id	sid	tid	token	lemma	pos
ejpam-6070	1	1	european	european	PROPN
ejpam-6070	1	2	journal	journal	PROPN
ejpam-6070	1	3	of	of	ADP
ejpam-6070	1	4	pure	pure	ADJ
ejpam-6070	1	5	and	and	CCONJ
ejpam-6070	1	6	applied	applied	ADJ
ejpam-6070	1	7	mathematics	mathematic	NOUN
ejpam-6070	1	8	2025	2025	NUM
ejpam-6070	1	9	,	,	PUNCT
ejpam-6070	1	10	vol	vol	NOUN
ejpam-6070	1	11	.	.	PROPN
ejpam-6070	1	12	18	18	NUM
ejpam-6070	1	13	,	,	PUNCT
ejpam-6070	1	14	issue	issue	NOUN
ejpam-6070	1	15	2	2	NUM
ejpam-6070	1	16	,	,	PUNCT
ejpam-6070	1	17	article	article	NOUN
ejpam-6070	1	18	number	number	NOUN
ejpam-6070	1	19	6070	6070	NUM
ejpam-6070	1	20	issn	issn	VERB
ejpam-6070	1	21	1307	1307	NUM
ejpam-6070	1	22	-	-	SYM
ejpam-6070	1	23	5543	5543	NUM
ejpam-6070	1	24	–	–	PUNCT
ejpam-6070	1	25	ejpam.com	ejpam.com	X
ejpam-6070	1	26	published	publish	VERB
ejpam-6070	1	27	by	by	ADP
ejpam-6070	1	28	new	new	PROPN
ejpam-6070	1	29	york	york	PROPN
ejpam-6070	1	30	business	business	PROPN
ejpam-6070	1	31	global	global	ADJ
ejpam-6070	1	32	overlapping	overlap	VERB
ejpam-6070	1	33	domain	domain	NOUN
ejpam-6070	1	34	decomposition	decomposition	NOUN
ejpam-6070	1	35	methods	method	NOUN
ejpam-6070	1	36	for	for	ADP
ejpam-6070	1	37	noncoercive	noncoercive	ADJ
ejpam-6070	1	38	hamilton	hamilton	PROPN
ejpam-6070	1	39	-	-	PUNCT
ejpam-6070	1	40	jacobi	jacobi	PROPN
ejpam-6070	1	41	-	-	PUNCT
ejpam-6070	1	42	bellman	bellman	NOUN
ejpam-6070	1	43	equation	equation	NOUN
ejpam-6070	1	44	samar	samar	PROPN
ejpam-6070	1	45	chebbah1,2,∗	chebbah1,2,∗	PROPN
ejpam-6070	1	46	,	,	PUNCT
ejpam-6070	1	47	sofiane	sofiane	ADJ
ejpam-6070	1	48	madi3	madi3	NOUN
ejpam-6070	1	49	,	,	PUNCT
ejpam-6070	1	50	mohamed	mohamed	PROPN
ejpam-6070	1	51	haiour4	haiour4	PROPN
ejpam-6070	1	52	1	1	NUM
ejpam-6070	1	53	department	department	NOUN
ejpam-6070	1	54	of	of	ADP
ejpam-6070	1	55	mathematics	mathematics	PROPN
ejpam-6070	1	56	,	,	PUNCT
ejpam-6070	1	57	institute	institute	NOUN
ejpam-6070	1	58	of	of	ADP
ejpam-6070	1	59	mathematics	mathematics	PROPN
ejpam-6070	1	60	and	and	CCONJ
ejpam-6070	1	61	computer	computer	NOUN
ejpam-6070	1	62	science	science	NOUN
ejpam-6070	1	63	,	,	PUNCT
ejpam-6070	1	64	abdelhafid	abdelhafid	ADV
ejpam-6070	1	65	boussouf	boussouf	PROPN
ejpam-6070	1	66	university	university	NOUN
ejpam-6070	1	67	center	center	NOUN
ejpam-6070	1	68	–	–	PUNCT
ejpam-6070	1	69	mila	mila	PROPN
ejpam-6070	1	70	,	,	PUNCT
ejpam-6070	1	71	mila	mila	PROPN
ejpam-6070	1	72	,	,	PUNCT
ejpam-6070	1	73	algeria	algeria	PROPN
ejpam-6070	1	74	2	2	NUM
ejpam-6070	1	75	laboratoire	laboratoire	X
ejpam-6070	1	76	des	des	X
ejpam-6070	1	77	mathématiques	mathématiques	PROPN
ejpam-6070	1	78	appliquées	appliquée	NOUN
ejpam-6070	1	79	et	et	NOUN
ejpam-6070	1	80	didactique	didactique	NOUN
ejpam-6070	1	81	(	(	PUNCT
ejpam-6070	1	82	mad	mad	ADJ
ejpam-6070	1	83	)	)	PUNCT
ejpam-6070	1	84	,	,	PUNCT
ejpam-6070	1	85	école	école	ADJ
ejpam-6070	1	86	normale	normale	PROPN
ejpam-6070	1	87	supérieure	supérieure	PROPN
ejpam-6070	1	88	el	el	PROPN
ejpam-6070	1	89	katiba	katiba	PROPN
ejpam-6070	1	90	assia	assia	PROPN
ejpam-6070	1	91	djebar	djebar	PROPN
ejpam-6070	1	92	(	(	PUNCT
ejpam-6070	1	93	ensc	ensc	ADV
ejpam-6070	1	94	)	)	PUNCT
ejpam-6070	1	95	–	–	PUNCT
ejpam-6070	1	96	constantine	constantine	PROPN
ejpam-6070	1	97	,	,	PUNCT
ejpam-6070	1	98	constantine	constantine	PROPN
ejpam-6070	1	99	,	,	PUNCT
ejpam-6070	1	100	algeria	algeria	PROPN
ejpam-6070	1	101	3	3	NUM
ejpam-6070	1	102	department	department	NOUN
ejpam-6070	1	103	of	of	ADP
ejpam-6070	1	104	mathematics	mathematic	NOUN
ejpam-6070	1	105	,	,	PUNCT
ejpam-6070	1	106	faculty	faculty	NOUN
ejpam-6070	1	107	of	of	ADP
ejpam-6070	1	108	mathematics	mathematic	NOUN
ejpam-6070	1	109	and	and	CCONJ
ejpam-6070	1	110	computer	computer	NOUN
ejpam-6070	1	111	science	science	NOUN
ejpam-6070	1	112	,	,	PUNCT
ejpam-6070	1	113	university	university	NOUN
ejpam-6070	1	114	of	of	ADP
ejpam-6070	1	115	batna	batna	PROPN
ejpam-6070	1	116	2	2	NUM
ejpam-6070	1	117	,	,	PUNCT
ejpam-6070	1	118	batna	batna	PROPN
ejpam-6070	1	119	,	,	PUNCT
ejpam-6070	1	120	algeria	algeria	PROPN
ejpam-6070	1	121	4	4	NUM
ejpam-6070	1	122	department	department	NOUN
ejpam-6070	1	123	of	of	ADP
ejpam-6070	1	124	mathematics	mathematic	NOUN
ejpam-6070	1	125	,	,	PUNCT
ejpam-6070	1	126	faculty	faculty	NOUN
ejpam-6070	1	127	of	of	ADP
ejpam-6070	1	128	the	the	DET
ejpam-6070	1	129	sciences	science	NOUN
ejpam-6070	1	130	,	,	PUNCT
ejpam-6070	1	131	university	university	NOUN
ejpam-6070	1	132	badji	badji	NOUN
ejpam-6070	1	133	mokhtar	mokhtar	PROPN
ejpam-6070	1	134	–	–	PUNCT
ejpam-6070	1	135	annaba	annaba	PROPN
ejpam-6070	1	136	,	,	PUNCT
ejpam-6070	1	137	p.o	p.o	PROPN
ejpam-6070	1	138	.	.	PROPN
ejpam-6070	1	139	23000	23000	NUM
ejpam-6070	1	140	annaba	annaba	PROPN
ejpam-6070	1	141	,	,	PUNCT
ejpam-6070	1	142	algeria	algeria	PROPN
ejpam-6070	1	143	abstract	abstract	NOUN
ejpam-6070	1	144	.	.	PUNCT
ejpam-6070	2	1	this	this	DET
ejpam-6070	2	2	study	study	NOUN
ejpam-6070	2	3	presents	present	VERB
ejpam-6070	2	4	an	an	DET
ejpam-6070	2	5	approach	approach	NOUN
ejpam-6070	2	6	to	to	PART
ejpam-6070	2	7	demonstrate	demonstrate	VERB
ejpam-6070	2	8	the	the	DET
ejpam-6070	2	9	monotonic	monotonic	ADJ
ejpam-6070	2	10	and	and	CCONJ
ejpam-6070	2	11	geometric	geometric	ADJ
ejpam-6070	2	12	convergence	convergence	NOUN
ejpam-6070	2	13	of	of	ADP
ejpam-6070	2	14	the	the	DET
ejpam-6070	2	15	non	non	ADJ
ejpam-6070	2	16	-	-	ADJ
ejpam-6070	2	17	coercive	coercive	ADJ
ejpam-6070	2	18	hamilton	hamilton	PROPN
ejpam-6070	2	19	-	-	PUNCT
ejpam-6070	2	20	jacobi	jacobi	PROPN
ejpam-6070	2	21	-	-	PUNCT
ejpam-6070	2	22	bellman	bellman	PROPN
ejpam-6070	2	23	problem	problem	NOUN
ejpam-6070	2	24	with	with	ADP
ejpam-6070	2	25	dirichlet	dirichlet	PROPN
ejpam-6070	2	26	boundary	boundary	ADJ
ejpam-6070	2	27	conditions	condition	NOUN
ejpam-6070	2	28	using	use	VERB
ejpam-6070	2	29	the	the	DET
ejpam-6070	2	30	finite	finite	ADJ
ejpam-6070	2	31	difference	difference	NOUN
ejpam-6070	2	32	method	method	NOUN
ejpam-6070	2	33	.	.	PUNCT
ejpam-6070	3	1	the	the	DET
ejpam-6070	3	2	approach	approach	NOUN
ejpam-6070	3	3	combines	combine	VERB
ejpam-6070	3	4	overlapping	overlap	VERB
ejpam-6070	3	5	domain	domain	NOUN
ejpam-6070	3	6	decomposition	decomposition	NOUN
ejpam-6070	3	7	with	with	ADP
ejpam-6070	3	8	a	a	DET
ejpam-6070	3	9	sequence	sequence	NOUN
ejpam-6070	3	10	of	of	ADP
ejpam-6070	3	11	lower	low	ADJ
ejpam-6070	3	12	and	and	CCONJ
ejpam-6070	3	13	upper	upper	ADJ
ejpam-6070	3	14	solutions	solution	NOUN
ejpam-6070	3	15	to	to	PART
ejpam-6070	3	16	characterize	characterize	VERB
ejpam-6070	3	17	the	the	DET
ejpam-6070	3	18	solution	solution	NOUN
ejpam-6070	3	19	in	in	ADP
ejpam-6070	3	20	a	a	DET
ejpam-6070	3	21	discrete	discrete	ADJ
ejpam-6070	3	22	setting	setting	NOUN
ejpam-6070	3	23	.	.	PUNCT
ejpam-6070	4	1	numerical	numerical	ADJ
ejpam-6070	4	2	experiments	experiment	NOUN
ejpam-6070	4	3	are	be	AUX
ejpam-6070	4	4	conducted	conduct	VERB
ejpam-6070	4	5	to	to	PART
ejpam-6070	4	6	validate	validate	VERB
ejpam-6070	4	7	the	the	DET
ejpam-6070	4	8	methodology	methodology	NOUN
ejpam-6070	4	9	and	and	CCONJ
ejpam-6070	4	10	illustrate	illustrate	VERB
ejpam-6070	4	11	the	the	DET
ejpam-6070	4	12	consistency	consistency	NOUN
ejpam-6070	4	13	of	of	ADP
ejpam-6070	4	14	the	the	DET
ejpam-6070	4	15	theoretical	theoretical	ADJ
ejpam-6070	4	16	findings	finding	NOUN
ejpam-6070	4	17	.	.	PUNCT
ejpam-6070	5	1	2020	2020	NUM
ejpam-6070	5	2	mathematics	mathematic	NOUN
ejpam-6070	5	3	subject	subject	NOUN
ejpam-6070	5	4	classifications	classification	NOUN
ejpam-6070	5	5	:	:	PUNCT
ejpam-6070	5	6	65n06	65n06	NUM
ejpam-6070	5	7	,	,	PUNCT
ejpam-6070	5	8	65n12	65n12	NUM
ejpam-6070	5	9	,	,	PUNCT
ejpam-6070	5	10	49l25	49l25	NUM
ejpam-6070	5	11	,	,	PUNCT
ejpam-6070	5	12	65n55	65n55	NOUN
ejpam-6070	5	13	key	key	ADJ
ejpam-6070	5	14	words	word	NOUN
ejpam-6070	5	15	and	and	CCONJ
ejpam-6070	5	16	phrases	phrase	NOUN
ejpam-6070	5	17	:	:	PUNCT
ejpam-6070	5	18	hamilton	hamilton	PROPN
ejpam-6070	5	19	-	-	PUNCT
ejpam-6070	5	20	jacobi	jacobi	PROPN
ejpam-6070	5	21	-	-	PUNCT
ejpam-6070	5	22	bellman	bellman	NOUN
ejpam-6070	5	23	equation	equation	NOUN
ejpam-6070	5	24	,	,	PUNCT
ejpam-6070	5	25	noncoercive	noncoercive	ADJ
ejpam-6070	5	26	problems	problem	NOUN
ejpam-6070	5	27	,	,	PUNCT
ejpam-6070	5	28	overlapping	overlap	VERB
ejpam-6070	5	29	domain	domain	NOUN
ejpam-6070	5	30	decomposition	decomposition	NOUN
ejpam-6070	5	31	,	,	PUNCT
ejpam-6070	5	32	convergence	convergence	NOUN
ejpam-6070	5	33	analysis	analysis	NOUN
ejpam-6070	5	34	,	,	PUNCT
ejpam-6070	5	35	lower	low	ADJ
ejpam-6070	5	36	and	and	CCONJ
ejpam-6070	5	37	upper	upper	ADJ
ejpam-6070	5	38	solutions	solution	NOUN
ejpam-6070	5	39	,	,	PUNCT
ejpam-6070	5	40	finite	finite	ADJ
ejpam-6070	5	41	difference	difference	NOUN
ejpam-6070	5	42	method	method	NOUN
ejpam-6070	5	43	1	1	NUM
ejpam-6070	5	44	.	.	PUNCT
ejpam-6070	6	1	introduction	introduction	NOUN
ejpam-6070	6	2	we	we	PRON
ejpam-6070	6	3	consider	consider	VERB
ejpam-6070	6	4	the	the	DET
ejpam-6070	6	5	following	follow	VERB
ejpam-6070	6	6	non	non	ADJ
ejpam-6070	6	7	-	-	ADJ
ejpam-6070	6	8	coercive	coercive	ADJ
ejpam-6070	6	9	hamilton	hamilton	PROPN
ejpam-6070	6	10	-	-	PUNCT
ejpam-6070	6	11	jacobi	jacobi	PROPN
ejpam-6070	6	12	-	-	PUNCT
ejpam-6070	6	13	bellman	bellman	NOUN
ejpam-6070	6	14	(	(	PUNCT
ejpam-6070	6	15	hjb	hjb	NOUN
ejpam-6070	6	16	)	)	PUNCT
ejpam-6070	6	17	equation	equation	NOUN
ejpam-6070	6	18	,	,	PUNCT
ejpam-6070	6	19	with	with	ADP
ejpam-6070	6	20	dirichlet	dirichlet	PROPN
ejpam-6070	6	21	boundary	boundary	ADJ
ejpam-6070	6	22	conditions	condition	NOUN
ejpam-6070	6	23	:	:	PUNCT
ejpam-6070	6	24	max	max	NOUN
ejpam-6070	6	25	1≤i≤n	1≤i≤n	NUM
ejpam-6070	6	26	(	(	PUNCT
ejpam-6070	6	27	aiξ	aiξ	ADP
ejpam-6070	6	28	−f	−f	PROPN
ejpam-6070	6	29	i	i	PROPN
ejpam-6070	6	30	)	)	PUNCT
ejpam-6070	7	1	=	=	SYM
ejpam-6070	7	2	0	0	NUM
ejpam-6070	7	3	,	,	PUNCT
ejpam-6070	7	4	inω	inω	ADJ
ejpam-6070	7	5	,	,	PUNCT
ejpam-6070	7	6	ξ	ξ	X
ejpam-6070	7	7	=	=	SYM
ejpam-6070	7	8	0	0	NUM
ejpam-6070	7	9	,	,	PUNCT
ejpam-6070	7	10	on	on	ADP
ejpam-6070	7	11	∂ω	∂ω	PROPN
ejpam-6070	7	12	,	,	PUNCT
ejpam-6070	7	13	(	(	PUNCT
ejpam-6070	7	14	1	1	X
ejpam-6070	7	15	)	)	PUNCT
ejpam-6070	7	16	∗corresponding	∗corresponde	VERB
ejpam-6070	7	17	author	author	NOUN
ejpam-6070	7	18	.	.	PUNCT
ejpam-6070	8	1	doi	doi	NOUN
ejpam-6070	8	2	:	:	PUNCT
ejpam-6070	8	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6070	https://doi.org/10.29020/nybg.ejpam.v18i2.6070	VERB
ejpam-6070	8	4	email	email	NOUN
ejpam-6070	8	5	addresses	address	NOUN
ejpam-6070	8	6	:	:	PUNCT
ejpam-6070	8	7	s.chebbah@centre-univ-mila.dz	s.chebbah@centre-univ-mila.dz	PROPN
ejpam-6070	8	8	(	(	PUNCT
ejpam-6070	8	9	s.	s.	PROPN
ejpam-6070	8	10	chebbah	chebbah	PROPN
ejpam-6070	8	11	)	)	PUNCT
ejpam-6070	8	12	,	,	PUNCT
ejpam-6070	8	13	s.madi@univ-batna2.dz	s.madi@univ-batna2.dz	PUNCT
ejpam-6070	8	14	(	(	PUNCT
ejpam-6070	8	15	s.madi	s.madi	NOUN
ejpam-6070	8	16	)	)	PUNCT
ejpam-6070	8	17	,	,	PUNCT
ejpam-6070	8	18	mohamed.haiour@univ-annaba.dz	mohamed.haiour@univ-annaba.dz	PROPN
ejpam-6070	8	19	(	(	PUNCT
ejpam-6070	8	20	m.	m.	NOUN
ejpam-6070	8	21	haiour	haiour	PROPN
ejpam-6070	8	22	)	)	PUNCT
ejpam-6070	8	23	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6070	9	1	1	1	NUM
ejpam-6070	9	2	copyright	copyright	NOUN
ejpam-6070	9	3	:	:	PUNCT
ejpam-6070	9	4	©	©	PROPN
ejpam-6070	9	5	2025	2025	NUM
ejpam-6070	9	6	the	the	DET
ejpam-6070	9	7	author(s	author(s	NOUN
ejpam-6070	9	8	)	)	PUNCT
ejpam-6070	9	9	.	.	PUNCT
ejpam-6070	10	1	(	(	PUNCT
ejpam-6070	10	2	cc	cc	NOUN
ejpam-6070	10	3	by	by	ADP
ejpam-6070	10	4	-	-	PUNCT
ejpam-6070	10	5	nc	nc	PROPN
ejpam-6070	10	6	4.0	4.0	NUM
ejpam-6070	10	7	)	)	PUNCT
ejpam-6070	10	8	s.	s.	PROPN
ejpam-6070	10	9	chebbah	chebbah	PROPN
ejpam-6070	10	10	,	,	PUNCT
ejpam-6070	10	11	s.	s.	PROPN
ejpam-6070	10	12	madi	madi	PROPN
ejpam-6070	10	13	,	,	PUNCT
ejpam-6070	10	14	m.	m.	NOUN
ejpam-6070	10	15	haiour	haiour	PROPN
ejpam-6070	10	16	/	/	SYM
ejpam-6070	10	17	eur	eur	PROPN
ejpam-6070	10	18	.	.	PUNCT
ejpam-6070	11	1	j.	j.	PROPN
ejpam-6070	11	2	pure	pure	PROPN
ejpam-6070	11	3	appl	appl	PROPN
ejpam-6070	11	4	.	.	PROPN
ejpam-6070	11	5	math	math	PROPN
ejpam-6070	11	6	,	,	PUNCT
ejpam-6070	11	7	18	18	NUM
ejpam-6070	11	8	(	(	PUNCT
ejpam-6070	11	9	2	2	NUM
ejpam-6070	11	10	)	)	PUNCT
ejpam-6070	11	11	(	(	PUNCT
ejpam-6070	11	12	2025	2025	NUM
ejpam-6070	11	13	)	)	PUNCT
ejpam-6070	11	14	,	,	PUNCT
ejpam-6070	11	15	6070	6070	NUM
ejpam-6070	11	16	2	2	NUM
ejpam-6070	11	17	of	of	ADP
ejpam-6070	11	18	20	20	NUM
ejpam-6070	11	19	where	where	SCONJ
ejpam-6070	11	20	ω	ω	PROPN
ejpam-6070	11	21	⊂	⊂	PROPN
ejpam-6070	11	22	rd	rd	PROPN
ejpam-6070	11	23	(	(	PUNCT
ejpam-6070	11	24	d	d	X
ejpam-6070	11	25	≥	≥	NUM
ejpam-6070	11	26	1	1	NUM
ejpam-6070	11	27	)	)	PUNCT
ejpam-6070	11	28	is	be	AUX
ejpam-6070	11	29	a	a	DET
ejpam-6070	11	30	bounded	bounded	ADJ
ejpam-6070	11	31	domain	domain	NOUN
ejpam-6070	11	32	with	with	ADP
ejpam-6070	11	33	a	a	DET
ejpam-6070	11	34	smooth	smooth	ADJ
ejpam-6070	11	35	boundary	boundary	ADJ
ejpam-6070	11	36	∂ω	∂ω	PROPN
ejpam-6070	11	37	.	.	PUNCT
ejpam-6070	12	1	the	the	DET
ejpam-6070	12	2	operators	operator	NOUN
ejpam-6070	12	3	ai	ai	VERB
ejpam-6070	12	4	are	be	AUX
ejpam-6070	12	5	uniformly	uniformly	ADV
ejpam-6070	12	6	elliptic	elliptic	ADJ
ejpam-6070	12	7	and	and	CCONJ
ejpam-6070	12	8	take	take	VERB
ejpam-6070	12	9	the	the	DET
ejpam-6070	12	10	form	form	NOUN
ejpam-6070	12	11	:	:	PUNCT
ejpam-6070	12	12	ai	ai	VERB
ejpam-6070	12	13	=	=	PUNCT
ejpam-6070	12	14	d∑	d∑	PROPN
ejpam-6070	12	15	t	t	PROPN
ejpam-6070	12	16	,	,	PUNCT
ejpam-6070	12	17	s=1	s=1	X
ejpam-6070	12	18	aits(x	aits(x	NOUN
ejpam-6070	12	19	)	)	PUNCT
ejpam-6070	12	20	∂2	∂2	NOUN
ejpam-6070	12	21	∂xt∂xs	∂xt∂xs	PROPN
ejpam-6070	13	1	+	+	X
ejpam-6070	13	2	d∑	d∑	PROPN
ejpam-6070	13	3	s=1	s=1	X
ejpam-6070	13	4	bis(x	bis(x	PROPN
ejpam-6070	13	5	)	)	PUNCT
ejpam-6070	14	1	∂	∂	NUM
ejpam-6070	15	1	∂xs	∂xs	PROPN
ejpam-6070	15	2	+	+	CCONJ
ejpam-6070	15	3	ai0(x	ai0(x	PROPN
ejpam-6070	15	4	)	)	PUNCT
ejpam-6070	15	5	,	,	PUNCT
ejpam-6070	15	6	where	where	SCONJ
ejpam-6070	15	7	the	the	DET
ejpam-6070	15	8	coefficients	coefficient	NOUN
ejpam-6070	15	9	aits(x	aits(x	PROPN
ejpam-6070	15	10	)	)	PUNCT
ejpam-6070	15	11	,	,	PUNCT
ejpam-6070	15	12	b	b	X
ejpam-6070	15	13	i	i	PROPN
ejpam-6070	15	14	s(x	s(x	PROPN
ejpam-6070	15	15	)	)	PUNCT
ejpam-6070	15	16	,	,	PUNCT
ejpam-6070	15	17	a	a	DET
ejpam-6070	15	18	i	i	PRON
ejpam-6070	15	19	0(x	0(x	NOUN
ejpam-6070	15	20	)	)	PUNCT
ejpam-6070	15	21	∈	∈	PROPN
ejpam-6070	15	22	c2(ω	c2(ω	PRON
ejpam-6070	15	23	)	)	PUNCT
ejpam-6070	15	24	satisfy	satisfy	VERB
ejpam-6070	15	25	the	the	DET
ejpam-6070	15	26	following	follow	VERB
ejpam-6070	15	27	conditions	condition	NOUN
ejpam-6070	15	28	:	:	PUNCT
ejpam-6070	15	29	d∑	d∑	PROPN
ejpam-6070	15	30	t	t	PROPN
ejpam-6070	15	31	,	,	PUNCT
ejpam-6070	15	32	s=1	s=1	X
ejpam-6070	15	33	aits(x)νtνs	aits(x)νtνs	NUM
ejpam-6070	15	34	≥	≥	NOUN
ejpam-6070	15	35	δ|ν|2	δ|ν|2	VERB
ejpam-6070	15	36	,	,	PUNCT
ejpam-6070	15	37	∀ν	∀ν	PROPN
ejpam-6070	15	38	∈	∈	PROPN
ejpam-6070	15	39	rd	rd	PROPN
ejpam-6070	15	40	,	,	PUNCT
ejpam-6070	15	41	δ	δ	PROPN
ejpam-6070	15	42	>	>	X
ejpam-6070	15	43	0	0	NUM
ejpam-6070	15	44	,	,	PUNCT
ejpam-6070	15	45	ai0(x	ai0(x	PROPN
ejpam-6070	15	46	)	)	PUNCT
ejpam-6070	15	47	≥	≥	NOUN
ejpam-6070	15	48	γ	γ	X
ejpam-6070	15	49	>	>	X
ejpam-6070	15	50	0	0	PROPN
ejpam-6070	15	51	.	.	PUNCT
ejpam-6070	16	1	the	the	DET
ejpam-6070	16	2	noncoercive	noncoercive	ADJ
ejpam-6070	16	3	bilinear	bilinear	NOUN
ejpam-6070	16	4	form	form	NOUN
ejpam-6070	16	5	for	for	ADP
ejpam-6070	16	6	u	u	NOUN
ejpam-6070	16	7	,	,	PUNCT
ejpam-6070	16	8	v	v	ADP
ejpam-6070	16	9	∈	∈	PROPN
ejpam-6070	16	10	h1(ω	h1(ω	PRON
ejpam-6070	16	11	)	)	PUNCT
ejpam-6070	16	12	is	be	AUX
ejpam-6070	16	13	expressed	express	VERB
ejpam-6070	16	14	as	as	SCONJ
ejpam-6070	16	15	follows	follow	VERB
ejpam-6070	16	16	:	:	PUNCT
ejpam-6070	16	17	ai⟨u	ai⟨u	NOUN
ejpam-6070	16	18	,	,	PUNCT
ejpam-6070	16	19	v⟩	v⟩	PUNCT
ejpam-6070	17	1	=	=	PUNCT
ejpam-6070	17	2	∫	∫	PROPN
ejpam-6070	18	1	ω	ω	X
ejpam-6070	18	2			PROPN
ejpam-6070	18	3	d∑	d∑	PROPN
ejpam-6070	18	4	t	t	PROPN
ejpam-6070	18	5	,	,	PUNCT
ejpam-6070	18	6	s=1	s=1	X
ejpam-6070	18	7	aits(x	aits(x	NOUN
ejpam-6070	18	8	)	)	PUNCT
ejpam-6070	19	1	∂u	∂u	PROPN
ejpam-6070	19	2	∂xt	∂xt	PROPN
ejpam-6070	19	3	∂v	∂v	PROPN
ejpam-6070	19	4	∂xs	∂xs	PROPN
ejpam-6070	19	5	+	+	CCONJ
ejpam-6070	19	6	d∑	d∑	PROPN
ejpam-6070	19	7	s=1	s=1	X
ejpam-6070	19	8	bis(x	bis(x	PROPN
ejpam-6070	19	9	)	)	PUNCT
ejpam-6070	19	10	∂u	∂u	PROPN
ejpam-6070	19	11	∂xs	∂xs	PROPN
ejpam-6070	19	12	v+	v+	ADV
ejpam-6070	19	13	ai0(x)uv	ai0(x)uv	VERB
ejpam-6070	20	1			PROPN
ejpam-6070	20	2	dx	dx	PROPN
ejpam-6070	20	3	.	.	PUNCT
ejpam-6070	21	1	additionally	additionally	ADV
ejpam-6070	21	2	,	,	PUNCT
ejpam-6070	21	3	the	the	DET
ejpam-6070	21	4	function	function	NOUN
ejpam-6070	21	5	f	f	PROPN
ejpam-6070	22	1	i	i	PRON
ejpam-6070	22	2	is	be	AUX
ejpam-6070	22	3	assumed	assume	VERB
ejpam-6070	22	4	to	to	PART
ejpam-6070	22	5	be	be	AUX
ejpam-6070	22	6	smooth	smooth	ADJ
ejpam-6070	22	7	and	and	CCONJ
ejpam-6070	22	8	nonnegative	nonnegative	ADJ
ejpam-6070	22	9	:	:	PUNCT
ejpam-6070	22	10	f	f	X
ejpam-6070	22	11	i	i	PROPN
ejpam-6070	22	12	∈	∈	PROPN
ejpam-6070	22	13	c2(ω	c2(ω	PRON
ejpam-6070	22	14	)	)	PUNCT
ejpam-6070	22	15	,	,	PUNCT
ejpam-6070	23	1	f	f	PROPN
ejpam-6070	23	2	i	i	PRON
ejpam-6070	23	3	≥	≥	VERB
ejpam-6070	23	4	0	0	NUM
ejpam-6070	23	5	.	.	PUNCT
ejpam-6070	24	1	this	this	DET
ejpam-6070	24	2	study	study	NOUN
ejpam-6070	24	3	examines	examine	VERB
ejpam-6070	24	4	the	the	DET
ejpam-6070	24	5	monotonic	monotonic	ADJ
ejpam-6070	24	6	and	and	CCONJ
ejpam-6070	24	7	geometric	geometric	ADJ
ejpam-6070	24	8	convergence	convergence	NOUN
ejpam-6070	24	9	of	of	ADP
ejpam-6070	24	10	problem	problem	NOUN
ejpam-6070	24	11	(	(	PUNCT
ejpam-6070	24	12	1	1	NUM
ejpam-6070	24	13	)	)	PUNCT
ejpam-6070	24	14	within	within	ADP
ejpam-6070	24	15	a	a	DET
ejpam-6070	24	16	discrete	discrete	ADJ
ejpam-6070	24	17	framework	framework	NOUN
ejpam-6070	24	18	using	use	VERB
ejpam-6070	24	19	the	the	DET
ejpam-6070	24	20	finite	finite	ADJ
ejpam-6070	24	21	difference	difference	NOUN
ejpam-6070	24	22	method	method	NOUN
ejpam-6070	24	23	.	.	PUNCT
ejpam-6070	25	1	we	we	PRON
ejpam-6070	25	2	employ	employ	VERB
ejpam-6070	25	3	the	the	DET
ejpam-6070	25	4	overlapping	overlap	VERB
ejpam-6070	25	5	domain	domain	NOUN
ejpam-6070	25	6	decomposition	decomposition	NOUN
ejpam-6070	25	7	approach	approach	NOUN
ejpam-6070	25	8	along	along	ADP
ejpam-6070	25	9	with	with	ADP
ejpam-6070	25	10	the	the	DET
ejpam-6070	25	11	characterization	characterization	NOUN
ejpam-6070	25	12	of	of	ADP
ejpam-6070	25	13	sequences	sequence	NOUN
ejpam-6070	25	14	of	of	ADP
ejpam-6070	25	15	lower	low	ADJ
ejpam-6070	25	16	and	and	CCONJ
ejpam-6070	25	17	upper	upper	ADJ
ejpam-6070	25	18	solutions	solution	NOUN
ejpam-6070	25	19	.	.	PUNCT
ejpam-6070	26	1	this	this	DET
ejpam-6070	26	2	approach	approach	NOUN
ejpam-6070	26	3	allows	allow	VERB
ejpam-6070	26	4	us	we	PRON
ejpam-6070	26	5	to	to	PART
ejpam-6070	26	6	analyze	analyze	VERB
ejpam-6070	26	7	the	the	DET
ejpam-6070	26	8	convergence	convergence	NOUN
ejpam-6070	26	9	properties	property	NOUN
ejpam-6070	26	10	of	of	ADP
ejpam-6070	26	11	the	the	DET
ejpam-6070	26	12	hamilton	hamilton	PROPN
ejpam-6070	26	13	-	-	PUNCT
ejpam-6070	26	14	jacobi	jacobi	PROPN
ejpam-6070	26	15	-	-	PUNCT
ejpam-6070	26	16	bellman	bellman	NOUN
ejpam-6070	26	17	(	(	PUNCT
ejpam-6070	26	18	hjb	hjb	NOUN
ejpam-6070	26	19	)	)	PUNCT
ejpam-6070	26	20	equation	equation	NOUN
ejpam-6070	26	21	,	,	PUNCT
ejpam-6070	26	22	particularly	particularly	ADV
ejpam-6070	26	23	in	in	ADP
ejpam-6070	26	24	its	its	PRON
ejpam-6070	26	25	non	non	ADJ
ejpam-6070	26	26	-	-	ADJ
ejpam-6070	26	27	coercive	coercive	ADJ
ejpam-6070	26	28	form	form	NOUN
ejpam-6070	26	29	.	.	PUNCT
ejpam-6070	27	1	the	the	DET
ejpam-6070	27	2	absence	absence	NOUN
ejpam-6070	27	3	of	of	ADP
ejpam-6070	27	4	a	a	DET
ejpam-6070	27	5	coercive	coercive	ADJ
ejpam-6070	27	6	condition	condition	NOUN
ejpam-6070	27	7	in	in	ADP
ejpam-6070	27	8	the	the	DET
ejpam-6070	27	9	hjb	hjb	NOUN
ejpam-6070	27	10	equation	equation	NOUN
ejpam-6070	27	11	presents	present	VERB
ejpam-6070	27	12	a	a	DET
ejpam-6070	27	13	significant	significant	ADJ
ejpam-6070	27	14	challenge	challenge	NOUN
ejpam-6070	27	15	,	,	PUNCT
ejpam-6070	27	16	making	make	VERB
ejpam-6070	27	17	the	the	DET
ejpam-6070	27	18	application	application	NOUN
ejpam-6070	27	19	of	of	ADP
ejpam-6070	27	20	conventional	conventional	ADJ
ejpam-6070	27	21	solution	solution	NOUN
ejpam-6070	27	22	methods	method	NOUN
ejpam-6070	27	23	more	more	ADV
ejpam-6070	27	24	complex	complex	ADJ
ejpam-6070	27	25	.	.	PUNCT
ejpam-6070	28	1	the	the	DET
ejpam-6070	28	2	numerical	numerical	PROPN
ejpam-6070	28	3	approximation	approximation	NOUN
ejpam-6070	28	4	of	of	ADP
ejpam-6070	28	5	hamilton	hamilton	PROPN
ejpam-6070	28	6	-	-	PUNCT
ejpam-6070	28	7	jacobi	jacobi	PROPN
ejpam-6070	28	8	-	-	PUNCT
ejpam-6070	28	9	bellman	bellman	NOUN
ejpam-6070	28	10	(	(	PUNCT
ejpam-6070	28	11	hjb	hjb	PROPN
ejpam-6070	28	12	)	)	PUNCT
ejpam-6070	28	13	equations	equation	NOUN
ejpam-6070	28	14	has	have	AUX
ejpam-6070	28	15	been	be	AUX
ejpam-6070	28	16	an	an	DET
ejpam-6070	28	17	active	active	ADJ
ejpam-6070	28	18	research	research	NOUN
ejpam-6070	28	19	area	area	NOUN
ejpam-6070	28	20	,	,	PUNCT
ejpam-6070	28	21	with	with	ADP
ejpam-6070	28	22	various	various	ADJ
ejpam-6070	28	23	methods	method	NOUN
ejpam-6070	28	24	proposed	propose	VERB
ejpam-6070	28	25	to	to	PART
ejpam-6070	28	26	enhance	enhance	VERB
ejpam-6070	28	27	accuracy	accuracy	NOUN
ejpam-6070	28	28	and	and	CCONJ
ejpam-6070	28	29	computational	computational	ADJ
ejpam-6070	28	30	efficiency	efficiency	NOUN
ejpam-6070	28	31	.	.	PUNCT
ejpam-6070	29	1	for	for	ADP
ejpam-6070	29	2	instance	instance	NOUN
ejpam-6070	29	3	,	,	PUNCT
ejpam-6070	29	4	the	the	DET
ejpam-6070	29	5	study	study	NOUN
ejpam-6070	29	6	in	in	ADP
ejpam-6070	29	7	[	[	X
ejpam-6070	29	8	1	1	NUM
ejpam-6070	29	9	]	]	PUNCT
ejpam-6070	29	10	explores	explore	NOUN
ejpam-6070	29	11	numerical	numerical	ADJ
ejpam-6070	29	12	schemes	scheme	NOUN
ejpam-6070	29	13	for	for	ADP
ejpam-6070	29	14	systems	system	NOUN
ejpam-6070	29	15	of	of	ADP
ejpam-6070	29	16	hjb	hjb	NOUN
ejpam-6070	29	17	equations	equation	NOUN
ejpam-6070	29	18	in	in	ADP
ejpam-6070	29	19	innovation	innovation	NOUN
ejpam-6070	29	20	dynamics	dynamic	NOUN
ejpam-6070	29	21	,	,	PUNCT
ejpam-6070	29	22	providing	provide	VERB
ejpam-6070	29	23	insights	insight	NOUN
ejpam-6070	29	24	into	into	ADP
ejpam-6070	29	25	their	their	PRON
ejpam-6070	29	26	stability	stability	NOUN
ejpam-6070	29	27	and	and	CCONJ
ejpam-6070	29	28	convergence	convergence	NOUN
ejpam-6070	29	29	.	.	PUNCT
ejpam-6070	30	1	mixed	mix	VERB
ejpam-6070	30	2	finite	finite	PROPN
ejpam-6070	30	3	element	element	NOUN
ejpam-6070	30	4	techniques	technique	NOUN
ejpam-6070	30	5	have	have	AUX
ejpam-6070	30	6	also	also	ADV
ejpam-6070	30	7	been	be	AUX
ejpam-6070	30	8	developed	develop	VERB
ejpam-6070	30	9	to	to	PART
ejpam-6070	30	10	handle	handle	VERB
ejpam-6070	30	11	hjb	hjb	NOUN
ejpam-6070	30	12	equations	equation	NOUN
ejpam-6070	30	13	with	with	ADP
ejpam-6070	30	14	cordes	corde	NOUN
ejpam-6070	30	15	coefficients	coefficient	NOUN
ejpam-6070	30	16	,	,	PUNCT
ejpam-6070	30	17	as	as	SCONJ
ejpam-6070	30	18	discussed	discuss	VERB
ejpam-6070	30	19	in	in	ADP
ejpam-6070	30	20	[	[	X
ejpam-6070	30	21	2	2	NUM
ejpam-6070	30	22	]	]	PUNCT
ejpam-6070	30	23	.	.	PUNCT
ejpam-6070	31	1	to	to	PART
ejpam-6070	31	2	address	address	VERB
ejpam-6070	31	3	challenges	challenge	NOUN
ejpam-6070	31	4	associated	associate	VERB
ejpam-6070	31	5	with	with	ADP
ejpam-6070	31	6	quasi	quasi	ADJ
ejpam-6070	31	7	-	-	ADJ
ejpam-6070	31	8	variational	variational	ADJ
ejpam-6070	31	9	inequalities	inequality	NOUN
ejpam-6070	31	10	,	,	PUNCT
ejpam-6070	31	11	domain	domain	NOUN
ejpam-6070	31	12	decomposition	decomposition	NOUN
ejpam-6070	31	13	strategies	strategy	NOUN
ejpam-6070	31	14	such	such	ADJ
ejpam-6070	31	15	as	as	ADP
ejpam-6070	31	16	the	the	DET
ejpam-6070	31	17	schwarz	schwarz	PROPN
ejpam-6070	31	18	method	method	NOUN
ejpam-6070	31	19	have	have	AUX
ejpam-6070	31	20	been	be	AUX
ejpam-6070	31	21	analyzed	analyze	VERB
ejpam-6070	31	22	in	in	ADP
ejpam-6070	31	23	[	[	X
ejpam-6070	31	24	3	3	NUM
ejpam-6070	31	25	]	]	PUNCT
ejpam-6070	31	26	.	.	PUNCT
ejpam-6070	32	1	furthermore	furthermore	ADV
ejpam-6070	32	2	,	,	PUNCT
ejpam-6070	32	3	overlapping	overlap	VERB
ejpam-6070	32	4	domain	domain	NOUN
ejpam-6070	32	5	decomposition	decomposition	NOUN
ejpam-6070	32	6	approaches	approach	NOUN
ejpam-6070	32	7	have	have	AUX
ejpam-6070	32	8	been	be	AUX
ejpam-6070	32	9	applied	apply	VERB
ejpam-6070	32	10	to	to	ADP
ejpam-6070	32	11	non	non	ADJ
ejpam-6070	32	12	-	-	ADJ
ejpam-6070	32	13	coercive	coercive	ADJ
ejpam-6070	32	14	quasi	quasi	ADJ
ejpam-6070	32	15	-	-	ADJ
ejpam-6070	32	16	variational	variational	ADJ
ejpam-6070	32	17	systems	system	NOUN
ejpam-6070	32	18	related	relate	VERB
ejpam-6070	32	19	to	to	ADP
ejpam-6070	32	20	hjb	hjb	VERB
ejpam-6070	32	21	equations	equation	NOUN
ejpam-6070	32	22	[	[	X
ejpam-6070	32	23	4	4	NUM
ejpam-6070	32	24	]	]	PUNCT
ejpam-6070	32	25	,	,	PUNCT
ejpam-6070	32	26	while	while	SCONJ
ejpam-6070	32	27	[	[	X
ejpam-6070	32	28	5	5	NUM
ejpam-6070	32	29	]	]	PUNCT
ejpam-6070	32	30	introduces	introduce	VERB
ejpam-6070	32	31	a	a	DET
ejpam-6070	32	32	contraction	contraction	NOUN
ejpam-6070	32	33	-	-	PUNCT
ejpam-6070	32	34	based	base	VERB
ejpam-6070	32	35	algorithmic	algorithmic	ADJ
ejpam-6070	32	36	approach	approach	NOUN
ejpam-6070	32	37	to	to	ADP
ejpam-6070	32	38	solving	solve	VERB
ejpam-6070	32	39	these	these	DET
ejpam-6070	32	40	equations	equation	NOUN
ejpam-6070	32	41	.	.	PUNCT
ejpam-6070	33	1	in	in	ADP
ejpam-6070	33	2	this	this	DET
ejpam-6070	33	3	work	work	NOUN
ejpam-6070	33	4	,	,	PUNCT
ejpam-6070	33	5	we	we	PRON
ejpam-6070	33	6	adopt	adopt	VERB
ejpam-6070	33	7	an	an	DET
ejpam-6070	33	8	overlapping	overlap	VERB
ejpam-6070	33	9	domain	domain	NOUN
ejpam-6070	33	10	decomposition	decomposition	NOUN
ejpam-6070	33	11	method	method	NOUN
ejpam-6070	33	12	that	that	PRON
ejpam-6070	33	13	ensures	ensure	VERB
ejpam-6070	33	14	stability	stability	NOUN
ejpam-6070	33	15	through	through	ADP
ejpam-6070	33	16	lower	low	ADJ
ejpam-6070	33	17	and	and	CCONJ
ejpam-6070	33	18	upper	upper	ADJ
ejpam-6070	33	19	solutions	solution	NOUN
ejpam-6070	33	20	,	,	PUNCT
ejpam-6070	33	21	providing	provide	VERB
ejpam-6070	33	22	a	a	DET
ejpam-6070	33	23	robust	robust	ADJ
ejpam-6070	33	24	numerical	numerical	ADJ
ejpam-6070	33	25	framework	framework	NOUN
ejpam-6070	33	26	for	for	ADP
ejpam-6070	33	27	solving	solve	VERB
ejpam-6070	33	28	hjb	hjb	NOUN
ejpam-6070	33	29	equations	equation	NOUN
ejpam-6070	33	30	efficiently	efficiently	ADV
ejpam-6070	33	31	.	.	PUNCT
ejpam-6070	34	1	s.	s.	PROPN
ejpam-6070	34	2	chebbah	chebbah	PROPN
ejpam-6070	34	3	,	,	PUNCT
ejpam-6070	34	4	s.	s.	PROPN
ejpam-6070	34	5	madi	madi	PROPN
ejpam-6070	34	6	,	,	PUNCT
ejpam-6070	34	7	m.	m.	NOUN
ejpam-6070	34	8	haiour	haiour	PROPN
ejpam-6070	34	9	/	/	SYM
ejpam-6070	34	10	eur	eur	PROPN
ejpam-6070	34	11	.	.	PUNCT
ejpam-6070	35	1	j.	j.	PROPN
ejpam-6070	35	2	pure	pure	PROPN
ejpam-6070	35	3	appl	appl	PROPN
ejpam-6070	35	4	.	.	PROPN
ejpam-6070	35	5	math	math	PROPN
ejpam-6070	35	6	,	,	PUNCT
ejpam-6070	35	7	18	18	NUM
ejpam-6070	35	8	(	(	PUNCT
ejpam-6070	35	9	2	2	NUM
ejpam-6070	35	10	)	)	PUNCT
ejpam-6070	35	11	(	(	PUNCT
ejpam-6070	35	12	2025	2025	NUM
ejpam-6070	35	13	)	)	PUNCT
ejpam-6070	35	14	,	,	PUNCT
ejpam-6070	35	15	6070	6070	NUM
ejpam-6070	35	16	3	3	NUM
ejpam-6070	35	17	of	of	ADP
ejpam-6070	35	18	20	20	NUM
ejpam-6070	35	19	in	in	ADP
ejpam-6070	35	20	this	this	DET
ejpam-6070	35	21	work	work	NOUN
ejpam-6070	35	22	,	,	PUNCT
ejpam-6070	35	23	we	we	PRON
ejpam-6070	35	24	adopt	adopt	VERB
ejpam-6070	35	25	an	an	DET
ejpam-6070	35	26	overlapping	overlap	VERB
ejpam-6070	35	27	domain	domain	NOUN
ejpam-6070	35	28	decomposition	decomposition	NOUN
ejpam-6070	35	29	approach	approach	NOUN
ejpam-6070	35	30	,	,	PUNCT
ejpam-6070	35	31	leveraging	leverage	VERB
ejpam-6070	35	32	the	the	DET
ejpam-6070	35	33	interaction	interaction	NOUN
ejpam-6070	35	34	between	between	ADP
ejpam-6070	35	35	lower	low	ADJ
ejpam-6070	35	36	and	and	CCONJ
ejpam-6070	35	37	upper	upper	ADJ
ejpam-6070	35	38	solutions	solution	NOUN
ejpam-6070	35	39	to	to	PART
ejpam-6070	35	40	ensure	ensure	VERB
ejpam-6070	35	41	numerical	numerical	ADJ
ejpam-6070	35	42	stability	stability	NOUN
ejpam-6070	35	43	and	and	CCONJ
ejpam-6070	35	44	convergence	convergence	NOUN
ejpam-6070	35	45	.	.	PUNCT
ejpam-6070	36	1	this	this	PRON
ejpam-6070	36	2	makes	make	VERB
ejpam-6070	36	3	it	it	PRON
ejpam-6070	36	4	a	a	DET
ejpam-6070	36	5	reliable	reliable	ADJ
ejpam-6070	36	6	method	method	NOUN
ejpam-6070	36	7	for	for	ADP
ejpam-6070	36	8	solving	solve	VERB
ejpam-6070	36	9	complex	complex	ADJ
ejpam-6070	36	10	problems	problem	NOUN
ejpam-6070	36	11	.	.	PUNCT
ejpam-6070	37	1	this	this	DET
ejpam-6070	37	2	paper	paper	NOUN
ejpam-6070	37	3	is	be	AUX
ejpam-6070	37	4	organized	organize	VERB
ejpam-6070	37	5	as	as	SCONJ
ejpam-6070	37	6	follows	follow	VERB
ejpam-6070	37	7	:	:	PUNCT
ejpam-6070	37	8	section	section	NOUN
ejpam-6070	37	9	2	2	NUM
ejpam-6070	37	10	provides	provide	VERB
ejpam-6070	37	11	a	a	DET
ejpam-6070	37	12	detailed	detailed	ADJ
ejpam-6070	37	13	analysis	analysis	NOUN
ejpam-6070	37	14	of	of	ADP
ejpam-6070	37	15	the	the	DET
ejpam-6070	37	16	transformation	transformation	NOUN
ejpam-6070	37	17	of	of	ADP
ejpam-6070	37	18	the	the	DET
ejpam-6070	37	19	non	non	ADJ
ejpam-6070	37	20	-	-	ADJ
ejpam-6070	37	21	coercive	coercive	ADJ
ejpam-6070	37	22	problem	problem	NOUN
ejpam-6070	37	23	(	(	PUNCT
ejpam-6070	37	24	1	1	NUM
ejpam-6070	37	25	)	)	PUNCT
ejpam-6070	37	26	into	into	ADP
ejpam-6070	37	27	the	the	DET
ejpam-6070	37	28	coercive	coercive	PROPN
ejpam-6070	37	29	hamilton	hamilton	PROPN
ejpam-6070	37	30	-	-	PUNCT
ejpam-6070	37	31	jacobi	jacobi	PROPN
ejpam-6070	37	32	-	-	PUNCT
ejpam-6070	37	33	bellman	bellman	NOUN
ejpam-6070	37	34	(	(	PUNCT
ejpam-6070	37	35	hjb	hjb	NOUN
ejpam-6070	37	36	)	)	PUNCT
ejpam-6070	37	37	equation	equation	NOUN
ejpam-6070	37	38	,	,	PUNCT
ejpam-6070	37	39	considering	consider	VERB
