id	sid	tid	token	lemma	pos
ejpam-6680	1	1	european	european	PROPN
ejpam-6680	1	2	journal	journal	PROPN
ejpam-6680	1	3	of	of	ADP
ejpam-6680	1	4	pure	pure	ADJ
ejpam-6680	1	5	and	and	CCONJ
ejpam-6680	1	6	applied	applied	ADJ
ejpam-6680	1	7	mathematics	mathematic	NOUN
ejpam-6680	1	8	2025	2025	NUM
ejpam-6680	1	9	,	,	PUNCT
ejpam-6680	1	10	vol	vol	NOUN
ejpam-6680	1	11	.	.	PROPN
ejpam-6680	1	12	18	18	NUM
ejpam-6680	1	13	,	,	PUNCT
ejpam-6680	1	14	issue	issue	NOUN
ejpam-6680	1	15	4	4	NUM
ejpam-6680	1	16	,	,	PUNCT
ejpam-6680	1	17	article	article	NOUN
ejpam-6680	1	18	number	number	NOUN
ejpam-6680	1	19	6680	6680	NUM
ejpam-6680	1	20	issn	issn	VERB
ejpam-6680	1	21	1307	1307	NUM
ejpam-6680	1	22	-	-	SYM
ejpam-6680	1	23	5543	5543	NUM
ejpam-6680	1	24	–	–	PUNCT
ejpam-6680	1	25	ejpam.com	ejpam.com	X
ejpam-6680	1	26	published	publish	VERB
ejpam-6680	1	27	by	by	ADP
ejpam-6680	1	28	new	new	PROPN
ejpam-6680	1	29	york	york	PROPN
ejpam-6680	1	30	business	business	PROPN
ejpam-6680	1	31	global	global	ADJ
ejpam-6680	1	32	some	some	DET
ejpam-6680	1	33	convergence	convergence	NOUN
ejpam-6680	1	34	results	result	VERB
ejpam-6680	1	35	for	for	ADP
ejpam-6680	1	36	the	the	DET
ejpam-6680	1	37	solution	solution	NOUN
ejpam-6680	1	38	of	of	ADP
ejpam-6680	1	39	new	new	ADJ
ejpam-6680	1	40	type	type	NOUN
ejpam-6680	1	41	of	of	ADP
ejpam-6680	1	42	variational	variational	ADJ
ejpam-6680	1	43	inequalities	inequality	NOUN
ejpam-6680	1	44	associated	associate	VERB
ejpam-6680	1	45	with	with	ADP
ejpam-6680	1	46	generalized	generalized	ADJ
ejpam-6680	1	47	pseudo	pseudo	NOUN
ejpam-6680	1	48	-	-	ADJ
ejpam-6680	1	49	monotone	monotone	ADJ
ejpam-6680	1	50	mappings	mapping	NOUN
ejpam-6680	1	51	in	in	ADP
ejpam-6680	1	52	complete	complete	ADJ
ejpam-6680	1	53	cat	cat	NOUN
ejpam-6680	1	54	(	(	PUNCT
ejpam-6680	1	55	0	0	NUM
ejpam-6680	1	56	)	)	PUNCT
ejpam-6680	1	57	spaces	space	NOUN
ejpam-6680	1	58	maliha	maliha	VERB
ejpam-6680	1	59	rashid1	rashid1	ADV
ejpam-6680	1	60	,	,	PUNCT
ejpam-6680	1	61	amna	amna	PROPN
ejpam-6680	1	62	kalsoom1	kalsoom1	PROPN
ejpam-6680	1	63	,	,	PUNCT
ejpam-6680	1	64	nida	nida	PROPN
ejpam-6680	1	65	masood1	masood1	PROPN
ejpam-6680	1	66	,	,	PUNCT
ejpam-6680	1	67	ahmad	ahmad	PROPN
ejpam-6680	1	68	aloqaily2	aloqaily2	PROPN
ejpam-6680	1	69	,	,	PUNCT
ejpam-6680	1	70	nabil	nabil	PROPN
ejpam-6680	1	71	mlaiki2,∗	mlaiki2,∗	PROPN
ejpam-6680	1	72	1	1	NUM
ejpam-6680	1	73	department	department	NOUN
ejpam-6680	1	74	of	of	ADP
ejpam-6680	1	75	mathematics	mathematic	NOUN
ejpam-6680	1	76	and	and	CCONJ
ejpam-6680	1	77	statistics	statistic	NOUN
ejpam-6680	1	78	,	,	PUNCT
ejpam-6680	1	79	international	international	ADJ
ejpam-6680	1	80	islamic	islamic	PROPN
ejpam-6680	1	81	university	university	PROPN
ejpam-6680	1	82	,	,	PUNCT
ejpam-6680	1	83	islamabad	islamabad	PROPN
ejpam-6680	1	84	,	,	PUNCT
ejpam-6680	1	85	pakistan	pakistan	PROPN
ejpam-6680	1	86	2	2	NUM
ejpam-6680	1	87	department	department	NOUN
ejpam-6680	1	88	of	of	ADP
ejpam-6680	1	89	mathematics	mathematic	NOUN
ejpam-6680	1	90	and	and	CCONJ
ejpam-6680	1	91	sciences	science	NOUN
ejpam-6680	1	92	,	,	PUNCT
ejpam-6680	1	93	prince	prince	PROPN
ejpam-6680	1	94	sultan	sultan	PROPN
ejpam-6680	1	95	university	university	PROPN
ejpam-6680	1	96	,	,	PUNCT
ejpam-6680	1	97	saudi	saudi	PROPN
ejpam-6680	1	98	arabia	arabia	PROPN
ejpam-6680	1	99	abstract	abstract	NOUN
ejpam-6680	1	100	.	.	PUNCT
ejpam-6680	2	1	the	the	DET
ejpam-6680	2	2	basic	basic	ADJ
ejpam-6680	2	3	purpose	purpose	NOUN
ejpam-6680	2	4	of	of	ADP
ejpam-6680	2	5	this	this	DET
ejpam-6680	2	6	article	article	NOUN
ejpam-6680	2	7	is	be	AUX
ejpam-6680	2	8	to	to	PART
ejpam-6680	2	9	introduce	introduce	VERB
ejpam-6680	2	10	a	a	DET
ejpam-6680	2	11	generalized	generalized	ADJ
ejpam-6680	2	12	version	version	NOUN
ejpam-6680	2	13	of	of	ADP
ejpam-6680	2	14	pseudomonotone	pseudomonotone	PROPN
ejpam-6680	2	15	variational	variational	ADJ
ejpam-6680	2	16	inequality	inequality	NOUN
ejpam-6680	2	17	in	in	ADP
ejpam-6680	2	18	the	the	DET
ejpam-6680	2	19	setting	setting	NOUN
ejpam-6680	2	20	of	of	ADP
ejpam-6680	2	21	complete	complete	ADJ
ejpam-6680	2	22	cat	cat	NOUN
ejpam-6680	2	23	(	(	PUNCT
ejpam-6680	2	24	0	0	NUM
ejpam-6680	2	25	)	)	PUNCT
ejpam-6680	2	26	spaces	space	NOUN
ejpam-6680	2	27	and	and	CCONJ
ejpam-6680	2	28	to	to	PART
ejpam-6680	2	29	present	present	VERB
ejpam-6680	2	30	some	some	DET
ejpam-6680	2	31	strong	strong	ADJ
ejpam-6680	2	32	and	and	CCONJ
ejpam-6680	2	33	∆-convergence	∆-convergence	NOUN
ejpam-6680	2	34	results	result	VERB
ejpam-6680	2	35	for	for	ADP
ejpam-6680	2	36	the	the	DET
ejpam-6680	2	37	existence	existence	NOUN
ejpam-6680	2	38	of	of	ADP
ejpam-6680	2	39	solutions	solution	NOUN
ejpam-6680	2	40	for	for	ADP
ejpam-6680	2	41	the	the	DET
ejpam-6680	2	42	respective	respective	ADJ
ejpam-6680	2	43	variational	variational	ADJ
ejpam-6680	2	44	inequality	inequality	NOUN
ejpam-6680	2	45	problem	problem	NOUN
ejpam-6680	2	46	.	.	PUNCT
ejpam-6680	3	1	algorithm	algorithm	NOUN
ejpam-6680	3	2	1	1	NUM
ejpam-6680	3	3	and	and	CCONJ
ejpam-6680	3	4	2	2	NUM
ejpam-6680	3	5	are	be	AUX
ejpam-6680	3	6	proposed	propose	VERB
ejpam-6680	3	7	in	in	ADP
ejpam-6680	3	8	accordance	accordance	NOUN
ejpam-6680	3	9	with	with	ADP
ejpam-6680	3	10	pseudo	pseudo	NOUN
ejpam-6680	3	11	-	-	ADJ
ejpam-6680	3	12	monotone	monotone	ADJ
ejpam-6680	3	13	and	and	CCONJ
ejpam-6680	3	14	α	α	NOUN
ejpam-6680	3	15	-	-	PUNCT
ejpam-6680	3	16	strongly	strongly	ADV
ejpam-6680	3	17	pseudo	pseudo	NOUN
ejpam-6680	3	18	-	-	ADJ
ejpam-6680	3	19	monotone	monotone	ADJ
ejpam-6680	3	20	mappings	mapping	NOUN
ejpam-6680	3	21	to	to	PART
ejpam-6680	3	22	prove	prove	VERB
ejpam-6680	3	23	our	our	PRON
ejpam-6680	3	24	results	result	NOUN
ejpam-6680	3	25	under	under	ADP
ejpam-6680	3	26	some	some	DET
ejpam-6680	3	27	conditions	condition	NOUN
ejpam-6680	3	28	.	.	PUNCT
ejpam-6680	4	1	a	a	DET
ejpam-6680	4	2	numerical	numerical	ADJ
ejpam-6680	4	3	implication	implication	NOUN
ejpam-6680	4	4	of	of	ADP
ejpam-6680	4	5	our	our	PRON
ejpam-6680	4	6	proposed	propose	VERB
ejpam-6680	4	7	algorithm	algorithm	NOUN
ejpam-6680	4	8	is	be	AUX
ejpam-6680	4	9	also	also	ADV
ejpam-6680	4	10	presented	present	VERB
ejpam-6680	4	11	.	.	PUNCT
ejpam-6680	5	1	2020	2020	NUM
ejpam-6680	5	2	mathematics	mathematics	PROPN
ejpam-6680	5	3	subject	subject	NOUN
ejpam-6680	5	4	classifications	classification	NOUN
ejpam-6680	5	5	:	:	PUNCT
ejpam-6680	5	6	47h10	47h10	NUM
ejpam-6680	5	7	,	,	PUNCT
ejpam-6680	5	8	47h09	47h09	NUM
ejpam-6680	5	9	,	,	PUNCT
ejpam-6680	5	10	47j25	47j25	NUM
ejpam-6680	5	11	key	key	ADJ
ejpam-6680	5	12	words	word	NOUN
ejpam-6680	5	13	and	and	CCONJ
ejpam-6680	5	14	phrases	phrase	NOUN
ejpam-6680	5	15	:	:	PUNCT
ejpam-6680	5	16	projection	projection	ADJ
ejpam-6680	5	17	type	type	NOUN
ejpam-6680	5	18	method	method	NOUN
ejpam-6680	5	19	,	,	PUNCT
ejpam-6680	5	20	variational	variational	ADJ
ejpam-6680	5	21	inequality	inequality	NOUN
ejpam-6680	5	22	,	,	PUNCT
ejpam-6680	5	23	pseudo	pseudo	NOUN
ejpam-6680	5	24	-	-	ADJ
ejpam-6680	5	25	monotone	monotone	ADJ
ejpam-6680	5	26	mapping	mapping	NOUN
ejpam-6680	5	27	1	1	NUM
ejpam-6680	5	28	.	.	PUNCT
ejpam-6680	6	1	introduction	introduction	NOUN
ejpam-6680	6	2	variational	variational	ADJ
ejpam-6680	6	3	inequalities	inequality	NOUN
ejpam-6680	6	4	originated	originate	VERB
ejpam-6680	6	5	in	in	ADP
ejpam-6680	6	6	the	the	DET
ejpam-6680	6	7	beginning	beginning	NOUN
ejpam-6680	6	8	of	of	ADP
ejpam-6680	6	9	1960s	1960	NOUN
ejpam-6680	6	10	through	through	ADP
ejpam-6680	6	11	the	the	DET
ejpam-6680	6	12	revolutionary	revolutionary	ADJ
ejpam-6680	6	13	work	work	NOUN
ejpam-6680	6	14	of	of	ADP
ejpam-6680	6	15	the	the	DET
ejpam-6680	6	16	italian	italian	ADJ
ejpam-6680	6	17	mathematician	mathematician	ADJ
ejpam-6680	6	18	guido	guido	NOUN
ejpam-6680	6	19	stampacchia	stampacchia	NOUN
ejpam-6680	7	1	[	[	X
ejpam-6680	7	2	1	1	NUM
ejpam-6680	7	3	]	]	PUNCT
ejpam-6680	7	4	,	,	PUNCT
ejpam-6680	7	5	who	who	PRON
ejpam-6680	7	6	analyse	analyse	VERB
ejpam-6680	7	7	free	free	ADJ
ejpam-6680	7	8	boundary	boundary	ADJ
ejpam-6680	7	9	problems	problem	NOUN
ejpam-6680	7	10	occuring	occur	VERB
ejpam-6680	7	11	in	in	ADP
ejpam-6680	7	12	elasticity	elasticity	NOUN
ejpam-6680	7	13	theory	theory	NOUN
ejpam-6680	7	14	and	and	CCONJ
ejpam-6680	7	15	mechanics	mechanic	NOUN
ejpam-6680	7	16	by	by	ADP
ejpam-6680	7	17	using	use	VERB
ejpam-6680	7	18	the	the	DET
ejpam-6680	7	19	variational	variational	ADJ
ejpam-6680	7	20	inequality	inequality	NOUN
ejpam-6680	7	21	as	as	ADP
ejpam-6680	7	22	an	an	DET
ejpam-6680	7	23	analytic	analytic	ADJ
ejpam-6680	7	24	tool	tool	NOUN
ejpam-6680	7	25	.	.	PUNCT
ejpam-6680	8	1	from	from	ADP
ejpam-6680	8	2	1960	1960	NUM
ejpam-6680	8	3	-	-	SYM
ejpam-6680	8	4	1975	1975	NUM
ejpam-6680	8	5	many	many	ADJ
ejpam-6680	8	6	foundational	foundational	ADJ
ejpam-6680	8	7	articles	article	NOUN
ejpam-6680	8	8	presented	present	VERB
ejpam-6680	8	9	in	in	ADP
ejpam-6680	8	10	the	the	DET
ejpam-6680	8	11	literature	literature	NOUN
ejpam-6680	8	12	emphasizing	emphasize	VERB
ejpam-6680	8	13	the	the	DET
ejpam-6680	8	14	association	association	NOUN
ejpam-6680	8	15	between	between	ADP
ejpam-6680	8	16	the	the	DET
ejpam-6680	8	17	complementarity	complementarity	NOUN
ejpam-6680	8	18	problems	problem	NOUN
ejpam-6680	8	19	and	and	CCONJ
ejpam-6680	8	20	the	the	DET
ejpam-6680	8	21	variational	variational	ADJ
ejpam-6680	8	22	inequalities	inequality	NOUN
ejpam-6680	8	23	.	.	PUNCT
ejpam-6680	9	1	for	for	ADP
ejpam-6680	9	2	the	the	DET
ejpam-6680	9	3	early	early	ADJ
ejpam-6680	9	4	advancement	advancement	NOUN
ejpam-6680	9	5	on	on	ADP
ejpam-6680	9	6	variational	variational	ADJ
ejpam-6680	9	7	inequalities	inequality	NOUN
ejpam-6680	9	8	readers	reader	NOUN
ejpam-6680	9	9	are	be	AUX
ejpam-6680	9	10	referred	refer	VERB
ejpam-6680	9	11	to	to	ADP
ejpam-6680	9	12	[	[	X
ejpam-6680	9	13	2–6	2–6	NOUN
ejpam-6680	9	14	]	]	X
ejpam-6680	9	15	.	.	PUNCT
ejpam-6680	10	1	∗corresponding	∗corresponde	VERB
ejpam-6680	10	2	author	author	NOUN
ejpam-6680	10	3	.	.	PUNCT
ejpam-6680	11	1	doi	doi	NOUN
ejpam-6680	11	2	:	:	PUNCT
ejpam-6680	11	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6680	https://doi.org/10.29020/nybg.ejpam.v18i4.6680	VERB
ejpam-6680	11	4	email	email	NOUN
ejpam-6680	11	5	addresses	address	NOUN
ejpam-6680	11	6	:	:	PUNCT
ejpam-6680	11	7	maliha.rashid@iiu.edu.pk	maliha.rashid@iiu.edu.pk	PROPN
ejpam-6680	11	8	(	(	PUNCT
ejpam-6680	11	9	m.	m.	NOUN
ejpam-6680	11	10	rashid	rashid	PROPN
ejpam-6680	11	11	)	)	PUNCT
ejpam-6680	11	12	,	,	PUNCT
ejpam-6680	11	13	amna.kalsoom@iiu.edu.pk	amna.kalsoom@iiu.edu.pk	PROPN
ejpam-6680	11	14	(	(	PUNCT
ejpam-6680	11	15	a.	a.	NOUN
ejpam-6680	11	16	kalsoom	kalsoom	PROPN
ejpam-6680	11	17	)	)	PUNCT
ejpam-6680	11	18	,	,	PUNCT
ejpam-6680	11	19	nida.msma673@iiu.edu.pk	nida.msma673@iiu.edu.pk	PRON
ejpam-6680	11	20	(	(	PUNCT
ejpam-6680	11	21	n.	n.	PROPN
ejpam-6680	11	22	masood	masood	PROPN
ejpam-6680	11	23	)	)	PUNCT
ejpam-6680	11	24	,	,	PUNCT
ejpam-6680	11	25	maloqaily@psu.edu.sa	maloqaily@psu.edu.sa	PROPN
ejpam-6680	11	26	(	(	PUNCT
ejpam-6680	11	27	a.	a.	NOUN
ejpam-6680	11	28	aloqaily	aloqaily	ADV
ejpam-6680	11	29	)	)	PUNCT
ejpam-6680	11	30	,	,	PUNCT
ejpam-6680	11	31	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-6680	11	32	(	(	PUNCT
ejpam-6680	11	33	n.	n.	PROPN
ejpam-6680	11	34	mlaiki	mlaiki	PROPN
ejpam-6680	11	35	)	)	PUNCT
ejpam-6680	11	36	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6680	12	1	1	1	NUM
ejpam-6680	12	2	copyright	copyright	NOUN
ejpam-6680	12	3	:	:	PUNCT
ejpam-6680	12	4	©	©	PROPN
ejpam-6680	12	5	2025	2025	NUM
ejpam-6680	12	6	the	the	DET
ejpam-6680	12	7	author(s	author(s	NOUN
ejpam-6680	12	8	)	)	PUNCT
ejpam-6680	12	9	.	.	PUNCT
ejpam-6680	13	1	(	(	PUNCT
ejpam-6680	13	2	cc	cc	NOUN
ejpam-6680	13	3	by	by	ADP
ejpam-6680	13	4	-	-	PUNCT
ejpam-6680	13	5	nc	nc	PROPN
ejpam-6680	13	6	4.0	4.0	NUM
ejpam-6680	13	7	)	)	PUNCT
ejpam-6680	13	8	m.	m.	NOUN
ejpam-6680	13	9	rashid	rashid	PROPN
ejpam-6680	13	10	et	et	PROPN
ejpam-6680	13	11	al	al	PROPN
ejpam-6680	13	12	.	.	PUNCT
ejpam-6680	13	13	/	/	SYM
ejpam-6680	13	14	eur	eur	PROPN
ejpam-6680	13	15	.	.	PUNCT
ejpam-6680	14	1	j.	j.	PROPN
ejpam-6680	14	2	pure	pure	PROPN
ejpam-6680	14	3	appl	appl	PROPN
ejpam-6680	14	4	.	.	PROPN
ejpam-6680	14	5	math	math	PROPN
ejpam-6680	14	6	,	,	PUNCT
ejpam-6680	14	7	18	18	NUM
ejpam-6680	14	8	(	(	PUNCT
ejpam-6680	14	9	4	4	NUM
ejpam-6680	14	10	)	)	PUNCT
ejpam-6680	14	11	(	(	PUNCT
ejpam-6680	14	12	2025	2025	NUM
ejpam-6680	14	13	)	)	PUNCT
ejpam-6680	14	14	,	,	PUNCT
ejpam-6680	14	15	6680	6680	NUM
ejpam-6680	14	16	2	2	NUM
ejpam-6680	14	17	of	of	ADP
ejpam-6680	14	18	24	24	NUM
ejpam-6680	14	19	a	a	DET
ejpam-6680	14	20	large	large	ADJ
ejpam-6680	14	21	number	number	NOUN
ejpam-6680	14	22	of	of	ADP
ejpam-6680	14	23	articles	article	NOUN
ejpam-6680	14	24	,	,	PUNCT
ejpam-6680	14	25	proposed	propose	VERB
ejpam-6680	14	26	in	in	ADP
ejpam-6680	14	27	second	second	ADJ
ejpam-6680	14	28	half	half	NOUN
ejpam-6680	14	29	of	of	ADP
ejpam-6680	14	30	1990s	1990s	NUM
ejpam-6680	14	31	,	,	PUNCT
ejpam-6680	14	32	was	be	AUX
ejpam-6680	14	33	dedicated	dedicate	VERB
ejpam-6680	14	34	to	to	ADP
ejpam-6680	14	35	the	the	DET
ejpam-6680	14	36	reformulation	reformulation	NOUN
ejpam-6680	14	37	of	of	ADP
ejpam-6680	14	38	the	the	DET
ejpam-6680	14	39	nonlinear	nonlinear	ADJ
ejpam-6680	14	40	complementarity	complementarity	NOUN
ejpam-6680	14	41	problem	problem	NOUN
ejpam-6680	14	42	in	in	ADP
ejpam-6680	14	43	terms	term	NOUN
ejpam-6680	14	44	of	of	ADP
ejpam-6680	14	45	the	the	DET
ejpam-6680	14	46	algorithms	algorithm	NOUN
ejpam-6680	14	47	produced	produce	VERB
ejpam-6680	14	48	through	through	ADP
ejpam-6680	14	49	a	a	DET
ejpam-6680	14	50	globally	globally	ADV
ejpam-6680	14	51	convergent	convergent	ADJ
ejpam-6680	14	52	newton	newton	PROPN
ejpam-6680	14	53	method	method	NOUN
ejpam-6680	14	54	.	.	PUNCT
ejpam-6680	15	1	after	after	ADP
ejpam-6680	15	2	that	that	PRON
ejpam-6680	15	3	,	,	PUNCT
ejpam-6680	15	4	many	many	ADJ
ejpam-6680	15	5	iterative	iterative	NOUN
ejpam-6680	15	6	schemes	scheme	NOUN
ejpam-6680	15	7	have	have	AUX
ejpam-6680	15	8	been	be	AUX
ejpam-6680	15	9	formulated	formulate	VERB
ejpam-6680	15	10	for	for	ADP
ejpam-6680	15	11	finding	find	VERB
ejpam-6680	15	12	the	the	DET
ejpam-6680	15	13	solutions	solution	NOUN
ejpam-6680	15	14	of	of	ADP
ejpam-6680	15	15	variational	variational	ADJ
ejpam-6680	15	16	inequalities	inequality	NOUN
ejpam-6680	15	17	and	and	CCONJ
ejpam-6680	15	18	their	their	PRON
ejpam-6680	15	19	relevant	relevant	ADJ
ejpam-6680	15	20	optimization	optimization	NOUN
ejpam-6680	15	21	problems	problem	NOUN
ejpam-6680	15	22	(	(	PUNCT
ejpam-6680	15	23	see	see	VERB
ejpam-6680	15	24	[	[	X
ejpam-6680	15	25	7	7	NUM
ejpam-6680	15	26	,	,	PUNCT
ejpam-6680	15	27	8	8	NUM
ejpam-6680	15	28	]	]	PUNCT
ejpam-6680	15	29	and	and	CCONJ
ejpam-6680	15	30	literature	literature	NOUN
ejpam-6680	15	31	cited	cite	VERB
ejpam-6680	15	32	in	in	ADP
ejpam-6680	15	33	)	)	PUNCT
ejpam-6680	15	34	.	.	PUNCT
ejpam-6680	16	1	one	one	NUM
ejpam-6680	16	2	of	of	ADP
ejpam-6680	16	3	the	the	DET
ejpam-6680	16	4	numerical	numerical	ADJ
ejpam-6680	16	5	methods	method	NOUN
ejpam-6680	16	6	for	for	ADP
ejpam-6680	16	7	solving	solve	VERB
ejpam-6680	16	8	variational	variational	ADJ
ejpam-6680	16	9	inequality	inequality	NOUN
ejpam-6680	16	10	problems	problem	NOUN
ejpam-6680	16	11	(	(	PUNCT
ejpam-6680	16	12	vip	vip	NOUN
ejpam-6680	16	13	’s	’s	PART
ejpam-6680	16	14	)	)	PUNCT
ejpam-6680	16	15	is	be	AUX
ejpam-6680	16	16	known	know	VERB
ejpam-6680	16	17	as	as	ADP
ejpam-6680	16	18	projection	projection	NOUN
ejpam-6680	16	19	method	method	NOUN
ejpam-6680	16	20	[	[	X
ejpam-6680	16	21	9–11	9–11	X
ejpam-6680	16	22	]	]	PUNCT
ejpam-6680	16	23	which	which	PRON
ejpam-6680	16	24	is	be	AUX
ejpam-6680	16	25	further	far	ADV
ejpam-6680	16	26	expanded	expand	VERB
ejpam-6680	16	27	to	to	ADP
ejpam-6680	16	28	gradient	gradient	NOUN
ejpam-6680	16	29	,	,	PUNCT
ejpam-6680	16	30	extragradient	extragradient	NOUN
ejpam-6680	16	31	and	and	CCONJ
ejpam-6680	16	32	subgradient	subgradient	ADJ
ejpam-6680	16	33	methods	method	NOUN
ejpam-6680	16	34	(	(	PUNCT
ejpam-6680	16	35	see	see	VERB
ejpam-6680	16	36	,	,	PUNCT
ejpam-6680	16	37	e.g.	e.g.	ADV
ejpam-6680	16	38	,	,	PUNCT
ejpam-6680	16	39	[	[	X
ejpam-6680	16	40	12–25	12–25	NUM
ejpam-6680	16	41	]	]	PUNCT
ejpam-6680	16	42	and	and	CCONJ
ejpam-6680	16	43	the	the	DET
ejpam-6680	16	44	references	reference	NOUN
ejpam-6680	16	45	therein	therein	ADV
ejpam-6680	16	46	)	)	PUNCT
ejpam-6680	16	47	.	.	PUNCT
ejpam-6680	17	1	extragradient	extragradient	PROPN
ejpam-6680	17	2	method	method	NOUN
ejpam-6680	17	3	is	be	AUX
ejpam-6680	17	4	not	not	PART
ejpam-6680	17	5	practically	practically	ADV
ejpam-6680	17	6	useful	useful	ADJ
ejpam-6680	17	7	for	for	ADP
ejpam-6680	17	8	the	the	DET
ejpam-6680	17	9	solution	solution	NOUN
ejpam-6680	17	10	of	of	ADP
ejpam-6680	17	11	variational	variational	ADJ
ejpam-6680	17	12	inequalities	inequality	NOUN
ejpam-6680	17	13	having	have	VERB
ejpam-6680	17	14	non	non	ADJ
ejpam-6680	17	15	-	-	ADJ
ejpam-6680	17	16	lipschitz	lipschitz	ADJ
ejpam-6680	17	17	mapping	mapping	NOUN
ejpam-6680	17	18	.	.	PUNCT
ejpam-6680	18	1	in	in	ADP
ejpam-6680	18	2	case	case	NOUN
ejpam-6680	18	3	of	of	ADP
ejpam-6680	18	4	extragradient	extragradient	NOUN
ejpam-6680	18	5	method	method	NOUN
ejpam-6680	18	6	,	,	PUNCT
ejpam-6680	18	7	the	the	DET
ejpam-6680	18	8	reforms	reform	NOUN
ejpam-6680	18	9	regarding	regard	VERB
ejpam-6680	18	10	[	[	X
ejpam-6680	18	11	26	26	NUM
ejpam-6680	18	12	,	,	PUNCT
ejpam-6680	18	13	27	27	NUM
ejpam-6680	18	14	]	]	PUNCT
ejpam-6680	18	15	mentioned	mention	VERB
ejpam-6680	18	16	in	in	ADP
ejpam-6680	18	17	[	[	X
ejpam-6680	18	18	28	28	NUM
ejpam-6680	18	19	,	,	PUNCT
ejpam-6680	18	20	29	29	NUM
ejpam-6680	18	21	]	]	PUNCT
ejpam-6680	18	22	ensured	ensure	VERB
ejpam-6680	18	23	the	the	DET
ejpam-6680	18	24	convergence	convergence	NOUN
ejpam-6680	18	25	without	without	ADP
ejpam-6680	18	26	lipschitz	lipschitz	VERB
ejpam-6680	18	27	continuity	continuity	NOUN
ejpam-6680	18	28	.	.	PUNCT
ejpam-6680	19	1	in	in	ADP
ejpam-6680	19	2	[	[	X
ejpam-6680	19	3	30	30	NUM
ejpam-6680	19	4	]	]	PUNCT
ejpam-6680	19	5	,	,	PUNCT
ejpam-6680	19	6	the	the	DET
ejpam-6680	19	7	authors	author	NOUN
ejpam-6680	19	8	discussed	discuss	VERB
ejpam-6680	19	9	strong	strong	ADJ
ejpam-6680	19	10	and	and	CCONJ
ejpam-6680	19	11	weak	weak	ADJ
ejpam-6680	19	12	convergence	convergence	NOUN
ejpam-6680	19	13	results	result	NOUN
ejpam-6680	19	14	for	for	ADP
ejpam-6680	19	15	a	a	DET
ejpam-6680	19	16	vip	vip	NOUN
ejpam-6680	19	17	in	in	ADP
ejpam-6680	19	18	the	the	DET
ejpam-6680	19	19	context	context	NOUN
ejpam-6680	19	20	of	of	ADP
ejpam-6680	19	21	a	a	DET
ejpam-6680	19	22	pseudo	pseudo	NOUN
ejpam-6680	19	23	-	-	NOUN
ejpam-6680	19	24	monotone	monotone	ADJ
ejpam-6680	19	25	,	,	PUNCT
ejpam-6680	19	26	classical	classical	ADJ
ejpam-6680	19	27	non	non	ADJ
ejpam-6680	19	28	-	-	ADJ
ejpam-6680	19	29	lipschitzian	lipschitzian	ADJ
ejpam-6680	19	30	,	,	PUNCT
ejpam-6680	19	31	continuous	continuous	ADJ
ejpam-6680	19	32	mapping	mapping	NOUN
ejpam-6680	19	33	in	in	ADP
ejpam-6680	19	34	hilbert	hilbert	PROPN
ejpam-6680	19	35	spaces	space	NOUN
ejpam-6680	19	36	over	over	ADP
ejpam-6680	19	37	r.	r.	PROPN
ejpam-6680	19	38	korpelevich	korpelevich	PUNCT
ejpam-6680	20	1	[	[	X
ejpam-6680	20	2	11	11	NUM
ejpam-6680	20	3	]	]	PUNCT
ejpam-6680	20	4	,	,	PUNCT
ejpam-6680	20	5	introduced	introduce	VERB
ejpam-6680	20	6	an	an	DET
ejpam-6680	20	7	extragradient	extragradient	NOUN
ejpam-6680	20	8	method	method	NOUN
ejpam-6680	20	9	in	in	ADP
ejpam-6680	20	10	finite	finite	ADJ
ejpam-6680	20	11	dimensional	dimensional	ADJ
ejpam-6680	20	12	euclidean	euclidean	ADJ
ejpam-6680	20	13	space	space	NOUN
ejpam-6680	20	14	to	to	PART
ejpam-6680	20	15	obtain	obtain	VERB
ejpam-6680	20	16	solution	solution	NOUN
ejpam-6680	20	17	of	of	ADP
ejpam-6680	20	18	variational	variational	ADJ
ejpam-6680	20	19	inequality	inequality	NOUN
ejpam-6680	20	20	problem	problem	NOUN
ejpam-6680	20	21	under	under	ADP
ejpam-6680	20	22	the	the	DET
ejpam-6680	20	23	mapping	mapping	NOUN
ejpam-6680	20	24	of	of	ADP
ejpam-6680	20	25	monotone	monotone	ADJ
ejpam-6680	20	26	and	and	CCONJ
ejpam-6680	20	27	lipschitz	lipschitz	NOUN
ejpam-6680	20	28	continuous	continuous	ADJ
ejpam-6680	20	29	.	.	PUNCT
ejpam-6680	21	1	the	the	DET
ejpam-6680	21	2	extragradient	extragradient	NOUN
ejpam-6680	21	3	method	method	NOUN
ejpam-6680	21	4	has	have	AUX
ejpam-6680	21	5	been	be	AUX
ejpam-6680	21	6	further	far	ADV
ejpam-6680	21	7	extended	extend	VERB
ejpam-6680	21	8	in	in	ADP
ejpam-6680	21	9	infinite	infinite	ADJ
ejpam-6680	21	10	dimensional	dimensional	ADJ
ejpam-6680	21	11	spaces	space	NOUN
ejpam-6680	21	12	by	by	ADP
ejpam-6680	21	13	many	many	ADJ
ejpam-6680	21	14	researchers	researcher	NOUN
ejpam-6680	21	15	(	(	PUNCT
ejpam-6680	21	16	see	see	VERB
ejpam-6680	21	17	[	[	X
ejpam-6680	21	18	12–15	12–15	NUM
ejpam-6680	21	19	,	,	PUNCT
ejpam-6680	21	20	22–25	22–25	NUM
ejpam-6680	21	21	]	]	PUNCT
ejpam-6680	21	22	and	and	CCONJ
ejpam-6680	21	23	the	the	DET
ejpam-6680	21	24	refferences	refference	NOUN
ejpam-6680	21	25	therein	therein	ADV
ejpam-6680	21	26	)	)	PUNCT
ejpam-6680	21	27	.	.	PUNCT
ejpam-6680	22	1	the	the	DET
ejpam-6680	22	2	modification	modification	NOUN
ejpam-6680	22	3	in	in	ADP
ejpam-6680	22	4	[	[	X
ejpam-6680	22	5	28	28	NUM
ejpam-6680	22	6	,	,	PUNCT
ejpam-6680	22	7	29	29	NUM
ejpam-6680	22	8	]	]	PUNCT
ejpam-6680	22	9	,	,	PUNCT
ejpam-6680	22	10	enables	enable	VERB
ejpam-6680	22	11	convergence	convergence	NOUN
ejpam-6680	22	12	in	in	ADP
ejpam-6680	22	13	finite	finite	ADJ
ejpam-6680	22	14	dimensional	dimensional	ADJ
ejpam-6680	22	15	euclidean	euclidean	ADJ
ejpam-6680	22	16	space	space	NOUN
ejpam-6680	22	17	without	without	ADP
ejpam-6680	22	18	lipschitz	lipschitz	VERB
ejpam-6680	22	19	continuity	continuity	NOUN
ejpam-6680	22	20	of	of	ADP
ejpam-6680	22	21	the	the	DET
ejpam-6680	22	22	mappings	mapping	NOUN
ejpam-6680	22	23	associated	associate	VERB
ejpam-6680	22	24	variational	variational	ADJ
ejpam-6680	22	25	inequality	inequality	NOUN
ejpam-6680	22	26	.	.	PUNCT
ejpam-6680	23	1	in	in	ADP
ejpam-6680	23	2	[	[	X
ejpam-6680	23	3	30	30	NUM
ejpam-6680	23	4	]	]	PUNCT
ejpam-6680	23	5	,	,	PUNCT
ejpam-6680	23	6	the	the	DET
ejpam-6680	23	7	extragradient	extragradient	NOUN
ejpam-6680	23	8	method	method	NOUN
ejpam-6680	23	9	has	have	AUX
ejpam-6680	23	10	been	be	AUX
ejpam-6680	23	11	expanded	expand	VERB
ejpam-6680	23	12	in	in	ADP
ejpam-6680	23	13	infinite	infinite	ADJ
ejpam-6680	23	14	dimensional	dimensional	ADJ
ejpam-6680	23	15	space	space	NOUN
ejpam-6680	23	16	to	to	PART
ejpam-6680	23	17	get	get	VERB
ejpam-6680	23	18	weak	weak	ADJ
ejpam-6680	23	19	and	and	CCONJ
ejpam-6680	23	20	strong	strong	ADJ
ejpam-6680	23	21	convergence	convergence	NOUN
ejpam-6680	23	22	results	result	NOUN
ejpam-6680	23	23	for	for	ADP
ejpam-6680	23	24	vip	vip	NOUN
ejpam-6680	23	25	under	under	ADP
ejpam-6680	23	26	the	the	DET
ejpam-6680	23	27	condition	condition	NOUN
ejpam-6680	23	28	of	of	ADP
ejpam-6680	23	29	classical	classical	ADJ
ejpam-6680	23	30	non	non	ADJ
ejpam-6680	23	31	-	-	ADJ
ejpam-6680	23	32	lipschitz	lipschitz	ADJ
ejpam-6680	23	33	,	,	PUNCT
ejpam-6680	23	34	pseudo	pseudo	NOUN
ejpam-6680	23	35	-	-	ADJ
ejpam-6680	23	36	monotone	monotone	ADJ
ejpam-6680	23	37	and	and	CCONJ
ejpam-6680	23	38	continuous	continuous	ADJ
ejpam-6680	23	39	mapping	mapping	NOUN
ejpam-6680	23	40	.	.	PUNCT
ejpam-6680	24	1	the	the	DET
ejpam-6680	24	2	following	follow	VERB
ejpam-6680	24	3	article	article	NOUN
ejpam-6680	24	4	is	be	AUX
ejpam-6680	24	5	dedicated	dedicate	VERB
ejpam-6680	24	6	to	to	ADP
ejpam-6680	24	7	the	the	DET
ejpam-6680	24	8	analysis	analysis	NOUN
ejpam-6680	24	9	of	of	ADP
ejpam-6680	24	10	a	a	DET
ejpam-6680	24	11	pseudo	pseudo	NOUN
ejpam-6680	24	12	-	-	ADJ
ejpam-6680	24	13	monotone	monotone	ADJ
ejpam-6680	24	14	vip	vip	NOUN
ejpam-6680	24	15	in	in	ADP
ejpam-6680	24	16	the	the	DET
ejpam-6680	24	17	setting	setting	NOUN
ejpam-6680	24	18	of	of	ADP
ejpam-6680	24	19	cat	cat	NOUN
ejpam-6680	24	20	(	(	PUNCT
ejpam-6680	24	21	0	0	NUM
ejpam-6680	24	22	)	)	PUNCT
ejpam-6680	24	23	space	space	NOUN
ejpam-6680	24	24	,	,	PUNCT
ejpam-6680	24	25	which	which	PRON
ejpam-6680	24	26	gives	give	VERB
ejpam-6680	24	27	a	a	DET
ejpam-6680	24	28	clear	clear	ADJ
ejpam-6680	24	29	modification	modification	NOUN
ejpam-6680	24	30	of	of	ADP
ejpam-6680	24	31	extragradient	extragradient	ADJ
ejpam-6680	24	32	algorithm	algorithm	NOUN
ejpam-6680	24	33	for	for	ADP
ejpam-6680	24	34	strong	strong	ADJ
ejpam-6680	24	35	and	and	CCONJ
ejpam-6680	24	36	∆-convergence	∆-convergence	NOUN
ejpam-6680	24	37	.	.	PUNCT
ejpam-6680	25	1	cat	cat	NOUN
ejpam-6680	25	2	(	(	PUNCT
ejpam-6680	25	3	0	0	NUM
ejpam-6680	25	4	)	)	PUNCT
ejpam-6680	25	5	spaces	space	NOUN
ejpam-6680	25	6	,	,	PUNCT
ejpam-6680	25	7	established	establish	VERB
ejpam-6680	25	8	by	by	ADP
ejpam-6680	25	9	alexandrov	alexandrov	PROPN
ejpam-6680	25	10	in	in	ADP
ejpam-6680	25	11	the	the	DET
ejpam-6680	25	12	1950	1950	NUM
ejpam-6680	25	13	’s	’s	NOUN
ejpam-6680	25	14	,	,	PUNCT
ejpam-6680	25	15	were	be	AUX
ejpam-6680	25	16	given	give	VERB
ejpam-6680	25	17	recognition	recognition	NOUN
ejpam-6680	25	18	by	by	ADP
ejpam-6680	25	19	m.	m.	NOUN
ejpam-6680	25	20	gromov	gromov	PROPN
ejpam-6680	25	21	,	,	PUNCT
ejpam-6680	25	22	who	who	PRON
ejpam-6680	25	23	displayed	display	VERB
ejpam-6680	25	24	that	that	SCONJ
ejpam-6680	25	25	a	a	DET
ejpam-6680	25	26	great	great	ADJ
ejpam-6680	25	27	deal	deal	NOUN
ejpam-6680	25	28	of	of	ADP
ejpam-6680	25	29	the	the	DET
ejpam-6680	25	30	theory	theory	NOUN
ejpam-6680	25	31	of	of	ADP
ejpam-6680	25	32	manifolds	manifold	NOUN
ejpam-6680	25	33	of	of	ADP
ejpam-6680	25	34	non	non	ADJ
ejpam-6680	25	35	-	-	ADJ
ejpam-6680	25	36	positive	positive	ADJ
ejpam-6680	25	37	sectional	sectional	ADJ
ejpam-6680	25	38	curvature	curvature	NOUN
ejpam-6680	25	39	could	could	AUX
ejpam-6680	25	40	be	be	AUX
ejpam-6680	25	41	designed	design	VERB
ejpam-6680	25	42	without	without	ADP
ejpam-6680	25	43	using	use	VERB
ejpam-6680	25	44	much	much	ADV
ejpam-6680	25	45	more	more	ADJ
ejpam-6680	25	46	than	than	ADP
ejpam-6680	25	47	the	the	DET
ejpam-6680	25	48	cat	cat	NOUN
ejpam-6680	25	49	(	(	PUNCT
ejpam-6680	25	50	0	0	NUM
ejpam-6680	25	51	)	)	PUNCT
ejpam-6680	25	52	condition	condition	NOUN
ejpam-6680	25	53	.	.	PUNCT
ejpam-6680	26	1	gromov	gromov	PROPN
ejpam-6680	26	2	described	describe	VERB
ejpam-6680	26	3	the	the	DET
ejpam-6680	26	4	key	key	ADJ
ejpam-6680	26	5	aspects	aspect	NOUN
ejpam-6680	26	6	of	of	ADP
ejpam-6680	26	7	the	the	DET
ejpam-6680	26	8	global	global	ADJ
ejpam-6680	26	9	geometry	geometry	NOUN
ejpam-6680	26	10	of	of	ADP
ejpam-6680	26	11	manifolds	manifold	NOUN
ejpam-6680	26	12	of	of	ADP
ejpam-6680	26	13	non	non	ADJ
ejpam-6680	26	14	-	-	ADJ
ejpam-6680	26	15	positive	positive	ADJ
ejpam-6680	26	16	curvature	curvature	NOUN
ejpam-6680	26	17	,	,	PUNCT
ejpam-6680	26	18	primarily	primarily	ADV
ejpam-6680	26	19	relying	rely	VERB
ejpam-6680	26	20	on	on	ADP
ejpam-6680	26	21	the	the	DET
ejpam-6680	26	22	cat	cat	NOUN
ejpam-6680	26	23	(	(	PUNCT
ejpam-6680	26	24	0	0	NUM
ejpam-6680	26	25	)	)	PUNCT
ejpam-6680	26	26	inequality(see	inequality(see	NOUN
ejpam-6680	27	1	[	[	X
ejpam-6680	27	2	31	31	NUM
ejpam-6680	27	3	]	]	PUNCT
ejpam-6680	27	4	)	)	PUNCT
ejpam-6680	27	5	.	.	PUNCT
ejpam-6680	28	1	let	let	AUX
ejpam-6680	28	2	(	(	PUNCT
ejpam-6680	28	3	y	y	NOUN
ejpam-6680	28	4	,	,	PUNCT
ejpam-6680	28	5	ϱ	ϱ	PROPN
ejpam-6680	28	6	)	)	PUNCT
ejpam-6680	28	7	be	be	AUX
ejpam-6680	28	8	a	a	DET
ejpam-6680	28	9	metric	metric	ADJ
ejpam-6680	28	10	space	space	NOUN
ejpam-6680	28	11	.	.	PUNCT
ejpam-6680	29	1	a	a	DET
ejpam-6680	29	2	geodesic	geodesic	ADJ
ejpam-6680	29	3	segment	segment	NOUN
ejpam-6680	29	4	connecting	connect	VERB
ejpam-6680	29	5	u1	u1	NOUN
ejpam-6680	29	6	∈	∈	PROPN
ejpam-6680	29	7	y	y	PROPN
ejpam-6680	29	8	to	to	ADP
ejpam-6680	29	9	u2	u2	PROPN
ejpam-6680	29	10	∈	∈	PROPN
ejpam-6680	29	11	y	y	PROPN
ejpam-6680	29	12	is	be	AUX
ejpam-6680	29	13	a	a	DET
ejpam-6680	29	14	mapping	mapping	NOUN
ejpam-6680	29	15	υ	υ	NOUN
ejpam-6680	29	16	:	:	PUNCT
ejpam-6680	30	1	[	[	X
ejpam-6680	30	2	0	0	NUM
ejpam-6680	30	3	,	,	PUNCT
ejpam-6680	30	4	ϱ(u1	ϱ(u1	NOUN
ejpam-6680	30	5	,	,	PUNCT
ejpam-6680	30	6	u2	u2	PROPN
ejpam-6680	30	7	)	)	PUNCT
ejpam-6680	30	8	]	]	PUNCT
ejpam-6680	31	1	→	→	PUNCT
ejpam-6680	31	2	y	y	PROPN
ejpam-6680	31	3	such	such	ADJ
ejpam-6680	31	4	that	that	DET
ejpam-6680	31	5	υ(0	υ(0	NOUN
ejpam-6680	31	6	)	)	PUNCT
ejpam-6680	31	7	=	=	SYM
ejpam-6680	31	8	u1,υ(ϱ(u1	u1,υ(ϱ(u1	NOUN
ejpam-6680	31	9	,	,	PUNCT
ejpam-6680	31	10	u2	u2	NOUN
ejpam-6680	31	11	)	)	PUNCT
ejpam-6680	31	12	)	)	PUNCT
ejpam-6680	32	1	=	=	SYM
ejpam-6680	32	2	u2	u2	NOUN
ejpam-6680	32	3	and	and	CCONJ
ejpam-6680	32	4	ϱ(υ(g1),υ(g2	ϱ(υ(g1),υ(g2	PROPN
ejpam-6680	32	5	)	)	PUNCT
ejpam-6680	32	6	=	=	SYM
ejpam-6680	32	7	|g1	|g1	PROPN
ejpam-6680	32	8	−	−	PROPN
ejpam-6680	32	9	g2|	g2|	PROPN
ejpam-6680	32	10	)	)	PUNCT
ejpam-6680	32	11	,	,	PUNCT
ejpam-6680	32	12	∀g1	∀g1	PROPN
ejpam-6680	32	13	,	,	PUNCT
ejpam-6680	32	14	g2	g2	PROPN
ejpam-6680	32	15	∈	∈	PROPN
ejpam-6680	33	1	[	[	X
ejpam-6680	33	2	0	0	NUM
ejpam-6680	33	3	,	,	PUNCT
ejpam-6680	33	4	ϱ(u1	ϱ(u1	NOUN
ejpam-6680	33	5	,	,	PUNCT
ejpam-6680	33	6	u2	u2	PROPN
ejpam-6680	33	7	)	)	PUNCT
ejpam-6680	33	8	]	]	PUNCT
ejpam-6680	33	9	.	.	PUNCT
ejpam-6680	34	1	a	a	DET
ejpam-6680	34	2	geodesic	geodesic	ADJ
ejpam-6680	34	3	segment	segment	NOUN
ejpam-6680	34	4	linking	link	VERB
ejpam-6680	34	5	any	any	DET
ejpam-6680	34	6	two	two	NUM
ejpam-6680	34	7	different	different	ADJ
ejpam-6680	34	8	points	point	NOUN
ejpam-6680	34	9	u1	u1	NOUN
ejpam-6680	34	10	,	,	PUNCT
ejpam-6680	34	11	u2	u2	PROPN
ejpam-6680	34	12	∈	∈	PROPN
ejpam-6680	34	13	y	y	PROPN
ejpam-6680	34	14	is	be	AUX
ejpam-6680	34	15	an	an	DET
ejpam-6680	34	16	isometry	isometry	NOUN
ejpam-6680	34	17	with	with	ADP
ejpam-6680	34	18	υ(0	υ(0	NOUN
ejpam-6680	34	19	)	)	PUNCT
ejpam-6680	34	20	=	=	SYM
ejpam-6680	34	21	u1,υ(u1	u1,υ(u1	PROPN
ejpam-6680	34	22	,	,	PUNCT
ejpam-6680	34	23	u2	u2	NOUN
ejpam-6680	34	24	)	)	PUNCT
ejpam-6680	34	25	=	=	SYM
ejpam-6680	34	26	u2	u2	PROPN
ejpam-6680	34	27	.	.	PUNCT
ejpam-6680	35	1	a	a	DET
ejpam-6680	35	2	unique	unique	ADJ
ejpam-6680	35	3	geodesic	geodesic	ADJ
ejpam-6680	35	4	segment	segment	NOUN
ejpam-6680	35	5	is	be	AUX
ejpam-6680	35	6	expressed	express	VERB
ejpam-6680	35	7	by	by	ADP
ejpam-6680	35	8	[	[	X
ejpam-6680	35	9	u1	u1	NOUN
ejpam-6680	35	10	,	,	PUNCT
ejpam-6680	35	11	u2	u2	PROPN
ejpam-6680	35	12	]	]	PUNCT
ejpam-6680	35	13	.	.	PUNCT
ejpam-6680	36	1	the	the	DET
ejpam-6680	36	2	metric	metric	ADJ
ejpam-6680	36	3	space	space	NOUN
ejpam-6680	36	4	(	(	PUNCT
ejpam-6680	36	5	y	y	PROPN
ejpam-6680	36	6	,	,	PUNCT
ejpam-6680	36	7	ϱ	ϱ	NOUN
ejpam-6680	36	8	)	)	PUNCT
ejpam-6680	36	9	is	be	AUX
ejpam-6680	36	10	known	know	VERB
ejpam-6680	36	11	as	as	ADP
ejpam-6680	36	12	a	a	DET
ejpam-6680	36	13	geodesic	geodesic	ADJ
ejpam-6680	36	14	metric	metric	ADJ
ejpam-6680	36	15	space	space	NOUN
ejpam-6680	36	16	if	if	SCONJ
ejpam-6680	36	17	any	any	DET
ejpam-6680	36	18	two	two	NUM
ejpam-6680	36	19	points	point	NOUN
ejpam-6680	36	20	are	be	AUX
ejpam-6680	36	21	joined	join	VERB
ejpam-6680	36	22	by	by	ADP
ejpam-6680	36	23	a	a	DET
ejpam-6680	36	24	geodesic	geodesic	ADJ
ejpam-6680	36	25	segment	segment	NOUN
ejpam-6680	36	26	and	and	CCONJ
ejpam-6680	36	27	the	the	DET
ejpam-6680	36	28	metric	metric	ADJ
ejpam-6680	36	29	(	(	PUNCT
ejpam-6680	36	30	y	y	PROPN
ejpam-6680	36	31	,	,	PUNCT
ejpam-6680	36	32	ϱ	ϱ	NOUN
ejpam-6680	36	33	)	)	PUNCT
ejpam-6680	36	34	is	be	AUX
ejpam-6680	36	35	a	a	DET
ejpam-6680	36	36	uniquely	uniquely	ADV
ejpam-6680	36	37	geodesic	geodesic	ADJ
ejpam-6680	36	38	if	if	SCONJ
ejpam-6680	36	39	there	there	PRON
ejpam-6680	36	40	is	be	VERB
ejpam-6680	36	41	exactly	exactly	ADV
ejpam-6680	36	42	one	one	NUM
ejpam-6680	36	43	geodesic	geodesic	ADJ
ejpam-6680	36	44	segment	segment	NOUN
ejpam-6680	36	45	to	to	PART
ejpam-6680	36	46	link	link	VERB
ejpam-6680	36	47	them	they	PRON
ejpam-6680	36	48	.	.	PUNCT
ejpam-6680	37	1	a	a	DET
ejpam-6680	37	2	subset	subset	NOUN
ejpam-6680	37	3	l	l	NOUN
ejpam-6680	37	4	⊆	⊆	NUM
ejpam-6680	37	5	y	y	PROPN
ejpam-6680	37	6	is	be	AUX
ejpam-6680	37	7	called	call	VERB
ejpam-6680	37	8	convex	convex	NOUN
ejpam-6680	37	9	if	if	SCONJ
ejpam-6680	37	10	any	any	DET
ejpam-6680	37	11	two	two	NUM
ejpam-6680	37	12	points	point	NOUN
ejpam-6680	37	13	in	in	ADP
ejpam-6680	37	14	y	y	PROPN
ejpam-6680	37	15	can	can	AUX
ejpam-6680	37	16	be	be	AUX
ejpam-6680	37	17	joined	join	VERB
ejpam-6680	37	18	by	by	ADP
ejpam-6680	37	19	a	a	DET
ejpam-6680	37	20	geodesic	geodesic	NOUN
ejpam-6680	37	21	and	and	CCONJ
ejpam-6680	37	22	the	the	DET
ejpam-6680	37	23	image	image	NOUN
ejpam-6680	37	24	of	of	ADP
ejpam-6680	37	25	every	every	DET
ejpam-6680	37	26	such	such	ADJ
ejpam-6680	37	27	geodesic	geodesic	NOUN
ejpam-6680	37	28	is	be	AUX
ejpam-6680	37	29	lying	lie	VERB
ejpam-6680	37	30	in	in	ADP
ejpam-6680	37	31	l.	l.	PROPN
ejpam-6680	37	32	suppose	suppose	VERB
ejpam-6680	37	33	(	(	PUNCT
ejpam-6680	37	34	y	y	PROPN
ejpam-6680	37	35	,	,	PUNCT
ejpam-6680	37	36	ϱ	ϱ	PROPN
ejpam-6680	37	37	)	)	PUNCT
ejpam-6680	37	38	be	be	VERB
ejpam-6680	37	39	the	the	DET
ejpam-6680	37	40	geodesic	geodesic	ADJ
ejpam-6680	37	41	metric	metric	ADJ
ejpam-6680	37	42	space	space	NOUN
ejpam-6680	37	43	.	.	PUNCT
ejpam-6680	38	1	in	in	ADP
ejpam-6680	38	2	a	a	DET
ejpam-6680	38	3	geodesic	geodesic	ADJ
ejpam-6680	38	4	metric	metric	ADJ
ejpam-6680	38	5	space	space	NOUN
ejpam-6680	38	6	,	,	PUNCT
ejpam-6680	38	7	a	a	DET
ejpam-6680	38	8	geodesic	geodesic	ADJ
ejpam-6680	38	9	triangle	triangle	NOUN
ejpam-6680	38	10	has	have	VERB
ejpam-6680	38	11	three	three	NUM
ejpam-6680	38	12	corners	corner	NOUN
ejpam-6680	38	13	u1	u1	NOUN
ejpam-6680	38	14	,	,	PUNCT
ejpam-6680	38	15	u2	u2	NOUN
ejpam-6680	38	16	,	,	PUNCT
ejpam-6680	38	17	u3	u3	NOUN
ejpam-6680	38	18	∈	∈	PROPN
ejpam-6680	38	19	y	y	PROPN
ejpam-6680	38	20	and	and	CCONJ
ejpam-6680	38	21	three	three	NUM
ejpam-6680	38	22	geodesic	geodesic	ADJ
ejpam-6680	38	23	segments	segment	NOUN
ejpam-6680	38	24	(	(	PUNCT
ejpam-6680	38	25	[	[	NOUN
ejpam-6680	38	26	u1	u1	NOUN
ejpam-6680	38	27	,	,	PUNCT
ejpam-6680	38	28	u2	u2	NOUN
ejpam-6680	38	29	]	]	PUNCT
ejpam-6680	38	30	,	,	PUNCT
ejpam-6680	39	1	[	[	X
ejpam-6680	39	2	u2	u2	NOUN
ejpam-6680	39	3	,	,	PUNCT
ejpam-6680	39	4	u3	u3	NOUN
ejpam-6680	39	5	]	]	PUNCT
ejpam-6680	39	6	,	,	PUNCT
ejpam-6680	39	7	[	[	X
ejpam-6680	39	8	u3	u3	NOUN
ejpam-6680	39	9	,	,	PUNCT
ejpam-6680	39	10	u1	u1	NOUN
ejpam-6680	39	11	]	]	PUNCT
ejpam-6680	39	12	)	)	PUNCT
ejpam-6680	39	13	joinm	joinm	NOUN
ejpam-6680	39	14	.	.	PUNCT
ejpam-6680	40	1	rashid	rashid	PROPN
ejpam-6680	40	2	et	et	PROPN
ejpam-6680	40	3	al	al	PROPN
ejpam-6680	40	4	.	.	PUNCT
ejpam-6680	40	5	/	/	SYM
ejpam-6680	40	6	eur	eur	PROPN
ejpam-6680	40	7	.	.	PUNCT
ejpam-6680	41	1	j.	j.	PROPN
ejpam-6680	41	2	pure	pure	PROPN
ejpam-6680	41	3	appl	appl	PROPN
ejpam-6680	41	4	.	.	PROPN
ejpam-6680	41	5	math	math	PROPN
ejpam-6680	41	6	,	,	PUNCT
ejpam-6680	41	7	18	18	NUM
ejpam-6680	41	8	(	(	PUNCT
ejpam-6680	41	9	4	4	NUM
ejpam-6680	41	10	)	)	PUNCT
ejpam-6680	41	11	(	(	PUNCT
ejpam-6680	41	12	2025	2025	NUM
ejpam-6680	41	13	)	)	PUNCT
ejpam-6680	41	14	,	,	PUNCT
ejpam-6680	41	15	6680	6680	NUM
ejpam-6680	41	16	3	3	NUM
ejpam-6680	41	17	of	of	ADP
ejpam-6680	41	18	24	24	NUM
ejpam-6680	41	19	ing	e	VERB
ejpam-6680	41	20	them	they	PRON
ejpam-6680	41	21	.	.	PUNCT
ejpam-6680	42	1	for	for	ADP
ejpam-6680	42	2	this	this	DET
ejpam-6680	42	3	triangle	triangle	NOUN
ejpam-6680	42	4	there	there	ADV
ejpam-6680	42	5	exist	exist	VERB
ejpam-6680	42	6	a	a	DET
ejpam-6680	42	7	comparison	comparison	NOUN
ejpam-6680	42	8	(	(	PUNCT
ejpam-6680	42	9	alexandrov	alexandrov	NOUN
ejpam-6680	42	10	)	)	PUNCT
ejpam-6680	42	11	triangle	triangle	NOUN
ejpam-6680	42	12	∆(u1	∆(u1	NOUN
ejpam-6680	42	13	,	,	PUNCT
ejpam-6680	42	14	u2	u2	NOUN
ejpam-6680	42	15	,	,	PUNCT
ejpam-6680	42	16	u3	u3	PROPN
ejpam-6680	42	17	)	)	PUNCT
ejpam-6680	42	18	⊂	⊂	PROPN
ejpam-6680	42	19	r2	r2	NOUN
ejpam-6680	43	1	such	such	ADJ
ejpam-6680	43	2	that	that	SCONJ
ejpam-6680	43	3	∗	∗	PROPN
ejpam-6680	43	4	ϱ(u1	ϱ(u1	PROPN
ejpam-6680	43	5	,	,	PUNCT
ejpam-6680	43	6	u2	u2	PROPN
ejpam-6680	43	7	)	)	PUNCT
ejpam-6680	43	8	=	=	SYM
ejpam-6680	43	9	ϱ(u1	ϱ(u1	PROPN
ejpam-6680	43	10	,	,	PUNCT
ejpam-6680	43	11	u2	u2	PROPN
ejpam-6680	43	12	)	)	PUNCT
ejpam-6680	43	13	,	,	PUNCT
ejpam-6680	43	14	∗	∗	PROPN
ejpam-6680	43	15	ϱ(u2	ϱ(u2	PROPN
ejpam-6680	43	16	,	,	PUNCT
ejpam-6680	43	17	u3	u3	PROPN
ejpam-6680	43	18	)	)	PUNCT
ejpam-6680	43	19	=	=	SYM
ejpam-6680	43	20	ϱ(u2	ϱ(u2	PROPN
ejpam-6680	43	21	,	,	PUNCT
ejpam-6680	43	22	u3	u3	PROPN
ejpam-6680	43	23	)	)	PUNCT
ejpam-6680	43	24	,	,	PUNCT
ejpam-6680	43	25	∗	∗	NOUN
ejpam-6680	43	26	ϱ(u3	ϱ(u3	NOUN
ejpam-6680	43	27	,	,	PUNCT
ejpam-6680	43	28	u1	u1	NOUN
ejpam-6680	43	29	)	)	PUNCT
ejpam-6680	43	30	=	=	SYM
ejpam-6680	43	31	ϱ(u3	ϱ(u3	ADJ
ejpam-6680	43	32	,	,	PUNCT
ejpam-6680	43	33	u1	u1	NOUN
ejpam-6680	43	34	)	)	PUNCT
ejpam-6680	43	35	.	.	PUNCT
ejpam-6680	44	1	when	when	SCONJ
ejpam-6680	44	2	all	all	DET
ejpam-6680	44	3	geodesic	geodesic	ADJ
ejpam-6680	44	4	triangles	triangle	NOUN
ejpam-6680	44	5	in	in	ADP
ejpam-6680	44	6	a	a	DET
ejpam-6680	44	7	geodesic	geodesic	ADJ
ejpam-6680	44	8	metric	metric	ADJ
ejpam-6680	44	9	space	space	NOUN
ejpam-6680	44	10	satisfy	satisfy	VERB
ejpam-6680	44	11	the	the	DET
ejpam-6680	44	12	following	follow	VERB
ejpam-6680	44	13	cat	cat	NOUN
ejpam-6680	44	14	(	(	PUNCT
ejpam-6680	44	15	0	0	NUM
ejpam-6680	44	16	)	)	PUNCT
ejpam-6680	44	17	comparison	comparison	NOUN
ejpam-6680	44	18	axiom	axiom	NOUN
ejpam-6680	44	19	then	then	ADV
ejpam-6680	44	20	geodesic	geodesic	ADJ
ejpam-6680	44	21	metric	metric	ADJ
ejpam-6680	44	22	space	space	NOUN
ejpam-6680	44	23	is	be	AUX
ejpam-6680	44	24	known	know	VERB
ejpam-6680	44	25	as	as	ADP
ejpam-6680	44	26	cat	cat	NOUN
ejpam-6680	44	27	(	(	PUNCT
ejpam-6680	44	28	0	0	NUM
ejpam-6680	44	29	)	)	PUNCT
ejpam-6680	44	30	space	space	NOUN
ejpam-6680	44	31	(	(	PUNCT
ejpam-6680	44	32	this	this	DET
ejpam-6680	44	33	term	term	NOUN
ejpam-6680	44	34	is	be	AUX
ejpam-6680	44	35	due	due	ADJ
ejpam-6680	44	36	to	to	ADP
ejpam-6680	44	37	m.gromov	m.gromov	ADJ
ejpam-6680	45	1	[	[	X
ejpam-6680	45	2	32	32	NUM
ejpam-6680	45	3	]	]	SYM
ejpam-6680	45	4	)	)	PUNCT
ejpam-6680	46	1	if	if	SCONJ
ejpam-6680	46	2	.	.	PUNCT
ejpam-6680	47	1	let	let	VERB
ejpam-6680	47	2	∆	∆	PROPN
ejpam-6680	47	3	and	and	CCONJ
ejpam-6680	47	4	∆	∆	PROPN
ejpam-6680	47	5	be	be	VERB
ejpam-6680	47	6	a	a	DET
ejpam-6680	47	7	geodesic	geodesic	NOUN
ejpam-6680	47	8	and	and	CCONJ
ejpam-6680	47	9	comparison	comparison	NOUN
ejpam-6680	47	10	triangle	triangle	NOUN
ejpam-6680	47	11	in	in	ADP
ejpam-6680	47	12	z	z	PROPN
ejpam-6680	47	13	,	,	PUNCT
ejpam-6680	47	14	respectively	respectively	ADV
ejpam-6680	47	15	.	.	PUNCT
ejpam-6680	48	1	if	if	SCONJ
ejpam-6680	48	2	the	the	DET
ejpam-6680	48	3	following	follow	VERB
ejpam-6680	48	4	inequality	inequality	NOUN
ejpam-6680	48	5	is	be	AUX
ejpam-6680	48	6	satisfied	satisfied	ADJ
ejpam-6680	48	7	for	for	ADP
ejpam-6680	48	8	all	all	DET
ejpam-6680	48	9	u1	u1	NOUN
ejpam-6680	48	10	,	,	PUNCT
ejpam-6680	48	11	u2	u2	PROPN
ejpam-6680	48	12	∈	∈	PROPN
ejpam-6680	48	13	∆	∆	PROPN
ejpam-6680	48	14	and	and	CCONJ
ejpam-6680	48	15	all	all	DET
ejpam-6680	48	16	comparison	comparison	NOUN
ejpam-6680	48	17	points	point	NOUN
ejpam-6680	48	18	u1	u1	NOUN
ejpam-6680	48	19	,	,	PUNCT
ejpam-6680	48	20	u2	u2	PROPN
ejpam-6680	48	21	∈	∈	PROPN
ejpam-6680	48	22	∆	∆	PROPN
ejpam-6680	48	23	,	,	PUNCT
ejpam-6680	48	24	ϱ(u1	ϱ(u1	NOUN
ejpam-6680	48	25	,	,	PUNCT
ejpam-6680	48	26	u2	u2	PROPN
ejpam-6680	48	27	)	)	PUNCT
ejpam-6680	48	28	≤	≤	NOUN
ejpam-6680	48	29	ϱ(u1	ϱ(u1	NOUN
ejpam-6680	48	30	,	,	PUNCT
ejpam-6680	48	31	u2	u2	PROPN
ejpam-6680	48	32	)	)	PUNCT
ejpam-6680	48	33	,	,	PUNCT
ejpam-6680	48	34	then	then	ADV
ejpam-6680	48	35	∆	∆	PROPN
ejpam-6680	48	36	is	be	AUX
ejpam-6680	48	37	said	say	VERB
ejpam-6680	48	38	to	to	PART
ejpam-6680	48	39	satisify	satisify	VERB
ejpam-6680	48	40	cat	cat	NOUN
ejpam-6680	48	41	(	(	PUNCT
ejpam-6680	48	42	0	0	NUM
ejpam-6680	48	43	)	)	PUNCT
ejpam-6680	48	44	inequality	inequality	NOUN
ejpam-6680	48	45	.	.	PUNCT
ejpam-6680	49	1	the	the	DET
ejpam-6680	49	2	motivation	motivation	NOUN
ejpam-6680	49	3	for	for	ADP
ejpam-6680	49	4	the	the	DET
ejpam-6680	49	5	conversion	conversion	NOUN
ejpam-6680	49	6	thus	thus	ADV
ejpam-6680	49	7	stems	stem	VERB
ejpam-6680	49	8	from	from	ADP
ejpam-6680	49	9	the	the	DET
ejpam-6680	49	10	need	need	NOUN
ejpam-6680	49	11	to	to	PART
ejpam-6680	49	12	improve	improve	VERB
ejpam-6680	49	13	robustness	robustness	NOUN
ejpam-6680	49	14	and	and	CCONJ
ejpam-6680	49	15	applicability	applicability	NOUN
ejpam-6680	49	16	of	of	ADP
ejpam-6680	49	17	results	result	NOUN
ejpam-6680	49	18	.	.	PUNCT
ejpam-6680	50	1	by	by	ADP
ejpam-6680	50	2	transiting	transit	VERB
ejpam-6680	50	3	to	to	ADP
ejpam-6680	50	4	cat	cat	NOUN
ejpam-6680	50	5	(	(	PUNCT
ejpam-6680	50	6	0	0	NUM
ejpam-6680	50	7	)	)	PUNCT
ejpam-6680	50	8	spaces	space	NOUN
ejpam-6680	50	9	,	,	PUNCT
ejpam-6680	50	10	researchers	researcher	NOUN
ejpam-6680	50	11	can	can	AUX
ejpam-6680	50	12	better	well	ADV
ejpam-6680	50	13	handle	handle	VERB
ejpam-6680	50	14	nonlinearities	nonlinearitie	NOUN
ejpam-6680	50	15	,	,	PUNCT
ejpam-6680	50	16	ensuring	ensure	VERB
ejpam-6680	50	17	more	more	ADV
ejpam-6680	50	18	meaningful	meaningful	ADJ
ejpam-6680	50	19	and	and	CCONJ
ejpam-6680	50	20	reliable	reliable	ADJ
ejpam-6680	50	21	insights	insight	NOUN
ejpam-6680	50	22	across	across	ADP
ejpam-6680	50	23	a	a	DET
ejpam-6680	50	24	broad	broad	ADJ
ejpam-6680	50	25	range	range	NOUN
ejpam-6680	50	26	of	of	ADP
ejpam-6680	50	27	applications	application	NOUN
ejpam-6680	50	28	.	.	PUNCT
ejpam-6680	51	1	we	we	PRON
ejpam-6680	51	2	introduce	introduce	VERB
ejpam-6680	51	3	two	two	NUM
ejpam-6680	51	4	algorithms	algorithm	NOUN
ejpam-6680	51	5	in	in	ADP
ejpam-6680	51	6	hadamard	hadamard	ADJ
ejpam-6680	51	7	spaces	space	NOUN
ejpam-6680	51	8	that	that	PRON
ejpam-6680	51	9	does	do	AUX
ejpam-6680	51	10	not	not	PART
ejpam-6680	51	11	require	require	VERB
ejpam-6680	51	12	to	to	PART
ejpam-6680	51	13	have	have	VERB
ejpam-6680	51	14	previous	previous	ADJ
ejpam-6680	51	15	knowledge	knowledge	NOUN
ejpam-6680	51	16	of	of	ADP
ejpam-6680	51	17	lipschitzlike	lipschitzlike	ADJ
ejpam-6680	51	18	constants	constant	NOUN
ejpam-6680	51	19	.	.	PUNCT
ejpam-6680	52	1	our	our	PRON
ejpam-6680	52	2	proposed	propose	VERB
ejpam-6680	52	3	algorithms	algorithm	NOUN
ejpam-6680	52	4	converges	converge	VERB
ejpam-6680	52	5	to	to	ADP
ejpam-6680	52	6	a	a	DET
ejpam-6680	52	7	solution	solution	NOUN
ejpam-6680	52	8	of	of	ADP
ejpam-6680	52	9	vip	vip	NOUN
ejpam-6680	52	10	.	.	PUNCT
ejpam-6680	53	1	moreover	moreover	ADV
ejpam-6680	53	2	,	,	PUNCT
ejpam-6680	53	3	we	we	PRON
ejpam-6680	53	4	present	present	VERB
ejpam-6680	53	5	a	a	DET
ejpam-6680	53	6	numerical	numerical	ADJ
ejpam-6680	53	7	example	example	NOUN
ejpam-6680	53	8	in	in	ADP
ejpam-6680	53	9	a	a	DET
ejpam-6680	53	10	hadamard	hadamard	ADJ
ejpam-6680	53	11	space	space	NOUN
ejpam-6680	53	12	to	to	PART
ejpam-6680	53	13	demonstrate	demonstrate	VERB
ejpam-6680	53	14	the	the	DET
ejpam-6680	53	15	performance	performance	NOUN
ejpam-6680	53	16	of	of	ADP
ejpam-6680	53	17	our	our	PRON
ejpam-6680	53	18	method	method	NOUN
ejpam-6680	53	19	.	.	PUNCT
ejpam-6680	54	1	question	question	NOUN
ejpam-6680	54	2	1	1	NUM
ejpam-6680	54	3	.	.	PUNCT
ejpam-6680	55	1	can	can	AUX
ejpam-6680	55	2	we	we	PRON
ejpam-6680	55	3	obtain	obtain	VERB
ejpam-6680	55	4	convergence	convergence	NOUN
ejpam-6680	55	5	results	result	NOUN
ejpam-6680	55	6	for	for	ADP
ejpam-6680	55	7	vip	vip	NOUN
ejpam-6680	55	8	using	use	VERB
ejpam-6680	55	9	an	an	DET
ejpam-6680	55	10	extragradient	extragradient	NOUN
ejpam-6680	55	11	algorithm	algorithm	NOUN
ejpam-6680	55	12	in	in	ADP
ejpam-6680	55	13	hadamard	hadamard	ADJ
ejpam-6680	55	14	space	space	NOUN
ejpam-6680	55	15	under	under	ADP
ejpam-6680	55	16	the	the	DET
ejpam-6680	55	17	condition	condition	NOUN
ejpam-6680	55	18	of	of	ADP
ejpam-6680	55	19	pseudo	pseudo	NOUN
ejpam-6680	55	20	-	-	NOUN
ejpam-6680	55	21	monotone	monotone	NOUN
ejpam-6680	55	22	.	.	PUNCT
ejpam-6680	56	1	our	our	PRON
ejpam-6680	56	2	contributions	contribution	NOUN
