
ejpam-5710	42	1	=	=	SYM
ejpam-5710	42	2	−	−	ADP
ejpam-5710	42	3	sin(ϕ)n(s	sin(ϕ)n(s	NUM
ejpam-5710	42	4	)	)	PUNCT
ejpam-5710	42	5	+	+	NUM
ejpam-5710	42	6	cos(ϕ)b(s	cos(ϕ)b(	NOUN
ejpam-5710	42	7	)	)	PUNCT
ejpam-5710	42	8	.	.	PUNCT
ejpam-5710	43	1	(	(	PUNCT
ejpam-5710	43	2	2.8	2.8	NUM
ejpam-5710	43	3	)	)	PUNCT
ejpam-5710	43	4	a	a	DET
ejpam-5710	43	5	ruled	rule	VERB
ejpam-5710	43	6	surface	surface	NOUN
ejpam-5710	43	7	w	w	NOUN
ejpam-5710	43	8	can	can	AUX
ejpam-5710	43	9	be	be	AUX
ejpam-5710	43	10	defined	define	VERB
ejpam-5710	43	11	as	as	ADP
ejpam-5710	43	12	a	a	DET
ejpam-5710	43	13	surface	surface	NOUN
ejpam-5710	43	14	formed	form	VERB
ejpam-5710	43	15	by	by	ADP
ejpam-5710	43	16	the	the	DET
ejpam-5710	43	17	movement	movement	NOUN
ejpam-5710	43	18	of	of	ADP
ejpam-5710	43	19	a	a	DET
ejpam-5710	43	20	line	line	NOUN
ejpam-5710	43	21	l	l	NOUN
ejpam-5710	43	22	in	in	ADP
ejpam-5710	43	23	space	space	NOUN
ejpam-5710	43	24	.	.	PUNCT
ejpam-5710	44	1	suppose	suppose	VERB
ejpam-5710	44	2	α(s	α(s	PROPN
ejpam-5710	44	3	)	)	PUNCT
ejpam-5710	44	4	represents	represent	VERB
ejpam-5710	44	5	a	a	DET
ejpam-5710	44	6	regular	regular	ADJ
ejpam-5710	44	7	curve	curve	NOUN
ejpam-5710	44	8	in	in	ADP
ejpam-5710	44	9	euclidean	euclidean	ADJ
ejpam-5710	44	10	3−space	3−space	NUM
ejpam-5710	44	11	and	and	CCONJ
ejpam-5710	44	12	y	y	PROPN
ejpam-5710	44	13	(	(	PUNCT
ejpam-5710	44	14	s	s	X
ejpam-5710	44	15	)	)	PUNCT
ejpam-5710	44	16	represents	represent	VERB
ejpam-5710	44	17	the	the	DET
ejpam-5710	44	18	direction	direction	NOUN
ejpam-5710	44	19	vector	vector	NOUN
ejpam-5710	44	20	of	of	ADP
ejpam-5710	44	21	the	the	DET
ejpam-5710	44	22	line	line	NOUN
ejpam-5710	44	23	l.	l.	PROPN
ejpam-5710	44	24	the	the	DET
ejpam-5710	44	25	parametric	parametric	ADJ
ejpam-5710	44	26	representation	representation	NOUN
ejpam-5710	44	27	of	of	ADP
ejpam-5710	44	28	the	the	DET
ejpam-5710	44	29	ruled	rule	VERB
ejpam-5710	44	30	surface	surface	NOUN
ejpam-5710	45	1	w	w	NOUN
ejpam-5710	45	2	can	can	AUX
ejpam-5710	45	3	be	be	AUX
ejpam-5710	45	4	given	give	VERB
ejpam-5710	45	5	by	by	ADP
ejpam-5710	45	6	w	w	PROPN
ejpam-5710	45	7	(	(	PUNCT
ejpam-5710	45	8	s	s	PROPN
ejpam-5710	45	9	,	,	PUNCT
ejpam-5710	45	10	u	u	NOUN
ejpam-5710	45	11	)	)	PUNCT
ejpam-5710	45	12	=	=	SYM
ejpam-5710	45	13	α(s	α(s	PROPN
ejpam-5710	45	14	)	)	PUNCT
ejpam-5710	46	1	+	+	CCONJ
ejpam-5710	46	2	uy	uy	X
ejpam-5710	46	3	(	(	PUNCT
ejpam-5710	46	4	s	s	NOUN
ejpam-5710	46	5	)	)	PUNCT
ejpam-5710	46	6	,	,	PUNCT
ejpam-5710	46	7	where	where	SCONJ
ejpam-5710	46	8	α(s	α(s	PROPN
ejpam-5710	46	9	)	)	PUNCT
ejpam-5710	46	10	denotes	denote	VERB
ejpam-5710	46	11	the	the	DET
ejpam-5710	46	12	base	base	NOUN
ejpam-5710	46	13	curve	curve	NOUN
ejpam-5710	46	14	[	[	X
ejpam-5710	46	15	2	2	NUM
ejpam-5710	46	16	]	]	PUNCT
ejpam-5710	46	17	.	.	PUNCT
ejpam-5710	47	1	the	the	DET
ejpam-5710	47	2	striction	striction	NOUN
ejpam-5710	47	3	line	line	NOUN
ejpam-5710	47	4	and	and	CCONJ
ejpam-5710	47	5	the	the	DET
ejpam-5710	47	6	distribution	distribution	NOUN
ejpam-5710	47	7	parameter	parameter	NOUN
ejpam-5710	47	8	of	of	ADP
ejpam-5710	47	9	the	the	DET
ejpam-5710	47	10	ruled	rule	VERB
ejpam-5710	47	11	surface	surface	NOUN
ejpam-5710	47	12	w	w	NOUN
ejpam-5710	47	13	can	can	AUX
ejpam-5710	47	14	be	be	AUX
ejpam-5710	47	15	given	give	VERB
ejpam-5710	47	16	respectively	respectively	ADV
ejpam-5710	47	17	as	as	ADP
ejpam-5710	47	18	α∗(s	α∗(s	NUM
ejpam-5710	47	19	)	)	PUNCT
ejpam-5710	47	20	=	=	SYM
ejpam-5710	47	21	α(s	α(s	PROPN
ejpam-5710	47	22	)	)	PUNCT
ejpam-5710	48	1	+	+	CCONJ
ejpam-5710	48	2	<	<	X
ejpam-5710	48	3	tq(s	tq(s	NUM
ejpam-5710	48	4	)	)	PUNCT
ejpam-5710	48	5	,	,	PUNCT
ejpam-5710	48	6	y	y	PROPN
ejpam-5710	48	7	′(s	′(s	NOUN
ejpam-5710	48	8	)	)	PUNCT
ejpam-5710	48	9	>	>	PUNCT
ejpam-5710	48	10	∥	∥	PROPN
ejpam-5710	48	11	y	y	PROPN
ejpam-5710	48	12	′(s	′(s	NOUN
ejpam-5710	48	13	)	)	PUNCT
ejpam-5710	48	14	∥2	∥2	NOUN
ejpam-5710	49	1	y	y	PROPN
ejpam-5710	49	2	(	(	PUNCT
ejpam-5710	49	3	s	s	PROPN
ejpam-5710	49	4	)	)	PUNCT
ejpam-5710	49	5	,	,	PUNCT
ejpam-5710	49	6	(	(	PUNCT
ejpam-5710	49	7	2.9	2.9	NUM
ejpam-5710	49	8	)	)	PUNCT
ejpam-5710	49	9	and	and	CCONJ
ejpam-5710	49	10	λ(s	λ(s	PROPN
ejpam-5710	49	11	)	)	PUNCT
ejpam-5710	49	12	=	=	SYM
ejpam-5710	49	13	det	det	PROPN
ejpam-5710	49	14	[	[	PUNCT
ejpam-5710	49	15	tq(s	tq(s	NUM
ejpam-5710	49	16	)	)	PUNCT
ejpam-5710	49	17	,	,	PUNCT
ejpam-5710	49	18	y	y	PROPN
ejpam-5710	49	19	(	(	PUNCT
ejpam-5710	49	20	s	s	PROPN
ejpam-5710	49	21	)	)	PUNCT
ejpam-5710	49	22	,	,	PUNCT
ejpam-5710	49	23	y	y	PROPN
ejpam-5710	49	24	′(s	′(s	NOUN
ejpam-5710	49	25	)	)	PUNCT
ejpam-5710	49	26	]	]	PUNCT
ejpam-5710	50	1	∥	∥	PUNCT
ejpam-5710	50	2	y	y	PROPN
ejpam-5710	50	3	′(s	′(s	NOUN
ejpam-5710	50	4	)	)	PUNCT
ejpam-5710	50	5	∥2	∥2	NOUN
ejpam-5710	50	6	,	,	PUNCT
ejpam-5710	50	7	(	(	PUNCT
ejpam-5710	50	8	2.10	2.10	NUM
ejpam-5710	50	9	)	)	PUNCT
ejpam-5710	50	10	where	where	SCONJ
ejpam-5710	50	11	tq(s	tq(s	NUM
ejpam-5710	50	12	)	)	PUNCT
ejpam-5710	50	13	is	be	AUX
ejpam-5710	50	14	unit	unit	NOUN
ejpam-5710	50	15	tangent	tangent	NOUN
ejpam-5710	50	16	vector	vector	NOUN
ejpam-5710	50	17	field	field	NOUN
ejpam-5710	50	18	of	of	ADP
ejpam-5710	50	19	the	the	DET
ejpam-5710	50	20	base	base	NOUN
ejpam-5710	50	21	curve	curve	NOUN
ejpam-5710	50	22	α(s	α(s	PROPN
ejpam-5710	50	23	)	)	PUNCT
ejpam-5710	50	24	.	.	PUNCT
ejpam-5710	51	1	the	the	DET
ejpam-5710	51	2	ruled	rule	VERB
ejpam-5710	51	3	surface	surface	NOUN
ejpam-5710	51	4	w	w	NOUN
ejpam-5710	51	5	is	be	AUX
ejpam-5710	51	6	developable	developable	ADJ
ejpam-5710	51	7	if	if	SCONJ
ejpam-5710	51	8	and	and	CCONJ
ejpam-5710	51	9	only	only	ADV
ejpam-5710	51	10	if	if	SCONJ
ejpam-5710	51	11	λ(s	λ(s	PROPN
ejpam-5710	51	12	)	)	PUNCT
ejpam-5710	51	13	=	=	PUNCT
ejpam-5710	52	1	0	0	X
ejpam-5710	52	2	.	.	PUNCT
ejpam-5710	53	1	if	if	SCONJ
ejpam-5710	53	2	∥	∥	PROPN
ejpam-5710	53	3	y	y	PROPN
ejpam-5710	53	4	′(s	′(s	NOUN
ejpam-5710	53	5	)	)	PUNCT
ejpam-5710	53	6	∥=	∥=	NOUN
ejpam-5710	53	7	0	0	NUM
ejpam-5710	53	8	,	,	PUNCT
ejpam-5710	53	9	then	then	ADV
ejpam-5710	53	10	the	the	DET
ejpam-5710	53	11	ruled	rule	VERB
ejpam-5710	53	12	surface	surface	NOUN
ejpam-5710	53	13	does	do	AUX
ejpam-5710	53	14	not	not	PART
ejpam-5710	53	15	have	have	VERB
ejpam-5710	53	16	any	any	DET
ejpam-5710	53	17	striction	striction	NOUN
ejpam-5710	53	18	curve	curve	NOUN
ejpam-5710	53	19	.	.	PUNCT
ejpam-5710	54	1	in	in	ADP
ejpam-5710	54	2	this	this	DET
ejpam-5710	54	3	case	case	NOUN
ejpam-5710	54	4	,	,	PUNCT
ejpam-5710	54	5	the	the	DET
ejpam-5710	54	6	ruled	rule	VERB
ejpam-5710	54	7	surface	surface	NOUN
ejpam-5710	54	8	is	be	AUX
ejpam-5710	54	9	cylindrical	cylindrical	ADJ
ejpam-5710	54	10	.	.	PUNCT
ejpam-5710	55	1	thus	thus	ADV
ejpam-5710	55	2	,	,	PUNCT
ejpam-5710	55	3	the	the	DET
ejpam-5710	55	4	base	base	NOUN
ejpam-5710	55	5	curve	curve	NOUN
ejpam-5710	55	6	can	can	AUX
ejpam-5710	55	7	be	be	AUX
ejpam-5710	55	8	taken	take	VERB
ejpam-5710	55	9	as	as	ADP
ejpam-5710	55	10	a	a	DET
ejpam-5710	55	11	striction	striction	NOUN
ejpam-5710	55	12	curve	curve	NOUN
ejpam-5710	55	13	[	[	X
ejpam-5710	55	14	3	3	NUM
ejpam-5710	55	15	]	]	PUNCT
ejpam-5710	55	16	.	.	PUNCT
ejpam-5710	56	1	the	the	DET
ejpam-5710	56	2	standard	standard	ADJ
ejpam-5710	56	3	unit	unit	NOUN
ejpam-5710	56	4	normal	normal	ADJ
ejpam-5710	56	5	vector	vector	NOUN
ejpam-5710	56	6	field	field	NOUN
ejpam-5710	56	7	n	n	CCONJ
ejpam-5710	56	8	on	on	ADP
ejpam-5710	56	9	a	a	DET
ejpam-5710	56	10	surface	surface	NOUN
ejpam-5710	56	11	w	w	NOUN
ejpam-5710	56	12	can	can	AUX
ejpam-5710	56	13	be	be	AUX
ejpam-5710	56	14	defined	define	VERB
ejpam-5710	56	15	by	by	ADP
ejpam-5710	56	16	n	n	PROPN
ejpam-5710	56	17	=	=	PROPN
ejpam-5710	56	18	ws	ws	PROPN
ejpam-5710	56	19	×wu	×wu	PROPN
ejpam-5710	56	20	∥	∥	PROPN
ejpam-5710	56	21	ws	ws	PROPN
ejpam-5710	56	22	×wu	×wu	PROPN
ejpam-5710	56	23	∥	∥	PROPN
ejpam-5710	56	24	,	,	PUNCT
ejpam-5710	56	25	(	(	PUNCT
ejpam-5710	56	26	2.11	2.11	NUM
ejpam-5710	56	27	)	)	PUNCT
ejpam-5710	56	28	where	where	SCONJ
ejpam-5710	56	29	ws	ws	NOUN
ejpam-5710	56	30	and	and	CCONJ
ejpam-5710	56	31	wu	wu	PROPN
ejpam-5710	56	32	are	be	AUX
ejpam-5710	56	33	partial	partial	ADJ
ejpam-5710	56	34	derivatives	derivative	NOUN
ejpam-5710	56	35	of	of	ADP
ejpam-5710	56	36	w	w	PROPN
ejpam-5710	56	37	(	(	PUNCT
ejpam-5710	56	38	s	s	PROPN
ejpam-5710	56	39	,	,	PUNCT
ejpam-5710	56	40	u	u	NOUN
ejpam-5710	56	41	)	)	PUNCT
ejpam-5710	56	42	with	with	ADP
ejpam-5710	56	43	respect	respect	NOUN
ejpam-5710	56	44	to	to	ADP
ejpam-5710	56	45	s	s	PRON
ejpam-5710	56	46	and	and	CCONJ
ejpam-5710	56	47	u.	u.	VERB
ejpam-5710	56	48	the	the	DET
ejpam-5710	56	49	1st	1st	PROPN
ejpam-5710	56	50	f.f	f.f	PROPN
ejpam-5710	56	51	,	,	PUNCT
ejpam-5710	56	52	the	the	DET
ejpam-5710	56	53	2nd	2nd	ADJ
ejpam-5710	56	54	f.f	f.f	PROPN
ejpam-5710	56	55	and	and	CCONJ
ejpam-5710	56	56	3rd	3rd	ADJ
ejpam-5710	56	57	f.f	f.f	PROPN
ejpam-5710	56	58	of	of	ADP
ejpam-5710	56	59	the	the	DET
ejpam-5710	56	60	surface	surface	NOUN
ejpam-5710	56	61	w	w	PROPN
ejpam-5710	56	62	(	(	PUNCT
ejpam-5710	56	63	s	s	PROPN
ejpam-5710	56	64	,	,	PUNCT
ejpam-5710	56	65	u	u	NOUN
ejpam-5710	56	66	)	)	PUNCT
ejpam-5710	56	67	are	be	AUX
ejpam-5710	56	68	given	give	VERB
ejpam-5710	56	69	,	,	PUNCT
ejpam-5710	56	70	respectively	respectively	ADV
ejpam-5710	56	71	,	,	PUNCT
ejpam-5710	56	72	by	by	ADP
ejpam-5710	56	73	i	i	PROPN
ejpam-5710	56	74	=	=	NOUN
ejpam-5710	56	75	e(ds)2	e(ds)2	PROPN
ejpam-5710	56	76	+	+	NUM
ejpam-5710	56	77	2f	2f	NUM
ejpam-5710	56	78	ds	ds	ADJ
ejpam-5710	56	79	du+g(du)2	du+g(du)2	NOUN
ejpam-5710	56	80	,	,	PUNCT
ejpam-5710	56	81	(	(	PUNCT
ejpam-5710	56	82	2.12	2.12	NUM
ejpam-5710	56	83	)	)	PUNCT
ejpam-5710	56	84	ii	ii	NOUN
ejpam-5710	56	85	=	=	NOUN
ejpam-5710	56	86	l(ds)2	l(ds)2	NOUN
ejpam-5710	56	87	+	+	NUM
ejpam-5710	56	88	2	2	NUM
ejpam-5710	56	89	m	m	NOUN
ejpam-5710	56	90	ds	ds	ADJ
ejpam-5710	56	91	du+n(du)2	du+n(du)2	NOUN
ejpam-5710	56	92	,	,	PUNCT
ejpam-5710	56	93	(	(	PUNCT
ejpam-5710	56	94	2.13	2.13	NUM
ejpam-5710	56	95	)	)	PUNCT
ejpam-5710	56	96	iii	iii	X
ejpam-5710	57	1	=	=	NOUN
ejpam-5710	57	2	e(ds)2	e(ds)2	PROPN
ejpam-5710	57	3	+	+	NUM
ejpam-5710	57	4	2f	2f	NUM
ejpam-5710	57	5	ds	ds	ADJ
ejpam-5710	57	6	du+	du+	NOUN
ejpam-5710	57	7	g(du)2	g(du)2	NOUN
ejpam-5710	57	8	,	,	PUNCT
ejpam-5710	57	9	(	(	PUNCT
ejpam-5710	57	10	2.14	2.14	NUM
ejpam-5710	57	11	)	)	PUNCT
ejpam-5710	57	12	a.	a.	NOUN
ejpam-5710	57	13	elsharkawy	elsharkawy	PROPN
ejpam-5710	57	14	,	,	PUNCT
ejpam-5710	57	15	h.	h.	PROPN
ejpam-5710	57	16	k.	k.	PROPN
ejpam-5710	57	17	elsayied	elsayied	PROPN
ejpam-5710	57	18	,	,	PUNCT
ejpam-5710	57	19	a.	a.	NOUN
ejpam-5710	57	20	refaat	refaat	PROPN
ejpam-5710	57	21	/	/	SYM
ejpam-5710	57	22	eur	eur	PROPN
ejpam-5710	57	23	.	.	PUNCT
ejpam-5710	58	1	j.	j.	PROPN
ejpam-5710	58	2	pure	pure	PROPN
ejpam-5710	58	3	appl	appl	PROPN
ejpam-5710	58	4	.	.	PROPN
ejpam-5710	58	5	math	math	PROPN
ejpam-5710	58	6	,	,	PUNCT
ejpam-5710	58	7	18	18	NUM
ejpam-5710	58	8	(	(	PUNCT
ejpam-5710	58	9	1	1	NUM
ejpam-5710	58	10	)	)	PUNCT
ejpam-5710	58	11	(	(	PUNCT
ejpam-5710	58	12	2025	2025	NUM
ejpam-5710	58	13	)	)	PUNCT
ejpam-5710	58	14	,	,	PUNCT
ejpam-5710	58	15	5710	5710	NUM
ejpam-5710	58	16	4	4	NUM
ejpam-5710	58	17	of	of	ADP
ejpam-5710	58	18	18	18	NUM
ejpam-5710	59	1	where	where	SCONJ
ejpam-5710	59	2	e	e	NOUN
ejpam-5710	59	3	=	=	NOUN
ejpam-5710	59	4	<	<	X
ejpam-5710	59	5	ws	ws	PROPN
ejpam-5710	59	6	,	,	PUNCT
ejpam-5710	59	7	ws	ws	PROPN
ejpam-5710	59	8	>	>	X
ejpam-5710	59	9	,	,	PUNCT
ejpam-5710	59	10	f	f	PROPN
ejpam-5710	59	11	=	=	X
ejpam-5710	59	12	<	<	X
ejpam-5710	59	13	ws	ws	PROPN
ejpam-5710	59	14	,	,	PUNCT
ejpam-5710	59	15	wu	wu	PROPN
ejpam-5710	59	16	>	>	X
ejpam-5710	59	17	,	,	PUNCT
ejpam-5710	59	18	g	g	PROPN
ejpam-5710	59	19	=	=	NOUN
ejpam-5710	59	20	<	<	X
ejpam-5710	59	21	wu	wu	PROPN
ejpam-5710	59	22	,	,	PUNCT
ejpam-5710	59	23	wu	wu	PROPN
ejpam-5710	59	24	>	>	PUNCT
ejpam-5710	59	25	,	,	PUNCT
ejpam-5710	59	26	l	l	X
ejpam-5710	59	27	=	=	X
ejpam-5710	59	28	<	<	X
ejpam-5710	59	29	wss	wss	NOUN
ejpam-5710	59	30	,	,	PUNCT
ejpam-5710	59	31	n	n	X
ejpam-5710	59	32	>	>	PUNCT
ejpam-5710	59	33	,	,	PUNCT
ejpam-5710	59	34	m	m	VERB
ejpam-5710	59	35	=	=	ADJ
ejpam-5710	59	36	<	<	X
ejpam-5710	59	37	wsu	wsu	PROPN
ejpam-5710	59	38	,	,	PUNCT
ejpam-5710	59	39	n	n	CCONJ
ejpam-5710	59	40	>	>	PUNCT
ejpam-5710	59	41	,	,	PUNCT
ejpam-5710	59	42	n	n	PROPN
ejpam-5710	59	43	=	=	NUM
ejpam-5710	59	44	<	<	X
ejpam-5710	59	45	wuu	wuu	PROPN
ejpam-5710	59	46	,	,	PUNCT
ejpam-5710	59	47	n	n	X
ejpam-5710	59	48	>	>	PUNCT
ejpam-5710	59	49	,	,	PUNCT
ejpam-5710	59	50	e	e	X
ejpam-5710	59	51	=	=	X
ejpam-5710	59	52	<	<	X
ejpam-5710	59	53	ns	ns	PROPN
ejpam-5710	59	54	,	,	PUNCT
ejpam-5710	59	55	ns	ns	INTJ
ejpam-5710	59	56	>	>	X
ejpam-5710	59	57	,	,	PUNCT
ejpam-5710	59	58	f	f	X
ejpam-5710	59	59	=	=	X
ejpam-5710	59	60	<	<	X
ejpam-5710	59	61	ns	ns	PROPN
ejpam-5710	59	62	,	,	PUNCT
ejpam-5710	59	63	nu	nu	NOUN
ejpam-5710	59	64	>	>	X
ejpam-5710	59	65	and	and	CCONJ
ejpam-5710	59	66	g	g	PROPN
ejpam-5710	59	67	=	=	PROPN
ejpam-5710	59	68	<	<	X
ejpam-5710	59	69	nu	nu	PROPN
ejpam-5710	59	70	,	,	PUNCT
ejpam-5710	59	71	nu	nu	X
ejpam-5710	59	72	>	>	X
ejpam-5710	59	73	.	.	PUNCT
ejpam-5710	60	1	also	also	ADV
ejpam-5710	60	2	,	,	PUNCT
ejpam-5710	60	3	the	the	DET
ejpam-5710	60	4	gaussian	gaussian	ADJ
ejpam-5710	60	5	curvature	curvature	NOUN
ejpam-5710	60	6	k	k	PROPN
ejpam-5710	60	7	and	and	CCONJ
ejpam-5710	60	8	the	the	DET
ejpam-5710	60	9	mean	mean	ADJ
ejpam-5710	60	10	curvature	curvature	NOUN
ejpam-5710	60	11	h	h	NOUN
ejpam-5710	60	12	are	be	AUX
ejpam-5710	60	13	given	give	VERB
ejpam-5710	60	14	,	,	PUNCT
ejpam-5710	60	15	respectively	respectively	ADV
ejpam-5710	60	16	,	,	PUNCT
ejpam-5710	60	17	by	by	ADP
ejpam-5710	60	18	k	k	PROPN
ejpam-5710	60	19	=	=	PUNCT
ejpam-5710	60	20	ln	ln	ADJ
ejpam-5710	60	21	−m2	−m2	NOUN
ejpam-5710	60	22	eg−	eg−	SYM
ejpam-5710	60	23	f	f	PROPN
ejpam-5710	60	24	2	2	NUM
ejpam-5710	60	25	,	,	PUNCT
ejpam-5710	60	26	h	h	NOUN
ejpam-5710	61	1	=	=	PUNCT
ejpam-5710	61	2	en	en	ADP
ejpam-5710	61	3	−	−	NOUN
ejpam-5710	61	4	2mf	2mf	NOUN
ejpam-5710	62	1	+	+	PROPN
ejpam-5710	62	2	gl	gl	NOUN
ejpam-5710	62	3	2(eg−	2(eg−	NUM
ejpam-5710	62	4	f	f	PROPN
ejpam-5710	62	5	2	2	NUM
ejpam-5710	62	6	)	)	PUNCT
ejpam-5710	62	7	.	.	PUNCT
ejpam-5710	63	1	(	(	PUNCT
ejpam-5710	63	2	2.15	2.15	NUM
ejpam-5710	63	3	)	)	PUNCT
ejpam-5710	63	4	the	the	DET
ejpam-5710	63	5	g−	g−	PROPN
ejpam-5710	63	6	curvature	curvature	NOUN
ejpam-5710	63	7	κg	κg	PROPN
ejpam-5710	63	8	,	,	PUNCT
ejpam-5710	63	9	the	the	DET
ejpam-5710	63	10	n−	n−	NOUN
ejpam-5710	63	11	curvature	curvature	NOUN
ejpam-5710	63	12	κn	κn	NOUN
ejpam-5710	63	13	and	and	CCONJ
ejpam-5710	63	14	the	the	DET
ejpam-5710	63	15	g−	g−	ADJ
ejpam-5710	63	16	torsion	torsion	NOUN
ejpam-5710	63	17	τg	τg	ADP
ejpam-5710	63	18	which	which	PRON
ejpam-5710	63	19	associate	associate	VERB
ejpam-5710	63	20	the	the	DET
ejpam-5710	63	21	curve	curve	NOUN
ejpam-5710	63	22	α(s	α(s	PROPN
ejpam-5710	63	23	)	)	PUNCT
ejpam-5710	63	24	on	on	ADP
ejpam-5710	63	25	the	the	DET
ejpam-5710	63	26	surface	surface	NOUN
ejpam-5710	63	27	w	w	NOUN
ejpam-5710	63	28	can	can	AUX
ejpam-5710	63	29	be	be	AUX
ejpam-5710	63	30	computed	compute	VERB
ejpam-5710	63	31	as	as	SCONJ
ejpam-5710	63	32	follows	follow	VERB
ejpam-5710	63	33	κg	κg	ADP
ejpam-5710	63	34	=	=	X
ejpam-5710	63	35	<	<	X
ejpam-5710	63	36	n(s)×	n(s)×	NOUN
ejpam-5710	63	37	tq(s	tq(s	NUM
ejpam-5710	63	38	)	)	PUNCT
ejpam-5710	63	39	,	,	PUNCT
ejpam-5710	63	40	t	t	PROPN
ejpam-5710	63	41	′	′	NUM
ejpam-5710	63	42	q(s	q(s	PROPN
ejpam-5710	63	43	)	)	PUNCT
ejpam-5710	63	44	>	>	PUNCT
ejpam-5710	63	45	,	,	PUNCT
ejpam-5710	63	46	κn	κn	NOUN
ejpam-5710	63	47	=	=	PROPN
ejpam-5710	63	48	<	<	X
ejpam-5710	63	49	n(s	n(s	PROPN
ejpam-5710	63	50	)	)	PUNCT
ejpam-5710	63	51	,	,	PUNCT
ejpam-5710	63	52	α′′(s	α′′(	VERB
ejpam-5710	63	53	)	)	PUNCT
ejpam-5710	63	54	>	>	PUNCT
ejpam-5710	63	55	,	,	PUNCT
ejpam-5710	63	56	τg	τg	PUNCT
ejpam-5710	64	1	=	=	NOUN
ejpam-5710	64	2	<	<	X
ejpam-5710	64	3	n	n	PRON
ejpam-5710	64	4	×n	×n	PROPN
ejpam-5710	64	5	′	′	PROPN
ejpam-5710	64	6	,	,	PUNCT
ejpam-5710	64	7	t′q(s	t′q(s	PROPN
ejpam-5710	64	8	)	)	PUNCT
ejpam-5710	64	9	>	>	X
ejpam-5710	64	10	(	(	PUNCT
ejpam-5710	64	11	2.16	2.16	NUM
ejpam-5710	64	12	)	)	PUNCT
ejpam-5710	64	13	where	where	SCONJ
ejpam-5710	64	14	n	n	PRON
ejpam-5710	64	15	represents	represent	VERB
ejpam-5710	64	16	the	the	DET
ejpam-5710	64	17	unit	unit	NOUN
ejpam-5710	64	18	normal	normal	ADJ
ejpam-5710	64	19	vector	vector	NOUN
ejpam-5710	64	20	of	of	ADP
ejpam-5710	64	21	the	the	DET
ejpam-5710	64	22	surface	surface	NOUN
ejpam-5710	64	23	along	along	ADP
ejpam-5710	64	24	the	the	DET
ejpam-5710	64	25	curve	curve	NOUN
ejpam-5710	64	26	α(s	α(s	PROPN
ejpam-5710	64	27	)	)	PUNCT
ejpam-5710	64	28	and	and	CCONJ
ejpam-5710	64	29	tq	tq	ADP
ejpam-5710	64	30	denotes	denote	VERB
ejpam-5710	64	31	the	the	DET
ejpam-5710	64	32	unit	unit	NOUN
ejpam-5710	64	33	tangent	tangent	PROPN
ejpam-5710	64	34	vector	vector	NOUN
ejpam-5710	64	35	of	of	ADP
ejpam-5710	64	36	α(s	α(s	PROPN
ejpam-5710	64	37	)	)	PUNCT
ejpam-5710	64	38	.	.	PUNCT
ejpam-5710	65	1	definition	definition	NOUN
ejpam-5710	65	2	2.1	2.1	NUM
ejpam-5710	65	3	.	.	PUNCT
ejpam-5710	66	1	[	[	X
ejpam-5710	66	2	16	16	NUM
ejpam-5710	66	3	]	]	PUNCT
ejpam-5710	66	4	let	let	AUX
ejpam-5710	66	5	α(s	α(s	PROPN
ejpam-5710	66	6	)	)	PUNCT
ejpam-5710	66	7	be	be	AUX
ejpam-5710	66	8	a	a	DET
ejpam-5710	66	9	regular	regular	ADJ
ejpam-5710	66	10	curve	curve	NOUN
ejpam-5710	66	11	lying	lie	VERB
ejpam-5710	66	12	on	on	ADP
ejpam-5710	66	13	a	a	DET
ejpam-5710	66	14	surface	surface	NOUN
ejpam-5710	66	15	w	w	ADP
ejpam-5710	66	16	(	(	PUNCT
ejpam-5710	66	17	s	s	PROPN
ejpam-5710	66	18	,	,	PUNCT
ejpam-5710	66	19	u	u	NOUN
ejpam-5710	66	20	)	)	PUNCT
ejpam-5710	66	21	.	.	PUNCT
ejpam-5710	67	1	(	(	PUNCT
ejpam-5710	67	2	a	a	X
ejpam-5710	67	3	)	)	PUNCT
ejpam-5710	67	4	the	the	DET
ejpam-5710	67	5	curve	curve	NOUN
ejpam-5710	67	6	α(s	α(s	PROPN
ejpam-5710	67	7	)	)	PUNCT
ejpam-5710	67	8	is	be	AUX
ejpam-5710	67	9	said	say	VERB
ejpam-5710	67	10	to	to	PART
ejpam-5710	67	11	be	be	AUX
ejpam-5710	67	12	geodesic	geodesic	ADJ
ejpam-5710	67	13	curve	curve	NOUN
ejpam-5710	67	14	if	if	SCONJ
ejpam-5710	67	15	only	only	ADV
ejpam-5710	67	16	if	if	SCONJ
ejpam-5710	67	17	g−	g−	ADJ
ejpam-5710	67	18	curvature	curvature	NOUN
ejpam-5710	67	19	vanishes	vanish	VERB
ejpam-5710	67	20	.	.	PUNCT
ejpam-5710	68	1	(	(	PUNCT
ejpam-5710	68	2	b	b	X
ejpam-5710	68	3	)	)	PUNCT
ejpam-5710	68	4	the	the	DET
ejpam-5710	68	5	curve	curve	NOUN
ejpam-5710	68	6	α(s	α(s	PROPN
ejpam-5710	68	7	)	)	PUNCT
ejpam-5710	68	8	is	be	AUX
ejpam-5710	68	9	said	say	VERB
ejpam-5710	68	10	to	to	PART
ejpam-5710	68	11	be	be	AUX
ejpam-5710	68	12	an	an	DET
ejpam-5710	68	13	asymptotic	asymptotic	ADJ
ejpam-5710	68	14	line	line	NOUN
ejpam-5710	68	15	if	if	SCONJ
ejpam-5710	68	16	and	and	CCONJ
ejpam-5710	68	17	only	only	ADV
ejpam-5710	68	18	if	if	SCONJ
ejpam-5710	68	19	n−	n−	NOUN
ejpam-5710	68	20	curvature	curvature	NOUN
ejpam-5710	68	21	vanishes	vanish	VERB
ejpam-5710	68	22	.	.	PUNCT
ejpam-5710	69	1	(	(	PUNCT
ejpam-5710	69	2	c	c	X
ejpam-5710	69	3	)	)	PUNCT
ejpam-5710	69	4	the	the	DET
ejpam-5710	69	5	curve	curve	NOUN
ejpam-5710	69	6	α(s	α(s	PROPN
ejpam-5710	69	7	)	)	PUNCT
ejpam-5710	69	8	is	be	AUX
ejpam-5710	69	9	said	say	VERB
ejpam-5710	69	10	to	to	PART
ejpam-5710	69	11	be	be	AUX
ejpam-5710	69	12	a	a	DET
ejpam-5710	69	13	principal	principal	ADJ
ejpam-5710	69	14	line	line	NOUN
ejpam-5710	69	15	if	if	SCONJ
ejpam-5710	69	16	and	and	CCONJ
ejpam-5710	69	17	only	only	ADV
ejpam-5710	69	18	if	if	SCONJ
ejpam-5710	69	19	g−	g−	ADJ
ejpam-5710	69	20	torsion	torsion	NOUN
ejpam-5710	69	21	vanishes	vanish	VERB
ejpam-5710	69	22	.	.	PUNCT
ejpam-5710	70	1	definition	definition	NOUN
ejpam-5710	70	2	2.2	2.2	NUM
ejpam-5710	70	3	.	.	PUNCT
ejpam-5710	71	1	(	(	PUNCT
ejpam-5710	71	2	a	a	X
ejpam-5710	71	3	)	)	PUNCT
ejpam-5710	71	4	a	a	DET
ejpam-5710	71	5	regular	regular	ADJ
ejpam-5710	71	6	surface	surface	NOUN
ejpam-5710	71	7	is	be	AUX
ejpam-5710	71	8	flat	flat	ADJ
ejpam-5710	71	9	(	(	PUNCT
ejpam-5710	71	10	developable	developable	ADJ
ejpam-5710	71	11	)	)	PUNCT
ejpam-5710	71	12	if	if	SCONJ
ejpam-5710	72	1	and	and	CCONJ
ejpam-5710	72	2	only	only	ADV
ejpam-5710	72	3	if	if	SCONJ
ejpam-5710	72	4	its	its	PRON
ejpam-5710	72	5	gaussian	gaussian	ADJ
ejpam-5710	72	6	curvature	curvature	NOUN
ejpam-5710	72	7	vanishes	vanish	VERB
ejpam-5710	72	8	identically	identically	ADV
ejpam-5710	72	9	.	.	PUNCT
ejpam-5710	73	1	(	(	PUNCT
ejpam-5710	73	2	b	b	X
ejpam-5710	73	3	)	)	PUNCT
ejpam-5710	73	4	a	a	DET
ejpam-5710	73	5	regular	regular	ADJ
ejpam-5710	73	6	surface	surface	NOUN
ejpam-5710	73	7	is	be	AUX
ejpam-5710	73	8	a	a	DET
ejpam-5710	73	9	minimal	minimal	ADJ
ejpam-5710	73	10	surface	surface	NOUN
ejpam-5710	73	11	if	if	SCONJ
ejpam-5710	73	12	and	and	CCONJ
ejpam-5710	73	13	only	only	ADV
ejpam-5710	73	14	if	if	SCONJ
ejpam-5710	73	15	the	the	DET
ejpam-5710	73	16	mean	mean	ADJ
ejpam-5710	73	17	curvature	curvature	NOUN
ejpam-5710	73	18	vanishes	vanish	VERB
ejpam-5710	73	19	identically	identically	ADV
ejpam-5710	73	20	.	.	PUNCT
ejpam-5710	74	1	3	3	X
ejpam-5710	74	2	.	.	X
ejpam-5710	74	3	main	main	ADJ
ejpam-5710	74	4	result	result	NOUN
ejpam-5710	74	5	this	this	DET
ejpam-5710	74	6	section	section	NOUN
ejpam-5710	74	7	has	have	VERB
ejpam-5710	74	8	three	three	NUM
ejpam-5710	74	9	subsections	subsection	NOUN
ejpam-5710	74	10	that	that	PRON
ejpam-5710	74	11	introduce	introduce	VERB
ejpam-5710	74	12	three	three	NUM
ejpam-5710	74	13	different	different	ADJ
ejpam-5710	74	14	types	type	NOUN
ejpam-5710	74	15	of	of	ADP
ejpam-5710	74	16	ruled	rule	VERB
ejpam-5710	74	17	surfaces	surface	NOUN
ejpam-5710	74	18	according	accord	VERB
ejpam-5710	74	19	to	to	ADP
ejpam-5710	74	20	the	the	DET
ejpam-5710	74	21	quasi	quasi	ADJ
ejpam-5710	74	22	frame	frame	NOUN
ejpam-5710	74	23	called	call	VERB
ejpam-5710	74	24	qrt	qrt	NOUN
ejpam-5710	74	25	-	-	PUNCT
ejpam-5710	74	26	surfaces	surface	NOUN
ejpam-5710	74	27	,	,	PUNCT
ejpam-5710	74	28	qrn	qrn	NOUN
ejpam-5710	74	29	-	-	PUNCT
ejpam-5710	74	30	surfaces	surface	NOUN
ejpam-5710	74	31	,	,	PUNCT
ejpam-5710	74	32	and	and	CCONJ
ejpam-5710	74	33	qrbsurfaces	qrbsurface	NOUN
ejpam-5710	74	34	,	,	PUNCT
ejpam-5710	74	35	respectively	respectively	ADV
ejpam-5710	74	36	.	.	PUNCT
ejpam-5710	75	1	also	also	ADV
ejpam-5710	75	2	,	,	PUNCT
ejpam-5710	75	3	discuss	discuss	VERB
ejpam-5710	75	4	their	their	PRON
ejpam-5710	75	5	fundamental	fundamental	ADJ
ejpam-5710	75	6	properties	property	NOUN
ejpam-5710	75	7	.	.	PUNCT
ejpam-5710	76	1	3.1	3.1	NUM
ejpam-5710	76	2	.	.	PUNCT
ejpam-5710	77	1	quasi	quasi	ADJ
ejpam-5710	77	2	-	-	ADJ
ejpam-5710	77	3	tangent	tangent	ADJ
ejpam-5710	77	4	ruled	rule	VERB
ejpam-5710	77	5	surfaces	surface	NOUN
ejpam-5710	77	6	according	accord	VERB
ejpam-5710	77	7	to	to	ADP
ejpam-5710	77	8	the	the	DET
ejpam-5710	77	9	quasi	quasi	ADJ
ejpam-5710	77	10	frame	frame	NOUN
ejpam-5710	77	11	in	in	ADP
ejpam-5710	77	12	this	this	DET
ejpam-5710	77	13	section	section	NOUN
ejpam-5710	78	1	,	,	PUNCT
ejpam-5710	78	2	we	we	PRON
ejpam-5710	78	3	establish	establish	VERB
ejpam-5710	78	4	the	the	DET
ejpam-5710	78	5	definition	definition	NOUN
ejpam-5710	78	6	of	of	ADP
ejpam-5710	78	7	ruled	rule	VERB
ejpam-5710	78	8	surfaces	surface	NOUN
ejpam-5710	78	9	that	that	PRON
ejpam-5710	78	10	arise	arise	VERB
ejpam-5710	78	11	from	from	ADP
ejpam-5710	78	12	a	a	DET
ejpam-5710	78	13	regular	regular	ADJ
ejpam-5710	78	14	curve	curve	NOUN
ejpam-5710	78	15	(	(	PUNCT
ejpam-5710	78	16	referred	refer	VERB
ejpam-5710	78	17	to	to	ADP
ejpam-5710	78	18	as	as	ADP
ejpam-5710	78	19	the	the	DET
ejpam-5710	78	20	base	base	NOUN
ejpam-5710	78	21	curve	curve	NOUN
ejpam-5710	78	22	)	)	PUNCT
ejpam-5710	78	23	and	and	CCONJ
ejpam-5710	78	24	are	be	AUX
ejpam-5710	78	25	generated	generate	VERB
ejpam-5710	78	26	by	by	ADP
ejpam-5710	78	27	the	the	DET
ejpam-5710	78	28	quasi	quasi	PROPN
ejpam-5710	78	29	tangent	tangent	PROPN
ejpam-5710	78	30	vector	vector	NOUN
ejpam-5710	78	31	tq	tq	ADP
ejpam-5710	78	32	,	,	PUNCT
ejpam-5710	78	33	which	which	PRON
ejpam-5710	78	34	represents	represent	VERB
ejpam-5710	78	35	the	the	DET
ejpam-5710	78	36	direction	direction	NOUN
ejpam-5710	78	37	vector	vector	NOUN
ejpam-5710	78	38	.	.	PUNCT
ejpam-5710	79	1	additionally	additionally	ADV
ejpam-5710	79	2	,	,	PUNCT
ejpam-5710	79	3	we	we	PRON
ejpam-5710	79	4	explore	explore	VERB
ejpam-5710	79	5	the	the	DET
ejpam-5710	79	6	fundamental	fundamental	ADJ
ejpam-5710	79	7	properties	property	NOUN
ejpam-5710	79	8	associated	associate	VERB
ejpam-5710	79	9	with	with	ADP
ejpam-5710	79	10	this	this	DET
ejpam-5710	79	11	particular	particular	ADJ
ejpam-5710	79	12	type	type	NOUN
ejpam-5710	79	13	of	of	ADP
ejpam-5710	79	14	ruled	rule	VERB
ejpam-5710	79	15	surface	surface	NOUN
ejpam-5710	79	16	.	.	PUNCT
ejpam-5710	80	1	definition	definition	NOUN
ejpam-5710	80	2	3.1	3.1	NUM
ejpam-5710	80	3	.	.	PUNCT
ejpam-5710	81	1	let	let	AUX
ejpam-5710	81	2	α(s	α(s	PROPN
ejpam-5710	81	3	)	)	PUNCT
ejpam-5710	81	4	be	be	AUX
ejpam-5710	81	5	a	a	DET
ejpam-5710	81	6	regular	regular	ADJ
ejpam-5710	81	7	curve	curve	NOUN
ejpam-5710	81	8	with	with	ADP
ejpam-5710	81	9	quasi	quasi	ADJ
ejpam-5710	81	10	frame	frame	NOUN
ejpam-5710	81	11	{	{	PUNCT
ejpam-5710	81	12	tq	tq	NOUN
ejpam-5710	81	13	,	,	PUNCT
ejpam-5710	81	14	nq	nq	PROPN
ejpam-5710	81	15	,	,	PUNCT
ejpam-5710	81	16	bq	bq	PROPN
ejpam-5710	81	17	}	}	PUNCT
ejpam-5710	81	18	,	,	PUNCT
ejpam-5710	81	19	then	then	ADV
ejpam-5710	81	20	the	the	DET
ejpam-5710	81	21	parametric	parametric	ADJ
ejpam-5710	81	22	representations	representation	NOUN
ejpam-5710	81	23	of	of	ADP
ejpam-5710	81	24	the	the	DET
ejpam-5710	81	25	qtr	qtr	NOUN
ejpam-5710	81	26	-	-	PUNCT
ejpam-5710	81	27	surface	surface	NOUN
ejpam-5710	81	28	w	w	PROPN
ejpam-5710	81	29	t	t	PROPN
ejpam-5710	81	30	(	(	PUNCT
ejpam-5710	81	31	s	s	PROPN
ejpam-5710	81	32	,	,	PUNCT
ejpam-5710	81	33	u	u	NOUN
ejpam-5710	81	34	)	)	PUNCT
ejpam-5710	81	35	with	with	ADP
ejpam-5710	81	36	the	the	DET
ejpam-5710	81	37	ruling	rule	VERB
ejpam-5710	81	38	u	u	NOUN
ejpam-5710	81	39	given	give	VERB
ejpam-5710	81	40	by	by	ADP
ejpam-5710	81	41	w	w	PROPN
ejpam-5710	81	42	t	t	PROPN
ejpam-5710	81	43	(	(	PUNCT
ejpam-5710	81	44	s	s	PROPN
ejpam-5710	81	45	,	,	PUNCT
ejpam-5710	81	46	u	u	NOUN
ejpam-5710	81	47	)	)	PUNCT
ejpam-5710	81	48	=	=	SYM
ejpam-5710	81	49	α(s	α(s	PROPN
ejpam-5710	81	50	)	)	PUNCT
ejpam-5710	82	1	+	+	CCONJ
ejpam-5710	82	2	u	u	NOUN
ejpam-5710	82	3	tq(s	tq(s	NUM
ejpam-5710	82	4	)	)	PUNCT
ejpam-5710	82	5	.	.	PUNCT
ejpam-5710	83	1	(	(	PUNCT
ejpam-5710	83	2	3.1	3.1	NUM
ejpam-5710	83	3	)	)	PUNCT
ejpam-5710	83	4	a.	a.	NOUN
ejpam-5710	83	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	83	6	,	,	PUNCT
ejpam-5710	83	7	h.	h.	PROPN
ejpam-5710	83	8	k.	k.	PROPN
ejpam-5710	83	9	elsayied	elsayied	PROPN
ejpam-5710	83	10	,	,	PUNCT
ejpam-5710	83	11	a.	a.	NOUN
ejpam-5710	83	12	refaat	refaat	PROPN
ejpam-5710	83	13	/	/	SYM
ejpam-5710	83	14	eur	eur	PROPN
ejpam-5710	83	15	.	.	PUNCT
ejpam-5710	84	1	j.	j.	PROPN
ejpam-5710	84	2	pure	pure	PROPN
ejpam-5710	84	3	appl	appl	PROPN
ejpam-5710	84	4	.	.	PROPN
ejpam-5710	84	5	math	math	PROPN
ejpam-5710	84	6	,	,	PUNCT
ejpam-5710	84	7	18	18	NUM
ejpam-5710	84	8	(	(	PUNCT
ejpam-5710	84	9	1	1	NUM
ejpam-5710	84	10	)	)	PUNCT
ejpam-5710	84	11	(	(	PUNCT
ejpam-5710	84	12	2025	2025	NUM
ejpam-5710	84	13	)	)	PUNCT
ejpam-5710	84	14	,	,	PUNCT
ejpam-5710	84	15	5710	5710	NUM
ejpam-5710	84	16	5	5	NUM
ejpam-5710	84	17	of	of	ADP
ejpam-5710	84	18	18	18	NUM
ejpam-5710	84	19	theorem	theorem	VERB