ejpam-6070	37	40	both	both	CCONJ
ejpam-6070	37	41	the	the	DET
ejpam-6070	37	42	continuous	continuous	ADJ
ejpam-6070	37	43	and	and	CCONJ
ejpam-6070	37	44	discrete	discrete	ADJ
ejpam-6070	37	45	cases	case	NOUN
ejpam-6070	37	46	using	use	VERB
ejpam-6070	37	47	the	the	DET
ejpam-6070	37	48	finite	finite	ADJ
ejpam-6070	37	49	difference	difference	NOUN
ejpam-6070	37	50	method	method	NOUN
ejpam-6070	37	51	.	.	PUNCT
ejpam-6070	38	1	section	section	NOUN
ejpam-6070	38	2	3	3	NUM
ejpam-6070	38	3	establishes	establish	VERB
ejpam-6070	38	4	the	the	DET
ejpam-6070	38	5	monotonic	monotonic	ADJ
ejpam-6070	38	6	and	and	CCONJ
ejpam-6070	38	7	geometric	geometric	ADJ
ejpam-6070	38	8	convergence	convergence	NOUN
ejpam-6070	38	9	of	of	ADP
ejpam-6070	38	10	the	the	DET
ejpam-6070	38	11	solutions	solution	NOUN
ejpam-6070	38	12	by	by	ADP
ejpam-6070	38	13	applying	apply	VERB
ejpam-6070	38	14	the	the	DET
ejpam-6070	38	15	overlapping	overlap	VERB
ejpam-6070	38	16	domain	domain	NOUN
ejpam-6070	38	17	decomposition	decomposition	NOUN
ejpam-6070	38	18	method	method	NOUN
ejpam-6070	38	19	along	along	ADP
ejpam-6070	38	20	with	with	ADP
ejpam-6070	38	21	a	a	DET
ejpam-6070	38	22	sequence	sequence	NOUN
ejpam-6070	38	23	of	of	ADP
ejpam-6070	38	24	lower	low	ADJ
ejpam-6070	38	25	and	and	CCONJ
ejpam-6070	38	26	upper	upper	ADJ
ejpam-6070	38	27	solutions	solution	NOUN
ejpam-6070	38	28	.	.	PUNCT
ejpam-6070	39	1	the	the	DET
ejpam-6070	39	2	final	final	ADJ
ejpam-6070	39	3	section	section	NOUN
ejpam-6070	39	4	presents	present	VERB
ejpam-6070	39	5	numerical	numerical	ADJ
ejpam-6070	39	6	experiments	experiment	NOUN
ejpam-6070	39	7	that	that	PRON
ejpam-6070	39	8	confirm	confirm	VERB
ejpam-6070	39	9	the	the	DET
ejpam-6070	39	10	theoretical	theoretical	ADJ
ejpam-6070	39	11	findings	finding	NOUN
ejpam-6070	39	12	,	,	PUNCT
ejpam-6070	39	13	illustrating	illustrate	VERB
ejpam-6070	39	14	the	the	DET
ejpam-6070	39	15	effectiveness	effectiveness	NOUN
ejpam-6070	39	16	of	of	ADP
ejpam-6070	39	17	domain	domain	NOUN
ejpam-6070	39	18	decomposition	decomposition	NOUN
ejpam-6070	39	19	methods	method	NOUN
ejpam-6070	39	20	in	in	ADP
ejpam-6070	39	21	solving	solve	VERB
ejpam-6070	39	22	hjb	hjb	NOUN
ejpam-6070	39	23	equations	equation	NOUN
ejpam-6070	39	24	and	and	CCONJ
ejpam-6070	39	25	evaluating	evaluate	VERB
ejpam-6070	39	26	the	the	DET
ejpam-6070	39	27	impact	impact	NOUN
ejpam-6070	39	28	of	of	ADP
ejpam-6070	39	29	overlapping	overlap	VERB
ejpam-6070	39	30	on	on	ADP
ejpam-6070	39	31	the	the	DET
ejpam-6070	39	32	convergence	convergence	NOUN
ejpam-6070	39	33	rate	rate	NOUN
ejpam-6070	39	34	.	.	PUNCT
ejpam-6070	40	1	2	2	X
ejpam-6070	40	2	.	.	X
ejpam-6070	40	3	coercive	coercive	ADJ
ejpam-6070	40	4	reformulation	reformulation	NOUN
ejpam-6070	40	5	of	of	ADP
ejpam-6070	40	6	the	the	DET
ejpam-6070	40	7	hjb	hjb	NOUN
ejpam-6070	40	8	equation	equation	NOUN
ejpam-6070	40	9	in	in	ADP
ejpam-6070	40	10	this	this	DET
ejpam-6070	40	11	section	section	NOUN
ejpam-6070	40	12	,	,	PUNCT
ejpam-6070	40	13	we	we	PRON
ejpam-6070	40	14	reformulate	reformulate	VERB
ejpam-6070	40	15	the	the	DET
ejpam-6070	40	16	hamilton	hamilton	PROPN
ejpam-6070	40	17	-	-	PUNCT
ejpam-6070	40	18	jacobi	jacobi	PROPN
ejpam-6070	40	19	-	-	PUNCT
ejpam-6070	40	20	bellman	bellman	NOUN
ejpam-6070	40	21	(	(	PUNCT
ejpam-6070	40	22	hjb	hjb	NOUN
ejpam-6070	40	23	)	)	PUNCT
ejpam-6070	40	24	equation	equation	NOUN
ejpam-6070	40	25	into	into	ADP
ejpam-6070	40	26	a	a	DET
ejpam-6070	40	27	coercive	coercive	ADJ
ejpam-6070	40	28	form	form	NOUN
ejpam-6070	40	29	to	to	PART
ejpam-6070	40	30	improve	improve	VERB
ejpam-6070	40	31	its	its	PRON
ejpam-6070	40	32	stability	stability	NOUN
ejpam-6070	40	33	and	and	CCONJ
ejpam-6070	40	34	numerical	numerical	ADJ
ejpam-6070	40	35	solvability	solvability	NOUN
ejpam-6070	40	36	.	.	PUNCT
ejpam-6070	41	1	following	follow	VERB
ejpam-6070	41	2	[	[	X
ejpam-6070	41	3	6	6	NUM
ejpam-6070	41	4	]	]	PUNCT
ejpam-6070	41	5	,	,	PUNCT
ejpam-6070	41	6	this	this	PRON
ejpam-6070	41	7	is	be	AUX
ejpam-6070	41	8	achieved	achieve	VERB
ejpam-6070	41	9	by	by	ADP
ejpam-6070	41	10	introducing	introduce	VERB
ejpam-6070	41	11	a	a	DET
ejpam-6070	41	12	regularization	regularization	NOUN
ejpam-6070	41	13	parameter	parameter	NOUN
ejpam-6070	41	14	µ	µ	X
ejpam-6070	41	15	>	>	X
ejpam-6070	41	16	0	0	PROPN
ejpam-6070	41	17	,	,	PUNCT
ejpam-6070	41	18	which	which	PRON
ejpam-6070	41	19	ensures	ensure	VERB
ejpam-6070	41	20	coercivity	coercivity	NOUN
ejpam-6070	41	21	and	and	CCONJ
ejpam-6070	41	22	enhances	enhance	VERB
ejpam-6070	41	23	the	the	DET
ejpam-6070	41	24	well	well	NOUN
ejpam-6070	41	25	-	-	PUNCT
ejpam-6070	41	26	posedness	posedness	NOUN
ejpam-6070	41	27	of	of	ADP
ejpam-6070	41	28	the	the	DET
ejpam-6070	41	29	problem	problem	NOUN
ejpam-6070	41	30	.	.	PUNCT
ejpam-6070	42	1	the	the	DET
ejpam-6070	42	2	modified	modify	VERB
ejpam-6070	42	3	equation	equation	NOUN
ejpam-6070	42	4	is	be	AUX
ejpam-6070	42	5	given	give	VERB
ejpam-6070	42	6	by:max	by:max	PROPN
ejpam-6070	42	7	1≤i≤n	1≤i≤n	NUM
ejpam-6070	42	8	(	(	PUNCT
ejpam-6070	42	9	biξ	biξ	NOUN
ejpam-6070	42	10	−	−	NOUN
ejpam-6070	42	11	gi(ξ	gi(ξ	NOUN
ejpam-6070	42	12	)	)	PUNCT
ejpam-6070	42	13	)	)	PUNCT
ejpam-6070	43	1	=	=	SYM
ejpam-6070	43	2	0	0	NUM
ejpam-6070	43	3	,	,	PUNCT
ejpam-6070	43	4	inω	inω	ADJ
ejpam-6070	43	5	,	,	PUNCT
ejpam-6070	43	6	ξ	ξ	X
ejpam-6070	43	7	=	=	SYM
ejpam-6070	43	8	0	0	NUM
ejpam-6070	43	9	,	,	PUNCT
ejpam-6070	43	10	on	on	ADP
ejpam-6070	43	11	∂ω	∂ω	PROPN
ejpam-6070	43	12	,	,	PUNCT
ejpam-6070	43	13	(	(	PUNCT
ejpam-6070	43	14	2	2	X
ejpam-6070	43	15	)	)	PUNCT
ejpam-6070	43	16	where	where	SCONJ
ejpam-6070	43	17	the	the	DET
ejpam-6070	43	18	coercive	coercive	ADJ
ejpam-6070	43	19	operators	operator	NOUN
ejpam-6070	43	20	b1	b1	VERB
ejpam-6070	43	21	,	,	PUNCT
ejpam-6070	43	22	·	·	PUNCT
ejpam-6070	43	23	·	·	PUNCT
ejpam-6070	43	24	·	·	PUNCT
ejpam-6070	43	25	,	,	PUNCT
ejpam-6070	43	26	bn	bn	NUM
ejpam-6070	43	27	are	be	AUX
ejpam-6070	43	28	defined	define	VERB
ejpam-6070	43	29	as	as	ADP
ejpam-6070	43	30	:	:	PUNCT
ejpam-6070	43	31	bi	bi	NOUN
ejpam-6070	43	32	=	=	PROPN
ejpam-6070	43	33	d∑	d∑	PROPN
ejpam-6070	43	34	t	t	PROPN
ejpam-6070	43	35	,	,	PUNCT
ejpam-6070	43	36	s=1	s=1	X
ejpam-6070	43	37	aits(x	aits(x	NOUN
ejpam-6070	43	38	)	)	PUNCT
ejpam-6070	43	39	∂2	∂2	NOUN
ejpam-6070	43	40	∂xt∂xs	∂xt∂xs	PROPN
ejpam-6070	43	41	+	+	X
ejpam-6070	43	42	d∑	d∑	PROPN
ejpam-6070	43	43	s=1	s=1	X
ejpam-6070	43	44	bis(x	bis(x	PROPN
ejpam-6070	43	45	)	)	PUNCT
ejpam-6070	43	46	∂	∂	PUNCT
ejpam-6070	43	47	∂xs	∂xs	PROPN
ejpam-6070	43	48	+	+	CCONJ
ejpam-6070	43	49	(	(	PUNCT
ejpam-6070	43	50	ai0(x	ai0(x	PROPN
ejpam-6070	43	51	)	)	PUNCT
ejpam-6070	43	52	+	+	X
ejpam-6070	43	53	µ	µ	X
ejpam-6070	43	54	)	)	PUNCT
ejpam-6070	43	55	,	,	PUNCT
ejpam-6070	43	56	and	and	CCONJ
ejpam-6070	43	57	the	the	DET
ejpam-6070	43	58	corresponding	corresponding	ADJ
ejpam-6070	43	59	equations	equation	NOUN
ejpam-6070	43	60	are	be	AUX
ejpam-6070	43	61	defined	define	VERB
ejpam-6070	43	62	as	as	ADP
ejpam-6070	43	63	:	:	PUNCT
ejpam-6070	43	64	bi	bi	NOUN
ejpam-6070	44	1	=	=	NOUN
ejpam-6070	44	2	ai	ai	PROPN
ejpam-6070	44	3	+	+	X
ejpam-6070	44	4	µi	µi	PROPN
ejpam-6070	44	5	and	and	CCONJ
ejpam-6070	44	6	gi(ξ	gi(ξ	PUNCT
ejpam-6070	44	7	)	)	PUNCT
ejpam-6070	45	1	=	=	PUNCT
ejpam-6070	45	2	f	f	X
ejpam-6070	46	1	i	i	PRON
ejpam-6070	46	2	+	+	X
ejpam-6070	46	3	µξ	µξ	ADP
ejpam-6070	46	4	,	,	PUNCT
ejpam-6070	46	5	i	i	NOUN
ejpam-6070	46	6	=	=	NOUN
ejpam-6070	46	7	1	1	NUM
ejpam-6070	46	8	,	,	PUNCT
ejpam-6070	46	9	n.	n.	VERB
ejpam-6070	46	10	the	the	DET
ejpam-6070	46	11	bilinear	bilinear	NOUN
ejpam-6070	46	12	form	form	NOUN
ejpam-6070	46	13	for	for	ADP
ejpam-6070	46	14	the	the	DET
ejpam-6070	46	15	operator	operator	NOUN
ejpam-6070	46	16	bi	bi	NOUN
ejpam-6070	46	17	is	be	AUX
ejpam-6070	46	18	expressed	express	VERB
ejpam-6070	46	19	as	as	ADP
ejpam-6070	46	20	:	:	PUNCT
ejpam-6070	46	21	bi⟨u	bi⟨u	NOUN
ejpam-6070	46	22	,	,	PUNCT
ejpam-6070	46	23	v⟩	v⟩	NOUN
ejpam-6070	46	24	=	=	SYM
ejpam-6070	46	25	ai⟨u	ai⟨u	NOUN
ejpam-6070	46	26	,	,	PUNCT
ejpam-6070	46	27	v⟩+	v⟩+	PROPN
ejpam-6070	46	28	µ⟨u	µ⟨u	NUM
ejpam-6070	46	29	,	,	PUNCT
ejpam-6070	46	30	v⟩	v⟩	NOUN
ejpam-6070	46	31	,	,	PUNCT
ejpam-6070	46	32	previous	previous	ADJ
ejpam-6070	46	33	studies	study	NOUN
ejpam-6070	46	34	have	have	AUX
ejpam-6070	46	35	established	establish	VERB
ejpam-6070	46	36	the	the	DET
ejpam-6070	46	37	existence	existence	NOUN
ejpam-6070	46	38	,	,	PUNCT
ejpam-6070	46	39	uniqueness	uniqueness	NOUN
ejpam-6070	46	40	,	,	PUNCT
ejpam-6070	46	41	and	and	CCONJ
ejpam-6070	46	42	regularity	regularity	NOUN
ejpam-6070	46	43	of	of	ADP
ejpam-6070	46	44	the	the	DET
ejpam-6070	46	45	solution	solution	NOUN
ejpam-6070	46	46	to	to	ADP
ejpam-6070	46	47	the	the	DET
ejpam-6070	46	48	continuous	continuous	ADJ
ejpam-6070	46	49	problem	problem	NOUN
ejpam-6070	46	50	(	(	PUNCT
ejpam-6070	46	51	2	2	NUM
ejpam-6070	46	52	)	)	PUNCT
ejpam-6070	46	53	(	(	PUNCT
ejpam-6070	46	54	see	see	VERB
ejpam-6070	46	55	[	[	X
ejpam-6070	46	56	7	7	NUM
ejpam-6070	46	57	,	,	PUNCT
ejpam-6070	46	58	8	8	NUM
ejpam-6070	46	59	]	]	NUM
ejpam-6070	46	60	)	)	PUNCT
ejpam-6070	46	61	.	.	PUNCT
ejpam-6070	47	1	to	to	PART
ejpam-6070	47	2	solve	solve	VERB
ejpam-6070	47	3	this	this	DET
ejpam-6070	47	4	problem	problem	NOUN
ejpam-6070	47	5	numerically	numerically	ADV
ejpam-6070	47	6	,	,	PUNCT
ejpam-6070	47	7	both	both	PRON
ejpam-6070	47	8	finite	finite	ADJ
ejpam-6070	47	9	element	element	NOUN
ejpam-6070	47	10	and	and	CCONJ
ejpam-6070	47	11	finite	finite	ADJ
ejpam-6070	47	12	difference	difference	NOUN
ejpam-6070	47	13	methods	method	NOUN
ejpam-6070	47	14	have	have	AUX
ejpam-6070	47	15	been	be	AUX
ejpam-6070	47	16	employed	employ	VERB
ejpam-6070	47	17	,	,	PUNCT
ejpam-6070	47	18	transforming	transform	VERB
ejpam-6070	47	19	the	the	DET
ejpam-6070	47	20	continuous	continuous	ADJ
ejpam-6070	47	21	problem	problem	NOUN
ejpam-6070	47	22	into	into	ADP
ejpam-6070	47	23	a	a	DET
ejpam-6070	47	24	system	system	NOUN
ejpam-6070	47	25	of	of	ADP
ejpam-6070	47	26	algebraic	algebraic	ADJ
ejpam-6070	47	27	equations	equation	NOUN
ejpam-6070	47	28	through	through	ADP
ejpam-6070	47	29	discretization	discretization	NOUN
ejpam-6070	47	30	.	.	PUNCT
ejpam-6070	48	1	this	this	DET
ejpam-6070	48	2	approach	approach	NOUN
ejpam-6070	48	3	simplifies	simplify	VERB
ejpam-6070	48	4	the	the	DET
ejpam-6070	48	5	problem	problem	NOUN
ejpam-6070	48	6	and	and	CCONJ
ejpam-6070	48	7	enhances	enhance	VERB
ejpam-6070	48	8	its	its	PRON
ejpam-6070	48	9	computational	computational	ADJ
ejpam-6070	48	10	feasibility	feasibility	NOUN
ejpam-6070	48	11	.	.	PUNCT
ejpam-6070	49	1	thus	thus	ADV
ejpam-6070	49	2	,	,	PUNCT
ejpam-6070	49	3	the	the	DET
ejpam-6070	49	4	discrete	discrete	ADJ
ejpam-6070	49	5	version	version	NOUN
ejpam-6070	49	6	of	of	ADP
ejpam-6070	49	7	the	the	DET
ejpam-6070	49	8	problem	problem	NOUN
ejpam-6070	49	9	is	be	AUX
ejpam-6070	49	10	formulated	formulate	VERB
ejpam-6070	49	11	as	as	ADP
ejpam-6070	49	12	:	:	PUNCT
ejpam-6070	49	13	s.	s.	PROPN
ejpam-6070	49	14	chebbah	chebbah	PROPN
ejpam-6070	49	15	,	,	PUNCT
ejpam-6070	49	16	s.	s.	PROPN
ejpam-6070	49	17	madi	madi	PROPN
ejpam-6070	49	18	,	,	PUNCT
ejpam-6070	49	19	m.	m.	NOUN
ejpam-6070	49	20	haiour	haiour	PROPN
ejpam-6070	49	21	/	/	SYM
ejpam-6070	49	22	eur	eur	PROPN
ejpam-6070	49	23	.	.	PUNCT
ejpam-6070	50	1	j.	j.	PROPN
ejpam-6070	50	2	pure	pure	PROPN
ejpam-6070	50	3	appl	appl	PROPN
ejpam-6070	50	4	.	.	PROPN
ejpam-6070	50	5	math	math	PROPN
ejpam-6070	50	6	,	,	PUNCT
ejpam-6070	50	7	18	18	NUM
ejpam-6070	50	8	(	(	PUNCT
ejpam-6070	50	9	2	2	NUM
ejpam-6070	50	10	)	)	PUNCT
ejpam-6070	50	11	(	(	PUNCT
ejpam-6070	50	12	2025	2025	NUM
ejpam-6070	50	13	)	)	PUNCT
ejpam-6070	50	14	,	,	PUNCT
ejpam-6070	50	15	6070	6070	NUM
ejpam-6070	50	16	4	4	NUM
ejpam-6070	50	17	of	of	ADP
ejpam-6070	50	18	20	20	NUM
ejpam-6070	50	19	max	max	NOUN
ejpam-6070	50	20	1≤i≤n	1≤i≤n	NUM
ejpam-6070	51	1	(	(	PUNCT
ejpam-6070	51	2	biζ	biζ	ADP
ejpam-6070	51	3	−	−	PROPN
ejpam-6070	51	4	g	g	PROPN
ejpam-6070	51	5	i(ζ	i(ζ	PROPN
ejpam-6070	51	6	)	)	PUNCT
ejpam-6070	51	7	)	)	PUNCT
ejpam-6070	52	1	=	=	SYM
ejpam-6070	52	2	0	0	NUM
ejpam-6070	52	3	,	,	PUNCT
ejpam-6070	52	4	inω	inω	ADJ
ejpam-6070	52	5	,	,	PUNCT
ejpam-6070	52	6	ζ	ζ	NOUN
ejpam-6070	52	7	=	=	SYM
ejpam-6070	52	8	0	0	NUM
ejpam-6070	52	9	,	,	PUNCT
ejpam-6070	52	10	on	on	ADP
ejpam-6070	52	11	∂ω	∂ω	PROPN
ejpam-6070	52	12	,	,	PUNCT
ejpam-6070	52	13	(	(	PUNCT
ejpam-6070	52	14	3	3	X
ejpam-6070	52	15	)	)	PUNCT
ejpam-6070	52	16	here	here	ADV
ejpam-6070	52	17	,	,	PUNCT
ejpam-6070	52	18	bi	bi	NOUN
ejpam-6070	52	19	and	and	CCONJ
ejpam-6070	52	20	g	g	PROPN
ejpam-6070	52	21	i(ζ	i(ζ	PROPN
ejpam-6070	52	22	)	)	PUNCT
ejpam-6070	52	23	are	be	AUX
ejpam-6070	52	24	the	the	DET
ejpam-6070	52	25	discrete	discrete	ADJ
ejpam-6070	52	26	approximations	approximation	NOUN
ejpam-6070	52	27	of	of	ADP
ejpam-6070	52	28	the	the	DET
ejpam-6070	52	29	continuous	continuous	ADJ
ejpam-6070	52	30	operators	operator	NOUN
ejpam-6070	52	31	,	,	PUNCT
ejpam-6070	52	32	facilitating	facilitate	VERB
ejpam-6070	52	33	the	the	DET
ejpam-6070	52	34	numerical	numerical	ADJ
ejpam-6070	52	35	solution	solution	NOUN
ejpam-6070	52	36	of	of	ADP
ejpam-6070	52	37	the	the	DET
ejpam-6070	52	38	hjb	hjb	NOUN
ejpam-6070	52	39	equation	equation	NOUN
ejpam-6070	52	40	.	.	PUNCT
ejpam-6070	53	1	these	these	PRON
ejpam-6070	53	2	are	be	AUX
ejpam-6070	53	3	given	give	VERB
ejpam-6070	53	4	by	by	ADP
ejpam-6070	53	5	:	:	PUNCT
ejpam-6070	53	6	bi	bi	NOUN
ejpam-6070	53	7	=	=	PROPN
ejpam-6070	53	8	a	a	PRON
ejpam-6070	54	1	i	i	X
ejpam-6070	54	2	+	+	X
ejpam-6070	54	3	µi	µi	PROPN
ejpam-6070	54	4	,	,	PUNCT
ejpam-6070	54	5	g	g	PROPN
ejpam-6070	54	6	i(ζ	i(ζ	PROPN
ejpam-6070	54	7	)	)	PUNCT
ejpam-6070	55	1	=	=	SYM
ejpam-6070	56	1	f	f	X
ejpam-6070	57	1	i	i	PRON
ejpam-6070	57	2	+	+	X
ejpam-6070	57	3	µζ	µζ	PROPN
ejpam-6070	57	4	.	.	PUNCT
ejpam-6070	58	1	the	the	DET
ejpam-6070	58	2	matrices	matrix	NOUN
ejpam-6070	58	3	bi	bi	NOUN
ejpam-6070	58	4	and	and	CCONJ
ejpam-6070	58	5	a	a	PRON
ejpam-6070	58	6	i	i	PRON
ejpam-6070	58	7	satisfy	satisfy	VERB
ejpam-6070	58	8	the	the	DET
ejpam-6070	58	9	discrete	discrete	ADJ
ejpam-6070	58	10	maximum	maximum	ADJ
ejpam-6070	58	11	principle	principle	NOUN
ejpam-6070	58	12	and	and	CCONJ
ejpam-6070	58	13	are	be	AUX
ejpam-6070	58	14	m	m	NOUN
ejpam-6070	58	15	-	-	PUNCT
ejpam-6070	58	16	matrices[7	matrices[7	X
ejpam-6070	58	17	]	]	PUNCT
ejpam-6070	58	18	,	,	PUNCT
ejpam-6070	58	19	ensuring	ensure	VERB
ejpam-6070	58	20	stability	stability	NOUN
ejpam-6070	58	21	and	and	CCONJ
ejpam-6070	58	22	convergence	convergence	NOUN
ejpam-6070	58	23	in	in	ADP
ejpam-6070	58	24	the	the	DET
ejpam-6070	58	25	numerical	numerical	ADJ
ejpam-6070	58	26	approximation	approximation	NOUN
ejpam-6070	58	27	of	of	ADP
ejpam-6070	58	28	the	the	DET
ejpam-6070	58	29	hjb	hjb	NOUN
ejpam-6070	58	30	equation	equation	NOUN
ejpam-6070	58	31	.	.	PUNCT
ejpam-6070	59	1	3	3	X
ejpam-6070	59	2	.	.	X
ejpam-6070	59	3	decomposition	decomposition	NOUN
ejpam-6070	59	4	of	of	ADP
ejpam-6070	59	5	the	the	DET
ejpam-6070	59	6	domain	domain	NOUN
ejpam-6070	59	7	into	into	ADP
ejpam-6070	59	8	overlapping	overlap	VERB
ejpam-6070	59	9	subdomains	subdomain	NOUN
ejpam-6070	59	10	in	in	ADP
ejpam-6070	59	11	this	this	DET
ejpam-6070	59	12	section	section	NOUN
ejpam-6070	59	13	,	,	PUNCT
ejpam-6070	59	14	we	we	PRON
ejpam-6070	59	15	introduce	introduce	VERB
ejpam-6070	59	16	an	an	DET
ejpam-6070	59	17	approach	approach	NOUN
ejpam-6070	59	18	that	that	PRON
ejpam-6070	59	19	combines	combine	VERB
ejpam-6070	59	20	domain	domain	NOUN
ejpam-6070	59	21	decomposition	decomposition	NOUN
ejpam-6070	59	22	with	with	ADP
ejpam-6070	59	23	overlapping	overlap	VERB
ejpam-6070	59	24	subdomains	subdomain	NOUN
ejpam-6070	59	25	and	and	CCONJ
ejpam-6070	59	26	the	the	DET
ejpam-6070	59	27	sequence	sequence	NOUN
ejpam-6070	59	28	of	of	ADP
ejpam-6070	59	29	lower	low	ADJ
ejpam-6070	59	30	and	and	CCONJ
ejpam-6070	59	31	upper	upper	ADJ
ejpam-6070	59	32	solutions	solution	NOUN
ejpam-6070	59	33	to	to	PART
ejpam-6070	59	34	efficiently	efficiently	ADV
ejpam-6070	59	35	solve	solve	VERB
ejpam-6070	59	36	the	the	DET
ejpam-6070	59	37	hamilton	hamilton	PROPN
ejpam-6070	59	38	-	-	PUNCT
ejpam-6070	59	39	jacobi	jacobi	PROPN
ejpam-6070	59	40	-	-	PUNCT
ejpam-6070	59	41	bellman	bellman	NOUN
ejpam-6070	59	42	(	(	PUNCT
ejpam-6070	59	43	hjb	hjb	NOUN
ejpam-6070	59	44	)	)	PUNCT
ejpam-6070	59	45	equation	equation	NOUN
ejpam-6070	59	46	.	.	PUNCT
ejpam-6070	60	1	the	the	DET
ejpam-6070	60	2	computational	computational	ADJ
ejpam-6070	60	3	domain	domain	NOUN
ejpam-6070	60	4	is	be	AUX
ejpam-6070	60	5	divided	divide	VERB
ejpam-6070	60	6	into	into	ADP
ejpam-6070	60	7	overlapping	overlap	VERB
ejpam-6070	60	8	subdomains	subdomain	NOUN
ejpam-6070	60	9	,	,	PUNCT
ejpam-6070	60	10	which	which	PRON
ejpam-6070	60	11	enhances	enhance	VERB
ejpam-6070	60	12	numerical	numerical	ADJ
ejpam-6070	60	13	stability	stability	NOUN
ejpam-6070	60	14	.	.	PUNCT
ejpam-6070	61	1	we	we	PRON
ejpam-6070	61	2	establish	establish	VERB
ejpam-6070	61	3	the	the	DET
ejpam-6070	61	4	geometric	geometric	ADJ
ejpam-6070	61	5	and	and	CCONJ
ejpam-6070	61	6	monotonic	monotonic	ADJ
ejpam-6070	61	7	convergence	convergence	NOUN
ejpam-6070	61	8	towards	towards	ADP
ejpam-6070	61	9	the	the	DET
ejpam-6070	61	10	discrete	discrete	ADJ
ejpam-6070	61	11	solution	solution	NOUN
ejpam-6070	61	12	of	of	ADP
ejpam-6070	61	13	the	the	DET
ejpam-6070	61	14	problem	problem	NOUN
ejpam-6070	61	15	.	.	PUNCT
ejpam-6070	62	1	3.1	3.1	NUM
ejpam-6070	62	2	.	.	PUNCT
ejpam-6070	62	3	definition	definition	NOUN
ejpam-6070	62	4	of	of	ADP
ejpam-6070	62	5	subdomain	subdomain	NOUN
ejpam-6070	62	6	decomposition	decomposition	NOUN
ejpam-6070	62	7	we	we	PRON
ejpam-6070	62	8	examine	examine	VERB
ejpam-6070	62	9	a	a	DET
ejpam-6070	62	10	regular	regular	ADJ
ejpam-6070	62	11	and	and	CCONJ
ejpam-6070	62	12	bounded	bounded	ADJ
ejpam-6070	62	13	domain	domain	PROPN
ejpam-6070	62	14	ω	ω	PROPN
ejpam-6070	62	15	in	in	ADP
ejpam-6070	62	16	r2	r2	PROPN
ejpam-6070	62	17	,	,	PUNCT
ejpam-6070	62	18	which	which	PRON
ejpam-6070	62	19	is	be	AUX
ejpam-6070	62	20	partitioned	partition	VERB
ejpam-6070	62	21	into	into	ADP
ejpam-6070	62	22	two	two	NUM
ejpam-6070	62	23	subdomains	subdomain	NOUN
ejpam-6070	62	24	,	,	PUNCT
ejpam-6070	62	25	ω1	ω1	PROPN
ejpam-6070	62	26	and	and	CCONJ
ejpam-6070	62	27	ω2	ω2	ADJ
ejpam-6070	62	28	,	,	PUNCT
ejpam-6070	62	29	that	that	PRON
ejpam-6070	62	30	overlap	overlap	VERB
ejpam-6070	62	31	along	along	ADP
ejpam-6070	62	32	the	the	DET
ejpam-6070	62	33	x	x	NOUN
ejpam-6070	62	34	-	-	NOUN
ejpam-6070	62	35	axis	axis	ADJ
ejpam-6070	62	36	.	.	PUNCT
ejpam-6070	63	1	these	these	DET
ejpam-6070	63	2	subdomains	subdomain	NOUN
ejpam-6070	63	3	are	be	AUX
ejpam-6070	63	4	defined	define	VERB
ejpam-6070	63	5	by	by	ADP
ejpam-6070	63	6	the	the	DET
ejpam-6070	63	7	following	follow	VERB
ejpam-6070	63	8	relations	relation	NOUN
ejpam-6070	63	9	:	:	PUNCT
ejpam-6070	63	10	ω	ω	NUM
ejpam-6070	63	11	=	=	SYM
ejpam-6070	63	12	ω1	ω1	PROPN
ejpam-6070	63	13	∪	∪	X
ejpam-6070	63	14	ω2	ω2	ADJ
ejpam-6070	63	15	and	and	CCONJ
ejpam-6070	63	16	ω1	ω1	ADJ
ejpam-6070	63	17	∩	∩	PROPN
ejpam-6070	63	18	ω2	ω2	ADJ
ejpam-6070	63	19	̸=	̸=	PROPN
ejpam-6070	63	20	∅.	∅.	ADP
ejpam-6070	63	21	the	the	DET
ejpam-6070	63	22	boundaries	boundary	NOUN
ejpam-6070	63	23	of	of	ADP
ejpam-6070	63	24	each	each	DET
ejpam-6070	63	25	subdomain	subdomain	NOUN
ejpam-6070	63	26	are	be	AUX
ejpam-6070	63	27	denoted	denote	VERB
ejpam-6070	63	28	by	by	ADP
ejpam-6070	63	29	γ1	γ1	PROPN
ejpam-6070	63	30	=	=	SYM
ejpam-6070	63	31	∂ω1	∂ω1	PROPN
ejpam-6070	63	32	and	and	CCONJ
ejpam-6070	63	33	γ2	γ2	NOUN
ejpam-6070	63	34	=	=	SYM
ejpam-6070	63	35	∂ω2	∂ω2	PROPN
ejpam-6070	63	36	,	,	PUNCT
ejpam-6070	63	37	and	and	CCONJ
ejpam-6070	63	38	the	the	DET
ejpam-6070	63	39	interface	interface	NOUN
ejpam-6070	63	40	where	where	SCONJ
ejpam-6070	63	41	the	the	DET
ejpam-6070	63	42	subdomains	subdomain	NOUN
ejpam-6070	63	43	meet	meet	VERB
ejpam-6070	63	44	is	be	AUX
ejpam-6070	63	45	represented	represent	VERB
ejpam-6070	63	46	by	by	ADP
ejpam-6070	63	47	:	:	PUNCT
ejpam-6070	63	48	σ1	σ1	PROPN
ejpam-6070	63	49	=	=	SYM
ejpam-6070	64	1	∂ω1	∂ω1	PROPN
ejpam-6070	64	2	∩	∩	PROPN
ejpam-6070	64	3	ω2	ω2	ADJ
ejpam-6070	64	4	,	,	PUNCT
ejpam-6070	64	5	σ2	σ2	NOUN
ejpam-6070	64	6	=	=	SYM
ejpam-6070	64	7	∂ω2	∂ω2	PROPN
ejpam-6070	64	8	∩	∩	ADJ
ejpam-6070	64	9	ω1	ω1	PROPN
ejpam-6070	64	10	.	.	PROPN
ejpam-6070	64	11	figure	figure	NOUN
ejpam-6070	64	12	1	1	NUM
ejpam-6070	64	13	:	:	PUNCT
ejpam-6070	64	14	illustration	illustration	NOUN
ejpam-6070	64	15	of	of	ADP
ejpam-6070	64	16	the	the	DET
ejpam-6070	64	17	domain	domain	NOUN
ejpam-6070	64	18	ω	ω	NOUN
ejpam-6070	64	19	and	and	CCONJ
ejpam-6070	64	20	its	its	PRON
ejpam-6070	64	21	subdomains	subdomain	NOUN
ejpam-6070	64	22	.	.	PUNCT
ejpam-6070	65	1	s.	s.	PROPN
ejpam-6070	65	2	chebbah	chebbah	PROPN
ejpam-6070	65	3	,	,	PUNCT
ejpam-6070	65	4	s.	s.	PROPN
ejpam-6070	65	5	madi	madi	PROPN
ejpam-6070	65	6	,	,	PUNCT
ejpam-6070	65	7	m.	m.	NOUN
ejpam-6070	65	8	haiour	haiour	PROPN
ejpam-6070	65	9	/	/	SYM
ejpam-6070	65	10	eur	eur	PROPN
ejpam-6070	65	11	.	.	PUNCT
ejpam-6070	66	1	j.	j.	PROPN
ejpam-6070	66	2	pure	pure	PROPN
ejpam-6070	66	3	appl	appl	PROPN
ejpam-6070	66	4	.	.	PROPN
ejpam-6070	66	5	math	math	PROPN
ejpam-6070	66	6	,	,	PUNCT
ejpam-6070	66	7	18	18	NUM
ejpam-6070	66	8	(	(	PUNCT
ejpam-6070	66	9	2	2	NUM
ejpam-6070	66	10	)	)	PUNCT
ejpam-6070	66	11	(	(	PUNCT
ejpam-6070	66	12	2025	2025	NUM
ejpam-6070	66	13	)	)	PUNCT
ejpam-6070	66	14	,	,	PUNCT
ejpam-6070	66	15	6070	6070	NUM
ejpam-6070	66	16	5	5	NUM
ejpam-6070	66	17	of	of	ADP
ejpam-6070	66	18	20	20	NUM
ejpam-6070	66	19	the	the	DET
ejpam-6070	66	20	specific	specific	ADJ
ejpam-6070	66	21	case	case	NOUN
ejpam-6070	66	22	considered	consider	VERB
ejpam-6070	66	23	here	here	ADV
ejpam-6070	66	24	is	be	AUX
ejpam-6070	66	25	where	where	SCONJ
ejpam-6070	66	26	the	the	DET
ejpam-6070	66	27	domain	domain	NOUN
ejpam-6070	66	28	ω	ω	NOUN
ejpam-6070	66	29	is	be	AUX
ejpam-6070	66	30	defined	define	VERB
ejpam-6070	66	31	as	as	ADP
ejpam-6070	66	32	[	[	X
ejpam-6070	66	33	0	0	NUM
ejpam-6070	66	34	,	,	PUNCT
ejpam-6070	66	35	1	1	NUM
ejpam-6070	66	36	]	]	SYM
ejpam-6070	66	37	×	×	NOUN
ejpam-6070	67	1	[	[	X
ejpam-6070	67	2	0	0	NUM
ejpam-6070	67	3	,	,	PUNCT
ejpam-6070	67	4	1	1	NUM
ejpam-6070	67	5	]	]	PUNCT
ejpam-6070	67	6	.	.	PUNCT
ejpam-6070	68	1	this	this	DET
ejpam-6070	68	2	domain	domain	NOUN
ejpam-6070	68	3	is	be	AUX
ejpam-6070	68	4	then	then	ADV
ejpam-6070	68	5	subdivided	subdivide	VERB
ejpam-6070	68	6	into	into	ADP
ejpam-6070	68	7	two	two	NUM
ejpam-6070	68	8	overlapping	overlap	VERB
ejpam-6070	68	9	subdomains	subdomain	NOUN
ejpam-6070	68	10	:	:	PUNCT
ejpam-6070	68	11	ω1	ω1	PROPN
ejpam-6070	68	12	=	=	PUNCT
ejpam-6070	69	1	[	[	X
ejpam-6070	69	2	0	0	NUM
ejpam-6070	69	3	,	,	PUNCT
ejpam-6070	69	4	β]×	β]×	NOUN
ejpam-6070	70	1	[	[	X
ejpam-6070	70	2	0	0	NUM
ejpam-6070	70	3	,	,	PUNCT
ejpam-6070	70	4	1	1	NUM
ejpam-6070	70	5	]	]	PUNCT
ejpam-6070	70	6	,	,	PUNCT
ejpam-6070	70	7	ω2	ω2	NOUN
ejpam-6070	70	8	=	=	PUNCT
ejpam-6070	71	1	[	[	X
ejpam-6070	71	2	α	α	X
ejpam-6070	71	3	,	,	PUNCT
ejpam-6070	71	4	1]×	1]×	NUM
ejpam-6070	72	1	[	[	X
ejpam-6070	72	2	0	0	NUM
ejpam-6070	72	3	,	,	PUNCT
ejpam-6070	72	4	1	1	NUM
ejpam-6070	72	5	]	]	PUNCT
ejpam-6070	72	6	,	,	PUNCT
ejpam-6070	72	7	where	where	SCONJ
ejpam-6070	72	8	α	α	NOUN
ejpam-6070	72	9	and	and	CCONJ
ejpam-6070	72	10	β	β	PROPN
ejpam-6070	72	11	represent	represent	VERB
ejpam-6070	72	12	the	the	DET
ejpam-6070	72	13	boundaries	boundary	NOUN
ejpam-6070	72	14	that	that	PRON
ejpam-6070	72	15	define	define	VERB
ejpam-6070	72	16	the	the	DET
ejpam-6070	72	17	partition	partition	NOUN
ejpam-6070	72	18	.	.	PUNCT
ejpam-6070	73	1	the	the	DET
ejpam-6070	73	2	region	region	NOUN
ejpam-6070	73	3	of	of	ADP
ejpam-6070	73	4	overlap	overlap	NOUN
ejpam-6070	73	5	between	between	ADP
ejpam-6070	73	6	ω1	ω1	PROPN
ejpam-6070	73	7	and	and	CCONJ
ejpam-6070	73	8	ω2	ω2	NOUN
ejpam-6070	73	9	is	be	AUX
ejpam-6070	73	10	given	give	VERB
ejpam-6070	73	11	by	by	ADP
ejpam-6070	73	12	the	the	DET
ejpam-6070	73	13	interval	interval	NOUN
ejpam-6070	73	14	:	:	PUNCT
ejpam-6070	73	15	τ	τ	X
ejpam-6070	73	16	=	=	PUNCT
ejpam-6070	73	17	β	β	X
ejpam-6070	73	18	−	−	PROPN
ejpam-6070	73	19	α	α	NOUN
ejpam-6070	73	20	,	,	PUNCT
ejpam-6070	73	21	with	with	ADP
ejpam-6070	73	22	τ	τ	PROPN
ejpam-6070	73	23	representing	represent	VERB
ejpam-6070	73	24	the	the	DET
ejpam-6070	73	25	length	length	NOUN
ejpam-6070	73	26	of	of	ADP
ejpam-6070	73	27	the	the	DET
ejpam-6070	73	28	overlap	overlap	NOUN
ejpam-6070	73	29	.	.	PUNCT
ejpam-6070	74	1	additionally	additionally	ADV
ejpam-6070	74	2	,	,	PUNCT
ejpam-6070	74	3	the	the	DET
ejpam-6070	74	4	geometric	geometric	ADJ
ejpam-6070	74	5	length	length	NOUN
ejpam-6070	74	6	of	of	ADP
ejpam-6070	74	7	the	the	DET
ejpam-6070	74	8	overlap	overlap	NOUN
ejpam-6070	74	9	region	region	NOUN
ejpam-6070	74	10	is	be	AUX
ejpam-6070	74	11	quantified	quantify	VERB
ejpam-6070	74	12	as	as	ADP
ejpam-6070	74	13	:	:	PUNCT
ejpam-6070	74	14	χ(h	χ(h	X
ejpam-6070	74	15	)	)	PUNCT
ejpam-6070	74	16	=	=	PUNCT
ejpam-6070	75	1	τ	τ	PROPN
ejpam-6070	75	2	×	×	PROPN
ejpam-6070	75	3	h	h	NOUN
ejpam-6070	75	4	,	,	PUNCT
ejpam-6070	75	5	where	where	SCONJ
ejpam-6070	75	6	h	h	NOUN
ejpam-6070	75	7	is	be	AUX
ejpam-6070	75	8	a	a	DET
ejpam-6070	75	9	scaling	scale	VERB
ejpam-6070	75	10	factor	factor	NOUN
ejpam-6070	75	11	.	.	PUNCT
ejpam-6070	76	1	3.2	3.2	NUM
ejpam-6070	76	2	.	.	PUNCT
ejpam-6070	77	1	block	block	NOUN
ejpam-6070	77	2	decomposition	decomposition	NOUN
ejpam-6070	77	3	of	of	ADP
ejpam-6070	77	4	the	the	DET
ejpam-6070	77	5	domain	domain	NOUN
ejpam-6070	77	6	matrix	matrix	NOUN
ejpam-6070	77	7	we	we	PRON
ejpam-6070	77	8	consider	consider	VERB
ejpam-6070	77	9	the	the	DET
ejpam-6070	77	10	matrices	matrix	NOUN
ejpam-6070	77	11	bi	bi	NOUN
ejpam-6070	77	12	of	of	ADP
ejpam-6070	77	13	dimension	dimension	NOUN
ejpam-6070	77	14	(	(	PUNCT
ejpam-6070	77	15	d×	d×	NOUN
ejpam-6070	77	16	d	d	PROPN
ejpam-6070	77	17	)	)	PUNCT
ejpam-6070	77	18	,	,	PUNCT
ejpam-6070	77	19	which	which	PRON
ejpam-6070	77	20	are	be	AUX
ejpam-6070	77	21	associated	associate	VERB
ejpam-6070	77	22	with	with	ADP
ejpam-6070	77	23	vectors	vector	NOUN
ejpam-6070	77	24	that	that	PRON
ejpam-6070	77	25	can	can	AUX
ejpam-6070	77	26	be	be	AUX
ejpam-6070	77	27	partitioned	partition	VERB
ejpam-6070	77	28	into	into	ADP
ejpam-6070	77	29	block	block	NOUN
ejpam-6070	77	30	form	form	NOUN
ejpam-6070	77	31	as	as	SCONJ
ejpam-6070	77	32	follows	follow	VERB
ejpam-6070	77	33	:	:	PUNCT
ejpam-6070	77	34	ζ	ζ	NOUN
ejpam-6070	77	35	=	=	SYM
ejpam-6070	77	36	(	(	PUNCT
ejpam-6070	77	37	ζ1	ζ1	NOUN
ejpam-6070	77	38	ζ2	ζ2	NOUN
ejpam-6070	77	39	)	)	PUNCT
ejpam-6070	77	40	,	,	PUNCT
ejpam-6070	77	41	g	g	PROPN
ejpam-6070	77	42	i(ζ	i(ζ	PROPN
ejpam-6070	77	43	)	)	PUNCT
ejpam-6070	78	1	=	=	PRON
ejpam-6070	78	2	(	(	PUNCT
ejpam-6070	78	3	g	g	PROPN
ejpam-6070	78	4	i(ζ1	i(ζ1	PROPN
ejpam-6070	78	5	)	)	PUNCT
ejpam-6070	78	6	g	g	PROPN
ejpam-6070	78	7	i(ζ2	i(ζ2	PROPN
ejpam-6070	78	8	)	)	PUNCT
ejpam-6070	78	9	)	)	PUNCT
ejpam-6070	78	10	,	,	PUNCT
ejpam-6070	78	11	bi	bi	NOUN
ejpam-6070	78	12	=	=	PRON
ejpam-6070	78	13	(	(	PUNCT
ejpam-6070	78	14	bi	bi	NOUN
ejpam-6070	78	15	1,1	1,1	NUM
ejpam-6070	78	16	−bi	−bi	NOUN
ejpam-6070	78	17	1,2	1,2	NUM
ejpam-6070	78	18	−bi	−bi	NOUN
ejpam-6070	78	19	2,1	2,1	NUM
ejpam-6070	78	20	bi	bi	NOUN
ejpam-6070	78	21	2,2	2,2	NUM
ejpam-6070	78	22	)	)	PUNCT
ejpam-6070	78	23	.	.	PUNCT
ejpam-6070	79	1	here	here	ADV
ejpam-6070	79	2	,	,	PUNCT
ejpam-6070	79	3	the	the	DET
ejpam-6070	79	4	vectors	vector	NOUN
ejpam-6070	79	5	ζ1	ζ1	NOUN
ejpam-6070	79	6	and	and	CCONJ
ejpam-6070	79	7	ζ2	ζ2	NOUN
ejpam-6070	79	8	are	be	AUX
ejpam-6070	79	9	defined	define	VERB
ejpam-6070	79	10	as	as	ADP
ejpam-6070	79	11	:	:	PUNCT
ejpam-6070	79	12	ζ1	ζ1	NOUN
ejpam-6070	79	13	=	=	SYM
ejpam-6070	79	14	(	(	PUNCT
ejpam-6070	79	15	(	(	PUNCT
ejpam-6070	79	16	ζ1)1	ζ1)1	NOUN
ejpam-6070	79	17	,	,	PUNCT
ejpam-6070	79	18	.	.	PUNCT
ejpam-6070	79	19	.	.	PUNCT
ejpam-6070	79	20	.	.	PUNCT
ejpam-6070	80	1	,	,	PUNCT
ejpam-6070	80	2	(	(	PUNCT
ejpam-6070	80	3	ζ1)β−1	ζ1)β−1	NOUN
ejpam-6070	80	4	)	)	PUNCT
ejpam-6070	80	5	t	t	NOUN
ejpam-6070	80	6	,	,	PUNCT
ejpam-6070	80	7	ζ2	ζ2	NOUN
ejpam-6070	80	8	=	=	SYM
ejpam-6070	80	9	(	(	PUNCT
ejpam-6070	80	10	(	(	PUNCT
ejpam-6070	80	11	ζ2)α+1	ζ2)α+1	NOUN
ejpam-6070	80	12	,	,	PUNCT
ejpam-6070	80	13	.	.	PUNCT
ejpam-6070	80	14	.	.	PUNCT
ejpam-6070	80	15	.	.	PUNCT
ejpam-6070	81	1	,	,	PUNCT
ejpam-6070	81	2	(	(	PUNCT
ejpam-6070	81	3	ζ2)d	ζ2)d	NOUN
ejpam-6070	81	4	)	)	PUNCT
ejpam-6070	81	5	t	t	NOUN
ejpam-6070	81	6	.	.	PUNCT
ejpam-6070	82	1	to	to	PART
ejpam-6070	82	2	construct	construct	VERB
ejpam-6070	82	3	the	the	DET
ejpam-6070	82	4	matrix	matrix	NOUN
ejpam-6070	82	5	bi	bi	NOUN
ejpam-6070	82	6	using	use	VERB
ejpam-6070	82	7	the	the	DET
ejpam-6070	82	8	domain	domain	NOUN
ejpam-6070	82	9	decomposition	decomposition	NOUN
ejpam-6070	82	10	method	method	NOUN
ejpam-6070	82	11	,	,	PUNCT
ejpam-6070	82	12	we	we	PRON
ejpam-6070	82	13	partition	partition	VERB
ejpam-6070	82	14	it	it	PRON
ejpam-6070	82	15	into	into	ADP
ejpam-6070	82	16	two	two	NUM
ejpam-6070	82	17	different	different	ADJ
ejpam-6070	82	18	forms	form	NOUN
ejpam-6070	82	19	within	within	ADP
ejpam-6070	82	20	each	each	DET
ejpam-6070	82	21	subdomain	subdomain	NOUN
ejpam-6070	82	22	.	.	PUNCT
ejpam-6070	83	1	the	the	DET
ejpam-6070	83	2	decomposition	decomposition	NOUN
ejpam-6070	83	3	for	for	ADP
ejpam-6070	83	4	the	the	DET
ejpam-6070	83	5	first	first	ADJ
ejpam-6070	83	6	subdomain	subdomain	NOUN
ejpam-6070	83	7	is	be	AUX
ejpam-6070	83	8	defined	define	VERB
ejpam-6070	83	9	as	as	SCONJ
ejpam-6070	83	10	follows	follow	VERB
ejpam-6070	83	11	:	:	PUNCT
ejpam-6070	84	1	bi	bi	NOUN
ejpam-6070	84	2	=	=	PRON
ejpam-6070	84	3	(	(	PUNCT
ejpam-6070	84	4	bi	bi	NOUN
ejpam-6070	84	5	1,1	1,1	NUM
ejpam-6070	84	6	−bi	−bi	NOUN
ejpam-6070	84	7	1,2	1,2	NUM
ejpam-6070	84	8	c	c	NOUN
ejpam-6070	84	9	i	i	PRON
ejpam-6070	84	10	1	1	NUM
ejpam-6070	84	11	d	d	NOUN
ejpam-6070	84	12	i	i	PRON
ejpam-6070	84	13	1	1	NUM
ejpam-6070	84	14	)	)	PUNCT
ejpam-6070	84	15	,	,	PUNCT
ejpam-6070	84	16	where	where	SCONJ
ejpam-6070	84	17	:	:	PUNCT
ejpam-6070	84	18	•	•	NUM
ejpam-6070	84	19	bi	bi	NOUN
ejpam-6070	84	20	1,1	1,1	NUM
ejpam-6070	85	1	and	and	CCONJ