ejpam-6680	56	3	in	in	ADP
ejpam-6680	56	4	this	this	DET
ejpam-6680	56	5	paper	paper	NOUN
ejpam-6680	56	6	are	be	AUX
ejpam-6680	56	7	briefly	briefly	ADV
ejpam-6680	56	8	highlighted	highlight	VERB
ejpam-6680	56	9	as	as	ADP
ejpam-6680	56	10	:	:	PUNCT
ejpam-6680	56	11	1	1	X
ejpam-6680	56	12	.	.	X
ejpam-6680	57	1	our	our	PRON
ejpam-6680	57	2	work	work	NOUN
ejpam-6680	57	3	extends	extend	VERB
ejpam-6680	57	4	algorithm	algorithm	NOUN
ejpam-6680	57	5	of	of	ADP
ejpam-6680	57	6	extragradient	extragradient	NOUN
ejpam-6680	57	7	for	for	ADP
ejpam-6680	57	8	pseudomonotone	pseudomonotone	NOUN
ejpam-6680	57	9	from	from	ADP
ejpam-6680	57	10	linear	linear	ADJ
ejpam-6680	57	11	spaces	space	NOUN
ejpam-6680	57	12	to	to	ADP
ejpam-6680	57	13	nonlinear	nonlinear	ADJ
ejpam-6680	57	14	spaces	space	NOUN
ejpam-6680	57	15	.	.	PUNCT
ejpam-6680	58	1	2	2	X
ejpam-6680	58	2	.	.	X
ejpam-6680	58	3	our	our	PRON
ejpam-6680	58	4	algorithm	algorithm	NOUN
ejpam-6680	58	5	not	not	PART
ejpam-6680	58	6	depends	depend	VERB
ejpam-6680	58	7	on	on	ADP
ejpam-6680	58	8	the	the	DET
ejpam-6680	58	9	lipschitz	lipschitz	NOUN
ejpam-6680	58	10	constant	constant	ADJ
ejpam-6680	58	11	.	.	PUNCT
ejpam-6680	59	1	2	2	X
ejpam-6680	59	2	.	.	X
ejpam-6680	59	3	preliminaries	preliminary	NOUN
ejpam-6680	59	4	in	in	ADP
ejpam-6680	59	5	this	this	DET
ejpam-6680	59	6	section	section	NOUN
ejpam-6680	59	7	,	,	PUNCT
ejpam-6680	59	8	we	we	PRON
ejpam-6680	59	9	display	display	VERB
ejpam-6680	59	10	some	some	DET
ejpam-6680	59	11	notations	notation	NOUN
ejpam-6680	59	12	,	,	PUNCT
ejpam-6680	59	13	familiar	familiar	ADJ
ejpam-6680	59	14	definitions	definition	NOUN
ejpam-6680	59	15	,	,	PUNCT
ejpam-6680	59	16	and	and	CCONJ
ejpam-6680	59	17	relevent	relevent	ADJ
ejpam-6680	59	18	results	result	NOUN
ejpam-6680	59	19	that	that	PRON
ejpam-6680	59	20	will	will	AUX
ejpam-6680	59	21	be	be	AUX
ejpam-6680	59	22	required	require	VERB
ejpam-6680	59	23	in	in	ADP
ejpam-6680	59	24	the	the	DET
ejpam-6680	59	25	proof	proof	NOUN
ejpam-6680	59	26	of	of	ADP
ejpam-6680	59	27	our	our	PRON
ejpam-6680	59	28	main	main	ADJ
ejpam-6680	59	29	results	result	NOUN
ejpam-6680	59	30	.	.	PUNCT
ejpam-6680	60	1	definition	definition	NOUN
ejpam-6680	60	2	1	1	NUM
ejpam-6680	60	3	.	.	PUNCT
ejpam-6680	61	1	a	a	DET
ejpam-6680	61	2	geodesically	geodesically	ADV
ejpam-6680	61	3	connected	connect	VERB
ejpam-6680	61	4	metric	metric	ADJ
ejpam-6680	61	5	space	space	NOUN
ejpam-6680	61	6	y	y	PROPN
ejpam-6680	61	7	is	be	AUX
ejpam-6680	61	8	known	know	VERB
ejpam-6680	61	9	as	as	ADP
ejpam-6680	61	10	cat	cat	NOUN
ejpam-6680	61	11	(	(	PUNCT
ejpam-6680	61	12	0	0	NUM
ejpam-6680	61	13	)	)	PUNCT
ejpam-6680	61	14	space	space	NOUN
ejpam-6680	61	15	and	and	CCONJ
ejpam-6680	61	16	every	every	DET
ejpam-6680	61	17	geodesic	geodesic	ADJ
ejpam-6680	61	18	triangle	triangle	NOUN
ejpam-6680	61	19	in	in	ADP
ejpam-6680	61	20	y	y	PROPN
ejpam-6680	61	21	is	be	AUX
ejpam-6680	61	22	at	at	ADV
ejpam-6680	61	23	least	least	ADJ
ejpam-6680	61	24	as	as	ADP
ejpam-6680	61	25	’	'	PUNCT
ejpam-6680	61	26	thin	thin	ADJ
ejpam-6680	61	27	’	'	PUNCT
ejpam-6680	61	28	as	as	ADP
ejpam-6680	61	29	its	its	PRON
ejpam-6680	61	30	comparison	comparison	NOUN
ejpam-6680	61	31	triangle	triangle	NOUN
ejpam-6680	61	32	in	in	ADP
ejpam-6680	61	33	the	the	DET
ejpam-6680	61	34	euclidean	euclidean	ADJ
ejpam-6680	61	35	plane	plane	NOUN
ejpam-6680	61	36	.	.	PUNCT
ejpam-6680	62	1	for	for	ADP
ejpam-6680	62	2	a	a	DET
ejpam-6680	62	3	systematic	systematic	ADJ
ejpam-6680	62	4	study	study	NOUN
ejpam-6680	62	5	of	of	ADP
ejpam-6680	62	6	geodesic	geodesic	ADJ
ejpam-6680	62	7	spaces	space	NOUN
ejpam-6680	62	8	and	and	CCONJ
ejpam-6680	62	9	cat	cat	NOUN
ejpam-6680	62	10	(	(	PUNCT
ejpam-6680	62	11	0	0	NUM
ejpam-6680	62	12	)	)	PUNCT
ejpam-6680	62	13	spaces	space	VERB
ejpam-6680	62	14	the	the	DET
ejpam-6680	62	15	readers	reader	NOUN
ejpam-6680	62	16	are	be	AUX
ejpam-6680	62	17	referred	refer	VERB
ejpam-6680	62	18	to	to	ADP
ejpam-6680	62	19	[	[	X
ejpam-6680	62	20	31	31	NUM
ejpam-6680	62	21	]	]	PUNCT
ejpam-6680	62	22	.	.	PUNCT
ejpam-6680	63	1	according	accord	VERB
ejpam-6680	63	2	to	to	ADP
ejpam-6680	63	3	bruhat	bruhat	ADP
ejpam-6680	63	4	and	and	CCONJ
ejpam-6680	63	5	tits	tit	NOUN
ejpam-6680	63	6	[	[	X
ejpam-6680	63	7	33	33	NUM
ejpam-6680	63	8	]	]	PUNCT
ejpam-6680	63	9	,	,	PUNCT
ejpam-6680	63	10	the	the	DET
ejpam-6680	63	11	(	(	PUNCT
ejpam-6680	63	12	cn	cn	NOUN
ejpam-6680	63	13	)	)	PUNCT
ejpam-6680	63	14	inequality	inequality	NOUN
ejpam-6680	63	15	is	be	AUX
ejpam-6680	63	16	defined	define	VERB
ejpam-6680	63	17	as	as	SCONJ
ejpam-6680	63	18	follows	follow	VERB
ejpam-6680	63	19	:	:	PUNCT
ejpam-6680	63	20	definition	definition	NOUN
ejpam-6680	63	21	2	2	NUM
ejpam-6680	63	22	.	.	PUNCT
ejpam-6680	64	1	if	if	SCONJ
ejpam-6680	64	2	u	u	NOUN
ejpam-6680	64	3	,	,	PUNCT
ejpam-6680	64	4	u1	u1	NOUN
ejpam-6680	64	5	,	,	PUNCT
ejpam-6680	64	6	u2	u2	PROPN
ejpam-6680	64	7	∈	∈	PROPN
ejpam-6680	64	8	cat	cat	NOUN
ejpam-6680	64	9	(	(	PUNCT
ejpam-6680	64	10	0	0	NUM
ejpam-6680	64	11	)	)	PUNCT
ejpam-6680	64	12	space	space	NOUN
ejpam-6680	64	13	and	and	CCONJ
ejpam-6680	64	14	if	if	SCONJ
ejpam-6680	64	15	u0	u0	PROPN
ejpam-6680	64	16	∈	∈	PROPN
ejpam-6680	64	17	[	[	X
ejpam-6680	64	18	u1	u1	NOUN
ejpam-6680	64	19	,	,	PUNCT
ejpam-6680	64	20	u2	u2	PROPN
ejpam-6680	64	21	]	]	PUNCT
ejpam-6680	64	22	be	be	VERB
ejpam-6680	64	23	the	the	DET
ejpam-6680	64	24	middle	middle	ADJ
ejpam-6680	64	25	point	point	NOUN
ejpam-6680	64	26	of	of	ADP
ejpam-6680	64	27	the	the	DET
ejpam-6680	64	28	segment	segment	NOUN
ejpam-6680	64	29	,	,	PUNCT
ejpam-6680	64	30	then	then	ADV
ejpam-6680	64	31	the	the	DET
ejpam-6680	64	32	cat	cat	NOUN
ejpam-6680	64	33	(	(	PUNCT
ejpam-6680	64	34	0	0	NUM
ejpam-6680	64	35	)	)	PUNCT
ejpam-6680	64	36	inequality	inequality	NOUN
ejpam-6680	64	37	yields	yield	NOUN
ejpam-6680	64	38	ϱ(u	ϱ(u	ADP
ejpam-6680	64	39	,	,	PUNCT
ejpam-6680	64	40	u0	u0	ADJ
ejpam-6680	64	41	)	)	PUNCT
ejpam-6680	64	42	2	2	NUM
ejpam-6680	64	43	≤	≤	NUM
ejpam-6680	64	44	1	1	NUM
ejpam-6680	64	45	2	2	NUM
ejpam-6680	64	46	ϱ(u	ϱ(u	ADP
ejpam-6680	64	47	,	,	PUNCT
ejpam-6680	64	48	u1	u1	NOUN
ejpam-6680	64	49	)	)	PUNCT
ejpam-6680	64	50	2	2	NUM
ejpam-6680	64	51	+	+	CCONJ
ejpam-6680	64	52	1	1	NUM
ejpam-6680	64	53	2	2	NUM
ejpam-6680	64	54	ϱ(u	ϱ(u	ADP
ejpam-6680	64	55	,	,	PUNCT
ejpam-6680	64	56	u2	u2	NOUN
ejpam-6680	64	57	)	)	PUNCT
ejpam-6680	64	58	2	2	NUM
ejpam-6680	64	59	−	−	NOUN
ejpam-6680	64	60	1	1	NUM
ejpam-6680	64	61	4	4	NUM
ejpam-6680	64	62	ϱ(u1	ϱ(u1	NUM
ejpam-6680	64	63	,	,	PUNCT
ejpam-6680	64	64	u2	u2	NOUN
ejpam-6680	64	65	)	)	PUNCT
ejpam-6680	64	66	2	2	NUM
ejpam-6680	64	67	.	.	PUNCT
ejpam-6680	64	68	m.	m.	NOUN
ejpam-6680	64	69	rashid	rashid	PROPN
ejpam-6680	64	70	et	et	PROPN
ejpam-6680	64	71	al	al	PROPN
ejpam-6680	64	72	.	.	PUNCT
ejpam-6680	64	73	/	/	SYM
ejpam-6680	64	74	eur	eur	PROPN
ejpam-6680	64	75	.	.	PUNCT
ejpam-6680	65	1	j.	j.	PROPN
ejpam-6680	65	2	pure	pure	PROPN
ejpam-6680	65	3	appl	appl	PROPN
ejpam-6680	65	4	.	.	PROPN
ejpam-6680	65	5	math	math	PROPN
ejpam-6680	65	6	,	,	PUNCT
ejpam-6680	65	7	18	18	NUM
ejpam-6680	65	8	(	(	PUNCT
ejpam-6680	65	9	4	4	NUM
ejpam-6680	65	10	)	)	PUNCT
ejpam-6680	65	11	(	(	PUNCT
ejpam-6680	65	12	2025	2025	NUM
ejpam-6680	65	13	)	)	PUNCT
ejpam-6680	65	14	,	,	PUNCT
ejpam-6680	65	15	6680	6680	NUM
ejpam-6680	65	16	4	4	NUM
ejpam-6680	65	17	of	of	ADP
ejpam-6680	65	18	24	24	NUM
ejpam-6680	65	19	in	in	ADP
ejpam-6680	65	20	recent	recent	ADJ
ejpam-6680	65	21	past	past	NOUN
ejpam-6680	65	22	,	,	PUNCT
ejpam-6680	65	23	cat	cat	NOUN
ejpam-6680	65	24	(	(	PUNCT
ejpam-6680	65	25	0	0	NUM
ejpam-6680	65	26	)	)	PUNCT
ejpam-6680	65	27	spaces	space	NOUN
ejpam-6680	65	28	have	have	AUX
ejpam-6680	65	29	appealed	appeal	VERB
ejpam-6680	65	30	many	many	ADJ
ejpam-6680	65	31	mathematicians	mathematician	NOUN
ejpam-6680	65	32	,	,	PUNCT
ejpam-6680	65	33	due	due	ADP
ejpam-6680	65	34	to	to	ADP
ejpam-6680	65	35	their	their	PRON
ejpam-6680	65	36	geometrical	geometrical	ADJ
ejpam-6680	65	37	relevance	relevance	NOUN
ejpam-6680	65	38	in	in	ADP
ejpam-6680	65	39	multiple	multiple	ADJ
ejpam-6680	65	40	directions	direction	NOUN
ejpam-6680	65	41	.	.	PUNCT
ejpam-6680	66	1	hadamard	hadamard	ADJ
ejpam-6680	66	2	spaces	space	NOUN
ejpam-6680	67	1	[	[	X
ejpam-6680	67	2	34	34	NUM
ejpam-6680	67	3	]	]	PUNCT
ejpam-6680	67	4	are	be	AUX
ejpam-6680	67	5	originally	originally	ADV
ejpam-6680	67	6	the	the	DET
ejpam-6680	67	7	complete	complete	ADJ
ejpam-6680	67	8	cat	cat	NOUN
ejpam-6680	67	9	(	(	PUNCT
ejpam-6680	67	10	0	0	NUM
ejpam-6680	67	11	)	)	PUNCT
ejpam-6680	67	12	spaces	space	NOUN
ejpam-6680	67	13	.	.	PUNCT
ejpam-6680	68	1	in	in	ADP
ejpam-6680	68	2	2008	2008	NUM
ejpam-6680	68	3	,	,	PUNCT
ejpam-6680	68	4	the	the	DET
ejpam-6680	68	5	notion	notion	NOUN
ejpam-6680	68	6	of	of	ADP
ejpam-6680	68	7	quasilinearization	quasilinearization	NOUN
ejpam-6680	68	8	was	be	AUX
ejpam-6680	68	9	initiated	initiate	VERB
ejpam-6680	68	10	by	by	ADP
ejpam-6680	68	11	berg	berg	PROPN
ejpam-6680	68	12	and	and	CCONJ
ejpam-6680	68	13	nikolaev	nikolaev	X
ejpam-6680	69	1	[	[	X
ejpam-6680	69	2	35	35	NUM
ejpam-6680	69	3	]	]	PUNCT
ejpam-6680	69	4	,	,	PUNCT
ejpam-6680	69	5	given	give	VERB
ejpam-6680	69	6	as	as	SCONJ
ejpam-6680	69	7	follows	follow	VERB
ejpam-6680	69	8	:	:	PUNCT
ejpam-6680	69	9	definition	definition	NOUN
ejpam-6680	69	10	3	3	NUM
ejpam-6680	69	11	.	.	PUNCT
ejpam-6680	70	1	denoting	denote	VERB
ejpam-6680	70	2	a	a	DET
ejpam-6680	70	3	vector	vector	NOUN
ejpam-6680	70	4	as	as	ADP
ejpam-6680	70	5	a	a	DET
ejpam-6680	70	6	pair	pair	NOUN
ejpam-6680	70	7	(	(	PUNCT
ejpam-6680	70	8	ξ	ξ	PROPN
ejpam-6680	70	9	,	,	PUNCT
ejpam-6680	70	10	η	η	NOUN
ejpam-6680	70	11	)	)	PUNCT
ejpam-6680	70	12	∈	∈	PROPN
ejpam-6680	70	13	y	y	PROPN
ejpam-6680	70	14	×	×	PROPN
ejpam-6680	70	15	y	y	NOUN
ejpam-6680	70	16	by	by	ADP
ejpam-6680	70	17	−→	−→	NOUN
ejpam-6680	70	18	ξη	ξη	NOUN
ejpam-6680	70	19	,	,	PUNCT
ejpam-6680	70	20	the	the	DET
ejpam-6680	70	21	quasilinearization	quasilinearization	NOUN
ejpam-6680	70	22	is	be	AUX
ejpam-6680	70	23	defined	define	VERB
ejpam-6680	70	24	as	as	ADP
ejpam-6680	70	25	a	a	DET
ejpam-6680	70	26	mapping	mapping	NOUN
ejpam-6680	70	27	⟨.	⟨.	NOUN
ejpam-6680	70	28	,	,	PUNCT
ejpam-6680	70	29	.⟩	.⟩	PROPN
ejpam-6680	70	30	:	:	PUNCT
ejpam-6680	71	1	(	(	PUNCT
ejpam-6680	71	2	y	y	NOUN
ejpam-6680	71	3	×	×	NOUN
ejpam-6680	71	4	y)×	y)×	NOUN
ejpam-6680	71	5	(	(	PUNCT
ejpam-6680	71	6	y	y	PROPN
ejpam-6680	71	7	×	×	PROPN
ejpam-6680	71	8	y	y	PROPN
ejpam-6680	71	9	)	)	PUNCT
ejpam-6680	71	10	→	→	PUNCT
ejpam-6680	71	11	r	r	NOUN
ejpam-6680	71	12	satisfying	satisfying	NOUN
ejpam-6680	71	13	⟨	⟨	VERB
ejpam-6680	71	14	−→	−→	NOUN
ejpam-6680	71	15	ξη	ξη	NOUN
ejpam-6680	71	16	,	,	PUNCT
ejpam-6680	71	17	−→	−→	ADV
ejpam-6680	71	18	γδ⟩	γδ⟩	NOUN
ejpam-6680	71	19	=	=	SYM
ejpam-6680	71	20	1	1	NUM
ejpam-6680	71	21	2	2	NUM
ejpam-6680	71	22	[	[	PUNCT
ejpam-6680	71	23	ϱ2(ξ	ϱ2(ξ	NUM
ejpam-6680	71	24	,	,	PUNCT
ejpam-6680	71	25	δ	δ	PROPN
ejpam-6680	71	26	)	)	PUNCT
ejpam-6680	71	27	+	+	CCONJ
ejpam-6680	72	1	ϱ2(η	ϱ2(η	X
ejpam-6680	72	2	,	,	PUNCT
ejpam-6680	72	3	γ)−	γ)−	PROPN
ejpam-6680	72	4	ϱ2(ξ	ϱ2(ξ	NUM
ejpam-6680	72	5	,	,	PUNCT
ejpam-6680	72	6	γ)−	γ)−	PROPN
ejpam-6680	72	7	ϱ2(η	ϱ2(η	PROPN
ejpam-6680	72	8	,	,	PUNCT
ejpam-6680	72	9	δ	δ	PROPN
ejpam-6680	72	10	)	)	PUNCT
ejpam-6680	72	11	]	]	PUNCT
ejpam-6680	72	12	,	,	PUNCT
ejpam-6680	72	13	where	where	SCONJ
ejpam-6680	72	14	ξ	ξ	X
ejpam-6680	72	15	,	,	PUNCT
ejpam-6680	72	16	η	η	PROPN
ejpam-6680	72	17	,	,	PUNCT
ejpam-6680	72	18	γ	γ	PROPN
ejpam-6680	72	19	,	,	PUNCT
ejpam-6680	72	20	δ	δ	PROPN
ejpam-6680	72	21	∈	∈	PROPN
ejpam-6680	72	22	y.	y.	NOUN
ejpam-6680	72	23	remark	remark	NOUN
ejpam-6680	72	24	1	1	NUM
ejpam-6680	72	25	.	.	PUNCT
ejpam-6680	73	1	it	it	PRON
ejpam-6680	73	2	can	can	AUX
ejpam-6680	73	3	easily	easily	ADV
ejpam-6680	73	4	verify	verify	VERB
ejpam-6680	73	5	that	that	SCONJ
ejpam-6680	73	6	for	for	ADP
ejpam-6680	73	7	all	all	DET
ejpam-6680	73	8	ξ	ξ	PROPN
ejpam-6680	73	9	,	,	PUNCT
ejpam-6680	73	10	η	η	PROPN
ejpam-6680	73	11	,	,	PUNCT
ejpam-6680	73	12	γ	γ	PROPN
ejpam-6680	73	13	,	,	PUNCT
ejpam-6680	73	14	δ	δ	PROPN
ejpam-6680	73	15	,	,	PUNCT
ejpam-6680	73	16	ζ	ζ	PROPN
ejpam-6680	73	17	∈	∈	PROPN
ejpam-6680	73	18	y	y	PROPN
ejpam-6680	73	19	,	,	PUNCT
ejpam-6680	73	20	(	(	PUNCT
ejpam-6680	73	21	i	i	NOUN
ejpam-6680	73	22	)	)	PUNCT
ejpam-6680	73	23	⟨	⟨	VERB
ejpam-6680	73	24	−→	−→	NOUN
ejpam-6680	73	25	ξη	ξη	NOUN
ejpam-6680	73	26	,	,	PUNCT
ejpam-6680	73	27	−→	−→	NOUN
ejpam-6680	73	28	γδ⟩	γδ⟩	NOUN
ejpam-6680	73	29	=	=	PUNCT
ejpam-6680	73	30	⟨	⟨	VERB
ejpam-6680	73	31	−→	−→	NOUN
ejpam-6680	73	32	γδ	γδ	ADP
ejpam-6680	73	33	,	,	PUNCT
ejpam-6680	73	34	−→	−→	ADJ
ejpam-6680	73	35	ξη⟩	ξη⟩	PROPN
ejpam-6680	73	36	,	,	PUNCT
ejpam-6680	73	37	(	(	PUNCT
ejpam-6680	73	38	ii	ii	NOUN
ejpam-6680	73	39	)	)	PUNCT
ejpam-6680	73	40	⟨	⟨	VERB
ejpam-6680	73	41	−→	−→	NOUN
ejpam-6680	73	42	ξη	ξη	NOUN
ejpam-6680	73	43	,	,	PUNCT
ejpam-6680	73	44	−→	−→	NOUN
ejpam-6680	73	45	γδ⟩	γδ⟩	NOUN
ejpam-6680	73	46	=	=	SYM
ejpam-6680	74	1	−⟨	−⟨	ADP
ejpam-6680	74	2	−→	−→	PROPN
ejpam-6680	74	3	ηξ	ηξ	PROPN
ejpam-6680	74	4	,	,	PUNCT
ejpam-6680	74	5	−→	−→	PROPN
ejpam-6680	74	6	γδ⟩	γδ⟩	PROPN
ejpam-6680	74	7	,	,	PUNCT
ejpam-6680	74	8	(	(	PUNCT
ejpam-6680	74	9	iii	iii	NOUN
ejpam-6680	74	10	)	)	PUNCT
ejpam-6680	74	11	⟨	⟨	VERB
ejpam-6680	74	12	−→	−→	ADJ
ejpam-6680	74	13	ξζ	ξζ	NOUN
ejpam-6680	74	14	,	,	PUNCT
ejpam-6680	74	15	−→	−→	NOUN
ejpam-6680	74	16	γδ⟩+	γδ⟩+	PROPN
ejpam-6680	74	17	⟨	⟨	VERB
ejpam-6680	74	18	−→	−→	PROPN
ejpam-6680	74	19	ζη	ζη	ADJ
ejpam-6680	74	20	,	,	PUNCT
ejpam-6680	74	21	−→	−→	NOUN
ejpam-6680	74	22	γδ⟩	γδ⟩	NOUN
ejpam-6680	74	23	=	=	PUNCT
ejpam-6680	75	1	⟨	⟨	VERB
ejpam-6680	75	2	−→	−→	NOUN
ejpam-6680	75	3	ξη	ξη	NOUN
ejpam-6680	75	4	,	,	PUNCT
ejpam-6680	75	5	−→	−→	PROPN
ejpam-6680	75	6	γδ⟩	γδ⟩	PROPN
ejpam-6680	75	7	,	,	PUNCT
ejpam-6680	75	8	(	(	PUNCT
ejpam-6680	75	9	iv	iv	X
ejpam-6680	75	10	)	)	PUNCT
ejpam-6680	75	11	y	y	PROPN
ejpam-6680	75	12	satisfies	satisfy	VERB
ejpam-6680	75	13	the	the	DET
ejpam-6680	75	14	cauchy	cauchy	PROPN
ejpam-6680	75	15	-	-	PUNCT
ejpam-6680	75	16	schwarz	schwarz	PROPN
ejpam-6680	75	17	inequality	inequality	NOUN
ejpam-6680	75	18	if	if	SCONJ
ejpam-6680	75	19	⟨	⟨	VERB
ejpam-6680	75	20	−→	−→	NOUN
ejpam-6680	75	21	ξη	ξη	NOUN
ejpam-6680	75	22	,	,	PUNCT
ejpam-6680	76	1	−→	−→	ADJ
ejpam-6680	76	2	γδ⟩	γδ⟩	PUNCT
ejpam-6680	76	3	≤	≤	PROPN
ejpam-6680	77	1	ϱ(ξ	ϱ(ξ	PROPN
ejpam-6680	77	2	,	,	PUNCT
ejpam-6680	77	3	η)ϱ(γ	η)ϱ(γ	PROPN
ejpam-6680	77	4	,	,	PUNCT
ejpam-6680	77	5	δ	δ	PROPN
ejpam-6680	77	6	)	)	PUNCT
ejpam-6680	77	7	.	.	PUNCT
ejpam-6680	78	1	remark	remark	PROPN
ejpam-6680	78	2	2	2	NUM
ejpam-6680	78	3	.	.	PUNCT
ejpam-6680	78	4	a	a	DET
ejpam-6680	78	5	geodesically	geodesically	ADV
ejpam-6680	78	6	connected	connect	VERB
ejpam-6680	78	7	metric	metric	ADJ
ejpam-6680	78	8	space	space	NOUN
ejpam-6680	78	9	is	be	AUX
ejpam-6680	78	10	a	a	DET
ejpam-6680	78	11	cat	cat	NOUN
ejpam-6680	78	12	(	(	PUNCT
ejpam-6680	78	13	0	0	NUM
ejpam-6680	78	14	)	)	PUNCT
ejpam-6680	78	15	space	space	NOUN
ejpam-6680	79	1	if	if	SCONJ
ejpam-6680	79	2	and	and	CCONJ
ejpam-6680	79	3	only	only	ADV
ejpam-6680	79	4	if	if	SCONJ
ejpam-6680	79	5	it	it	PRON
ejpam-6680	79	6	satisfies	satisfy	VERB
ejpam-6680	79	7	the	the	DET
ejpam-6680	79	8	cauchy	cauchy	PROPN
ejpam-6680	79	9	-	-	PUNCT
ejpam-6680	79	10	schwarz	schwarz	PROPN
ejpam-6680	79	11	inequality	inequality	NOUN
ejpam-6680	79	12	(	(	PUNCT
ejpam-6680	79	13	[	[	X
ejpam-6680	79	14	35	35	NUM
ejpam-6680	79	15	]	]	PUNCT
ejpam-6680	79	16	,	,	PUNCT
ejpam-6680	79	17	corollary	corollary	ADJ
ejpam-6680	79	18	3	3	NUM
ejpam-6680	79	19	)	)	PUNCT
ejpam-6680	79	20	.	.	PUNCT
ejpam-6680	80	1	in	in	ADP
ejpam-6680	80	2	2010	2010	NUM
ejpam-6680	80	3	kakavandi	kakavandi	NOUN
ejpam-6680	80	4	and	and	CCONJ
ejpam-6680	80	5	amini[36	amini[36	NOUN
ejpam-6680	80	6	]	]	X
ejpam-6680	80	7	develop	develop	VERB
ejpam-6680	80	8	dual	dual	ADJ
ejpam-6680	80	9	space	space	NOUN
ejpam-6680	80	10	of	of	ADP
ejpam-6680	80	11	hadamard	hadamard	ADJ
ejpam-6680	80	12	space	space	NOUN
ejpam-6680	80	13	z	z	NOUN
ejpam-6680	80	14	by	by	ADP
ejpam-6680	80	15	using	use	VERB
ejpam-6680	80	16	the	the	DET
ejpam-6680	80	17	concept	concept	NOUN
ejpam-6680	80	18	of	of	ADP
ejpam-6680	80	19	quasilinearization	quasilinearization	NOUN
ejpam-6680	80	20	and	and	CCONJ
ejpam-6680	80	21	by	by	ADP
ejpam-6680	80	22	initiating	initiate	VERB
ejpam-6680	80	23	the	the	DET
ejpam-6680	80	24	concept	concept	NOUN
ejpam-6680	80	25	of	of	ADP
ejpam-6680	80	26	pseudometric	pseudometric	ADJ
ejpam-6680	80	27	space	space	NOUN
ejpam-6680	80	28	.	.	PUNCT
ejpam-6680	81	1	definition	definition	NOUN
ejpam-6680	81	2	4	4	NUM
ejpam-6680	81	3	.	.	PUNCT
ejpam-6680	81	4	to	to	PART
ejpam-6680	81	5	explain	explain	VERB
ejpam-6680	81	6	the	the	DET
ejpam-6680	81	7	conjugate	conjugate	ADJ
ejpam-6680	81	8	space	space	NOUN
ejpam-6680	81	9	of	of	ADP
ejpam-6680	81	10	hadamard	hadamard	ADJ
ejpam-6680	81	11	space	space	NOUN
ejpam-6680	81	12	z	z	NOUN
ejpam-6680	81	13	,	,	PUNCT
ejpam-6680	81	14	consider	consider	VERB
ejpam-6680	81	15	the	the	DET
ejpam-6680	81	16	map	map	NOUN
ejpam-6680	81	17	φ	φ	X
ejpam-6680	81	18	:	:	PUNCT
ejpam-6680	82	1	r×z	r×z	ADJ
ejpam-6680	82	2	×z	×z	ADP
ejpam-6680	82	3	→	→	SYM
ejpam-6680	82	4	h(z	h(z	NOUN
ejpam-6680	82	5	,	,	PUNCT
ejpam-6680	82	6	r	r	NOUN
ejpam-6680	82	7	)	)	PUNCT
ejpam-6680	82	8	defined	define	VERB
ejpam-6680	82	9	by	by	ADP
ejpam-6680	82	10	φ(t	φ(t	PROPN
ejpam-6680	82	11	,	,	PUNCT
ejpam-6680	82	12	ξ	ξ	PROPN
ejpam-6680	82	13	,	,	PUNCT
ejpam-6680	82	14	η	η	NOUN
ejpam-6680	82	15	)	)	PUNCT
ejpam-6680	82	16	=	=	PUNCT
ejpam-6680	82	17	t⟨	t⟨	VERB
ejpam-6680	82	18	−→	−→	NOUN
ejpam-6680	82	19	ξη	ξη	VERB
ejpam-6680	82	20	,	,	PUNCT
ejpam-6680	82	21	−→	−→	NOUN
ejpam-6680	82	22	ξα⟩	ξα⟩	PROPN
ejpam-6680	82	23	(	(	PUNCT
ejpam-6680	82	24	t	t	PROPN
ejpam-6680	82	25	∈	∈	PROPN
ejpam-6680	82	26	r	r	PROPN
ejpam-6680	82	27	,	,	PUNCT
ejpam-6680	82	28	ξ	ξ	PROPN
ejpam-6680	82	29	,	,	PUNCT
ejpam-6680	82	30	η	η	PROPN
ejpam-6680	82	31	,	,	PUNCT
ejpam-6680	82	32	γ	γ	PROPN
ejpam-6680	82	33	∈	∈	PROPN
ejpam-6680	82	34	z	z	PROPN
ejpam-6680	82	35	)	)	PUNCT
ejpam-6680	82	36	(	(	PUNCT
ejpam-6680	82	37	1	1	X
ejpam-6680	82	38	)	)	PUNCT
ejpam-6680	82	39	where	where	SCONJ
ejpam-6680	82	40	h(z	h(z	NOUN
ejpam-6680	82	41	,	,	PUNCT
ejpam-6680	82	42	r	r	NOUN
ejpam-6680	82	43	)	)	PUNCT
ejpam-6680	82	44	is	be	AUX
ejpam-6680	82	45	the	the	DET
ejpam-6680	82	46	space	space	NOUN
ejpam-6680	82	47	of	of	ADP
ejpam-6680	82	48	all	all	DET
ejpam-6680	82	49	continuous	continuous	ADJ
ejpam-6680	82	50	real	real	ADV
ejpam-6680	82	51	-	-	PUNCT
ejpam-6680	82	52	valued	value	VERB
ejpam-6680	82	53	functions	function	NOUN
ejpam-6680	82	54	on	on	ADP
ejpam-6680	82	55	z.	z.	PROPN
ejpam-6680	82	56	then	then	ADV
ejpam-6680	82	57	the	the	DET
ejpam-6680	82	58	cauchyschwartz	cauchyschwartz	NOUN
ejpam-6680	82	59	inequality	inequality	NOUN
ejpam-6680	82	60	implies	imply	VERB
ejpam-6680	82	61	that	that	SCONJ
ejpam-6680	82	62	φ(t	φ(t	PROPN
ejpam-6680	82	63	,	,	PUNCT
ejpam-6680	82	64	ξ	ξ	PROPN
ejpam-6680	82	65	,	,	PUNCT
ejpam-6680	82	66	η	η	NOUN
ejpam-6680	82	67	)	)	PUNCT
ejpam-6680	82	68	is	be	AUX
ejpam-6680	82	69	a	a	DET
ejpam-6680	82	70	lipschitz	lipschitz	NOUN
ejpam-6680	82	71	function	function	NOUN
ejpam-6680	82	72	with	with	ADP
ejpam-6680	82	73	lipschitz	lipschitz	NOUN
ejpam-6680	82	74	semi	semi	ADJ
ejpam-6680	82	75	-	-	ADJ
ejpam-6680	82	76	norm	norm	ADJ
ejpam-6680	82	77	h(φ(t	h(φ(t	NOUN
ejpam-6680	82	78	,	,	PUNCT
ejpam-6680	82	79	ξ	ξ	PROPN
ejpam-6680	82	80	,	,	PUNCT
ejpam-6680	82	81	η	η	NOUN
ejpam-6680	82	82	)	)	PUNCT
ejpam-6680	82	83	)	)	PUNCT
ejpam-6680	83	1	=	=	SYM
ejpam-6680	83	2	tϱ(ξ	tϱ(ξ	NOUN
ejpam-6680	83	3	,	,	PUNCT
ejpam-6680	83	4	η	η	NOUN
ejpam-6680	83	5	)	)	PUNCT
ejpam-6680	83	6	,	,	PUNCT
ejpam-6680	83	7	for	for	ADP
ejpam-6680	83	8	all	all	DET
ejpam-6680	83	9	t	t	NOUN
ejpam-6680	83	10	∈	∈	NOUN
ejpam-6680	83	11	r	r	NOUN
ejpam-6680	83	12	and	and	CCONJ
ejpam-6680	83	13	ξ	ξ	PROPN
ejpam-6680	83	14	,	,	PUNCT
ejpam-6680	83	15	η	η	PROPN
ejpam-6680	83	16	∈	∈	PROPN
ejpam-6680	83	17	z	z	PROPN
ejpam-6680	83	18	,	,	PUNCT
ejpam-6680	83	19	where	where	SCONJ
ejpam-6680	83	20	h(ψ	h(ψ	NOUN
ejpam-6680	83	21	)	)	PUNCT
ejpam-6680	83	22	=	=	SYM
ejpam-6680	83	23	sup{ψ(ξ)−ψ(η	sup{ψ(ξ)−ψ(η	X
ejpam-6680	83	24	)	)	PUNCT
ejpam-6680	83	25	ϱ(ξ	ϱ(ξ	PROPN
ejpam-6680	83	26	,	,	PUNCT
ejpam-6680	83	27	η	η	PROPN
ejpam-6680	83	28	)	)	PUNCT
ejpam-6680	83	29	;	;	PUNCT
ejpam-6680	83	30	ξ	ξ	X
ejpam-6680	83	31	,	,	PUNCT
ejpam-6680	83	32	η	η	PROPN
ejpam-6680	83	33	∈	∈	PROPN
ejpam-6680	83	34	z	z	PROPN
ejpam-6680	83	35	,	,	PUNCT
ejpam-6680	83	36	ξ	ξ	PROPN
ejpam-6680	83	37	̸=	̸=	PROPN
ejpam-6680	83	38	η	η	PROPN
ejpam-6680	83	39	}	}	PUNCT
ejpam-6680	83	40	is	be	AUX
ejpam-6680	83	41	the	the	DET
ejpam-6680	83	42	lipschitz	lipschitz	NOUN
ejpam-6680	83	43	semi	semi	NOUN
ejpam-6680	83	44	-	-	NOUN
ejpam-6680	83	45	norm	norm	ADJ
ejpam-6680	83	46	,	,	PUNCT
ejpam-6680	83	47	for	for	ADP
ejpam-6680	83	48	any	any	DET
ejpam-6680	83	49	function	function	NOUN
ejpam-6680	83	50	ψ	ψ	NOUN
ejpam-6680	83	51	:	:	PUNCT
ejpam-6680	83	52	z	z	X
ejpam-6680	83	53	→	→	SYM
ejpam-6680	83	54	r.	r.	PROPN
ejpam-6680	83	55	now	now	ADV
ejpam-6680	83	56	,	,	PUNCT
ejpam-6680	83	57	we	we	PRON
ejpam-6680	83	58	present	present	VERB
ejpam-6680	83	59	the	the	DET
ejpam-6680	83	60	pseudometric	pseudometric	ADJ
ejpam-6680	83	61	d	d	PROPN
ejpam-6680	83	62	on	on	ADP
ejpam-6680	83	63	r×z	r×z	PROPN
ejpam-6680	83	64	×z	×z	ADV
ejpam-6680	83	65	by	by	ADP
ejpam-6680	83	66	d((t	d((t	NOUN
ejpam-6680	83	67	,	,	PUNCT
ejpam-6680	83	68	ξ	ξ	PROPN
ejpam-6680	83	69	,	,	PUNCT
ejpam-6680	83	70	η	η	NOUN
ejpam-6680	83	71	)	)	PUNCT
ejpam-6680	83	72	,	,	PUNCT
ejpam-6680	83	73	(	(	PUNCT
ejpam-6680	83	74	s	s	X
ejpam-6680	83	75	,	,	PUNCT
ejpam-6680	83	76	γ	γ	X
ejpam-6680	83	77	,	,	PUNCT
ejpam-6680	83	78	δ	δ	PROPN
ejpam-6680	83	79	)	)	PUNCT
ejpam-6680	83	80	)	)	PUNCT
ejpam-6680	84	1	=	=	SYM
ejpam-6680	84	2	h(φ(t	h(φ(t	PROPN
ejpam-6680	84	3	,	,	PUNCT
ejpam-6680	84	4	ξ	ξ	PROPN
ejpam-6680	84	5	,	,	PUNCT
ejpam-6680	84	6	η)−	η)−	PROPN
ejpam-6680	84	7	φ(s	φ(s	NOUN
ejpam-6680	84	8	,	,	PUNCT
ejpam-6680	84	9	γ	γ	PROPN
ejpam-6680	84	10	,	,	PUNCT
ejpam-6680	84	11	δ	δ	PROPN
ejpam-6680	84	12	)	)	PUNCT
ejpam-6680	84	13	)	)	PUNCT
ejpam-6680	84	14	(	(	PUNCT
ejpam-6680	84	15	t	t	PROPN
ejpam-6680	84	16	,	,	PUNCT
ejpam-6680	84	17	s	s	PART
ejpam-6680	84	18	∈	∈	PROPN
ejpam-6680	84	19	r	r	PROPN
ejpam-6680	84	20	,	,	PUNCT
ejpam-6680	84	21	ξ	ξ	PROPN
ejpam-6680	84	22	,	,	PUNCT
ejpam-6680	84	23	η	η	PROPN
ejpam-6680	84	24	,	,	PUNCT
ejpam-6680	84	25	γ	γ	PROPN
ejpam-6680	84	26	,	,	PUNCT
ejpam-6680	84	27	δ	δ	PROPN
ejpam-6680	84	28	∈	∈	PROPN
ejpam-6680	84	29	z	z	PROPN
ejpam-6680	84	30	)	)	PUNCT
ejpam-6680	84	31	.	.	PUNCT
ejpam-6680	85	1	(	(	PUNCT
ejpam-6680	85	2	2	2	X
ejpam-6680	85	3	)	)	PUNCT
ejpam-6680	85	4	m.	m.	NOUN
ejpam-6680	85	5	rashid	rashid	PROPN
ejpam-6680	85	6	et	et	PROPN
ejpam-6680	85	7	al	al	PROPN
ejpam-6680	85	8	.	.	PUNCT
ejpam-6680	85	9	/	/	SYM
ejpam-6680	85	10	eur	eur	PROPN
ejpam-6680	85	11	.	.	PUNCT
ejpam-6680	86	1	j.	j.	PROPN
ejpam-6680	86	2	pure	pure	PROPN
ejpam-6680	86	3	appl	appl	PROPN
ejpam-6680	86	4	.	.	PROPN
ejpam-6680	86	5	math	math	PROPN
ejpam-6680	86	6	,	,	PUNCT
ejpam-6680	86	7	18	18	NUM
ejpam-6680	86	8	(	(	PUNCT
ejpam-6680	86	9	4	4	NUM
ejpam-6680	86	10	)	)	PUNCT
ejpam-6680	86	11	(	(	PUNCT
ejpam-6680	86	12	2025	2025	NUM
ejpam-6680	86	13	)	)	PUNCT
ejpam-6680	86	14	,	,	PUNCT
ejpam-6680	86	15	6680	6680	NUM
ejpam-6680	86	16	5	5	NUM
ejpam-6680	86	17	of	of	ADP
ejpam-6680	86	18	24	24	NUM
ejpam-6680	86	19	lemma	lemma	PROPN
ejpam-6680	86	20	1	1	NUM
ejpam-6680	86	21	.	.	PUNCT
ejpam-6680	87	1	[	[	X
ejpam-6680	87	2	36	36	NUM
ejpam-6680	87	3	]	]	X
ejpam-6680	87	4	d((t	d((t	NOUN
ejpam-6680	87	5	,	,	PUNCT
ejpam-6680	87	6	ξ	ξ	PROPN
ejpam-6680	87	7	,	,	PUNCT
ejpam-6680	87	8	η	η	NOUN
ejpam-6680	87	9	)	)	PUNCT
ejpam-6680	87	10	,	,	PUNCT
ejpam-6680	87	11	(	(	PUNCT
ejpam-6680	87	12	s	s	X
ejpam-6680	87	13	,	,	PUNCT
ejpam-6680	87	14	γ	γ	X
ejpam-6680	87	15	,	,	PUNCT
ejpam-6680	87	16	δ	δ	PROPN
ejpam-6680	87	17	)	)	PUNCT
ejpam-6680	87	18	)	)	PUNCT
ejpam-6680	88	1	=	=	SYM
ejpam-6680	88	2	0	0	PUNCT
ejpam-6680	89	1	if	if	SCONJ
ejpam-6680	89	2	and	and	CCONJ
ejpam-6680	89	3	only	only	ADV
ejpam-6680	89	4	if	if	SCONJ
ejpam-6680	89	5	t⟨ξη,−→er⟩	t⟨ξη,−→er⟩	PROPN
ejpam-6680	89	6	=	=	SYM
ejpam-6680	89	7	s⟨γδ,−→er⟩	s⟨γδ,−→er⟩	PROPN
ejpam-6680	89	8	,	,	PUNCT
ejpam-6680	89	9	for	for	ADP
ejpam-6680	89	10	all	all	DET
ejpam-6680	89	11	e	e	NOUN
ejpam-6680	89	12	,	,	PUNCT
ejpam-6680	89	13	r	r	NOUN
ejpam-6680	89	14	∈	∈	PROPN
ejpam-6680	89	15	z.	z.	NOUN
ejpam-6680	89	16	proof	proof	NOUN
ejpam-6680	89	17	.	.	PUNCT
ejpam-6680	90	1	by	by	ADP
ejpam-6680	90	2	(	(	PUNCT
ejpam-6680	90	3	1	1	NUM
ejpam-6680	90	4	)	)	PUNCT
ejpam-6680	90	5	and	and	CCONJ
ejpam-6680	90	6	(	(	PUNCT
ejpam-6680	90	7	2	2	NUM
ejpam-6680	90	8	)	)	PUNCT
ejpam-6680	90	9	and	and	CCONJ
ejpam-6680	90	10	formulation	formulation	NOUN
ejpam-6680	90	11	of	of	ADP
ejpam-6680	90	12	lipschitz	lipschitz	NOUN
ejpam-6680	90	13	semi	semi	NOUN
ejpam-6680	90	14	-	-	NOUN
ejpam-6680	90	15	norm	norm	ADJ
ejpam-6680	90	16	,	,	PUNCT
ejpam-6680	90	17	d((t	d((t	NOUN
ejpam-6680	90	18	,	,	PUNCT
ejpam-6680	90	19	ξ	ξ	PROPN
ejpam-6680	90	20	,	,	PUNCT
ejpam-6680	90	21	η	η	NOUN
ejpam-6680	90	22	)	)	PUNCT
ejpam-6680	90	23	,	,	PUNCT
ejpam-6680	90	24	(	(	PUNCT
ejpam-6680	90	25	s	s	X
ejpam-6680	90	26	,	,	PUNCT
ejpam-6680	90	27	γ	γ	X
ejpam-6680	90	28	,	,	PUNCT
ejpam-6680	90	29	δ	δ	PROPN
ejpam-6680	90	30	)	)	PUNCT
ejpam-6680	90	31	)	)	PUNCT
ejpam-6680	91	1	=	=	SYM
ejpam-6680	91	2	0	0	PUNCT
ejpam-6680	92	1	if	if	SCONJ
ejpam-6680	92	2	and	and	CCONJ
ejpam-6680	92	3	only	only	ADV
ejpam-6680	92	4	if	if	SCONJ
ejpam-6680	92	5	there	there	PRON
ejpam-6680	92	6	exist	exist	VERB
ejpam-6680	92	7	a	a	DET
ejpam-6680	92	8	constant	constant	ADJ
ejpam-6680	92	9	κ	κ	NOUN
ejpam-6680	92	10	∈	∈	PROPN
ejpam-6680	92	11	r	r	NOUN
ejpam-6680	92	12	such	such	ADJ
ejpam-6680	92	13	that	that	SCONJ
ejpam-6680	92	14	t⟨ξη,−→ξe⟩	t⟨ξη,−→ξe⟩	PROPN
ejpam-6680	92	15	=	=	PUNCT
ejpam-6680	92	16	s⟨γδ,−→γe⟩+κ	s⟨γδ,−→γe⟩+κ	NOUN
ejpam-6680	92	17	,	,	PUNCT
ejpam-6680	92	18	for	for	ADP
ejpam-6680	92	19	all	all	DET
ejpam-6680	92	20	e	e	PROPN
ejpam-6680	92	21	∈	∈	PROPN
ejpam-6680	92	22	z.	z.	PROPN
ejpam-6680	92	23	therefore	therefore	ADV
ejpam-6680	92	24	,	,	PUNCT
ejpam-6680	92	25	for	for	ADP
ejpam-6680	92	26	all	all	DET
ejpam-6680	92	27	e	e	NOUN
ejpam-6680	92	28	,	,	PUNCT
ejpam-6680	92	29	r	r	NOUN
ejpam-6680	92	30	∈	∈	PROPN
ejpam-6680	92	31	z	z	NOUN
ejpam-6680	92	32	t⟨ξη,−→er⟩	t⟨ξη,−→er⟩	PROPN
ejpam-6680	93	1	=	=	PUNCT
ejpam-6680	93	2	t⟨ξη	t⟨ξη	NOUN
ejpam-6680	93	3	,	,	PUNCT
ejpam-6680	93	4	−→	−→	ADJ
ejpam-6680	93	5	ξr⟩	ξr⟩	NOUN
ejpam-6680	94	1	−	−	ADP
ejpam-6680	94	2	t⟨ξη	t⟨ξη	PROPN
ejpam-6680	94	3	,	,	PUNCT
ejpam-6680	94	4	−→	−→	ADJ
ejpam-6680	94	5	ξe⟩	ξe⟩	NOUN
ejpam-6680	94	6	=	=	SYM
ejpam-6680	94	7	s⟨γδ,−→γe⟩	s⟨γδ,−→γe⟩	ADJ
ejpam-6680	94	8	−	−	PROPN
ejpam-6680	94	9	s⟨γδ,−→γe⟩	s⟨γδ,−→γe⟩	PROPN
ejpam-6680	94	10	=	=	PUNCT
ejpam-6680	94	11	s⟨γδ,−→er⟩.	s⟨γδ,−→er⟩.	NOUN
ejpam-6680	94	12	conversely	conversely	ADV
ejpam-6680	94	13	if	if	SCONJ
ejpam-6680	94	14	t⟨ξη,−→er⟩	t⟨ξη,−→er⟩	PROPN
ejpam-6680	94	15	=	=	SYM
ejpam-6680	94	16	s⟨γδ,−→er⟩	s⟨γδ,−→er⟩	PROPN
ejpam-6680	94	17	,	,	PUNCT
ejpam-6680	94	18	for	for	ADP
ejpam-6680	94	19	all	all	DET
ejpam-6680	94	20	e	e	NOUN
ejpam-6680	94	21	,	,	PUNCT
ejpam-6680	94	22	r	r	NOUN
ejpam-6680	94	23	∈	∈	PROPN
ejpam-6680	94	24	z	z	PROPN
ejpam-6680	94	25	,	,	PUNCT
ejpam-6680	94	26	then	then	ADV
ejpam-6680	94	27	φ(t	φ(t	PROPN
ejpam-6680	94	28	,	,	PUNCT
ejpam-6680	94	29	ξ	ξ	PROPN
ejpam-6680	94	30	,	,	PUNCT
ejpam-6680	94	31	η)(e	η)(e	ADJ
ejpam-6680	94	32	)	)	PUNCT
ejpam-6680	95	1	=	=	SYM
ejpam-6680	95	2	t⟨ξη	t⟨ξη	PROPN
ejpam-6680	95	3	,	,	PUNCT
ejpam-6680	95	4	ξe⟩	ξe⟩	NUM
ejpam-6680	95	5	=	=	SYM
ejpam-6680	95	6	s⟨γδ	s⟨γδ	PROPN
ejpam-6680	95	7	,	,	PUNCT
ejpam-6680	95	8	ξe⟩	ξe⟩	NUM
ejpam-6680	95	9	=	=	SYM
ejpam-6680	95	10	φ(s	φ(s	NOUN
ejpam-6680	95	11	,	,	PUNCT
ejpam-6680	95	12	γ	γ	X
ejpam-6680	95	13	,	,	PUNCT
ejpam-6680	95	14	δ)(e)−	δ)(e)−	ADJ
ejpam-6680	95	15	s⟨γδ	s⟨γδ	PROPN
ejpam-6680	95	16	,	,	PUNCT
ejpam-6680	95	17	γξ⟩	γξ⟩	NOUN
ejpam-6680	95	18	,	,	PUNCT
ejpam-6680	95	19	for	for	ADP
ejpam-6680	95	20	all	all	DET
ejpam-6680	95	21	e	e	PROPN
ejpam-6680	95	22	∈	∈	PROPN
ejpam-6680	95	23	z	z	PROPN
ejpam-6680	95	24	,	,	PUNCT
ejpam-6680	95	25	which	which	PRON
ejpam-6680	95	26	yields	yield	VERB
ejpam-6680	95	27	d((t	d((t	VERB
ejpam-6680	95	28	,	,	PUNCT
ejpam-6680	95	29	ξ	ξ	PROPN
ejpam-6680	95	30	,	,	PUNCT
ejpam-6680	95	31	η	η	NOUN
ejpam-6680	95	32	)	)	PUNCT
ejpam-6680	95	33	,	,	PUNCT
ejpam-6680	95	34	(	(	PUNCT
ejpam-6680	95	35	s	s	X
ejpam-6680	95	36	,	,	PUNCT
ejpam-6680	95	37	γ	γ	X
ejpam-6680	95	38	,	,	PUNCT
ejpam-6680	95	39	δ	δ	PROPN
ejpam-6680	95	40	)	)	PUNCT
ejpam-6680	95	41	)	)	PUNCT
ejpam-6680	96	1	=	=	PUNCT
ejpam-6680	96	2	0	0	X
ejpam-6680	96	3	.	.	PUNCT
ejpam-6680	97	1	definition	definition	NOUN
ejpam-6680	97	2	5	5	NUM
ejpam-6680	97	3	.	.	PUNCT
ejpam-6680	98	1	for	for	ADP
ejpam-6680	98	2	a	a	DET
ejpam-6680	98	3	hadamard	hadamard	ADJ
ejpam-6680	98	4	space	space	NOUN
ejpam-6680	98	5	(	(	PUNCT
ejpam-6680	98	6	z	z	NOUN
ejpam-6680	98	7	,	,	PUNCT
ejpam-6680	98	8	ϱ	ϱ	PROPN
ejpam-6680	98	9	)	)	PUNCT
ejpam-6680	98	10	,	,	PUNCT
ejpam-6680	98	11	the	the	DET
ejpam-6680	98	12	pseudometric	pseudometric	ADJ
ejpam-6680	98	13	space	space	NOUN
ejpam-6680	98	14	(	(	PUNCT
ejpam-6680	98	15	r×z	r×z	ADJ
ejpam-6680	98	16	×z	×z	ADV
ejpam-6680	98	17	,	,	PUNCT
ejpam-6680	98	18	d	d	NOUN
ejpam-6680	98	19	)	)	PUNCT
ejpam-6680	98	20	can	can	AUX
ejpam-6680	98	21	be	be	AUX
ejpam-6680	98	22	considered	consider	VERB
ejpam-6680	98	23	as	as	ADP
ejpam-6680	98	24	a	a	DET
ejpam-6680	98	25	subspace	subspace	NOUN
ejpam-6680	98	26	of	of	ADP
ejpam-6680	98	27	the	the	DET
ejpam-6680	98	28	pseudometric	pseudometric	ADJ
ejpam-6680	98	29	space	space	NOUN
ejpam-6680	98	30	(	(	PUNCT
ejpam-6680	98	31	lip(z	lip(z	PROPN
ejpam-6680	98	32	,	,	PUNCT
ejpam-6680	98	33	r),h	r),h	PROPN
ejpam-6680	98	34	)	)	PUNCT
ejpam-6680	98	35	of	of	ADP
ejpam-6680	98	36	all	all	DET
ejpam-6680	98	37	real	real	ADV
ejpam-6680	98	38	-	-	PUNCT
ejpam-6680	98	39	valued	value	VERB
ejpam-6680	98	40	lipschitz	lipschitz	NOUN
ejpam-6680	98	41	functions	function	NOUN
ejpam-6680	98	42	.	.	PUNCT
ejpam-6680	99	1	also	also	ADV
ejpam-6680	99	2	,	,	PUNCT
ejpam-6680	99	3	d	d	PRON
ejpam-6680	99	4	explain	explain	VERB
ejpam-6680	99	5	an	an	DET
ejpam-6680	99	6	equivalence	equivalence	NOUN
ejpam-6680	99	7	relation	relation	NOUN
ejpam-6680	99	8	on	on	ADP
ejpam-6680	99	9	r	r	PROPN
ejpam-6680	99	10	×	×	PROPN
ejpam-6680	99	11	z	z	NOUN
ejpam-6680	99	12	×	×	NOUN
ejpam-6680	99	13	z	z	NOUN
ejpam-6680	99	14	,	,	PUNCT
ejpam-6680	99	15	where	where	SCONJ
ejpam-6680	99	16	the	the	DET
ejpam-6680	99	17	equivalence	equivalence	NOUN
ejpam-6680	99	18	class	class	NOUN
ejpam-6680	99	19	of	of	ADP
ejpam-6680	99	20	(	(	PUNCT
ejpam-6680	99	21	t	t	PROPN
ejpam-6680	99	22	,	,	PUNCT
ejpam-6680	99	23	ξ	ξ	PROPN
ejpam-6680	99	24	,	,	PUNCT
ejpam-6680	99	25	η	η	NOUN
ejpam-6680	99	26	)	)	PUNCT
ejpam-6680	99	27	is	be	AUX
ejpam-6680	99	28	[	[	X
ejpam-6680	99	29	t	t	NOUN
ejpam-6680	99	30	−→	−→	NOUN
ejpam-6680	99	31	ξη	ξη	VERB
ejpam-6680	99	32	]	]	X
ejpam-6680	99	33	=	=	PUNCT
ejpam-6680	99	34	{	{	PUNCT
ejpam-6680	99	35	s	s	AUX
ejpam-6680	99	36	−→	−→	NOUN
ejpam-6680	99	37	γδ	γδ	ADV
ejpam-6680	99	38	;	;	PUNCT
ejpam-6680	99	39	t⟨	t⟨	PROPN
ejpam-6680	99	40	−→	−→	NOUN
ejpam-6680	99	41	ξη	ξη	VERB
ejpam-6680	99	42	,	,	PUNCT
ejpam-6680	99	43	−→	−→	ADJ
ejpam-6680	99	44	γδ⟩	γδ⟩	NOUN
ejpam-6680	99	45	=	=	PUNCT
ejpam-6680	99	46	s⟨	s⟨	ADV
ejpam-6680	99	47	−→	−→	NOUN
ejpam-6680	99	48	γδ	γδ	ADP
ejpam-6680	99	49	,	,	PUNCT
ejpam-6680	99	50	−→	−→	ADJ
ejpam-6680	99	51	γδ⟩	γδ⟩	X
ejpam-6680	99	52	(	(	PUNCT
ejpam-6680	99	53	γ	γ	X
ejpam-6680	99	54	,	,	PUNCT
ejpam-6680	99	55	δ	δ	PROPN
ejpam-6680	99	56	∈	∈	PROPN
ejpam-6680	99	57	z	z	PROPN
ejpam-6680	99	58	)	)	PUNCT
ejpam-6680	99	59	}	}	PUNCT
ejpam-6680	99	60	.	.	PUNCT
ejpam-6680	100	1	the	the	DET
ejpam-6680	100	2	set	set	NOUN
ejpam-6680	100	3	y	y	PROPN
ejpam-6680	100	4	∗	∗	NOUN
ejpam-6680	100	5	=	=	PUNCT
ejpam-6680	100	6	{	{	PUNCT
ejpam-6680	100	7	t	t	NOUN
ejpam-6680	100	8	−→	−→	NOUN
ejpam-6680	100	9	ξη	ξη	VERB
ejpam-6680	100	10	;	;	PUNCT
ejpam-6680	100	11	(	(	PUNCT
ejpam-6680	100	12	t	t	PROPN
ejpam-6680	100	13	,	,	PUNCT
ejpam-6680	100	14	γ	γ	X
ejpam-6680	100	15	,	,	PUNCT
ejpam-6680	100	16	δ	δ	PROPN
ejpam-6680	100	17	)	)	PUNCT
ejpam-6680	100	18	∈	∈	PROPN
ejpam-6680	101	1	r×z	r×z	PROPN
ejpam-6680	101	2	×z	×z	NOUN
ejpam-6680	101	3	}	}	PUNCT
ejpam-6680	101	4	is	be	AUX
ejpam-6680	101	5	a	a	DET
ejpam-6680	101	6	metric	metric	ADJ
ejpam-6680	101	7	space	space	NOUN
ejpam-6680	101	8	with	with	ADP
ejpam-6680	101	9	metric	metric	ADJ
ejpam-6680	101	10	d	d	PROPN
ejpam-6680	101	11	,	,	PUNCT
ejpam-6680	101	12	which	which	PRON
ejpam-6680	101	13	is	be	AUX
ejpam-6680	101	14	called	call	VERB
ejpam-6680	101	15	the	the	DET
ejpam-6680	101	16	dual	dual	ADJ
ejpam-6680	101	17	metric	metric	ADJ
ejpam-6680	101	18	space	space	NOUN
ejpam-6680	101	19	of	of	ADP
ejpam-6680	101	20	(	(	PUNCT
ejpam-6680	101	21	z	z	NOUN
ejpam-6680	101	22	,	,	PUNCT
ejpam-6680	101	23	ϱ	ϱ	NOUN
ejpam-6680	101	24	)	)	PUNCT
ejpam-6680	101	25	.	.	PUNCT
ejpam-6680	102	1	in	in	ADP
ejpam-6680	102	2	[	[	X
ejpam-6680	102	3	37	37	NUM
ejpam-6680	102	4	]	]	PUNCT
ejpam-6680	102	5	,	,	PUNCT
ejpam-6680	102	6	theorem	theorem	VERB
ejpam-6680	102	7	2.3	2.3	NUM
ejpam-6680	102	8	,	,	PUNCT
ejpam-6680	102	9	the	the	DET
ejpam-6680	102	10	projection	projection	NOUN
ejpam-6680	102	11	operator	operator	NOUN
ejpam-6680	102	12	is	be	AUX
ejpam-6680	102	13	utilized	utilize	VERB
ejpam-6680	102	14	for	for	ADP
ejpam-6680	102	15	the	the	DET
ejpam-6680	102	16	existence	existence	NOUN
ejpam-6680	102	17	of	of	ADP
ejpam-6680	102	18	solution	solution	NOUN
ejpam-6680	102	19	of	of	ADP
ejpam-6680	102	20	the	the	DET
ejpam-6680	102	21	respective	respective	ADJ
ejpam-6680	102	22	variational	variational	ADJ
ejpam-6680	102	23	inequality	inequality	NOUN
ejpam-6680	102	24	in	in	ADP
ejpam-6680	102	25	a	a	DET
ejpam-6680	102	26	hilbert	hilbert	NOUN
ejpam-6680	102	27	space	space	NOUN
ejpam-6680	102	28	over	over	ADP
ejpam-6680	102	29	r.	r.	NOUN
ejpam-6680	102	30	by	by	ADP
ejpam-6680	102	31	using	use	VERB
ejpam-6680	102	32	the	the	DET
ejpam-6680	102	33	concept	concept	NOUN
ejpam-6680	102	34	of	of	ADP
ejpam-6680	102	35	quasilinearization	quasilinearization	NOUN
ejpam-6680	102	36	,	,	PUNCT
ejpam-6680	102	37	authors	author	NOUN
ejpam-6680	102	38	in	in	ADP
ejpam-6680	102	39	[	[	X
ejpam-6680	102	40	38	38	NUM
ejpam-6680	102	41	]	]	PUNCT
ejpam-6680	102	42	extended	extend	VERB
ejpam-6680	102	43	the	the	DET
ejpam-6680	102	44	above	above	ADV
ejpam-6680	102	45	mentioned	mention	VERB
ejpam-6680	102	46	result	result	NOUN
ejpam-6680	102	47	in	in	ADP
ejpam-6680	102	48	cat	cat	NOUN
ejpam-6680	102	49	(	(	PUNCT
ejpam-6680	102	50	0	0	NUM
ejpam-6680	102	51	)	)	PUNCT
ejpam-6680	102	52	space	space	NOUN
ejpam-6680	102	53	that	that	PRON
ejpam-6680	102	54	is	be	AUX
ejpam-6680	102	55	as	as	SCONJ
ejpam-6680	102	56	follows	follow	VERB
ejpam-6680	102	57	:	:	PUNCT
ejpam-6680	102	58	theorem	theorem	NOUN
ejpam-6680	102	59	1	1	NUM
ejpam-6680	102	60	.	.	PUNCT
ejpam-6680	103	1	[	[	X
ejpam-6680	103	2	38	38	NUM
ejpam-6680	103	3	]	]	PUNCT
ejpam-6680	103	4	let	let	AUX
ejpam-6680	103	5	(	(	PUNCT
ejpam-6680	103	6	z	z	NOUN
ejpam-6680	103	7	,	,	PUNCT
ejpam-6680	103	8	ϱ	ϱ	PROPN
ejpam-6680	103	9	)	)	PUNCT
ejpam-6680	103	10	be	be	VERB
ejpam-6680	103	11	a	a	DET
ejpam-6680	103	12	complete	complete	ADJ
ejpam-6680	103	13	cat	cat	NOUN
ejpam-6680	103	14	(	(	PUNCT
ejpam-6680	103	15	0	0	NUM
ejpam-6680	103	16	)	)	PUNCT
ejpam-6680	103	17	space	space	NOUN
ejpam-6680	103	18	and	and	CCONJ
ejpam-6680	103	19	∅	∅	NOUN
ejpam-6680	103	20	̸=	̸=	PROPN
ejpam-6680	103	21	l	l	NOUN
ejpam-6680	103	22	⊆	⊆	NUM
ejpam-6680	103	23	z	z	NOUN
ejpam-6680	103	24	is	be	AUX
ejpam-6680	103	25	convex	convex	PROPN
ejpam-6680	103	26	.	.	PUNCT
ejpam-6680	104	1	then	then	ADV
ejpam-6680	104	2	w	w	PROPN
ejpam-6680	104	3	=	=	PROPN
ejpam-6680	104	4	plw2	plw2	PROPN
ejpam-6680	104	5	⇔	⇔	PROPN
ejpam-6680	104	6	⟨−−→w1w	⟨−−→w1w	PROPN
ejpam-6680	104	7	,	,	PUNCT
ejpam-6680	104	8	−−→ww2⟩	−−→ww2⟩	PRON
ejpam-6680	104	9	≥	≥	NUM
ejpam-6680	104	10	0	0	NUM
ejpam-6680	104	11	,	,	PUNCT
ejpam-6680	104	12	∀	∀	X
ejpam-6680	104	13	w1	w1	NOUN
ejpam-6680	104	14	∈	∈	PROPN
ejpam-6680	104	15	l	l	NOUN
ejpam-6680	104	16	,	,	PUNCT
ejpam-6680	104	17	w2	w2	NOUN
ejpam-6680	104	18	∈	∈	PROPN
ejpam-6680	104	19	z	z	PROPN
ejpam-6680	104	20	,	,	PUNCT
ejpam-6680	104	21	and	and	CCONJ
ejpam-6680	104	22	w	w	PROPN
ejpam-6680	104	23	∈	∈	PROPN
ejpam-6680	104	24	l.	l.	NOUN
ejpam-6680	104	25	in	in	ADP
ejpam-6680	104	26	the	the	DET
ejpam-6680	104	27	following	following	NOUN
ejpam-6680	104	28	,	,	PUNCT
ejpam-6680	104	29	(	(	PUNCT
ejpam-6680	104	30	y	y	NOUN
ejpam-6680	104	31	,	,	PUNCT
ejpam-6680	104	32	ϱ	ϱ	PROPN
ejpam-6680	104	33	)	)	PUNCT
ejpam-6680	104	34	and	and	CCONJ
ejpam-6680	104	35	(	(	PUNCT
ejpam-6680	104	36	z	z	NOUN
ejpam-6680	104	37	,	,	PUNCT
ejpam-6680	104	38	ϱ	ϱ	NOUN
ejpam-6680	104	39	)	)	PUNCT
ejpam-6680	104	40	will	will	AUX
ejpam-6680	104	41	represent	represent	VERB
ejpam-6680	104	42	cat	cat	NOUN
ejpam-6680	104	43	(	(	PUNCT
ejpam-6680	104	44	0	0	NUM
ejpam-6680	104	45	)	)	PUNCT
ejpam-6680	104	46	space	space	NOUN
ejpam-6680	104	47	and	and	CCONJ
ejpam-6680	104	48	complete	complete	ADJ
ejpam-6680	104	49	cat	cat	NOUN
ejpam-6680	104	50	(	(	PUNCT
ejpam-6680	104	51	0	0	NUM
ejpam-6680	104	52	)	)	PUNCT
ejpam-6680	104	53	space	space	NOUN
ejpam-6680	104	54	respectively	respectively	ADV
ejpam-6680	104	55	.	.	PUNCT
ejpam-6680	105	1	these	these	PRON
ejpam-6680	105	2	are	be	AUX
ejpam-6680	105	3	some	some	DET
ejpam-6680	105	4	lemma	lemma	PROPN
ejpam-6680	105	5	’s	’	VERB
ejpam-6680	105	6	taken	take	VERB
ejpam-6680	105	7	from	from	ADP
ejpam-6680	105	8	literature	literature	NOUN
ejpam-6680	105	9	which	which	PRON
ejpam-6680	105	10	are	be	AUX
ejpam-6680	105	11	helpful	helpful	ADJ
ejpam-6680	105	12	in	in	ADP
ejpam-6680	105	13	our	our	PRON
ejpam-6680	105	14	main	main	ADJ
ejpam-6680	105	15	results	result	NOUN
ejpam-6680	105	16	.	.	PUNCT
ejpam-6680	106	1	lemma	lemma	PROPN
ejpam-6680	106	2	2	2	NUM
ejpam-6680	106	3	.	.	PUNCT
ejpam-6680	107	1	[	[	X
ejpam-6680	107	2	39	39	NUM
ejpam-6680	107	3	]	]	PUNCT
ejpam-6680	107	4	let	let	VERB
ejpam-6680	107	5	u1	u1	NOUN
ejpam-6680	107	6	,	,	PUNCT
ejpam-6680	107	7	u2	u2	PROPN
ejpam-6680	107	8	,	,	PUNCT
ejpam-6680	107	9	u	u	NOUN
ejpam-6680	107	10	∈	∈	PROPN
ejpam-6680	107	11	y	y	PROPN
ejpam-6680	107	12	and	and	CCONJ
ejpam-6680	107	13	τ	τ	PROPN
ejpam-6680	107	14	∈	∈	PROPN
ejpam-6680	108	1	[	[	X
ejpam-6680	108	2	0	0	NUM
ejpam-6680	108	3	,	,	PUNCT
ejpam-6680	108	4	1	1	NUM
ejpam-6680	108	5	]	]	PUNCT
ejpam-6680	108	6	.	.	PUNCT
ejpam-6680	109	1	then	then	ADV
ejpam-6680	109	2	(	(	PUNCT
ejpam-6680	109	3	i	i	NOUN
ejpam-6680	109	4	)	)	PUNCT
ejpam-6680	109	5	ϱ(τu1	ϱ(τu1	PROPN
ejpam-6680	109	6	⊕	⊕	PROPN
ejpam-6680	109	7	(	(	PUNCT
ejpam-6680	109	8	1−	1−	NUM
ejpam-6680	109	9	τ)u2	τ)u2	NOUN
ejpam-6680	109	10	,	,	PUNCT
ejpam-6680	109	11	u	u	NOUN
ejpam-6680	109	12	)	)	PUNCT
ejpam-6680	109	13	≤	≤	NUM
ejpam-6680	109	14	τϱ(u1	τϱ(u1	NOUN
ejpam-6680	109	15	,	,	PUNCT
ejpam-6680	109	16	u	u	NOUN
ejpam-6680	109	17	)	)	PUNCT
ejpam-6680	109	18	+	+	CCONJ
ejpam-6680	109	19	(	(	PUNCT
ejpam-6680	109	20	1−	1−	NUM
ejpam-6680	109	21	τ)ϱ(u2	τ)ϱ(u2	NUM
ejpam-6680	109	22	,	,	PUNCT
ejpam-6680	109	23	u	u	NOUN
ejpam-6680	109	24	)	)	PUNCT
ejpam-6680	109	25	,	,	PUNCT
ejpam-6680	109	26	(	(	PUNCT
ejpam-6680	109	27	ii	ii	NOUN
ejpam-6680	109	28	)	)	PUNCT
ejpam-6680	109	29	ϱ2(τu1	ϱ2(τu1	VERB
ejpam-6680	109	30	⊕	⊕	PROPN
ejpam-6680	109	31	(	(	PUNCT
ejpam-6680	109	32	1−	1−	NUM
ejpam-6680	109	33	τ)u2	τ)u2	NOUN
ejpam-6680	109	34	,	,	PUNCT
ejpam-6680	109	35	u	u	NOUN
ejpam-6680	109	36	)	)	PUNCT
ejpam-6680	109	37	≤	≤	NOUN
ejpam-6680	109	38	τϱ2(u1	τϱ2(u1	ADJ
ejpam-6680	109	39	,	,	PUNCT
ejpam-6680	109	40	u	u	NOUN
ejpam-6680	109	41	)	)	PUNCT
ejpam-6680	110	1	+	+	CCONJ
ejpam-6680	110	2	(	(	PUNCT
ejpam-6680	110	3	1−	1−	NUM
ejpam-6680	110	4	τ)ϱ2(u2	τ)ϱ2(u2	PROPN
ejpam-6680	110	5	,	,	PUNCT
ejpam-6680	110	6	u)−	u)−	PROPN
ejpam-6680	110	7	τ(1−	τ(1−	ADJ
ejpam-6680	110	8	τ)ϱ2(u1	τ)ϱ2(u1	NOUN
ejpam-6680	110	9	,	,	PUNCT
ejpam-6680	110	10	u2	u2	PROPN
ejpam-6680	110	11	)	)	PUNCT
ejpam-6680	110	12	.	.	PUNCT
ejpam-6680	111	1	lemma	lemma	PROPN
ejpam-6680	111	2	3	3	X
ejpam-6680	111	3	.	.	PUNCT
ejpam-6680	112	1	[	[	X
ejpam-6680	112	2	39	39	NUM
ejpam-6680	112	3	]	]	PUNCT
ejpam-6680	112	4	let	let	VERB
ejpam-6680	112	5	u1	u1	NOUN
ejpam-6680	112	6	,	,	PUNCT
ejpam-6680	112	7	u2	u2	PROPN
ejpam-6680	112	8	,	,	PUNCT
ejpam-6680	112	9	u	u	NOUN
ejpam-6680	112	10	∈	∈	PROPN
ejpam-6680	112	11	y	y	PROPN
ejpam-6680	112	12	and	and	CCONJ
ejpam-6680	112	13	τ	τ	PROPN
ejpam-6680	112	14	∈	∈	PROPN
ejpam-6680	113	1	[	[	X
ejpam-6680	113	2	0	0	NUM
ejpam-6680	113	3	,	,	PUNCT
ejpam-6680	113	4	1	1	NUM
ejpam-6680	113	5	]	]	PUNCT
ejpam-6680	113	6	.	.	PUNCT
ejpam-6680	114	1	then	then	ADV
ejpam-6680	114	2	(	(	PUNCT
ejpam-6680	114	3	i	i	NOUN
ejpam-6680	114	4	)	)	PUNCT
ejpam-6680	114	5	ϱ(τu1	ϱ(τu1	PROPN
ejpam-6680	114	6	⊕	⊕	PROPN
ejpam-6680	114	7	(	(	PUNCT
ejpam-6680	114	8	1−	1−	NUM
ejpam-6680	114	9	τ)u2	τ)u2	NOUN
ejpam-6680	114	10	,	,	PUNCT
ejpam-6680	114	11	γu1	γu1	PROPN
ejpam-6680	114	12	⊕	⊕	PROPN
ejpam-6680	114	13	(	(	PUNCT
ejpam-6680	114	14	1−	1−	NUM
ejpam-6680	114	15	γ)u2	γ)u2	PROPN
ejpam-6680	114	16	)	)	PUNCT
ejpam-6680	114	17	=	=	SYM
ejpam-6680	114	18	|τ	|τ	ADJ
ejpam-6680	114	19	−	−	NOUN
ejpam-6680	114	20	γ|ϱ(u1	γ|ϱ(u1	NOUN
ejpam-6680	114	21	,	,	PUNCT
ejpam-6680	114	22	u2	u2	PROPN
ejpam-6680	114	23	)	)	PUNCT
ejpam-6680	114	24	,	,	PUNCT
ejpam-6680	114	25	m.	m.	NOUN
ejpam-6680	114	26	rashid	rashid	PROPN
ejpam-6680	114	27	et	et	PROPN
ejpam-6680	114	28	al	al	PROPN
ejpam-6680	114	29	.	.	PUNCT
ejpam-6680	114	30	/	/	SYM
ejpam-6680	114	31	eur	eur	PROPN
ejpam-6680	114	32	.	.	PUNCT
ejpam-6680	115	1	j.	j.	PROPN
ejpam-6680	115	2	pure	pure	PROPN
ejpam-6680	115	3	appl	appl	PROPN
ejpam-6680	115	4	.	.	PROPN
ejpam-6680	115	5	math	math	PROPN
ejpam-6680	115	6	,	,	PUNCT
ejpam-6680	115	7	18	18	NUM
ejpam-6680	115	8	(	(	PUNCT
ejpam-6680	115	9	4	4	NUM
ejpam-6680	115	10	)	)	PUNCT
ejpam-6680	115	11	(	(	PUNCT
ejpam-6680	115	12	2025	2025	NUM
ejpam-6680	115	13	)	)	PUNCT
ejpam-6680	115	14	,	,	PUNCT
ejpam-6680	115	15	6680	6680	NUM
ejpam-6680	115	16	6	6	NUM
ejpam-6680	115	17	of	of	ADP
ejpam-6680	115	18	24	24	NUM
ejpam-6680	115	19	(	(	PUNCT
ejpam-6680	115	20	ii	ii	NOUN
ejpam-6680	115	21	)	)	PUNCT
ejpam-6680	115	22	ϱ(τu1	ϱ(τu1	PROPN
ejpam-6680	115	23	⊕	⊕	PROPN
ejpam-6680	115	24	(	(	PUNCT
ejpam-6680	115	25	1−	1−	NUM
ejpam-6680	115	26	τ)u2	τ)u2	NOUN
ejpam-6680	115	27	,	,	PUNCT
ejpam-6680	115	28	τu1	τu1	X
ejpam-6680	115	29	⊕	⊕	PROPN
ejpam-6680	115	30	(	(	PUNCT
ejpam-6680	115	31	1−	1−	NUM
ejpam-6680	115	32	τ)q	τ)q	NOUN
ejpam-6680	115	33	)	)	PUNCT
ejpam-6680	115	34	≤	≤	NOUN
ejpam-6680	115	35	(	(	PUNCT
ejpam-6680	115	36	1−	1−	NUM
ejpam-6680	115	37	τ)ϱ(u2	τ)ϱ(u2	NUM
ejpam-6680	115	38	,	,	PUNCT
ejpam-6680	115	39	u	u	NOUN
ejpam-6680	115	40	)	)	PUNCT
ejpam-6680	115	41	.	.	PUNCT
ejpam-6680	116	1	lemma	lemma	PROPN
ejpam-6680	116	2	4	4	NUM
ejpam-6680	116	3	.	.	PUNCT
ejpam-6680	117	1	[	[	X
ejpam-6680	117	2	40	40	NUM
ejpam-6680	117	3	]	]	PUNCT
ejpam-6680	117	4	in	in	ADP
ejpam-6680	117	5	(	(	PUNCT
ejpam-6680	117	6	z	z	NOUN
ejpam-6680	117	7	,	,	PUNCT
ejpam-6680	117	8	ϱ	ϱ	NOUN
ejpam-6680	117	9	)	)	PUNCT
ejpam-6680	117	10	space	space	NOUN
ejpam-6680	117	11	,	,	PUNCT
ejpam-6680	117	12	every	every	DET
ejpam-6680	117	13	bounded	bounded	ADJ
ejpam-6680	117	14	sequence	sequence	NOUN
ejpam-6680	117	15	always	always	ADV
ejpam-6680	117	16	has	have	VERB
ejpam-6680	117	17	a	a	DET
ejpam-6680	117	18	∆-convergent	∆-convergent	ADJ
ejpam-6680	117	19	subsequence	subsequence	NOUN
ejpam-6680	117	20	.	.	PUNCT
ejpam-6680	118	1	lemma	lemma	PROPN
ejpam-6680	118	2	5	5	NUM
ejpam-6680	118	3	.	.	PUNCT
ejpam-6680	119	1	[	[	X
ejpam-6680	119	2	41	41	NUM
ejpam-6680	119	3	]	]	PUNCT
ejpam-6680	119	4	assume	assume	VERB
