id	sid	tid	token	lemma	pos
ejpam-3471	1	1	european	european	PROPN
ejpam-3471	1	2	journal	journal	PROPN
ejpam-3471	1	3	of	of	ADP
ejpam-3471	1	4	pure	pure	ADJ
ejpam-3471	1	5	and	and	CCONJ
ejpam-3471	1	6	applied	apply	VERB
ejpam-3471	1	7	mathematics	mathematic	NOUN
ejpam-3471	1	8	vol	vol	NOUN
ejpam-3471	1	9	.	.	PROPN
ejpam-3471	2	1	12	12	NUM
ejpam-3471	2	2	,	,	PUNCT
ejpam-3471	2	3	no	no	INTJ
ejpam-3471	2	4	.	.	NOUN
ejpam-3471	2	5	3	3	NUM
ejpam-3471	2	6	,	,	PUNCT
ejpam-3471	2	7	2019	2019	NUM
ejpam-3471	2	8	,	,	PUNCT
ejpam-3471	2	9	1260	1260	NUM
ejpam-3471	2	10	-	-	SYM
ejpam-3471	2	11	1276	1276	NUM
ejpam-3471	2	12	issn	issn	PROPN
ejpam-3471	2	13	1307	1307	NUM
ejpam-3471	2	14	-	-	SYM
ejpam-3471	2	15	5543	5543	NUM
ejpam-3471	2	16	–	–	PUNCT
ejpam-3471	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3471	2	18	published	publish	VERB
ejpam-3471	2	19	by	by	ADP
ejpam-3471	2	20	new	new	PROPN
ejpam-3471	2	21	york	york	PROPN
ejpam-3471	2	22	business	business	PROPN
ejpam-3471	2	23	global	global	ADJ
ejpam-3471	2	24	comparison	comparison	NOUN
ejpam-3471	2	25	of	of	ADP
ejpam-3471	2	26	sba	sba	PROPN
ejpam-3471	2	27	numerical	numerical	PROPN
ejpam-3471	2	28	method	method	PROPN
ejpam-3471	2	29	and	and	CCONJ
ejpam-3471	2	30	method	method	NOUN
ejpam-3471	2	31	of	of	ADP
ejpam-3471	2	32	separation	separation	NOUN
ejpam-3471	2	33	of	of	ADP
ejpam-3471	2	34	variables	variable	NOUN
ejpam-3471	2	35	(	(	PUNCT
ejpam-3471	2	36	fourier	fourier	NOUN
ejpam-3471	2	37	)	)	PUNCT
ejpam-3471	2	38	on	on	ADP
ejpam-3471	2	39	wave	wave	NOUN
ejpam-3471	2	40	equations	equation	NOUN
ejpam-3471	2	41	.	.	PUNCT
ejpam-3471	3	1	rasmane	rasmane	NOUN
ejpam-3471	3	2	yaro1	yaro1	PROPN
ejpam-3471	3	3	,	,	PUNCT
ejpam-3471	3	4	youssouf	youssouf	PROPN
ejpam-3471	3	5	paré2,∗	paré2,∗	PROPN
ejpam-3471	3	6	,	,	PUNCT
ejpam-3471	3	7	bakari	bakari	PROPN
ejpam-3471	3	8	abbo3	abbo3	PROPN
ejpam-3471	3	9	1	1	NUM
ejpam-3471	3	10	université	université	NOUN
ejpam-3471	3	11	de	de	X
ejpam-3471	3	12	dédougou	dédougou	PROPN
ejpam-3471	3	13	,	,	PUNCT
ejpam-3471	3	14	dédougou	dédougou	PROPN
ejpam-3471	3	15	,	,	PUNCT
ejpam-3471	3	16	burkina	burkina	PROPN
ejpam-3471	3	17	-	-	PUNCT
ejpam-3471	3	18	faso	faso	PROPN
ejpam-3471	3	19	2	2	NUM
ejpam-3471	3	20	département	département	PROPN
ejpam-3471	3	21	de	de	X
ejpam-3471	3	22	mathématiques	mathématiques	PROPN
ejpam-3471	3	23	,	,	PUNCT
ejpam-3471	3	24	ufr	ufr	PROPN
ejpam-3471	3	25	/	/	SYM
ejpam-3471	3	26	sciences	science	NOUN
ejpam-3471	3	27	exactes	exact	VERB
ejpam-3471	3	28	et	et	NOUN
ejpam-3471	3	29	appliquées	appliquée	NOUN
ejpam-3471	3	30	,	,	PUNCT
ejpam-3471	3	31	université	université	ADJ
ejpam-3471	3	32	joseph	joseph	PROPN
ejpam-3471	3	33	ki	ki	PROPN
ejpam-3471	3	34	-	-	PUNCT
ejpam-3471	3	35	zerbo	zerbo	PROPN
ejpam-3471	3	36	,	,	PUNCT
ejpam-3471	3	37	ouagadougou	ouagadougou	PROPN
ejpam-3471	3	38	,	,	PUNCT
ejpam-3471	3	39	burkina	burkina	PROPN
ejpam-3471	3	40	-	-	PUNCT
ejpam-3471	3	41	faso	faso	PROPN
ejpam-3471	3	42	2	2	NUM
ejpam-3471	3	43	département	département	PROPN
ejpam-3471	3	44	de	de	X
ejpam-3471	3	45	mathématiques	mathématiques	PROPN
ejpam-3471	3	46	,	,	PUNCT
ejpam-3471	3	47	facultés	facultés	PROPN
ejpam-3471	3	48	des	des	PROPN
ejpam-3471	3	49	sciences	sciences	PROPN
ejpam-3471	3	50	et	et	NOUN
ejpam-3471	3	51	techniques	technique	NOUN
ejpam-3471	3	52	,	,	PUNCT
ejpam-3471	3	53	université	université	NOUN
ejpam-3471	3	54	de	de	X
ejpam-3471	3	55	ndjaména	ndjaména	PROPN
ejpam-3471	3	56	,	,	PUNCT
ejpam-3471	3	57	ndjaména	ndjaména	ADV
ejpam-3471	3	58	,	,	PUNCT
ejpam-3471	3	59	tchad	tchad	VERB
ejpam-3471	3	60	abstract	abstract	NOUN
ejpam-3471	3	61	.	.	PUNCT
ejpam-3471	4	1	in	in	ADP
ejpam-3471	4	2	this	this	DET
ejpam-3471	4	3	paper	paper	NOUN
ejpam-3471	4	4	,	,	PUNCT
ejpam-3471	4	5	our	our	PRON
ejpam-3471	4	6	aim	aim	NOUN
ejpam-3471	4	7	is	be	AUX
ejpam-3471	4	8	to	to	PART
ejpam-3471	4	9	use	use	VERB
ejpam-3471	4	10	the	the	DET
ejpam-3471	4	11	sba	sba	PROPN
ejpam-3471	4	12	numerical	numerical	PROPN
ejpam-3471	4	13	method	method	PROPN
ejpam-3471	4	14	(	(	PUNCT
ejpam-3471	4	15	combination	combination	NOUN
ejpam-3471	4	16	of	of	ADP
ejpam-3471	4	17	adomian	adomian	NOUN
ejpam-3471	4	18	method	method	NOUN
ejpam-3471	4	19	and	and	CCONJ
ejpam-3471	4	20	picard	picard	NOUN
ejpam-3471	4	21	successive	successive	ADJ
ejpam-3471	4	22	approximations	approximation	NOUN
ejpam-3471	4	23	)	)	PUNCT
ejpam-3471	4	24	and	and	CCONJ
ejpam-3471	4	25	fourier	fouri	ADJ
ejpam-3471	4	26	method	method	NOUN
ejpam-3471	4	27	or	or	CCONJ
ejpam-3471	4	28	method	method	NOUN
ejpam-3471	4	29	of	of	ADP
ejpam-3471	4	30	separation	separation	NOUN
ejpam-3471	4	31	of	of	ADP
ejpam-3471	4	32	variables	variable	NOUN
ejpam-3471	4	33	to	to	PART
ejpam-3471	4	34	construct	construct	VERB
ejpam-3471	4	35	the	the	DET
ejpam-3471	4	36	solution	solution	NOUN
ejpam-3471	4	37	of	of	ADP
ejpam-3471	4	38	some	some	DET
ejpam-3471	4	39	wave	wave	NOUN
ejpam-3471	4	40	equations	equation	NOUN
ejpam-3471	4	41	.	.	PUNCT
ejpam-3471	5	1	we	we	PRON
ejpam-3471	5	2	compare	compare	VERB
ejpam-3471	5	3	the	the	DET
ejpam-3471	5	4	two	two	NUM
ejpam-3471	5	5	methods	method	NOUN
ejpam-3471	5	6	and	and	CCONJ
ejpam-3471	5	7	apply	apply	VERB
ejpam-3471	5	8	them	they	PRON
ejpam-3471	5	9	to	to	ADP
ejpam-3471	5	10	some	some	DET
ejpam-3471	5	11	wave	wave	NOUN
ejpam-3471	5	12	equations	equation	NOUN
ejpam-3471	5	13	.	.	PUNCT
ejpam-3471	6	1	2010	2010	NUM
ejpam-3471	6	2	mathematics	mathematic	NOUN
ejpam-3471	6	3	subject	subject	NOUN
ejpam-3471	6	4	classifications	classification	NOUN
ejpam-3471	6	5	:	:	PUNCT
ejpam-3471	6	6	65l07	65l07	NUM
ejpam-3471	6	7	,	,	PUNCT
ejpam-3471	6	8	65p40	65p40	NUM
ejpam-3471	6	9	,	,	PUNCT
ejpam-3471	6	10	40a05	40a05	NUM
ejpam-3471	6	11	,	,	PUNCT
ejpam-3471	6	12	34f05	34f05	NUM
ejpam-3471	6	13	key	key	ADJ
ejpam-3471	6	14	words	word	NOUN
ejpam-3471	6	15	and	and	CCONJ
ejpam-3471	6	16	phrases	phrase	NOUN
ejpam-3471	6	17	:	:	PUNCT
ejpam-3471	6	18	numerical	numerical	PROPN
ejpam-3471	6	19	sba	sba	PROPN
ejpam-3471	6	20	method	method	PROPN
ejpam-3471	6	21	,	,	PUNCT
ejpam-3471	6	22	adomian	adomian	NOUN
ejpam-3471	6	23	method	method	NOUN
ejpam-3471	6	24	,	,	PUNCT
ejpam-3471	6	25	dynamical	dynamical	ADJ
ejpam-3471	6	26	model	model	NOUN
ejpam-3471	6	27	,	,	PUNCT
ejpam-3471	6	28	picard	picard	PROPN
ejpam-3471	6	29	’s	’s	PART
ejpam-3471	6	30	principle	principle	NOUN
ejpam-3471	6	31	,	,	PUNCT
ejpam-3471	6	32	successive	successive	ADJ
ejpam-3471	6	33	approximations	approximation	NOUN
ejpam-3471	6	34	and	and	CCONJ
ejpam-3471	6	35	wave	wave	NOUN
ejpam-3471	6	36	equations	equation	NOUN
ejpam-3471	6	37	1	1	NUM
ejpam-3471	6	38	.	.	PUNCT
ejpam-3471	7	1	introduction	introduction	NOUN
ejpam-3471	7	2	many	many	ADJ
ejpam-3471	7	3	problems	problem	NOUN
ejpam-3471	7	4	are	be	AUX
ejpam-3471	7	5	governed	govern	VERB
ejpam-3471	7	6	by	by	ADP
ejpam-3471	7	7	partial	partial	ADJ
ejpam-3471	7	8	differential	differential	NOUN
ejpam-3471	7	9	equations	equation	NOUN
ejpam-3471	7	10	,	,	PUNCT
ejpam-3471	7	11	or	or	CCONJ
ejpam-3471	7	12	by	by	ADP
ejpam-3471	7	13	systems	system	NOUN
ejpam-3471	7	14	of	of	ADP
ejpam-3471	7	15	partial	partial	ADJ
ejpam-3471	7	16	differential	differential	NOUN
ejpam-3471	7	17	equations	equation	NOUN
ejpam-3471	7	18	.	.	PUNCT
ejpam-3471	8	1	it	it	PRON
ejpam-3471	8	2	is	be	AUX
ejpam-3471	8	3	difficult	difficult	ADJ
ejpam-3471	8	4	to	to	PART
ejpam-3471	8	5	find	find	VERB
ejpam-3471	8	6	their	their	PRON
ejpam-3471	8	7	exact	exact	ADJ
ejpam-3471	8	8	solutions	solution	NOUN
ejpam-3471	8	9	.	.	PUNCT
ejpam-3471	9	1	in	in	ADP
ejpam-3471	9	2	this	this	DET
ejpam-3471	9	3	work	work	NOUN
ejpam-3471	9	4	,	,	PUNCT
ejpam-3471	9	5	the	the	DET
ejpam-3471	9	6	sba	sba	PROPN
ejpam-3471	9	7	numerical	numerical	PROPN
ejpam-3471	9	8	method	method	PROPN
ejpam-3471	9	9	,	,	PUNCT
ejpam-3471	9	10	[	[	X
ejpam-3471	9	11	3	3	NUM
ejpam-3471	9	12	,	,	PUNCT
ejpam-3471	9	13	9	9	NUM
ejpam-3471	9	14	]	]	PUNCT
ejpam-3471	9	15	and	and	CCONJ
ejpam-3471	9	16	fourier	fourier	ADJ
ejpam-3471	9	17	method	method	NOUN
ejpam-3471	9	18	permitted	permit	VERB
ejpam-3471	9	19	us	we	PRON
ejpam-3471	9	20	to	to	PART
ejpam-3471	9	21	find	find	VERB
ejpam-3471	9	22	the	the	DET
ejpam-3471	9	23	exact	exact	ADJ
ejpam-3471	9	24	solution	solution	NOUN
ejpam-3471	9	25	of	of	ADP
ejpam-3471	9	26	some	some	DET
ejpam-3471	9	27	wave	wave	NOUN
ejpam-3471	9	28	equations	equation	NOUN
ejpam-3471	9	29	.	.	PUNCT
ejpam-3471	10	1	2	2	X
ejpam-3471	10	2	.	.	X
ejpam-3471	10	3	description	description	NOUN
ejpam-3471	10	4	of	of	ADP
ejpam-3471	10	5	the	the	DET
ejpam-3471	10	6	methods	method	NOUN
ejpam-3471	10	7	2.1	2.1	NUM
ejpam-3471	10	8	.	.	PUNCT
ejpam-3471	11	1	description	description	NOUN
ejpam-3471	11	2	of	of	ADP
ejpam-3471	11	3	the	the	DET
ejpam-3471	11	4	sba	sba	PROPN
ejpam-3471	11	5	numerical	numerical	PROPN
ejpam-3471	11	6	method	method	PROPN
ejpam-3471	11	7	let	let	VERB
ejpam-3471	11	8	’s	’s	NOUN
ejpam-3471	11	9	consider	consider	VERB
ejpam-3471	11	10	the	the	DET
ejpam-3471	11	11	following	follow	VERB
ejpam-3471	11	12	functional	functional	ADJ
ejpam-3471	11	13	equation	equation	NOUN
ejpam-3471	11	14	au	au	X
ejpam-3471	11	15	=	=	SYM
ejpam-3471	11	16	f	f	PROPN
ejpam-3471	11	17	(	(	PUNCT
ejpam-3471	11	18	1	1	X
ejpam-3471	11	19	)	)	PUNCT
ejpam-3471	11	20	∗corresponding	∗corresponde	VERB
ejpam-3471	11	21	author	author	NOUN
ejpam-3471	11	22	.	.	PUNCT
ejpam-3471	12	1	doi	doi	NOUN
ejpam-3471	12	2	:	:	PUNCT
ejpam-3471	12	3	https://doi.org/10.29020/nybg.ejpam.v12i3.3471	https://doi.org/10.29020/nybg.ejpam.v12i3.3471	PRON
ejpam-3471	12	4	email	email	NOUN
ejpam-3471	12	5	addresses	address	NOUN
ejpam-3471	12	6	:	:	PUNCT
ejpam-3471	12	7	yarorasmane@yahoo.fr	yarorasmane@yahoo.fr	PROPN
ejpam-3471	12	8	(	(	PUNCT
ejpam-3471	12	9	r.	r.	PROPN
ejpam-3471	12	10	yaro	yaro	PROPN
ejpam-3471	12	11	)	)	PUNCT
ejpam-3471	12	12	,	,	PUNCT
ejpam-3471	12	13	pareyoussouf@yahoo.fr	pareyoussouf@yahoo.fr	PROPN
ejpam-3471	12	14	(	(	PUNCT
ejpam-3471	12	15	y.	y.	PROPN
ejpam-3471	12	16	paré	paré	NOUN
ejpam-3471	12	17	)	)	PUNCT
ejpam-3471	12	18	,	,	PUNCT
ejpam-3471	12	19	bakariabbo@yahoo.fr	bakariabbo@yahoo.fr	PROPN
ejpam-3471	12	20	(	(	PUNCT
ejpam-3471	12	21	b.	b.	PROPN
ejpam-3471	12	22	abbo	abbo	PROPN
ejpam-3471	12	23	)	)	PUNCT
ejpam-3471	12	24	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3471	13	1	1260	1260	NUM
ejpam-3471	13	2	c	c	NOUN
ejpam-3471	13	3	©	©	PROPN
ejpam-3471	13	4	2019	2019	NUM
ejpam-3471	13	5	ejpam	ejpam	NOUN
ejpam-3471	13	6	all	all	DET
ejpam-3471	13	7	rights	right	NOUN
ejpam-3471	13	8	reserved	reserve	VERB
ejpam-3471	13	9	.	.	PUNCT
ejpam-3471	14	1	r.	r.	PROPN
ejpam-3471	14	2	yaro	yaro	PROPN
ejpam-3471	14	3	,	,	PUNCT
ejpam-3471	14	4	y.	y.	PROPN
ejpam-3471	14	5	paré	paré	NOUN
ejpam-3471	14	6	,	,	PUNCT
ejpam-3471	14	7	b.	b.	PROPN
ejpam-3471	14	8	abbo	abbo	PROPN
ejpam-3471	14	9	/	/	SYM
ejpam-3471	14	10	eur	eur	PROPN
ejpam-3471	14	11	.	.	PUNCT
ejpam-3471	15	1	j.	j.	PROPN
ejpam-3471	15	2	pure	pure	PROPN
ejpam-3471	15	3	appl	appl	PROPN
ejpam-3471	15	4	.	.	PROPN
ejpam-3471	15	5	math	math	PROPN
ejpam-3471	15	6	,	,	PUNCT
ejpam-3471	15	7	12	12	NUM
ejpam-3471	15	8	(	(	PUNCT
ejpam-3471	15	9	3	3	NUM
ejpam-3471	15	10	)	)	PUNCT
ejpam-3471	15	11	(	(	PUNCT
ejpam-3471	15	12	2019	2019	NUM
ejpam-3471	15	13	)	)	PUNCT
ejpam-3471	15	14	,	,	PUNCT
ejpam-3471	15	15	1260	1260	NUM
ejpam-3471	15	16	-	-	SYM
ejpam-3471	15	17	1276	1276	NUM
ejpam-3471	15	18	1261	1261	NUM
ejpam-3471	15	19	where	where	SCONJ
ejpam-3471	15	20	a	a	DET
ejpam-3471	15	21	:	:	PUNCT
ejpam-3471	15	22	h	h	NOUN
ejpam-3471	15	23	→	→	SYM
ejpam-3471	15	24	h	h	NOUN
ejpam-3471	15	25	is	be	AUX
ejpam-3471	15	26	an	an	DET
ejpam-3471	15	27	operator	operator	NOUN
ejpam-3471	15	28	not	not	PART
ejpam-3471	15	29	necessarily	necessarily	ADV
ejpam-3471	15	30	linear	linear	ADJ
ejpam-3471	15	31	and	and	CCONJ
ejpam-3471	15	32	h	h	NOUN
ejpam-3471	15	33	is	be	AUX
ejpam-3471	15	34	a	a	DET
ejpam-3471	15	35	hilbert	hilbert	NOUN
ejpam-3471	15	36	space	space	NOUN
ejpam-3471	15	37	adequately	adequately	ADV
ejpam-3471	15	38	chosen	choose	VERB
ejpam-3471	15	39	given	give	VERB
ejpam-3471	15	40	the	the	DET
ejpam-3471	15	41	operator	operator	NOUN
ejpam-3471	15	42	a.	a.	NOUN
ejpam-3471	15	43	let	let	VERB
ejpam-3471	15	44	:	:	PUNCT
ejpam-3471	15	45	a	a	DET
ejpam-3471	15	46	=	=	X
ejpam-3471	15	47	l−r−n	l−r−n	PROPN
ejpam-3471	15	48	(	(	PUNCT
ejpam-3471	15	49	2	2	NUM
ejpam-3471	15	50	)	)	PUNCT
ejpam-3471	15	51	where	where	SCONJ
ejpam-3471	15	52	l	l	NOUN
ejpam-3471	15	53	is	be	AUX
ejpam-3471	15	54	an	an	DET
ejpam-3471	15	55	invertible	invertible	ADJ
ejpam-3471	15	56	operator	operator	NOUN
ejpam-3471	15	57	in	in	ADP
ejpam-3471	15	58	the	the	DET
ejpam-3471	15	59	adomian	adomian	NOUN
ejpam-3471	15	60	sense	sense	NOUN
ejpam-3471	15	61	,	,	PUNCT
ejpam-3471	15	62	r	r	NOUN
ejpam-3471	15	63	the	the	DET
ejpam-3471	15	64	linear	linear	ADJ
ejpam-3471	15	65	remainder	remainder	NOUN
ejpam-3471	15	66	and	and	CCONJ
ejpam-3471	15	67	n	n	DET
ejpam-3471	15	68	a	a	DET
ejpam-3471	15	69	nonlinear	nonlinear	ADJ
ejpam-3471	15	70	operator	operator	NOUN
ejpam-3471	15	71	.	.	PUNCT
ejpam-3471	16	1	equation	equation	NOUN
ejpam-3471	16	2	(	(	PUNCT
ejpam-3471	16	3	2	2	X
ejpam-3471	16	4	)	)	PUNCT
ejpam-3471	16	5	therefore	therefore	ADV
ejpam-3471	16	6	becomes	become	VERB
ejpam-3471	16	7	:	:	PUNCT
ejpam-3471	17	1	lu−ru−nu	lu−ru−nu	PROPN
ejpam-3471	17	2	=	=	PUNCT
ejpam-3471	17	3	f	f	X
ejpam-3471	17	4	⇐	⇐	ADJ
ejpam-3471	17	5	⇒	⇒	NOUN
ejpam-3471	17	6	u	u	NOUN
ejpam-3471	17	7	=	=	SYM
ejpam-3471	17	8	θ	θ	PROPN
ejpam-3471	17	9	+	+	PUNCT
ejpam-3471	17	10	l−1(f	l−1(f	ADJ
ejpam-3471	17	11	)	)	PUNCT
ejpam-3471	17	12	+	+	SYM
ejpam-3471	17	13	l−1(ru	l−1(ru	PROPN
ejpam-3471	17	14	)	)	PUNCT
ejpam-3471	17	15	+	+	SYM
ejpam-3471	17	16	l−1(nu	l−1(nu	NOUN
ejpam-3471	17	17	)	)	PUNCT
ejpam-3471	17	18	(	(	PUNCT
ejpam-3471	17	19	3	3	X
ejpam-3471	17	20	)	)	PUNCT
ejpam-3471	17	21	where	where	SCONJ
ejpam-3471	17	22	θ	θ	PROPN
ejpam-3471	17	23	is	be	AUX
ejpam-3471	17	24	such	such	ADJ
ejpam-3471	17	25	that	that	SCONJ
ejpam-3471	17	26	lθ	lθ	NOUN
ejpam-3471	17	27	=	=	SYM
ejpam-3471	17	28	0	0	NUM
ejpam-3471	17	29	equation	equation	NOUN
ejpam-3471	17	30	(	(	PUNCT
ejpam-3471	17	31	3	3	X
ejpam-3471	17	32	)	)	PUNCT
ejpam-3471	17	33	is	be	AUX
ejpam-3471	17	34	the	the	DET
ejpam-3471	17	35	adomian	adomian	ADJ
ejpam-3471	17	36	canonical	canonical	ADJ
ejpam-3471	17	37	form	form	NOUN
ejpam-3471	17	38	[	[	X
ejpam-3471	17	39	2	2	NUM
ejpam-3471	17	40	,	,	PUNCT
ejpam-3471	17	41	6–8	6–8	NOUN
ejpam-3471	17	42	]	]	X
ejpam-3471	17	43	using	use	VERB
ejpam-3471	17	44	the	the	DET
ejpam-3471	17	45	successive	successive	ADJ
ejpam-3471	17	46	approximations	approximation	NOUN
ejpam-3471	17	47	[	[	X
ejpam-3471	17	48	1	1	NUM
ejpam-3471	17	49	,	,	PUNCT
ejpam-3471	17	50	4	4	NUM
ejpam-3471	17	51	]	]	PUNCT
ejpam-3471	17	52	,	,	PUNCT
ejpam-3471	17	53	we	we	PRON
ejpam-3471	17	54	get	get	VERB
ejpam-3471	17	55	:	:	PUNCT
ejpam-3471	17	56	uk	uk	PROPN
ejpam-3471	17	57	=	=	SYM
ejpam-3471	17	58	θk	θk	PROPN
ejpam-3471	17	59	+	+	CCONJ
ejpam-3471	17	60	l−1(fk	l−1(fk	PROPN
ejpam-3471	17	61	)	)	PUNCT
ejpam-3471	18	1	+	+	CCONJ
ejpam-3471	18	2	l−1(r(uk	l−1(r(uk	PROPN
ejpam-3471	18	3	)	)	PUNCT
ejpam-3471	18	4	)	)	PUNCT
ejpam-3471	19	1	+	+	CCONJ
ejpam-3471	19	2	l−1(n(uk−1	l−1(n(uk−1	PROPN
ejpam-3471	19	3	)	)	PUNCT
ejpam-3471	19	4	)	)	PUNCT
ejpam-3471	19	5	;	;	PUNCT
ejpam-3471	19	6	k	k	X
ejpam-3471	19	7	≥	≥	NUM
ejpam-3471	19	8	1	1	NUM
ejpam-3471	19	9	(	(	PUNCT
ejpam-3471	19	10	4	4	X
ejpam-3471	19	11	)	)	PUNCT
ejpam-3471	19	12	this	this	PRON
ejpam-3471	19	13	yields	yield	VERB
ejpam-3471	19	14	the	the	DET
ejpam-3471	19	15	following	follow	VERB
ejpam-3471	19	16	adomian	adomian	NOUN
ejpam-3471	19	17	algorithm	algorithm	NOUN
ejpam-3471	20	1	[	[	X
ejpam-3471	20	2	5	5	NUM
ejpam-3471	20	3	]	]	X
ejpam-3471	20	4	{	{	PUNCT
ejpam-3471	20	5	uk0	uk0	ADJ
ejpam-3471	20	6	=	=	NOUN
ejpam-3471	20	7	θk	θk	NOUN
ejpam-3471	20	8	+	+	X
ejpam-3471	20	9	l−1(fk	l−1(fk	PROPN
ejpam-3471	20	10	)	)	PUNCT
ejpam-3471	20	11	+	+	CCONJ
ejpam-3471	20	12	l−1(n(uk−1	l−1(n(uk−1	PROPN
ejpam-3471	20	13	)	)	PUNCT
ejpam-3471	20	14	)	)	PUNCT
ejpam-3471	20	15	;	;	PUNCT
ejpam-3471	20	16	k	k	PROPN
ejpam-3471	20	17	≥	≥	PROPN
ejpam-3471	20	18	1	1	NUM
ejpam-3471	20	19	ukn	ukn	NOUN
ejpam-3471	20	20	=	=	SYM
ejpam-3471	20	21	l−1(r(ukn−1	l−1(r(ukn−1	PROPN
ejpam-3471	20	22	)	)	PUNCT
ejpam-3471	20	23	)	)	PUNCT
ejpam-3471	20	24	;	;	PUNCT
ejpam-3471	21	1	n	n	PRON
ejpam-3471	21	2	≥	≥	NOUN
ejpam-3471	21	3	1	1	NUM
ejpam-3471	21	4	(	(	PUNCT
ejpam-3471	21	5	5	5	NUM
ejpam-3471	21	6	)	)	PUNCT
ejpam-3471	21	7	the	the	DET
ejpam-3471	21	8	picard	picard	PROPN
ejpam-3471	21	9	principle	principle	NOUN
ejpam-3471	21	10	is	be	AUX
ejpam-3471	21	11	then	then	ADV
ejpam-3471	21	12	applied	apply	VERB
ejpam-3471	21	13	to	to	ADP
ejpam-3471	21	14	equation	equation	NOUN
ejpam-3471	21	15	(	(	PUNCT
ejpam-3471	21	16	5	5	NUM
ejpam-3471	21	17	)	)	PUNCT
ejpam-3471	21	18	:	:	PUNCT
ejpam-3471	21	19	let	let	VERB
ejpam-3471	21	20	u0	u0	ADJ
ejpam-3471	21	21	be	be	AUX
ejpam-3471	21	22	such	such	ADJ
ejpam-3471	21	23	that	that	DET
ejpam-3471	21	24	n(u0	n(u0	NOUN
ejpam-3471	21	25	)	)	PUNCT
ejpam-3471	21	26	=	=	SYM
ejpam-3471	21	27	0	0	NUM
ejpam-3471	22	1	for	for	ADP
ejpam-3471	22	2	k	k	PROPN
ejpam-3471	22	3	=	=	SYM
ejpam-3471	22	4	1	1	NUM
ejpam-3471	22	5	,	,	PUNCT
ejpam-3471	22	6	we	we	PRON
ejpam-3471	22	7	get	get	VERB
ejpam-3471	22	8	:	:	PUNCT
ejpam-3471	22	9	{	{	PUNCT
ejpam-3471	22	10	u10	u10	PROPN
ejpam-3471	22	11	=	=	SYM
ejpam-3471	22	12	θ1	θ1	PROPN
ejpam-3471	22	13	+	+	CCONJ
ejpam-3471	22	14	l−1(f1	l−1(f1	NOUN
ejpam-3471	22	15	)	)	PUNCT
ejpam-3471	23	1	+	+	NUM
ejpam-3471	23	2	l−1(n(u0	l−1(n(u0	NOUN
ejpam-3471	23	3	)	)	PUNCT
ejpam-3471	23	4	)	)	PUNCT
ejpam-3471	24	1	u1n	u1n	X
ejpam-3471	24	2	=	=	SYM
ejpam-3471	24	3	l−1(r(u1n−1	l−1(r(u1n−1	PROPN
ejpam-3471	24	4	)	)	PUNCT
ejpam-3471	24	5	)	)	PUNCT
ejpam-3471	24	6	;	;	PUNCT
ejpam-3471	25	1	n	n	PRON
ejpam-3471	25	2	≥	≥	NOUN
ejpam-3471	25	3	1	1	NUM
ejpam-3471	25	4	if	if	SCONJ
ejpam-3471	25	5	the	the	DET
ejpam-3471	25	6	series	series	NOUN
ejpam-3471	25	7	(	(	PUNCT
ejpam-3471	25	8	∑	∑	PROPN
ejpam-3471	25	9	n≥0	n≥0	ADJ
ejpam-3471	25	10	u	u	NOUN
ejpam-3471	25	11	1	1	NUM
ejpam-3471	25	12	n	n	NOUN
ejpam-3471	25	13	)	)	PUNCT
ejpam-3471	25	14	converges	converge	NOUN
ejpam-3471	25	15	,	,	PUNCT
ejpam-3471	25	16	then	then	ADV
ejpam-3471	25	17	u1	u1	PROPN
ejpam-3471	25	18	=	=	PUNCT
ejpam-3471	25	19	∑	∑	PROPN
ejpam-3471	25	20	n≥0	n≥0	PROPN
ejpam-3471	25	21	u	u	PROPN
ejpam-3471	25	22	1	1	NUM
ejpam-3471	25	23	n	n	NOUN
ejpam-3471	25	24	for	for	ADP
ejpam-3471	25	25	k	k	PROPN
ejpam-3471	25	26	=	=	SYM
ejpam-3471	25	27	2,we	2,we	NUM
ejpam-3471	25	28	get	get	VERB
ejpam-3471	25	29	:	:	PUNCT
ejpam-3471	25	30	{	{	PUNCT
ejpam-3471	25	31	u20	u20	PROPN
ejpam-3471	25	32	=	=	PUNCT
ejpam-3471	25	33	θ2	θ2	PROPN
ejpam-3471	25	34	+	+	CCONJ
ejpam-3471	25	35	l−1(f2	l−1(f2	NOUN
ejpam-3471	25	36	)	)	PUNCT
ejpam-3471	26	1	+	+	CCONJ
ejpam-3471	26	2	l−1(n(u1	l−1(n(u1	NOUN
ejpam-3471	26	3	)	)	PUNCT
ejpam-3471	26	4	)	)	PUNCT
ejpam-3471	26	5	u2n	u2n	PROPN
ejpam-3471	27	1	=	=	SYM
ejpam-3471	27	2	l−1(r(u2n−1	l−1(r(u2n−1	PROPN
ejpam-3471	27	3	)	)	PUNCT
ejpam-3471	27	4	)	)	PUNCT
ejpam-3471	27	5	;	;	PUNCT
ejpam-3471	28	1	n	n	PRON
ejpam-3471	28	2	≥	≥	NOUN
ejpam-3471	28	3	1	1	NUM
ejpam-3471	28	4	if	if	SCONJ
ejpam-3471	28	5	the	the	DET
ejpam-3471	28	6	series	series	NOUN
ejpam-3471	28	7	(	(	PUNCT
ejpam-3471	28	8	∑	∑	PROPN
ejpam-3471	28	9	n≥0	n≥0	ADJ
ejpam-3471	28	10	u	u	NOUN
ejpam-3471	28	11	2	2	NUM
ejpam-3471	28	12	n	n	NOUN
ejpam-3471	28	13	)	)	PUNCT
ejpam-3471	28	14	converges	converge	NOUN
ejpam-3471	28	15	,	,	PUNCT
ejpam-3471	28	16	then	then	ADV
ejpam-3471	28	17	u2	u2	PROPN
ejpam-3471	28	18	=	=	PUNCT
ejpam-3471	28	19	∑	∑	PROPN
ejpam-3471	28	20	n≥0	n≥0	PROPN
ejpam-3471	28	21	u	u	PROPN
ejpam-3471	28	22	2	2	NUM
ejpam-3471	28	23	n.	n.	NOUN
ejpam-3471	28	24	this	this	DET
ejpam-3471	28	25	process	process	NOUN
ejpam-3471	28	26	is	be	AUX
ejpam-3471	28	27	repeated	repeat	VERB
ejpam-3471	28	28	to	to	ADP
ejpam-3471	28	29	k.	k.	PROPN
ejpam-3471	28	30	if	if	SCONJ
ejpam-3471	28	31	the	the	DET
ejpam-3471	28	32	series	series	NOUN
ejpam-3471	28	33	(	(	PUNCT
ejpam-3471	28	34	∑	∑	PROPN
ejpam-3471	28	35	n≥0	n≥0	PROPN
ejpam-3471	28	36	u	u	PROPN
ejpam-3471	28	37	k	k	PROPN
ejpam-3471	28	38	n	n	PROPN
ejpam-3471	28	39	)	)	PUNCT
ejpam-3471	28	40	converges	converge	NOUN
ejpam-3471	28	41	,	,	PUNCT
ejpam-3471	28	42	then	then	ADV
ejpam-3471	28	43	uk	uk	PROPN
ejpam-3471	28	44	=	=	SYM
ejpam-3471	28	45	∑	∑	PROPN
ejpam-3471	28	46	n≥0	n≥0	PROPN
ejpam-3471	28	47	u	u	PROPN
ejpam-3471	28	48	k	k	PROPN
ejpam-3471	28	49	n.	n.	PROPN
ejpam-3471	28	50	therefore	therefore	ADV
ejpam-3471	28	51	u	u	PROPN
ejpam-3471	29	1	=	=	PROPN
ejpam-3471	29	2	lim	lim	PROPN
ejpam-3471	29	3	k→+∞	k→+∞	PROPN
ejpam-3471	29	4	uk	uk	PROPN
ejpam-3471	29	5	is	be	AUX
ejpam-3471	29	6	the	the	DET
ejpam-3471	29	7	solution	solution	NOUN
ejpam-3471	29	8	of	of	ADP
ejpam-3471	29	9	the	the	DET
ejpam-3471	29	10	problem	problem	NOUN
ejpam-3471	29	11	.	.	PUNCT
ejpam-3471	30	1	thus	thus	ADV
ejpam-3471	30	2	,	,	PUNCT
ejpam-3471	30	3	given	give	VERB
ejpam-3471	30	4	the	the	DET
ejpam-3471	30	5	problem	problem	NOUN
ejpam-3471	30	6	(	(	PUNCT
ejpam-3471	30	7	p	p	NOUN
ejpam-3471	30	8	)	)	PUNCT
ejpam-3471	30	9	:	:	PUNCT
ejpam-3471	30	10	au	au	X
ejpam-3471	30	11	=	=	SYM