ejpam-6070	85	2	d	d	NOUN
ejpam-6070	85	3	i	i	PRON
ejpam-6070	85	4	1	1	NUM
ejpam-6070	85	5	are	be	AUX
ejpam-6070	85	6	square	square	ADJ
ejpam-6070	85	7	matrices	matrix	NOUN
ejpam-6070	85	8	of	of	ADP
ejpam-6070	85	9	dimensions	dimension	NOUN
ejpam-6070	85	10	(	(	PUNCT
ejpam-6070	85	11	β−	β−	NOUN
ejpam-6070	85	12	1)×	1)×	NUM
ejpam-6070	85	13	(	(	PUNCT
ejpam-6070	85	14	β−	β−	NOUN
ejpam-6070	85	15	1	1	NUM
ejpam-6070	85	16	)	)	PUNCT
ejpam-6070	85	17	and	and	CCONJ
ejpam-6070	85	18	(	(	PUNCT
ejpam-6070	85	19	d−	d−	PROPN
ejpam-6070	85	20	β+1)×	β+1)×	PROPN
ejpam-6070	85	21	(	(	PUNCT
ejpam-6070	85	22	d−	d−	PROPN
ejpam-6070	85	23	β	β	X
ejpam-6070	85	24	+	+	NOUN
ejpam-6070	85	25	1	1	NUM
ejpam-6070	85	26	)	)	PUNCT
ejpam-6070	85	27	respectively	respectively	ADV
ejpam-6070	85	28	.	.	PUNCT
ejpam-6070	86	1	•	•	NUM
ejpam-6070	86	2	bi	bi	NOUN
ejpam-6070	86	3	1,2	1,2	NUM
ejpam-6070	86	4	and	and	CCONJ
ejpam-6070	86	5	c	c	NOUN
ejpam-6070	86	6	i	i	PRON
ejpam-6070	86	7	1	1	NUM
ejpam-6070	86	8	are	be	AUX
ejpam-6070	86	9	of	of	ADP
ejpam-6070	86	10	dimensions	dimension	NOUN
ejpam-6070	86	11	(	(	PUNCT
ejpam-6070	86	12	β	β	NOUN
ejpam-6070	86	13	−	−	NOUN
ejpam-6070	86	14	1	1	NUM
ejpam-6070	86	15	)	)	PUNCT
ejpam-6070	86	16	×	×	NOUN
ejpam-6070	86	17	(	(	PUNCT
ejpam-6070	86	18	d	d	NOUN
ejpam-6070	86	19	−	−	X
ejpam-6070	86	20	β	β	NOUN
ejpam-6070	87	1	+	+	NOUN
ejpam-6070	87	2	1	1	NUM
ejpam-6070	87	3	)	)	PUNCT
ejpam-6070	87	4	and	and	CCONJ
ejpam-6070	87	5	(	(	PUNCT
ejpam-6070	87	6	d	d	PART
ejpam-6070	87	7	−	−	X
ejpam-6070	87	8	β	β	NOUN
ejpam-6070	87	9	+	+	NOUN
ejpam-6070	87	10	1	1	X
ejpam-6070	87	11	)	)	PUNCT
ejpam-6070	87	12	×	×	NOUN
ejpam-6070	87	13	(	(	PUNCT
ejpam-6070	87	14	β	β	NOUN
ejpam-6070	87	15	−	−	NOUN
ejpam-6070	87	16	1	1	NUM
ejpam-6070	87	17	)	)	PUNCT
ejpam-6070	87	18	respectively	respectively	ADV
ejpam-6070	87	19	.	.	PUNCT
ejpam-6070	88	1	the	the	DET
ejpam-6070	88	2	second	second	ADJ
ejpam-6070	88	3	partition	partition	NOUN
ejpam-6070	88	4	of	of	ADP
ejpam-6070	88	5	the	the	DET
ejpam-6070	88	6	matrix	matrix	NOUN
ejpam-6070	88	7	bi	bi	NOUN
ejpam-6070	88	8	is	be	AUX
ejpam-6070	88	9	as	as	SCONJ
ejpam-6070	88	10	follows	follow	VERB
ejpam-6070	88	11	:	:	PUNCT
ejpam-6070	88	12	bi	bi	NOUN
ejpam-6070	88	13	=	=	PRON
ejpam-6070	88	14	(	(	PUNCT
ejpam-6070	88	15	d	d	X
ejpam-6070	88	16	i	i	PRON
ejpam-6070	88	17	2	2	NUM
ejpam-6070	88	18	c	c	NOUN
ejpam-6070	88	19	i	i	NOUN
ejpam-6070	88	20	2	2	NUM
ejpam-6070	88	21	−bi	−bi	NOUN
ejpam-6070	88	22	2,1	2,1	NUM
ejpam-6070	88	23	bi	bi	NOUN
ejpam-6070	88	24	2,2	2,2	NUM
ejpam-6070	88	25	)	)	PUNCT
ejpam-6070	88	26	,	,	PUNCT
ejpam-6070	88	27	where	where	SCONJ
ejpam-6070	88	28	:	:	PUNCT
ejpam-6070	88	29	s.	s.	PROPN
ejpam-6070	88	30	chebbah	chebbah	PROPN
ejpam-6070	88	31	,	,	PUNCT
ejpam-6070	88	32	s.	s.	PROPN
ejpam-6070	88	33	madi	madi	PROPN
ejpam-6070	88	34	,	,	PUNCT
ejpam-6070	88	35	m.	m.	NOUN
ejpam-6070	88	36	haiour	haiour	PROPN
ejpam-6070	88	37	/	/	SYM
ejpam-6070	88	38	eur	eur	PROPN
ejpam-6070	88	39	.	.	PUNCT
ejpam-6070	89	1	j.	j.	PROPN
ejpam-6070	89	2	pure	pure	PROPN
ejpam-6070	89	3	appl	appl	PROPN
ejpam-6070	89	4	.	.	PROPN
ejpam-6070	89	5	math	math	PROPN
ejpam-6070	89	6	,	,	PUNCT
ejpam-6070	89	7	18	18	NUM
ejpam-6070	89	8	(	(	PUNCT
ejpam-6070	89	9	2	2	NUM
ejpam-6070	89	10	)	)	PUNCT
ejpam-6070	89	11	(	(	PUNCT
ejpam-6070	89	12	2025	2025	NUM
ejpam-6070	89	13	)	)	PUNCT
ejpam-6070	89	14	,	,	PUNCT
ejpam-6070	89	15	6070	6070	NUM
ejpam-6070	89	16	6	6	NUM
ejpam-6070	89	17	of	of	ADP
ejpam-6070	89	18	20	20	NUM
ejpam-6070	89	19	•	•	NOUN
ejpam-6070	89	20	bi	bi	NOUN
ejpam-6070	89	21	2,2	2,2	NUM
ejpam-6070	89	22	and	and	CCONJ
ejpam-6070	89	23	d	d	NOUN
ejpam-6070	89	24	i	i	PRON
ejpam-6070	89	25	2	2	NUM
ejpam-6070	89	26	are	be	AUX
ejpam-6070	89	27	square	square	ADJ
ejpam-6070	89	28	matrices	matrix	NOUN
ejpam-6070	89	29	of	of	ADP
ejpam-6070	89	30	dimensions	dimension	NOUN
ejpam-6070	89	31	(	(	PUNCT
ejpam-6070	89	32	d	d	NOUN
ejpam-6070	89	33	−	−	PROPN
ejpam-6070	89	34	α	α	NUM
ejpam-6070	89	35	)	)	PUNCT
ejpam-6070	89	36	×	×	NOUN
ejpam-6070	89	37	(	(	PUNCT
ejpam-6070	89	38	d	d	NOUN
ejpam-6070	89	39	−	−	PROPN
ejpam-6070	89	40	α	α	NUM
ejpam-6070	89	41	)	)	PUNCT
ejpam-6070	89	42	and	and	CCONJ
ejpam-6070	89	43	α	α	DET
ejpam-6070	89	44	×	×	NOUN
ejpam-6070	89	45	α	α	PRON
ejpam-6070	89	46	respectively	respectively	ADV
ejpam-6070	89	47	.	.	PUNCT
ejpam-6070	90	1	•	•	NUM
ejpam-6070	90	2	bi	bi	NOUN
ejpam-6070	90	3	2,1	2,1	NUM
ejpam-6070	91	1	and	and	CCONJ
ejpam-6070	91	2	c	c	NOUN
ejpam-6070	91	3	i	i	PRON
ejpam-6070	91	4	2	2	NUM
ejpam-6070	91	5	are	be	AUX
ejpam-6070	91	6	of	of	ADP
ejpam-6070	91	7	dimensions	dimension	NOUN
ejpam-6070	91	8	(	(	PUNCT
ejpam-6070	91	9	d−	d−	PROPN
ejpam-6070	91	10	α)×	α)×	NUM
ejpam-6070	91	11	α	α	NOUN
ejpam-6070	91	12	and	and	CCONJ
ejpam-6070	91	13	α×	α×	PROPN
ejpam-6070	91	14	(	(	PUNCT
ejpam-6070	91	15	d−	d−	PROPN
ejpam-6070	91	16	α	α	NUM
ejpam-6070	91	17	)	)	PUNCT
ejpam-6070	91	18	respectively	respectively	ADV
ejpam-6070	91	19	.	.	PUNCT
ejpam-6070	92	1	when	when	SCONJ
ejpam-6070	92	2	β	β	X
ejpam-6070	92	3	=	=	PUNCT
ejpam-6070	92	4	α	α	PROPN
ejpam-6070	92	5	+	+	NOUN
ejpam-6070	92	6	1	1	NUM
ejpam-6070	92	7	(	(	PUNCT
ejpam-6070	92	8	i.e.	i.e.	X
ejpam-6070	92	9	,	,	PUNCT
ejpam-6070	92	10	τ	τ	PROPN
ejpam-6070	92	11	=	=	SYM
ejpam-6070	92	12	1	1	NUM
ejpam-6070	92	13	)	)	PUNCT
ejpam-6070	92	14	,	,	PUNCT
ejpam-6070	92	15	the	the	DET
ejpam-6070	92	16	matrices	matrix	NOUN
ejpam-6070	92	17	bi	bi	NOUN
ejpam-6070	92	18	1,1	1,1	NUM
ejpam-6070	93	1	and	and	CCONJ
ejpam-6070	93	2	d	d	NOUN
ejpam-6070	93	3	i	i	PROPN
ejpam-6070	93	4	2	2	NUM
ejpam-6070	93	5	coincide	coincide	NOUN
ejpam-6070	93	6	,	,	PUNCT
ejpam-6070	93	7	and	and	CCONJ
ejpam-6070	93	8	similarly	similarly	ADV
ejpam-6070	93	9	,	,	PUNCT
ejpam-6070	93	10	bi	bi	NOUN
ejpam-6070	93	11	2,2	2,2	NUM
ejpam-6070	93	12	and	and	CCONJ
ejpam-6070	93	13	d	d	NOUN
ejpam-6070	93	14	i	i	PROPN
ejpam-6070	93	15	1	1	NUM
ejpam-6070	93	16	coincide	coincide	NOUN
ejpam-6070	93	17	.	.	PUNCT
ejpam-6070	94	1	this	this	DET
ejpam-6070	94	2	results	result	VERB
ejpam-6070	94	3	in	in	ADP
ejpam-6070	94	4	minimal	minimal	ADJ
ejpam-6070	94	5	geometric	geometric	ADJ
ejpam-6070	94	6	overlap	overlap	NOUN
ejpam-6070	94	7	and	and	CCONJ
ejpam-6070	94	8	complete	complete	ADJ
ejpam-6070	94	9	exclusion	exclusion	NOUN
ejpam-6070	94	10	of	of	ADP
ejpam-6070	94	11	algebraic	algebraic	ADJ
ejpam-6070	94	12	overlap	overlap	NOUN
ejpam-6070	94	13	.	.	PUNCT
ejpam-6070	95	1	additionally	additionally	ADV
ejpam-6070	95	2	:	:	PUNCT
ejpam-6070	95	3	bi	bi	PROPN
ejpam-6070	95	4	1,1	1,1	NUM
ejpam-6070	95	5	and	and	CCONJ
ejpam-6070	95	6	bi	bi	PROPN
ejpam-6070	95	7	2,2	2,2	PROPN
ejpam-6070	95	8	correspond	correspond	NOUN
ejpam-6070	95	9	to	to	ADP
ejpam-6070	95	10	the	the	DET
ejpam-6070	95	11	discretized	discretized	ADJ
ejpam-6070	95	12	operators	operator	NOUN
ejpam-6070	95	13	under	under	ADP
ejpam-6070	95	14	homogeneous	homogeneous	ADJ
ejpam-6070	95	15	dirichlet	dirichlet	PROPN
ejpam-6070	95	16	boundary	boundary	PROPN
ejpam-6070	95	17	conditions	condition	NOUN
ejpam-6070	95	18	.	.	PUNCT
ejpam-6070	96	1	to	to	PART
ejpam-6070	96	2	ensure	ensure	VERB
ejpam-6070	96	3	that	that	SCONJ
ejpam-6070	96	4	the	the	DET
ejpam-6070	96	5	enhanced	enhanced	ADJ
ejpam-6070	96	6	system	system	NOUN
ejpam-6070	96	7	remains	remain	VERB
ejpam-6070	96	8	consistent	consistent	ADJ
ejpam-6070	96	9	with	with	ADP
ejpam-6070	96	10	the	the	DET
ejpam-6070	96	11	original	original	ADJ
ejpam-6070	96	12	system	system	NOUN
ejpam-6070	96	13	despite	despite	SCONJ
ejpam-6070	96	14	the	the	DET
ejpam-6070	96	15	overlapping	overlap	VERB
ejpam-6070	96	16	region	region	NOUN
ejpam-6070	96	17	,	,	PUNCT
ejpam-6070	96	18	the	the	DET
ejpam-6070	96	19	non	non	ADJ
ejpam-6070	96	20	-	-	ADJ
ejpam-6070	96	21	diagonal	diagonal	ADJ
ejpam-6070	96	22	blocks	block	NOUN
ejpam-6070	96	23	bi	bi	PROPN
ejpam-6070	96	24	2,1	2,1	NUM
ejpam-6070	96	25	and	and	CCONJ
ejpam-6070	96	26	bi	bi	NOUN
ejpam-6070	96	27	1,2	1,2	NUM
ejpam-6070	96	28	are	be	AUX
ejpam-6070	96	29	extended	extend	VERB
ejpam-6070	96	30	by	by	ADP
ejpam-6070	96	31	adding	add	VERB
ejpam-6070	96	32	rows	row	NOUN
ejpam-6070	96	33	and	and	CCONJ
ejpam-6070	96	34	columns	column	NOUN
ejpam-6070	96	35	filled	fill	VERB
ejpam-6070	96	36	with	with	ADP
ejpam-6070	96	37	zeros	zero	NOUN
ejpam-6070	96	38	.	.	PUNCT
ejpam-6070	97	1	the	the	DET
ejpam-6070	97	2	resulting	result	VERB
ejpam-6070	97	3	extended	extend	VERB
ejpam-6070	97	4	matrices	matrix	NOUN
ejpam-6070	97	5	are	be	AUX
ejpam-6070	97	6	defined	define	VERB
ejpam-6070	97	7	as	as	SCONJ
ejpam-6070	97	8	follows	follow	VERB
ejpam-6070	97	9	:	:	PUNCT
ejpam-6070	97	10	b̃i	b̃i	ADP
ejpam-6070	97	11	1,2	1,2	NUM
ejpam-6070	97	12	=	=	SYM
ejpam-6070	97	13	[	[	PUNCT
ejpam-6070	97	14	0β−1,τ−1	0β−1,τ−1	NUM
ejpam-6070	97	15	bi	bi	NOUN
ejpam-6070	97	16	1,2	1,2	NUM
ejpam-6070	97	17	]	]	PUNCT
ejpam-6070	97	18	,	,	PUNCT
ejpam-6070	97	19	b̃i	b̃i	ADP
ejpam-6070	97	20	2,1	2,1	NUM
ejpam-6070	97	21	=	=	SYM
ejpam-6070	97	22	[	[	PUNCT
ejpam-6070	97	23	bi	bi	NOUN
ejpam-6070	97	24	2,1	2,1	NUM
ejpam-6070	97	25	0d−α	0d−α	NOUN
ejpam-6070	97	26	,	,	PUNCT
ejpam-6070	97	27	τ−1	τ−1	PROPN
ejpam-6070	97	28	]	]	PUNCT
ejpam-6070	97	29	.	.	PUNCT
ejpam-6070	98	1	where	where	SCONJ
ejpam-6070	98	2	:	:	PUNCT
ejpam-6070	98	3	•	•	NUM
ejpam-6070	98	4	b̃i	b̃i	ADP
ejpam-6070	98	5	1,2	1,2	NUM
ejpam-6070	98	6	is	be	AUX
ejpam-6070	98	7	a	a	DET
ejpam-6070	98	8	matrix	matrix	NOUN
ejpam-6070	98	9	of	of	ADP
ejpam-6070	98	10	size	size	NOUN
ejpam-6070	98	11	(	(	PUNCT
ejpam-6070	98	12	β−1)×	β−1)×	PROPN
ejpam-6070	98	13	(	(	PUNCT
ejpam-6070	98	14	d−α	d−α	NOUN
ejpam-6070	98	15	)	)	PUNCT
ejpam-6070	98	16	that	that	PRON
ejpam-6070	98	17	connects	connect	VERB
ejpam-6070	98	18	a	a	DET
ejpam-6070	98	19	vector	vector	NOUN
ejpam-6070	98	20	from	from	ADP
ejpam-6070	98	21	ω2	ω2	ADJ
ejpam-6070	98	22	to	to	ADP
ejpam-6070	98	23	ω1	ω1	PROPN
ejpam-6070	98	24	with	with	ADP
ejpam-6070	98	25	zero	zero	NUM
ejpam-6070	98	26	entries	entry	NOUN
ejpam-6070	98	27	outside	outside	ADP
ejpam-6070	98	28	of	of	ADP
ejpam-6070	98	29	ω2	ω2	ADJ
ejpam-6070	98	30	.	.	PUNCT
ejpam-6070	98	31	•	•	NUM
ejpam-6070	98	32	b̃i	b̃i	SCONJ
ejpam-6070	98	33	2,1	2,1	NUM
ejpam-6070	98	34	is	be	AUX
ejpam-6070	98	35	a	a	DET
ejpam-6070	98	36	matrix	matrix	NOUN
ejpam-6070	98	37	of	of	ADP
ejpam-6070	98	38	size	size	NOUN
ejpam-6070	98	39	(	(	PUNCT
ejpam-6070	98	40	d	d	NOUN
ejpam-6070	98	41	−	−	PROPN
ejpam-6070	98	42	α	α	NUM
ejpam-6070	98	43	)	)	PUNCT
ejpam-6070	98	44	×	×	NOUN
ejpam-6070	98	45	(	(	PUNCT
ejpam-6070	98	46	β	β	NOUN
ejpam-6070	98	47	−	−	NOUN
ejpam-6070	98	48	1	1	NUM
ejpam-6070	98	49	)	)	PUNCT
ejpam-6070	98	50	that	that	PRON
ejpam-6070	98	51	connects	connect	VERB
ejpam-6070	98	52	a	a	DET
ejpam-6070	98	53	vector	vector	NOUN
ejpam-6070	98	54	from	from	ADP
ejpam-6070	98	55	ω1	ω1	PROPN
ejpam-6070	98	56	to	to	ADP
ejpam-6070	98	57	ω2	ω2	NUM
ejpam-6070	98	58	,	,	PUNCT
ejpam-6070	98	59	with	with	ADP
ejpam-6070	98	60	zero	zero	NUM
ejpam-6070	98	61	entries	entry	NOUN
ejpam-6070	98	62	outside	outside	ADP
ejpam-6070	98	63	of	of	ADP
ejpam-6070	98	64	ω1	ω1	PROPN
ejpam-6070	98	65	.	.	PUNCT
ejpam-6070	99	1	the	the	DET
ejpam-6070	99	2	extended	extended	ADJ
ejpam-6070	99	3	system	system	NOUN
ejpam-6070	99	4	satisfies	satisfy	VERB
ejpam-6070	99	5	the	the	DET
ejpam-6070	99	6	following	follow	VERB
ejpam-6070	99	7	equations:max	equations:max	PROPN
ejpam-6070	99	8	1≤i≤n	1≤i≤n	NUM
ejpam-6070	99	9	(	(	PUNCT
ejpam-6070	99	10	b̃iζ	b̃iζ	PROPN
ejpam-6070	99	11	−	−	NOUN
ejpam-6070	99	12	g	g	NOUN
ejpam-6070	99	13	i(ζ	i(ζ	NOUN
ejpam-6070	99	14	)	)	PUNCT
ejpam-6070	99	15	)	)	PUNCT
ejpam-6070	100	1	=	=	SYM
ejpam-6070	100	2	0	0	NUM
ejpam-6070	100	3	,	,	PUNCT
ejpam-6070	100	4	inω	inω	ADJ
ejpam-6070	100	5	,	,	PUNCT
ejpam-6070	100	6	ζ	ζ	NOUN
ejpam-6070	100	7	=	=	SYM
ejpam-6070	100	8	0	0	NUM
ejpam-6070	100	9	,	,	PUNCT
ejpam-6070	100	10	on	on	ADP
ejpam-6070	100	11	∂ω	∂ω	PROPN
ejpam-6070	100	12	.	.	PUNCT
ejpam-6070	101	1	in	in	ADP
ejpam-6070	101	2	the	the	DET
ejpam-6070	101	3	minimal	minimal	ADJ
ejpam-6070	101	4	overlap	overlap	NOUN
ejpam-6070	101	5	case	case	NOUN
ejpam-6070	101	6	(	(	PUNCT
ejpam-6070	101	7	τ	τ	X
ejpam-6070	101	8	=	=	SYM
ejpam-6070	101	9	1	1	NUM
ejpam-6070	101	10	)	)	PUNCT
ejpam-6070	101	11	,	,	PUNCT
ejpam-6070	101	12	the	the	DET
ejpam-6070	101	13	extended	extended	ADJ
ejpam-6070	101	14	system	system	NOUN
ejpam-6070	101	15	simplifies	simplifie	NOUN
ejpam-6070	101	16	to	to	ADP
ejpam-6070	101	17	the	the	DET
ejpam-6070	101	18	original	original	ADJ
ejpam-6070	101	19	matrix	matrix	NOUN
ejpam-6070	101	20	associated	associate	VERB
ejpam-6070	101	21	with	with	ADP
ejpam-6070	101	22	the	the	DET
ejpam-6070	101	23	domain	domain	NOUN
ejpam-6070	101	24	partition	partition	NOUN
ejpam-6070	101	25	without	without	ADP
ejpam-6070	101	26	any	any	DET
ejpam-6070	101	27	overlap	overlap	NOUN
ejpam-6070	101	28	.	.	PUNCT
ejpam-6070	102	1	this	this	PRON
ejpam-6070	102	2	is	be	AUX
ejpam-6070	102	3	expressed	express	VERB
ejpam-6070	102	4	by	by	ADP
ejpam-6070	102	5	the	the	DET
ejpam-6070	102	6	following	follow	VERB
ejpam-6070	102	7	relation	relation	NOUN
ejpam-6070	102	8	:	:	PUNCT
ejpam-6070	102	9	b̃i	b̃i	X
ejpam-6070	102	10	=	=	SYM
ejpam-6070	102	11	(	(	PUNCT
ejpam-6070	102	12	bi	bi	NOUN
ejpam-6070	102	13	1,1	1,1	NUM
ejpam-6070	102	14	−b̃i	−b̃i	SYM
ejpam-6070	102	15	1,2	1,2	NUM
ejpam-6070	102	16	−b̃i	−b̃i	ADP
ejpam-6070	102	17	2,1	2,1	NUM
ejpam-6070	102	18	bi	bi	NOUN
ejpam-6070	102	19	2,2	2,2	NUM
ejpam-6070	102	20	)	)	PUNCT
ejpam-6070	102	21	=	=	PUNCT
ejpam-6070	103	1	(	(	PUNCT
ejpam-6070	103	2	bi	bi	NOUN
ejpam-6070	103	3	1,1	1,1	NUM
ejpam-6070	103	4	−bi	−bi	NOUN
ejpam-6070	103	5	1,2	1,2	NUM
ejpam-6070	103	6	−bi	−bi	NOUN
ejpam-6070	103	7	2,1	2,1	NUM
ejpam-6070	103	8	bi	bi	NOUN
ejpam-6070	103	9	2,2	2,2	NUM
ejpam-6070	103	10	)	)	PUNCT
ejpam-6070	104	1	=	=	SYM
ejpam-6070	104	2	bi	bi	NOUN
ejpam-6070	104	3	.	.	PROPN
ejpam-6070	104	4	3.3	3.3	NUM
ejpam-6070	104	5	.	.	PUNCT
ejpam-6070	105	1	iterative	iterative	ADJ
ejpam-6070	105	2	algorithm	algorithm	NOUN
ejpam-6070	105	3	for	for	ADP
ejpam-6070	105	4	domain	domain	NOUN
ejpam-6070	105	5	decomposition	decomposition	NOUN
ejpam-6070	105	6	the	the	DET
ejpam-6070	105	7	iterative	iterative	NOUN
ejpam-6070	105	8	process	process	NOUN
ejpam-6070	105	9	begins	begin	VERB
ejpam-6070	105	10	with	with	ADP
ejpam-6070	105	11	selecting	select	VERB
ejpam-6070	105	12	an	an	DET
ejpam-6070	105	13	initial	initial	ADJ
ejpam-6070	105	14	solution	solution	NOUN
ejpam-6070	105	15	,	,	PUNCT
ejpam-6070	105	16	either	either	CCONJ
ejpam-6070	105	17	a	a	DET
ejpam-6070	105	18	lower	low	ADJ
ejpam-6070	105	19	or	or	CCONJ
ejpam-6070	105	20	an	an	DET
ejpam-6070	105	21	upper	upper	ADJ
ejpam-6070	105	22	one	one	NOUN
ejpam-6070	105	23	,	,	PUNCT
ejpam-6070	105	24	depending	depend	VERB
ejpam-6070	105	25	on	on	ADP
ejpam-6070	105	26	the	the	DET
ejpam-6070	105	27	nature	nature	NOUN
ejpam-6070	105	28	of	of	ADP
ejpam-6070	105	29	the	the	DET
ejpam-6070	105	30	problem	problem	NOUN
ejpam-6070	105	31	.	.	PUNCT
ejpam-6070	106	1	we	we	PRON
ejpam-6070	106	2	first	first	ADV
ejpam-6070	106	3	define	define	VERB
ejpam-6070	106	4	the	the	DET
ejpam-6070	106	5	notions	notion	NOUN
ejpam-6070	106	6	of	of	ADP
ejpam-6070	106	7	subsolution	subsolution	NOUN
ejpam-6070	106	8	and	and	CCONJ
ejpam-6070	106	9	supersolution	supersolution	NOUN
ejpam-6070	106	10	:	:	PUNCT
ejpam-6070	106	11	•	•	ADP
ejpam-6070	106	12	a	a	DET
ejpam-6070	106	13	subsolution	subsolution	NOUN
ejpam-6070	106	14	ζ̌	ζ̌	PROPN
ejpam-6070	106	15	∈	∈	PROPN
ejpam-6070	106	16	rm	rm	NOUN
ejpam-6070	106	17	satisfies	satisfy	VERB
ejpam-6070	106	18	the	the	DET
ejpam-6070	106	19	inequality	inequality	NOUN
ejpam-6070	106	20	:	:	PUNCT
ejpam-6070	106	21	max	max	PROPN
ejpam-6070	106	22	1≤i≤n	1≤i≤n	NUM
ejpam-6070	106	23	{	{	PUNCT
ejpam-6070	106	24	biζ̌	biζ̌	ADP
ejpam-6070	106	25	−	−	PROPN
ejpam-6070	106	26	g	g	PROPN
ejpam-6070	106	27	i(ζ̌	i(ζ̌	PROPN
ejpam-6070	106	28	)	)	PUNCT
ejpam-6070	106	29	}	}	PUNCT
ejpam-6070	106	30	≤	≤	NUM
ejpam-6070	106	31	0	0	NUM
ejpam-6070	106	32	.	.	PUNCT
ejpam-6070	107	1	s.	s.	PROPN
ejpam-6070	107	2	chebbah	chebbah	PROPN
ejpam-6070	107	3	,	,	PUNCT
ejpam-6070	107	4	s.	s.	PROPN
ejpam-6070	107	5	madi	madi	PROPN
ejpam-6070	107	6	,	,	PUNCT
ejpam-6070	107	7	m.	m.	NOUN
ejpam-6070	107	8	haiour	haiour	PROPN
ejpam-6070	107	9	/	/	SYM
ejpam-6070	107	10	eur	eur	PROPN
ejpam-6070	107	11	.	.	PUNCT
ejpam-6070	108	1	j.	j.	PROPN
ejpam-6070	108	2	pure	pure	PROPN
ejpam-6070	108	3	appl	appl	PROPN
ejpam-6070	108	4	.	.	PROPN
ejpam-6070	108	5	math	math	PROPN
ejpam-6070	108	6	,	,	PUNCT
ejpam-6070	108	7	18	18	NUM
ejpam-6070	108	8	(	(	PUNCT
ejpam-6070	108	9	2	2	NUM
ejpam-6070	108	10	)	)	PUNCT
ejpam-6070	108	11	(	(	PUNCT
ejpam-6070	108	12	2025	2025	NUM
ejpam-6070	108	13	)	)	PUNCT
ejpam-6070	108	14	,	,	PUNCT
ejpam-6070	108	15	6070	6070	NUM
ejpam-6070	108	16	7	7	NUM
ejpam-6070	108	17	of	of	ADP
ejpam-6070	108	18	20	20	NUM
ejpam-6070	108	19	•	•	NUM
ejpam-6070	108	20	a	a	DET
ejpam-6070	108	21	supersolution	supersolution	NOUN
ejpam-6070	108	22	ζ̂	ζ̂	ADP
ejpam-6070	108	23	∈	∈	PROPN
ejpam-6070	108	24	rm	rm	NOUN
ejpam-6070	108	25	satisfies	satisfy	VERB
ejpam-6070	108	26	the	the	DET
ejpam-6070	108	27	inequality	inequality	NOUN
ejpam-6070	108	28	:	:	PUNCT
ejpam-6070	108	29	max	max	PROPN
ejpam-6070	108	30	1≤i≤n	1≤i≤n	NUM
ejpam-6070	108	31	{	{	PUNCT
ejpam-6070	108	32	biζ̂	biζ̂	PROPN
ejpam-6070	108	33	−	−	PROPN
ejpam-6070	108	34	g	g	PROPN
ejpam-6070	108	35	i(ζ̂	i(ζ̂	PROPN
ejpam-6070	108	36	)	)	PUNCT
ejpam-6070	108	37	}	}	PUNCT
ejpam-6070	108	38	≥	≥	NOUN
ejpam-6070	108	39	0	0	NUM
ejpam-6070	108	40	.	.	PUNCT
ejpam-6070	109	1	following	follow	VERB
ejpam-6070	109	2	these	these	DET
ejpam-6070	109	3	definitions	definition	NOUN
ejpam-6070	109	4	,	,	PUNCT
ejpam-6070	109	5	and	and	CCONJ
ejpam-6070	109	6	based	base	VERB
ejpam-6070	109	7	on	on	ADP
ejpam-6070	109	8	the	the	DET
ejpam-6070	109	9	approach	approach	NOUN
ejpam-6070	109	10	in	in	ADP
ejpam-6070	109	11	[	[	X
ejpam-6070	109	12	9	9	NUM
ejpam-6070	109	13	]	]	PUNCT
ejpam-6070	109	14	,	,	PUNCT
ejpam-6070	109	15	the	the	DET
ejpam-6070	109	16	initial	initial	ADJ
ejpam-6070	109	17	subsolution	subsolution	NOUN
ejpam-6070	109	18	is	be	AUX
ejpam-6070	109	19	chosen	choose	VERB
ejpam-6070	109	20	as	as	ADP
ejpam-6070	109	21	:	:	PUNCT
ejpam-6070	109	22	ζ̌0	ζ̌0	NOUN
ejpam-6070	109	23	=	=	SYM
ejpam-6070	109	24	(	(	PUNCT
ejpam-6070	109	25	0	0	NUM
ejpam-6070	109	26	,	,	PUNCT
ejpam-6070	109	27	0	0	NUM
ejpam-6070	109	28	,	,	PUNCT
ejpam-6070	109	29	.	.	PUNCT
ejpam-6070	109	30	.	.	PUNCT
ejpam-6070	109	31	.	.	PUNCT
ejpam-6070	110	1	,	,	PUNCT
ejpam-6070	110	2	0	0	NUM
ejpam-6070	110	3	)	)	PUNCT
ejpam-6070	110	4	,	,	PUNCT
ejpam-6070	110	5	if	if	SCONJ
ejpam-6070	110	6	g	g	PROPN
ejpam-6070	110	7	i	i	PRON
ejpam-6070	110	8	≥	≥	VERB
ejpam-6070	110	9	0	0	NUM
ejpam-6070	110	10	for	for	ADP
ejpam-6070	110	11	all	all	DET
ejpam-6070	110	12	i	i	PRON
ejpam-6070	110	13	=	=	NOUN
ejpam-6070	111	1	1	1	NUM
ejpam-6070	111	2	,	,	PUNCT
ejpam-6070	111	3	.	.	PUNCT
ejpam-6070	111	4	.	.	PUNCT
ejpam-6070	112	1	.	.	PUNCT
ejpam-6070	113	1	,	,	PUNCT
ejpam-6070	113	2	n.	n.	NOUN
ejpam-6070	113	3	to	to	PART
ejpam-6070	113	4	compute	compute	VERB
ejpam-6070	113	5	the	the	DET
ejpam-6070	113	6	corresponding	corresponding	ADJ
ejpam-6070	113	7	initial	initial	ADJ
ejpam-6070	113	8	supersolution	supersolution	NOUN
ejpam-6070	113	9	ζ̂0	ζ̂0	PROPN
ejpam-6070	113	10	,	,	PUNCT
ejpam-6070	113	11	we	we	PRON
ejpam-6070	113	12	solve	solve	VERB
ejpam-6070	113	13	the	the	DET
ejpam-6070	113	14	nonlinear	nonlinear	ADJ
ejpam-6070	113	15	system	system	NOUN
ejpam-6070	113	16	:	:	PUNCT
ejpam-6070	113	17	biζ̂0	biζ̂0	NOUN
ejpam-6070	113	18	=	=	PUNCT
ejpam-6070	113	19	g	g	PROPN
ejpam-6070	113	20	i(ζ̂0	i(ζ̂0	PROPN
ejpam-6070	113	21	)	)	PUNCT
ejpam-6070	113	22	,	,	PUNCT
ejpam-6070	113	23	for	for	ADP
ejpam-6070	113	24	each	each	DET
ejpam-6070	113	25	i	i	NOUN
ejpam-6070	113	26	=	=	NOUN
ejpam-6070	113	27	1	1	NUM
ejpam-6070	113	28	,	,	PUNCT
ejpam-6070	113	29	.	.	PUNCT
ejpam-6070	113	30	.	.	PUNCT
ejpam-6070	114	1	.	.	PUNCT
ejpam-6070	115	1	,	,	PUNCT
ejpam-6070	115	2	n.	n.	VERB
ejpam-6070	115	3	the	the	DET
ejpam-6070	115	4	discrete	discrete	ADJ
ejpam-6070	115	5	hamilton	hamilton	PROPN
ejpam-6070	115	6	-	-	PUNCT
ejpam-6070	115	7	jacobi	jacobi	PROPN
ejpam-6070	115	8	-	-	PUNCT
ejpam-6070	115	9	bellman	bellman	NOUN
ejpam-6070	115	10	(	(	PUNCT
ejpam-6070	115	11	hjb	hjb	NOUN
ejpam-6070	115	12	)	)	PUNCT
ejpam-6070	115	13	problem	problem	NOUN
ejpam-6070	115	14	,	,	PUNCT
ejpam-6070	115	15	as	as	SCONJ
ejpam-6070	115	16	expressed	express	VERB
ejpam-6070	115	17	in	in	ADP
ejpam-6070	115	18	equation	equation	NOUN
ejpam-6070	115	19	(	(	PUNCT
ejpam-6070	115	20	3	3	X
ejpam-6070	115	21	)	)	PUNCT
ejpam-6070	115	22	can	can	AUX
ejpam-6070	115	23	be	be	AUX
ejpam-6070	115	24	reformulated	reformulate	VERB
ejpam-6070	115	25	using	use	VERB
ejpam-6070	115	26	an	an	DET
ejpam-6070	115	27	overlapping	overlap	VERB
ejpam-6070	115	28	domain	domain	NOUN
ejpam-6070	115	29	decomposition	decomposition	NOUN
ejpam-6070	115	30	strategy	strategy	NOUN
ejpam-6070	115	31	,	,	PUNCT
ejpam-6070	115	32	as	as	SCONJ
ejpam-6070	115	33	follows	follow	VERB
ejpam-6070	115	34	:	:	PUNCT
ejpam-6070	115	35	•	•	NUM
ejpam-6070	115	36	solution	solution	NOUN
ejpam-6070	115	37	for	for	ADP
ejpam-6070	115	38	the	the	DET
ejpam-6070	115	39	domain	domain	NOUN
ejpam-6070	115	40	ω1	ω1	PROPN
ejpam-6070	115	41	:	:	PUNCT
ejpam-6070	115	42	to	to	PART
ejpam-6070	115	43	compute	compute	VERB
ejpam-6070	115	44	ζk+1	ζk+1	NUM
ejpam-6070	115	45	1	1	NUM
ejpam-6070	115	46	,	,	PUNCT
ejpam-6070	115	47	we	we	PRON
ejpam-6070	115	48	solve	solve	VERB
ejpam-6070	115	49	the	the	DET
ejpam-6070	115	50	following	follow	VERB
ejpam-6070	115	51	system:	system:	PROPN
ejpam-6070	115	52	max	max	PROPN
ejpam-6070	115	53	1≤i≤n	1≤i≤n	NUM
ejpam-6070	115	54	(	(	PUNCT
ejpam-6070	115	55	bi	bi	NOUN
ejpam-6070	115	56	1,1ζ	1,1ζ	PROPN
ejpam-6070	115	57	k+1	k+1	NOUN
ejpam-6070	115	58	1	1	NUM
ejpam-6070	115	59	−	−	PROPN
ejpam-6070	115	60	g	g	PROPN
ejpam-6070	115	61	i(ζk1	i(ζk1	PROPN
ejpam-6070	115	62	)	)	PUNCT
ejpam-6070	115	63	)	)	PUNCT
ejpam-6070	116	1	=	=	PUNCT
ejpam-6070	116	2	0	0	NUM
ejpam-6070	116	3	,	,	PUNCT
ejpam-6070	116	4	in	in	ADP
ejpam-6070	116	5	ω1	ω1	PROPN
ejpam-6070	116	6	,	,	PUNCT
ejpam-6070	116	7	(	(	PUNCT
ejpam-6070	116	8	ζk+1	ζk+1	NUM
ejpam-6070	116	9	1	1	NUM
ejpam-6070	116	10	)	)	PUNCT
ejpam-6070	116	11	β	β	NOUN
ejpam-6070	116	12	=	=	PUNCT
ejpam-6070	116	13	(	(	PUNCT
ejpam-6070	116	14	ζk2	ζk2	NOUN
ejpam-6070	116	15	)	)	PUNCT
ejpam-6070	116	16	β	β	PROPN
ejpam-6070	116	17	,	,	PUNCT
ejpam-6070	116	18	on	on	ADP
ejpam-6070	116	19	σ1	σ1	PROPN
ejpam-6070	116	20	.	.	PUNCT
ejpam-6070	117	1	•	•	NUM
ejpam-6070	117	2	solution	solution	NOUN
ejpam-6070	117	3	for	for	ADP
ejpam-6070	117	4	the	the	DET
ejpam-6070	117	5	domain	domain	NOUN
ejpam-6070	117	6	ω2	ω2	NOUN
ejpam-6070	117	7	:	:	PUNCT
ejpam-6070	117	8	to	to	PART
ejpam-6070	117	9	compute	compute	VERB
ejpam-6070	117	10	ζk+1	ζk+1	NUM
ejpam-6070	117	11	2	2	NUM
ejpam-6070	117	12	,	,	PUNCT
ejpam-6070	117	13	we	we	PRON
ejpam-6070	117	14	solve	solve	VERB
ejpam-6070	117	15	the	the	DET
ejpam-6070	117	16	following	follow	VERB
ejpam-6070	117	17	system	system	NOUN
ejpam-6070	117	18	:	:	PUNCT
ejpam-6070	117	19	max	max	NOUN
ejpam-6070	117	20	1≤i≤n	1≤i≤n	NUM
ejpam-6070	118	1	(	(	PUNCT
ejpam-6070	118	2	bi	bi	NOUN
ejpam-6070	118	3	2,2ζ	2,2ζ	NOUN
ejpam-6070	118	4	k+1	k+1	NOUN
ejpam-6070	118	5	2	2	NUM
ejpam-6070	118	6	−	−	NOUN
ejpam-6070	118	7	g	g	NOUN
ejpam-6070	118	8	i(ζk2	i(ζk2	NOUN
ejpam-6070	118	9	)	)	PUNCT
ejpam-6070	118	10	)	)	PUNCT
ejpam-6070	119	1	=	=	PUNCT
ejpam-6070	119	2	0	0	NUM
ejpam-6070	119	3	,	,	PUNCT
ejpam-6070	119	4	in	in	ADP
ejpam-6070	119	5	ω2	ω2	ADJ
ejpam-6070	119	6	,	,	PUNCT
ejpam-6070	119	7	(	(	PUNCT
ejpam-6070	119	8	ζk+1	ζk+1	NUM
ejpam-6070	119	9	2	2	NUM
ejpam-6070	119	10	)	)	PUNCT
ejpam-6070	119	11	α	α	NOUN
ejpam-6070	119	12	=	=	PUNCT
ejpam-6070	119	13	(	(	PUNCT
ejpam-6070	119	14	ζk+1	ζk+1	NUM
ejpam-6070	119	15	1	1	NUM
ejpam-6070	119	16	)	)	PUNCT
ejpam-6070	119	17	α	α	NOUN
ejpam-6070	119	18	,	,	PUNCT
ejpam-6070	119	19	on	on	ADP
ejpam-6070	119	20	σ2	σ2	PROPN
ejpam-6070	119	21	.	.	PUNCT
ejpam-6070	120	1	upon	upon	SCONJ
ejpam-6070	120	2	incorporating	incorporate	VERB
ejpam-6070	120	3	boundary	boundary	ADJ
ejpam-6070	120	4	conditions	condition	NOUN
ejpam-6070	120	5	,	,	PUNCT
ejpam-6070	120	6	the	the	DET
ejpam-6070	120	7	system	system	NOUN
ejpam-6070	120	8	becomes:	becomes:	PROPN
ejpam-6070	120	9	max	max	PROPN
ejpam-6070	120	10	1≤i≤n	1≤i≤n	NUM
ejpam-6070	120	11	{	{	PUNCT
ejpam-6070	120	12	bi	bi	PROPN
ejpam-6070	120	13	1,1ζ	1,1ζ	PROPN
ejpam-6070	120	14	k+1	k+1	NOUN
ejpam-6070	120	15	1	1	NUM
ejpam-6070	120	16	−	−	NOUN
ejpam-6070	120	17	b̃i	b̃i	ADP
ejpam-6070	120	18	1,2ζ	1,2ζ	NUM
ejpam-6070	120	19	k	k	NOUN
ejpam-6070	120	20	2	2	NUM
ejpam-6070	120	21	−	−	PROPN
ejpam-6070	120	22	g	g	PROPN
ejpam-6070	120	23	i(ζk1	i(ζk1	PROPN
ejpam-6070	120	24	)	)	PUNCT
ejpam-6070	120	25	}	}	PUNCT
ejpam-6070	121	1	=	=	PUNCT
ejpam-6070	121	2	0	0	NUM
ejpam-6070	121	3	,	,	PUNCT
ejpam-6070	121	4	in	in	ADP
ejpam-6070	121	5	ω1	ω1	PROPN
ejpam-6070	121	6	,	,	PUNCT
ejpam-6070	121	7	max	max	PROPN
ejpam-6070	121	8	1≤i≤n	1≤i≤n	NUM
ejpam-6070	121	9	{	{	PUNCT
ejpam-6070	121	10	bi	bi	NOUN
ejpam-6070	121	11	2,2ζ	2,2ζ	NOUN
ejpam-6070	121	12	k+1	k+1	X
ejpam-6070	121	13	2	2	NUM
ejpam-6070	121	14	−	−	NOUN
ejpam-6070	121	15	b̃i	b̃i	ADP
ejpam-6070	121	16	2,1ζ	2,1ζ	NUM
ejpam-6070	121	17	k+1	k+1	NOUN
ejpam-6070	121	18	1	1	NUM
ejpam-6070	121	19	−	−	NOUN
ejpam-6070	121	20	g	g	NOUN
ejpam-6070	121	21	i(ζk2	i(ζk2	NOUN
ejpam-6070	121	22	)	)	PUNCT
ejpam-6070	121	23	}	}	PUNCT
ejpam-6070	121	24	=	=	SYM
ejpam-6070	121	25	0	0	NUM
ejpam-6070	121	26	,	,	PUNCT
ejpam-6070	121	27	in	in	ADP
ejpam-6070	121	28	ω2	ω2	ADJ
ejpam-6070	121	29	.	.	PUNCT
ejpam-6070	122	1	we	we	PRON
ejpam-6070	122	2	reformulate	reformulate	VERB
ejpam-6070	122	3	the	the	DET
ejpam-6070	122	4	iterative	iterative	NOUN
ejpam-6070	122	5	process	process	NOUN
ejpam-6070	122	6	derived	derive	VERB
ejpam-6070	122	7	from	from	ADP
ejpam-6070	122	8	the	the	DET
ejpam-6070	122	9	overlapping	overlap	VERB
ejpam-6070	122	10	domain	domain	NOUN
ejpam-6070	122	11	decomposition	decomposition	NOUN
ejpam-6070	122	12	method	method	NOUN
ejpam-6070	122	13	into	into	ADP
ejpam-6070	122	14	the	the	DET
ejpam-6070	122	15	following	follow	VERB
ejpam-6070	122	16	matrix	matrix	NOUN
ejpam-6070	122	17	-	-	PUNCT
ejpam-6070	122	18	based	base	VERB
ejpam-6070	122	19	nonlinear	nonlinear	ADJ
ejpam-6070	122	20	system	system	NOUN
ejpam-6070	122	21	:(	:(	PUNCT
ejpam-6070	122	22	bi	bi	NOUN
ejpam-6070	122	23	1,1	1,1	NUM
ejpam-6070	122	24	0	0	NUM
ejpam-6070	122	25	−b̃i	−b̃i	NUM
ejpam-6070	122	26	2,1	2,1	NUM
ejpam-6070	122	27	bi	bi	NOUN
ejpam-6070	122	28	2,2	2,2	NUM
ejpam-6070	122	29	)	)	PUNCT
ejpam-6070	122	30	(	(	PUNCT
ejpam-6070	122	31	ζk+1	ζk+1	NUM
ejpam-6070	122	32	1	1	NUM
ejpam-6070	122	33	ζk+1	ζk+1	NUM
ejpam-6070	122	34	2	2	NUM
ejpam-6070	122	35	)	)	PUNCT
ejpam-6070	122	36	=	=	SYM
ejpam-6070	122	37	(	(	PUNCT
ejpam-6070	122	38	b̃i	b̃i	ADP
ejpam-6070	123	1	1,2	1,2	NUM
ejpam-6070	123	2	0	0	NUM
ejpam-6070	123	3	0	0	NUM
ejpam-6070	123	4	0	0	NUM
ejpam-6070	123	5	)	)	PUNCT
ejpam-6070	123	6	(	(	PUNCT
ejpam-6070	123	7	ζk1	ζk1	X
ejpam-6070	123	8	ζk2	ζk2	NOUN
ejpam-6070	123	9	)	)	PUNCT
ejpam-6070	124	1	+	+	CCONJ
ejpam-6070	124	2	(	(	PUNCT
ejpam-6070	124	3	g	g	NOUN
ejpam-6070	124	4	i(ζk1	i(ζk1	NOUN
ejpam-6070	124	5	)	)	PUNCT
ejpam-6070	124	6	g	g	PROPN
ejpam-6070	124	7	i(ζk2	i(ζk2	NOUN
ejpam-6070	124	8	)	)	PUNCT
ejpam-6070	124	9	)	)	PUNCT
ejpam-6070	124	10	.	.	PUNCT
ejpam-6070	125	1	(	(	PUNCT
ejpam-6070	125	2	4	4	X
ejpam-6070	125	3	)	)	PUNCT
ejpam-6070	125	4	to	to	PART
ejpam-6070	125	5	better	well	ADV
ejpam-6070	125	6	understand	understand	VERB
ejpam-6070	125	7	this	this	DET
ejpam-6070	125	8	formulation	formulation	NOUN
ejpam-6070	125	9	,	,	PUNCT
ejpam-6070	125	10	we	we	PRON
ejpam-6070	125	11	recast	recast	VERB
ejpam-6070	125	12	it	it	PRON
ejpam-6070	125	13	in	in	ADP
ejpam-6070	125	14	the	the	DET
ejpam-6070	125	15	context	context	NOUN
ejpam-6070	125	16	of	of	ADP
ejpam-6070	125	17	the	the	DET
ejpam-6070	125	18	block	block	NOUN
ejpam-6070	125	19	gaussseidel	gaussseidel	NOUN
ejpam-6070	125	20	method	method	NOUN
ejpam-6070	125	21	.	.	PUNCT
ejpam-6070	126	1	the	the	DET
ejpam-6070	126	2	general	general	ADJ
ejpam-6070	126	3	form	form	NOUN
ejpam-6070	126	4	of	of	ADP
ejpam-6070	126	5	this	this	DET
ejpam-6070	126	6	iterative	iterative	NOUN
ejpam-6070	126	7	scheme	scheme	NOUN
ejpam-6070	126	8	is	be	AUX
ejpam-6070	126	9	given	give	VERB
ejpam-6070	126	10	by:	by:	NUM
ejpam-6070	126	11	ζ(0	ζ(0	NOUN
ejpam-6070	126	12	)	)	PUNCT
ejpam-6070	126	13	∈	∈	PROPN
ejpam-6070	126	14	rm	rm	PROPN
ejpam-6070	126	15	,	,	PUNCT
ejpam-6070	126	16	bt	bt	PROPN
ejpam-6070	126	17	,	,	PUNCT
ejpam-6070	126	18	t	t	PROPN
ejpam-6070	126	19	ζ	ζ	PROPN
ejpam-6070	126	20	(	(	PUNCT
ejpam-6070	126	21	k+1	k+1	NOUN
ejpam-6070	126	22	)	)	PUNCT
ejpam-6070	126	23	t	t	NOUN
ejpam-6070	126	24	=	=	PUNCT
ejpam-6070	126	25	−	−	PROPN
ejpam-6070	126	26	m∑	m∑	INTJ
ejpam-6070	126	27	s	s	X
ejpam-6070	126	28	<	<	X
ejpam-6070	126	29	t	t	NOUN
ejpam-6070	126	30	bt	bt	PROPN
ejpam-6070	126	31	,	,	PUNCT
ejpam-6070	126	32	s	s	VERB
ejpam-6070	126	33	ζ	ζ	NOUN
ejpam-6070	126	34	(	(	PUNCT
ejpam-6070	126	35	k+1	k+1	NOUN
ejpam-6070	126	36	)	)	PUNCT
ejpam-6070	126	37	s	s	PART
ejpam-6070	126	38	−	−	NOUN
ejpam-6070	126	39	m∑	m∑	NOUN
ejpam-6070	126	40	s	s	PART
ejpam-6070	126	41	>	>	X
ejpam-6070	126	42	t	t	PROPN
ejpam-6070	126	43	bt	bt	PROPN
ejpam-6070	126	44	,	,	PUNCT
ejpam-6070	126	45	s	s	VERB
ejpam-6070	126	46	ζ	ζ	NOUN
ejpam-6070	126	47	(	(	PUNCT
ejpam-6070	126	48	k	k	NOUN
ejpam-6070	126	49	)	)	PUNCT
ejpam-6070	126	50	s	s	PART
ejpam-6070	126	51	+	+	NUM
ejpam-6070	126	52	gt	gt	PROPN
ejpam-6070	126	53	,	,	PUNCT
ejpam-6070	126	54	t	t	NOUN
ejpam-6070	127	1	=	=	SYM
ejpam-6070	128	1	1	1	NUM
ejpam-6070	128	2	,	,	PUNCT
ejpam-6070	128	3	.	.	PUNCT
ejpam-6070	128	4	.	.	PUNCT
ejpam-6070	128	5	.	.	PUNCT
ejpam-6070	129	1	,	,	PUNCT
ejpam-6070	129	2	m.	m.	NOUN
ejpam-6070	129	3	(	(	PUNCT
ejpam-6070	129	4	5	5	NUM
ejpam-6070	129	5	)	)	PUNCT
ejpam-6070	129	6	s.	s.	PROPN
ejpam-6070	129	7	chebbah	chebbah	PROPN