ejpam-6680	119	5	{	{	PUNCT
ejpam-6680	119	6	ℵn	ℵn	NOUN
ejpam-6680	119	7	}	}	PUNCT
ejpam-6680	119	8	,	,	PUNCT
ejpam-6680	119	9	{	{	PUNCT
ejpam-6680	119	10	ℑn	ℑn	PROPN
ejpam-6680	119	11	}	}	PUNCT
ejpam-6680	119	12	,	,	PUNCT
ejpam-6680	119	13	{	{	PUNCT
ejpam-6680	119	14	cn	cn	NOUN
ejpam-6680	119	15	}	}	PUNCT
ejpam-6680	119	16	and	and	CCONJ
ejpam-6680	119	17	{	{	PUNCT
ejpam-6680	119	18	σn	σn	NOUN
ejpam-6680	119	19	}	}	PUNCT
ejpam-6680	119	20	be	be	AUX
ejpam-6680	119	21	nonnegative	nonnegative	ADJ
ejpam-6680	119	22	sequences	sequence	NOUN
ejpam-6680	120	1	such	such	ADJ
ejpam-6680	120	2	that	that	DET
ejpam-6680	120	3	ℵn+1	ℵn+1	NOUN
ejpam-6680	120	4	≤	≤	NOUN
ejpam-6680	120	5	(	(	PUNCT
ejpam-6680	120	6	1−	1−	NUM
ejpam-6680	120	7	σn)ℵn	σn)ℵn	PUNCT
ejpam-6680	120	8	+	+	NUM
ejpam-6680	121	1	σnℑn	σnℑn	PROPN
ejpam-6680	121	2	+	+	CCONJ
ejpam-6680	121	3	cn	cn	PROPN
ejpam-6680	121	4	,	,	PUNCT
ejpam-6680	121	5	n	n	PRON
ejpam-6680	121	6	≥	≥	NOUN
ejpam-6680	121	7	0	0	NUM
ejpam-6680	121	8	with	with	ADP
ejpam-6680	121	9	{	{	PUNCT
ejpam-6680	121	10	σn	σn	X
ejpam-6680	121	11	}	}	PUNCT
ejpam-6680	121	12	⊂	⊂	PROPN
ejpam-6680	122	1	[	[	X
ejpam-6680	122	2	0	0	NUM
ejpam-6680	122	3	,	,	PUNCT
ejpam-6680	122	4	1],σ∞	1],σ∞	NUM
ejpam-6680	122	5	n	n	CCONJ
ejpam-6680	122	6	=	=	PRON
ejpam-6680	122	7	oσn	oσn	NOUN
ejpam-6680	122	8	=	=	SYM
ejpam-6680	122	9	∞	∞	PROPN
ejpam-6680	122	10	,	,	PUNCT
ejpam-6680	122	11	limn→∞ℑn	limn→∞ℑn	ADJ
ejpam-6680	122	12	=	=	SYM
ejpam-6680	122	13	0	0	NUM
ejpam-6680	122	14	and	and	CCONJ
ejpam-6680	122	15	σ∞n=0cn	σ∞n=0cn	NUM
ejpam-6680	122	16	<	<	X
ejpam-6680	122	17	∞.	∞.	PROPN
ejpam-6680	122	18	then	then	ADV
ejpam-6680	122	19	limn→∞	limn→∞	X
ejpam-6680	122	20	ℵn	ℵn	NOUN
ejpam-6680	122	21	=	=	SYM
ejpam-6680	122	22	0	0	PROPN
ejpam-6680	122	23	.	.	PUNCT
ejpam-6680	123	1	lemma	lemma	PROPN
ejpam-6680	123	2	6	6	NUM
ejpam-6680	123	3	.	.	PUNCT
ejpam-6680	124	1	[	[	X
ejpam-6680	124	2	42	42	NUM
ejpam-6680	124	3	]	]	PUNCT
ejpam-6680	124	4	for	for	ADP
ejpam-6680	124	5	(	(	PUNCT
ejpam-6680	124	6	z	z	NOUN
ejpam-6680	124	7	,	,	PUNCT
ejpam-6680	124	8	ϱ	ϱ	PROPN
ejpam-6680	124	9	)	)	PUNCT
ejpam-6680	124	10	,	,	PUNCT
ejpam-6680	124	11	the	the	DET
ejpam-6680	124	12	inequality	inequality	NOUN
ejpam-6680	124	13	stated	state	VERB
ejpam-6680	124	14	below	below	ADV
ejpam-6680	124	15	holds	hold	VERB
ejpam-6680	124	16	ϱ2(u	ϱ2(u	PROPN
ejpam-6680	124	17	,	,	PUNCT
ejpam-6680	124	18	w	w	NOUN
ejpam-6680	124	19	)	)	PUNCT
ejpam-6680	124	20	≤	≤	NOUN
ejpam-6680	124	21	ϱ2(r	ϱ2(r	PROPN
ejpam-6680	124	22	,	,	PUNCT
ejpam-6680	124	23	w	w	NOUN
ejpam-6680	124	24	)	)	PUNCT
ejpam-6680	124	25	+	+	CCONJ
ejpam-6680	125	1	2⟨−→ur,−→uw⟩	2⟨−→ur,−→uw⟩	NUM
ejpam-6680	125	2	,	,	PUNCT
ejpam-6680	125	3	∀	∀	X
ejpam-6680	125	4	u	u	NOUN
ejpam-6680	125	5	,	,	PUNCT
ejpam-6680	125	6	r	r	NOUN
ejpam-6680	125	7	,	,	PUNCT
ejpam-6680	125	8	w	w	PROPN
ejpam-6680	125	9	∈	∈	PROPN
ejpam-6680	125	10	z.	z.	PROPN
ejpam-6680	125	11	lemma	lemma	PROPN
ejpam-6680	126	1	7	7	X
ejpam-6680	126	2	.	.	PUNCT
ejpam-6680	127	1	[	[	X
ejpam-6680	127	2	42	42	NUM
ejpam-6680	127	3	]	]	PUNCT
ejpam-6680	127	4	for	for	ADP
ejpam-6680	127	5	any	any	DET
ejpam-6680	127	6	ℓ	ℓ	PROPN
ejpam-6680	127	7	∈	∈	PROPN
ejpam-6680	127	8	(	(	PUNCT
ejpam-6680	127	9	0	0	NUM
ejpam-6680	127	10	,	,	PUNCT
ejpam-6680	127	11	1	1	NUM
ejpam-6680	127	12	)	)	PUNCT
ejpam-6680	127	13	and	and	CCONJ
ejpam-6680	127	14	s	s	PROPN
ejpam-6680	127	15	,	,	PUNCT
ejpam-6680	127	16	t	t	PROPN
ejpam-6680	127	17	∈	∈	PROPN
ejpam-6680	127	18	y	y	PROPN
ejpam-6680	127	19	,	,	PUNCT
ejpam-6680	127	20	assume	assume	VERB
ejpam-6680	127	21	sℓ	sℓ	NOUN
ejpam-6680	127	22	=	=	NOUN
ejpam-6680	127	23	ℓs⊕	ℓs⊕	X
ejpam-6680	127	24	(	(	PUNCT
ejpam-6680	127	25	1−	1−	NUM
ejpam-6680	127	26	ℓ)t	ℓ)t	X
ejpam-6680	127	27	.	.	PUNCT
ejpam-6680	128	1	then	then	ADV
ejpam-6680	128	2	,	,	PUNCT
ejpam-6680	128	3	for	for	ADP
ejpam-6680	128	4	all	all	DET
ejpam-6680	128	5	u	u	NOUN
ejpam-6680	128	6	,	,	PUNCT
ejpam-6680	128	7	v	v	PROPN
ejpam-6680	128	8	∈	∈	PROPN
ejpam-6680	128	9	y	y	PROPN
ejpam-6680	128	10	,	,	PUNCT
ejpam-6680	128	11	(	(	PUNCT
ejpam-6680	128	12	i	i	NOUN
ejpam-6680	128	13	)	)	PUNCT
ejpam-6680	128	14	⟨−→sℓu,−→sℓv⟩	⟨−→sℓu,−→sℓv⟩	PUNCT
ejpam-6680	129	1	≤	≤	NUM
ejpam-6680	129	2	ℓ⟨−→su,−→sℓv⟩+	ℓ⟨−→su,−→sℓv⟩+	NOUN
ejpam-6680	129	3	(	(	PUNCT
ejpam-6680	129	4	1−	1−	NUM
ejpam-6680	129	5	ℓ)⟨−→tu,−→sℓv⟩	ℓ)⟨−→tu,−→sℓv⟩	NOUN
ejpam-6680	129	6	(	(	PUNCT
ejpam-6680	129	7	ii	ii	NOUN
ejpam-6680	129	8	)	)	PUNCT
ejpam-6680	129	9	⟨−→sℓu,−→sv⟩	⟨−→sℓu,−→sv⟩	VERB
ejpam-6680	129	10	≤	≤	NUM
ejpam-6680	129	11	ℓ⟨−→su,−→sv⟩+	ℓ⟨−→su,−→sv⟩+	PUNCT
ejpam-6680	129	12	(	(	PUNCT
ejpam-6680	129	13	1−	1−	NUM
ejpam-6680	129	14	ℓ)⟨−→tu,−→sv⟩	ℓ)⟨−→tu,−→sv⟩	PROPN
ejpam-6680	129	15	and	and	CCONJ
ejpam-6680	129	16	⟨−→sℓu	⟨−→sℓu	PROPN
ejpam-6680	129	17	,	,	PUNCT
ejpam-6680	129	18	−→	−→	ADJ
ejpam-6680	129	19	tv⟩	tv⟩	X
ejpam-6680	129	20	≤	≤	NOUN
ejpam-6680	129	21	ℓ⟨−→su,−→tv⟩+	ℓ⟨−→su,−→tv⟩+	PUNCT
ejpam-6680	129	22	(	(	PUNCT
ejpam-6680	129	23	1−	1−	NUM
ejpam-6680	129	24	ℓ)⟨−→tu,−→tv⟩.	ℓ)⟨−→tu,−→tv⟩.	PROPN
ejpam-6680	129	25	lemma	lemma	PROPN
ejpam-6680	129	26	8	8	NUM
ejpam-6680	129	27	.	.	PUNCT
ejpam-6680	130	1	[	[	X
ejpam-6680	130	2	43	43	NUM
ejpam-6680	130	3	]	]	PUNCT
ejpam-6680	130	4	assume	assume	VERB
ejpam-6680	130	5	a	a	DET
ejpam-6680	130	6	non	non	ADJ
ejpam-6680	130	7	-	-	ADJ
ejpam-6680	130	8	negative	negative	ADJ
ejpam-6680	130	9	sequence	sequence	NOUN
ejpam-6680	130	10	{	{	PUNCT
ejpam-6680	130	11	bn	bn	NOUN
ejpam-6680	130	12	}	}	PUNCT
ejpam-6680	130	13	of	of	ADP
ejpam-6680	130	14	real	real	ADJ
ejpam-6680	130	15	numbers	number	NOUN
ejpam-6680	130	16	,	,	PUNCT
ejpam-6680	130	17	such	such	ADJ
ejpam-6680	130	18	that	that	SCONJ
ejpam-6680	130	19	there	there	PRON
ejpam-6680	130	20	exist	exist	VERB
ejpam-6680	130	21	a	a	DET
ejpam-6680	130	22	subsequence	subsequence	NOUN
ejpam-6680	130	23	{	{	PUNCT
ejpam-6680	130	24	bnl	bnl	PROPN
ejpam-6680	130	25	}	}	PUNCT
ejpam-6680	130	26	of	of	ADP
ejpam-6680	130	27	the	the	DET
ejpam-6680	130	28	sequence	sequence	NOUN
ejpam-6680	130	29	{	{	PUNCT
ejpam-6680	130	30	bn	bn	ADP
ejpam-6680	130	31	}	}	PUNCT
ejpam-6680	130	32	satisfying	satisfy	VERB
ejpam-6680	130	33	bnl	bnl	PROPN
ejpam-6680	130	34	<	<	X
ejpam-6680	130	35	bnl+1	bnl+1	PROPN
ejpam-6680	130	36	,	,	PUNCT
ejpam-6680	130	37	for	for	ADP
ejpam-6680	130	38	all	all	DET
ejpam-6680	130	39	l	l	NOUN
ejpam-6680	130	40	∈	∈	PROPN
ejpam-6680	130	41	n.	n.	NOUN
ejpam-6680	130	42	so	so	SCONJ
ejpam-6680	130	43	there	there	PRON
ejpam-6680	130	44	is	be	VERB
ejpam-6680	130	45	a	a	DET
ejpam-6680	130	46	non	non	ADJ
ejpam-6680	130	47	-	-	ADJ
ejpam-6680	130	48	decreasing	decrease	VERB
ejpam-6680	130	49	sequence	sequence	NOUN
ejpam-6680	130	50	{	{	PUNCT
ejpam-6680	130	51	ak	ak	NOUN
ejpam-6680	130	52	}	}	PUNCT
ejpam-6680	130	53	of	of	ADP
ejpam-6680	130	54	natural	natural	ADJ
ejpam-6680	130	55	numbers	number	NOUN
ejpam-6680	130	56	in	in	ADP
ejpam-6680	130	57	such	such	DET
ejpam-6680	130	58	a	a	DET
ejpam-6680	130	59	way	way	NOUN
ejpam-6680	130	60	that	that	PRON
ejpam-6680	130	61	ak	ak	PROPN
ejpam-6680	130	62	→	→	SYM
ejpam-6680	130	63	∞	∞	PROPN
ejpam-6680	130	64	as	as	ADP
ejpam-6680	130	65	k	k	PROPN
ejpam-6680	130	66	→	→	SYM
ejpam-6680	130	67	∞	∞	PROPN
ejpam-6680	130	68	,	,	PUNCT
ejpam-6680	130	69	and	and	CCONJ
ejpam-6680	130	70	for	for	ADP
ejpam-6680	130	71	all	all	DET
ejpam-6680	130	72	k	k	PROPN
ejpam-6680	130	73	∈	∈	PROPN
ejpam-6680	130	74	n	n	AUX
ejpam-6680	130	75	satisfy	satisfy	VERB
ejpam-6680	130	76	the	the	DET
ejpam-6680	130	77	conditions	condition	NOUN
ejpam-6680	130	78	stated	state	VERB
ejpam-6680	130	79	below	below	ADV
ejpam-6680	130	80	:	:	PUNCT
ejpam-6680	130	81	bak	bak	VERB
ejpam-6680	130	82	≤	≤	NOUN
ejpam-6680	130	83	bak+1	bak+1	NOUN
ejpam-6680	130	84	and	and	CCONJ
ejpam-6680	130	85	bk	bk	VERB
ejpam-6680	130	86	≤	≤	NOUN
ejpam-6680	130	87	bak+1	bak+1	NOUN
ejpam-6680	130	88	.	.	PUNCT
ejpam-6680	131	1	indeed	indeed	ADV
ejpam-6680	131	2	,	,	PUNCT
ejpam-6680	131	3	ak	ak	PROPN
ejpam-6680	131	4	=	=	PUNCT
ejpam-6680	131	5	max{l	max{l	NOUN
ejpam-6680	131	6	≤	≤	NUM
ejpam-6680	132	1	k	k	PROPN
ejpam-6680	132	2	:	:	PUNCT
ejpam-6680	133	1	bl	bl	PROPN
ejpam-6680	133	2	≤	≤	NUM
ejpam-6680	133	3	bl+1	bl+1	NOUN
ejpam-6680	133	4	}	}	PUNCT
ejpam-6680	133	5	.	.	PUNCT
ejpam-6680	134	1	lemma	lemma	PROPN
ejpam-6680	134	2	9	9	NUM
ejpam-6680	134	3	.	.	PUNCT
ejpam-6680	135	1	[	[	X
ejpam-6680	135	2	44	44	NUM
ejpam-6680	135	3	]	]	PUNCT
ejpam-6680	135	4	consider	consider	VERB
ejpam-6680	135	5	a	a	DET
ejpam-6680	135	6	sequence	sequence	NOUN
ejpam-6680	135	7	{	{	PUNCT
ejpam-6680	135	8	bn	bn	NOUN
ejpam-6680	135	9	}	}	PUNCT
ejpam-6680	135	10	∈	∈	PROPN
ejpam-6680	135	11	z	z	NOUN
ejpam-6680	135	12	and	and	CCONJ
ejpam-6680	135	13	if	if	SCONJ
ejpam-6680	135	14	a	a	DET
ejpam-6680	135	15	nonempty	nonempty	NOUN
ejpam-6680	135	16	subset	subset	VERB
ejpam-6680	135	17	l	l	NOUN
ejpam-6680	135	18	⊆	⊆	NUM
ejpam-6680	135	19	z	z	VERB
ejpam-6680	135	20	satisfying	satisfy	VERB
ejpam-6680	135	21	the	the	DET
ejpam-6680	135	22	following	follow	VERB
ejpam-6680	135	23	conditions	condition	NOUN
ejpam-6680	135	24	:	:	PUNCT
ejpam-6680	135	25	(	(	PUNCT
ejpam-6680	135	26	i	i	NOUN
ejpam-6680	135	27	)	)	PUNCT
ejpam-6680	135	28	for	for	ADP
ejpam-6680	135	29	every	every	DET
ejpam-6680	135	30	ω	ω	PROPN
ejpam-6680	135	31	∈	∈	PROPN
ejpam-6680	135	32	l	l	NOUN
ejpam-6680	135	33	,	,	PUNCT
ejpam-6680	135	34	limn→∞	limn→∞	PROPN
ejpam-6680	135	35	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	135	36	,	,	PUNCT
ejpam-6680	135	37	ω	ω	NOUN
ejpam-6680	135	38	)	)	PUNCT
ejpam-6680	135	39	exists	exist	VERB
ejpam-6680	135	40	;	;	PUNCT
ejpam-6680	135	41	(	(	PUNCT
ejpam-6680	135	42	ii	ii	NOUN
ejpam-6680	135	43	)	)	PUNCT
ejpam-6680	135	44	if	if	SCONJ
ejpam-6680	135	45	{	{	PUNCT
ejpam-6680	135	46	bnj	bnj	NOUN
ejpam-6680	135	47	}	}	PUNCT
ejpam-6680	135	48	is	be	AUX
ejpam-6680	135	49	a	a	DET
ejpam-6680	135	50	subsequence	subsequence	NOUN
ejpam-6680	135	51	of	of	ADP
ejpam-6680	135	52	{	{	PUNCT
ejpam-6680	135	53	bn	bn	NOUN
ejpam-6680	135	54	}	}	PUNCT
ejpam-6680	135	55	which	which	PRON
ejpam-6680	135	56	is	be	AUX
ejpam-6680	135	57	∆-convergent	∆-convergent	ADJ
ejpam-6680	135	58	to	to	ADP
ejpam-6680	135	59	v	v	NOUN
ejpam-6680	135	60	,	,	PUNCT
ejpam-6680	135	61	then	then	ADV
ejpam-6680	135	62	v	v	X
ejpam-6680	135	63	∈	∈	PROPN
ejpam-6680	135	64	l.	l.	NOUN
ejpam-6680	135	65	then	then	ADV
ejpam-6680	135	66	{	{	PUNCT
ejpam-6680	135	67	bn	bn	NOUN
ejpam-6680	135	68	}	}	PUNCT
ejpam-6680	135	69	∆-converges	∆-converge	NOUN
ejpam-6680	135	70	to	to	ADP
ejpam-6680	135	71	an	an	DET
ejpam-6680	135	72	element	element	NOUN
ejpam-6680	135	73	of	of	ADP
ejpam-6680	135	74	l.	l.	PROPN
ejpam-6680	135	75	m.	m.	PROPN
ejpam-6680	135	76	rashid	rashid	PROPN
ejpam-6680	135	77	et	et	PROPN
ejpam-6680	135	78	al	al	PROPN
ejpam-6680	135	79	.	.	PUNCT
ejpam-6680	135	80	/	/	SYM
ejpam-6680	135	81	eur	eur	PROPN
ejpam-6680	135	82	.	.	PUNCT
ejpam-6680	136	1	j.	j.	PROPN
ejpam-6680	136	2	pure	pure	PROPN
ejpam-6680	136	3	appl	appl	PROPN
ejpam-6680	136	4	.	.	PROPN
ejpam-6680	136	5	math	math	PROPN
ejpam-6680	136	6	,	,	PUNCT
ejpam-6680	136	7	18	18	NUM
ejpam-6680	136	8	(	(	PUNCT
ejpam-6680	136	9	4	4	NUM
ejpam-6680	136	10	)	)	PUNCT
ejpam-6680	136	11	(	(	PUNCT
ejpam-6680	136	12	2025	2025	NUM
ejpam-6680	136	13	)	)	PUNCT
ejpam-6680	136	14	,	,	PUNCT
ejpam-6680	136	15	6680	6680	NUM
ejpam-6680	136	16	7	7	NUM
ejpam-6680	136	17	of	of	ADP
ejpam-6680	136	18	24	24	NUM
ejpam-6680	136	19	3	3	NUM
ejpam-6680	136	20	.	.	PUNCT
ejpam-6680	136	21	variational	variational	ADJ
ejpam-6680	136	22	inequality	inequality	NOUN
ejpam-6680	136	23	and	and	CCONJ
ejpam-6680	136	24	some	some	DET
ejpam-6680	136	25	crucial	crucial	ADJ
ejpam-6680	136	26	lemmas	lemma	NOUN
ejpam-6680	136	27	in	in	ADP
ejpam-6680	136	28	this	this	DET
ejpam-6680	136	29	section	section	NOUN
ejpam-6680	136	30	we	we	PRON
ejpam-6680	136	31	introduce	introduce	VERB
ejpam-6680	136	32	variational	variational	ADJ
ejpam-6680	136	33	inequality	inequality	NOUN
ejpam-6680	136	34	and	and	CCONJ
ejpam-6680	136	35	several	several	ADJ
ejpam-6680	136	36	lemmas	lemma	NOUN
ejpam-6680	136	37	which	which	PRON
ejpam-6680	136	38	are	be	AUX
ejpam-6680	136	39	essential	essential	ADJ
ejpam-6680	136	40	for	for	ADP
ejpam-6680	136	41	our	our	PRON
ejpam-6680	136	42	main	main	ADJ
ejpam-6680	136	43	results	result	NOUN
ejpam-6680	136	44	.	.	PUNCT
ejpam-6680	137	1	consider	consider	VERB
ejpam-6680	137	2	a	a	DET
ejpam-6680	137	3	closed	closed	ADJ
ejpam-6680	137	4	,	,	PUNCT
ejpam-6680	137	5	convex	convex	NOUN
ejpam-6680	137	6	subset	subset	NOUN
ejpam-6680	137	7	l	l	NOUN
ejpam-6680	137	8	⊆	⊆	NUM
ejpam-6680	137	9	z	z	NUM
ejpam-6680	137	10	,	,	PUNCT
ejpam-6680	137	11	and	and	CCONJ
ejpam-6680	137	12	define	define	VERB
ejpam-6680	137	13	a	a	DET
ejpam-6680	137	14	map	map	NOUN
ejpam-6680	137	15	a1	a1	NOUN
ejpam-6680	137	16	:	:	PUNCT
ejpam-6680	137	17	l	l	NOUN
ejpam-6680	137	18	→	→	SYM
ejpam-6680	137	19	z∗	z∗	PROPN
ejpam-6680	137	20	,	,	PUNCT
ejpam-6680	137	21	a2	a2	PROPN
ejpam-6680	137	22	:	:	PUNCT
ejpam-6680	137	23	z∗	z∗	PROPN
ejpam-6680	137	24	→	→	SYM
ejpam-6680	137	25	l	l	NOUN
ejpam-6680	137	26	and	and	CCONJ
ejpam-6680	137	27	a	a	DET
ejpam-6680	137	28	:	:	PUNCT
ejpam-6680	137	29	l	l	NOUN
ejpam-6680	137	30	→	→	SYM
ejpam-6680	137	31	l.	l.	PROPN
ejpam-6680	137	32	finding	find	VERB
ejpam-6680	137	33	a	a	DET
ejpam-6680	137	34	point	point	NOUN
ejpam-6680	137	35	w∗	w∗	NOUN
ejpam-6680	137	36	∈	∈	PROPN
ejpam-6680	137	37	l	l	NOUN
ejpam-6680	137	38	such	such	ADJ
ejpam-6680	137	39	that	that	PRON
ejpam-6680	137	40	⟨	⟨	X
ejpam-6680	137	41	−−−−→	−−−−→	PUNCT
ejpam-6680	137	42	waw∗	waw∗	NOUN
ejpam-6680	137	43	,	,	PUNCT
ejpam-6680	137	44	−−→	−−→	X
ejpam-6680	137	45	ww∗⟩	ww∗⟩	NOUN
ejpam-6680	137	46	≥	≥	NUM
ejpam-6680	137	47	0	0	NUM
ejpam-6680	137	48	,	,	PUNCT
ejpam-6680	137	49	for	for	ADP
ejpam-6680	137	50	all	all	DET
ejpam-6680	137	51	w	w	PROPN
ejpam-6680	137	52	∈	∈	PROPN
ejpam-6680	137	53	l.	l.	NOUN
ejpam-6680	137	54	(	(	PUNCT
ejpam-6680	137	55	3	3	NUM
ejpam-6680	137	56	)	)	PUNCT
ejpam-6680	137	57	problem	problem	NOUN
ejpam-6680	137	58	(	(	PUNCT
ejpam-6680	137	59	3	3	X
ejpam-6680	137	60	)	)	PUNCT
ejpam-6680	137	61	is	be	AUX
ejpam-6680	137	62	referred	refer	VERB
ejpam-6680	137	63	as	as	ADP
ejpam-6680	137	64	variational	variational	ADJ
ejpam-6680	137	65	inequality	inequality	NOUN
ejpam-6680	137	66	and	and	CCONJ
ejpam-6680	137	67	denoted	denote	VERB
ejpam-6680	137	68	by	by	ADP
ejpam-6680	137	69	v	v	ADP
ejpam-6680	137	70	i(l	i(l	PROPN
ejpam-6680	137	71	,	,	PUNCT
ejpam-6680	137	72	a	a	PRON
ejpam-6680	137	73	)	)	PUNCT
ejpam-6680	137	74	.	.	PUNCT
ejpam-6680	138	1	definition	definition	NOUN
ejpam-6680	138	2	6	6	NUM
ejpam-6680	138	3	.	.	PUNCT
ejpam-6680	139	1	the	the	DET
ejpam-6680	139	2	map	map	NOUN
ejpam-6680	139	3	a	a	DET
ejpam-6680	139	4	:	:	PUNCT
ejpam-6680	139	5	l	l	NOUN
ejpam-6680	139	6	→	→	PUNCT
ejpam-6680	139	7	l	l	NOUN
ejpam-6680	139	8	is	be	AUX
ejpam-6680	139	9	known	know	VERB
ejpam-6680	139	10	as	as	ADP
ejpam-6680	139	11	(	(	PUNCT
ejpam-6680	139	12	i	i	NOUN
ejpam-6680	139	13	)	)	PUNCT
ejpam-6680	139	14	monotone	monotone	ADJ
ejpam-6680	139	15	if	if	SCONJ
ejpam-6680	139	16	⟨	⟨	VERB
ejpam-6680	139	17	−−−−−−→	−−−−−−→	X
ejpam-6680	139	18	aw1aw2	aw1aw2	PROPN
ejpam-6680	139	19	,	,	PUNCT
ejpam-6680	139	20	−−−→w1w2⟩	−−−→w1w2⟩	PRON
ejpam-6680	139	21	≥	≥	NOUN
ejpam-6680	139	22	0	0	NUM
ejpam-6680	139	23	,	,	PUNCT
ejpam-6680	139	24	∀	∀	X
ejpam-6680	139	25	w1	w1	NOUN
ejpam-6680	139	26	,	,	PUNCT
ejpam-6680	139	27	w2	w2	NOUN
ejpam-6680	139	28	∈	∈	PROPN
ejpam-6680	139	29	l.	l.	PROPN
ejpam-6680	139	30	(	(	PUNCT
ejpam-6680	139	31	ii	ii	NOUN
ejpam-6680	139	32	)	)	PUNCT
ejpam-6680	139	33	pseudo	pseudo	NOUN
ejpam-6680	139	34	-	-	NOUN
ejpam-6680	139	35	monotone	monotone	ADJ
ejpam-6680	139	36	if	if	SCONJ
ejpam-6680	139	37	⟨	⟨	VERB
ejpam-6680	139	38	−−−−→	−−−−→	X
ejpam-6680	139	39	w1aw	w1aw	X
ejpam-6680	139	40	∗	∗	PROPN
ejpam-6680	139	41	1	1	NUM
ejpam-6680	139	42	,	,	PUNCT
ejpam-6680	139	43	−−−→	−−−→	PROPN
ejpam-6680	139	44	w1w	w1w	PROPN
ejpam-6680	139	45	∗	∗	NOUN
ejpam-6680	139	46	1⟩	1⟩	NUM
ejpam-6680	139	47	≥	≥	NOUN
ejpam-6680	139	48	0	0	NUM
ejpam-6680	139	49	⇒	⇒	PROPN
ejpam-6680	139	50	⟨	⟨	VERB
ejpam-6680	139	51	−−−−→	−−−−→	X
ejpam-6680	139	52	w∗	w∗	PROPN
ejpam-6680	139	53	1aw1	1aw1	NUM
ejpam-6680	139	54	,	,	PUNCT
ejpam-6680	139	55	−−−→	−−−→	ADJ
ejpam-6680	139	56	w∗	w∗	NOUN
ejpam-6680	139	57	1w1⟩	1w1⟩	NUM
ejpam-6680	139	58	≥	≥	NOUN
ejpam-6680	139	59	0	0	NUM
ejpam-6680	139	60	,	,	PUNCT
ejpam-6680	139	61	∀	∀	X
ejpam-6680	139	62	w1	w1	NOUN
ejpam-6680	139	63	,	,	PUNCT
ejpam-6680	139	64	w	w	PROPN
ejpam-6680	139	65	∗	∗	NOUN
ejpam-6680	139	66	1	1	NUM
ejpam-6680	139	67	∈	∈	PROPN
ejpam-6680	139	68	l.	l.	NOUN
ejpam-6680	139	69	definition	definition	NOUN
ejpam-6680	139	70	7	7	NUM
ejpam-6680	139	71	.	.	PUNCT
ejpam-6680	139	72	consider	consider	VERB
ejpam-6680	139	73	the	the	DET
ejpam-6680	139	74	space	space	NOUN
ejpam-6680	139	75	(	(	PUNCT
ejpam-6680	139	76	z	z	NOUN
ejpam-6680	139	77	,	,	PUNCT
ejpam-6680	139	78	ϱ	ϱ	NOUN
ejpam-6680	139	79	)	)	PUNCT
ejpam-6680	139	80	.	.	PUNCT
ejpam-6680	140	1	for	for	ADP
ejpam-6680	140	2	α	α	PROPN
ejpam-6680	140	3	>	>	X
ejpam-6680	140	4	0	0	PROPN
ejpam-6680	140	5	,	,	PUNCT
ejpam-6680	140	6	map	map	VERB
ejpam-6680	140	7	a	a	PRON
ejpam-6680	140	8	is	be	AUX
ejpam-6680	140	9	known	know	VERB
ejpam-6680	140	10	as	as	ADP
ejpam-6680	140	11	α−strongly	α−strongly	ADV
ejpam-6680	140	12	pseudo	pseudo	NOUN
ejpam-6680	140	13	-	-	NOUN
ejpam-6680	140	14	monotone	monotone	ADJ
ejpam-6680	140	15	if	if	SCONJ
ejpam-6680	140	16	⟨	⟨	VERB
ejpam-6680	140	17	−−−−−−→	−−−−−−→	X
ejpam-6680	140	18	aw1aw2	aw1aw2	PROPN
ejpam-6680	140	19	,	,	PUNCT
ejpam-6680	140	20	−−−→w1w2⟩	−−−→w1w2⟩	PROPN
ejpam-6680	140	21	≥	≥	NOUN
ejpam-6680	140	22	αϱ2(w1	αϱ2(w1	NUM
ejpam-6680	140	23	,	,	PUNCT
ejpam-6680	140	24	w2	w2	NOUN
ejpam-6680	140	25	)	)	PUNCT
ejpam-6680	140	26	,	,	PUNCT
ejpam-6680	140	27	∀	∀	X
ejpam-6680	140	28	w1	w1	NOUN
ejpam-6680	140	29	,	,	PUNCT
ejpam-6680	140	30	w2	w2	NOUN
ejpam-6680	140	31	∈	∈	PROPN
ejpam-6680	140	32	l.	l.	NOUN
ejpam-6680	141	1	the	the	DET
ejpam-6680	141	2	convergence	convergence	NOUN
ejpam-6680	141	3	of	of	ADP
ejpam-6680	141	4	the	the	DET
ejpam-6680	141	5	approaches	approach	NOUN
ejpam-6680	141	6	is	be	AUX
ejpam-6680	141	7	assumed	assume	VERB
ejpam-6680	141	8	to	to	PART
ejpam-6680	141	9	meet	meet	VERB
ejpam-6680	141	10	the	the	DET
ejpam-6680	141	11	following	following	ADJ
ejpam-6680	141	12	conditions	condition	NOUN
ejpam-6680	141	13	.	.	PUNCT
ejpam-6680	142	1	condition	condition	NOUN
ejpam-6680	142	2	1	1	NUM
ejpam-6680	142	3	.	.	PUNCT
ejpam-6680	143	1	the	the	DET
ejpam-6680	143	2	subset	subset	ADJ
ejpam-6680	143	3	l	l	NOUN
ejpam-6680	143	4	of	of	ADP
ejpam-6680	143	5	a	a	DET
ejpam-6680	143	6	hadamard	hadamard	ADJ
ejpam-6680	143	7	space	space	NOUN
ejpam-6680	143	8	(	(	PUNCT
ejpam-6680	143	9	z	z	NOUN
ejpam-6680	143	10	,	,	PUNCT
ejpam-6680	143	11	ϱ	ϱ	NOUN
ejpam-6680	143	12	)	)	PUNCT
ejpam-6680	143	13	is	be	AUX
ejpam-6680	143	14	nonempty	nonempty	ADJ
ejpam-6680	143	15	,	,	PUNCT
ejpam-6680	143	16	closed	closed	ADJ
ejpam-6680	143	17	and	and	CCONJ
ejpam-6680	143	18	convex	convex	NOUN
ejpam-6680	143	19	.	.	PUNCT
ejpam-6680	144	1	condition	condition	NOUN
ejpam-6680	144	2	2	2	NUM
ejpam-6680	144	3	.	.	PUNCT
ejpam-6680	145	1	the	the	DET
ejpam-6680	145	2	mapping	mapping	NOUN
ejpam-6680	145	3	a	a	DET
ejpam-6680	145	4	:	:	PUNCT
ejpam-6680	145	5	l	l	NOUN
ejpam-6680	145	6	→	→	PUNCT
ejpam-6680	145	7	l	l	NOUN
ejpam-6680	145	8	is	be	AUX
ejpam-6680	145	9	a	a	DET
ejpam-6680	145	10	pseudo	pseudo	NOUN
ejpam-6680	145	11	-	-	ADJ
ejpam-6680	145	12	monotone	monotone	ADJ
ejpam-6680	145	13	,	,	PUNCT
ejpam-6680	145	14	uniformly	uniformly	ADV
ejpam-6680	145	15	continuous	continuous	ADJ
ejpam-6680	145	16	on	on	ADP
ejpam-6680	145	17	l.	l.	PROPN
ejpam-6680	145	18	condition	condition	PROPN
ejpam-6680	145	19	3	3	X
ejpam-6680	145	20	.	.	PUNCT
ejpam-6680	146	1	the	the	DET
ejpam-6680	146	2	solution	solution	NOUN
ejpam-6680	146	3	set	set	VERB
ejpam-6680	146	4	of	of	ADP
ejpam-6680	146	5	vi(3	vi(3	PROPN
ejpam-6680	146	6	)	)	PUNCT
ejpam-6680	146	7	is	be	AUX
ejpam-6680	146	8	non	non	ADJ
ejpam-6680	146	9	-	-	ADJ
ejpam-6680	146	10	empty	empty	ADJ
ejpam-6680	146	11	,	,	PUNCT
ejpam-6680	146	12	that	that	PRON
ejpam-6680	146	13	is	be	AUX
ejpam-6680	146	14	v	v	ADP
ejpam-6680	146	15	i(l	i(l	PROPN
ejpam-6680	146	16	,	,	PUNCT
ejpam-6680	146	17	a	a	PRON
ejpam-6680	146	18	)	)	PUNCT
ejpam-6680	146	19	̸=	̸=	PROPN
ejpam-6680	146	20	ϕ.	ϕ.	ADJ
ejpam-6680	146	21	condition	condition	NOUN
ejpam-6680	146	22	4	4	X
ejpam-6680	146	23	.	.	PUNCT
ejpam-6680	147	1	let	let	VERB
ejpam-6680	147	2	ϖ	ϖ	PRON
ejpam-6680	147	3	:	:	PUNCT
ejpam-6680	147	4	l	l	X
ejpam-6680	147	5	→	→	PUNCT
ejpam-6680	147	6	z	z	X
ejpam-6680	147	7	be	be	AUX
ejpam-6680	147	8	a	a	DET
ejpam-6680	147	9	contraction	contraction	NOUN
ejpam-6680	147	10	map	map	NOUN
ejpam-6680	147	11	.	.	PUNCT
ejpam-6680	148	1	let	let	VERB
ejpam-6680	148	2	’s	’s	NOUN
ejpam-6680	148	3	say	say	VERB
ejpam-6680	148	4	there	there	PRON
ejpam-6680	148	5	’s	’	VERB
ejpam-6680	148	6	a	a	DET
ejpam-6680	148	7	sequence	sequence	NOUN
ejpam-6680	148	8	{	{	PUNCT
ejpam-6680	148	9	ξn	ξn	NOUN
ejpam-6680	148	10	}	}	PUNCT
ejpam-6680	148	11	of	of	ADP
ejpam-6680	148	12	real	real	ADJ
ejpam-6680	148	13	numbers	number	NOUN
ejpam-6680	148	14	in	in	ADP
ejpam-6680	148	15	an	an	DET
ejpam-6680	148	16	open	open	ADJ
ejpam-6680	148	17	interval	interval	NOUN
ejpam-6680	148	18	(	(	PUNCT
ejpam-6680	148	19	0	0	NUM
ejpam-6680	148	20	,	,	PUNCT
ejpam-6680	148	21	1	1	NUM
ejpam-6680	148	22	)	)	PUNCT
ejpam-6680	148	23	in	in	ADP
ejpam-6680	148	24	such	such	DET
ejpam-6680	148	25	a	a	DET
ejpam-6680	148	26	way	way	NOUN
ejpam-6680	148	27	that	that	PRON
ejpam-6680	148	28	lim	lim	PROPN
ejpam-6680	148	29	n→∞	n→∞	PRON
ejpam-6680	148	30	ξn	ξn	PROPN
ejpam-6680	148	31	=	=	SYM
ejpam-6680	148	32	0	0	NUM
ejpam-6680	148	33	,	,	PUNCT
ejpam-6680	148	34	σ∞	σ∞	PROPN
ejpam-6680	148	35	n=1ξn	n=1ξn	X
ejpam-6680	149	1	=	=	SYM
ejpam-6680	149	2	∞.	∞.	PROPN
ejpam-6680	149	3	now	now	ADV
ejpam-6680	149	4	we	we	PRON
ejpam-6680	149	5	will	will	AUX
ejpam-6680	149	6	discuss	discuss	VERB
ejpam-6680	149	7	some	some	DET
ejpam-6680	149	8	lemmas	lemma	NOUN
ejpam-6680	149	9	which	which	PRON
ejpam-6680	149	10	are	be	AUX
ejpam-6680	149	11	crucial	crucial	ADJ
ejpam-6680	149	12	for	for	ADP
ejpam-6680	149	13	our	our	PRON
ejpam-6680	149	14	main	main	ADJ
ejpam-6680	149	15	results	result	NOUN
ejpam-6680	149	16	.	.	PUNCT
ejpam-6680	150	1	these	these	DET
ejpam-6680	150	2	lemmas	lemmas	PROPN
ejpam-6680	150	3	has	have	AUX
ejpam-6680	150	4	been	be	AUX
ejpam-6680	150	5	established	establish	VERB
ejpam-6680	150	6	by	by	ADP
ejpam-6680	150	7	authors	author	NOUN
ejpam-6680	150	8	in	in	ADP
ejpam-6680	150	9	the	the	DET
ejpam-6680	150	10	framework	framework	NOUN
ejpam-6680	150	11	of	of	ADP
ejpam-6680	150	12	hilbert	hilbert	PROPN
ejpam-6680	150	13	space	space	NOUN
ejpam-6680	150	14	.	.	PUNCT
ejpam-6680	151	1	here	here	ADV
ejpam-6680	151	2	,	,	PUNCT
ejpam-6680	151	3	we	we	PRON
ejpam-6680	151	4	explain	explain	VERB
ejpam-6680	151	5	these	these	DET
ejpam-6680	151	6	lemmas	lemma	NOUN
ejpam-6680	151	7	in	in	ADP
ejpam-6680	151	8	a	a	DET
ejpam-6680	151	9	complete	complete	ADJ
ejpam-6680	151	10	cat	cat	NOUN
ejpam-6680	151	11	(	(	PUNCT
ejpam-6680	151	12	0	0	NUM
ejpam-6680	151	13	)	)	PUNCT
ejpam-6680	151	14	space	space	NOUN
ejpam-6680	151	15	setting	setting	NOUN
ejpam-6680	151	16	and	and	CCONJ
ejpam-6680	151	17	provide	provide	VERB
ejpam-6680	151	18	the	the	DET
ejpam-6680	151	19	proof	proof	NOUN
ejpam-6680	151	20	.	.	PUNCT
ejpam-6680	152	1	m.	m.	NOUN
ejpam-6680	152	2	rashid	rashid	PROPN
ejpam-6680	152	3	et	et	PROPN
ejpam-6680	152	4	al	al	PROPN
ejpam-6680	152	5	.	.	PUNCT
ejpam-6680	152	6	/	/	SYM
ejpam-6680	152	7	eur	eur	PROPN
ejpam-6680	152	8	.	.	PUNCT
ejpam-6680	153	1	j.	j.	PROPN
ejpam-6680	153	2	pure	pure	PROPN
ejpam-6680	153	3	appl	appl	PROPN
ejpam-6680	153	4	.	.	PROPN
ejpam-6680	153	5	math	math	PROPN
ejpam-6680	153	6	,	,	PUNCT
ejpam-6680	153	7	18	18	NUM
ejpam-6680	153	8	(	(	PUNCT
ejpam-6680	153	9	4	4	NUM
ejpam-6680	153	10	)	)	PUNCT
ejpam-6680	153	11	(	(	PUNCT
ejpam-6680	153	12	2025	2025	NUM
ejpam-6680	153	13	)	)	PUNCT
ejpam-6680	153	14	,	,	PUNCT
ejpam-6680	153	15	6680	6680	NUM
ejpam-6680	153	16	8	8	NUM
ejpam-6680	153	17	of	of	ADP
ejpam-6680	153	18	24	24	NUM
ejpam-6680	153	19	lemma	lemma	PROPN
ejpam-6680	153	20	10	10	NUM
ejpam-6680	153	21	.	.	PUNCT
ejpam-6680	154	1	let	let	VERB
ejpam-6680	154	2	u1	u1	PROPN
ejpam-6680	154	3	∈	∈	PROPN
ejpam-6680	154	4	z.	z.	PROPN
ejpam-6680	154	5	then	then	ADV
ejpam-6680	154	6	ϱ2(plu1	ϱ2(plu1	PROPN
ejpam-6680	154	7	,	,	PUNCT
ejpam-6680	154	8	u2	u2	NOUN
ejpam-6680	154	9	)	)	PUNCT
ejpam-6680	154	10	≤	≤	NUM
ejpam-6680	154	11	ϱ2(u1	ϱ2(u1	NOUN
ejpam-6680	154	12	,	,	PUNCT
ejpam-6680	154	13	u2)−	u2)−	X
ejpam-6680	154	14	ϱ2(u1	ϱ2(u1	NOUN
ejpam-6680	154	15	,	,	PUNCT
ejpam-6680	154	16	plu2	plu2	NOUN
ejpam-6680	154	17	)	)	PUNCT
ejpam-6680	154	18	,	,	PUNCT
ejpam-6680	154	19	for	for	ADP
ejpam-6680	154	20	all	all	DET
ejpam-6680	154	21	u2	u2	PROPN
ejpam-6680	154	22	∈	∈	PROPN
ejpam-6680	154	23	l.	l.	NOUN
ejpam-6680	154	24	proof	proof	NOUN
ejpam-6680	154	25	.	.	PUNCT
ejpam-6680	155	1	consider	consider	VERB
ejpam-6680	155	2	⟨−−→u1u2	⟨−−→u1u2	NOUN
ejpam-6680	155	3	,	,	PUNCT
ejpam-6680	155	4	−−→u1u2⟩	−−→u1u2⟩	NOUN
ejpam-6680	155	5	=	=	PUNCT
ejpam-6680	155	6	⟨	⟨	VERB
ejpam-6680	155	7	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	8	u1plu1	u1plu1	NOUN
ejpam-6680	155	9	,	,	PUNCT
ejpam-6680	155	10	−−→u1u2⟩+	−−→u1u2⟩+	NOUN
ejpam-6680	155	11	⟨	⟨	VERB
ejpam-6680	155	12	−−−−−→	−−−−−→	NOUN
ejpam-6680	155	13	plu1u2	plu1u2	PROPN
ejpam-6680	155	14	,	,	PUNCT
ejpam-6680	155	15	−−→u1u2⟩	−−→u1u2⟩	NOUN
ejpam-6680	155	16	,	,	PUNCT
ejpam-6680	155	17	=	=	PUNCT
ejpam-6680	155	18	⟨	⟨	VERB
ejpam-6680	155	19	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	20	u1plu1	u1plu1	NOUN
ejpam-6680	155	21	,	,	PUNCT
ejpam-6680	155	22	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	23	u1plu1⟩+	u1plu1⟩+	PROPN
ejpam-6680	155	24	⟨	⟨	VERB
ejpam-6680	155	25	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	26	u1plu1	u1plu1	NOUN
ejpam-6680	155	27	,	,	PUNCT
ejpam-6680	155	28	−−−−−→	−−−−−→	X
ejpam-6680	155	29	plu1u2⟩+	plu1u2⟩+	NOUN
ejpam-6680	155	30	⟨	⟨	VERB
ejpam-6680	155	31	−−−−−→	−−−−−→	NOUN
ejpam-6680	155	32	plu1u2	plu1u2	ADV
ejpam-6680	155	33	,	,	PUNCT
ejpam-6680	155	34	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	35	u1plu1⟩	u1plu1⟩	PROPN
ejpam-6680	155	36	+	+	PROPN
ejpam-6680	155	37	⟨	⟨	ADJ
ejpam-6680	155	38	−−−−−→	−−−−−→	NOUN
ejpam-6680	155	39	plu1u2	plu1u2	ADJ
ejpam-6680	155	40	,	,	PUNCT
ejpam-6680	155	41	−−−−−→	−−−−−→	X
ejpam-6680	155	42	plu1u2⟩	plu1u2⟩	NOUN
ejpam-6680	155	43	,	,	PUNCT
ejpam-6680	155	44	=	=	SYM
ejpam-6680	155	45	⟨	⟨	VERB
ejpam-6680	155	46	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	47	u1plu2	u1plu2	NOUN
ejpam-6680	155	48	,	,	PUNCT
ejpam-6680	155	49	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	50	u1plu2⟩+	u1plu2⟩+	NOUN
ejpam-6680	155	51	⟨	⟨	NOUN
ejpam-6680	155	52	−−−−−→	−−−−−→	NOUN
ejpam-6680	155	53	plu1u2	plu1u2	ADJ
ejpam-6680	155	54	,	,	PUNCT
ejpam-6680	155	55	−−−−−→	−−−−−→	X
ejpam-6680	155	56	plu1u2⟩+	plu1u2⟩+	NOUN
ejpam-6680	155	57	2⟨	2⟨	NUM
ejpam-6680	155	58	−−−−−→	−−−−−→	X
ejpam-6680	155	59	u1plu1	u1plu1	NOUN
ejpam-6680	155	60	,	,	PUNCT
ejpam-6680	155	61	−−−−−→	−−−−−→	X
ejpam-6680	155	62	plu1u2⟩	plu1u2⟩	NOUN
ejpam-6680	155	63	,	,	PUNCT
ejpam-6680	155	64	=	=	SYM
ejpam-6680	155	65	⟨	⟨	VERB
ejpam-6680	155	66	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	67	u1plu1	u1plu1	NOUN
ejpam-6680	155	68	,	,	PUNCT
ejpam-6680	155	69	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	70	u1plu1⟩+	u1plu1⟩+	PROPN
ejpam-6680	155	71	⟨	⟨	VERB
ejpam-6680	155	72	−−−−−→	−−−−−→	NOUN
ejpam-6680	155	73	plu1u2	plu1u2	ADJ
ejpam-6680	155	74	,	,	PUNCT
ejpam-6680	155	75	−−−−−→	−−−−−→	X
ejpam-6680	155	76	plu1u2⟩+	plu1u2⟩+	NOUN
ejpam-6680	155	77	2⟨	2⟨	NUM
ejpam-6680	155	78	−−−−−→	−−−−−→	X
ejpam-6680	155	79	u2plu1	u2plu1	NOUN
ejpam-6680	155	80	,	,	PUNCT
ejpam-6680	155	81	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	82	plu1u1⟩.	plu1u1⟩.	X
ejpam-6680	155	83	by	by	ADP
ejpam-6680	155	84	theorem	theorem	NOUN
ejpam-6680	155	85	1	1	NUM
ejpam-6680	155	86	,	,	PUNCT
ejpam-6680	155	87	we	we	PRON
ejpam-6680	155	88	have	have	AUX
ejpam-6680	155	89	⟨	⟨	NOUN
ejpam-6680	155	90	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	91	u2plu1	u2plu1	NOUN
ejpam-6680	155	92	,	,	PUNCT
ejpam-6680	155	93	−−−−−→	−−−−−→	PUNCT
ejpam-6680	155	94	plu1u1⟩	plu1u1⟩	X
ejpam-6680	155	95	≥	≥	NOUN
ejpam-6680	155	96	0	0	NUM
ejpam-6680	155	97	.	.	PUNCT
ejpam-6680	156	1	we	we	PRON
ejpam-6680	156	2	have	have	VERB
ejpam-6680	156	3	⟨−−→u1u2	⟨−−→u1u2	NOUN
ejpam-6680	156	4	,	,	PUNCT
ejpam-6680	156	5	−−→u1u2⟩	−−→u1u2⟩	PROPN
ejpam-6680	156	6	≥	≥	PROPN
ejpam-6680	156	7	⟨	⟨	VERB
ejpam-6680	156	8	−−−−−→	−−−−−→	PUNCT
ejpam-6680	156	9	u1plu1	u1plu1	NOUN
ejpam-6680	156	10	,	,	PUNCT
ejpam-6680	156	11	−−−−−→	−−−−−→	PUNCT
ejpam-6680	156	12	u1plu1⟩+	u1plu1⟩+	PROPN
ejpam-6680	156	13	⟨	⟨	VERB
ejpam-6680	156	14	−−−−−→	−−−−−→	NOUN
ejpam-6680	156	15	plu1u2	plu1u2	ADJ
ejpam-6680	156	16	,	,	PUNCT
ejpam-6680	156	17	−−−−−→	−−−−−→	PUNCT
ejpam-6680	156	18	plu1u2⟩	plu1u2⟩	NOUN
ejpam-6680	156	19	,	,	PUNCT
ejpam-6680	156	20	ϱ2(u1	ϱ2(u1	X
ejpam-6680	156	21	,	,	PUNCT
ejpam-6680	156	22	u2	u2	PROPN
ejpam-6680	156	23	)	)	PUNCT
ejpam-6680	157	1	≥	≥	NOUN
ejpam-6680	157	2	ϱ2(u1	ϱ2(u1	NOUN
ejpam-6680	157	3	,	,	PUNCT
ejpam-6680	157	4	plu1	plu1	PROPN
ejpam-6680	157	5	)	)	PUNCT
ejpam-6680	158	1	+	+	CCONJ
ejpam-6680	159	1	ϱ2(u2	ϱ2(u2	NUM
ejpam-6680	159	2	,	,	PUNCT
ejpam-6680	159	3	plu1	plu1	PROPN
ejpam-6680	159	4	)	)	PUNCT
ejpam-6680	159	5	,	,	PUNCT
ejpam-6680	159	6	ϱ2(u2	ϱ2(u2	NOUN
ejpam-6680	159	7	,	,	PUNCT
ejpam-6680	159	8	plu1	plu1	PROPN
ejpam-6680	159	9	)	)	PUNCT
ejpam-6680	159	10	≤	≤	NUM
ejpam-6680	159	11	ϱ2(u1	ϱ2(u1	NOUN
ejpam-6680	159	12	,	,	PUNCT
ejpam-6680	159	13	u2)−	u2)−	X
ejpam-6680	159	14	ϱ2(u1	ϱ2(u1	NOUN
ejpam-6680	159	15	,	,	PUNCT
ejpam-6680	159	16	plu1	plu1	PROPN
ejpam-6680	159	17	)	)	PUNCT
ejpam-6680	159	18	.	.	PUNCT
ejpam-6680	160	1	lemma	lemma	PROPN
ejpam-6680	160	2	11	11	NUM
ejpam-6680	160	3	.	.	PUNCT
ejpam-6680	161	1	consider	consider	VERB
ejpam-6680	161	2	a	a	DET
ejpam-6680	161	3	closed	closed	ADJ
ejpam-6680	161	4	,	,	PUNCT
ejpam-6680	161	5	convex	convex	NOUN
ejpam-6680	161	6	subset	subset	NOUN
ejpam-6680	161	7	l	l	PROPN
ejpam-6680	161	8	⊂	⊂	PROPN
ejpam-6680	161	9	z	z	X
ejpam-6680	161	10	and	and	CCONJ
ejpam-6680	161	11	defined	define	VERB
ejpam-6680	161	12	c	c	NOUN
ejpam-6680	161	13	:	:	PUNCT
ejpam-6680	161	14	=	=	SYM
ejpam-6680	161	15	{	{	PUNCT
ejpam-6680	161	16	u	u	NOUN
ejpam-6680	161	17	∈	∈	PROPN
ejpam-6680	161	18	z	z	NOUN
ejpam-6680	161	19	:	:	PUNCT
ejpam-6680	161	20	ψ(u	ψ(u	PROPN
ejpam-6680	161	21	)	)	PUNCT
ejpam-6680	161	22	≤	≤	ADV
ejpam-6680	161	23	0	0	NUM
ejpam-6680	161	24	}	}	PUNCT
ejpam-6680	161	25	.	.	PUNCT
ejpam-6680	162	1	if	if	SCONJ
ejpam-6680	162	2	l	l	NOUN
ejpam-6680	162	3	is	be	AUX
ejpam-6680	162	4	nonempty	nonempty	ADJ
ejpam-6680	162	5	and	and	CCONJ
ejpam-6680	162	6	a	a	DET
ejpam-6680	162	7	real	real	ADV
ejpam-6680	162	8	valued	value	VERB
ejpam-6680	162	9	function	function	NOUN
ejpam-6680	162	10	ψ	ψ	NOUN
ejpam-6680	162	11	is	be	AUX
ejpam-6680	162	12	lipschitz	lipschitz	ADJ
ejpam-6680	162	13	continuous	continuous	ADJ
ejpam-6680	162	14	on	on	ADP
ejpam-6680	162	15	z	z	NOUN
ejpam-6680	162	16	with	with	ADP
ejpam-6680	162	17	modulus	modulus	ADJ
ejpam-6680	162	18	θ	θ	PROPN
ejpam-6680	162	19	>	>	X
ejpam-6680	162	20	0	0	NUM
ejpam-6680	162	21	,	,	PUNCT
ejpam-6680	162	22	then	then	ADV
ejpam-6680	162	23	ϱ(u	ϱ(u	ADP
ejpam-6680	162	24	,	,	PUNCT
ejpam-6680	162	25	c	c	NOUN
ejpam-6680	162	26	)	)	PUNCT
ejpam-6680	162	27	≥	≥	NOUN
ejpam-6680	162	28	θ−1max{ψ(u	θ−1max{ψ(u	PROPN
ejpam-6680	162	29	)	)	PUNCT
ejpam-6680	162	30	,	,	PUNCT
ejpam-6680	162	31	0	0	NUM
ejpam-6680	162	32	}	}	PUNCT
ejpam-6680	162	33	,	,	PUNCT
ejpam-6680	162	34	for	for	ADP
ejpam-6680	162	35	all	all	DET
ejpam-6680	162	36	u	u	PRON
ejpam-6680	162	37	∈	∈	PROPN
ejpam-6680	162	38	l	l	NOUN
ejpam-6680	162	39	,	,	PUNCT
ejpam-6680	162	40	(	(	PUNCT
ejpam-6680	162	41	4	4	X
ejpam-6680	162	42	)	)	PUNCT
ejpam-6680	162	43	the	the	DET
ejpam-6680	162	44	distance	distance	NOUN
ejpam-6680	162	45	from	from	ADP
ejpam-6680	162	46	u	u	PRON
ejpam-6680	162	47	to	to	ADP
ejpam-6680	162	48	c	c	PROPN
ejpam-6680	162	49	is	be	AUX
ejpam-6680	162	50	denoted	denote	VERB
ejpam-6680	162	51	by	by	ADP
ejpam-6680	162	52	d(u	d(u	PROPN
ejpam-6680	162	53	,	,	PUNCT
ejpam-6680	162	54	c	c	NOUN
ejpam-6680	162	55	)	)	PUNCT
ejpam-6680	162	56	.	.	PUNCT
ejpam-6680	163	1	proof	proof	NOUN
ejpam-6680	163	2	.	.	PUNCT
ejpam-6680	164	1	clearly	clearly	ADV
ejpam-6680	164	2	(	(	PUNCT
ejpam-6680	164	3	4	4	X
ejpam-6680	164	4	)	)	PUNCT
ejpam-6680	164	5	holds	hold	VERB
ejpam-6680	164	6	for	for	ADP
ejpam-6680	164	7	all	all	DET
ejpam-6680	164	8	u	u	NOUN
ejpam-6680	164	9	∈	∈	PROPN
ejpam-6680	164	10	c	c	NOUN
ejpam-6680	164	11	and	and	CCONJ
ejpam-6680	164	12	we	we	PRON
ejpam-6680	164	13	are	be	AUX
ejpam-6680	164	14	left	leave	VERB
ejpam-6680	164	15	to	to	ADP
ejpam-6680	164	16	proof	proof	NOUN
ejpam-6680	164	17	that	that	SCONJ
ejpam-6680	164	18	(	(	PUNCT
ejpam-6680	164	19	4	4	X
ejpam-6680	164	20	)	)	PUNCT
ejpam-6680	164	21	holds	hold	VERB
ejpam-6680	164	22	for	for	ADP
ejpam-6680	164	23	every	every	DET
ejpam-6680	164	24	u	u	PROPN
ejpam-6680	164	25	∈	∈	PROPN
ejpam-6680	164	26	l	l	PROPN
ejpam-6680	164	27	/	/	SYM
ejpam-6680	164	28	c.	c.	PROPN
ejpam-6680	164	29	assume	assume	VERB
ejpam-6680	164	30	u	u	PROPN
ejpam-6680	164	31	̸∈	̸∈	PROPN
ejpam-6680	164	32	c	c	PROPN
ejpam-6680	165	1	but	but	CCONJ
ejpam-6680	165	2	u	u	PROPN
ejpam-6680	165	3	∈	∈	PROPN
ejpam-6680	165	4	l.	l.	NOUN
ejpam-6680	165	5	since	since	SCONJ
ejpam-6680	165	6	c	c	PROPN
ejpam-6680	165	7	is	be	AUX
ejpam-6680	165	8	closed	closed	ADJ
ejpam-6680	165	9	,	,	PUNCT
ejpam-6680	165	10	there	there	PRON
ejpam-6680	165	11	exist	exist	VERB
ejpam-6680	165	12	ω(u	ω(u	NUM
ejpam-6680	165	13	)	)	PUNCT
ejpam-6680	165	14	∈	∈	PROPN
ejpam-6680	165	15	c	c	NOUN
ejpam-6680	165	16	such	such	ADJ
ejpam-6680	165	17	that	that	PRON
ejpam-6680	165	18	ϱ(u	ϱ(u	ADP
ejpam-6680	165	19	,	,	PUNCT
ejpam-6680	165	20	ω	ω	NOUN
ejpam-6680	165	21	)	)	PUNCT
ejpam-6680	165	22	=	=	PUNCT
ejpam-6680	165	23	ϱ(u	ϱ(u	ADP
ejpam-6680	165	24	,	,	PUNCT
ejpam-6680	165	25	c	c	NOUN
ejpam-6680	165	26	)	)	PUNCT
ejpam-6680	165	27	.	.	PUNCT
ejpam-6680	166	1	since	since	SCONJ
ejpam-6680	166	2	ψ	ψ	NOUN
ejpam-6680	166	3	is	be	AUX
ejpam-6680	166	4	lipschitz	lipschitz	ADJ
ejpam-6680	166	5	continuous	continuous	ADJ
ejpam-6680	166	6	,	,	PUNCT
ejpam-6680	166	7	we	we	PRON
ejpam-6680	166	8	have	have	AUX
ejpam-6680	166	9	ϱ(ψ(u	ϱ(ψ(u	NOUN
ejpam-6680	166	10	)	)	PUNCT
ejpam-6680	166	11	,	,	PUNCT
ejpam-6680	166	12	ψ(ω(u	ψ(ω(u	PROPN
ejpam-6680	166	13	)	)	PUNCT
ejpam-6680	166	14	)	)	PUNCT
ejpam-6680	166	15	)	)	PUNCT
ejpam-6680	167	1	≤	≤	NOUN
ejpam-6680	167	2	θϱ(u	θϱ(u	NUM
ejpam-6680	167	3	,	,	PUNCT
ejpam-6680	167	4	ω	ω	NOUN
ejpam-6680	167	5	)	)	PUNCT
ejpam-6680	167	6	,	,	PUNCT
ejpam-6680	167	7	=	=	SYM
ejpam-6680	167	8	θϱ(u	θϱ(u	X
ejpam-6680	167	9	,	,	PUNCT
ejpam-6680	167	10	c	c	NOUN
ejpam-6680	167	11	)	)	PUNCT
ejpam-6680	167	12	.	.	PUNCT
ejpam-6680	168	1	since	since	SCONJ
ejpam-6680	168	2	u	u	PRON
ejpam-6680	168	3	̸∈	̸∈	PROPN
ejpam-6680	168	4	c	c	PROPN
ejpam-6680	168	5	and	and	CCONJ
ejpam-6680	168	6	ω(u	ω(u	PROPN
ejpam-6680	168	7	)	)	PUNCT
ejpam-6680	168	8	∈	∈	PROPN
ejpam-6680	168	9	l	l	NOUN
ejpam-6680	168	10	,	,	PUNCT
ejpam-6680	168	11	we	we	PRON
ejpam-6680	168	12	have	have	VERB
ejpam-6680	168	13	ψ(u	ψ(u	PROPN
ejpam-6680	168	14	)	)	PUNCT
ejpam-6680	168	15	>	>	X
ejpam-6680	168	16	0	0	PUNCT
ejpam-6680	168	17	and	and	CCONJ
ejpam-6680	168	18	ψ(y(u	ψ(y(u	NUM
ejpam-6680	168	19	)	)	PUNCT
ejpam-6680	168	20	)	)	PUNCT
ejpam-6680	169	1	≤	≤	NUM
ejpam-6680	169	2	0	0	X
ejpam-6680	169	3	.	.	PUNCT
ejpam-6680	170	1	then	then	ADV
ejpam-6680	170	2	ψ(u	ψ(u	PROPN
ejpam-6680	170	3	)	)	PUNCT
ejpam-6680	170	4	≤	≤	NUM
ejpam-6680	170	5	ψ(u)−	ψ(u)−	PROPN
ejpam-6680	170	6	ψ(ω(u	ψ(ω(u	PROPN
ejpam-6680	170	7	)	)	PUNCT
ejpam-6680	170	8	)	)	PUNCT
ejpam-6680	171	1	≤	≤	NUM
ejpam-6680	171	2	|ψ(u)−	|ψ(u)−	NOUN
ejpam-6680	171	3	ψ(ω(u))|	ψ(ω(u))|	PROPN
ejpam-6680	171	4	,	,	PUNCT
ejpam-6680	171	5	=	=	PUNCT
ejpam-6680	171	6	ϱ(ψ(u	ϱ(ψ(u	PROPN
ejpam-6680	171	7	)	)	PUNCT
ejpam-6680	171	8	,	,	PUNCT
ejpam-6680	171	9	ψ(ω(u	ψ(ω(u	PROPN
ejpam-6680	171	10	)	)	PUNCT
ejpam-6680	171	11	)	)	PUNCT
ejpam-6680	171	12	)	)	PUNCT
ejpam-6680	172	1	≤	≤	NOUN
ejpam-6680	172	2	θϱ(u	θϱ(u	NOUN
ejpam-6680	172	3	,	,	PUNCT
ejpam-6680	172	4	c	c	NOUN
ejpam-6680	172	5	)	)	PUNCT
ejpam-6680	172	6	.	.	PUNCT
ejpam-6680	173	1	lemma	lemma	PROPN
ejpam-6680	173	2	12	12	NUM
ejpam-6680	173	3	.	.	PUNCT
ejpam-6680	174	1	let	let	VERB
ejpam-6680	174	2	l	l	NOUN
ejpam-6680	174	3	be	be	AUX
ejpam-6680	174	4	a	a	DET
ejpam-6680	174	5	nonempty	nonempty	ADJ
ejpam-6680	174	6	,	,	PUNCT
ejpam-6680	174	7	closed	closed	ADJ
ejpam-6680	174	8	and	and	CCONJ
ejpam-6680	174	9	convex	convex	NOUN
ejpam-6680	174	10	subset	subset	NOUN
ejpam-6680	174	11	of	of	ADP
ejpam-6680	174	12	a	a	DET
ejpam-6680	174	13	complete	complete	ADJ
ejpam-6680	174	14	cat	cat	NOUN
ejpam-6680	174	15	(	(	PUNCT
ejpam-6680	174	16	0	0	NUM
ejpam-6680	174	17	)	)	PUNCT
ejpam-6680	174	18	space	space	NOUN
ejpam-6680	174	19	z	z	NOUN
ejpam-6680	174	20	and	and	CCONJ
ejpam-6680	174	21	a	a	PRON
ejpam-6680	174	22	be	be	AUX
ejpam-6680	174	23	a	a	DET
ejpam-6680	174	24	pseudo	pseudo	NOUN
ejpam-6680	174	25	-	-	ADJ
ejpam-6680	174	26	monotone	monotone	ADJ
ejpam-6680	174	27	map	map	NOUN
ejpam-6680	174	28	.	.	PUNCT
ejpam-6680	175	1	if	if	SCONJ
ejpam-6680	175	2	⟨	⟨	VERB
ejpam-6680	175	3	−−→	−−→	PROPN
ejpam-6680	175	4	uau	uau	PROPN
ejpam-6680	175	5	,	,	PUNCT
ejpam-6680	175	6	−−→	−−→	PROPN
ejpam-6680	175	7	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	175	8	≥	≥	NOUN
ejpam-6680	175	9	0	0	NUM
ejpam-6680	175	10	,	,	PUNCT
ejpam-6680	175	11	∀	∀	VERB
ejpam-6680	175	12	u	u	NOUN
ejpam-6680	175	13	∈	∈	PROPN
ejpam-6680	175	14	l.	l.	NOUN
ejpam-6680	175	15	(	(	PUNCT
ejpam-6680	175	16	5	5	NUM
ejpam-6680	175	17	)	)	PUNCT
ejpam-6680	175	18	then	then	ADV
ejpam-6680	175	19	u∗	u∗	ADV
ejpam-6680	175	20	is	be	AUX
ejpam-6680	175	21	the	the	DET
ejpam-6680	175	22	solution	solution	NOUN
ejpam-6680	175	23	of	of	ADP
ejpam-6680	175	24	v	v	ADP
ejpam-6680	175	25	i(l	i(l	PROPN
ejpam-6680	175	26	,	,	PUNCT
ejpam-6680	175	27	a	a	PRON
ejpam-6680	175	28	)	)	PUNCT
ejpam-6680	175	29	.	.	PUNCT
ejpam-6680	176	1	m.	m.	PROPN
ejpam-6680	176	2	rashid	rashid	PROPN
ejpam-6680	176	3	et	et	PROPN
ejpam-6680	176	4	al	al	PROPN
ejpam-6680	176	5	.	.	PUNCT
ejpam-6680	176	6	/	/	SYM
ejpam-6680	176	7	eur	eur	PROPN
ejpam-6680	176	8	.	.	PUNCT
ejpam-6680	177	1	j.	j.	PROPN
ejpam-6680	177	2	pure	pure	PROPN
ejpam-6680	177	3	appl	appl	PROPN
ejpam-6680	177	4	.	.	PROPN
ejpam-6680	177	5	math	math	PROPN
ejpam-6680	177	6	,	,	PUNCT
ejpam-6680	177	7	18	18	NUM
ejpam-6680	177	8	(	(	PUNCT
ejpam-6680	177	9	4	4	NUM
ejpam-6680	177	10	)	)	PUNCT
ejpam-6680	177	11	(	(	PUNCT
ejpam-6680	177	12	2025	2025	NUM
ejpam-6680	177	13	)	)	PUNCT
ejpam-6680	177	14	,	,	PUNCT
ejpam-6680	177	15	6680	6680	NUM
ejpam-6680	177	16	9	9	NUM
ejpam-6680	177	17	of	of	ADP
ejpam-6680	177	18	24	24	NUM
ejpam-6680	177	19	proof	proof	NOUN
ejpam-6680	177	20	.	.	PUNCT
ejpam-6680	178	1	suppose	suppose	VERB
ejpam-6680	178	2	⟨	⟨	VERB
ejpam-6680	178	3	−−→	−−→	PROPN
ejpam-6680	178	4	uau	uau	PROPN
ejpam-6680	178	5	,	,	PUNCT
ejpam-6680	178	6	−−→	−−→	PROPN
ejpam-6680	178	7	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	178	8	≥	≥	NUM
ejpam-6680	178	9	0	0	NUM
ejpam-6680	178	10	holds	hold	VERB
ejpam-6680	178	11	for	for	SCONJ
ejpam-6680	178	12	all	all	DET
ejpam-6680	178	13	u	u	PROPN
ejpam-6680	178	14	∈	∈	PROPN
ejpam-6680	178	15	l.	l.	NOUN
ejpam-6680	178	16	thus	thus	ADV
ejpam-6680	178	17	⟨	⟨	VERB
ejpam-6680	178	18	−−−−−→	−−−−−→	X
ejpam-6680	178	19	uλ	uλ	ADP
ejpam-6680	178	20	∗auλ	∗auλ	PROPN
ejpam-6680	178	21	∗	∗	NOUN
ejpam-6680	178	22	,	,	PUNCT
ejpam-6680	178	23	−−−→	−−−→	ADJ
ejpam-6680	178	24	uλ	uλ	PRON
ejpam-6680	178	25	∗u∗⟩	∗u∗⟩	NUM
ejpam-6680	178	26	≥	≥	NOUN
ejpam-6680	178	27	0	0	NUM
ejpam-6680	178	28	,	,	PUNCT
ejpam-6680	178	29	uλ	uλ	ADP
ejpam-6680	178	30	∗	∗	NOUN
ejpam-6680	178	31	∈	∈	PROPN
ejpam-6680	178	32	l	l	NOUN
ejpam-6680	178	33	⟨	⟨	VERB
ejpam-6680	178	34	−−−→	−−−→	VERB
ejpam-6680	178	35	uλ	uλ	ADP
ejpam-6680	178	36	∗u∗	∗u∗	NUM
ejpam-6680	178	37	,	,	PUNCT
ejpam-6680	178	38	−−−−−→	−−−−−→	X
ejpam-6680	178	39	uλ	uλ	ADP
ejpam-6680	178	40	∗auλ	∗auλ	ADP
ejpam-6680	178	41	∗⟩	∗⟩	X
ejpam-6680	178	42	≥	≥	NOUN
ejpam-6680	178	43	0	0	NUM
ejpam-6680	178	44	.	.	PUNCT
ejpam-6680	179	1	by	by	ADP
ejpam-6680	179	2	using	use	VERB
ejpam-6680	179	3	lemma	lemma	PROPN
ejpam-6680	179	4	7	7	NUM
ejpam-6680	179	5	and	and	CCONJ
ejpam-6680	179	6	applying	apply	VERB
ejpam-6680	179	7	limit	limit	NOUN
ejpam-6680	179	8	,	,	PUNCT
ejpam-6680	179	9	we	we	PRON
ejpam-6680	179	10	obtain	obtain	VERB
ejpam-6680	179	11	⟨	⟨	VERB
ejpam-6680	179	12	−−−→	−−−→	PROPN
ejpam-6680	179	13	uλ	uλ	ADP
ejpam-6680	179	14	∗u∗	∗u∗	NUM
ejpam-6680	179	15	,	,	PUNCT
ejpam-6680	179	16	−−−−−→	−−−−−→	X
ejpam-6680	179	17	uλ	uλ	ADP
ejpam-6680	179	18	∗auλ	∗auλ	PROPN
ejpam-6680	179	19	∗⟩	∗⟩	PUNCT
ejpam-6680	179	20	≤	≤	PUNCT
ejpam-6680	179	21	λ⟨	λ⟨	PUNCT
ejpam-6680	179	22	−−→	−−→	PROPN
ejpam-6680	179	23	uu∗	uu∗	PROPN
ejpam-6680	179	24	,	,	PUNCT
ejpam-6680	179	25	−−−−−→	−−−−−→	PUNCT
ejpam-6680	179	26	uλ	uλ	ADP
ejpam-6680	179	27	∗auλ	∗auλ	PROPN
ejpam-6680	179	28	∗⟩+	∗⟩+	PROPN
ejpam-6680	179	29	(	(	PUNCT
ejpam-6680	179	30	1−	1−	NUM
ejpam-6680	179	31	λ)⟨	λ)⟨	PROPN
ejpam-6680	179	32	−−→	−−→	PROPN
ejpam-6680	179	33	u∗u∗	u∗u∗	PROPN
ejpam-6680	179	34	,	,	PUNCT
ejpam-6680	179	35	−−−−−→	−−−−−→	PUNCT
ejpam-6680	179	36	uλ	uλ	ADP
ejpam-6680	179	37	∗auλ	∗auλ	PROPN
ejpam-6680	179	38	∗⟩.	∗⟩.	NOUN
ejpam-6680	179	39	=	=	SYM
ejpam-6680	179	40	λ⟨	λ⟨	NOUN
ejpam-6680	179	41	−−→	−−→	PROPN
ejpam-6680	179	42	uu∗	uu∗	PROPN
ejpam-6680	179	43	,	,	PUNCT
ejpam-6680	179	44	−−−−−→	−−−−−→	PUNCT
ejpam-6680	179	45	uλ	uλ	ADP
ejpam-6680	179	46	∗auλ	∗auλ	PROPN
ejpam-6680	179	47	∗⟩	∗⟩	PUNCT
ejpam-6680	179	48	≤	≤	NUM
ejpam-6680	179	49	⟨	⟨	VERB
ejpam-6680	179	50	−−−−−→	−−−−−→	X
ejpam-6680	179	51	uλ	uλ	ADP
ejpam-6680	179	52	∗auλ	∗auλ	PROPN
ejpam-6680	179	53	∗	∗	NOUN
ejpam-6680	179	54	,	,	PUNCT
ejpam-6680	179	55	−−→	−−→	PROPN
ejpam-6680	179	56	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	179	57	,	,	PUNCT
ejpam-6680	179	58	≤	≤	ADJ
ejpam-6680	179	59	λ⟨	λ⟨	NOUN
ejpam-6680	179	60	−−−−→	−−−−→	X
ejpam-6680	179	61	uauλ	uauλ	ADJ
ejpam-6680	179	62	∗	∗	NOUN
ejpam-6680	179	63	,	,	PUNCT
ejpam-6680	179	64	−−→	−−→	X
ejpam-6680	179	65	uu∗⟩+	uu∗⟩+	NOUN
ejpam-6680	179	66	(	(	PUNCT
ejpam-6680	179	67	1−	1−	NUM
ejpam-6680	179	68	λ)⟨	λ)⟨	NOUN
ejpam-6680	179	69	−−−−−→	−−−−−→	PUNCT
ejpam-6680	179	70	u∗auλ	u∗auλ	ADJ
ejpam-6680	179	71	∗	∗	NOUN
ejpam-6680	179	72	,	,	PUNCT
ejpam-6680	179	73	−−→	−−→	PROPN
ejpam-6680	179	74	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	179	75	,	,	PUNCT
ejpam-6680	179	76	=	=	PUNCT
ejpam-6680	179	77	λ⟨	λ⟨	NOUN
ejpam-6680	179	78	−−−→	−−−→	NUM
ejpam-6680	179	79	uau∗	uau∗	PROPN
ejpam-6680	179	80	,	,	PUNCT
ejpam-6680	179	81	−−→	−−→	X
ejpam-6680	179	82	uu∗⟩+	uu∗⟩+	NOUN
ejpam-6680	179	83	(	(	PUNCT
ejpam-6680	179	84	1−	1−	NUM
ejpam-6680	179	85	λ)⟨	λ)⟨	PROPN
ejpam-6680	179	86	−−−−→	−−−−→	PRON
ejpam-6680	179	87	u∗au∗	u∗au∗	PROPN
ejpam-6680	179	88	,	,	PUNCT
ejpam-6680	179	89	−−→	−−→	PROPN
ejpam-6680	179	90	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	179	91	,	,	PUNCT
ejpam-6680	179	92	=	=	PUNCT
ejpam-6680	179	93	λ⟨	λ⟨	NOUN
ejpam-6680	179	94	−−−→	−−−→	NUM
ejpam-6680	179	95	uau∗	uau∗	PROPN
ejpam-6680	179	96	,	,	PUNCT
ejpam-6680	179	97	−−→	−−→	X
ejpam-6680	179	98	uu∗⟩+	uu∗⟩+	NOUN
ejpam-6680	179	99	(	(	PUNCT
ejpam-6680	179	100	1−	1−	NUM
ejpam-6680	179	101	λ)⟨	λ)⟨	NOUN
ejpam-6680	179	102	−−→	−−→	PROPN
ejpam-6680	179	103	u∗u	u∗u	PROPN
ejpam-6680	179	104	,	,	PUNCT
ejpam-6680	179	105	−−→	−−→	X
ejpam-6680	179	106	uu∗⟩+	uu∗⟩+	NOUN