ejpam-3471	30	12	f	f	X
ejpam-3471	30	13	,	,	PUNCT
ejpam-3471	30	14	we	we	PRON
ejpam-3471	30	15	combine	combine	VERB
ejpam-3471	30	16	ideas	idea	NOUN
ejpam-3471	30	17	from	from	ADP
ejpam-3471	30	18	the	the	DET
ejpam-3471	30	19	classical	classical	ADJ
ejpam-3471	30	20	techniques	technique	NOUN
ejpam-3471	30	21	to	to	PART
ejpam-3471	30	22	derive	derive	VERB
ejpam-3471	30	23	the	the	DET
ejpam-3471	30	24	following	follow	VERB
ejpam-3471	30	25	appropriate	appropriate	ADJ
ejpam-3471	30	26	approximate	approximate	ADJ
ejpam-3471	30	27	scheme	scheme	NOUN
ejpam-3471	30	28	.	.	PUNCT
ejpam-3471	31	1	r.	r.	PROPN
ejpam-3471	31	2	yaro	yaro	PROPN
ejpam-3471	31	3	,	,	PUNCT
ejpam-3471	31	4	y.	y.	PROPN
ejpam-3471	31	5	paré	paré	NOUN
ejpam-3471	31	6	,	,	PUNCT
ejpam-3471	31	7	b.	b.	PROPN
ejpam-3471	31	8	abbo	abbo	PROPN
ejpam-3471	31	9	/	/	SYM
ejpam-3471	31	10	eur	eur	PROPN
ejpam-3471	31	11	.	.	PUNCT
ejpam-3471	32	1	j.	j.	PROPN
ejpam-3471	32	2	pure	pure	PROPN
ejpam-3471	32	3	appl	appl	PROPN
ejpam-3471	32	4	.	.	PROPN
ejpam-3471	32	5	math	math	PROPN
ejpam-3471	32	6	,	,	PUNCT
ejpam-3471	32	7	12	12	NUM
ejpam-3471	32	8	(	(	PUNCT
ejpam-3471	32	9	3	3	NUM
ejpam-3471	32	10	)	)	PUNCT
ejpam-3471	32	11	(	(	PUNCT
ejpam-3471	32	12	2019	2019	NUM
ejpam-3471	32	13	)	)	PUNCT
ejpam-3471	32	14	,	,	PUNCT
ejpam-3471	32	15	1260	1260	NUM
ejpam-3471	32	16	-	-	SYM
ejpam-3471	32	17	1276	1276	NUM
ejpam-3471	32	18	1262	1262	NUM
ejpam-3471	32	19	{	{	PUNCT
ejpam-3471	32	20	uk0	uk0	ADJ
ejpam-3471	32	21	=	=	NOUN
ejpam-3471	32	22	θk	θk	NOUN
ejpam-3471	32	23	+	+	X
ejpam-3471	32	24	l−1(fk	l−1(fk	PROPN
ejpam-3471	32	25	)	)	PUNCT
ejpam-3471	32	26	+	+	CCONJ
ejpam-3471	32	27	l−1(n(uk−1	l−1(n(uk−1	PROPN
ejpam-3471	32	28	)	)	PUNCT
ejpam-3471	32	29	)	)	PUNCT
ejpam-3471	32	30	;	;	PUNCT
ejpam-3471	33	1	k	k	PROPN
ejpam-3471	33	2	≥	≥	PROPN
ejpam-3471	33	3	1	1	NUM
ejpam-3471	33	4	ukn	ukn	NOUN
ejpam-3471	33	5	=	=	SYM
ejpam-3471	33	6	l−1(r(ukn−1	l−1(r(ukn−1	PROPN
ejpam-3471	33	7	)	)	PUNCT
ejpam-3471	33	8	)	)	PUNCT
ejpam-3471	33	9	;	;	PUNCT
ejpam-3471	33	10	n	n	PRON
ejpam-3471	33	11	≥	≥	NOUN
ejpam-3471	33	12	1	1	NUM
ejpam-3471	33	13	(	(	PUNCT
ejpam-3471	33	14	6	6	NUM
ejpam-3471	33	15	)	)	PUNCT
ejpam-3471	33	16	called	call	VERB
ejpam-3471	33	17	sba	sba	PROPN
ejpam-3471	33	18	algorithm	algorithm	PROPN
ejpam-3471	33	19	.	.	PUNCT
ejpam-3471	34	1	2.2	2.2	NUM
ejpam-3471	34	2	.	.	PUNCT
ejpam-3471	34	3	description	description	NOUN
ejpam-3471	34	4	of	of	ADP
ejpam-3471	34	5	the	the	DET
ejpam-3471	34	6	fourier	fourier	NOUN
ejpam-3471	34	7	method	method	NOUN
ejpam-3471	34	8	or	or	CCONJ
ejpam-3471	34	9	method	method	NOUN
ejpam-3471	34	10	of	of	ADP
ejpam-3471	34	11	separation	separation	NOUN
ejpam-3471	34	12	of	of	ADP
ejpam-3471	34	13	variables	variable	NOUN
ejpam-3471	34	14	the	the	DET
ejpam-3471	34	15	method	method	NOUN
ejpam-3471	34	16	of	of	ADP
ejpam-3471	34	17	separation	separation	NOUN
ejpam-3471	34	18	of	of	ADP
ejpam-3471	34	19	variable	variable	NOUN
ejpam-3471	34	20	(	(	PUNCT
ejpam-3471	34	21	also	also	ADV
ejpam-3471	34	22	known	know	VERB
ejpam-3471	34	23	as	as	ADP
ejpam-3471	34	24	fourier	fourier	NOUN
ejpam-3471	34	25	method	method	NOUN
ejpam-3471	34	26	)	)	PUNCT
ejpam-3471	34	27	is	be	AUX
ejpam-3471	34	28	one	one	NUM
ejpam-3471	34	29	of	of	ADP
ejpam-3471	34	30	several	several	ADJ
ejpam-3471	34	31	methods	method	NOUN
ejpam-3471	34	32	for	for	ADP
ejpam-3471	34	33	solving	solve	VERB
ejpam-3471	34	34	ordinary	ordinary	ADJ
ejpam-3471	34	35	and	and	CCONJ
ejpam-3471	34	36	partial	partial	ADJ
ejpam-3471	34	37	differential	differential	ADJ
ejpam-3471	34	38	equations	equation	NOUN
ejpam-3471	34	39	.	.	PUNCT
ejpam-3471	35	1	this	this	DET
ejpam-3471	35	2	method	method	NOUN
ejpam-3471	35	3	can	can	AUX
ejpam-3471	35	4	not	not	PART
ejpam-3471	35	5	always	always	ADV
ejpam-3471	35	6	be	be	AUX
ejpam-3471	35	7	used	use	VERB
ejpam-3471	35	8	,	,	PUNCT
ejpam-3471	35	9	even	even	ADV
ejpam-3471	35	10	when	when	SCONJ
ejpam-3471	35	11	it	it	PRON
ejpam-3471	35	12	can	can	AUX
ejpam-3471	35	13	be	be	AUX
ejpam-3471	35	14	used	use	VERB
ejpam-3471	35	15	it	it	PRON
ejpam-3471	35	16	will	will	AUX
ejpam-3471	35	17	not	not	PART
ejpam-3471	35	18	always	always	ADV
ejpam-3471	35	19	be	be	AUX
ejpam-3471	35	20	possible	possible	ADJ
ejpam-3471	35	21	to	to	PART
ejpam-3471	35	22	get	get	VERB
ejpam-3471	35	23	the	the	DET
ejpam-3471	35	24	solution	solution	NOUN
ejpam-3471	35	25	of	of	ADP
ejpam-3471	35	26	the	the	DET
ejpam-3471	35	27	problem	problem	NOUN
ejpam-3471	35	28	.	.	PUNCT
ejpam-3471	36	1	however	however	ADV
ejpam-3471	36	2	,	,	PUNCT
ejpam-3471	36	3	it	it	PRON
ejpam-3471	36	4	can	can	AUX
ejpam-3471	36	5	be	be	AUX
ejpam-3471	36	6	used	use	VERB
ejpam-3471	36	7	to	to	PART
ejpam-3471	36	8	easily	easily	ADV
ejpam-3471	36	9	in	in	ADP
ejpam-3471	36	10	the	the	DET
ejpam-3471	36	11	(	(	PUNCT
ejpam-3471	36	12	1−d	1−d	NUM
ejpam-3471	36	13	)	)	PUNCT
ejpam-3471	36	14	heat	heat	NOUN
ejpam-3471	36	15	equation	equation	NOUN
ejpam-3471	36	16	with	with	ADP
ejpam-3471	36	17	no	no	DET
ejpam-3471	36	18	sources	source	NOUN
ejpam-3471	36	19	,	,	PUNCT
ejpam-3471	36	20	in	in	ADP
ejpam-3471	36	21	the	the	DET
ejpam-3471	36	22	(	(	PUNCT
ejpam-3471	36	23	1−d	1−d	NUM
ejpam-3471	36	24	)	)	PUNCT
ejpam-3471	36	25	wave	wave	NOUN
ejpam-3471	36	26	equation	equation	NOUN
ejpam-3471	36	27	and	and	CCONJ
ejpam-3471	36	28	in	in	ADP
ejpam-3471	36	29	the	the	DET
ejpam-3471	36	30	(	(	PUNCT
ejpam-3471	36	31	2−d	2−d	NUM
ejpam-3471	36	32	)	)	PUNCT
ejpam-3471	36	33	heat	heat	NOUN
ejpam-3471	36	34	and	and	CCONJ
ejpam-3471	36	35	wave	wave	NOUN
ejpam-3471	36	36	equations	equation	NOUN
ejpam-3471	36	37	.	.	PUNCT
ejpam-3471	37	1	let	let	VERB
ejpam-3471	37	2	’s	’s	NOUN
ejpam-3471	37	3	consider	consider	VERB
ejpam-3471	37	4	the	the	DET
ejpam-3471	37	5	following	follow	VERB
ejpam-3471	37	6	general	general	ADJ
ejpam-3471	37	7	functional	functional	ADJ
ejpam-3471	37	8	equation	equation	NOUN
ejpam-3471	37	9	au	au	X
ejpam-3471	37	10	=	=	SYM
ejpam-3471	37	11	f	f	PROPN
ejpam-3471	37	12	(	(	PUNCT
ejpam-3471	37	13	7	7	NUM
ejpam-3471	37	14	)	)	PUNCT
ejpam-3471	37	15	the	the	DET
ejpam-3471	37	16	method	method	NOUN
ejpam-3471	37	17	of	of	ADP
ejpam-3471	37	18	separation	separation	NOUN
ejpam-3471	37	19	of	of	ADP
ejpam-3471	37	20	variables	variable	NOUN
ejpam-3471	37	21	relies	rely	VERB
ejpam-3471	37	22	upon	upon	SCONJ
ejpam-3471	37	23	the	the	DET
ejpam-3471	37	24	assumption	assumption	NOUN
ejpam-3471	38	1	that	that	SCONJ
ejpam-3471	38	2	a	a	DET
ejpam-3471	38	3	function	function	NOUN
ejpam-3471	38	4	of	of	ADP
ejpam-3471	38	5	the	the	DET
ejpam-3471	38	6	form	form	NOUN
ejpam-3471	38	7	:	:	PUNCT
ejpam-3471	38	8	u(x	u(x	PROPN
ejpam-3471	38	9	,	,	PUNCT
ejpam-3471	38	10	t	t	PROPN
ejpam-3471	38	11	)	)	PUNCT
ejpam-3471	38	12	=	=	SYM
ejpam-3471	38	13	x(x)t	x(x)t	PROPN
ejpam-3471	38	14	(	(	PUNCT
ejpam-3471	38	15	t	t	PROPN
ejpam-3471	38	16	)	)	PUNCT
ejpam-3471	38	17	(	(	PUNCT
ejpam-3471	38	18	8)	8)	NUM
ejpam-3471	38	19	if	if	SCONJ
ejpam-3471	38	20	we	we	PRON
ejpam-3471	38	21	are	be	AUX
ejpam-3471	38	22	in	in	ADP
ejpam-3471	38	23	the	the	DET
ejpam-3471	38	24	case	case	NOUN
ejpam-3471	38	25	of	of	ADP
ejpam-3471	38	26	one	one	NUM
ejpam-3471	38	27	-dimension	-dimension	NOUN
ejpam-3471	38	28	x	x	X
ejpam-3471	38	29	of	of	ADP
ejpam-3471	38	30	space(1−d	space(1−d	NUM
ejpam-3471	38	31	)	)	PUNCT
ejpam-3471	38	32	and	and	CCONJ
ejpam-3471	38	33	u(x	u(x	PROPN
ejpam-3471	38	34	,	,	PUNCT
ejpam-3471	38	35	y	y	PROPN
ejpam-3471	38	36	,	,	PUNCT
ejpam-3471	38	37	t	t	PROPN
ejpam-3471	38	38	)	)	PUNCT
ejpam-3471	38	39	=	=	SYM
ejpam-3471	38	40	u(x	u(x	NOUN
ejpam-3471	38	41	,	,	PUNCT
ejpam-3471	38	42	y)t	y)t	PUNCT
ejpam-3471	38	43	(	(	PUNCT
ejpam-3471	38	44	t	t	NOUN
ejpam-3471	38	45	)	)	PUNCT
ejpam-3471	38	46	=	=	SYM
ejpam-3471	39	1	x(x)y	x(x)y	PROPN
ejpam-3471	39	2	(	(	PUNCT
ejpam-3471	39	3	y)t	y)t	X
ejpam-3471	39	4	(	(	PUNCT
ejpam-3471	39	5	t	t	NOUN
ejpam-3471	39	6	)	)	PUNCT
ejpam-3471	39	7	(	(	PUNCT
ejpam-3471	39	8	9	9	X
ejpam-3471	39	9	)	)	PUNCT
ejpam-3471	39	10	if	if	SCONJ
ejpam-3471	39	11	we	we	PRON
ejpam-3471	39	12	are	be	AUX
ejpam-3471	39	13	in	in	ADP
ejpam-3471	39	14	the	the	DET
ejpam-3471	39	15	case	case	NOUN
ejpam-3471	39	16	of	of	ADP
ejpam-3471	39	17	two	two	NUM
ejpam-3471	39	18	dimension	dimension	NOUN
ejpam-3471	39	19	x	x	PUNCT
ejpam-3471	39	20	and	and	CCONJ
ejpam-3471	39	21	y	y	PROPN
ejpam-3471	39	22	of	of	ADP
ejpam-3471	39	23	space	space	NOUN
ejpam-3471	39	24	(	(	PUNCT
ejpam-3471	39	25	2	2	NUM
ejpam-3471	39	26	−d	−d	ADJ
ejpam-3471	39	27	)	)	PUNCT
ejpam-3471	39	28	will	will	AUX
ejpam-3471	39	29	be	be	AUX
ejpam-3471	39	30	a	a	DET
ejpam-3471	39	31	solution	solution	NOUN
ejpam-3471	39	32	to	to	PART
ejpam-3471	39	33	linear	linear	VERB
ejpam-3471	39	34	homogeneous	homogeneous	ADJ
ejpam-3471	39	35	partial	partial	ADJ
ejpam-3471	39	36	differential	differential	NOUN
ejpam-3471	39	37	equation	equation	NOUN
ejpam-3471	39	38	in	in	ADP
ejpam-3471	39	39	x	x	PUNCT
ejpam-3471	39	40	and	and	CCONJ
ejpam-3471	39	41	t	t	PROPN
ejpam-3471	39	42	when	when	SCONJ
ejpam-3471	39	43	when	when	SCONJ
ejpam-3471	39	44	we	we	PRON
ejpam-3471	39	45	are	be	AUX
ejpam-3471	39	46	in	in	ADP
ejpam-3471	39	47	(	(	PUNCT
ejpam-3471	39	48	1−d	1−d	NUM
ejpam-3471	39	49	)	)	PUNCT
ejpam-3471	39	50	and	and	CCONJ
ejpam-3471	39	51	x	x	X
ejpam-3471	39	52	,	,	PUNCT
ejpam-3471	39	53	y	y	PROPN
ejpam-3471	39	54	and	and	CCONJ
ejpam-3471	39	55	t	t	PROPN
ejpam-3471	39	56	when	when	SCONJ
ejpam-3471	39	57	when	when	SCONJ
ejpam-3471	39	58	we	we	PRON
ejpam-3471	39	59	are	be	AUX
ejpam-3471	39	60	in	in	ADP
ejpam-3471	39	61	(	(	PUNCT
ejpam-3471	39	62	2.−d	2.−d	NUM
ejpam-3471	39	63	)	)	PUNCT
ejpam-3471	39	64	.	.	PUNCT
ejpam-3471	40	1	this	this	PRON
ejpam-3471	40	2	is	be	AUX
ejpam-3471	40	3	called	call	VERB
ejpam-3471	40	4	a	a	DET
ejpam-3471	40	5	product	product	NOUN
ejpam-3471	40	6	solution	solution	NOUN
ejpam-3471	40	7	and	and	CCONJ
ejpam-3471	40	8	provided	provide	VERB
ejpam-3471	40	9	the	the	DET
ejpam-3471	40	10	boundary	boundary	ADJ
ejpam-3471	40	11	conditions	condition	NOUN
ejpam-3471	40	12	are	be	AUX
ejpam-3471	40	13	also	also	ADV
ejpam-3471	40	14	linear	linear	ADJ
ejpam-3471	40	15	and	and	CCONJ
ejpam-3471	40	16	homogeneous	homogeneous	ADJ
ejpam-3471	40	17	this	this	PRON
ejpam-3471	40	18	will	will	AUX
ejpam-3471	40	19	also	also	ADV
ejpam-3471	40	20	satisfy	satisfy	VERB
ejpam-3471	40	21	the	the	DET
ejpam-3471	40	22	boundary	boundary	ADJ
ejpam-3471	40	23	conditions	condition	NOUN
ejpam-3471	40	24	.	.	PUNCT
ejpam-3471	41	1	however	however	ADV
ejpam-3471	41	2	,	,	PUNCT
ejpam-3471	41	3	as	as	SCONJ
ejpam-3471	41	4	noted	note	VERB
ejpam-3471	41	5	above	above	ADP
ejpam-3471	41	6	this	this	PRON
ejpam-3471	41	7	will	will	AUX
ejpam-3471	41	8	only	only	ADV
ejpam-3471	41	9	rarely	rarely	ADV
ejpam-3471	41	10	satisfy	satisfy	VERB
ejpam-3471	41	11	the	the	DET
ejpam-3471	41	12	initial	initial	ADJ
ejpam-3471	41	13	condition	condition	NOUN
ejpam-3471	41	14	,	,	PUNCT
ejpam-3471	41	15	but	but	CCONJ
ejpam-3471	41	16	that	that	PRON
ejpam-3471	41	17	is	be	AUX
ejpam-3471	41	18	something	something	PRON
ejpam-3471	41	19	for	for	SCONJ
ejpam-3471	41	20	us	we	PRON
ejpam-3471	41	21	to	to	PART
ejpam-3471	41	22	worry	worry	VERB
ejpam-3471	41	23	about	about	ADP
ejpam-3471	41	24	in	in	ADP
ejpam-3471	41	25	the	the	DET
ejpam-3471	41	26	next	next	ADJ
ejpam-3471	41	27	section	section	NOUN
ejpam-3471	41	28	.	.	PUNCT
ejpam-3471	42	1	r.	r.	PROPN
ejpam-3471	42	2	yaro	yaro	PROPN
ejpam-3471	42	3	,	,	PUNCT
ejpam-3471	42	4	y.	y.	PROPN
ejpam-3471	42	5	paré	paré	NOUN
ejpam-3471	42	6	,	,	PUNCT
ejpam-3471	42	7	b.	b.	PROPN
ejpam-3471	42	8	abbo	abbo	PROPN
ejpam-3471	42	9	/	/	SYM
ejpam-3471	42	10	eur	eur	PROPN
ejpam-3471	42	11	.	.	PUNCT
ejpam-3471	43	1	j.	j.	PROPN
ejpam-3471	43	2	pure	pure	PROPN
ejpam-3471	43	3	appl	appl	PROPN
ejpam-3471	43	4	.	.	PROPN
ejpam-3471	43	5	math	math	PROPN
ejpam-3471	43	6	,	,	PUNCT
ejpam-3471	43	7	12	12	NUM
ejpam-3471	43	8	(	(	PUNCT
ejpam-3471	43	9	3	3	NUM
ejpam-3471	43	10	)	)	PUNCT
ejpam-3471	43	11	(	(	PUNCT
ejpam-3471	43	12	2019	2019	NUM
ejpam-3471	43	13	)	)	PUNCT
ejpam-3471	43	14	,	,	PUNCT
ejpam-3471	43	15	1260	1260	NUM
ejpam-3471	43	16	-	-	SYM
ejpam-3471	43	17	1276	1276	NUM
ejpam-3471	43	18	1263	1263	NUM
ejpam-3471	43	19	3	3	NUM
ejpam-3471	43	20	.	.	PUNCT
ejpam-3471	43	21	applications	application	NOUN
ejpam-3471	43	22	3.1	3.1	NUM
ejpam-3471	43	23	.	.	PUNCT
ejpam-3471	44	1	problem	problem	NOUN
ejpam-3471	44	2	1	1	NUM
ejpam-3471	44	3	let	let	VERB
ejpam-3471	44	4	’s	’s	NOUN
ejpam-3471	44	5	consider	consider	VERB
ejpam-3471	44	6	the	the	DET
ejpam-3471	44	7	following	follow	VERB
ejpam-3471	44	8	wave	wave	NOUN
ejpam-3471	44	9	’s	’s	PART
ejpam-3471	44	10	model	model	NOUN
ejpam-3471	44	11	of	of	ADP
ejpam-3471	44	12	one	one	NUM
ejpam-3471	44	13	-	-	PUNCT
ejpam-3471	44	14	dimension	dimension	NOUN
ejpam-3471	44	15	of	of	ADP
ejpam-3471	44	16	space	space	NOUN
ejpam-3471	44	17	:	:	PUNCT
ejpam-3471	44	18	(	(	PUNCT
ejpam-3471	44	19	p1	p1	NOUN
ejpam-3471	44	20	)	)	PUNCT
ejpam-3471	44	21			NUM
ejpam-3471	44	22	∂2u(x	∂2u(x	PROPN
ejpam-3471	44	23	,	,	PUNCT
ejpam-3471	44	24	t	t	NOUN
ejpam-3471	44	25	)	)	PUNCT
ejpam-3471	44	26	∂t2	∂t2	NOUN
ejpam-3471	45	1	=	=	SYM
ejpam-3471	45	2	c2	c2	PROPN
ejpam-3471	45	3	4	4	NUM
ejpam-3471	45	4	u(x	u(x	NOUN
ejpam-3471	45	5	,	,	PUNCT
ejpam-3471	45	6	t	t	PROPN
ejpam-3471	45	7	)	)	PUNCT
ejpam-3471	45	8	,	,	PUNCT
ejpam-3471	45	9	c	c	X
ejpam-3471	45	10	>	>	X
ejpam-3471	45	11	0	0	NUM
ejpam-3471	45	12	u(x	u(x	NOUN
ejpam-3471	45	13	,	,	PUNCT
ejpam-3471	45	14	0	0	NUM
ejpam-3471	45	15	)	)	PUNCT
ejpam-3471	45	16	=	=	SYM
ejpam-3471	45	17	ϕ(x	ϕ(x	X
ejpam-3471	45	18	)	)	PUNCT
ejpam-3471	45	19	=	=	PUNCT
ejpam-3471	45	20	sin	sin	NOUN
ejpam-3471	45	21	(	(	PUNCT
ejpam-3471	45	22	πx	πx	NOUN
ejpam-3471	45	23	l	l	NOUN
ejpam-3471	45	24	)	)	PUNCT
ejpam-3471	45	25	ut(x	ut(x	NOUN
ejpam-3471	45	26	,	,	PUNCT
ejpam-3471	45	27	0	0	NUM
ejpam-3471	45	28	)	)	PUNCT
ejpam-3471	45	29	=	=	SYM
ejpam-3471	45	30	φ(x	φ(x	NOUN
ejpam-3471	45	31	)	)	PUNCT
ejpam-3471	45	32	=	=	PUNCT
ejpam-3471	46	1	π	π	X
ejpam-3471	46	2	sin	sin	NOUN
ejpam-3471	46	3	(	(	PUNCT
ejpam-3471	46	4	πx	πx	NOUN
ejpam-3471	46	5	l	l	NOUN
ejpam-3471	46	6	)	)	PUNCT
ejpam-3471	46	7	u(0	u(0	PROPN
ejpam-3471	46	8	,	,	PUNCT
ejpam-3471	46	9	t	t	PROPN
ejpam-3471	46	10	)	)	PUNCT
ejpam-3471	46	11	=	=	SYM
ejpam-3471	46	12	0	0	X
ejpam-3471	46	13	u(l	u(l	ADJ
ejpam-3471	46	14	,	,	PUNCT
ejpam-3471	46	15	t	t	PROPN
ejpam-3471	46	16	)	)	PUNCT
ejpam-3471	46	17	=	=	SYM
ejpam-3471	46	18	0	0	NUM
ejpam-3471	46	19	,	,	PUNCT
ejpam-3471	46	20	l	l	NOUN
ejpam-3471	46	21	>	>	X
ejpam-3471	46	22	0	0	PUNCT
ejpam-3471	46	23	(	(	PUNCT
ejpam-3471	46	24	10	10	NUM
ejpam-3471	46	25	)	)	PUNCT
ejpam-3471	46	26	solving	solve	VERB
ejpam-3471	46	27	yhe	yhe	NOUN
ejpam-3471	46	28	wave	wave	NOUN
ejpam-3471	46	29	equation	equation	NOUN
ejpam-3471	46	30	involves	involves	AUX
ejpam-3471	46	31	identifyinf	identifyinf	VERB
ejpam-3471	46	32	the	the	DET
ejpam-3471	46	33	functions	function	NOUN
ejpam-3471	46	34	u(x	u(x	NOUN
ejpam-3471	46	35	,	,	PUNCT
ejpam-3471	46	36	t	t	PROPN
ejpam-3471	46	37	)	)	PUNCT
ejpam-3471	46	38	that	that	PRON
ejpam-3471	46	39	solve	solve	VERB
ejpam-3471	46	40	the	the	DET
ejpam-3471	46	41	partial	partial	ADJ
ejpam-3471	46	42	differential	differential	NOUN
ejpam-3471	46	43	equation	equation	NOUN
ejpam-3471	46	44	that	that	PRON
ejpam-3471	46	45	represent	represent	VERB
ejpam-3471	46	46	the	the	DET
ejpam-3471	46	47	amplitude	amplitude	NOUN
ejpam-3471	46	48	of	of	ADP
ejpam-3471	46	49	the	the	DET
ejpam-3471	46	50	wave	wave	NOUN
ejpam-3471	46	51	at	at	ADP
ejpam-3471	46	52	any	any	DET
ejpam-3471	46	53	position	position	NOUN
ejpam-3471	46	54	x	x	PUNCT
ejpam-3471	46	55	at	at	ADP
ejpam-3471	46	56	any	any	DET
ejpam-3471	46	57	time	time	NOUN
ejpam-3471	46	58	t.	t.	NOUN
ejpam-3471	46	59	•	•	NOUN
ejpam-3471	46	60	solving	solving	NOUN
ejpam-3471	46	61	by	by	ADP
ejpam-3471	46	62	sba	sba	PROPN
ejpam-3471	46	63	method	method	NOUN
ejpam-3471	46	64	by	by	ADP
ejpam-3471	46	65	integrating	integrate	VERB
ejpam-3471	46	66	(	(	PUNCT
ejpam-3471	46	67	10	10	NUM
ejpam-3471	46	68	)	)	PUNCT
ejpam-3471	46	69	we	we	PRON
ejpam-3471	46	70	get	get	VERB
ejpam-3471	46	71	the	the	DET
ejpam-3471	46	72	adomian	adomian	NOUN
ejpam-3471	46	73	canonical	canonical	ADJ
ejpam-3471	46	74	form	form	NOUN
ejpam-3471	46	75	[	[	X
ejpam-3471	46	76	2	2	NUM
ejpam-3471	46	77	,	,	PUNCT
ejpam-3471	46	78	9	9	NUM
ejpam-3471	46	79	]	]	PUNCT
ejpam-3471	46	80	of	of	ADP
ejpam-3471	46	81	the	the	DET
ejpam-3471	46	82	problem	problem	NOUN
ejpam-3471	46	83	(	(	PUNCT
ejpam-3471	46	84	10	10	NUM
ejpam-3471	46	85	)	)	PUNCT
ejpam-3471	46	86	:	:	PUNCT
ejpam-3471	47	1	u(x	u(x	PROPN
ejpam-3471	47	2	,	,	PUNCT
ejpam-3471	47	3	t	t	PROPN
ejpam-3471	47	4	)	)	PUNCT
ejpam-3471	47	5	=	=	PUNCT
ejpam-3471	48	1	u(0	u(0	PROPN
ejpam-3471	48	2	,	,	PUNCT
ejpam-3471	48	3	x	x	NOUN
ejpam-3471	48	4	)	)	PUNCT
ejpam-3471	48	5	+	+	NUM
ejpam-3471	48	6	t	t	PROPN
ejpam-3471	48	7	∂u(0	∂u(0	PROPN
ejpam-3471	48	8	,	,	PUNCT
ejpam-3471	48	9	x	x	NOUN
ejpam-3471	48	10	)	)	PUNCT
ejpam-3471	48	11	∂t	∂t	PROPN
ejpam-3471	49	1	+	+	CCONJ
ejpam-3471	49	2	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	49	3	(	(	PUNCT
ejpam-3471	49	4	4u(x	4u(x	PROPN
ejpam-3471	49	5	,	,	PUNCT
ejpam-3471	49	6	t	t	PROPN
ejpam-3471	49	7	)	)	PUNCT
ejpam-3471	49	8	)	)	PUNCT
ejpam-3471	49	9	(	(	PUNCT
ejpam-3471	49	10	11	11	X
ejpam-3471	49	11	)	)	PUNCT
ejpam-3471	49	12	applying	apply	VERB
ejpam-3471	49	13	successive	successive	ADJ
ejpam-3471	49	14	approximations	approximation	NOUN
ejpam-3471	49	15	method	method	NOUN
ejpam-3471	49	16	to	to	ADP
ejpam-3471	49	17	(	(	PUNCT
ejpam-3471	49	18	11	11	NUM
ejpam-3471	49	19	)	)	PUNCT
ejpam-3471	49	20	,	,	PUNCT
ejpam-3471	49	21	we	we	PRON
ejpam-3471	49	22	get	get	VERB
ejpam-3471	49	23	:	:	PUNCT
ejpam-3471	49	24	uk(x	uk(x	ADP
ejpam-3471	49	25	,	,	PUNCT
ejpam-3471	49	26	t	t	PROPN
ejpam-3471	49	27	)	)	PUNCT
ejpam-3471	49	28	=	=	SYM
ejpam-3471	50	1	uk(0	uk(0	PROPN
ejpam-3471	50	2	,	,	PUNCT
ejpam-3471	50	3	x	x	X
ejpam-3471	50	4	)	)	PUNCT
ejpam-3471	50	5	+	+	NUM
ejpam-3471	50	6	t	t	PROPN
ejpam-3471	50	7	∂uk(0	∂uk(0	PROPN
ejpam-3471	50	8	,	,	PUNCT
ejpam-3471	50	9	x	x	NOUN
ejpam-3471	50	10	)	)	PUNCT
ejpam-3471	51	1	∂t	∂t	PROPN
ejpam-3471	52	1	+	+	CCONJ
ejpam-3471	52	2	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	52	3	(	(	PUNCT
ejpam-3471	52	4	4uk(x	4uk(x	NUM
ejpam-3471	52	5	,	,	PUNCT
ejpam-3471	52	6	t	t	PROPN
ejpam-3471	52	7	)	)	PUNCT
ejpam-3471	52	8	)	)	PUNCT
ejpam-3471	53	1	+	+	CCONJ
ejpam-3471	53	2	ñ(uk−1(x	ñ(uk−1(x	NOUN
ejpam-3471	53	3	,	,	PUNCT
ejpam-3471	53	4	t	t	PROPN
ejpam-3471	53	5	)	)	PUNCT
ejpam-3471	53	6	)	)	PUNCT
ejpam-3471	53	7	,	,	PUNCT
ejpam-3471	54	1	k	k	PROPN
ejpam-3471	54	2	≥	≥	NUM
ejpam-3471	54	3	1	1	NUM
ejpam-3471	54	4	(	(	PUNCT
ejpam-3471	54	5	12	12	NUM
ejpam-3471	54	6	)	)	PUNCT
ejpam-3471	54	7	where	where	SCONJ
ejpam-3471	54	8	ñ(uk(x	ñ(uk(x	PROPN
ejpam-3471	54	9	,	,	PUNCT
ejpam-3471	54	10	t	t	PROPN
ejpam-3471	54	11	)	)	PUNCT
ejpam-3471	54	12	)	)	PUNCT
ejpam-3471	55	1	=	=	SYM
ejpam-3471	55	2	0	0	NUM
ejpam-3471	55	3	∀	∀	NOUN
ejpam-3471	55	4	k	k	NOUN
ejpam-3471	55	5	∈	∈	PROPN
ejpam-3471	55	6	n	n	ADP
ejpam-3471	55	7	applying	apply	VERB
ejpam-3471	55	8	the	the	DET
ejpam-3471	55	9	sba	sba	PROPN
ejpam-3471	55	10	algorithm	algorithm	NOUN
ejpam-3471	55	11	to	to	ADP
ejpam-3471	55	12	(	(	PUNCT
ejpam-3471	55	13	12	12	NUM
ejpam-3471	55	14	)	)	PUNCT
ejpam-3471	55	15	,	,	PUNCT
ejpam-3471	55	16	we	we	PRON
ejpam-3471	55	17	get	get	VERB
ejpam-3471	55	18	:	:	PUNCT
ejpam-3471	55	19	(	(	PUNCT
ejpam-3471	55	20	p	p	NOUN
ejpam-3471	55	21	ksba	ksba	NOUN
ejpam-3471	55	22	)	)	PUNCT
ejpam-3471	55	23			PUNCT
ejpam-3471	55	24	uk0(x	uk0(x	PROPN
ejpam-3471	55	25	,	,	PUNCT
ejpam-3471	55	26	t	t	PROPN
ejpam-3471	55	27	)	)	PUNCT
ejpam-3471	55	28	=	=	PUNCT
ejpam-3471	56	1	uk(x	uk(x	ADP
ejpam-3471	56	2	,	,	PUNCT
ejpam-3471	56	3	0	0	NUM
ejpam-3471	56	4	)	)	PUNCT
ejpam-3471	56	5	+	+	NUM
ejpam-3471	56	6	t	t	PROPN
ejpam-3471	56	7	∂uk(0	∂uk(0	PROPN
ejpam-3471	56	8	,	,	PUNCT
ejpam-3471	56	9	x	x	NOUN
ejpam-3471	56	10	)	)	PUNCT
ejpam-3471	57	1	∂t	∂t	PROPN
ejpam-3471	57	2	,	,	PUNCT
ejpam-3471	57	3	k	k	PROPN
ejpam-3471	57	4	≥	≥	NUM
ejpam-3471	57	5	1	1	NUM
ejpam-3471	57	6	ukn(x	ukn(x	PROPN
ejpam-3471	57	7	,	,	PUNCT
ejpam-3471	57	8	t	t	PROPN
ejpam-3471	57	9	)	)	PUNCT
ejpam-3471	57	10	=	=	VERB
ejpam-3471	58	1	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	58	2	(	(	PUNCT
ejpam-3471	58	3	4ukn−1(x	4ukn−1(x	NUM
ejpam-3471	58	4	,	,	PUNCT
ejpam-3471	58	5	t	t	PROPN
ejpam-3471	58	6	)	)	PUNCT
ejpam-3471	58	7	)	)	PUNCT
ejpam-3471	58	8	,	,	PUNCT
ejpam-3471	58	9	n	n	X
ejpam-3471	58	10	≥	≥	NOUN
ejpam-3471	58	11	1	1	NUM
ejpam-3471	58	12	(	(	PUNCT
ejpam-3471	58	13	13	13	NUM
ejpam-3471	58	14	)	)	PUNCT
ejpam-3471	58	15	for	for	ADP
ejpam-3471	58	16	k	k	PROPN
ejpam-3471	58	17	=	=	SYM
ejpam-3471	58	18	1	1	NUM
ejpam-3471	58	19	,	,	PUNCT
ejpam-3471	58	20	we	we	PRON
ejpam-3471	58	21	have	have	AUX
ejpam-3471	58	22	:	:	PUNCT
ejpam-3471	58	23	(	(	PUNCT
ejpam-3471	58	24	p	p	NOUN
ejpam-3471	58	25	1	1	NUM
ejpam-3471	58	26	sba	sba	NOUN
ejpam-3471	58	27	)	)	PUNCT
ejpam-3471	58	28	{	{	PUNCT
ejpam-3471	58	29	u10(x	u10(x	NOUN
ejpam-3471	58	30	,	,	PUNCT
ejpam-3471	58	31	t	t	PROPN
ejpam-3471	58	32	)	)	PUNCT
ejpam-3471	58	33	=	=	PUNCT
ejpam-3471	59	1	u1(x	u1(x	PROPN
ejpam-3471	59	2	,	,	PUNCT