ejpam-6070	129	8	,	,	PUNCT
ejpam-6070	129	9	s.	s.	PROPN
ejpam-6070	129	10	madi	madi	PROPN
ejpam-6070	129	11	,	,	PUNCT
ejpam-6070	129	12	m.	m.	NOUN
ejpam-6070	129	13	haiour	haiour	PROPN
ejpam-6070	129	14	/	/	SYM
ejpam-6070	129	15	eur	eur	PROPN
ejpam-6070	129	16	.	.	PUNCT
ejpam-6070	130	1	j.	j.	PROPN
ejpam-6070	130	2	pure	pure	PROPN
ejpam-6070	130	3	appl	appl	PROPN
ejpam-6070	130	4	.	.	PROPN
ejpam-6070	130	5	math	math	PROPN
ejpam-6070	130	6	,	,	PUNCT
ejpam-6070	130	7	18	18	NUM
ejpam-6070	130	8	(	(	PUNCT
ejpam-6070	130	9	2	2	NUM
ejpam-6070	130	10	)	)	PUNCT
ejpam-6070	130	11	(	(	PUNCT
ejpam-6070	130	12	2025	2025	NUM
ejpam-6070	130	13	)	)	PUNCT
ejpam-6070	130	14	,	,	PUNCT
ejpam-6070	130	15	6070	6070	NUM
ejpam-6070	130	16	8	8	NUM
ejpam-6070	130	17	of	of	ADP
ejpam-6070	130	18	20	20	NUM
ejpam-6070	130	19	by	by	ADP
ejpam-6070	130	20	comparing	compare	VERB
ejpam-6070	130	21	systems	system	NOUN
ejpam-6070	130	22	(	(	PUNCT
ejpam-6070	130	23	4	4	NUM
ejpam-6070	130	24	)	)	PUNCT
ejpam-6070	130	25	and	and	CCONJ
ejpam-6070	130	26	(	(	PUNCT
ejpam-6070	130	27	5	5	NUM
ejpam-6070	130	28	)	)	PUNCT
ejpam-6070	131	1	,	,	PUNCT
ejpam-6070	131	2	it	it	PRON
ejpam-6070	131	3	becomes	become	VERB
ejpam-6070	131	4	clear	clear	ADJ
ejpam-6070	131	5	that	that	SCONJ
ejpam-6070	131	6	they	they	PRON
ejpam-6070	131	7	are	be	AUX
ejpam-6070	131	8	structurally	structurally	ADV
ejpam-6070	131	9	equivalent	equivalent	ADJ
ejpam-6070	131	10	in	in	ADP
ejpam-6070	131	11	the	the	DET
ejpam-6070	131	12	nonlinear	nonlinear	ADJ
ejpam-6070	131	13	context	context	NOUN
ejpam-6070	131	14	,	,	PUNCT
ejpam-6070	131	15	where	where	SCONJ
ejpam-6070	131	16	the	the	DET
ejpam-6070	131	17	source	source	NOUN
ejpam-6070	131	18	term	term	NOUN
ejpam-6070	131	19	g	g	PROPN
ejpam-6070	131	20	is	be	AUX
ejpam-6070	131	21	replaced	replace	VERB
ejpam-6070	131	22	by	by	ADP
ejpam-6070	131	23	the	the	DET
ejpam-6070	131	24	nonlinear	nonlinear	ADJ
ejpam-6070	131	25	expression	expression	NOUN
ejpam-6070	131	26	g	g	PROPN
ejpam-6070	131	27	k	k	PROPN
ejpam-6070	131	28	at	at	ADP
ejpam-6070	131	29	each	each	DET
ejpam-6070	131	30	iteration	iteration	NOUN
ejpam-6070	131	31	.	.	PUNCT
ejpam-6070	132	1	the	the	DET
ejpam-6070	132	2	algorithm	algorithm	NOUN
ejpam-6070	132	3	below	below	ADP
ejpam-6070	132	4	outlines	outline	VERB
ejpam-6070	132	5	the	the	DET
ejpam-6070	132	6	iterative	iterative	ADJ
ejpam-6070	132	7	steps	step	NOUN
ejpam-6070	132	8	of	of	ADP
ejpam-6070	132	9	the	the	DET
ejpam-6070	132	10	proposed	propose	VERB
ejpam-6070	132	11	method	method	NOUN
ejpam-6070	132	12	.	.	PUNCT
ejpam-6070	133	1	algorithm	algorithm	NOUN
ejpam-6070	133	2	overlapping	overlap	VERB
ejpam-6070	133	3	domain	domain	NOUN
ejpam-6070	133	4	decomposition	decomposition	NOUN
ejpam-6070	133	5	initialize	initialize	NOUN
ejpam-6070	133	6	:	:	PUNCT
ejpam-6070	133	7	set	set	VERB
ejpam-6070	133	8	the	the	DET
ejpam-6070	133	9	initial	initial	ADJ
ejpam-6070	133	10	guess	guess	NOUN
ejpam-6070	133	11	as	as	ADP
ejpam-6070	133	12	ζ̌0	ζ̌0	NOUN
ejpam-6070	133	13	=	=	SYM
ejpam-6070	133	14	(	(	PUNCT
ejpam-6070	133	15	0	0	NUM
ejpam-6070	133	16	,	,	PUNCT
ejpam-6070	133	17	0	0	NUM
ejpam-6070	133	18	,	,	PUNCT
ejpam-6070	133	19	.	.	PUNCT
ejpam-6070	133	20	.	.	PUNCT
ejpam-6070	134	1	.	.	PUNCT
ejpam-6070	135	1	,	,	PUNCT
ejpam-6070	135	2	0	0	NUM
ejpam-6070	135	3	)	)	PUNCT
ejpam-6070	135	4	,	,	PUNCT
ejpam-6070	135	5	and	and	CCONJ
ejpam-6070	135	6	set	set	VERB
ejpam-6070	135	7	k	k	PROPN
ejpam-6070	135	8	=	=	PUNCT
ejpam-6070	135	9	0	0	X
ejpam-6070	135	10	.	.	PUNCT
ejpam-6070	136	1	step	step	NOUN
ejpam-6070	136	2	1	1	NUM
ejpam-6070	136	3	:	:	PUNCT
ejpam-6070	136	4	compute	compute	VERB
ejpam-6070	136	5	the	the	DET
ejpam-6070	136	6	updated	update	VERB
ejpam-6070	136	7	solution	solution	NOUN
ejpam-6070	136	8	ζ̌k+1	ζ̌k+1	NOUN
ejpam-6070	136	9	1	1	NUM
ejpam-6070	136	10	by	by	ADP
ejpam-6070	136	11	solving	solve	VERB
ejpam-6070	136	12	the	the	DET
ejpam-6070	136	13	system	system	NOUN
ejpam-6070	136	14	:	:	PUNCT
ejpam-6070	136	15	max	max	PROPN
ejpam-6070	136	16	1≤i≤n	1≤i≤n	NUM
ejpam-6070	136	17	{	{	PUNCT
ejpam-6070	136	18	bi	bi	NOUN
ejpam-6070	136	19	1,1ζ̌	1,1ζ̌	NUM
ejpam-6070	136	20	k+1	k+1	NOUN
ejpam-6070	136	21	1	1	NUM
ejpam-6070	136	22	−	−	NOUN
ejpam-6070	136	23	b̃i	b̃i	ADP
ejpam-6070	136	24	1,2ζ̌	1,2ζ̌	NUM
ejpam-6070	136	25	k	k	NOUN
ejpam-6070	136	26	2	2	NUM
ejpam-6070	136	27	−	−	NOUN
ejpam-6070	136	28	g	g	NOUN
ejpam-6070	136	29	i(ζ̌k1	i(ζ̌k1	NOUN
ejpam-6070	136	30	)	)	PUNCT
ejpam-6070	136	31	}	}	PUNCT
ejpam-6070	137	1	=	=	SYM
ejpam-6070	137	2	0	0	X
ejpam-6070	137	3	.	.	X
ejpam-6070	138	1	step	step	NOUN
ejpam-6070	138	2	2	2	NUM
ejpam-6070	138	3	:	:	PUNCT
ejpam-6070	138	4	calculate	calculate	VERB
ejpam-6070	138	5	the	the	DET
ejpam-6070	138	6	updated	update	VERB
ejpam-6070	138	7	value	value	NOUN
ejpam-6070	138	8	ζ̌k+1	ζ̌k+1	NOUN
ejpam-6070	138	9	2	2	NUM
ejpam-6070	138	10	using	use	VERB
ejpam-6070	138	11	the	the	DET
ejpam-6070	138	12	most	most	ADV
ejpam-6070	138	13	recent	recent	ADJ
ejpam-6070	138	14	value	value	NOUN
ejpam-6070	138	15	of	of	ADP
ejpam-6070	138	16	ζ̌k+1	ζ̌k+1	PROPN
ejpam-6070	138	17	1	1	NUM
ejpam-6070	138	18	:	:	PUNCT
ejpam-6070	138	19	max	max	PROPN
ejpam-6070	138	20	1≤i≤n	1≤i≤n	NUM
ejpam-6070	138	21	{	{	PUNCT
ejpam-6070	138	22	−b̃i	−b̃i	PROPN
ejpam-6070	138	23	2,1ζ̌	2,1ζ̌	NUM
ejpam-6070	138	24	k+1	k+1	NOUN
ejpam-6070	138	25	1	1	NUM
ejpam-6070	139	1	+	+	CCONJ
ejpam-6070	139	2	bi	bi	NOUN
ejpam-6070	139	3	2,2ζ̌	2,2ζ̌	PROPN
ejpam-6070	139	4	k+1	k+1	NOUN
ejpam-6070	139	5	2	2	NUM
ejpam-6070	139	6	−	−	NOUN
ejpam-6070	139	7	g	g	PROPN
ejpam-6070	139	8	i(ζ̌k2	i(ζ̌k2	PROPN
ejpam-6070	139	9	)	)	PUNCT
ejpam-6070	139	10	}	}	PUNCT
ejpam-6070	140	1	=	=	SYM
ejpam-6070	140	2	0	0	X
ejpam-6070	140	3	.	.	X
ejpam-6070	141	1	step	step	NOUN
ejpam-6070	141	2	3	3	NUM
ejpam-6070	141	3	:	:	PUNCT
ejpam-6070	141	4	verify	verify	VERB
ejpam-6070	141	5	convergence	convergence	NOUN
ejpam-6070	141	6	of	of	ADP
ejpam-6070	141	7	the	the	DET
ejpam-6070	141	8	solution	solution	NOUN
ejpam-6070	141	9	.	.	PUNCT
ejpam-6070	142	1	if	if	SCONJ
ejpam-6070	142	2	the	the	DET
ejpam-6070	142	3	solution	solution	NOUN
ejpam-6070	142	4	has	have	AUX
ejpam-6070	142	5	not	not	PART
ejpam-6070	142	6	converged	converge	VERB
ejpam-6070	142	7	,	,	PUNCT
ejpam-6070	142	8	increment	increment	NOUN
ejpam-6070	142	9	k	k	PROPN
ejpam-6070	142	10	by	by	ADP
ejpam-6070	142	11	1	1	NUM
ejpam-6070	142	12	and	and	CCONJ
ejpam-6070	142	13	repeat	repeat	VERB
ejpam-6070	142	14	from	from	ADP
ejpam-6070	142	15	step	step	NOUN
ejpam-6070	142	16	1	1	NUM
ejpam-6070	142	17	.	.	X
ejpam-6070	142	18	3.4	3.4	NUM
ejpam-6070	142	19	.	.	PUNCT
ejpam-6070	143	1	monotonic	monotonic	ADJ
ejpam-6070	143	2	and	and	CCONJ
ejpam-6070	143	3	geometric	geometric	ADJ
ejpam-6070	143	4	convergence	convergence	NOUN
ejpam-6070	143	5	to	to	PART
ejpam-6070	143	6	validate	validate	VERB
ejpam-6070	143	7	the	the	DET
ejpam-6070	143	8	proposed	propose	VERB
ejpam-6070	143	9	algorithm	algorithm	NOUN
ejpam-6070	143	10	,	,	PUNCT
ejpam-6070	143	11	we	we	PRON
ejpam-6070	143	12	establish	establish	VERB
ejpam-6070	143	13	its	its	PRON
ejpam-6070	143	14	monotonic	monotonic	ADJ
ejpam-6070	143	15	and	and	CCONJ
ejpam-6070	143	16	geometric	geometric	ADJ
ejpam-6070	143	17	convergence	convergence	NOUN
ejpam-6070	143	18	using	use	VERB
ejpam-6070	143	19	lower	low	ADJ
ejpam-6070	143	20	and	and	CCONJ
ejpam-6070	143	21	upper	upper	ADJ
ejpam-6070	143	22	solutions	solution	NOUN
ejpam-6070	143	23	.	.	PUNCT
ejpam-6070	144	1	the	the	DET
ejpam-6070	144	2	following	follow	VERB
ejpam-6070	144	3	theorem	theorem	NOUN
ejpam-6070	144	4	presents	present	VERB
ejpam-6070	144	5	the	the	DET
ejpam-6070	144	6	proof	proof	NOUN
ejpam-6070	144	7	.	.	PUNCT
ejpam-6070	145	1	theorem	theorem	NOUN
ejpam-6070	145	2	1	1	NUM
ejpam-6070	145	3	.	.	PUNCT
ejpam-6070	146	1	the	the	DET
ejpam-6070	146	2	iterative	iterative	NOUN
ejpam-6070	146	3	process	process	NOUN
ejpam-6070	146	4	described	describe	VERB
ejpam-6070	146	5	in	in	ADP
ejpam-6070	146	6	algorithm	algorithm	NOUN
ejpam-6070	146	7	generates	generate	VERB
ejpam-6070	146	8	two	two	NUM
ejpam-6070	146	9	sequences	sequence	NOUN
ejpam-6070	146	10	,	,	PUNCT
ejpam-6070	146	11	(	(	PUNCT
ejpam-6070	146	12	ζ̌k	ζ̌k	PROPN
ejpam-6070	146	13	)	)	PUNCT
ejpam-6070	146	14	and	and	CCONJ
ejpam-6070	146	15	(	(	PUNCT
ejpam-6070	146	16	ζ̂k	ζ̂k	NOUN
ejpam-6070	146	17	)	)	PUNCT
ejpam-6070	146	18	,	,	PUNCT
ejpam-6070	146	19	which	which	PRON
ejpam-6070	146	20	exhibit	exhibit	VERB
ejpam-6070	146	21	monotonic	monotonic	ADJ
ejpam-6070	146	22	behavior	behavior	NOUN
ejpam-6070	146	23	.	.	PUNCT
ejpam-6070	147	1	more	more	ADV
ejpam-6070	147	2	precisely	precisely	ADV
ejpam-6070	147	3	,	,	PUNCT
ejpam-6070	147	4	the	the	DET
ejpam-6070	147	5	sequence	sequence	NOUN
ejpam-6070	147	6	(	(	PUNCT
ejpam-6070	147	7	ζ̌k	ζ̌k	PROPN
ejpam-6070	147	8	)	)	PUNCT
ejpam-6070	147	9	increases	increase	NOUN
ejpam-6070	147	10	,	,	PUNCT
ejpam-6070	147	11	while	while	SCONJ
ejpam-6070	147	12	(	(	PUNCT
ejpam-6070	147	13	ζ̂k	ζ̂k	NOUN
ejpam-6070	147	14	)	)	PUNCT
ejpam-6070	147	15	decreases	decrease	VERB
ejpam-6070	147	16	,	,	PUNCT
ejpam-6070	147	17	both	both	PRON
ejpam-6070	147	18	converging	converge	VERB
ejpam-6070	147	19	toward	toward	ADP
ejpam-6070	147	20	the	the	DET
ejpam-6070	147	21	unique	unique	ADJ
ejpam-6070	147	22	solution	solution	NOUN
ejpam-6070	147	23	ζ	ζ	NOUN
ejpam-6070	147	24	of	of	ADP
ejpam-6070	147	25	the	the	DET
ejpam-6070	147	26	hamiltonjacobi	hamiltonjacobi	NOUN
ejpam-6070	147	27	-	-	PUNCT
ejpam-6070	147	28	bellman	bellman	NOUN
ejpam-6070	147	29	system	system	NOUN
ejpam-6070	147	30	(	(	PUNCT
ejpam-6070	147	31	3	3	NUM
ejpam-6070	147	32	)	)	PUNCT
ejpam-6070	147	33	.	.	PUNCT
ejpam-6070	148	1	proof	proof	NOUN
ejpam-6070	148	2	.	.	PUNCT
ejpam-6070	149	1	the	the	DET
ejpam-6070	149	2	proof	proof	NOUN
ejpam-6070	149	3	is	be	AUX
ejpam-6070	149	4	structured	structure	VERB
ejpam-6070	149	5	into	into	ADP
ejpam-6070	149	6	five	five	NUM
ejpam-6070	149	7	consecutive	consecutive	ADJ
ejpam-6070	149	8	steps	step	NOUN
ejpam-6070	149	9	.	.	PUNCT
ejpam-6070	150	1	•	•	NUM
ejpam-6070	150	2	step	step	NOUN
ejpam-6070	150	3	1	1	NUM
ejpam-6070	150	4	:	:	PUNCT
ejpam-6070	150	5	we	we	PRON
ejpam-6070	150	6	establish	establish	VERB
ejpam-6070	150	7	that	that	SCONJ
ejpam-6070	150	8	the	the	DET
ejpam-6070	150	9	sequence	sequence	NOUN
ejpam-6070	150	10	(	(	PUNCT
ejpam-6070	150	11	ζ̌k	ζ̌k	PROPN
ejpam-6070	150	12	)	)	PUNCT
ejpam-6070	150	13	,	,	PUNCT
ejpam-6070	150	14	produced	produce	VERB
ejpam-6070	150	15	by	by	ADP
ejpam-6070	150	16	the	the	DET
ejpam-6070	150	17	algorithm	algorithm	NOUN
ejpam-6070	150	18	is	be	AUX
ejpam-6070	150	19	monotonic	monotonic	ADJ
ejpam-6070	150	20	and	and	CCONJ
ejpam-6070	150	21	converges	converge	VERB
ejpam-6070	150	22	to	to	ADP
ejpam-6070	150	23	the	the	DET
ejpam-6070	150	24	unique	unique	ADJ
ejpam-6070	150	25	solution	solution	NOUN
ejpam-6070	150	26	of	of	ADP
ejpam-6070	150	27	the	the	DET
ejpam-6070	150	28	system	system	NOUN
ejpam-6070	150	29	(	(	PUNCT
ejpam-6070	150	30	3	3	NUM
ejpam-6070	150	31	)	)	PUNCT
ejpam-6070	150	32	.	.	PUNCT
ejpam-6070	151	1	initially	initially	ADV
ejpam-6070	151	2	,	,	PUNCT
ejpam-6070	151	3	for	for	ADP
ejpam-6070	151	4	k	k	PROPN
ejpam-6070	151	5	=	=	SYM
ejpam-6070	151	6	0	0	PROPN
ejpam-6070	151	7	,	,	PUNCT
ejpam-6070	151	8	we	we	PRON
ejpam-6070	151	9	solve	solve	VERB
ejpam-6070	151	10	the	the	DET
ejpam-6070	151	11	problem	problem	NOUN
ejpam-6070	151	12	in	in	ADP
ejpam-6070	151	13	the	the	DET
ejpam-6070	151	14	first	first	ADJ
ejpam-6070	151	15	subdomain	subdomain	NOUN
ejpam-6070	151	16	to	to	PART
ejpam-6070	151	17	compute	compute	VERB
ejpam-6070	151	18	ζ̌11	ζ̌11	ADJ
ejpam-6070	151	19	as	as	SCONJ
ejpam-6070	151	20	follows	follow	VERB
ejpam-6070	151	21	:	:	PUNCT
ejpam-6070	151	22	max	max	PROPN
ejpam-6070	151	23	1≤i≤n	1≤i≤n	NUM
ejpam-6070	151	24	{	{	PUNCT
ejpam-6070	151	25	bi	bi	PROPN
ejpam-6070	151	26	1,1ζ̌	1,1ζ̌	NUM
ejpam-6070	151	27	1	1	NUM
ejpam-6070	151	28	1	1	NUM
ejpam-6070	151	29	−	−	NUM
ejpam-6070	151	30	b̃i	b̃i	ADP
ejpam-6070	151	31	1,2ζ̌	1,2ζ̌	NUM
ejpam-6070	151	32	0	0	NUM
ejpam-6070	151	33	2	2	NUM
ejpam-6070	151	34	−	−	NOUN
ejpam-6070	151	35	g	g	PROPN
ejpam-6070	151	36	i(ζ̌01	i(ζ̌01	PROPN
ejpam-6070	151	37	)	)	PUNCT
ejpam-6070	151	38	}	}	PUNCT
ejpam-6070	152	1	=	=	PUNCT
ejpam-6070	152	2	0	0	X
ejpam-6070	152	3	.	.	PUNCT
ejpam-6070	153	1	since	since	SCONJ
ejpam-6070	153	2	ζ̌0	ζ̌0	NOUN
ejpam-6070	153	3	is	be	AUX
ejpam-6070	153	4	a	a	DET
ejpam-6070	153	5	lower	low	ADJ
ejpam-6070	153	6	solution	solution	NOUN
ejpam-6070	153	7	,	,	PUNCT
ejpam-6070	153	8	the	the	DET
ejpam-6070	153	9	following	follow	VERB
ejpam-6070	153	10	inequality	inequality	NOUN
ejpam-6070	153	11	holds	hold	VERB
ejpam-6070	153	12	:	:	PUNCT
ejpam-6070	153	13	max	max	PROPN
ejpam-6070	153	14	1≤i≤n	1≤i≤n	NUM
ejpam-6070	153	15	{	{	PUNCT
ejpam-6070	153	16	bi	bi	PROPN
ejpam-6070	153	17	1,1ζ̌	1,1ζ̌	NUM
ejpam-6070	153	18	0	0	NUM
ejpam-6070	153	19	1	1	NUM
ejpam-6070	153	20	−	−	NOUN
ejpam-6070	153	21	b̃i	b̃i	ADP
ejpam-6070	153	22	1,2ζ̌	1,2ζ̌	NUM
ejpam-6070	153	23	0	0	NUM
ejpam-6070	153	24	2	2	NUM
ejpam-6070	153	25	−	−	NOUN
ejpam-6070	153	26	g	g	PROPN
ejpam-6070	153	27	i(ζ̌01	i(ζ̌01	PROPN
ejpam-6070	153	28	)	)	PUNCT
ejpam-6070	153	29	}	}	PUNCT
ejpam-6070	153	30	≤	≤	NUM
ejpam-6070	153	31	0	0	NUM
ejpam-6070	153	32	.	.	PUNCT
ejpam-6070	154	1	from	from	ADP
ejpam-6070	154	2	this	this	PRON
ejpam-6070	154	3	,	,	PUNCT
ejpam-6070	154	4	we	we	PRON
ejpam-6070	154	5	deduce	deduce	VERB
ejpam-6070	154	6	that	that	SCONJ
ejpam-6070	154	7	:	:	PUNCT
ejpam-6070	155	1	ζ̌01	ζ̌01	PROPN
ejpam-6070	155	2	≤	≤	PUNCT
ejpam-6070	155	3	ζ̌11	ζ̌11	ADJ
ejpam-6070	155	4	.	.	PUNCT
ejpam-6070	156	1	next	next	ADV
ejpam-6070	156	2	,	,	PUNCT
ejpam-6070	156	3	we	we	PRON
ejpam-6070	156	4	proceed	proceed	VERB
ejpam-6070	156	5	to	to	PART
ejpam-6070	156	6	solve	solve	VERB
ejpam-6070	156	7	the	the	DET
ejpam-6070	156	8	problem	problem	NOUN
ejpam-6070	156	9	in	in	ADP
ejpam-6070	156	10	the	the	DET
ejpam-6070	156	11	second	second	ADJ
ejpam-6070	156	12	subdomain	subdomain	NOUN
ejpam-6070	156	13	to	to	PART
ejpam-6070	156	14	determine	determine	VERB
ejpam-6070	156	15	ζ̌12	ζ̌12	PROPN
ejpam-6070	156	16	:	:	PUNCT
ejpam-6070	156	17	max	max	PROPN
ejpam-6070	156	18	1≤i≤n	1≤i≤n	NUM
ejpam-6070	156	19	{	{	PUNCT
ejpam-6070	156	20	−b̃i	−b̃i	SYM
ejpam-6070	156	21	2,1ζ̌	2,1ζ̌	NUM
ejpam-6070	156	22	1	1	NUM
ejpam-6070	156	23	1	1	NUM
ejpam-6070	156	24	+	+	CCONJ
ejpam-6070	156	25	bi	bi	NOUN
ejpam-6070	156	26	2,2ζ̌	2,2ζ̌	NUM
ejpam-6070	156	27	1	1	NUM
ejpam-6070	156	28	2	2	NUM
ejpam-6070	156	29	−	−	NOUN
ejpam-6070	156	30	g	g	PROPN
ejpam-6070	156	31	i(ζ̌02	i(ζ̌02	PROPN
ejpam-6070	156	32	)	)	PUNCT
ejpam-6070	156	33	}	}	PUNCT
ejpam-6070	157	1	=	=	PUNCT
ejpam-6070	157	2	0	0	X
ejpam-6070	157	3	.	.	PUNCT
ejpam-6070	158	1	(	(	PUNCT
ejpam-6070	158	2	6	6	X
ejpam-6070	158	3	)	)	PUNCT
ejpam-6070	158	4	s.	s.	PROPN
ejpam-6070	158	5	chebbah	chebbah	PROPN
ejpam-6070	158	6	,	,	PUNCT
ejpam-6070	158	7	s.	s.	PROPN
ejpam-6070	158	8	madi	madi	PROPN
ejpam-6070	158	9	,	,	PUNCT
ejpam-6070	158	10	m.	m.	NOUN
ejpam-6070	158	11	haiour	haiour	PROPN
ejpam-6070	158	12	/	/	SYM
ejpam-6070	158	13	eur	eur	PROPN
ejpam-6070	158	14	.	.	PUNCT
ejpam-6070	159	1	j.	j.	PROPN
ejpam-6070	159	2	pure	pure	PROPN
ejpam-6070	159	3	appl	appl	PROPN
ejpam-6070	159	4	.	.	PROPN
ejpam-6070	159	5	math	math	PROPN
ejpam-6070	159	6	,	,	PUNCT
ejpam-6070	159	7	18	18	NUM
ejpam-6070	159	8	(	(	PUNCT
ejpam-6070	159	9	2	2	NUM
ejpam-6070	159	10	)	)	PUNCT
ejpam-6070	159	11	(	(	PUNCT
ejpam-6070	159	12	2025	2025	NUM
ejpam-6070	159	13	)	)	PUNCT
ejpam-6070	159	14	,	,	PUNCT
ejpam-6070	159	15	6070	6070	NUM
ejpam-6070	159	16	9	9	NUM
ejpam-6070	159	17	of	of	ADP
ejpam-6070	159	18	20	20	NUM
ejpam-6070	159	19	since	since	SCONJ
ejpam-6070	159	20	ζ̌0	ζ̌0	NOUN
ejpam-6070	159	21	is	be	AUX
ejpam-6070	159	22	also	also	ADV
ejpam-6070	159	23	a	a	DET
ejpam-6070	159	24	lower	low	ADJ
ejpam-6070	159	25	solution	solution	NOUN
ejpam-6070	159	26	,	,	PUNCT
ejpam-6070	159	27	we	we	PRON
ejpam-6070	159	28	obtain	obtain	VERB
ejpam-6070	159	29	:	:	PUNCT
ejpam-6070	159	30	max	max	PROPN
ejpam-6070	159	31	1≤i≤n	1≤i≤n	NUM
ejpam-6070	159	32	{	{	PUNCT
ejpam-6070	159	33	−b̃i	−b̃i	SYM
ejpam-6070	159	34	2,1ζ̌	2,1ζ̌	NUM
ejpam-6070	159	35	0	0	NUM
ejpam-6070	160	1	1	1	NUM
ejpam-6070	161	1	+	+	CCONJ
ejpam-6070	161	2	bi	bi	ADJ
ejpam-6070	161	3	2,2ζ̌	2,2ζ̌	NUM
ejpam-6070	161	4	0	0	NUM
ejpam-6070	161	5	2	2	NUM
ejpam-6070	161	6	−	−	NOUN
ejpam-6070	161	7	g	g	PROPN
ejpam-6070	161	8	i(ζ̌02	i(ζ̌02	PROPN
ejpam-6070	161	9	)	)	PUNCT
ejpam-6070	161	10	}	}	PUNCT
ejpam-6070	161	11	≤	≤	NUM
ejpam-6070	161	12	0	0	NUM
ejpam-6070	161	13	.	.	PUNCT
ejpam-6070	162	1	(	(	PUNCT
ejpam-6070	162	2	7	7	X
ejpam-6070	162	3	)	)	PUNCT
ejpam-6070	162	4	comparing	compare	VERB
ejpam-6070	162	5	equations	equation	NOUN
ejpam-6070	162	6	(	(	PUNCT
ejpam-6070	162	7	6	6	NUM
ejpam-6070	162	8	)	)	PUNCT
ejpam-6070	162	9	and	and	CCONJ
ejpam-6070	162	10	(	(	PUNCT
ejpam-6070	162	11	7	7	NUM
ejpam-6070	162	12	)	)	PUNCT
ejpam-6070	162	13	,	,	PUNCT
ejpam-6070	162	14	we	we	PRON
ejpam-6070	162	15	deduce	deduce	VERB
ejpam-6070	162	16	:	:	PUNCT
ejpam-6070	162	17	ζ̌02	ζ̌02	ADJ
ejpam-6070	162	18	≤	≤	ADJ
ejpam-6070	162	19	ζ̌12	ζ̌12	NOUN
ejpam-6070	162	20	.	.	PUNCT
ejpam-6070	163	1	thus	thus	ADV
ejpam-6070	163	2	,	,	PUNCT
ejpam-6070	163	3	we	we	PRON
ejpam-6070	163	4	conclude	conclude	VERB
ejpam-6070	163	5	that	that	PRON
ejpam-6070	163	6	:	:	PUNCT
ejpam-6070	163	7	ζ̌0	ζ̌0	NUM
ejpam-6070	163	8	≤	≤	NOUN
ejpam-6070	163	9	ζ̌1	ζ̌1	NUM
ejpam-6070	163	10	.	.	PUNCT
ejpam-6070	164	1	this	this	PRON
ejpam-6070	164	2	confirms	confirm	VERB
ejpam-6070	164	3	that	that	SCONJ
ejpam-6070	164	4	ζ̌1	ζ̌1	NUM
ejpam-6070	164	5	is	be	AUX
ejpam-6070	164	6	also	also	ADV
ejpam-6070	164	7	a	a	DET
ejpam-6070	164	8	lower	low	ADJ
ejpam-6070	164	9	solution	solution	NOUN
ejpam-6070	164	10	.	.	PUNCT
ejpam-6070	165	1	by	by	ADP
ejpam-6070	165	2	mathematical	mathematical	ADJ
ejpam-6070	165	3	induction	induction	NOUN
ejpam-6070	165	4	,	,	PUNCT
ejpam-6070	165	5	assuming	assume	VERB
ejpam-6070	165	6	that	that	SCONJ
ejpam-6070	165	7	ζ̌k	ζ̌k	PROPN
ejpam-6070	165	8	≤	≤	PROPN
ejpam-6070	165	9	ζ̌k+1	ζ̌k+1	NOUN
ejpam-6070	165	10	holds	hold	VERB
ejpam-6070	165	11	for	for	ADP
ejpam-6070	165	12	some	some	DET
ejpam-6070	165	13	k	k	NOUN
ejpam-6070	165	14	,	,	PUNCT
ejpam-6070	165	15	we	we	PRON
ejpam-6070	165	16	extend	extend	VERB
ejpam-6070	165	17	this	this	DET
ejpam-6070	165	18	property	property	NOUN
ejpam-6070	165	19	to	to	ADP
ejpam-6070	165	20	all	all	DET
ejpam-6070	165	21	iterations	iteration	NOUN
ejpam-6070	165	22	:	:	PUNCT
ejpam-6070	165	23	ζ̌0	ζ̌0	NUM
ejpam-6070	165	24	≤	≤	NOUN
ejpam-6070	165	25	ζ̌1	ζ̌1	NUM
ejpam-6070	165	26	≤	≤	NUM
ejpam-6070	165	27	·	·	PUNCT
ejpam-6070	165	28	·	·	PUNCT
ejpam-6070	165	29	·	·	PUNCT
ejpam-6070	165	30	≤	≤	NUM
ejpam-6070	165	31	ζ̌k	ζ̌k	PROPN
ejpam-6070	165	32	≤	≤	PROPN
ejpam-6070	165	33	ζ̌k+1	ζ̌k+1	NOUN
ejpam-6070	165	34	.	.	PUNCT
ejpam-6070	166	1	hence	hence	ADV
ejpam-6070	166	2	,	,	PUNCT
ejpam-6070	166	3	the	the	DET
ejpam-6070	166	4	sequence	sequence	NOUN
ejpam-6070	166	5	(	(	PUNCT
ejpam-6070	166	6	ζ̌k	ζ̌k	PROPN
ejpam-6070	166	7	)	)	PUNCT
ejpam-6070	166	8	is	be	AUX
ejpam-6070	166	9	non	non	ADJ
ejpam-6070	166	10	-	-	ADJ
ejpam-6070	166	11	decreasing	decrease	VERB
ejpam-6070	166	12	.	.	PUNCT
ejpam-6070	167	1	•	•	NUM
ejpam-6070	167	2	step	step	NOUN
ejpam-6070	167	3	2	2	NUM
ejpam-6070	167	4	:	:	PUNCT
ejpam-6070	167	5	establishing	establish	VERB
ejpam-6070	167	6	the	the	DET
ejpam-6070	167	7	convergence	convergence	NOUN
ejpam-6070	167	8	of	of	ADP
ejpam-6070	167	9	the	the	DET
ejpam-6070	167	10	sequence	sequence	NOUN
ejpam-6070	167	11	(	(	PUNCT
ejpam-6070	167	12	ζ̌k	ζ̌k	PROPN
ejpam-6070	167	13	)	)	PUNCT
ejpam-6070	167	14	to	to	ADP
ejpam-6070	167	15	the	the	DET
ejpam-6070	167	16	solution	solution	NOUN
ejpam-6070	167	17	of	of	ADP
ejpam-6070	167	18	system	system	NOUN
ejpam-6070	167	19	(	(	PUNCT
ejpam-6070	167	20	3	3	NUM
ejpam-6070	167	21	)	)	PUNCT
ejpam-6070	167	22	.	.	PUNCT
ejpam-6070	168	1	since	since	SCONJ
ejpam-6070	168	2	ζ̌k	ζ̌k	PROPN
ejpam-6070	168	3	is	be	AUX
ejpam-6070	168	4	considered	consider	VERB
ejpam-6070	168	5	a	a	DET
ejpam-6070	168	6	lower	low	ADJ
ejpam-6070	168	7	solution	solution	NOUN
ejpam-6070	168	8	,	,	PUNCT
ejpam-6070	168	9	the	the	DET
ejpam-6070	168	10	following	follow	VERB
ejpam-6070	168	11	inequality	inequality	NOUN
ejpam-6070	168	12	holds	hold	VERB
ejpam-6070	168	13	:	:	PUNCT
ejpam-6070	168	14	max	max	PROPN
ejpam-6070	168	15	1≤i≤n	1≤i≤n	NUM
ejpam-6070	168	16	{	{	PUNCT
ejpam-6070	168	17	biζ̌k	biζ̌k	PROPN
ejpam-6070	168	18	−	−	NOUN
ejpam-6070	168	19	g	g	PROPN
ejpam-6070	168	20	i(ζ̌k	i(ζ̌k	PROPN
ejpam-6070	168	21	)	)	PUNCT
ejpam-6070	168	22	}	}	PUNCT
ejpam-6070	168	23	≤	≤	NUM
ejpam-6070	168	24	0	0	NUM
ejpam-6070	168	25	.	.	PUNCT
ejpam-6070	169	1	(	(	PUNCT
ejpam-6070	169	2	8)	8)	NUM
ejpam-6070	169	3	this	this	PRON
ejpam-6070	169	4	directly	directly	ADV
ejpam-6070	169	5	implies	imply	VERB
ejpam-6070	169	6	the	the	DET
ejpam-6070	169	7	relation	relation	NOUN
ejpam-6070	169	8	:	:	PUNCT
ejpam-6070	169	9	biζ̌k	biζ̌k	PROPN
ejpam-6070	169	10	−	−	NOUN
ejpam-6070	169	11	g	g	PROPN
ejpam-6070	169	12	i(ζ̌k	i(ζ̌k	PROPN
ejpam-6070	169	13	)	)	PUNCT
ejpam-6070	169	14	≤	≤	NOUN
ejpam-6070	169	15	0	0	NUM
ejpam-6070	169	16	⇒	⇒	NOUN
ejpam-6070	169	17	biζ̌k	biζ̌k	PROPN
ejpam-6070	169	18	−	−	PROPN
ejpam-6070	170	1	f	f	NOUN
ejpam-6070	171	1	i	i	PRON
ejpam-6070	171	2	−	−	PROPN
ejpam-6070	171	3	µζ̌k	µζ̌k	VERB
ejpam-6070	171	4	≤	≤	NUM
ejpam-6070	171	5	0	0	NUM
ejpam-6070	171	6	.	.	PUNCT
ejpam-6070	172	1	(	(	PUNCT
ejpam-6070	172	2	9	9	X
ejpam-6070	172	3	)	)	PUNCT
ejpam-6070	172	4	now	now	ADV
ejpam-6070	172	5	,	,	PUNCT
ejpam-6070	172	6	let	let	VERB
ejpam-6070	172	7	us	we	PRON
ejpam-6070	172	8	assume	assume	VERB
ejpam-6070	172	9	the	the	DET
ejpam-6070	172	10	existence	existence	NOUN
ejpam-6070	172	11	of	of	ADP
ejpam-6070	172	12	a	a	DET
ejpam-6070	172	13	solution	solution	NOUN
ejpam-6070	172	14	ζ̌∗	ζ̌∗	NOUN
ejpam-6070	172	15	satisfying	satisfying	NOUN
ejpam-6070	172	16	:	:	PUNCT
ejpam-6070	172	17	biζ̌∗	biζ̌∗	PROPN
ejpam-6070	173	1	−	−	PROPN
ejpam-6070	173	2	f	f	PROPN
ejpam-6070	174	1	i	i	PRON
ejpam-6070	174	2	−	−	VERB
ejpam-6070	174	3	µζ̌∗	µζ̌∗	PROPN
ejpam-6070	174	4	=	=	NOUN
ejpam-6070	174	5	0	0	PROPN
ejpam-6070	174	6	.	.	PUNCT
ejpam-6070	175	1	(	(	PUNCT
ejpam-6070	175	2	10	10	NUM
ejpam-6070	175	3	)	)	PUNCT
ejpam-6070	175	4	from	from	ADP
ejpam-6070	175	5	equation	equation	NOUN
ejpam-6070	175	6	(	(	PUNCT
ejpam-6070	175	7	10	10	NUM
ejpam-6070	175	8	)	)	PUNCT
ejpam-6070	175	9	,	,	PUNCT
ejpam-6070	175	10	we	we	PRON
ejpam-6070	175	11	express	express	VERB
ejpam-6070	175	12	:	:	PUNCT
ejpam-6070	175	13	f	f	PROPN
ejpam-6070	175	14	i	i	PRON
ejpam-6070	175	15	=	=	PUNCT
ejpam-6070	175	16	biζ̌∗	biζ̌∗	NOUN
ejpam-6070	175	17	−	−	NOUN
ejpam-6070	175	18	µζ̌∗.	µζ̌∗.	NOUN
ejpam-6070	175	19	by	by	ADP
ejpam-6070	175	20	substituting	substitute	VERB
ejpam-6070	175	21	this	this	PRON
ejpam-6070	175	22	into	into	ADP
ejpam-6070	175	23	equation	equation	NOUN
ejpam-6070	175	24	(	(	PUNCT
ejpam-6070	175	25	9	9	NUM
ejpam-6070	175	26	)	)	PUNCT
ejpam-6070	175	27	,	,	PUNCT
ejpam-6070	175	28	we	we	PRON
ejpam-6070	175	29	obtain	obtain	VERB
ejpam-6070	175	30	:	:	PUNCT
ejpam-6070	175	31	biζ̌k	biζ̌k	PROPN
ejpam-6070	175	32	−	−	PROPN
ejpam-6070	175	33	biζ̌∗	biζ̌∗	NOUN
ejpam-6070	176	1	+	+	CCONJ
ejpam-6070	176	2	µζ̌∗	µζ̌∗	PROPN
ejpam-6070	176	3	−	−	PROPN
ejpam-6070	176	4	µζ̌k	µζ̌k	VERB
ejpam-6070	176	5	≤	≤	NUM
ejpam-6070	176	6	0	0	NUM
ejpam-6070	176	7	.	.	PUNCT
ejpam-6070	177	1	rearranging	rearrange	VERB
ejpam-6070	177	2	,	,	PUNCT
ejpam-6070	177	3	we	we	PRON
ejpam-6070	177	4	get	get	VERB
ejpam-6070	177	5	:	:	PUNCT
ejpam-6070	177	6	(	(	PUNCT
ejpam-6070	177	7	bi	bi	INTJ
ejpam-6070	177	8	−	−	PROPN
ejpam-6070	177	9	µi)(ζ̌k	µi)(ζ̌k	PROPN
ejpam-6070	177	10	−	−	PROPN
ejpam-6070	177	11	ζ̌∗	ζ̌∗	NOUN
ejpam-6070	177	12	)	)	PUNCT
ejpam-6070	177	13	≤	≤	NOUN
ejpam-6070	177	14	0	0	NUM
ejpam-6070	177	15	.	.	PUNCT
ejpam-6070	178	1	since	since	SCONJ
ejpam-6070	178	2	bi	bi	NOUN
ejpam-6070	178	3	can	can	AUX
ejpam-6070	178	4	be	be	AUX
ejpam-6070	178	5	rewritten	rewrite	VERB
ejpam-6070	178	6	as	as	ADP
ejpam-6070	178	7	a	a	DET
ejpam-6070	178	8	i	i	NOUN
ejpam-6070	178	9	+	+	PROPN
ejpam-6070	178	10	µi	µi	PROPN
ejpam-6070	178	11	,	,	PUNCT
ejpam-6070	178	12	it	it	PRON
ejpam-6070	178	13	follows	follow	VERB
ejpam-6070	178	14	that	that	SCONJ
ejpam-6070	178	15	:	:	PUNCT
ejpam-6070	178	16	a	a	DET
ejpam-6070	178	17	i(ζ̌k	i(ζ̌k	PROPN
ejpam-6070	178	18	−	−	PROPN
ejpam-6070	178	19	ζ̌∗	ζ̌∗	NOUN
ejpam-6070	178	20	)	)	PUNCT
ejpam-6070	178	21	≤	≤	NOUN
ejpam-6070	178	22	0	0	NUM
ejpam-6070	178	23	.	.	PUNCT
ejpam-6070	179	1	s.	s.	PROPN
ejpam-6070	179	2	chebbah	chebbah	PROPN
ejpam-6070	179	3	,	,	PUNCT
ejpam-6070	179	4	s.	s.	PROPN
ejpam-6070	179	5	madi	madi	PROPN
ejpam-6070	179	6	,	,	PUNCT
ejpam-6070	179	7	m.	m.	NOUN
ejpam-6070	179	8	haiour	haiour	PROPN
ejpam-6070	179	9	/	/	SYM
ejpam-6070	179	10	eur	eur	PROPN
ejpam-6070	179	11	.	.	PUNCT
ejpam-6070	180	1	j.	j.	PROPN
ejpam-6070	180	2	pure	pure	PROPN
ejpam-6070	180	3	appl	appl	PROPN
ejpam-6070	180	4	.	.	PROPN
ejpam-6070	180	5	math	math	PROPN
ejpam-6070	180	6	,	,	PUNCT
ejpam-6070	180	7	18	18	NUM
ejpam-6070	180	8	(	(	PUNCT
ejpam-6070	180	9	2	2	NUM
ejpam-6070	180	10	)	)	PUNCT
ejpam-6070	180	11	(	(	PUNCT
ejpam-6070	180	12	2025	2025	NUM
ejpam-6070	180	13	)	)	PUNCT
ejpam-6070	180	14	,	,	PUNCT
ejpam-6070	180	15	6070	6070	NUM
ejpam-6070	180	16	10	10	NUM
ejpam-6070	180	17	of	of	ADP
ejpam-6070	180	18	20	20	NUM
ejpam-6070	180	19	given	give	VERB
ejpam-6070	180	20	that	that	SCONJ
ejpam-6070	180	21	a	a	PRON
ejpam-6070	180	22	i	i	PRON
ejpam-6070	180	23	is	be	AUX
ejpam-6070	180	24	an	an	DET
ejpam-6070	180	25	m	m	NOUN
ejpam-6070	180	26	-	-	NOUN
ejpam-6070	180	27	matrix	matrix	NOUN
ejpam-6070	180	28	,	,	PUNCT
ejpam-6070	180	29	we	we	PRON
ejpam-6070	180	30	deduce	deduce	VERB
ejpam-6070	180	31	:	:	PUNCT
ejpam-6070	180	32	ζ̌k	ζ̌k	PROPN
ejpam-6070	180	33	≤	≤	NUM
ejpam-6070	180	34	ζ̌∗.	ζ̌∗.	ADV
ejpam-6070	180	35	thus	thus	ADV
ejpam-6070	180	36	,	,	PUNCT
ejpam-6070	180	37	the	the	DET
ejpam-6070	180	38	sequence	sequence	NOUN
ejpam-6070	180	39	(	(	PUNCT
ejpam-6070	180	40	ζ̌k	ζ̌k	PROPN
ejpam-6070	180	41	)	)	PUNCT
ejpam-6070	180	42	is	be	AUX
ejpam-6070	180	43	bounded	bound	VERB
ejpam-6070	180	44	below	below	ADV
ejpam-6070	180	45	by	by	ADP
ejpam-6070	180	46	ζ̌∗.	ζ̌∗.	PROPN
ejpam-6070	180	47	since	since	SCONJ
ejpam-6070	180	48	(	(	PUNCT
ejpam-6070	180	49	ζ̌k	ζ̌k	PROPN
ejpam-6070	180	50	)	)	PUNCT
ejpam-6070	180	51	is	be	AUX
ejpam-6070	180	52	a	a	DET
ejpam-6070	180	53	monotonically	monotonically	ADV
ejpam-6070	180	54	increasing	increase	VERB
ejpam-6070	180	55	and	and	CCONJ
ejpam-6070	180	56	lower	lower	ADV
ejpam-6070	180	57	-	-	PUNCT
ejpam-6070	180	58	bounded	bound	VERB
ejpam-6070	180	59	sequence	sequence	NOUN
ejpam-6070	180	60	,	,	PUNCT
ejpam-6070	180	61	it	it	PRON
ejpam-6070	180	62	necessarily	necessarily	ADV
ejpam-6070	180	63	converges	converge	VERB
ejpam-6070	180	64	.	.	PUNCT
ejpam-6070	181	1	therefore	therefore	ADV
ejpam-6070	181	2	,	,	PUNCT
ejpam-6070	181	3	we	we	PRON
ejpam-6070	181	4	conclude	conclude	VERB
ejpam-6070	181	5	:	:	PUNCT
ejpam-6070	181	6	lim	lim	PROPN
ejpam-6070	181	7	k→∞	k→∞	NOUN
ejpam-6070	181	8	ζ̌k	ζ̌k	PROPN
ejpam-6070	181	9	=	=	PUNCT
ejpam-6070	181	10	ζ̌∗.	ζ̌∗.	X
ejpam-6070	181	11	(	(	PUNCT
ejpam-6070	181	12	11	11	NUM
ejpam-6070	181	13	)	)	PUNCT
ejpam-6070	181	14	•	•	NUM
ejpam-6070	181	15	step	step	NOUN
ejpam-6070	181	16	3	3	NUM
ejpam-6070	181	17	:	:	PUNCT
ejpam-6070	181	18	the	the	DET
ejpam-6070	181	19	vector	vector	NOUN
ejpam-6070	181	20	ζ̌∗	ζ̌∗	NOUN
ejpam-6070	181	21	=	=	PUNCT
ejpam-6070	181	22	(	(	PUNCT
ejpam-6070	181	23	ζ̌∗1	ζ̌∗1	NOUN
ejpam-6070	181	24	,	,	PUNCT
ejpam-6070	181	25	ζ̌	ζ̌	PROPN
ejpam-6070	181	26	∗	∗	NOUN
ejpam-6070	181	27	2	2	NUM
ejpam-6070	181	28	)	)	PUNCT
ejpam-6070	181	29	corresponds	correspond	VERB
ejpam-6070	181	30	to	to	ADP
ejpam-6070	181	31	the	the	DET
ejpam-6070	181	32	solution	solution	NOUN
ejpam-6070	181	33	of	of	ADP
ejpam-6070	181	34	system	system	NOUN
ejpam-6070	181	35	(	(	PUNCT
ejpam-6070	181	36	3	3	NUM
ejpam-6070	181	37	)	)	PUNCT
ejpam-6070	181	38	.	.	PUNCT
ejpam-6070	182	1	from	from	ADP
ejpam-6070	182	2	the	the	DET
ejpam-6070	182	3	iterative	iterative	NOUN
ejpam-6070	182	4	scheme	scheme	NOUN
ejpam-6070	182	5	described	describe	VERB
ejpam-6070	182	6	in	in	ADP
ejpam-6070	182	7	algorithm	algorithm	NOUN
ejpam-6070	182	8	,	,	PUNCT
ejpam-6070	182	9	we	we	PRON
ejpam-6070	182	10	derive	derive	VERB
ejpam-6070	182	11	the	the	DET
ejpam-6070	182	12	following	follow	VERB
ejpam-6070	182	13	conditions	condition	NOUN
ejpam-6070	182	14	:	:	PUNCT
ejpam-6070	182	15	max	max	PROPN
ejpam-6070	182	16	1≤i≤n	1≤i≤n	NUM
ejpam-6070	182	17	{	{	PUNCT
ejpam-6070	182	18	bi	bi	NOUN
ejpam-6070	182	19	1,1ζ̌	1,1ζ̌	NUM
ejpam-6070	182	20	k+1	k+1	NOUN
ejpam-6070	182	21	1	1	NUM
ejpam-6070	182	22	−	−	NOUN
ejpam-6070	182	23	b̃i	b̃i	ADP
ejpam-6070	182	24	1,2ζ̌	1,2ζ̌	NUM
ejpam-6070	182	25	k	k	NOUN
ejpam-6070	182	26	2	2	NUM
ejpam-6070	182	27	−	−	NOUN
ejpam-6070	182	28	g	g	NOUN
ejpam-6070	182	29	i(ζ̌k1	i(ζ̌k1	NOUN
ejpam-6070	182	30	)	)	PUNCT
ejpam-6070	182	31	}	}	PUNCT
ejpam-6070	183	1	=	=	SYM
ejpam-6070	183	2	0	0	NUM
ejpam-6070	183	3	,	,	PUNCT
ejpam-6070	183	4	max	max	PROPN
ejpam-6070	183	5	1≤i≤n	1≤i≤n	NUM
ejpam-6070	183	6	{	{	PUNCT
ejpam-6070	183	7	−b̃i	−b̃i	SYM
ejpam-6070	183	8	2,1ζ̌	2,1ζ̌	NUM
ejpam-6070	183	9	k+1	k+1	NOUN
ejpam-6070	183	10	1	1	NUM
ejpam-6070	183	11	+	+	CCONJ
ejpam-6070	183	12	bi	bi	NOUN
ejpam-6070	183	13	2,2ζ̌	2,2ζ̌	PROPN
ejpam-6070	184	1	k+1	k+1	NOUN
ejpam-6070	184	2	2	2	NUM
ejpam-6070	184	3	−	−	NOUN
ejpam-6070	184	4	g	g	PROPN
ejpam-6070	184	5	i(ζ̌k2	i(ζ̌k2	PROPN
ejpam-6070	184	6	)	)	PUNCT
ejpam-6070	184	7	}	}	PUNCT
ejpam-6070	185	1	=	=	SYM
ejpam-6070	185	2	0	0	X
ejpam-6070	185	3	.	.	PUNCT
ejpam-6070	186	1	taking	take	VERB
ejpam-6070	186	2	the	the	DET
ejpam-6070	186	3	limit	limit	NOUN
ejpam-6070	186	4	as	as	ADP
ejpam-6070	186	5	k	k	PROPN
ejpam-6070	186	6	→	→	SYM
ejpam-6070	186	7	∞	∞	PROPN
ejpam-6070	186	8	and	and	CCONJ
ejpam-6070	186	9	employing	employ	VERB
ejpam-6070	186	10	equation	equation	NOUN
ejpam-6070	186	11	(	(	PUNCT
ejpam-6070	186	12	11	11	NUM
ejpam-6070	186	13	)	)	PUNCT
