id	sid	tid	token	lemma	pos
ejpam-4403	1	1	european	european	PROPN
ejpam-4403	1	2	journal	journal	PROPN
ejpam-4403	1	3	of	of	ADP
ejpam-4403	1	4	pure	pure	ADJ
ejpam-4403	1	5	and	and	CCONJ
ejpam-4403	1	6	applied	apply	VERB
ejpam-4403	1	7	mathematics	mathematic	NOUN
ejpam-4403	1	8	vol	vol	NOUN
ejpam-4403	1	9	.	.	PROPN
ejpam-4403	2	1	15	15	NUM
ejpam-4403	2	2	,	,	PUNCT
ejpam-4403	2	3	no	no	INTJ
ejpam-4403	2	4	.	.	NOUN
ejpam-4403	2	5	3	3	NUM
ejpam-4403	2	6	,	,	PUNCT
ejpam-4403	2	7	2022	2022	NUM
ejpam-4403	2	8	,	,	PUNCT
ejpam-4403	2	9	1348	1348	NUM
ejpam-4403	2	10	-	-	SYM
ejpam-4403	2	11	1362	1362	NUM
ejpam-4403	2	12	issn	issn	PROPN
ejpam-4403	2	13	1307	1307	NUM
ejpam-4403	2	14	-	-	SYM
ejpam-4403	2	15	5543	5543	NUM
ejpam-4403	2	16	–	–	PUNCT
ejpam-4403	2	17	ejpam.com	ejpam.com	X
ejpam-4403	2	18	published	publish	VERB
ejpam-4403	2	19	by	by	ADP
ejpam-4403	2	20	new	new	PROPN
ejpam-4403	2	21	york	york	PROPN
ejpam-4403	2	22	business	business	PROPN
ejpam-4403	2	23	global	global	PROPN
ejpam-4403	2	24	on	on	ADP
ejpam-4403	2	25	the	the	DET
ejpam-4403	2	26	existence	existence	NOUN
ejpam-4403	2	27	,	,	PUNCT
ejpam-4403	2	28	uniqueness	uniqueness	NOUN
ejpam-4403	2	29	and	and	CCONJ
ejpam-4403	2	30	application	application	NOUN
ejpam-4403	2	31	of	of	ADP
ejpam-4403	2	32	the	the	DET
ejpam-4403	2	33	finite	finite	ADJ
ejpam-4403	2	34	difference	difference	NOUN
ejpam-4403	2	35	method	method	NOUN
ejpam-4403	2	36	for	for	ADP
ejpam-4403	2	37	solving	solve	VERB
ejpam-4403	2	38	cauchy	cauchy	NOUN
ejpam-4403	2	39	-	-	PUNCT
ejpam-4403	2	40	dirichlet	dirichlet	PROPN
ejpam-4403	2	41	problem	problem	NOUN
ejpam-4403	2	42	diogène	diogène	PROPN
ejpam-4403	2	43	vianney	vianney	PROPN
ejpam-4403	2	44	pongui	pongui	PROPN
ejpam-4403	2	45	ngoma1,∗	ngoma1,∗	PROPN
ejpam-4403	2	46	,	,	PUNCT
ejpam-4403	2	47	germain	germain	PROPN
ejpam-4403	2	48	nguimbi1	nguimbi1	PROPN
ejpam-4403	2	49	,	,	PUNCT
ejpam-4403	2	50	vital	vital	ADJ
ejpam-4403	2	51	delmas	delmas	PROPN
ejpam-4403	2	52	mabonzo2	mabonzo2	PROPN
ejpam-4403	2	53	,	,	PUNCT
ejpam-4403	2	54	bienaime	bienaime	NOUN
ejpam-4403	2	55	bervi	bervi	PROPN
ejpam-4403	2	56	bamvi	bamvi	NOUN
ejpam-4403	2	57	madzou	madzou	NOUN
ejpam-4403	2	58	1	1	NUM
ejpam-4403	2	59	ecole	ecole	PROPN
ejpam-4403	2	60	nationale	nationale	PROPN
ejpam-4403	2	61	superieure	superieure	PROPN
ejpam-4403	2	62	polytechnique	polytechnique	PROPN
ejpam-4403	2	63	,	,	PUNCT
ejpam-4403	2	64	marien	marien	PROPN
ejpam-4403	2	65	ngouabi	ngouabi	PROPN
ejpam-4403	2	66	university	university	PROPN
ejpam-4403	2	67	,	,	PUNCT
ejpam-4403	2	68	brazzaville	brazzaville	PROPN
ejpam-4403	2	69	,	,	PUNCT
ejpam-4403	2	70	congo	congo	PROPN
ejpam-4403	2	71	2	2	NUM
ejpam-4403	2	72	ecole	ecole	PROPN
ejpam-4403	2	73	normale	normale	PROPN
ejpam-4403	2	74	superieure	superieure	PROPN
ejpam-4403	2	75	,	,	PUNCT
ejpam-4403	2	76	marien	marien	PROPN
ejpam-4403	2	77	ngouabi	ngouabi	PROPN
ejpam-4403	2	78	university	university	PROPN
ejpam-4403	2	79	,	,	PUNCT
ejpam-4403	2	80	brazzaville	brazzaville	PROPN
ejpam-4403	2	81	,	,	PUNCT
ejpam-4403	2	82	congo	congo	PROPN
ejpam-4403	2	83	abstract	abstract	NOUN
ejpam-4403	2	84	.	.	PUNCT
ejpam-4403	3	1	in	in	ADP
ejpam-4403	3	2	this	this	DET
ejpam-4403	3	3	paper	paper	NOUN
ejpam-4403	3	4	we	we	PRON
ejpam-4403	3	5	treat	treat	VERB
ejpam-4403	3	6	the	the	DET
ejpam-4403	3	7	existence	existence	NOUN
ejpam-4403	3	8	,	,	PUNCT
ejpam-4403	3	9	the	the	DET
ejpam-4403	3	10	uniqueness	uniqueness	NOUN
ejpam-4403	3	11	and	and	CCONJ
ejpam-4403	3	12	the	the	DET
ejpam-4403	3	13	numerical	numerical	ADJ
ejpam-4403	3	14	resolution	resolution	NOUN
ejpam-4403	3	15	of	of	ADP
ejpam-4403	3	16	the	the	DET
ejpam-4403	3	17	problem	problem	NOUN
ejpam-4403	3	18	at	at	ADP
ejpam-4403	3	19	the	the	DET
ejpam-4403	3	20	elliptic	elliptic	ADJ
ejpam-4403	3	21	limits	limit	NOUN
ejpam-4403	3	22	case	case	NOUN
ejpam-4403	3	23	of	of	ADP
ejpam-4403	3	24	the	the	DET
ejpam-4403	3	25	cauchy	cauchy	PROPN
ejpam-4403	3	26	-	-	PUNCT
ejpam-4403	3	27	dirichlet	dirichlet	PROPN
ejpam-4403	3	28	problem	problem	NOUN
ejpam-4403	3	29	of	of	ADP
ejpam-4403	3	30	the	the	DET
ejpam-4403	3	31	type	type	NOUN
ejpam-4403	3	32	the	the	DET
ejpam-4403	3	33	stationary	stationary	ADJ
ejpam-4403	3	34	convection	convection	NOUN
ejpam-4403	3	35	-	-	PUNCT
ejpam-4403	3	36	diffusion	diffusion	NOUN
ejpam-4403	3	37	equation	equation	NOUN
ejpam-4403	3	38	.	.	PUNCT
ejpam-4403	4	1	by	by	ADP
ejpam-4403	4	2	applying	apply	VERB
ejpam-4403	4	3	the	the	DET
ejpam-4403	4	4	lax	lax	PROPN
ejpam-4403	4	5	-	-	PUNCT
ejpam-4403	4	6	milgram	milgram	NOUN
ejpam-4403	4	7	theorem	theorem	NOUN
ejpam-4403	4	8	,	,	PUNCT
ejpam-4403	4	9	we	we	PRON
ejpam-4403	4	10	proved	prove	VERB
ejpam-4403	4	11	the	the	DET
ejpam-4403	4	12	existence	existence	NOUN
ejpam-4403	4	13	and	and	CCONJ
ejpam-4403	4	14	the	the	DET
ejpam-4403	4	15	uniqueness	uniqueness	NOUN
ejpam-4403	4	16	of	of	ADP
ejpam-4403	4	17	the	the	DET
ejpam-4403	4	18	problem	problem	NOUN
ejpam-4403	4	19	,	,	PUNCT
ejpam-4403	4	20	then	then	ADV
ejpam-4403	4	21	we	we	PRON
ejpam-4403	4	22	solved	solve	VERB
ejpam-4403	4	23	the	the	DET
ejpam-4403	4	24	problem	problem	NOUN
ejpam-4403	4	25	numerically	numerically	ADV
ejpam-4403	4	26	by	by	ADP
ejpam-4403	4	27	the	the	DET
ejpam-4403	4	28	finite	finite	ADJ
ejpam-4403	4	29	difference	difference	NOUN
ejpam-4403	4	30	method	method	NOUN
ejpam-4403	4	31	.	.	PUNCT
ejpam-4403	5	1	in	in	ADP
ejpam-4403	5	2	addition	addition	NOUN
ejpam-4403	5	3	,	,	PUNCT
ejpam-4403	5	4	we	we	PRON
ejpam-4403	5	5	solved	solve	VERB
ejpam-4403	5	6	the	the	DET
ejpam-4403	5	7	problem	problem	NOUN
ejpam-4403	5	8	analytically	analytically	ADV
ejpam-4403	5	9	using	use	VERB
ejpam-4403	5	10	the	the	DET
ejpam-4403	5	11	method	method	NOUN
ejpam-4403	5	12	of	of	ADP
ejpam-4403	5	13	variation	variation	NOUN
ejpam-4403	5	14	of	of	ADP
ejpam-4403	5	15	constants	constant	NOUN
ejpam-4403	5	16	.	.	PUNCT
ejpam-4403	6	1	finally	finally	ADV
ejpam-4403	6	2	,	,	PUNCT
ejpam-4403	6	3	we	we	PRON
ejpam-4403	6	4	performed	perform	VERB
ejpam-4403	6	5	a	a	DET
ejpam-4403	6	6	numerical	numerical	ADJ
ejpam-4403	6	7	simulation	simulation	NOUN
ejpam-4403	6	8	of	of	ADP
ejpam-4403	6	9	said	say	VERB
ejpam-4403	6	10	problem	problem	NOUN
ejpam-4403	6	11	to	to	PART
ejpam-4403	6	12	approach	approach	VERB
ejpam-4403	6	13	the	the	DET
ejpam-4403	6	14	exact	exact	ADJ
ejpam-4403	6	15	solution	solution	NOUN
ejpam-4403	6	16	by	by	ADP
ejpam-4403	6	17	the	the	DET
ejpam-4403	6	18	numerical	numerical	ADJ
ejpam-4403	6	19	solution	solution	NOUN
ejpam-4403	6	20	using	use	VERB
ejpam-4403	6	21	the	the	DET
ejpam-4403	6	22	software	software	NOUN
ejpam-4403	6	23	scilab	scilab	VERB
ejpam-4403	6	24	2020	2020	NUM
ejpam-4403	6	25	mathematics	mathematic	NOUN
ejpam-4403	6	26	subject	subject	NOUN
ejpam-4403	6	27	classifications	classification	NOUN
ejpam-4403	6	28	:	:	PUNCT
ejpam-4403	6	29	65m06	65m06	NUM
ejpam-4403	6	30	,	,	PUNCT
ejpam-4403	6	31	65m12	65m12	NUM
ejpam-4403	6	32	,	,	PUNCT
ejpam-4403	6	33	65k05	65k05	NUM
ejpam-4403	6	34	key	key	ADJ
ejpam-4403	6	35	words	word	NOUN
ejpam-4403	6	36	and	and	CCONJ
ejpam-4403	6	37	phrases	phrase	NOUN
ejpam-4403	6	38	:	:	PUNCT
ejpam-4403	6	39	cauchy	cauchy	PROPN
ejpam-4403	6	40	-	-	PUNCT
ejpam-4403	6	41	dirichlet	dirichlet	PROPN
ejpam-4403	6	42	problem	problem	NOUN
ejpam-4403	6	43	,	,	PUNCT
ejpam-4403	6	44	convection	convection	NOUN
ejpam-4403	6	45	-	-	PUNCT
ejpam-4403	6	46	diffusion	diffusion	NOUN
ejpam-4403	6	47	equation	equation	NOUN
ejpam-4403	6	48	,	,	PUNCT
ejpam-4403	6	49	finite	finite	ADJ
ejpam-4403	6	50	difference	difference	NOUN
ejpam-4403	6	51	method	method	NOUN
ejpam-4403	6	52	,	,	PUNCT
ejpam-4403	6	53	numerical	numerical	PROPN
ejpam-4403	6	54	simulation	simulation	PROPN
ejpam-4403	6	55	1	1	NUM
ejpam-4403	6	56	.	.	PUNCT
ejpam-4403	7	1	introduction	introduction	NOUN
ejpam-4403	7	2	partial	partial	ADJ
ejpam-4403	7	3	differential	differential	NOUN
ejpam-4403	7	4	equations	equation	NOUN
ejpam-4403	7	5	(	(	PUNCT
ejpam-4403	7	6	pdes	pde	NOUN
ejpam-4403	7	7	)	)	PUNCT
ejpam-4403	7	8	are	be	AUX
ejpam-4403	7	9	used	use	VERB
ejpam-4403	7	10	in	in	ADP
ejpam-4403	7	11	several	several	ADJ
ejpam-4403	7	12	fields	field	NOUN
ejpam-4403	7	13	,	,	PUNCT
ejpam-4403	7	14	including	include	VERB
ejpam-4403	7	15	engineering	engineering	NOUN
ejpam-4403	7	16	,	,	PUNCT
ejpam-4403	7	17	mechanics	mechanic	NOUN
ejpam-4403	7	18	,	,	PUNCT
ejpam-4403	7	19	physics	physics	NOUN
ejpam-4403	7	20	,	,	PUNCT
ejpam-4403	7	21	aeronautics	aeronautic	NOUN
ejpam-4403	7	22	,	,	PUNCT
ejpam-4403	7	23	petroleum	petroleum	NOUN
ejpam-4403	7	24	industry	industry	NOUN
ejpam-4403	7	25	,	,	PUNCT
ejpam-4403	7	26	but	but	CCONJ
ejpam-4403	7	27	also	also	ADV
ejpam-4403	7	28	in	in	ADP
ejpam-4403	7	29	economics	economic	NOUN
ejpam-4403	7	30	,	,	PUNCT
ejpam-4403	7	31	chemistry	chemistry	NOUN
ejpam-4403	7	32	,	,	PUNCT
ejpam-4403	7	33	biology	biology	NOUN
ejpam-4403	7	34	;	;	PUNCT
ejpam-4403	7	35	in	in	ADP
ejpam-4403	7	36	medicine	medicine	NOUN
ejpam-4403	7	37	...	...	PUNCT
ejpam-4403	7	38	they	they	PRON
ejpam-4403	7	39	are	be	AUX
ejpam-4403	7	40	defined	define	VERB
ejpam-4403	7	41	in	in	ADP
ejpam-4403	7	42	an	an	DET
ejpam-4403	7	43	open	open	ADJ
ejpam-4403	7	44	ω	ω	NOUN
ejpam-4403	7	45	of	of	ADP
ejpam-4403	7	46	space	space	NOUN
ejpam-4403	7	47	rn	rn	PROPN
ejpam-4403	7	48	,	,	PUNCT
ejpam-4403	7	49	n	n	PRON
ejpam-4403	7	50	≥	≥	NOUN
ejpam-4403	7	51	1	1	NUM
ejpam-4403	7	52	(	(	PUNCT
ejpam-4403	7	53	pfes	pfe	NOUN
ejpam-4403	7	54	integration	integration	NOUN
ejpam-4403	7	55	domain	domain	NOUN
ejpam-4403	7	56	)	)	PUNCT
ejpam-4403	7	57	of	of	ADP
ejpam-4403	7	58	border	border	NOUN
ejpam-4403	7	59	∂ω	∂ω	PROPN
ejpam-4403	7	60	.	.	PUNCT
ejpam-4403	8	1	they	they	PRON
ejpam-4403	8	2	can	can	AUX
ejpam-4403	8	3	be	be	AUX
ejpam-4403	8	4	listed	list	VERB
ejpam-4403	8	5	by	by	ADP
ejpam-4403	8	6	type	type	NOUN
ejpam-4403	8	7	.	.	PUNCT
ejpam-4403	9	1	thus	thus	ADV
ejpam-4403	9	2	,	,	PUNCT
ejpam-4403	9	3	the	the	DET
ejpam-4403	9	4	equations	equation	NOUN
ejpam-4403	9	5	of	of	ADP
ejpam-4403	9	6	the	the	DET
ejpam-4403	9	7	elliptical	elliptical	ADJ
ejpam-4403	9	8	type	type	NOUN
ejpam-4403	9	9	describe	describe	VERB
ejpam-4403	9	10	the	the	DET
ejpam-4403	9	11	phenomena	phenomenon	NOUN
ejpam-4403	9	12	of	of	ADP
ejpam-4403	9	13	stationary	stationary	ADJ
ejpam-4403	9	14	diffusion	diffusion	NOUN
ejpam-4403	9	15	,	,	PUNCT
ejpam-4403	9	16	the	the	DET
ejpam-4403	9	17	equations	equation	NOUN
ejpam-4403	9	18	of	of	ADP
ejpam-4403	9	19	the	the	DET
ejpam-4403	9	20	parabolic	parabolic	ADJ
ejpam-4403	9	21	type	type	NOUN
ejpam-4403	9	22	describe	describe	VERB
ejpam-4403	9	23	the	the	DET
ejpam-4403	9	24	phenomena	phenomenon	NOUN
ejpam-4403	9	25	of	of	ADP
ejpam-4403	9	26	diffusion	diffusion	NOUN
ejpam-4403	9	27	and	and	CCONJ
ejpam-4403	9	28	the	the	DET
ejpam-4403	9	29	equations	equation	NOUN
ejpam-4403	9	30	of	of	ADP
ejpam-4403	9	31	the	the	DET
ejpam-4403	9	32	hyperbolic	hyperbolic	ADJ
ejpam-4403	9	33	type	type	NOUN
ejpam-4403	9	34	describe	describe	VERB
ejpam-4403	9	35	the	the	DET
ejpam-4403	9	36	phenomena	phenomenon	NOUN
ejpam-4403	9	37	of	of	ADP
ejpam-4403	9	38	transport	transport	NOUN
ejpam-4403	9	39	at	at	ADP
ejpam-4403	9	40	finite	finite	ADJ
ejpam-4403	9	41	speed	speed	NOUN
ejpam-4403	9	42	.	.	PUNCT
ejpam-4403	10	1	as	as	ADP
ejpam-4403	10	2	a	a	DET
ejpam-4403	10	3	general	general	ADJ
ejpam-4403	10	4	rule	rule	NOUN
ejpam-4403	10	5	,	,	PUNCT
ejpam-4403	10	6	it	it	PRON
ejpam-4403	10	7	is	be	AUX
ejpam-4403	10	8	difficult	difficult	ADJ
ejpam-4403	10	9	to	to	PART
ejpam-4403	10	10	find	find	VERB
ejpam-4403	10	11	a	a	DET
ejpam-4403	10	12	unique	unique	ADJ
ejpam-4403	10	13	solution	solution	NOUN
ejpam-4403	10	14	to	to	ADP
ejpam-4403	10	15	an	an	DET
ejpam-4403	10	16	edp	edp	NOUN
ejpam-4403	10	17	without	without	ADP
ejpam-4403	10	18	boundary	boundary	ADJ
ejpam-4403	10	19	conditions	condition	NOUN
ejpam-4403	10	20	(	(	PUNCT
ejpam-4403	10	21	additional	additional	ADJ
ejpam-4403	10	22	information	information	NOUN
ejpam-4403	10	23	on	on	ADP
ejpam-4403	10	24	the	the	DET
ejpam-4403	10	25	border	border	NOUN
ejpam-4403	10	26	∂ω	∂ω	PROPN
ejpam-4403	10	27	)	)	PUNCT
ejpam-4403	10	28	.	.	PUNCT
ejpam-4403	11	1	thus	thus	ADV
ejpam-4403	11	2	,	,	PUNCT
ejpam-4403	11	3	we	we	PRON
ejpam-4403	11	4	speak	speak	VERB
ejpam-4403	11	5	of	of	ADP
ejpam-4403	11	6	dirichlet	dirichlet	PROPN
ejpam-4403	11	7	’s	’s	PART
ejpam-4403	11	8	boundary	boundary	ADJ
ejpam-4403	11	9	condition	condition	NOUN
ejpam-4403	11	10	,	,	PUNCT
ejpam-4403	11	11	of	of	ADP
ejpam-4403	11	12	cauchy	cauchy	ADJ
ejpam-4403	11	13	condition	condition	NOUN
ejpam-4403	11	14	(	(	PUNCT
ejpam-4403	11	15	that	that	PRON
ejpam-4403	11	16	is	be	AUX
ejpam-4403	11	17	to	to	PART
ejpam-4403	11	18	say	say	VERB
ejpam-4403	11	19	of	of	ADP
ejpam-4403	11	20	dirichlet	dirichlet	PROPN
ejpam-4403	11	21	type	type	NOUN
ejpam-4403	11	22	on	on	ADP
ejpam-4403	11	23	a	a	DET
ejpam-4403	11	24	part	part	NOUN
ejpam-4403	11	25	of	of	ADP
ejpam-4403	11	26	the	the	DET
ejpam-4403	11	27	edge	edge	NOUN
ejpam-4403	11	28	∂ω	∂ω	PROPN
ejpam-4403	11	29	and	and	CCONJ
ejpam-4403	11	30	of	of	ADP
ejpam-4403	11	31	cauchy	cauchy	ADJ
ejpam-4403	11	32	type	type	NOUN
ejpam-4403	11	33	on	on	ADP
ejpam-4403	11	34	the	the	DET
ejpam-4403	11	35	other	other	ADJ
ejpam-4403	11	36	part	part	NOUN
ejpam-4403	11	37	)	)	PUNCT
ejpam-4403	11	38	.	.	PUNCT
ejpam-4403	12	1	∗corresponding	∗corresponde	VERB
ejpam-4403	12	2	author	author	NOUN
ejpam-4403	12	3	.	.	PUNCT
ejpam-4403	13	1	doi	doi	NOUN
ejpam-4403	13	2	:	:	PUNCT
ejpam-4403	13	3	https://doi.org/10.29020/nybg.ejpam.v15i3.4403	https://doi.org/10.29020/nybg.ejpam.v15i3.4403	NUM
ejpam-4403	13	4	email	email	NOUN
ejpam-4403	13	5	addresses	address	NOUN
ejpam-4403	13	6	:	:	PUNCT
ejpam-4403	13	7	diogene.ponguingoma@umng.cg	diogene.ponguingoma@umng.cg	PROPN
ejpam-4403	13	8	(	(	PUNCT
ejpam-4403	13	9	d.v	d.v	PROPN
ejpam-4403	13	10	.	.	PROPN
ejpam-4403	13	11	pongui	pongui	PROPN
ejpam-4403	13	12	ngoma	ngoma	PROPN
ejpam-4403	13	13	)	)	PUNCT
ejpam-4403	13	14	,	,	PUNCT
ejpam-4403	13	15	germain.nguimbi@umng.cg	germain.nguimbi@umng.cg	NOUN
ejpam-4403	13	16	(	(	PUNCT
ejpam-4403	13	17	g.	g.	PROPN
ejpam-4403	13	18	nguimbi	nguimbi	PROPN
ejpam-4403	13	19	)	)	PUNCT
ejpam-4403	13	20	,	,	PUNCT
ejpam-4403	13	21	vital.mabonzo@umng.cg	vital.mabonzo@umng.cg	NOUN
ejpam-4403	13	22	(	(	PUNCT
ejpam-4403	13	23	v.d	v.d	PROPN
ejpam-4403	13	24	.	.	PROPN
ejpam-4403	13	25	mabonzo	mabonzo	PROPN
ejpam-4403	13	26	)	)	PUNCT
ejpam-4403	13	27	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4403	13	28	1348	1348	NUM
ejpam-4403	14	1	©	©	ADP
ejpam-4403	14	2	2022	2022	NUM
ejpam-4403	14	3	ejpam	ejpam	VERB
ejpam-4403	14	4	all	all	DET
ejpam-4403	14	5	rights	right	NOUN
ejpam-4403	14	6	reserved	reserve	VERB
ejpam-4403	14	7	.	.	PUNCT
ejpam-4403	15	1	d.	d.	PROPN
ejpam-4403	15	2	v.	v.	PROPN
ejpam-4403	15	3	pongui	pongui	PROPN
ejpam-4403	15	4	ngoma	ngoma	PROPN
ejpam-4403	15	5	et	et	PROPN
ejpam-4403	15	6	al	al	PROPN
ejpam-4403	15	7	.	.	PROPN
ejpam-4403	15	8	,	,	PUNCT
ejpam-4403	15	9	/	/	SYM
ejpam-4403	15	10	eur	eur	NOUN
ejpam-4403	15	11	.	.	PUNCT
ejpam-4403	16	1	j.	j.	PROPN
ejpam-4403	16	2	pure	pure	PROPN
ejpam-4403	16	3	appl	appl	PROPN
ejpam-4403	16	4	.	.	PROPN
ejpam-4403	16	5	math	math	PROPN
ejpam-4403	16	6	,	,	PUNCT
ejpam-4403	16	7	15	15	NUM
ejpam-4403	16	8	(	(	PUNCT
ejpam-4403	16	9	3	3	NUM
ejpam-4403	16	10	)	)	PUNCT
ejpam-4403	16	11	(	(	PUNCT
ejpam-4403	16	12	2022	2022	NUM
ejpam-4403	16	13	)	)	PUNCT
ejpam-4403	16	14	,	,	PUNCT
ejpam-4403	16	15	1348	1348	NUM
ejpam-4403	16	16	-	-	SYM
ejpam-4403	16	17	1362	1362	NUM
ejpam-4403	16	18	1349	1349	NUM
ejpam-4403	16	19	furthermore	furthermore	ADV
ejpam-4403	16	20	,	,	PUNCT
ejpam-4403	16	21	a	a	DET
ejpam-4403	16	22	boundary	boundary	ADJ
ejpam-4403	16	23	problem	problem	NOUN
ejpam-4403	16	24	is	be	AUX
ejpam-4403	16	25	broken	break	VERB
ejpam-4403	16	26	down	down	ADP
ejpam-4403	16	27	into	into	ADP
ejpam-4403	16	28	a	a	DET
ejpam-4403	16	29	pdes	pde	NOUN
ejpam-4403	16	30	(	(	PUNCT
ejpam-4403	16	31	or	or	CCONJ
ejpam-4403	16	32	ode	ode	ADJ
ejpam-4403	16	33	)	)	PUNCT
ejpam-4403	16	34	inside	inside	ADP
ejpam-4403	16	35	the	the	DET
ejpam-4403	16	36	ω	ω	PROPN
ejpam-4403	16	37	domain	domain	NOUN
ejpam-4403	16	38	and	and	CCONJ
ejpam-4403	16	39	the	the	DET
ejpam-4403	16	40	boundary	boundary	ADJ
ejpam-4403	16	41	conditions	condition	NOUN
ejpam-4403	16	42	of	of	ADP
ejpam-4403	16	43	the	the	DET
ejpam-4403	16	44	problem	problem	NOUN
ejpam-4403	16	45	.	.	PUNCT
ejpam-4403	17	1	we	we	PRON
ejpam-4403	17	2	speak	speak	VERB
ejpam-4403	17	3	in	in	ADP
ejpam-4403	17	4	this	this	DET
ejpam-4403	17	5	case	case	NOUN
ejpam-4403	17	6	of	of	ADP
ejpam-4403	17	7	the	the	DET
ejpam-4403	17	8	dirichlet	dirichlet	PROPN
ejpam-4403	17	9	problem	problem	NOUN
ejpam-4403	17	10	,	,	PUNCT
ejpam-4403	17	11	cauchy	cauchy	PROPN
ejpam-4403	17	12	problem	problem	NOUN
ejpam-4403	17	13	,	,	PUNCT
ejpam-4403	17	14	cauchy	cauchy	PROPN
ejpam-4403	17	15	-	-	PUNCT
ejpam-4403	17	16	dirichlet	dirichlet	PROPN
ejpam-4403	17	17	problem	problem	NOUN
ejpam-4403	17	18	(	(	PUNCT
ejpam-4403	17	19	problem	problem	NOUN
ejpam-4403	17	20	whose	whose	DET
ejpam-4403	17	21	boundary	boundary	ADJ
ejpam-4403	17	22	conditions	condition	NOUN
ejpam-4403	17	23	are	be	AUX
ejpam-4403	17	24	a	a	DET
ejpam-4403	17	25	combination	combination	NOUN
ejpam-4403	17	26	of	of	ADP
ejpam-4403	17	27	a	a	DET
ejpam-4403	17	28	cauchy	cauchy	ADJ
ejpam-4403	17	29	condition	condition	NOUN
ejpam-4403	17	30	and	and	CCONJ
ejpam-4403	17	31	a	a	DET
ejpam-4403	17	32	dirichlet	dirichlet	NOUN
ejpam-4403	17	33	condition	condition	NOUN
ejpam-4403	17	34	)	)	PUNCT
ejpam-4403	17	35	.	.	PUNCT
ejpam-4403	18	1	in	in	ADP
ejpam-4403	18	2	addition	addition	NOUN
ejpam-4403	18	3	,	,	PUNCT
ejpam-4403	18	4	it	it	PRON
ejpam-4403	18	5	is	be	AUX
ejpam-4403	18	6	necessary	necessary	ADJ
ejpam-4403	18	7	,	,	PUNCT
ejpam-4403	18	8	to	to	PART
ejpam-4403	18	9	approach	approach	VERB
ejpam-4403	18	10	the	the	DET
ejpam-4403	18	11	theoretical	theoretical	ADJ
ejpam-4403	18	12	(	(	PUNCT
ejpam-4403	18	13	mathematical	mathematical	ADJ
ejpam-4403	18	14	)	)	PUNCT
ejpam-4403	18	15	study	study	NOUN
ejpam-4403	18	16	of	of	ADP
ejpam-4403	18	17	these	these	DET
ejpam-4403	18	18	type	type	NOUN
ejpam-4403	18	19	of	of	ADP
ejpam-4403	18	20	problems	problem	NOUN
ejpam-4403	18	21	,	,	PUNCT
ejpam-4403	18	22	to	to	PART
ejpam-4403	18	23	have	have	VERB
ejpam-4403	18	24	a	a	DET
ejpam-4403	18	25	good	good	ADJ
ejpam-4403	18	26	knowledge	knowledge	NOUN
ejpam-4403	18	27	of	of	ADP
ejpam-4403	18	28	vector	vector	NOUN
ejpam-4403	18	29	and	and	CCONJ
ejpam-4403	18	30	functional	functional	ADJ
ejpam-4403	18	31	analysis	analysis	NOUN
ejpam-4403	18	32	(	(	PUNCT
ejpam-4403	18	33	normed	normed	ADJ
ejpam-4403	18	34	vector	vector	NOUN
ejpam-4403	18	35	spaces	space	NOUN
ejpam-4403	18	36	,	,	PUNCT
ejpam-4403	18	37	lebesgue	lebesgue	NOUN
ejpam-4403	18	38	spaces	space	NOUN
ejpam-4403	18	39	)	)	PUNCT
ejpam-4403	18	40	,	,	PUNCT
ejpam-4403	18	41	hilbert	hilbert	NOUN
ejpam-4403	18	42	analysis	analysis	NOUN
ejpam-4403	18	43	,	,	PUNCT
ejpam-4403	18	44	matrix	matrix	NOUN
ejpam-4403	18	45	numerical	numerical	ADJ
ejpam-4403	18	46	analysis	analysis	NOUN
ejpam-4403	18	47	and	and	CCONJ
ejpam-4403	18	48	also	also	ADV
ejpam-4403	18	49	some	some	DET
ejpam-4403	18	50	knowledge	knowledge	NOUN
ejpam-4403	18	51	of	of	ADP
ejpam-4403	18	52	distributions	distribution	NOUN
ejpam-4403	18	53	,	,	PUNCT
ejpam-4403	18	54	sobolev	sobolev	NOUN
ejpam-4403	18	55	spaces	space	NOUN
ejpam-4403	18	56	,	,	PUNCT
ejpam-4403	18	57	traces	trace	NOUN
ejpam-4403	18	58	,	,	PUNCT
ejpam-4403	18	59	green	green	PROPN
ejpam-4403	18	60	’s	’s	PART
ejpam-4403	18	61	formulas	formula	NOUN
ejpam-4403	18	62	,	,	PUNCT
ejpam-4403	18	63	the	the	DET
ejpam-4403	18	64	use	use	NOUN
ejpam-4403	18	65	of	of	ADP
ejpam-4403	18	66	the	the	DET
ejpam-4403	18	67	lax	lax	PROPN
ejpam-4403	18	68	-	-	PUNCT
ejpam-4403	18	69	milgram	milgram	NOUN
ejpam-4403	18	70	theorem	theorem	NOUN
ejpam-4403	18	71	and	and	CCONJ
ejpam-4403	18	72	some	some	DET
ejpam-4403	18	73	fundamental	fundamental	ADJ
ejpam-4403	18	74	inequalities	inequality	NOUN
ejpam-4403	18	75	(	(	PUNCT
ejpam-4403	18	76	cauchy	cauchy	NOUN
ejpam-4403	18	77	-	-	PUNCT
ejpam-4403	18	78	schwartz	schwartz	PROPN
ejpam-4403	18	79	,	,	PUNCT