ejpam-3471	59	3	0	0	NUM
ejpam-3471	59	4	)	)	PUNCT
ejpam-3471	59	5	u1n(x	u1n(x	PROPN
ejpam-3471	59	6	,	,	PUNCT
ejpam-3471	59	7	t	t	PROPN
ejpam-3471	59	8	)	)	PUNCT
ejpam-3471	59	9	=	=	VERB
ejpam-3471	60	1	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	60	2	(	(	PUNCT
ejpam-3471	60	3	4ukn−1(x	4ukn−1(x	NUM
ejpam-3471	60	4	,	,	PUNCT
ejpam-3471	60	5	t	t	PROPN
ejpam-3471	60	6	)	)	PUNCT
ejpam-3471	60	7	)	)	PUNCT
ejpam-3471	60	8	,	,	PUNCT
ejpam-3471	60	9	n	n	X
ejpam-3471	60	10	≥	≥	NOUN
ejpam-3471	60	11	1	1	NUM
ejpam-3471	60	12	(	(	PUNCT
ejpam-3471	60	13	14	14	NUM
ejpam-3471	60	14	)	)	PUNCT
ejpam-3471	60	15	r.	r.	PROPN
ejpam-3471	60	16	yaro	yaro	PROPN
ejpam-3471	60	17	,	,	PUNCT
ejpam-3471	60	18	y.	y.	PROPN
ejpam-3471	60	19	paré	paré	NOUN
ejpam-3471	60	20	,	,	PUNCT
ejpam-3471	60	21	b.	b.	PROPN
ejpam-3471	60	22	abbo	abbo	PROPN
ejpam-3471	60	23	/	/	SYM
ejpam-3471	60	24	eur	eur	PROPN
ejpam-3471	60	25	.	.	PUNCT
ejpam-3471	61	1	j.	j.	PROPN
ejpam-3471	61	2	pure	pure	PROPN
ejpam-3471	61	3	appl	appl	PROPN
ejpam-3471	61	4	.	.	PROPN
ejpam-3471	61	5	math	math	PROPN
ejpam-3471	61	6	,	,	PUNCT
ejpam-3471	61	7	12	12	NUM
ejpam-3471	61	8	(	(	PUNCT
ejpam-3471	61	9	3	3	NUM
ejpam-3471	61	10	)	)	PUNCT
ejpam-3471	61	11	(	(	PUNCT
ejpam-3471	61	12	2019	2019	NUM
ejpam-3471	61	13	)	)	PUNCT
ejpam-3471	61	14	,	,	PUNCT
ejpam-3471	61	15	1260	1260	NUM
ejpam-3471	61	16	-	-	SYM
ejpam-3471	61	17	1276	1276	NUM
ejpam-3471	61	18	1264	1264	NUM
ejpam-3471	61	19	we	we	PRON
ejpam-3471	61	20	obtain	obtain	VERB
ejpam-3471	61	21	:	:	PUNCT
ejpam-3471	61	22			NOUN
ejpam-3471	61	23	u10(x	u10(x	NOUN
ejpam-3471	61	24	,	,	PUNCT
ejpam-3471	61	25	t	t	PROPN
ejpam-3471	61	26	)	)	PUNCT
ejpam-3471	61	27	=	=	PUNCT
ejpam-3471	61	28	ϕ(x	ϕ(x	X
ejpam-3471	61	29	)	)	PUNCT
ejpam-3471	61	30	+	+	NUM
ejpam-3471	61	31	tφ(x	tφ(x	X
ejpam-3471	61	32	)	)	PUNCT
ejpam-3471	61	33	u11(x	u11(x	NOUN
ejpam-3471	61	34	,	,	PUNCT
ejpam-3471	61	35	t	t	PROPN
ejpam-3471	61	36	)	)	PUNCT
ejpam-3471	61	37	=	=	SYM
ejpam-3471	61	38	c2(ϕ2(x	c2(ϕ2(x	PROPN
ejpam-3471	61	39	)	)	PUNCT
ejpam-3471	61	40	t2	t2	NOUN
ejpam-3471	61	41	2	2	NUM
ejpam-3471	61	42	!	!	PUNCT
ejpam-3471	62	1	+	+	NUM
ejpam-3471	62	2	φ2(x	φ2(x	X
ejpam-3471	62	3	)	)	PUNCT
ejpam-3471	62	4	t3	t3	NOUN
ejpam-3471	62	5	3	3	NUM
ejpam-3471	62	6	!	!	PUNCT
ejpam-3471	62	7	)	)	PUNCT
ejpam-3471	63	1	u12(x	u12(x	PROPN
ejpam-3471	63	2	,	,	PUNCT
ejpam-3471	63	3	t	t	PROPN
ejpam-3471	63	4	)	)	PUNCT
ejpam-3471	63	5	=	=	SYM
ejpam-3471	63	6	c4(ϕ4(x	c4(ϕ4(x	PROPN
ejpam-3471	63	7	)	)	PUNCT
ejpam-3471	63	8	t4	t4	PROPN
ejpam-3471	63	9	4	4	NUM
ejpam-3471	63	10	!	!	PUNCT
ejpam-3471	64	1	+	+	CCONJ
ejpam-3471	64	2	φ4(x	φ4(x	X
ejpam-3471	64	3	)	)	PUNCT
ejpam-3471	64	4	t5	t5	PROPN
ejpam-3471	64	5	5	5	NUM
ejpam-3471	64	6	!	!	PUNCT
ejpam-3471	64	7	)	)	PUNCT
ejpam-3471	65	1	u13(x	u13(x	PROPN
ejpam-3471	65	2	,	,	PUNCT
ejpam-3471	65	3	t	t	PROPN
ejpam-3471	65	4	)	)	PUNCT
ejpam-3471	65	5	=	=	SYM
ejpam-3471	65	6	c6(ϕ6(x	c6(ϕ6(x	PROPN
ejpam-3471	65	7	)	)	PUNCT
ejpam-3471	65	8	t6	t6	PROPN
ejpam-3471	65	9	6	6	NUM
ejpam-3471	65	10	!	!	PUNCT
ejpam-3471	66	1	+	+	CCONJ
ejpam-3471	66	2	φ6(x	φ6(x	NOUN
ejpam-3471	66	3	)	)	PUNCT
ejpam-3471	66	4	t7	t7	PROPN
ejpam-3471	66	5	7	7	NUM
ejpam-3471	66	6	!	!	PUNCT
ejpam-3471	66	7	)	)	PUNCT
ejpam-3471	66	8	...	...	PUNCT
ejpam-3471	67	1	u1n(x	u1n(x	PROPN
ejpam-3471	67	2	,	,	PUNCT
ejpam-3471	67	3	t	t	PROPN
ejpam-3471	67	4	)	)	PUNCT
ejpam-3471	67	5	=	=	SYM
ejpam-3471	67	6	c2n(ϕ2n(x	c2n(ϕ2n(x	X
ejpam-3471	67	7	)	)	PUNCT
ejpam-3471	67	8	t2n	t2n	PROPN
ejpam-3471	67	9	(	(	PUNCT
ejpam-3471	67	10	2n	2n	NUM
ejpam-3471	67	11	)	)	PUNCT
ejpam-3471	67	12	!	!	PUNCT
ejpam-3471	68	1	+	+	CCONJ
ejpam-3471	68	2	φ2n(x	φ2n(x	PROPN
ejpam-3471	68	3	)	)	PUNCT
ejpam-3471	68	4	t2n+1	t2n+1	NOUN
ejpam-3471	68	5	(	(	PUNCT
ejpam-3471	68	6	2n+	2n+	NUM
ejpam-3471	68	7	1	1	NUM
ejpam-3471	68	8	)	)	PUNCT
ejpam-3471	68	9	!	!	PUNCT
ejpam-3471	68	10	)	)	PUNCT
ejpam-3471	69	1	we	we	PRON
ejpam-3471	69	2	have	have	VERB
ejpam-3471	69	3			PRON
ejpam-3471	69	4	ϕ(x	ϕ(x	X
ejpam-3471	69	5	)	)	PUNCT
ejpam-3471	69	6	=	=	PUNCT
ejpam-3471	69	7	sin	sin	NOUN
ejpam-3471	69	8	(	(	PUNCT
ejpam-3471	69	9	πx	πx	NOUN
ejpam-3471	69	10	l	l	NOUN
ejpam-3471	69	11	)	)	PUNCT
ejpam-3471	69	12	⇒	⇒	PROPN
ejpam-3471	69	13	ϕ2n(x	ϕ2n(x	PROPN
ejpam-3471	69	14	)	)	PUNCT
ejpam-3471	70	1	=	=	PRON
ejpam-3471	70	2	(	(	PUNCT
ejpam-3471	70	3	−1)n	−1)n	X
ejpam-3471	70	4	(	(	PUNCT
ejpam-3471	70	5	π	π	NOUN
ejpam-3471	70	6	l	l	NOUN
ejpam-3471	70	7	)	)	PUNCT
ejpam-3471	70	8	2n	2n	NUM
ejpam-3471	70	9	sin	sin	NOUN
ejpam-3471	70	10	(	(	PUNCT
ejpam-3471	70	11	πx	πx	NOUN
ejpam-3471	70	12	l	l	NOUN
ejpam-3471	70	13	)	)	PUNCT
ejpam-3471	70	14	φ(x	φ(x	NOUN
ejpam-3471	70	15	)	)	PUNCT
ejpam-3471	70	16	=	=	PUNCT
ejpam-3471	71	1	π	π	X
ejpam-3471	71	2	sin	sin	NOUN
ejpam-3471	71	3	(	(	PUNCT
ejpam-3471	71	4	πx	πx	NOUN
ejpam-3471	71	5	l	l	NOUN
ejpam-3471	71	6	)	)	PUNCT
ejpam-3471	71	7	⇒	⇒	PROPN
ejpam-3471	71	8	φ2n(x	φ2n(x	PROPN
ejpam-3471	71	9	)	)	PUNCT
ejpam-3471	71	10	=	=	SYM
ejpam-3471	71	11	π(−1)n	π(−1)n	NOUN
ejpam-3471	71	12	(	(	PUNCT
ejpam-3471	71	13	π	π	NOUN
ejpam-3471	71	14	l	l	NOUN
ejpam-3471	71	15	)	)	PUNCT
ejpam-3471	71	16	2n	2n	NUM
ejpam-3471	71	17	sin	sin	NOUN
ejpam-3471	71	18	(	(	PUNCT
ejpam-3471	71	19	πx	πx	NOUN
ejpam-3471	71	20	l	l	NOUN
ejpam-3471	71	21	)	)	PUNCT
ejpam-3471	72	1	then	then	ADV
ejpam-3471	72	2	u1n(x	u1n(x	PROPN
ejpam-3471	72	3	,	,	PUNCT
ejpam-3471	72	4	t	t	PROPN
ejpam-3471	72	5	)	)	PUNCT
ejpam-3471	72	6	=	=	VERB
ejpam-3471	72	7	sin	sin	NOUN
ejpam-3471	72	8	(	(	PUNCT
ejpam-3471	72	9	πx	πx	NOUN
ejpam-3471	72	10	l	l	NOUN
ejpam-3471	72	11	)	)	PUNCT
ejpam-3471	72	12	(−1)n	(−1)n	X
ejpam-3471	72	13	(	(	PUNCT
ejpam-3471	72	14	cπt	cπt	PROPN
ejpam-3471	72	15	l	l	NOUN
ejpam-3471	72	16	)	)	PUNCT
ejpam-3471	72	17	2n	2n	NUM
ejpam-3471	72	18	(	(	PUNCT
ejpam-3471	72	19	2n	2n	NUM
ejpam-3471	72	20	)	)	PUNCT
ejpam-3471	72	21	!	!	PUNCT
ejpam-3471	73	1	+	+	CCONJ
ejpam-3471	73	2	(	(	PUNCT
ejpam-3471	73	3	−1)n	−1)n	X
ejpam-3471	73	4	l	l	NOUN
ejpam-3471	73	5	c	c	PROPN
ejpam-3471	73	6	(	(	PUNCT
ejpam-3471	73	7	cπt	cπt	PROPN
ejpam-3471	73	8	l	l	NOUN
ejpam-3471	73	9	)	)	PUNCT
ejpam-3471	73	10	2n+1	2n+1	NOUN
ejpam-3471	73	11	(	(	PUNCT
ejpam-3471	73	12	2n+	2n+	NUM
ejpam-3471	73	13	1	1	NUM
ejpam-3471	73	14	)	)	PUNCT
ejpam-3471	73	15	!	!	PUNCT
ejpam-3471	74	1			NUM
ejpam-3471	74	2	ϕ1	ϕ1	PROPN
ejpam-3471	74	3	m(x	m(x	PROPN
ejpam-3471	74	4	,	,	PUNCT
ejpam-3471	74	5	t	t	PROPN
ejpam-3471	74	6	)	)	PUNCT
ejpam-3471	74	7	=	=	SYM
ejpam-3471	75	1	m−1∑	m−1∑	PROPN
ejpam-3471	75	2	n=0	n=0	SYM
ejpam-3471	75	3	u1n(x	u1n(x	PROPN
ejpam-3471	75	4	,	,	PUNCT
ejpam-3471	75	5	t	t	PROPN
ejpam-3471	75	6	)	)	PUNCT
ejpam-3471	75	7	let	let	VERB
ejpam-3471	75	8	’s	’s	NOUN
ejpam-3471	75	9	put	put	VERB
ejpam-3471	75	10	then	then	ADV
ejpam-3471	75	11	the	the	DET
ejpam-3471	75	12	approached	approach	VERB
ejpam-3471	75	13	solution	solution	NOUN
ejpam-3471	75	14	at	at	ADP
ejpam-3471	75	15	the	the	DET
ejpam-3471	75	16	the	the	DET
ejpam-3471	75	17	first	first	ADJ
ejpam-3471	75	18	step	step	NOUN
ejpam-3471	75	19	is	be	AUX
ejpam-3471	75	20	:	:	PUNCT
ejpam-3471	75	21	u1(x	u1(x	PROPN
ejpam-3471	75	22	,	,	PUNCT
ejpam-3471	75	23	t	t	PROPN
ejpam-3471	75	24	)	)	PUNCT
ejpam-3471	76	1	=	=	PROPN
ejpam-3471	76	2	lim	lim	PROPN
ejpam-3471	76	3	m→+∞	m→+∞	PROPN
ejpam-3471	76	4	ϕ1	ϕ1	PROPN
ejpam-3471	76	5	m(x	m(x	PROPN
ejpam-3471	76	6	,	,	PUNCT
ejpam-3471	76	7	t	t	PROPN
ejpam-3471	76	8	)	)	PUNCT
ejpam-3471	76	9	=	=	VERB
ejpam-3471	76	10	sin	sin	NOUN
ejpam-3471	76	11	(	(	PUNCT
ejpam-3471	76	12	πx	πx	NOUN
ejpam-3471	76	13	l	l	NOUN
ejpam-3471	76	14	)	)	PUNCT
ejpam-3471	77	1	cos	cos	PROPN
ejpam-3471	77	2	(	(	PUNCT
ejpam-3471	77	3	cπt	cπt	PROPN
ejpam-3471	77	4	l	l	NOUN
ejpam-3471	77	5	)	)	PUNCT
ejpam-3471	78	1	+	+	CCONJ
ejpam-3471	78	2	l	l	NOUN
ejpam-3471	78	3	c	c	NOUN
ejpam-3471	78	4	sin	sin	NOUN
ejpam-3471	78	5	(	(	PUNCT
ejpam-3471	78	6	cπt	cπt	PROPN
ejpam-3471	78	7	l	l	NOUN
ejpam-3471	78	8	)	)	PUNCT
ejpam-3471	78	9	such	such	ADJ
ejpam-3471	78	10	us	us	PROPN
ejpam-3471	78	11	ñ(uk(x	ñ(uk(x	PROPN
ejpam-3471	78	12	,	,	PUNCT
ejpam-3471	78	13	t	t	PROPN
ejpam-3471	78	14	)	)	PUNCT
ejpam-3471	78	15	)	)	PUNCT
ejpam-3471	79	1	=	=	SYM
ejpam-3471	79	2	0	0	NUM
ejpam-3471	79	3	,	,	PUNCT
ejpam-3471	79	4	∀k	∀k	NOUN
ejpam-3471	79	5	≥	≥	NUM
ejpam-3471	79	6	0	0	NUM
ejpam-3471	79	7	at	at	ADP
ejpam-3471	79	8	the	the	DET
ejpam-3471	79	9	step	step	NOUN
ejpam-3471	79	10	k	k	PROPN
ejpam-3471	79	11	,	,	PUNCT
ejpam-3471	79	12	we	we	PRON
ejpam-3471	79	13	have	have	VERB
ejpam-3471	79	14	:	:	PUNCT
ejpam-3471	79	15	(	(	PUNCT
ejpam-3471	79	16	p	p	NOUN
ejpam-3471	79	17	ksba	ksba	NOUN
ejpam-3471	79	18	)	)	PUNCT
ejpam-3471	79	19			PUNCT
ejpam-3471	79	20	uk0(x	uk0(x	PROPN
ejpam-3471	79	21	,	,	PUNCT
ejpam-3471	79	22	t	t	PROPN
ejpam-3471	79	23	)	)	PUNCT
ejpam-3471	79	24	=	=	PUNCT
ejpam-3471	80	1	uk(x	uk(x	ADP
ejpam-3471	80	2	,	,	PUNCT
ejpam-3471	80	3	0	0	NUM
ejpam-3471	80	4	)	)	PUNCT
ejpam-3471	80	5	+	+	NUM
ejpam-3471	80	6	t	t	PROPN
ejpam-3471	80	7	∂uk(0	∂uk(0	PROPN
ejpam-3471	80	8	,	,	PUNCT
ejpam-3471	80	9	x	x	NOUN
ejpam-3471	80	10	)	)	PUNCT
ejpam-3471	81	1	∂t	∂t	PROPN
ejpam-3471	81	2	,	,	PUNCT
ejpam-3471	81	3	k	k	PROPN
ejpam-3471	81	4	≥	≥	NUM
ejpam-3471	81	5	1	1	NUM
ejpam-3471	81	6	ukn(x	ukn(x	PROPN
ejpam-3471	81	7	,	,	PUNCT
ejpam-3471	81	8	t	t	PROPN
ejpam-3471	81	9	)	)	PUNCT
ejpam-3471	81	10	=	=	VERB
ejpam-3471	82	1	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	82	2	(	(	PUNCT
ejpam-3471	82	3	4ukn−1(x	4ukn−1(x	NUM
ejpam-3471	82	4	,	,	PUNCT
ejpam-3471	82	5	t	t	PROPN
ejpam-3471	82	6	)	)	PUNCT
ejpam-3471	82	7	)	)	PUNCT
ejpam-3471	82	8	,	,	PUNCT
ejpam-3471	82	9	n	n	X
ejpam-3471	82	10	≥	≥	NOUN
ejpam-3471	82	11	1	1	NUM
ejpam-3471	82	12	(	(	PUNCT
ejpam-3471	82	13	15	15	NUM
ejpam-3471	82	14	)	)	PUNCT
ejpam-3471	82	15	r.	r.	PROPN
ejpam-3471	82	16	yaro	yaro	PROPN
ejpam-3471	82	17	,	,	PUNCT
ejpam-3471	82	18	y.	y.	PROPN
ejpam-3471	82	19	paré	paré	NOUN
ejpam-3471	82	20	,	,	PUNCT
ejpam-3471	82	21	b.	b.	PROPN
ejpam-3471	82	22	abbo	abbo	PROPN
ejpam-3471	82	23	/	/	SYM
ejpam-3471	82	24	eur	eur	PROPN
ejpam-3471	82	25	.	.	PUNCT
ejpam-3471	83	1	j.	j.	PROPN
ejpam-3471	83	2	pure	pure	PROPN
ejpam-3471	83	3	appl	appl	PROPN
ejpam-3471	83	4	.	.	PROPN
ejpam-3471	83	5	math	math	PROPN
ejpam-3471	83	6	,	,	PUNCT
ejpam-3471	83	7	12	12	NUM
ejpam-3471	83	8	(	(	PUNCT
ejpam-3471	83	9	3	3	NUM
ejpam-3471	83	10	)	)	PUNCT
ejpam-3471	83	11	(	(	PUNCT
ejpam-3471	83	12	2019	2019	NUM
ejpam-3471	83	13	)	)	PUNCT
ejpam-3471	83	14	,	,	PUNCT
ejpam-3471	83	15	1260	1260	NUM
ejpam-3471	83	16	-	-	SYM
ejpam-3471	83	17	1276	1276	NUM
ejpam-3471	83	18	1265	1265	NUM
ejpam-3471	83	19	by	by	ADP
ejpam-3471	83	20	unfolding	unfold	VERB
ejpam-3471	83	21	:	:	PUNCT
ejpam-3471	83	22			VERB
ejpam-3471	83	23	uk0(x	uk0(x	PROPN
ejpam-3471	83	24	,	,	PUNCT
ejpam-3471	83	25	t	t	PROPN
ejpam-3471	83	26	)	)	PUNCT
ejpam-3471	83	27	=	=	PUNCT
ejpam-3471	83	28	ϕ(x	ϕ(x	X
ejpam-3471	83	29	)	)	PUNCT
ejpam-3471	84	1	+	+	NUM
ejpam-3471	84	2	tφ(x	tφ(x	X
ejpam-3471	84	3	)	)	PUNCT
ejpam-3471	84	4	uk1(x	uk1(x	PROPN
ejpam-3471	84	5	,	,	PUNCT
ejpam-3471	84	6	t	t	PROPN
ejpam-3471	84	7	)	)	PUNCT
ejpam-3471	84	8	=	=	SYM
ejpam-3471	84	9	c2(ϕ2(x	c2(ϕ2(x	PROPN
ejpam-3471	84	10	)	)	PUNCT
ejpam-3471	84	11	t2	t2	NOUN
ejpam-3471	84	12	2	2	NUM
ejpam-3471	84	13	!	!	PUNCT
ejpam-3471	85	1	+	+	NUM
ejpam-3471	85	2	φ2(x	φ2(x	X
ejpam-3471	85	3	)	)	PUNCT
ejpam-3471	85	4	t3	t3	NOUN
ejpam-3471	85	5	3	3	NUM
ejpam-3471	85	6	!	!	PUNCT
ejpam-3471	85	7	)	)	PUNCT
ejpam-3471	86	1	uk2(x	uk2(x	PROPN
ejpam-3471	86	2	,	,	PUNCT
ejpam-3471	86	3	t	t	PROPN
ejpam-3471	86	4	)	)	PUNCT
ejpam-3471	86	5	=	=	SYM
ejpam-3471	86	6	c4(ϕ4(x	c4(ϕ4(x	PROPN
ejpam-3471	86	7	)	)	PUNCT
ejpam-3471	86	8	t4	t4	PROPN
ejpam-3471	86	9	4	4	NUM
ejpam-3471	86	10	!	!	PUNCT
ejpam-3471	87	1	+	+	CCONJ
ejpam-3471	87	2	φ4(x	φ4(x	X
ejpam-3471	87	3	)	)	PUNCT
ejpam-3471	87	4	t5	t5	PROPN
ejpam-3471	87	5	5	5	NUM
ejpam-3471	87	6	!	!	PUNCT
ejpam-3471	87	7	)	)	PUNCT
ejpam-3471	88	1	uk3(x	uk3(x	PROPN
ejpam-3471	88	2	,	,	PUNCT
ejpam-3471	88	3	t	t	PROPN
ejpam-3471	88	4	)	)	PUNCT
ejpam-3471	88	5	=	=	SYM
ejpam-3471	88	6	c6(ϕ6(x	c6(ϕ6(x	PROPN
ejpam-3471	88	7	)	)	PUNCT
ejpam-3471	88	8	t6	t6	PROPN
ejpam-3471	88	9	6	6	NUM
ejpam-3471	88	10	!	!	PUNCT
ejpam-3471	89	1	+	+	CCONJ
ejpam-3471	89	2	φ6(x	φ6(x	NOUN
ejpam-3471	89	3	)	)	PUNCT
ejpam-3471	89	4	t7	t7	PROPN
ejpam-3471	89	5	7	7	NUM
ejpam-3471	89	6	!	!	PUNCT
ejpam-3471	89	7	)	)	PUNCT
ejpam-3471	90	1	·	·	PUNCT
ejpam-3471	90	2	·	·	PUNCT
ejpam-3471	90	3	·	·	PUNCT
ejpam-3471	90	4	ukn(x	ukn(x	PROPN
ejpam-3471	90	5	,	,	PUNCT
ejpam-3471	90	6	t	t	PROPN
ejpam-3471	90	7	)	)	PUNCT
ejpam-3471	90	8	=	=	SYM
ejpam-3471	90	9	c2n(ϕ2n(x	c2n(ϕ2n(x	X
ejpam-3471	90	10	)	)	PUNCT
ejpam-3471	90	11	t2n	t2n	PROPN
ejpam-3471	90	12	(	(	PUNCT
ejpam-3471	90	13	2n	2n	NUM
ejpam-3471	90	14	)	)	PUNCT
ejpam-3471	90	15	!	!	PUNCT
ejpam-3471	91	1	+	+	CCONJ
ejpam-3471	91	2	φ2n(x	φ2n(x	PROPN
ejpam-3471	91	3	)	)	PUNCT
ejpam-3471	91	4	t2n+1	t2n+1	NOUN
ejpam-3471	91	5	(	(	PUNCT
ejpam-3471	91	6	2n+	2n+	NUM
ejpam-3471	91	7	1	1	NUM
ejpam-3471	91	8	)	)	PUNCT
ejpam-3471	91	9	!	!	PUNCT
ejpam-3471	91	10	)	)	PUNCT
ejpam-3471	92	1	then	then	ADV
ejpam-3471	92	2	ukn(x	ukn(x	PROPN
ejpam-3471	92	3	,	,	PUNCT
ejpam-3471	92	4	t	t	PROPN
ejpam-3471	92	5	)	)	PUNCT
ejpam-3471	92	6	=	=	SYM
ejpam-3471	92	7	sin	sin	NOUN
ejpam-3471	92	8	(	(	PUNCT
ejpam-3471	92	9	πx	πx	NOUN
ejpam-3471	92	10	l	l	NOUN
ejpam-3471	92	11	)	)	PUNCT
ejpam-3471	92	12	(	(	PUNCT
ejpam-3471	92	13	(	(	PUNCT
ejpam-3471	92	14	−1)n	−1)n	X
ejpam-3471	92	15	(	(	PUNCT
ejpam-3471	92	16	cπtl	cπtl	NOUN
ejpam-3471	92	17	)	)	PUNCT
ejpam-3471	92	18	2n	2n	NUM
ejpam-3471	92	19	(	(	PUNCT
ejpam-3471	92	20	2n	2n	NUM
ejpam-3471	92	21	)	)	PUNCT
ejpam-3471	92	22	!	!	PUNCT
ejpam-3471	93	1	+	+	CCONJ
ejpam-3471	93	2	(	(	PUNCT
ejpam-3471	93	3	−1)n	−1)n	X
ejpam-3471	93	4	l	l	NOUN
ejpam-3471	93	5	c	c	PROPN
ejpam-3471	93	6	(	(	PUNCT
ejpam-3471	93	7	cπtl	cπtl	NOUN
ejpam-3471	93	8	)	)	PUNCT
ejpam-3471	93	9	2n+1	2n+1	PROPN
ejpam-3471	93	10	(	(	PUNCT
ejpam-3471	93	11	2n+	2n+	NUM
ejpam-3471	93	12	1	1	NUM
ejpam-3471	93	13	)	)	PUNCT
ejpam-3471	93	14	!	!	PUNCT
ejpam-3471	94	1	ϕkm(x	ϕkm(x	PROPN
ejpam-3471	94	2	,	,	PUNCT
ejpam-3471	94	3	t	t	PROPN
ejpam-3471	94	4	)	)	PUNCT
ejpam-3471	94	5	=	=	SYM
ejpam-3471	95	1	m−1∑	m−1∑	PROPN
ejpam-3471	95	2	n=0	n=0	SYM
ejpam-3471	95	3	ukn(x	ukn(x	PROPN
ejpam-3471	95	4	,	,	PUNCT
ejpam-3471	95	5	t	t	PROPN
ejpam-3471	95	6	)	)	PUNCT
ejpam-3471	95	7	then	then	ADV
ejpam-3471	95	8	the	the	DET
ejpam-3471	95	9	approached	approach	VERB
ejpam-3471	95	10	solution	solution	NOUN
ejpam-3471	95	11	at	at	ADP
ejpam-3471	95	12	the	the	DET
ejpam-3471	95	13	the	the	DET
ejpam-3471	95	14	first	first	ADJ
ejpam-3471	95	15	step	step	NOUN
ejpam-3471	95	16	is	be	AUX
ejpam-3471	95	17	:	:	PUNCT
ejpam-3471	95	18	uk(x	uk(x	ADP
ejpam-3471	95	19	,	,	PUNCT
ejpam-3471	95	20	t	t	PROPN
ejpam-3471	95	21	)	)	PUNCT
ejpam-3471	96	1	=	=	SYM
ejpam-3471	96	2	lim	lim	PROPN
ejpam-3471	96	3	m→+∞	m→+∞	PROPN
ejpam-3471	96	4	ϕkm(t	ϕkm(t	PROPN
ejpam-3471	96	5	)	)	PUNCT
ejpam-3471	97	1	=	=	VERB
ejpam-3471	97	2	sin	sin	NOUN
ejpam-3471	97	3	(	(	PUNCT
ejpam-3471	97	4	πx	πx	NOUN
ejpam-3471	97	5	l	l	NOUN
ejpam-3471	97	6	)	)	PUNCT
ejpam-3471	97	7	(	(	PUNCT
ejpam-3471	97	8	cos	cos	PROPN
ejpam-3471	97	9	(	(	PUNCT
ejpam-3471	97	10	cπt	cπt	PROPN
ejpam-3471	97	11	l	l	NOUN
ejpam-3471	97	12	)	)	PUNCT
ejpam-3471	98	1	+	+	CCONJ
ejpam-3471	98	2	l	l	NOUN
ejpam-3471	98	3	c	c	NOUN
ejpam-3471	98	4	sin	sin	NOUN
ejpam-3471	98	5	(	(	PUNCT
ejpam-3471	98	6	cπt	cπt	PROPN
ejpam-3471	98	7	l	l	NOUN
ejpam-3471	98	8	)	)	PUNCT
ejpam-3471	98	9	therefore	therefore	ADV
ejpam-3471	98	10	,	,	PUNCT
ejpam-3471	98	11	we	we	PRON
ejpam-3471	98	12	obtain	obtain	VERB
ejpam-3471	98	13	the	the	DET
ejpam-3471	98	14	exact	exact	ADJ
ejpam-3471	98	15	solution	solution	NOUN
ejpam-3471	98	16	of	of	ADP
ejpam-3471	98	17	the	the	DET
ejpam-3471	98	18	problem	problem	NOUN
ejpam-3471	98	19	(	(	PUNCT
ejpam-3471	98	20	p1	p1	PROPN
ejpam-3471	98	21	)	)	PUNCT
ejpam-3471	98	22	:	:	PUNCT
ejpam-3471	99	1	u(x	u(x	PROPN
ejpam-3471	99	2	,	,	PUNCT
ejpam-3471	99	3	t	t	NOUN
ejpam-3471	99	4	)	)	PUNCT
ejpam-3471	99	5	=	=	VERB
ejpam-3471	100	1	lim	lim	PROPN
ejpam-3471	100	2	k→+∞	k→+∞	PROPN
ejpam-3471	100	3	uk(x	uk(x	ADP
ejpam-3471	100	4	,	,	PUNCT
ejpam-3471	100	5	t	t	PROPN
ejpam-3471	100	6	)	)	PUNCT
ejpam-3471	100	7	=	=	SYM
ejpam-3471	100	8	(	(	PUNCT
ejpam-3471	100	9	cos	cos	PROPN
ejpam-3471	100	10	(	(	PUNCT
ejpam-3471	100	11	cπt	cπt	PROPN
ejpam-3471	100	12	l	l	NOUN
ejpam-3471	100	13	)	)	PUNCT
ejpam-3471	101	1	+	+	CCONJ
ejpam-3471	101	2	l	l	NOUN
ejpam-3471	101	3	c	c	NOUN
ejpam-3471	101	4	sin	sin	NOUN
ejpam-3471	101	5	(	(	PUNCT
ejpam-3471	101	6	cπt	cπt	PROPN
ejpam-3471	101	7	l	l	NOUN
ejpam-3471	101	8	)	)	PUNCT
ejpam-3471	101	9	)	)	PUNCT
ejpam-3471	101	10	sin	sin	NOUN
ejpam-3471	101	11	(	(	PUNCT
ejpam-3471	101	12	πx	πx	NOUN
ejpam-3471	101	13	l	l	NOUN
ejpam-3471	101	14	)	)	PUNCT
ejpam-3471	101	15	•	•	ADP
ejpam-3471	101	16	solving	solve	VERB
ejpam-3471	101	17	by	by	ADP
ejpam-3471	101	18	fourier	fourier	ADJ
ejpam-3471	101	19	method	method	NOUN
ejpam-3471	101	20	we	we	PRON
ejpam-3471	101	21	find	find	VERB
ejpam-3471	101	22	all	all	DET
ejpam-3471	101	23	solutions	solution	NOUN
ejpam-3471	101	24	of	of	ADP
ejpam-3471	101	25	the	the	DET
ejpam-3471	101	26	wave	wave	NOUN
ejpam-3471	101	27	equation	equation	NOUN
ejpam-3471	101	28	(	(	PUNCT
ejpam-3471	101	29	p1	p1	PROPN
ejpam-3471	101	30	)	)	PUNCT
ejpam-3471	101	31	with	with	ADP
ejpam-3471	101	32	the	the	DET
ejpam-3471	101	33	general	general	ADJ
ejpam-3471	101	34	form	form	NOUN
ejpam-3471	101	35	:	:	PUNCT
ejpam-3471	101	36	u(x	u(x	PROPN
ejpam-3471	101	37	,	,	PUNCT
ejpam-3471	101	38	t	t	PROPN
ejpam-3471	101	39	)	)	PUNCT
ejpam-3471	101	40	=	=	SYM
ejpam-3471	101	41	t	t	PROPN
ejpam-3471	101	42	(	(	PUNCT
ejpam-3471	101	43	t)x(x	t)x(x	PROPN
ejpam-3471	101	44	)	)	PUNCT
ejpam-3471	101	45	(	(	PUNCT
ejpam-3471	101	46	16	16	NUM
ejpam-3471	101	47	)	)	PUNCT
ejpam-3471	101	48	for	for	ADP
ejpam-3471	101	49	some	some	DET
ejpam-3471	101	50	function	function	NOUN
ejpam-3471	101	51	x(x	x(x	PROPN
ejpam-3471	101	52	)	)	PUNCT
ejpam-3471	101	53	that	that	PRON
ejpam-3471	101	54	depends	depend	VERB
ejpam-3471	101	55	on	on	ADP
ejpam-3471	101	56	x	x	X
ejpam-3471	101	57	but	but	CCONJ
ejpam-3471	101	58	not	not	PART
ejpam-3471	101	59	t	t	PROPN
ejpam-3471	101	60	and	and	CCONJ
ejpam-3471	101	61	some	some	DET
ejpam-3471	101	62	function	function	NOUN
ejpam-3471	101	63	t	t	PROPN
ejpam-3471	101	64	(	(	PUNCT
ejpam-3471	101	65	t	t	PROPN
ejpam-3471	101	66	)	)	PUNCT
ejpam-3471	101	67	that	that	PRON
ejpam-3471	101	68	depends	depend	VERB
ejpam-3471	101	69	only	only	ADV
ejpam-3471	101	70	on	on	ADP
ejpam-3471	101	71	t	t	PROPN
ejpam-3471	101	72	but	but	CCONJ
ejpam-3471	101	73	not	not	PART
ejpam-3471	101	74	x.	x.	PROPN
ejpam-3471	101	75	r.	r.	PROPN
ejpam-3471	101	76	yaro	yaro	PROPN
ejpam-3471	101	77	,	,	PUNCT
ejpam-3471	101	78	y.	y.	PROPN
ejpam-3471	101	79	paré	paré	NOUN
ejpam-3471	101	80	,	,	PUNCT
ejpam-3471	101	81	b.	b.	PROPN
ejpam-3471	101	82	abbo	abbo	PROPN
ejpam-3471	101	83	/	/	SYM
ejpam-3471	101	84	eur	eur	PROPN
ejpam-3471	101	85	.	.	PUNCT
ejpam-3471	102	1	j.	j.	PROPN
ejpam-3471	102	2	pure	pure	PROPN
ejpam-3471	102	3	appl	appl	PROPN
ejpam-3471	102	4	.	.	PROPN
ejpam-3471	102	5	math	math	PROPN
ejpam-3471	102	6	,	,	PUNCT
ejpam-3471	102	7	12	12	NUM
ejpam-3471	102	8	(	(	PUNCT
ejpam-3471	102	9	3	3	NUM
ejpam-3471	102	10	)	)	PUNCT
ejpam-3471	102	11	(	(	PUNCT
ejpam-3471	102	12	2019	2019	NUM
ejpam-3471	102	13	)	)	PUNCT
ejpam-3471	102	14	,	,	PUNCT
ejpam-3471	102	15	1260	1260	NUM
ejpam-3471	102	16	-	-	SYM
ejpam-3471	102	17	1276	1276	NUM
ejpam-3471	102	18	1266	1266	NUM
ejpam-3471	102	19	substitute	substitute	NOUN
ejpam-3471	102	20	equation	equation	NOUN
ejpam-3471	102	21	(	(	PUNCT
ejpam-3471	102	22	16	16	NUM
ejpam-3471	102	23	)	)	PUNCT
ejpam-3471	102	24	into	into	ADP
ejpam-3471	102	25	the	the	DET
ejpam-3471	102	26	one	one	NUM
ejpam-3471	102	27	-	-	PUNCT
ejpam-3471	102	28	dimensional	dimensional	ADJ
ejpam-3471	102	29	equation	equation	NOUN
ejpam-3471	102	30	(	(	PUNCT
ejpam-3471	102	31	10	10	NUM
ejpam-3471	102	32	)	)	PUNCT
ejpam-3471	102	33	,	,	PUNCT
ejpam-3471	102	34	we	we	PRON
ejpam-3471	102	35	get	get	VERB
ejpam-3471	102	36	x(x)t	x(x)t	PROPN
ejpam-3471	103	1	′′	′′	PROPN
ejpam-3471	103	2	(	(	PUNCT
ejpam-3471	103	3	t	t	PROPN
ejpam-3471	103	4	)	)	PUNCT
ejpam-3471	103	5	=	=	SYM
ejpam-3471	104	1	c2	c2	PROPN
ejpam-3471	104	2	t	t	PROPN
ejpam-3471	104	3	(	(	PUNCT
ejpam-3471	104	4	t)x	t)x	NOUN
ejpam-3471	104	5	′′	′′	PROPN
ejpam-3471	104	6	(	(	PUNCT
ejpam-3471	104	7	x)	x)	NUM
ejpam-3471	104	8	⇐	⇐	ADJ
ejpam-3471	104	9	⇒	⇒	NOUN
ejpam-3471	104	10	t	t	X
ejpam-3471	104	11	′′	′′	PROPN
ejpam-3471	104	12	(	(	PUNCT
ejpam-3471	104	13	t	t	PROPN
ejpam-3471	104	14	)	)	PUNCT
ejpam-3471	104	15	c2	c2	PROPN
ejpam-3471	104	16	t	t	PROPN
ejpam-3471	104	17	(	(	PUNCT
ejpam-3471	104	18	t	t	PROPN
ejpam-3471	104	19	)	)	PUNCT
ejpam-3471	104	20	=	=	PUNCT
ejpam-3471	105	1	x	x	X
ejpam-3471	105	2	′′	′′	PROPN
ejpam-3471	105	3	(	(	PUNCT
ejpam-3471	105	4	x	x	X
ejpam-3471	105	5	)	)	PUNCT
ejpam-3471	105	6	x(t	x(t	PROPN
ejpam-3471	105	7	)	)	PUNCT
ejpam-3471	105	8	(	(	PUNCT
ejpam-3471	105	9	17	17	NUM
ejpam-3471	105	10	)	)	PUNCT
ejpam-3471	105	11	such	such	ADJ
ejpam-3471	105	12	t	t	PROPN
ejpam-3471	105	13	′′	′′	PROPN