ejpam-6070	186	14	,	,	PUNCT
ejpam-6070	186	15	we	we	PRON
ejpam-6070	186	16	obtain	obtain	VERB
ejpam-6070	186	17	the	the	DET
ejpam-6070	186	18	following	follow	VERB
ejpam-6070	186	19	system	system	NOUN
ejpam-6070	186	20	:	:	PUNCT
ejpam-6070	186	21	max	max	PROPN
ejpam-6070	186	22	1≤i≤n	1≤i≤n	NUM
ejpam-6070	186	23	{	{	PUNCT
ejpam-6070	186	24	bi	bi	PROPN
ejpam-6070	186	25	1,1ζ̌	1,1ζ̌	NUM
ejpam-6070	186	26	∗	∗	NOUN
ejpam-6070	186	27	1	1	NUM
ejpam-6070	186	28	−	−	NOUN
ejpam-6070	186	29	b̃i	b̃i	ADP
ejpam-6070	186	30	1,2ζ̌	1,2ζ̌	NUM
ejpam-6070	186	31	∗	∗	NOUN
ejpam-6070	186	32	2	2	NUM
ejpam-6070	186	33	−	−	NOUN
ejpam-6070	186	34	g	g	NOUN
ejpam-6070	186	35	i(ζ̌∗1	i(ζ̌∗1	ADJ
ejpam-6070	186	36	)	)	PUNCT
ejpam-6070	186	37	}	}	PUNCT
ejpam-6070	187	1	=	=	SYM
ejpam-6070	187	2	0	0	NUM
ejpam-6070	187	3	,	,	PUNCT
ejpam-6070	187	4	max	max	PROPN
ejpam-6070	187	5	1≤i≤n	1≤i≤n	NUM
ejpam-6070	187	6	{	{	PUNCT
ejpam-6070	187	7	−b̃i	−b̃i	SYM
ejpam-6070	187	8	2,1ζ̌	2,1ζ̌	NUM
ejpam-6070	187	9	∗	∗	NOUN
ejpam-6070	187	10	1	1	NUM
ejpam-6070	187	11	+	+	CCONJ
ejpam-6070	187	12	bi	bi	PROPN
ejpam-6070	187	13	2,2ζ̌	2,2ζ̌	PROPN
ejpam-6070	187	14	∗	∗	NOUN
ejpam-6070	187	15	2	2	NUM
ejpam-6070	187	16	−	−	NOUN
ejpam-6070	187	17	g	g	NOUN
ejpam-6070	187	18	i(ζ̌∗2	i(ζ̌∗2	ADV
ejpam-6070	187	19	)	)	PUNCT
ejpam-6070	187	20	}	}	PUNCT
ejpam-6070	188	1	=	=	PUNCT
ejpam-6070	188	2	0	0	X
ejpam-6070	188	3	.	.	PUNCT
ejpam-6070	189	1	this	this	DET
ejpam-6070	189	2	system	system	NOUN
ejpam-6070	189	3	can	can	AUX
ejpam-6070	189	4	be	be	AUX
ejpam-6070	189	5	rewritten	rewrite	VERB
ejpam-6070	189	6	in	in	ADP
ejpam-6070	189	7	a	a	DET
ejpam-6070	189	8	more	more	ADV
ejpam-6070	189	9	compact	compact	ADJ
ejpam-6070	189	10	form	form	NOUN
ejpam-6070	189	11	as	as	ADP
ejpam-6070	189	12	:	:	PUNCT
ejpam-6070	189	13	max	max	PROPN
ejpam-6070	189	14	1≤i≤n	1≤i≤n	NUM
ejpam-6070	189	15	{	{	PUNCT
ejpam-6070	189	16	biζ̌∗	biζ̌∗	ADV
ejpam-6070	189	17	−	−	PROPN
ejpam-6070	189	18	g	g	PROPN
ejpam-6070	189	19	i(ζ̌∗	i(ζ̌∗	PROPN
ejpam-6070	189	20	)	)	PUNCT
ejpam-6070	189	21	}	}	PUNCT
ejpam-6070	189	22	=	=	PUNCT
ejpam-6070	190	1	0	0	X
ejpam-6070	190	2	.	.	PUNCT
ejpam-6070	191	1	consequently	consequently	ADV
ejpam-6070	191	2	,	,	PUNCT
ejpam-6070	191	3	we	we	PRON
ejpam-6070	191	4	establish	establish	VERB
ejpam-6070	191	5	that	that	DET
ejpam-6070	191	6	ζ̌∗	ζ̌∗	NOUN
ejpam-6070	191	7	is	be	AUX
ejpam-6070	191	8	the	the	DET
ejpam-6070	191	9	unique	unique	ADJ
ejpam-6070	191	10	solution	solution	NOUN
ejpam-6070	191	11	to	to	ADP
ejpam-6070	191	12	system	system	NOUN
ejpam-6070	191	13	(	(	PUNCT
ejpam-6070	191	14	3	3	NUM
ejpam-6070	191	15	)	)	PUNCT
ejpam-6070	191	16	.	.	PUNCT
ejpam-6070	192	1	•	•	NUM
ejpam-6070	192	2	step	step	NOUN
ejpam-6070	192	3	4	4	NUM
ejpam-6070	192	4	:	:	PUNCT
ejpam-6070	192	5	uniqueness	uniqueness	NOUN
ejpam-6070	192	6	of	of	ADP
ejpam-6070	192	7	the	the	DET
ejpam-6070	192	8	discrete	discrete	ADJ
ejpam-6070	192	9	solution	solution	NOUN
ejpam-6070	192	10	to	to	ADP
ejpam-6070	192	11	the	the	DET
ejpam-6070	192	12	hamilton	hamilton	PROPN
ejpam-6070	192	13	-	-	PUNCT
ejpam-6070	192	14	jacobi	jacobi	PROPN
ejpam-6070	192	15	-	-	PUNCT
ejpam-6070	192	16	bellman	bellman	NOUN
ejpam-6070	192	17	system	system	NOUN
ejpam-6070	192	18	(	(	PUNCT
ejpam-6070	192	19	3	3	NUM
ejpam-6070	192	20	)	)	PUNCT
ejpam-6070	192	21	.	.	PUNCT
ejpam-6070	193	1	assume	assume	VERB
ejpam-6070	193	2	that	that	SCONJ
ejpam-6070	193	3	the	the	DET
ejpam-6070	193	4	system	system	NOUN
ejpam-6070	193	5	(	(	PUNCT
ejpam-6070	193	6	3	3	X
ejpam-6070	193	7	)	)	PUNCT
ejpam-6070	193	8	admits	admit	VERB
ejpam-6070	193	9	two	two	NUM
ejpam-6070	193	10	possible	possible	ADJ
ejpam-6070	193	11	solutions	solution	NOUN
ejpam-6070	193	12	,	,	PUNCT
ejpam-6070	193	13	denoted	denote	VERB
ejpam-6070	193	14	by	by	ADP
ejpam-6070	193	15	ζ−	ζ−	NOUN
ejpam-6070	193	16	and	and	CCONJ
ejpam-6070	193	17	ζ+	ζ+	NOUN
ejpam-6070	193	18	.	.	PUNCT
ejpam-6070	194	1	this	this	PRON
ejpam-6070	194	2	leads	lead	VERB
ejpam-6070	194	3	to	to	ADP
ejpam-6070	194	4	the	the	DET
ejpam-6070	194	5	following	follow	VERB
ejpam-6070	194	6	two	two	NUM
ejpam-6070	194	7	conditions	condition	NOUN
ejpam-6070	194	8	:	:	PUNCT
ejpam-6070	194	9	max	max	PROPN
ejpam-6070	194	10	1≤i≤n	1≤i≤n	NUM
ejpam-6070	194	11	{	{	PUNCT
ejpam-6070	194	12	biζ−	biζ−	PROPN
ejpam-6070	194	13	−	−	PROPN
ejpam-6070	194	14	g	g	PROPN
ejpam-6070	194	15	i(ζ−	i(ζ−	NOUN
ejpam-6070	194	16	)	)	PUNCT
ejpam-6070	194	17	}	}	PUNCT
ejpam-6070	195	1	=	=	SYM
ejpam-6070	195	2	0	0	NUM
ejpam-6070	195	3	,	,	PUNCT
ejpam-6070	195	4	max	max	PROPN
ejpam-6070	195	5	1≤i≤n	1≤i≤n	NUM
ejpam-6070	195	6	{	{	PUNCT
ejpam-6070	195	7	biζ+	biζ+	VERB
ejpam-6070	195	8	−	−	NOUN
ejpam-6070	195	9	g	g	NOUN
ejpam-6070	195	10	i(ζ+	i(ζ+	NOUN
ejpam-6070	195	11	)	)	PUNCT
ejpam-6070	195	12	}	}	PUNCT
ejpam-6070	196	1	=	=	PUNCT
ejpam-6070	196	2	0	0	X
ejpam-6070	196	3	.	.	PUNCT
ejpam-6070	197	1	from	from	ADP
ejpam-6070	197	2	these	these	DET
ejpam-6070	197	3	relations	relation	NOUN
ejpam-6070	197	4	,	,	PUNCT
ejpam-6070	197	5	it	it	PRON
ejpam-6070	197	6	follows	follow	VERB
ejpam-6070	197	7	that	that	PRON
ejpam-6070	197	8	:	:	PUNCT
ejpam-6070	197	9	biζ+	biζ+	VERB
ejpam-6070	197	10	−	−	NOUN
ejpam-6070	197	11	g	g	NOUN
ejpam-6070	197	12	i(ζ+	i(ζ+	NOUN
ejpam-6070	197	13	)	)	PUNCT
ejpam-6070	198	1	=	=	SYM
ejpam-6070	198	2	0	0	NUM
ejpam-6070	198	3	⇔	⇔	X
ejpam-6070	198	4	biζ+	biζ+	PROPN
ejpam-6070	198	5	−	−	NOUN
ejpam-6070	199	1	f	f	NOUN
ejpam-6070	200	1	i	i	PRON
ejpam-6070	200	2	−	−	VERB
ejpam-6070	200	3	µζ+	µζ+	NOUN
ejpam-6070	200	4	=	=	NOUN
ejpam-6070	200	5	0	0	NUM
ejpam-6070	200	6	,	,	PUNCT
ejpam-6070	200	7	biζ−	biζ−	NOUN
ejpam-6070	200	8	−	−	PROPN
ejpam-6070	200	9	g	g	PROPN
ejpam-6070	200	10	i(ζ−	i(ζ−	NOUN
ejpam-6070	200	11	)	)	PUNCT
ejpam-6070	200	12	=	=	SYM
ejpam-6070	200	13	0	0	NUM
ejpam-6070	200	14	⇔	⇔	PROPN
ejpam-6070	200	15	biζ−	biζ−	PROPN
ejpam-6070	200	16	−	−	PROPN
ejpam-6070	201	1	f	f	PROPN
ejpam-6070	202	1	i	i	PRON
ejpam-6070	202	2	−	−	PROPN
ejpam-6070	202	3	µζ−	µζ−	PUNCT
ejpam-6070	202	4	=	=	SYM
ejpam-6070	202	5	0	0	PROPN
ejpam-6070	202	6	.	.	PUNCT
ejpam-6070	203	1	s.	s.	PROPN
ejpam-6070	203	2	chebbah	chebbah	PROPN
ejpam-6070	203	3	,	,	PUNCT
ejpam-6070	203	4	s.	s.	PROPN
ejpam-6070	203	5	madi	madi	PROPN
ejpam-6070	203	6	,	,	PUNCT
ejpam-6070	203	7	m.	m.	NOUN
ejpam-6070	203	8	haiour	haiour	PROPN
ejpam-6070	203	9	/	/	SYM
ejpam-6070	203	10	eur	eur	PROPN
ejpam-6070	203	11	.	.	PUNCT
ejpam-6070	204	1	j.	j.	PROPN
ejpam-6070	204	2	pure	pure	PROPN
ejpam-6070	204	3	appl	appl	PROPN
ejpam-6070	204	4	.	.	PROPN
ejpam-6070	204	5	math	math	PROPN
ejpam-6070	204	6	,	,	PUNCT
ejpam-6070	204	7	18	18	NUM
ejpam-6070	204	8	(	(	PUNCT
ejpam-6070	204	9	2	2	NUM
ejpam-6070	204	10	)	)	PUNCT
ejpam-6070	204	11	(	(	PUNCT
ejpam-6070	204	12	2025	2025	NUM
ejpam-6070	204	13	)	)	PUNCT
ejpam-6070	204	14	,	,	PUNCT
ejpam-6070	204	15	6070	6070	NUM
ejpam-6070	204	16	11	11	NUM
ejpam-6070	204	17	of	of	ADP
ejpam-6070	204	18	20	20	NUM
ejpam-6070	204	19	by	by	ADP
ejpam-6070	204	20	subtracting	subtract	VERB
ejpam-6070	204	21	these	these	DET
ejpam-6070	204	22	two	two	NUM
ejpam-6070	204	23	equations	equation	NOUN
ejpam-6070	204	24	and	and	CCONJ
ejpam-6070	204	25	considering	consider	VERB
ejpam-6070	204	26	the	the	DET
ejpam-6070	204	27	decomposition	decomposition	NOUN
ejpam-6070	204	28	bi	bi	NOUN
ejpam-6070	205	1	=	=	PUNCT
ejpam-6070	205	2	a	a	PRON
ejpam-6070	205	3	i+	i+	INTJ
ejpam-6070	205	4	µi	µi	PROPN
ejpam-6070	205	5	,	,	PUNCT
ejpam-6070	205	6	we	we	PRON
ejpam-6070	205	7	obtain	obtain	VERB
ejpam-6070	205	8	:	:	PUNCT
ejpam-6070	205	9	(	(	PUNCT
ejpam-6070	205	10	bi	bi	NOUN
ejpam-6070	205	11	−	−	PROPN
ejpam-6070	205	12	µi)(ζ+	µi)(ζ+	PROPN
ejpam-6070	205	13	−	−	PROPN
ejpam-6070	205	14	ζ−	ζ−	NOUN
ejpam-6070	205	15	)	)	PUNCT
ejpam-6070	205	16	=	=	SYM
ejpam-6070	205	17	0	0	NUM
ejpam-6070	205	18	⇔	⇔	PROPN
ejpam-6070	205	19	a	a	PRON
ejpam-6070	205	20	i(ζ+	i(ζ+	NOUN
ejpam-6070	205	21	−	−	PROPN
ejpam-6070	206	1	ζ−	ζ−	NOUN
ejpam-6070	206	2	)	)	PUNCT
ejpam-6070	206	3	=	=	SYM
ejpam-6070	206	4	0	0	X
ejpam-6070	206	5	.	.	PUNCT
ejpam-6070	207	1	given	give	VERB
ejpam-6070	207	2	that	that	SCONJ
ejpam-6070	207	3	the	the	DET
ejpam-6070	207	4	matrices	matrix	NOUN
ejpam-6070	207	5	a	a	PRON
ejpam-6070	207	6	i	i	PRON
ejpam-6070	207	7	are	be	AUX
ejpam-6070	207	8	m	m	NOUN
ejpam-6070	207	9	-	-	NOUN
ejpam-6070	207	10	matrices	matrix	NOUN
ejpam-6070	207	11	,	,	PUNCT
ejpam-6070	207	12	we	we	PRON
ejpam-6070	207	13	conclude	conclude	VERB
ejpam-6070	207	14	that	that	PRON
ejpam-6070	207	15	:	:	PUNCT
ejpam-6070	207	16	ζ−	ζ−	NOUN
ejpam-6070	207	17	−	−	PROPN
ejpam-6070	207	18	ζ+	ζ+	NOUN
ejpam-6070	207	19	=	=	SYM
ejpam-6070	207	20	0	0	NUM
ejpam-6070	207	21	⇒	⇒	NOUN
ejpam-6070	207	22	ζ−	ζ−	NOUN
ejpam-6070	207	23	=	=	SYM
ejpam-6070	207	24	ζ+	ζ+	NOUN
ejpam-6070	207	25	.	.	PUNCT
ejpam-6070	208	1	thus	thus	ADV
ejpam-6070	208	2	,	,	PUNCT
ejpam-6070	208	3	the	the	DET
ejpam-6070	208	4	solution	solution	NOUN
ejpam-6070	208	5	to	to	ADP
ejpam-6070	208	6	the	the	DET
ejpam-6070	208	7	system	system	NOUN
ejpam-6070	208	8	(	(	PUNCT
ejpam-6070	208	9	3	3	X
ejpam-6070	208	10	)	)	PUNCT
ejpam-6070	208	11	is	be	AUX
ejpam-6070	208	12	uniquely	uniquely	ADV
ejpam-6070	208	13	determined	determine	VERB
ejpam-6070	208	14	.	.	PUNCT
ejpam-6070	209	1	•	•	NUM
ejpam-6070	209	2	step	step	NOUN
ejpam-6070	209	3	5	5	NUM
ejpam-6070	209	4	:	:	PUNCT
ejpam-6070	209	5	demonstrating	demonstrate	VERB
ejpam-6070	209	6	the	the	DET
ejpam-6070	209	7	monotonicity	monotonicity	NOUN
ejpam-6070	209	8	of	of	ADP
ejpam-6070	209	9	the	the	DET
ejpam-6070	209	10	upper	upper	ADJ
ejpam-6070	209	11	sequence	sequence	NOUN
ejpam-6070	209	12	(	(	PUNCT
ejpam-6070	209	13	ζ̂k	ζ̂k	NOUN
ejpam-6070	209	14	)	)	PUNCT
ejpam-6070	209	15	follows	follow	VERB
ejpam-6070	209	16	an	an	DET
ejpam-6070	209	17	approach	approach	NOUN
ejpam-6070	209	18	similar	similar	ADJ
ejpam-6070	209	19	to	to	ADP
ejpam-6070	209	20	that	that	PRON
ejpam-6070	209	21	used	use	VERB
ejpam-6070	209	22	for	for	ADP
ejpam-6070	209	23	the	the	DET
ejpam-6070	209	24	lower	low	ADJ
ejpam-6070	209	25	sequence	sequence	NOUN
ejpam-6070	209	26	(	(	PUNCT
ejpam-6070	209	27	ζ̌k	ζ̌k	PROPN
ejpam-6070	209	28	)	)	PUNCT
ejpam-6070	209	29	.	.	PUNCT
ejpam-6070	210	1	the	the	DET
ejpam-6070	210	2	goal	goal	NOUN
ejpam-6070	210	3	here	here	ADV
ejpam-6070	210	4	is	be	AUX
ejpam-6070	210	5	to	to	PART
ejpam-6070	210	6	establish	establish	VERB
ejpam-6070	210	7	that	that	SCONJ
ejpam-6070	210	8	the	the	DET
ejpam-6070	210	9	two	two	NUM
ejpam-6070	210	10	sequences	sequence	NOUN
ejpam-6070	210	11	,	,	PUNCT
ejpam-6070	210	12	(	(	PUNCT
ejpam-6070	210	13	ζ̂k	ζ̂k	NOUN
ejpam-6070	210	14	)	)	PUNCT
ejpam-6070	210	15	and	and	CCONJ
ejpam-6070	210	16	(	(	PUNCT
ejpam-6070	210	17	ζ̌k	ζ̌k	PROPN
ejpam-6070	210	18	)	)	PUNCT
ejpam-6070	210	19	,	,	PUNCT
ejpam-6070	210	20	maintain	maintain	VERB
ejpam-6070	210	21	an	an	DET
ejpam-6070	210	22	ordering	ordering	NOUN
ejpam-6070	210	23	relationship	relationship	NOUN
ejpam-6070	210	24	across	across	ADP
ejpam-6070	210	25	all	all	DET
ejpam-6070	210	26	subdomains	subdomain	NOUN
ejpam-6070	210	27	.	.	PUNCT
ejpam-6070	211	1	specifically	specifically	ADV
ejpam-6070	211	2	,	,	PUNCT
ejpam-6070	211	3	we	we	PRON
ejpam-6070	211	4	aim	aim	VERB
ejpam-6070	211	5	to	to	PART
ejpam-6070	211	6	show	show	VERB
ejpam-6070	211	7	:	:	PUNCT
ejpam-6070	211	8	ζ̌k	ζ̌k	PROPN
ejpam-6070	211	9	≤	≤	NOUN
ejpam-6070	211	10	ζ̂k	ζ̂k	NOUN
ejpam-6070	211	11	,	,	PUNCT
ejpam-6070	211	12	∀k	∀k	NOUN
ejpam-6070	211	13	∈	∈	PROPN
ejpam-6070	211	14	n.	n.	NOUN
ejpam-6070	211	15	for	for	ADP
ejpam-6070	211	16	the	the	DET
ejpam-6070	211	17	initial	initial	ADJ
ejpam-6070	211	18	iteration	iteration	NOUN
ejpam-6070	211	19	k	k	PROPN
ejpam-6070	212	1	=	=	SYM
ejpam-6070	212	2	0	0	PROPN
ejpam-6070	212	3	,	,	PUNCT
ejpam-6070	212	4	we	we	PRON
ejpam-6070	212	5	assume	assume	VERB
ejpam-6070	212	6	that	that	SCONJ
ejpam-6070	212	7	ζ̌0	ζ̌0	PRON
ejpam-6070	212	8	≤	≤	X
ejpam-6070	212	9	ζ̂0	ζ̂0	NOUN
ejpam-6070	212	10	.	.	PUNCT
ejpam-6070	213	1	in	in	ADP
ejpam-6070	213	2	the	the	DET
ejpam-6070	213	3	first	first	ADJ
ejpam-6070	213	4	subdomain	subdomain	NOUN
ejpam-6070	213	5	,	,	PUNCT
ejpam-6070	213	6	since	since	SCONJ
ejpam-6070	213	7	ζ̌1	ζ̌1	NUM
ejpam-6070	213	8	is	be	AUX
ejpam-6070	213	9	a	a	DET
ejpam-6070	213	10	lower	low	ADJ
ejpam-6070	213	11	solution	solution	NOUN
ejpam-6070	213	12	,	,	PUNCT
ejpam-6070	213	13	it	it	PRON
ejpam-6070	213	14	satisfies	satisfy	VERB
ejpam-6070	213	15	the	the	DET
ejpam-6070	213	16	inequality	inequality	NOUN
ejpam-6070	213	17	:	:	PUNCT
ejpam-6070	213	18	max	max	PROPN
ejpam-6070	213	19	1≤i≤n	1≤i≤n	NUM
ejpam-6070	213	20	{	{	PUNCT
ejpam-6070	213	21	bi	bi	PROPN
ejpam-6070	213	22	1,1ζ̌	1,1ζ̌	NUM
ejpam-6070	213	23	1	1	NUM
ejpam-6070	213	24	1	1	NUM
ejpam-6070	213	25	−	−	NUM
ejpam-6070	213	26	b̃i	b̃i	ADP
ejpam-6070	213	27	1,2ζ̌	1,2ζ̌	NUM
ejpam-6070	213	28	0	0	NUM
ejpam-6070	213	29	2	2	NUM
ejpam-6070	213	30	−	−	NOUN
ejpam-6070	213	31	g	g	PROPN
ejpam-6070	213	32	i(ζ̌01	i(ζ̌01	PROPN
ejpam-6070	213	33	)	)	PUNCT
ejpam-6070	213	34	}	}	PUNCT
ejpam-6070	213	35	≤	≤	NUM
ejpam-6070	213	36	0	0	NUM
ejpam-6070	213	37	.	.	PUNCT
ejpam-6070	214	1	(	(	PUNCT
ejpam-6070	214	2	12	12	NUM
ejpam-6070	214	3	)	)	PUNCT
ejpam-6070	214	4	on	on	ADP
ejpam-6070	214	5	the	the	DET
ejpam-6070	214	6	other	other	ADJ
ejpam-6070	214	7	hand	hand	NOUN
ejpam-6070	214	8	,	,	PUNCT
ejpam-6070	214	9	since	since	SCONJ
ejpam-6070	214	10	ζ̂1	ζ̂1	ADV
ejpam-6070	214	11	is	be	AUX
ejpam-6070	214	12	an	an	DET
ejpam-6070	214	13	upper	upper	ADJ
ejpam-6070	214	14	solution	solution	NOUN
ejpam-6070	214	15	,	,	PUNCT
ejpam-6070	214	16	it	it	PRON
ejpam-6070	214	17	must	must	AUX
ejpam-6070	214	18	satisfy	satisfy	VERB
ejpam-6070	214	19	:	:	PUNCT
ejpam-6070	214	20	max	max	PROPN
ejpam-6070	214	21	1≤i≤n	1≤i≤n	NUM
ejpam-6070	214	22	{	{	PUNCT
ejpam-6070	214	23	bi	bi	NOUN
ejpam-6070	214	24	1,1ζ̂	1,1ζ̂	NOUN
ejpam-6070	214	25	1	1	NUM
ejpam-6070	214	26	1	1	NUM
ejpam-6070	214	27	−	−	NUM
ejpam-6070	214	28	b̃i	b̃i	ADP
ejpam-6070	214	29	1,2ζ̂	1,2ζ̂	NUM
ejpam-6070	214	30	0	0	SYM
ejpam-6070	214	31	2	2	NUM
ejpam-6070	214	32	−	−	NOUN
ejpam-6070	214	33	g	g	NOUN
ejpam-6070	214	34	i(ζ̂01	i(ζ̂01	PROPN
ejpam-6070	214	35	)	)	PUNCT
ejpam-6070	214	36	}	}	PUNCT
ejpam-6070	214	37	≥	≥	NOUN
ejpam-6070	214	38	0	0	NUM
ejpam-6070	214	39	.	.	PUNCT
ejpam-6070	215	1	(	(	PUNCT
ejpam-6070	215	2	13	13	NUM
ejpam-6070	215	3	)	)	PUNCT
ejpam-6070	215	4	by	by	ADP
ejpam-6070	215	5	comparing	compare	VERB
ejpam-6070	215	6	the	the	DET
ejpam-6070	215	7	inequalities	inequality	NOUN
ejpam-6070	215	8	in	in	ADP
ejpam-6070	215	9	equations	equation	NOUN
ejpam-6070	215	10	(	(	PUNCT
ejpam-6070	215	11	12	12	NUM
ejpam-6070	215	12	)	)	PUNCT
ejpam-6070	215	13	and	and	CCONJ
ejpam-6070	215	14	(	(	PUNCT
ejpam-6070	215	15	13	13	NUM
ejpam-6070	215	16	)	)	PUNCT
ejpam-6070	215	17	,	,	PUNCT
ejpam-6070	215	18	we	we	PRON
ejpam-6070	215	19	deduce	deduce	VERB
ejpam-6070	215	20	that	that	PRON
ejpam-6070	215	21	:	:	PUNCT
ejpam-6070	215	22	max	max	PROPN
ejpam-6070	215	23	1≤i≤n	1≤i≤n	NUM
ejpam-6070	215	24	{	{	PUNCT
ejpam-6070	215	25	bi	bi	PROPN
ejpam-6070	215	26	1,1ζ̌	1,1ζ̌	NUM
ejpam-6070	215	27	1	1	NUM
ejpam-6070	215	28	1	1	NUM
ejpam-6070	215	29	−	−	NUM
ejpam-6070	215	30	b̃i	b̃i	ADP
ejpam-6070	215	31	1,2ζ̌	1,2ζ̌	NUM
ejpam-6070	215	32	0	0	NUM
ejpam-6070	215	33	2	2	NUM
ejpam-6070	215	34	−	−	NOUN
ejpam-6070	215	35	g	g	PROPN
ejpam-6070	215	36	i(ζ̌01	i(ζ̌01	PROPN
ejpam-6070	215	37	)	)	PUNCT
ejpam-6070	215	38	}	}	PUNCT
ejpam-6070	215	39	≤	≤	NUM
ejpam-6070	215	40	max	max	PROPN
ejpam-6070	215	41	1≤i≤n	1≤i≤n	NUM
ejpam-6070	215	42	{	{	PUNCT
ejpam-6070	215	43	bi	bi	NOUN
ejpam-6070	215	44	1,1ζ̂	1,1ζ̂	NOUN
ejpam-6070	215	45	1	1	NUM
ejpam-6070	215	46	1	1	NUM
ejpam-6070	215	47	−	−	NUM
ejpam-6070	215	48	b̃i	b̃i	ADP
ejpam-6070	215	49	1,2ζ̂	1,2ζ̂	NUM
ejpam-6070	215	50	0	0	SYM
ejpam-6070	215	51	2	2	NUM
ejpam-6070	215	52	−	−	NOUN
ejpam-6070	215	53	g	g	NOUN
ejpam-6070	215	54	i(ζ̂01	i(ζ̂01	PROPN
ejpam-6070	215	55	)	)	PUNCT
ejpam-6070	215	56	}	}	PUNCT
ejpam-6070	215	57	.	.	PUNCT
ejpam-6070	216	1	thus	thus	ADV
ejpam-6070	216	2	,	,	PUNCT
ejpam-6070	216	3	we	we	PRON
ejpam-6070	216	4	obtain	obtain	VERB
ejpam-6070	216	5	ζ̌02	ζ̌02	ADJ
ejpam-6070	216	6	≤	≤	NOUN
ejpam-6070	216	7	ζ̂02	ζ̂02	NOUN
ejpam-6070	216	8	and	and	CCONJ
ejpam-6070	216	9	ζ̌01	ζ̌01	PROPN
ejpam-6070	216	10	≤	≤	ADJ
ejpam-6070	216	11	ζ̂01	ζ̂01	NOUN
ejpam-6070	216	12	,	,	PUNCT
ejpam-6070	216	13	leading	lead	VERB
ejpam-6070	216	14	to	to	ADP
ejpam-6070	216	15	:	:	PUNCT
ejpam-6070	216	16	ζ̌11	ζ̌11	PROPN
ejpam-6070	216	17	≤	≤	NUM
ejpam-6070	216	18	ζ̂11	ζ̂11	PROPN
ejpam-6070	216	19	.	.	PUNCT
ejpam-6070	217	1	next	next	ADV
ejpam-6070	217	2	,	,	PUNCT
ejpam-6070	217	3	solving	solve	VERB
ejpam-6070	217	4	the	the	DET
ejpam-6070	217	5	problem	problem	NOUN
ejpam-6070	217	6	in	in	ADP
ejpam-6070	217	7	the	the	DET
ejpam-6070	217	8	second	second	ADJ
ejpam-6070	217	9	subdomain	subdomain	NOUN
ejpam-6070	217	10	gives	give	VERB
ejpam-6070	217	11	the	the	DET
ejpam-6070	217	12	following	follow	VERB
ejpam-6070	217	13	inequalities	inequality	NOUN
ejpam-6070	217	14	:	:	PUNCT
ejpam-6070	217	15	max	max	PROPN
ejpam-6070	217	16	1≤i≤n	1≤i≤n	NUM
ejpam-6070	217	17	{	{	PUNCT
ejpam-6070	217	18	−b̃i	−b̃i	SYM
ejpam-6070	217	19	2,1ζ̌	2,1ζ̌	NUM
ejpam-6070	217	20	1	1	NUM
ejpam-6070	217	21	1	1	NUM
ejpam-6070	217	22	+	+	CCONJ
ejpam-6070	217	23	bi	bi	NOUN
ejpam-6070	217	24	2,2ζ̌	2,2ζ̌	NUM
ejpam-6070	217	25	1	1	NUM
ejpam-6070	217	26	2	2	NUM
ejpam-6070	217	27	−	−	NOUN
ejpam-6070	217	28	g	g	PROPN
ejpam-6070	217	29	i(ζ̌02	i(ζ̌02	PROPN
ejpam-6070	217	30	)	)	PUNCT
ejpam-6070	217	31	}	}	PUNCT
ejpam-6070	217	32	≤	≤	NUM
ejpam-6070	217	33	0	0	NUM
ejpam-6070	217	34	,	,	PUNCT
ejpam-6070	217	35	(	(	PUNCT
ejpam-6070	217	36	14	14	NUM
ejpam-6070	217	37	)	)	PUNCT
ejpam-6070	217	38	and	and	CCONJ
ejpam-6070	217	39	max	max	PROPN
ejpam-6070	217	40	1≤i≤n	1≤i≤n	NUM
ejpam-6070	217	41	{	{	PUNCT
ejpam-6070	217	42	−b̃i	−b̃i	SYM
ejpam-6070	217	43	2,1ζ̂	2,1ζ̂	NUM
ejpam-6070	217	44	1	1	NUM
ejpam-6070	217	45	1	1	NUM
ejpam-6070	217	46	+	+	NUM
ejpam-6070	217	47	bi	bi	NOUN
ejpam-6070	217	48	2,2ζ̂	2,2ζ̂	NUM
ejpam-6070	217	49	1	1	NUM
ejpam-6070	217	50	2	2	NUM
ejpam-6070	217	51	−	−	NOUN
ejpam-6070	217	52	g	g	PROPN
ejpam-6070	217	53	i(ζ̂02	i(ζ̂02	PROPN
ejpam-6070	217	54	)	)	PUNCT
ejpam-6070	217	55	}	}	PUNCT
ejpam-6070	217	56	≥	≥	NOUN
ejpam-6070	217	57	0	0	NUM
ejpam-6070	217	58	.	.	PUNCT
ejpam-6070	218	1	(	(	PUNCT
ejpam-6070	218	2	15	15	NUM
ejpam-6070	218	3	)	)	PUNCT
ejpam-6070	218	4	by	by	ADP
ejpam-6070	218	5	comparing	compare	VERB
ejpam-6070	218	6	equations	equation	NOUN
ejpam-6070	218	7	(	(	PUNCT
ejpam-6070	218	8	14	14	NUM
ejpam-6070	218	9	)	)	PUNCT
ejpam-6070	218	10	and	and	CCONJ
ejpam-6070	218	11	(	(	PUNCT
ejpam-6070	218	12	15	15	NUM
ejpam-6070	218	13	)	)	PUNCT
ejpam-6070	218	14	,	,	PUNCT
ejpam-6070	218	15	we	we	PRON
ejpam-6070	218	16	obtain	obtain	VERB
ejpam-6070	218	17	:	:	PUNCT
ejpam-6070	218	18	max	max	PROPN
ejpam-6070	218	19	1≤i≤n	1≤i≤n	NUM
ejpam-6070	218	20	{	{	PUNCT
ejpam-6070	218	21	−b̃i	−b̃i	SYM
ejpam-6070	218	22	2,1ζ̌	2,1ζ̌	NUM
ejpam-6070	218	23	1	1	NUM
ejpam-6070	218	24	1	1	NUM
ejpam-6070	218	25	+	+	CCONJ
ejpam-6070	218	26	bi	bi	NOUN
ejpam-6070	218	27	2,2ζ̌	2,2ζ̌	NUM
ejpam-6070	218	28	1	1	NUM
ejpam-6070	218	29	2	2	NUM
ejpam-6070	218	30	−	−	NOUN
ejpam-6070	218	31	g	g	PROPN
ejpam-6070	218	32	i(ζ̌02	i(ζ̌02	PROPN
ejpam-6070	218	33	)	)	PUNCT
ejpam-6070	218	34	}	}	PUNCT
ejpam-6070	218	35	≤	≤	NUM
ejpam-6070	218	36	max	max	PROPN
ejpam-6070	218	37	1≤i≤n	1≤i≤n	NUM
ejpam-6070	218	38	{	{	PUNCT
ejpam-6070	218	39	−b̃i	−b̃i	SYM
ejpam-6070	218	40	2,1ζ̂	2,1ζ̂	NUM
ejpam-6070	218	41	1	1	NUM
ejpam-6070	218	42	1	1	NUM
ejpam-6070	218	43	+	+	NUM
ejpam-6070	218	44	bi	bi	NOUN
ejpam-6070	218	45	2,2ζ̂	2,2ζ̂	NUM
ejpam-6070	218	46	1	1	NUM
ejpam-6070	218	47	2	2	NUM
ejpam-6070	218	48	−	−	NOUN
ejpam-6070	218	49	g	g	PROPN
ejpam-6070	218	50	i(ζ̂02	i(ζ̂02	PROPN
ejpam-6070	218	51	)	)	PUNCT
ejpam-6070	218	52	}	}	PUNCT
ejpam-6070	218	53	.	.	PUNCT
ejpam-6070	219	1	s.	s.	PROPN
ejpam-6070	219	2	chebbah	chebbah	PROPN
ejpam-6070	219	3	,	,	PUNCT
ejpam-6070	219	4	s.	s.	PROPN
ejpam-6070	219	5	madi	madi	PROPN
ejpam-6070	219	6	,	,	PUNCT
ejpam-6070	219	7	m.	m.	NOUN
ejpam-6070	219	8	haiour	haiour	PROPN
ejpam-6070	219	9	/	/	SYM
ejpam-6070	219	10	eur	eur	PROPN
ejpam-6070	219	11	.	.	PUNCT
ejpam-6070	220	1	j.	j.	PROPN
ejpam-6070	220	2	pure	pure	PROPN
ejpam-6070	220	3	appl	appl	PROPN
ejpam-6070	220	4	.	.	PROPN
ejpam-6070	220	5	math	math	PROPN
ejpam-6070	220	6	,	,	PUNCT
ejpam-6070	220	7	18	18	NUM
ejpam-6070	220	8	(	(	PUNCT
ejpam-6070	220	9	2	2	NUM
ejpam-6070	220	10	)	)	PUNCT
ejpam-6070	220	11	(	(	PUNCT
ejpam-6070	220	12	2025	2025	NUM
ejpam-6070	220	13	)	)	PUNCT
ejpam-6070	220	14	,	,	PUNCT
ejpam-6070	220	15	6070	6070	NUM
ejpam-6070	220	16	12	12	NUM
ejpam-6070	220	17	of	of	ADP
ejpam-6070	220	18	20	20	NUM
ejpam-6070	220	19	from	from	ADP
ejpam-6070	220	20	the	the	DET
ejpam-6070	220	21	assumption	assumption	NOUN
ejpam-6070	220	22	ζ̌11	ζ̌11	PROPN
ejpam-6070	220	23	≤	≤	PUNCT
ejpam-6070	220	24	ζ̂11	ζ̂11	NOUN
ejpam-6070	220	25	and	and	CCONJ
ejpam-6070	220	26	ζ̌02	ζ̌02	ADJ
ejpam-6070	220	27	≤	≤	ADJ
ejpam-6070	220	28	ζ̂02	ζ̂02	NOUN
ejpam-6070	220	29	,	,	PUNCT
ejpam-6070	220	30	we	we	PRON
ejpam-6070	220	31	conclude	conclude	VERB
ejpam-6070	220	32	that	that	SCONJ
ejpam-6070	220	33	:	:	PUNCT
ejpam-6070	220	34	ζ̌12	ζ̌12	ADJ
ejpam-6070	220	35	≤	≤	PUNCT
ejpam-6070	220	36	ζ̂12	ζ̂12	ADV
ejpam-6070	220	37	.	.	PUNCT
ejpam-6070	221	1	therefore	therefore	ADV
ejpam-6070	221	2	,	,	PUNCT
ejpam-6070	221	3	we	we	PRON
ejpam-6070	221	4	can	can	AUX
ejpam-6070	221	5	conclude	conclude	VERB
ejpam-6070	221	6	that	that	PRON
ejpam-6070	221	7	:	:	PUNCT
ejpam-6070	221	8	ζ̌1	ζ̌1	NUM
ejpam-6070	221	9	≤	≤	NUM
ejpam-6070	221	10	ζ̂1	ζ̂1	PROPN
ejpam-6070	221	11	.	.	PUNCT
ejpam-6070	222	1	by	by	ADP
ejpam-6070	222	2	applying	apply	VERB
ejpam-6070	222	3	induction	induction	NOUN
ejpam-6070	222	4	,	,	PUNCT
ejpam-6070	222	5	we	we	PRON
ejpam-6070	222	6	prove	prove	VERB
ejpam-6070	222	7	that	that	SCONJ
ejpam-6070	222	8	ζ̌k	ζ̌k	PROPN
ejpam-6070	222	9	≤	≤	NOUN
ejpam-6070	222	10	ζ̂k	ζ̂k	X
ejpam-6070	222	11	for	for	ADP
ejpam-6070	222	12	all	all	DET
ejpam-6070	222	13	k.	k.	PROPN
ejpam-6070	222	14	since	since	SCONJ
ejpam-6070	222	15	the	the	DET
ejpam-6070	222	16	sequence	sequence	NOUN
ejpam-6070	222	17	(	(	PUNCT
ejpam-6070	222	18	ζ̌k	ζ̌k	PROPN
ejpam-6070	222	19	)	)	PUNCT
ejpam-6070	222	20	is	be	AUX
ejpam-6070	222	21	increasing	increase	VERB
ejpam-6070	222	22	and	and	CCONJ
ejpam-6070	222	23	bounded	bound	VERB
ejpam-6070	222	24	above	above	ADV
ejpam-6070	222	25	,	,	PUNCT
ejpam-6070	222	26	while	while	SCONJ
ejpam-6070	222	27	the	the	DET
ejpam-6070	222	28	sequence	sequence	NOUN
ejpam-6070	222	29	(	(	PUNCT
ejpam-6070	222	30	ζ̂k	ζ̂k	NOUN
ejpam-6070	222	31	)	)	PUNCT
ejpam-6070	222	32	is	be	AUX
ejpam-6070	222	33	decreasing	decrease	VERB
ejpam-6070	222	34	and	and	CCONJ
ejpam-6070	222	35	bounded	bound	VERB
ejpam-6070	222	36	below	below	ADV
ejpam-6070	222	37	,	,	PUNCT
ejpam-6070	222	38	and	and	CCONJ
ejpam-6070	222	39	given	give	VERB
ejpam-6070	222	40	that	that	SCONJ
ejpam-6070	222	41	these	these	DET
ejpam-6070	222	42	two	two	NUM
ejpam-6070	222	43	sequences	sequence	NOUN
ejpam-6070	222	44	are	be	AUX
ejpam-6070	222	45	interdependent	interdependent	ADJ
ejpam-6070	222	46	,	,	PUNCT
ejpam-6070	222	47	it	it	PRON
ejpam-6070	222	48	can	can	AUX
ejpam-6070	222	49	be	be	AUX
ejpam-6070	222	50	concluded	conclude	VERB
ejpam-6070	222	51	that	that	SCONJ
ejpam-6070	222	52	both	both	DET
ejpam-6070	222	53	sequences	sequence	NOUN
ejpam-6070	222	54	converge	converge	VERB
ejpam-6070	222	55	to	to	ADP
ejpam-6070	222	56	the	the	DET
ejpam-6070	222	57	unique	unique	ADJ
ejpam-6070	222	58	solution	solution	NOUN
ejpam-6070	222	59	of	of	ADP
ejpam-6070	222	60	the	the	DET
ejpam-6070	222	61	discrete	discrete	ADJ
ejpam-6070	222	62	problem	problem	NOUN
ejpam-6070	222	63	(	(	PUNCT
ejpam-6070	222	64	3	3	NUM
ejpam-6070	222	65	)	)	PUNCT
ejpam-6070	222	66	.	.	PUNCT
ejpam-6070	223	1	thus	thus	ADV
ejpam-6070	223	2	,	,	PUNCT
ejpam-6070	223	3	we	we	PRON
ejpam-6070	223	4	obtain	obtain	VERB
ejpam-6070	223	5	:	:	PUNCT
ejpam-6070	223	6	lim	lim	PROPN
ejpam-6070	223	7	k→∞	k→∞	NOUN
ejpam-6070	223	8	ζ̂k	ζ̂k	X
ejpam-6070	224	1	=	=	SYM
ejpam-6070	224	2	lim	lim	PROPN
ejpam-6070	224	3	k→∞	k→∞	NOUN
ejpam-6070	224	4	ζ̌k	ζ̌k	PROPN
ejpam-6070	224	5	=	=	PUNCT
ejpam-6070	224	6	ζ	ζ	NOUN
ejpam-6070	224	7	theorem	theorem	NOUN
ejpam-6070	224	8	2	2	NUM
ejpam-6070	224	9	.	.	X
ejpam-6070	224	10	for	for	ADP
ejpam-6070	224	11	any	any	DET
ejpam-6070	224	12	initial	initial	ADJ
ejpam-6070	224	13	solution	solution	NOUN
ejpam-6070	224	14	ζ0	ζ0	VERB
ejpam-6070	224	15	,	,	PUNCT
ejpam-6070	224	16	the	the	DET
ejpam-6070	224	17	iterative	iterative	NOUN
ejpam-6070	224	18	sequence	sequence	NOUN
ejpam-6070	224	19	(	(	PUNCT
ejpam-6070	224	20	ζk	ζk	NOUN
ejpam-6070	224	21	)	)	PUNCT
ejpam-6070	224	22	,	,	PUNCT
ejpam-6070	224	23	generated	generate	VERB
ejpam-6070	224	24	by	by	ADP
ejpam-6070	224	25	the	the	DET
ejpam-6070	224	26	algorithm	algorithm	NOUN
ejpam-6070	224	27	converges	converge	VERB
ejpam-6070	224	28	geometrically	geometrically	ADV
ejpam-6070	224	29	to	to	ADP
ejpam-6070	224	30	the	the	DET
ejpam-6070	224	31	unique	unique	ADJ
ejpam-6070	224	32	solution	solution	NOUN
ejpam-6070	224	33	of	of	ADP
ejpam-6070	224	34	the	the	DET
ejpam-6070	224	35	system	system	NOUN
ejpam-6070	224	36	(	(	PUNCT
ejpam-6070	224	37	3	3	NUM
ejpam-6070	224	38	)	)	PUNCT
ejpam-6070	224	39	,	,	PUNCT
ejpam-6070	224	40	with	with	ADP
ejpam-6070	224	41	a	a	DET
ejpam-6070	224	42	positive	positive	ADJ
ejpam-6070	224	43	constant	constant	ADJ
ejpam-6070	224	44	0	0	NUM
ejpam-6070	224	45	<	<	X
ejpam-6070	224	46	η	η	X
ejpam-6070	224	47	<	<	X
ejpam-6070	224	48	1	1	NUM
ejpam-6070	224	49	such	such	ADJ
ejpam-6070	224	50	that	that	PRON
ejpam-6070	224	51	:	:	PUNCT
ejpam-6070	224	52	∥ζk+1	∥ζk+1	ADP
ejpam-6070	224	53	−	−	ADP
ejpam-6070	224	54	ζk∥l∞(ω	ζk∥l∞(ω	NOUN
ejpam-6070	224	55	)	)	PUNCT
ejpam-6070	224	56	≤	≤	NOUN
ejpam-6070	224	57	cηk	cηk	PROPN
ejpam-6070	224	58	,	,	PUNCT
ejpam-6070	224	59	k	k	PROPN
ejpam-6070	224	60	∈	∈	PROPN
ejpam-6070	224	61	n.	n.	NOUN
ejpam-6070	224	62	proof	proof	NOUN
ejpam-6070	224	63	.	.	PUNCT
ejpam-6070	225	1	we	we	PRON
ejpam-6070	225	2	begin	begin	VERB
ejpam-6070	225	3	by	by	ADP
ejpam-6070	225	4	examining	examine	VERB
ejpam-6070	225	5	the	the	DET
ejpam-6070	225	6	formulation	formulation	NOUN
ejpam-6070	225	7	of	of	ADP
ejpam-6070	225	8	the	the	DET
ejpam-6070	225	9	system	system	NOUN
ejpam-6070	225	10	and	and	CCONJ
ejpam-6070	225	11	noting	note	VERB
ejpam-6070	225	12	the	the	DET
ejpam-6070	225	13	following	follow	VERB
ejpam-6070	225	14	relations	relation	NOUN
ejpam-6070	225	15	:	:	PUNCT
ejpam-6070	225	16	max	max	PROPN
ejpam-6070	225	17	1≤i≤n	1≤i≤n	NUM
ejpam-6070	225	18	{	{	PUNCT
ejpam-6070	225	19	bi	bi	PROPN
ejpam-6070	225	20	1,1ζ	1,1ζ	PROPN
ejpam-6070	225	21	k+1	k+1	NOUN
ejpam-6070	225	22	1	1	NUM
ejpam-6070	225	23	−	−	NOUN
ejpam-6070	225	24	b̃i	b̃i	ADP
ejpam-6070	225	25	1,2ζ	1,2ζ	NUM
ejpam-6070	225	26	k	k	NOUN
ejpam-6070	225	27	2	2	NUM
ejpam-6070	225	28	−	−	PROPN
ejpam-6070	225	29	g	g	PROPN
ejpam-6070	225	30	i(ζk1	i(ζk1	PROPN
ejpam-6070	225	31	)	)	PUNCT
ejpam-6070	225	32	}	}	PUNCT
ejpam-6070	226	1	=	=	PUNCT
ejpam-6070	226	2	0	0	NUM
ejpam-6070	226	3	,	,	PUNCT
ejpam-6070	226	4	and	and	CCONJ
ejpam-6070	226	5	max	max	PROPN
ejpam-6070	226	6	1≤i≤n	1≤i≤n	NUM
ejpam-6070	226	7	{	{	PUNCT
ejpam-6070	226	8	bi	bi	PROPN
ejpam-6070	226	9	1,1ζ	1,1ζ	NUM
ejpam-6070	226	10	k	k	NOUN
ejpam-6070	226	11	1	1	NUM
ejpam-6070	226	12	−	−	NOUN
ejpam-6070	226	13	b̃i	b̃i	X
ejpam-6070	226	14	1,2ζ	1,2ζ	NUM
ejpam-6070	226	15	k−1	k−1	PROPN
ejpam-6070	226	16	2	2	NUM
ejpam-6070	226	17	−	−	NOUN
ejpam-6070	226	18	g	g	PROPN
ejpam-6070	226	19	i(ζk−1	i(ζk−1	PROPN
ejpam-6070	226	20	1	1	NUM
ejpam-6070	226	21	)	)	PUNCT
ejpam-6070	226	22	}	}	PUNCT
ejpam-6070	227	1	=	=	PUNCT
ejpam-6070	227	2	0	0	X
ejpam-6070	227	3	.	.	PUNCT
ejpam-6070	228	1	these	these	DET
ejpam-6070	228	2	conditions	condition	NOUN
ejpam-6070	228	3	correspond	correspond	VERB
ejpam-6070	228	4	to	to	ADP
ejpam-6070	228	5	solving	solve	VERB
ejpam-6070	228	6	the	the	DET
ejpam-6070	228	7	following	follow	VERB
ejpam-6070	228	8	problems:	problems:	PROPN
ejpam-6070	228	9	max	max	PROPN
ejpam-6070	228	10	1≤i≤n	1≤i≤n	NUM
ejpam-6070	228	11	(	(	PUNCT
ejpam-6070	228	12	bi	bi	NOUN
ejpam-6070	228	13	1,1ζ	1,1ζ	PROPN
ejpam-6070	228	14	k+1	k+1	NOUN
ejpam-6070	228	15	1	1	NUM
ejpam-6070	228	16	−	−	PROPN
ejpam-6070	228	17	g	g	PROPN
ejpam-6070	228	18	i(ζk1	i(ζk1	PROPN
ejpam-6070	228	19	)	)	PUNCT
ejpam-6070	228	20	)	)	PUNCT
ejpam-6070	229	1	=	=	PUNCT
ejpam-6070	229	2	0	0	NUM
ejpam-6070	229	3	,	,	PUNCT
ejpam-6070	229	4	in	in	ADP
ejpam-6070	229	5	ω1	ω1	PROPN
ejpam-6070	229	6	,	,	PUNCT
ejpam-6070	229	7	(	(	PUNCT
ejpam-6070	229	8	ζk+1	ζk+1	NUM
ejpam-6070	229	9	1	1	NUM
ejpam-6070	229	10	)	)	PUNCT
ejpam-6070	229	11	β	β	NOUN
ejpam-6070	229	12	=	=	PUNCT
ejpam-6070	229	13	(	(	PUNCT
ejpam-6070	229	14	ζk2	ζk2	NOUN
ejpam-6070	229	15	)	)	PUNCT
ejpam-6070	229	16	β	β	PROPN
ejpam-6070	229	17	,	,	PUNCT
ejpam-6070	229	18	on	on	ADP
ejpam-6070	229	19	σ1	σ1	PROPN
ejpam-6070	229	20	,	,	PUNCT
ejpam-6070	229	21	and	and	CCONJ
ejpam-6070	229	22			PRON
ejpam-6070	229	23	max	max	PROPN
ejpam-6070	229	24	1≤i≤n	1≤i≤n	NUM
ejpam-6070	229	25	(	(	PUNCT
ejpam-6070	229	26	bi	bi	PROPN
ejpam-6070	229	27	1,1ζ	1,1ζ	NUM
ejpam-6070	229	28	k	k	NOUN
ejpam-6070	230	1	1	1	NUM
ejpam-6070	230	2	−	−	PROPN
ejpam-6070	230	3	g	g	PROPN
ejpam-6070	230	4	i(ζk−1	i(ζk−1	PROPN
ejpam-6070	230	5	1	1	NUM
ejpam-6070	230	6	)	)	PUNCT
ejpam-6070	230	7	)	)	PUNCT
ejpam-6070	231	1	=	=	PUNCT
ejpam-6070	231	2	0	0	NUM
ejpam-6070	231	3	,	,	PUNCT
ejpam-6070	231	4	in	in	ADP
ejpam-6070	231	5	ω1	ω1	PROPN
ejpam-6070	231	6	,	,	PUNCT
ejpam-6070	231	7	(	(	PUNCT
ejpam-6070	231	8	ζk1	ζk1	X
ejpam-6070	231	9	)	)	PUNCT
ejpam-6070	231	10	β	β	X
ejpam-6070	231	11	=	=	PUNCT
ejpam-6070	231	12	(	(	PUNCT
ejpam-6070	231	13	ζk−1	ζk−1	PROPN
ejpam-6070	231	14	2	2	NUM
ejpam-6070	231	15	)	)	PUNCT
ejpam-6070	231	16	β	β	NOUN
ejpam-6070	231	17	,	,	PUNCT
ejpam-6070	231	18	on	on	ADP
ejpam-6070	231	19	σ1	σ1	PROPN
ejpam-6070	231	20	.	.	PUNCT
ejpam-6070	232	1	by	by	ADP
ejpam-6070	232	2	analyzing	analyze	VERB
ejpam-6070	232	3	the	the	DET