ejpam-4403	18	80	hölder	hölder	NOUN
ejpam-4403	18	81	,	,	PUNCT
ejpam-4403	18	82	poincaré	poincaré	ADJ
ejpam-4403	18	83	,	,	PUNCT
ejpam-4403	18	84	etc	etc	X
ejpam-4403	18	85	.	.	X
ejpam-4403	18	86	)	)	PUNCT
ejpam-4403	18	87	which	which	PRON
ejpam-4403	18	88	emanate	emanate	VERB
ejpam-4403	18	89	from	from	ADP
ejpam-4403	18	90	the	the	DET
ejpam-4403	18	91	analysis	analysis	NOUN
ejpam-4403	18	92	and	and	CCONJ
ejpam-4403	18	93	which	which	PRON
ejpam-4403	18	94	are	be	AUX
ejpam-4403	18	95	generally	generally	ADV
ejpam-4403	18	96	used	use	VERB
ejpam-4403	18	97	in	in	ADP
ejpam-4403	18	98	the	the	DET
ejpam-4403	18	99	framework	framework	NOUN
ejpam-4403	18	100	of	of	ADP
ejpam-4403	18	101	functional	functional	ADJ
ejpam-4403	18	102	analysis	analysis	NOUN
ejpam-4403	18	103	of	of	ADP
ejpam-4403	18	104	pde	pde	NOUN
ejpam-4403	19	1	[	[	X
ejpam-4403	19	2	2–6	2–6	NOUN
ejpam-4403	19	3	,	,	PUNCT
ejpam-4403	19	4	8	8	NUM
ejpam-4403	19	5	]	]	PUNCT
ejpam-4403	19	6	.	.	PUNCT
ejpam-4403	20	1	the	the	DET
ejpam-4403	20	2	pde	pde	PROPN
ejpam-4403	20	3	numerical	numerical	PROPN
ejpam-4403	20	4	resolution	resolution	NOUN
ejpam-4403	20	5	represents	represent	VERB
ejpam-4403	20	6	a	a	DET
ejpam-4403	20	7	field	field	NOUN
ejpam-4403	20	8	of	of	ADP
ejpam-4403	20	9	research	research	NOUN
ejpam-4403	20	10	in	in	ADP
ejpam-4403	20	11	mathematical	mathematical	ADJ
ejpam-4403	20	12	sciences	science	NOUN
ejpam-4403	20	13	.	.	PUNCT
ejpam-4403	21	1	there	there	PRON
ejpam-4403	21	2	are	be	VERB
ejpam-4403	21	3	several	several	ADJ
ejpam-4403	21	4	numerical	numerical	ADJ
ejpam-4403	21	5	methods	method	NOUN
ejpam-4403	21	6	of	of	ADP
ejpam-4403	21	7	resolution	resolution	NOUN
ejpam-4403	21	8	available	available	ADJ
ejpam-4403	21	9	for	for	ADP
ejpam-4403	21	10	each	each	DET
ejpam-4403	21	11	type	type	NOUN
ejpam-4403	21	12	of	of	ADP
ejpam-4403	21	13	boundary	boundary	ADJ
ejpam-4403	21	14	problem	problem	NOUN
ejpam-4403	21	15	,	,	PUNCT
ejpam-4403	21	16	classified	classify	VERB
ejpam-4403	21	17	by	by	ADP
ejpam-4403	21	18	categories	category	NOUN
ejpam-4403	21	19	[	[	X
ejpam-4403	21	20	1	1	NUM
ejpam-4403	21	21	,	,	PUNCT
ejpam-4403	21	22	12–18	12–18	NUM
ejpam-4403	21	23	]	]	PUNCT
ejpam-4403	21	24	.	.	PUNCT
ejpam-4403	22	1	thus	thus	ADV
ejpam-4403	22	2	,	,	PUNCT
ejpam-4403	22	3	we	we	PRON
ejpam-4403	22	4	speak	speak	VERB
ejpam-4403	22	5	of	of	ADP
ejpam-4403	22	6	finite	finite	ADJ
ejpam-4403	22	7	difference	difference	NOUN
ejpam-4403	22	8	method	method	NOUN
ejpam-4403	22	9	,	,	PUNCT
ejpam-4403	22	10	finite	finite	PROPN
ejpam-4403	22	11	element	element	NOUN
ejpam-4403	22	12	method	method	NOUN
ejpam-4403	22	13	,	,	PUNCT
ejpam-4403	22	14	finite	finite	ADJ
ejpam-4403	22	15	volume	volume	NOUN
ejpam-4403	22	16	method	method	NOUN
ejpam-4403	22	17	,	,	PUNCT
ejpam-4403	22	18	etc	etc	X
ejpam-4403	22	19	.	.	X
ejpam-4403	23	1	the	the	DET
ejpam-4403	23	2	manipulation	manipulation	NOUN
ejpam-4403	23	3	of	of	ADP
ejpam-4403	23	4	these	these	DET
ejpam-4403	23	5	resolution	resolution	NOUN
ejpam-4403	23	6	methods	method	NOUN
ejpam-4403	23	7	and	and	CCONJ
ejpam-4403	23	8	the	the	DET
ejpam-4403	23	9	implementation	implementation	NOUN
ejpam-4403	23	10	of	of	ADP
ejpam-4403	23	11	numerical	numerical	ADJ
ejpam-4403	23	12	simulations	simulation	NOUN
ejpam-4403	23	13	depend	depend	VERB
ejpam-4403	23	14	on	on	ADP
ejpam-4403	23	15	the	the	DET
ejpam-4403	23	16	type	type	NOUN
ejpam-4403	23	17	of	of	ADP
ejpam-4403	23	18	problem	problem	NOUN
ejpam-4403	23	19	studied	study	VERB
ejpam-4403	23	20	.	.	PUNCT
ejpam-4403	24	1	however	however	ADV
ejpam-4403	24	2	,	,	PUNCT
ejpam-4403	24	3	incontestably	incontestably	ADJ
ejpam-4403	24	4	few	few	ADJ
ejpam-4403	24	5	numerical	numerical	ADJ
ejpam-4403	24	6	methods	method	NOUN
ejpam-4403	24	7	have	have	AUX
ejpam-4403	24	8	been	be	AUX
ejpam-4403	24	9	used	use	VERB
ejpam-4403	24	10	to	to	PART
ejpam-4403	24	11	solve	solve	VERB
ejpam-4403	24	12	the	the	DET
ejpam-4403	24	13	cauchy	cauchy	NOUN
ejpam-4403	24	14	-	-	PUNCT
ejpam-4403	24	15	dirichlet	dirichlet	PROPN
ejpam-4403	24	16	problem	problem	NOUN
ejpam-4403	24	17	.	.	PUNCT
ejpam-4403	25	1	the	the	DET
ejpam-4403	25	2	object	object	NOUN
ejpam-4403	25	3	of	of	ADP
ejpam-4403	25	4	our	our	PRON
ejpam-4403	25	5	work	work	NOUN
ejpam-4403	25	6	is	be	AUX
ejpam-4403	25	7	to	to	PART
ejpam-4403	25	8	propose	propose	VERB
ejpam-4403	25	9	a	a	DET
ejpam-4403	25	10	theoretical	theoretical	ADJ
ejpam-4403	25	11	(	(	PUNCT
ejpam-4403	25	12	mathematical	mathematical	ADJ
ejpam-4403	25	13	)	)	PUNCT
ejpam-4403	25	14	and	and	CCONJ
ejpam-4403	25	15	numerical	numerical	ADJ
ejpam-4403	25	16	study	study	NOUN
ejpam-4403	25	17	of	of	ADP
ejpam-4403	25	18	the	the	DET
ejpam-4403	25	19	solution	solution	NOUN
ejpam-4403	25	20	of	of	ADP
ejpam-4403	25	21	the	the	DET
ejpam-4403	25	22	cauchy	cauchy	PROPN
ejpam-4403	25	23	-	-	PUNCT
ejpam-4403	25	24	dirichlet	dirichlet	PROPN
ejpam-4403	25	25	problem	problem	NOUN
ejpam-4403	25	26	of	of	ADP
ejpam-4403	25	27	the	the	DET
ejpam-4403	25	28	type	type	NOUN
ejpam-4403	25	29	of	of	ADP
ejpam-4403	25	30	stationary	stationary	ADJ
ejpam-4403	25	31	convection	convection	NOUN
ejpam-4403	25	32	-	-	PUNCT
ejpam-4403	25	33	diffusion	diffusion	NOUN
ejpam-4403	25	34	equation	equation	NOUN
ejpam-4403	25	35	by	by	ADP
ejpam-4403	25	36	the	the	DET
ejpam-4403	25	37	method	method	NOUN
ejpam-4403	25	38	of	of	ADP
ejpam-4403	25	39	finite	finite	ADJ
ejpam-4403	25	40	differences	difference	NOUN
ejpam-4403	25	41	and	and	CCONJ
ejpam-4403	25	42	to	to	PART
ejpam-4403	25	43	implement	implement	VERB
ejpam-4403	25	44	numerical	numerical	ADJ
ejpam-4403	25	45	simulations	simulation	NOUN
ejpam-4403	25	46	using	use	VERB
ejpam-4403	25	47	the	the	DET
ejpam-4403	25	48	scilab	scilab	PROPN
ejpam-4403	25	49	software	software	NOUN
ejpam-4403	25	50	,	,	PUNCT
ejpam-4403	25	51	via	via	ADP
ejpam-4403	25	52	the	the	DET
ejpam-4403	25	53	analytical	analytical	ADJ
ejpam-4403	25	54	and	and	CCONJ
ejpam-4403	25	55	numerical	numerical	ADJ
ejpam-4403	25	56	solutions	solution	NOUN
ejpam-4403	25	57	obtained	obtain	VERB
ejpam-4403	25	58	by	by	ADP
ejpam-4403	25	59	solving	solve	VERB
ejpam-4403	25	60	the	the	DET
ejpam-4403	25	61	problem	problem	NOUN
ejpam-4403	25	62	.	.	PUNCT
ejpam-4403	26	1	2	2	X
ejpam-4403	26	2	.	.	X
ejpam-4403	26	3	cauchydirichlet	cauchydirichlet	NOUN
ejpam-4403	26	4	problem	problem	NOUN
ejpam-4403	26	5	in	in	ADP
ejpam-4403	26	6	mathematics	mathematic	NOUN
ejpam-4403	26	7	,	,	PUNCT
ejpam-4403	26	8	a	a	DET
ejpam-4403	26	9	cauchy	cauchy	PROPN
ejpam-4403	26	10	–	–	PUNCT
ejpam-4403	26	11	dirichlet	dirichlet	PROPN
ejpam-4403	26	12	problem	problem	NOUN
ejpam-4403	26	13	is	be	AUX
ejpam-4403	26	14	the	the	DET
ejpam-4403	26	15	problem	problem	NOUN
ejpam-4403	26	16	of	of	ADP
ejpam-4403	26	17	finding	find	VERB
ejpam-4403	26	18	a	a	DET
ejpam-4403	26	19	function	function	NOUN
ejpam-4403	26	20	that	that	PRON
ejpam-4403	26	21	solves	solve	VERB
ejpam-4403	26	22	a	a	DET
ejpam-4403	26	23	specified	specify	VERB
ejpam-4403	26	24	partial	partial	ADJ
ejpam-4403	26	25	differential	differential	NOUN
ejpam-4403	26	26	equation	equation	NOUN
ejpam-4403	26	27	(	(	PUNCT
ejpam-4403	26	28	pde	pde	NOUN
ejpam-4403	26	29	)	)	PUNCT
ejpam-4403	26	30	inside	inside	ADP
ejpam-4403	26	31	a	a	DET
ejpam-4403	26	32	given	give	VERB
ejpam-4403	26	33	region	region	NOUN
ejpam-4403	26	34	that	that	PRON
ejpam-4403	26	35	takes	take	VERB
ejpam-4403	26	36	on	on	ADP
ejpam-4403	26	37	prescribed	prescribed	ADJ
ejpam-4403	26	38	values	value	NOUN
ejpam-4403	26	39	at	at	ADP
ejpam-4403	26	40	the	the	DET
ejpam-4403	26	41	boundary	boundary	NOUN
ejpam-4403	26	42	of	of	ADP
ejpam-4403	26	43	the	the	DET
ejpam-4403	26	44	region	region	NOUN
ejpam-4403	26	45	.	.	PUNCT
ejpam-4403	27	1	the	the	DET
ejpam-4403	27	2	problem	problem	NOUN
ejpam-4403	27	3	finds	find	VERB
ejpam-4403	27	4	its	its	PRON
ejpam-4403	27	5	applications	application	NOUN
ejpam-4403	27	6	in	in	ADP
ejpam-4403	27	7	several	several	ADJ
ejpam-4403	27	8	fields	field	NOUN
ejpam-4403	27	9	of	of	ADP
ejpam-4403	27	10	engineering	engineering	NOUN
ejpam-4403	27	11	sciences	science	NOUN
ejpam-4403	27	12	(	(	PUNCT
ejpam-4403	27	13	for	for	ADP
ejpam-4403	27	14	example	example	NOUN
ejpam-4403	27	15	in	in	ADP
ejpam-4403	27	16	aeronautics	aeronautic	NOUN
ejpam-4403	27	17	)	)	PUNCT
ejpam-4403	27	18	and	and	CCONJ
ejpam-4403	27	19	is	be	AUX
ejpam-4403	27	20	often	often	ADV
ejpam-4403	27	21	presented	present	VERB
ejpam-4403	27	22	in	in	ADP
ejpam-4403	27	23	the	the	DET
ejpam-4403	27	24	form	form	NOUN
ejpam-4403	27	25	:	:	PUNCT
ejpam-4403	27	26	let	let	VERB
ejpam-4403	27	27	ω	ω	PRON
ejpam-4403	27	28	be	be	AUX
ejpam-4403	27	29	a	a	DET
ejpam-4403	27	30	bounded	bounded	ADJ
ejpam-4403	27	31	non	non	ADJ
ejpam-4403	27	32	-	-	ADJ
ejpam-4403	27	33	empty	empty	ADJ
ejpam-4403	27	34	domain	domain	NOUN
ejpam-4403	27	35	of	of	ADP
ejpam-4403	27	36	class	class	NOUN
ejpam-4403	27	37	c1	c1	PROPN
ejpam-4403	27	38	of	of	ADP
ejpam-4403	27	39	rn	rn	PROPN
ejpam-4403	27	40	(	(	PUNCT
ejpam-4403	27	41	n	n	CCONJ
ejpam-4403	27	42	≥	≥	NOUN
ejpam-4403	27	43	1	1	NUM
ejpam-4403	27	44	)	)	PUNCT
ejpam-4403	27	45	,	,	PUNCT
ejpam-4403	27	46	f	f	PROPN
ejpam-4403	27	47	and	and	CCONJ
ejpam-4403	27	48	c	c	PROPN
ejpam-4403	27	49	are	be	AUX
ejpam-4403	27	50	two	two	NUM
ejpam-4403	27	51	functions	function	NOUN
ejpam-4403	27	52	defined	define	VERB
ejpam-4403	27	53	respectively	respectively	ADV
ejpam-4403	27	54	on	on	ADP
ejpam-4403	27	55	ω	ω	NUM
ejpam-4403	27	56	and	and	CCONJ
ejpam-4403	27	57	on	on	ADP
ejpam-4403	27	58	∂ω	∂ω	ADJ
ejpam-4403	27	59	=	=	PUNCT
ejpam-4403	27	60	γ	γ	X
ejpam-4403	27	61	(	(	PUNCT
ejpam-4403	27	62	the	the	DET
ejpam-4403	27	63	border	border	NOUN
ejpam-4403	27	64	of	of	ADP
ejpam-4403	27	65	ω	ω	NUM
ejpam-4403	27	66	)	)	PUNCT
ejpam-4403	27	67	.	.	PUNCT
ejpam-4403	28	1	the	the	DET
ejpam-4403	28	2	cauchy	cauchy	PROPN
ejpam-4403	28	3	-	-	PUNCT
ejpam-4403	28	4	dirichlet	dirichlet	PROPN
ejpam-4403	28	5	problem	problem	NOUN
ejpam-4403	28	6	[	[	X
ejpam-4403	28	7	2	2	NUM
ejpam-4403	28	8	,	,	PUNCT
ejpam-4403	28	9	9	9	NUM
ejpam-4403	28	10	,	,	PUNCT
ejpam-4403	28	11	10	10	NUM
ejpam-4403	28	12	]	]	PUNCT
ejpam-4403	28	13	is	be	AUX
ejpam-4403	28	14	an	an	DET
ejpam-4403	28	15	elliptical	elliptical	ADJ
ejpam-4403	28	16	boundary	boundary	ADJ
ejpam-4403	28	17	problem	problem	NOUN
ejpam-4403	28	18	of	of	ADP
ejpam-4403	28	19	solution	solution	NOUN
ejpam-4403	28	20	u	u	NOUN
ejpam-4403	28	21	=	=	SYM
ejpam-4403	28	22	u(x	u(x	PROPN
ejpam-4403	28	23	,	,	PUNCT
ejpam-4403	28	24	t	t	PROPN
ejpam-4403	28	25	)	)	PUNCT
ejpam-4403	28	26	which	which	PRON
ejpam-4403	28	27	presents	present	VERB
ejpam-4403	28	28	itself	itself	PRON
ejpam-4403	28	29	in	in	ADP
ejpam-4403	28	30	the	the	DET
ejpam-4403	28	31	following	follow	VERB
ejpam-4403	28	32	way:	way:	NUM
ejpam-4403	28	33	−∇(µ∇u	−∇(µ∇u	NUM
ejpam-4403	28	34	)	)	PUNCT
ejpam-4403	28	35	+	+	NUM
ejpam-4403	28	36	c(x)∇u	c(x)∇u	NOUN
ejpam-4403	28	37	=	=	SYM
ejpam-4403	28	38	f(x	f(x	PROPN
ejpam-4403	28	39	)	)	PUNCT
ejpam-4403	28	40	,	,	PUNCT
ejpam-4403	28	41	x	x	X
ejpam-4403	28	42	∈]0	∈]0	X
ejpam-4403	28	43	;	;	PUNCT
ejpam-4403	28	44	1	1	NUM
ejpam-4403	28	45	[	[	PUNCT
ejpam-4403	28	46	u(0	u(0	PROPN
ejpam-4403	28	47	,	,	PUNCT
ejpam-4403	28	48	t	t	PROPN
ejpam-4403	28	49	)	)	PUNCT
ejpam-4403	28	50	=	=	SYM
ejpam-4403	29	1	u(1	u(1	PROPN
ejpam-4403	29	2	,	,	PUNCT
ejpam-4403	29	3	t	t	PROPN
ejpam-4403	29	4	)	)	PUNCT
ejpam-4403	29	5	=	=	SYM
ejpam-4403	29	6	0	0	NUM
ejpam-4403	29	7	u(x	u(x	NOUN
ejpam-4403	29	8	,	,	PUNCT
ejpam-4403	29	9	0	0	NUM
ejpam-4403	29	10	)	)	PUNCT
ejpam-4403	29	11	=	=	SYM
ejpam-4403	29	12	u0(x	u0(x	NOUN
ejpam-4403	29	13	)	)	PUNCT
ejpam-4403	29	14	=	=	SYM
ejpam-4403	29	15	sin(19πx	sin(19πx	NOUN
ejpam-4403	29	16	)	)	PUNCT
ejpam-4403	29	17	(	(	PUNCT
ejpam-4403	29	18	1	1	X
ejpam-4403	29	19	)	)	PUNCT
ejpam-4403	29	20	where	where	SCONJ
ejpam-4403	29	21	−∇(µ∇u	−∇(µ∇u	NOUN
ejpam-4403	29	22	)	)	PUNCT
ejpam-4403	29	23	and	and	CCONJ
ejpam-4403	29	24	c(x)∇u	c(x)∇u	NOUN
ejpam-4403	29	25	represent	represent	VERB
ejpam-4403	29	26	respectively	respectively	ADV
ejpam-4403	29	27	,	,	PUNCT
ejpam-4403	29	28	the	the	DET
ejpam-4403	29	29	diffusion	diffusion	NOUN
ejpam-4403	29	30	and	and	CCONJ
ejpam-4403	29	31	convection	convection	NOUN
ejpam-4403	29	32	terms	term	NOUN
ejpam-4403	29	33	,	,	PUNCT
ejpam-4403	29	34	f(x	f(x	PROPN
ejpam-4403	29	35	)	)	PUNCT
ejpam-4403	29	36	=	=	SYM
ejpam-4403	29	37	5	5	NUM
ejpam-4403	29	38	cos(πx	cos(πx	NOUN
ejpam-4403	29	39	)	)	PUNCT
ejpam-4403	30	1	+	+	CCONJ
ejpam-4403	30	2	(	(	PUNCT
ejpam-4403	30	3	x−	x−	PROPN
ejpam-4403	30	4	5	5	NUM
ejpam-4403	30	5	)	)	PUNCT
ejpam-4403	30	6	,	,	PUNCT
ejpam-4403	30	7	c(x	c(x	NOUN
ejpam-4403	30	8	)	)	PUNCT
ejpam-4403	30	9	=	=	SYM
ejpam-4403	30	10	sin(2x	sin(2x	PROPN
ejpam-4403	30	11	)	)	PUNCT
ejpam-4403	30	12	,	,	PUNCT
ejpam-4403	30	13	µ	µ	X
ejpam-4403	30	14	>	>	SYM
ejpam-4403	30	15	0	0	NUM
ejpam-4403	30	16	fixed	fix	VERB
ejpam-4403	30	17	positive	positive	ADJ
ejpam-4403	30	18	real	real	NOUN
ejpam-4403	30	19	.	.	PUNCT
ejpam-4403	31	1	d.	d.	PROPN
ejpam-4403	31	2	v.	v.	PROPN
ejpam-4403	31	3	pongui	pongui	PROPN
ejpam-4403	31	4	ngoma	ngoma	PROPN
ejpam-4403	31	5	et	et	PROPN
ejpam-4403	31	6	al	al	PROPN
ejpam-4403	31	7	.	.	PROPN
ejpam-4403	31	8	,	,	PUNCT
ejpam-4403	31	9	/	/	SYM
ejpam-4403	31	10	eur	eur	NOUN
ejpam-4403	31	11	.	.	PUNCT
ejpam-4403	32	1	j.	j.	PROPN
ejpam-4403	32	2	pure	pure	PROPN
ejpam-4403	32	3	appl	appl	PROPN
ejpam-4403	32	4	.	.	PROPN
ejpam-4403	32	5	math	math	PROPN
ejpam-4403	32	6	,	,	PUNCT
ejpam-4403	32	7	15	15	NUM
ejpam-4403	32	8	(	(	PUNCT
ejpam-4403	32	9	3	3	NUM
ejpam-4403	32	10	)	)	PUNCT
ejpam-4403	32	11	(	(	PUNCT
ejpam-4403	32	12	2022	2022	NUM
ejpam-4403	32	13	)	)	PUNCT
ejpam-4403	32	14	,	,	PUNCT
ejpam-4403	32	15	1348	1348	NUM
ejpam-4403	32	16	-	-	SYM
ejpam-4403	32	17	1362	1362	NUM
ejpam-4403	32	18	1350	1350	NUM
ejpam-4403	32	19	variational	variational	ADJ
ejpam-4403	32	20	formulation	formulation	NOUN
ejpam-4403	32	21	of	of	ADP
ejpam-4403	32	22	the	the	DET
ejpam-4403	32	23	boundary	boundary	ADJ
ejpam-4403	32	24	value	value	NOUN
ejpam-4403	32	25	problems	problem	NOUN
ejpam-4403	32	26	let	let	VERB
ejpam-4403	32	27	us	we	PRON
ejpam-4403	32	28	transform	transform	VERB
ejpam-4403	32	29	the	the	DET
ejpam-4403	32	30	problem	problem	NOUN
ejpam-4403	32	31	(	(	PUNCT
ejpam-4403	32	32	1	1	NUM
ejpam-4403	32	33	)	)	PUNCT
ejpam-4403	32	34	into	into	ADP
ejpam-4403	32	35	a	a	DET
ejpam-4403	32	36	variational	variational	ADJ
ejpam-4403	32	37	problem	problem	NOUN
ejpam-4403	32	38	as	as	ADP
ejpam-4403	32	39	f	f	PROPN
ejpam-4403	32	40	∈	∈	PROPN
ejpam-4403	32	41	l2(ω	l2(ω	PROPN
ejpam-4403	32	42	)	)	PUNCT
ejpam-4403	32	43	then	then	ADV
ejpam-4403	32	44	−µ∆u	−µ∆u	PROPN
ejpam-4403	32	45	∈	∈	PROPN
ejpam-4403	32	46	l2(ω	l2(ω	NOUN
ejpam-4403	32	47	)	)	PUNCT
ejpam-4403	32	48	u	u	NOUN
ejpam-4403	32	49	∈	∈	PROPN
ejpam-4403	32	50	h1(ω	h1(ω	PROPN
ejpam-4403	32	51	)	)	PUNCT
ejpam-4403	32	52	u	u	NOUN
ejpam-4403	32	53	∈	∈	PROPN
ejpam-4403	32	54	h1(ω	h1(ω	PROPN
ejpam-4403	32	55	)	)	PUNCT
ejpam-4403	32	56	and	and	CCONJ
ejpam-4403	32	57	u	u	X
ejpam-4403	32	58	=	=	NOUN
ejpam-4403	32	59	0	0	NUM
ejpam-4403	32	60	on	on	ADP
ejpam-4403	32	61	∂ω	∂ω	PROPN
ejpam-4403	32	62	,	,	PUNCT
ejpam-4403	32	63	then	then	ADV
ejpam-4403	32	64	u	u	PROPN
ejpam-4403	32	65	∈	∈	PROPN
ejpam-4403	32	66	h1	h1	NOUN
ejpam-4403	32	67	0	0	NUM
ejpam-4403	32	68	(	(	PUNCT
ejpam-4403	32	69	ω	ω	NOUN
ejpam-4403	32	70	)	)	PUNCT
ejpam-4403	32	71	.	.	PUNCT
ejpam-4403	33	1	now	now	ADV
ejpam-4403	33	2	,	,	PUNCT
ejpam-4403	33	3	let	let	VERB
ejpam-4403	33	4	’s	’s	PRON
ejpam-4403	33	5	give	give	VERB
ejpam-4403	33	6	the	the	DET
ejpam-4403	33	7	variational	variational	ADJ
ejpam-4403	33	8	formulation	formulation	NOUN
ejpam-4403	33	9	of	of	ADP
ejpam-4403	33	10	the	the	DET
ejpam-4403	33	11	problem	problem	NOUN
ejpam-4403	33	12	(	(	PUNCT
ejpam-4403	33	13	1	1	X
ejpam-4403	33	14	)	)	PUNCT
ejpam-4403	33	15	let	let	VERB
ejpam-4403	33	16	v	v	NUM
ejpam-4403	33	17	∈	∈	PROPN
ejpam-4403	33	18	h1	h1	NOUN
ejpam-4403	33	19	0	0	NUM
ejpam-4403	33	20	(	(	PUNCT
ejpam-4403	33	21	ω	ω	NOUN
ejpam-4403	33	22	)	)	PUNCT
ejpam-4403	33	23	multiply	multiply	ADP
ejpam-4403	33	24	the	the	DET
ejpam-4403	33	25	first	first	ADJ
ejpam-4403	33	26	equation	equation	NOUN
ejpam-4403	33	27	of	of	ADP
ejpam-4403	33	28	the	the	DET
ejpam-4403	33	29	system	system	NOUN
ejpam-4403	33	30	(	(	PUNCT
ejpam-4403	33	31	1	1	NUM
ejpam-4403	33	32	)	)	PUNCT
ejpam-4403	33	33	by	by	ADP
ejpam-4403	33	34	v	v	NOUN
ejpam-4403	33	35	and	and	CCONJ
ejpam-4403	33	36	integrate	integrate	VERB
ejpam-4403	33	37	member	member	NOUN
ejpam-4403	33	38	to	to	PART
ejpam-4403	33	39	member	member	NOUN
ejpam-4403	33	40	on	on	ADP
ejpam-4403	33	41	ω	ω	PROPN
ejpam-4403	33	42	∫	∫	PROPN
ejpam-4403	34	1	ω	ω	NUM
ejpam-4403	34	2	−µ∆u.v	−µ∆u.v	PROPN
ejpam-4403	34	3	dω+	dω+	PROPN
ejpam-4403	34	4	∫	∫	PROPN
ejpam-4403	35	1	ω	ω	PROPN
ejpam-4403	35	2	c∇u.v	c∇u.v	PROPN
ejpam-4403	35	3	dω	dω	PROPN
ejpam-4403	35	4	=	=	SYM
ejpam-4403	35	5	∫	∫	PROPN
ejpam-4403	35	6	ω	ω	PROPN
ejpam-4403	35	7	f.v	f.v	PROPN
ejpam-4403	35	8	dω	dω	PROPN
ejpam-4403	35	9	(	(	PUNCT
ejpam-4403	35	10	2	2	X
ejpam-4403	35	11	)	)	PUNCT
ejpam-4403	35	12	let	let	VERB
ejpam-4403	35	13	’s	’s	NOUN
ejpam-4403	35	14	use	use	VERB
ejpam-4403	35	15	green	green	NOUN
ejpam-4403	35	16	’s	’s	PART
ejpam-4403	35	17	formula	formula	NOUN
ejpam-4403	35	18	[	[	X
ejpam-4403	35	19	8	8	NUM
ejpam-4403	35	20	,	,	PUNCT
ejpam-4403	35	21	11	11	NUM
ejpam-4403	35	22	]	]	PUNCT
ejpam-4403	36	1	,	,	PUNCT
ejpam-4403	36	2	then	then	ADV
ejpam-4403	36	3	µ	µ	X
ejpam-4403	36	4	∫	∫	PROPN
ejpam-4403	36	5	ω	ω	PROPN
ejpam-4403	36	6	∇u.∇v	∇u.∇v	PROPN
ejpam-4403	37	1	dω+	dω+	PROPN
ejpam-4403	37	2	∫	∫	PROPN
ejpam-4403	37	3	ω	ω	PROPN
ejpam-4403	37	4	c∇u.v	c∇u.v	PROPN
ejpam-4403	37	5	dω	dω	PROPN
ejpam-4403	37	6	=	=	SYM
ejpam-4403	37	7	∫	∫	PROPN
ejpam-4403	37	8	ω	ω	PROPN
ejpam-4403	37	9	f.v	f.v	PROPN
ejpam-4403	37	10	dω	dω	ADP
ejpam-4403	37	11	(	(	PUNCT
ejpam-4403	37	12	3	3	X
ejpam-4403	37	13	)	)	PUNCT
ejpam-4403	37	14	we	we	PRON
ejpam-4403	37	15	thus	thus	ADV
ejpam-4403	37	16	obtain	obtain	VERB
ejpam-4403	37	17	the	the	DET
ejpam-4403	37	18	following	follow	VERB
ejpam-4403	37	19	variational	variational	ADJ
ejpam-4403	37	20	formulation	formulation	NOUN
ejpam-4403	37	21	{	{	PUNCT
ejpam-4403	37	22	u	u	NOUN
ejpam-4403	37	23	∈	∈	PROPN
ejpam-4403	37	24	h1	h1	NOUN
ejpam-4403	37	25	0	0	NUM
ejpam-4403	37	26	(	(	PUNCT
ejpam-4403	37	27	ω	ω	NOUN
ejpam-4403	37	28	)	)	PUNCT
ejpam-4403	37	29	a(u	a(u	PROPN
ejpam-4403	37	30	,	,	PUNCT
ejpam-4403	37	31	v	v	NOUN
ejpam-4403	37	32	)	)	PUNCT
ejpam-4403	37	33	=	=	SYM
ejpam-4403	37	34	l(v	l(v	NOUN
ejpam-4403	37	35	)	)	PUNCT
ejpam-4403	37	36	∀v	∀v	PROPN
ejpam-4403	37	37	∈	∈	PROPN
ejpam-4403	37	38	h1	h1	NOUN
ejpam-4403	37	39	0	0	NUM
ejpam-4403	37	40	(	(	PUNCT
ejpam-4403	37	41	ω	ω	NOUN
ejpam-4403	37	42	)	)	PUNCT
ejpam-4403	37	43	(	(	PUNCT
ejpam-4403	37	44	4	4	X
ejpam-4403	37	45	)	)	PUNCT
ejpam-4403	37	46	where	where	SCONJ
ejpam-4403	37	47	a(u	a(u	PROPN
ejpam-4403	37	48	,	,	PUNCT
ejpam-4403	37	49	v	v	NOUN
ejpam-4403	37	50	)	)	PUNCT
ejpam-4403	37	51	=	=	SYM
ejpam-4403	37	52	µ	µ	PRON
ejpam-4403	37	53	∫	∫	PROPN
ejpam-4403	37	54	ω	ω	PROPN
ejpam-4403	37	55	∇u.∇v	∇u.∇v	PROPN
ejpam-4403	38	1	dω+	dω+	PROPN
ejpam-4403	38	2	∫	∫	PROPN
ejpam-4403	38	3	ω	ω	PROPN
ejpam-4403	38	4	c∇u.v	c∇u.v	PROPN
ejpam-4403	38	5	dω	dω	PROPN
ejpam-4403	38	6	and	and	CCONJ
ejpam-4403	38	7	l(v	l(v	NOUN
ejpam-4403	38	8	)	)	PUNCT
ejpam-4403	39	1	=	=	SYM
ejpam-4403	40	1	∫	∫	PROPN
ejpam-4403	41	1	ω	ω	PROPN
ejpam-4403	42	1	f.v	f.v	PROPN
ejpam-4403	42	2	dω	dω	PROPN
ejpam-4403	42	3	3	3	NUM
ejpam-4403	42	4	.	.	PUNCT
ejpam-4403	42	5	existence	existence	NOUN
ejpam-4403	42	6	and	and	CCONJ
ejpam-4403	42	7	uniqueness	uniqueness	NOUN
ejpam-4403	42	8	of	of	ADP
ejpam-4403	42	9	the	the	DET
ejpam-4403	42	10	solution	solution	NOUN
ejpam-4403	42	11	let	let	VERB
ejpam-4403	42	12	us	we	PRON
ejpam-4403	42	13	prove	prove	VERB
ejpam-4403	42	14	the	the	DET
ejpam-4403	42	15	existence	existence	NOUN
ejpam-4403	42	16	and	and	CCONJ
ejpam-4403	42	17	the	the	DET
ejpam-4403	42	18	uniqueness	uniqueness	NOUN
ejpam-4403	42	19	of	of	ADP
ejpam-4403	42	20	the	the	DET
ejpam-4403	42	21	solution	solution	NOUN
ejpam-4403	42	22	u	u	PROPN
ejpam-4403	42	23	∈	∈	PROPN