ejpam-3471	105	14	(	(	PUNCT
ejpam-3471	105	15	t	t	PROPN
ejpam-3471	105	16	)	)	PUNCT
ejpam-3471	105	17	c2	c2	PROPN
ejpam-3471	105	18	t	t	PROPN
ejpam-3471	105	19	(	(	PUNCT
ejpam-3471	105	20	t	t	PROPN
ejpam-3471	105	21	)	)	PUNCT
ejpam-3471	105	22	depends	depend	VERB
ejpam-3471	105	23	on	on	ADP
ejpam-3471	105	24	t	t	PROPN
ejpam-3471	105	25	and	and	CCONJ
ejpam-3471	105	26	x	x	PART
ejpam-3471	105	27	′′	′′	PROPN
ejpam-3471	105	28	(	(	PUNCT
ejpam-3471	105	29	x	x	X
ejpam-3471	105	30	)	)	PUNCT
ejpam-3471	105	31	x(t	x(t	PROPN
ejpam-3471	105	32	)	)	PUNCT
ejpam-3471	105	33	depends	depend	VERB
ejpam-3471	105	34	on	on	ADP
ejpam-3471	105	35	x	x	PRON
ejpam-3471	105	36	,	,	PUNCT
ejpam-3471	105	37	we	we	PRON
ejpam-3471	105	38	can	can	AUX
ejpam-3471	105	39	put	put	VERB
ejpam-3471	105	40	:	:	PUNCT
ejpam-3471	105	41	t	t	PROPN
ejpam-3471	105	42	′′	′′	PROPN
ejpam-3471	105	43	(	(	PUNCT
ejpam-3471	105	44	t	t	PROPN
ejpam-3471	105	45	)	)	PUNCT
ejpam-3471	105	46	c2	c2	PROPN
ejpam-3471	105	47	t	t	PROPN
ejpam-3471	105	48	(	(	PUNCT
ejpam-3471	105	49	t	t	PROPN
ejpam-3471	105	50	)	)	PUNCT
ejpam-3471	105	51	=	=	PUNCT
ejpam-3471	106	1	x	x	X
ejpam-3471	106	2	′′	′′	PROPN
ejpam-3471	106	3	(	(	PUNCT
ejpam-3471	106	4	x	x	X
ejpam-3471	106	5	)	)	PUNCT
ejpam-3471	106	6	x(t	x(t	PROPN
ejpam-3471	106	7	)	)	PUNCT
ejpam-3471	106	8	=	=	SYM
ejpam-3471	107	1	−k2	−k2	NOUN
ejpam-3471	107	2	(	(	PUNCT
ejpam-3471	107	3	18	18	NUM
ejpam-3471	107	4	)	)	PUNCT
ejpam-3471	107	5	then	then	ADV
ejpam-3471	107	6			PUNCT
ejpam-3471	107	7	t	t	X
ejpam-3471	108	1	′′	′′	PROPN
ejpam-3471	108	2	(	(	PUNCT
ejpam-3471	108	3	t	t	PROPN
ejpam-3471	108	4	)	)	PUNCT
ejpam-3471	108	5	=	=	VERB
ejpam-3471	108	6	−(ck)2	−(ck)2	PROPN
ejpam-3471	108	7	t	t	PROPN
ejpam-3471	108	8	(	(	PUNCT
ejpam-3471	108	9	t	t	PROPN
ejpam-3471	108	10	)	)	PUNCT
ejpam-3471	108	11	and	and	CCONJ
ejpam-3471	108	12	x	x	PUNCT
ejpam-3471	108	13	′′	′′	PROPN
ejpam-3471	108	14	(	(	PUNCT
ejpam-3471	108	15	x	x	X
ejpam-3471	108	16	)	)	PUNCT
ejpam-3471	108	17	=	=	SYM
ejpam-3471	108	18	−k2x(x	−k2x(x	NOUN
ejpam-3471	108	19	)	)	PUNCT
ejpam-3471	108	20	⇐	⇐	ADJ
ejpam-3471	108	21	⇒	⇒	NOUN
ejpam-3471	108	22			PUNCT
ejpam-3471	108	23	t	t	PROPN
ejpam-3471	108	24	′′	′′	PROPN
ejpam-3471	108	25	(	(	PUNCT
ejpam-3471	108	26	t	t	PROPN
ejpam-3471	108	27	)	)	PUNCT
ejpam-3471	108	28	+	+	CCONJ
ejpam-3471	108	29	(	(	PUNCT
ejpam-3471	108	30	ck)2	ck)2	PROPN
ejpam-3471	108	31	t	t	PROPN
ejpam-3471	108	32	(	(	PUNCT
ejpam-3471	108	33	t	t	PROPN
ejpam-3471	108	34	)	)	PUNCT
ejpam-3471	108	35	=	=	SYM
ejpam-3471	108	36	0	0	PUNCT
ejpam-3471	108	37	and	and	CCONJ
ejpam-3471	108	38	x	x	SYM
ejpam-3471	108	39	′′	′′	PROPN
ejpam-3471	108	40	(	(	PUNCT
ejpam-3471	108	41	x	x	X
ejpam-3471	108	42	)	)	PUNCT
ejpam-3471	108	43	+	+	CCONJ
ejpam-3471	108	44	k2x(x	k2x(x	NOUN
ejpam-3471	108	45	)	)	PUNCT
ejpam-3471	108	46	=	=	SYM
ejpam-3471	108	47	0	0	PUNCT
ejpam-3471	108	48	(	(	PUNCT
ejpam-3471	108	49	19	19	NUM
ejpam-3471	108	50	)	)	PUNCT
ejpam-3471	108	51	then	then	ADV
ejpam-3471	108	52			PUNCT
ejpam-3471	108	53	t	t	PROPN
ejpam-3471	108	54	(	(	PUNCT
ejpam-3471	108	55	t	t	PROPN
ejpam-3471	108	56	)	)	PUNCT
ejpam-3471	108	57	=	=	NOUN
ejpam-3471	108	58	a	a	DET
ejpam-3471	108	59	cos(ckt	cos(ckt	NOUN
ejpam-3471	108	60	)	)	PUNCT
ejpam-3471	109	1	+	+	PROPN
ejpam-3471	109	2	b	b	X
ejpam-3471	109	3	sin(ckt	sin(ckt	NOUN
ejpam-3471	109	4	)	)	PUNCT
ejpam-3471	109	5	and	and	CCONJ
ejpam-3471	109	6	x(x	x(x	PROPN
ejpam-3471	109	7	)	)	PUNCT
ejpam-3471	110	1	=	=	SYM
ejpam-3471	110	2	c	c	NOUN
ejpam-3471	110	3	cos(kx	cos(kx	X
ejpam-3471	110	4	)	)	PUNCT
ejpam-3471	111	1	+	+	PUNCT
ejpam-3471	111	2	d	d	NOUN
ejpam-3471	111	3	sin(kx	sin(kx	NOUN
ejpam-3471	111	4	)	)	PUNCT
ejpam-3471	111	5	(	(	PUNCT
ejpam-3471	111	6	20	20	NUM
ejpam-3471	111	7	)	)	PUNCT
ejpam-3471	111	8	where	where	SCONJ
ejpam-3471	111	9	a	a	DET
ejpam-3471	111	10	,	,	PUNCT
ejpam-3471	111	11	b	b	NOUN
ejpam-3471	111	12	,	,	PUNCT
ejpam-3471	111	13	c	c	PROPN
ejpam-3471	111	14	and	and	CCONJ
ejpam-3471	111	15	d	d	PROPN
ejpam-3471	111	16	are	be	AUX
ejpam-3471	111	17	arbibrairy	arbibrairy	ADJ
ejpam-3471	111	18	constantes	constante	NOUN
ejpam-3471	111	19	.	.	PUNCT
ejpam-3471	112	1	we	we	PRON
ejpam-3471	112	2	have	have	VERB
ejpam-3471	112	3	u(x	u(x	NOUN
ejpam-3471	112	4	,	,	PUNCT
ejpam-3471	112	5	t	t	PROPN
ejpam-3471	112	6	)	)	PUNCT
ejpam-3471	112	7	=	=	PUNCT
ejpam-3471	112	8	(	(	PUNCT
ejpam-3471	112	9	a	a	DET
ejpam-3471	112	10	cos(ckt	cos(ckt	NOUN
ejpam-3471	112	11	)	)	PUNCT
ejpam-3471	113	1	+	+	PROPN
ejpam-3471	113	2	b	b	X
ejpam-3471	113	3	sin(ckt	sin(ckt	NOUN
ejpam-3471	113	4	)	)	PUNCT
ejpam-3471	113	5	)	)	PUNCT
ejpam-3471	114	1	(	(	PUNCT
ejpam-3471	114	2	c	c	NOUN
ejpam-3471	114	3	cos(kx	cos(kx	X
ejpam-3471	114	4	)	)	PUNCT
ejpam-3471	115	1	+	+	PUNCT
ejpam-3471	115	2	d	d	NOUN
ejpam-3471	115	3	sin(kx	sin(kx	NOUN
ejpam-3471	115	4	)	)	PUNCT
ejpam-3471	115	5	)	)	PUNCT
ejpam-3471	115	6	(	(	PUNCT
ejpam-3471	115	7	21	21	X
ejpam-3471	115	8	)	)	PUNCT
ejpam-3471	115	9	let	let	VERB
ejpam-3471	115	10	’s	’s	NOUN
ejpam-3471	115	11	calculate	calculate	VERB
ejpam-3471	115	12	the	the	DET
ejpam-3471	115	13	constantes	constante	NOUN
ejpam-3471	115	14			PUNCT
ejpam-3471	115	15	u(t	u(t	NOUN
ejpam-3471	115	16	,	,	PUNCT
ejpam-3471	115	17	0	0	NUM
ejpam-3471	115	18	)	)	PUNCT
ejpam-3471	115	19	=	=	SYM
ejpam-3471	115	20	0	0	NUM
ejpam-3471	115	21	and	and	CCONJ
ejpam-3471	115	22	u(t	u(t	NOUN
ejpam-3471	115	23	,	,	PUNCT
ejpam-3471	115	24	l	l	NOUN
ejpam-3471	115	25	)	)	PUNCT
ejpam-3471	115	26	=	=	SYM
ejpam-3471	115	27	0	0	PUNCT
ejpam-3471	116	1	=	=	NOUN
ejpam-3471	116	2	⇒	⇒	NOUN
ejpam-3471	116	3	{	{	PUNCT
ejpam-3471	116	4	c	c	NOUN
ejpam-3471	116	5	=	=	SYM
ejpam-3471	116	6	0	0	NUM
ejpam-3471	116	7	d	d	NOUN
ejpam-3471	116	8	sin(kl	sin(kl	X
ejpam-3471	116	9	)	)	PUNCT
ejpam-3471	116	10	=	=	SYM
ejpam-3471	116	11	0	0	NUM
ejpam-3471	116	12	d	d	NOUN
ejpam-3471	116	13	sin(kl	sin(kl	X
ejpam-3471	116	14	)	)	PUNCT
ejpam-3471	116	15	=	=	PUNCT
ejpam-3471	116	16	0	0	PUNCT
ejpam-3471	117	1	=	=	NOUN
ejpam-3471	117	2	⇒	⇒	NOUN
ejpam-3471	117	3	{	{	PUNCT
ejpam-3471	117	4	d	d	NOUN
ejpam-3471	117	5	6=	6=	ADP
ejpam-3471	117	6	0	0	NUM
ejpam-3471	117	7	sin(kl	sin(kl	X
ejpam-3471	117	8	)	)	PUNCT
ejpam-3471	117	9	=	=	SYM
ejpam-3471	117	10	0	0	NUM
ejpam-3471	117	11	sin(kl	sin(kl	NOUN
ejpam-3471	117	12	)	)	PUNCT
ejpam-3471	117	13	=	=	SYM
ejpam-3471	117	14	0	0	NUM
ejpam-3471	117	15	⇐	⇐	ADJ
ejpam-3471	117	16	⇒	⇒	NOUN
ejpam-3471	117	17	k	k	PROPN
ejpam-3471	117	18	=	=	PUNCT
ejpam-3471	117	19	nπ	nπ	NOUN
ejpam-3471	117	20	l	l	NOUN
ejpam-3471	117	21	(	(	PUNCT
ejpam-3471	117	22	n	n	X
ejpam-3471	117	23	∈	∈	PROPN
ejpam-3471	117	24	z	z	PROPN
ejpam-3471	117	25	)	)	PUNCT
ejpam-3471	117	26	then	then	ADV
ejpam-3471	117	27	∀n	∀n	NUM
ejpam-3471	117	28	≥	≥	NOUN
ejpam-3471	117	29	1	1	NUM
ejpam-3471	117	30	,	,	PUNCT
ejpam-3471	117	31	we	we	PRON
ejpam-3471	117	32	have	have	VERB
ejpam-3471	117	33	r.	r.	PROPN
ejpam-3471	117	34	yaro	yaro	PROPN
ejpam-3471	117	35	,	,	PUNCT
ejpam-3471	117	36	y.	y.	PROPN
ejpam-3471	117	37	paré	paré	NOUN
ejpam-3471	117	38	,	,	PUNCT
ejpam-3471	117	39	b.	b.	PROPN
ejpam-3471	117	40	abbo	abbo	PROPN
ejpam-3471	117	41	/	/	SYM
ejpam-3471	117	42	eur	eur	PROPN
ejpam-3471	117	43	.	.	PUNCT
ejpam-3471	118	1	j.	j.	PROPN
ejpam-3471	118	2	pure	pure	PROPN
ejpam-3471	118	3	appl	appl	PROPN
ejpam-3471	118	4	.	.	PROPN
ejpam-3471	118	5	math	math	PROPN
ejpam-3471	118	6	,	,	PUNCT
ejpam-3471	118	7	12	12	NUM
ejpam-3471	118	8	(	(	PUNCT
ejpam-3471	118	9	3	3	NUM
ejpam-3471	118	10	)	)	PUNCT
ejpam-3471	118	11	(	(	PUNCT
ejpam-3471	118	12	2019	2019	NUM
ejpam-3471	118	13	)	)	PUNCT
ejpam-3471	118	14	,	,	PUNCT
ejpam-3471	118	15	1260	1260	NUM
ejpam-3471	118	16	-	-	SYM
ejpam-3471	118	17	1276	1276	NUM
ejpam-3471	118	18	1267	1267	NUM
ejpam-3471	118	19	un(x	un(x	PROPN
ejpam-3471	118	20	,	,	PUNCT
ejpam-3471	118	21	t	t	PROPN
ejpam-3471	118	22	)	)	PUNCT
ejpam-3471	118	23	=	=	PUNCT
ejpam-3471	118	24	(	(	PUNCT
ejpam-3471	118	25	an	an	DET
ejpam-3471	118	26	cos	cos	PROPN
ejpam-3471	118	27	(	(	PUNCT
ejpam-3471	118	28	cnπt	cnπt	PROPN
ejpam-3471	118	29	l	l	NOUN
ejpam-3471	118	30	)	)	PUNCT
ejpam-3471	119	1	+	+	ADP
ejpam-3471	119	2	bn	bn	X
ejpam-3471	119	3	sin	sin	NOUN
ejpam-3471	119	4	(	(	PUNCT
ejpam-3471	119	5	cnπt	cnπt	PROPN
ejpam-3471	119	6	l	l	NOUN
ejpam-3471	119	7	)	)	PUNCT
ejpam-3471	119	8	)	)	PUNCT
ejpam-3471	119	9	sin	sin	NOUN
ejpam-3471	119	10	(	(	PUNCT
ejpam-3471	119	11	nπx	nπx	NOUN
ejpam-3471	119	12	l	l	NOUN
ejpam-3471	119	13	)	)	PUNCT
ejpam-3471	119	14	(	(	PUNCT
ejpam-3471	119	15	22	22	NUM
ejpam-3471	119	16	)	)	PUNCT
ejpam-3471	119	17	then	then	ADV
ejpam-3471	119	18	u(x	u(x	PROPN
ejpam-3471	119	19	,	,	PUNCT
ejpam-3471	119	20	t	t	PROPN
ejpam-3471	119	21	)	)	PUNCT
ejpam-3471	119	22	=	=	PUNCT
ejpam-3471	120	1	+	+	ADP
ejpam-3471	120	2	∞∑	∞∑	NUM
ejpam-3471	120	3	n=1	n=1	PROPN
ejpam-3471	120	4	(	(	PUNCT
ejpam-3471	120	5	an	an	DET
ejpam-3471	120	6	cos	cos	PROPN
ejpam-3471	120	7	(	(	PUNCT
ejpam-3471	120	8	cnπt	cnπt	PROPN
ejpam-3471	120	9	l	l	NOUN
ejpam-3471	120	10	)	)	PUNCT
ejpam-3471	121	1	+	+	ADP
ejpam-3471	121	2	bn	bn	X
ejpam-3471	121	3	sin	sin	NOUN
ejpam-3471	121	4	(	(	PUNCT
ejpam-3471	121	5	cnπt	cnπt	PROPN
ejpam-3471	121	6	l	l	NOUN
ejpam-3471	121	7	)	)	PUNCT
ejpam-3471	121	8	)	)	PUNCT
ejpam-3471	121	9	sin	sin	NOUN
ejpam-3471	121	10	(	(	PUNCT
ejpam-3471	121	11	nπx	nπx	NOUN
ejpam-3471	121	12	l	l	NOUN
ejpam-3471	121	13	)	)	PUNCT
ejpam-3471	121	14	(	(	PUNCT
ejpam-3471	121	15	23	23	NUM
ejpam-3471	121	16	)	)	PUNCT
ejpam-3471	121	17	we	we	PRON
ejpam-3471	121	18	can	can	AUX
ejpam-3471	121	19	noticed	notice	VERB
ejpam-3471	121	20	that	that	SCONJ
ejpam-3471	121	21	if	if	SCONJ
ejpam-3471	121	22	we	we	PRON
ejpam-3471	121	23	choose	choose	VERB
ejpam-3471	121	24	k2	k2	PROPN
ejpam-3471	121	25	instead	instead	ADV
ejpam-3471	121	26	of	of	ADP
ejpam-3471	121	27	−k2	−k2	PROPN
ejpam-3471	121	28	the	the	DET
ejpam-3471	121	29	solution	solution	NOUN
ejpam-3471	121	30	of	of	ADP
ejpam-3471	121	31	the	the	DET
ejpam-3471	121	32	equation	equation	NOUN
ejpam-3471	121	33	x	x	PUNCT
ejpam-3471	122	1	′′	′′	PROPN
ejpam-3471	122	2	(	(	PUNCT
ejpam-3471	122	3	x	x	X
ejpam-3471	122	4	)	)	PUNCT
ejpam-3471	122	5	+	+	CCONJ
ejpam-3471	122	6	k2x(x	k2x(x	NOUN
ejpam-3471	122	7	)	)	PUNCT
ejpam-3471	122	8	=	=	SYM
ejpam-3471	122	9	0	0	PUNCT
ejpam-3471	122	10	(	(	PUNCT
ejpam-3471	122	11	24	24	NUM
ejpam-3471	122	12	)	)	PUNCT
ejpam-3471	122	13	which	which	PRON
ejpam-3471	122	14	is	be	AUX
ejpam-3471	122	15	x(x	x(x	NOUN
ejpam-3471	122	16	)	)	PUNCT
ejpam-3471	122	17	=	=	PRON
ejpam-3471	122	18	aekx	aekx	VERB
ejpam-3471	122	19	+	+	SYM
ejpam-3471	122	20	be−kx	be−kx	NOUN
ejpam-3471	122	21	do	do	AUX
ejpam-3471	122	22	n’t	not	PART
ejpam-3471	122	23	verify	verify	VERB
ejpam-3471	122	24	the	the	DET
ejpam-3471	122	25	initial	initial	ADJ
ejpam-3471	122	26	condition	condition	NOUN
ejpam-3471	122	27	:	:	PUNCT
ejpam-3471	122	28	u(t	u(t	NOUN
ejpam-3471	122	29	,	,	PUNCT
ejpam-3471	122	30	0	0	NUM
ejpam-3471	122	31	)	)	PUNCT
ejpam-3471	122	32	=	=	SYM
ejpam-3471	122	33	u(t	u(t	NOUN
ejpam-3471	122	34	,	,	PUNCT
ejpam-3471	122	35	l	l	NOUN
ejpam-3471	122	36	)	)	PUNCT
ejpam-3471	122	37	=	=	SYM
ejpam-3471	122	38	0	0	PUNCT
ejpam-3471	123	1	so	so	ADV
ejpam-3471	123	2	choosing	choose	VERB
ejpam-3471	123	3	k2	k2	NOUN
ejpam-3471	123	4	is	be	AUX
ejpam-3471	123	5	impossible	impossible	ADJ
ejpam-3471	123	6	.	.	PUNCT
ejpam-3471	124	1	we	we	PRON
ejpam-3471	124	2	have	have	VERB
ejpam-3471	124	3	∂u(x	∂u(x	PROPN
ejpam-3471	124	4	,	,	PUNCT
ejpam-3471	124	5	t	t	PROPN
ejpam-3471	124	6	)	)	PUNCT
ejpam-3471	124	7	∂t	∂t	PROPN
ejpam-3471	125	1	=	=	PUNCT
ejpam-3471	126	1	+	+	PROPN
ejpam-3471	126	2	∞∑	∞∑	NUM
ejpam-3471	126	3	n=1	n=1	PROPN
ejpam-3471	126	4	(	(	PUNCT
ejpam-3471	126	5	−cnπ	−cnπ	PROPN
ejpam-3471	126	6	l	l	PROPN
ejpam-3471	126	7	an	an	DET
ejpam-3471	126	8	cos	cos	PROPN
ejpam-3471	126	9	(	(	PUNCT
ejpam-3471	126	10	cnπt	cnπt	PROPN
ejpam-3471	126	11	l	l	NOUN
ejpam-3471	126	12	)	)	PUNCT
ejpam-3471	127	1	+	+	CCONJ
ejpam-3471	127	2	cnπ	cnπ	VERB
ejpam-3471	127	3	l	l	PROPN
ejpam-3471	127	4	bn	bn	NOUN
ejpam-3471	127	5	sin	sin	NOUN
ejpam-3471	127	6	(	(	PUNCT
ejpam-3471	127	7	cnπt	cnπt	PROPN
ejpam-3471	127	8	l	l	NOUN
ejpam-3471	127	9	)	)	PUNCT
ejpam-3471	127	10	)	)	PUNCT
ejpam-3471	127	11	sin	sin	NOUN
ejpam-3471	127	12	(	(	PUNCT
ejpam-3471	127	13	nπx	nπx	NOUN
ejpam-3471	127	14	l	l	NOUN
ejpam-3471	127	15	)	)	PUNCT
ejpam-3471	127	16	(	(	PUNCT
ejpam-3471	127	17	25	25	NUM
ejpam-3471	127	18	)	)	PUNCT
ejpam-3471	127	19	for	for	ADP
ejpam-3471	127	20	t	t	NOUN
ejpam-3471	127	21	=	=	SYM
ejpam-3471	127	22	0	0	NUM
ejpam-3471	127	23	,	,	PUNCT
ejpam-3471	127	24	we	we	PRON
ejpam-3471	127	25	have	have	VERB
ejpam-3471	127	26	+	+	NOUN
ejpam-3471	127	27	∞∑	∞∑	NUM
ejpam-3471	127	28	n=1	n=1	PROPN
ejpam-3471	127	29	cnπ	cnπ	VERB
ejpam-3471	127	30	l	l	PROPN
ejpam-3471	127	31	bn	bn	NOUN
ejpam-3471	127	32	sin	sin	NOUN
ejpam-3471	127	33	(	(	PUNCT
ejpam-3471	127	34	nπx	nπx	NOUN
ejpam-3471	127	35	l	l	NOUN
ejpam-3471	127	36	)	)	PUNCT
ejpam-3471	128	1	=	=	SYM
ejpam-3471	128	2	φ(x	φ(x	NOUN
ejpam-3471	128	3	)	)	PUNCT
ejpam-3471	128	4	(	(	PUNCT
ejpam-3471	128	5	26	26	NUM
ejpam-3471	128	6	)	)	PUNCT
ejpam-3471	128	7	u(0	u(0	NOUN
ejpam-3471	128	8	,	,	PUNCT
ejpam-3471	128	9	x	x	NOUN
ejpam-3471	128	10	)	)	PUNCT
ejpam-3471	128	11	=	=	SYM
ejpam-3471	128	12	ϕ(x)	ϕ(x)	PROPN
ejpam-3471	128	13	⇐	⇐	ADJ
ejpam-3471	128	14	⇒	⇒	PROPN
ejpam-3471	128	15	ϕ(x	ϕ(x	X
ejpam-3471	128	16	)	)	PUNCT
ejpam-3471	128	17	=	=	PUNCT
ejpam-3471	129	1	+	+	ADP
ejpam-3471	129	2	∞∑	∞∑	NUM
ejpam-3471	129	3	n=1	n=1	ADP
ejpam-3471	129	4	an	an	DET
ejpam-3471	129	5	sin	sin	NOUN
ejpam-3471	129	6	(	(	PUNCT
ejpam-3471	129	7	nπx	nπx	NOUN
ejpam-3471	129	8	l	l	NOUN
ejpam-3471	129	9	)	)	PUNCT
ejpam-3471	129	10	(	(	PUNCT
ejpam-3471	129	11	27	27	NUM
ejpam-3471	129	12	)	)	PUNCT
ejpam-3471	129	13	we	we	PRON
ejpam-3471	129	14	have	have	AUX
ejpam-3471	129	15			VERB
ejpam-3471	129	16	an	an	DET
ejpam-3471	129	17	=	=	SYM
ejpam-3471	129	18	2	2	NUM
ejpam-3471	129	19	l	l	NOUN
ejpam-3471	129	20	∫	∫	NOUN
ejpam-3471	129	21	l	l	NOUN
ejpam-3471	129	22	0	0	PUNCT
ejpam-3471	129	23	ϕ(z	ϕ(z	PROPN
ejpam-3471	129	24	)	)	PUNCT
ejpam-3471	129	25	sin	sin	NOUN
ejpam-3471	129	26	(	(	PUNCT
ejpam-3471	129	27	nπz	nπz	NOUN
ejpam-3471	129	28	l	l	NOUN
ejpam-3471	129	29	)	)	PUNCT
ejpam-3471	129	30	dz	dz	PROPN
ejpam-3471	129	31	and	and	CCONJ
ejpam-3471	129	32	bn	bn	NOUN
ejpam-3471	129	33	=	=	SYM
ejpam-3471	129	34	2	2	NUM
ejpam-3471	129	35	cnπ	cnπ	NOUN
ejpam-3471	129	36	∫	∫	PROPN
ejpam-3471	129	37	l	l	PROPN
ejpam-3471	129	38	0	0	NUM
ejpam-3471	129	39	φ(z	φ(z	ADJ
ejpam-3471	129	40	)	)	PUNCT
ejpam-3471	129	41	sin	sin	NOUN
ejpam-3471	129	42	(	(	PUNCT
ejpam-3471	129	43	nπz	nπz	NOUN
ejpam-3471	129	44	l	l	NOUN
ejpam-3471	129	45	)	)	PUNCT
ejpam-3471	129	46	dz	dz	PROPN
ejpam-3471	129	47	(	(	PUNCT
ejpam-3471	129	48	28	28	NUM
ejpam-3471	129	49	)	)	PUNCT
ejpam-3471	129	50	r.	r.	PROPN
ejpam-3471	129	51	yaro	yaro	PROPN
ejpam-3471	129	52	,	,	PUNCT
ejpam-3471	129	53	y.	y.	PROPN
ejpam-3471	129	54	paré	paré	NOUN
ejpam-3471	129	55	,	,	PUNCT
ejpam-3471	129	56	b.	b.	PROPN
ejpam-3471	129	57	abbo	abbo	PROPN
ejpam-3471	129	58	/	/	SYM
ejpam-3471	129	59	eur	eur	PROPN
ejpam-3471	129	60	.	.	PUNCT
ejpam-3471	130	1	j.	j.	PROPN
ejpam-3471	130	2	pure	pure	PROPN
ejpam-3471	130	3	appl	appl	PROPN
ejpam-3471	130	4	.	.	PROPN
ejpam-3471	130	5	math	math	PROPN
ejpam-3471	130	6	,	,	PUNCT
ejpam-3471	130	7	12	12	NUM
ejpam-3471	130	8	(	(	PUNCT
ejpam-3471	130	9	3	3	NUM
ejpam-3471	130	10	)	)	PUNCT
ejpam-3471	130	11	(	(	PUNCT
ejpam-3471	130	12	2019	2019	NUM
ejpam-3471	130	13	)	)	PUNCT
ejpam-3471	130	14	,	,	PUNCT
ejpam-3471	130	15	1260	1260	NUM
ejpam-3471	130	16	-	-	SYM
ejpam-3471	130	17	1276	1276	NUM
ejpam-3471	130	18	1268	1268	NUM
ejpam-3471	130	19	3.2	3.2	NUM
ejpam-3471	130	20	.	.	PUNCT
ejpam-3471	131	1	problem	problem	NOUN
ejpam-3471	131	2	2	2	NUM
ejpam-3471	131	3	let	let	VERB
ejpam-3471	131	4	’s	’s	NOUN
ejpam-3471	131	5	consider	consider	VERB
ejpam-3471	131	6	the	the	DET
ejpam-3471	131	7	following	follow	VERB
ejpam-3471	131	8	wave	wave	NOUN
ejpam-3471	131	9	’s	’s	PART
ejpam-3471	131	10	model	model	NOUN
ejpam-3471	131	11	:	:	PUNCT
ejpam-3471	131	12	(	(	PUNCT
ejpam-3471	131	13	p2	p2	X
ejpam-3471	131	14	)	)	PUNCT
ejpam-3471	131	15			PROPN
ejpam-3471	131	16	∂2u(x	∂2u(x	NOUN
ejpam-3471	131	17	,	,	PUNCT
ejpam-3471	131	18	y	y	PROPN
ejpam-3471	131	19	,	,	PUNCT
ejpam-3471	131	20	t	t	PROPN
ejpam-3471	131	21	)	)	PUNCT
ejpam-3471	131	22	∂t2	∂t2	NOUN
ejpam-3471	131	23	=	=	SYM
ejpam-3471	131	24	c2	c2	PROPN
ejpam-3471	131	25	4	4	NUM
ejpam-3471	131	26	u(x	u(x	NOUN
ejpam-3471	131	27	,	,	PUNCT
ejpam-3471	131	28	y	y	PROPN
ejpam-3471	131	29	,	,	PUNCT
ejpam-3471	131	30	t	t	PROPN
ejpam-3471	131	31	)	)	PUNCT
ejpam-3471	131	32	,	,	PUNCT
ejpam-3471	132	1	c	c	X
ejpam-3471	132	2	>	>	X
ejpam-3471	132	3	0	0	NUM
ejpam-3471	133	1	u(x	u(x	PROPN
ejpam-3471	133	2	,	,	PUNCT
ejpam-3471	133	3	y	y	NOUN
ejpam-3471	133	4	,	,	PUNCT
ejpam-3471	133	5	0	0	NUM
ejpam-3471	133	6	)	)	PUNCT
ejpam-3471	133	7	=	=	SYM
ejpam-3471	134	1	f1(x	f1(x	PROPN
ejpam-3471	134	2	,	,	PUNCT
ejpam-3471	134	3	y	y	NOUN
ejpam-3471	134	4	)	)	PUNCT
ejpam-3471	134	5	ut(x	ut(x	NOUN
ejpam-3471	134	6	,	,	PUNCT
ejpam-3471	134	7	y	y	NOUN
ejpam-3471	134	8	,	,	PUNCT
ejpam-3471	134	9	0	0	NUM
ejpam-3471	134	10	)	)	PUNCT
ejpam-3471	134	11	=	=	SYM
ejpam-3471	135	1	f2(x	f2(x	PROPN
ejpam-3471	135	2	,	,	PUNCT
ejpam-3471	135	3	y	y	NOUN
ejpam-3471	135	4	)	)	PUNCT
ejpam-3471	135	5	u(0	u(0	PROPN
ejpam-3471	135	6	,	,	PUNCT
ejpam-3471	135	7	y	y	PROPN
ejpam-3471	135	8	,	,	PUNCT
ejpam-3471	135	9	t	t	PROPN
ejpam-3471	135	10	)	)	PUNCT
ejpam-3471	135	11	)	)	PUNCT
ejpam-3471	136	1	=	=	SYM
ejpam-3471	136	2	h1(0	h1(0	PROPN
ejpam-3471	136	3	,	,	PUNCT
ejpam-3471	136	4	y	y	PROPN
ejpam-3471	136	5	,	,	PUNCT
ejpam-3471	136	6	t	t	PROPN
ejpam-3471	136	7	)	)	PUNCT
ejpam-3471	136	8	u(l	u(l	PROPN
ejpam-3471	136	9	,	,	PUNCT
ejpam-3471	136	10	y	y	PROPN
ejpam-3471	136	11	,	,	PUNCT
ejpam-3471	136	12	t	t	PROPN
ejpam-3471	136	13	)	)	PUNCT
ejpam-3471	136	14	)	)	PUNCT
ejpam-3471	137	1	=	=	PUNCT
ejpam-3471	137	2	h2(l	h2(l	NOUN
ejpam-3471	137	3	,	,	PUNCT
ejpam-3471	137	4	y	y	PROPN
ejpam-3471	137	5	,	,	PUNCT
ejpam-3471	137	6	t	t	PROPN
ejpam-3471	137	7	)	)	PUNCT
ejpam-3471	137	8	u(x	u(x	NOUN
ejpam-3471	137	9	,	,	PUNCT
ejpam-3471	137	10	0	0	NUM
ejpam-3471	137	11	,	,	PUNCT
ejpam-3471	137	12	t	t	PROPN
ejpam-3471	137	13	)	)	PUNCT
ejpam-3471	137	14	)	)	PUNCT
ejpam-3471	138	1	=	=	PUNCT
ejpam-3471	139	1	g1(x	g1(x	NOUN
ejpam-3471	139	2	,	,	PUNCT
ejpam-3471	139	3	0	0	NUM
ejpam-3471	139	4	,	,	PUNCT
ejpam-3471	139	5	t	t	NOUN
ejpam-3471	139	6	)	)	PUNCT
ejpam-3471	139	7	u(x	u(x	PROPN
ejpam-3471	139	8	,	,	PUNCT
ejpam-3471	139	9	l	l	NOUN
ejpam-3471	139	10	,	,	PUNCT
ejpam-3471	139	11	t	t	PROPN
ejpam-3471	139	12	)	)	PUNCT
ejpam-3471	139	13	)	)	PUNCT
ejpam-3471	140	1	=	=	SYM
ejpam-3471	140	2	g2(x	g2(x	PROPN
ejpam-3471	140	3	,	,	PUNCT
ejpam-3471	140	4	l	l	PROPN
ejpam-3471	140	5	,	,	PUNCT
ejpam-3471	140	6	t	t	PROPN
ejpam-3471	140	7	)	)	PUNCT
ejpam-3471	140	8	(	(	PUNCT
ejpam-3471	140	9	29	29	NUM
ejpam-3471	140	10	)	)	PUNCT
ejpam-3471	140	11	where	where	SCONJ
ejpam-3471	140	12			PROPN
ejpam-3471	140	13	4u(x	4u(x	PROPN
ejpam-3471	140	14	,	,	PUNCT
ejpam-3471	140	15	y	y	PROPN
ejpam-3471	140	16	,	,	PUNCT
ejpam-3471	140	17	t	t	PROPN
ejpam-3471	140	18	)	)	PUNCT
ejpam-3471	140	19	=	=	SYM
ejpam-3471	140	20	∂2u(x	∂2u(x	PROPN
ejpam-3471	140	21	,	,	PUNCT
ejpam-3471	140	22	y	y	PROPN
ejpam-3471	140	23	,	,	PUNCT
ejpam-3471	140	24	t	t	PROPN
ejpam-3471	140	25	)	)	PUNCT
ejpam-3471	140	26	∂x2	∂x2	NOUN
ejpam-3471	140	27	+	+	CCONJ
ejpam-3471	140	28	∂2u(x	∂2u(x	NOUN
ejpam-3471	140	29	,	,	PUNCT
ejpam-3471	140	30	y	y	PROPN
ejpam-3471	140	31	,	,	PUNCT
ejpam-3471	140	32	t	t	PROPN
ejpam-3471	140	33	)	)	PUNCT
ejpam-3471	140	34	∂y2	∂y2	ADJ
ejpam-3471	140	35	f1(x	f1(x	PROPN
ejpam-3471	140	36	,	,	PUNCT
ejpam-3471	140	37	t	t	PROPN
ejpam-3471	140	38	)	)	PUNCT
ejpam-3471	140	39	=	=	VERB
ejpam-3471	140	40	sin	sin	NOUN
ejpam-3471	140	41	(	(	PUNCT
ejpam-3471	140	42	πx	πx	NOUN
ejpam-3471	140	43	l	l	NOUN
ejpam-3471	140	44	)	)	PUNCT
ejpam-3471	140	45	sin	sin	NOUN
ejpam-3471	140	46	(	(	PUNCT
ejpam-3471	140	47	πy	πy	NOUN
ejpam-3471	140	48	l	l	NOUN
ejpam-3471	140	49	)	)	PUNCT
ejpam-3471	141	1	f2(x	f2(x	PROPN
ejpam-3471	141	2	,	,	PUNCT
ejpam-3471	141	3	t	t	PROPN
ejpam-3471	141	4	)	)	PUNCT
ejpam-3471	141	5	=	=	SYM
ejpam-3471	141	6	0	0	PUNCT
ejpam-3471	142	1	h1(x	h1(x	NOUN
ejpam-3471	142	2	,	,	PUNCT
ejpam-3471	142	3	t	t	PROPN
ejpam-3471	142	4	)	)	PUNCT
ejpam-3471	143	1	=	=	SYM
ejpam-3471	143	2	0	0	NUM
ejpam-3471	144	1	h2(x	h2(x	PROPN
ejpam-3471	144	2	,	,	PUNCT
ejpam-3471	144	3	t	t	PROPN
ejpam-3471	144	4	)	)	PUNCT
ejpam-3471	144	5	=	=	SYM
ejpam-3471	144	6	0	0	NUM
ejpam-3471	145	1	g1(x	g1(x	NOUN
ejpam-3471	145	2	,	,	PUNCT
ejpam-3471	145	3	t	t	PROPN
ejpam-3471	145	4	)	)	PUNCT
ejpam-3471	145	5	=	=	SYM
ejpam-3471	145	6	0	0	NUM
ejpam-3471	146	1	g2(x	g2(x	PROPN
ejpam-3471	146	2	,	,	PUNCT
ejpam-3471	146	3	t	t	PROPN
ejpam-3471	146	4	)	)	PUNCT
ejpam-3471	146	5	=	=	SYM
ejpam-3471	146	6	0	0	NUM
ejpam-3471	146	7	(	(	PUNCT
ejpam-3471	146	8	30	30	NUM
ejpam-3471	146	9	)	)	PUNCT
ejpam-3471	146	10	solving	solve	VERB
ejpam-3471	146	11	yhe	yhe	NOUN
ejpam-3471	146	12	wave	wave	NOUN
ejpam-3471	146	13	equation	equation	NOUN
ejpam-3471	146	14	involves	involves	AUX
ejpam-3471	146	15	identifyinf	identifyinf	VERB