ejpam-5710	84	20	3.1	3.1	NUM
ejpam-5710	84	21	.	.	PUNCT
ejpam-5710	85	1	the	the	DET
ejpam-5710	85	2	striction	striction	NOUN
ejpam-5710	85	3	curve	curve	NOUN
ejpam-5710	85	4	of	of	ADP
ejpam-5710	85	5	the	the	DET
ejpam-5710	85	6	quasi	quasi	NOUN
ejpam-5710	85	7	-	-	ADJ
ejpam-5710	85	8	tangent	tangent	ADJ
ejpam-5710	85	9	ruled	rule	VERB
ejpam-5710	85	10	surface	surface	NOUN
ejpam-5710	85	11	is	be	AUX
ejpam-5710	85	12	also	also	ADV
ejpam-5710	85	13	a	a	DET
ejpam-5710	85	14	base	base	NOUN
ejpam-5710	85	15	function	function	NOUN
ejpam-5710	85	16	of	of	ADP
ejpam-5710	85	17	the	the	DET
ejpam-5710	85	18	surface	surface	NOUN
ejpam-5710	85	19	.	.	PUNCT
ejpam-5710	86	1	proof	proof	NOUN
ejpam-5710	86	2	.	.	PUNCT
ejpam-5710	87	1	let	let	VERB
ejpam-5710	87	2	w	w	PROPN
ejpam-5710	87	3	t	t	PROPN
ejpam-5710	87	4	(	(	PUNCT
ejpam-5710	87	5	s	s	PROPN
ejpam-5710	87	6	,	,	PUNCT
ejpam-5710	87	7	u	u	NOUN
ejpam-5710	87	8	)	)	PUNCT
ejpam-5710	87	9	be	be	VERB
ejpam-5710	87	10	a	a	DET
ejpam-5710	87	11	qtr	qtr	NOUN
ejpam-5710	87	12	-	-	PUNCT
ejpam-5710	87	13	surface	surface	NOUN
ejpam-5710	87	14	with	with	ADP
ejpam-5710	87	15	base	base	NOUN
ejpam-5710	87	16	curve	curve	NOUN
ejpam-5710	87	17	α(s	α(s	PROPN
ejpam-5710	87	18	)	)	PUNCT
ejpam-5710	87	19	from	from	ADP
ejpam-5710	87	20	equation	equation	NOUN
ejpam-5710	87	21	(	(	PUNCT
ejpam-5710	87	22	2.9	2.9	NUM
ejpam-5710	87	23	)	)	PUNCT
ejpam-5710	87	24	the	the	DET
ejpam-5710	87	25	striction	striction	NOUN
ejpam-5710	87	26	curve	curve	NOUN
ejpam-5710	87	27	defined	define	VERB
ejpam-5710	87	28	by	by	ADP
ejpam-5710	87	29	α∗(s	α∗(s	PROPN
ejpam-5710	87	30	)	)	PUNCT
ejpam-5710	87	31	=	=	SYM
ejpam-5710	87	32	α(s	α(s	PROPN
ejpam-5710	87	33	)	)	PUNCT
ejpam-5710	88	1	+	+	CCONJ
ejpam-5710	88	2	<	<	X
ejpam-5710	88	3	tq(s	tq(s	NUM
ejpam-5710	88	4	)	)	PUNCT
ejpam-5710	88	5	,	,	PUNCT
ejpam-5710	88	6	t	t	PROPN
ejpam-5710	88	7	′	′	NUM
ejpam-5710	88	8	q(s	q(s	PROPN
ejpam-5710	88	9	)	)	PUNCT
ejpam-5710	88	10	>	>	PUNCT
ejpam-5710	89	1	∥	∥	PROPN
ejpam-5710	89	2	t′q(s	t′q(s	NOUN
ejpam-5710	89	3	)	)	PUNCT
ejpam-5710	89	4	∥2	∥2	NOUN
ejpam-5710	89	5	tq	tq	ADP
ejpam-5710	89	6	.	.	PUNCT
ejpam-5710	90	1	by	by	ADP
ejpam-5710	90	2	the	the	DET
ejpam-5710	90	3	equations	equation	NOUN
ejpam-5710	90	4	in	in	ADP
ejpam-5710	90	5	(	(	PUNCT
ejpam-5710	90	6	2.2	2.2	NUM
ejpam-5710	90	7	)	)	PUNCT
ejpam-5710	90	8	α∗(s	α∗(s	PROPN
ejpam-5710	90	9	)	)	PUNCT
ejpam-5710	90	10	=	=	SYM
ejpam-5710	90	11	α(s	α(s	PROPN
ejpam-5710	90	12	)	)	PUNCT
ejpam-5710	91	1	+	+	CCONJ
ejpam-5710	91	2	<	<	X
ejpam-5710	91	3	tq(s	tq(s	NUM
ejpam-5710	91	4	)	)	PUNCT
ejpam-5710	91	5	,	,	PUNCT
ejpam-5710	91	6	(	(	PUNCT
ejpam-5710	91	7	κ1	κ1	NOUN
ejpam-5710	91	8	nq(s	nq(s	PUNCT
ejpam-5710	91	9	)	)	PUNCT
ejpam-5710	91	10	+	+	CCONJ
ejpam-5710	92	1	κ2	κ2	NOUN
ejpam-5710	92	2	bq(s	bq(s	NUM
ejpam-5710	92	3	)	)	PUNCT
ejpam-5710	92	4	)	)	PUNCT
ejpam-5710	92	5	>	>	PUNCT
ejpam-5710	92	6	∥	∥	PROPN
ejpam-5710	92	7	t′q(s	t′q(s	NOUN
ejpam-5710	92	8	)	)	PUNCT
ejpam-5710	92	9	∥2	∥2	NOUN
ejpam-5710	92	10	tq	tq	ADP
ejpam-5710	92	11	,	,	PUNCT
ejpam-5710	92	12	or	or	CCONJ
ejpam-5710	92	13	α∗(s	α∗(s	NUM
ejpam-5710	92	14	)	)	PUNCT
ejpam-5710	92	15	=	=	SYM
ejpam-5710	92	16	α(s	α(s	PROPN
ejpam-5710	92	17	)	)	PUNCT
ejpam-5710	93	1	+	+	CCONJ
ejpam-5710	93	2	κ1	κ1	NOUN
ejpam-5710	93	3	<	<	X
ejpam-5710	93	4	tq(s	tq(s	NUM
ejpam-5710	93	5	)	)	PUNCT
ejpam-5710	93	6	,	,	PUNCT
ejpam-5710	93	7	nq(s	nq(s	NUM
ejpam-5710	93	8	)	)	PUNCT
ejpam-5710	93	9	>	>	PUNCT
ejpam-5710	94	1	+	+	NUM
ejpam-5710	94	2	κ2	κ2	NOUN
ejpam-5710	94	3	<	<	X
ejpam-5710	94	4	tq(s	tq(s	NUM
ejpam-5710	94	5	)	)	PUNCT
ejpam-5710	94	6	,	,	PUNCT
ejpam-5710	94	7	bq(s	bq(s	PROPN
ejpam-5710	94	8	)	)	PUNCT
ejpam-5710	94	9	>	>	PUNCT
ejpam-5710	94	10	∥	∥	PROPN
ejpam-5710	94	11	t′q(s	t′q(s	NOUN
ejpam-5710	94	12	)	)	PUNCT
ejpam-5710	94	13	∥2	∥2	NOUN
ejpam-5710	94	14	tq	tq	ADP
ejpam-5710	94	15	,	,	PUNCT
ejpam-5710	94	16	therefore	therefore	ADV
ejpam-5710	94	17	,	,	PUNCT
ejpam-5710	94	18	α∗(s	α∗(s	PROPN
ejpam-5710	94	19	)	)	PUNCT
ejpam-5710	94	20	=	=	SYM
ejpam-5710	94	21	α(s	α(s	PROPN
ejpam-5710	94	22	)	)	PUNCT
ejpam-5710	94	23	.	.	PUNCT
ejpam-5710	95	1	theorem	theorem	VERB
ejpam-5710	95	2	3.2	3.2	NUM
ejpam-5710	95	3	.	.	PUNCT
ejpam-5710	96	1	the	the	DET
ejpam-5710	96	2	first	first	ADJ
ejpam-5710	96	3	fundamental	fundamental	ADJ
ejpam-5710	96	4	form	form	NOUN
ejpam-5710	96	5	of	of	ADP
ejpam-5710	96	6	the	the	DET
ejpam-5710	96	7	quasi	quasi	NOUN
ejpam-5710	96	8	-	-	ADJ
ejpam-5710	96	9	tangent	tangent	ADJ
ejpam-5710	96	10	ruled	rule	VERB
ejpam-5710	96	11	surface	surface	PROPN
ejpam-5710	96	12	w	w	PROPN
ejpam-5710	96	13	t	t	PROPN
ejpam-5710	96	14	(	(	PUNCT
ejpam-5710	96	15	s	s	PROPN
ejpam-5710	96	16	,	,	PUNCT
ejpam-5710	96	17	u	u	NOUN
ejpam-5710	96	18	)	)	PUNCT
ejpam-5710	96	19	is	be	AUX
ejpam-5710	96	20	given	give	VERB
ejpam-5710	96	21	by	by	ADP
ejpam-5710	96	22	i	i	NOUN
ejpam-5710	96	23	=	=	NOUN
ejpam-5710	96	24	1	1	NUM
ejpam-5710	96	25	+	+	CCONJ
ejpam-5710	96	26	u2	u2	PROPN
ejpam-5710	96	27	(	(	PUNCT
ejpam-5710	96	28	κ1	κ1	NOUN
ejpam-5710	96	29	2	2	NUM
ejpam-5710	96	30	+	+	NUM
ejpam-5710	96	31	κ2	κ2	NOUN
ejpam-5710	96	32	2)(ds)2	2)(ds)2	NUM
ejpam-5710	96	33	+	+	CCONJ
ejpam-5710	96	34	2	2	NUM
ejpam-5710	96	35	dsdu+	dsdu+	NOUN
ejpam-5710	96	36	(	(	PUNCT
ejpam-5710	96	37	du)2	du)2	NOUN
ejpam-5710	96	38	.	.	PUNCT
ejpam-5710	97	1	proof	proof	NOUN
ejpam-5710	97	2	.	.	PUNCT
ejpam-5710	98	1	let	let	VERB
ejpam-5710	98	2	w	w	PROPN
ejpam-5710	98	3	t	t	PROPN
ejpam-5710	98	4	(	(	PUNCT
ejpam-5710	98	5	s	s	PROPN
ejpam-5710	98	6	,	,	PUNCT
ejpam-5710	98	7	u	u	NOUN
ejpam-5710	98	8	)	)	PUNCT
ejpam-5710	98	9	be	be	VERB
ejpam-5710	98	10	a	a	DET
ejpam-5710	98	11	qtr	qtr	NOUN
ejpam-5710	98	12	-	-	PUNCT
ejpam-5710	98	13	surface	surface	NOUN
ejpam-5710	98	14	with	with	ADP
ejpam-5710	98	15	base	base	NOUN
ejpam-5710	98	16	curve	curve	NOUN
ejpam-5710	98	17	α(s	α(s	PROPN
ejpam-5710	98	18	)	)	PUNCT
ejpam-5710	98	19	.	.	PUNCT
ejpam-5710	99	1	considering	consider	VERB
ejpam-5710	99	2	equations	equation	NOUN
ejpam-5710	99	3	(	(	PUNCT
ejpam-5710	99	4	2.2	2.2	NUM
ejpam-5710	99	5	)	)	PUNCT
ejpam-5710	99	6	and	and	CCONJ
ejpam-5710	99	7	(	(	PUNCT
ejpam-5710	99	8	2.6	2.6	NUM
ejpam-5710	99	9	)	)	PUNCT
ejpam-5710	99	10	,	,	PUNCT
ejpam-5710	99	11	the	the	DET
ejpam-5710	99	12	first	first	ADJ
ejpam-5710	99	13	partial	partial	ADJ
ejpam-5710	99	14	derivatives	derivative	NOUN
ejpam-5710	99	15	of	of	ADP
ejpam-5710	99	16	the	the	DET
ejpam-5710	99	17	qtr	qtr	NOUN
ejpam-5710	99	18	-	-	NOUN
ejpam-5710	99	19	surface	surface	NOUN
ejpam-5710	99	20	with	with	ADP
ejpam-5710	99	21	respect	respect	NOUN
ejpam-5710	99	22	to	to	ADP
ejpam-5710	99	23	s	s	PRON
ejpam-5710	99	24	and	and	CCONJ
ejpam-5710	99	25	u	u	NOUN
ejpam-5710	99	26	are	be	AUX
ejpam-5710	99	27	given	give	VERB
ejpam-5710	99	28	by	by	ADP
ejpam-5710	99	29	w	w	PROPN
ejpam-5710	99	30	t	t	PROPN
ejpam-5710	99	31	s	s	PART
ejpam-5710	99	32	=	=	NOUN
ejpam-5710	99	33	tq(s	tq(s	NUM
ejpam-5710	99	34	)	)	PUNCT
ejpam-5710	100	1	+	+	CCONJ
ejpam-5710	100	2	u	u	SYM
ejpam-5710	100	3	(	(	PUNCT
ejpam-5710	100	4	κ1	κ1	NOUN
ejpam-5710	100	5	nq(s	nq(s	PUNCT
ejpam-5710	100	6	)	)	PUNCT
ejpam-5710	101	1	+	+	CCONJ
ejpam-5710	101	2	κ2	κ2	NOUN
ejpam-5710	101	3	bq(s	bq(s	NUM
ejpam-5710	101	4	)	)	PUNCT
ejpam-5710	101	5	)	)	PUNCT
ejpam-5710	101	6	,	,	PUNCT
ejpam-5710	101	7	(	(	PUNCT
ejpam-5710	101	8	3.2	3.2	NUM
ejpam-5710	101	9	)	)	PUNCT
ejpam-5710	101	10	w	w	PROPN
ejpam-5710	101	11	t	t	PROPN
ejpam-5710	101	12	u	u	NOUN
ejpam-5710	101	13	=	=	PROPN
ejpam-5710	101	14	tq(s	tq(s	NUM
ejpam-5710	101	15	)	)	PUNCT
ejpam-5710	101	16	.	.	PUNCT
ejpam-5710	102	1	(	(	PUNCT
ejpam-5710	102	2	3.3	3.3	NUM
ejpam-5710	102	3	)	)	PUNCT
ejpam-5710	102	4	from	from	ADP
ejpam-5710	102	5	equations	equation	NOUN
ejpam-5710	102	6	(	(	PUNCT
ejpam-5710	102	7	2.12),(3.2	2.12),(3.2	NUM
ejpam-5710	102	8	)	)	PUNCT
ejpam-5710	102	9	and	and	CCONJ
ejpam-5710	102	10	(	(	PUNCT
ejpam-5710	102	11	3.3	3.3	NUM
ejpam-5710	102	12	)	)	PUNCT
ejpam-5710	102	13	the	the	DET
ejpam-5710	102	14	coefficients	coefficient	NOUN
ejpam-5710	102	15	of	of	ADP
ejpam-5710	102	16	the	the	DET
ejpam-5710	102	17	1st	1st	ADJ
ejpam-5710	102	18	f.f	f.f	PROPN
ejpam-5710	102	19	are	be	AUX
ejpam-5710	102	20	given	give	VERB
ejpam-5710	102	21	by	by	ADP
ejpam-5710	102	22	e	e	X
ejpam-5710	102	23	=	=	NOUN
ejpam-5710	102	24	<	<	X
ejpam-5710	102	25	w	w	PROPN
ejpam-5710	102	26	t	t	PROPN
ejpam-5710	102	27	s	s	PROPN
ejpam-5710	102	28	,	,	PUNCT
ejpam-5710	102	29	w	w	PROPN
ejpam-5710	102	30	t	t	PROPN
ejpam-5710	102	31	s	s	X
ejpam-5710	102	32	>	>	X
ejpam-5710	102	33	=	=	SYM
ejpam-5710	102	34	1	1	NUM
ejpam-5710	102	35	+	+	CCONJ
ejpam-5710	102	36	u2	u2	PROPN
ejpam-5710	102	37	(	(	PUNCT
ejpam-5710	102	38	κ1	κ1	NOUN
ejpam-5710	102	39	2	2	NUM
ejpam-5710	102	40	+	+	NUM
ejpam-5710	102	41	κ2	κ2	NOUN
ejpam-5710	102	42	2	2	NUM
ejpam-5710	102	43	)	)	PUNCT
ejpam-5710	102	44	,	,	PUNCT
ejpam-5710	102	45	f	f	X
ejpam-5710	103	1	=	=	PUNCT
ejpam-5710	103	2	<	<	X
ejpam-5710	103	3	w	w	PROPN
ejpam-5710	103	4	t	t	PROPN
ejpam-5710	103	5	s	s	PROPN
ejpam-5710	103	6	,	,	PUNCT
ejpam-5710	103	7	w	w	PROPN
ejpam-5710	103	8	t	t	PROPN
ejpam-5710	103	9	u	u	X
ejpam-5710	103	10	>	>	X
ejpam-5710	103	11	=	=	PUNCT
ejpam-5710	103	12	1	1	NUM
ejpam-5710	103	13	,	,	PUNCT
ejpam-5710	103	14	(	(	PUNCT
ejpam-5710	103	15	3.4	3.4	NUM
ejpam-5710	103	16	)	)	PUNCT
ejpam-5710	104	1	g	g	NOUN
ejpam-5710	105	1	=	=	PUNCT
ejpam-5710	105	2	<	<	X
ejpam-5710	105	3	w	w	PROPN
ejpam-5710	105	4	t	t	PROPN
ejpam-5710	105	5	u	u	PROPN
ejpam-5710	105	6	,	,	PUNCT
ejpam-5710	105	7	w	w	PROPN
ejpam-5710	105	8	t	t	PROPN
ejpam-5710	105	9	u	u	X
ejpam-5710	105	10	>	>	X
ejpam-5710	105	11	=	=	SYM
ejpam-5710	105	12	1	1	X
ejpam-5710	105	13	.	.	PUNCT
ejpam-5710	105	14	theorem	theorem	VERB
ejpam-5710	105	15	3.3	3.3	NUM
ejpam-5710	105	16	.	.	PUNCT
ejpam-5710	106	1	the	the	DET
ejpam-5710	106	2	second	second	ADJ
ejpam-5710	106	3	fundamental	fundamental	ADJ
ejpam-5710	106	4	form	form	NOUN
ejpam-5710	106	5	of	of	ADP
ejpam-5710	106	6	the	the	DET
ejpam-5710	106	7	quasi	quasi	NOUN
ejpam-5710	106	8	-	-	ADJ
ejpam-5710	106	9	tangent	tangent	ADJ
ejpam-5710	106	10	ruled	rule	VERB
ejpam-5710	106	11	surface	surface	PROPN
ejpam-5710	106	12	w	w	PROPN
ejpam-5710	106	13	t	t	PROPN
ejpam-5710	106	14	(	(	PUNCT
ejpam-5710	106	15	s	s	PROPN
ejpam-5710	106	16	,	,	PUNCT
ejpam-5710	106	17	u	u	NOUN
ejpam-5710	106	18	)	)	PUNCT
ejpam-5710	106	19	is	be	AUX
ejpam-5710	106	20	given	give	VERB
ejpam-5710	106	21	by	by	ADP
ejpam-5710	106	22	ii	ii	NOUN
ejpam-5710	106	23	=	=	SYM
ejpam-5710	107	1	−	−	PROPN
ejpam-5710	107	2	u	u	NOUN
ejpam-5710	107	3	(	(	PUNCT
ejpam-5710	107	4	κ2	κ2	PROPN
ejpam-5710	107	5	(	(	PUNCT
ejpam-5710	107	6	κ2	κ2	NOUN
ejpam-5710	107	7	κ3	κ3	PROPN
ejpam-5710	107	8	−	−	PROPN
ejpam-5710	107	9	κ1	κ1	PROPN
ejpam-5710	107	10	′	′	PROPN
ejpam-5710	107	11	)	)	PUNCT
ejpam-5710	108	1	+	+	CCONJ
ejpam-5710	108	2	κ1	κ1	PROPN
ejpam-5710	108	3	κ2	κ2	NOUN
ejpam-5710	108	4	′	′	NUM
ejpam-5710	109	1	+	+	CCONJ
ejpam-5710	109	2	κ1	κ1	PROPN
ejpam-5710	109	3	2	2	NUM
ejpam-5710	109	4	κ3	κ3	PROPN
ejpam-5710	109	5	)	)	PUNCT
ejpam-5710	109	6	√	√	VERB
ejpam-5710	110	1	κ12	κ12	VERB
ejpam-5710	110	2	+	+	CCONJ
ejpam-5710	110	3	κ22	κ22	NOUN
ejpam-5710	110	4	(	(	PUNCT
ejpam-5710	110	5	ds)2	ds)2	PROPN
ejpam-5710	110	6	.	.	PUNCT
ejpam-5710	110	7	a.	a.	NOUN
ejpam-5710	110	8	elsharkawy	elsharkawy	PROPN
ejpam-5710	110	9	,	,	PUNCT
ejpam-5710	110	10	h.	h.	PROPN
ejpam-5710	110	11	k.	k.	PROPN
ejpam-5710	110	12	elsayied	elsayied	PROPN
ejpam-5710	110	13	,	,	PUNCT
ejpam-5710	110	14	a.	a.	NOUN
ejpam-5710	110	15	refaat	refaat	PROPN
ejpam-5710	110	16	/	/	SYM
ejpam-5710	110	17	eur	eur	PROPN
ejpam-5710	110	18	.	.	PUNCT
ejpam-5710	111	1	j.	j.	PROPN
ejpam-5710	111	2	pure	pure	PROPN
ejpam-5710	111	3	appl	appl	PROPN
ejpam-5710	111	4	.	.	PROPN
ejpam-5710	111	5	math	math	PROPN
ejpam-5710	111	6	,	,	PUNCT
ejpam-5710	111	7	18	18	NUM
ejpam-5710	111	8	(	(	PUNCT
ejpam-5710	111	9	1	1	NUM
ejpam-5710	111	10	)	)	PUNCT
ejpam-5710	111	11	(	(	PUNCT
ejpam-5710	111	12	2025	2025	NUM
ejpam-5710	111	13	)	)	PUNCT
ejpam-5710	111	14	,	,	PUNCT
ejpam-5710	111	15	5710	5710	NUM
ejpam-5710	111	16	6	6	NUM
ejpam-5710	111	17	of	of	ADP
ejpam-5710	111	18	18	18	NUM
ejpam-5710	111	19	proof	proof	NOUN
ejpam-5710	111	20	.	.	PUNCT
ejpam-5710	112	1	let	let	VERB
ejpam-5710	112	2	w	w	PROPN
ejpam-5710	112	3	t	t	PROPN
ejpam-5710	112	4	(	(	PUNCT
ejpam-5710	112	5	s	s	PROPN
ejpam-5710	112	6	,	,	PUNCT
ejpam-5710	112	7	u	u	NOUN
ejpam-5710	112	8	)	)	PUNCT
ejpam-5710	112	9	be	be	VERB
ejpam-5710	112	10	a	a	DET
ejpam-5710	112	11	qtr	qtr	NOUN
ejpam-5710	112	12	-	-	PUNCT
ejpam-5710	112	13	surface	surface	NOUN
ejpam-5710	112	14	with	with	ADP
ejpam-5710	112	15	base	base	NOUN
ejpam-5710	112	16	curve	curve	NOUN
ejpam-5710	112	17	α(s	α(s	PROPN
ejpam-5710	112	18	)	)	PUNCT
ejpam-5710	112	19	.	.	PUNCT
ejpam-5710	113	1	the	the	DET
ejpam-5710	113	2	cross	cross	NOUN
ejpam-5710	113	3	product	product	NOUN
ejpam-5710	113	4	of	of	ADP
ejpam-5710	113	5	equations	equation	NOUN
ejpam-5710	113	6	(	(	PUNCT
ejpam-5710	113	7	3.2	3.2	NUM
ejpam-5710	113	8	)	)	PUNCT
ejpam-5710	113	9	and	and	CCONJ
ejpam-5710	113	10	(	(	PUNCT
ejpam-5710	113	11	3.3	3.3	NUM
ejpam-5710	113	12	)	)	PUNCT
ejpam-5710	113	13	given	give	VERB
ejpam-5710	113	14	by	by	ADP
ejpam-5710	113	15	w	w	PROPN
ejpam-5710	113	16	t	t	PROPN
ejpam-5710	113	17	s	s	PART
ejpam-5710	113	18	×w	×w	NOUN
ejpam-5710	113	19	t	t	PROPN
ejpam-5710	113	20	u	u	NOUN
ejpam-5710	113	21	=	=	PROPN
ejpam-5710	113	22	u	u	PROPN
ejpam-5710	113	23	(	(	PUNCT
ejpam-5710	113	24	κ2	κ2	NOUN
ejpam-5710	113	25	nq(s)−	nq(s)−	ADP
ejpam-5710	113	26	κ1	κ1	PROPN
ejpam-5710	113	27	bq(s	bq(s	PROPN
ejpam-5710	113	28	)	)	PUNCT
ejpam-5710	113	29	)	)	PUNCT
ejpam-5710	113	30	,	,	PUNCT
ejpam-5710	113	31	(	(	PUNCT
ejpam-5710	113	32	3.5	3.5	X
ejpam-5710	113	33	)	)	PUNCT
ejpam-5710	113	34	taking	take	VERB
ejpam-5710	113	35	the	the	DET
ejpam-5710	113	36	norm	norm	NOUN
ejpam-5710	113	37	we	we	PRON
ejpam-5710	113	38	get	get	VERB
ejpam-5710	113	39	∥	∥	PROPN
ejpam-5710	113	40	w	w	ADP
ejpam-5710	113	41	t	t	NOUN
ejpam-5710	113	42	s	s	PART
ejpam-5710	113	43	×w	×w	NOUN
ejpam-5710	113	44	t	t	PROPN
ejpam-5710	113	45	u	u	PRON
ejpam-5710	113	46	∥=	∥=	ADJ
ejpam-5710	113	47	u2(κ1	u2(κ1	ADV
ejpam-5710	113	48	2	2	NUM
ejpam-5710	113	49	+	+	NUM
ejpam-5710	113	50	κ2	κ2	NOUN
ejpam-5710	113	51	2	2	NUM
ejpam-5710	113	52	)	)	PUNCT
ejpam-5710	113	53	.	.	PUNCT
ejpam-5710	114	1	(	(	PUNCT
ejpam-5710	114	2	3.6	3.6	NUM
ejpam-5710	114	3	)	)	PUNCT
ejpam-5710	114	4	from	from	ADP
ejpam-5710	114	5	equations	equation	NOUN
ejpam-5710	114	6	(	(	PUNCT
ejpam-5710	114	7	2.11	2.11	NUM
ejpam-5710	114	8	)	)	PUNCT
ejpam-5710	114	9	,	,	PUNCT
ejpam-5710	114	10	(	(	PUNCT
ejpam-5710	114	11	3.5	3.5	NUM
ejpam-5710	114	12	)	)	PUNCT
ejpam-5710	114	13	and	and	CCONJ
ejpam-5710	114	14	(	(	PUNCT
ejpam-5710	114	15	3.6	3.6	NUM
ejpam-5710	114	16	)	)	PUNCT
ejpam-5710	114	17	,	,	PUNCT
ejpam-5710	114	18	the	the	DET
ejpam-5710	114	19	unit	unit	NOUN
ejpam-5710	114	20	normal	normal	ADJ
ejpam-5710	114	21	vector	vector	NOUN
ejpam-5710	114	22	can	can	AUX
ejpam-5710	114	23	be	be	AUX
ejpam-5710	114	24	defined	define	VERB
ejpam-5710	114	25	by	by	ADP
ejpam-5710	114	26	nt	not	PART
ejpam-5710	114	27	=	=	PROPN
ejpam-5710	114	28	w	w	PROPN
ejpam-5710	114	29	t	t	PROPN
ejpam-5710	114	30	s	s	PART
ejpam-5710	114	31	×w	×w	NOUN
ejpam-5710	114	32	t	t	PROPN
ejpam-5710	114	33	u	u	PROPN
ejpam-5710	114	34	∥	∥	PROPN
ejpam-5710	114	35	w	w	PROPN
ejpam-5710	114	36	t	t	NOUN
ejpam-5710	114	37	s	s	PART
ejpam-5710	114	38	×w	×w	NOUN
ejpam-5710	114	39	t	t	PROPN
ejpam-5710	114	40	u	u	NOUN
ejpam-5710	114	41	∥	∥	PROPN
ejpam-5710	114	42	=	=	SYM
ejpam-5710	114	43	u	u	PROPN
ejpam-5710	114	44	(	(	PUNCT
ejpam-5710	114	45	κ2	κ2	NOUN
ejpam-5710	114	46	nq(s	nq(s	PUNCT
ejpam-5710	114	47	)	)	PUNCT
ejpam-5710	114	48	−	−	PROPN
ejpam-5710	114	49	κ1	κ1	PROPN
ejpam-5710	114	50	bq(s	bq(s	PROPN
ejpam-5710	114	51	)	)	PUNCT
ejpam-5710	114	52	)	)	PUNCT
ejpam-5710	115	1	√	√	PUNCT
ejpam-5710	116	1	e	e	X
ejpam-5710	116	2	−	−	PROPN
ejpam-5710	116	3	1	1	NUM
ejpam-5710	116	4	,	,	PUNCT
ejpam-5710	116	5	(	(	PUNCT
ejpam-5710	116	6	3.7	3.7	NUM
ejpam-5710	116	7	)	)	PUNCT
ejpam-5710	116	8	where	where	SCONJ
ejpam-5710	116	9	e	e	NOUN
ejpam-5710	116	10	=	=	SYM
ejpam-5710	116	11	1	1	NUM
ejpam-5710	116	12	+	+	NUM
ejpam-5710	116	13	u2	u2	NOUN
ejpam-5710	116	14	(	(	PUNCT
ejpam-5710	116	15	κ1	κ1	NOUN
ejpam-5710	116	16	2	2	NUM
ejpam-5710	116	17	+	+	NUM
ejpam-5710	116	18	κ2	κ2	NOUN
ejpam-5710	116	19	2	2	NUM
ejpam-5710	116	20	)	)	PUNCT
ejpam-5710	116	21	.	.	PUNCT
ejpam-5710	117	1	considering	consider	VERB
ejpam-5710	117	2	equations	equation	NOUN
ejpam-5710	117	3	(	(	PUNCT
ejpam-5710	117	4	2.2),(3.2	2.2),(3.2	NUM
ejpam-5710	117	5	)	)	PUNCT
ejpam-5710	117	6	and	and	CCONJ
ejpam-5710	117	7	(	(	PUNCT
ejpam-5710	117	8	3.3	3.3	NUM
ejpam-5710	117	9	)	)	PUNCT
ejpam-5710	117	10	,	,	PUNCT
ejpam-5710	117	11	the	the	DET
ejpam-5710	117	12	second	second	ADJ
ejpam-5710	117	13	partial	partial	ADJ
ejpam-5710	117	14	derivatives	derivative	NOUN
ejpam-5710	117	15	of	of	ADP
ejpam-5710	117	16	the	the	DET
ejpam-5710	117	17	qtr	qtr	NOUN
ejpam-5710	117	18	-	-	NOUN
ejpam-5710	117	19	surface	surface	NOUN
ejpam-5710	117	20	with	with	ADP
ejpam-5710	117	21	respect	respect	NOUN
ejpam-5710	117	22	to	to	ADP
ejpam-5710	117	23	s	s	PRON
ejpam-5710	117	24	and	and	CCONJ
ejpam-5710	117	25	u	u	NOUN
ejpam-5710	117	26	are	be	AUX
ejpam-5710	117	27	given	give	VERB
ejpam-5710	117	28	by	by	ADP
ejpam-5710	117	29	w	w	PROPN
ejpam-5710	117	30	t	t	PROPN
ejpam-5710	117	31	ss	ss	NOUN
ejpam-5710	118	1	=	=	PUNCT
ejpam-5710	118	2	−u	−u	PROPN
ejpam-5710	118	3	(	(	PUNCT
ejpam-5710	118	4	κ1	κ1	NOUN
ejpam-5710	118	5	2	2	NUM
ejpam-5710	118	6	+	+	NUM
ejpam-5710	118	7	κ2	κ2	NOUN
ejpam-5710	118	8	2)tq(s	2)tq(s	NUM
ejpam-5710	118	9	)	)	PUNCT
ejpam-5710	119	1	+	+	CCONJ
ejpam-5710	119	2	(	(	PUNCT
ejpam-5710	119	3	κ1	κ1	NOUN
ejpam-5710	119	4	+	+	CCONJ
ejpam-5710	119	5	u(−κ2κ3	u(−κ2κ3	PROPN
ejpam-5710	119	6	+	+	PROPN
ejpam-5710	119	7	κ1	κ1	PROPN
ejpam-5710	119	8	′)nq(s	′)nq(s	PROPN
ejpam-5710	119	9	)	)	PUNCT
ejpam-5710	120	1	+	+	PROPN
ejpam-5710	120	2	(	(	PUNCT
ejpam-5710	120	3	κ2	κ2	NOUN
ejpam-5710	120	4	+	+	CCONJ
ejpam-5710	120	5	u(−κ1κ3	u(−κ1κ3	ADJ
ejpam-5710	120	6	+	+	NUM
ejpam-5710	120	7	κ2	κ2	NOUN
ejpam-5710	120	8	′))bq(s	′))bq(s	ADJ
ejpam-5710	120	9	)	)	PUNCT
ejpam-5710	120	10	,	,	PUNCT
ejpam-5710	120	11	(	(	PUNCT
ejpam-5710	120	12	3.8	3.8	NUM
ejpam-5710	120	13	)	)	PUNCT
ejpam-5710	120	14	w	w	PROPN
ejpam-5710	120	15	t	t	PROPN
ejpam-5710	120	16	su	su	PROPN
ejpam-5710	121	1	=	=	PROPN
ejpam-5710	121	2	κ1	κ1	PROPN
ejpam-5710	121	3	nq(s	nq(s	PUNCT
ejpam-5710	121	4	)	)	PUNCT
ejpam-5710	122	1	+	+	CCONJ
ejpam-5710	122	2	κ2	κ2	NOUN
ejpam-5710	122	3	bq(s	bq(s	NUM
ejpam-5710	122	4	)	)	PUNCT
ejpam-5710	122	5	,	,	PUNCT
ejpam-5710	122	6	w	w	PROPN
ejpam-5710	122	7	t	t	PROPN
ejpam-5710	122	8	uu	uu	PROPN
ejpam-5710	122	9	=	=	SYM
ejpam-5710	122	10	0	0	PROPN
ejpam-5710	122	11	.	.	PUNCT
ejpam-5710	122	12	from	from	ADP
ejpam-5710	122	13	equations	equation	NOUN
ejpam-5710	122	14	(	(	PUNCT
ejpam-5710	122	15	2.13	2.13	NUM
ejpam-5710	122	16	)	)	PUNCT
ejpam-5710	122	17	,	,	PUNCT
ejpam-5710	122	18	and	and	CCONJ
ejpam-5710	122	19	(	(	PUNCT
ejpam-5710	122	20	3.8	3.8	NUM
ejpam-5710	122	21	)	)	PUNCT
ejpam-5710	122	22	the	the	DET
ejpam-5710	122	23	coefficients	coefficient	NOUN
ejpam-5710	122	24	of	of	ADP
ejpam-5710	122	25	the	the	DET
ejpam-5710	122	26	2nd	2nd	ADJ
ejpam-5710	122	27	f.f	f.f	PROPN
ejpam-5710	122	28	are	be	AUX
ejpam-5710	122	29	given	give	VERB
ejpam-5710	122	30	by	by	ADP
ejpam-5710	122	31	l	l	NOUN
ejpam-5710	122	32	=	=	X
ejpam-5710	122	33	<	<	X
ejpam-5710	122	34	w	w	PROPN
ejpam-5710	122	35	t	t	PROPN
ejpam-5710	122	36	ss	ss	PROPN
ejpam-5710	122	37	,	,	PUNCT
ejpam-5710	122	38	n	n	X
ejpam-5710	122	39	>	>	PUNCT
ejpam-5710	122	40	=	=	SYM
ejpam-5710	122	41	−u2	−u2	PROPN
ejpam-5710	122	42	(	(	PUNCT
ejpam-5710	122	43	κ2	κ2	PROPN
ejpam-5710	122	44	(	(	PUNCT
ejpam-5710	122	45	κ2	κ2	NOUN
ejpam-5710	122	46	κ3	κ3	PROPN
ejpam-5710	122	47	−	−	PROPN
ejpam-5710	122	48	κ1	κ1	PROPN
ejpam-5710	122	49	′	′	PROPN
ejpam-5710	122	50	)	)	PUNCT
ejpam-5710	123	1	+	+	CCONJ
ejpam-5710	123	2	κ1	κ1	PROPN
ejpam-5710	123	3	κ2	κ2	NOUN
ejpam-5710	123	4	′	′	NUM
ejpam-5710	124	1	+	+	CCONJ
ejpam-5710	124	2	κ1	κ1	PROPN
ejpam-5710	124	3	2	2	NUM
ejpam-5710	124	4	κ3	κ3	PROPN
ejpam-5710	124	5	)	)	PUNCT
ejpam-5710	124	6	√	√	PUNCT
ejpam-5710	125	1	e	e	NOUN
ejpam-5710	125	2	−	−	PROPN
ejpam-5710	125	3	1	1	NUM
ejpam-5710	125	4	,	,	PUNCT
ejpam-5710	125	5	m	m	VERB
ejpam-5710	125	6	=	=	NOUN
ejpam-5710	125	7	<	<	X
ejpam-5710	125	8	w	w	PROPN
ejpam-5710	125	9	t	t	PROPN
ejpam-5710	125	10	su	su	PROPN
ejpam-5710	125	11	,	,	PUNCT
ejpam-5710	125	12	n	n	X
ejpam-5710	125	13	>	>	PUNCT
ejpam-5710	125	14	=	=	SYM
ejpam-5710	125	15	0	0	PROPN
ejpam-5710	125	16	,	,	PUNCT
ejpam-5710	125	17	(	(	PUNCT
ejpam-5710	125	18	3.9	3.9	NUM
ejpam-5710	125	19	)	)	PUNCT
ejpam-5710	125	20	n	n	NOUN
ejpam-5710	125	21	=	=	NUM
ejpam-5710	125	22	<	<	X
ejpam-5710	125	23	w	w	PROPN
ejpam-5710	125	24	t	t	PROPN
ejpam-5710	125	25	uu	uu	PROPN
ejpam-5710	125	26	,	,	PUNCT
ejpam-5710	125	27	n	n	X
ejpam-5710	125	28	>	>	PUNCT
ejpam-5710	125	29	=	=	SYM
ejpam-5710	125	30	0	0	X
ejpam-5710	125	31	.	.	PUNCT
ejpam-5710	125	32	theorem	theorem	VERB
ejpam-5710	125	33	3.4	3.4	NUM
ejpam-5710	125	34	.	.	PUNCT
ejpam-5710	126	1	the	the	DET
ejpam-5710	126	2	third	third	ADJ
ejpam-5710	126	3	fundamental	fundamental	ADJ
ejpam-5710	126	4	form	form	NOUN
ejpam-5710	126	5	of	of	ADP
ejpam-5710	126	6	the	the	DET
ejpam-5710	126	7	quasi	quasi	NOUN
ejpam-5710	126	8	-	-	ADJ
ejpam-5710	126	9	tangent	tangent	ADJ
ejpam-5710	126	10	ruled	rule	VERB
ejpam-5710	126	11	surface	surface	PROPN
ejpam-5710	126	12	w	w	PROPN
ejpam-5710	126	13	t	t	PROPN
ejpam-5710	126	14	(	(	PUNCT
ejpam-5710	126	15	s	s	PROPN
ejpam-5710	126	16	,	,	PUNCT
ejpam-5710	126	17	u	u	NOUN
ejpam-5710	126	18	)	)	PUNCT
ejpam-5710	126	19	is	be	AUX
ejpam-5710	126	20	given	give	VERB
ejpam-5710	126	21	by	by	ADP
ejpam-5710	126	22	iii	iii	NOUN
ejpam-5710	126	23	=	=	SYM
ejpam-5710	126	24	(	(	PUNCT
ejpam-5710	126	25	κ2	κ2	NOUN
ejpam-5710	126	26	(	(	PUNCT
ejpam-5710	126	27	κ2κ3	κ2κ3	ADP
ejpam-5710	126	28	−	−	PROPN
ejpam-5710	126	29	κ1	κ1	NOUN
ejpam-5710	126	30	′	′	NOUN
ejpam-5710	126	31	)	)	PUNCT
ejpam-5710	127	1	+	+	CCONJ
ejpam-5710	127	2	κ1κ2	κ1κ2	ADP
ejpam-5710	127	3	′	′	NOUN
ejpam-5710	127	4	+	+	CCONJ
ejpam-5710	127	5	κ1	κ1	NOUN
ejpam-5710	127	6	2κ3	2κ3	NUM
ejpam-5710	127	7	)	)	PUNCT
ejpam-5710	127	8	2	2	NUM
ejpam-5710	127	9	(	(	PUNCT
ejpam-5710	127	10	κ12	κ12	X
ejpam-5710	127	11	+	+	CCONJ
ejpam-5710	127	12	κ22	κ22	NOUN
ejpam-5710	127	13	)	)	PUNCT
ejpam-5710	127	14	2	2	NUM
ejpam-5710	127	15	(	(	PUNCT
ejpam-5710	127	16	ds)2	ds)2	NOUN
ejpam-5710	127	17	.	.	PUNCT
ejpam-5710	127	18	proof	proof	NOUN
ejpam-5710	127	19	.	.	PUNCT
ejpam-5710	128	1	let	let	VERB
ejpam-5710	128	2	w	w	PROPN
ejpam-5710	128	3	t	t	PROPN
ejpam-5710	128	4	(	(	PUNCT
ejpam-5710	128	5	s	s	PROPN
ejpam-5710	128	6	,	,	PUNCT
ejpam-5710	128	7	u	u	NOUN
ejpam-5710	128	8	)	)	PUNCT
ejpam-5710	128	9	be	be	VERB
ejpam-5710	128	10	a	a	DET
ejpam-5710	128	11	qtr	qtr	NOUN
ejpam-5710	128	12	-	-	PUNCT
ejpam-5710	128	13	surface	surface	NOUN
ejpam-5710	128	14	with	with	ADP
ejpam-5710	128	15	base	base	NOUN
ejpam-5710	128	16	curve	curve	NOUN
ejpam-5710	128	17	α(s	α(s	PROPN
ejpam-5710	128	18	)	)	PUNCT
ejpam-5710	128	19	.	.	PUNCT
ejpam-5710	129	1	the	the	DET
ejpam-5710	129	2	first	first	ADJ
ejpam-5710	129	3	partial	partial	ADJ
ejpam-5710	129	4	derivatives	derivative	NOUN
ejpam-5710	129	5	of	of	ADP
ejpam-5710	129	6	equation	equation	NOUN
ejpam-5710	129	7	(	(	PUNCT
ejpam-5710	129	8	3.7	3.7	NUM
ejpam-5710	129	9	)	)	PUNCT
ejpam-5710	129	10	with	with	ADP
ejpam-5710	129	11	respect	respect	NOUN
ejpam-5710	129	12	to	to	ADP
ejpam-5710	129	13	s	s	PRON
ejpam-5710	129	14	and	and	CCONJ
ejpam-5710	129	15	u	u	PRON
ejpam-5710	129	16	given	give	VERB
ejpam-5710	129	17	by	by	ADP
ejpam-5710	129	18	(	(	PUNCT
ejpam-5710	129	19	nt	not	PART
ejpam-5710	129	20	)	)	PUNCT
ejpam-5710	129	21	s	s	PART
ejpam-5710	129	22	=	=	PROPN
ejpam-5710	129	23	κ1	κ1	NOUN
ejpam-5710	129	24	(	(	PUNCT
ejpam-5710	129	25	κ2	κ2	NOUN
ejpam-5710	129	26	(	(	PUNCT
ejpam-5710	129	27	κ2κ3	κ2κ3	ADP
ejpam-5710	129	28	−	−	PROPN
ejpam-5710	129	29	κ1	κ1	NOUN
ejpam-5710	129	30	′	′	NOUN
ejpam-5710	129	31	)	)	PUNCT
ejpam-5710	130	1	+	+	CCONJ
ejpam-5710	130	2	κ1κ2	κ1κ2	ADP
ejpam-5710	130	3	′	′	NOUN
ejpam-5710	130	4	+	+	CCONJ
ejpam-5710	130	5	κ1	κ1	NOUN
ejpam-5710	130	6	2κ3	2κ3	NUM
ejpam-5710	130	7	)	)	PUNCT
ejpam-5710	130	8	(	(	PUNCT
ejpam-5710	130	9	κ12	κ12	NOUN
ejpam-5710	130	10	+	+	CCONJ
ejpam-5710	130	11	κ22	κ22	NOUN
ejpam-5710	130	12	)	)	PUNCT
ejpam-5710	130	13	3/2	3/2	NUM
ejpam-5710	130	14	nq(s	nq(s	NUM
ejpam-5710	130	15	)	)	PUNCT
ejpam-5710	131	1	+	+	CCONJ
ejpam-5710	131	2	κ2	κ2	NOUN
ejpam-5710	131	3	(	(	PUNCT
ejpam-5710	131	4	κ2	κ2	NOUN
ejpam-5710	131	5	(	(	PUNCT
ejpam-5710	131	6	κ2κ3	κ2κ3	ADP
ejpam-5710	131	7	−	−	PROPN
ejpam-5710	131	8	κ1	κ1	NOUN
ejpam-5710	131	9	′	′	NOUN
ejpam-5710	131	10	)	)	PUNCT
ejpam-5710	132	1	+	+	CCONJ
ejpam-5710	132	2	κ1κ2	κ1κ2	ADP
ejpam-5710	132	3	′	′	NOUN
ejpam-5710	132	4	+	+	CCONJ
ejpam-5710	132	5	κ1	κ1	NOUN
ejpam-5710	132	6	2κ3	2κ3	NUM
ejpam-5710	132	7	)	)	PUNCT
ejpam-5710	132	8	(	(	PUNCT
ejpam-5710	132	9	κ12	κ12	NOUN
ejpam-5710	132	10	+	+	CCONJ
ejpam-5710	132	11	κ22	κ22	NOUN
ejpam-5710	132	12	)	)	PUNCT
ejpam-5710	132	13	3/2	3/2	NUM
ejpam-5710	132	14	bq(s	bq(s	NOUN
ejpam-5710	132	15	)	)	PUNCT
ejpam-5710	132	16	,	,	PUNCT
ejpam-5710	132	17	(	(	PUNCT
ejpam-5710	132	18	3.10	3.10	NUM
ejpam-5710	132	19	)	)	PUNCT
ejpam-5710	132	20	a.	a.	NOUN
ejpam-5710	132	21	elsharkawy	elsharkawy	PROPN
ejpam-5710	132	22	,	,	PUNCT
ejpam-5710	132	23	h.	h.	PROPN
ejpam-5710	132	24	k.	k.	PROPN
ejpam-5710	132	25	elsayied	elsayied	PROPN
ejpam-5710	132	26	,	,	PUNCT
ejpam-5710	132	27	a.	a.	NOUN
ejpam-5710	132	28	refaat	refaat	PROPN
ejpam-5710	132	29	/	/	SYM
ejpam-5710	132	30	eur	eur	PROPN
ejpam-5710	132	31	.	.	PUNCT
ejpam-5710	133	1	j.	j.	PROPN
ejpam-5710	133	2	pure	pure	PROPN
ejpam-5710	133	3	appl	appl	PROPN
ejpam-5710	133	4	.	.	PROPN
ejpam-5710	133	5	math	math	PROPN
ejpam-5710	133	6	,	,	PUNCT
ejpam-5710	133	7	18	18	NUM
ejpam-5710	133	8	(	(	PUNCT
ejpam-5710	133	9	1	1	NUM
ejpam-5710	133	10	)	)	PUNCT
ejpam-5710	133	11	(	(	PUNCT
ejpam-5710	133	12	2025	2025	NUM
ejpam-5710	133	13	)	)	PUNCT
ejpam-5710	133	14	,	,	PUNCT
ejpam-5710	133	15	5710	5710	NUM
ejpam-5710	133	16	7	7	NUM
ejpam-5710	133	17	of	of	ADP
ejpam-5710	133	18	18	18	NUM
ejpam-5710	133	19	and	and	CCONJ
ejpam-5710	133	20	(	(	PUNCT
ejpam-5710	133	21	nt	not	PART
ejpam-5710	133	22	)	)	PUNCT
ejpam-5710	133	23	u	u	NOUN
ejpam-5710	133	24	=	=	NOUN
ejpam-5710	133	25	0	0	PROPN
ejpam-5710	133	26	.	.	PUNCT
ejpam-5710	134	1	(	(	PUNCT
ejpam-5710	134	2	3.11	3.11	NUM
ejpam-5710	134	3	)	)	PUNCT
ejpam-5710	134	4	from	from	ADP
ejpam-5710	134	5	equations	equation	NOUN
ejpam-5710	134	6	(	(	PUNCT
ejpam-5710	134	7	2.14	2.14	NUM
ejpam-5710	134	8	)	)	PUNCT
ejpam-5710	134	9	,	,	PUNCT
ejpam-5710	134	10	(	(	PUNCT
ejpam-5710	134	11	3.10	3.10	NUM
ejpam-5710	134	12	)	)	PUNCT
ejpam-5710	134	13	and	and	CCONJ
ejpam-5710	134	14	(	(	PUNCT
ejpam-5710	134	15	3.11	3.11	NUM
ejpam-5710	134	16	)	)	PUNCT
ejpam-5710	134	17	the	the	DET
ejpam-5710	134	18	coefficients	coefficient	NOUN
ejpam-5710	134	19	of	of	ADP
ejpam-5710	134	20	3rd	3rd	PROPN
ejpam-5710	134	21	f.f	f.f	PROPN
ejpam-5710	134	22	are	be	AUX
ejpam-5710	134	23	given	give	VERB