ejpam-6680	179	107	(	(	PUNCT
ejpam-6680	179	108	1−	1−	NUM
ejpam-6680	179	109	λ)⟨	λ)⟨	NOUN
ejpam-6680	179	110	−−−→	−−−→	NUM
ejpam-6680	179	111	uau∗	uau∗	PROPN
ejpam-6680	179	112	,	,	PUNCT
ejpam-6680	179	113	−−→	−−→	PROPN
ejpam-6680	179	114	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	179	115	,	,	PUNCT
ejpam-6680	179	116	=	=	PRON
ejpam-6680	179	117	⟨	⟨	VERB
ejpam-6680	179	118	−−−→	−−−→	NUM
ejpam-6680	179	119	uau∗	uau∗	NOUN
ejpam-6680	179	120	,	,	PUNCT
ejpam-6680	179	121	−−→	−−→	X
ejpam-6680	179	122	uu∗⟩+	uu∗⟩+	NOUN
ejpam-6680	179	123	(	(	PUNCT
ejpam-6680	179	124	1−	1−	NUM
ejpam-6680	179	125	λ)⟨	λ)⟨	NOUN
ejpam-6680	179	126	−−→	−−→	PROPN
ejpam-6680	179	127	u∗u	u∗u	PROPN
ejpam-6680	179	128	,	,	PUNCT
ejpam-6680	179	129	−−→	−−→	PROPN
ejpam-6680	179	130	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	179	131	,	,	PUNCT
ejpam-6680	179	132	≤	≤	NUM
ejpam-6680	179	133	⟨	⟨	VERB
ejpam-6680	179	134	−−−→	−−−→	PROPN
ejpam-6680	179	135	bau∗	bau∗	NOUN
ejpam-6680	179	136	,	,	PUNCT
ejpam-6680	179	137	−−→	−−→	X
ejpam-6680	179	138	uu∗⟩+	uu∗⟩+	NOUN
ejpam-6680	179	139	(	(	PUNCT
ejpam-6680	179	140	1−	1−	NUM
ejpam-6680	179	141	λ)ϱ2(u	λ)ϱ2(u	NUM
ejpam-6680	179	142	,	,	PUNCT
ejpam-6680	179	143	u∗	u∗	PROPN
ejpam-6680	179	144	)	)	PUNCT
ejpam-6680	179	145	.	.	PUNCT
ejpam-6680	180	1	this	this	PRON
ejpam-6680	180	2	implies	imply	VERB
ejpam-6680	180	3	⟨	⟨	VERB
ejpam-6680	180	4	−−−→	−−−→	PROPN
ejpam-6680	180	5	uau∗	uau∗	PROPN
ejpam-6680	180	6	,	,	PUNCT
ejpam-6680	180	7	−−→	−−→	PROPN
ejpam-6680	180	8	uu∗⟩	uu∗⟩	PROPN
ejpam-6680	180	9	≥	≥	NOUN
ejpam-6680	180	10	0	0	NUM
ejpam-6680	180	11	.	.	PUNCT
ejpam-6680	181	1	thus	thus	ADV
ejpam-6680	181	2	u∗	u∗	ADV
ejpam-6680	181	3	is	be	AUX
ejpam-6680	181	4	a	a	DET
ejpam-6680	181	5	solution	solution	NOUN
ejpam-6680	181	6	of	of	ADP
ejpam-6680	181	7	(	(	PUNCT
ejpam-6680	181	8	5	5	NUM
ejpam-6680	181	9	)	)	PUNCT
ejpam-6680	181	10	.	.	PUNCT
ejpam-6680	182	1	now	now	ADV
ejpam-6680	182	2	,	,	PUNCT
ejpam-6680	182	3	we	we	PRON
ejpam-6680	182	4	introduce	introduce	VERB
ejpam-6680	182	5	our	our	PRON
ejpam-6680	182	6	algorithm	algorithm	NOUN
ejpam-6680	182	7	as	as	SCONJ
ejpam-6680	182	8	follows	follow	VERB
ejpam-6680	182	9	:	:	PUNCT
ejpam-6680	182	10	algorithm	algorithm	NOUN
ejpam-6680	182	11	1	1	NUM
ejpam-6680	182	12	.	.	PUNCT
ejpam-6680	182	13	initialization	initialization	NOUN
ejpam-6680	182	14	:	:	PUNCT
ejpam-6680	182	15	given	give	VERB
ejpam-6680	182	16	µ	µ	PRON
ejpam-6680	182	17	,	,	PUNCT
ejpam-6680	182	18	ν	ν	NOUN
ejpam-6680	182	19	,	,	PUNCT
ejpam-6680	182	20	ς	ς	PROPN
ejpam-6680	182	21	∈	∈	PROPN
ejpam-6680	182	22	(	(	PUNCT
ejpam-6680	182	23	0	0	NUM
ejpam-6680	182	24	,	,	PUNCT
ejpam-6680	182	25	1	1	NUM
ejpam-6680	182	26	)	)	PUNCT
ejpam-6680	182	27	.	.	PUNCT
ejpam-6680	183	1	let	let	VERB
ejpam-6680	183	2	b1	b1	PROPN
ejpam-6680	183	3	∈	∈	PROPN
ejpam-6680	183	4	l	l	NOUN
ejpam-6680	183	5	be	be	AUX
ejpam-6680	183	6	arbitrary	arbitrary	ADJ
ejpam-6680	183	7	iterative	iterative	NOUN
ejpam-6680	183	8	steps	step	NOUN
ejpam-6680	183	9	:	:	PUNCT
ejpam-6680	183	10	for	for	ADP
ejpam-6680	183	11	the	the	DET
ejpam-6680	183	12	given	give	VERB
ejpam-6680	183	13	iteration	iteration	NOUN
ejpam-6680	183	14	bn	bn	NOUN
ejpam-6680	183	15	,	,	PUNCT
ejpam-6680	183	16	we	we	PRON
ejpam-6680	183	17	first	first	ADV
ejpam-6680	183	18	calculate	calculate	VERB
ejpam-6680	183	19	bn+1	bn+1	NUM
ejpam-6680	183	20	as	as	SCONJ
ejpam-6680	183	21	stated	state	VERB
ejpam-6680	183	22	below	below	ADV
ejpam-6680	183	23	:	:	PUNCT
ejpam-6680	183	24	step	step	NOUN
ejpam-6680	183	25	1	1	NUM
ejpam-6680	183	26	.	.	PUNCT
ejpam-6680	184	1	compute	compute	VERB
ejpam-6680	184	2	sn	sn	PROPN
ejpam-6680	184	3	=	=	SYM
ejpam-6680	184	4	pl(ξnbn	pl(ξnbn	PROPN
ejpam-6680	184	5	⊕	⊕	PROPN
ejpam-6680	184	6	(	(	PUNCT
ejpam-6680	184	7	1−	1−	NUM
ejpam-6680	184	8	ξn)abn	ξn)abn	NOUN
ejpam-6680	184	9	)	)	PUNCT
ejpam-6680	184	10	,	,	PUNCT
ejpam-6680	184	11	where	where	SCONJ
ejpam-6680	184	12	ξn	ξn	ADJ
ejpam-6680	184	13	:	:	PUNCT
ejpam-6680	184	14	=	=	SYM
ejpam-6680	184	15	ςνmn	ςνmn	PROPN
ejpam-6680	184	16	,	,	PUNCT
ejpam-6680	184	17	with	with	ADP
ejpam-6680	184	18	mn	mn	PROPN
ejpam-6680	184	19	is	be	AUX
ejpam-6680	184	20	the	the	DET
ejpam-6680	184	21	minimal	minimal	ADJ
ejpam-6680	184	22	nonnegative	nonnegative	ADJ
ejpam-6680	184	23	integer	integer	NOUN
ejpam-6680	184	24	satisfying	satisfy	VERB
ejpam-6680	184	25	⟨	⟨	VERB
ejpam-6680	184	26	−−−−−→	−−−−−→	X
ejpam-6680	184	27	abnasn	abnasn	NOUN
ejpam-6680	184	28	,	,	PUNCT
ejpam-6680	184	29	−−→	−−→	PROPN
ejpam-6680	184	30	bnsn⟩	bnsn⟩	PROPN
ejpam-6680	184	31	≤	≤	PUNCT
ejpam-6680	184	32	µϱ2(bn	µϱ2(bn	PROPN
ejpam-6680	184	33	,	,	PUNCT
ejpam-6680	184	34	sn	sn	PROPN
ejpam-6680	184	35	)	)	PUNCT
ejpam-6680	184	36	.	.	PUNCT
ejpam-6680	185	1	if	if	SCONJ
ejpam-6680	185	2	asn	asn	PROPN
ejpam-6680	185	3	=	=	PUNCT
ejpam-6680	185	4	0	0	NUM
ejpam-6680	185	5	or	or	CCONJ
ejpam-6680	185	6	bn	bn	NOUN
ejpam-6680	185	7	=	=	SYM
ejpam-6680	185	8	sn	sn	PROPN
ejpam-6680	185	9	holds	hold	VERB
ejpam-6680	185	10	then	then	ADV
ejpam-6680	185	11	algorithm	algorithm	NOUN
ejpam-6680	185	12	stops	stop	NOUN
ejpam-6680	185	13	and	and	CCONJ
ejpam-6680	185	14	sn	sn	PROPN
ejpam-6680	185	15	is	be	AUX
ejpam-6680	185	16	a	a	DET
ejpam-6680	185	17	solution	solution	NOUN
ejpam-6680	185	18	of	of	ADP
ejpam-6680	185	19	vi	vi	PROPN
ejpam-6680	185	20	.	.	PUNCT
ejpam-6680	185	21	else	else	ADJ
ejpam-6680	185	22	step	step	NOUN
ejpam-6680	185	23	2	2	NUM
ejpam-6680	185	24	.	.	PUNCT
ejpam-6680	185	25	calculate	calculate	NOUN
ejpam-6680	185	26	bn+1	bn+1	NOUN
ejpam-6680	185	27	=	=	PUNCT
ejpam-6680	185	28	pln(bn	pln(bn	X
ejpam-6680	185	29	)	)	PUNCT
ejpam-6680	185	30	,	,	PUNCT
ejpam-6680	185	31	where	where	SCONJ
ejpam-6680	185	32	ln	ln	ADV
ejpam-6680	185	33	:	:	PUNCT
ejpam-6680	185	34	=	=	SYM
ejpam-6680	185	35	{	{	PUNCT
ejpam-6680	185	36	l	l	NOUN
ejpam-6680	185	37	∈	∈	PROPN
ejpam-6680	185	38	z	z	NOUN
ejpam-6680	185	39	:	:	PUNCT
ejpam-6680	185	40	hn(b	hn(b	X
ejpam-6680	185	41	)	)	PUNCT
ejpam-6680	185	42	≤	≤	NOUN
ejpam-6680	185	43	0	0	NUM
ejpam-6680	185	44	}	}	PUNCT
ejpam-6680	185	45	and	and	CCONJ
ejpam-6680	185	46	hn(b	hn(b	NUM
ejpam-6680	185	47	)	)	PUNCT
ejpam-6680	185	48	=	=	VERB
ejpam-6680	185	49	⟨	⟨	VERB
ejpam-6680	185	50	−→	−→	NOUN
ejpam-6680	185	51	bsn	bsn	NOUN
ejpam-6680	185	52	,	,	PUNCT
ejpam-6680	185	53	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	PRON
ejpam-6680	185	54	(	(	PUNCT
ejpam-6680	185	55	ξnbn	ξnbn	PROPN
ejpam-6680	185	56	⊕	⊕	PROPN
ejpam-6680	185	57	(	(	PUNCT
ejpam-6680	185	58	1−	1−	NUM
ejpam-6680	185	59	ξn)abn)abn⟩.	ξn)abn)abn⟩.	NOUN
ejpam-6680	185	60	(	(	PUNCT
ejpam-6680	185	61	6	6	NUM
ejpam-6680	185	62	)	)	PUNCT
ejpam-6680	185	63	place	place	NOUN
ejpam-6680	185	64	n	n	NOUN
ejpam-6680	185	65	:	:	PUNCT
ejpam-6680	185	66	=	=	SYM
ejpam-6680	185	67	n+	n+	ADP
ejpam-6680	185	68	1	1	NUM
ejpam-6680	185	69	and	and	CCONJ
ejpam-6680	185	70	repeat	repeat	VERB
ejpam-6680	185	71	the	the	DET
ejpam-6680	185	72	step	step	NOUN
ejpam-6680	185	73	1	1	NUM
ejpam-6680	185	74	.	.	PUNCT
ejpam-6680	186	1	m.	m.	NOUN
ejpam-6680	186	2	rashid	rashid	PROPN
ejpam-6680	186	3	et	et	PROPN
ejpam-6680	186	4	al	al	PROPN
ejpam-6680	186	5	.	.	PUNCT
ejpam-6680	186	6	/	/	SYM
ejpam-6680	186	7	eur	eur	PROPN
ejpam-6680	186	8	.	.	PUNCT
ejpam-6680	187	1	j.	j.	PROPN
ejpam-6680	187	2	pure	pure	PROPN
ejpam-6680	187	3	appl	appl	PROPN
ejpam-6680	187	4	.	.	PROPN
ejpam-6680	187	5	math	math	PROPN
ejpam-6680	187	6	,	,	PUNCT
ejpam-6680	187	7	18	18	NUM
ejpam-6680	187	8	(	(	PUNCT
ejpam-6680	187	9	4	4	NUM
ejpam-6680	187	10	)	)	PUNCT
ejpam-6680	187	11	(	(	PUNCT
ejpam-6680	187	12	2025	2025	NUM
ejpam-6680	187	13	)	)	PUNCT
ejpam-6680	187	14	,	,	PUNCT
ejpam-6680	187	15	6680	6680	NUM
ejpam-6680	187	16	10	10	NUM
ejpam-6680	187	17	of	of	ADP
ejpam-6680	187	18	24	24	NUM
ejpam-6680	187	19	lemma	lemma	PROPN
ejpam-6680	187	20	13	13	NUM
ejpam-6680	187	21	.	.	PUNCT
ejpam-6680	187	22	suppose	suppose	VERB
ejpam-6680	187	23	that	that	SCONJ
ejpam-6680	187	24	conditions	condition	NOUN
ejpam-6680	187	25	1	1	NUM
ejpam-6680	187	26	-	-	SYM
ejpam-6680	187	27	3	3	NUM
ejpam-6680	187	28	hold	hold	NOUN
ejpam-6680	187	29	.	.	PUNCT
ejpam-6680	188	1	let	let	VERB
ejpam-6680	188	2	b∗	b∗	ADJ
ejpam-6680	188	3	be	be	AUX
ejpam-6680	188	4	a	a	DET
ejpam-6680	188	5	solution	solution	NOUN
ejpam-6680	188	6	of	of	ADP
ejpam-6680	188	7	v	v	ADP
ejpam-6680	188	8	i(l	i(l	PROPN
ejpam-6680	188	9	,	,	PUNCT
ejpam-6680	188	10	a	a	PRON
ejpam-6680	188	11	)	)	PUNCT
ejpam-6680	188	12	and	and	CCONJ
ejpam-6680	188	13	the	the	DET
ejpam-6680	188	14	function	function	NOUN
ejpam-6680	188	15	hn	hn	PRON
ejpam-6680	188	16	be	be	AUX
ejpam-6680	188	17	defined	define	VERB
ejpam-6680	188	18	by	by	ADP
ejpam-6680	188	19	(	(	PUNCT
ejpam-6680	188	20	6	6	NUM
ejpam-6680	188	21	)	)	PUNCT
ejpam-6680	188	22	.	.	PUNCT
ejpam-6680	189	1	then	then	ADV
ejpam-6680	189	2	hn(b	hn(b	VERB
ejpam-6680	189	3	∗	∗	NOUN
ejpam-6680	189	4	)	)	PUNCT
ejpam-6680	189	5	≤	≤	NOUN
ejpam-6680	189	6	0	0	NUM
ejpam-6680	190	1	and	and	CCONJ
ejpam-6680	190	2	hn(bn	hn(bn	NOUN
ejpam-6680	190	3	)	)	PUNCT
ejpam-6680	190	4	≥	≥	NOUN
ejpam-6680	190	5	(	(	PUNCT
ejpam-6680	190	6	1−	1−	NUM
ejpam-6680	190	7	µ)ϱ2(bn	µ)ϱ2(bn	NUM
ejpam-6680	190	8	,	,	PUNCT
ejpam-6680	190	9	sn	sn	PROPN
ejpam-6680	190	10	)	)	PUNCT
ejpam-6680	190	11	.	.	PUNCT
ejpam-6680	191	1	proof	proof	NOUN
ejpam-6680	191	2	.	.	PUNCT
ejpam-6680	192	1	since	since	SCONJ
ejpam-6680	192	2	b∗	b∗	PROPN
ejpam-6680	192	3	∈	∈	PROPN
ejpam-6680	192	4	v	v	ADP
ejpam-6680	192	5	i(l	i(l	PROPN
ejpam-6680	192	6	,	,	PUNCT
ejpam-6680	192	7	a	a	PRON
ejpam-6680	192	8	)	)	PUNCT
ejpam-6680	192	9	,	,	PUNCT
ejpam-6680	192	10	we	we	PRON
ejpam-6680	192	11	have	have	VERB
ejpam-6680	192	12	⟨	⟨	NOUN
ejpam-6680	192	13	−−−→	−−−→	PROPN
ejpam-6680	192	14	snab	snab	ADJ
ejpam-6680	192	15	∗	∗	NOUN
ejpam-6680	192	16	,	,	PUNCT
ejpam-6680	192	17	−−→	−−→	PROPN
ejpam-6680	192	18	b∗sn⟩	b∗sn⟩	VERB
ejpam-6680	192	19	≤	≤	NOUN
ejpam-6680	192	20	0	0	NUM
ejpam-6680	192	21	.	.	PUNCT
ejpam-6680	193	1	(	(	PUNCT
ejpam-6680	193	2	7	7	X
ejpam-6680	193	3	)	)	PUNCT
ejpam-6680	193	4	it	it	PRON
ejpam-6680	193	5	is	be	AUX
ejpam-6680	193	6	implied	imply	VERB
ejpam-6680	193	7	from	from	ADP
ejpam-6680	193	8	lemma	lemma	PROPN
ejpam-6680	193	9	7	7	NUM
ejpam-6680	193	10	and	and	CCONJ
ejpam-6680	193	11	(	(	PUNCT
ejpam-6680	193	12	7	7	X
ejpam-6680	193	13	)	)	PUNCT
ejpam-6680	193	14	that	that	PRON
ejpam-6680	193	15	hn(b	hn(b	VERB
ejpam-6680	193	16	∗	∗	NOUN
ejpam-6680	193	17	)	)	PUNCT
ejpam-6680	193	18	=	=	PRON
ejpam-6680	194	1	⟨	⟨	VERB
ejpam-6680	194	2	−−→	−−→	PROPN
ejpam-6680	194	3	b∗sn	b∗sn	PROPN
ejpam-6680	194	4	,	,	PUNCT
ejpam-6680	194	5	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	PROPN
ejpam-6680	194	6	(	(	PUNCT
ejpam-6680	194	7	ξnbn	ξnbn	PROPN
ejpam-6680	194	8	⊕	⊕	PROPN
ejpam-6680	194	9	(	(	PUNCT
ejpam-6680	194	10	1−	1−	NUM
ejpam-6680	194	11	ξn)abn)abn⟩	ξn)abn)abn⟩	NOUN
ejpam-6680	194	12	,	,	PUNCT
ejpam-6680	194	13	≤	≤	NUM
ejpam-6680	194	14	ξn⟨	ξn⟨	PROPN
ejpam-6680	194	15	−−→	−−→	PROPN
ejpam-6680	194	16	b∗sn	b∗sn	PROPN
ejpam-6680	194	17	,	,	PUNCT
ejpam-6680	194	18	−−−→	−−−→	ADJ
ejpam-6680	194	19	bnabn⟩+	bnabn⟩+	PROPN
ejpam-6680	194	20	(	(	PUNCT
ejpam-6680	194	21	1−	1−	NUM
ejpam-6680	194	22	ξn)⟨	ξn)⟨	NUM
ejpam-6680	194	23	−−→	−−→	PROPN
ejpam-6680	194	24	b∗sn	b∗sn	PROPN
ejpam-6680	194	25	,	,	PUNCT
ejpam-6680	194	26	−−−−−→	−−−−−→	PUNCT
ejpam-6680	194	27	abnabn⟩	abnabn⟩	PROPN
ejpam-6680	194	28	,	,	PUNCT
ejpam-6680	194	29	≤	≤	NUM
ejpam-6680	194	30	ξn⟨	ξn⟨	PROPN
ejpam-6680	194	31	−−→	−−→	PROPN
ejpam-6680	194	32	b∗sn	b∗sn	PROPN
ejpam-6680	194	33	,	,	PUNCT
ejpam-6680	194	34	−−→	−−→	PROPN
ejpam-6680	194	35	bnsn⟩+	bnsn⟩+	PROPN
ejpam-6680	194	36	⟨	⟨	VERB
ejpam-6680	194	37	−−→	−−→	PROPN
ejpam-6680	194	38	b∗sn	b∗sn	PROPN
ejpam-6680	194	39	,	,	PUNCT
ejpam-6680	194	40	−−−→	−−−→	VERB
ejpam-6680	194	41	snab	snab	ADJ
ejpam-6680	194	42	∗⟩+	∗⟩+	PROPN
ejpam-6680	194	43	ξn⟨	ξn⟨	PROPN
ejpam-6680	194	44	−−→	−−→	PROPN
ejpam-6680	194	45	b∗sn	b∗sn	PROPN
ejpam-6680	194	46	,	,	PUNCT
ejpam-6680	194	47	−−−−−→	−−−−−→	X
ejpam-6680	194	48	ab∗abn⟩	ab∗abn⟩	NOUN
ejpam-6680	194	49	,	,	PUNCT
ejpam-6680	194	50	by	by	ADP
ejpam-6680	194	51	taking	take	VERB
ejpam-6680	194	52	limit	limit	NOUN
ejpam-6680	194	53	,	,	PUNCT
ejpam-6680	194	54	we	we	PRON
ejpam-6680	194	55	get	get	VERB
ejpam-6680	194	56	hn(b	hn(b	PUNCT
ejpam-6680	194	57	∗	∗	NOUN
ejpam-6680	194	58	)	)	PUNCT
ejpam-6680	194	59	≤	≤	NOUN
ejpam-6680	194	60	0	0	NUM
ejpam-6680	194	61	.	.	PUNCT
ejpam-6680	195	1	thus	thus	ADV
ejpam-6680	195	2	claim	claim	VERB
ejpam-6680	195	3	1	1	NUM
ejpam-6680	195	4	of	of	ADP
ejpam-6680	195	5	lemma	lemma	PROPN
ejpam-6680	195	6	13	13	NUM
ejpam-6680	195	7	holds	hold	NOUN
ejpam-6680	195	8	.	.	PUNCT
ejpam-6680	196	1	now	now	ADV
ejpam-6680	196	2	,	,	PUNCT
ejpam-6680	196	3	to	to	PART
ejpam-6680	196	4	prove	prove	VERB
ejpam-6680	196	5	claim	claim	NOUN
ejpam-6680	196	6	2	2	NUM
ejpam-6680	196	7	,	,	PUNCT
ejpam-6680	196	8	from	from	ADP
ejpam-6680	196	9	(	(	PUNCT
ejpam-6680	196	10	6	6	NUM
ejpam-6680	196	11	)	)	PUNCT
ejpam-6680	196	12	,	,	PUNCT
ejpam-6680	196	13	we	we	PRON
ejpam-6680	196	14	have	have	VERB
ejpam-6680	196	15	hn(bn	hn(bn	NOUN
ejpam-6680	196	16	)	)	PUNCT
ejpam-6680	196	17	=	=	PUNCT
ejpam-6680	197	1	⟨	⟨	VERB
ejpam-6680	197	2	−−→	−−→	NOUN
ejpam-6680	197	3	bnsn	bnsn	NOUN
ejpam-6680	197	4	,	,	PUNCT
ejpam-6680	197	5	−−−−→	−−−−→	PRON
ejpam-6680	197	6	snabn⟩	snabn⟩	VERB
ejpam-6680	197	7	=	=	SYM
ejpam-6680	197	8	⟨	⟨	VERB
ejpam-6680	197	9	−−→	−−→	NOUN
ejpam-6680	197	10	bnsn	bnsn	NOUN
ejpam-6680	197	11	,	,	PUNCT
ejpam-6680	197	12	−−→	−−→	PROPN
ejpam-6680	197	13	snbn⟩+	snbn⟩+	PROPN
ejpam-6680	197	14	⟨	⟨	VERB
ejpam-6680	197	15	−−→	−−→	NOUN
ejpam-6680	197	16	bnsn	bnsn	NOUN
ejpam-6680	197	17	,	,	PUNCT
ejpam-6680	197	18	−−−−→	−−−−→	PUNCT
ejpam-6680	197	19	bnasn⟩+	bnasn⟩+	NOUN
ejpam-6680	197	20	⟨	⟨	VERB
ejpam-6680	197	21	−−→	−−→	NOUN
ejpam-6680	197	22	bnsn	bnsn	NOUN
ejpam-6680	197	23	,	,	PUNCT
ejpam-6680	197	24	−−−−−→	−−−−−→	X
ejpam-6680	197	25	asnabn⟩.	asnabn⟩.	NOUN
ejpam-6680	197	26	as	as	ADP
ejpam-6680	197	27	⟨	⟨	NOUN
ejpam-6680	197	28	−−→	−−→	NOUN
ejpam-6680	197	29	bnsn	bnsn	NOUN
ejpam-6680	197	30	,	,	PUNCT
ejpam-6680	197	31	−−−−→	−−−−→	PRON
ejpam-6680	197	32	bnasn⟩	bnasn⟩	X
ejpam-6680	197	33	≥	≥	NOUN
ejpam-6680	197	34	0	0	NUM
ejpam-6680	197	35	,	,	PUNCT
ejpam-6680	197	36	we	we	PRON
ejpam-6680	197	37	have	have	VERB
ejpam-6680	197	38	hn(bn	hn(bn	NOUN
ejpam-6680	197	39	)	)	PUNCT
ejpam-6680	197	40	≥	≥	NOUN
ejpam-6680	197	41	⟨	⟨	VERB
ejpam-6680	197	42	−−→	−−→	NOUN
ejpam-6680	197	43	bnsn	bnsn	NOUN
ejpam-6680	197	44	,	,	PUNCT
ejpam-6680	197	45	−−→	−−→	PROPN
ejpam-6680	197	46	snbn⟩+	snbn⟩+	PROPN
ejpam-6680	197	47	⟨	⟨	VERB
ejpam-6680	197	48	−−→	−−→	NOUN
ejpam-6680	197	49	bnsn	bnsn	NOUN
ejpam-6680	197	50	,	,	PUNCT
ejpam-6680	197	51	−−−−−→	−−−−−→	X
ejpam-6680	197	52	asnabn⟩	asnabn⟩	PROPN
ejpam-6680	197	53	,	,	PUNCT
ejpam-6680	197	54	≥	≥	X
ejpam-6680	197	55	−ϱ2(bn	−ϱ2(bn	PROPN
ejpam-6680	197	56	,	,	PUNCT
ejpam-6680	197	57	sn)−	sn)−	PRON
ejpam-6680	197	58	µϱ2(bn	µϱ2(bn	PROPN
ejpam-6680	197	59	,	,	PUNCT
ejpam-6680	197	60	sn	sn	PROPN
ejpam-6680	197	61	)	)	PUNCT
ejpam-6680	197	62	,	,	PUNCT
ejpam-6680	197	63	=	=	SYM
ejpam-6680	197	64	(	(	PUNCT
ejpam-6680	197	65	−1−	−1−	PROPN
ejpam-6680	197	66	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	197	67	,	,	PUNCT
ejpam-6680	197	68	sn	sn	PROPN
ejpam-6680	197	69	)	)	PUNCT
ejpam-6680	197	70	.	.	PUNCT
ejpam-6680	198	1	lemma	lemma	PROPN
ejpam-6680	198	2	14	14	NUM
ejpam-6680	198	3	.	.	PUNCT
ejpam-6680	198	4	consider	consider	VERB
ejpam-6680	198	5	a	a	DET
ejpam-6680	198	6	nonempty	nonempty	ADJ
ejpam-6680	198	7	,	,	PUNCT
ejpam-6680	198	8	closed	closed	ADJ
ejpam-6680	198	9	and	and	CCONJ
ejpam-6680	198	10	convex	convex	PROPN
ejpam-6680	198	11	subset	subset	NOUN
ejpam-6680	198	12	of	of	ADP
ejpam-6680	198	13	a	a	DET
ejpam-6680	198	14	hadamard	hadamard	ADJ
ejpam-6680	198	15	space	space	NOUN
ejpam-6680	198	16	z	z	AUX
ejpam-6680	198	17	be	be	AUX
ejpam-6680	198	18	l.	l.	PROPN
ejpam-6680	198	19	the	the	DET
ejpam-6680	198	20	map	map	NOUN
ejpam-6680	198	21	a	a	PRON
ejpam-6680	198	22	is	be	AUX
ejpam-6680	198	23	uniformly	uniformly	ADV
ejpam-6680	198	24	continuous	continuous	ADJ
ejpam-6680	198	25	and	and	CCONJ
ejpam-6680	198	26	pseudo	pseudo	NOUN
ejpam-6680	198	27	-	-	NOUN
ejpam-6680	198	28	monotone	monotone	ADJ
ejpam-6680	198	29	on	on	ADP
ejpam-6680	198	30	l.	l.	PROPN
ejpam-6680	198	31	the	the	DET
ejpam-6680	198	32	solution	solution	NOUN
ejpam-6680	198	33	set	set	VERB
ejpam-6680	198	34	of	of	ADP
ejpam-6680	198	35	the	the	DET
ejpam-6680	198	36	v	v	PROPN
ejpam-6680	198	37	i(l	i(l	PROPN
ejpam-6680	198	38	,	,	PUNCT
ejpam-6680	198	39	a	a	PRON
ejpam-6680	198	40	)	)	PUNCT
ejpam-6680	198	41	is	be	AUX
ejpam-6680	198	42	nonempty	nonempty	ADJ
ejpam-6680	198	43	and	and	CCONJ
ejpam-6680	198	44	suppose	suppose	VERB
ejpam-6680	198	45	a	a	DET
ejpam-6680	198	46	sequence	sequence	NOUN
ejpam-6680	198	47	produced	produce	VERB
ejpam-6680	198	48	by	by	ADP
ejpam-6680	198	49	algorithm	algorithm	NOUN
ejpam-6680	198	50	1	1	NUM
ejpam-6680	198	51	is	be	AUX
ejpam-6680	198	52	{	{	PUNCT
ejpam-6680	198	53	bn	bn	NOUN
ejpam-6680	198	54	}	}	PUNCT
ejpam-6680	198	55	.	.	PUNCT
ejpam-6680	199	1	if	if	SCONJ
ejpam-6680	199	2	there	there	PRON
ejpam-6680	199	3	is	be	VERB
ejpam-6680	199	4	a	a	DET
ejpam-6680	199	5	subsequence	subsequence	NOUN
ejpam-6680	199	6	{	{	PUNCT
ejpam-6680	199	7	bnk	bnk	PROPN
ejpam-6680	199	8	}	}	PUNCT
ejpam-6680	199	9	of	of	ADP
ejpam-6680	199	10	{	{	PUNCT
ejpam-6680	199	11	bn	bn	ADP
ejpam-6680	199	12	}	}	PUNCT
ejpam-6680	199	13	such	such	ADJ
ejpam-6680	199	14	that	that	SCONJ
ejpam-6680	199	15	{	{	PUNCT
ejpam-6680	199	16	bnk	bnk	NOUN
ejpam-6680	199	17	}	}	PUNCT
ejpam-6680	199	18	∆-converges	∆-converge	VERB
ejpam-6680	199	19	to	to	ADP
ejpam-6680	199	20	z	z	PROPN
ejpam-6680	199	21	∈	∈	PROPN
ejpam-6680	199	22	z	z	NOUN
ejpam-6680	199	23	and	and	CCONJ
ejpam-6680	199	24	limk→∞	limk→∞	PROPN
ejpam-6680	199	25	ϱ(bnk	ϱ(bnk	NOUN
ejpam-6680	199	26	,	,	PUNCT
ejpam-6680	199	27	snk	snk	PROPN
ejpam-6680	199	28	)	)	PUNCT
ejpam-6680	199	29	=	=	SYM
ejpam-6680	199	30	0	0	NUM
ejpam-6680	199	31	,	,	PUNCT
ejpam-6680	199	32	then	then	ADV
ejpam-6680	199	33	z	z	PROPN
ejpam-6680	199	34	∈	∈	PROPN
ejpam-6680	199	35	v	v	ADP
ejpam-6680	199	36	i(l	i(l	PROPN
ejpam-6680	199	37	,	,	PUNCT
ejpam-6680	199	38	a	a	PRON
ejpam-6680	199	39	)	)	PUNCT
ejpam-6680	199	40	.	.	PUNCT
ejpam-6680	200	1	proof	proof	NOUN
ejpam-6680	200	2	.	.	PUNCT
ejpam-6680	201	1	from	from	ADP
ejpam-6680	201	2	∆−	∆−	NOUN
ejpam-6680	201	3	limn→∞	limn→∞	PRON
ejpam-6680	201	4	bnk	bnk	PROPN
ejpam-6680	201	5	=	=	SYM
ejpam-6680	201	6	z	z	NOUN
ejpam-6680	201	7	,	,	PUNCT
ejpam-6680	201	8	limk→∞	limk→∞	ADJ
ejpam-6680	201	9	ϱ(bnk	ϱ(bnk	NOUN
ejpam-6680	201	10	,	,	PUNCT
ejpam-6680	201	11	snk	snk	PROPN
ejpam-6680	201	12	)	)	PUNCT
ejpam-6680	201	13	=	=	SYM
ejpam-6680	201	14	0	0	NUM
ejpam-6680	201	15	,	,	PUNCT
ejpam-6680	201	16	and	and	CCONJ
ejpam-6680	201	17	sn	sn	PROPN
ejpam-6680	201	18	⊂	⊂	PROPN
ejpam-6680	201	19	l	l	NOUN
ejpam-6680	201	20	,	,	PUNCT
ejpam-6680	201	21	we	we	PRON
ejpam-6680	201	22	have	have	VERB
ejpam-6680	201	23	z	z	NOUN
ejpam-6680	201	24	∈	∈	PROPN
ejpam-6680	201	25	l	l	NOUN
ejpam-6680	201	26	and	and	CCONJ
ejpam-6680	201	27	snk	snk	PROPN
ejpam-6680	201	28	=	=	SYM
ejpam-6680	201	29	pl(ξnk	pl(ξnk	VERB
ejpam-6680	201	30	bnk	bnk	PROPN
ejpam-6680	201	31	⊕	⊕	PROPN
ejpam-6680	201	32	(	(	PUNCT
ejpam-6680	201	33	1−	1−	NUM
ejpam-6680	201	34	ξnk	ξnk	NOUN
ejpam-6680	201	35	)	)	PUNCT
ejpam-6680	201	36	abnk	abnk	NOUN
ejpam-6680	201	37	)	)	PUNCT
ejpam-6680	201	38	thus	thus	ADV
ejpam-6680	201	39	,	,	PUNCT
ejpam-6680	201	40	0	0	NUM
ejpam-6680	201	41	≤	≤	NOUN
ejpam-6680	201	42	⟨	⟨	VERB
ejpam-6680	201	43	−−→	−−→	PROPN
ejpam-6680	201	44	bsnk	bsnk	NOUN
ejpam-6680	201	45	,	,	PUNCT
ejpam-6680	201	46	−−−−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−−−−→	PROPN
ejpam-6680	201	47	snk	snk	PROPN
ejpam-6680	201	48	(	(	PUNCT
ejpam-6680	201	49	ξnk	ξnk	PROPN
ejpam-6680	201	50	bnk	bnk	PROPN
ejpam-6680	201	51	⊕	⊕	PROPN
ejpam-6680	201	52	(	(	PUNCT
ejpam-6680	201	53	1−	1−	NUM
ejpam-6680	201	54	ξnk	ξnk	NOUN
ejpam-6680	201	55	)	)	PUNCT
ejpam-6680	201	56	abnk	abnk	PROPN
ejpam-6680	201	57	)	)	PUNCT
ejpam-6680	201	58	⟩	⟩	NOUN
ejpam-6680	201	59	,	,	PUNCT
ejpam-6680	201	60	∀b	∀b	NOUN
ejpam-6680	201	61	∈	∈	PROPN
ejpam-6680	201	62	l.	l.	NOUN
ejpam-6680	201	63	by	by	ADP
ejpam-6680	201	64	lemma	lemma	PROPN
ejpam-6680	201	65	7	7	NUM
ejpam-6680	201	66	and	and	CCONJ
ejpam-6680	201	67	remark	remark	NOUN
ejpam-6680	201	68	1	1	NUM
ejpam-6680	201	69	,	,	PUNCT
ejpam-6680	201	70	we	we	PRON
ejpam-6680	201	71	get	get	VERB
ejpam-6680	201	72	⟨	⟨	ADJ
ejpam-6680	201	73	−−−−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−−−−→	X
ejpam-6680	201	74	(	(	PUNCT
ejpam-6680	201	75	ξnk	ξnk	PROPN
ejpam-6680	201	76	bnk	bnk	PROPN
ejpam-6680	201	77	⊕	⊕	PROPN
ejpam-6680	201	78	(	(	PUNCT
ejpam-6680	201	79	1−	1−	NUM
ejpam-6680	201	80	ξnk	ξnk	NOUN
ejpam-6680	201	81	)	)	PUNCT
ejpam-6680	201	82	abnk	abnk	PROPN
ejpam-6680	201	83	)	)	PUNCT
ejpam-6680	201	84	snk	snk	PROPN
ejpam-6680	201	85	,	,	PUNCT
ejpam-6680	201	86	−−→	−−→	PROPN
ejpam-6680	201	87	snk	snk	PROPN
ejpam-6680	201	88	b⟩	b⟩	PROPN
ejpam-6680	201	89	≤	≤	NUM
ejpam-6680	201	90	ξnk	ξnk	VERB
ejpam-6680	201	91	⟨	⟨	VERB
ejpam-6680	201	92	−−−−→	−−−−→	X
ejpam-6680	201	93	bnk	bnk	PROPN
ejpam-6680	201	94	snk	snk	PROPN
ejpam-6680	201	95	,	,	PUNCT
ejpam-6680	201	96	−−→	−−→	PROPN
ejpam-6680	201	97	snk	snk	PROPN
ejpam-6680	201	98	b⟩+	b⟩+	X
ejpam-6680	201	99	(	(	PUNCT
ejpam-6680	201	100	1−	1−	NUM
ejpam-6680	201	101	ξnk	ξnk	NOUN
ejpam-6680	201	102	)	)	PUNCT
ejpam-6680	201	103	⟨	⟨	VERB
ejpam-6680	201	104	−−−−−→	−−−−−→	NUM
ejpam-6680	201	105	abnk	abnk	PROPN
ejpam-6680	201	106	snk	snk	PROPN
ejpam-6680	201	107	,	,	PUNCT
ejpam-6680	201	108	−−→	−−→	PROPN
ejpam-6680	201	109	snk	snk	PROPN
ejpam-6680	201	110	b⟩	b⟩	PROPN
ejpam-6680	201	111	,	,	PUNCT
ejpam-6680	201	112	=	=	PRON
ejpam-6680	201	113	ξnk	ξnk	VERB
ejpam-6680	201	114	⟨	⟨	VERB
ejpam-6680	201	115	−−−−→	−−−−→	X
ejpam-6680	201	116	bnk	bnk	PROPN
ejpam-6680	201	117	snk	snk	PROPN
ejpam-6680	201	118	,	,	PUNCT
ejpam-6680	201	119	−−→	−−→	PROPN
ejpam-6680	201	120	snk	snk	PROPN
ejpam-6680	201	121	b⟩+	b⟩+	X
ejpam-6680	201	122	(	(	PUNCT
ejpam-6680	201	123	1−	1−	NUM
ejpam-6680	201	124	ξnk	ξnk	NOUN
ejpam-6680	201	125	)	)	PUNCT
ejpam-6680	201	126	⟨	⟨	VERB
ejpam-6680	201	127	−−→	−−→	PROPN
ejpam-6680	201	128	snk	snk	PROPN
ejpam-6680	201	129	b	b	PROPN
ejpam-6680	201	130	,	,	PUNCT
ejpam-6680	201	131	−−→	−−→	PROPN
ejpam-6680	202	1	bsnk	bsnk	NOUN
ejpam-6680	203	1	⟩+	⟩+	NOUN
ejpam-6680	203	2	(	(	PUNCT
ejpam-6680	203	3	1−	1−	NUM
ejpam-6680	203	4	ξnk	ξnk	NOUN
ejpam-6680	203	5	)	)	PUNCT
ejpam-6680	203	6	⟨	⟨	VERB
ejpam-6680	203	7	−−−→	−−−→	PROPN
ejpam-6680	203	8	babnk	babnk	NOUN
ejpam-6680	203	9	,	,	PUNCT
ejpam-6680	203	10	−−→	−−→	PROPN
ejpam-6680	203	11	bsnk	bsnk	PROPN
ejpam-6680	203	12	⟩	⟩	NOUN
ejpam-6680	203	13	,	,	PUNCT
ejpam-6680	203	14	m.	m.	NOUN
ejpam-6680	203	15	rashid	rashid	PROPN
ejpam-6680	203	16	et	et	PROPN
ejpam-6680	203	17	al	al	PROPN
ejpam-6680	203	18	.	.	PUNCT
ejpam-6680	203	19	/	/	SYM
ejpam-6680	203	20	eur	eur	PROPN
ejpam-6680	203	21	.	.	PUNCT
ejpam-6680	204	1	j.	j.	PROPN
ejpam-6680	204	2	pure	pure	PROPN
ejpam-6680	204	3	appl	appl	PROPN
ejpam-6680	204	4	.	.	PROPN
ejpam-6680	204	5	math	math	PROPN
ejpam-6680	204	6	,	,	PUNCT
ejpam-6680	204	7	18	18	NUM
ejpam-6680	204	8	(	(	PUNCT
ejpam-6680	204	9	4	4	NUM
ejpam-6680	204	10	)	)	PUNCT
ejpam-6680	204	11	(	(	PUNCT
ejpam-6680	204	12	2025	2025	NUM
ejpam-6680	204	13	)	)	PUNCT
ejpam-6680	204	14	,	,	PUNCT
ejpam-6680	204	15	6680	6680	NUM
ejpam-6680	204	16	11	11	NUM
ejpam-6680	204	17	of	of	ADP
ejpam-6680	204	18	24	24	NUM
ejpam-6680	204	19	=	=	SYM
ejpam-6680	204	20	ξnk	ξnk	X
ejpam-6680	204	21	⟨	⟨	VERB
ejpam-6680	204	22	−−−−→	−−−−→	PUNCT
ejpam-6680	204	23	bnk	bnk	PROPN
ejpam-6680	204	24	snk	snk	PROPN
ejpam-6680	204	25	,	,	PUNCT
ejpam-6680	204	26	−−→	−−→	PROPN
ejpam-6680	204	27	snk	snk	PROPN
ejpam-6680	204	28	b⟩+	b⟩+	X
ejpam-6680	204	29	(	(	PUNCT
ejpam-6680	204	30	1−	1−	NUM
ejpam-6680	204	31	ξnk	ξnk	NOUN
ejpam-6680	204	32	)	)	PUNCT
ejpam-6680	204	33	⟨	⟨	VERB
ejpam-6680	204	34	−−→	−−→	PROPN
ejpam-6680	204	35	snk	snk	PROPN
ejpam-6680	204	36	b	b	PROPN
ejpam-6680	204	37	,	,	PUNCT
ejpam-6680	204	38	−−→	−−→	PROPN
ejpam-6680	205	1	bsnk	bsnk	NOUN
ejpam-6680	206	1	⟩+	⟩+	NOUN
ejpam-6680	206	2	(	(	PUNCT
ejpam-6680	206	3	1−	1−	NUM
ejpam-6680	206	4	ξnk	ξnk	NOUN
ejpam-6680	206	5	)	)	PUNCT
ejpam-6680	206	6	⟨	⟨	VERB
ejpam-6680	206	7	−−−→	−−−→	PROPN
ejpam-6680	206	8	babnk	babnk	NOUN
ejpam-6680	206	9	,	,	PUNCT
ejpam-6680	206	10	−−→	−−→	PROPN
ejpam-6680	206	11	bbnk	bbnk	NOUN
ejpam-6680	207	1	⟩+	⟩+	NOUN
ejpam-6680	207	2	(	(	PUNCT
ejpam-6680	207	3	1−	1−	NUM
ejpam-6680	207	4	ξnk	ξnk	NOUN
ejpam-6680	207	5	)	)	PUNCT
ejpam-6680	207	6	⟨	⟨	VERB
ejpam-6680	207	7	−−−→	−−−→	PROPN
ejpam-6680	207	8	babnk	babnk	NOUN
ejpam-6680	207	9	,	,	PUNCT
ejpam-6680	207	10	−−−−→	−−−−→	X
ejpam-6680	207	11	bnk	bnk	PROPN
ejpam-6680	207	12	snk	snk	PROPN
ejpam-6680	207	13	⟩	⟩	PROPN
ejpam-6680	207	14	,	,	PUNCT
ejpam-6680	207	15	≤	≤	NUM
ejpam-6680	207	16	⟨	⟨	VERB
ejpam-6680	207	17	−−−−→	−−−−→	X
ejpam-6680	207	18	bnk	bnk	PROPN
ejpam-6680	207	19	snk	snk	PROPN
ejpam-6680	207	20	,	,	PUNCT
ejpam-6680	207	21	−−→	−−→	PROPN
ejpam-6680	207	22	snk	snk	PROPN
ejpam-6680	207	23	b⟩	b⟩	PUNCT
ejpam-6680	207	24	−	−	PROPN
ejpam-6680	208	1	ϱ2(snk	ϱ2(snk	NOUN
ejpam-6680	208	2	,	,	PUNCT
ejpam-6680	208	3	b	b	NOUN
ejpam-6680	208	4	)	)	PUNCT
ejpam-6680	209	1	+	+	CCONJ
ejpam-6680	209	2	⟨	⟨	VERB
ejpam-6680	209	3	−−−→	−−−→	ADJ
ejpam-6680	209	4	babnk	babnk	NOUN
ejpam-6680	209	5	,	,	PUNCT
ejpam-6680	209	6	−−→	−−→	PROPN
ejpam-6680	209	7	bbnk	bbnk	NOUN
ejpam-6680	209	8	⟩+	⟩+	NOUN
ejpam-6680	209	9	⟨	⟨	VERB
ejpam-6680	209	10	−−−→	−−−→	NUM
ejpam-6680	209	11	babnk	babnk	NOUN
ejpam-6680	209	12	,	,	PUNCT
ejpam-6680	209	13	−−−−→	−−−−→	X
ejpam-6680	209	14	bnk	bnk	PROPN
ejpam-6680	209	15	snk	snk	PROPN
ejpam-6680	209	16	⟩.	⟩.	PROPN
ejpam-6680	209	17	this	this	PRON
ejpam-6680	209	18	implies	imply	VERB
ejpam-6680	209	19	that	that	SCONJ
ejpam-6680	209	20	⟨	⟨	VERB
ejpam-6680	209	21	−−−−→	−−−−→	PUNCT
ejpam-6680	209	22	bnk	bnk	PROPN
ejpam-6680	209	23	snk	snk	PROPN
ejpam-6680	209	24	,	,	PUNCT
ejpam-6680	209	25	−−→	−−→	PROPN
ejpam-6680	209	26	snk	snk	PROPN
ejpam-6680	209	27	b⟩+	b⟩+	PROPN
ejpam-6680	209	28	⟨	⟨	VERB
ejpam-6680	209	29	−−−→	−−−→	PROPN
ejpam-6680	209	30	babnk	babnk	NOUN
ejpam-6680	209	31	,	,	PUNCT
ejpam-6680	209	32	−−→	−−→	PROPN
ejpam-6680	209	33	bbnk	bbnk	NOUN
ejpam-6680	209	34	⟩+	⟩+	NOUN
ejpam-6680	209	35	⟨	⟨	VERB
ejpam-6680	209	36	−−−→	−−−→	NUM
ejpam-6680	209	37	babnk	babnk	NOUN
ejpam-6680	209	38	,	,	PUNCT
ejpam-6680	209	39	−−−−→	−−−−→	X
ejpam-6680	209	40	bnk	bnk	PROPN
ejpam-6680	209	41	snk	snk	PROPN
ejpam-6680	209	42	⟩	⟩	PROPN
ejpam-6680	209	43	≥	≥	NOUN
ejpam-6680	209	44	0	0	NUM
ejpam-6680	209	45	,	,	PUNCT
ejpam-6680	209	46	∀b	∀b	NOUN
ejpam-6680	209	47	∈	∈	PROPN
ejpam-6680	209	48	l.	l.	NOUN
ejpam-6680	209	49	(	(	PUNCT
ejpam-6680	209	50	8)	8)	NUM
ejpam-6680	209	51	now	now	ADV
ejpam-6680	209	52	,	,	PUNCT
ejpam-6680	209	53	we	we	PRON
ejpam-6680	209	54	will	will	AUX
ejpam-6680	209	55	prove	prove	VERB
ejpam-6680	209	56	lim	lim	PROPN
ejpam-6680	209	57	inf⟨	inf⟨	PROPN
ejpam-6680	209	58	−−−→	−−−→	PROPN
ejpam-6680	209	59	babnk	babnk	NOUN
ejpam-6680	209	60	,	,	PUNCT
ejpam-6680	209	61	−−→	−−→	PROPN
ejpam-6680	209	62	bbnk	bbnk	PROPN
ejpam-6680	209	63	⟩	⟩	PROPN
ejpam-6680	209	64	≥	≥	NOUN
ejpam-6680	209	65	0	0	NUM
ejpam-6680	209	66	.	.	PUNCT
ejpam-6680	210	1	(	(	PUNCT
ejpam-6680	210	2	9	9	X
ejpam-6680	210	3	)	)	PUNCT
ejpam-6680	210	4	taking	take	VERB
ejpam-6680	210	5	k	k	X
ejpam-6680	210	6	→	→	SYM
ejpam-6680	210	7	∞	∞	NUM
ejpam-6680	210	8	in	in	ADP
ejpam-6680	210	9	(	(	PUNCT
ejpam-6680	210	10	8)	8)	NUM
ejpam-6680	210	11	,	,	PUNCT
ejpam-6680	210	12	we	we	PRON
ejpam-6680	210	13	get	get	VERB
ejpam-6680	210	14	lim	lim	PROPN
ejpam-6680	210	15	inf⟨	inf⟨	PROPN
ejpam-6680	210	16	−−−→	−−−→	PROPN
ejpam-6680	210	17	babnk	babnk	NOUN
ejpam-6680	210	18	,	,	PUNCT
ejpam-6680	210	19	−−→	−−→	PROPN
ejpam-6680	210	20	bbnk	bbnk	PROPN
ejpam-6680	210	21	⟩	⟩	PROPN
ejpam-6680	210	22	≥	≥	NOUN
ejpam-6680	210	23	0	0	NUM
ejpam-6680	210	24	.	.	PUNCT
ejpam-6680	211	1	since	since	SCONJ
ejpam-6680	211	2	a	a	PRON
ejpam-6680	211	3	is	be	AUX
ejpam-6680	211	4	uniformly	uniformly	ADV
ejpam-6680	211	5	continuous	continuous	ADJ
ejpam-6680	211	6	map	map	NOUN
ejpam-6680	211	7	,	,	PUNCT
ejpam-6680	211	8	thus	thus	ADV
ejpam-6680	211	9	we	we	PRON
ejpam-6680	211	10	have	have	VERB
ejpam-6680	211	11	ϱ(abnk	ϱ(abnk	NOUN
ejpam-6680	211	12	,	,	PUNCT
ejpam-6680	211	13	asnk	asnk	NOUN
ejpam-6680	211	14	)	)	PUNCT
ejpam-6680	211	15	→	→	SYM
ejpam-6680	211	16	0	0	PUNCT
ejpam-6680	211	17	as	as	SCONJ
ejpam-6680	211	18	k	k	PROPN
ejpam-6680	211	19	→	→	SYM
ejpam-6680	211	20	∞.	∞.	PROPN
ejpam-6680	211	21	(	(	PUNCT
ejpam-6680	211	22	10	10	NUM
ejpam-6680	211	23	)	)	PUNCT
ejpam-6680	211	24	on	on	ADP
ejpam-6680	211	25	the	the	DET
ejpam-6680	211	26	other	other	ADJ
ejpam-6680	211	27	,	,	PUNCT
ejpam-6680	211	28	hand	hand	NOUN
ejpam-6680	211	29	we	we	PRON
ejpam-6680	211	30	have	have	VERB
ejpam-6680	211	31	⟨	⟨	NOUN
ejpam-6680	211	32	−−−→	−−−→	PROPN
ejpam-6680	211	33	basnk	basnk	NOUN
ejpam-6680	211	34	,	,	PUNCT
ejpam-6680	212	1	−−→	−−→	PROPN
ejpam-6680	212	2	bsnk	bsnk	NOUN
ejpam-6680	212	3	⟩	⟩	NOUN
ejpam-6680	212	4	=	=	PUNCT
ejpam-6680	212	5	⟨	⟨	AUX
ejpam-6680	212	6	−−−→	−−−→	PROPN
ejpam-6680	212	7	babnk	babnk	NOUN
ejpam-6680	212	8	,	,	PUNCT
ejpam-6680	212	9	−−→	−−→	PROPN
ejpam-6680	212	10	bsnk	bsnk	NOUN
ejpam-6680	213	1	⟩+	⟩+	ADJ
ejpam-6680	213	2	⟨	⟨	NOUN
ejpam-6680	213	3	−−−−−−→	−−−−−−→	X
ejpam-6680	213	4	abnk	abnk	PROPN
ejpam-6680	213	5	asnk	asnk	PROPN
ejpam-6680	213	6	,	,	PUNCT
ejpam-6680	213	7	−−→	−−→	PROPN
ejpam-6680	213	8	bsnk	bsnk	NOUN
ejpam-6680	213	9	⟩	⟩	NOUN
ejpam-6680	213	10	=	=	PUNCT
ejpam-6680	213	11	⟨	⟨	VERB
ejpam-6680	213	12	−−−→	−−−→	PROPN
ejpam-6680	213	13	babnk	babnk	NOUN
ejpam-6680	213	14	,	,	PUNCT
ejpam-6680	213	15	−−→	−−→	PROPN
ejpam-6680	213	16	bbnk	bbnk	NOUN
ejpam-6680	213	17	⟩+	⟩+	NOUN
ejpam-6680	213	18	⟨	⟨	VERB
ejpam-6680	213	19	−−−→	−−−→	NUM
ejpam-6680	213	20	babnk	babnk	NOUN
ejpam-6680	213	21	,	,	PUNCT
ejpam-6680	213	22	−−−−→	−−−−→	X
ejpam-6680	213	23	bnk	bnk	PROPN
ejpam-6680	213	24	snk	snk	NOUN
ejpam-6680	213	25	⟩+	⟩+	NOUN
ejpam-6680	213	26	⟨	⟨	VERB
ejpam-6680	213	27	−−−−−−→	−−−−−−→	X
ejpam-6680	213	28	abnk	abnk	PROPN
ejpam-6680	213	29	asnk	asnk	NOUN
ejpam-6680	213	30	,	,	PUNCT
ejpam-6680	213	31	−−→	−−→	PROPN
ejpam-6680	213	32	bsnk	bsnk	PROPN
ejpam-6680	213	33	⟩	⟩	NOUN
ejpam-6680	213	34	,	,	PUNCT
ejpam-6680	213	35	which	which	PRON
ejpam-6680	213	36	together	together	ADV
ejpam-6680	213	37	with	with	ADP
ejpam-6680	213	38	(	(	PUNCT
ejpam-6680	213	39	9	9	NUM
ejpam-6680	213	40	)	)	PUNCT
ejpam-6680	213	41	and	and	CCONJ
ejpam-6680	213	42	(	(	PUNCT
ejpam-6680	213	43	10	10	NUM
ejpam-6680	213	44	)	)	PUNCT
ejpam-6680	213	45	gives	give	VERB
ejpam-6680	213	46	lim	lim	PROPN
ejpam-6680	213	47	inf⟨	inf⟨	PROPN
ejpam-6680	213	48	−−−→	−−−→	PROPN
ejpam-6680	213	49	basnk	basnk	NOUN
ejpam-6680	213	50	,	,	PUNCT
ejpam-6680	213	51	−−→	−−→	PROPN
ejpam-6680	213	52	bsnk	bsnk	NOUN
ejpam-6680	213	53	⟩	⟩	PROPN
ejpam-6680	213	54	≥	≥	NOUN
ejpam-6680	213	55	0	0	NUM
ejpam-6680	213	56	.	.	PUNCT
ejpam-6680	214	1	now	now	ADV
ejpam-6680	214	2	,	,	PUNCT
ejpam-6680	214	3	we	we	PRON
ejpam-6680	214	4	have	have	VERB
ejpam-6680	214	5	to	to	PART
ejpam-6680	214	6	prove	prove	VERB
ejpam-6680	214	7	that	that	SCONJ
ejpam-6680	214	8	v	v	NUM
ejpam-6680	214	9	∈	∈	PRON
ejpam-6680	214	10	v	v	ADP
ejpam-6680	214	11	i(l	i(l	PROPN
ejpam-6680	214	12	,	,	PUNCT
ejpam-6680	214	13	a	a	PRON
ejpam-6680	214	14	)	)	PUNCT
ejpam-6680	214	15	.	.	PUNCT
ejpam-6680	215	1	since	since	SCONJ
ejpam-6680	215	2	a	a	PRON
ejpam-6680	215	3	is	be	AUX
ejpam-6680	215	4	pseudo	pseudo	NOUN
ejpam-6680	215	5	-	-	ADJ
ejpam-6680	215	6	monotone	monotone	ADJ
ejpam-6680	215	7	,	,	PUNCT
ejpam-6680	215	8	so	so	SCONJ
ejpam-6680	215	9	we	we	PRON
ejpam-6680	215	10	get	get	VERB
ejpam-6680	215	11	⟨	⟨	NOUN
ejpam-6680	215	12	−−→	−−→	PROPN
ejpam-6680	215	13	vab	vab	PROPN
ejpam-6680	215	14	,	,	PUNCT
ejpam-6680	215	15	−→	−→	ADJ
ejpam-6680	215	16	vb⟩	vb⟩	PROPN
ejpam-6680	215	17	=	=	SYM
ejpam-6680	215	18	lim	lim	PROPN
ejpam-6680	215	19	k→∞	k→∞	PROPN
ejpam-6680	215	20	⟨	⟨	VERB
ejpam-6680	215	21	−−−→	−−−→	PROPN
ejpam-6680	215	22	snk	snk	PROPN
ejpam-6680	215	23	ab	ab	PROPN
ejpam-6680	215	24	,	,	PUNCT
ejpam-6680	215	25	−−→	−−→	PROPN
ejpam-6680	215	26	snk	snk	PROPN
ejpam-6680	215	27	b⟩	b⟩	PUNCT
ejpam-6680	216	1	=	=	PROPN
ejpam-6680	216	2	lim	lim	PROPN
ejpam-6680	216	3	k→∞	k→∞	PROPN
ejpam-6680	217	1	inf⟨	inf⟨	PROPN
ejpam-6680	217	2	−−−→	−−−→	PROPN
ejpam-6680	217	3	snk	snk	PROPN
ejpam-6680	217	4	ab	ab	PROPN
ejpam-6680	217	5	,	,	PUNCT
ejpam-6680	217	6	−−→	−−→	PROPN
ejpam-6680	217	7	snk	snk	PROPN
ejpam-6680	217	8	b⟩	b⟩	PROPN
ejpam-6680	217	9	≥	≥	NOUN
ejpam-6680	217	10	0	0	NUM
ejpam-6680	217	11	.	.	PUNCT
ejpam-6680	218	1	using	use	VERB
ejpam-6680	218	2	lemma	lemma	PROPN
ejpam-6680	218	3	12	12	NUM
ejpam-6680	218	4	,	,	PUNCT
ejpam-6680	218	5	we	we	PRON
ejpam-6680	218	6	get	get	VERB
ejpam-6680	218	7	v	v	ADP
ejpam-6680	218	8	∈	∈	NOUN
ejpam-6680	218	9	v	v	ADP
ejpam-6680	218	10	i(l	i(l	PROPN
ejpam-6680	218	11	,	,	PUNCT
ejpam-6680	218	12	a	a	PRON
ejpam-6680	218	13	)	)	PUNCT
ejpam-6680	218	14	and	and	CCONJ
ejpam-6680	218	15	the	the	DET
ejpam-6680	218	16	proof	proof	NOUN
ejpam-6680	218	17	is	be	AUX
ejpam-6680	218	18	finished	finish	VERB
ejpam-6680	218	19	.	.	PUNCT
ejpam-6680	219	1	4	4	X
ejpam-6680	219	2	.	.	X
ejpam-6680	219	3	convergence	convergence	NOUN
ejpam-6680	219	4	results	result	NOUN
ejpam-6680	219	5	in	in	ADP
ejpam-6680	219	6	this	this	DET
ejpam-6680	219	7	section	section	NOUN
ejpam-6680	219	8	we	we	PRON
ejpam-6680	219	9	prove	prove	VERB
ejpam-6680	219	10	the	the	DET
ejpam-6680	219	11	results	result	NOUN
ejpam-6680	219	12	of	of	ADP
ejpam-6680	219	13	strong	strong	ADJ
ejpam-6680	219	14	and	and	CCONJ
ejpam-6680	219	15	∆-convergence	∆-convergence	NOUN
ejpam-6680	219	16	.	.	PUNCT
ejpam-6680	220	1	theorem	theorem	NOUN
ejpam-6680	220	2	2	2	NUM
ejpam-6680	220	3	.	.	X
ejpam-6680	220	4	consider	consider	VERB
ejpam-6680	220	5	a	a	DET
ejpam-6680	220	6	nonempty	nonempty	ADJ
ejpam-6680	220	7	,	,	PUNCT
ejpam-6680	220	8	closed	closed	ADJ
ejpam-6680	220	9	and	and	CCONJ
ejpam-6680	220	10	convex	convex	PROPN
ejpam-6680	220	11	subset	subset	NOUN
ejpam-6680	220	12	of	of	ADP
ejpam-6680	220	13	a	a	DET
ejpam-6680	220	14	hadamard	hadamard	ADJ
ejpam-6680	220	15	space	space	NOUN
ejpam-6680	220	16	z	z	AUX
ejpam-6680	220	17	be	be	AUX
ejpam-6680	220	18	l.	l.	NOUN
ejpam-6680	220	19	the	the	DET
ejpam-6680	220	20	map	map	NOUN
ejpam-6680	220	21	a	a	DET
ejpam-6680	220	22	:	:	PUNCT
ejpam-6680	220	23	l	l	NOUN
ejpam-6680	220	24	→	→	PUNCT
ejpam-6680	220	25	l	l	NOUN
ejpam-6680	220	26	is	be	AUX
ejpam-6680	220	27	a	a	DET
ejpam-6680	220	28	pseudo	pseudo	NOUN
ejpam-6680	220	29	-	-	ADJ
ejpam-6680	220	30	monotone	monotone	ADJ
ejpam-6680	220	31	,	,	PUNCT
ejpam-6680	220	32	uniformly	uniformly	ADV
ejpam-6680	220	33	continuous	continuous	ADJ
ejpam-6680	220	34	on	on	ADP
ejpam-6680	220	35	l.	l.	PROPN
ejpam-6680	220	36	the	the	DET
ejpam-6680	220	37	solution	solution	NOUN
ejpam-6680	220	38	set	set	VERB
ejpam-6680	220	39	of	of	ADP
ejpam-6680	220	40	the	the	DET
ejpam-6680	220	41	v	v	PROPN
ejpam-6680	220	42	i(l	i(l	PROPN
ejpam-6680	220	43	,	,	PUNCT
ejpam-6680	220	44	a	a	PRON
ejpam-6680	220	45	)	)	PUNCT
ejpam-6680	220	46	is	be	AUX
ejpam-6680	220	47	nonempty	nonempty	ADJ
ejpam-6680	220	48	,	,	PUNCT
ejpam-6680	220	49	that	that	PRON
ejpam-6680	220	50	is	be	AUX
ejpam-6680	220	51	v	v	ADP
ejpam-6680	220	52	i(l	i(l	PROPN
ejpam-6680	220	53	,	,	PUNCT
ejpam-6680	220	54	a	a	PRON
ejpam-6680	220	55	)	)	PUNCT
ejpam-6680	220	56	̸=	̸=	PROPN
ejpam-6680	220	57	ϕ.	ϕ.	NOUN
ejpam-6680	220	58	then	then	ADV
ejpam-6680	220	59	any	any	DET
ejpam-6680	220	60	sequence	sequence	NOUN
ejpam-6680	220	61	{	{	PUNCT
ejpam-6680	220	62	bn	bn	NOUN
ejpam-6680	220	63	}	}	PUNCT
ejpam-6680	220	64	∆-convergent	∆-convergent	NOUN
ejpam-6680	220	65	in	in	ADP
ejpam-6680	220	66	v	v	ADP
ejpam-6680	220	67	i(l	i(l	PROPN
ejpam-6680	220	68	,	,	PUNCT
ejpam-6680	220	69	a	a	PRON
ejpam-6680	220	70	)	)	PUNCT
ejpam-6680	220	71	.	.	PUNCT
ejpam-6680	221	1	m.	m.	PROPN
ejpam-6680	221	2	rashid	rashid	PROPN
ejpam-6680	221	3	et	et	PROPN
ejpam-6680	221	4	al	al	PROPN
ejpam-6680	221	5	.	.	PUNCT
ejpam-6680	221	6	/	/	SYM
ejpam-6680	221	7	eur	eur	PROPN
ejpam-6680	221	8	.	.	PUNCT
ejpam-6680	222	1	j.	j.	PROPN
ejpam-6680	222	2	pure	pure	PROPN
ejpam-6680	222	3	appl	appl	PROPN
ejpam-6680	222	4	.	.	PROPN
ejpam-6680	222	5	math	math	PROPN
ejpam-6680	222	6	,	,	PUNCT
ejpam-6680	222	7	18	18	NUM
ejpam-6680	222	8	(	(	PUNCT
ejpam-6680	222	9	4	4	NUM
ejpam-6680	222	10	)	)	PUNCT
ejpam-6680	222	11	(	(	PUNCT
ejpam-6680	222	12	2025	2025	NUM
ejpam-6680	222	13	)	)	PUNCT
ejpam-6680	222	14	,	,	PUNCT
ejpam-6680	222	15	6680	6680	NUM
ejpam-6680	222	16	12	12	NUM
ejpam-6680	222	17	of	of	ADP
ejpam-6680	222	18	24	24	NUM
ejpam-6680	222	19	proof	proof	NOUN
ejpam-6680	222	20	.	.	PUNCT
ejpam-6680	223	1	claim	claim	NOUN
ejpam-6680	223	2	1	1	NUM
ejpam-6680	223	3	.	.	PUNCT
ejpam-6680	224	1	the	the	DET
ejpam-6680	224	2	sequence	sequence	NOUN
ejpam-6680	224	3	{	{	PUNCT
ejpam-6680	224	4	bn	bn	NUM
ejpam-6680	224	5	}	}	PUNCT
ejpam-6680	224	6	is	be	AUX
ejpam-6680	224	7	a	a	DET
ejpam-6680	224	8	bounded	bound	VERB
ejpam-6680	224	9	.	.	PUNCT
ejpam-6680	225	1	to	to	PART
ejpam-6680	225	2	proof	proof	VERB
ejpam-6680	225	3	the	the	DET
ejpam-6680	225	4	claim	claim	NOUN
ejpam-6680	225	5	,	,	PUNCT
ejpam-6680	225	6	assume	assume	VERB
ejpam-6680	225	7	v	v	ADP
ejpam-6680	225	8	∈	∈	PROPN
ejpam-6680	225	9	v	v	ADP
ejpam-6680	225	10	i(l	i(l	PROPN
ejpam-6680	225	11	,	,	PUNCT
ejpam-6680	225	12	a	a	PRON
ejpam-6680	225	13	)	)	PUNCT
ejpam-6680	225	14	,	,	PUNCT
ejpam-6680	225	15	we	we	PRON
ejpam-6680	225	16	have	have	VERB
ejpam-6680	225	17	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	225	18	,	,	PUNCT
ejpam-6680	225	19	v	v	NOUN
ejpam-6680	225	20	)	)	PUNCT
ejpam-6680	225	21	=	=	SYM
ejpam-6680	225	22	ϱ2(plnbn	ϱ2(plnbn	PROPN
ejpam-6680	225	23	,	,	PUNCT
ejpam-6680	225	24	v	v	NOUN
ejpam-6680	225	25	)	)	PUNCT
ejpam-6680	225	26	≤	≤	NUM
ejpam-6680	225	27	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	225	28	,	,	PUNCT
ejpam-6680	225	29	v)−	v)−	PROPN
ejpam-6680	225	30	ϱ2(plnbn	ϱ2(plnbn	PROPN
ejpam-6680	225	31	,	,	PUNCT
ejpam-6680	225	32	bn	bn	NOUN
ejpam-6680	225	33	)	)	PUNCT
ejpam-6680	225	34	,	,	PUNCT
ejpam-6680	225	35	(	(	PUNCT
ejpam-6680	225	36	11	11	NUM
ejpam-6680	225	37	)	)	PUNCT
ejpam-6680	225	38	ϱ2(bn+1	ϱ2(bn+1	PROPN
ejpam-6680	225	39	,	,	PUNCT
ejpam-6680	225	40	v	v	NOUN
ejpam-6680	225	41	)	)	PUNCT
ejpam-6680	225	42	≤	≤	NUM
ejpam-6680	225	43	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	225	44	,	,	PUNCT
ejpam-6680	225	45	v)−	v)−	PROPN
ejpam-6680	225	46	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	225	47	,	,	PUNCT
ejpam-6680	225	48	ln	ln	ADJ
ejpam-6680	225	49	)	)	PUNCT
ejpam-6680	225	50	.	.	PUNCT
ejpam-6680	226	1	this	this	PRON
ejpam-6680	226	2	implies	imply	VERB
ejpam-6680	226	3	that	that	SCONJ
ejpam-6680	226	4	ϱ(bn+1	ϱ(bn+1	NOUN
ejpam-6680	226	5	,	,	PUNCT
ejpam-6680	226	6	v	v	NOUN
ejpam-6680	226	7	)	)	PUNCT
ejpam-6680	226	8	≤	≤	NOUN
ejpam-6680	226	9	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	226	10	,	,	PUNCT
ejpam-6680	226	11	v	v	NOUN
ejpam-6680	226	12	)	)	PUNCT
ejpam-6680	226	13	.	.	PUNCT
ejpam-6680	227	1	thus	thus	ADV
ejpam-6680	227	2	limn→∞	limn→∞	PROPN
ejpam-6680	227	3	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	227	4	,	,	PUNCT
ejpam-6680	227	5	v	v	NOUN
ejpam-6680	227	6	)	)	PUNCT
ejpam-6680	227	7	exists	exist	VERB
ejpam-6680	227	8	.	.	PUNCT
ejpam-6680	228	1	therefore	therefore	ADV
ejpam-6680	228	2	,	,	PUNCT
ejpam-6680	228	3	the	the	DET
ejpam-6680	228	4	sequence	sequence	NOUN
ejpam-6680	228	5	{	{	PUNCT
ejpam-6680	228	6	bn	bn	NUM
ejpam-6680	228	7	}	}	PUNCT
ejpam-6680	228	8	is	be	AUX
ejpam-6680	228	9	bounded	bound	VERB
ejpam-6680	228	10	and	and	CCONJ
ejpam-6680	228	11	implies	imply	VERB
ejpam-6680	228	12	that	that	SCONJ
ejpam-6680	228	13	the	the	DET
ejpam-6680	228	14	sequence	sequence	NOUN
ejpam-6680	228	15	{	{	PUNCT
ejpam-6680	228	16	sn	sn	NOUN
ejpam-6680	228	17	}	}	PUNCT
ejpam-6680	228	18	is	be	AUX
ejpam-6680	228	19	also	also	ADV
ejpam-6680	228	20	bounded	bound	VERB
ejpam-6680	228	21	.	.	PUNCT
ejpam-6680	229	1	claim	claim	NOUN
ejpam-6680	229	2	2	2	NUM
ejpam-6680	229	3	.	.	PUNCT
ejpam-6680	230	1	[	[	PUNCT
ejpam-6680	230	2	1	1	NUM
ejpam-6680	230	3	m	m	PROPN
ejpam-6680	230	4	(	(	PUNCT
ejpam-6680	230	5	1−	1−	NUM
ejpam-6680	230	6	µ)ϱ2(bn	µ)ϱ2(bn	NUM
ejpam-6680	230	7	,	,	PUNCT
ejpam-6680	230	8	sn	sn	PROPN
ejpam-6680	230	9	)	)	PUNCT
ejpam-6680	230	10	]	]	PUNCT
ejpam-6680	230	11	2	2	NUM
ejpam-6680	230	12	≤	≤	NUM
ejpam-6680	230	13	ϱ2(bn	ϱ2(bn	NUM
ejpam-6680	230	14	,	,	PUNCT
ejpam-6680	230	15	v)−	v)−	PROPN
ejpam-6680	230	16	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	230	17	,	,	PUNCT
ejpam-6680	230	18	v	v	NOUN
ejpam-6680	230	19	)	)	PUNCT
ejpam-6680	230	20	,	,	PUNCT
ejpam-6680	230	21	for	for	ADP
ejpam-6680	230	22	some	some	DET
ejpam-6680	230	23	m	m	NOUN
ejpam-6680	230	24	>	>	X
ejpam-6680	230	25	0	0	X
ejpam-6680	230	26	.	.	PUNCT
ejpam-6680	231	1	indeed	indeed	ADV
ejpam-6680	231	2	,	,	PUNCT
ejpam-6680	231	3	the	the	DET
ejpam-6680	231	4	bounded	bounded	ADJ
ejpam-6680	231	5	sequences	sequence	NOUN
ejpam-6680	231	6	{	{	PUNCT
ejpam-6680	231	7	bn	bn	NUM
ejpam-6680	231	8	}	}	PUNCT
ejpam-6680	231	9	,	,	PUNCT
ejpam-6680	231	10	{	{	PUNCT
ejpam-6680	231	11	sn	sn	NOUN
ejpam-6680	231	12	}	}	PUNCT
ejpam-6680	231	13	implies	imply	VERB
ejpam-6680	231	14	that	that	SCONJ
ejpam-6680	231	15	{	{	PUNCT
ejpam-6680	231	16	abn	abn	PROPN
ejpam-6680	231	17	}	}	PUNCT
ejpam-6680	231	18	,	,	PUNCT
ejpam-6680	231	19	{	{	PUNCT
ejpam-6680	231	20	asn	asn	PROPN
ejpam-6680	231	21	}	}	PUNCT
ejpam-6680	231	22	are	be	AUX
ejpam-6680	231	23	also	also	ADV
ejpam-6680	231	24	bounded	bound	VERB
ejpam-6680	231	25	,	,	PUNCT
ejpam-6680	231	26	so	so	ADV
ejpam-6680	231	27	for	for	SCONJ
ejpam-6680	231	28	all	all	PRON
ejpam-6680	231	29	n	n	PRON
ejpam-6680	231	30	there	there	ADV
ejpam-6680	231	31	exists	exist	VERB
ejpam-6680	231	32	m	m	VERB
ejpam-6680	231	33	>	>	X
ejpam-6680	231	34	0	0	NUM
ejpam-6680	231	35	such	such	ADJ
ejpam-6680	231	36	that	that	DET
ejpam-6680	231	37	ξnd(bn	ξnd(bn	NOUN
ejpam-6680	231	38	,	,	PUNCT
ejpam-6680	231	39	abn	abn	PROPN
ejpam-6680	231	40	)	)	PUNCT
ejpam-6680	231	41	≤	≤	NUM
ejpam-6680	231	42	m.	m.	NOUN
ejpam-6680	231	43	therefore	therefore	ADV
ejpam-6680	231	44	,	,	PUNCT
ejpam-6680	231	45	for	for	ADP
ejpam-6680	231	46	all	all	DET
ejpam-6680	231	47	u	u	NOUN
ejpam-6680	231	48	,	,	PUNCT
ejpam-6680	231	49	q	q	PROPN
ejpam-6680	231	50	∈	∈	PROPN
ejpam-6680	231	51	z	z	X
ejpam-6680	231	52	,	,	PUNCT
ejpam-6680	231	53	we	we	PRON
ejpam-6680	231	54	have	have	VERB
ejpam-6680	231	55	ϱ(hn(u	ϱ(hn(u	NUM
ejpam-6680	231	56	)	)	PUNCT
ejpam-6680	231	57	,	,	PUNCT
ejpam-6680	231	58	hn(q	hn(q	NOUN
ejpam-6680	231	59	)	)	PUNCT
ejpam-6680	231	60	)	)	PUNCT
ejpam-6680	232	1	=	=	SYM
ejpam-6680	232	2	|hn(u)−	|hn(u)−	NOUN
ejpam-6680	232	3	hn(q)|	hn(q)|	X
ejpam-6680	232	4	,	,	PUNCT
ejpam-6680	232	5	=	=	PUNCT
ejpam-6680	232	6	∣∣∣⟨−−→usn,−−−−−−−−−−−−−−−−−−→(ξnbn	∣∣∣⟨−−→usn,−−−−−−−−−−−−−−−−−−→(ξnbn	PROPN
ejpam-6680	232	7	⊕	⊕	PROPN
ejpam-6680	232	8	(	(	PUNCT
ejpam-6680	232	9	1−	1−	NUM
ejpam-6680	232	10	ξn)abn)abn⟩	ξn)abn)abn⟩	NOUN
ejpam-6680	232	11	−⟨−→qsn	−⟨−→qsn	NOUN
ejpam-6680	232	12	,	,	PUNCT
ejpam-6680	232	13	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	PROPN
ejpam-6680	232	14	(	(	PUNCT
ejpam-6680	232	15	ξnbn	ξnbn	PROPN
ejpam-6680	232	16	⊕	⊕	PROPN
ejpam-6680	232	17	(	(	PUNCT
ejpam-6680	232	18	1−	1−	NUM
ejpam-6680	232	19	ξn)abn)abn⟩	ξn)abn)abn⟩	NOUN
ejpam-6680	232	20	∣∣∣	∣∣∣	ADJ
ejpam-6680	232	21	.	.	PUNCT
ejpam-6680	233	1	by	by	ADP
ejpam-6680	233	2	using	use	VERB
ejpam-6680	233	3	remark	remark	NOUN
ejpam-6680	233	4	1	1	NUM