ejpam-4403	42	24	h1	h1	NOUN
ejpam-4403	42	25	0	0	NUM
ejpam-4403	42	26	(	(	PUNCT
ejpam-4403	42	27	ω	ω	NOUN
ejpam-4403	42	28	)	)	PUNCT
ejpam-4403	42	29	by	by	ADP
ejpam-4403	42	30	laxmilgram	laxmilgram	NOUN
ejpam-4403	42	31	theorem	theorem	ADJ
ejpam-4403	42	32	[	[	X
ejpam-4403	42	33	8	8	NUM
ejpam-4403	42	34	,	,	PUNCT
ejpam-4403	42	35	9	9	NUM
ejpam-4403	42	36	,	,	PUNCT
ejpam-4403	42	37	11	11	NUM
ejpam-4403	42	38	]	]	PUNCT
ejpam-4403	42	39	.	.	PUNCT
ejpam-4403	43	1	let	let	VERB
ejpam-4403	43	2	u	u	PRON
ejpam-4403	43	3	∈	∈	PROPN
ejpam-4403	43	4	v	v	ADP
ejpam-4403	43	5	=	=	X
ejpam-4403	43	6	h1	h1	NOUN
ejpam-4403	43	7	0	0	NUM
ejpam-4403	43	8	(	(	PUNCT
ejpam-4403	43	9	ω	ω	NOUN
ejpam-4403	43	10	)	)	PUNCT
ejpam-4403	43	11	•	•	ADP
ejpam-4403	43	12	let	let	VERB
ejpam-4403	43	13	us	we	PRON
ejpam-4403	43	14	show	show	VERB
ejpam-4403	43	15	that	that	SCONJ
ejpam-4403	43	16	the	the	DET
ejpam-4403	43	17	bilinear	bilinear	NOUN
ejpam-4403	43	18	form	form	NOUN
ejpam-4403	43	19	a	a	PRON
ejpam-4403	43	20	is	be	AUX
ejpam-4403	43	21	continuous	continuous	ADJ
ejpam-4403	43	22	we	we	PRON
ejpam-4403	43	23	have	have	VERB
ejpam-4403	43	24	|	|	ADV
ejpam-4403	43	25	a(u	a(u	NOUN
ejpam-4403	43	26	,	,	PUNCT
ejpam-4403	43	27	v	v	NOUN
ejpam-4403	43	28	)	)	PUNCT
ejpam-4403	43	29	|=|	|=|	PROPN
ejpam-4403	43	30	µ	µ	DET
ejpam-4403	43	31	∫	∫	PROPN
ejpam-4403	43	32	ω	ω	PROPN
ejpam-4403	43	33	∇u.∇v	∇u.∇v	PROPN
ejpam-4403	44	1	dω+	dω+	PROPN
ejpam-4403	44	2	∫	∫	PROPN
ejpam-4403	44	3	ω	ω	PROPN
ejpam-4403	44	4	c∇u.v	c∇u.v	PROPN
ejpam-4403	44	5	dω	dω	ADP
ejpam-4403	44	6	|	|	ADV
ejpam-4403	44	7	(	(	PUNCT
ejpam-4403	44	8	5	5	NUM
ejpam-4403	44	9	)	)	PUNCT
ejpam-4403	44	10	|	|	ADV
ejpam-4403	44	11	a(u	a(u	PROPN
ejpam-4403	44	12	,	,	PUNCT
ejpam-4403	44	13	v	v	NOUN
ejpam-4403	44	14	)	)	PUNCT
ejpam-4403	44	15	|≤|	|≤|	X
ejpam-4403	44	16	µ	µ	X
ejpam-4403	44	17	|	|	ADV
ejpam-4403	44	18	∫	∫	PROPN
ejpam-4403	44	19	ω	ω	NUM
ejpam-4403	45	1	|	|	NOUN
ejpam-4403	45	2	∇u.∇v	∇u.∇v	PROPN
ejpam-4403	45	3	|	|	ADV
ejpam-4403	45	4	dω+	dω+	PROPN
ejpam-4403	45	5	∫	∫	PROPN
ejpam-4403	46	1	ω	ω	NUM
ejpam-4403	46	2	|	|	ADV
ejpam-4403	46	3	c∇u.v	c∇u.v	PROPN
ejpam-4403	46	4	|	|	ADV
ejpam-4403	46	5	dω	dω	VERB
ejpam-4403	46	6	(	(	PUNCT
ejpam-4403	46	7	6	6	NUM
ejpam-4403	46	8	)	)	PUNCT
ejpam-4403	46	9	since	since	SCONJ
ejpam-4403	46	10	c	c	PROPN
ejpam-4403	46	11	∈	∈	PROPN
ejpam-4403	46	12	l∞(ω	l∞(ω	NOUN
ejpam-4403	46	13	)	)	PUNCT
ejpam-4403	46	14	,	,	PUNCT
ejpam-4403	46	15	then	then	ADV
ejpam-4403	46	16	|	|	ADV
ejpam-4403	46	17	c	c	PROPN
ejpam-4403	46	18	|≤	|≤	PROPN
ejpam-4403	46	19	m	m	PROPN
ejpam-4403	46	20	d.	d.	PROPN
ejpam-4403	46	21	v.	v.	PROPN
ejpam-4403	46	22	pongui	pongui	PROPN
ejpam-4403	46	23	ngoma	ngoma	PROPN
ejpam-4403	46	24	et	et	PROPN
ejpam-4403	46	25	al	al	PROPN
ejpam-4403	46	26	.	.	PROPN
ejpam-4403	46	27	,	,	PUNCT
ejpam-4403	46	28	/	/	SYM
ejpam-4403	46	29	eur	eur	NOUN
ejpam-4403	46	30	.	.	PUNCT
ejpam-4403	47	1	j.	j.	PROPN
ejpam-4403	47	2	pure	pure	PROPN
ejpam-4403	47	3	appl	appl	PROPN
ejpam-4403	47	4	.	.	PROPN
ejpam-4403	47	5	math	math	PROPN
ejpam-4403	47	6	,	,	PUNCT
ejpam-4403	47	7	15	15	NUM
ejpam-4403	47	8	(	(	PUNCT
ejpam-4403	47	9	3	3	NUM
ejpam-4403	47	10	)	)	PUNCT
ejpam-4403	47	11	(	(	PUNCT
ejpam-4403	47	12	2022	2022	NUM
ejpam-4403	47	13	)	)	PUNCT
ejpam-4403	47	14	,	,	PUNCT
ejpam-4403	47	15	1348	1348	NUM
ejpam-4403	47	16	-	-	SYM
ejpam-4403	47	17	1362	1362	NUM
ejpam-4403	47	18	1351	1351	NUM
ejpam-4403	47	19	thus	thus	ADV
ejpam-4403	47	20	|	|	ADV
ejpam-4403	47	21	a(u	a(u	PROPN
ejpam-4403	47	22	,	,	PUNCT
ejpam-4403	47	23	v	v	NOUN
ejpam-4403	47	24	)	)	PUNCT
ejpam-4403	47	25	|≤|	|≤|	X
ejpam-4403	47	26	µ	µ	X
ejpam-4403	47	27	|	|	ADV
ejpam-4403	47	28	∫	∫	PROPN
ejpam-4403	47	29	ω	ω	NUM
ejpam-4403	48	1	|	|	NOUN
ejpam-4403	48	2	∇u.∇v	∇u.∇v	PROPN
ejpam-4403	49	1	|	|	ADV
ejpam-4403	50	1	dω+m	dω+m	PROPN
ejpam-4403	51	1	∫	∫	PROPN
ejpam-4403	52	1	ω	ω	NUM
ejpam-4403	53	1	|	|	ADV
ejpam-4403	53	2	∇u.v	∇u.v	NOUN
ejpam-4403	53	3	|	|	ADV
ejpam-4403	53	4	dω	dω	VERB
ejpam-4403	53	5	(	(	PUNCT
ejpam-4403	53	6	7	7	NUM
ejpam-4403	53	7	)	)	PUNCT
ejpam-4403	53	8	according	accord	VERB
ejpam-4403	53	9	to	to	ADP
ejpam-4403	53	10	the	the	DET
ejpam-4403	53	11	cauchy	cauchy	PROPN
ejpam-4403	53	12	-	-	PUNCT
ejpam-4403	53	13	schwarz	schwarz	PROPN
ejpam-4403	53	14	inequality	inequality	NOUN
ejpam-4403	53	15	[	[	X
ejpam-4403	53	16	8	8	NUM
ejpam-4403	53	17	,	,	PUNCT
ejpam-4403	53	18	10	10	NUM
ejpam-4403	53	19	,	,	PUNCT
ejpam-4403	53	20	11	11	NUM
ejpam-4403	53	21	]	]	PUNCT
ejpam-4403	53	22	|	|	ADV
ejpam-4403	53	23	a(u	a(u	PROPN
ejpam-4403	53	24	,	,	PUNCT
ejpam-4403	53	25	v	v	NOUN
ejpam-4403	53	26	)	)	PUNCT
ejpam-4403	53	27	|	|	ADV
ejpam-4403	53	28	≤|	≤|	VERB
ejpam-4403	53	29	µ	µ	PRON
ejpam-4403	53	30	|	|	ADV
ejpam-4403	53	31	(	(	PUNCT
ejpam-4403	53	32	∫	∫	PROPN
ejpam-4403	53	33	ω	ω	NUM
ejpam-4403	54	1	|	|	PROPN
ejpam-4403	54	2	∇u	∇u	PROPN
ejpam-4403	54	3	|2	|2	NUM
ejpam-4403	54	4	dω	dω	NOUN
ejpam-4403	54	5	)	)	PUNCT
ejpam-4403	54	6	1	1	NUM
ejpam-4403	54	7	2	2	NUM
ejpam-4403	54	8	(	(	PUNCT
ejpam-4403	54	9	∫	∫	PROPN
ejpam-4403	54	10	ω	ω	NUM
ejpam-4403	54	11	|	|	PROPN
ejpam-4403	54	12	∇v	∇v	PROPN
ejpam-4403	54	13	|2	|2	NUM
ejpam-4403	54	14	dω	dω	NOUN
ejpam-4403	54	15	)	)	PUNCT
ejpam-4403	54	16	1	1	NUM
ejpam-4403	54	17	2	2	NUM
ejpam-4403	55	1	+	+	NOUN
ejpam-4403	55	2	m	m	PROPN
ejpam-4403	55	3	(	(	PUNCT
ejpam-4403	55	4	∫	∫	PROPN
ejpam-4403	55	5	ω	ω	NUM
ejpam-4403	56	1	|	|	PROPN
ejpam-4403	56	2	∇u	∇u	PROPN
ejpam-4403	56	3	|2	|2	NUM
ejpam-4403	56	4	dω	dω	NOUN
ejpam-4403	56	5	)	)	PUNCT
ejpam-4403	56	6	1	1	NUM
ejpam-4403	56	7	2	2	NUM
ejpam-4403	56	8	(	(	PUNCT
ejpam-4403	56	9	∫	∫	PROPN
ejpam-4403	56	10	ω	ω	NUM
ejpam-4403	56	11	|	|	NOUN
ejpam-4403	56	12	v	v	ADP
ejpam-4403	56	13	|2	|2	NUM
ejpam-4403	56	14	dω	dω	NOUN
ejpam-4403	56	15	)	)	PUNCT
ejpam-4403	56	16	1	1	NUM
ejpam-4403	56	17	2	2	NUM
ejpam-4403	56	18	(	(	PUNCT
ejpam-4403	56	19	8)	8)	NUM
ejpam-4403	56	20	≤|	≤|	NOUN
ejpam-4403	56	21	µ	µ	PRON
ejpam-4403	56	22	|∥	|∥	PROPN
ejpam-4403	56	23	∇u	∇u	NOUN
ejpam-4403	56	24	∥l2(ω	∥l2(ω	ADV
ejpam-4403	56	25	)	)	PUNCT
ejpam-4403	56	26	.	.	PUNCT
ejpam-4403	57	1	∥	∥	X
ejpam-4403	58	1	∇v	∇v	ADV
ejpam-4403	58	2	∥l2(ω	∥l2(ω	ADV
ejpam-4403	58	3	)	)	PUNCT
ejpam-4403	59	1	+	+	VERB
ejpam-4403	59	2	m	m	VERB
ejpam-4403	59	3	∥	∥	NOUN
ejpam-4403	59	4	∇u	∇u	PROPN
ejpam-4403	59	5	∥l2(ω	∥l2(ω	ADV
ejpam-4403	59	6	)	)	PUNCT
ejpam-4403	59	7	.	.	PUNCT
ejpam-4403	60	1	∥	∥	NOUN
ejpam-4403	60	2	v	v	ADP
ejpam-4403	60	3	∥l2(ω	∥l2(ω	ADV
ejpam-4403	60	4	)	)	PUNCT
ejpam-4403	60	5	(	(	PUNCT
ejpam-4403	60	6	9	9	X
ejpam-4403	60	7	)	)	PUNCT
ejpam-4403	60	8	≤|	≤|	NOUN
ejpam-4403	60	9	µ	µ	DET
ejpam-4403	60	10	|∥	|∥	PROPN
ejpam-4403	60	11	u	u	PROPN
ejpam-4403	60	12	∥h1	∥h1	ADJ
ejpam-4403	60	13	0	0	NUM
ejpam-4403	60	14	(	(	PUNCT
ejpam-4403	60	15	ω	ω	NOUN
ejpam-4403	60	16	)	)	PUNCT
ejpam-4403	60	17	.	.	PUNCT
ejpam-4403	61	1	∥	∥	NUM
ejpam-4403	61	2	v	v	NOUN
ejpam-4403	61	3	∥h1	∥h1	NOUN
ejpam-4403	61	4	0	0	NUM
ejpam-4403	61	5	(	(	PUNCT
ejpam-4403	61	6	ω	ω	X
ejpam-4403	61	7	)	)	PUNCT
ejpam-4403	62	1	+	+	NOUN
ejpam-4403	62	2	mc	mc	PROPN
ejpam-4403	62	3	∥	∥	PROPN
ejpam-4403	62	4	u	u	PROPN
ejpam-4403	62	5	∥h1	∥h1	ADJ
ejpam-4403	62	6	0	0	NUM
ejpam-4403	62	7	(	(	PUNCT
ejpam-4403	62	8	ω	ω	NOUN
ejpam-4403	62	9	)	)	PUNCT
ejpam-4403	62	10	.	.	PUNCT
ejpam-4403	63	1	∥	∥	NUM
ejpam-4403	63	2	v	v	NOUN
ejpam-4403	63	3	∥h1	∥h1	NOUN
ejpam-4403	63	4	0ω	0ω	NOUN
ejpam-4403	63	5	)	)	PUNCT
ejpam-4403	63	6	(	(	PUNCT
ejpam-4403	63	7	10	10	NUM
ejpam-4403	63	8	)	)	PUNCT
ejpam-4403	63	9	≤|	≤|	NOUN
ejpam-4403	63	10	µ	µ	DET
ejpam-4403	63	11	|∥	|∥	PROPN
ejpam-4403	63	12	u	u	PROPN
ejpam-4403	63	13	∥h1	∥h1	ADJ
ejpam-4403	63	14	0	0	NUM
ejpam-4403	63	15	(	(	PUNCT
ejpam-4403	63	16	ω	ω	NOUN
ejpam-4403	63	17	)	)	PUNCT
ejpam-4403	63	18	.	.	PUNCT
ejpam-4403	64	1	∥	∥	NUM
ejpam-4403	64	2	v	v	NOUN
ejpam-4403	64	3	∥h1	∥h1	NOUN
ejpam-4403	64	4	0	0	NUM
ejpam-4403	64	5	(	(	PUNCT
ejpam-4403	64	6	ω	ω	NOUN
ejpam-4403	64	7	)	)	PUNCT
ejpam-4403	65	1	+	+	NOUN
ejpam-4403	65	2	m	m	VERB
ejpam-4403	65	3	′	′	ADJ
ejpam-4403	65	4	∥	∥	NUM
ejpam-4403	65	5	u	u	NOUN
ejpam-4403	65	6	∥h1	∥h1	ADJ
ejpam-4403	65	7	0	0	NUM
ejpam-4403	65	8	(	(	PUNCT
ejpam-4403	65	9	ω	ω	NOUN
ejpam-4403	65	10	)	)	PUNCT
ejpam-4403	65	11	.	.	PUNCT
ejpam-4403	66	1	∥	∥	NUM
ejpam-4403	66	2	v	v	NOUN
ejpam-4403	66	3	∥h1	∥h1	NOUN
ejpam-4403	66	4	0ω	0ω	NOUN
ejpam-4403	66	5	)	)	PUNCT
ejpam-4403	66	6	(	(	PUNCT
ejpam-4403	66	7	11	11	NUM
ejpam-4403	66	8	)	)	PUNCT
ejpam-4403	66	9	≤	≤	NOUN
ejpam-4403	66	10	(	(	PUNCT
ejpam-4403	66	11	|	|	ADV
ejpam-4403	66	12	µ	µ	X
ejpam-4403	67	1	|	|	NOUN
ejpam-4403	67	2	+	+	NOUN
ejpam-4403	67	3	m	m	NOUN
ejpam-4403	67	4	′	′	NUM
ejpam-4403	67	5	)	)	PUNCT
ejpam-4403	67	6	∥	∥	NUM
ejpam-4403	67	7	u	u	NOUN
ejpam-4403	67	8	∥h1	∥h1	ADJ
ejpam-4403	67	9	0	0	NUM
ejpam-4403	67	10	(	(	PUNCT
ejpam-4403	67	11	ω	ω	NOUN
ejpam-4403	67	12	)	)	PUNCT
ejpam-4403	67	13	.	.	PUNCT
ejpam-4403	68	1	∥	∥	NUM
ejpam-4403	68	2	v	v	NOUN
ejpam-4403	68	3	∥h1	∥h1	NOUN
ejpam-4403	68	4	0	0	NUM
ejpam-4403	68	5	(	(	PUNCT
ejpam-4403	68	6	ω	ω	NOUN
ejpam-4403	68	7	)	)	PUNCT
ejpam-4403	68	8	(	(	PUNCT
ejpam-4403	68	9	12	12	NUM
ejpam-4403	68	10	)	)	PUNCT
ejpam-4403	68	11	|	|	ADV
ejpam-4403	68	12	a(u	a(u	PROPN
ejpam-4403	68	13	,	,	PUNCT
ejpam-4403	68	14	v	v	NOUN
ejpam-4403	68	15	)	)	PUNCT
ejpam-4403	69	1	|	|	ADV
ejpam-4403	69	2	≤	≤	NUM
ejpam-4403	69	3	c	c	X
ejpam-4403	69	4	∥	∥	X
ejpam-4403	69	5	u	u	PROPN
ejpam-4403	69	6	∥h1	∥h1	ADJ
ejpam-4403	69	7	0	0	NUM
ejpam-4403	69	8	(	(	PUNCT
ejpam-4403	69	9	ω	ω	NOUN
ejpam-4403	69	10	)	)	PUNCT
ejpam-4403	69	11	.	.	PUNCT
ejpam-4403	70	1	∥	∥	NUM
ejpam-4403	70	2	v	v	NOUN
ejpam-4403	70	3	∥h1	∥h1	NOUN
ejpam-4403	70	4	0	0	NUM
ejpam-4403	70	5	(	(	PUNCT
ejpam-4403	70	6	ω	ω	NOUN
ejpam-4403	70	7	)	)	PUNCT
ejpam-4403	70	8	,	,	PUNCT
ejpam-4403	70	9	where	where	SCONJ
ejpam-4403	70	10	c	c	NOUN
ejpam-4403	70	11	=|	=|	X
ejpam-4403	70	12	µ	µ	X
ejpam-4403	71	1	|	|	NOUN
ejpam-4403	72	1	+	+	NOUN
ejpam-4403	72	2	m	m	PROPN
ejpam-4403	72	3	′,whith	′,whith	NOUN
ejpam-4403	72	4	m	m	VERB
ejpam-4403	72	5	′	′	NOUN
ejpam-4403	72	6	=	=	PUNCT
ejpam-4403	72	7	constant	constant	ADJ
ejpam-4403	72	8	(	(	PUNCT
ejpam-4403	72	9	13	13	NUM
ejpam-4403	72	10	)	)	PUNCT
ejpam-4403	72	11	therefore	therefore	ADV
ejpam-4403	72	12	a	a	PRON
ejpam-4403	72	13	is	be	AUX
ejpam-4403	72	14	continue	continue	ADJ
ejpam-4403	72	15	.	.	PUNCT
ejpam-4403	73	1	•	•	INTJ
ejpam-4403	73	2	let	let	VERB
ejpam-4403	73	3	us	we	PRON
ejpam-4403	73	4	show	show	VERB
ejpam-4403	73	5	that	that	SCONJ
ejpam-4403	73	6	the	the	DET
ejpam-4403	73	7	bilinear	bilinear	NOUN
ejpam-4403	73	8	form	form	NOUN
ejpam-4403	73	9	a	a	PRON
ejpam-4403	73	10	is	be	AUX
ejpam-4403	73	11	coercive	coercive	ADJ
ejpam-4403	73	12	let	let	NOUN
ejpam-4403	73	13	v	v	NOUN
ejpam-4403	73	14	=	=	SYM
ejpam-4403	73	15	u	u	NOUN
ejpam-4403	73	16	,	,	PUNCT
ejpam-4403	73	17	then	then	ADV
ejpam-4403	73	18	a(u	a(u	NOUN
ejpam-4403	73	19	,	,	PUNCT
ejpam-4403	73	20	u	u	NOUN
ejpam-4403	73	21	)	)	PUNCT
ejpam-4403	73	22	=	=	SYM
ejpam-4403	73	23	µ	µ	PRON
ejpam-4403	73	24	∫	∫	PROPN
ejpam-4403	73	25	ω	ω	PROPN
ejpam-4403	73	26	(	(	PUNCT
ejpam-4403	73	27	∇u)2	∇u)2	ADV
ejpam-4403	73	28	dω+	dω+	PROPN
ejpam-4403	73	29	∫	∫	PROPN
ejpam-4403	73	30	ω	ω	PROPN
ejpam-4403	73	31	c∇u.u	c∇u.u	PROPN
ejpam-4403	73	32	dω	dω	ADP
ejpam-4403	73	33	(	(	PUNCT
ejpam-4403	73	34	14	14	NUM
ejpam-4403	73	35	)	)	PUNCT
ejpam-4403	73	36	assuming	assume	VERB
ejpam-4403	73	37	that	that	SCONJ
ejpam-4403	73	38	,	,	PUNCT
ejpam-4403	73	39	c	c	PROPN
ejpam-4403	73	40	≥	≥	PROPN
ejpam-4403	73	41	c0	c0	X
ejpam-4403	73	42	>	>	X
ejpam-4403	73	43	0	0	PROPN
ejpam-4403	73	44	,	,	PUNCT
ejpam-4403	73	45	therefore	therefore	ADV
ejpam-4403	73	46	a(u	a(u	X
ejpam-4403	73	47	,	,	PUNCT
ejpam-4403	73	48	u	u	NOUN
ejpam-4403	73	49	)	)	PUNCT
ejpam-4403	73	50	≥	≥	PROPN
ejpam-4403	73	51	µ	µ	PROPN
ejpam-4403	73	52	∫	∫	PROPN
ejpam-4403	73	53	ω	ω	PROPN
ejpam-4403	73	54	(	(	PUNCT
ejpam-4403	73	55	∇u)2	∇u)2	ADV
ejpam-4403	73	56	dω+	dω+	PROPN
ejpam-4403	73	57	c0	c0	PROPN
ejpam-4403	73	58	∫	∫	PROPN
ejpam-4403	73	59	ω	ω	PROPN
ejpam-4403	73	60	∇u.u	∇u.u	NOUN
ejpam-4403	73	61	dω	dω	PROPN
ejpam-4403	73	62	(	(	PUNCT
ejpam-4403	73	63	15	15	NUM
ejpam-4403	73	64	)	)	PUNCT
ejpam-4403	73	65	a(u	a(u	NOUN
ejpam-4403	73	66	,	,	PUNCT
ejpam-4403	73	67	u	u	NOUN
ejpam-4403	73	68	)	)	PUNCT
ejpam-4403	73	69	≥	≥	PROPN
ejpam-4403	73	70	µ	µ	PROPN
ejpam-4403	73	71	∫	∫	PROPN
ejpam-4403	73	72	ω	ω	PROPN
ejpam-4403	73	73	(	(	PUNCT
ejpam-4403	73	74	∇u)2	∇u)2	ADV
ejpam-4403	73	75	dω	dω	VERB
ejpam-4403	73	76	(	(	PUNCT
ejpam-4403	73	77	16	16	NUM
ejpam-4403	73	78	)	)	PUNCT
ejpam-4403	73	79	a(u	a(u	PROPN
ejpam-4403	73	80	,	,	PUNCT
ejpam-4403	73	81	u	u	NOUN
ejpam-4403	73	82	)	)	PUNCT
ejpam-4403	73	83	≥	≥	X
ejpam-4403	73	84	µ	µ	X
ejpam-4403	73	85	∥	∥	X
ejpam-4403	73	86	u	u	NOUN
ejpam-4403	73	87	∥2h1	∥2h1	NOUN
ejpam-4403	73	88	0	0	NUM
ejpam-4403	73	89	(	(	PUNCT
ejpam-4403	73	90	ω	ω	NOUN
ejpam-4403	73	91	)	)	PUNCT
ejpam-4403	73	92	(	(	PUNCT
ejpam-4403	73	93	17	17	NUM
ejpam-4403	73	94	)	)	PUNCT
ejpam-4403	73	95	a(u	a(u	PROPN
ejpam-4403	73	96	,	,	PUNCT
ejpam-4403	73	97	u	u	NOUN
ejpam-4403	73	98	)	)	PUNCT
ejpam-4403	73	99	≥	≥	PROPN
ejpam-4403	73	100	α	α	NOUN
ejpam-4403	73	101	∥	∥	X
ejpam-4403	73	102	u	u	NOUN
ejpam-4403	73	103	∥2h1	∥2h1	NOUN
ejpam-4403	73	104	0	0	NUM
ejpam-4403	73	105	(	(	PUNCT
ejpam-4403	73	106	ω),withµ	ω),withµ	NOUN
ejpam-4403	73	107	=	=	SYM
ejpam-4403	73	108	α	α	PROPN
ejpam-4403	73	109	(	(	PUNCT
ejpam-4403	73	110	18	18	NUM
ejpam-4403	73	111	)	)	PUNCT
ejpam-4403	73	112	therefore	therefore	ADV
ejpam-4403	73	113	a	a	PRON
ejpam-4403	73	114	is	be	AUX
ejpam-4403	73	115	coercive	coercive	ADJ
ejpam-4403	73	116	.	.	PUNCT
ejpam-4403	74	1	(	(	PUNCT
ejpam-4403	74	2	19	19	NUM
ejpam-4403	74	3	)	)	PUNCT
ejpam-4403	74	4	(	(	PUNCT
ejpam-4403	74	5	20	20	NUM
ejpam-4403	74	6	)	)	PUNCT
ejpam-4403	74	7	•	•	NOUN
ejpam-4403	74	8	let	let	VERB
ejpam-4403	74	9	us	we	PRON
ejpam-4403	74	10	show	show	VERB
ejpam-4403	74	11	that	that	SCONJ
ejpam-4403	74	12	the	the	DET
ejpam-4403	74	13	linear	linear	ADJ
ejpam-4403	74	14	form	form	NOUN
ejpam-4403	74	15	l	l	NOUN
ejpam-4403	74	16	is	be	AUX
ejpam-4403	74	17	continuous	continuous	ADJ
ejpam-4403	74	18	on	on	ADP
ejpam-4403	74	19	v	v	NOUN
ejpam-4403	74	20	=	=	PUNCT
ejpam-4403	74	21	h1	h1	NOUN
ejpam-4403	74	22	0	0	NUM
ejpam-4403	74	23	(	(	PUNCT
ejpam-4403	74	24	ω	ω	NOUN
ejpam-4403	74	25	)	)	PUNCT
ejpam-4403	74	26	we	we	PRON
ejpam-4403	74	27	have	have	VERB
ejpam-4403	74	28	,	,	PUNCT
ejpam-4403	74	29	l(v	l(v	NOUN
ejpam-4403	74	30	)	)	PUNCT
ejpam-4403	75	1	=	=	SYM
ejpam-4403	75	2	∫	∫	PROPN
ejpam-4403	76	1	ω	ω	PROPN
ejpam-4403	76	2	f.v	f.v	PROPN
ejpam-4403	76	3	dω	dω	PROPN
ejpam-4403	76	4	(	(	PUNCT
ejpam-4403	76	5	21	21	NUM
ejpam-4403	76	6	)	)	PUNCT
ejpam-4403	76	7	=|	=|	NOUN
ejpam-4403	77	1	∫	∫	PROPN
ejpam-4403	77	2	ω	ω	PROPN
ejpam-4403	77	3	f.v	f.v	PROPN
ejpam-4403	77	4	dω	dω	PROPN
ejpam-4403	77	5	|	|	ADV
ejpam-4403	77	6	(	(	PUNCT
ejpam-4403	77	7	22	22	NUM
ejpam-4403	77	8	)	)	PUNCT
ejpam-4403	77	9	d.	d.	PROPN
ejpam-4403	77	10	v.	v.	PROPN
ejpam-4403	77	11	pongui	pongui	PROPN
ejpam-4403	77	12	ngoma	ngoma	PROPN
ejpam-4403	77	13	et	et	PROPN
ejpam-4403	77	14	al	al	PROPN
ejpam-4403	77	15	.	.	PROPN
ejpam-4403	77	16	,	,	PUNCT
ejpam-4403	77	17	/	/	SYM
ejpam-4403	77	18	eur	eur	NOUN
ejpam-4403	77	19	.	.	PUNCT
ejpam-4403	78	1	j.	j.	PROPN
ejpam-4403	78	2	pure	pure	PROPN
ejpam-4403	78	3	appl	appl	PROPN
ejpam-4403	78	4	.	.	PROPN
ejpam-4403	78	5	math	math	PROPN
ejpam-4403	78	6	,	,	PUNCT
ejpam-4403	78	7	15	15	NUM
ejpam-4403	78	8	(	(	PUNCT
ejpam-4403	78	9	3	3	NUM
ejpam-4403	78	10	)	)	PUNCT
ejpam-4403	78	11	(	(	PUNCT
ejpam-4403	78	12	2022	2022	NUM
ejpam-4403	78	13	)	)	PUNCT
ejpam-4403	78	14	,	,	PUNCT
ejpam-4403	78	15	1348	1348	NUM
ejpam-4403	78	16	-	-	SYM
ejpam-4403	78	17	1362	1362	NUM
ejpam-4403	78	18	1352	1352	NUM
ejpam-4403	78	19	≤	≤	NUM
ejpam-4403	78	20	∫	∫	PROPN
ejpam-4403	79	1	ω	ω	NUM
ejpam-4403	79	2	|	|	PROPN
ejpam-4403	79	3	f.v	f.v	PROPN
ejpam-4403	79	4	|	|	ADV
ejpam-4403	79	5	dω	dω	VERB
ejpam-4403	79	6	(	(	PUNCT
ejpam-4403	79	7	23	23	NUM
ejpam-4403	79	8	)	)	PUNCT
ejpam-4403	79	9	according	accord	VERB
ejpam-4403	79	10	to	to	ADP
ejpam-4403	79	11	the	the	DET
ejpam-4403	79	12	cauchy	cauchy	PROPN
ejpam-4403	79	13	-	-	PUNCT
ejpam-4403	79	14	schwartz	schwartz	PROPN
ejpam-4403	79	15	inequality	inequality	NOUN
ejpam-4403	79	16	|	|	ADP
ejpam-4403	79	17	l(v	l(v	NOUN
ejpam-4403	79	18	)	)	PUNCT
ejpam-4403	79	19	|≤	|≤	PROPN
ejpam-4403	79	20	(	(	PUNCT
ejpam-4403	79	21	∫	∫	PROPN
ejpam-4403	79	22	ω	ω	NUM
ejpam-4403	79	23	|	|	PROPN
ejpam-4403	79	24	f	f	PROPN
ejpam-4403	79	25	|2	|2	NUM
ejpam-4403	79	26	dω	dω	NOUN
ejpam-4403	79	27	)	)	PUNCT
ejpam-4403	79	28	1	1	NUM
ejpam-4403	79	29	2	2	NUM
ejpam-4403	79	30	(	(	PUNCT
ejpam-4403	79	31	∫	∫	PROPN
ejpam-4403	79	32	ω	ω	NUM
ejpam-4403	79	33	|	|	NOUN
ejpam-4403	79	34	v	v	ADP
ejpam-4403	79	35	|2	|2	NUM
ejpam-4403	79	36	dω	dω	NOUN
ejpam-4403	79	37	)	)	PUNCT
ejpam-4403	79	38	1	1	NUM
ejpam-4403	79	39	2	2	NUM
ejpam-4403	79	40	(	(	PUNCT
ejpam-4403	79	41	24	24	NUM
ejpam-4403	79	42	)	)	PUNCT
ejpam-4403	79	43	|	|	ADV
ejpam-4403	79	44	l(v	l(v	NOUN
ejpam-4403	79	45	)	)	PUNCT
ejpam-4403	79	46	|≤∥	|≤∥	PROPN
ejpam-4403	79	47	f	f	PROPN
ejpam-4403	79	48	∥l2(ω	∥l2(ω	ADV
ejpam-4403	79	49	)	)	PUNCT
ejpam-4403	79	50	.	.	PUNCT
ejpam-4403	80	1	∥	∥	NOUN
ejpam-4403	80	2	v	v	ADP
ejpam-4403	80	3	∥l2(ω	∥l2(ω	ADV
ejpam-4403	80	4	)	)	PUNCT
ejpam-4403	80	5	(	(	PUNCT
ejpam-4403	80	6	25	25	NUM
ejpam-4403	80	7	)	)	PUNCT
ejpam-4403	80	8	(	(	PUNCT
ejpam-4403	80	9	26	26	NUM
ejpam-4403	80	10	)	)	PUNCT
ejpam-4403	80	11	since	since	SCONJ
ejpam-4403	80	12	f	f	PROPN
ejpam-4403	80	13	∈	∈	PROPN
ejpam-4403	80	14	l2(ω	l2(ω	PROPN
ejpam-4403	80	15	)	)	PUNCT
ejpam-4403	80	16	then	then	ADV
ejpam-4403	80	17	∥	∥	PROPN
ejpam-4403	80	18	f	f	PROPN
ejpam-4403	80	19	∥l2(ω)≤	∥l2(ω)≤	PROPN
ejpam-4403	80	20	m1	m1	PROPN
ejpam-4403	80	21	and	and	CCONJ
ejpam-4403	80	22	∥	∥	NUM
ejpam-4403	80	23	v	v	NOUN
ejpam-4403	81	1	∥l2(ω)≤	∥l2(ω)≤	ADP
ejpam-4403	81	2	c	c	NOUN
ejpam-4403	81	3	∥	∥	NOUN
ejpam-4403	81	4	v	v	NOUN
ejpam-4403	81	5	∥h1	∥h1	NOUN
ejpam-4403	81	6	0	0	NUM
ejpam-4403	81	7	(	(	PUNCT
ejpam-4403	81	8	ω	ω	NOUN
ejpam-4403	81	9	)	)	PUNCT
ejpam-4403	81	10	therefore	therefore	ADV
ejpam-4403	81	11	|	|	ADV
ejpam-4403	81	12	l(v	l(v	NOUN
ejpam-4403	81	13	)	)	PUNCT
ejpam-4403	81	14	|≤	|≤	PROPN
ejpam-4403	81	15	m1c	m1c	PROPN
ejpam-4403	81	16	∥	∥	PUNCT
ejpam-4403	81	17	v	v	NOUN
ejpam-4403	81	18	∥h1	∥h1	NOUN
ejpam-4403	81	19	0	0	NUM
ejpam-4403	82	1	(	(	PUNCT
ejpam-4403	82	2	ω	ω	NOUN
ejpam-4403	82	3	)	)	PUNCT
ejpam-4403	82	4	hence	hence	ADV
ejpam-4403	82	5	|	|	ADV
ejpam-4403	82	6	l(v	l(v	NOUN
ejpam-4403	82	7	)	)	PUNCT
ejpam-4403	82	8	|≤	|≤	PROPN
ejpam-4403	82	9	β	β	X
ejpam-4403	82	10	∥	∥	NOUN
ejpam-4403	82	11	v	v	NOUN
ejpam-4403	82	12	∥h1	∥h1	NOUN
ejpam-4403	82	13	0	0	NUM
ejpam-4403	83	1	(	(	PUNCT
ejpam-4403	83	2	ω	ω	NOUN
ejpam-4403	83	3	)	)	PUNCT
ejpam-4403	83	4	withβ	withβ	NOUN
ejpam-4403	83	5	=	=	SYM
ejpam-4403	83	6	m1c	m1c	PROPN
ejpam-4403	83	7	thus	thus	ADV
ejpam-4403	83	8	l	l	NOUN
ejpam-4403	83	9	is	be	AUX
ejpam-4403	83	10	continue	continue	ADJ
ejpam-4403	83	11	.	.	PUNCT
ejpam-4403	84	1	all	all	DET
ejpam-4403	84	2	the	the	DET
ejpam-4403	84	3	hypotheses	hypothesis	NOUN
ejpam-4403	84	4	of	of	ADP
ejpam-4403	84	5	the	the	DET
ejpam-4403	84	6	lax	lax	PROPN
ejpam-4403	84	7	-	-	PUNCT
ejpam-4403	84	8	milgram	milgram	NOUN
ejpam-4403	84	9	theorem	theorem	NOUN
ejpam-4403	84	10	being	be	AUX
ejpam-4403	84	11	satisfied	satisfied	ADJ
ejpam-4403	84	12	,	,	PUNCT
ejpam-4403	84	13	we	we	PRON
ejpam-4403	84	14	deduce	deduce	VERB
ejpam-4403	84	15	that	that	SCONJ
ejpam-4403	84	16	the	the	DET
ejpam-4403	84	17	variational	variational	ADJ
ejpam-4403	84	18	problem	problem	NOUN
ejpam-4403	84	19	admits	admit	VERB
ejpam-4403	84	20	a	a	DET
ejpam-4403	84	21	unique	unique	ADJ
ejpam-4403	84	22	solution	solution	NOUN
ejpam-4403	84	23	u	u	NOUN
ejpam-4403	84	24	∈	∈	PROPN
ejpam-4403	84	25	h1	h1	NOUN
ejpam-4403	84	26	0	0	NUM
ejpam-4403	84	27	(	(	PUNCT
ejpam-4403	84	28	ω	ω	NOUN
ejpam-4403	84	29	)	)	PUNCT
ejpam-4403	84	30	.	.	PUNCT
ejpam-4403	85	1	4	4	X
ejpam-4403	85	2	.	.	X
ejpam-4403	85	3	numerical	numerical	ADJ
ejpam-4403	85	4	resolution	resolution	NOUN