ejpam-5710	134	24	by	by	ADP
ejpam-5710	134	25	e	e	X
ejpam-5710	134	26	=	=	X
ejpam-5710	134	27	<	<	X
ejpam-5710	134	28	nt	nt	PROPN
ejpam-5710	134	29	s	s	PROPN
ejpam-5710	134	30	,	,	PUNCT
ejpam-5710	134	31	n	n	PROPN
ejpam-5710	134	32	t	t	PROPN
ejpam-5710	134	33	s	s	X
ejpam-5710	134	34	>	>	X
ejpam-5710	134	35	=	=	SYM
ejpam-5710	134	36	(	(	PUNCT
ejpam-5710	134	37	κ2	κ2	NOUN
ejpam-5710	134	38	(	(	PUNCT
ejpam-5710	134	39	κ2κ3	κ2κ3	ADP
ejpam-5710	134	40	−	−	PROPN
ejpam-5710	134	41	κ1	κ1	NOUN
ejpam-5710	134	42	′	′	NOUN
ejpam-5710	134	43	)	)	PUNCT
ejpam-5710	135	1	+	+	CCONJ
ejpam-5710	135	2	κ1κ2	κ1κ2	ADP
ejpam-5710	135	3	′	′	NOUN
ejpam-5710	135	4	+	+	CCONJ
ejpam-5710	135	5	κ1	κ1	NOUN
ejpam-5710	135	6	2κ3	2κ3	NUM
ejpam-5710	135	7	)	)	PUNCT
ejpam-5710	135	8	2	2	NUM
ejpam-5710	135	9	(	(	PUNCT
ejpam-5710	135	10	κ12	κ12	X
ejpam-5710	135	11	+	+	CCONJ
ejpam-5710	135	12	κ22	κ22	NOUN
ejpam-5710	135	13	)	)	PUNCT
ejpam-5710	135	14	2	2	NUM
ejpam-5710	135	15	=	=	SYM
ejpam-5710	135	16	l√	l√	NOUN
ejpam-5710	135	17	e	e	NOUN
ejpam-5710	135	18	−	−	PROPN
ejpam-5710	135	19	1	1	NUM
ejpam-5710	135	20	,	,	PUNCT
ejpam-5710	135	21	f	f	X
ejpam-5710	136	1	=	=	X
ejpam-5710	136	2	<	<	X
ejpam-5710	136	3	nt	nt	PROPN
ejpam-5710	136	4	s	s	PROPN
ejpam-5710	136	5	,	,	PUNCT
ejpam-5710	136	6	n	n	PROPN
ejpam-5710	136	7	t	t	NOUN
ejpam-5710	136	8	u	u	X
ejpam-5710	136	9	>	>	X
ejpam-5710	136	10	=	=	PUNCT
ejpam-5710	136	11	0	0	PROPN
ejpam-5710	136	12	,	,	PUNCT
ejpam-5710	136	13	g	g	NOUN
ejpam-5710	136	14	=	=	NOUN
ejpam-5710	136	15	<	<	X
ejpam-5710	136	16	nt	not	PART
ejpam-5710	136	17	u	u	PROPN
ejpam-5710	136	18	,	,	PUNCT
ejpam-5710	136	19	n	n	PROPN
ejpam-5710	136	20	t	t	NOUN
ejpam-5710	136	21	u	u	X
ejpam-5710	136	22	>	>	X
ejpam-5710	136	23	=	=	PUNCT
ejpam-5710	136	24	0	0	PROPN
ejpam-5710	136	25	,	,	PUNCT
ejpam-5710	136	26	where	where	SCONJ
ejpam-5710	136	27	e	e	NOUN
ejpam-5710	136	28	=	=	NOUN
ejpam-5710	136	29	1	1	NUM
ejpam-5710	136	30	+	+	CCONJ
ejpam-5710	136	31	u2	u2	PROPN
ejpam-5710	136	32	(	(	PUNCT
ejpam-5710	136	33	κ1	κ1	NOUN
ejpam-5710	136	34	2	2	NUM
ejpam-5710	136	35	+	+	NUM
ejpam-5710	136	36	κ2	κ2	NOUN
ejpam-5710	136	37	2	2	NUM
ejpam-5710	136	38	)	)	PUNCT
ejpam-5710	136	39	.	.	PUNCT
ejpam-5710	137	1	theorem	theorem	VERB
ejpam-5710	137	2	3.5	3.5	NUM
ejpam-5710	137	3	.	.	PUNCT
ejpam-5710	138	1	the	the	DET
ejpam-5710	138	2	gaussian	gaussian	ADJ
ejpam-5710	138	3	curvature	curvature	NOUN
ejpam-5710	138	4	k	k	PROPN
ejpam-5710	138	5	and	and	CCONJ
ejpam-5710	138	6	the	the	DET
ejpam-5710	138	7	mean	mean	ADJ
ejpam-5710	138	8	curvature	curvature	NOUN
ejpam-5710	138	9	h	h	NOUN
ejpam-5710	138	10	of	of	ADP
ejpam-5710	138	11	the	the	DET
ejpam-5710	138	12	quasitangent	quasitangent	NOUN
ejpam-5710	138	13	ruled	rule	VERB
ejpam-5710	138	14	surface	surface	PROPN
ejpam-5710	138	15	w	w	PROPN
ejpam-5710	138	16	t	t	PROPN
ejpam-5710	138	17	(	(	PUNCT
ejpam-5710	138	18	s	s	PROPN
ejpam-5710	138	19	,	,	PUNCT
ejpam-5710	138	20	u	u	NOUN
ejpam-5710	138	21	)	)	PUNCT
ejpam-5710	138	22	are	be	AUX
ejpam-5710	138	23	given	give	VERB
ejpam-5710	138	24	,	,	PUNCT
ejpam-5710	138	25	respectively	respectively	ADV
ejpam-5710	138	26	,	,	PUNCT
ejpam-5710	138	27	by	by	ADP
ejpam-5710	138	28	k	k	PROPN
ejpam-5710	138	29	=	=	SYM
ejpam-5710	138	30	0	0	PROPN
ejpam-5710	138	31	,	,	PUNCT
ejpam-5710	138	32	h	h	NOUN
ejpam-5710	138	33	=	=	SYM
ejpam-5710	138	34	κ2	κ2	NOUN
ejpam-5710	138	35	(	(	PUNCT
ejpam-5710	138	36	κ1	κ1	NOUN
ejpam-5710	138	37	′	′	NUM
ejpam-5710	138	38	−	−	PROPN
ejpam-5710	138	39	κ2κ3	κ2κ3	NOUN
ejpam-5710	138	40	)	)	PUNCT
ejpam-5710	139	1	+	+	CCONJ
ejpam-5710	139	2	κ1	κ1	NOUN
ejpam-5710	139	3	(	(	PUNCT
ejpam-5710	139	4	−κ2	−κ2	PROPN
ejpam-5710	139	5	′)−	′)−	PROPN
ejpam-5710	139	6	κ1	κ1	NOUN
ejpam-5710	139	7	2κ3	2κ3	NUM
ejpam-5710	139	8	2u	2u	NOUN
ejpam-5710	139	9	(	(	PUNCT
ejpam-5710	139	10	κ12	κ12	X
ejpam-5710	139	11	+	+	CCONJ
ejpam-5710	139	12	κ22	κ22	NOUN
ejpam-5710	139	13	)	)	PUNCT
ejpam-5710	139	14	3/2	3/2	NUM
ejpam-5710	139	15	.	.	PUNCT
ejpam-5710	140	1	proof	proof	NOUN
ejpam-5710	140	2	.	.	PUNCT
ejpam-5710	141	1	let	let	VERB
ejpam-5710	141	2	w	w	PROPN
ejpam-5710	141	3	t	t	PROPN
ejpam-5710	141	4	(	(	PUNCT
ejpam-5710	141	5	s	s	PROPN
ejpam-5710	141	6	,	,	PUNCT
ejpam-5710	141	7	u	u	NOUN
ejpam-5710	141	8	)	)	PUNCT
ejpam-5710	141	9	be	be	VERB
ejpam-5710	141	10	a	a	DET
ejpam-5710	141	11	qtr	qtr	NOUN
ejpam-5710	141	12	-	-	PUNCT
ejpam-5710	141	13	surface	surface	NOUN
ejpam-5710	141	14	with	with	ADP
ejpam-5710	141	15	base	base	NOUN
ejpam-5710	141	16	curve	curve	NOUN
ejpam-5710	141	17	α(s	α(s	PROPN
ejpam-5710	141	18	)	)	PUNCT
ejpam-5710	141	19	.	.	PUNCT
ejpam-5710	142	1	from	from	ADP
ejpam-5710	142	2	equations	equation	NOUN
ejpam-5710	142	3	(	(	PUNCT
ejpam-5710	142	4	2.15	2.15	NUM
ejpam-5710	142	5	)	)	PUNCT
ejpam-5710	142	6	,	,	PUNCT
ejpam-5710	142	7	(	(	PUNCT
ejpam-5710	142	8	3.4	3.4	NUM
ejpam-5710	142	9	)	)	PUNCT
ejpam-5710	142	10	and	and	CCONJ
ejpam-5710	142	11	(	(	PUNCT
ejpam-5710	142	12	3.9	3.9	NUM
ejpam-5710	142	13	)	)	PUNCT
ejpam-5710	142	14	we	we	PRON
ejpam-5710	142	15	deduce	deduce	VERB
ejpam-5710	142	16	the	the	DET
ejpam-5710	142	17	result	result	NOUN
ejpam-5710	142	18	.	.	PUNCT
ejpam-5710	143	1	theorem	theorem	VERB
ejpam-5710	143	2	3.6	3.6	NUM
ejpam-5710	143	3	.	.	PUNCT
ejpam-5710	144	1	the	the	DET
ejpam-5710	144	2	geodesic	geodesic	ADJ
ejpam-5710	144	3	curvature	curvature	NOUN
ejpam-5710	144	4	κg	κg	PROPN
ejpam-5710	144	5	,	,	PUNCT
ejpam-5710	144	6	the	the	DET
ejpam-5710	144	7	normal	normal	ADJ
ejpam-5710	144	8	curvature	curvature	NOUN
ejpam-5710	144	9	κn	κn	NOUN
ejpam-5710	144	10	and	and	CCONJ
ejpam-5710	144	11	the	the	DET
ejpam-5710	144	12	geodesic	geodesic	ADJ
ejpam-5710	144	13	torsion	torsion	NOUN
ejpam-5710	144	14	τg	τg	ADP
ejpam-5710	144	15	which	which	PRON
ejpam-5710	144	16	associate	associate	VERB
ejpam-5710	144	17	the	the	DET
ejpam-5710	144	18	base	base	NOUN
ejpam-5710	144	19	curve	curve	NOUN
ejpam-5710	144	20	on	on	ADP
ejpam-5710	144	21	the	the	DET
ejpam-5710	144	22	quasi	quasi	NOUN
ejpam-5710	144	23	-	-	ADJ
ejpam-5710	144	24	tangent	tangent	ADJ
ejpam-5710	144	25	ruled	rule	VERB
ejpam-5710	144	26	surface	surface	PROPN
ejpam-5710	144	27	w	w	PROPN
ejpam-5710	144	28	t	t	PROPN
ejpam-5710	144	29	(	(	PUNCT
ejpam-5710	144	30	s	s	PROPN
ejpam-5710	144	31	,	,	PUNCT
ejpam-5710	144	32	u	u	NOUN
ejpam-5710	144	33	)	)	PUNCT
ejpam-5710	144	34	are	be	AUX
ejpam-5710	144	35	given	give	VERB
ejpam-5710	144	36	,	,	PUNCT
ejpam-5710	144	37	respectively	respectively	ADV
ejpam-5710	144	38	,	,	PUNCT
ejpam-5710	144	39	by	by	ADP
ejpam-5710	144	40	κg	κg	PROPN
ejpam-5710	144	41	=	=	SYM
ejpam-5710	144	42	−	−	PROPN
ejpam-5710	144	43	√	√	PROPN
ejpam-5710	144	44	κ12	κ12	VERB
ejpam-5710	144	45	+	+	CCONJ
ejpam-5710	144	46	κ22	κ22	NOUN
ejpam-5710	144	47	,	,	PUNCT
ejpam-5710	144	48	κn	κn	NOUN
ejpam-5710	144	49	=	=	PROPN
ejpam-5710	144	50	0	0	NUM
ejpam-5710	144	51	,	,	PUNCT
ejpam-5710	144	52	τg	τg	NOUN
ejpam-5710	145	1	=	=	NOUN
ejpam-5710	145	2	0	0	X
ejpam-5710	145	3	.	.	PUNCT
ejpam-5710	145	4	proof	proof	NOUN
ejpam-5710	145	5	.	.	PUNCT
ejpam-5710	146	1	let	let	VERB
ejpam-5710	146	2	w	w	PROPN
ejpam-5710	146	3	t	t	PROPN
ejpam-5710	146	4	(	(	PUNCT
ejpam-5710	146	5	s	s	PROPN
ejpam-5710	146	6	,	,	PUNCT
ejpam-5710	146	7	u	u	NOUN
ejpam-5710	146	8	)	)	PUNCT
ejpam-5710	146	9	be	be	VERB
ejpam-5710	146	10	a	a	DET
ejpam-5710	146	11	qtr	qtr	NOUN
ejpam-5710	146	12	-	-	PUNCT
ejpam-5710	146	13	surface	surface	NOUN
ejpam-5710	146	14	with	with	ADP
ejpam-5710	146	15	base	base	NOUN
ejpam-5710	146	16	curve	curve	NOUN
ejpam-5710	146	17	α(s	α(s	PROPN
ejpam-5710	146	18	)	)	PUNCT
ejpam-5710	146	19	.	.	PUNCT
ejpam-5710	147	1	from	from	ADP
ejpam-5710	147	2	equations	equation	NOUN
ejpam-5710	147	3	(	(	PUNCT
ejpam-5710	147	4	2.2	2.2	NUM
ejpam-5710	147	5	)	)	PUNCT
ejpam-5710	147	6	and	and	CCONJ
ejpam-5710	147	7	(	(	PUNCT
ejpam-5710	147	8	2.16	2.16	NUM
ejpam-5710	147	9	)	)	PUNCT
ejpam-5710	147	10	we	we	PRON
ejpam-5710	147	11	deduce	deduce	VERB
ejpam-5710	147	12	the	the	DET
ejpam-5710	147	13	result	result	NOUN
ejpam-5710	147	14	.	.	PUNCT
ejpam-5710	148	1	corollary	corollary	ADJ
ejpam-5710	148	2	3.1	3.1	NUM
ejpam-5710	148	3	.	.	PUNCT
ejpam-5710	149	1	let	let	AUX
ejpam-5710	149	2	α(s	α(s	PROPN
ejpam-5710	149	3	)	)	PUNCT
ejpam-5710	149	4	be	be	AUX
ejpam-5710	149	5	a	a	DET
ejpam-5710	149	6	regular	regular	ADJ
ejpam-5710	149	7	curve	curve	NOUN
ejpam-5710	149	8	lying	lie	VERB
ejpam-5710	149	9	on	on	ADP
ejpam-5710	149	10	a	a	DET
ejpam-5710	149	11	surface	surface	NOUN
ejpam-5710	149	12	w	w	PROPN
ejpam-5710	149	13	t	t	PROPN
ejpam-5710	149	14	(	(	PUNCT
ejpam-5710	149	15	s	s	PROPN
ejpam-5710	149	16	,	,	PUNCT
ejpam-5710	149	17	u	u	NOUN
ejpam-5710	149	18	)	)	PUNCT
ejpam-5710	149	19	.	.	PUNCT
ejpam-5710	150	1	(	(	PUNCT
ejpam-5710	150	2	a	a	X
ejpam-5710	150	3	)	)	PUNCT
ejpam-5710	150	4	the	the	DET
ejpam-5710	150	5	curve	curve	NOUN
ejpam-5710	150	6	α(s	α(s	PROPN
ejpam-5710	150	7	)	)	PUNCT
ejpam-5710	150	8	is	be	AUX
ejpam-5710	150	9	said	say	VERB
ejpam-5710	150	10	to	to	PART
ejpam-5710	150	11	be	be	AUX
ejpam-5710	150	12	a	a	DET
ejpam-5710	150	13	geodesic	geodesic	ADJ
ejpam-5710	150	14	curve	curve	NOUN
ejpam-5710	150	15	if	if	SCONJ
ejpam-5710	150	16	only	only	ADV
ejpam-5710	150	17	if	if	SCONJ
ejpam-5710	150	18	α(s	α(s	PROPN
ejpam-5710	150	19	)	)	PUNCT
ejpam-5710	150	20	is	be	AUX
ejpam-5710	150	21	a	a	DET
ejpam-5710	150	22	straight	straight	ADJ
ejpam-5710	150	23	line	line	NOUN
ejpam-5710	150	24	.	.	PUNCT
ejpam-5710	151	1	(	(	PUNCT
ejpam-5710	151	2	b	b	X
ejpam-5710	151	3	)	)	PUNCT
ejpam-5710	151	4	the	the	DET
ejpam-5710	151	5	curve	curve	NOUN
ejpam-5710	151	6	α(s	α(s	PROPN
ejpam-5710	151	7	)	)	PUNCT
ejpam-5710	151	8	is	be	AUX
ejpam-5710	151	9	always	always	ADV
ejpam-5710	151	10	asymptotic	asymptotic	ADJ
ejpam-5710	151	11	line	line	NOUN
ejpam-5710	151	12	.	.	PUNCT
ejpam-5710	152	1	(	(	PUNCT
ejpam-5710	152	2	c	c	X
ejpam-5710	152	3	)	)	PUNCT
ejpam-5710	152	4	the	the	DET
ejpam-5710	152	5	curve	curve	NOUN
ejpam-5710	152	6	α(s	α(s	PROPN
ejpam-5710	152	7	)	)	PUNCT
ejpam-5710	152	8	is	be	AUX
ejpam-5710	152	9	a	a	DET
ejpam-5710	152	10	always	always	ADV
ejpam-5710	152	11	principal	principal	ADJ
ejpam-5710	152	12	line	line	NOUN
ejpam-5710	152	13	.	.	PUNCT
ejpam-5710	153	1	corollary	corollary	ADJ
ejpam-5710	153	2	3.2	3.2	NUM
ejpam-5710	153	3	.	.	PUNCT
ejpam-5710	154	1	(	(	PUNCT
ejpam-5710	154	2	a	a	X
ejpam-5710	154	3	)	)	PUNCT
ejpam-5710	154	4	the	the	DET
ejpam-5710	154	5	qtr	qtr	NOUN
ejpam-5710	154	6	-	-	PUNCT
ejpam-5710	154	7	surface	surface	NOUN
ejpam-5710	154	8	is	be	AUX
ejpam-5710	154	9	always	always	ADV
ejpam-5710	154	10	flat	flat	ADJ
ejpam-5710	154	11	(	(	PUNCT
ejpam-5710	154	12	developable	developable	ADJ
ejpam-5710	154	13	)	)	PUNCT
ejpam-5710	154	14	surface	surface	NOUN
ejpam-5710	154	15	.	.	PUNCT
ejpam-5710	155	1	(	(	PUNCT
ejpam-5710	155	2	b	b	X
ejpam-5710	155	3	)	)	PUNCT
ejpam-5710	155	4	for	for	ADP
ejpam-5710	155	5	non	non	ADJ
ejpam-5710	155	6	-	-	ADJ
ejpam-5710	155	7	straight	straight	ADJ
ejpam-5710	155	8	lines	line	NOUN
ejpam-5710	155	9	the	the	DET
ejpam-5710	155	10	qtr	qtr	NOUN
ejpam-5710	155	11	-	-	PUNCT
ejpam-5710	155	12	surface	surface	NOUN
ejpam-5710	155	13	is	be	AUX
ejpam-5710	155	14	a	a	DET
ejpam-5710	155	15	minimal	minimal	ADJ
ejpam-5710	155	16	surface	surface	NOUN
ejpam-5710	155	17	if	if	SCONJ
ejpam-5710	155	18	and	and	CCONJ
ejpam-5710	155	19	only	only	ADV
ejpam-5710	155	20	if	if	SCONJ
ejpam-5710	155	21	κ3	κ3	PROPN
ejpam-5710	155	22	=	=	SYM
ejpam-5710	155	23	−κ21	−κ21	PROPN
ejpam-5710	155	24	d	d	X
ejpam-5710	155	25	du	du	X
ejpam-5710	155	26	(	(	PUNCT
ejpam-5710	155	27	κ2	κ2	NOUN
ejpam-5710	155	28	κ1	κ1	PROPN
ejpam-5710	155	29	)	)	PUNCT
ejpam-5710	155	30	κ21	κ21	PROPN
ejpam-5710	155	31	+	+	NUM
ejpam-5710	155	32	κ22	κ22	NOUN
ejpam-5710	155	33	.	.	PUNCT
ejpam-5710	156	1	a.	a.	NOUN
ejpam-5710	156	2	elsharkawy	elsharkawy	PROPN
ejpam-5710	156	3	,	,	PUNCT
ejpam-5710	156	4	h.	h.	PROPN
ejpam-5710	156	5	k.	k.	PROPN
ejpam-5710	156	6	elsayied	elsayied	PROPN
ejpam-5710	156	7	,	,	PUNCT
ejpam-5710	156	8	a.	a.	NOUN
ejpam-5710	156	9	refaat	refaat	PROPN
ejpam-5710	156	10	/	/	SYM
ejpam-5710	156	11	eur	eur	PROPN
ejpam-5710	156	12	.	.	PUNCT
ejpam-5710	157	1	j.	j.	PROPN
ejpam-5710	157	2	pure	pure	PROPN
ejpam-5710	157	3	appl	appl	PROPN
ejpam-5710	157	4	.	.	PROPN
ejpam-5710	157	5	math	math	PROPN
ejpam-5710	157	6	,	,	PUNCT
ejpam-5710	157	7	18	18	NUM
ejpam-5710	157	8	(	(	PUNCT
ejpam-5710	157	9	1	1	NUM
ejpam-5710	157	10	)	)	PUNCT
ejpam-5710	157	11	(	(	PUNCT
ejpam-5710	157	12	2025	2025	NUM
ejpam-5710	157	13	)	)	PUNCT
ejpam-5710	157	14	,	,	PUNCT
ejpam-5710	157	15	5710	5710	NUM
ejpam-5710	157	16	8	8	NUM
ejpam-5710	157	17	of	of	ADP
ejpam-5710	157	18	18	18	NUM
ejpam-5710	157	19	3.2	3.2	NUM
ejpam-5710	157	20	.	.	PUNCT
ejpam-5710	158	1	quasi	quasi	ADJ
ejpam-5710	158	2	-	-	ADJ
ejpam-5710	158	3	normal	normal	ADJ
ejpam-5710	158	4	ruled	rule	VERB
ejpam-5710	158	5	surfaces	surface	NOUN
ejpam-5710	158	6	according	accord	VERB
ejpam-5710	158	7	to	to	ADP
ejpam-5710	158	8	the	the	DET
ejpam-5710	158	9	quasi	quasi	ADJ
ejpam-5710	158	10	frame	frame	NOUN
ejpam-5710	158	11	in	in	ADP
ejpam-5710	158	12	this	this	DET
ejpam-5710	158	13	section	section	NOUN
ejpam-5710	159	1	,	,	PUNCT
ejpam-5710	159	2	we	we	PRON
ejpam-5710	159	3	outline	outline	VERB
ejpam-5710	159	4	the	the	DET
ejpam-5710	159	5	characteristics	characteristic	NOUN
ejpam-5710	159	6	of	of	ADP
ejpam-5710	159	7	qnr	qnr	NOUN
ejpam-5710	159	8	-	-	PUNCT
ejpam-5710	159	9	surfaces	surface	NOUN
ejpam-5710	159	10	.	.	PUNCT
ejpam-5710	160	1	these	these	DET
ejpam-5710	160	2	surfaces	surface	NOUN
ejpam-5710	160	3	are	be	AUX
ejpam-5710	160	4	formed	form	VERB
ejpam-5710	160	5	by	by	ADP
ejpam-5710	160	6	a	a	DET
ejpam-5710	160	7	regular	regular	ADJ
ejpam-5710	160	8	curve	curve	NOUN
ejpam-5710	160	9	(	(	PUNCT
ejpam-5710	160	10	known	know	VERB
ejpam-5710	160	11	as	as	ADP
ejpam-5710	160	12	the	the	DET
ejpam-5710	160	13	base	base	NOUN
ejpam-5710	160	14	curve	curve	NOUN
ejpam-5710	160	15	)	)	PUNCT
ejpam-5710	160	16	and	and	CCONJ
ejpam-5710	160	17	are	be	AUX
ejpam-5710	160	18	generated	generate	VERB
ejpam-5710	160	19	using	use	VERB
ejpam-5710	160	20	the	the	DET
ejpam-5710	160	21	quasinormal	quasinormal	ADJ
ejpam-5710	160	22	vector	vector	NOUN
ejpam-5710	160	23	nq	nq	PROPN
ejpam-5710	160	24	,	,	PUNCT
ejpam-5710	160	25	which	which	PRON
ejpam-5710	160	26	represents	represent	VERB
ejpam-5710	160	27	the	the	DET
ejpam-5710	160	28	direction	direction	NOUN
ejpam-5710	160	29	vector	vector	NOUN
ejpam-5710	160	30	.	.	PUNCT
ejpam-5710	161	1	furthermore	furthermore	ADV
ejpam-5710	161	2	,	,	PUNCT
ejpam-5710	161	3	we	we	PRON
ejpam-5710	161	4	will	will	AUX
ejpam-5710	161	5	examine	examine	VERB
ejpam-5710	161	6	the	the	DET
ejpam-5710	161	7	fundamental	fundamental	ADJ
ejpam-5710	161	8	properties	property	NOUN
ejpam-5710	161	9	that	that	PRON
ejpam-5710	161	10	are	be	AUX
ejpam-5710	161	11	inherent	inherent	ADJ
ejpam-5710	161	12	to	to	ADP
ejpam-5710	161	13	this	this	DET
ejpam-5710	161	14	type	type	NOUN
ejpam-5710	161	15	of	of	ADP
ejpam-5710	161	16	ruled	rule	VERB
ejpam-5710	161	17	surface	surface	NOUN
ejpam-5710	161	18	.	.	PUNCT
ejpam-5710	162	1	definition	definition	NOUN
ejpam-5710	162	2	3.2	3.2	NUM
ejpam-5710	162	3	.	.	PUNCT
ejpam-5710	163	1	let	let	VERB
ejpam-5710	163	2	η(s	η(	NOUN
ejpam-5710	163	3	)	)	PUNCT
ejpam-5710	163	4	be	be	VERB
ejpam-5710	163	5	a	a	DET
ejpam-5710	163	6	regular	regular	ADJ
ejpam-5710	163	7	curve	curve	NOUN
ejpam-5710	163	8	with	with	ADP
ejpam-5710	163	9	quasi	quasi	ADJ
ejpam-5710	163	10	frame	frame	NOUN
ejpam-5710	163	11	{	{	PUNCT
ejpam-5710	163	12	tq	tq	NOUN
ejpam-5710	163	13	,	,	PUNCT
ejpam-5710	163	14	nq	nq	PROPN
ejpam-5710	163	15	,	,	PUNCT
ejpam-5710	163	16	bq	bq	PROPN
ejpam-5710	163	17	}	}	PUNCT
ejpam-5710	163	18	,	,	PUNCT
ejpam-5710	163	19	then	then	ADV
ejpam-5710	163	20	the	the	DET
ejpam-5710	163	21	parametric	parametric	ADJ
ejpam-5710	163	22	representations	representation	NOUN
ejpam-5710	163	23	of	of	ADP
ejpam-5710	163	24	the	the	DET
ejpam-5710	163	25	qnr	qnr	NOUN
ejpam-5710	163	26	-	-	PUNCT
ejpam-5710	163	27	surface	surface	NOUN
ejpam-5710	163	28	wn	wn	NOUN
ejpam-5710	163	29	(	(	PUNCT
ejpam-5710	163	30	s	s	PROPN
ejpam-5710	163	31	,	,	PUNCT
ejpam-5710	163	32	u	u	NOUN
ejpam-5710	163	33	)	)	PUNCT
ejpam-5710	163	34	with	with	ADP
ejpam-5710	163	35	the	the	DET
ejpam-5710	163	36	ruling	rule	VERB
ejpam-5710	163	37	u	u	NOUN
ejpam-5710	163	38	given	give	VERB
ejpam-5710	163	39	by	by	ADP
ejpam-5710	163	40	wn	wn	PROPN
ejpam-5710	163	41	(	(	PUNCT
ejpam-5710	163	42	s	s	PROPN
ejpam-5710	163	43	,	,	PUNCT
ejpam-5710	163	44	u	u	NOUN
ejpam-5710	163	45	)	)	PUNCT
ejpam-5710	163	46	=	=	SYM
ejpam-5710	163	47	η(s	η(s	PROPN
ejpam-5710	163	48	)	)	PUNCT
ejpam-5710	164	1	+	+	NUM
ejpam-5710	164	2	u	u	NOUN
ejpam-5710	164	3	nq(s	nq(s	PUNCT
ejpam-5710	164	4	)	)	PUNCT
ejpam-5710	164	5	.	.	PUNCT
ejpam-5710	165	1	(	(	PUNCT
ejpam-5710	165	2	3.12	3.12	NUM
ejpam-5710	165	3	)	)	PUNCT
ejpam-5710	165	4	the	the	DET
ejpam-5710	165	5	theories	theory	NOUN
ejpam-5710	165	6	presented	present	VERB
ejpam-5710	165	7	in	in	ADP
ejpam-5710	165	8	this	this	DET
ejpam-5710	165	9	section	section	NOUN
ejpam-5710	165	10	are	be	AUX
ejpam-5710	165	11	built	build	VERB
ejpam-5710	165	12	upon	upon	SCONJ
ejpam-5710	165	13	the	the	DET
ejpam-5710	165	14	same	same	ADJ
ejpam-5710	165	15	foundational	foundational	ADJ
ejpam-5710	165	16	evidence	evidence	NOUN
ejpam-5710	165	17	as	as	ADP
ejpam-5710	165	18	those	those	PRON
ejpam-5710	165	19	discussed	discuss	VERB
ejpam-5710	165	20	in	in	ADP
ejpam-5710	165	21	the	the	DET
ejpam-5710	165	22	first	first	ADJ
ejpam-5710	165	23	section	section	NOUN
ejpam-5710	165	24	.	.	PUNCT
ejpam-5710	166	1	theorem	theorem	VERB
ejpam-5710	166	2	3.7	3.7	NUM
ejpam-5710	166	3	.	.	PUNCT
ejpam-5710	167	1	the	the	DET
ejpam-5710	167	2	striction	striction	NOUN
ejpam-5710	167	3	curve	curve	NOUN
ejpam-5710	167	4	of	of	ADP
ejpam-5710	167	5	the	the	DET
ejpam-5710	167	6	quasi	quasi	ADJ
ejpam-5710	167	7	-	-	ADJ
ejpam-5710	167	8	normal	normal	ADJ
ejpam-5710	167	9	ruled	rule	VERB
ejpam-5710	167	10	surface	surface	NOUN
ejpam-5710	167	11	is	be	AUX
ejpam-5710	167	12	given	give	VERB
ejpam-5710	167	13	by	by	ADP
ejpam-5710	167	14	η∗(s	η∗(s	PROPN
ejpam-5710	167	15	)	)	PUNCT
ejpam-5710	167	16	=	=	SYM
ejpam-5710	167	17	η(s)−	η(s)−	PROPN
ejpam-5710	167	18	κ1	κ1	NOUN
ejpam-5710	167	19	κ12	κ12	VERB
ejpam-5710	167	20	+	+	CCONJ
ejpam-5710	167	21	κ32	κ32	PROPN
ejpam-5710	167	22	nq	nq	PROPN
ejpam-5710	167	23	theorem	theorem	VERB
ejpam-5710	167	24	3.8	3.8	NUM
ejpam-5710	167	25	.	.	PUNCT
ejpam-5710	168	1	the	the	DET
ejpam-5710	168	2	first	first	ADJ
ejpam-5710	168	3	fundamental	fundamental	ADJ
ejpam-5710	168	4	form	form	NOUN
ejpam-5710	168	5	of	of	ADP
ejpam-5710	168	6	the	the	DET
ejpam-5710	168	7	quasi	quasi	ADJ
ejpam-5710	168	8	-	-	ADJ
ejpam-5710	168	9	normal	normal	ADJ
ejpam-5710	168	10	ruled	rule	VERB
ejpam-5710	168	11	surface	surface	PROPN
ejpam-5710	168	12	w	w	PROPN
ejpam-5710	168	13	t	t	PROPN
ejpam-5710	168	14	(	(	PUNCT
ejpam-5710	168	15	s	s	PROPN
ejpam-5710	168	16	,	,	PUNCT
ejpam-5710	168	17	u	u	NOUN
ejpam-5710	168	18	)	)	PUNCT
ejpam-5710	168	19	is	be	AUX
ejpam-5710	168	20	given	give	VERB
ejpam-5710	168	21	by	by	ADP
ejpam-5710	168	22	i	i	PRON
ejpam-5710	168	23	=	=	PUNCT
ejpam-5710	168	24	(	(	PUNCT
ejpam-5710	168	25	u2κ3	u2κ3	PROPN
ejpam-5710	168	26	2	2	NUM
ejpam-5710	168	27	+	+	CCONJ
ejpam-5710	168	28	(	(	PUNCT
ejpam-5710	168	29	1−	1−	NUM
ejpam-5710	168	30	u	u	NOUN
ejpam-5710	168	31	κ1	κ1	NOUN
ejpam-5710	168	32	2))(ds)2	2))(ds)2	PROPN
ejpam-5710	168	33	+	+	CCONJ
ejpam-5710	168	34	(	(	PUNCT
ejpam-5710	168	35	du)2	du)2	PROPN
ejpam-5710	168	36	,	,	PUNCT
ejpam-5710	168	37	where	where	SCONJ
ejpam-5710	168	38	e	e	NOUN
ejpam-5710	168	39	=	=	NOUN
ejpam-5710	168	40	<	<	X
ejpam-5710	168	41	wn	wn	PROPN
ejpam-5710	168	42	s	s	PROPN
ejpam-5710	168	43	,	,	PUNCT
ejpam-5710	168	44	w	w	PROPN
ejpam-5710	168	45	n	n	ADP
ejpam-5710	168	46	s	s	X
ejpam-5710	168	47	>	>	X
ejpam-5710	168	48	=	=	X
ejpam-5710	168	49	u2κ3	u2κ3	PROPN
ejpam-5710	168	50	2	2	NUM
ejpam-5710	168	51	+	+	CCONJ
ejpam-5710	168	52	(	(	PUNCT
ejpam-5710	168	53	1−	1−	NUM
ejpam-5710	168	54	u	u	NOUN
ejpam-5710	168	55	κ1	κ1	NOUN
ejpam-5710	168	56	2	2	NUM
ejpam-5710	168	57	)	)	PUNCT
ejpam-5710	168	58	,	,	PUNCT
ejpam-5710	168	59	f	f	X
ejpam-5710	169	1	=	=	X
ejpam-5710	169	2	<	<	X
ejpam-5710	169	3	wn	wn	PROPN
ejpam-5710	169	4	s	s	PROPN
ejpam-5710	169	5	,	,	PUNCT
ejpam-5710	169	6	w	w	PROPN
ejpam-5710	169	7	n	n	ADP
ejpam-5710	169	8	u	u	X
ejpam-5710	169	9	>	>	X
ejpam-5710	169	10	=	=	PROPN
ejpam-5710	169	11	0	0	PROPN
ejpam-5710	169	12	,	,	PUNCT
ejpam-5710	169	13	g	g	NOUN
ejpam-5710	169	14	=	=	PUNCT
ejpam-5710	169	15	<	<	X
ejpam-5710	169	16	wn	wn	PROPN
ejpam-5710	169	17	u	u	PROPN
ejpam-5710	169	18	,	,	PUNCT
ejpam-5710	169	19	w	w	PROPN
ejpam-5710	169	20	n	n	ADP
ejpam-5710	169	21	u	u	X
ejpam-5710	169	22	>	>	X
ejpam-5710	169	23	=	=	PROPN
ejpam-5710	169	24	1	1	NUM
ejpam-5710	169	25	.	.	PUNCT
ejpam-5710	169	26	theorem	theorem	VERB
ejpam-5710	169	27	3.9	3.9	NUM
ejpam-5710	169	28	.	.	PUNCT
ejpam-5710	170	1	the	the	DET
ejpam-5710	170	2	second	second	ADJ
ejpam-5710	170	3	fundamental	fundamental	ADJ
ejpam-5710	170	4	form	form	NOUN
ejpam-5710	170	5	of	of	ADP
ejpam-5710	170	6	the	the	DET
ejpam-5710	170	7	quasi	quasi	ADJ
ejpam-5710	170	8	-	-	ADJ
ejpam-5710	170	9	normal	normal	ADJ
ejpam-5710	170	10	ruled	rule	VERB
ejpam-5710	170	11	surface	surface	PROPN
ejpam-5710	170	12	wn	wn	PROPN
ejpam-5710	170	13	(	(	PUNCT
ejpam-5710	170	14	s	s	PROPN
ejpam-5710	170	15	,	,	PUNCT
ejpam-5710	170	16	u	u	NOUN
ejpam-5710	170	17	)	)	PUNCT
ejpam-5710	170	18	is	be	AUX
ejpam-5710	170	19	given	give	VERB
ejpam-5710	170	20	by	by	ADP
ejpam-5710	170	21	ii	ii	PROPN
ejpam-5710	170	22	=	=	SYM
ejpam-5710	170	23	(	(	PUNCT
ejpam-5710	170	24	κ2	κ2	NOUN
ejpam-5710	170	25	(	(	PUNCT
ejpam-5710	170	26	u2κ1	u2κ1	X
ejpam-5710	170	27	2	2	NUM
ejpam-5710	170	28	+	+	CCONJ
ejpam-5710	170	29	u2κ3	u2κ3	PROPN
ejpam-5710	170	30	2	2	NUM
ejpam-5710	170	31	−	−	NOUN
ejpam-5710	170	32	2uκ1	2uκ1	NUM
ejpam-5710	170	33	+	+	CCONJ
ejpam-5710	170	34	1	1	NUM
ejpam-5710	170	35	)	)	PUNCT
ejpam-5710	171	1	+	+	CCONJ
ejpam-5710	171	2	u	u	SYM
ejpam-5710	171	3	(	(	PUNCT
ejpam-5710	171	4	uκ3κ1	uκ3κ1	PROPN
ejpam-5710	171	5	′	′	NOUN
ejpam-5710	171	6	+	+	CCONJ
ejpam-5710	171	7	κ3	κ3	PROPN
ejpam-5710	171	8	′(1−	′(1−	NOUN
ejpam-5710	171	9	uκ1))√	uκ1))√	PROPN
ejpam-5710	171	10	u2κ12	u2κ12	VERB
ejpam-5710	171	11	+	+	CCONJ
ejpam-5710	171	12	u2κ32	u2κ32	NUM
ejpam-5710	171	13	−	−	PROPN
ejpam-5710	171	14	2uκ1	2uκ1	NUM
ejpam-5710	171	15	+	+	CCONJ
ejpam-5710	171	16	1	1	NUM
ejpam-5710	171	17	)	)	PUNCT
ejpam-5710	171	18	(	(	PUNCT
ejpam-5710	171	19	ds)2	ds)2	NOUN
ejpam-5710	171	20	+	+	PROPN
ejpam-5710	171	21	2κ3√	2κ3√	NUM
ejpam-5710	171	22	u2κ12	u2κ12	VERB
ejpam-5710	171	23	+	+	CCONJ
ejpam-5710	171	24	u2κ32	u2κ32	ADJ
ejpam-5710	171	25	−	−	PROPN
ejpam-5710	171	26	2uκ1	2uκ1	NUM
ejpam-5710	171	27	+	+	SYM
ejpam-5710	171	28	1	1	NUM
ejpam-5710	171	29	ds	ds	ADJ
ejpam-5710	171	30	du	du	NOUN
ejpam-5710	171	31	,	,	PUNCT
ejpam-5710	171	32	where	where	SCONJ
ejpam-5710	171	33	l	l	NOUN
ejpam-5710	172	1	=	=	PUNCT
ejpam-5710	172	2	<	<	X
ejpam-5710	172	3	wn	wn	PROPN
ejpam-5710	172	4	ss	ss	PROPN
ejpam-5710	172	5	,	,	PUNCT
ejpam-5710	172	6	n	n	CCONJ
ejpam-5710	172	7	>	>	PUNCT
ejpam-5710	172	8	=	=	PUNCT
ejpam-5710	172	9	κ2	κ2	NOUN
ejpam-5710	172	10	(	(	PUNCT
ejpam-5710	172	11	u2κ1	u2κ1	X
ejpam-5710	172	12	2	2	NUM
ejpam-5710	172	13	+	+	CCONJ
ejpam-5710	172	14	u2κ3	u2κ3	PROPN
ejpam-5710	172	15	2	2	NUM
ejpam-5710	172	16	−	−	NOUN
ejpam-5710	172	17	2uκ1	2uκ1	NUM
ejpam-5710	172	18	+	+	CCONJ
ejpam-5710	172	19	1	1	NUM
ejpam-5710	172	20	)	)	PUNCT
ejpam-5710	172	21	+	+	CCONJ
ejpam-5710	172	22	u	u	SYM
ejpam-5710	172	23	(	(	PUNCT
ejpam-5710	172	24	uκ3κ1	uκ3κ1	PROPN
ejpam-5710	172	25	′	′	NOUN
ejpam-5710	172	26	+	+	CCONJ
ejpam-5710	172	27	κ3	κ3	PROPN
ejpam-5710	172	28	′(1−	′(1−	NOUN
ejpam-5710	172	29	uκ1))√	uκ1))√	PROPN
ejpam-5710	172	30	u2κ12	u2κ12	VERB
ejpam-5710	172	31	+	+	CCONJ
ejpam-5710	172	32	u2κ32	u2κ32	NUM
ejpam-5710	172	33	−	−	PROPN
ejpam-5710	172	34	2uκ1	2uκ1	NUM
ejpam-5710	172	35	+	+	CCONJ
ejpam-5710	172	36	1	1	NUM
ejpam-5710	172	37	,	,	PUNCT
ejpam-5710	172	38	m	m	VERB
ejpam-5710	172	39	=	=	X
ejpam-5710	172	40	<	<	X
ejpam-5710	172	41	wn	wn	PROPN
ejpam-5710	172	42	su	su	PROPN
ejpam-5710	172	43	,	,	PUNCT
ejpam-5710	172	44	n	n	X
ejpam-5710	172	45	>	>	PUNCT
ejpam-5710	172	46	=	=	PUNCT
ejpam-5710	173	1	κ3√	κ3√	VERB
ejpam-5710	173	2	u2κ12	u2κ12	ADV
ejpam-5710	173	3	+	+	CCONJ
ejpam-5710	173	4	u2κ32	u2κ32	PRON
ejpam-5710	173	5	−	−	PROPN
ejpam-5710	173	6	2uκ1	2uκ1	NUM
ejpam-5710	173	7	+	+	CCONJ
ejpam-5710	173	8	1	1	NUM
ejpam-5710	173	9	,	,	PUNCT
ejpam-5710	173	10	n	n	NOUN
ejpam-5710	173	11	=	=	SYM
ejpam-5710	173	12	<	<	X
ejpam-5710	173	13	wn	wn	X
ejpam-5710	173	14	uu	uu	PROPN
ejpam-5710	173	15	,	,	PUNCT
ejpam-5710	173	16	n	n	X
ejpam-5710	173	17	>	>	PUNCT
ejpam-5710	173	18	=	=	SYM
ejpam-5710	173	19	0	0	PROPN
ejpam-5710	173	20	.	.	PUNCT
ejpam-5710	173	21	a.	a.	NOUN
ejpam-5710	173	22	elsharkawy	elsharkawy	PROPN
ejpam-5710	173	23	,	,	PUNCT
ejpam-5710	173	24	h.	h.	PROPN
ejpam-5710	173	25	k.	k.	PROPN
ejpam-5710	173	26	elsayied	elsayied	PROPN
ejpam-5710	173	27	,	,	PUNCT
ejpam-5710	173	28	a.	a.	NOUN
ejpam-5710	173	29	refaat	refaat	PROPN
ejpam-5710	173	30	/	/	SYM
ejpam-5710	173	31	eur	eur	PROPN
ejpam-5710	173	32	.	.	PUNCT
ejpam-5710	174	1	j.	j.	PROPN
ejpam-5710	174	2	pure	pure	PROPN
ejpam-5710	174	3	appl	appl	PROPN
ejpam-5710	174	4	.	.	PROPN
ejpam-5710	174	5	math	math	PROPN
ejpam-5710	174	6	,	,	PUNCT
ejpam-5710	174	7	18	18	NUM
ejpam-5710	174	8	(	(	PUNCT
ejpam-5710	174	9	1	1	NUM
ejpam-5710	174	10	)	)	PUNCT
ejpam-5710	174	11	(	(	PUNCT
ejpam-5710	174	12	2025	2025	NUM
ejpam-5710	174	13	)	)	PUNCT
ejpam-5710	174	14	,	,	PUNCT
ejpam-5710	174	15	5710	5710	NUM
ejpam-5710	174	16	9	9	NUM
ejpam-5710	174	17	of	of	ADP
ejpam-5710	174	18	18	18	NUM
ejpam-5710	174	19	theorem	theorem	VERB
ejpam-5710	174	20	3.10	3.10	NUM
ejpam-5710	174	21	.	.	PUNCT
ejpam-5710	175	1	the	the	DET
ejpam-5710	175	2	third	third	ADJ
ejpam-5710	175	3	fundamental	fundamental	ADJ
ejpam-5710	175	4	form	form	NOUN
ejpam-5710	175	5	of	of	ADP
ejpam-5710	175	6	the	the	DET
ejpam-5710	175	7	quasi	quasi	ADJ
ejpam-5710	175	8	-	-	ADJ
ejpam-5710	175	9	normal	normal	ADJ
ejpam-5710	175	10	ruled	rule	VERB
ejpam-5710	175	11	surface	surface	PROPN
ejpam-5710	175	12	wn	wn	PROPN
ejpam-5710	175	13	(	(	PUNCT
ejpam-5710	175	14	s	s	PROPN
ejpam-5710	175	15	,	,	PUNCT
ejpam-5710	175	16	u	u	NOUN
ejpam-5710	175	17	)	)	PUNCT
ejpam-5710	175	18	is	be	AUX
ejpam-5710	175	19	given	give	VERB
ejpam-5710	175	20	by	by	ADP
ejpam-5710	175	21	iii	iii	X
ejpam-5710	175	22	=	=	SYM
ejpam-5710	175	23	e(ds)2	e(ds)2	PROPN
ejpam-5710	175	24	+	+	NUM
ejpam-5710	175	25	2f	2f	NUM
ejpam-5710	175	26	dsdu+	dsdu+	NOUN
ejpam-5710	175	27	g(du)2	g(du)2	NUM
ejpam-5710	175	28	,	,	PUNCT
ejpam-5710	176	1	where	where	SCONJ
ejpam-5710	176	2	e	e	NOUN
ejpam-5710	176	3	=	=	NOUN
ejpam-5710	176	4	<	<	X
ejpam-5710	176	5	nn	nn	X
ejpam-5710	176	6	s	s	PROPN
ejpam-5710	176	7	,	,	PUNCT
ejpam-5710	176	8	n	n	CCONJ
ejpam-5710	176	9	n	n	PROPN
ejpam-5710	176	10	s	s	PART
ejpam-5710	176	11	>	>	X
ejpam-5710	176	12	=	=	SYM
ejpam-5710	176	13	κ23	κ23	NOUN
ejpam-5710	176	14	(	(	PUNCT
ejpam-5710	176	15	u4κ1	u4κ1	ADP
ejpam-5710	176	16	′2	′2	X
ejpam-5710	176	17	+	+	CCONJ
ejpam-5710	176	18	(	(	PUNCT
ejpam-5710	176	19	uκ1	uκ1	PROPN
ejpam-5710	176	20	−	−	PROPN
ejpam-5710	176	21	1)2	1)2	NUM
ejpam-5710	176	22	)	)	PUNCT
ejpam-5710	176	23	−	−	PROPN