ejpam-6680	233	5	,	,	PUNCT
ejpam-6680	233	6	we	we	PRON
ejpam-6680	233	7	have	have	VERB
ejpam-6680	233	8	ϱ(hn(u	ϱ(hn(u	NUM
ejpam-6680	233	9	)	)	PUNCT
ejpam-6680	233	10	,	,	PUNCT
ejpam-6680	233	11	hn(q	hn(q	NOUN
ejpam-6680	233	12	)	)	PUNCT
ejpam-6680	233	13	)	)	PUNCT
ejpam-6680	234	1	=	=	SYM
ejpam-6680	234	2	∣∣∣⟨−→uq,−−−−−−−−−−−−−−−−−−→(ξnbn	∣∣∣⟨−→uq,−−−−−−−−−−−−−−−−−−→(ξnbn	PUNCT
ejpam-6680	234	3	⊕	⊕	PROPN
ejpam-6680	234	4	(	(	PUNCT
ejpam-6680	234	5	1−	1−	NUM
ejpam-6680	234	6	ξn)abn)abn⟩	ξn)abn)abn⟩	NOUN
ejpam-6680	234	7	∣∣∣	∣∣∣	ADJ
ejpam-6680	234	8	.	.	PUNCT
ejpam-6680	235	1	by	by	ADP
ejpam-6680	235	2	lemma	lemma	PROPN
ejpam-6680	235	3	7	7	NUM
ejpam-6680	235	4	and	and	CCONJ
ejpam-6680	235	5	cauchy	cauchy	PROPN
ejpam-6680	235	6	schwartz	schwartz	PROPN
ejpam-6680	235	7	inequality	inequality	PROPN
ejpam-6680	235	8	,	,	PUNCT
ejpam-6680	235	9	we	we	PRON
ejpam-6680	235	10	get	get	VERB
ejpam-6680	235	11	⟨−→uq	⟨−→uq	NUM
ejpam-6680	235	12	,	,	PUNCT
ejpam-6680	235	13	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	PROPN
ejpam-6680	235	14	(	(	PUNCT
ejpam-6680	235	15	ξnbn	ξnbn	PROPN
ejpam-6680	235	16	⊕	⊕	PROPN
ejpam-6680	235	17	(	(	PUNCT
ejpam-6680	235	18	1−	1−	NUM
ejpam-6680	235	19	ξn)abn)abn⟩	ξn)abn)abn⟩	VERB
ejpam-6680	235	20	≤	≤	NOUN
ejpam-6680	235	21	ξn⟨−→uq	ξn⟨−→uq	NUM
ejpam-6680	235	22	,	,	PUNCT
ejpam-6680	235	23	−−−→	−−−→	ADJ
ejpam-6680	235	24	bnabn⟩+	bnabn⟩+	PROPN
ejpam-6680	235	25	[	[	PUNCT
ejpam-6680	235	26	(	(	PUNCT
ejpam-6680	235	27	1−	1−	NUM
ejpam-6680	235	28	ξn	ξn	NOUN
ejpam-6680	235	29	)	)	PUNCT
ejpam-6680	235	30	×⟨−→uq	×⟨−→uq	NOUN
ejpam-6680	235	31	,	,	PUNCT
ejpam-6680	235	32	−−−−−→	−−−−−→	PUNCT
ejpam-6680	235	33	abnabn⟩	abnabn⟩	NOUN
ejpam-6680	235	34	]	]	PUNCT
ejpam-6680	235	35	,	,	PUNCT
ejpam-6680	235	36	=	=	SYM
ejpam-6680	235	37	ξn⟨−→uq	ξn⟨−→uq	NUM
ejpam-6680	235	38	,	,	PUNCT
ejpam-6680	235	39	−−−→	−−−→	ADJ
ejpam-6680	235	40	bnabn⟩	bnabn⟩	NOUN
ejpam-6680	235	41	≤	≤	X
ejpam-6680	235	42	ξnd(u	ξnd(u	PROPN
ejpam-6680	235	43	,	,	PUNCT
ejpam-6680	235	44	q)d(bn	q)d(bn	NUM
ejpam-6680	235	45	,	,	PUNCT
ejpam-6680	235	46	abn	abn	PROPN
ejpam-6680	235	47	)	)	PUNCT
ejpam-6680	235	48	,	,	PUNCT
ejpam-6680	235	49	≤	≤	NOUN
ejpam-6680	235	50	mϱ(u	mϱ(u	PRON
ejpam-6680	235	51	,	,	PUNCT
ejpam-6680	235	52	q	q	NOUN
ejpam-6680	235	53	)	)	PUNCT
ejpam-6680	235	54	.	.	PUNCT
ejpam-6680	236	1	thus	thus	ADV
ejpam-6680	236	2	we	we	PRON
ejpam-6680	236	3	have	have	VERB
ejpam-6680	236	4	hn	hn	PROPN
ejpam-6680	236	5	(	(	PUNCT
ejpam-6680	236	6	.	.	PUNCT
ejpam-6680	236	7	)	)	PUNCT
ejpam-6680	236	8	is	be	AUX
ejpam-6680	236	9	m	m	NOUN
ejpam-6680	236	10	-	-	PUNCT
ejpam-6680	236	11	lipschitz	lipschitz	NOUN
ejpam-6680	236	12	continuous	continuous	ADJ
ejpam-6680	236	13	on	on	ADP
ejpam-6680	236	14	z	z	PROPN
ejpam-6680	236	15	and	and	CCONJ
ejpam-6680	236	16	by	by	ADP
ejpam-6680	236	17	lemma	lemma	PROPN
ejpam-6680	236	18	11	11	NUM
ejpam-6680	236	19	,	,	PUNCT
ejpam-6680	236	20	we	we	PRON
ejpam-6680	236	21	get	get	VERB
ejpam-6680	236	22	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	236	23	,	,	PUNCT
ejpam-6680	236	24	ln	ln	ADJ
ejpam-6680	236	25	)	)	PUNCT
ejpam-6680	236	26	≥	≥	NOUN
ejpam-6680	236	27	1	1	NUM
ejpam-6680	236	28	m	m	NOUN
ejpam-6680	236	29	hn(bn	hn(bn	NOUN
ejpam-6680	236	30	)	)	PUNCT
ejpam-6680	236	31	,	,	PUNCT
ejpam-6680	236	32	(	(	PUNCT
ejpam-6680	236	33	12	12	NUM
ejpam-6680	236	34	)	)	PUNCT
ejpam-6680	236	35	which	which	PRON
ejpam-6680	236	36	,	,	PUNCT
ejpam-6680	236	37	together	together	ADV
ejpam-6680	236	38	with	with	ADP
ejpam-6680	236	39	lemma	lemma	PROPN
ejpam-6680	236	40	13	13	NUM
ejpam-6680	236	41	,	,	PUNCT
ejpam-6680	236	42	we	we	PRON
ejpam-6680	236	43	get	get	VERB
ejpam-6680	236	44	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	236	45	,	,	PUNCT
ejpam-6680	236	46	ln	ln	ADJ
ejpam-6680	236	47	)	)	PUNCT
ejpam-6680	236	48	≥	≥	NOUN
ejpam-6680	236	49	1	1	NUM
ejpam-6680	236	50	m	m	VERB
ejpam-6680	236	51	(	(	PUNCT
ejpam-6680	236	52	−1−	−1−	PROPN
ejpam-6680	236	53	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	236	54	,	,	PUNCT
ejpam-6680	236	55	sn	sn	PROPN
ejpam-6680	236	56	)	)	PUNCT
ejpam-6680	236	57	.	.	PUNCT
ejpam-6680	237	1	m.	m.	PROPN
ejpam-6680	237	2	rashid	rashid	PROPN
ejpam-6680	237	3	et	et	PROPN
ejpam-6680	237	4	al	al	PROPN
ejpam-6680	237	5	.	.	PUNCT
ejpam-6680	237	6	/	/	SYM
ejpam-6680	237	7	eur	eur	PROPN
ejpam-6680	237	8	.	.	PUNCT
ejpam-6680	238	1	j.	j.	PROPN
ejpam-6680	238	2	pure	pure	PROPN
ejpam-6680	238	3	appl	appl	PROPN
ejpam-6680	238	4	.	.	PROPN
ejpam-6680	238	5	math	math	PROPN
ejpam-6680	238	6	,	,	PUNCT
ejpam-6680	238	7	18	18	NUM
ejpam-6680	238	8	(	(	PUNCT
ejpam-6680	238	9	4	4	NUM
ejpam-6680	238	10	)	)	PUNCT
ejpam-6680	238	11	(	(	PUNCT
ejpam-6680	238	12	2025	2025	NUM
ejpam-6680	238	13	)	)	PUNCT
ejpam-6680	238	14	,	,	PUNCT
ejpam-6680	238	15	6680	6680	NUM
ejpam-6680	238	16	13	13	NUM
ejpam-6680	238	17	of	of	ADP
ejpam-6680	238	18	24	24	NUM
ejpam-6680	238	19	combining	combine	VERB
ejpam-6680	238	20	(	(	PUNCT
ejpam-6680	238	21	11	11	NUM
ejpam-6680	238	22	)	)	PUNCT
ejpam-6680	238	23	and	and	CCONJ
ejpam-6680	238	24	(	(	PUNCT
ejpam-6680	238	25	12	12	NUM
ejpam-6680	238	26	)	)	PUNCT
ejpam-6680	238	27	,	,	PUNCT
ejpam-6680	238	28	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	238	29	,	,	PUNCT
ejpam-6680	238	30	v	v	NOUN
ejpam-6680	238	31	)	)	PUNCT
ejpam-6680	238	32	≤	≤	NUM
ejpam-6680	238	33	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	238	34	,	,	PUNCT
ejpam-6680	238	35	v)−	v)−	PROPN
ejpam-6680	238	36	[	[	PUNCT
ejpam-6680	238	37	1	1	NUM
ejpam-6680	238	38	m	m	VERB
ejpam-6680	238	39	(	(	PUNCT
ejpam-6680	238	40	−1−	−1−	PROPN
ejpam-6680	238	41	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	238	42	,	,	PUNCT
ejpam-6680	238	43	sn	sn	PROPN
ejpam-6680	238	44	)	)	PUNCT
ejpam-6680	238	45	]	]	PUNCT
ejpam-6680	238	46	2	2	X
ejpam-6680	238	47	.	.	PUNCT
ejpam-6680	239	1	thus	thus	ADV
ejpam-6680	239	2	,	,	PUNCT
ejpam-6680	239	3	claim	claim	NOUN
ejpam-6680	239	4	2	2	NUM
ejpam-6680	239	5	is	be	AUX
ejpam-6680	239	6	proven	prove	VERB
ejpam-6680	239	7	.	.	PUNCT
ejpam-6680	240	1	claim	claim	VERB
ejpam-6680	240	2	3	3	NUM
ejpam-6680	240	3	the	the	DET
ejpam-6680	240	4	sequence	sequence	NOUN
ejpam-6680	240	5	{	{	PUNCT
ejpam-6680	240	6	bn	bn	NOUN
ejpam-6680	240	7	}	}	PUNCT
ejpam-6680	240	8	∆-converges	∆-converge	NOUN
ejpam-6680	240	9	in	in	ADP
ejpam-6680	240	10	v	v	ADP
ejpam-6680	240	11	i(l	i(l	PROPN
ejpam-6680	240	12	,	,	PUNCT
ejpam-6680	240	13	a	a	PRON
ejpam-6680	240	14	)	)	PUNCT
ejpam-6680	240	15	.	.	PUNCT
ejpam-6680	241	1	indeed	indeed	ADV
ejpam-6680	241	2	,	,	PUNCT
ejpam-6680	241	3	by	by	ADP
ejpam-6680	241	4	lemma	lemma	PROPN
ejpam-6680	241	5	4	4	NUM
ejpam-6680	241	6	,	,	PUNCT
ejpam-6680	241	7	there	there	PRON
ejpam-6680	241	8	exists	exist	VERB
ejpam-6680	241	9	the	the	DET
ejpam-6680	241	10	subsequence	subsequence	NOUN
ejpam-6680	241	11	{	{	PUNCT
ejpam-6680	241	12	bnk	bnk	PROPN
ejpam-6680	241	13	}	}	PUNCT
ejpam-6680	241	14	of	of	ADP
ejpam-6680	241	15	bounded	bounded	ADJ
ejpam-6680	241	16	sequence	sequence	NOUN
ejpam-6680	241	17	{	{	PUNCT
ejpam-6680	241	18	bn	bn	NOUN
ejpam-6680	241	19	}	}	PUNCT
ejpam-6680	241	20	such	such	ADJ
ejpam-6680	241	21	that	that	SCONJ
ejpam-6680	241	22	the	the	DET
ejpam-6680	241	23	subsequence	subsequence	NOUN
ejpam-6680	241	24	{	{	PUNCT
ejpam-6680	241	25	bnk	bnk	NOUN
ejpam-6680	241	26	}	}	PUNCT
ejpam-6680	241	27	∆converges	∆converge	NOUN
ejpam-6680	241	28	to	to	ADP
ejpam-6680	241	29	v	v	NUM
ejpam-6680	241	30	∈	∈	NOUN
ejpam-6680	241	31	z.	z.	NOUN
ejpam-6680	241	32	using	use	VERB
ejpam-6680	241	33	claim	claim	NOUN
ejpam-6680	241	34	2	2	NUM
ejpam-6680	241	35	,	,	PUNCT
ejpam-6680	241	36	we	we	PRON
ejpam-6680	241	37	can	can	AUX
ejpam-6680	241	38	find	find	VERB
ejpam-6680	241	39	lim	lim	PROPN
ejpam-6680	241	40	n→∞	n→∞	X
ejpam-6680	241	41	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	241	42	,	,	PUNCT
ejpam-6680	241	43	sn	sn	PROPN
ejpam-6680	241	44	)	)	PUNCT
ejpam-6680	241	45	=	=	SYM
ejpam-6680	242	1	0	0	X
ejpam-6680	242	2	.	.	PUNCT
ejpam-6680	243	1	it	it	PRON
ejpam-6680	243	2	is	be	AUX
ejpam-6680	243	3	implied	imply	VERB
ejpam-6680	243	4	from	from	ADP
ejpam-6680	243	5	lemma	lemma	PROPN
ejpam-6680	243	6	14	14	NUM
ejpam-6680	243	7	that	that	SCONJ
ejpam-6680	243	8	v	v	ADP
ejpam-6680	243	9	∈	∈	PRON
ejpam-6680	243	10	v	v	ADP
ejpam-6680	243	11	i(l	i(l	PROPN
ejpam-6680	243	12	,	,	PUNCT
ejpam-6680	243	13	a	a	PRON
ejpam-6680	243	14	)	)	PUNCT
ejpam-6680	243	15	.	.	PUNCT
ejpam-6680	244	1	therefore	therefore	ADV
ejpam-6680	244	2	,	,	PUNCT
ejpam-6680	244	3	we	we	PRON
ejpam-6680	244	4	proved	prove	VERB
ejpam-6680	244	5	that	that	SCONJ
ejpam-6680	244	6	:	:	PUNCT
ejpam-6680	244	7	(	(	PUNCT
ejpam-6680	244	8	i	i	NOUN
ejpam-6680	244	9	)	)	PUNCT
ejpam-6680	244	10	limn→∞	limn→∞	PROPN
ejpam-6680	244	11	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	244	12	,	,	PUNCT
ejpam-6680	244	13	v	v	NOUN
ejpam-6680	244	14	)	)	PUNCT
ejpam-6680	244	15	exists	exist	VERB
ejpam-6680	244	16	,	,	PUNCT
ejpam-6680	244	17	for	for	ADP
ejpam-6680	244	18	every	every	PRON
ejpam-6680	244	19	v	v	NUM
ejpam-6680	244	20	∈	∈	PROPN
ejpam-6680	244	21	v	v	NOUN
ejpam-6680	244	22	(	(	PUNCT
ejpam-6680	244	23	l	l	NOUN
ejpam-6680	244	24	,	,	PUNCT
ejpam-6680	244	25	a	a	NOUN
ejpam-6680	244	26	)	)	PUNCT
ejpam-6680	244	27	;	;	PUNCT
ejpam-6680	244	28	(	(	PUNCT
ejpam-6680	244	29	ii	ii	NOUN
ejpam-6680	244	30	)	)	PUNCT
ejpam-6680	244	31	each	each	DET
ejpam-6680	244	32	∆-limit	∆-limit	NOUN
ejpam-6680	244	33	of	of	ADP
ejpam-6680	244	34	the	the	DET
ejpam-6680	244	35	sequence	sequence	NOUN
ejpam-6680	244	36	{	{	PUNCT
ejpam-6680	244	37	bn	bn	NOUN
ejpam-6680	244	38	}	}	PUNCT
ejpam-6680	244	39	∈	∈	PROPN
ejpam-6680	244	40	v	v	ADP
ejpam-6680	244	41	i(l	i(l	PROPN
ejpam-6680	244	42	,	,	PUNCT
ejpam-6680	244	43	a	a	PRON
ejpam-6680	244	44	)	)	PUNCT
ejpam-6680	244	45	.	.	PUNCT
ejpam-6680	245	1	thus	thus	ADV
ejpam-6680	245	2	,	,	PUNCT
ejpam-6680	245	3	by	by	ADP
ejpam-6680	245	4	lemma	lemma	PROPN
ejpam-6680	245	5	9	9	NUM
ejpam-6680	245	6	,	,	PUNCT
ejpam-6680	245	7	the	the	DET
ejpam-6680	245	8	sequence	sequence	NOUN
ejpam-6680	245	9	{	{	PUNCT
ejpam-6680	245	10	bn	bn	NUM
ejpam-6680	245	11	}	}	PUNCT
ejpam-6680	245	12	is	be	AUX
ejpam-6680	245	13	∆-convergent	∆-convergent	ADJ
ejpam-6680	245	14	in	in	ADP
ejpam-6680	245	15	v	v	ADP
ejpam-6680	245	16	i(l	i(l	PROPN
ejpam-6680	245	17	,	,	PUNCT
ejpam-6680	245	18	a	a	PRON
ejpam-6680	245	19	)	)	PUNCT
ejpam-6680	245	20	.	.	PUNCT
ejpam-6680	246	1	now	now	ADV
ejpam-6680	246	2	we	we	PRON
ejpam-6680	246	3	introduce	introduce	VERB
ejpam-6680	246	4	an	an	DET
ejpam-6680	246	5	algorithm	algorithm	NOUN
ejpam-6680	246	6	for	for	ADP
ejpam-6680	246	7	strong	strong	ADJ
ejpam-6680	246	8	convergence	convergence	NOUN
ejpam-6680	246	9	:	:	PUNCT
ejpam-6680	246	10	algorithm	algorithm	NOUN
ejpam-6680	246	11	2	2	NUM
ejpam-6680	246	12	.	.	PUNCT
ejpam-6680	246	13	initialization	initialization	NOUN
ejpam-6680	246	14	:	:	PUNCT
ejpam-6680	246	15	given	give	VERB
ejpam-6680	246	16	µ	µ	PRON
ejpam-6680	246	17	,	,	PUNCT
ejpam-6680	246	18	ν	ν	NOUN
ejpam-6680	246	19	,	,	PUNCT
ejpam-6680	246	20	ς	ς	PROPN
ejpam-6680	246	21	∈	∈	PROPN
ejpam-6680	246	22	(	(	PUNCT
ejpam-6680	246	23	0	0	NUM
ejpam-6680	246	24	,	,	PUNCT
ejpam-6680	246	25	1	1	NUM
ejpam-6680	246	26	)	)	PUNCT
ejpam-6680	246	27	.	.	PUNCT
ejpam-6680	247	1	let	let	VERB
ejpam-6680	247	2	b1	b1	NOUN
ejpam-6680	247	3	be	be	AUX
ejpam-6680	247	4	the	the	DET
ejpam-6680	247	5	arbitrary	arbitrary	ADJ
ejpam-6680	247	6	element	element	NOUN
ejpam-6680	247	7	of	of	ADP
ejpam-6680	247	8	l.	l.	PROPN
ejpam-6680	247	9	iterative	iterative	PROPN
ejpam-6680	247	10	steps	step	NOUN
ejpam-6680	247	11	:	:	PUNCT
ejpam-6680	247	12	for	for	ADP
ejpam-6680	247	13	the	the	DET
ejpam-6680	247	14	given	give	VERB
ejpam-6680	247	15	iteration	iteration	NOUN
ejpam-6680	247	16	bn	bn	NOUN
ejpam-6680	247	17	,	,	PUNCT
ejpam-6680	247	18	first	first	ADJ
ejpam-6680	247	19	calculate	calculate	NOUN
ejpam-6680	247	20	bn+1	bn+1	NUM
ejpam-6680	247	21	as	as	SCONJ
ejpam-6680	247	22	stated	state	VERB
ejpam-6680	247	23	below	below	ADV
ejpam-6680	247	24	:	:	PUNCT
ejpam-6680	247	25	step	step	NOUN
ejpam-6680	247	26	1	1	NUM
ejpam-6680	247	27	.	.	PUNCT
ejpam-6680	248	1	compute	compute	VERB
ejpam-6680	248	2	sn	sn	PROPN
ejpam-6680	248	3	=	=	SYM
ejpam-6680	248	4	pl(ξnbn	pl(ξnbn	PROPN
ejpam-6680	248	5	⊕	⊕	PROPN
ejpam-6680	248	6	(	(	PUNCT
ejpam-6680	248	7	1−	1−	NUM
ejpam-6680	248	8	ξn)abn	ξn)abn	NOUN
ejpam-6680	248	9	)	)	PUNCT
ejpam-6680	248	10	,	,	PUNCT
ejpam-6680	248	11	where	where	SCONJ
ejpam-6680	248	12	ξn	ξn	ADJ
ejpam-6680	248	13	:	:	PUNCT
ejpam-6680	248	14	=	=	SYM
ejpam-6680	248	15	ςνmn	ςνmn	PROPN
ejpam-6680	248	16	,	,	PUNCT
ejpam-6680	248	17	with	with	ADP
ejpam-6680	248	18	mn	mn	PROPN
ejpam-6680	248	19	is	be	AUX
ejpam-6680	248	20	the	the	DET
ejpam-6680	248	21	minimal	minimal	ADJ
ejpam-6680	248	22	nonnegative	nonnegative	ADJ
ejpam-6680	248	23	integer	integer	NOUN
ejpam-6680	248	24	satisfying	satisfy	VERB
ejpam-6680	248	25	⟨	⟨	VERB
ejpam-6680	248	26	−−−−−→	−−−−−→	X
ejpam-6680	248	27	abnasn	abnasn	NOUN
ejpam-6680	248	28	,	,	PUNCT
ejpam-6680	248	29	−−→	−−→	PROPN
ejpam-6680	248	30	bnsn⟩	bnsn⟩	PROPN
ejpam-6680	248	31	≤	≤	PUNCT
ejpam-6680	248	32	µϱ2(bn	µϱ2(bn	PROPN
ejpam-6680	248	33	,	,	PUNCT
ejpam-6680	248	34	sn	sn	PROPN
ejpam-6680	248	35	)	)	PUNCT
ejpam-6680	248	36	.	.	PUNCT
ejpam-6680	249	1	if	if	SCONJ
ejpam-6680	249	2	bn	bn	NOUN
ejpam-6680	249	3	=	=	VERB
ejpam-6680	249	4	sn	sn	PROPN
ejpam-6680	249	5	or	or	CCONJ
ejpam-6680	249	6	asn	asn	PROPN
ejpam-6680	249	7	=	=	SYM
ejpam-6680	249	8	0	0	PUNCT
ejpam-6680	249	9	then	then	ADV
ejpam-6680	249	10	algorithm	algorithm	NOUN
ejpam-6680	249	11	stops	stop	VERB
ejpam-6680	249	12	and	and	CCONJ
ejpam-6680	249	13	sn	sn	PROPN
ejpam-6680	249	14	is	be	AUX
ejpam-6680	249	15	a	a	DET
ejpam-6680	249	16	solution	solution	NOUN
ejpam-6680	249	17	of	of	ADP
ejpam-6680	249	18	vi	vi	PROPN
ejpam-6680	249	19	.	.	PUNCT
ejpam-6680	250	1	otherwise	otherwise	ADV
ejpam-6680	250	2	step	step	VERB
ejpam-6680	250	3	2	2	NUM
ejpam-6680	250	4	.	.	PUNCT
ejpam-6680	250	5	calculate	calculate	NOUN
ejpam-6680	250	6	bn+1	bn+1	NOUN
ejpam-6680	250	7	=	=	SYM
ejpam-6680	250	8	ξnϖ(bn)⊕	ξnϖ(bn)⊕	PROPN
ejpam-6680	250	9	(	(	PUNCT
ejpam-6680	250	10	1−	1−	NUM
ejpam-6680	250	11	ξn)pln(bn	ξn)pln(bn	NOUN
ejpam-6680	250	12	)	)	PUNCT
ejpam-6680	250	13	,	,	PUNCT
ejpam-6680	250	14	where	where	SCONJ
ejpam-6680	250	15	ln	ln	ADV
ejpam-6680	250	16	:	:	PUNCT
ejpam-6680	250	17	=	=	SYM
ejpam-6680	250	18	{	{	PUNCT
ejpam-6680	250	19	b	b	PROPN
ejpam-6680	250	20	∈	∈	PROPN
ejpam-6680	250	21	z	z	NOUN
ejpam-6680	250	22	:	:	PUNCT
ejpam-6680	250	23	hn(b	hn(b	X
ejpam-6680	250	24	)	)	PUNCT
ejpam-6680	250	25	≤	≤	NOUN
ejpam-6680	250	26	0	0	NUM
ejpam-6680	250	27	}	}	PUNCT
ejpam-6680	250	28	and	and	CCONJ
ejpam-6680	250	29	hn(b	hn(b	NUM
ejpam-6680	250	30	)	)	PUNCT
ejpam-6680	250	31	=	=	VERB
ejpam-6680	250	32	⟨	⟨	VERB
ejpam-6680	250	33	−→	−→	NOUN
ejpam-6680	250	34	bsn	bsn	NOUN
ejpam-6680	250	35	,	,	PUNCT
ejpam-6680	250	36	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	PRON
ejpam-6680	250	37	(	(	PUNCT
ejpam-6680	250	38	ξnbn	ξnbn	PROPN
ejpam-6680	250	39	⊕	⊕	PROPN
ejpam-6680	250	40	(	(	PUNCT
ejpam-6680	250	41	1−	1−	NUM
ejpam-6680	250	42	ξn)abn)abn⟩.	ξn)abn)abn⟩.	NOUN
ejpam-6680	250	43	place	place	NOUN
ejpam-6680	250	44	n	n	NOUN
ejpam-6680	250	45	:	:	PUNCT
ejpam-6680	250	46	=	=	SYM
ejpam-6680	250	47	n+	n+	X
ejpam-6680	250	48	1	1	NUM
ejpam-6680	250	49	and	and	CCONJ
ejpam-6680	250	50	move	move	VERB
ejpam-6680	250	51	to	to	PART
ejpam-6680	250	52	step	step	VERB
ejpam-6680	250	53	1	1	NUM
ejpam-6680	250	54	.	.	PUNCT
ejpam-6680	251	1	theorem	theorem	NOUN
ejpam-6680	251	2	3	3	X
ejpam-6680	251	3	.	.	PUNCT
ejpam-6680	251	4	consider	consider	VERB
ejpam-6680	251	5	a	a	DET
ejpam-6680	251	6	nonempty	nonempty	ADJ
ejpam-6680	251	7	,	,	PUNCT
ejpam-6680	251	8	closed	closed	ADJ
ejpam-6680	251	9	and	and	CCONJ
ejpam-6680	251	10	convex	convex	PROPN
ejpam-6680	251	11	subset	subset	NOUN
ejpam-6680	251	12	of	of	ADP
ejpam-6680	251	13	a	a	DET
ejpam-6680	251	14	hadamard	hadamard	ADJ
ejpam-6680	251	15	space	space	NOUN
ejpam-6680	251	16	z	z	AUX
ejpam-6680	251	17	be	be	AUX
ejpam-6680	251	18	l.	l.	NOUN
ejpam-6680	251	19	the	the	DET
ejpam-6680	251	20	mapping	mapping	NOUN
ejpam-6680	251	21	a	a	DET
ejpam-6680	251	22	:	:	PUNCT
ejpam-6680	251	23	l	l	NOUN
ejpam-6680	251	24	→	→	PUNCT
ejpam-6680	251	25	l	l	NOUN
ejpam-6680	251	26	is	be	AUX
ejpam-6680	251	27	a	a	DET
ejpam-6680	251	28	pseudo	pseudo	NOUN
ejpam-6680	251	29	-	-	ADJ
ejpam-6680	251	30	monotone	monotone	ADJ
ejpam-6680	251	31	,	,	PUNCT
ejpam-6680	251	32	uniformly	uniformly	ADV
ejpam-6680	251	33	continuous	continuous	ADJ
ejpam-6680	251	34	on	on	ADP
ejpam-6680	251	35	z.	z.	PROPN
ejpam-6680	251	36	the	the	DET
ejpam-6680	251	37	solution	solution	NOUN
ejpam-6680	251	38	set	set	VERB
ejpam-6680	251	39	of	of	ADP
ejpam-6680	251	40	vi	vi	PROPN
ejpam-6680	251	41	is	be	AUX
ejpam-6680	251	42	nonempty	nonempty	ADJ
ejpam-6680	251	43	,	,	PUNCT
ejpam-6680	251	44	that	that	PRON
ejpam-6680	251	45	is	be	AUX
ejpam-6680	251	46	v	v	ADP
ejpam-6680	251	47	i(l	i(l	PROPN
ejpam-6680	251	48	,	,	PUNCT
ejpam-6680	251	49	a	a	PRON
ejpam-6680	251	50	)	)	PUNCT
ejpam-6680	251	51	̸=	̸=	PROPN
ejpam-6680	251	52	∅.	∅.	ADV
ejpam-6680	251	53	let	let	VERB
ejpam-6680	251	54	{	{	PUNCT
ejpam-6680	251	55	ξn	ξn	NOUN
ejpam-6680	251	56	}	}	PUNCT
ejpam-6680	251	57	be	be	AUX
ejpam-6680	251	58	the	the	DET
ejpam-6680	251	59	sequences	sequence	NOUN
ejpam-6680	251	60	of	of	ADP
ejpam-6680	251	61	real	real	ADJ
ejpam-6680	251	62	numbers	number	NOUN
ejpam-6680	251	63	in	in	ADP
ejpam-6680	251	64	(	(	PUNCT
ejpam-6680	251	65	0	0	NUM
ejpam-6680	251	66	,	,	PUNCT
ejpam-6680	251	67	1	1	NUM
ejpam-6680	251	68	)	)	PUNCT
ejpam-6680	251	69	such	such	ADJ
ejpam-6680	251	70	that	that	SCONJ
ejpam-6680	251	71	lim	lim	PROPN
ejpam-6680	251	72	n→∞	n→∞	PRON
ejpam-6680	251	73	ξn	ξn	PROPN
ejpam-6680	251	74	=	=	PUNCT
ejpam-6680	251	75	0,σ∞	0,σ∞	NUM
ejpam-6680	251	76	n=1ξn	n=1ξn	NOUN
ejpam-6680	252	1	=	=	PUNCT
ejpam-6680	252	2	∞.	∞.	PROPN
ejpam-6680	252	3	then	then	ADV
ejpam-6680	252	4	any	any	DET
ejpam-6680	252	5	sequence	sequence	NOUN
ejpam-6680	252	6	{	{	PUNCT
ejpam-6680	252	7	bn	bn	NOUN
ejpam-6680	252	8	}	}	PUNCT
ejpam-6680	252	9	converges	converge	VERB
ejpam-6680	252	10	strongly	strongly	ADV
ejpam-6680	252	11	to	to	ADP
ejpam-6680	252	12	v	v	NOUN
ejpam-6680	252	13	∈	∈	NOUN
ejpam-6680	252	14	v	v	ADP
ejpam-6680	252	15	i(l	i(l	PROPN
ejpam-6680	252	16	,	,	PUNCT
ejpam-6680	252	17	a	a	PRON
ejpam-6680	252	18	)	)	PUNCT
ejpam-6680	252	19	,	,	PUNCT
ejpam-6680	252	20	where	where	SCONJ
ejpam-6680	252	21	v	v	NOUN
ejpam-6680	252	22	=	=	SYM
ejpam-6680	252	23	pv	pv	NOUN
ejpam-6680	252	24	i(l	i(l	PROPN
ejpam-6680	252	25	,	,	PUNCT
ejpam-6680	252	26	a)ϖ(v	a)ϖ(v	NOUN
ejpam-6680	252	27	)	)	PUNCT
ejpam-6680	252	28	.	.	PUNCT
ejpam-6680	253	1	m.	m.	PROPN
ejpam-6680	253	2	rashid	rashid	PROPN
ejpam-6680	253	3	et	et	PROPN
ejpam-6680	253	4	al	al	PROPN
ejpam-6680	253	5	.	.	PUNCT
ejpam-6680	253	6	/	/	SYM
ejpam-6680	253	7	eur	eur	PROPN
ejpam-6680	253	8	.	.	PUNCT
ejpam-6680	254	1	j.	j.	PROPN
ejpam-6680	254	2	pure	pure	PROPN
ejpam-6680	254	3	appl	appl	PROPN
ejpam-6680	254	4	.	.	PROPN
ejpam-6680	254	5	math	math	PROPN
ejpam-6680	254	6	,	,	PUNCT
ejpam-6680	254	7	18	18	NUM
ejpam-6680	254	8	(	(	PUNCT
ejpam-6680	254	9	4	4	NUM
ejpam-6680	254	10	)	)	PUNCT
ejpam-6680	254	11	(	(	PUNCT
ejpam-6680	254	12	2025	2025	NUM
ejpam-6680	254	13	)	)	PUNCT
ejpam-6680	254	14	,	,	PUNCT
ejpam-6680	254	15	6680	6680	NUM
ejpam-6680	254	16	14	14	NUM
ejpam-6680	254	17	of	of	ADP
ejpam-6680	254	18	24	24	NUM
ejpam-6680	254	19	proof	proof	NOUN
ejpam-6680	254	20	.	.	PUNCT
ejpam-6680	255	1	claim	claim	NOUN
ejpam-6680	255	2	1	1	NUM
ejpam-6680	255	3	.	.	PUNCT
ejpam-6680	256	1	the	the	DET
ejpam-6680	256	2	sequence	sequence	NOUN
ejpam-6680	256	3	{	{	PUNCT
ejpam-6680	256	4	bn	bn	NOUN
ejpam-6680	256	5	}	}	PUNCT
ejpam-6680	256	6	is	be	AUX
ejpam-6680	256	7	bounded	bound	VERB
ejpam-6680	256	8	.	.	PUNCT
ejpam-6680	257	1	to	to	PART
ejpam-6680	257	2	prove	prove	VERB
ejpam-6680	257	3	the	the	DET
ejpam-6680	257	4	claim	claim	NOUN
ejpam-6680	257	5	,	,	PUNCT
ejpam-6680	257	6	assume	assume	VERB
ejpam-6680	257	7	zn	zn	PROPN
ejpam-6680	257	8	=	=	PUNCT
ejpam-6680	257	9	pln(bn	pln(bn	X
ejpam-6680	257	10	)	)	PUNCT
ejpam-6680	257	11	,	,	PUNCT
ejpam-6680	257	12	using	use	VERB
ejpam-6680	257	13	lemma	lemma	PROPN
ejpam-6680	257	14	10	10	NUM
ejpam-6680	257	15	,	,	PUNCT
ejpam-6680	257	16	we	we	PRON
ejpam-6680	257	17	have	have	VERB
ejpam-6680	257	18	ϱ2(zn	ϱ2(zn	PROPN
ejpam-6680	257	19	,	,	PUNCT
ejpam-6680	257	20	v	v	NOUN
ejpam-6680	257	21	)	)	PUNCT
ejpam-6680	257	22	=	=	SYM
ejpam-6680	257	23	ϱ2(plnbn	ϱ2(plnbn	PROPN
ejpam-6680	257	24	,	,	PUNCT
ejpam-6680	257	25	v	v	NOUN
ejpam-6680	257	26	)	)	PUNCT
ejpam-6680	257	27	≤	≤	NUM
ejpam-6680	257	28	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	257	29	,	,	PUNCT
ejpam-6680	257	30	v)−	v)−	PROPN
ejpam-6680	257	31	ϱ2(plnbn	ϱ2(plnbn	PROPN
ejpam-6680	257	32	,	,	PUNCT
ejpam-6680	257	33	bn	bn	NOUN
ejpam-6680	257	34	)	)	PUNCT
ejpam-6680	257	35	,	,	PUNCT
ejpam-6680	257	36	according	accord	VERB
ejpam-6680	257	37	to	to	ADP
ejpam-6680	257	38	claim	claim	NOUN
ejpam-6680	257	39	1	1	NUM
ejpam-6680	257	40	in	in	ADP
ejpam-6680	257	41	theorem	theorem	NOUN
ejpam-6680	257	42	1	1	NUM
ejpam-6680	257	43	,	,	PUNCT
ejpam-6680	257	44	we	we	PRON
ejpam-6680	257	45	get	get	VERB
ejpam-6680	257	46	ϱ2(zn	ϱ2(zn	PROPN
ejpam-6680	257	47	,	,	PUNCT
ejpam-6680	257	48	v	v	NOUN
ejpam-6680	257	49	)	)	PUNCT
ejpam-6680	258	1	=	=	SYM
ejpam-6680	258	2	ϱ2(plnbn	ϱ2(plnbn	PROPN
ejpam-6680	258	3	,	,	PUNCT
ejpam-6680	258	4	v	v	NOUN
ejpam-6680	258	5	)	)	PUNCT
ejpam-6680	258	6	≤	≤	NUM
ejpam-6680	258	7	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	258	8	,	,	PUNCT
ejpam-6680	258	9	v)−	v)−	PROPN
ejpam-6680	258	10	[	[	PUNCT
ejpam-6680	258	11	1	1	NUM
ejpam-6680	258	12	m	m	VERB
ejpam-6680	258	13	(	(	PUNCT
ejpam-6680	258	14	−1−	−1−	PROPN
ejpam-6680	258	15	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	258	16	,	,	PUNCT
ejpam-6680	258	17	sn	sn	PROPN
ejpam-6680	258	18	)	)	PUNCT
ejpam-6680	258	19	]	]	PUNCT
ejpam-6680	258	20	2	2	X
ejpam-6680	258	21	.	.	PUNCT
ejpam-6680	259	1	this	this	PRON
ejpam-6680	259	2	implies	imply	VERB
ejpam-6680	259	3	that	that	SCONJ
ejpam-6680	259	4	ϱ(zn	ϱ(zn	PROPN
ejpam-6680	259	5	,	,	PUNCT
ejpam-6680	259	6	v	v	NOUN
ejpam-6680	259	7	)	)	PUNCT
ejpam-6680	259	8	≤	≤	NOUN
ejpam-6680	259	9	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	259	10	,	,	PUNCT
ejpam-6680	259	11	v	v	NOUN
ejpam-6680	259	12	)	)	PUNCT
ejpam-6680	259	13	.	.	PUNCT
ejpam-6680	260	1	(	(	PUNCT
ejpam-6680	260	2	13	13	X
ejpam-6680	260	3	)	)	PUNCT
ejpam-6680	260	4	consider	consider	VERB
ejpam-6680	260	5	ϱ(bn+1	ϱ(bn+1	NOUN
ejpam-6680	260	6	,	,	PUNCT
ejpam-6680	260	7	v	v	NOUN
ejpam-6680	260	8	)	)	PUNCT
ejpam-6680	260	9	=	=	SYM
ejpam-6680	260	10	ϱ(ξnϖ(bn)⊕	ϱ(ξnϖ(bn)⊕	PROPN
ejpam-6680	260	11	(	(	PUNCT
ejpam-6680	260	12	1−	1−	NUM
ejpam-6680	260	13	ξn)pln(bn	ξn)pln(bn	NOUN
ejpam-6680	260	14	)	)	PUNCT
ejpam-6680	260	15	,	,	PUNCT
ejpam-6680	260	16	v	v	NOUN
ejpam-6680	260	17	)	)	PUNCT
ejpam-6680	260	18	and	and	CCONJ
ejpam-6680	260	19	by	by	ADP
ejpam-6680	260	20	using	use	VERB
ejpam-6680	260	21	lemma	lemma	PROPN
ejpam-6680	260	22	2-(i),we	2-(i),we	PROPN
ejpam-6680	260	23	get	get	VERB
ejpam-6680	260	24	ϱ(ξnϖ(bn)⊕(1−	ϱ(ξnϖ(bn)⊕(1−	ADJ
ejpam-6680	260	25	ξn)pln(bn	ξn)pln(bn	NOUN
ejpam-6680	260	26	)	)	PUNCT
ejpam-6680	260	27	,	,	PUNCT
ejpam-6680	260	28	v	v	NOUN
ejpam-6680	260	29	)	)	PUNCT
ejpam-6680	260	30	≤	≤	NOUN
ejpam-6680	260	31	ξnϱ(ϖ(bn	ξnϱ(ϖ(bn	NOUN
ejpam-6680	260	32	)	)	PUNCT
ejpam-6680	260	33	,	,	PUNCT
ejpam-6680	260	34	v	v	NOUN
ejpam-6680	260	35	)	)	PUNCT
ejpam-6680	261	1	+	+	CCONJ
ejpam-6680	261	2	(	(	PUNCT
ejpam-6680	261	3	1−	1−	NUM
ejpam-6680	261	4	ξn)ϱ(plnbn	ξn)ϱ(plnbn	NOUN
ejpam-6680	261	5	,	,	PUNCT
ejpam-6680	261	6	v	v	NOUN
ejpam-6680	261	7	)	)	PUNCT
ejpam-6680	261	8	,	,	PUNCT
ejpam-6680	261	9	≤	≤	ADJ
ejpam-6680	261	10	ξn(ϱ(ϖ(bn	ξn(ϱ(ϖ(bn	NOUN
ejpam-6680	261	11	)	)	PUNCT
ejpam-6680	261	12	,	,	PUNCT
ejpam-6680	261	13	ϖ(v	ϖ(v	NOUN
ejpam-6680	261	14	)	)	PUNCT
ejpam-6680	262	1	+	+	NUM
ejpam-6680	263	1	ϱ(ϖ(v	ϱ(ϖ(v	PROPN
ejpam-6680	263	2	)	)	PUNCT
ejpam-6680	263	3	,	,	PUNCT
ejpam-6680	263	4	v	v	NOUN
ejpam-6680	263	5	)	)	PUNCT
ejpam-6680	263	6	)	)	PUNCT
ejpam-6680	264	1	+	+	CCONJ
ejpam-6680	264	2	[	[	PUNCT
ejpam-6680	264	3	(	(	PUNCT
ejpam-6680	264	4	1−	1−	NUM
ejpam-6680	264	5	ξn)ϱ(plnbn	ξn)ϱ(plnbn	NOUN
ejpam-6680	264	6	,	,	PUNCT
ejpam-6680	264	7	v	v	NOUN
ejpam-6680	264	8	)	)	PUNCT
ejpam-6680	264	9	]	]	PUNCT
ejpam-6680	264	10	,	,	PUNCT
ejpam-6680	264	11	≤	≤	NUM
ejpam-6680	264	12	ξnϱ(ϖ(bn	ξnϱ(ϖ(bn	NOUN
ejpam-6680	264	13	)	)	PUNCT
ejpam-6680	264	14	,	,	PUNCT
ejpam-6680	264	15	ϖ(v	ϖ(v	NOUN
ejpam-6680	264	16	)	)	PUNCT
ejpam-6680	264	17	)	)	PUNCT
ejpam-6680	265	1	+	+	CCONJ
ejpam-6680	265	2	ξnϱ(ϖ(v	ξnϱ(ϖ(v	NOUN
ejpam-6680	265	3	)	)	PUNCT
ejpam-6680	265	4	,	,	PUNCT
ejpam-6680	265	5	v	v	NOUN
ejpam-6680	265	6	)	)	PUNCT
ejpam-6680	265	7	+	+	CCONJ
ejpam-6680	265	8	[	[	PUNCT
ejpam-6680	265	9	(	(	PUNCT
ejpam-6680	265	10	1−	1−	NUM
ejpam-6680	265	11	ξn)ϱ(plnbn	ξn)ϱ(plnbn	NOUN
ejpam-6680	265	12	,	,	PUNCT
ejpam-6680	265	13	v	v	NOUN
ejpam-6680	265	14	)	)	PUNCT
ejpam-6680	265	15	]	]	PUNCT
ejpam-6680	265	16	,	,	PUNCT
ejpam-6680	265	17	≤	≤	PROPN
ejpam-6680	265	18	ξnρϱ(bn	ξnρϱ(bn	PROPN
ejpam-6680	265	19	,	,	PUNCT
ejpam-6680	265	20	v	v	NOUN
ejpam-6680	265	21	)	)	PUNCT
ejpam-6680	265	22	+	+	CCONJ
ejpam-6680	265	23	ξnϱ(ϖ(v	ξnϱ(ϖ(v	NOUN
ejpam-6680	265	24	)	)	PUNCT
ejpam-6680	265	25	,	,	PUNCT
ejpam-6680	265	26	v	v	NOUN
ejpam-6680	265	27	)	)	PUNCT
ejpam-6680	265	28	+	+	CCONJ
ejpam-6680	265	29	(	(	PUNCT
ejpam-6680	265	30	1−	1−	NUM
ejpam-6680	265	31	ξn)ϱ(zn	ξn)ϱ(zn	PROPN
ejpam-6680	265	32	,	,	PUNCT
ejpam-6680	265	33	v	v	NOUN
ejpam-6680	265	34	)	)	PUNCT
ejpam-6680	265	35	,	,	PUNCT
ejpam-6680	265	36	≤	≤	PROPN
ejpam-6680	265	37	ξnρϱ(bn	ξnρϱ(bn	PROPN
ejpam-6680	265	38	,	,	PUNCT
ejpam-6680	265	39	v	v	NOUN
ejpam-6680	265	40	)	)	PUNCT
ejpam-6680	265	41	+	+	CCONJ
ejpam-6680	265	42	ξnϱ(ϖ(v	ξnϱ(ϖ(v	NOUN
ejpam-6680	265	43	)	)	PUNCT
ejpam-6680	265	44	,	,	PUNCT
ejpam-6680	265	45	v	v	NOUN
ejpam-6680	265	46	)	)	PUNCT
ejpam-6680	265	47	+	+	CCONJ
ejpam-6680	265	48	(	(	PUNCT
ejpam-6680	265	49	1−	1−	NUM
ejpam-6680	265	50	ξn)ϱ(bn	ξn)ϱ(bn	NUM
ejpam-6680	265	51	,	,	PUNCT
ejpam-6680	265	52	v	v	NOUN
ejpam-6680	265	53	)	)	PUNCT
ejpam-6680	265	54	,	,	PUNCT
ejpam-6680	265	55	=	=	PRON
ejpam-6680	265	56	(	(	PUNCT
ejpam-6680	265	57	ξnρ+	ξnρ+	PROPN
ejpam-6680	265	58	(	(	PUNCT
ejpam-6680	265	59	1−	1−	NUM
ejpam-6680	265	60	ξn))ϱ(bn	ξn))ϱ(bn	PROPN
ejpam-6680	265	61	,	,	PUNCT
ejpam-6680	265	62	v	v	NOUN
ejpam-6680	265	63	)	)	PUNCT
ejpam-6680	265	64	+	+	CCONJ
ejpam-6680	265	65	ξnϱ(ϖ(v	ξnϱ(ϖ(v	NOUN
ejpam-6680	265	66	)	)	PUNCT
ejpam-6680	265	67	,	,	PUNCT
ejpam-6680	265	68	v	v	NOUN
ejpam-6680	265	69	)	)	PUNCT
ejpam-6680	265	70	,	,	PUNCT
ejpam-6680	265	71	=	=	SYM
ejpam-6680	265	72	(	(	PUNCT
ejpam-6680	265	73	1−	1−	NUM
ejpam-6680	265	74	ξn(1−	ξn(1−	PROPN
ejpam-6680	265	75	ρ))ϱ(bn	ρ))ϱ(bn	NUM
ejpam-6680	265	76	,	,	PUNCT
ejpam-6680	265	77	v	v	NOUN
ejpam-6680	265	78	)	)	PUNCT
ejpam-6680	265	79	+	+	CCONJ
ejpam-6680	265	80	ξn(1−	ξn(1−	PROPN
ejpam-6680	265	81	ρ	ρ	PROPN
ejpam-6680	265	82	)	)	PUNCT
ejpam-6680	265	83	ϱ(ϖ(v	ϱ(ϖ(v	PROPN
ejpam-6680	265	84	)	)	PUNCT
ejpam-6680	265	85	,	,	PUNCT
ejpam-6680	265	86	v	v	NOUN
ejpam-6680	265	87	)	)	PUNCT
ejpam-6680	265	88	(	(	PUNCT
ejpam-6680	265	89	1−	1−	NUM
ejpam-6680	265	90	ρ	ρ	NUM
ejpam-6680	265	91	)	)	PUNCT
ejpam-6680	265	92	,	,	PUNCT
ejpam-6680	265	93	≤	≤	NUM
ejpam-6680	265	94	max	max	PROPN
ejpam-6680	265	95	{	{	PUNCT
ejpam-6680	265	96	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	265	97	,	,	PUNCT
ejpam-6680	265	98	v	v	NOUN
ejpam-6680	265	99	)	)	PUNCT
ejpam-6680	265	100	,	,	PUNCT
ejpam-6680	265	101	ϱ(ϖ(v	ϱ(ϖ(v	PROPN
ejpam-6680	265	102	)	)	PUNCT
ejpam-6680	265	103	,	,	PUNCT
ejpam-6680	265	104	v	v	NOUN
ejpam-6680	265	105	)	)	PUNCT
ejpam-6680	265	106	(	(	PUNCT
ejpam-6680	265	107	1−	1−	NUM
ejpam-6680	265	108	ρ	ρ	NUM
ejpam-6680	265	109	)	)	PUNCT
ejpam-6680	265	110	}	}	PUNCT
ejpam-6680	265	111	,	,	PUNCT
ejpam-6680	265	112	...	...	PUNCT
ejpam-6680	265	113	≤	≤	NUM
ejpam-6680	265	114	max	max	PROPN
ejpam-6680	265	115	{	{	PUNCT
ejpam-6680	265	116	ϱ(b1	ϱ(b1	NOUN
ejpam-6680	265	117	,	,	PUNCT
ejpam-6680	265	118	v	v	NOUN
ejpam-6680	265	119	)	)	PUNCT
ejpam-6680	265	120	,	,	PUNCT
ejpam-6680	265	121	ϱ(ϖ(v	ϱ(ϖ(v	PROPN
ejpam-6680	265	122	)	)	PUNCT
ejpam-6680	265	123	,	,	PUNCT
ejpam-6680	265	124	v	v	NOUN
ejpam-6680	265	125	)	)	PUNCT
ejpam-6680	265	126	(	(	PUNCT
ejpam-6680	265	127	1−	1−	NUM
ejpam-6680	265	128	ρ	ρ	NUM
ejpam-6680	265	129	)	)	PUNCT
ejpam-6680	265	130	}	}	PUNCT
ejpam-6680	265	131	,	,	PUNCT
ejpam-6680	265	132	for	for	ADP
ejpam-6680	265	133	0	0	NUM
ejpam-6680	265	134	≤	≤	NOUN
ejpam-6680	265	135	ξn(1−	ξn(1−	PROPN
ejpam-6680	265	136	ρ	ρ	NOUN
ejpam-6680	265	137	)	)	PUNCT
ejpam-6680	265	138	≤	≤	NUM
ejpam-6680	265	139	1	1	NUM
ejpam-6680	265	140	.	.	PUNCT
ejpam-6680	266	1	thus	thus	ADV
ejpam-6680	266	2	we	we	PRON
ejpam-6680	266	3	proved	prove	VERB
ejpam-6680	266	4	the	the	DET
ejpam-6680	266	5	claim	claim	NOUN
ejpam-6680	266	6	1	1	X
ejpam-6680	266	7	.	.	X
ejpam-6680	266	8	claim	claim	NOUN
ejpam-6680	266	9	2	2	NUM
ejpam-6680	266	10	.	.	PUNCT
ejpam-6680	266	11	to	to	PART
ejpam-6680	266	12	prove	prove	VERB
ejpam-6680	266	13	ϱ2(zn	ϱ2(zn	PROPN
ejpam-6680	266	14	,	,	PUNCT
ejpam-6680	266	15	bn	bn	NOUN
ejpam-6680	266	16	)	)	PUNCT
ejpam-6680	266	17	≤	≤	NUM
ejpam-6680	266	18	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	266	19	,	,	PUNCT
ejpam-6680	266	20	v)−	v)−	PROPN
ejpam-6680	266	21	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	266	22	,	,	PUNCT
ejpam-6680	266	23	v	v	NOUN
ejpam-6680	266	24	)	)	PUNCT
ejpam-6680	266	25	+	+	CCONJ
ejpam-6680	266	26	2ξn⟨	2ξn⟨	NUM
ejpam-6680	266	27	−−−−→	−−−−→	NOUN
ejpam-6680	266	28	ϖ(bn)v	ϖ(bn)v	VERB
ejpam-6680	266	29	,	,	PUNCT
ejpam-6680	266	30	−−−→	−−−→	VERB
ejpam-6680	266	31	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	266	32	let	let	VERB
ejpam-6680	266	33	sn	sn	PROPN
ejpam-6680	266	34	=	=	SYM
ejpam-6680	266	35	ξnv	ξnv	PROPN
ejpam-6680	266	36	⊕	⊕	PROPN
ejpam-6680	266	37	(	(	PUNCT
ejpam-6680	266	38	1−	1−	NUM
ejpam-6680	266	39	ξn)zn	ξn)zn	NOUN
ejpam-6680	266	40	.	.	PUNCT
ejpam-6680	267	1	it	it	PRON
ejpam-6680	267	2	follows	follow	VERB
ejpam-6680	267	3	from	from	ADP
ejpam-6680	267	4	lemmas	lemmas	PROPN
ejpam-6680	267	5	6	6	NUM
ejpam-6680	267	6	and	and	CCONJ
ejpam-6680	267	7	7	7	NUM
ejpam-6680	267	8	that	that	DET
ejpam-6680	267	9	ϱ2(bn+1	ϱ2(bn+1	VERB
ejpam-6680	267	10	,	,	PUNCT
ejpam-6680	267	11	v	v	NOUN
ejpam-6680	267	12	)	)	PUNCT
ejpam-6680	267	13	=	=	SYM
ejpam-6680	267	14	ϱ2(ξnϖ(bn)⊕	ϱ2(ξnϖ(bn)⊕	X
ejpam-6680	267	15	(	(	PUNCT
ejpam-6680	267	16	1−	1−	NUM
ejpam-6680	267	17	ξn)zn	ξn)zn	NOUN
ejpam-6680	267	18	,	,	PUNCT
ejpam-6680	267	19	v	v	NOUN
ejpam-6680	267	20	)	)	PUNCT
ejpam-6680	267	21	≤	≤	NOUN
ejpam-6680	267	22	ϱ2(sn	ϱ2(sn	PROPN
ejpam-6680	267	23	,	,	PUNCT
ejpam-6680	267	24	v	v	NOUN
ejpam-6680	267	25	)	)	PUNCT
ejpam-6680	268	1	+	+	CCONJ
ejpam-6680	268	2	2⟨	2⟨	NUM
ejpam-6680	268	3	−−−−→	−−−−→	SYM
ejpam-6680	268	4	bn+1sn	bn+1sn	NOUN
ejpam-6680	268	5	,	,	PUNCT
ejpam-6680	268	6	−−−→	−−−→	ADJ
ejpam-6680	268	7	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	268	8	,	,	PUNCT
ejpam-6680	268	9	=	=	PUNCT
ejpam-6680	269	1	[	[	X
ejpam-6680	269	2	ϱ(ξnv	ϱ(ξnv	PROPN
ejpam-6680	269	3	+	+	CCONJ
ejpam-6680	269	4	(	(	PUNCT
ejpam-6680	269	5	1−	1−	NUM
ejpam-6680	269	6	ξn)zn	ξn)zn	NOUN
ejpam-6680	269	7	,	,	PUNCT
ejpam-6680	269	8	v	v	NOUN
ejpam-6680	269	9	)	)	PUNCT
ejpam-6680	269	10	]	]	PUNCT
ejpam-6680	269	11	2	2	NUM
ejpam-6680	269	12	m.	m.	NOUN
ejpam-6680	269	13	rashid	rashid	PROPN
ejpam-6680	269	14	et	et	PROPN
ejpam-6680	269	15	al	al	PROPN
ejpam-6680	269	16	.	.	PUNCT
ejpam-6680	269	17	/	/	SYM
ejpam-6680	269	18	eur	eur	PROPN
ejpam-6680	269	19	.	.	PUNCT
ejpam-6680	270	1	j.	j.	PROPN
ejpam-6680	270	2	pure	pure	PROPN
ejpam-6680	270	3	appl	appl	PROPN
ejpam-6680	270	4	.	.	PROPN
ejpam-6680	270	5	math	math	PROPN
ejpam-6680	270	6	,	,	PUNCT
ejpam-6680	270	7	18	18	NUM
ejpam-6680	270	8	(	(	PUNCT
ejpam-6680	270	9	4	4	NUM
ejpam-6680	270	10	)	)	PUNCT
ejpam-6680	270	11	(	(	PUNCT
ejpam-6680	270	12	2025	2025	NUM
ejpam-6680	270	13	)	)	PUNCT
ejpam-6680	270	14	,	,	PUNCT
ejpam-6680	270	15	6680	6680	NUM
ejpam-6680	270	16	15	15	NUM
ejpam-6680	270	17	of	of	ADP
ejpam-6680	270	18	24	24	NUM
ejpam-6680	270	19	+2⟨	+2⟨	NOUN
ejpam-6680	270	20	(	(	PUNCT
ejpam-6680	270	21	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	NUM
ejpam-6680	270	22	ξnϖ(bn)⊕	ξnϖ(bn)⊕	PROPN
ejpam-6680	270	23	(	(	PUNCT
ejpam-6680	270	24	1−	1−	NUM
ejpam-6680	270	25	ξn)zn))sn	ξn)zn))sn	NOUN
ejpam-6680	270	26	,	,	PUNCT
ejpam-6680	270	27	−−−→	−−−→	PROPN
ejpam-6680	270	28	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	270	29	,	,	PUNCT
ejpam-6680	270	30	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	270	31	,	,	PUNCT
ejpam-6680	270	32	v	v	NOUN
ejpam-6680	270	33	)	)	PUNCT
ejpam-6680	270	34	≤	≤	NOUN
ejpam-6680	271	1	[	[	X
ejpam-6680	271	2	ξnd(v	ξnd(v	PROPN
ejpam-6680	271	3	,	,	PUNCT
ejpam-6680	271	4	v	v	NOUN
ejpam-6680	271	5	)	)	PUNCT
ejpam-6680	272	1	+	+	CCONJ
ejpam-6680	272	2	(	(	PUNCT
ejpam-6680	272	3	1−	1−	NUM
ejpam-6680	272	4	ξn)ϱ(zn	ξn)ϱ(zn	PROPN
ejpam-6680	272	5	,	,	PUNCT
ejpam-6680	272	6	v	v	NOUN
ejpam-6680	272	7	)	)	PUNCT
ejpam-6680	272	8	]	]	PUNCT
ejpam-6680	272	9	2	2	NUM
ejpam-6680	272	10	+	+	NUM
ejpam-6680	272	11	2[ξn⟨	2[ξn⟨	NUM
ejpam-6680	272	12	−−−−−→	−−−−−→	NOUN
ejpam-6680	272	13	ϖ(bn)sn	ϖ(bn)sn	NOUN
ejpam-6680	272	14	,	,	PUNCT
ejpam-6680	272	15	−−−→	−−−→	ADJ
ejpam-6680	272	16	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	17	+	+	PROPN
ejpam-6680	272	18	(	(	PUNCT
ejpam-6680	272	19	1−	1−	NUM
ejpam-6680	272	20	ξn)⟨−−→znsn	ξn)⟨−−→znsn	PROPN
ejpam-6680	272	21	,	,	PUNCT
ejpam-6680	272	22	−−−→	−−−→	ADJ
ejpam-6680	272	23	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	24	]	]	PUNCT
ejpam-6680	272	25	,	,	PUNCT
ejpam-6680	272	26	=	=	SYM
ejpam-6680	272	27	(	(	PUNCT
ejpam-6680	272	28	1−	1−	NUM
ejpam-6680	272	29	ξn	ξn	NOUN
ejpam-6680	272	30	)	)	PUNCT
ejpam-6680	272	31	2ϱ2(zn	2ϱ2(zn	PROPN
ejpam-6680	272	32	,	,	PUNCT
ejpam-6680	272	33	v	v	NOUN
ejpam-6680	272	34	)	)	PUNCT
ejpam-6680	272	35	+	+	NUM
ejpam-6680	272	36	2[ξn⟨	2[ξn⟨	NUM
ejpam-6680	272	37	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	PUNCT
ejpam-6680	272	38	ϖ(bn)(ξnv	ϖ(bn)(ξnv	PROPN
ejpam-6680	272	39	⊕	⊕	PROPN
ejpam-6680	272	40	(	(	PUNCT
ejpam-6680	272	41	1−	1−	NUM
ejpam-6680	272	42	ξn)zn	ξn)zn	NOUN
ejpam-6680	272	43	)	)	PUNCT
ejpam-6680	272	44	,	,	PUNCT
ejpam-6680	272	45	−−−→	−−−→	PROPN
ejpam-6680	272	46	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	47	+	+	PROPN
ejpam-6680	272	48	(	(	PUNCT
ejpam-6680	272	49	1−	1−	NUM
ejpam-6680	272	50	ξn)⟨	ξn)⟨	NUM
ejpam-6680	272	51	−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−→	SYM
ejpam-6680	272	52	zn(ξnv	zn(ξnv	PROPN
ejpam-6680	272	53	⊕	⊕	PROPN
ejpam-6680	272	54	(	(	PUNCT
ejpam-6680	272	55	1−	1−	NUM
ejpam-6680	272	56	ξn)zn	ξn)zn	NOUN
ejpam-6680	272	57	)	)	PUNCT
ejpam-6680	272	58	,	,	PUNCT
ejpam-6680	272	59	−−−→	−−−→	PROPN
ejpam-6680	272	60	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	61	]	]	PUNCT
ejpam-6680	272	62	,	,	PUNCT
ejpam-6680	272	63	≤	≤	NUM
ejpam-6680	272	64	(	(	PUNCT
ejpam-6680	272	65	1−	1−	NUM
ejpam-6680	272	66	ξn	ξn	NOUN
ejpam-6680	272	67	)	)	PUNCT
ejpam-6680	272	68	2ϱ2(zn	2ϱ2(zn	PROPN
ejpam-6680	272	69	,	,	PUNCT
ejpam-6680	272	70	v	v	NOUN
ejpam-6680	272	71	)	)	PUNCT
ejpam-6680	272	72	+	+	CCONJ
ejpam-6680	272	73	2	2	NUM
ejpam-6680	272	74	[	[	PUNCT
ejpam-6680	272	75	ξ2n⟨	ξ2n⟨	NUM
ejpam-6680	272	76	−−−−→	−−−−→	PUNCT
ejpam-6680	272	77	ϖ(bn)v	ϖ(bn)v	NOUN
ejpam-6680	272	78	,	,	PUNCT
ejpam-6680	272	79	−−−→	−−−→	ADJ
ejpam-6680	272	80	bn+1v⟩+	bn+1v⟩+	NOUN
ejpam-6680	272	81	{	{	PUNCT
ejpam-6680	272	82	ξn(1−	ξn(1−	PROPN
ejpam-6680	272	83	ξn	ξn	PROPN
ejpam-6680	272	84	)	)	PUNCT
ejpam-6680	272	85	×⟨	×⟨	PROPN
ejpam-6680	272	86	−−−−−→	−−−−−→	NUM
ejpam-6680	272	87	ϖ(bn)zn	ϖ(bn)zn	NOUN
ejpam-6680	272	88	,	,	PUNCT
ejpam-6680	272	89	−−−→	−−−→	ADJ
ejpam-6680	272	90	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	91	}	}	PUNCT
ejpam-6680	272	92	+	+	CCONJ
ejpam-6680	272	93	ξn(1−	ξn(1−	PROPN
ejpam-6680	272	94	ξn)⟨−→znv	ξn)⟨−→znv	PROPN
ejpam-6680	272	95	,	,	PUNCT
ejpam-6680	272	96	−−→	−−→	PROPN
ejpam-6680	272	97	bn+1⟩+	bn+1⟩+	PROPN
ejpam-6680	272	98	{	{	PUNCT
ejpam-6680	272	99	(	(	PUNCT
ejpam-6680	272	100	1−	1−	NUM
ejpam-6680	272	101	ξn	ξn	NOUN
ejpam-6680	272	102	)	)	PUNCT
ejpam-6680	272	103	2	2	NUM
ejpam-6680	272	104	×⟨−−→znzn	×⟨−−→znzn	NOUN
ejpam-6680	272	105	,	,	PUNCT
ejpam-6680	272	106	−−−→	−−−→	ADJ
ejpam-6680	272	107	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	108	}	}	PUNCT
ejpam-6680	272	109	]	]	PUNCT
ejpam-6680	272	110	,	,	PUNCT
ejpam-6680	272	111	=	=	SYM
ejpam-6680	272	112	(	(	PUNCT
ejpam-6680	272	113	1−	1−	NUM
ejpam-6680	272	114	ξn	ξn	NOUN
ejpam-6680	272	115	)	)	PUNCT
ejpam-6680	272	116	2ϱ2(zn	2ϱ2(zn	PROPN
ejpam-6680	272	117	,	,	PUNCT
ejpam-6680	272	118	v	v	NOUN
ejpam-6680	272	119	)	)	PUNCT
ejpam-6680	272	120	+	+	CCONJ
ejpam-6680	272	121	2ξ2n⟨	2ξ2n⟨	NUM
ejpam-6680	272	122	−−−−→	−−−−→	SYM
ejpam-6680	272	123	ϖ(bn)v	ϖ(bn)v	NOUN
ejpam-6680	272	124	,	,	PUNCT
ejpam-6680	272	125	−−−→	−−−→	NUM
ejpam-6680	272	126	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	127	+2ξn(1−	+2ξn(1−	PROPN
ejpam-6680	272	128	ξn)⟨	ξn)⟨	NUM
ejpam-6680	272	129	−−−−→	−−−−→	PRON
ejpam-6680	272	130	ϖ(bn)v	ϖ(bn)v	NOUN
ejpam-6680	272	131	,	,	PUNCT
ejpam-6680	272	132	−−−→	−−−→	ADJ
ejpam-6680	272	133	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	134	,	,	PUNCT
ejpam-6680	272	135	=	=	PUNCT
ejpam-6680	272	136	(	(	PUNCT
ejpam-6680	272	137	1−	1−	NUM
ejpam-6680	272	138	ξn	ξn	NOUN
ejpam-6680	272	139	)	)	PUNCT
ejpam-6680	272	140	2ϱ2(zn	2ϱ2(zn	PROPN
ejpam-6680	272	141	,	,	PUNCT
ejpam-6680	272	142	v	v	NOUN
ejpam-6680	272	143	)	)	PUNCT
ejpam-6680	272	144	+	+	CCONJ
ejpam-6680	272	145	2ξ2n⟨	2ξ2n⟨	NUM
ejpam-6680	272	146	−−−−→	−−−−→	SYM
ejpam-6680	272	147	ϖ(bn)v	ϖ(bn)v	NOUN
ejpam-6680	272	148	,	,	PUNCT
ejpam-6680	272	149	−−−→	−−−→	NUM
ejpam-6680	272	150	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	151	+2ξn⟨	+2ξn⟨	PROPN
ejpam-6680	272	152	−−−−→	−−−−→	PUNCT
ejpam-6680	272	153	ϖ(bn)v	ϖ(bn)v	NOUN
ejpam-6680	272	154	,	,	PUNCT
ejpam-6680	272	155	−−−→	−−−→	NUM
ejpam-6680	272	156	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	157	−	−	PROPN
ejpam-6680	272	158	2ξ2n⟨	2ξ2n⟨	NUM
ejpam-6680	272	159	−−−−→	−−−−→	NOUN
ejpam-6680	272	160	ϖ(bn)v	ϖ(bn)v	NOUN
ejpam-6680	272	161	,	,	PUNCT
ejpam-6680	272	162	−−−→	−−−→	ADJ
ejpam-6680	272	163	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	164	,	,	PUNCT
ejpam-6680	272	165	=	=	PUNCT
ejpam-6680	272	166	(	(	PUNCT
ejpam-6680	272	167	1−	1−	NUM
ejpam-6680	272	168	ξn	ξn	NOUN
ejpam-6680	272	169	)	)	PUNCT
ejpam-6680	272	170	2ϱ2(zn	2ϱ2(zn	PROPN
ejpam-6680	272	171	,	,	PUNCT
ejpam-6680	272	172	v	v	NOUN
ejpam-6680	272	173	)	)	PUNCT
ejpam-6680	272	174	+	+	CCONJ
ejpam-6680	272	175	2ξn⟨	2ξn⟨	NUM
ejpam-6680	272	176	−−−−→	−−−−→	NOUN
ejpam-6680	272	177	ϖ(bn)v	ϖ(bn)v	VERB
ejpam-6680	272	178	,	,	PUNCT
ejpam-6680	272	179	−−−→	−−−→	VERB
ejpam-6680	272	180	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	272	181	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	272	182	,	,	PUNCT
ejpam-6680	272	183	v	v	NOUN
ejpam-6680	272	184	)	)	PUNCT
ejpam-6680	272	185	≤	≤	NOUN
ejpam-6680	272	186	(	(	PUNCT
ejpam-6680	272	187	1−	1−	NUM
ejpam-6680	272	188	ξn	ξn	NOUN
ejpam-6680	272	189	)	)	PUNCT
ejpam-6680	272	190	d	d	NOUN
ejpam-6680	272	191	2(zn	2(zn	PROPN
ejpam-6680	272	192	,	,	PUNCT
ejpam-6680	272	193	v	v	NOUN
ejpam-6680	272	194	)	)	PUNCT
ejpam-6680	272	195	+	+	CCONJ
ejpam-6680	272	196	2ξn⟨	2ξn⟨	NUM
ejpam-6680	272	197	−−−−→	−−−−→	NOUN
ejpam-6680	272	198	ϖ(bn)v	ϖ(bn)v	VERB
ejpam-6680	272	199	,	,	PUNCT
ejpam-6680	272	200	−−−→	−−−→	NUM
ejpam-6680	272	201	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	272	202	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	272	203	,	,	PUNCT
ejpam-6680	272	204	v	v	NOUN
ejpam-6680	272	205	)	)	PUNCT
ejpam-6680	272	206	≤	≤	NOUN
ejpam-6680	273	1	ϱ2(zn	ϱ2(zn	PROPN
ejpam-6680	273	2	,	,	PUNCT
ejpam-6680	273	3	v	v	NOUN
ejpam-6680	273	4	)	)	PUNCT
ejpam-6680	273	5	+	+	CCONJ
ejpam-6680	273	6	2ξn⟨	2ξn⟨	NUM
ejpam-6680	273	7	−−−−→	−−−−→	NOUN
ejpam-6680	273	8	ϖ(bn)v	ϖ(bn)v	VERB
ejpam-6680	273	9	,	,	PUNCT
ejpam-6680	273	10	−−−→	−−−→	VERB
ejpam-6680	273	11	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	273	12	(	(	PUNCT
ejpam-6680	273	13	14	14	NUM
ejpam-6680	273	14	)	)	PUNCT
ejpam-6680	273	15	on	on	ADP
ejpam-6680	273	16	the	the	DET
ejpam-6680	273	17	other	other	ADJ
ejpam-6680	273	18	hand	hand	NOUN
ejpam-6680	273	19	,	,	PUNCT
ejpam-6680	273	20	we	we	PRON
ejpam-6680	273	21	have	have	VERB
ejpam-6680	273	22	ϱ2(zn	ϱ2(zn	PROPN
ejpam-6680	273	23	,	,	PUNCT
ejpam-6680	273	24	v	v	NOUN
ejpam-6680	273	25	)	)	PUNCT
ejpam-6680	273	26	≤	≤	NUM
ejpam-6680	273	27	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	273	28	,	,	PUNCT
ejpam-6680	273	29	v)−	v)−	PROPN
ejpam-6680	273	30	ϱ2(zn	ϱ2(zn	PROPN
ejpam-6680	273	31	,	,	PUNCT
ejpam-6680	273	32	bn	bn	NOUN
ejpam-6680	273	33	)	)	PUNCT
ejpam-6680	273	34	,	,	PUNCT
ejpam-6680	273	35	by	by	ADP
ejpam-6680	273	36	putting	put	VERB
ejpam-6680	273	37	above	above	ADV
ejpam-6680	273	38	in	in	ADP
ejpam-6680	273	39	(	(	PUNCT
ejpam-6680	273	40	4.3	4.3	NUM
ejpam-6680	273	41	)	)	PUNCT
ejpam-6680	273	42	,	,	PUNCT
ejpam-6680	273	43	we	we	PRON
ejpam-6680	273	44	have	have	VERB
ejpam-6680	273	45	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	273	46	,	,	PUNCT
ejpam-6680	273	47	v	v	NOUN
ejpam-6680	273	48	)	)	PUNCT
ejpam-6680	273	49	≤	≤	NUM
ejpam-6680	273	50	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	273	51	,	,	PUNCT
ejpam-6680	273	52	v)−	v)−	PROPN
ejpam-6680	273	53	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	273	54	,	,	PUNCT
ejpam-6680	273	55	zn	zn	PROPN
ejpam-6680	273	56	)	)	PUNCT
ejpam-6680	274	1	+	+	CCONJ
ejpam-6680	274	2	2ξn⟨	2ξn⟨	NUM
ejpam-6680	274	3	−−−−→	−−−−→	NOUN
ejpam-6680	274	4	ϖ(bn)v	ϖ(bn)v	VERB
ejpam-6680	274	5	,	,	PUNCT
ejpam-6680	274	6	−−−→	−−−→	ADJ
ejpam-6680	274	7	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	274	8	,	,	PUNCT
ejpam-6680	274	9	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	274	10	,	,	PUNCT
ejpam-6680	274	11	zn	zn	NOUN
ejpam-6680	274	12	)	)	PUNCT
ejpam-6680	274	13	≤	≤	PROPN
ejpam-6680	274	14	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	274	15	,	,	PUNCT
ejpam-6680	274	16	v)−	v)−	PROPN
ejpam-6680	274	17	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	274	18	,	,	PUNCT
ejpam-6680	274	19	v	v	NOUN
ejpam-6680	274	20	)	)	PUNCT
ejpam-6680	274	21	+	+	CCONJ
ejpam-6680	274	22	2ξn⟨	2ξn⟨	NUM
ejpam-6680	274	23	−−−−→	−−−−→	NOUN
ejpam-6680	274	24	ϖ(bn)v	ϖ(bn)v	VERB
ejpam-6680	274	25	,	,	PUNCT
ejpam-6680	274	26	−−−→	−−−→	VERB
ejpam-6680	274	27	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	274	28	claim	claim	NOUN
ejpam-6680	274	29	3	3	NUM
ejpam-6680	274	30	.	.	PUNCT
ejpam-6680	274	31	to	to	PART
ejpam-6680	274	32	prove	prove	VERB
ejpam-6680	274	33	(	(	PUNCT
ejpam-6680	274	34	1−	1−	NUM
ejpam-6680	274	35	ξn	ξn	NOUN
ejpam-6680	274	36	)	)	PUNCT
ejpam-6680	274	37	[	[	PUNCT
ejpam-6680	274	38	1	1	NUM
ejpam-6680	274	39	m	m	PROPN
ejpam-6680	274	40	ξn(−1−	ξn(−1−	PROPN
ejpam-6680	274	41	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	274	42	,	,	PUNCT
ejpam-6680	274	43	sn	sn	PROPN
ejpam-6680	274	44	)	)	PUNCT
ejpam-6680	274	45	]	]	PUNCT
ejpam-6680	274	46	2	2	NUM
ejpam-6680	274	47	≤	≤	NUM
ejpam-6680	274	48	ϱ2(bn	ϱ2(bn	NUM
ejpam-6680	274	49	,	,	PUNCT
ejpam-6680	274	50	v)−	v)−	PROPN
ejpam-6680	274	51	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	274	52	,	,	PUNCT
ejpam-6680	274	53	v	v	NOUN
ejpam-6680	274	54	)	)	PUNCT
ejpam-6680	274	55	+	+	CCONJ
ejpam-6680	274	56	ξnϱ	ξnϱ	NOUN
ejpam-6680	274	57	2(ϖ(bn	2(ϖ(bn	NUM
ejpam-6680	274	58	)	)	PUNCT
ejpam-6680	274	59	,	,	PUNCT
ejpam-6680	274	60	v	v	NOUN
ejpam-6680	274	61	)	)	PUNCT
ejpam-6680	274	62	.	.	PUNCT
ejpam-6680	275	1	consider	consider	VERB