ejpam-4403	85	5	of	of	ADP
ejpam-4403	85	6	the	the	DET
ejpam-4403	85	7	problem	problem	NOUN
ejpam-4403	85	8	in	in	ADP
ejpam-4403	85	9	this	this	DET
ejpam-4403	85	10	section	section	NOUN
ejpam-4403	85	11	,	,	PUNCT
ejpam-4403	85	12	we	we	PRON
ejpam-4403	85	13	will	will	AUX
ejpam-4403	85	14	try	try	VERB
ejpam-4403	85	15	to	to	PART
ejpam-4403	85	16	solve	solve	VERB
ejpam-4403	85	17	the	the	DET
ejpam-4403	85	18	cauchy	cauchy	PROPN
ejpam-4403	85	19	-	-	PUNCT
ejpam-4403	85	20	dirichlet	dirichlet	PROPN
ejpam-4403	85	21	problem	problem	NOUN
ejpam-4403	85	22	by	by	ADP
ejpam-4403	85	23	a	a	DET
ejpam-4403	85	24	numerical	numerical	ADJ
ejpam-4403	85	25	method	method	NOUN
ejpam-4403	85	26	,	,	PUNCT
ejpam-4403	85	27	in	in	ADP
ejpam-4403	85	28	particular	particular	ADJ
ejpam-4403	85	29	the	the	DET
ejpam-4403	85	30	finite	finite	ADJ
ejpam-4403	85	31	difference	difference	NOUN
ejpam-4403	85	32	method	method	NOUN
ejpam-4403	85	33	.	.	PUNCT
ejpam-4403	86	1	to	to	PART
ejpam-4403	86	2	do	do	VERB
ejpam-4403	86	3	this	this	PRON
ejpam-4403	86	4	,	,	PUNCT
ejpam-4403	86	5	let	let	VERB
ejpam-4403	86	6	’s	’s	PRON
ejpam-4403	86	7	use	use	VERB
ejpam-4403	86	8	the	the	DET
ejpam-4403	86	9	cauchydirichlet	cauchydirichlet	NOUN
ejpam-4403	86	10	problem	problem	NOUN
ejpam-4403	86	11	in	in	ADP
ejpam-4403	86	12	dimension	dimension	NOUN
ejpam-4403	86	13	one	one	NUM
ejpam-4403	86	14	,	,	PUNCT
ejpam-4403	86	15	which	which	PRON
ejpam-4403	86	16	is	be	AUX
ejpam-4403	86	17	presented	present	VERB
ejpam-4403	86	18	in	in	ADP
ejpam-4403	86	19	the	the	DET
ejpam-4403	86	20	following	following	ADJ
ejpam-4403	86	21	way	way	NOUN
ejpam-4403	86	22	:	:	PUNCT
ejpam-4403	86	23	{	{	PUNCT
ejpam-4403	86	24	−µu′′(x	−µu′′(x	NOUN
ejpam-4403	86	25	)	)	PUNCT
ejpam-4403	87	1	+	+	NUM
ejpam-4403	87	2	c(x)u′(x	c(x)u′(x	NOUN
ejpam-4403	87	3	)	)	PUNCT
ejpam-4403	87	4	=	=	SYM
ejpam-4403	87	5	f(x	f(x	PROPN
ejpam-4403	87	6	)	)	PUNCT
ejpam-4403	87	7	,	,	PUNCT
ejpam-4403	87	8	x	x	X
ejpam-4403	87	9	∈]0	∈]0	X
ejpam-4403	87	10	;	;	PUNCT
ejpam-4403	87	11	1	1	NUM
ejpam-4403	87	12	[	[	PUNCT
ejpam-4403	87	13	u(0	u(0	PROPN
ejpam-4403	87	14	,	,	PUNCT
ejpam-4403	87	15	t	t	PROPN
ejpam-4403	87	16	)	)	PUNCT
ejpam-4403	87	17	=	=	SYM
ejpam-4403	88	1	u(1	u(1	PROPN
ejpam-4403	88	2	,	,	PUNCT
ejpam-4403	88	3	t	t	PROPN
ejpam-4403	88	4	)	)	PUNCT
ejpam-4403	88	5	(	(	PUNCT
ejpam-4403	88	6	27	27	NUM
ejpam-4403	88	7	)	)	PUNCT
ejpam-4403	88	8	one	one	NOUN
ejpam-4403	88	9	describes	describe	VERB
ejpam-4403	88	10	the	the	DET
ejpam-4403	88	11	method	method	NOUN
ejpam-4403	88	12	in	in	ADP
ejpam-4403	88	13	three	three	NUM
ejpam-4403	88	14	parts	part	NOUN
ejpam-4403	88	15	:	:	PUNCT
ejpam-4403	88	16	choice	choice	NOUN
ejpam-4403	88	17	of	of	ADP
ejpam-4403	88	18	the	the	DET
ejpam-4403	88	19	mesh	mesh	NOUN
ejpam-4403	88	20	,	,	PUNCT
ejpam-4403	88	21	choice	choice	NOUN
ejpam-4403	88	22	of	of	ADP
ejpam-4403	88	23	the	the	DET
ejpam-4403	88	24	numerical	numerical	ADJ
ejpam-4403	88	25	scheme	scheme	NOUN
ejpam-4403	88	26	and	and	CCONJ
ejpam-4403	88	27	discretization	discretization	NOUN
ejpam-4403	88	28	of	of	ADP
ejpam-4403	88	29	the	the	DET
ejpam-4403	88	30	problem	problem	NOUN
ejpam-4403	88	31	.	.	PUNCT
ejpam-4403	89	1	first	first	ADJ
ejpam-4403	89	2	step	step	NOUN
ejpam-4403	89	3	:	:	PUNCT
ejpam-4403	89	4	choice	choice	NOUN
ejpam-4403	89	5	of	of	ADP
ejpam-4403	89	6	the	the	DET
ejpam-4403	89	7	discretization	discretization	NOUN
ejpam-4403	89	8	.	.	PUNCT
ejpam-4403	90	1	we	we	PRON
ejpam-4403	90	2	consider	consider	VERB
ejpam-4403	90	3	a	a	DET
ejpam-4403	90	4	subdivision	subdivision	NOUN
ejpam-4403	90	5	,	,	PUNCT
ejpam-4403	90	6	0	0	PUNCT
ejpam-4403	91	1	=	=	SYM
ejpam-4403	91	2	x0	x0	PROPN
ejpam-4403	91	3	<	<	X
ejpam-4403	92	1	x1	x1	X
ejpam-4403	92	2	<	<	X
ejpam-4403	92	3	x2	x2	X
ejpam-4403	92	4	<	<	X
ejpam-4403	92	5	...	...	PUNCT
ejpam-4403	93	1	<	<	X
ejpam-4403	93	2	xn	xn	X
ejpam-4403	93	3	<	<	X
ejpam-4403	93	4	xn+1	xn+1	PROPN
ejpam-4403	93	5	=	=	SYM
ejpam-4403	93	6	1	1	NUM
ejpam-4403	93	7	,	,	PUNCT
ejpam-4403	93	8	of	of	ADP
ejpam-4403	93	9	the	the	DET
ejpam-4403	93	10	interval	interval	NOUN
ejpam-4403	93	11	[	[	X
ejpam-4403	93	12	0	0	NUM
ejpam-4403	93	13	,	,	PUNCT
ejpam-4403	93	14	1	1	NUM
ejpam-4403	93	15	]	]	PUNCT
ejpam-4403	93	16	,	,	PUNCT
ejpam-4403	93	17	where	where	SCONJ
ejpam-4403	93	18	n	n	X
ejpam-4403	93	19	∈	∈	PROPN
ejpam-4403	93	20	n.	n.	NOUN
ejpam-4403	93	21	for	for	ADP
ejpam-4403	93	22	i	i	PROPN
ejpam-4403	93	23	=	=	NOUN
ejpam-4403	93	24	0	0	NUM
ejpam-4403	93	25	,	,	PUNCT
ejpam-4403	93	26	...	...	PUNCT
ejpam-4403	93	27	,	,	PUNCT
ejpam-4403	93	28	n	n	X
ejpam-4403	93	29	,	,	PUNCT
ejpam-4403	93	30	we	we	PRON
ejpam-4403	93	31	put	put	VERB
ejpam-4403	93	32	,	,	PUNCT
ejpam-4403	93	33	∆xi	∆xi	PROPN
ejpam-4403	93	34	=	=	PUNCT
ejpam-4403	94	1	xi+1	xi+1	PROPN
ejpam-4403	95	1	−	−	NOUN
ejpam-4403	95	2	xi	xi	PROPN
ejpam-4403	95	3	,	,	PUNCT
ejpam-4403	95	4	with	with	ADP
ejpam-4403	95	5	∆x	∆x	PROPN
ejpam-4403	95	6	=	=	SYM
ejpam-4403	95	7	max	max	PROPN
ejpam-4403	95	8	1⩽i⩽n	1⩽i⩽n	NUM
ejpam-4403	95	9	∆xi	∆xi	PROPN
ejpam-4403	95	10	,	,	PUNCT
ejpam-4403	95	11	the	the	DET
ejpam-4403	95	12	mesh	mesh	NOUN
ejpam-4403	95	13	step	step	NOUN
ejpam-4403	95	14	.	.	PUNCT
ejpam-4403	96	1	the	the	DET
ejpam-4403	96	2	first	first	ADJ
ejpam-4403	96	3	step	step	NOUN
ejpam-4403	96	4	of	of	ADP
ejpam-4403	96	5	discretization	discretization	NOUN
ejpam-4403	96	6	consists	consist	VERB
ejpam-4403	96	7	in	in	ADP
ejpam-4403	96	8	approximating	approximate	VERB
ejpam-4403	96	9	the	the	DET
ejpam-4403	96	10	functions	function	NOUN
ejpam-4403	96	11	u	u	NOUN
ejpam-4403	96	12	,	,	PUNCT
ejpam-4403	96	13	c	c	PROPN
ejpam-4403	96	14	and	and	CCONJ
ejpam-4403	96	15	f	f	PROPN
ejpam-4403	96	16	at	at	ADP
ejpam-4403	96	17	the	the	DET
ejpam-4403	96	18	nodes	node	NOUN
ejpam-4403	96	19	xi	xi	PROPN
ejpam-4403	96	20	,	,	PUNCT
ejpam-4403	96	21	that	that	PRON
ejpam-4403	96	22	is	be	AUX
ejpam-4403	96	23	to	to	PART
ejpam-4403	96	24	say	say	VERB
ejpam-4403	96	25	:	:	PUNCT
ejpam-4403	96	26	u(xi	u(xi	NOUN
ejpam-4403	96	27	)	)	PUNCT
ejpam-4403	96	28	≃	≃	NOUN
ejpam-4403	96	29	ui	ui	PROPN
ejpam-4403	96	30	,	,	PUNCT
ejpam-4403	96	31	c(xi	c(xi	PROPN
ejpam-4403	96	32	)	)	PUNCT
ejpam-4403	96	33	≃	≃	PROPN
ejpam-4403	96	34	ci	ci	PROPN
ejpam-4403	96	35	,	,	PUNCT
ejpam-4403	96	36	f(xi	f(xi	PROPN
ejpam-4403	96	37	)	)	PUNCT
ejpam-4403	96	38	≃	≃	NOUN
ejpam-4403	96	39	fi	fi	NOUN
ejpam-4403	96	40	the	the	DET
ejpam-4403	96	41	problem	problem	NOUN
ejpam-4403	96	42	(	(	PUNCT
ejpam-4403	96	43	27	27	NUM
ejpam-4403	96	44	)	)	PUNCT
ejpam-4403	96	45	become	become	VERB
ejpam-4403	96	46	{	{	PUNCT
ejpam-4403	96	47	−µ.u′′i	−µ.u′′i	X
ejpam-4403	96	48	+	+	CCONJ
ejpam-4403	96	49	ci.u	ci.u	VERB
ejpam-4403	96	50	′	′	NUM
ejpam-4403	97	1	i	i	PRON
ejpam-4403	97	2	=	=	PUNCT
ejpam-4403	98	1	fi,∀i	fi,∀i	NOUN
ejpam-4403	98	2	=	=	SYM
ejpam-4403	98	3	1	1	NUM
ejpam-4403	98	4	,	,	PUNCT
ejpam-4403	98	5	...	...	PUNCT
ejpam-4403	98	6	,	,	PUNCT
ejpam-4403	98	7	n	n	PROPN
ejpam-4403	98	8	u(0	u(0	NOUN
ejpam-4403	98	9	)	)	PUNCT
ejpam-4403	98	10	=	=	SYM
ejpam-4403	99	1	un+1	un+1	X
ejpam-4403	99	2	(	(	PUNCT
ejpam-4403	99	3	28	28	NUM
ejpam-4403	99	4	)	)	PUNCT
ejpam-4403	99	5	d.	d.	PROPN
ejpam-4403	99	6	v.	v.	PROPN
ejpam-4403	99	7	pongui	pongui	PROPN
ejpam-4403	99	8	ngoma	ngoma	PROPN
ejpam-4403	99	9	et	et	PROPN
ejpam-4403	99	10	al	al	PROPN
ejpam-4403	99	11	.	.	PROPN
ejpam-4403	99	12	,	,	PUNCT
ejpam-4403	99	13	/	/	SYM
ejpam-4403	99	14	eur	eur	NOUN
ejpam-4403	99	15	.	.	PUNCT
ejpam-4403	100	1	j.	j.	PROPN
ejpam-4403	100	2	pure	pure	PROPN
ejpam-4403	100	3	appl	appl	PROPN
ejpam-4403	100	4	.	.	PROPN
ejpam-4403	100	5	math	math	PROPN
ejpam-4403	100	6	,	,	PUNCT
ejpam-4403	100	7	15	15	NUM
ejpam-4403	100	8	(	(	PUNCT
ejpam-4403	100	9	3	3	NUM
ejpam-4403	100	10	)	)	PUNCT
ejpam-4403	100	11	(	(	PUNCT
ejpam-4403	100	12	2022	2022	NUM
ejpam-4403	100	13	)	)	PUNCT
ejpam-4403	100	14	,	,	PUNCT
ejpam-4403	100	15	1348	1348	NUM
ejpam-4403	100	16	-	-	SYM
ejpam-4403	100	17	1362	1362	NUM
ejpam-4403	100	18	1353	1353	NUM
ejpam-4403	100	19	second	second	ADJ
ejpam-4403	100	20	step	step	NOUN
ejpam-4403	100	21	:	:	PUNCT
ejpam-4403	100	22	construction	construction	NOUN
ejpam-4403	100	23	of	of	ADP
ejpam-4403	100	24	the	the	DET
ejpam-4403	100	25	numerical	numerical	ADJ
ejpam-4403	100	26	scheme	scheme	NOUN
ejpam-4403	100	27	assuming	assume	VERB
ejpam-4403	100	28	that	that	SCONJ
ejpam-4403	100	29	,	,	PUNCT
ejpam-4403	100	30	u	u	PROPN
ejpam-4403	100	31	∈	∈	PROPN
ejpam-4403	100	32	c2([0	c2([0	PROPN
ejpam-4403	100	33	;	;	PUNCT
ejpam-4403	100	34	1	1	NUM
ejpam-4403	100	35	]	]	NUM
ejpam-4403	100	36	)	)	PUNCT
ejpam-4403	100	37	,	,	PUNCT
ejpam-4403	100	38	then	then	ADV
ejpam-4403	100	39	u	u	PRON
ejpam-4403	100	40	admits	admit	VERB
ejpam-4403	100	41	a	a	DET
ejpam-4403	100	42	taylor	taylor	PROPN
ejpam-4403	100	43	expansion	expansion	NOUN
ejpam-4403	100	44	in	in	ADP
ejpam-4403	100	45	the	the	DET
ejpam-4403	100	46	neighborhood	neighborhood	NOUN
ejpam-4403	100	47	of	of	ADP
ejpam-4403	100	48	xi	xi	PROPN
ejpam-4403	100	49	in	in	ADP
ejpam-4403	100	50	the	the	DET
ejpam-4403	100	51	form	form	NOUN
ejpam-4403	100	52	:	:	PUNCT
ejpam-4403	100	53	u(xi	u(xi	PROPN
ejpam-4403	100	54	+	+	X
ejpam-4403	100	55	1)−	1)−	NUM
ejpam-4403	100	56	u(xi	u(xi	PROPN
ejpam-4403	100	57	+	+	ADJ
ejpam-4403	100	58	∆x	∆x	PROPN
ejpam-4403	100	59	)	)	PUNCT
ejpam-4403	101	1	=	=	X
ejpam-4403	101	2	u(xi)−	u(xi)−	NOUN
ejpam-4403	101	3	∆x	∆x	PROPN
ejpam-4403	101	4	1	1	NUM
ejpam-4403	101	5	!	!	PUNCT
ejpam-4403	102	1	u′(xi	u′(xi	PROPN
ejpam-4403	102	2	)	)	PUNCT
ejpam-4403	103	1	+	+	CCONJ
ejpam-4403	103	2	∆x2	∆x2	NOUN
ejpam-4403	103	3	2	2	X
ejpam-4403	103	4	!	!	NOUN
ejpam-4403	103	5	u′′(xi	u′′(xi	INTJ
ejpam-4403	103	6	)	)	PUNCT
ejpam-4403	104	1	+	+	NUM
ejpam-4403	104	2	0(∆x3	0(∆x3	NUM
ejpam-4403	104	3	)	)	PUNCT
ejpam-4403	104	4	(	(	PUNCT
ejpam-4403	104	5	29	29	NUM
ejpam-4403	104	6	)	)	PUNCT
ejpam-4403	104	7	u(xi	u(xi	PROPN
ejpam-4403	104	8	−	−	PROPN
ejpam-4403	104	9	1)−	1)−	NUM
ejpam-4403	104	10	u(xi	u(xi	PROPN
ejpam-4403	104	11	−∆x	−∆x	NOUN
ejpam-4403	104	12	)	)	PUNCT
ejpam-4403	104	13	=	=	SYM
ejpam-4403	104	14	u(xi)−	u(xi)−	NOUN
ejpam-4403	104	15	∆x	∆x	PROPN
ejpam-4403	104	16	1	1	NUM
ejpam-4403	104	17	!	!	PUNCT
ejpam-4403	105	1	u′(xi	u′(xi	PROPN
ejpam-4403	105	2	)	)	PUNCT
ejpam-4403	106	1	+	+	CCONJ
ejpam-4403	106	2	∆x2	∆x2	NOUN
ejpam-4403	106	3	2	2	X
ejpam-4403	106	4	!	!	NOUN
ejpam-4403	106	5	u′′(xi	u′′(xi	INTJ
ejpam-4403	106	6	)	)	PUNCT
ejpam-4403	107	1	+	+	NUM
ejpam-4403	107	2	0(∆x3	0(∆x3	NUM
ejpam-4403	107	3	)	)	PUNCT
ejpam-4403	107	4	(	(	PUNCT
ejpam-4403	107	5	30	30	X
ejpam-4403	107	6	)	)	PUNCT
ejpam-4403	107	7	going	go	VERB
ejpam-4403	107	8	to	to	ADP
ejpam-4403	107	9	the	the	DET
ejpam-4403	107	10	approximations	approximation	NOUN
ejpam-4403	107	11	,	,	PUNCT
ejpam-4403	107	12	we	we	PRON
ejpam-4403	107	13	have	have	VERB
ejpam-4403	107	14	:	:	PUNCT
ejpam-4403	107	15	ui+1	ui+1	PROPN
ejpam-4403	107	16	=	=	PUNCT
ejpam-4403	107	17	ui	ui	PROPN
ejpam-4403	108	1	+	+	CCONJ
ejpam-4403	108	2	∆x	∆x	PROPN
ejpam-4403	108	3	1	1	NUM
ejpam-4403	108	4	!	!	PUNCT
ejpam-4403	108	5	u′i	u′i	PROPN
ejpam-4403	109	1	+	+	PUNCT
ejpam-4403	109	2	∆x2	∆x2	PRON
ejpam-4403	109	3	2	2	X
ejpam-4403	109	4	!	!	X
ejpam-4403	109	5	u′′i	u′′i	PROPN
ejpam-4403	109	6	+	+	CCONJ
ejpam-4403	109	7	0(∆x3	0(∆x3	NUM
ejpam-4403	109	8	)	)	PUNCT
ejpam-4403	109	9	(	(	PUNCT
ejpam-4403	109	10	31	31	NUM
ejpam-4403	109	11	)	)	PUNCT
ejpam-4403	109	12	ui−1	ui−1	PROPN
ejpam-4403	109	13	=	=	SYM
ejpam-4403	109	14	ui	ui	PROPN
ejpam-4403	110	1	−	−	PROPN
ejpam-4403	110	2	∆x	∆x	PROPN
ejpam-4403	110	3	1	1	NUM
ejpam-4403	110	4	!	!	PUNCT
ejpam-4403	110	5	u′i	u′i	PROPN
ejpam-4403	111	1	+	+	PUNCT
ejpam-4403	111	2	∆x2	∆x2	PRON
ejpam-4403	111	3	2	2	X
ejpam-4403	111	4	!	!	X
ejpam-4403	111	5	u′′i	u′′i	PROPN
ejpam-4403	111	6	+	+	CCONJ
ejpam-4403	111	7	0(∆x3	0(∆x3	NUM
ejpam-4403	111	8	)	)	PUNCT
ejpam-4403	111	9	(	(	PUNCT
ejpam-4403	111	10	32	32	NUM
ejpam-4403	111	11	)	)	PUNCT
ejpam-4403	111	12	adding	add	VERB
ejpam-4403	111	13	the	the	DET
ejpam-4403	111	14	two	two	NUM
ejpam-4403	111	15	equalities	equality	NOUN
ejpam-4403	111	16	,	,	PUNCT
ejpam-4403	111	17	to	to	PART
ejpam-4403	111	18	obtain	obtain	VERB
ejpam-4403	111	19	the	the	DET
ejpam-4403	111	20	following	follow	VERB
ejpam-4403	111	21	expression	expression	NOUN
ejpam-4403	111	22	u′′i	u′′i	PROPN
ejpam-4403	111	23	=	=	PUNCT
ejpam-4403	111	24	ui+1	ui+1	PROPN
ejpam-4403	112	1	−	−	NOUN
ejpam-4403	112	2	2ui	2ui	NOUN
ejpam-4403	113	1	+	+	CCONJ
ejpam-4403	113	2	ui−1	ui−1	PROPN
ejpam-4403	113	3	∆x2	∆x2	PROPN
ejpam-4403	113	4	(	(	PUNCT
ejpam-4403	113	5	33	33	NUM
ejpam-4403	113	6	)	)	PUNCT
ejpam-4403	113	7	the	the	DET
ejpam-4403	113	8	first	first	ADJ
ejpam-4403	113	9	derivative	derivative	NOUN
ejpam-4403	113	10	has	have	AUX
ejpam-4403	113	11	been	be	AUX
ejpam-4403	113	12	approximated	approximate	VERB
ejpam-4403	113	13	using	use	VERB
ejpam-4403	113	14	the	the	DET
ejpam-4403	113	15	forward	forward	ADJ
ejpam-4403	113	16	finite	finite	ADJ
ejpam-4403	113	17	difference	difference	NOUN
ejpam-4403	113	18	method	method	NOUN
ejpam-4403	113	19	of	of	ADP
ejpam-4403	113	20	order	order	NOUN
ejpam-4403	113	21	1	1	NUM
ejpam-4403	113	22	,	,	PUNCT
ejpam-4403	113	23	that	that	PRON
ejpam-4403	113	24	is	be	AUX
ejpam-4403	113	25	to	to	PART
ejpam-4403	113	26	say	say	VERB
ejpam-4403	113	27	(	(	PUNCT
ejpam-4403	113	28	∂u	∂u	PROPN
ejpam-4403	113	29	∂x	∂x	PROPN
ejpam-4403	113	30	)	)	PUNCT
ejpam-4403	114	1	i	i	PRON
ejpam-4403	114	2	≃	≃	VERB
ejpam-4403	114	3	ui+1	ui+1	PROPN
ejpam-4403	114	4	−	−	PROPN
ejpam-4403	114	5	ui	ui	PROPN
ejpam-4403	114	6	∆x	∆x	PROPN
ejpam-4403	114	7	,	,	PUNCT
ejpam-4403	114	8	(	(	PUNCT
ejpam-4403	114	9	34	34	NUM
ejpam-4403	114	10	)	)	PUNCT
ejpam-4403	114	11	with	with	ADP
ejpam-4403	114	12	u0	u0	ADJ
ejpam-4403	114	13	=	=	SYM
ejpam-4403	114	14	un+1	un+1	PROPN
ejpam-4403	114	15	=	=	SYM
ejpam-4403	114	16	0	0	X
ejpam-4403	114	17	.	.	PUNCT
ejpam-4403	115	1	we	we	PRON
ejpam-4403	115	2	have	have	VERB
ejpam-4403	115	3	−µu′′(x	−µu′′(x	NOUN
ejpam-4403	115	4	)	)	PUNCT
ejpam-4403	116	1	+	+	NUM
ejpam-4403	116	2	c(x)u′(x	c(x)u′(x	NOUN
ejpam-4403	116	3	)	)	PUNCT
ejpam-4403	116	4	=	=	SYM
ejpam-4403	116	5	f(x	f(x	PROPN
ejpam-4403	116	6	)	)	PUNCT
ejpam-4403	116	7	,	,	PUNCT
ejpam-4403	116	8	(	(	PUNCT
ejpam-4403	116	9	35	35	NUM
ejpam-4403	116	10	)	)	PUNCT
ejpam-4403	116	11	that	that	PRON
ejpam-4403	116	12	is	be	AUX
ejpam-4403	116	13	to	to	PART
ejpam-4403	116	14	say	say	VERB
ejpam-4403	116	15	−µ	−µ	PROPN
ejpam-4403	116	16	(	(	PUNCT
ejpam-4403	116	17	ui+1	ui+1	ADV
ejpam-4403	116	18	−	−	NOUN
ejpam-4403	116	19	2ui	2ui	NOUN
ejpam-4403	117	1	+	+	PUNCT
ejpam-4403	117	2	ui−1	ui−1	PROPN
ejpam-4403	117	3	∆x2	∆x2	NOUN
ejpam-4403	117	4	)	)	PUNCT
ejpam-4403	118	1	+	+	CCONJ
ejpam-4403	118	2	ci	ci	NOUN
ejpam-4403	118	3	(	(	PUNCT
ejpam-4403	118	4	ui+1	ui+1	NOUN
ejpam-4403	118	5	−	−	PROPN
ejpam-4403	118	6	ui	ui	PROPN
ejpam-4403	118	7	∆x	∆x	PROPN
ejpam-4403	118	8	)	)	PUNCT
ejpam-4403	119	1	=	=	NOUN
ejpam-4403	120	1	fi	fi	NOUN
ejpam-4403	120	2	(	(	PUNCT
ejpam-4403	120	3	36	36	NUM
ejpam-4403	120	4	)	)	PUNCT
ejpam-4403	120	5	therefore	therefore	ADV
ejpam-4403	120	6	,	,	PUNCT
ejpam-4403	120	7	−µ	−µ	ADV
ejpam-4403	120	8	∆x2	∆x2	PRON
ejpam-4403	120	9	(	(	PUNCT
ejpam-4403	120	10	ui+1	ui+1	NOUN
ejpam-4403	120	11	−	−	NOUN
ejpam-4403	120	12	2ui	2ui	ADJ
ejpam-4403	120	13	−	−	PROPN
ejpam-4403	120	14	ui−1	ui−1	PROPN
ejpam-4403	120	15	)	)	PUNCT
ejpam-4403	120	16	+	+	NUM
ejpam-4403	120	17	ci	ci	PROPN
ejpam-4403	120	18	∆x	∆x	PROPN
ejpam-4403	120	19	(	(	PUNCT
ejpam-4403	120	20	ui+1	ui+1	NUM
ejpam-4403	120	21	−	−	PROPN
ejpam-4403	120	22	ui	ui	NOUN
ejpam-4403	120	23	)	)	PUNCT
ejpam-4403	120	24	=	=	NOUN
ejpam-4403	120	25	fi	fi	NOUN
ejpam-4403	120	26	(	(	PUNCT
ejpam-4403	120	27	37	37	NUM
ejpam-4403	120	28	)	)	PUNCT
ejpam-4403	120	29	multiplying	multiply	VERB
ejpam-4403	120	30	the	the	DET
ejpam-4403	120	31	equation	equation	NOUN
ejpam-4403	120	32	(	(	PUNCT
ejpam-4403	120	33	37	37	NUM
ejpam-4403	120	34	)	)	PUNCT
ejpam-4403	120	35	by	by	ADP
ejpam-4403	120	36	∆x2	∆x2	PRON
ejpam-4403	120	37	µ	µ	NOUN
ejpam-4403	120	38	,	,	PUNCT
ejpam-4403	120	39	to	to	PART
ejpam-4403	120	40	obtain	obtain	VERB
ejpam-4403	120	41	(	(	PUNCT
ejpam-4403	120	42	λci	λci	ADJ
ejpam-4403	120	43	−	−	PROPN
ejpam-4403	120	44	1)ui+1	1)ui+1	NUM
ejpam-4403	121	1	+	+	CCONJ
ejpam-4403	122	1	(	(	PUNCT
ejpam-4403	122	2	2−	2−	NUM
ejpam-4403	122	3	λci)ui	λci)ui	NOUN
ejpam-4403	122	4	−	−	PROPN
ejpam-4403	122	5	ui−1	ui−1	PROPN
ejpam-4403	122	6	=	=	SYM
ejpam-4403	122	7	λ∆xfi	λ∆xfi	PROPN
ejpam-4403	122	8	,	,	PUNCT
ejpam-4403	122	9	with	with	ADP
ejpam-4403	122	10	λ	λ	PROPN
ejpam-4403	122	11	=	=	SYM
ejpam-4403	122	12	∆x	∆x	PROPN
ejpam-4403	122	13	µ	µ	X
ejpam-4403	122	14	(	(	PUNCT
ejpam-4403	122	15	38	38	NUM
ejpam-4403	122	16	)	)	PUNCT
ejpam-4403	122	17	for	for	ADP
ejpam-4403	122	18	i	i	PROPN
ejpam-4403	122	19	=	=	NOUN
ejpam-4403	122	20	1	1	NUM
ejpam-4403	122	21	,	,	PUNCT
ejpam-4403	122	22	(	(	PUNCT
ejpam-4403	122	23	λc1	λc1	ADP
ejpam-4403	122	24	−	−	PROPN
ejpam-4403	122	25	1)u2	1)u2	NUM
ejpam-4403	122	26	+	+	CCONJ
ejpam-4403	122	27	(	(	PUNCT
ejpam-4403	122	28	2−	2−	NUM
ejpam-4403	122	29	λc1)u1	λc1)u1	NOUN
ejpam-4403	122	30	−	−	NOUN
ejpam-4403	122	31	u0	u0	ADJ
ejpam-4403	122	32	=	=	SYM
ejpam-4403	122	33	λ∆xf1	λ∆xf1	X
ejpam-4403	122	34	for	for	ADP
ejpam-4403	122	35	i	i	PROPN
ejpam-4403	122	36	=	=	SYM
ejpam-4403	122	37	2	2	NUM
ejpam-4403	122	38	,	,	PUNCT
ejpam-4403	122	39	(	(	PUNCT
ejpam-4403	122	40	λc2	λc2	VERB
ejpam-4403	122	41	−	−	PROPN
ejpam-4403	122	42	1)u3	1)u3	NUM
ejpam-4403	122	43	+	+	CCONJ
ejpam-4403	122	44	(	(	PUNCT
ejpam-4403	122	45	2−	2−	NUM
ejpam-4403	122	46	λc2)u2	λc2)u2	NOUN
ejpam-4403	122	47	−	−	PROPN
ejpam-4403	122	48	u1	u1	NOUN
ejpam-4403	122	49	=	=	PRON
ejpam-4403	122	50	λ∆xf2	λ∆xf2	PROPN
ejpam-4403	122	51	for	for	ADP
ejpam-4403	122	52	i	i	PRON
ejpam-4403	122	53	=	=	SYM
ejpam-4403	122	54	3	3	NUM
ejpam-4403	122	55	,	,	PUNCT
ejpam-4403	122	56	(	(	PUNCT
ejpam-4403	122	57	λc3	λc3	NOUN
ejpam-4403	122	58	−	−	ADP
ejpam-4403	122	59	1)u4	1)u4	NUM
ejpam-4403	122	60	+	+	CCONJ
ejpam-4403	122	61	(	(	PUNCT
ejpam-4403	122	62	2−	2−	NUM
ejpam-4403	122	63	λc3)u3	λc3)u3	NOUN
ejpam-4403	122	64	−	−	PROPN
ejpam-4403	122	65	u2	u2	PROPN
ejpam-4403	122	66	=	=	SYM
ejpam-4403	122	67	λ∆xf3	λ∆xf3	PROPN
ejpam-4403	122	68	...	...	PUNCT
ejpam-4403	122	69	for	for	ADP
ejpam-4403	122	70	i	i	PRON
ejpam-4403	122	71	=	=	SYM
ejpam-4403	122	72	n	n	PROPN
ejpam-4403	122	73	,	,	PUNCT
ejpam-4403	122	74	(	(	PUNCT
ejpam-4403	122	75	λcn	λcn	PRON
ejpam-4403	122	76	−	−	PROPN
ejpam-4403	123	1	1)un+1	1)un+1	PROPN
ejpam-4403	123	2	+	+	CCONJ
ejpam-4403	123	3	(	(	PUNCT
ejpam-4403	123	4	2−	2−	NUM
ejpam-4403	123	5	λcn	λcn	NOUN
ejpam-4403	123	6	)	)	PUNCT
ejpam-4403	123	7	un	un	PROPN
ejpam-4403	123	8	−	−	PROPN
ejpam-4403	123	9	un−1	un−1	PROPN
ejpam-4403	124	1	=	=	SYM
ejpam-4403	124	2	λ∆xfn	λ∆xfn	PROPN
ejpam-4403	124	3	d.	d.	PROPN
ejpam-4403	124	4	v.	v.	PROPN
ejpam-4403	124	5	pongui	pongui	PROPN
ejpam-4403	124	6	ngoma	ngoma	PROPN
ejpam-4403	124	7	et	et	PROPN
ejpam-4403	124	8	al	al	PROPN
ejpam-4403	124	9	.	.	PROPN
ejpam-4403	124	10	,	,	PUNCT
ejpam-4403	124	11	/	/	SYM
ejpam-4403	124	12	eur	eur	NOUN
ejpam-4403	124	13	.	.	PUNCT
ejpam-4403	125	1	j.	j.	PROPN
ejpam-4403	125	2	pure	pure	PROPN
ejpam-4403	125	3	appl	appl	PROPN
ejpam-4403	125	4	.	.	PROPN
ejpam-4403	125	5	math	math	PROPN
ejpam-4403	125	6	,	,	PUNCT
ejpam-4403	125	7	15	15	NUM
ejpam-4403	125	8	(	(	PUNCT
ejpam-4403	125	9	3	3	NUM
ejpam-4403	125	10	)	)	PUNCT
ejpam-4403	125	11	(	(	PUNCT
ejpam-4403	125	12	2022	2022	NUM
ejpam-4403	125	13	)	)	PUNCT
ejpam-4403	125	14	,	,	PUNCT
ejpam-4403	125	15	1348	1348	NUM
ejpam-4403	125	16	-	-	SYM
ejpam-4403	125	17	1362	1362	NUM
ejpam-4403	125	18	1354	1354	NUM
ejpam-4403	125	19	third	third	ADJ
ejpam-4403	125	20	step	step	NOUN
ejpam-4403	125	21	:	:	PUNCT
ejpam-4403	125	22	writing	write	VERB
ejpam-4403	125	23	matrix	matrix	NOUN
ejpam-4403	125	24	taking	take	VERB
ejpam-4403	125	25	into	into	ADP
ejpam-4403	125	26	account	account	NOUN
ejpam-4403	125	27	the	the	DET
ejpam-4403	125	28	boundary	boundary	ADJ
ejpam-4403	125	29	conditions	condition	NOUN
ejpam-4403	125	30	,	,	PUNCT
ejpam-4403	125	31	we	we	PRON
ejpam-4403	125	32	obtain	obtain	VERB
ejpam-4403	125	33	the	the	DET