ejpam-3471	146	16	the	the	DET
ejpam-3471	146	17	functions	function	NOUN
ejpam-3471	146	18	u(x	u(x	NOUN
ejpam-3471	146	19	,	,	PUNCT
ejpam-3471	146	20	y	y	PROPN
ejpam-3471	146	21	,	,	PUNCT
ejpam-3471	146	22	t	t	PROPN
ejpam-3471	146	23	)	)	PUNCT
ejpam-3471	146	24	that	that	PRON
ejpam-3471	146	25	solve	solve	VERB
ejpam-3471	146	26	the	the	DET
ejpam-3471	146	27	partial	partial	ADJ
ejpam-3471	146	28	differential	differential	NOUN
ejpam-3471	146	29	equation	equation	NOUN
ejpam-3471	146	30	that	that	PRON
ejpam-3471	146	31	represent	represent	VERB
ejpam-3471	146	32	the	the	DET
ejpam-3471	146	33	amplitude	amplitude	NOUN
ejpam-3471	146	34	of	of	ADP
ejpam-3471	146	35	the	the	DET
ejpam-3471	146	36	wave	wave	NOUN
ejpam-3471	146	37	at	at	ADP
ejpam-3471	146	38	any	any	DET
ejpam-3471	146	39	position	position	NOUN
ejpam-3471	146	40	x	x	PUNCT
ejpam-3471	146	41	and	and	CCONJ
ejpam-3471	146	42	y	y	PROPN
ejpam-3471	146	43	at	at	ADP
ejpam-3471	146	44	any	any	DET
ejpam-3471	146	45	time	time	NOUN
ejpam-3471	146	46	t.	t.	NOUN
ejpam-3471	146	47	•	•	NOUN
ejpam-3471	146	48	solving	solving	NOUN
ejpam-3471	146	49	by	by	ADP
ejpam-3471	146	50	sba	sba	PROPN
ejpam-3471	146	51	method	method	NOUN
ejpam-3471	146	52	by	by	ADP
ejpam-3471	146	53	integrating	integrate	VERB
ejpam-3471	146	54	(	(	PUNCT
ejpam-3471	146	55	29	29	NUM
ejpam-3471	146	56	)	)	PUNCT
ejpam-3471	146	57	we	we	PRON
ejpam-3471	146	58	get	get	VERB
ejpam-3471	146	59	the	the	DET
ejpam-3471	146	60	adomian	adomian	NOUN
ejpam-3471	146	61	canonical	canonical	ADJ
ejpam-3471	146	62	form	form	NOUN
ejpam-3471	146	63	[	[	X
ejpam-3471	146	64	2	2	NUM
ejpam-3471	146	65	,	,	PUNCT
ejpam-3471	146	66	9	9	NUM
ejpam-3471	146	67	]	]	PUNCT
ejpam-3471	146	68	of	of	ADP
ejpam-3471	146	69	the	the	DET
ejpam-3471	146	70	problem	problem	NOUN
ejpam-3471	146	71	(	(	PUNCT
ejpam-3471	146	72	29	29	NUM
ejpam-3471	146	73	)	)	PUNCT
ejpam-3471	146	74	:	:	PUNCT
ejpam-3471	147	1	u(x	u(x	PROPN
ejpam-3471	147	2	,	,	PUNCT
ejpam-3471	147	3	y	y	PROPN
ejpam-3471	147	4	,	,	PUNCT
ejpam-3471	147	5	t	t	PROPN
ejpam-3471	147	6	)	)	PUNCT
ejpam-3471	147	7	=	=	SYM
ejpam-3471	147	8	u(x	u(x	PROPN
ejpam-3471	147	9	,	,	PUNCT
ejpam-3471	147	10	y	y	NOUN
ejpam-3471	147	11	,	,	PUNCT
ejpam-3471	147	12	0	0	NUM
ejpam-3471	147	13	)	)	PUNCT
ejpam-3471	147	14	+	+	NUM
ejpam-3471	147	15	t	t	PROPN
ejpam-3471	147	16	∂u(x	∂u(x	PROPN
ejpam-3471	147	17	,	,	PUNCT
ejpam-3471	147	18	y	y	PROPN
ejpam-3471	147	19	,	,	PUNCT
ejpam-3471	147	20	0	0	NUM
ejpam-3471	147	21	)	)	PUNCT
ejpam-3471	147	22	∂t	∂t	PROPN
ejpam-3471	148	1	+	+	CCONJ
ejpam-3471	148	2	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	148	3	(	(	PUNCT
ejpam-3471	148	4	4u(x	4u(x	NUM
ejpam-3471	148	5	,	,	PUNCT
ejpam-3471	148	6	y	y	PROPN
ejpam-3471	148	7	,	,	PUNCT
ejpam-3471	148	8	t	t	PROPN
ejpam-3471	148	9	)	)	PUNCT
ejpam-3471	148	10	)	)	PUNCT
ejpam-3471	148	11	(	(	PUNCT
ejpam-3471	148	12	31	31	X
ejpam-3471	148	13	)	)	PUNCT
ejpam-3471	148	14	applying	apply	VERB
ejpam-3471	148	15	successive	successive	ADJ
ejpam-3471	148	16	approximations	approximation	NOUN
ejpam-3471	148	17	method	method	NOUN
ejpam-3471	148	18	to	to	ADP
ejpam-3471	148	19	(	(	PUNCT
ejpam-3471	148	20	31	31	NUM
ejpam-3471	148	21	)	)	PUNCT
ejpam-3471	148	22	,	,	PUNCT
ejpam-3471	148	23	we	we	PRON
ejpam-3471	148	24	get	get	VERB
ejpam-3471	148	25	:	:	PUNCT
ejpam-3471	148	26	uk(x	uk(x	ADP
ejpam-3471	148	27	,	,	PUNCT
ejpam-3471	148	28	y	y	PROPN
ejpam-3471	148	29	,	,	PUNCT
ejpam-3471	148	30	t	t	PROPN
ejpam-3471	148	31	)	)	PUNCT
ejpam-3471	148	32	=	=	PUNCT
ejpam-3471	149	1	uk(x	uk(x	PROPN
ejpam-3471	149	2	,	,	PUNCT
ejpam-3471	149	3	y	y	PROPN
ejpam-3471	149	4	,	,	PUNCT
ejpam-3471	149	5	0)+t	0)+t	PROPN
ejpam-3471	149	6	∂uk(x	∂uk(x	PROPN
ejpam-3471	149	7	,	,	PUNCT
ejpam-3471	149	8	y	y	PROPN
ejpam-3471	149	9	,	,	PUNCT
ejpam-3471	149	10	0	0	NUM
ejpam-3471	149	11	)	)	PUNCT
ejpam-3471	150	1	∂t	∂t	PROPN
ejpam-3471	150	2	+	+	PROPN
ejpam-3471	150	3	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	150	4	(	(	PUNCT
ejpam-3471	150	5	4uk(x	4uk(x	NUM
ejpam-3471	150	6	,	,	PUNCT
ejpam-3471	150	7	y	y	NOUN
ejpam-3471	150	8	,	,	PUNCT
ejpam-3471	150	9	t))+ñ(uk−1(x	t))+ñ(uk−1(x	NOUN
ejpam-3471	150	10	,	,	PUNCT
ejpam-3471	150	11	y	y	PROPN
ejpam-3471	150	12	,	,	PUNCT
ejpam-3471	150	13	t	t	PROPN
ejpam-3471	150	14	)	)	PUNCT
ejpam-3471	150	15	)	)	PUNCT
ejpam-3471	150	16	,	,	PUNCT
ejpam-3471	150	17	k	k	PROPN
ejpam-3471	150	18	≥	≥	NUM
ejpam-3471	150	19	1	1	NUM
ejpam-3471	150	20	(	(	PUNCT
ejpam-3471	150	21	32	32	NUM
ejpam-3471	150	22	)	)	PUNCT
ejpam-3471	150	23	where	where	SCONJ
ejpam-3471	150	24	n∼(uk(x	n∼(uk(x	PROPN
ejpam-3471	150	25	,	,	PUNCT
ejpam-3471	150	26	y	y	PROPN
ejpam-3471	150	27	,	,	PUNCT
ejpam-3471	150	28	t	t	PROPN
ejpam-3471	150	29	)	)	PUNCT
ejpam-3471	150	30	)	)	PUNCT
ejpam-3471	150	31	=	=	SYM
ejpam-3471	150	32	0	0	NUM
ejpam-3471	151	1	∀k	∀k	X
ejpam-3471	151	2	∈	∈	PROPN
ejpam-3471	151	3	n	n	ADP
ejpam-3471	151	4	applying	apply	VERB
ejpam-3471	151	5	the	the	DET
ejpam-3471	151	6	sba	sba	PROPN
ejpam-3471	151	7	algorithm	algorithm	NOUN
ejpam-3471	151	8	to	to	ADP
ejpam-3471	151	9	(	(	PUNCT
ejpam-3471	151	10	32	32	NUM
ejpam-3471	151	11	)	)	PUNCT
ejpam-3471	151	12	,	,	PUNCT
ejpam-3471	151	13	we	we	PRON
ejpam-3471	151	14	get	get	VERB
ejpam-3471	151	15	:	:	PUNCT
ejpam-3471	151	16	r.	r.	PROPN
ejpam-3471	151	17	yaro	yaro	PROPN
ejpam-3471	151	18	,	,	PUNCT
ejpam-3471	151	19	y.	y.	PROPN
ejpam-3471	151	20	paré	paré	NOUN
ejpam-3471	151	21	,	,	PUNCT
ejpam-3471	151	22	b.	b.	PROPN
ejpam-3471	151	23	abbo	abbo	PROPN
ejpam-3471	151	24	/	/	SYM
ejpam-3471	151	25	eur	eur	PROPN
ejpam-3471	151	26	.	.	PUNCT
ejpam-3471	152	1	j.	j.	PROPN
ejpam-3471	152	2	pure	pure	PROPN
ejpam-3471	152	3	appl	appl	PROPN
ejpam-3471	152	4	.	.	PROPN
ejpam-3471	152	5	math	math	PROPN
ejpam-3471	152	6	,	,	PUNCT
ejpam-3471	152	7	12	12	NUM
ejpam-3471	152	8	(	(	PUNCT
ejpam-3471	152	9	3	3	NUM
ejpam-3471	152	10	)	)	PUNCT
ejpam-3471	152	11	(	(	PUNCT
ejpam-3471	152	12	2019	2019	NUM
ejpam-3471	152	13	)	)	PUNCT
ejpam-3471	152	14	,	,	PUNCT
ejpam-3471	152	15	1260	1260	NUM
ejpam-3471	152	16	-	-	SYM
ejpam-3471	152	17	1276	1276	NUM
ejpam-3471	152	18	1269	1269	NUM
ejpam-3471	152	19	(	(	PUNCT
ejpam-3471	152	20	p	p	NOUN
ejpam-3471	152	21	ksba	ksba	NOUN
ejpam-3471	152	22	)	)	PUNCT
ejpam-3471	152	23			PUNCT
ejpam-3471	152	24	uk0(x	uk0(x	PROPN
ejpam-3471	152	25	,	,	PUNCT
ejpam-3471	152	26	y	y	PROPN
ejpam-3471	152	27	,	,	PUNCT
ejpam-3471	152	28	t	t	PROPN
ejpam-3471	152	29	)	)	PUNCT
ejpam-3471	152	30	=	=	PUNCT
ejpam-3471	153	1	uk(x	uk(x	PROPN
ejpam-3471	153	2	,	,	PUNCT
ejpam-3471	153	3	y	y	PROPN
ejpam-3471	153	4	,	,	PUNCT
ejpam-3471	153	5	0	0	NUM
ejpam-3471	153	6	)	)	PUNCT
ejpam-3471	153	7	+	+	NUM
ejpam-3471	153	8	t	t	NOUN
ejpam-3471	153	9	∂uk(x	∂uk(x	NOUN
ejpam-3471	153	10	,	,	PUNCT
ejpam-3471	153	11	y	y	PROPN
ejpam-3471	153	12	,	,	PUNCT
ejpam-3471	153	13	0	0	NUM
ejpam-3471	153	14	)	)	PUNCT
ejpam-3471	154	1	∂t	∂t	PROPN
ejpam-3471	154	2	+	+	NUM
ejpam-3471	154	3	ñ(uk−1(x	ñ(uk−1(x	NOUN
ejpam-3471	154	4	,	,	PUNCT
ejpam-3471	154	5	y	y	PROPN
ejpam-3471	154	6	,	,	PUNCT
ejpam-3471	154	7	t	t	PROPN
ejpam-3471	154	8	)	)	PUNCT
ejpam-3471	154	9	)	)	PUNCT
ejpam-3471	154	10	,	,	PUNCT
ejpam-3471	154	11	k	k	PROPN
ejpam-3471	154	12	≥	≥	NUM
ejpam-3471	154	13	1	1	NUM
ejpam-3471	154	14	,	,	PUNCT
ejpam-3471	154	15	k	k	X
ejpam-3471	154	16	≥	≥	NUM
ejpam-3471	154	17	1	1	NUM
ejpam-3471	154	18	ukn(x	ukn(x	PROPN
ejpam-3471	154	19	,	,	PUNCT
ejpam-3471	154	20	t	t	PROPN
ejpam-3471	154	21	)	)	PUNCT
ejpam-3471	155	1	=	=	VERB
ejpam-3471	155	2	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	155	3	(	(	PUNCT
ejpam-3471	155	4	4ukn−1(x	4ukn−1(x	NUM
ejpam-3471	155	5	,	,	PUNCT
ejpam-3471	155	6	y	y	PROPN
ejpam-3471	155	7	,	,	PUNCT
ejpam-3471	155	8	t	t	PROPN
ejpam-3471	155	9	)	)	PUNCT
ejpam-3471	155	10	)	)	PUNCT
ejpam-3471	155	11	,	,	PUNCT
ejpam-3471	155	12	n	n	X
ejpam-3471	155	13	≥	≥	NOUN
ejpam-3471	155	14	1	1	NUM
ejpam-3471	155	15	(	(	PUNCT
ejpam-3471	155	16	33	33	NUM
ejpam-3471	155	17	)	)	PUNCT
ejpam-3471	155	18	for	for	ADP
ejpam-3471	155	19	k	k	PROPN
ejpam-3471	155	20	=	=	SYM
ejpam-3471	155	21	1	1	NUM
ejpam-3471	155	22	,	,	PUNCT
ejpam-3471	155	23	we	we	PRON
ejpam-3471	155	24	have	have	AUX
ejpam-3471	155	25	:	:	PUNCT
ejpam-3471	155	26	(	(	PUNCT
ejpam-3471	155	27	p	p	NOUN
ejpam-3471	155	28	1	1	NUM
ejpam-3471	155	29	sba	sba	NOUN
ejpam-3471	155	30	)	)	PUNCT
ejpam-3471	155	31			PUNCT
ejpam-3471	155	32	u10(x	u10(x	NOUN
ejpam-3471	155	33	,	,	PUNCT
ejpam-3471	155	34	y	y	PROPN
ejpam-3471	155	35	,	,	PUNCT
ejpam-3471	155	36	t	t	PROPN
ejpam-3471	155	37	)	)	PUNCT
ejpam-3471	155	38	=	=	PUNCT
ejpam-3471	156	1	u1(x	u1(x	PROPN
ejpam-3471	156	2	,	,	PUNCT
ejpam-3471	156	3	,	,	PUNCT
ejpam-3471	156	4	y	y	PROPN
ejpam-3471	156	5	,	,	PUNCT
ejpam-3471	156	6	0	0	NUM
ejpam-3471	156	7	)	)	PUNCT
ejpam-3471	156	8	+	+	NUM
ejpam-3471	156	9	t	t	PROPN
ejpam-3471	156	10	∂u1(x	∂u1(x	NOUN
ejpam-3471	156	11	,	,	PUNCT
ejpam-3471	156	12	y	y	PROPN
ejpam-3471	156	13	,	,	PUNCT
ejpam-3471	156	14	0	0	NUM
ejpam-3471	156	15	)	)	PUNCT
ejpam-3471	156	16	∂t	∂t	PROPN
ejpam-3471	156	17	u1n(x	u1n(x	PROPN
ejpam-3471	156	18	,	,	PUNCT
ejpam-3471	156	19	t	t	PROPN
ejpam-3471	156	20	)	)	PUNCT
ejpam-3471	156	21	=	=	VERB
ejpam-3471	157	1	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	157	2	(	(	PUNCT
ejpam-3471	157	3	4ukn−1(x	4ukn−1(x	NUM
ejpam-3471	157	4	,	,	PUNCT
ejpam-3471	157	5	y	y	PROPN
ejpam-3471	157	6	,	,	PUNCT
ejpam-3471	157	7	t	t	PROPN
ejpam-3471	157	8	)	)	PUNCT
ejpam-3471	157	9	)	)	PUNCT
ejpam-3471	157	10	,	,	PUNCT
ejpam-3471	157	11	n	n	X
ejpam-3471	157	12	≥	≥	NOUN
ejpam-3471	157	13	1	1	NUM
ejpam-3471	157	14	(	(	PUNCT
ejpam-3471	157	15	34	34	NUM
ejpam-3471	157	16	)	)	PUNCT
ejpam-3471	157	17	we	we	PRON
ejpam-3471	157	18	obtain	obtain	VERB
ejpam-3471	157	19	:	:	PUNCT
ejpam-3471	157	20			NOUN
ejpam-3471	157	21	u10(x	u10(x	NOUN
ejpam-3471	157	22	,	,	PUNCT
ejpam-3471	157	23	t	t	PROPN
ejpam-3471	157	24	)	)	PUNCT
ejpam-3471	157	25	=	=	SYM
ejpam-3471	157	26	sin(πxl	sin(πxl	NOUN
ejpam-3471	157	27	)	)	PUNCT
ejpam-3471	157	28	sin(πyl	sin(πyl	NOUN
ejpam-3471	157	29	)	)	PUNCT
ejpam-3471	157	30	u11(x	u11(x	NOUN
ejpam-3471	157	31	,	,	PUNCT
ejpam-3471	157	32	y	y	PROPN
ejpam-3471	157	33	,	,	PUNCT
ejpam-3471	157	34	t	t	PROPN
ejpam-3471	157	35	)	)	PUNCT
ejpam-3471	157	36	=	=	SYM
ejpam-3471	157	37	−c2	−c2	PROPN
ejpam-3471	157	38	(	(	PUNCT
ejpam-3471	157	39	π2	π2	ADJ
ejpam-3471	157	40	l2	l2	NOUN
ejpam-3471	157	41	+	+	CCONJ
ejpam-3471	157	42	π2	π2	ADJ
ejpam-3471	157	43	l2	l2	NOUN
ejpam-3471	157	44	)	)	PUNCT
ejpam-3471	157	45	sin(πxl	sin(πxl	NOUN
ejpam-3471	157	46	)	)	PUNCT
ejpam-3471	157	47	sin(πyl	sin(πyl	NOUN
ejpam-3471	157	48	)	)	PUNCT
ejpam-3471	157	49	t2	t2	NOUN
ejpam-3471	157	50	2	2	NUM
ejpam-3471	157	51	!	!	PUNCT
ejpam-3471	158	1	u12(x	u12(x	PROPN
ejpam-3471	158	2	,	,	PUNCT
ejpam-3471	158	3	y	y	PROPN
ejpam-3471	158	4	,	,	PUNCT
ejpam-3471	158	5	t	t	PROPN
ejpam-3471	158	6	)	)	PUNCT
ejpam-3471	158	7	=	=	SYM
ejpam-3471	158	8	c4	c4	NOUN
ejpam-3471	158	9	(	(	PUNCT
ejpam-3471	158	10	π	π	PROPN
ejpam-3471	158	11	2	2	NUM
ejpam-3471	158	12	l2	l2	NOUN
ejpam-3471	158	13	+	+	CCONJ
ejpam-3471	158	14	π2	π2	ADJ
ejpam-3471	158	15	l2	l2	NOUN
ejpam-3471	158	16	)	)	PUNCT
ejpam-3471	158	17	2	2	NUM
ejpam-3471	158	18	sin(πxl	sin(πxl	NOUN
ejpam-3471	158	19	)	)	PUNCT
ejpam-3471	158	20	sin(πyl	sin(πyl	NOUN
ejpam-3471	158	21	)	)	PUNCT
ejpam-3471	158	22	t4	t4	PROPN
ejpam-3471	158	23	4	4	NUM
ejpam-3471	158	24	!	!	X
ejpam-3471	159	1	u13(x	u13(x	PROPN
ejpam-3471	159	2	,	,	PUNCT
ejpam-3471	159	3	y	y	PROPN
ejpam-3471	159	4	,	,	PUNCT
ejpam-3471	159	5	t	t	PROPN
ejpam-3471	159	6	)	)	PUNCT
ejpam-3471	159	7	=	=	SYM
ejpam-3471	160	1	−c6	−c6	PROPN
ejpam-3471	160	2	(	(	PUNCT
ejpam-3471	160	3	π2	π2	ADJ
ejpam-3471	160	4	l2	l2	NOUN
ejpam-3471	160	5	+	+	CCONJ
ejpam-3471	160	6	π2	π2	ADJ
ejpam-3471	160	7	l2	l2	NOUN
ejpam-3471	160	8	)	)	PUNCT
ejpam-3471	160	9	3	3	NUM
ejpam-3471	160	10	sin(πxl	sin(πxl	NOUN
ejpam-3471	160	11	)	)	PUNCT
ejpam-3471	160	12	sin(πyl	sin(πyl	NOUN
ejpam-3471	160	13	)	)	PUNCT
ejpam-3471	160	14	t6	t6	PROPN
ejpam-3471	160	15	6	6	NUM
ejpam-3471	160	16	!	!	PUNCT
ejpam-3471	160	17	...	...	PUNCT
ejpam-3471	161	1	u1n(x	u1n(x	PROPN
ejpam-3471	161	2	,	,	PUNCT
ejpam-3471	161	3	y	y	PROPN
ejpam-3471	161	4	,	,	PUNCT
ejpam-3471	161	5	t	t	PROPN
ejpam-3471	161	6	)	)	PUNCT
ejpam-3471	161	7	=	=	SYM
ejpam-3471	161	8	(	(	PUNCT
ejpam-3471	161	9	−1)nc2n6	−1)nc2n6	PROPN
ejpam-3471	161	10	(	(	PUNCT
ejpam-3471	161	11	π	π	PROPN
ejpam-3471	161	12	2	2	NUM
ejpam-3471	161	13	l2	l2	NOUN
ejpam-3471	161	14	+	+	CCONJ
ejpam-3471	161	15	π2	π2	ADJ
ejpam-3471	161	16	l2	l2	NOUN
ejpam-3471	161	17	)	)	PUNCT
ejpam-3471	161	18	n	n	NOUN
ejpam-3471	161	19	sin(πxl	sin(πxl	NOUN
ejpam-3471	161	20	)	)	PUNCT
ejpam-3471	161	21	sin(πyl	sin(πyl	NOUN
ejpam-3471	161	22	)	)	PUNCT
ejpam-3471	161	23	t2n	t2n	PROPN
ejpam-3471	161	24	(	(	PUNCT
ejpam-3471	161	25	2n	2n	NUM
ejpam-3471	161	26	)	)	PUNCT
ejpam-3471	161	27	!	!	PUNCT
ejpam-3471	162	1	let	let	VERB
ejpam-3471	162	2	’s	’s	NOUN
ejpam-3471	162	3	put	put	VERB
ejpam-3471	162	4	ϕ1	ϕ1	NOUN
ejpam-3471	162	5	m(x	m(x	PROPN
ejpam-3471	162	6	,	,	PUNCT
ejpam-3471	162	7	y	y	PROPN
ejpam-3471	162	8	,	,	PUNCT
ejpam-3471	162	9	t	t	PROPN
ejpam-3471	162	10	)	)	PUNCT
ejpam-3471	162	11	=	=	SYM
ejpam-3471	163	1	m−1∑	m−1∑	PROPN
ejpam-3471	163	2	n=0	n=0	SYM
ejpam-3471	163	3	u1n(x	u1n(x	PROPN
ejpam-3471	163	4	,	,	PUNCT
ejpam-3471	163	5	y	y	PROPN
ejpam-3471	163	6	,	,	PUNCT
ejpam-3471	163	7	t	t	PROPN
ejpam-3471	163	8	)	)	PUNCT
ejpam-3471	163	9	ϕ1	ϕ1	NOUN
ejpam-3471	163	10	m(x	m(x	PROPN
ejpam-3471	163	11	,	,	PUNCT
ejpam-3471	163	12	y	y	PROPN
ejpam-3471	163	13	,	,	PUNCT
ejpam-3471	163	14	t	t	PROPN
ejpam-3471	163	15	)	)	PUNCT
ejpam-3471	163	16	=	=	X
ejpam-3471	163	17	sin	sin	NOUN
ejpam-3471	163	18	(	(	PUNCT
ejpam-3471	163	19	πx	πx	NOUN
ejpam-3471	163	20	l	l	NOUN
ejpam-3471	163	21	)	)	PUNCT
ejpam-3471	163	22	sin	sin	NOUN
ejpam-3471	163	23	(	(	PUNCT
ejpam-3471	163	24	πy	πy	NOUN
ejpam-3471	163	25	l	l	NOUN
ejpam-3471	163	26	)	)	PUNCT
ejpam-3471	163	27	m−1∑	m−1∑	PROPN
ejpam-3471	163	28	n=0	n=0	NUM
ejpam-3471	163	29	(	(	PUNCT
ejpam-3471	163	30	−1)n	−1)n	X
ejpam-3471	163	31	(	(	PUNCT
ejpam-3471	163	32	cπt	cπt	PROPN
ejpam-3471	163	33	ll	ll	AUX
ejpam-3471	163	34	√	√	VERB
ejpam-3471	163	35	l2	l2	VERB
ejpam-3471	163	36	+	+	CCONJ
ejpam-3471	163	37	l2	l2	NOUN
ejpam-3471	163	38	)	)	PUNCT
ejpam-3471	163	39	2n	2n	NUM
ejpam-3471	163	40	(	(	PUNCT
ejpam-3471	163	41	2n	2n	NUM
ejpam-3471	163	42	)	)	PUNCT
ejpam-3471	163	43	!	!	PUNCT
ejpam-3471	164	1	let	let	VERB
ejpam-3471	164	2	’s	’s	NOUN
ejpam-3471	164	3	put	put	VERB
ejpam-3471	164	4	then	then	ADV
ejpam-3471	164	5	the	the	DET
ejpam-3471	164	6	approached	approach	VERB
ejpam-3471	164	7	solution	solution	NOUN
ejpam-3471	164	8	at	at	ADP
ejpam-3471	164	9	the	the	DET
ejpam-3471	164	10	the	the	DET
ejpam-3471	164	11	first	first	ADJ
ejpam-3471	164	12	step	step	NOUN
ejpam-3471	164	13	is	be	AUX
ejpam-3471	164	14	:	:	PUNCT
ejpam-3471	164	15	u1(x	u1(x	PROPN
ejpam-3471	164	16	,	,	PUNCT
ejpam-3471	164	17	y	y	PROPN
ejpam-3471	164	18	,	,	PUNCT
ejpam-3471	164	19	t	t	PROPN
ejpam-3471	164	20	)	)	PUNCT
ejpam-3471	165	1	=	=	PROPN
ejpam-3471	165	2	lim	lim	PROPN
ejpam-3471	165	3	m→+∞	m→+∞	PROPN
ejpam-3471	165	4	ϕ1	ϕ1	PROPN
ejpam-3471	165	5	m(x	m(x	PROPN
ejpam-3471	165	6	,	,	PUNCT
ejpam-3471	165	7	y	y	PROPN
ejpam-3471	165	8	,	,	PUNCT
ejpam-3471	165	9	t	t	PROPN
ejpam-3471	165	10	)	)	PUNCT
ejpam-3471	165	11	=	=	X
ejpam-3471	165	12	sin	sin	NOUN
ejpam-3471	165	13	(	(	PUNCT
ejpam-3471	165	14	πx	πx	NOUN
ejpam-3471	165	15	l	l	NOUN
ejpam-3471	165	16	)	)	PUNCT
ejpam-3471	165	17	sin	sin	NOUN
ejpam-3471	165	18	(	(	PUNCT
ejpam-3471	165	19	πy	πy	NOUN
ejpam-3471	165	20	l	l	NOUN
ejpam-3471	165	21	)	)	PUNCT
ejpam-3471	166	1	cos	cos	PROPN
ejpam-3471	166	2	(	(	PUNCT
ejpam-3471	166	3	cπt	cπt	PROPN
ejpam-3471	166	4	ll	ll	AUX
ejpam-3471	166	5	√	√	VERB
ejpam-3471	166	6	l2	l2	VERB
ejpam-3471	166	7	+	+	CCONJ
ejpam-3471	166	8	l2	l2	NOUN
ejpam-3471	166	9	)	)	PUNCT
ejpam-3471	166	10	r.	r.	PROPN
ejpam-3471	166	11	yaro	yaro	PROPN
ejpam-3471	166	12	,	,	PUNCT
ejpam-3471	166	13	y.	y.	PROPN
ejpam-3471	166	14	paré	paré	NOUN
ejpam-3471	166	15	,	,	PUNCT
ejpam-3471	166	16	b.	b.	PROPN
ejpam-3471	166	17	abbo	abbo	PROPN
ejpam-3471	166	18	/	/	SYM
ejpam-3471	166	19	eur	eur	PROPN
ejpam-3471	166	20	.	.	PUNCT
ejpam-3471	167	1	j.	j.	PROPN
ejpam-3471	167	2	pure	pure	PROPN
ejpam-3471	167	3	appl	appl	PROPN
ejpam-3471	167	4	.	.	PROPN
ejpam-3471	167	5	math	math	PROPN
ejpam-3471	167	6	,	,	PUNCT
ejpam-3471	167	7	12	12	NUM
ejpam-3471	167	8	(	(	PUNCT
ejpam-3471	167	9	3	3	NUM
ejpam-3471	167	10	)	)	PUNCT
ejpam-3471	167	11	(	(	PUNCT
ejpam-3471	167	12	2019	2019	NUM
ejpam-3471	167	13	)	)	PUNCT
ejpam-3471	167	14	,	,	PUNCT
ejpam-3471	167	15	1260	1260	NUM
ejpam-3471	167	16	-	-	SYM
ejpam-3471	167	17	1276	1276	NUM
ejpam-3471	167	18	1270	1270	NUM
ejpam-3471	167	19	.	.	PUNCT
ejpam-3471	168	1	such	such	ADJ
ejpam-3471	168	2	us	we	PRON
ejpam-3471	168	3	n∼(uk(x	n∼(uk(x	PROPN
ejpam-3471	168	4	,	,	PUNCT
ejpam-3471	168	5	y	y	PROPN
ejpam-3471	168	6	,	,	PUNCT
ejpam-3471	168	7	t	t	PROPN
ejpam-3471	168	8	)	)	PUNCT
ejpam-3471	168	9	)	)	PUNCT
ejpam-3471	169	1	=	=	SYM
ejpam-3471	169	2	0	0	NUM
ejpam-3471	169	3	∀k	∀k	NOUN
ejpam-3471	169	4	≥	≥	NOUN
ejpam-3471	169	5	0	0	NUM
ejpam-3471	169	6	at	at	ADP
ejpam-3471	169	7	the	the	DET
ejpam-3471	169	8	step	step	NOUN
ejpam-3471	169	9	k	k	PROPN
ejpam-3471	169	10	,	,	PUNCT
ejpam-3471	169	11	we	we	PRON
ejpam-3471	169	12	have	have	VERB
ejpam-3471	169	13	:	:	PUNCT
ejpam-3471	169	14	(	(	PUNCT
ejpam-3471	169	15	p	p	NOUN
ejpam-3471	169	16	ksba	ksba	NOUN
ejpam-3471	169	17	)	)	PUNCT
ejpam-3471	169	18			PUNCT
ejpam-3471	169	19	uk0(x	uk0(x	PROPN
ejpam-3471	169	20	,	,	PUNCT
ejpam-3471	169	21	y	y	PROPN
ejpam-3471	169	22	,	,	PUNCT
ejpam-3471	169	23	t	t	PROPN
ejpam-3471	169	24	)	)	PUNCT
ejpam-3471	169	25	=	=	PUNCT
ejpam-3471	170	1	uk(x	uk(x	ADP
ejpam-3471	170	2	,	,	PUNCT
ejpam-3471	170	3	,	,	PUNCT
ejpam-3471	170	4	y	y	PROPN
ejpam-3471	170	5	,	,	PUNCT
ejpam-3471	170	6	0	0	NUM
ejpam-3471	170	7	)	)	PUNCT
ejpam-3471	170	8	+	+	NUM
ejpam-3471	170	9	t	t	NOUN
ejpam-3471	170	10	∂uk(x	∂uk(x	NOUN
ejpam-3471	170	11	,	,	PUNCT
ejpam-3471	170	12	y	y	PROPN
ejpam-3471	170	13	,	,	PUNCT
ejpam-3471	170	14	0	0	NUM
ejpam-3471	170	15	)	)	PUNCT
ejpam-3471	170	16	∂t	∂t	PROPN
ejpam-3471	170	17	u1n(x	u1n(x	PROPN
ejpam-3471	170	18	,	,	PUNCT
ejpam-3471	170	19	y	y	PROPN
ejpam-3471	170	20	,	,	PUNCT
ejpam-3471	170	21	t	t	PROPN
ejpam-3471	170	22	)	)	PUNCT
ejpam-3471	170	23	=	=	VERB
ejpam-3471	171	1	c2l−1tt	c2l−1tt	NOUN
ejpam-3471	171	2	(	(	PUNCT
ejpam-3471	171	3	4ukn−1(x	4ukn−1(x	NUM
ejpam-3471	171	4	,	,	PUNCT
ejpam-3471	171	5	y	y	PROPN
ejpam-3471	171	6	,	,	PUNCT
ejpam-3471	171	7	t	t	PROPN
ejpam-3471	171	8	)	)	PUNCT
ejpam-3471	171	9	)	)	PUNCT
ejpam-3471	171	10	,	,	PUNCT
ejpam-3471	171	11	n	n	X
ejpam-3471	171	12	≥	≥	NOUN
ejpam-3471	171	13	1	1	NUM
ejpam-3471	171	14	(	(	PUNCT
ejpam-3471	171	15	35	35	NUM
ejpam-3471	171	16	)	)	PUNCT
ejpam-3471	171	17	by	by	ADP
ejpam-3471	171	18	unfolding	unfold	VERB
ejpam-3471	171	19	:	:	PUNCT
ejpam-3471	171	20			NUM
ejpam-3471	171	21	uk0(x	uk0(x	NOUN
ejpam-3471	171	22	,	,	PUNCT
ejpam-3471	171	23	t	t	PROPN
ejpam-3471	171	24	)	)	PUNCT
ejpam-3471	171	25	=	=	VERB
ejpam-3471	171	26	sin	sin	NOUN
ejpam-3471	171	27	(	(	PUNCT
ejpam-3471	171	28	πx	πx	NOUN
ejpam-3471	171	29	l	l	NOUN
ejpam-3471	171	30	)	)	PUNCT
ejpam-3471	171	31	sin	sin	NOUN
ejpam-3471	171	32	(	(	PUNCT
ejpam-3471	171	33	πy	πy	NOUN
ejpam-3471	171	34	l	l	NOUN
ejpam-3471	171	35	)	)	PUNCT
ejpam-3471	172	1	uk1(x	uk1(x	PROPN
ejpam-3471	172	2	,	,	PUNCT
ejpam-3471	172	3	y	y	PROPN
ejpam-3471	172	4	,	,	PUNCT
ejpam-3471	172	5	t	t	PROPN
ejpam-3471	172	6	)	)	PUNCT
ejpam-3471	172	7	=	=	SYM
ejpam-3471	173	1	−c2	−c2	PROPN
ejpam-3471	173	2	(	(	PUNCT
ejpam-3471	173	3	π2	π2	ADJ
ejpam-3471	173	4	l2	l2	NOUN
ejpam-3471	173	5	+	+	CCONJ
ejpam-3471	173	6	π2	π2	ADJ
ejpam-3471	173	7	l2	l2	NOUN
ejpam-3471	173	8	)	)	PUNCT
ejpam-3471	173	9	sin	sin	NOUN
ejpam-3471	173	10	(	(	PUNCT
ejpam-3471	173	11	πx	πx	NOUN
ejpam-3471	173	12	l	l	NOUN
ejpam-3471	173	13	)	)	PUNCT
ejpam-3471	173	14	sin	sin	NOUN
ejpam-3471	173	15	(	(	PUNCT
ejpam-3471	173	16	πy	πy	NOUN
ejpam-3471	173	17	l	l	NOUN
ejpam-3471	173	18	)	)	PUNCT
ejpam-3471	173	19	t2	t2	PROPN
ejpam-3471	173	20	2	2	NUM
ejpam-3471	173	21	!	!	X
ejpam-3471	174	1	uk2(x	uk2(x	PROPN
ejpam-3471	174	2	,	,	PUNCT
ejpam-3471	174	3	y	y	PROPN
ejpam-3471	174	4	,	,	PUNCT
ejpam-3471	174	5	t	t	PROPN
ejpam-3471	174	6	)	)	PUNCT
ejpam-3471	174	7	=	=	NOUN
ejpam-3471	174	8	c4	c4	NOUN
ejpam-3471	174	9	(	(	PUNCT
ejpam-3471	174	10	π2	π2	ADJ
ejpam-3471	174	11	l2	l2	NOUN
ejpam-3471	174	12	+	+	CCONJ
ejpam-3471	174	13	π2	π2	ADJ
ejpam-3471	174	14	l2	l2	NOUN
ejpam-3471	174	15	)	)	PUNCT
ejpam-3471	174	16	2	2	NUM
ejpam-3471	174	17	sin	sin	NOUN
ejpam-3471	174	18	(	(	PUNCT
ejpam-3471	174	19	πx	πx	NOUN
ejpam-3471	174	20	l	l	NOUN
ejpam-3471	174	21	)	)	PUNCT
ejpam-3471	174	22	sin	sin	NOUN
ejpam-3471	174	23	(	(	PUNCT
ejpam-3471	174	24	πy	πy	NOUN
ejpam-3471	174	25	l	l	NOUN
ejpam-3471	174	26	)	)	PUNCT
ejpam-3471	174	27	t′4	t′4	NOUN
ejpam-3471	175	1	4	4	X
ejpam-3471	175	2	!	!	X
ejpam-3471	175	3	uk3(x	uk3(x	PROPN
ejpam-3471	175	4	,	,	PUNCT
ejpam-3471	175	5	y	y	PROPN
ejpam-3471	175	6	,	,	PUNCT
ejpam-3471	175	7	t	t	PROPN
ejpam-3471	175	8	)	)	PUNCT
ejpam-3471	175	9	=	=	SYM