ejpam-6070	232	4	boundary	boundary	ADJ
ejpam-6070	232	5	conditions	condition	NOUN
ejpam-6070	232	6	of	of	ADP
ejpam-6070	232	7	both	both	DET
ejpam-6070	232	8	problems	problem	NOUN
ejpam-6070	232	9	and	and	CCONJ
ejpam-6070	232	10	using	use	VERB
ejpam-6070	232	11	the	the	DET
ejpam-6070	232	12	results	result	NOUN
ejpam-6070	232	13	from	from	ADP
ejpam-6070	232	14	[	[	X
ejpam-6070	232	15	10	10	NUM
ejpam-6070	232	16	]	]	PUNCT
ejpam-6070	232	17	applied	apply	VERB
ejpam-6070	232	18	to	to	ADP
ejpam-6070	232	19	the	the	DET
ejpam-6070	232	20	hamilton	hamilton	PROPN
ejpam-6070	232	21	-	-	PUNCT
ejpam-6070	232	22	jacobi	jacobi	PROPN
ejpam-6070	232	23	-	-	PUNCT
ejpam-6070	232	24	bellman	bellman	NOUN
ejpam-6070	232	25	equation	equation	NOUN
ejpam-6070	232	26	,	,	PUNCT
ejpam-6070	232	27	we	we	PRON
ejpam-6070	232	28	deduce	deduce	VERB
ejpam-6070	232	29	the	the	DET
ejpam-6070	232	30	existence	existence	NOUN
ejpam-6070	232	31	of	of	ADP
ejpam-6070	232	32	a	a	DET
ejpam-6070	232	33	constant	constant	ADJ
ejpam-6070	232	34	κ1	κ1	NOUN
ejpam-6070	232	35	∈	∈	PROPN
ejpam-6070	232	36	(	(	PUNCT
ejpam-6070	232	37	0	0	NUM
ejpam-6070	232	38	,	,	PUNCT
ejpam-6070	232	39	1	1	NUM
ejpam-6070	232	40	)	)	PUNCT
ejpam-6070	232	41	such	such	ADJ
ejpam-6070	232	42	that	that	SCONJ
ejpam-6070	232	43	:	:	PUNCT
ejpam-6070	232	44	κ1	κ1	NOUN
ejpam-6070	232	45	=	=	SYM
ejpam-6070	232	46	sup{v(x	sup{v(x	PROPN
ejpam-6070	232	47	)	)	PUNCT
ejpam-6070	232	48	:	:	PUNCT
ejpam-6070	232	49	x	x	X
ejpam-6070	232	50	∈	∈	PROPN
ejpam-6070	232	51	σ1	σ1	PROPN
ejpam-6070	232	52	}	}	PUNCT
ejpam-6070	232	53	.	.	PUNCT
ejpam-6070	233	1	s.	s.	PROPN
ejpam-6070	233	2	chebbah	chebbah	PROPN
ejpam-6070	233	3	,	,	PUNCT
ejpam-6070	233	4	s.	s.	PROPN
ejpam-6070	233	5	madi	madi	PROPN
ejpam-6070	233	6	,	,	PUNCT
ejpam-6070	233	7	m.	m.	NOUN
ejpam-6070	233	8	haiour	haiour	PROPN
ejpam-6070	233	9	/	/	SYM
ejpam-6070	233	10	eur	eur	PROPN
ejpam-6070	233	11	.	.	PUNCT
ejpam-6070	234	1	j.	j.	PROPN
ejpam-6070	234	2	pure	pure	PROPN
ejpam-6070	234	3	appl	appl	PROPN
ejpam-6070	234	4	.	.	PROPN
ejpam-6070	234	5	math	math	PROPN
ejpam-6070	234	6	,	,	PUNCT
ejpam-6070	234	7	18	18	NUM
ejpam-6070	234	8	(	(	PUNCT
ejpam-6070	234	9	2	2	NUM
ejpam-6070	234	10	)	)	PUNCT
ejpam-6070	234	11	(	(	PUNCT
ejpam-6070	234	12	2025	2025	NUM
ejpam-6070	234	13	)	)	PUNCT
ejpam-6070	234	14	,	,	PUNCT
ejpam-6070	234	15	6070	6070	NUM
ejpam-6070	234	16	13	13	NUM
ejpam-6070	234	17	of	of	ADP
ejpam-6070	234	18	20	20	NUM
ejpam-6070	234	19	thus	thus	ADV
ejpam-6070	234	20	,	,	PUNCT
ejpam-6070	234	21	we	we	PRON
ejpam-6070	234	22	obtain	obtain	VERB
ejpam-6070	234	23	the	the	DET
ejpam-6070	234	24	following	follow	VERB
ejpam-6070	234	25	inequality	inequality	NOUN
ejpam-6070	234	26	:	:	PUNCT
ejpam-6070	234	27	∥ζk+1	∥ζk+1	ADP
ejpam-6070	234	28	1	1	NUM
ejpam-6070	234	29	−	−	NOUN
ejpam-6070	234	30	ζk1	ζk1	NOUN
ejpam-6070	234	31	∥l∞(σ1	∥l∞(σ1	NOUN
ejpam-6070	234	32	)	)	PUNCT
ejpam-6070	234	33	≤	≤	NOUN
ejpam-6070	234	34	κ1∥ζk2	κ1∥ζk2	VERB
ejpam-6070	234	35	−	−	PROPN
ejpam-6070	234	36	ζk−1	ζk−1	PROPN
ejpam-6070	234	37	2	2	NUM
ejpam-6070	234	38	∥l∞(ω2	∥l∞(ω2	NOUN
ejpam-6070	234	39	)	)	PUNCT
ejpam-6070	234	40	.	.	PUNCT
ejpam-6070	235	1	similarly	similarly	ADV
ejpam-6070	235	2	,	,	PUNCT
ejpam-6070	235	3	analyzing	analyze	VERB
ejpam-6070	235	4	the	the	DET
ejpam-6070	235	5	second	second	ADJ
ejpam-6070	235	6	part	part	NOUN
ejpam-6070	235	7	of	of	ADP
ejpam-6070	235	8	the	the	DET
ejpam-6070	235	9	system	system	NOUN
ejpam-6070	235	10	,	,	PUNCT
ejpam-6070	235	11	we	we	PRON
ejpam-6070	235	12	have	have	VERB
ejpam-6070	235	13	:	:	PUNCT
ejpam-6070	235	14	max	max	PROPN
ejpam-6070	235	15	1≤i≤n	1≤i≤n	NUM
ejpam-6070	235	16	{	{	PUNCT
ejpam-6070	235	17	−b̃i	−b̃i	PROPN
ejpam-6070	235	18	2,1ζ	2,1ζ	NUM
ejpam-6070	235	19	k+1	k+1	NOUN
ejpam-6070	235	20	1	1	NUM
ejpam-6070	236	1	+	+	NUM
ejpam-6070	236	2	bi	bi	NOUN
ejpam-6070	236	3	2,2ζ	2,2ζ	NOUN
ejpam-6070	236	4	k+1	k+1	NOUN
ejpam-6070	236	5	2	2	NUM
ejpam-6070	236	6	−	−	NOUN
ejpam-6070	236	7	g	g	NOUN
ejpam-6070	236	8	i(ζk2	i(ζk2	NOUN
ejpam-6070	236	9	)	)	PUNCT
ejpam-6070	236	10	}	}	PUNCT
ejpam-6070	236	11	=	=	SYM
ejpam-6070	236	12	0	0	NUM
ejpam-6070	236	13	,	,	PUNCT
ejpam-6070	236	14	and	and	CCONJ
ejpam-6070	236	15	max	max	PROPN
ejpam-6070	236	16	1≤i≤n	1≤i≤n	NUM
ejpam-6070	236	17	{	{	PUNCT
ejpam-6070	236	18	−b̃i	−b̃i	PROPN
ejpam-6070	236	19	2,1ζ	2,1ζ	NUM
ejpam-6070	236	20	k	k	NOUN
ejpam-6070	236	21	1	1	NUM
ejpam-6070	236	22	+	+	NUM
ejpam-6070	236	23	bi	bi	NOUN
ejpam-6070	236	24	2,2ζ	2,2ζ	NOUN
ejpam-6070	236	25	k	k	NOUN
ejpam-6070	236	26	2	2	NUM
ejpam-6070	236	27	−	−	NOUN
ejpam-6070	236	28	g	g	PROPN
ejpam-6070	236	29	i(ζk−1	i(ζk−1	X
ejpam-6070	236	30	2	2	NUM
ejpam-6070	236	31	)	)	PUNCT
ejpam-6070	236	32	}	}	PUNCT
ejpam-6070	237	1	=	=	PUNCT
ejpam-6070	237	2	0	0	X
ejpam-6070	237	3	.	.	PUNCT
ejpam-6070	238	1	by	by	ADP
ejpam-6070	238	2	applying	apply	VERB
ejpam-6070	238	3	the	the	DET
ejpam-6070	238	4	results	result	NOUN
ejpam-6070	238	5	from	from	ADP
ejpam-6070	238	6	[	[	X
ejpam-6070	238	7	10	10	NUM
ejpam-6070	238	8	]	]	PUNCT
ejpam-6070	238	9	,	,	PUNCT
ejpam-6070	238	10	we	we	PRON
ejpam-6070	238	11	conclude	conclude	VERB
ejpam-6070	238	12	the	the	DET
ejpam-6070	238	13	existence	existence	NOUN
ejpam-6070	238	14	of	of	ADP
ejpam-6070	238	15	a	a	DET
ejpam-6070	238	16	constant	constant	ADJ
ejpam-6070	238	17	κ2	κ2	NOUN
ejpam-6070	238	18	∈	∈	PROPN
ejpam-6070	238	19	(	(	PUNCT
ejpam-6070	238	20	0	0	NUM
ejpam-6070	238	21	,	,	PUNCT
ejpam-6070	238	22	1	1	NUM
ejpam-6070	238	23	)	)	PUNCT
ejpam-6070	238	24	such	such	ADJ
ejpam-6070	238	25	that	that	SCONJ
ejpam-6070	238	26	:	:	PUNCT
ejpam-6070	238	27	κ2	κ2	NOUN
ejpam-6070	238	28	=	=	SYM
ejpam-6070	238	29	sup{v(x	sup{v(x	PROPN
ejpam-6070	238	30	)	)	PUNCT
ejpam-6070	238	31	:	:	PUNCT
ejpam-6070	238	32	x	x	X
ejpam-6070	238	33	∈	∈	PROPN
ejpam-6070	238	34	σ2	σ2	PROPN
ejpam-6070	238	35	}	}	PUNCT
ejpam-6070	238	36	.	.	PUNCT
ejpam-6070	239	1	this	this	PRON
ejpam-6070	239	2	implies	imply	VERB
ejpam-6070	239	3	the	the	DET
ejpam-6070	239	4	following	follow	VERB
ejpam-6070	239	5	relationship	relationship	NOUN
ejpam-6070	239	6	:	:	PUNCT
ejpam-6070	239	7	∥ζk+1	∥ζk+1	ADP
ejpam-6070	239	8	2	2	NUM
ejpam-6070	239	9	−	−	NOUN
ejpam-6070	239	10	ζk2	ζk2	NOUN
ejpam-6070	239	11	∥l∞(σ2	∥l∞(σ2	PROPN
ejpam-6070	239	12	)	)	PUNCT
ejpam-6070	239	13	≤	≤	NUM
ejpam-6070	239	14	κ2∥ζk+1	κ2∥ζk+1	VERB
ejpam-6070	239	15	1	1	NUM
ejpam-6070	239	16	−	−	NOUN
ejpam-6070	239	17	ζk1	ζk1	PRON
ejpam-6070	239	18	∥l∞(ω1	∥l∞(ω1	ADJ
ejpam-6070	239	19	)	)	PUNCT
ejpam-6070	239	20	.	.	PUNCT
ejpam-6070	240	1	by	by	ADP
ejpam-6070	240	2	applying	apply	VERB
ejpam-6070	240	3	the	the	DET
ejpam-6070	240	4	maximum	maximum	ADJ
ejpam-6070	240	5	principle	principle	NOUN
ejpam-6070	240	6	,	,	PUNCT
ejpam-6070	240	7	we	we	PRON
ejpam-6070	240	8	obtain	obtain	VERB
ejpam-6070	240	9	:	:	PUNCT
ejpam-6070	240	10	∥ζk+1	∥ζk+1	ADP
ejpam-6070	240	11	2	2	NUM
ejpam-6070	240	12	−	−	NOUN
ejpam-6070	240	13	ζk2	ζk2	NOUN
ejpam-6070	240	14	∥l∞(ω2	∥l∞(ω2	NOUN
ejpam-6070	240	15	)	)	PUNCT
ejpam-6070	240	16	≤	≤	NUM
ejpam-6070	240	17	∥ζk+1	∥ζk+1	VERB
ejpam-6070	240	18	2	2	NUM
ejpam-6070	240	19	−	−	NOUN
ejpam-6070	240	20	ζk2	ζk2	NOUN
ejpam-6070	240	21	∥l∞(σ2	∥l∞(σ2	PROPN
ejpam-6070	240	22	)	)	PUNCT
ejpam-6070	240	23	,	,	PUNCT
ejpam-6070	240	24	∥ζk+1	∥ζk+1	VERB
ejpam-6070	240	25	2	2	NUM
ejpam-6070	240	26	−	−	NOUN
ejpam-6070	240	27	ζk2	ζk2	NOUN
ejpam-6070	240	28	∥l∞(σ2	∥l∞(σ2	PROPN
ejpam-6070	240	29	)	)	PUNCT
ejpam-6070	240	30	≤	≤	NUM
ejpam-6070	240	31	κ2∥ζk+1	κ2∥ζk+1	VERB
ejpam-6070	240	32	1	1	NUM
ejpam-6070	240	33	−	−	NOUN
ejpam-6070	240	34	ζk1	ζk1	X
ejpam-6070	240	35	∥l∞(ω1	∥l∞(ω1	ADJ
ejpam-6070	240	36	)	)	PUNCT
ejpam-6070	240	37	,	,	PUNCT
ejpam-6070	240	38	≤	≤	NUM
ejpam-6070	240	39	κ2∥ζk+1	κ2∥ζk+1	VERB
ejpam-6070	240	40	1	1	NUM
ejpam-6070	240	41	−	−	NOUN
ejpam-6070	240	42	ζk1	ζk1	NOUN
ejpam-6070	240	43	∥l∞(σ1	∥l∞(σ1	NOUN
ejpam-6070	240	44	)	)	PUNCT
ejpam-6070	240	45	,	,	PUNCT
ejpam-6070	240	46	≤	≤	NOUN
ejpam-6070	240	47	κ1κ2∥ζk2	κ1κ2∥ζk2	NOUN
ejpam-6070	240	48	−	−	PROPN
ejpam-6070	240	49	ζk−1	ζk−1	PROPN
ejpam-6070	240	50	2	2	NUM
ejpam-6070	240	51	∥l∞(ω2	∥l∞(ω2	NOUN
ejpam-6070	240	52	)	)	PUNCT
ejpam-6070	240	53	.	.	PUNCT
ejpam-6070	241	1	similarly	similarly	ADV
ejpam-6070	241	2	,	,	PUNCT
ejpam-6070	241	3	we	we	PRON
ejpam-6070	241	4	derive	derive	VERB
ejpam-6070	241	5	:	:	PUNCT
ejpam-6070	241	6	∥ζk+1	∥ζk+1	ADP
ejpam-6070	241	7	1	1	NUM
ejpam-6070	241	8	−	−	NOUN
ejpam-6070	241	9	ζk1	ζk1	X
ejpam-6070	241	10	∥l∞(ω1	∥l∞(ω1	ADJ
ejpam-6070	241	11	)	)	PUNCT
ejpam-6070	241	12	≤	≤	NOUN
ejpam-6070	241	13	∥ζk+1	∥ζk+1	VERB
ejpam-6070	241	14	1	1	NUM
ejpam-6070	241	15	−	−	NOUN
ejpam-6070	241	16	ζk1	ζk1	NOUN
ejpam-6070	241	17	∥l∞(σ1	∥l∞(σ1	NOUN
ejpam-6070	241	18	)	)	PUNCT
ejpam-6070	241	19	,	,	PUNCT
ejpam-6070	241	20	∥ζk+1	∥ζk+1	ADP
ejpam-6070	241	21	1	1	NUM
ejpam-6070	241	22	−	−	NOUN
ejpam-6070	241	23	ζk1	ζk1	NOUN
ejpam-6070	241	24	∥l∞(σ1	∥l∞(σ1	NOUN
ejpam-6070	241	25	)	)	PUNCT
ejpam-6070	241	26	≤	≤	NOUN
ejpam-6070	241	27	κ1∥ζk2	κ1∥ζk2	VERB
ejpam-6070	242	1	−	−	PROPN
ejpam-6070	242	2	ζk−1	ζk−1	PROPN
ejpam-6070	242	3	2	2	NUM
ejpam-6070	242	4	∥l∞(ω2	∥l∞(ω2	NOUN
ejpam-6070	242	5	)	)	PUNCT
ejpam-6070	242	6	,	,	PUNCT
ejpam-6070	242	7	≤	≤	NUM
ejpam-6070	242	8	κ1∥ζk2	κ1∥ζk2	VERB
ejpam-6070	243	1	−	−	PROPN
ejpam-6070	243	2	ζk−1	ζk−1	PROPN
ejpam-6070	243	3	2	2	NUM
ejpam-6070	243	4	∥l∞(σ2	∥l∞(σ2	NUM
ejpam-6070	243	5	)	)	PUNCT
ejpam-6070	243	6	,	,	PUNCT
ejpam-6070	243	7	≤	≤	X
ejpam-6070	243	8	κ1κ2∥ζk1	κ1κ2∥ζk1	VERB
ejpam-6070	243	9	−	−	PROPN
ejpam-6070	243	10	ζk−1	ζk−1	VERB
ejpam-6070	243	11	1	1	NUM
ejpam-6070	243	12	∥l∞(ω1	∥l∞(ω1	NOUN
ejpam-6070	243	13	)	)	PUNCT
ejpam-6070	243	14	.	.	PUNCT
ejpam-6070	244	1	finally	finally	ADV
ejpam-6070	244	2	,	,	PUNCT
ejpam-6070	244	3	we	we	PRON
ejpam-6070	244	4	conclude	conclude	VERB
ejpam-6070	244	5	with	with	ADP
ejpam-6070	244	6	the	the	DET
ejpam-6070	244	7	inequality	inequality	NOUN
ejpam-6070	244	8	:	:	PUNCT
ejpam-6070	244	9	∥ζk+1	∥ζk+1	ADP
ejpam-6070	244	10	−	−	ADP
ejpam-6070	244	11	ζk∥l∞(ω	ζk∥l∞(ω	NOUN
ejpam-6070	244	12	)	)	PUNCT
ejpam-6070	244	13	≤	≤	NOUN
ejpam-6070	244	14	κ1κ2∥ζk	κ1κ2∥ζk	PROPN
ejpam-6070	244	15	−	−	PROPN
ejpam-6070	244	16	ζk−1∥l∞(ω	ζk−1∥l∞(ω	PROPN
ejpam-6070	244	17	)	)	PUNCT
ejpam-6070	244	18	.	.	PUNCT
ejpam-6070	245	1	by	by	ADP
ejpam-6070	245	2	induction	induction	NOUN
ejpam-6070	245	3	and	and	CCONJ
ejpam-6070	245	4	noting	note	VERB
ejpam-6070	245	5	that	that	SCONJ
ejpam-6070	245	6	η	η	PROPN
ejpam-6070	245	7	=	=	PROPN
ejpam-6070	245	8	κ1κ2	κ1κ2	PROPN
ejpam-6070	245	9	∈	∈	PROPN
ejpam-6070	245	10	(	(	PUNCT
ejpam-6070	245	11	0	0	NUM
ejpam-6070	245	12	,	,	PUNCT
ejpam-6070	245	13	1	1	NUM
ejpam-6070	245	14	)	)	PUNCT
ejpam-6070	245	15	,	,	PUNCT
ejpam-6070	245	16	we	we	PRON
ejpam-6070	245	17	conclude	conclude	VERB
ejpam-6070	245	18	:	:	PUNCT
ejpam-6070	245	19	∥ζk+1	∥ζk+1	ADP
ejpam-6070	245	20	−	−	ADP
ejpam-6070	245	21	ζk∥l∞(ω	ζk∥l∞(ω	NOUN
ejpam-6070	245	22	)	)	PUNCT
ejpam-6070	245	23	≤	≤	NOUN
ejpam-6070	245	24	ηk∥ζ1	ηk∥ζ1	PROPN
ejpam-6070	245	25	−	−	PROPN
ejpam-6070	245	26	ζ0∥l∞(ω	ζ0∥l∞(ω	NOUN
ejpam-6070	245	27	)	)	PUNCT
ejpam-6070	245	28	.	.	PUNCT
ejpam-6070	246	1	thus	thus	ADV
ejpam-6070	246	2	,	,	PUNCT
ejpam-6070	246	3	we	we	PRON
ejpam-6070	246	4	obtain	obtain	VERB
ejpam-6070	246	5	:	:	PUNCT
ejpam-6070	246	6	∥ζk+1	∥ζk+1	ADP
ejpam-6070	247	1	−	−	ADP
ejpam-6070	247	2	ζk∥l∞(ω	ζk∥l∞(ω	NOUN
ejpam-6070	247	3	)	)	PUNCT
ejpam-6070	247	4	≤	≤	NOUN
ejpam-6070	247	5	cηk	cηk	PROPN
ejpam-6070	247	6	,	,	PUNCT
ejpam-6070	247	7	k	k	PROPN
ejpam-6070	247	8	∈	∈	PROPN
ejpam-6070	247	9	n.	n.	PROPN
ejpam-6070	247	10	therefore	therefore	ADV
ejpam-6070	247	11	,	,	PUNCT
ejpam-6070	247	12	the	the	DET
ejpam-6070	247	13	sequence	sequence	NOUN
ejpam-6070	247	14	(	(	PUNCT
ejpam-6070	247	15	ζk	ζk	NOUN
ejpam-6070	247	16	)	)	PUNCT
ejpam-6070	247	17	converges	converge	VERB
ejpam-6070	247	18	geometrically	geometrically	ADV
ejpam-6070	247	19	to	to	ADP
ejpam-6070	247	20	the	the	DET
ejpam-6070	247	21	solution	solution	NOUN
ejpam-6070	247	22	of	of	ADP
ejpam-6070	247	23	the	the	DET
ejpam-6070	247	24	system	system	NOUN
ejpam-6070	247	25	(	(	PUNCT
ejpam-6070	247	26	3	3	NUM
ejpam-6070	247	27	)	)	PUNCT
ejpam-6070	247	28	.	.	PUNCT
ejpam-6070	248	1	s.	s.	PROPN
ejpam-6070	248	2	chebbah	chebbah	PROPN
ejpam-6070	248	3	,	,	PUNCT
ejpam-6070	248	4	s.	s.	PROPN
ejpam-6070	248	5	madi	madi	PROPN
ejpam-6070	248	6	,	,	PUNCT
ejpam-6070	248	7	m.	m.	NOUN
ejpam-6070	248	8	haiour	haiour	PROPN
ejpam-6070	248	9	/	/	SYM
ejpam-6070	248	10	eur	eur	PROPN
ejpam-6070	248	11	.	.	PUNCT
ejpam-6070	249	1	j.	j.	PROPN
ejpam-6070	249	2	pure	pure	PROPN
ejpam-6070	249	3	appl	appl	PROPN
ejpam-6070	249	4	.	.	PROPN
ejpam-6070	249	5	math	math	PROPN
ejpam-6070	249	6	,	,	PUNCT
ejpam-6070	249	7	18	18	NUM
ejpam-6070	249	8	(	(	PUNCT
ejpam-6070	249	9	2	2	NUM
ejpam-6070	249	10	)	)	PUNCT
ejpam-6070	249	11	(	(	PUNCT
ejpam-6070	249	12	2025	2025	NUM
ejpam-6070	249	13	)	)	PUNCT
ejpam-6070	249	14	,	,	PUNCT
ejpam-6070	249	15	6070	6070	NUM
ejpam-6070	249	16	14	14	NUM
ejpam-6070	249	17	of	of	ADP
ejpam-6070	249	18	20	20	NUM
ejpam-6070	249	19	4	4	NUM
ejpam-6070	249	20	.	.	PUNCT
ejpam-6070	249	21	numerical	numerical	ADJ
ejpam-6070	249	22	applications	application	NOUN
ejpam-6070	249	23	and	and	CCONJ
ejpam-6070	249	24	computational	computational	ADJ
ejpam-6070	249	25	results	result	NOUN
ejpam-6070	249	26	in	in	ADP
ejpam-6070	249	27	this	this	DET
ejpam-6070	249	28	section	section	NOUN
ejpam-6070	249	29	,	,	PUNCT
ejpam-6070	249	30	we	we	PRON
ejpam-6070	249	31	formulate	formulate	VERB
ejpam-6070	249	32	the	the	DET
ejpam-6070	249	33	hamilton	hamilton	PROPN
ejpam-6070	249	34	-	-	PUNCT
ejpam-6070	249	35	jacobi	jacobi	PROPN
ejpam-6070	249	36	-	-	PUNCT
ejpam-6070	249	37	bellman	bellman	NOUN
ejpam-6070	249	38	(	(	PUNCT
ejpam-6070	249	39	hjb	hjb	NOUN
ejpam-6070	249	40	)	)	PUNCT
ejpam-6070	249	41	equation	equation	NOUN
ejpam-6070	249	42	using	use	VERB
ejpam-6070	249	43	an	an	DET
ejpam-6070	249	44	overlapping	overlap	VERB
ejpam-6070	249	45	domain	domain	NOUN
ejpam-6070	249	46	decomposition	decomposition	NOUN
ejpam-6070	249	47	method	method	NOUN
ejpam-6070	249	48	.	.	PUNCT
ejpam-6070	250	1	the	the	DET
ejpam-6070	250	2	computational	computational	ADJ
ejpam-6070	250	3	domain	domain	NOUN
ejpam-6070	250	4	ω	ω	NOUN
ejpam-6070	250	5	=	=	PUNCT
ejpam-6070	251	1	[	[	X
ejpam-6070	251	2	0	0	NUM
ejpam-6070	251	3	,	,	PUNCT
ejpam-6070	251	4	1]×[0	1]×[0	NUM
ejpam-6070	251	5	,	,	PUNCT
ejpam-6070	251	6	1	1	NUM
ejpam-6070	251	7	]	]	PUNCT
ejpam-6070	251	8	is	be	AUX
ejpam-6070	251	9	discretized	discretize	VERB
ejpam-6070	251	10	on	on	ADP
ejpam-6070	251	11	a	a	DET
ejpam-6070	251	12	uniform	uniform	ADJ
ejpam-6070	251	13	grid	grid	NOUN
ejpam-6070	251	14	with	with	ADP
ejpam-6070	251	15	step	step	NOUN
ejpam-6070	251	16	size	size	NOUN
ejpam-6070	251	17	h	h	NOUN
ejpam-6070	251	18	based	base	VERB
ejpam-6070	251	19	on	on	ADP
ejpam-6070	251	20	the	the	DET
ejpam-6070	251	21	finite	finite	ADJ
ejpam-6070	251	22	difference	difference	NOUN
ejpam-6070	251	23	method	method	NOUN
ejpam-6070	251	24	.	.	PUNCT
ejpam-6070	252	1	the	the	DET
ejpam-6070	252	2	initial	initial	ADJ
ejpam-6070	252	3	solution	solution	NOUN
ejpam-6070	252	4	can	can	AUX
ejpam-6070	252	5	be	be	AUX
ejpam-6070	252	6	selected	select	VERB
ejpam-6070	252	7	as	as	ADP
ejpam-6070	252	8	either	either	CCONJ
ejpam-6070	252	9	a	a	DET
ejpam-6070	252	10	lower	low	ADJ
ejpam-6070	252	11	or	or	CCONJ
ejpam-6070	252	12	upper	upper	ADJ
ejpam-6070	252	13	solution	solution	NOUN
ejpam-6070	252	14	,	,	PUNCT
ejpam-6070	252	15	both	both	PRON
ejpam-6070	252	16	ensuring	ensure	VERB
ejpam-6070	252	17	convergence	convergence	NOUN
ejpam-6070	252	18	to	to	ADP
ejpam-6070	252	19	the	the	DET
ejpam-6070	252	20	discrete	discrete	ADJ
ejpam-6070	252	21	solution	solution	NOUN
ejpam-6070	252	22	.	.	PUNCT
ejpam-6070	253	1	the	the	DET
ejpam-6070	253	2	iterative	iterative	NOUN
ejpam-6070	253	3	process	process	NOUN
ejpam-6070	253	4	continues	continue	VERB
ejpam-6070	253	5	until	until	ADP
ejpam-6070	253	6	the	the	DET
ejpam-6070	253	7	stopping	stopping	NOUN
ejpam-6070	253	8	criterion	criterion	NOUN
ejpam-6070	253	9	ε	ε	PROPN
ejpam-6070	253	10	=	=	SYM
ejpam-6070	253	11	10−6	10−6	PROPN
ejpam-6070	253	12	is	be	AUX
ejpam-6070	253	13	satisfied	satisfied	ADJ
ejpam-6070	253	14	.	.	PUNCT
ejpam-6070	254	1	the	the	DET
ejpam-6070	254	2	system	system	NOUN
ejpam-6070	254	3	is	be	AUX
ejpam-6070	254	4	governed	govern	VERB
ejpam-6070	254	5	by	by	ADP
ejpam-6070	254	6	the	the	DET
ejpam-6070	254	7	following	follow	VERB
ejpam-6070	254	8	equations	equation	NOUN
ejpam-6070	254	9	:	:	PUNCT
ejpam-6070	254	10	{	{	PUNCT
ejpam-6070	254	11	max	max	X
ejpam-6070	254	12	{	{	PUNCT
ejpam-6070	254	13	b1ζ	b1ζ	PROPN
ejpam-6070	254	14	−	−	PROPN
ejpam-6070	254	15	g	g	NOUN
ejpam-6070	254	16	1,b2ζ	1,b2ζ	NUM
ejpam-6070	254	17	−	−	PROPN
ejpam-6070	254	18	g	g	NOUN
ejpam-6070	254	19	2	2	NUM
ejpam-6070	254	20	}	}	PUNCT
ejpam-6070	254	21	in	in	ADP
ejpam-6070	254	22	ω	ω	NUM
ejpam-6070	254	23	,	,	PUNCT
ejpam-6070	254	24	ζ	ζ	NOUN
ejpam-6070	254	25	=	=	SYM
ejpam-6070	254	26	0	0	NUM
ejpam-6070	254	27	on	on	ADP
ejpam-6070	254	28	∂ω	∂ω	PROPN
ejpam-6070	254	29	.	.	PUNCT
ejpam-6070	255	1	(	(	PUNCT
ejpam-6070	255	2	16	16	NUM
ejpam-6070	255	3	)	)	PUNCT
ejpam-6070	255	4	to	to	PART
ejpam-6070	255	5	facilitate	facilitate	VERB
ejpam-6070	255	6	the	the	DET
ejpam-6070	255	7	numerical	numerical	ADJ
ejpam-6070	255	8	treatment	treatment	NOUN
ejpam-6070	255	9	,	,	PUNCT
ejpam-6070	255	10	we	we	PRON
ejpam-6070	255	11	introduce	introduce	VERB
ejpam-6070	255	12	the	the	DET
ejpam-6070	255	13	following	following	ADJ
ejpam-6070	255	14	notations	notation	NOUN
ejpam-6070	255	15	:	:	PUNCT
ejpam-6070	255	16	•	•	NUM
ejpam-6070	255	17	b1	b1	NOUN
ejpam-6070	255	18	=	=	SYM
ejpam-6070	255	19	b	b	PROPN
ejpam-6070	256	1	+	+	CCONJ
ejpam-6070	256	2	µi	µi	PROPN
ejpam-6070	256	3	,	,	PUNCT
ejpam-6070	256	4	g	g	PROPN
ejpam-6070	256	5	1	1	NUM
ejpam-6070	256	6	=	=	SYM
ejpam-6070	256	7	g	g	PROPN
ejpam-6070	256	8	+	+	X
ejpam-6070	256	9	µζ	µζ	CCONJ
ejpam-6070	256	10	,	,	PUNCT
ejpam-6070	256	11	with	with	ADP
ejpam-6070	256	12	µ	µ	NOUN
ejpam-6070	256	13	=	=	SYM
ejpam-6070	256	14	1	1	NUM
ejpam-6070	256	15	.	.	NOUN
ejpam-6070	256	16	•	•	NUM
ejpam-6070	256	17	b2	b2	NOUN
ejpam-6070	256	18	=	=	SYM
ejpam-6070	256	19	i	i	PROPN
ejpam-6070	256	20	,	,	PUNCT
ejpam-6070	256	21	where	where	SCONJ
ejpam-6070	256	22	i	i	PRON
ejpam-6070	256	23	is	be	AUX
ejpam-6070	256	24	the	the	DET
ejpam-6070	256	25	identity	identity	NOUN
ejpam-6070	256	26	matrix	matrix	NOUN
ejpam-6070	256	27	,	,	PUNCT
ejpam-6070	256	28	and	and	CCONJ
ejpam-6070	256	29	g	g	PROPN
ejpam-6070	256	30	2	2	NUM
ejpam-6070	256	31	=	=	SYM
ejpam-6070	256	32	0	0	NUM
ejpam-6070	256	33	.	.	PUNCT
ejpam-6070	257	1	the	the	DET
ejpam-6070	257	2	operator	operator	NOUN
ejpam-6070	257	3	b	b	NOUN
ejpam-6070	257	4	,	,	PUNCT
ejpam-6070	257	5	which	which	PRON
ejpam-6070	257	6	is	be	AUX
ejpam-6070	257	7	non	non	ADJ
ejpam-6070	257	8	-	-	ADJ
ejpam-6070	257	9	coercive	coercive	ADJ
ejpam-6070	257	10	,	,	PUNCT
ejpam-6070	257	11	is	be	AUX
ejpam-6070	257	12	defined	define	VERB
ejpam-6070	257	13	as	as	ADP
ejpam-6070	257	14	:	:	PUNCT
ejpam-6070	257	15	b	b	X
ejpam-6070	257	16	=	=	SYM
ejpam-6070	257	17	−	−	PROPN
ejpam-6070	257	18	∂2	∂2	PROPN
ejpam-6070	257	19	∂x2	∂x2	NOUN
ejpam-6070	257	20	−	−	NOUN
ejpam-6070	257	21	∂2	∂2	NOUN
ejpam-6070	257	22	∂y2	∂y2	NOUN
ejpam-6070	257	23	+	+	PUNCT
ejpam-6070	257	24	0.5x	0.5x	NUM
ejpam-6070	257	25	∂	∂	NOUN
ejpam-6070	257	26	∂x	∂x	NOUN
ejpam-6070	258	1	+	+	CCONJ
ejpam-6070	258	2	0.5y	0.5y	NUM
ejpam-6070	258	3	∂	∂	X
ejpam-6070	258	4	∂y	∂y	NOUN
ejpam-6070	259	1	+	+	ADV
ejpam-6070	259	2	0.045	0.045	NUM
ejpam-6070	259	3	.	.	PUNCT
ejpam-6070	260	1	the	the	DET
ejpam-6070	260	2	function	function	NOUN
ejpam-6070	260	3	g	g	NOUN
ejpam-6070	260	4	is	be	AUX
ejpam-6070	260	5	given	give	VERB
ejpam-6070	260	6	by	by	ADP
ejpam-6070	260	7	:	:	PUNCT
ejpam-6070	260	8	g	g	PROPN
ejpam-6070	260	9	=	=	SYM
ejpam-6070	260	10	sin(2πx	sin(2πx	NOUN
ejpam-6070	260	11	)	)	PUNCT
ejpam-6070	260	12	sin(2πy	sin(2πy	NOUN
ejpam-6070	260	13	)	)	PUNCT
ejpam-6070	260	14	.	.	PUNCT
ejpam-6070	261	1	to	to	PART
ejpam-6070	261	2	evaluate	evaluate	VERB
ejpam-6070	261	3	the	the	DET
ejpam-6070	261	4	efficiency	efficiency	NOUN
ejpam-6070	261	5	of	of	ADP
ejpam-6070	261	6	the	the	DET
ejpam-6070	261	7	domain	domain	NOUN
ejpam-6070	261	8	decomposition	decomposition	NOUN
ejpam-6070	261	9	methods	method	NOUN
ejpam-6070	261	10	,	,	PUNCT
ejpam-6070	261	11	we	we	PRON
ejpam-6070	261	12	compare	compare	VERB
ejpam-6070	261	13	the	the	DET
ejpam-6070	261	14	performance	performance	NOUN
ejpam-6070	261	15	of	of	ADP
ejpam-6070	261	16	the	the	DET
ejpam-6070	261	17	non	non	ADJ
ejpam-6070	261	18	-	-	ADJ
ejpam-6070	261	19	overlapping	overlapping	ADJ
ejpam-6070	261	20	domain	domain	NOUN
ejpam-6070	261	21	decomposition	decomposition	NOUN
ejpam-6070	261	22	(	(	PUNCT
ejpam-6070	261	23	τ	τ	X
ejpam-6070	261	24	=	=	SYM
ejpam-6070	261	25	1	1	NUM
ejpam-6070	261	26	)	)	PUNCT
ejpam-6070	261	27	(	(	PUNCT
ejpam-6070	261	28	see	see	VERB
ejpam-6070	261	29	[	[	X
ejpam-6070	261	30	11	11	NUM
ejpam-6070	261	31	]	]	PUNCT
ejpam-6070	261	32	)	)	PUNCT
ejpam-6070	261	33	with	with	ADP
ejpam-6070	261	34	the	the	DET
ejpam-6070	261	35	newly	newly	ADV
ejpam-6070	261	36	introduced	introduce	VERB
ejpam-6070	261	37	overlapping	overlap	VERB
ejpam-6070	261	38	domain	domain	NOUN
ejpam-6070	261	39	decomposition	decomposition	NOUN
ejpam-6070	261	40	method	method	NOUN
ejpam-6070	261	41	(	(	PUNCT
ejpam-6070	261	42	τ	τ	X
ejpam-6070	261	43	>	>	X
ejpam-6070	261	44	1	1	NUM
ejpam-6070	261	45	)	)	PUNCT
ejpam-6070	261	46	.	.	PUNCT
ejpam-6070	262	1	this	this	DET
ejpam-6070	262	2	comparative	comparative	ADJ
ejpam-6070	262	3	study	study	NOUN
ejpam-6070	262	4	aims	aim	VERB
ejpam-6070	262	5	to	to	PART
ejpam-6070	262	6	assess	assess	VERB
ejpam-6070	262	7	the	the	DET
ejpam-6070	262	8	accuracy	accuracy	NOUN
ejpam-6070	262	9	and	and	CCONJ
ejpam-6070	262	10	convergence	convergence	NOUN
ejpam-6070	262	11	of	of	ADP
ejpam-6070	262	12	both	both	DET
ejpam-6070	262	13	methods	method	NOUN
ejpam-6070	262	14	,	,	PUNCT
ejpam-6070	262	15	verifying	verify	VERB
ejpam-6070	262	16	their	their	PRON
ejpam-6070	262	17	effectiveness	effectiveness	NOUN
ejpam-6070	262	18	against	against	ADP
ejpam-6070	262	19	theoretical	theoretical	ADJ
ejpam-6070	262	20	expectations	expectation	NOUN
ejpam-6070	262	21	.	.	PUNCT
ejpam-6070	263	1	the	the	DET
ejpam-6070	263	2	numerical	numerical	ADJ
ejpam-6070	263	3	results	result	NOUN
ejpam-6070	263	4	,	,	PUNCT
ejpam-6070	263	5	illustrating	illustrate	VERB
ejpam-6070	263	6	the	the	DET
ejpam-6070	263	7	efficiency	efficiency	NOUN
ejpam-6070	263	8	of	of	ADP
ejpam-6070	263	9	these	these	DET
ejpam-6070	263	10	approaches	approach	NOUN
ejpam-6070	263	11	,	,	PUNCT
ejpam-6070	263	12	are	be	AUX
ejpam-6070	263	13	presented	present	VERB
ejpam-6070	263	14	in	in	ADP
ejpam-6070	263	15	tables	table	NOUN
ejpam-6070	263	16	and	and	CCONJ
ejpam-6070	263	17	figures	figure	NOUN
ejpam-6070	263	18	generated	generate	VERB
ejpam-6070	263	19	using	use	VERB
ejpam-6070	263	20	matlab	matlab	PROPN
ejpam-6070	263	21	r2018a	r2018a	PROPN
ejpam-6070	263	22	.	.	PROPN
ejpam-6070	263	23	table	table	NOUN
ejpam-6070	263	24	1	1	NUM
ejpam-6070	263	25	:	:	PUNCT
ejpam-6070	263	26	residual	residual	ADJ
ejpam-6070	263	27	error	error	NOUN
ejpam-6070	263	28	using	use	VERB
ejpam-6070	263	29	ddm	ddm	NOUN
ejpam-6070	263	30	for	for	ADP
ejpam-6070	263	31	various	various	ADJ
ejpam-6070	263	32	overlap	overlap	NOUN
ejpam-6070	263	33	values	value	NOUN
ejpam-6070	263	34	.	.	PUNCT
ejpam-6070	264	1	∥r∥∞	∥r∥∞	CCONJ
ejpam-6070	264	2	iteration	iteration	NOUN
ejpam-6070	264	3	ddm	ddm	PROPN
ejpam-6070	264	4	:	:	PUNCT
ejpam-6070	264	5	τ	τ	PROPN
ejpam-6070	264	6	>	>	X
ejpam-6070	264	7	1	1	NUM
ejpam-6070	264	8	ddm	ddm	PROPN
ejpam-6070	264	9	:	:	PUNCT
ejpam-6070	264	10	τ	τ	X
ejpam-6070	264	11	=	=	SYM
ejpam-6070	264	12	1	1	NUM
ejpam-6070	264	13	1	1	NUM
ejpam-6070	264	14	7.391048136608375e-04	7.391048136608375e-04	NUM
ejpam-6070	264	15	9.591296770784198e-04	9.591296770784198e-04	NUM
ejpam-6070	264	16	4	4	NUM
ejpam-6070	264	17	1.608036639652848e-04	1.608036639652848e-04	NUM
ejpam-6070	264	18	2.363530936250824e-04	2.363530936250824e-04	NUM
ejpam-6070	264	19	8	8	NUM
ejpam-6070	264	20	3.630680843518114e-05	3.630680843518114e-05	NUM
ejpam-6070	264	21	5.836710081515498e-05	5.836710081515498e-05	NUM
ejpam-6070	264	22	last	last	ADJ
ejpam-6070	264	23	iteration	iteration	NOUN
ejpam-6070	264	24	2.162254986382806e-05	2.162254986382806e-05	NUM
ejpam-6070	264	25	3.666961301803263e-05	3.666961301803263e-05	NUM
ejpam-6070	264	26	the	the	DET
ejpam-6070	264	27	table	table	NOUN
ejpam-6070	264	28	(	(	PUNCT
ejpam-6070	264	29	1	1	X
ejpam-6070	264	30	)	)	PUNCT
ejpam-6070	264	31	presents	present	VERB
ejpam-6070	264	32	the	the	DET
ejpam-6070	264	33	infinity	infinity	NOUN
ejpam-6070	264	34	norm	norm	NOUN
ejpam-6070	264	35	of	of	ADP
ejpam-6070	264	36	the	the	DET
ejpam-6070	264	37	residual	residual	ADJ
ejpam-6070	264	38	error	error	NOUN
ejpam-6070	264	39	for	for	ADP
ejpam-6070	264	40	the	the	DET
ejpam-6070	264	41	approximate	approximate	ADJ
ejpam-6070	264	42	solutions	solution	NOUN
ejpam-6070	264	43	obtained	obtain	VERB
ejpam-6070	264	44	using	use	VERB
ejpam-6070	264	45	finite	finite	ADJ
ejpam-6070	264	46	difference	difference	NOUN
ejpam-6070	264	47	methods	method	NOUN
ejpam-6070	264	48	with	with	ADP
ejpam-6070	264	49	h	h	NOUN
ejpam-6070	264	50	=	=	NOUN
ejpam-6070	264	51	1	1	NUM
ejpam-6070	264	52	20	20	NUM
ejpam-6070	264	53	under	under	ADP
ejpam-6070	264	54	various	various	ADJ
ejpam-6070	264	55	overlap	overlap	NOUN
ejpam-6070	264	56	configurations	configuration	NOUN
ejpam-6070	264	57	.	.	PUNCT
ejpam-6070	265	1	the	the	DET
ejpam-6070	265	2	residual	residual	ADJ
ejpam-6070	265	3	is	be	AUX
ejpam-6070	265	4	computed	compute	VERB
ejpam-6070	265	5	as	as	ADP
ejpam-6070	265	6	r	r	NOUN
ejpam-6070	265	7	=	=	SYM
ejpam-6070	265	8	max	max	PROPN
ejpam-6070	265	9	1≤i≤2	1≤i≤2	NOUN
ejpam-6070	265	10	{	{	PUNCT
ejpam-6070	265	11	biζ̌k	biζ̌k	PROPN
ejpam-6070	265	12	−	−	NOUN
ejpam-6070	265	13	g	g	PROPN
ejpam-6070	266	1	i	i	PRON
ejpam-6070	266	2	(	(	PUNCT
ejpam-6070	266	3	ζ̌k−1	ζ̌k−1	PROPN
ejpam-6070	266	4	)	)	PUNCT
ejpam-6070	266	5	}	}	PUNCT
ejpam-6070	266	6	.	.	PUNCT
ejpam-6070	267	1	s.	s.	PROPN
ejpam-6070	267	2	chebbah	chebbah	PROPN
ejpam-6070	267	3	,	,	PUNCT
ejpam-6070	267	4	s.	s.	PROPN
ejpam-6070	267	5	madi	madi	PROPN
ejpam-6070	267	6	,	,	PUNCT
ejpam-6070	267	7	m.	m.	NOUN
ejpam-6070	267	8	haiour	haiour	PROPN
ejpam-6070	267	9	/	/	SYM
ejpam-6070	267	10	eur	eur	PROPN
ejpam-6070	267	11	.	.	PUNCT
ejpam-6070	268	1	j.	j.	PROPN
ejpam-6070	268	2	pure	pure	PROPN
ejpam-6070	268	3	appl	appl	PROPN
ejpam-6070	268	4	.	.	PROPN
ejpam-6070	268	5	math	math	PROPN
ejpam-6070	268	6	,	,	PUNCT
ejpam-6070	268	7	18	18	NUM
ejpam-6070	268	8	(	(	PUNCT
ejpam-6070	268	9	2	2	NUM
ejpam-6070	268	10	)	)	PUNCT
ejpam-6070	268	11	(	(	PUNCT
ejpam-6070	268	12	2025	2025	NUM
ejpam-6070	268	13	)	)	PUNCT
ejpam-6070	268	14	,	,	PUNCT
ejpam-6070	268	15	6070	6070	NUM
ejpam-6070	268	16	15	15	NUM
ejpam-6070	268	17	of	of	ADP
ejpam-6070	268	18	20	20	NUM
ejpam-6070	268	19	the	the	DET
ejpam-6070	268	20	results	result	NOUN
ejpam-6070	268	21	indicate	indicate	VERB
ejpam-6070	268	22	that	that	SCONJ
ejpam-6070	268	23	the	the	DET
ejpam-6070	268	24	residual	residual	ADJ
ejpam-6070	268	25	errors	error	NOUN
ejpam-6070	268	26	are	be	AUX
ejpam-6070	268	27	remarkably	remarkably	ADV
ejpam-6070	268	28	small	small	ADJ
ejpam-6070	268	29	and	and	CCONJ
ejpam-6070	268	30	consistently	consistently	ADV
ejpam-6070	268	31	decrease	decrease	VERB
ejpam-6070	268	32	across	across	ADP
ejpam-6070	268	33	iterations	iteration	NOUN
ejpam-6070	268	34	.	.	PUNCT
ejpam-6070	269	1	notably	notably	ADV
ejpam-6070	269	2	,	,	PUNCT
ejpam-6070	269	3	configurations	configuration	NOUN
ejpam-6070	269	4	with	with	ADP
ejpam-6070	269	5	overlap	overlap	NOUN
ejpam-6070	269	6	(	(	PUNCT
ejpam-6070	269	7	τ	τ	X
ejpam-6070	269	8	>	>	X
ejpam-6070	269	9	1	1	NUM
ejpam-6070	269	10	)	)	PUNCT
ejpam-6070	269	11	result	result	NOUN
ejpam-6070	269	12	in	in	ADP
ejpam-6070	269	13	a	a	DET
ejpam-6070	269	14	faster	fast	ADJ
ejpam-6070	269	15	reduction	reduction	NOUN
ejpam-6070	269	16	in	in	ADP
ejpam-6070	269	17	error	error	NOUN
ejpam-6070	269	18	compared	compare	VERB
ejpam-6070	269	19	to	to	ADP
ejpam-6070	269	20	the	the	DET
ejpam-6070	269	21	non	non	ADJ
ejpam-6070	269	22	-	-	ADJ
ejpam-6070	269	23	overlapping	overlapping	ADJ
ejpam-6070	269	24	case	case	NOUN
ejpam-6070	269	25	(	(	PUNCT
ejpam-6070	269	26	τ	τ	X
ejpam-6070	269	27	=	=	SYM
ejpam-6070	269	28	1	1	NUM
ejpam-6070	269	29	)	)	PUNCT
ejpam-6070	269	30	.	.	PUNCT
ejpam-6070	270	1	this	this	PRON
ejpam-6070	270	2	emphasizes	emphasize	VERB
ejpam-6070	270	3	the	the	DET
ejpam-6070	270	4	importance	importance	NOUN
ejpam-6070	270	5	of	of	ADP
ejpam-6070	270	6	overlap	overlap	NOUN
ejpam-6070	270	7	in	in	ADP
ejpam-6070	270	8	accelerating	accelerate	VERB
ejpam-6070	270	9	convergence	convergence	NOUN
ejpam-6070	270	10	and	and	CCONJ
ejpam-6070	270	11	improving	improve	VERB
ejpam-6070	270	12	the	the	DET
ejpam-6070	270	13	accuracy	accuracy	NOUN
ejpam-6070	270	14	of	of	ADP
ejpam-6070	270	15	the	the	DET
ejpam-6070	270	16	solution	solution	NOUN
ejpam-6070	270	17	approximation	approximation	NOUN
ejpam-6070	270	18	.	.	PUNCT
ejpam-6070	271	1	table	table	NOUN
ejpam-6070	271	2	2	2	NUM
ejpam-6070	271	3	:	:	PUNCT
ejpam-6070	271	4	value	value	NOUN
ejpam-6070	271	5	of	of	ADP
ejpam-6070	271	6	ζ̂k	ζ̂k	PROPN
ejpam-6070	271	7	at	at	ADP
ejpam-6070	271	8	(	(	PUNCT
ejpam-6070	271	9	x	x	NOUN
ejpam-6070	271	10	,	,	PUNCT
ejpam-6070	271	11	y)t	y)t	PUNCT
ejpam-6070	271	12	=	=	PUNCT
ejpam-6070	271	13	(	(	PUNCT
ejpam-6070	271	14	0.5	0.5	NUM
ejpam-6070	271	15	,	,	PUNCT
ejpam-6070	271	16	0.25)t	0.25)t	NOUN
ejpam-6070	271	17	for	for	ADP
ejpam-6070	271	18	h	h	NOUN
ejpam-6070	271	19	=	=	NOUN
ejpam-6070	271	20	1	1	NUM
ejpam-6070	271	21	20	20	NUM
ejpam-6070	271	22	.	.	PUNCT
ejpam-6070	272	1	iteration	iteration	PROPN
ejpam-6070	272	2	ddm	ddm	PROPN
ejpam-6070	272	3	:	:	PUNCT
ejpam-6070	272	4	τ	τ	X
ejpam-6070	272	5	>	>	X
ejpam-6070	272	6	1	1	NUM
ejpam-6070	272	7	ddm	ddm	NOUN
ejpam-6070	272	8	:	:	PUNCT
ejpam-6070	272	9	τ	τ	X