ejpam-4403	125	34	following	follow	VERB
ejpam-4403	125	35	linear	linear	PROPN
ejpam-4403	125	36	system	system	PROPN
ejpam-4403	125	37	(	(	PUNCT
ejpam-4403	125	38	2−	2−	NUM
ejpam-4403	125	39	λc1)u1	λc1)u1	NOUN
ejpam-4403	125	40	+	+	CCONJ
ejpam-4403	125	41	(	(	PUNCT
ejpam-4403	125	42	λc1	λc1	ADP
ejpam-4403	125	43	−	−	PROPN
ejpam-4403	125	44	1)u2	1)u2	NUM
ejpam-4403	125	45	=	=	PUNCT
ejpam-4403	125	46	λ∆xf1	λ∆xf1	PUNCT
ejpam-4403	125	47	−u1	−u1	PROPN
ejpam-4403	125	48	+	+	CCONJ
ejpam-4403	125	49	(	(	PUNCT
ejpam-4403	125	50	2−	2−	NUM
ejpam-4403	125	51	λc2)u2	λc2)u2	NOUN
ejpam-4403	125	52	+	+	CCONJ
ejpam-4403	125	53	(	(	PUNCT
ejpam-4403	125	54	λc3	λc3	NOUN
ejpam-4403	125	55	−	−	PROPN
ejpam-4403	125	56	1)u3	1)u3	NUM
ejpam-4403	125	57	=	=	SYM
ejpam-4403	125	58	λ∆xf2	λ∆xf2	X
ejpam-4403	125	59	−u2	−u2	PROPN
ejpam-4403	125	60	+	+	CCONJ
ejpam-4403	126	1	(	(	PUNCT
ejpam-4403	126	2	2−	2−	NUM
ejpam-4403	126	3	λc3)u3	λc3)u3	NOUN
ejpam-4403	126	4	+	+	CCONJ
ejpam-4403	126	5	(	(	PUNCT
ejpam-4403	126	6	λc3	λc3	NOUN
ejpam-4403	126	7	−	−	PROPN
ejpam-4403	126	8	1)u4	1)u4	NUM
ejpam-4403	126	9	=	=	SYM
ejpam-4403	126	10	λ∆xf3	λ∆xf3	PROPN
ejpam-4403	126	11	...	...	PUNCT
ejpam-4403	126	12	−un−1	−un−1	PUNCT
ejpam-4403	127	1	+	+	CCONJ
ejpam-4403	127	2	(	(	PUNCT
ejpam-4403	127	3	2−	2−	NUM
ejpam-4403	127	4	λcn	λcn	NOUN
ejpam-4403	127	5	)	)	PUNCT
ejpam-4403	127	6	un	un	PROPN
ejpam-4403	128	1	=	=	PROPN
ejpam-4403	128	2	λ∆xfn	λ∆xfn	PROPN
ejpam-4403	128	3	(	(	PUNCT
ejpam-4403	128	4	39	39	NUM
ejpam-4403	128	5	)	)	PUNCT
ejpam-4403	128	6	hence	hence	ADV
ejpam-4403	128	7	the	the	DET
ejpam-4403	128	8	matrix	matrix	NOUN
ejpam-4403	128	9	below:	below:	NOUN
ejpam-4403	128	10	2−	2−	NUM
ejpam-4403	128	11	λc1	λc1	NOUN
ejpam-4403	128	12	λc1	λc1	NOUN
ejpam-4403	128	13	−	−	NUM
ejpam-4403	128	14	1	1	NUM
ejpam-4403	128	15	0	0	NUM
ejpam-4403	128	16	0	0	NUM
ejpam-4403	128	17	...	...	SYM
ejpam-4403	128	18	0	0	NUM
ejpam-4403	128	19	−1	−1	NOUN
ejpam-4403	128	20	2−	2−	NUM
ejpam-4403	128	21	λc2	λc2	NOUN
ejpam-4403	128	22	λc2	λc2	NOUN
ejpam-4403	128	23	−	−	PROPN
ejpam-4403	128	24	1	1	NUM
ejpam-4403	128	25	0	0	NUM
ejpam-4403	128	26	...	...	PUNCT
ejpam-4403	128	27	0	0	NUM
ejpam-4403	128	28	0	0	NUM
ejpam-4403	128	29	−1	−1	NOUN
ejpam-4403	128	30	2−	2−	NUM
ejpam-4403	129	1	λc3	λc3	NOUN
ejpam-4403	129	2	λc3	λc3	NOUN
ejpam-4403	129	3	−	−	NOUN
ejpam-4403	129	4	1	1	NUM
ejpam-4403	129	5	...	...	PUNCT
ejpam-4403	129	6	...	...	PUNCT
ejpam-4403	129	7	...	...	PUNCT
ejpam-4403	129	8	...	...	PUNCT
ejpam-4403	129	9	...	...	PUNCT
ejpam-4403	129	10	...	...	PUNCT
ejpam-4403	129	11	...	...	PUNCT
ejpam-4403	130	1	λcn−1	λcn−1	ADV
ejpam-4403	130	2	0	0	NUM
ejpam-4403	130	3	0	0	NUM
ejpam-4403	130	4	...	...	PUNCT
ejpam-4403	130	5	−1	−1	NOUN
ejpam-4403	130	6	2−	2−	NUM
ejpam-4403	130	7	λcn	λcn	NOUN
ejpam-4403	130	8			ADP
ejpam-4403	130	9			ADJ
ejpam-4403	130	10	u1	u1	NOUN
ejpam-4403	130	11	u2	u2	PROPN
ejpam-4403	130	12	u3	u3	PROPN
ejpam-4403	130	13	...	...	PUNCT
ejpam-4403	130	14	un	un	PROPN
ejpam-4403	130	15			PROPN
ejpam-4403	130	16	=	=	NOUN
ejpam-4403	130	17	λ∆x	λ∆x	ADJ
ejpam-4403	130	18			ADJ
ejpam-4403	130	19	f1	f1	NOUN
ejpam-4403	130	20	f2	f2	PROPN
ejpam-4403	130	21	f3	f3	PROPN
ejpam-4403	130	22	...	...	PUNCT
ejpam-4403	131	1	fn	fn	INTJ
ejpam-4403	131	2			NOUN
ejpam-4403	131	3	(	(	PUNCT
ejpam-4403	131	4	40	40	NUM
ejpam-4403	131	5	)	)	PUNCT
ejpam-4403	131	6	thus	thus	ADV
ejpam-4403	131	7	,	,	PUNCT
ejpam-4403	131	8	the	the	DET
ejpam-4403	131	9	problem	problem	NOUN
ejpam-4403	131	10	(	(	PUNCT
ejpam-4403	131	11	40	40	NUM
ejpam-4403	131	12	)	)	PUNCT
ejpam-4403	131	13	boils	boil	VERB
ejpam-4403	131	14	down	down	ADP
ejpam-4403	131	15	to	to	ADP
ejpam-4403	131	16	the	the	DET
ejpam-4403	131	17	following	follow	VERB
ejpam-4403	131	18	linear	linear	ADJ
ejpam-4403	131	19	system	system	NOUN
ejpam-4403	131	20	:	:	PUNCT
ejpam-4403	131	21	aλu	aλu	PROPN
ejpam-4403	131	22	=	=	SYM
ejpam-4403	131	23	b	b	PROPN
ejpam-4403	131	24	(	(	PUNCT
ejpam-4403	131	25	41	41	NUM
ejpam-4403	131	26	)	)	PUNCT
ejpam-4403	131	27	it	it	PRON
ejpam-4403	131	28	remains	remain	VERB
ejpam-4403	131	29	to	to	PART
ejpam-4403	131	30	verify	verify	VERB
ejpam-4403	131	31	that	that	SCONJ
ejpam-4403	131	32	if	if	SCONJ
ejpam-4403	131	33	aλ	aλ	PROPN
ejpam-4403	131	34	is	be	AUX
ejpam-4403	131	35	symmetric	symmetric	ADJ
ejpam-4403	131	36	positive	positive	ADJ
ejpam-4403	131	37	definite	definite	ADJ
ejpam-4403	131	38	to	to	PART
ejpam-4403	131	39	prove	prove	VERB
ejpam-4403	131	40	the	the	DET
ejpam-4403	131	41	existence	existence	NOUN
ejpam-4403	131	42	and	and	CCONJ
ejpam-4403	131	43	the	the	DET
ejpam-4403	131	44	uniqueness	uniqueness	NOUN
ejpam-4403	131	45	of	of	ADP
ejpam-4403	131	46	the	the	DET
ejpam-4403	131	47	solution	solution	NOUN
ejpam-4403	131	48	u	u	NOUN
ejpam-4403	131	49	of	of	ADP
ejpam-4403	131	50	the	the	DET
ejpam-4403	131	51	system	system	NOUN
ejpam-4403	131	52	(	(	PUNCT
ejpam-4403	131	53	41	41	NUM
ejpam-4403	131	54	)	)	PUNCT
ejpam-4403	131	55	.	.	PUNCT
ejpam-4403	132	1	that	that	PRON
ejpam-4403	132	2	is	be	AUX
ejpam-4403	132	3	to	to	PART
ejpam-4403	132	4	say:	say:	VERB
ejpam-4403	132	5	at	at	ADP
ejpam-4403	132	6	λ	λ	X
ejpam-4403	132	7	=	=	SYM
ejpam-4403	132	8	aλ	aλ	PROPN
ejpam-4403	132	9	(	(	PUNCT
ejpam-4403	132	10	1	1	NUM
ejpam-4403	132	11	)	)	PUNCT
ejpam-4403	132	12	∀v	∀v	PROPN
ejpam-4403	132	13	∈	∈	PROPN
ejpam-4403	132	14	rn	rn	PROPN
ejpam-4403	132	15	,	,	PUNCT
ejpam-4403	132	16	aλv.v	aλv.v	PROPN
ejpam-4403	132	17	>	>	X
ejpam-4403	132	18	0	0	PUNCT
ejpam-4403	133	1	(	(	PUNCT
ejpam-4403	133	2	2	2	X
ejpam-4403	133	3	)	)	PUNCT
ejpam-4403	133	4	aλv.v	aλv.v	X
ejpam-4403	133	5	=	=	SYM
ejpam-4403	133	6	0	0	PUNCT
ejpam-4403	134	1	=	=	NOUN
ejpam-4403	134	2	⇒	⇒	X
ejpam-4403	134	3	v	v	X
ejpam-4403	134	4	=	=	SYM
ejpam-4403	134	5	0	0	NUM
ejpam-4403	134	6	(	(	PUNCT
ejpam-4403	134	7	3	3	X
ejpam-4403	134	8	)	)	PUNCT
ejpam-4403	134	9	let	let	VERB
ejpam-4403	134	10	’s	’s	NOUN
ejpam-4403	134	11	suppose	suppose	VERB
ejpam-4403	134	12	that	that	SCONJ
ejpam-4403	134	13	λci	λci	PROPN
ejpam-4403	134	14	−	−	PROPN
ejpam-4403	134	15	1	1	NUM
ejpam-4403	134	16	=	=	SYM
ejpam-4403	134	17	−1	−1	NOUN
ejpam-4403	134	18	,	,	PUNCT
ejpam-4403	134	19	that	that	PRON
ejpam-4403	134	20	is	be	AUX
ejpam-4403	134	21	to	to	PART
ejpam-4403	134	22	say	say	VERB
ejpam-4403	134	23	λci	λci	PROPN
ejpam-4403	134	24	=	=	SYM
ejpam-4403	134	25	0	0	NUM
ejpam-4403	134	26	for	for	ADP
ejpam-4403	134	27	all	all	PRON
ejpam-4403	134	28	i	i	PRON
ejpam-4403	134	29	∈	∈	PROPN
ejpam-4403	134	30	{	{	PUNCT
ejpam-4403	134	31	1	1	NUM
ejpam-4403	134	32	,	,	PUNCT
ejpam-4403	134	33	2	2	NUM
ejpam-4403	134	34	,	,	PUNCT
ejpam-4403	134	35	3	3	NUM
ejpam-4403	134	36	,	,	PUNCT
ejpam-4403	134	37	...	...	PUNCT
ejpam-4403	134	38	,	,	PUNCT
ejpam-4403	134	39	n	n	CCONJ
ejpam-4403	134	40	}	}	PUNCT
ejpam-4403	134	41	,	,	PUNCT
ejpam-4403	134	42	c	c	NOUN
ejpam-4403	134	43	=	=	SYM
ejpam-4403	134	44	0	0	NUM
ejpam-4403	134	45	and	and	CCONJ
ejpam-4403	134	46	λ	λ	X
ejpam-4403	134	47	̸=	̸=	PROPN
ejpam-4403	134	48	0	0	NUM
ejpam-4403	134	49	.	.	PUNCT
ejpam-4403	135	1	the	the	DET
ejpam-4403	135	2	relation	relation	NOUN
ejpam-4403	135	3	(	(	PUNCT
ejpam-4403	135	4	1	1	X
ejpam-4403	135	5	)	)	PUNCT
ejpam-4403	135	6	is	be	AUX
ejpam-4403	135	7	trivial	trivial	ADJ
ejpam-4403	135	8	because	because	SCONJ
ejpam-4403	135	9	the	the	DET
ejpam-4403	135	10	matrix	matrix	NOUN
ejpam-4403	135	11	aλ	aλ	ADP
ejpam-4403	135	12	is	be	AUX
ejpam-4403	135	13	tridiagonal	tridiagonal	ADJ
ejpam-4403	135	14	with	with	ADP
ejpam-4403	135	15	the	the	DET
ejpam-4403	135	16	values	value	NOUN
ejpam-4403	135	17	of	of	ADP
ejpam-4403	135	18	the	the	DET
ejpam-4403	135	19	overdiagonal	overdiagonal	ADJ
ejpam-4403	135	20	which	which	PRON
ejpam-4403	135	21	are	be	AUX
ejpam-4403	135	22	equal	equal	ADJ
ejpam-4403	135	23	to	to	ADP
ejpam-4403	135	24	the	the	DET
ejpam-4403	135	25	values	value	NOUN
ejpam-4403	135	26	of	of	ADP
ejpam-4403	135	27	the	the	DET
ejpam-4403	135	28	subdiagonal	subdiagonal	ADJ
ejpam-4403	135	29	.	.	PUNCT
ejpam-4403	136	1	admitting	admit	VERB
ejpam-4403	136	2	λci	λci	PROPN
ejpam-4403	136	3	=	=	SYM
ejpam-4403	136	4	0	0	PUNCT
ejpam-4403	136	5	et	et	NOUN
ejpam-4403	136	6	v0	v0	NOUN
ejpam-4403	136	7	=	=	SYM
ejpam-4403	136	8	vn+1	vn+1	PROPN
ejpam-4403	136	9	=	=	SYM
ejpam-4403	136	10	0	0	NUM
ejpam-4403	136	11	,	,	PUNCT
ejpam-4403	136	12	to	to	PART
ejpam-4403	136	13	get	get	VERB
ejpam-4403	136	14	:	:	PUNCT
ejpam-4403	136	15	aλv	aλv	NOUN
ejpam-4403	136	16	=	=	PUNCT
ejpam-4403	136	17			NOUN
ejpam-4403	136	18	2	2	NUM
ejpam-4403	136	19	−1	−1	NOUN
ejpam-4403	136	20	0	0	NUM
ejpam-4403	136	21	...	...	PUNCT
ejpam-4403	136	22	0	0	NUM
ejpam-4403	136	23	−1	−1	NOUN
ejpam-4403	136	24	2	2	NUM
ejpam-4403	136	25	−1	−1	NOUN
ejpam-4403	136	26	...	...	PUNCT
ejpam-4403	136	27	0	0	NUM
ejpam-4403	136	28	0	0	NUM
ejpam-4403	136	29	−1	−1	NOUN
ejpam-4403	136	30	2	2	NUM
ejpam-4403	136	31	.	.	PUNCT
ejpam-4403	136	32	.	.	PUNCT
ejpam-4403	137	1	.	.	PUNCT
ejpam-4403	137	2	0	0	NUM
ejpam-4403	137	3	...	...	PUNCT
ejpam-4403	137	4	.	.	PUNCT
ejpam-4403	137	5	.	.	PUNCT
ejpam-4403	138	1	.	.	PUNCT
ejpam-4403	138	2	.	.	PUNCT
ejpam-4403	139	1	.	.	PUNCT
ejpam-4403	139	2	.	.	PUNCT
ejpam-4403	140	1	.	.	PUNCT
ejpam-4403	140	2	.	.	PUNCT
ejpam-4403	141	1	.	.	PUNCT
ejpam-4403	142	1	−1	−1	NOUN
ejpam-4403	142	2	0	0	NUM
ejpam-4403	142	3	0	0	NUM
ejpam-4403	142	4	...	...	PUNCT
ejpam-4403	143	1	−1	−1	NOUN
ejpam-4403	143	2	2	2	NUM
ejpam-4403	143	3			ADP
ejpam-4403	143	4			NOUN
ejpam-4403	143	5	v1	v1	PROPN
ejpam-4403	143	6	v2	v2	PROPN
ejpam-4403	143	7	v3	v3	PROPN
ejpam-4403	143	8	...	...	PUNCT
ejpam-4403	144	1	vn−1	vn−1	PROPN
ejpam-4403	144	2	vn	vn	PROPN
ejpam-4403	144	3			PROPN
ejpam-4403	145	1	d.	d.	PROPN
ejpam-4403	145	2	v.	v.	PROPN
ejpam-4403	145	3	pongui	pongui	PROPN
ejpam-4403	145	4	ngoma	ngoma	PROPN
ejpam-4403	145	5	et	et	PROPN
ejpam-4403	145	6	al	al	PROPN
ejpam-4403	145	7	.	.	PROPN
ejpam-4403	145	8	,	,	PUNCT
ejpam-4403	145	9	/	/	SYM
ejpam-4403	145	10	eur	eur	NOUN
ejpam-4403	145	11	.	.	PUNCT
ejpam-4403	146	1	j.	j.	PROPN
ejpam-4403	146	2	pure	pure	PROPN
ejpam-4403	146	3	appl	appl	PROPN
ejpam-4403	146	4	.	.	PROPN
ejpam-4403	146	5	math	math	PROPN
ejpam-4403	146	6	,	,	PUNCT
ejpam-4403	146	7	15	15	NUM
ejpam-4403	146	8	(	(	PUNCT
ejpam-4403	146	9	3	3	NUM
ejpam-4403	146	10	)	)	PUNCT
ejpam-4403	146	11	(	(	PUNCT
ejpam-4403	146	12	2022	2022	NUM
ejpam-4403	146	13	)	)	PUNCT
ejpam-4403	146	14	,	,	PUNCT
ejpam-4403	146	15	1348	1348	NUM
ejpam-4403	146	16	-	-	SYM
ejpam-4403	146	17	1362	1362	NUM
ejpam-4403	146	18	1355	1355	NUM
ejpam-4403	146	19	<	<	X
ejpam-4403	146	20	aλv	aλv	PROPN
ejpam-4403	146	21	,	,	PUNCT
ejpam-4403	146	22	v	v	X
ejpam-4403	146	23	>	>	X
ejpam-4403	146	24	=	=	SYM
ejpam-4403	146	25			NOUN
ejpam-4403	146	26	2v1	2v1	NUM
ejpam-4403	146	27	−	−	PROPN
ejpam-4403	146	28	v2	v2	PROPN
ejpam-4403	146	29	−	−	PROPN
ejpam-4403	146	30	v1	v1	NOUN
ejpam-4403	146	31	+	+	CCONJ
ejpam-4403	146	32	2v2	2v2	NUM
ejpam-4403	146	33	−	−	NOUN
ejpam-4403	146	34	v3	v3	PROPN
ejpam-4403	146	35	−v2	−v2	PROPN
ejpam-4403	146	36	+	+	CCONJ
ejpam-4403	146	37	2v3	2v3	NUM
ejpam-4403	146	38	−	−	PROPN
ejpam-4403	146	39	v4	v4	NOUN
ejpam-4403	146	40	...	...	PUNCT
ejpam-4403	146	41	−vn−2	−vn−2	PUNCT
ejpam-4403	147	1	+	+	ADV
ejpam-4403	147	2	2vn−1	2vn−1	NUM
ejpam-4403	147	3	−	−	NOUN
ejpam-4403	147	4	vn	vn	X
ejpam-4403	147	5	−vn−1	−vn−1	X
ejpam-4403	148	1	+	+	CCONJ
ejpam-4403	148	2	2vn	2vn	ADJ
ejpam-4403	148	3			ADJ
ejpam-4403	148	4			ADJ
ejpam-4403	148	5	v1	v1	PROPN
ejpam-4403	148	6	v2	v2	PROPN
ejpam-4403	148	7	v3	v3	PROPN
ejpam-4403	148	8	...	...	PUNCT
ejpam-4403	149	1	vn−1	vn−1	ADJ
ejpam-4403	149	2	vn	vn	PROPN
ejpam-4403	149	3			PROPN
ejpam-4403	149	4	;	;	PUNCT
ejpam-4403	149	5	<	<	X
ejpam-4403	149	6	aλv	aλv	PROPN
ejpam-4403	149	7	,	,	PUNCT
ejpam-4403	149	8	v	v	X
ejpam-4403	149	9	>	>	X
ejpam-4403	149	10	=	=	PUNCT
ejpam-4403	149	11	(	(	PUNCT
ejpam-4403	149	12	2v1−v2)v1+(−v1	2v1−v2)v1+(−v1	NUM
ejpam-4403	149	13	+	+	NOUN
ejpam-4403	149	14	2v2−v3)v2+(−v2	2v2−v3)v2+(−v2	NUM
ejpam-4403	149	15	+	+	ADJ
ejpam-4403	149	16	2v3−v4)v3+(−vn−2	2v3−v4)v3+(−vn−2	NUM
ejpam-4403	149	17	+	+	NOUN
ejpam-4403	149	18	2vn−1−vn	2vn−1−vn	NOUN
ejpam-4403	149	19	)	)	PUNCT
ejpam-4403	150	1	vn−1+(−vn−1	vn−1+(−vn−1	PROPN
ejpam-4403	150	2	+	+	NOUN
ejpam-4403	150	3	2vn	2vn	NOUN
ejpam-4403	150	4	)	)	PUNCT
ejpam-4403	150	5	vn	vn	PROPN
ejpam-4403	150	6	<	<	X
ejpam-4403	150	7	aλv	aλv	PROPN
ejpam-4403	150	8	,	,	PUNCT
ejpam-4403	150	9	v	v	X
ejpam-4403	150	10	>	>	PUNCT
ejpam-4403	150	11	=	=	PROPN
ejpam-4403	151	1	n∑	n∑	NOUN
ejpam-4403	151	2	i=1	i=1	X
ejpam-4403	152	1	[	[	X
ejpam-4403	152	2	−vi−1	−vi−1	NUM
ejpam-4403	152	3	+	+	NOUN
ejpam-4403	152	4	2vi	2vi	ADJ
ejpam-4403	152	5	−	−	NOUN
ejpam-4403	152	6	vi+1]vi	vi+1]vi	NOUN
ejpam-4403	152	7	<	<	X
ejpam-4403	152	8	aλv	aλv	PROPN
ejpam-4403	152	9	,	,	PUNCT
ejpam-4403	152	10	v	v	X
ejpam-4403	152	11	>	>	PUNCT
ejpam-4403	152	12	=	=	PROPN
ejpam-4403	153	1	n∑	n∑	PROPN
ejpam-4403	153	2	i=1	i=1	PROPN
ejpam-4403	153	3	(	(	PUNCT
ejpam-4403	153	4	−vi−1vi	−vi−1vi	NOUN
ejpam-4403	153	5	)	)	PUNCT
ejpam-4403	154	1	+	+	CCONJ
ejpam-4403	154	2	n∑	n∑	ADV
ejpam-4403	154	3	i=1	i=1	PROPN
ejpam-4403	154	4	(	(	PUNCT
ejpam-4403	154	5	2v2i	2v2i	NOUN
ejpam-4403	154	6	)	)	PUNCT
ejpam-4403	155	1	+	+	CCONJ
ejpam-4403	155	2	n∑	n∑	ADJ
ejpam-4403	155	3	i=1	i=1	PROPN
ejpam-4403	155	4	(	(	PUNCT
ejpam-4403	155	5	−vi+1vi	−vi+1vi	NOUN
ejpam-4403	155	6	)	)	PUNCT
ejpam-4403	155	7	or	or	CCONJ
ejpam-4403	155	8	n∑	n∑	NOUN
ejpam-4403	155	9	i=1	i=1	PROPN
ejpam-4403	156	1	(	(	PUNCT
ejpam-4403	156	2	−vi+1vi	−vi+1vi	NOUN
ejpam-4403	156	3	)	)	PUNCT
ejpam-4403	156	4	=	=	SYM
ejpam-4403	156	5	n+1∑	n+1∑	PROPN
ejpam-4403	156	6	i=2	i=2	PROPN
ejpam-4403	156	7	(	(	PUNCT
ejpam-4403	156	8	−vi−1vi	−vi−1vi	NOUN
ejpam-4403	156	9	)	)	PUNCT
ejpam-4403	156	10	n+1∑	n+1∑	ADP
ejpam-4403	156	11	i=2	i=2	PROPN
ejpam-4403	156	12	(	(	PUNCT
ejpam-4403	156	13	−vivi−1	−vivi−1	PROPN
ejpam-4403	156	14	)	)	PUNCT
ejpam-4403	157	1	+	+	PROPN
ejpam-4403	157	2	n∑	n∑	ADJ
ejpam-4403	157	3	i=1	i=1	PROPN
ejpam-4403	157	4	(	(	PUNCT
ejpam-4403	157	5	−vi−1vi	−vi−1vi	NOUN
ejpam-4403	157	6	)	)	PUNCT
ejpam-4403	157	7	=	=	PUNCT
ejpam-4403	158	1	n∑	n∑	NOUN
ejpam-4403	158	2	i=1	i=1	PROPN
ejpam-4403	158	3	(	(	PUNCT
ejpam-4403	158	4	−vi−1vi	−vi−1vi	NOUN
ejpam-4403	158	5	)	)	PUNCT
ejpam-4403	158	6	and	and	CCONJ
ejpam-4403	158	7	n∑	n∑	NOUN
ejpam-4403	158	8	i=1	i=1	PROPN
ejpam-4403	158	9	(	(	PUNCT
ejpam-4403	158	10	2v2i	2v2i	NOUN
ejpam-4403	158	11	)	)	PUNCT
ejpam-4403	159	1	=	=	PUNCT
ejpam-4403	159	2	n∑	n∑	NOUN
ejpam-4403	159	3	i=1	i=1	PROPN
ejpam-4403	160	1	(	(	PUNCT
ejpam-4403	160	2	−v2i	−v2i	X
ejpam-4403	160	3	+	+	CCONJ
ejpam-4403	160	4	v2i−1	v2i−1	PROPN
ejpam-4403	160	5	)	)	PUNCT
ejpam-4403	160	6	+	+	CCONJ
ejpam-4403	160	7	v2n	v2n	NOUN
ejpam-4403	160	8	thus	thus	ADV
ejpam-4403	160	9	<	<	X
ejpam-4403	160	10	aλv	aλv	PROPN
ejpam-4403	160	11	,	,	PUNCT
ejpam-4403	160	12	v	v	X
ejpam-4403	160	13	>	>	PUNCT
ejpam-4403	161	1	=	=	PROPN
ejpam-4403	161	2	n∑	n∑	PROPN
ejpam-4403	161	3	i=1	i=1	PROPN
ejpam-4403	161	4	(	(	PUNCT
ejpam-4403	161	5	−2vi−1vi	−2vi−1vi	NUM
ejpam-4403	161	6	)	)	PUNCT
ejpam-4403	162	1	+	+	CCONJ
ejpam-4403	162	2	n∑	n∑	ADJ
ejpam-4403	162	3	i=1	i=1	PROPN
ejpam-4403	162	4	(	(	PUNCT
ejpam-4403	162	5	v2i	v2i	PROPN
ejpam-4403	162	6	+	+	CCONJ
ejpam-4403	162	7	v2i−1	v2i−1	PROPN
ejpam-4403	162	8	)	)	PUNCT
ejpam-4403	163	1	+	+	CCONJ
ejpam-4403	163	2	v2n	v2n	PROPN
ejpam-4403	163	3	<	<	X
ejpam-4403	163	4	aλv	aλv	PROPN
ejpam-4403	163	5	,	,	PUNCT
ejpam-4403	163	6	v	v	X
ejpam-4403	163	7	>	>	PUNCT
ejpam-4403	164	1	=	=	PROPN
ejpam-4403	164	2	n∑	n∑	PROPN
ejpam-4403	164	3	i=1	i=1	PROPN
ejpam-4403	164	4	(	(	PUNCT
ejpam-4403	164	5	v2i	v2i	PROPN
ejpam-4403	164	6	−	−	PROPN
ejpam-4403	164	7	2vivi−1	2vivi−1	NUM
ejpam-4403	164	8	+	+	CCONJ
ejpam-4403	164	9	v2i−1	v2i−1	PROPN
ejpam-4403	164	10	)	)	PUNCT
ejpam-4403	165	1	+	+	CCONJ
ejpam-4403	165	2	v2n	v2n	PROPN
ejpam-4403	165	3	<	<	X
ejpam-4403	165	4	aλv	aλv	PROPN
ejpam-4403	165	5	,	,	PUNCT
ejpam-4403	165	6	v	v	X
ejpam-4403	165	7	>	>	X
ejpam-4403	165	8	=	=	PUNCT
ejpam-4403	166	1	[	[	PUNCT
ejpam-4403	166	2	n∑	n∑	NOUN
ejpam-4403	166	3	i=1	i=1	PROPN
ejpam-4403	166	4	(	(	PUNCT
ejpam-4403	166	5	vi	vi	PROPN
ejpam-4403	166	6	−	−	PROPN
ejpam-4403	166	7	vi−1	vi−1	PROPN
ejpam-4403	166	8	)	)	PUNCT
ejpam-4403	166	9	2	2	NUM
ejpam-4403	167	1	+	+	CCONJ
ejpam-4403	167	2	v2n	v2n	PROPN
ejpam-4403	167	3	]	]	PUNCT
ejpam-4403	167	4	≥	≥	NOUN
ejpam-4403	167	5	0	0	NUM
ejpam-4403	168	1	the	the	DET
ejpam-4403	168	2	relation	relation	NOUN
ejpam-4403	168	3	(	(	PUNCT
ejpam-4403	168	4	3	3	X
ejpam-4403	168	5	)	)	PUNCT
ejpam-4403	168	6	gives	give	VERB
ejpam-4403	168	7	:	:	PUNCT
ejpam-4403	168	8	<	<	X
ejpam-4403	168	9	aλv	aλv	PROPN
ejpam-4403	168	10	,	,	PUNCT
ejpam-4403	168	11	v	v	X
ejpam-4403	168	12	>	>	X
ejpam-4403	168	13	=	=	SYM
ejpam-4403	168	14	0	0	PUNCT
ejpam-4403	169	1	=	=	NOUN
ejpam-4403	169	2	⇒	⇒	NOUN
ejpam-4403	169	3			PROPN
ejpam-4403	169	4	vi	vi	PROPN
ejpam-4403	169	5	−	−	PROPN
ejpam-4403	169	6	vi−1	vi−1	PROPN
ejpam-4403	169	7	=	=	SYM
ejpam-4403	169	8	0	0	NUM
ejpam-4403	169	9	vi	vi	NOUN
ejpam-4403	169	10	=	=	NOUN
ejpam-4403	169	11	0	0	NUM
ejpam-4403	169	12	...	...	PUNCT
ejpam-4403	169	13	v1	v1	NOUN
ejpam-4403	169	14	=	=	SYM
ejpam-4403	169	15	0	0	PUNCT
ejpam-4403	170	1	=	=	NOUN
ejpam-4403	170	2	⇒	⇒	NOUN
ejpam-4403	170	3	v	v	X
ejpam-4403	170	4	=	=	SYM
ejpam-4403	170	5	0	0	NUM
ejpam-4403	170	6	(	(	PUNCT
ejpam-4403	170	7	1),(2	1),(2	NUM
ejpam-4403	170	8	)	)	PUNCT
ejpam-4403	170	9	et	et	NOUN
ejpam-4403	170	10	(	(	PUNCT
ejpam-4403	170	11	3	3	X
ejpam-4403	170	12	)	)	PUNCT
ejpam-4403	170	13	being	be	AUX
ejpam-4403	170	14	verified	verify	VERB
ejpam-4403	170	15	,	,	PUNCT
ejpam-4403	170	16	then	then	ADV
ejpam-4403	170	17	the	the	DET
ejpam-4403	170	18	problem	problem	NOUN
ejpam-4403	170	19	(	(	PUNCT
ejpam-4403	170	20	41	41	NUM
ejpam-4403	170	21	)	)	PUNCT
ejpam-4403	170	22	admits	admit	VERB
ejpam-4403	170	23	a	a	DET
ejpam-4403	170	24	unique	unique	ADJ
ejpam-4403	170	25	solution	solution	NOUN
ejpam-4403	170	26	.	.	PUNCT
ejpam-4403	171	1	d.	d.	PROPN
ejpam-4403	171	2	v.	v.	PROPN
ejpam-4403	171	3	pongui	pongui	PROPN
ejpam-4403	171	4	ngoma	ngoma	PROPN
ejpam-4403	171	5	et	et	PROPN
ejpam-4403	171	6	al	al	PROPN
ejpam-4403	171	7	.	.	PROPN
ejpam-4403	171	8	,	,	PUNCT
ejpam-4403	171	9	/	/	SYM
ejpam-4403	171	10	eur	eur	NOUN
ejpam-4403	171	11	.	.	PUNCT
ejpam-4403	172	1	j.	j.	PROPN
ejpam-4403	172	2	pure	pure	PROPN
ejpam-4403	172	3	appl	appl	PROPN
ejpam-4403	172	4	.	.	PROPN
ejpam-4403	172	5	math	math	PROPN
ejpam-4403	172	6	,	,	PUNCT
ejpam-4403	172	7	15	15	NUM
ejpam-4403	172	8	(	(	PUNCT
ejpam-4403	172	9	3	3	NUM
ejpam-4403	172	10	)	)	PUNCT
ejpam-4403	172	11	(	(	PUNCT
ejpam-4403	172	12	2022	2022	NUM
ejpam-4403	172	13	)	)	PUNCT
ejpam-4403	172	14	,	,	PUNCT
ejpam-4403	172	15	1348	1348	NUM
ejpam-4403	172	16	-	-	SYM
ejpam-4403	172	17	1362	1362	NUM
ejpam-4403	172	18	1356	1356	NUM
ejpam-4403	172	19	5	5	NUM
ejpam-4403	172	20	.	.	PUNCT
ejpam-4403	172	21	analytical	analytical	ADJ
ejpam-4403	172	22	resolution	resolution	NOUN
ejpam-4403	172	23	of	of	ADP
ejpam-4403	172	24	the	the	DET
ejpam-4403	172	25	problem	problem	NOUN
ejpam-4403	172	26	to	to	PART
ejpam-4403	172	27	solve	solve	VERB
ejpam-4403	172	28	the	the	DET
ejpam-4403	172	29	problem	problem	NOUN
ejpam-4403	172	30	analytically	analytically	ADV
ejpam-4403	172	31	,	,	PUNCT
ejpam-4403	172	32	we	we	PRON
ejpam-4403	172	33	are	be	AUX
ejpam-4403	172	34	going	go	VERB
ejpam-4403	172	35	to	to	PART
ejpam-4403	172	36	use	use	VERB
ejpam-4403	172	37	the	the	DET
ejpam-4403	172	38	method	method	NOUN
ejpam-4403	172	39	of	of	ADP
ejpam-4403	172	40	variation	variation	NOUN
ejpam-4403	172	41	of	of	ADP
ejpam-4403	172	42	constants	constant	NOUN
ejpam-4403	172	43	which	which	PRON
ejpam-4403	172	44	is	be	AUX
ejpam-4403	172	45	done	do	VERB
ejpam-4403	172	46	in	in	ADP
ejpam-4403	172	47	three	three	NUM
ejpam-4403	172	48	steps	step	NOUN
ejpam-4403	172	49	:	:	PUNCT
ejpam-4403	172	50	first	first	ADJ
ejpam-4403	172	51	step	step	NOUN
ejpam-4403	172	52	:	:	PUNCT
ejpam-4403	172	53	resolution	resolution	NOUN
ejpam-4403	172	54	of	of	ADP
ejpam-4403	172	55	the	the	DET
ejpam-4403	172	56	associated	associate	VERB
ejpam-4403	172	57	homogeneous	homogeneous	ADJ
ejpam-4403	172	58	equation	equation	NOUN