ejpam-5710	176	24	2u3κ3κ1	2u3κ3κ1	NUM
ejpam-5710	176	25	′κ3	′κ3	ADJ
ejpam-5710	176	26	′(uκ1	′(uκ1	NOUN
ejpam-5710	176	27	−	−	NOUN
ejpam-5710	176	28	1	1	NUM
ejpam-5710	176	29	)	)	PUNCT
ejpam-5710	176	30	(	(	PUNCT
ejpam-5710	176	31	u2κ32	u2κ32	X
ejpam-5710	176	32	+	+	CCONJ
ejpam-5710	176	33	(	(	PUNCT
ejpam-5710	176	34	1−	1−	NUM
ejpam-5710	176	35	uκ1)2	uκ1)2	PROPN
ejpam-5710	176	36	)	)	PUNCT
ejpam-5710	176	37	2	2	NUM
ejpam-5710	176	38	+	+	NUM
ejpam-5710	176	39	2uκ2	2uκ2	NUM
ejpam-5710	176	40	(	(	PUNCT
ejpam-5710	176	41	u2κ23	u2κ23	ADP
ejpam-5710	176	42	+	+	CCONJ
ejpam-5710	176	43	(	(	PUNCT
ejpam-5710	176	44	uκ1	uκ1	PROPN
ejpam-5710	176	45	−	−	PROPN
ejpam-5710	176	46	1)2	1)2	NUM
ejpam-5710	176	47	)	)	PUNCT
ejpam-5710	176	48	(	(	PUNCT
ejpam-5710	176	49	uκ3κ1	uκ3κ1	PROPN
ejpam-5710	176	50	′	′	NOUN
ejpam-5710	176	51	+	+	CCONJ
ejpam-5710	176	52	κ3	κ3	PROPN
ejpam-5710	176	53	′(1−	′(1−	PROPN
ejpam-5710	176	54	uκ1	uκ1	PROPN
ejpam-5710	176	55	)	)	PUNCT
ejpam-5710	176	56	)	)	PUNCT
ejpam-5710	177	1	(	(	PUNCT
ejpam-5710	177	2	u2κ32	u2κ32	X
ejpam-5710	177	3	+	+	CCONJ
ejpam-5710	177	4	(	(	PUNCT
ejpam-5710	177	5	1−	1−	NUM
ejpam-5710	177	6	uκ1)2	uκ1)2	PROPN
ejpam-5710	177	7	)	)	PUNCT
ejpam-5710	177	8	2	2	NUM
ejpam-5710	178	1	+	+	NUM
ejpam-5710	178	2	κ22	κ22	NOUN
ejpam-5710	178	3	(	(	PUNCT
ejpam-5710	178	4	u2κ23	u2κ23	ADP
ejpam-5710	178	5	+	+	CCONJ
ejpam-5710	178	6	(	(	PUNCT
ejpam-5710	178	7	uκ1	uκ1	PROPN
ejpam-5710	178	8	−	−	PROPN
ejpam-5710	178	9	1)2	1)2	NUM
ejpam-5710	178	10	)	)	PUNCT
ejpam-5710	178	11	2	2	NUM
ejpam-5710	178	12	+	+	CCONJ
ejpam-5710	178	13	u2κ3	u2κ3	PROPN
ejpam-5710	178	14	′2(uκ1	′2(uκ1	NOUN
ejpam-5710	178	15	−	−	PROPN
ejpam-5710	178	16	1)2	1)2	NUM
ejpam-5710	178	17	+	+	CCONJ
ejpam-5710	178	18	u2κ43	u2κ43	NOUN
ejpam-5710	178	19	(	(	PUNCT
ejpam-5710	178	20	u2κ32	u2κ32	NOUN
ejpam-5710	178	21	+	+	CCONJ
ejpam-5710	178	22	(	(	PUNCT
ejpam-5710	178	23	1−	1−	NUM
ejpam-5710	178	24	uκ1)2	uκ1)2	PROPN
ejpam-5710	178	25	)	)	PUNCT
ejpam-5710	178	26	2	2	NUM
ejpam-5710	178	27	=	=	SYM
ejpam-5710	178	28	l2	l2	NOUN
ejpam-5710	178	29	e	e	NOUN
ejpam-5710	178	30	+	+	CCONJ
ejpam-5710	178	31	m2	m2	PROPN
ejpam-5710	178	32	,	,	PUNCT
ejpam-5710	178	33	f	f	X
ejpam-5710	178	34	=	=	X
ejpam-5710	178	35	<	<	X
ejpam-5710	178	36	nn	nn	X
ejpam-5710	178	37	s	s	PROPN
ejpam-5710	178	38	,	,	PUNCT
ejpam-5710	178	39	n	n	CCONJ
ejpam-5710	178	40	n	n	PRON
ejpam-5710	178	41	u	u	NOUN
ejpam-5710	178	42	>	>	X
ejpam-5710	178	43	=	=	PROPN
ejpam-5710	178	44	κ3	κ3	PROPN
ejpam-5710	178	45	(	(	PUNCT
ejpam-5710	178	46	κ2	κ2	PROPN
ejpam-5710	178	47	(	(	PUNCT
ejpam-5710	178	48	u2κ21	u2κ21	ADJ
ejpam-5710	178	49	+	+	ADJ
ejpam-5710	178	50	u2κ23	u2κ23	ADP
ejpam-5710	178	51	−	−	PROPN
ejpam-5710	178	52	2uκ1	2uκ1	NUM
ejpam-5710	178	53	+	+	CCONJ
ejpam-5710	178	54	1	1	NUM
ejpam-5710	178	55	)	)	PUNCT
ejpam-5710	179	1	+	+	CCONJ
ejpam-5710	179	2	u	u	SYM
ejpam-5710	179	3	(	(	PUNCT
ejpam-5710	179	4	uκ3κ1	uκ3κ1	PROPN
ejpam-5710	179	5	′	′	NOUN
ejpam-5710	179	6	+	+	CCONJ
ejpam-5710	179	7	κ3	κ3	PROPN
ejpam-5710	179	8	′(1−	′(1−	PROPN
ejpam-5710	179	9	uκ1	uκ1	PROPN
ejpam-5710	179	10	)	)	PUNCT
ejpam-5710	179	11	)	)	PUNCT
ejpam-5710	179	12	)	)	PUNCT
ejpam-5710	180	1	(	(	PUNCT
ejpam-5710	180	2	u2κ32	u2κ32	X
ejpam-5710	180	3	+	+	CCONJ
ejpam-5710	180	4	(	(	PUNCT
ejpam-5710	180	5	1−	1−	NUM
ejpam-5710	180	6	uκ1)2	uκ1)2	PROPN
ejpam-5710	180	7	)	)	PUNCT
ejpam-5710	180	8	2	2	NUM
ejpam-5710	180	9	=	=	SYM
ejpam-5710	180	10	lm	lm	X
ejpam-5710	180	11	e	e	NOUN
ejpam-5710	180	12	,	,	PUNCT
ejpam-5710	180	13	g	g	PROPN
ejpam-5710	180	14	=	=	PROPN
ejpam-5710	180	15	<	<	X
ejpam-5710	180	16	nn	nn	X
ejpam-5710	180	17	u	u	PROPN
ejpam-5710	180	18	,	,	PUNCT
ejpam-5710	180	19	n	n	CCONJ
ejpam-5710	180	20	n	n	PRON
ejpam-5710	180	21	u	u	NOUN
ejpam-5710	180	22	>	>	X
ejpam-5710	180	23	=	=	SYM
ejpam-5710	180	24	κ23	κ23	NOUN
ejpam-5710	180	25	(	(	PUNCT
ejpam-5710	180	26	u2κ32	u2κ32	SYM
ejpam-5710	180	27	+	+	CCONJ
ejpam-5710	180	28	(	(	PUNCT
ejpam-5710	180	29	1−	1−	NUM
ejpam-5710	180	30	uκ1)2	uκ1)2	PROPN
ejpam-5710	180	31	)	)	PUNCT
ejpam-5710	180	32	2	2	NUM
ejpam-5710	180	33	=	=	SYM
ejpam-5710	180	34	m2	m2	PROPN
ejpam-5710	180	35	e	e	PROPN
ejpam-5710	180	36	.	.	PUNCT
ejpam-5710	180	37	theorem	theorem	VERB
ejpam-5710	180	38	3.11	3.11	NUM
ejpam-5710	180	39	.	.	PUNCT
ejpam-5710	181	1	the	the	DET
ejpam-5710	181	2	gaussian	gaussian	ADJ
ejpam-5710	181	3	curvature	curvature	NOUN
ejpam-5710	181	4	k	k	PROPN
ejpam-5710	181	5	and	and	CCONJ
ejpam-5710	181	6	the	the	DET
ejpam-5710	181	7	mean	mean	ADJ
ejpam-5710	181	8	curvature	curvature	NOUN
ejpam-5710	181	9	h	h	NOUN
ejpam-5710	181	10	of	of	ADP
ejpam-5710	181	11	the	the	DET
ejpam-5710	181	12	quasinormal	quasinormal	PROPN
ejpam-5710	181	13	ruled	rule	VERB
ejpam-5710	181	14	surface	surface	PROPN
ejpam-5710	181	15	wn	wn	PROPN
ejpam-5710	181	16	(	(	PUNCT
ejpam-5710	181	17	s	s	PROPN
ejpam-5710	181	18	,	,	PUNCT
ejpam-5710	181	19	u	u	NOUN
ejpam-5710	181	20	)	)	PUNCT
ejpam-5710	181	21	are	be	AUX
ejpam-5710	181	22	given	give	VERB
ejpam-5710	181	23	,	,	PUNCT
ejpam-5710	181	24	respectively	respectively	ADV
ejpam-5710	181	25	,	,	PUNCT
ejpam-5710	181	26	by	by	ADP
ejpam-5710	181	27	k	k	PROPN
ejpam-5710	181	28	=	=	PUNCT
ejpam-5710	181	29	−κ3	−κ3	PROPN
ejpam-5710	181	30	2	2	NUM
ejpam-5710	181	31	(	(	PUNCT
ejpam-5710	181	32	u2κ32	u2κ32	NOUN
ejpam-5710	181	33	+	+	CCONJ
ejpam-5710	181	34	(	(	PUNCT
ejpam-5710	181	35	1−	1−	NUM
ejpam-5710	181	36	uκ1)2	uκ1)2	PROPN
ejpam-5710	181	37	)	)	PUNCT
ejpam-5710	181	38	2	2	NUM
ejpam-5710	181	39	=	=	SYM
ejpam-5710	181	40	−m2	−m2	NOUN
ejpam-5710	181	41	e	e	NOUN
ejpam-5710	181	42	,	,	PUNCT
ejpam-5710	181	43	h	h	NOUN
ejpam-5710	181	44	=	=	SYM
ejpam-5710	181	45	κ2	κ2	NOUN
ejpam-5710	181	46	(	(	PUNCT
ejpam-5710	181	47	u2κ23	u2κ23	ADP
ejpam-5710	181	48	+	+	CCONJ
ejpam-5710	181	49	(	(	PUNCT
ejpam-5710	181	50	uκ1	uκ1	PROPN
ejpam-5710	181	51	−	−	PROPN
ejpam-5710	181	52	1)2	1)2	NUM
ejpam-5710	181	53	)	)	PUNCT
ejpam-5710	182	1	+	+	CCONJ
ejpam-5710	182	2	u	u	SYM
ejpam-5710	182	3	(	(	PUNCT
ejpam-5710	182	4	uκ3κ1	uκ3κ1	PROPN
ejpam-5710	182	5	′	′	NOUN
ejpam-5710	182	6	+	+	CCONJ
ejpam-5710	182	7	κ3	κ3	PROPN
ejpam-5710	182	8	′(1−	′(1−	PROPN
ejpam-5710	182	9	uκ1	uκ1	PROPN
ejpam-5710	182	10	)	)	PUNCT
ejpam-5710	182	11	)	)	PUNCT
ejpam-5710	182	12	2	2	NUM
ejpam-5710	182	13	(	(	PUNCT
ejpam-5710	182	14	u2κ23	u2κ23	ADP
ejpam-5710	182	15	+	+	CCONJ
ejpam-5710	182	16	(	(	PUNCT
ejpam-5710	182	17	uκ1	uκ1	PROPN
ejpam-5710	182	18	−	−	PROPN
ejpam-5710	182	19	1)2	1)2	NUM
ejpam-5710	182	20	)	)	PUNCT
ejpam-5710	182	21	3/2	3/2	NUM
ejpam-5710	182	22	=	=	SYM
ejpam-5710	182	23	l	l	NOUN
ejpam-5710	182	24	2e	2e	NOUN
ejpam-5710	182	25	.	.	PUNCT
ejpam-5710	183	1	theorem	theorem	VERB
ejpam-5710	183	2	3.12	3.12	NUM
ejpam-5710	183	3	.	.	PUNCT
ejpam-5710	184	1	the	the	DET
ejpam-5710	184	2	geodesic	geodesic	ADJ
ejpam-5710	184	3	curvature	curvature	NOUN
ejpam-5710	184	4	κg	κg	PROPN
ejpam-5710	184	5	,	,	PUNCT
ejpam-5710	184	6	the	the	DET
ejpam-5710	184	7	normal	normal	ADJ
ejpam-5710	184	8	curvature	curvature	NOUN
ejpam-5710	184	9	κn	κn	NOUN
ejpam-5710	184	10	and	and	CCONJ
ejpam-5710	184	11	the	the	DET
ejpam-5710	184	12	geodesic	geodesic	ADJ
ejpam-5710	184	13	torsion	torsion	NOUN
ejpam-5710	184	14	τg	τg	ADP
ejpam-5710	184	15	which	which	PRON
ejpam-5710	184	16	associate	associate	VERB
ejpam-5710	184	17	the	the	DET
ejpam-5710	184	18	base	base	NOUN
ejpam-5710	184	19	curve	curve	NOUN
ejpam-5710	184	20	on	on	ADP
ejpam-5710	184	21	the	the	DET
ejpam-5710	184	22	quasi	quasi	ADJ
ejpam-5710	184	23	-	-	ADJ
ejpam-5710	184	24	normal	normal	ADJ
ejpam-5710	184	25	ruled	rule	VERB
ejpam-5710	184	26	surface	surface	PROPN
ejpam-5710	184	27	wn	wn	PROPN
ejpam-5710	184	28	(	(	PUNCT
ejpam-5710	184	29	s	s	PROPN
ejpam-5710	184	30	,	,	PUNCT
ejpam-5710	184	31	u	u	NOUN
ejpam-5710	184	32	)	)	PUNCT
ejpam-5710	184	33	are	be	AUX
ejpam-5710	184	34	given	give	VERB
ejpam-5710	184	35	,	,	PUNCT
ejpam-5710	184	36	respectively	respectively	ADV
ejpam-5710	184	37	,	,	PUNCT
ejpam-5710	184	38	by	by	ADP
ejpam-5710	184	39	κg	κg	PROPN
ejpam-5710	184	40	=	=	SYM
ejpam-5710	184	41	κ1	κ1	PROPN
ejpam-5710	184	42	−	−	PROPN
ejpam-5710	184	43	uκ21√	uκ21√	NOUN
ejpam-5710	184	44	u2κ23	u2κ23	ADP
ejpam-5710	184	45	+	+	CCONJ
ejpam-5710	184	46	(	(	PUNCT
ejpam-5710	184	47	uκ1	uκ1	PROPN
ejpam-5710	184	48	−	−	PROPN
ejpam-5710	184	49	1)2	1)2	NUM
ejpam-5710	184	50	,	,	PUNCT
ejpam-5710	184	51	κn	κn	NOUN
ejpam-5710	184	52	=	=	PUNCT
ejpam-5710	184	53	κ2(1−	κ2(1−	PROPN
ejpam-5710	184	54	uκ1)√	uκ1)√	NOUN
ejpam-5710	184	55	u2κ23	u2κ23	ADP
ejpam-5710	184	56	+	+	CCONJ
ejpam-5710	185	1	(	(	PUNCT
ejpam-5710	186	1	1−	1−	NUM
ejpam-5710	186	2	uκ1)2	uκ1)2	PROPN
ejpam-5710	186	3	,	,	PUNCT
ejpam-5710	186	4	τg	τg	NUM
ejpam-5710	186	5	=	=	SYM
ejpam-5710	186	6	−κ1	−κ1	PROPN
ejpam-5710	186	7	(	(	PUNCT
ejpam-5710	186	8	κ2	κ2	NOUN
ejpam-5710	186	9	(	(	PUNCT
ejpam-5710	186	10	u2κ23	u2κ23	ADP
ejpam-5710	186	11	+	+	CCONJ
ejpam-5710	186	12	1	1	NUM
ejpam-5710	186	13	)	)	PUNCT
ejpam-5710	187	1	+	+	CCONJ
ejpam-5710	187	2	u	u	SYM
ejpam-5710	187	3	(	(	PUNCT
ejpam-5710	187	4	κ3	κ3	PROPN
ejpam-5710	187	5	′	′	NUM
ejpam-5710	187	6	+	+	CCONJ
ejpam-5710	187	7	uκ3κ1	uκ3κ1	PROPN
ejpam-5710	187	8	′	′	NUM
ejpam-5710	187	9	)	)	PUNCT
ejpam-5710	187	10	)	)	PUNCT
ejpam-5710	188	1	−	−	ADP
ejpam-5710	188	2	u2κ31κ2	u2κ31κ2	PROPN
ejpam-5710	189	1	+	+	PROPN
ejpam-5710	189	2	uκ21	uκ21	PROPN
ejpam-5710	189	3	(	(	PUNCT
ejpam-5710	189	4	2κ2	2κ2	NUM
ejpam-5710	189	5	+	+	CCONJ
ejpam-5710	189	6	uκ3	uκ3	PROPN
ejpam-5710	189	7	′	′	NUM
ejpam-5710	189	8	)	)	PUNCT
ejpam-5710	190	1	+	+	CCONJ
ejpam-5710	191	1	uκ2κ	uκ2κ	ADJ
ejpam-5710	191	2	2	2	NUM
ejpam-5710	191	3	3	3	NUM
ejpam-5710	191	4	u2κ23	u2κ23	ADP
ejpam-5710	191	5	+	+	CCONJ
ejpam-5710	191	6	(	(	PUNCT
ejpam-5710	191	7	uκ1	uκ1	PROPN
ejpam-5710	191	8	−	−	PROPN
ejpam-5710	191	9	1)2	1)2	NUM
ejpam-5710	191	10	.	.	PUNCT
ejpam-5710	192	1	corollary	corollary	ADJ
ejpam-5710	192	2	3.3	3.3	NUM
ejpam-5710	192	3	.	.	PUNCT
ejpam-5710	193	1	let	let	VERB
ejpam-5710	193	2	η(s	η(	NOUN
ejpam-5710	193	3	)	)	PUNCT
ejpam-5710	193	4	be	be	VERB
ejpam-5710	193	5	a	a	DET
ejpam-5710	193	6	regular	regular	ADJ
ejpam-5710	193	7	curve	curve	NOUN
ejpam-5710	193	8	lying	lie	VERB
ejpam-5710	193	9	on	on	ADP
ejpam-5710	193	10	a	a	DET
ejpam-5710	193	11	surface	surface	NOUN
ejpam-5710	193	12	wn	wn	NOUN
ejpam-5710	193	13	(	(	PUNCT
ejpam-5710	193	14	s	s	PROPN
ejpam-5710	193	15	,	,	PUNCT
ejpam-5710	193	16	u	u	NOUN
ejpam-5710	193	17	)	)	PUNCT
ejpam-5710	193	18	.	.	PUNCT
ejpam-5710	194	1	(	(	PUNCT
ejpam-5710	194	2	a	a	X
ejpam-5710	194	3	)	)	PUNCT
ejpam-5710	194	4	the	the	DET
ejpam-5710	194	5	curve	curve	NOUN
ejpam-5710	194	6	η(s	η(s	PROPN
ejpam-5710	194	7	)	)	PUNCT
ejpam-5710	194	8	is	be	AUX
ejpam-5710	194	9	a	a	DET
ejpam-5710	194	10	geodesic	geodesic	ADJ
ejpam-5710	194	11	curve	curve	NOUN
ejpam-5710	194	12	if	if	SCONJ
ejpam-5710	194	13	only	only	ADV
ejpam-5710	194	14	if	if	SCONJ
ejpam-5710	194	15	κ1	κ1	NOUN
ejpam-5710	194	16	=	=	SYM
ejpam-5710	194	17	0	0	NUM
ejpam-5710	194	18	or	or	CCONJ
ejpam-5710	194	19	κ1	κ1	NOUN
ejpam-5710	194	20	=	=	SYM
ejpam-5710	194	21	1	1	NUM
ejpam-5710	194	22	u	u	NOUN
ejpam-5710	194	23	.	.	PUNCT
ejpam-5710	195	1	a.	a.	NOUN
ejpam-5710	195	2	elsharkawy	elsharkawy	PROPN
ejpam-5710	195	3	,	,	PUNCT
ejpam-5710	195	4	h.	h.	PROPN
ejpam-5710	195	5	k.	k.	PROPN
ejpam-5710	195	6	elsayied	elsayied	PROPN
ejpam-5710	195	7	,	,	PUNCT
ejpam-5710	195	8	a.	a.	NOUN
ejpam-5710	195	9	refaat	refaat	PROPN
ejpam-5710	195	10	/	/	SYM
ejpam-5710	195	11	eur	eur	PROPN
ejpam-5710	195	12	.	.	PUNCT
ejpam-5710	196	1	j.	j.	PROPN
ejpam-5710	196	2	pure	pure	PROPN
ejpam-5710	196	3	appl	appl	PROPN
ejpam-5710	196	4	.	.	PROPN
ejpam-5710	196	5	math	math	PROPN
ejpam-5710	196	6	,	,	PUNCT
ejpam-5710	196	7	18	18	NUM
ejpam-5710	196	8	(	(	PUNCT
ejpam-5710	196	9	1	1	NUM
ejpam-5710	196	10	)	)	PUNCT
ejpam-5710	196	11	(	(	PUNCT
ejpam-5710	196	12	2025	2025	NUM
ejpam-5710	196	13	)	)	PUNCT
ejpam-5710	196	14	,	,	PUNCT
ejpam-5710	196	15	5710	5710	NUM
ejpam-5710	196	16	10	10	NUM
ejpam-5710	196	17	of	of	ADP
ejpam-5710	196	18	18	18	NUM
ejpam-5710	196	19	(	(	PUNCT
ejpam-5710	196	20	b	b	NOUN
ejpam-5710	196	21	)	)	PUNCT
ejpam-5710	196	22	the	the	DET
ejpam-5710	196	23	curve	curve	NOUN
ejpam-5710	196	24	η(s	η(s	PROPN
ejpam-5710	196	25	)	)	PUNCT
ejpam-5710	196	26	is	be	AUX
ejpam-5710	196	27	an	an	DET
ejpam-5710	196	28	asymptotic	asymptotic	ADJ
ejpam-5710	196	29	line	line	NOUN
ejpam-5710	196	30	if	if	SCONJ
ejpam-5710	196	31	only	only	ADV
ejpam-5710	196	32	if	if	SCONJ
ejpam-5710	196	33	κ2	κ2	NOUN
ejpam-5710	196	34	=	=	SYM
ejpam-5710	196	35	0	0	NUM
ejpam-5710	196	36	or	or	CCONJ
ejpam-5710	196	37	κ1	κ1	NOUN
ejpam-5710	196	38	=	=	SYM
ejpam-5710	196	39	1	1	NUM
ejpam-5710	196	40	u	u	NOUN
ejpam-5710	196	41	.	.	PUNCT
ejpam-5710	197	1	(	(	PUNCT
ejpam-5710	197	2	c	c	X
ejpam-5710	197	3	)	)	PUNCT
ejpam-5710	197	4	the	the	DET
ejpam-5710	197	5	curve	curve	NOUN
ejpam-5710	197	6	η(s	η(s	PROPN
ejpam-5710	197	7	)	)	PUNCT
ejpam-5710	197	8	is	be	AUX
ejpam-5710	197	9	a	a	DET
ejpam-5710	197	10	principal	principal	ADJ
ejpam-5710	197	11	line	line	NOUN
ejpam-5710	197	12	if	if	SCONJ
ejpam-5710	197	13	and	and	CCONJ
ejpam-5710	197	14	only	only	ADV
ejpam-5710	197	15	if	if	SCONJ
ejpam-5710	197	16	κ2(s	κ2(s	NOUN
ejpam-5710	197	17	)	)	PUNCT
ejpam-5710	197	18	=	=	SYM
ejpam-5710	197	19	uκ1(s	uκ1(s	PROPN
ejpam-5710	197	20	)	)	PUNCT
ejpam-5710	197	21	(	(	PUNCT
ejpam-5710	197	22	dκ3(s	dκ3(s	PROPN
ejpam-5710	197	23	)	)	PUNCT
ejpam-5710	197	24	dt	dt	NOUN
ejpam-5710	197	25	+	+	CCONJ
ejpam-5710	197	26	uκ3(s	uκ3(s	NOUN
ejpam-5710	197	27	)	)	PUNCT
ejpam-5710	197	28	dκ1(s	dκ1(s	PROPN
ejpam-5710	197	29	)	)	PUNCT
ejpam-5710	197	30	dt	dt	NOUN
ejpam-5710	197	31	)	)	PUNCT
ejpam-5710	198	1	−	−	PUNCT
ejpam-5710	199	1	u2κ1(s	u2κ1(s	ADJ
ejpam-5710	199	2	)	)	PUNCT
ejpam-5710	199	3	2	2	NUM
ejpam-5710	199	4	dκ3(s	dκ3(	NOUN
ejpam-5710	199	5	)	)	PUNCT
ejpam-5710	199	6	dt	dt	PUNCT
ejpam-5710	199	7	−κ1(s	−κ1(s	PROPN
ejpam-5710	199	8	)	)	PUNCT
ejpam-5710	199	9	(	(	PUNCT
ejpam-5710	199	10	u2κ23(s	u2κ23(s	ADP
ejpam-5710	199	11	)	)	PUNCT
ejpam-5710	199	12	+	+	CCONJ
ejpam-5710	199	13	1	1	X
ejpam-5710	199	14	)	)	PUNCT
ejpam-5710	199	15	−	−	NOUN
ejpam-5710	199	16	u2κ1(s)3	u2κ1(s)3	ADJ
ejpam-5710	199	17	+	+	X
ejpam-5710	199	18	2uκ21(s	2uκ21(s	NUM
ejpam-5710	199	19	)	)	PUNCT
ejpam-5710	199	20	+	+	X
ejpam-5710	199	21	uκ23(s	uκ23(	NOUN
ejpam-5710	199	22	)	)	PUNCT
ejpam-5710	199	23	.	.	PUNCT
ejpam-5710	200	1	corollary	corollary	ADJ
ejpam-5710	200	2	3.4	3.4	NUM
ejpam-5710	200	3	.	.	PUNCT
ejpam-5710	201	1	(	(	PUNCT
ejpam-5710	201	2	a	a	X
ejpam-5710	201	3	)	)	PUNCT
ejpam-5710	201	4	the	the	DET
ejpam-5710	201	5	qnr	qnr	NOUN
ejpam-5710	201	6	-	-	PUNCT
ejpam-5710	201	7	surface	surface	NOUN
ejpam-5710	201	8	is	be	AUX
ejpam-5710	201	9	a	a	DET
ejpam-5710	201	10	flat	flat	ADJ
ejpam-5710	201	11	(	(	PUNCT
ejpam-5710	201	12	developable)surface	developable)surface	NOUN
ejpam-5710	201	13	if	if	SCONJ
ejpam-5710	201	14	and	and	CCONJ
ejpam-5710	201	15	only	only	ADV
ejpam-5710	201	16	if	if	SCONJ
ejpam-5710	201	17	κ3	κ3	PROPN
ejpam-5710	201	18	=	=	SYM
ejpam-5710	201	19	0	0	PROPN
ejpam-5710	201	20	.	.	PUNCT
ejpam-5710	202	1	(	(	PUNCT
ejpam-5710	202	2	b	b	X
ejpam-5710	202	3	)	)	PUNCT
ejpam-5710	202	4	a	a	DET
ejpam-5710	202	5	qnr	qnr	NOUN
ejpam-5710	202	6	-	-	PUNCT
ejpam-5710	202	7	surface	surface	NOUN
ejpam-5710	202	8	is	be	AUX
ejpam-5710	202	9	a	a	DET
ejpam-5710	202	10	minimal	minimal	ADJ
ejpam-5710	202	11	surface	surface	NOUN
ejpam-5710	202	12	if	if	SCONJ
ejpam-5710	202	13	and	and	CCONJ
ejpam-5710	202	14	only	only	ADV
ejpam-5710	202	15	if	if	SCONJ
ejpam-5710	202	16	κ2(s	κ2(s	NOUN
ejpam-5710	202	17	)	)	PUNCT
ejpam-5710	203	1	=	=	SYM
ejpam-5710	204	1	−	−	PROPN
ejpam-5710	204	2	u	u	NOUN
ejpam-5710	204	3	(	(	PUNCT
ejpam-5710	204	4	uκ3(s	uκ3(s	PROPN
ejpam-5710	204	5	)	)	PUNCT
ejpam-5710	204	6	dκ1(s	dκ1(s	PROPN
ejpam-5710	204	7	)	)	PUNCT
ejpam-5710	204	8	dt	dt	NOUN
ejpam-5710	205	1	+	+	CCONJ
ejpam-5710	205	2	dκ3(s	dκ3(	NOUN
ejpam-5710	205	3	)	)	PUNCT
ejpam-5710	205	4	dt	dt	X
ejpam-5710	205	5	(	(	PUNCT
ejpam-5710	205	6	1−	1−	NUM
ejpam-5710	205	7	uκ1(s	uκ1(s	PROPN
ejpam-5710	205	8	)	)	PUNCT
ejpam-5710	205	9	)	)	PUNCT
ejpam-5710	205	10	)	)	PUNCT
ejpam-5710	206	1	u2κ1(s)2	u2κ1(s)2	PROPN
ejpam-5710	207	1	+	+	CCONJ
ejpam-5710	207	2	u2κ3(s)2	u2κ3(s)2	PRON
ejpam-5710	207	3	−	−	NOUN
ejpam-5710	207	4	2uκ1(s	2uκ1(s	NUM
ejpam-5710	207	5	)	)	PUNCT
ejpam-5710	207	6	+	+	CCONJ
ejpam-5710	207	7	1	1	NUM
ejpam-5710	207	8	.	.	X
ejpam-5710	207	9	3.3	3.3	NUM
ejpam-5710	207	10	.	.	PUNCT
ejpam-5710	208	1	quasi	quasi	ADJ
ejpam-5710	208	2	-	-	ADJ
ejpam-5710	208	3	binormal	binormal	ADJ
ejpam-5710	208	4	ruled	rule	VERB
ejpam-5710	208	5	surfaces	surface	NOUN
ejpam-5710	208	6	according	accord	VERB
ejpam-5710	208	7	to	to	ADP
ejpam-5710	208	8	the	the	DET
ejpam-5710	208	9	quasi	quasi	ADJ
ejpam-5710	208	10	frame	frame	NOUN
ejpam-5710	208	11	in	in	ADP
ejpam-5710	208	12	this	this	DET
ejpam-5710	208	13	section	section	NOUN
ejpam-5710	208	14	,	,	PUNCT
ejpam-5710	208	15	we	we	PRON
ejpam-5710	208	16	define	define	VERB
ejpam-5710	208	17	the	the	DET
ejpam-5710	208	18	qbr	qbr	NOUN
ejpam-5710	208	19	-	-	PUNCT
ejpam-5710	208	20	surfaces	surface	NOUN
ejpam-5710	208	21	that	that	PRON
ejpam-5710	208	22	are	be	AUX
ejpam-5710	208	23	created	create	VERB
ejpam-5710	208	24	by	by	ADP
ejpam-5710	208	25	combining	combine	VERB
ejpam-5710	208	26	a	a	DET
ejpam-5710	208	27	regular	regular	ADJ
ejpam-5710	208	28	curve	curve	NOUN
ejpam-5710	208	29	(	(	PUNCT
ejpam-5710	208	30	referred	refer	VERB
ejpam-5710	208	31	to	to	ADP
ejpam-5710	208	32	as	as	ADP
ejpam-5710	208	33	the	the	DET
ejpam-5710	208	34	base	base	NOUN
ejpam-5710	208	35	curve	curve	NOUN
ejpam-5710	208	36	)	)	PUNCT
ejpam-5710	208	37	with	with	ADP
ejpam-5710	208	38	the	the	DET
ejpam-5710	208	39	quasi	quasi	ADJ
ejpam-5710	208	40	binormal	binormal	PROPN
ejpam-5710	208	41	vector	vector	PROPN
ejpam-5710	208	42	bq	bq	PROPN
ejpam-5710	208	43	,	,	PUNCT
ejpam-5710	208	44	which	which	PRON
ejpam-5710	208	45	determines	determine	VERB
ejpam-5710	208	46	the	the	DET
ejpam-5710	208	47	direction	direction	NOUN
ejpam-5710	208	48	.	.	PUNCT
ejpam-5710	209	1	additionally	additionally	ADV
ejpam-5710	209	2	,	,	PUNCT
ejpam-5710	209	3	we	we	PRON
ejpam-5710	209	4	explore	explore	VERB
ejpam-5710	209	5	and	and	CCONJ
ejpam-5710	209	6	discuss	discuss	VERB
ejpam-5710	209	7	the	the	DET
ejpam-5710	209	8	fundamental	fundamental	ADJ
ejpam-5710	209	9	properties	property	NOUN
ejpam-5710	209	10	associated	associate	VERB
ejpam-5710	209	11	with	with	ADP
ejpam-5710	209	12	this	this	DET
ejpam-5710	209	13	particular	particular	ADJ
ejpam-5710	209	14	type	type	NOUN
ejpam-5710	209	15	of	of	ADP
ejpam-5710	209	16	ruled	rule	VERB
ejpam-5710	209	17	surface	surface	NOUN
ejpam-5710	209	18	.	.	PUNCT
ejpam-5710	210	1	definition	definition	NOUN
ejpam-5710	210	2	3.3	3.3	NUM
ejpam-5710	210	3	.	.	PUNCT
ejpam-5710	211	1	let	let	VERB
ejpam-5710	211	2	γ(s	γ(	NOUN
ejpam-5710	211	3	)	)	PUNCT
ejpam-5710	211	4	be	be	AUX
ejpam-5710	211	5	a	a	DET
ejpam-5710	211	6	regular	regular	ADJ
ejpam-5710	211	7	curve	curve	NOUN
ejpam-5710	211	8	with	with	ADP
ejpam-5710	211	9	quasi	quasi	ADJ
ejpam-5710	211	10	frame	frame	NOUN
ejpam-5710	211	11	{	{	PUNCT
ejpam-5710	211	12	tq	tq	NOUN
ejpam-5710	211	13	,	,	PUNCT
ejpam-5710	211	14	nq	nq	PROPN
ejpam-5710	211	15	,	,	PUNCT
ejpam-5710	211	16	bq	bq	NOUN
ejpam-5710	211	17	}	}	PUNCT
ejpam-5710	211	18	.	.	PUNCT
ejpam-5710	212	1	then	then	ADV
ejpam-5710	212	2	the	the	DET
ejpam-5710	212	3	parametric	parametric	ADJ
ejpam-5710	212	4	representations	representation	NOUN
ejpam-5710	212	5	of	of	ADP
ejpam-5710	212	6	the	the	DET
ejpam-5710	212	7	qbr	qbr	ADJ
ejpam-5710	212	8	-	-	PUNCT
ejpam-5710	212	9	surface	surface	NOUN
ejpam-5710	212	10	wb(s	wb(	NOUN
ejpam-5710	212	11	,	,	PUNCT
ejpam-5710	212	12	u	u	NOUN
ejpam-5710	212	13	)	)	PUNCT
ejpam-5710	212	14	with	with	ADP
ejpam-5710	212	15	the	the	DET
ejpam-5710	212	16	ruling	rule	VERB
ejpam-5710	212	17	u	u	NOUN
ejpam-5710	212	18	is	be	AUX
ejpam-5710	212	19	given	give	VERB
ejpam-5710	212	20	by	by	ADP
ejpam-5710	212	21	wb(s	wb(	NOUN
ejpam-5710	212	22	,	,	PUNCT
ejpam-5710	212	23	u	u	NOUN
ejpam-5710	212	24	)	)	PUNCT
ejpam-5710	212	25	=	=	SYM
ejpam-5710	212	26	γ(s	γ(	NOUN
ejpam-5710	212	27	)	)	PUNCT
ejpam-5710	213	1	+	+	CCONJ
ejpam-5710	213	2	u	u	NOUN
ejpam-5710	213	3	bq(s	bq(s	NOUN
ejpam-5710	213	4	)	)	PUNCT
ejpam-5710	213	5	.	.	PUNCT
ejpam-5710	214	1	(	(	PUNCT
ejpam-5710	214	2	3.13	3.13	NUM
ejpam-5710	214	3	)	)	PUNCT
ejpam-5710	214	4	the	the	DET
ejpam-5710	214	5	theories	theory	NOUN
ejpam-5710	214	6	presented	present	VERB
ejpam-5710	214	7	in	in	ADP
ejpam-5710	214	8	this	this	DET
ejpam-5710	214	9	section	section	NOUN
ejpam-5710	214	10	are	be	AUX
ejpam-5710	214	11	built	build	VERB
ejpam-5710	214	12	upon	upon	SCONJ
ejpam-5710	214	13	the	the	DET
ejpam-5710	214	14	same	same	ADJ
ejpam-5710	214	15	foundational	foundational	ADJ
ejpam-5710	214	16	evidence	evidence	NOUN
ejpam-5710	214	17	as	as	ADP
ejpam-5710	214	18	those	those	PRON
ejpam-5710	214	19	discussed	discuss	VERB
ejpam-5710	214	20	in	in	ADP
ejpam-5710	214	21	the	the	DET
ejpam-5710	214	22	first	first	ADJ
ejpam-5710	214	23	section	section	NOUN
ejpam-5710	214	24	.	.	PUNCT
ejpam-5710	215	1	theorem	theorem	VERB
ejpam-5710	215	2	3.13	3.13	NUM
ejpam-5710	215	3	.	.	PUNCT
ejpam-5710	216	1	the	the	DET
ejpam-5710	216	2	striction	striction	NOUN
ejpam-5710	216	3	curve	curve	NOUN
ejpam-5710	216	4	of	of	ADP
ejpam-5710	216	5	the	the	DET
ejpam-5710	216	6	quasi	quasi	ADJ
ejpam-5710	216	7	-	-	ADJ
ejpam-5710	216	8	binormal	binormal	ADJ
ejpam-5710	216	9	ruled	rule	VERB
ejpam-5710	216	10	surface	surface	NOUN
ejpam-5710	216	11	is	be	AUX
ejpam-5710	216	12	given	give	VERB
ejpam-5710	216	13	by	by	ADP
ejpam-5710	216	14	γ∗(s	γ∗(s	PROPN
ejpam-5710	216	15	)	)	PUNCT
ejpam-5710	216	16	=	=	SYM
ejpam-5710	216	17	γ(s)−	γ(s)−	PROPN
ejpam-5710	216	18	κ2	κ2	NOUN
ejpam-5710	216	19	κ22	κ22	NOUN
ejpam-5710	216	20	+	+	CCONJ
ejpam-5710	216	21	κ32	κ32	PROPN
ejpam-5710	216	22	bq	bq	PROPN
ejpam-5710	216	23	.	.	PUNCT
ejpam-5710	216	24	theorem	theorem	VERB
ejpam-5710	216	25	3.14	3.14	NUM
ejpam-5710	216	26	.	.	PUNCT
ejpam-5710	217	1	the	the	DET
ejpam-5710	217	2	first	first	ADJ
ejpam-5710	217	3	fundamental	fundamental	ADJ
ejpam-5710	217	4	form	form	NOUN
ejpam-5710	217	5	of	of	ADP
ejpam-5710	217	6	the	the	DET
ejpam-5710	217	7	quasi	quasi	ADJ
ejpam-5710	217	8	-	-	ADJ
ejpam-5710	217	9	binormal	binormal	ADJ
ejpam-5710	217	10	ruled	rule	VERB
ejpam-5710	217	11	surface	surface	NOUN
ejpam-5710	217	12	wb(s	wb(	NOUN
ejpam-5710	217	13	,	,	PUNCT
ejpam-5710	217	14	u	u	NOUN
ejpam-5710	217	15	)	)	PUNCT
ejpam-5710	217	16	is	be	AUX
ejpam-5710	217	17	given	give	VERB
ejpam-5710	217	18	by	by	ADP
ejpam-5710	217	19	i	i	PRON
ejpam-5710	217	20	=	=	PUNCT
ejpam-5710	217	21	(	(	PUNCT
ejpam-5710	217	22	u2κ3	u2κ3	PROPN
ejpam-5710	217	23	2	2	NUM
ejpam-5710	217	24	+	+	CCONJ
ejpam-5710	217	25	(	(	PUNCT
ejpam-5710	217	26	1−	1−	NUM
ejpam-5710	217	27	u	u	PROPN
ejpam-5710	217	28	κ2	κ2	NOUN
ejpam-5710	217	29	2))(ds)2	2))(ds)2	PROPN
ejpam-5710	217	30	+	+	CCONJ
ejpam-5710	217	31	(	(	PUNCT
ejpam-5710	217	32	du)2	du)2	NOUN
ejpam-5710	217	33	,	,	PUNCT
ejpam-5710	217	34	theorem	theorem	VERB
ejpam-5710	217	35	3.15	3.15	NUM
ejpam-5710	217	36	.	.	PUNCT
ejpam-5710	218	1	the	the	DET
ejpam-5710	218	2	second	second	ADJ
ejpam-5710	218	3	fundamental	fundamental	ADJ
ejpam-5710	218	4	form	form	NOUN
ejpam-5710	218	5	of	of	ADP
ejpam-5710	218	6	the	the	DET
ejpam-5710	218	7	quasi	quasi	ADJ
ejpam-5710	218	8	-	-	ADJ
ejpam-5710	218	9	binormal	binormal	ADJ
ejpam-5710	218	10	ruled	rule	VERB
ejpam-5710	218	11	surface	surface	NOUN
ejpam-5710	218	12	wb(s	wb(	NOUN
ejpam-5710	218	13	,	,	PUNCT
ejpam-5710	218	14	u	u	NOUN
ejpam-5710	218	15	)	)	PUNCT
ejpam-5710	218	16	is	be	AUX
ejpam-5710	218	17	given	give	VERB
ejpam-5710	218	18	by	by	ADP
ejpam-5710	218	19	ii	ii	PROPN
ejpam-5710	218	20	=	=	SYM
ejpam-5710	218	21	(	(	PUNCT
ejpam-5710	218	22	−κ1	−κ1	PROPN
ejpam-5710	218	23	(	(	PUNCT
ejpam-5710	218	24	u2κ3	u2κ3	PROPN
ejpam-5710	218	25	2	2	NUM
ejpam-5710	218	26	+	+	CCONJ
ejpam-5710	218	27	(	(	PUNCT
ejpam-5710	218	28	1−	1−	NUM
ejpam-5710	218	29	u	u	PROPN
ejpam-5710	218	30	κ2	κ2	NOUN
ejpam-5710	218	31	2	2	NUM
ejpam-5710	218	32	)	)	PUNCT
ejpam-5710	219	1	+	+	CCONJ
ejpam-5710	219	2	u	u	NOUN
ejpam-5710	219	3	(	(	PUNCT
ejpam-5710	219	4	uκ3κ2	uκ3κ2	ADV
ejpam-5710	219	5	′	′	NUM
ejpam-5710	220	1	+	+	CCONJ
ejpam-5710	220	2	κ3	κ3	PROPN
ejpam-5710	220	3	′(1−	′(1−	NOUN
ejpam-5710	220	4	uκ2))√	uκ2))√	PROPN
ejpam-5710	220	5	u2κ32	u2κ32	NOUN
ejpam-5710	221	1	+	+	CCONJ
ejpam-5710	221	2	(	(	PUNCT
ejpam-5710	221	3	1−	1−	NUM
ejpam-5710	221	4	u	u	NOUN
ejpam-5710	221	5	κ2)2	κ2)2	X
ejpam-5710	221	6	)	)	PUNCT
ejpam-5710	221	7	(	(	PUNCT
ejpam-5710	221	8	ds)2	ds)2	NOUN
ejpam-5710	221	9	+	+	PROPN
ejpam-5710	221	10	2κ3√	2κ3√	NUM
ejpam-5710	221	11	u2κ32	u2κ32	NOUN
ejpam-5710	221	12	+	+	CCONJ
ejpam-5710	221	13	(	(	PUNCT
ejpam-5710	221	14	1−	1−	NUM
ejpam-5710	221	15	u	u	NOUN
ejpam-5710	221	16	κ2)2	κ2)2	X
ejpam-5710	221	17	ds	ds	PROPN
ejpam-5710	221	18	du	du	X
ejpam-5710	221	19	,	,	PUNCT
ejpam-5710	221	20	a.	a.	NOUN
ejpam-5710	221	21	elsharkawy	elsharkawy	PROPN
ejpam-5710	221	22	,	,	PUNCT
ejpam-5710	221	23	h.	h.	PROPN
ejpam-5710	221	24	k.	k.	PROPN
ejpam-5710	221	25	elsayied	elsayied	PROPN
ejpam-5710	221	26	,	,	PUNCT
ejpam-5710	221	27	a.	a.	NOUN
ejpam-5710	221	28	refaat	refaat	PROPN
ejpam-5710	221	29	/	/	SYM
ejpam-5710	221	30	eur	eur	PROPN
ejpam-5710	221	31	.	.	PUNCT
ejpam-5710	222	1	j.	j.	PROPN
ejpam-5710	222	2	pure	pure	PROPN
ejpam-5710	222	3	appl	appl	PROPN
ejpam-5710	222	4	.	.	PROPN
ejpam-5710	222	5	math	math	PROPN
ejpam-5710	222	6	,	,	PUNCT
ejpam-5710	222	7	18	18	NUM
ejpam-5710	222	8	(	(	PUNCT
ejpam-5710	222	9	1	1	NUM
ejpam-5710	222	10	)	)	PUNCT
ejpam-5710	222	11	(	(	PUNCT
ejpam-5710	222	12	2025	2025	NUM
ejpam-5710	222	13	)	)	PUNCT
ejpam-5710	222	14	,	,	PUNCT
ejpam-5710	222	15	5710	5710	NUM
ejpam-5710	222	16	11	11	NUM
ejpam-5710	222	17	of	of	ADP
ejpam-5710	222	18	18	18	NUM
ejpam-5710	222	19	theorem	theorem	VERB
ejpam-5710	222	20	3.16	3.16	NUM
ejpam-5710	222	21	.	.	PUNCT
ejpam-5710	223	1	the	the	DET
ejpam-5710	223	2	third	third	ADJ
ejpam-5710	223	3	fundamental	fundamental	ADJ
ejpam-5710	223	4	form	form	NOUN
ejpam-5710	223	5	of	of	ADP
ejpam-5710	223	6	the	the	DET
ejpam-5710	223	7	quasi	quasi	ADJ
ejpam-5710	223	8	-	-	ADJ
ejpam-5710	223	9	binormal	binormal	ADJ
ejpam-5710	223	10	ruled	rule	VERB
ejpam-5710	223	11	surface	surface	NOUN
ejpam-5710	223	12	wb(s	wb(	NOUN
ejpam-5710	223	13	,	,	PUNCT
ejpam-5710	223	14	u	u	NOUN
ejpam-5710	223	15	)	)	PUNCT
ejpam-5710	223	16	is	be	AUX
ejpam-5710	223	17	given	give	VERB
ejpam-5710	223	18	by	by	ADP
ejpam-5710	223	19	iii	iii	X
ejpam-5710	223	20	=	=	SYM
ejpam-5710	223	21	e(ds)2	e(ds)2	PROPN
ejpam-5710	223	22	+	+	NUM
ejpam-5710	223	23	2f	2f	NUM
ejpam-5710	223	24	dsdu+	dsdu+	NOUN
ejpam-5710	223	25	g(du)2	g(du)2	NUM
ejpam-5710	223	26	.	.	PUNCT
ejpam-5710	224	1	where	where	SCONJ
ejpam-5710	224	2	e	e	X
ejpam-5710	224	3	=	=	AUX
ejpam-5710	224	4	<	<	X
ejpam-5710	224	5	nn	nn	X
ejpam-5710	224	6	s	s	PROPN
ejpam-5710	224	7	,	,	PUNCT
ejpam-5710	224	8	n	n	CCONJ
ejpam-5710	224	9	n	n	PROPN
ejpam-5710	224	10	s	s	PART
ejpam-5710	224	11	>	>	X
ejpam-5710	224	12	=	=	SYM
ejpam-5710	224	13	κ23	κ23	PROPN
ejpam-5710	224	14	(	(	PUNCT
ejpam-5710	224	15	u4κ2	u4κ2	X
ejpam-5710	224	16	′2	′2	X
ejpam-5710	224	17	+	+	CCONJ
ejpam-5710	224	18	(	(	PUNCT
ejpam-5710	224	19	1−	1−	NUM
ejpam-5710	224	20	uκ2	uκ2	NOUN