ejpam-6070	272	10	=	=	SYM
ejpam-6070	272	11	1	1	NUM
ejpam-6070	272	12	1	1	NUM
ejpam-6070	272	13	-0.003915453822399	-0.003915453822399	NOUN
ejpam-6070	272	14	-0.003375478664288	-0.003375478664288	VERB
ejpam-6070	272	15	4	4	NUM
ejpam-6070	272	16	-0.005478666922059	-0.005478666922059	NOUN
ejpam-6070	272	17	-0.005035539613455	-0.005035539613455	NOUN
ejpam-6070	272	18	8	8	NUM
ejpam-6070	272	19	-0.005493072486538	-0.005493072486538	NOUN
ejpam-6070	272	20	-0.005428621964170	-0.005428621964170	NOUN
ejpam-6070	273	1	last	last	ADJ
ejpam-6070	273	2	iteration	iteration	NOUN
ejpam-6070	273	3	-0.005493166542087	-0.005493166542087	NOUN
ejpam-6070	273	4	-0.005493095359904	-0.005493095359904	ADJ
ejpam-6070	273	5	table	table	NOUN
ejpam-6070	273	6	3	3	NUM
ejpam-6070	273	7	:	:	PUNCT
ejpam-6070	273	8	value	value	NOUN
ejpam-6070	273	9	of	of	ADP
ejpam-6070	273	10	ζ̌k	ζ̌k	PROPN
ejpam-6070	273	11	at	at	ADP
ejpam-6070	273	12	(	(	PUNCT
ejpam-6070	273	13	x	x	NOUN
ejpam-6070	273	14	,	,	PUNCT
ejpam-6070	273	15	y)t	y)t	PUNCT
ejpam-6070	273	16	=	=	PUNCT
ejpam-6070	273	17	(	(	PUNCT
ejpam-6070	273	18	0.5	0.5	NUM
ejpam-6070	273	19	,	,	PUNCT
ejpam-6070	273	20	0.25)t	0.25)t	NOUN
ejpam-6070	273	21	for	for	ADP
ejpam-6070	273	22	h	h	NOUN
ejpam-6070	273	23	=	=	NOUN
ejpam-6070	273	24	1	1	NUM
ejpam-6070	273	25	20	20	NUM
ejpam-6070	273	26	.	.	PUNCT
ejpam-6070	274	1	iteration	iteration	PROPN
ejpam-6070	274	2	ddm	ddm	PROPN
ejpam-6070	274	3	:	:	PUNCT
ejpam-6070	274	4	τ	τ	X
ejpam-6070	274	5	>	>	X
ejpam-6070	274	6	1	1	NUM
ejpam-6070	274	7	ddm	ddm	NOUN
ejpam-6070	274	8	:	:	PUNCT
ejpam-6070	274	9	τ	τ	X
ejpam-6070	274	10	=	=	SYM
ejpam-6070	274	11	1	1	NUM
ejpam-6070	274	12	1	1	NUM
ejpam-6070	274	13	-0.137907986376806	-0.137907986376806	NOUN
ejpam-6070	274	14	-1.035248717772950	-1.035248717772950	NOUN
ejpam-6070	274	15	4	4	NUM
ejpam-6070	274	16	-0.012726797737372	-0.012726797737372	NOUN
ejpam-6070	274	17	-0.386671348701684	-0.386671348701684	NOUN
ejpam-6070	274	18	8	8	NUM
ejpam-6070	274	19	-0.005505924360092	-0.005505924360092	NOUN
ejpam-6070	274	20	-0.098756491226852	-0.098756491226852	NOUN
ejpam-6070	274	21	last	last	ADJ
ejpam-6070	274	22	iteration	iteration	PROPN
ejpam-6070	274	23	-0.005493173019551	-0.005493173019551	PRON
ejpam-6070	274	24	-0.005493282229003	-0.005493282229003	PUNCT
ejpam-6070	275	1	the	the	DET
ejpam-6070	275	2	numerical	numerical	ADJ
ejpam-6070	275	3	results	result	NOUN
ejpam-6070	275	4	presented	present	VERB
ejpam-6070	275	5	in	in	ADP
ejpam-6070	275	6	tables	table	NOUN
ejpam-6070	275	7	(	(	PUNCT
ejpam-6070	275	8	2	2	NUM
ejpam-6070	275	9	)	)	PUNCT
ejpam-6070	275	10	and	and	CCONJ
ejpam-6070	275	11	(	(	PUNCT
ejpam-6070	275	12	3	3	X
ejpam-6070	275	13	)	)	PUNCT
ejpam-6070	275	14	illustrate	illustrate	VERB
ejpam-6070	275	15	the	the	DET
ejpam-6070	275	16	convergence	convergence	NOUN
ejpam-6070	275	17	properties	property	NOUN
ejpam-6070	275	18	of	of	ADP
ejpam-6070	275	19	the	the	DET
ejpam-6070	275	20	lower	low	ADJ
ejpam-6070	275	21	and	and	CCONJ
ejpam-6070	275	22	upper	upper	ADJ
ejpam-6070	275	23	solutions	solution	NOUN
ejpam-6070	275	24	for	for	ADP
ejpam-6070	275	25	the	the	DET
ejpam-6070	275	26	hamilton	hamilton	PROPN
ejpam-6070	275	27	-	-	PUNCT
ejpam-6070	275	28	jacobi	jacobi	PROPN
ejpam-6070	275	29	-	-	PUNCT
ejpam-6070	275	30	bellman	bellman	NOUN
ejpam-6070	275	31	(	(	PUNCT
ejpam-6070	275	32	hjb	hjb	NOUN
ejpam-6070	275	33	)	)	PUNCT
ejpam-6070	275	34	equation	equation	NOUN
ejpam-6070	275	35	.	.	PUNCT
ejpam-6070	276	1	as	as	SCONJ
ejpam-6070	276	2	expected	expect	VERB
ejpam-6070	276	3	,	,	PUNCT
ejpam-6070	276	4	the	the	DET
ejpam-6070	276	5	lower	low	ADJ
ejpam-6070	276	6	solution	solution	NOUN
ejpam-6070	276	7	ζ̌k	ζ̌k	PROPN
ejpam-6070	276	8	exhibits	exhibit	VERB
ejpam-6070	276	9	a	a	DET
ejpam-6070	276	10	monotonic	monotonic	ADJ
ejpam-6070	276	11	increase	increase	NOUN
ejpam-6070	276	12	,	,	PUNCT
ejpam-6070	276	13	while	while	SCONJ
ejpam-6070	276	14	the	the	DET
ejpam-6070	276	15	upper	upper	ADJ
ejpam-6070	276	16	solution	solution	NOUN
ejpam-6070	276	17	ζ̂k	ζ̂k	PROPN
ejpam-6070	276	18	follows	follow	VERB
ejpam-6070	276	19	a	a	DET
ejpam-6070	276	20	monotonic	monotonic	ADJ
ejpam-6070	276	21	decrease	decrease	NOUN
ejpam-6070	276	22	,	,	PUNCT
ejpam-6070	276	23	ensuring	ensure	VERB
ejpam-6070	276	24	a	a	DET
ejpam-6070	276	25	stable	stable	ADJ
ejpam-6070	276	26	convergence	convergence	NOUN
ejpam-6070	276	27	towards	towards	ADP
ejpam-6070	276	28	the	the	DET
ejpam-6070	276	29	exact	exact	ADJ
ejpam-6070	276	30	solution	solution	NOUN
ejpam-6070	276	31	.	.	PUNCT
ejpam-6070	277	1	moreover	moreover	ADV
ejpam-6070	277	2	,	,	PUNCT
ejpam-6070	277	3	the	the	DET
ejpam-6070	277	4	comparison	comparison	NOUN
ejpam-6070	277	5	between	between	ADP
ejpam-6070	277	6	the	the	DET
ejpam-6070	277	7	overlapping	overlapping	NOUN
ejpam-6070	277	8	(	(	PUNCT
ejpam-6070	277	9	τ	τ	X
ejpam-6070	277	10	>	>	X
ejpam-6070	277	11	1	1	NUM
ejpam-6070	277	12	)	)	PUNCT
ejpam-6070	277	13	and	and	CCONJ
ejpam-6070	277	14	non	non	ADJ
ejpam-6070	277	15	-	-	ADJ
ejpam-6070	277	16	overlapping	overlapping	ADJ
ejpam-6070	277	17	(	(	PUNCT
ejpam-6070	277	18	τ	τ	X
ejpam-6070	277	19	=	=	SYM
ejpam-6070	277	20	1	1	X
ejpam-6070	277	21	)	)	PUNCT
ejpam-6070	277	22	domain	domain	NOUN
ejpam-6070	277	23	decomposition	decomposition	NOUN
ejpam-6070	277	24	methods	method	NOUN
ejpam-6070	277	25	confirms	confirm	VERB
ejpam-6070	277	26	that	that	SCONJ
ejpam-6070	277	27	increasing	increase	VERB
ejpam-6070	277	28	the	the	DET
ejpam-6070	277	29	overlap	overlap	NOUN
ejpam-6070	277	30	parameter	parameter	NOUN
ejpam-6070	277	31	significantly	significantly	ADV
ejpam-6070	277	32	enhances	enhance	VERB
ejpam-6070	277	33	the	the	DET
ejpam-6070	277	34	convergence	convergence	NOUN
ejpam-6070	277	35	rate	rate	NOUN
ejpam-6070	277	36	,	,	PUNCT
ejpam-6070	277	37	reducing	reduce	VERB
ejpam-6070	277	38	the	the	DET
ejpam-6070	277	39	number	number	NOUN
ejpam-6070	277	40	of	of	ADP
ejpam-6070	277	41	iterations	iteration	NOUN
ejpam-6070	277	42	required	require	VERB
ejpam-6070	277	43	to	to	PART
ejpam-6070	277	44	reach	reach	VERB
ejpam-6070	277	45	the	the	DET
ejpam-6070	277	46	desired	desire	VERB
ejpam-6070	277	47	accuracy	accuracy	NOUN
ejpam-6070	277	48	.	.	PUNCT
ejpam-6070	278	1	s.	s.	PROPN
ejpam-6070	278	2	chebbah	chebbah	PROPN
ejpam-6070	278	3	,	,	PUNCT
ejpam-6070	278	4	s.	s.	PROPN
ejpam-6070	278	5	madi	madi	PROPN
ejpam-6070	278	6	,	,	PUNCT
ejpam-6070	278	7	m.	m.	NOUN
ejpam-6070	278	8	haiour	haiour	PROPN
ejpam-6070	278	9	/	/	SYM
ejpam-6070	278	10	eur	eur	PROPN
ejpam-6070	278	11	.	.	PUNCT
ejpam-6070	279	1	j.	j.	PROPN
ejpam-6070	279	2	pure	pure	PROPN
ejpam-6070	279	3	appl	appl	PROPN
ejpam-6070	279	4	.	.	PROPN
ejpam-6070	279	5	math	math	PROPN
ejpam-6070	279	6	,	,	PUNCT
ejpam-6070	279	7	18	18	NUM
ejpam-6070	279	8	(	(	PUNCT
ejpam-6070	279	9	2	2	NUM
ejpam-6070	279	10	)	)	PUNCT
ejpam-6070	279	11	(	(	PUNCT
ejpam-6070	279	12	2025	2025	NUM
ejpam-6070	279	13	)	)	PUNCT
ejpam-6070	279	14	,	,	PUNCT
ejpam-6070	279	15	6070	6070	NUM
ejpam-6070	279	16	16	16	NUM
ejpam-6070	279	17	of	of	ADP
ejpam-6070	279	18	20	20	NUM
ejpam-6070	279	19	figure	figure	NOUN
ejpam-6070	279	20	2	2	NUM
ejpam-6070	279	21	:	:	PUNCT
ejpam-6070	279	22	approximated	approximate	VERB
ejpam-6070	279	23	solutions	solution	NOUN
ejpam-6070	279	24	(	(	PUNCT
ejpam-6070	279	25	ddm	ddm	PROPN
ejpam-6070	279	26	)	)	PUNCT
ejpam-6070	279	27	.	.	PUNCT
ejpam-6070	280	1	figure	figure	NOUN
ejpam-6070	280	2	(	(	PUNCT
ejpam-6070	280	3	2	2	NUM
ejpam-6070	280	4	)	)	PUNCT
ejpam-6070	280	5	represents	represent	VERB
ejpam-6070	280	6	the	the	DET
ejpam-6070	280	7	numerical	numerical	ADJ
ejpam-6070	280	8	solution	solution	NOUN
ejpam-6070	280	9	of	of	ADP
ejpam-6070	280	10	the	the	DET
ejpam-6070	280	11	problem	problem	NOUN
ejpam-6070	280	12	using	use	VERB
ejpam-6070	280	13	the	the	DET
ejpam-6070	280	14	overlapping	overlap	VERB
ejpam-6070	280	15	schwarz	schwarz	PROPN
ejpam-6070	280	16	domain	domain	NOUN
ejpam-6070	280	17	decomposition	decomposition	NOUN
ejpam-6070	280	18	method	method	NOUN
ejpam-6070	280	19	.	.	PUNCT
ejpam-6070	281	1	the	the	DET
ejpam-6070	281	2	red	red	ADJ
ejpam-6070	281	3	and	and	CCONJ
ejpam-6070	281	4	blue	blue	ADJ
ejpam-6070	281	5	lines	line	NOUN
ejpam-6070	281	6	indicate	indicate	VERB
ejpam-6070	281	7	the	the	DET
ejpam-6070	281	8	overlapping	overlap	VERB
ejpam-6070	281	9	subdomains	subdomain	NOUN
ejpam-6070	281	10	along	along	ADP
ejpam-6070	281	11	the	the	DET
ejpam-6070	281	12	x	x	NOUN
ejpam-6070	281	13	-	-	NOUN
ejpam-6070	281	14	axis	axis	ADJ
ejpam-6070	281	15	.	.	PUNCT
ejpam-6070	282	1	figure	figure	NOUN
ejpam-6070	282	2	3	3	NUM
ejpam-6070	282	3	:	:	PUNCT
ejpam-6070	282	4	convergence	convergence	NOUN
ejpam-6070	282	5	behavior	behavior	NOUN
ejpam-6070	282	6	of	of	ADP
ejpam-6070	282	7	the	the	DET
ejpam-6070	282	8	iterative	iterative	NOUN
ejpam-6070	282	9	scheme	scheme	NOUN
ejpam-6070	282	10	.	.	PUNCT
ejpam-6070	283	1	figure	figure	NOUN
ejpam-6070	283	2	(	(	PUNCT
ejpam-6070	283	3	3	3	NUM
ejpam-6070	283	4	)	)	PUNCT
ejpam-6070	283	5	demonstrates	demonstrate	VERB
ejpam-6070	283	6	the	the	DET
ejpam-6070	283	7	geometric	geometric	ADJ
ejpam-6070	283	8	convergence	convergence	NOUN
ejpam-6070	283	9	of	of	ADP
ejpam-6070	283	10	the	the	DET
ejpam-6070	283	11	iterative	iterative	NOUN
ejpam-6070	283	12	method	method	NOUN
ejpam-6070	283	13	for	for	ADP
ejpam-6070	283	14	h	h	NOUN
ejpam-6070	283	15	=	=	NOUN
ejpam-6070	283	16	1	1	NUM
ejpam-6070	283	17	20	20	NUM
ejpam-6070	283	18	.	.	PUNCT
ejpam-6070	284	1	the	the	DET
ejpam-6070	284	2	graph	graph	NOUN
ejpam-6070	284	3	displays	display	VERB
ejpam-6070	284	4	the	the	DET
ejpam-6070	284	5	evolution	evolution	NOUN
ejpam-6070	284	6	of	of	ADP
ejpam-6070	284	7	the	the	DET
ejpam-6070	284	8	infinity	infinity	NOUN
ejpam-6070	284	9	norm	norm	NOUN
ejpam-6070	284	10	of	of	ADP
ejpam-6070	284	11	the	the	DET
ejpam-6070	284	12	error	error	NOUN
ejpam-6070	284	13	∥ζk+1	∥ζk+1	ADP
ejpam-6070	284	14	−	−	PRON
ejpam-6070	284	15	ζk∥∞	ζk∥∞	NOUN
ejpam-6070	284	16	as	as	ADP
ejpam-6070	284	17	a	a	DET
ejpam-6070	284	18	function	function	NOUN
ejpam-6070	284	19	of	of	ADP
ejpam-6070	284	20	the	the	DET
ejpam-6070	284	21	iteration	iteration	NOUN
ejpam-6070	284	22	number	number	NOUN
ejpam-6070	284	23	.	.	PUNCT
ejpam-6070	285	1	we	we	PRON
ejpam-6070	285	2	observe	observe	VERB
ejpam-6070	285	3	a	a	DET
ejpam-6070	285	4	rapid	rapid	ADJ
ejpam-6070	285	5	exponential	exponential	ADJ
ejpam-6070	285	6	decrease	decrease	NOUN
ejpam-6070	285	7	in	in	ADP
ejpam-6070	285	8	the	the	DET
ejpam-6070	285	9	error	error	NOUN
ejpam-6070	285	10	,	,	PUNCT
ejpam-6070	285	11	indicating	indicate	VERB
ejpam-6070	285	12	that	that	SCONJ
ejpam-6070	285	13	the	the	DET
ejpam-6070	285	14	approximate	approximate	ADJ
ejpam-6070	285	15	solution	solution	NOUN
ejpam-6070	285	16	is	be	AUX
ejpam-6070	285	17	approaching	approach	VERB
ejpam-6070	285	18	a	a	DET
ejpam-6070	285	19	stable	stable	ADJ
ejpam-6070	285	20	fixed	fix	VERB
ejpam-6070	285	21	point	point	NOUN
ejpam-6070	285	22	.	.	PUNCT
ejpam-6070	286	1	furthermore	furthermore	ADV
ejpam-6070	286	2	,	,	PUNCT
ejpam-6070	286	3	using	use	VERB
ejpam-6070	286	4	a	a	DET
ejpam-6070	286	5	larger	large	ADJ
ejpam-6070	286	6	overlap	overlap	NOUN
ejpam-6070	286	7	(	(	PUNCT
ejpam-6070	286	8	blue	blue	ADJ
ejpam-6070	286	9	curve	curve	NOUN
ejpam-6070	286	10	)	)	PUNCT
ejpam-6070	286	11	significantly	significantly	ADV
ejpam-6070	286	12	improves	improve	VERB
ejpam-6070	286	13	the	the	DET
ejpam-6070	286	14	convergence	convergence	NOUN
ejpam-6070	286	15	rate	rate	NOUN
ejpam-6070	286	16	by	by	ADP
ejpam-6070	286	17	reducing	reduce	VERB
ejpam-6070	286	18	both	both	CCONJ
ejpam-6070	286	19	the	the	DET
ejpam-6070	286	20	number	number	NOUN
ejpam-6070	286	21	of	of	ADP
ejpam-6070	286	22	iterations	iteration	NOUN
ejpam-6070	286	23	and	and	CCONJ
ejpam-6070	286	24	the	the	DET
ejpam-6070	286	25	total	total	ADJ
ejpam-6070	286	26	computational	computational	ADJ
ejpam-6070	286	27	effort	effort	NOUN
ejpam-6070	286	28	.	.	PUNCT
ejpam-6070	287	1	s.	s.	PROPN
ejpam-6070	287	2	chebbah	chebbah	PROPN
ejpam-6070	287	3	,	,	PUNCT
ejpam-6070	287	4	s.	s.	PROPN
ejpam-6070	287	5	madi	madi	PROPN
ejpam-6070	287	6	,	,	PUNCT
ejpam-6070	287	7	m.	m.	NOUN
ejpam-6070	287	8	haiour	haiour	PROPN
ejpam-6070	287	9	/	/	SYM
ejpam-6070	287	10	eur	eur	PROPN
ejpam-6070	287	11	.	.	PUNCT
ejpam-6070	288	1	j.	j.	PROPN
ejpam-6070	288	2	pure	pure	PROPN
ejpam-6070	288	3	appl	appl	PROPN
ejpam-6070	288	4	.	.	PROPN
ejpam-6070	288	5	math	math	PROPN
ejpam-6070	288	6	,	,	PUNCT
ejpam-6070	288	7	18	18	NUM
ejpam-6070	288	8	(	(	PUNCT
ejpam-6070	288	9	2	2	NUM
ejpam-6070	288	10	)	)	PUNCT
ejpam-6070	288	11	(	(	PUNCT
ejpam-6070	288	12	2025	2025	NUM
ejpam-6070	288	13	)	)	PUNCT
ejpam-6070	288	14	,	,	PUNCT
ejpam-6070	288	15	6070	6070	NUM
ejpam-6070	288	16	17	17	NUM
ejpam-6070	288	17	of	of	ADP
ejpam-6070	288	18	20	20	NUM
ejpam-6070	288	19	figure	figure	NOUN
ejpam-6070	288	20	4	4	NUM
ejpam-6070	288	21	:	:	PUNCT
ejpam-6070	288	22	residuals	residual	VERB
ejpam-6070	288	23	evolution	evolution	NOUN
ejpam-6070	288	24	for	for	ADP
ejpam-6070	288	25	the	the	DET
ejpam-6070	288	26	overlapping	overlap	VERB
ejpam-6070	288	27	domain	domain	NOUN
ejpam-6070	288	28	decomposition	decomposition	NOUN
ejpam-6070	288	29	.	.	PUNCT
ejpam-6070	289	1	figure	figure	NOUN
ejpam-6070	289	2	(	(	PUNCT
ejpam-6070	289	3	4	4	NUM
ejpam-6070	289	4	)	)	PUNCT
ejpam-6070	289	5	illustrates	illustrate	VERB
ejpam-6070	289	6	the	the	DET
ejpam-6070	289	7	residuals	residual	NOUN
ejpam-6070	289	8	r1	r1	NOUN
ejpam-6070	289	9	and	and	CCONJ
ejpam-6070	289	10	r2	r2	NOUN
ejpam-6070	289	11	,	,	PUNCT
ejpam-6070	289	12	representing	represent	VERB
ejpam-6070	289	13	the	the	DET
ejpam-6070	289	14	error	error	NOUN
ejpam-6070	289	15	distribution	distribution	NOUN
ejpam-6070	289	16	in	in	ADP
ejpam-6070	289	17	the	the	DET
ejpam-6070	289	18	approximate	approximate	ADJ
ejpam-6070	289	19	solution	solution	NOUN
ejpam-6070	289	20	while	while	SCONJ
ejpam-6070	289	21	highlighting	highlight	VERB
ejpam-6070	289	22	the	the	DET
ejpam-6070	289	23	active	active	ADJ
ejpam-6070	289	24	and	and	CCONJ
ejpam-6070	289	25	inactive	inactive	ADJ
ejpam-6070	289	26	points	point	NOUN
ejpam-6070	289	27	at	at	ADP
ejpam-6070	289	28	the	the	DET
ejpam-6070	289	29	boundaries	boundary	NOUN
ejpam-6070	289	30	.	.	PUNCT
ejpam-6070	290	1	these	these	DET
ejpam-6070	290	2	plots	plot	NOUN
ejpam-6070	290	3	demonstrate	demonstrate	VERB
ejpam-6070	290	4	the	the	DET
ejpam-6070	290	5	error	error	NOUN
ejpam-6070	290	6	evolution	evolution	NOUN
ejpam-6070	290	7	through	through	ADP
ejpam-6070	290	8	iterations	iteration	NOUN
ejpam-6070	290	9	within	within	ADP
ejpam-6070	290	10	each	each	DET
ejpam-6070	290	11	subdomain	subdomain	NOUN
ejpam-6070	290	12	,	,	PUNCT
ejpam-6070	290	13	where	where	SCONJ
ejpam-6070	290	14	these	these	DET
ejpam-6070	290	15	values	value	NOUN
ejpam-6070	290	16	are	be	AUX
ejpam-6070	290	17	utilized	utilize	VERB
ejpam-6070	290	18	to	to	PART
ejpam-6070	290	19	adjust	adjust	VERB
ejpam-6070	290	20	and	and	CCONJ
ejpam-6070	290	21	refine	refine	VERB
ejpam-6070	290	22	the	the	DET
ejpam-6070	290	23	solution	solution	NOUN
ejpam-6070	290	24	at	at	ADP
ejpam-6070	290	25	each	each	DET
ejpam-6070	290	26	step	step	NOUN
ejpam-6070	290	27	.	.	PUNCT
ejpam-6070	291	1	figure	figure	VERB
ejpam-6070	291	2	5	5	NUM
ejpam-6070	291	3	:	:	PUNCT
ejpam-6070	291	4	maximum	maximum	ADJ
ejpam-6070	291	5	residual	residual	ADJ
ejpam-6070	291	6	over	over	ADP
ejpam-6070	291	7	the	the	DET
ejpam-6070	291	8	computational	computational	ADJ
ejpam-6070	291	9	domain	domain	NOUN
ejpam-6070	291	10	.	.	PUNCT
ejpam-6070	292	1	figure	figure	NOUN
ejpam-6070	292	2	(	(	PUNCT
ejpam-6070	292	3	5	5	NUM
ejpam-6070	292	4	)	)	PUNCT
ejpam-6070	292	5	illustrates	illustrate	VERB
ejpam-6070	292	6	the	the	DET
ejpam-6070	292	7	distribution	distribution	NOUN
ejpam-6070	292	8	of	of	ADP
ejpam-6070	292	9	the	the	DET
ejpam-6070	292	10	maximum	maximum	ADJ
ejpam-6070	292	11	residual	residual	ADJ
ejpam-6070	292	12	over	over	ADP
ejpam-6070	292	13	the	the	DET
ejpam-6070	292	14	computational	computational	ADJ
ejpam-6070	292	15	domain	domain	NOUN
ejpam-6070	292	16	.	.	PUNCT
ejpam-6070	293	1	the	the	DET
ejpam-6070	293	2	error	error	NOUN
ejpam-6070	293	3	is	be	AUX
ejpam-6070	293	4	clearly	clearly	ADV
ejpam-6070	293	5	concentrated	concentrate	VERB
ejpam-6070	293	6	in	in	ADP
ejpam-6070	293	7	the	the	DET
ejpam-6070	293	8	overlapping	overlap	VERB
ejpam-6070	293	9	region	region	NOUN
ejpam-6070	293	10	between	between	ADP
ejpam-6070	293	11	the	the	DET
ejpam-6070	293	12	two	two	NUM
ejpam-6070	293	13	subdomains	subdomain	NOUN
ejpam-6070	293	14	ω1	ω1	ADJ
ejpam-6070	293	15	and	and	CCONJ
ejpam-6070	293	16	ω2	ω2	ADJ
ejpam-6070	293	17	,	,	PUNCT
ejpam-6070	293	18	where	where	SCONJ
ejpam-6070	293	19	it	it	PRON
ejpam-6070	293	20	drops	drop	VERB
ejpam-6070	293	21	to	to	ADP
ejpam-6070	293	22	a	a	DET
ejpam-6070	293	23	minimal	minimal	ADJ
ejpam-6070	293	24	value	value	NOUN
ejpam-6070	293	25	of	of	ADP
ejpam-6070	293	26	approximately	approximately	ADV
ejpam-6070	293	27	10−5	10−5	NUM
ejpam-6070	293	28	.	.	PUNCT
ejpam-6070	294	1	this	this	PRON
ejpam-6070	294	2	confirms	confirm	VERB
ejpam-6070	294	3	the	the	DET
ejpam-6070	294	4	efficiency	efficiency	NOUN
ejpam-6070	294	5	of	of	ADP
ejpam-6070	294	6	the	the	DET
ejpam-6070	294	7	iterative	iterative	NOUN
ejpam-6070	294	8	method	method	NOUN
ejpam-6070	294	9	in	in	ADP
ejpam-6070	294	10	reducing	reduce	VERB
ejpam-6070	294	11	the	the	DET
ejpam-6070	294	12	residual	residual	ADJ
ejpam-6070	294	13	specifically	specifically	ADV
ejpam-6070	294	14	within	within	ADP
ejpam-6070	294	15	the	the	DET
ejpam-6070	294	16	interface	interface	NOUN
ejpam-6070	294	17	area	area	NOUN
ejpam-6070	294	18	,	,	PUNCT
ejpam-6070	294	19	thereby	thereby	ADV
ejpam-6070	294	20	enhancing	enhance	VERB
ejpam-6070	294	21	the	the	DET
ejpam-6070	294	22	accuracy	accuracy	NOUN
ejpam-6070	294	23	of	of	ADP
ejpam-6070	294	24	the	the	DET
ejpam-6070	294	25	solution	solution	NOUN
ejpam-6070	294	26	and	and	CCONJ
ejpam-6070	294	27	accelerating	accelerate	VERB
ejpam-6070	294	28	convergence	convergence	NOUN
ejpam-6070	294	29	.	.	PUNCT
ejpam-6070	295	1	s.	s.	PROPN
ejpam-6070	295	2	chebbah	chebbah	PROPN
ejpam-6070	295	3	,	,	PUNCT
ejpam-6070	295	4	s.	s.	PROPN
ejpam-6070	295	5	madi	madi	PROPN
ejpam-6070	295	6	,	,	PUNCT
ejpam-6070	295	7	m.	m.	NOUN
ejpam-6070	295	8	haiour	haiour	PROPN
ejpam-6070	295	9	/	/	SYM
ejpam-6070	295	10	eur	eur	PROPN
ejpam-6070	295	11	.	.	PUNCT
ejpam-6070	296	1	j.	j.	PROPN
ejpam-6070	296	2	pure	pure	PROPN
ejpam-6070	296	3	appl	appl	PROPN
ejpam-6070	296	4	.	.	PROPN
ejpam-6070	296	5	math	math	PROPN
ejpam-6070	296	6	,	,	PUNCT
ejpam-6070	296	7	18	18	NUM
ejpam-6070	296	8	(	(	PUNCT
ejpam-6070	296	9	2	2	NUM
ejpam-6070	296	10	)	)	PUNCT
ejpam-6070	296	11	(	(	PUNCT
ejpam-6070	296	12	2025	2025	NUM
ejpam-6070	296	13	)	)	PUNCT
ejpam-6070	296	14	,	,	PUNCT
ejpam-6070	296	15	6070	6070	NUM
ejpam-6070	296	16	18	18	NUM
ejpam-6070	296	17	of	of	ADP
ejpam-6070	296	18	20	20	NUM
ejpam-6070	296	19	5	5	NUM
ejpam-6070	296	20	.	.	PUNCT
ejpam-6070	297	1	conclusion	conclusion	NOUN
ejpam-6070	297	2	in	in	ADP
ejpam-6070	297	3	this	this	DET
ejpam-6070	297	4	work	work	NOUN
ejpam-6070	298	1	,	,	PUNCT
ejpam-6070	298	2	we	we	PRON
ejpam-6070	298	3	solved	solve	VERB
ejpam-6070	298	4	the	the	DET
ejpam-6070	298	5	noncoercive	noncoercive	ADJ
ejpam-6070	298	6	hamilton	hamilton	PROPN
ejpam-6070	298	7	-	-	PUNCT
ejpam-6070	298	8	jacobi	jacobi	PROPN
ejpam-6070	298	9	-	-	PUNCT
ejpam-6070	298	10	bellman	bellman	NOUN
ejpam-6070	298	11	equation	equation	NOUN
ejpam-6070	298	12	directly	directly	ADV
ejpam-6070	298	13	,	,	PUNCT
ejpam-6070	298	14	without	without	ADP
ejpam-6070	298	15	transforming	transform	VERB
ejpam-6070	298	16	it	it	PRON
ejpam-6070	298	17	into	into	ADP
ejpam-6070	298	18	a	a	DET
ejpam-6070	298	19	quasi	quasi	ADJ
ejpam-6070	298	20	-	-	ADJ
ejpam-6070	298	21	variational	variational	ADJ
ejpam-6070	298	22	inequality	inequality	NOUN
ejpam-6070	298	23	system	system	NOUN
ejpam-6070	298	24	.	.	PUNCT
ejpam-6070	299	1	this	this	DET
ejpam-6070	299	2	approach	approach	NOUN
ejpam-6070	299	3	preserves	preserve	VERB
ejpam-6070	299	4	the	the	DET
ejpam-6070	299	5	structure	structure	NOUN
ejpam-6070	299	6	of	of	ADP
ejpam-6070	299	7	the	the	DET
ejpam-6070	299	8	original	original	ADJ
ejpam-6070	299	9	problem	problem	NOUN
ejpam-6070	299	10	and	and	CCONJ
ejpam-6070	299	11	simplifies	simplify	VERB
ejpam-6070	299	12	the	the	DET
ejpam-6070	299	13	numerical	numerical	ADJ
ejpam-6070	299	14	treatment	treatment	PROPN
ejpam-6070	299	15	.	.	PUNCT
ejpam-6070	300	1	the	the	DET
ejpam-6070	300	2	method	method	NOUN
ejpam-6070	300	3	is	be	AUX
ejpam-6070	300	4	based	base	VERB
ejpam-6070	300	5	on	on	ADP
ejpam-6070	300	6	constructing	construct	VERB
ejpam-6070	300	7	lower	low	ADJ
ejpam-6070	300	8	and	and	CCONJ
ejpam-6070	300	9	upper	upper	ADJ
ejpam-6070	300	10	solutions	solution	NOUN
ejpam-6070	300	11	that	that	PRON
ejpam-6070	300	12	converge	converge	VERB
ejpam-6070	300	13	to	to	ADP
ejpam-6070	300	14	the	the	DET
ejpam-6070	300	15	discrete	discrete	ADJ
ejpam-6070	300	16	solution	solution	NOUN
ejpam-6070	300	17	within	within	ADP
ejpam-6070	300	18	the	the	DET
ejpam-6070	300	19	finite	finite	ADJ
ejpam-6070	300	20	difference	difference	NOUN
ejpam-6070	300	21	framework	framework	NOUN
ejpam-6070	300	22	.	.	PUNCT
ejpam-6070	301	1	the	the	DET
ejpam-6070	301	2	overlapping	overlap	VERB
ejpam-6070	301	3	domain	domain	NOUN
ejpam-6070	301	4	decomposition	decomposition	NOUN
ejpam-6070	301	5	method	method	NOUN
ejpam-6070	301	6	was	be	AUX
ejpam-6070	301	7	applied	apply	VERB
ejpam-6070	301	8	,	,	PUNCT
ejpam-6070	301	9	which	which	PRON
ejpam-6070	301	10	contributed	contribute	VERB
ejpam-6070	301	11	to	to	ADP
ejpam-6070	301	12	improving	improve	VERB
ejpam-6070	301	13	the	the	DET
ejpam-6070	301	14	convergence	convergence	NOUN
ejpam-6070	301	15	rate	rate	NOUN
ejpam-6070	301	16	compared	compare	VERB
ejpam-6070	301	17	to	to	ADP
ejpam-6070	301	18	the	the	DET
ejpam-6070	301	19	non	non	ADJ
ejpam-6070	301	20	-	-	ADJ
ejpam-6070	301	21	overlapping	overlapping	ADJ
ejpam-6070	301	22	case	case	NOUN
ejpam-6070	301	23	.	.	PUNCT
ejpam-6070	302	1	theoretical	theoretical	ADJ
ejpam-6070	302	2	analysis	analysis	NOUN
ejpam-6070	302	3	confirms	confirm	VERB
ejpam-6070	302	4	that	that	SCONJ
ejpam-6070	302	5	this	this	DET
ejpam-6070	302	6	method	method	NOUN
ejpam-6070	302	7	ensures	ensure	VERB
ejpam-6070	302	8	monotonic	monotonic	ADJ
ejpam-6070	302	9	and	and	CCONJ
ejpam-6070	302	10	geometric	geometric	ADJ
ejpam-6070	302	11	convergence	convergence	NOUN
ejpam-6070	302	12	.	.	PUNCT
ejpam-6070	303	1	furthermore	furthermore	ADV
ejpam-6070	303	2	,	,	PUNCT
ejpam-6070	303	3	numerical	numerical	ADJ
ejpam-6070	303	4	results	result	NOUN
ejpam-6070	303	5	demonstrated	demonstrate	VERB
ejpam-6070	303	6	that	that	SCONJ
ejpam-6070	303	7	the	the	DET
ejpam-6070	303	8	performance	performance	NOUN
ejpam-6070	303	9	achieved	achieve	VERB
ejpam-6070	303	10	by	by	ADP
ejpam-6070	303	11	this	this	DET
ejpam-6070	303	12	method	method	NOUN
ejpam-6070	303	13	is	be	AUX
ejpam-6070	303	14	characterized	characterize	VERB
ejpam-6070	303	15	by	by	ADP
ejpam-6070	303	16	high	high	ADJ
ejpam-6070	303	17	accuracy	accuracy	NOUN
ejpam-6070	303	18	and	and	CCONJ
ejpam-6070	303	19	exhibits	exhibit	VERB
ejpam-6070	303	20	significant	significant	ADJ
ejpam-6070	303	21	similarity	similarity	NOUN
ejpam-6070	303	22	to	to	ADP
ejpam-6070	303	23	methods	method	NOUN
ejpam-6070	303	24	such	such	ADJ
ejpam-6070	303	25	as	as	ADP
ejpam-6070	303	26	the	the	DET
ejpam-6070	303	27	two	two	NUM
ejpam-6070	303	28	-	-	PUNCT
ejpam-6070	303	29	level	level	NOUN
ejpam-6070	303	30	and	and	CCONJ
ejpam-6070	303	31	multi	multi	ADJ
ejpam-6070	303	32	-	-	ADJ
ejpam-6070	303	33	grid	grid	ADJ
ejpam-6070	303	34	approaches	approach	NOUN
ejpam-6070	303	35	,	,	PUNCT
ejpam-6070	303	36	in	in	ADP
ejpam-6070	303	37	terms	term	NOUN
ejpam-6070	303	38	of	of	ADP
ejpam-6070	303	39	convergence	convergence	NOUN
ejpam-6070	303	40	speed	speed	NOUN
ejpam-6070	303	41	and	and	CCONJ
ejpam-6070	303	42	result	result	VERB
ejpam-6070	303	43	precision	precision	NOUN
ejpam-6070	303	44	.	.	PUNCT
ejpam-6070	304	1	in	in	ADP
ejpam-6070	304	2	future	future	ADJ
ejpam-6070	304	3	work	work	NOUN
ejpam-6070	304	4	,	,	PUNCT
ejpam-6070	304	5	we	we	PRON
ejpam-6070	304	6	plan	plan	VERB
ejpam-6070	304	7	to	to	PART
ejpam-6070	304	8	extend	extend	VERB
ejpam-6070	304	9	this	this	DET
ejpam-6070	304	10	method	method	NOUN
ejpam-6070	304	11	to	to	ADP
ejpam-6070	304	12	q	q	NOUN
ejpam-6070	304	13	overlapping	overlap	VERB
ejpam-6070	304	14	subdomains	subdomain	NOUN
ejpam-6070	304	15	in	in	ADP
ejpam-6070	304	16	higherdimensional	higherdimensional	ADJ
ejpam-6070	304	17	spaces	space	NOUN
ejpam-6070	304	18	,	,	PUNCT
ejpam-6070	304	19	particularly	particularly	ADV
ejpam-6070	304	20	for	for	ADP
ejpam-6070	304	21	non	non	ADJ
ejpam-6070	304	22	-	-	ADJ
ejpam-6070	304	23	matching	matching	ADJ
ejpam-6070	304	24	grids	grid	NOUN
ejpam-6070	304	25	.	.	PUNCT
ejpam-6070	305	1	additionally	additionally	ADV
ejpam-6070	305	2	,	,	PUNCT
ejpam-6070	305	3	we	we	PRON
ejpam-6070	305	4	plan	plan	VERB
ejpam-6070	305	5	to	to	PART
ejpam-6070	305	6	combine	combine	VERB
ejpam-6070	305	7	finite	finite	PROPN
ejpam-6070	305	8	element	element	NOUN
ejpam-6070	305	9	discretizations	discretization	NOUN
ejpam-6070	305	10	with	with	ADP
ejpam-6070	305	11	different	different	ADJ
ejpam-6070	305	12	boundary	boundary	ADJ
ejpam-6070	305	13	conditions	condition	NOUN
ejpam-6070	305	14	,	,	PUNCT
ejpam-6070	305	15	integrating	integrate	VERB
ejpam-6070	305	16	the	the	DET
ejpam-6070	305	17	domain	domain	NOUN
ejpam-6070	305	18	decomposition	decomposition	NOUN
ejpam-6070	305	19	method	method	NOUN
ejpam-6070	305	20	with	with	ADP
ejpam-6070	305	21	nonlinear	nonlinear	ADJ
ejpam-6070	305	22	multigrid	multigrid	NOUN
ejpam-6070	305	23	techniques	technique	NOUN
ejpam-6070	305	24	to	to	PART
ejpam-6070	305	25	further	far	ADV
ejpam-6070	305	26	improve	improve	VERB
ejpam-6070	305	27	efficiency	efficiency	NOUN
ejpam-6070	305	28	and	and	CCONJ
ejpam-6070	305	29	scalability	scalability	NOUN
ejpam-6070	305	30	for	for	ADP
ejpam-6070	305	31	large	large	ADJ
ejpam-6070	305	32	-	-	PUNCT
ejpam-6070	305	33	scale	scale	NOUN
ejpam-6070	305	34	problems	problem	NOUN
ejpam-6070	305	35	.	.	PUNCT
ejpam-6070	306	1	we	we	PRON
ejpam-6070	306	2	will	will	AUX
ejpam-6070	306	3	also	also	ADV
ejpam-6070	306	4	investigate	investigate	VERB
ejpam-6070	306	5	parallel	parallel	ADJ
ejpam-6070	306	6	implementations	implementation	NOUN
ejpam-6070	306	7	to	to	PART
ejpam-6070	306	8	enhance	enhance	VERB
ejpam-6070	306	9	performance	performance	NOUN
ejpam-6070	306	10	and	and	CCONJ
ejpam-6070	306	11	tackle	tackle	VERB
ejpam-6070	306	12	more	more	ADV
ejpam-6070	306	13	complex	complex	ADJ
ejpam-6070	306	14	problems	problem	NOUN
ejpam-6070	306	15	.	.	PUNCT
ejpam-6070	307	1	acknowledgements	acknowledgement	NOUN
ejpam-6070	307	2	the	the	DET
ejpam-6070	307	3	authors	author	NOUN
ejpam-6070	307	4	thank	thank	VERB
ejpam-6070	307	5	the	the	DET
ejpam-6070	307	6	reviewers	reviewer	NOUN
ejpam-6070	307	7	and	and	CCONJ
ejpam-6070	307	8	editors	editor	NOUN
ejpam-6070	307	9	for	for	ADP
ejpam-6070	307	10	their	their	PRON
ejpam-6070	307	11	valuable	valuable	ADJ
ejpam-6070	307	12	feedback	feedback	NOUN
ejpam-6070	307	13	and	and	CCONJ
ejpam-6070	307	14	support	support	NOUN
ejpam-6070	307	15	.	.	PUNCT
ejpam-6070	308	1	references	reference	NOUN
ejpam-6070	308	2	[	[	X
ejpam-6070	308	3	1	1	NUM
ejpam-6070	308	4	]	]	PUNCT
ejpam-6070	308	5	l’ubomı́r	l’ubomı́r	PROPN
ejpam-6070	308	6	baňas	baňas	PROPN
ejpam-6070	308	7	,	,	PUNCT
ejpam-6070	308	8	herbert	herbert	PROPN
ejpam-6070	308	9	dawid	dawid	PROPN
ejpam-6070	308	10	,	,	PUNCT
ejpam-6070	308	11	tsiry	tsiry	NOUN
ejpam-6070	308	12	avisoa	avisoa	VERB
ejpam-6070	308	13	randrianasolo	randrianasolo	NOUN
ejpam-6070	308	14	,	,	PUNCT
ejpam-6070	308	15	johannes	johanne	NOUN
ejpam-6070	308	16	storn	storn	ADJ
ejpam-6070	308	17	,	,	PUNCT
ejpam-6070	308	18	and	and	CCONJ
ejpam-6070	308	19	xingang	xingang	PROPN
ejpam-6070	308	20	wen	wen	PROPN
ejpam-6070	308	21	.	.	PROPN
ejpam-6070	309	1	numerical	numerical	PROPN
ejpam-6070	309	2	approximation	approximation	NOUN
ejpam-6070	309	3	of	of	ADP
ejpam-6070	309	4	a	a	DET
ejpam-6070	309	5	system	system	NOUN
ejpam-6070	309	6	of	of	ADP
ejpam-6070	309	7	hamilton	hamilton	PROPN
ejpam-6070	309	8	–	–	PUNCT
ejpam-6070	309	9	jacobi	jacobi	PROPN
ejpam-6070	309	10	–	–	PUNCT
ejpam-6070	309	11	bellman	bellman	NOUN
ejpam-6070	309	12	equations	equation	NOUN
ejpam-6070	309	13	arising	arise	VERB
ejpam-6070	309	14	in	in	ADP
ejpam-6070	309	15	innovation	innovation	NOUN
ejpam-6070	309	16	dynamics	dynamic	NOUN
ejpam-6070	309	17	.	.	PUNCT
ejpam-6070	310	1	journal	journal	NOUN
ejpam-6070	310	2	of	of	ADP
ejpam-6070	310	3	scientific	scientific	ADJ
ejpam-6070	310	4	computing	computing	NOUN
ejpam-6070	310	5	,	,	PUNCT
ejpam-6070	310	6	92:54	92:54	NUM
ejpam-6070	310	7	,	,	PUNCT
ejpam-6070	310	8	2022	2022	NUM
ejpam-6070	310	9	.	.	PUNCT
ejpam-6070	311	1	[	[	X
ejpam-6070	311	2	2	2	NUM
ejpam-6070	311	3	]	]	PUNCT
ejpam-6070	311	4	dietmar	dietmar	PROPN
ejpam-6070	311	5	gallistl	gallistl	PROPN
ejpam-6070	311	6	and	and	CCONJ
ejpam-6070	311	7	endre	endre	PROPN
ejpam-6070	311	8	süli	süli	NOUN
ejpam-6070	311	9	.	.	PUNCT
ejpam-6070	312	1	mixed	mix	VERB
ejpam-6070	312	2	finite	finite	PROPN
ejpam-6070	312	3	element	element	NOUN
ejpam-6070	312	4	approximation	approximation	NOUN
ejpam-6070	312	5	of	of	ADP
ejpam-6070	312	6	the	the	DET
ejpam-6070	312	7	hamilton	hamilton	PROPN
ejpam-6070	312	8	–	–	PUNCT
ejpam-6070	312	9	jacobi	jacobi	PROPN
ejpam-6070	312	10	–	–	PUNCT
ejpam-6070	312	11	bellman	bellman	NOUN
ejpam-6070	312	12	equation	equation	NOUN
ejpam-6070	312	13	with	with	ADP
ejpam-6070	312	14	cordes	corde	NOUN
ejpam-6070	312	15	coefficients	coefficient	NOUN
ejpam-6070	312	16	.	.	PUNCT
ejpam-6070	313	1	siam	siam	PROPN
ejpam-6070	313	2	journal	journal	PROPN
ejpam-6070	313	3	on	on	ADP
ejpam-6070	313	4	numerical	numerical	ADJ
ejpam-6070	313	5	analysis	analysis	NOUN
ejpam-6070	313	6	,	,	PUNCT
ejpam-6070	313	7	57(2):592–614	57(2):592–614	NUM
ejpam-6070	313	8	,	,	PUNCT
ejpam-6070	313	9	2019	2019	NUM
ejpam-6070	313	10	.	.	PUNCT
ejpam-6070	314	1	[	[	X