ejpam-4403	172	59	consider	consider	VERB
ejpam-4403	172	60	:	:	PUNCT
ejpam-4403	172	61	f(x	f(x	PROPN
ejpam-4403	172	62	)	)	PUNCT
ejpam-4403	172	63	=	=	SYM
ejpam-4403	172	64	5	5	NUM
ejpam-4403	172	65	cos(πx	cos(πx	NOUN
ejpam-4403	172	66	)	)	PUNCT
ejpam-4403	173	1	+	+	CCONJ
ejpam-4403	173	2	(	(	PUNCT
ejpam-4403	173	3	x−	x−	PROPN
ejpam-4403	173	4	5	5	NUM
ejpam-4403	173	5	)	)	PUNCT
ejpam-4403	173	6	,	,	PUNCT
ejpam-4403	173	7	h(x	h(x	PROPN
ejpam-4403	173	8	)	)	PUNCT
ejpam-4403	173	9	=	=	SYM
ejpam-4403	173	10	sin(19πx	sin(19πx	NOUN
ejpam-4403	173	11	)	)	PUNCT
ejpam-4403	173	12	et	et	NOUN
ejpam-4403	173	13	c(x	c(x	NOUN
ejpam-4403	173	14	)	)	PUNCT
ejpam-4403	173	15	=	=	SYM
ejpam-4403	173	16	c0	c0	NOUN
ejpam-4403	173	17	.	.	PUNCT
ejpam-4403	174	1	thus	thus	ADV
ejpam-4403	174	2	,	,	PUNCT
ejpam-4403	174	3	we	we	PRON
ejpam-4403	174	4	obtain	obtain	VERB
ejpam-4403	174	5	:	:	PUNCT
ejpam-4403	174	6	{	{	PUNCT
ejpam-4403	174	7	−µu′′(x	−µu′′(x	NOUN
ejpam-4403	174	8	)	)	PUNCT
ejpam-4403	175	1	+	+	CCONJ
ejpam-4403	175	2	c0u	c0u	NOUN
ejpam-4403	175	3	′(x	′(x	NOUN
ejpam-4403	175	4	)	)	PUNCT
ejpam-4403	175	5	=	=	SYM
ejpam-4403	175	6	5	5	NUM
ejpam-4403	175	7	cos(πx	cos(πx	NOUN
ejpam-4403	175	8	)	)	PUNCT
ejpam-4403	176	1	+	+	CCONJ
ejpam-4403	176	2	(	(	PUNCT
ejpam-4403	176	3	x−	x−	PROPN
ejpam-4403	176	4	5	5	NUM
ejpam-4403	176	5	)	)	PUNCT
ejpam-4403	176	6	u(0	u(0	NOUN
ejpam-4403	176	7	)	)	PUNCT
ejpam-4403	176	8	=	=	SYM
ejpam-4403	176	9	0	0	NUM
ejpam-4403	176	10	,	,	PUNCT
ejpam-4403	176	11	u(1	u(1	PROPN
ejpam-4403	176	12	)	)	PUNCT
ejpam-4403	176	13	=	=	SYM
ejpam-4403	176	14	0	0	NUM
ejpam-4403	177	1	solving	solve	VERB
ejpam-4403	177	2	the	the	DET
ejpam-4403	177	3	associated	associated	ADJ
ejpam-4403	177	4	homogeneous	homogeneous	ADJ
ejpam-4403	177	5	equation	equation	NOUN
ejpam-4403	177	6	−µu′′(x	−µu′′(x	NOUN
ejpam-4403	177	7	)	)	PUNCT
ejpam-4403	178	1	+	+	CCONJ
ejpam-4403	178	2	c0u	c0u	NOUN
ejpam-4403	178	3	′(x	′(x	NOUN
ejpam-4403	178	4	)	)	PUNCT
ejpam-4403	179	1	=	=	SYM
ejpam-4403	179	2	0	0	PUNCT
ejpam-4403	179	3	to	to	PART
ejpam-4403	179	4	get	get	VERB
ejpam-4403	179	5	the	the	DET
ejpam-4403	179	6	solution	solution	NOUN
ejpam-4403	179	7	:	:	PUNCT
ejpam-4403	179	8	u(x	u(x	PROPN
ejpam-4403	179	9	)	)	PUNCT
ejpam-4403	180	1	=	=	SYM
ejpam-4403	180	2	c1	c1	NOUN
ejpam-4403	180	3	+	+	CCONJ
ejpam-4403	180	4	c2e	c2e	PROPN
ejpam-4403	180	5	βx	βx	X
ejpam-4403	180	6	with	with	ADP
ejpam-4403	180	7	β	β	X
ejpam-4403	180	8	=	=	PUNCT
ejpam-4403	180	9	co	co	X
ejpam-4403	180	10	µ	µ	X
ejpam-4403	180	11	,	,	PUNCT
ejpam-4403	180	12	c1	c1	PROPN
ejpam-4403	180	13	,	,	PUNCT
ejpam-4403	180	14	c2	c2	PROPN
ejpam-4403	180	15	∈	∈	PROPN
ejpam-4403	180	16	r	r	NOUN
ejpam-4403	180	17	second	second	ADJ
ejpam-4403	180	18	step	step	NOUN
ejpam-4403	180	19	:	:	PUNCT
ejpam-4403	180	20	variation	variation	NOUN
ejpam-4403	180	21	of	of	ADP
ejpam-4403	180	22	constants	constant	NOUN
ejpam-4403	180	23	let	let	VERB
ejpam-4403	180	24	us	we	PRON
ejpam-4403	180	25	determine	determine	VERB
ejpam-4403	180	26	c1(x	c1(x	NOUN
ejpam-4403	180	27	)	)	PUNCT
ejpam-4403	180	28	and	and	CCONJ
ejpam-4403	180	29	c2(x	c2(x	NOUN
ejpam-4403	180	30	)	)	PUNCT
ejpam-4403	180	31	such	such	ADJ
ejpam-4403	180	32	that	that	SCONJ
ejpam-4403	180	33	:	:	PUNCT
ejpam-4403	180	34	u(x	u(x	PROPN
ejpam-4403	180	35	)	)	PUNCT
ejpam-4403	180	36	=	=	SYM
ejpam-4403	181	1	c1(x	c1(x	X
ejpam-4403	181	2	)	)	PUNCT
ejpam-4403	181	3	+	+	CCONJ
ejpam-4403	181	4	c2(x)e	c2(x)e	PROPN
ejpam-4403	181	5	βx	βx	NOUN
ejpam-4403	181	6	,	,	PUNCT
ejpam-4403	181	7	(	(	PUNCT
ejpam-4403	181	8	42	42	X
ejpam-4403	181	9	)	)	PUNCT
ejpam-4403	181	10	let	let	AUX
ejpam-4403	181	11	be	be	AUX
ejpam-4403	181	12	the	the	DET
ejpam-4403	181	13	solution	solution	NOUN
ejpam-4403	181	14	of	of	ADP
ejpam-4403	181	15	the	the	DET
ejpam-4403	181	16	equation	equation	NOUN
ejpam-4403	181	17	with	with	ADP
ejpam-4403	181	18	second	second	ADJ
ejpam-4403	181	19	member	member	NOUN
ejpam-4403	181	20	.	.	PUNCT
ejpam-4403	182	1	for	for	ADP
ejpam-4403	182	2	that	that	PRON
ejpam-4403	182	3	,	,	PUNCT
ejpam-4403	182	4	it	it	PRON
ejpam-4403	182	5	is	be	AUX
ejpam-4403	182	6	a	a	DET
ejpam-4403	182	7	question	question	NOUN
ejpam-4403	182	8	of	of	ADP
ejpam-4403	182	9	solving	solve	VERB
ejpam-4403	182	10	the	the	DET
ejpam-4403	182	11	following	follow	VERB
ejpam-4403	182	12	system	system	NOUN
ejpam-4403	182	13	:	:	PUNCT
ejpam-4403	182	14	{	{	PUNCT
ejpam-4403	182	15	c′1(x	c′1(x	NOUN
ejpam-4403	182	16	)	)	PUNCT
ejpam-4403	182	17	+	+	CCONJ
ejpam-4403	182	18	c′2(x)e	c′2(x)e	ADJ
ejpam-4403	182	19	βx	βx	X
ejpam-4403	182	20	=	=	SYM
ejpam-4403	182	21	0	0	PROPN
ejpam-4403	182	22	βc′2(x)e	βc′2(x)e	VERB
ejpam-4403	182	23	βx	βx	ADP
ejpam-4403	183	1	=	=	SYM
ejpam-4403	183	2	f(x	f(x	PROPN
ejpam-4403	183	3	)	)	PUNCT
ejpam-4403	183	4	a	a	DET
ejpam-4403	183	5	=	=	PUNCT
ejpam-4403	183	6	−5	−5	ADP
ejpam-4403	183	7	cos(πx)+(x−5	cos(πx)+(x−5	PROPN
ejpam-4403	183	8	)	)	PUNCT
ejpam-4403	183	9	µ	µ	X
ejpam-4403	183	10	(	(	PUNCT
ejpam-4403	183	11	43	43	NUM
ejpam-4403	183	12	)	)	PUNCT
ejpam-4403	183	13	we	we	PRON
ejpam-4403	183	14	obtain	obtain	VERB
ejpam-4403	183	15	c1(x	c1(x	NOUN
ejpam-4403	183	16	)	)	PUNCT
ejpam-4403	183	17	=	=	SYM
ejpam-4403	183	18	5	5	NUM
ejpam-4403	183	19	µβπ	µβπ	NOUN
ejpam-4403	183	20	sin(πx	sin(πx	NOUN
ejpam-4403	183	21	)	)	PUNCT
ejpam-4403	184	1	+	+	CCONJ
ejpam-4403	184	2	1	1	NUM
ejpam-4403	184	3	µβ	µβ	NOUN
ejpam-4403	184	4	(	(	PUNCT
ejpam-4403	184	5	x2	x2	NOUN
ejpam-4403	184	6	2	2	NUM
ejpam-4403	184	7	−	−	NOUN
ejpam-4403	184	8	5x	5x	NUM
ejpam-4403	184	9	)	)	PUNCT
ejpam-4403	185	1	+	+	CCONJ
ejpam-4403	185	2	α1	α1	PROPN
ejpam-4403	185	3	with	with	ADP
ejpam-4403	185	4	α1	α1	PROPN
ejpam-4403	185	5	∈	∈	PROPN
ejpam-4403	185	6	r	r	NOUN
ejpam-4403	185	7	(	(	PUNCT
ejpam-4403	185	8	44	44	NUM
ejpam-4403	185	9	)	)	PUNCT
ejpam-4403	185	10	c2(x	c2(x	PROPN
ejpam-4403	185	11	)	)	PUNCT
ejpam-4403	185	12	=	=	SYM
ejpam-4403	185	13	1	1	NUM
ejpam-4403	185	14	co	co	NOUN
ejpam-4403	185	15	[	[	PUNCT
ejpam-4403	185	16	−5	−5	ADP
ejpam-4403	185	17	π2	π2	NOUN
ejpam-4403	185	18	+	+	CCONJ
ejpam-4403	185	19	β2	β2	NOUN
ejpam-4403	185	20	(	(	PUNCT
ejpam-4403	185	21	π	π	PROPN
ejpam-4403	185	22	sinπx−	sinπx−	ADV
ejpam-4403	185	23	β	β	X
ejpam-4403	185	24	cosπx	cosπx	PROPN
ejpam-4403	185	25	)	)	PUNCT
ejpam-4403	186	1	+	+	CCONJ
ejpam-4403	186	2	1	1	NUM
ejpam-4403	186	3	β2	β2	ADJ
ejpam-4403	186	4	+	+	CCONJ
ejpam-4403	186	5	1	1	NUM
ejpam-4403	186	6	β	β	X
ejpam-4403	186	7	(	(	PUNCT
ejpam-4403	186	8	x−	x−	PROPN
ejpam-4403	186	9	5	5	NUM
ejpam-4403	186	10	)	)	PUNCT
ejpam-4403	186	11	]	]	PUNCT
ejpam-4403	187	1	e−βx	e−βx	PROPN
ejpam-4403	187	2	+	+	ADV
ejpam-4403	187	3	α2	α2	ADJ
ejpam-4403	187	4	with	with	ADP
ejpam-4403	187	5	α2	α2	PROPN
ejpam-4403	187	6	∈	∈	PROPN
ejpam-4403	187	7	r	r	NOUN
ejpam-4403	187	8	(	(	PUNCT
ejpam-4403	187	9	45	45	NUM
ejpam-4403	187	10	)	)	PUNCT
ejpam-4403	187	11	thus	thus	ADV
ejpam-4403	187	12	,	,	PUNCT
ejpam-4403	187	13	the	the	DET
ejpam-4403	187	14	relation	relation	NOUN
ejpam-4403	187	15	(	(	PUNCT
ejpam-4403	187	16	42	42	NUM
ejpam-4403	187	17	)	)	PUNCT
ejpam-4403	187	18	becomes	becomes	AUX
ejpam-4403	187	19	:	:	PUNCT
ejpam-4403	188	1	d.	d.	PROPN
ejpam-4403	188	2	v.	v.	PROPN
ejpam-4403	188	3	pongui	pongui	PROPN
ejpam-4403	188	4	ngoma	ngoma	PROPN
ejpam-4403	188	5	et	et	PROPN
ejpam-4403	188	6	al	al	PROPN
ejpam-4403	188	7	.	.	PROPN
ejpam-4403	188	8	,	,	PUNCT
ejpam-4403	188	9	/	/	SYM
ejpam-4403	188	10	eur	eur	NOUN
ejpam-4403	188	11	.	.	PUNCT
ejpam-4403	189	1	j.	j.	PROPN
ejpam-4403	189	2	pure	pure	PROPN
ejpam-4403	189	3	appl	appl	PROPN
ejpam-4403	189	4	.	.	PROPN
ejpam-4403	189	5	math	math	PROPN
ejpam-4403	189	6	,	,	PUNCT
ejpam-4403	189	7	15	15	NUM
ejpam-4403	189	8	(	(	PUNCT
ejpam-4403	189	9	3	3	NUM
ejpam-4403	189	10	)	)	PUNCT
ejpam-4403	189	11	(	(	PUNCT
ejpam-4403	189	12	2022	2022	NUM
ejpam-4403	189	13	)	)	PUNCT
ejpam-4403	189	14	,	,	PUNCT
ejpam-4403	189	15	1348	1348	NUM
ejpam-4403	189	16	-	-	SYM
ejpam-4403	189	17	1362	1362	NUM
ejpam-4403	189	18	1357	1357	NUM
ejpam-4403	189	19	u(x	u(x	NOUN
ejpam-4403	189	20	)	)	PUNCT
ejpam-4403	189	21	=	=	SYM
ejpam-4403	190	1	5	5	NUM
ejpam-4403	190	2	coπ	coπ	NOUN
ejpam-4403	190	3	sin(πx)+	sin(πx)+	NOUN
ejpam-4403	190	4	1	1	NUM
ejpam-4403	190	5	co	co	NOUN
ejpam-4403	190	6	(	(	PUNCT
ejpam-4403	190	7	x2	x2	PROPN
ejpam-4403	190	8	2	2	NUM
ejpam-4403	190	9	−5x)+	−5x)+	NUM
ejpam-4403	190	10	1	1	NUM
ejpam-4403	190	11	co	co	NOUN
ejpam-4403	190	12	[	[	PUNCT
ejpam-4403	190	13	−5	−5	ADP
ejpam-4403	190	14	π2	π2	NOUN
ejpam-4403	190	15	+	+	CCONJ
ejpam-4403	190	16	β2	β2	NOUN
ejpam-4403	190	17	(	(	PUNCT
ejpam-4403	190	18	π	π	PROPN
ejpam-4403	190	19	sinπx−	sinπx−	ADV
ejpam-4403	190	20	β	β	X
ejpam-4403	190	21	cosπx	cosπx	PROPN
ejpam-4403	190	22	)	)	PUNCT
ejpam-4403	190	23	+	+	CCONJ
ejpam-4403	190	24	1	1	NUM
ejpam-4403	190	25	β2	β2	ADJ
ejpam-4403	190	26	+	+	CCONJ
ejpam-4403	190	27	1	1	NUM
ejpam-4403	190	28	β	β	X
ejpam-4403	190	29	(	(	PUNCT
ejpam-4403	190	30	x−	x−	PROPN
ejpam-4403	190	31	5	5	NUM
ejpam-4403	190	32	)	)	PUNCT
ejpam-4403	190	33	]	]	PUNCT
ejpam-4403	191	1	+	+	ADP
ejpam-4403	191	2	α1+α2e	α1+α2e	X
ejpam-4403	191	3	−βx	−βx	NOUN
ejpam-4403	191	4	(	(	PUNCT
ejpam-4403	191	5	46	46	NUM
ejpam-4403	191	6	)	)	PUNCT
ejpam-4403	191	7	third	third	ADJ
ejpam-4403	191	8	step	step	NOUN
ejpam-4403	191	9	:	:	PUNCT
ejpam-4403	191	10	general	general	ADJ
ejpam-4403	191	11	solution	solution	NOUN
ejpam-4403	191	12	of	of	ADP
ejpam-4403	191	13	the	the	DET
ejpam-4403	191	14	complete	complete	ADJ
ejpam-4403	191	15	equation	equation	NOUN
ejpam-4403	191	16	let	let	VERB
ejpam-4403	191	17	’s	’s	NOUN
ejpam-4403	191	18	find	find	VERB
ejpam-4403	191	19	α1	α1	PROPN
ejpam-4403	191	20	and	and	CCONJ
ejpam-4403	191	21	α2	α2	NOUN
ejpam-4403	191	22	using	use	VERB
ejpam-4403	191	23	the	the	DET
ejpam-4403	191	24	boundary	boundary	ADJ
ejpam-4403	191	25	conditions	condition	NOUN
ejpam-4403	191	26	,	,	PUNCT
ejpam-4403	191	27	we	we	PRON
ejpam-4403	191	28	have	have	VERB
ejpam-4403	191	29	:	:	PUNCT
ejpam-4403	191	30	{	{	PUNCT
ejpam-4403	191	31	5β	5β	PROPN
ejpam-4403	191	32	co(π2+β2	co(π2+β2	X
ejpam-4403	191	33	)	)	PUNCT
ejpam-4403	191	34	+	+	CCONJ
ejpam-4403	191	35	1	1	NUM
ejpam-4403	191	36	coβ2	coβ2	NOUN
ejpam-4403	191	37	−	−	PROPN
ejpam-4403	191	38	5	5	NUM
ejpam-4403	191	39	coβ	coβ	ADJ
ejpam-4403	191	40	+	+	CCONJ
ejpam-4403	191	41	α1	α1	PROPN
ejpam-4403	191	42	+	+	CCONJ
ejpam-4403	191	43	α2	α2	ADJ
ejpam-4403	191	44	=	=	SYM
ejpam-4403	191	45	0	0	PUNCT
ejpam-4403	192	1	−9	−9	NOUN
ejpam-4403	192	2	2c0	2c0	NUM
ejpam-4403	192	3	−	−	PROPN
ejpam-4403	192	4	5β	5β	NUM
ejpam-4403	192	5	c0(π2+β2	c0(π2+β2	NOUN
ejpam-4403	192	6	)	)	PUNCT
ejpam-4403	193	1	+	+	CCONJ
ejpam-4403	193	2	1	1	NUM
ejpam-4403	193	3	c0β2	c0β2	SYM
ejpam-4403	193	4	−	−	NOUN
ejpam-4403	193	5	4	4	NUM
ejpam-4403	193	6	c0β	c0β	PROPN
ejpam-4403	193	7	+	+	CCONJ
ejpam-4403	193	8	α1	α1	PROPN
ejpam-4403	193	9	+	+	CCONJ
ejpam-4403	193	10	α2e	α2e	NOUN
ejpam-4403	193	11	β	β	X
ejpam-4403	193	12	=	=	SYM
ejpam-4403	193	13	0	0	PUNCT
ejpam-4403	193	14	(	(	PUNCT
ejpam-4403	193	15	47	47	NUM
ejpam-4403	193	16	)	)	PUNCT
ejpam-4403	193	17	solving	solve	VERB
ejpam-4403	193	18	the	the	DET
ejpam-4403	193	19	equation	equation	NOUN
ejpam-4403	193	20	(	(	PUNCT
ejpam-4403	193	21	47	47	NUM
ejpam-4403	193	22	)	)	PUNCT
ejpam-4403	193	23	,	,	PUNCT
ejpam-4403	193	24	to	to	PART
ejpam-4403	193	25	obtain	obtain	VERB
ejpam-4403	193	26	α1	α1	PROPN
ejpam-4403	193	27	=	=	SYM
ejpam-4403	193	28	1	1	NUM
ejpam-4403	193	29	co(eβ	co(eβ	NOUN
ejpam-4403	193	30	−	−	NOUN
ejpam-4403	193	31	1	1	X
ejpam-4403	193	32	)	)	PUNCT
ejpam-4403	193	33	[	[	PUNCT
ejpam-4403	193	34	−9	−9	NOUN
ejpam-4403	193	35	2	2	NUM
ejpam-4403	193	36	+	+	SYM
ejpam-4403	193	37	1−	1−	NUM
ejpam-4403	193	38	4β	4β	NOUN
ejpam-4403	193	39	+	+	CCONJ
ejpam-4403	193	40	(	(	PUNCT
ejpam-4403	193	41	5β	5β	NUM
ejpam-4403	193	42	−	−	PROPN
ejpam-4403	193	43	1)eβ	1)eβ	NUM
ejpam-4403	193	44	β2	β2	NOUN
ejpam-4403	193	45	−	−	PROPN
ejpam-4403	193	46	5β(1	5β(1	NUM
ejpam-4403	193	47	+	+	NUM
ejpam-4403	193	48	eβ	eβ	NOUN
ejpam-4403	193	49	)	)	PUNCT
ejpam-4403	193	50	β2	β2	NOUN
ejpam-4403	194	1	+	+	CCONJ
ejpam-4403	194	2	π2	π2	X
ejpam-4403	194	3	]	]	PUNCT
ejpam-4403	194	4	(	(	PUNCT
ejpam-4403	194	5	48	48	NUM
ejpam-4403	194	6	)	)	PUNCT
ejpam-4403	194	7	α2	α2	NOUN
ejpam-4403	194	8	=	=	SYM
ejpam-4403	194	9	1	1	NUM
ejpam-4403	194	10	co(eβ	co(eβ	NOUN
ejpam-4403	194	11	−	−	NOUN
ejpam-4403	194	12	1	1	X
ejpam-4403	194	13	)	)	PUNCT
ejpam-4403	194	14	[	[	PUNCT
ejpam-4403	194	15	9	9	NUM
ejpam-4403	194	16	2	2	NUM
ejpam-4403	194	17	+	+	NUM
ejpam-4403	194	18	10β	10β	X
ejpam-4403	194	19	β2	β2	NOUN
ejpam-4403	194	20	+	+	CCONJ
ejpam-4403	195	1	π2	π2	ADV
ejpam-4403	195	2	−	−	PROPN
ejpam-4403	195	3	−1	−1	NOUN
ejpam-4403	195	4	β	β	X
ejpam-4403	195	5	]	]	X
ejpam-4403	195	6	(	(	PUNCT
ejpam-4403	195	7	49	49	NUM
ejpam-4403	195	8	)	)	PUNCT
ejpam-4403	195	9	thus	thus	ADV
ejpam-4403	195	10	,	,	PUNCT
ejpam-4403	195	11	replacing	replace	VERB
ejpam-4403	195	12	(	(	PUNCT
ejpam-4403	195	13	49	49	NUM
ejpam-4403	195	14	)	)	PUNCT
ejpam-4403	195	15	and	and	CCONJ
ejpam-4403	195	16	(	(	PUNCT
ejpam-4403	195	17	48	48	NUM
ejpam-4403	195	18	)	)	PUNCT
ejpam-4403	195	19	in	in	ADP
ejpam-4403	195	20	(	(	PUNCT
ejpam-4403	195	21	46	46	NUM
ejpam-4403	195	22	)	)	PUNCT
ejpam-4403	195	23	,	,	PUNCT
ejpam-4403	195	24	u(x	u(x	PROPN
ejpam-4403	195	25	)	)	PUNCT
ejpam-4403	195	26	=	=	SYM
ejpam-4403	195	27	5	5	NUM
ejpam-4403	195	28	coπ	coπ	NOUN
ejpam-4403	195	29	sin(πx	sin(πx	NOUN
ejpam-4403	195	30	)	)	PUNCT
ejpam-4403	196	1	+	+	CCONJ
ejpam-4403	196	2	1	1	NUM
ejpam-4403	196	3	co	co	NOUN
ejpam-4403	196	4	(	(	PUNCT
ejpam-4403	196	5	x2	x2	PROPN
ejpam-4403	196	6	2	2	NUM
ejpam-4403	196	7	−	−	NOUN
ejpam-4403	196	8	5x	5x	NUM
ejpam-4403	196	9	)	)	PUNCT
ejpam-4403	196	10	+	+	CCONJ
ejpam-4403	196	11	1	1	NUM
ejpam-4403	196	12	co	co	NOUN
ejpam-4403	196	13	[	[	PUNCT
ejpam-4403	196	14	−5	−5	ADP
ejpam-4403	196	15	π2	π2	NOUN
ejpam-4403	196	16	+	+	CCONJ
ejpam-4403	196	17	β2	β2	NOUN
ejpam-4403	196	18	(	(	PUNCT
ejpam-4403	196	19	π	π	PROPN
ejpam-4403	196	20	sinπx−	sinπx−	ADV
ejpam-4403	196	21	β	β	X
ejpam-4403	196	22	cosπx	cosπx	PROPN
ejpam-4403	196	23	)	)	PUNCT
ejpam-4403	196	24	+	+	CCONJ
ejpam-4403	196	25	1	1	NUM
ejpam-4403	196	26	β2	β2	ADJ
ejpam-4403	196	27	+	+	CCONJ
ejpam-4403	196	28	1	1	NUM
ejpam-4403	196	29	β	β	X
ejpam-4403	196	30	(	(	PUNCT
ejpam-4403	196	31	x−	x−	PROPN
ejpam-4403	196	32	5	5	NUM
ejpam-4403	196	33	)	)	PUNCT
ejpam-4403	196	34	]	]	PUNCT
ejpam-4403	197	1	+	+	CCONJ
ejpam-4403	197	2	+	+	NUM
ejpam-4403	197	3	1	1	NUM
ejpam-4403	197	4	co(eβ	co(eβ	NOUN
ejpam-4403	197	5	−	−	NOUN
ejpam-4403	197	6	1	1	X
ejpam-4403	197	7	)	)	PUNCT
ejpam-4403	197	8	[	[	PUNCT
ejpam-4403	197	9	9	9	NUM
ejpam-4403	197	10	2	2	NUM
ejpam-4403	197	11	(	(	PUNCT
ejpam-4403	197	12	eβ	eβ	NOUN
ejpam-4403	197	13	−	−	PROPN
ejpam-4403	197	14	1	1	NUM
ejpam-4403	197	15	)	)	PUNCT
ejpam-4403	197	16	+	+	CCONJ
ejpam-4403	197	17	1−	1−	NUM
ejpam-4403	197	18	4β	4β	NOUN
ejpam-4403	197	19	+	+	CCONJ
ejpam-4403	197	20	(	(	PUNCT
ejpam-4403	197	21	5β	5β	NUM
ejpam-4403	197	22	−	−	PROPN
ejpam-4403	197	23	1)eβ	1)eβ	NUM
ejpam-4403	197	24	β2	β2	NOUN
ejpam-4403	197	25	+	+	CCONJ
ejpam-4403	197	26	5β(eβ	5β(eβ	NUM
ejpam-4403	197	27	−	−	NOUN
ejpam-4403	197	28	1	1	X
ejpam-4403	197	29	)	)	PUNCT
ejpam-4403	197	30	β2	β2	NOUN
ejpam-4403	197	31	+	+	CCONJ
ejpam-4403	197	32	π2	π2	ADJ
ejpam-4403	197	33	−	−	PROPN
ejpam-4403	197	34	eβ	eβ	NOUN
ejpam-4403	197	35	β	β	X
ejpam-4403	197	36	]	]	PUNCT
ejpam-4403	197	37	.	.	PUNCT
ejpam-4403	198	1	(	(	PUNCT
ejpam-4403	198	2	50	50	NUM
ejpam-4403	198	3	)	)	PUNCT
ejpam-4403	198	4	6	6	NUM
ejpam-4403	198	5	.	.	PUNCT
ejpam-4403	198	6	numerical	numerical	PROPN
ejpam-4403	198	7	simulation	simulation	PROPN
ejpam-4403	198	8	the	the	DET
ejpam-4403	198	9	goal	goal	NOUN
ejpam-4403	198	10	here	here	ADV
ejpam-4403	198	11	is	be	AUX
ejpam-4403	198	12	to	to	PART
ejpam-4403	198	13	represent	represent	VERB
ejpam-4403	198	14	on	on	ADP
ejpam-4403	198	15	the	the	DET
ejpam-4403	198	16	same	same	ADJ
ejpam-4403	198	17	graph	graph	NOUN
ejpam-4403	198	18	the	the	DET
ejpam-4403	198	19	solutions	solution	NOUN
ejpam-4403	198	20	(	(	PUNCT
ejpam-4403	198	21	50	50	NUM
ejpam-4403	198	22	)	)	PUNCT
ejpam-4403	198	23	and	and	CCONJ
ejpam-4403	198	24	(	(	PUNCT
ejpam-4403	198	25	41	41	NUM
ejpam-4403	198	26	)	)	PUNCT
ejpam-4403	198	27	exact	exact	ADJ
ejpam-4403	198	28	and	and	CCONJ
ejpam-4403	198	29	numeric	numeric	ADJ
ejpam-4403	198	30	,	,	PUNCT
ejpam-4403	198	31	respectively	respectively	ADV
ejpam-4403	198	32	,	,	PUNCT
ejpam-4403	198	33	taking	take	VERB
ejpam-4403	198	34	into	into	ADP
ejpam-4403	198	35	account	account	NOUN
ejpam-4403	198	36	the	the	DET
ejpam-4403	198	37	number	number	NOUN
ejpam-4403	198	38	of	of	ADP
ejpam-4403	198	39	points	point	NOUN
ejpam-4403	198	40	n	n	PRON
ejpam-4403	198	41	and	and	CCONJ
ejpam-4403	198	42	the	the	DET
ejpam-4403	198	43	step	step	NOUN
ejpam-4403	198	44	h	h	NOUN
ejpam-4403	198	45	of	of	ADP
ejpam-4403	198	46	the	the	DET
ejpam-4403	198	47	finite	finite	ADJ
ejpam-4403	198	48	difference	difference	NOUN
ejpam-4403	198	49	method	method	NOUN
ejpam-4403	198	50	with	with	ADP
ejpam-4403	198	51	the	the	DET
ejpam-4403	198	52	objective	objective	NOUN
ejpam-4403	198	53	of	of	ADP
ejpam-4403	198	54	making	make	VERB
ejpam-4403	198	55	the	the	DET
ejpam-4403	198	56	two	two	NUM
ejpam-4403	198	57	solutions	solution	NOUN
ejpam-4403	198	58	converge	converge	NOUN
ejpam-4403	198	59	(	(	PUNCT
ejpam-4403	198	60	exact	exact	ADJ
ejpam-4403	198	61	and	and	CCONJ
ejpam-4403	198	62	numerical	numerical	ADJ
ejpam-4403	198	63	)	)	PUNCT
ejpam-4403	198	64	.	.	PUNCT
ejpam-4403	199	1	this	this	DET
ejpam-4403	199	2	simulation	simulation	NOUN
ejpam-4403	199	3	will	will	AUX
ejpam-4403	199	4	be	be	AUX
ejpam-4403	199	5	implemented	implement	VERB
ejpam-4403	199	6	in	in	ADP
ejpam-4403	199	7	scilab	scilab	PROPN
ejpam-4403	199	8	.	.	PUNCT
ejpam-4403	200	1	the	the	DET
ejpam-4403	200	2	figure	figure	NOUN
ejpam-4403	200	3	1	1	NUM
ejpam-4403	200	4	illustrates	illustrate	VERB
ejpam-4403	200	5	the	the	DET
ejpam-4403	200	6	exact	exact	ADJ
ejpam-4403	200	7	solution	solution	NOUN
ejpam-4403	200	8	(	(	PUNCT
ejpam-4403	200	9	50	50	NUM
ejpam-4403	200	10	)	)	PUNCT
ejpam-4403	200	11	for	for	ADP
ejpam-4403	200	12	µ	µ	NOUN
ejpam-4403	200	13	=	=	SYM
ejpam-4403	200	14	1	1	NUM
ejpam-4403	200	15	and	and	CCONJ
ejpam-4403	200	16	c0	c0	NOUN
ejpam-4403	200	17	=	=	PUNCT
ejpam-4403	201	1	3	3	X
ejpam-4403	201	2	.	.	X
ejpam-4403	201	3	d.	d.	PROPN
ejpam-4403	201	4	v.	v.	PROPN
ejpam-4403	201	5	pongui	pongui	PROPN
ejpam-4403	201	6	ngoma	ngoma	PROPN
ejpam-4403	201	7	et	et	PROPN
ejpam-4403	201	8	al	al	PROPN
ejpam-4403	201	9	.	.	PROPN
ejpam-4403	201	10	,	,	PUNCT
ejpam-4403	201	11	/	/	SYM
ejpam-4403	201	12	eur	eur	NOUN
ejpam-4403	201	13	.	.	PUNCT
ejpam-4403	202	1	j.	j.	PROPN
ejpam-4403	202	2	pure	pure	PROPN
ejpam-4403	202	3	appl	appl	PROPN
ejpam-4403	202	4	.	.	PROPN
ejpam-4403	202	5	math	math	PROPN
ejpam-4403	202	6	,	,	PUNCT
ejpam-4403	202	7	15	15	NUM
ejpam-4403	202	8	(	(	PUNCT
ejpam-4403	202	9	3	3	NUM
ejpam-4403	202	10	)	)	PUNCT
ejpam-4403	202	11	(	(	PUNCT
ejpam-4403	202	12	2022	2022	NUM
ejpam-4403	202	13	)	)	PUNCT
ejpam-4403	202	14	,	,	PUNCT
ejpam-4403	202	15	1348	1348	NUM
ejpam-4403	202	16	-	-	SYM
ejpam-4403	202	17	1362	1362	NUM
ejpam-4403	202	18	1358	1358	NUM
ejpam-4403	202	19	by	by	ADP
ejpam-4403	202	20	fixing	fix	VERB
ejpam-4403	202	21	the	the	DET
ejpam-4403	202	22	number	number	NOUN
ejpam-4403	202	23	of	of	ADP
ejpam-4403	202	24	points	point	NOUN
ejpam-4403	202	25	n	n	X
ejpam-4403	202	26	=	=	SYM
ejpam-4403	202	27	5	5	NUM
ejpam-4403	202	28	in	in	ADP
ejpam-4403	202	29	the	the	DET
ejpam-4403	202	30	finite	finite	ADJ
ejpam-4403	202	31	difference	difference	NOUN
ejpam-4403	202	32	method	method	NOUN
ejpam-4403	202	33	(	(	PUNCT
ejpam-4403	202	34	41	41	NUM
ejpam-4403	202	35	)	)	PUNCT
ejpam-4403	203	1	,	,	PUNCT
ejpam-4403	203	2	we	we	PRON
ejpam-4403	203	3	sought	seek	VERB
ejpam-4403	203	4	to	to	PART
ejpam-4403	203	5	figure	figure	VERB
ejpam-4403	203	6	1	1	NUM
ejpam-4403	203	7	:	:	PUNCT
ejpam-4403	203	8	representation	representation	NOUN
ejpam-4403	203	9	of	of	ADP
ejpam-4403	203	10	the	the	DET
ejpam-4403	203	11	exact	exact	ADJ
ejpam-4403	203	12	solution	solution	NOUN