ejpam-5710	224	21	)	)	PUNCT
ejpam-5710	224	22	2	2	NUM
ejpam-5710	224	23	)	)	PUNCT
ejpam-5710	224	24	+	+	CCONJ
ejpam-5710	224	25	2u3κ3κ2	2u3κ3κ2	NUM
ejpam-5710	224	26	′κ3	′κ3	ADJ
ejpam-5710	224	27	′(1−	′(1−	NOUN
ejpam-5710	224	28	uκ2	uκ2	NOUN
ejpam-5710	224	29	)	)	PUNCT
ejpam-5710	224	30	(	(	PUNCT
ejpam-5710	224	31	u2κ32	u2κ32	X
ejpam-5710	224	32	+	+	CCONJ
ejpam-5710	224	33	(	(	PUNCT
ejpam-5710	224	34	1−	1−	NUM
ejpam-5710	224	35	uκ2)2	uκ2)2	PROPN
ejpam-5710	224	36	)	)	PUNCT
ejpam-5710	224	37	2	2	NUM
ejpam-5710	224	38	−	−	NOUN
ejpam-5710	224	39	2uκ1	2uκ1	NUM
ejpam-5710	224	40	(	(	PUNCT
ejpam-5710	224	41	u2κ23	u2κ23	ADP
ejpam-5710	224	42	+	+	CCONJ
ejpam-5710	224	43	(	(	PUNCT
ejpam-5710	224	44	1−	1−	NUM
ejpam-5710	224	45	uκ2	uκ2	NOUN
ejpam-5710	224	46	)	)	PUNCT
ejpam-5710	224	47	2	2	NUM
ejpam-5710	224	48	)	)	PUNCT
ejpam-5710	224	49	(	(	PUNCT
ejpam-5710	224	50	uκ3κ2	uκ3κ2	ADV
ejpam-5710	224	51	′	′	NOUN
ejpam-5710	225	1	+	+	CCONJ
ejpam-5710	225	2	κ3	κ3	PROPN
ejpam-5710	225	3	′(1−	′(1−	ADJ
ejpam-5710	225	4	uκ2	uκ2	NOUN
ejpam-5710	225	5	)	)	PUNCT
ejpam-5710	225	6	)	)	PUNCT
ejpam-5710	226	1	(	(	PUNCT
ejpam-5710	226	2	u2κ32	u2κ32	X
ejpam-5710	226	3	+	+	CCONJ
ejpam-5710	226	4	(	(	PUNCT
ejpam-5710	226	5	1−	1−	NUM
ejpam-5710	226	6	uκ2)2	uκ2)2	PROPN
ejpam-5710	226	7	)	)	PUNCT
ejpam-5710	226	8	2	2	NUM
ejpam-5710	227	1	+	+	X
ejpam-5710	227	2	κ21	κ21	NOUN
ejpam-5710	227	3	(	(	PUNCT
ejpam-5710	227	4	u2κ23	u2κ23	ADP
ejpam-5710	227	5	+	+	CCONJ
ejpam-5710	227	6	(	(	PUNCT
ejpam-5710	227	7	1−	1−	NUM
ejpam-5710	227	8	uκ2	uκ2	NOUN
ejpam-5710	227	9	)	)	PUNCT
ejpam-5710	227	10	2	2	NUM
ejpam-5710	227	11	)	)	SYM
ejpam-5710	227	12	2	2	NUM
ejpam-5710	227	13	+	+	CCONJ
ejpam-5710	227	14	u2κ3	u2κ3	PROPN
ejpam-5710	227	15	′2(1−	′2(1−	PROPN
ejpam-5710	227	16	uκ2	uκ2	NOUN
ejpam-5710	227	17	)	)	PUNCT
ejpam-5710	227	18	2	2	NUM
ejpam-5710	227	19	+	+	CCONJ
ejpam-5710	227	20	u2κ43	u2κ43	NOUN
ejpam-5710	227	21	(	(	PUNCT
ejpam-5710	227	22	u2κ32	u2κ32	NOUN
ejpam-5710	227	23	+	+	CCONJ
ejpam-5710	227	24	(	(	PUNCT
ejpam-5710	227	25	1−	1−	NUM
ejpam-5710	227	26	uκ2)2	uκ2)2	PROPN
ejpam-5710	227	27	)	)	PUNCT
ejpam-5710	227	28	2	2	NUM
ejpam-5710	227	29	=	=	SYM
ejpam-5710	227	30	l2	l2	NOUN
ejpam-5710	227	31	e	e	NOUN
ejpam-5710	227	32	+	+	CCONJ
ejpam-5710	227	33	m2	m2	PROPN
ejpam-5710	227	34	,	,	PUNCT
ejpam-5710	227	35	f	f	X
ejpam-5710	228	1	=	=	X
ejpam-5710	228	2	<	<	X
ejpam-5710	228	3	nn	nn	X
ejpam-5710	228	4	s	s	PROPN
ejpam-5710	228	5	,	,	PUNCT
ejpam-5710	228	6	n	n	CCONJ
ejpam-5710	228	7	n	n	PRON
ejpam-5710	228	8	u	u	NOUN
ejpam-5710	228	9	>	>	X
ejpam-5710	228	10	=	=	PROPN
ejpam-5710	228	11	κ3	κ3	PROPN
ejpam-5710	228	12	(	(	PUNCT
ejpam-5710	228	13	κ1	κ1	NOUN
ejpam-5710	228	14	(	(	PUNCT
ejpam-5710	228	15	u2κ23	u2κ23	ADP
ejpam-5710	228	16	+	+	CCONJ
ejpam-5710	228	17	(	(	PUNCT
ejpam-5710	228	18	1−	1−	NUM
ejpam-5710	228	19	uκ2	uκ2	NOUN
ejpam-5710	228	20	)	)	PUNCT
ejpam-5710	228	21	2	2	NUM
ejpam-5710	228	22	)	)	PUNCT
ejpam-5710	228	23	+	+	CCONJ
ejpam-5710	228	24	u	u	NOUN
ejpam-5710	228	25	(	(	PUNCT
ejpam-5710	228	26	uκ3κ2	uκ3κ2	ADV
ejpam-5710	228	27	′	′	NUM
ejpam-5710	228	28	+	+	CCONJ
ejpam-5710	228	29	κ3	κ3	PROPN
ejpam-5710	228	30	′(1−	′(1−	ADJ
ejpam-5710	228	31	uκ2	uκ2	NOUN
ejpam-5710	228	32	)	)	PUNCT
ejpam-5710	228	33	)	)	PUNCT
ejpam-5710	228	34	)	)	PUNCT
ejpam-5710	229	1	(	(	PUNCT
ejpam-5710	229	2	u2κ32	u2κ32	X
ejpam-5710	229	3	+	+	CCONJ
ejpam-5710	229	4	(	(	PUNCT
ejpam-5710	229	5	1−	1−	NUM
ejpam-5710	229	6	uκ2)2	uκ2)2	PROPN
ejpam-5710	229	7	)	)	PUNCT
ejpam-5710	229	8	2	2	NUM
ejpam-5710	229	9	=	=	SYM
ejpam-5710	229	10	lm	lm	X
ejpam-5710	229	11	e	e	NOUN
ejpam-5710	229	12	,	,	PUNCT
ejpam-5710	229	13	g	g	PROPN
ejpam-5710	229	14	=	=	PROPN
ejpam-5710	229	15	<	<	X
ejpam-5710	229	16	nn	nn	X
ejpam-5710	229	17	u	u	PROPN
ejpam-5710	229	18	,	,	PUNCT
ejpam-5710	229	19	n	n	CCONJ
ejpam-5710	229	20	n	n	PRON
ejpam-5710	229	21	u	u	NOUN
ejpam-5710	229	22	>	>	X
ejpam-5710	229	23	=	=	SYM
ejpam-5710	229	24	κ23	κ23	NOUN
ejpam-5710	229	25	(	(	PUNCT
ejpam-5710	229	26	u2κ32	u2κ32	SYM
ejpam-5710	229	27	+	+	CCONJ
ejpam-5710	229	28	(	(	PUNCT
ejpam-5710	229	29	1−	1−	NUM
ejpam-5710	229	30	uκ2)2	uκ2)2	PROPN
ejpam-5710	229	31	)	)	PUNCT
ejpam-5710	229	32	2	2	NUM
ejpam-5710	229	33	=	=	SYM
ejpam-5710	229	34	m2	m2	PROPN
ejpam-5710	229	35	e	e	PROPN
ejpam-5710	229	36	.	.	PUNCT
ejpam-5710	229	37	theorem	theorem	VERB
ejpam-5710	229	38	3.17	3.17	NUM
ejpam-5710	229	39	.	.	PUNCT
ejpam-5710	230	1	the	the	DET
ejpam-5710	230	2	gaussian	gaussian	ADJ
ejpam-5710	230	3	curvature	curvature	NOUN
ejpam-5710	230	4	k	k	PROPN
ejpam-5710	230	5	and	and	CCONJ
ejpam-5710	230	6	the	the	DET
ejpam-5710	230	7	mean	mean	ADJ
ejpam-5710	230	8	curvature	curvature	NOUN
ejpam-5710	230	9	h	h	NOUN
ejpam-5710	230	10	of	of	ADP
ejpam-5710	230	11	the	the	DET
ejpam-5710	230	12	quasibinormal	quasibinormal	PROPN
ejpam-5710	230	13	ruled	rule	VERB
ejpam-5710	230	14	surface	surface	NOUN
ejpam-5710	230	15	wb(s	wb(	NOUN
ejpam-5710	230	16	,	,	PUNCT
ejpam-5710	230	17	u	u	NOUN
ejpam-5710	230	18	)	)	PUNCT
ejpam-5710	230	19	are	be	AUX
ejpam-5710	230	20	given	give	VERB
ejpam-5710	230	21	,	,	PUNCT
ejpam-5710	230	22	respectively	respectively	ADV
ejpam-5710	230	23	,	,	PUNCT
ejpam-5710	230	24	by	by	ADP
ejpam-5710	230	25	k	k	X
ejpam-5710	230	26	=	=	SYM
ejpam-5710	230	27	−m2	−m2	NOUN
ejpam-5710	230	28	e	e	NOUN
ejpam-5710	230	29	=	=	SYM
ejpam-5710	230	30	−κ3	−κ3	PROPN
ejpam-5710	230	31	2	2	NUM
ejpam-5710	230	32	(	(	PUNCT
ejpam-5710	230	33	u2κ32	u2κ32	NOUN
ejpam-5710	231	1	+	+	CCONJ
ejpam-5710	231	2	(	(	PUNCT
ejpam-5710	231	3	1−	1−	NUM
ejpam-5710	231	4	uκ2)2	uκ2)2	PROPN
ejpam-5710	231	5	)	)	PUNCT
ejpam-5710	231	6	2	2	NUM
ejpam-5710	231	7	,	,	PUNCT
ejpam-5710	231	8	h	h	NOUN
ejpam-5710	231	9	=	=	SYM
ejpam-5710	231	10	l	l	NOUN
ejpam-5710	231	11	2e	2e	NOUN
ejpam-5710	231	12	=	=	SYM
ejpam-5710	231	13	−κ1	−κ1	NOUN
ejpam-5710	231	14	(	(	PUNCT
ejpam-5710	231	15	u2κ23	u2κ23	ADP
ejpam-5710	231	16	+	+	CCONJ
ejpam-5710	231	17	(	(	PUNCT
ejpam-5710	231	18	1−	1−	NUM
ejpam-5710	231	19	uκ2	uκ2	NOUN
ejpam-5710	231	20	)	)	PUNCT
ejpam-5710	231	21	2	2	NUM
ejpam-5710	231	22	)	)	PUNCT
ejpam-5710	232	1	+	+	CCONJ
ejpam-5710	232	2	u	u	NOUN
ejpam-5710	232	3	(	(	PUNCT
ejpam-5710	232	4	uκ3κ2	uκ3κ2	ADV
ejpam-5710	232	5	′	′	NUM
ejpam-5710	233	1	+	+	CCONJ
ejpam-5710	233	2	κ3	κ3	PROPN
ejpam-5710	233	3	′(1−	′(1−	ADJ
ejpam-5710	233	4	uκ2	uκ2	NOUN
ejpam-5710	233	5	)	)	PUNCT
ejpam-5710	233	6	)	)	PUNCT
ejpam-5710	233	7	2	2	NUM
ejpam-5710	233	8	(	(	PUNCT
ejpam-5710	233	9	u2κ23	u2κ23	ADP
ejpam-5710	233	10	+	+	CCONJ
ejpam-5710	233	11	(	(	PUNCT
ejpam-5710	233	12	1−	1−	NUM
ejpam-5710	233	13	uκ2)2	uκ2)2	PROPN
ejpam-5710	233	14	)	)	PUNCT
ejpam-5710	233	15	3/2	3/2	NUM
ejpam-5710	233	16	.	.	PUNCT
ejpam-5710	233	17	theorem	theorem	VERB
ejpam-5710	233	18	3.18	3.18	NUM
ejpam-5710	233	19	.	.	PUNCT
ejpam-5710	234	1	the	the	DET
ejpam-5710	234	2	geodesic	geodesic	ADJ
ejpam-5710	234	3	curvature	curvature	NOUN
ejpam-5710	234	4	κg	κg	PROPN
ejpam-5710	234	5	,	,	PUNCT
ejpam-5710	234	6	the	the	DET
ejpam-5710	234	7	normal	normal	ADJ
ejpam-5710	234	8	curvature	curvature	NOUN
ejpam-5710	234	9	κn	κn	NOUN
ejpam-5710	234	10	and	and	CCONJ
ejpam-5710	234	11	the	the	DET
ejpam-5710	234	12	geodesic	geodesic	ADJ
ejpam-5710	234	13	torsion	torsion	NOUN
ejpam-5710	234	14	τg	τg	ADP
ejpam-5710	234	15	which	which	PRON
ejpam-5710	234	16	associate	associate	VERB
ejpam-5710	234	17	the	the	DET
ejpam-5710	234	18	base	base	NOUN
ejpam-5710	234	19	curve	curve	NOUN
ejpam-5710	234	20	on	on	ADP
ejpam-5710	234	21	the	the	DET
ejpam-5710	234	22	quasi	quasi	ADJ
ejpam-5710	234	23	-	-	ADJ
ejpam-5710	234	24	binormal	binormal	ADJ
ejpam-5710	234	25	ruled	rule	VERB
ejpam-5710	234	26	surface	surface	NOUN
ejpam-5710	234	27	wb(s	wb(	NOUN
ejpam-5710	234	28	,	,	PUNCT
ejpam-5710	234	29	u	u	NOUN
ejpam-5710	234	30	)	)	PUNCT
ejpam-5710	234	31	are	be	AUX
ejpam-5710	234	32	given	give	VERB
ejpam-5710	234	33	,	,	PUNCT
ejpam-5710	234	34	respectively	respectively	ADV
ejpam-5710	234	35	,	,	PUNCT
ejpam-5710	234	36	by	by	ADP
ejpam-5710	234	37	κg	κg	X
ejpam-5710	234	38	=	=	SYM
ejpam-5710	234	39	κ2(1−	κ2(1−	PROPN
ejpam-5710	234	40	uκ2)√	uκ2)√	NOUN
ejpam-5710	234	41	u2κ23	u2κ23	ADP
ejpam-5710	234	42	+	+	CCONJ
ejpam-5710	234	43	(	(	PUNCT
ejpam-5710	234	44	1−	1−	NUM
ejpam-5710	234	45	uκ2)2	uκ2)2	PROPN
ejpam-5710	234	46	,	,	PUNCT
ejpam-5710	234	47	κn	κn	NOUN
ejpam-5710	234	48	=	=	PUNCT
ejpam-5710	234	49	−κ1(1−	−κ1(1−	ADJ
ejpam-5710	234	50	uκ2)√	uκ2)√	NOUN
ejpam-5710	234	51	u2κ23	u2κ23	ADP
ejpam-5710	234	52	+	+	CCONJ
ejpam-5710	234	53	(	(	PUNCT
ejpam-5710	234	54	1−	1−	NUM
ejpam-5710	234	55	uκ2)2	uκ2)2	PROPN
ejpam-5710	234	56	,	,	PUNCT
ejpam-5710	234	57	τg	τg	NOUN
ejpam-5710	234	58	=	=	SYM
ejpam-5710	234	59	−κ2	−κ2	PROPN
ejpam-5710	234	60	(	(	PUNCT
ejpam-5710	234	61	κ1	κ1	NOUN
ejpam-5710	234	62	(	(	PUNCT
ejpam-5710	234	63	u2κ23	u2κ23	ADP
ejpam-5710	234	64	+	+	CCONJ
ejpam-5710	234	65	1	1	NUM
ejpam-5710	234	66	)	)	PUNCT
ejpam-5710	235	1	+	+	CCONJ
ejpam-5710	235	2	u	u	SYM
ejpam-5710	235	3	(	(	PUNCT
ejpam-5710	235	4	κ3	κ3	PROPN
ejpam-5710	235	5	′	′	NOUN
ejpam-5710	235	6	+	+	CCONJ
ejpam-5710	235	7	uκ3κ2	uκ3κ2	PROPN
ejpam-5710	235	8	′	′	NUM
ejpam-5710	235	9	)	)	PUNCT
ejpam-5710	235	10	)	)	PUNCT
ejpam-5710	236	1	−	−	ADP
ejpam-5710	236	2	u2κ32κ1	u2κ32κ1	NOUN
ejpam-5710	236	3	+	+	X
ejpam-5710	237	1	uκ22	uκ22	PROPN
ejpam-5710	237	2	(	(	PUNCT
ejpam-5710	237	3	2κ1	2κ1	NUM
ejpam-5710	237	4	+	+	CCONJ
ejpam-5710	237	5	uκ3	uκ3	PROPN
ejpam-5710	237	6	′	′	NUM
ejpam-5710	237	7	)	)	PUNCT
ejpam-5710	238	1	+	+	CCONJ
ejpam-5710	239	1	uκ1κ	uκ1κ	ADJ
ejpam-5710	239	2	2	2	NUM
ejpam-5710	239	3	3	3	NUM
ejpam-5710	239	4	u2κ23	u2κ23	ADP
ejpam-5710	239	5	+	+	CCONJ
ejpam-5710	239	6	(	(	PUNCT
ejpam-5710	239	7	1−	1−	NUM
ejpam-5710	239	8	uκ2)2	uκ2)2	PROPN
ejpam-5710	239	9	.	.	PUNCT
ejpam-5710	239	10	a.	a.	NOUN
ejpam-5710	239	11	elsharkawy	elsharkawy	PROPN
ejpam-5710	239	12	,	,	PUNCT
ejpam-5710	239	13	h.	h.	PROPN
ejpam-5710	239	14	k.	k.	PROPN
ejpam-5710	239	15	elsayied	elsayied	PROPN
ejpam-5710	239	16	,	,	PUNCT
ejpam-5710	239	17	a.	a.	NOUN
ejpam-5710	239	18	refaat	refaat	PROPN
ejpam-5710	239	19	/	/	SYM
ejpam-5710	239	20	eur	eur	PROPN
ejpam-5710	239	21	.	.	PUNCT
ejpam-5710	240	1	j.	j.	PROPN
ejpam-5710	240	2	pure	pure	PROPN
ejpam-5710	240	3	appl	appl	PROPN
ejpam-5710	240	4	.	.	PROPN
ejpam-5710	240	5	math	math	PROPN
ejpam-5710	240	6	,	,	PUNCT
ejpam-5710	240	7	18	18	NUM
ejpam-5710	240	8	(	(	PUNCT
ejpam-5710	240	9	1	1	NUM
ejpam-5710	240	10	)	)	PUNCT
ejpam-5710	240	11	(	(	PUNCT
ejpam-5710	240	12	2025	2025	NUM
ejpam-5710	240	13	)	)	PUNCT
ejpam-5710	240	14	,	,	PUNCT
ejpam-5710	240	15	5710	5710	NUM
ejpam-5710	240	16	12	12	NUM
ejpam-5710	240	17	of	of	ADP
ejpam-5710	240	18	18	18	NUM
ejpam-5710	240	19	corollary	corollary	ADJ
ejpam-5710	240	20	3.5	3.5	NUM
ejpam-5710	240	21	.	.	PUNCT
ejpam-5710	241	1	let	let	VERB
ejpam-5710	241	2	γ(s	γ(	NOUN
ejpam-5710	241	3	)	)	PUNCT
ejpam-5710	241	4	be	be	AUX
ejpam-5710	241	5	a	a	DET
ejpam-5710	241	6	regular	regular	ADJ
ejpam-5710	241	7	curve	curve	NOUN
ejpam-5710	241	8	lying	lie	VERB
ejpam-5710	241	9	on	on	ADP
ejpam-5710	241	10	a	a	DET
ejpam-5710	241	11	surface	surface	NOUN
ejpam-5710	241	12	wn	wn	NOUN
ejpam-5710	241	13	(	(	PUNCT
ejpam-5710	241	14	s	s	PROPN
ejpam-5710	241	15	,	,	PUNCT
ejpam-5710	241	16	u	u	NOUN
ejpam-5710	241	17	)	)	PUNCT
ejpam-5710	241	18	.	.	PUNCT
ejpam-5710	242	1	(	(	PUNCT
ejpam-5710	242	2	a	a	X
ejpam-5710	242	3	)	)	PUNCT
ejpam-5710	242	4	the	the	DET
ejpam-5710	242	5	curve	curve	NOUN
ejpam-5710	242	6	γ(s	γ(	NOUN
ejpam-5710	242	7	)	)	PUNCT
ejpam-5710	242	8	is	be	AUX
ejpam-5710	242	9	a	a	DET
ejpam-5710	242	10	geodesic	geodesic	ADJ
ejpam-5710	242	11	curve	curve	NOUN
ejpam-5710	242	12	if	if	SCONJ
ejpam-5710	242	13	only	only	ADV
ejpam-5710	242	14	if	if	SCONJ
ejpam-5710	242	15	κ2	κ2	NOUN
ejpam-5710	242	16	=	=	SYM
ejpam-5710	242	17	0	0	NUM
ejpam-5710	242	18	or	or	CCONJ
ejpam-5710	242	19	κ2	κ2	NOUN
ejpam-5710	242	20	=	=	SYM
ejpam-5710	242	21	1	1	NUM
ejpam-5710	242	22	u	u	NOUN
ejpam-5710	242	23	.	.	PUNCT
ejpam-5710	243	1	(	(	PUNCT
ejpam-5710	243	2	b	b	X
ejpam-5710	243	3	)	)	PUNCT
ejpam-5710	243	4	the	the	DET
ejpam-5710	243	5	curve	curve	NOUN
ejpam-5710	243	6	γ(s	γ(	NOUN
ejpam-5710	243	7	)	)	PUNCT
ejpam-5710	243	8	is	be	AUX
ejpam-5710	243	9	an	an	DET
ejpam-5710	243	10	asymptotic	asymptotic	ADJ
ejpam-5710	243	11	line	line	NOUN
ejpam-5710	243	12	if	if	SCONJ
ejpam-5710	243	13	only	only	ADV
ejpam-5710	243	14	if	if	SCONJ
ejpam-5710	243	15	κ1	κ1	NOUN
ejpam-5710	243	16	=	=	SYM
ejpam-5710	243	17	0	0	NUM
ejpam-5710	243	18	or	or	CCONJ
ejpam-5710	243	19	κ2	κ2	NOUN
ejpam-5710	243	20	=	=	SYM
ejpam-5710	243	21	1	1	NUM
ejpam-5710	243	22	u	u	NOUN
ejpam-5710	243	23	.	.	PUNCT
ejpam-5710	244	1	(	(	PUNCT
ejpam-5710	244	2	c	c	X
ejpam-5710	244	3	)	)	PUNCT
ejpam-5710	244	4	the	the	DET
ejpam-5710	244	5	curve	curve	NOUN
ejpam-5710	244	6	γ(s	γ(	NOUN
ejpam-5710	244	7	)	)	PUNCT
ejpam-5710	244	8	is	be	AUX
ejpam-5710	244	9	a	a	DET
ejpam-5710	244	10	principal	principal	ADJ
ejpam-5710	244	11	line	line	NOUN
ejpam-5710	244	12	if	if	SCONJ
ejpam-5710	244	13	and	and	CCONJ
ejpam-5710	244	14	only	only	ADV
ejpam-5710	244	15	if	if	SCONJ
ejpam-5710	244	16	κ1(s	κ1(s	ADP
ejpam-5710	244	17	)	)	PUNCT
ejpam-5710	244	18	=	=	SYM
ejpam-5710	244	19	−	−	PROPN
ejpam-5710	244	20	uκ2(s	uκ2(s	PROPN
ejpam-5710	244	21	)	)	PUNCT
ejpam-5710	244	22	(	(	PUNCT
ejpam-5710	244	23	−κ2(s	−κ2(s	NOUN
ejpam-5710	244	24	)	)	PUNCT
ejpam-5710	245	1	+	+	X
ejpam-5710	246	1	uκ2(s	uκ2(s	NOUN
ejpam-5710	246	2	)	)	PUNCT
ejpam-5710	246	3	2	2	NUM
ejpam-5710	247	1	+	+	SYM
ejpam-5710	247	2	uκ3(s	uκ3(	NOUN
ejpam-5710	247	3	)	)	PUNCT
ejpam-5710	247	4	2	2	NUM
ejpam-5710	247	5	)	)	PUNCT
ejpam-5710	247	6	(	(	PUNCT
ejpam-5710	247	7	κ′3(s)(uκ2(s)−	κ′3(s)(uκ2(s)−	PROPN
ejpam-5710	247	8	1)−	1)−	PROPN
ejpam-5710	247	9	uκ3(s)κ	uκ3(s)κ	PROPN
ejpam-5710	247	10	′	′	NUM
ejpam-5710	247	11	2(s	2(s	NUM
ejpam-5710	247	12	)	)	PUNCT
ejpam-5710	247	13	)	)	PUNCT
ejpam-5710	248	1	uκ2(s)−	uκ2(s)−	ADJ
ejpam-5710	248	2	1	1	NUM
ejpam-5710	248	3	.	.	PUNCT
ejpam-5710	249	1	corollary	corollary	ADJ
ejpam-5710	249	2	3.6	3.6	NUM
ejpam-5710	249	3	.	.	PUNCT
ejpam-5710	250	1	(	(	PUNCT
ejpam-5710	250	2	a	a	X
ejpam-5710	250	3	)	)	PUNCT
ejpam-5710	250	4	the	the	DET
ejpam-5710	250	5	qbr	qbr	NOUN
ejpam-5710	250	6	-	-	PUNCT
ejpam-5710	250	7	surface	surface	NOUN
ejpam-5710	250	8	is	be	AUX
ejpam-5710	250	9	a	a	DET
ejpam-5710	250	10	flat	flat	ADJ
ejpam-5710	250	11	(	(	PUNCT
ejpam-5710	250	12	developable)surface	developable)surface	NOUN
ejpam-5710	250	13	if	if	SCONJ
ejpam-5710	250	14	and	and	CCONJ
ejpam-5710	250	15	only	only	ADV
ejpam-5710	250	16	if	if	SCONJ
ejpam-5710	250	17	κ3	κ3	PROPN
ejpam-5710	250	18	=	=	SYM
ejpam-5710	250	19	0	0	PROPN
ejpam-5710	250	20	.	.	PUNCT
ejpam-5710	251	1	(	(	PUNCT
ejpam-5710	251	2	b	b	X
ejpam-5710	251	3	)	)	PUNCT
ejpam-5710	251	4	a	a	DET
ejpam-5710	251	5	qbr	qbr	NOUN
ejpam-5710	251	6	-	-	PUNCT
ejpam-5710	251	7	surface	surface	NOUN
ejpam-5710	251	8	is	be	AUX
ejpam-5710	251	9	a	a	DET
ejpam-5710	251	10	minimal	minimal	ADJ
ejpam-5710	251	11	surface	surface	NOUN
ejpam-5710	251	12	if	if	SCONJ
ejpam-5710	251	13	and	and	CCONJ
ejpam-5710	251	14	only	only	ADV
ejpam-5710	251	15	if	if	SCONJ
ejpam-5710	251	16	κ1(s	κ1(s	ADP
ejpam-5710	251	17	)	)	PUNCT
ejpam-5710	251	18	=	=	SYM
ejpam-5710	252	1	−	−	PROPN
ejpam-5710	252	2	u	u	NOUN
ejpam-5710	252	3	(	(	PUNCT
ejpam-5710	252	4	uκ3(s	uκ3(s	PROPN
ejpam-5710	252	5	)	)	PUNCT
ejpam-5710	252	6	dκ2(s	dκ2(s	NOUN
ejpam-5710	252	7	)	)	PUNCT
ejpam-5710	252	8	ds	ds	ADJ
ejpam-5710	252	9	+	+	CCONJ
ejpam-5710	252	10	dκ3(s	dκ3(	NOUN
ejpam-5710	252	11	)	)	PUNCT
ejpam-5710	252	12	ds	ds	X
ejpam-5710	252	13	(	(	PUNCT
ejpam-5710	252	14	1−	1−	NUM
ejpam-5710	252	15	uκ2(s	uκ2(s	PROPN
ejpam-5710	252	16	)	)	PUNCT
ejpam-5710	252	17	)	)	PUNCT
ejpam-5710	252	18	)	)	PUNCT
ejpam-5710	252	19	−u2κ3(s)2	−u2κ3(s)2	ADP
ejpam-5710	252	20	−	−	PROPN
ejpam-5710	252	21	(	(	PUNCT
ejpam-5710	252	22	uκ2(s)−	uκ2(s)−	ADJ
ejpam-5710	252	23	1)2	1)2	NUM
ejpam-5710	252	24	.	.	PUNCT
ejpam-5710	252	25	example	example	NOUN
ejpam-5710	252	26	3.1	3.1	NUM
ejpam-5710	252	27	.	.	PUNCT
ejpam-5710	252	28	let	let	VERB
ejpam-5710	252	29	ζ(s	ζ(s	PROPN
ejpam-5710	252	30	)	)	PUNCT
ejpam-5710	252	31	be	be	VERB
ejpam-5710	252	32	a	a	DET
ejpam-5710	252	33	general	general	ADJ
ejpam-5710	252	34	helix	helix	NOUN
ejpam-5710	252	35	curve	curve	NOUN
ejpam-5710	252	36	given	give	VERB
ejpam-5710	252	37	by	by	ADP
ejpam-5710	252	38	the	the	DET
ejpam-5710	252	39	parametrization	parametrization	NOUN
ejpam-5710	252	40	ζ(s	ζ(	VERB
ejpam-5710	252	41	)	)	PUNCT
ejpam-5710	252	42	=	=	SYM
ejpam-5710	252	43	(	(	PUNCT
ejpam-5710	252	44	4	4	NUM
ejpam-5710	252	45	cos	cos	X
ejpam-5710	252	46	(	(	PUNCT
ejpam-5710	252	47	s	s	NOUN
ejpam-5710	252	48	5	5	NUM
ejpam-5710	252	49	)	)	PUNCT
ejpam-5710	252	50	,	,	PUNCT
ejpam-5710	252	51	4	4	NUM
ejpam-5710	252	52	sin	sin	NOUN
ejpam-5710	252	53	(	(	PUNCT
ejpam-5710	252	54	s	s	NOUN
ejpam-5710	252	55	5	5	NUM
ejpam-5710	252	56	)	)	PUNCT
ejpam-5710	252	57	,	,	PUNCT
ejpam-5710	252	58	3s	3s	NUM
ejpam-5710	252	59	5	5	NUM
ejpam-5710	252	60	)	)	PUNCT
ejpam-5710	252	61	.	.	PUNCT
ejpam-5710	253	1	by	by	ADP
ejpam-5710	253	2	equation	equation	NOUN
ejpam-5710	253	3	(	(	PUNCT
ejpam-5710	253	4	2.1	2.1	NUM
ejpam-5710	253	5	)	)	PUNCT
ejpam-5710	253	6	where	where	SCONJ
ejpam-5710	253	7	choose	choose	VERB
ejpam-5710	253	8	m	m	NOUN
ejpam-5710	253	9	=	=	SYM
ejpam-5710	253	10	(	(	PUNCT
ejpam-5710	253	11	0	0	NUM
ejpam-5710	253	12	,	,	PUNCT
ejpam-5710	253	13	1	1	NUM
ejpam-5710	253	14	,	,	PUNCT
ejpam-5710	253	15	0	0	NUM
ejpam-5710	253	16	)	)	PUNCT
ejpam-5710	253	17	the	the	DET
ejpam-5710	253	18	quasi	quasi	NOUN
ejpam-5710	253	19	-	-	NOUN
ejpam-5710	253	20	frame	frame	NOUN
ejpam-5710	253	21	obtained	obtain	VERB
ejpam-5710	253	22	by	by	ADP
ejpam-5710	253	23	t	t	PROPN
ejpam-5710	253	24	=	=	SYM
ejpam-5710	253	25	(	(	PUNCT
ejpam-5710	253	26	−4	−4	PROPN
ejpam-5710	253	27	5	5	NUM
ejpam-5710	253	28	sin	sin	NOUN
ejpam-5710	253	29	(	(	PUNCT
ejpam-5710	253	30	s	s	NOUN
ejpam-5710	253	31	5	5	NUM
ejpam-5710	253	32	)	)	PUNCT
ejpam-5710	253	33	,	,	PUNCT
ejpam-5710	253	34	4	4	NUM
ejpam-5710	253	35	5	5	NUM
ejpam-5710	253	36	cos	cos	X
ejpam-5710	253	37	(	(	PUNCT
ejpam-5710	253	38	s	s	PROPN
ejpam-5710	253	39	5	5	NUM
ejpam-5710	253	40	)	)	PUNCT
ejpam-5710	253	41	,	,	PUNCT
ejpam-5710	253	42	3	3	NUM
ejpam-5710	253	43	5	5	NUM
ejpam-5710	253	44	)	)	PUNCT
ejpam-5710	253	45	,	,	PUNCT
ejpam-5710	253	46	nq	nq	NOUN
ejpam-5710	253	47	=	=	SYM
ejpam-5710	253	48	(	(	PUNCT
ejpam-5710	253	49	0	0	NUM
ejpam-5710	253	50	,	,	PUNCT
ejpam-5710	253	51	3√	3√	NOUN
ejpam-5710	253	52	8	8	NUM
ejpam-5710	253	53	cos	cos	NOUN
ejpam-5710	253	54	(	(	PUNCT
ejpam-5710	253	55	2s	2s	NUM
ejpam-5710	253	56	5	5	NUM
ejpam-5710	253	57	)	)	PUNCT
ejpam-5710	253	58	+	+	CCONJ
ejpam-5710	253	59	17	17	NUM
ejpam-5710	253	60	,	,	PUNCT
ejpam-5710	253	61	−	−	PROPN
ejpam-5710	253	62	4	4	NUM
ejpam-5710	253	63	cos	cos	PROPN
ejpam-5710	253	64	(	(	PUNCT
ejpam-5710	253	65	s	s	NOUN
ejpam-5710	253	66	5	5	NUM
ejpam-5710	253	67	)	)	PUNCT
ejpam-5710	253	68	√	√	PROPN
ejpam-5710	253	69	8	8	NUM
ejpam-5710	253	70	cos	cos	PROPN
ejpam-5710	253	71	(	(	PUNCT
ejpam-5710	253	72	2s	2s	NUM
ejpam-5710	253	73	5	5	NUM
ejpam-5710	253	74	)	)	PUNCT
ejpam-5710	253	75	+	+	CCONJ
ejpam-5710	253	76	17	17	NUM
ejpam-5710	253	77	)	)	PUNCT
ejpam-5710	253	78	,	,	PUNCT
ejpam-5710	253	79	bq	bq	INTJ
ejpam-5710	253	80	=	=	SYM
ejpam-5710	253	81	(	(	PUNCT
ejpam-5710	253	82	−8	−8	X
ejpam-5710	253	83	cos	cos	PROPN
ejpam-5710	253	84	(	(	PUNCT
ejpam-5710	253	85	2s	2s	NUM
ejpam-5710	253	86	5	5	NUM
ejpam-5710	253	87	)	)	PUNCT
ejpam-5710	253	88	−	−	PROPN
ejpam-5710	253	89	17	17	NUM
ejpam-5710	253	90	5	5	NUM
ejpam-5710	253	91	√	√	NUM
ejpam-5710	253	92	8	8	NUM
ejpam-5710	253	93	cos	cos	PROPN
ejpam-5710	253	94	(	(	PUNCT
ejpam-5710	253	95	2s	2s	NUM
ejpam-5710	253	96	5	5	NUM
ejpam-5710	253	97	)	)	PUNCT
ejpam-5710	253	98	+	+	CCONJ
ejpam-5710	253	99	17	17	NUM
ejpam-5710	253	100	,	,	PUNCT
ejpam-5710	253	101	−	−	PROPN
ejpam-5710	253	102	8	8	NUM
ejpam-5710	253	103	sin	sin	NOUN
ejpam-5710	253	104	(	(	PUNCT
ejpam-5710	253	105	2s	2s	NUM
ejpam-5710	253	106	5	5	NUM
ejpam-5710	253	107	)	)	PUNCT
ejpam-5710	253	108	5	5	NUM
ejpam-5710	253	109	√	√	NUM
ejpam-5710	253	110	8	8	NUM
ejpam-5710	253	111	cos	cos	PROPN
ejpam-5710	253	112	(	(	PUNCT
ejpam-5710	253	113	2s	2s	NUM
ejpam-5710	253	114	5	5	NUM
ejpam-5710	253	115	)	)	PUNCT
ejpam-5710	253	116	+	+	CCONJ
ejpam-5710	253	117	17	17	NUM
ejpam-5710	253	118	,	,	PUNCT
ejpam-5710	253	119	−	−	PROPN
ejpam-5710	253	120	12	12	NUM
ejpam-5710	253	121	sin	sin	NOUN
ejpam-5710	253	122	(	(	PUNCT
ejpam-5710	253	123	s	s	NOUN
ejpam-5710	253	124	5	5	NUM
ejpam-5710	253	125	)	)	PUNCT
ejpam-5710	253	126	5	5	NUM
ejpam-5710	253	127	√	√	NUM
ejpam-5710	253	128	8	8	NUM
ejpam-5710	253	129	cos	cos	PROPN
ejpam-5710	253	130	(	(	PUNCT
ejpam-5710	253	131	2s	2s	NUM
ejpam-5710	253	132	5	5	NUM
ejpam-5710	253	133	)	)	PUNCT
ejpam-5710	253	134	+	+	CCONJ
ejpam-5710	253	135	17	17	NUM
ejpam-5710	253	136	)	)	PUNCT
ejpam-5710	253	137	.	.	PUNCT
ejpam-5710	254	1	also	also	ADV
ejpam-5710	254	2	by	by	ADP
ejpam-5710	254	3	equation	equation	NOUN
ejpam-5710	254	4	(	(	PUNCT
ejpam-5710	254	5	2.3	2.3	NUM
ejpam-5710	254	6	)	)	PUNCT
ejpam-5710	254	7	the	the	DET
ejpam-5710	254	8	quasi	quasi	NOUN
ejpam-5710	254	9	-	-	NOUN
ejpam-5710	254	10	curvatures	curvature	NOUN
ejpam-5710	254	11	along	along	ADP
ejpam-5710	254	12	ζ(s	ζ(s	PROPN
ejpam-5710	254	13	)	)	PUNCT
ejpam-5710	254	14	are	be	AUX
ejpam-5710	254	15	obtained	obtain	VERB
ejpam-5710	254	16	by	by	ADP
ejpam-5710	254	17	κ1	κ1	NOUN
ejpam-5710	254	18	=	=	PROPN
ejpam-5710	254	19	−	−	PROPN
ejpam-5710	254	20	12	12	NUM
ejpam-5710	254	21	sin	sin	NOUN
ejpam-5710	254	22	(	(	PUNCT
ejpam-5710	254	23	s	s	NOUN
ejpam-5710	254	24	5	5	NUM
ejpam-5710	254	25	)	)	PUNCT
ejpam-5710	254	26	25	25	NUM
ejpam-5710	254	27	√	√	NUM
ejpam-5710	254	28	8	8	NUM
ejpam-5710	254	29	cos	cos	PROPN
ejpam-5710	254	30	(	(	PUNCT
ejpam-5710	254	31	2s	2s	NUM
ejpam-5710	254	32	5	5	NUM
ejpam-5710	254	33	)	)	PUNCT
ejpam-5710	254	34	+	+	CCONJ
ejpam-5710	254	35	17	17	NUM
ejpam-5710	254	36	,	,	PUNCT
ejpam-5710	254	37	κ2	κ2	NOUN
ejpam-5710	254	38	=	=	SYM
ejpam-5710	254	39	4	4	NUM
ejpam-5710	254	40	cos	cos	X
ejpam-5710	254	41	(	(	PUNCT
ejpam-5710	254	42	s	s	NOUN
ejpam-5710	254	43	5	5	NUM
ejpam-5710	254	44	)	)	PUNCT
ejpam-5710	255	1	5	5	NUM
ejpam-5710	255	2	√	√	NUM
ejpam-5710	255	3	8	8	NUM
ejpam-5710	255	4	cos	cos	PROPN
ejpam-5710	255	5	(	(	PUNCT
ejpam-5710	255	6	2s	2s	NUM
ejpam-5710	255	7	5	5	NUM
ejpam-5710	255	8	)	)	PUNCT
ejpam-5710	255	9	+	+	CCONJ
ejpam-5710	255	10	17	17	NUM
ejpam-5710	255	11	,	,	PUNCT
ejpam-5710	255	12	κ3	κ3	PROPN
ejpam-5710	255	13	=	=	PUNCT
ejpam-5710	255	14	−	−	PROPN
ejpam-5710	255	15	48	48	NUM
ejpam-5710	255	16	sin2	sin2	NOUN
ejpam-5710	255	17	(	(	PUNCT
ejpam-5710	255	18	s	s	NOUN
ejpam-5710	255	19	5	5	NUM
ejpam-5710	255	20	)	)	PUNCT
ejpam-5710	255	21	25	25	NUM
ejpam-5710	255	22	(	(	PUNCT
ejpam-5710	255	23	8	8	NUM
ejpam-5710	255	24	cos	cos	NOUN
ejpam-5710	255	25	(	(	PUNCT
ejpam-5710	255	26	2s	2s	NUM
ejpam-5710	255	27	5	5	NUM
ejpam-5710	255	28	)	)	PUNCT
ejpam-5710	255	29	+	+	CCONJ
ejpam-5710	255	30	17	17	NUM
ejpam-5710	255	31	)	)	PUNCT
ejpam-5710	255	32	.	.	PUNCT
ejpam-5710	256	1	a.	a.	NOUN
ejpam-5710	256	2	elsharkawy	elsharkawy	PROPN
ejpam-5710	256	3	,	,	PUNCT
ejpam-5710	256	4	h.	h.	PROPN
ejpam-5710	256	5	k.	k.	PROPN
ejpam-5710	256	6	elsayied	elsayied	PROPN
ejpam-5710	256	7	,	,	PUNCT
ejpam-5710	256	8	a.	a.	NOUN
ejpam-5710	256	9	refaat	refaat	PROPN
ejpam-5710	256	10	/	/	SYM
ejpam-5710	256	11	eur	eur	PROPN
ejpam-5710	256	12	.	.	PUNCT
ejpam-5710	257	1	j.	j.	PROPN
ejpam-5710	257	2	pure	pure	PROPN
ejpam-5710	257	3	appl	appl	PROPN
ejpam-5710	257	4	.	.	PROPN
ejpam-5710	257	5	math	math	PROPN
ejpam-5710	257	6	,	,	PUNCT
ejpam-5710	257	7	18	18	NUM
ejpam-5710	257	8	(	(	PUNCT
ejpam-5710	257	9	1	1	NUM
ejpam-5710	257	10	)	)	PUNCT
ejpam-5710	257	11	(	(	PUNCT
ejpam-5710	257	12	2025	2025	NUM
ejpam-5710	257	13	)	)	PUNCT
ejpam-5710	257	14	,	,	PUNCT
ejpam-5710	257	15	5710	5710	NUM
ejpam-5710	257	16	13	13	NUM
ejpam-5710	257	17	of	of	ADP
ejpam-5710	257	18	18	18	NUM
ejpam-5710	257	19	the	the	DET
ejpam-5710	257	20	qtr	qtr	NOUN
ejpam-5710	257	21	-	-	PUNCT
ejpam-5710	257	22	surface	surface	NOUN
ejpam-5710	257	23	,	,	PUNCT
ejpam-5710	257	24	the	the	DET
ejpam-5710	257	25	qnr	qnr	NOUN
ejpam-5710	257	26	-	-	PUNCT
ejpam-5710	257	27	surface	surface	NOUN
ejpam-5710	257	28	,	,	PUNCT
ejpam-5710	257	29	and	and	CCONJ
ejpam-5710	257	30	the	the	DET
ejpam-5710	257	31	qbr	qbr	NOUN
ejpam-5710	257	32	-	-	PUNCT
ejpam-5710	257	33	surface	surface	NOUN
ejpam-5710	257	34	are	be	AUX
ejpam-5710	257	35	,	,	PUNCT
ejpam-5710	257	36	respectively	respectively	ADV
ejpam-5710	257	37	,	,	PUNCT
ejpam-5710	257	38	given	give	VERB
ejpam-5710	257	39	in	in	ADP
ejpam-5710	257	40	figure	figure	NOUN
ejpam-5710	257	41	3.1	3.1	NUM
ejpam-5710	257	42	by	by	ADP
ejpam-5710	257	43	w	w	PROPN
ejpam-5710	257	44	t	t	PROPN
ejpam-5710	257	45	(	(	PUNCT
ejpam-5710	257	46	s	s	PROPN
ejpam-5710	257	47	,	,	PUNCT
ejpam-5710	257	48	u	u	NOUN
ejpam-5710	257	49	)	)	PUNCT
ejpam-5710	257	50	=	=	SYM
ejpam-5710	257	51	(	(	PUNCT
ejpam-5710	257	52	4	4	NUM
ejpam-5710	257	53	cos	cos	X
ejpam-5710	257	54	(	(	PUNCT
ejpam-5710	257	55	s	s	NOUN
ejpam-5710	257	56	5	5	NUM
ejpam-5710	257	57	)	)	PUNCT
ejpam-5710	257	58	−	−	NOUN
ejpam-5710	257	59	4	4	NUM
ejpam-5710	257	60	5	5	NUM
ejpam-5710	257	61	u	u	NOUN
ejpam-5710	257	62	sin	sin	NOUN
ejpam-5710	257	63	(	(	PUNCT
ejpam-5710	257	64	s	s	NOUN
ejpam-5710	257	65	5	5	NUM
ejpam-5710	257	66	)	)	PUNCT
ejpam-5710	257	67	,	,	PUNCT
ejpam-5710	257	68	4	4	NUM
ejpam-5710	257	69	5	5	NUM
ejpam-5710	257	70	u	u	NOUN
ejpam-5710	257	71	cos	cos	PROPN
ejpam-5710	257	72	(	(	PUNCT
ejpam-5710	257	73	s	s	NOUN
ejpam-5710	257	74	5	5	NUM
ejpam-5710	257	75	)	)	PUNCT
ejpam-5710	257	76	+	+	CCONJ
ejpam-5710	257	77	4	4	NUM
ejpam-5710	257	78	sin	sin	NOUN
ejpam-5710	257	79	(	(	PUNCT
ejpam-5710	257	80	s	s	NOUN
ejpam-5710	257	81	5	5	NUM
ejpam-5710	257	82	)	)	PUNCT
ejpam-5710	257	83	,	,	PUNCT
ejpam-5710	257	84	3s	3s	NUM
ejpam-5710	257	85	5	5	NUM
ejpam-5710	257	86	+	+	CCONJ
ejpam-5710	257	87	3u	3u	NUM
ejpam-5710	257	88	5	5	NUM
ejpam-5710	257	89	)	)	PUNCT
ejpam-5710	257	90	,	,	PUNCT
ejpam-5710	257	91	wn	wn	PROPN
ejpam-5710	257	92	(	(	PUNCT
ejpam-5710	257	93	s	s	PROPN
ejpam-5710	257	94	,	,	PUNCT
ejpam-5710	257	95	u	u	NOUN
ejpam-5710	257	96	)	)	PUNCT
ejpam-5710	257	97	=	=	SYM
ejpam-5710	257	98	(	(	PUNCT
ejpam-5710	257	99	4	4	NUM
ejpam-5710	257	100	cos	cos	X
ejpam-5710	257	101	(	(	PUNCT
ejpam-5710	257	102	s	s	NOUN
ejpam-5710	257	103	5	5	NUM
ejpam-5710	257	104	)	)	PUNCT
ejpam-5710	257	105	,	,	PUNCT
ejpam-5710	257	106	3u√	3u√	NUM
ejpam-5710	257	107	8	8	NUM
ejpam-5710	257	108	cos	cos	NOUN
ejpam-5710	257	109	(	(	PUNCT
ejpam-5710	257	110	2s	2s	NUM
ejpam-5710	257	111	5	5	NUM
ejpam-5710	257	112	)	)	PUNCT
ejpam-5710	258	1	+	+	CCONJ
ejpam-5710	258	2	17	17	NUM
ejpam-5710	258	3	+	+	SYM
ejpam-5710	258	4	4	4	NUM
ejpam-5710	258	5	sin	sin	NOUN
ejpam-5710	258	6	(	(	PUNCT
ejpam-5710	258	7	s	s	NOUN
ejpam-5710	258	8	5	5	NUM
ejpam-5710	258	9	)	)	PUNCT
ejpam-5710	258	10	,	,	PUNCT
ejpam-5710	258	11	3s	3s	NUM
ejpam-5710	258	12	5	5	NUM
ejpam-5710	258	13	−	−	NOUN
ejpam-5710	258	14	4u	4u	NOUN
ejpam-5710	258	15	cos	cos	ADP
ejpam-5710	258	16	(	(	PUNCT
ejpam-5710	258	17	s	s	NOUN
ejpam-5710	258	18	5	5	NUM
ejpam-5710	258	19	)	)	PUNCT
ejpam-5710	258	20	√	√	PROPN
ejpam-5710	258	21	8	8	NUM
ejpam-5710	258	22	cos	cos	PROPN
ejpam-5710	258	23	(	(	PUNCT