ejpam-6680	275	2	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	275	3	,	,	PUNCT
ejpam-6680	275	4	v	v	NOUN
ejpam-6680	275	5	)	)	PUNCT
ejpam-6680	275	6	=	=	SYM
ejpam-6680	275	7	ϱ2(ξnϖ(bn)⊕	ϱ2(ξnϖ(bn)⊕	X
ejpam-6680	275	8	(	(	PUNCT
ejpam-6680	275	9	1−	1−	NUM
ejpam-6680	275	10	ξn)zn	ξn)zn	NOUN
ejpam-6680	275	11	,	,	PUNCT
ejpam-6680	275	12	v	v	NOUN
ejpam-6680	275	13	)	)	PUNCT
ejpam-6680	275	14	and	and	CCONJ
ejpam-6680	275	15	by	by	ADP
ejpam-6680	275	16	using	use	VERB
ejpam-6680	275	17	lemma	lemma	PROPN
ejpam-6680	275	18	2-(ii	2-(ii	NUM
ejpam-6680	275	19	)	)	PUNCT
ejpam-6680	275	20	,	,	PUNCT
ejpam-6680	275	21	we	we	PRON
ejpam-6680	275	22	have	have	VERB
ejpam-6680	275	23	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	275	24	,	,	PUNCT
ejpam-6680	275	25	v	v	NOUN
ejpam-6680	275	26	)	)	PUNCT
ejpam-6680	275	27	≤	≤	NUM
ejpam-6680	275	28	ξnϱ	ξnϱ	NOUN
ejpam-6680	275	29	2(ϖ(bn	2(ϖ(bn	NUM
ejpam-6680	275	30	)	)	PUNCT
ejpam-6680	275	31	,	,	PUNCT
ejpam-6680	275	32	v	v	NOUN
ejpam-6680	275	33	)	)	PUNCT
ejpam-6680	276	1	+	+	CCONJ
ejpam-6680	276	2	(	(	PUNCT
ejpam-6680	276	3	1−	1−	NUM
ejpam-6680	276	4	ξn)ϱ	ξn)ϱ	NUM
ejpam-6680	276	5	2(zn	2(zn	NUM
ejpam-6680	276	6	,	,	PUNCT
ejpam-6680	276	7	v	v	NOUN
ejpam-6680	276	8	)	)	PUNCT
ejpam-6680	276	9	−ξn(1−	−ξn(1−	PROPN
ejpam-6680	276	10	ξn)ϱ	ξn)ϱ	PROPN
ejpam-6680	276	11	2(ϖ(bn	2(ϖ(bn	NUM
ejpam-6680	276	12	)	)	PUNCT
ejpam-6680	276	13	,	,	PUNCT
ejpam-6680	276	14	zn	zn	PROPN
ejpam-6680	276	15	)	)	PUNCT
ejpam-6680	276	16	,	,	PUNCT
ejpam-6680	276	17	≤	≤	NUM
ejpam-6680	276	18	ξnϱ	ξnϱ	NOUN
ejpam-6680	276	19	2(ϖ(bn	2(ϖ(bn	NUM
ejpam-6680	276	20	)	)	PUNCT
ejpam-6680	276	21	,	,	PUNCT
ejpam-6680	276	22	v	v	NOUN
ejpam-6680	276	23	)	)	PUNCT
ejpam-6680	276	24	+	+	CCONJ
ejpam-6680	276	25	(	(	PUNCT
ejpam-6680	276	26	1−	1−	NUM
ejpam-6680	276	27	ξn)ϱ	ξn)ϱ	NUM
ejpam-6680	276	28	2(zn	2(zn	NUM
ejpam-6680	276	29	,	,	PUNCT
ejpam-6680	276	30	v	v	NOUN
ejpam-6680	276	31	)	)	PUNCT
ejpam-6680	276	32	.	.	PUNCT
ejpam-6680	277	1	by	by	ADP
ejpam-6680	277	2	using	use	VERB
ejpam-6680	277	3	(	(	PUNCT
ejpam-6680	277	4	13	13	NUM
ejpam-6680	277	5	)	)	PUNCT
ejpam-6680	277	6	,	,	PUNCT
ejpam-6680	277	7	we	we	PRON
ejpam-6680	277	8	obtain	obtain	VERB
ejpam-6680	277	9	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	277	10	,	,	PUNCT
ejpam-6680	277	11	v	v	NOUN
ejpam-6680	277	12	)	)	PUNCT
ejpam-6680	277	13	≤	≤	NUM
ejpam-6680	277	14	ξnϱ	ξnϱ	NOUN
ejpam-6680	277	15	2(ϖ(bn	2(ϖ(bn	NUM
ejpam-6680	277	16	)	)	PUNCT
ejpam-6680	277	17	,	,	PUNCT
ejpam-6680	277	18	v	v	NOUN
ejpam-6680	277	19	)	)	PUNCT
ejpam-6680	277	20	+	+	CCONJ
ejpam-6680	277	21	(	(	PUNCT
ejpam-6680	277	22	1−	1−	NUM
ejpam-6680	277	23	ξn)ϱ	ξn)ϱ	NUM
ejpam-6680	277	24	2(bn	2(bn	NUM
ejpam-6680	277	25	,	,	PUNCT
ejpam-6680	277	26	v	v	NOUN
ejpam-6680	277	27	)	)	PUNCT
ejpam-6680	277	28	m.	m.	NOUN
ejpam-6680	277	29	rashid	rashid	PROPN
ejpam-6680	277	30	et	et	PROPN
ejpam-6680	277	31	al	al	PROPN
ejpam-6680	277	32	.	.	PUNCT
ejpam-6680	277	33	/	/	SYM
ejpam-6680	277	34	eur	eur	PROPN
ejpam-6680	277	35	.	.	PUNCT
ejpam-6680	278	1	j.	j.	PROPN
ejpam-6680	278	2	pure	pure	PROPN
ejpam-6680	278	3	appl	appl	PROPN
ejpam-6680	278	4	.	.	PROPN
ejpam-6680	278	5	math	math	PROPN
ejpam-6680	278	6	,	,	PUNCT
ejpam-6680	278	7	18	18	NUM
ejpam-6680	278	8	(	(	PUNCT
ejpam-6680	278	9	4	4	NUM
ejpam-6680	278	10	)	)	PUNCT
ejpam-6680	278	11	(	(	PUNCT
ejpam-6680	278	12	2025	2025	NUM
ejpam-6680	278	13	)	)	PUNCT
ejpam-6680	278	14	,	,	PUNCT
ejpam-6680	278	15	6680	6680	NUM
ejpam-6680	278	16	16	16	NUM
ejpam-6680	278	17	of	of	ADP
ejpam-6680	278	18	24	24	NUM
ejpam-6680	278	19	−(1−	−(1−	NOUN
ejpam-6680	278	20	ξn	ξn	NOUN
ejpam-6680	278	21	)	)	PUNCT
ejpam-6680	278	22	[	[	PUNCT
ejpam-6680	278	23	1	1	NUM
ejpam-6680	278	24	m	m	VERB
ejpam-6680	278	25	(	(	PUNCT
ejpam-6680	278	26	−1−	−1−	PROPN
ejpam-6680	278	27	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	278	28	,	,	PUNCT
ejpam-6680	278	29	sn	sn	PROPN
ejpam-6680	278	30	)	)	PUNCT
ejpam-6680	278	31	]	]	SYM
ejpam-6680	278	32	2	2	NUM
ejpam-6680	278	33	,	,	PUNCT
ejpam-6680	278	34	≤	≤	NUM
ejpam-6680	278	35	ξnϱ	ξnϱ	NOUN
ejpam-6680	278	36	2(ϖ(bn	2(ϖ(bn	NUM
ejpam-6680	278	37	)	)	PUNCT
ejpam-6680	278	38	,	,	PUNCT
ejpam-6680	278	39	v	v	NOUN
ejpam-6680	278	40	)	)	PUNCT
ejpam-6680	278	41	+	+	CCONJ
ejpam-6680	278	42	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	278	43	,	,	PUNCT
ejpam-6680	278	44	v)−	v)−	PROPN
ejpam-6680	278	45	(	(	PUNCT
ejpam-6680	278	46	1−	1−	NUM
ejpam-6680	278	47	ξn	ξn	NOUN
ejpam-6680	278	48	)	)	PUNCT
ejpam-6680	278	49	×	×	NOUN
ejpam-6680	278	50	[	[	PUNCT
ejpam-6680	278	51	1	1	NUM
ejpam-6680	278	52	m	m	VERB
ejpam-6680	278	53	(	(	PUNCT
ejpam-6680	278	54	−1−	−1−	PROPN
ejpam-6680	278	55	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	278	56	,	,	PUNCT
ejpam-6680	278	57	sn	sn	PROPN
ejpam-6680	278	58	)	)	PUNCT
ejpam-6680	278	59	]	]	PUNCT
ejpam-6680	278	60	2	2	X
ejpam-6680	278	61	.	.	PUNCT
ejpam-6680	279	1	this	this	PRON
ejpam-6680	279	2	implies	imply	VERB
ejpam-6680	279	3	that	that	SCONJ
ejpam-6680	279	4	(	(	PUNCT
ejpam-6680	279	5	1−	1−	NUM
ejpam-6680	279	6	ξn	ξn	NOUN
ejpam-6680	279	7	)	)	PUNCT
ejpam-6680	279	8	[	[	PUNCT
ejpam-6680	279	9	1	1	NUM
ejpam-6680	279	10	m	m	VERB
ejpam-6680	279	11	(	(	PUNCT
ejpam-6680	279	12	−1−	−1−	PROPN
ejpam-6680	279	13	µ)ϱ2(bn	µ)ϱ2(bn	PROPN
ejpam-6680	279	14	,	,	PUNCT
ejpam-6680	279	15	sn	sn	PROPN
ejpam-6680	279	16	)	)	PUNCT
ejpam-6680	279	17	]	]	PUNCT
ejpam-6680	279	18	2	2	NUM
ejpam-6680	279	19	≤	≤	NUM
ejpam-6680	279	20	ξnϱ	ξnϱ	NOUN
ejpam-6680	279	21	2(ϖ(bn	2(ϖ(bn	NUM
ejpam-6680	279	22	)	)	PUNCT
ejpam-6680	279	23	,	,	PUNCT
ejpam-6680	279	24	v	v	NOUN
ejpam-6680	279	25	)	)	PUNCT
ejpam-6680	279	26	+	+	CCONJ
ejpam-6680	279	27	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	279	28	,	,	PUNCT
ejpam-6680	279	29	v)−	v)−	PROPN
ejpam-6680	279	30	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	279	31	,	,	PUNCT
ejpam-6680	279	32	v	v	NOUN
ejpam-6680	279	33	)	)	PUNCT
ejpam-6680	279	34	.	.	PUNCT
ejpam-6680	280	1	claim	claim	NOUN
ejpam-6680	280	2	4	4	NUM
ejpam-6680	280	3	.	.	PUNCT
ejpam-6680	280	4	to	to	PART
ejpam-6680	280	5	prove	prove	VERB
ejpam-6680	280	6	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	280	7	,	,	PUNCT
ejpam-6680	280	8	v	v	NOUN
ejpam-6680	280	9	)	)	PUNCT
ejpam-6680	280	10	≤	≤	NOUN
ejpam-6680	280	11	(	(	PUNCT
ejpam-6680	280	12	1−	1−	NUM
ejpam-6680	280	13	(	(	PUNCT
ejpam-6680	280	14	1−	1−	NUM
ejpam-6680	280	15	ρ)ξn	ρ)ξn	PROPN
ejpam-6680	280	16	)	)	PUNCT
ejpam-6680	280	17	1−	1−	NUM
ejpam-6680	280	18	ξnρ	ξnρ	NOUN
ejpam-6680	280	19	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	280	20	,	,	PUNCT
ejpam-6680	280	21	v	v	NOUN
ejpam-6680	280	22	)	)	PUNCT
ejpam-6680	280	23	+	+	CCONJ
ejpam-6680	281	1	2ξn	2ξn	ADJ
ejpam-6680	281	2	1−	1−	NUM
ejpam-6680	281	3	ξnρ	ξnρ	NOUN
ejpam-6680	281	4	⟨	⟨	VERB
ejpam-6680	281	5	−−−−→	−−−−→	X
ejpam-6680	281	6	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	281	7	,	,	PUNCT
ejpam-6680	281	8	−−−→	−−−→	VERB
ejpam-6680	281	9	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	281	10	consider	consider	VERB
ejpam-6680	281	11	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	281	12	,	,	PUNCT
ejpam-6680	281	13	v	v	NOUN
ejpam-6680	281	14	)	)	PUNCT
ejpam-6680	281	15	≤	≤	NOUN
ejpam-6680	281	16	(	(	PUNCT
ejpam-6680	281	17	1−	1−	NUM
ejpam-6680	281	18	ξn)ϱ	ξn)ϱ	NUM
ejpam-6680	281	19	2(zn	2(zn	NUM
ejpam-6680	281	20	,	,	PUNCT
ejpam-6680	281	21	v	v	NOUN
ejpam-6680	281	22	)	)	PUNCT
ejpam-6680	281	23	+	+	CCONJ
ejpam-6680	281	24	2ξn⟨	2ξn⟨	NUM
ejpam-6680	281	25	−−−−→	−−−−→	NOUN
ejpam-6680	281	26	ϖ(bn)v	ϖ(bn)v	VERB
ejpam-6680	281	27	,	,	PUNCT
ejpam-6680	281	28	−−−→	−−−→	VERB
ejpam-6680	281	29	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	281	30	(	(	PUNCT
ejpam-6680	281	31	15	15	NUM
ejpam-6680	281	32	)	)	PUNCT
ejpam-6680	281	33	by	by	ADP
ejpam-6680	281	34	cauchy	cauchy	PROPN
ejpam-6680	281	35	schwartz	schwartz	PROPN
ejpam-6680	281	36	inequality	inequality	PROPN
ejpam-6680	281	37	,	,	PUNCT
ejpam-6680	281	38	we	we	PRON
ejpam-6680	281	39	have	have	AUX
ejpam-6680	281	40	⟨	⟨	NOUN
ejpam-6680	281	41	−−−−→	−−−−→	PUNCT
ejpam-6680	281	42	ϖ(bn)v	ϖ(bn)v	NOUN
ejpam-6680	281	43	,	,	PUNCT
ejpam-6680	281	44	−−−→	−−−→	ADJ
ejpam-6680	281	45	bn+1v⟩	bn+1v⟩	X
ejpam-6680	281	46	=	=	PRON
ejpam-6680	281	47	⟨	⟨	VERB
ejpam-6680	281	48	−−−−−−−→	−−−−−−−→	X
ejpam-6680	281	49	ϖ(bn)ϖ(v	ϖ(bn)ϖ(v	PROPN
ejpam-6680	281	50	)	)	PUNCT
ejpam-6680	281	51	,	,	PUNCT
ejpam-6680	281	52	−−−→	−−−→	ADJ
ejpam-6680	281	53	bn+1v⟩+	bn+1v⟩+	PROPN
ejpam-6680	281	54	⟨	⟨	VERB
ejpam-6680	281	55	−−−−→	−−−−→	X
ejpam-6680	281	56	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	281	57	,	,	PUNCT
ejpam-6680	281	58	−−−→	−−−→	ADJ
ejpam-6680	281	59	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	281	60	,	,	PUNCT
ejpam-6680	281	61	≤	≤	NOUN
ejpam-6680	281	62	d(ϖ(bn	d(ϖ(bn	NOUN
ejpam-6680	281	63	)	)	PUNCT
ejpam-6680	281	64	,	,	PUNCT
ejpam-6680	281	65	ϖ(v))d(bn+1	ϖ(v))d(bn+1	PROPN
ejpam-6680	281	66	,	,	PUNCT
ejpam-6680	281	67	v	v	NOUN
ejpam-6680	281	68	)	)	PUNCT
ejpam-6680	282	1	+	+	CCONJ
ejpam-6680	282	2	⟨	⟨	ADJ
ejpam-6680	282	3	−−−−→	−−−−→	X
ejpam-6680	282	4	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	282	5	,	,	PUNCT
ejpam-6680	282	6	−−−→	−−−→	ADJ
ejpam-6680	282	7	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	282	8	,	,	PUNCT
ejpam-6680	282	9	≤	≤	ADJ
ejpam-6680	282	10	ρd(bn	ρd(bn	PROPN
ejpam-6680	282	11	,	,	PUNCT
ejpam-6680	282	12	v)d(bn+1	v)d(bn+1	NOUN
ejpam-6680	282	13	,	,	PUNCT
ejpam-6680	282	14	v	v	NOUN
ejpam-6680	282	15	)	)	PUNCT
ejpam-6680	283	1	+	+	CCONJ
ejpam-6680	283	2	⟨	⟨	ADJ
ejpam-6680	283	3	−−−−→	−−−−→	X
ejpam-6680	283	4	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	283	5	,	,	PUNCT
ejpam-6680	283	6	−−−→	−−−→	ADJ
ejpam-6680	283	7	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	283	8	,	,	PUNCT
ejpam-6680	283	9	≤	≤	NUM
ejpam-6680	283	10	ρ	ρ	NUM
ejpam-6680	283	11	2	2	NUM
ejpam-6680	283	12	[	[	X
ejpam-6680	283	13	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	283	14	,	,	PUNCT
ejpam-6680	283	15	v	v	NOUN
ejpam-6680	283	16	)	)	PUNCT
ejpam-6680	283	17	+	+	CCONJ
ejpam-6680	283	18	ϱ2(bn+1	ϱ2(bn+1	PROPN
ejpam-6680	283	19	,	,	PUNCT
ejpam-6680	283	20	v	v	NOUN
ejpam-6680	283	21	)	)	PUNCT
ejpam-6680	283	22	]	]	PUNCT
ejpam-6680	284	1	+	+	CCONJ
ejpam-6680	284	2	⟨	⟨	X
ejpam-6680	284	3	−−−−→	−−−−→	PUNCT
ejpam-6680	284	4	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	284	5	,	,	PUNCT
ejpam-6680	284	6	−−−→	−−−→	ADJ
ejpam-6680	284	7	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	284	8	,	,	PUNCT
ejpam-6680	284	9	by	by	ADP
ejpam-6680	284	10	putting	put	VERB
ejpam-6680	284	11	above	above	ADV
ejpam-6680	284	12	in	in	ADP
ejpam-6680	284	13	(	(	PUNCT
ejpam-6680	284	14	15	15	NUM
ejpam-6680	284	15	)	)	PUNCT
ejpam-6680	284	16	,	,	PUNCT
ejpam-6680	284	17	we	we	PRON
ejpam-6680	284	18	have	have	VERB
ejpam-6680	284	19	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	284	20	,	,	PUNCT
ejpam-6680	284	21	v	v	NOUN
ejpam-6680	284	22	)	)	PUNCT
ejpam-6680	284	23	≤	≤	NOUN
ejpam-6680	284	24	(	(	PUNCT
ejpam-6680	284	25	1−	1−	NUM
ejpam-6680	284	26	ξn)ϱ	ξn)ϱ	NUM
ejpam-6680	284	27	2(zn	2(zn	NUM
ejpam-6680	284	28	,	,	PUNCT
ejpam-6680	284	29	v	v	NOUN
ejpam-6680	284	30	)	)	PUNCT
ejpam-6680	284	31	+	+	CCONJ
ejpam-6680	284	32	ξnρϱ	ξnρϱ	PROPN
ejpam-6680	284	33	2(bn	2(bn	PROPN
ejpam-6680	284	34	,	,	PUNCT
ejpam-6680	284	35	v	v	NOUN
ejpam-6680	284	36	)	)	PUNCT
ejpam-6680	284	37	+	+	CCONJ
ejpam-6680	284	38	ξnρϱ	ξnρϱ	PROPN
ejpam-6680	284	39	2(bn+1	2(bn+1	NUM
ejpam-6680	284	40	,	,	PUNCT
ejpam-6680	284	41	v	v	NOUN
ejpam-6680	284	42	)	)	PUNCT
ejpam-6680	284	43	+	+	CCONJ
ejpam-6680	284	44	2ξn⟨	2ξn⟨	NUM
ejpam-6680	284	45	−−−−→	−−−−→	SYM
ejpam-6680	284	46	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	284	47	,	,	PUNCT
ejpam-6680	284	48	−−−→	−−−→	ADJ
ejpam-6680	284	49	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	284	50	,	,	PUNCT
ejpam-6680	284	51	ϱ2(bn+1	ϱ2(bn+1	PROPN
ejpam-6680	284	52	,	,	PUNCT
ejpam-6680	284	53	v)−	v)−	PROPN
ejpam-6680	284	54	ξnρϱ	ξnρϱ	PROPN
ejpam-6680	284	55	2(bn+1	2(bn+1	PROPN
ejpam-6680	284	56	,	,	PUNCT
ejpam-6680	284	57	v	v	NOUN
ejpam-6680	284	58	)	)	PUNCT
ejpam-6680	284	59	≤	≤	NOUN
ejpam-6680	284	60	(	(	PUNCT
ejpam-6680	284	61	1−	1−	NUM
ejpam-6680	284	62	ξn	ξn	NOUN
ejpam-6680	284	63	+	+	CCONJ
ejpam-6680	284	64	ξnρ)ϱ	ξnρ)ϱ	PROPN
ejpam-6680	284	65	2(bn	2(bn	PROPN
ejpam-6680	284	66	,	,	PUNCT
ejpam-6680	284	67	v	v	NOUN
ejpam-6680	284	68	)	)	PUNCT
ejpam-6680	284	69	+	+	CCONJ
ejpam-6680	284	70	2ξn⟨	2ξn⟨	NUM
ejpam-6680	284	71	−−−−→	−−−−→	SYM
ejpam-6680	284	72	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	284	73	,	,	PUNCT
ejpam-6680	284	74	−−−→	−−−→	ADJ
ejpam-6680	284	75	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	284	76	(	(	PUNCT
ejpam-6680	284	77	1−	1−	NUM
ejpam-6680	284	78	ξnρ)ϱ	ξnρ)ϱ	NOUN
ejpam-6680	284	79	2(bn+1	2(bn+1	PROPN
ejpam-6680	284	80	,	,	PUNCT
ejpam-6680	284	81	v	v	NOUN
ejpam-6680	284	82	)	)	PUNCT
ejpam-6680	284	83	≤	≤	NOUN
ejpam-6680	284	84	(	(	PUNCT
ejpam-6680	284	85	1−	1−	NUM
ejpam-6680	284	86	(	(	PUNCT
ejpam-6680	284	87	1−	1−	NUM
ejpam-6680	284	88	ρ)ξn)ϱ	ρ)ξn)ϱ	PROPN
ejpam-6680	284	89	2(bn	2(bn	PROPN
ejpam-6680	284	90	,	,	PUNCT
ejpam-6680	284	91	v	v	NOUN
ejpam-6680	284	92	)	)	PUNCT
ejpam-6680	284	93	+	+	CCONJ
ejpam-6680	284	94	2ξn⟨	2ξn⟨	NUM
ejpam-6680	284	95	−−−−→	−−−−→	SYM
ejpam-6680	284	96	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	284	97	,	,	PUNCT
ejpam-6680	284	98	−−−→	−−−→	ADJ
ejpam-6680	284	99	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	284	100	,	,	PUNCT
ejpam-6680	284	101	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	284	102	,	,	PUNCT
ejpam-6680	284	103	v	v	NOUN
ejpam-6680	284	104	)	)	PUNCT
ejpam-6680	284	105	≤	≤	NOUN
ejpam-6680	284	106	(	(	PUNCT
ejpam-6680	284	107	1−	1−	NUM
ejpam-6680	284	108	(	(	PUNCT
ejpam-6680	284	109	1−	1−	NUM
ejpam-6680	284	110	ρ)ξn	ρ)ξn	PROPN
ejpam-6680	284	111	)	)	PUNCT
ejpam-6680	284	112	1−	1−	NUM
ejpam-6680	284	113	ξnρ	ξnρ	NOUN
ejpam-6680	284	114	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	284	115	,	,	PUNCT
ejpam-6680	284	116	v	v	NOUN
ejpam-6680	284	117	)	)	PUNCT
ejpam-6680	284	118	+	+	CCONJ
ejpam-6680	284	119	2ξn	2ξn	ADJ
ejpam-6680	284	120	1−	1−	NUM
ejpam-6680	284	121	ξnρ	ξnρ	NOUN
ejpam-6680	284	122	⟨	⟨	VERB
ejpam-6680	284	123	−−−−→	−−−−→	X
ejpam-6680	284	124	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	284	125	,	,	PUNCT
ejpam-6680	284	126	−−−→	−−−→	VERB
ejpam-6680	284	127	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	284	128	claim	claim	NOUN
ejpam-6680	284	129	5	5	NUM
ejpam-6680	284	130	.	.	PUNCT
ejpam-6680	285	1	the	the	DET
ejpam-6680	285	2	sequence	sequence	NOUN
ejpam-6680	285	3	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	285	4	,	,	PUNCT
ejpam-6680	285	5	v	v	NOUN
ejpam-6680	285	6	)	)	PUNCT
ejpam-6680	285	7	converges	converge	VERB
ejpam-6680	285	8	to	to	ADP
ejpam-6680	285	9	zero	zero	NUM
ejpam-6680	285	10	.	.	PUNCT
ejpam-6680	286	1	there	there	PRON
ejpam-6680	286	2	are	be	VERB
ejpam-6680	286	3	two	two	NUM
ejpam-6680	286	4	scenarios	scenario	NOUN
ejpam-6680	286	5	for	for	ADP
ejpam-6680	286	6	the	the	DET
ejpam-6680	286	7	proof	proof	NOUN
ejpam-6680	286	8	of	of	ADP
ejpam-6680	286	9	convergence	convergence	NOUN
ejpam-6680	286	10	of	of	ADP
ejpam-6680	286	11	sequence	sequence	NOUN
ejpam-6680	286	12	{	{	PUNCT
ejpam-6680	286	13	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	286	14	,	,	PUNCT
ejpam-6680	286	15	v	v	NOUN
ejpam-6680	286	16	)	)	PUNCT
ejpam-6680	286	17	}	}	PUNCT
ejpam-6680	286	18	.	.	PUNCT
ejpam-6680	287	1	case	case	NOUN
ejpam-6680	287	2	1	1	X
ejpam-6680	287	3	.	.	X
ejpam-6680	288	1	there	there	PRON
ejpam-6680	288	2	exist	exist	VERB
ejpam-6680	288	3	a	a	DET
ejpam-6680	288	4	natural	natural	ADJ
ejpam-6680	288	5	number	number	NOUN
ejpam-6680	288	6	n	n	ADP
ejpam-6680	288	7	such	such	ADJ
ejpam-6680	288	8	that	that	DET
ejpam-6680	288	9	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	288	10	,	,	PUNCT
ejpam-6680	288	11	v	v	NOUN
ejpam-6680	288	12	)	)	PUNCT
ejpam-6680	288	13	≤	≤	NUM
ejpam-6680	288	14	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	288	15	,	,	PUNCT
ejpam-6680	288	16	v	v	NOUN
ejpam-6680	288	17	)	)	PUNCT
ejpam-6680	288	18	for	for	ADP
ejpam-6680	288	19	all	all	DET
ejpam-6680	288	20	n	n	DET
ejpam-6680	288	21	≥	≥	NOUN
ejpam-6680	288	22	n.	n.	NOUN
ejpam-6680	288	23	this	this	PRON
ejpam-6680	288	24	implies	imply	VERB
ejpam-6680	288	25	that	that	SCONJ
ejpam-6680	288	26	limn→∞	limn→∞	PROPN
ejpam-6680	288	27	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	288	28	,	,	PUNCT
ejpam-6680	288	29	v	v	NOUN
ejpam-6680	288	30	)	)	PUNCT
ejpam-6680	288	31	exist	exist	VERB
ejpam-6680	288	32	.	.	PUNCT
ejpam-6680	289	1	from	from	ADP
ejpam-6680	289	2	claim	claim	NOUN
ejpam-6680	289	3	2	2	NUM
ejpam-6680	289	4	,	,	PUNCT
ejpam-6680	289	5	we	we	PRON
ejpam-6680	289	6	have	have	VERB
ejpam-6680	289	7	lim	lim	PROPN
ejpam-6680	289	8	n→∞	n→∞	X
ejpam-6680	289	9	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	289	10	,	,	PUNCT
ejpam-6680	289	11	zn	zn	NOUN
ejpam-6680	289	12	)	)	PUNCT
ejpam-6680	289	13	=	=	SYM
ejpam-6680	290	1	0	0	X
ejpam-6680	290	2	.	.	PUNCT
ejpam-6680	290	3	m.	m.	NOUN
ejpam-6680	290	4	rashid	rashid	PROPN
ejpam-6680	290	5	et	et	PROPN
ejpam-6680	290	6	al	al	PROPN
ejpam-6680	290	7	.	.	PUNCT
ejpam-6680	290	8	/	/	SYM
ejpam-6680	290	9	eur	eur	PROPN
ejpam-6680	290	10	.	.	PUNCT
ejpam-6680	291	1	j.	j.	PROPN
ejpam-6680	291	2	pure	pure	PROPN
ejpam-6680	291	3	appl	appl	PROPN
ejpam-6680	291	4	.	.	PROPN
ejpam-6680	291	5	math	math	PROPN
ejpam-6680	291	6	,	,	PUNCT
ejpam-6680	291	7	18	18	NUM
ejpam-6680	291	8	(	(	PUNCT
ejpam-6680	291	9	4	4	NUM
ejpam-6680	291	10	)	)	PUNCT
ejpam-6680	291	11	(	(	PUNCT
ejpam-6680	291	12	2025	2025	NUM
ejpam-6680	291	13	)	)	PUNCT
ejpam-6680	291	14	,	,	PUNCT
ejpam-6680	291	15	6680	6680	NUM
ejpam-6680	291	16	17	17	NUM
ejpam-6680	291	17	of	of	ADP
ejpam-6680	291	18	24	24	NUM
ejpam-6680	291	19	now	now	ADV
ejpam-6680	291	20	,	,	PUNCT
ejpam-6680	291	21	according	accord	VERB
ejpam-6680	291	22	to	to	ADP
ejpam-6680	291	23	claim	claim	NOUN
ejpam-6680	291	24	3	3	NUM
ejpam-6680	291	25	,	,	PUNCT
ejpam-6680	291	26	lim	lim	PROPN
ejpam-6680	291	27	n→∞	n→∞	NUM
ejpam-6680	291	28	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	291	29	,	,	PUNCT
ejpam-6680	291	30	sn	sn	NOUN
ejpam-6680	291	31	)	)	PUNCT
ejpam-6680	291	32	=	=	SYM
ejpam-6680	292	1	0	0	X
ejpam-6680	292	2	.	.	PUNCT
ejpam-6680	293	1	since	since	SCONJ
ejpam-6680	293	2	the	the	DET
ejpam-6680	293	3	sequence	sequence	NOUN
ejpam-6680	293	4	{	{	PUNCT
ejpam-6680	293	5	bn	bn	NUM
ejpam-6680	293	6	}	}	PUNCT
ejpam-6680	293	7	is	be	AUX
ejpam-6680	293	8	bounded	bound	VERB
ejpam-6680	293	9	.	.	PUNCT
ejpam-6680	294	1	it	it	PRON
ejpam-6680	294	2	is	be	AUX
ejpam-6680	294	3	implied	imply	VERB
ejpam-6680	294	4	by	by	ADP
ejpam-6680	294	5	lemma	lemma	PROPN
ejpam-6680	294	6	4	4	NUM
ejpam-6680	294	7	,	,	PUNCT
ejpam-6680	294	8	that	that	SCONJ
ejpam-6680	294	9	every	every	DET
ejpam-6680	294	10	bounded	bounded	ADJ
ejpam-6680	294	11	sequence	sequence	NOUN
ejpam-6680	294	12	in	in	ADP
ejpam-6680	294	13	(	(	PUNCT
ejpam-6680	294	14	z	z	NOUN
ejpam-6680	294	15	,	,	PUNCT
ejpam-6680	294	16	ϱ	ϱ	NOUN
ejpam-6680	294	17	)	)	PUNCT
ejpam-6680	294	18	always	always	ADV
ejpam-6680	294	19	has	have	VERB
ejpam-6680	294	20	a	a	DET
ejpam-6680	294	21	∆-convergent	∆-convergent	ADJ
ejpam-6680	294	22	subsequence	subsequence	NOUN
ejpam-6680	294	23	,	,	PUNCT
ejpam-6680	294	24	say	say	VERB
ejpam-6680	294	25	bnk	bnk	PROPN
ejpam-6680	294	26	∆-converges	∆-converge	VERB
ejpam-6680	294	27	to	to	ADP
ejpam-6680	294	28	z	z	NOUN
ejpam-6680	294	29	such	such	ADJ
ejpam-6680	294	30	that	that	SCONJ
ejpam-6680	294	31	lim	lim	PROPN
ejpam-6680	294	32	n→∞	n→∞	X
ejpam-6680	295	1	sup⟨	sup⟨	ADJ
ejpam-6680	295	2	−−−−→	−−−−→	PUNCT
ejpam-6680	295	3	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	295	4	,	,	PUNCT
ejpam-6680	295	5	−→	−→	NOUN
ejpam-6680	295	6	bnv⟩	bnv⟩	NOUN
ejpam-6680	295	7	=	=	SYM
ejpam-6680	295	8	lim	lim	PROPN
ejpam-6680	295	9	n→∞	n→∞	X
ejpam-6680	295	10	⟨	⟨	VERB
ejpam-6680	295	11	−−−−→	−−−−→	X
ejpam-6680	295	12	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	295	13	,	,	PUNCT
ejpam-6680	295	14	−−→	−−→	PROPN
ejpam-6680	295	15	bnk	bnk	PROPN
ejpam-6680	295	16	v⟩	v⟩	PUNCT
ejpam-6680	296	1	=	=	PUNCT
ejpam-6680	296	2	⟨	⟨	NOUN
ejpam-6680	296	3	−−−−→	−−−−→	X
ejpam-6680	296	4	ϖ(v)v,−→zv⟩.	ϖ(v)v,−→zv⟩.	X
ejpam-6680	296	5	(	(	PUNCT
ejpam-6680	296	6	16	16	NUM
ejpam-6680	296	7	)	)	PUNCT
ejpam-6680	296	8	since	since	SCONJ
ejpam-6680	296	9	bnk	bnk	PROPN
ejpam-6680	296	10	∆-converges	∆-converge	VERB
ejpam-6680	296	11	to	to	ADP
ejpam-6680	296	12	z	z	PROPN
ejpam-6680	296	13	and	and	CCONJ
ejpam-6680	296	14	ϱ(bn	ϱ(bn	PROPN
ejpam-6680	296	15	,	,	PUNCT
ejpam-6680	296	16	sn	sn	PROPN
ejpam-6680	296	17	)	)	PUNCT
ejpam-6680	296	18	=	=	SYM
ejpam-6680	297	1	0	0	NUM
ejpam-6680	297	2	,	,	PUNCT
ejpam-6680	297	3	it	it	PRON
ejpam-6680	297	4	implies	imply	VERB
ejpam-6680	297	5	from	from	ADP
ejpam-6680	297	6	lemma14	lemma14	NOUN
ejpam-6680	297	7	that	that	SCONJ
ejpam-6680	297	8	z	z	PROPN
ejpam-6680	297	9	∈	∈	PROPN
ejpam-6680	297	10	v	v	ADP
ejpam-6680	297	11	i(l	i(l	PROPN
ejpam-6680	297	12	,	,	PUNCT
ejpam-6680	297	13	a	a	PRON
ejpam-6680	297	14	)	)	PUNCT
ejpam-6680	297	15	.	.	PUNCT
ejpam-6680	298	1	on	on	ADP
ejpam-6680	298	2	the	the	DET
ejpam-6680	298	3	other	other	ADJ
ejpam-6680	298	4	hand	hand	NOUN
ejpam-6680	298	5	,	,	PUNCT
ejpam-6680	298	6	ϱ(bn+1	ϱ(bn+1	PROPN
ejpam-6680	298	7	,	,	PUNCT
ejpam-6680	298	8	zn	zn	NOUN
ejpam-6680	298	9	)	)	PUNCT
ejpam-6680	298	10	=	=	SYM
ejpam-6680	298	11	ϱ(ξnϖ(bn)⊕	ϱ(ξnϖ(bn)⊕	PROPN
ejpam-6680	298	12	(	(	PUNCT
ejpam-6680	298	13	1−	1−	NUM
ejpam-6680	298	14	ξn)zn	ξn)zn	NOUN
ejpam-6680	298	15	,	,	PUNCT
ejpam-6680	298	16	zn	zn	NOUN
ejpam-6680	298	17	)	)	PUNCT
ejpam-6680	298	18	≤	≤	NOUN
ejpam-6680	298	19	ξnϱ(ϖ(bn	ξnϱ(ϖ(bn	NOUN
ejpam-6680	298	20	)	)	PUNCT
ejpam-6680	298	21	,	,	PUNCT
ejpam-6680	298	22	zn	zn	X
ejpam-6680	298	23	)	)	PUNCT
ejpam-6680	299	1	+	+	CCONJ
ejpam-6680	299	2	(	(	PUNCT
ejpam-6680	299	3	1−	1−	NUM
ejpam-6680	299	4	ξn)ϱ(zn	ξn)ϱ(zn	PROPN
ejpam-6680	299	5	,	,	PUNCT
ejpam-6680	299	6	zn	zn	PROPN
ejpam-6680	299	7	)	)	PUNCT
ejpam-6680	299	8	=	=	PUNCT
ejpam-6680	299	9	ξnϱ(ϖ(bn	ξnϱ(ϖ(bn	NOUN
ejpam-6680	299	10	)	)	PUNCT
ejpam-6680	299	11	,	,	PUNCT
ejpam-6680	299	12	zn	zn	X
ejpam-6680	299	13	)	)	PUNCT
ejpam-6680	299	14	→	→	SYM
ejpam-6680	299	15	0	0	NUM
ejpam-6680	299	16	as	as	ADP
ejpam-6680	299	17	n→	n→	PROPN
ejpam-6680	299	18	∞.	∞.	PROPN
ejpam-6680	299	19	thus	thus	ADV
ejpam-6680	299	20	,	,	PUNCT
ejpam-6680	299	21	ϱ(bn+1	ϱ(bn+1	PROPN
ejpam-6680	299	22	,	,	PUNCT
ejpam-6680	299	23	bn	bn	NOUN
ejpam-6680	299	24	)	)	PUNCT
ejpam-6680	299	25	≤	≤	NOUN
ejpam-6680	299	26	ϱ(bn+1	ϱ(bn+1	PROPN
ejpam-6680	299	27	,	,	PUNCT
ejpam-6680	299	28	zn	zn	X
ejpam-6680	299	29	)	)	PUNCT
ejpam-6680	300	1	+	+	CCONJ
ejpam-6680	300	2	ϱ(zn	ϱ(zn	PROPN
ejpam-6680	300	3	,	,	PUNCT
ejpam-6680	300	4	bn	bn	NOUN
ejpam-6680	300	5	)	)	PUNCT
ejpam-6680	300	6	→	→	SYM
ejpam-6680	300	7	0	0	NUM
ejpam-6680	300	8	as	as	ADP
ejpam-6680	300	9	n→	n→	PUNCT
ejpam-6680	300	10	∞.	∞.	PROPN
ejpam-6680	300	11	since	since	SCONJ
ejpam-6680	300	12	v	v	NOUN
ejpam-6680	300	13	=	=	SYM
ejpam-6680	300	14	pv	pv	NOUN
ejpam-6680	300	15	i(l	i(l	PROPN
ejpam-6680	300	16	,	,	PUNCT
ejpam-6680	300	17	a)ϖ(v	a)ϖ(v	NOUN
ejpam-6680	300	18	)	)	PUNCT
ejpam-6680	300	19	and	and	CCONJ
ejpam-6680	300	20	bnk	bnk	PROPN
ejpam-6680	300	21	∆-converges	∆-converge	VERB
ejpam-6680	300	22	to	to	ADP
ejpam-6680	300	23	z	z	PROPN
ejpam-6680	300	24	∈	∈	PROPN
ejpam-6680	300	25	v	v	ADP
ejpam-6680	300	26	i(l	i(l	PROPN
ejpam-6680	300	27	,	,	PUNCT
ejpam-6680	300	28	a	a	PRON
ejpam-6680	300	29	)	)	PUNCT
ejpam-6680	300	30	,	,	PUNCT
ejpam-6680	300	31	using	use	VERB
ejpam-6680	300	32	(	(	PUNCT
ejpam-6680	300	33	16	16	NUM
ejpam-6680	300	34	)	)	PUNCT
ejpam-6680	300	35	,	,	PUNCT
ejpam-6680	300	36	we	we	PRON
ejpam-6680	300	37	get	get	VERB
ejpam-6680	300	38	lim	lim	PROPN
ejpam-6680	300	39	n→∞	n→∞	X
ejpam-6680	301	1	sup⟨	sup⟨	ADJ
ejpam-6680	301	2	−−−−→	−−−−→	PUNCT
ejpam-6680	301	3	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	301	4	,	,	PUNCT
ejpam-6680	301	5	−→	−→	NOUN
ejpam-6680	301	6	bnv⟩	bnv⟩	NOUN
ejpam-6680	301	7	=	=	PUNCT
ejpam-6680	301	8	⟨	⟨	VERB
ejpam-6680	301	9	−−−−→	−−−−→	X
ejpam-6680	301	10	ϖ(v)v,−→zv⟩	ϖ(v)v,−→zv⟩	NOUN
ejpam-6680	301	11	≤	≤	ADV
ejpam-6680	301	12	0	0	X
ejpam-6680	301	13	.	.	PUNCT
ejpam-6680	302	1	this	this	PRON
ejpam-6680	302	2	implies	imply	VERB
ejpam-6680	302	3	that	that	SCONJ
ejpam-6680	302	4	lim	lim	PROPN
ejpam-6680	302	5	n→∞	n→∞	X
ejpam-6680	302	6	sup⟨	sup⟨	ADJ
ejpam-6680	302	7	−−−−→	−−−−→	PUNCT
ejpam-6680	302	8	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	302	9	,	,	PUNCT
ejpam-6680	302	10	−−−→	−−−→	NUM
ejpam-6680	302	11	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	302	12	≤	≤	ADJ
ejpam-6680	302	13	lim	lim	PROPN
ejpam-6680	302	14	n→∞	n→∞	X
ejpam-6680	303	1	sup⟨	sup⟨	ADJ
ejpam-6680	303	2	−−−−→	−−−−→	PUNCT
ejpam-6680	303	3	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	303	4	,	,	PUNCT
ejpam-6680	303	5	−−−−→	−−−−→	X
ejpam-6680	303	6	bn+1bn⟩+	bn+1bn⟩+	PROPN
ejpam-6680	303	7	lim	lim	PROPN
ejpam-6680	303	8	n→∞	n→∞	X
ejpam-6680	304	1	sup⟨	sup⟨	ADJ
ejpam-6680	304	2	−−−−→	−−−−→	PUNCT
ejpam-6680	304	3	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	304	4	,	,	PUNCT
ejpam-6680	304	5	−→	−→	NOUN
ejpam-6680	304	6	bnv⟩	bnv⟩	NOUN
ejpam-6680	304	7	≤	≤	ADJ
ejpam-6680	304	8	0	0	NUM
ejpam-6680	304	9	.	.	PUNCT
ejpam-6680	305	1	from	from	ADP
ejpam-6680	305	2	claim	claim	NOUN
ejpam-6680	305	3	4	4	NUM
ejpam-6680	305	4	ϱ2(bn+1	ϱ2(bn+1	NOUN
ejpam-6680	305	5	,	,	PUNCT
ejpam-6680	305	6	v	v	NOUN
ejpam-6680	305	7	)	)	PUNCT
ejpam-6680	305	8	≤	≤	NOUN
ejpam-6680	305	9	1−	1−	NUM
ejpam-6680	305	10	(	(	PUNCT
ejpam-6680	305	11	ξn	ξn	PROPN
ejpam-6680	305	12	−	−	PROPN
ejpam-6680	305	13	2ξnρ	2ξnρ	NUM
ejpam-6680	305	14	)	)	PUNCT
ejpam-6680	305	15	1−	1−	NUM
ejpam-6680	305	16	ξnρ	ξnρ	NOUN
ejpam-6680	305	17	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	305	18	,	,	PUNCT
ejpam-6680	305	19	v	v	NOUN
ejpam-6680	305	20	)	)	PUNCT
ejpam-6680	305	21	+	+	CCONJ
ejpam-6680	305	22	2ξn	2ξn	ADJ
ejpam-6680	305	23	1−	1−	NUM
ejpam-6680	305	24	ξnρ	ξnρ	NOUN
ejpam-6680	305	25	⟨	⟨	VERB
ejpam-6680	305	26	−−−−→	−−−−→	X
ejpam-6680	305	27	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	305	28	,	,	PUNCT
ejpam-6680	306	1	−−−→	−−−→	ADJ
ejpam-6680	306	2	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	306	3	=	=	SYM
ejpam-6680	306	4	1−	1−	NUM
ejpam-6680	306	5	(	(	PUNCT
ejpam-6680	306	6	1−	1−	NUM
ejpam-6680	306	7	2ρ)ξn	2ρ)ξn	NUM
ejpam-6680	306	8	1−	1−	NUM
ejpam-6680	306	9	ξnρ	ξnρ	NOUN
ejpam-6680	306	10	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	306	11	,	,	PUNCT
ejpam-6680	306	12	v	v	NOUN
ejpam-6680	306	13	)	)	PUNCT
ejpam-6680	306	14	+	+	CCONJ
ejpam-6680	306	15	2	2	NUM
ejpam-6680	306	16	(	(	PUNCT
ejpam-6680	306	17	1−	1−	NUM
ejpam-6680	306	18	2ρ)ξn	2ρ)ξn	NUM
ejpam-6680	306	19	(	(	PUNCT
ejpam-6680	306	20	1−	1−	NUM
ejpam-6680	306	21	ξnρ)(1−	ξnρ)(1−	NOUN
ejpam-6680	306	22	2ρ	2ρ	NOUN
ejpam-6680	306	23	)	)	PUNCT
ejpam-6680	306	24	⟨	⟨	VERB
ejpam-6680	306	25	−−−−→	−−−−→	X
ejpam-6680	306	26	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	306	27	,	,	PUNCT
ejpam-6680	306	28	−−−→	−−−→	VERB
ejpam-6680	306	29	bn+1v⟩.	bn+1v⟩.	NOUN
ejpam-6680	306	30	now	now	ADV
ejpam-6680	306	31	,	,	PUNCT
ejpam-6680	306	32	taking	take	VERB
ejpam-6680	306	33	λn	λn	X
ejpam-6680	306	34	=	=	PUNCT
ejpam-6680	306	35	(	(	PUNCT
ejpam-6680	306	36	1−	1−	NUM
ejpam-6680	306	37	2ρ)ξn	2ρ)ξn	NUM
ejpam-6680	306	38	1−	1−	NUM
ejpam-6680	306	39	ξnρ	ξnρ	NOUN
ejpam-6680	306	40	,	,	PUNCT
ejpam-6680	306	41	ℑn	ℑn	PROPN
ejpam-6680	306	42	=	=	PUNCT
ejpam-6680	306	43	2⟨	2⟨	NUM
ejpam-6680	306	44	−−−−→	−−−−→	X
ejpam-6680	306	45	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	306	46	,	,	PUNCT
ejpam-6680	306	47	−−−→	−−−→	ADJ
ejpam-6680	306	48	bn+1v⟩	bn+1v⟩	PROPN
ejpam-6680	306	49	1−	1−	NUM
ejpam-6680	306	50	2ρ	2ρ	NOUN
ejpam-6680	306	51	,	,	PUNCT
ejpam-6680	306	52	by	by	ADP
ejpam-6680	306	53	lemma	lemma	PROPN
ejpam-6680	306	54	5	5	NUM
ejpam-6680	306	55	,	,	PUNCT
ejpam-6680	306	56	we	we	PRON
ejpam-6680	306	57	can	can	AUX
ejpam-6680	306	58	conclude	conclude	VERB
ejpam-6680	306	59	that	that	PRON
ejpam-6680	306	60	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	306	61	,	,	PUNCT
ejpam-6680	306	62	v	v	NOUN
ejpam-6680	306	63	)	)	PUNCT
ejpam-6680	306	64	=	=	SYM
ejpam-6680	307	1	0	0	X
ejpam-6680	307	2	.	.	PUNCT
ejpam-6680	307	3	⇒	⇒	PROPN
ejpam-6680	307	4	bn	bn	INTJ
ejpam-6680	307	5	→	→	SYM
ejpam-6680	307	6	v	v	NOUN
ejpam-6680	307	7	as	as	ADP
ejpam-6680	307	8	n→	n→	PUNCT
ejpam-6680	307	9	∞.	∞.	PROPN
ejpam-6680	307	10	case	case	NOUN
ejpam-6680	307	11	2	2	X
ejpam-6680	307	12	.	.	X
ejpam-6680	307	13	there	there	PRON
ejpam-6680	307	14	exist	exist	VERB
ejpam-6680	307	15	a	a	DET
ejpam-6680	307	16	subsequence	subsequence	NOUN
ejpam-6680	307	17	{	{	PUNCT
ejpam-6680	307	18	ϱ2(bnj	ϱ2(bnj	PROPN
ejpam-6680	307	19	,	,	PUNCT
ejpam-6680	307	20	v	v	NOUN
ejpam-6680	307	21	)	)	PUNCT
ejpam-6680	307	22	}	}	PUNCT
ejpam-6680	307	23	of	of	ADP
ejpam-6680	307	24	{	{	PUNCT
ejpam-6680	307	25	ϱ2(bn	ϱ2(bn	PROPN
ejpam-6680	307	26	,	,	PUNCT
ejpam-6680	307	27	v	v	NOUN
ejpam-6680	307	28	)	)	PUNCT
ejpam-6680	307	29	}	}	PUNCT
ejpam-6680	307	30	such	such	ADJ
ejpam-6680	307	31	that	that	SCONJ
ejpam-6680	307	32	ϱ2(bnj	ϱ2(bnj	PROPN
ejpam-6680	307	33	,	,	PUNCT
ejpam-6680	307	34	v	v	NOUN
ejpam-6680	307	35	)	)	PUNCT
ejpam-6680	307	36	<	<	X
ejpam-6680	307	37	ϱ2(bnj+1	ϱ2(bnj+1	X
ejpam-6680	307	38	,	,	PUNCT
ejpam-6680	307	39	v	v	NOUN
ejpam-6680	307	40	)	)	PUNCT
ejpam-6680	307	41	,	,	PUNCT
ejpam-6680	307	42	for	for	ADP
ejpam-6680	307	43	all	all	DET
ejpam-6680	307	44	j	j	PROPN
ejpam-6680	307	45	∈	∈	PROPN
ejpam-6680	307	46	n.	n.	NOUN
ejpam-6680	307	47	in	in	ADP
ejpam-6680	307	48	this	this	DET
ejpam-6680	307	49	case	case	NOUN
ejpam-6680	307	50	,	,	PUNCT
ejpam-6680	307	51	from	from	ADP
ejpam-6680	307	52	lemma	lemma	PROPN
ejpam-6680	307	53	8	8	NUM
ejpam-6680	307	54	that	that	SCONJ
ejpam-6680	307	55	there	there	PRON
ejpam-6680	307	56	exist	exist	VERB
ejpam-6680	307	57	a	a	DET
ejpam-6680	307	58	nondecreasing	nondecrease	VERB
ejpam-6680	307	59	sequence	sequence	NOUN
ejpam-6680	307	60	of	of	ADP
ejpam-6680	307	61	natural	natural	ADJ
ejpam-6680	307	62	numbers	number	NOUN
ejpam-6680	307	63	{	{	PUNCT
ejpam-6680	307	64	ak	ak	PROPN
ejpam-6680	307	65	}	}	PUNCT
ejpam-6680	307	66	such	such	ADJ
ejpam-6680	307	67	that	that	SCONJ
ejpam-6680	307	68	lim	lim	PROPN
ejpam-6680	307	69	k→∞	k→∞	PROPN
ejpam-6680	307	70	ak	ak	PROPN
ejpam-6680	307	71	=	=	SYM
ejpam-6680	307	72	∞	∞	PROPN
ejpam-6680	307	73	,	,	PUNCT
ejpam-6680	307	74	and	and	CCONJ
ejpam-6680	307	75	the	the	DET
ejpam-6680	307	76	inequalities	inequality	NOUN
ejpam-6680	307	77	stated	state	VERB
ejpam-6680	307	78	below	below	ADP
ejpam-6680	307	79	holds	hold	VERB
ejpam-6680	307	80	for	for	ADP
ejpam-6680	307	81	all	all	DET
ejpam-6680	307	82	values	value	NOUN
ejpam-6680	307	83	of	of	ADP
ejpam-6680	307	84	k	k	PROPN
ejpam-6680	307	85	∈	∈	PROPN
ejpam-6680	307	86	n	n	CCONJ
ejpam-6680	307	87	:	:	PUNCT
ejpam-6680	308	1	m.	m.	NOUN
ejpam-6680	308	2	rashid	rashid	PROPN
ejpam-6680	308	3	et	et	PROPN
ejpam-6680	308	4	al	al	PROPN
ejpam-6680	308	5	.	.	PUNCT
ejpam-6680	308	6	/	/	SYM
ejpam-6680	308	7	eur	eur	PROPN
ejpam-6680	308	8	.	.	PUNCT
ejpam-6680	309	1	j.	j.	PROPN
ejpam-6680	309	2	pure	pure	PROPN
ejpam-6680	309	3	appl	appl	PROPN
ejpam-6680	309	4	.	.	PROPN
ejpam-6680	309	5	math	math	PROPN
ejpam-6680	309	6	,	,	PUNCT
ejpam-6680	309	7	18	18	NUM
ejpam-6680	309	8	(	(	PUNCT
ejpam-6680	309	9	4	4	NUM
ejpam-6680	309	10	)	)	PUNCT
ejpam-6680	309	11	(	(	PUNCT
ejpam-6680	309	12	2025	2025	NUM
ejpam-6680	309	13	)	)	PUNCT
ejpam-6680	309	14	,	,	PUNCT
ejpam-6680	309	15	6680	6680	NUM
ejpam-6680	309	16	18	18	NUM
ejpam-6680	309	17	of	of	ADP
ejpam-6680	309	18	24	24	NUM
ejpam-6680	309	19	(	(	PUNCT
ejpam-6680	309	20	i	i	NOUN
ejpam-6680	309	21	)	)	PUNCT
ejpam-6680	309	22	ϱ2(bak	ϱ2(bak	NOUN
ejpam-6680	309	23	,	,	PUNCT
ejpam-6680	309	24	v	v	NOUN
ejpam-6680	309	25	)	)	PUNCT
ejpam-6680	309	26	≤	≤	NOUN
ejpam-6680	309	27	ϱ2(bak+1	ϱ2(bak+1	NOUN
ejpam-6680	309	28	,	,	PUNCT
ejpam-6680	309	29	v	v	NOUN
ejpam-6680	309	30	)	)	PUNCT
ejpam-6680	309	31	,	,	PUNCT
ejpam-6680	309	32	(	(	PUNCT
ejpam-6680	309	33	ii	ii	NOUN
ejpam-6680	309	34	)	)	PUNCT
ejpam-6680	309	35	ϱ2(bk	ϱ2(bk	PROPN
ejpam-6680	309	36	,	,	PUNCT
ejpam-6680	309	37	v	v	NOUN
ejpam-6680	309	38	)	)	PUNCT
ejpam-6680	309	39	≤	≤	NOUN
ejpam-6680	309	40	ϱ2(bak+1	ϱ2(bak+1	NOUN
ejpam-6680	309	41	,	,	PUNCT
ejpam-6680	309	42	v	v	NOUN
ejpam-6680	309	43	)	)	PUNCT
ejpam-6680	309	44	.	.	PUNCT
ejpam-6680	310	1	according	accord	VERB
ejpam-6680	310	2	to	to	ADP
ejpam-6680	310	3	claim	claim	NOUN
ejpam-6680	310	4	2	2	NUM
ejpam-6680	310	5	,	,	PUNCT
ejpam-6680	310	6	we	we	PRON
ejpam-6680	310	7	have	have	VERB
ejpam-6680	310	8	ϱ2(zak	ϱ2(zak	NOUN
ejpam-6680	310	9	,	,	PUNCT
ejpam-6680	310	10	bak	bak	NOUN
ejpam-6680	310	11	)	)	PUNCT
ejpam-6680	310	12	≤	≤	NOUN
ejpam-6680	310	13	ϱ2(bak	ϱ2(bak	NOUN
ejpam-6680	310	14	,	,	PUNCT
ejpam-6680	310	15	v)−	v)−	PROPN
ejpam-6680	310	16	ϱ2(bak+1	ϱ2(bak+1	NOUN
ejpam-6680	310	17	,	,	PUNCT
ejpam-6680	310	18	v	v	NOUN
ejpam-6680	310	19	)	)	PUNCT
ejpam-6680	310	20	+	+	NUM
ejpam-6680	310	21	2ξak⟨	2ξak⟨	NUM
ejpam-6680	310	22	−−−−−→	−−−−−→	X
ejpam-6680	310	23	ϖ(bak)v	ϖ(bak)v	NOUN
ejpam-6680	310	24	,	,	PUNCT
ejpam-6680	310	25	−−−−→	−−−−→	PRON
ejpam-6680	310	26	bak+1	bak+1	VERB
ejpam-6680	310	27	v⟩	v⟩	NOUN
ejpam-6680	310	28	,	,	PUNCT
ejpam-6680	310	29	≤	≤	NUM
ejpam-6680	310	30	ϱ2(bak+1	ϱ2(bak+1	X
ejpam-6680	310	31	,	,	PUNCT
ejpam-6680	310	32	v)−	v)−	PROPN
ejpam-6680	310	33	ϱ2(bak+1	ϱ2(bak+1	X
ejpam-6680	310	34	,	,	PUNCT
ejpam-6680	310	35	v	v	NOUN
ejpam-6680	310	36	)	)	PUNCT
ejpam-6680	310	37	+	+	NUM
ejpam-6680	310	38	2ξak⟨	2ξak⟨	NUM
ejpam-6680	310	39	−−−−−→	−−−−−→	X
ejpam-6680	310	40	ϖ(bak)v	ϖ(bak)v	NOUN
ejpam-6680	310	41	,	,	PUNCT
ejpam-6680	310	42	−−−−→	−−−−→	PRON
ejpam-6680	310	43	bak+1	bak+1	VERB
ejpam-6680	310	44	v⟩	v⟩	NOUN
ejpam-6680	310	45	,	,	PUNCT
ejpam-6680	310	46	≤	≤	NUM
ejpam-6680	310	47	ξak⟨	ξak⟨	NOUN
ejpam-6680	310	48	−−−−−→	−−−−−→	X
ejpam-6680	310	49	ϖ(bak)v	ϖ(bak)v	NOUN
ejpam-6680	310	50	,	,	PUNCT
ejpam-6680	310	51	−−−−→	−−−−→	PRON
ejpam-6680	310	52	bak+1	bak+1	VERB
ejpam-6680	310	53	v⟩	v⟩	NOUN
ejpam-6680	310	54	,	,	PUNCT
ejpam-6680	310	55	≤	≤	NOUN
ejpam-6680	310	56	ξakϱ(ϖ(bak	ξakϱ(ϖ(bak	NOUN
ejpam-6680	310	57	)	)	PUNCT
ejpam-6680	310	58	,	,	PUNCT
ejpam-6680	310	59	v)ϱ(bak+1	v)ϱ(bak+1	NOUN
ejpam-6680	310	60	,	,	PUNCT
ejpam-6680	310	61	v	v	NOUN
ejpam-6680	310	62	)	)	PUNCT
ejpam-6680	310	63	→	→	SYM
ejpam-6680	310	64	0	0	PUNCT
ejpam-6680	310	65	as	as	ADP
ejpam-6680	310	66	k	k	PROPN
ejpam-6680	310	67	→	→	SYM
ejpam-6680	310	68	∞.	∞.	PROPN
ejpam-6680	310	69	according	accord	VERB
ejpam-6680	310	70	to	to	ADP
ejpam-6680	310	71	claim	claim	NOUN
ejpam-6680	310	72	3	3	NUM
ejpam-6680	310	73	,	,	PUNCT
ejpam-6680	310	74	we	we	PRON
ejpam-6680	310	75	have	have	VERB
ejpam-6680	310	76	(	(	PUNCT
ejpam-6680	310	77	1−	1−	NUM
ejpam-6680	310	78	ξak	ξak	NOUN
ejpam-6680	310	79	)	)	PUNCT
ejpam-6680	310	80	[	[	PUNCT
ejpam-6680	310	81	1	1	NUM
ejpam-6680	310	82	m	m	NOUN
ejpam-6680	310	83	ξn(−1−	ξn(−1−	PROPN
ejpam-6680	310	84	µ)ϱ2(bak	µ)ϱ2(bak	NOUN
ejpam-6680	310	85	,	,	PUNCT
ejpam-6680	310	86	sak	sak	PROPN
ejpam-6680	310	87	)	)	PUNCT
ejpam-6680	310	88	]	]	PUNCT
ejpam-6680	310	89	2	2	NUM
ejpam-6680	310	90	≤	≤	NUM
ejpam-6680	310	91	ϱ2(bak	ϱ2(bak	NOUN
ejpam-6680	310	92	,	,	PUNCT
ejpam-6680	310	93	v)−	v)−	PROPN
ejpam-6680	310	94	ϱ2(bak+1	ϱ2(bak+1	NOUN
ejpam-6680	310	95	,	,	PUNCT
ejpam-6680	310	96	v	v	NOUN
ejpam-6680	310	97	)	)	PUNCT
ejpam-6680	310	98	+	+	CCONJ
ejpam-6680	310	99	ξakϱ	ξakϱ	PROPN
ejpam-6680	310	100	2(ϖ(bak	2(ϖ(bak	NUM
ejpam-6680	310	101	)	)	PUNCT
ejpam-6680	310	102	,	,	PUNCT
ejpam-6680	310	103	v	v	NOUN
ejpam-6680	310	104	)	)	PUNCT
ejpam-6680	310	105	,	,	PUNCT
ejpam-6680	310	106	≤	≤	NUM
ejpam-6680	310	107	ϱ2(bak+1	ϱ2(bak+1	X
ejpam-6680	310	108	,	,	PUNCT
ejpam-6680	310	109	v)−	v)−	PROPN
ejpam-6680	310	110	ϱ2(bak+1	ϱ2(bak+1	X
ejpam-6680	310	111	,	,	PUNCT
ejpam-6680	310	112	v	v	NOUN
ejpam-6680	310	113	)	)	PUNCT
ejpam-6680	310	114	+	+	CCONJ
ejpam-6680	310	115	ξakd	ξakd	NOUN
ejpam-6680	310	116	2(ϖ(bak	2(ϖ(bak	NOUN
ejpam-6680	310	117	)	)	PUNCT
ejpam-6680	310	118	,	,	PUNCT
ejpam-6680	310	119	v	v	NOUN
ejpam-6680	310	120	)	)	PUNCT
ejpam-6680	310	121	,	,	PUNCT
ejpam-6680	310	122	≤	≤	ADJ
ejpam-6680	310	123	ξakϱ	ξakϱ	PROPN
ejpam-6680	310	124	2(ϖ(bak	2(ϖ(bak	NUM
ejpam-6680	310	125	)	)	PUNCT
ejpam-6680	310	126	,	,	PUNCT
ejpam-6680	310	127	v	v	NOUN
ejpam-6680	310	128	)	)	PUNCT
ejpam-6680	310	129	→	→	SYM
ejpam-6680	310	130	0	0	PUNCT
ejpam-6680	310	131	as	as	SCONJ
ejpam-6680	310	132	k	k	PROPN
ejpam-6680	310	133	→	→	SYM
ejpam-6680	310	134	∞.	∞.	PROPN
ejpam-6680	310	135	using	use	VERB
ejpam-6680	310	136	the	the	DET
ejpam-6680	310	137	same	same	ADJ
ejpam-6680	310	138	argument	argument	NOUN
ejpam-6680	310	139	as	as	ADP
ejpam-6680	310	140	in	in	ADP
ejpam-6680	310	141	the	the	DET
ejpam-6680	310	142	proof	proof	NOUN
ejpam-6680	310	143	of	of	ADP
ejpam-6680	310	144	case	case	NOUN
ejpam-6680	310	145	1	1	NUM
ejpam-6680	310	146	,	,	PUNCT
ejpam-6680	310	147	we	we	PRON
ejpam-6680	310	148	obtain	obtain	VERB
ejpam-6680	310	149	ϱ(bak+1	ϱ(bak+1	X
ejpam-6680	310	150	,	,	PUNCT
ejpam-6680	310	151	bak	bak	NOUN
ejpam-6680	310	152	)	)	PUNCT
ejpam-6680	310	153	→	→	SYM
ejpam-6680	310	154	0	0	NUM
ejpam-6680	311	1	and	and	CCONJ
ejpam-6680	311	2	lim	lim	PROPN
ejpam-6680	311	3	sup	sup	PROPN
ejpam-6680	311	4	k→∞	k→∞	NOUN
ejpam-6680	311	5	⟨	⟨	VERB
ejpam-6680	311	6	−−−−→	−−−−→	X
ejpam-6680	311	7	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	311	8	,	,	PUNCT
ejpam-6680	311	9	−−−→	−−−→	VERB
ejpam-6680	311	10	ba+1v⟩	ba+1v⟩	NOUN
ejpam-6680	311	11	≤	≤	NOUN
ejpam-6680	311	12	0	0	NUM
ejpam-6680	311	13	.	.	PUNCT
ejpam-6680	312	1	from	from	ADP
ejpam-6680	312	2	claim	claim	NOUN
ejpam-6680	312	3	4	4	NUM
ejpam-6680	312	4	ϱ2(bmk+1	ϱ2(bmk+1	ADJ
ejpam-6680	312	5	,	,	PUNCT
ejpam-6680	312	6	v	v	NOUN
ejpam-6680	312	7	)	)	PUNCT
ejpam-6680	312	8	≤	≤	NOUN
ejpam-6680	312	9	(	(	PUNCT
ejpam-6680	312	10	1−	1−	NUM
ejpam-6680	312	11	(	(	PUNCT
ejpam-6680	312	12	1−	1−	NUM
ejpam-6680	312	13	ρ)ξmk	ρ)ξmk	NOUN
ejpam-6680	312	14	)	)	PUNCT
ejpam-6680	312	15	(	(	PUNCT
ejpam-6680	312	16	1−	1−	NUM
ejpam-6680	312	17	ξmk	ξmk	NUM
ejpam-6680	312	18	ρ	ρ	NUM
ejpam-6680	312	19	)	)	PUNCT
ejpam-6680	312	20	ϱ2(bmk	ϱ2(bmk	PROPN
ejpam-6680	312	21	,	,	PUNCT
ejpam-6680	312	22	v	v	NOUN
ejpam-6680	312	23	)	)	PUNCT
ejpam-6680	312	24	+	+	NOUN
ejpam-6680	312	25	2ξmk	2ξmk	NUM
ejpam-6680	312	26	1−	1−	NUM
ejpam-6680	312	27	ξmk	ξmk	NOUN
ejpam-6680	312	28	ρ	ρ	NOUN
ejpam-6680	312	29	⟨	⟨	VERB
ejpam-6680	312	30	−−−−→	−−−−→	X
ejpam-6680	312	31	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	312	32	,	,	PUNCT
ejpam-6680	312	33	−−−−→	−−−−→	PRON
ejpam-6680	312	34	bmk+1	bmk+1	VERB
ejpam-6680	312	35	v⟩	v⟩	ADV
ejpam-6680	312	36	,	,	PUNCT
ejpam-6680	312	37	since	since	SCONJ
ejpam-6680	312	38	ϱ2(bk	ϱ2(bk	PROPN
ejpam-6680	312	39	,	,	PUNCT
ejpam-6680	312	40	v	v	NOUN
ejpam-6680	312	41	)	)	PUNCT
ejpam-6680	312	42	≤	≤	NOUN
ejpam-6680	312	43	ϱ2(bmk+1	ϱ2(bmk+1	VERB
ejpam-6680	312	44	,	,	PUNCT
ejpam-6680	312	45	v	v	NOUN
ejpam-6680	312	46	)	)	PUNCT
ejpam-6680	312	47	,	,	PUNCT
ejpam-6680	312	48	we	we	PRON
ejpam-6680	312	49	have	have	AUX
ejpam-6680	312	50	ϱ2(bmk+1	ϱ2(bmk+1	VERB
ejpam-6680	312	51	,	,	PUNCT
ejpam-6680	312	52	v	v	NOUN
ejpam-6680	312	53	)	)	PUNCT
ejpam-6680	312	54	≤	≤	NOUN
ejpam-6680	312	55	(	(	PUNCT
ejpam-6680	312	56	1−	1−	NUM
ejpam-6680	312	57	(	(	PUNCT
ejpam-6680	312	58	1−	1−	NUM
ejpam-6680	312	59	ρ)ξmk	ρ)ξmk	NOUN
ejpam-6680	312	60	)	)	PUNCT
ejpam-6680	313	1	1−	1−	NUM
ejpam-6680	313	2	ξmk	ξmk	NOUN
ejpam-6680	313	3	ρ	ρ	PROPN
ejpam-6680	313	4	ϱ2(bmk+1	ϱ2(bmk+1	PROPN
ejpam-6680	313	5	,	,	PUNCT
ejpam-6680	313	6	v	v	NOUN
ejpam-6680	313	7	)	)	PUNCT
ejpam-6680	313	8	+	+	NOUN
ejpam-6680	314	1	2ξmk	2ξmk	NUM
ejpam-6680	314	2	1−	1−	NUM
ejpam-6680	314	3	ξmk	ξmk	NOUN
ejpam-6680	314	4	ρ	ρ	NOUN
ejpam-6680	314	5	⟨	⟨	VERB
ejpam-6680	314	6	−−−−→	−−−−→	X
ejpam-6680	314	7	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	314	8	,	,	PUNCT
ejpam-6680	314	9	−−−−→	−−−−→	PRON
ejpam-6680	314	10	bmk+1	bmk+1	VERB
ejpam-6680	314	11	v⟩	v⟩	ADJ
ejpam-6680	314	12	,	,	PUNCT
ejpam-6680	314	13	ξmk	ξmk	PROPN
ejpam-6680	314	14	(	(	PUNCT
ejpam-6680	314	15	1−	1−	NUM
ejpam-6680	314	16	2ρ)ϱ2(bmk+1	2ρ)ϱ2(bmk+1	NUM
ejpam-6680	314	17	,	,	PUNCT
ejpam-6680	314	18	v	v	NOUN
ejpam-6680	314	19	)	)	PUNCT
ejpam-6680	314	20	≤	≤	NOUN
ejpam-6680	314	21	2ξmk	2ξmk	NUM
ejpam-6680	314	22	⟨	⟨	NOUN
ejpam-6680	314	23	−−−−→	−−−−→	X
ejpam-6680	314	24	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	314	25	,	,	PUNCT
ejpam-6680	314	26	−−−−→	−−−−→	PRON
ejpam-6680	314	27	bmk+1	bmk+1	VERB
ejpam-6680	314	28	v⟩	v⟩	ADV
ejpam-6680	314	29	,	,	PUNCT
ejpam-6680	314	30	ϱ2(bk	ϱ2(bk	PROPN
ejpam-6680	314	31	,	,	PUNCT
ejpam-6680	314	32	v	v	NOUN
ejpam-6680	314	33	)	)	PUNCT
ejpam-6680	314	34	≤	≤	NUM
ejpam-6680	314	35	2	2	NUM
ejpam-6680	314	36	1−	1−	NUM
ejpam-6680	314	37	2ρ	2ρ	NOUN
ejpam-6680	314	38	⟨	⟨	VERB
ejpam-6680	314	39	−−−−→	−−−−→	PUNCT
ejpam-6680	314	40	ϖ(v)v	ϖ(v)v	PROPN
ejpam-6680	314	41	,	,	PUNCT
ejpam-6680	314	42	−−−−→	−−−−→	PRON
ejpam-6680	314	43	bmk+1	bmk+1	AUX
ejpam-6680	314	44	v⟩.	v⟩.	VERB
ejpam-6680	314	45	therefore	therefore	ADV
ejpam-6680	314	46	,	,	PUNCT
ejpam-6680	314	47	lim	lim	PROPN
ejpam-6680	314	48	k→∞	k→∞	PROPN
ejpam-6680	314	49	sup	sup	PROPN
ejpam-6680	314	50	ϱ2(bk	ϱ2(bk	PROPN
ejpam-6680	314	51	,	,	PUNCT
ejpam-6680	314	52	v	v	NOUN
ejpam-6680	314	53	)	)	PUNCT
ejpam-6680	314	54	≤	≤	NOUN
ejpam-6680	314	55	0	0	NUM
ejpam-6680	314	56	,	,	PUNCT
ejpam-6680	314	57	that	that	ADV
ejpam-6680	314	58	is	is	ADV
ejpam-6680	314	59	,	,	PUNCT
ejpam-6680	314	60	bk	bk	INTJ
ejpam-6680	314	61	→	→	SYM
ejpam-6680	314	62	v.	v.	PROPN
ejpam-6680	314	63	m.	m.	PROPN
ejpam-6680	314	64	rashid	rashid	PROPN
ejpam-6680	314	65	et	et	PROPN
ejpam-6680	314	66	al	al	PROPN
ejpam-6680	314	67	.	.	PUNCT
ejpam-6680	314	68	/	/	SYM
ejpam-6680	314	69	eur	eur	PROPN
ejpam-6680	314	70	.	.	PUNCT
ejpam-6680	315	1	j.	j.	PROPN
ejpam-6680	315	2	pure	pure	PROPN
ejpam-6680	315	3	appl	appl	PROPN
ejpam-6680	315	4	.	.	PROPN
ejpam-6680	315	5	math	math	PROPN
ejpam-6680	315	6	,	,	PUNCT
ejpam-6680	315	7	18	18	NUM
ejpam-6680	315	8	(	(	PUNCT
ejpam-6680	315	9	4	4	NUM
ejpam-6680	315	10	)	)	PUNCT
ejpam-6680	315	11	(	(	PUNCT
ejpam-6680	315	12	2025	2025	NUM
ejpam-6680	315	13	)	)	PUNCT
ejpam-6680	315	14	,	,	PUNCT
ejpam-6680	315	15	6680	6680	NUM
ejpam-6680	315	16	19	19	NUM
ejpam-6680	315	17	of	of	ADP
ejpam-6680	315	18	24	24	NUM
ejpam-6680	315	19	5	5	NUM
ejpam-6680	315	20	.	.	PUNCT
ejpam-6680	316	1	some	some	DET
ejpam-6680	316	2	consequences	consequence	NOUN
ejpam-6680	316	3	and	and	CCONJ
ejpam-6680	316	4	numerical	numerical	ADJ
ejpam-6680	316	5	illustrations	illustration	NOUN
ejpam-6680	316	6	in	in	ADP
ejpam-6680	316	7	this	this	DET
ejpam-6680	316	8	section	section	NOUN
ejpam-6680	316	9	,	,	PUNCT
ejpam-6680	316	10	we	we	PRON
ejpam-6680	316	11	first	first	ADV
ejpam-6680	316	12	derive	derive	VERB
ejpam-6680	316	13	1	1	NUM
ejpam-6680	316	14	and	and	CCONJ
ejpam-6680	316	15	2	2	NUM
ejpam-6680	316	16	corollaries	corollary	NOUN
ejpam-6680	316	17	of	of	ADP
ejpam-6680	316	18	theorem	theorem	ADJ
ejpam-6680	316	19	2	2	NUM
ejpam-6680	316	20	and	and	CCONJ
ejpam-6680	316	21	3	3	NUM
ejpam-6680	316	22	respectively	respectively	ADV
ejpam-6680	316	23	.	.	PUNCT
ejpam-6680	317	1	we	we	PRON
ejpam-6680	317	2	then	then	ADV
ejpam-6680	317	3	illustrate	illustrate	VERB
ejpam-6680	317	4	a	a	DET
ejpam-6680	317	5	numerical	numerical	ADJ
ejpam-6680	317	6	experiment	experiment	NOUN
ejpam-6680	317	7	to	to	PART
ejpam-6680	317	8	demonstrate	demonstrate	VERB
ejpam-6680	317	9	the	the	DET
ejpam-6680	317	10	performance	performance	NOUN
ejpam-6680	317	11	of	of	ADP
ejpam-6680	317	12	our	our	PRON
ejpam-6680	317	13	method	method	NOUN
ejpam-6680	317	14	.	.	PUNCT
ejpam-6680	318	1	corollary	corollary	ADJ
ejpam-6680	318	2	1	1	NUM
ejpam-6680	318	3	.	.	PUNCT