ejpam-4403	203	13	.	.	PUNCT
ejpam-4403	204	1	vary	vary	VERB
ejpam-4403	204	2	the	the	DET
ejpam-4403	204	3	step	step	NOUN
ejpam-4403	204	4	h	h	NOUN
ejpam-4403	204	5	of	of	ADP
ejpam-4403	204	6	the	the	DET
ejpam-4403	204	7	method	method	NOUN
ejpam-4403	204	8	to	to	PART
ejpam-4403	204	9	verify	verify	VERB
ejpam-4403	204	10	the	the	DET
ejpam-4403	204	11	numerical	numerical	ADJ
ejpam-4403	204	12	convergence	convergence	NOUN
ejpam-4403	204	13	of	of	ADP
ejpam-4403	204	14	(	(	PUNCT
ejpam-4403	204	15	41	41	NUM
ejpam-4403	204	16	)	)	PUNCT
ejpam-4403	204	17	on	on	ADP
ejpam-4403	204	18	(	(	PUNCT
ejpam-4403	204	19	50	50	NUM
ejpam-4403	204	20	)	)	PUNCT
ejpam-4403	204	21	.	.	PUNCT
ejpam-4403	205	1	(	(	PUNCT
ejpam-4403	205	2	cf	cf	NOUN
ejpam-4403	205	3	fig	fig	NOUN
ejpam-4403	205	4	2	2	NUM
ejpam-4403	205	5	)	)	PUNCT
ejpam-4403	205	6	.	.	PUNCT
ejpam-4403	206	1	•	•	NUM
ejpam-4403	206	2	taking	take	VERB
ejpam-4403	206	3	for	for	ADP
ejpam-4403	206	4	step	step	NOUN
ejpam-4403	206	5	h	h	NOUN
ejpam-4403	207	1	=	=	NOUN
ejpam-4403	207	2	0.001	0.001	NUM
ejpam-4403	207	3	,	,	PUNCT
ejpam-4403	207	4	on	on	ADP
ejpam-4403	207	5	can	can	AUX
ejpam-4403	207	6	notice	notice	VERB
ejpam-4403	207	7	that	that	SCONJ
ejpam-4403	207	8	both	both	CCONJ
ejpam-4403	207	9	exact	exact	ADJ
ejpam-4403	207	10	and	and	CCONJ
ejpam-4403	207	11	numerical	numerical	ADJ
ejpam-4403	207	12	solutions	solution	NOUN
ejpam-4403	207	13	converge	converge	VERB
ejpam-4403	207	14	almost	almost	ADV
ejpam-4403	207	15	everywhere	everywhere	ADV
ejpam-4403	207	16	numerically	numerically	ADV
ejpam-4403	207	17	(	(	PUNCT
ejpam-4403	207	18	figure	figure	NOUN
ejpam-4403	207	19	2	2	NUM
ejpam-4403	207	20	a	a	NOUN
ejpam-4403	207	21	)	)	PUNCT
ejpam-4403	207	22	.	.	PUNCT
ejpam-4403	208	1	•	•	NUM
ejpam-4403	209	1	taking	take	VERB
ejpam-4403	209	2	for	for	ADP
ejpam-4403	209	3	step	step	NOUN
ejpam-4403	209	4	h	h	NOUN
ejpam-4403	210	1	=	=	NOUN
ejpam-4403	210	2	0.01	0.01	NUM
ejpam-4403	210	3	,	,	PUNCT
ejpam-4403	210	4	we	we	PRON
ejpam-4403	210	5	note	note	VERB
ejpam-4403	210	6	that	that	SCONJ
ejpam-4403	210	7	at	at	ADP
ejpam-4403	210	8	the	the	DET
ejpam-4403	210	9	beginning	beginning	NOUN
ejpam-4403	210	10	the	the	DET
ejpam-4403	210	11	two	two	NUM
ejpam-4403	210	12	solutions	solution	NOUN
ejpam-4403	210	13	(	(	PUNCT
ejpam-4403	210	14	exact	exact	ADJ
ejpam-4403	210	15	and	and	CCONJ
ejpam-4403	210	16	numerical	numerical	ADJ
ejpam-4403	210	17	)	)	PUNCT
ejpam-4403	210	18	tend	tend	VERB
ejpam-4403	210	19	to	to	PART
ejpam-4403	210	20	move	move	VERB
ejpam-4403	210	21	away	away	ADV
ejpam-4403	210	22	and	and	CCONJ
ejpam-4403	210	23	at	at	ADP
ejpam-4403	210	24	a	a	DET
ejpam-4403	210	25	moment	moment	NOUN
ejpam-4403	210	26	converge	converge	VERB
ejpam-4403	210	27	and	and	CCONJ
ejpam-4403	210	28	move	move	VERB
ejpam-4403	210	29	away	away	ADV
ejpam-4403	210	30	very	very	ADV
ejpam-4403	210	31	quickly	quickly	ADV
ejpam-4403	210	32	after	after	ADP
ejpam-4403	210	33	(	(	PUNCT
ejpam-4403	210	34	figure	figure	NOUN
ejpam-4403	210	35	ref	ref	NOUN
ejpam-4403	210	36	fig2	fig2	PROPN
ejpam-4403	210	37	b	b	PROPN
ejpam-4403	210	38	)	)	PUNCT
ejpam-4403	210	39	,	,	PUNCT
ejpam-4403	210	40	which	which	PRON
ejpam-4403	210	41	is	be	AUX
ejpam-4403	210	42	explained	explain	VERB
ejpam-4403	210	43	by	by	ADP
ejpam-4403	210	44	a	a	DET
ejpam-4403	210	45	weak	weak	ADJ
ejpam-4403	210	46	numerical	numerical	ADJ
ejpam-4403	210	47	convergence	convergence	NOUN
ejpam-4403	210	48	.	.	PUNCT
ejpam-4403	211	1	•	•	NUM
ejpam-4403	211	2	taking	take	VERB
ejpam-4403	211	3	for	for	ADP
ejpam-4403	211	4	step	step	NOUN
ejpam-4403	211	5	h	h	NOUN
ejpam-4403	212	1	=	=	NOUN
ejpam-4403	212	2	0.5	0.5	NUM
ejpam-4403	213	1	,	,	PUNCT
ejpam-4403	213	2	one	one	PRON
ejpam-4403	213	3	can	can	AUX
ejpam-4403	213	4	notice	notice	VERB
ejpam-4403	213	5	that	that	SCONJ
ejpam-4403	213	6	both	both	CCONJ
ejpam-4403	213	7	exact	exact	ADJ
ejpam-4403	213	8	and	and	CCONJ
ejpam-4403	213	9	numerical	numerical	ADJ
ejpam-4403	213	10	solutions	solution	NOUN
ejpam-4403	213	11	respectively	respectively	ADV
ejpam-4403	213	12	tend	tend	VERB
ejpam-4403	213	13	not	not	PART
ejpam-4403	213	14	to	to	PART
ejpam-4403	213	15	converge	converge	VERB
ejpam-4403	213	16	except	except	SCONJ
ejpam-4403	213	17	on	on	ADP
ejpam-4403	213	18	almost	almost	ADV
ejpam-4403	213	19	negligible	negligible	ADJ
ejpam-4403	213	20	points	point	NOUN
ejpam-4403	213	21	,	,	PUNCT
ejpam-4403	213	22	which	which	PRON
ejpam-4403	213	23	is	be	AUX
ejpam-4403	213	24	explained	explain	VERB
ejpam-4403	213	25	by	by	ADP
ejpam-4403	213	26	a	a	DET
ejpam-4403	213	27	numerical	numerical	ADJ
ejpam-4403	213	28	divergence	divergence	NOUN
ejpam-4403	213	29	(	(	PUNCT
ejpam-4403	213	30	figure	figure	NOUN
ejpam-4403	213	31	2	2	NUM
ejpam-4403	213	32	c	c	NOUN
ejpam-4403	213	33	)	)	PUNCT
ejpam-4403	213	34	.	.	PUNCT
ejpam-4403	214	1	d.	d.	PROPN
ejpam-4403	214	2	v.	v.	PROPN
ejpam-4403	214	3	pongui	pongui	PROPN
ejpam-4403	214	4	ngoma	ngoma	PROPN
ejpam-4403	214	5	et	et	PROPN
ejpam-4403	214	6	al	al	PROPN
ejpam-4403	214	7	.	.	PROPN
ejpam-4403	214	8	,	,	PUNCT
ejpam-4403	214	9	/	/	SYM
ejpam-4403	214	10	eur	eur	NOUN
ejpam-4403	214	11	.	.	PUNCT
ejpam-4403	215	1	j.	j.	PROPN
ejpam-4403	215	2	pure	pure	PROPN
ejpam-4403	215	3	appl	appl	PROPN
ejpam-4403	215	4	.	.	PROPN
ejpam-4403	215	5	math	math	PROPN
ejpam-4403	215	6	,	,	PUNCT
ejpam-4403	215	7	15	15	NUM
ejpam-4403	215	8	(	(	PUNCT
ejpam-4403	215	9	3	3	NUM
ejpam-4403	215	10	)	)	PUNCT
ejpam-4403	215	11	(	(	PUNCT
ejpam-4403	215	12	2022	2022	NUM
ejpam-4403	215	13	)	)	PUNCT
ejpam-4403	215	14	,	,	PUNCT
ejpam-4403	215	15	1348	1348	NUM
ejpam-4403	215	16	-	-	SYM
ejpam-4403	215	17	1362	1362	NUM
ejpam-4403	215	18	1359	1359	NUM
ejpam-4403	215	19	(	(	PUNCT
ejpam-4403	215	20	a	a	NOUN
ejpam-4403	215	21	)	)	PUNCT
ejpam-4403	215	22	(	(	PUNCT
ejpam-4403	215	23	b	b	X
ejpam-4403	215	24	)	)	PUNCT
ejpam-4403	215	25	(	(	PUNCT
ejpam-4403	215	26	c	c	X
ejpam-4403	215	27	)	)	PUNCT
ejpam-4403	215	28	figure	figure	NOUN
ejpam-4403	215	29	2	2	NUM
ejpam-4403	215	30	:	:	PUNCT
ejpam-4403	215	31	representation	representation	NOUN
ejpam-4403	215	32	of	of	ADP
ejpam-4403	215	33	the	the	DET
ejpam-4403	215	34	exact	exact	ADJ
ejpam-4403	215	35	and	and	CCONJ
ejpam-4403	215	36	numerical	numerical	ADJ
ejpam-4403	215	37	solution	solution	NOUN
ejpam-4403	215	38	for	for	ADP
ejpam-4403	215	39	n	n	NOUN
ejpam-4403	215	40	=	=	SYM
ejpam-4403	215	41	5	5	NUM
ejpam-4403	215	42	.	.	PUNCT
ejpam-4403	216	1	in	in	ADP
ejpam-4403	216	2	the	the	DET
ejpam-4403	216	3	figure	figure	NOUN
ejpam-4403	216	4	3	3	NUM
ejpam-4403	216	5	,	,	PUNCT
ejpam-4403	216	6	let	let	VERB
ejpam-4403	216	7	’s	’s	PRON
ejpam-4403	216	8	fix	fix	VERB
ejpam-4403	216	9	n	n	NOUN
ejpam-4403	216	10	=	=	NOUN
ejpam-4403	216	11	10	10	NUM
ejpam-4403	216	12	.	.	PUNCT
ejpam-4403	216	13	•	•	NUM
ejpam-4403	216	14	by	by	ADP
ejpam-4403	216	15	taking	take	VERB
ejpam-4403	216	16	h	h	NOUN
ejpam-4403	216	17	=	=	NOUN
ejpam-4403	216	18	0.001	0.001	NUM
ejpam-4403	216	19	and	and	CCONJ
ejpam-4403	216	20	h	h	NOUN
ejpam-4403	217	1	=	=	NOUN
ejpam-4403	217	2	0.01	0.01	NUM
ejpam-4403	217	3	,	,	PUNCT
ejpam-4403	217	4	we	we	PRON
ejpam-4403	217	5	note	note	VERB
ejpam-4403	217	6	that	that	SCONJ
ejpam-4403	217	7	both	both	CCONJ
ejpam-4403	217	8	exact	exact	ADJ
ejpam-4403	217	9	and	and	CCONJ
ejpam-4403	217	10	numerical	numerical	ADJ
ejpam-4403	217	11	solutions	solution	NOUN
ejpam-4403	217	12	respectively	respectively	ADV
ejpam-4403	217	13	(	(	PUNCT
ejpam-4403	217	14	figure	figure	NOUN
ejpam-4403	217	15	3	3	NUM
ejpam-4403	217	16	d	d	NOUN
ejpam-4403	217	17	and	and	CCONJ
ejpam-4403	217	18	figure	figure	VERB
ejpam-4403	217	19	3	3	NUM
ejpam-4403	217	20	e	e	NOUN
ejpam-4403	217	21	)	)	PUNCT
ejpam-4403	217	22	converge	converge	VERB
ejpam-4403	217	23	very	very	ADV
ejpam-4403	217	24	fast	fast	ADV
ejpam-4403	217	25	numerically	numerically	ADV
ejpam-4403	217	26	.	.	PUNCT
ejpam-4403	218	1	•	•	NUM
ejpam-4403	218	2	by	by	ADP
ejpam-4403	218	3	taking	take	VERB
ejpam-4403	218	4	h	h	NOUN
ejpam-4403	218	5	=	=	NUM
ejpam-4403	218	6	0.5	0.5	NUM
ejpam-4403	218	7	,	,	PUNCT
ejpam-4403	218	8	one	one	PRON
ejpam-4403	218	9	can	can	AUX
ejpam-4403	218	10	see	see	VERB
ejpam-4403	218	11	that	that	SCONJ
ejpam-4403	218	12	the	the	DET
ejpam-4403	218	13	exact	exact	ADJ
ejpam-4403	218	14	and	and	CCONJ
ejpam-4403	218	15	numerical	numerical	ADJ
ejpam-4403	218	16	solutions	solution	NOUN
ejpam-4403	218	17	respectively	respectively	ADV
ejpam-4403	218	18	converge	converge	VERB
ejpam-4403	218	19	numerically	numerically	ADV
ejpam-4403	218	20	almost	almost	ADV
ejpam-4403	218	21	everywhere	everywhere	ADV
ejpam-4403	218	22	.	.	PUNCT
ejpam-4403	219	1	(	(	PUNCT
ejpam-4403	219	2	figure	figure	NOUN
ejpam-4403	219	3	3f	3f	PROPN
ejpam-4403	219	4	)	)	PUNCT
ejpam-4403	220	1	d.	d.	PROPN
ejpam-4403	220	2	v.	v.	PROPN
ejpam-4403	220	3	pongui	pongui	PROPN
ejpam-4403	220	4	ngoma	ngoma	PROPN
ejpam-4403	220	5	et	et	PROPN
ejpam-4403	220	6	al	al	PROPN
ejpam-4403	220	7	.	.	PROPN
ejpam-4403	220	8	,	,	PUNCT
ejpam-4403	220	9	/	/	SYM
ejpam-4403	220	10	eur	eur	NOUN
ejpam-4403	220	11	.	.	PUNCT
ejpam-4403	221	1	j.	j.	PROPN
ejpam-4403	221	2	pure	pure	PROPN
ejpam-4403	221	3	appl	appl	PROPN
ejpam-4403	221	4	.	.	PROPN
ejpam-4403	221	5	math	math	PROPN
ejpam-4403	221	6	,	,	PUNCT
ejpam-4403	221	7	15	15	NUM
ejpam-4403	221	8	(	(	PUNCT
ejpam-4403	221	9	3	3	NUM
ejpam-4403	221	10	)	)	PUNCT
ejpam-4403	221	11	(	(	PUNCT
ejpam-4403	221	12	2022	2022	NUM
ejpam-4403	221	13	)	)	PUNCT
ejpam-4403	221	14	,	,	PUNCT
ejpam-4403	221	15	1348	1348	NUM
ejpam-4403	221	16	-	-	SYM
ejpam-4403	221	17	1362	1362	NUM
ejpam-4403	221	18	1360	1360	NUM
ejpam-4403	221	19	(	(	PUNCT
ejpam-4403	221	20	d	d	NOUN
ejpam-4403	221	21	)	)	PUNCT
ejpam-4403	221	22	(	(	PUNCT
ejpam-4403	221	23	e	e	NOUN
ejpam-4403	221	24	)	)	PUNCT
ejpam-4403	221	25	(	(	PUNCT
ejpam-4403	221	26	f	f	X
ejpam-4403	221	27	)	)	PUNCT
ejpam-4403	221	28	figure	figure	NOUN
ejpam-4403	221	29	3	3	NUM
ejpam-4403	221	30	:	:	PUNCT
ejpam-4403	221	31	representation	representation	NOUN
ejpam-4403	221	32	of	of	ADP
ejpam-4403	221	33	the	the	DET
ejpam-4403	221	34	exact	exact	ADJ
ejpam-4403	221	35	and	and	CCONJ
ejpam-4403	221	36	numerical	numerical	ADJ
ejpam-4403	221	37	solution	solution	NOUN
ejpam-4403	221	38	for	for	ADP
ejpam-4403	221	39	n	n	NOUN
ejpam-4403	221	40	=	=	SYM
ejpam-4403	221	41	10	10	NUM
ejpam-4403	221	42	the	the	DET
ejpam-4403	221	43	finite	finite	ADJ
ejpam-4403	221	44	difference	difference	NOUN
ejpam-4403	221	45	method	method	NOUN
ejpam-4403	221	46	being	be	AUX
ejpam-4403	221	47	linked	link	VERB
ejpam-4403	221	48	to	to	ADP
ejpam-4403	221	49	a	a	DET
ejpam-4403	221	50	multiplicative	multiplicative	ADJ
ejpam-4403	221	51	term	term	NOUN
ejpam-4403	221	52	of	of	ADP
ejpam-4403	221	53	the	the	DET
ejpam-4403	221	54	form	form	NOUN
ejpam-4403	221	55	1	1	NUM
ejpam-4403	221	56	h2	h2	NOUN
ejpam-4403	221	57	,	,	PUNCT
ejpam-4403	221	58	ensuring	ensure	VERB
ejpam-4403	221	59	its	its	PRON
ejpam-4403	221	60	convergence	convergence	NOUN
ejpam-4403	221	61	towards	towards	ADP
ejpam-4403	221	62	the	the	DET
ejpam-4403	221	63	exact	exact	ADJ
ejpam-4403	221	64	solution	solution	NOUN
ejpam-4403	221	65	requires	require	VERB
ejpam-4403	221	66	a	a	DET
ejpam-4403	221	67	very	very	ADV
ejpam-4403	221	68	large	large	ADJ
ejpam-4403	221	69	number	number	NOUN
ejpam-4403	221	70	of	of	ADP
ejpam-4403	221	71	points	point	NOUN
ejpam-4403	221	72	n	n	PRON
ejpam-4403	221	73	and	and	CCONJ
ejpam-4403	221	74	a	a	DET
ejpam-4403	221	75	very	very	ADV
ejpam-4403	221	76	good	good	ADJ
ejpam-4403	221	77	choice	choice	NOUN
ejpam-4403	221	78	of	of	ADP
ejpam-4403	221	79	the	the	DET
ejpam-4403	221	80	step	step	NOUN
ejpam-4403	221	81	h	h	NOUN
ejpam-4403	221	82	of	of	ADP
ejpam-4403	221	83	the	the	DET
ejpam-4403	221	84	method	method	NOUN
ejpam-4403	221	85	.	.	PUNCT
ejpam-4403	222	1	conclusion	conclusion	NOUN
ejpam-4403	222	2	the	the	DET
ejpam-4403	222	3	resolution	resolution	NOUN
ejpam-4403	222	4	of	of	ADP
ejpam-4403	222	5	the	the	DET
ejpam-4403	222	6	problem	problem	NOUN
ejpam-4403	222	7	of	of	ADP
ejpam-4403	222	8	cauchy	cauchy	PROPN
ejpam-4403	222	9	-	-	PUNCT
ejpam-4403	222	10	dirichlet	dirichlet	PROPN
ejpam-4403	222	11	remains	remain	VERB
ejpam-4403	222	12	a	a	DET
ejpam-4403	222	13	challenge	challenge	NOUN
ejpam-4403	222	14	to	to	PART
ejpam-4403	222	15	be	be	AUX
ejpam-4403	222	16	taken	take	VERB
ejpam-4403	222	17	up	up	ADP
ejpam-4403	222	18	of	of	ADP
ejpam-4403	222	19	which	which	PRON
ejpam-4403	222	20	several	several	ADJ
ejpam-4403	222	21	authors	author	NOUN
ejpam-4403	222	22	introduced	introduce	VERB
ejpam-4403	222	23	the	the	DET
ejpam-4403	222	24	concept	concept	NOUN
ejpam-4403	222	25	of	of	ADP
ejpam-4403	222	26	very	very	ADV
ejpam-4403	222	27	weak	weak	ADJ
ejpam-4403	222	28	solution	solution	NOUN
ejpam-4403	222	29	to	to	ADP
ejpam-4403	222	30	a	a	DET
ejpam-4403	222	31	problem	problem	NOUN
ejpam-4403	222	32	of	of	ADP
ejpam-4403	222	33	cauchy	cauchy	NOUN
ejpam-4403	222	34	for	for	ADP
ejpam-4403	222	35	the	the	DET
ejpam-4403	222	36	elliptic	elliptic	ADJ
ejpam-4403	222	37	equations	equation	NOUN
ejpam-4403	222	38	.	.	PUNCT
ejpam-4403	223	1	the	the	DET
ejpam-4403	223	2	cauchy	cauchy	PROPN
ejpam-4403	223	3	-	-	PUNCT
ejpam-4403	223	4	dirichlet	dirichlet	PROPN
ejpam-4403	223	5	problem	problem	NOUN
ejpam-4403	223	6	is	be	AUX
ejpam-4403	223	7	regularized	regularize	VERB
ejpam-4403	223	8	by	by	ADP
ejpam-4403	223	9	a	a	DET
ejpam-4403	223	10	nonlocal	nonlocal	ADJ
ejpam-4403	223	11	boundary	boundary	ADJ
ejpam-4403	223	12	value	value	NOUN
ejpam-4403	223	13	problem	problem	NOUN
ejpam-4403	223	14	whose	whose	DET
ejpam-4403	223	15	solution	solution	NOUN
ejpam-4403	223	16	is	be	AUX
ejpam-4403	223	17	understood	understand	VERB
ejpam-4403	223	18	in	in	ADP
ejpam-4403	223	19	this	this	DET
ejpam-4403	223	20	very	very	ADV
ejpam-4403	223	21	weak	weak	ADJ
ejpam-4403	223	22	sense	sense	NOUN
ejpam-4403	223	23	[	[	X
ejpam-4403	223	24	7	7	NUM
ejpam-4403	223	25	]	]	PUNCT
ejpam-4403	223	26	.	.	PUNCT
ejpam-4403	224	1	in	in	ADP
ejpam-4403	224	2	our	our	PRON
ejpam-4403	224	3	this	this	DET
ejpam-4403	224	4	work	work	NOUN
ejpam-4403	224	5	we	we	PRON
ejpam-4403	224	6	have	have	AUX
ejpam-4403	224	7	numerically	numerically	ADV
ejpam-4403	224	8	solved	solve	VERB
ejpam-4403	224	9	the	the	DET
ejpam-4403	224	10	cauchy	cauchy	PROPN
ejpam-4403	224	11	-	-	PUNCT
ejpam-4403	224	12	dirichlet	dirichlet	PROPN
ejpam-4403	224	13	problem	problem	NOUN
ejpam-4403	224	14	by	by	ADP
ejpam-4403	224	15	the	the	DET
ejpam-4403	224	16	finite	finite	ADJ
ejpam-4403	224	17	difference	difference	NOUN
ejpam-4403	224	18	method	method	NOUN
ejpam-4403	224	19	.	.	PUNCT
ejpam-4403	225	1	in	in	ADP
ejpam-4403	225	2	addition	addition	NOUN
ejpam-4403	225	3	to	to	PART
ejpam-4403	225	4	prove	prove	VERB
ejpam-4403	225	5	the	the	DET
ejpam-4403	225	6	existence	existence	NOUN
ejpam-4403	225	7	and	and	CCONJ
ejpam-4403	225	8	the	the	DET
ejpam-4403	225	9	uniqueness	uniqueness	NOUN
ejpam-4403	225	10	of	of	ADP
ejpam-4403	225	11	the	the	DET
ejpam-4403	225	12	solution	solution	NOUN
ejpam-4403	225	13	to	to	ADP
ejpam-4403	225	14	the	the	DET
ejpam-4403	225	15	linear	linear	ADJ
ejpam-4403	225	16	system	system	NOUN
ejpam-4403	225	17	obtained	obtain	VERB
ejpam-4403	225	18	we	we	PRON
ejpam-4403	225	19	set	set	VERB
ejpam-4403	225	20	λci	λci	ADJ
ejpam-4403	225	21	−	−	PROPN
ejpam-4403	225	22	1	1	NUM
ejpam-4403	225	23	=	=	SYM
ejpam-4403	225	24	−1	−1	NOUN
ejpam-4403	225	25	,	,	PUNCT
ejpam-4403	225	26	i	i	PRON
ejpam-4403	225	27	=	=	NOUN
ejpam-4403	225	28	1	1	NUM
ejpam-4403	225	29	,	,	PUNCT
ejpam-4403	225	30	2	2	NUM
ejpam-4403	225	31	,	,	PUNCT
ejpam-4403	225	32	...	...	PUNCT
ejpam-4403	225	33	,	,	PUNCT
ejpam-4403	225	34	n	n	CCONJ
ejpam-4403	225	35	so	so	SCONJ
ejpam-4403	225	36	that	that	SCONJ
ejpam-4403	225	37	the	the	DET
ejpam-4403	225	38	matrix	matrix	NOUN
ejpam-4403	225	39	is	be	AUX
ejpam-4403	225	40	symmetrical	symmetrical	ADJ
ejpam-4403	225	41	.	.	PUNCT
ejpam-4403	226	1	we	we	PRON
ejpam-4403	226	2	then	then	ADV
ejpam-4403	226	3	solved	solve	VERB
ejpam-4403	226	4	the	the	DET
ejpam-4403	226	5	problem	problem	NOUN
ejpam-4403	226	6	analytically	analytically	ADV
ejpam-4403	226	7	using	use	VERB
ejpam-4403	226	8	the	the	DET
ejpam-4403	226	9	method	method	NOUN
ejpam-4403	226	10	of	of	ADP
ejpam-4403	226	11	the	the	DET
ejpam-4403	226	12	variation	variation	NOUN
ejpam-4403	226	13	of	of	ADP
ejpam-4403	226	14	the	the	DET
ejpam-4403	226	15	constants	constant	NOUN
ejpam-4403	226	16	.	.	PUNCT
ejpam-4403	227	1	finally	finally	ADV
ejpam-4403	227	2	,	,	PUNCT
ejpam-4403	227	3	we	we	PRON
ejpam-4403	227	4	have	have	AUX
ejpam-4403	227	5	implemented	implement	VERB
ejpam-4403	227	6	numerical	numerical	ADJ
ejpam-4403	227	7	simulations	simulation	NOUN
ejpam-4403	227	8	in	in	ADP
ejpam-4403	227	9	order	order	NOUN
ejpam-4403	227	10	to	to	PART
ejpam-4403	227	11	make	make	VERB
ejpam-4403	227	12	the	the	DET
ejpam-4403	227	13	numerical	numerical	ADJ
ejpam-4403	227	14	solution	solution	NOUN
ejpam-4403	227	15	converge	converge	VERB
ejpam-4403	227	16	towards	towards	ADP
ejpam-4403	227	17	the	the	DET
ejpam-4403	227	18	exact	exact	ADJ
ejpam-4403	227	19	solution	solution	NOUN
ejpam-4403	227	20	,	,	PUNCT
ejpam-4403	227	21	using	use	VERB
ejpam-4403	227	22	the	the	DET
ejpam-4403	227	23	scilab	scilab	PROPN
ejpam-4403	227	24	software	software	PROPN
ejpam-4403	227	25	.	.	PUNCT
ejpam-4403	228	1	references	reference	NOUN
ejpam-4403	228	2	1361	1361	NUM
ejpam-4403	228	3	acknowledgements	acknowledgement	NOUN
ejpam-4403	228	4	the	the	DET
ejpam-4403	228	5	authors	author	NOUN
ejpam-4403	228	6	thank	thank	VERB
ejpam-4403	228	7	the	the	DET
ejpam-4403	228	8	anonym	anonym	NOUN
ejpam-4403	228	9	referees	referee	NOUN
ejpam-4403	228	10	of	of	ADP
ejpam-4403	228	11	european	european	PROPN
ejpam-4403	228	12	journal	journal	PROPN
ejpam-4403	228	13	of	of	ADP
ejpam-4403	228	14	pure	pure	ADJ
ejpam-4403	228	15	and	and	CCONJ
ejpam-4403	228	16	applied	applied	ADJ
ejpam-4403	228	17	mathematics	mathematic	NOUN
ejpam-4403	228	18	,	,	PUNCT
ejpam-4403	228	19	for	for	ADP
ejpam-4403	228	20	their	their	PRON
ejpam-4403	228	21	valuable	valuable	ADJ
ejpam-4403	228	22	comments	comment	NOUN
ejpam-4403	228	23	and	and	CCONJ
ejpam-4403	228	24	suggestions	suggestion	NOUN
ejpam-4403	228	25	which	which	PRON
ejpam-4403	228	26	have	have	AUX
ejpam-4403	228	27	led	lead	VERB
ejpam-4403	228	28	to	to	ADP
ejpam-4403	228	29	an	an	DET
ejpam-4403	228	30	improvement	improvement	NOUN
ejpam-4403	228	31	of	of	ADP
ejpam-4403	228	32	the	the	DET
ejpam-4403	228	33	presentation	presentation	NOUN
ejpam-4403	228	34	.	.	PUNCT
ejpam-4403	229	1	references	reference	NOUN
ejpam-4403	229	2	[	[	X
ejpam-4403	229	3	1	1	NUM
ejpam-4403	229	4	]	]	PUNCT
ejpam-4403	229	5	paolo	paolo	PROPN
ejpam-4403	229	6	baroni	baroni	PROPN
ejpam-4403	229	7	and	and	CCONJ
ejpam-4403	229	8	casimir	casimir	PROPN
ejpam-4403	229	9	lindforsb	lindforsb	PROPN
ejpam-4403	229	10	.	.	PUNCT
ejpam-4403	230	1	the	the	DET
ejpam-4403	230	2	cauchy	cauchy	PROPN
ejpam-4403	230	3	-	-	PUNCT
ejpam-4403	230	4	dirichlet	dirichlet	PROPN
ejpam-4403	230	5	problem	problem	NOUN
ejpam-4403	230	6	for	for	ADP
ejpam-4403	230	7	a	a	DET
ejpam-4403	230	8	general	general	ADJ
ejpam-4403	230	9	class	class	NOUN
ejpam-4403	230	10	of	of	ADP
ejpam-4403	230	11	parabolic	parabolic	ADJ
ejpam-4403	230	12	equations	equation	NOUN
ejpam-4403	230	13	.	.	PUNCT
ejpam-4403	231	1	annales	annales	PROPN
ejpam-4403	231	2	de	de	PROPN
ejpam-4403	231	3	l’institut	l’institut	PROPN
ejpam-4403	231	4	henri	henri	PROPN
ejpam-4403	231	5	poincaré	poincaré	ADJ
ejpam-4403	231	6	c	c	X
ejpam-4403	231	7	,	,	PUNCT
ejpam-4403	231	8	analyse	analyse	VERB
ejpam-4403	231	9	non	non	ADJ
ejpam-4403	231	10	linéaire	linéaire	NOUN
ejpam-4403	231	11	,	,	PUNCT
ejpam-4403	231	12	34(3):593–624	34(3):593–624	PROPN
ejpam-4403	231	13	,	,	PUNCT
ejpam-4403	231	14	2017	2017	NUM
ejpam-4403	231	15	.	.	PUNCT
ejpam-4403	232	1	[	[	X
ejpam-4403	232	2	2	2	NUM
ejpam-4403	232	3	]	]	PUNCT
ejpam-4403	232	4	h	h	NOUN
ejpam-4403	232	5	beghr	beghr	NOUN
ejpam-4403	232	6	and	and	CCONJ
ejpam-4403	232	7	g	g	PROPN
ejpam-4403	232	8	harutjunjan	harutjunjan	PROPN
ejpam-4403	232	9	.	.	PUNCT
ejpam-4403	233	1	robin	robin	PROPN
ejpam-4403	233	2	boundary	boundary	ADJ
ejpam-4403	233	3	value	value	NOUN
ejpam-4403	233	4	problem	problem	NOUN