ejpam-5710	258	24	2s	2s	NUM
ejpam-5710	258	25	5	5	NUM
ejpam-5710	258	26	)	)	PUNCT
ejpam-5710	258	27	+	+	CCONJ
ejpam-5710	258	28	17	17	NUM
ejpam-5710	258	29	)	)	PUNCT
ejpam-5710	258	30	,	,	PUNCT
ejpam-5710	258	31	wb(s	wb(s	X
ejpam-5710	258	32	,	,	PUNCT
ejpam-5710	258	33	u	u	NOUN
ejpam-5710	258	34	)	)	PUNCT
ejpam-5710	258	35	=	=	SYM
ejpam-5710	258	36	(	(	PUNCT
ejpam-5710	258	37	4	4	NUM
ejpam-5710	258	38	cos	cos	NOUN
ejpam-5710	258	39	s	s	PROPN
ejpam-5710	258	40	5	5	NUM
ejpam-5710	258	41	−	−	NOUN
ejpam-5710	258	42	1	1	NUM
ejpam-5710	258	43	5	5	NUM
ejpam-5710	258	44	u	u	NOUN
ejpam-5710	258	45	√	√	ADP
ejpam-5710	258	46	8	8	NUM
ejpam-5710	258	47	cos	cos	ADP
ejpam-5710	258	48	2s	2s	NOUN
ejpam-5710	258	49	5	5	NUM
ejpam-5710	258	50	+	+	NUM
ejpam-5710	258	51	17	17	NUM
ejpam-5710	258	52	,	,	PUNCT
ejpam-5710	258	53	4	4	NUM
ejpam-5710	258	54	sin	sin	NOUN
ejpam-5710	258	55	(	(	PUNCT
ejpam-5710	258	56	s	s	NOUN
ejpam-5710	258	57	5	5	NUM
ejpam-5710	258	58	)	)	PUNCT
ejpam-5710	258	59	−	−	PROPN
ejpam-5710	258	60	8u	8u	PROPN
ejpam-5710	258	61	sin	sin	NOUN
ejpam-5710	258	62	(	(	PUNCT
ejpam-5710	258	63	2s	2s	NUM
ejpam-5710	258	64	5	5	NUM
ejpam-5710	258	65	)	)	PUNCT
ejpam-5710	258	66	5	5	NUM
ejpam-5710	258	67	√	√	NUM
ejpam-5710	258	68	8	8	NUM
ejpam-5710	258	69	cos	cos	PROPN
ejpam-5710	258	70	(	(	PUNCT
ejpam-5710	258	71	2s	2s	NUM
ejpam-5710	258	72	5	5	NUM
ejpam-5710	258	73	)	)	PUNCT
ejpam-5710	258	74	+	+	CCONJ
ejpam-5710	258	75	17	17	NUM
ejpam-5710	258	76	,	,	PUNCT
ejpam-5710	258	77	3	3	NUM
ejpam-5710	258	78	5	5	NUM
ejpam-5710	258	79	(	(	PUNCT
ejpam-5710	258	80	s−	s−	PROPN
ejpam-5710	258	81	4u	4u	NOUN
ejpam-5710	258	82	sin	sin	NOUN
ejpam-5710	258	83	(	(	PUNCT
ejpam-5710	258	84	s	s	NOUN
ejpam-5710	258	85	5	5	NUM
ejpam-5710	258	86	)	)	PUNCT
ejpam-5710	258	87	√	√	PROPN
ejpam-5710	258	88	8	8	NUM
ejpam-5710	258	89	cos	cos	PROPN
ejpam-5710	258	90	(	(	PUNCT
ejpam-5710	258	91	2s	2s	NUM
ejpam-5710	258	92	5	5	NUM
ejpam-5710	258	93	)	)	PUNCT
ejpam-5710	258	94	+	+	CCONJ
ejpam-5710	258	95	17	17	NUM
ejpam-5710	258	96	)	)	PUNCT
ejpam-5710	258	97	)	)	PUNCT
ejpam-5710	258	98	.	.	PUNCT
ejpam-5710	259	1	figure	figure	VERB
ejpam-5710	259	2	1	1	NUM
ejpam-5710	259	3	:	:	PUNCT
ejpam-5710	259	4	ruled	rule	VERB
ejpam-5710	259	5	surfaces	surface	NOUN
ejpam-5710	259	6	generated	generate	VERB
ejpam-5710	259	7	by	by	ADP
ejpam-5710	259	8	a	a	DET
ejpam-5710	259	9	general	general	ADJ
ejpam-5710	259	10	helix	helix	NOUN
ejpam-5710	259	11	example	example	NOUN
ejpam-5710	259	12	3.2	3.2	NUM
ejpam-5710	259	13	.	.	PUNCT
ejpam-5710	260	1	let	let	VERB
ejpam-5710	260	2	ξ(s	ξ(s	PROPN
ejpam-5710	260	3	)	)	PUNCT
ejpam-5710	260	4	be	be	AUX
ejpam-5710	260	5	a	a	DET
ejpam-5710	260	6	regular	regular	ADJ
ejpam-5710	260	7	curve	curve	NOUN
ejpam-5710	260	8	parameterized	parameterize	VERB
ejpam-5710	260	9	by	by	ADP
ejpam-5710	260	10	ξ	ξ	PROPN
ejpam-5710	260	11	=	=	SYM
ejpam-5710	260	12	(	(	PUNCT
ejpam-5710	260	13	3	3	NUM
ejpam-5710	260	14	2	2	NUM
ejpam-5710	260	15	cos	cos	X
ejpam-5710	260	16	(	(	PUNCT
ejpam-5710	260	17	s	s	NOUN
ejpam-5710	260	18	2	2	NUM
ejpam-5710	260	19	)	)	PUNCT
ejpam-5710	261	1	+	+	CCONJ
ejpam-5710	261	2	1	1	NUM
ejpam-5710	261	3	6	6	NUM
ejpam-5710	261	4	cos	cos	PROPN
ejpam-5710	261	5	(	(	PUNCT
ejpam-5710	261	6	3s	3s	NUM
ejpam-5710	261	7	2	2	NUM
ejpam-5710	261	8	)	)	PUNCT
ejpam-5710	261	9	,	,	PUNCT
ejpam-5710	261	10	3	3	NUM
ejpam-5710	261	11	2	2	NUM
ejpam-5710	261	12	sin	sin	NOUN
ejpam-5710	261	13	(	(	PUNCT
ejpam-5710	261	14	s	s	NOUN
ejpam-5710	261	15	2	2	NUM
ejpam-5710	261	16	)	)	PUNCT
ejpam-5710	261	17	+	+	CCONJ
ejpam-5710	261	18	1	1	NUM
ejpam-5710	261	19	6	6	NUM
ejpam-5710	261	20	sin	sin	NOUN
ejpam-5710	261	21	(	(	PUNCT
ejpam-5710	261	22	3s	3s	NUM
ejpam-5710	261	23	2	2	NUM
ejpam-5710	261	24	)	)	PUNCT
ejpam-5710	261	25	,	,	PUNCT
ejpam-5710	261	26	√	√	PROPN
ejpam-5710	261	27	3	3	NUM
ejpam-5710	261	28	cos	cos	X
ejpam-5710	261	29	(	(	PUNCT
ejpam-5710	261	30	s	s	PROPN
ejpam-5710	261	31	2	2	NUM
ejpam-5710	261	32	)	)	PUNCT
ejpam-5710	261	33	)	)	PUNCT
ejpam-5710	261	34	.	.	PUNCT
ejpam-5710	262	1	a.	a.	NOUN
ejpam-5710	262	2	elsharkawy	elsharkawy	PROPN
ejpam-5710	262	3	,	,	PUNCT
ejpam-5710	262	4	h.	h.	PROPN
ejpam-5710	262	5	k.	k.	PROPN
ejpam-5710	262	6	elsayied	elsayied	PROPN
ejpam-5710	262	7	,	,	PUNCT
ejpam-5710	262	8	a.	a.	NOUN
ejpam-5710	262	9	refaat	refaat	PROPN
ejpam-5710	262	10	/	/	SYM
ejpam-5710	262	11	eur	eur	PROPN
ejpam-5710	262	12	.	.	PUNCT
ejpam-5710	263	1	j.	j.	PROPN
ejpam-5710	263	2	pure	pure	PROPN
ejpam-5710	263	3	appl	appl	PROPN
ejpam-5710	263	4	.	.	PROPN
ejpam-5710	263	5	math	math	PROPN
ejpam-5710	263	6	,	,	PUNCT
ejpam-5710	263	7	18	18	NUM
ejpam-5710	263	8	(	(	PUNCT
ejpam-5710	263	9	1	1	NUM
ejpam-5710	263	10	)	)	PUNCT
ejpam-5710	263	11	(	(	PUNCT
ejpam-5710	263	12	2025	2025	NUM
ejpam-5710	263	13	)	)	PUNCT
ejpam-5710	263	14	,	,	PUNCT
ejpam-5710	263	15	5710	5710	NUM
ejpam-5710	263	16	14	14	NUM
ejpam-5710	263	17	of	of	ADP
ejpam-5710	263	18	18	18	NUM
ejpam-5710	263	19	by	by	ADP
ejpam-5710	263	20	equation	equation	NOUN
ejpam-5710	263	21	(	(	PUNCT
ejpam-5710	263	22	2.1	2.1	NUM
ejpam-5710	263	23	)	)	PUNCT
ejpam-5710	263	24	where	where	SCONJ
ejpam-5710	263	25	choose	choose	VERB
ejpam-5710	263	26	m	m	NOUN
ejpam-5710	263	27	=	=	SYM
ejpam-5710	263	28	(	(	PUNCT
ejpam-5710	263	29	0	0	NUM
ejpam-5710	263	30	,	,	PUNCT
ejpam-5710	263	31	0	0	NUM
ejpam-5710	263	32	,	,	PUNCT
ejpam-5710	263	33	1	1	NUM
ejpam-5710	263	34	)	)	PUNCT
ejpam-5710	263	35	the	the	DET
ejpam-5710	263	36	quasi	quasi	NOUN
ejpam-5710	263	37	-	-	NOUN
ejpam-5710	263	38	frame	frame	NOUN
ejpam-5710	263	39	obtained	obtain	VERB
ejpam-5710	263	40	by	by	ADP
ejpam-5710	263	41	t	t	PROPN
ejpam-5710	263	42	=	=	PUNCT
ejpam-5710	263	43	(	(	PUNCT
ejpam-5710	263	44	1	1	NUM
ejpam-5710	263	45	4	4	NUM
ejpam-5710	263	46	(	(	PUNCT
ejpam-5710	263	47	−3	−3	NOUN
ejpam-5710	263	48	sin	sin	NOUN
ejpam-5710	263	49	(	(	PUNCT
ejpam-5710	263	50	s	s	NOUN
ejpam-5710	263	51	2	2	NUM
ejpam-5710	263	52	)	)	PUNCT
ejpam-5710	263	53	−	−	NOUN
ejpam-5710	264	1	sin	sin	NOUN
ejpam-5710	264	2	(	(	PUNCT
ejpam-5710	264	3	3s	3s	NUM
ejpam-5710	264	4	2	2	NUM
ejpam-5710	264	5	)	)	PUNCT
ejpam-5710	264	6	)	)	PUNCT
ejpam-5710	264	7	,	,	PUNCT
ejpam-5710	264	8	cos3	cos3	PROPN
ejpam-5710	264	9	(	(	PUNCT
ejpam-5710	264	10	s	s	NOUN
ejpam-5710	264	11	2	2	NUM
ejpam-5710	264	12	)	)	PUNCT
ejpam-5710	264	13	,	,	PUNCT
ejpam-5710	264	14	−1	−1	NOUN
ejpam-5710	264	15	2	2	NUM
ejpam-5710	264	16	√	√	NUM
ejpam-5710	264	17	3	3	NUM
ejpam-5710	264	18	sin	sin	NOUN
ejpam-5710	264	19	(	(	PUNCT
ejpam-5710	264	20	s	s	NOUN
ejpam-5710	264	21	2	2	NUM
ejpam-5710	264	22	)	)	PUNCT
ejpam-5710	264	23	)	)	PUNCT
ejpam-5710	264	24	,	,	PUNCT
ejpam-5710	264	25	nq	nq	NOUN
ejpam-5710	264	26	=	=	PUNCT
ejpam-5710	264	27	(	(	PUNCT
ejpam-5710	264	28	2	2	NUM
ejpam-5710	264	29	√	√	NUM
ejpam-5710	264	30	2	2	NUM
ejpam-5710	264	31	cos3	cos3	NOUN
ejpam-5710	264	32	(	(	PUNCT
ejpam-5710	264	33	s	s	NOUN
ejpam-5710	264	34	2	2	NUM
ejpam-5710	264	35	)	)	PUNCT
ejpam-5710	264	36	√	√	NOUN
ejpam-5710	264	37	3	3	NUM
ejpam-5710	264	38	cos(s	cos(s	NOUN
ejpam-5710	264	39	)	)	PUNCT
ejpam-5710	265	1	+	+	CCONJ
ejpam-5710	265	2	5	5	NUM
ejpam-5710	265	3	,	,	PUNCT
ejpam-5710	265	4	3	3	NUM
ejpam-5710	265	5	sin	sin	NOUN
ejpam-5710	265	6	(	(	PUNCT
ejpam-5710	265	7	s	s	NOUN
ejpam-5710	265	8	2	2	NUM
ejpam-5710	265	9	)	)	PUNCT
ejpam-5710	265	10	+	+	CCONJ
ejpam-5710	265	11	sin	sin	NOUN
ejpam-5710	265	12	(	(	PUNCT
ejpam-5710	265	13	3s	3s	NUM
ejpam-5710	265	14	2	2	NUM
ejpam-5710	265	15	)	)	PUNCT
ejpam-5710	265	16	√	√	PROPN
ejpam-5710	265	17	6	6	NUM
ejpam-5710	265	18	cos(s	cos(s	NOUN
ejpam-5710	265	19	)	)	PUNCT
ejpam-5710	266	1	+	+	CCONJ
ejpam-5710	266	2	10	10	NUM
ejpam-5710	266	3	,	,	PUNCT
ejpam-5710	266	4	0	0	NUM
ejpam-5710	266	5	)	)	PUNCT
ejpam-5710	266	6	,	,	PUNCT
ejpam-5710	266	7	bq	bq	INTJ
ejpam-5710	266	8	=	=	SYM
ejpam-5710	266	9	(	(	PUNCT
ejpam-5710	266	10	sin2	sin2	NOUN
ejpam-5710	266	11	(	(	PUNCT
ejpam-5710	266	12	s	s	NOUN
ejpam-5710	266	13	2	2	NUM
ejpam-5710	266	14	)	)	PUNCT
ejpam-5710	266	15	(	(	PUNCT
ejpam-5710	266	16	cos(s	cos(s	X
ejpam-5710	266	17	)	)	PUNCT
ejpam-5710	267	1	+	+	CCONJ
ejpam-5710	267	2	2)√	2)√	NUM
ejpam-5710	267	3	2	2	NUM
ejpam-5710	267	4	cos(s	cos(s	NOUN
ejpam-5710	267	5	)	)	PUNCT
ejpam-5710	267	6	+	+	CCONJ
ejpam-5710	267	7	10	10	NUM
ejpam-5710	267	8	3	3	NUM
ejpam-5710	267	9	,	,	PUNCT
ejpam-5710	267	10	−sin(s)(cos(s	−sin(s)(cos(s	NOUN
ejpam-5710	267	11	)	)	PUNCT
ejpam-5710	268	1	+	+	CCONJ
ejpam-5710	268	2	1	1	X
ejpam-5710	268	3	)	)	SYM
ejpam-5710	268	4	2	2	NUM
ejpam-5710	268	5	√	√	NUM
ejpam-5710	268	6	2	2	NUM
ejpam-5710	268	7	cos(s	cos(	NOUN
ejpam-5710	268	8	)	)	PUNCT
ejpam-5710	268	9	+	+	CCONJ
ejpam-5710	268	10	10	10	NUM
ejpam-5710	268	11	3	3	NUM
ejpam-5710	268	12	,	,	PUNCT
ejpam-5710	268	13	−	−	PROPN
ejpam-5710	268	14	√	√	PROPN
ejpam-5710	268	15	3	3	NUM
ejpam-5710	268	16	cos(s	cos(s	NOUN
ejpam-5710	268	17	)	)	PUNCT
ejpam-5710	269	1	+	+	CCONJ
ejpam-5710	269	2	5	5	NUM
ejpam-5710	269	3	2	2	NUM
ejpam-5710	269	4	√	√	NUM
ejpam-5710	269	5	2	2	NUM
ejpam-5710	269	6	)	)	PUNCT
ejpam-5710	269	7	.	.	PUNCT
ejpam-5710	270	1	also	also	ADV
ejpam-5710	270	2	by	by	ADP
ejpam-5710	270	3	equation	equation	NOUN
ejpam-5710	270	4	(	(	PUNCT
ejpam-5710	270	5	2.3	2.3	NUM
ejpam-5710	270	6	)	)	PUNCT
ejpam-5710	270	7	the	the	DET
ejpam-5710	270	8	quasi	quasi	NOUN
ejpam-5710	270	9	-	-	NOUN
ejpam-5710	270	10	curvatures	curvature	NOUN
ejpam-5710	270	11	along	along	ADP
ejpam-5710	270	12	ξ(s	ξ(s	PROPN
ejpam-5710	270	13	)	)	PUNCT
ejpam-5710	270	14	are	be	AUX
ejpam-5710	270	15	obtained	obtain	VERB
ejpam-5710	270	16	by	by	ADP
ejpam-5710	270	17	κ1	κ1	NOUN
ejpam-5710	270	18	=	=	PROPN
ejpam-5710	270	19	−	−	PROPN
ejpam-5710	270	20	3	3	NUM
ejpam-5710	270	21	cos2	cos2	NOUN
ejpam-5710	270	22	(	(	PUNCT
ejpam-5710	270	23	s	s	NOUN
ejpam-5710	270	24	2	2	NUM
ejpam-5710	270	25	)	)	PUNCT
ejpam-5710	270	26	√	√	NOUN
ejpam-5710	270	27	6	6	NUM
ejpam-5710	270	28	cos(s	cos(s	NOUN
ejpam-5710	270	29	)	)	PUNCT
ejpam-5710	271	1	+	+	CCONJ
ejpam-5710	271	2	10	10	NUM
ejpam-5710	271	3	,	,	PUNCT
ejpam-5710	271	4	κ2	κ2	NOUN
ejpam-5710	271	5	=	=	SYM
ejpam-5710	271	6	cos	cos	PROPN
ejpam-5710	271	7	(	(	PUNCT
ejpam-5710	271	8	s	s	NOUN
ejpam-5710	271	9	2	2	NUM
ejpam-5710	271	10	)	)	PUNCT
ejpam-5710	271	11	√	√	PROPN
ejpam-5710	271	12	2	2	NUM
ejpam-5710	271	13	cos(s	cos(s	NOUN
ejpam-5710	271	14	)	)	PUNCT
ejpam-5710	271	15	+	+	CCONJ
ejpam-5710	271	16	10	10	NUM
ejpam-5710	271	17	3	3	NUM
ejpam-5710	271	18	,	,	PUNCT
ejpam-5710	271	19	κ3	κ3	PROPN
ejpam-5710	271	20	=	=	PROPN
ejpam-5710	271	21	−	−	PROPN
ejpam-5710	271	22	3	3	NUM
ejpam-5710	271	23	√	√	PROPN
ejpam-5710	271	24	3	3	NUM
ejpam-5710	271	25	sin2(s	sin2(s	NUM
ejpam-5710	271	26	)	)	PUNCT
ejpam-5710	271	27	csc	csc	PROPN
ejpam-5710	271	28	(	(	PUNCT
ejpam-5710	271	29	s	s	PROPN
ejpam-5710	271	30	2	2	NUM
ejpam-5710	271	31	)	)	PUNCT
ejpam-5710	271	32	12	12	NUM
ejpam-5710	271	33	cos(s	cos(s	NOUN
ejpam-5710	271	34	)	)	PUNCT
ejpam-5710	271	35	+	+	CCONJ
ejpam-5710	271	36	20	20	NUM
ejpam-5710	271	37	.	.	PUNCT
ejpam-5710	272	1	the	the	DET
ejpam-5710	272	2	qtr	qtr	NOUN
ejpam-5710	272	3	-	-	PUNCT
ejpam-5710	272	4	surface	surface	NOUN
ejpam-5710	272	5	,	,	PUNCT
ejpam-5710	272	6	the	the	DET
ejpam-5710	272	7	qnr	qnr	NOUN
ejpam-5710	272	8	-	-	PUNCT
ejpam-5710	272	9	surface	surface	NOUN
ejpam-5710	272	10	,	,	PUNCT
ejpam-5710	272	11	and	and	CCONJ
ejpam-5710	272	12	the	the	DET
ejpam-5710	272	13	qbr	qbr	NOUN
ejpam-5710	272	14	-	-	PUNCT
ejpam-5710	272	15	surface	surface	NOUN
ejpam-5710	272	16	are	be	AUX
ejpam-5710	272	17	,	,	PUNCT
ejpam-5710	272	18	respectively	respectively	ADV
ejpam-5710	272	19	,	,	PUNCT
ejpam-5710	272	20	given	give	VERB
ejpam-5710	272	21	in	in	ADP
ejpam-5710	272	22	figure	figure	NOUN
ejpam-5710	272	23	3.2	3.2	NUM
ejpam-5710	272	24	by	by	ADP
ejpam-5710	272	25	w	w	PROPN
ejpam-5710	272	26	t	t	PROPN
ejpam-5710	272	27	(	(	PUNCT
ejpam-5710	272	28	s	s	PROPN
ejpam-5710	272	29	,	,	PUNCT
ejpam-5710	272	30	u	u	NOUN
ejpam-5710	272	31	)	)	PUNCT
ejpam-5710	272	32	=	=	PUNCT
ejpam-5710	272	33	(	(	PUNCT
ejpam-5710	272	34	1	1	NUM
ejpam-5710	272	35	12	12	NUM
ejpam-5710	272	36	(	(	PUNCT
ejpam-5710	272	37	−3u	−3u	PROPN
ejpam-5710	272	38	(	(	PUNCT
ejpam-5710	272	39	3	3	NUM
ejpam-5710	272	40	sin	sin	NOUN
ejpam-5710	272	41	(	(	PUNCT
ejpam-5710	272	42	s	s	NOUN
ejpam-5710	272	43	2	2	NUM
ejpam-5710	272	44	)	)	PUNCT
ejpam-5710	272	45	+	+	CCONJ
ejpam-5710	272	46	sin	sin	NOUN
ejpam-5710	272	47	(	(	PUNCT
ejpam-5710	272	48	3s	3s	NUM
ejpam-5710	272	49	2	2	NUM
ejpam-5710	272	50	)	)	PUNCT
ejpam-5710	272	51	)	)	PUNCT
ejpam-5710	273	1	+	+	CCONJ
ejpam-5710	273	2	18	18	NUM
ejpam-5710	273	3	cos	co	NOUN
ejpam-5710	273	4	(	(	PUNCT
ejpam-5710	273	5	s	s	NOUN
ejpam-5710	273	6	2	2	NUM
ejpam-5710	273	7	)	)	PUNCT
ejpam-5710	273	8	+	+	CCONJ
ejpam-5710	273	9	2	2	NUM
ejpam-5710	273	10	cos	cos	X
ejpam-5710	273	11	(	(	PUNCT
ejpam-5710	273	12	3s	3s	NUM
ejpam-5710	273	13	2	2	NUM
ejpam-5710	273	14	)	)	PUNCT
ejpam-5710	273	15	)	)	PUNCT
ejpam-5710	273	16	,	,	PUNCT
ejpam-5710	273	17	1	1	NUM
ejpam-5710	273	18	12	12	NUM
ejpam-5710	273	19	(	(	PUNCT
ejpam-5710	273	20	9u	9u	X
ejpam-5710	273	21	cos	cos	PROPN
ejpam-5710	273	22	(	(	PUNCT
ejpam-5710	273	23	s	s	NOUN
ejpam-5710	273	24	2	2	NUM
ejpam-5710	273	25	)	)	PUNCT
ejpam-5710	273	26	+	+	CCONJ
ejpam-5710	273	27	3u	3u	PROPN
ejpam-5710	273	28	cos	cos	PROPN
ejpam-5710	273	29	(	(	PUNCT
ejpam-5710	273	30	3s	3s	NUM
ejpam-5710	273	31	2	2	NUM
ejpam-5710	273	32	)	)	PUNCT
ejpam-5710	273	33	+	+	CCONJ
ejpam-5710	273	34	2	2	NUM
ejpam-5710	273	35	(	(	PUNCT
ejpam-5710	273	36	9	9	NUM
ejpam-5710	273	37	sin	sin	NOUN
ejpam-5710	273	38	(	(	PUNCT
ejpam-5710	273	39	s	s	NOUN
ejpam-5710	273	40	2	2	NUM
ejpam-5710	273	41	)	)	PUNCT
ejpam-5710	273	42	+	+	CCONJ
ejpam-5710	273	43	sin	sin	NOUN
ejpam-5710	273	44	(	(	PUNCT
ejpam-5710	273	45	3s	3s	NUM
ejpam-5710	273	46	2	2	NUM
ejpam-5710	273	47	)	)	PUNCT
ejpam-5710	273	48	)	)	PUNCT
ejpam-5710	273	49	)	)	PUNCT
ejpam-5710	273	50	,	,	PUNCT
ejpam-5710	273	51	−	−	PROPN
ejpam-5710	273	52	1	1	NUM
ejpam-5710	273	53	2	2	NUM
ejpam-5710	273	54	√	√	NUM
ejpam-5710	273	55	3	3	NUM
ejpam-5710	273	56	(	(	PUNCT
ejpam-5710	273	57	u	u	NOUN
ejpam-5710	273	58	sin	sin	NOUN
ejpam-5710	273	59	(	(	PUNCT
ejpam-5710	273	60	s	s	NOUN
ejpam-5710	273	61	2	2	NUM
ejpam-5710	273	62	)	)	PUNCT
ejpam-5710	273	63	−	−	PROPN
ejpam-5710	273	64	2	2	NUM
ejpam-5710	273	65	cos	cos	X
ejpam-5710	273	66	(	(	PUNCT
ejpam-5710	273	67	s	s	NOUN
ejpam-5710	273	68	2	2	NUM
ejpam-5710	273	69	)	)	PUNCT
ejpam-5710	273	70	)	)	PUNCT
ejpam-5710	273	71	)	)	PUNCT
ejpam-5710	273	72	,	,	PUNCT
ejpam-5710	273	73	wn	wn	PROPN
ejpam-5710	273	74	(	(	PUNCT
ejpam-5710	273	75	s	s	PROPN
ejpam-5710	273	76	,	,	PUNCT
ejpam-5710	273	77	u	u	NOUN
ejpam-5710	273	78	)	)	PUNCT
ejpam-5710	273	79	=	=	SYM
ejpam-5710	273	80	(	(	PUNCT
ejpam-5710	273	81	1	1	NUM
ejpam-5710	273	82	6	6	NUM
ejpam-5710	273	83	(	(	PUNCT
ejpam-5710	273	84	12	12	NUM
ejpam-5710	273	85	√	√	PROPN
ejpam-5710	273	86	2u	2u	PROPN
ejpam-5710	273	87	cos3	cos3	PROPN
ejpam-5710	273	88	(	(	PUNCT
ejpam-5710	273	89	s	s	NOUN
ejpam-5710	273	90	2	2	NUM
ejpam-5710	273	91	)	)	PUNCT
ejpam-5710	273	92	√	√	NOUN
ejpam-5710	273	93	3	3	NUM
ejpam-5710	273	94	cos(s	cos(s	NOUN
ejpam-5710	273	95	)	)	PUNCT
ejpam-5710	274	1	+	+	CCONJ
ejpam-5710	274	2	5	5	NUM
ejpam-5710	274	3	+	+	SYM
ejpam-5710	274	4	9	9	NUM
ejpam-5710	274	5	cos	cos	X
ejpam-5710	274	6	(	(	PUNCT
ejpam-5710	274	7	s	s	NOUN
ejpam-5710	274	8	2	2	NUM
ejpam-5710	274	9	)	)	PUNCT
ejpam-5710	274	10	+	+	CCONJ
ejpam-5710	274	11	cos	cos	X
ejpam-5710	274	12	(	(	PUNCT
ejpam-5710	274	13	3s	3s	NUM
ejpam-5710	274	14	2	2	NUM
ejpam-5710	274	15	)	)	PUNCT
ejpam-5710	274	16	)	)	PUNCT
ejpam-5710	274	17	,	,	PUNCT
ejpam-5710	274	18	u	u	NOUN
ejpam-5710	274	19	(	(	PUNCT
ejpam-5710	274	20	3	3	NUM
ejpam-5710	274	21	sin	sin	NOUN
ejpam-5710	274	22	(	(	PUNCT
ejpam-5710	274	23	s	s	NOUN
ejpam-5710	274	24	2	2	NUM
ejpam-5710	274	25	)	)	PUNCT
ejpam-5710	274	26	+	+	CCONJ
ejpam-5710	274	27	sin	sin	NOUN
ejpam-5710	274	28	(	(	PUNCT
ejpam-5710	274	29	3s	3s	NUM
ejpam-5710	274	30	2	2	NUM
ejpam-5710	274	31	)	)	PUNCT
ejpam-5710	274	32	)	)	PUNCT
ejpam-5710	274	33	√	√	ADP
ejpam-5710	274	34	6	6	NUM
ejpam-5710	274	35	cos(s	cos(s	NOUN
ejpam-5710	274	36	)	)	PUNCT
ejpam-5710	275	1	+	+	CCONJ
ejpam-5710	275	2	10	10	NUM
ejpam-5710	275	3	+	+	SYM
ejpam-5710	275	4	3	3	NUM
ejpam-5710	275	5	2	2	NUM
ejpam-5710	275	6	sin	sin	NOUN
ejpam-5710	275	7	(	(	PUNCT
ejpam-5710	275	8	s	s	NOUN
ejpam-5710	275	9	2	2	NUM
ejpam-5710	275	10	)	)	PUNCT
ejpam-5710	275	11	+	+	CCONJ
ejpam-5710	275	12	1	1	NUM
ejpam-5710	275	13	6	6	NUM
ejpam-5710	275	14	sin	sin	NOUN
ejpam-5710	275	15	(	(	PUNCT
ejpam-5710	275	16	3s	3s	NUM
ejpam-5710	275	17	2	2	NUM
ejpam-5710	275	18	)	)	PUNCT
ejpam-5710	275	19	,	,	PUNCT
ejpam-5710	275	20	√	√	PROPN
ejpam-5710	275	21	3	3	NUM
ejpam-5710	275	22	cos	cos	X
ejpam-5710	275	23	(	(	PUNCT
ejpam-5710	275	24	s	s	NOUN
ejpam-5710	275	25	2	2	NUM
ejpam-5710	275	26	)	)	PUNCT
ejpam-5710	275	27	)	)	PUNCT
ejpam-5710	275	28	,	,	PUNCT
ejpam-5710	275	29	wb(s	wb(s	X
ejpam-5710	275	30	,	,	PUNCT
ejpam-5710	275	31	u	u	NOUN
ejpam-5710	275	32	)	)	PUNCT
ejpam-5710	275	33	=	=	SYM
ejpam-5710	275	34	(	(	PUNCT
ejpam-5710	275	35	u	u	NOUN
ejpam-5710	275	36	sin2	sin2	NOUN
ejpam-5710	275	37	(	(	PUNCT
ejpam-5710	275	38	s	s	NOUN
ejpam-5710	275	39	2	2	NUM
ejpam-5710	275	40	)	)	PUNCT
ejpam-5710	275	41	(	(	PUNCT
ejpam-5710	275	42	cos(s	cos(s	X
ejpam-5710	275	43	)	)	PUNCT
ejpam-5710	276	1	+	+	CCONJ
ejpam-5710	276	2	2)√	2)√	NUM
ejpam-5710	276	3	2	2	NUM
ejpam-5710	276	4	cos(s	cos(s	NOUN
ejpam-5710	276	5	)	)	PUNCT
ejpam-5710	276	6	+	+	CCONJ
ejpam-5710	276	7	10	10	NUM
ejpam-5710	276	8	3	3	NUM
ejpam-5710	276	9	+	+	CCONJ
ejpam-5710	276	10	3	3	NUM
ejpam-5710	276	11	2	2	NUM
ejpam-5710	276	12	cos	cos	X
ejpam-5710	276	13	(	(	PUNCT
ejpam-5710	276	14	s	s	NOUN
ejpam-5710	276	15	2	2	NUM
ejpam-5710	276	16	)	)	PUNCT
ejpam-5710	276	17	+	+	CCONJ
ejpam-5710	276	18	1	1	NUM
ejpam-5710	276	19	6	6	NUM
ejpam-5710	276	20	cos	cos	PROPN
ejpam-5710	276	21	(	(	PUNCT
ejpam-5710	276	22	3s	3s	NUM
ejpam-5710	276	23	2	2	NUM
ejpam-5710	276	24	)	)	PUNCT
ejpam-5710	276	25	,	,	PUNCT
ejpam-5710	276	26	−	−	PROPN
ejpam-5710	276	27	u	u	PROPN
ejpam-5710	276	28	sin(s)(cos(s	sin(s)(cos(s	PUNCT
ejpam-5710	276	29	)	)	PUNCT
ejpam-5710	277	1	+	+	CCONJ
ejpam-5710	277	2	1	1	X
ejpam-5710	277	3	)	)	SYM
ejpam-5710	277	4	2	2	NUM
ejpam-5710	277	5	√	√	NUM
ejpam-5710	277	6	2	2	NUM
ejpam-5710	277	7	cos(s	cos(	NOUN
ejpam-5710	277	8	)	)	PUNCT
ejpam-5710	277	9	+	+	CCONJ
ejpam-5710	277	10	10	10	NUM
ejpam-5710	277	11	3	3	NUM
ejpam-5710	277	12	+	+	CCONJ
ejpam-5710	277	13	3	3	NUM
ejpam-5710	277	14	2	2	NUM
ejpam-5710	277	15	sin	sin	NOUN
ejpam-5710	277	16	(	(	PUNCT
ejpam-5710	277	17	s	s	NOUN
ejpam-5710	277	18	2	2	NUM
ejpam-5710	277	19	)	)	PUNCT
ejpam-5710	277	20	+	+	CCONJ
ejpam-5710	277	21	1	1	NUM
ejpam-5710	277	22	6	6	NUM
ejpam-5710	277	23	sin	sin	NOUN
ejpam-5710	277	24	(	(	PUNCT
ejpam-5710	277	25	3s	3s	NUM
ejpam-5710	277	26	2	2	NUM
ejpam-5710	277	27	)	)	PUNCT
ejpam-5710	277	28	,	,	PUNCT
ejpam-5710	277	29	a.	a.	NOUN
ejpam-5710	277	30	elsharkawy	elsharkawy	PROPN
ejpam-5710	277	31	,	,	PUNCT
ejpam-5710	277	32	h.	h.	PROPN
ejpam-5710	277	33	k.	k.	PROPN
ejpam-5710	277	34	elsayied	elsayied	PROPN
ejpam-5710	277	35	,	,	PUNCT
ejpam-5710	277	36	a.	a.	NOUN
ejpam-5710	277	37	refaat	refaat	PROPN
ejpam-5710	277	38	/	/	SYM
ejpam-5710	277	39	eur	eur	PROPN
ejpam-5710	277	40	.	.	PUNCT
ejpam-5710	278	1	j.	j.	PROPN
ejpam-5710	278	2	pure	pure	PROPN
ejpam-5710	278	3	appl	appl	PROPN
ejpam-5710	278	4	.	.	PROPN
ejpam-5710	278	5	math	math	PROPN
ejpam-5710	278	6	,	,	PUNCT
ejpam-5710	278	7	18	18	NUM
ejpam-5710	278	8	(	(	PUNCT
ejpam-5710	278	9	1	1	NUM
ejpam-5710	278	10	)	)	PUNCT
ejpam-5710	278	11	(	(	PUNCT
ejpam-5710	278	12	2025	2025	NUM
ejpam-5710	278	13	)	)	PUNCT
ejpam-5710	278	14	,	,	PUNCT
ejpam-5710	278	15	5710	5710	NUM
ejpam-5710	278	16	15	15	NUM
ejpam-5710	278	17	of	of	ADP
ejpam-5710	278	18	18	18	NUM
ejpam-5710	278	19	√	√	NUM
ejpam-5710	278	20	3	3	NUM
ejpam-5710	278	21	cos	cos	X
ejpam-5710	278	22	(	(	PUNCT
ejpam-5710	278	23	s	s	NOUN
ejpam-5710	278	24	2	2	NUM
ejpam-5710	278	25	)	)	PUNCT
ejpam-5710	278	26	−	−	PROPN
ejpam-5710	278	27	u	u	NOUN
ejpam-5710	278	28	√	√	PROPN
ejpam-5710	278	29	3	3	NUM
ejpam-5710	278	30	cos(s	cos(s	NOUN
ejpam-5710	278	31	)	)	PUNCT
ejpam-5710	279	1	+	+	CCONJ
ejpam-5710	279	2	5	5	NUM
ejpam-5710	279	3	2	2	NUM
ejpam-5710	279	4	√	√	NUM
ejpam-5710	279	5	2	2	NUM
ejpam-5710	279	6	)	)	PUNCT
ejpam-5710	279	7	.	.	PUNCT
ejpam-5710	280	1	figure	figure	VERB
ejpam-5710	280	2	2	2	NUM
ejpam-5710	280	3	:	:	PUNCT
ejpam-5710	280	4	ruled	rule	VERB
ejpam-5710	280	5	surfaces	surface	NOUN
ejpam-5710	280	6	generated	generate	VERB
ejpam-5710	280	7	by	by	ADP
ejpam-5710	280	8	ξ(s	ξ(s	PROPN
ejpam-5710	280	9	)	)	PUNCT
ejpam-5710	280	10	abbreviation	abbreviation	NOUN
ejpam-5710	280	11	full	full	ADJ
ejpam-5710	280	12	form	form	NOUN
ejpam-5710	280	13	qrt	qrt	NOUN
ejpam-5710	280	14	quasi	quasi	ADJ
ejpam-5710	280	15	-	-	ADJ
ejpam-5710	280	16	tangent	tangent	ADJ
ejpam-5710	280	17	ruled	rule	VERB
ejpam-5710	280	18	surface	surface	PROPN
ejpam-5710	280	19	qrn	qrn	ADJ
ejpam-5710	280	20	quasi	quasi	ADJ
ejpam-5710	280	21	-	-	ADJ
ejpam-5710	280	22	normal	normal	ADJ
ejpam-5710	280	23	ruled	rule	VERB
ejpam-5710	280	24	surface	surface	NOUN
ejpam-5710	280	25	qrb	qrb	NOUN
ejpam-5710	280	26	quasi	quasi	ADJ
ejpam-5710	280	27	-	-	ADJ
ejpam-5710	280	28	binormal	binormal	ADJ
ejpam-5710	280	29	ruled	rule	VERB
ejpam-5710	280	30	surface	surface	NOUN
ejpam-5710	280	31	f.f	f.f	ADJ
ejpam-5710	280	32	fundamental	fundamental	ADJ
ejpam-5710	280	33	form	form	NOUN
ejpam-5710	280	34	gcurvature	gcurvature	NOUN
ejpam-5710	280	35	geodesic	geodesic	NOUN
ejpam-5710	280	36	curvature	curvature	NOUN
ejpam-5710	280	37	ncurvature	ncurvature	NOUN
ejpam-5710	280	38	normal	normal	ADJ
ejpam-5710	280	39	curvature	curvature	NOUN
ejpam-5710	280	40	gtorsion	gtorsion	NOUN
ejpam-5710	280	41	geodesic	geodesic	ADJ
ejpam-5710	280	42	torsion	torsion	NOUN
ejpam-5710	280	43	table	table	NOUN
ejpam-5710	280	44	1	1	NUM
ejpam-5710	280	45	:	:	PUNCT
ejpam-5710	280	46	list	list	NOUN
ejpam-5710	280	47	of	of	ADP
ejpam-5710	280	48	abbreviations	abbreviation	NOUN
ejpam-5710	280	49	4	4	NUM
ejpam-5710	280	50	.	.	PUNCT
ejpam-5710	281	1	conclusion	conclusion	NOUN
ejpam-5710	281	2	this	this	DET
ejpam-5710	281	3	paper	paper	NOUN
ejpam-5710	281	4	introduced	introduce	VERB
ejpam-5710	281	5	three	three	NUM
ejpam-5710	281	6	distinct	distinct	ADJ
ejpam-5710	281	7	types	type	NOUN
ejpam-5710	281	8	of	of	ADP
ejpam-5710	281	9	ruled	rule	VERB
ejpam-5710	281	10	surfaces	surface	NOUN
ejpam-5710	281	11	based	base	VERB
ejpam-5710	281	12	on	on	ADP
ejpam-5710	281	13	the	the	DET
ejpam-5710	281	14	quasiframe	quasiframe	NOUN
ejpam-5710	281	15	:	:	PUNCT
ejpam-5710	281	16	quasi	quasi	ADJ
ejpam-5710	281	17	-	-	NOUN
ejpam-5710	281	18	tangent	tangent	ADJ
ejpam-5710	281	19	(	(	PUNCT
ejpam-5710	281	20	qrt	qrt	PROPN
ejpam-5710	281	21	)	)	PUNCT
ejpam-5710	281	22	,	,	PUNCT
ejpam-5710	281	23	quasi	quasi	ADJ
ejpam-5710	281	24	-	-	ADJ
ejpam-5710	281	25	normal	normal	ADJ
ejpam-5710	281	26	(	(	PUNCT
ejpam-5710	281	27	qrn	qrn	NOUN
ejpam-5710	281	28	)	)	PUNCT
ejpam-5710	281	29	,	,	PUNCT
ejpam-5710	281	30	and	and	CCONJ
ejpam-5710	281	31	quasi	quasi	NOUN
ejpam-5710	281	32	-	-	NOUN
ejpam-5710	281	33	binormal	binormal	ADJ
ejpam-5710	281	34	(	(	PUNCT
ejpam-5710	281	35	qrb	qrb	NOUN
ejpam-5710	281	36	)	)	PUNCT
ejpam-5710	281	37	surfaces	surface	NOUN
ejpam-5710	281	38	.	.	PUNCT
ejpam-5710	282	1	these	these	DET
ejpam-5710	282	2	surfaces	surface	NOUN
ejpam-5710	282	3	are	be	AUX
ejpam-5710	282	4	generated	generate	VERB
ejpam-5710	282	5	by	by	ADP
ejpam-5710	282	6	the	the	DET
ejpam-5710	282	7	motion	motion	NOUN
ejpam-5710	282	8	of	of	ADP
ejpam-5710	282	9	a	a	DET
ejpam-5710	282	10	straight	straight	ADJ
ejpam-5710	282	11	line	line	NOUN
ejpam-5710	282	12	(	(	PUNCT
ejpam-5710	282	13	ruling	ruling	NOUN
ejpam-5710	282	14	)	)	PUNCT
ejpam-5710	282	15	along	along	ADP
ejpam-5710	282	16	a	a	DET
ejpam-5710	282	17	base	base	NOUN
ejpam-5710	282	18	curve	curve	NOUN
ejpam-5710	282	19	,	,	PUNCT
ejpam-5710	282	20	with	with	ADP
ejpam-5710	282	21	the	the	DET
ejpam-5710	282	22	direction	direction	NOUN
ejpam-5710	282	23	of	of	ADP
ejpam-5710	282	24	the	the	DET
ejpam-5710	282	25	ruling	ruling	NOUN
ejpam-5710	282	26	determined	determine	VERB
ejpam-5710	282	27	by	by	ADP
ejpam-5710	282	28	the	the	DET
ejpam-5710	282	29	quasi	quasi	NOUN
ejpam-5710	282	30	-	-	NOUN
ejpam-5710	282	31	tangent	tangent	ADJ
ejpam-5710	282	32	,	,	PUNCT
ejpam-5710	282	33	quasi	quasi	ADJ
ejpam-5710	282	34	-	-	ADJ
ejpam-5710	282	35	normal	normal	ADJ
ejpam-5710	282	36	,	,	PUNCT
ejpam-5710	282	37	and	and	CCONJ
ejpam-5710	282	38	quasibinormal	quasibinormal	ADJ
ejpam-5710	282	39	vectors	vector	NOUN
ejpam-5710	282	40	,	,	PUNCT
ejpam-5710	282	41	respectively	respectively	ADV
ejpam-5710	282	42	.	.	PUNCT
ejpam-5710	283	1	we	we	PRON
ejpam-5710	283	2	have	have	AUX
ejpam-5710	283	3	thoroughly	thoroughly	ADV
ejpam-5710	283	4	investigated	investigate	VERB
ejpam-5710	283	5	their	their	PRON
ejpam-5710	283	6	first	first	ADJ
ejpam-5710	283	7	,	,	PUNCT
ejpam-5710	283	8	second	second	ADJ
ejpam-5710	283	9	,	,	PUNCT
ejpam-5710	283	10	and	and	CCONJ
ejpam-5710	283	11	third	third	ADJ
ejpam-5710	283	12	fundamental	fundamental	ADJ
ejpam-5710	283	13	forms	form	NOUN
ejpam-5710	283	14	,	,	PUNCT
ejpam-5710	283	15	as	as	ADV
ejpam-5710	283	16	well	well	ADV
ejpam-5710	283	17	as	as	ADP
ejpam-5710	283	18	their	their	PRON
ejpam-5710	283	19	gaussian	gaussian	NOUN
ejpam-5710	283	20	and	and	CCONJ
ejpam-5710	283	21	mean	mean	ADJ
ejpam-5710	283	22	curvatures	curvature	NOUN
ejpam-5710	283	23	.	.	PUNCT
ejpam-5710	284	1	in	in	ADP
ejpam-5710	284	2	addition	addition	NOUN
ejpam-5710	284	3	,	,	PUNCT
ejpam-5710	284	4	we	we	PRON
ejpam-5710	284	5	have	have	AUX
ejpam-5710	284	6	also	also	ADV
ejpam-5710	284	7	explored	explore	VERB
ejpam-5710	284	8	the	the	DET
ejpam-5710	284	9	geodesic	geodesic	ADJ
ejpam-5710	284	10	curvature	curvature	NOUN
ejpam-5710	284	11	,	,	PUNCT
ejpam-5710	284	12	normal	normal	ADJ
ejpam-5710	284	13	curvature	curvature	NOUN
ejpam-5710	284	14	,	,	PUNCT
ejpam-5710	284	15	and	and	CCONJ
ejpam-5710	284	16	geodesic	geodesic	ADJ
ejpam-5710	284	17	torsion	torsion	NOUN
ejpam-5710	284	18	associated	associate	VERB
ejpam-5710	284	19	with	with	ADP
ejpam-5710	284	20	the	the	DET
ejpam-5710	284	21	base	base	NOUN
ejpam-5710	284	22	curve	curve	NOUN
ejpam-5710	284	23	for	for	ADP
ejpam-5710	284	24	each	each	DET
ejpam-5710	284	25	type	type	NOUN
ejpam-5710	284	26	of	of	ADP
ejpam-5710	284	27	surface	surface	NOUN
ejpam-5710	284	28	.	.	PUNCT
ejpam-5710	285	1	furthermore	furthermore	ADV
ejpam-5710	285	2	,	,	PUNCT
ejpam-5710	285	3	we	we	PRON
ejpam-5710	285	4	have	have	AUX
ejpam-5710	285	5	established	establish	VERB
ejpam-5710	285	6	a.	a.	NOUN
ejpam-5710	285	7	elsharkawy	elsharkawy	PROPN
ejpam-5710	285	8	,	,	PUNCT
ejpam-5710	285	9	h.	h.	PROPN
ejpam-5710	285	10	k.	k.	PROPN
ejpam-5710	285	11	elsayied	elsayied	PROPN
ejpam-5710	285	12	,	,	PUNCT
ejpam-5710	285	13	a.	a.	NOUN
ejpam-5710	285	14	refaat	refaat	PROPN
ejpam-5710	285	15	/	/	SYM
ejpam-5710	285	16	eur	eur	PROPN
ejpam-5710	285	17	.	.	PUNCT
ejpam-5710	286	1	j.	j.	PROPN
ejpam-5710	286	2	pure	pure	PROPN
ejpam-5710	286	3	appl	appl	PROPN
ejpam-5710	286	4	.	.	PROPN
ejpam-5710	286	5	math	math	PROPN
ejpam-5710	286	6	,	,	PUNCT
ejpam-5710	286	7	18	18	NUM
ejpam-5710	286	8	(	(	PUNCT
ejpam-5710	286	9	1	1	NUM
ejpam-5710	286	10	)	)	PUNCT
ejpam-5710	286	11	(	(	PUNCT