ejpam-6680	318	4	consider	consider	VERB
ejpam-6680	318	5	a	a	DET
ejpam-6680	318	6	nonempty	nonempty	ADJ
ejpam-6680	318	7	,	,	PUNCT
ejpam-6680	318	8	closed	closed	ADJ
ejpam-6680	318	9	and	and	CCONJ
ejpam-6680	318	10	convex	convex	PROPN
ejpam-6680	318	11	subset	subset	NOUN
ejpam-6680	318	12	of	of	ADP
ejpam-6680	318	13	a	a	DET
ejpam-6680	318	14	hadamard	hadamard	ADJ
ejpam-6680	318	15	space	space	NOUN
ejpam-6680	319	1	z	z	PROPN
ejpam-6680	319	2	be	be	AUX
ejpam-6680	319	3	l.	l.	NOUN
ejpam-6680	319	4	let	let	VERB
ejpam-6680	319	5	z∗	z∗	PROPN
ejpam-6680	319	6	be	be	AUX
ejpam-6680	319	7	a	a	DET
ejpam-6680	319	8	metric	metric	ADJ
ejpam-6680	319	9	space	space	NOUN
ejpam-6680	319	10	and	and	CCONJ
ejpam-6680	319	11	a2	a2	PROPN
ejpam-6680	319	12	:	:	PUNCT
ejpam-6680	320	1	l	l	X
ejpam-6680	320	2	→	→	SYM
ejpam-6680	320	3	z∗	z∗	PROPN
ejpam-6680	320	4	,	,	PUNCT
ejpam-6680	320	5	a1	a1	NOUN
ejpam-6680	320	6	:	:	PUNCT
ejpam-6680	320	7	z∗	z∗	PROPN
ejpam-6680	320	8	→	→	SYM
ejpam-6680	320	9	l.	l.	PROPN
ejpam-6680	320	10	the	the	DET
ejpam-6680	320	11	map	map	NOUN
ejpam-6680	320	12	a2	a2	PROPN
ejpam-6680	320	13	is	be	AUX
ejpam-6680	320	14	a	a	DET
ejpam-6680	320	15	uniformly	uniformly	ADV
ejpam-6680	320	16	continuous	continuous	ADJ
ejpam-6680	320	17	on	on	ADP
ejpam-6680	320	18	l	l	NOUN
ejpam-6680	320	19	and	and	CCONJ
ejpam-6680	320	20	a1	a1	NOUN
ejpam-6680	320	21	is	be	AUX
ejpam-6680	320	22	uniformly	uniformly	ADV
ejpam-6680	320	23	continuous	continuous	ADJ
ejpam-6680	320	24	on	on	ADP
ejpam-6680	320	25	a2(l	a2(l	NOUN
ejpam-6680	320	26	)	)	PUNCT
ejpam-6680	320	27	,	,	PUNCT
ejpam-6680	320	28	a	a	PRON
ejpam-6680	320	29	is	be	AUX
ejpam-6680	320	30	a	a	DET
ejpam-6680	320	31	pseudo	pseudo	NOUN
ejpam-6680	320	32	-	-	NOUN
ejpam-6680	320	33	monotone	monotone	ADJ
ejpam-6680	320	34	on	on	ADP
ejpam-6680	320	35	l.	l.	PROPN
ejpam-6680	320	36	the	the	DET
ejpam-6680	320	37	solution	solution	NOUN
ejpam-6680	320	38	set	set	VERB
ejpam-6680	320	39	of	of	ADP
ejpam-6680	320	40	the	the	DET
ejpam-6680	320	41	v	v	PROPN
ejpam-6680	320	42	i(l	i(l	PROPN
ejpam-6680	320	43	,	,	PUNCT
ejpam-6680	320	44	a	a	PRON
ejpam-6680	320	45	)	)	PUNCT
ejpam-6680	320	46	is	be	AUX
ejpam-6680	320	47	nonempty	nonempty	ADJ
ejpam-6680	320	48	,	,	PUNCT
ejpam-6680	320	49	that	that	PRON
ejpam-6680	320	50	is	be	AUX
ejpam-6680	320	51	v	v	ADP
ejpam-6680	320	52	i(l	i(l	PROPN
ejpam-6680	320	53	,	,	PUNCT
ejpam-6680	320	54	a	a	PRON
ejpam-6680	320	55	)	)	PUNCT
ejpam-6680	320	56	̸=	̸=	PROPN
ejpam-6680	320	57	ϕ.	ϕ.	NOUN
ejpam-6680	320	58	then	then	ADV
ejpam-6680	320	59	any	any	DET
ejpam-6680	320	60	sequence	sequence	NOUN
ejpam-6680	320	61	bn	bn	NOUN
ejpam-6680	320	62	is	be	AUX
ejpam-6680	320	63	∆-convergent	∆-convergent	ADJ
ejpam-6680	320	64	in	in	ADP
ejpam-6680	320	65	v	v	ADP
ejpam-6680	320	66	i(l	i(l	PROPN
ejpam-6680	320	67	,	,	PUNCT
ejpam-6680	320	68	a	a	PRON
ejpam-6680	320	69	)	)	PUNCT
ejpam-6680	320	70	.	.	PUNCT
ejpam-6680	321	1	corollary	corollary	ADJ
ejpam-6680	321	2	2	2	NUM
ejpam-6680	321	3	.	.	PUNCT
ejpam-6680	322	1	let	let	VERB
ejpam-6680	322	2	l	l	NOUN
ejpam-6680	322	3	be	be	AUX
ejpam-6680	322	4	a	a	DET
ejpam-6680	322	5	nonempty	nonempty	ADJ
ejpam-6680	322	6	,	,	PUNCT
ejpam-6680	322	7	closed	closed	ADJ
ejpam-6680	322	8	and	and	CCONJ
ejpam-6680	322	9	convex	convex	PROPN
ejpam-6680	322	10	subset	subset	NOUN
ejpam-6680	322	11	of	of	ADP
ejpam-6680	322	12	a	a	DET
ejpam-6680	322	13	hadamard	hadamard	ADJ
ejpam-6680	322	14	space	space	NOUN
ejpam-6680	322	15	z.	z.	PROPN
ejpam-6680	322	16	consider	consider	VERB
ejpam-6680	322	17	the	the	DET
ejpam-6680	322	18	mappings	mapping	NOUN
ejpam-6680	322	19	a1	a1	NOUN
ejpam-6680	322	20	:	:	PUNCT
ejpam-6680	322	21	l	l	NOUN
ejpam-6680	322	22	→	→	SYM
ejpam-6680	322	23	l	l	NOUN
ejpam-6680	322	24	and	and	CCONJ
ejpam-6680	322	25	a2	a2	PROPN
ejpam-6680	322	26	:	:	PUNCT
ejpam-6680	323	1	l	l	X
ejpam-6680	323	2	→	→	PUNCT
ejpam-6680	323	3	l	l	NOUN
ejpam-6680	323	4	such	such	ADJ
ejpam-6680	323	5	that	that	DET
ejpam-6680	323	6	a1oa2	a1oa2	NOUN
ejpam-6680	323	7	=	=	PUNCT
ejpam-6680	323	8	a.	a.	NOUN
ejpam-6680	323	9	the	the	DET
ejpam-6680	323	10	mapping	mapping	NOUN
ejpam-6680	323	11	a	a	PRON
ejpam-6680	323	12	is	be	AUX
ejpam-6680	323	13	a	a	DET
ejpam-6680	323	14	pseudo	pseudo	NOUN
ejpam-6680	323	15	-	-	ADJ
ejpam-6680	323	16	monotone	monotone	ADJ
ejpam-6680	323	17	,	,	PUNCT
ejpam-6680	323	18	uniformly	uniformly	ADV
ejpam-6680	323	19	continuous	continuous	ADJ
ejpam-6680	323	20	on	on	ADP
ejpam-6680	323	21	z.	z.	PROPN
ejpam-6680	323	22	the	the	DET
ejpam-6680	323	23	solution	solution	NOUN
ejpam-6680	323	24	set	set	VERB
ejpam-6680	323	25	of	of	ADP
ejpam-6680	323	26	vi	vi	PROPN
ejpam-6680	323	27	is	be	AUX
ejpam-6680	323	28	nonempty	nonempty	ADJ
ejpam-6680	323	29	,	,	PUNCT
ejpam-6680	323	30	that	that	PRON
ejpam-6680	323	31	is	be	AUX
ejpam-6680	323	32	v	v	ADP
ejpam-6680	323	33	i(l	i(l	PROPN
ejpam-6680	323	34	,	,	PUNCT
ejpam-6680	323	35	a	a	PRON
ejpam-6680	323	36	)	)	PUNCT
ejpam-6680	323	37	̸=	̸=	PROPN
ejpam-6680	323	38	∅.	∅.	ADV
ejpam-6680	323	39	let	let	VERB
ejpam-6680	323	40	{	{	PUNCT
ejpam-6680	323	41	ξn	ξn	NOUN
ejpam-6680	323	42	}	}	PUNCT
ejpam-6680	323	43	be	be	AUX
ejpam-6680	323	44	the	the	DET
ejpam-6680	323	45	sequences	sequence	NOUN
ejpam-6680	323	46	of	of	ADP
ejpam-6680	323	47	real	real	ADJ
ejpam-6680	323	48	numbers	number	NOUN
ejpam-6680	323	49	in	in	ADP
ejpam-6680	323	50	(	(	PUNCT
ejpam-6680	323	51	0	0	NUM
ejpam-6680	323	52	,	,	PUNCT
ejpam-6680	323	53	1	1	NUM
ejpam-6680	323	54	)	)	PUNCT
ejpam-6680	323	55	such	such	ADJ
ejpam-6680	323	56	that	that	SCONJ
ejpam-6680	323	57	lim	lim	PROPN
ejpam-6680	323	58	n→∞	n→∞	PRON
ejpam-6680	323	59	ξn	ξn	PROPN
ejpam-6680	323	60	=	=	PUNCT
ejpam-6680	323	61	0,σ∞	0,σ∞	NUM
ejpam-6680	323	62	n=1ξn	n=1ξn	NOUN
ejpam-6680	324	1	=	=	PUNCT
ejpam-6680	324	2	∞.	∞.	PROPN
ejpam-6680	324	3	then	then	ADV
ejpam-6680	324	4	the	the	DET
ejpam-6680	324	5	sequence	sequence	NOUN
ejpam-6680	324	6	{	{	PUNCT
ejpam-6680	324	7	bn	bn	PART
ejpam-6680	324	8	}	}	PUNCT
ejpam-6680	324	9	converges	converge	VERB
ejpam-6680	324	10	strongly	strongly	ADV
ejpam-6680	324	11	to	to	ADP
ejpam-6680	324	12	v	v	NOUN
ejpam-6680	324	13	∈	∈	NOUN
ejpam-6680	324	14	v	v	ADP
ejpam-6680	324	15	i(l	i(l	PROPN
ejpam-6680	324	16	,	,	PUNCT
ejpam-6680	324	17	a	a	PRON
ejpam-6680	324	18	)	)	PUNCT
ejpam-6680	324	19	,	,	PUNCT
ejpam-6680	324	20	where	where	SCONJ
ejpam-6680	324	21	v	v	NOUN
ejpam-6680	324	22	=	=	SYM
ejpam-6680	324	23	pv	pv	NOUN
ejpam-6680	324	24	i(l	i(l	PROPN
ejpam-6680	324	25	,	,	PUNCT
ejpam-6680	324	26	a)ϖ(v	a)ϖ(v	NOUN
ejpam-6680	324	27	)	)	PUNCT
ejpam-6680	324	28	.	.	PUNCT
ejpam-6680	325	1	example	example	NOUN
ejpam-6680	326	1	1	1	X
ejpam-6680	326	2	.	.	PUNCT
ejpam-6680	326	3	let	let	VERB
ejpam-6680	326	4	z	z	NOUN
ejpam-6680	326	5	=	=	PUNCT
ejpam-6680	326	6	r2,l	r2,l	PROPN
ejpam-6680	326	7	=	=	PUNCT
ejpam-6680	326	8	{	{	PUNCT
ejpam-6680	326	9	u	u	NOUN
ejpam-6680	326	10	∈	∈	PROPN
ejpam-6680	326	11	r2	r2	NOUN
ejpam-6680	326	12	:	:	PUNCT
ejpam-6680	326	13	−1	−1	NOUN
ejpam-6680	326	14	≤	≤	NOUN
ejpam-6680	326	15	ui	ui	NOUN
ejpam-6680	327	1	≤	≤	NUM
ejpam-6680	327	2	1	1	NUM
ejpam-6680	327	3	,	,	PUNCT
ejpam-6680	327	4	i	i	PRON
ejpam-6680	327	5	=	=	NOUN
ejpam-6680	327	6	1	1	NUM
ejpam-6680	327	7	,	,	PUNCT
ejpam-6680	327	8	2	2	NUM
ejpam-6680	327	9	}	}	PUNCT
ejpam-6680	327	10	.	.	PUNCT
ejpam-6680	328	1	define	define	VERB
ejpam-6680	328	2	the	the	DET
ejpam-6680	328	3	maps	map	NOUN
ejpam-6680	328	4	a1	a1	NOUN
ejpam-6680	328	5	:	:	PUNCT
ejpam-6680	328	6	l	l	NOUN
ejpam-6680	328	7	→	→	PUNCT
ejpam-6680	328	8	(	(	PUNCT
ejpam-6680	328	9	r2)∗	r2)∗	ADJ
ejpam-6680	328	10	,	,	PUNCT
ejpam-6680	328	11	and	and	CCONJ
ejpam-6680	328	12	a2	a2	PROPN
ejpam-6680	328	13	:	:	PUNCT
ejpam-6680	328	14	(	(	PUNCT
ejpam-6680	328	15	r2)∗	r2)∗	NOUN
ejpam-6680	328	16	→	→	SYM
ejpam-6680	328	17	l	l	NOUN
ejpam-6680	328	18	such	such	ADJ
ejpam-6680	328	19	that	that	PRON
ejpam-6680	328	20	a1(b	a1(b	NOUN
ejpam-6680	328	21	)	)	PUNCT
ejpam-6680	328	22	=	=	SYM
ejpam-6680	328	23	f	f	X
ejpam-6680	328	24	,	,	PUNCT
ejpam-6680	328	25	f	f	PROPN
ejpam-6680	328	26	∈	∈	PROPN
ejpam-6680	328	27	(	(	PUNCT
ejpam-6680	328	28	r2)∗	r2)∗	PROPN
ejpam-6680	328	29	,	,	PUNCT
ejpam-6680	328	30	a2(b	a2(b	ADJ
ejpam-6680	328	31	)	)	PUNCT
ejpam-6680	328	32	=	=	NOUN
ejpam-6680	328	33	s′	s′	VERB
ejpam-6680	328	34	respectively	respectively	ADV
ejpam-6680	328	35	.	.	PUNCT
ejpam-6680	329	1	let	let	VERB
ejpam-6680	329	2	b1	b1	NOUN
ejpam-6680	329	3	=	=	SYM
ejpam-6680	329	4	(	(	PUNCT
ejpam-6680	329	5	0.1	0.1	NUM
ejpam-6680	329	6	,	,	PUNCT
ejpam-6680	329	7	0.2	0.2	NUM
ejpam-6680	329	8	)	)	PUNCT
ejpam-6680	329	9	∈	∈	NOUN
ejpam-6680	329	10	l	l	NOUN
ejpam-6680	329	11	be	be	AUX
ejpam-6680	329	12	arbitrary	arbitrary	ADJ
ejpam-6680	329	13	and	and	CCONJ
ejpam-6680	329	14	define	define	VERB
ejpam-6680	329	15	gi	gi	INTJ
ejpam-6680	329	16	:	:	PUNCT
ejpam-6680	329	17	r2	r2	PROPN
ejpam-6680	329	18	→	→	PUNCT
ejpam-6680	329	19	r	r	NOUN
ejpam-6680	329	20	such	such	ADJ
ejpam-6680	329	21	that	that	DET
ejpam-6680	329	22	g1(b1	g1(b1	NOUN
ejpam-6680	329	23	,	,	PUNCT
ejpam-6680	329	24	b2	b2	NOUN
ejpam-6680	329	25	)	)	PUNCT
ejpam-6680	330	1	=	=	SYM
ejpam-6680	330	2	cos(b1	cos(b1	PROPN
ejpam-6680	330	3	)	)	PUNCT
ejpam-6680	330	4	,	,	PUNCT
ejpam-6680	330	5	g2(b1	g2(b1	NOUN
ejpam-6680	330	6	,	,	PUNCT
ejpam-6680	330	7	b2	b2	NOUN
ejpam-6680	330	8	)	)	PUNCT
ejpam-6680	330	9	=	=	SYM
ejpam-6680	330	10	cos(b2	cos(b2	NOUN
ejpam-6680	330	11	)	)	PUNCT
ejpam-6680	330	12	.	.	PUNCT
ejpam-6680	331	1	then	then	ADV
ejpam-6680	331	2	we	we	PRON
ejpam-6680	331	3	have	have	VERB
ejpam-6680	331	4	ab1	ab1	ADV
ejpam-6680	331	5	=	=	SYM
ejpam-6680	331	6	(	(	PUNCT
ejpam-6680	331	7	cos(b1	cos(b1	PROPN
ejpam-6680	331	8	)	)	PUNCT
ejpam-6680	331	9	+	+	SYM
ejpam-6680	331	10	cos(b2	cos(b2	NOUN
ejpam-6680	331	11	)	)	PUNCT
ejpam-6680	331	12	2	2	NUM
ejpam-6680	331	13	,	,	PUNCT
ejpam-6680	331	14	cos(b1)−	cos(b1)−	NOUN
ejpam-6680	331	15	cos(b2	cos(b2	NOUN
ejpam-6680	331	16	)	)	PUNCT
ejpam-6680	331	17	2	2	NUM
ejpam-6680	331	18	)	)	PUNCT
ejpam-6680	331	19	=	=	SYM
ejpam-6680	331	20	(	(	PUNCT
ejpam-6680	331	21	cos(0.1	cos(0.1	NUM
ejpam-6680	331	22	)	)	PUNCT
ejpam-6680	332	1	+	+	NUM
ejpam-6680	332	2	cos(0.2	cos(0.2	NUM
ejpam-6680	332	3	)	)	PUNCT
ejpam-6680	332	4	2	2	NUM
ejpam-6680	332	5	,	,	PUNCT
ejpam-6680	332	6	cos(0.1)−	cos(0.1)−	PROPN
ejpam-6680	332	7	cos(0.2	cos(0.2	NUM
ejpam-6680	332	8	)	)	PUNCT
ejpam-6680	332	9	2	2	NUM
ejpam-6680	332	10	)	)	PUNCT
ejpam-6680	333	1	=	=	SYM
ejpam-6680	333	2	(	(	PUNCT
ejpam-6680	333	3	0.98754	0.98754	NUM
ejpam-6680	333	4	,	,	PUNCT
ejpam-6680	333	5	0.00747	0.00747	NUM
ejpam-6680	333	6	)	)	PUNCT
ejpam-6680	333	7	.	.	PUNCT
ejpam-6680	334	1	step	step	NOUN
ejpam-6680	334	2	1	1	NUM
ejpam-6680	334	3	for	for	ADP
ejpam-6680	334	4	n	n	NOUN
ejpam-6680	334	5	=	=	SYM
ejpam-6680	334	6	1	1	NUM
ejpam-6680	334	7	,	,	PUNCT
ejpam-6680	334	8	and	and	CCONJ
ejpam-6680	334	9	ξ1	ξ1	NOUN
ejpam-6680	334	10	=	=	SYM
ejpam-6680	334	11	0.2	0.2	NUM
ejpam-6680	334	12	,	,	PUNCT
ejpam-6680	334	13	s1	s1	PROPN
ejpam-6680	334	14	=	=	SYM
ejpam-6680	334	15	pl(ξ1b1	pl(ξ1b1	PROPN
ejpam-6680	334	16	⊕	⊕	PROPN
ejpam-6680	334	17	(	(	PUNCT
ejpam-6680	334	18	1−	1−	NUM
ejpam-6680	334	19	ξ1)ab1	ξ1)ab1	X
ejpam-6680	334	20	)	)	PUNCT
ejpam-6680	335	1	=	=	SYM
ejpam-6680	335	2	pl((0.2)(0.1	pl((0.2)(0.1	NOUN
ejpam-6680	335	3	,	,	PUNCT
ejpam-6680	335	4	0.2)⊕	0.2)⊕	PROPN
ejpam-6680	335	5	(	(	PUNCT
ejpam-6680	335	6	1−	1−	NUM
ejpam-6680	335	7	0.2)(0.98754	0.2)(0.98754	NUM
ejpam-6680	335	8	,	,	PUNCT
ejpam-6680	335	9	0.00747	0.00747	NUM
ejpam-6680	335	10	)	)	PUNCT
ejpam-6680	335	11	)	)	PUNCT
ejpam-6680	336	1	=	=	SYM
ejpam-6680	336	2	pl((0.02	pl((0.02	NOUN
ejpam-6680	336	3	,	,	PUNCT
ejpam-6680	336	4	0.04)⊕	0.04)⊕	PROPN
ejpam-6680	336	5	(	(	PUNCT
ejpam-6680	336	6	0.790032	0.790032	NUM
ejpam-6680	336	7	,	,	PUNCT
ejpam-6680	336	8	0.005976	0.005976	NUM
ejpam-6680	336	9	)	)	PUNCT
ejpam-6680	336	10	)	)	PUNCT
ejpam-6680	337	1	=	=	SYM
ejpam-6680	337	2	pl(0.810032	pl(0.810032	PROPN
ejpam-6680	337	3	,	,	PUNCT
ejpam-6680	337	4	0.045976	0.045976	NUM
ejpam-6680	337	5	)	)	PUNCT
ejpam-6680	337	6	.	.	PUNCT
ejpam-6680	338	1	as	as	ADP
ejpam-6680	338	2	(	(	PUNCT
ejpam-6680	338	3	0.810032	0.810032	NUM
ejpam-6680	338	4	,	,	PUNCT
ejpam-6680	338	5	0.045976	0.045976	NUM
ejpam-6680	338	6	)	)	PUNCT
ejpam-6680	338	7	∈	∈	PROPN
ejpam-6680	338	8	l	l	NOUN
ejpam-6680	338	9	,	,	PUNCT
ejpam-6680	338	10	so	so	SCONJ
ejpam-6680	338	11	it	it	PRON
ejpam-6680	338	12	’s	’	VERB
ejpam-6680	338	13	unique	unique	ADJ
ejpam-6680	338	14	nearest	near	ADJ
ejpam-6680	338	15	point	point	NOUN
ejpam-6680	338	16	in	in	ADP
ejpam-6680	338	17	l	l	NOUN
ejpam-6680	338	18	is	be	AUX
ejpam-6680	338	19	(	(	PUNCT
ejpam-6680	338	20	0.810032	0.810032	NUM
ejpam-6680	338	21	,	,	PUNCT
ejpam-6680	338	22	0.045976	0.045976	NUM
ejpam-6680	338	23	)	)	PUNCT
ejpam-6680	338	24	implies	imply	VERB
ejpam-6680	338	25	s1	s1	NOUN
ejpam-6680	338	26	=	=	SYM
ejpam-6680	338	27	(	(	PUNCT
ejpam-6680	338	28	0.810032	0.810032	NUM
ejpam-6680	338	29	,	,	PUNCT
ejpam-6680	338	30	0.045976	0.045976	NUM
ejpam-6680	338	31	)	)	PUNCT
ejpam-6680	338	32	.	.	PUNCT
ejpam-6680	339	1	as1	as1	PROPN
ejpam-6680	339	2	=	=	PROPN
ejpam-6680	339	3	(	(	PUNCT
ejpam-6680	339	4	0.68948	0.68948	NUM
ejpam-6680	339	5	+	+	CCONJ
ejpam-6680	339	6	0.99894	0.99894	NUM
ejpam-6680	339	7	2	2	NUM
ejpam-6680	339	8	,	,	PUNCT
ejpam-6680	339	9	0.68948−	0.68948−	NUM
ejpam-6680	339	10	0.99894	0.99894	NUM
ejpam-6680	339	11	2	2	NUM
ejpam-6680	339	12	)	)	PUNCT
ejpam-6680	339	13	=	=	SYM
ejpam-6680	339	14	(	(	PUNCT
ejpam-6680	339	15	0.84421,−0.15473	0.84421,−0.15473	NUM
ejpam-6680	339	16	)	)	PUNCT
ejpam-6680	339	17	.	.	PUNCT
ejpam-6680	340	1	m.	m.	PROPN
ejpam-6680	340	2	rashid	rashid	PROPN
ejpam-6680	340	3	et	et	PROPN
ejpam-6680	340	4	al	al	PROPN
ejpam-6680	340	5	.	.	PUNCT
ejpam-6680	340	6	/	/	SYM
ejpam-6680	340	7	eur	eur	PROPN
ejpam-6680	340	8	.	.	PUNCT
ejpam-6680	341	1	j.	j.	PROPN
ejpam-6680	341	2	pure	pure	PROPN
ejpam-6680	341	3	appl	appl	PROPN
ejpam-6680	341	4	.	.	PROPN
ejpam-6680	341	5	math	math	PROPN
ejpam-6680	341	6	,	,	PUNCT
ejpam-6680	341	7	18	18	NUM
ejpam-6680	341	8	(	(	PUNCT
ejpam-6680	341	9	4	4	NUM
ejpam-6680	341	10	)	)	PUNCT
ejpam-6680	341	11	(	(	PUNCT
ejpam-6680	341	12	2025	2025	NUM
ejpam-6680	341	13	)	)	PUNCT
ejpam-6680	341	14	,	,	PUNCT
ejpam-6680	341	15	6680	6680	NUM
ejpam-6680	341	16	20	20	NUM
ejpam-6680	341	17	of	of	ADP
ejpam-6680	341	18	24	24	NUM
ejpam-6680	341	19	now	now	ADV
ejpam-6680	341	20	to	to	PART
ejpam-6680	341	21	prove	prove	VERB
ejpam-6680	341	22	⟨	⟨	NOUN
ejpam-6680	341	23	−−−−−→	−−−−−→	PUNCT
ejpam-6680	341	24	ab1as1	ab1as1	PROPN
ejpam-6680	341	25	,	,	PUNCT
ejpam-6680	341	26	−−→	−−→	X
ejpam-6680	342	1	b1s1⟩	b1s1⟩	NOUN
ejpam-6680	342	2	≤	≤	ADJ
ejpam-6680	342	3	µϱ2(b1	µϱ2(b1	NOUN
ejpam-6680	342	4	,	,	PUNCT
ejpam-6680	342	5	s1	s1	NOUN
ejpam-6680	342	6	)	)	PUNCT
ejpam-6680	342	7	.	.	PUNCT
ejpam-6680	343	1	(	(	PUNCT
ejpam-6680	343	2	17	17	NUM
ejpam-6680	343	3	)	)	PUNCT
ejpam-6680	343	4	consider	consider	VERB
ejpam-6680	343	5	left	leave	VERB
ejpam-6680	343	6	hand	hand	NOUN
ejpam-6680	343	7	side	side	NOUN
ejpam-6680	343	8	of	of	ADP
ejpam-6680	343	9	(	(	PUNCT
ejpam-6680	343	10	17	17	NUM
ejpam-6680	343	11	)	)	PUNCT
ejpam-6680	343	12	,	,	PUNCT
ejpam-6680	343	13	⟨	⟨	VERB
ejpam-6680	343	14	−−−−−→	−−−−−→	PUNCT
ejpam-6680	343	15	ab1as1	ab1as1	PROPN
ejpam-6680	343	16	,	,	PUNCT
ejpam-6680	343	17	−−→	−−→	X
ejpam-6680	343	18	b1s1⟩	b1s1⟩	X
ejpam-6680	343	19	=	=	PUNCT
ejpam-6680	343	20	1	1	NUM
ejpam-6680	343	21	2	2	NUM
ejpam-6680	343	22	[	[	PUNCT
ejpam-6680	343	23	ϱ2(ab1	ϱ2(ab1	PROPN
ejpam-6680	343	24	,	,	PUNCT
ejpam-6680	343	25	s1	s1	NOUN
ejpam-6680	343	26	)	)	PUNCT
ejpam-6680	343	27	+	+	SYM
ejpam-6680	343	28	ϱ2(as1	ϱ2(as1	NOUN
ejpam-6680	343	29	,	,	PUNCT
ejpam-6680	343	30	b1)−	b1)−	PROPN
ejpam-6680	343	31	ϱ2(ab1	ϱ2(ab1	PROPN
ejpam-6680	343	32	,	,	PUNCT
ejpam-6680	343	33	b1	b1	NOUN
ejpam-6680	343	34	)	)	PUNCT
ejpam-6680	343	35	−ϱ2(πay1	−ϱ2(πay1	PROPN
ejpam-6680	343	36	,	,	PUNCT
ejpam-6680	343	37	y1	y1	NOUN
ejpam-6680	343	38	)	)	PUNCT
ejpam-6680	343	39	]	]	PUNCT
ejpam-6680	344	1	=	=	PUNCT
ejpam-6680	344	2	−0.0932945	−0.0932945	PROPN
ejpam-6680	344	3	and	and	CCONJ
ejpam-6680	344	4	ϱ2(b1	ϱ2(b1	ADV
ejpam-6680	344	5	,	,	PUNCT
ejpam-6680	344	6	s1	s1	NOUN
ejpam-6680	344	7	)	)	PUNCT
ejpam-6680	344	8	=	=	SYM
ejpam-6680	344	9	(	(	PUNCT
ejpam-6680	344	10	0.1−	0.1−	NOUN
ejpam-6680	344	11	0.810032)2	0.810032)2	NOUN
ejpam-6680	344	12	+	+	CCONJ
ejpam-6680	344	13	(	(	PUNCT
ejpam-6680	344	14	0.2−	0.2−	NOUN
ejpam-6680	344	15	0.045976)2	0.045976)2	NUM
ejpam-6680	344	16	=	=	SYM
ejpam-6680	345	1	0.527873	0.527873	NUM
ejpam-6680	345	2	µϱ2(b1	µϱ2(b1	NOUN
ejpam-6680	345	3	,	,	PUNCT
ejpam-6680	345	4	s1	s1	NOUN
ejpam-6680	345	5	)	)	PUNCT
ejpam-6680	345	6	=	=	SYM
ejpam-6680	345	7	0.2(0.527873	0.2(0.527873	X
ejpam-6680	345	8	)	)	PUNCT
ejpam-6680	345	9	=	=	PUNCT
ejpam-6680	345	10	0.1055746	0.1055746	NUM
ejpam-6680	345	11	thus	thus	ADV
ejpam-6680	345	12	,	,	PUNCT
ejpam-6680	345	13	we	we	PRON
ejpam-6680	345	14	have	have	AUX
ejpam-6680	345	15	⟨	⟨	NOUN
ejpam-6680	345	16	−−−−−→	−−−−−→	PUNCT
ejpam-6680	345	17	ab1as1	ab1as1	PROPN
ejpam-6680	345	18	,	,	PUNCT
ejpam-6680	345	19	−−→	−−→	X
ejpam-6680	345	20	b1s1⟩	b1s1⟩	NOUN
ejpam-6680	345	21	≤	≤	ADJ
ejpam-6680	345	22	µϱ2(b1	µϱ2(b1	NOUN
ejpam-6680	345	23	,	,	PUNCT
ejpam-6680	345	24	s1	s1	NOUN
ejpam-6680	345	25	)	)	PUNCT
ejpam-6680	345	26	.	.	PUNCT
ejpam-6680	346	1	step	step	NOUN
ejpam-6680	346	2	2	2	NUM
ejpam-6680	346	3	now	now	ADV
ejpam-6680	346	4	,	,	PUNCT
ejpam-6680	346	5	for	for	ADP
ejpam-6680	346	6	b2	b2	NOUN
ejpam-6680	346	7	=	=	SYM
ejpam-6680	346	8	pln(b1	pln(b1	NOUN
ejpam-6680	346	9	)	)	PUNCT
ejpam-6680	346	10	,	,	PUNCT
ejpam-6680	346	11	hn(b	hn(b	X
ejpam-6680	346	12	)	)	PUNCT
ejpam-6680	346	13	=	=	VERB
ejpam-6680	346	14	⟨	⟨	VERB
ejpam-6680	346	15	−→	−→	NOUN
ejpam-6680	346	16	bsn	bsn	NOUN
ejpam-6680	346	17	,	,	PUNCT
ejpam-6680	346	18	−−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−−→	PRON
ejpam-6680	346	19	(	(	PUNCT
ejpam-6680	346	20	ξnbn	ξnbn	PROPN
ejpam-6680	346	21	⊕	⊕	PROPN
ejpam-6680	346	22	(	(	PUNCT
ejpam-6680	346	23	1−	1−	NUM
ejpam-6680	346	24	ξn)abn)abn⟩	ξn)abn)abn⟩	NOUN
ejpam-6680	346	25	and	and	CCONJ
ejpam-6680	346	26	ln	ln	NOUN
ejpam-6680	346	27	=	=	PUNCT
ejpam-6680	346	28	{	{	PUNCT
ejpam-6680	346	29	b	b	PROPN
ejpam-6680	346	30	∈	∈	PROPN
ejpam-6680	346	31	z	z	NOUN
ejpam-6680	346	32	:	:	PUNCT
ejpam-6680	346	33	hn(b	hn(b	X
ejpam-6680	346	34	)	)	PUNCT
ejpam-6680	346	35	≤	≤	NOUN
ejpam-6680	346	36	0	0	NUM
ejpam-6680	346	37	}	}	PUNCT
ejpam-6680	346	38	.	.	PUNCT
ejpam-6680	347	1	let	let	VERB
ejpam-6680	347	2	b	b	X
ejpam-6680	347	3	=	=	SYM
ejpam-6680	347	4	(	(	PUNCT
ejpam-6680	347	5	µ1	µ1	PROPN
ejpam-6680	347	6	,	,	PUNCT
ejpam-6680	347	7	µ2	µ2	PROPN
ejpam-6680	347	8	)	)	PUNCT
ejpam-6680	347	9	,	,	PUNCT
ejpam-6680	347	10	h1(b	h1(b	NUM
ejpam-6680	347	11	)	)	PUNCT
ejpam-6680	347	12	=	=	SYM
ejpam-6680	348	1	0	0	X
ejpam-6680	348	2	.	.	PUNCT
ejpam-6680	349	1	then	then	ADV
ejpam-6680	349	2	h1(b	h1(b	NUM
ejpam-6680	349	3	)	)	PUNCT
ejpam-6680	349	4	=	=	VERB
ejpam-6680	349	5	⟨	⟨	VERB
ejpam-6680	349	6	−→	−→	ADJ
ejpam-6680	349	7	bs1	bs1	NOUN
ejpam-6680	349	8	,	,	PUNCT
ejpam-6680	349	9	−−−−−−−−−−−−−−−−−→	−−−−−−−−−−−−−−−−−→	PUNCT
ejpam-6680	349	10	(	(	PUNCT
ejpam-6680	349	11	ξ1b1	ξ1b1	PROPN
ejpam-6680	349	12	⊕	⊕	PROPN
ejpam-6680	349	13	(	(	PUNCT
ejpam-6680	349	14	1−	1−	NUM
ejpam-6680	349	15	ξ1)ab1)ab1⟩	ξ1)ab1)ab1⟩	NOUN
ejpam-6680	349	16	=	=	SYM
ejpam-6680	349	17	0	0	NUM
ejpam-6680	349	18	1	1	NUM
ejpam-6680	349	19	2	2	NUM
ejpam-6680	349	20	[	[	PUNCT
ejpam-6680	349	21	d2(b	d2(b	PROPN
ejpam-6680	349	22	,	,	PUNCT
ejpam-6680	349	23	ab1	ab1	X
ejpam-6680	349	24	)	)	PUNCT
ejpam-6680	350	1	+	+	CCONJ
ejpam-6680	350	2	d2(s1	d2(s1	PROPN
ejpam-6680	350	3	,	,	PUNCT
ejpam-6680	350	4	ξ1b1	ξ1b1	PROPN
ejpam-6680	350	5	⊕	⊕	PROPN
ejpam-6680	350	6	(	(	PUNCT
ejpam-6680	350	7	1−	1−	NUM
ejpam-6680	350	8	ξ1)ab1	ξ1)ab1	NOUN
ejpam-6680	350	9	)	)	PUNCT
ejpam-6680	350	10	−d2(b	−d2(b	ADJ
ejpam-6680	350	11	,	,	PUNCT
ejpam-6680	350	12	ξ1b1	ξ1b1	PROPN
ejpam-6680	350	13	⊕	⊕	PROPN
ejpam-6680	350	14	(	(	PUNCT
ejpam-6680	350	15	1−	1−	NUM
ejpam-6680	350	16	ξ1)ab1)−	ξ1)ab1)−	PROPN
ejpam-6680	350	17	d2(s1	d2(s1	PROPN
ejpam-6680	350	18	,	,	PUNCT
ejpam-6680	350	19	ab1	ab1	X
ejpam-6680	350	20	)	)	PUNCT
ejpam-6680	350	21	]	]	PUNCT
ejpam-6680	351	1	=	=	SYM
ejpam-6680	351	2	0	0	NUM
ejpam-6680	351	3	−0.355016µ1	−0.355016µ1	NOUN
ejpam-6680	352	1	+	+	CCONJ
ejpam-6680	353	1	0.77012µ2	0.77012µ2	NUM
ejpam-6680	354	1	+	+	PUNCT
ejpam-6680	354	2	0.2845414	0.2845414	NUM
ejpam-6680	354	3	=	=	SYM
ejpam-6680	354	4	0	0	NUM
ejpam-6680	354	5	.	.	PUNCT
ejpam-6680	355	1	(	(	PUNCT
ejpam-6680	355	2	18	18	NUM
ejpam-6680	355	3	)	)	PUNCT
ejpam-6680	355	4	from	from	ADP
ejpam-6680	355	5	(	(	PUNCT
ejpam-6680	355	6	18	18	NUM
ejpam-6680	355	7	)	)	PUNCT
ejpam-6680	355	8	,	,	PUNCT
ejpam-6680	355	9	we	we	PRON
ejpam-6680	355	10	have	have	VERB
ejpam-6680	355	11	µ1	µ1	NOUN
ejpam-6680	355	12	=	=	SYM
ejpam-6680	355	13	0.21993µ2	0.21993µ2	NUM
ejpam-6680	355	14	+	+	NOUN
ejpam-6680	355	15	0.801164	0.801164	NUM
ejpam-6680	355	16	.	.	PUNCT
ejpam-6680	356	1	if	if	SCONJ
ejpam-6680	356	2	µ1	µ1	PROPN
ejpam-6680	356	3	=	=	SYM
ejpam-6680	356	4	0	0	PROPN
ejpam-6680	356	5	,	,	PUNCT
ejpam-6680	356	6	then	then	ADV
ejpam-6680	356	7	µ2	µ2	PROPN
ejpam-6680	356	8	=	=	PROPN
ejpam-6680	356	9	3.6428	3.6428	NUM
ejpam-6680	356	10	and	and	CCONJ
ejpam-6680	356	11	if	if	SCONJ
ejpam-6680	356	12	µ2	µ2	PROPN
ejpam-6680	356	13	=	=	PROPN
ejpam-6680	356	14	0	0	NUM
ejpam-6680	356	15	,	,	PUNCT
ejpam-6680	356	16	then	then	ADV
ejpam-6680	356	17	µ1	µ1	PROPN
ejpam-6680	356	18	=	=	NOUN
ejpam-6680	356	19	0.801164	0.801164	NUM
ejpam-6680	356	20	.	.	PUNCT
ejpam-6680	357	1	since	since	SCONJ
ejpam-6680	357	2	b2	b2	NOUN
ejpam-6680	357	3	=	=	SYM
ejpam-6680	357	4	{	{	PUNCT
ejpam-6680	357	5	s′	s′	NOUN
ejpam-6680	357	6	∈	∈	PROPN
ejpam-6680	357	7	l1	l1	PROPN
ejpam-6680	357	8	:	:	PUNCT
ejpam-6680	357	9	ϱ(b1	ϱ(b1	VERB
ejpam-6680	357	10	,	,	PUNCT
ejpam-6680	357	11	s	s	NOUN
ejpam-6680	357	12	′	′	NOUN
ejpam-6680	357	13	)	)	PUNCT
ejpam-6680	357	14	=	=	SYM
ejpam-6680	357	15	ϱ(b1,l1	ϱ(b1,l1	NOUN
ejpam-6680	357	16	)	)	PUNCT
ejpam-6680	357	17	}	}	PUNCT
ejpam-6680	357	18	and	and	CCONJ
ejpam-6680	357	19	ϱ((0.1	ϱ((0.1	NOUN
ejpam-6680	357	20	,	,	PUNCT
ejpam-6680	357	21	0.2),l1	0.2),l1	NUM
ejpam-6680	357	22	)	)	PUNCT
ejpam-6680	358	1	=	=	SYM
ejpam-6680	358	2	−0.355016(0.1	−0.355016(0.1	PROPN
ejpam-6680	358	3	)	)	PUNCT
ejpam-6680	358	4	+	+	CCONJ
ejpam-6680	358	5	0.77012(0.2	0.77012(0.2	NUM
ejpam-6680	358	6	)	)	PUNCT
ejpam-6680	358	7	+	+	CCONJ
ejpam-6680	358	8	0.2845414	0.2845414	NUM
ejpam-6680	358	9	2	2	NUM
ejpam-6680	358	10	√	√	NUM
ejpam-6680	358	11	(	(	PUNCT
ejpam-6680	358	12	−0.355016)2	−0.355016)2	NOUN
ejpam-6680	358	13	+	+	CCONJ
ejpam-6680	358	14	(	(	PUNCT
ejpam-6680	358	15	0.77012)2	0.77012)2	NUM
ejpam-6680	358	16	=	=	SYM
ejpam-6680	358	17	0.727949	0.727949	NUM
ejpam-6680	358	18	let	let	VERB
ejpam-6680	358	19	s′(µ1	s′(µ1	NOUN
ejpam-6680	358	20	,	,	PUNCT
ejpam-6680	358	21	µ2)t	µ2)t	PROPN
ejpam-6680	358	22	.	.	PUNCT
ejpam-6680	359	1	then	then	ADV
ejpam-6680	359	2	s′	s′	PROPN
ejpam-6680	359	3	is	be	AUX
ejpam-6680	359	4	point	point	NOUN
ejpam-6680	359	5	of	of	ADP
ejpam-6680	359	6	intersection	intersection	NOUN
ejpam-6680	359	7	of	of	ADP
ejpam-6680	359	8	line	line	NOUN
ejpam-6680	359	9	l1	l1	PROPN
ejpam-6680	359	10	with	with	ADP
ejpam-6680	359	11	the	the	DET
ejpam-6680	359	12	perpendicular	perpendicular	ADJ
ejpam-6680	359	13	line	line	NOUN
ejpam-6680	359	14	.	.	PUNCT
ejpam-6680	360	1	the	the	DET
ejpam-6680	360	2	equation	equation	NOUN
ejpam-6680	360	3	of	of	ADP
ejpam-6680	360	4	perpendicular	perpendicular	ADJ
ejpam-6680	360	5	line	line	NOUN
ejpam-6680	360	6	is	be	AUX
ejpam-6680	360	7	µ1	µ1	NOUN
ejpam-6680	360	8	=	=	SYM
ejpam-6680	360	9	−	−	PROPN
ejpam-6680	360	10	1	1	NUM
ejpam-6680	360	11	0.21993	0.21993	NUM
ejpam-6680	361	1	µ2	µ2	NOUN
ejpam-6680	361	2	+	+	CCONJ
ejpam-6680	361	3	0.801164	0.801164	NUM
ejpam-6680	361	4	(	(	PUNCT
ejpam-6680	361	5	19	19	NUM
ejpam-6680	361	6	)	)	PUNCT
ejpam-6680	361	7	if	if	SCONJ
ejpam-6680	361	8	µ1	µ1	PROPN
ejpam-6680	361	9	=	=	SYM
ejpam-6680	361	10	0	0	PROPN
ejpam-6680	361	11	,	,	PUNCT
ejpam-6680	361	12	then	then	ADV
ejpam-6680	361	13	µ2	µ2	PROPN
ejpam-6680	361	14	=	=	PUNCT
ejpam-6680	361	15	0.176199	0.176199	NUM
ejpam-6680	361	16	and	and	CCONJ
ejpam-6680	361	17	if	if	SCONJ
ejpam-6680	361	18	µ2	µ2	PROPN
ejpam-6680	361	19	=	=	PROPN
ejpam-6680	361	20	0	0	NUM
ejpam-6680	361	21	,	,	PUNCT
ejpam-6680	361	22	then	then	ADV
ejpam-6680	361	23	µ1	µ1	PROPN
ejpam-6680	361	24	=	=	NOUN
ejpam-6680	361	25	0.801164	0.801164	NUM
ejpam-6680	361	26	.	.	PUNCT
ejpam-6680	362	1	to	to	PART
ejpam-6680	362	2	find	find	VERB
ejpam-6680	362	3	point	point	NOUN
ejpam-6680	362	4	of	of	ADP
ejpam-6680	362	5	intersection	intersection	NOUN
ejpam-6680	362	6	,	,	PUNCT
ejpam-6680	362	7	subtracting	subtract	VERB
ejpam-6680	362	8	(	(	PUNCT
ejpam-6680	362	9	18	18	NUM
ejpam-6680	362	10	)	)	PUNCT
ejpam-6680	362	11	and	and	CCONJ
ejpam-6680	362	12	(	(	PUNCT
ejpam-6680	362	13	19	19	NUM
ejpam-6680	362	14	)	)	PUNCT
ejpam-6680	362	15	,	,	PUNCT
ejpam-6680	362	16	we	we	PRON
ejpam-6680	362	17	get	get	VERB
ejpam-6680	362	18	µ2	µ2	PROPN
ejpam-6680	362	19	=	=	PROPN
ejpam-6680	362	20	0	0	NUM
ejpam-6680	362	21	,	,	PUNCT
ejpam-6680	362	22	µ1	µ1	PROPN
ejpam-6680	362	23	=	=	SYM
ejpam-6680	362	24	0.801164	0.801164	NUM
ejpam-6680	362	25	and	and	CCONJ
ejpam-6680	362	26	s′	s′	ADJ
ejpam-6680	362	27	=	=	NOUN
ejpam-6680	362	28	b2	b2	NOUN
ejpam-6680	362	29	=	=	SYM
ejpam-6680	362	30	(	(	PUNCT
ejpam-6680	362	31	0.801164	0.801164	NUM
ejpam-6680	362	32	,	,	PUNCT
ejpam-6680	362	33	0	0	NUM
ejpam-6680	362	34	)	)	PUNCT
ejpam-6680	362	35	.	.	PUNCT
ejpam-6680	363	1	m.	m.	PROPN
ejpam-6680	363	2	rashid	rashid	PROPN
ejpam-6680	363	3	et	et	PROPN
ejpam-6680	363	4	al	al	PROPN
ejpam-6680	363	5	.	.	PUNCT
ejpam-6680	363	6	/	/	SYM
ejpam-6680	363	7	eur	eur	PROPN
ejpam-6680	363	8	.	.	PUNCT
ejpam-6680	364	1	j.	j.	PROPN
ejpam-6680	364	2	pure	pure	PROPN
ejpam-6680	364	3	appl	appl	PROPN
ejpam-6680	364	4	.	.	PROPN
ejpam-6680	364	5	math	math	PROPN
ejpam-6680	364	6	,	,	PUNCT
ejpam-6680	364	7	18	18	NUM
ejpam-6680	364	8	(	(	PUNCT
ejpam-6680	364	9	4	4	NUM
ejpam-6680	364	10	)	)	PUNCT
ejpam-6680	364	11	(	(	PUNCT
ejpam-6680	364	12	2025	2025	NUM
ejpam-6680	364	13	)	)	PUNCT
ejpam-6680	364	14	,	,	PUNCT
ejpam-6680	364	15	6680	6680	NUM
ejpam-6680	364	16	21	21	NUM
ejpam-6680	364	17	of	of	ADP
ejpam-6680	364	18	24	24	NUM
ejpam-6680	364	19	example	example	NOUN
ejpam-6680	364	20	2	2	NUM
ejpam-6680	364	21	.	.	PUNCT
ejpam-6680	365	1	let	let	VERB
ejpam-6680	365	2	l	l	NOUN
ejpam-6680	365	3	=	=	PRON
ejpam-6680	365	4	{	{	PUNCT
ejpam-6680	365	5	(	(	PUNCT
ejpam-6680	365	6	x1	x1	PROPN
ejpam-6680	365	7	,	,	PUNCT
ejpam-6680	365	8	0	0	NUM
ejpam-6680	365	9	,	,	PUNCT
ejpam-6680	365	10	0	0	NUM
ejpam-6680	365	11	,	,	PUNCT
ejpam-6680	365	12	.	.	PUNCT
ejpam-6680	365	13	.	.	PUNCT
ejpam-6680	365	14	.	.	PUNCT
ejpam-6680	365	15	)	)	PUNCT
ejpam-6680	366	1	∈	∈	PROPN
ejpam-6680	366	2	ℓ2	ℓ2	NOUN
ejpam-6680	366	3	:	:	PUNCT
ejpam-6680	366	4	0	0	NUM
ejpam-6680	366	5	≤	≤	NUM
ejpam-6680	366	6	x1	x1	NUM
ejpam-6680	366	7	≤	≤	NUM
ejpam-6680	366	8	1	1	NUM
ejpam-6680	366	9	}	}	PUNCT
ejpam-6680	366	10	,	,	PUNCT
ejpam-6680	366	11	which	which	PRON
ejpam-6680	366	12	is	be	AUX
ejpam-6680	366	13	convex	convex	ADJ
ejpam-6680	366	14	(	(	PUNCT
ejpam-6680	366	15	if	if	SCONJ
ejpam-6680	366	16	x	x	X
ejpam-6680	366	17	=	=	SYM
ejpam-6680	366	18	(	(	PUNCT
ejpam-6680	366	19	x1	x1	PROPN
ejpam-6680	366	20	,	,	PUNCT
ejpam-6680	366	21	0	0	NUM
ejpam-6680	366	22	,	,	PUNCT
ejpam-6680	366	23	.	.	PUNCT
ejpam-6680	366	24	.	.	PUNCT
ejpam-6680	366	25	.	.	PUNCT
ejpam-6680	366	26	)	)	PUNCT
ejpam-6680	366	27	,	,	PUNCT
ejpam-6680	366	28	y	y	PROPN
ejpam-6680	366	29	=	=	SYM
ejpam-6680	366	30	(	(	PUNCT
ejpam-6680	366	31	y1	y1	PROPN
ejpam-6680	366	32	,	,	PUNCT
ejpam-6680	366	33	0	0	NUM
ejpam-6680	366	34	,	,	PUNCT
ejpam-6680	366	35	.	.	PUNCT
ejpam-6680	366	36	.	.	PUNCT
ejpam-6680	366	37	.	.	PUNCT
ejpam-6680	366	38	)	)	PUNCT
ejpam-6680	367	1	∈	∈	PROPN
ejpam-6680	367	2	l	l	NOUN
ejpam-6680	367	3	and	and	CCONJ
ejpam-6680	367	4	λ	λ	X
ejpam-6680	367	5	∈	∈	PROPN
ejpam-6680	368	1	[	[	X
ejpam-6680	368	2	0	0	NUM
ejpam-6680	368	3	,	,	PUNCT
ejpam-6680	368	4	1	1	NUM
ejpam-6680	368	5	]	]	PUNCT
ejpam-6680	368	6	,	,	PUNCT
ejpam-6680	368	7	then	then	ADV
ejpam-6680	368	8	λx+	λx+	INTJ
ejpam-6680	368	9	(	(	PUNCT
ejpam-6680	368	10	1−	1−	NUM
ejpam-6680	368	11	λ)y	λ)y	NOUN
ejpam-6680	368	12	=	=	SYM
ejpam-6680	368	13	(	(	PUNCT
ejpam-6680	368	14	λx1	λx1	X
ejpam-6680	368	15	+	+	PUNCT
ejpam-6680	368	16	(	(	PUNCT
ejpam-6680	368	17	1−	1−	NUM
ejpam-6680	368	18	λ)y1	λ)y1	PROPN
ejpam-6680	368	19	,	,	PUNCT
ejpam-6680	368	20	0	0	NUM
ejpam-6680	368	21	,	,	PUNCT
ejpam-6680	368	22	.	.	PUNCT
ejpam-6680	368	23	.	.	PUNCT
ejpam-6680	368	24	.	.	PUNCT
ejpam-6680	368	25	)	)	PUNCT
ejpam-6680	369	1	∈	∈	PROPN
ejpam-6680	369	2	l.	l.	NOUN
ejpam-6680	369	3	for	for	ADP
ejpam-6680	369	4	a	a	DET
ejpam-6680	369	5	concrete	concrete	ADJ
ejpam-6680	369	6	test	test	NOUN
ejpam-6680	369	7	,	,	PUNCT
ejpam-6680	369	8	we	we	PRON
ejpam-6680	369	9	work	work	VERB
ejpam-6680	369	10	with	with	ADP
ejpam-6680	369	11	a	a	DET
ejpam-6680	369	12	simple	simple	ADJ
ejpam-6680	369	13	diagonal	diagonal	ADJ
ejpam-6680	369	14	operator	operator	NOUN
ejpam-6680	369	15	a1	a1	NOUN
ejpam-6680	369	16	:	:	PUNCT
ejpam-6680	369	17	l	l	NOUN
ejpam-6680	369	18	→	→	SYM
ejpam-6680	369	19	ℓ2	ℓ2	NOUN
ejpam-6680	369	20	given	give	VERB
ejpam-6680	369	21	by	by	ADP
ejpam-6680	369	22	a1(x	a1(x	PRON
ejpam-6680	369	23	)	)	PUNCT
ejpam-6680	369	24	=	=	SYM
ejpam-6680	369	25	(	(	PUNCT
ejpam-6680	369	26	αnxn	αnxn	NOUN
ejpam-6680	369	27	)	)	PUNCT
ejpam-6680	369	28	,	,	PUNCT
ejpam-6680	370	1	αn	αn	NOUN
ejpam-6680	370	2	=	=	SYM
ejpam-6680	370	3	1	1	NUM
ejpam-6680	370	4	n+	n+	SYM
ejpam-6680	370	5	1	1	NUM
ejpam-6680	370	6	(	(	PUNCT
ejpam-6680	370	7	so	so	ADV
ejpam-6680	370	8	α1	α1	PROPN
ejpam-6680	370	9	=	=	SYM
ejpam-6680	370	10	1	1	NUM
ejpam-6680	370	11	2	2	NUM
ejpam-6680	370	12	)	)	PUNCT
ejpam-6680	370	13	,	,	PUNCT
ejpam-6680	370	14	and	and	CCONJ
ejpam-6680	370	15	a2(y	a2(y	X
ejpam-6680	370	16	)	)	PUNCT
ejpam-6680	370	17	=	=	SYM
ejpam-6680	370	18	pl(y	pl(y	NOUN
ejpam-6680	370	19	)	)	PUNCT
ejpam-6680	370	20	.	.	PUNCT
ejpam-6680	371	1	choose	choose	VERB
ejpam-6680	371	2	ξn	ξn	NOUN
ejpam-6680	371	3	=	=	SYM
ejpam-6680	371	4	ξ	ξ	PROPN
ejpam-6680	371	5	=	=	SYM
ejpam-6680	371	6	0.2	0.2	NUM
ejpam-6680	371	7	and	and	CCONJ
ejpam-6680	371	8	an	an	DET
ejpam-6680	371	9	initial	initial	ADJ
ejpam-6680	371	10	vector	vector	NOUN
ejpam-6680	371	11	b1	b1	NOUN
ejpam-6680	371	12	∈	∈	PROPN
ejpam-6680	371	13	l	l	NOUN
ejpam-6680	371	14	with	with	ADP
ejpam-6680	371	15	first	first	ADJ
ejpam-6680	371	16	coordinate	coordinate	NOUN
ejpam-6680	371	17	x1	x1	NOUN
ejpam-6680	371	18	=	=	PUNCT
ejpam-6680	371	19	0.8	0.8	NUM
ejpam-6680	371	20	.	.	PUNCT
ejpam-6680	372	1	the	the	DET
ejpam-6680	372	2	orthogonal	orthogonal	ADJ
ejpam-6680	372	3	projection	projection	NOUN
ejpam-6680	372	4	pl	pl	X
ejpam-6680	372	5	onto	onto	ADP
ejpam-6680	372	6	set	set	ADJ
ejpam-6680	372	7	l	l	NOUN
ejpam-6680	372	8	can	can	AUX
ejpam-6680	372	9	be	be	AUX
ejpam-6680	372	10	described	describe	VERB
ejpam-6680	372	11	explicitly	explicitly	ADV
ejpam-6680	372	12	pl(v	pl(v	X
ejpam-6680	372	13	)	)	PUNCT
ejpam-6680	373	1	=	=	SYM
ejpam-6680	373	2	(	(	PUNCT
ejpam-6680	373	3	π[0,1](v1	π[0,1](v1	NOUN
ejpam-6680	373	4	)	)	PUNCT
ejpam-6680	373	5	,	,	PUNCT
ejpam-6680	373	6	0	0	NUM
ejpam-6680	373	7	,	,	PUNCT
ejpam-6680	373	8	0	0	NUM
ejpam-6680	373	9	,	,	PUNCT
ejpam-6680	373	10	.	.	PUNCT
ejpam-6680	373	11	.	.	PUNCT
ejpam-6680	373	12	.	.	PUNCT
ejpam-6680	373	13	)	)	PUNCT
ejpam-6680	374	1	,	,	PUNCT
ejpam-6680	374	2	so	so	CCONJ
ejpam-6680	374	3	the	the	DET
ejpam-6680	374	4	algorithm	algorithm	NOUN
ejpam-6680	374	5	1	1	NUM
ejpam-6680	374	6	update	update	NOUN
ejpam-6680	374	7	sn	sn	NOUN
ejpam-6680	374	8	=	=	PUNCT
ejpam-6680	375	1	pl(ξbn	pl(ξbn	VERB
ejpam-6680	375	2	+	+	CCONJ
ejpam-6680	375	3	(	(	PUNCT
ejpam-6680	375	4	1	1	NUM
ejpam-6680	375	5	−	−	PROPN
ejpam-6680	375	6	ξ)abn	ξ)abn	PROPN
ejpam-6680	375	7	)	)	PUNCT
ejpam-6680	375	8	,	,	PUNCT
ejpam-6680	375	9	the	the	DET
ejpam-6680	375	10	entire	entire	ADJ
ejpam-6680	375	11	iteration	iteration	NOUN
ejpam-6680	375	12	is	be	AUX
ejpam-6680	375	13	governed	govern	VERB
ejpam-6680	375	14	solely	solely	ADV
ejpam-6680	375	15	by	by	ADP
ejpam-6680	375	16	the	the	DET
ejpam-6680	375	17	first	first	ADJ
ejpam-6680	375	18	coordinate	coordinate	NOUN
ejpam-6680	375	19	,	,	PUNCT
ejpam-6680	375	20	leading	lead	VERB
ejpam-6680	375	21	to	to	ADP
ejpam-6680	375	22	a	a	DET
ejpam-6680	375	23	simple	simple	ADJ
ejpam-6680	375	24	one	one	NUM
ejpam-6680	375	25	-	-	PUNCT
ejpam-6680	375	26	dimensional	dimensional	ADJ
ejpam-6680	375	27	recurrence	recurrence	NOUN
ejpam-6680	375	28	relation	relation	NOUN
ejpam-6680	375	29	.	.	PUNCT
ejpam-6680	376	1	for	for	ADP
ejpam-6680	376	2	the	the	DET
ejpam-6680	376	3	purpose	purpose	NOUN
ejpam-6680	376	4	of	of	ADP
ejpam-6680	376	5	demonstration	demonstration	NOUN
ejpam-6680	376	6	we	we	PRON
ejpam-6680	376	7	will	will	AUX
ejpam-6680	376	8	take	take	VERB
ejpam-6680	376	9	the	the	DET
ejpam-6680	376	10	simplified	simplified	ADJ
ejpam-6680	376	11	update	update	NOUN
ejpam-6680	376	12	bn+1	bn+1	NOUN
ejpam-6680	376	13	=	=	SYM
ejpam-6680	376	14	sn	sn	PROPN
ejpam-6680	376	15	,	,	PUNCT
ejpam-6680	376	16	where	where	SCONJ
ejpam-6680	376	17	sn	sn	PROPN
ejpam-6680	376	18	=	=	PUNCT
ejpam-6680	376	19	pl(ξbn	pl(ξbn	VERB
ejpam-6680	376	20	+	+	CCONJ
ejpam-6680	376	21	(	(	PUNCT
ejpam-6680	376	22	1−	1−	NUM
ejpam-6680	376	23	ξ)abn	ξ)abn	NOUN
ejpam-6680	376	24	)	)	PUNCT
ejpam-6680	376	25	.	.	PUNCT
ejpam-6680	377	1	with	with	ADP
ejpam-6680	377	2	ξ	ξ	PROPN
ejpam-6680	377	3	=	=	SYM
ejpam-6680	377	4	0.2	0.2	NUM
ejpam-6680	377	5	and	and	CCONJ
ejpam-6680	377	6	α1	α1	PROPN
ejpam-6680	377	7	=	=	SYM
ejpam-6680	377	8	1/2	1/2	NUM
ejpam-6680	377	9	one	one	NOUN
ejpam-6680	377	10	gets	get	VERB
ejpam-6680	377	11	xn+1	xn+1	NOUN
ejpam-6680	377	12	=	=	SYM
ejpam-6680	377	13	0.6xn	0.6xn	PROPN
ejpam-6680	377	14	,	,	PUNCT
ejpam-6680	377	15	x1	x1	NOUN
ejpam-6680	377	16	=	=	NOUN
ejpam-6680	377	17	0.8	0.8	NUM
ejpam-6680	377	18	,	,	PUNCT
ejpam-6680	377	19	hence	hence	ADV
ejpam-6680	377	20	xn	xn	PUNCT
ejpam-6680	378	1	=	=	PUNCT
ejpam-6680	378	2	0.6n−1x1	0.6n−1x1	NOUN
ejpam-6680	378	3	and	and	CCONJ
ejpam-6680	378	4	bn	bn	NOUN
ejpam-6680	378	5	=	=	SYM
ejpam-6680	378	6	(	(	PUNCT
ejpam-6680	378	7	xn	xn	PROPN
ejpam-6680	378	8	,	,	PUNCT
ejpam-6680	378	9	0	0	NUM
ejpam-6680	378	10	,	,	PUNCT
ejpam-6680	378	11	0	0	NUM
ejpam-6680	378	12	,	,	PUNCT
ejpam-6680	378	13	.	.	PUNCT
ejpam-6680	378	14	.	.	PUNCT
ejpam-6680	378	15	.	.	PUNCT
ejpam-6680	378	16	)	)	PUNCT
ejpam-6680	379	1	→	→	SYM
ejpam-6680	379	2	0	0	NUM
ejpam-6680	379	3	strongly	strongly	ADV
ejpam-6680	379	4	in	in	ADP
ejpam-6680	379	5	ℓ2	ℓ2	NOUN
ejpam-6680	379	6	.	.	PUNCT
ejpam-6680	380	1	this	this	DET
ejpam-6680	380	2	worked	work	VERB
ejpam-6680	380	3	-	-	PUNCT
ejpam-6680	380	4	out	out	ADP
ejpam-6680	380	5	example	example	NOUN
ejpam-6680	380	6	provides	provide	VERB
ejpam-6680	380	7	a	a	DET
ejpam-6680	380	8	straightforward	straightforward	ADJ
ejpam-6680	380	9	demonstration	demonstration	NOUN
ejpam-6680	380	10	in	in	ADP
ejpam-6680	380	11	the	the	DET
ejpam-6680	380	12	infinite	infinite	ADJ
ejpam-6680	380	13	-	-	PUNCT
ejpam-6680	380	14	dimensional	dimensional	ADJ
ejpam-6680	380	15	framework	framework	NOUN
ejpam-6680	380	16	(	(	PUNCT
ejpam-6680	380	17	implemented	implement	VERB
ejpam-6680	380	18	by	by	ADP
ejpam-6680	380	19	truncation	truncation	NOUN
ejpam-6680	380	20	for	for	ADP
ejpam-6680	380	21	computations	computation	NOUN
ejpam-6680	380	22	)	)	PUNCT
ejpam-6680	380	23	validating	validate	VERB
ejpam-6680	380	24	the	the	DET
ejpam-6680	380	25	convergence	convergence	NOUN
ejpam-6680	380	26	behaviour	behaviour	NOUN
ejpam-6680	380	27	asserted	assert	VERB
ejpam-6680	380	28	in	in	ADP
ejpam-6680	380	29	theorem	theorem	NOUN
ejpam-6680	380	30	2	2	NUM
ejpam-6680	380	31	.	.	PUNCT
ejpam-6680	380	32	conclusion	conclusion	NOUN
ejpam-6680	380	33	1	1	NUM
ejpam-6680	380	34	.	.	PUNCT
ejpam-6680	381	1	the	the	DET
ejpam-6680	381	2	variational	variational	ADJ
ejpam-6680	381	3	inequality	inequality	NOUN
ejpam-6680	381	4	is	be	AUX
ejpam-6680	381	5	defined	define	VERB
ejpam-6680	381	6	for	for	ADP
ejpam-6680	381	7	asymptotically	asymptotically	ADV
ejpam-6680	381	8	nonexpansive	nonexpansive	ADJ
ejpam-6680	381	9	mapping	mapping	NOUN
ejpam-6680	381	10	in	in	ADP
ejpam-6680	381	11	cat	cat	NOUN
ejpam-6680	381	12	(	(	PUNCT
ejpam-6680	381	13	0	0	NUM
ejpam-6680	381	14	)	)	PUNCT
ejpam-6680	381	15	spaces	space	NOUN
ejpam-6680	381	16	.	.	PUNCT
ejpam-6680	382	1	we	we	PRON
ejpam-6680	382	2	acquire	acquire	VERB
ejpam-6680	382	3	strong	strong	ADJ
ejpam-6680	382	4	and	and	CCONJ
ejpam-6680	382	5	∆-convergence	∆-convergence	NOUN
ejpam-6680	382	6	of	of	ADP
ejpam-6680	382	7	two	two	NUM
ejpam-6680	382	8	projection	projection	NOUN
ejpam-6680	382	9	type	type	NOUN
ejpam-6680	382	10	methods	method	NOUN
ejpam-6680	382	11	for	for	ADP
ejpam-6680	382	12	variational	variational	ADJ
ejpam-6680	382	13	inequality	inequality	NOUN
ejpam-6680	382	14	problem	problem	NOUN
ejpam-6680	382	15	using	use	VERB
ejpam-6680	382	16	pseudo	pseudo	NOUN
ejpam-6680	382	17	-	-	ADJ
ejpam-6680	382	18	monotone	monotone	ADJ
ejpam-6680	382	19	mapping	mapping	NOUN
ejpam-6680	382	20	.	.	PUNCT
ejpam-6680	383	1	numerical	numerical	ADJ
ejpam-6680	383	2	experiment	experiment	NOUN
ejpam-6680	383	3	performed	perform	VERB
ejpam-6680	383	4	for	for	ADP
ejpam-6680	383	5	our	our	PRON
ejpam-6680	383	6	perposed	perpose	VERB
ejpam-6680	383	7	algorithm	algorithm	NOUN
ejpam-6680	383	8	.	.	PUNCT
ejpam-6680	384	1	acknowledgements	acknowledgement	NOUN
ejpam-6680	384	2	the	the	DET
ejpam-6680	384	3	authors	author	NOUN
ejpam-6680	384	4	a.	a.	PROPN
ejpam-6680	384	5	aloqaily	aloqaily	ADV
ejpam-6680	384	6	and	and	CCONJ
ejpam-6680	384	7	n.	n.	PROPN
ejpam-6680	384	8	mlaiki	mlaiki	PROPN
ejpam-6680	384	9	would	would	AUX
ejpam-6680	384	10	like	like	VERB
ejpam-6680	384	11	to	to	PART
ejpam-6680	384	12	thank	thank	VERB
ejpam-6680	384	13	prince	prince	PROPN
ejpam-6680	384	14	sultan	sultan	PROPN
ejpam-6680	384	15	university	university	PROPN
ejpam-6680	384	16	for	for	ADP
ejpam-6680	384	17	paying	pay	VERB
ejpam-6680	384	18	the	the	DET
ejpam-6680	384	19	publication	publication	NOUN
ejpam-6680	384	20	fees	fee	NOUN
ejpam-6680	384	21	for	for	ADP
ejpam-6680	384	22	this	this	DET
ejpam-6680	384	23	work	work	NOUN
ejpam-6680	384	24	through	through	ADP
ejpam-6680	384	25	tas	ta	NOUN
ejpam-6680	384	26	lab	lab	NOUN
ejpam-6680	384	27	.	.	PUNCT
ejpam-6680	385	1	competing	compete	VERB
ejpam-6680	385	2	interests	interest	NOUN
ejpam-6680	385	3	there	there	PRON
ejpam-6680	385	4	are	be	VERB
ejpam-6680	385	5	no	no	DET
ejpam-6680	385	6	conflicting	conflict	VERB
ejpam-6680	385	7	interests	interest	NOUN
ejpam-6680	385	8	,	,	PUNCT
ejpam-6680	385	9	according	accord	VERB
ejpam-6680	385	10	to	to	ADP
ejpam-6680	385	11	the	the	DET
ejpam-6680	385	12	authors	author	NOUN
ejpam-6680	385	13	.	.	PUNCT
ejpam-6680	386	1	author	author	NOUN
ejpam-6680	386	2	’s	’s	PART
ejpam-6680	386	3	contributions	contribution	NOUN
ejpam-6680	386	4	each	each	DET
ejpam-6680	386	5	author	author	NOUN
ejpam-6680	386	6	contributed	contribute	VERB
ejpam-6680	386	7	equally	equally	ADV
ejpam-6680	386	8	to	to	ADP
ejpam-6680	386	9	the	the	DET
ejpam-6680	386	10	writing	writing	NOUN
ejpam-6680	386	11	of	of	ADP
ejpam-6680	386	12	this	this	DET
ejpam-6680	386	13	work	work	NOUN
ejpam-6680	386	14	,	,	PUNCT
ejpam-6680	386	15	and	and	CCONJ
ejpam-6680	386	16	they	they	PRON
ejpam-6680	386	17	have	have	AUX
ejpam-6680	386	18	all	all	ADV
ejpam-6680	386	19	read	read	VERB
ejpam-6680	386	20	and	and	CCONJ
ejpam-6680	386	21	approved	approve	VERB
ejpam-6680	386	22	the	the	DET
ejpam-6680	386	23	finished	finished	ADJ
ejpam-6680	386	24	work	work	NOUN
ejpam-6680	386	25	.	.	PUNCT
ejpam-6680	387	1	m.	m.	NOUN
ejpam-6680	387	2	rashid	rashid	PROPN
ejpam-6680	387	3	et	et	PROPN
ejpam-6680	387	4	al	al	PROPN
ejpam-6680	387	5	.	.	PUNCT
ejpam-6680	387	6	/	/	SYM
ejpam-6680	387	7	eur	eur	PROPN
ejpam-6680	387	8	.	.	PUNCT
ejpam-6680	388	1	j.	j.	PROPN
ejpam-6680	388	2	pure	pure	PROPN
ejpam-6680	388	3	appl	appl	PROPN
ejpam-6680	388	4	.	.	PROPN
ejpam-6680	388	5	math	math	PROPN
ejpam-6680	388	6	,	,	PUNCT
ejpam-6680	388	7	18	18	NUM
ejpam-6680	388	8	(	(	PUNCT
ejpam-6680	388	9	4	4	NUM
ejpam-6680	388	10	)	)	PUNCT
ejpam-6680	388	11	(	(	PUNCT
ejpam-6680	388	12	2025	2025	NUM
ejpam-6680	388	13	)	)	PUNCT
ejpam-6680	388	14	,	,	PUNCT
ejpam-6680	388	15	6680	6680	NUM
ejpam-6680	388	16	22	22	NUM
ejpam-6680	388	17	of	of	ADP
ejpam-6680	388	18	24	24	NUM
ejpam-6680	388	19	declarations	declaration	NOUN
ejpam-6680	388	20	ethical	ethical	ADJ
ejpam-6680	388	21	approval	approval	NOUN
ejpam-6680	388	22	not	not	PART
ejpam-6680	388	23	applicable	applicable	ADJ
ejpam-6680	388	24	.	.	PUNCT
ejpam-6680	389	1	funding	fund	VERB
ejpam-6680	389	2	not	not	PART
ejpam-6680	389	3	applicable	applicable	ADJ
ejpam-6680	389	4	.	.	PUNCT
ejpam-6680	390	1	availability	availability	NOUN
ejpam-6680	390	2	of	of	ADP
ejpam-6680	390	3	data	datum	NOUN
ejpam-6680	390	4	and	and	CCONJ
ejpam-6680	390	5	materialsdata	materialsdata	NOUN
ejpam-6680	390	6	sharing	sharing	NOUN
ejpam-6680	390	7	is	be	AUX
ejpam-6680	390	8	not	not	PART
ejpam-6680	390	9	applicable	applicable	ADJ
ejpam-6680	390	10	to	to	ADP
ejpam-6680	390	11	this	this	DET
ejpam-6680	390	12	article	article	NOUN
ejpam-6680	390	13	as	as	SCONJ
ejpam-6680	390	14	no	no	DET
ejpam-6680	390	15	data	data	NOUN
ejpam-6680	390	16	sets	set	NOUN
ejpam-6680	390	17	were	be	AUX
ejpam-6680	390	18	generated	generate	VERB
ejpam-6680	390	19	or	or	CCONJ
ejpam-6680	390	20	analyzed	analyze	VERB
ejpam-6680	390	21	during	during	ADP
ejpam-6680	390	22	the	the	DET
ejpam-6680	390	23	current	current	ADJ
ejpam-6680	390	24	study	study	NOUN
ejpam-6680	390	25	.	.	PUNCT
ejpam-6680	391	1	references	reference	NOUN
ejpam-6680	391	2	[	[	X
ejpam-6680	391	3	1	1	X
ejpam-6680	391	4	]	]	PUNCT
ejpam-6680	391	5	d.	d.	PROPN
ejpam-6680	391	6	kinderlehrer	kinderlehrer	PROPN
ejpam-6680	391	7	and	and	CCONJ
ejpam-6680	391	8	g.	g.	PROPN
ejpam-6680	391	9	stampacchia	stampacchia	PROPN
ejpam-6680	391	10	.	.	PUNCT
ejpam-6680	392	1	an	an	DET
ejpam-6680	392	2	introduction	introduction	NOUN
ejpam-6680	392	3	to	to	ADP
ejpam-6680	392	4	variational	variational	ADJ
ejpam-6680	392	5	inequalities	inequality	NOUN
ejpam-6680	392	6	and	and	CCONJ
ejpam-6680	392	7	their	their	PRON
ejpam-6680	392	8	applications	application	NOUN
ejpam-6680	392	9	.	.	PUNCT
ejpam-6680	393	1	academic	academic	ADJ
ejpam-6680	393	2	press	press	NOUN
ejpam-6680	393	3	,	,	PUNCT
ejpam-6680	393	4	new	new	PROPN
ejpam-6680	393	5	york	york	PROPN
ejpam-6680	393	6	,	,	PUNCT
ejpam-6680	393	7	1980	1980	NUM
ejpam-6680	393	8	.	.	PUNCT
ejpam-6680	394	1	[	[	X
ejpam-6680	394	2	2	2	NUM
ejpam-6680	394	3	]	]	PUNCT
ejpam-6680	394	4	p.	p.	PROPN
ejpam-6680	394	5	hartman	hartman	PROPN
ejpam-6680	394	6	and	and	CCONJ
ejpam-6680	394	7	g.	g.	PROPN
ejpam-6680	394	8	stampacchia	stampacchia	PROPN
ejpam-6680	394	9	.	.	PUNCT
ejpam-6680	395	1	on	on	ADP
ejpam-6680	395	2	some	some	DET
ejpam-6680	395	3	nonlinear	nonlinear	ADJ
ejpam-6680	395	4	elliptic	elliptic	ADJ
ejpam-6680	395	5	differential	differential	ADJ
ejpam-6680	395	6	functional	functional	ADJ
ejpam-6680	395	7	equations	equation	NOUN
ejpam-6680	395	8	.	.	PUNCT
ejpam-6680	396	1	acta	acta	PROPN
ejpam-6680	396	2	mathematica	mathematica	PROPN
ejpam-6680	396	3	,	,	PUNCT
ejpam-6680	396	4	115:153–188	115:153–188	NUM
ejpam-6680	396	5	,	,	PUNCT
ejpam-6680	396	6	1969	1969	NUM
ejpam-6680	396	7	.	.	PUNCT
ejpam-6680	397	1	[	[	X
ejpam-6680	397	2	3	3	X
ejpam-6680	397	3	]	]	X
ejpam-6680	397	4	j.	j.	PROPN
ejpam-6680	397	5	l.	l.	PROPN
ejpam-6680	397	6	lions	lions	PROPN
ejpam-6680	397	7	and	and	CCONJ
ejpam-6680	397	8	g.	g.	PROPN
ejpam-6680	397	9	stampacchia	stampacchia	PROPN
ejpam-6680	397	10	.	.	PUNCT