ejpam-3471	176	1	−c6	−c6	ADJ
ejpam-3471	176	2	(	(	PUNCT
ejpam-3471	176	3	π2	π2	ADJ
ejpam-3471	176	4	l2	l2	NOUN
ejpam-3471	176	5	+	+	CCONJ
ejpam-3471	176	6	π2	π2	ADJ
ejpam-3471	176	7	l2	l2	NOUN
ejpam-3471	176	8	)	)	PUNCT
ejpam-3471	176	9	3	3	NUM
ejpam-3471	176	10	sin	sin	NOUN
ejpam-3471	176	11	(	(	PUNCT
ejpam-3471	176	12	πx	πx	NOUN
ejpam-3471	176	13	l	l	NOUN
ejpam-3471	176	14	)	)	PUNCT
ejpam-3471	176	15	sin	sin	NOUN
ejpam-3471	176	16	(	(	PUNCT
ejpam-3471	176	17	πy	πy	NOUN
ejpam-3471	176	18	l	l	NOUN
ejpam-3471	176	19	)	)	PUNCT
ejpam-3471	176	20	t′6	t′6	X
ejpam-3471	176	21	6	6	NUM
ejpam-3471	176	22	!	!	PUNCT
ejpam-3471	176	23	...	...	PUNCT
ejpam-3471	177	1	ukn(x	ukn(x	PROPN
ejpam-3471	177	2	,	,	PUNCT
ejpam-3471	177	3	y	y	PROPN
ejpam-3471	177	4	,	,	PUNCT
ejpam-3471	177	5	t	t	PROPN
ejpam-3471	177	6	)	)	PUNCT
ejpam-3471	177	7	=	=	PUNCT
ejpam-3471	177	8	(	(	PUNCT
ejpam-3471	177	9	−1)nc2n6	−1)nc2n6	NOUN
ejpam-3471	177	10	(	(	PUNCT
ejpam-3471	177	11	π2	π2	ADJ
ejpam-3471	177	12	l2	l2	NOUN
ejpam-3471	177	13	+	+	CCONJ
ejpam-3471	177	14	π2	π2	ADJ
ejpam-3471	177	15	l2	l2	NOUN
ejpam-3471	177	16	)	)	PUNCT
ejpam-3471	177	17	n	n	NOUN
ejpam-3471	177	18	sin	sin	NOUN
ejpam-3471	177	19	(	(	PUNCT
ejpam-3471	177	20	πx	πx	NOUN
ejpam-3471	177	21	l	l	NOUN
ejpam-3471	177	22	)	)	PUNCT
ejpam-3471	177	23	sin	sin	NOUN
ejpam-3471	177	24	(	(	PUNCT
ejpam-3471	177	25	πy	πy	NOUN
ejpam-3471	177	26	l	l	NOUN
ejpam-3471	177	27	)	)	PUNCT
ejpam-3471	177	28	t	t	PROPN
ejpam-3471	177	29	′2n	′2n	PROPN
ejpam-3471	177	30	(	(	PUNCT
ejpam-3471	177	31	2n	2n	NUM
ejpam-3471	177	32	)	)	PUNCT
ejpam-3471	177	33	!	!	PUNCT
ejpam-3471	178	1	then	then	ADV
ejpam-3471	178	2	let	let	VERB
ejpam-3471	178	3	’s	’s	NOUN
ejpam-3471	178	4	put	put	VERB
ejpam-3471	178	5	ϕkm(x	ϕkm(x	PROPN
ejpam-3471	178	6	,	,	PUNCT
ejpam-3471	178	7	y	y	PROPN
ejpam-3471	178	8	,	,	PUNCT
ejpam-3471	178	9	t	t	PROPN
ejpam-3471	178	10	)	)	PUNCT
ejpam-3471	178	11	=	=	SYM
ejpam-3471	179	1	m−1∑	m−1∑	PROPN
ejpam-3471	179	2	n=0	n=0	SYM
ejpam-3471	179	3	u1n(x	u1n(x	PROPN
ejpam-3471	179	4	,	,	PUNCT
ejpam-3471	179	5	y	y	PROPN
ejpam-3471	179	6	,	,	PUNCT
ejpam-3471	179	7	t	t	PROPN
ejpam-3471	179	8	)	)	PUNCT
ejpam-3471	179	9	ϕkm(x	ϕkm(x	PROPN
ejpam-3471	179	10	,	,	PUNCT
ejpam-3471	179	11	y	y	PROPN
ejpam-3471	179	12	,	,	PUNCT
ejpam-3471	179	13	t	t	PROPN
ejpam-3471	179	14	)	)	PUNCT
ejpam-3471	179	15	=	=	SYM
ejpam-3471	179	16	sin	sin	NOUN
ejpam-3471	179	17	(	(	PUNCT
ejpam-3471	179	18	πx	πx	NOUN
ejpam-3471	179	19	l	l	NOUN
ejpam-3471	179	20	)	)	PUNCT
ejpam-3471	179	21	sin	sin	NOUN
ejpam-3471	179	22	(	(	PUNCT
ejpam-3471	179	23	πy	πy	NOUN
ejpam-3471	179	24	l	l	NOUN
ejpam-3471	179	25	)	)	PUNCT
ejpam-3471	179	26	m−1∑	m−1∑	PROPN
ejpam-3471	179	27	n=0	n=0	NUM
ejpam-3471	179	28	(	(	PUNCT
ejpam-3471	179	29	−1)n	−1)n	X
ejpam-3471	179	30	(	(	PUNCT
ejpam-3471	179	31	cπtll	cπtll	NOUN
ejpam-3471	179	32	√	√	NOUN
ejpam-3471	179	33	l2	l2	NOUN
ejpam-3471	179	34	+	+	CCONJ
ejpam-3471	179	35	l2)2n	l2)2n	PROPN
ejpam-3471	179	36	(	(	PUNCT
ejpam-3471	179	37	2n	2n	NUM
ejpam-3471	179	38	)	)	PUNCT
ejpam-3471	179	39	!	!	PUNCT
ejpam-3471	180	1	then	then	ADV
ejpam-3471	180	2	the	the	DET
ejpam-3471	180	3	approached	approach	VERB
ejpam-3471	180	4	solution	solution	NOUN
ejpam-3471	180	5	at	at	ADP
ejpam-3471	180	6	the	the	DET
ejpam-3471	180	7	the	the	DET
ejpam-3471	180	8	first	first	ADJ
ejpam-3471	180	9	step	step	NOUN
ejpam-3471	180	10	is	be	AUX
ejpam-3471	180	11	:	:	PUNCT
ejpam-3471	180	12	uk(x	uk(x	ADP
ejpam-3471	180	13	,	,	PUNCT
ejpam-3471	180	14	y	y	PROPN
ejpam-3471	180	15	,	,	PUNCT
ejpam-3471	180	16	t	t	PROPN
ejpam-3471	180	17	)	)	PUNCT
ejpam-3471	181	1	=	=	SYM
ejpam-3471	181	2	lim	lim	PROPN
ejpam-3471	181	3	m→+∞	m→+∞	PROPN
ejpam-3471	181	4	ϕkm(x	ϕkm(x	PROPN
ejpam-3471	181	5	,	,	PUNCT
ejpam-3471	181	6	y	y	PROPN
ejpam-3471	181	7	,	,	PUNCT
ejpam-3471	181	8	t	t	PROPN
ejpam-3471	181	9	)	)	PUNCT
ejpam-3471	181	10	=	=	SYM
ejpam-3471	181	11	sin	sin	NOUN
ejpam-3471	181	12	(	(	PUNCT
ejpam-3471	181	13	πx	πx	NOUN
ejpam-3471	181	14	l	l	NOUN
ejpam-3471	181	15	)	)	PUNCT
ejpam-3471	181	16	sin	sin	NOUN
ejpam-3471	181	17	(	(	PUNCT
ejpam-3471	181	18	πy	πy	NOUN
ejpam-3471	181	19	l	l	NOUN
ejpam-3471	181	20	)	)	PUNCT
ejpam-3471	181	21	cos	cos	PROPN
ejpam-3471	181	22	(	(	PUNCT
ejpam-3471	181	23	cπt	cπt	PROPN
ejpam-3471	181	24	ll	ll	AUX
ejpam-3471	181	25	√	√	VERB
ejpam-3471	181	26	l2	l2	VERB
ejpam-3471	181	27	+	+	CCONJ
ejpam-3471	181	28	l2	l2	NOUN
ejpam-3471	181	29	)	)	PUNCT
ejpam-3471	181	30	therefore	therefore	ADV
ejpam-3471	181	31	,	,	PUNCT
ejpam-3471	181	32	we	we	PRON
ejpam-3471	181	33	obtain	obtain	VERB
ejpam-3471	181	34	the	the	DET
ejpam-3471	181	35	exact	exact	ADJ
ejpam-3471	181	36	solution	solution	NOUN
ejpam-3471	181	37	of	of	ADP
ejpam-3471	181	38	the	the	DET
ejpam-3471	181	39	problem	problem	NOUN
ejpam-3471	181	40	(	(	PUNCT
ejpam-3471	181	41	p2	p2	PROPN
ejpam-3471	181	42	)	)	PUNCT
ejpam-3471	181	43	:	:	PUNCT
ejpam-3471	182	1	u(x	u(x	PROPN
ejpam-3471	182	2	,	,	PUNCT
ejpam-3471	182	3	y	y	PROPN
ejpam-3471	182	4	,	,	PUNCT
ejpam-3471	182	5	t	t	PROPN
ejpam-3471	182	6	)	)	PUNCT
ejpam-3471	182	7	=	=	VERB
ejpam-3471	183	1	lim	lim	PROPN
ejpam-3471	183	2	k→+∞	k→+∞	PROPN
ejpam-3471	183	3	uk(x	uk(x	ADP
ejpam-3471	183	4	,	,	PUNCT
ejpam-3471	183	5	y	y	PROPN
ejpam-3471	183	6	,	,	PUNCT
ejpam-3471	183	7	t	t	PROPN
ejpam-3471	183	8	)	)	PUNCT
ejpam-3471	183	9	(	(	PUNCT
ejpam-3471	183	10	36	36	NUM
ejpam-3471	183	11	)	)	PUNCT
ejpam-3471	183	12	r.	r.	PROPN
ejpam-3471	183	13	yaro	yaro	PROPN
ejpam-3471	183	14	,	,	PUNCT
ejpam-3471	183	15	y.	y.	PROPN
ejpam-3471	183	16	paré	paré	NOUN
ejpam-3471	183	17	,	,	PUNCT
ejpam-3471	183	18	b.	b.	PROPN
ejpam-3471	183	19	abbo	abbo	PROPN
ejpam-3471	183	20	/	/	SYM
ejpam-3471	183	21	eur	eur	PROPN
ejpam-3471	183	22	.	.	PUNCT
ejpam-3471	184	1	j.	j.	PROPN
ejpam-3471	184	2	pure	pure	PROPN
ejpam-3471	184	3	appl	appl	PROPN
ejpam-3471	184	4	.	.	PROPN
ejpam-3471	184	5	math	math	PROPN
ejpam-3471	184	6	,	,	PUNCT
ejpam-3471	184	7	12	12	NUM
ejpam-3471	184	8	(	(	PUNCT
ejpam-3471	184	9	3	3	NUM
ejpam-3471	184	10	)	)	PUNCT
ejpam-3471	184	11	(	(	PUNCT
ejpam-3471	184	12	2019	2019	NUM
ejpam-3471	184	13	)	)	PUNCT
ejpam-3471	184	14	,	,	PUNCT
ejpam-3471	184	15	1260	1260	NUM
ejpam-3471	184	16	-	-	SYM
ejpam-3471	184	17	1276	1276	NUM
ejpam-3471	184	18	1271	1271	NUM
ejpam-3471	184	19	=	=	SYM
ejpam-3471	184	20	sin	sin	NOUN
ejpam-3471	184	21	(	(	PUNCT
ejpam-3471	184	22	πx	πx	NOUN
ejpam-3471	184	23	l	l	NOUN
ejpam-3471	184	24	)	)	PUNCT
ejpam-3471	184	25	sin	sin	NOUN
ejpam-3471	184	26	(	(	PUNCT
ejpam-3471	184	27	πy	πy	NOUN
ejpam-3471	184	28	l	l	NOUN
ejpam-3471	184	29	)	)	PUNCT
ejpam-3471	185	1	cos	cos	PROPN
ejpam-3471	185	2	(	(	PUNCT
ejpam-3471	185	3	cπt	cπt	PROPN
ejpam-3471	185	4	ll	ll	AUX
ejpam-3471	185	5	√	√	VERB
ejpam-3471	185	6	l2	l2	VERB
ejpam-3471	185	7	+	+	CCONJ
ejpam-3471	185	8	l2	l2	NOUN
ejpam-3471	185	9	)	)	PUNCT
ejpam-3471	185	10	•	•	ADP
ejpam-3471	185	11	solving	solve	VERB
ejpam-3471	185	12	by	by	ADP
ejpam-3471	185	13	fourier	fourier	ADJ
ejpam-3471	185	14	method	method	NOUN
ejpam-3471	185	15	or	or	CCONJ
ejpam-3471	185	16	separation	separation	NOUN
ejpam-3471	185	17	of	of	ADP
ejpam-3471	185	18	variables	variable	NOUN
ejpam-3471	185	19	method	method	NOUN
ejpam-3471	185	20	we	we	PRON
ejpam-3471	185	21	find	find	VERB
ejpam-3471	185	22	all	all	DET
ejpam-3471	185	23	solutions	solution	NOUN
ejpam-3471	185	24	of	of	ADP
ejpam-3471	185	25	the	the	DET
ejpam-3471	185	26	wave	wave	NOUN
ejpam-3471	185	27	equation	equation	NOUN
ejpam-3471	185	28	(	(	PUNCT
ejpam-3471	185	29	p2	p2	PROPN
ejpam-3471	185	30	)	)	PUNCT
ejpam-3471	185	31	with	with	ADP
ejpam-3471	185	32	the	the	DET
ejpam-3471	185	33	general	general	ADJ
ejpam-3471	185	34	form	form	NOUN
ejpam-3471	185	35	:	:	PUNCT
ejpam-3471	185	36	u(x	u(x	PROPN
ejpam-3471	185	37	,	,	PUNCT
ejpam-3471	185	38	y	y	PROPN
ejpam-3471	185	39	,	,	PUNCT
ejpam-3471	185	40	t	t	PROPN
ejpam-3471	185	41	)	)	PUNCT
ejpam-3471	185	42	=	=	SYM
ejpam-3471	185	43	t	t	PROPN
ejpam-3471	185	44	(	(	PUNCT
ejpam-3471	185	45	t)u(x	t)u(x	PROPN
ejpam-3471	185	46	,	,	PUNCT
ejpam-3471	185	47	y	y	NOUN
ejpam-3471	185	48	)	)	PUNCT
ejpam-3471	185	49	(	(	PUNCT
ejpam-3471	185	50	37	37	NUM
ejpam-3471	185	51	)	)	PUNCT
ejpam-3471	185	52	where	where	SCONJ
ejpam-3471	185	53	u	u	NOUN
ejpam-3471	185	54	depends	depend	VERB
ejpam-3471	185	55	on	on	ADP
ejpam-3471	185	56	x	x	PUNCT
ejpam-3471	185	57	and	and	CCONJ
ejpam-3471	185	58	y	y	PROPN
ejpam-3471	185	59	:	:	PUNCT
ejpam-3471	185	60	u(x	u(x	PROPN
ejpam-3471	185	61	,	,	PUNCT
ejpam-3471	185	62	y	y	NOUN
ejpam-3471	185	63	)	)	PUNCT
ejpam-3471	185	64	=	=	SYM
ejpam-3471	186	1	x(x)y	x(x)y	PROPN
ejpam-3471	186	2	(	(	PUNCT
ejpam-3471	186	3	y	y	NOUN
ejpam-3471	186	4	)	)	PUNCT
ejpam-3471	186	5	(	(	PUNCT
ejpam-3471	186	6	38	38	NUM
ejpam-3471	186	7	)	)	PUNCT
ejpam-3471	186	8	for	for	ADP
ejpam-3471	186	9	some	some	DET
ejpam-3471	186	10	function	function	NOUN
ejpam-3471	186	11	x(x	x(x	PROPN
ejpam-3471	186	12	)	)	PUNCT
ejpam-3471	186	13	that	that	PRON
ejpam-3471	186	14	depends	depend	VERB
ejpam-3471	186	15	on	on	ADP
ejpam-3471	186	16	x	x	PRON
ejpam-3471	186	17	,	,	PUNCT
ejpam-3471	186	18	some	some	DET
ejpam-3471	186	19	function	function	NOUN
ejpam-3471	186	20	(	(	PUNCT
ejpam-3471	186	21	y	y	NOUN
ejpam-3471	186	22	)	)	PUNCT
ejpam-3471	186	23	that	that	PRON
ejpam-3471	186	24	depends	depend	VERB
ejpam-3471	186	25	on	on	ADP
ejpam-3471	186	26	y	y	PROPN
ejpam-3471	186	27	and	and	CCONJ
ejpam-3471	186	28	some	some	DET
ejpam-3471	186	29	function	function	NOUN
ejpam-3471	186	30	t	t	PROPN
ejpam-3471	186	31	(	(	PUNCT
ejpam-3471	186	32	t	t	PROPN
ejpam-3471	186	33	)	)	PUNCT
ejpam-3471	186	34	that	that	PRON
ejpam-3471	186	35	depends	depend	VERB
ejpam-3471	186	36	only	only	ADV
ejpam-3471	186	37	on	on	ADP
ejpam-3471	186	38	t	t	PROPN
ejpam-3471	186	39	but	but	CCONJ
ejpam-3471	186	40	not	not	PART
ejpam-3471	186	41	x	x	PROPN
ejpam-3471	186	42	and	and	CCONJ
ejpam-3471	186	43	y.	y.	PROPN
ejpam-3471	186	44	substitute	substitute	PROPN
ejpam-3471	186	45	equation	equation	NOUN
ejpam-3471	186	46	(	(	PUNCT
ejpam-3471	186	47	37	37	NUM
ejpam-3471	186	48	)	)	PUNCT
ejpam-3471	186	49	and	and	CCONJ
ejpam-3471	186	50	(	(	PUNCT
ejpam-3471	186	51	38	38	NUM
ejpam-3471	186	52	)	)	PUNCT
ejpam-3471	186	53	into	into	ADP
ejpam-3471	186	54	the	the	DET
ejpam-3471	186	55	two	two	NUM
ejpam-3471	186	56	-	-	PUNCT
ejpam-3471	186	57	dimensional	dimensional	ADJ
ejpam-3471	186	58	equation	equation	NOUN
ejpam-3471	186	59	(	(	PUNCT
ejpam-3471	186	60	31	31	NUM
ejpam-3471	186	61	)	)	PUNCT
ejpam-3471	186	62	we	we	PRON
ejpam-3471	186	63	get	get	VERB
ejpam-3471	186	64	:	:	PUNCT
ejpam-3471	186	65			PROPN
ejpam-3471	186	66	∂2u(x	∂2u(x	PROPN
ejpam-3471	186	67	,	,	PUNCT
ejpam-3471	186	68	y	y	PROPN
ejpam-3471	186	69	,	,	PUNCT
ejpam-3471	186	70	t	t	PROPN
ejpam-3471	186	71	)	)	PUNCT
ejpam-3471	186	72	∂t2	∂t2	NOUN
ejpam-3471	186	73	=	=	SYM
ejpam-3471	186	74	t	t	X
ejpam-3471	186	75	′′	′′	PROPN
ejpam-3471	186	76	(	(	PUNCT
ejpam-3471	186	77	t)u(x	t)u(x	PROPN
ejpam-3471	186	78	,	,	PUNCT
ejpam-3471	186	79	y	y	NOUN
ejpam-3471	186	80	)	)	PUNCT
ejpam-3471	186	81	∂2u(x	∂2u(x	PROPN
ejpam-3471	186	82	,	,	PUNCT
ejpam-3471	186	83	y	y	PROPN
ejpam-3471	186	84	,	,	PUNCT
ejpam-3471	186	85	t	t	PROPN
ejpam-3471	186	86	)	)	PUNCT
ejpam-3471	186	87	∂x2	∂x2	NOUN
ejpam-3471	186	88	=	=	SYM
ejpam-3471	186	89	t	t	PROPN
ejpam-3471	186	90	(	(	PUNCT
ejpam-3471	186	91	t	t	PROPN
ejpam-3471	186	92	)	)	PUNCT
ejpam-3471	186	93	∂2u(x	∂2u(x	PROPN
ejpam-3471	186	94	,	,	PUNCT
ejpam-3471	186	95	y	y	NOUN
ejpam-3471	186	96	)	)	PUNCT
ejpam-3471	186	97	∂x2	∂x2	NOUN
ejpam-3471	186	98	∂2u(x	∂2u(x	NOUN
ejpam-3471	186	99	,	,	PUNCT
ejpam-3471	186	100	y	y	PROPN
ejpam-3471	186	101	,	,	PUNCT
ejpam-3471	186	102	t	t	PROPN
ejpam-3471	186	103	)	)	PUNCT
ejpam-3471	186	104	∂y2	∂y2	NOUN
ejpam-3471	186	105	=	=	SYM
ejpam-3471	186	106	t	t	PROPN
ejpam-3471	186	107	(	(	PUNCT
ejpam-3471	186	108	t	t	PROPN
ejpam-3471	186	109	)	)	PUNCT
ejpam-3471	186	110	∂2u(x	∂2u(x	PROPN
ejpam-3471	186	111	,	,	PUNCT
ejpam-3471	186	112	y	y	NOUN
ejpam-3471	186	113	)	)	PUNCT
ejpam-3471	186	114	∂y2	∂y2	NOUN
ejpam-3471	186	115	and	and	CCONJ
ejpam-3471	186	116	t	t	NOUN
ejpam-3471	186	117	′′	′′	PROPN
ejpam-3471	186	118	(	(	PUNCT
ejpam-3471	186	119	t)u(x	t)u(x	PROPN
ejpam-3471	186	120	,	,	PUNCT
ejpam-3471	186	121	y	y	NOUN
ejpam-3471	186	122	)	)	PUNCT
ejpam-3471	186	123	=	=	SYM
ejpam-3471	186	124	c2	c2	PROPN
ejpam-3471	186	125	t	t	PROPN
ejpam-3471	186	126	(	(	PUNCT
ejpam-3471	186	127	t	t	PROPN
ejpam-3471	186	128	)	)	PUNCT
ejpam-3471	186	129	(	(	PUNCT
ejpam-3471	186	130	∂2u(x	∂2u(x	PROPN
ejpam-3471	186	131	,	,	PUNCT
ejpam-3471	186	132	y	y	NOUN
ejpam-3471	186	133	)	)	PUNCT
ejpam-3471	186	134	∂x2	∂x2	NOUN
ejpam-3471	186	135	+	+	SYM
ejpam-3471	186	136	∂2u(x	∂2u(x	NOUN
ejpam-3471	186	137	,	,	PUNCT
ejpam-3471	186	138	y	y	NOUN
ejpam-3471	186	139	)	)	PUNCT
ejpam-3471	186	140	∂y2	∂y2	NOUN
ejpam-3471	186	141	)	)	PUNCT
ejpam-3471	186	142	then	then	ADV
ejpam-3471	186	143	t	t	X
ejpam-3471	186	144	′′	′′	PROPN
ejpam-3471	186	145	(	(	PUNCT
ejpam-3471	186	146	t	t	PROPN
ejpam-3471	186	147	)	)	PUNCT
ejpam-3471	186	148	c2	c2	PROPN
ejpam-3471	186	149	t	t	PROPN
ejpam-3471	186	150	(	(	PUNCT
ejpam-3471	186	151	t	t	PROPN
ejpam-3471	186	152	)	)	PUNCT
ejpam-3471	186	153	=	=	SYM
ejpam-3471	186	154	∂2u(x	∂2u(x	PROPN
ejpam-3471	186	155	,	,	PUNCT
ejpam-3471	186	156	y	y	NOUN
ejpam-3471	186	157	)	)	PUNCT
ejpam-3471	186	158	∂x2	∂x2	NOUN
ejpam-3471	186	159	+	+	SYM
ejpam-3471	186	160	∂2u(x	∂2u(x	NOUN
ejpam-3471	186	161	,	,	PUNCT
ejpam-3471	186	162	y	y	NOUN
ejpam-3471	186	163	)	)	PUNCT
ejpam-3471	186	164	∂y2	∂y2	ADJ
ejpam-3471	186	165	u(x	u(x	PROPN
ejpam-3471	186	166	,	,	PUNCT
ejpam-3471	186	167	y	y	NOUN
ejpam-3471	186	168	)	)	PUNCT
ejpam-3471	187	1	=	=	SYM
ejpam-3471	187	2	−λ2	−λ2	NOUN
ejpam-3471	187	3	(	(	PUNCT
ejpam-3471	187	4	39	39	NUM
ejpam-3471	187	5	)	)	PUNCT
ejpam-3471	187	6	then	then	ADV
ejpam-3471	187	7	we	we	PRON
ejpam-3471	187	8	have	have	VERB
ejpam-3471	187	9	t	t	NOUN
ejpam-3471	187	10	′′	′′	PROPN
ejpam-3471	187	11	(	(	PUNCT
ejpam-3471	187	12	t	t	PROPN
ejpam-3471	187	13	)	)	PUNCT
ejpam-3471	187	14	+	+	CCONJ
ejpam-3471	187	15	(	(	PUNCT
ejpam-3471	187	16	λc)2	λc)2	PROPN
ejpam-3471	187	17	t	t	PROPN
ejpam-3471	187	18	(	(	PUNCT
ejpam-3471	187	19	t	t	PROPN
ejpam-3471	187	20	)	)	PUNCT
ejpam-3471	187	21	=	=	SYM
ejpam-3471	187	22	0	0	PUNCT
ejpam-3471	188	1	=	=	NOUN
ejpam-3471	188	2	⇒	⇒	X
ejpam-3471	188	3	t	t	PROPN
ejpam-3471	188	4	(	(	PUNCT
ejpam-3471	188	5	t	t	PROPN
ejpam-3471	188	6	)	)	PUNCT
ejpam-3471	188	7	=	=	SYM
ejpam-3471	188	8	α	α	PROPN
ejpam-3471	188	9	cos(λct	cos(λct	PROPN
ejpam-3471	188	10	)	)	PUNCT
ejpam-3471	189	1	+	+	CCONJ
ejpam-3471	189	2	β	β	X
ejpam-3471	189	3	sin(λct	sin(λct	NOUN
ejpam-3471	189	4	)	)	PUNCT
ejpam-3471	189	5	(	(	PUNCT
ejpam-3471	189	6	40	40	NUM
ejpam-3471	189	7	)	)	PUNCT
ejpam-3471	189	8	where	where	SCONJ
ejpam-3471	189	9	α	α	NOUN
ejpam-3471	189	10	and	and	CCONJ
ejpam-3471	189	11	β	β	PROPN
ejpam-3471	189	12	are	be	AUX
ejpam-3471	189	13	arbibrairy	arbibrairy	ADJ
ejpam-3471	189	14	constantes	constante	NOUN
ejpam-3471	189	15	.	.	PUNCT
ejpam-3471	190	1	and	and	CCONJ
ejpam-3471	190	2	we	we	PRON
ejpam-3471	190	3	get	get	VERB
ejpam-3471	190	4	r.	r.	PROPN
ejpam-3471	190	5	yaro	yaro	PROPN
ejpam-3471	190	6	,	,	PUNCT
ejpam-3471	190	7	y.	y.	PROPN
ejpam-3471	190	8	paré	paré	NOUN
ejpam-3471	190	9	,	,	PUNCT
ejpam-3471	190	10	b.	b.	PROPN
ejpam-3471	190	11	abbo	abbo	PROPN
ejpam-3471	190	12	/	/	SYM
ejpam-3471	190	13	eur	eur	PROPN
ejpam-3471	190	14	.	.	PUNCT
ejpam-3471	191	1	j.	j.	PROPN
ejpam-3471	191	2	pure	pure	PROPN
ejpam-3471	191	3	appl	appl	PROPN
ejpam-3471	191	4	.	.	PROPN
ejpam-3471	191	5	math	math	PROPN
ejpam-3471	191	6	,	,	PUNCT
ejpam-3471	191	7	12	12	NUM
ejpam-3471	191	8	(	(	PUNCT
ejpam-3471	191	9	3	3	NUM
ejpam-3471	191	10	)	)	PUNCT
ejpam-3471	191	11	(	(	PUNCT
ejpam-3471	191	12	2019	2019	NUM
ejpam-3471	191	13	)	)	PUNCT
ejpam-3471	191	14	,	,	PUNCT
ejpam-3471	191	15	1260	1260	NUM
ejpam-3471	191	16	-	-	SYM
ejpam-3471	191	17	1276	1276	NUM
ejpam-3471	191	18	1272	1272	NUM
ejpam-3471	191	19	u(x	u(x	NOUN
ejpam-3471	191	20	,	,	PUNCT
ejpam-3471	191	21	y	y	PROPN
ejpam-3471	191	22	,	,	PUNCT
ejpam-3471	191	23	t	t	PROPN
ejpam-3471	191	24	)	)	PUNCT
ejpam-3471	191	25	=	=	SYM
ejpam-3471	191	26	(	(	PUNCT
ejpam-3471	191	27	α	α	NOUN
ejpam-3471	191	28	cos(λct	cos(λct	PROPN
ejpam-3471	191	29	)	)	PUNCT
ejpam-3471	192	1	+	+	CCONJ
ejpam-3471	192	2	β	β	X
ejpam-3471	192	3	sin(λct))u(x	sin(λct))u(x	NOUN
ejpam-3471	192	4	,	,	PUNCT
ejpam-3471	192	5	y	y	NOUN
ejpam-3471	192	6	)	)	PUNCT
ejpam-3471	192	7	(	(	PUNCT
ejpam-3471	192	8	41	41	NUM
ejpam-3471	192	9	)	)	PUNCT
ejpam-3471	192	10	then	then	ADV
ejpam-3471	192	11	we	we	PRON
ejpam-3471	192	12	have	have	VERB
ejpam-3471	192	13	∂2u(x	∂2u(x	NOUN
ejpam-3471	192	14	,	,	PUNCT
ejpam-3471	192	15	y	y	NOUN
ejpam-3471	192	16	)	)	PUNCT
ejpam-3471	192	17	∂x2	∂x2	NOUN
ejpam-3471	192	18	+	+	SYM
ejpam-3471	192	19	∂2u(x	∂2u(x	NOUN
ejpam-3471	192	20	,	,	PUNCT
ejpam-3471	192	21	y	y	NOUN
ejpam-3471	192	22	)	)	PUNCT
ejpam-3471	192	23	∂y2	∂y2	ADJ
ejpam-3471	192	24	u(x	u(x	PROPN
ejpam-3471	192	25	,	,	PUNCT
ejpam-3471	192	26	y	y	NOUN
ejpam-3471	192	27	)	)	PUNCT
ejpam-3471	193	1	=	=	PUNCT
ejpam-3471	193	2	−λ2	−λ2	NOUN
ejpam-3471	193	3	=	=	SYM
ejpam-3471	193	4	⇒	⇒	VERB
ejpam-3471	193	5	x	x	PUNCT
ejpam-3471	194	1	′′	′′	PROPN
ejpam-3471	194	2	y	y	PROPN
ejpam-3471	194	3	(	(	PUNCT
ejpam-3471	194	4	y	y	PROPN
ejpam-3471	194	5	)	)	PUNCT
ejpam-3471	194	6	+	+	PROPN
ejpam-3471	194	7	x(x)y	x(x)y	PROPN
ejpam-3471	194	8	′′	′′	PROPN
ejpam-3471	194	9	(	(	PUNCT
ejpam-3471	194	10	y	y	PROPN
ejpam-3471	194	11	)	)	PUNCT
ejpam-3471	194	12	x(x)y	x(x)y	PROPN
ejpam-3471	194	13	(	(	PUNCT
ejpam-3471	194	14	y	y	X
ejpam-3471	194	15	)	)	PUNCT
ejpam-3471	194	16	=	=	SYM
ejpam-3471	194	17	−λ2	−λ2	NOUN
ejpam-3471	194	18	(	(	PUNCT
ejpam-3471	194	19	42	42	NUM
ejpam-3471	194	20	)	)	PUNCT
ejpam-3471	194	21	then	then	ADV
ejpam-3471	194	22	x	x	X
ejpam-3471	194	23	′′	′′	PROPN
ejpam-3471	194	24	y	y	PROPN
ejpam-3471	194	25	(	(	PUNCT
ejpam-3471	194	26	y	y	PROPN
ejpam-3471	194	27	)	)	PUNCT
ejpam-3471	195	1	+	+	PROPN
ejpam-3471	195	2	x(x)y	x(x)y	PROPN
ejpam-3471	195	3	′′	′′	PROPN
ejpam-3471	195	4	(	(	PUNCT
ejpam-3471	195	5	y	y	PROPN
ejpam-3471	195	6	)	)	PUNCT
ejpam-3471	195	7	+	+	CCONJ
ejpam-3471	195	8	λ2x(x)y	λ2x(x)y	PROPN
ejpam-3471	195	9	(	(	PUNCT
ejpam-3471	195	10	y	y	NOUN
ejpam-3471	195	11	)	)	PUNCT
ejpam-3471	195	12	=	=	SYM
ejpam-3471	195	13	0	0	PUNCT
ejpam-3471	195	14	(	(	PUNCT
ejpam-3471	195	15	43	43	NUM
ejpam-3471	195	16	)	)	PUNCT
ejpam-3471	195	17	let	let	VERB
ejpam-3471	195	18	’s	’s	NOUN
ejpam-3471	195	19	put	put	VERB
ejpam-3471	195	20	x	x	PUNCT
ejpam-3471	196	1	′′	′′	PROPN
ejpam-3471	196	2	(	(	PUNCT
ejpam-3471	196	3	x	x	NOUN
ejpam-3471	196	4	)	)	PUNCT
ejpam-3471	196	5	x(x	x(x	NOUN
ejpam-3471	196	6	)	)	PUNCT
ejpam-3471	196	7	=	=	SYM
ejpam-3471	196	8	y	y	PROPN
ejpam-3471	196	9	′′	′′	PROPN
ejpam-3471	196	10	(	(	PUNCT
ejpam-3471	196	11	y	y	PROPN
ejpam-3471	196	12	)	)	PUNCT
ejpam-3471	196	13	+	+	CCONJ
ejpam-3471	196	14	λ2y	λ2y	PUNCT
ejpam-3471	196	15	(	(	PUNCT
ejpam-3471	196	16	y	y	NOUN
ejpam-3471	196	17	)	)	PUNCT
ejpam-3471	196	18	y	y	PROPN
ejpam-3471	196	19	(	(	PUNCT
ejpam-3471	196	20	y	y	NOUN
ejpam-3471	196	21	)	)	PUNCT
ejpam-3471	196	22	=	=	SYM
ejpam-3471	197	1	−µ2	−µ2	NOUN
ejpam-3471	197	2	(	(	PUNCT
ejpam-3471	197	3	44	44	NUM
ejpam-3471	197	4	)	)	PUNCT
ejpam-3471	197	5	we	we	PRON
ejpam-3471	197	6	obtain	obtain	VERB
ejpam-3471	197	7			PUNCT
ejpam-3471	197	8	x	x	SYM
ejpam-3471	197	9	′′	′′	PROPN
ejpam-3471	197	10	(	(	PUNCT
ejpam-3471	197	11	x	x	X
ejpam-3471	197	12	)	)	PUNCT
ejpam-3471	197	13	+	+	CCONJ
ejpam-3471	197	14	µ2x(x	µ2x(x	PROPN
ejpam-3471	197	15	)	)	PUNCT
ejpam-3471	197	16	=	=	SYM
ejpam-3471	197	17	0	0	PUNCT
ejpam-3471	197	18	and	and	CCONJ
ejpam-3471	197	19	y	y	PROPN
ejpam-3471	197	20	′′	′′	PROPN
ejpam-3471	197	21	(	(	PUNCT
ejpam-3471	197	22	y	y	PROPN
ejpam-3471	197	23	)	)	PUNCT
ejpam-3471	197	24	+	+	CCONJ
ejpam-3471	197	25	ς2x(y	ς2x(y	PROPN
ejpam-3471	197	26	)	)	PUNCT
ejpam-3471	197	27	=	=	PUNCT
ejpam-3471	197	28	0	0	NUM
ejpam-3471	197	29	;	;	PUNCT
ejpam-3471	197	30	ς2	ς2	PROPN
ejpam-3471	197	31	=	=	SYM
ejpam-3471	197	32	λ2	λ2	PROPN
ejpam-3471	197	33	+	+	CCONJ
ejpam-3471	197	34	µ2	µ2	PROPN
ejpam-3471	197	35	(	(	PUNCT
ejpam-3471	197	36	45	45	NUM
ejpam-3471	197	37	)	)	PUNCT
ejpam-3471	197	38	then	then	ADV
ejpam-3471	197	39			PUNCT
ejpam-3471	197	40	x(x	x(x	PROPN
ejpam-3471	197	41	)	)	PUNCT
ejpam-3471	197	42	=	=	PUNCT
ejpam-3471	197	43	a	a	DET
ejpam-3471	197	44	cos(µx	cos(µx	NOUN
ejpam-3471	197	45	)	)	PUNCT
ejpam-3471	198	1	+	+	NOUN
ejpam-3471	198	2	b	b	NOUN
ejpam-3471	198	3	sin(µx	sin(µx	NOUN
ejpam-3471	198	4	)	)	PUNCT
ejpam-3471	198	5	and	and	CCONJ
ejpam-3471	198	6	y	y	PROPN
ejpam-3471	198	7	(	(	PUNCT
ejpam-3471	198	8	y	y	NOUN
ejpam-3471	198	9	)	)	PUNCT
ejpam-3471	198	10	=	=	SYM
ejpam-3471	198	11	c	c	NOUN
ejpam-3471	198	12	cos(ςy	cos(ςy	PROPN
ejpam-3471	198	13	)	)	PUNCT
ejpam-3471	199	1	+	+	PROPN
ejpam-3471	199	2	d	d	NOUN
ejpam-3471	199	3	sin(ςy	sin(ςy	PRON
ejpam-3471	199	4	)	)	PUNCT
ejpam-3471	199	5	(	(	PUNCT
ejpam-3471	199	6	46	46	NUM
ejpam-3471	199	7	)	)	PUNCT
ejpam-3471	199	8	where	where	SCONJ
ejpam-3471	199	9	a	a	DET
ejpam-3471	199	10	,	,	PUNCT
ejpam-3471	199	11	b	b	NOUN
ejpam-3471	199	12	,	,	PUNCT
ejpam-3471	199	13	c	c	PROPN