ejpam-5710	286	12	2025	2025	NUM
ejpam-5710	286	13	)	)	PUNCT
ejpam-5710	286	14	,	,	PUNCT
ejpam-5710	286	15	5710	5710	NUM
ejpam-5710	286	16	16	16	NUM
ejpam-5710	286	17	of	of	ADP
ejpam-5710	286	18	18	18	NUM
ejpam-5710	286	19	the	the	DET
ejpam-5710	286	20	conditions	condition	NOUN
ejpam-5710	286	21	under	under	ADP
ejpam-5710	286	22	which	which	PRON
ejpam-5710	286	23	the	the	DET
ejpam-5710	286	24	base	base	NOUN
ejpam-5710	286	25	curve	curve	NOUN
ejpam-5710	286	26	can	can	AUX
ejpam-5710	286	27	be	be	AUX
ejpam-5710	286	28	classified	classify	VERB
ejpam-5710	286	29	as	as	ADP
ejpam-5710	286	30	a	a	DET
ejpam-5710	286	31	geodesic	geodesic	NOUN
ejpam-5710	286	32	,	,	PUNCT
ejpam-5710	286	33	an	an	DET
ejpam-5710	286	34	asymptotic	asymptotic	ADJ
ejpam-5710	286	35	line	line	NOUN
ejpam-5710	286	36	,	,	PUNCT
ejpam-5710	286	37	or	or	CCONJ
ejpam-5710	286	38	a	a	DET
ejpam-5710	286	39	principal	principal	ADJ
ejpam-5710	286	40	line	line	NOUN
ejpam-5710	286	41	on	on	ADP
ejpam-5710	286	42	each	each	DET
ejpam-5710	286	43	type	type	NOUN
ejpam-5710	286	44	of	of	ADP
ejpam-5710	286	45	surface	surface	NOUN
ejpam-5710	286	46	.	.	PUNCT
ejpam-5710	287	1	we	we	PRON
ejpam-5710	287	2	have	have	AUX
ejpam-5710	287	3	also	also	ADV
ejpam-5710	287	4	derived	derive	VERB
ejpam-5710	287	5	the	the	DET
ejpam-5710	287	6	conditions	condition	NOUN
ejpam-5710	287	7	for	for	SCONJ
ejpam-5710	287	8	these	these	DET
ejpam-5710	287	9	surfaces	surface	NOUN
ejpam-5710	287	10	to	to	PART
ejpam-5710	287	11	be	be	AUX
ejpam-5710	287	12	developable	developable	ADJ
ejpam-5710	287	13	or	or	CCONJ
ejpam-5710	287	14	minimal	minimal	ADJ
ejpam-5710	287	15	.	.	PUNCT
ejpam-5710	288	1	to	to	PART
ejpam-5710	288	2	illustrate	illustrate	VERB
ejpam-5710	288	3	the	the	DET
ejpam-5710	288	4	theoretical	theoretical	ADJ
ejpam-5710	288	5	results	result	NOUN
ejpam-5710	288	6	,	,	PUNCT
ejpam-5710	288	7	we	we	PRON
ejpam-5710	288	8	provided	provide	VERB
ejpam-5710	288	9	two	two	NUM
ejpam-5710	288	10	detailed	detailed	ADJ
ejpam-5710	288	11	examples	example	NOUN
ejpam-5710	288	12	.	.	PUNCT
ejpam-5710	289	1	all	all	DET
ejpam-5710	289	2	the	the	DET
ejpam-5710	289	3	results	result	NOUN
ejpam-5710	289	4	derived	derive	VERB
ejpam-5710	289	5	in	in	ADP
ejpam-5710	289	6	this	this	DET
ejpam-5710	289	7	paper	paper	NOUN
ejpam-5710	289	8	can	can	AUX
ejpam-5710	289	9	be	be	AUX
ejpam-5710	289	10	specialized	specialize	VERB
ejpam-5710	289	11	to	to	ADP
ejpam-5710	289	12	the	the	DET
ejpam-5710	289	13	frenet	frenet	ADJ
ejpam-5710	289	14	frame	frame	NOUN
ejpam-5710	289	15	by	by	ADP
ejpam-5710	289	16	setting	set	VERB
ejpam-5710	289	17	κ2	κ2	NOUN
ejpam-5710	289	18	=	=	PUNCT
ejpam-5710	290	1	0	0	X
ejpam-5710	290	2	.	.	PUNCT
ejpam-5710	291	1	this	this	DET
ejpam-5710	291	2	connection	connection	NOUN
ejpam-5710	291	3	between	between	ADP
ejpam-5710	291	4	the	the	DET
ejpam-5710	291	5	quasi	quasi	NOUN
ejpam-5710	291	6	-	-	NOUN
ejpam-5710	291	7	frame	frame	NOUN
ejpam-5710	291	8	and	and	CCONJ
ejpam-5710	291	9	the	the	DET
ejpam-5710	291	10	frenet	frenet	ADJ
ejpam-5710	291	11	frame	frame	NOUN
ejpam-5710	291	12	allows	allow	VERB
ejpam-5710	291	13	for	for	ADP
ejpam-5710	291	14	a	a	DET
ejpam-5710	291	15	broader	broad	ADJ
ejpam-5710	291	16	interpretation	interpretation	NOUN
ejpam-5710	291	17	of	of	ADP
ejpam-5710	291	18	the	the	DET
ejpam-5710	291	19	results	result	NOUN
ejpam-5710	291	20	and	and	CCONJ
ejpam-5710	291	21	provides	provide	VERB
ejpam-5710	291	22	a	a	DET
ejpam-5710	291	23	bridge	bridge	NOUN
ejpam-5710	291	24	between	between	ADP
ejpam-5710	291	25	different	different	ADJ
ejpam-5710	291	26	geometric	geometric	ADJ
ejpam-5710	291	27	frameworks	framework	NOUN
ejpam-5710	291	28	.	.	PUNCT
ejpam-5710	292	1	future	future	ADJ
ejpam-5710	292	2	research	research	NOUN
ejpam-5710	292	3	could	could	AUX
ejpam-5710	292	4	explore	explore	VERB
ejpam-5710	292	5	the	the	DET
ejpam-5710	292	6	application	application	NOUN
ejpam-5710	292	7	of	of	ADP
ejpam-5710	292	8	quasi	quasi	NOUN
ejpam-5710	292	9	-	-	NOUN
ejpam-5710	292	10	frames	frame	NOUN
ejpam-5710	292	11	in	in	ADP
ejpam-5710	292	12	higher	high	ADJ
ejpam-5710	292	13	-	-	PUNCT
ejpam-5710	292	14	dimensional	dimensional	ADJ
ejpam-5710	292	15	spaces	space	NOUN
ejpam-5710	292	16	,	,	PUNCT
ejpam-5710	292	17	such	such	ADJ
ejpam-5710	292	18	as	as	ADP
ejpam-5710	292	19	minkowski	minkowski	ADJ
ejpam-5710	292	20	and	and	CCONJ
ejpam-5710	292	21	galilean	galilean	PROPN
ejpam-5710	292	22	spaces	space	NOUN
ejpam-5710	292	23	.	.	PUNCT
ejpam-5710	293	1	additionally	additionally	ADV
ejpam-5710	293	2	,	,	PUNCT
ejpam-5710	293	3	the	the	DET
ejpam-5710	293	4	study	study	NOUN
ejpam-5710	293	5	of	of	ADP
ejpam-5710	293	6	quasi	quasi	ADJ
ejpam-5710	293	7	-	-	ADJ
ejpam-5710	293	8	ruled	rule	VERB
ejpam-5710	293	9	surfaces	surface	NOUN
ejpam-5710	293	10	in	in	ADP
ejpam-5710	293	11	the	the	DET
ejpam-5710	293	12	context	context	NOUN
ejpam-5710	293	13	of	of	ADP
ejpam-5710	293	14	computer	computer	NOUN
ejpam-5710	293	15	-	-	PUNCT
ejpam-5710	293	16	aided	aid	VERB
ejpam-5710	293	17	design	design	NOUN
ejpam-5710	293	18	and	and	CCONJ
ejpam-5710	293	19	architecture	architecture	NOUN
ejpam-5710	293	20	could	could	AUX
ejpam-5710	293	21	lead	lead	VERB
ejpam-5710	293	22	to	to	ADP
ejpam-5710	293	23	new	new	ADJ
ejpam-5710	293	24	practical	practical	ADJ
ejpam-5710	293	25	applications	application	NOUN
ejpam-5710	293	26	.	.	PUNCT
ejpam-5710	294	1	further	further	ADJ
ejpam-5710	294	2	investigations	investigation	NOUN
ejpam-5710	294	3	into	into	ADP
ejpam-5710	294	4	the	the	DET
ejpam-5710	294	5	singularities	singularity	NOUN
ejpam-5710	294	6	of	of	ADP
ejpam-5710	294	7	the	the	DET
ejpam-5710	294	8	quasi	quasi	NOUN
ejpam-5710	294	9	-	-	NOUN
ejpam-5710	294	10	frame	frame	NOUN
ejpam-5710	294	11	and	and	CCONJ
ejpam-5710	294	12	their	their	PRON
ejpam-5710	294	13	implications	implication	NOUN
ejpam-5710	294	14	for	for	ADP
ejpam-5710	294	15	geometric	geometric	ADJ
ejpam-5710	294	16	modeling	modeling	NOUN
ejpam-5710	294	17	are	be	AUX
ejpam-5710	294	18	also	also	ADV
ejpam-5710	294	19	warranted	warrant	VERB
ejpam-5710	294	20	.	.	PUNCT
ejpam-5710	295	1	references	reference	NOUN
ejpam-5710	295	2	[	[	X
ejpam-5710	295	3	1	1	NUM
ejpam-5710	295	4	]	]	X
ejpam-5710	295	5	n.	n.	PROPN
ejpam-5710	295	6	h.	h.	PROPN
ejpam-5710	295	7	abdel	abdel	PROPN
ejpam-5710	295	8	-	-	PUNCT
ejpam-5710	295	9	all	all	PROPN
ejpam-5710	295	10	,	,	PUNCT
ejpam-5710	295	11	r.	r.	PROPN
ejpam-5710	295	12	a.	a.	PROPN
ejpam-5710	295	13	abdel	abdel	PROPN
ejpam-5710	295	14	-	-	PUNCT
ejpam-5710	295	15	baky	baky	PROPN
ejpam-5710	295	16	,	,	PUNCT
ejpam-5710	295	17	and	and	CCONJ
ejpam-5710	295	18	f.	f.	PROPN
ejpam-5710	295	19	m.	m.	PROPN
ejpam-5710	295	20	hamdoon	hamdoon	NOUN
ejpam-5710	295	21	.	.	PUNCT
ejpam-5710	296	1	ruled	rule	VERB
ejpam-5710	296	2	surfaces	surface	NOUN
ejpam-5710	296	3	with	with	ADP
ejpam-5710	296	4	timelike	timelike	NOUN
ejpam-5710	296	5	rulings	ruling	NOUN
ejpam-5710	296	6	.	.	PUNCT
ejpam-5710	297	1	applied	apply	VERB
ejpam-5710	297	2	mathematics	mathematic	NOUN
ejpam-5710	297	3	and	and	CCONJ
ejpam-5710	297	4	computation	computation	NOUN
ejpam-5710	297	5	,	,	PUNCT
ejpam-5710	297	6	147:241–253	147:241–253	NUM
ejpam-5710	297	7	,	,	PUNCT
ejpam-5710	297	8	2004	2004	NUM
ejpam-5710	297	9	.	.	PUNCT
ejpam-5710	298	1	[	[	X
ejpam-5710	298	2	2	2	NUM
ejpam-5710	298	3	]	]	PUNCT
ejpam-5710	298	4	p.	p.	NOUN
ejpam-5710	298	5	alegre	alegre	PROPN
ejpam-5710	298	6	,	,	PUNCT
ejpam-5710	298	7	k.	k.	PROPN
ejpam-5710	298	8	arslan	arslan	PROPN
ejpam-5710	298	9	,	,	PUNCT
ejpam-5710	298	10	a.	a.	NOUN
ejpam-5710	298	11	carriazo	carriazo	PROPN
ejpam-5710	298	12	,	,	PUNCT
ejpam-5710	298	13	c.	c.	PROPN
ejpam-5710	298	14	murathan	murathan	PROPN
ejpam-5710	298	15	,	,	PUNCT
ejpam-5710	298	16	and	and	CCONJ
ejpam-5710	298	17	g.	g.	PROPN
ejpam-5710	298	18	ozturk	ozturk	PROPN
ejpam-5710	298	19	.	.	PUNCT
ejpam-5710	299	1	some	some	DET
ejpam-5710	299	2	special	special	ADJ
ejpam-5710	299	3	types	type	NOUN
ejpam-5710	299	4	of	of	ADP
ejpam-5710	299	5	developable	developable	ADJ
ejpam-5710	299	6	ruled	rule	VERB
ejpam-5710	299	7	surface	surface	NOUN
ejpam-5710	299	8	.	.	PUNCT
ejpam-5710	300	1	hacettepe	hacettepe	PROPN
ejpam-5710	300	2	journal	journal	PROPN
ejpam-5710	300	3	of	of	ADP
ejpam-5710	300	4	mathematics	mathematic	NOUN
ejpam-5710	300	5	and	and	CCONJ
ejpam-5710	300	6	statistics	statistic	NOUN
ejpam-5710	300	7	,	,	PUNCT
ejpam-5710	300	8	39(3):319–325	39(3):319–325	PROPN
ejpam-5710	300	9	,	,	PUNCT
ejpam-5710	300	10	2010	2010	NUM
ejpam-5710	300	11	.	.	PUNCT
ejpam-5710	301	1	[	[	X
ejpam-5710	301	2	3	3	NUM
ejpam-5710	301	3	]	]	X
ejpam-5710	301	4	a.	a.	NOUN
ejpam-5710	301	5	t.	t.	PROPN
ejpam-5710	301	6	ali	ali	PROPN
ejpam-5710	301	7	,	,	PUNCT
ejpam-5710	301	8	h.	h.	PROPN
ejpam-5710	301	9	s.	s.	PROPN
ejpam-5710	301	10	a.	a.	PROPN
ejpam-5710	301	11	aziz	aziz	PROPN
ejpam-5710	301	12	,	,	PUNCT
ejpam-5710	301	13	and	and	CCONJ
ejpam-5710	301	14	a.	a.	PROPN
ejpam-5710	301	15	h.	h.	PROPN
ejpam-5710	301	16	sorour	sorour	PROPN
ejpam-5710	301	17	.	.	PUNCT
ejpam-5710	301	18	ruled	rule	VERB
ejpam-5710	301	19	surfaces	surface	NOUN
ejpam-5710	301	20	generated	generate	VERB
ejpam-5710	301	21	by	by	ADP
ejpam-5710	301	22	some	some	DET
ejpam-5710	301	23	special	special	ADJ
ejpam-5710	301	24	curves	curve	NOUN
ejpam-5710	301	25	in	in	ADP
ejpam-5710	301	26	euclidean	euclidean	ADJ
ejpam-5710	301	27	3	3	NUM
ejpam-5710	301	28	-	-	PUNCT
ejpam-5710	301	29	space	space	NOUN
ejpam-5710	301	30	.	.	PUNCT
ejpam-5710	302	1	journal	journal	NOUN
ejpam-5710	302	2	of	of	ADP
ejpam-5710	302	3	the	the	DET
ejpam-5710	302	4	egyptian	egyptian	PROPN
ejpam-5710	302	5	mathematical	mathematical	PROPN
ejpam-5710	302	6	society	society	NOUN
ejpam-5710	302	7	,	,	PUNCT
ejpam-5710	302	8	21(3):285–294	21(3):285–294	NOUN
ejpam-5710	302	9	,	,	PUNCT
ejpam-5710	302	10	2013	2013	NUM
ejpam-5710	302	11	.	.	PUNCT
ejpam-5710	303	1	[	[	X
ejpam-5710	303	2	4	4	NUM
ejpam-5710	303	3	]	]	PUNCT
ejpam-5710	303	4	a.	a.	NOUN
ejpam-5710	303	5	a.	a.	NOUN
ejpam-5710	303	6	almoneef	almoneef	PROPN
ejpam-5710	303	7	and	and	CCONJ
ejpam-5710	303	8	r.	r.	PROPN
ejpam-5710	303	9	a.	a.	PROPN
ejpam-5710	303	10	abdel	abdel	PROPN
ejpam-5710	303	11	-	-	PUNCT
ejpam-5710	303	12	baky	baky	PROPN
ejpam-5710	303	13	.	.	PUNCT
ejpam-5710	304	1	timelike	timelike	PROPN
ejpam-5710	304	2	constant	constant	ADJ
ejpam-5710	304	3	axis	axis	NOUN
ejpam-5710	304	4	ruled	rule	VERB
ejpam-5710	304	5	surface	surface	NOUN
ejpam-5710	304	6	family	family	NOUN
ejpam-5710	304	7	in	in	ADP
ejpam-5710	304	8	minkowski	minkowski	ADJ
ejpam-5710	304	9	3	3	NUM
ejpam-5710	304	10	-	-	PUNCT
ejpam-5710	304	11	space	space	NOUN
ejpam-5710	304	12	.	.	PUNCT
ejpam-5710	305	1	symmetry	symmetry	NOUN
ejpam-5710	305	2	,	,	PUNCT
ejpam-5710	305	3	16(6):677	16(6):677	NUM
ejpam-5710	305	4	,	,	PUNCT
ejpam-5710	305	5	2024	2024	NUM
ejpam-5710	305	6	.	.	PUNCT
ejpam-5710	306	1	[	[	X
ejpam-5710	306	2	5	5	NUM
ejpam-5710	306	3	]	]	PUNCT
ejpam-5710	306	4	c.	c.	PROPN
ejpam-5710	306	5	andradas	andradas	PROPN
ejpam-5710	306	6	,	,	PUNCT
ejpam-5710	306	7	t.	t.	PROPN
ejpam-5710	306	8	recio	recio	PROPN
ejpam-5710	306	9	,	,	PUNCT
ejpam-5710	306	10	l.	l.	PROPN
ejpam-5710	306	11	f.	f.	PROPN
ejpam-5710	306	12	tabera	tabera	PROPN
ejpam-5710	306	13	,	,	PUNCT
ejpam-5710	306	14	j.	j.	PROPN
ejpam-5710	306	15	r.	r.	PROPN
ejpam-5710	306	16	sendra	sendra	PROPN
ejpam-5710	306	17	,	,	PUNCT
ejpam-5710	306	18	and	and	CCONJ
ejpam-5710	306	19	c.	c.	PROPN
ejpam-5710	306	20	villarino	villarino	PROPN
ejpam-5710	306	21	.	.	PUNCT
ejpam-5710	307	1	proper	proper	ADJ
ejpam-5710	307	2	real	real	ADJ
ejpam-5710	307	3	reparametrization	reparametrization	NOUN
ejpam-5710	307	4	of	of	ADP
ejpam-5710	307	5	rational	rational	ADJ
ejpam-5710	307	6	ruled	rule	VERB
ejpam-5710	307	7	surfaces	surface	NOUN
ejpam-5710	307	8	.	.	PUNCT
ejpam-5710	308	1	computer	computer	NOUN
ejpam-5710	308	2	aided	aid	VERB
ejpam-5710	308	3	geometric	geometric	ADJ
ejpam-5710	308	4	design	design	NOUN
ejpam-5710	308	5	,	,	PUNCT
ejpam-5710	308	6	28(2):102–113	28(2):102–113	PROPN
ejpam-5710	308	7	,	,	PUNCT
ejpam-5710	308	8	2011	2011	NUM
ejpam-5710	308	9	.	.	PUNCT
ejpam-5710	309	1	[	[	X
ejpam-5710	309	2	6	6	NUM
ejpam-5710	309	3	]	]	PUNCT
ejpam-5710	309	4	l.	l.	PROPN
ejpam-5710	309	5	buse	buse	PROPN
ejpam-5710	309	6	,	,	PUNCT
ejpam-5710	309	7	m.	m.	NOUN
ejpam-5710	309	8	elkadi	elkadi	NOUN
ejpam-5710	309	9	,	,	PUNCT
ejpam-5710	309	10	and	and	CCONJ
ejpam-5710	309	11	a.	a.	NOUN
ejpam-5710	309	12	galligo	galligo	PROPN
ejpam-5710	309	13	.	.	PUNCT
ejpam-5710	310	1	a	a	DET
ejpam-5710	310	2	computational	computational	ADJ
ejpam-5710	310	3	study	study	NOUN
ejpam-5710	310	4	of	of	ADP
ejpam-5710	310	5	ruled	rule	VERB
ejpam-5710	310	6	surfaces	surface	NOUN
ejpam-5710	310	7	.	.	PUNCT
ejpam-5710	311	1	journal	journal	PROPN
ejpam-5710	311	2	of	of	ADP
ejpam-5710	311	3	symbolic	symbolic	ADJ
ejpam-5710	311	4	computation	computation	NOUN
ejpam-5710	311	5	,	,	PUNCT
ejpam-5710	311	6	44(3):232–241	44(3):232–241	NOUN
ejpam-5710	311	7	,	,	PUNCT
ejpam-5710	311	8	2009	2009	NUM
ejpam-5710	311	9	.	.	PUNCT
ejpam-5710	312	1	[	[	X
ejpam-5710	312	2	7	7	X
ejpam-5710	312	3	]	]	X
ejpam-5710	312	4	y.	y.	PROPN
ejpam-5710	312	5	chen	chen	PROPN
ejpam-5710	312	6	,	,	PUNCT
ejpam-5710	312	7	l.	l.	PROPN
ejpam-5710	312	8	y.	y.	PROPN
ejpam-5710	312	9	shen	shen	PROPN
ejpam-5710	312	10	,	,	PUNCT
ejpam-5710	312	11	and	and	CCONJ
ejpam-5710	312	12	c.	c.	PROPN
ejpam-5710	312	13	m.	m.	PROPN
ejpam-5710	312	14	yuan	yuan	PROPN
ejpam-5710	312	15	.	.	PUNCT
ejpam-5710	313	1	collision	collision	NOUN
ejpam-5710	313	2	and	and	CCONJ
ejpam-5710	313	3	intersection	intersection	NOUN
ejpam-5710	313	4	detection	detection	NOUN
ejpam-5710	313	5	of	of	ADP
ejpam-5710	313	6	two	two	NUM
ejpam-5710	313	7	ruled	rule	VERB
ejpam-5710	313	8	surfaces	surface	NOUN
ejpam-5710	313	9	using	use	VERB
ejpam-5710	313	10	bracket	bracket	NOUN
ejpam-5710	313	11	method	method	NOUN
ejpam-5710	313	12	.	.	PUNCT
ejpam-5710	314	1	computer	computer	NOUN
ejpam-5710	314	2	aided	aid	VERB
ejpam-5710	314	3	geometric	geometric	ADJ
ejpam-5710	314	4	design	design	NOUN
ejpam-5710	314	5	,	,	PUNCT
ejpam-5710	314	6	28(2):114	28(2):114	NOUN
ejpam-5710	314	7	–	–	PUNCT
ejpam-5710	314	8	126	126	NUM
ejpam-5710	314	9	,	,	PUNCT
ejpam-5710	314	10	2011	2011	NUM
ejpam-5710	314	11	.	.	PUNCT
ejpam-5710	315	1	[	[	X
ejpam-5710	315	2	8	8	X
ejpam-5710	315	3	]	]	PUNCT
ejpam-5710	315	4	t.	t.	PROPN
ejpam-5710	315	5	h.	h.	PROPN
ejpam-5710	315	6	colding	colding	PROPN
ejpam-5710	315	7	and	and	CCONJ
ejpam-5710	315	8	c.	c.	PROPN
ejpam-5710	315	9	d.	d.	PROPN
ejpam-5710	315	10	lellis	lellis	PROPN
ejpam-5710	315	11	.	.	PUNCT
ejpam-5710	316	1	the	the	DET
ejpam-5710	316	2	min	min	PROPN
ejpam-5710	316	3	-	-	ADJ
ejpam-5710	316	4	max	max	PROPN
ejpam-5710	316	5	construction	construction	NOUN
ejpam-5710	316	6	of	of	ADP
ejpam-5710	316	7	minimal	minimal	ADJ
ejpam-5710	316	8	surfaces	surface	NOUN
ejpam-5710	316	9	.	.	PUNCT
ejpam-5710	317	1	surveys	survey	NOUN
ejpam-5710	317	2	in	in	ADP
ejpam-5710	317	3	differential	differential	ADJ
ejpam-5710	317	4	geometry	geometry	NOUN
ejpam-5710	317	5	,	,	PUNCT
ejpam-5710	317	6	8(1):75–107	8(1):75–107	NUM
ejpam-5710	317	7	,	,	PUNCT
ejpam-5710	317	8	2003	2003	NUM
ejpam-5710	317	9	.	.	PUNCT
ejpam-5710	318	1	[	[	X
ejpam-5710	318	2	9	9	NUM
ejpam-5710	318	3	]	]	X
ejpam-5710	318	4	f.	f.	PROPN
ejpam-5710	318	5	dillen	dillen	PROPN
ejpam-5710	318	6	and	and	CCONJ
ejpam-5710	318	7	w.	w.	PROPN
ejpam-5710	318	8	sodsiri	sodsiri	PROPN
ejpam-5710	318	9	.	.	PUNCT
ejpam-5710	319	1	ruled	rule	VERB
ejpam-5710	319	2	surfaces	surface	NOUN
ejpam-5710	319	3	of	of	ADP
ejpam-5710	319	4	weingarten	weingarten	ADJ
ejpam-5710	319	5	type	type	NOUN
ejpam-5710	319	6	in	in	ADP
ejpam-5710	319	7	minkowski	minkowski	ADJ
ejpam-5710	319	8	3	3	NUM
ejpam-5710	319	9	-	-	PUNCT
ejpam-5710	319	10	space	space	NOUN
ejpam-5710	319	11	.	.	PUNCT
ejpam-5710	320	1	journal	journal	PROPN
ejpam-5710	320	2	of	of	ADP
ejpam-5710	320	3	geometry	geometry	NOUN
ejpam-5710	320	4	,	,	PUNCT
ejpam-5710	320	5	83:10–21	83:10–21	NUM
ejpam-5710	320	6	,	,	PUNCT
ejpam-5710	320	7	2005	2005	NUM
ejpam-5710	320	8	.	.	PUNCT
ejpam-5710	321	1	[	[	X
ejpam-5710	321	2	10	10	NUM
ejpam-5710	321	3	]	]	X
ejpam-5710	321	4	h.	h.	PROPN
ejpam-5710	321	5	k.	k.	PROPN
ejpam-5710	321	6	elsayied	elsayied	PROPN
ejpam-5710	321	7	,	,	PUNCT
ejpam-5710	321	8	a.	a.	NOUN
ejpam-5710	321	9	a.	a.	NOUN
ejpam-5710	321	10	altaha	altaha	NOUN
ejpam-5710	321	11	,	,	PUNCT
ejpam-5710	321	12	and	and	CCONJ
ejpam-5710	321	13	a.	a.	NOUN
ejpam-5710	321	14	elsharkawy	elsharkawy	PROPN
ejpam-5710	321	15	.	.	PUNCT
ejpam-5710	322	1	bertrand	bertrand	PROPN
ejpam-5710	322	2	curves	curve	VERB
ejpam-5710	322	3	with	with	ADP
ejpam-5710	322	4	the	the	DET
ejpam-5710	322	5	modified	modify	VERB
ejpam-5710	322	6	orthogonal	orthogonal	ADJ
ejpam-5710	322	7	frame	frame	NOUN
ejpam-5710	322	8	in	in	ADP
ejpam-5710	322	9	minkowski	minkowski	ADJ
ejpam-5710	322	10	3	3	NUM
ejpam-5710	322	11	-	-	PUNCT
ejpam-5710	322	12	space	space	NOUN
ejpam-5710	322	13	e3	e3	NOUN
ejpam-5710	322	14	1	1	NUM
ejpam-5710	322	15	.	.	PUNCT
ejpam-5710	322	16	revista	revista	PROPN
ejpam-5710	322	17	de	de	PROPN
ejpam-5710	322	18	educacion	educacion	PROPN
ejpam-5710	322	19	,	,	PUNCT
ejpam-5710	322	20	392(6):43–55	392(6):43–55	ADV
ejpam-5710	322	21	,	,	PUNCT
ejpam-5710	322	22	2022	2022	NUM
ejpam-5710	322	23	.	.	PUNCT
ejpam-5710	323	1	[	[	X
ejpam-5710	323	2	11	11	NUM
ejpam-5710	323	3	]	]	PUNCT
ejpam-5710	323	4	h.	h.	PROPN
ejpam-5710	323	5	k.	k.	PROPN
ejpam-5710	323	6	elsayied	elsayied	PROPN
ejpam-5710	323	7	,	,	PUNCT
ejpam-5710	323	8	m.	m.	NOUN
ejpam-5710	323	9	elzawy	elzawy	PROPN
ejpam-5710	323	10	,	,	PUNCT
ejpam-5710	323	11	and	and	CCONJ
ejpam-5710	323	12	a.	a.	NOUN
ejpam-5710	323	13	elsharkawy	elsharkawy	PROPN
ejpam-5710	323	14	.	.	PUNCT
ejpam-5710	324	1	equiform	equiform	PROPN
ejpam-5710	324	2	timelike	timelike	PROPN
ejpam-5710	324	3	normal	normal	ADJ
ejpam-5710	324	4	curves	curve	NOUN
ejpam-5710	324	5	in	in	ADP
ejpam-5710	324	6	minkowski	minkowski	ADJ
ejpam-5710	324	7	space	space	NOUN
ejpam-5710	324	8	e3	e3	NOUN
ejpam-5710	324	9	1	1	NUM
ejpam-5710	324	10	.	.	PUNCT
ejpam-5710	325	1	far	far	PROPN
ejpam-5710	325	2	east	east	PROPN
ejpam-5710	325	3	journal	journal	PROPN
ejpam-5710	325	4	of	of	ADP
ejpam-5710	325	5	mathematical	mathematical	ADJ
ejpam-5710	325	6	sciences	science	NOUN
ejpam-5710	325	7	,	,	PUNCT
ejpam-5710	325	8	101:1619–1629	101:1619–1629	NUM
ejpam-5710	325	9	,	,	PUNCT
ejpam-5710	325	10	2017	2017	NUM
ejpam-5710	325	11	.	.	PUNCT
ejpam-5710	326	1	a.	a.	NOUN
ejpam-5710	326	2	elsharkawy	elsharkawy	PROPN
ejpam-5710	326	3	,	,	PUNCT
ejpam-5710	326	4	h.	h.	PROPN
ejpam-5710	326	5	k.	k.	PROPN
ejpam-5710	326	6	elsayied	elsayied	PROPN
ejpam-5710	326	7	,	,	PUNCT
ejpam-5710	326	8	a.	a.	NOUN
ejpam-5710	326	9	refaat	refaat	PROPN
ejpam-5710	326	10	/	/	SYM
ejpam-5710	326	11	eur	eur	PROPN
ejpam-5710	326	12	.	.	PUNCT
ejpam-5710	327	1	j.	j.	PROPN
ejpam-5710	327	2	pure	pure	PROPN
ejpam-5710	327	3	appl	appl	PROPN
ejpam-5710	327	4	.	.	PROPN
ejpam-5710	327	5	math	math	PROPN
ejpam-5710	327	6	,	,	PUNCT
ejpam-5710	327	7	18	18	NUM
ejpam-5710	327	8	(	(	PUNCT
ejpam-5710	327	9	1	1	NUM
ejpam-5710	327	10	)	)	PUNCT
ejpam-5710	327	11	(	(	PUNCT
ejpam-5710	327	12	2025	2025	NUM
ejpam-5710	327	13	)	)	PUNCT
ejpam-5710	327	14	,	,	PUNCT
ejpam-5710	327	15	5710	5710	NUM
ejpam-5710	327	16	17	17	NUM
ejpam-5710	327	17	of	of	ADP
ejpam-5710	327	18	18	18	NUM
ejpam-5710	327	19	[	[	X
ejpam-5710	327	20	12	12	NUM
ejpam-5710	327	21	]	]	PUNCT
ejpam-5710	327	22	h.	h.	PROPN
ejpam-5710	327	23	k.	k.	PROPN
ejpam-5710	327	24	elsayied	elsayied	PROPN
ejpam-5710	327	25	,	,	PUNCT
ejpam-5710	327	26	m.	m.	NOUN
ejpam-5710	327	27	elzawy	elzawy	PROPN
ejpam-5710	327	28	,	,	PUNCT
ejpam-5710	327	29	and	and	CCONJ
ejpam-5710	327	30	a.	a.	NOUN
ejpam-5710	327	31	elsharkawy	elsharkawy	PROPN
ejpam-5710	327	32	.	.	PUNCT
ejpam-5710	328	1	equiform	equiform	PROPN
ejpam-5710	328	2	spacelike	spacelike	VERB
ejpam-5710	328	3	normal	normal	ADJ
ejpam-5710	328	4	curves	curve	NOUN
ejpam-5710	328	5	according	accord	VERB
ejpam-5710	328	6	to	to	ADP
ejpam-5710	328	7	equiform	equiform	NOUN
ejpam-5710	328	8	-	-	PUNCT
ejpam-5710	328	9	bishop	bishop	PROPN
ejpam-5710	328	10	frame	frame	NOUN
ejpam-5710	328	11	in	in	ADP
ejpam-5710	328	12	e3	e3	PROPN
ejpam-5710	328	13	1	1	NUM
ejpam-5710	328	14	.	.	PUNCT
ejpam-5710	329	1	mathematical	mathematical	ADJ
ejpam-5710	329	2	methods	method	NOUN
ejpam-5710	329	3	in	in	ADP
ejpam-5710	329	4	the	the	DET
ejpam-5710	329	5	applied	apply	VERB
ejpam-5710	329	6	sciences	science	NOUN
ejpam-5710	329	7	,	,	PUNCT
ejpam-5710	329	8	41(15):5754–5760	41(15):5754–5760	NUM
ejpam-5710	329	9	,	,	PUNCT
ejpam-5710	329	10	2018	2018	NUM
ejpam-5710	329	11	.	.	PUNCT
ejpam-5710	330	1	[	[	X
ejpam-5710	330	2	13	13	NUM
ejpam-5710	330	3	]	]	X
ejpam-5710	330	4	h.	h.	PROPN
ejpam-5710	330	5	k.	k.	PROPN
ejpam-5710	330	6	elsayied	elsayied	PROPN
ejpam-5710	330	7	,	,	PUNCT
ejpam-5710	330	8	a.	a.	PROPN
ejpam-5710	330	9	m.	m.	PROPN
ejpam-5710	330	10	tawfiq	tawfiq	PROPN
ejpam-5710	330	11	,	,	PUNCT
ejpam-5710	330	12	and	and	CCONJ
ejpam-5710	330	13	a.	a.	NOUN
ejpam-5710	330	14	elsharkawy	elsharkawy	PROPN
ejpam-5710	330	15	.	.	PUNCT
ejpam-5710	331	1	special	special	ADJ
ejpam-5710	331	2	smarandach	smarandach	ADJ
ejpam-5710	331	3	curves	curve	NOUN
ejpam-5710	331	4	according	accord	VERB
ejpam-5710	331	5	to	to	ADP
ejpam-5710	331	6	the	the	DET
ejpam-5710	331	7	quasi	quasi	ADJ
ejpam-5710	331	8	frame	frame	NOUN
ejpam-5710	331	9	in	in	ADP
ejpam-5710	331	10	4	4	NUM
ejpam-5710	331	11	-	-	PUNCT
ejpam-5710	331	12	dimensional	dimensional	ADJ
ejpam-5710	331	13	euclidean	euclidean	ADJ
ejpam-5710	331	14	space	space	NOUN
ejpam-5710	331	15	e4	e4	PROPN
ejpam-5710	331	16	.	.	PUNCT
ejpam-5710	332	1	houstoun	houstoun	PROPN
ejpam-5710	332	2	journal	journal	PROPN
ejpam-5710	332	3	of	of	ADP
ejpam-5710	332	4	mathematics	mathematic	NOUN
ejpam-5710	332	5	,	,	PUNCT
ejpam-5710	332	6	74:467–482	74:467–482	PROPN
ejpam-5710	332	7	,	,	PUNCT
ejpam-5710	332	8	2021	2021	NUM
ejpam-5710	332	9	.	.	PUNCT
ejpam-5710	333	1	[	[	X
ejpam-5710	333	2	14	14	NUM
ejpam-5710	333	3	]	]	X
ejpam-5710	333	4	h.	h.	PROPN
ejpam-5710	333	5	k.	k.	PROPN
ejpam-5710	333	6	elsayied	elsayied	PROPN
ejpam-5710	333	7	,	,	PUNCT
ejpam-5710	333	8	a.	a.	PROPN
ejpam-5710	333	9	m.	m.	PROPN
ejpam-5710	333	10	tawfiq	tawfiq	PROPN
ejpam-5710	333	11	,	,	PUNCT
ejpam-5710	333	12	and	and	CCONJ
ejpam-5710	333	13	a.	a.	NOUN
ejpam-5710	333	14	elsharkawy	elsharkawy	PROPN
ejpam-5710	333	15	.	.	PUNCT
ejpam-5710	334	1	the	the	DET
ejpam-5710	334	2	quasi	quasi	ADJ
ejpam-5710	334	3	frame	frame	NOUN
ejpam-5710	334	4	and	and	CCONJ
ejpam-5710	334	5	equations	equation	NOUN
ejpam-5710	334	6	of	of	ADP
ejpam-5710	334	7	non	non	ADJ
ejpam-5710	334	8	-	-	ADJ
ejpam-5710	334	9	lightlike	lightlike	ADJ
ejpam-5710	334	10	curves	curve	NOUN
ejpam-5710	334	11	in	in	ADP
ejpam-5710	334	12	minkowski	minkowski	ADJ
ejpam-5710	334	13	e3	e3	NOUN
ejpam-5710	334	14	1	1	NUM
ejpam-5710	334	15	and	and	CCONJ
ejpam-5710	334	16	e4	e4	PROPN
ejpam-5710	334	17	1	1	NUM
ejpam-5710	334	18	.	.	PUNCT
ejpam-5710	335	1	italian	italian	ADJ
ejpam-5710	335	2	journal	journal	NOUN
ejpam-5710	335	3	of	of	ADP
ejpam-5710	335	4	pure	pure	ADJ
ejpam-5710	335	5	and	and	CCONJ
ejpam-5710	335	6	applied	applied	ADJ
ejpam-5710	335	7	mathematics	mathematic	NOUN
ejpam-5710	335	8	,	,	PUNCT
ejpam-5710	335	9	225	225	NUM
ejpam-5710	335	10	,	,	PUNCT
ejpam-5710	335	11	2023	2023	NUM
ejpam-5710	335	12	.	.	PUNCT
ejpam-5710	336	1	[	[	X
ejpam-5710	336	2	15	15	NUM
ejpam-5710	336	3	]	]	PUNCT
ejpam-5710	336	4	a.	a.	NOUN
ejpam-5710	336	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	336	6	.	.	PUNCT
ejpam-5710	337	1	generalized	generalized	ADJ
ejpam-5710	337	2	involute	involute	NOUN
ejpam-5710	337	3	and	and	CCONJ
ejpam-5710	337	4	evolute	evolute	PROPN
ejpam-5710	337	5	curves	curve	NOUN
ejpam-5710	337	6	of	of	ADP
ejpam-5710	337	7	equiform	equiform	NOUN
ejpam-5710	337	8	spacelike	spacelike	PROPN
ejpam-5710	337	9	curves	curve	NOUN
ejpam-5710	337	10	with	with	ADP
ejpam-5710	337	11	a	a	DET
ejpam-5710	337	12	timelike	timelike	PROPN
ejpam-5710	337	13	equiform	equiform	NOUN
ejpam-5710	337	14	principal	principal	NOUN
ejpam-5710	337	15	normal	normal	ADJ
ejpam-5710	337	16	in	in	ADP
ejpam-5710	337	17	e3	e3	PROPN
ejpam-5710	337	18	1	1	NUM
ejpam-5710	337	19	.	.	PUNCT
ejpam-5710	338	1	journal	journal	NOUN
ejpam-5710	338	2	of	of	ADP
ejpam-5710	338	3	the	the	DET
ejpam-5710	338	4	egyptian	egyptian	PROPN
ejpam-5710	338	5	mathematical	mathematical	PROPN
ejpam-5710	338	6	society	society	NOUN
ejpam-5710	338	7	,	,	PUNCT
ejpam-5710	338	8	28(1):26	28(1):26	NUM
ejpam-5710	338	9	,	,	PUNCT
ejpam-5710	338	10	2020	2020	NUM
ejpam-5710	338	11	.	.	PUNCT
ejpam-5710	339	1	[	[	X
ejpam-5710	339	2	16	16	NUM
ejpam-5710	339	3	]	]	PUNCT
ejpam-5710	339	4	a.	a.	NOUN
ejpam-5710	339	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	339	6	.	.	PUNCT
ejpam-5710	340	1	exploring	explore	VERB
ejpam-5710	340	2	hasimoto	hasimoto	NOUN
ejpam-5710	340	3	surfaces	surface	NOUN
ejpam-5710	340	4	within	within	ADP
ejpam-5710	340	5	equiform	equiform	NOUN
ejpam-5710	340	6	geometry	geometry	NOUN
ejpam-5710	340	7	in	in	ADP
ejpam-5710	340	8	minkowski	minkowski	ADJ
ejpam-5710	340	9	space	space	NOUN
ejpam-5710	340	10	.	.	PUNCT
ejpam-5710	341	1	physica	physica	PROPN
ejpam-5710	341	2	scripta	scripta	PROPN
ejpam-5710	341	3	,	,	PUNCT
ejpam-5710	341	4	100(1):016101	100(1):016101	NUM
ejpam-5710	341	5	,	,	PUNCT
ejpam-5710	341	6	2024	2024	NUM
ejpam-5710	341	7	.	.	PUNCT
ejpam-5710	342	1	[	[	X
ejpam-5710	342	2	17	17	NUM
ejpam-5710	342	3	]	]	PUNCT
ejpam-5710	342	4	a.	a.	NOUN
ejpam-5710	342	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	342	6	,	,	PUNCT
ejpam-5710	342	7	c.	c.	PROPN
ejpam-5710	342	8	cesarano	cesarano	PROPN
ejpam-5710	342	9	,	,	PUNCT
ejpam-5710	342	10	and	and	CCONJ
ejpam-5710	342	11	h.	h.	PROPN
ejpam-5710	342	12	alhazmi	alhazmi	PROPN
ejpam-5710	342	13	.	.	PUNCT
ejpam-5710	343	1	on	on	ADP
ejpam-5710	343	2	the	the	DET
ejpam-5710	343	3	jerk	jerk	NOUN
ejpam-5710	343	4	and	and	CCONJ
ejpam-5710	343	5	snap	snap	VERB
ejpam-5710	343	6	in	in	ADP
ejpam-5710	343	7	motion	motion	NOUN
ejpam-5710	343	8	along	along	ADP
ejpam-5710	343	9	non	non	ADJ
ejpam-5710	343	10	-	-	ADJ
ejpam-5710	343	11	lightlike	lightlike	ADJ
ejpam-5710	343	12	curves	curve	NOUN
ejpam-5710	343	13	in	in	ADP
ejpam-5710	343	14	minkowski	minkowski	ADJ
ejpam-5710	343	15	3	3	NUM
ejpam-5710	343	16	-	-	PUNCT
ejpam-5710	343	17	space	space	NOUN
ejpam-5710	343	18	.	.	PUNCT
ejpam-5710	344	1	mathematical	mathematical	ADJ
ejpam-5710	344	2	methods	method	NOUN
ejpam-5710	344	3	in	in	ADP
ejpam-5710	344	4	the	the	DET
ejpam-5710	344	5	applied	apply	VERB
ejpam-5710	344	6	sciences	science	NOUN
ejpam-5710	344	7	,	,	PUNCT
ejpam-5710	344	8	pages	page	NOUN
ejpam-5710	344	9	1–13	1–13	NOUN
ejpam-5710	344	10	,	,	PUNCT
ejpam-5710	344	11	2024	2024	NUM
ejpam-5710	344	12	.	.	PUNCT
ejpam-5710	345	1	[	[	X
ejpam-5710	345	2	18	18	NUM
ejpam-5710	345	3	]	]	PUNCT
ejpam-5710	345	4	a.	a.	NOUN
ejpam-5710	345	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	345	6	,	,	PUNCT
ejpam-5710	345	7	c.	c.	PROPN
ejpam-5710	345	8	cesarano	cesarano	PROPN
ejpam-5710	345	9	,	,	PUNCT
ejpam-5710	345	10	a.	a.	PROPN
ejpam-5710	345	11	tawfiq	tawfiq	PROPN
ejpam-5710	345	12	,	,	PUNCT
ejpam-5710	345	13	and	and	CCONJ
ejpam-5710	345	14	a.	a.	NOUN
ejpam-5710	345	15	a.	a.	PROPN
ejpam-5710	345	16	ismail	ismail	PROPN
ejpam-5710	345	17	.	.	PUNCT
ejpam-5710	346	1	the	the	DET
ejpam-5710	346	2	non	non	ADJ