ejpam-4403	233	5	for	for	ADP
ejpam-4403	233	6	the	the	DET
ejpam-4403	233	7	poisson	poisson	NOUN
ejpam-4403	233	8	equation	equation	NOUN
ejpam-4403	233	9	.	.	PUNCT
ejpam-4403	234	1	j	j	PROPN
ejpam-4403	234	2	anal	anal	PROPN
ejpam-4403	234	3	appl	appl	PROPN
ejpam-4403	234	4	,	,	PUNCT
ejpam-4403	234	5	04:29–45	04:29–45	PROPN
ejpam-4403	234	6	,	,	PUNCT
ejpam-4403	234	7	2006	2006	NUM
ejpam-4403	234	8	.	.	PUNCT
ejpam-4403	235	1	[	[	X
ejpam-4403	235	2	3	3	NUM
ejpam-4403	235	3	]	]	X
ejpam-4403	235	4	bourchra	bourchra	PROPN
ejpam-4403	235	5	bensiali	bensiali	PROPN
ejpam-4403	235	6	,	,	PUNCT
ejpam-4403	235	7	guillaume	guillaume	PROPN
ejpam-4403	235	8	chiavassa	chiavassa	NOUN
ejpam-4403	235	9	,	,	PUNCT
ejpam-4403	235	10	and	and	CCONJ
ejpam-4403	235	11	jacques	jacques	PROPN
ejpam-4403	235	12	liandrat	liandrat	PROPN
ejpam-4403	235	13	.	.	PUNCT
ejpam-4403	236	1	penalization	penalization	NOUN
ejpam-4403	236	2	of	of	ADP
ejpam-4403	236	3	robin	robin	PROPN
ejpam-4403	236	4	boundary	boundary	PROPN
ejpam-4403	236	5	conditions	condition	NOUN
ejpam-4403	236	6	.	.	PUNCT
ejpam-4403	237	1	applied	apply	VERB
ejpam-4403	237	2	numerical	numerical	ADJ
ejpam-4403	237	3	mathematics	mathematic	NOUN
ejpam-4403	237	4	,	,	PUNCT
ejpam-4403	237	5	96(3):134–152	96(3):134–152	NUM
ejpam-4403	237	6	,	,	PUNCT
ejpam-4403	237	7	2006	2006	NUM
ejpam-4403	237	8	.	.	PUNCT
ejpam-4403	238	1	[	[	X
ejpam-4403	238	2	4	4	NUM
ejpam-4403	238	3	]	]	X
ejpam-4403	238	4	shao	shao	PROPN
ejpam-4403	238	5	-	-	PUNCT
ejpam-4403	238	6	gao	gao	PROPN
ejpam-4403	238	7	deng	deng	PROPN
ejpam-4403	238	8	.	.	PUNCT
ejpam-4403	238	9	positive	positive	ADJ
ejpam-4403	238	10	solutions	solution	NOUN
ejpam-4403	238	11	for	for	ADP
ejpam-4403	238	12	robin	robin	PROPN
ejpam-4403	238	13	problem	problem	NOUN
ejpam-4403	238	14	involving	involve	VERB
ejpam-4403	238	15	the	the	DET
ejpam-4403	238	16	p(x)-laplacian	p(x)-laplacian	PROPN
ejpam-4403	238	17	.	.	PUNCT
ejpam-4403	239	1	j	j	PROPN
ejpam-4403	239	2	math	math	PROPN
ejpam-4403	239	3	anal	anal	PROPN
ejpam-4403	239	4	appll	appll	PROPN
ejpam-4403	239	5	,	,	PUNCT
ejpam-4403	239	6	360:548–560	360:548–560	NUM
ejpam-4403	239	7	,	,	PUNCT
ejpam-4403	239	8	2009	2009	NUM
ejpam-4403	239	9	.	.	PUNCT
ejpam-4403	240	1	[	[	X
ejpam-4403	240	2	5	5	NUM
ejpam-4403	240	3	]	]	PUNCT
ejpam-4403	240	4	bishnu	bishnu	NOUN
ejpam-4403	240	5	prasad	prasad	PROPN
ejpam-4403	240	6	dhungana	dhungana	PROPN
ejpam-4403	240	7	and	and	CCONJ
ejpam-4403	240	8	tadato	tadato	PROPN
ejpam-4403	240	9	matsuzawa	matsuzawa	PROPN
ejpam-4403	240	10	.	.	PUNCT
ejpam-4403	241	1	an	an	DET
ejpam-4403	241	2	existence	existence	NOUN
ejpam-4403	241	3	result	result	NOUN
ejpam-4403	241	4	of	of	ADP
ejpam-4403	241	5	the	the	DET
ejpam-4403	241	6	cauchy	cauchy	ADJ
ejpam-4403	241	7	dirichlet	dirichlet	PROPN
ejpam-4403	241	8	problem	problem	NOUN
ejpam-4403	241	9	for	for	ADP
ejpam-4403	241	10	the	the	DET
ejpam-4403	241	11	hermite	hermite	ADJ
ejpam-4403	241	12	heat	heat	NOUN
ejpam-4403	241	13	equation	equation	NOUN
ejpam-4403	241	14	.	.	PUNCT
ejpam-4403	242	1	proc	proc	PROPN
ejpam-4403	242	2	japan	japan	PROPN
ejpam-4403	242	3	acad	acad	PROPN
ejpam-4403	242	4	ser	ser	PROPN
ejpam-4403	242	5	a	a	DET
ejpam-4403	242	6	math	math	NOUN
ejpam-4403	242	7	,	,	PUNCT
ejpam-4403	242	8	86(2):45–47	86(2):45–47	NUM
ejpam-4403	242	9	,	,	PUNCT
ejpam-4403	242	10	2010	2010	NUM
ejpam-4403	242	11	.	.	PUNCT
ejpam-4403	243	1	[	[	X
ejpam-4403	243	2	6	6	X
ejpam-4403	243	3	]	]	PUNCT
ejpam-4403	243	4	marc	marc	PROPN
ejpam-4403	243	5	ethier	ethier	NOUN
ejpam-4403	243	6	and	and	CCONJ
ejpam-4403	243	7	y	y	PROPN
ejpam-4403	243	8	bourgault	bourgault	NOUN
ejpam-4403	243	9	.	.	PUNCT
ejpam-4403	244	1	semi	semi	ADJ
ejpam-4403	244	2	-	-	ADJ
ejpam-4403	244	3	implicit	implicit	ADJ
ejpam-4403	244	4	time	time	NOUN
ejpam-4403	244	5	-	-	PUNCT
ejpam-4403	244	6	discretization	discretization	NOUN
ejpam-4403	244	7	schemes	scheme	NOUN
ejpam-4403	244	8	for	for	ADP
ejpam-4403	244	9	the	the	DET
ejpam-4403	244	10	bidomaine	bidomaine	ADJ
ejpam-4403	244	11	model	model	NOUN
ejpam-4403	244	12	.	.	PUNCT
ejpam-4403	245	1	siam	siam	PROPN
ejpam-4403	245	2	j	j	PROPN
ejpam-4403	245	3	numer	numer	PROPN
ejpam-4403	245	4	anal	anal	PROPN
ejpam-4403	245	5	,	,	PUNCT
ejpam-4403	245	6	46:2443–2468	46:2443–2468	PROPN
ejpam-4403	245	7	,	,	PUNCT
ejpam-4403	245	8	2008	2008	NUM
ejpam-4403	245	9	.	.	PUNCT
ejpam-4403	246	1	[	[	X
ejpam-4403	246	2	7	7	NUM
ejpam-4403	246	3	]	]	SYM
ejpam-4403	246	4	dinh	dinh	NOUN
ejpam-4403	246	5	nho	nho	NOUN
ejpam-4403	246	6	hao	hao	PROPN
ejpam-4403	246	7	,	,	PUNCT
ejpam-4403	246	8	le	le	PROPN
ejpam-4403	246	9	thi	thi	VERB
ejpam-4403	246	10	thu	thu	PROPN
ejpam-4403	246	11	giang	giang	PROPN
ejpam-4403	246	12	,	,	PUNCT
ejpam-4403	246	13	sergey	sergey	PROPN
ejpam-4403	246	14	kabanikhin	kabanikhin	PROPN
ejpam-4403	246	15	,	,	PUNCT
ejpam-4403	246	16	and	and	CCONJ
ejpam-4403	246	17	maxim	maxim	NOUN
ejpam-4403	246	18	shishlenin	shishlenin	NOUN
ejpam-4403	246	19	.	.	PUNCT
ejpam-4403	247	1	a	a	DET
ejpam-4403	247	2	finite	finite	ADJ
ejpam-4403	247	3	difference	difference	NOUN
ejpam-4403	247	4	method	method	NOUN
ejpam-4403	247	5	for	for	ADP
ejpam-4403	247	6	the	the	DET
ejpam-4403	247	7	very	very	ADV
ejpam-4403	247	8	weak	weak	ADJ
ejpam-4403	247	9	solution	solution	NOUN
ejpam-4403	247	10	to	to	ADP
ejpam-4403	247	11	a	a	DET
ejpam-4403	247	12	cauchy	cauchy	ADJ
ejpam-4403	247	13	problem	problem	NOUN
ejpam-4403	247	14	for	for	ADP
ejpam-4403	247	15	an	an	DET
ejpam-4403	247	16	elliptic	elliptic	ADJ
ejpam-4403	247	17	equation	equation	NOUN
ejpam-4403	247	18	.	.	PUNCT
ejpam-4403	248	1	journal	journal	PROPN
ejpam-4403	248	2	of	of	ADP
ejpam-4403	248	3	inverse	inverse	NOUN
ejpam-4403	248	4	and	and	CCONJ
ejpam-4403	248	5	ill	ill	ADV
ejpam-4403	248	6	-	-	PUNCT
ejpam-4403	248	7	posed	pose	VERB
ejpam-4403	248	8	problems	problem	NOUN
ejpam-4403	248	9	,	,	PUNCT
ejpam-4403	248	10	29(6):1–23	29(6):1–23	NOUN
ejpam-4403	248	11	,	,	PUNCT
ejpam-4403	248	12	2018	2018	NUM
ejpam-4403	248	13	.	.	PUNCT
ejpam-4403	249	1	[	[	X
ejpam-4403	249	2	8	8	NUM
ejpam-4403	249	3	]	]	X
ejpam-4403	249	4	m	m	VERB
ejpam-4403	249	5	hinze	hinze	NOUN
ejpam-4403	249	6	,	,	PUNCT
ejpam-4403	249	7	r	r	NOUN
ejpam-4403	249	8	pinnau	pinnau	NOUN
ejpam-4403	249	9	,	,	PUNCT
ejpam-4403	249	10	m	m	VERB
ejpam-4403	249	11	ulbrich	ulbrich	ADJ
ejpam-4403	249	12	,	,	PUNCT
ejpam-4403	249	13	and	and	CCONJ
ejpam-4403	249	14	s	s	VERB
ejpam-4403	249	15	ulbrich	ulbrich	NOUN
ejpam-4403	249	16	.	.	PUNCT
ejpam-4403	250	1	mathematical	mathematical	ADJ
ejpam-4403	250	2	modelling	modelling	NOUN
ejpam-4403	250	3	:	:	PUNCT
ejpam-4403	250	4	theory	theory	NOUN
ejpam-4403	250	5	and	and	CCONJ
ejpam-4403	250	6	applications	application	NOUN
ejpam-4403	250	7	.	.	PUNCT
ejpam-4403	251	1	springer	springer	NOUN
ejpam-4403	251	2	,	,	PUNCT
ejpam-4403	251	3	2009	2009	NUM
ejpam-4403	251	4	.	.	PUNCT
ejpam-4403	252	1	[	[	X
ejpam-4403	252	2	9	9	NUM
ejpam-4403	252	3	]	]	PUNCT
ejpam-4403	252	4	a	a	DET
ejpam-4403	252	5	v	v	NOUN
ejpam-4403	252	6	ivanov	ivanov	NOUN
ejpam-4403	252	7	,	,	PUNCT
ejpam-4403	252	8	p	p	NOUN
ejpam-4403	252	9	z	z	NOUN
ejpam-4403	252	10	mkrtychan	mkrtychan	NOUN
ejpam-4403	252	11	,	,	PUNCT
ejpam-4403	252	12	and	and	CCONJ
ejpam-4403	252	13	w	w	PROPN
ejpam-4403	252	14	jäger	jäger	PROPN
ejpam-4403	252	15	.	.	PUNCT
ejpam-4403	253	1	existence	existence	NOUN
ejpam-4403	253	2	and	and	CCONJ
ejpam-4403	253	3	uniqueness	uniqueness	NOUN
ejpam-4403	253	4	of	of	ADP
ejpam-4403	253	5	a	a	DET
ejpam-4403	253	6	regular	regular	ADJ
ejpam-4403	253	7	solution	solution	NOUN
ejpam-4403	253	8	of	of	ADP
ejpam-4403	253	9	the	the	DET
ejpam-4403	253	10	cauchy	cauchy	PROPN
ejpam-4403	253	11	-	-	PUNCT
ejpam-4403	253	12	dirichlet	dirichlet	PROPN
ejpam-4403	253	13	problem	problem	NOUN
ejpam-4403	253	14	for	for	ADP
ejpam-4403	253	15	a	a	DET
ejpam-4403	253	16	class	class	NOUN
ejpam-4403	253	17	of	of	ADP
ejpam-4403	253	18	doubly	doubly	ADV
ejpam-4403	253	19	nonlinear	nonlinear	ADJ
ejpam-4403	253	20	parabolic	parabolic	ADJ
ejpam-4403	253	21	equations	equation	NOUN
ejpam-4403	253	22	.	.	PUNCT
ejpam-4403	254	1	journal	journal	PROPN
ejpam-4403	254	2	of	of	ADP
ejpam-4403	254	3	mathematical	mathematical	ADJ
ejpam-4403	254	4	sciences	science	NOUN
ejpam-4403	254	5	,	,	PUNCT
ejpam-4403	254	6	84(1):845–855	84(1):845–855	PROPN
ejpam-4403	254	7	,	,	PUNCT
ejpam-4403	254	8	1997	1997	NUM
ejpam-4403	254	9	.	.	PUNCT
ejpam-4403	255	1	[	[	X
ejpam-4403	255	2	10	10	NUM
ejpam-4403	255	3	]	]	X
ejpam-4403	255	4	peter	peter	PROPN
ejpam-4403	255	5	knabner	knabner	PROPN
ejpam-4403	255	6	and	and	CCONJ
ejpam-4403	255	7	lutz	lutz	PROPN
ejpam-4403	255	8	angermann	angermann	PROPN
ejpam-4403	255	9	.	.	PUNCT
ejpam-4403	256	1	numerical	numerical	ADJ
ejpam-4403	256	2	methods	method	NOUN
ejpam-4403	256	3	for	for	ADP
ejpam-4403	256	4	elliptic	elliptic	ADJ
ejpam-4403	256	5	and	and	CCONJ
ejpam-4403	256	6	parabolic	parabolic	ADJ
ejpam-4403	256	7	partial	partial	ADJ
ejpam-4403	256	8	differential	differential	NOUN
ejpam-4403	256	9	equations	equation	NOUN
ejpam-4403	256	10	.	.	PUNCT
ejpam-4403	257	1	springer	springer	NOUN
ejpam-4403	257	2	,	,	PUNCT
ejpam-4403	257	3	2000	2000	NUM
ejpam-4403	257	4	.	.	PUNCT
ejpam-4403	258	1	[	[	X
ejpam-4403	258	2	11	11	NUM
ejpam-4403	258	3	]	]	X
ejpam-4403	258	4	brigitte	brigitte	PROPN
ejpam-4403	258	5	lucquin	lucquin	PROPN
ejpam-4403	258	6	.	.	PUNCT
ejpam-4403	259	1	equations	equation	NOUN
ejpam-4403	259	2	aux	aux	PROPN
ejpam-4403	259	3	derivees	derive	VERB
ejpam-4403	259	4	partielles	partielle	NOUN
ejpam-4403	259	5	et	et	PROPN
ejpam-4403	259	6	leurs	leurs	PROPN
ejpam-4403	259	7	approximations	approximation	NOUN
ejpam-4403	259	8	.	.	PUNCT
ejpam-4403	260	1	ellipses	ellipsis	NOUN
ejpam-4403	260	2	,	,	PUNCT
ejpam-4403	260	3	2004	2004	NUM
ejpam-4403	260	4	.	.	PUNCT
ejpam-4403	261	1	[	[	X
ejpam-4403	261	2	12	12	NUM
ejpam-4403	261	3	]	]	X
ejpam-4403	261	4	g	g	PROPN
ejpam-4403	261	5	nguimbi	nguimbi	PROPN
ejpam-4403	261	6	,	,	PUNCT
ejpam-4403	261	7	d	d	PROPN
ejpam-4403	261	8	v	v	NUM
ejpam-4403	261	9	pongui	pongui	PROPN
ejpam-4403	261	10	ngoma	ngoma	PROPN
ejpam-4403	261	11	,	,	PUNCT
ejpam-4403	261	12	and	and	CCONJ
ejpam-4403	261	13	r	r	NOUN
ejpam-4403	261	14	b	b	PROPN
ejpam-4403	261	15	pellat	pellat	NOUN
ejpam-4403	261	16	likibi	likibi	NOUN
ejpam-4403	261	17	.	.	PUNCT
ejpam-4403	262	1	the	the	DET
ejpam-4403	262	2	effect	effect	NOUN
ejpam-4403	262	3	of	of	ADP
ejpam-4403	262	4	numerical	numerical	ADJ
ejpam-4403	262	5	integration	integration	NOUN
ejpam-4403	262	6	in	in	ADP
ejpam-4403	262	7	galerkin	galerkin	ADJ
ejpam-4403	262	8	methods	method	NOUN
ejpam-4403	262	9	for	for	ADP
ejpam-4403	262	10	compressible	compressible	ADJ
ejpam-4403	262	11	miscible	miscible	ADJ
ejpam-4403	262	12	displacement	displacement	NOUN
ejpam-4403	262	13	in	in	ADP
ejpam-4403	262	14	porous	porous	ADJ
ejpam-4403	262	15	media	medium	NOUN
ejpam-4403	262	16	.	.	PUNCT
ejpam-4403	263	1	nonlinear	nonlinear	ADJ
ejpam-4403	263	2	analysis	analysis	NOUN
ejpam-4403	263	3	and	and	CCONJ
ejpam-4403	263	4	differential	differential	ADJ
ejpam-4403	263	5	equations	equation	NOUN
ejpam-4403	263	6	,	,	PUNCT
ejpam-4403	263	7	5:17–35	5:17–35	NUM
ejpam-4403	263	8	,	,	PUNCT
ejpam-4403	263	9	2017	2017	NUM
ejpam-4403	263	10	.	.	PUNCT
ejpam-4403	264	1	references	reference	NOUN
ejpam-4403	264	2	1362	1362	NUM
ejpam-4403	265	1	[	[	X
ejpam-4403	265	2	13	13	NUM
ejpam-4403	265	3	]	]	SYM
ejpam-4403	265	4	g	g	PROPN
ejpam-4403	265	5	nguimbi	nguimbi	PROPN
ejpam-4403	265	6	,	,	PUNCT
ejpam-4403	265	7	d	d	PROPN
ejpam-4403	265	8	v	v	NUM
ejpam-4403	265	9	pongui	pongui	PROPN
ejpam-4403	265	10	ngoma	ngoma	PROPN
ejpam-4403	265	11	,	,	PUNCT
ejpam-4403	265	12	and	and	CCONJ
ejpam-4403	265	13	r	r	NOUN
ejpam-4403	265	14	b	b	PROPN
ejpam-4403	265	15	pellat	pellat	NOUN
ejpam-4403	265	16	likibi	likibi	NOUN
ejpam-4403	265	17	.	.	PUNCT
ejpam-4403	266	1	the	the	DET
ejpam-4403	266	2	effect	effect	NOUN
ejpam-4403	266	3	of	of	ADP
ejpam-4403	266	4	numerical	numerical	ADJ
ejpam-4403	266	5	integration	integration	NOUN
ejpam-4403	266	6	in	in	ADP
ejpam-4403	266	7	mixed	mixed	ADJ
ejpam-4403	266	8	finite	finite	ADJ
ejpam-4403	266	9	element	element	NOUN
ejpam-4403	266	10	approximation	approximation	NOUN
ejpam-4403	266	11	in	in	ADP
ejpam-4403	266	12	the	the	DET
ejpam-4403	266	13	simulation	simulation	NOUN
ejpam-4403	266	14	of	of	ADP
ejpam-4403	266	15	miscible	miscible	ADJ
ejpam-4403	266	16	displacement	displacement	NOUN
ejpam-4403	266	17	.	.	PUNCT
ejpam-4403	267	1	international	international	ADJ
ejpam-4403	267	2	journal	journal	PROPN
ejpam-4403	267	3	of	of	ADP
ejpam-4403	267	4	applied	apply	VERB
ejpam-4403	267	5	mathematical	mathematical	ADJ
ejpam-4403	267	6	research	research	NOUN
ejpam-4403	267	7	,	,	PUNCT
ejpam-4403	267	8	6:44–48	6:44–48	NOUN
ejpam-4403	267	9	,	,	PUNCT
ejpam-4403	267	10	2017	2017	NUM
ejpam-4403	267	11	.	.	PUNCT
ejpam-4403	268	1	[	[	X
ejpam-4403	268	2	14	14	NUM
ejpam-4403	268	3	]	]	X
ejpam-4403	268	4	g	g	PROPN
ejpam-4403	268	5	nguimbi	nguimbi	PROPN
ejpam-4403	268	6	,	,	PUNCT
ejpam-4403	268	7	d	d	PROPN
ejpam-4403	268	8	v	v	NUM
ejpam-4403	268	9	pongui	pongui	PROPN
ejpam-4403	268	10	ngoma	ngoma	PROPN
ejpam-4403	268	11	,	,	PUNCT
ejpam-4403	268	12	v	v	PROPN
ejpam-4403	268	13	d	d	X
ejpam-4403	268	14	mabonzo	mabonzo	NOUN
ejpam-4403	268	15	,	,	PUNCT
ejpam-4403	268	16	b	b	PROPN
ejpam-4403	268	17	b	b	PROPN
ejpam-4403	268	18	b	b	PROPN
ejpam-4403	268	19	madzou	madzou	NOUN
ejpam-4403	268	20	,	,	PUNCT
ejpam-4403	268	21	and	and	CCONJ
ejpam-4403	268	22	l	l	NOUN
ejpam-4403	268	23	g	g	PROPN
ejpam-4403	268	24	ngoma	ngoma	PROPN
ejpam-4403	268	25	bouanga	bouanga	NOUN
ejpam-4403	268	26	.	.	PUNCT
ejpam-4403	269	1	mathematical	mathematical	ADJ
ejpam-4403	269	2	and	and	CCONJ
ejpam-4403	269	3	numerical	numerical	ADJ
ejpam-4403	269	4	analysis	analysis	NOUN
ejpam-4403	269	5	for	for	ADP
ejpam-4403	269	6	neumann	neumann	PROPN
ejpam-4403	269	7	boundary	boundary	ADJ
ejpam-4403	269	8	value	value	NOUN
ejpam-4403	269	9	problem	problem	NOUN
ejpam-4403	269	10	of	of	ADP
ejpam-4403	269	11	the	the	DET
ejpam-4403	269	12	poisson	poisson	NOUN
ejpam-4403	269	13	equation	equation	NOUN
ejpam-4403	269	14	.	.	PUNCT
ejpam-4403	270	1	journal	journal	PROPN
ejpam-4403	270	2	of	of	ADP
ejpam-4403	270	3	advnces	advnce	NOUN
ejpam-4403	270	4	in	in	ADP
ejpam-4403	270	5	mathemtics	mathemtic	NOUN
ejpam-4403	270	6	and	and	CCONJ
ejpam-4403	270	7	computer	computer	NOUN
ejpam-4403	270	8	science	science	NOUN
ejpam-4403	270	9	,	,	PUNCT
ejpam-4403	270	10	30:1–13	30:1–13	NUM
ejpam-4403	270	11	,	,	PUNCT
ejpam-4403	270	12	2019	2019	NUM
ejpam-4403	270	13	.	.	PUNCT
ejpam-4403	271	1	[	[	X
ejpam-4403	271	2	15	15	NUM
ejpam-4403	271	3	]	]	X
ejpam-4403	271	4	g	g	PROPN
ejpam-4403	271	5	nguimbi	nguimbi	PROPN
ejpam-4403	271	6	,	,	PUNCT
ejpam-4403	271	7	d	d	PROPN
ejpam-4403	271	8	v	v	NUM
ejpam-4403	271	9	pongui	pongui	PROPN
ejpam-4403	271	10	ngoma	ngoma	PROPN
ejpam-4403	271	11	,	,	PUNCT
ejpam-4403	271	12	v	v	NOUN
ejpam-4403	271	13	dmabonzo	dmabonzo	NOUN
ejpam-4403	271	14	,	,	PUNCT
ejpam-4403	271	15	b	b	PROPN
ejpam-4403	271	16	b	b	X
ejpam-4403	271	17	bmadzou	bmadzou	NOUN
ejpam-4403	271	18	,	,	PUNCT
ejpam-4403	271	19	and	and	CCONJ
ejpam-4403	271	20	m	m	PROPN
ejpam-4403	271	21	j	j	PROPN
ejpam-4403	272	1	j	j	PROPN
ejpam-4403	272	2	kokolo	kokolo	INTJ
ejpam-4403	272	3	.	.	PUNCT
ejpam-4403	273	1	on	on	ADP
ejpam-4403	273	2	the	the	DET
ejpam-4403	273	3	existence	existence	NOUN
ejpam-4403	273	4	,	,	PUNCT
ejpam-4403	273	5	uniqueness	uniqueness	NOUN
ejpam-4403	273	6	and	and	CCONJ
ejpam-4403	273	7	application	application	NOUN
ejpam-4403	273	8	of	of	ADP
ejpam-4403	273	9	the	the	DET
ejpam-4403	273	10	finite	finite	ADJ
ejpam-4403	273	11	difference	difference	NOUN
ejpam-4403	273	12	method	method	NOUN
ejpam-4403	273	13	for	for	ADP
ejpam-4403	273	14	solving	solve	VERB
ejpam-4403	273	15	robin	robin	PROPN
ejpam-4403	273	16	elliptic	elliptic	ADJ
ejpam-4403	273	17	boundary	boundary	ADJ
ejpam-4403	273	18	value	value	NOUN
ejpam-4403	273	19	problem	problem	NOUN
ejpam-4403	273	20	.	.	PUNCT
ejpam-4403	274	1	journal	journal	NOUN
ejpam-4403	274	2	of	of	ADP
ejpam-4403	274	3	mathematics	mathematics	PROPN
ejpam-4403	274	4	research	research	NOUN
ejpam-4403	274	5	,	,	PUNCT
ejpam-4403	274	6	11:26–36	11:26–36	NUM
ejpam-4403	274	7	,	,	PUNCT
ejpam-4403	274	8	2019	2019	NUM
ejpam-4403	274	9	.	.	PUNCT
ejpam-4403	275	1	[	[	X
ejpam-4403	275	2	16	16	NUM
ejpam-4403	275	3	]	]	X
ejpam-4403	275	4	t	t	NOUN
ejpam-4403	275	5	a	a	DET
ejpam-4403	275	6	randrianasolo	randrianasolo	NOUN
ejpam-4403	275	7	,	,	PUNCT
ejpam-4403	275	8	g	g	PROPN
ejpam-4403	275	9	nguimbi	nguimbi	NOUN
ejpam-4403	275	10	,	,	PUNCT
ejpam-4403	275	11	and	and	CCONJ
ejpam-4403	275	12	d	d	X
ejpam-4403	275	13	v	v	NUM
ejpam-4403	275	14	pongui	pongui	PROPN
ejpam-4403	275	15	ngoma	ngoma	PROPN
ejpam-4403	275	16	.	.	PUNCT
ejpam-4403	276	1	one	one	NUM
ejpam-4403	276	2	-	-	PUNCT
ejpam-4403	276	3	step	step	NOUN
ejpam-4403	276	4	hermite	hermite	ADJ
ejpam-4403	276	5	-	-	PUNCT
ejpam-4403	276	6	birkhofftaylor	birkhofftaylor	NOUN
ejpam-4403	276	7	methods	method	NOUN
ejpam-4403	276	8	.	.	PUNCT
ejpam-4403	277	1	pioneer	pioneer	PROPN
ejpam-4403	277	2	journal	journal	PROPN
ejpam-4403	277	3	of	of	ADP
ejpam-4403	277	4	mathematics	mathematics	PROPN
ejpam-4403	277	5	and	and	CCONJ
ejpam-4403	277	6	mathematical	mathematical	ADJ
ejpam-4403	277	7	sciences	science	NOUN
ejpam-4403	277	8	,	,	PUNCT
ejpam-4403	277	9	24:73	24:73	NUM
ejpam-4403	277	10	–	–	PUNCT
ejpam-4403	277	11	111	111	NUM
ejpam-4403	277	12	,	,	PUNCT
ejpam-4403	277	13	2018	2018	NUM
ejpam-4403	277	14	.	.	PUNCT
ejpam-4403	278	1	[	[	X
ejpam-4403	278	2	17	17	NUM
ejpam-4403	278	3	]	]	X
ejpam-4403	278	4	gerardo	gerardo	PROPN
ejpam-4403	278	5	rubio	rubio	PROPN
ejpam-4403	278	6	.	.	PUNCT
ejpam-4403	279	1	the	the	DET
ejpam-4403	279	2	cauchy	cauchy	PROPN
ejpam-4403	279	3	-	-	PUNCT
ejpam-4403	279	4	dirichlet	dirichlet	PROPN
ejpam-4403	279	5	problem	problem	NOUN
ejpam-4403	279	6	for	for	ADP
ejpam-4403	279	7	a	a	DET
ejpam-4403	279	8	class	class	NOUN
ejpam-4403	279	9	of	of	ADP
ejpam-4403	279	10	linear	linear	PROPN
ejpam-4403	279	11	parabolic	parabolic	PROPN
ejpam-4403	279	12	differential	differential	NOUN
ejpam-4403	279	13	equations	equation	NOUN
ejpam-4403	279	14	with	with	ADP
ejpam-4403	279	15	unbounded	unbounded	ADJ
ejpam-4403	279	16	coefficients	coefficient	NOUN
ejpam-4403	279	17	in	in	ADP
ejpam-4403	279	18	an	an	DET
ejpam-4403	279	19	unbounded	unbounded	ADJ
ejpam-4403	279	20	domain	domain	NOUN
ejpam-4403	279	21	.	.	PUNCT
ejpam-4403	280	1	international	international	ADJ
ejpam-4403	280	2	journal	journal	NOUN
ejpam-4403	280	3	of	of	ADP
ejpam-4403	280	4	stochastic	stochastic	ADJ
ejpam-4403	280	5	analysis	analysis	NOUN
ejpam-4403	280	6	,	,	PUNCT
ejpam-4403	280	7	2011(469806):1–35	2011(469806):1–35	NUM
ejpam-4403	280	8	,	,	PUNCT
ejpam-4403	280	9	2011	2011	NUM
ejpam-4403	280	10	.	.	PUNCT
ejpam-4403	281	1	[	[	X
ejpam-4403	281	2	18	18	NUM
ejpam-4403	281	3	]	]	X
ejpam-4403	281	4	r	r	NOUN
ejpam-4403	281	5	shanthi	shanthi	PROPN
ejpam-4403	281	6	,	,	PUNCT
ejpam-4403	281	7	t	t	PROPN
ejpam-4403	281	8	iswarya	iswarya	PROPN
ejpam-4403	281	9	,	,	PUNCT
ejpam-4403	281	10	j	j	PROPN
ejpam-4403	281	11	visuvasam	visuvasam	NOUN
ejpam-4403	281	12	,	,	PUNCT
ejpam-4403	281	13	l	l	NOUN
ejpam-4403	281	14	rajendran	rajendran	NOUN
ejpam-4403	281	15	,	,	PUNCT
ejpam-4403	281	16	and	and	CCONJ
ejpam-4403	281	17	michael	michael	PROPN
ejpam-4403	281	18	e	e	PROPN
ejpam-4403	281	19	g	g	PROPN
ejpam-4403	281	20	lyo	lyo	PROPN
ejpam-4403	281	21	.	.	PUNCT
ejpam-4403	282	1	voltammetric	voltammetric	ADJ
ejpam-4403	282	2	and	and	CCONJ
ejpam-4403	282	3	mathematical	mathematical	ADJ
ejpam-4403	282	4	analysis	analysis	NOUN
ejpam-4403	282	5	of	of	ADP
ejpam-4403	282	6	adsorption	adsorption	NOUN
ejpam-4403	282	7	of	of	ADP
ejpam-4403	282	8	enzymes	enzyme	NOUN
ejpam-4403	282	9	at	at	ADP
ejpam-4403	282	10	rotating	rotate	VERB
ejpam-4403	282	11	disk	disk	NOUN
ejpam-4403	282	12	electrode	electrode	NOUN
ejpam-4403	282	13	.	.	PUNCT
ejpam-4403	283	1	springer	springer	NOUN
ejpam-4403	283	2	-	-	PUNCT
ejpam-4403	283	3	verlag	verlag	PROPN
ejpam-4403	283	4	,	,	PUNCT
ejpam-4403	283	5	17(220433):1–16	17(220433):1–16	NUM
ejpam-4403	283	6	,	,	PUNCT
ejpam-4403	283	7	2022	2022	NUM
ejpam-4403	283	8	.	.	PUNCT