ejpam-3471	199	14	and	and	CCONJ
ejpam-3471	199	15	d	d	PROPN
ejpam-3471	199	16	are	be	AUX
ejpam-3471	199	17	arbibrairy	arbibrairy	ADJ
ejpam-3471	199	18	constantes	constante	NOUN
ejpam-3471	199	19	.	.	PUNCT
ejpam-3471	200	1	we	we	PRON
ejpam-3471	200	2	have	have	VERB
ejpam-3471	200	3	u(x	u(x	NOUN
ejpam-3471	200	4	,	,	PUNCT
ejpam-3471	200	5	y	y	PROPN
ejpam-3471	200	6	,	,	PUNCT
ejpam-3471	200	7	t	t	PROPN
ejpam-3471	200	8	)	)	PUNCT
ejpam-3471	200	9	=	=	SYM
ejpam-3471	200	10	(	(	PUNCT
ejpam-3471	200	11	(	(	PUNCT
ejpam-3471	200	12	α	α	PROPN
ejpam-3471	200	13	cos(λct	cos(λct	PROPN
ejpam-3471	200	14	)	)	PUNCT
ejpam-3471	201	1	+	+	CCONJ
ejpam-3471	201	2	β	β	X
ejpam-3471	201	3	sin(λct))x(x)y	sin(λct))x(x)y	PROPN
ejpam-3471	201	4	(	(	PUNCT
ejpam-3471	201	5	y	y	NOUN
ejpam-3471	201	6	)	)	PUNCT
ejpam-3471	201	7	(	(	PUNCT
ejpam-3471	201	8	47	47	NUM
ejpam-3471	201	9	)	)	PUNCT
ejpam-3471	201	10	let	let	VERB
ejpam-3471	201	11	’s	’s	NOUN
ejpam-3471	201	12	calculate	calculate	VERB
ejpam-3471	201	13	the	the	DET
ejpam-3471	201	14	constantes	constante	NOUN
ejpam-3471	201	15	with	with	ADP
ejpam-3471	201	16	the	the	DET
ejpam-3471	201	17	initial	initial	ADJ
ejpam-3471	201	18	condition	condition	PROPN
ejpam-3471	201	19	u(x	u(x	PROPN
ejpam-3471	201	20	,	,	PUNCT
ejpam-3471	201	21	y	y	PROPN
ejpam-3471	201	22	,	,	PUNCT
ejpam-3471	201	23	0	0	NUM
ejpam-3471	201	24	)	)	PUNCT
ejpam-3471	201	25	=	=	VERB
ejpam-3471	202	1	sin	sin	NOUN
ejpam-3471	202	2	(	(	PUNCT
ejpam-3471	202	3	πx	πx	NOUN
ejpam-3471	202	4	l	l	NOUN
ejpam-3471	202	5	)	)	PUNCT
ejpam-3471	202	6	sin	sin	NOUN
ejpam-3471	202	7	(	(	PUNCT
ejpam-3471	202	8	πy	πy	NOUN
ejpam-3471	202	9	l	l	NOUN
ejpam-3471	202	10	)	)	PUNCT
ejpam-3471	202	11	ut(x	ut(x	NOUN
ejpam-3471	202	12	,	,	PUNCT
ejpam-3471	202	13	y	y	NOUN
ejpam-3471	202	14	,	,	PUNCT
ejpam-3471	202	15	0	0	NUM
ejpam-3471	202	16	)	)	PUNCT
ejpam-3471	202	17	=	=	SYM
ejpam-3471	202	18	0	0	X
ejpam-3471	203	1	u(0	u(0	PROPN
ejpam-3471	203	2	,	,	PUNCT
ejpam-3471	203	3	y	y	PROPN
ejpam-3471	203	4	,	,	PUNCT
ejpam-3471	203	5	t	t	PROPN
ejpam-3471	203	6	)	)	PUNCT
ejpam-3471	203	7	)	)	PUNCT
ejpam-3471	204	1	=	=	SYM
ejpam-3471	204	2	0	0	X
ejpam-3471	205	1	u(l	u(l	ADJ
ejpam-3471	205	2	,	,	PUNCT
ejpam-3471	205	3	y	y	PROPN
ejpam-3471	205	4	,	,	PUNCT
ejpam-3471	205	5	t	t	PROPN
ejpam-3471	205	6	)	)	PUNCT
ejpam-3471	205	7	)	)	PUNCT
ejpam-3471	206	1	=	=	SYM
ejpam-3471	206	2	0	0	NUM
ejpam-3471	206	3	u(x	u(x	NOUN
ejpam-3471	206	4	,	,	PUNCT
ejpam-3471	206	5	0	0	NUM
ejpam-3471	206	6	,	,	PUNCT
ejpam-3471	206	7	t	t	PROPN
ejpam-3471	206	8	)	)	PUNCT
ejpam-3471	206	9	)	)	PUNCT
ejpam-3471	207	1	=	=	SYM
ejpam-3471	207	2	0	0	NUM
ejpam-3471	207	3	u(x	u(x	NOUN
ejpam-3471	207	4	,	,	PUNCT
ejpam-3471	207	5	l	l	NOUN
ejpam-3471	207	6	,	,	PUNCT
ejpam-3471	207	7	t	t	PROPN
ejpam-3471	207	8	)	)	PUNCT
ejpam-3471	207	9	)	)	PUNCT
ejpam-3471	208	1	=	=	SYM
ejpam-3471	208	2	0	0	PROPN
ejpam-3471	208	3	r.	r.	PROPN
ejpam-3471	208	4	yaro	yaro	PROPN
ejpam-3471	208	5	,	,	PUNCT
ejpam-3471	208	6	y.	y.	PROPN
ejpam-3471	208	7	paré	paré	NOUN
ejpam-3471	208	8	,	,	PUNCT
ejpam-3471	208	9	b.	b.	PROPN
ejpam-3471	208	10	abbo	abbo	PROPN
ejpam-3471	208	11	/	/	SYM
ejpam-3471	208	12	eur	eur	PROPN
ejpam-3471	208	13	.	.	PUNCT
ejpam-3471	209	1	j.	j.	PROPN
ejpam-3471	209	2	pure	pure	PROPN
ejpam-3471	209	3	appl	appl	PROPN
ejpam-3471	209	4	.	.	PROPN
ejpam-3471	209	5	math	math	PROPN
ejpam-3471	209	6	,	,	PUNCT
ejpam-3471	209	7	12	12	NUM
ejpam-3471	209	8	(	(	PUNCT
ejpam-3471	209	9	3	3	NUM
ejpam-3471	209	10	)	)	PUNCT
ejpam-3471	209	11	(	(	PUNCT
ejpam-3471	209	12	2019	2019	NUM
ejpam-3471	209	13	)	)	PUNCT
ejpam-3471	209	14	,	,	PUNCT
ejpam-3471	209	15	1260	1260	NUM
ejpam-3471	209	16	-	-	SYM
ejpam-3471	209	17	1276	1276	NUM
ejpam-3471	209	18	1273	1273	NUM
ejpam-3471	209	19	we	we	PRON
ejpam-3471	209	20	get	get	VERB
ejpam-3471	209	21			PROPN
ejpam-3471	209	22	αx(x)y	αx(x)y	NUM
ejpam-3471	209	23	(	(	PUNCT
ejpam-3471	209	24	y	y	NOUN
ejpam-3471	209	25	)	)	PUNCT
ejpam-3471	209	26	=	=	AUX
ejpam-3471	209	27	sin	sin	NOUN
ejpam-3471	209	28	(	(	PUNCT
ejpam-3471	209	29	πx	πx	NOUN
ejpam-3471	209	30	l	l	NOUN
ejpam-3471	209	31	)	)	PUNCT
ejpam-3471	209	32	sin	sin	NOUN
ejpam-3471	209	33	(	(	PUNCT
ejpam-3471	209	34	πy	πy	NOUN
ejpam-3471	209	35	l	l	NOUN
ejpam-3471	209	36	)	)	PUNCT
ejpam-3471	210	1	x(0	x(0	PROPN
ejpam-3471	210	2	)	)	PUNCT
ejpam-3471	210	3	=	=	PUNCT
ejpam-3471	210	4	0	0	NUM
ejpam-3471	210	5	x(l	x(l	NOUN
ejpam-3471	210	6	)	)	PUNCT
ejpam-3471	211	1	=	=	SYM
ejpam-3471	211	2	0	0	NUM
ejpam-3471	211	3	y	y	PROPN
ejpam-3471	211	4	(	(	PUNCT
ejpam-3471	211	5	0	0	NUM
ejpam-3471	211	6	)	)	PUNCT
ejpam-3471	211	7	=	=	SYM
ejpam-3471	212	1	0	0	PUNCT
ejpam-3471	212	2	y	y	PROPN
ejpam-3471	212	3	(	(	PUNCT
ejpam-3471	212	4	l	l	NOUN
ejpam-3471	212	5	)	)	PUNCT
ejpam-3471	212	6	=	=	SYM
ejpam-3471	212	7	0	0	NUM
ejpam-3471	212	8	βcλ	βcλ	NOUN
ejpam-3471	212	9	=	=	SYM
ejpam-3471	212	10	0	0	PUNCT
ejpam-3471	213	1	=	=	AUX
ejpam-3471	213	2	⇒	⇒	X
ejpam-3471	213	3			PROPN
ejpam-3471	213	4	αx(x)y	αx(x)y	NUM
ejpam-3471	213	5	(	(	PUNCT
ejpam-3471	213	6	y	y	NOUN
ejpam-3471	213	7	)	)	PUNCT
ejpam-3471	213	8	=	=	AUX
ejpam-3471	213	9	sin	sin	NOUN
ejpam-3471	213	10	(	(	PUNCT
ejpam-3471	213	11	πx	πx	NOUN
ejpam-3471	213	12	l	l	NOUN
ejpam-3471	213	13	)	)	PUNCT
ejpam-3471	213	14	sin	sin	NOUN
ejpam-3471	213	15	(	(	PUNCT
ejpam-3471	213	16	πy	πy	NOUN
ejpam-3471	213	17	l	l	NOUN
ejpam-3471	213	18	)	)	PUNCT
ejpam-3471	213	19	x(0	x(0	PROPN
ejpam-3471	213	20	)	)	PUNCT
ejpam-3471	213	21	=	=	PUNCT
ejpam-3471	213	22	0	0	NUM
ejpam-3471	213	23	x(l	x(l	NOUN
ejpam-3471	213	24	)	)	PUNCT
ejpam-3471	214	1	=	=	SYM
ejpam-3471	214	2	0	0	NUM
ejpam-3471	214	3	y	y	PROPN
ejpam-3471	214	4	(	(	PUNCT
ejpam-3471	214	5	0	0	NUM
ejpam-3471	214	6	)	)	PUNCT
ejpam-3471	214	7	=	=	SYM
ejpam-3471	215	1	0	0	PUNCT
ejpam-3471	215	2	y	y	PROPN
ejpam-3471	215	3	(	(	PUNCT
ejpam-3471	215	4	l	l	NOUN
ejpam-3471	215	5	)	)	PUNCT
ejpam-3471	215	6	=	=	SYM
ejpam-3471	215	7	0	0	NUM
ejpam-3471	215	8	βcλ	βcλ	NOUN
ejpam-3471	215	9	=	=	SYM
ejpam-3471	215	10	0	0	NUM
ejpam-3471	215	11	we	we	PRON
ejpam-3471	215	12	obtain	obtain	VERB
ejpam-3471	215	13	by	by	ADP
ejpam-3471	215	14	unfoilding	unfoilding	PROPN
ejpam-3471	216	1	a	a	DET
ejpam-3471	216	2	=	=	NOUN
ejpam-3471	216	3	0	0	NUM
ejpam-3471	216	4	sin(µl	sin(µl	NOUN
ejpam-3471	216	5	)	)	PUNCT
ejpam-3471	216	6	=	=	SYM
ejpam-3471	216	7	0	0	PUNCT
ejpam-3471	216	8	c	c	NOUN
ejpam-3471	216	9	=	=	SYM
ejpam-3471	216	10	0	0	NUM
ejpam-3471	216	11	sin(ςl	sin(ςl	NOUN
ejpam-3471	216	12	)	)	PUNCT
ejpam-3471	216	13	=	=	SYM
ejpam-3471	216	14	0	0	PUNCT
ejpam-3471	216	15	β	β	X
ejpam-3471	216	16	=	=	SYM
ejpam-3471	216	17	0	0	PUNCT
ejpam-3471	217	1	=	=	NOUN
ejpam-3471	217	2	⇒	⇒	NOUN
ejpam-3471	217	3			VERB
ejpam-3471	217	4	a	a	DET
ejpam-3471	217	5	=	=	SYM
ejpam-3471	217	6	0	0	NUM
ejpam-3471	217	7	µ	µ	X
ejpam-3471	217	8	=	=	SYM
ejpam-3471	217	9	nπ	nπ	NOUN
ejpam-3471	217	10	l	l	NOUN
ejpam-3471	217	11	;	;	PUNCT
ejpam-3471	217	12	∀n	∀n	X
ejpam-3471	217	13	≥	≥	NOUN
ejpam-3471	217	14	1	1	NUM
ejpam-3471	217	15	c	c	NOUN
ejpam-3471	217	16	=	=	SYM
ejpam-3471	217	17	0	0	PUNCT
ejpam-3471	218	1	ς	ς	PROPN
ejpam-3471	218	2	=	=	PUNCT
ejpam-3471	218	3	nπ	nπ	NOUN
ejpam-3471	218	4	l	l	NOUN
ejpam-3471	218	5	;	;	PUNCT
ejpam-3471	219	1	∀n	∀n	X
ejpam-3471	219	2	≥	≥	NOUN
ejpam-3471	219	3	1	1	NUM
ejpam-3471	219	4	β	β	X
ejpam-3471	219	5	then	then	ADV
ejpam-3471	219	6	we	we	PRON
ejpam-3471	219	7	get	get	VERB
ejpam-3471	219	8			PUNCT
ejpam-3471	219	9	x(x	x(x	PROPN
ejpam-3471	219	10	)	)	PUNCT
ejpam-3471	219	11	=	=	SYM
ejpam-3471	219	12	sin(nπxl	sin(nπxl	NOUN
ejpam-3471	219	13	)	)	PUNCT
ejpam-3471	219	14	and	and	CCONJ
ejpam-3471	219	15	y	y	PROPN
ejpam-3471	219	16	(	(	PUNCT
ejpam-3471	219	17	y	y	NOUN
ejpam-3471	219	18	)	)	PUNCT
ejpam-3471	219	19	=	=	SYM
ejpam-3471	219	20	sin(nπyl	sin(nπyl	NOUN
ejpam-3471	219	21	)	)	PUNCT
ejpam-3471	219	22	(	(	PUNCT
ejpam-3471	219	23	48	48	NUM
ejpam-3471	219	24	)	)	PUNCT
ejpam-3471	219	25	then	then	ADV
ejpam-3471	219	26	∀n	∀n	NUM
ejpam-3471	219	27	≥	≥	NOUN
ejpam-3471	219	28	1	1	NUM
ejpam-3471	219	29	,	,	PUNCT
ejpam-3471	219	30	we	we	PRON
ejpam-3471	219	31	have	have	VERB
ejpam-3471	219	32	un(x	un(x	NOUN
ejpam-3471	219	33	,	,	PUNCT
ejpam-3471	219	34	y	y	PROPN
ejpam-3471	219	35	;	;	PUNCT
ejpam-3471	219	36	t	t	PROPN
ejpam-3471	219	37	)	)	PUNCT
ejpam-3471	219	38	=	=	SYM
ejpam-3471	220	1	(	(	PUNCT
ejpam-3471	220	2	(	(	PUNCT
ejpam-3471	220	3	αn	αn	NOUN
ejpam-3471	220	4	cos(λnct	cos(λnct	PUNCT
ejpam-3471	220	5	)	)	PUNCT
ejpam-3471	221	1	+	+	CCONJ
ejpam-3471	221	2	βn	βn	ADJ
ejpam-3471	221	3	sin(λnct	sin(λnct	NOUN
ejpam-3471	221	4	)	)	PUNCT
ejpam-3471	221	5	)	)	PUNCT
ejpam-3471	221	6	sin	sin	NOUN
ejpam-3471	221	7	(	(	PUNCT
ejpam-3471	221	8	nπx	nπx	NOUN
ejpam-3471	221	9	l	l	NOUN
ejpam-3471	221	10	)	)	PUNCT
ejpam-3471	221	11	sin	sin	NOUN
ejpam-3471	221	12	(	(	PUNCT
ejpam-3471	221	13	nπy	nπy	NOUN
ejpam-3471	221	14	l	l	PROPN
ejpam-3471	221	15	)	)	PUNCT
ejpam-3471	221	16	;	;	PUNCT
ejpam-3471	221	17	∀n	∀n	NUM
ejpam-3471	221	18	≥	≥	NOUN
ejpam-3471	221	19	1	1	NUM
ejpam-3471	221	20	(	(	PUNCT
ejpam-3471	221	21	49	49	NUM
ejpam-3471	221	22	)	)	PUNCT
ejpam-3471	221	23	and	and	CCONJ
ejpam-3471	221	24	λ2n	λ2n	SYM
ejpam-3471	221	25	=	=	SYM
ejpam-3471	221	26	(	(	PUNCT
ejpam-3471	221	27	nπ	nπ	NOUN
ejpam-3471	221	28	ll	ll	NOUN
ejpam-3471	221	29	)	)	PUNCT
ejpam-3471	221	30	2(l2	2(l2	PROPN
ejpam-3471	222	1	+	+	NUM
ejpam-3471	222	2	l2	l2	NOUN
ejpam-3471	222	3	)	)	PUNCT
ejpam-3471	222	4	(	(	PUNCT
ejpam-3471	222	5	50	50	NUM
ejpam-3471	222	6	)	)	PUNCT
ejpam-3471	222	7	let	let	VERB
ejpam-3471	222	8	’s	’s	NOUN
ejpam-3471	222	9	put	put	VERB
ejpam-3471	222	10	tn(t	tn(t	NUM
ejpam-3471	222	11	)	)	PUNCT
ejpam-3471	222	12	=	=	SYM
ejpam-3471	223	1	(	(	PUNCT
ejpam-3471	223	2	(	(	PUNCT
ejpam-3471	223	3	αn	αn	NOUN
ejpam-3471	223	4	cos(λnct	cos(λnct	PUNCT
ejpam-3471	223	5	)	)	PUNCT
ejpam-3471	224	1	+	+	CCONJ
ejpam-3471	224	2	βn	βn	PROPN
ejpam-3471	224	3	sin(λnct));∀n	sin(λnct));∀n	NOUN
ejpam-3471	224	4	≥	≥	NUM
ejpam-3471	224	5	1	1	NUM
ejpam-3471	224	6	(	(	PUNCT
ejpam-3471	224	7	51	51	NUM
ejpam-3471	224	8	)	)	PUNCT
ejpam-3471	224	9	we	we	PRON
ejpam-3471	224	10	obtain	obtain	VERB
ejpam-3471	224	11	u(x	u(x	NOUN
ejpam-3471	224	12	,	,	PUNCT
ejpam-3471	224	13	y	y	PROPN
ejpam-3471	224	14	,	,	PUNCT
ejpam-3471	224	15	t	t	PROPN
ejpam-3471	224	16	)	)	PUNCT
ejpam-3471	224	17	=	=	PUNCT
ejpam-3471	225	1	+	+	ADP
ejpam-3471	225	2	∞∑	∞∑	NUM
ejpam-3471	225	3	n=1	n=1	ADP
ejpam-3471	225	4	tn(t	tn(t	NUM
ejpam-3471	225	5	)	)	PUNCT
ejpam-3471	225	6	sin	sin	NOUN
ejpam-3471	225	7	(	(	PUNCT
ejpam-3471	225	8	nπx	nπx	NOUN
ejpam-3471	225	9	l	l	NOUN
ejpam-3471	225	10	)	)	PUNCT
ejpam-3471	225	11	sin	sin	NOUN
ejpam-3471	225	12	(	(	PUNCT
ejpam-3471	225	13	nπy	nπy	PROPN
ejpam-3471	225	14	l	l	PROPN
ejpam-3471	225	15	)	)	PUNCT
ejpam-3471	225	16	(	(	PUNCT
ejpam-3471	225	17	52	52	NUM
ejpam-3471	225	18	)	)	PUNCT
ejpam-3471	225	19	such	such	ADJ
ejpam-3471	225	20	r.	r.	PROPN
ejpam-3471	225	21	yaro	yaro	PROPN
ejpam-3471	225	22	,	,	PUNCT
ejpam-3471	225	23	y.	y.	PROPN
ejpam-3471	225	24	paré	paré	NOUN
ejpam-3471	225	25	,	,	PUNCT
ejpam-3471	225	26	b.	b.	PROPN
ejpam-3471	225	27	abbo	abbo	PROPN
ejpam-3471	225	28	/	/	SYM
ejpam-3471	225	29	eur	eur	PROPN
ejpam-3471	225	30	.	.	PUNCT
ejpam-3471	226	1	j.	j.	PROPN
ejpam-3471	226	2	pure	pure	PROPN
ejpam-3471	226	3	appl	appl	PROPN
ejpam-3471	226	4	.	.	PROPN
ejpam-3471	226	5	math	math	PROPN
ejpam-3471	226	6	,	,	PUNCT
ejpam-3471	226	7	12	12	NUM
ejpam-3471	226	8	(	(	PUNCT
ejpam-3471	226	9	3	3	NUM
ejpam-3471	226	10	)	)	PUNCT
ejpam-3471	226	11	(	(	PUNCT
ejpam-3471	226	12	2019	2019	NUM
ejpam-3471	226	13	)	)	PUNCT
ejpam-3471	226	14	,	,	PUNCT
ejpam-3471	226	15	1260	1260	NUM
ejpam-3471	226	16	-	-	SYM
ejpam-3471	226	17	1276	1276	NUM
ejpam-3471	226	18	1274	1274	NUM
ejpam-3471	226	19			PRON
ejpam-3471	226	20	u(x	u(x	VERB
ejpam-3471	226	21	;	;	PUNCT
ejpam-3471	226	22	y	y	PROPN
ejpam-3471	226	23	,	,	PUNCT
ejpam-3471	226	24	0	0	NUM
ejpam-3471	226	25	)	)	PUNCT
ejpam-3471	226	26	=	=	SYM
ejpam-3471	227	1	f1(x	f1(x	PROPN
ejpam-3471	227	2	,	,	PUNCT
ejpam-3471	227	3	y	y	NOUN
ejpam-3471	227	4	)	)	PUNCT
ejpam-3471	227	5	=	=	NOUN
ejpam-3471	228	1	sin	sin	NOUN
ejpam-3471	228	2	(	(	PUNCT
ejpam-3471	228	3	nπx	nπx	NOUN
ejpam-3471	228	4	l	l	NOUN
ejpam-3471	228	5	)	)	PUNCT
ejpam-3471	228	6	sin	sin	NOUN
ejpam-3471	228	7	(	(	PUNCT
ejpam-3471	228	8	nπy	nπy	NOUN
ejpam-3471	228	9	l	l	PROPN
ejpam-3471	228	10	)	)	PUNCT
ejpam-3471	228	11	and	and	CCONJ
ejpam-3471	228	12	ut(x	ut(x	NOUN
ejpam-3471	228	13	,	,	PUNCT
ejpam-3471	228	14	y	y	NOUN
ejpam-3471	228	15	,	,	PUNCT
ejpam-3471	228	16	0	0	NUM
ejpam-3471	228	17	)	)	PUNCT
ejpam-3471	228	18	=	=	SYM
ejpam-3471	229	1	f2(x	f2(x	PROPN
ejpam-3471	229	2	,	,	PUNCT
ejpam-3471	229	3	y	y	NOUN
ejpam-3471	229	4	)	)	PUNCT
ejpam-3471	229	5	=	=	SYM
ejpam-3471	229	6	0	0	NUM
ejpam-3471	230	1	we	we	PRON
ejpam-3471	230	2	have	have	VERB
ejpam-3471	230	3			NUM
ejpam-3471	230	4	f1(x	f1(x	PROPN
ejpam-3471	230	5	,	,	PUNCT
ejpam-3471	230	6	y	y	NOUN
ejpam-3471	230	7	)	)	PUNCT
ejpam-3471	230	8	=	=	PUNCT
ejpam-3471	231	1	+	+	ADP
ejpam-3471	231	2	∞∑	∞∑	NUM
ejpam-3471	231	3	n=1	n=1	PART
ejpam-3471	231	4	αn	αn	NOUN
ejpam-3471	231	5	sin	sin	NOUN
ejpam-3471	231	6	(	(	PUNCT
ejpam-3471	231	7	nπx	nπx	NOUN
ejpam-3471	231	8	l	l	NOUN
ejpam-3471	231	9	)	)	PUNCT
ejpam-3471	231	10	sin	sin	NOUN
ejpam-3471	231	11	(	(	PUNCT
ejpam-3471	231	12	nπy	nπy	NOUN
ejpam-3471	231	13	l	l	PROPN
ejpam-3471	231	14	)	)	PUNCT
ejpam-3471	231	15	and	and	CCONJ
ejpam-3471	231	16	αn	αn	NOUN
ejpam-3471	231	17	=	=	SYM
ejpam-3471	231	18	∫	∫	PROPN
ejpam-3471	231	19	l	l	NOUN
ejpam-3471	231	20	0	0	NUM
ejpam-3471	231	21	.	.	PUNCT
ejpam-3471	231	22	∫	∫	PROPN
ejpam-3471	232	1	l	l	NOUN
ejpam-3471	232	2	0	0	PUNCT
ejpam-3471	233	1	f1(x	f1(x	PROPN
ejpam-3471	233	2	,	,	PUNCT
ejpam-3471	233	3	y	y	NOUN
ejpam-3471	233	4	)	)	PUNCT
ejpam-3471	233	5	sin	sin	NOUN
ejpam-3471	233	6	(	(	PUNCT
ejpam-3471	233	7	nπx	nπx	NOUN
ejpam-3471	233	8	l	l	NOUN
ejpam-3471	233	9	)	)	PUNCT
ejpam-3471	233	10	sin	sin	NOUN
ejpam-3471	233	11	(	(	PUNCT
ejpam-3471	233	12	nπy	nπy	PROPN
ejpam-3471	233	13	l	l	PROPN
ejpam-3471	233	14	)	)	PUNCT
ejpam-3471	233	15	dxdy	dxdy	PROPN
ejpam-3471	233	16	(	(	PUNCT
ejpam-3471	233	17	53	53	NUM
ejpam-3471	233	18	)	)	PUNCT
ejpam-3471	233	19	then	then	ADV
ejpam-3471	233	20	by	by	ADP
ejpam-3471	233	21	unfolding	unfold	VERB
ejpam-3471	233	22	,	,	PUNCT
ejpam-3471	233	23	we	we	PRON
ejpam-3471	233	24	get	get	VERB
ejpam-3471	233	25	α1	α1	PROPN
ejpam-3471	233	26	=	=	SYM
ejpam-3471	233	27	∫	∫	PROPN
ejpam-3471	233	28	l	l	NOUN
ejpam-3471	233	29	0	0	NUM
ejpam-3471	233	30	.	.	PUNCT
ejpam-3471	234	1	sin2	sin2	NOUN
ejpam-3471	234	2	(	(	PUNCT
ejpam-3471	234	3	πx	πx	NOUN
ejpam-3471	234	4	l	l	NOUN
ejpam-3471	234	5	)	)	PUNCT
ejpam-3471	235	1	dx	dx	PROPN
ejpam-3471	236	1	∫	∫	PROPN
ejpam-3471	236	2	l	l	PROPN
ejpam-3471	236	3	0	0	NUM
ejpam-3471	236	4	sin2	sin2	NOUN
ejpam-3471	236	5	(	(	PUNCT
ejpam-3471	236	6	πy	πy	NOUN
ejpam-3471	236	7	l	l	NOUN
ejpam-3471	236	8	)	)	PUNCT
ejpam-3471	236	9	dy	dy	NOUN
ejpam-3471	236	10	=	=	SYM
ejpam-3471	236	11	1	1	NUM
ejpam-3471	236	12	and	and	CCONJ
ejpam-3471	236	13	αn	αn	NOUN
ejpam-3471	236	14	=	=	SYM
ejpam-3471	236	15	∫	∫	PROPN
ejpam-3471	236	16	l	l	NOUN
ejpam-3471	236	17	0	0	NUM
ejpam-3471	236	18	.	.	PUNCT
ejpam-3471	237	1	∫	∫	PROPN
ejpam-3471	238	1	l	l	NOUN
ejpam-3471	238	2	0	0	PUNCT
ejpam-3471	239	1	f1(x	f1(x	PROPN
ejpam-3471	239	2	,	,	PUNCT
ejpam-3471	239	3	y	y	NOUN
ejpam-3471	239	4	)	)	PUNCT
ejpam-3471	239	5	sin	sin	NOUN
ejpam-3471	239	6	(	(	PUNCT
ejpam-3471	239	7	nπx	nπx	NOUN
ejpam-3471	239	8	l	l	NOUN
ejpam-3471	239	9	)	)	PUNCT
ejpam-3471	239	10	sin	sin	NOUN
ejpam-3471	239	11	(	(	PUNCT
ejpam-3471	239	12	nπy	nπy	PROPN
ejpam-3471	239	13	l	l	PROPN
ejpam-3471	239	14	)	)	PUNCT
ejpam-3471	239	15	dxdy	dxdy	PROPN
ejpam-3471	239	16	=	=	SYM
ejpam-3471	239	17	0;∀n	0;∀n	PROPN
ejpam-3471	239	18	6=	6=	NUM
ejpam-3471	239	19	0	0	PUNCT
ejpam-3471	239	20	therefore	therefore	ADV
ejpam-3471	239	21	,	,	PUNCT
ejpam-3471	239	22	we	we	PRON
ejpam-3471	239	23	obtain	obtain	VERB
ejpam-3471	239	24	the	the	DET
ejpam-3471	239	25	exact	exact	ADJ
ejpam-3471	239	26	solution	solution	NOUN
ejpam-3471	239	27	of	of	ADP
ejpam-3471	239	28	the	the	DET
ejpam-3471	239	29	problem	problem	NOUN
ejpam-3471	239	30	(	(	PUNCT
ejpam-3471	239	31	p2	p2	PROPN
ejpam-3471	239	32	)	)	PUNCT
ejpam-3471	239	33	:	:	PUNCT
ejpam-3471	240	1	u(x	u(x	PROPN
ejpam-3471	240	2	,	,	PUNCT
ejpam-3471	240	3	y	y	PROPN
ejpam-3471	240	4	,	,	PUNCT
ejpam-3471	240	5	t	t	PROPN
ejpam-3471	240	6	)	)	PUNCT
ejpam-3471	240	7	=	=	PUNCT
ejpam-3471	241	1	+	+	ADP
ejpam-3471	241	2	∞∑	∞∑	NUM
ejpam-3471	241	3	n=1	n=1	ADP
ejpam-3471	241	4	un(x	un(x	PROPN
ejpam-3471	241	5	,	,	PUNCT
ejpam-3471	241	6	y	y	PROPN
ejpam-3471	241	7	,	,	PUNCT
ejpam-3471	241	8	t	t	PROPN
ejpam-3471	241	9	)	)	PUNCT
ejpam-3471	241	10	=	=	SYM
ejpam-3471	241	11	cos(λ1ct	cos(λ1ct	PROPN
ejpam-3471	241	12	)	)	PUNCT
ejpam-3471	241	13	sin	sin	NOUN
ejpam-3471	241	14	(	(	PUNCT
ejpam-3471	241	15	πx	πx	NOUN
ejpam-3471	241	16	l	l	NOUN
ejpam-3471	241	17	)	)	PUNCT
ejpam-3471	241	18	sin	sin	NOUN
ejpam-3471	241	19	(	(	PUNCT
ejpam-3471	241	20	πy	πy	NOUN
ejpam-3471	241	21	l	l	NOUN
ejpam-3471	241	22	)	)	PUNCT
ejpam-3471	241	23	where	where	SCONJ
ejpam-3471	241	24	λ2n	λ2n	NOUN
ejpam-3471	241	25	=	=	SYM
ejpam-3471	241	26	(	(	PUNCT
ejpam-3471	241	27	nπ	nπ	NOUN
ejpam-3471	241	28	ll	ll	NOUN
ejpam-3471	241	29	)	)	PUNCT
ejpam-3471	241	30	2(l2	2(l2	PROPN
ejpam-3471	242	1	+	+	NUM
ejpam-3471	242	2	l2	l2	NOUN
ejpam-3471	242	3	)	)	PUNCT
ejpam-3471	242	4	(	(	PUNCT
ejpam-3471	242	5	54	54	NUM
ejpam-3471	242	6	)	)	PUNCT
ejpam-3471	242	7	λ1	λ1	PROPN
ejpam-3471	242	8	=	=	PUNCT
ejpam-3471	242	9	nπ	nπ	NOUN
ejpam-3471	242	10	√	√	NOUN
ejpam-3471	242	11	l2	l2	NOUN
ejpam-3471	242	12	+	+	CCONJ
ejpam-3471	242	13	l2	l2	NOUN
ejpam-3471	242	14	ll	ll	NOUN
ejpam-3471	242	15	(	(	PUNCT
ejpam-3471	242	16	55	55	NUM
ejpam-3471	242	17	)	)	PUNCT
ejpam-3471	242	18	therefore	therefore	ADV
ejpam-3471	242	19	,	,	PUNCT
ejpam-3471	242	20	we	we	PRON
ejpam-3471	242	21	obtain	obtain	VERB
ejpam-3471	242	22	the	the	DET
ejpam-3471	242	23	exact	exact	ADJ
ejpam-3471	242	24	solution	solution	NOUN
ejpam-3471	242	25	of	of	ADP
ejpam-3471	242	26	the	the	DET
ejpam-3471	242	27	problem	problem	NOUN
ejpam-3471	242	28	(	(	PUNCT
ejpam-3471	242	29	p2	p2	PROPN
ejpam-3471	242	30	)	)	PUNCT
ejpam-3471	242	31	:	:	PUNCT
ejpam-3471	243	1	u(x	u(x	PROPN
ejpam-3471	243	2	,	,	PUNCT
ejpam-3471	243	3	y	y	PROPN
ejpam-3471	243	4	,	,	PUNCT
ejpam-3471	243	5	t	t	PROPN
ejpam-3471	243	6	)	)	PUNCT
ejpam-3471	243	7	=	=	X
ejpam-3471	243	8	sin	sin	NOUN
ejpam-3471	243	9	(	(	PUNCT
ejpam-3471	243	10	πx	πx	NOUN
ejpam-3471	243	11	l	l	NOUN
ejpam-3471	243	12	)	)	PUNCT
ejpam-3471	243	13	sin	sin	NOUN
ejpam-3471	243	14	(	(	PUNCT
ejpam-3471	243	15	πy	πy	NOUN
ejpam-3471	243	16	l	l	NOUN
ejpam-3471	243	17	)	)	PUNCT
ejpam-3471	244	1	cos	cos	PROPN
ejpam-3471	244	2	(	(	PUNCT
ejpam-3471	244	3	cπt	cπt	PART
ejpam-3471	244	4	√	√	VERB
ejpam-3471	244	5	l2	l2	NOUN
ejpam-3471	244	6	+	+	CCONJ
ejpam-3471	244	7	l2	l2	NOUN
ejpam-3471	244	8	ll	ll	NOUN
ejpam-3471	244	9	)	)	PUNCT
ejpam-3471	244	10	(	(	PUNCT
ejpam-3471	244	11	56	56	X
ejpam-3471	244	12	)	)	PUNCT
ejpam-3471	244	13	we	we	PRON
ejpam-3471	244	14	can	can	AUX
ejpam-3471	244	15	noticed	notice	VERB
ejpam-3471	244	16	that	that	SCONJ
ejpam-3471	244	17	if	if	SCONJ
ejpam-3471	244	18	we	we	PRON
ejpam-3471	244	19	choose	choose	VERB
ejpam-3471	244	20	λ2	λ2	NOUN
ejpam-3471	244	21	and	and	CCONJ
ejpam-3471	244	22	µ2	µ2	PROPN
ejpam-3471	244	23	instead	instead	ADV
ejpam-3471	244	24	of	of	ADP
ejpam-3471	244	25	−λ2	−λ2	NOUN
ejpam-3471	244	26	and	and	CCONJ
ejpam-3471	244	27	−µ2	−µ2	PROPN
ejpam-3471	244	28	the	the	DET
ejpam-3471	244	29	solution	solution	NOUN
ejpam-3471	244	30	of	of	ADP
ejpam-3471	244	31	the	the	DET
ejpam-3471	244	32	equation	equation	NOUN
ejpam-3471	244	33	do	do	AUX
ejpam-3471	244	34	n’t	not	PART
ejpam-3471	244	35	verify	verify	VERB
ejpam-3471	244	36	the	the	DET
ejpam-3471	244	37	initial	initial	ADJ
ejpam-3471	244	38	condition	condition	NOUN
ejpam-3471	244	39	:	:	PUNCT
ejpam-3471	244	40	r.	r.	PROPN
ejpam-3471	244	41	yaro	yaro	PROPN
ejpam-3471	244	42	,	,	PUNCT
ejpam-3471	244	43	y.	y.	PROPN
ejpam-3471	244	44	paré	paré	NOUN
ejpam-3471	244	45	,	,	PUNCT
ejpam-3471	244	46	b.	b.	PROPN
ejpam-3471	244	47	abbo	abbo	PROPN
ejpam-3471	244	48	/	/	SYM
ejpam-3471	244	49	eur	eur	PROPN
ejpam-3471	244	50	.	.	PUNCT
ejpam-3471	245	1	j.	j.	PROPN
ejpam-3471	245	2	pure	pure	PROPN
ejpam-3471	245	3	appl	appl	PROPN
ejpam-3471	245	4	.	.	PROPN
ejpam-3471	245	5	math	math	PROPN
ejpam-3471	245	6	,	,	PUNCT
ejpam-3471	245	7	12	12	NUM
ejpam-3471	245	8	(	(	PUNCT
ejpam-3471	245	9	3	3	NUM
ejpam-3471	245	10	)	)	PUNCT
ejpam-3471	245	11	(	(	PUNCT
ejpam-3471	245	12	2019	2019	NUM
ejpam-3471	245	13	)	)	PUNCT
ejpam-3471	245	14	,	,	PUNCT
ejpam-3471	245	15	1260	1260	NUM
ejpam-3471	245	16	-	-	SYM
ejpam-3471	245	17	1276	1276	NUM
ejpam-3471	245	18	1275	1275	NUM
ejpam-3471	245	19	u(0	u(0	PROPN
ejpam-3471	245	20	,	,	PUNCT
ejpam-3471	245	21	y	y	PROPN
ejpam-3471	245	22	,	,	PUNCT
ejpam-3471	245	23	t	t	PROPN
ejpam-3471	245	24	)	)	PUNCT
ejpam-3471	245	25	=	=	SYM
ejpam-3471	246	1	u(l	u(l	PROPN
ejpam-3471	246	2	,	,	PUNCT
ejpam-3471	246	3	y	y	PROPN
ejpam-3471	246	4	,	,	PUNCT
ejpam-3471	246	5	0	0	NUM
ejpam-3471	246	6	)	)	PUNCT
ejpam-3471	246	7	=	=	SYM