ejpam-5710	346	3	-	-	ADJ
ejpam-5710	346	4	linear	linear	ADJ
ejpam-5710	346	5	schrodinger	schrodinger	NOUN
ejpam-5710	346	6	equation	equation	NOUN
ejpam-5710	346	7	associated	associate	VERB
ejpam-5710	346	8	with	with	ADP
ejpam-5710	346	9	the	the	DET
ejpam-5710	346	10	soliton	soliton	NOUN
ejpam-5710	346	11	surfaces	surface	NOUN
ejpam-5710	346	12	in	in	ADP
ejpam-5710	346	13	minkowski	minkowski	ADJ
ejpam-5710	346	14	3	3	NUM
ejpam-5710	346	15	-	-	PUNCT
ejpam-5710	346	16	space	space	NOUN
ejpam-5710	346	17	.	.	PUNCT
ejpam-5710	346	18	aims	aim	VERB
ejpam-5710	346	19	mathematics	mathematic	NOUN
ejpam-5710	346	20	,	,	PUNCT
ejpam-5710	346	21	7:17879–17893	7:17879–17893	NUM
ejpam-5710	346	22	,	,	PUNCT
ejpam-5710	346	23	2022	2022	NUM
ejpam-5710	346	24	.	.	PUNCT
ejpam-5710	347	1	[	[	X
ejpam-5710	347	2	19	19	NUM
ejpam-5710	347	3	]	]	PUNCT
ejpam-5710	347	4	a.	a.	NOUN
ejpam-5710	347	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	347	6	and	and	CCONJ
ejpam-5710	347	7	a.	a.	NOUN
ejpam-5710	347	8	m.	m.	PROPN
ejpam-5710	347	9	elshenhab	elshenhab	PROPN
ejpam-5710	347	10	.	.	PUNCT
ejpam-5710	348	1	mannheim	mannheim	NOUN
ejpam-5710	348	2	curves	curve	NOUN
ejpam-5710	348	3	and	and	CCONJ
ejpam-5710	348	4	their	their	PRON
ejpam-5710	348	5	partner	partner	NOUN
ejpam-5710	348	6	curves	curve	NOUN
ejpam-5710	348	7	in	in	ADP
ejpam-5710	348	8	minkowski	minkowski	ADJ
ejpam-5710	348	9	3	3	NUM
ejpam-5710	348	10	-	-	PUNCT
ejpam-5710	348	11	space	space	NOUN
ejpam-5710	348	12	e3	e3	NOUN
ejpam-5710	348	13	1	1	NUM
ejpam-5710	348	14	.	.	PUNCT
ejpam-5710	348	15	demonstratio	demonstratio	PROPN
ejpam-5710	348	16	mathematica	mathematica	PROPN
ejpam-5710	348	17	,	,	PUNCT
ejpam-5710	348	18	55(1):798–811	55(1):798–811	PROPN
ejpam-5710	348	19	,	,	PUNCT
ejpam-5710	348	20	2022	2022	NUM
ejpam-5710	348	21	.	.	PUNCT
ejpam-5710	349	1	[	[	X
ejpam-5710	349	2	20	20	NUM
ejpam-5710	349	3	]	]	PUNCT
ejpam-5710	349	4	a.	a.	NOUN
ejpam-5710	349	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	349	6	,	,	PUNCT
ejpam-5710	349	7	y.	y.	PROPN
ejpam-5710	349	8	tashkandy	tashkandy	PROPN
ejpam-5710	349	9	,	,	PUNCT
ejpam-5710	349	10	w.	w.	PROPN
ejpam-5710	349	11	emam	emam	PROPN
ejpam-5710	349	12	,	,	PUNCT
ejpam-5710	349	13	c.	c.	PROPN
ejpam-5710	349	14	cesarano	cesarano	PROPN
ejpam-5710	349	15	,	,	PUNCT
ejpam-5710	349	16	and	and	CCONJ
ejpam-5710	349	17	n.	n.	NOUN
ejpam-5710	349	18	elsharkawy	elsharkawy	NOUN
ejpam-5710	349	19	.	.	PUNCT
ejpam-5710	350	1	on	on	ADP
ejpam-5710	350	2	some	some	DET
ejpam-5710	350	3	quasi	quasi	NOUN
ejpam-5710	350	4	-	-	NOUN
ejpam-5710	350	5	curves	curve	NOUN
ejpam-5710	350	6	in	in	ADP
ejpam-5710	350	7	galilean	galilean	PROPN
ejpam-5710	350	8	three	three	NUM
ejpam-5710	350	9	-	-	PUNCT
ejpam-5710	350	10	space	space	NOUN
ejpam-5710	350	11	.	.	PUNCT
ejpam-5710	351	1	axioms	axiom	NOUN
ejpam-5710	351	2	,	,	PUNCT
ejpam-5710	351	3	12(9):823	12(9):823	NUM
ejpam-5710	351	4	,	,	PUNCT
ejpam-5710	351	5	2023	2023	NUM
ejpam-5710	351	6	.	.	PUNCT
ejpam-5710	352	1	[	[	X
ejpam-5710	352	2	21	21	NUM
ejpam-5710	352	3	]	]	X
ejpam-5710	352	4	n.	n.	NOUN
ejpam-5710	352	5	elsharkawy	elsharkawy	PROPN
ejpam-5710	352	6	,	,	PUNCT
ejpam-5710	352	7	c.	c.	PROPN
ejpam-5710	352	8	cesarano	cesarano	PROPN
ejpam-5710	352	9	,	,	PUNCT
ejpam-5710	352	10	r.	r.	PROPN
ejpam-5710	352	11	dmytryshyn	dmytryshyn	PROPN
ejpam-5710	352	12	,	,	PUNCT
ejpam-5710	352	13	and	and	CCONJ
ejpam-5710	352	14	a.	a.	NOUN
ejpam-5710	352	15	elsharkawy	elsharkawy	PROPN
ejpam-5710	352	16	.	.	PUNCT
ejpam-5710	353	1	timelike	timelike	PROPN
ejpam-5710	353	2	spherical	spherical	ADJ
ejpam-5710	353	3	curves	curve	NOUN
ejpam-5710	353	4	according	accord	VERB
ejpam-5710	353	5	to	to	ADP
ejpam-5710	353	6	equiform	equiform	NOUN
ejpam-5710	353	7	bishop	bishop	PROPN
ejpam-5710	353	8	frame	frame	NOUN
ejpam-5710	353	9	in	in	ADP
ejpam-5710	353	10	3	3	NUM
ejpam-5710	353	11	-	-	PUNCT
ejpam-5710	353	12	dimensional	dimensional	ADJ
ejpam-5710	353	13	minkowski	minkowski	ADJ
ejpam-5710	353	14	space	space	NOUN
ejpam-5710	353	15	.	.	PUNCT
ejpam-5710	354	1	carpathian	carpathian	ADJ
ejpam-5710	354	2	mathematical	mathematical	ADJ
ejpam-5710	354	3	publications	publication	NOUN
ejpam-5710	354	4	,	,	PUNCT
ejpam-5710	354	5	15(2):88–95	15(2):88–95	NUM
ejpam-5710	354	6	,	,	PUNCT
ejpam-5710	354	7	2023	2023	NUM
ejpam-5710	354	8	.	.	PUNCT
ejpam-5710	355	1	[	[	X
ejpam-5710	355	2	22	22	NUM
ejpam-5710	355	3	]	]	PUNCT
ejpam-5710	355	4	a.	a.	NOUN
ejpam-5710	355	5	m.	m.	PROPN
ejpam-5710	355	6	elshenhab	elshenhab	PROPN
ejpam-5710	355	7	,	,	PUNCT
ejpam-5710	355	8	o.	o.	PROPN
ejpam-5710	355	9	moaaz	moaaz	PROPN
ejpam-5710	355	10	,	,	PUNCT
ejpam-5710	355	11	i.	i.	NOUN
ejpam-5710	355	12	dassios	dassios	PROPN
ejpam-5710	355	13	,	,	PUNCT
ejpam-5710	355	14	and	and	CCONJ
ejpam-5710	355	15	a.	a.	NOUN
ejpam-5710	355	16	elsharkawy	elsharkawy	PROPN
ejpam-5710	355	17	.	.	PUNCT
ejpam-5710	356	1	motion	motion	NOUN
ejpam-5710	356	2	along	along	ADP
ejpam-5710	356	3	a	a	DET
ejpam-5710	356	4	space	space	NOUN
ejpam-5710	356	5	curve	curve	NOUN
ejpam-5710	356	6	with	with	ADP
ejpam-5710	356	7	a	a	DET
ejpam-5710	356	8	quasi	quasi	NOUN
ejpam-5710	356	9	-	-	NOUN
ejpam-5710	356	10	frame	frame	NOUN
ejpam-5710	356	11	in	in	ADP
ejpam-5710	356	12	euclidean	euclidean	ADJ
ejpam-5710	356	13	3	3	NUM
ejpam-5710	356	14	-	-	PUNCT
ejpam-5710	356	15	space	space	NOUN
ejpam-5710	356	16	:	:	PUNCT
ejpam-5710	356	17	acceleration	acceleration	NOUN
ejpam-5710	356	18	and	and	CCONJ
ejpam-5710	356	19	jerk	jerk	NOUN
ejpam-5710	356	20	.	.	PUNCT
ejpam-5710	357	1	symmetry	symmetry	PROPN
ejpam-5710	357	2	,	,	PUNCT
ejpam-5710	357	3	14:1610	14:1610	NUM
ejpam-5710	357	4	,	,	PUNCT
ejpam-5710	357	5	2022	2022	NUM
ejpam-5710	357	6	.	.	PUNCT
ejpam-5710	358	1	[	[	X
ejpam-5710	358	2	23	23	NUM
ejpam-5710	358	3	]	]	X
ejpam-5710	358	4	r.	r.	PROPN
ejpam-5710	358	5	evans	evans	PROPN
ejpam-5710	358	6	.	.	PUNCT
ejpam-5710	359	1	the	the	DET
ejpam-5710	359	2	projective	projective	ADJ
ejpam-5710	359	3	cast	cast	NOUN
ejpam-5710	359	4	:	:	PUNCT
ejpam-5710	359	5	architecture	architecture	NOUN
ejpam-5710	359	6	and	and	CCONJ
ejpam-5710	359	7	its	its	PRON
ejpam-5710	359	8	three	three	NUM
ejpam-5710	359	9	geometries	geometry	NOUN
ejpam-5710	359	10	.	.	PUNCT
ejpam-5710	360	1	mit	mit	PROPN
ejpam-5710	360	2	press	press	PROPN
ejpam-5710	360	3	,	,	PUNCT
ejpam-5710	360	4	2000	2000	NUM
ejpam-5710	360	5	.	.	PUNCT
ejpam-5710	361	1	[	[	X
ejpam-5710	361	2	24	24	NUM
ejpam-5710	361	3	]	]	PUNCT
ejpam-5710	361	4	e.	e.	PROPN
ejpam-5710	361	5	hamouda	hamouda	PROPN
ejpam-5710	361	6	,	,	PUNCT
ejpam-5710	361	7	c.	c.	PROPN
ejpam-5710	361	8	cesarano	cesarano	PROPN
ejpam-5710	361	9	,	,	PUNCT
ejpam-5710	361	10	s.	s.	PROPN
ejpam-5710	361	11	askar	askar	PROPN
ejpam-5710	361	12	,	,	PUNCT
ejpam-5710	361	13	and	and	CCONJ
ejpam-5710	361	14	a.	a.	NOUN
ejpam-5710	361	15	elsharkawy	elsharkawy	NOUN
ejpam-5710	361	16	.	.	PUNCT
ejpam-5710	362	1	resolutions	resolution	NOUN
ejpam-5710	362	2	of	of	ADP
ejpam-5710	362	3	the	the	DET
ejpam-5710	362	4	jerk	jerk	NOUN
ejpam-5710	362	5	and	and	CCONJ
ejpam-5710	362	6	snap	snap	VERB
ejpam-5710	362	7	vectors	vector	NOUN
ejpam-5710	362	8	for	for	ADP
ejpam-5710	362	9	a	a	DET
ejpam-5710	362	10	quasi	quasi	ADJ
ejpam-5710	362	11	curve	curve	NOUN
ejpam-5710	362	12	in	in	ADP
ejpam-5710	362	13	euclidean	euclidean	ADJ
ejpam-5710	362	14	3	3	NUM
ejpam-5710	362	15	-	-	PUNCT
ejpam-5710	362	16	space	space	NOUN
ejpam-5710	362	17	.	.	PUNCT
ejpam-5710	363	1	mathematics	mathematic	NOUN
ejpam-5710	363	2	,	,	PUNCT
ejpam-5710	363	3	9(23):3128	9(23):3128	NOUN
ejpam-5710	363	4	,	,	PUNCT
ejpam-5710	363	5	2021	2021	NUM
ejpam-5710	363	6	.	.	PUNCT
ejpam-5710	364	1	[	[	X
ejpam-5710	364	2	25	25	NUM
ejpam-5710	364	3	]	]	PUNCT
ejpam-5710	364	4	e.	e.	PROPN
ejpam-5710	364	5	hamouda	hamouda	PROPN
ejpam-5710	364	6	,	,	PUNCT
ejpam-5710	364	7	o.	o.	PROPN
ejpam-5710	364	8	moaaz	moaaz	PROPN
ejpam-5710	364	9	,	,	PUNCT
ejpam-5710	364	10	c.	c.	PROPN
ejpam-5710	364	11	cesarano	cesarano	PROPN
ejpam-5710	364	12	,	,	PUNCT
ejpam-5710	364	13	s.	s.	PROPN
ejpam-5710	364	14	askar	askar	PROPN
ejpam-5710	364	15	,	,	PUNCT
ejpam-5710	364	16	and	and	CCONJ
ejpam-5710	364	17	a.	a.	NOUN
ejpam-5710	364	18	elsharkawy	elsharkawy	PROPN
ejpam-5710	364	19	.	.	PUNCT
ejpam-5710	365	1	geometry	geometry	NOUN
ejpam-5710	365	2	of	of	ADP
ejpam-5710	365	3	solutions	solution	NOUN
ejpam-5710	365	4	of	of	ADP
ejpam-5710	365	5	the	the	DET
ejpam-5710	365	6	quasi	quasi	ADJ
ejpam-5710	365	7	-	-	ADJ
ejpam-5710	365	8	vortex	vortex	ADJ
ejpam-5710	365	9	filament	filament	NOUN
ejpam-5710	365	10	equation	equation	NOUN
ejpam-5710	365	11	in	in	ADP
ejpam-5710	365	12	euclidean	euclidean	ADJ
ejpam-5710	365	13	3	3	NUM
ejpam-5710	365	14	-	-	PUNCT
ejpam-5710	365	15	space	space	NOUN
ejpam-5710	365	16	e3	e3	NOUN
ejpam-5710	365	17	.	.	PUNCT
ejpam-5710	366	1	mathematics	mathematic	NOUN
ejpam-5710	366	2	,	,	PUNCT
ejpam-5710	366	3	10:891	10:891	NUM
ejpam-5710	366	4	,	,	PUNCT
ejpam-5710	366	5	2022	2022	NUM
ejpam-5710	366	6	.	.	PUNCT
ejpam-5710	367	1	[	[	X
ejpam-5710	367	2	26	26	NUM
ejpam-5710	367	3	]	]	X
ejpam-5710	367	4	g.	g.	PROPN
ejpam-5710	367	5	hu	hu	PROPN
ejpam-5710	367	6	,	,	PUNCT
ejpam-5710	367	7	h.	h.	PROPN
ejpam-5710	367	8	cao	cao	PROPN
ejpam-5710	367	9	,	,	PUNCT
ejpam-5710	367	10	j.	j.	PROPN
ejpam-5710	367	11	wu	wu	PROPN
ejpam-5710	367	12	,	,	PUNCT
ejpam-5710	367	13	and	and	CCONJ
ejpam-5710	367	14	g.	g.	PROPN
ejpam-5710	367	15	wei	wei	PROPN
ejpam-5710	367	16	.	.	PUNCT
ejpam-5710	368	1	construction	construction	NOUN
ejpam-5710	368	2	of	of	ADP
ejpam-5710	368	3	developable	developable	ADJ
ejpam-5710	368	4	surfaces	surface	NOUN
ejpam-5710	368	5	using	use	VERB
ejpam-5710	368	6	generalized	generalized	ADJ
ejpam-5710	368	7	c	c	NOUN
ejpam-5710	368	8	-	-	PUNCT
ejpam-5710	368	9	bezier	bezier	NOUN
ejpam-5710	368	10	bases	basis	NOUN
ejpam-5710	368	11	with	with	ADP
ejpam-5710	368	12	shape	shape	NOUN
ejpam-5710	368	13	parameters	parameter	NOUN
ejpam-5710	368	14	.	.	PUNCT
ejpam-5710	369	1	computational	computational	ADJ
ejpam-5710	369	2	and	and	CCONJ
ejpam-5710	369	3	applied	applied	ADJ
ejpam-5710	369	4	mathematics	mathematic	NOUN
ejpam-5710	369	5	,	,	PUNCT
ejpam-5710	369	6	39(3	39(3	NUM
ejpam-5710	369	7	)	)	PUNCT
ejpam-5710	369	8	,	,	PUNCT
ejpam-5710	369	9	2020	2020	NUM
ejpam-5710	369	10	.	.	PUNCT
ejpam-5710	370	1	[	[	X
ejpam-5710	370	2	27	27	NUM
ejpam-5710	370	3	]	]	PUNCT
ejpam-5710	370	4	a.	a.	NOUN
ejpam-5710	370	5	karger	karger	PROPN
ejpam-5710	370	6	and	and	CCONJ
ejpam-5710	370	7	j.	j.	PROPN
ejpam-5710	370	8	novak	novak	PROPN
ejpam-5710	370	9	.	.	PUNCT
ejpam-5710	370	10	space	space	NOUN
ejpam-5710	370	11	kinematics	kinematic	NOUN
ejpam-5710	370	12	and	and	CCONJ
ejpam-5710	370	13	lie	lie	NOUN
ejpam-5710	370	14	groups	group	NOUN
ejpam-5710	370	15	.	.	PUNCT
ejpam-5710	371	1	stnl	stnl	ADJ
ejpam-5710	371	2	publishers	publisher	NOUN
ejpam-5710	371	3	of	of	ADP
ejpam-5710	371	4	technical	technical	ADJ
ejpam-5710	371	5	literature	literature	PROPN
ejpam-5710	371	6	,	,	PUNCT
ejpam-5710	371	7	prague	prague	PROPN
ejpam-5710	371	8	,	,	PUNCT
ejpam-5710	371	9	1978	1978	NUM
ejpam-5710	371	10	.	.	PUNCT
ejpam-5710	372	1	[	[	X
ejpam-5710	372	2	28	28	NUM
ejpam-5710	372	3	]	]	X
ejpam-5710	372	4	y.	y.	PROPN
ejpam-5710	372	5	h.	h.	PROPN
ejpam-5710	372	6	kim	kim	PROPN
ejpam-5710	372	7	and	and	CCONJ
ejpam-5710	372	8	w.	w.	PROPN
ejpam-5710	372	9	d.	d.	PROPN
ejpam-5710	372	10	yoon	yoon	PROPN
ejpam-5710	372	11	.	.	PUNCT
ejpam-5710	373	1	classification	classification	NOUN
ejpam-5710	373	2	of	of	ADP
ejpam-5710	373	3	ruled	rule	VERB
ejpam-5710	373	4	surfaces	surface	NOUN
ejpam-5710	373	5	in	in	ADP
ejpam-5710	373	6	minkowski	minkowski	ADJ
ejpam-5710	373	7	3	3	NUM
ejpam-5710	373	8	-	-	PUNCT
ejpam-5710	373	9	space	space	NOUN
ejpam-5710	373	10	.	.	PUNCT
ejpam-5710	374	1	a.	a.	NOUN
ejpam-5710	374	2	elsharkawy	elsharkawy	PROPN
ejpam-5710	374	3	,	,	PUNCT
ejpam-5710	374	4	h.	h.	PROPN
ejpam-5710	374	5	k.	k.	PROPN
ejpam-5710	374	6	elsayied	elsayied	PROPN
ejpam-5710	374	7	,	,	PUNCT
ejpam-5710	374	8	a.	a.	NOUN
ejpam-5710	374	9	refaat	refaat	PROPN
ejpam-5710	374	10	/	/	SYM
ejpam-5710	374	11	eur	eur	PROPN
ejpam-5710	374	12	.	.	PUNCT
ejpam-5710	375	1	j.	j.	PROPN
ejpam-5710	375	2	pure	pure	PROPN
ejpam-5710	375	3	appl	appl	PROPN
ejpam-5710	375	4	.	.	PROPN
ejpam-5710	375	5	math	math	PROPN
ejpam-5710	375	6	,	,	PUNCT
ejpam-5710	375	7	18	18	NUM
ejpam-5710	375	8	(	(	PUNCT
ejpam-5710	375	9	1	1	NUM
ejpam-5710	375	10	)	)	PUNCT
ejpam-5710	375	11	(	(	PUNCT
ejpam-5710	375	12	2025	2025	NUM
ejpam-5710	375	13	)	)	PUNCT
ejpam-5710	375	14	,	,	PUNCT
ejpam-5710	375	15	5710	5710	NUM
ejpam-5710	375	16	18	18	NUM
ejpam-5710	375	17	of	of	ADP
ejpam-5710	375	18	18	18	NUM
ejpam-5710	375	19	journal	journal	NOUN
ejpam-5710	375	20	of	of	ADP
ejpam-5710	375	21	geometry	geometry	NOUN
ejpam-5710	375	22	and	and	CCONJ
ejpam-5710	375	23	physics	physics	NOUN
ejpam-5710	375	24	,	,	PUNCT
ejpam-5710	375	25	49:89–100	49:89–100	NUM
ejpam-5710	375	26	,	,	PUNCT
ejpam-5710	375	27	2004	2004	NUM
ejpam-5710	375	28	.	.	PUNCT
ejpam-5710	376	1	[	[	X
ejpam-5710	376	2	29	29	NUM
ejpam-5710	376	3	]	]	X
ejpam-5710	376	4	y.	y.	PROPN
ejpam-5710	376	5	lam	lam	PROPN
ejpam-5710	376	6	,	,	PUNCT
ejpam-5710	376	7	wai	wai	PROPN
ejpam-5710	376	8	.	.	PROPN
ejpam-5710	376	9	minimal	minimal	ADJ
ejpam-5710	376	10	surfaces	surface	NOUN
ejpam-5710	376	11	from	from	ADP
ejpam-5710	376	12	infinitesimal	infinitesimal	ADJ
ejpam-5710	376	13	deformations	deformation	NOUN
ejpam-5710	376	14	of	of	ADP
ejpam-5710	376	15	circle	circle	NOUN
ejpam-5710	376	16	packings	packing	NOUN
ejpam-5710	376	17	.	.	PUNCT
ejpam-5710	377	1	advances	advance	NOUN
ejpam-5710	377	2	in	in	ADP
ejpam-5710	377	3	mathematics	mathematic	NOUN
ejpam-5710	377	4	,	,	PUNCT
ejpam-5710	377	5	362:106939	362:106939	NUM
ejpam-5710	377	6	,	,	PUNCT
ejpam-5710	377	7	2020	2020	NUM
ejpam-5710	377	8	.	.	PUNCT
ejpam-5710	378	1	[	[	X
ejpam-5710	378	2	30	30	NUM
ejpam-5710	378	3	]	]	X
ejpam-5710	378	4	y.	y.	PROPN
ejpam-5710	378	5	li	li	PROPN
ejpam-5710	378	6	,	,	PUNCT
ejpam-5710	378	7	h.s	h.s	PROPN
ejpam-5710	378	8	.	.	PROPN
ejpam-5710	378	9	abdel	abdel	PROPN
ejpam-5710	378	10	-	-	PUNCT
ejpam-5710	378	11	aziz	aziz	PROPN
ejpam-5710	378	12	,	,	PUNCT
ejpam-5710	378	13	h.m	h.m	PROPN
ejpam-5710	378	14	.	.	PROPN
ejpam-5710	378	15	serry	serry	PROPN
ejpam-5710	378	16	,	,	PUNCT
ejpam-5710	378	17	f.m	f.m	PROPN
ejpam-5710	378	18	.	.	PROPN
ejpam-5710	378	19	el	el	PROPN
ejpam-5710	378	20	-	-	ADJ
ejpam-5710	378	21	adawy	adawy	ADJ
ejpam-5710	378	22	,	,	PUNCT
ejpam-5710	378	23	and	and	CCONJ
ejpam-5710	378	24	m.k	m.k	PROPN
ejpam-5710	378	25	.	.	PROPN
ejpam-5710	378	26	saad	saad	PROPN
ejpam-5710	378	27	.	.	PUNCT
ejpam-5710	379	1	geometric	geometric	ADJ
ejpam-5710	379	2	visualization	visualization	NOUN
ejpam-5710	379	3	of	of	ADP
ejpam-5710	379	4	evolved	evolved	ADJ
ejpam-5710	379	5	ruled	rule	VERB
ejpam-5710	379	6	surfaces	surface	NOUN
ejpam-5710	379	7	via	via	ADP
ejpam-5710	379	8	alternative	alternative	ADJ
ejpam-5710	379	9	frame	frame	NOUN
ejpam-5710	379	10	in	in	ADP
ejpam-5710	379	11	lorentz	lorentz	PROPN
ejpam-5710	379	12	-	-	PUNCT
ejpam-5710	379	13	minkowski	minkowski	ADJ
ejpam-5710	379	14	3	3	NUM
ejpam-5710	379	15	-	-	PUNCT
ejpam-5710	379	16	space	space	NOUN
ejpam-5710	379	17	.	.	PUNCT
ejpam-5710	380	1	space	space	NOUN
ejpam-5710	380	2	,	,	PUNCT
ejpam-5710	380	3	3:1	3:1	NUM
ejpam-5710	380	4	,	,	PUNCT
ejpam-5710	380	5	2024	2024	NUM
ejpam-5710	380	6	.	.	PUNCT
ejpam-5710	381	1	[	[	X
ejpam-5710	381	2	31	31	NUM
ejpam-5710	381	3	]	]	X
ejpam-5710	381	4	y.	y.	PROPN
ejpam-5710	381	5	li	li	PROPN
ejpam-5710	381	6	,	,	PUNCT
ejpam-5710	381	7	h.	h.	PROPN
ejpam-5710	381	8	pottmann	pottmann	PROPN
ejpam-5710	381	9	,	,	PUNCT
ejpam-5710	381	10	j.	j.	PROPN
ejpam-5710	381	11	wallner	wallner	PROPN
ejpam-5710	381	12	,	,	PUNCT
ejpam-5710	381	13	y.	y.	PROPN
ejpam-5710	381	14	yang	yang	PROPN
ejpam-5710	381	15	,	,	PUNCT
ejpam-5710	381	16	and	and	CCONJ
ejpam-5710	381	17	w.	w.	PROPN
ejpam-5710	381	18	wang	wang	PROPN
ejpam-5710	381	19	.	.	PUNCT
ejpam-5710	382	1	geometric	geometric	ADJ
ejpam-5710	382	2	modeling	modeling	NOUN
ejpam-5710	382	3	with	with	ADP
ejpam-5710	382	4	conical	conical	ADJ
ejpam-5710	382	5	meshes	mesh	NOUN
ejpam-5710	382	6	and	and	CCONJ
ejpam-5710	382	7	developable	developable	ADJ
ejpam-5710	382	8	surfaces	surface	NOUN
ejpam-5710	382	9	.	.	PUNCT
ejpam-5710	383	1	acm	acm	NOUN
ejpam-5710	383	2	transactions	transaction	NOUN
ejpam-5710	383	3	on	on	ADP
ejpam-5710	383	4	graphics	graphic	NOUN
ejpam-5710	383	5	,	,	PUNCT
ejpam-5710	383	6	25(3):681	25(3):681	NUM
ejpam-5710	383	7	–	–	PUNCT
ejpam-5710	383	8	689	689	NUM
ejpam-5710	383	9	,	,	PUNCT
ejpam-5710	383	10	2006	2006	NUM
ejpam-5710	383	11	.	.	PUNCT
ejpam-5710	384	1	[	[	X
ejpam-5710	384	2	32	32	NUM
ejpam-5710	384	3	]	]	PUNCT
ejpam-5710	384	4	t.	t.	PROPN
ejpam-5710	384	5	g.	g.	PROPN
ejpam-5710	384	6	nelson	nelson	PROPN
ejpam-5710	384	7	,	,	PUNCT
ejpam-5710	384	8	t.	t.	PROPN
ejpam-5710	384	9	zimmerman	zimmerman	PROPN
ejpam-5710	384	10	,	,	PUNCT
ejpam-5710	384	11	s.	s.	PROPN
ejpam-5710	384	12	p.	p.	PROPN
ejpam-5710	384	13	magleby	magleby	PROPN
ejpam-5710	384	14	,	,	PUNCT
ejpam-5710	384	15	r.	r.	PROPN
ejpam-5710	384	16	j.	j.	PROPN
ejpam-5710	384	17	lang	lang	PROPN
ejpam-5710	384	18	,	,	PUNCT
ejpam-5710	384	19	and	and	CCONJ
ejpam-5710	384	20	l.	l.	PROPN
ejpam-5710	384	21	l.	l.	PROPN
ejpam-5710	384	22	howell	howell	PROPN
ejpam-5710	384	23	.	.	PUNCT
ejpam-5710	385	1	developable	developable	ADJ
ejpam-5710	385	2	mechanisms	mechanism	NOUN
ejpam-5710	385	3	on	on	ADP
ejpam-5710	385	4	developable	developable	ADJ
ejpam-5710	385	5	surfaces	surface	NOUN
ejpam-5710	385	6	.	.	PUNCT
ejpam-5710	386	1	science	science	NOUN
ejpam-5710	386	2	robotics	robotic	NOUN
ejpam-5710	386	3	,	,	PUNCT
ejpam-5710	386	4	4(27	4(27	NUM
ejpam-5710	386	5	)	)	PUNCT
ejpam-5710	386	6	,	,	PUNCT
ejpam-5710	386	7	2019	2019	NUM
ejpam-5710	386	8	.	.	PUNCT
ejpam-5710	387	1	[	[	X
ejpam-5710	387	2	33	33	NUM
ejpam-5710	387	3	]	]	PUNCT
ejpam-5710	387	4	m.	m.	NOUN
ejpam-5710	387	5	peternel	peternel	PROPN
ejpam-5710	387	6	,	,	PUNCT
ejpam-5710	387	7	h.	h.	PROPN
ejpam-5710	387	8	pottmann	pottmann	PROPN
ejpam-5710	387	9	,	,	PUNCT
ejpam-5710	387	10	and	and	CCONJ
ejpam-5710	387	11	b.	b.	PROPN
ejpam-5710	387	12	ravani	ravani	PROPN
ejpam-5710	387	13	.	.	PUNCT
ejpam-5710	388	1	on	on	ADP
ejpam-5710	388	2	the	the	DET
ejpam-5710	388	3	computational	computational	ADJ
ejpam-5710	388	4	geometry	geometry	NOUN
ejpam-5710	388	5	of	of	ADP
ejpam-5710	388	6	ruled	rule	VERB
ejpam-5710	388	7	surfaces	surface	NOUN
ejpam-5710	388	8	.	.	PUNCT
ejpam-5710	389	1	computer	computer	NOUN
ejpam-5710	389	2	aided	aid	VERB
ejpam-5710	389	3	geometric	geometric	ADJ
ejpam-5710	389	4	design	design	NOUN
ejpam-5710	389	5	,	,	PUNCT
ejpam-5710	389	6	31:17–32	31:17–32	PROPN
ejpam-5710	389	7	,	,	PUNCT
ejpam-5710	389	8	1999	1999	NUM
ejpam-5710	389	9	.	.	PUNCT
ejpam-5710	390	1	[	[	X
ejpam-5710	390	2	34	34	NUM
ejpam-5710	390	3	]	]	X
ejpam-5710	390	4	h.	h.	PROPN
ejpam-5710	390	5	pottmann	pottmann	PROPN
ejpam-5710	390	6	,	,	PUNCT
ejpam-5710	390	7	w.	w.	PROPN
ejpam-5710	390	8	lu	lu	PROPN
ejpam-5710	390	9	,	,	PUNCT
ejpam-5710	390	10	and	and	CCONJ
ejpam-5710	390	11	b.	b.	PROPN
ejpam-5710	390	12	ravani	ravani	PROPN
ejpam-5710	390	13	.	.	PUNCT
ejpam-5710	391	1	rational	rational	ADJ
ejpam-5710	391	2	ruled	rule	VERB
ejpam-5710	391	3	surfaces	surface	NOUN
ejpam-5710	391	4	and	and	CCONJ
ejpam-5710	391	5	their	their	PRON
ejpam-5710	391	6	offsets	offset	NOUN
ejpam-5710	391	7	.	.	PUNCT
ejpam-5710	392	1	graphical	graphical	ADJ
ejpam-5710	392	2	models	model	NOUN
ejpam-5710	392	3	and	and	CCONJ
ejpam-5710	392	4	image	image	NOUN
ejpam-5710	392	5	processing	processing	NOUN
ejpam-5710	392	6	,	,	PUNCT
ejpam-5710	392	7	58(6):544–552	58(6):544–552	NOUN
ejpam-5710	392	8	,	,	PUNCT
ejpam-5710	392	9	1996	1996	NUM
ejpam-5710	392	10	.	.	PUNCT
ejpam-5710	393	1	[	[	X
ejpam-5710	393	2	35	35	NUM
ejpam-5710	393	3	]	]	X
ejpam-5710	393	4	e.	e.	PROPN
ejpam-5710	393	5	solouma	solouma	PROPN
ejpam-5710	393	6	,	,	PUNCT
ejpam-5710	393	7	i.	i.	PROPN
ejpam-5710	393	8	al	al	PROPN
ejpam-5710	393	9	-	-	PUNCT
ejpam-5710	393	10	dayel	dayel	PROPN
ejpam-5710	393	11	,	,	PUNCT
ejpam-5710	393	12	m.	m.	NOUN
ejpam-5710	393	13	a.	a.	PROPN
ejpam-5710	393	14	khan	khan	PROPN
ejpam-5710	393	15	,	,	PUNCT
ejpam-5710	393	16	and	and	CCONJ
ejpam-5710	393	17	m.	m.	NOUN
ejpam-5710	393	18	abdelkawy	abdelkawy	PROPN
ejpam-5710	393	19	.	.	PUNCT
ejpam-5710	394	1	investigation	investigation	NOUN
ejpam-5710	394	2	of	of	ADP
ejpam-5710	394	3	special	special	ADJ
ejpam-5710	394	4	type	type	NOUN
ejpam-5710	394	5	-	-	PUNCT
ejpam-5710	394	6	î	î	NOUN
ejpam-5710	394	7	smarandache	smarandache	NOUN
ejpam-5710	394	8	ruled	rule	VERB
ejpam-5710	394	9	surfaces	surface	NOUN
ejpam-5710	394	10	due	due	ADJ
ejpam-5710	394	11	to	to	ADP
ejpam-5710	394	12	rotation	rotation	NOUN
ejpam-5710	394	13	minimizing	minimize	VERB
ejpam-5710	394	14	darboux	darboux	VERB
ejpam-5710	394	15	frame	frame	NOUN
ejpam-5710	394	16	in	in	ADP
ejpam-5710	394	17	e3	e3	NOUN
ejpam-5710	394	18	.	.	PUNCT
ejpam-5710	394	19	symmetry	symmetry	NOUN
ejpam-5710	394	20	,	,	PUNCT
ejpam-5710	394	21	15(12):2207	15(12):2207	NUM
ejpam-5710	394	22	,	,	PUNCT
ejpam-5710	394	23	2023	2023	NUM
ejpam-5710	394	24	.	.	PUNCT
ejpam-5710	395	1	[	[	X
ejpam-5710	395	2	36	36	NUM
ejpam-5710	395	3	]	]	X
ejpam-5710	395	4	e.	e.	PROPN
ejpam-5710	395	5	solouma	solouma	PROPN
ejpam-5710	395	6	,	,	PUNCT
ejpam-5710	395	7	i.	i.	PROPN
ejpam-5710	395	8	al	al	PROPN
ejpam-5710	395	9	-	-	PUNCT
ejpam-5710	395	10	dayel	dayel	PROPN
ejpam-5710	395	11	,	,	PUNCT
ejpam-5710	395	12	m.	m.	NOUN
ejpam-5710	395	13	a.	a.	PROPN
ejpam-5710	395	14	khan	khan	PROPN
ejpam-5710	395	15	,	,	PUNCT
ejpam-5710	395	16	and	and	CCONJ
ejpam-5710	395	17	y.	y.	NOUN
ejpam-5710	395	18	a.	a.	NOUN
ejpam-5710	395	19	lazer	lazer	NOUN
ejpam-5710	395	20	.	.	PUNCT
ejpam-5710	396	1	characterization	characterization	NOUN
ejpam-5710	396	2	of	of	ADP
ejpam-5710	396	3	imbricate	imbricate	NOUN
ejpam-5710	396	4	-	-	PUNCT
ejpam-5710	396	5	ruled	rule	VERB
ejpam-5710	396	6	surfaces	surface	NOUN
ejpam-5710	396	7	via	via	ADP
ejpam-5710	396	8	rotation	rotation	NOUN
ejpam-5710	396	9	-	-	PUNCT
ejpam-5710	396	10	minimizing	minimize	VERB
ejpam-5710	396	11	darboux	darboux	VERB
ejpam-5710	396	12	frame	frame	NOUN
ejpam-5710	396	13	in	in	ADP
ejpam-5710	396	14	minkowski	minkowski	PROPN
ejpam-5710	396	15	3space	3space	NUM
ejpam-5710	396	16	e3	e3	NOUN
ejpam-5710	396	17	1	1	NUM
ejpam-5710	396	18	.	.	PUNCT
ejpam-5710	397	1	aims	aim	VERB
ejpam-5710	397	2	mathematics	mathematic	NOUN
ejpam-5710	397	3	,	,	PUNCT
ejpam-5710	397	4	9(5):13028–13042	9(5):13028–13042	NUM
ejpam-5710	397	5	,	,	PUNCT
ejpam-5710	397	6	2024	2024	NUM
ejpam-5710	397	7	.	.	PUNCT
ejpam-5710	398	1	[	[	X
ejpam-5710	398	2	37	37	NUM
ejpam-5710	398	3	]	]	X
ejpam-5710	398	4	y.	y.	PROPN
ejpam-5710	398	5	tashkandy	tashkandy	PROPN
ejpam-5710	398	6	,	,	PUNCT
ejpam-5710	398	7	w.	w.	PROPN
ejpam-5710	398	8	emam	emam	PROPN
ejpam-5710	398	9	,	,	PUNCT
ejpam-5710	398	10	c.	c.	PROPN
ejpam-5710	398	11	cesarano	cesarano	PROPN
ejpam-5710	398	12	,	,	PUNCT
ejpam-5710	398	13	m.	m.	PROPN
ejpam-5710	398	14	a.	a.	PROPN
ejpam-5710	398	15	el	el	PROPN
ejpam-5710	398	16	-	-	PROPN
ejpam-5710	398	17	raouf	raouf	PROPN
ejpam-5710	398	18	,	,	PUNCT
ejpam-5710	398	19	and	and	CCONJ
ejpam-5710	398	20	a.	a.	NOUN
ejpam-5710	398	21	elsharkawy	elsharkawy	PROPN
ejpam-5710	398	22	.	.	PUNCT
ejpam-5710	399	1	generalized	generalize	VERB
ejpam-5710	399	2	spacelike	spacelike	VERB
ejpam-5710	399	3	normal	normal	ADJ
ejpam-5710	399	4	curves	curve	NOUN
ejpam-5710	399	5	in	in	ADP
ejpam-5710	399	6	minkowski	minkowski	ADJ
ejpam-5710	399	7	three	three	NUM
ejpam-5710	399	8	-	-	PUNCT
ejpam-5710	399	9	space	space	NOUN
ejpam-5710	399	10	.	.	PUNCT
ejpam-5710	400	1	mathematics	mathematic	NOUN
ejpam-5710	400	2	,	,	PUNCT
ejpam-5710	400	3	10(21):4145	10(21):4145	NUM
ejpam-5710	400	4	,	,	PUNCT
ejpam-5710	400	5	2022	2022	NUM
ejpam-5710	400	6	.	.	PUNCT
ejpam-5710	401	1	[	[	X
ejpam-5710	401	2	38	38	NUM
ejpam-5710	401	3	]	]	PUNCT
ejpam-5710	401	4	a.	a.	NOUN
ejpam-5710	401	5	m.	m.	PROPN
ejpam-5710	401	6	tawfiq	tawfiq	PROPN
ejpam-5710	401	7	,	,	PUNCT
ejpam-5710	401	8	c.	c.	PROPN
ejpam-5710	401	9	cesarano	cesarano	PROPN
ejpam-5710	401	10	,	,	PUNCT
ejpam-5710	401	11	and	and	CCONJ
ejpam-5710	401	12	a.	a.	NOUN
ejpam-5710	401	13	elsharkawy	elsharkawy	PROPN
ejpam-5710	401	14	.	.	PUNCT
ejpam-5710	402	1	a	a	DET
ejpam-5710	402	2	new	new	ADJ
ejpam-5710	402	3	method	method	NOUN
ejpam-5710	402	4	for	for	ADP
ejpam-5710	402	5	resolving	resolve	VERB
ejpam-5710	402	6	the	the	DET
ejpam-5710	402	7	jerk	jerk	NOUN
ejpam-5710	402	8	and	and	CCONJ
ejpam-5710	402	9	jounce	jounce	NOUN
ejpam-5710	402	10	vectors	vector	NOUN
ejpam-5710	402	11	in	in	ADP
ejpam-5710	402	12	euclidean	euclidean	ADJ
ejpam-5710	402	13	3	3	NUM
ejpam-5710	402	14	-	-	PUNCT
ejpam-5710	402	15	space	space	NOUN
ejpam-5710	402	16	.	.	PUNCT
ejpam-5710	403	1	mathematical	mathematical	ADJ
ejpam-5710	403	2	methods	method	NOUN
ejpam-5710	403	3	in	in	ADP
ejpam-5710	403	4	the	the	DET
ejpam-5710	403	5	applied	apply	VERB
ejpam-5710	403	6	sciences	science	NOUN
ejpam-5710	403	7	,	,	PUNCT
ejpam-5710	403	8	46(8):8779–8792	46(8):8779–8792	NUM
ejpam-5710	403	9	,	,	PUNCT
ejpam-5710	403	10	2023	2023	NUM
ejpam-5710	403	11	.	.	PUNCT
ejpam-5710	404	1	[	[	X
ejpam-5710	404	2	39	39	NUM
ejpam-5710	404	3	]	]	PUNCT
ejpam-5710	404	4	a.	a.	NOUN
ejpam-5710	404	5	turgut	turgut	PROPN
ejpam-5710	404	6	and	and	CCONJ
ejpam-5710	404	7	h.	h.	PROPN
ejpam-5710	404	8	h.	h.	PROPN
ejpam-5710	404	9	hacisalihoglu	hacisalihoglu	PROPN
ejpam-5710	404	10	.	.	PUNCT
ejpam-5710	405	1	timelike	timelike	PROPN
ejpam-5710	405	2	ruled	rule	VERB
ejpam-5710	405	3	surfaces	surface	NOUN
ejpam-5710	405	4	in	in	ADP
ejpam-5710	405	5	the	the	DET
ejpam-5710	405	6	minkowski	minkowski	ADJ
ejpam-5710	405	7	3space	3space	NUM
ejpam-5710	405	8	.	.	PUNCT
ejpam-5710	406	1	far	far	PROPN
ejpam-5710	406	2	east	east	PROPN
ejpam-5710	406	3	journal	journal	PROPN
ejpam-5710	406	4	of	of	ADP
ejpam-5710	406	5	mathematical	mathematical	ADJ
ejpam-5710	406	6	sciences	science	NOUN
ejpam-5710	406	7	,	,	PUNCT
ejpam-5710	406	8	5(1):83–90	5(1):83–90	NUM
ejpam-5710	406	9	,	,	PUNCT
ejpam-5710	406	10	1997	1997	NUM
ejpam-5710	406	11	.	.	PUNCT
ejpam-5710	407	1	introduction	introduction	NOUN
ejpam-5710	407	2	preliminaries	preliminary	NOUN
ejpam-5710	407	3	main	main	ADJ
ejpam-5710	407	4	result	result	NOUN
ejpam-5710	407	5	quasi	quasi	ADJ
ejpam-5710	407	6	-	-	ADJ
ejpam-5710	407	7	tangent	tangent	ADJ
ejpam-5710	407	8	ruled	rule	VERB
ejpam-5710	407	9	surfaces	surface	NOUN
ejpam-5710	407	10	according	accord	VERB
ejpam-5710	407	11	to	to	ADP
ejpam-5710	407	12	the	the	DET
ejpam-5710	407	13	quasi	quasi	ADJ
ejpam-5710	407	14	frame	frame	NOUN
ejpam-5710	407	15	quasi	quasi	ADJ
ejpam-5710	407	16	-	-	ADJ
ejpam-5710	407	17	normal	normal	ADJ
ejpam-5710	407	18	ruled	rule	VERB
ejpam-5710	407	19	surfaces	surface	NOUN
ejpam-5710	407	20	according	accord	VERB
ejpam-5710	407	21	to	to	ADP
ejpam-5710	407	22	the	the	DET
ejpam-5710	407	23	quasi	quasi	ADJ
ejpam-5710	407	24	frame	frame	NOUN
ejpam-5710	407	25	quasi	quasi	ADJ
ejpam-5710	407	26	-	-	ADJ
ejpam-5710	407	27	binormal	binormal	ADJ
ejpam-5710	407	28	ruled	rule	VERB
ejpam-5710	407	29	surfaces	surface	NOUN
ejpam-5710	407	30	according	accord	VERB
ejpam-5710	407	31	to	to	ADP
ejpam-5710	407	32	the	the	DET
ejpam-5710	407	33	quasi	quasi	ADJ
ejpam-5710	407	34	frame	frame	NOUN
ejpam-5710	407	35	conclusion	conclusion	NOUN