ejpam-6070	314	2	3	3	X
ejpam-6070	314	3	]	]	X
ejpam-6070	314	4	mohammed	mohammed	PROPN
ejpam-6070	314	5	beggas	beggas	PROPN
ejpam-6070	314	6	and	and	CCONJ
ejpam-6070	314	7	mohamed	mohamed	ADJ
ejpam-6070	314	8	haiour	haiour	PROPN
ejpam-6070	314	9	.	.	PUNCT
ejpam-6070	315	1	the	the	DET
ejpam-6070	315	2	maximum	maximum	ADJ
ejpam-6070	315	3	norm	norm	NOUN
ejpam-6070	315	4	analysis	analysis	NOUN
ejpam-6070	315	5	of	of	ADP
ejpam-6070	315	6	schwarz	schwarz	PROPN
ejpam-6070	315	7	method	method	NOUN
ejpam-6070	315	8	for	for	ADP
ejpam-6070	315	9	elliptic	elliptic	ADJ
ejpam-6070	315	10	quasi	quasi	ADJ
ejpam-6070	315	11	-	-	ADJ
ejpam-6070	315	12	variational	variational	ADJ
ejpam-6070	315	13	inequalities	inequality	NOUN
ejpam-6070	315	14	.	.	PUNCT
ejpam-6070	316	1	kragujevac	kragujevac	PROPN
ejpam-6070	316	2	journal	journal	PROPN
ejpam-6070	316	3	of	of	ADP
ejpam-6070	316	4	mathematics	mathematic	NOUN
ejpam-6070	316	5	,	,	PUNCT
ejpam-6070	316	6	45(4):635–645	45(4):635–645	PROPN
ejpam-6070	316	7	,	,	PUNCT
ejpam-6070	316	8	2021	2021	NUM
ejpam-6070	316	9	.	.	PUNCT
ejpam-6070	317	1	[	[	X
ejpam-6070	317	2	4	4	X
ejpam-6070	317	3	]	]	PUNCT
ejpam-6070	317	4	l.	l.	PROPN
ejpam-6070	317	5	djemaoune	djemaoune	PROPN
ejpam-6070	317	6	and	and	CCONJ
ejpam-6070	317	7	m.	m.	NOUN
ejpam-6070	317	8	haiour	haiour	NOUN
ejpam-6070	317	9	.	.	PUNCT
ejpam-6070	318	1	overlapping	overlap	VERB
ejpam-6070	318	2	domain	domain	NOUN
ejpam-6070	318	3	decomposition	decomposition	NOUN
ejpam-6070	318	4	method	method	NOUN
ejpam-6070	318	5	for	for	ADP
ejpam-6070	318	6	a	a	DET
ejpam-6070	318	7	noncoercive	noncoercive	ADJ
ejpam-6070	318	8	system	system	NOUN
ejpam-6070	318	9	of	of	ADP
ejpam-6070	318	10	quasi	quasi	ADJ
ejpam-6070	318	11	-	-	ADJ
ejpam-6070	318	12	variational	variational	ADJ
ejpam-6070	318	13	inequalities	inequality	NOUN
ejpam-6070	318	14	related	relate	VERB
ejpam-6070	318	15	to	to	ADP
ejpam-6070	318	16	the	the	DET
ejpam-6070	318	17	hamilton	hamilton	PROPN
ejpam-6070	318	18	–	–	PUNCT
ejpam-6070	318	19	jacobi	jacobi	PROPN
ejpam-6070	318	20	–	–	PUNCT
ejpam-6070	318	21	bellman	bellman	NOUN
ejpam-6070	318	22	equation	equation	NOUN
ejpam-6070	318	23	.	.	PUNCT
ejpam-6070	319	1	computational	computational	ADJ
ejpam-6070	319	2	mathematics	mathematic	NOUN
ejpam-6070	319	3	and	and	CCONJ
ejpam-6070	319	4	modeling	modeling	NOUN
ejpam-6070	319	5	,	,	PUNCT
ejpam-6070	319	6	27(2	27(2	PRON
ejpam-6070	319	7	)	)	PUNCT
ejpam-6070	319	8	,	,	PUNCT
ejpam-6070	319	9	2016	2016	NUM
ejpam-6070	319	10	.	.	PUNCT
ejpam-6070	320	1	s.	s.	PROPN
ejpam-6070	320	2	chebbah	chebbah	PROPN
ejpam-6070	320	3	,	,	PUNCT
ejpam-6070	320	4	s.	s.	PROPN
ejpam-6070	320	5	madi	madi	PROPN
ejpam-6070	320	6	,	,	PUNCT
ejpam-6070	320	7	m.	m.	NOUN
ejpam-6070	320	8	haiour	haiour	PROPN
ejpam-6070	320	9	/	/	SYM
ejpam-6070	320	10	eur	eur	PROPN
ejpam-6070	320	11	.	.	PUNCT
ejpam-6070	321	1	j.	j.	PROPN
ejpam-6070	321	2	pure	pure	PROPN
ejpam-6070	321	3	appl	appl	PROPN
ejpam-6070	321	4	.	.	PROPN
ejpam-6070	321	5	math	math	PROPN
ejpam-6070	321	6	,	,	PUNCT
ejpam-6070	321	7	18	18	NUM
ejpam-6070	321	8	(	(	PUNCT
ejpam-6070	321	9	2	2	NUM
ejpam-6070	321	10	)	)	PUNCT
ejpam-6070	321	11	(	(	PUNCT
ejpam-6070	321	12	2025	2025	NUM
ejpam-6070	321	13	)	)	PUNCT
ejpam-6070	321	14	,	,	PUNCT
ejpam-6070	321	15	6070	6070	NUM
ejpam-6070	321	16	19	19	NUM
ejpam-6070	321	17	of	of	ADP
ejpam-6070	321	18	20	20	NUM
ejpam-6070	321	19	[	[	SYM
ejpam-6070	321	20	5	5	NUM
ejpam-6070	321	21	]	]	PUNCT
ejpam-6070	321	22	madjda	madjda	NOUN
ejpam-6070	321	23	miloudi	miloudi	PROPN
ejpam-6070	321	24	,	,	PUNCT
ejpam-6070	321	25	samira	samira	PROPN
ejpam-6070	321	26	saadi	saadi	PROPN
ejpam-6070	321	27	,	,	PUNCT
ejpam-6070	321	28	and	and	CCONJ
ejpam-6070	321	29	mohamed	mohamed	PROPN
ejpam-6070	321	30	haiour	haiour	PROPN
ejpam-6070	321	31	.	.	PUNCT
ejpam-6070	322	1	hamilton	hamilton	PROPN
ejpam-6070	322	2	-	-	PUNCT
ejpam-6070	322	3	jacobi	jacobi	PROPN
ejpam-6070	322	4	-	-	PUNCT
ejpam-6070	322	5	bellman	bellman	PROPN
ejpam-6070	322	6	equations	equation	NOUN
ejpam-6070	322	7	:	:	PUNCT
ejpam-6070	322	8	an	an	DET
ejpam-6070	322	9	algorithmic	algorithmic	ADJ
ejpam-6070	322	10	contraction	contraction	NOUN
ejpam-6070	322	11	new	new	ADJ
ejpam-6070	322	12	approach	approach	NOUN
ejpam-6070	322	13	.	.	PUNCT
ejpam-6070	323	1	applied	apply	VERB
ejpam-6070	323	2	mathematics	mathematics	PROPN
ejpam-6070	323	3	&	&	CCONJ
ejpam-6070	323	4	information	information	NOUN
ejpam-6070	323	5	sciences	sciences	PROPN
ejpam-6070	323	6	,	,	PUNCT
ejpam-6070	323	7	15(1):83–88	15(1):83–88	NUM
ejpam-6070	323	8	,	,	PUNCT
ejpam-6070	323	9	2021	2021	NUM
ejpam-6070	323	10	.	.	PUNCT
ejpam-6070	324	1	[	[	X
ejpam-6070	324	2	6	6	NUM
ejpam-6070	324	3	]	]	X
ejpam-6070	324	4	philippe	philippe	PROPN
ejpam-6070	324	5	cortey	cortey	PROPN
ejpam-6070	324	6	-	-	PUNCT
ejpam-6070	324	7	dumont	dumont	NOUN
ejpam-6070	324	8	.	.	PUNCT
ejpam-6070	325	1	sur	sur	PROPN
ejpam-6070	325	2	les	les	PROPN
ejpam-6070	325	3	inéquations	inéquations	PROPN
ejpam-6070	325	4	variationnelles	variationnelle	NOUN
ejpam-6070	325	5	à	à	PROPN
ejpam-6070	325	6	opérateur	opérateur	PROPN
ejpam-6070	325	7	non	non	ADJ
ejpam-6070	325	8	coercif	coercif	PROPN
ejpam-6070	325	9	.	.	PUNCT
ejpam-6070	326	1	mathematical	mathematical	ADJ
ejpam-6070	326	2	modelling	modelling	NOUN
ejpam-6070	326	3	and	and	CCONJ
ejpam-6070	326	4	numerical	numerical	ADJ
ejpam-6070	326	5	analysis	analysis	NOUN
ejpam-6070	326	6	modélisation	modélisation	PROPN
ejpam-6070	326	7	mathématique	mathématique	PROPN
ejpam-6070	326	8	et	et	NOUN
ejpam-6070	326	9	analyse	analyse	PROPN
ejpam-6070	326	10	numérique	numérique	NOUN
ejpam-6070	326	11	,	,	PUNCT
ejpam-6070	326	12	19(2):195–212	19(2):195–212	NUM
ejpam-6070	326	13	,	,	PUNCT
ejpam-6070	326	14	1985	1985	NUM
ejpam-6070	326	15	.	.	PUNCT
ejpam-6070	327	1	[	[	X
ejpam-6070	327	2	7	7	X
ejpam-6070	327	3	]	]	X
ejpam-6070	327	4	p.	p.	NOUN
ejpam-6070	327	5	g.	g.	PROPN
ejpam-6070	327	6	ciarlet	ciarlet	PROPN
ejpam-6070	327	7	and	and	CCONJ
ejpam-6070	327	8	p.	p.	NOUN
ejpam-6070	327	9	a.	a.	NOUN
ejpam-6070	327	10	raviart	raviart	PROPN
ejpam-6070	327	11	.	.	PUNCT
ejpam-6070	328	1	maximum	maximum	ADJ
ejpam-6070	328	2	principle	principle	NOUN
ejpam-6070	328	3	and	and	CCONJ
ejpam-6070	328	4	uniform	uniform	ADJ
ejpam-6070	328	5	convergence	convergence	NOUN
ejpam-6070	328	6	for	for	ADP
ejpam-6070	328	7	the	the	DET
ejpam-6070	328	8	finite	finite	ADJ
ejpam-6070	328	9	element	element	NOUN
ejpam-6070	328	10	method	method	NOUN
ejpam-6070	328	11	.	.	PUNCT
ejpam-6070	329	1	computer	computer	NOUN
ejpam-6070	329	2	methods	method	NOUN
ejpam-6070	329	3	in	in	ADP
ejpam-6070	329	4	applied	applied	ADJ
ejpam-6070	329	5	mechanics	mechanic	NOUN
ejpam-6070	329	6	and	and	CCONJ
ejpam-6070	329	7	engineering	engineering	NOUN
ejpam-6070	329	8	,	,	PUNCT
ejpam-6070	329	9	2(1):17–31	2(1):17–31	NUM
ejpam-6070	329	10	,	,	PUNCT
ejpam-6070	329	11	1973	1973	NUM
ejpam-6070	329	12	.	.	PUNCT
ejpam-6070	330	1	[	[	X
ejpam-6070	330	2	8	8	NUM
ejpam-6070	330	3	]	]	X
ejpam-6070	330	4	p.	p.	NOUN
ejpam-6070	330	5	l.	l.	PROPN
ejpam-6070	330	6	lions	lion	NOUN
ejpam-6070	330	7	and	and	CCONJ
ejpam-6070	330	8	j.	j.	PROPN
ejpam-6070	330	9	l.	l.	PROPN
ejpam-6070	330	10	menaldi	menaldi	PROPN
ejpam-6070	330	11	.	.	PUNCT
ejpam-6070	331	1	optimal	optimal	ADJ
ejpam-6070	331	2	control	control	NOUN
ejpam-6070	331	3	of	of	ADP
ejpam-6070	331	4	stochastic	stochastic	ADJ
ejpam-6070	331	5	integrals	integral	NOUN
ejpam-6070	331	6	and	and	CCONJ
ejpam-6070	331	7	hamilton	hamilton	PROPN
ejpam-6070	331	8	-	-	PUNCT
ejpam-6070	331	9	jacobi	jacobi	PROPN
ejpam-6070	331	10	-	-	PUNCT
ejpam-6070	331	11	bellman	bellman	PROPN
ejpam-6070	331	12	equations	equation	NOUN
ejpam-6070	331	13	(	(	PUNCT
ejpam-6070	331	14	part	part	NOUN
ejpam-6070	331	15	i	i	PROPN
ejpam-6070	331	16	)	)	PUNCT
ejpam-6070	331	17	.	.	PUNCT
ejpam-6070	332	1	siam	siam	PROPN
ejpam-6070	332	2	journal	journal	PROPN
ejpam-6070	332	3	on	on	ADP
ejpam-6070	332	4	control	control	NOUN
ejpam-6070	332	5	and	and	CCONJ
ejpam-6070	332	6	optimization	optimization	NOUN
ejpam-6070	332	7	,	,	PUNCT
ejpam-6070	332	8	20:58–81	20:58–81	NUM
ejpam-6070	332	9	,	,	PUNCT
ejpam-6070	332	10	1982	1982	NUM
ejpam-6070	332	11	.	.	PUNCT
ejpam-6070	333	1	[	[	X
ejpam-6070	333	2	9	9	NUM
ejpam-6070	333	3	]	]	PUNCT
ejpam-6070	333	4	m.	m.	NOUN
ejpam-6070	333	5	boulbrachene	boulbrachene	NOUN
ejpam-6070	333	6	and	and	CCONJ
ejpam-6070	333	7	m.	m.	NOUN
ejpam-6070	333	8	haiour	haiour	NOUN
ejpam-6070	333	9	.	.	PUNCT
ejpam-6070	334	1	the	the	DET
ejpam-6070	334	2	finite	finite	PROPN
ejpam-6070	334	3	element	element	NOUN
ejpam-6070	334	4	approximation	approximation	NOUN
ejpam-6070	334	5	of	of	ADP
ejpam-6070	334	6	hamiltonjacobi	hamiltonjacobi	NOUN
ejpam-6070	334	7	-	-	PUNCT
ejpam-6070	334	8	bellman	bellman	NOUN
ejpam-6070	334	9	equations	equation	NOUN
ejpam-6070	334	10	.	.	PUNCT
ejpam-6070	335	1	computers	computer	NOUN
ejpam-6070	335	2	and	and	CCONJ
ejpam-6070	335	3	mathematics	mathematic	NOUN
ejpam-6070	335	4	with	with	ADP
ejpam-6070	335	5	applications	application	NOUN
ejpam-6070	335	6	,	,	PUNCT
ejpam-6070	335	7	41(78):993–1007	41(78):993–1007	NUM
ejpam-6070	335	8	,	,	PUNCT
ejpam-6070	335	9	2001	2001	NUM
ejpam-6070	335	10	.	.	PUNCT
ejpam-6070	336	1	[	[	X
ejpam-6070	336	2	10	10	NUM
ejpam-6070	336	3	]	]	X
ejpam-6070	336	4	mohamed	mohamed	PROPN
ejpam-6070	336	5	haiour	haiour	PROPN
ejpam-6070	336	6	and	and	CCONJ
ejpam-6070	336	7	salah	salah	PROPN
ejpam-6070	336	8	boulaaras	boulaaras	PROPN
ejpam-6070	336	9	.	.	PUNCT
ejpam-6070	337	1	overlapping	overlap	VERB
ejpam-6070	337	2	domain	domain	NOUN
ejpam-6070	337	3	decomposition	decomposition	NOUN
ejpam-6070	337	4	methods	method	NOUN
ejpam-6070	337	5	for	for	ADP
ejpam-6070	337	6	elliptic	elliptic	ADJ
ejpam-6070	337	7	quasi	quasi	ADJ
ejpam-6070	337	8	-	-	ADJ
ejpam-6070	337	9	variational	variational	ADJ
ejpam-6070	337	10	inequalities	inequality	NOUN
ejpam-6070	337	11	related	relate	VERB
ejpam-6070	337	12	to	to	ADP
ejpam-6070	337	13	impulse	impulse	ADJ
ejpam-6070	337	14	control	control	NOUN
ejpam-6070	337	15	problem	problem	NOUN
ejpam-6070	337	16	with	with	ADP
ejpam-6070	337	17	mixed	mixed	ADJ
ejpam-6070	337	18	boundary	boundary	ADJ
ejpam-6070	337	19	conditions	condition	NOUN
ejpam-6070	337	20	.	.	PUNCT
ejpam-6070	338	1	proceedings	proceeding	NOUN
ejpam-6070	338	2	of	of	ADP
ejpam-6070	338	3	the	the	DET
ejpam-6070	338	4	indian	indian	PROPN
ejpam-6070	338	5	academy	academy	PROPN
ejpam-6070	338	6	of	of	ADP
ejpam-6070	338	7	sciences	sciences	PROPN
ejpam-6070	338	8	(	(	PUNCT
ejpam-6070	338	9	mathematical	mathematical	ADJ
ejpam-6070	338	10	sciences	science	NOUN
ejpam-6070	338	11	)	)	PUNCT
ejpam-6070	338	12	,	,	PUNCT
ejpam-6070	338	13	121(4):481–493	121(4):481–493	NUM
ejpam-6070	338	14	,	,	PUNCT
ejpam-6070	338	15	2011	2011	NUM
ejpam-6070	338	16	.	.	PUNCT
ejpam-6070	339	1	[	[	X
ejpam-6070	339	2	11	11	NUM
ejpam-6070	339	3	]	]	PUNCT
ejpam-6070	339	4	m.	m.	NOUN
ejpam-6070	339	5	sun	sun	PROPN
ejpam-6070	339	6	.	.	PUNCT
ejpam-6070	339	7	domain	domain	NOUN
ejpam-6070	339	8	decomposition	decomposition	NOUN
ejpam-6070	339	9	algorithms	algorithm	NOUN
ejpam-6070	339	10	for	for	ADP
ejpam-6070	339	11	solving	solve	VERB
ejpam-6070	339	12	hamilton	hamilton	PROPN
ejpam-6070	339	13	-	-	PUNCT
ejpam-6070	339	14	jacobi	jacobi	PROPN
ejpam-6070	339	15	-	-	PUNCT
ejpam-6070	339	16	bellman	bellman	PROPN
ejpam-6070	339	17	equations	equation	NOUN
ejpam-6070	339	18	.	.	PUNCT
ejpam-6070	340	1	numerical	numerical	ADJ
ejpam-6070	340	2	functional	functional	ADJ
ejpam-6070	340	3	analysis	analysis	NOUN
ejpam-6070	340	4	and	and	CCONJ
ejpam-6070	340	5	optimization	optimization	NOUN
ejpam-6070	340	6	,	,	PUNCT
ejpam-6070	340	7	14(1	14(1	NUM
ejpam-6070	340	8	-	-	SYM
ejpam-6070	340	9	2	2	NUM
ejpam-6070	340	10	)	)	PUNCT
ejpam-6070	340	11	,	,	PUNCT
ejpam-6070	340	12	1993	1993	NUM
ejpam-6070	340	13	.	.	PUNCT
ejpam-6070	341	1	[	[	X
ejpam-6070	341	2	12	12	NUM
ejpam-6070	341	3	]	]	PUNCT
ejpam-6070	341	4	m.	m.	NOUN
ejpam-6070	341	5	boulbrachene	boulbrachene	NOUN
ejpam-6070	341	6	.	.	PUNCT
ejpam-6070	342	1	a	a	DET
ejpam-6070	342	2	contraction	contraction	NOUN
ejpam-6070	342	3	approach	approach	NOUN
ejpam-6070	342	4	for	for	ADP
ejpam-6070	342	5	noncoercive	noncoercive	ADJ
ejpam-6070	342	6	hamilton	hamilton	PROPN
ejpam-6070	342	7	-	-	PUNCT
ejpam-6070	342	8	jacobi	jacobi	PROPN
ejpam-6070	342	9	-	-	PUNCT
ejpam-6070	342	10	bellman	bellman	PROPN
ejpam-6070	342	11	equations	equation	NOUN
ejpam-6070	342	12	.	.	PUNCT
ejpam-6070	343	1	applied	apply	VERB
ejpam-6070	343	2	mathematics	mathematics	PROPN
ejpam-6070	343	3	information	information	NOUN
ejpam-6070	343	4	sciences	sciences	PROPN
ejpam-6070	343	5	,	,	PUNCT
ejpam-6070	343	6	4(2):261–269	4(2):261–269	NUM
ejpam-6070	343	7	,	,	PUNCT
ejpam-6070	343	8	2010	2010	NUM
ejpam-6070	343	9	.	.	PUNCT
ejpam-6070	344	1	[	[	X
ejpam-6070	344	2	13	13	NUM
ejpam-6070	344	3	]	]	PUNCT
ejpam-6070	344	4	m.	m.	NOUN
ejpam-6070	344	5	boulbrachene	boulbrachene	NOUN
ejpam-6070	344	6	,	,	PUNCT
ejpam-6070	344	7	m.	m.	NOUN
ejpam-6070	344	8	haiour	haiour	NOUN
ejpam-6070	344	9	,	,	PUNCT
ejpam-6070	344	10	and	and	CCONJ
ejpam-6070	344	11	b.	b.	PROPN
ejpam-6070	344	12	chentouf	chentouf	PROPN
ejpam-6070	344	13	.	.	PUNCT
ejpam-6070	345	1	on	on	ADP
ejpam-6070	345	2	a	a	DET
ejpam-6070	345	3	noncoercive	noncoercive	ADJ
ejpam-6070	345	4	system	system	NOUN
ejpam-6070	345	5	of	of	ADP
ejpam-6070	345	6	quasivariational	quasivariational	ADJ
ejpam-6070	345	7	inequalities	inequality	NOUN
ejpam-6070	345	8	related	relate	VERB
ejpam-6070	345	9	to	to	ADP
ejpam-6070	345	10	stochastic	stochastic	ADJ
ejpam-6070	345	11	control	control	NOUN
ejpam-6070	345	12	problems	problem	NOUN
ejpam-6070	345	13	.	.	PUNCT
ejpam-6070	346	1	journal	journal	PROPN
ejpam-6070	346	2	of	of	ADP
ejpam-6070	346	3	inequalities	inequality	NOUN
ejpam-6070	346	4	in	in	ADP
ejpam-6070	346	5	pure	pure	ADJ
ejpam-6070	346	6	and	and	CCONJ
ejpam-6070	346	7	applied	applied	ADJ
ejpam-6070	346	8	mathematics	mathematic	NOUN
ejpam-6070	346	9	,	,	PUNCT
ejpam-6070	346	10	3(2):article	3(2):article	NUM
ejpam-6070	346	11	30	30	NUM
ejpam-6070	346	12	,	,	PUNCT
ejpam-6070	346	13	14	14	NUM
ejpam-6070	346	14	p	p	NOUN
ejpam-6070	346	15	,	,	PUNCT
ejpam-6070	346	16	2002	2002	NUM
ejpam-6070	346	17	.	.	PUNCT
ejpam-6070	347	1	[	[	X
ejpam-6070	347	2	14	14	NUM
ejpam-6070	347	3	]	]	SYM
ejpam-6070	347	4	salah	salah	PROPN
ejpam-6070	347	5	boulaaras	boulaaras	NOUN
ejpam-6070	347	6	and	and	CCONJ
ejpam-6070	347	7	mohamed	mohamed	PROPN
ejpam-6070	347	8	haiour	haiour	PROPN
ejpam-6070	347	9	.	.	PUNCT
ejpam-6070	348	1	a	a	DET
ejpam-6070	348	2	general	general	ADJ
ejpam-6070	348	3	case	case	NOUN
ejpam-6070	348	4	for	for	ADP
ejpam-6070	348	5	the	the	DET
ejpam-6070	348	6	maximum	maximum	ADJ
ejpam-6070	348	7	norm	norm	NOUN
ejpam-6070	348	8	analysis	analysis	NOUN
ejpam-6070	348	9	of	of	ADP
ejpam-6070	348	10	an	an	DET
ejpam-6070	348	11	overlapping	overlap	VERB
ejpam-6070	348	12	schwarz	schwarz	NOUN
ejpam-6070	348	13	methods	method	NOUN
ejpam-6070	348	14	of	of	ADP
ejpam-6070	348	15	evolutionary	evolutionary	ADJ
ejpam-6070	348	16	hjb	hjb	NOUN
ejpam-6070	348	17	equation	equation	NOUN
ejpam-6070	348	18	with	with	ADP
ejpam-6070	348	19	nonlinear	nonlinear	ADJ
ejpam-6070	348	20	source	source	NOUN
ejpam-6070	348	21	terms	term	NOUN
ejpam-6070	348	22	with	with	ADP
ejpam-6070	348	23	the	the	DET
ejpam-6070	348	24	mixed	mixed	ADJ
ejpam-6070	348	25	boundary	boundary	ADJ
ejpam-6070	348	26	conditions	condition	NOUN
ejpam-6070	348	27	.	.	PUNCT
ejpam-6070	349	1	applied	apply	VERB
ejpam-6070	349	2	mathematics	mathematics	PROPN
ejpam-6070	349	3	&	&	CCONJ
ejpam-6070	349	4	information	information	NOUN
ejpam-6070	349	5	sciences	sciences	PROPN
ejpam-6070	349	6	,	,	PUNCT
ejpam-6070	349	7	9(3):1247–1257	9(3):1247–1257	NOUN
ejpam-6070	349	8	,	,	PUNCT
ejpam-6070	349	9	2015	2015	NUM
ejpam-6070	349	10	.	.	PUNCT
ejpam-6070	350	1	[	[	X
ejpam-6070	350	2	15	15	NUM
ejpam-6070	350	3	]	]	X
ejpam-6070	350	4	mohamed	mohamed	ADJ
ejpam-6070	350	5	haiour	haiour	PROPN
ejpam-6070	350	6	and	and	CCONJ
ejpam-6070	350	7	salah	salah	PROPN
ejpam-6070	350	8	boulaaras	boulaaras	PROPN
ejpam-6070	350	9	.	.	PUNCT
ejpam-6070	351	1	uniform	uniform	ADJ
ejpam-6070	351	2	convergence	convergence	NOUN
ejpam-6070	351	3	of	of	ADP
ejpam-6070	351	4	schwarz	schwarz	PROPN
ejpam-6070	351	5	method	method	NOUN
ejpam-6070	351	6	for	for	ADP
ejpam-6070	351	7	elliptic	elliptic	ADJ
ejpam-6070	351	8	quasi	quasi	ADJ
ejpam-6070	351	9	-	-	ADJ
ejpam-6070	351	10	variational	variational	ADJ
ejpam-6070	351	11	inequalities	inequality	NOUN
ejpam-6070	351	12	related	relate	VERB
ejpam-6070	351	13	to	to	ADP
ejpam-6070	351	14	impulse	impulse	ADJ
ejpam-6070	351	15	control	control	NOUN
ejpam-6070	351	16	problem	problem	NOUN
ejpam-6070	351	17	.	.	PUNCT
ejpam-6070	352	1	annajah	annajah	PROPN
ejpam-6070	352	2	university	university	PROPN
ejpam-6070	352	3	journal	journal	NOUN
ejpam-6070	352	4	of	of	ADP
ejpam-6070	352	5	research	research	PROPN
ejpam-6070	352	6	(	(	PUNCT
ejpam-6070	352	7	n.	n.	PROPN
ejpam-6070	352	8	sc	sc	PROPN
ejpam-6070	352	9	.	.	PROPN
ejpam-6070	352	10	)	)	PUNCT
ejpam-6070	352	11	,	,	PUNCT
ejpam-6070	352	12	24	24	NUM
ejpam-6070	352	13	,	,	PUNCT
ejpam-6070	352	14	2010	2010	NUM
ejpam-6070	352	15	.	.	PUNCT
ejpam-6070	353	1	[	[	X
ejpam-6070	353	2	16	16	NUM
ejpam-6070	353	3	]	]	X
ejpam-6070	353	4	salah	salah	PROPN
ejpam-6070	353	5	boulaaras	boulaaras	PROPN
ejpam-6070	353	6	,	,	PUNCT
ejpam-6070	353	7	mohamed	mohamed	PROPN
ejpam-6070	353	8	el	el	PROPN
ejpam-6070	353	9	amine	amine	PROPN
ejpam-6070	353	10	bencheikh	bencheikh	PROPN
ejpam-6070	353	11	le	le	X
ejpam-6070	353	12	hocine	hocine	PROPN
ejpam-6070	353	13	,	,	PUNCT
ejpam-6070	353	14	and	and	CCONJ
ejpam-6070	353	15	mohamed	mohamed	ADJ
ejpam-6070	353	16	haiour	haiour	PROPN
ejpam-6070	353	17	.	.	PUNCT
ejpam-6070	354	1	a	a	DET
ejpam-6070	354	2	new	new	ADJ
ejpam-6070	354	3	error	error	NOUN
ejpam-6070	354	4	estimate	estimate	NOUN
ejpam-6070	354	5	on	on	ADP
ejpam-6070	354	6	uniform	uniform	ADJ
ejpam-6070	354	7	norm	norm	NOUN
ejpam-6070	354	8	of	of	ADP
ejpam-6070	354	9	a	a	DET
ejpam-6070	354	10	parabolic	parabolic	ADJ
ejpam-6070	354	11	variational	variational	ADJ
ejpam-6070	354	12	inequality	inequality	NOUN
ejpam-6070	354	13	with	with	ADP
ejpam-6070	354	14	nonlinear	nonlinear	ADJ
ejpam-6070	354	15	source	source	NOUN
ejpam-6070	354	16	terms	term	NOUN
ejpam-6070	354	17	via	via	ADP
ejpam-6070	354	18	the	the	DET
ejpam-6070	354	19	subsolution	subsolution	NOUN
ejpam-6070	354	20	concepts	concept	NOUN
ejpam-6070	354	21	.	.	PUNCT
ejpam-6070	355	1	journal	journal	PROPN
ejpam-6070	355	2	of	of	ADP
ejpam-6070	355	3	inequalities	inequality	NOUN
ejpam-6070	355	4	and	and	CCONJ
ejpam-6070	355	5	applications	application	NOUN
ejpam-6070	355	6	,	,	PUNCT
ejpam-6070	355	7	2020:78	2020:78	NUM
ejpam-6070	355	8	,	,	PUNCT
ejpam-6070	355	9	2020	2020	NUM
ejpam-6070	355	10	.	.	PUNCT
ejpam-6070	356	1	[	[	X
ejpam-6070	356	2	17	17	NUM
ejpam-6070	356	3	]	]	SYM
ejpam-6070	356	4	ph	ph	PROPN
ejpam-6070	356	5	.	.	PROPN
ejpam-6070	356	6	cortey	cortey	PROPN
ejpam-6070	356	7	-	-	PUNCT
ejpam-6070	356	8	dumont	dumont	NOUN
ejpam-6070	356	9	.	.	PUNCT
ejpam-6070	357	1	sur	sur	PROPN
ejpam-6070	357	2	l’analyse	l’analyse	PROPN
ejpam-6070	357	3	numérique	numérique	NOUN
ejpam-6070	357	4	des	des	X
ejpam-6070	357	5	équations	équations	PROPN
ejpam-6070	357	6	de	de	PROPN
ejpam-6070	357	7	hamilton	hamilton	PROPN
ejpam-6070	357	8	-	-	PUNCT
ejpam-6070	357	9	jacobibellman	jacobibellman	NOUN
ejpam-6070	357	10	.	.	PUNCT
ejpam-6070	358	1	mathematical	mathematical	ADJ
ejpam-6070	358	2	methods	method	NOUN
ejpam-6070	358	3	in	in	ADP
ejpam-6070	358	4	the	the	DET
ejpam-6070	358	5	applied	apply	VERB
ejpam-6070	358	6	sciences	science	NOUN
ejpam-6070	358	7	,	,	PUNCT
ejpam-6070	358	8	9:198–209	9:198–209	NOUN
ejpam-6070	358	9	,	,	PUNCT
ejpam-6070	358	10	1987	1987	NUM
ejpam-6070	358	11	.	.	PUNCT
ejpam-6070	359	1	[	[	X
ejpam-6070	359	2	18	18	NUM
ejpam-6070	359	3	]	]	X
ejpam-6070	359	4	lawrence	lawrence	PROPN
ejpam-6070	359	5	c.	c.	PROPN
ejpam-6070	359	6	evans	evans	PROPN
ejpam-6070	359	7	and	and	CCONJ
ejpam-6070	359	8	avner	avner	PROPN
ejpam-6070	359	9	friedman	friedman	PROPN
ejpam-6070	359	10	.	.	PUNCT
ejpam-6070	360	1	optimal	optimal	ADJ
ejpam-6070	360	2	stochastic	stochastic	NOUN
ejpam-6070	360	3	switching	switching	NOUN
ejpam-6070	360	4	and	and	CCONJ
ejpam-6070	360	5	the	the	DET
ejpam-6070	360	6	dirichlet	dirichlet	PROPN
ejpam-6070	360	7	problem	problem	NOUN
ejpam-6070	360	8	for	for	ADP
ejpam-6070	360	9	the	the	DET
ejpam-6070	360	10	bellman	bellman	PROPN
ejpam-6070	360	11	equations	equation	NOUN
ejpam-6070	360	12	.	.	PUNCT
ejpam-6070	361	1	transactions	transaction	NOUN
ejpam-6070	361	2	of	of	ADP
ejpam-6070	361	3	the	the	DET
ejpam-6070	361	4	american	american	PROPN
ejpam-6070	361	5	mathematical	mathematical	PROPN
ejpam-6070	361	6	society	society	NOUN
ejpam-6070	361	7	,	,	PUNCT
ejpam-6070	361	8	253:365–389	253:365–389	NUM
ejpam-6070	361	9	,	,	PUNCT
ejpam-6070	361	10	1979	1979	NUM
ejpam-6070	361	11	.	.	PUNCT
ejpam-6070	362	1	[	[	X
ejpam-6070	362	2	19	19	NUM
ejpam-6070	362	3	]	]	PUNCT
ejpam-6070	362	4	m.	m.	NOUN
ejpam-6070	362	5	j.	j.	PROPN
ejpam-6070	362	6	gander	gander	PROPN
ejpam-6070	362	7	and	and	CCONJ
ejpam-6070	362	8	l.	l.	PROPN
ejpam-6070	362	9	halpren	halpren	PROPN
ejpam-6070	362	10	.	.	PUNCT
ejpam-6070	363	1	méthodes	méthodes	PROPN
ejpam-6070	363	2	de	de	ADP
ejpam-6070	363	3	décomposition	décomposition	PROPN
ejpam-6070	363	4	de	de	X
ejpam-6070	363	5	domaines	domaines	PROPN
ejpam-6070	363	6	notions	notion	NOUN
ejpam-6070	363	7	s.	s.	PROPN
ejpam-6070	363	8	chebbah	chebbah	PROPN
ejpam-6070	363	9	,	,	PUNCT
ejpam-6070	363	10	s.	s.	PROPN
ejpam-6070	363	11	madi	madi	PROPN
ejpam-6070	363	12	,	,	PUNCT
ejpam-6070	363	13	m.	m.	NOUN
ejpam-6070	363	14	haiour	haiour	PROPN
ejpam-6070	363	15	/	/	SYM
ejpam-6070	363	16	eur	eur	PROPN
ejpam-6070	363	17	.	.	PUNCT
ejpam-6070	364	1	j.	j.	PROPN
ejpam-6070	364	2	pure	pure	PROPN
ejpam-6070	364	3	appl	appl	PROPN
ejpam-6070	364	4	.	.	PROPN
ejpam-6070	364	5	math	math	PROPN
ejpam-6070	364	6	,	,	PUNCT
ejpam-6070	364	7	18	18	NUM
ejpam-6070	364	8	(	(	PUNCT
ejpam-6070	364	9	2	2	NUM
ejpam-6070	364	10	)	)	PUNCT
ejpam-6070	364	11	(	(	PUNCT
ejpam-6070	364	12	2025	2025	NUM
ejpam-6070	364	13	)	)	PUNCT
ejpam-6070	364	14	,	,	PUNCT
ejpam-6070	364	15	6070	6070	NUM
ejpam-6070	364	16	20	20	NUM
ejpam-6070	364	17	of	of	ADP
ejpam-6070	364	18	20	20	NUM
ejpam-6070	364	19	de	de	ADJ
ejpam-6070	364	20	base	base	NOUN
ejpam-6070	364	21	.	.	PUNCT
ejpam-6070	365	1	sciences	science	NOUN
ejpam-6070	365	2	fondamentales	fondamentale	VERB
ejpam-6070	365	3	mathematics	mathematic	NOUN
ejpam-6070	365	4	,	,	PUNCT
ejpam-6070	365	5	af1375(v1	af1375(v1	NOUN
ejpam-6070	365	6	)	)	PUNCT
ejpam-6070	365	7	,	,	PUNCT
ejpam-6070	365	8	2012	2012	NUM
ejpam-6070	365	9	.	.	PUNCT
ejpam-6070	366	1	[	[	X
ejpam-6070	366	2	20	20	NUM
ejpam-6070	366	3	]	]	PUNCT
ejpam-6070	366	4	abida	abida	PROPN
ejpam-6070	366	5	harbi	harbi	PROPN
ejpam-6070	366	6	,	,	PUNCT
ejpam-6070	366	7	nasreddine	nasreddine	ADJ
ejpam-6070	366	8	nemis	nemis	NOUN
ejpam-6070	366	9	,	,	PUNCT
ejpam-6070	366	10	and	and	CCONJ
ejpam-6070	366	11	mohamed	mohamed	ADJ
ejpam-6070	366	12	haiour	haiour	NOUN
ejpam-6070	366	13	.	.	PUNCT
ejpam-6070	367	1	optimal	optimal	ADJ
ejpam-6070	367	2	error	error	NOUN
ejpam-6070	367	3	estimates	estimate	NOUN
ejpam-6070	367	4	of	of	ADP
ejpam-6070	367	5	a	a	DET
ejpam-6070	367	6	class	class	NOUN
ejpam-6070	367	7	of	of	ADP
ejpam-6070	367	8	system	system	NOUN
ejpam-6070	367	9	of	of	ADP
ejpam-6070	367	10	two	two	NUM
ejpam-6070	367	11	quasi	quasi	ADJ
ejpam-6070	367	12	-	-	ADJ
ejpam-6070	367	13	variational	variational	ADJ
ejpam-6070	367	14	inequalities	inequality	NOUN
ejpam-6070	367	15	.	.	PUNCT
ejpam-6070	368	1	aims	aim	VERB
ejpam-6070	368	2	mathematics	mathematic	NOUN
ejpam-6070	368	3	,	,	PUNCT
ejpam-6070	368	4	6(6):5977	6(6):5977	NUM
ejpam-6070	368	5	–	–	PUNCT
ejpam-6070	368	6	6002	6002	NUM
ejpam-6070	368	7	,	,	PUNCT
ejpam-6070	368	8	2021	2021	NUM
ejpam-6070	368	9	.	.	PUNCT
ejpam-6070	369	1	[	[	X
ejpam-6070	369	2	21	21	NUM
ejpam-6070	369	3	]	]	X
ejpam-6070	369	4	ronald	ronald	PROPN
ejpam-6070	369	5	h.	h.	PROPN
ejpam-6070	369	6	w.	w.	PROPN
ejpam-6070	369	7	hoppe	hoppe	PROPN
ejpam-6070	369	8	.	.	PUNCT
ejpam-6070	370	1	multi	multi	ADJ
ejpam-6070	370	2	-	-	ADJ
ejpam-6070	370	3	grid	grid	ADJ
ejpam-6070	370	4	methods	method	NOUN
ejpam-6070	370	5	for	for	ADP
ejpam-6070	370	6	hamilton	hamilton	PROPN
ejpam-6070	370	7	-	-	PUNCT
ejpam-6070	370	8	jacobi	jacobi	PROPN
ejpam-6070	370	9	-	-	PUNCT
ejpam-6070	370	10	bellman	bellman	PROPN
ejpam-6070	370	11	equations	equation	NOUN
ejpam-6070	370	12	.	.	PUNCT
ejpam-6070	371	1	numerische	numerische	PROPN
ejpam-6070	371	2	mathematik	mathematik	PROPN
ejpam-6070	371	3	,	,	PUNCT
ejpam-6070	371	4	49:239–254	49:239–254	PROPN
ejpam-6070	371	5	,	,	PUNCT
ejpam-6070	371	6	1986	1986	NUM
ejpam-6070	371	7	.	.	PUNCT
ejpam-6070	372	1	[	[	X
ejpam-6070	372	2	22	22	NUM
ejpam-6070	372	3	]	]	X
ejpam-6070	372	4	p.	p.	NOUN
ejpam-6070	372	5	l.	l.	PROPN
ejpam-6070	372	6	lions	lion	NOUN
ejpam-6070	372	7	and	and	CCONJ
ejpam-6070	372	8	b.	b.	PROPN
ejpam-6070	372	9	mercier	mercier	PROPN
ejpam-6070	372	10	.	.	PUNCT
ejpam-6070	373	1	approximation	approximation	NOUN
ejpam-6070	373	2	numérique	numérique	NOUN
ejpam-6070	373	3	des	des	X
ejpam-6070	373	4	équations	équations	PROPN
ejpam-6070	373	5	de	de	X
ejpam-6070	373	6	hamiltonjacobi	hamiltonjacobi	NOUN
ejpam-6070	373	7	-	-	PUNCT
ejpam-6070	373	8	bellman	bellman	NOUN
ejpam-6070	373	9	.	.	PUNCT
ejpam-6070	374	1	rairo	rairo	PROPN
ejpam-6070	374	2	.	.	PUNCT
ejpam-6070	375	1	analyse	analyse	PROPN
ejpam-6070	375	2	numérique	numérique	PROPN
ejpam-6070	375	3	,	,	PUNCT
ejpam-6070	375	4	14(4):369–393	14(4):369–393	NUM
ejpam-6070	375	5	,	,	PUNCT
ejpam-6070	375	6	1980	1980	NUM
ejpam-6070	375	7	.	.	PUNCT
ejpam-6070	376	1	[	[	X
ejpam-6070	376	2	23	23	NUM
ejpam-6070	376	3	]	]	PUNCT
ejpam-6070	376	4	madjda	madjda	NOUN
ejpam-6070	376	5	miloudi	miloudi	PROPN
ejpam-6070	376	6	,	,	PUNCT
ejpam-6070	376	7	samira	samira	PROPN
ejpam-6070	376	8	saadi	saadi	PROPN
ejpam-6070	376	9	,	,	PUNCT
ejpam-6070	376	10	and	and	CCONJ
ejpam-6070	376	11	mohamed	mohamed	ADJ
ejpam-6070	376	12	haiour	haiour	PROPN
ejpam-6070	376	13	.	.	PUNCT
ejpam-6070	377	1	l∞-error	l∞-error	PROPN
ejpam-6070	377	2	estimates	estimate	NOUN
ejpam-6070	377	3	of	of	ADP
ejpam-6070	377	4	a	a	DET
ejpam-6070	377	5	finite	finite	ADJ
ejpam-6070	377	6	element	element	NOUN
ejpam-6070	377	7	method	method	NOUN
ejpam-6070	377	8	for	for	ADP
ejpam-6070	377	9	hamilton	hamilton	PROPN
ejpam-6070	377	10	–	–	PUNCT
ejpam-6070	377	11	jacobi	jacobi	PROPN
ejpam-6070	377	12	–	–	PUNCT
ejpam-6070	377	13	bellman	bellman	NOUN
ejpam-6070	377	14	equations	equation	NOUN
ejpam-6070	377	15	with	with	ADP
ejpam-6070	377	16	nonlinear	nonlinear	ADJ
ejpam-6070	377	17	source	source	NOUN
ejpam-6070	377	18	terms	term	NOUN
ejpam-6070	377	19	with	with	ADP
ejpam-6070	377	20	mixed	mixed	ADJ
ejpam-6070	377	21	boundary	boundary	ADJ
ejpam-6070	377	22	condition	condition	NOUN
ejpam-6070	377	23	.	.	PUNCT
ejpam-6070	378	1	demonstratio	demonstratio	PROPN
ejpam-6070	378	2	mathematica	mathematica	PROPN
ejpam-6070	378	3	,	,	PUNCT
ejpam-6070	378	4	54(1):452–461	54(1):452–461	NUM
ejpam-6070	378	5	,	,	PUNCT
ejpam-6070	378	6	2021	2021	NUM
ejpam-6070	378	7	.	.	PUNCT
ejpam-6070	379	1	[	[	X
ejpam-6070	379	2	24	24	NUM
ejpam-6070	379	3	]	]	X
ejpam-6070	379	4	p.	p.	NOUN
ejpam-6070	379	5	spiteri	spiteri	PROPN
ejpam-6070	379	6	,	,	PUNCT
ejpam-6070	379	7	j.	j.	PROPN
ejpam-6070	379	8	c.	c.	PROPN
ejpam-6070	379	9	miellou	miellou	PROPN
ejpam-6070	379	10	,	,	PUNCT
ejpam-6070	379	11	and	and	CCONJ
ejpam-6070	379	12	d.	d.	PROPN
ejpam-6070	379	13	el	el	PROPN
ejpam-6070	379	14	baz	baz	PROPN
ejpam-6070	379	15	.	.	PUNCT
ejpam-6070	380	1	asynchronous	asynchronous	ADJ
ejpam-6070	380	2	schwarz	schwarz	PROPN
ejpam-6070	380	3	alternating	alternate	VERB
ejpam-6070	380	4	methods	method	NOUN
ejpam-6070	380	5	with	with	ADP
ejpam-6070	380	6	flexible	flexible	ADJ
ejpam-6070	380	7	communication	communication	NOUN
ejpam-6070	380	8	for	for	ADP
ejpam-6070	380	9	the	the	DET
ejpam-6070	380	10	obstacle	obstacle	NOUN
ejpam-6070	380	11	problem	problem	NOUN
ejpam-6070	380	12	.	.	PUNCT
ejpam-6070	381	1	calculateurs	calculateur	VERB
ejpam-6070	381	2	parallèles	parallèle	NOUN
ejpam-6070	381	3	,	,	PUNCT
ejpam-6070	381	4	réseaux	réseaux	PROPN
ejpam-6070	381	5	et	et	NOUN
ejpam-6070	381	6	systèmes	systèmes	PRON
ejpam-6070	381	7	répartis	répartis	PROPN
ejpam-6070	381	8	,	,	PUNCT
ejpam-6070	381	9	13(1):47–66	13(1):47–66	NUM
ejpam-6070	381	10	,	,	PUNCT
ejpam-6070	381	11	2001	2001	NUM
ejpam-6070	381	12	.	.	PUNCT
ejpam-6070	382	1	introduction	introduction	NOUN
ejpam-6070	382	2	coercive	coercive	ADJ
ejpam-6070	382	3	reformulation	reformulation	NOUN
ejpam-6070	382	4	of	of	ADP
ejpam-6070	382	5	the	the	DET
ejpam-6070	382	6	hjb	hjb	NOUN
ejpam-6070	382	7	equation	equation	NOUN
ejpam-6070	382	8	decomposition	decomposition	NOUN
ejpam-6070	382	9	of	of	ADP
ejpam-6070	382	10	the	the	DET
ejpam-6070	382	11	domain	domain	NOUN
ejpam-6070	382	12	into	into	ADP
ejpam-6070	382	13	overlapping	overlap	VERB
ejpam-6070	382	14	subdomains	subdomain	NOUN
ejpam-6070	382	15	definition	definition	NOUN
ejpam-6070	382	16	of	of	ADP
ejpam-6070	382	17	subdomain	subdomain	NOUN
ejpam-6070	382	18	decomposition	decomposition	NOUN
ejpam-6070	382	19	block	block	NOUN
ejpam-6070	382	20	decomposition	decomposition	NOUN
ejpam-6070	382	21	of	of	ADP
ejpam-6070	382	22	the	the	DET
ejpam-6070	382	23	domain	domain	NOUN
ejpam-6070	382	24	matrix	matrix	NOUN
ejpam-6070	382	25	iterative	iterative	NOUN
ejpam-6070	382	26	algorithm	algorithm	NOUN
ejpam-6070	382	27	for	for	ADP
ejpam-6070	382	28	domain	domain	NOUN
ejpam-6070	382	29	decomposition	decomposition	NOUN
ejpam-6070	382	30	monotonic	monotonic	ADJ
ejpam-6070	382	31	and	and	CCONJ
ejpam-6070	382	32	geometric	geometric	ADJ
ejpam-6070	382	33	convergence	convergence	NOUN
ejpam-6070	382	34	numerical	numerical	ADJ
ejpam-6070	382	35	applications	application	NOUN
ejpam-6070	382	36	and	and	CCONJ
ejpam-6070	382	37	computational	computational	ADJ
ejpam-6070	382	38	results	result	NOUN
ejpam-6070	382	39	conclusion	conclusion	NOUN