ejpam-3471	246	8	u(x	u(x	NOUN
ejpam-3471	246	9	,	,	PUNCT
ejpam-3471	246	10	0	0	NUM
ejpam-3471	246	11	,	,	PUNCT
ejpam-3471	246	12	t	t	PROPN
ejpam-3471	246	13	)	)	PUNCT
ejpam-3471	246	14	=	=	SYM
ejpam-3471	246	15	u(x	u(x	NOUN
ejpam-3471	246	16	,	,	PUNCT
ejpam-3471	246	17	l	l	NOUN
ejpam-3471	246	18	,	,	PUNCT
ejpam-3471	246	19	0	0	NUM
ejpam-3471	246	20	)	)	PUNCT
ejpam-3471	246	21	=	=	SYM
ejpam-3471	246	22	0	0	PUNCT
ejpam-3471	247	1	so	so	ADV
ejpam-3471	247	2	choosing	choose	VERB
ejpam-3471	247	3	λ2	λ2	NOUN
ejpam-3471	247	4	and	and	CCONJ
ejpam-3471	247	5	µ2	µ2	PROPN
ejpam-3471	247	6	is	be	AUX
ejpam-3471	247	7	impossible	impossible	ADJ
ejpam-3471	247	8	.	.	PUNCT
ejpam-3471	248	1	where	where	SCONJ
ejpam-3471	248	2			PROPN
ejpam-3471	248	3	a1	a1	NOUN
ejpam-3471	248	4	=	=	SYM
ejpam-3471	248	5	2	2	NUM
ejpam-3471	248	6	l	l	NOUN
ejpam-3471	248	7	∫	∫	PROPN
ejpam-3471	248	8	l	l	NOUN
ejpam-3471	248	9	0	0	NUM
ejpam-3471	248	10	sin2	sin2	NOUN
ejpam-3471	248	11	(	(	PUNCT
ejpam-3471	248	12	πz	πz	X
ejpam-3471	248	13	l	l	NOUN
ejpam-3471	248	14	)	)	PUNCT
ejpam-3471	248	15	dz	dz	PROPN
ejpam-3471	248	16	=	=	NOUN
ejpam-3471	248	17	1	1	NUM
ejpam-3471	248	18	an	an	DET
ejpam-3471	248	19	=	=	SYM
ejpam-3471	248	20	2	2	NUM
ejpam-3471	248	21	l	l	NOUN
ejpam-3471	248	22	∫	∫	NOUN
ejpam-3471	248	23	l	l	NOUN
ejpam-3471	248	24	0	0	PUNCT
ejpam-3471	248	25	ϕ(z	ϕ(z	PROPN
ejpam-3471	248	26	)	)	PUNCT
ejpam-3471	248	27	sin	sin	NOUN
ejpam-3471	248	28	(	(	PUNCT
ejpam-3471	248	29	nπz	nπz	NOUN
ejpam-3471	248	30	l	l	NOUN
ejpam-3471	248	31	)	)	PUNCT
ejpam-3471	248	32	dz	dz	PROPN
ejpam-3471	249	1	=	=	NOUN
ejpam-3471	249	2	0	0	PUNCT
ejpam-3471	250	1	if	if	SCONJ
ejpam-3471	250	2	n	n	NUM
ejpam-3471	250	3	6=	6=	NUM
ejpam-3471	250	4	1	1	NUM
ejpam-3471	250	5	and	and	CCONJ
ejpam-3471	250	6	bn	bn	NOUN
ejpam-3471	250	7	=	=	SYM
ejpam-3471	250	8	2	2	NUM
ejpam-3471	250	9	c	c	NOUN
ejpam-3471	250	10	∫	∫	PROPN
ejpam-3471	250	11	l	l	NOUN
ejpam-3471	250	12	0	0	NUM
ejpam-3471	250	13	sin2	sin2	NOUN
ejpam-3471	250	14	(	(	PUNCT
ejpam-3471	250	15	πz	πz	X
ejpam-3471	250	16	l	l	NOUN
ejpam-3471	250	17	)	)	PUNCT
ejpam-3471	250	18	dz	dz	PROPN
ejpam-3471	250	19	=	=	PUNCT
ejpam-3471	250	20	l	l	NOUN
ejpam-3471	250	21	c	c	NOUN
ejpam-3471	250	22	bn	bn	NOUN
ejpam-3471	250	23	=	=	SYM
ejpam-3471	250	24	2	2	NUM
ejpam-3471	250	25	cnπ	cnπ	NOUN
ejpam-3471	250	26	∫	∫	PROPN
ejpam-3471	250	27	l	l	PROPN
ejpam-3471	250	28	0	0	NUM
ejpam-3471	250	29	φ(z	φ(z	ADJ
ejpam-3471	250	30	)	)	PUNCT
ejpam-3471	250	31	sin	sin	NOUN
ejpam-3471	250	32	(	(	PUNCT
ejpam-3471	250	33	nπz	nπz	NOUN
ejpam-3471	250	34	l	l	NOUN
ejpam-3471	250	35	)	)	PUNCT
ejpam-3471	250	36	dz	dz	PROPN
ejpam-3471	251	1	=	=	NOUN
ejpam-3471	251	2	0	0	PUNCT
ejpam-3471	252	1	if	if	SCONJ
ejpam-3471	252	2	n	n	NUM
ejpam-3471	252	3	6=	6=	NUM
ejpam-3471	252	4	1	1	NUM
ejpam-3471	252	5	we	we	PRON
ejpam-3471	252	6	obtain	obtain	VERB
ejpam-3471	252	7			NUM
ejpam-3471	252	8	a1	a1	NOUN
ejpam-3471	252	9	=	=	NOUN
ejpam-3471	252	10	1	1	NUM
ejpam-3471	252	11	an	an	DET
ejpam-3471	252	12	=	=	SYM
ejpam-3471	252	13	0	0	NUM
ejpam-3471	252	14	∀	∀	NOUN
ejpam-3471	252	15	n	n	NOUN
ejpam-3471	252	16	6=	6=	NUM
ejpam-3471	252	17	1	1	NUM
ejpam-3471	252	18	and	and	CCONJ
ejpam-3471	252	19	bn	bn	NOUN
ejpam-3471	252	20	=	=	NOUN
ejpam-3471	252	21	l	l	NOUN
ejpam-3471	252	22	c	c	NOUN
ejpam-3471	253	1	bn	bn	NOUN
ejpam-3471	253	2	=	=	SYM
ejpam-3471	253	3	0	0	NUM
ejpam-3471	253	4	∀	∀	NOUN
ejpam-3471	253	5	n	n	NOUN
ejpam-3471	253	6	6=	6=	NUM
ejpam-3471	253	7	1	1	NUM
ejpam-3471	253	8	therefore	therefore	ADV
ejpam-3471	253	9	,	,	PUNCT
ejpam-3471	253	10	we	we	PRON
ejpam-3471	253	11	obtain	obtain	VERB
ejpam-3471	253	12	the	the	DET
ejpam-3471	253	13	exact	exact	ADJ
ejpam-3471	253	14	solution	solution	NOUN
ejpam-3471	253	15	of	of	ADP
ejpam-3471	253	16	the	the	DET
ejpam-3471	253	17	problem	problem	NOUN
ejpam-3471	253	18	(	(	PUNCT
ejpam-3471	253	19	p1	p1	PROPN
ejpam-3471	253	20	)	)	PUNCT
ejpam-3471	253	21	:	:	PUNCT
ejpam-3471	254	1	u(x	u(x	PROPN
ejpam-3471	254	2	,	,	PUNCT
ejpam-3471	254	3	t	t	NOUN
ejpam-3471	254	4	)	)	PUNCT
ejpam-3471	254	5	=	=	PUNCT
ejpam-3471	255	1	+	+	ADP
ejpam-3471	255	2	∞∑	∞∑	NUM
ejpam-3471	255	3	n=1	n=1	PROPN
ejpam-3471	255	4	(	(	PUNCT
ejpam-3471	255	5	an	an	DET
ejpam-3471	255	6	cos	cos	PROPN
ejpam-3471	255	7	(	(	PUNCT
ejpam-3471	255	8	cnπt	cnπt	PROPN
ejpam-3471	255	9	l	l	NOUN
ejpam-3471	255	10	)	)	PUNCT
ejpam-3471	256	1	+	+	ADP
ejpam-3471	256	2	bn	bn	X
ejpam-3471	256	3	sin	sin	NOUN
ejpam-3471	256	4	(	(	PUNCT
ejpam-3471	256	5	cnπt	cnπt	PROPN
ejpam-3471	256	6	l	l	NOUN
ejpam-3471	256	7	)	)	PUNCT
ejpam-3471	256	8	)	)	PUNCT
ejpam-3471	256	9	sin	sin	NOUN
ejpam-3471	256	10	(	(	PUNCT
ejpam-3471	256	11	nπx	nπx	NOUN
ejpam-3471	256	12	l	l	NOUN
ejpam-3471	256	13	)	)	PUNCT
ejpam-3471	256	14	(	(	PUNCT
ejpam-3471	256	15	57	57	NUM
ejpam-3471	256	16	)	)	PUNCT
ejpam-3471	256	17	=	=	PRON
ejpam-3471	256	18	(	(	PUNCT
ejpam-3471	256	19	cos	cos	PROPN
ejpam-3471	256	20	(	(	PUNCT
ejpam-3471	256	21	cπt	cπt	PROPN
ejpam-3471	256	22	l	l	NOUN
ejpam-3471	256	23	)	)	PUNCT
ejpam-3471	257	1	+	+	CCONJ
ejpam-3471	257	2	l	l	NOUN
ejpam-3471	257	3	c	c	NOUN
ejpam-3471	257	4	sin	sin	NOUN
ejpam-3471	257	5	(	(	PUNCT
ejpam-3471	257	6	cπt	cπt	PROPN
ejpam-3471	257	7	l	l	NOUN
ejpam-3471	257	8	)	)	PUNCT
ejpam-3471	257	9	)	)	PUNCT
ejpam-3471	257	10	sin	sin	NOUN
ejpam-3471	257	11	(	(	PUNCT
ejpam-3471	257	12	πx	πx	NOUN
ejpam-3471	257	13	l	l	NOUN
ejpam-3471	257	14	)	)	PUNCT
ejpam-3471	257	15	3.3	3.3	NUM
ejpam-3471	257	16	.	.	PUNCT
ejpam-3471	258	1	comparison	comparison	NOUN
ejpam-3471	258	2	of	of	ADP
ejpam-3471	258	3	the	the	DET
ejpam-3471	258	4	solution	solution	NOUN
ejpam-3471	258	5	method	method	PROPN
ejpam-3471	258	6	sba	sba	PROPN
ejpam-3471	258	7	method	method	PROPN
ejpam-3471	258	8	problem	problem	NOUN
ejpam-3471	258	9	1	1	NUM
ejpam-3471	258	10	u(x	u(x	NOUN
ejpam-3471	258	11	,	,	PUNCT
ejpam-3471	258	12	t	t	NOUN
ejpam-3471	258	13	)	)	PUNCT
ejpam-3471	258	14	=	=	SYM
ejpam-3471	259	1	(	(	PUNCT
ejpam-3471	259	2	cos	cos	X
ejpam-3471	259	3	(	(	PUNCT
ejpam-3471	259	4	cπt	cπt	PROPN
ejpam-3471	259	5	l	l	NOUN
ejpam-3471	259	6	)	)	PUNCT
ejpam-3471	260	1	+	+	CCONJ
ejpam-3471	260	2	l	l	NOUN
ejpam-3471	260	3	c	c	NOUN
ejpam-3471	260	4	sin	sin	NOUN
ejpam-3471	260	5	(	(	PUNCT
ejpam-3471	260	6	cπt	cπt	PROPN
ejpam-3471	260	7	l	l	NOUN
ejpam-3471	260	8	)	)	PUNCT
ejpam-3471	260	9	)	)	PUNCT
ejpam-3471	260	10	sin	sin	NOUN
ejpam-3471	260	11	(	(	PUNCT
ejpam-3471	260	12	πx	πx	NOUN
ejpam-3471	260	13	l	l	NOUN
ejpam-3471	260	14	)	)	PUNCT
ejpam-3471	260	15	problem	problem	NOUN
ejpam-3471	260	16	2	2	NUM
ejpam-3471	260	17	u(x	u(x	NOUN
ejpam-3471	260	18	,	,	PUNCT
ejpam-3471	260	19	y	y	PROPN
ejpam-3471	260	20	,	,	PUNCT
ejpam-3471	260	21	t	t	PROPN
ejpam-3471	260	22	)	)	PUNCT
ejpam-3471	260	23	=	=	X
ejpam-3471	260	24	sin	sin	NOUN
ejpam-3471	260	25	(	(	PUNCT
ejpam-3471	260	26	πx	πx	NOUN
ejpam-3471	260	27	l	l	NOUN
ejpam-3471	260	28	)	)	PUNCT
ejpam-3471	260	29	sin	sin	NOUN
ejpam-3471	260	30	(	(	PUNCT
ejpam-3471	260	31	πy	πy	NOUN
ejpam-3471	260	32	l	l	NOUN
ejpam-3471	260	33	)	)	PUNCT
ejpam-3471	261	1	cos	cos	PROPN
ejpam-3471	261	2	(	(	PUNCT
ejpam-3471	261	3	cπt	cπt	PART
ejpam-3471	261	4	√	√	VERB
ejpam-3471	261	5	l2	l2	NOUN
ejpam-3471	261	6	+	+	CCONJ
ejpam-3471	261	7	l2	l2	NOUN
ejpam-3471	261	8	ll	ll	NOUN
ejpam-3471	261	9	)	)	PUNCT
ejpam-3471	261	10	references	reference	VERB
ejpam-3471	261	11	1276	1276	NUM
ejpam-3471	261	12	method	method	NOUN
ejpam-3471	261	13	fourier	fourier	NOUN
ejpam-3471	261	14	method	method	NOUN
ejpam-3471	261	15	problem	problem	NOUN
ejpam-3471	261	16	1	1	NUM
ejpam-3471	261	17	u(x	u(x	NOUN
ejpam-3471	261	18	,	,	PUNCT
ejpam-3471	261	19	t	t	NOUN
ejpam-3471	261	20	)	)	PUNCT
ejpam-3471	261	21	=	=	SYM
ejpam-3471	262	1	(	(	PUNCT
ejpam-3471	262	2	cos	cos	X
ejpam-3471	262	3	(	(	PUNCT
ejpam-3471	262	4	cπt	cπt	PROPN
ejpam-3471	262	5	l	l	NOUN
ejpam-3471	262	6	)	)	PUNCT
ejpam-3471	263	1	+	+	CCONJ
ejpam-3471	263	2	l	l	NOUN
ejpam-3471	263	3	c	c	NOUN
ejpam-3471	263	4	sin	sin	NOUN
ejpam-3471	263	5	(	(	PUNCT
ejpam-3471	263	6	cπt	cπt	PROPN
ejpam-3471	263	7	l	l	NOUN
ejpam-3471	263	8	)	)	PUNCT
ejpam-3471	263	9	)	)	PUNCT
ejpam-3471	263	10	sin	sin	NOUN
ejpam-3471	263	11	(	(	PUNCT
ejpam-3471	263	12	πx	πx	NOUN
ejpam-3471	263	13	l	l	NOUN
ejpam-3471	263	14	)	)	PUNCT
ejpam-3471	263	15	problem	problem	NOUN
ejpam-3471	263	16	2	2	NUM
ejpam-3471	263	17	u(x	u(x	NOUN
ejpam-3471	263	18	,	,	PUNCT
ejpam-3471	263	19	y	y	PROPN
ejpam-3471	263	20	,	,	PUNCT
ejpam-3471	263	21	t	t	PROPN
ejpam-3471	263	22	)	)	PUNCT
ejpam-3471	263	23	=	=	X
ejpam-3471	263	24	sin	sin	NOUN
ejpam-3471	263	25	(	(	PUNCT
ejpam-3471	263	26	πx	πx	NOUN
ejpam-3471	263	27	l	l	NOUN
ejpam-3471	263	28	)	)	PUNCT
ejpam-3471	263	29	sin	sin	NOUN
ejpam-3471	263	30	(	(	PUNCT
ejpam-3471	263	31	πy	πy	NOUN
ejpam-3471	263	32	l	l	NOUN
ejpam-3471	263	33	)	)	PUNCT
ejpam-3471	264	1	cos	cos	PROPN
ejpam-3471	264	2	(	(	PUNCT
ejpam-3471	264	3	cπt	cπt	PART
ejpam-3471	264	4	√	√	VERB
ejpam-3471	264	5	l2	l2	NOUN
ejpam-3471	264	6	+	+	CCONJ
ejpam-3471	264	7	l2	l2	NOUN
ejpam-3471	264	8	ll	ll	NOUN
ejpam-3471	264	9	)	)	PUNCT
ejpam-3471	264	10	4	4	X
ejpam-3471	264	11	.	.	X
ejpam-3471	264	12	conclusion	conclusion	VERB
ejpam-3471	264	13	the	the	DET
ejpam-3471	264	14	numerical	numerical	PROPN
ejpam-3471	264	15	method	method	PROPN
ejpam-3471	264	16	sba	sba	PROPN
ejpam-3471	264	17	and	and	CCONJ
ejpam-3471	264	18	fourier	fourier	NOUN
ejpam-3471	264	19	method	method	NOUN
ejpam-3471	264	20	or	or	CCONJ
ejpam-3471	264	21	method	method	NOUN
ejpam-3471	264	22	of	of	ADP
ejpam-3471	264	23	separation	separation	NOUN
ejpam-3471	264	24	of	of	ADP
ejpam-3471	264	25	variable	variable	NOUN
ejpam-3471	264	26	permitted	permit	VERB
ejpam-3471	264	27	us	we	PRON
ejpam-3471	264	28	to	to	PART
ejpam-3471	264	29	resolve	resolve	VERB
ejpam-3471	264	30	some	some	DET
ejpam-3471	264	31	partial	partial	ADJ
ejpam-3471	264	32	differential	differential	ADJ
ejpam-3471	264	33	equations	equation	NOUN
ejpam-3471	264	34	in	in	ADP
ejpam-3471	264	35	this	this	DET
ejpam-3471	264	36	paper	paper	NOUN
ejpam-3471	264	37	.	.	PUNCT
ejpam-3471	265	1	in	in	ADP
ejpam-3471	265	2	this	this	DET
ejpam-3471	265	3	paper	paper	NOUN
ejpam-3471	265	4	,	,	PUNCT
ejpam-3471	265	5	we	we	PRON
ejpam-3471	265	6	showed	show	VERB
ejpam-3471	265	7	that	that	SCONJ
ejpam-3471	265	8	using	use	VERB
ejpam-3471	265	9	the	the	DET
ejpam-3471	265	10	both	both	DET
ejpam-3471	265	11	methods	method	NOUN
ejpam-3471	265	12	,	,	PUNCT
ejpam-3471	265	13	we	we	PRON
ejpam-3471	265	14	get	get	VERB
ejpam-3471	265	15	the	the	DET
ejpam-3471	265	16	same	same	ADJ
ejpam-3471	265	17	solution	solution	NOUN
ejpam-3471	265	18	.	.	PUNCT
ejpam-3471	266	1	there	there	PRON
ejpam-3471	266	2	are	be	VERB
ejpam-3471	266	3	then	then	ADV
ejpam-3471	266	4	some	some	DET
ejpam-3471	266	5	very	very	ADV
ejpam-3471	266	6	powerful	powerful	ADJ
ejpam-3471	266	7	numerical	numerical	ADJ
ejpam-3471	266	8	tools	tool	NOUN
ejpam-3471	266	9	of	of	ADP
ejpam-3471	266	10	analysis	analysis	NOUN
ejpam-3471	266	11	for	for	ADP
ejpam-3471	266	12	the	the	DET
ejpam-3471	266	13	resolution	resolution	NOUN
ejpam-3471	266	14	of	of	ADP
ejpam-3471	266	15	partial	partial	ADJ
ejpam-3471	266	16	differential	differential	ADJ
ejpam-3471	266	17	equations	equation	NOUN
ejpam-3471	266	18	.	.	PUNCT
ejpam-3471	267	1	references	reference	NOUN
ejpam-3471	267	2	[	[	X
ejpam-3471	267	3	1	1	NUM
ejpam-3471	267	4	]	]	PUNCT
ejpam-3471	267	5	k.	k.	PROPN
ejpam-3471	267	6	abbaoui	abbaoui	PROPN
ejpam-3471	267	7	and	and	CCONJ
ejpam-3471	267	8	y.	y.	PROPN
ejpam-3471	267	9	cherruault	cherruault	PROPN
ejpam-3471	267	10	.	.	PUNCT
ejpam-3471	268	1	convergence	convergence	NOUN
ejpam-3471	268	2	of	of	ADP
ejpam-3471	268	3	adomian	adomian	NOUN
ejpam-3471	268	4	method	method	NOUN
ejpam-3471	268	5	applied	apply	VERB
ejpam-3471	268	6	to	to	ADP
ejpam-3471	268	7	differential	differential	ADJ
ejpam-3471	268	8	equations	equation	NOUN
ejpam-3471	268	9	.	.	PUNCT
ejpam-3471	269	1	math	math	NOUN
ejpam-3471	269	2	.	.	PUNCT
ejpam-3471	270	1	comput	comput	NOUN
ejpam-3471	270	2	.	.	PUNCT
ejpam-3471	271	1	modelling	modelling	NOUN
ejpam-3471	271	2	,	,	PUNCT
ejpam-3471	271	3	28(5):103–109	28(5):103–109	NUM
ejpam-3471	271	4	,	,	PUNCT
ejpam-3471	271	5	1994	1994	NUM
ejpam-3471	271	6	.	.	PUNCT
ejpam-3471	272	1	[	[	X
ejpam-3471	272	2	2	2	NUM
ejpam-3471	272	3	]	]	PUNCT
ejpam-3471	272	4	k.	k.	PROPN
ejpam-3471	272	5	abbaoui	abbaoui	PROPN
ejpam-3471	272	6	and	and	CCONJ
ejpam-3471	272	7	y.	y.	PROPN
ejpam-3471	272	8	cherruault	cherruault	PROPN
ejpam-3471	272	9	.	.	PUNCT
ejpam-3471	273	1	the	the	DET
ejpam-3471	273	2	decomposition	decomposition	NOUN
ejpam-3471	273	3	method	method	NOUN
ejpam-3471	273	4	applied	apply	VERB
ejpam-3471	273	5	to	to	ADP
ejpam-3471	273	6	the	the	DET
ejpam-3471	273	7	cauchy	cauchy	PROPN
ejpam-3471	273	8	problem	problem	NOUN
ejpam-3471	273	9	.	.	PUNCT
ejpam-3471	274	1	kybernetes	kybernete	NOUN
ejpam-3471	274	2	,	,	PUNCT
ejpam-3471	274	3	28(1):68–74	28(1):68–74	NUM
ejpam-3471	274	4	,	,	PUNCT
ejpam-3471	274	5	1999	1999	NUM
ejpam-3471	274	6	.	.	PUNCT
ejpam-3471	275	1	[	[	X
ejpam-3471	275	2	3	3	X
ejpam-3471	275	3	]	]	X
ejpam-3471	275	4	b.	b.	PROPN
ejpam-3471	275	5	abbo	abbo	PROPN
ejpam-3471	275	6	,	,	PUNCT
ejpam-3471	275	7	n.	n.	PROPN
ejpam-3471	275	8	ngarhasta	ngarhasta	PROPN
ejpam-3471	275	9	,	,	PUNCT
ejpam-3471	275	10	b.	b.	PROPN
ejpam-3471	275	11	mampassi	mampassi	PROPN
ejpam-3471	275	12	,	,	PUNCT
ejpam-3471	275	13	b.some	b.some	NOUN
ejpam-3471	275	14	,	,	PUNCT
ejpam-3471	275	15	and	and	CCONJ
ejpam-3471	275	16	l.	l.	PROPN
ejpam-3471	275	17	some	some	PRON
ejpam-3471	275	18	.	.	PUNCT
ejpam-3471	276	1	a	a	DET
ejpam-3471	276	2	new	new	ADJ
ejpam-3471	276	3	approach	approach	NOUN
ejpam-3471	276	4	of	of	ADP
ejpam-3471	276	5	the	the	DET
ejpam-3471	276	6	adomian	adomian	NOUN
ejpam-3471	276	7	algorithm	algorithm	NOUN
ejpam-3471	276	8	for	for	ADP
ejpam-3471	276	9	solving	solve	VERB
ejpam-3471	276	10	nonlinear	nonlinear	ADJ
ejpam-3471	276	11	ordinary	ordinary	ADJ
ejpam-3471	276	12	or	or	CCONJ
ejpam-3471	276	13	partial	partial	ADJ
ejpam-3471	276	14	differential	differential	ADJ
ejpam-3471	276	15	equations	equation	NOUN
ejpam-3471	276	16	.	.	PUNCT
ejpam-3471	277	1	far	far	PROPN
ejpam-3471	277	2	east	east	PROPN
ejpam-3471	277	3	j.appl.math	j.appl.math	PROPN
ejpam-3471	277	4	,	,	PUNCT
ejpam-3471	277	5	23(3):299–312	23(3):299–312	NUM
ejpam-3471	277	6	,	,	PUNCT
ejpam-3471	277	7	2006	2006	NUM
ejpam-3471	277	8	.	.	PUNCT
ejpam-3471	278	1	[	[	X
ejpam-3471	278	2	4	4	X
ejpam-3471	278	3	]	]	PUNCT
ejpam-3471	278	4	pierre	pierre	X
ejpam-3471	278	5	baki	baki	PROPN
ejpam-3471	278	6	-	-	PUNCT
ejpam-3471	278	7	tangou	tangou	VERB
ejpam-3471	278	8	and	and	CCONJ
ejpam-3471	278	9	gabriel	gabriel	PROPN
ejpam-3471	278	10	bissanga	bissanga	PROPN
ejpam-3471	278	11	.	.	PUNCT
ejpam-3471	279	1	application	application	NOUN
ejpam-3471	279	2	of	of	ADP
ejpam-3471	279	3	adomian	adomian	ADJ
ejpam-3471	279	4	decomposition	decomposition	NOUN
ejpam-3471	279	5	method	method	NOUN
ejpam-3471	279	6	to	to	ADP
ejpam-3471	279	7	solving	solve	VERB
ejpam-3471	279	8	the	the	DET
ejpam-3471	279	9	duffing	duffing	NOUN
ejpam-3471	279	10	-	-	PUNCT
ejpam-3471	279	11	van	van	PROPN
ejpam-3471	279	12	der	der	ADJ
ejpam-3471	279	13	pol	pol	NOUN
ejpam-3471	279	14	equation	equation	NOUN
ejpam-3471	279	15	.	.	PUNCT
ejpam-3471	280	1	communications	communication	NOUN
ejpam-3471	280	2	in	in	ADP
ejpam-3471	280	3	mathematical	mathematical	ADJ
ejpam-3471	280	4	analysis	analysis	NOUN
ejpam-3471	280	5	,	,	PUNCT
ejpam-3471	280	6	4(1):30–40	4(1):30–40	NUM
ejpam-3471	280	7	,	,	PUNCT
ejpam-3471	280	8	2008	2008	NUM
ejpam-3471	280	9	.	.	PUNCT
ejpam-3471	281	1	[	[	X
ejpam-3471	281	2	5	5	NUM
ejpam-3471	281	3	]	]	PUNCT
ejpam-3471	281	4	francis	francis	PROPN
ejpam-3471	281	5	bassono	bassono	PROPN
ejpam-3471	281	6	,	,	PUNCT
ejpam-3471	281	7	pare	pare	PROPN
ejpam-3471	281	8	youssouf	youssouf	PROPN
ejpam-3471	281	9	,	,	PUNCT
ejpam-3471	281	10	gabriel	gabriel	PROPN
ejpam-3471	281	11	bissanga	bissanga	PROPN
ejpam-3471	281	12	,	,	PUNCT
ejpam-3471	281	13	and	and	CCONJ
ejpam-3471	281	14	blaise	blaise	PROPN
ejpam-3471	281	15	some	some	PRON
ejpam-3471	281	16	.	.	PUNCT
ejpam-3471	282	1	application	application	NOUN
ejpam-3471	282	2	of	of	ADP
ejpam-3471	282	3	the	the	DET
ejpam-3471	282	4	adomian	adomian	NOUN
ejpam-3471	282	5	decomposition	decomposition	NOUN
ejpam-3471	282	6	method	method	NOUN
ejpam-3471	282	7	and	and	CCONJ
ejpam-3471	282	8	the	the	DET
ejpam-3471	282	9	perturbation	perturbation	NOUN
ejpam-3471	282	10	method	method	NOUN
ejpam-3471	282	11	to	to	ADP
ejpam-3471	282	12	solving	solve	VERB
ejpam-3471	282	13	a	a	DET
ejpam-3471	282	14	sytem	sytem	NOUN
ejpam-3471	282	15	of	of	ADP
ejpam-3471	282	16	perturbation	perturbation	NOUN
ejpam-3471	282	17	equations	equation	NOUN
ejpam-3471	282	18	.	.	PUNCT
ejpam-3471	283	1	far	far	PROPN
ejpam-3471	283	2	east	east	PROPN
ejpam-3471	283	3	journal	journal	PROPN
ejpam-3471	283	4	of	of	ADP
ejpam-3471	283	5	applied	apply	VERB
ejpam-3471	283	6	mathematics	mathematic	NOUN
ejpam-3471	283	7	,	,	PUNCT
ejpam-3471	283	8	72(2):91–99	72(2):91–99	NUM
ejpam-3471	283	9	,	,	PUNCT
ejpam-3471	283	10	2012	2012	NUM
ejpam-3471	283	11	.	.	PUNCT
ejpam-3471	284	1	[	[	X
ejpam-3471	284	2	6	6	NUM
ejpam-3471	284	3	]	]	PUNCT
ejpam-3471	284	4	m.	m.	NOUN
ejpam-3471	284	5	hussain	hussain	PROPN
ejpam-3471	284	6	and	and	CCONJ
ejpam-3471	284	7	majid	majid	PROPN
ejpam-3471	284	8	khan	khan	PROPN
ejpam-3471	284	9	.	.	PUNCT
ejpam-3471	285	1	modified	modify	VERB
ejpam-3471	285	2	laplace	laplace	NOUN
ejpam-3471	285	3	decomposition	decomposition	NOUN
ejpam-3471	285	4	method	method	NOUN
ejpam-3471	285	5	.	.	PUNCT
ejpam-3471	286	1	applied	apply	VERB
ejpam-3471	286	2	mathematical	mathematical	ADJ
ejpam-3471	286	3	sciences	sciences	PROPN
ejpam-3471	286	4	,	,	PUNCT
ejpam-3471	286	5	4(36):1769–1783	4(36):1769–1783	NUM
ejpam-3471	286	6	,	,	PUNCT
ejpam-3471	286	7	2010	2010	NUM
ejpam-3471	286	8	.	.	PUNCT
ejpam-3471	287	1	[	[	X
ejpam-3471	287	2	7	7	X
ejpam-3471	287	3	]	]	X
ejpam-3471	287	4	s.	s.	PROPN
ejpam-3471	287	5	khelifa	khelifa	PROPN
ejpam-3471	287	6	and	and	CCONJ
ejpam-3471	287	7	yves	yve	NOUN
ejpam-3471	287	8	cherruault	cherruault	NOUN
ejpam-3471	287	9	.	.	PUNCT
ejpam-3471	288	1	the	the	DET
ejpam-3471	288	2	decomposition	decomposition	NOUN
ejpam-3471	288	3	method	method	NOUN
ejpam-3471	288	4	for	for	ADP
ejpam-3471	288	5	solving	solve	VERB
ejpam-3471	288	6	first	first	ADJ
ejpam-3471	288	7	order	order	NOUN
ejpam-3471	288	8	partial	partial	ADJ
ejpam-3471	288	9	differential	differential	NOUN
ejpam-3471	288	10	equations	equation	NOUN
ejpam-3471	288	11	.	.	PUNCT
ejpam-3471	289	1	kybernetes	kybernete	NOUN
ejpam-3471	289	2	,	,	PUNCT
ejpam-3471	289	3	31(6):844–871	31(6):844–871	PROPN
ejpam-3471	289	4	,	,	PUNCT
ejpam-3471	289	5	2002	2002	NUM
ejpam-3471	289	6	.	.	PUNCT
ejpam-3471	290	1	[	[	X
ejpam-3471	290	2	8	8	NUM
ejpam-3471	290	3	]	]	X
ejpam-3471	290	4	n.	n.	NOUN
ejpam-3471	290	5	ngarhasta	ngarhasta	PROPN
ejpam-3471	290	6	,	,	PUNCT
ejpam-3471	290	7	b.	b.	PROPN
ejpam-3471	290	8	some	some	PRON
ejpam-3471	290	9	,	,	PUNCT
ejpam-3471	290	10	k.	k.	PROPN
ejpam-3471	290	11	abbaoui	abbaoui	PROPN
ejpam-3471	290	12	,	,	PUNCT
ejpam-3471	290	13	and	and	CCONJ
ejpam-3471	290	14	y.	y.	PROPN
ejpam-3471	290	15	cherruault	cherruault	PROPN
ejpam-3471	290	16	.	.	PUNCT
ejpam-3471	291	1	new	new	ADJ
ejpam-3471	291	2	numerical	numerical	PROPN
ejpam-3471	291	3	study	study	PROPN
ejpam-3471	291	4	of	of	ADP
ejpam-3471	291	5	adomian	adomian	PROPN
ejpam-3471	291	6	method	method	NOUN
ejpam-3471	291	7	applied	apply	VERB
ejpam-3471	291	8	to	to	ADP
ejpam-3471	291	9	a	a	DET
ejpam-3471	291	10	diffusion	diffusion	NOUN
ejpam-3471	291	11	model	model	NOUN
ejpam-3471	291	12	.	.	PUNCT
ejpam-3471	292	1	kybernetes	kybernete	NOUN
ejpam-3471	292	2	,	,	PUNCT
ejpam-3471	292	3	31(1):61–75	31(1):61–75	NUM
ejpam-3471	292	4	,	,	PUNCT
ejpam-3471	292	5	2002	2002	NUM
ejpam-3471	292	6	.	.	PUNCT
ejpam-3471	293	1	[	[	X
ejpam-3471	293	2	9	9	NUM
ejpam-3471	293	3	]	]	PUNCT
ejpam-3471	293	4	pare	pare	PROPN
ejpam-3471	293	5	youssouf	youssouf	PROPN
ejpam-3471	293	6	,	,	PUNCT
ejpam-3471	293	7	francis	francis	PROPN
ejpam-3471	293	8	bassono	bassono	PROPN
ejpam-3471	293	9	,	,	PUNCT
ejpam-3471	293	10	and	and	CCONJ
ejpam-3471	293	11	blaise	blaise	PROPN
ejpam-3471	293	12	some	some	PRON
ejpam-3471	293	13	.	.	PUNCT
ejpam-3471	294	1	a	a	DET
ejpam-3471	294	2	new	new	ADJ
ejpam-3471	294	3	technique	technique	NOUN
ejpam-3471	294	4	for	for	ADP
ejpam-3471	294	5	numerical	numerical	ADJ
ejpam-3471	294	6	resolution	resolution	NOUN
ejpam-3471	294	7	of	of	ADP
ejpam-3471	294	8	few	few	ADJ
ejpam-3471	294	9	nonlinear	nonlinear	ADJ
ejpam-3471	294	10	integral	integral	ADJ
ejpam-3471	294	11	equations	equation	NOUN
ejpam-3471	294	12	of	of	ADP
ejpam-3471	294	13	fredholm	fredholm	NOUN
ejpam-3471	294	14	by	by	ADP
ejpam-3471	294	15	sba	sba	PROPN
ejpam-3471	294	16	method	method	PROPN
ejpam-3471	294	17	.	.	PUNCT
ejpam-3471	295	1	international	international	ADJ
ejpam-3471	295	2	journal	journal	PROPN
ejpam-3471	295	3	of	of	ADP
ejpam-3471	295	4	applied	apply	VERB
ejpam-3471	295	5	mathematical	mathematical	ADJ
ejpam-3471	295	6	research	research	NOUN
ejpam-3471	295	7	,	,	PUNCT
ejpam-3471	295	8	70(1):21–33	70(1):21–33	NUM
ejpam-3471	295	9	,	,	PUNCT
ejpam-3471	295	10	2012	2012	NUM
ejpam-3471	295	11	.	.	PUNCT