ejpam-6680	398	1	variational	variational	ADJ
ejpam-6680	398	2	inequalities	inequality	NOUN
ejpam-6680	398	3	.	.	PUNCT
ejpam-6680	399	1	communications	communication	NOUN
ejpam-6680	399	2	on	on	ADP
ejpam-6680	399	3	pure	pure	ADJ
ejpam-6680	399	4	and	and	CCONJ
ejpam-6680	399	5	applied	applied	ADJ
ejpam-6680	399	6	mathematics	mathematic	NOUN
ejpam-6680	399	7	,	,	PUNCT
ejpam-6680	399	8	20:493–519	20:493–519	NUM
ejpam-6680	399	9	,	,	PUNCT
ejpam-6680	399	10	1967	1967	NUM
ejpam-6680	399	11	.	.	PUNCT
ejpam-6680	400	1	[	[	X
ejpam-6680	400	2	4	4	X
ejpam-6680	400	3	]	]	PUNCT
ejpam-6680	400	4	m.	m.	NOUN
ejpam-6680	400	5	mancino	mancino	NOUN
ejpam-6680	400	6	and	and	CCONJ
ejpam-6680	400	7	g.	g.	PROPN
ejpam-6680	400	8	stampacchia	stampacchia	PROPN
ejpam-6680	400	9	.	.	PUNCT
ejpam-6680	401	1	convex	convex	NOUN
ejpam-6680	401	2	programming	programming	NOUN
ejpam-6680	401	3	and	and	CCONJ
ejpam-6680	401	4	variational	variational	ADJ
ejpam-6680	401	5	inequalities	inequality	NOUN
ejpam-6680	401	6	.	.	PUNCT
ejpam-6680	402	1	journal	journal	PROPN
ejpam-6680	402	2	of	of	ADP
ejpam-6680	402	3	optimization	optimization	NOUN
ejpam-6680	402	4	theory	theory	NOUN
ejpam-6680	402	5	and	and	CCONJ
ejpam-6680	402	6	applications	application	NOUN
ejpam-6680	402	7	,	,	PUNCT
ejpam-6680	402	8	9:3–23	9:3–23	NUM
ejpam-6680	402	9	,	,	PUNCT
ejpam-6680	402	10	1972	1972	NUM
ejpam-6680	402	11	.	.	PUNCT
ejpam-6680	403	1	[	[	X
ejpam-6680	403	2	5	5	X
ejpam-6680	403	3	]	]	X
ejpam-6680	403	4	g.	g.	PROPN
ejpam-6680	403	5	stampacchia	stampacchia	PROPN
ejpam-6680	403	6	.	.	PUNCT
ejpam-6680	404	1	formes	forme	NOUN
ejpam-6680	404	2	bilineaires	bilineaire	VERB
ejpam-6680	404	3	coercives	coercive	NOUN
ejpam-6680	404	4	sur	sur	VERB
ejpam-6680	404	5	les	le	NOUN
ejpam-6680	404	6	ensembles	ensemble	NOUN
ejpam-6680	404	7	convexes	convexe	NOUN
ejpam-6680	404	8	.	.	PUNCT
ejpam-6680	405	1	comptes	compte	VERB
ejpam-6680	405	2	rendus	rendus	PROPN
ejpam-6680	405	3	de	de	PROPN
ejpam-6680	405	4	l’académie	l’académie	PROPN
ejpam-6680	405	5	des	des	PROPN
ejpam-6680	405	6	sciences	sciences	PROPN
ejpam-6680	405	7	de	de	PROPN
ejpam-6680	405	8	paris	paris	PROPN
ejpam-6680	405	9	,	,	PUNCT
ejpam-6680	405	10	258:4413–4416	258:4413–4416	NUM
ejpam-6680	405	11	,	,	PUNCT
ejpam-6680	405	12	1964	1964	NUM
ejpam-6680	405	13	.	.	PUNCT
ejpam-6680	406	1	[	[	X
ejpam-6680	406	2	6	6	NUM
ejpam-6680	406	3	]	]	X
ejpam-6680	406	4	g.	g.	PROPN
ejpam-6680	406	5	stampacchia	stampacchia	PROPN
ejpam-6680	406	6	.	.	PUNCT
ejpam-6680	407	1	variational	variational	ADJ
ejpam-6680	407	2	inequalities	inequality	NOUN
ejpam-6680	407	3	.	.	PUNCT
ejpam-6680	408	1	in	in	ADP
ejpam-6680	408	2	theory	theory	NOUN
ejpam-6680	408	3	and	and	CCONJ
ejpam-6680	408	4	applications	application	NOUN
ejpam-6680	408	5	of	of	ADP
ejpam-6680	408	6	monotone	monotone	ADJ
ejpam-6680	408	7	operators	operator	NOUN
ejpam-6680	408	8	:	:	PUNCT
ejpam-6680	408	9	proceedings	proceeding	NOUN
ejpam-6680	408	10	of	of	ADP
ejpam-6680	408	11	the	the	DET
ejpam-6680	408	12	nato	nato	PROPN
ejpam-6680	408	13	advanced	advanced	ADJ
ejpam-6680	408	14	study	study	PROPN
ejpam-6680	408	15	institute	institute	NOUN
ejpam-6680	408	16	,	,	PUNCT
ejpam-6680	408	17	pages	page	NOUN
ejpam-6680	408	18	101–192	101–192	NUM
ejpam-6680	408	19	,	,	PUNCT
ejpam-6680	408	20	venice	venice	PROPN
ejpam-6680	408	21	,	,	PUNCT
ejpam-6680	408	22	italy	italy	PROPN
ejpam-6680	408	23	,	,	PUNCT
ejpam-6680	408	24	1969	1969	NUM
ejpam-6680	408	25	.	.	PUNCT
ejpam-6680	409	1	nato	nato	PROPN
ejpam-6680	409	2	,	,	PUNCT
ejpam-6680	409	3	edizioni	edizioni	NOUN
ejpam-6680	409	4	oderisi	oderisi	ADJ
ejpam-6680	409	5	.	.	PUNCT
ejpam-6680	410	1	[	[	X
ejpam-6680	410	2	7	7	X
ejpam-6680	410	3	]	]	X
ejpam-6680	410	4	f.	f.	PROPN
ejpam-6680	410	5	facchinei	facchinei	PROPN
ejpam-6680	410	6	and	and	CCONJ
ejpam-6680	410	7	j.	j.	PROPN
ejpam-6680	410	8	s.	s.	PROPN
ejpam-6680	410	9	pang	pang	PROPN
ejpam-6680	410	10	.	.	PUNCT
ejpam-6680	411	1	finite	finite	ADJ
ejpam-6680	411	2	-	-	ADJ
ejpam-6680	411	3	dimensional	dimensional	ADJ
ejpam-6680	411	4	variational	variational	ADJ
ejpam-6680	411	5	inequalities	inequality	NOUN
ejpam-6680	411	6	and	and	CCONJ
ejpam-6680	411	7	complementarity	complementarity	NOUN
ejpam-6680	411	8	problems	problem	NOUN
ejpam-6680	411	9	.	.	PUNCT
ejpam-6680	412	1	springer	springer	NOUN
ejpam-6680	412	2	,	,	PUNCT
ejpam-6680	412	3	new	new	PROPN
ejpam-6680	412	4	york	york	PROPN
ejpam-6680	412	5	,	,	PUNCT
ejpam-6680	412	6	2003	2003	NUM
ejpam-6680	412	7	.	.	PUNCT
ejpam-6680	413	1	[	[	X
ejpam-6680	413	2	8	8	NUM
ejpam-6680	413	3	]	]	X
ejpam-6680	413	4	i.	i.	PROPN
ejpam-6680	413	5	v.	v.	PROPN
ejpam-6680	413	6	konnov	konnov	PROPN
ejpam-6680	413	7	.	.	PUNCT
ejpam-6680	414	1	combined	combine	VERB
ejpam-6680	414	2	relaxation	relaxation	NOUN
ejpam-6680	414	3	methods	method	NOUN
ejpam-6680	414	4	for	for	ADP
ejpam-6680	414	5	variational	variational	ADJ
ejpam-6680	414	6	inequalities	inequality	NOUN
ejpam-6680	414	7	.	.	PUNCT
ejpam-6680	415	1	springer	springer	PROPN
ejpam-6680	415	2	,	,	PUNCT
ejpam-6680	415	3	berlin	berlin	PROPN
ejpam-6680	415	4	,	,	PUNCT
ejpam-6680	415	5	2001	2001	NUM
ejpam-6680	415	6	.	.	PUNCT
ejpam-6680	416	1	[	[	X
ejpam-6680	416	2	9	9	NUM
ejpam-6680	416	3	]	]	X
ejpam-6680	416	4	r.	r.	PROPN
ejpam-6680	416	5	glowinski	glowinski	PROPN
ejpam-6680	416	6	.	.	PUNCT
ejpam-6680	417	1	numerical	numerical	ADJ
ejpam-6680	417	2	methods	method	NOUN
ejpam-6680	417	3	for	for	ADP
ejpam-6680	417	4	variational	variational	ADJ
ejpam-6680	417	5	problems	problem	NOUN
ejpam-6680	417	6	.	.	PUNCT
ejpam-6680	418	1	springer	springer	NOUN
ejpam-6680	418	2	,	,	PUNCT
ejpam-6680	418	3	new	new	PROPN
ejpam-6680	418	4	york	york	PROPN
ejpam-6680	418	5	,	,	PUNCT
ejpam-6680	418	6	1984	1984	NUM
ejpam-6680	418	7	.	.	PUNCT
ejpam-6680	419	1	[	[	X
ejpam-6680	419	2	10	10	NUM
ejpam-6680	419	3	]	]	X
ejpam-6680	419	4	m.	m.	NOUN
ejpam-6680	419	5	v.	v.	ADP
ejpam-6680	419	6	solodov	solodov	PROPN
ejpam-6680	419	7	and	and	CCONJ
ejpam-6680	419	8	p.	p.	PROPN
ejpam-6680	419	9	tseng	tseng	PROPN
ejpam-6680	419	10	.	.	PUNCT
ejpam-6680	420	1	modified	modify	VERB
ejpam-6680	420	2	projection	projection	NOUN
ejpam-6680	420	3	methods	method	NOUN
ejpam-6680	420	4	for	for	ADP
ejpam-6680	420	5	monotone	monotone	ADJ
ejpam-6680	420	6	variational	variational	ADJ
ejpam-6680	420	7	inequalities	inequality	NOUN
ejpam-6680	420	8	.	.	PUNCT
ejpam-6680	421	1	siam	siam	PROPN
ejpam-6680	421	2	journal	journal	PROPN
ejpam-6680	421	3	on	on	ADP
ejpam-6680	421	4	control	control	NOUN
ejpam-6680	421	5	and	and	CCONJ
ejpam-6680	421	6	optimization	optimization	NOUN
ejpam-6680	421	7	,	,	PUNCT
ejpam-6680	421	8	34:1814–1830	34:1814–1830	NUM
ejpam-6680	421	9	,	,	PUNCT
ejpam-6680	421	10	1996	1996	NUM
ejpam-6680	421	11	.	.	PUNCT
ejpam-6680	422	1	[	[	X
ejpam-6680	422	2	11	11	NUM
ejpam-6680	422	3	]	]	X
ejpam-6680	422	4	g.	g.	PROPN
ejpam-6680	422	5	m.	m.	PROPN
ejpam-6680	422	6	korpelevich	korpelevich	PROPN
ejpam-6680	422	7	.	.	PUNCT
ejpam-6680	423	1	the	the	DET
ejpam-6680	423	2	extragradient	extragradient	NOUN
ejpam-6680	423	3	method	method	NOUN
ejpam-6680	423	4	for	for	ADP
ejpam-6680	423	5	finding	find	VERB
ejpam-6680	423	6	saddle	saddle	NOUN
ejpam-6680	423	7	points	point	NOUN
ejpam-6680	423	8	and	and	CCONJ
ejpam-6680	423	9	other	other	ADJ
ejpam-6680	423	10	problems	problem	NOUN
ejpam-6680	423	11	.	.	PUNCT
ejpam-6680	424	1	metacon	metacon	PROPN
ejpam-6680	424	2	,	,	PUNCT
ejpam-6680	424	3	12:747–756	12:747–756	PROPN
ejpam-6680	424	4	,	,	PUNCT
ejpam-6680	424	5	1976	1976	NUM
ejpam-6680	424	6	.	.	PUNCT
ejpam-6680	425	1	[	[	X
ejpam-6680	425	2	12	12	NUM
ejpam-6680	425	3	]	]	X
ejpam-6680	425	4	y.	y.	NOUN
ejpam-6680	425	5	censor	censor	PROPN
ejpam-6680	425	6	,	,	PUNCT
ejpam-6680	425	7	a.	a.	NOUN
ejpam-6680	425	8	gibali	gibali	PROPN
ejpam-6680	425	9	,	,	PUNCT
ejpam-6680	425	10	and	and	CCONJ
ejpam-6680	425	11	s.	s.	PROPN
ejpam-6680	425	12	reich	reich	PROPN
ejpam-6680	425	13	.	.	PUNCT
ejpam-6680	426	1	the	the	DET
ejpam-6680	426	2	subgradient	subgradient	ADJ
ejpam-6680	426	3	extragradient	extragradient	NOUN
ejpam-6680	426	4	method	method	NOUN
ejpam-6680	426	5	for	for	ADP
ejpam-6680	426	6	solving	solve	VERB
ejpam-6680	426	7	variational	variational	ADJ
ejpam-6680	426	8	inequalities	inequality	NOUN
ejpam-6680	426	9	in	in	ADP
ejpam-6680	426	10	hilbert	hilbert	PROPN
ejpam-6680	426	11	spaces	space	NOUN
ejpam-6680	426	12	.	.	PUNCT
ejpam-6680	427	1	journal	journal	NOUN
ejpam-6680	427	2	of	of	ADP
ejpam-6680	427	3	optimization	optimization	NOUN
ejpam-6680	427	4	theory	theory	NOUN
ejpam-6680	427	5	and	and	CCONJ
ejpam-6680	427	6	applications	application	NOUN
ejpam-6680	427	7	,	,	PUNCT
ejpam-6680	427	8	148:318–335	148:318–335	NUM
ejpam-6680	427	9	,	,	PUNCT
ejpam-6680	427	10	2011	2011	NUM
ejpam-6680	427	11	.	.	PUNCT
ejpam-6680	428	1	[	[	X
ejpam-6680	428	2	13	13	NUM
ejpam-6680	428	3	]	]	X
ejpam-6680	428	4	y.	y.	NOUN
ejpam-6680	428	5	censor	censor	PROPN
ejpam-6680	428	6	,	,	PUNCT
ejpam-6680	428	7	a.	a.	NOUN
ejpam-6680	428	8	gibali	gibali	PROPN
ejpam-6680	428	9	,	,	PUNCT
ejpam-6680	428	10	and	and	CCONJ
ejpam-6680	428	11	s.	s.	PROPN
ejpam-6680	428	12	reich	reich	PROPN
ejpam-6680	428	13	.	.	PUNCT
ejpam-6680	429	1	strong	strong	ADJ
ejpam-6680	429	2	convergence	convergence	NOUN
ejpam-6680	429	3	of	of	ADP
ejpam-6680	429	4	subgradient	subgradient	NOUN
ejpam-6680	429	5	and	and	CCONJ
ejpam-6680	429	6	extragradient	extragradient	NOUN
ejpam-6680	429	7	methods	method	NOUN
ejpam-6680	429	8	for	for	ADP
ejpam-6680	429	9	the	the	DET
ejpam-6680	429	10	variational	variational	ADJ
ejpam-6680	429	11	inequality	inequality	NOUN
ejpam-6680	429	12	problem	problem	NOUN
ejpam-6680	429	13	in	in	ADP
ejpam-6680	429	14	hilbert	hilbert	NOUN
ejpam-6680	429	15	space	space	NOUN
ejpam-6680	429	16	.	.	PUNCT
ejpam-6680	430	1	optimization	optimization	NOUN
ejpam-6680	430	2	methods	method	NOUN
ejpam-6680	430	3	and	and	CCONJ
ejpam-6680	430	4	software	software	NOUN
ejpam-6680	430	5	,	,	PUNCT
ejpam-6680	430	6	26:827–845	26:827–845	PROPN
ejpam-6680	430	7	,	,	PUNCT
ejpam-6680	430	8	2011	2011	NUM
ejpam-6680	430	9	.	.	PUNCT
ejpam-6680	431	1	[	[	X
ejpam-6680	431	2	14	14	NUM
ejpam-6680	431	3	]	]	X
ejpam-6680	431	4	y.	y.	NOUN
ejpam-6680	431	5	censor	censor	PROPN
ejpam-6680	431	6	,	,	PUNCT
ejpam-6680	431	7	a.	a.	NOUN
ejpam-6680	431	8	gibali	gibali	PROPN
ejpam-6680	431	9	,	,	PUNCT
ejpam-6680	431	10	and	and	CCONJ
ejpam-6680	431	11	s.	s.	PROPN
ejpam-6680	431	12	reich	reich	PROPN
ejpam-6680	431	13	.	.	PUNCT
ejpam-6680	432	1	extensions	extension	NOUN
ejpam-6680	432	2	of	of	ADP
ejpam-6680	432	3	korpelevich	korpelevich	PROPN
ejpam-6680	432	4	’s	’s	PART
ejpam-6680	432	5	extragradient	extragradient	NOUN
ejpam-6680	432	6	method	method	NOUN
ejpam-6680	432	7	for	for	ADP
ejpam-6680	432	8	the	the	DET
ejpam-6680	432	9	variational	variational	ADJ
ejpam-6680	432	10	inequality	inequality	NOUN
ejpam-6680	432	11	problems	problem	NOUN
ejpam-6680	432	12	in	in	ADP
ejpam-6680	432	13	euclidean	euclidean	ADJ
ejpam-6680	432	14	space	space	NOUN
ejpam-6680	432	15	.	.	PUNCT
ejpam-6680	433	1	optimization	optimization	NOUN
ejpam-6680	433	2	,	,	PUNCT
ejpam-6680	433	3	61:1119	61:1119	NUM
ejpam-6680	433	4	–	–	PUNCT
ejpam-6680	433	5	1132	1132	NUM
ejpam-6680	433	6	,	,	PUNCT
ejpam-6680	433	7	2011	2011	NUM
ejpam-6680	433	8	.	.	PUNCT
ejpam-6680	434	1	[	[	X
ejpam-6680	434	2	15	15	NUM
ejpam-6680	434	3	]	]	X
ejpam-6680	434	4	y.	y.	NOUN
ejpam-6680	434	5	censor	censor	PROPN
ejpam-6680	434	6	,	,	PUNCT
ejpam-6680	434	7	a.	a.	NOUN
ejpam-6680	434	8	gibali	gibali	PROPN
ejpam-6680	434	9	,	,	PUNCT
ejpam-6680	434	10	and	and	CCONJ
ejpam-6680	434	11	s.	s.	PROPN
ejpam-6680	434	12	reich	reich	PROPN
ejpam-6680	434	13	.	.	PUNCT
ejpam-6680	435	1	algorithms	algorithm	NOUN
ejpam-6680	435	2	for	for	ADP
ejpam-6680	435	3	the	the	DET
ejpam-6680	435	4	split	split	ADJ
ejpam-6680	435	5	variational	variational	ADJ
ejpam-6680	435	6	inequality	inequality	NOUN
ejpam-6680	435	7	problem	problem	NOUN
ejpam-6680	435	8	.	.	PUNCT
ejpam-6680	436	1	numerical	numerical	ADJ
ejpam-6680	436	2	algorithms	algorithms	PROPN
ejpam-6680	436	3	,	,	PUNCT
ejpam-6680	436	4	56:301–323	56:301–323	NUM
ejpam-6680	436	5	,	,	PUNCT
ejpam-6680	436	6	2012	2012	NUM
ejpam-6680	436	7	.	.	PUNCT
ejpam-6680	437	1	m.	m.	NOUN
ejpam-6680	437	2	rashid	rashid	PROPN
ejpam-6680	437	3	et	et	PROPN
ejpam-6680	437	4	al	al	PROPN
ejpam-6680	437	5	.	.	PUNCT
ejpam-6680	437	6	/	/	SYM
ejpam-6680	437	7	eur	eur	PROPN
ejpam-6680	437	8	.	.	PUNCT
ejpam-6680	438	1	j.	j.	PROPN
ejpam-6680	438	2	pure	pure	PROPN
ejpam-6680	438	3	appl	appl	PROPN
ejpam-6680	438	4	.	.	PROPN
ejpam-6680	438	5	math	math	PROPN
ejpam-6680	438	6	,	,	PUNCT
ejpam-6680	438	7	18	18	NUM
ejpam-6680	438	8	(	(	PUNCT
ejpam-6680	438	9	4	4	NUM
ejpam-6680	438	10	)	)	PUNCT
ejpam-6680	438	11	(	(	PUNCT
ejpam-6680	438	12	2025	2025	NUM
ejpam-6680	438	13	)	)	PUNCT
ejpam-6680	438	14	,	,	PUNCT
ejpam-6680	438	15	6680	6680	NUM
ejpam-6680	438	16	23	23	NUM
ejpam-6680	438	17	of	of	ADP
ejpam-6680	438	18	24	24	NUM
ejpam-6680	438	19	[	[	X
ejpam-6680	438	20	16	16	NUM
ejpam-6680	438	21	]	]	PUNCT
ejpam-6680	438	22	a.	a.	NOUN
ejpam-6680	438	23	n.	n.	PROPN
ejpam-6680	438	24	iusem	iusem	PROPN
ejpam-6680	438	25	and	and	CCONJ
ejpam-6680	438	26	b.	b.	PROPN
ejpam-6680	438	27	f.	f.	PROPN
ejpam-6680	438	28	svaiter	svaiter	PROPN
ejpam-6680	438	29	.	.	PUNCT
ejpam-6680	439	1	a	a	DET
ejpam-6680	439	2	variant	variant	NOUN
ejpam-6680	439	3	of	of	ADP
ejpam-6680	439	4	korpelevich	korpelevich	PROPN
ejpam-6680	439	5	’s	’s	PART
ejpam-6680	439	6	method	method	NOUN
ejpam-6680	439	7	for	for	ADP
ejpam-6680	439	8	variational	variational	ADJ
ejpam-6680	439	9	inequalities	inequality	NOUN
ejpam-6680	439	10	with	with	ADP
ejpam-6680	439	11	a	a	DET
ejpam-6680	439	12	new	new	ADJ
ejpam-6680	439	13	search	search	NOUN
ejpam-6680	439	14	strategy	strategy	NOUN
ejpam-6680	439	15	.	.	PUNCT
ejpam-6680	440	1	optimization	optimization	NOUN
ejpam-6680	440	2	,	,	PUNCT
ejpam-6680	440	3	42:309–321	42:309–321	PROPN
ejpam-6680	440	4	,	,	PUNCT
ejpam-6680	440	5	1997	1997	NUM
ejpam-6680	440	6	.	.	PUNCT
ejpam-6680	441	1	[	[	X
ejpam-6680	441	2	17	17	NUM
ejpam-6680	441	3	]	]	PUNCT
ejpam-6680	441	4	a.	a.	NOUN
ejpam-6680	441	5	n.	n.	PROPN
ejpam-6680	441	6	iusem	iusem	PROPN
ejpam-6680	441	7	and	and	CCONJ
ejpam-6680	441	8	m.	m.	PROPN
ejpam-6680	441	9	nasri	nasri	PROPN
ejpam-6680	441	10	.	.	PUNCT
ejpam-6680	442	1	korpelevich	korpelevich	PROPN
ejpam-6680	442	2	’s	’s	PART
ejpam-6680	442	3	method	method	NOUN
ejpam-6680	442	4	for	for	ADP
ejpam-6680	442	5	variational	variational	ADJ
ejpam-6680	442	6	inequality	inequality	NOUN
ejpam-6680	442	7	problems	problem	NOUN
ejpam-6680	442	8	in	in	ADP
ejpam-6680	442	9	banach	banach	NOUN
ejpam-6680	442	10	spaces	space	NOUN
ejpam-6680	442	11	.	.	PUNCT
ejpam-6680	443	1	journal	journal	NOUN
ejpam-6680	443	2	of	of	ADP
ejpam-6680	443	3	global	global	ADJ
ejpam-6680	443	4	optimization	optimization	NOUN
ejpam-6680	443	5	,	,	PUNCT
ejpam-6680	443	6	50:59–76	50:59–76	PROPN
ejpam-6680	443	7	,	,	PUNCT
ejpam-6680	443	8	2011	2011	NUM
ejpam-6680	443	9	.	.	PUNCT
ejpam-6680	444	1	[	[	X
ejpam-6680	444	2	18	18	NUM
ejpam-6680	444	3	]	]	X
ejpam-6680	444	4	c.	c.	PROPN
ejpam-6680	444	5	kanzow	kanzow	PROPN
ejpam-6680	444	6	and	and	CCONJ
ejpam-6680	444	7	y.	y.	PROPN
ejpam-6680	444	8	shehu	shehu	PROPN
ejpam-6680	444	9	.	.	PUNCT
ejpam-6680	445	1	strong	strong	ADJ
ejpam-6680	445	2	convergence	convergence	NOUN
ejpam-6680	445	3	of	of	ADP
ejpam-6680	445	4	a	a	DET
ejpam-6680	445	5	double	double	ADJ
ejpam-6680	445	6	projection	projection	NOUN
ejpam-6680	445	7	-	-	PUNCT
ejpam-6680	445	8	type	type	NOUN
ejpam-6680	445	9	method	method	NOUN
ejpam-6680	445	10	for	for	ADP
ejpam-6680	445	11	monotone	monotone	ADJ
ejpam-6680	445	12	variational	variational	ADJ
ejpam-6680	445	13	inequalities	inequality	NOUN
ejpam-6680	445	14	in	in	ADP
ejpam-6680	445	15	hilbert	hilbert	PROPN
ejpam-6680	445	16	spaces	space	NOUN
ejpam-6680	445	17	.	.	PUNCT
ejpam-6680	446	1	journal	journal	NOUN
ejpam-6680	446	2	of	of	ADP
ejpam-6680	446	3	fixed	fix	VERB
ejpam-6680	446	4	point	point	NOUN
ejpam-6680	446	5	theory	theory	NOUN
ejpam-6680	446	6	and	and	CCONJ
ejpam-6680	446	7	applications	application	NOUN
ejpam-6680	446	8	,	,	PUNCT
ejpam-6680	446	9	20	20	NUM
ejpam-6680	446	10	:	:	PUNCT
ejpam-6680	446	11	article	article	NOUN
ejpam-6680	446	12	51	51	NUM
ejpam-6680	446	13	,	,	PUNCT
ejpam-6680	446	14	2018	2018	NUM
ejpam-6680	446	15	.	.	PUNCT
ejpam-6680	447	1	[	[	X
ejpam-6680	447	2	19	19	NUM
ejpam-6680	447	3	]	]	X
ejpam-6680	447	4	y.	y.	PROPN
ejpam-6680	447	5	v.	v.	PROPN
ejpam-6680	447	6	malitsky	malitsky	PROPN
ejpam-6680	447	7	.	.	PUNCT
ejpam-6680	448	1	projected	project	VERB
ejpam-6680	448	2	reflected	reflect	VERB
ejpam-6680	448	3	gradient	gradient	ADJ
ejpam-6680	448	4	methods	method	NOUN
ejpam-6680	448	5	for	for	ADP
ejpam-6680	448	6	monotone	monotone	ADJ
ejpam-6680	448	7	variational	variational	ADJ
ejpam-6680	448	8	inequalities	inequality	NOUN
ejpam-6680	448	9	.	.	PUNCT
ejpam-6680	449	1	siam	siam	PROPN
ejpam-6680	449	2	journal	journal	PROPN
ejpam-6680	449	3	on	on	ADP
ejpam-6680	449	4	optimization	optimization	NOUN
ejpam-6680	449	5	,	,	PUNCT
ejpam-6680	449	6	25:502–520	25:502–520	PROPN
ejpam-6680	449	7	,	,	PUNCT
ejpam-6680	449	8	2015	2015	NUM
ejpam-6680	449	9	.	.	PUNCT
ejpam-6680	450	1	[	[	X
ejpam-6680	450	2	20	20	NUM
ejpam-6680	450	3	]	]	X
ejpam-6680	450	4	y.	y.	PROPN
ejpam-6680	450	5	v.	v.	PROPN
ejpam-6680	450	6	malitsky	malitsky	PROPN
ejpam-6680	450	7	and	and	CCONJ
ejpam-6680	450	8	v.	v.	ADP
ejpam-6680	450	9	v.	v.	CCONJ
ejpam-6680	450	10	semenov	semenov	PROPN
ejpam-6680	450	11	.	.	PUNCT
ejpam-6680	451	1	a	a	DET
ejpam-6680	451	2	hybrid	hybrid	ADJ
ejpam-6680	451	3	method	method	NOUN
ejpam-6680	451	4	without	without	ADP
ejpam-6680	451	5	extrapolation	extrapolation	NOUN
ejpam-6680	451	6	step	step	NOUN
ejpam-6680	451	7	for	for	ADP
ejpam-6680	451	8	solving	solve	VERB
ejpam-6680	451	9	variational	variational	ADJ
ejpam-6680	451	10	inequality	inequality	NOUN
ejpam-6680	451	11	problems	problem	NOUN
ejpam-6680	451	12	.	.	PUNCT
ejpam-6680	452	1	journal	journal	PROPN
ejpam-6680	452	2	of	of	ADP
ejpam-6680	452	3	global	global	ADJ
ejpam-6680	452	4	optimization	optimization	NOUN
ejpam-6680	452	5	,	,	PUNCT
ejpam-6680	452	6	61:193–202	61:193–202	PROPN
ejpam-6680	452	7	,	,	PUNCT
ejpam-6680	452	8	2015	2015	NUM
ejpam-6680	452	9	.	.	PUNCT
ejpam-6680	453	1	[	[	X
ejpam-6680	453	2	21	21	NUM
ejpam-6680	453	3	]	]	X
ejpam-6680	453	4	m.	m.	NOUN
ejpam-6680	453	5	v.	v.	ADP
ejpam-6680	453	6	solodov	solodov	PROPN
ejpam-6680	453	7	and	and	CCONJ
ejpam-6680	453	8	b.	b.	PROPN
ejpam-6680	453	9	f.	f.	PROPN
ejpam-6680	453	10	svaiter	svaiter	PROPN
ejpam-6680	453	11	.	.	PUNCT
ejpam-6680	454	1	a	a	DET
ejpam-6680	454	2	new	new	ADJ
ejpam-6680	454	3	projection	projection	NOUN
ejpam-6680	454	4	method	method	NOUN
ejpam-6680	454	5	for	for	ADP
ejpam-6680	454	6	variational	variational	ADJ
ejpam-6680	454	7	inequality	inequality	NOUN
ejpam-6680	454	8	problems	problem	NOUN
ejpam-6680	454	9	.	.	PUNCT
ejpam-6680	455	1	siam	siam	PROPN
ejpam-6680	455	2	journal	journal	PROPN
ejpam-6680	455	3	on	on	ADP
ejpam-6680	455	4	control	control	NOUN
ejpam-6680	455	5	and	and	CCONJ
ejpam-6680	455	6	optimization	optimization	NOUN
ejpam-6680	455	7	,	,	PUNCT
ejpam-6680	455	8	37:765–776	37:765–776	PROPN
ejpam-6680	455	9	,	,	PUNCT
ejpam-6680	455	10	1999	1999	NUM
ejpam-6680	455	11	.	.	PUNCT
ejpam-6680	456	1	[	[	X
ejpam-6680	456	2	22	22	NUM
ejpam-6680	456	3	]	]	X
ejpam-6680	456	4	d.	d.	PROPN
ejpam-6680	456	5	v.	v.	PROPN
ejpam-6680	456	6	thong	thong	PROPN
ejpam-6680	456	7	and	and	CCONJ
ejpam-6680	456	8	d.	d.	PROPN
ejpam-6680	456	9	v.	v.	PROPN
ejpam-6680	456	10	hieu	hieu	PROPN
ejpam-6680	456	11	.	.	PUNCT
ejpam-6680	457	1	strong	strong	ADJ
ejpam-6680	457	2	and	and	CCONJ
ejpam-6680	457	3	weak	weak	ADJ
ejpam-6680	457	4	convergence	convergence	NOUN
ejpam-6680	457	5	theorems	theorem	NOUN
ejpam-6680	457	6	for	for	ADP
ejpam-6680	457	7	variational	variational	ADJ
ejpam-6680	457	8	inequality	inequality	NOUN
ejpam-6680	457	9	problems	problem	NOUN
ejpam-6680	457	10	.	.	PUNCT
ejpam-6680	458	1	numerical	numerical	ADJ
ejpam-6680	458	2	algorithms	algorithms	PROPN
ejpam-6680	458	3	,	,	PUNCT
ejpam-6680	458	4	78:1045–1060	78:1045–1060	NUM
ejpam-6680	458	5	,	,	PUNCT
ejpam-6680	458	6	2018	2018	NUM
ejpam-6680	458	7	.	.	PUNCT
ejpam-6680	459	1	[	[	X
ejpam-6680	459	2	23	23	NUM
ejpam-6680	459	3	]	]	X
ejpam-6680	459	4	d.	d.	PROPN
ejpam-6680	459	5	v.	v.	PROPN
ejpam-6680	459	6	thong	thong	PROPN
ejpam-6680	459	7	and	and	CCONJ
ejpam-6680	459	8	d.	d.	PROPN
ejpam-6680	459	9	v.	v.	PROPN
ejpam-6680	459	10	hieu	hieu	PROPN
ejpam-6680	459	11	.	.	PUNCT
ejpam-6680	460	1	modified	modify	VERB
ejpam-6680	460	2	subgradient	subgradient	ADJ
ejpam-6680	460	3	extragradient	extragradient	NOUN
ejpam-6680	460	4	algorithms	algorithm	NOUN
ejpam-6680	460	5	for	for	ADP
ejpam-6680	460	6	variational	variational	ADJ
ejpam-6680	460	7	inequality	inequality	NOUN
ejpam-6680	460	8	problems	problem	NOUN
ejpam-6680	460	9	and	and	CCONJ
ejpam-6680	460	10	fixed	fix	VERB
ejpam-6680	460	11	point	point	NOUN
ejpam-6680	460	12	problems	problem	NOUN
ejpam-6680	460	13	.	.	PUNCT
ejpam-6680	461	1	optimization	optimization	NOUN
ejpam-6680	461	2	,	,	PUNCT
ejpam-6680	461	3	67:83–102	67:83–102	NUM
ejpam-6680	461	4	,	,	PUNCT
ejpam-6680	461	5	2018	2018	NUM
ejpam-6680	461	6	.	.	PUNCT
ejpam-6680	462	1	[	[	X
ejpam-6680	462	2	24	24	NUM
ejpam-6680	462	3	]	]	X
ejpam-6680	462	4	d.	d.	PROPN
ejpam-6680	462	5	v.	v.	PROPN
ejpam-6680	462	6	thong	thong	PROPN
ejpam-6680	462	7	and	and	CCONJ
ejpam-6680	462	8	d.	d.	PROPN
ejpam-6680	462	9	v.	v.	PROPN
ejpam-6680	462	10	hieu	hieu	PROPN
ejpam-6680	462	11	.	.	PUNCT
ejpam-6680	463	1	modified	modify	VERB
ejpam-6680	463	2	subgradient	subgradient	ADJ
ejpam-6680	463	3	extragradient	extragradient	NOUN
ejpam-6680	463	4	method	method	NOUN
ejpam-6680	463	5	for	for	ADP
ejpam-6680	463	6	variational	variational	ADJ
ejpam-6680	463	7	inequality	inequality	NOUN
ejpam-6680	463	8	problems	problem	NOUN
ejpam-6680	463	9	.	.	PUNCT
ejpam-6680	464	1	numerical	numerical	ADJ
ejpam-6680	464	2	algorithms	algorithms	PROPN
ejpam-6680	464	3	,	,	PUNCT
ejpam-6680	464	4	79:597–610	79:597–610	PROPN
ejpam-6680	464	5	,	,	PUNCT
ejpam-6680	464	6	2018	2018	NUM
ejpam-6680	464	7	.	.	PUNCT
ejpam-6680	465	1	[	[	X
ejpam-6680	465	2	25	25	NUM
ejpam-6680	465	3	]	]	X
ejpam-6680	465	4	d.	d.	PROPN
ejpam-6680	465	5	v.	v.	PROPN
ejpam-6680	465	6	thong	thong	PROPN
ejpam-6680	465	7	and	and	CCONJ
ejpam-6680	465	8	d.	d.	PROPN
ejpam-6680	465	9	v.	v.	PROPN
ejpam-6680	465	10	hieu	hieu	PROPN
ejpam-6680	465	11	.	.	PUNCT
ejpam-6680	466	1	inertial	inertial	ADJ
ejpam-6680	466	2	extragradient	extragradient	NOUN
ejpam-6680	466	3	algorithms	algorithm	NOUN
ejpam-6680	466	4	for	for	ADP
ejpam-6680	466	5	strongly	strongly	ADV
ejpam-6680	466	6	pseudomonotone	pseudomonotone	VERB
ejpam-6680	466	7	variational	variational	ADJ
ejpam-6680	466	8	inequalities	inequality	NOUN
ejpam-6680	466	9	.	.	PUNCT
ejpam-6680	467	1	journal	journal	PROPN
ejpam-6680	467	2	of	of	ADP
ejpam-6680	467	3	computational	computational	ADJ
ejpam-6680	467	4	and	and	CCONJ
ejpam-6680	467	5	applied	applied	ADJ
ejpam-6680	467	6	mathematics	mathematic	NOUN
ejpam-6680	467	7	,	,	PUNCT
ejpam-6680	467	8	341:80–98	341:80–98	NUM
ejpam-6680	467	9	,	,	PUNCT
ejpam-6680	467	10	2018	2018	NUM
ejpam-6680	467	11	.	.	PUNCT
ejpam-6680	468	1	[	[	X
ejpam-6680	468	2	26	26	NUM
ejpam-6680	468	3	]	]	PUNCT
ejpam-6680	468	4	e.	e.	PROPN
ejpam-6680	468	5	n.	n.	PROPN
ejpam-6680	468	6	khobotov	khobotov	PROPN
ejpam-6680	468	7	.	.	PUNCT
ejpam-6680	469	1	modification	modification	NOUN
ejpam-6680	469	2	of	of	ADP
ejpam-6680	469	3	extragradient	extragradient	NOUN
ejpam-6680	469	4	method	method	NOUN
ejpam-6680	469	5	for	for	ADP
ejpam-6680	469	6	solving	solve	VERB
ejpam-6680	469	7	variational	variational	ADJ
ejpam-6680	469	8	inequalities	inequality	NOUN
ejpam-6680	469	9	and	and	CCONJ
ejpam-6680	469	10	certain	certain	ADJ
ejpam-6680	469	11	optimization	optimization	NOUN
ejpam-6680	469	12	problems	problem	NOUN
ejpam-6680	469	13	.	.	PUNCT
ejpam-6680	470	1	ussr	ussr	ADJ
ejpam-6680	470	2	computational	computational	ADJ
ejpam-6680	470	3	mathematics	mathematic	NOUN
ejpam-6680	470	4	and	and	CCONJ
ejpam-6680	470	5	mathematical	mathematical	ADJ
ejpam-6680	470	6	physics	physics	NOUN
ejpam-6680	470	7	,	,	PUNCT
ejpam-6680	470	8	27:120–127	27:120–127	PROPN
ejpam-6680	470	9	,	,	PUNCT
ejpam-6680	470	10	1987	1987	NUM
ejpam-6680	470	11	.	.	PUNCT
ejpam-6680	471	1	[	[	X
ejpam-6680	471	2	27	27	NUM
ejpam-6680	471	3	]	]	X
ejpam-6680	471	4	p.	p.	PROPN
ejpam-6680	471	5	marcotte	marcotte	PROPN
ejpam-6680	471	6	.	.	PUNCT
ejpam-6680	472	1	application	application	NOUN
ejpam-6680	472	2	of	of	ADP
ejpam-6680	472	3	khobotov	khobotov	PROPN
ejpam-6680	472	4	’s	’s	PART
ejpam-6680	472	5	algorithm	algorithm	NOUN
ejpam-6680	472	6	to	to	ADP
ejpam-6680	472	7	variational	variational	ADJ
ejpam-6680	472	8	inequalities	inequality	NOUN
ejpam-6680	472	9	and	and	CCONJ
ejpam-6680	472	10	network	network	NOUN
ejpam-6680	472	11	equilibrium	equilibrium	NOUN
ejpam-6680	472	12	problems	problem	NOUN
ejpam-6680	472	13	.	.	PUNCT
ejpam-6680	473	1	information	information	NOUN
ejpam-6680	473	2	systems	system	NOUN
ejpam-6680	473	3	and	and	CCONJ
ejpam-6680	473	4	operational	operational	ADJ
ejpam-6680	473	5	research	research	NOUN
ejpam-6680	473	6	,	,	PUNCT
ejpam-6680	473	7	29:258	29:258	NUM
ejpam-6680	473	8	–	–	PUNCT
ejpam-6680	473	9	270	270	NUM
ejpam-6680	473	10	,	,	PUNCT
ejpam-6680	473	11	1991	1991	NUM
ejpam-6680	473	12	.	.	PUNCT
ejpam-6680	474	1	[	[	X
ejpam-6680	474	2	28	28	NUM
ejpam-6680	474	3	]	]	PUNCT
ejpam-6680	474	4	a.	a.	NOUN
ejpam-6680	474	5	n.	n.	PROPN
ejpam-6680	474	6	iusem	iusem	PROPN
ejpam-6680	474	7	.	.	PUNCT
ejpam-6680	475	1	an	an	DET
ejpam-6680	475	2	iterative	iterative	NOUN
ejpam-6680	475	3	algorithm	algorithm	NOUN
ejpam-6680	475	4	for	for	ADP
ejpam-6680	475	5	the	the	DET
ejpam-6680	475	6	variational	variational	ADJ
ejpam-6680	475	7	inequality	inequality	NOUN
ejpam-6680	475	8	problems	problem	NOUN
ejpam-6680	475	9	.	.	PUNCT
ejpam-6680	476	1	computational	computational	ADJ
ejpam-6680	476	2	and	and	CCONJ
ejpam-6680	476	3	applied	applied	ADJ
ejpam-6680	476	4	mathematics	mathematic	NOUN
ejpam-6680	476	5	,	,	PUNCT
ejpam-6680	476	6	13:103–114	13:103–114	NUM
ejpam-6680	476	7	,	,	PUNCT
ejpam-6680	476	8	1994	1994	NUM
ejpam-6680	476	9	.	.	PUNCT
ejpam-6680	477	1	[	[	X
ejpam-6680	477	2	29	29	NUM
ejpam-6680	477	3	]	]	X
ejpam-6680	477	4	i.	i.	PROPN
ejpam-6680	477	5	v.	v.	PROPN
ejpam-6680	477	6	konnov	konnov	PROPN
ejpam-6680	477	7	.	.	PUNCT
ejpam-6680	477	8	combined	combine	VERB
ejpam-6680	477	9	relation	relation	NOUN
ejpam-6680	477	10	methods	method	NOUN
ejpam-6680	477	11	for	for	ADP
ejpam-6680	477	12	finding	find	VERB
ejpam-6680	477	13	equilibrium	equilibrium	NOUN
ejpam-6680	477	14	points	point	NOUN
ejpam-6680	477	15	and	and	CCONJ
ejpam-6680	477	16	solving	solve	VERB
ejpam-6680	477	17	related	related	ADJ
ejpam-6680	477	18	problems	problem	NOUN
ejpam-6680	477	19	.	.	PUNCT
ejpam-6680	478	1	russian	russian	ADJ
ejpam-6680	478	2	mathematics	mathematics	PROPN
ejpam-6680	478	3	,	,	PUNCT
ejpam-6680	478	4	37:44–51	37:44–51	NUM
ejpam-6680	478	5	,	,	PUNCT
ejpam-6680	478	6	1993	1993	NUM
ejpam-6680	478	7	.	.	PUNCT
ejpam-6680	479	1	[	[	X
ejpam-6680	479	2	30	30	NUM
ejpam-6680	479	3	]	]	X
ejpam-6680	479	4	d.	d.	PROPN
ejpam-6680	479	5	v.	v.	PROPN
ejpam-6680	479	6	thong	thong	PROPN
ejpam-6680	479	7	,	,	PUNCT
ejpam-6680	479	8	y.	y.	PROPN
ejpam-6680	479	9	shehu	shehu	PROPN
ejpam-6680	479	10	,	,	PUNCT
ejpam-6680	479	11	and	and	CCONJ
ejpam-6680	479	12	o.	o.	PROPN
ejpam-6680	479	13	s.	s.	PROPN
ejpam-6680	479	14	iyiola	iyiola	PROPN
ejpam-6680	479	15	.	.	PUNCT
ejpam-6680	480	1	weak	weak	ADJ
ejpam-6680	480	2	and	and	CCONJ
ejpam-6680	480	3	strong	strong	ADJ
ejpam-6680	480	4	convergence	convergence	NOUN
ejpam-6680	480	5	theorems	theorem	NOUN
ejpam-6680	480	6	for	for	ADP
ejpam-6680	480	7	solving	solve	VERB
ejpam-6680	480	8	pseudomonotone	pseudomonotone	ADP
ejpam-6680	480	9	variational	variational	ADJ
ejpam-6680	480	10	inequalities	inequality	NOUN
ejpam-6680	480	11	with	with	ADP
ejpam-6680	480	12	non	non	ADJ
ejpam-6680	480	13	-	-	ADJ
ejpam-6680	480	14	lipschitz	lipschitz	ADJ
ejpam-6680	480	15	mappings	mapping	NOUN
ejpam-6680	480	16	.	.	PUNCT
ejpam-6680	481	1	numerical	numerical	ADJ
ejpam-6680	481	2	algorithms	algorithms	PROPN
ejpam-6680	481	3	,	,	PUNCT
ejpam-6680	481	4	84(2):795–823	84(2):795–823	NUM
ejpam-6680	481	5	,	,	PUNCT
ejpam-6680	481	6	2020	2020	NUM
ejpam-6680	481	7	.	.	PUNCT
ejpam-6680	482	1	[	[	X
ejpam-6680	482	2	31	31	NUM
ejpam-6680	482	3	]	]	PUNCT
ejpam-6680	482	4	m.	m.	PROPN
ejpam-6680	482	5	r.	r.	PROPN
ejpam-6680	482	6	bridson	bridson	PROPN
ejpam-6680	482	7	and	and	CCONJ
ejpam-6680	482	8	a.	a.	NOUN
ejpam-6680	482	9	haefliger	haefliger	NOUN
ejpam-6680	482	10	.	.	PUNCT
ejpam-6680	483	1	metric	metric	ADJ
ejpam-6680	483	2	spaces	space	NOUN
ejpam-6680	483	3	of	of	ADP
ejpam-6680	483	4	non	non	ADJ
ejpam-6680	483	5	-	-	ADJ
ejpam-6680	483	6	positive	positive	ADJ
ejpam-6680	483	7	curvature	curvature	NOUN
ejpam-6680	483	8	.	.	PUNCT
ejpam-6680	484	1	springer	springer	NOUN
ejpam-6680	484	2	science	science	NOUN
ejpam-6680	484	3	and	and	CCONJ
ejpam-6680	484	4	business	business	NOUN
ejpam-6680	484	5	media	medium	NOUN
ejpam-6680	484	6	,	,	PUNCT
ejpam-6680	484	7	2013	2013	NUM
ejpam-6680	484	8	.	.	PUNCT
ejpam-6680	485	1	[	[	X
ejpam-6680	485	2	32	32	NUM
ejpam-6680	485	3	]	]	PUNCT
ejpam-6680	485	4	m.	m.	NOUN
ejpam-6680	485	5	gromov	gromov	NOUN
ejpam-6680	485	6	.	.	PUNCT
ejpam-6680	486	1	hyperbolic	hyperbolic	ADJ
ejpam-6680	486	2	groups	group	NOUN
ejpam-6680	486	3	,	,	PUNCT
ejpam-6680	486	4	essays	essay	NOUN
ejpam-6680	486	5	in	in	ADP
ejpam-6680	486	6	group	group	NOUN
ejpam-6680	486	7	theory	theory	NOUN
ejpam-6680	486	8	.	.	PUNCT
ejpam-6680	487	1	in	in	ADP
ejpam-6680	487	2	advances	advance	NOUN
ejpam-6680	487	3	in	in	ADP
ejpam-6680	487	4	econometrics	econometric	NOUN
ejpam-6680	487	5	,	,	PUNCT
ejpam-6680	487	6	pages	page	NOUN
ejpam-6680	487	7	75–263	75–263	PROPN
ejpam-6680	487	8	.	.	PUNCT
ejpam-6680	487	9	springer	springer	NOUN
ejpam-6680	487	10	,	,	PUNCT
ejpam-6680	487	11	new	new	PROPN
ejpam-6680	487	12	york	york	PROPN
ejpam-6680	487	13	,	,	PUNCT
ejpam-6680	487	14	ny	ny	PROPN
ejpam-6680	487	15	,	,	PUNCT
ejpam-6680	487	16	1987	1987	NUM
ejpam-6680	487	17	.	.	PUNCT
ejpam-6680	488	1	[	[	X
ejpam-6680	488	2	33	33	NUM
ejpam-6680	488	3	]	]	PUNCT
ejpam-6680	488	4	f.	f.	NOUN
ejpam-6680	488	5	bruhat	bruhat	PROPN
ejpam-6680	488	6	and	and	CCONJ
ejpam-6680	488	7	j.	j.	PROPN
ejpam-6680	488	8	tits	tits	PROPN
ejpam-6680	488	9	.	.	PUNCT
ejpam-6680	489	1	groupes	groupes	PROPN
ejpam-6680	489	2	reductifs	reductifs	PROPN
ejpam-6680	489	3	sur	sur	PROPN
ejpam-6680	489	4	un	un	PROPN
ejpam-6680	489	5	corps	corps	PROPN
ejpam-6680	489	6	local	local	PROPN
ejpam-6680	489	7	.	.	PUNCT
ejpam-6680	490	1	publications	publication	NOUN
ejpam-6680	490	2	mathématiques	mathématiques	PROPN
ejpam-6680	490	3	de	de	X
ejpam-6680	490	4	l’institut	l’institut	PROPN
ejpam-6680	490	5	des	des	PROPN
ejpam-6680	490	6	hautes	haute	NOUN
ejpam-6680	490	7	études	étude	NOUN
ejpam-6680	490	8	scientifiques	scientifique	NOUN
ejpam-6680	490	9	,	,	PUNCT
ejpam-6680	490	10	41(1):5–251	41(1):5–251	NUM
ejpam-6680	490	11	,	,	PUNCT
ejpam-6680	490	12	1972	1972	NUM
ejpam-6680	490	13	.	.	PUNCT
ejpam-6680	491	1	m.	m.	NOUN
ejpam-6680	491	2	rashid	rashid	PROPN
ejpam-6680	491	3	et	et	PROPN
ejpam-6680	491	4	al	al	PROPN
ejpam-6680	491	5	.	.	PUNCT
ejpam-6680	491	6	/	/	SYM
ejpam-6680	491	7	eur	eur	PROPN
ejpam-6680	491	8	.	.	PUNCT
ejpam-6680	492	1	j.	j.	PROPN
ejpam-6680	492	2	pure	pure	PROPN
ejpam-6680	492	3	appl	appl	PROPN
ejpam-6680	492	4	.	.	PROPN
ejpam-6680	492	5	math	math	PROPN
ejpam-6680	492	6	,	,	PUNCT
ejpam-6680	492	7	18	18	NUM
ejpam-6680	492	8	(	(	PUNCT
ejpam-6680	492	9	4	4	NUM
ejpam-6680	492	10	)	)	PUNCT
ejpam-6680	492	11	(	(	PUNCT
ejpam-6680	492	12	2025	2025	NUM
ejpam-6680	492	13	)	)	PUNCT
ejpam-6680	492	14	,	,	PUNCT
ejpam-6680	492	15	6680	6680	NUM
ejpam-6680	492	16	24	24	NUM
ejpam-6680	492	17	of	of	ADP
ejpam-6680	492	18	24	24	NUM
ejpam-6680	492	19	[	[	SYM
ejpam-6680	492	20	34	34	NUM
ejpam-6680	492	21	]	]	PUNCT
ejpam-6680	492	22	w.	w.	PROPN
ejpam-6680	492	23	a.	a.	PROPN
ejpam-6680	492	24	kirk	kirk	PROPN
ejpam-6680	492	25	.	.	PUNCT
ejpam-6680	493	1	fixed	fix	VERB
ejpam-6680	493	2	point	point	NOUN
ejpam-6680	493	3	theorems	theorem	NOUN
ejpam-6680	493	4	in	in	ADP
ejpam-6680	493	5	spaces	space	NOUN
ejpam-6680	493	6	and	and	CCONJ
ejpam-6680	493	7	r	r	NOUN
ejpam-6680	493	8	-	-	PUNCT
ejpam-6680	493	9	trees	tree	NOUN
ejpam-6680	493	10	.	.	PUNCT
ejpam-6680	494	1	fixed	fix	VERB
ejpam-6680	494	2	point	point	NOUN
ejpam-6680	494	3	theory	theory	NOUN
ejpam-6680	494	4	and	and	CCONJ
ejpam-6680	494	5	applications	application	NOUN
ejpam-6680	494	6	,	,	PUNCT
ejpam-6680	494	7	pages	page	NOUN
ejpam-6680	494	8	1–8	1–8	NUM
ejpam-6680	494	9	,	,	PUNCT
ejpam-6680	494	10	2004	2004	NUM
ejpam-6680	494	11	.	.	PUNCT
ejpam-6680	495	1	[	[	X
ejpam-6680	495	2	35	35	NUM
ejpam-6680	495	3	]	]	X
ejpam-6680	495	4	i.	i.	PROPN
ejpam-6680	495	5	d.	d.	PROPN
ejpam-6680	495	6	berg	berg	PROPN
ejpam-6680	495	7	and	and	CCONJ
ejpam-6680	495	8	i.	i.	PROPN
ejpam-6680	495	9	g.	g.	PROPN
ejpam-6680	495	10	nikolaev	nikolaev	PROPN
ejpam-6680	495	11	.	.	PUNCT
ejpam-6680	496	1	quasilinearization	quasilinearization	NOUN
ejpam-6680	496	2	and	and	CCONJ
ejpam-6680	496	3	curvature	curvature	NOUN
ejpam-6680	496	4	of	of	ADP
ejpam-6680	496	5	alexandrov	alexandrov	PROPN
ejpam-6680	496	6	spaces	space	NOUN
ejpam-6680	496	7	.	.	PUNCT
ejpam-6680	497	1	geometriae	geometriae	PROPN
ejpam-6680	497	2	dedicata	dedicata	PROPN
ejpam-6680	497	3	,	,	PUNCT
ejpam-6680	497	4	133(1):195–218	133(1):195–218	NUM
ejpam-6680	497	5	,	,	PUNCT
ejpam-6680	497	6	2008	2008	NUM
ejpam-6680	497	7	.	.	PUNCT
ejpam-6680	498	1	[	[	X
ejpam-6680	498	2	36	36	NUM
ejpam-6680	498	3	]	]	X
ejpam-6680	498	4	b.	b.	PROPN
ejpam-6680	498	5	a.	a.	PROPN
ejpam-6680	498	6	kakavandi	kakavandi	PROPN
ejpam-6680	498	7	and	and	CCONJ
ejpam-6680	498	8	m.	m.	PROPN
ejpam-6680	498	9	amini	amini	PROPN
ejpam-6680	498	10	.	.	PUNCT
ejpam-6680	498	11	duality	duality	NOUN
ejpam-6680	498	12	and	and	CCONJ
ejpam-6680	498	13	subdifferential	subdifferential	ADJ
ejpam-6680	498	14	for	for	ADP
ejpam-6680	498	15	convex	convex	NOUN
ejpam-6680	498	16	functions	function	NOUN
ejpam-6680	498	17	on	on	ADP
ejpam-6680	498	18	complete	complete	ADJ
ejpam-6680	498	19	cat(0	cat(0	NOUN
ejpam-6680	498	20	)	)	PUNCT
ejpam-6680	498	21	metric	metric	ADJ
ejpam-6680	498	22	spaces	space	NOUN
ejpam-6680	498	23	.	.	PUNCT
ejpam-6680	499	1	nonlinear	nonlinear	ADJ
ejpam-6680	499	2	analysis	analysis	NOUN
ejpam-6680	499	3	:	:	PUNCT
ejpam-6680	499	4	theory	theory	NOUN
ejpam-6680	499	5	,	,	PUNCT
ejpam-6680	499	6	methods	method	NOUN
ejpam-6680	499	7	and	and	CCONJ
ejpam-6680	499	8	applications	application	NOUN
ejpam-6680	499	9	,	,	PUNCT
ejpam-6680	499	10	73(10):3450–3455	73(10):3450–3455	NUM
ejpam-6680	499	11	,	,	PUNCT
ejpam-6680	499	12	2010	2010	NUM
ejpam-6680	499	13	.	.	PUNCT
ejpam-6680	500	1	[	[	X
ejpam-6680	500	2	37	37	NUM
ejpam-6680	500	3	]	]	X
ejpam-6680	500	4	d.	d.	PROPN
ejpam-6680	500	5	kinderlehrer	kinderlehrer	PROPN
ejpam-6680	500	6	and	and	CCONJ
ejpam-6680	500	7	g.	g.	PROPN
ejpam-6680	500	8	stampacchia	stampacchia	PROPN
ejpam-6680	500	9	.	.	PUNCT
ejpam-6680	501	1	an	an	DET
ejpam-6680	501	2	introduction	introduction	NOUN
ejpam-6680	501	3	to	to	ADP
ejpam-6680	501	4	variational	variational	ADJ
ejpam-6680	501	5	inequalities	inequality	NOUN
ejpam-6680	501	6	and	and	CCONJ
ejpam-6680	501	7	their	their	PRON
ejpam-6680	501	8	applications	application	NOUN
ejpam-6680	501	9	.	.	PUNCT
ejpam-6680	502	1	society	society	NOUN
ejpam-6680	502	2	for	for	ADP
ejpam-6680	502	3	industrial	industrial	ADJ
ejpam-6680	502	4	and	and	CCONJ
ejpam-6680	502	5	applied	applied	ADJ
ejpam-6680	502	6	mathematics	mathematic	NOUN
ejpam-6680	502	7	,	,	PUNCT
ejpam-6680	502	8	2000	2000	NUM
ejpam-6680	502	9	.	.	PUNCT
ejpam-6680	503	1	[	[	X
ejpam-6680	503	2	38	38	NUM
ejpam-6680	503	3	]	]	X
ejpam-6680	503	4	h.	h.	PROPN
ejpam-6680	503	5	dehghan	dehghan	PROPN
ejpam-6680	503	6	and	and	CCONJ
ejpam-6680	503	7	j.	j.	PROPN
ejpam-6680	503	8	rooin	rooin	PROPN
ejpam-6680	503	9	.	.	PUNCT
ejpam-6680	504	1	a	a	DET
ejpam-6680	504	2	characterization	characterization	NOUN
ejpam-6680	504	3	of	of	ADP
ejpam-6680	504	4	metric	metric	ADJ
ejpam-6680	504	5	projection	projection	NOUN
ejpam-6680	504	6	in	in	ADP
ejpam-6680	504	7	cat(0	cat(0	ADJ
ejpam-6680	504	8	)	)	PUNCT
ejpam-6680	504	9	spaces	space	NOUN
ejpam-6680	504	10	.	.	PUNCT
ejpam-6680	505	1	arxiv	arxiv	PROPN
ejpam-6680	505	2	preprint	preprint	PROPN
ejpam-6680	505	3	arxiv:1311.4174	arxiv:1311.4174	PROPN
ejpam-6680	505	4	,	,	PUNCT
ejpam-6680	505	5	2013	2013	NUM
ejpam-6680	505	6	.	.	PUNCT
ejpam-6680	506	1	[	[	X
ejpam-6680	506	2	39	39	NUM
ejpam-6680	506	3	]	]	PUNCT
ejpam-6680	506	4	s.	s.	PROPN
ejpam-6680	506	5	dhompongsa	dhompongsa	VERB
ejpam-6680	506	6	and	and	CCONJ
ejpam-6680	506	7	b.	b.	PROPN
ejpam-6680	506	8	panyanak	panyanak	PROPN
ejpam-6680	506	9	.	.	PUNCT
ejpam-6680	507	1	on	on	ADP
ejpam-6680	507	2	δ	δ	PROPN
ejpam-6680	507	3	-	-	PUNCT
ejpam-6680	507	4	convergence	convergence	NOUN
ejpam-6680	507	5	theorems	theorem	NOUN
ejpam-6680	507	6	in	in	ADP
ejpam-6680	507	7	cat(0	cat(0	ADJ
ejpam-6680	507	8	)	)	PUNCT
ejpam-6680	507	9	spaces	space	NOUN
ejpam-6680	507	10	.	.	PUNCT
ejpam-6680	508	1	computers	computer	NOUN
ejpam-6680	508	2	and	and	CCONJ
ejpam-6680	508	3	mathematics	mathematic	NOUN
ejpam-6680	508	4	with	with	ADP
ejpam-6680	508	5	applications	application	NOUN
ejpam-6680	508	6	,	,	PUNCT
ejpam-6680	508	7	56(10):2572–2579	56(10):2572–2579	NUM
ejpam-6680	508	8	,	,	PUNCT
ejpam-6680	508	9	2008	2008	NUM
ejpam-6680	508	10	.	.	PUNCT
ejpam-6680	509	1	[	[	X
ejpam-6680	509	2	40	40	NUM
ejpam-6680	509	3	]	]	PUNCT
ejpam-6680	509	4	a.	a.	NOUN
ejpam-6680	509	5	kalsoom	kalsoom	PROPN
ejpam-6680	509	6	,	,	PUNCT
ejpam-6680	509	7	m.	m.	NOUN
ejpam-6680	509	8	rashid	rashid	PROPN
ejpam-6680	509	9	,	,	PUNCT
ejpam-6680	509	10	o.	o.	PROPN
ejpam-6680	509	11	bagdasar	bagdasar	PROPN
ejpam-6680	509	12	,	,	PUNCT
ejpam-6680	509	13	and	and	CCONJ
ejpam-6680	509	14	z.	z.	PROPN
ejpam-6680	509	15	u.	u.	PROPN
ejpam-6680	509	16	nisa	nisa	PROPN
ejpam-6680	509	17	.	.	PUNCT
ejpam-6680	510	1	a	a	DET
ejpam-6680	510	2	new	new	ADJ
ejpam-6680	510	3	algorithm	algorithm	NOUN
ejpam-6680	510	4	for	for	ADP
ejpam-6680	510	5	variational	variational	ADJ
ejpam-6680	510	6	inequality	inequality	NOUN
ejpam-6680	510	7	problems	problem	NOUN
ejpam-6680	510	8	in	in	ADP
ejpam-6680	510	9	cat(0	cat(0	ADJ
ejpam-6680	510	10	)	)	PUNCT
ejpam-6680	510	11	spaces	space	NOUN
ejpam-6680	510	12	.	.	PUNCT
ejpam-6680	511	1	mathematics	mathematic	NOUN
ejpam-6680	511	2	,	,	PUNCT
ejpam-6680	511	3	12(14):2193	12(14):2193	NUM
ejpam-6680	511	4	,	,	PUNCT
ejpam-6680	511	5	2024	2024	NUM
ejpam-6680	511	6	.	.	PUNCT
ejpam-6680	512	1	[	[	X
ejpam-6680	512	2	41	41	NUM
ejpam-6680	512	3	]	]	PUNCT
ejpam-6680	512	4	l.	l.	PROPN
ejpam-6680	512	5	s.	s.	PROPN
ejpam-6680	512	6	liu	liu	PROPN
ejpam-6680	512	7	.	.	PUNCT
ejpam-6680	513	1	ishikawa	ishikawa	PROPN
ejpam-6680	513	2	and	and	CCONJ
ejpam-6680	513	3	mann	mann	PROPN
ejpam-6680	513	4	iterative	iterative	NOUN
ejpam-6680	513	5	process	process	NOUN
ejpam-6680	513	6	with	with	ADP
ejpam-6680	513	7	errors	error	NOUN
ejpam-6680	513	8	for	for	ADP
ejpam-6680	513	9	nonlinear	nonlinear	ADJ
ejpam-6680	513	10	strongly	strongly	ADV
ejpam-6680	513	11	accretive	accretive	ADJ
ejpam-6680	513	12	mappings	mapping	NOUN
ejpam-6680	513	13	in	in	ADP
ejpam-6680	513	14	banach	banach	NOUN
ejpam-6680	513	15	spaces	space	NOUN
ejpam-6680	513	16	.	.	PUNCT
ejpam-6680	514	1	journal	journal	NOUN
ejpam-6680	514	2	of	of	ADP
ejpam-6680	514	3	mathematical	mathematical	ADJ
ejpam-6680	514	4	analysis	analysis	NOUN
ejpam-6680	514	5	and	and	CCONJ
ejpam-6680	514	6	applications	application	NOUN
ejpam-6680	514	7	,	,	PUNCT
ejpam-6680	514	8	194(1):114–125	194(1):114–125	NUM
ejpam-6680	514	9	,	,	PUNCT
ejpam-6680	514	10	1995	1995	NUM
ejpam-6680	514	11	.	.	PUNCT
ejpam-6680	515	1	[	[	X
ejpam-6680	515	2	42	42	NUM
ejpam-6680	515	3	]	]	PUNCT
ejpam-6680	515	4	r.	r.	PROPN
ejpam-6680	515	5	wangkeeree	wangkeeree	PROPN
ejpam-6680	515	6	,	,	PUNCT
ejpam-6680	515	7	u.	u.	PROPN
ejpam-6680	515	8	boonkong	boonkong	PROPN
ejpam-6680	515	9	,	,	PUNCT
ejpam-6680	515	10	and	and	CCONJ
ejpam-6680	515	11	p.	p.	PROPN
ejpam-6680	515	12	preechasilp	preechasilp	PROPN
ejpam-6680	515	13	.	.	PUNCT
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ejpam-6680	516	2	approximation	approximation	NOUN
ejpam-6680	516	3	methods	method	NOUN
ejpam-6680	516	4	for	for	ADP
ejpam-6680	516	5	asymptotically	asymptotically	ADV
ejpam-6680	516	6	nonexpansive	nonexpansive	ADJ
ejpam-6680	516	7	mapping	mapping	NOUN
ejpam-6680	516	8	in	in	ADP
ejpam-6680	516	9	cat(0	cat(0	ADJ
ejpam-6680	516	10	)	)	PUNCT
ejpam-6680	516	11	spaces	space	NOUN
ejpam-6680	516	12	.	.	PUNCT
ejpam-6680	517	1	fixed	fix	VERB
ejpam-6680	517	2	point	point	NOUN
ejpam-6680	517	3	theory	theory	NOUN
ejpam-6680	517	4	and	and	CCONJ
ejpam-6680	517	5	applications	application	NOUN
ejpam-6680	517	6	,	,	PUNCT
ejpam-6680	517	7	1:1–15	1:1–15	NUM
ejpam-6680	517	8	,	,	PUNCT
ejpam-6680	517	9	2015	2015	NUM
ejpam-6680	517	10	.	.	PUNCT
ejpam-6680	518	1	[	[	X
ejpam-6680	518	2	43	43	NUM
ejpam-6680	518	3	]	]	PUNCT
ejpam-6680	518	4	m.	m.	NOUN
ejpam-6680	518	5	rashid	rashid	PROPN
ejpam-6680	518	6	,	,	PUNCT
ejpam-6680	518	7	a.	a.	NOUN
ejpam-6680	518	8	kalsoom	kalsoom	PROPN
ejpam-6680	518	9	,	,	PUNCT
ejpam-6680	518	10	a.	a.	PROPN
ejpam-6680	518	11	h.	h.	PROPN
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ejpam-6680	518	13	,	,	PUNCT
ejpam-6680	518	14	a.	a.	NOUN
ejpam-6680	518	15	hussain	hussain	PROPN
ejpam-6680	518	16	,	,	PUNCT
ejpam-6680	518	17	and	and	CCONJ
ejpam-6680	518	18	h.	h.	PROPN
ejpam-6680	518	19	sundas	sundas	PROPN
ejpam-6680	518	20	.	.	PUNCT
ejpam-6680	519	1	convergence	convergence	NOUN
ejpam-6680	519	2	result	result	NOUN
ejpam-6680	519	3	for	for	ADP
ejpam-6680	519	4	solving	solve	VERB
ejpam-6680	519	5	the	the	DET
ejpam-6680	519	6	split	split	ADJ
ejpam-6680	519	7	fixed	fix	VERB
ejpam-6680	519	8	point	point	NOUN
ejpam-6680	519	9	problem	problem	NOUN
ejpam-6680	519	10	with	with	ADP
ejpam-6680	519	11	multiple	multiple	ADJ
ejpam-6680	519	12	output	output	NOUN
ejpam-6680	519	13	sets	set	NOUN
ejpam-6680	519	14	in	in	ADP
ejpam-6680	519	15	nonlinear	nonlinear	ADJ
ejpam-6680	519	16	spaces	space	NOUN
ejpam-6680	519	17	.	.	PUNCT
ejpam-6680	520	1	mathematics	mathematic	NOUN
ejpam-6680	520	2	,	,	PUNCT
ejpam-6680	520	3	12(12):18–25	12(12):18–25	NUM
ejpam-6680	520	4	,	,	PUNCT
ejpam-6680	520	5	2024	2024	NUM
ejpam-6680	520	6	.	.	PUNCT
ejpam-6680	521	1	[	[	X
ejpam-6680	521	2	44	44	NUM
ejpam-6680	521	3	]	]	PUNCT
ejpam-6680	521	4	a.	a.	NOUN
ejpam-6680	521	5	tassaddiq	tassaddiq	NOUN
ejpam-6680	521	6	,	,	PUNCT
ejpam-6680	521	7	a.	a.	NOUN
ejpam-6680	521	8	kalsoom	kalsoom	PROPN
ejpam-6680	521	9	,	,	PUNCT
ejpam-6680	521	10	a.	a.	NOUN
ejpam-6680	521	11	batool	batool	PROPN
ejpam-6680	521	12	,	,	PUNCT
ejpam-6680	521	13	d.	d.	PROPN
ejpam-6680	521	14	k.	k.	PROPN
ejpam-6680	521	15	almutairi	almutairi	PROPN
ejpam-6680	521	16	,	,	PUNCT
ejpam-6680	521	17	and	and	CCONJ
ejpam-6680	521	18	s.	s.	PROPN
ejpam-6680	521	19	afsheen	afsheen	PROPN
ejpam-6680	521	20	.	.	PUNCT
ejpam-6680	522	1	an	an	DET
ejpam-6680	522	2	algorithm	algorithm	NOUN
ejpam-6680	522	3	for	for	ADP
ejpam-6680	522	4	solving	solve	VERB
ejpam-6680	522	5	pseudomonotone	pseudomonotone	ADP
ejpam-6680	522	6	variational	variational	ADJ
ejpam-6680	522	7	inequality	inequality	NOUN
ejpam-6680	522	8	problems	problem	NOUN
ejpam-6680	522	9	in	in	ADP
ejpam-6680	522	10	cat(0	cat(0	ADJ
ejpam-6680	522	11	)	)	PUNCT
ejpam-6680	522	12	spaces	space	NOUN
ejpam-6680	522	13	.	.	PUNCT
ejpam-6680	523	1	contemporary	contemporary	ADJ
ejpam-6680	523	2	mathematics	mathematic	NOUN
ejpam-6680	523	3	,	,	PUNCT
ejpam-6680	523	4	pages	page	NOUN
ejpam-6680	523	5	590–601	590–601	NUM
ejpam-6680	523	6	,	,	PUNCT
ejpam-6680	523	7	2024	2024	NUM
ejpam-6680	523	8	.	.	PUNCT